LMFDB - Embedded newform 43.2.g.a.25.3

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			25.3
Character	$\chi$	$=$	43.25
Dual form			43.2.g.a.31.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.94880 + 0.938491i) q^{2} +(-2.41097 - 1.64377i) q^{3} +(1.67006 + 2.09419i) q^{4} +(-2.00127 + 1.85691i) q^{5} +(-3.15582 - 5.46604i) q^{6} +(1.01083 - 1.75082i) q^{7} +(0.326607 + 1.43096i) q^{8} +(2.01476 + 5.13352i) q^{9} +O(q^{10})$	\(q+(1.94880 + 0.938491i) q^{2} +(-2.41097 - 1.64377i) q^{3} +(1.67006 + 2.09419i) q^{4} +(-2.00127 + 1.85691i) q^{5} +(-3.15582 - 5.46604i) q^{6} +(1.01083 - 1.75082i) q^{7} +(0.326607 + 1.43096i) q^{8} +(2.01476 + 5.13352i) q^{9} +(-5.64276 + 1.74056i) q^{10} +(-0.515533 + 0.646459i) q^{11} +(-0.584097 - 7.79423i) q^{12} +(3.02110 + 0.931885i) q^{13} +(3.61304 - 2.46333i) q^{14} +(7.87733 - 1.18732i) q^{15} +(0.485626 - 2.12767i) q^{16} +(-2.50278 - 2.32224i) q^{17} +(-0.891409 + 11.8950i) q^{18} +(-1.08222 + 2.75745i) q^{19} +(-7.23098 - 1.08990i) q^{20} +(-5.31503 + 2.55958i) q^{21} +(-1.61137 + 0.775993i) q^{22} +(1.21045 + 0.182446i) q^{23} +(1.56473 - 3.98686i) q^{24} +(0.183328 - 2.44634i) q^{25} +(5.01294 + 4.65133i) q^{26} +(1.63286 - 7.15403i) q^{27} +(5.35471 - 0.807093i) q^{28} +(-7.00539 + 4.77619i) q^{29} +(16.4656 + 5.07896i) q^{30} +(-0.399005 - 5.32435i) q^{31} +(4.77345 - 5.98572i) q^{32} +(2.30556 - 0.711172i) q^{33} +(-2.69801 - 6.87441i) q^{34} +(1.22815 + 5.38089i) q^{35} +(-7.38582 + 12.7926i) q^{36} +(-1.73217 - 3.00021i) q^{37} +(-4.69687 + 4.35806i) q^{38} +(-5.75196 - 7.21273i) q^{39} +(-3.31079 - 2.25726i) q^{40} +(6.20561 + 2.98847i) q^{41} -12.7601 q^{42} +(-3.02108 - 5.82006i) q^{43} -2.21478 q^{44} +(-13.5646 - 6.53235i) q^{45} +(2.18770 + 1.49155i) q^{46} +(2.33951 + 2.93365i) q^{47} +(-4.66822 + 4.33148i) q^{48} +(1.45643 + 2.52260i) q^{49} +(2.65314 - 4.59537i) q^{50} +(2.21689 + 9.71283i) q^{51} +(3.09388 + 7.88307i) q^{52} +(8.47611 - 2.61454i) q^{53} +(9.89611 - 12.4093i) q^{54} +(-0.168692 - 2.25104i) q^{55} +(2.83550 + 0.874635i) q^{56} +(7.14181 - 4.86920i) q^{57} +(-18.1345 + 2.73333i) q^{58} +(-0.633519 + 2.77563i) q^{59} +(15.6421 + 14.5138i) q^{60} +(0.573465 - 7.65235i) q^{61} +(4.21927 - 10.7505i) q^{62} +(11.0245 + 1.66167i) q^{63} +(10.9875 - 5.29131i) q^{64} +(-7.77646 + 3.74495i) q^{65} +(5.16050 + 0.777821i) q^{66} +(-3.76698 + 9.59812i) q^{67} +(0.683419 - 9.11959i) q^{68} +(-2.61846 - 2.42957i) q^{69} +(-2.65650 + 11.6389i) q^{70} +(-11.9877 + 1.80685i) q^{71} +(-6.68783 + 4.55969i) q^{72} +(11.9045 + 3.67204i) q^{73} +(-0.559982 - 7.47244i) q^{74} +(-4.46321 + 5.59669i) q^{75} +(-7.58201 + 2.33874i) q^{76} +(0.610712 + 1.55607i) q^{77} +(-4.44032 - 19.4543i) q^{78} +(-2.34287 + 4.05797i) q^{79} +(2.97901 + 5.15980i) q^{80} +(-3.56858 + 3.31116i) q^{81} +(9.28883 + 11.6478i) q^{82} +(-3.94401 - 2.68898i) q^{83} +(-14.2367 - 6.85604i) q^{84} +9.32092 q^{85} +(-0.425398 - 14.1774i) q^{86} +24.7407 q^{87} +(-1.09343 - 0.526570i) q^{88} +(-1.70700 - 1.16382i) q^{89} +(-20.3040 - 25.4605i) q^{90} +(4.68539 - 4.34741i) q^{91} +(1.63945 + 2.83962i) q^{92} +(-7.79001 + 13.4927i) q^{93} +(1.80602 + 7.91270i) q^{94} +(-2.95452 - 7.52799i) q^{95} +(-21.3478 + 6.58491i) q^{96} +(-7.51296 + 9.42095i) q^{97} +(0.470837 + 6.28288i) q^{98} +(-4.35729 - 1.34404i) 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 $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{4}{21}\right)$

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 $

$2$	1.94880	+	0.938491i	1.37801	+	0.663613i	0.968574	−	0.248726i	$-0.0800120\pi$
$2$	1.94880	+	0.938491i	1.37801	+	0.663613i	0.409434	+	0.912340i	$0.365726\pi$
$3$	−2.41097	−	1.64377i	−1.39197	−	0.949031i	−0.999573	−	0.0292358i	$-0.990693\pi$
$3$	−2.41097	−	1.64377i	−1.39197	−	0.949031i	−0.392400	−	0.919795i	$-0.628355\pi$
$4$	1.67006	+	2.09419i	0.835032	+	1.04710i
$5$	−2.00127	+	1.85691i	−0.894996	+	0.830435i	−0.986227	−	0.165395i	$-0.947110\pi$
$5$	−2.00127	+	1.85691i	−0.894996	+	0.830435i	0.0912316	+	0.995830i	$0.470920\pi$
$6$	−3.15582	−	5.46604i	−1.28836	−	2.23150i
$7$	1.01083	−	1.75082i	0.382060	−	0.661747i	−0.609297	−	0.792942i	$-0.708548\pi$
$7$	1.01083	−	1.75082i	0.382060	−	0.661747i	0.991357	+	0.131195i	$0.0418815\pi$
$8$	0.326607	+	1.43096i	0.115473	+	0.505921i
$9$	2.01476	+	5.13352i	0.671587	+	1.71117i
$10$	−5.64276	+	1.74056i	−1.78440	+	0.550414i
$11$	−0.515533	+	0.646459i	−0.155439	+	0.194915i	−0.853453	−	0.521170i	$-0.825496\pi$
$11$	−0.515533	+	0.646459i	−0.155439	+	0.194915i	0.698014	+	0.716084i	$0.254067\pi$
$12$	−0.584097	−	7.79423i	−0.168614	−	2.25000i
$13$	3.02110	+	0.931885i	0.837901	+	0.258458i	0.683867	−	0.729607i	$-0.260297\pi$
$13$	3.02110	+	0.931885i	0.837901	+	0.258458i	0.154035	+	0.988065i	$0.450773\pi$
$14$	3.61304	−	2.46333i	0.965625	−	0.658352i
$15$	7.87733	−	1.18732i	2.03392	−	0.306564i
$16$	0.485626	−	2.12767i	0.121407	−	0.531917i
$17$	−2.50278	−	2.32224i	−0.607013	−	0.563226i	0.315629	−	0.948883i	$-0.397784\pi$
$17$	−2.50278	−	2.32224i	−0.607013	−	0.563226i	−0.922642	+	0.385657i	$0.873975\pi$
$18$	−0.891409	+	11.8950i	−0.210107	+	2.80369i
$19$	−1.08222	+	2.75745i	−0.248278	+	0.632603i	−0.999627	−	0.0273025i	$-0.991308\pi$
$19$	−1.08222	+	2.75745i	−0.248278	+	0.632603i	0.751349	+	0.659905i	$0.229403\pi$
$20$	−7.23098	−	1.08990i	−1.61690	−	0.243708i
$21$	−5.31503	+	2.55958i	−1.15983	+	0.558547i
$22$	−1.61137	+	0.775993i	−0.343544	+	0.165442i
$23$	1.21045	+	0.182446i	0.252396	+	0.0380426i	0.274022	−	0.961724i	$-0.411646\pi$
$23$	1.21045	+	0.182446i	0.252396	+	0.0380426i	−0.0216253	+	0.999766i	$0.506884\pi$
$24$	1.56473	−	3.98686i	0.319399	−	0.813815i
$25$	0.183328	−	2.44634i	0.0366655	−	0.489268i
$26$	5.01294	+	4.65133i	0.983118	+	0.912200i
$27$	1.63286	−	7.15403i	0.314244	−	1.37679i
$28$	5.35471	−	0.807093i	1.01195	−	0.152526i
$29$	−7.00539	+	4.77619i	−1.30087	+	0.886916i	−0.997816	−	0.0660577i	$-0.978958\pi$
$29$	−7.00539	+	4.77619i	−1.30087	+	0.886916i	−0.303052	+	0.952974i	$0.598005\pi$
$30$	16.4656	+	5.07896i	3.00619	+	0.927288i
$31$	−0.399005	−	5.32435i	−0.0716634	−	0.956281i	−0.910930	−	0.412561i	$-0.864634\pi$
$31$	−0.399005	−	5.32435i	−0.0716634	−	0.956281i	0.839267	−	0.543720i	$-0.182985\pi$
$32$	4.77345	−	5.98572i	0.843835	−	1.05814i
$33$	2.30556	−	0.711172i	0.401347	−	0.123799i
$34$	−2.69801	−	6.87441i	−0.462704	−	1.17895i
$35$	1.22815	+	5.38089i	0.207596	+	0.909536i
$36$	−7.38582	+	12.7926i	−1.23097	+	2.13210i
$37$	−1.73217	−	3.00021i	−0.284768	−	0.493232i	0.687785	−	0.725914i	$-0.258583\pi$
$37$	−1.73217	−	3.00021i	−0.284768	−	0.493232i	−0.972553	+	0.232682i	$0.925250\pi$
$38$	−4.69687	+	4.35806i	−0.761933	+	0.706970i
$39$	−5.75196	−	7.21273i	−0.921051	−	1.15496i
$40$	−3.31079	−	2.25726i	−0.523482	−	0.356904i
$41$	6.20561	+	2.98847i	0.969154	+	0.466720i	0.850361	−	0.526199i	$-0.176383\pi$
$41$	6.20561	+	2.98847i	0.969154	+	0.466720i	0.118793	+	0.992919i	$0.462098\pi$
$42$	−12.7601			−1.96892
$43$	−3.02108	−	5.82006i	−0.460710	−	0.887551i
$43$	−3.02108	−	5.82006i	−0.460710	−	0.887551i
$44$	−2.21478			−0.333891
$45$	−13.5646	−	6.53235i	−2.02209	−	0.973785i
$46$	2.18770	+	1.49155i	0.322558	+	0.219917i
$47$	2.33951	+	2.93365i	0.341252	+	0.427917i	0.922612	−	0.385730i	$-0.126050\pi$
$47$	2.33951	+	2.93365i	0.341252	+	0.427917i	−0.581359	+	0.813647i	$0.697479\pi$
$48$	−4.66822	+	4.33148i	−0.673800	+	0.625195i
$49$	1.45643	+	2.52260i	0.208061	+	0.360372i
$50$	2.65314	−	4.59537i	0.375210	−	0.649883i
$51$	2.21689	+	9.71283i	0.310427	+	1.36007i
$52$	3.09388	+	7.88307i	0.429044	+	1.09319i
$53$	8.47611	−	2.61454i	1.16428	−	0.359134i	0.348398	−	0.937347i	$-0.386726\pi$
$53$	8.47611	−	2.61454i	1.16428	−	0.359134i	0.815886	+	0.578213i	$0.196250\pi$
$54$	9.89611	−	12.4093i	1.34669	−	1.68870i
$55$	−0.168692	−	2.25104i	−0.0227464	−	0.303530i
$56$	2.83550	+	0.874635i	0.378909	+	0.116878i
$57$	7.14181	−	4.86920i	0.945956	−	0.644942i
$58$	−18.1345	+	2.73333i	−2.38117	+	0.358904i
$59$	−0.633519	+	2.77563i	−0.0824772	+	0.361356i	−0.999278	−	0.0379881i	$-0.987905\pi$
$59$	−0.633519	+	2.77563i	−0.0824772	+	0.361356i	0.916801	+	0.399344i	$0.130762\pi$
$60$	15.6421	+	14.5138i	2.01939	+	1.87372i
$61$	0.573465	−	7.65235i	0.0734246	−	0.979783i	−0.831862	−	0.554982i	$-0.812725\pi$
$61$	0.573465	−	7.65235i	0.0734246	−	0.979783i	0.905287	−	0.424801i	$-0.139656\pi$
$62$	4.21927	−	10.7505i	0.535848	−	1.36532i
$63$	11.0245	+	1.66167i	1.38895	+	0.209351i
$64$	10.9875	−	5.29131i	1.37344	−	0.661413i
$65$	−7.77646	+	3.74495i	−0.964551	+	0.464503i
$66$	5.16050	+	0.777821i	0.635214	+	0.0957431i
$67$	−3.76698	+	9.59812i	−0.460210	+	1.17260i	0.492930	+	0.870069i	$0.335926\pi$
$67$	−3.76698	+	9.59812i	−0.460210	+	1.17260i	−0.953141	+	0.302528i	$0.902169\pi$
$68$	0.683419	−	9.11959i	0.0828767	−	1.10591i
$69$	−2.61846	−	2.42957i	−0.315225	−	0.292486i
$70$	−2.65650	+	11.6389i	−0.317512	+	1.39111i
$71$	−11.9877	+	1.80685i	−1.42268	+	0.214434i	−0.814867	−	0.579648i	$-0.803190\pi$
$71$	−11.9877	+	1.80685i	−1.42268	+	0.214434i	−0.607811	+	0.794082i	$0.707952\pi$
$72$	−6.68783	+	4.55969i	−0.788169	+	0.537364i
$73$	11.9045	+	3.67204i	1.39331	+	0.429779i	0.898405	−	0.439167i	$-0.144726\pi$
$73$	11.9045	+	3.67204i	1.39331	+	0.429779i	0.494906	+	0.868947i	$0.335203\pi$
$74$	−0.559982	−	7.47244i	−0.0650966	−	0.868654i
$75$	−4.46321	+	5.59669i	−0.515367	+	0.646250i
$76$	−7.58201	+	2.33874i	−0.869717	+	0.268272i
$77$	0.610712	+	1.55607i	0.0695971	+	0.177330i
$78$	−4.44032	−	19.4543i	−0.502767	−	2.20277i
$79$	−2.34287	+	4.05797i	−0.263593	+	0.456557i	−0.967194	−	0.254038i	$-0.918241\pi$
$79$	−2.34287	+	4.05797i	−0.263593	+	0.456557i	0.703601	+	0.710596i	$0.251574\pi$
$80$	2.97901	+	5.15980i	0.333064	+	0.576884i
$81$	−3.56858	+	3.31116i	−0.396509	+	0.367907i
$82$	9.28883	+	11.6478i	1.02578	+	1.28629i
$83$	−3.94401	−	2.68898i	−0.432912	−	0.295154i	0.327190	−	0.944959i	$-0.393898\pi$
$83$	−3.94401	−	2.68898i	−0.432912	−	0.295154i	−0.760101	+	0.649805i	$0.774851\pi$
$84$	−14.2367	−	6.85604i	−1.55335	−	0.748055i
$85$	9.32092			1.01100
$86$	−0.425398	−	14.1774i	−0.0458719	−	1.52878i
$87$	24.7407			2.65248
$88$	−1.09343	−	0.526570i	−0.116560	−	0.0561325i
$89$	−1.70700	−	1.16382i	−0.180942	−	0.123364i	0.469462	−	0.882953i	$-0.344448\pi$
$89$	−1.70700	−	1.16382i	−0.180942	−	0.123364i	−0.650404	+	0.759589i	$0.725400\pi$
$90$	−20.3040	−	25.4605i	−2.14023	−	2.68377i
$91$	4.68539	−	4.34741i	0.491162	−	0.455732i
$92$	1.63945	+	2.83962i	0.170925	+	0.296050i
$93$	−7.79001	+	13.4927i	−0.807787	+	1.39913i
$94$	1.80602	+	7.91270i	0.186277	+	0.816132i
$95$	−2.95452	−	7.52799i	−0.303127	−	0.772355i
$96$	−21.3478	+	6.58491i	−2.17880	+	0.672070i
$97$	−7.51296	+	9.42095i	−0.762825	+	0.956552i	−0.999888	−	0.0149418i	$-0.995244\pi$
$97$	−7.51296	+	9.42095i	−0.762825	+	0.956552i	0.237063	+	0.971494i	$0.423815\pi$
$98$	0.470837	+	6.28288i	0.0475617	+	0.634667i
$99$	−4.35729	−	1.34404i	−0.437924	−	0.135082i
$100$	5.42928	−	3.70162i	0.542928	−	0.370162i
$101$	−2.52020	+	0.379859i	−0.250769	+	0.0377974i	−0.273224	−	0.961951i	$-0.588090\pi$
$101$	−2.52020	+	0.379859i	−0.250769	+	0.0377974i	0.0224547	+	0.999748i	$0.492852\pi$
$102$	−4.79514	+	21.0089i	−0.474789	+	2.08019i
$103$	−5.76522	−	5.34934i	−0.568064	−	0.527086i	0.343009	−	0.939332i	$-0.388554\pi$
$103$	−5.76522	−	5.34934i	−0.568064	−	0.527086i	−0.911073	+	0.412246i	$0.864744\pi$
$104$	−0.346778	+	4.62743i	−0.0340044	+	0.453757i
$105$	5.88391	−	14.9919i	0.574210	−	1.46306i
$106$	18.9719	+	2.85956i	1.84272	+	0.277745i
$107$	7.55616	−	3.63886i	0.730482	−	0.351782i	−0.0313918	−	0.999507i	$-0.509994\pi$
$107$	7.55616	−	3.63886i	0.730482	−	0.351782i	0.761874	+	0.647726i	$0.224280\pi$
$108$	17.7089	−	8.52816i	1.70404	−	0.820623i
$109$	5.60910	+	0.845435i	0.537254	+	0.0809780i	0.412064	−	0.911155i	$-0.364808\pi$
$109$	5.60910	+	0.845435i	0.537254	+	0.0809780i	0.125190	+	0.992133i	$0.460046\pi$
$110$	1.78383	−	4.54513i	0.170082	−	0.433361i
$111$	−0.755445	+	10.0807i	−0.0717037	+	0.956819i
$112$	−3.23427	−	3.00096i	−0.305610	−	0.283564i
$113$	3.99341	−	17.4963i	0.375669	−	1.64591i	−0.334877	−	0.942262i	$-0.608695\pi$
$113$	3.99341	−	17.4963i	0.375669	−	1.64591i	0.710546	−	0.703651i	$-0.248448\pi$
$114$	18.4876	−	2.78656i	1.73153	−	0.260986i
$115$	−2.76123	+	1.88257i	−0.257486	+	0.175551i
$116$	−21.7017	−	6.69409i	−2.01495	−	0.621531i
$117$	1.30293	+	17.3864i	0.120456	+	1.60737i
$118$	−3.83951	+	4.81459i	−0.353455	+	0.443219i
$119$	−6.59571	+	2.03451i	−0.604628	+	0.186503i
$120$	4.27180	+	10.8844i	0.389960	+	0.993601i
$121$	2.29560	+	10.0577i	0.208691	+	0.914333i
$122$	8.29923	−	14.3747i	0.751377	−	1.30142i
$123$	−10.0492	−	17.4057i	−0.906104	−	1.56942i
$124$	10.4839	−	9.72760i	0.941478	−	0.873564i
$125$	−4.33507	−	5.43600i	−0.387740	−	0.486211i
$126$	19.9250	+	13.5846i	1.77506	+	1.21021i
$127$	−17.6508	−	8.50017i	−1.56625	−	0.754268i	−0.568593	−	0.822619i	$-0.692512\pi$
$127$	−17.6508	−	8.50017i	−1.56625	−	0.754268i	−0.997661	+	0.0683509i	$0.978226\pi$
$128$	11.0662			0.978126
$129$	−2.28311	+	18.9979i	−0.201017	+	1.67267i
$130$	−18.6693			−1.63741
$131$	10.9256	+	5.26150i	0.954576	+	0.459700i	0.845288	−	0.534310i	$-0.179429\pi$
$131$	10.9256	+	5.26150i	0.954576	+	0.459700i	0.109288	+	0.994010i	$0.465143\pi$
$132$	5.33977	+	3.64059i	0.464767	+	0.316873i
$133$	3.73385	+	4.68210i	0.323766	+	0.405989i
$134$	−16.3488	+	15.1695i	−1.41232	+	1.31045i
$135$	10.0166	+	17.3492i	0.862090	+	1.49318i
$136$	2.50561	−	4.33984i	0.214854	−	0.372138i
$137$	−1.32721	−	5.81487i	−0.113391	−	0.496798i	−0.999448	−	0.0332220i	$-0.989423\pi$
$137$	−1.32721	−	5.81487i	−0.113391	−	0.496798i	0.886057	−	0.463576i	$-0.153434\pi$
$138$	−2.82271	−	7.19214i	−0.240285	−	0.612236i
$139$	2.97091	−	0.916404i	0.251989	−	0.0777284i	−0.166187	−	0.986094i	$-0.553146\pi$
$139$	2.97091	−	0.916404i	0.251989	−	0.0777284i	0.418176	+	0.908366i	$0.362669\pi$
$140$	−9.21754	+	11.5584i	−0.779024	+	0.976865i
$141$	−0.818232	−	10.9185i	−0.0689075	−	0.919507i
$142$	−25.0573	−	7.72916i	−2.10276	−	0.648616i
$143$	−2.15990	+	1.47260i	−0.180620	+	0.123145i
$144$	11.9009	−	1.79376i	0.991738	−	0.149480i
$145$	5.15073	−	22.5668i	0.427745	−	1.87407i
$146$	19.7532	+	18.3283i	1.63479	+	1.51686i
$147$	0.635184	−	8.47594i	0.0523891	−	0.699084i
$148$	3.39019	−	8.63806i	0.278672	−	0.710045i
$149$	1.59287	+	0.240086i	0.130493	+	0.0196686i	0.213964	−	0.976842i	$-0.431363\pi$
$149$	1.59287	+	0.240086i	0.130493	+	0.0196686i	−0.0834711	+	0.996510i	$0.526601\pi$
$150$	−13.9503	+	6.71813i	−1.13904	+	0.548533i
$151$	3.99279	−	1.92283i	0.324929	−	0.156477i	−0.264307	−	0.964439i	$-0.585143\pi$
$151$	3.99279	−	1.92283i	0.324929	−	0.156477i	0.589236	+	0.807961i	$0.299429\pi$
$152$	−4.29926	−	0.648010i	−0.348716	−	0.0525605i
$153$	6.87877	−	17.5268i	0.556116	−	1.41696i
$154$	−0.270203	+	3.60561i	−0.0217736	+	0.290548i
$155$	10.6853	+	9.91455i	0.858267	+	0.796356i
$156$	5.49872	−	24.0914i	0.440250	−	1.92886i
$157$	−3.60721	+	0.543700i	−0.287887	+	0.0433920i	−0.291398	−	0.956602i	$-0.594120\pi$
$157$	−3.60721	+	0.543700i	−0.287887	+	0.0433920i	0.00351117	+	0.999994i	$0.498882\pi$
$158$	−8.37415	+	5.70940i	−0.666211	+	0.454215i
$159$	−24.7333	−	7.62922i	−1.96148	−	0.605036i
$160$	1.56196	+	20.8429i	0.123484	+	1.64778i
$161$	1.54300	−	1.93485i	0.121605	−	0.152488i
$162$	−10.0619	+	3.10370i	−0.790540	+	0.243849i
$163$	2.81502	+	7.17257i	0.220490	+	0.561799i	0.997725	−	0.0674110i	$-0.0214739\pi$
$163$	2.81502	+	7.17257i	0.220490	+	0.561799i	−0.777236	+	0.629210i	$0.783379\pi$
$164$	4.10535	+	17.9867i	0.320574	+	1.40452i
$165$	−3.29348	+	5.70447i	−0.256397	+	0.444092i
$166$	−5.16249	−	8.94170i	−0.400687	−	0.694011i
$167$	3.60763	−	3.34739i	0.279167	−	0.259029i	−0.528145	−	0.849154i	$-0.677112\pi$
$167$	3.60763	−	3.34739i	0.279167	−	0.259029i	0.807312	+	0.590125i	$0.200922\pi$
$168$	−5.39859	−	6.76962i	−0.416510	−	0.522287i
$169$	−2.48249	−	1.69253i	−0.190961	−	0.130195i
$170$	18.1646	+	8.74761i	1.39316	+	0.670911i
$171$	−16.3359			−1.24923
$172$	7.14294	−	16.0466i	0.544644	−	1.22354i
$173$	−21.5624			−1.63936			−0.819680	−	0.572821i	$-0.805849\pi$
$173$	−21.5624			−1.63936			−0.819680	+	0.572821i	$0.805849\pi$
$174$	48.2146	+	23.2189i	3.65514	+	1.76022i
$175$	−4.09778	−	2.79382i	−0.309763	−	0.211193i
$176$	1.12509	+	1.41082i	0.0848070	+	0.106345i
$177$	6.08989	−	5.65059i	0.457744	−	0.424725i
$178$	−2.23437	−	3.87005i	−0.167473	−	0.290072i
$179$	8.40248	−	14.5535i	0.628031	−	1.08778i	−0.359915	−	0.932985i	$-0.617194\pi$
$179$	8.40248	−	14.5535i	0.628031	−	1.08778i	0.987946	−	0.154797i	$-0.0494723\pi$
$180$	−8.97369	−	39.3163i	−0.668859	−	2.93046i
$181$	0.294349	+	0.749988i	0.0218788	+	0.0557462i	0.941396	−	0.337304i	$-0.109515\pi$
$181$	0.294349	+	0.749988i	0.0218788	+	0.0557462i	−0.919517	+	0.393050i	$0.871420\pi$
$182$	13.2109	−	4.07502i	0.979255	−	0.302060i
$183$	−13.9613	+	17.5069i	−1.03205	+	1.29415i
$184$	0.134269	+	1.79169i	0.00989844	+	0.132085i
$185$	9.03768	+	2.78775i	0.664463	+	0.204960i
$186$	−27.8439	+	18.9837i	−2.04162	+	1.39195i
$187$	2.79150	−	0.420750i	0.204134	−	0.0307683i
$188$	−2.23651	+	9.79877i	−0.163114	+	0.714649i
$189$	−10.8748	−	10.0904i	−0.791029	−	0.733968i
$190$	1.30720	−	17.4433i	0.0948339	−	1.26547i
$191$	−4.22806	+	10.7729i	−0.305931	+	0.779500i	0.692387	+	0.721527i	$0.256559\pi$
$191$	−4.22806	+	10.7729i	−0.305931	+	0.779500i	−0.998318	+	0.0579738i	$0.981536\pi$
$192$	−35.1882	−	5.30377i	−2.53949	−	0.382766i
$193$	5.28929	−	2.54719i	0.380732	−	0.183351i	−0.233722	−	0.972303i	$-0.575091\pi$
$193$	5.28929	−	2.54719i	0.380732	−	0.183351i	0.614454	+	0.788953i	$0.289376\pi$
$194$	−23.4827	+	11.3087i	−1.68596	+	0.811915i
$195$	24.9046	+	3.75377i	1.78346	+	0.268813i
$196$	−2.85050	+	7.26295i	−0.203607	+	0.518782i
$197$	0.412103	−	5.49913i	0.0293611	−	0.391797i	−0.963092	−	0.269172i	$-0.913250\pi$
$197$	0.412103	−	5.49913i	0.0293611	−	0.391797i	0.992453	−	0.122624i	$-0.0391310\pi$
$198$	−7.23009	−	6.70855i	−0.513820	−	0.476756i
$199$	−4.37361	+	19.1620i	−0.310037	+	1.35836i	0.544409	+	0.838820i	$0.316754\pi$
$199$	−4.37361	+	19.1620i	−0.310037	+	1.35836i	−0.854446	+	0.519540i	$0.826103\pi$
$200$	3.56049	−	0.536657i	0.251765	−	0.0379474i
$201$	24.8592	−	16.9487i	1.75343	−	1.19547i
$202$	−5.26785	−	1.62492i	−0.370645	−	0.114329i
$203$	1.28095	+	17.0931i	0.0899051	+	1.19970i
$204$	−16.6382	+	20.8637i	−1.16491	+	1.46075i
$205$	−17.9684	+	5.54252i	−1.25497	+	0.387107i
$206$	−6.21493	−	15.8354i	−0.433015	−	1.10330i
$207$	1.50218	+	6.58146i	0.104408	+	0.457443i
$208$	3.44986	−	5.97534i	0.239205	−	0.414315i
$209$	−1.22466	−	2.12117i	−0.0847113	−	0.146724i
$210$	25.5363	−	23.6943i	1.76218	−	1.63506i
$211$	10.8591	+	13.6169i	0.747574	+	0.937428i	0.999541	−	0.0303076i	$-0.00964869\pi$
$211$	10.8591	+	13.6169i	0.747574	+	0.937428i	−0.251966	+	0.967736i	$0.581077\pi$
$212$	19.6310	+	13.3842i	1.34826	+	0.919230i
$213$	31.8720	+	15.3487i	2.18383	+	1.05168i
$214$	18.1405			1.24006
$215$	16.8533	+	6.03765i	1.14939	+	0.411764i
$216$	10.7704			0.732835
$217$	−9.72529	−	4.68345i	−0.660196	−	0.317933i
$218$	10.1376	+	6.91167i	0.686602	+	0.468117i
$219$	−22.6653	−	28.4213i	−1.53158	−	1.92054i
$220$	4.43238	−	4.11265i	0.298831	−	0.277275i
$221$	−5.39708	−	9.34801i	−0.363047	−	0.628815i
$222$	−10.9329	+	18.9363i	−0.733766	+	1.27092i
$223$	3.36182	+	14.7291i	0.225124	+	0.986333i	0.953556	+	0.301215i	$0.0973922\pi$
$223$	3.36182	+	14.7291i	0.225124	+	0.986333i	−0.728432	+	0.685118i	$0.759751\pi$
$224$	−5.65473	−	14.4080i	−0.377822	−	0.962676i
$225$	12.9277	−	3.98767i	0.861847	−	0.265844i
$226$	24.2025	−	30.3489i	1.60992	−	2.01878i
$227$	−0.937088	−	12.5046i	−0.0621967	−	0.829957i	−0.937855	−	0.347027i	$-0.887191\pi$
$227$	−0.937088	−	12.5046i	−0.0621967	−	0.829957i	0.875659	−	0.482931i	$-0.160428\pi$
$228$	22.1243	+	6.82445i	1.46522	+	0.451961i
$229$	16.8194	−	11.4673i	1.11146	−	0.757778i	0.138868	−	0.990311i	$-0.455654\pi$
$229$	16.8194	−	11.4673i	1.11146	−	0.757778i	0.972589	+	0.232533i	$0.0747012\pi$
$230$	−7.14785	+	1.07736i	−0.471315	+	0.0710393i
$231$	1.08541	−	4.75550i	0.0714148	−	0.312889i
$232$	−9.12255	−	8.46449i	−0.598925	−	0.555721i
$233$	−2.20664	+	29.4455i	−0.144562	+	1.92904i	0.180930	+	0.983496i	$0.442089\pi$
$233$	−2.20664	+	29.4455i	−0.144562	+	1.92904i	−0.325491	+	0.945545i	$0.605530\pi$
$234$	−13.7778	+	35.1053i	−0.900685	+	2.29491i
$235$	−10.1295	−	1.52678i	−0.660776	−	0.0995960i
$236$	−6.87073	+	3.30877i	−0.447246	+	0.215382i
$237$	12.3189	−	5.93249i	0.800202	−	0.385357i
$238$	−14.7631	−	2.22518i	−0.956948	−	0.144237i
$239$	−8.80723	+	22.4405i	−0.569692	+	1.45155i	0.298056	+	0.954548i	$0.403662\pi$
$239$	−8.80723	+	22.4405i	−0.569692	+	1.45155i	−0.867748	+	0.497004i	$0.834433\pi$
$240$	1.29922	−	17.3369i	0.0838645	−	1.11909i
$241$	4.34963	+	4.03587i	0.280184	+	0.259973i	0.807729	−	0.589554i	$-0.200697\pi$
$241$	4.34963	+	4.03587i	0.280184	+	0.259973i	−0.527544	+	0.849528i	$0.676887\pi$
$242$	−4.96538	+	21.7547i	−0.319187	+	1.39845i
$243$	−7.72164	+	1.16385i	−0.495343	+	0.0746610i
$244$	16.9832	−	11.5790i	1.08724	−	0.741268i
$245$	−7.59894	−	2.34396i	−0.485479	−	0.149750i
$246$	−3.24872	−	43.3512i	−0.207131	−	2.76397i
$247$	−5.83912	+	7.32202i	−0.371534	+	0.465889i
$248$	7.48861	−	2.30993i	0.475527	−	0.146681i
$249$	5.08882	+	12.9661i	0.322491	+	0.821693i
$250$	−3.34653	−	14.6621i	−0.211653	−	0.927312i
$251$	7.19242	−	12.4576i	0.453982	−	0.786319i	−0.544647	−	0.838665i	$-0.683337\pi$
$251$	7.19242	−	12.4576i	0.453982	−	0.786319i	0.998629	+	0.0523460i	$0.0166699\pi$
$252$	14.9317	+	25.8624i	0.940608	+	1.62918i
$253$	−0.741972	+	0.688449i	−0.0466473	+	0.0432824i
$254$	−26.4205	−	33.1302i	−1.65777	−	2.07877i
$255$	−22.4724	−	15.3214i	−1.40728	−	0.959466i
$256$	−0.409185	−	0.197053i	−0.0255740	−	0.0123158i
$257$	−18.1706			−1.13345			−0.566724	−	0.823908i	$-0.691789\pi$
$257$	−18.1706			−1.13345			−0.566724	+	0.823908i	$0.691789\pi$
$258$	−22.2787	+	34.8804i	−1.38701	+	2.17156i
$259$	−7.00377			−0.435193
$260$	−20.8298	−	10.0311i	−1.29181	−	0.622104i
$261$	−38.6329	−	26.3394i	−2.39131	−	1.63037i
$262$	16.3540	+	20.5072i	1.01035	+	1.26694i
$263$	11.6213	−	10.7830i	0.716598	−	0.664906i	−0.235089	−	0.971974i	$-0.575538\pi$
$263$	11.6213	−	10.7830i	0.716598	−	0.664906i	0.951688	+	0.307068i	$0.0993478\pi$
$264$	1.77067	+	3.06689i	0.108977	+	0.188754i
$265$	−12.1081	+	20.9718i	−0.743792	+	1.28829i
$266$	2.88240	+	12.6286i	0.176732	+	0.774311i
$267$	2.20249	+	5.61184i	0.134790	+	0.343439i
$268$	−26.3914	+	8.14068i	−1.61211	+	0.497271i
$269$	6.59147	−	8.26544i	0.401889	−	0.503953i	−0.539169	−	0.842197i	$-0.681262\pi$
$269$	6.59147	−	8.26544i	0.401889	−	0.503953i	0.941058	+	0.338245i	$0.109833\pi$
$270$	3.23819	+	43.2106i	0.197070	+	2.62971i
$271$	−1.69682	−	0.523401i	−0.103075	−	0.0317943i	0.242789	−	0.970079i	$-0.421938\pi$
$271$	−1.69682	−	0.523401i	−0.103075	−	0.0317943i	−0.345864	+	0.938285i	$0.612414\pi$
$272$	−6.15637	+	4.19734i	−0.373284	+	0.254501i
$273$	−18.4425	+	2.77975i	−1.11619	+	0.168238i
$274$	2.87075	−	12.5776i	0.173428	−	0.759839i
$275$	1.48694	+	1.37968i	0.0896661	+	0.0831980i
$276$	0.715007	−	9.54110i	0.0430383	−	0.574307i
$277$	0.682551	−	1.73911i	0.0410105	−	0.104493i	−0.908901	−	0.417012i	$-0.863077\pi$
$277$	0.682551	−	1.73911i	0.0410105	−	0.104493i	0.949912	+	0.312519i	$0.101173\pi$
$278$	6.64974	+	1.00229i	0.398825	+	0.0601132i
$279$	26.5288	−	12.7756i	1.58824	−	0.764854i
$280$	−7.29872	+	3.51488i	−0.436182	+	0.210054i
$281$	5.38800	+	0.812110i	0.321421	+	0.0484464i	0.307771	−	0.951460i	$-0.400417\pi$
$281$	5.38800	+	0.812110i	0.321421	+	0.0484464i	0.0136498	+	0.999907i	$0.495655\pi$
$282$	8.65239	−	22.0459i	0.515242	−	1.31282i
$283$	0.707816	−	9.44514i	0.0420753	−	0.561456i	−0.935836	−	0.352436i	$-0.885354\pi$
$283$	0.707816	−	9.44514i	0.0420753	−	0.561456i	0.977911	−	0.209020i	$-0.0670274\pi$
$284$	−23.8041	−	22.0870i	−1.41252	−	1.31062i
$285$	−5.25103	+	23.0063i	−0.311044	+	1.36277i
$286$	−5.59123	+	0.842742i	−0.330616	+	0.0498324i
$287$	11.5051	−	7.84405i	0.679125	−	0.463020i
$288$	40.3452	+	12.4448i	2.37736	+	0.733319i
$289$	−0.399306	−	5.32837i	−0.0234886	−	0.313433i
$290$	31.2165	−	39.1442i	1.83310	−	2.29863i
$291$	33.5994	−	10.3640i	1.96963	−	0.607550i
$292$	12.1912	+	31.0628i	0.713439	+	1.81781i
$293$	−2.12778	−	9.32241i	−0.124306	−	0.544621i	−0.998279	−	0.0586458i	$-0.981322\pi$
$293$	−2.12778	−	9.32241i	−0.124306	−	0.544621i	0.873973	−	0.485975i	$-0.161535\pi$
$294$	9.19244	−	15.9218i	0.536114	−	0.928576i
$295$	−3.88625	−	6.73118i	−0.226266	−	0.391904i
$296$	3.72745	−	3.45857i	0.216653	−	0.201025i
$297$	3.78299	+	4.74372i	0.219511	+	0.275258i
$298$	2.87886	+	1.96277i	0.166768	+	0.113700i
$299$	3.48687	+	1.67919i	0.201651	+	0.0971099i
$300$	−19.1744			−1.10704
$301$	−13.2437	−	0.593759i	−0.763353	−	0.0342237i
$302$	9.58569			0.551594
$303$	6.70051	+	3.22680i	0.384934	+	0.185375i
$304$	5.34138	+	3.64169i	0.306349	+	0.208865i
$305$	13.0621	+	16.3793i	0.747931	+	0.937876i
$306$	29.8541	−	27.7006i	1.70665	−	1.58354i
$307$	8.96235	+	15.5232i	0.511508	+	0.885959i	0.999911	+	0.0133402i	$0.00424644\pi$
$307$	8.96235	+	15.5232i	0.511508	+	0.885959i	−0.488403	+	0.872618i	$0.662420\pi$
$308$	−2.23878	+	3.87768i	−0.127566	+	0.220952i
$309$	5.10667	+	22.3738i	0.290508	+	1.27280i
$310$	11.5188	+	29.3495i	0.654227	+	1.66694i
$311$	11.9150	−	3.67529i	0.675638	−	0.208407i	0.0620976	−	0.998070i	$-0.480221\pi$
$311$	11.9150	−	3.67529i	0.675638	−	0.208407i	0.613540	+	0.789663i	$0.289745\pi$
$312$	8.44250	−	10.5866i	0.477962	−	0.599346i
$313$	1.95694	+	26.1136i	0.110613	+	1.47603i	0.725941	+	0.687757i	$0.241405\pi$
$313$	1.95694	+	26.1136i	0.110613	+	1.47603i	−0.615328	+	0.788271i	$0.710976\pi$
$314$	−7.53999	−	2.32578i	−0.425506	−	0.131251i
$315$	−25.1485	+	17.1460i	−1.41696	+	0.966065i
$316$	−12.4109	+	1.87065i	−0.698169	+	0.105232i
$317$	−2.01390	+	8.82346i	−0.113112	+	0.495575i	0.886358	+	0.463001i	$0.153227\pi$
$317$	−2.01390	+	8.82346i	−0.113112	+	0.495575i	−0.999469	+	0.0325735i	$0.989630\pi$
$318$	−41.0403	−	38.0798i	−2.30142	−	2.13541i
$319$	0.523901	−	6.99098i	0.0293328	−	0.391420i
$320$	−12.1635	+	30.9921i	−0.679961	+	1.73251i
$321$	−24.1991	−	3.64743i	−1.35066	−	0.203580i
$322$	4.82283	−	2.32255i	0.268766	−	0.129431i
$323$	9.11201	−	4.38811i	0.507006	−	0.244161i
$324$	−12.8940	−	1.94345i	−0.716332	−	0.107970i
$325$	2.83356	−	7.21978i	0.157177	−	0.400482i
$326$	−1.24548	+	16.6198i	−0.0689807	+	0.920483i
$327$	−12.1336	−	11.2584i	−0.670992	−	0.622590i
$328$	−2.24958	+	9.85604i	−0.124212	+	0.544209i
$329$	7.50114	−	1.13062i	0.413551	−	0.0623328i
$330$	−11.7719	+	8.02595i	−0.648022	+	0.441814i
$331$	−3.33977	−	1.03018i	−0.183571	−	0.0566240i	0.201607	−	0.979466i	$-0.435384\pi$
$331$	−3.33977	−	1.03018i	−0.183571	−	0.0566240i	−0.385178	+	0.922842i	$0.625860\pi$
$332$	−0.955503	−	12.7503i	−0.0524400	−	0.699764i
$333$	11.9118	−	14.9369i	0.652760	−	0.818536i
$334$	10.1720	−	3.13766i	0.556589	−	0.171685i
$335$	−10.2841	−	26.2034i	−0.561879	−	1.43164i
$336$	2.86482	+	12.5516i	0.156289	+	0.684747i
$337$	−2.60035	+	4.50393i	−0.141650	+	0.245345i	−0.928118	−	0.372286i	$-0.878574\pi$
$337$	−2.60035	+	4.50393i	−0.141650	+	0.245345i	0.786468	+	0.617631i	$0.211907\pi$
$338$	−3.24944	−	5.62820i	−0.176746	−	0.306134i
$339$	−38.3879	+	35.6187i	−2.08494	+	1.93454i
$340$	15.5665	+	19.5198i	0.844214	+	1.05861i
$341$	3.64767	+	2.48694i	0.197532	+	0.134675i
$342$	−31.8353	−	15.3311i	−1.72145	−	0.829008i
$343$	20.0405			1.08209
$344$	7.34156	−	6.22392i	0.395831	−	0.335571i
$345$	9.75174			0.525016
$346$	−42.0208	−	20.2361i	−2.25905	−	1.08790i
$347$	6.33995	+	4.32251i	0.340346	+	0.232044i	0.721416	−	0.692502i	$-0.243492\pi$
$347$	6.33995	+	4.32251i	0.340346	+	0.232044i	−0.381069	+	0.924546i	$0.624444\pi$
$348$	41.3186	+	51.8119i	2.21491	+	2.77741i
$349$	19.3740	−	17.9765i	1.03707	−	0.962257i	0.0377526	−	0.999287i	$-0.487980\pi$
$349$	19.3740	−	17.9765i	1.03707	−	0.962257i	0.999314	+	0.0370298i	$0.0117896\pi$
$350$	−5.36376	−	9.29031i	−0.286705	−	0.496588i
$351$	11.5998	−	20.0914i	0.619150	−	1.07240i
$352$	1.40864	+	6.17168i	0.0750810	+	0.328951i
$353$	−3.64148	−	9.27834i	−0.193817	−	0.493836i	0.800620	−	0.599172i	$-0.204504\pi$
$353$	−3.64148	−	9.27834i	−0.193817	−	0.493836i	−0.994437	+	0.105336i	$0.966408\pi$
$354$	17.1710	−	5.29655i	0.912628	−	0.281508i
$355$	20.6355	−	25.8761i	1.09522	−	1.37336i
$356$	−0.413550	−	5.51845i	−0.0219181	−	0.292477i
$357$	19.2463	+	5.93670i	1.01862	+	0.314203i
$358$	30.0331	−	20.4762i	1.58730	−	1.08220i
$359$	1.39816	−	0.210739i	0.0737921	−	0.0111224i	−0.112042	−	0.993703i	$-0.535739\pi$
$359$	1.39816	−	0.210739i	0.0737921	−	0.0111224i	0.185835	+	0.982581i	$0.440501\pi$
$360$	4.91725	−	21.5439i	0.259162	−	1.13546i
$361$	7.49565	+	6.95495i	0.394508	+	0.366050i
$362$	−0.130232	+	1.73782i	−0.00684482	+	0.0913377i
$363$	10.9979	−	28.0221i	0.577239	−	1.47078i
$364$	16.9292	+	2.55167i	0.887332	+	0.133744i
$365$	−30.6427	+	14.7567i	−1.60391	+	0.772403i
$366$	−43.6378	+	21.0149i	−2.28099	+	1.09847i
$367$	−28.0262	−	4.22427i	−1.46295	−	0.220505i	−0.631188	−	0.775630i	$-0.717432\pi$
$367$	−28.0262	−	4.22427i	−1.46295	−	0.220505i	−0.831767	+	0.555125i	$0.812670\pi$
$368$	0.976011	−	2.48683i	0.0508781	−	0.129635i
$369$	−2.83854	+	37.8777i	−0.147769	+	1.97183i
$370$	14.9963	+	13.9145i	0.779621	+	0.723383i
$371$	3.99038	−	17.4830i	0.207170	−	0.907672i
$372$	−41.2662	+	6.21987i	−2.13955	+	0.322485i
$373$	−19.4695	+	13.2741i	−1.00809	+	0.687304i	−0.950400	−	0.311030i	$-0.899326\pi$
$373$	−19.4695	+	13.2741i	−1.00809	+	0.687304i	−0.0576903	+	0.998335i	$0.518374\pi$
$374$	5.83493	+	1.79984i	0.301717	+	0.0930674i
$375$	1.51617	+	20.2319i	0.0782946	+	1.04477i
$376$	−3.43384	+	4.30589i	−0.177087	+	0.222060i
$377$	−25.6148	+	7.90112i	−1.31923	+	0.406928i
$378$	−11.7231	−	29.8701i	−0.602973	−	1.53635i
$379$	0.506526	+	2.21924i	0.0260185	+	0.113995i	0.986270	−	0.165143i	$-0.0528086\pi$
$379$	0.506526	+	2.21924i	0.0260185	+	0.113995i	−0.960251	+	0.279138i	$0.909951\pi$
$380$	10.8308	−	18.7596i	0.555610	−	0.962345i
$381$	28.5831	+	49.5075i	1.46436	+	2.53634i
$382$	−18.3499	+	17.0262i	−0.938863	+	0.871137i
$383$	−12.2178	−	15.3206i	−0.624299	−	0.782846i	0.364643	−	0.931147i	$-0.381191\pi$
$383$	−12.2178	−	15.3206i	−0.624299	−	0.782846i	−0.988942	+	0.148301i	$0.952620\pi$
$384$	−26.6803	−	18.1903i	−1.36152	−	0.928271i
$385$	−4.11168	−	1.98008i	−0.209550	−	0.100914i
$386$	12.6983			0.646325
$387$	23.7907	−	27.2348i	1.20935	−	1.38442i
$388$	−32.2764			−1.63859
$389$	−0.649494	−	0.312780i	−0.0329306	−	0.0158586i	0.417346	−	0.908748i	$-0.362960\pi$
$389$	−0.649494	−	0.312780i	−0.0329306	−	0.0158586i	−0.450277	+	0.892889i	$0.648675\pi$
$390$	45.0112	+	30.6881i	2.27923	+	1.55395i
$391$	−2.60581	−	3.26758i	−0.131781	−	0.165248i
$392$	−3.13406	+	2.90799i	−0.158294	+	0.146876i
$393$	−17.6926	−	30.6445i	−0.892475	−	1.54581i
$394$	5.96399	−	10.3299i	0.300461	−	0.520414i
$395$	−2.84656	−	12.4716i	−0.143226	−	0.627514i
$396$	−4.46226	−	11.3696i	−0.224237	−	0.571346i
$397$	−8.02091	+	2.47412i	−0.402558	+	0.124173i	−0.489421	−	0.872048i	$-0.662792\pi$
$397$	−8.02091	+	2.47412i	−0.402558	+	0.124173i	0.0868631	+	0.996220i	$0.472316\pi$
$398$	−26.5067	+	33.2383i	−1.32866	+	1.66609i
$399$	−1.30590	−	17.4260i	−0.0653765	−	0.872389i
$400$	−5.11596	−	1.57807i	−0.255798	−	0.0789033i
$401$	23.6148	−	16.1003i	1.17927	−	0.804011i	0.195019	−	0.980800i	$-0.437523\pi$
$401$	23.6148	−	16.1003i	1.17927	−	0.804011i	0.984249	+	0.176789i	$0.0565709\pi$
$402$	64.3517	−	9.69945i	3.20957	−	0.483765i
$403$	3.75625	−	16.4572i	0.187112	−	0.819791i
$404$	−5.00439	−	4.64340i	−0.248978	−	0.231018i
$405$	0.993180	−	13.2531i	0.0493515	−	0.658550i
$406$	−13.5454	+	34.5131i	−0.672247	+	1.71286i
$407$	2.83251	+	0.426932i	0.140402	+	0.0211622i
$408$	−13.1746	+	6.34456i	−0.652241	+	0.314103i
$409$	9.56120	−	4.60443i	0.472771	−	0.227674i	−0.182299	−	0.983243i	$-0.558354\pi$
$409$	9.56120	−	4.60443i	0.472771	−	0.227674i	0.655069	+	0.755569i	$0.272639\pi$
$410$	−40.2184	−	6.06195i	−1.98625	−	0.299378i
$411$	−6.35846	+	16.2011i	−0.313640	+	0.799141i
$412$	1.57427	−	21.0072i	0.0775589	−	1.03495i
$413$	4.21924	+	3.91488i	0.207615	+	0.192639i
$414$	−3.24921	+	14.2357i	−0.159690	+	0.699647i
$415$	12.8862	−	1.94229i	0.632560	−	0.0953431i
$416$	19.9991	−	13.6351i	0.980534	−	0.668517i
$417$	−8.66912	−	2.67407i	−0.424529	−	0.130950i
$418$	−0.395910	−	5.28306i	−0.0193646	−	0.258403i
$419$	−11.9692	+	15.0089i	−0.584735	+	0.733235i	−0.982912	−	0.184074i	$-0.941071\pi$
$419$	−11.9692	+	15.0089i	−0.584735	+	0.733235i	0.398177	+	0.917309i	$0.369643\pi$
$420$	41.2226	−	12.7155i	2.01145	−	0.620452i
$421$	−10.9213	−	27.8270i	−0.532272	−	1.35621i	−0.903868	−	0.427812i	$-0.859285\pi$
$421$	−10.9213	−	27.8270i	−0.532272	−	1.35621i	0.371596	−	0.928395i	$-0.378811\pi$
$422$	8.38289	+	36.7278i	0.408073	+	1.78788i
$423$	−10.3464	+	17.9205i	−0.503060	+	0.871326i
$424$	6.50966	+	11.2751i	0.316137	+	0.547565i
$425$	−6.13981	+	5.69691i	−0.297825	+	0.276341i
$426$	47.7074	+	59.8232i	2.31143	+	2.89844i
$427$	−12.8182	−	8.73930i	−0.620316	−	0.422924i
$428$	20.2398	+	9.74695i	0.978325	+	0.471137i
$429$	7.62806			0.368286
$430$	27.1774	+	27.5828i	1.31061	+	1.33016i
$431$	20.3418			0.979832			0.489916	−	0.871770i	$-0.337028\pi$
$431$	20.3418			0.979832			0.489916	+	0.871770i	$0.337028\pi$
$432$	−14.4284	−	6.94837i	−0.694188	−	0.334304i
$433$	−22.7969	−	15.5427i	−1.09555	−	0.746932i	−0.126049	−	0.992024i	$-0.540230\pi$
$433$	−22.7969	−	15.5427i	−1.09555	−	0.746932i	−0.969500	+	0.245092i	$0.921182\pi$
$434$	−14.5572	−	18.2542i	−0.698770	−	0.876229i
$435$	−49.5129	+	45.9412i	−2.37396	+	2.20271i
$436$	7.59705	+	13.1585i	0.363833	+	0.630176i
$437$	−1.81306	+	3.14031i	−0.0867304	+	0.150221i
$438$	−17.4968	−	76.6586i	−0.836030	−	3.66289i
$439$	−9.38354	−	23.9089i	−0.447852	−	1.14111i	−0.959449	−	0.281883i	$-0.909041\pi$
$439$	−9.38354	−	23.9089i	−0.447852	−	1.14111i	0.511597	−	0.859226i	$-0.329054\pi$
$440$	3.16605	−	0.976597i	0.150935	−	0.0465574i
$441$	−10.0155	+	12.5590i	−0.476928	+	0.598049i
$442$	−1.74478	−	23.2825i	−0.0829908	−	1.10743i
$443$	0.266159	+	0.0820992i	0.0126456	+	0.00390065i	0.301072	−	0.953602i	$-0.402656\pi$
$443$	0.266159	+	0.0820992i	0.0126456	+	0.00390065i	−0.288426	+	0.957502i	$0.593132\pi$
$444$	−22.3726	+	15.2534i	−1.06176	+	0.723894i
$445$	5.57728	−	0.840639i	0.264388	−	0.0398501i
$446$	−7.27162	+	31.8590i	−0.344321	+	1.50857i
$447$	−3.44570	−	3.19715i	−0.162976	−	0.151220i
$448$	1.84245	−	24.5858i	0.0870475	−	1.16157i
$449$	4.94037	−	12.5878i	0.233150	−	0.594057i	−0.765638	−	0.643272i	$-0.777577\pi$
$449$	4.94037	−	12.5878i	0.233150	−	0.594057i	0.998788	+	0.0492145i	$0.0156718\pi$
$450$	28.9358	+	4.36138i	1.36405	+	0.205597i
$451$	−5.13112	+	2.47102i	−0.241615	+	0.116356i
$452$	43.3099	−	20.8570i	2.03713	−	0.981028i
$453$	−12.7872	−	1.92735i	−0.600793	−	0.0905550i
$454$	9.90923	−	25.2483i	0.465063	−	1.18496i
$455$	−1.30400	+	17.4007i	−0.0611325	+	0.815757i
$456$	9.30020	+	8.62933i	0.435522	+	0.404105i
$457$	3.82680	−	16.7663i	0.179010	−	0.784295i	−0.803078	−	0.595874i	$-0.796806\pi$
$457$	3.82680	−	16.7663i	0.179010	−	0.784295i	0.982088	−	0.188421i	$-0.0603370\pi$
$458$	43.5395	−	6.56253i	2.03447	−	0.306647i
$459$	−20.7001	+	14.1131i	−0.966196	+	0.658741i
$460$	−8.55390	−	2.63853i	−0.398828	−	0.123022i
$461$	−0.242881	−	3.24102i	−0.0113121	−	0.150949i	−1.00000		0.000958913i	$-0.999695\pi$
$461$	−0.242881	−	3.24102i	−0.0113121	−	0.150949i	0.988687	−	0.149990i	$-0.0479243\pi$
$462$	6.57824	−	8.24885i	0.306047	−	0.383771i
$463$	32.6129	−	10.0597i	1.51565	−	0.467516i	0.578275	−	0.815842i	$-0.303726\pi$
$463$	32.6129	−	10.0597i	1.51565	−	0.467516i	0.937373	+	0.348326i	$0.113250\pi$
$464$	6.76015	+	17.2246i	0.313832	+	0.799631i
$465$	−9.46477	−	41.4679i	−0.438918	−	1.92303i
$466$	−31.9347	+	55.3125i	−1.47934	+	2.56230i
$467$	17.3380	+	30.0303i	0.802308	+	1.38964i	0.918094	+	0.396364i	$0.129728\pi$
$467$	17.3380	+	30.0303i	0.802308	+	1.38964i	−0.115786	+	0.993274i	$0.536939\pi$
$468$	−34.2345	+	31.7650i	−1.58249	+	1.46834i
$469$	12.9968	+	16.2974i	0.600134	+	0.752545i
$470$	−18.3075	−	12.4818i	−0.844462	−	0.575744i
$471$	9.59059	+	4.61858i	0.441911	+	0.212813i
$472$	−4.17873			−0.192342
$473$	5.31989	+	1.04743i	0.244609	+	0.0481610i
$474$	29.5747			1.35841
$475$	6.54726	+	3.15299i	0.300409	+	0.144669i
$476$	−15.2759	−	10.4149i	−0.700171	−	0.477368i
$477$	30.4991	+	38.2447i	1.39646	+	1.75110i
$478$	−38.2237	+	35.4664i	−1.74831	+	1.62219i
$479$	−3.86193	−	6.68907i	−0.176456	−	0.305631i	0.764208	−	0.644970i	$-0.223130\pi$
$479$	−3.86193	−	6.68907i	−0.176456	−	0.305631i	−0.940664	+	0.339339i	$0.889797\pi$
$480$	30.4951	−	52.8191i	1.39190	−	2.41085i
$481$	−2.43721	−	10.6781i	−0.111127	−	0.486881i
$482$	4.68892	+	11.9472i	0.213575	+	0.544179i
$483$	−6.90057	+	2.12854i	−0.313987	+	0.0968520i
$484$	−17.2289	+	21.6044i	−0.783132	+	0.982017i
$485$	−2.45838	−	32.8048i	−0.111629	−	1.48959i
$486$	−16.1402	−	4.97858i	−0.732133	−	0.225833i
$487$	−19.0696	+	13.0014i	−0.864125	+	0.589151i	−0.912224	−	0.409692i	$-0.865636\pi$
$487$	−19.0696	+	13.0014i	−0.864125	+	0.589151i	0.0480986	+	0.998843i	$0.484684\pi$
$488$	11.1375	−	1.67871i	0.504171	−	0.0759916i
$489$	5.00311	−	21.9201i	0.226249	−	0.991260i
$490$	−12.6090	−	11.6995i	−0.569617	−	0.528527i
$491$	−0.737039	+	9.83511i	−0.0332621	+	0.443852i	0.955565	+	0.294782i	$0.0952470\pi$
$491$	−0.737039	+	9.83511i	−0.0332621	+	0.443852i	−0.988827	+	0.149070i	$0.952372\pi$
$492$	19.6681	−	50.1136i	0.886707	−	2.25929i
$493$	28.6244	+	4.31443i	1.28918	+	0.194312i
$494$	−18.2509	+	8.78917i	−0.821147	+	0.395444i
$495$	11.2159	−	5.40128i	0.504116	−	0.242770i
$496$	−11.5222	−	1.73669i	−0.517362	−	0.0779798i
$497$	−8.95411	+	22.8147i	−0.401647	+	1.02338i
$498$	−2.25149	+	30.0441i	−0.100892	+	1.34631i
$499$	30.3095	+	28.1231i	1.35684	+	1.25896i	0.936079	+	0.351790i	$0.114427\pi$
$499$	30.3095	+	28.1231i	1.35684	+	1.25896i	0.420759	+	0.907172i	$0.361764\pi$
$500$	4.14421	−	18.1570i	0.185335	−	0.812004i
$501$	−14.2002	+	2.14034i	−0.634419	+	0.0956233i
$502$	25.7079	−	17.5274i	1.14740	−	0.782285i
$503$	13.2126	+	4.07554i	0.589120	+	0.181720i	0.574962	−	0.818180i	$-0.305017\pi$
$503$	13.2126	+	4.07554i	0.589120	+	0.181720i	0.0141584	+	0.999900i	$0.495493\pi$
$504$	1.22289	+	16.3183i	0.0544716	+	0.726873i
$505$	4.33824	−	5.43998i	0.193049	−	0.242076i
$506$	−2.09206	+	0.645314i	−0.0930032	+	0.0286877i
$507$	3.20307	+	8.16128i	0.142253	+	0.362455i
$508$	−11.6769	−	51.1600i	−0.518080	−	2.26986i
$509$	12.1089	−	20.9732i	0.536716	−	0.929619i	−0.462362	−	0.886691i	$-0.652998\pi$
$509$	12.1089	−	20.9732i	0.536716	−	0.929619i	0.999078	−	0.0429280i	$-0.0136686\pi$
$510$	−29.4152	−	50.9486i	−1.30253	−	2.25604i
$511$	18.4625	−	17.1307i	0.816733	−	0.757818i
$512$	−14.4118	−	18.0719i	−0.636920	−	0.798672i
$513$	17.9598	+	12.2448i	0.792943	+	0.540620i
$514$	−35.4107	−	17.0529i	−1.56190	−	0.752171i
$515$	21.4710			0.946125
$516$	−43.5983	+	26.9465i	−1.91931	+	1.18625i
$517$	−3.10258			−0.136451
$518$	−13.6489	−	6.57298i	−0.599700	−	0.288800i
$519$	51.9863	+	35.4436i	2.28194	+	1.55580i
$520$	−7.89872	−	9.90468i	−0.346382	−	0.434349i
$521$	−4.41210	+	4.09383i	−0.193297	+	0.179354i	−0.770884	−	0.636976i	$-0.780185\pi$
$521$	−4.41210	+	4.09383i	−0.193297	+	0.179354i	0.577586	+	0.816330i	$0.303995\pi$
$522$	−50.5683	−	87.5868i	−2.21331	−	3.83357i
$523$	−18.5046	+	32.0509i	−0.809149	+	1.40149i	0.104305	+	0.994545i	$0.466738\pi$
$523$	−18.5046	+	32.0509i	−0.809149	+	1.40149i	−0.913454	+	0.406942i	$0.866595\pi$
$524$	7.22789	+	31.6674i	0.315752	+	1.38340i
$525$	5.28721	+	13.4716i	0.230753	+	0.587949i
$526$	32.7672	−	10.1073i	1.42872	−	0.440701i
$527$	−11.3658	+	14.2522i	−0.495101	+	0.620838i
$528$	−0.393496	−	5.25083i	−0.0171247	−	0.228513i
$529$	−20.5463	−	6.33769i	−0.893316	−	0.275552i
$530$	−43.2780	+	29.5064i	−1.87987	+	1.28168i
$531$	−15.5252	+	2.34004i	−0.673734	+	0.101549i
$532$	−3.56946	+	15.6388i	−0.154756	+	0.678028i
$533$	15.9628	+	14.8114i	0.691428	+	0.641551i
$534$	−0.974466	+	13.0034i	−0.0421693	+	0.562710i
$535$	−8.36491	+	21.3134i	−0.361647	+	0.921461i
$536$	−14.9648	−	2.25559i	−0.646383	−	0.0974266i
$537$	−44.1808	+	21.2763i	−1.90654	+	0.918141i
$538$	20.6025	−	9.92163i	0.888235	−	0.427752i
$539$	−2.38159	−	0.358968i	−0.102583	−	0.0154618i
$540$	−19.6043	+	49.9510i	−0.843636	+	2.14955i
$541$	−0.253692	+	3.38529i	−0.0109071	+	0.145545i	−0.999998	−	0.00175845i	$-0.999440\pi$
$541$	−0.253692	+	3.38529i	−0.0109071	+	0.145545i	0.989091	+	0.147303i	$0.0470593\pi$
$542$	−2.81556	−	2.61246i	−0.120939	−	0.112215i
$543$	0.523143	−	2.29204i	0.0224502	−	0.0983608i
$544$	−25.8472	+	3.89583i	−1.10819	+	0.167032i
$545$	−12.7952	+	8.72363i	−0.548087	+	0.373679i
$546$	−38.5494	−	11.8909i	−1.64976	−	0.508884i
$547$	−1.91085	−	25.4985i	−0.0817021	−	1.09024i	−0.875872	−	0.482543i	$-0.839713\pi$
$547$	−1.91085	−	25.4985i	−0.0817021	−	1.09024i	0.794170	−	0.607696i	$-0.207906\pi$
$548$	9.96096	−	12.4906i	0.425511	−	0.533574i
$549$	40.4389	−	12.4738i	1.72589	−	0.532367i
$550$	1.60293	+	4.08421i	0.0683493	+	0.174151i
$551$	−5.58874	−	24.4859i	−0.238089	−	1.04313i
$552$	2.62141	−	4.54042i	0.111575	−	0.193253i
$553$	4.73651	+	8.20387i	0.201417	+	0.348864i
$554$	2.96230	−	2.74861i	0.125856	−	0.116777i
$555$	−17.2071	−	21.5770i	−0.730401	−	0.915894i
$556$	6.88074	+	4.69121i	0.291808	+	0.198952i
$557$	−18.9148	−	9.10888i	−0.801445	−	0.385955i	−0.0121162	−	0.999927i	$-0.503857\pi$
$557$	−18.9148	−	9.10888i	−0.801445	−	0.385955i	−0.789328	+	0.613971i	$0.789571\pi$
$558$	63.6890			2.69617
$559$	−3.70335	−	20.3983i	−0.156635	−	0.862754i
$560$	12.0452			0.509001
$561$	−7.42182	−	3.57416i	−0.313350	−	0.150901i
$562$	9.73795	+	6.63922i	0.410771	+	0.280059i
$563$	−16.8730	−	21.1580i	−0.711111	−	0.891705i	0.286688	−	0.958024i	$-0.407446\pi$
$563$	−16.8730	−	21.1580i	−0.711111	−	0.891705i	−0.997798	+	0.0663195i	$0.978874\pi$
$564$	21.4991	−	19.9482i	0.905274	−	0.839971i
$565$	24.4971	+	42.4302i	1.03060	+	1.78505i
$566$	10.2436	−	17.7424i	0.430570	−	0.745768i
$567$	2.18999	+	9.59497i	0.0919709	+	0.402951i
$568$	−6.50081	−	16.5638i	−0.272768	−	0.695001i
$569$	−26.2872	+	8.10851i	−1.10201	+	0.339927i	−0.791825	−	0.610748i	$-0.790869\pi$
$569$	−26.2872	+	8.10851i	−1.10201	+	0.339927i	−0.310190	+	0.950675i	$0.600393\pi$
$570$	−31.8244	+	39.9065i	−1.33298	+	1.67150i
$571$	2.56665	+	34.2495i	0.107411	+	1.43330i	0.747124	+	0.664685i	$0.231434\pi$
$571$	2.56665	+	34.2495i	0.107411	+	1.43330i	−0.639713	+	0.768614i	$0.720947\pi$
$572$	−6.69108	−	2.06392i	−0.279768	−	0.0862970i
$573$	27.9019	−	19.0232i	1.16562	−	0.794705i
$574$	29.7827	−	4.48902i	1.24311	−	0.187368i
$575$	0.668234	−	2.92772i	0.0278673	−	0.122095i
$576$	49.3002	+	45.7439i	2.05418	+	1.90600i
$577$	−0.0405171	+	0.540663i	−0.00168675	+	0.0225081i	−0.997984	−	0.0634713i	$-0.979783\pi$
$577$	−0.0405171	+	0.540663i	−0.00168675	+	0.0225081i	0.996297	+	0.0859794i	$0.0274019\pi$
$578$	4.22246	−	10.7587i	0.175631	−	0.447501i
$579$	−16.9393	−	2.55319i	−0.703973	−	0.106107i
$580$	55.8614	−	26.9014i	2.31952	−	1.11702i
$581$	−8.69466	+	4.18713i	−0.360715	+	0.173711i
$582$	75.2049	+	11.3353i	3.11734	+	0.469864i
$583$	−2.67953	+	6.82734i	−0.110975	+	0.282759i
$584$	−1.36646	+	18.2341i	−0.0565444	+	0.754533i
$585$	−34.8925	−	32.3755i	−1.44263	−	1.33856i
$586$	4.60239	−	20.1644i	0.190123	−	0.832983i
$587$	9.72187	−	1.46534i	0.401265	−	0.0604809i	0.0546901	−	0.998503i	$-0.482583\pi$
$587$	9.72187	−	1.46534i	0.401265	−	0.0604809i	0.346574	+	0.938022i	$0.387345\pi$
$588$	18.8111	−	12.8252i	0.775755	−	0.528901i
$589$	15.1134	+	4.66188i	0.622738	+	0.192089i
$590$	−1.25636	−	16.7649i	−0.0517234	−	0.690200i
$591$	−10.0329	+	12.5808i	−0.412697	+	0.517505i
$592$	−7.22465	+	2.22851i	−0.296931	+	0.0915911i
$593$	10.5629	+	26.9139i	0.433767	+	1.10522i	0.965981	+	0.258611i	$0.0832649\pi$
$593$	10.5629	+	26.9139i	0.433767	+	1.10522i	−0.532214	+	0.846610i	$0.678640\pi$
$594$	2.92034	+	12.7948i	0.119823	+	0.524979i
$595$	9.42192	−	16.3192i	0.386261	−	0.669024i
$596$	2.15740	+	3.73673i	0.0883707	+	0.153063i
$597$	42.0426	−	39.0098i	1.72069	−	1.59657i
$598$	5.21930	+	6.54479i	0.213433	+	0.267636i
$599$	−1.58885	−	1.08326i	−0.0649188	−	0.0442609i	0.530426	−	0.847731i	$-0.322032\pi$
$599$	−1.58885	−	1.08326i	−0.0649188	−	0.0442609i	−0.595345	+	0.803470i	$0.702984\pi$
$600$	−9.46636	−	4.55876i	−0.386463	−	0.186111i
$601$	−45.9528			−1.87446			−0.937228	−	0.348718i	$-0.886617\pi$
$601$	−45.9528			−1.87446			−0.937228	+	0.348718i	$0.886617\pi$
$602$	−25.2520	−	13.5862i	−1.02919	−	0.553732i
$603$	−56.8617			−2.31559
$604$	10.6950	+	5.15043i	0.435173	+	0.209568i
$605$	−23.2703	−	15.8654i	−0.946071	−	0.645020i
$606$	10.0296	+	12.5767i	0.407425	+	0.510895i
$607$	21.6805	−	20.1166i	0.879986	−	0.816508i	−0.104032	−	0.994574i	$-0.533175\pi$
$607$	21.6805	−	20.1166i	0.879986	−	0.816508i	0.984019	+	0.178066i	$0.0569841\pi$
$608$	11.3394	+	19.6404i	0.459873	+	0.796524i
$609$	25.0088	−	43.3165i	1.01341	−	1.75527i
$610$	10.0835	+	44.1786i	0.408268	+	1.78874i
$611$	4.33406	+	11.0430i	0.175337	+	0.446752i
$612$	48.1926	−	14.8654i	1.94807	−	0.600900i
$613$	−1.83476	+	2.30071i	−0.0741052	+	0.0929250i	−0.817502	−	0.575925i	$-0.804642\pi$
$613$	−1.83476	+	2.30071i	−0.0741052	+	0.0929250i	0.743397	+	0.668850i	$0.233213\pi$
$614$	2.89737	+	38.6627i	0.116928	+	1.56030i
$615$	52.4319	+	16.1731i	2.11426	+	0.652162i
$616$	−2.02721	+	1.38213i	−0.0816786	+	0.0556875i
$617$	9.18497	−	1.38441i	0.369773	−	0.0557343i	0.0384726	−	0.999260i	$-0.487751\pi$
$617$	9.18497	−	1.38441i	0.369773	−	0.0557343i	0.331300	+	0.943525i	$0.392513\pi$
$618$	−11.0457	+	48.3945i	−0.444324	+	1.94671i
$619$	−28.9452	−	26.8572i	−1.16341	−	1.07948i	−0.995604	−	0.0936630i	$-0.970142\pi$
$619$	−28.9452	−	26.8572i	−1.16341	−	1.07948i	−0.167803	−	0.985821i	$-0.553667\pi$
$620$	−2.91778	+	38.9351i	−0.117181	+	1.56367i
$621$	3.28172	−	8.36169i	0.131691	−	0.335543i
$622$	26.6692	+	4.01973i	1.06934	+	0.161176i
$623$	−3.76313	+	1.81223i	−0.150767	+	0.0726053i
$624$	−18.1396	+	8.73556i	−0.726165	+	0.349702i
$625$	30.8988	+	4.65724i	1.23595	+	0.186290i
$626$	−20.6937	+	52.7267i	−0.827087	+	2.10738i
$627$	−0.534104	+	7.12712i	−0.0213300	+	0.284630i
$628$	−7.16289	−	6.64619i	−0.285831	−	0.265212i
$629$	−2.63197	+	11.5314i	−0.104943	+	0.459787i
$630$	−65.1006	+	9.81234i	−2.59367	+	0.390933i
$631$	−18.1097	+	12.3470i	−0.720936	+	0.491526i	−0.867351	−	0.497698i	$-0.834179\pi$
$631$	−18.1097	+	12.3470i	−0.720936	+	0.491526i	0.146415	+	0.989223i	$0.453227\pi$
$632$	−6.57199	−	2.02719i	−0.261420	−	0.0806373i
$633$	−3.79793	−	50.6799i	−0.150954	−	2.01435i
$634$	−12.2054	+	15.3051i	−0.484739	+	0.607843i
$635$	51.1081	−	15.7647i	2.02816	−	0.625605i
$636$	−25.3292	−	64.5377i	−1.00437	−	2.55909i
$637$	2.04923	+	8.97825i	0.0811933	+	0.355731i
$638$	7.58195	−	13.1323i	0.300172	−	0.519914i
$639$	−33.4279	−	57.8988i	−1.32239	−	2.29044i
$640$	−22.1465	+	20.5490i	−0.875418	+	0.812270i
$641$	14.4602	+	18.1325i	0.571143	+	0.716191i	0.980574	−	0.196151i	$-0.0628441\pi$
$641$	14.4602	+	18.1325i	0.571143	+	0.716191i	−0.409431	+	0.912341i	$0.634273\pi$
$642$	−43.7360	−	29.8187i	−1.72612	−	1.17685i
$643$	−18.3605	−	8.84194i	−0.724067	−	0.348692i	0.0352809	−	0.999377i	$-0.488767\pi$
$643$	−18.3605	−	8.84194i	−0.724067	−	0.348692i	−0.759347	+	0.650685i	$0.774482\pi$
$644$	6.62887			0.261214
$645$	−30.7083	−	42.2595i	−1.20914	−	1.66397i
$646$	21.8757			0.860687
$647$	−0.758290	−	0.365173i	−0.0298114	−	0.0143564i	0.418919	−	0.908024i	$-0.362409\pi$
$647$	−0.758290	−	0.365173i	−0.0298114	−	0.0143564i	−0.448730	+	0.893667i	$0.648124\pi$
$648$	−5.90366	−	4.02505i	−0.231918	−	0.158119i
$649$	−1.46773	−	1.84047i	−0.0576134	−	0.0722449i
$650$	12.2977	−	11.4106i	0.482357	−	0.447562i
$651$	15.7488	+	27.2778i	0.617245	+	1.06910i
$652$	−10.3195	+	17.8739i	−0.404142	+	0.699994i
$653$	−8.94329	−	39.1831i	−0.349978	−	1.53335i	−0.777227	−	0.629220i	$-0.783375\pi$
$653$	−8.94329	−	39.1831i	−0.349978	−	1.53335i	0.427250	−	0.904134i	$-0.359483\pi$
$654$	−13.0801	−	33.3276i	−0.511473	−	1.30321i
$655$	−31.6353	+	9.75819i	−1.23609	+	0.381284i
$656$	9.37207	−	11.7522i	0.365918	−	0.458846i
$657$	5.13412	+	68.5101i	0.200301	+	2.67283i
$658$	15.6793	+	4.83642i	0.611242	+	0.188543i
$659$	−16.9744	+	11.5729i	−0.661229	+	0.450818i	−0.846870	−	0.531800i	$-0.821516\pi$
$659$	−16.9744	+	11.5729i	−0.661229	+	0.450818i	0.185642	+	0.982617i	$0.440564\pi$
$660$	−17.4466	+	2.62965i	−0.679107	+	0.102359i
$661$	−4.27999	+	18.7519i	−0.166472	+	0.729364i	0.820916	+	0.571049i	$0.193463\pi$
$661$	−4.27999	+	18.7519i	−0.166472	+	0.729364i	−0.987389	+	0.158315i	$0.949394\pi$
$662$	−5.54172	−	5.14197i	−0.215385	−	0.199848i
$663$	−2.35380	+	31.4093i	−0.0914140	+	1.21984i
$664$	2.55968	−	6.52197i	0.0993350	−	0.253101i
$665$	−16.1667	−	2.43673i	−0.626916	−	0.0944925i
$666$	37.2317	−	17.9299i	1.44270	−	0.694768i
$667$	−9.35107	+	4.50324i	−0.362075	+	0.174366i
$668$	13.0351	+	1.96472i	0.504342	+	0.0760173i
$669$	16.1060	−	41.0374i	0.622694	−	1.58660i
$670$	4.55008	−	60.7166i	0.175785	−	2.34569i
$671$	4.65129	+	4.31576i	0.179561	+	0.166608i
$672$	−10.0501	+	44.0323i	−0.387691	+	1.69858i
$673$	11.6700	−	1.75897i	0.449846	−	0.0678033i	0.0797875	−	0.996812i	$-0.474576\pi$
$673$	11.6700	−	1.75897i	0.449846	−	0.0678033i	0.370058	+	0.929009i	$0.379338\pi$
$674$	−9.29445	+	6.33685i	−0.358009	+	0.244086i
$675$	−17.2018	−	5.30606i	−0.662099	−	0.204230i
$676$	−0.601425	−	8.02546i	−0.0231317	−	0.308671i
$677$	−5.08538	+	6.37687i	−0.195447	+	0.245083i	−0.869892	−	0.493242i	$-0.835812\pi$
$677$	−5.08538	+	6.37687i	−0.195447	+	0.245083i	0.674445	+	0.738325i	$0.264383\pi$
$678$	−108.238	+	33.3870i	−4.15686	+	1.28222i
$679$	8.90000	+	22.6768i	0.341551	+	0.870257i
$680$	3.04428	+	13.3379i	0.116743	+	0.511484i
$681$	−18.2953	+	31.6885i	−0.701079	+	1.21430i
$682$	4.77460	+	8.26985i	0.182829	+	0.316669i
$683$	4.30555	−	3.99496i	0.164747	−	0.152863i	−0.593491	−	0.804841i	$-0.702251\pi$
$683$	4.30555	−	3.99496i	0.164747	−	0.152863i	0.758238	+	0.651977i	$0.226060\pi$
$684$	−27.2819	−	34.2105i	−1.04315	−	1.30807i
$685$	13.4538	+	9.17264i	0.514043	+	0.350469i
$686$	39.0549	+	18.8078i	1.49112	+	0.718087i
$687$	−59.4005			−2.26627
$688$	−13.8503	+	3.60148i	−0.528036	+	0.137305i
$689$	28.0436			1.06838
$690$	19.0042	+	9.15192i	0.723476	+	0.348408i
$691$	30.4990	+	20.7939i	1.16024	+	0.791037i	0.981236	−	0.192812i	$-0.0617607\pi$
$691$	30.4990	+	20.7939i	1.16024	+	0.791037i	0.179002	+	0.983849i	$0.442713\pi$
$692$	−36.0106	−	45.1559i	−1.36892	−	1.71657i
$693$	−6.75768	+	6.27021i	−0.256703	+	0.238185i
$694$	8.29865	+	14.3737i	0.315012	+	0.545617i
$695$	−4.24392	+	7.35068i	−0.160981	+	0.278827i
$696$	8.08050	+	35.4030i	0.306290	+	1.34195i
$697$	−8.59134	−	21.8904i	−0.325420	−	0.829157i
$698$	54.6267	−	16.8501i	2.06765	−	0.637786i
$699$	53.7218	−	67.3650i	2.03194	−	2.54798i
$700$	−0.992755	−	13.2474i	−0.0375226	−	0.500705i
$701$	−13.3574	−	4.12021i	−0.504502	−	0.155618i	0.0320488	−	0.999486i	$-0.489797\pi$
$701$	−13.3574	−	4.12021i	−0.504502	−	0.155618i	−0.536551	+	0.843868i	$0.680273\pi$
$702$	41.4612	−	28.2677i	1.56485	−	1.06690i
$703$	10.1475	−	1.52950i	0.382722	−	0.0576860i
$704$	−2.24382	+	9.83081i	−0.0845671	+	0.370513i
$705$	21.9122	+	20.3316i	0.825263	+	0.765732i
$706$	1.61114	−	21.4991i	0.0606359	−	0.809130i
$707$	−1.88244	+	4.79638i	−0.0707965	+	0.180387i
$708$	22.0039	+	3.31656i	0.826959	+	0.124644i
$709$	−26.8924	+	12.9507i	−1.00997	+	0.486374i	−0.864309	−	0.502962i	$-0.832244\pi$
$709$	−26.8924	+	12.9507i	−1.00997	+	0.486374i	−0.145656	+	0.989335i	$0.546529\pi$
$710$	64.4988	−	31.0610i	2.42060	−	1.16570i
$711$	−25.5520	−	3.85134i	−0.958275	−	0.144437i
$712$	1.10785	−	2.82277i	0.0415186	−	0.105788i
$713$	0.488431	−	6.51765i	0.0182919	−	0.244088i
$714$	31.9356	+	29.6319i	1.19516	+	1.10895i
$715$	1.58807	−	6.95780i	0.0593906	−	0.260207i
$716$	44.5106	−	6.70890i	1.66344	−	0.250723i
$717$	58.1209	−	39.6261i	2.17056	−	1.47987i
$718$	2.92251	+	0.901474i	0.109067	+	0.0336427i
$719$	0.700233	+	9.34396i	0.0261143	+	0.348471i	0.994921	+	0.100655i	$0.0320938\pi$
$719$	0.700233	+	9.34396i	0.0261143	+	0.348471i	−0.968807	+	0.247816i	$0.920287\pi$
$720$	−20.4860	+	25.6886i	−0.763467	+	0.957358i
$721$	−15.1934	+	4.68654i	−0.565832	+	0.174536i
$722$	8.08035	+	20.5884i	0.300719	+	0.766220i
$723$	−3.85278	−	16.8801i	−0.143286	−	0.627779i
$724$	−1.07904	+	1.86895i	−0.0401022	+	0.0694591i
$725$	10.3999	+	18.0132i	0.386243	+	0.668992i
$726$	47.7311	−	44.2880i	1.77147	−	1.64368i
$727$	−32.3793	−	40.6024i	−1.20088	−	1.50586i	−0.811054	−	0.584971i	$-0.801106\pi$
$727$	−32.3793	−	40.6024i	−1.20088	−	1.50586i	−0.389828	−	0.920888i	$-0.627466\pi$
$728$	7.75125	+	5.28471i	0.287280	+	0.195864i
$729$	33.6878	+	16.2232i	1.24770	+	0.600858i
$730$	−73.5654			−2.72278
$731$	−5.95447	+	21.5820i	−0.220234	+	0.798238i
$732$	−59.9792			−2.21689
$733$	14.5273	+	6.99597i	0.536577	+	0.258402i	0.682489	−	0.730896i	$-0.260897\pi$
$733$	14.5273	+	6.99597i	0.536577	+	0.258402i	−0.145912	+	0.989298i	$0.546612\pi$
$734$	−50.6529	−	34.5346i	−1.86963	−	1.27469i
$735$	14.4679	+	18.1421i	0.533655	+	0.669183i
$736$	6.87010	−	6.37452i	0.253235	−	0.234968i
$737$	−4.26278	−	7.38335i	−0.157021	−	0.271969i
$738$	−41.0796	+	71.1520i	−1.51216	+	2.61914i
$739$	−2.96821	−	13.0046i	−0.109187	−	0.478381i	−0.999725	−	0.0234707i	$-0.992528\pi$
$739$	−2.96821	−	13.0046i	−0.109187	−	0.478381i	0.890537	−	0.454911i	$-0.150329\pi$
$740$	9.25540	+	23.5824i	0.340235	+	0.866906i
$741$	26.1136	−	8.05499i	0.959308	−	0.295907i
$742$	24.1841	−	30.3259i	0.887825	−	1.11330i
$743$	0.266334	+	3.55398i	0.00977085	+	0.130383i	0.999956	−	0.00937874i	$-0.00298539\pi$
$743$	0.266334	+	3.55398i	0.00977085	+	0.130383i	−0.990185	+	0.139762i	$0.955366\pi$
$744$	−21.8518	−	6.74038i	−0.801125	−	0.247114i
$745$	−3.63358	+	2.47733i	−0.133124	+	0.0907624i
$746$	−50.3996	+	7.59652i	−1.84526	+	0.278128i
$747$	5.85772	−	25.6643i	0.214323	−	0.939009i
$748$	5.54311	+	5.14326i	0.202676	+	0.188056i
$749$	1.26706	−	16.9077i	0.0462974	−	0.617796i
$750$	−16.0327	+	40.8507i	−0.585432	+	1.49166i
$751$	0.730912	+	0.110167i	0.0266714	+	0.00402006i	0.162364	−	0.986731i	$-0.448088\pi$
$751$	0.730912	+	0.110167i	0.0266714	+	0.00402006i	−0.135693	+	0.990751i	$0.543326\pi$
$752$	7.37796	−	3.55304i	0.269046	−	0.129566i
$753$	−37.8182	+	18.2123i	−1.37817	+	0.663692i
$754$	−57.3332	−	8.64159i	−2.08795	−	0.314708i
$755$	−4.42014	+	11.2623i	−0.160865	+	0.409879i
$756$	2.96953	−	39.6256i	0.108001	−	1.44117i
$757$	−4.16657	−	3.86601i	−0.151436	−	0.140513i	0.600816	−	0.799387i	$-0.294842\pi$
$757$	−4.16657	−	3.86601i	−0.151436	−	0.140513i	−0.752253	+	0.658875i	$0.771033\pi$
$758$	−1.09562	+	4.80021i	−0.0397946	+	0.174352i
$759$	2.92052	−	0.440198i	0.106008	−	0.0159782i
$760$	9.80729	−	6.68650i	0.355748	−	0.242545i
$761$	−23.9356	−	7.38315i	−0.867665	−	0.267639i	−0.171205	−	0.985235i	$-0.554766\pi$
$761$	−23.9356	−	7.38315i	−0.867665	−	0.267639i	−0.696459	+	0.717596i	$0.745242\pi$
$762$	9.24043	+	123.305i	0.334746	+	4.46687i
$763$	7.15007	−	8.96591i	0.258850	−	0.324588i
$764$	−29.6217	+	9.13708i	−1.07168	+	0.330568i
$765$	18.7794	+	47.8492i	0.678972	+	1.72999i
$766$	−9.43171	−	41.3230i	−0.340781	−	1.49306i
$767$	−4.50049	+	7.79508i	−0.162503	+	0.281464i
$768$	0.662621	+	1.14769i	0.0239103	+	0.0414138i
$769$	−19.8037	+	18.3752i	−0.714140	+	0.662625i	−0.951096	−	0.308895i	$-0.900041\pi$
$769$	−19.8037	+	18.3752i	−0.714140	+	0.662625i	0.236956	+	0.971520i	$0.423850\pi$
$770$	−6.15454	−	7.71754i	−0.221794	−	0.278121i
$771$	43.8086	+	29.8682i	1.57773	+	1.07568i
$772$	14.1678	+	6.82284i	0.509909	+	0.245559i
$773$	31.0614			1.11720			0.558600	−	0.829437i	$-0.311339\pi$
$773$	31.0614			1.11720			0.558600	+	0.829437i	$0.311339\pi$
$774$	71.9228	−	30.7478i	2.58521	−	1.10521i
$775$	−13.0983			−0.470505
$776$	−15.9348	−	7.67379i	−0.572026	−	0.275473i
$777$	16.8859	+	11.5126i	0.605777	+	0.413012i
$778$	−0.972191	−	1.21909i	−0.0348547	−	0.0437064i
$779$	−14.9564	+	13.8775i	−0.535868	+	0.497213i
$780$	33.7312	+	58.4241i	1.20777	+	2.09192i
$781$	5.01200	−	8.68104i	0.179344	−	0.310632i
$782$	−2.01159	−	8.81337i	−0.0719345	−	0.315165i
$783$	22.7302	+	57.9156i	0.812311	+	2.06973i
$784$	6.07454	−	1.87375i	0.216948	−	0.0669195i
$785$	6.20941	−	7.78636i	0.221623	−	0.277907i
$786$	−5.71972	−	76.3243i	−0.204016	−	2.72240i
$787$	−10.8315	−	3.34108i	−0.386102	−	0.119097i	0.0956261	−	0.995417i	$-0.469515\pi$
$787$	−10.8315	−	3.34108i	−0.386102	−	0.119097i	−0.481729	+	0.876321i	$0.659991\pi$
$788$	12.2045	−	8.32087i	0.434767	−	0.296419i
$789$	−45.7432	+	6.89468i	−1.62850	+	0.245457i
$790$	6.15711	−	26.9761i	0.219060	−	0.959766i
$791$	−26.5961	−	24.6776i	−0.945650	−	0.877435i
$792$	0.500153	−	6.67408i	0.0177722	−	0.237153i
$793$	8.86360	−	22.5841i	0.314756	−	0.801985i
$794$	−17.9531	−	2.70599i	−0.637131	−	0.0960320i
$795$	63.6649	−	30.6594i	2.25796	−	1.08738i
$796$	−47.4332	+	22.8426i	−1.68123	+	0.809636i
$797$	10.6905	+	1.61133i	0.378675	+	0.0570761i	0.335622	−	0.941997i	$-0.391053\pi$
$797$	10.6905	+	1.61133i	0.378675	+	0.0570761i	0.0430532	+	0.999073i	$0.486292\pi$
$798$	13.8092	−	35.1852i	0.488840	−	1.24554i
$799$	0.957367	−	12.7752i	0.0338692	−	0.451953i
$800$	−13.7680	−	12.7748i	−0.486772	−	0.451658i
$801$	2.53527	−	11.1078i	0.0895794	−	0.392473i
$802$	61.1305	−	9.21394i	2.15859	−	0.325355i
$803$	−8.51096	+	5.80268i	−0.300345	+	0.204772i
$804$	77.0103	+	23.7545i	2.71594	+	0.837757i
$805$	0.504896	+	6.73737i	0.0177953	+	0.237461i
$806$	22.7651	−	28.5465i	0.801866	−	1.00551i
$807$	−29.4783	+	9.09284i	−1.03768	+	0.320083i
$808$	−1.36668	−	3.48224i	−0.0480796	−	0.122505i
$809$	8.65541	+	37.9218i	0.304308	+	1.33326i	0.863553	+	0.504258i	$0.168234\pi$
$809$	8.65541	+	37.9218i	0.304308	+	1.33326i	−0.559245	+	0.829002i	$0.688909\pi$
$810$	14.3734	−	24.8954i	0.505029	−	0.874736i
$811$	−2.39529	−	4.14876i	−0.0841100	−	0.145683i	0.820902	−	0.571070i	$-0.193471\pi$
$811$	−2.39529	−	4.14876i	−0.0841100	−	0.145683i	−0.905012	+	0.425387i	$0.860138\pi$
$812$	−33.6570	+	31.2291i	−1.18113	+	1.09593i
$813$	3.23063	+	4.05109i	0.113303	+	0.142078i
$814$	5.11931	+	3.49029i	0.179432	+	0.122335i
$815$	−18.9524	−	9.12701i	−0.663875	−	0.319705i
$816$	21.7422			0.761131
$817$	19.3180	−	2.03190i	0.675851	−	0.0710871i
$818$	22.9540			0.802569
$819$	31.7575	+	15.2936i	1.10970	+	0.534401i
$820$	−41.6156	−	28.3730i	−1.45328	−	0.990828i
$821$	−32.6933	−	40.9962i	−1.14101	−	1.43078i	−0.885908	−	0.463860i	$-0.846464\pi$
$821$	−32.6933	−	40.9962i	−1.14101	−	1.43078i	−0.255097	−	0.966915i	$-0.582107\pi$
$822$	−27.5959	+	25.6053i	−0.962518	+	0.893086i
$823$	4.68633	+	8.11696i	0.163355	+	0.282940i	0.936070	−	0.351814i	$-0.114435\pi$
$823$	4.68633	+	8.11696i	0.163355	+	0.282940i	−0.772715	+	0.634753i	$0.781102\pi$
$824$	5.77173	−	9.99693i	0.201068	−	0.348260i
$825$	−1.31709	−	5.77056i	−0.0458553	−	0.200905i
$826$	4.54836	+	11.5890i	0.158258	+	0.403234i
$827$	−45.0728	+	13.9031i	−1.56733	+	0.483459i	−0.952331	−	0.305066i	$-0.901322\pi$
$827$	−45.0728	+	13.9031i	−1.56733	+	0.483459i	−0.615003	+	0.788524i	$0.710845\pi$
$828$	−11.2741	+	14.1373i	−0.391803	+	0.491306i
$829$	0.496542	+	6.62590i	0.0172456	+	0.230127i	0.999166	+	0.0408325i	$0.0130010\pi$
$829$	0.496542	+	6.62590i	0.0172456	+	0.230127i	−0.981920	+	0.189294i	$0.939380\pi$
$830$	26.9355	+	8.30849i	0.934944	+	0.288392i
$831$	−4.50431	+	3.07099i	−0.156253	+	0.106531i
$832$	38.1252	−	5.74645i	1.32175	−	0.199222i
$833$	2.21298	−	9.69568i	0.0766751	−	0.335935i
$834$	−14.3848	−	13.3471i	−0.498104	−	0.462173i
$835$	−1.00405	+	13.3981i	−0.0347465	+	0.463660i
$836$	2.39688	−	6.10716i	0.0828979	−	0.211220i
$837$	−38.7421	−	5.83943i	−1.33912	−	0.201840i
$838$	−37.4114	+	18.0164i	−1.29235	+	0.622365i
$839$	20.9640	−	10.0957i	0.723757	−	0.348543i	−0.0354681	−	0.999371i	$-0.511292\pi$
$839$	20.9640	−	10.0957i	0.723757	−	0.348543i	0.759226	+	0.650828i	$0.225578\pi$
$840$	23.3746	+	3.52315i	0.806500	+	0.121560i
$841$	15.6685	−	39.9228i	0.540294	−	1.37665i
$842$	4.83202	−	64.4788i	0.166522	−	2.22209i
$843$	−11.6554	−	10.8146i	−0.401432	−	0.372474i
$844$	−10.3810	+	45.4823i	−0.357330	+	1.56557i
$845$	8.11101	−	1.22254i	0.279027	−	0.0420566i
$846$	−36.9813	+	25.2134i	−1.27144	+	0.866856i
$847$	19.9296	+	6.14747i	0.684789	+	0.211230i
$848$	−1.44664	−	19.3040i	−0.0496777	−	0.662903i
$849$	−17.2322	+	21.6084i	−0.591406	+	0.741600i
$850$	−17.3117	+	5.33997i	−0.593788	+	0.183159i
$851$	−1.54933	−	3.94764i	−0.0531105	−	0.135323i
$852$	21.0850	+	92.3796i	0.722361	+	3.16487i
$853$	−22.6689	+	39.2637i	−0.776168	+	1.34436i	0.157968	+	0.987444i	$0.449506\pi$
$853$	−22.6689	+	39.2637i	−0.776168	+	1.34436i	−0.934136	+	0.356918i	$0.883828\pi$
$854$	−16.7783	−	29.0609i	−0.574142	−	0.994443i
$855$	32.6925	−	30.3342i	1.11806	−	1.03741i
$856$	7.67496	+	9.62409i	0.262325	+	0.328945i
$857$	24.0494	+	16.3966i	0.821511	+	0.560097i	0.899532	−	0.436855i	$-0.143908\pi$
$857$	24.0494	+	16.3966i	0.821511	+	0.560097i	−0.0780208	+	0.996952i	$0.524860\pi$
$858$	14.8655	+	7.15886i	0.507501	+	0.244400i
$859$	34.6694			1.18290			0.591452	−	0.806340i	$-0.298555\pi$
$859$	34.6694			1.18290			0.591452	+	0.806340i	$0.298555\pi$
$860$	15.5021	+	45.3774i	0.528618	+	1.54736i
$861$	−40.6322			−1.38474
$862$	39.6421	+	19.0906i	1.35022	+	0.650229i
$863$	−8.65784	−	5.90282i	−0.294716	−	0.200934i	0.406930	−	0.913459i	$-0.366599\pi$
$863$	−8.65784	−	5.90282i	−0.294716	−	0.200934i	−0.701647	+	0.712525i	$0.747552\pi$
$864$	−35.0276	−	43.9233i	−1.19166	−	1.49430i
$865$	43.1523	−	40.0394i	1.46722	−	1.36138i
$866$	−29.8399	−	51.6842i	−1.01400	−	1.75630i
$867$	−7.79589	+	13.5029i	−0.264762	+	0.458582i
$868$	−6.43380	−	28.1883i	−0.218377	−	0.956774i
$869$	−1.41548	−	3.60659i	−0.0480169	−	0.122345i
$870$	−139.606	+	43.0627i	−4.73309	+	1.45996i
$871$	−20.3248	+	25.4864i	−0.688678	+	0.863575i
$872$	0.622188	+	8.30252i	0.0210699	+	0.281159i
$873$	−63.4995	−	19.5870i	−2.14913	−	0.662919i
$874$	−6.48044	+	4.41829i	−0.219204	+	0.149451i
$875$	−13.8995	+	2.09501i	−0.469888	+	0.0708243i
$876$	21.6674	−	94.9309i	0.732072	−	3.20742i
$877$	8.34914	+	7.74687i	0.281930	+	0.261593i	0.808443	−	0.588574i	$-0.200310\pi$
$877$	8.34914	+	7.74687i	0.281930	+	0.261593i	−0.526513	+	0.850167i	$0.676501\pi$
$878$	4.15165	−	55.3999i	0.140111	−	1.86966i
$879$	−10.1939	+	25.9736i	−0.343831	+	0.876067i
$880$	−4.87138	−	0.734242i	−0.164214	−	0.0247513i
$881$	−5.10037	+	2.45621i	−0.171836	+	0.0827518i	−0.517824	−	0.855487i	$-0.673258\pi$
$881$	−5.10037	+	2.45621i	−0.171836	+	0.0827518i	0.345988	+	0.938239i	$0.387544\pi$
$882$	−31.3047	+	15.0756i	−1.05408	+	0.507620i
$883$	15.4143	+	2.32333i	0.518732	+	0.0781863i	0.403190	−	0.915116i	$-0.367901\pi$
$883$	15.4143	+	2.32333i	0.518732	+	0.0781863i	0.115542	+	0.993303i	$0.463139\pi$
$884$	10.5631	−	26.9143i	0.355275	−	0.905226i
$885$	−1.69489	+	22.6167i	−0.0569731	+	0.760253i
$886$	0.441641	+	0.409783i	0.0148372	+	0.0137669i
$887$	3.43965	−	15.0701i	0.115492	−	0.506004i	−0.883782	−	0.467900i	$-0.845011\pi$
$887$	3.43965	−	15.0701i	0.115492	−	0.506004i	0.999274	−	0.0381046i	$-0.0121320\pi$
$888$	−14.6718	+	2.21142i	−0.492355	+	0.0742105i
$889$	−32.7243	+	22.3110i	−1.09754	+	0.748288i
$890$	11.6579	+	3.59599i	0.390774	+	0.120538i
$891$	−0.300804	−	4.01395i	−0.0100773	−	0.134473i
$892$	−25.2311	+	31.6388i	−0.844801	+	1.05935i
$893$	−10.6213	+	3.27622i	−0.355427	+	0.109635i
$894$	−3.71448	−	9.46435i	−0.124231	−	0.316535i
$895$	10.2089	+	44.7282i	0.341247	+	1.49510i
$896$	11.1861	−	19.3749i	0.373702	−	0.647272i
$897$	−5.64653	−	9.78007i	−0.188532	−	0.326547i
$898$	21.4414	−	19.8947i	0.715507	−	0.663894i
$899$	28.2253	+	35.3934i	0.941366	+	1.18044i
$900$	29.9410	+	20.4135i	0.998035	+	0.680449i
$901$	−27.2854	−	13.1400i	−0.909009	−	0.437756i
$902$	−12.3185			−0.410163
$903$	30.9541	+	23.2011i	1.03009	+	0.772083i
$904$	26.3408			0.876081
$905$	−1.98173	−	0.954352i	−0.0658750	−	0.0317237i
$906$	−23.1108	−	15.7567i	−0.767804	−	0.523480i
$907$	30.3903	+	38.1082i	1.00909	+	1.26536i	0.963867	+	0.266385i	$0.0858294\pi$
$907$	30.3903	+	38.1082i	1.00909	+	1.26536i	0.0452260	+	0.998977i	$0.485599\pi$
$908$	24.6220	−	22.8459i	0.817110	−	0.758167i
$909$	−7.02761	−	12.1722i	−0.233091	−	0.403726i
$910$	−18.8716	+	32.6866i	−0.625588	+	1.08355i
$911$	2.90180	+	12.7136i	0.0961408	+	0.421220i	0.999978	−	0.00665648i	$-0.00211884\pi$
$911$	2.90180	+	12.7136i	0.0961408	+	0.421220i	−0.903837	+	0.427877i	$0.859262\pi$
$912$	−6.89179	−	17.5600i	−0.228210	−	0.581470i
$913$	3.77159	−	1.16338i	0.124821	−	0.0385023i
$914$	23.1927	−	29.0827i	0.767146	−	0.961971i
$915$	−4.56839	−	60.9610i	−0.151026	−	2.01531i
$916$	52.1042	+	16.0720i	1.72157	+	0.531034i
$917$	20.2559	−	13.8103i	0.668910	−	0.456055i
$918$	−53.5852	+	8.07667i	−1.76857	+	0.266570i
$919$	−4.83091	+	21.1656i	−0.159357	+	0.698189i	0.830606	+	0.556861i	$0.187994\pi$
$919$	−4.83091	+	21.1656i	−0.159357	+	0.698189i	−0.989963	+	0.141328i	$0.954863\pi$
$920$	−3.59572	−	3.33634i	−0.118547	−	0.109996i
$921$	3.90871	−	52.1581i	0.128796	−	1.71867i
$922$	2.56834	−	6.54403i	0.0845839	−	0.215516i
$923$	−37.8998	−	5.71247i	−1.24749	−	0.188028i
$924$	11.7716	−	5.66892i	0.387259	−	0.186494i
$925$	−7.65710	+	3.68746i	−0.251764	+	0.121243i
$926$	72.9968	+	11.0025i	2.39882	+	0.361565i
$927$	15.8454	−	40.3735i	0.520433	−	1.32604i
$928$	−4.85093	+	64.7312i	−0.159240	+	2.12490i
$929$	23.6472	+	21.9414i	0.775839	+	0.719873i	0.965051	−	0.262063i	$-0.0844029\pi$
$929$	23.6472	+	21.9414i	0.775839	+	0.719873i	−0.189212	+	0.981936i	$0.560593\pi$
$930$	20.4723	−	89.6951i	0.671314	−	2.94122i
$931$	−8.53212	+	1.28601i	−0.279629	+	0.0421473i
$932$	−65.3499	+	44.5548i	−2.14061	+	1.45944i
$933$	−34.7680	−	10.7245i	−1.13825	−	0.351105i
$934$	5.60508	+	74.7946i	0.183404	+	2.44735i
$935$	−4.80525	+	6.02559i	−0.157148	+	0.197058i
$936$	−24.4537	+	7.54297i	−0.799294	+	0.246550i
$937$	−4.03376	−	10.2779i	−0.131777	−	0.335763i	0.849721	−	0.527232i	$-0.176770\pi$
$937$	−4.03376	−	10.2779i	−0.131777	−	0.335763i	−0.981499	+	0.191469i	$0.938675\pi$
$938$	10.0331	+	43.9577i	0.327591	+	1.43527i
$939$	38.2066	−	66.1758i	1.24683	−	2.15957i
$940$	−13.7196	−	23.7630i	−0.447483	−	0.775063i
$941$	24.4771	−	22.7114i	0.797931	−	0.740372i	−0.171646	−	0.985159i	$-0.554908\pi$
$941$	24.4771	−	22.7114i	0.797931	−	0.740372i	0.969577	+	0.244787i	$0.0787180\pi$
$942$	14.3556	+	18.0014i	0.467731	+	0.586516i
$943$	6.96635	+	4.74958i	0.226856	+	0.154668i
$944$	5.59796	+	2.69584i	0.182198	+	0.0877420i
$945$	40.5005			1.31748
$946$	9.38439	+	7.03391i	0.305113	+	0.228692i
$947$	14.9637			0.486256			0.243128	−	0.969994i	$-0.421827\pi$
$947$	14.9637			0.486256			0.243128	+	0.969994i	$0.421827\pi$
$948$	32.9972	+	15.8906i	1.07170	+	0.516104i
$949$	32.5426	+	22.1872i	1.05638	+	0.720226i
$950$	9.80022	+	12.2891i	0.317961	+	0.398711i
$951$	19.3592	−	17.9627i	0.627764	−	0.582480i
$952$	−5.06551	−	8.77372i	−0.164174	−	0.284358i
$953$	−10.3374	+	17.9049i	−0.334862	+	0.579997i	−0.983458	−	0.181135i	$-0.942023\pi$
$953$	−10.3374	+	17.9049i	−0.334862	+	0.579997i	0.648597	+	0.761132i	$0.275356\pi$
$954$	23.5443	+	103.154i	0.762274	+	3.33974i
$955$	−11.5428	−	29.4106i	−0.373517	−	0.951706i
$956$	−61.7033	+	19.0330i	−1.99563	+	0.615570i
$957$	−12.7547	+	15.9938i	−0.412300	+	0.517007i
$958$	−1.24850	−	16.6600i	−0.0403371	−	0.538261i
$959$	−11.5224	−	3.55418i	−0.372077	−	0.114770i
$960$	80.2698	−	54.7270i	2.59070	−	1.76631i
$961$	2.46429	−	0.371432i	0.0794932	−	0.0119817i
$962$	5.27169	−	23.0968i	0.169966	−	0.744671i
$963$	33.9040	+	31.4583i	1.09254	+	1.01373i
$964$	−1.18773	+	15.8491i	−0.0382542	+	0.510466i
$965$	−5.85542	+	14.9194i	−0.188492	+	0.480271i
$966$	−15.4454	−	2.32802i	−0.496948	−	0.0749029i
$967$	9.85181	−	4.74438i	0.316813	−	0.152569i	−0.268719	−	0.963219i	$-0.586600\pi$
$967$	9.85181	−	4.74438i	0.316813	−	0.152569i	0.585531	+	0.810650i	$0.300886\pi$
$968$	−13.6424	+	6.56981i	−0.438482	+	0.211162i
$969$	−29.1818	−	4.39845i	−0.937455	−	0.141299i
$970$	25.9961	−	66.2370i	0.834684	−	2.12674i
$971$	−1.61481	+	21.5482i	−0.0518218	+	0.691513i	0.909433	+	0.415851i	$0.136516\pi$
$971$	−1.61481	+	21.5482i	−0.0518218	+	0.691513i	−0.961255	+	0.275662i	$0.911103\pi$
$972$	−15.3330	−	14.2269i	−0.491805	−	0.456328i
$973$	1.39864	−	6.12785i	0.0448384	−	0.196450i
$974$	−49.3645	+	7.44050i	−1.58174	+	0.238409i
$975$	−18.6993	+	12.7489i	−0.598856	+	0.408293i
$976$	−16.0032	−	4.93632i	−0.512249	−	0.158008i
$977$	0.119768	+	1.59820i	0.00383172	+	0.0511308i	0.998792	−	0.0491401i	$-0.0156481\pi$
$977$	0.119768	+	1.59820i	0.00383172	+	0.0511308i	−0.994960	+	0.100271i	$0.968029\pi$
$978$	30.3218	−	38.0224i	0.969586	−	1.21582i
$979$	1.63238	−	0.503521i	0.0521710	−	0.0160926i
$980$	−7.78201	−	19.8282i	−0.248587	−	0.633390i
$981$	6.96092	+	30.4978i	0.222245	+	0.973719i
$982$	−10.6665	+	18.4749i	−0.340382	+	0.589558i
$983$	0.512227	+	0.887204i	0.0163375	+	0.0282974i	0.874079	−	0.485785i	$-0.161466\pi$
$983$	0.512227	+	0.887204i	0.0163375	+	0.0282974i	−0.857741	+	0.514082i	$0.828133\pi$
$984$	21.6247	−	20.0648i	0.689371	−	0.639642i
$985$	9.38665	+	11.7705i	0.299083	+	0.375039i
$986$	51.7341	+	35.2717i	1.64755	+	1.12328i
$987$	−19.9435	−	9.60427i	−0.634808	−	0.305707i
$988$	−25.0854			−0.798074
$989$	−2.59502	−	7.59608i	−0.0825169	−	0.241541i
$990$	26.9265			0.855782
$991$	−13.1752	−	6.34486i	−0.418525	−	0.201551i	0.212756	−	0.977105i	$-0.431756\pi$
$991$	−13.1752	−	6.34486i	−0.418525	−	0.201551i	−0.631281	+	0.775554i	$0.717470\pi$
$992$	−33.7747	−	23.0272i	−1.07235	−	0.731114i
$993$	6.35870	+	7.97355i	0.201787	+	0.253033i
$994$	−38.8611	+	36.0579i	−1.23260	+	1.14369i
$995$	−26.8294	−	46.4698i	−0.850548	−	1.47319i
$996$	−18.6549	+	32.3112i	−0.591102	+	1.02382i
$997$	−0.782739	−	3.42941i	−0.0247896	−	0.108610i	0.961019	−	0.276481i	$-0.0891682\pi$
$997$	−0.782739	−	3.42941i	−0.0247896	−	0.108610i	−0.985809	+	0.167870i	$0.946311\pi$
$998$	32.6737	+	83.2514i	1.03427	+	2.63528i
$999$	−24.2920	+	7.49310i	−0.768566	+	0.237071i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.2.g.a.25.3	✓	36
3.2	odd	2		387.2.y.c.154.1		36
4.3	odd	2		688.2.bg.c.369.3		36
43.17	even	21		1849.2.a.n.1.4		18
43.26	odd	42		1849.2.a.o.1.15		18
43.31	even	21	inner	43.2.g.a.31.3	yes	36
129.74	odd	42		387.2.y.c.289.1		36
172.31	odd	42		688.2.bg.c.289.3		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.2.g.a.25.3	✓	36	1.1	even	1	trivial
43.2.g.a.31.3	yes	36	43.31	even	21	inner
387.2.y.c.154.1		36	3.2	odd	2
387.2.y.c.289.1		36	129.74	odd	42
688.2.bg.c.289.3		36	172.31	odd	42
688.2.bg.c.369.3		36	4.3	odd	2
1849.2.a.n.1.4		18	43.17	even	21
1849.2.a.o.1.15		18	43.26	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)

\(f(q)\)	\(=\)	\(q+(1.94880 + 0.938491i) q^{2} +(-2.41097 - 1.64377i) q^{3} +(1.67006 + 2.09419i) q^{4} +(-2.00127 + 1.85691i) q^{5} +(-3.15582 - 5.46604i) q^{6} +(1.01083 - 1.75082i) q^{7} +(0.326607 + 1.43096i) q^{8} +(2.01476 + 5.13352i) q^{9} +O(q^{10})\)	\(q+(1.94880 + 0.938491i) q^{2} +(-2.41097 - 1.64377i) q^{3} +(1.67006 + 2.09419i) q^{4} +(-2.00127 + 1.85691i) q^{5} +(-3.15582 - 5.46604i) q^{6} +(1.01083 - 1.75082i) q^{7} +(0.326607 + 1.43096i) q^{8} +(2.01476 + 5.13352i) q^{9} +(-5.64276 + 1.74056i) q^{10} +(-0.515533 + 0.646459i) q^{11} +(-0.584097 - 7.79423i) q^{12} +(3.02110 + 0.931885i) q^{13} +(3.61304 - 2.46333i) q^{14} +(7.87733 - 1.18732i) q^{15} +(0.485626 - 2.12767i) q^{16} +(-2.50278 - 2.32224i) q^{17} +(-0.891409 + 11.8950i) q^{18} +(-1.08222 + 2.75745i) q^{19} +(-7.23098 - 1.08990i) q^{20} +(-5.31503 + 2.55958i) q^{21} +(-1.61137 + 0.775993i) q^{22} +(1.21045 + 0.182446i) q^{23} +(1.56473 - 3.98686i) q^{24} +(0.183328 - 2.44634i) q^{25} +(5.01294 + 4.65133i) q^{26} +(1.63286 - 7.15403i) q^{27} +(5.35471 - 0.807093i) q^{28} +(-7.00539 + 4.77619i) q^{29} +(16.4656 + 5.07896i) q^{30} +(-0.399005 - 5.32435i) q^{31} +(4.77345 - 5.98572i) q^{32} +(2.30556 - 0.711172i) q^{33} +(-2.69801 - 6.87441i) q^{34} +(1.22815 + 5.38089i) q^{35} +(-7.38582 + 12.7926i) q^{36} +(-1.73217 - 3.00021i) q^{37} +(-4.69687 + 4.35806i) q^{38} +(-5.75196 - 7.21273i) q^{39} +(-3.31079 - 2.25726i) q^{40} +(6.20561 + 2.98847i) q^{41} -12.7601 q^{42} +(-3.02108 - 5.82006i) q^{43} -2.21478 q^{44} +(-13.5646 - 6.53235i) q^{45} +(2.18770 + 1.49155i) q^{46} +(2.33951 + 2.93365i) q^{47} +(-4.66822 + 4.33148i) q^{48} +(1.45643 + 2.52260i) q^{49} +(2.65314 - 4.59537i) q^{50} +(2.21689 + 9.71283i) q^{51} +(3.09388 + 7.88307i) q^{52} +(8.47611 - 2.61454i) q^{53} +(9.89611 - 12.4093i) q^{54} +(-0.168692 - 2.25104i) q^{55} +(2.83550 + 0.874635i) q^{56} +(7.14181 - 4.86920i) q^{57} +(-18.1345 + 2.73333i) q^{58} +(-0.633519 + 2.77563i) q^{59} +(15.6421 + 14.5138i) q^{60} +(0.573465 - 7.65235i) q^{61} +(4.21927 - 10.7505i) q^{62} +(11.0245 + 1.66167i) q^{63} +(10.9875 - 5.29131i) q^{64} +(-7.77646 + 3.74495i) q^{65} +(5.16050 + 0.777821i) q^{66} +(-3.76698 + 9.59812i) q^{67} +(0.683419 - 9.11959i) q^{68} +(-2.61846 - 2.42957i) q^{69} +(-2.65650 + 11.6389i) q^{70} +(-11.9877 + 1.80685i) q^{71} +(-6.68783 + 4.55969i) q^{72} +(11.9045 + 3.67204i) q^{73} +(-0.559982 - 7.47244i) q^{74} +(-4.46321 + 5.59669i) q^{75} +(-7.58201 + 2.33874i) q^{76} +(0.610712 + 1.55607i) q^{77} +(-4.44032 - 19.4543i) q^{78} +(-2.34287 + 4.05797i) q^{79} +(2.97901 + 5.15980i) q^{80} +(-3.56858 + 3.31116i) q^{81} +(9.28883 + 11.6478i) q^{82} +(-3.94401 - 2.68898i) q^{83} +(-14.2367 - 6.85604i) q^{84} +9.32092 q^{85} +(-0.425398 - 14.1774i) q^{86} +24.7407 q^{87} +(-1.09343 - 0.526570i) q^{88} +(-1.70700 - 1.16382i) q^{89} +(-20.3040 - 25.4605i) q^{90} +(4.68539 - 4.34741i) q^{91} +(1.63945 + 2.83962i) q^{92} +(-7.79001 + 13.4927i) q^{93} +(1.80602 + 7.91270i) q^{94} +(-2.95452 - 7.52799i) q^{95} +(-21.3478 + 6.58491i) q^{96} +(-7.51296 + 9.42095i) q^{97} +(0.470837 + 6.28288i) q^{98} +(-4.35729 - 1.34404i) 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

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