LMFDB - Embedded newform 804.2.j.b.499.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(499,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("804.499");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.j (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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			499.9
Character	$\chi$	$=$	804.499
Dual form			804.2.j.b.775.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.02913 - 0.969995i) q^{2} +1.00000 q^{3} +(0.118221 + 1.99650i) q^{4} -4.16950i q^{5} +(-1.02913 - 0.969995i) q^{6} +(0.853071 - 1.47756i) q^{7} +(1.81493 - 2.16934i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-1.02913 - 0.969995i) q^{2} +1.00000 q^{3} +(0.118221 + 1.99650i) q^{4} -4.16950i q^{5} +(-1.02913 - 0.969995i) q^{6} +(0.853071 - 1.47756i) q^{7} +(1.81493 - 2.16934i) q^{8} +1.00000 q^{9} +(-4.04439 + 4.29096i) q^{10} +(2.31815 - 4.01516i) q^{11} +(0.118221 + 1.99650i) q^{12} +(1.43191 - 0.826711i) q^{13} +(-2.31115 + 0.693131i) q^{14} -4.16950i q^{15} +(-3.97205 + 0.472056i) q^{16} +(2.55705 + 4.42894i) q^{17} +(-1.02913 - 0.969995i) q^{18} +(-3.35198 + 1.93527i) q^{19} +(8.32441 - 0.492921i) q^{20} +(0.853071 - 1.47756i) q^{21} +(-6.28037 + 1.88353i) q^{22} +(4.99547 - 2.88414i) q^{23} +(1.81493 - 2.16934i) q^{24} -12.3847 q^{25} +(-2.27552 - 0.538147i) q^{26} +1.00000 q^{27} +(3.05081 + 1.52848i) q^{28} +(-5.06928 + 8.78025i) q^{29} +(-4.04439 + 4.29096i) q^{30} +(2.38328 - 4.12796i) q^{31} +(4.54565 + 3.36706i) q^{32} +(2.31815 - 4.01516i) q^{33} +(1.66451 - 7.03829i) q^{34} +(-6.16069 - 3.55688i) q^{35} +(0.118221 + 1.99650i) q^{36} +(3.63265 + 6.29193i) q^{37} +(5.32683 + 1.25976i) q^{38} +(1.43191 - 0.826711i) q^{39} +(-9.04504 - 7.56735i) q^{40} +(-7.26972 - 4.19717i) q^{41} +(-2.31115 + 0.693131i) q^{42} -2.95503 q^{43} +(8.29033 + 4.15353i) q^{44} -4.16950i q^{45} +(-7.93859 - 1.87743i) q^{46} +(-0.472829 - 0.272988i) q^{47} +(-3.97205 + 0.472056i) q^{48} +(2.04454 + 3.54125i) q^{49} +(12.7455 + 12.0131i) q^{50} +(2.55705 + 4.42894i) q^{51} +(1.81981 + 2.76107i) q^{52} -3.50033i q^{53} +(-1.02913 - 0.969995i) q^{54} +(-16.7412 - 9.66553i) q^{55} +(-1.65706 - 4.53227i) q^{56} +(-3.35198 + 1.93527i) q^{57} +(13.7338 - 4.11885i) q^{58} -10.5316i q^{59} +(8.32441 - 0.492921i) q^{60} +(6.74319 - 3.89318i) q^{61} +(-6.45681 + 1.93644i) q^{62} +(0.853071 - 1.47756i) q^{63} +(-1.41204 - 7.87440i) q^{64} +(-3.44697 - 5.97032i) q^{65} +(-6.28037 + 1.88353i) q^{66} +(7.70268 - 2.76925i) q^{67} +(-8.54010 + 5.62875i) q^{68} +(4.99547 - 2.88414i) q^{69} +(2.89001 + 9.63633i) q^{70} +(3.04145 + 1.75598i) q^{71} +(1.81493 - 2.16934i) q^{72} +(-0.636897 - 1.10314i) q^{73} +(2.36467 - 9.99887i) q^{74} -12.3847 q^{75} +(-4.26004 - 6.46346i) q^{76} +(-3.95510 - 6.85043i) q^{77} +(-2.27552 - 0.538147i) q^{78} +(-7.40343 + 12.8231i) q^{79} +(1.96824 + 16.5614i) q^{80} +1.00000 q^{81} +(3.41026 + 11.3710i) q^{82} +(1.29893 - 0.749938i) q^{83} +(3.05081 + 1.52848i) q^{84} +(18.4665 - 10.6616i) q^{85} +(3.04112 + 2.86637i) q^{86} +(-5.06928 + 8.78025i) q^{87} +(-4.50294 - 12.3161i) q^{88} -6.03812 q^{89} +(-4.04439 + 4.29096i) q^{90} -2.82097i q^{91} +(6.34875 + 9.63250i) q^{92} +(2.38328 - 4.12796i) q^{93} +(0.221806 + 0.739582i) q^{94} +(8.06910 + 13.9761i) q^{95} +(4.54565 + 3.36706i) q^{96} +(-13.8362 + 7.98831i) q^{97} +(1.33089 - 5.62760i) q^{98} +(2.31815 - 4.01516i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 68 q^{3} - 2 q^{4} - 4 q^{7} + 6 q^{8} + 68 q^{9}+O(q^{10}) $ 68 * q + 68 * q^3 - 2 * q^4 - 4 * q^7 + 6 * q^8 + 68 * q^9	$ 68 q + 68 q^{3} - 2 q^{4} - 4 q^{7} + 6 q^{8} + 68 q^{9} - 6 q^{10} - 2 q^{12} + 6 q^{13} + 10 q^{14} - 2 q^{16} - 12 q^{20} - 4 q^{21} - 22 q^{22} + 6 q^{24} - 68 q^{25} - 19 q^{26} + 68 q^{27} - 7 q^{28} - 8 q^{29} - 6 q^{30} - 2 q^{31} + 15 q^{32} - 2 q^{36} + 12 q^{37} + 4 q^{38} + 6 q^{39} + 18 q^{40} + 10 q^{42} + 4 q^{43} - 5 q^{44} + 16 q^{46} - 2 q^{48} - 46 q^{49} + 27 q^{50} + 28 q^{52} - 17 q^{56} - 4 q^{58} - 12 q^{60} + 6 q^{61} - 34 q^{62} - 4 q^{63} + 16 q^{64} - 22 q^{66} + 18 q^{67} + 34 q^{68} - 56 q^{70} + 36 q^{71} + 6 q^{72} + 6 q^{73} + 11 q^{74} - 68 q^{75} + 14 q^{76} - 4 q^{77} - 19 q^{78} - 6 q^{79} - 25 q^{80} + 68 q^{81} - 26 q^{82} - 12 q^{83} - 7 q^{84} - 33 q^{86} - 8 q^{87} + 22 q^{88} - 6 q^{90} + 10 q^{92} - 2 q^{93} + 16 q^{94} - 20 q^{95} + 15 q^{96} + 18 q^{97} - 32 q^{98}+O(q^{100}) $ 68 * q + 68 * q^3 - 2 * q^4 - 4 * q^7 + 6 * q^8 + 68 * q^9 - 6 * q^10 - 2 * q^12 + 6 * q^13 + 10 * q^14 - 2 * q^16 - 12 * q^20 - 4 * q^21 - 22 * q^22 + 6 * q^24 - 68 * q^25 - 19 * q^26 + 68 * q^27 - 7 * q^28 - 8 * q^29 - 6 * q^30 - 2 * q^31 + 15 * q^32 - 2 * q^36 + 12 * q^37 + 4 * q^38 + 6 * q^39 + 18 * q^40 + 10 * q^42 + 4 * q^43 - 5 * q^44 + 16 * q^46 - 2 * q^48 - 46 * q^49 + 27 * q^50 + 28 * q^52 - 17 * q^56 - 4 * q^58 - 12 * q^60 + 6 * q^61 - 34 * q^62 - 4 * q^63 + 16 * q^64 - 22 * q^66 + 18 * q^67 + 34 * q^68 - 56 * q^70 + 36 * q^71 + 6 * q^72 + 6 * q^73 + 11 * q^74 - 68 * q^75 + 14 * q^76 - 4 * q^77 - 19 * q^78 - 6 * q^79 - 25 * q^80 + 68 * q^81 - 26 * q^82 - 12 * q^83 - 7 * q^84 - 33 * q^86 - 8 * q^87 + 22 * q^88 - 6 * q^90 + 10 * q^92 - 2 * q^93 + 16 * q^94 - 20 * q^95 + 15 * q^96 + 18 * q^97 - 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.02913	−	0.969995i	−0.727705	−	0.685890i
$2$	−1.02913	−	0.969995i	−0.727705	−	0.685890i
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	0.118221	+	1.99650i	0.0591103	+	0.998251i
$5$		−	4.16950i		−	1.86466i	−0.361615	−	0.932328i	$-0.617774\pi$
$5$		−	4.16950i		−	1.86466i	0.361615	−	0.932328i	$-0.382226\pi$
$6$	−1.02913	−	0.969995i	−0.420141	−	0.395999i
$7$	0.853071	−	1.47756i	0.322431	−	0.558466i	−0.658558	−	0.752530i	$-0.728833\pi$
$7$	0.853071	−	1.47756i	0.322431	−	0.558466i	0.980989	+	0.194064i	$0.0621668\pi$
$8$	1.81493	−	2.16934i	0.641676	−	0.766976i
$9$	1.00000			0.333333
$10$	−4.04439	+	4.29096i	−1.27895	+	1.35692i
$11$	2.31815	−	4.01516i	0.698950	−	1.21062i	−0.269881	−	0.962894i	$-0.586984\pi$
$11$	2.31815	−	4.01516i	0.698950	−	1.21062i	0.968831	−	0.247723i	$-0.0796823\pi$
$12$	0.118221	+	1.99650i	0.0341274	+	0.576341i
$13$	1.43191	−	0.826711i	0.397139	−	0.229288i	−0.288110	−	0.957597i	$-0.593027\pi$
$13$	1.43191	−	0.826711i	0.397139	−	0.229288i	0.685249	+	0.728309i	$0.259693\pi$
$14$	−2.31115	+	0.693131i	−0.617681	+	0.185247i
$15$		−	4.16950i		−	1.07656i
$16$	−3.97205	+	0.472056i	−0.993012	+	0.118014i
$17$	2.55705	+	4.42894i	0.620176	+	1.07418i	0.989453	+	0.144857i	$0.0462721\pi$
$17$	2.55705	+	4.42894i	0.620176	+	1.07418i	−0.369277	+	0.929319i	$0.620395\pi$
$18$	−1.02913	−	0.969995i	−0.242568	−	0.228630i
$19$	−3.35198	+	1.93527i	−0.768998	+	0.443981i	−0.832517	−	0.553999i	$-0.813101\pi$
$19$	−3.35198	+	1.93527i	−0.768998	+	0.443981i	0.0635191	+	0.997981i	$0.479768\pi$
$20$	8.32441	−	0.492921i	1.86139	−	0.110220i
$21$	0.853071	−	1.47756i	0.186155	−	0.322431i
$22$	−6.28037	+	1.88353i	−1.33898	+	0.401570i
$23$	4.99547	−	2.88414i	1.04163	−	0.601384i	0.121333	−	0.992612i	$-0.461283\pi$
$23$	4.99547	−	2.88414i	1.04163	−	0.601384i	0.920294	+	0.391228i	$0.127950\pi$
$24$	1.81493	−	2.16934i	0.370472	−	0.442814i
$25$	−12.3847			−2.47694
$26$	−2.27552	−	0.538147i	−0.446267	−	0.105539i
$27$	1.00000			0.192450
$28$	3.05081	+	1.52848i	0.576549	+	0.288856i
$29$	−5.06928	+	8.78025i	−0.941342	+	1.63045i	−0.178427	+	0.983953i	$0.557101\pi$
$29$	−5.06928	+	8.78025i	−0.941342	+	1.63045i	−0.762915	+	0.646499i	$0.776232\pi$
$30$	−4.04439	+	4.29096i	−0.738401	+	0.783418i
$31$	2.38328	−	4.12796i	0.428050	−	0.741404i	−0.568650	−	0.822580i	$-0.692534\pi$
$31$	2.38328	−	4.12796i	0.428050	−	0.741404i	0.996700	+	0.0811755i	$0.0258674\pi$
$32$	4.54565	+	3.36706i	0.803565	+	0.595217i
$33$	2.31815	−	4.01516i	0.403539	−	0.698950i
$34$	1.66451	−	7.03829i	0.285461	−	1.20706i
$35$	−6.16069	−	3.55688i	−1.04135	−	0.601222i
$36$	0.118221	+	1.99650i	0.0197034	+	0.332750i
$37$	3.63265	+	6.29193i	0.597204	+	1.03439i	0.993232	+	0.116149i	$0.0370549\pi$
$37$	3.63265	+	6.29193i	0.597204	+	1.03439i	−0.396028	+	0.918238i	$0.629612\pi$
$38$	5.32683	+	1.25976i	0.864126	+	0.204360i
$39$	1.43191	−	0.826711i	0.229288	−	0.132380i
$40$	−9.04504	−	7.56735i	−1.43015	−	1.19650i
$41$	−7.26972	−	4.19717i	−1.13534	−	0.655488i	−0.190067	−	0.981771i	$-0.560871\pi$
$41$	−7.26972	−	4.19717i	−1.13534	−	0.655488i	−0.945272	+	0.326283i	$0.894204\pi$
$42$	−2.31115	+	0.693131i	−0.356618	+	0.106952i
$43$	−2.95503			−0.450638			−0.225319	−	0.974285i	$-0.572343\pi$
$43$	−2.95503			−0.450638			−0.225319	+	0.974285i	$0.572343\pi$
$44$	8.29033	+	4.15353i	1.24982	+	0.626168i
$45$		−	4.16950i		−	0.621552i
$46$	−7.93859	−	1.87743i	−1.17048	−	0.276811i
$47$	−0.472829	−	0.272988i	−0.0689692	−	0.0398194i	0.465119	−	0.885248i	$-0.346012\pi$
$47$	−0.472829	−	0.272988i	−0.0689692	−	0.0398194i	−0.534088	+	0.845429i	$0.679345\pi$
$48$	−3.97205	+	0.472056i	−0.573316	+	0.0681354i
$49$	2.04454	+	3.54125i	0.292077	+	0.505892i
$50$	12.7455	+	12.0131i	1.80248	+	1.69891i
$51$	2.55705	+	4.42894i	0.358059	+	0.620176i
$52$	1.81981	+	2.76107i	0.252362	+	0.382891i
$53$		−	3.50033i		−	0.480807i	−0.970673	−	0.240404i	$-0.922720\pi$
$53$		−	3.50033i		−	0.480807i	0.970673	−	0.240404i	$-0.0772798\pi$
$54$	−1.02913	−	0.969995i	−0.140047	−	0.132000i
$55$	−16.7412	−	9.66553i	−2.25738	−	1.30330i
$56$	−1.65706	−	4.53227i	−0.221434	−	0.605651i
$57$	−3.35198	+	1.93527i	−0.443981	+	0.256333i
$58$	13.7338	−	4.11885i	1.80333	−	0.540832i
$59$		−	10.5316i		−	1.37110i	−0.728026	−	0.685550i	$-0.759562\pi$
$59$		−	10.5316i		−	1.37110i	0.728026	−	0.685550i	$-0.240438\pi$
$60$	8.32441	−	0.492921i	1.07468	−	0.0636358i
$61$	6.74319	−	3.89318i	0.863377	−	0.498471i	−0.00176477	−	0.999998i	$-0.500562\pi$
$61$	6.74319	−	3.89318i	0.863377	−	0.498471i	0.865142	+	0.501528i	$0.167228\pi$
$62$	−6.45681	+	1.93644i	−0.820016	+	0.245929i
$63$	0.853071	−	1.47756i	0.107477	−	0.186155i
$64$	−1.41204	−	7.87440i	−0.176505	−	0.984300i
$65$	−3.44697	−	5.97032i	−0.427544	−	0.740527i
$66$	−6.28037	+	1.88353i	−0.773060	+	0.231846i
$67$	7.70268	−	2.76925i	0.941032	−	0.338318i
$67$	7.70268	−	2.76925i	0.941032	−	0.338318i
$68$	−8.54010	+	5.62875i	−1.03564	+	0.682586i
$69$	4.99547	−	2.88414i	0.601384	−	0.347209i
$70$	2.89001	+	9.63633i	0.345422	+	1.15176i
$71$	3.04145	+	1.75598i	0.360953	+	0.208396i	0.669499	−	0.742813i	$-0.266509\pi$
$71$	3.04145	+	1.75598i	0.360953	+	0.208396i	−0.308546	+	0.951210i	$0.599842\pi$
$72$	1.81493	−	2.16934i	0.213892	−	0.255659i
$73$	−0.636897	−	1.10314i	−0.0745431	−	0.129113i	0.826344	−	0.563165i	$-0.190417\pi$
$73$	−0.636897	−	1.10314i	−0.0745431	−	0.129113i	−0.900888	+	0.434053i	$0.857083\pi$
$74$	2.36467	−	9.99887i	0.274887	−	1.16235i
$75$	−12.3847			−1.43006
$76$	−4.26004	−	6.46346i	−0.488661	−	0.741409i
$77$	−3.95510	−	6.85043i	−0.450726	−	0.780680i
$78$	−2.27552	−	0.538147i	−0.257652	−	0.0609331i
$79$	−7.40343	+	12.8231i	−0.832951	+	1.44271i	0.0627362	+	0.998030i	$0.480017\pi$
$79$	−7.40343	+	12.8231i	−0.832951	+	1.44271i	−0.895688	+	0.444684i	$0.853316\pi$
$80$	1.96824	+	16.5614i	0.220055	+	1.85162i
$81$	1.00000			0.111111
$82$	3.41026	+	11.3710i	0.376600	+	1.25572i
$83$	1.29893	−	0.749938i	0.142576	−	0.0823164i	−0.427015	−	0.904245i	$-0.640435\pi$
$83$	1.29893	−	0.749938i	0.142576	−	0.0823164i	0.569591	+	0.821928i	$0.307102\pi$
$84$	3.05081	+	1.52848i	0.332870	+	0.166771i
$85$	18.4665	−	10.6616i	2.00297	−	1.15641i
$86$	3.04112	+	2.86637i	0.327932	+	0.309088i
$87$	−5.06928	+	8.78025i	−0.543484	+	0.941342i
$88$	−4.50294	−	12.3161i	−0.480015	−	1.31290i
$89$	−6.03812			−0.640039			−0.320020	−	0.947411i	$-0.603690\pi$
$89$	−6.03812			−0.640039			−0.320020	+	0.947411i	$0.603690\pi$
$90$	−4.04439	+	4.29096i	−0.426316	+	0.452307i
$91$		−	2.82097i		−	0.295718i
$92$	6.34875	+	9.63250i	0.661903	+	1.00426i
$93$	2.38328	−	4.12796i	0.247135	−	0.428050i
$94$	0.221806	+	0.739582i	0.0228776	+	0.0762821i
$95$	8.06910	+	13.9761i	0.827872	+	1.43392i
$96$	4.54565	+	3.36706i	0.463938	+	0.343649i
$97$	−13.8362	+	7.98831i	−1.40485	+	0.811090i	−0.994885	−	0.101012i	$-0.967792\pi$
$97$	−13.8362	+	7.98831i	−1.40485	+	0.811090i	−0.409963	+	0.912102i	$0.634459\pi$
$98$	1.33089	−	5.62760i	0.134440	−	0.568473i
$99$	2.31815	−	4.01516i	0.232983	−	0.403539i
$100$	−1.46413	−	24.7261i	−0.146413	−	2.47261i
$101$	13.2530	+	7.65165i	1.31873	+	0.761367i	0.983524	−	0.180778i	$-0.0578617\pi$
$101$	13.2530	+	7.65165i	1.31873	+	0.761367i	0.335203	+	0.942146i	$0.391195\pi$
$102$	1.66451	−	7.03829i	0.164811	−	0.696894i
$103$	−6.64821	−	3.83835i	−0.655068	−	0.378204i	0.135327	−	0.990801i	$-0.456791\pi$
$103$	−6.64821	−	3.83835i	−0.655068	−	0.378204i	−0.790395	+	0.612597i	$0.790125\pi$
$104$	0.805398	−	4.60671i	0.0789757	−	0.451725i
$105$	−6.16069	−	3.55688i	−0.601222	−	0.347116i
$106$	−3.39530	+	3.60230i	−0.329781	+	0.349886i
$107$		−	0.478532i		−	0.0462614i	−0.999732	−	0.0231307i	$-0.992637\pi$
$107$		−	0.478532i		−	0.0462614i	0.999732	−	0.0231307i	$-0.00736339\pi$
$108$	0.118221	+	1.99650i	0.0113758	+	0.192114i
$109$			6.64012i			0.636008i	0.948089	+	0.318004i	$0.103013\pi$
$109$			6.64012i			0.636008i	−0.948089	+	0.318004i	$0.896987\pi$
$110$	7.85337	+	26.1860i	0.748789	+	2.49673i
$111$	3.63265	+	6.29193i	0.344796	+	0.597204i
$112$	−2.69095	+	6.27164i	−0.254271	+	0.592615i
$113$	−6.98854	−	4.03484i	−0.657427	−	0.379566i	0.133869	−	0.990999i	$-0.457260\pi$
$113$	−6.98854	−	4.03484i	−0.657427	−	0.379566i	−0.791296	+	0.611434i	$0.790593\pi$
$114$	5.32683	+	1.25976i	0.498903	+	0.117987i
$115$	−12.0254	−	20.8286i	−1.12137	−	1.94228i
$116$	−18.1291	−	9.08283i	−1.68324	−	0.843319i
$117$	1.43191	−	0.826711i	0.132380	−	0.0764294i
$118$	−10.2156	+	10.8384i	−0.940423	+	0.997756i
$119$	8.72538			0.799855
$120$	−9.04504	−	7.56735i	−0.825695	−	0.690802i
$121$	−5.24768	−	9.08925i	−0.477062	−	0.826295i
$122$	−10.7160	−	2.53426i	−0.970180	−	0.229441i
$123$	−7.26972	−	4.19717i	−0.655488	−	0.378446i
$124$	8.52324	+	4.27022i	0.765410	+	0.383477i
$125$			30.7904i			2.75398i
$126$	−2.31115	+	0.693131i	−0.205894	+	0.0617490i
$127$	−5.52839	−	3.19182i	−0.490566	−	0.283228i	0.234244	−	0.972178i	$-0.424739\pi$
$127$	−5.52839	−	3.19182i	−0.490566	−	0.283228i	−0.724809	+	0.688950i	$0.758072\pi$
$128$	−6.18495	+	9.47346i	−0.546678	+	0.837343i
$129$	−2.95503			−0.260176
$130$	−2.24380	+	9.48778i	−0.196794	+	0.832134i
$131$			12.7546i			1.11437i	0.830387	+	0.557187i	$0.188119\pi$
$131$			12.7546i			1.11437i	−0.830387	+	0.557187i	$0.811881\pi$
$132$	8.29033	+	4.15353i	0.721581	+	0.361518i
$133$			6.60369i			0.572612i
$134$	−10.6132	−	4.62163i	−0.916843	−	0.399248i
$135$		−	4.16950i		−	0.358853i
$136$	14.2487	+	2.49113i	1.22182	+	0.213612i
$137$		−	5.96671i		−	0.509771i	−0.966971	−	0.254885i	$-0.917962\pi$
$137$		−	5.96671i		−	0.509771i	0.966971	−	0.254885i	$-0.0820377\pi$
$138$	−7.93859	−	1.87743i	−0.675777	−	0.159817i
$139$	−8.17487			−0.693383			−0.346692	−	0.937979i	$-0.612695\pi$
$139$	−8.17487			−0.693383			−0.346692	+	0.937979i	$0.612695\pi$
$140$	6.37299	−	12.7203i	0.538616	−	1.07506i
$141$	−0.472829	−	0.272988i	−0.0398194	−	0.0229897i
$142$	−1.42675	−	4.75732i	−0.119731	−	0.399225i
$143$		−	7.66577i		−	0.641044i
$144$	−3.97205	+	0.472056i	−0.331004	+	0.0393380i
$145$	36.6092	+	21.1363i	3.04023	+	1.75528i
$146$	−0.414587	+	1.75306i	−0.0343115	+	0.145084i
$147$	2.04454	+	3.54125i	0.168631	+	0.292077i
$148$	−12.1324	+	7.99643i	−0.997278	+	0.657302i
$149$	14.2624			1.16842			0.584211	−	0.811601i	$-0.301404\pi$
$149$	14.2624			1.16842			0.584211	+	0.811601i	$0.301404\pi$
$150$	12.7455	+	12.0131i	1.04066	+	0.980864i
$151$	5.11146	−	2.95110i	0.415965	−	0.240157i	−0.277385	−	0.960759i	$-0.589468\pi$
$151$	5.11146	−	2.95110i	0.415965	−	0.240157i	0.693349	+	0.720602i	$0.256134\pi$
$152$	−1.88538	+	10.7840i	−0.152924	+	0.874695i
$153$	2.55705	+	4.42894i	0.206725	+	0.358059i
$154$	−2.57457	+	10.8864i	−0.207465	+	0.877253i
$155$	−17.2115	−	9.93708i	−1.38246	−	0.798165i
$156$	1.81981	+	2.76107i	0.145702	+	0.221062i
$157$	7.55154	+	13.0796i	0.602678	+	1.04387i	0.992414	+	0.122942i	$0.0392331\pi$
$157$	7.55154	+	13.0796i	0.602678	+	1.04387i	−0.389736	+	0.920927i	$0.627434\pi$
$158$	20.0575	−	6.01538i	1.59569	−	0.478558i
$159$		−	3.50033i		−	0.277594i
$160$	14.0389	−	18.9531i	1.10988	−	1.49837i
$161$		−	9.84149i		−	0.775618i
$162$	−1.02913	−	0.969995i	−0.0808562	−	0.0762100i
$163$	18.3058	+	10.5688i	1.43382	+	0.827815i	0.997409	−	0.0719336i	$-0.0229170\pi$
$163$	18.3058	+	10.5688i	1.43382	+	0.827815i	0.436408	+	0.899749i	$0.356250\pi$
$164$	7.52024	−	15.0102i	0.587232	−	1.17210i
$165$	−16.7412	−	9.66553i	−1.30330	−	0.752461i
$166$	−2.06421	−	0.488172i	−0.160214	−	0.0378895i
$167$	3.00682	+	1.73599i	0.232674	+	0.134335i	0.611805	−	0.791008i	$-0.290444\pi$
$167$	3.00682	+	1.73599i	0.232674	+	0.134335i	−0.379131	+	0.925343i	$0.623777\pi$
$168$	−1.65706	−	4.53227i	−0.127845	−	0.349673i
$169$	−5.13310	+	8.89079i	−0.394854	+	0.683907i
$170$	−29.3461	−	6.94017i	−2.25074	−	0.532287i
$171$	−3.35198	+	1.93527i	−0.256333	+	0.147994i
$172$	−0.349346	−	5.89973i	−0.0266374	−	0.449850i
$173$	−6.45025	−	11.1722i	−0.490403	−	0.849403i	0.509536	−	0.860449i	$-0.329817\pi$
$173$	−6.45025	−	11.1722i	−0.490403	−	0.849403i	−0.999939	+	0.0110462i	$0.996484\pi$
$174$	13.7338	−	4.11885i	1.04115	−	0.312249i
$175$	−10.5650	+	18.2992i	−0.798641	+	1.38329i
$176$	−7.31244	+	17.0427i	−0.551196	+	1.28464i
$177$		−	10.5316i		−	0.791605i
$178$	6.21401	+	5.85694i	0.465760	+	0.438996i
$179$	25.2737			1.88905			0.944523	−	0.328446i	$-0.106525\pi$
$179$	25.2737			1.88905			0.944523	+	0.328446i	$0.106525\pi$
$180$	8.32441	−	0.492921i	0.620465	−	0.0367401i
$181$	5.09990	−	8.83329i	0.379073	−	0.656573i	−0.611855	−	0.790970i	$-0.709576\pi$
$181$	5.09990	−	8.83329i	0.379073	−	0.656573i	0.990928	+	0.134397i	$0.0429097\pi$
$182$	−2.73633	+	2.90315i	−0.202830	+	0.215196i
$183$	6.74319	−	3.89318i	0.498471	−	0.287792i
$184$	2.80978	−	16.0714i	0.207140	−	1.18480i
$185$	26.2342	−	15.1463i	1.92878	−	1.11358i
$186$	−6.45681	+	1.93644i	−0.473436	+	0.141987i
$187$	23.7106			1.73389
$188$	0.489123	−	0.976277i	0.0356730	−	0.0712023i
$189$	0.853071	−	1.47756i	0.0620518	−	0.107477i
$190$	5.25257	−	22.2102i	0.381062	−	1.61130i
$191$	−4.28464	−	7.42121i	−0.310026	−	0.536980i	0.668342	−	0.743854i	$-0.267004\pi$
$191$	−4.28464	−	7.42121i	−0.310026	−	0.536980i	−0.978368	+	0.206874i	$0.933671\pi$
$192$	−1.41204	−	7.87440i	−0.101905	−	0.568286i
$193$	3.85697			0.277631			0.138816	−	0.990318i	$-0.455670\pi$
$193$	3.85697			0.277631			0.138816	+	0.990318i	$0.455670\pi$
$194$	21.9878	+	5.19998i	1.57863	+	0.373337i
$195$	−3.44697	−	5.97032i	−0.246842	−	0.427544i
$196$	−6.82840	+	4.50058i	−0.487743	+	0.321470i
$197$	0.862773	+	0.498122i	0.0614700	+	0.0354897i	0.530420	−	0.847735i	$-0.322034\pi$
$197$	0.862773	+	0.498122i	0.0614700	+	0.0354897i	−0.468950	+	0.883225i	$0.655368\pi$
$198$	−6.28037	+	1.88353i	−0.446326	+	0.133857i
$199$	18.3581	−	10.5990i	1.30137	−	0.751347i	0.320731	−	0.947170i	$-0.396071\pi$
$199$	18.3581	−	10.5990i	1.30137	−	0.751347i	0.980639	+	0.195824i	$0.0627380\pi$
$200$	−22.4774	+	26.8666i	−1.58939	+	1.89975i
$201$	7.70268	−	2.76925i	0.543305	−	0.195328i
$202$	−6.21706	−	20.7299i	−0.437431	−	1.45855i
$203$	8.64891	+	14.9804i	0.607035	+	1.05141i
$204$	−8.54010	+	5.62875i	−0.597926	+	0.394091i
$205$	−17.5001	+	30.3111i	−1.22226	+	2.11702i
$206$	3.11871	+	10.3989i	0.217290	+	0.724525i
$207$	4.99547	−	2.88414i	0.347209	−	0.200461i
$208$	−5.29734	+	3.95967i	−0.367305	+	0.274554i
$209$			17.9450i			1.24128i
$210$	2.89001	+	9.63633i	0.199429	+	0.664970i
$211$	5.20080	−	3.00268i	0.358038	−	0.206713i	−0.310182	−	0.950677i	$-0.600390\pi$
$211$	5.20080	−	3.00268i	0.358038	−	0.206713i	0.668220	+	0.743964i	$0.267057\pi$
$212$	6.98842	−	0.413811i	0.479967	−	0.0284207i
$213$	3.04145	+	1.75598i	0.208396	+	0.120318i
$214$	−0.464173	+	0.492472i	−0.0317302	+	0.0336647i
$215$			12.3210i			0.840285i
$216$	1.81493	−	2.16934i	0.123491	−	0.147605i
$217$	−4.06621	−	7.04289i	−0.276033	−	0.478103i
$218$	6.44088	−	6.83355i	0.436231	−	0.462827i
$219$	−0.636897	−	1.10314i	−0.0430375	−	0.0745431i
$220$	17.3181	−	34.5665i	1.16759	−	2.33047i
$221$	7.32291	+	4.22788i	0.492592	+	0.284398i
$222$	2.36467	−	9.99887i	0.158706	−	0.671080i
$223$			22.0870i			1.47905i	0.673127	+	0.739527i	$0.264951\pi$
$223$			22.0870i			1.47905i	−0.673127	+	0.739527i	$0.735049\pi$
$224$	8.85280	−	3.84414i	0.591502	−	0.256847i
$225$	−12.3847			−0.825646
$226$	3.27835	+	10.9312i	0.218073	+	0.727134i
$227$	0.343477	+	0.198307i	0.0227974	+	0.0131621i	0.511355	−	0.859369i	$-0.329144\pi$
$227$	0.343477	+	0.198307i	0.0227974	+	0.0131621i	−0.488558	+	0.872531i	$0.662477\pi$
$228$	−4.26004	−	6.46346i	−0.282128	−	0.428053i
$229$	14.4225	−	8.32684i	0.953066	−	0.550253i	0.0590341	−	0.998256i	$-0.481198\pi$
$229$	14.4225	−	8.32684i	0.953066	−	0.550253i	0.894032	+	0.448003i	$0.147865\pi$
$230$	−7.82792	+	33.0999i	−0.516158	+	2.18254i
$231$	−3.95510	−	6.85043i	−0.260227	−	0.450726i
$232$	9.84692	+	26.9325i	0.646482	+	1.76821i
$233$	−2.51365	−	1.45126i	−0.164675	−	0.0950751i	0.415398	−	0.909640i	$-0.363642\pi$
$233$	−2.51365	−	1.45126i	−0.164675	−	0.0950751i	−0.580073	+	0.814565i	$0.696976\pi$
$234$	−2.27552	−	0.538147i	−0.148756	−	0.0351797i
$235$	−1.13822	+	1.97146i	−0.0742494	+	0.128604i
$236$	21.0264	−	1.24505i	1.36870	−	0.0810461i
$237$	−7.40343	+	12.8231i	−0.480905	+	0.832951i
$238$	−8.97956	−	8.46357i	−0.582058	−	0.548612i
$239$	11.8629	−	20.5472i	0.767349	−	1.32909i	−0.171646	−	0.985159i	$-0.554909\pi$
$239$	11.8629	−	20.5472i	0.767349	−	1.32909i	0.938995	−	0.343930i	$-0.111758\pi$
$240$	1.96824	+	16.5614i	0.127049	+	1.06904i
$241$	−9.42863			−0.607351			−0.303676	−	0.952775i	$-0.598214\pi$
$241$	−9.42863			−0.607351			−0.303676	+	0.952775i	$0.598214\pi$
$242$	−3.41597	+	14.4442i	−0.219587	+	0.928511i
$243$	1.00000			0.0641500
$244$	8.56993	+	13.0025i	0.548634	+	0.832402i
$245$	14.7652	−	8.52470i	0.943315	−	0.544623i
$246$	3.41026	+	11.3710i	0.217430	+	0.724990i
$247$	−3.19982	+	5.54224i	−0.203599	+	0.352644i
$248$	−4.62945	−	12.6621i	−0.293970	−	0.804045i
$249$	1.29893	−	0.749938i	0.0823164	−	0.0475254i
$250$	29.8666	−	31.6874i	1.88893	−	2.00409i
$251$	−1.99614	−	3.45742i	−0.125995	−	0.218230i	0.796126	−	0.605130i	$-0.206879\pi$
$251$	−1.99614	−	3.45742i	−0.125995	−	0.218230i	−0.922122	+	0.386900i	$0.873546\pi$
$252$	3.05081	+	1.52848i	0.192183	+	0.0962852i
$253$		−	26.7435i		−	1.68135i
$254$	2.59339	+	8.64731i	0.162724	+	0.542581i
$255$	18.4665	−	10.6616i	1.15641	−	0.667656i
$256$	15.5543	−	3.75006i	0.972145	−	0.234379i
$257$	1.11377	−	1.92910i	0.0694749	−	0.120334i	−0.829195	−	0.558959i	$-0.811201\pi$
$257$	1.11377	−	1.92910i	0.0694749	−	0.120334i	0.898670	+	0.438625i	$0.144534\pi$
$258$	3.04112	+	2.86637i	0.189332	+	0.178452i
$259$	12.3956			0.770227
$260$	11.5123	−	7.58769i	0.713960	−	0.470569i
$261$	−5.06928	+	8.78025i	−0.313781	+	0.543484i
$262$	12.3719	−	13.1261i	0.764337	−	0.810935i
$263$			11.3715i			0.701197i	0.936526	+	0.350599i	$0.114022\pi$
$263$			11.3715i			0.701197i	−0.936526	+	0.350599i	$0.885978\pi$
$264$	−4.50294	−	12.3161i	−0.277137	−	0.758004i
$265$	−14.5946			−0.896540
$266$	6.40554	−	6.79606i	0.392749	−	0.416693i
$267$	−6.03812			−0.369527
$268$	6.43944	+	15.0510i	0.393351	+	0.919388i
$269$	4.46275			0.272099			0.136049	−	0.990702i	$-0.456559\pi$
$269$	4.46275			0.272099			0.136049	+	0.990702i	$0.456559\pi$
$270$	−4.04439	+	4.29096i	−0.246134	+	0.261139i
$271$	−21.3867			−1.29915			−0.649574	−	0.760298i	$-0.725053\pi$
$271$	−21.3867			−1.29915			−0.649574	+	0.760298i	$0.725053\pi$
$272$	−12.2474	−	16.3849i	−0.742610	−	0.993480i
$273$		−	2.82097i		−	0.170733i
$274$	−5.78768	+	6.14053i	−0.349647	+	0.370963i
$275$	−28.7096	+	49.7265i	−1.73126	+	2.99862i
$276$	6.34875	+	9.63250i	0.382150	+	0.579809i
$277$	−14.3293			−0.860966			−0.430483	−	0.902599i	$-0.641657\pi$
$277$	−14.3293			−0.860966			−0.430483	+	0.902599i	$0.641657\pi$
$278$	8.41301	+	7.92958i	0.504579	+	0.475584i
$279$	2.38328	−	4.12796i	0.142683	−	0.247135i
$280$	−18.8973	+	6.90912i	−1.12933	+	0.412899i
$281$	15.7947	−	9.11906i	0.942231	−	0.543998i	0.0515723	−	0.998669i	$-0.483577\pi$
$281$	15.7947	−	9.11906i	0.942231	−	0.543998i	0.890659	+	0.454672i	$0.150243\pi$
$282$	0.221806	+	0.739582i	0.0132084	+	0.0440415i
$283$			13.3972i			0.796378i	0.917303	+	0.398189i	$0.130361\pi$
$283$			13.3972i			0.796378i	−0.917303	+	0.398189i	$0.869639\pi$
$284$	−3.14626	+	6.27985i	−0.186696	+	0.372640i
$285$	8.06910	+	13.9761i	0.477972	+	0.827872i
$286$	−7.43576	+	7.88908i	−0.439686	+	0.466491i
$287$	−12.4032	+	7.16097i	−0.732136	+	0.422699i
$288$	4.54565	+	3.36706i	0.267855	+	0.198406i
$289$	−4.57702	+	7.92762i	−0.269236	+	0.466331i
$290$	−17.1735	−	57.2628i	−1.00847	−	3.36259i
$291$	−13.8362	+	7.98831i	−0.811090	+	0.468283i
$292$	2.12712	−	1.40198i	0.124480	−	0.0820447i
$293$	−27.6590			−1.61586			−0.807929	−	0.589280i	$-0.799411\pi$
$293$	−27.6590			−1.61586			−0.807929	+	0.589280i	$0.799411\pi$
$294$	1.33089	−	5.62760i	0.0776192	−	0.328208i
$295$	−43.9115			−2.55663
$296$	20.2423	+	3.53900i	1.17656	+	0.205700i
$297$	2.31815	−	4.01516i	0.134513	−	0.232983i
$298$	−14.6779	−	13.8345i	−0.850268	−	0.801409i
$299$	4.76869	−	8.25961i	0.275781	−	0.477666i
$300$	−1.46413	−	24.7261i	−0.0845314	−	1.42756i
$301$	−2.52085	+	4.36625i	−0.145300	+	0.251666i
$302$	−8.12292	−	1.92102i	−0.467421	−	0.110542i
$303$	13.2530	+	7.65165i	0.761367	+	0.439576i
$304$	12.4007	−	9.26930i	0.711228	−	0.531631i
$305$	−16.2326	−	28.1157i	−0.929476	−	1.60990i
$306$	1.66451	−	7.03829i	0.0951537	−	0.402352i
$307$	−9.84151	+	5.68200i	−0.561685	+	0.324289i	−0.753821	−	0.657079i	$-0.771792\pi$
$307$	−9.84151	+	5.68200i	−0.561685	+	0.324289i	0.192137	+	0.981368i	$0.438458\pi$
$308$	13.2093	−	8.70623i	0.752672	−	0.496084i
$309$	−6.64821	−	3.83835i	−0.378204	−	0.218356i
$310$	8.07400	+	26.9216i	0.458572	+	1.52905i
$311$	13.9433			0.790652			0.395326	−	0.918541i	$-0.370632\pi$
$311$	13.9433			0.790652			0.395326	+	0.918541i	$0.370632\pi$
$312$	0.805398	−	4.60671i	0.0455967	−	0.260803i
$313$		−	1.88468i		−	0.106529i	−0.998580	−	0.0532643i	$-0.983037\pi$
$313$		−	1.88468i		−	0.106529i	0.998580	−	0.0532643i	$-0.0169626\pi$
$314$	4.91567	−	20.7856i	0.277407	−	1.17300i
$315$	−6.16069	−	3.55688i	−0.347116	−	0.200407i
$316$	−26.4766	−	13.2650i	−1.48943	−	0.746216i
$317$	2.47017	+	4.27846i	0.138739	+	0.240302i	0.927019	−	0.375013i	$-0.122362\pi$
$317$	2.47017	+	4.27846i	0.138739	+	0.240302i	−0.788281	+	0.615316i	$0.789029\pi$
$318$	−3.39530	+	3.60230i	−0.190399	+	0.202007i
$319$	23.5028	+	40.7080i	1.31590	+	2.27921i
$320$	−32.8323	+	5.88749i	−1.83538	+	0.329121i
$321$		−	0.478532i		−	0.0267090i
$322$	−9.54619	+	10.1282i	−0.531988	+	0.564421i
$323$	−17.1424	−	9.89716i	−0.953828	−	0.550693i
$324$	0.118221	+	1.99650i	0.00656782	+	0.110917i
$325$	−17.7337	+	10.2386i	−0.983689	+	0.567933i
$326$	−8.58731	−	28.6332i	−0.475607	−	1.58585i
$327$			6.64012i			0.367199i
$328$	−22.2991	+	8.15288i	−1.23126	+	0.450167i
$329$	−0.806713	+	0.465756i	−0.0444756	+	0.0256780i
$330$	7.85337	+	26.1860i	0.432314	+	1.44149i
$331$	−0.946179	+	1.63883i	−0.0520067	+	0.0900783i	−0.890857	−	0.454284i	$-0.849895\pi$
$331$	−0.946179	+	1.63883i	−0.0520067	+	0.0900783i	0.838850	+	0.544363i	$0.183228\pi$
$332$	1.65081	+	2.50466i	0.0906002	+	0.137461i
$333$	3.63265	+	6.29193i	0.199068	+	0.344796i
$334$	−1.41051	−	4.70315i	−0.0771797	−	0.257345i
$335$	−11.5464	−	32.1163i	−0.630847	−	1.75470i
$336$	−2.69095	+	6.27164i	−0.146803	+	0.342146i
$337$	7.02297	−	4.05471i	0.382565	−	0.220874i	−0.296368	−	0.955074i	$-0.595776\pi$
$337$	7.02297	−	4.05471i	0.382565	−	0.220874i	0.678934	+	0.734199i	$0.262442\pi$
$338$	13.9066	−	4.17071i	0.756422	−	0.226856i
$339$	−6.98854	−	4.03484i	−0.379566	−	0.219142i
$340$	23.4691	+	35.6079i	1.27279	+	1.93111i
$341$	−11.0496	−	19.1385i	−0.598371	−	1.03641i
$342$	5.32683	+	1.25976i	0.288042	+	0.0681201i
$343$	18.9195			1.02156
$344$	−5.36319	+	6.41046i	−0.289164	+	0.345629i
$345$	−12.0254	−	20.8286i	−0.647425	−	1.12137i
$346$	−4.19878	+	17.7543i	−0.225728	+	0.954478i
$347$	−5.03228	+	8.71616i	−0.270147	+	0.467908i	−0.968899	−	0.247456i	$-0.920406\pi$
$347$	−5.03228	+	8.71616i	−0.270147	+	0.467908i	0.698753	+	0.715363i	$0.253739\pi$
$348$	−18.1291	−	9.08283i	−0.971821	−	0.486891i
$349$	34.7269			1.85889			0.929443	−	0.368965i	$-0.120288\pi$
$349$	34.7269			1.85889			0.929443	+	0.368965i	$0.120288\pi$
$350$	28.6229	−	8.58421i	1.52996	−	0.458845i
$351$	1.43191	−	0.826711i	0.0764294	−	0.0441266i
$352$	24.0568	−	10.4462i	1.28223	−	0.556782i
$353$	−16.0075	+	9.24196i	−0.851996	+	0.491900i	−0.861324	−	0.508056i	$-0.830364\pi$
$353$	−16.0075	+	9.24196i	−0.851996	+	0.491900i	0.00932794	+	0.999956i	$0.497031\pi$
$354$	−10.2156	+	10.8384i	−0.542953	+	0.576055i
$355$	7.32155	−	12.6813i	0.388587	−	0.673053i
$356$	−0.713831	−	12.0551i	−0.0378329	−	0.638920i
$357$	8.72538			0.461796
$358$	−26.0099	−	24.5154i	−1.37467	−	1.29568i
$359$		−	9.11105i		−	0.480863i	−0.970666	−	0.240431i	$-0.922711\pi$
$359$		−	9.11105i		−	0.480863i	0.970666	−	0.240431i	$-0.0772889\pi$
$360$	−9.04504	−	7.56735i	−0.476715	−	0.398835i
$361$	−2.00947	+	3.48050i	−0.105762	+	0.183184i
$362$	−13.8167	+	4.14373i	−0.726190	+	0.217790i
$363$	−5.24768	−	9.08925i	−0.275432	−	0.477062i
$364$	5.63208	−	0.333497i	0.295201	−	0.0174800i
$365$	−4.59953	+	2.65554i	−0.240750	+	0.138997i
$366$	−10.7160	−	2.53426i	−0.560134	−	0.132468i
$367$	−12.0486	+	20.8689i	−0.628934	+	1.08935i	0.358832	+	0.933402i	$0.383175\pi$
$367$	−12.0486	+	20.8689i	−0.628934	+	1.08935i	−0.987766	+	0.155943i	$0.950158\pi$
$368$	−18.4808	+	13.8141i	−0.963377	+	0.720108i
$369$	−7.26972	−	4.19717i	−0.378446	−	0.218496i
$370$	−41.6902	−	9.85948i	−2.16737	−	0.512570i
$371$	−5.17195	−	2.98603i	−0.268515	−	0.155027i
$372$	8.52324	+	4.27022i	0.441910	+	0.221400i
$373$	15.1386	+	8.74029i	0.783848	+	0.452555i	0.837792	−	0.545989i	$-0.183846\pi$
$373$	15.1386	+	8.74029i	0.783848	+	0.452555i	−0.0539441	+	0.998544i	$0.517179\pi$
$374$	−24.4013	−	22.9991i	−1.26176	−	1.18926i
$375$			30.7904i			1.59001i
$376$	−1.45036	+	0.530270i	−0.0747964	+	0.0273466i
$377$			16.7633i			0.863355i
$378$	−2.31115	+	0.693131i	−0.118873	+	0.0356508i
$379$	−10.3448	−	17.9177i	−0.531377	−	0.920373i	−0.999329	−	0.0366187i	$-0.988341\pi$
$379$	−10.3448	−	17.9177i	−0.531377	−	0.920373i	0.467952	−	0.883754i	$-0.344992\pi$
$380$	−26.9494	+	17.7622i	−1.38247	+	0.911183i
$381$	−5.52839	−	3.19182i	−0.283228	−	0.163522i
$382$	−2.78908	+	11.7935i	−0.142702	+	0.603407i
$383$	−10.2473	−	17.7489i	−0.523615	−	0.906928i	−0.999622	−	0.0274863i	$-0.991250\pi$
$383$	−10.2473	−	17.7489i	−0.523615	−	0.906928i	0.476007	−	0.879441i	$-0.342084\pi$
$384$	−6.18495	+	9.47346i	−0.315624	+	0.483440i
$385$	−28.5629	+	16.4908i	−1.45570	+	0.840448i
$386$	−3.96933	−	3.74124i	−0.202034	−	0.190424i
$387$	−2.95503			−0.150213
$388$	−17.5844	−	26.6795i	−0.892713	−	1.35445i
$389$	−8.16640	−	14.1446i	−0.414053	−	0.717161i	0.581276	−	0.813707i	$-0.302554\pi$
$389$	−8.16640	−	14.1446i	−0.414053	−	0.717161i	−0.995329	+	0.0965459i	$0.969221\pi$
$390$	−2.24380	+	9.48778i	−0.113619	+	0.480433i
$391$	25.5473	+	14.7498i	1.29198	+	0.745927i
$392$	11.3929	+	1.99183i	0.575426	+	0.100603i
$393$			12.7546i			0.643384i
$394$	−0.404730	−	1.34952i	−0.0203900	−	0.0679877i
$395$	53.4660	+	30.8686i	2.69016	+	1.55317i
$396$	8.29033	+	4.15353i	0.416605	+	0.208723i
$397$	7.46142			0.374478			0.187239	−	0.982314i	$-0.440046\pi$
$397$	7.46142			0.374478			0.187239	+	0.982314i	$0.440046\pi$
$398$	−29.1739	−	6.89944i	−1.46236	−	0.345838i
$399$			6.60369i			0.330598i
$400$	49.1926	−	5.84627i	2.45963	−	0.292313i
$401$			21.9869i			1.09797i	0.835831	+	0.548987i	$0.184986\pi$
$401$			21.9869i			1.09797i	−0.835831	+	0.548987i	$0.815014\pi$
$402$	−10.6132	−	4.62163i	−0.529340	−	0.230506i
$403$		−	7.88113i		−	0.392587i
$404$	−13.7098	+	27.3643i	−0.682086	+	1.36143i
$405$		−	4.16950i		−	0.207184i
$406$	5.63000	−	23.8061i	0.279412	−	1.18148i
$407$	33.6842			1.66966
$408$	14.2487	+	2.49113i	0.705418	+	0.123329i
$409$	10.1078	+	5.83576i	0.499800	+	0.288560i	0.728631	−	0.684906i	$-0.240157\pi$
$409$	10.1078	+	5.83576i	0.499800	+	0.288560i	−0.228831	+	0.973466i	$0.573490\pi$
$410$	47.4115	−	14.2190i	2.34149	−	0.702229i
$411$		−	5.96671i		−	0.294316i
$412$	6.87732	−	13.7270i	0.338821	−	0.676278i
$413$	−15.5611	−	8.98421i	−0.765712	−	0.442084i
$414$	−7.93859	−	1.87743i	−0.390160	−	0.0922704i
$415$	−3.12686	−	5.41589i	−0.153492	−	0.265856i
$416$	9.29252	+	1.06337i	0.455603	+	0.0521360i
$417$	−8.17487			−0.400325
$418$	17.4066	−	18.4678i	0.851383	−	0.903288i
$419$	−10.2137	+	5.89691i	−0.498974	+	0.288083i	−0.728290	−	0.685269i	$-0.759685\pi$
$419$	−10.2137	+	5.89691i	−0.498974	+	0.288083i	0.229316	+	0.973352i	$0.426351\pi$
$420$	6.37299	−	12.7203i	0.310970	−	0.620689i
$421$	6.61403	+	11.4558i	0.322348	+	0.558323i	0.980972	−	0.194149i	$-0.0621946\pi$
$421$	6.61403	+	11.4558i	0.322348	+	0.558323i	−0.658624	+	0.752472i	$0.728861\pi$
$422$	−8.26489	−	1.95459i	−0.402329	−	0.0951481i
$423$	−0.472829	−	0.272988i	−0.0229897	−	0.0132731i
$424$	−7.59339	−	6.35286i	−0.368768	−	0.308522i
$425$	−31.6683	−	54.8511i	−1.53614	−	2.66067i
$426$	−1.42675	−	4.75732i	−0.0691265	−	0.230493i
$427$		−	13.2846i		−	0.642889i
$428$	0.955390	−	0.0565723i	0.0461805	−	0.00273453i
$429$		−	7.66577i		−	0.370107i
$430$	11.9513	−	12.6799i	0.576343	−	0.611480i
$431$	−33.9419	−	19.5964i	−1.63492	−	0.943923i	−0.982544	−	0.186030i	$-0.940438\pi$
$431$	−33.9419	−	19.5964i	−1.63492	−	0.943923i	−0.652379	−	0.757893i	$-0.726229\pi$
$432$	−3.97205	+	0.472056i	−0.191105	+	0.0227118i
$433$	−27.8113	−	16.0569i	−1.33653	−	0.771643i	−0.350235	−	0.936662i	$-0.613898\pi$
$433$	−27.8113	−	16.0569i	−1.33653	−	0.771643i	−0.986290	+	0.165019i	$0.947232\pi$
$434$	−2.64690	+	11.1923i	−0.127055	+	0.537246i
$435$	36.6092	+	21.1363i	1.75528	+	1.01341i
$436$	−13.2570	+	0.784999i	−0.634896	+	0.0375947i
$437$	−11.1632	+	19.3351i	−0.534006	+	0.924926i
$438$	−0.414587	+	1.75306i	−0.0198098	+	0.0837644i
$439$	12.5976	−	7.27325i	0.601253	−	0.347133i	−0.168282	−	0.985739i	$-0.553822\pi$
$439$	12.5976	−	7.27325i	0.601253	−	0.347133i	0.769534	+	0.638606i	$0.220488\pi$
$440$	−51.3519	+	18.7750i	−2.44811	+	0.895063i
$441$	2.04454	+	3.54125i	0.0973590	+	0.168631i
$442$	−3.43521	−	11.4542i	−0.163396	−	0.544822i
$443$	−0.670339	+	1.16106i	−0.0318488	+	0.0551637i	−0.881510	−	0.472165i	$-0.843473\pi$
$443$	−0.670339	+	1.16106i	−0.0318488	+	0.0551637i	0.849662	+	0.527328i	$0.176806\pi$
$444$	−12.1324	+	7.99643i	−0.575778	+	0.379494i
$445$			25.1759i			1.19345i
$446$	21.4243	−	22.7304i	1.01447	−	1.07632i
$447$	14.2624			0.674589
$448$	−12.8395	−	4.63104i	−0.606609	−	0.218796i
$449$	8.92592	−	15.4601i	0.421240	−	0.729609i	−0.574821	−	0.818279i	$-0.694928\pi$
$449$	8.92592	−	15.4601i	0.421240	−	0.729609i	0.996061	+	0.0886699i	$0.0282616\pi$
$450$	12.7455	+	12.0131i	0.600827	+	0.566302i
$451$	−33.7047	+	19.4594i	−1.58709	+	0.916307i
$452$	7.22937	−	14.4296i	0.340041	−	0.678713i
$453$	5.11146	−	2.95110i	0.240157	−	0.138655i
$454$	−0.161127	−	0.537254i	−0.00756204	−	0.0252146i
$455$	−11.7620			−0.551412
$456$	−1.88538	+	10.7840i	−0.0882908	+	0.505005i
$457$	12.1291	−	21.0083i	0.567377	−	0.982726i	−0.429447	−	0.903092i	$-0.641291\pi$
$457$	12.1291	−	21.0083i	0.567377	−	0.982726i	0.996824	−	0.0796341i	$-0.0253752\pi$
$458$	−22.9196	−	5.42035i	−1.07096	−	0.253276i
$459$	2.55705	+	4.42894i	0.119353	+	0.206725i
$460$	40.1627	−	26.4711i	1.87259	−	1.23422i
$461$	−10.1386			−0.472200			−0.236100	−	0.971729i	$-0.575869\pi$
$461$	−10.1386			−0.472200			−0.236100	+	0.971729i	$0.575869\pi$
$462$	−2.57457	+	10.8864i	−0.119780	+	0.506482i
$463$	15.7638	+	27.3037i	0.732605	+	1.26891i	0.955766	+	0.294128i	$0.0950291\pi$
$463$	15.7638	+	27.3037i	0.732605	+	1.26891i	−0.223161	+	0.974782i	$0.571638\pi$
$464$	15.9907	−	37.2686i	0.742348	−	1.73015i
$465$	−17.2115	−	9.93708i	−0.798165	−	0.460821i
$466$	1.17917	+	3.93177i	0.0546238	+	0.182136i
$467$	5.31715	−	3.06986i	0.246049	−	0.142056i	−0.371905	−	0.928271i	$-0.621295\pi$
$467$	5.31715	−	3.06986i	0.246049	−	0.142056i	0.617954	+	0.786215i	$0.287962\pi$
$468$	1.81981	+	2.76107i	0.0841208	+	0.127630i
$469$	2.47918	−	13.7436i	0.114478	−	0.634618i
$470$	3.08368	−	0.924819i	0.142240	−	0.0426587i
$471$	7.55154	+	13.0796i	0.347956	+	0.602678i
$472$	−22.8466	−	19.1142i	−1.05160	−	0.879801i
$473$	−6.85022	+	11.8649i	−0.314974	+	0.545550i
$474$	20.0575	−	6.01538i	0.921270	−	0.276296i
$475$	41.5133	−	23.9677i	1.90476	−	1.09971i
$476$	1.03152	+	17.4203i	0.0472797	+	0.798456i
$477$		−	3.50033i		−	0.160269i
$478$	−32.1392	+	9.63878i	−1.47001	+	0.440868i
$479$	10.5122	−	6.06919i	0.480312	−	0.277309i	−0.240234	−	0.970715i	$-0.577224\pi$
$479$	10.5122	−	6.06919i	0.480312	−	0.277309i	0.720547	+	0.693406i	$0.243891\pi$
$480$	14.0389	−	18.9531i	0.640787	−	0.865085i
$481$	10.4032	+	6.00630i	0.474346	+	0.273864i
$482$	9.70329	+	9.14572i	0.441973	+	0.416576i
$483$		−	9.84149i		−	0.447803i
$484$	17.5263	−	11.5515i	0.796651	−	0.525070i
$485$	33.3072	+	57.6898i	1.51240	+	2.61956i
$486$	−1.02913	−	0.969995i	−0.0466823	−	0.0439999i
$487$	−6.63771	−	11.4968i	−0.300783	−	0.520972i	0.675530	−	0.737332i	$-0.263915\pi$
$487$	−6.63771	−	11.4968i	−0.300783	−	0.520972i	−0.976314	+	0.216360i	$0.930581\pi$
$488$	3.79281	−	21.6941i	0.171693	−	0.982046i
$489$	18.3058	+	10.5688i	0.827815	+	0.477939i
$490$	−23.4643	−	5.54915i	−1.06001	−	0.250685i
$491$		−	11.5281i		−	0.520256i	−0.965574	−	0.260128i	$-0.916235\pi$
$491$		−	11.5281i		−	0.520256i	0.965574	−	0.260128i	$-0.0837648\pi$
$492$	7.52024	−	15.0102i	0.339039	−	0.676712i
$493$	−51.8496			−2.33519
$494$	8.66897	−	2.59989i	0.390036	−	0.116975i
$495$	−16.7412	−	9.66553i	−0.752461	−	0.434433i
$496$	−7.51788	+	17.5215i	−0.337563	+	0.786739i
$497$	5.18914	−	2.99595i	0.232765	−	0.134387i
$498$	−2.06421	−	0.488172i	−0.0924993	−	0.0218755i
$499$	2.18106	+	3.77771i	0.0976378	+	0.169114i	0.910706	−	0.413054i	$-0.135538\pi$
$499$	2.18106	+	3.77771i	0.0976378	+	0.169114i	−0.813069	+	0.582168i	$0.802205\pi$
$500$	−61.4732	+	3.64007i	−2.74917	+	0.162789i
$501$	3.00682	+	1.73599i	0.134335	+	0.0775581i
$502$	−1.29939	+	5.49438i	−0.0579944	+	0.245226i
$503$	0.541291	−	0.937543i	0.0241350	−	0.0418030i	−0.853706	−	0.520756i	$-0.825650\pi$
$503$	0.541291	−	0.937543i	0.0241350	−	0.0418030i	0.877841	+	0.478953i	$0.158984\pi$
$504$	−1.65706	−	4.53227i	−0.0738115	−	0.201884i
$505$	31.9035	−	55.2585i	1.41969	−	2.45897i
$506$	−25.9410	+	27.5225i	−1.15322	+	1.22353i
$507$	−5.13310	+	8.89079i	−0.227969	+	0.394854i
$508$	5.71891	−	11.4148i	0.253735	−	0.506449i
$509$	11.2846			0.500180			0.250090	−	0.968223i	$-0.419540\pi$
$509$	11.2846			0.500180			0.250090	+	0.968223i	$0.419540\pi$
$510$	−29.3461	−	6.94017i	−1.29947	−	0.307316i
$511$	−2.17327			−0.0961399
$512$	−19.6450	−	11.2283i	−0.868193	−	0.496226i
$513$	−3.35198	+	1.93527i	−0.147994	+	0.0854442i
$514$	−3.01743	+	0.904950i	−0.133093	+	0.0399156i
$515$	−16.0040	+	27.7197i	−0.705219	+	1.22148i
$516$	−0.349346	−	5.89973i	−0.0153791	−	0.259721i
$517$	−2.19218	+	1.26566i	−0.0964120	+	0.0556635i
$518$	−12.7567	−	12.0237i	−0.560498	−	0.528291i
$519$	−6.45025	−	11.1722i	−0.283134	−	0.490403i
$520$	−19.2076	−	3.35810i	−0.842311	−	0.147262i
$521$		−	30.7942i		−	1.34912i	−0.738221	−	0.674559i	$-0.764334\pi$
$521$		−	30.7942i		−	1.34912i	0.738221	−	0.674559i	$-0.235666\pi$
$522$	13.7338	−	4.11885i	0.601110	−	0.180277i
$523$	33.7241	−	19.4706i	1.47465	−	0.851391i	0.475061	−	0.879953i	$-0.342426\pi$
$523$	33.7241	−	19.4706i	1.47465	−	0.851391i	0.999592	+	0.0285614i	$0.00909260\pi$
$524$	−25.4646	+	1.50786i	−1.11242	+	0.0658710i
$525$	−10.5650	+	18.2992i	−0.461095	+	0.798641i
$526$	11.0303	−	11.7028i	0.480944	−	0.510265i
$527$	24.3767			1.06186
$528$	−7.31244	+	17.0427i	−0.318233	+	0.741689i
$529$	5.13647	−	8.89663i	0.223325	−	0.386810i
$530$	15.0198	+	14.1567i	0.652417	+	0.614927i
$531$		−	10.5316i		−	0.457033i
$532$	−13.1843	+	0.780692i	−0.571611	+	0.0338473i
$533$	−13.8794			−0.601183
$534$	6.21401	+	5.85694i	0.268907	+	0.253455i
$535$	−1.99524			−0.0862615
$536$	7.97240	−	21.7357i	0.344355	−	0.938839i
$537$	25.2737			1.09064
$538$	−4.59275	−	4.32884i	−0.198008	−	0.186630i
$539$	18.9582			0.816589
$540$	8.32441	−	0.492921i	0.358226	−	0.0212119i
$541$			19.0662i			0.819722i	0.912148	+	0.409861i	$0.134423\pi$
$541$			19.0662i			0.819722i	−0.912148	+	0.409861i	$0.865577\pi$
$542$	22.0097	+	20.7450i	0.945397	+	0.891073i
$543$	5.09990	−	8.83329i	0.218858	−	0.379073i
$544$	−3.28905	+	28.7421i	−0.141017	+	1.23231i
$545$	27.6859			1.18594
$546$	−2.73633	+	2.90315i	−0.117104	+	0.124243i
$547$	8.86084	−	15.3474i	0.378862	−	0.656208i	−0.612035	−	0.790831i	$-0.709649\pi$
$547$	8.86084	−	15.3474i	0.378862	−	0.656208i	0.990897	+	0.134622i	$0.0429821\pi$
$548$	11.9126	−	0.705389i	0.508879	−	0.0301327i
$549$	6.74319	−	3.89318i	0.287792	−	0.166157i
$550$	77.7805	−	23.3269i	3.31657	−	0.994664i
$551$		−	39.2417i		−	1.67175i
$552$	2.80978	−	16.0714i	0.119592	−	0.684043i
$553$	12.6313	+	21.8781i	0.537138	+	0.930350i
$554$	14.7468	+	13.8994i	0.626530	+	0.590528i
$555$	26.2342	−	15.1463i	1.11358	−	0.642925i
$556$	−0.966438	−	16.3211i	−0.0409861	−	0.692171i
$557$	−17.4038	+	30.1442i	−0.737421	+	1.27725i	0.216232	+	0.976342i	$0.430623\pi$
$557$	−17.4038	+	30.1442i	−0.737421	+	1.27725i	−0.953653	+	0.300909i	$0.902710\pi$
$558$	−6.45681	+	1.93644i	−0.273339	+	0.0819762i
$559$	−4.23133	+	2.44296i	−0.178966	+	0.103326i
$560$	26.1496	+	11.2199i	1.10502	+	0.474127i
$561$	23.7106			1.00106
$562$	−25.1002	−	5.93604i	−1.05879	−	0.250397i
$563$	−12.4444			−0.524467			−0.262234	−	0.965004i	$-0.584459\pi$
$563$	−12.4444			−0.524467			−0.262234	+	0.965004i	$0.584459\pi$
$564$	0.489123	−	0.976277i	0.0205958	−	0.0411087i
$565$	−16.8232	+	29.1387i	−0.707759	+	1.22587i
$566$	12.9952	−	13.7874i	0.546228	−	0.579529i
$567$	0.853071	−	1.47756i	0.0358256	−	0.0620518i
$568$	9.32933	−	3.41093i	0.391450	−	0.143120i
$569$	−7.94945	+	13.7688i	−0.333258	+	0.577220i	−0.983149	−	0.182808i	$-0.941481\pi$
$569$	−7.94945	+	13.7688i	−0.333258	+	0.577220i	0.649890	+	0.760028i	$0.274815\pi$
$570$	5.25257	−	22.2102i	0.220006	−	0.930283i
$571$	2.35850	+	1.36168i	0.0987002	+	0.0569846i	0.548538	−	0.836126i	$-0.315185\pi$
$571$	2.35850	+	1.36168i	0.0987002	+	0.0569846i	−0.449837	+	0.893110i	$0.648518\pi$
$572$	15.3047	−	0.906253i	0.639923	−	0.0378923i
$573$	−4.28464	−	7.42121i	−0.178993	−	0.310026i
$574$	19.7106	+	4.66143i	0.822704	+	0.194564i
$575$	−61.8673	+	35.7191i	−2.58005	+	1.48959i
$576$	−1.41204	−	7.87440i	−0.0588350	−	0.328100i
$577$	−7.93997	−	4.58414i	−0.330545	−	0.190840i	0.325538	−	0.945529i	$-0.394455\pi$
$577$	−7.93997	−	4.58414i	−0.330545	−	0.190840i	−0.656083	+	0.754689i	$0.727788\pi$
$578$	12.4001	−	3.71888i	0.515776	−	0.154685i
$579$	3.85697			0.160290
$580$	−37.8708	+	75.5892i	−1.57250	+	3.13867i
$581$		−	2.55900i		−	0.106165i
$582$	21.9878	+	5.19998i	0.911425	+	0.215546i
$583$	−14.0544	−	8.11430i	−0.582073	−	0.336060i
$584$	−3.54900	−	0.620477i	−0.146859	−	0.0256755i
$585$	−3.44697	−	5.97032i	−0.142515	−	0.246842i
$586$	28.4648	+	26.8291i	1.17587	+	1.10830i
$587$	−8.50625	−	14.7333i	−0.351091	−	0.608107i	0.635350	−	0.772224i	$-0.280856\pi$
$587$	−8.50625	−	14.7333i	−0.351091	−	0.608107i	−0.986441	+	0.164117i	$0.947522\pi$
$588$	−6.82840	+	4.50058i	−0.281599	+	0.185601i
$589$			18.4492i			0.760184i
$590$	45.1907	+	42.5939i	1.86047	+	1.75356i
$591$	0.862773	+	0.498122i	0.0354897	+	0.0204900i
$592$	−17.3992	−	23.2770i	−0.715103	−	0.956680i
$593$	−6.59437	+	3.80726i	−0.270798	+	0.156345i	−0.629250	−	0.777203i	$-0.716638\pi$
$593$	−6.59437	+	3.80726i	−0.270798	+	0.156345i	0.358452	+	0.933548i	$0.383305\pi$
$594$	−6.28037	+	1.88353i	−0.257687	+	0.0772821i
$595$		−	36.3804i		−	1.49145i
$596$	1.68611	+	28.4750i	0.0690659	+	1.16638i
$597$	18.3581	−	10.5990i	0.751347	−	0.433790i
$598$	−12.9194	+	3.87462i	−0.528313	+	0.158445i
$599$	−10.0070	+	17.3326i	−0.408875	+	0.708192i	−0.994764	−	0.102199i	$-0.967412\pi$
$599$	−10.0070	+	17.3326i	−0.408875	+	0.708192i	0.585889	+	0.810391i	$0.300745\pi$
$600$	−22.4774	+	26.8666i	−0.917635	+	1.09682i
$601$	18.9857	+	32.8842i	0.774443	+	1.34138i	0.935107	+	0.354366i	$0.115303\pi$
$601$	18.9857	+	32.8842i	0.774443	+	1.34138i	−0.160663	+	0.987009i	$0.551363\pi$
$602$	6.82952	−	2.04822i	0.278351	−	0.0834794i
$603$	7.70268	−	2.76925i	0.313677	−	0.112773i
$604$	6.49617	+	9.85617i	0.264325	+	0.401042i
$605$	−37.8976	+	21.8802i	−1.54076	+	0.889556i
$606$	−6.21706	−	20.7299i	−0.252551	−	0.842096i
$607$	−16.1381	−	9.31735i	−0.655026	−	0.378179i	0.135353	−	0.990797i	$-0.456783\pi$
$607$	−16.1381	−	9.31735i	−0.655026	−	0.378179i	−0.790379	+	0.612618i	$0.790116\pi$
$608$	−21.7531	−	2.48927i	−0.882205	−	0.100953i
$609$	8.64891	+	14.9804i	0.350472	+	0.607035i
$610$	−10.5666	+	44.6803i	−0.427829	+	1.80905i
$611$	−0.902728			−0.0365205
$612$	−8.54010	+	5.62875i	−0.345213	+	0.227529i
$613$	15.9728	+	27.6657i	0.645136	+	1.11741i	0.984270	+	0.176670i	$0.0565326\pi$
$613$	15.9728	+	27.6657i	0.645136	+	1.11741i	−0.339134	+	0.940738i	$0.610134\pi$
$614$	15.6397	+	3.69869i	0.631168	+	0.149267i
$615$	−17.5001	+	30.3111i	−0.705672	+	1.22226i
$616$	−22.0391	−	3.85314i	−0.887982	−	0.155247i
$617$	−29.2728			−1.17848			−0.589239	−	0.807959i	$-0.700572\pi$
$617$	−29.2728			−1.17848			−0.589239	+	0.807959i	$0.700572\pi$
$618$	3.11871	+	10.3989i	0.125453	+	0.418305i
$619$	−33.9365	+	19.5933i	−1.36402	+	0.787520i	−0.990157	−	0.139962i	$-0.955302\pi$
$619$	−33.9365	+	19.5933i	−1.36402	+	0.787520i	−0.373868	+	0.927482i	$0.621969\pi$
$620$	17.8046	−	35.5376i	0.715052	−	1.42723i
$621$	4.99547	−	2.88414i	0.200461	−	0.115736i
$622$	−14.3495	−	13.5249i	−0.575362	−	0.542300i
$623$	−5.15094	+	8.92170i	−0.206368	+	0.357440i
$624$	−5.29734	+	3.95967i	−0.212063	+	0.158514i
$625$	66.4572			2.65829
$626$	−1.82813	+	1.93959i	−0.0730669	+	0.0775214i
$627$			17.9450i			0.716655i
$628$	−25.2208	+	16.6229i	−1.00642	+	0.663328i
$629$	−18.5777	+	32.1776i	−0.740743	+	1.28300i
$630$	2.89001	+	9.63633i	0.115141	+	0.383920i
$631$	−18.5384	−	32.1094i	−0.738000	−	1.27825i	−0.953394	−	0.301727i	$-0.902437\pi$
$631$	−18.5384	−	32.1094i	−0.738000	−	1.27825i	0.215394	−	0.976527i	$-0.430896\pi$
$632$	14.3809	+	39.3336i	0.572043	+	1.56461i
$633$	5.20080	−	3.00268i	0.206713	−	0.119346i
$634$	1.60796	−	6.79915i	0.0638601	−	0.270029i
$635$	−13.3083	+	23.0506i	−0.528123	+	0.914736i
$636$	6.98842	−	0.413811i	0.277109	−	0.0164087i
$637$	5.85517	+	3.38049i	0.231990	+	0.133940i
$638$	15.2991	−	64.6914i	0.605697	−	2.56116i
$639$	3.04145	+	1.75598i	0.120318	+	0.0694655i
$640$	39.4995	+	25.7881i	1.56136	+	1.01937i
$641$	17.1212	+	9.88492i	0.676246	+	0.390431i	0.798439	−	0.602076i	$-0.205659\pi$
$641$	17.1212	+	9.88492i	0.676246	+	0.390431i	−0.122193	+	0.992506i	$0.538993\pi$
$642$	−0.464173	+	0.492472i	−0.0183194	+	0.0194363i
$643$		−	38.1300i		−	1.50370i	−0.659333	−	0.751851i	$-0.729161\pi$
$643$		−	38.1300i		−	1.50370i	0.659333	−	0.751851i	$-0.270839\pi$
$644$	19.6486	−	1.16347i	0.774262	−	0.0458470i
$645$			12.3210i			0.485139i
$646$	8.04156	+	26.8135i	0.316391	+	1.05496i
$647$	21.5950	+	37.4036i	0.848986	+	1.47049i	0.882114	+	0.471035i	$0.156120\pi$
$647$	21.5950	+	37.4036i	0.848986	+	1.47049i	−0.0331286	+	0.999451i	$0.510547\pi$
$648$	1.81493	−	2.16934i	0.0712973	−	0.0852196i
$649$	−42.2861	−	24.4139i	−1.65988	−	0.958330i
$650$	28.1817	+	6.66478i	1.10538	+	0.261414i
$651$	−4.06621	−	7.04289i	−0.159368	−	0.276033i
$652$	−18.9366	+	37.7970i	−0.741614	+	1.48024i
$653$	16.7917	−	9.69467i	0.657108	−	0.379382i	−0.134066	−	0.990972i	$-0.542803\pi$
$653$	16.7917	−	9.69467i	0.657108	−	0.379382i	0.791174	+	0.611591i	$0.209470\pi$
$654$	6.44088	−	6.83355i	0.251858	−	0.267213i
$655$	53.1802			2.07792
$656$	30.8570	+	13.2397i	1.20476	+	0.516922i
$657$	−0.636897	−	1.10314i	−0.0248477	−	0.0430375i
$658$	1.28199	+	0.303184i	0.0499774	+	0.0118193i
$659$	−16.2607	−	9.38809i	−0.633425	−	0.365708i	0.148652	−	0.988890i	$-0.452507\pi$
$659$	−16.2607	−	9.38809i	−0.633425	−	0.365708i	−0.782077	+	0.623181i	$0.785840\pi$
$660$	17.3181	−	34.5665i	0.674107	−	1.34550i
$661$		−	7.15199i		−	0.278180i	−0.990280	−	0.139090i	$-0.955582\pi$
$661$		−	7.15199i		−	0.278180i	0.990280	−	0.139090i	$-0.0444177\pi$
$662$	2.56340	−	0.768782i	0.0996293	−	0.0298796i
$663$	7.32291	+	4.22788i	0.284398	+	0.164197i
$664$	0.730604	−	4.17891i	0.0283530	−	0.162173i
$665$	27.5340			1.06772
$666$	2.36467	−	9.99887i	0.0916291	−	0.387448i
$667$			58.4820i			2.26443i
$668$	−3.11043	+	6.20835i	−0.120346	+	0.240208i
$669$			22.0870i			0.853932i
$670$	−19.2699	+	44.2518i	−0.744460	+	1.70960i
$671$		−	36.1000i		−	1.39362i
$672$	8.85280	−	3.84414i	0.341504	−	0.148291i
$673$		−	7.78300i		−	0.300013i	−0.988685	−	0.150006i	$-0.952071\pi$
$673$		−	7.78300i		−	0.300013i	0.988685	−	0.150006i	$-0.0479294\pi$
$674$	−11.1606	−	2.63941i	−0.429890	−	0.101666i
$675$	−12.3847			−0.476687
$676$	−18.3573	−	9.19717i	−0.706051	−	0.353737i
$677$	−36.6838	−	21.1794i	−1.40987	−	0.813990i	−0.414497	−	0.910051i	$-0.636042\pi$
$677$	−36.6838	−	21.1794i	−1.40987	−	0.813990i	−0.995375	+	0.0960607i	$0.969376\pi$
$678$	3.27835	+	10.9312i	0.125904	+	0.419811i
$679$			27.2584i			1.04608i
$680$	10.3867	−	59.4101i	0.398314	−	2.27827i
$681$	0.343477	+	0.198307i	0.0131621	+	0.00759913i
$682$	−7.19274	+	30.4141i	−0.275424	+	1.16462i
$683$	−15.9567	−	27.6378i	−0.610566	−	1.05753i	−0.991145	−	0.132783i	$-0.957609\pi$
$683$	−15.9567	−	27.6378i	−0.610566	−	1.05753i	0.380579	−	0.924748i	$-0.375725\pi$
$684$	−4.26004	−	6.46346i	−0.162887	−	0.247136i
$685$	−24.8782			−0.950547
$686$	−19.4707	−	18.3519i	−0.743394	−	0.700677i
$687$	14.4225	−	8.32684i	0.550253	−	0.317689i
$688$	11.7375	−	1.39494i	0.447489	−	0.0531816i
$689$	−2.89376	−	5.01214i	−0.110243	−	0.190947i
$690$	−7.82792	+	33.0999i	−0.298004	+	1.26009i
$691$	18.2527	+	10.5382i	0.694367	+	0.400893i	0.805246	−	0.592941i	$-0.202033\pi$
$691$	18.2527	+	10.5382i	0.694367	+	0.400893i	−0.110879	+	0.993834i	$0.535367\pi$
$692$	21.5427	−	14.1987i	0.818930	−	0.539754i
$693$	−3.95510	−	6.85043i	−0.150242	−	0.260227i
$694$	13.6335	−	4.08879i	0.517520	−	0.155208i
$695$			34.0851i			1.29292i
$696$	9.84692	+	26.9325i	0.373246	+	1.02088i
$697$		−	42.9295i		−	1.62607i
$698$	−35.7385	−	33.6849i	−1.35272	−	1.27499i
$699$	−2.51365	−	1.45126i	−0.0950751	−	0.0548916i
$700$	−37.7833	−	18.9298i	−1.42808	−	0.715478i
$701$	30.4377	+	17.5732i	1.14961	+	0.663730i	0.948793	−	0.315898i	$-0.102306\pi$
$701$	30.4377	+	17.5732i	1.14961	+	0.663730i	0.200821	+	0.979628i	$0.435639\pi$
$702$	−2.27552	−	0.538147i	−0.0858841	−	0.0203110i
$703$	−24.3532	−	14.0603i	−0.918497	−	0.530294i
$704$	−34.8903	−	12.5845i	−1.31498	−	0.474296i
$705$	−1.13822	+	1.97146i	−0.0428679	+	0.0742494i
$706$	25.4385	+	6.01605i	0.957391	+	0.226417i
$707$	22.6116	−	13.0548i	0.850396	−	0.490976i
$708$	21.0264	−	1.24505i	0.790220	−	0.0467920i
$709$	−3.69484	−	6.39965i	−0.138763	−	0.240344i	0.788266	−	0.615335i	$-0.210979\pi$
$709$	−3.69484	−	6.39965i	−0.138763	−	0.240344i	−0.927029	+	0.374991i	$0.877646\pi$
$710$	−19.8356	+	5.94885i	−0.744418	+	0.223256i
$711$	−7.40343	+	12.8231i	−0.277650	+	0.480905i
$712$	−10.9588	+	13.0987i	−0.410698	+	0.490895i
$713$		−	27.4948i		−	1.02969i
$714$	−8.97956	−	8.46357i	−0.336052	−	0.316741i
$715$	−31.9624			−1.19533
$716$	2.98787	+	50.4590i	0.111662	+	1.88574i
$717$	11.8629	−	20.5472i	0.443029	−	0.767349i
$718$	−8.83767	+	9.37646i	−0.329819	+	0.349926i
$719$	−9.46958	+	5.46727i	−0.353156	+	0.203895i	−0.666074	−	0.745885i	$-0.732027\pi$
$719$	−9.46958	+	5.46727i	−0.353156	+	0.203895i	0.312918	+	0.949780i	$0.398693\pi$
$720$	1.96824	+	16.5614i	0.0733518	+	0.617208i
$721$	−11.3428	+	6.54877i	−0.422428	+	0.243889i
$722$	5.44407	−	1.63272i	0.202607	−	0.0607635i
$723$	−9.42863			−0.350654
$724$	18.2386	+	9.13769i	0.677832	+	0.339600i
$725$	62.7815	−	108.741i	2.33165	−	4.03853i
$726$	−3.41597	+	14.4442i	−0.126779	+	0.536076i
$727$	−8.20134	−	14.2051i	−0.304171	−	0.526839i	0.672906	−	0.739728i	$-0.265046\pi$
$727$	−8.20134	−	14.2051i	−0.304171	−	0.526839i	−0.977076	+	0.212889i	$0.931713\pi$
$728$	−6.11964	−	5.11987i	−0.226809	−	0.189755i
$729$	1.00000			0.0370370
$730$	7.30937	+	1.72862i	0.270532	+	0.0639791i
$731$	−7.55617	−	13.0877i	−0.279475	−	0.484065i
$732$	8.56993	+	13.0025i	0.316754	+	0.480588i
$733$	23.0097	+	13.2847i	0.849884	+	0.490681i	0.860612	−	0.509262i	$-0.170082\pi$
$733$	23.0097	+	13.2847i	0.849884	+	0.490681i	−0.0107280	+	0.999942i	$0.503415\pi$
$734$	32.6423	−	9.78967i	1.20485	−	0.361343i
$735$	14.7652	−	8.52470i	0.544623	−	0.314438i
$736$	32.4187	+	3.70977i	1.19497	+	0.136744i
$737$	6.73699	−	37.3470i	0.248160	−	1.37570i
$738$	3.41026	+	11.3710i	0.125533	+	0.418573i
$739$	−14.7697	−	25.5818i	−0.543311	−	0.941042i	−0.998711	−	0.0507555i	$-0.983837\pi$
$739$	−14.7697	−	25.5818i	−0.543311	−	0.941042i	0.455400	−	0.890287i	$-0.349496\pi$
$740$	33.3411	+	50.5860i	1.22564	+	1.85958i
$741$	−3.19982	+	5.54224i	−0.117548	+	0.203599i
$742$	2.42619	+	8.08978i	0.0890681	+	0.296985i
$743$	−31.7258	+	18.3169i	−1.16391	+	0.671981i	−0.952237	−	0.305360i	$-0.901223\pi$
$743$	−31.7258	+	18.3169i	−1.16391	+	0.671981i	−0.211669	+	0.977341i	$0.567890\pi$
$744$	−4.62945	−	12.6621i	−0.169724	−	0.464216i
$745$		−	59.4671i		−	2.17871i
$746$	−7.10159	−	23.6793i	−0.260008	−	0.866960i
$747$	1.29893	−	0.749938i	0.0475254	−	0.0274388i
$748$	2.80308	+	47.3382i	0.102491	+	1.73086i
$749$	−0.707060	−	0.408221i	−0.0258354	−	0.0149161i
$750$	29.8666	−	31.6874i	1.09057	−	1.15706i
$751$		−	2.16041i		−	0.0788346i	−0.999223	−	0.0394173i	$-0.987450\pi$
$751$		−	2.16041i		−	0.0788346i	0.999223	−	0.0394173i	$-0.0125502\pi$
$752$	2.00697	+	0.861120i	0.0731865	+	0.0314018i
$753$	−1.99614	−	3.45742i	−0.0727434	−	0.125995i
$754$	16.2603	−	17.2516i	0.592166	−	0.628268i
$755$	−12.3046	−	21.3122i	−0.447811	−	0.775631i
$756$	3.05081	+	1.52848i	0.110957	+	0.0555903i
$757$	−6.76318	−	3.90473i	−0.245812	−	0.141920i	0.372033	−	0.928219i	$-0.378661\pi$
$757$	−6.76318	−	3.90473i	−0.245812	−	0.141920i	−0.617845	+	0.786300i	$0.711994\pi$
$758$	−6.73395	+	28.4741i	−0.244588	+	1.03423i
$759$		−	26.7435i		−	0.970727i
$760$	44.9637	+	7.86107i	1.63100	+	0.285151i
$761$	1.59990			0.0579963			0.0289982	−	0.999579i	$-0.490768\pi$
$761$	1.59990			0.0579963			0.0289982	+	0.999579i	$0.490768\pi$
$762$	2.59339	+	8.64731i	0.0939487	+	0.313259i
$763$	9.81119	+	5.66449i	0.355189	+	0.205068i
$764$	14.3099	−	9.43164i	0.517716	−	0.341225i
$765$	18.4665	−	10.6616i	0.667656	−	0.385471i
$766$	−6.67050	+	28.2058i	−0.241015	+	1.01912i
$767$	−8.70660	−	15.0803i	−0.314377	−	0.544517i
$768$	15.5543	−	3.75006i	0.561268	−	0.135319i
$769$	28.0130	+	16.1733i	1.01017	+	0.583225i	0.911243	−	0.411870i	$-0.135124\pi$
$769$	28.0130	+	16.1733i	1.01017	+	0.583225i	0.0989319	+	0.995094i	$0.468457\pi$
$770$	45.3909	+	10.7347i	1.63577	+	0.386850i
$771$	1.11377	−	1.92910i	0.0401114	−	0.0694749i
$772$	0.455974	+	7.70046i	0.0164109	+	0.277146i
$773$	9.20107	−	15.9367i	0.330940	−	0.573204i	−0.651757	−	0.758428i	$-0.725968\pi$
$773$	9.20107	−	15.9367i	0.330940	−	0.573204i	0.982696	+	0.185224i	$0.0593010\pi$
$774$	3.04112	+	2.86637i	0.109311	+	0.103029i
$775$	−29.5162	+	51.1236i	−1.06025	+	1.83641i
$776$	−7.78236	+	44.5135i	−0.279371	+	1.59794i
$777$	12.3956			0.444691
$778$	−5.31591	+	22.4780i	−0.190585	+	0.805877i
$779$	32.4906			1.16410
$780$	11.5123	−	7.58769i	0.412205	−	0.271683i
$781$	14.1011	−	8.14126i	0.504576	−	0.291317i
$782$	−11.9844	−	39.9602i	−0.428560	−	1.42897i
$783$	−5.06928	+	8.78025i	−0.181161	+	0.313781i
$784$	−9.79268	−	13.1009i	−0.349738	−	0.467888i
$785$	54.5355	−	31.4861i	1.94646	−	1.12379i
$786$	12.3719	−	13.1261i	0.441290	−	0.468194i
$787$	11.2554	+	19.4950i	0.401212	+	0.694920i	0.993873	−	0.110532i	$-0.0352556\pi$
$787$	11.2554	+	19.4950i	0.401212	+	0.694920i	−0.592660	+	0.805453i	$0.701922\pi$
$788$	−0.892505	+	1.78142i	−0.0317942	+	0.0634604i
$789$			11.3715i			0.404836i
$790$	−25.0811	−	83.6295i	−0.892346	−	2.97540i
$791$	−11.9234	+	6.88400i	−0.423949	+	0.244767i
$792$	−4.50294	−	12.3161i	−0.160005	−	0.437634i
$793$	6.43707	−	11.1493i	0.228587	−	0.395924i
$794$	−7.67878	−	7.23754i	−0.272510	−	0.256851i
$795$	−14.5946			−0.517617
$796$	23.3313	+	35.3990i	0.826957	+	1.25468i
$797$	16.4943	−	28.5689i	0.584257	−	1.01196i	−0.410710	−	0.911766i	$-0.634719\pi$
$797$	16.4943	−	28.5689i	0.584257	−	1.01196i	0.994968	−	0.100197i	$-0.0319474\pi$
$798$	6.40554	−	6.79606i	0.226754	−	0.240578i
$799$		−	2.79218i		−	0.0987801i
$800$	−56.2965	−	41.7000i	−1.99038	−	1.47432i
$801$	−6.03812			−0.213346
$802$	21.3272	−	22.6274i	0.753089	−	0.799002i
$803$	−5.90570			−0.208408
$804$	6.43944	+	15.0510i	0.227102	+	0.530809i
$805$	−41.0340			−1.44626
$806$	−7.64466	+	8.11072i	−0.269272	+	0.285688i
$807$	4.46275			0.157096
$808$	40.6524	−	14.8631i	1.43015	−	0.522881i
$809$			30.9716i			1.08890i	0.838792	+	0.544452i	$0.183262\pi$
$809$			30.9716i			1.08890i	−0.838792	+	0.544452i	$0.816738\pi$
$810$	−4.04439	+	4.29096i	−0.142105	+	0.150769i
$811$	−3.96469	+	6.86705i	−0.139219	+	0.241135i	−0.927201	−	0.374564i	$-0.877793\pi$
$811$	−3.96469	+	6.86705i	−0.139219	+	0.241135i	0.787982	+	0.615698i	$0.211126\pi$
$812$	−28.8858	+	19.0386i	−1.01369	+	0.668123i
$813$	−21.3867			−0.750064
$814$	−34.6654	−	32.6735i	−1.21502	−	1.14520i
$815$	44.0667	−	76.3258i	1.54359	−	2.67358i
$816$	−12.2474	−	16.3849i	−0.428746	−	0.573586i
$817$	9.90523	−	5.71879i	0.346540	−	0.200075i
$818$	−4.74163	−	15.8103i	−0.165787	−	0.552794i
$819$		−	2.82097i		−	0.0985727i
$820$	−62.5850	−	31.3556i	−2.18556	−	1.09499i
$821$	7.63477	+	13.2238i	0.266455	+	0.461514i	0.967944	−	0.251167i	$-0.0808142\pi$
$821$	7.63477	+	13.2238i	0.266455	+	0.461514i	−0.701489	+	0.712681i	$0.747481\pi$
$822$	−5.78768	+	6.14053i	−0.201869	+	0.214176i
$823$	41.4942	−	23.9567i	1.44640	−	0.835077i	0.448131	−	0.893968i	$-0.352090\pi$
$823$	41.4942	−	23.9567i	1.44640	−	0.835077i	0.998264	+	0.0588909i	$0.0187564\pi$
$824$	−20.3927	+	7.45587i	−0.710414	+	0.259737i
$825$	−28.7096	+	49.7265i	−0.999541	+	1.73126i
$826$	7.29978	+	24.3401i	0.253992	+	0.846901i
$827$	−44.2782	+	25.5640i	−1.53970	+	0.888948i	−0.540848	+	0.841121i	$0.681896\pi$
$827$	−44.2782	+	25.5640i	−1.53970	+	0.888948i	−0.998856	+	0.0478275i	$0.984770\pi$
$828$	6.34875	+	9.63250i	0.220634	+	0.334753i
$829$	−53.6112			−1.86199			−0.930996	−	0.365028i	$-0.881059\pi$
$829$	−53.6112			−1.86199			−0.930996	+	0.365028i	$0.881059\pi$
$830$	−2.03543	+	8.60670i	−0.0706508	+	0.298743i
$831$	−14.3293			−0.497079
$832$	−8.53176	−	10.1080i	−0.295785	−	0.350433i
$833$	−10.4560	+	18.1103i	−0.362278	+	0.627485i
$834$	8.41301	+	7.92958i	0.291319	+	0.274579i
$835$	7.23819	−	12.5369i	0.250488	−	0.433858i
$836$	−35.8273	+	2.12147i	−1.23911	+	0.0733726i
$837$	2.38328	−	4.12796i	0.0823782	−	0.142683i
$838$	16.2313	+	3.83859i	0.560699	+	0.132602i
$839$	−21.7923	−	12.5818i	−0.752354	−	0.434372i	0.0741901	−	0.997244i	$-0.476363\pi$
$839$	−21.7923	−	12.5818i	−0.752354	−	0.434372i	−0.826544	+	0.562873i	$0.809696\pi$
$840$	−18.8973	+	6.90912i	−0.652019	+	0.238387i
$841$	−36.8952	−	63.9044i	−1.27225	−	2.20360i
$842$	4.30540	−	18.2051i	0.148374	−	0.627390i
$843$	15.7947	−	9.11906i	0.543998	−	0.314077i
$844$	6.60971	+	10.0284i	0.227516	+	0.345193i
$845$	37.0701	+	21.4024i	1.27525	+	0.736266i
$846$	0.221806	+	0.739582i	0.00762585	+	0.0254274i
$847$	−17.9066			−0.615277
$848$	1.65235	+	13.9035i	0.0567420	+	0.477447i
$849$			13.3972i			0.459789i
$850$	−20.6144	+	87.1670i	−0.707070	+	2.98980i
$851$	36.2936	+	20.9541i	1.24413	+	0.718297i
$852$	−3.14626	+	6.27985i	−0.107789	+	0.215144i
$853$	18.7245	+	32.4318i	0.641115	+	1.11044i	0.985184	+	0.171499i	$0.0548610\pi$
$853$	18.7245	+	32.4318i	0.641115	+	1.11044i	−0.344070	+	0.938944i	$0.611806\pi$
$854$	−12.8860	+	13.6716i	−0.440951	+	0.467834i
$855$	8.06910	+	13.9761i	0.275957	+	0.477972i
$856$	−1.03810	−	0.868503i	−0.0354814	−	0.0296848i
$857$		−	4.88340i		−	0.166814i	−0.996516	−	0.0834069i	$-0.973420\pi$
$857$		−	4.88340i		−	0.166814i	0.996516	−	0.0834069i	$-0.0265801\pi$
$858$	−7.43576	+	7.88908i	−0.253853	+	0.269329i
$859$	15.6722	+	9.04836i	0.534729	+	0.308726i	0.742940	−	0.669358i	$-0.233431\pi$
$859$	15.6722	+	9.04836i	0.534729	+	0.308726i	−0.208211	+	0.978084i	$0.566764\pi$
$860$	−24.5989	+	1.45660i	−0.838816	+	0.0496696i
$861$	−12.4032	+	7.16097i	−0.422699	+	0.244045i
$862$	15.9223	+	53.0907i	0.542315	+	1.80827i
$863$		−	11.9646i		−	0.407281i	−0.979046	−	0.203640i	$-0.934723\pi$
$863$		−	11.9646i		−	0.407281i	0.979046	−	0.203640i	$-0.0652773\pi$
$864$	4.54565	+	3.36706i	0.154646	+	0.114550i
$865$	−46.5823	+	26.8943i	−1.58384	+	0.914433i
$866$	13.0464	+	43.5014i	0.443335	+	1.47824i
$867$	−4.57702	+	7.92762i	−0.155444	+	0.269236i
$868$	13.5804	−	8.95083i	0.460950	−	0.303811i
$869$	34.3246	+	59.4520i	1.16438	+	2.01677i
$870$	−17.1735	−	57.2628i	−0.582238	−	1.94139i
$871$	8.74013	−	10.3332i	0.296148	−	0.350127i
$872$	14.4047	+	12.0514i	0.487803	+	0.408111i
$873$	−13.8362	+	7.98831i	−0.468283	+	0.270363i
$874$	30.2433	−	9.07020i	1.02300	−	0.306804i
$875$	45.4948	+	26.2664i	1.53801	+	0.887968i
$876$	2.12712	−	1.40198i	0.0718688	−	0.0473685i
$877$	−2.65364	−	4.59623i	−0.0896069	−	0.155204i	0.817738	−	0.575590i	$-0.195228\pi$
$877$	−2.65364	−	4.59623i	−0.0896069	−	0.155204i	−0.907345	+	0.420387i	$0.861894\pi$
$878$	−20.0196	−	4.73452i	−0.675630	−	0.159782i
$879$	−27.6590			−0.932916
$880$	71.0595	+	30.4892i	2.39542	+	1.02779i
$881$	26.4430	+	45.8006i	0.890886	+	1.54306i	0.838815	+	0.544416i	$0.183249\pi$
$881$	26.4430	+	45.8006i	0.890886	+	1.54306i	0.0520710	+	0.998643i	$0.483418\pi$
$882$	1.33089	−	5.62760i	0.0448134	−	0.189491i
$883$	−5.23475	+	9.06686i	−0.176163	+	0.305124i	−0.940563	−	0.339618i	$-0.889702\pi$
$883$	−5.23475	+	9.06686i	−0.176163	+	0.305124i	0.764400	+	0.644743i	$0.223035\pi$
$884$	−7.57526	+	15.1200i	−0.254784	+	0.508542i
$885$	−43.9115			−1.47607
$886$	1.81609	−	0.544658i	0.0610127	−	0.0182982i
$887$	33.6020	−	19.4001i	1.12825	−	0.651393i	0.184753	−	0.982785i	$-0.440852\pi$
$887$	33.6020	−	19.4001i	1.12825	−	0.651393i	0.943493	+	0.331392i	$0.107518\pi$
$888$	20.2423	+	3.53900i	0.679288	+	0.118761i
$889$	−9.43222	+	5.44570i	−0.316347	+	0.182643i
$890$	24.4205	−	25.9093i	0.818577	−	0.868482i
$891$	2.31815	−	4.01516i	0.0776611	−	0.134513i
$892$	−44.0967	+	2.61114i	−1.47647	+	0.0874274i
$893$	2.11322			0.0707162
$894$	−14.6779	−	13.8345i	−0.490902	−	0.462694i
$895$		−	105.379i		−	3.52242i
$896$	8.72142	+	17.2202i	0.291362	+	0.575286i
$897$	4.76869	−	8.25961i	0.159222	−	0.275781i
$898$	−24.1822	+	7.25242i	−0.806970	+	0.242016i
$899$	24.1630	+	41.8516i	0.805883	+	1.39583i
$900$	−1.46413	−	24.7261i	−0.0488042	−	0.824203i
$901$	15.5028	−	8.95052i	0.516472	−	0.298185i
$902$	53.5620	+	12.6671i	1.78342	+	0.421768i
$903$	−2.52085	+	4.36625i	−0.0838888	+	0.145300i
$904$	−21.4367	+	7.83754i	−0.712972	+	0.260673i
$905$	−36.8303	−	21.2640i	−1.22428	−	0.706840i
$906$	−8.12292	−	1.92102i	−0.269866	−	0.0638216i
$907$	4.47580	+	2.58411i	0.148617	+	0.0858038i	0.572464	−	0.819930i	$-0.305987\pi$
$907$	4.47580	+	2.58411i	0.148617	+	0.0858038i	−0.423848	+	0.905733i	$0.639321\pi$
$908$	−0.355314	+	0.709197i	−0.0117915	+	0.0235355i
$909$	13.2530	+	7.65165i	0.439576	+	0.253789i
$910$	12.1047	+	11.4091i	0.401266	+	0.378208i
$911$			49.6189i			1.64395i	0.569524	+	0.821974i	$0.307127\pi$
$911$			49.6189i			1.64395i	−0.569524	+	0.821974i	$0.692873\pi$
$912$	12.4007	−	9.26930i	0.410628	−	0.306937i
$913$		−	6.95389i		−	0.230140i
$914$	−32.8604	+	9.85507i	−1.08693	+	0.325977i
$915$	−16.2326	−	28.1157i	−0.536633	−	0.929476i
$916$	18.3296	+	27.8102i	0.605627	+	0.918874i
$917$	18.8457	+	10.8806i	0.622340	+	0.359308i
$918$	1.66451	−	7.03829i	0.0549370	−	0.232298i
$919$	5.22770	+	9.05464i	0.172446	+	0.298685i	0.939274	−	0.343167i	$-0.111500\pi$
$919$	5.22770	+	9.05464i	0.172446	+	0.298685i	−0.766828	+	0.641852i	$0.778166\pi$
$920$	−67.0095	−	11.7154i	−2.20924	−	0.386244i
$921$	−9.84151	+	5.68200i	−0.324289	+	0.187228i
$922$	10.4339	+	9.83436i	0.343623	+	0.323877i
$923$	5.80675			0.191131
$924$	13.2093	−	8.70623i	0.434555	−	0.286414i
$925$	−44.9892	−	77.9236i	−1.47924	−	2.56211i
$926$	10.2614	−	43.3898i	0.337211	−	1.42588i
$927$	−6.64821	−	3.83835i	−0.218356	−	0.126068i
$928$	−52.6068	+	22.8434i	−1.72690	+	0.749871i
$929$			10.4003i			0.341224i	0.985338	+	0.170612i	$0.0545744\pi$
$929$			10.4003i			0.341224i	−0.985338	+	0.170612i	$0.945426\pi$
$930$	8.07400	+	26.9216i	0.264757	+	0.882795i
$931$	−13.7065	−	7.91347i	−0.449213	−	0.259353i
$932$	2.60028	−	5.19009i	0.0851749	−	0.170007i
$933$	13.9433			0.456483
$934$	−8.44980	−	1.99832i	−0.276486	−	0.0653871i
$935$		−	98.8610i		−	3.23310i
$936$	0.805398	−	4.60671i	0.0263252	−	0.150575i
$937$		−	3.29602i		−	0.107676i	−0.998550	−	0.0538381i	$-0.982854\pi$
$937$		−	3.29602i		−	0.107676i	0.998550	−	0.0538381i	$-0.0171455\pi$
$938$	−15.8826	+	11.7391i	−0.518585	+	0.383296i
$939$		−	1.88468i		−	0.0615043i
$940$	−4.07058	−	2.03940i	−0.132768	−	0.0665178i
$941$			17.2797i			0.563301i	0.959517	+	0.281651i	$0.0908819\pi$
$941$			17.2797i			0.563301i	−0.959517	+	0.281651i	$0.909118\pi$
$942$	4.91567	−	20.7856i	0.160161	−	0.677232i
$943$	−48.4209			−1.57680
$944$	4.97151	+	41.8321i	0.161809	+	1.36152i
$945$	−6.16069	−	3.55688i	−0.200407	−	0.115705i
$946$	18.5587	−	5.56589i	0.603396	−	0.180963i
$947$			33.4709i			1.08766i	0.839196	+	0.543829i	$0.183026\pi$
$947$			33.4709i			1.08766i	−0.839196	+	0.543829i	$0.816974\pi$
$948$	−26.4766	−	13.2650i	−0.859921	−	0.430828i
$949$	−1.82395	−	1.05306i	−0.0592080	−	0.0341837i
$950$	−65.9712	−	15.6018i	−2.14039	−	0.506188i
$951$	2.47017	+	4.27846i	0.0801008	+	0.138739i
$952$	15.8360	−	18.9283i	0.513247	−	0.613469i
$953$	−13.6873			−0.443376			−0.221688	−	0.975118i	$-0.571157\pi$
$953$	−13.6873			−0.443376			−0.221688	+	0.975118i	$0.571157\pi$
$954$	−3.39530	+	3.60230i	−0.109927	+	0.116629i
$955$	−30.9427	+	17.8648i	−1.00128	+	0.578091i
$956$	42.4250	+	21.2553i	1.37212	+	0.687445i
$957$	23.5028	+	40.7080i	0.759736	+	1.31590i
$958$	−16.7055	−	3.95074i	−0.539729	−	0.127643i
$959$	−8.81619	−	5.09003i	−0.284690	−	0.164366i
$960$	−32.8323	+	5.88749i	−1.05966	+	0.190018i
$961$	4.13995	+	7.17060i	0.133547	+	0.231310i
$962$	−4.88019	−	16.2723i	−0.157344	−	0.524641i
$963$		−	0.478532i		−	0.0154205i
$964$	−1.11466	−	18.8243i	−0.0359007	−	0.606289i
$965$		−	16.0816i		−	0.517686i
$966$	−9.54619	+	10.1282i	−0.307144	+	0.325869i
$967$	26.1761	+	15.1128i	0.841768	+	0.485995i	0.857865	−	0.513875i	$-0.171791\pi$
$967$	26.1761	+	15.1128i	0.841768	+	0.485995i	−0.0160967	+	0.999870i	$0.505124\pi$
$968$	−29.2418	−	5.11239i	−0.939868	−	0.164318i
$969$	−17.1424	−	9.89716i	−0.550693	−	0.317943i
$970$	21.6813	−	91.6782i	0.696145	−	2.94361i
$971$	−51.9851	−	30.0136i	−1.66828	−	0.963183i	−0.968564	−	0.248764i	$-0.919976\pi$
$971$	−51.9851	−	30.0136i	−1.66828	−	0.963183i	−0.699718	−	0.714419i	$-0.746691\pi$
$972$	0.118221	+	1.99650i	0.00379193	+	0.0640379i
$973$	−6.97374	+	12.0789i	−0.223568	+	0.387231i
$974$	−4.32081	+	18.2703i	−0.138448	+	0.585418i
$975$	−17.7337	+	10.2386i	−0.567933	+	0.327896i
$976$	−24.9465	+	18.6471i	−0.798517	+	0.596878i
$977$	25.7852	+	44.6613i	0.824943	+	1.42884i	0.901963	+	0.431813i	$0.142126\pi$
$977$	25.7852	+	44.6613i	0.824943	+	1.42884i	−0.0770207	+	0.997029i	$0.524541\pi$
$978$	−8.58731	−	28.6332i	−0.274592	−	0.915589i
$979$	−13.9973	+	24.2440i	−0.447355	+	0.774842i
$980$	18.7651	+	28.4710i	0.599430	+	0.909473i
$981$			6.64012i			0.212003i
$982$	−11.1822	+	11.8639i	−0.356838	+	0.378593i
$983$	−8.71918			−0.278099			−0.139049	−	0.990285i	$-0.544405\pi$
$983$	−8.71918			−0.278099			−0.139049	+	0.990285i	$0.544405\pi$
$984$	−22.2991	+	8.15288i	−0.710870	+	0.259904i
$985$	2.07692	−	3.59733i	0.0661761	−	0.114620i
$986$	53.3601	+	50.2939i	1.69933	+	1.60168i
$987$	−0.806713	+	0.465756i	−0.0256780	+	0.0148252i
$988$	−11.4434	−	5.73323i	−0.364063	−	0.182398i
$989$	−14.7618	+	8.52272i	−0.469397	+	0.271007i
$990$	7.85337	+	26.1860i	0.249596	+	0.832245i
$991$	2.48474			0.0789305			0.0394653	−	0.999221i	$-0.487435\pi$
$991$	2.48474			0.0789305			0.0394653	+	0.999221i	$0.487435\pi$
$992$	24.7326	−	10.7396i	0.785262	−	0.340983i
$993$	−0.946179	+	1.63883i	−0.0300261	+	0.0520067i
$994$	−8.24636	−	1.95021i	−0.261559	−	0.0618569i
$995$	−44.1927	−	76.5440i	−1.40100	−	2.42661i
$996$	1.65081	+	2.50466i	0.0523081	+	0.0793633i
$997$	−1.00170			−0.0317242			−0.0158621	−	0.999874i	$-0.505049\pi$
$997$	−1.00170			−0.0317242			−0.0158621	+	0.999874i	$0.505049\pi$
$998$	1.41976	−	6.00338i	0.0449418	−	0.190034i
$999$	3.63265	+	6.29193i	0.114932	+	0.199068i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.j.b.499.9	yes	68
4.3	odd	2		804.2.j.a.499.20	✓	68
67.38	odd	6		804.2.j.a.775.20	yes	68
268.239	even	6	inner	804.2.j.b.775.9	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.j.a.499.20	✓	68	4.3	odd	2
804.2.j.a.775.20	yes	68	67.38	odd	6
804.2.j.b.499.9	yes	68	1.1	even	1	trivial
804.2.j.b.775.9	yes	68	268.239	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.02913 - 0.969995i) q^{2} +1.00000 q^{3} +(0.118221 + 1.99650i) q^{4} -4.16950i q^{5} +(-1.02913 - 0.969995i) q^{6} +(0.853071 - 1.47756i) q^{7} +(1.81493 - 2.16934i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-1.02913 - 0.969995i) q^{2} +1.00000 q^{3} +(0.118221 + 1.99650i) q^{4} -4.16950i q^{5} +(-1.02913 - 0.969995i) q^{6} +(0.853071 - 1.47756i) q^{7} +(1.81493 - 2.16934i) q^{8} +1.00000 q^{9} +(-4.04439 + 4.29096i) q^{10} +(2.31815 - 4.01516i) q^{11} +(0.118221 + 1.99650i) q^{12} +(1.43191 - 0.826711i) q^{13} +(-2.31115 + 0.693131i) q^{14} -4.16950i q^{15} +(-3.97205 + 0.472056i) q^{16} +(2.55705 + 4.42894i) q^{17} +(-1.02913 - 0.969995i) q^{18} +(-3.35198 + 1.93527i) q^{19} +(8.32441 - 0.492921i) q^{20} +(0.853071 - 1.47756i) q^{21} +(-6.28037 + 1.88353i) q^{22} +(4.99547 - 2.88414i) q^{23} +(1.81493 - 2.16934i) q^{24} -12.3847 q^{25} +(-2.27552 - 0.538147i) q^{26} +1.00000 q^{27} +(3.05081 + 1.52848i) q^{28} +(-5.06928 + 8.78025i) q^{29} +(-4.04439 + 4.29096i) q^{30} +(2.38328 - 4.12796i) q^{31} +(4.54565 + 3.36706i) q^{32} +(2.31815 - 4.01516i) q^{33} +(1.66451 - 7.03829i) q^{34} +(-6.16069 - 3.55688i) q^{35} +(0.118221 + 1.99650i) q^{36} +(3.63265 + 6.29193i) q^{37} +(5.32683 + 1.25976i) q^{38} +(1.43191 - 0.826711i) q^{39} +(-9.04504 - 7.56735i) q^{40} +(-7.26972 - 4.19717i) q^{41} +(-2.31115 + 0.693131i) q^{42} -2.95503 q^{43} +(8.29033 + 4.15353i) q^{44} -4.16950i q^{45} +(-7.93859 - 1.87743i) q^{46} +(-0.472829 - 0.272988i) q^{47} +(-3.97205 + 0.472056i) q^{48} +(2.04454 + 3.54125i) q^{49} +(12.7455 + 12.0131i) q^{50} +(2.55705 + 4.42894i) q^{51} +(1.81981 + 2.76107i) q^{52} -3.50033i q^{53} +(-1.02913 - 0.969995i) q^{54} +(-16.7412 - 9.66553i) q^{55} +(-1.65706 - 4.53227i) q^{56} +(-3.35198 + 1.93527i) q^{57} +(13.7338 - 4.11885i) q^{58} -10.5316i q^{59} +(8.32441 - 0.492921i) q^{60} +(6.74319 - 3.89318i) q^{61} +(-6.45681 + 1.93644i) q^{62} +(0.853071 - 1.47756i) q^{63} +(-1.41204 - 7.87440i) q^{64} +(-3.44697 - 5.97032i) q^{65} +(-6.28037 + 1.88353i) q^{66} +(7.70268 - 2.76925i) q^{67} +(-8.54010 + 5.62875i) q^{68} +(4.99547 - 2.88414i) q^{69} +(2.89001 + 9.63633i) q^{70} +(3.04145 + 1.75598i) q^{71} +(1.81493 - 2.16934i) q^{72} +(-0.636897 - 1.10314i) q^{73} +(2.36467 - 9.99887i) q^{74} -12.3847 q^{75} +(-4.26004 - 6.46346i) q^{76} +(-3.95510 - 6.85043i) q^{77} +(-2.27552 - 0.538147i) q^{78} +(-7.40343 + 12.8231i) q^{79} +(1.96824 + 16.5614i) q^{80} +1.00000 q^{81} +(3.41026 + 11.3710i) q^{82} +(1.29893 - 0.749938i) q^{83} +(3.05081 + 1.52848i) q^{84} +(18.4665 - 10.6616i) q^{85} +(3.04112 + 2.86637i) q^{86} +(-5.06928 + 8.78025i) q^{87} +(-4.50294 - 12.3161i) q^{88} -6.03812 q^{89} +(-4.04439 + 4.29096i) q^{90} -2.82097i q^{91} +(6.34875 + 9.63250i) q^{92} +(2.38328 - 4.12796i) q^{93} +(0.221806 + 0.739582i) q^{94} +(8.06910 + 13.9761i) q^{95} +(4.54565 + 3.36706i) q^{96} +(-13.8362 + 7.98831i) q^{97} +(1.33089 - 5.62760i) q^{98} +(2.31815 - 4.01516i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 68 q^{3} - 2 q^{4} - 4 q^{7} + 6 q^{8} + 68 q^{9}+O(q^{10}) \) 68 * q + 68 * q^3 - 2 * q^4 - 4 * q^7 + 6 * q^8 + 68 * q^9	\( 68 q + 68 q^{3} - 2 q^{4} - 4 q^{7} + 6 q^{8} + 68 q^{9} - 6 q^{10} - 2 q^{12} + 6 q^{13} + 10 q^{14} - 2 q^{16} - 12 q^{20} - 4 q^{21} - 22 q^{22} + 6 q^{24} - 68 q^{25} - 19 q^{26} + 68 q^{27} - 7 q^{28} - 8 q^{29} - 6 q^{30} - 2 q^{31} + 15 q^{32} - 2 q^{36} + 12 q^{37} + 4 q^{38} + 6 q^{39} + 18 q^{40} + 10 q^{42} + 4 q^{43} - 5 q^{44} + 16 q^{46} - 2 q^{48} - 46 q^{49} + 27 q^{50} + 28 q^{52} - 17 q^{56} - 4 q^{58} - 12 q^{60} + 6 q^{61} - 34 q^{62} - 4 q^{63} + 16 q^{64} - 22 q^{66} + 18 q^{67} + 34 q^{68} - 56 q^{70} + 36 q^{71} + 6 q^{72} + 6 q^{73} + 11 q^{74} - 68 q^{75} + 14 q^{76} - 4 q^{77} - 19 q^{78} - 6 q^{79} - 25 q^{80} + 68 q^{81} - 26 q^{82} - 12 q^{83} - 7 q^{84} - 33 q^{86} - 8 q^{87} + 22 q^{88} - 6 q^{90} + 10 q^{92} - 2 q^{93} + 16 q^{94} - 20 q^{95} + 15 q^{96} + 18 q^{97} - 32 q^{98}+O(q^{100}) \) 68 * q + 68 * q^3 - 2 * q^4 - 4 * q^7 + 6 * q^8 + 68 * q^9 - 6 * q^10 - 2 * q^12 + 6 * q^13 + 10 * q^14 - 2 * q^16 - 12 * q^20 - 4 * q^21 - 22 * q^22 + 6 * q^24 - 68 * q^25 - 19 * q^26 + 68 * q^27 - 7 * q^28 - 8 * q^29 - 6 * q^30 - 2 * q^31 + 15 * q^32 - 2 * q^36 + 12 * q^37 + 4 * q^38 + 6 * q^39 + 18 * q^40 + 10 * q^42 + 4 * q^43 - 5 * q^44 + 16 * q^46 - 2 * q^48 - 46 * q^49 + 27 * q^50 + 28 * q^52 - 17 * q^56 - 4 * q^58 - 12 * q^60 + 6 * q^61 - 34 * q^62 - 4 * q^63 + 16 * q^64 - 22 * q^66 + 18 * q^67 + 34 * q^68 - 56 * q^70 + 36 * q^71 + 6 * q^72 + 6 * q^73 + 11 * q^74 - 68 * q^75 + 14 * q^76 - 4 * q^77 - 19 * q^78 - 6 * q^79 - 25 * q^80 + 68 * q^81 - 26 * q^82 - 12 * q^83 - 7 * q^84 - 33 * q^86 - 8 * q^87 + 22 * q^88 - 6 * q^90 + 10 * q^92 - 2 * q^93 + 16 * q^94 - 20 * q^95 + 15 * q^96 + 18 * q^97 - 32 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more