LMFDB - Embedded newform 418.2.u.b.5.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(5,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(90))

chi = DirichletCharacter(H, H._module([36, 80]))

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

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

chi := DirichletCharacter("418.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.u (of order $45$, degree $24$, 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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$264$
Relative dimension:	$11$ over $\Q(\zeta_{45})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{45}]$

Embedding invariants

Embedding label			5.5
Character	$\chi$	$=$	418.5
Dual form			418.2.u.b.251.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.615661 - 0.788011i) q^{2} +(-0.215741 + 0.208339i) q^{3} +(-0.241922 + 0.970296i) q^{4} +(-0.160523 + 0.100306i) q^{5} +(0.296996 + 0.0417401i) q^{6} +(-1.81207 - 0.806787i) q^{7} +(0.913545 - 0.406737i) q^{8} +(-0.101559 + 2.90828i) q^{9} +O(q^{10})$	\(q+(-0.615661 - 0.788011i) q^{2} +(-0.215741 + 0.208339i) q^{3} +(-0.241922 + 0.970296i) q^{4} +(-0.160523 + 0.100306i) q^{5} +(0.296996 + 0.0417401i) q^{6} +(-1.81207 - 0.806787i) q^{7} +(0.913545 - 0.406737i) q^{8} +(-0.101559 + 2.90828i) q^{9} +(0.177870 + 0.0647394i) q^{10} +(-2.25551 - 2.43160i) q^{11} +(-0.149958 - 0.259734i) q^{12} +(-2.74105 + 1.45744i) q^{13} +(0.479867 + 1.92464i) q^{14} +(0.0137338 - 0.0550832i) q^{15} +(-0.882948 - 0.469472i) q^{16} +(-0.0244707 - 0.700748i) q^{17} +(2.35428 - 1.71048i) q^{18} +(-4.35542 - 0.174113i) q^{19} +(-0.0584924 - 0.180021i) q^{20} +(0.559023 - 0.203468i) q^{21} +(-0.527495 + 3.27441i) q^{22} +(0.196066 - 0.164519i) q^{23} +(-0.112350 + 0.278077i) q^{24} +(-2.17615 + 4.46177i) q^{25} +(2.83604 + 1.26269i) q^{26} +(-1.18604 - 1.31723i) q^{27} +(1.22120 - 1.56307i) q^{28} +(-8.18525 + 2.34708i) q^{29} +(-0.0518615 + 0.0230902i) q^{30} +(0.876837 - 0.973827i) q^{31} +(0.173648 + 0.984808i) q^{32} +(0.993202 + 0.0546856i) q^{33} +(-0.537132 + 0.450707i) q^{34} +(0.371805 - 0.0522538i) q^{35} +(-2.79732 - 0.802119i) q^{36} +(-1.02976 + 0.748166i) q^{37} +(2.54426 + 3.53931i) q^{38} +(0.287715 - 0.885496i) q^{39} +(-0.105847 + 0.156925i) q^{40} +(-1.49356 + 1.44231i) q^{41} +(-0.504504 - 0.315249i) q^{42} +(-0.430035 - 0.360842i) q^{43} +(2.90503 - 1.60026i) q^{44} +(-0.275415 - 0.477033i) q^{45} +(-0.250353 - 0.0532141i) q^{46} +(4.83523 + 7.16853i) q^{47} +(0.288297 - 0.0826678i) q^{48} +(-2.05121 - 2.27810i) q^{49} +(4.85569 - 1.03211i) q^{50} +(0.151272 + 0.146082i) q^{51} +(-0.751030 - 3.01221i) q^{52} +(6.32283 + 3.95094i) q^{53} +(-0.307794 + 1.74559i) q^{54} +(0.605965 + 0.164087i) q^{55} -1.98356 q^{56} +(0.975917 - 0.869839i) q^{57} +(6.88887 + 5.00506i) q^{58} +(-2.40614 + 3.56726i) q^{59} +(0.0501245 + 0.0266517i) q^{60} +(-1.78117 - 4.40856i) q^{61} +(-1.30722 - 0.0914098i) q^{62} +(2.53039 - 5.18808i) q^{63} +(0.669131 - 0.743145i) q^{64} +(0.293811 - 0.508896i) q^{65} +(-0.568383 - 0.816322i) q^{66} +(-7.50231 - 2.73062i) q^{67} +(0.685853 + 0.145783i) q^{68} +(-0.00802381 + 0.0763415i) q^{69} +(-0.270082 - 0.260816i) q^{70} +(11.9870 - 7.49029i) q^{71} +(1.09012 + 2.69815i) q^{72} +(0.166785 + 0.341959i) q^{73} +(1.22355 + 0.350847i) q^{74} +(-0.460074 - 1.41596i) q^{75} +(1.22261 - 4.18392i) q^{76} +(2.12537 + 6.22595i) q^{77} +(-0.874916 + 0.318443i) q^{78} +(-3.75945 + 0.528356i) q^{79} +(0.188824 - 0.0132039i) q^{80} +(-8.17858 - 0.571902i) q^{81} +(2.05609 + 0.288964i) q^{82} +(13.5235 - 2.87451i) q^{83} +(0.0621840 + 0.591641i) q^{84} +(0.0742173 + 0.110032i) q^{85} +(-0.0195916 + 0.561029i) q^{86} +(1.27691 - 2.21167i) q^{87} +(-3.04953 - 1.30398i) q^{88} +(-1.30973 - 7.42784i) q^{89} +(-0.206344 + 0.510720i) q^{90} +(6.14283 - 0.429548i) q^{91} +(0.112199 + 0.230042i) q^{92} +(0.0137160 + 0.392773i) q^{93} +(2.67201 - 8.22360i) q^{94} +(0.716610 - 0.408925i) q^{95} +(-0.242637 - 0.176286i) q^{96} +(-2.30385 - 2.94879i) q^{97} +(-0.532316 + 3.01891i) q^{98} +(7.30083 - 6.31270i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 264 q + 6 q^{3} - 9 q^{6} - 15 q^{7} + 33 q^{8} + 6 q^{9}+O(q^{10}) $ 264 * q + 6 * q^3 - 9 * q^6 - 15 * q^7 + 33 * q^8 + 6 * q^9	$ 264 q + 6 q^{3} - 9 q^{6} - 15 q^{7} + 33 q^{8} + 6 q^{9} + 3 q^{11} - 6 q^{13} + 18 q^{14} - 39 q^{15} - 3 q^{17} - 78 q^{18} - 45 q^{19} - 24 q^{20} + 48 q^{21} + 6 q^{23} - 9 q^{24} + 30 q^{25} + 18 q^{26} - 24 q^{27} + 6 q^{28} - 3 q^{31} - 63 q^{33} - 36 q^{34} + 42 q^{35} - 9 q^{36} + 60 q^{37} - 3 q^{38} + 36 q^{39} + 39 q^{41} + 6 q^{42} - 60 q^{43} + 60 q^{44} - 108 q^{45} - 12 q^{46} - 24 q^{47} - 12 q^{48} + 6 q^{49} + 18 q^{50} + 96 q^{51} + 3 q^{52} - 117 q^{53} + 54 q^{54} + 102 q^{55} - 96 q^{57} - 60 q^{58} - 141 q^{59} + 36 q^{60} + 24 q^{61} - 27 q^{62} - 81 q^{63} + 33 q^{64} - 102 q^{65} + 72 q^{66} + 102 q^{67} - 21 q^{68} - 6 q^{69} - 33 q^{70} - 66 q^{71} - 12 q^{72} + 36 q^{73} + 18 q^{74} + 6 q^{76} - 174 q^{77} + 18 q^{78} + 36 q^{79} + 60 q^{81} - 36 q^{82} - 24 q^{83} + 48 q^{84} + 174 q^{85} - 21 q^{86} + 12 q^{87} + 3 q^{88} + 30 q^{89} - 48 q^{90} - 18 q^{91} + 18 q^{92} - 123 q^{93} - 120 q^{94} - 18 q^{95} - 24 q^{97} - 84 q^{98} - 141 q^{99}+O(q^{100}) $ 264 * q + 6 * q^3 - 9 * q^6 - 15 * q^7 + 33 * q^8 + 6 * q^9 + 3 * q^11 - 6 * q^13 + 18 * q^14 - 39 * q^15 - 3 * q^17 - 78 * q^18 - 45 * q^19 - 24 * q^20 + 48 * q^21 + 6 * q^23 - 9 * q^24 + 30 * q^25 + 18 * q^26 - 24 * q^27 + 6 * q^28 - 3 * q^31 - 63 * q^33 - 36 * q^34 + 42 * q^35 - 9 * q^36 + 60 * q^37 - 3 * q^38 + 36 * q^39 + 39 * q^41 + 6 * q^42 - 60 * q^43 + 60 * q^44 - 108 * q^45 - 12 * q^46 - 24 * q^47 - 12 * q^48 + 6 * q^49 + 18 * q^50 + 96 * q^51 + 3 * q^52 - 117 * q^53 + 54 * q^54 + 102 * q^55 - 96 * q^57 - 60 * q^58 - 141 * q^59 + 36 * q^60 + 24 * q^61 - 27 * q^62 - 81 * q^63 + 33 * q^64 - 102 * q^65 + 72 * q^66 + 102 * q^67 - 21 * q^68 - 6 * q^69 - 33 * q^70 - 66 * q^71 - 12 * q^72 + 36 * q^73 + 18 * q^74 + 6 * q^76 - 174 * q^77 + 18 * q^78 + 36 * q^79 + 60 * q^81 - 36 * q^82 - 24 * q^83 + 48 * q^84 + 174 * q^85 - 21 * q^86 + 12 * q^87 + 3 * q^88 + 30 * q^89 - 48 * q^90 - 18 * q^91 + 18 * q^92 - 123 * q^93 - 120 * q^94 - 18 * q^95 - 24 * q^97 - 84 * q^98 - 141 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.615661	−	0.788011i	−0.435338	−	0.557208i
$2$	−0.615661	−	0.788011i	−0.435338	−	0.557208i
$3$	−0.215741	+	0.208339i	−0.124558	+	0.120284i	−0.754329	−	0.656497i	$-0.772038\pi$
$3$	−0.215741	+	0.208339i	−0.124558	+	0.120284i	0.629771	+	0.776781i	$0.283149\pi$
$4$	−0.241922	+	0.970296i	−0.120961	+	0.485148i
$5$	−0.160523	+	0.100306i	−0.0717881	+	0.0448582i	−0.565338	−	0.824859i	$-0.691254\pi$
$5$	−0.160523	+	0.100306i	−0.0717881	+	0.0448582i	0.493550	+	0.869717i	$0.335699\pi$
$6$	0.296996	+	0.0417401i	0.121248	+	0.0170403i
$7$	−1.81207	−	0.806787i	−0.684899	−	0.304937i	0.0346288	−	0.999400i	$-0.488975\pi$
$7$	−1.81207	−	0.806787i	−0.684899	−	0.304937i	−0.719528	+	0.694463i	$0.755642\pi$
$8$	0.913545	−	0.406737i	0.322987	−	0.143803i
$9$	−0.101559	+	2.90828i	−0.0338531	+	0.969426i
$10$	0.177870	+	0.0647394i	0.0562474	+	0.0204724i
$11$	−2.25551	−	2.43160i	−0.680062	−	0.733155i
$11$	−2.25551	−	2.43160i	−0.680062	−	0.733155i
$12$	−0.149958	−	0.259734i	−0.0432890	−	0.0749788i
$13$	−2.74105	+	1.45744i	−0.760230	+	0.404222i	−0.803854	−	0.594826i	$-0.797221\pi$
$13$	−2.74105	+	1.45744i	−0.760230	+	0.404222i	0.0436240	+	0.999048i	$0.486110\pi$
$14$	0.479867	+	1.92464i	0.128250	+	0.514382i
$15$	0.0137338	−	0.0550832i	0.00354605	−	0.0142224i
$16$	−0.882948	−	0.469472i	−0.220737	−	0.117368i
$17$	−0.0244707	−	0.700748i	−0.00593501	−	0.169956i	−0.998739	−	0.0502051i	$-0.984012\pi$
$17$	−0.0244707	−	0.700748i	−0.00593501	−	0.169956i	0.992804	−	0.119751i	$-0.0382097\pi$
$18$	2.35428	−	1.71048i	0.554909	−	0.403165i
$19$	−4.35542	−	0.174113i	−0.999202	−	0.0399444i
$19$	−4.35542	−	0.174113i	−0.999202	−	0.0399444i
$20$	−0.0584924	−	0.180021i	−0.0130793	−	0.0402539i
$21$	0.559023	−	0.203468i	0.121989	−	0.0444003i
$22$	−0.527495	+	3.27441i	−0.112462	+	0.698106i
$23$	0.196066	−	0.164519i	0.0408825	−	0.0343045i	−0.622117	−	0.782924i	$-0.713727\pi$
$23$	0.196066	−	0.164519i	0.0408825	−	0.0343045i	0.663000	+	0.748619i	$0.269283\pi$
$24$	−0.112350	+	0.278077i	−0.0229334	+	0.0567621i
$25$	−2.17615	+	4.46177i	−0.435230	+	0.892353i
$26$	2.83604	+	1.26269i	0.556193	+	0.247633i
$27$	−1.18604	−	1.31723i	−0.228254	−	0.253502i
$28$	1.22120	−	1.56307i	0.230785	−	0.295392i
$29$	−8.18525	+	2.34708i	−1.51996	+	0.435842i	−0.928760	−	0.370681i	$-0.879124\pi$
$29$	−8.18525	+	2.34708i	−1.51996	+	0.435842i	−0.591203	+	0.806523i	$0.701347\pi$
$30$	−0.0518615	+	0.0230902i	−0.00946858	+	0.00421568i
$31$	0.876837	−	0.973827i	0.157485	−	0.174904i	−0.659239	−	0.751934i	$-0.729121\pi$
$31$	0.876837	−	0.973827i	0.157485	−	0.174904i	0.816724	+	0.577029i	$0.195788\pi$
$32$	0.173648	+	0.984808i	0.0306970	+	0.174091i
$33$	0.993202	+	0.0546856i	0.172894	+	0.00951953i
$34$	−0.537132	+	0.450707i	−0.0921173	+	0.0772956i
$35$	0.371805	−	0.0522538i	0.0628465	−	0.00883250i
$36$	−2.79732	−	0.802119i	−0.466220	−	0.133686i
$37$	−1.02976	+	0.748166i	−0.169292	+	0.122998i	−0.669205	−	0.743078i	$-0.733365\pi$
$37$	−1.02976	+	0.748166i	−0.169292	+	0.122998i	0.499913	+	0.866075i	$0.333365\pi$
$38$	2.54426	+	3.53931i	0.412734	+	0.574152i
$39$	0.287715	−	0.885496i	0.0460713	−	0.141793i
$40$	−0.105847	+	0.156925i	−0.0167359	+	0.0248120i
$41$	−1.49356	+	1.44231i	−0.233255	+	0.225252i	−0.802095	−	0.597196i	$-0.796281\pi$
$41$	−1.49356	+	1.44231i	−0.233255	+	0.225252i	0.568840	+	0.822448i	$0.307392\pi$
$42$	−0.504504	−	0.315249i	−0.0778466	−	0.0486440i
$43$	−0.430035	−	0.360842i	−0.0655798	−	0.0550279i	0.609409	−	0.792856i	$-0.291407\pi$
$43$	−0.430035	−	0.360842i	−0.0655798	−	0.0550279i	−0.674988	+	0.737828i	$0.735851\pi$
$44$	2.90503	−	1.60026i	0.437949	−	0.241248i
$45$	−0.275415	−	0.477033i	−0.0410564	−	0.0711118i
$46$	−0.250353	−	0.0532141i	−0.0369125	−	0.00784599i
$47$	4.83523	+	7.16853i	0.705291	+	1.04564i	0.996046	+	0.0888398i	$0.0283159\pi$
$47$	4.83523	+	7.16853i	0.705291	+	1.04564i	−0.290755	+	0.956798i	$0.593906\pi$
$48$	0.288297	−	0.0826678i	0.0416121	−	0.0119321i
$49$	−2.05121	−	2.27810i	−0.293030	−	0.325443i
$50$	4.85569	−	1.03211i	0.686699	−	0.145962i
$51$	0.151272	+	0.146082i	0.0211824	+	0.0204556i
$52$	−0.751030	−	3.01221i	−0.104149	−	0.417719i
$53$	6.32283	+	3.95094i	0.868507	+	0.542704i	0.889427	−	0.457078i	$-0.151104\pi$
$53$	6.32283	+	3.95094i	0.868507	+	0.542704i	−0.0209196	+	0.999781i	$0.506659\pi$
$54$	−0.307794	+	1.74559i	−0.0418854	+	0.237544i
$55$	0.605965	+	0.164087i	0.0817083	+	0.0221254i
$56$	−1.98356			−0.265064
$57$	0.975917	−	0.869839i	0.129263	−	0.115213i
$58$	6.88887	+	5.00506i	0.904553	+	0.657196i
$59$	−2.40614	+	3.56726i	−0.313253	+	0.464417i	−0.952480	−	0.304601i	$-0.901477\pi$
$59$	−2.40614	+	3.56726i	−0.313253	+	0.464417i	0.639227	+	0.769018i	$0.279255\pi$
$60$	0.0501245	+	0.0266517i	0.00647105	+	0.00344072i
$61$	−1.78117	−	4.40856i	−0.228056	−	0.564458i	0.769158	−	0.639059i	$-0.220676\pi$
$61$	−1.78117	−	4.40856i	−0.228056	−	0.564458i	−0.997213	+	0.0746011i	$0.976232\pi$
$62$	−1.30722	−	0.0914098i	−0.166017	−	0.0116091i
$63$	2.53039	−	5.18808i	0.318800	−	0.653636i
$64$	0.669131	−	0.743145i	0.0836413	−	0.0928931i
$65$	0.293811	−	0.508896i	0.0364428	−	0.0631208i
$66$	−0.568383	−	0.816322i	−0.0699632	−	0.100482i
$67$	−7.50231	−	2.73062i	−0.916553	−	0.333598i	−0.159687	−	0.987168i	$-0.551048\pi$
$67$	−7.50231	−	2.73062i	−0.916553	−	0.333598i	−0.756866	+	0.653570i	$0.773271\pi$
$68$	0.685853	+	0.145783i	0.0831719	+	0.0176787i
$69$	−0.00802381	+	0.0763415i	−0.000965953	+	0.00919043i
$70$	−0.270082	−	0.260816i	−0.0322810	−	0.0311734i
$71$	11.9870	−	7.49029i	1.42259	−	0.888934i	0.422742	−	0.906250i	$-0.361068\pi$
$71$	11.9870	−	7.49029i	1.42259	−	0.888934i	0.999850	+	0.0173164i	$0.00551225\pi$
$72$	1.09012	+	2.69815i	0.128472	+	0.317980i
$73$	0.166785	+	0.341959i	0.0195207	+	0.0400233i	0.908332	−	0.418251i	$-0.137357\pi$
$73$	0.166785	+	0.341959i	0.0195207	+	0.0400233i	−0.888811	+	0.458274i	$0.848468\pi$
$74$	1.22355	+	0.350847i	0.142235	+	0.0407851i
$75$	−0.460074	−	1.41596i	−0.0531248	−	0.163501i
$76$	1.22261	−	4.18392i	0.140243	−	0.479929i
$77$	2.12537	+	6.22595i	0.242208	+	0.709513i
$78$	−0.874916	+	0.318443i	−0.0990647	+	0.0360566i
$79$	−3.75945	+	0.528356i	−0.422971	+	0.0594446i	−0.347448	−	0.937699i	$-0.612952\pi$
$79$	−3.75945	+	0.528356i	−0.422971	+	0.0594446i	−0.0755230	+	0.997144i	$0.524063\pi$
$80$	0.188824	−	0.0132039i	0.0211112	−	0.00147624i
$81$	−8.17858	−	0.571902i	−0.908731	−	0.0635446i
$82$	2.05609	+	0.288964i	0.227057	+	0.0319108i
$83$	13.5235	−	2.87451i	1.48440	−	0.315519i	0.606777	−	0.794872i	$-0.292462\pi$
$83$	13.5235	−	2.87451i	1.48440	−	0.315519i	0.877622	+	0.479353i	$0.159129\pi$
$84$	0.0621840	+	0.591641i	0.00678483	+	0.0645533i
$85$	0.0742173	+	0.110032i	0.00805000	+	0.0119346i
$86$	−0.0195916	+	0.561029i	−0.00211261	+	0.0604973i
$87$	1.27691	−	2.21167i	0.136899	−	0.237116i
$88$	−3.04953	−	1.30398i	−0.325081	−	0.139004i
$89$	−1.30973	−	7.42784i	−0.138831	−	0.787349i	−0.972115	−	0.234504i	$-0.924653\pi$
$89$	−1.30973	−	7.42784i	−0.138831	−	0.787349i	0.833284	−	0.552845i	$-0.186458\pi$
$90$	−0.206344	+	0.510720i	−0.0217506	+	0.0538347i
$91$	6.14283	−	0.429548i	0.643943	−	0.0450289i
$92$	0.112199	+	0.230042i	0.0116976	+	0.0239836i
$93$	0.0137160	+	0.392773i	0.00142228	+	0.0407287i
$94$	2.67201	−	8.22360i	0.275597	−	0.848200i
$95$	0.716610	−	0.408925i	0.0735226	−	0.0419548i
$96$	−0.242637	−	0.176286i	−0.0247640	−	0.0179921i
$97$	−2.30385	−	2.94879i	−0.233921	−	0.299405i	0.656700	−	0.754152i	$-0.271952\pi$
$97$	−2.30385	−	2.94879i	−0.233921	−	0.299405i	−0.890621	+	0.454747i	$0.849730\pi$
$98$	−0.532316	+	3.01891i	−0.0537721	+	0.304956i
$99$	7.30083	−	6.31270i	0.733761	−	0.634450i
$100$	−3.80278	−	3.19091i	−0.380278	−	0.319091i
$101$	4.57883	−	2.43460i	0.455610	−	0.242252i	−0.225772	−	0.974180i	$-0.572490\pi$
$101$	4.57883	−	2.43460i	0.455610	−	0.242252i	0.681382	+	0.731928i	$0.261379\pi$
$102$	0.0219816	−	0.209141i	0.00217651	−	0.0207081i
$103$	−0.279165	−	2.65608i	−0.0275070	−	0.261711i	−0.999629	−	0.0272360i	$-0.991329\pi$
$103$	−0.279165	−	2.65608i	−0.0275070	−	0.261711i	0.972122	−	0.234475i	$-0.0753372\pi$
$104$	−1.91128	+	2.44632i	−0.187416	+	0.239882i
$105$	−0.0693271	+	0.0887346i	−0.00676563	+	0.00865961i
$106$	−0.779337	−	7.41490i	−0.0756959	−	0.720199i
$107$	1.43121	−	13.6171i	0.138361	−	1.31641i	−0.676365	−	0.736567i	$-0.736446\pi$
$107$	1.43121	−	13.6171i	0.138361	−	1.31641i	0.814725	−	0.579847i	$-0.196888\pi$
$108$	1.56504	−	0.832145i	0.150596	−	0.0800732i
$109$	−9.83619	−	8.25354i	−0.942136	−	0.790546i	0.0358199	−	0.999358i	$-0.488596\pi$
$109$	−9.83619	−	8.25354i	−0.942136	−	0.790546i	−0.977956	+	0.208813i	$0.933040\pi$
$110$	−0.243767	−	0.578529i	−0.0232423	−	0.0551605i
$111$	0.0662900	−	0.375949i	0.00629197	−	0.0356835i
$112$	1.22120	+	1.56307i	0.115393	+	0.147696i
$113$	5.17143	+	3.75726i	0.486487	+	0.353454i	0.803832	−	0.594857i	$-0.202791\pi$
$113$	5.17143	+	3.75726i	0.486487	+	0.353454i	−0.317345	+	0.948310i	$0.602791\pi$
$114$	−1.28628	−	0.233507i	−0.120471	−	0.0218699i
$115$	−0.0149709	+	0.0460756i	−0.00139604	+	0.00429657i
$116$	−0.297173	−	8.50993i	−0.0275918	−	0.790127i
$117$	−3.96027	−	8.11975i	−0.366127	−	0.750671i
$118$	4.29241	−	0.300154i	0.395148	−	0.0276314i
$119$	−0.521012	+	1.28955i	−0.0477611	+	0.118213i
$120$	−0.00985793	−	0.0559071i	−0.000899901	−	0.00510359i
$121$	−0.825346	+	10.9690i	−0.0750315	+	0.997181i
$122$	−2.37739	+	4.11776i	−0.215239	+	0.372805i
$123$	0.0217323	−	0.622333i	0.00195954	−	0.0561139i
$124$	0.732774	+	1.08638i	0.0658050	+	0.0975599i
$125$	−0.197148	−	1.87574i	−0.0176335	−	0.167771i
$126$	−5.64612	+	1.20012i	−0.502997	+	0.106915i
$127$	5.36716	+	0.754305i	0.476258	+	0.0669337i	0.373218	−	0.927743i	$-0.378254\pi$
$127$	5.36716	+	0.754305i	0.476258	+	0.0669337i	0.103040	+	0.994677i	$0.467143\pi$
$128$	−0.997564	−	0.0697565i	−0.0881730	−	0.00616566i
$129$	0.167954	−	0.0117445i	0.0147875	−	0.00103404i
$130$	−0.581904	+	0.0817813i	−0.0510364	+	0.00717269i
$131$	−12.6510	+	4.60458i	−1.10532	+	0.402304i	−0.829275	−	0.558840i	$-0.811247\pi$
$131$	−12.6510	+	4.60458i	−1.10532	+	0.402304i	−0.276046	+	0.961144i	$0.589024\pi$
$132$	−0.293338	+	0.950470i	−0.0255318	+	0.0827278i
$133$	7.75187	+	3.82940i	0.672172	+	0.332051i
$134$	2.46713	+	7.59303i	0.213127	+	0.655938i
$135$	0.322514	+	0.0924793i	0.0277576	+	0.00795935i
$136$	−0.307375	−	0.630212i	−0.0263572	−	0.0540403i
$137$	3.41058	+	8.44148i	0.291385	+	0.721204i	0.999880	+	0.0154880i	$0.00493017\pi$
$137$	3.41058	+	8.44148i	0.291385	+	0.721204i	−0.708495	+	0.705716i	$0.750625\pi$
$138$	0.0650978	−	0.0406777i	0.00554150	−	0.00346271i
$139$	8.85886	+	8.55491i	0.751399	+	0.725618i	0.968085	−	0.250624i	$-0.0806357\pi$
$139$	8.85886	+	8.55491i	0.751399	+	0.725618i	−0.216686	+	0.976241i	$0.569525\pi$
$140$	−0.0392461	+	0.373402i	−0.00331690	+	0.0315582i
$141$	−2.53664	−	0.539179i	−0.213624	−	0.0454071i
$142$	−13.2823	−	4.83438i	−1.11463	−	0.405692i
$143$	9.72638	+	3.37786i	0.813361	+	0.282471i
$144$	1.45503	−	2.52018i	0.121252	−	0.210015i
$145$	1.07849	−	1.19779i	0.0895641	−	0.0994710i
$146$	0.166785	−	0.341959i	0.0138032	−	0.0283008i
$147$	0.917147	+	0.0641331i	0.0756450	+	0.00528961i
$148$	−0.476820	−	1.18017i	−0.0391944	−	0.0970095i
$149$	19.3455	+	10.2862i	1.58484	+	0.842677i	0.999491	+	0.0318985i	$0.0101553\pi$
$149$	19.3455	+	10.2862i	1.58484	+	0.842677i	0.585353	+	0.810778i	$0.300956\pi$
$150$	−0.832544	+	1.23430i	−0.0679769	+	0.100780i
$151$	−15.1844	−	11.0321i	−1.23569	−	0.897779i	−0.238384	−	0.971171i	$-0.576618\pi$
$151$	−15.1844	−	11.0321i	−1.23569	−	0.897779i	−0.997303	+	0.0733920i	$0.976618\pi$
$152$	−4.04969	+	1.61245i	−0.328473	+	0.130787i
$153$	2.04046			0.164961
$154$	3.59761	−	5.50789i	0.289904	−	0.443838i
$155$	−0.0430720	+	0.244274i	−0.00345963	+	0.0196205i
$156$	0.789589	+	0.493390i	0.0632177	+	0.0395028i
$157$	5.07836	+	20.3682i	0.405297	+	1.62556i	0.732615	+	0.680643i	$0.238300\pi$
$157$	5.07836	+	20.3682i	0.405297	+	1.62556i	−0.327318	+	0.944914i	$0.606145\pi$
$158$	2.73090	+	2.63719i	0.217258	+	0.209804i
$159$	−2.18723	+	0.464909i	−0.173458	+	0.0368697i
$160$	−0.126657	−	0.140666i	−0.0100131	−	0.0111207i
$161$	−0.488017	+	0.139937i	−0.0384611	+	0.0110285i
$162$	4.58457	+	6.79690i	0.360198	+	0.534015i
$163$	−16.1320	−	3.42897i	−1.26356	−	0.268578i	−0.473054	−	0.881033i	$-0.656849\pi$
$163$	−16.1320	−	3.42897i	−1.26356	−	0.268578i	−0.790505	+	0.612455i	$0.790182\pi$
$164$	−1.03815	−	1.79812i	−0.0810656	−	0.140410i
$165$	−0.164917	+	0.0908457i	−0.0128388	+	0.00707233i
$166$	−10.5911	−	8.88695i	−0.822025	−	0.689761i
$167$	16.2835	+	10.1750i	1.26005	+	0.787368i	0.984748	−	0.173989i	$-0.0556656\pi$
$167$	16.2835	+	10.1750i	1.26005	+	0.787368i	0.275305	+	0.961357i	$0.411221\pi$
$168$	0.427935	−	0.413252i	0.0330159	−	0.0318831i
$169$	−1.88030	+	2.78765i	−0.144638	+	0.214435i
$170$	0.0410134	−	0.126226i	0.00314559	−	0.00968112i
$171$	0.948704	−	12.6491i	0.0725492	−	0.967300i
$172$	0.454159	−	0.329966i	0.0346293	−	0.0251596i
$173$	−10.5897	−	3.03655i	−0.805120	−	0.230864i	−0.152257	−	0.988341i	$-0.548654\pi$
$173$	−10.5897	−	3.03655i	−0.805120	−	0.230864i	−0.652863	+	0.757476i	$0.726432\pi$
$174$	−2.52896	+	0.355422i	−0.191720	+	0.0269445i
$175$	7.54304	−	6.32936i	0.570200	−	0.478455i
$176$	0.849931	+	3.20587i	0.0640660	+	0.241652i
$177$	−0.224093	−	1.27090i	−0.0168439	−	0.0955264i
$178$	−5.04687	+	5.60511i	−0.378279	+	0.420121i
$179$	−14.7683	+	6.57527i	−1.10383	+	0.491459i	−0.876034	−	0.482249i	$-0.839820\pi$
$179$	−14.7683	+	6.57527i	−1.10383	+	0.491459i	−0.227800	+	0.973708i	$0.573153\pi$
$180$	0.529491	−	0.151829i	0.0394660	−	0.0113167i
$181$	2.27514	−	2.91205i	0.169110	−	0.216451i	−0.695989	−	0.718053i	$-0.745034\pi$
$181$	2.27514	−	2.91205i	0.169110	−	0.216451i	0.865098	+	0.501602i	$0.167256\pi$
$182$	−4.12039	−	4.57616i	−0.305424	−	0.339207i
$183$	1.30275	+	0.580020i	0.0963017	+	0.0428763i
$184$	0.112199	−	0.230042i	0.00827143	−	0.0169589i
$185$	0.0902550	−	0.223389i	0.00663568	−	0.0164239i
$186$	0.301065	−	0.252624i	0.0220752	−	0.0185233i
$187$	−1.64875	+	1.64005i	−0.120568	+	0.119932i
$188$	−8.12534	+	2.95738i	−0.592602	+	0.215689i
$189$	1.08647	+	3.34381i	0.0790290	+	0.243226i
$190$	−0.763426	−	0.312937i	−0.0553848	−	0.0227028i
$191$	−5.97042	+	4.33777i	−0.432005	+	0.313870i	−0.782450	−	0.622713i	$-0.786030\pi$
$191$	−5.97042	+	4.33777i	−0.432005	+	0.313870i	0.350445	+	0.936583i	$0.386030\pi$
$192$	0.0104669	+	0.299733i	0.000755383	+	0.0216313i
$193$	−8.95376	−	4.76080i	−0.644506	−	0.342690i	0.114834	−	0.993385i	$-0.463367\pi$
$193$	−8.95376	−	4.76080i	−0.644506	−	0.342690i	−0.759339	+	0.650695i	$0.774478\pi$
$194$	−0.905289	+	3.63092i	−0.0649960	+	0.260685i
$195$	0.0426356	+	0.171002i	0.00305320	+	0.0122457i
$196$	2.70666	−	1.43916i	0.193333	−	0.102797i
$197$	9.18177	+	15.9033i	0.654174	+	1.13306i	0.982100	+	0.188360i	$0.0603170\pi$
$197$	9.18177	+	15.9033i	0.654174	+	1.13306i	−0.327926	+	0.944703i	$0.606350\pi$
$198$	−9.46932	−	1.86665i	−0.672955	−	0.132657i
$199$	−1.00582	−	0.366088i	−0.0713005	−	0.0259513i	0.306124	−	0.951992i	$-0.400968\pi$
$199$	−1.00582	−	0.366088i	−0.0713005	−	0.0259513i	−0.377424	+	0.926040i	$0.623190\pi$
$200$	−0.173247	+	4.96115i	−0.0122504	+	0.350806i
$201$	2.18745	−	0.973915i	0.154291	−	0.0686946i
$202$	−4.73750	−	2.10927i	−0.333329	−	0.148408i
$203$	16.7259	+	2.35067i	1.17393	+	0.164985i
$204$	−0.178339	+	0.111438i	−0.0124862	+	0.00780225i
$205$	0.0950781	−	0.381338i	0.00664055	−	0.0266338i
$206$	−1.92115	+	1.85523i	−0.133853	+	0.129260i
$207$	0.458554	+	0.586922i	0.0318717	+	0.0407939i
$208$	3.10443			0.215253
$209$	9.40032	+	10.9833i	0.650234	+	0.759734i
$210$	0.112606			0.00777054
$211$	−12.0247	−	15.3909i	−0.827813	−	1.05955i	−0.997257	−	0.0740121i	$-0.976420\pi$
$211$	−12.0247	−	15.3909i	−0.827813	−	1.05955i	0.169445	−	0.985540i	$-0.445803\pi$
$212$	−5.36321	+	5.17919i	−0.368347	+	0.355708i
$213$	−1.02556	+	4.11331i	−0.0702705	+	0.281839i
$214$	−11.6116	+	7.25571i	−0.793750	+	0.495990i
$215$	0.105225	+	0.0147884i	0.00717630	+	0.00100856i
$216$	−1.61927	−	0.720947i	−0.110178	−	0.0490542i
$217$	−2.37456	+	1.05722i	−0.161196	+	0.0717690i
$218$	−0.448118	+	12.8324i	−0.0303503	+	0.869120i
$219$	−0.107226	−	0.0390270i	−0.00724564	−	0.00263720i
$220$	−0.305809	+	0.548269i	−0.0206176	+	0.0369643i
$221$	1.08838	+	1.88512i	0.0732120	+	0.126807i
$222$	−0.337064	+	0.179220i	−0.0226223	+	0.0120285i
$223$	4.54580	+	18.2322i	0.304409	+	1.22092i	0.906401	+	0.422417i	$0.138818\pi$
$223$	4.54580	+	18.2322i	0.304409	+	1.22092i	−0.601992	+	0.798502i	$0.705626\pi$
$224$	0.479867	−	1.92464i	0.0320624	−	0.128595i
$225$	−12.7551	−	6.78198i	−0.850337	−	0.452132i
$226$	−0.223086	−	6.38834i	−0.0148395	−	0.424946i
$227$	1.63721	−	1.18950i	0.108665	−	0.0789499i	−0.532126	−	0.846665i	$-0.678607\pi$
$227$	1.63721	−	1.18950i	0.108665	−	0.0789499i	0.640791	+	0.767716i	$0.278607\pi$
$228$	0.607905	+	1.15736i	0.0402595	+	0.0766481i
$229$	8.71046	+	26.8080i	0.575604	+	1.77153i	0.634115	+	0.773239i	$0.281365\pi$
$229$	8.71046	+	26.8080i	0.575604	+	1.77153i	−0.0585115	+	0.998287i	$0.518635\pi$
$230$	0.0455250	−	0.0165698i	0.00300183	−	0.00109258i
$231$	−1.75563	−	0.900397i	−0.115512	−	0.0592417i
$232$	−6.52295	+	5.47341i	−0.428253	+	0.359347i
$233$	−1.30604	+	3.23257i	−0.0855617	+	0.211773i	−0.963899	−	0.266269i	$-0.914209\pi$
$233$	−1.30604	+	3.23257i	−0.0855617	+	0.211773i	0.878337	+	0.478042i	$0.158653\pi$
$234$	−3.96027	+	8.11975i	−0.258891	+	0.530805i
$235$	−1.49521	−	0.665711i	−0.0975369	−	0.0434262i
$236$	−2.87919	−	3.19767i	−0.187420	−	0.208151i
$237$	0.700989	−	0.897226i	0.0455342	−	0.0582811i
$238$	1.33695	−	0.383363i	0.0866614	−	0.0248497i
$239$	−4.50058	+	2.00379i	−0.291118	+	0.129614i	−0.547100	−	0.837067i	$-0.684268\pi$
$239$	−4.50058	+	2.00379i	−0.291118	+	0.129614i	0.255981	+	0.966682i	$0.417601\pi$
$240$	−0.0379862	+	0.0421880i	−0.00245200	+	0.00272322i
$241$	3.82287	+	21.6806i	0.246253	+	1.39657i	0.817566	+	0.575835i	$0.195323\pi$
$241$	3.82287	+	21.6806i	0.246253	+	1.39657i	−0.571313	+	0.820732i	$0.693566\pi$
$242$	9.15182	−	6.10280i	0.588301	−	0.392303i
$243$	5.95708	−	4.99858i	0.382147	−	0.320659i
$244$	4.70851	−	0.661738i	0.301431	−	0.0423634i
$245$	0.557773	+	0.159939i	0.0356348	+	0.0102181i
$246$	−0.503785	+	0.366021i	−0.0321201	+	0.0233366i
$247$	12.1922	−	5.87052i	0.775770	−	0.373532i
$248$	0.404940	−	1.24628i	0.0257137	−	0.0791387i
$249$	−2.31870	+	3.43762i	−0.146942	+	0.217850i
$250$	−1.35673	+	1.31017i	−0.0858069	+	0.0828627i
$251$	−16.9226	−	10.5744i	−1.06815	−	0.667452i	−0.122440	−	0.992476i	$-0.539072\pi$
$251$	−16.9226	−	10.5744i	−1.06815	−	0.667452i	−0.945706	+	0.325024i	$0.894628\pi$
$252$	4.42181	+	3.71034i	0.278548	+	0.233729i
$253$	−0.842271	−	0.105680i	−0.0529532	−	0.00664402i
$254$	−2.70995	−	4.69378i	−0.170038	−	0.294514i
$255$	−0.0389356	−	0.00827601i	−0.00243824	−	0.000518264i
$256$	0.559193	+	0.829038i	0.0349496	+	0.0518148i
$257$	−30.6836	+	8.79838i	−1.91399	+	0.548828i	−0.931053	+	0.364883i	$0.881109\pi$
$257$	−30.6836	+	8.79838i	−1.91399	+	0.548828i	−0.982937	+	0.183945i	$0.941113\pi$
$258$	−0.112657	−	0.125119i	−0.00701374	−	0.00778955i
$259$	2.46961	−	0.524933i	0.153454	−	0.0326177i
$260$	0.422700	+	0.408197i	0.0262148	+	0.0253153i
$261$	−5.99468	−	24.0434i	−0.371062	−	1.48825i
$262$	11.4172	+	7.13425i	0.705356	+	0.440755i
$263$	0.580192	−	3.29043i	0.0357762	−	0.202897i	−0.961680	−	0.274173i	$-0.911596\pi$
$263$	0.580192	−	3.29043i	0.0357762	−	0.202897i	0.997457	+	0.0712760i	$0.0227071\pi$
$264$	0.929578	−	0.354014i	0.0572116	−	0.0217880i
$265$	−1.41126			−0.0866931
$266$	−1.75492	−	8.46617i	−0.107601	−	0.519094i
$267$	1.83007	+	1.32962i	0.111998	+	0.0813716i
$268$	4.46448	−	6.61886i	0.272711	−	0.404311i
$269$	−18.6987	−	9.94228i	−1.14008	−	0.606192i	−0.211521	−	0.977374i	$-0.567842\pi$
$269$	−18.6987	−	9.94228i	−1.14008	−	0.606192i	−0.928560	+	0.371182i	$0.878953\pi$
$270$	−0.125685	−	0.311080i	−0.00764892	−	0.0189317i
$271$	−10.2299	−	0.715346i	−0.621423	−	0.0434541i	−0.244425	−	0.969668i	$-0.578599\pi$
$271$	−10.2299	−	0.715346i	−0.621423	−	0.0434541i	−0.376998	+	0.926214i	$0.623044\pi$
$272$	−0.307375	+	0.630212i	−0.0186374	+	0.0382122i
$273$	−1.23577	+	1.37246i	−0.0747921	+	0.0830650i
$274$	4.55221	−	7.88467i	0.275009	−	0.476330i
$275$	15.7576	−	4.77204i	0.950216	−	0.287765i
$276$	−0.0721327	−	0.0262541i	−0.00434188	−	0.00158031i
$277$	−12.6862	−	2.69653i	−0.762238	−	0.162019i	−0.189639	−	0.981854i	$-0.560732\pi$
$277$	−12.6862	−	2.69653i	−0.762238	−	0.162019i	−0.572599	+	0.819835i	$0.694065\pi$
$278$	1.28730	−	12.2478i	0.0772069	−	0.734575i
$279$	2.74311	+	2.64899i	0.164226	+	0.158591i
$280$	0.318407	−	0.198963i	0.0190285	−	0.0118903i
$281$	0.356294	+	0.881860i	0.0212547	+	0.0526073i	0.937438	−	0.348152i	$-0.113191\pi$
$281$	0.356294	+	0.881860i	0.0212547	+	0.0526073i	−0.916183	+	0.400759i	$0.868746\pi$
$282$	1.13683	+	2.33085i	0.0676974	+	0.138800i
$283$	−7.99109	−	2.29141i	−0.475021	−	0.136210i	0.0295804	−	0.999562i	$-0.490583\pi$
$283$	−7.99109	−	2.29141i	−0.475021	−	0.136210i	−0.504602	+	0.863352i	$0.668361\pi$
$284$	4.36789	+	13.4430i	0.259186	+	0.797694i
$285$	−0.0694072	+	0.237519i	−0.00411133	+	0.0140694i
$286$	−3.32637	−	9.74411i	−0.196692	−	0.576181i
$287$	3.87008	−	1.40859i	0.228444	−	0.0831467i
$288$	−2.88173	+	0.405001i	−0.169808	+	0.0238649i
$289$	16.4681	−	1.15156i	0.968714	−	0.0677391i
$290$	−1.60786	−	0.112432i	−0.0944167	−	0.00660226i
$291$	1.11138	+	0.156195i	0.0651504	+	0.00915629i
$292$	−0.372151	+	0.0791031i	−0.0217785	+	0.00462916i
$293$	−0.718104	−	6.83230i	−0.0419521	−	0.399147i	−0.995268	−	0.0971715i	$-0.969020\pi$
$293$	−0.718104	−	6.83230i	−0.0419521	−	0.399147i	0.953316	−	0.301976i	$-0.0976462\pi$
$294$	−0.514114	−	0.762206i	−0.0299838	−	0.0444527i
$295$	0.0284247	−	0.813977i	0.00165495	−	0.0473916i
$296$	−0.636428	+	1.10233i	−0.0369916	+	0.0640714i
$297$	−0.527853	+	5.85502i	−0.0306292	+	0.339743i
$298$	−3.80465	−	21.5773i	−0.220398	−	1.24994i
$299$	−0.297649	+	0.736708i	−0.0172135	+	0.0426049i
$300$	1.48520	−	0.103856i	0.0857483	−	0.00599610i
$301$	0.488132	+	1.00082i	0.0281355	+	0.0576863i
$302$	0.655026	+	18.7575i	0.0376925	+	1.07937i
$303$	−0.480618	+	1.47919i	−0.0276108	+	0.0849773i
$304$	3.76387	+	2.19848i	0.215873	+	0.126091i
$305$	0.728124	+	0.529013i	0.0416922	+	0.0302912i
$306$	−1.25623	−	1.60790i	−0.0718139	−	0.0919176i
$307$	2.69921	−	15.3080i	0.154052	−	0.873672i	−0.805596	−	0.592466i	$-0.798154\pi$
$307$	2.69921	−	15.3080i	0.154052	−	0.873672i	0.959647	−	0.281206i	$-0.0907344\pi$
$308$	−6.55519	+	0.556041i	−0.373516	+	0.0316834i
$309$	0.613592	+	0.514864i	0.0349060	+	0.0292896i
$310$	0.219008	−	0.116449i	0.0124388	−	0.00661384i
$311$	1.29934	−	12.3624i	0.0736790	−	0.701009i	−0.893870	−	0.448326i	$-0.852020\pi$
$311$	1.29934	−	12.3624i	0.0736790	−	0.701009i	0.967549	−	0.252683i	$-0.0813129\pi$
$312$	−0.0973229	−	0.925965i	−0.00550982	−	0.0524225i
$313$	−1.35046	+	1.72851i	−0.0763324	+	0.0977010i	−0.824661	−	0.565627i	$-0.808634\pi$
$313$	−1.35046	+	1.72851i	−0.0763324	+	0.0977010i	0.748329	+	0.663328i	$0.230857\pi$
$314$	12.9238	−	16.5417i	0.729332	−	0.933502i
$315$	0.114208	+	1.08662i	0.00643491	+	0.0612240i
$316$	0.396831	−	3.77559i	0.0223235	−	0.212394i
$317$	12.2451	−	6.51082i	0.687752	−	0.365684i	−0.0885270	−	0.996074i	$-0.528216\pi$
$317$	12.2451	−	6.51082i	0.687752	−	0.365684i	0.776279	+	0.630390i	$0.217105\pi$
$318$	1.71294	+	1.43733i	0.0960572	+	0.0806015i
$319$	24.1691	+	14.6094i	1.35321	+	0.817968i
$320$	−0.0328690	+	0.186410i	−0.00183744	+	0.0104206i
$321$	2.52820	+	3.23594i	0.141110	+	0.180613i
$322$	0.410725	+	0.298409i	0.0228888	+	0.0166297i
$323$	−0.0154296	+	3.05631i	−0.000858527	+	0.170058i
$324$	2.53349	−	7.79728i	0.140749	−	0.433182i
$325$	−0.537833	−	15.4015i	−0.0298336	−	0.854323i
$326$	7.22981	+	14.8233i	0.400422	+	0.820987i
$327$	3.84160	−	0.268631i	0.212441	−	0.0148553i
$328$	−0.777793	+	1.92511i	−0.0429464	+	0.106296i
$329$	−2.97832	−	16.8909i	−0.164200	−	0.931226i
$330$	0.173120	+	0.0740262i	0.00952997	+	0.00407501i
$331$	−3.17272	+	5.49530i	−0.174388	+	0.302049i	−0.939949	−	0.341314i	$-0.889128\pi$
$331$	−3.17272	+	5.49530i	−0.174388	+	0.302049i	0.765561	+	0.643363i	$0.222461\pi$
$332$	−0.482508	+	13.8172i	−0.0264811	+	0.758318i
$333$	−2.07129	−	3.07082i	−0.113506	−	0.168280i
$334$	−2.00706	−	19.0959i	−0.109822	−	1.04488i
$335$	1.47819	−	0.314199i	0.0807621	−	0.0171665i
$336$	−0.589111	−	0.0827941i	−0.0321386	−	0.00451679i
$337$	18.1796	+	1.27124i	0.990308	+	0.0692491i	0.555711	−	0.831376i	$-0.312446\pi$
$337$	18.1796	+	1.27124i	0.990308	+	0.0692491i	0.434597	+	0.900625i	$0.356891\pi$
$338$	3.35432	−	0.234557i	0.182451	−	0.0127582i
$339$	−1.89847	+	0.266813i	−0.103111	+	0.0144913i
$340$	−0.124718	+	0.0453937i	−0.00676379	+	0.00246182i
$341$	−4.34567	+	0.0643591i	−0.235331	+	0.00348524i
$342$	−10.5517	+	7.03997i	−0.570571	+	0.380678i
$343$	6.16968	+	18.9883i	0.333131	+	1.02527i
$344$	−0.539625	−	0.154735i	−0.0290946	−	0.00834274i
$345$	−0.00636949	−	0.0130594i	−0.000342922	−	0.000703094i
$346$	4.12684	+	10.2143i	0.221860	+	0.549123i
$347$	−22.1482	+	13.8397i	−1.18898	+	0.742956i	−0.972402	−	0.233310i	$-0.925044\pi$
$347$	−22.1482	+	13.8397i	−1.18898	+	0.742956i	−0.216576	+	0.976266i	$0.569489\pi$
$348$	1.83706	+	1.77403i	0.0984767	+	0.0950978i
$349$	1.83736	−	17.4813i	0.0983516	−	0.935753i	−0.828415	−	0.560115i	$-0.810757\pi$
$349$	1.83736	−	17.4813i	0.0983516	−	0.935753i	0.926766	−	0.375638i	$-0.122576\pi$
$350$	−9.63156	−	2.04725i	−0.514829	−	0.109430i
$351$	5.17080	+	1.88202i	0.275997	+	0.100455i
$352$	2.00299	−	2.64349i	0.106760	−	0.140898i
$353$	−1.40856	+	2.43969i	−0.0749699	+	0.129852i	−0.901073	−	0.433667i	$-0.857219\pi$
$353$	−1.40856	+	2.43969i	−0.0749699	+	0.129852i	0.826103	+	0.563519i	$0.190553\pi$
$354$	−0.863514	+	0.959030i	−0.0458953	+	0.0509719i
$355$	−1.17286	+	2.40473i	−0.0622492	+	0.127630i
$356$	7.52405	+	0.526133i	0.398774	+	0.0278850i
$357$	−0.156259	−	0.386756i	−0.00827013	−	0.0204693i
$358$	14.2737	+	7.58944i	0.754386	+	0.401114i
$359$	1.41152	−	2.09266i	0.0744971	−	0.110447i	−0.789948	−	0.613174i	$-0.789892\pi$
$359$	1.41152	−	2.09266i	0.0744971	−	0.110447i	0.864445	+	0.502728i	$0.167670\pi$
$360$	−0.445631	−	0.323770i	−0.0234868	−	0.0170642i
$361$	18.9394	+	1.51667i	0.996809	+	0.0798249i
$362$	−3.69544			−0.194228
$363$	−2.10720	−	2.53841i	−0.110600	−	0.133232i
$364$	−1.06930	+	6.06427i	−0.0560463	+	0.317854i
$365$	−0.0610733	−	0.0381629i	−0.00319672	−	0.00199754i
$366$	−0.344988	−	1.38367i	−0.0180328	−	0.0723257i
$367$	−6.65392	−	6.42561i	−0.347332	−	0.335414i	0.500444	−	0.865769i	$-0.333170\pi$
$367$	−6.65392	−	6.42561i	−0.347332	−	0.335414i	−0.847776	+	0.530354i	$0.822059\pi$
$368$	−0.250353	+	0.0532141i	−0.0130505	+	0.00277398i
$369$	−4.04297	−	4.49017i	−0.210468	−	0.233749i
$370$	−0.231599	+	0.0664101i	−0.0120403	+	0.00345250i
$371$	−8.26986	−	12.2606i	−0.429350	−	0.636537i
$372$	−0.384425	−	0.0817120i	−0.0199315	−	0.00423657i
$373$	−8.10742	−	14.0425i	−0.419786	−	0.727091i	0.576131	−	0.817357i	$-0.304562\pi$
$373$	−8.10742	−	14.0425i	−0.419786	−	0.727091i	−0.995918	+	0.0902658i	$0.971228\pi$
$374$	2.30744	+	0.289514i	0.119315	+	0.0149704i
$375$	0.433322	+	0.363600i	0.0223766	+	0.0187762i
$376$	7.33291	+	4.58211i	0.378166	+	0.236304i
$377$	19.0154	−	18.3630i	0.979345	−	0.945742i
$378$	1.96606	−	2.91480i	0.101123	−	0.149921i
$379$	5.07678	−	15.6247i	0.260777	−	0.802588i	−0.731860	−	0.681455i	$-0.761347\pi$
$379$	5.07678	−	15.6247i	0.260777	−	0.802588i	0.992636	−	0.121133i	$-0.0386526\pi$
$380$	0.223415	+	0.794251i	0.0114609	+	0.0407442i
$381$	−1.31507	+	0.955452i	−0.0673729	+	0.0489493i
$382$	7.09397	+	2.03416i	0.362959	+	0.104077i
$383$	−2.95858	+	0.415802i	−0.151177	+	0.0212465i	−0.214355	−	0.976756i	$-0.568765\pi$
$383$	−2.95858	+	0.415802i	−0.151177	+	0.0212465i	0.0631788	+	0.998002i	$0.479876\pi$
$384$	0.229748	−	0.192782i	0.0117243	−	0.00983786i
$385$	−0.965670	−	0.786221i	−0.0492151	−	0.0400696i
$386$	1.76092	+	9.98670i	0.0896287	+	0.508309i
$387$	1.09310	−	1.21402i	0.0555656	−	0.0617119i
$388$	3.41855	−	1.52204i	0.173551	−	0.0772698i
$389$	−19.6789	+	5.64283i	−0.997760	+	0.286103i	−0.734490	−	0.678619i	$-0.762579\pi$
$389$	−19.6789	+	5.64283i	−0.997760	+	0.286103i	−0.263269	+	0.964722i	$0.584801\pi$
$390$	0.108502	−	0.138877i	0.00549423	−	0.00703229i
$391$	−0.120084	−	0.133367i	−0.00607291	−	0.00674465i
$392$	−2.80046	−	1.24685i	−0.141445	−	0.0629752i
$393$	1.77002	−	3.62909i	0.0892859	−	0.183063i
$394$	6.87910	−	17.0264i	0.346564	−	0.857777i
$395$	0.550480	−	0.461908i	0.0276977	−	0.0232411i
$396$	4.35895	+	8.61115i	0.219046	+	0.432726i
$397$	10.3522	−	3.76788i	0.519561	−	0.189105i	−0.0689104	−	0.997623i	$-0.521952\pi$
$397$	10.3522	−	3.76788i	0.519561	−	0.189105i	0.588471	+	0.808518i	$0.299730\pi$
$398$	0.330762	+	1.01798i	0.0165796	+	0.0510268i
$399$	−2.47021	+	0.788854i	−0.123665	+	0.0394921i
$400$	4.01610	−	2.91787i	0.200805	−	0.145893i
$401$	−1.16944	−	33.4884i	−0.0583991	−	1.67233i	−0.576564	−	0.817052i	$-0.695607\pi$
$401$	−1.16944	−	33.4884i	−0.0583991	−	1.67233i	0.518165	−	0.855281i	$-0.326615\pi$
$402$	−2.11418	−	1.12413i	−0.105446	−	0.0560666i
$403$	−0.984159	+	3.94725i	−0.0490244	+	0.196626i
$404$	1.25457	+	5.03180i	0.0624171	+	0.250341i
$405$	1.37021	−	0.728556i	0.0680865	−	0.0362022i
$406$	−8.44512	−	14.6274i	−0.419124	−	0.725945i
$407$	4.14188	+	0.816472i	0.205305	+	0.0404710i
$408$	0.197611	+	0.0719245i	0.00978320	+	0.00356079i
$409$	−0.0255918	+	0.732853i	−0.00126543	+	0.0362373i	−0.999859	−	0.0167751i	$-0.994660\pi$
$409$	−0.0255918	+	0.732853i	−0.00126543	+	0.0362373i	0.998594	+	0.0530124i	$0.0168823\pi$
$410$	−0.359034	+	0.159852i	−0.0177314	+	0.00789454i
$411$	−2.49449	−	1.11062i	−0.123044	−	0.0547827i
$412$	2.64472	+	0.371691i	0.130296	+	0.0183119i
$413$	7.23812	−	4.52288i	0.356165	−	0.222556i
$414$	0.180187	−	0.722690i	0.00885571	−	0.0355183i
$415$	−1.88250	+	1.81791i	−0.0924085	+	0.0892379i
$416$	−1.91128	−	2.44632i	−0.0937081	−	0.119941i
$417$	−3.69354			−0.180873
$418$	2.86758	−	14.1696i	0.140258	−	0.693057i
$419$	5.95186			0.290767			0.145384	−	0.989375i	$-0.453558\pi$
$419$	5.95186			0.290767			0.145384	+	0.989375i	$0.453558\pi$
$420$	−0.0693271	−	0.0887346i	−0.00338281	−	0.00432980i
$421$	−10.3875	+	10.0311i	−0.506257	+	0.488887i	−0.903357	−	0.428888i	$-0.858905\pi$
$421$	−10.3875	+	10.0311i	−0.506257	+	0.488887i	0.397100	+	0.917775i	$0.370016\pi$
$422$	−4.72505	+	18.9511i	−0.230012	+	0.922527i
$423$	−21.3391	+	13.3342i	−1.03754	+	0.648330i
$424$	7.38318	+	1.03764i	0.358559	+	0.0503922i
$425$	3.17983	+	1.41575i	0.154244	+	0.0686740i
$426$	3.87273	−	1.72425i	0.187635	−	0.0835403i
$427$	−0.329151	+	9.42566i	−0.0159287	+	0.456140i
$428$	12.8664	+	4.68297i	0.621919	+	0.226360i
$429$	−2.80212	+	1.29764i	−0.135287	+	0.0626506i
$430$	−0.0531296	−	0.0920232i	−0.00256214	−	0.00443775i
$431$	−6.03478	+	3.20875i	−0.290685	+	0.154560i	−0.608410	−	0.793623i	$-0.708192\pi$
$431$	−6.03478	+	3.20875i	−0.290685	+	0.154560i	0.317725	+	0.948183i	$0.397081\pi$
$432$	0.428810	+	1.71986i	0.0206311	+	0.0827470i
$433$	−3.41088	+	13.6803i	−0.163917	+	0.657433i	0.830960	+	0.556333i	$0.187792\pi$
$433$	−3.41088	+	13.6803i	−0.163917	+	0.657433i	−0.994876	+	0.101101i	$0.967764\pi$
$434$	2.29503	+	1.22029i	0.110165	+	0.0585758i
$435$	0.0168704	+	0.483104i	0.000808873	+	0.0231631i
$436$	10.3880	−	7.54730i	0.497493	−	0.361450i
$437$	−0.882593	+	0.682410i	−0.0422202	+	0.0326441i
$438$	0.0352611	+	0.108522i	0.00168484	+	0.00518540i
$439$	−14.0338	+	5.10788i	−0.669796	+	0.243786i	−0.654460	−	0.756097i	$-0.727104\pi$
$439$	−14.0338	+	5.10788i	−0.669796	+	0.243786i	−0.0153357	+	0.999882i	$0.504882\pi$
$440$	0.620317	−	0.0965676i	0.0295724	−	0.00460368i
$441$	6.83367	−	5.73413i	0.325413	−	0.273054i
$442$	0.815425	−	2.01825i	0.0387858	−	0.0959983i
$443$	14.4586	−	29.6445i	0.686949	−	1.40845i	−0.215002	−	0.976614i	$-0.568976\pi$
$443$	14.4586	−	29.6445i	0.686949	−	1.40845i	0.901950	−	0.431840i	$-0.142135\pi$
$444$	0.348745	+	0.155271i	0.0165507	+	0.00736885i
$445$	0.955298	+	1.06097i	0.0452854	+	0.0502946i
$446$	11.5685	−	14.8070i	0.547785	−	0.701133i
$447$	−6.31662	+	1.81126i	−0.298766	+	0.0856698i
$448$	−1.81207	+	0.806787i	−0.0856124	+	0.0381171i
$449$	3.61502	−	4.01489i	0.170603	−	0.189474i	−0.651780	−	0.758408i	$-0.725977\pi$
$449$	3.61502	−	4.01489i	0.170603	−	0.189474i	0.822383	+	0.568934i	$0.192644\pi$
$450$	2.50852	+	14.2265i	0.118253	+	0.670645i
$451$	6.87587	+	0.378585i	0.323772	+	0.0178269i
$452$	−4.89674	+	4.10885i	−0.230323	+	0.193264i
$453$	5.57430	−	0.783417i	0.261904	−	0.0368082i
$454$	−1.94530	−	0.557807i	−0.0912976	−	0.0261792i
$455$	−0.942978	+	0.685114i	−0.0442075	+	0.0321186i
$456$	0.537749	−	1.19158i	0.0251824	−	0.0558008i
$457$	−4.37686	+	13.4706i	−0.204741	+	0.630128i	0.794983	+	0.606632i	$0.207480\pi$
$457$	−4.37686	+	13.4706i	−0.204741	+	0.630128i	−0.999724	+	0.0234959i	$0.992520\pi$
$458$	15.7623	−	23.3686i	0.736525	−	1.09194i
$459$	−0.894027	+	0.863352i	−0.0417296	+	0.0402978i
$460$	−0.0410851	−	0.0256728i	−0.00191560	−	0.00119700i
$461$	20.6565	+	17.3329i	0.962070	+	0.807272i	0.981289	−	0.192543i	$-0.0616735\pi$
$461$	20.6565	+	17.3329i	0.962070	+	0.807272i	−0.0192189	+	0.999815i	$0.506118\pi$
$462$	0.371355	+	1.93780i	0.0172770	+	0.0901546i
$463$	3.33073	+	5.76899i	0.154792	+	0.268108i	0.932983	−	0.359920i	$-0.117196\pi$
$463$	3.33073	+	5.76899i	0.154792	+	0.268108i	−0.778191	+	0.628027i	$0.783863\pi$
$464$	8.32904	+	1.77039i	0.386666	+	0.0821884i
$465$	−0.0415992	−	0.0616734i	−0.00192912	−	0.00286003i
$466$	3.35138	−	0.960992i	0.155250	−	0.0445171i
$467$	9.16225	+	10.1757i	0.423979	+	0.470876i	0.916853	−	0.399224i	$-0.130721\pi$
$467$	9.16225	+	10.1757i	0.423979	+	0.470876i	−0.492875	+	0.870100i	$0.664054\pi$
$468$	8.83663	−	1.87828i	0.408473	−	0.0868237i
$469$	11.3917	+	11.0008i	0.526020	+	0.507972i
$470$	0.395957	+	1.58810i	0.0182641	+	0.0732534i
$471$	−5.33909	−	3.33623i	−0.246012	−	0.153725i
$472$	−0.747189	+	4.23752i	−0.0343921	+	0.195048i
$473$	0.0925249	+	1.85956i	0.00425430	+	0.0855025i
$474$	−1.13860			−0.0522974
$475$	10.2549	−	19.0540i	0.470527	−	0.874256i
$476$	−1.12520	−	0.817506i	−0.0515735	−	0.0374703i
$477$	−12.1326	+	17.9873i	−0.555513	+	0.823581i
$478$	4.34984	+	2.31285i	0.198957	+	0.105787i
$479$	7.40013	+	18.3160i	0.338120	+	0.836878i	0.996453	+	0.0841504i	$0.0268176\pi$
$479$	7.40013	+	18.3160i	0.338120	+	0.836878i	−0.658333	+	0.752727i	$0.728738\pi$
$480$	0.0566312	+	0.00396004i	0.00258485	+	0.000180750i
$481$	1.73222	−	3.55158i	0.0789824	−	0.161938i
$482$	14.7309	−	16.3603i	0.670975	−	0.745193i
$483$	0.0761310	−	0.131863i	0.00346408	−	0.00599997i
$484$	−10.4435	−	3.45447i	−0.474704	−	0.157021i
$485$	0.665602	+	0.242259i	0.0302234	+	0.0110004i
$486$	−7.60648	−	1.61681i	−0.345037	−	0.0733399i
$487$	−0.248828	+	2.36744i	−0.0112755	+	0.107279i	−0.998712	−	0.0507369i	$-0.983843\pi$
$487$	−0.248828	+	2.36744i	−0.0112755	+	0.107279i	0.987437	+	0.158016i	$0.0505097\pi$
$488$	−3.42031	−	3.30295i	−0.154830	−	0.149518i
$489$	4.19473	−	2.62116i	0.189692	−	0.118533i
$490$	−0.217366	−	0.538000i	−0.00981959	−	0.0243043i
$491$	−5.42311	−	11.1190i	−0.244742	−	0.501795i	0.740694	−	0.671842i	$-0.234497\pi$
$491$	−5.42311	−	11.1190i	−0.244742	−	0.501795i	−0.985436	+	0.170047i	$0.945608\pi$
$492$	0.598589	+	0.171643i	0.0269865	+	0.00773825i
$493$	1.84501	+	5.67837i	0.0830952	+	0.255741i
$494$	−12.1323	−	5.99332i	−0.545857	−	0.269652i
$495$	−0.538751	+	1.74565i	−0.0242150	+	0.0784611i
$496$	−1.23139	+	0.448188i	−0.0552908	+	0.0201242i
$497$	−27.7643	+	3.90202i	−1.24540	+	0.175030i
$498$	4.13642	−	0.289247i	0.185357	−	0.0129615i
$499$	−34.1696	−	2.38937i	−1.52964	−	0.106963i	−0.720037	−	0.693936i	$-0.755875\pi$
$499$	−34.1696	−	2.38937i	−1.52964	−	0.106963i	−0.809607	+	0.586973i	$0.800319\pi$
$500$	1.86772	+	0.262490i	0.0835268	+	0.0117389i
$501$	−5.63287	+	1.19730i	−0.251658	+	0.0534915i
$502$	2.08584	+	19.8455i	0.0930957	+	0.885747i
$503$	19.7149	+	29.2286i	0.879046	+	1.30324i	0.952061	+	0.305908i	$0.0989600\pi$
$503$	19.7149	+	29.2286i	0.879046	+	1.30324i	−0.0730155	+	0.997331i	$0.523262\pi$
$504$	0.201449	−	5.76875i	0.00897325	−	0.256960i
$505$	−0.490802	+	0.850093i	−0.0218404	+	0.0378287i
$506$	0.435277	+	0.728782i	0.0193504	+	0.0323983i
$507$	−0.175119	−	0.993149i	−0.00777731	−	0.0441073i
$508$	−2.03033	+	5.02525i	−0.0900814	+	0.222959i
$509$	−33.3080	+	2.32912i	−1.47635	+	0.103236i	−0.785095	−	0.619375i	$-0.787386\pi$
$509$	−33.3080	+	2.32912i	−1.47635	+	0.103236i	−0.691254	+	0.722612i	$0.742942\pi$
$510$	0.0174495	+	0.0357769i	0.000772679	+	0.00158423i
$511$	−0.0263378	−	0.754215i	−0.00116511	−	0.0333645i
$512$	0.309017	−	0.951057i	0.0136568	−	0.0420312i
$513$	4.93637	+	5.94362i	0.217946	+	0.262417i
$514$	25.8239	+	18.7622i	1.13904	+	0.827564i
$515$	0.311233	+	0.398360i	0.0137146	+	0.0175538i
$516$	−0.0292361	+	0.165806i	−0.00128705	+	0.00729920i
$517$	6.52507	−	27.9260i	0.286972	−	1.22819i
$518$	−1.93410	−	1.62290i	−0.0849794	−	0.0713062i
$519$	2.91726	−	1.55114i	0.128054	−	0.0680873i
$520$	0.0614233	−	0.584404i	0.00269359	−	0.0256278i
$521$	−1.68067	−	15.9905i	−0.0736315	−	0.700557i	−0.967610	−	0.252448i	$-0.918764\pi$
$521$	−1.68067	−	15.9905i	−0.0736315	−	0.700557i	0.893979	−	0.448109i	$-0.147902\pi$
$522$	−15.2557	+	19.5264i	−0.667725	+	0.854649i
$523$	−19.3652	+	24.7864i	−0.846782	+	1.08383i	0.148700	+	0.988882i	$0.452491\pi$
$523$	−19.3652	+	24.7864i	−0.846782	+	1.08383i	−0.995482	+	0.0949497i	$0.969731\pi$
$524$	−1.40726	−	13.3891i	−0.0614763	−	0.584908i
$525$	−0.308692	+	2.93701i	−0.0134724	+	0.128182i
$526$	−2.95010	+	1.56859i	−0.128630	+	0.0683940i
$527$	−0.703864	−	0.590612i	−0.0306608	−	0.0257275i
$528$	−0.851272	−	0.514565i	−0.0370469	−	0.0223935i
$529$	−3.98253	+	22.5861i	−0.173154	+	0.982003i
$530$	0.868860	+	1.11209i	0.0377409	+	0.0483061i
$531$	−10.1302	−	7.36003i	−0.439613	−	0.319398i
$532$	−5.59100	+	6.59519i	−0.242401	+	0.285938i
$533$	1.99183	−	6.13023i	0.0862759	−	0.265530i
$534$	−0.0789457	−	2.26071i	−0.00341632	−	0.0978305i
$535$	1.13613	+	2.32942i	0.0491193	+	0.100709i
$536$	−7.96434	+	0.556921i	−0.344007	+	0.0240553i
$537$	1.81624	−	4.49536i	0.0783767	−	0.193989i
$538$	3.67745	+	20.8559i	0.158546	+	0.899160i
$539$	−0.912899	+	10.1260i	−0.0393214	+	0.436158i
$540$	−0.167755	+	0.290561i	−0.00721904	+	0.0125037i
$541$	0.364871	−	10.4485i	0.0156870	−	0.449218i	−0.965980	−	0.258616i	$-0.916734\pi$
$541$	0.364871	−	10.4485i	0.0156870	−	0.449218i	0.981667	−	0.190602i	$-0.0610441\pi$
$542$	5.73447	+	8.50170i	0.246316	+	0.365179i
$543$	0.115851	+	1.10225i	0.00497164	+	0.0473020i
$544$	0.685853	−	0.145783i	0.0294057	−	0.00625038i
$545$	2.40681	+	0.338255i	0.103097	+	0.0144893i
$546$	1.84233	+	0.128828i	0.0788443	+	0.00551333i
$547$	−19.3583	+	1.35367i	−0.827702	+	0.0578786i	−0.477322	−	0.878729i	$-0.658392\pi$
$547$	−19.3583	+	1.35367i	−0.827702	+	0.0578786i	−0.350381	+	0.936607i	$0.613948\pi$
$548$	−9.01582	+	1.26709i	−0.385137	+	0.0541275i
$549$	13.0022	−	4.73242i	0.554921	−	0.201975i
$550$	−13.4617	−	9.47916i	−0.574010	−	0.404193i
$551$	36.0589	−	8.79737i	1.53616	−	0.374781i
$552$	0.0237208	+	0.0730050i	0.00100962	+	0.00310730i
$553$	7.23866	+	2.07565i	0.307819	+	0.0882657i
$554$	5.68549	+	11.6570i	0.241553	+	0.495258i
$555$	0.0270689	+	0.0669978i	0.00114901	+	0.00284390i
$556$	−10.4439	+	6.52610i	−0.442922	+	0.276768i
$557$	−30.7444	−	29.6896i	−1.30268	−	1.25799i	−0.946159	−	0.323701i	$-0.895073\pi$
$557$	−30.7444	−	29.6896i	−1.30268	−	1.25799i	−0.356524	−	0.934286i	$-0.616038\pi$
$558$	0.398606	−	3.79248i	0.0168743	−	0.160548i
$559$	1.70465	+	0.362335i	0.0720992	+	0.0153252i
$560$	−0.352816	−	0.128414i	−0.0149092	−	0.00542650i
$561$	0.0140165	−	0.697323i	0.000591777	−	0.0294410i
$562$	0.475558	−	0.823691i	0.0200602	−	0.0347453i
$563$	−15.8723	+	17.6280i	−0.668939	+	0.742932i	−0.978113	−	0.208073i	$-0.933281\pi$
$563$	−15.8723	+	17.6280i	−0.668939	+	0.742932i	0.309174	+	0.951006i	$0.399947\pi$
$564$	1.13683	−	2.33085i	0.0478693	−	0.0981466i
$565$	−1.20701	−	0.0844023i	−0.0507792	−	0.00355083i
$566$	3.11415	+	7.70780i	0.130898	+	0.323983i
$567$	14.3588	+	7.63470i	0.603012	+	0.320627i
$568$	7.90407	−	11.7183i	0.331647	−	0.491687i
$569$	−7.31452	−	5.31431i	−0.306641	−	0.222787i	0.423813	−	0.905750i	$-0.360691\pi$
$569$	−7.31452	−	5.31431i	−0.306641	−	0.222787i	−0.730454	+	0.682962i	$0.760691\pi$
$570$	0.229899	−	0.0915379i	0.00962942	−	0.00383410i
$571$	−42.9002			−1.79532			−0.897660	−	0.440689i	$-0.854734\pi$
$571$	−42.9002			−1.79532			−0.897660	+	0.440689i	$0.854734\pi$
$572$	−5.63054	+	8.62028i	−0.235425	+	0.360432i
$573$	0.384341	−	2.17970i	0.0160561	−	0.0910584i
$574$	−3.49265	−	2.18245i	−0.145780	−	0.0910936i
$575$	0.307376	+	1.23282i	0.0128185	+	0.0514120i
$576$	2.09332	+	2.02149i	0.0872215	+	0.0842288i
$577$	28.2618	−	6.00723i	1.17655	−	0.250084i	0.422170	−	0.906517i	$-0.361269\pi$
$577$	28.2618	−	6.00723i	1.17655	−	0.250084i	0.754385	+	0.656432i	$0.227935\pi$
$578$	−11.0462	−	12.2681i	−0.459463	−	0.510286i
$579$	2.92355	−	0.838315i	0.121499	−	0.0348392i
$580$	0.901299	+	1.33623i	0.0374244	+	0.0554840i
$581$	−26.8247	−	5.70177i	−1.11288	−	0.236549i
$582$	−0.561152	−	0.971945i	−0.0232605	−	0.0402884i
$583$	−4.65410	−	24.2860i	−0.192753	−	1.00582i
$584$	0.291453	+	0.244558i	0.0120604	+	0.0101199i
$585$	1.45017	+	0.906168i	0.0599573	+	0.0374654i
$586$	−4.94182	+	4.77226i	−0.204145	+	0.197140i
$587$	23.5373	−	34.8955i	0.971488	−	1.44029i	0.0750204	−	0.997182i	$-0.476098\pi$
$587$	23.5373	−	34.8955i	0.971488	−	1.44029i	0.896468	−	0.443109i	$-0.146124\pi$
$588$	−0.284106	+	0.874388i	−0.0117163	+	0.0360592i
$589$	−3.98855	+	4.08875i	−0.164345	+	0.168474i
$590$	−0.658923	+	0.478735i	−0.0271274	+	0.0197092i
$591$	−5.29416	−	1.51807i	−0.217772	−	0.0624452i
$592$	1.26047	−	0.177147i	0.0518049	−	0.00728071i
$593$	3.06648	−	2.57308i	0.125925	−	0.105664i	−0.577650	−	0.816284i	$-0.696030\pi$
$593$	3.06648	−	2.57308i	0.125925	−	0.105664i	0.703575	+	0.710621i	$0.251586\pi$
$594$	4.93880	−	3.18876i	0.202641	−	0.130836i
$595$	−0.0457151	−	0.259263i	−0.00187413	−	0.0106287i
$596$	−14.6607	+	16.2824i	−0.600527	+	0.666953i
$597$	0.293266	−	0.130571i	0.0120026	−	0.00534390i
$598$	0.763785	−	0.219012i	0.0312335	−	0.00895606i
$599$	−8.84493	+	11.3210i	−0.361394	+	0.462563i	−0.934003	−	0.357266i	$-0.883709\pi$
$599$	−8.84493	+	11.3210i	−0.361394	+	0.462563i	0.572609	+	0.819829i	$0.305931\pi$
$600$	−0.996222	−	1.10642i	−0.0406706	−	0.0451693i
$601$	27.4887	+	12.2388i	1.12129	+	0.499230i	0.881778	−	0.471664i	$-0.156347\pi$
$601$	27.4887	+	12.2388i	1.12129	+	0.499230i	0.239510	+	0.970894i	$0.423013\pi$
$602$	0.488132	−	1.00082i	0.0198948	−	0.0407904i
$603$	8.70332	−	21.5415i	0.354427	−	0.877237i
$604$	14.3778	−	12.0644i	0.585025	−	0.490895i
$605$	−0.967768	−	1.84356i	−0.0393453	−	0.0749515i
$606$	1.46152	−	0.531948i	0.0593700	−	0.0216089i
$607$	12.7485	+	39.2359i	0.517447	+	1.59254i	0.778786	+	0.627290i	$0.215836\pi$
$607$	12.7485	+	39.2359i	0.517447	+	1.59254i	−0.261339	+	0.965247i	$0.584164\pi$
$608$	−0.584843	−	4.31949i	−0.0237185	−	0.175178i
$609$	−4.09819	+	2.97751i	−0.166067	+	0.120655i
$610$	−0.0314099	−	0.899462i	−0.00127175	−	0.0364182i
$611$	−23.7013	−	12.6022i	−0.958853	−	0.509831i
$612$	−0.493631	+	1.97985i	−0.0199539	+	0.0800305i
$613$	3.29204	+	13.2036i	0.132964	+	0.533290i	0.999421	+	0.0340372i	$0.0108365\pi$
$613$	3.29204	+	13.2036i	0.132964	+	0.533290i	−0.866457	+	0.499253i	$0.833608\pi$
$614$	−13.7246	+	7.29752i	−0.553881	+	0.294504i
$615$	0.0589351	+	0.102079i	0.00237649	+	0.00411621i
$616$	4.47394	+	4.82322i	0.180260	+	0.194333i
$617$	1.71530	+	0.624319i	0.0690555	+	0.0251341i	0.376317	−	0.926491i	$-0.377190\pi$
$617$	1.71530	+	0.624319i	0.0690555	+	0.0251341i	−0.307261	+	0.951625i	$0.599413\pi$
$618$	0.0279540	−	0.800499i	0.00112448	−	0.0322008i
$619$	−30.1004	+	13.4016i	−1.20984	+	0.538654i	−0.909710	−	0.415245i	$-0.863696\pi$
$619$	−30.1004	+	13.4016i	−1.20984	+	0.538654i	−0.300128	+	0.953899i	$0.597029\pi$
$620$	−0.226597	−	0.100888i	−0.00910037	−	0.00405175i
$621$	−0.449252	−	0.0631383i	−0.0180279	−	0.00253365i
$622$	−10.5417	+	6.58717i	−0.422683	+	0.264122i
$623$	−3.61936	+	14.5165i	−0.145007	+	0.581590i
$624$	−0.669753	+	0.646773i	−0.0268116	+	0.0258916i
$625$	−15.0615	−	19.2778i	−0.602458	−	0.771111i
$626$	2.19351			0.0876702
$627$	−4.31629	−	0.411108i	−0.172376	−	0.0164181i
$628$	−20.9917			−0.837661
$629$	0.549475	+	0.703296i	0.0219090	+	0.0280422i
$630$	0.785954	−	0.758987i	0.0313131	−	0.0302388i
$631$	6.82916	−	27.3902i	0.271864	−	1.09039i	−0.666712	−	0.745316i	$-0.732299\pi$
$631$	6.82916	−	27.3902i	0.271864	−	1.09039i	0.938576	−	0.345073i	$-0.112146\pi$
$632$	−3.21952	+	2.01178i	−0.128066	+	0.0800243i
$633$	5.80073	+	0.815239i	0.230558	+	0.0324029i
$634$	−12.6694	−	5.64079i	−0.503167	−	0.224024i
$635$	−0.937214	+	0.417274i	−0.0371922	+	0.0165590i
$636$	0.0780384	−	2.23473i	0.00309443	−	0.0886128i
$637$	8.94267	+	3.25486i	0.354321	+	0.128962i
$638$	−3.36763	−	28.0399i	−0.133326	−	1.11011i
$639$	20.5665	+	35.6222i	0.813597	+	1.40919i
$640$	0.167129	−	0.0888640i	0.00660635	−	0.00351266i
$641$	−4.33275	−	17.3777i	−0.171133	−	0.686378i	−0.993143	−	0.116905i	$-0.962703\pi$
$641$	−4.33275	−	17.3777i	−0.171133	−	0.686378i	0.822010	−	0.569473i	$-0.192853\pi$
$642$	0.993445	−	3.98449i	0.0392081	−	0.157255i
$643$	−16.8084	−	8.93718i	−0.662858	−	0.352448i	0.103713	−	0.994607i	$-0.466928\pi$
$643$	−16.8084	−	8.93718i	−0.662858	−	0.352448i	−0.766571	+	0.642159i	$0.778039\pi$
$644$	−0.0177179	−	0.507374i	−0.000698183	−	0.0199933i
$645$	−0.0257824	+	0.0187320i	−0.00101518	+	0.000737572i
$646$	2.41791	−	1.86950i	0.0951313	−	0.0735544i
$647$	5.48128	+	16.8696i	0.215491	+	0.663214i	0.999118	+	0.0419825i	$0.0133674\pi$
$647$	5.48128	+	16.8696i	0.215491	+	0.663214i	−0.783627	+	0.621232i	$0.786633\pi$
$648$	−7.70412	+	2.80407i	−0.302646	+	0.110154i
$649$	14.1012	−	2.19520i	0.553521	−	0.0861693i
$650$	−11.8055	+	9.90595i	−0.463048	+	0.388543i
$651$	0.292030	−	0.722800i	0.0114456	−	0.0283288i
$652$	7.22981	−	14.8233i	0.283141	−	0.580526i
$653$	36.8944	+	16.4264i	1.44379	+	0.642816i	0.971156	−	0.238443i	$-0.0766370\pi$
$653$	36.8944	+	16.4264i	1.44379	+	0.642816i	0.472633	+	0.881259i	$0.343304\pi$
$654$	−2.57681	−	2.86184i	−0.100761	−	0.111907i
$655$	1.56891	−	2.00811i	0.0613023	−	0.0784633i
$656$	1.99586	−	0.572304i	0.0779253	−	0.0223447i
$657$	−1.01145	+	0.450327i	−0.0394605	+	0.0175689i
$658$	−11.4766	+	12.7460i	−0.447403	+	0.496892i
$659$	5.06067	+	28.7005i	0.197136	+	1.11801i	0.909344	+	0.416044i	$0.136584\pi$
$659$	5.06067	+	28.7005i	0.197136	+	1.11801i	−0.712209	+	0.701968i	$0.752305\pi$
$660$	−0.0482502	−	0.181996i	−0.00187814	−	0.00708418i
$661$	17.0692	−	14.3228i	0.663915	−	0.557091i	−0.247342	−	0.968928i	$-0.579557\pi$
$661$	17.0692	−	14.3228i	0.663915	−	0.557091i	0.911257	+	0.411837i	$0.135113\pi$
$662$	6.28368	−	0.883113i	0.244222	−	0.0343232i
$663$	−0.627551	−	0.179947i	−0.0243720	−	0.00698857i
$664$	11.1852	−	8.12651i	0.434069	−	0.315370i
$665$	−1.62846	+	0.162851i	−0.0631491	+	0.00631509i
$666$	−1.14462	+	3.52278i	−0.0443532	+	0.136505i
$667$	−1.21871	+	1.80681i	−0.0471886	+	0.0699599i
$668$	−13.8121	+	13.3382i	−0.534407	+	0.516071i
$669$	−4.77919	−	2.98637i	−0.184774	−	0.115460i
$670$	−1.15766	−	0.971389i	−0.0447242	−	0.0375280i
$671$	−6.70239	+	14.2746i	−0.258743	+	0.551067i
$672$	0.297450	+	0.515199i	0.0114744	+	0.0198742i
$673$	−37.3213	−	7.93288i	−1.43863	−	0.305790i	−0.578424	−	0.815736i	$-0.696332\pi$
$673$	−37.3213	−	7.93288i	−1.43863	−	0.305790i	−0.860206	+	0.509946i	$0.829665\pi$
$674$	−10.1907	−	15.1084i	−0.392533	−	0.581954i
$675$	8.45820	−	2.42535i	0.325556	−	0.0933518i
$676$	−2.24996	−	2.49884i	−0.0865370	−	0.0961091i
$677$	−11.3641	+	2.41552i	−0.436760	+	0.0928361i	−0.421044	−	0.907040i	$-0.638336\pi$
$677$	−11.3641	+	2.41552i	−0.436760	+	0.0928361i	−0.0157160	+	0.999876i	$0.505003\pi$
$678$	1.37907	+	1.33175i	0.0529628	+	0.0511456i
$679$	1.79570	+	7.20215i	0.0689125	+	0.276393i
$680$	0.112555	+	0.0703320i	0.00431628	+	0.00269711i
$681$	−0.105394	+	0.597717i	−0.00403869	+	0.0229046i
$682$	2.72618	+	3.38481i	0.104391	+	0.129611i
$683$	−16.6749			−0.638048			−0.319024	−	0.947747i	$-0.603355\pi$
$683$	−16.6749			−0.638048			−0.319024	+	0.947747i	$0.603355\pi$
$684$	12.0438	+	3.98061i	0.460508	+	0.152203i
$685$	−1.39421	−	1.01295i	−0.0532699	−	0.0387028i
$686$	11.1646	−	16.5522i	0.426265	−	0.631964i
$687$	−7.46436	−	3.96887i	−0.284783	−	0.151422i
$688$	0.210293	+	0.520494i	0.00801736	+	0.0198437i
$689$	−23.0894	−	1.61457i	−0.879638	−	0.0615103i
$690$	−0.00636949	+	0.0130594i	−0.000242482	+	0.000497163i
$691$	−4.23438	+	4.70275i	−0.161083	+	0.178901i	−0.818283	−	0.574815i	$-0.805074\pi$
$691$	−4.23438	+	4.70275i	−0.161083	+	0.178901i	0.657200	+	0.753716i	$0.271741\pi$
$692$	5.50823	−	9.54053i	0.209391	−	0.362677i
$693$	−18.3226	+	5.54886i	−0.696020	+	0.210784i
$694$	24.5417	+	8.93243i	0.931589	+	0.339071i
$695$	−2.28016	−	0.484663i	−0.0864914	−	0.0183843i
$696$	0.266946	−	2.53982i	0.0101186	−	0.0962717i
$697$	1.04725	+	1.01132i	0.0396674	+	0.0383063i
$698$	−14.9067	+	9.31471i	−0.564225	+	0.352567i
$699$	−0.391702	−	0.969496i	−0.0148155	−	0.0366697i
$700$	4.31652	+	8.85019i	0.163149	+	0.334506i
$701$	14.9086	+	4.27496i	0.563088	+	0.161463i	0.545094	−	0.838375i	$-0.316494\pi$
$701$	14.9086	+	4.27496i	0.563088	+	0.161463i	0.0179945	+	0.999838i	$0.494272\pi$
$702$	−1.70041	−	5.23333i	−0.0641779	−	0.197519i
$703$	4.61531	−	3.07928i	0.174070	−	0.116137i
$704$	−3.31626	+	0.0491136i	−0.124986	+	0.00185104i
$705$	0.461272	−	0.167889i	0.0173725	−	0.00632307i
$706$	2.78970	−	0.392066i	0.104992	−	0.0147556i
$707$	−10.2614	+	0.717545i	−0.385919	+	0.0269861i
$708$	1.28736	+	0.0900209i	0.0483819	+	0.00338319i
$709$	12.4931	+	1.75579i	0.469188	+	0.0659401i	0.369806	−	0.929109i	$-0.379424\pi$
$709$	12.4931	+	1.75579i	0.469188	+	0.0659401i	0.0993828	+	0.995049i	$0.468313\pi$
$710$	2.61704	−	0.556269i	0.0982157	−	0.0208764i
$711$	−1.15480	−	10.9872i	−0.0433083	−	0.412051i
$712$	−4.21767	−	6.25295i	−0.158064	−	0.234339i
$713$	0.0117051	−	0.335190i	0.000438359	−	0.0125530i
$714$	−0.208565	+	0.361245i	−0.00780534	+	0.0135192i
$715$	−1.90013	+	0.433389i	−0.0710607	+	0.0162078i
$716$	−2.80718	−	15.9203i	−0.104909	−	0.594970i
$717$	0.553493	−	1.36994i	0.0206706	−	0.0511615i
$718$	−2.51806	+	0.176080i	−0.0939731	+	0.00657124i
$719$	−11.9615	−	24.5247i	−0.446088	−	0.914616i	−0.996801	−	0.0799214i	$-0.974533\pi$
$719$	−11.9615	−	24.5247i	−0.446088	−	0.914616i	0.550713	−	0.834695i	$-0.314356\pi$
$720$	0.0192237	+	0.550494i	0.000716424	+	0.0205157i
$721$	−1.63702	+	5.03824i	−0.0609659	+	0.187634i
$722$	−10.4651	−	15.8582i	−0.389470	−	0.590181i
$723$	−5.34165	−	3.88093i	−0.198658	−	0.144333i
$724$	2.27514	+	2.91205i	0.0845549	+	0.108225i
$725$	7.34019	−	41.6283i	0.272608	−	1.54604i
$726$	−0.702972	+	3.22330i	−0.0260897	+	0.119628i
$727$	20.4229	+	17.1368i	0.757444	+	0.635571i	0.937460	−	0.348093i	$-0.113171\pi$
$727$	20.4229	+	17.1368i	0.757444	+	0.635571i	−0.180016	+	0.983664i	$0.557615\pi$
$728$	5.43704	−	2.89092i	0.201510	−	0.107145i
$729$	2.32716	−	22.1414i	0.0861910	−	0.820053i
$730$	0.00752776	+	0.0716218i	0.000278615	+	0.00265084i
$731$	−0.242336	+	0.310177i	−0.00896314	+	0.0114723i
$732$	−0.877953	+	1.12373i	−0.0324501	+	0.0415342i
$733$	4.31188	+	41.0248i	0.159263	+	1.51528i	0.723877	+	0.689929i	$0.242358\pi$
$733$	4.31188	+	41.0248i	0.159263	+	1.51528i	−0.564614	+	0.825355i	$0.690975\pi$
$734$	−0.966892	+	9.19936i	−0.0356886	+	0.339555i
$735$	−0.153656	+	0.0817004i	−0.00566769	+	0.00301356i
$736$	0.196066	+	0.164519i	0.00722708	+	0.00606424i
$737$	10.2818	+	24.4015i	0.378734	+	0.898842i
$738$	−1.04920	+	5.95033i	−0.0386217	+	0.219035i
$739$	14.7147	+	18.8340i	0.541290	+	0.692820i	0.978431	−	0.206573i	$-0.0662312\pi$
$739$	14.7147	+	18.8340i	0.541290	+	0.692820i	−0.437141	+	0.899393i	$0.644009\pi$
$740$	0.194919	+	0.141617i	0.00716536	+	0.00520594i
$741$	−1.40730	+	3.80661i	−0.0516984	+	0.139839i
$742$	−4.57003	+	14.0651i	−0.167771	+	0.516346i
$743$	1.35053	+	38.6742i	0.0495463	+	1.41882i	0.728705	+	0.684828i	$0.240123\pi$
$743$	1.35053	+	38.6742i	0.0495463	+	1.41882i	−0.679158	+	0.733992i	$0.737655\pi$
$744$	0.172285	+	0.353238i	0.00631629	+	0.0129503i
$745$	−4.13716	+	0.289298i	−0.151574	+	0.0105991i
$746$	−6.07419	+	15.0341i	−0.222392	+	0.550439i
$747$	6.98644	+	39.6221i	0.255621	+	1.44970i
$748$	−1.19246	−	1.99653i	−0.0436008	−	0.0730005i
$749$	−13.5796	+	23.5205i	−0.496186	+	0.859420i
$750$	0.0197413	−	0.565317i	0.000720850	−	0.0206424i
$751$	8.11082	+	12.0248i	0.295968	+	0.438791i	0.947465	−	0.319861i	$-0.103636\pi$
$751$	8.11082	+	12.0248i	0.295968	+	0.438791i	−0.651496	+	0.758652i	$0.725858\pi$
$752$	−0.903838	−	8.59944i	−0.0329596	−	0.313589i
$753$	5.85396	−	1.24430i	0.213330	−	0.0453447i
$754$	−26.1773	−	3.67898i	−0.953321	−	0.133981i
$755$	3.54403	+	0.247822i	0.128980	+	0.00901918i
$756$	−3.50733	+	0.245256i	−0.127560	+	0.00891988i
$757$	34.8470	−	4.89742i	1.26653	−	0.178000i	0.526271	−	0.850317i	$-0.323590\pi$
$757$	34.8470	−	4.89742i	1.26653	−	0.178000i	0.740264	+	0.672317i	$0.234701\pi$
$758$	−15.4380	+	5.61898i	−0.560734	+	0.204091i
$759$	0.203730	−	0.152678i	0.00739492	−	0.00554187i
$760$	0.488331	−	0.665043i	0.0177136	−	0.0241236i
$761$	−14.0531	−	43.2509i	−0.509423	−	1.56784i	−0.793205	−	0.608955i	$-0.791589\pi$
$761$	−14.0531	−	43.2509i	−0.509423	−	1.56784i	0.283781	−	0.958889i	$-0.408411\pi$
$762$	1.56254	+	0.448052i	0.0566049	+	0.0162312i
$763$	11.1650	+	22.8917i	0.404202	+	0.828736i
$764$	−2.76454	−	6.84248i	−0.100018	−	0.247552i
$765$	−0.327540	+	0.204670i	−0.0118422	+	0.00739985i
$766$	2.14914	+	2.07540i	0.0776517	+	0.0749873i
$767$	1.39629	−	13.2848i	0.0504172	−	0.479688i
$768$	−0.293361	−	0.0623559i	−0.0105858	−	0.00225007i
$769$	13.6242	+	4.95880i	0.491300	+	0.178819i	0.575777	−	0.817607i	$-0.304700\pi$
$769$	13.6242	+	4.95880i	0.491300	+	0.178819i	−0.0844766	+	0.996425i	$0.526922\pi$
$770$	−0.0250251	+	1.24500i	−0.000901843	+	0.0448668i
$771$	4.78667	−	8.29075i	0.172388	−	0.298584i
$772$	6.78549	−	7.53605i	0.244215	−	0.271228i
$773$	11.7015	−	23.9916i	0.420873	−	0.862918i	−0.578026	−	0.816018i	$-0.696177\pi$
$773$	11.7015	−	23.9916i	0.420873	−	0.862918i	0.998900	−	0.0468999i	$-0.0149342\pi$
$774$	−1.62964	−	0.113955i	−0.0585762	−	0.00409604i
$775$	2.43686	+	6.03144i	0.0875345	+	0.216656i
$776$	−3.30405	−	1.75680i	−0.118609	−	0.0630653i
$777$	−0.423433	+	0.627766i	−0.0151906	+	0.0225210i
$778$	16.5621	+	12.0331i	0.593782	+	0.431408i
$779$	6.75621	−	6.02184i	0.242066	−	0.215755i
$780$	−0.176237			−0.00631030
$781$	−45.2501	−	12.2531i	−1.61918	−	0.438450i
$782$	−0.0311634	+	0.176736i	−0.00111440	+	0.00632008i
$783$	12.7997	+	7.99816i	0.457425	+	0.285831i
$784$	0.741608	+	2.97443i	0.0264860	+	0.106230i
$785$	−2.85824	−	2.76017i	−0.102015	−	0.0985147i
$786$	−3.94949	+	0.839491i	−0.140874	+	0.0299437i
$787$	10.2202	+	11.3506i	0.364309	+	0.404607i	0.897233	−	0.441557i	$-0.145574\pi$
$787$	10.2202	+	11.3506i	0.364309	+	0.404607i	−0.532924	+	0.846163i	$0.678907\pi$
$788$	−17.6522	+	5.06168i	−0.628833	+	0.180315i
$789$	0.560353	+	0.830757i	0.0199491	+	0.0295757i
$790$	−0.702898	−	0.149406i	−0.0250080	−	0.00531561i
$791$	−6.33970	−	10.9807i	−0.225414	−	0.390428i
$792$	4.10204	−	8.73645i	0.145760	−	0.310436i
$793$	11.3075	+	9.48812i	0.401541	+	0.336933i
$794$	−9.34257	−	5.83788i	−0.331555	−	0.207179i
$795$	0.304467	−	0.294020i	0.0107983	−	0.0104278i
$796$	0.598543	−	0.887376i	0.0212148	−	0.0314522i
$797$	3.17980	−	9.78643i	0.112634	−	0.346653i	−0.878812	−	0.477168i	$-0.841663\pi$
$797$	3.17980	−	9.78643i	0.112634	−	0.346653i	0.991446	+	0.130515i	$0.0416631\pi$
$798$	2.14244	+	1.46088i	0.0758415	+	0.0517147i
$799$	4.90501	−	3.56370i	0.173527	−	0.126075i
$800$	−4.77187	−	1.36831i	−0.168711	−	0.0483771i
$801$	21.7352	−	3.05469i	0.767977	−	0.107932i
$802$	−25.6693	+	21.5391i	−0.906413	+	0.760571i
$803$	0.455323	−	1.17685i	0.0160680	−	0.0415300i
$804$	0.415794	+	2.35808i	0.0146639	+	0.0831632i
$805$	0.0643015	−	0.0714140i	0.00226633	−	0.00251701i
$806$	3.71638	−	1.65464i	0.130904	−	0.0582822i
$807$	6.10544	−	1.75071i	0.214922	−	0.0616278i
$808$	3.19272	−	4.08650i	0.112320	−	0.143763i
$809$	−7.24984	−	8.05176i	−0.254891	−	0.283085i	0.602096	−	0.798424i	$-0.294333\pi$
$809$	−7.24984	−	8.05176i	−0.254891	−	0.283085i	−0.856986	+	0.515339i	$0.827666\pi$
$810$	−1.41770	−	0.631200i	−0.0498128	−	0.0221781i
$811$	−7.81509	+	16.0233i	−0.274425	+	0.562654i	−0.990843	−	0.135016i	$-0.956891\pi$
$811$	−7.81509	+	16.0233i	−0.274425	+	0.562654i	0.716418	+	0.697671i	$0.245780\pi$
$812$	−6.32720	+	15.6604i	−0.222041	+	0.549571i
$813$	2.35605	−	1.97696i	0.0826302	−	0.0693349i
$814$	−1.90661	−	3.76652i	−0.0668265	−	0.132016i
$815$	2.93351	−	1.06771i	0.102756	−	0.0374003i
$816$	−0.0649842	−	0.200001i	−0.00227490	−	0.00700143i
$817$	1.81016	+	1.64650i	0.0633294	+	0.0576036i
$818$	0.593252	−	0.431023i	0.0207426	−	0.0150704i
$819$	0.625384	+	17.9087i	0.0218527	+	0.625780i
$820$	0.347009	+	0.184508i	0.0121181	+	0.00644329i
$821$	−5.76213	+	23.1106i	−0.201100	+	0.806567i	0.781967	+	0.623320i	$0.214216\pi$
$821$	−5.76213	+	23.1106i	−0.201100	+	0.806567i	−0.983067	+	0.183247i	$0.941339\pi$
$822$	0.660581	+	2.64945i	0.0230404	+	0.0924101i
$823$	22.4711	−	11.9481i	0.783292	−	0.416484i	−0.0291138	−	0.999576i	$-0.509269\pi$
$823$	22.4711	−	11.9481i	0.783292	−	0.416484i	0.812406	+	0.583092i	$0.198157\pi$
$824$	−1.33536	−	2.31290i	−0.0465193	−	0.0805738i
$825$	−2.40535	+	4.31243i	−0.0837435	+	0.150140i
$826$	−8.02031	−	2.91916i	−0.279062	−	0.101570i
$827$	1.77406	−	50.8024i	0.0616901	−	1.76657i	−0.436689	−	0.899613i	$-0.643849\pi$
$827$	1.77406	−	50.8024i	0.0616901	−	1.76657i	0.498379	−	0.866959i	$-0.333929\pi$
$828$	−0.680422	+	0.302943i	−0.0236463	+	0.0105280i
$829$	49.2001	+	21.9053i	1.70879	+	0.760802i	0.998373	+	0.0570200i	$0.0181599\pi$
$829$	49.2001	+	21.9053i	1.70879	+	0.760802i	0.710416	+	0.703782i	$0.248507\pi$
$830$	2.59152	+	0.364215i	0.0899530	+	0.0126421i
$831$	3.29872	−	2.06127i	0.114431	−	0.0715046i
$832$	−0.751030	+	3.01221i	−0.0260373	+	0.104430i
$833$	−1.54618	+	1.49313i	−0.0535720	+	0.0517339i
$834$	2.27397	+	2.91055i	0.0787411	+	0.100784i
$835$	−3.63449			−0.125777
$836$	−12.9312	+	6.46398i	−0.447236	+	0.223561i
$837$	−2.32273			−0.0802851
$838$	−3.66433	−	4.69013i	−0.126582	−	0.162018i
$839$	14.8466	−	14.3372i	0.512561	−	0.494974i	−0.392796	−	0.919626i	$-0.628492\pi$
$839$	14.8466	−	14.3372i	0.512561	−	0.494974i	0.905357	+	0.424651i	$0.139603\pi$
$840$	−0.0272418	+	0.109261i	−0.000939932	+	0.00376986i
$841$	36.8962	−	23.0553i	1.27228	−	0.795010i
$842$	14.2998	+	2.00971i	0.492805	+	0.0692592i
$843$	−0.260593	−	0.116023i	−0.00897529	−	0.00399606i
$844$	17.8427	−	7.94410i	0.614172	−	0.273447i
$845$	0.0222126	−	0.636087i	0.000764138	−	0.0218821i
$846$	23.6452	+	8.60613i	0.812937	+	0.295885i
$847$	10.3452	−	19.2107i	0.355466	−	0.660089i
$848$	−3.72787	−	6.45686i	−0.128016	−	0.221730i
$849$	2.20140	−	1.17050i	0.0755517	−	0.0401716i
$850$	−0.842071	−	3.37736i	−0.0288828	−	0.115843i
$851$	−0.0788138	+	0.316105i	−0.00270170	+	0.0108359i
$852$	−3.74302	−	1.99020i	−0.128234	−	0.0681831i
$853$	0.271532	+	7.77565i	0.00929707	+	0.266233i	0.995134	+	0.0985281i	$0.0314134\pi$
$853$	0.271532	+	7.77565i	0.00929707	+	0.266233i	−0.985837	+	0.167705i	$0.946364\pi$
$854$	7.63016	−	5.54364i	0.261099	−	0.189699i
$855$	1.11649	+	2.12563i	0.0381831	+	0.0726950i
$856$	−4.23109	−	13.0220i	−0.144616	−	0.445081i
$857$	47.9198	−	17.4414i	1.63691	−	0.595786i	0.650415	−	0.759579i	$-0.274595\pi$
$857$	47.9198	−	17.4414i	1.63691	−	0.595786i	0.986495	+	0.163793i	$0.0523729\pi$
$858$	2.74771	+	1.40919i	0.0938052	+	0.0481090i
$859$	7.09533	−	5.95369i	0.242090	−	0.203137i	−0.513667	−	0.857989i	$-0.671713\pi$
$859$	7.09533	−	5.95369i	0.242090	−	0.203137i	0.755757	+	0.654852i	$0.227269\pi$
$860$	−0.0398054	+	0.0985219i	−0.00135735	+	0.00335957i
$861$	−0.541470	+	1.11018i	−0.0184533	+	0.0378348i
$862$	6.24391	+	2.77997i	0.212668	+	0.0946861i
$863$	7.13072	+	7.91947i	0.242733	+	0.269582i	0.852185	−	0.523241i	$-0.175277\pi$
$863$	7.13072	+	7.91947i	0.242733	+	0.269582i	−0.609452	+	0.792823i	$0.708611\pi$
$864$	1.09127	−	1.39676i	0.0371257	−	0.0475188i
$865$	2.00447	−	0.574774i	0.0681542	−	0.0195429i
$866$	12.8802	−	5.73462i	0.437686	−	0.194870i
$867$	−3.31294	+	3.67939i	−0.112513	+	0.124959i
$868$	−0.451361	−	2.55979i	−0.0153202	−	0.0868851i
$869$	9.76422	+	7.94975i	0.331228	+	0.269677i
$870$	0.370305	−	0.310723i	0.0125545	−	0.0105345i
$871$	24.5439	−	3.44942i	0.831639	−	0.116879i
$872$	−12.3428	−	3.53925i	−0.417981	−	0.119854i
$873$	8.80989	−	6.40076i	0.298170	−	0.216633i
$874$	1.08113	+	0.275359i	0.0365696	+	0.00931417i
$875$	−1.15607	+	3.55803i	−0.0390825	+	0.120283i
$876$	0.0638079	−	0.0945991i	0.00215587	−	0.00319621i
$877$	16.3719	−	15.8102i	0.552841	−	0.533872i	−0.364903	−	0.931046i	$-0.618898\pi$
$877$	16.3719	−	15.8102i	0.552841	−	0.533872i	0.917744	+	0.397174i	$0.130009\pi$
$878$	12.6651	+	7.91404i	0.427427	+	0.267086i
$879$	1.57836	+	1.32440i	0.0532367	+	0.0446709i
$880$	−0.458001	−	0.429363i	−0.0154392	−	0.0144738i
$881$	−3.00167	−	5.19905i	−0.101129	−	0.175161i	0.811021	−	0.585017i	$-0.198912\pi$
$881$	−3.00167	−	5.19905i	−0.101129	−	0.175161i	−0.912150	+	0.409856i	$0.865579\pi$
$882$	−8.72578	−	1.85472i	−0.293812	−	0.0624517i
$883$	−17.0334	−	25.2531i	−0.573221	−	0.849835i	0.425252	−	0.905075i	$-0.360185\pi$
$883$	−17.0334	−	25.2531i	−0.573221	−	0.849835i	−0.998473	+	0.0552402i	$0.982408\pi$
$884$	−2.09243	+	0.599994i	−0.0703759	+	0.0201800i
$885$	0.163451	+	0.181530i	0.00549433	+	0.00610207i
$886$	−32.2618	+	6.85746i	−1.08386	+	0.230381i
$887$	−25.5904	−	24.7123i	−0.859240	−	0.829758i	0.127538	−	0.991834i	$-0.459292\pi$
$887$	−25.5904	−	24.7123i	−0.859240	−	0.829758i	−0.986778	+	0.162075i	$0.948181\pi$
$888$	−0.0923534	−	0.370409i	−0.00309918	−	0.0124301i
$889$	−9.11712	−	5.69701i	−0.305778	−	0.191072i
$890$	0.247912	−	1.40598i	0.00831004	−	0.0471286i
$891$	17.0562	+	21.1769i	0.571405	+	0.709455i
$892$	−18.7904			−0.629148
$893$	−19.8113	−	32.0638i	−0.662961	−	1.07298i
$894$	5.31620	+	3.86244i	0.177800	+	0.129179i
$895$	1.71111	−	2.53683i	0.0571962	−	0.0847969i
$896$	1.75138	+	0.931225i	0.0585095	+	0.0311101i
$897$	−0.0892696	−	0.220950i	−0.00298062	−	0.00737730i
$898$	−5.38940	−	0.376864i	−0.179847	−	0.0125761i
$899$	−4.89148	+	10.0290i	−0.163140	+	0.334487i
$900$	9.66625	−	10.7355i	0.322208	−	0.357849i
$901$	2.61389	−	4.52739i	0.0870814	−	0.150829i
$902$	−3.93488	−	5.65134i	−0.131017	−	0.188169i
$903$	−0.313820	−	0.114221i	−0.0104433	−	0.00380104i
$904$	6.25255	+	1.32902i	0.207957	+	0.0442026i
$905$	−0.0731168	+	0.695660i	−0.00243049	+	0.0231245i
$906$	−4.04922	−	3.91029i	−0.134526	−	0.129911i
$907$	−17.1080	+	10.6903i	−0.568062	+	0.354965i	−0.783345	−	0.621587i	$-0.786488\pi$
$907$	−17.1080	+	10.6903i	−0.568062	+	0.354965i	0.215283	+	0.976552i	$0.430933\pi$
$908$	0.758090	+	1.87634i	0.0251581	+	0.0622685i
$909$	6.61549	+	13.5638i	0.219422	+	0.449881i
$910$	1.12043	+	0.321279i	0.0371420	+	0.0106503i
$911$	1.25362	+	3.85826i	0.0415344	+	0.127830i	0.969674	−	0.244404i	$-0.0785922\pi$
$911$	1.25362	+	3.85826i	0.0415344	+	0.127830i	−0.928139	+	0.372233i	$0.878592\pi$
$912$	−1.27005	+	0.309857i	−0.0420555	+	0.0102604i
$913$	−37.4921	−	26.4003i	−1.24081	−	0.873722i
$914$	13.3096	−	4.84431i	0.440243	−	0.160236i
$915$	−0.267300	+	0.0375666i	−0.00883666	+	0.00124191i
$916$	−28.1190	+	1.96627i	−0.929077	+	0.0649674i
$917$	26.6394	+	1.86281i	0.879711	+	0.0615154i
$918$	1.23075	+	0.172970i	0.0406208	+	0.00570887i
$919$	−49.3777	+	10.4956i	−1.62882	+	0.346216i	−0.929565	−	0.368657i	$-0.879818\pi$
$919$	−49.3777	+	10.4956i	−1.62882	+	0.346216i	−0.699254	+	0.714873i	$0.746484\pi$
$920$	0.00506406	+	0.0481813i	0.000166957	+	0.00158849i
$921$	2.60691	+	3.86491i	0.0859006	+	0.127353i
$922$	0.941070	−	26.9487i	0.0309925	−	0.887509i
$923$	−21.9402	+	38.0016i	−0.722171	+	1.25084i
$924$	1.29838	−	1.48566i	0.0427135	−	0.0488746i
$925$	−1.09723	−	6.22268i	−0.0360766	−	0.204600i
$926$	2.49542	−	6.17639i	0.0820047	−	0.202969i
$927$	7.75297	−	0.542141i	0.254641	−	0.0178062i
$928$	−3.73278	−	7.65333i	−0.122535	−	0.251233i
$929$	1.75544	+	50.2692i	0.0575941	+	1.64928i	0.593378	+	0.804924i	$0.297794\pi$
$929$	1.75544	+	50.2692i	0.0575941	+	1.64928i	−0.535784	+	0.844355i	$0.679984\pi$
$930$	−0.0229882	+	0.0707506i	−0.000753814	+	0.00232000i
$931$	8.53724	+	10.2792i	0.279797	+	0.336888i
$932$	−2.82059	−	2.04928i	−0.0923914	−	0.0671263i
$933$	2.29525	+	2.93779i	0.0751431	+	0.0961788i
$934$	2.37773	−	13.4848i	0.0778015	−	0.441235i
$935$	0.100155	−	0.428644i	0.00327542	−	0.0140182i
$936$	−6.92048	−	5.80697i	−0.226203	−	0.189807i
$937$	−8.01843	+	4.26347i	−0.261951	+	0.139282i	−0.595253	−	0.803538i	$-0.702948\pi$
$937$	−8.01843	+	4.26347i	−0.261951	+	0.139282i	0.333302	+	0.942820i	$0.391837\pi$
$938$	1.65535	−	15.7496i	0.0540490	−	0.514242i
$939$	−0.0687658	−	0.654263i	−0.00224409	−	0.0213511i
$940$	1.00766	−	1.28975i	0.0328663	−	0.0420669i
$941$	−19.2463	+	24.6342i	−0.627413	+	0.803051i	−0.991746	−	0.128217i	$-0.959075\pi$
$941$	−19.2463	+	24.6342i	−0.627413	+	0.803051i	0.364334	+	0.931269i	$0.381297\pi$
$942$	0.658084	+	6.26125i	0.0214415	+	0.204003i
$943$	−0.0555483	+	0.528507i	−0.00180890	+	0.0172106i
$944$	3.79922	−	2.02008i	0.123654	−	0.0657481i
$945$	−0.509807	−	0.427779i	−0.0165840	−	0.0139157i
$946$	1.40839	−	1.21777i	0.0457906	−	0.0395931i
$947$	7.40539	−	41.9980i	0.240643	−	1.36475i	−0.589755	−	0.807582i	$-0.700776\pi$
$947$	7.40539	−	41.9980i	0.240643	−	1.36475i	0.830398	−	0.557171i	$-0.188113\pi$
$948$	0.700989	+	0.897226i	0.0227671	+	0.0291405i
$949$	−0.955551	−	0.694248i	−0.0310185	−	0.0225363i
$950$	−21.3283	+	3.64983i	−0.691981	+	0.118416i
$951$	−1.28531	+	3.95577i	−0.0416790	+	0.128275i
$952$	0.0485391	+	1.38998i	0.00157316	+	0.0450494i
$953$	−14.9381	−	30.6276i	−0.483892	−	0.992125i	−0.991448	−	0.130506i	$-0.958340\pi$
$953$	−14.9381	−	30.6276i	−0.483892	−	0.992125i	0.507556	−	0.861619i	$-0.330549\pi$
$954$	21.6437	−	1.51348i	0.700742	−	0.0490006i
$955$	0.523287	−	1.29518i	0.0169332	−	0.0419110i
$956$	−0.855478	−	4.85166i	−0.0276681	−	0.156914i
$957$	−8.25796	+	1.88351i	−0.266942	+	0.0608853i
$958$	9.87720	−	17.1078i	0.319118	−	0.552728i
$959$	0.630256	−	18.0482i	0.0203520	−	0.582806i
$960$	−0.0317451	−	0.0470641i	−0.00102457	−	0.00151899i
$961$	3.06089	+	29.1224i	0.0987383	+	0.939432i
$962$	−3.86514	+	0.821561i	−0.124617	+	0.0264882i
$963$	39.4569	+	5.54531i	1.27148	+	0.178695i
$964$	−21.9614	−	1.53569i	−0.707329	−	0.0494612i
$965$	1.91482	−	0.133897i	0.0616402	−	0.00431030i
$966$	−0.150780	+	0.0211908i	−0.00485127	+	0.000681802i
$967$	−2.98012	+	1.08467i	−0.0958341	+	0.0348808i	−0.389492	−	0.921030i	$-0.627349\pi$
$967$	−2.98012	+	1.08467i	−0.0958341	+	0.0348808i	0.293658	+	0.955911i	$0.405127\pi$
$968$	3.70750	+	10.3564i	0.119164	+	0.332866i
$969$	−0.633420	−	0.662587i	−0.0203484	−	0.0212854i
$970$	−0.218883	−	0.673652i	−0.00702790	−	0.0216297i
$971$	11.5248	+	3.30468i	0.369849	+	0.106052i	0.455413	−	0.890280i	$-0.349492\pi$
$971$	11.5248	+	3.30468i	0.369849	+	0.106052i	−0.0855645	+	0.996333i	$0.527269\pi$
$972$	3.40896	+	6.98939i	0.109342	+	0.224185i
$973$	−9.15092	−	22.6493i	−0.293365	−	0.726104i
$974$	2.01876	−	1.26146i	0.0646853	−	0.0404199i
$975$	3.32477	+	3.21069i	0.106478	+	0.102824i
$976$	−0.497010	+	4.72874i	−0.0159089	+	0.151363i
$977$	19.8611	+	4.22161i	0.635414	+	0.135061i	0.514346	−	0.857583i	$-0.328035\pi$
$977$	19.8611	+	4.22161i	0.635414	+	0.135061i	0.121068	+	0.992644i	$0.461368\pi$
$978$	−4.64804	−	1.69175i	−0.148628	−	0.0540961i
$979$	−15.1074	+	19.9383i	−0.482835	+	0.637231i
$980$	−0.290126	+	0.502512i	−0.00926773	+	0.0160522i
$981$	25.0025	−	27.7681i	0.798270	−	0.886568i
$982$	−5.42311	+	11.1190i	−0.173059	+	0.354823i
$983$	33.2654	+	2.32614i	1.06100	+	0.0741924i	0.589575	−	0.807713i	$-0.299295\pi$
$983$	33.2654	+	2.32614i	1.06100	+	0.0741924i	0.471426	+	0.881906i	$0.343740\pi$
$984$	−0.233272	−	0.577369i	−0.00743644	−	0.0184058i
$985$	−3.06908	−	1.63186i	−0.0977890	−	0.0519953i
$986$	3.33871	−	4.94984i	0.106326	−	0.157635i
$987$	4.16157	+	3.02356i	0.132464	+	0.0962410i
$988$	2.74658	+	13.2502i	0.0873804	+	0.421546i
$989$	−0.143680			−0.00456877
$990$	1.70728	−	0.650188i	0.0542609	−	0.0206643i
$991$	8.20353	−	46.5245i	0.260594	−	1.47790i	−0.520702	−	0.853738i	$-0.674330\pi$
$991$	8.20353	−	46.5245i	0.260594	−	1.47790i	0.781296	−	0.624161i	$-0.214559\pi$
$992$	1.11129	+	0.694413i	0.0352836	+	0.0220476i
$993$	−0.460399	−	1.84656i	−0.0146103	−	0.0585989i
$994$	20.1683	+	19.4763i	0.639699	+	0.617750i
$995$	0.198178	−	0.0421239i	0.00628265	−	0.00133542i
$996$	−2.77456	−	3.08147i	−0.0879154	−	0.0976400i
$997$	36.9427	−	10.5931i	1.16999	−	0.335488i	0.366274	−	0.930507i	$-0.380633\pi$
$997$	36.9427	−	10.5931i	1.16999	−	0.335488i	0.803712	+	0.595019i	$0.202855\pi$
$998$	19.1541	+	28.3971i	0.606312	+	0.898894i
$999$	2.20685	+	0.469081i	0.0698217	+	0.0148411i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.u.b.5.5	✓	264
11.9	even	5	inner	418.2.u.b.119.7	yes	264
19.4	even	9	inner	418.2.u.b.137.7	yes	264
209.42	even	45	inner	418.2.u.b.251.5	yes	264

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.u.b.5.5	✓	264	1.1	even	1	trivial
418.2.u.b.119.7	yes	264	11.9	even	5	inner
418.2.u.b.137.7	yes	264	19.4	even	9	inner
418.2.u.b.251.5	yes	264	209.42	even	45	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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.u (of order \(45\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.615661 - 0.788011i) q^{2} +(-0.215741 + 0.208339i) q^{3} +(-0.241922 + 0.970296i) q^{4} +(-0.160523 + 0.100306i) q^{5} +(0.296996 + 0.0417401i) q^{6} +(-1.81207 - 0.806787i) q^{7} +(0.913545 - 0.406737i) q^{8} +(-0.101559 + 2.90828i) q^{9} +O(q^{10})\)	\(q+(-0.615661 - 0.788011i) q^{2} +(-0.215741 + 0.208339i) q^{3} +(-0.241922 + 0.970296i) q^{4} +(-0.160523 + 0.100306i) q^{5} +(0.296996 + 0.0417401i) q^{6} +(-1.81207 - 0.806787i) q^{7} +(0.913545 - 0.406737i) q^{8} +(-0.101559 + 2.90828i) q^{9} +(0.177870 + 0.0647394i) q^{10} +(-2.25551 - 2.43160i) q^{11} +(-0.149958 - 0.259734i) q^{12} +(-2.74105 + 1.45744i) q^{13} +(0.479867 + 1.92464i) q^{14} +(0.0137338 - 0.0550832i) q^{15} +(-0.882948 - 0.469472i) q^{16} +(-0.0244707 - 0.700748i) q^{17} +(2.35428 - 1.71048i) q^{18} +(-4.35542 - 0.174113i) q^{19} +(-0.0584924 - 0.180021i) q^{20} +(0.559023 - 0.203468i) q^{21} +(-0.527495 + 3.27441i) q^{22} +(0.196066 - 0.164519i) q^{23} +(-0.112350 + 0.278077i) q^{24} +(-2.17615 + 4.46177i) q^{25} +(2.83604 + 1.26269i) q^{26} +(-1.18604 - 1.31723i) q^{27} +(1.22120 - 1.56307i) q^{28} +(-8.18525 + 2.34708i) q^{29} +(-0.0518615 + 0.0230902i) q^{30} +(0.876837 - 0.973827i) q^{31} +(0.173648 + 0.984808i) q^{32} +(0.993202 + 0.0546856i) q^{33} +(-0.537132 + 0.450707i) q^{34} +(0.371805 - 0.0522538i) q^{35} +(-2.79732 - 0.802119i) q^{36} +(-1.02976 + 0.748166i) q^{37} +(2.54426 + 3.53931i) q^{38} +(0.287715 - 0.885496i) q^{39} +(-0.105847 + 0.156925i) q^{40} +(-1.49356 + 1.44231i) q^{41} +(-0.504504 - 0.315249i) q^{42} +(-0.430035 - 0.360842i) q^{43} +(2.90503 - 1.60026i) q^{44} +(-0.275415 - 0.477033i) q^{45} +(-0.250353 - 0.0532141i) q^{46} +(4.83523 + 7.16853i) q^{47} +(0.288297 - 0.0826678i) q^{48} +(-2.05121 - 2.27810i) q^{49} +(4.85569 - 1.03211i) q^{50} +(0.151272 + 0.146082i) q^{51} +(-0.751030 - 3.01221i) q^{52} +(6.32283 + 3.95094i) q^{53} +(-0.307794 + 1.74559i) q^{54} +(0.605965 + 0.164087i) q^{55} -1.98356 q^{56} +(0.975917 - 0.869839i) q^{57} +(6.88887 + 5.00506i) q^{58} +(-2.40614 + 3.56726i) q^{59} +(0.0501245 + 0.0266517i) q^{60} +(-1.78117 - 4.40856i) q^{61} +(-1.30722 - 0.0914098i) q^{62} +(2.53039 - 5.18808i) q^{63} +(0.669131 - 0.743145i) q^{64} +(0.293811 - 0.508896i) q^{65} +(-0.568383 - 0.816322i) q^{66} +(-7.50231 - 2.73062i) q^{67} +(0.685853 + 0.145783i) q^{68} +(-0.00802381 + 0.0763415i) q^{69} +(-0.270082 - 0.260816i) q^{70} +(11.9870 - 7.49029i) q^{71} +(1.09012 + 2.69815i) q^{72} +(0.166785 + 0.341959i) q^{73} +(1.22355 + 0.350847i) q^{74} +(-0.460074 - 1.41596i) q^{75} +(1.22261 - 4.18392i) q^{76} +(2.12537 + 6.22595i) q^{77} +(-0.874916 + 0.318443i) q^{78} +(-3.75945 + 0.528356i) q^{79} +(0.188824 - 0.0132039i) q^{80} +(-8.17858 - 0.571902i) q^{81} +(2.05609 + 0.288964i) q^{82} +(13.5235 - 2.87451i) q^{83} +(0.0621840 + 0.591641i) q^{84} +(0.0742173 + 0.110032i) q^{85} +(-0.0195916 + 0.561029i) q^{86} +(1.27691 - 2.21167i) q^{87} +(-3.04953 - 1.30398i) q^{88} +(-1.30973 - 7.42784i) q^{89} +(-0.206344 + 0.510720i) q^{90} +(6.14283 - 0.429548i) q^{91} +(0.112199 + 0.230042i) q^{92} +(0.0137160 + 0.392773i) q^{93} +(2.67201 - 8.22360i) q^{94} +(0.716610 - 0.408925i) q^{95} +(-0.242637 - 0.176286i) q^{96} +(-2.30385 - 2.94879i) q^{97} +(-0.532316 + 3.01891i) q^{98} +(7.30083 - 6.31270i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 264 q + 6 q^{3} - 9 q^{6} - 15 q^{7} + 33 q^{8} + 6 q^{9}+O(q^{10}) \) 264 * q + 6 * q^3 - 9 * q^6 - 15 * q^7 + 33 * q^8 + 6 * q^9	\( 264 q + 6 q^{3} - 9 q^{6} - 15 q^{7} + 33 q^{8} + 6 q^{9} + 3 q^{11} - 6 q^{13} + 18 q^{14} - 39 q^{15} - 3 q^{17} - 78 q^{18} - 45 q^{19} - 24 q^{20} + 48 q^{21} + 6 q^{23} - 9 q^{24} + 30 q^{25} + 18 q^{26} - 24 q^{27} + 6 q^{28} - 3 q^{31} - 63 q^{33} - 36 q^{34} + 42 q^{35} - 9 q^{36} + 60 q^{37} - 3 q^{38} + 36 q^{39} + 39 q^{41} + 6 q^{42} - 60 q^{43} + 60 q^{44} - 108 q^{45} - 12 q^{46} - 24 q^{47} - 12 q^{48} + 6 q^{49} + 18 q^{50} + 96 q^{51} + 3 q^{52} - 117 q^{53} + 54 q^{54} + 102 q^{55} - 96 q^{57} - 60 q^{58} - 141 q^{59} + 36 q^{60} + 24 q^{61} - 27 q^{62} - 81 q^{63} + 33 q^{64} - 102 q^{65} + 72 q^{66} + 102 q^{67} - 21 q^{68} - 6 q^{69} - 33 q^{70} - 66 q^{71} - 12 q^{72} + 36 q^{73} + 18 q^{74} + 6 q^{76} - 174 q^{77} + 18 q^{78} + 36 q^{79} + 60 q^{81} - 36 q^{82} - 24 q^{83} + 48 q^{84} + 174 q^{85} - 21 q^{86} + 12 q^{87} + 3 q^{88} + 30 q^{89} - 48 q^{90} - 18 q^{91} + 18 q^{92} - 123 q^{93} - 120 q^{94} - 18 q^{95} - 24 q^{97} - 84 q^{98} - 141 q^{99}+O(q^{100}) \) 264 * q + 6 * q^3 - 9 * q^6 - 15 * q^7 + 33 * q^8 + 6 * q^9 + 3 * q^11 - 6 * q^13 + 18 * q^14 - 39 * q^15 - 3 * q^17 - 78 * q^18 - 45 * q^19 - 24 * q^20 + 48 * q^21 + 6 * q^23 - 9 * q^24 + 30 * q^25 + 18 * q^26 - 24 * q^27 + 6 * q^28 - 3 * q^31 - 63 * q^33 - 36 * q^34 + 42 * q^35 - 9 * q^36 + 60 * q^37 - 3 * q^38 + 36 * q^39 + 39 * q^41 + 6 * q^42 - 60 * q^43 + 60 * q^44 - 108 * q^45 - 12 * q^46 - 24 * q^47 - 12 * q^48 + 6 * q^49 + 18 * q^50 + 96 * q^51 + 3 * q^52 - 117 * q^53 + 54 * q^54 + 102 * q^55 - 96 * q^57 - 60 * q^58 - 141 * q^59 + 36 * q^60 + 24 * q^61 - 27 * q^62 - 81 * q^63 + 33 * q^64 - 102 * q^65 + 72 * q^66 + 102 * q^67 - 21 * q^68 - 6 * q^69 - 33 * q^70 - 66 * q^71 - 12 * q^72 + 36 * q^73 + 18 * q^74 + 6 * q^76 - 174 * q^77 + 18 * q^78 + 36 * q^79 + 60 * q^81 - 36 * q^82 - 24 * q^83 + 48 * q^84 + 174 * q^85 - 21 * q^86 + 12 * q^87 + 3 * q^88 + 30 * q^89 - 48 * q^90 - 18 * q^91 + 18 * q^92 - 123 * q^93 - 120 * q^94 - 18 * q^95 - 24 * q^97 - 84 * q^98 - 141 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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