LMFDB - Embedded newform 43.2.g.a.17.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,2,Mod(9,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("43.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	43.g (of order $21$, degree $12$, 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:	$0.343356728692$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$3$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			17.2
Character	$\chi$	$=$	43.17
Dual form			43.2.g.a.38.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.178150 - 0.780524i) q^{2} +(-0.711521 + 0.219475i) q^{3} +(1.22446 - 0.589667i) q^{4} +(0.511972 - 1.30448i) q^{5} +(0.298063 + 0.516260i) q^{6} +(-2.37928 + 4.12103i) q^{7} +(-1.67671 - 2.10253i) q^{8} +(-2.02062 + 1.37764i) q^{9} +O(q^{10})$	\(q+(-0.178150 - 0.780524i) q^{2} +(-0.711521 + 0.219475i) q^{3} +(1.22446 - 0.589667i) q^{4} +(0.511972 - 1.30448i) q^{5} +(0.298063 + 0.516260i) q^{6} +(-2.37928 + 4.12103i) q^{7} +(-1.67671 - 2.10253i) q^{8} +(-2.02062 + 1.37764i) q^{9} +(-1.10939 - 0.167213i) q^{10} +(2.39760 + 1.15462i) q^{11} +(-0.741809 + 0.688298i) q^{12} +(0.611008 - 0.0920946i) q^{13} +(3.64044 + 1.12293i) q^{14} +(-0.0779770 + 1.04053i) q^{15} +(0.352328 - 0.441805i) q^{16} +(-2.15975 - 5.50296i) q^{17} +(1.43525 + 1.33172i) q^{18} +(-1.48286 - 1.01100i) q^{19} +(-0.142323 - 1.89917i) q^{20} +(0.788443 - 3.45439i) q^{21} +(0.474081 - 2.07708i) q^{22} +(0.178184 + 2.37770i) q^{23} +(1.65447 + 1.12800i) q^{24} +(2.22570 + 2.06515i) q^{25} +(-0.180733 - 0.460500i) q^{26} +(2.52811 - 3.17015i) q^{27} +(-0.483287 + 6.44901i) q^{28} +(-1.79980 - 0.555165i) q^{29} +(0.826051 - 0.124507i) q^{30} +(5.49565 - 5.09922i) q^{31} +(-5.25345 - 2.52993i) q^{32} +(-1.95935 - 0.295325i) q^{33} +(-3.91044 + 2.66609i) q^{34} +(4.15769 + 5.21358i) q^{35} +(-1.66182 + 2.87835i) q^{36} +(1.11406 + 1.92960i) q^{37} +(-0.524936 + 1.33752i) q^{38} +(-0.414532 + 0.199628i) q^{39} +(-3.60115 + 1.11081i) q^{40} +(-0.583954 - 2.55847i) q^{41} -2.83670 q^{42} +(-6.54183 + 0.452170i) q^{43} +3.61660 q^{44} +(0.762602 + 3.34118i) q^{45} +(1.82411 - 0.562664i) q^{46} +(-8.07377 + 3.88812i) q^{47} +(-0.153723 + 0.391681i) q^{48} +(-7.82195 - 13.5480i) q^{49} +(1.21539 - 2.10512i) q^{50} +(2.74447 + 3.44146i) q^{51} +(0.693847 - 0.473057i) q^{52} +(13.5894 + 2.04828i) q^{53} +(-2.92476 - 1.40849i) q^{54} +(2.73369 - 2.53650i) q^{55} +(12.6540 - 1.90728i) q^{56} +(1.27697 + 0.393894i) q^{57} +(-0.112686 + 1.50369i) q^{58} +(-4.23034 + 5.30467i) q^{59} +(0.518087 + 1.32007i) q^{60} +(3.03226 + 2.81353i) q^{61} +(-4.95912 - 3.38107i) q^{62} +(-0.869663 - 11.6048i) q^{63} +(-0.787282 + 3.44931i) q^{64} +(0.192683 - 0.844198i) q^{65} +(0.118550 + 1.58194i) q^{66} +(4.65539 + 3.17399i) q^{67} +(-5.88944 - 5.46460i) q^{68} +(-0.648628 - 1.65268i) q^{69} +(3.32864 - 4.17398i) q^{70} +(-0.641465 + 8.55975i) q^{71} +(6.28454 + 1.93852i) q^{72} +(8.41561 - 1.26845i) q^{73} +(1.30763 - 1.21331i) q^{74} +(-2.03688 - 0.980910i) q^{75} +(-2.41185 - 0.363527i) q^{76} +(-10.4628 + 7.13343i) q^{77} +(0.229663 + 0.287989i) q^{78} +(3.09616 - 5.36270i) q^{79} +(-0.395945 - 0.685797i) q^{80} +(1.57737 - 4.01906i) q^{81} +(-1.89292 + 0.911581i) q^{82} +(-1.21371 + 0.374380i) q^{83} +(-1.07153 - 4.69467i) q^{84} -8.28425 q^{85} +(1.51835 + 5.02550i) q^{86} +1.40244 q^{87} +(-1.59246 - 6.97702i) q^{88} +(-9.04506 + 2.79003i) q^{89} +(2.47202 - 1.19046i) q^{90} +(-1.07423 + 2.73710i) q^{91} +(1.62023 + 2.80632i) q^{92} +(-2.79112 + 4.83436i) q^{93} +(4.47311 + 5.60911i) q^{94} +(-2.07801 + 1.41676i) q^{95} +(4.29319 + 0.647095i) q^{96} +(4.06114 + 1.95574i) q^{97} +(-9.18108 + 8.51880i) q^{98} +(-6.43531 + 0.969967i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 10 q^{2} - 16 q^{3} - 18 q^{4} - 17 q^{5} - 4 q^{6} + 6 q^{7} + 18 q^{8} - q^{9}+O(q^{10}) $ 36 * q - 10 * q^2 - 16 * q^3 - 18 * q^4 - 17 * q^5 - 4 * q^6 + 6 * q^7 + 18 * q^8 - q^9	\( 36 q - 10 q^{2} - 16 q^{3} - 18 q^{4} - 17 q^{5} - 4 q^{6} + 6 q^{7} + 18 q^{8} - q^{9} - 7 q^{10} - 4 q^{11} + 2 q^{12} + 18 q^{14} - 3 q^{15} - 10 q^{16} - 10 q^{17} + 11 q^{18} + 10 q^{19} - 3 q^{20} - 21 q^{21} - 3 q^{22} + 4 q^{23} + 31 q^{24} - 2 q^{25} - 15 q^{26} - 4 q^{27} + 20 q^{28} + 9 q^{29} + 88 q^{30} + 40 q^{31} + 48 q^{32} - 11 q^{33} - 42 q^{34} + 11 q^{35} - 47 q^{36} - 19 q^{37} - 21 q^{38} - q^{39} - 97 q^{40} - 28 q^{41} + 2 q^{42} - 8 q^{43} + 14 q^{44} - 46 q^{45} - 61 q^{46} - 30 q^{47} - 97 q^{48} + 6 q^{49} - 3 q^{50} + 57 q^{51} - 8 q^{52} - 24 q^{53} + 6 q^{54} + 14 q^{55} + 39 q^{56} + 52 q^{57} + 64 q^{58} - q^{59} + 111 q^{60} - 14 q^{61} + 33 q^{62} + 47 q^{63} + 48 q^{64} + 38 q^{65} + 79 q^{66} + 66 q^{67} + 66 q^{68} - 7 q^{69} + 47 q^{70} - 33 q^{71} + 26 q^{72} + 29 q^{73} - 40 q^{74} - 55 q^{75} - 39 q^{76} - 27 q^{77} - 126 q^{78} - 17 q^{79} + 8 q^{80} + 38 q^{81} - 54 q^{82} - 23 q^{83} - 155 q^{84} - 56 q^{85} - 45 q^{86} - 86 q^{87} - 17 q^{88} - 19 q^{89} - 127 q^{90} - 13 q^{91} - 18 q^{92} - 30 q^{93} + 44 q^{94} + q^{95} - 36 q^{96} - 31 q^{97} - 5 q^{98} - 31 q^{99}+O(q^{100}) \) 36 * q - 10 * q^2 - 16 * q^3 - 18 * q^4 - 17 * q^5 - 4 * q^6 + 6 * q^7 + 18 * q^8 - q^9 - 7 * q^10 - 4 * q^11 + 2 * q^12 + 18 * q^14 - 3 * q^15 - 10 * q^16 - 10 * q^17 + 11 * q^18 + 10 * q^19 - 3 * q^20 - 21 * q^21 - 3 * q^22 + 4 * q^23 + 31 * q^24 - 2 * q^25 - 15 * q^26 - 4 * q^27 + 20 * q^28 + 9 * q^29 + 88 * q^30 + 40 * q^31 + 48 * q^32 - 11 * q^33 - 42 * q^34 + 11 * q^35 - 47 * q^36 - 19 * q^37 - 21 * q^38 - q^39 - 97 * q^40 - 28 * q^41 + 2 * q^42 - 8 * q^43 + 14 * q^44 - 46 * q^45 - 61 * q^46 - 30 * q^47 - 97 * q^48 + 6 * q^49 - 3 * q^50 + 57 * q^51 - 8 * q^52 - 24 * q^53 + 6 * q^54 + 14 * q^55 + 39 * q^56 + 52 * q^57 + 64 * q^58 - q^59 + 111 * q^60 - 14 * q^61 + 33 * q^62 + 47 * q^63 + 48 * q^64 + 38 * q^65 + 79 * q^66 + 66 * q^67 + 66 * q^68 - 7 * q^69 + 47 * q^70 - 33 * q^71 + 26 * q^72 + 29 * q^73 - 40 * q^74 - 55 * q^75 - 39 * q^76 - 27 * q^77 - 126 * q^78 - 17 * q^79 + 8 * q^80 + 38 * q^81 - 54 * q^82 - 23 * q^83 - 155 * q^84 - 56 * q^85 - 45 * q^86 - 86 * q^87 - 17 * q^88 - 19 * q^89 - 127 * q^90 - 13 * q^91 - 18 * q^92 - 30 * q^93 + 44 * q^94 + q^95 - 36 * q^96 - 31 * q^97 - 5 * q^98 - 31 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{19}{21}\right)$

Coefficient data

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

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

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

$2$	−0.178150	−	0.780524i	−0.125971	−	0.551914i	−0.998043	−	0.0625363i	$-0.980081\pi$
$2$	−0.178150	−	0.780524i	−0.125971	−	0.551914i	0.872072	−	0.489378i	$-0.162776\pi$
$3$	−0.711521	+	0.219475i	−0.410797	+	0.126714i	−0.493264	−	0.869880i	$-0.664196\pi$
$3$	−0.711521	+	0.219475i	−0.410797	+	0.126714i	0.0824671	+	0.996594i	$0.473720\pi$
$4$	1.22446	−	0.589667i	0.612228	−	0.294834i
$5$	0.511972	−	1.30448i	0.228961	−	0.583382i	−0.769512	−	0.638632i	$-0.779500\pi$
$5$	0.511972	−	1.30448i	0.228961	−	0.583382i	0.998473	+	0.0552503i	$0.0175957\pi$
$6$	0.298063	+	0.516260i	0.121684	+	0.210762i
$7$	−2.37928	+	4.12103i	−0.899283	+	1.55760i	−0.0708714	+	0.997485i	$0.522578\pi$
$7$	−2.37928	+	4.12103i	−0.899283	+	1.55760i	−0.828412	+	0.560119i	$0.810755\pi$
$8$	−1.67671	−	2.10253i	−0.592808	−	0.743358i
$9$	−2.02062	+	1.37764i	−0.673541	+	0.459213i
$10$	−1.10939	−	0.167213i	−0.350819	−	0.0528775i
$11$	2.39760	+	1.15462i	0.722904	+	0.348132i	0.758889	−	0.651220i	$-0.225742\pi$
$11$	2.39760	+	1.15462i	0.722904	+	0.348132i	−0.0359847	+	0.999352i	$0.511457\pi$
$12$	−0.741809	+	0.688298i	−0.214142	+	0.198695i
$13$	0.611008	−	0.0920946i	0.169463	−	0.0255424i	−0.0637626	−	0.997965i	$-0.520310\pi$
$13$	0.611008	−	0.0920946i	0.169463	−	0.0255424i	0.233226	+	0.972423i	$0.425072\pi$
$14$	3.64044	+	1.12293i	0.972947	+	0.300115i
$15$	−0.0779770	+	1.04053i	−0.0201336	+	0.268664i
$16$	0.352328	−	0.441805i	0.0880820	−	0.110451i
$17$	−2.15975	−	5.50296i	−0.523817	−	1.33466i	−0.910903	−	0.412621i	$-0.864613\pi$
$17$	−2.15975	−	5.50296i	−0.523817	−	1.33466i	0.387086	−	0.922044i	$-0.373482\pi$
$18$	1.43525	+	1.33172i	0.338293	+	0.313890i
$19$	−1.48286	−	1.01100i	−0.340191	−	0.231938i	0.381158	−	0.924510i	$-0.375525\pi$
$19$	−1.48286	−	1.01100i	−0.340191	−	0.231938i	−0.721349	+	0.692572i	$0.756478\pi$
$20$	−0.142323	−	1.89917i	−0.0318245	−	0.424668i
$21$	0.788443	−	3.45439i	0.172052	−	0.753810i
$22$	0.474081	−	2.07708i	0.101074	−	0.442836i
$23$	0.178184	+	2.37770i	0.0371540	+	0.495785i	0.984478	+	0.175508i	$0.0561569\pi$
$23$	0.178184	+	2.37770i	0.0371540	+	0.495785i	−0.947324	+	0.320277i	$0.896224\pi$
$24$	1.65447	+	1.12800i	0.337717	+	0.230252i
$25$	2.22570	+	2.06515i	0.445140	+	0.413030i
$26$	−0.180733	−	0.460500i	−0.0354446	−	0.0903114i
$27$	2.52811	−	3.17015i	0.486535	−	0.610096i
$28$	−0.483287	+	6.44901i	−0.0913326	+	1.21875i
$29$	−1.79980	−	0.555165i	−0.334215	−	0.103092i	0.123106	−	0.992394i	$-0.460715\pi$
$29$	−1.79980	−	0.555165i	−0.334215	−	0.103092i	−0.457320	+	0.889302i	$0.651191\pi$
$30$	0.826051	−	0.124507i	0.150816	−	0.0227318i
$31$	5.49565	−	5.09922i	0.987048	−	0.915847i	−0.00940813	−	0.999956i	$-0.502995\pi$
$31$	5.49565	−	5.09922i	0.987048	−	0.915847i	0.996457	+	0.0841086i	$0.0268043\pi$
$32$	−5.25345	−	2.52993i	−0.928688	−	0.447232i
$33$	−1.95935	−	0.295325i	−0.341080	−	0.0514095i
$34$	−3.91044	+	2.66609i	−0.670635	+	0.457231i
$35$	4.15769	+	5.21358i	0.702778	+	0.881256i
$36$	−1.66182	+	2.87835i	−0.276970	+	0.479726i
$37$	1.11406	+	1.92960i	0.183150	+	0.317225i	0.942951	−	0.332930i	$-0.108037\pi$
$37$	1.11406	+	1.92960i	0.183150	+	0.317225i	−0.759802	+	0.650155i	$0.774704\pi$
$38$	−0.524936	+	1.33752i	−0.0851559	+	0.216974i
$39$	−0.414532	+	0.199628i	−0.0663783	+	0.0319661i
$40$	−3.60115	+	1.11081i	−0.569391	+	0.175634i
$41$	−0.583954	−	2.55847i	−0.0911984	−	0.399566i	0.908639	−	0.417582i	$-0.137122\pi$
$41$	−0.583954	−	2.55847i	−0.0911984	−	0.399566i	−0.999838	+	0.0180157i	$0.994265\pi$
$42$	−2.83670			−0.437712
$43$	−6.54183	+	0.452170i	−0.997620	+	0.0689553i
$43$	−6.54183	+	0.452170i	−0.997620	+	0.0689553i
$44$	3.61660			0.545224
$45$	0.762602	+	3.34118i	0.113682	+	0.498074i
$46$	1.82411	−	0.562664i	0.268951	−	0.0829603i
$47$	−8.07377	+	3.88812i	−1.17768	+	0.567141i	−0.917235	−	0.398348i	$-0.869584\pi$
$47$	−8.07377	+	3.88812i	−1.17768	+	0.567141i	−0.260446	+	0.965489i	$0.583869\pi$
$48$	−0.153723	+	0.391681i	−0.0221881	+	0.0565342i
$49$	−7.82195	−	13.5480i	−1.11742	−	1.93543i
$50$	1.21539	−	2.10512i	0.171882	−	0.297709i
$51$	2.74447	+	3.44146i	0.384303	+	0.481901i
$52$	0.693847	−	0.473057i	0.0962193	−	0.0656012i
$53$	13.5894	+	2.04828i	1.86665	+	0.281352i	0.982558	−	0.185957i	$-0.0595386\pi$
$53$	13.5894	+	2.04828i	1.86665	+	0.281352i	0.884094	+	0.467310i	$0.154777\pi$
$54$	−2.92476	−	1.40849i	−0.398010	−	0.191671i
$55$	2.73369	−	2.53650i	0.368611	−	0.342021i
$56$	12.6540	−	1.90728i	1.69096	−	0.254871i
$57$	1.27697	+	0.393894i	0.169139	+	0.0521725i
$58$	−0.112686	+	1.50369i	−0.0147964	+	0.197444i
$59$	−4.23034	+	5.30467i	−0.550743	+	0.690610i	−0.976816	−	0.214079i	$-0.931325\pi$
$59$	−4.23034	+	5.30467i	−0.550743	+	0.690610i	0.426073	+	0.904689i	$0.359897\pi$
$60$	0.518087	+	1.32007i	0.0668848	+	0.170420i
$61$	3.03226	+	2.81353i	0.388242	+	0.360236i	0.850011	−	0.526764i	$-0.176595\pi$
$61$	3.03226	+	2.81353i	0.388242	+	0.360236i	−0.461770	+	0.887000i	$0.652785\pi$
$62$	−4.95912	−	3.38107i	−0.629808	−	0.429396i
$63$	−0.869663	−	11.6048i	−0.109567	−	1.46207i
$64$	−0.787282	+	3.44931i	−0.0984103	+	0.431164i
$65$	0.192683	−	0.844198i	0.0238994	−	0.104710i
$66$	0.118550	+	1.58194i	0.0145925	+	0.194723i
$67$	4.65539	+	3.17399i	0.568747	+	0.387765i	0.813277	−	0.581877i	$-0.197681\pi$
$67$	4.65539	+	3.17399i	0.568747	+	0.387765i	−0.244530	+	0.969642i	$0.578634\pi$
$68$	−5.88944	−	5.46460i	−0.714200	−	0.662681i
$69$	−0.648628	−	1.65268i	−0.0780856	−	0.198959i
$70$	3.32864	−	4.17398i	0.397848	−	0.498886i
$71$	−0.641465	+	8.55975i	−0.0761278	+	1.01586i	0.820088	+	0.572237i	$0.193924\pi$
$71$	−0.641465	+	8.55975i	−0.0761278	+	1.01586i	−0.896216	+	0.443618i	$0.853695\pi$
$72$	6.28454	+	1.93852i	0.740640	+	0.228457i
$73$	8.41561	−	1.26845i	0.984972	−	0.148461i	0.363244	−	0.931694i	$-0.381669\pi$
$73$	8.41561	−	1.26845i	0.984972	−	0.148461i	0.621728	+	0.783233i	$0.286431\pi$
$74$	1.30763	−	1.21331i	0.152009	−	0.141044i
$75$	−2.03688	−	0.980910i	−0.235199	−	0.113266i
$76$	−2.41185	−	0.363527i	−0.276658	−	0.0416994i
$77$	−10.4628	+	7.13343i	−1.19235	+	0.812930i
$78$	0.229663	+	0.287989i	0.0260043	+	0.0326083i
$79$	3.09616	−	5.36270i	0.348345	−	0.603351i	−0.637611	−	0.770359i	$-0.720077\pi$
$79$	3.09616	−	5.36270i	0.348345	−	0.603351i	0.985956	+	0.167007i	$0.0534104\pi$
$80$	−0.395945	−	0.685797i	−0.0442680	−	0.0766745i
$81$	1.57737	−	4.01906i	0.175263	−	0.446563i
$82$	−1.89292	+	0.911581i	−0.209038	+	0.100667i
$83$	−1.21371	+	0.374380i	−0.133222	+	0.0410935i	−0.360649	−	0.932702i	$-0.617445\pi$
$83$	−1.21371	+	0.374380i	−0.133222	+	0.0410935i	0.227427	+	0.973795i	$0.426969\pi$
$84$	−1.07153	−	4.69467i	−0.116913	−	0.512231i
$85$	−8.28425			−0.898553
$86$	1.51835	+	5.02550i	0.163728	+	0.541914i
$87$	1.40244			0.150357
$88$	−1.59246	−	6.97702i	−0.169757	−	0.743752i
$89$	−9.04506	+	2.79003i	−0.958774	+	0.295743i	−0.734367	−	0.678753i	$-0.762521\pi$
$89$	−9.04506	+	2.79003i	−0.958774	+	0.295743i	−0.224408	+	0.974495i	$0.572045\pi$
$90$	2.47202	−	1.19046i	0.260573	−	0.125485i
$91$	−1.07423	+	2.73710i	−0.112610	+	0.286926i
$92$	1.62023	+	2.80632i	0.168921	+	0.292579i
$93$	−2.79112	+	4.83436i	−0.289426	+	0.501300i
$94$	4.47311	+	5.60911i	0.461366	+	0.578535i
$95$	−2.07801	+	1.41676i	−0.213199	+	0.145357i
$96$	4.29319	+	0.647095i	0.438172	+	0.0660439i
$97$	4.06114	+	1.95574i	0.412346	+	0.198575i	0.628544	−	0.777774i	$-0.283651\pi$
$97$	4.06114	+	1.95574i	0.412346	+	0.198575i	−0.216198	+	0.976350i	$0.569366\pi$
$98$	−9.18108	+	8.51880i	−0.927429	+	0.860528i
$99$	−6.43531	+	0.969967i	−0.646773	+	0.0974853i
$100$	3.94302	+	1.21626i	0.394302	+	0.121626i
$101$	−0.836983	+	11.1688i	−0.0832829	+	1.11133i	0.786398	+	0.617720i	$0.211943\pi$
$101$	−0.836983	+	11.1688i	−0.0832829	+	1.11133i	−0.869681	+	0.493614i	$0.835676\pi$
$102$	2.19722	−	2.75522i	0.217557	−	0.272808i
$103$	−3.78337	−	9.63986i	−0.372786	−	0.949844i	−0.987002	−	0.160706i	$-0.948623\pi$
$103$	−3.78337	−	9.63986i	−0.372786	−	0.949844i	0.614216	−	0.789138i	$-0.289472\pi$
$104$	−1.21812	−	1.13025i	−0.119446	−	0.110830i
$105$	−4.10253	−	2.79706i	−0.400366	−	0.272965i
$106$	−0.822221	−	10.9718i	−0.0798612	−	1.06567i
$107$	1.06717	−	4.67559i	0.103168	−	0.452007i	−0.896787	−	0.442463i	$-0.854105\pi$
$107$	1.06717	−	4.67559i	0.103168	−	0.452007i	0.999954	−	0.00954399i	$-0.00303799\pi$
$108$	1.22623	−	5.37246i	0.117994	−	0.516965i
$109$	1.33576	+	17.8244i	0.127942	+	1.70727i	0.579453	+	0.815006i	$0.303266\pi$
$109$	1.33576	+	17.8244i	0.127942	+	1.70727i	−0.451511	+	0.892266i	$0.649115\pi$
$110$	−2.46680	−	1.68184i	−0.235200	−	0.160357i
$111$	−1.21617	−	1.12844i	−0.115434	−	0.107107i
$112$	0.982408	+	2.50313i	0.0928288	+	0.236524i
$113$	0.802598	−	1.00643i	0.0755021	−	0.0946766i	−0.742646	−	0.669684i	$-0.766429\pi$
$113$	0.802598	−	1.00643i	0.0755021	−	0.0946766i	0.818148	+	0.575008i	$0.195001\pi$
$114$	0.0799516	−	1.06688i	0.00748815	−	0.0999224i
$115$	3.19290	+	0.984878i	0.297739	+	0.0918403i
$116$	−2.53114	+	0.381508i	−0.235011	+	0.0354221i
$117$	−1.10774	+	1.02784i	−0.102411	+	0.0950235i
$118$	4.89406	+	2.35686i	0.450535	+	0.216966i
$119$	27.8166	+	4.19267i	2.54994	+	0.384342i
$120$	2.31850	−	1.58072i	0.211649	−	0.144300i
$121$	−2.44305	−	3.06348i	−0.222095	−	0.278499i
$122$	1.65583	−	2.86799i	0.149912	−	0.259655i
$123$	0.977016	+	1.69224i	0.0880946	+	0.152584i
$124$	3.72235	−	9.48438i	0.334276	−	0.851723i
$125$	10.1463	−	4.88621i	0.907514	−	0.437036i
$126$	−8.90294	+	2.74619i	−0.793137	+	0.244650i
$127$	−0.977712	−	4.28364i	−0.0867579	−	0.380111i	0.912844	−	0.408307i	$-0.133881\pi$
$127$	−0.977712	−	4.28364i	−0.0867579	−	0.380111i	−0.999602	+	0.0281961i	$0.991024\pi$
$128$	−8.82926			−0.780404
$129$	4.55541	−	1.75750i	0.401081	−	0.154739i
$130$	−0.693244			−0.0608015
$131$	−3.14191	−	13.7656i	−0.274510	−	1.20271i	−0.904626	−	0.426206i	$-0.859850\pi$
$131$	−3.14191	−	13.7656i	−0.274510	−	1.20271i	0.630116	−	0.776501i	$-0.283007\pi$
$132$	−2.57329	+	0.793754i	−0.223976	+	0.0690875i
$133$	7.69448	−	3.70547i	0.667196	−	0.321305i
$134$	1.64802	−	4.19909i	0.142367	−	0.362746i
$135$	−2.84109	−	4.92090i	−0.244522	−	0.423524i
$136$	−7.94887	+	13.7679i	−0.681610	+	1.18058i
$137$	−5.86675	−	7.35668i	−0.501231	−	0.628523i	0.465276	−	0.885166i	$-0.345955\pi$
$137$	−5.86675	−	7.35668i	−0.501231	−	0.628523i	−0.966506	+	0.256642i	$0.917384\pi$
$138$	−1.17440	+	0.800694i	−0.0999717	+	0.0681596i
$139$	−16.5348	−	2.49223i	−1.40247	−	0.211388i	−0.596151	−	0.802873i	$-0.703304\pi$
$139$	−16.5348	−	2.49223i	−1.40247	−	0.211388i	−0.806316	+	0.591485i	$0.798542\pi$
$140$	8.16519	+	3.93215i	0.690085	+	0.332327i
$141$	4.89131	−	4.53847i	0.411922	−	0.382208i
$142$	6.79537	−	1.02424i	0.570255	−	0.0859521i
$143$	1.57129	+	0.484678i	0.131398	+	0.0405308i
$144$	−0.103275	+	1.37810i	−0.00860621	+	0.114842i
$145$	−1.64565	+	2.06358i	−0.136664	+	0.171371i
$146$	−2.48929	−	6.34261i	−0.206015	−	0.524918i
$147$	8.53893	+	7.92297i	0.704279	+	0.653475i
$148$	2.50194	+	1.70579i	0.205658	+	0.140215i
$149$	0.871916	+	11.6349i	0.0714302	+	0.953169i	0.911662	+	0.410942i	$0.134800\pi$
$149$	0.871916	+	11.6349i	0.0714302	+	0.953169i	−0.840231	+	0.542228i	$0.817581\pi$
$150$	−0.402755	+	1.76458i	−0.0328848	+	0.144078i
$151$	−1.79030	+	7.84381i	−0.145692	+	0.638320i	0.848360	+	0.529419i	$0.177590\pi$
$151$	−1.79030	+	7.84381i	−0.145692	+	0.638320i	−0.994053	+	0.108901i	$0.965267\pi$
$152$	0.360678	+	4.81291i	0.0292548	+	0.390378i
$153$	11.9451	+	8.14406i	0.965708	+	0.658408i
$154$	7.43176	+	6.89567i	0.598868	+	0.555669i
$155$	−3.83823	−	9.77964i	−0.308294	−	0.785519i
$156$	−0.389862	+	0.488872i	−0.0312140	+	0.0391411i
$157$	0.566002	−	7.55278i	0.0451719	−	0.602777i	−0.927982	−	0.372624i	$-0.878458\pi$
$157$	0.566002	−	7.55278i	0.0451719	−	0.602777i	0.973154	−	0.230153i	$-0.0739228\pi$
$158$	−4.73730	−	1.46126i	−0.376879	−	0.116252i
$159$	−10.1187	+	1.52515i	−0.802465	+	0.120952i
$160$	−5.98987	+	5.55778i	−0.473540	+	0.439381i
$161$	−10.2225	−	4.92292i	−0.805649	−	0.387980i
$162$	−3.41798	−	0.515178i	−0.268542	−	0.0404762i
$163$	5.09936	−	3.47669i	0.399413	−	0.272315i	−0.346911	−	0.937898i	$-0.612769\pi$
$163$	5.09936	−	3.47669i	0.399413	−	0.272315i	0.746324	+	0.665583i	$0.231817\pi$
$164$	−2.22367	−	2.78840i	−0.173640	−	0.217737i
$165$	−1.38838	+	2.40475i	−0.108085	+	0.187209i
$166$	0.508435	+	0.880635i	0.0394622	+	0.0683505i
$167$	−3.21985	+	8.20404i	−0.249159	+	0.634848i	−0.999661	−	0.0260204i	$-0.991717\pi$
$167$	−3.21985	+	8.20404i	−0.249159	+	0.634848i	0.750502	+	0.660868i	$0.229812\pi$
$168$	−8.58497	+	4.13430i	−0.662345	+	0.318968i
$169$	−12.0576	+	3.71928i	−0.927508	+	0.286098i
$170$	1.47584	+	6.46606i	0.113191	+	0.495924i
$171$	4.38908			0.335642
$172$	−7.74356	+	4.41117i	−0.590441	+	0.336348i
$173$	6.12350			0.465561			0.232780	−	0.972529i	$-0.425218\pi$
$173$	6.12350			0.465561			0.232780	+	0.972529i	$0.425218\pi$
$174$	−0.249844	−	1.09464i	−0.0189406	−	0.0829844i
$175$	−13.8061	+	4.25862i	−1.04364	+	0.321922i
$176$	1.35486	−	0.652467i	0.102127	−	0.0491816i
$177$	1.84573	−	4.70284i	0.138733	−	0.353487i
$178$	3.78906	+	6.56285i	0.284002	+	0.491906i
$179$	12.2987	−	21.3020i	0.919250	−	1.59219i	0.118693	−	0.992931i	$-0.462130\pi$
$179$	12.2987	−	21.3020i	0.919250	−	1.59219i	0.800557	−	0.599257i	$-0.204537\pi$
$180$	2.90396	+	3.64145i	0.216448	+	0.271418i
$181$	−4.71852	+	3.21703i	−0.350725	+	0.239120i	−0.725848	−	0.687855i	$-0.758553\pi$
$181$	−4.71852	+	3.21703i	−0.350725	+	0.239120i	0.375124	+	0.926975i	$0.377600\pi$
$182$	2.32775	+	0.350852i	0.172544	+	0.0260069i
$183$	−2.77502	−	1.33638i	−0.205135	−	0.0987879i
$184$	4.70043	−	4.36137i	0.346521	−	0.321524i
$185$	3.08750	−	0.465365i	0.226997	−	0.0342143i
$186$	4.27057	+	1.31730i	0.313134	+	0.0965889i
$187$	1.17562	−	15.6876i	0.0859702	−	1.14719i
$188$	−7.59328	+	9.52167i	−0.553797	+	0.694439i
$189$	7.04922	+	17.9611i	0.512755	+	1.30648i
$190$	1.47601	+	1.36954i	0.107081	+	0.0993568i
$191$	0.303915	+	0.207206i	0.0219905	+	0.0149929i	0.574265	−	0.818669i	$-0.305288\pi$
$191$	0.303915	+	0.207206i	0.0219905	+	0.0149929i	−0.552275	+	0.833662i	$0.686240\pi$
$192$	−0.196870	−	2.62704i	−0.0142078	−	0.189590i
$193$	1.96944	−	8.62869i	0.141764	−	0.621107i	−0.853262	−	0.521483i	$-0.825379\pi$
$193$	1.96944	−	8.62869i	0.141764	−	0.621107i	0.995025	−	0.0996237i	$-0.0317639\pi$
$194$	0.803013	−	3.51823i	0.0576530	−	0.252594i
$195$	0.0481827	+	0.642954i	0.00345044	+	0.0460429i
$196$	−17.5665	−	11.9766i	−1.25475	−	0.855472i
$197$	2.76426	+	2.56486i	0.196945	+	0.182738i	0.772480	−	0.635039i	$-0.219016\pi$
$197$	2.76426	+	2.56486i	0.196945	+	0.182738i	−0.575535	+	0.817777i	$0.695206\pi$
$198$	1.90353	+	4.85012i	0.135278	+	0.344683i
$199$	7.05704	−	8.84925i	0.500260	−	0.627307i	−0.466028	−	0.884770i	$-0.654315\pi$
$199$	7.05704	−	8.84925i	0.500260	−	0.627307i	0.966288	+	0.257464i	$0.0828867\pi$
$200$	0.610179	−	8.14227i	0.0431462	−	0.575746i
$201$	−4.00902	−	1.23662i	−0.282774	−	0.0872244i
$202$	8.86660	−	1.33642i	0.623852	−	0.0940305i
$203$	6.57009	−	6.09615i	0.461130	−	0.427866i
$204$	5.38980	+	2.59559i	0.377362	+	0.181728i
$205$	−3.63645	−	0.548106i	−0.253981	−	0.0382814i
$206$	−6.85014	+	4.67035i	−0.477272	+	0.325399i
$207$	−3.63566	−	4.55897i	−0.252696	−	0.316870i
$208$	0.174587	−	0.302394i	0.0121054	−	0.0209672i
$209$	−2.38798	−	4.13611i	−0.165180	−	0.286101i
$210$	−1.45231	+	3.70042i	−0.100219	+	0.255353i
$211$	2.57368	−	1.23942i	0.177180	−	0.0853253i	−0.343191	−	0.939266i	$-0.611508\pi$
$211$	2.57368	−	1.23942i	0.177180	−	0.0853253i	0.520371	+	0.853940i	$0.325794\pi$
$212$	17.8475	−	5.50521i	1.22577	−	0.378100i
$213$	−1.42224	−	6.23122i	−0.0974500	−	0.426956i
$214$	−3.83953			−0.262465
$215$	−2.75938	+	8.76520i	−0.188188	+	0.597782i
$216$	−10.9043			−0.741942
$217$	7.93837	+	34.7803i	0.538891	+	2.36104i
$218$	13.6744	−	4.21801i	0.926150	−	0.285679i
$219$	−5.70948	+	2.74954i	−0.385811	+	0.185797i
$220$	1.85160	−	4.71780i	0.124835	−	0.318074i
$221$	−1.82642	−	3.16345i	−0.122858	−	0.212797i
$222$	−0.664117	+	1.15029i	−0.0445726	+	0.0772021i
$223$	2.73391	+	3.42821i	0.183076	+	0.229570i	0.864897	−	0.501949i	$-0.167383\pi$
$223$	2.73391	+	3.42821i	0.183076	+	0.229570i	−0.681822	+	0.731519i	$0.738812\pi$
$224$	22.9254	−	15.6302i	1.53177	−	1.04434i
$225$	−7.34233	−	1.10668i	−0.489489	−	0.0737786i
$226$	−0.928523	−	0.447153i	−0.0617644	−	0.0297442i
$227$	9.09730	−	8.44106i	0.603809	−	0.560253i	−0.317905	−	0.948122i	$-0.602979\pi$
$227$	9.09730	−	8.44106i	0.603809	−	0.560253i	0.921714	+	0.387870i	$0.126789\pi$
$228$	1.79586	−	0.270683i	0.118934	−	0.0179264i
$229$	9.76205	+	3.01119i	0.645094	+	0.198985i	0.600003	−	0.799998i	$-0.295166\pi$
$229$	9.76205	+	3.01119i	0.645094	+	0.198985i	0.0450911	+	0.998983i	$0.485642\pi$
$230$	0.199908	−	2.66759i	0.0131816	−	0.175896i
$231$	5.87890	−	7.37191i	0.386803	−	0.485036i
$232$	1.85050	+	4.71500i	0.121491	+	0.309555i
$233$	−14.9717	−	13.8917i	−0.980830	−	0.910077i	0.0151294	−	0.999886i	$-0.495184\pi$
$233$	−14.9717	−	13.8917i	−0.980830	−	0.910077i	−0.995959	+	0.0898086i	$0.971374\pi$
$234$	0.999595	+	0.681513i	0.0653456	+	0.0445519i
$235$	0.938446	+	12.5227i	0.0612175	+	0.816891i
$236$	−2.05187	+	8.98984i	−0.133565	+	0.585188i
$237$	−1.02600	+	4.49520i	−0.0666459	+	0.291995i
$238$	−1.68303	−	22.4584i	−0.109094	−	1.45576i
$239$	1.59638	+	1.08839i	0.103261	+	0.0704022i	0.613850	−	0.789423i	$-0.289620\pi$
$239$	1.59638	+	1.08839i	0.103261	+	0.0704022i	−0.510589	+	0.859825i	$0.670572\pi$
$240$	0.432239	+	0.401059i	0.0279009	+	0.0258882i
$241$	5.18733	+	13.2171i	0.334145	+	0.851388i	0.994907	+	0.100793i	$0.0321380\pi$
$241$	5.18733	+	13.2171i	0.334145	+	0.851388i	−0.660762	+	0.750595i	$0.729767\pi$
$242$	−1.95590	+	2.45262i	−0.125730	+	0.157660i
$243$	−1.14929	+	15.3362i	−0.0737267	+	0.983815i
$244$	5.37192	+	1.65702i	0.343902	+	0.106080i
$245$	−21.6778	+	3.26740i	−1.38494	+	0.208746i
$246$	1.14678	−	1.06406i	0.0731161	−	0.0678418i
$247$	−0.999145	−	0.481163i	−0.0635741	−	0.0306157i
$248$	−19.9359	−	3.00486i	−1.26593	−	0.190809i
$249$	0.781412	−	0.532758i	0.0495200	−	0.0337622i
$250$	−5.62137	−	7.04897i	−0.355527	−	0.445816i
$251$	−4.31293	+	7.47021i	−0.272230	+	0.471516i	−0.969432	−	0.245358i	$-0.921094\pi$
$251$	−4.31293	+	7.47021i	−0.272230	+	0.471516i	0.697203	+	0.716874i	$0.254428\pi$
$252$	−7.90786	−	13.6968i	−0.498149	−	0.862819i
$253$	−2.31814	+	5.90652i	−0.145740	+	0.371340i
$254$	−3.16930	+	1.52626i	−0.198860	+	0.0957658i
$255$	5.89441	−	1.81819i	0.369123	−	0.113859i
$256$	3.14749	+	13.7901i	0.196718	+	0.861879i
$257$	12.4670			0.777670			0.388835	−	0.921307i	$-0.372878\pi$
$257$	12.4670			0.777670			0.388835	+	0.921307i	$0.372878\pi$
$258$	−2.18331	−	3.24251i	−0.135927	−	0.201870i
$259$	−10.6026			−0.658814
$260$	−0.261864	−	1.14730i	−0.0162401	−	0.0711527i
$261$	4.40154	−	1.35769i	0.272448	−	0.0840392i
$262$	−10.1847	+	4.90468i	−0.629211	+	0.303012i
$263$	−6.48661	+	16.5276i	−0.399982	+	1.01914i	0.579025	+	0.815310i	$0.303433\pi$
$263$	−6.48661	+	16.5276i	−0.399982	+	1.01914i	−0.979007	+	0.203827i	$0.934662\pi$
$264$	2.66435	+	4.61478i	0.163979	+	0.284020i
$265$	9.62934	−	16.6785i	0.591526	−	1.02455i
$266$	−4.26298	−	5.34560i	−0.261380	−	0.327760i
$267$	5.82340	−	3.97033i	0.356387	−	0.242980i
$268$	7.57193	+	1.14128i	0.462529	+	0.0697150i
$269$	−25.8191	−	12.4338i	−1.57422	−	0.758105i	−0.575984	−	0.817461i	$-0.695381\pi$
$269$	−25.8191	−	12.4338i	−1.57422	−	0.758105i	−0.998237	+	0.0593567i	$0.981095\pi$
$270$	−3.33475	+	3.09419i	−0.202946	+	0.188307i
$271$	−18.1205	+	2.73123i	−1.10074	+	0.165910i	−0.674194	−	0.738554i	$-0.735509\pi$
$271$	−18.1205	+	2.73123i	−1.10074	+	0.165910i	−0.426549	+	0.904464i	$0.640271\pi$
$272$	−3.19218	−	0.984657i	−0.193554	−	0.0597036i
$273$	0.163614	−	2.18327i	0.00990235	−	0.132138i
$274$	−4.69691	+	5.88973i	−0.283750	+	0.355812i
$275$	2.95187	+	7.52125i	0.178005	+	0.453549i
$276$	−1.76875	−	1.64116i	−0.106466	−	0.0987860i
$277$	5.46901	+	3.72871i	0.328601	+	0.224036i	0.716371	−	0.697720i	$-0.245802\pi$
$277$	5.46901	+	3.72871i	0.328601	+	0.224036i	−0.387770	+	0.921756i	$0.626754\pi$
$278$	1.00043	+	13.3498i	0.0600019	+	0.800670i
$279$	−4.07977	+	17.8746i	−0.244249	+	1.07013i
$280$	3.99047	−	17.4834i	0.238476	−	1.04483i
$281$	−0.962331	−	12.8414i	−0.0574079	−	0.766055i	−0.949413	−	0.314030i	$-0.898321\pi$
$281$	−0.962331	−	12.8414i	−0.0574079	−	0.766055i	0.892005	−	0.452025i	$-0.149298\pi$
$282$	−4.41377	−	3.00926i	−0.262836	−	0.179199i
$283$	−0.459412	−	0.426272i	−0.0273092	−	0.0253393i	0.666400	−	0.745594i	$-0.267834\pi$
$283$	−0.459412	−	0.426272i	−0.0273092	−	0.0253393i	−0.693709	+	0.720255i	$0.744025\pi$
$284$	4.26196	+	10.8593i	0.252901	+	0.644380i
$285$	1.16760	−	1.46412i	0.0691627	−	0.0867273i
$286$	0.0983788	−	1.31277i	0.00581726	−	0.0776260i
$287$	11.9329	+	3.68082i	0.704379	+	0.217272i
$288$	14.1006	−	2.12532i	0.830885	−	0.125236i
$289$	−13.1562	+	12.2072i	−0.773893	+	0.718068i
$290$	1.90385	+	0.916844i	0.111798	+	0.0538389i
$291$	−3.31882	−	0.500231i	−0.194553	−	0.0293241i
$292$	9.55658	−	6.51557i	0.559257	−	0.381295i
$293$	13.5001	+	16.9285i	0.788682	+	0.988976i	0.999933	+	0.0115444i	$0.00367477\pi$
$293$	13.5001	+	16.9285i	0.788682	+	0.988976i	−0.211251	+	0.977432i	$0.567754\pi$
$294$	4.66286	−	8.07632i	0.271944	−	0.471020i
$295$	4.75404	+	8.23424i	0.276791	+	0.479416i
$296$	2.18910	−	5.57773i	0.127239	−	0.324199i
$297$	9.72174	−	4.68174i	0.564113	−	0.271662i
$298$	8.92600	−	2.75331i	0.517070	−	0.159495i
$299$	0.327845	+	1.43638i	0.0189598	+	0.0830683i
$300$	−3.07248			−0.177390
$301$	13.7014	−	28.0349i	0.789738	−	1.61591i
$302$	6.44123			0.370651
$303$	−1.85573	−	8.13050i	−0.106609	−	0.467085i
$304$	−0.969115	+	0.298932i	−0.0555826	+	0.0171450i
$305$	5.22263	−	2.51509i	0.299047	−	0.144013i
$306$	4.22862	−	10.7743i	0.241734	−	0.615928i
$307$	4.16103	+	7.20711i	0.237482	+	0.411332i	0.959991	−	0.280030i	$-0.0903445\pi$
$307$	4.16103	+	7.20711i	0.237482	+	0.411332i	−0.722509	+	0.691362i	$0.757011\pi$
$308$	−8.60492	+	14.9042i	−0.490311	+	0.849243i
$309$	4.80765	+	6.02860i	0.273498	+	0.342955i
$310$	−6.94947	+	4.73807i	−0.394703	+	0.269104i
$311$	−13.6228	−	2.05331i	−0.772481	−	0.116433i	−0.249038	−	0.968494i	$-0.580114\pi$
$311$	−13.6228	−	2.05331i	−0.772481	−	0.116433i	−0.523443	+	0.852061i	$0.675353\pi$
$312$	1.11478	+	0.536848i	0.0631118	+	0.0303930i
$313$	−3.60094	+	3.34119i	−0.203537	+	0.188855i	−0.775355	−	0.631526i	$-0.782429\pi$
$313$	−3.60094	+	3.34119i	−0.203537	+	0.188855i	0.571818	+	0.820381i	$0.306238\pi$
$314$	−5.99596	+	0.903745i	−0.338372	+	0.0510013i
$315$	−15.5836	−	4.80689i	−0.878034	−	0.270838i
$316$	0.628901	−	8.39210i	0.0353785	−	0.472093i
$317$	11.7522	−	14.7368i	0.660071	−	0.827703i	−0.333280	−	0.942828i	$-0.608155\pi$
$317$	11.7522	−	14.7368i	0.660071	−	0.827703i	0.993351	+	0.115125i	$0.0367269\pi$
$318$	2.99306	+	7.62619i	0.167842	+	0.427655i
$319$	−3.67420	−	3.40916i	−0.205716	−	0.190876i
$320$	4.09650	+	2.79294i	0.229001	+	0.156130i
$321$	0.266860	+	3.56100i	0.0148947	+	0.198756i
$322$	−2.02132	+	8.85596i	−0.112643	+	0.493523i
$323$	−2.36086	+	10.3436i	−0.131362	+	0.575534i
$324$	−0.438494	−	5.85129i	−0.0243608	−	0.325072i
$325$	1.55011	+	1.05685i	0.0859846	+	0.0586233i
$326$	−3.62209	−	3.36081i	−0.200609	−	0.186138i
$327$	−4.86244	−	12.3893i	−0.268893	−	0.685129i
$328$	−4.40015	+	5.51761i	−0.242957	+	0.304659i
$329$	3.18667	−	42.5232i	0.175687	−	2.34438i
$330$	2.12430	+	0.655260i	0.116939	+	0.0360709i
$331$	−3.20077	+	0.482439i	−0.175930	+	0.0265172i	−0.236416	−	0.971652i	$-0.575973\pi$
$331$	−3.20077	+	0.482439i	−0.175930	+	0.0265172i	0.0604862	+	0.998169i	$0.480735\pi$
$332$	−1.26538	+	1.17410i	−0.0694465	+	0.0644369i
$333$	−4.90938	−	2.36423i	−0.269033	−	0.129559i
$334$	6.97707	+	1.05162i	0.381768	+	0.0575423i
$335$	6.52385	−	4.44788i	0.356436	−	0.243014i
$336$	−1.24838	−	1.56542i	−0.0681046	−	0.0854005i
$337$	−4.83669	+	8.37738i	−0.263471	+	0.456345i	−0.967162	−	0.254161i	$-0.918201\pi$
$337$	−4.83669	+	8.37738i	−0.263471	+	0.456345i	0.703691	+	0.710506i	$0.251534\pi$
$338$	5.05104	+	8.74866i	0.274740	+	0.475864i
$339$	−0.350180	+	0.892243i	−0.0190192	+	0.0484600i
$340$	−10.1437	+	4.88495i	−0.550120	+	0.264924i
$341$	19.0641	−	5.88049i	1.03238	−	0.318446i
$342$	−0.781914	−	3.42579i	−0.0422810	−	0.185245i
$343$	41.1325			2.22095
$344$	11.9195	+	12.9963i	0.642655	+	0.700711i
$345$	−2.48797			−0.133948
$346$	−1.09090	−	4.77954i	−0.0586471	−	0.256950i
$347$	10.4815	−	3.23310i	0.562674	−	0.173562i	−0.000353651	−	1.00000i	$-0.500113\pi$
$347$	10.4815	−	3.23310i	0.562674	−	0.173562i	0.563028	+	0.826438i	$0.309636\pi$
$348$	1.71723	−	0.826973i	0.0920531	−	0.0443304i
$349$	7.84116	−	19.9790i	0.419728	−	1.06945i	−0.552104	−	0.833775i	$-0.686175\pi$
$349$	7.84116	−	19.9790i	0.419728	−	1.06945i	0.971832	−	0.235674i	$-0.0757297\pi$
$350$	5.78351	+	10.0173i	0.309142	+	0.535449i
$351$	1.25274	−	2.16981i	0.0668664	−	0.115816i
$352$	−9.67457	−	12.1315i	−0.515656	−	0.646613i
$353$	−27.5239	+	18.7655i	−1.46495	+	0.998785i	−0.471828	+	0.881690i	$0.656406\pi$
$353$	−27.5239	+	18.7655i	−1.46495	+	0.998785i	−0.993121	+	0.117095i	$0.962642\pi$
$354$	−3.99950	−	0.602827i	−0.212571	−	0.0320399i
$355$	10.8376	+	5.21913i	0.575202	+	0.277003i
$356$	−9.43009	+	8.74985i	−0.499794	+	0.463741i
$357$	−20.7122	+	3.12187i	−1.09621	+	0.165227i
$358$	−18.8178	−	5.80451i	−0.994550	−	0.306778i
$359$	−0.560334	+	7.47713i	−0.0295733	+	0.394628i	0.962701	+	0.270567i	$0.0872110\pi$
$359$	−0.560334	+	7.47713i	−0.0295733	+	0.394628i	−0.992275	+	0.124061i	$0.960408\pi$
$360$	5.74628	−	7.20560i	0.302855	−	0.379769i
$361$	−5.76472	−	14.6883i	−0.303407	−	0.773067i
$362$	3.35158	+	3.10981i	0.176155	+	0.163448i
$363$	2.41064	+	1.64354i	0.126526	+	0.0862637i
$364$	0.298627	+	3.98490i	0.0156523	+	0.208866i
$365$	2.65388	−	11.6274i	0.138911	−	0.608607i
$366$	−0.548707	+	2.40404i	−0.0286814	+	0.125661i
$367$	−0.382393	−	5.10269i	−0.0199608	−	0.266358i	−0.998251	−	0.0591184i	$-0.981171\pi$
$367$	−0.382393	−	5.10269i	−0.0199608	−	0.266358i	0.978290	−	0.207240i	$-0.0664480\pi$
$368$	1.11326	+	0.759008i	0.0580327	+	0.0395660i
$369$	4.70460	+	4.36523i	0.244912	+	0.227245i
$370$	−0.913265	−	2.32696i	−0.0474784	−	0.120973i
$371$	−40.7741	+	51.1291i	−2.11688	+	2.65449i
$372$	−0.566940	+	7.56529i	−0.0293945	+	0.392242i
$373$	−31.4395	−	9.69781i	−1.62788	−	0.502134i	−0.659517	−	0.751690i	$-0.729239\pi$
$373$	−31.4395	−	9.69781i	−1.62788	−	0.502134i	−0.968360	+	0.249556i	$0.919715\pi$
$374$	−12.4540	+	1.87714i	−0.643982	+	0.0970646i
$375$	−6.14691	+	5.70350i	−0.317425	+	0.294528i
$376$	21.7123	+	10.4561i	1.11973	+	0.539232i
$377$	−1.15082	−	0.173458i	−0.0592703	−	0.00893355i
$378$	12.7633	−	8.70185i	0.656472	−	0.447575i
$379$	−5.54243	−	6.94999i	−0.284695	−	0.356997i	0.618835	−	0.785521i	$-0.287605\pi$
$379$	−5.54243	−	6.94999i	−0.284695	−	0.356997i	−0.903530	+	0.428524i	$0.859034\pi$
$380$	−1.70901	+	2.96009i	−0.0876704	+	0.151850i
$381$	1.63581	+	2.83331i	0.0838053	+	0.145155i
$382$	0.107587	−	0.274127i	0.00550463	−	0.0140256i
$383$	12.2349	−	5.89201i	0.625173	−	0.301067i	−0.0943467	−	0.995539i	$-0.530076\pi$
$383$	12.2349	−	5.89201i	0.625173	−	0.301067i	0.719520	+	0.694472i	$0.244362\pi$
$384$	6.28220	−	1.93780i	0.320587	−	0.0988880i
$385$	3.94876	+	17.3007i	0.201248	+	0.881724i
$386$	−7.08576			−0.360656
$387$	12.5957	−	9.92594i	0.640273	−	0.504564i
$388$	6.12592			0.310997
$389$	0.872197	+	3.82135i	0.0442222	+	0.193750i	0.992214	−	0.124545i	$-0.0397470\pi$
$389$	0.872197	+	3.82135i	0.0442222	+	0.193750i	−0.947992	+	0.318295i	$0.896890\pi$
$390$	0.493257	−	0.152150i	0.0249771	−	0.00770440i
$391$	12.6996	−	6.11579i	0.642245	−	0.309289i
$392$	−15.3700	+	39.1621i	−0.776301	+	1.97798i
$393$	5.25674	+	9.10494i	0.265168	+	0.459284i
$394$	1.50948	−	2.61450i	0.0760466	−	0.131717i
$395$	−5.41041	−	6.78444i	−0.272227	−	0.341362i
$396$	−7.30780	+	4.98237i	−0.367231	+	0.250374i
$397$	0.912545	+	0.137544i	0.0457993	+	0.00690313i	0.171902	−	0.985114i	$-0.445009\pi$
$397$	0.912545	+	0.137544i	0.0457993	+	0.00690313i	−0.126103	+	0.992017i	$0.540247\pi$
$398$	−8.16426	−	3.93170i	−0.409238	−	0.197078i
$399$	−4.66152	+	4.32526i	−0.233368	+	0.216534i
$400$	1.69657	−	0.255717i	0.0848285	−	0.0127858i
$401$	−12.9927	−	4.00771i	−0.648823	−	0.200136i	−0.0471626	−	0.998887i	$-0.515018\pi$
$401$	−12.9927	−	4.00771i	−0.648823	−	0.200136i	−0.601661	+	0.798752i	$0.705494\pi$
$402$	−0.251006	+	3.34944i	−0.0125190	+	0.167055i
$403$	2.88828	−	3.62178i	0.143875	−	0.180414i
$404$	5.56100	+	14.1692i	0.276670	+	0.704944i
$405$	−4.43523	−	4.11529i	−0.220388	−	0.204490i
$406$	−5.92865	−	4.04209i	−0.294234	−	0.200605i
$407$	0.443098	+	5.91274i	0.0219636	+	0.293083i
$408$	2.63409	−	11.5407i	0.130407	−	0.571349i
$409$	−3.60394	+	15.7899i	−0.178204	+	0.780761i	0.804256	+	0.594283i	$0.202564\pi$
$409$	−3.60394	+	15.7899i	−0.178204	+	0.780761i	−0.982459	+	0.186477i	$0.940293\pi$
$410$	0.220021	+	2.93598i	0.0108661	+	0.144998i
$411$	5.78892	+	3.94682i	0.285546	+	0.194682i
$412$	−10.3169	−	9.57266i	−0.508276	−	0.471611i
$413$	−11.7956	−	30.0547i	−0.580423	−	1.47889i
$414$	−2.91070	+	3.64990i	−0.143053	+	0.179383i
$415$	−0.133013	+	1.77493i	−0.00652935	+	0.0871281i
$416$	−3.44289	−	1.06199i	−0.168802	−	0.0520684i
$417$	12.3119	−	1.85571i	0.602914	−	0.0908747i
$418$	−2.80292	+	2.60073i	−0.137095	+	0.127206i
$419$	22.4254	+	10.7995i	1.09555	+	0.527590i	0.892257	−	0.451527i	$-0.149121\pi$
$419$	22.4254	+	10.7995i	1.09555	+	0.527590i	0.203295	+	0.979117i	$0.434835\pi$
$420$	−6.67271	−	1.00575i	−0.325595	−	0.0490755i
$421$	25.5011	−	17.3863i	1.24285	−	0.847359i	0.250175	−	0.968201i	$-0.419512\pi$
$421$	25.5011	−	17.3863i	1.24285	−	0.847359i	0.992672	+	0.120842i	$0.0385594\pi$
$422$	−1.42590	−	1.78802i	−0.0694117	−	0.0870395i
$423$	10.9576	−	18.9792i	0.532778	−	0.922799i
$424$	−18.4790	−	32.0066i	−0.897421	−	1.55438i
$425$	6.55747	−	16.7082i	0.318084	−	0.810465i
$426$	−4.61025	+	2.22018i	−0.223367	+	0.107568i
$427$	−18.8093	+	5.80189i	−0.910244	+	0.280773i
$428$	−1.45034	−	6.35434i	−0.0701047	−	0.307149i
$429$	−1.22438			−0.0591136
$430$	7.33304	+	0.592249i	0.353630	+	0.0285608i
$431$	−2.13534			−0.102856			−0.0514278	−	0.998677i	$-0.516377\pi$
$431$	−2.13534			−0.102856			−0.0514278	+	0.998677i	$0.516377\pi$
$432$	−0.509865	−	2.23387i	−0.0245309	−	0.107477i
$433$	18.6448	−	5.75116i	0.896012	−	0.276383i	0.187653	−	0.982235i	$-0.439912\pi$
$433$	18.6448	−	5.75116i	0.896012	−	0.276383i	0.708359	+	0.705852i	$0.249436\pi$
$434$	25.7326	−	12.3922i	1.23521	−	0.594844i
$435$	0.718010	−	1.82946i	0.0344259	−	0.0877158i
$436$	12.1461	+	21.0376i	0.581691	+	1.00752i
$437$	2.13962	−	3.70594i	0.102352	−	0.177279i
$438$	3.16323	+	3.96656i	0.151145	+	0.189530i
$439$	11.8985	−	8.11229i	0.567887	−	0.387179i	−0.245068	−	0.969506i	$-0.578810\pi$
$439$	11.8985	−	8.11229i	0.567887	−	0.387179i	0.812954	+	0.582327i	$0.197858\pi$
$440$	−9.91669	−	1.49470i	−0.472759	−	0.0712570i
$441$	34.4695	+	16.5996i	1.64140	+	0.790459i
$442$	−2.14378	+	1.98913i	−0.101969	+	0.0946134i
$443$	−20.4362	+	3.08026i	−0.970951	+	0.146347i	−0.615319	−	0.788278i	$-0.710973\pi$
$443$	−20.4362	+	3.08026i	−0.970951	+	0.146347i	−0.355633	+	0.934626i	$0.615735\pi$
$444$	−2.15456	−	0.664593i	−0.102251	−	0.0315402i
$445$	−0.991267	+	13.2275i	−0.0469906	+	0.627045i
$446$	2.18876	−	2.74462i	0.103641	−	0.129961i
$447$	−3.17396	−	8.08712i	−0.150123	−	0.382508i
$448$	−12.3416	−	11.4513i	−0.583084	−	0.541023i
$449$	27.0107	+	18.4156i	1.27471	+	0.869084i	0.995829	−	0.0912409i	$-0.0290833\pi$
$449$	27.0107	+	18.4156i	1.27471	+	0.869084i	0.278883	+	0.960325i	$0.410036\pi$
$450$	0.444244	+	5.92802i	0.0209419	+	0.279450i
$451$	1.55398	−	6.80845i	0.0731742	−	0.320597i
$452$	0.389290	−	1.70559i	0.0183107	−	0.0802243i
$453$	−0.447686	−	5.97396i	−0.0210341	−	0.280681i
$454$	−8.20913	−	5.59689i	−0.385274	−	0.262675i
$455$	3.02052	+	2.80264i	0.141604	+	0.131390i
$456$	−1.31294	−	3.34532i	−0.0614842	−	0.156659i
$457$	1.92198	−	2.41009i	0.0899066	−	0.112739i	−0.734843	−	0.678237i	$-0.762744\pi$
$457$	1.92198	−	2.41009i	0.0899066	−	0.112739i	0.824750	+	0.565497i	$0.191316\pi$
$458$	0.611205	−	8.15596i	0.0285597	−	0.381103i
$459$	−22.9053	−	7.06536i	−1.06913	−	0.329783i
$460$	4.49031	−	0.676806i	0.209362	−	0.0315562i
$461$	15.8067	−	14.6665i	0.736193	−	0.683087i	−0.220107	−	0.975476i	$-0.570641\pi$
$461$	15.8067	−	14.6665i	0.736193	−	0.683087i	0.956300	+	0.292389i	$0.0944501\pi$
$462$	−6.80128	−	3.27532i	−0.316424	−	0.152382i
$463$	−27.1728	−	4.09564i	−1.26283	−	0.190340i	−0.516713	−	0.856159i	$-0.672844\pi$
$463$	−27.1728	−	4.09564i	−1.26283	−	0.190340i	−0.746114	+	0.665818i	$0.768083\pi$
$464$	−0.879395	+	0.599562i	−0.0408249	+	0.0278339i
$465$	4.87736	+	6.11602i	0.226182	+	0.283624i
$466$	−8.17562	+	14.1606i	−0.378728	+	0.655977i
$467$	15.8517	+	27.4559i	0.733529	+	1.27051i	0.955366	+	0.295426i	$0.0954616\pi$
$467$	15.8517	+	27.4559i	0.733529	+	1.27051i	−0.221836	+	0.975084i	$0.571205\pi$
$468$	−0.750303	+	1.91174i	−0.0346828	+	0.0883703i
$469$	−24.1566	+	11.6332i	−1.11545	+	0.537172i
$470$	9.60709	−	2.96339i	0.443142	−	0.136691i
$471$	1.25492	+	5.49818i	0.0578238	+	0.253343i
$472$	18.2463			0.839855
$473$	−16.2068	−	6.46923i	−0.745189	−	0.297456i
$474$	3.69140			0.169552
$475$	−1.21254	−	5.31249i	−0.0556352	−	0.243754i
$476$	36.5325	−	11.2688i	1.67446	−	0.516503i
$477$	−30.2809	+	14.5825i	−1.38647	+	0.667688i
$478$	0.565122	−	1.43991i	0.0258481	−	0.0658598i
$479$	−1.49373	−	2.58721i	−0.0682502	−	0.118213i	0.829881	−	0.557941i	$-0.188408\pi$
$479$	−1.49373	−	2.58721i	−0.0682502	−	0.118213i	−0.898131	+	0.439728i	$0.855075\pi$
$480$	3.04212	−	5.26910i	0.138853	−	0.240501i
$481$	0.858403	+	1.07640i	0.0391398	+	0.0490798i
$482$	9.39215	−	6.40346i	0.427801	−	0.291670i
$483$	8.35401	+	1.25916i	0.380120	+	0.0572939i
$484$	−4.79784	−	2.31052i	−0.218084	−	0.105024i
$485$	4.63041	−	4.29640i	0.210256	−	0.195089i
$486$	12.1750	−	1.83508i	0.552269	−	0.0832411i
$487$	−30.1329	−	9.29475i	−1.36545	−	0.421186i	−0.476494	−	0.879178i	$-0.658093\pi$
$487$	−30.1329	−	9.29475i	−1.36545	−	0.421186i	−0.888956	+	0.457992i	$0.848569\pi$
$488$	0.831300	−	11.0929i	0.0376312	−	0.502153i
$489$	−2.86526	+	3.59292i	−0.129571	+	0.162477i
$490$	6.41217	+	16.3379i	0.289672	+	0.738073i
$491$	13.8180	+	12.8213i	0.623600	+	0.578616i	0.927378	−	0.374127i	$-0.122058\pi$
$491$	13.8180	+	12.8213i	0.623600	+	0.578616i	−0.303778	+	0.952743i	$0.598248\pi$
$492$	2.19417	+	1.49596i	0.0989210	+	0.0674432i
$493$	0.832074	+	11.1033i	0.0374747	+	0.500066i
$494$	−0.197562	+	0.865576i	−0.00888874	+	0.0389441i
$495$	−2.02939	+	8.89134i	−0.0912143	+	0.399636i
$496$	−0.316591	−	4.22461i	−0.0142153	−	0.189690i
$497$	−33.7488	−	23.0095i	−1.51384	−	1.03212i
$498$	−0.555039	−	0.515001i	−0.0248719	−	0.0230777i
$499$	11.4840	+	29.2608i	0.514096	+	1.30989i	0.918539	+	0.395331i	$0.129370\pi$
$499$	11.4840	+	29.2608i	0.514096	+	1.30989i	−0.404443	+	0.914563i	$0.632535\pi$
$500$	9.54249	−	11.9659i	0.426753	−	0.535131i
$501$	0.490407	−	6.54402i	0.0219097	−	0.292365i
$502$	6.59903	+	2.03553i	0.294529	+	0.0908502i
$503$	22.4500	−	3.38379i	1.00100	−	0.150876i	0.371957	−	0.928250i	$-0.378687\pi$
$503$	22.4500	−	3.38379i	1.00100	−	0.150876i	0.629039	+	0.777374i	$0.283449\pi$
$504$	−22.9414	+	21.2865i	−1.02189	+	0.948177i
$505$	14.1409	+	6.80992i	0.629263	+	0.303037i
$506$	5.02316	+	0.757119i	0.223307	+	0.0336581i
$507$	7.76294	−	5.29268i	0.344764	−	0.235056i
$508$	−3.72309	−	4.66860i	−0.165185	−	0.207136i
$509$	−8.84121	+	15.3134i	−0.391880	+	0.678755i	−0.992697	−	0.120631i	$-0.961508\pi$
$509$	−8.84121	+	15.3134i	−0.391880	+	0.678755i	0.600818	+	0.799386i	$0.294842\pi$
$510$	−2.46923	−	4.27682i	−0.109339	−	0.189381i
$511$	−14.7958	+	37.6990i	−0.654526	+	1.66771i
$512$	−5.70701	+	2.74835i	−0.252217	+	0.121461i
$513$	−6.95384	+	2.14498i	−0.307019	+	0.0947030i
$514$	−2.22099	−	9.73080i	−0.0979637	−	0.429207i
$515$	−14.5120			−0.639475
$516$	4.54156	−	4.83815i	0.199931	−	0.212988i
$517$	−23.8470			−1.04879
$518$	1.88885	+	8.27560i	0.0829913	+	0.363609i
$519$	−4.35699	+	1.34395i	−0.191251	+	0.0589931i
$520$	−2.09803	+	1.01036i	−0.0920047	+	0.0443071i
$521$	−12.4384	+	31.6925i	−0.544936	+	1.38847i	0.347662	+	0.937620i	$0.386976\pi$
$521$	−12.4384	+	31.6925i	−0.544936	+	1.38847i	−0.892598	+	0.450854i	$0.851120\pi$
$522$	−1.84385	−	3.19364i	−0.0807030	−	0.139782i
$523$	4.21809	−	7.30594i	0.184444	−	0.319466i	−0.758945	−	0.651155i	$-0.774285\pi$
$523$	4.21809	−	7.30594i	0.184444	−	0.319466i	0.943389	+	0.331688i	$0.107618\pi$
$524$	−11.9643	−	15.0027i	−0.522661	−	0.655397i
$525$	8.88867	−	6.06019i	0.387933	−	0.264489i
$526$	14.0558	+	2.11857i	0.612862	+	0.0923741i
$527$	−39.9301	−	19.2293i	−1.73938	−	0.837642i
$528$	−0.820812	+	0.761602i	−0.0357212	+	0.0331445i
$529$	17.1214	−	2.58063i	0.744408	−	0.112201i
$530$	−14.7334	−	4.54467i	−0.639980	−	0.197408i
$531$	1.24000	−	16.5466i	0.0538113	−	0.718062i
$532$	7.23657	−	9.07437i	0.313745	−	0.393424i
$533$	−0.592422	−	1.50947i	−0.0256606	−	0.0653823i
$534$	−4.13638	−	3.83800i	−0.178999	−	0.166086i
$535$	−5.55287	−	3.78588i	−0.240071	−	0.163678i
$536$	−1.13234	−	15.1100i	−0.0489095	−	0.652652i
$537$	−4.07554	+	17.8561i	−0.175872	+	0.770547i
$538$	−5.10525	+	22.3675i	−0.220103	+	0.964333i
$539$	−3.11106	−	41.5142i	−0.134003	−	1.78814i
$540$	−6.38048	−	4.35014i	−0.274572	−	0.187200i
$541$	−7.39584	−	6.86234i	−0.317972	−	0.295035i	0.504997	−	0.863121i	$-0.331494\pi$
$541$	−7.39584	−	6.86234i	−0.317972	−	0.295035i	−0.822969	+	0.568086i	$0.807684\pi$
$542$	5.35995	+	13.6569i	0.230230	+	0.586616i
$543$	2.65127	−	3.32458i	0.113777	−	0.142671i
$544$	−2.57594	+	34.3736i	−0.110443	+	1.47375i
$545$	23.9355	+	7.38313i	1.02529	+	0.316259i
$546$	−1.73324	+	0.261245i	−0.0741760	+	0.0111802i
$547$	13.5257	−	12.5500i	0.578318	−	0.536600i	−0.335861	−	0.941911i	$-0.609027\pi$
$547$	13.5257	−	12.5500i	0.578318	−	0.536600i	0.914179	+	0.405311i	$0.132837\pi$
$548$	−11.5216	−	5.54850i	−0.492177	−	0.237020i
$549$	−10.0031	−	1.50772i	−0.426922	−	0.0643481i
$550$	5.34465	−	3.64392i	0.227896	−	0.155377i
$551$	2.10758	+	2.64282i	0.0897859	+	0.112588i
$552$	−2.38724	+	4.13483i	−0.101608	+	0.175990i
$553$	14.7333	+	25.5188i	0.626522	+	1.08517i
$554$	1.93605	−	4.93296i	0.0822547	−	0.209582i
$555$	−2.09468	+	1.00875i	−0.0889143	+	0.0428189i
$556$	−21.7158	+	6.69843i	−0.920954	+	0.284077i
$557$	0.981857	+	4.30180i	0.0416026	+	0.182273i	0.991460	−	0.130410i	$-0.0416294\pi$
$557$	0.981857	+	4.30180i	0.0416026	+	0.182273i	−0.949858	+	0.312683i	$0.898772\pi$
$558$	14.6784			0.621386
$559$	−3.95547	+	0.878747i	−0.167298	+	0.0371670i
$560$	3.76826			0.159238
$561$	2.60656	+	11.4201i	0.110049	+	0.482156i
$562$	−9.85160	+	3.03882i	−0.415565	+	0.128185i
$563$	8.26616	−	3.98077i	0.348377	−	0.167769i	−0.251509	−	0.967855i	$-0.580927\pi$
$563$	8.26616	−	3.98077i	0.348377	−	0.167769i	0.599886	+	0.800085i	$0.295213\pi$
$564$	3.31301	−	8.44140i	0.139503	−	0.355447i
$565$	−0.901958	−	1.56224i	−0.0379457	−	0.0657238i
$566$	−0.250872	+	0.434523i	−0.0105449	+	0.0182644i
$567$	12.8097	+	16.0629i	0.537957	+	0.674577i
$568$	19.0727	−	13.0036i	0.800273	−	0.545617i
$569$	2.08305	+	0.313969i	0.0873259	+	0.0131623i	0.192560	−	0.981285i	$-0.438321\pi$
$569$	2.08305	+	0.313969i	0.0873259	+	0.0131623i	−0.105234	+	0.994447i	$0.533559\pi$
$570$	−1.35079	−	0.650507i	−0.0565785	−	0.0272468i
$571$	21.4978	−	19.9470i	0.899654	−	0.834757i	−0.0872298	−	0.996188i	$-0.527801\pi$
$571$	21.4978	−	19.9470i	0.899654	−	0.834757i	0.986884	+	0.161431i	$0.0516110\pi$
$572$	2.20977	−	0.333070i	0.0923953	−	0.0139263i
$573$	−0.261719	−	0.0807295i	−0.0109335	−	0.00337252i
$574$	0.747125	−	9.96969i	0.0311844	−	0.416127i
$575$	−4.51372	+	5.66003i	−0.188235	+	0.236040i
$576$	−3.16110	−	8.05435i	−0.131712	−	0.335598i
$577$	−12.2136	−	11.3326i	−0.508459	−	0.471781i	0.383729	−	0.923446i	$-0.374640\pi$
$577$	−12.2136	−	11.3326i	−0.508459	−	0.471781i	−0.892188	+	0.451665i	$0.850830\pi$
$578$	11.8718	+	8.09402i	0.493800	+	0.336667i
$579$	0.492483	+	6.57173i	0.0204669	+	0.273112i
$580$	−0.798202	+	3.49715i	−0.0331435	+	0.145211i
$581$	1.34492	−	5.89249i	0.0557968	−	0.244462i
$582$	0.200803	+	2.67953i	0.00832357	+	0.111070i
$583$	30.2171	+	20.6016i	1.25146	+	0.853233i
$584$	−16.7775	−	15.5673i	−0.694259	−	0.644178i
$585$	0.773661	+	1.97125i	0.0319869	+	0.0815014i
$586$	10.8081	−	13.5529i	0.446479	−	0.559867i
$587$	1.69281	−	22.5890i	0.0698698	−	0.932348i	−0.846596	−	0.532236i	$-0.821352\pi$
$587$	1.69281	−	22.5890i	0.0698698	−	0.932348i	0.916466	−	0.400112i	$-0.131029\pi$
$588$	15.1275	+	4.66620i	0.623846	+	0.192431i
$589$	−13.3046	+	2.00534i	−0.548205	+	0.0826286i
$590$	5.58010	−	5.17757i	0.229729	−	0.213157i
$591$	−2.52975	−	1.21826i	−0.104060	−	0.0501126i
$592$	1.24502	+	0.187657i	0.0511701	+	0.00771265i
$593$	−29.4226	+	20.0600i	−1.20824	+	0.823765i	−0.988415	−	0.151775i	$-0.951501\pi$
$593$	−29.4226	+	20.0600i	−1.20824	+	0.823765i	−0.219826	+	0.975539i	$0.570549\pi$
$594$	−5.38614	−	6.75401i	−0.220996	−	0.277120i
$595$	19.7106	−	34.1397i	0.808054	−	1.39959i
$596$	7.92835	+	13.7323i	0.324758	+	0.562497i
$597$	−3.07904	+	7.84527i	−0.126017	+	0.321085i
$598$	1.06273	−	0.511783i	0.0434582	−	0.0209283i
$599$	29.6180	−	9.13596i	1.21016	−	0.373285i	0.376946	−	0.926235i	$-0.376974\pi$
$599$	29.6180	−	9.13596i	1.21016	−	0.373285i	0.833214	+	0.552950i	$0.186498\pi$
$600$	1.35287	+	5.92731i	0.0552307	+	0.241982i
$601$	21.0632			0.859187			0.429594	−	0.903022i	$-0.358657\pi$
$601$	21.0632			0.859187			0.429594	+	0.903022i	$0.358657\pi$
$602$	−24.3229	−	5.69989i	−0.991326	−	0.232310i
$603$	−13.7794			−0.561141
$604$	2.43310	+	10.6601i	0.0990012	+	0.433753i
$605$	−5.24703	+	1.61849i	−0.213322	+	0.0658012i
$606$	−6.01545	+	2.89689i	−0.244361	+	0.117678i
$607$	1.57042	−	4.00136i	0.0637413	−	0.162410i	−0.895454	−	0.445153i	$-0.853149\pi$
$607$	1.57042	−	4.00136i	0.0637413	−	0.162410i	0.959196	+	0.282743i	$0.0912444\pi$
$608$	5.23238	+	9.06274i	0.212201	+	0.367543i
$609$	−3.33680	+	5.77951i	−0.135214	+	0.234197i
$610$	−2.89350	−	3.62833i	−0.117154	−	0.146907i
$611$	−4.57506	+	3.11922i	−0.185087	+	0.126190i
$612$	19.4286	+	2.92839i	0.785354	+	0.118373i
$613$	0.154163	+	0.0742412i	0.00622660	+	0.00299857i	0.436994	−	0.899464i	$-0.356043\pi$
$613$	0.154163	+	0.0742412i	0.00622660	+	0.00299857i	−0.430768	+	0.902463i	$0.641757\pi$
$614$	4.88404	−	4.53173i	0.197104	−	0.182886i
$615$	2.70770	−	0.408121i	0.109185	−	0.0164570i
$616$	32.5414	+	10.0377i	1.31113	+	0.404430i
$617$	0.435808	−	5.81545i	0.0175450	−	0.234121i	−0.981537	−	0.191274i	$-0.938738\pi$
$617$	0.435808	−	5.81545i	0.0175450	−	0.234121i	0.999082	−	0.0428472i	$-0.0136429\pi$
$618$	3.84899	−	4.82648i	0.154829	−	0.194150i
$619$	0.320011	+	0.815375i	0.0128623	+	0.0327727i	0.937161	−	0.348898i	$-0.113444\pi$
$619$	0.320011	+	0.815375i	0.0128623	+	0.0327727i	−0.924298	+	0.381671i	$0.875349\pi$
$620$	−10.4665	−	9.71147i	−0.420344	−	0.390022i
$621$	7.98815	+	5.44623i	0.320553	+	0.218550i
$622$	0.824243	+	10.9988i	0.0330491	+	0.441010i
$623$	10.0229	−	43.9133i	0.401560	−	1.75935i
$624$	−0.0578545	+	0.253477i	−0.00231603	+	0.0101472i
$625$	−0.0448653	−	0.598685i	−0.00179461	−	0.0239474i
$626$	3.24938	+	2.21539i	0.129871	+	0.0885449i
$627$	2.60687	+	2.41882i	0.104108	+	0.0965985i
$628$	−3.76058	−	9.58180i	−0.150063	−	0.382355i
$629$	8.21244	−	10.2981i	0.327452	−	0.410611i
$630$	−0.975691	+	13.0197i	−0.0388725	+	0.518717i
$631$	−21.9032	−	6.75624i	−0.871953	−	0.268962i	−0.173687	−	0.984801i	$-0.555568\pi$
$631$	−21.9032	−	6.75624i	−0.871953	−	0.268962i	−0.698265	+	0.715839i	$0.746044\pi$
$632$	−16.4666	+	2.48195i	−0.655008	+	0.0987265i
$633$	−1.55921	+	1.44673i	−0.0619729	+	0.0575025i
$634$	−13.5961	−	6.54754i	−0.539970	−	0.260036i
$635$	−6.08849	−	0.917692i	−0.241614	−	0.0364175i
$636$	−11.4906	+	7.83415i	−0.455631	+	0.310644i
$637$	−6.02697	−	7.55758i	−0.238797	−	0.299442i
$638$	−2.00638	+	3.47514i	−0.0794332	+	0.137582i
$639$	−10.4961	−	18.1797i	−0.415218	−	0.719180i
$640$	−4.52033	+	11.5176i	−0.178682	+	0.455274i
$641$	29.9739	−	14.4347i	1.18390	−	0.570136i	0.264854	−	0.964288i	$-0.414676\pi$
$641$	29.9739	−	14.4347i	1.18390	−	0.570136i	0.919045	+	0.394153i	$0.128962\pi$
$642$	2.73191	−	0.842681i	0.107820	−	0.0332580i
$643$	8.85495	+	38.7961i	0.349205	+	1.52997i	0.778990	+	0.627037i	$0.215732\pi$
$643$	8.85495	+	38.7961i	0.349205	+	1.52997i	−0.429785	+	0.902931i	$0.641410\pi$
$644$	−15.4199			−0.607631
$645$	0.0396153	−	6.84223i	0.00155985	−	0.269413i
$646$	8.49403			0.334193
$647$	−1.59035	−	6.96776i	−0.0625229	−	0.273931i	0.933998	−	0.357279i	$-0.116296\pi$
$647$	−1.59035	−	6.96776i	−0.0625229	−	0.273931i	−0.996520	+	0.0833487i	$0.973438\pi$
$648$	−11.0950	+	3.42236i	−0.435853	+	0.134443i
$649$	−16.2676	+	7.83405i	−0.638558	+	0.307513i
$650$	0.548743	−	1.39817i	0.0215235	−	0.0548409i
$651$	−13.2817	−	23.0046i	−0.520551	−	0.901621i
$652$	4.19386	−	7.26398i	0.164244	−	0.284479i
$653$	13.6325	+	17.0946i	0.533482	+	0.668965i	0.973411	−	0.229068i	$-0.0735677\pi$
$653$	13.6325	+	17.0946i	0.533482	+	0.668965i	−0.439929	+	0.898033i	$0.644996\pi$
$654$	−8.80390	+	6.00240i	−0.344260	+	0.234712i
$655$	−19.5656	−	2.94903i	−0.764490	−	0.115228i
$656$	−1.33609	−	0.643427i	−0.0521655	−	0.0251216i
$657$	−15.2573	+	14.1567i	−0.595245	+	0.552306i
$658$	−33.7581	+	5.08822i	−1.31603	+	0.198359i
$659$	22.0315	+	6.79582i	0.858225	+	0.264727i	0.692476	−	0.721441i	$-0.256520\pi$
$659$	22.0315	+	6.79582i	0.858225	+	0.264727i	0.165749	+	0.986168i	$0.446996\pi$
$660$	−0.282012	+	3.76319i	−0.0109773	+	0.146482i
$661$	12.0427	−	15.1011i	0.468407	−	0.587364i	−0.490373	−	0.871513i	$-0.663139\pi$
$661$	12.0427	−	15.1011i	0.468407	−	0.587364i	0.958780	+	0.284149i	$0.0917109\pi$
$662$	0.946771	+	2.41233i	0.0367973	+	0.0937580i
$663$	1.99383	+	1.85001i	0.0774341	+	0.0718483i
$664$	2.82219	+	1.92414i	0.109522	+	0.0746710i
$665$	−0.894360	−	11.9344i	−0.0346818	−	0.462796i
$666$	−0.970738	+	4.25308i	−0.0376153	+	0.164804i
$667$	0.999321	−	4.37831i	0.0386939	−	0.169529i
$668$	0.895089	+	11.9441i	0.0346320	+	0.462132i
$669$	−2.69764	−	1.83922i	−0.104297	−	0.0711083i
$670$	−4.63390	−	4.29963i	−0.179023	−	0.166109i
$671$	4.02159	+	10.2469i	0.155252	+	0.395575i
$672$	−12.8814	+	16.1528i	−0.496911	+	0.623107i
$673$	−0.885315	+	11.8137i	−0.0341264	+	0.455385i	0.953798	+	0.300448i	$0.0971363\pi$
$673$	−0.885315	+	11.8137i	−0.0341264	+	0.455385i	−0.987924	+	0.154936i	$0.950483\pi$
$674$	7.40041	+	2.28272i	0.285053	+	0.0879272i
$675$	12.1737	−	1.83488i	0.468564	−	0.0706247i
$676$	−12.5709	+	11.6641i	−0.483495	+	0.448618i
$677$	39.6619	+	19.1002i	1.52433	+	0.734079i	0.993546	−	0.113428i	$-0.0361830\pi$
$677$	39.6619	+	19.1002i	1.52433	+	0.734079i	0.530785	+	0.847507i	$0.321897\pi$
$678$	0.758802	+	0.114371i	0.0291416	+	0.00439239i
$679$	−17.7223	+	12.0828i	−0.680118	+	0.463696i
$680$	13.8903	+	17.4179i	0.532670	+	0.667946i
$681$	−4.62031	+	8.00261i	−0.177051	+	0.306661i
$682$	−7.98612	−	13.8324i	−0.305804	−	0.529669i
$683$	−3.21492	+	8.19149i	−0.123016	+	0.313439i	−0.979094	−	0.203407i	$-0.934799\pi$
$683$	−3.21492	+	8.19149i	−0.123016	+	0.313439i	0.856079	+	0.516845i	$0.172894\pi$
$684$	5.37424	−	2.58810i	0.205489	−	0.0989584i
$685$	−12.6003	+	3.88667i	−0.481431	+	0.148502i
$686$	−7.32774	−	32.1049i	−0.279775	−	1.22577i
$687$	−7.60678			−0.290217
$688$	−2.10510	+	3.04953i	−0.0802561	+	0.116262i
$689$	8.49188			0.323515
$690$	0.443230	+	1.94192i	0.0168735	+	0.0739276i
$691$	−23.4565	+	7.23537i	−0.892327	+	0.275247i	−0.706818	−	0.707396i	$-0.749870\pi$
$691$	−23.4565	+	7.23537i	−0.892327	+	0.275247i	−0.185510	+	0.982642i	$0.559394\pi$
$692$	7.49796	−	3.61083i	0.285030	−	0.137263i
$693$	11.3141	−	28.8280i	0.429789	−	1.09508i
$694$	−4.39078	−	7.60506i	−0.166672	−	0.288684i
$695$	−11.7164	+	20.2935i	−0.444430	+	0.769775i
$696$	−2.35149	−	2.94868i	−0.0891331	−	0.111769i
$697$	−12.8180	+	8.73915i	−0.485515	+	0.331019i
$698$	−16.9910	−	2.56098i	−0.643117	−	0.0969343i
$699$	13.7016	+	6.59833i	0.518241	+	0.249572i
$700$	−14.3938	+	13.3555i	−0.544035	+	0.504791i
$701$	−7.74950	+	1.16805i	−0.292695	+	0.0441166i	−0.293748	−	0.955883i	$-0.594903\pi$
$701$	−7.74950	+	1.16805i	−0.292695	+	0.0441166i	0.00105353	+	0.999999i	$0.499665\pi$
$702$	−1.91677	−	0.591244i	−0.0723437	−	0.0223151i
$703$	0.298832	−	3.98763i	0.0112707	−	0.150396i
$704$	−5.87025	+	7.36106i	−0.221243	+	0.277430i
$705$	−3.41614	−	8.70419i	−0.128659	−	0.327819i
$706$	19.5503	+	18.1400i	0.735784	+	0.682708i
$707$	−44.0354	−	30.0228i	−1.65612	−	1.12913i
$708$	−0.513096	−	6.84679i	−0.0192833	−	0.257318i
$709$	−1.33852	+	5.86443i	−0.0502691	+	0.220243i	−0.993823	−	0.110975i	$-0.964603\pi$
$709$	−1.33852	+	5.86443i	−0.0502691	+	0.220243i	0.943554	+	0.331218i	$0.107460\pi$
$710$	2.14294	−	9.38882i	0.0804230	−	0.352356i
$711$	1.13169	+	15.1014i	0.0424418	+	0.566347i
$712$	21.0321	+	14.3395i	0.788212	+	0.537394i
$713$	13.1037	+	12.1584i	0.490736	+	0.455337i
$714$	6.12657	+	15.6103i	0.229281	+	0.584199i
$715$	1.43671	−	1.80158i	0.0537299	−	0.0673751i
$716$	2.49815	−	33.3356i	0.0933604	−	1.24581i
$717$	−1.37473	−	0.424048i	−0.0513402	−	0.0158364i
$718$	5.93591	−	0.894694i	0.221526	−	0.0333897i
$719$	10.4800	−	9.72406i	0.390840	−	0.362646i	−0.460139	−	0.887847i	$-0.652200\pi$
$719$	10.4800	−	9.72406i	0.390840	−	0.362646i	0.850978	+	0.525201i	$0.176010\pi$
$720$	1.74484	+	0.840269i	0.0650262	+	0.0313150i
$721$	48.7279	+	7.34455i	1.81472	+	0.273525i
$722$	−10.4376	+	7.11622i	−0.388446	+	0.264838i
$723$	−6.59172	−	8.26575i	−0.245149	−	0.307407i
$724$	−3.88064	+	6.72147i	−0.144223	+	0.249802i
$725$	−2.85932	−	4.95249i	−0.106192	−	0.183931i
$726$	0.853372	−	2.17436i	0.0316716	−	0.0806980i
$727$	−6.01941	+	2.89879i	−0.223247	+	0.107510i	−0.542165	−	0.840272i	$-0.682395\pi$
$727$	−6.01941	+	2.89879i	−0.223247	+	0.107510i	0.318917	+	0.947783i	$0.396681\pi$
$728$	7.55603	−	2.33073i	0.280045	−	0.0863825i
$729$	0.334052	+	1.46358i	0.0123723	+	0.0542065i
$730$	−9.54827			−0.353397
$731$	16.6170	+	35.0229i	0.614603	+	1.29537i
$732$	−4.18591			−0.154716
$733$	−8.12555	−	35.6004i	−0.300124	−	1.31493i	−0.869940	−	0.493157i	$-0.835843\pi$
$733$	−8.12555	−	35.6004i	−0.300124	−	1.31493i	0.569816	−	0.821772i	$-0.307014\pi$
$734$	−3.91465	+	1.20751i	−0.144492	+	0.0445700i
$735$	14.7071	−	7.08255i	0.542478	−	0.261244i
$736$	5.07934	−	12.9419i	0.187227	−	0.477046i
$737$	7.49701	+	12.9852i	0.276156	+	0.478316i
$738$	2.56905	−	4.44972i	0.0945679	−	0.163796i
$739$	−12.8940	−	16.1686i	−0.474313	−	0.594770i	0.485908	−	0.874010i	$-0.338489\pi$
$739$	−12.8940	−	16.1686i	−0.474313	−	0.594770i	−0.960221	+	0.279240i	$0.909917\pi$
$740$	3.50610	−	2.39042i	0.128887	−	0.0878734i
$741$	0.816515	+	0.123070i	0.0299954	+	0.00452108i
$742$	47.1714	+	22.7165i	1.73172	+	0.833950i
$743$	4.99436	−	4.63408i	0.183225	−	0.170008i	−0.583228	−	0.812309i	$-0.698210\pi$
$743$	4.99436	−	4.63408i	0.183225	−	0.170008i	0.766453	+	0.642301i	$0.222020\pi$
$744$	14.8443	−	2.23742i	0.544219	−	0.0820278i
$745$	15.6239	+	4.81935i	0.572417	+	0.176567i
$746$	−1.96844	+	26.2670i	−0.0720696	+	0.961702i
$747$	1.93669	−	2.42853i	0.0708598	−	0.0888554i
$748$	−7.81098	−	19.9020i	−0.285598	−	0.727691i
$749$	16.7292	+	15.5224i	0.611271	+	0.567177i
$750$	5.54679	+	3.78174i	0.202540	+	0.138090i
$751$	−1.46930	−	19.6065i	−0.0536156	−	0.715450i	−0.957640	−	0.287969i	$-0.907020\pi$
$751$	−1.46930	−	19.6065i	−0.0536156	−	0.715450i	0.904024	−	0.427481i	$-0.140599\pi$
$752$	−1.12682	+	4.93693i	−0.0410910	+	0.180031i
$753$	1.42921	−	6.26179i	0.0520834	−	0.228192i
$754$	0.0696298	+	0.929145i	0.00253577	+	0.0338375i
$755$	9.31553	+	6.35122i	0.339027	+	0.231145i
$756$	19.2225	+	17.8359i	0.699117	+	0.648686i
$757$	−14.3182	−	36.4821i	−0.520403	−	1.32597i	−0.913638	−	0.406528i	$-0.866739\pi$
$757$	−14.3182	−	36.4821i	−0.520403	−	1.32597i	0.393235	−	0.919438i	$-0.371356\pi$
$758$	−4.43725	+	5.56414i	−0.161168	+	0.202099i
$759$	0.353069	−	4.71138i	0.0128156	−	0.171012i
$760$	6.46301	+	1.99357i	0.234438	+	0.0723145i
$761$	−42.8441	+	6.45772i	−1.55310	+	0.234092i	−0.868820	−	0.495128i	$-0.835121\pi$
$761$	−42.8441	+	6.45772i	−1.55310	+	0.234092i	−0.684279	+	0.729220i	$0.739883\pi$
$762$	1.92005	−	1.78155i	0.0695561	−	0.0645386i
$763$	−76.6333	−	36.9046i	−2.77431	−	1.33604i
$764$	0.494314	+	0.0745058i	0.0178836	+	0.00269553i
$765$	16.7394	−	11.4127i	0.605213	−	0.412627i
$766$	−6.77849	−	8.49996i	−0.244917	−	0.307116i
$767$	−2.09624	+	3.63079i	−0.0756907	+	0.131100i
$768$	−5.26608	−	9.12112i	−0.190023	−	0.329130i
$769$	17.9092	−	45.6318i	0.645821	−	1.64553i	−0.112505	−	0.993651i	$-0.535888\pi$
$769$	17.9092	−	45.6318i	0.645821	−	1.64553i	0.758327	−	0.651875i	$-0.226017\pi$
$770$	12.8001	−	6.16422i	0.461284	−	0.222143i
$771$	−8.87053	+	2.73620i	−0.319464	+	0.0985417i
$772$	−2.67656	−	11.7268i	−0.0963315	−	0.422056i
$773$	−45.8099			−1.64767			−0.823833	−	0.566832i	$-0.808169\pi$
$773$	−45.8099			−1.64767			−0.823833	+	0.566832i	$0.808169\pi$
$774$	−9.99135	−	8.06291i	−0.359132	−	0.289815i
$775$	22.7623			0.817647
$776$	−2.69736	−	11.8179i	−0.0968295	−	0.424238i
$777$	7.54398	−	2.32701i	0.270639	−	0.0834810i
$778$	2.82727	−	1.36154i	0.101363	−	0.0488137i
$779$	−1.72068	+	4.38422i	−0.0616498	+	0.157081i
$780$	0.438126	+	0.758857i	0.0156874	+	0.0271714i
$781$	−11.4213	+	19.7822i	−0.408685	+	0.707864i
$782$	−7.03595	−	8.82280i	−0.251605	−	0.315503i
$783$	−6.31006	+	4.30212i	−0.225503	+	0.153745i
$784$	−8.74148	−	1.31757i	−0.312196	−	0.0470559i
$785$	−9.56269	−	4.60515i	−0.341307	−	0.164365i
$786$	6.17014	−	5.72506i	0.220082	−	0.204206i
$787$	47.1951	−	7.11352i	1.68233	−	0.253570i	0.762810	−	0.646623i	$-0.223819\pi$
$787$	47.1951	−	7.11352i	1.68233	−	0.253570i	0.919516	+	0.393053i	$0.128581\pi$
$788$	4.89713	+	1.51056i	0.174453	+	0.0538116i
$789$	0.987958	−	13.1834i	0.0351722	−	0.469341i
$790$	−4.33156	+	5.43160i	−0.154110	+	0.193248i
$791$	2.23791	+	5.70211i	0.0795710	+	0.202744i
$792$	12.8296	+	11.9041i	0.455879	+	0.422994i
$793$	2.11185	+	1.43983i	0.0749939	+	0.0511300i
$794$	−0.0552130	−	0.736767i	−0.00195944	−	0.0261469i
$795$	−3.19096	+	13.9805i	−0.113172	+	0.495837i
$796$	3.42293	−	14.9968i	0.121322	−	0.531548i
$797$	2.36014	+	31.4939i	0.0836004	+	1.11557i	0.868415	+	0.495839i	$0.165139\pi$
$797$	2.36014	+	31.4939i	0.0836004	+	1.11557i	−0.784814	+	0.619731i	$0.787242\pi$
$798$	4.20642	+	2.86789i	0.148906	+	0.101522i
$799$	38.8335	+	36.0323i	1.37383	+	1.27473i
$800$	−6.46793	−	16.4800i	−0.228676	−	0.582657i
$801$	14.4330	−	18.0984i	0.509965	−	0.639476i
$802$	−0.813475	+	10.8551i	−0.0287248	+	0.383306i
$803$	21.6419	+	6.67563i	0.763725	+	0.235578i
$804$	−5.63806	+	0.849801i	−0.198839	+	0.0299702i
$805$	−11.6555	+	10.8147i	−0.410803	+	0.381169i
$806$	−3.34144	−	1.60915i	−0.117697	−	0.0566799i
$807$	21.0998	+	3.18028i	0.742747	+	0.111951i
$808$	24.8861	−	16.9670i	0.875489	−	0.596898i
$809$	31.3024	+	39.2520i	1.10054	+	1.38003i	0.917883	+	0.396850i	$0.129897\pi$
$809$	31.3024	+	39.2520i	1.10054	+	1.38003i	0.182652	+	0.983178i	$0.441532\pi$
$810$	−2.42195	+	4.19494i	−0.0850987	+	0.147395i
$811$	−18.3687	−	31.8155i	−0.645012	−	1.11719i	−0.984299	−	0.176511i	$-0.943519\pi$
$811$	−18.3687	−	31.8155i	−0.645012	−	1.11719i	0.339287	−	0.940683i	$-0.389814\pi$
$812$	4.45009	−	11.3386i	0.156167	−	0.397908i
$813$	12.2937	−	5.92033i	0.431158	−	0.207635i
$814$	4.53610	−	1.39920i	0.158990	−	0.0490420i
$815$	−1.92455	−	8.43199i	−0.0674140	−	0.295360i
$816$	2.48741			0.0870767
$817$	10.1577	+	5.94326i	0.355375	+	0.207928i
$818$	12.9664			0.453361
$819$	−1.60011	−	7.01056i	−0.0559125	−	0.244969i
$820$	−4.77587	+	1.47316i	−0.166781	+	0.0514450i
$821$	−8.74383	+	4.21081i	−0.305162	+	0.146958i	−0.580197	−	0.814476i	$-0.697025\pi$
$821$	−8.74383	+	4.21081i	−0.305162	+	0.146958i	0.275036	+	0.961434i	$0.411310\pi$
$822$	2.04930	−	5.22152i	0.0714774	−	0.182121i
$823$	5.78962	+	10.0279i	0.201814	+	0.349551i	0.949113	−	0.314936i	$-0.101983\pi$
$823$	5.78962	+	10.0279i	0.201814	+	0.349551i	−0.747299	+	0.664488i	$0.768650\pi$
$824$	−13.9245	+	24.1179i	−0.485083	+	0.840188i
$825$	−3.75105	−	4.70366i	−0.130595	−	0.163761i
$826$	−21.3570	+	14.5610i	−0.743106	+	0.506641i
$827$	13.5650	+	2.04459i	0.471701	+	0.0710974i	0.380591	−	0.924743i	$-0.375721\pi$
$827$	13.5650	+	2.04459i	0.471701	+	0.0710974i	0.0911095	+	0.995841i	$0.470959\pi$
$828$	−7.13998	−	3.43843i	−0.248131	−	0.119494i
$829$	−25.3708	+	23.5407i	−0.881166	+	0.817602i	−0.984197	−	0.177076i	$-0.943336\pi$
$829$	−25.3708	+	23.5407i	−0.881166	+	0.817602i	0.103031	+	0.994678i	$0.467146\pi$
$830$	1.40908	−	0.212384i	0.0489097	−	0.00737196i
$831$	−4.70967	−	1.45274i	−0.163377	−	0.0503950i
$832$	−0.163373	+	2.18006i	−0.00566393	+	0.0755799i
$833$	−57.6607	+	72.3043i	−1.99783	+	2.50519i
$834$	−3.64178	−	9.27911i	−0.126105	−	0.321309i
$835$	9.05356	+	8.40047i	0.313311	+	0.290710i
$836$	−5.36291	−	3.65637i	−0.185480	−	0.126458i
$837$	−2.27168	−	30.3135i	−0.0785207	−	1.04779i
$838$	4.43420	−	19.4275i	0.153177	−	0.671112i
$839$	5.36544	−	23.5075i	0.185235	−	0.811570i	−0.793849	−	0.608115i	$-0.791926\pi$
$839$	5.36544	−	23.5075i	0.185235	−	0.811570i	0.979084	−	0.203455i	$-0.0652169\pi$
$840$	0.997865	+	13.3156i	0.0344296	+	0.459431i
$841$	−21.0298	−	14.3379i	−0.725167	−	0.494411i
$842$	−18.1135	−	16.8069i	−0.624232	−	0.579202i
$843$	3.50309	+	8.92573i	0.120653	+	0.307418i
$844$	2.42052	−	3.03523i	0.0833177	−	0.104477i
$845$	−1.32142	+	17.6331i	−0.0454581	+	0.606597i
$846$	−16.7658	−	5.17156i	−0.576420	−	0.177802i
$847$	18.4374	−	2.77899i	0.633517	−	0.0954874i
$848$	5.69287	−	5.28222i	0.195494	−	0.181392i
$849$	0.420437	+	0.202472i	0.0144294	+	0.00694882i
$850$	−14.2093	−	2.14171i	−0.487376	−	0.0734601i
$851$	−4.38951	+	2.99272i	−0.150471	+	0.102589i
$852$	−5.41581	−	6.79122i	−0.185543	−	0.232663i
$853$	−7.47416	+	12.9456i	−0.255911	+	0.443250i	−0.965142	−	0.261725i	$-0.915709\pi$
$853$	−7.47416	+	12.9456i	−0.255911	+	0.443250i	0.709232	+	0.704975i	$0.249042\pi$
$854$	7.87938	+	13.6475i	0.269627	+	0.467007i
$855$	2.24709	−	5.72548i	0.0768487	−	0.195807i
$856$	−11.6199	+	5.59587i	−0.397161	+	0.191263i
$857$	−33.2780	+	10.2649i	−1.13675	+	0.350642i	−0.805322	−	0.592837i	$-0.798008\pi$
$857$	−33.2780	+	10.2649i	−1.13675	+	0.350642i	−0.331431	+	0.943479i	$0.607531\pi$
$858$	0.218123	+	0.955657i	0.00744658	+	0.0326256i
$859$	−34.5111			−1.17750			−0.588752	−	0.808314i	$-0.700381\pi$
$859$	−34.5111			−1.17750			−0.588752	+	0.808314i	$0.700381\pi$
$860$	1.78981	+	12.3597i	0.0610319	+	0.421463i
$861$	−9.29838			−0.316888
$862$	0.380410	+	1.66668i	0.0129568	+	0.0567675i
$863$	−19.4875	+	6.01110i	−0.663363	+	0.204620i	−0.608111	−	0.793852i	$-0.708072\pi$
$863$	−19.4875	+	6.01110i	−0.663363	+	0.204620i	−0.0552518	+	0.998472i	$0.517596\pi$
$864$	−21.3016	+	10.2583i	−0.724694	+	0.348994i
$865$	3.13506	−	7.98799i	0.106595	−	0.271600i
$866$	−7.81049	−	13.5282i	−0.265411	−	0.459706i
$867$	6.68173	−	11.5731i	0.226923	−	0.393043i
$868$	30.2290	+	37.9059i	1.02604	+	1.28661i
$869$	13.6153	−	9.28273i	0.461866	−	0.314895i
$870$	−1.55585	−	0.234507i	−0.0527483	−	0.00795052i
$871$	3.13679	+	1.51060i	0.106286	+	0.0511846i
$872$	35.2368	−	32.6950i	1.19327	−	1.10719i
$873$	−10.9003	+	1.64296i	−0.368920	+	0.0556058i
$874$	−3.27375	−	1.00982i	−0.110736	−	0.0341576i
$875$	−4.00470	+	53.4390i	−0.135384	+	1.80657i
$876$	−5.36970	+	6.73339i	−0.181425	+	0.227500i
$877$	12.4401	+	31.6968i	0.420072	+	1.07032i	0.971697	+	0.236233i	$0.0759128\pi$
$877$	12.4401	+	31.6968i	0.420072	+	1.07032i	−0.551625	+	0.834092i	$0.685992\pi$
$878$	−8.45156	−	7.84191i	−0.285226	−	0.264651i
$879$	−13.3210	−	9.08208i	−0.449305	−	0.306331i
$880$	−0.157481	−	2.10144i	−0.00530868	−	0.0708394i
$881$	−6.70780	+	29.3888i	−0.225991	+	0.990133i	0.726881	+	0.686763i	$0.240969\pi$
$881$	−6.70780	+	29.3888i	−0.225991	+	0.990133i	−0.952873	+	0.303370i	$0.901888\pi$
$882$	6.81569	−	29.8615i	0.229496	−	1.00549i
$883$	3.54420	+	47.2941i	0.119272	+	1.59157i	0.660585	+	0.750751i	$0.270308\pi$
$883$	3.54420	+	47.2941i	0.119272	+	1.59157i	−0.541313	+	0.840821i	$0.682073\pi$
$884$	−4.10175	−	2.79653i	−0.137957	−	0.0940575i
$885$	−5.18981	−	4.81544i	−0.174454	−	0.161869i
$886$	6.04491	+	15.4022i	0.203083	+	0.517446i
$887$	−5.58398	+	7.00209i	−0.187492	+	0.235107i	−0.866689	−	0.498848i	$-0.833756\pi$
$887$	−5.58398	+	7.00209i	−0.187492	+	0.235107i	0.679198	+	0.733955i	$0.262328\pi$
$888$	−0.333416	+	4.44912i	−0.0111887	+	0.149303i
$889$	19.9793	+	6.16279i	0.670083	+	0.206693i
$890$	10.5010	−	1.58277i	0.351995	−	0.0530547i
$891$	8.42241	−	7.81485i	0.282161	−	0.261807i
$892$	5.36905	+	2.58560i	0.179769	+	0.0865723i
$893$	15.9031	+	2.39701i	0.532178	+	0.0802129i
$894$	−5.74675	+	3.91807i	−0.192200	+	0.131040i
$895$	−21.4915	−	26.9495i	−0.718382	−	0.900822i
$896$	21.0073	−	36.3857i	0.701804	−	1.21556i
$897$	−0.548519	−	0.950063i	−0.0183145	−	0.0317217i
$898$	9.56186	−	24.3632i	0.319083	−	0.813011i
$899$	−12.7220	+	6.12659i	−0.424302	+	0.204333i
$900$	−9.64294	+	2.97445i	−0.321431	+	0.0991484i
$901$	−18.0782	−	79.2059i	−0.602273	−	2.63873i
$902$	−5.59100			−0.186160
$903$	−3.59588	+	22.9546i	−0.119664	+	0.763880i
$904$	−3.46177			−0.115137
$905$	1.78081	+	7.80225i	0.0591963	+	0.259356i
$906$	−4.58306	+	1.41369i	−0.152262	+	0.0469666i
$907$	17.1208	−	8.24496i	0.568488	−	0.273769i	−0.127481	−	0.991841i	$-0.540689\pi$
$907$	17.1208	−	8.24496i	0.568488	−	0.273769i	0.695969	+	0.718072i	$0.254975\pi$
$908$	6.16183	−	15.7001i	0.204488	−	0.521026i
$909$	−13.6953	−	23.7209i	−0.454244	−	0.786773i
$910$	1.64942	−	2.85688i	0.0546778	−	0.0947047i
$911$	−21.2968	−	26.7054i	−0.705595	−	0.884788i	0.291832	−	0.956469i	$-0.405735\pi$
$911$	−21.2968	−	26.7054i	−0.705595	−	0.884788i	−0.997428	+	0.0716811i	$0.977164\pi$
$912$	0.623937	−	0.425393i	0.0206606	−	0.0140862i
$913$	−3.34226	−	0.503765i	−0.110613	−	0.0166722i
$914$	−2.22354	−	1.07080i	−0.0735481	−	0.0354189i
$915$	−3.16401	+	2.93577i	−0.104599	+	0.0970537i
$916$	13.7288	−	2.06928i	0.453612	−	0.0683711i
$917$	64.2040	+	19.8043i	2.12020	+	0.653996i
$918$	−1.43411	+	19.1369i	−0.0473327	+	0.631611i
$919$	28.1861	−	35.3443i	0.929774	−	1.16590i	−0.0561022	−	0.998425i	$-0.517867\pi$
$919$	28.1861	−	35.3443i	0.929774	−	1.16590i	0.985876	−	0.167475i	$-0.0535613\pi$
$920$	−3.28284	−	8.36453i	−0.108232	−	0.275770i
$921$	−4.54244	−	4.21477i	−0.149678	−	0.138881i
$922$	−14.2635	−	9.72471i	−0.469744	−	0.320266i
$923$	0.396367	+	5.28915i	0.0130466	+	0.174094i
$924$	2.85149	−	12.4932i	0.0938070	−	0.410995i
$925$	−1.50536	+	6.59541i	−0.0494959	+	0.216856i
$926$	1.64408	+	21.9387i	0.0540277	+	0.720949i
$927$	20.9250	+	14.2664i	0.687267	+	0.468571i
$928$	8.05064	+	7.46990i	0.264275	+	0.245212i
$929$	−7.73067	−	19.6974i	−0.253635	−	0.646251i	0.746175	−	0.665750i	$-0.231888\pi$
$929$	−7.73067	−	19.6974i	−0.253635	−	0.646251i	−0.999810	+	0.0194985i	$0.993793\pi$
$930$	3.90480	−	4.89647i	0.128043	−	0.160561i
$931$	−2.09814	+	27.9977i	−0.0687638	+	0.917589i
$932$	−26.5237	−	8.18148i	−0.868813	−	0.267993i
$933$	10.1436	−	1.52890i	0.332086	−	0.0500539i
$934$	18.6061	−	17.2639i	0.608809	−	0.564892i
$935$	−19.8623	−	9.56520i	−0.649568	−	0.312815i
$936$	4.01843	+	0.605681i	0.131346	+	0.0197973i
$937$	−41.6658	+	28.4073i	−1.36116	+	0.928025i	−0.999990	−	0.00447367i	$-0.998576\pi$
$937$	−41.6658	+	28.4073i	−1.36116	+	0.928025i	−0.361173	+	0.932499i	$0.617624\pi$
$938$	13.3835	+	16.7824i	0.436987	+	0.547964i
$939$	1.82884	−	3.16764i	0.0596818	−	0.103372i
$940$	8.53331	+	14.7801i	0.278326	+	0.482075i
$941$	−7.34488	+	18.7144i	−0.239436	+	0.610074i	−0.999194	−	0.0401322i	$-0.987222\pi$
$941$	−7.34488	+	18.7144i	−0.239436	+	0.610074i	0.759758	+	0.650206i	$0.225317\pi$
$942$	4.06790	−	1.95900i	0.132539	−	0.0638276i
$943$	5.97923	−	1.84435i	0.194711	−	0.0600603i
$944$	0.853167	+	3.73797i	0.0277682	+	0.121661i
$945$	27.0390			0.879577
$946$	−2.16216	+	13.8023i	−0.0702979	+	0.448751i
$947$	11.6359			0.378117			0.189059	−	0.981966i	$-0.439456\pi$
$947$	11.6359			0.378117			0.189059	+	0.981966i	$0.439456\pi$
$948$	1.39438	+	6.10918i	0.0452874	+	0.198417i
$949$	5.02518	−	1.55006i	0.163124	−	0.0503172i
$950$	−3.93052	+	1.89284i	−0.127523	+	0.0614118i
$951$	−5.12759	+	13.0649i	−0.166273	+	0.423658i
$952$	−37.8252	−	65.5152i	−1.22592	−	2.12336i
$953$	21.3921	−	37.0523i	0.692959	−	1.20024i	−0.277905	−	0.960609i	$-0.589640\pi$
$953$	21.3921	−	37.0523i	0.692959	−	1.20024i	0.970864	−	0.239632i	$-0.0770267\pi$
$954$	16.7765	+	21.0371i	0.543161	+	0.681102i
$955$	0.425893	−	0.290369i	0.0137816	−	0.00939611i
$956$	2.59648	+	0.391357i	0.0839762	+	0.0126574i
$957$	3.36250	+	1.61929i	0.108694	+	0.0523443i
$958$	−1.75328	+	1.62680i	−0.0566458	+	0.0525596i
$959$	44.2758	−	6.67350i	1.42974	−	0.215499i
$960$	−3.52772	−	1.08816i	−0.113857	−	0.0351202i
$961$	1.88352	−	25.1338i	0.0607586	−	0.810767i
$962$	0.687235	−	0.861765i	0.0221573	−	0.0277844i
$963$	4.28492	+	10.9178i	0.138080	+	0.351821i
$964$	14.1454	+	13.1250i	0.455591	+	0.422727i
$965$	−10.2477	−	6.98675i	−0.329884	−	0.224911i
$966$	−0.505455	−	6.74483i	−0.0162627	−	0.217011i
$967$	−11.0286	+	48.3194i	−0.354655	+	1.55385i	0.411633	+	0.911350i	$0.364958\pi$
$967$	−11.0286	+	48.3194i	−0.354655	+	1.55385i	−0.766289	+	0.642497i	$0.777899\pi$
$968$	−2.34479	+	10.2732i	−0.0753643	+	0.330192i
$969$	−0.590363	−	7.87784i	−0.0189652	−	0.253073i
$970$	−4.17835	−	2.84875i	−0.134159	−	0.0914679i
$971$	−16.0648	−	14.9060i	−0.515544	−	0.478355i	0.378961	−	0.925413i	$-0.376281\pi$
$971$	−16.0648	−	14.9060i	−0.515544	−	0.478355i	−0.894505	+	0.447058i	$0.852472\pi$
$972$	7.63598	+	19.4562i	0.244924	+	0.624056i
$973$	49.6116	−	62.2109i	1.59047	−	1.99439i
$974$	−1.88663	+	25.1753i	−0.0604514	+	0.806668i
$975$	−1.33489	−	0.411758i	−0.0427506	−	0.0131868i
$976$	2.31138	−	0.348385i	0.0739856	−	0.0111515i
$977$	21.5917	−	20.0342i	0.690781	−	0.640951i	−0.254551	−	0.967059i	$-0.581928\pi$
$977$	21.5917	−	20.0342i	0.690781	−	0.640951i	0.945333	+	0.326108i	$0.105737\pi$
$978$	3.31480	+	1.59633i	0.105996	+	0.0510449i
$979$	−24.9079	−	3.75426i	−0.796060	−	0.119987i
$980$	−24.6168	+	16.7835i	−0.786355	+	0.536128i
$981$	−27.2547	−	34.1763i	−0.870175	−	1.09117i
$982$	7.54564	−	13.0694i	0.240791	−	0.417062i
$983$	−2.13856	−	3.70410i	−0.0682095	−	0.118142i	0.829904	−	0.557907i	$-0.188395\pi$
$983$	−2.13856	−	3.70410i	−0.0682095	−	0.118142i	−0.898113	+	0.439764i	$0.855062\pi$
$984$	1.91982	−	4.89161i	0.0612015	−	0.155939i
$985$	4.76103	−	2.29279i	0.151699	−	0.0730544i
$986$	8.51813	−	2.62750i	0.271273	−	0.0836765i
$987$	7.06540	+	30.9555i	0.224894	+	0.985325i
$988$	−1.50714			−0.0479484
$989$	−2.24078	−	15.4740i	−0.0712525	−	0.492043i
$990$	7.30144			0.232055
$991$	11.3481	+	49.7191i	0.360483	+	1.57938i	0.751971	+	0.659197i	$0.229103\pi$
$991$	11.3481	+	49.7191i	0.360483	+	1.57938i	−0.391487	+	0.920183i	$0.628039\pi$
$992$	−41.7718	+	12.8849i	−1.32626	+	0.409096i
$993$	2.17153	−	1.04575i	0.0689114	−	0.0331860i
$994$	−11.9472	+	30.4409i	−0.378941	+	0.965527i
$995$	−7.93068	−	13.7363i	−0.251420	−	0.435471i
$996$	0.642656	−	1.11311i	0.0203633	−	0.0352703i
$997$	25.9035	+	32.4820i	0.820373	+	1.02872i	0.998996	+	0.0447976i	$0.0142643\pi$
$997$	25.9035	+	32.4820i	0.820373	+	1.02872i	−0.178623	+	0.983918i	$0.557164\pi$
$998$	20.7929	−	14.1764i	0.658188	−	0.448745i
$999$	8.93359	+	1.34652i	0.282646	+	0.0426021i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.2.g.a.17.2	✓	36
3.2	odd	2		387.2.y.c.361.2		36
4.3	odd	2		688.2.bg.c.17.2		36
43.9	even	21		1849.2.a.n.1.12		18
43.34	odd	42		1849.2.a.o.1.7		18
43.38	even	21	inner	43.2.g.a.38.2	yes	36
129.38	odd	42		387.2.y.c.253.2		36
172.167	odd	42		688.2.bg.c.81.2		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.2.g.a.17.2	✓	36	1.1	even	1	trivial
43.2.g.a.38.2	yes	36	43.38	even	21	inner
387.2.y.c.253.2		36	129.38	odd	42
387.2.y.c.361.2		36	3.2	odd	2
688.2.bg.c.17.2		36	4.3	odd	2
688.2.bg.c.81.2		36	172.167	odd	42
1849.2.a.n.1.12		18	43.9	even	21
1849.2.a.o.1.7		18	43.34	odd	42

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:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	43.g (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.178150 - 0.780524i) q^{2} +(-0.711521 + 0.219475i) q^{3} +(1.22446 - 0.589667i) q^{4} +(0.511972 - 1.30448i) q^{5} +(0.298063 + 0.516260i) q^{6} +(-2.37928 + 4.12103i) q^{7} +(-1.67671 - 2.10253i) q^{8} +(-2.02062 + 1.37764i) q^{9} +O(q^{10})\)	\(q+(-0.178150 - 0.780524i) q^{2} +(-0.711521 + 0.219475i) q^{3} +(1.22446 - 0.589667i) q^{4} +(0.511972 - 1.30448i) q^{5} +(0.298063 + 0.516260i) q^{6} +(-2.37928 + 4.12103i) q^{7} +(-1.67671 - 2.10253i) q^{8} +(-2.02062 + 1.37764i) q^{9} +(-1.10939 - 0.167213i) q^{10} +(2.39760 + 1.15462i) q^{11} +(-0.741809 + 0.688298i) q^{12} +(0.611008 - 0.0920946i) q^{13} +(3.64044 + 1.12293i) q^{14} +(-0.0779770 + 1.04053i) q^{15} +(0.352328 - 0.441805i) q^{16} +(-2.15975 - 5.50296i) q^{17} +(1.43525 + 1.33172i) q^{18} +(-1.48286 - 1.01100i) q^{19} +(-0.142323 - 1.89917i) q^{20} +(0.788443 - 3.45439i) q^{21} +(0.474081 - 2.07708i) q^{22} +(0.178184 + 2.37770i) q^{23} +(1.65447 + 1.12800i) q^{24} +(2.22570 + 2.06515i) q^{25} +(-0.180733 - 0.460500i) q^{26} +(2.52811 - 3.17015i) q^{27} +(-0.483287 + 6.44901i) q^{28} +(-1.79980 - 0.555165i) q^{29} +(0.826051 - 0.124507i) q^{30} +(5.49565 - 5.09922i) q^{31} +(-5.25345 - 2.52993i) q^{32} +(-1.95935 - 0.295325i) q^{33} +(-3.91044 + 2.66609i) q^{34} +(4.15769 + 5.21358i) q^{35} +(-1.66182 + 2.87835i) q^{36} +(1.11406 + 1.92960i) q^{37} +(-0.524936 + 1.33752i) q^{38} +(-0.414532 + 0.199628i) q^{39} +(-3.60115 + 1.11081i) q^{40} +(-0.583954 - 2.55847i) q^{41} -2.83670 q^{42} +(-6.54183 + 0.452170i) q^{43} +3.61660 q^{44} +(0.762602 + 3.34118i) q^{45} +(1.82411 - 0.562664i) q^{46} +(-8.07377 + 3.88812i) q^{47} +(-0.153723 + 0.391681i) q^{48} +(-7.82195 - 13.5480i) q^{49} +(1.21539 - 2.10512i) q^{50} +(2.74447 + 3.44146i) q^{51} +(0.693847 - 0.473057i) q^{52} +(13.5894 + 2.04828i) q^{53} +(-2.92476 - 1.40849i) q^{54} +(2.73369 - 2.53650i) q^{55} +(12.6540 - 1.90728i) q^{56} +(1.27697 + 0.393894i) q^{57} +(-0.112686 + 1.50369i) q^{58} +(-4.23034 + 5.30467i) q^{59} +(0.518087 + 1.32007i) q^{60} +(3.03226 + 2.81353i) q^{61} +(-4.95912 - 3.38107i) q^{62} +(-0.869663 - 11.6048i) q^{63} +(-0.787282 + 3.44931i) q^{64} +(0.192683 - 0.844198i) q^{65} +(0.118550 + 1.58194i) q^{66} +(4.65539 + 3.17399i) q^{67} +(-5.88944 - 5.46460i) q^{68} +(-0.648628 - 1.65268i) q^{69} +(3.32864 - 4.17398i) q^{70} +(-0.641465 + 8.55975i) q^{71} +(6.28454 + 1.93852i) q^{72} +(8.41561 - 1.26845i) q^{73} +(1.30763 - 1.21331i) q^{74} +(-2.03688 - 0.980910i) q^{75} +(-2.41185 - 0.363527i) q^{76} +(-10.4628 + 7.13343i) q^{77} +(0.229663 + 0.287989i) q^{78} +(3.09616 - 5.36270i) q^{79} +(-0.395945 - 0.685797i) q^{80} +(1.57737 - 4.01906i) q^{81} +(-1.89292 + 0.911581i) q^{82} +(-1.21371 + 0.374380i) q^{83} +(-1.07153 - 4.69467i) q^{84} -8.28425 q^{85} +(1.51835 + 5.02550i) q^{86} +1.40244 q^{87} +(-1.59246 - 6.97702i) q^{88} +(-9.04506 + 2.79003i) q^{89} +(2.47202 - 1.19046i) q^{90} +(-1.07423 + 2.73710i) q^{91} +(1.62023 + 2.80632i) q^{92} +(-2.79112 + 4.83436i) q^{93} +(4.47311 + 5.60911i) q^{94} +(-2.07801 + 1.41676i) q^{95} +(4.29319 + 0.647095i) q^{96} +(4.06114 + 1.95574i) q^{97} +(-9.18108 + 8.51880i) q^{98} +(-6.43531 + 0.969967i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 10 q^{2} - 16 q^{3} - 18 q^{4} - 17 q^{5} - 4 q^{6} + 6 q^{7} + 18 q^{8} - q^{9}+O(q^{10}) \) 36 * q - 10 * q^2 - 16 * q^3 - 18 * q^4 - 17 * q^5 - 4 * q^6 + 6 * q^7 + 18 * q^8 - q^9	\( 36 q - 10 q^{2} - 16 q^{3} - 18 q^{4} - 17 q^{5} - 4 q^{6} + 6 q^{7} + 18 q^{8} - q^{9} - 7 q^{10} - 4 q^{11} + 2 q^{12} + 18 q^{14} - 3 q^{15} - 10 q^{16} - 10 q^{17} + 11 q^{18} + 10 q^{19} - 3 q^{20} - 21 q^{21} - 3 q^{22} + 4 q^{23} + 31 q^{24} - 2 q^{25} - 15 q^{26} - 4 q^{27} + 20 q^{28} + 9 q^{29} + 88 q^{30} + 40 q^{31} + 48 q^{32} - 11 q^{33} - 42 q^{34} + 11 q^{35} - 47 q^{36} - 19 q^{37} - 21 q^{38} - q^{39} - 97 q^{40} - 28 q^{41} + 2 q^{42} - 8 q^{43} + 14 q^{44} - 46 q^{45} - 61 q^{46} - 30 q^{47} - 97 q^{48} + 6 q^{49} - 3 q^{50} + 57 q^{51} - 8 q^{52} - 24 q^{53} + 6 q^{54} + 14 q^{55} + 39 q^{56} + 52 q^{57} + 64 q^{58} - q^{59} + 111 q^{60} - 14 q^{61} + 33 q^{62} + 47 q^{63} + 48 q^{64} + 38 q^{65} + 79 q^{66} + 66 q^{67} + 66 q^{68} - 7 q^{69} + 47 q^{70} - 33 q^{71} + 26 q^{72} + 29 q^{73} - 40 q^{74} - 55 q^{75} - 39 q^{76} - 27 q^{77} - 126 q^{78} - 17 q^{79} + 8 q^{80} + 38 q^{81} - 54 q^{82} - 23 q^{83} - 155 q^{84} - 56 q^{85} - 45 q^{86} - 86 q^{87} - 17 q^{88} - 19 q^{89} - 127 q^{90} - 13 q^{91} - 18 q^{92} - 30 q^{93} + 44 q^{94} + q^{95} - 36 q^{96} - 31 q^{97} - 5 q^{98} - 31 q^{99}+O(q^{100}) \) 36 * q - 10 * q^2 - 16 * q^3 - 18 * q^4 - 17 * q^5 - 4 * q^6 + 6 * q^7 + 18 * q^8 - q^9 - 7 * q^10 - 4 * q^11 + 2 * q^12 + 18 * q^14 - 3 * q^15 - 10 * q^16 - 10 * q^17 + 11 * q^18 + 10 * q^19 - 3 * q^20 - 21 * q^21 - 3 * q^22 + 4 * q^23 + 31 * q^24 - 2 * q^25 - 15 * q^26 - 4 * q^27 + 20 * q^28 + 9 * q^29 + 88 * q^30 + 40 * q^31 + 48 * q^32 - 11 * q^33 - 42 * q^34 + 11 * q^35 - 47 * q^36 - 19 * q^37 - 21 * q^38 - q^39 - 97 * q^40 - 28 * q^41 + 2 * q^42 - 8 * q^43 + 14 * q^44 - 46 * q^45 - 61 * q^46 - 30 * q^47 - 97 * q^48 + 6 * q^49 - 3 * q^50 + 57 * q^51 - 8 * q^52 - 24 * q^53 + 6 * q^54 + 14 * q^55 + 39 * q^56 + 52 * q^57 + 64 * q^58 - q^59 + 111 * q^60 - 14 * q^61 + 33 * q^62 + 47 * q^63 + 48 * q^64 + 38 * q^65 + 79 * q^66 + 66 * q^67 + 66 * q^68 - 7 * q^69 + 47 * q^70 - 33 * q^71 + 26 * q^72 + 29 * q^73 - 40 * q^74 - 55 * q^75 - 39 * q^76 - 27 * q^77 - 126 * q^78 - 17 * q^79 + 8 * q^80 + 38 * q^81 - 54 * q^82 - 23 * q^83 - 155 * q^84 - 56 * q^85 - 45 * q^86 - 86 * q^87 - 17 * q^88 - 19 * q^89 - 127 * q^90 - 13 * q^91 - 18 * q^92 - 30 * q^93 + 44 * q^94 + q^95 - 36 * q^96 - 31 * q^97 - 5 * q^98 - 31 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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