LMFDB - Embedded newform 637.2.bl.b.53.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(53,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([10, 0]))

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

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

chi := DirichletCharacter("637.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bl (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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$348$
Relative dimension:	$29$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			53.16
Character	$\chi$	$=$	637.53
Dual form			637.2.bl.b.625.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.371774 + 0.253471i) q^{2} +(-0.182364 - 0.169209i) q^{3} +(-0.656714 - 1.67328i) q^{4} +(3.18926 - 0.983757i) q^{5} +(-0.0249085 - 0.109131i) q^{6} +(2.51832 - 0.811213i) q^{7} +(0.380230 - 1.66590i) q^{8} +(-0.219565 - 2.92990i) q^{9} +O(q^{10})$	\(q+(0.371774 + 0.253471i) q^{2} +(-0.182364 - 0.169209i) q^{3} +(-0.656714 - 1.67328i) q^{4} +(3.18926 - 0.983757i) q^{5} +(-0.0249085 - 0.109131i) q^{6} +(2.51832 - 0.811213i) q^{7} +(0.380230 - 1.66590i) q^{8} +(-0.219565 - 2.92990i) q^{9} +(1.43504 + 0.442650i) q^{10} +(-0.272444 + 3.63551i) q^{11} +(-0.163373 + 0.416267i) q^{12} +(-0.900969 + 0.433884i) q^{13} +(1.14186 + 0.336734i) q^{14} +(-0.748066 - 0.360250i) q^{15} +(-2.07176 + 1.92231i) q^{16} +(0.940735 - 0.141793i) q^{17} +(0.661015 - 1.14491i) q^{18} +(-0.376207 - 0.651609i) q^{19} +(-3.74053 - 4.69048i) q^{20} +(-0.596515 - 0.278186i) q^{21} +(-1.02279 + 1.28253i) q^{22} +(-6.41865 - 0.967456i) q^{23} +(-0.351224 + 0.239461i) q^{24} +(5.07241 - 3.45831i) q^{25} +(-0.444934 - 0.0670630i) q^{26} +(-0.921047 + 1.15496i) q^{27} +(-3.01120 - 3.68112i) q^{28} +(2.15036 + 2.69646i) q^{29} +(-0.186798 - 0.323544i) q^{30} +(1.78101 - 3.08479i) q^{31} +(-4.63678 + 0.698882i) q^{32} +(0.664845 - 0.616886i) q^{33} +(0.385681 + 0.185734i) q^{34} +(7.23354 - 5.06458i) q^{35} +(-4.75834 + 2.29150i) q^{36} +(1.37154 - 3.49463i) q^{37} +(0.0253003 - 0.337609i) q^{38} +(0.237721 + 0.0733272i) q^{39} +(-0.426184 - 5.68703i) q^{40} +(-0.462122 + 2.02469i) q^{41} +(-0.151256 - 0.254622i) q^{42} +(2.64853 + 11.6040i) q^{43} +(6.26215 - 1.93162i) q^{44} +(-3.58256 - 9.12821i) q^{45} +(-2.14106 - 1.98662i) q^{46} +(10.0819 + 6.87372i) q^{47} +0.703086 q^{48} +(5.68387 - 4.08579i) q^{49} +2.76237 q^{50} +(-0.195549 - 0.133323i) q^{51} +(1.31769 + 1.22264i) q^{52} +(-1.70342 - 4.34024i) q^{53} +(-0.635169 + 0.195924i) q^{54} +(2.70757 + 11.8626i) q^{55} +(-0.393856 - 4.50370i) q^{56} +(-0.0416516 + 0.182487i) q^{57} +(0.115971 + 1.54753i) q^{58} +(-7.49100 - 2.31067i) q^{59} +(-0.111533 + 1.48830i) q^{60} +(1.58485 - 4.03814i) q^{61} +(1.44404 - 0.695412i) q^{62} +(-2.92971 - 7.20030i) q^{63} +(3.19168 + 1.53703i) q^{64} +(-2.44659 + 2.27010i) q^{65} +(0.403535 - 0.0608231i) q^{66} +(5.91404 - 10.2434i) q^{67} +(-0.855053 - 1.48099i) q^{68} +(1.00683 + 1.26252i) q^{69} +(3.97297 - 0.0493856i) q^{70} +(-0.194644 + 0.244076i) q^{71} +(-4.96439 - 0.748261i) q^{72} +(-3.94854 + 2.69207i) q^{73} +(1.39569 - 0.951565i) q^{74} +(-1.51020 - 0.227626i) q^{75} +(-0.843265 + 1.05742i) q^{76} +(2.26307 + 9.37640i) q^{77} +(0.0697921 + 0.0875166i) q^{78} +(3.46430 + 6.00034i) q^{79} +(-4.71629 + 8.16886i) q^{80} +(-8.35249 + 1.25894i) q^{81} +(-0.685005 + 0.635592i) q^{82} +(-13.7687 - 6.63067i) q^{83} +(-0.0737438 + 1.18082i) q^{84} +(2.86076 - 1.37767i) q^{85} +(-1.95662 + 4.98538i) q^{86} +(0.0641181 - 0.855596i) q^{87} +(5.95280 + 1.83619i) q^{88} +(0.448266 + 5.98169i) q^{89} +(0.981835 - 4.30170i) q^{90} +(-1.91696 + 1.82354i) q^{91} +(2.59639 + 11.3755i) q^{92} +(-0.846765 + 0.261192i) q^{93} +(2.00590 + 5.11094i) q^{94} +(-1.84085 - 1.70806i) q^{95} +(0.963838 + 0.657133i) q^{96} +7.46151 q^{97} +(3.14874 - 0.0782923i) q^{98} +10.7115 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9}+O(q^{10}) $ 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9	\( 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9} - 5 q^{10} + 2 q^{11} - 40 q^{12} - 58 q^{13} - 45 q^{14} - 14 q^{15} + 27 q^{16} - 12 q^{17} - 59 q^{18} - 24 q^{19} - 99 q^{20} - 2 q^{21} - 10 q^{22} - 14 q^{23} + 28 q^{25} + 3 q^{26} - 9 q^{27} - 37 q^{28} - 26 q^{29} - 83 q^{30} - 49 q^{31} + 33 q^{32} + 2 q^{33} - 130 q^{34} - 38 q^{35} - 74 q^{36} - 4 q^{37} + 92 q^{38} + 24 q^{40} + 20 q^{41} - 52 q^{42} + 2 q^{43} + 226 q^{44} - 23 q^{45} + 71 q^{46} + 24 q^{47} + 86 q^{48} + 25 q^{49} + 114 q^{50} - 54 q^{51} + 31 q^{52} + 36 q^{53} + 75 q^{54} + 38 q^{55} + 126 q^{56} + 27 q^{57} - 33 q^{58} + q^{59} - 179 q^{60} - 15 q^{61} + 158 q^{62} - 5 q^{63} - 24 q^{64} + q^{65} - 150 q^{66} - 151 q^{67} + 140 q^{68} - 98 q^{69} - 126 q^{70} - 31 q^{71} - 149 q^{72} - 9 q^{73} + 39 q^{74} + 85 q^{75} - 81 q^{76} + 46 q^{77} - 25 q^{78} - 69 q^{79} - 64 q^{80} + 71 q^{81} - 52 q^{82} - q^{83} - 47 q^{84} + 62 q^{85} + 97 q^{86} + 150 q^{87} - 12 q^{88} + 23 q^{89} + 107 q^{90} - q^{91} - 43 q^{92} + 316 q^{93} - 86 q^{94} - 29 q^{95} + 177 q^{96} + 114 q^{97} - 336 q^{98} + 102 q^{99}+O(q^{100}) \) 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9 - 5 * q^10 + 2 * q^11 - 40 * q^12 - 58 * q^13 - 45 * q^14 - 14 * q^15 + 27 * q^16 - 12 * q^17 - 59 * q^18 - 24 * q^19 - 99 * q^20 - 2 * q^21 - 10 * q^22 - 14 * q^23 + 28 * q^25 + 3 * q^26 - 9 * q^27 - 37 * q^28 - 26 * q^29 - 83 * q^30 - 49 * q^31 + 33 * q^32 + 2 * q^33 - 130 * q^34 - 38 * q^35 - 74 * q^36 - 4 * q^37 + 92 * q^38 + 24 * q^40 + 20 * q^41 - 52 * q^42 + 2 * q^43 + 226 * q^44 - 23 * q^45 + 71 * q^46 + 24 * q^47 + 86 * q^48 + 25 * q^49 + 114 * q^50 - 54 * q^51 + 31 * q^52 + 36 * q^53 + 75 * q^54 + 38 * q^55 + 126 * q^56 + 27 * q^57 - 33 * q^58 + q^59 - 179 * q^60 - 15 * q^61 + 158 * q^62 - 5 * q^63 - 24 * q^64 + q^65 - 150 * q^66 - 151 * q^67 + 140 * q^68 - 98 * q^69 - 126 * q^70 - 31 * q^71 - 149 * q^72 - 9 * q^73 + 39 * q^74 + 85 * q^75 - 81 * q^76 + 46 * q^77 - 25 * q^78 - 69 * q^79 - 64 * q^80 + 71 * q^81 - 52 * q^82 - q^83 - 47 * q^84 + 62 * q^85 + 97 * q^86 + 150 * q^87 - 12 * q^88 + 23 * q^89 + 107 * q^90 - q^91 - 43 * q^92 + 316 * q^93 - 86 * q^94 - 29 * q^95 + 177 * q^96 + 114 * q^97 - 336 * q^98 + 102 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$1$	$e\left(\frac{5}{21}\right)$

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 $

$2$	0.371774	+	0.253471i	0.262884	+	0.179231i	0.687588	−	0.726101i	$-0.258670\pi$
$2$	0.371774	+	0.253471i	0.262884	+	0.179231i	−0.424704	+	0.905332i	$0.639622\pi$
$3$	−0.182364	−	0.169209i	−0.105288	−	0.0976928i	0.625773	−	0.780006i	$-0.284784\pi$
$3$	−0.182364	−	0.169209i	−0.105288	−	0.0976928i	−0.731060	+	0.682313i	$0.760974\pi$
$4$	−0.656714	−	1.67328i	−0.328357	−	0.836640i
$5$	3.18926	−	0.983757i	1.42628	−	0.439949i	0.516947	−	0.856017i	$-0.327068\pi$
$5$	3.18926	−	0.983757i	1.42628	−	0.439949i	0.909334	+	0.416068i	$0.136592\pi$
$6$	−0.0249085	−	0.109131i	−0.0101689	−	0.0445527i
$7$	2.51832	−	0.811213i	0.951835	−	0.306610i
$7$	2.51832	−	0.811213i	0.951835	−	0.306610i
$8$	0.380230	−	1.66590i	0.134432	−	0.588983i
$9$	−0.219565	−	2.92990i	−0.0731885	−	0.976632i
$10$	1.43504	+	0.442650i	0.453799	+	0.139978i
$11$	−0.272444	+	3.63551i	−0.0821450	+	1.09615i	0.792012	+	0.610506i	$0.209034\pi$
$11$	−0.272444	+	3.63551i	−0.0821450	+	1.09615i	−0.874157	+	0.485643i	$0.838585\pi$
$12$	−0.163373	+	0.416267i	−0.0471617	+	0.120166i
$13$	−0.900969	+	0.433884i	−0.249884	+	0.120338i
$13$	−0.900969	+	0.433884i	−0.249884	+	0.120338i
$14$	1.14186	+	0.336734i	0.305176	+	0.0899958i
$15$	−0.748066	−	0.360250i	−0.193150	−	0.0930161i
$16$	−2.07176	+	1.92231i	−0.517940	+	0.480578i
$17$	0.940735	−	0.141793i	0.228162	−	0.0343898i	−0.0339662	−	0.999423i	$-0.510814\pi$
$17$	0.940735	−	0.141793i	0.228162	−	0.0343898i	0.262128	+	0.965033i	$0.415576\pi$
$18$	0.661015	−	1.14491i	0.155803	−	0.269858i
$19$	−0.376207	−	0.651609i	−0.0863078	−	0.149489i	0.819640	−	0.572879i	$-0.194174\pi$
$19$	−0.376207	−	0.651609i	−0.0863078	−	0.149489i	−0.905948	+	0.423390i	$0.860840\pi$
$20$	−3.74053	−	4.69048i	−0.836408	−	1.04882i
$21$	−0.596515	−	0.278186i	−0.130170	−	0.0607052i
$22$	−1.02279	+	1.28253i	−0.218059	+	0.273437i
$23$	−6.41865	−	0.967456i	−1.33838	−	0.201728i	−0.559463	−	0.828855i	$-0.688993\pi$
$23$	−6.41865	−	0.967456i	−1.33838	−	0.201728i	−0.778917	+	0.627127i	$0.784231\pi$
$24$	−0.351224	+	0.239461i	−0.0716934	+	0.0488797i
$25$	5.07241	−	3.45831i	1.01448	−	0.691663i
$26$	−0.444934	−	0.0670630i	−0.0872587	−	0.0131521i
$27$	−0.921047	+	1.15496i	−0.177255	+	0.222271i
$28$	−3.01120	−	3.68112i	−0.569064	−	0.695666i
$29$	2.15036	+	2.69646i	0.399311	+	0.500720i	0.940318	−	0.340298i	$-0.110528\pi$
$29$	2.15036	+	2.69646i	0.399311	+	0.500720i	−0.541007	+	0.841018i	$0.681957\pi$
$30$	−0.186798	−	0.323544i	−0.0341046	−	0.0590709i
$31$	1.78101	−	3.08479i	0.319878	−	0.554045i	−0.660584	−	0.750752i	$-0.729691\pi$
$31$	1.78101	−	3.08479i	0.319878	−	0.554045i	0.980462	+	0.196707i	$0.0630247\pi$
$32$	−4.63678	+	0.698882i	−0.819675	+	0.123546i
$33$	0.664845	−	0.616886i	0.115735	−	0.107386i
$34$	0.385681	+	0.185734i	0.0661437	+	0.0318531i
$35$	7.23354	−	5.06458i	1.22269	−	0.856071i
$36$	−4.75834	+	2.29150i	−0.793057	+	0.381916i
$37$	1.37154	−	3.49463i	0.225480	−	0.574513i	−0.772703	−	0.634767i	$-0.781096\pi$
$37$	1.37154	−	3.49463i	0.225480	−	0.574513i	0.998183	+	0.0602544i	$0.0191912\pi$
$38$	0.0253003	−	0.337609i	0.00410425	−	0.0547674i
$39$	0.237721	+	0.0733272i	0.0380658	+	0.0117418i
$40$	−0.426184	−	5.68703i	−0.0673856	−	0.899198i
$41$	−0.462122	+	2.02469i	−0.0721713	+	0.316203i	−0.998109	−	0.0614738i	$-0.980420\pi$
$41$	−0.462122	+	2.02469i	−0.0721713	+	0.316203i	0.925937	+	0.377677i	$0.123277\pi$
$42$	−0.151256	−	0.254622i	−0.0233394	−	0.0392890i
$43$	2.64853	+	11.6040i	0.403897	+	1.76959i	0.611367	+	0.791347i	$0.290620\pi$
$43$	2.64853	+	11.6040i	0.403897	+	1.76959i	−0.207470	+	0.978241i	$0.566523\pi$
$44$	6.26215	−	1.93162i	0.944055	−	0.291202i
$45$	−3.58256	−	9.12821i	−0.534056	−	1.36075i
$46$	−2.14106	−	1.98662i	−0.315683	−	0.292911i
$47$	10.0819	+	6.87372i	1.47060	+	1.00264i	0.992222	+	0.124479i	$0.0397259\pi$
$47$	10.0819	+	6.87372i	1.47060	+	1.00264i	0.478374	+	0.878156i	$0.341226\pi$
$48$	0.703086			0.101482
$49$	5.68387	−	4.08579i	0.811981	−	0.583684i
$50$	2.76237			0.390659
$51$	−0.195549	−	0.133323i	−0.0273823	−	0.0186689i
$52$	1.31769	+	1.22264i	0.182730	+	0.169549i
$53$	−1.70342	−	4.34024i	−0.233983	−	0.596178i	0.764864	−	0.644192i	$-0.222806\pi$
$53$	−1.70342	−	4.34024i	−0.233983	−	0.596178i	−0.998847	+	0.0480135i	$0.984711\pi$
$54$	−0.635169	+	0.195924i	−0.0864355	+	0.0266618i
$55$	2.70757	+	11.8626i	0.365088	+	1.59956i
$56$	−0.393856	−	4.50370i	−0.0526312	−	0.601833i
$57$	−0.0416516	+	0.182487i	−0.00551689	+	0.0241711i
$58$	0.115971	+	1.54753i	0.0152277	+	0.203200i
$59$	−7.49100	−	2.31067i	−0.975245	−	0.300823i	−0.234133	−	0.972205i	$-0.575225\pi$
$59$	−7.49100	−	2.31067i	−0.975245	−	0.300823i	−0.741112	+	0.671381i	$0.765701\pi$
$60$	−0.111533	+	1.48830i	−0.0143988	+	0.192139i
$61$	1.58485	−	4.03814i	0.202920	−	0.517031i	−0.792797	−	0.609485i	$-0.791376\pi$
$61$	1.58485	−	4.03814i	0.202920	−	0.517031i	0.995717	+	0.0924546i	$0.0294713\pi$
$62$	1.44404	−	0.695412i	0.183393	−	0.0883174i
$63$	−2.92971	−	7.20030i	−0.369108	−	0.907153i
$64$	3.19168	+	1.53703i	0.398960	+	0.192129i
$65$	−2.44659	+	2.27010i	−0.303462	+	0.281572i
$66$	0.403535	−	0.0608231i	0.0496717	−	0.00748681i
$67$	5.91404	−	10.2434i	0.722515	−	1.25143i	−0.237473	−	0.971394i	$-0.576319\pi$
$67$	5.91404	−	10.2434i	0.722515	−	1.25143i	0.959989	−	0.280039i	$-0.0903475\pi$
$68$	−0.855053	−	1.48099i	−0.103690	−	0.179597i
$69$	1.00683	+	1.26252i	0.121208	+	0.151990i
$70$	3.97297	−	0.0493856i	0.474860	−	0.00590270i
$71$	−0.194644	+	0.244076i	−0.0231000	+	0.0289665i	−0.793247	−	0.608900i	$-0.791611\pi$
$71$	−0.194644	+	0.244076i	−0.0231000	+	0.0289665i	0.770147	+	0.637866i	$0.220183\pi$
$72$	−4.96439	−	0.748261i	−0.585058	−	0.0881834i
$73$	−3.94854	+	2.69207i	−0.462142	+	0.315083i	−0.771913	−	0.635728i	$-0.780700\pi$
$73$	−3.94854	+	2.69207i	−0.462142	+	0.315083i	0.309771	+	0.950811i	$0.399748\pi$
$74$	1.39569	−	0.951565i	0.162246	−	0.110617i
$75$	−1.51020	−	0.227626i	−0.174383	−	0.0262840i
$76$	−0.843265	+	1.05742i	−0.0967291	+	0.121294i
$77$	2.26307	+	9.37640i	0.257901	+	1.06854i
$78$	0.0697921	+	0.0875166i	0.00790240	+	0.00990930i
$79$	3.46430	+	6.00034i	0.389764	+	0.675091i	0.992418	−	0.122912i	$-0.0392233\pi$
$79$	3.46430	+	6.00034i	0.389764	+	0.675091i	−0.602654	+	0.798003i	$0.705890\pi$
$80$	−4.71629	+	8.16886i	−0.527298	+	0.913307i
$81$	−8.35249	+	1.25894i	−0.928055	+	0.139882i
$82$	−0.685005	+	0.635592i	−0.0756462	+	0.0701894i
$83$	−13.7687	−	6.63067i	−1.51131	−	0.727810i	−0.519377	−	0.854545i	$-0.673836\pi$
$83$	−13.7687	−	6.63067i	−1.51131	−	0.727810i	−0.991937	+	0.126735i	$0.959550\pi$
$84$	−0.0737438	+	1.18082i	−0.00804610	+	0.128839i
$85$	2.86076	−	1.37767i	0.310293	−	0.149429i
$86$	−1.95662	+	4.98538i	−0.210987	+	0.537587i
$87$	0.0641181	−	0.855596i	0.00687418	−	0.0917295i
$88$	5.95280	+	1.83619i	0.634570	+	0.195739i
$89$	0.448266	+	5.98169i	0.0475161	+	0.634058i	0.969225	+	0.246176i	$0.0791742\pi$
$89$	0.448266	+	5.98169i	0.0475161	+	0.634058i	−0.921709	+	0.387882i	$0.873207\pi$
$90$	0.981835	−	4.30170i	0.103495	−	0.453439i
$91$	−1.91696	+	1.82354i	−0.200952	+	0.191158i
$92$	2.59639	+	11.3755i	0.270693	+	1.18598i
$93$	−0.846765	+	0.261192i	−0.0878055	+	0.0270844i
$94$	2.00590	+	5.11094i	0.206892	+	0.527153i
$95$	−1.84085	−	1.70806i	−0.188867	−	0.175243i
$96$	0.963838	+	0.657133i	0.0983713	+	0.0670684i
$97$	7.46151			0.757602			0.378801	−	0.925478i	$-0.376337\pi$
$97$	7.46151			0.757602			0.378801	+	0.925478i	$0.376337\pi$
$98$	3.14874	−	0.0782923i	0.318071	−	0.00790872i
$99$	10.7115			1.07655
$100$	−9.11785	−	6.21645i	−0.911785	−	0.621645i
$101$	3.05425	+	2.83393i	0.303909	+	0.281986i	0.817353	−	0.576137i	$-0.195440\pi$
$101$	3.05425	+	2.83393i	0.303909	+	0.281986i	−0.513445	+	0.858123i	$0.671631\pi$
$102$	−0.0389064	−	0.0991318i	−0.00385230	−	0.00981551i
$103$	−11.6862	+	3.60473i	−1.15148	+	0.355185i	−0.810988	−	0.585063i	$-0.801070\pi$
$103$	−11.6862	+	3.60473i	−1.15148	+	0.355185i	−0.340492	+	0.940247i	$0.610594\pi$
$104$	0.380230	+	1.66590i	0.0372846	+	0.163354i
$105$	−2.17611	−	0.300383i	−0.212366	−	0.0293144i
$106$	0.466839	−	2.04536i	0.0453434	−	0.198663i
$107$	1.29364	+	17.2624i	0.125061	+	1.66882i	0.608585	+	0.793488i	$0.291737\pi$
$107$	1.29364	+	17.2624i	0.125061	+	1.66882i	−0.483525	+	0.875331i	$0.660644\pi$
$108$	2.53743	+	0.782693i	0.244164	+	0.0753147i
$109$	0.486232	−	6.48831i	0.0465726	−	0.621468i	−0.924268	−	0.381743i	$-0.875324\pi$
$109$	0.486232	−	6.48831i	0.0465726	−	0.621468i	0.970841	−	0.239724i	$-0.0770571\pi$
$110$	−2.00023	+	5.09650i	−0.190714	+	0.485932i
$111$	−0.841441	+	0.405217i	−0.0798660	+	0.0384615i
$112$	−3.65795	+	6.52163i	−0.345644	+	0.616236i
$113$	12.2323	+	5.89078i	1.15072	+	0.554158i	0.909250	−	0.416250i	$-0.136656\pi$
$113$	12.2323	+	5.89078i	1.15072	+	0.554158i	0.241471	+	0.970408i	$0.422370\pi$
$114$	−0.0617403	+	0.0572866i	−0.00578251	+	0.00536538i
$115$	−21.4225	+	3.22892i	−1.99766	+	0.301098i
$116$	3.09976	−	5.36895i	0.287806	−	0.498495i
$117$	1.46906	+	2.54448i	0.135814	+	0.235237i
$118$	−2.19927	−	2.75780i	−0.202459	−	0.253876i
$119$	2.25405	−	1.12022i	0.206628	−	0.102690i
$120$	−0.884575	+	1.10922i	−0.0807503	+	0.101258i
$121$	−2.26560	−	0.341485i	−0.205964	−	0.0310441i
$122$	1.61276	−	1.09956i	0.146012	−	0.0995495i
$123$	0.426870	−	0.291035i	0.0384895	−	0.0262417i
$124$	−6.33133	−	0.954295i	−0.568570	−	0.0856982i
$125$	2.37051	−	2.97252i	0.212025	−	0.265871i
$126$	0.735880	−	3.41948i	0.0655574	−	0.304631i
$127$	2.28938	+	2.87079i	0.203150	+	0.254742i	0.872961	−	0.487789i	$-0.162197\pi$
$127$	2.28938	+	2.87079i	0.203150	+	0.254742i	−0.669812	+	0.742531i	$0.733625\pi$
$128$	5.48614	+	9.50228i	0.484911	+	0.839891i
$129$	1.48050	−	2.56430i	0.130351	−	0.225774i
$130$	−1.48498	+	0.223825i	−0.130242	+	0.0196308i
$131$	−4.82940	+	4.48103i	−0.421947	+	0.391510i	−0.862368	−	0.506282i	$-0.831020\pi$
$131$	−4.82940	+	4.48103i	−0.421947	+	0.391510i	0.440421	+	0.897791i	$0.354829\pi$
$132$	−1.46884	−	0.707354i	−0.127846	−	0.0615673i
$133$	−1.47600	−	1.33578i	−0.127986	−	0.115827i
$134$	4.79510	−	2.30920i	0.414233	−	0.199484i
$135$	−1.80126	+	4.58954i	−0.155028	+	0.395005i
$136$	0.121483	−	1.62108i	0.0104171	−	0.139006i
$137$	4.69339	+	1.44772i	0.400984	+	0.123687i	0.488686	−	0.872460i	$-0.337476\pi$
$137$	4.69339	+	1.44772i	0.400984	+	0.123687i	−0.0877026	+	0.996147i	$0.527953\pi$
$138$	0.0542993	+	0.724574i	0.00462226	+	0.0616798i
$139$	−2.83001	+	12.3991i	−0.240038	+	1.05168i	0.700943	+	0.713218i	$0.252763\pi$
$139$	−2.83001	+	12.3991i	−0.240038	+	1.05168i	−0.940981	+	0.338459i	$0.890094\pi$
$140$	−13.2248	−	8.77776i	−1.11770	−	0.741856i
$141$	−0.675478	−	2.95946i	−0.0568855	−	0.249232i
$142$	−0.134230	+	0.0414044i	−0.0112643	+	0.00347458i
$143$	−1.33193	−	3.39369i	−0.111381	−	0.283795i
$144$	6.08706	+	5.64797i	0.507255	+	0.470664i
$145$	9.51071	+	6.48429i	0.789821	+	0.538491i
$146$	−2.15033			−0.177962
$147$	−1.72788	−	0.216661i	−0.142513	−	0.0178699i
$148$	−6.74820			−0.554698
$149$	−17.3923	−	11.8579i	−1.42484	−	0.971437i	−0.997737	−	0.0672321i	$-0.978583\pi$
$149$	−17.3923	−	11.8579i	−1.42484	−	0.971437i	−0.427099	−	0.904205i	$-0.640464\pi$
$150$	−0.503757	−	0.467418i	−0.0411316	−	0.0381645i
$151$	2.12580	+	5.41644i	0.172995	+	0.440784i	0.990905	−	0.134562i	$-0.0429628\pi$
$151$	2.12580	+	5.41644i	0.172995	+	0.440784i	−0.817910	+	0.575346i	$0.804868\pi$
$152$	−1.22856	+	0.378960i	−0.0996492	+	0.0307377i
$153$	−0.621991	−	2.72512i	−0.0502850	−	0.220313i
$154$	−1.53529	+	4.05952i	−0.123718	+	0.327126i
$155$	2.64541	−	11.5903i	0.212484	−	0.930954i
$156$	−0.0334177	−	0.445929i	−0.00267556	−	0.0357029i
$157$	−16.3297	−	5.03703i	−1.30325	−	0.401999i	−0.436032	−	0.899931i	$-0.643617\pi$
$157$	−16.3297	−	5.03703i	−1.30325	−	0.401999i	−0.867216	+	0.497932i	$0.834093\pi$
$158$	−0.232977	+	3.10887i	−0.0185347	+	0.247328i
$159$	−0.423766	+	1.07974i	−0.0336068	+	0.0856287i
$160$	−14.1004	+	6.79038i	−1.11473	+	0.536827i
$161$	−16.9490	+	2.77053i	−1.33577	+	0.218348i
$162$	−3.42434	−	1.64908i	−0.269042	−	0.129564i
$163$	10.9835	−	10.1912i	0.860295	−	0.798237i	−0.120615	−	0.992699i	$-0.538487\pi$
$163$	10.9835	−	10.1912i	0.860295	−	0.798237i	0.980910	+	0.194462i	$0.0622961\pi$
$164$	3.69135	−	0.556382i	0.288246	−	0.0434461i
$165$	1.51350	−	2.62146i	0.117826	−	0.204080i
$166$	−3.43817	−	5.95508i	−0.266854	−	0.462204i
$167$	14.8711	+	18.6478i	1.15076	+	1.44301i	0.876529	+	0.481349i	$0.159853\pi$
$167$	14.8711	+	18.6478i	1.15076	+	1.44301i	0.274235	+	0.961663i	$0.411576\pi$
$168$	−0.690242	+	0.887956i	−0.0532533	+	0.0685073i
$169$	0.623490	−	0.781831i	0.0479608	−	0.0601409i
$170$	1.41275	+	0.212938i	0.108353	+	0.0163316i
$171$	−1.82655	+	1.24532i	−0.139679	+	0.0952318i
$172$	17.6774	−	12.0522i	1.34789	−	0.918973i
$173$	−1.98273	−	0.298848i	−0.150744	−	0.0227210i	0.0732366	−	0.997315i	$-0.476667\pi$
$173$	−1.98273	−	0.298848i	−0.150744	−	0.0227210i	−0.223981	+	0.974594i	$0.571905\pi$
$174$	0.240706	−	0.301836i	0.0182479	−	0.0228821i
$175$	9.96853	−	12.8239i	0.753550	−	0.969399i
$176$	−6.42415	−	8.05563i	−0.484239	−	0.607216i
$177$	0.975101	+	1.68893i	0.0732931	+	0.126947i
$178$	−1.34953	+	2.33746i	−0.101152	+	0.175200i
$179$	13.4272	−	2.02382i	1.00359	−	0.151268i	0.373372	−	0.927682i	$-0.378202\pi$
$179$	13.4272	−	2.02382i	1.00359	−	0.151268i	0.630223	+	0.776414i	$0.282964\pi$
$180$	−12.9213	+	11.9892i	−0.963099	+	0.893625i
$181$	−16.5745	−	7.98186i	−1.23197	−	0.593287i	−0.299352	−	0.954143i	$-0.596770\pi$
$181$	−16.5745	−	7.98186i	−1.23197	−	0.593287i	−0.932622	+	0.360855i	$0.882485\pi$
$182$	−1.17489	+	0.192050i	−0.0870884	+	0.0142357i
$183$	−0.972309	+	0.468239i	−0.0718751	+	0.0346132i
$184$	−4.05224	+	10.3249i	−0.298735	+	0.761165i
$185$	0.936336	−	12.4945i	0.0688408	−	0.918617i
$186$	−0.381010	−	0.117526i	−0.0279370	−	0.00861742i
$187$	0.259193	+	3.45868i	0.0189540	+	0.252924i
$188$	4.88074	−	21.3839i	0.355964	−	1.55958i
$189$	−1.38257	+	3.65571i	−0.100568	+	0.265914i
$190$	−0.251436	−	1.10161i	−0.0182411	−	0.0799193i
$191$	19.6594	−	6.06411i	1.42250	−	0.438784i	0.514407	−	0.857546i	$-0.328012\pi$
$191$	19.6594	−	6.06411i	1.42250	−	0.438784i	0.908096	+	0.418762i	$0.137536\pi$
$192$	−0.321967	−	0.820359i	−0.0232360	−	0.0592043i
$193$	12.6534	+	11.7406i	0.910808	+	0.845106i	0.988399	−	0.151879i	$-0.0485323\pi$
$193$	12.6534	+	11.7406i	0.910808	+	0.845106i	−0.0775910	+	0.996985i	$0.524723\pi$
$194$	2.77399	+	1.89128i	0.199161	+	0.135786i
$195$	0.830291			0.0594583
$196$	−10.5693	−	6.82751i	−0.754953	−	0.487679i
$197$	−4.89717			−0.348909			−0.174454	−	0.984665i	$-0.555816\pi$
$197$	−4.89717			−0.348909			−0.174454	+	0.984665i	$0.555816\pi$
$198$	3.98226	+	2.71506i	0.283007	+	0.192951i
$199$	−8.12955	−	7.54312i	−0.576288	−	0.534718i	0.337279	−	0.941405i	$-0.390493\pi$
$199$	−8.12955	−	7.54312i	−0.576288	−	0.534718i	−0.913567	+	0.406687i	$0.866684\pi$
$200$	−3.83251	−	9.76507i	−0.270999	−	0.690494i
$201$	−2.81179	+	0.867321i	−0.198328	+	0.0611761i
$202$	0.417170	+	1.82774i	0.0293520	+	0.128600i
$203$	7.60269	+	5.04615i	0.533604	+	0.354171i
$204$	−0.0946668	+	0.414762i	−0.00662800	+	0.0290392i
$205$	0.517974	+	6.91188i	0.0361768	+	0.482746i
$206$	−5.25834	−	1.62198i	−0.366366	−	0.113009i
$207$	−1.42523	+	19.0184i	−0.0990605	+	1.32187i
$208$	1.03253	−	2.63085i	0.0715931	−	0.182416i
$209$	2.47143	−	1.19018i	0.170952	−	0.0823264i
$210$	−0.732882	−	0.663255i	−0.0505736	−	0.0457689i
$211$	1.84438	+	0.888208i	0.126973	+	0.0611468i	0.496292	−	0.868156i	$-0.334695\pi$
$211$	1.84438	+	0.888208i	0.126973	+	0.0611468i	−0.369319	+	0.929303i	$0.620409\pi$
$212$	−6.14378	+	5.70060i	−0.421957	+	0.391519i
$213$	0.0767958	−	0.0115751i	0.00526196	−	0.000793113i
$214$	−3.89458	+	6.74561i	−0.266228	+	0.461120i
$215$	19.8623	+	34.4026i	1.35460	+	2.34624i
$216$	1.57383	+	1.97352i	0.107085	+	0.134281i
$217$	1.98272	−	9.21327i	0.134596	−	0.625437i
$218$	1.82537	−	2.28894i	0.123630	−	0.155027i
$219$	1.17559	+	0.177192i	0.0794393	+	0.0119735i
$220$	18.0714	−	12.3209i	1.21837	−	0.830673i
$221$	−0.786051	+	0.535920i	−0.0528755	+	0.0360499i
$222$	−0.415536	−	0.0626320i	−0.0278890	−	0.00420359i
$223$	−0.526293	+	0.659950i	−0.0352432	+	0.0441935i	−0.799141	−	0.601144i	$-0.794712\pi$
$223$	−0.526293	+	0.659950i	−0.0352432	+	0.0441935i	0.763898	+	0.645338i	$0.223283\pi$
$224$	−11.1100	+	5.52142i	−0.742315	+	0.368916i
$225$	−11.2462	−	14.1023i	−0.749748	−	0.940155i
$226$	3.05452	+	5.29058i	0.203184	+	0.351924i
$227$	12.1441	−	21.0342i	0.806031	−	1.39609i	−0.109561	−	0.993980i	$-0.534945\pi$
$227$	12.1441	−	21.0342i	0.806031	−	1.39609i	0.915593	−	0.402107i	$-0.131722\pi$
$228$	0.332706	−	0.0501473i	0.0220340	−	0.00332109i
$229$	−7.51155	+	6.96970i	−0.496377	+	0.460571i	−0.888191	−	0.459474i	$-0.848038\pi$
$229$	−7.51155	+	6.96970i	−0.496377	+	0.460571i	0.391814	+	0.920044i	$0.371848\pi$
$230$	−8.78276	−	4.22955i	−0.579118	−	0.278888i
$231$	1.17387	−	2.09285i	0.0772348	−	0.137699i
$232$	5.30965	−	2.55699i	0.348596	−	0.167875i
$233$	−4.80261	+	12.2369i	−0.314630	+	0.801663i	0.682840	+	0.730568i	$0.260745\pi$
$233$	−4.80261	+	12.2369i	−0.314630	+	0.801663i	−0.997470	+	0.0710951i	$0.977351\pi$
$234$	−0.0987955	+	1.31833i	−0.00645846	+	0.0861822i
$235$	38.9159	+	12.0040i	2.53859	+	0.783052i
$236$	1.05305	+	14.0520i	0.0685477	+	0.914706i
$237$	0.383548	−	1.68043i	0.0249141	−	0.109156i
$238$	1.12194	+	0.154869i	0.0727244	+	0.0100386i
$239$	4.77122	+	20.9041i	0.308625	+	1.35217i	0.856731	+	0.515764i	$0.172492\pi$
$239$	4.77122	+	20.9041i	0.308625	+	1.35217i	−0.548106	+	0.836409i	$0.684651\pi$
$240$	2.24233	−	0.691666i	0.144741	−	0.0446468i
$241$	2.46944	+	6.29204i	0.159071	+	0.405306i	0.988082	−	0.153926i	$-0.0491916\pi$
$241$	2.46944	+	6.29204i	0.159071	+	0.405306i	−0.829012	+	0.559231i	$0.811096\pi$
$242$	−0.755735	−	0.701220i	−0.0485805	−	0.0450761i
$243$	5.39788	+	3.68021i	0.346274	+	0.236086i
$244$	−7.79773			−0.499199
$245$	14.1079	−	18.6222i	0.901322	−	1.18973i
$246$	0.232468			0.0148216
$247$	0.621673	+	0.423850i	0.0395561	+	0.0269689i
$248$	−4.46175	−	4.13990i	−0.283321	−	0.262884i
$249$	1.38895	+	3.53898i	0.0880211	+	0.224274i
$250$	1.63474	−	0.504251i	0.103390	−	0.0318916i
$251$	2.96244	+	12.9793i	0.186988	+	0.819247i	0.978193	+	0.207697i	$0.0665966\pi$
$251$	2.96244	+	12.9793i	0.186988	+	0.819247i	−0.791206	+	0.611550i	$0.790546\pi$
$252$	−10.1241	+	9.63075i	−0.637761	+	0.606680i
$253$	5.26592	−	23.0715i	0.331066	−	1.45049i
$254$	0.123469	+	1.64758i	0.00774713	+	0.103378i
$255$	−0.754812	−	0.232829i	−0.0472682	−	0.0145803i
$256$	0.160513	−	2.14190i	0.0100321	−	0.133869i
$257$	9.15338	−	23.3224i	0.570972	−	1.45481i	−0.295380	−	0.955380i	$-0.595446\pi$
$257$	9.15338	−	23.3224i	0.570972	−	1.45481i	0.866352	−	0.499433i	$-0.166458\pi$
$258$	1.20039	−	0.578075i	0.0747327	−	0.0359894i
$259$	0.619090	−	9.91320i	0.0384684	−	0.615976i
$260$	5.40523	+	2.60302i	0.335218	+	0.161432i
$261$	7.42821	−	6.89237i	0.459794	−	0.426627i
$262$	−2.93126	+	0.441816i	−0.181094	+	0.0272955i
$263$	−6.49776	+	11.2545i	−0.400669	+	0.693979i	−0.993807	−	0.111122i	$-0.964556\pi$
$263$	−6.49776	+	11.2545i	−0.400669	+	0.693979i	0.593138	+	0.805101i	$0.297889\pi$
$264$	−0.774874	−	1.34212i	−0.0476902	−	0.0826018i
$265$	−9.70240	−	12.1664i	−0.596013	−	0.747377i
$266$	−0.210158	−	0.870731i	−0.0128856	−	0.0533879i
$267$	0.930408	−	1.16669i	0.0569400	−	0.0714006i
$268$	−21.0239	−	3.16885i	−1.28424	−	0.193568i
$269$	−10.3191	+	7.03545i	−0.629167	+	0.428959i	−0.835475	−	0.549528i	$-0.814807\pi$
$269$	−10.3191	+	7.03545i	−0.629167	+	0.428959i	0.206308	+	0.978487i	$0.433855\pi$
$270$	−1.83298	+	1.24970i	−0.111552	+	0.0760545i
$271$	−19.3223	−	2.91238i	−1.17375	−	0.176914i	−0.466921	−	0.884299i	$-0.654637\pi$
$271$	−19.3223	−	2.91238i	−1.17375	−	0.176914i	−0.706828	+	0.707385i	$0.749875\pi$
$272$	−1.67641	+	2.10215i	−0.101647	+	0.127461i
$273$	0.658142	−	0.00818096i	0.0398325	−	0.000495134i
$274$	1.37793	+	1.72786i	0.0832435	+	0.104384i
$275$	11.1908	+	19.3830i	0.674831	+	1.16884i
$276$	1.45135	−	2.51382i	0.0873612	−	0.151314i
$277$	3.48758	−	0.525668i	0.209548	−	0.0315844i	−0.0434290	−	0.999057i	$-0.513828\pi$
$277$	3.48758	−	0.525668i	0.209548	−	0.0315844i	0.252978	+	0.967472i	$0.418590\pi$
$278$	−4.19493	+	3.89233i	−0.251595	+	0.233446i
$279$	−9.42917	−	4.54085i	−0.564510	−	0.271854i
$280$	−5.68666	−	13.9760i	−0.339843	−	0.835227i
$281$	23.1344	−	11.1409i	1.38008	−	0.664612i	0.411065	−	0.911606i	$-0.365157\pi$
$281$	23.1344	−	11.1409i	1.38008	−	0.664612i	0.969017	+	0.246994i	$0.0794428\pi$
$282$	0.499013	−	1.27147i	0.0297158	−	0.0757147i
$283$	1.82814	−	24.3948i	0.108671	−	1.45012i	−0.630283	−	0.776365i	$-0.717061\pi$
$283$	1.82814	−	24.3948i	0.108671	−	1.45012i	0.738955	−	0.673755i	$-0.235320\pi$
$284$	0.536232	+	0.165406i	0.0318195	+	0.00981503i
$285$	0.0466855	+	0.622975i	0.00276541	+	0.0369019i
$286$	0.365028	−	1.59929i	0.0215846	−	0.0945681i
$287$	0.478683	+	5.47369i	0.0282557	+	0.323102i
$288$	3.06573	+	13.4318i	0.180650	+	0.791478i
$289$	−15.3799	+	4.74406i	−0.904698	+	0.279062i
$290$	1.89225	+	4.82138i	0.111117	+	0.283121i
$291$	−1.36071	−	1.26255i	−0.0797662	−	0.0740122i
$292$	7.09765	+	4.83910i	0.415359	+	0.283187i
$293$	−12.2775			−0.717257			−0.358628	−	0.933480i	$-0.616755\pi$
$293$	−12.2775			−0.717257			−0.358628	+	0.933480i	$0.616755\pi$
$294$	−0.587464	−	0.518517i	−0.0342616	−	0.0302405i
$295$	−26.1639			−1.52332
$296$	−5.30018	−	3.61360i	−0.308067	−	0.210036i
$297$	−3.94793	−	3.66314i	−0.229082	−	0.212557i
$298$	−3.46038	−	8.81691i	−0.200455	−	0.510750i
$299$	6.20277	−	1.91330i	0.358715	−	0.110649i
$300$	0.610888	+	2.67648i	0.0352696	+	0.154526i
$301$	16.0831	+	27.0740i	0.927016	+	1.56052i
$302$	−0.582596	+	2.55252i	−0.0335246	+	0.146881i
$303$	−0.0774584	−	1.03361i	−0.00444987	−	0.0593794i
$304$	2.03201	+	0.626791i	0.116544	+	0.0359489i
$305$	1.08196	−	14.4378i	0.0619530	−	0.826706i
$306$	0.459500	−	1.17079i	0.0262678	−	0.0669294i
$307$	−31.0583	+	14.9569i	−1.77259	+	0.853636i	−0.808313	+	0.588753i	$0.799619\pi$
$307$	−31.0583	+	14.9569i	−1.77259	+	0.853636i	−0.964281	+	0.264883i	$0.914667\pi$
$308$	14.2031	−	9.94437i	0.809299	−	0.566633i
$309$	2.74110	+	1.32004i	0.155936	+	0.0750947i
$310$	3.92130	−	3.63843i	0.222715	−	0.206649i
$311$	10.9060	−	1.64381i	0.618421	−	0.0932120i	0.167643	−	0.985848i	$-0.446384\pi$
$311$	10.9060	−	1.64381i	0.618421	−	0.0932120i	0.450779	+	0.892636i	$0.351146\pi$
$312$	0.212544	−	0.368137i	0.0120329	−	0.0208417i
$313$	−13.0605	−	22.6214i	−0.738223	−	1.27864i	−0.953295	−	0.302041i	$-0.902332\pi$
$313$	−13.0605	−	22.6214i	−0.738223	−	1.27864i	0.215072	−	0.976598i	$-0.431001\pi$
$314$	−4.79419	−	6.01173i	−0.270552	−	0.339262i
$315$	−16.4269	−	20.0815i	−0.925553	−	1.13147i
$316$	7.76519	−	9.73725i	0.436826	−	0.547763i
$317$	0.939697	+	0.141637i	0.0527787	+	0.00795510i	0.175379	−	0.984501i	$-0.443885\pi$
$317$	0.939697	+	0.141637i	0.0527787	+	0.00795510i	−0.122600	+	0.992456i	$0.539123\pi$
$318$	−0.431227	+	0.294006i	−0.0241820	+	0.0164870i
$319$	−10.3889	+	7.08302i	−0.581665	+	0.396573i
$320$	11.6912	+	1.76216i	0.653555	+	0.0985076i
$321$	2.68504	−	3.36693i	0.149864	−	0.187924i
$322$	−7.00345	−	3.26608i	−0.390287	−	0.182011i
$323$	−0.446304	−	0.559648i	−0.0248330	−	0.0311396i
$324$	7.59175	+	13.1493i	0.421764	+	0.730516i
$325$	−3.06958	+	5.31667i	−0.170270	+	0.294916i
$326$	6.66656	−	1.00482i	0.369227	−	0.0556520i
$327$	−1.18655	+	1.10096i	−0.0656164	+	0.0608831i
$328$	3.19721	+	1.53969i	0.176536	+	0.0850154i
$329$	30.9655	+	9.13166i	1.70718	+	0.503445i
$330$	1.22714	−	0.590961i	0.0675520	−	0.0325313i
$331$	−1.12153	+	2.85761i	−0.0616448	+	0.157068i	−0.958377	−	0.285504i	$-0.907839\pi$
$331$	−1.12153	+	2.85761i	−0.0616448	+	0.157068i	0.896733	+	0.442573i	$0.145934\pi$
$332$	−2.05285	+	27.3934i	−0.112665	+	1.50341i
$333$	−10.5400	−	3.25117i	−0.577590	−	0.178163i
$334$	0.802017	+	10.7022i	0.0438844	+	0.585597i
$335$	8.78439	−	38.4869i	0.479943	−	2.10277i
$336$	1.77060	−	0.570352i	0.0965939	−	0.0311153i
$337$	−6.92073	−	30.3217i	−0.376996	−	1.65173i	−0.706602	−	0.707611i	$-0.749773\pi$
$337$	−6.92073	−	30.3217i	−0.376996	−	1.65173i	0.329606	−	0.944119i	$-0.393084\pi$
$338$	0.429969	−	0.132628i	0.0233872	−	0.00721400i
$339$	−1.23396	−	3.14408i	−0.0670196	−	0.170763i
$340$	−4.18392	−	3.88211i	−0.226905	−	0.210537i
$341$	10.7296	+	7.31531i	0.581040	+	0.396146i
$342$	−0.994714			−0.0537880
$343$	10.9994	−	14.9001i	0.593909	−	0.804532i
$344$	20.3380			1.09655
$345$	4.45305	+	3.03604i	0.239744	+	0.163455i
$346$	−0.661377	−	0.613668i	−0.0355559	−	0.0329910i
$347$	1.90648	+	4.85762i	0.102345	+	0.260771i	0.972870	−	0.231354i	$-0.0743156\pi$
$347$	1.90648	+	4.85762i	0.102345	+	0.260771i	−0.870525	+	0.492125i	$0.836220\pi$
$348$	−1.47376	+	0.454594i	−0.0790018	+	0.0243688i
$349$	5.51078	+	24.1443i	0.294985	+	1.29241i	0.877493	+	0.479589i	$0.159214\pi$
$349$	5.51078	+	24.1443i	0.294985	+	1.29241i	−0.582508	+	0.812825i	$0.697929\pi$
$350$	6.95654	−	2.24087i	0.371843	−	0.119780i
$351$	0.328718	−	1.44021i	0.0175457	−	0.0768725i
$352$	−1.27753	−	17.0475i	−0.0680927	−	0.908634i
$353$	16.5633	+	5.10910i	0.881575	+	0.271930i	0.702310	−	0.711871i	$-0.252152\pi$
$353$	16.5633	+	5.10910i	0.881575	+	0.271930i	0.179265	+	0.983801i	$0.442628\pi$
$354$	−0.0655765	+	0.875058i	−0.00348535	+	0.0465088i
$355$	−0.380659	+	0.969903i	−0.0202033	+	0.0514771i
$356$	9.71466	−	4.67834i	0.514876	−	0.247951i
$357$	−0.600607	−	0.177118i	−0.0317875	−	0.00937407i
$358$	5.50485	+	2.65100i	0.290941	+	0.140110i
$359$	−11.2459	+	10.4346i	−0.593534	+	0.550719i	−0.918709	−	0.394935i	$-0.870767\pi$
$359$	−11.2459	+	10.4346i	−0.593534	+	0.550719i	0.325175	+	0.945654i	$0.394577\pi$
$360$	−16.5688	+	2.49735i	−0.873254	+	0.131622i
$361$	9.21694	−	15.9642i	0.485102	−	0.840221i
$362$	−4.13880	−	7.16861i	−0.217530	−	0.376774i
$363$	0.355382	+	0.445634i	0.0186527	+	0.0233897i
$364$	4.31018	+	2.01006i	0.225915	+	0.105356i
$365$	−9.94459	+	12.4701i	−0.520524	+	0.652716i
$366$	−0.480164	−	0.0723731i	−0.0250986	−	0.00378300i
$367$	17.6923	−	12.0624i	0.923529	−	0.629651i	−0.00536954	−	0.999986i	$-0.501709\pi$
$367$	17.6923	−	12.0624i	0.923529	−	0.629651i	0.928899	+	0.370334i	$0.120757\pi$
$368$	15.1576	−	10.3343i	0.790147	−	0.538713i
$369$	6.03360	+	0.909418i	0.314096	+	0.0473424i
$370$	3.51511	−	4.40781i	0.182742	−	0.229151i
$371$	−7.81062	−	9.54828i	−0.405507	−	0.495722i
$372$	0.993130	+	1.24535i	0.0514914	+	0.0645682i
$373$	−12.4527	−	21.5687i	−0.644775	−	1.11678i	−0.984353	−	0.176206i	$-0.943618\pi$
$373$	−12.4527	−	21.5687i	−0.644775	−	1.11678i	0.339578	−	0.940578i	$-0.389716\pi$
$374$	−0.780316	+	1.35155i	−0.0403492	+	0.0698868i
$375$	−0.935272	+	0.140970i	−0.0482973	+	0.00727964i
$376$	15.2843	−	14.1818i	0.788229	−	0.731370i
$377$	−3.10735	−	1.49642i	−0.160037	−	0.0770697i
$378$	−1.44062	+	1.00866i	−0.0740976	+	0.0518796i
$379$	−26.0051	+	12.5234i	−1.33579	+	0.643285i	−0.959104	−	0.283055i	$-0.908652\pi$
$379$	−26.0051	+	12.5234i	−1.33579	+	0.643285i	−0.376691	+	0.926339i	$0.622938\pi$
$380$	−1.64915	+	4.20196i	−0.0845994	+	0.215556i
$381$	0.0682635	−	0.910913i	0.00349724	−	0.0466675i
$382$	8.84592	+	2.72860i	0.452597	+	0.139608i
$383$	0.227935	+	3.04158i	0.0116469	+	0.155418i	0.999995	+	0.00320598i	$0.00102050\pi$
$383$	0.227935	+	3.04158i	0.0116469	+	0.155418i	−0.988348	+	0.152212i	$0.951360\pi$
$384$	0.607396	−	2.66118i	0.0309960	−	0.135803i
$385$	16.4416	+	27.6775i	0.837943	+	1.41057i
$386$	1.72828	+	7.57210i	0.0879673	+	0.385410i
$387$	33.4169	−	10.3077i	1.69868	−	0.523972i
$388$	−4.90008	−	12.4852i	−0.248764	−	0.633840i
$389$	−14.9236	−	13.8471i	−0.756656	−	0.702075i	0.204259	−	0.978917i	$-0.434522\pi$
$389$	−14.9236	−	13.8471i	−0.756656	−	0.702075i	−0.960915	+	0.276842i	$0.910712\pi$
$390$	0.308680	+	0.210455i	0.0156306	+	0.0106568i
$391$	−6.17542			−0.312305
$392$	−4.64532	−	11.0223i	−0.234624	−	0.556708i
$393$	1.63894			0.0826735
$394$	−1.82064	−	1.24129i	−0.0917225	−	0.0625353i
$395$	16.9514	+	15.7286i	0.852919	+	0.791393i
$396$	−7.03439	−	17.9233i	−0.353491	−	0.900682i
$397$	0.155298	−	0.0479031i	0.00779418	−	0.00240419i	−0.290856	−	0.956767i	$-0.593940\pi$
$397$	0.155298	−	0.0479031i	0.00779418	−	0.00240419i	0.298650	+	0.954363i	$0.403464\pi$
$398$	−1.11039	−	4.86494i	−0.0556589	−	0.243857i
$399$	0.0431442	+	0.493350i	0.00215991	+	0.0246984i
$400$	−3.86087	+	16.9156i	−0.193043	+	0.845778i
$401$	−1.95808	−	26.1288i	−0.0977820	−	1.30481i	−0.803068	−	0.595887i	$-0.796801\pi$
$401$	−1.95808	−	26.1288i	−0.0977820	−	1.30481i	0.705286	−	0.708923i	$-0.250818\pi$
$402$	−1.26519	−	0.390259i	−0.0631019	−	0.0194644i
$403$	−0.266189	+	3.55205i	−0.0132598	+	0.176940i
$404$	2.73619	−	6.97169i	0.136130	−	0.346854i
$405$	−25.3998	+	12.2319i	−1.26213	+	0.607808i
$406$	1.54743	+	3.80309i	0.0767974	+	0.188744i
$407$	12.3311	+	5.93834i	0.611230	+	0.294353i
$408$	−0.296455	+	0.275070i	−0.0146767	+	0.0136180i
$409$	−18.9860	+	2.86168i	−0.938797	+	0.141501i	−0.600578	−	0.799567i	$-0.705063\pi$
$409$	−18.9860	+	2.86168i	−0.938797	+	0.141501i	−0.338219	+	0.941067i	$0.609825\pi$
$410$	−1.55939	+	2.70095i	−0.0770129	+	0.133390i
$411$	−0.610938	−	1.05818i	−0.0301353	−	0.0521959i
$412$	13.7062	+	17.1871i	0.675258	+	0.846747i
$413$	−20.7392	+	0.257796i	−1.02051	+	0.0126853i
$414$	−5.35048	+	6.70929i	−0.262962	+	0.329743i
$415$	−50.4350	−	7.60186i	−2.47576	−	0.373160i
$416$	3.87436	−	2.64149i	0.189956	−	0.129510i
$417$	2.61413	−	1.78228i	0.128014	−	0.0872787i
$418$	1.22049	+	0.183959i	0.0596961	+	0.00899774i
$419$	13.1324	−	16.4676i	0.641562	−	0.804493i	−0.349635	−	0.936886i	$-0.613695\pi$
$419$	13.1324	−	16.4676i	0.641562	−	0.804493i	0.991197	+	0.132393i	$0.0422660\pi$
$420$	0.926456	+	3.83850i	0.0452064	+	0.187300i
$421$	7.12585	+	8.93554i	0.347293	+	0.435491i	0.924544	−	0.381075i	$-0.124446\pi$
$421$	7.12585	+	8.93554i	0.347293	+	0.435491i	−0.577251	+	0.816567i	$0.695875\pi$
$422$	0.460558	+	0.797710i	0.0224196	+	0.0388319i
$423$	17.9257	−	31.0481i	0.871575	−	1.50961i
$424$	−7.87808	+	1.18743i	−0.382594	+	0.0576667i
$425$	4.28143	−	3.97259i	0.207680	−	0.192699i
$426$	0.0314846	+	0.0151622i	0.00152543	+	0.000734610i
$427$	0.715376	−	11.4550i	0.0346195	−	0.554345i
$428$	28.0353	−	13.5011i	1.35514	−	0.652599i
$429$	−0.331348	+	0.844261i	−0.0159976	+	0.0407613i
$430$	−1.33576	+	17.8245i	−0.0644161	+	0.859574i
$431$	−7.47931	−	2.30706i	−0.360266	−	0.111127i	0.109338	−	0.994005i	$-0.465127\pi$
$431$	−7.47931	−	2.30706i	−0.360266	−	0.111127i	−0.469604	+	0.882877i	$0.655603\pi$
$432$	−0.311998	−	4.16333i	−0.0150110	−	0.200308i
$433$	3.09612	−	13.5650i	0.148790	−	0.651892i	−0.844432	−	0.535662i	$-0.820062\pi$
$433$	3.09612	−	13.5650i	0.148790	−	0.651892i	0.993222	−	0.116230i	$-0.0370809\pi$
$434$	3.07242	−	2.92269i	0.147481	−	0.140294i
$435$	−0.637209	−	2.79180i	−0.0305518	−	0.133856i
$436$	−11.1761	+	3.44736i	−0.535237	+	0.165099i
$437$	1.78434	+	4.54642i	0.0853564	+	0.217485i
$438$	0.392142	+	0.363854i	0.0187373	+	0.0173856i
$439$	−16.5058	−	11.2535i	−0.787779	−	0.537099i	0.101298	−	0.994856i	$-0.467700\pi$
$439$	−16.5058	−	11.2535i	−0.787779	−	0.537099i	−0.889077	+	0.457757i	$0.848653\pi$
$440$	20.7914			0.991190
$441$	−13.2189	−	15.7560i	−0.629472	−	0.750288i
$442$	−0.428073			−0.0203614
$443$	6.66109	+	4.54145i	0.316478	+	0.215771i	0.711132	−	0.703059i	$-0.248183\pi$
$443$	6.66109	+	4.54145i	0.316478	+	0.215771i	−0.394654	+	0.918830i	$0.629135\pi$
$444$	1.23063	+	1.14185i	0.0584029	+	0.0541900i
$445$	7.31417	+	18.6362i	0.346725	+	0.883440i
$446$	−0.362940	+	0.111952i	−0.0171857	+	0.00530109i
$447$	1.16527	+	5.10539i	0.0551155	+	0.241477i
$448$	9.28452	+	1.28161i	0.438652	+	0.0605501i
$449$	−7.06972	+	30.9744i	−0.333641	+	1.46177i	0.478384	+	0.878151i	$0.341223\pi$
$449$	−7.06972	+	30.9744i	−0.333641	+	1.46177i	−0.812024	+	0.583624i	$0.801634\pi$
$450$	−0.606522	−	8.09347i	−0.0285917	−	0.381530i
$451$	−7.23488	−	2.23167i	−0.340677	−	0.105085i
$452$	1.82378	−	24.3367i	0.0857835	−	1.14470i
$453$	0.528841	−	1.34747i	0.0248471	−	0.0633095i
$454$	9.84641	−	4.74178i	0.462115	−	0.222543i
$455$	−4.31976	+	7.70155i	−0.202513	+	0.361054i
$456$	0.288168	+	0.138774i	0.0134947	+	0.00649870i
$457$	−6.03207	+	5.59695i	−0.282169	+	0.261814i	−0.808541	−	0.588440i	$-0.799742\pi$
$457$	−6.03207	+	5.59695i	−0.282169	+	0.261814i	0.526372	+	0.850254i	$0.323552\pi$
$458$	−4.55921	+	0.687191i	−0.213038	+	0.0321103i
$459$	−0.702696	+	1.21710i	−0.0327990	+	0.0568096i
$460$	19.4713	+	33.7253i	0.907856	+	1.57245i
$461$	9.28231	+	11.6396i	0.432320	+	0.542112i	0.949501	−	0.313764i	$-0.101590\pi$
$461$	9.28231	+	11.6396i	0.432320	+	0.542112i	−0.517181	+	0.855876i	$0.673019\pi$
$462$	0.966889	−	0.480525i	0.0449838	−	0.0223560i
$463$	3.18381	−	3.99237i	0.147964	−	0.185541i	−0.702326	−	0.711856i	$-0.747855\pi$
$463$	3.18381	−	3.99237i	0.147964	−	0.185541i	0.850290	+	0.526314i	$0.176426\pi$
$464$	−9.63846	−	1.45276i	−0.447454	−	0.0674429i
$465$	−2.44361	+	1.66602i	−0.113319	+	0.0772599i
$466$	−4.88717	+	3.33202i	−0.226394	+	0.154353i
$467$	17.9071	+	2.69907i	0.828644	+	0.124898i	0.549650	−	0.835395i	$-0.314761\pi$
$467$	17.9071	+	2.69907i	0.828644	+	0.124898i	0.278994	+	0.960293i	$0.409999\pi$
$468$	3.29288	−	4.12914i	0.152213	−	0.190869i
$469$	6.58385	−	30.5938i	0.304014	−	1.41269i
$470$	11.4252	+	14.3268i	0.527007	+	0.660846i
$471$	2.12563	+	3.68169i	0.0979437	+	0.169643i
$472$	−6.69763	+	11.6006i	−0.308283	+	0.533962i
$473$	−42.9080	+	6.46734i	−1.97291	+	0.297368i
$474$	0.568535	−	0.527523i	0.0261137	−	0.0242299i
$475$	−4.16175	−	2.00419i	−0.190954	−	0.0919586i
$476$	−3.35470	−	3.03599i	−0.153762	−	0.139154i
$477$	−12.3425	+	5.94381i	−0.565122	+	0.272148i
$478$	−3.52477	+	8.98095i	−0.161219	+	0.410779i
$479$	0.516150	−	6.88754i	0.0235835	−	0.314700i	−0.972920	−	0.231144i	$-0.925753\pi$
$479$	0.516150	−	6.88754i	0.0235835	−	0.314700i	0.996503	−	0.0835560i	$-0.0266277\pi$
$480$	3.72039	+	1.14759i	0.169812	+	0.0523800i
$481$	0.280547	+	3.74364i	0.0127918	+	0.170695i
$482$	−0.676776	+	2.96515i	−0.0308263	+	0.135059i
$483$	3.55969	+	2.36268i	0.161971	+	0.107506i
$484$	0.916453	+	4.01524i	0.0416570	+	0.182511i
$485$	23.7967	−	7.34031i	1.08055	−	0.333306i
$486$	1.07396	+	2.73642i	0.0487160	+	0.124126i
$487$	−28.4943	−	26.4389i	−1.29120	−	1.19806i	−0.967778	−	0.251805i	$-0.918976\pi$
$487$	−28.4943	−	26.4389i	−1.29120	−	1.19806i	−0.323423	−	0.946255i	$-0.604834\pi$
$488$	−6.12451	−	4.17562i	−0.277244	−	0.189021i
$489$	−3.72744			−0.168561
$490$	9.96514	−	3.34729i	0.450179	−	0.151215i
$491$	−1.45354			−0.0655972			−0.0327986	−	0.999462i	$-0.510442\pi$
$491$	−1.45354			−0.0655972			−0.0327986	+	0.999462i	$0.510442\pi$
$492$	−0.767314	−	0.523146i	−0.0345932	−	0.0235852i
$493$	2.40525	+	2.23175i	0.108327	+	0.100513i
$494$	0.123688	+	0.315152i	0.00556500	+	0.0141794i
$495$	34.1618	−	10.5375i	1.53546	−	0.473626i
$496$	2.24012	+	9.81460i	0.100584	+	0.440688i
$497$	−0.292178	+	0.772558i	−0.0131060	+	0.0346540i
$498$	−0.380655	+	1.66776i	−0.0170576	+	0.0747341i
$499$	2.43583	+	32.5039i	0.109043	+	1.45507i	0.736508	+	0.676429i	$0.236474\pi$
$499$	2.43583	+	32.5039i	0.109043	+	1.45507i	−0.627465	+	0.778645i	$0.715907\pi$
$500$	−6.53061	−	2.01443i	−0.292058	−	0.0900879i
$501$	0.443419	−	5.91702i	0.0198105	−	0.264353i
$502$	−2.18852	+	5.57626i	−0.0976785	+	0.248881i
$503$	−16.8174	+	8.09883i	−0.749851	+	0.361109i	−0.769457	−	0.638699i	$-0.779473\pi$
$503$	−16.8174	+	8.09883i	−0.749851	+	0.361109i	0.0196063	+	0.999808i	$0.493759\pi$
$504$	−13.1089	+	2.14281i	−0.583917	+	0.0954485i
$505$	12.5287	+	6.03350i	0.557519	+	0.268487i
$506$	7.80569	−	7.24263i	0.347005	−	0.321974i
$507$	−0.245995	+	0.0370777i	−0.0109250	+	0.00164668i
$508$	3.30017	−	5.71607i	0.146422	−	0.253610i
$509$	−11.3639	−	19.6829i	−0.503696	−	0.872428i	−0.999991	−	0.00427351i	$-0.998640\pi$
$509$	−11.3639	−	19.6829i	−0.503696	−	0.872428i	0.496294	−	0.868154i	$-0.334694\pi$
$510$	−0.221604	−	0.277883i	−0.00981279	−	0.0123049i
$511$	−7.75985	+	9.98261i	−0.343276	+	0.441604i
$512$	14.2848	−	17.9126i	0.631305	−	0.791631i
$513$	1.09908	+	0.165660i	0.0485258	+	0.00731408i
$514$	9.31455	−	6.35055i	0.410847	−	0.280111i
$515$	−33.7243	+	22.9929i	−1.48607	+	1.01319i
$516$	−5.26305	−	0.793277i	−0.231693	−	0.0349221i
$517$	−27.7363	+	34.7802i	−1.21984	+	1.52963i
$518$	2.74287	−	3.52855i	0.120515	−	0.155035i
$519$	0.311010	+	0.389994i	0.0136518	+	0.0171189i
$520$	2.85149	+	4.93892i	0.125046	+	0.216586i
$521$	−17.8452	+	30.9088i	−0.781812	+	1.35414i	0.149074	+	0.988826i	$0.452371\pi$
$521$	−17.8452	+	30.9088i	−0.781812	+	1.35414i	−0.930885	+	0.365311i	$0.880963\pi$
$522$	4.50863	−	0.679567i	0.197337	−	0.0297438i
$523$	−24.4353	+	22.6727i	−1.06848	+	0.991407i	−0.999981	−	0.00624424i	$-0.998012\pi$
$523$	−24.4353	+	22.6727i	−1.06848	+	0.991407i	−0.0685019	+	0.997651i	$0.521822\pi$
$524$	10.6696	+	5.13819i	0.466102	+	0.224463i
$525$	−3.98782	+	0.651859i	−0.174043	+	0.0284495i
$526$	−5.26838	+	2.53712i	−0.229712	+	0.110624i
$527$	1.23805	−	3.15450i	0.0539304	−	0.137412i
$528$	−0.191552	+	2.55608i	−0.00833622	+	0.111239i
$529$	18.2849	+	5.64015i	0.794996	+	0.245224i
$530$	−0.523261	−	6.98243i	−0.0227290	−	0.303297i
$531$	−5.12525	+	22.4552i	−0.222417	+	0.974472i
$532$	−1.26582	+	3.34699i	−0.0548801	+	0.145110i
$533$	−0.462122	−	2.02469i	−0.0200167	−	0.0876990i
$534$	0.641625	−	0.197915i	0.0277658	−	0.00856462i
$535$	21.1078	+	53.7817i	0.912568	+	2.32518i
$536$	−14.8158	−	13.7470i	−0.639944	−	0.593781i
$537$	−2.79108	−	1.90293i	−0.120444	−	0.0821173i
$538$	−5.61966			−0.242281
$539$	13.3054	+	21.7769i	0.573104	+	0.937999i
$540$	8.86250			0.381381
$541$	−13.5172	−	9.21584i	−0.581148	−	0.396220i	0.236761	−	0.971568i	$-0.423914\pi$
$541$	−13.5172	−	9.21584i	−0.581148	−	0.396220i	−0.817909	+	0.575348i	$0.804867\pi$
$542$	−6.44534	−	5.98040i	−0.276851	−	0.256880i
$543$	1.67199	+	4.26016i	0.0717519	+	0.182821i
$544$	−4.26288	+	1.31493i	−0.182770	+	0.0563769i
$545$	−4.83220	−	21.1713i	−0.206989	−	0.906877i
$546$	0.246753	+	0.163778i	0.0105601	+	0.00700907i
$547$	0.247994	−	1.08653i	0.0106035	−	0.0464569i	−0.969349	−	0.245686i	$-0.920987\pi$
$547$	0.247994	−	1.08653i	0.0106035	−	0.0464569i	0.979953	+	0.199229i	$0.0638439\pi$
$548$	−0.659776	−	8.80409i	−0.0281842	−	0.376092i
$549$	−12.1793	−	3.75682i	−0.519800	−	0.160337i
$550$	−0.752593	+	10.0426i	−0.0320907	+	0.428220i
$551$	0.948061	−	2.41562i	0.0403887	−	0.102909i
$552$	2.48605	−	1.19722i	0.105813	−	0.0509571i
$553$	13.5918	+	12.3005i	0.577980	+	0.523070i
$554$	1.42983	+	0.688571i	0.0607478	+	0.0292546i
$555$	−2.28494	+	2.12011i	−0.0969903	+	0.0899938i
$556$	22.6056	−	3.40725i	0.958693	−	0.144500i
$557$	0.0397184	−	0.0687942i	0.00168292	−	0.00291490i	−0.865183	−	0.501457i	$-0.832798\pi$
$557$	0.0397184	−	0.0687942i	0.00168292	−	0.00291490i	0.866866	+	0.498542i	$0.166131\pi$
$558$	−2.35454	−	4.07819i	−0.0996758	−	0.172644i
$559$	−7.42101	−	9.30566i	−0.313875	−	0.393587i
$560$	−5.25045	+	24.3977i	−0.221872	+	1.03099i
$561$	0.537973	−	0.674597i	0.0227132	−	0.0284815i
$562$	11.4247	+	1.72199i	0.481920	+	0.0726378i
$563$	−4.64297	+	3.16552i	−0.195678	+	0.133411i	−0.657196	−	0.753720i	$-0.728257\pi$
$563$	−4.64297	+	3.16552i	−0.195678	+	0.133411i	0.461518	+	0.887131i	$0.347305\pi$
$564$	−4.50842	+	3.07379i	−0.189839	+	0.129430i
$565$	44.8072	+	6.75360i	1.88505	+	0.284126i
$566$	6.86303	−	8.60597i	0.288475	−	0.361736i
$567$	−20.0130	+	9.94605i	−0.840466	+	0.417695i
$568$	0.332595	+	0.417061i	0.0139554	+	0.0174995i
$569$	9.29479	+	16.0990i	0.389658	+	0.674907i	0.992403	−	0.123026i	$-0.0392600\pi$
$569$	9.29479	+	16.0990i	0.389658	+	0.674907i	−0.602746	+	0.797933i	$0.705927\pi$
$570$	−0.140550	+	0.243439i	−0.00588698	+	0.0101966i
$571$	−15.6936	+	2.36542i	−0.656755	+	0.0989898i	−0.468961	−	0.883219i	$-0.655372\pi$
$571$	−15.6936	+	2.36542i	−0.656755	+	0.0989898i	−0.187793	+	0.982209i	$0.560134\pi$
$572$	−4.80391	+	4.45737i	−0.200861	+	0.186372i
$573$	−4.61126	−	2.22067i	−0.192638	−	0.0927696i
$574$	−1.20946	+	2.15631i	−0.0504819	+	0.0900026i
$575$	−35.9038	+	17.2904i	−1.49729	+	0.721058i
$576$	3.80256	−	9.68876i	0.158440	−	0.403698i
$577$	1.58477	−	21.1473i	0.0659750	−	0.880375i	−0.861803	−	0.507243i	$-0.830665\pi$
$577$	1.58477	−	21.1473i	0.0659750	−	0.880375i	0.927778	−	0.373132i	$-0.121716\pi$
$578$	−6.92031	−	2.13463i	−0.287847	−	0.0887890i
$579$	−0.320900	−	4.28212i	−0.0133362	−	0.177959i
$580$	4.60422	−	20.1724i	0.191180	−	0.837613i
$581$	−40.0529	−	5.52878i	−1.66168	−	0.229372i
$582$	−0.185855	−	0.814285i	−0.00770395	−	0.0337532i
$583$	16.2431	−	5.01034i	0.672721	−	0.207507i
$584$	2.98336	+	7.60147i	0.123452	+	0.314551i
$585$	7.18835	+	6.66982i	0.297202	+	0.275763i
$586$	−4.56444	−	3.11198i	−0.188555	−	0.128555i
$587$	2.01581			0.0832013			0.0416006	−	0.999134i	$-0.486754\pi$
$587$	2.01581			0.0832013			0.0416006	+	0.999134i	$0.486754\pi$
$588$	0.772190	+	3.03352i	0.0318446	+	0.125100i
$589$	−2.68011			−0.110432
$590$	−9.72705	−	6.63179i	−0.400456	−	0.273026i
$591$	0.893066	+	0.828644i	0.0367358	+	0.0340859i
$592$	3.87626	+	9.87655i	0.159313	+	0.405924i
$593$	9.56987	−	2.95191i	0.392987	−	0.121221i	−0.0919626	−	0.995762i	$-0.529314\pi$
$593$	9.56987	−	2.95191i	0.392987	−	0.121221i	0.484950	+	0.874542i	$0.338838\pi$
$594$	−0.539235	−	2.36254i	−0.0221251	−	0.0969364i
$595$	6.08672	−	5.79009i	0.249531	−	0.237371i
$596$	−8.41979	+	36.8895i	−0.344888	+	1.51105i
$597$	0.206173	+	2.75118i	0.00843809	+	0.112598i
$598$	2.79099	+	0.860907i	0.114132	+	0.0352051i
$599$	−0.356830	+	4.76157i	−0.0145797	+	0.194552i	0.985158	+	0.171650i	$0.0549098\pi$
$599$	−0.356830	+	4.76157i	−0.0145797	+	0.194552i	−0.999738	+	0.0229025i	$0.992709\pi$
$600$	−0.953425	+	2.42929i	−0.0389234	+	0.0991753i
$601$	16.5579	−	7.97389i	0.675413	−	0.325262i	−0.0645452	−	0.997915i	$-0.520560\pi$
$601$	16.5579	−	7.97389i	0.675413	−	0.325262i	0.739958	+	0.672653i	$0.234845\pi$
$602$	−0.883183	+	14.1420i	−0.0359959	+	0.576385i
$603$	−31.3107	−	15.0784i	−1.27507	−	0.614041i
$604$	7.66718	−	7.11410i	0.311973	−	0.289469i
$605$	−7.56154	+	1.13972i	−0.307420	+	0.0463361i
$606$	0.233193	−	0.403903i	0.00947284	−	0.0164074i
$607$	−16.2859	−	28.2080i	−0.661024	−	1.14493i	−0.980347	−	0.197281i	$-0.936789\pi$
$607$	−16.2859	−	28.2080i	−0.661024	−	1.14493i	0.319323	−	0.947646i	$-0.396544\pi$
$608$	2.19979	+	2.75845i	0.0892131	+	0.111870i
$609$	−0.532601	−	2.20668i	−0.0215821	−	0.0894191i
$610$	4.06181	−	5.09335i	0.164458	−	0.206224i
$611$	−12.0659	−	1.81864i	−0.488133	−	0.0735742i
$612$	−4.15142	+	2.83039i	−0.167811	+	0.114412i
$613$	35.2886	−	24.0593i	1.42529	−	0.971747i	0.427591	−	0.903972i	$-0.359362\pi$
$613$	35.2886	−	24.0593i	1.42529	−	0.971747i	0.997701	−	0.0677747i	$-0.0215899\pi$
$614$	−15.3378	−	2.31180i	−0.618984	−	0.0932969i
$615$	1.07509	−	1.34812i	0.0433519	−	0.0543615i
$616$	16.4806	−	0.204860i	0.664022	−	0.00825405i
$617$	−26.9984	−	33.8549i	−1.08691	−	1.36295i	−0.926673	−	0.375868i	$-0.877345\pi$
$617$	−26.9984	−	33.8549i	−1.08691	−	1.36295i	−0.160240	−	0.987078i	$-0.551227\pi$
$618$	0.684476	+	1.18555i	0.0275337	+	0.0476897i
$619$	7.34678	−	12.7250i	0.295292	−	0.511461i	−0.679761	−	0.733434i	$-0.737916\pi$
$619$	7.34678	−	12.7250i	0.295292	−	0.511461i	0.975053	+	0.221973i	$0.0712497\pi$
$620$	−21.1311	+	3.18500i	−0.848644	+	0.127912i
$621$	7.02924	−	6.52218i	0.282074	−	0.261726i
$622$	4.47122	+	2.15322i	0.179279	+	0.0863364i
$623$	5.98130	+	14.7002i	0.239636	+	0.588950i
$624$	−0.633459	+	0.305058i	−0.0253586	+	0.0122121i
$625$	−6.57851	+	16.7618i	−0.263140	+	0.670471i
$626$	0.878332	−	11.7205i	0.0351052	−	0.468446i
$627$	−0.652088	−	0.201143i	−0.0260419	−	0.00803286i
$628$	2.29555	+	30.6320i	0.0916023	+	1.22235i
$629$	0.794741	−	3.48199i	0.0316884	−	0.138836i
$630$	−1.01702	−	11.6295i	−0.0405191	−	0.463332i
$631$	−4.72946	−	20.7211i	−0.188277	−	0.824895i	−0.977525	−	0.210820i	$-0.932387\pi$
$631$	−4.72946	−	20.7211i	−0.188277	−	0.824895i	0.789248	−	0.614075i	$-0.210471\pi$
$632$	11.3132	−	3.48965i	0.450014	−	0.138811i
$633$	−0.186056	−	0.474063i	−0.00739506	−	0.0188423i
$634$	0.313454	+	0.290843i	0.0124489	+	0.0115508i
$635$	10.1256	+	6.90352i	0.401822	+	0.273958i
$636$	2.08499			0.0826754
$637$	−3.34823	+	6.14730i	−0.132662	+	0.243565i
$638$	−5.65765			−0.223989
$639$	0.757854	+	0.516696i	0.0299802	+	0.0204402i
$640$	26.8447	+	24.9082i	1.06113	+	0.984584i
$641$	5.09161	+	12.9732i	0.201107	+	0.512411i	0.995475	−	0.0950252i	$-0.0302932\pi$
$641$	5.09161	+	12.9732i	0.201107	+	0.512411i	−0.794368	+	0.607436i	$0.792198\pi$
$642$	1.85165	−	0.571157i	0.0730787	−	0.0225418i
$643$	−2.78251	−	12.1910i	−0.109732	−	0.480765i	−0.999694	−	0.0247317i	$-0.992127\pi$
$643$	−2.78251	−	12.1910i	−0.109732	−	0.480765i	0.889963	−	0.456034i	$-0.150730\pi$
$644$	15.7665	+	26.5410i	0.621288	+	1.04586i
$645$	2.19905	−	9.63466i	0.0865875	−	0.379365i
$646$	−0.0240697	−	0.321188i	−0.000947009	−	0.0126370i
$647$	−22.6303	−	6.98052i	−0.889689	−	0.274433i	−0.183976	−	0.982931i	$-0.558897\pi$
$647$	−22.6303	−	6.98052i	−0.889689	−	0.274433i	−0.705713	+	0.708498i	$0.749373\pi$
$648$	−1.07861	+	14.3931i	−0.0423718	+	0.565413i
$649$	10.4413	−	26.6041i	0.409859	−	1.04430i
$650$	−2.48881	+	1.19855i	−0.0976193	+	0.0470110i
$651$	−1.92054	+	1.34467i	−0.0752720	+	0.0527019i
$652$	−24.2658	−	11.6858i	−0.950321	−	0.457650i
$653$	−29.6345	+	27.4968i	−1.15969	+	1.07603i	−0.163704	+	0.986510i	$0.552344\pi$
$653$	−29.6345	+	27.4968i	−1.15969	+	1.07603i	−0.995985	+	0.0895239i	$0.971465\pi$
$654$	−0.720190	+	0.108551i	−0.0281616	+	0.00424469i
$655$	−10.9940	+	19.0421i	−0.429571	+	0.744038i
$656$	−2.93468	−	5.08301i	−0.114580	−	0.198458i
$657$	8.75445	+	10.9777i	0.341544	+	0.428282i
$658$	9.19755	+	11.2438i	0.358558	+	0.438328i
$659$	5.08093	−	6.37128i	0.197925	−	0.248190i	−0.672958	−	0.739681i	$-0.734976\pi$
$659$	5.08093	−	6.37128i	0.197925	−	0.248190i	0.870883	+	0.491491i	$0.163548\pi$
$660$	−5.38037	−	0.810960i	−0.209430	−	0.0315666i
$661$	5.64677	−	3.84991i	0.219634	−	0.149744i	−0.448505	−	0.893780i	$-0.648043\pi$
$661$	5.64677	−	3.84991i	0.219634	−	0.149744i	0.668139	+	0.744036i	$0.267091\pi$
$662$	−1.14128	+	0.778109i	−0.0443570	+	0.0302421i
$663$	0.234030	+	0.0352743i	0.00908896	+	0.00136994i
$664$	−16.2813	+	20.4161i	−0.631836	+	0.792297i
$665$	−6.02144	−	2.80811i	−0.233501	−	0.108894i
$666$	−3.09443	−	3.88029i	−0.119907	−	0.150358i
$667$	−11.1937	−	19.3880i	−0.433421	−	0.750707i
$668$	21.4369	−	37.1299i	0.829420	−	1.43660i
$669$	0.207646	−	0.0312976i	0.00802806	−	0.00121004i
$670$	13.0211	−	12.0818i	0.503050	−	0.466762i
$671$	14.2489	+	6.86192i	0.550074	+	0.264902i
$672$	2.96033	+	0.872994i	0.114197	+	0.0336765i
$673$	12.4547	−	5.99788i	0.480095	−	0.231201i	−0.178153	−	0.984003i	$-0.557012\pi$
$673$	12.4547	−	5.99788i	0.480095	−	0.231201i	0.658248	+	0.752801i	$0.271298\pi$
$674$	5.11273	−	13.0270i	0.196935	−	0.501782i
$675$	−0.677730	+	9.04368i	−0.0260859	+	0.348092i
$676$	−1.71768	−	0.529833i	−0.0660645	−	0.0203782i
$677$	−3.87445	−	51.7009i	−0.148907	−	1.98703i	−0.160157	−	0.987092i	$-0.551200\pi$
$677$	−3.87445	−	51.7009i	−0.148907	−	1.98703i	0.0112495	−	0.999937i	$-0.496419\pi$
$678$	0.338180	−	1.48166i	0.0129877	−	0.0569029i
$679$	18.7905	−	6.05287i	0.721112	−	0.232288i
$680$	−1.20731	−	5.28955i	−0.0462981	−	0.202845i
$681$	−5.77381	+	1.78098i	−0.221253	+	0.0682475i
$682$	2.13476	+	5.43928i	0.0817442	+	0.208281i
$683$	−16.8631	−	15.6467i	−0.645249	−	0.598703i	0.288132	−	0.957591i	$-0.406966\pi$
$683$	−16.8631	−	15.6467i	−0.645249	−	0.598703i	−0.933381	+	0.358887i	$0.883156\pi$
$684$	3.28328	+	2.23850i	0.125539	+	0.0855914i
$685$	16.3927			0.626331
$686$	7.86603	−	2.75146i	0.300326	−	0.105051i
$687$	2.54917			0.0972569
$688$	−27.7936	−	18.9493i	−1.05962	−	0.722436i
$689$	3.41789	+	3.17134i	0.130211	+	0.120818i
$690$	0.885979	+	2.25744i	0.0337286	+	0.0859392i
$691$	−9.38065	+	2.89355i	−0.356857	+	0.110076i	−0.468000	−	0.883729i	$-0.655025\pi$
$691$	−9.38065	+	2.89355i	−0.356857	+	0.110076i	0.111143	+	0.993804i	$0.464549\pi$
$692$	0.802029	+	3.51392i	0.0304886	+	0.133579i
$693$	26.9750	−	8.68931i	1.02469	−	0.330079i
$694$	−0.522489	+	2.28917i	−0.0198334	+	0.0868959i
$695$	3.17204	+	42.3280i	0.120322	+	1.60559i
$696$	−1.40095	−	0.432137i	−0.0531030	−	0.0163801i
$697$	−0.147648	+	1.97022i	−0.00559255	+	0.0746274i
$698$	−4.07112	+	10.3730i	−0.154094	+	0.392625i
$699$	2.94641	−	1.41891i	0.111443	−	0.0536683i
$700$	−28.0045	−	8.25848i	−1.05847	−	0.312141i
$701$	18.8370	+	9.07140i	0.711462	+	0.342622i	0.754363	−	0.656457i	$-0.227946\pi$
$701$	18.8370	+	9.07140i	0.711462	+	0.342622i	−0.0429010	+	0.999079i	$0.513660\pi$
$702$	0.487259	−	0.452111i	0.0183904	−	0.0170638i
$703$	−2.79311	+	0.420994i	−0.105344	+	0.0158781i
$704$	−6.45745	+	11.1846i	−0.243374	+	0.421537i
$705$	−5.06567	−	8.77400i	−0.190784	−	0.330448i
$706$	4.86279	+	6.09775i	0.183013	+	0.229492i
$707$	9.99049	+	4.65909i	0.375731	+	0.175223i
$708$	2.18568	−	2.74076i	0.0821429	−	0.103004i
$709$	30.6924	+	4.62613i	1.15268	+	0.173738i	0.697447	−	0.716636i	$-0.254319\pi$
$709$	30.6924	+	4.62613i	1.15268	+	0.173738i	0.455229	+	0.890374i	$0.349557\pi$
$710$	−0.387362	+	0.264099i	−0.0145374	+	0.00991144i
$711$	16.8197	−	11.4675i	0.630789	−	0.430065i
$712$	10.1353	+	1.52765i	0.379837	+	0.0572512i
$713$	−14.4161	+	18.0772i	−0.539885	+	0.676995i
$714$	−0.178396	−	0.218084i	−0.00667629	−	0.00816160i
$715$	−7.58643	−	9.51309i	−0.283717	−	0.355769i
$716$	−12.2042	−	21.1384i	−0.456094	−	0.789977i
$717$	2.66706	−	4.61948i	0.0996031	−	0.172518i
$718$	−6.82580	+	1.02882i	−0.254737	+	0.0383954i
$719$	−8.94256	+	8.29748i	−0.333501	+	0.309444i	−0.829092	−	0.559112i	$-0.811142\pi$
$719$	−8.94256	+	8.29748i	−0.333501	+	0.309444i	0.495591	+	0.868556i	$0.334952\pi$
$720$	24.9695	+	12.0247i	0.930557	+	0.448132i
$721$	−26.5055	+	18.5579i	−0.987117	+	0.691132i
$722$	7.47308	−	3.59885i	0.278119	−	0.133935i
$723$	0.614332	−	1.56529i	0.0228472	−	0.0582138i
$724$	−2.47118	+	32.9756i	−0.0918406	+	1.22553i
$725$	20.2327	+	6.24096i	0.751424	+	0.231784i
$726$	0.0191661	+	0.255754i	0.000711322	+	0.00949193i
$727$	−4.26119	+	18.6695i	−0.158039	+	0.692413i	0.832367	+	0.554225i	$0.186985\pi$
$727$	−4.26119	+	18.6695i	−0.158039	+	0.692413i	−0.990406	+	0.138189i	$0.955872\pi$
$728$	2.30894	+	3.88681i	0.0855748	+	0.144055i
$729$	5.27714	+	23.1207i	0.195450	+	0.856321i
$730$	−6.85795	+	2.11540i	−0.253824	+	0.0782944i
$731$	4.13692	+	10.5407i	0.153010	+	0.389862i
$732$	1.42202	+	1.31945i	0.0525595	+	0.0487681i
$733$	6.14370	+	4.18870i	0.226923	+	0.154713i	0.671445	−	0.741055i	$-0.265674\pi$
$733$	6.14370	+	4.18870i	0.226923	+	0.154713i	−0.444522	+	0.895768i	$0.646626\pi$
$734$	9.63499			0.355634
$735$	−5.72381	+	1.00883i	−0.211126	+	0.0372111i
$736$	30.4380			1.12196
$737$	35.6289	+	24.2914i	1.31241	+	0.894784i
$738$	2.01262	+	1.86744i	0.0740856	+	0.0687414i
$739$	16.1985	+	41.2731i	0.595872	+	1.51826i	0.836685	+	0.547685i	$0.184491\pi$
$739$	16.1985	+	41.2731i	0.595872	+	1.51826i	−0.240813	+	0.970572i	$0.577414\pi$
$740$	−21.5218	+	6.63858i	−0.791156	+	0.244039i
$741$	−0.0416516	−	0.182487i	−0.00153011	−	0.00670385i
$742$	−0.483569	−	5.52957i	−0.0177524	−	0.202997i
$743$	−3.00721	+	13.1754i	−0.110324	+	0.483360i	0.889336	+	0.457255i	$0.151167\pi$
$743$	−3.00721	+	13.1754i	−0.110324	+	0.483360i	−0.999659	+	0.0261045i	$0.991690\pi$
$744$	0.113154	+	1.50994i	0.00414843	+	0.0553569i
$745$	−67.1340	−	20.7081i	−2.45960	−	0.758686i
$746$	0.837455	−	11.1751i	0.0306614	−	0.409148i
$747$	−16.4040	+	41.7968i	−0.600192	+	1.52927i
$748$	5.61713	−	2.70507i	0.205383	−	0.0989071i
$749$	17.2613	+	42.4228i	0.630713	+	1.55010i
$750$	−0.383441	−	0.184656i	−0.0140013	−	0.00674267i
$751$	9.77930	−	9.07386i	0.356852	−	0.331110i	−0.481291	−	0.876561i	$-0.659832\pi$
$751$	9.77930	−	9.07386i	0.356852	−	0.331110i	0.838143	+	0.545451i	$0.183642\pi$
$752$	−34.1007	+	5.13985i	−1.24352	+	0.187431i
$753$	1.65597	−	2.86823i	0.0603470	−	0.104524i
$754$	−0.775933	−	1.34396i	−0.0282578	−	0.0489440i
$755$	12.1082	+	15.1832i	0.440662	+	0.552572i
$756$	7.02499	−	0.0873234i	0.255496	−	0.00317592i
$757$	−22.4073	+	28.0979i	−0.814409	+	1.02124i	0.184851	+	0.982767i	$0.440820\pi$
$757$	−22.4073	+	28.0979i	−0.814409	+	1.02124i	−0.999260	+	0.0384697i	$0.987752\pi$
$758$	−12.8424	−	1.93567i	−0.466455	−	0.0703068i
$759$	−4.86422	+	3.31637i	−0.176560	+	0.120377i
$760$	−3.54539	+	2.41720i	−0.128605	+	0.0876812i
$761$	−17.6814	−	2.66504i	−0.640949	−	0.0966075i	−0.179477	−	0.983762i	$-0.557440\pi$
$761$	−17.6814	−	2.66504i	−0.640949	−	0.0966075i	−0.461472	+	0.887155i	$0.652679\pi$
$762$	0.256269	−	0.321351i	0.00928363	−	0.0116413i
$763$	−4.03892	−	16.7341i	−0.146219	−	0.605814i
$764$	−23.0575	−	28.9132i	−0.834193	−	1.04604i
$765$	−4.66455	−	8.07924i	−0.168647	−	0.292105i
$766$	−0.686213	+	1.18856i	−0.0247939	+	0.0429443i
$767$	7.75172	−	1.16838i	0.279898	−	0.0421879i
$768$	−0.391700	+	0.363445i	−0.0141343	+	0.0131147i
$769$	−7.28874	−	3.51007i	−0.262839	−	0.126577i	0.297824	−	0.954621i	$-0.403739\pi$
$769$	−7.28874	−	3.51007i	−0.262839	−	0.126577i	−0.560663	+	0.828044i	$0.689454\pi$
$770$	−0.902870	+	14.4572i	−0.0325372	+	0.521003i
$771$	−5.61561	+	2.70433i	−0.202241	+	0.0973942i
$772$	11.3357	−	28.8828i	0.407980	−	1.03951i
$773$	0.482978	−	6.44490i	0.0173715	−	0.231807i	−0.981759	−	0.190127i	$-0.939110\pi$
$773$	0.482978	−	6.44490i	0.0173715	−	0.231807i	0.999131	−	0.0416798i	$-0.0132709\pi$
$774$	15.0362	+	4.63807i	0.540466	+	0.166712i
$775$	−1.63418	−	21.8066i	−0.0587015	−	0.783317i
$776$	2.83709	−	12.4301i	0.101846	−	0.446214i
$777$	−1.79030	+	1.70305i	−0.0642267	+	0.0610967i
$778$	−2.03837	−	8.93068i	−0.0730791	−	0.320180i
$779$	1.49316	−	0.460579i	0.0534980	−	0.0165019i
$780$	−0.545263	−	1.38931i	−0.0195236	−	0.0497452i
$781$	−0.834311	−	0.774128i	−0.0298540	−	0.0277005i
$782$	−2.29586	−	1.56529i	−0.0820998	−	0.0559747i
$783$	−5.09487			−0.182076
$784$	−3.92145	+	19.3909i	−0.140052	+	0.692533i
$785$	−57.0347			−2.03566
$786$	0.609315	+	0.415424i	0.0217335	+	0.0148177i
$787$	3.56472	+	3.30758i	0.127069	+	0.117902i	0.741147	−	0.671342i	$-0.234282\pi$
$787$	3.56472	+	3.30758i	0.127069	+	0.117902i	−0.614079	+	0.789245i	$0.710472\pi$
$788$	3.21604	+	8.19433i	0.114567	+	0.291911i
$789$	3.08931	−	0.952926i	0.109982	−	0.0339251i
$790$	2.31534	+	10.1442i	0.0823763	+	0.360914i
$791$	35.5836	+	4.91185i	1.26521	+	0.174645i
$792$	4.07283	−	17.8442i	0.144722	−	0.634067i
$793$	0.324180	+	4.32588i	0.0115120	+	0.153617i
$794$	0.0698777	+	0.0215544i	0.00247987	+	0.000764938i
$795$	−0.289300	+	3.86045i	−0.0102604	+	0.136916i
$796$	−7.28296	+	18.5567i	−0.258138	+	0.657724i
$797$	16.0634	−	7.73573i	0.568995	−	0.274014i	−0.127187	−	0.991879i	$-0.540595\pi$
$797$	16.0634	−	7.73573i	0.568995	−	0.274014i	0.696182	+	0.717865i	$0.254881\pi$
$798$	−0.109010	+	0.194350i	−0.00385892	+	0.00687993i
$799$	10.4590	+	5.03681i	0.370014	+	0.178189i
$800$	−21.1027	+	19.5805i	−0.746094	+	0.692274i
$801$	17.4273	−	2.62675i	0.615764	−	0.0928115i
$802$	5.89493	−	10.2103i	0.208157	−	0.360539i
$803$	−8.71131	−	15.0884i	−0.307415	−	0.532459i
$804$	3.29781	+	4.13532i	0.116305	+	0.145842i
$805$	−51.3293	+	25.5097i	−1.80912	+	0.899097i
$806$	−0.999305	+	1.25309i	−0.0351990	+	0.0441382i
$807$	3.07229	+	0.463073i	0.108150	+	0.0163010i
$808$	5.88234	−	4.01051i	0.206940	−	0.141089i
$809$	−13.8171	+	9.42031i	−0.485782	+	0.331201i	−0.781320	−	0.624130i	$-0.785453\pi$
$809$	−13.8171	+	9.42031i	−0.485782	+	0.331201i	0.295538	+	0.955331i	$0.404501\pi$
$810$	−12.5434	−	1.89061i	−0.440730	−	0.0664294i
$811$	23.6179	−	29.6159i	0.829336	−	1.03995i	−0.169184	−	0.985584i	$-0.554113\pi$
$811$	23.6179	−	29.6159i	0.829336	−	1.03995i	0.998521	−	0.0543705i	$-0.0173152\pi$
$812$	3.45084	−	16.0353i	0.121101	−	0.562729i
$813$	3.03090	+	3.80062i	0.106298	+	0.133294i
$814$	3.07918	+	5.33330i	0.107925	+	0.186932i
$815$	25.0036	−	43.3075i	0.875839	−	1.51700i
$816$	0.661417	−	0.0996926i	0.0231542	−	0.00348994i
$817$	6.56486	−	6.09130i	0.229675	−	0.213108i
$818$	−7.78385	−	3.74850i	−0.272156	−	0.131063i
$819$	5.76367	+	5.21610i	0.201399	+	0.182265i
$820$	11.2253	−	5.40584i	0.392006	−	0.188780i
$821$	2.66365	−	6.78687i	0.0929620	−	0.236863i	−0.876828	−	0.480804i	$-0.840345\pi$
$821$	2.66365	−	6.78687i	0.0929620	−	0.236863i	0.969790	+	0.243940i	$0.0784402\pi$
$822$	0.0410862	−	0.548257i	0.00143304	−	0.0191227i
$823$	−33.8337	−	10.4363i	−1.17937	−	0.363787i	−0.357746	−	0.933819i	$-0.616455\pi$
$823$	−33.8337	−	10.4363i	−1.17937	−	0.363787i	−0.821622	+	0.570032i	$0.806931\pi$
$824$	1.56164	+	20.8387i	0.0544024	+	0.725950i
$825$	1.23898	−	5.42835i	0.0431359	−	0.188991i
$826$	−7.77562	−	5.16094i	−0.270549	−	0.179572i
$827$	−3.83654	−	16.8090i	−0.133410	−	0.584506i	−0.996798	−	0.0799652i	$-0.974519\pi$
$827$	−3.83654	−	16.8090i	−0.133410	−	0.584506i	0.863388	−	0.504540i	$-0.168338\pi$
$828$	32.7591	−	10.1048i	1.13846	−	0.351167i
$829$	11.1088	+	28.3047i	0.385824	+	0.983064i	0.983432	+	0.181276i	$0.0580227\pi$
$829$	11.1088	+	28.3047i	0.385824	+	0.983064i	−0.597608	+	0.801788i	$0.703882\pi$
$830$	−16.8236	−	15.6100i	−0.583955	−	0.541831i
$831$	−0.724956	−	0.494267i	−0.0251485	−	0.0171459i
$832$	−3.54249			−0.122814
$833$	4.76767	−	4.64957i	0.165190	−	0.161098i
$834$	1.42362			0.0492959
$835$	65.7729	+	44.8432i	2.27616	+	1.55186i
$836$	−3.61452	−	3.35379i	−0.125011	−	0.115993i
$837$	1.92241	+	4.89822i	0.0664482	+	0.169307i
$838$	9.05635	−	2.79351i	0.312846	−	0.0965003i
$839$	−9.85702	−	43.1864i	−0.340302	−	1.49096i	−0.798437	−	0.602079i	$-0.794339\pi$
$839$	−9.85702	−	43.1864i	−0.340302	−	1.49096i	0.458134	−	0.888883i	$-0.348518\pi$
$840$	−1.32783	+	3.51095i	−0.0458144	+	0.121139i
$841$	3.80624	−	16.6762i	0.131250	−	0.575042i
$842$	0.384305	+	5.12820i	0.0132440	+	0.176729i
$843$	−6.10402	−	1.88284i	−0.210234	−	0.0648485i
$844$	0.274989	−	3.66947i	0.00946550	−	0.126308i
$845$	1.21934	−	3.10683i	0.0419466	−	0.106878i
$846$	14.5341	−	6.99925i	0.499693	−	0.240639i
$847$	−5.98253	+	0.977919i	−0.205562	+	0.0336017i
$848$	11.8724	+	5.71744i	0.407699	+	0.196338i
$849$	−4.46120	+	4.13939i	−0.153108	+	0.142064i
$850$	2.59866	−	0.391685i	0.0891333	−	0.0134347i
$851$	−12.1843	+	21.1039i	−0.417673	+	0.723431i
$852$	−0.0698012	−	0.120899i	−0.00239135	−	0.00414194i
$853$	−28.0380	−	35.1585i	−0.960003	−	1.20381i	−0.978974	−	0.203985i	$-0.934611\pi$
$853$	−28.0380	−	35.1585i	−0.960003	−	1.20381i	0.0189714	−	0.999820i	$-0.493961\pi$
$854$	3.16946	−	4.07733i	0.108457	−	0.139524i
$855$	−4.60024	+	5.76852i	−0.157325	+	0.197279i
$856$	29.2492	+	4.40861i	0.999718	+	0.150683i
$857$	−9.40770	+	6.41406i	−0.321361	+	0.219100i	−0.713246	−	0.700914i	$-0.752776\pi$
$857$	−9.40770	+	6.41406i	−0.321361	+	0.219100i	0.391885	+	0.920014i	$0.371823\pi$
$858$	−0.337182	+	0.229887i	−0.0115112	+	0.00784821i
$859$	−30.0196	−	4.52472i	−1.02426	−	0.154382i	−0.384632	−	0.923070i	$-0.625672\pi$
$859$	−30.0196	−	4.52472i	−1.02426	−	0.154382i	−0.639623	+	0.768688i	$0.720910\pi$
$860$	44.5212	−	55.8279i	1.51816	−	1.90371i
$861$	0.838903	−	1.07920i	0.0285897	−	0.0367791i
$862$	−2.19584	−	2.75350i	−0.0747906	−	0.0937844i
$863$	10.8472	+	18.7880i	0.369244	+	0.639549i	0.989448	−	0.144892i	$-0.0462833\pi$
$863$	10.8472	+	18.7880i	0.369244	+	0.639549i	−0.620204	+	0.784441i	$0.712950\pi$
$864$	3.46351	−	5.99898i	0.117831	−	0.204089i
$865$	−6.61743	+	0.997418i	−0.225000	+	0.0339132i
$866$	4.58939	−	4.25833i	0.155954	−	0.144704i
$867$	3.60747	+	1.73726i	0.122516	+	0.0590006i
$868$	−16.7185	+	2.73284i	−0.567461	+	0.0927586i
$869$	−22.7582	+	10.9597i	−0.772017	+	0.371784i
$870$	0.470742	−	1.19943i	0.0159596	−	0.0406645i
$871$	−0.883914	+	11.7950i	−0.0299503	+	0.399659i
$872$	−10.6240	−	3.27706i	−0.359773	−	0.110975i
$873$	−1.63829	−	21.8615i	−0.0554477	−	0.739898i
$874$	−0.489015	+	2.14252i	−0.0165412	+	0.0724717i
$875$	3.55835	−	9.40875i	0.120294	−	0.318074i
$876$	−0.475536	−	2.08346i	−0.0160669	−	0.0703936i
$877$	46.2599	−	14.2693i	1.56209	−	0.481840i	0.611225	−	0.791457i	$-0.290677\pi$
$877$	46.2599	−	14.2693i	1.56209	−	0.481840i	0.950861	+	0.309617i	$0.100201\pi$
$878$	−3.28400	−	8.36749i	−0.110830	−	0.282389i
$879$	2.23896	+	2.07746i	0.0755184	+	0.0700708i
$880$	−28.4131	−	19.3717i	−0.957805	−	0.653020i
$881$	2.55851			0.0861983			0.0430991	−	0.999071i	$-0.486277\pi$
$881$	2.55851			0.0861983			0.0430991	+	0.999071i	$0.486277\pi$
$882$	−0.920743	−	9.20830i	−0.0310030	−	0.310059i
$883$	−14.1777			−0.477118			−0.238559	−	0.971128i	$-0.576675\pi$
$883$	−14.1777			−0.477118			−0.238559	+	0.971128i	$0.576675\pi$
$884$	1.41296	+	0.963337i	0.0475228	+	0.0324005i
$885$	4.77134	+	4.42716i	0.160387	+	0.148817i
$886$	1.32529	+	3.37679i	0.0445240	+	0.113445i
$887$	18.3918	−	5.67311i	0.617535	−	0.190484i	0.0298238	−	0.999555i	$-0.490505\pi$
$887$	18.3918	−	5.67311i	0.617535	−	0.190484i	0.587711	+	0.809071i	$0.300029\pi$
$888$	0.355107	+	1.55583i	0.0119166	+	0.0522102i
$889$	8.09422	+	5.37240i	0.271472	+	0.180185i
$890$	−2.00452	+	8.78238i	−0.0671917	+	0.294386i
$891$	−2.30129	−	30.7086i	−0.0770962	−	1.02878i
$892$	1.44990	+	0.447236i	0.0485464	+	0.0149746i
$893$	0.686102	−	9.15540i	0.0229595	−	0.306374i
$894$	−0.860851	+	2.19341i	−0.0287912	+	0.0733587i
$895$	40.8318	−	19.6636i	1.36486	−	0.657281i
$896$	21.5242	+	19.4793i	0.719074	+	0.650759i
$897$	−1.45491	−	0.700646i	−0.0485779	−	0.0233939i
$898$	−10.4795	+	9.72352i	−0.349704	+	0.324478i
$899$	12.1478	−	1.83099i	0.405152	−	0.0610669i
$900$	−16.2116	+	28.0793i	−0.540386	+	0.935976i
$901$	−2.21788	−	3.84148i	−0.0738884	−	0.127978i
$902$	−2.12408	−	2.66351i	−0.0707241	−	0.0886852i
$903$	1.64818	−	7.65872i	0.0548479	−	0.254866i
$904$	14.4645	−	18.1379i	0.481083	−	0.603259i
$905$	−60.7127	−	9.15096i	−2.01816	−	0.304188i
$906$	0.538153	−	0.366907i	0.0178789	−	0.0121897i
$907$	−9.86693	+	6.72716i	−0.327626	+	0.223372i	−0.715951	−	0.698151i	$-0.754006\pi$
$907$	−9.86693	+	6.72716i	−0.327626	+	0.223372i	0.388324	+	0.921523i	$0.373054\pi$
$908$	−43.1712	−	6.50702i	−1.43269	−	0.215943i
$909$	7.63250	−	9.57086i	0.253154	−	0.317445i
$910$	−3.55809	+	1.76830i	−0.117950	+	0.0586186i
$911$	9.35344	+	11.7288i	0.309893	+	0.388594i	0.912251	−	0.409633i	$-0.134343\pi$
$911$	9.35344	+	11.7288i	0.309893	+	0.388594i	−0.602357	+	0.798227i	$0.705772\pi$
$912$	−0.264506	−	0.458137i	−0.00875866	−	0.0151704i
$913$	27.8571	−	48.2499i	0.921936	−	1.59684i
$914$	−3.66123	+	0.551842i	−0.121103	+	0.0182533i
$915$	−2.64031	+	2.44985i	−0.0872861	+	0.0809896i
$916$	16.5952	+	7.99182i	0.548321	+	0.264057i
$917$	−8.52691	+	15.2023i	−0.281584	+	0.502026i
$918$	−0.569745	+	0.274375i	−0.0188044	+	0.00905571i
$919$	0.755739	−	1.92559i	0.0249295	−	0.0635194i	−0.917867	−	0.396888i	$-0.870090\pi$
$919$	0.755739	−	1.92559i	0.0249295	−	0.0635194i	0.942797	+	0.333369i	$0.108185\pi$
$920$	−2.76642	+	36.9154i	−0.0912063	+	1.21706i
$921$	8.19476	+	2.52775i	0.270026	+	0.0832921i
$922$	0.500605	+	6.68011i	0.0164866	+	0.219998i
$923$	0.0694676	−	0.304357i	0.00228655	−	0.0100180i
$924$	−4.27281	−	0.589805i	−0.140565	−	0.0194032i
$925$	−5.12850	−	22.4694i	−0.168624	−	0.738790i
$926$	2.19561	−	0.677255i	0.0721522	−	0.0222560i
$927$	13.1274	+	33.4480i	0.431160	+	1.09858i
$928$	−11.8552	−	11.0001i	−0.389167	−	0.361094i
$929$	−19.3199	−	13.1721i	−0.633865	−	0.432162i	0.203297	−	0.979117i	$-0.434834\pi$
$929$	−19.3199	−	13.1721i	−0.633865	−	0.432162i	−0.837162	+	0.546955i	$0.815787\pi$
$930$	−1.33076			−0.0436372
$931$	−4.80065	−	2.16656i	−0.157335	−	0.0710062i
$932$	23.6296			0.774014
$933$	−2.26700	−	1.54562i	−0.0742183	−	0.0506012i
$934$	5.97327	+	5.54239i	0.195451	+	0.181352i
$935$	4.22914	+	10.7757i	0.138308	+	0.352402i
$936$	4.79741	−	1.47981i	0.156808	−	0.0483690i
$937$	−6.24450	−	27.3590i	−0.203999	−	0.893778i	−0.968472	−	0.249122i	$-0.919858\pi$
$937$	−6.24450	−	27.3590i	−0.203999	−	0.893778i	0.764473	−	0.644656i	$-0.222999\pi$
$938$	10.2023	−	9.70514i	0.333118	−	0.316884i
$939$	−1.44599	+	6.33528i	−0.0471880	+	0.206744i
$940$	−5.47062	−	73.0003i	−0.178432	−	2.38101i
$941$	−17.5232	−	5.40518i	−0.571238	−	0.176204i	−0.00433876	−	0.999991i	$-0.501381\pi$
$941$	−17.5232	−	5.40518i	−0.571238	−	0.176204i	−0.566900	+	0.823787i	$0.691857\pi$
$942$	−0.142951	+	1.90754i	−0.00465758	+	0.0621511i
$943$	4.92500	−	12.5487i	0.160380	−	0.408641i
$944$	19.9614	−	9.61289i	0.649687	−	0.312873i
$945$	−0.813059	+	13.0191i	−0.0264488	+	0.423513i
$946$	−17.5913	−	8.47154i	−0.571944	−	0.275434i
$947$	−1.16278	+	1.07890i	−0.0377852	+	0.0350596i	−0.698839	−	0.715279i	$-0.746300\pi$
$947$	−1.16278	+	1.07890i	−0.0377852	+	0.0350596i	0.661054	+	0.750338i	$0.270109\pi$
$948$	−3.06372	+	0.461781i	−0.0995049	+	0.0149980i
$949$	2.38947	−	4.13868i	0.0775654	−	0.134347i
$950$	−1.03922	−	1.79999i	−0.0337169	−	0.0583993i
$951$	−0.147401	−	0.184834i	−0.00477979	−	0.00599367i
$952$	−1.00911	−	4.18094i	−0.0327053	−	0.135505i
$953$	31.5122	−	39.5150i	1.02078	−	1.28002i	0.0613346	−	0.998117i	$-0.480464\pi$
$953$	31.5122	−	39.5150i	1.02078	−	1.28002i	0.959444	−	0.281899i	$-0.0909642\pi$
$954$	−6.09518	−	0.918701i	−0.197339	−	0.0297441i
$955$	56.7333	−	38.6801i	1.83585	−	1.25166i
$956$	31.8450	−	21.7116i	1.02994	−	0.702203i
$957$	3.09306	+	0.466204i	0.0999845	+	0.0150702i
$958$	1.93768	−	2.42978i	0.0626037	−	0.0785026i
$959$	12.9939	−	0.161519i	0.419594	−	0.00521572i
$960$	−1.83387	−	2.29960i	−0.0591879	−	0.0742193i
$961$	9.15604	+	15.8587i	0.295356	+	0.511572i
$962$	−0.844604	+	1.46290i	−0.0272311	+	0.0471657i
$963$	50.2930	−	7.58045i	1.62067	−	0.244277i
$964$	8.90662	−	8.26414i	0.286863	−	0.266170i
$965$	51.9047	+	24.9960i	1.67087	+	0.804650i
$966$	0.724527	+	1.78066i	0.0233113	+	0.0572918i
$967$	48.9045	−	23.5512i	1.57266	−	0.757354i	0.574532	−	0.818482i	$-0.305184\pi$
$967$	48.9045	−	23.5512i	1.57266	−	0.757354i	0.998130	+	0.0611279i	$0.0194698\pi$
$968$	−1.43033	+	3.64441i	−0.0459725	+	0.117136i
$969$	−0.0133076	+	0.177578i	−0.000427503	+	0.00570463i
$970$	10.7075	+	3.30284i	0.343799	+	0.106048i
$971$	−4.23203	−	56.4725i	−0.135812	−	1.81229i	−0.484222	−	0.874945i	$-0.660897\pi$
$971$	−4.23203	−	56.4725i	−0.135812	−	1.81229i	0.348410	−	0.937342i	$-0.386722\pi$
$972$	2.61316	−	11.4490i	0.0838173	−	0.367227i
$973$	2.93143	+	33.5206i	0.0939772	+	1.07462i
$974$	−3.89195	−	17.0518i	−0.124706	−	0.546374i
$975$	1.45941	−	0.450168i	0.0467385	−	0.0144169i
$976$	4.47913	+	11.4126i	0.143373	+	0.365310i
$977$	5.70972	+	5.29785i	0.182670	+	0.169493i	0.766208	−	0.642593i	$-0.222141\pi$
$977$	5.70972	+	5.29785i	0.182670	+	0.169493i	−0.583537	+	0.812086i	$0.698332\pi$
$978$	−1.38576	−	0.944798i	−0.0443118	−	0.0302113i
$979$	−21.8687			−0.698926
$980$	−40.4250	−	11.3770i	−1.29133	−	0.363426i
$981$	−19.1168			−0.610354
$982$	−0.540387	−	0.368429i	−0.0172444	−	0.0117571i
$983$	−14.2643	−	13.2353i	−0.454961	−	0.422142i	0.419114	−	0.907934i	$-0.362341\pi$
$983$	−14.2643	−	13.2353i	−0.454961	−	0.422142i	−0.874075	+	0.485792i	$0.838531\pi$
$984$	−0.322525	−	0.821780i	−0.0102817	−	0.0261974i
$985$	−15.6184	+	4.81762i	−0.497642	+	0.153502i
$986$	0.328526	+	1.43937i	0.0104624	+	0.0458388i
$987$	−4.10183	−	6.90492i	−0.130563	−	0.219786i
$988$	0.300958	−	1.31858i	0.00957474	−	0.0419497i
$989$	−5.77366	−	77.0441i	−0.183592	−	2.44986i
$990$	15.3714	+	4.74145i	0.488535	+	0.150693i
$991$	3.21207	−	42.8620i	0.102035	−	1.36156i	−0.677650	−	0.735385i	$-0.737001\pi$
$991$	3.21207	−	42.8620i	0.102035	−	1.36156i	0.779684	−	0.626173i	$-0.215380\pi$
$992$	−6.10223	+	15.5482i	−0.193746	+	0.493656i
$993$	0.688059	−	0.331352i	0.0218349	−	0.0105151i
$994$	−0.304445	+	0.213158i	−0.00965642	+	0.00676097i
$995$	−33.3478	−	16.0595i	−1.05720	−	0.509120i
$996$	5.00957	−	4.64820i	0.158734	−	0.147284i
$997$	30.6596	−	4.62120i	0.971000	−	0.146355i	0.355659	−	0.934616i	$-0.384256\pi$
$997$	30.6596	−	4.62120i	0.971000	−	0.146355i	0.615341	+	0.788261i	$0.289018\pi$
$998$	−7.33322	+	12.7015i	−0.232129	+	0.402059i
$999$	2.77289	+	4.80278i	0.0877303	+	0.151953i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bl.b.53.16	✓	348
49.37	even	21	inner	637.2.bl.b.625.16	yes	348

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.bl.b.53.16	✓	348	1.1	even	1	trivial
637.2.bl.b.625.16	yes	348	49.37	even	21	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.bl (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.371774 + 0.253471i) q^{2} +(-0.182364 - 0.169209i) q^{3} +(-0.656714 - 1.67328i) q^{4} +(3.18926 - 0.983757i) q^{5} +(-0.0249085 - 0.109131i) q^{6} +(2.51832 - 0.811213i) q^{7} +(0.380230 - 1.66590i) q^{8} +(-0.219565 - 2.92990i) q^{9} +O(q^{10})\)	\(q+(0.371774 + 0.253471i) q^{2} +(-0.182364 - 0.169209i) q^{3} +(-0.656714 - 1.67328i) q^{4} +(3.18926 - 0.983757i) q^{5} +(-0.0249085 - 0.109131i) q^{6} +(2.51832 - 0.811213i) q^{7} +(0.380230 - 1.66590i) q^{8} +(-0.219565 - 2.92990i) q^{9} +(1.43504 + 0.442650i) q^{10} +(-0.272444 + 3.63551i) q^{11} +(-0.163373 + 0.416267i) q^{12} +(-0.900969 + 0.433884i) q^{13} +(1.14186 + 0.336734i) q^{14} +(-0.748066 - 0.360250i) q^{15} +(-2.07176 + 1.92231i) q^{16} +(0.940735 - 0.141793i) q^{17} +(0.661015 - 1.14491i) q^{18} +(-0.376207 - 0.651609i) q^{19} +(-3.74053 - 4.69048i) q^{20} +(-0.596515 - 0.278186i) q^{21} +(-1.02279 + 1.28253i) q^{22} +(-6.41865 - 0.967456i) q^{23} +(-0.351224 + 0.239461i) q^{24} +(5.07241 - 3.45831i) q^{25} +(-0.444934 - 0.0670630i) q^{26} +(-0.921047 + 1.15496i) q^{27} +(-3.01120 - 3.68112i) q^{28} +(2.15036 + 2.69646i) q^{29} +(-0.186798 - 0.323544i) q^{30} +(1.78101 - 3.08479i) q^{31} +(-4.63678 + 0.698882i) q^{32} +(0.664845 - 0.616886i) q^{33} +(0.385681 + 0.185734i) q^{34} +(7.23354 - 5.06458i) q^{35} +(-4.75834 + 2.29150i) q^{36} +(1.37154 - 3.49463i) q^{37} +(0.0253003 - 0.337609i) q^{38} +(0.237721 + 0.0733272i) q^{39} +(-0.426184 - 5.68703i) q^{40} +(-0.462122 + 2.02469i) q^{41} +(-0.151256 - 0.254622i) q^{42} +(2.64853 + 11.6040i) q^{43} +(6.26215 - 1.93162i) q^{44} +(-3.58256 - 9.12821i) q^{45} +(-2.14106 - 1.98662i) q^{46} +(10.0819 + 6.87372i) q^{47} +0.703086 q^{48} +(5.68387 - 4.08579i) q^{49} +2.76237 q^{50} +(-0.195549 - 0.133323i) q^{51} +(1.31769 + 1.22264i) q^{52} +(-1.70342 - 4.34024i) q^{53} +(-0.635169 + 0.195924i) q^{54} +(2.70757 + 11.8626i) q^{55} +(-0.393856 - 4.50370i) q^{56} +(-0.0416516 + 0.182487i) q^{57} +(0.115971 + 1.54753i) q^{58} +(-7.49100 - 2.31067i) q^{59} +(-0.111533 + 1.48830i) q^{60} +(1.58485 - 4.03814i) q^{61} +(1.44404 - 0.695412i) q^{62} +(-2.92971 - 7.20030i) q^{63} +(3.19168 + 1.53703i) q^{64} +(-2.44659 + 2.27010i) q^{65} +(0.403535 - 0.0608231i) q^{66} +(5.91404 - 10.2434i) q^{67} +(-0.855053 - 1.48099i) q^{68} +(1.00683 + 1.26252i) q^{69} +(3.97297 - 0.0493856i) q^{70} +(-0.194644 + 0.244076i) q^{71} +(-4.96439 - 0.748261i) q^{72} +(-3.94854 + 2.69207i) q^{73} +(1.39569 - 0.951565i) q^{74} +(-1.51020 - 0.227626i) q^{75} +(-0.843265 + 1.05742i) q^{76} +(2.26307 + 9.37640i) q^{77} +(0.0697921 + 0.0875166i) q^{78} +(3.46430 + 6.00034i) q^{79} +(-4.71629 + 8.16886i) q^{80} +(-8.35249 + 1.25894i) q^{81} +(-0.685005 + 0.635592i) q^{82} +(-13.7687 - 6.63067i) q^{83} +(-0.0737438 + 1.18082i) q^{84} +(2.86076 - 1.37767i) q^{85} +(-1.95662 + 4.98538i) q^{86} +(0.0641181 - 0.855596i) q^{87} +(5.95280 + 1.83619i) q^{88} +(0.448266 + 5.98169i) q^{89} +(0.981835 - 4.30170i) q^{90} +(-1.91696 + 1.82354i) q^{91} +(2.59639 + 11.3755i) q^{92} +(-0.846765 + 0.261192i) q^{93} +(2.00590 + 5.11094i) q^{94} +(-1.84085 - 1.70806i) q^{95} +(0.963838 + 0.657133i) q^{96} +7.46151 q^{97} +(3.14874 - 0.0782923i) q^{98} +10.7115 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9}+O(q^{10}) \) 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9	\( 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9} - 5 q^{10} + 2 q^{11} - 40 q^{12} - 58 q^{13} - 45 q^{14} - 14 q^{15} + 27 q^{16} - 12 q^{17} - 59 q^{18} - 24 q^{19} - 99 q^{20} - 2 q^{21} - 10 q^{22} - 14 q^{23} + 28 q^{25} + 3 q^{26} - 9 q^{27} - 37 q^{28} - 26 q^{29} - 83 q^{30} - 49 q^{31} + 33 q^{32} + 2 q^{33} - 130 q^{34} - 38 q^{35} - 74 q^{36} - 4 q^{37} + 92 q^{38} + 24 q^{40} + 20 q^{41} - 52 q^{42} + 2 q^{43} + 226 q^{44} - 23 q^{45} + 71 q^{46} + 24 q^{47} + 86 q^{48} + 25 q^{49} + 114 q^{50} - 54 q^{51} + 31 q^{52} + 36 q^{53} + 75 q^{54} + 38 q^{55} + 126 q^{56} + 27 q^{57} - 33 q^{58} + q^{59} - 179 q^{60} - 15 q^{61} + 158 q^{62} - 5 q^{63} - 24 q^{64} + q^{65} - 150 q^{66} - 151 q^{67} + 140 q^{68} - 98 q^{69} - 126 q^{70} - 31 q^{71} - 149 q^{72} - 9 q^{73} + 39 q^{74} + 85 q^{75} - 81 q^{76} + 46 q^{77} - 25 q^{78} - 69 q^{79} - 64 q^{80} + 71 q^{81} - 52 q^{82} - q^{83} - 47 q^{84} + 62 q^{85} + 97 q^{86} + 150 q^{87} - 12 q^{88} + 23 q^{89} + 107 q^{90} - q^{91} - 43 q^{92} + 316 q^{93} - 86 q^{94} - 29 q^{95} + 177 q^{96} + 114 q^{97} - 336 q^{98} + 102 q^{99}+O(q^{100}) \) 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9 - 5 * q^10 + 2 * q^11 - 40 * q^12 - 58 * q^13 - 45 * q^14 - 14 * q^15 + 27 * q^16 - 12 * q^17 - 59 * q^18 - 24 * q^19 - 99 * q^20 - 2 * q^21 - 10 * q^22 - 14 * q^23 + 28 * q^25 + 3 * q^26 - 9 * q^27 - 37 * q^28 - 26 * q^29 - 83 * q^30 - 49 * q^31 + 33 * q^32 + 2 * q^33 - 130 * q^34 - 38 * q^35 - 74 * q^36 - 4 * q^37 + 92 * q^38 + 24 * q^40 + 20 * q^41 - 52 * q^42 + 2 * q^43 + 226 * q^44 - 23 * q^45 + 71 * q^46 + 24 * q^47 + 86 * q^48 + 25 * q^49 + 114 * q^50 - 54 * q^51 + 31 * q^52 + 36 * q^53 + 75 * q^54 + 38 * q^55 + 126 * q^56 + 27 * q^57 - 33 * q^58 + q^59 - 179 * q^60 - 15 * q^61 + 158 * q^62 - 5 * q^63 - 24 * q^64 + q^65 - 150 * q^66 - 151 * q^67 + 140 * q^68 - 98 * q^69 - 126 * q^70 - 31 * q^71 - 149 * q^72 - 9 * q^73 + 39 * q^74 + 85 * q^75 - 81 * q^76 + 46 * q^77 - 25 * q^78 - 69 * q^79 - 64 * q^80 + 71 * q^81 - 52 * q^82 - q^83 - 47 * q^84 + 62 * q^85 + 97 * q^86 + 150 * q^87 - 12 * q^88 + 23 * q^89 + 107 * q^90 - q^91 - 43 * q^92 + 316 * q^93 - 86 * q^94 - 29 * q^95 + 177 * q^96 + 114 * q^97 - 336 * q^98 + 102 * q^99

Introduction

L-functions

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