LMFDB - Embedded newform 637.2.bl.b.53.28

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			53.28
Character	$\chi$	$=$	637.53
Dual form			637.2.bl.b.625.28

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.27734 + 1.55266i) q^{2} +(-1.64682 - 1.52803i) q^{3} +(2.04482 + 5.21012i) q^{4} +(3.15635 - 0.973606i) q^{5} +(-1.37786 - 6.03678i) q^{6} +(-0.157452 + 2.64106i) q^{7} +(-2.20615 + 9.66579i) q^{8} +(0.152964 + 2.04116i) q^{9} +O(q^{10})$	\(q+(2.27734 + 1.55266i) q^{2} +(-1.64682 - 1.52803i) q^{3} +(2.04482 + 5.21012i) q^{4} +(3.15635 - 0.973606i) q^{5} +(-1.37786 - 6.03678i) q^{6} +(-0.157452 + 2.64106i) q^{7} +(-2.20615 + 9.66579i) q^{8} +(0.152964 + 2.04116i) q^{9} +(8.69976 + 2.68352i) q^{10} +(0.246240 - 3.28585i) q^{11} +(4.59375 - 11.7047i) q^{12} +(-0.900969 + 0.433884i) q^{13} +(-4.45925 + 5.77012i) q^{14} +(-6.68564 - 3.21963i) q^{15} +(-11.8260 + 10.9730i) q^{16} +(3.84221 - 0.579120i) q^{17} +(-2.82088 + 4.88590i) q^{18} +(1.43526 + 2.48594i) q^{19} +(11.5268 + 14.4541i) q^{20} +(4.29491 - 4.10876i) q^{21} +(5.66259 - 7.10066i) q^{22} +(-4.29295 - 0.647058i) q^{23} +(18.4027 - 12.5468i) q^{24} +(4.88346 - 3.32949i) q^{25} +(-2.72548 - 0.410801i) q^{26} +(-1.33502 + 1.67406i) q^{27} +(-14.0822 + 4.58016i) q^{28} +(0.847456 + 1.06268i) q^{29} +(-10.2265 - 17.7127i) q^{30} +(5.02617 - 8.70558i) q^{31} +(-24.3619 + 3.67197i) q^{32} +(-5.42638 + 5.03494i) q^{33} +(9.64918 + 4.64680i) q^{34} +(2.07438 + 8.48942i) q^{35} +(-10.3219 + 4.97076i) q^{36} +(-2.62863 + 6.69764i) q^{37} +(-0.591258 + 7.88979i) q^{38} +(2.14672 + 0.662175i) q^{39} +(2.44727 + 32.6565i) q^{40} +(0.276573 - 1.21174i) q^{41} +(16.1605 - 2.68850i) q^{42} +(-0.691842 - 3.03116i) q^{43} +(17.6232 - 5.43603i) q^{44} +(2.47009 + 6.29369i) q^{45} +(-8.77183 - 8.13907i) q^{46} +(-5.08918 - 3.46974i) q^{47} +36.2423 q^{48} +(-6.95042 - 0.831682i) q^{49} +16.2908 q^{50} +(-7.21234 - 4.91729i) q^{51} +(-4.10291 - 3.80694i) q^{52} +(1.88758 + 4.80947i) q^{53} +(-5.63955 + 1.73957i) q^{54} +(-2.42190 - 10.6110i) q^{55} +(-25.1806 - 7.34848i) q^{56} +(1.43497 - 6.28700i) q^{57} +(0.279966 + 3.73588i) q^{58} +(-6.62469 - 2.04345i) q^{59} +(3.10374 - 41.4166i) q^{60} +(4.53500 - 11.5550i) q^{61} +(24.9631 - 12.0216i) q^{62} +(-5.41491 + 0.0826017i) q^{63} +(-32.1116 - 15.4641i) q^{64} +(-2.42134 + 2.24668i) q^{65} +(-20.1753 + 3.04093i) q^{66} +(5.54457 - 9.60347i) q^{67} +(10.8739 + 18.8342i) q^{68} +(6.08100 + 7.62533i) q^{69} +(-8.45714 + 22.5541i) q^{70} +(-7.46067 + 9.35538i) q^{71} +(-20.0668 - 3.02459i) q^{72} +(0.694714 - 0.473648i) q^{73} +(-16.3854 + 11.1714i) q^{74} +(-13.1297 - 1.97899i) q^{75} +(-10.0172 + 12.5612i) q^{76} +(8.63936 + 1.16770i) q^{77} +(3.86067 + 4.84113i) q^{78} +(-5.29798 - 9.17638i) q^{79} +(-26.6438 + 46.1484i) q^{80} +(10.8286 - 1.63215i) q^{81} +(2.51128 - 2.33013i) q^{82} +(-9.66512 - 4.65448i) q^{83} +(30.1895 + 13.9753i) q^{84} +(11.5635 - 5.56870i) q^{85} +(3.13080 - 7.97716i) q^{86} +(0.228189 - 3.04497i) q^{87} +(31.2171 + 9.62919i) q^{88} +(-0.916329 - 12.2276i) q^{89} +(-4.14674 + 18.1681i) q^{90} +(-1.00405 - 2.44783i) q^{91} +(-5.40707 - 23.6899i) q^{92} +(-21.5795 + 6.65641i) q^{93} +(-6.20243 - 15.8035i) q^{94} +(6.95050 + 6.44912i) q^{95} +(45.7305 + 31.1786i) q^{96} -3.19724 q^{97} +(-14.5371 - 12.6857i) q^{98} +6.74460 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 $

$2$	2.27734	+	1.55266i	1.61032	+	1.09790i	0.931590	+	0.363510i	$0.118422\pi$
$2$	2.27734	+	1.55266i	1.61032	+	1.09790i	0.678730	+	0.734388i	$0.262531\pi$
$3$	−1.64682	−	1.52803i	−0.950792	−	0.882206i	0.0423519	−	0.999103i	$-0.486515\pi$
$3$	−1.64682	−	1.52803i	−0.950792	−	0.882206i	−0.993144	+	0.116897i	$0.962705\pi$
$4$	2.04482	+	5.21012i	1.02241	+	2.60506i
$5$	3.15635	−	0.973606i	1.41156	−	0.435410i	0.507073	−	0.861903i	$-0.330727\pi$
$5$	3.15635	−	0.973606i	1.41156	−	0.435410i	0.904491	+	0.426493i	$0.140251\pi$
$6$	−1.37786	−	6.03678i	−0.562508	−	2.46451i
$7$	−0.157452	+	2.64106i	−0.0595113	+	0.998228i
$7$	−0.157452	+	2.64106i	−0.0595113	+	0.998228i
$8$	−2.20615	+	9.66579i	−0.779993	+	3.41737i
$9$	0.152964	+	2.04116i	0.0509879	+	0.680386i
$10$	8.69976	+	2.68352i	2.75111	+	0.848604i
$11$	0.246240	−	3.28585i	0.0742443	−	0.990721i	−0.828345	−	0.560218i	$-0.810717\pi$
$11$	0.246240	−	3.28585i	0.0742443	−	0.990721i	0.902589	−	0.430503i	$-0.141664\pi$
$12$	4.59375	−	11.7047i	1.32610	−	3.37885i
$13$	−0.900969	+	0.433884i	−0.249884	+	0.120338i
$13$	−0.900969	+	0.433884i	−0.249884	+	0.120338i
$14$	−4.45925	+	5.77012i	−1.19178	+	1.54213i
$15$	−6.68564	−	3.21963i	−1.72622	−	0.831306i
$16$	−11.8260	+	10.9730i	−2.95651	+	2.74324i
$17$	3.84221	−	0.579120i	0.931872	−	0.140457i	0.334477	−	0.942404i	$-0.391440\pi$
$17$	3.84221	−	0.579120i	0.931872	−	0.140457i	0.597395	+	0.801947i	$0.296202\pi$
$18$	−2.82088	+	4.88590i	−0.664887	+	1.15162i
$19$	1.43526	+	2.48594i	0.329271	+	0.570313i	0.982367	−	0.186961i	$-0.0598638\pi$
$19$	1.43526	+	2.48594i	0.329271	+	0.570313i	−0.653097	+	0.757274i	$0.726531\pi$
$20$	11.5268	+	14.4541i	2.57747	+	3.23204i
$21$	4.29491	−	4.10876i	0.937226	−	0.896606i
$22$	5.66259	−	7.10066i	1.20727	−	1.51387i
$23$	−4.29295	−	0.647058i	−0.895142	−	0.134921i	−0.314670	−	0.949201i	$-0.601894\pi$
$23$	−4.29295	−	0.647058i	−0.895142	−	0.134921i	−0.580472	+	0.814280i	$0.697132\pi$
$24$	18.4027	−	12.5468i	3.75644	−	2.56110i
$25$	4.88346	−	3.32949i	0.976692	−	0.665897i
$26$	−2.72548	−	0.410801i	−0.534511	−	0.0805646i
$27$	−1.33502	+	1.67406i	−0.256925	+	0.322174i
$28$	−14.0822	+	4.58016i	−2.66129	+	0.865568i
$29$	0.847456	+	1.06268i	0.157369	+	0.197334i	0.854265	−	0.519838i	$-0.174008\pi$
$29$	0.847456	+	1.06268i	0.157369	+	0.197334i	−0.696896	+	0.717172i	$0.745436\pi$
$30$	−10.2265	−	17.7127i	−1.86709	−	3.23389i
$31$	5.02617	−	8.70558i	0.902726	−	1.56357i	0.0787853	−	0.996892i	$-0.474896\pi$
$31$	5.02617	−	8.70558i	0.902726	−	1.56357i	0.823941	−	0.566676i	$-0.191771\pi$
$32$	−24.3619	+	3.67197i	−4.30662	+	0.649118i
$33$	−5.42638	+	5.03494i	−0.944611	+	0.876471i
$34$	9.64918	+	4.64680i	1.65482	+	0.796920i
$35$	2.07438	+	8.48942i	0.350634	+	1.43497i
$36$	−10.3219	+	4.97076i	−1.72032	+	0.828460i
$37$	−2.62863	+	6.69764i	−0.432144	+	1.10108i	0.534547	+	0.845139i	$0.320482\pi$
$37$	−2.62863	+	6.69764i	−0.432144	+	1.10108i	−0.966691	+	0.255946i	$0.917613\pi$
$38$	−0.591258	+	7.88979i	−0.0959147	+	1.27989i
$39$	2.14672	+	0.662175i	0.343750	+	0.106033i
$40$	2.44727	+	32.6565i	0.386947	+	5.16345i
$41$	0.276573	−	1.21174i	0.0431934	−	0.189243i	−0.948729	−	0.316092i	$-0.897629\pi$
$41$	0.276573	−	1.21174i	0.0431934	−	0.189243i	0.991922	+	0.126849i	$0.0404864\pi$
$42$	16.1605	−	2.68850i	2.49361	−	0.414845i
$43$	−0.691842	−	3.03116i	−0.105505	−	0.462247i	−0.999888	−	0.0149459i	$-0.995242\pi$
$43$	−0.691842	−	3.03116i	−0.105505	−	0.462247i	0.894383	−	0.447301i	$-0.147615\pi$
$44$	17.6232	−	5.43603i	2.65680	−	0.819513i
$45$	2.47009	+	6.29369i	0.368219	+	0.938207i
$46$	−8.77183	−	8.13907i	−1.29334	−	1.20004i
$47$	−5.08918	−	3.46974i	−0.742333	−	0.506114i	0.132115	−	0.991234i	$-0.457823\pi$
$47$	−5.08918	−	3.46974i	−0.742333	−	0.506114i	−0.874447	+	0.485121i	$0.838776\pi$
$48$	36.2423			5.23113
$49$	−6.95042	−	0.831682i	−0.992917	−	0.118812i
$50$	16.2908			2.30387
$51$	−7.21234	−	4.91729i	−1.00993	−	0.688558i
$52$	−4.10291	−	3.80694i	−0.568971	−	0.527928i
$53$	1.88758	+	4.80947i	0.259279	+	0.660632i	0.999937	−	0.0112506i	$-0.00358126\pi$
$53$	1.88758	+	4.80947i	0.259279	+	0.660632i	−0.740658	+	0.671882i	$0.765486\pi$
$54$	−5.63955	+	1.73957i	−0.767445	+	0.236725i
$55$	−2.42190	−	10.6110i	−0.326569	−	1.43079i
$56$	−25.1806	−	7.34848i	−3.36490	−	0.981983i
$57$	1.43497	−	6.28700i	0.190066	−	0.832734i
$58$	0.279966	+	3.73588i	0.0367613	+	0.490545i
$59$	−6.62469	−	2.04345i	−0.862461	−	0.266034i	−0.168196	−	0.985754i	$-0.553794\pi$
$59$	−6.62469	−	2.04345i	−0.862461	−	0.266034i	−0.694265	+	0.719720i	$0.744270\pi$
$60$	3.10374	−	41.4166i	0.400691	−	5.34686i
$61$	4.53500	−	11.5550i	0.580647	−	1.47947i	−0.274762	−	0.961512i	$-0.588599\pi$
$61$	4.53500	−	11.5550i	0.580647	−	1.47947i	0.855409	−	0.517953i	$-0.173306\pi$
$62$	24.9631	−	12.0216i	3.17032	−	1.52674i
$63$	−5.41491	+	0.0826017i	−0.682214	+	0.0104068i
$64$	−32.1116	−	15.4641i	−4.01395	−	1.93302i
$65$	−2.42134	+	2.24668i	−0.300331	+	0.278666i
$66$	−20.1753	+	3.04093i	−2.48340	+	0.374313i
$67$	5.54457	−	9.60347i	0.677377	−	1.17325i	−0.298391	−	0.954444i	$-0.596450\pi$
$67$	5.54457	−	9.60347i	0.677377	−	1.17325i	0.975768	−	0.218807i	$-0.0702166\pi$
$68$	10.8739	+	18.8342i	1.31866	+	2.28398i
$69$	6.08100	+	7.62533i	0.732066	+	0.917982i
$70$	−8.45714	+	22.5541i	−1.01082	+	2.69573i
$71$	−7.46067	+	9.35538i	−0.885418	+	1.11028i	0.107818	+	0.994171i	$0.465614\pi$
$71$	−7.46067	+	9.35538i	−0.885418	+	1.11028i	−0.993236	+	0.116109i	$0.962958\pi$
$72$	−20.0668	−	3.02459i	−2.36490	−	0.356451i
$73$	0.694714	−	0.473648i	0.0813101	−	0.0554363i	−0.521983	−	0.852956i	$-0.674807\pi$
$73$	0.694714	−	0.473648i	0.0813101	−	0.0554363i	0.603293	+	0.797520i	$0.293855\pi$
$74$	−16.3854	+	11.1714i	−1.90477	+	1.29865i
$75$	−13.1297	−	1.97899i	−1.51609	−	0.228514i
$76$	−10.0172	+	12.5612i	−1.14905	+	1.44086i
$77$	8.63936	+	1.16770i	0.984547	+	0.133072i
$78$	3.86067	+	4.84113i	0.437135	+	0.548150i
$79$	−5.29798	−	9.17638i	−0.596070	−	1.03242i	−0.993395	−	0.114745i	$-0.963395\pi$
$79$	−5.29798	−	9.17638i	−0.596070	−	1.03242i	0.397325	−	0.917678i	$-0.369939\pi$
$80$	−26.6438	+	46.1484i	−2.97887	+	5.15955i
$81$	10.8286	−	1.63215i	1.20318	−	0.181350i
$82$	2.51128	−	2.33013i	0.277324	−	0.257319i
$83$	−9.66512	−	4.65448i	−1.06089	−	0.510895i	−0.179727	−	0.983717i	$-0.557521\pi$
$83$	−9.66512	−	4.65448i	−1.06089	−	0.510895i	−0.881158	+	0.472821i	$0.843236\pi$
$84$	30.1895	+	13.9753i	3.29394	+	1.52483i
$85$	11.5635	−	5.56870i	1.25424	−	0.604011i
$86$	3.13080	−	7.97716i	0.337603	−	0.860199i
$87$	0.228189	−	3.04497i	0.0244644	−	0.326455i
$88$	31.2171	+	9.62919i	3.32775	+	1.02648i
$89$	−0.916329	−	12.2276i	−0.0971307	−	1.29612i	−0.806480	−	0.591262i	$-0.798630\pi$
$89$	−0.916329	−	12.2276i	−0.0971307	−	1.29612i	0.709349	−	0.704857i	$-0.248989\pi$
$90$	−4.14674	+	18.1681i	−0.437105	+	1.91508i
$91$	−1.00405	−	2.44783i	−0.105254	−	0.256602i
$92$	−5.40707	−	23.6899i	−0.563726	−	2.46984i
$93$	−21.5795	+	6.65641i	−2.23769	+	0.690237i
$94$	−6.20243	−	15.8035i	−0.639732	−	1.63001i
$95$	6.95050	+	6.44912i	0.713106	+	0.661666i
$96$	45.7305	+	31.1786i	4.66735	+	3.18215i
$97$	−3.19724			−0.324631			−0.162315	−	0.986739i	$-0.551896\pi$
$97$	−3.19724			−0.324631			−0.162315	+	0.986739i	$0.551896\pi$
$98$	−14.5371	−	12.6857i	−1.46847	−	1.28145i
$99$	6.74460			0.677858
$100$	27.3328	+	18.6352i	2.73328	+	1.86352i
$101$	−2.17460	−	2.01773i	−0.216381	−	0.200772i	0.564534	−	0.825410i	$-0.309056\pi$
$101$	−2.17460	−	2.01773i	−0.216381	−	0.200772i	−0.780914	+	0.624638i	$0.785247\pi$
$102$	−8.79003	−	22.3966i	−0.870343	−	2.21760i
$103$	5.96267	−	1.83924i	0.587519	−	0.181226i	0.0132781	−	0.999912i	$-0.495773\pi$
$103$	5.96267	−	1.83924i	0.587519	−	0.181226i	0.574241	+	0.818686i	$0.305297\pi$
$104$	−2.20615	−	9.66579i	−0.216331	−	0.947808i
$105$	9.55592	−	17.1503i	0.932563	−	1.67369i
$106$	−3.16883	+	13.8836i	−0.307784	+	1.34849i
$107$	0.862305	+	11.5067i	0.0833622	+	1.11239i	0.869366	+	0.494169i	$0.164528\pi$
$107$	0.862305	+	11.5067i	0.0833622	+	1.11239i	−0.786003	+	0.618222i	$0.787853\pi$
$108$	−11.4520	−	3.53246i	−1.10196	−	0.339911i
$109$	0.497862	−	6.64351i	0.0476865	−	0.636332i	−0.921242	−	0.388991i	$-0.872824\pi$
$109$	0.497862	−	6.64351i	0.0476865	−	0.636332i	0.968928	−	0.247342i	$-0.0795571\pi$
$110$	10.9599	−	27.9253i	1.04498	−	2.66257i
$111$	14.5630	−	7.01319i	1.38226	−	0.665663i
$112$	−27.1182	−	32.9610i	−2.56243	−	3.11452i
$113$	11.9973	+	5.77760i	1.12861	+	0.543511i	0.902543	−	0.430600i	$-0.141698\pi$
$113$	11.9973	+	5.77760i	1.12861	+	0.543511i	0.226070	+	0.974111i	$0.427412\pi$
$114$	13.0295	−	12.0896i	1.22032	−	1.13230i
$115$	−14.1800	+	2.13730i	−1.32230	+	0.199304i
$116$	−3.80377	+	6.58833i	−0.353171	+	0.611711i
$117$	−1.02344	−	1.77265i	−0.0946171	−	0.163882i
$118$	−11.9139	−	14.9395i	−1.09676	−	1.37529i
$119$	0.924527	+	10.2387i	0.0847513	+	0.938579i
$120$	45.8698	−	57.5190i	4.18732	−	5.25074i
$121$	0.140965	+	0.0212470i	0.0128150	+	0.00193155i
$122$	28.2687	−	19.2733i	2.55933	−	1.74492i
$123$	−2.30704	+	1.57291i	−0.208019	+	0.141825i
$124$	55.6347	+	8.38558i	4.99614	+	0.753048i
$125$	1.87507	−	2.35126i	0.167711	−	0.210303i
$126$	−12.4598	−	8.21941i	−1.11001	−	0.732243i
$127$	−3.84555	−	4.82217i	−0.341237	−	0.427898i	0.581370	−	0.813640i	$-0.302517\pi$
$127$	−3.84555	−	4.82217i	−0.341237	−	0.427898i	−0.922607	+	0.385742i	$0.873946\pi$
$128$	−24.4813	−	42.4029i	−2.16386	−	3.74792i
$129$	−3.49235	+	6.04892i	−0.307484	+	0.532578i
$130$	−9.00255	+	1.35692i	−0.789576	+	0.119009i
$131$	−1.68741	+	1.56568i	−0.147429	+	0.136794i	−0.750440	−	0.660939i	$-0.770158\pi$
$131$	−1.68741	+	1.56568i	−0.147429	+	0.136794i	0.603010	+	0.797733i	$0.293968\pi$
$132$	−37.3286	−	17.9765i	−3.24904	−	1.56466i
$133$	−6.79150	+	3.39919i	−0.588898	+	0.294747i
$134$	27.5378	−	13.2615i	2.37890	−	1.14562i
$135$	−2.58392	+	6.58372i	−0.222388	+	0.566636i
$136$	−2.87885	+	38.4156i	−0.246859	+	3.29411i
$137$	−0.723317	−	0.223114i	−0.0617972	−	0.0190619i	0.263702	−	0.964604i	$-0.415056\pi$
$137$	−0.723317	−	0.223114i	−0.0617972	−	0.0190619i	−0.325500	+	0.945542i	$0.605532\pi$
$138$	2.00892	+	26.8072i	0.171011	+	2.28198i
$139$	0.302257	−	1.32427i	0.0256371	−	0.112323i	−0.960490	−	0.278313i	$-0.910225\pi$
$139$	0.302257	−	1.32427i	0.0256371	−	0.112323i	0.986127	+	0.165990i	$0.0530818\pi$
$140$	−39.9892	+	28.1671i	−3.37970	+	2.38056i
$141$	3.07910	+	13.4904i	0.259307	+	1.13610i
$142$	−31.5162	+	9.72146i	−2.64478	+	0.815807i
$143$	1.20382	+	3.06729i	0.100669	+	0.256500i
$144$	−24.2065	−	22.4603i	−2.01721	−	1.87169i
$145$	3.70950	+	2.52909i	0.308057	+	0.210030i
$146$	2.31751			0.191799
$147$	10.1753	+	11.9900i	0.839241	+	0.988923i
$148$	−40.2706			−3.31022
$149$	7.07436	+	4.82322i	0.579554	+	0.395133i	0.817316	−	0.576190i	$-0.195461\pi$
$149$	7.07436	+	4.82322i	0.579554	+	0.395133i	−0.237761	+	0.971324i	$0.576414\pi$
$150$	−26.8281	−	24.8928i	−2.19050	−	2.03249i
$151$	5.96143	+	15.1895i	0.485134	+	1.23610i	0.938655	+	0.344856i	$0.112072\pi$
$151$	5.96143	+	15.1895i	0.485134	+	1.23610i	−0.453521	+	0.891245i	$0.649832\pi$
$152$	−27.1949	+	8.38853i	−2.20580	+	0.680400i
$153$	1.76979	+	7.75397i	0.143079	+	0.626871i
$154$	17.8617	+	16.0733i	1.43934	+	1.29522i
$155$	7.38855	−	32.3714i	0.593463	−	2.60013i
$156$	0.939645	+	12.5387i	0.0752318	+	1.00390i
$157$	−20.6645	−	6.37416i	−1.64921	−	0.508713i	−0.675664	−	0.737210i	$-0.736143\pi$
$157$	−20.6645	−	6.37416i	−1.64921	−	0.508713i	−0.973545	+	0.228496i	$0.926619\pi$
$158$	2.18252	−	29.1237i	0.173632	−	2.31696i
$159$	4.24050	−	10.8046i	0.336293	−	0.856861i
$160$	−73.3197	+	35.3089i	−5.79643	+	2.79141i
$161$	2.38486	−	11.2361i	0.187953	−	0.885526i
$162$	27.1946	+	13.0962i	2.13661	+	1.02894i
$163$	−8.26316	+	7.66709i	−0.647220	+	0.600533i	−0.933918	−	0.357489i	$-0.883633\pi$
$163$	−8.26316	+	7.66709i	−0.647220	+	0.600533i	0.286697	+	0.958021i	$0.407443\pi$
$164$	6.87887	−	1.03682i	0.537150	−	0.0809623i
$165$	−12.2255	+	21.1752i	−0.951755	+	1.64849i
$166$	−14.7839	−	25.6065i	−1.14745	−	1.98745i
$167$	11.3612	+	14.2464i	0.879153	+	1.10242i	0.994037	+	0.109044i	$0.0347790\pi$
$167$	11.3612	+	14.2464i	0.879153	+	1.10242i	−0.114884	+	0.993379i	$0.536650\pi$
$168$	30.2392	+	50.5782i	2.33301	+	3.90219i
$169$	0.623490	−	0.781831i	0.0479608	−	0.0601409i
$170$	34.9804	+	5.27244i	2.68287	+	0.404378i
$171$	−4.85465	+	3.30984i	−0.371244	+	0.253110i
$172$	14.3780	−	9.80275i	1.09631	−	0.747453i
$173$	−8.36325	−	1.26056i	−0.635846	−	0.0958383i	−0.176794	−	0.984248i	$-0.556573\pi$
$173$	−8.36325	−	1.26056i	−0.635846	−	0.0958383i	−0.459052	+	0.888410i	$0.651811\pi$
$174$	5.24747	−	6.58012i	0.397810	−	0.498838i
$175$	8.02447	+	13.4218i	0.606593	+	1.01459i
$176$	33.1434	+	41.5606i	2.49828	+	3.13274i
$177$	7.78723	+	13.4879i	0.585324	+	1.01381i
$178$	16.8985	−	29.2690i	1.26659	−	2.19381i
$179$	−4.65371	+	0.701434i	−0.347834	+	0.0524276i	−0.320636	−	0.947202i	$-0.603897\pi$
$179$	−4.65371	+	0.701434i	−0.347834	+	0.0524276i	−0.0271984	+	0.999630i	$0.508659\pi$
$180$	−27.7400	+	25.7389i	−2.06761	+	1.91847i
$181$	5.08039	+	2.44659i	0.377623	+	0.181853i	0.613061	−	0.790036i	$-0.289938\pi$
$181$	5.08039	+	2.44659i	0.377623	+	0.181853i	−0.235438	+	0.971889i	$0.575652\pi$
$182$	1.51408	−	7.13349i	0.112231	−	0.528770i
$183$	−25.1247	+	12.0994i	−1.85727	+	0.894413i
$184$	15.7252	−	40.0672i	1.15928	−	2.95380i
$185$	−1.77602	+	23.6994i	−0.130576	+	1.74241i
$186$	−59.4790	−	18.3468i	−4.36121	−	1.34526i
$187$	−0.956793	−	12.7675i	−0.0699677	−	0.933654i
$188$	7.67131	−	33.6102i	0.559488	−	2.45128i
$189$	−4.21110	−	3.78946i	−0.306313	−	0.275643i
$190$	5.81532	+	25.4786i	0.421888	+	1.84841i
$191$	−22.9519	+	7.07973i	−1.66074	+	0.512271i	−0.976231	−	0.216731i	$-0.930461\pi$
$191$	−22.9519	+	7.07973i	−1.66074	+	0.512271i	−0.684512	+	0.729002i	$0.739984\pi$
$192$	29.2525	+	74.5341i	2.11112	+	5.37903i
$193$	13.7168	+	12.7273i	0.987355	+	0.916131i	0.996480	−	0.0838271i	$-0.0267143\pi$
$193$	13.7168	+	12.7273i	0.987355	+	0.916131i	−0.00912563	+	0.999958i	$0.502905\pi$
$194$	−7.28119	−	4.96423i	−0.522759	−	0.356411i
$195$	7.42050			0.531393
$196$	−9.87920	−	37.9132i	−0.705657	−	2.70808i
$197$	15.9994			1.13991			0.569956	−	0.821675i	$-0.306960\pi$
$197$	15.9994			1.13991			0.569956	+	0.821675i	$0.306960\pi$
$198$	15.3597	+	10.4721i	1.09157	+	0.744219i
$199$	6.86157	+	6.36661i	0.486404	+	0.451317i	0.884851	−	0.465874i	$-0.154260\pi$
$199$	6.86157	+	6.36661i	0.486404	+	0.451317i	−0.398447	+	0.917191i	$0.630451\pi$
$200$	21.4084	+	54.5478i	1.51381	+	3.85711i
$201$	−23.8053	+	7.34295i	−1.67909	+	0.517932i
$202$	−1.81944	−	7.97147i	−0.128015	−	0.560871i
$203$	−2.94003	+	2.07086i	−0.206349	+	0.145346i
$204$	10.8717	−	47.6321i	0.761173	−	3.33491i
$205$	−0.306800	−	4.09396i	−0.0214279	−	0.285935i
$206$	16.4347	+	5.06944i	1.14506	+	0.353205i
$207$	0.664082	−	8.86156i	0.0461569	−	0.615921i
$208$	5.89390	−	15.0174i	0.408669	−	1.04127i
$209$	8.52184	−	4.10390i	0.589468	−	0.283873i
$210$	48.3906	−	24.2198i	3.33927	−	1.67132i
$211$	1.47202	+	0.708885i	0.101338	+	0.0488017i	0.483866	−	0.875142i	$-0.339232\pi$
$211$	1.47202	+	0.708885i	0.101338	+	0.0488017i	−0.382528	+	0.923944i	$0.624947\pi$
$212$	−21.1982	+	19.6690i	−1.45590	+	1.35087i
$213$	26.5816	−	4.00654i	1.82134	−	0.274524i
$214$	−15.9022	+	27.5434i	−1.08705	+	1.88283i
$215$	−5.13485	−	8.89382i	−0.350194	−	0.606553i
$216$	−13.2359	−	16.5973i	−0.900587	−	1.12930i
$217$	22.2006	+	14.6451i	1.50707	+	0.994176i
$218$	11.4489	−	14.3565i	0.775419	−	0.972344i
$219$	−1.86782	−	0.281528i	−0.126215	−	0.0190239i
$220$	50.3324	−	34.3161i	3.39341	−	2.31359i
$221$	−3.21044	+	2.18884i	−0.215958	+	0.147237i
$222$	44.0541	+	6.64008i	2.95672	+	0.445653i
$223$	2.57880	−	3.23372i	0.172689	−	0.216546i	−0.687953	−	0.725755i	$-0.741491\pi$
$223$	2.57880	−	3.23372i	0.172689	−	0.216546i	0.860643	+	0.509209i	$0.170062\pi$
$224$	−5.86206	−	64.9195i	−0.391675	−	4.33761i
$225$	7.54300	+	9.45862i	0.502866	+	0.630575i
$226$	18.3513	+	31.7853i	1.22071	+	2.11433i
$227$	−11.4120	+	19.7662i	−0.757441	+	1.31193i	0.186710	+	0.982415i	$0.440218\pi$
$227$	−11.4120	+	19.7662i	−0.757441	+	1.31193i	−0.944151	+	0.329512i	$0.893116\pi$
$228$	35.6903	−	5.37945i	2.36365	−	0.356263i
$229$	−8.43854	+	7.82982i	−0.557634	+	0.517409i	−0.907870	−	0.419253i	$-0.862292\pi$
$229$	−8.43854	+	7.82982i	−0.557634	+	0.517409i	0.350235	+	0.936662i	$0.386102\pi$
$230$	−35.6112	−	17.1495i	−2.34814	−	1.13080i
$231$	−12.4432	−	15.1242i	−0.818703	−	0.995097i
$232$	−12.1412	+	5.84690i	−0.797110	+	0.383868i
$233$	5.12552	−	13.0596i	0.335784	−	0.855564i	−0.658866	−	0.752260i	$-0.728964\pi$
$233$	5.12552	−	13.0596i	0.335784	−	0.855564i	0.994650	−	0.103303i	$-0.0329412\pi$
$234$	0.421609	−	5.62598i	0.0275614	−	0.367782i
$235$	−19.4414	−	5.99688i	−1.26822	−	0.391193i
$236$	−2.89971	−	38.6939i	−0.188755	−	2.51876i
$237$	−5.29692	+	23.2073i	−0.344072	+	1.50748i
$238$	−13.7918	+	24.7524i	−0.893988	+	1.60446i
$239$	4.33989	+	19.0143i	0.280724	+	1.22993i	0.896867	+	0.442299i	$0.145837\pi$
$239$	4.33989	+	19.0143i	0.280724	+	1.22993i	−0.616143	+	0.787634i	$0.711306\pi$
$240$	114.394	−	35.2857i	7.38407	−	2.27768i
$241$	7.69605	+	19.6092i	0.495746	+	1.26314i	0.931719	+	0.363181i	$0.118309\pi$
$241$	7.69605	+	19.6092i	0.495746	+	1.26314i	−0.435972	+	0.899960i	$0.643595\pi$
$242$	0.288035	+	0.267257i	0.0185156	+	0.0171800i
$243$	−15.0193	−	10.2400i	−0.963488	−	0.656895i
$244$	69.4762			4.44776
$245$	−22.7477	+	4.14189i	−1.45330	+	0.264615i
$246$	−7.69612			−0.490686
$247$	−2.37173	−	1.61702i	−0.150910	−	0.102888i
$248$	73.0577	+	67.7877i	4.63917	+	4.30452i
$249$	8.80456	+	22.4337i	0.557966	+	1.42167i
$250$	7.92086	−	2.44326i	0.500959	−	0.154526i
$251$	2.17759	+	9.54062i	0.137448	+	0.602199i	0.995991	+	0.0894568i	$0.0285131\pi$
$251$	2.17759	+	9.54062i	0.137448	+	0.602199i	−0.858543	+	0.512742i	$0.828630\pi$
$252$	−11.5029	−	28.0434i	−0.724614	−	1.76657i
$253$	−3.18323	+	13.9467i	−0.200128	+	0.876819i
$254$	−1.27042	−	16.9525i	−0.0797130	−	1.06370i
$255$	−27.5522	−	8.49872i	−1.72538	−	0.532211i
$256$	4.75820	−	63.4938i	0.297388	−	3.96836i
$257$	−2.00203	+	5.10109i	−0.124883	+	0.318197i	−0.979619	−	0.200867i	$-0.935624\pi$
$257$	−2.00203	+	5.10109i	−0.124883	+	0.318197i	0.854735	+	0.519064i	$0.173719\pi$
$258$	−17.3452	+	8.35300i	−1.07986	+	0.520035i
$259$	−17.2750	−	7.99693i	−1.07342	−	0.496905i
$260$	−16.6567	−	8.02143i	−1.03300	−	0.497468i
$261$	−2.03946	+	1.89234i	−0.126239	+	0.117133i
$262$	−6.27377	+	0.945618i	−0.387595	+	0.0584205i
$263$	14.7015	−	25.4638i	0.906534	−	1.57016i	0.0876888	−	0.996148i	$-0.472052\pi$
$263$	14.7015	−	25.4638i	0.906534	−	1.57016i	0.818845	−	0.574015i	$-0.194615\pi$
$264$	−36.6953	−	63.5581i	−2.25844	−	3.91173i
$265$	10.6404	+	13.3426i	0.653634	+	0.819631i
$266$	−20.7443	−	2.80381i	−1.27192	−	0.171913i
$267$	−17.1750	+	21.5368i	−1.05109	+	1.31803i
$268$	61.3729	+	9.25048i	3.74895	+	0.565063i
$269$	0.813053	−	0.554330i	0.0495727	−	0.0337981i	−0.538280	−	0.842766i	$-0.680926\pi$
$269$	0.813053	−	0.554330i	0.0495727	−	0.0337981i	0.587853	+	0.808968i	$0.299973\pi$
$270$	−16.1067	+	10.9814i	−0.980225	+	0.668306i
$271$	12.8662	+	1.93927i	0.781565	+	0.117802i	0.527692	−	0.849436i	$-0.323057\pi$
$271$	12.8662	+	1.93927i	0.781565	+	0.117802i	0.253873	+	0.967238i	$0.418295\pi$
$272$	−39.0834	+	49.0091i	−2.36978	+	2.97161i
$273$	−2.08685	+	5.56536i	−0.126302	+	0.336831i
$274$	−1.30082	−	1.63117i	−0.0785852	−	0.0985427i
$275$	−9.73769	−	16.8662i	−0.587205	−	1.01707i
$276$	−27.2943	+	47.2752i	−1.64293	+	2.84563i
$277$	2.67476	−	0.403155i	0.160711	−	0.0242232i	−0.0681941	−	0.997672i	$-0.521724\pi$
$277$	2.67476	−	0.403155i	0.160711	−	0.0242232i	0.228905	+	0.973449i	$0.426486\pi$
$278$	2.74449	−	2.54652i	0.164604	−	0.152730i
$279$	18.5383	+	8.92756i	1.10986	+	0.534479i
$280$	−86.6333	+	1.32155i	−5.17733	+	0.0789776i
$281$	−6.00696	+	2.89280i	−0.358345	+	0.172570i	−0.604390	−	0.796688i	$-0.706583\pi$
$281$	−6.00696	+	2.89280i	−0.358345	+	0.172570i	0.246045	+	0.969258i	$0.420869\pi$
$282$	−13.9339	+	35.5031i	−0.829753	+	2.11418i
$283$	−0.736606	+	9.82933i	−0.0437867	+	0.584293i	0.931556	+	0.363598i	$0.118452\pi$
$283$	−0.736606	+	9.82933i	−0.0437867	+	0.584293i	−0.975343	+	0.220695i	$0.929167\pi$
$284$	−63.9984	−	19.7409i	−3.79761	−	1.17141i
$285$	−1.59180	−	21.2411i	−0.0942901	−	1.25821i
$286$	−2.02095	+	8.85438i	−0.119501	+	0.523570i
$287$	3.15674	+	0.921237i	0.186337	+	0.0543789i
$288$	−11.2215	−	49.1648i	−0.661236	−	2.89706i
$289$	−1.81755	+	0.560641i	−0.106915	+	0.0329789i
$290$	4.52095	+	11.5192i	0.265479	+	0.676430i
$291$	5.26528	+	4.88547i	0.308656	+	0.286391i
$292$	3.88833	+	2.65102i	0.227547	+	0.155139i
$293$	−21.1959			−1.23828			−0.619139	−	0.785282i	$-0.712518\pi$
$293$	−21.1959			−1.23828			−0.619139	+	0.785282i	$0.712518\pi$
$294$	4.55600	+	43.1041i	0.265711	+	2.51388i
$295$	−22.8994			−1.33325
$296$	−58.9388	−	40.1838i	−3.42575	−	2.33563i
$297$	5.17198	+	4.79890i	0.300109	+	0.278460i
$298$	8.62188	+	21.9682i	0.499452	+	1.27258i
$299$	4.14856	−	1.27966i	0.239918	−	0.0740048i
$300$	−16.5372	−	72.4541i	−0.954774	−	4.18314i
$301$	8.11440	−	1.34993i	0.467706	−	0.0778089i
$302$	−10.0079	+	43.8476i	−0.575892	+	2.52315i
$303$	0.498025	+	6.64569i	0.0286108	+	0.381785i
$304$	−44.2515	−	13.6498i	−2.53800	−	0.782868i
$305$	3.06405	−	40.8869i	0.175447	−	2.34118i
$306$	−8.00888	+	20.4063i	−0.457837	+	1.16655i
$307$	13.7433	−	6.61842i	0.784372	−	0.377733i	0.00156514	−	0.999999i	$-0.499502\pi$
$307$	13.7433	−	6.61842i	0.784372	−	0.377733i	0.782806	+	0.622265i	$0.213788\pi$
$308$	11.5821	+	47.3999i	0.659951	+	2.70086i
$309$	−12.6299	−	6.08222i	−0.718487	−	0.346005i
$310$	67.0880	−	62.2486i	3.81034	−	3.53548i
$311$	−9.20049	+	1.38675i	−0.521712	+	0.0786354i	−0.404619	−	0.914486i	$-0.632596\pi$
$311$	−9.20049	+	1.38675i	−0.521712	+	0.0786354i	−0.117093	+	0.993121i	$0.537358\pi$
$312$	−11.1364	+	19.2889i	−0.630476	+	1.09202i
$313$	14.6867	+	25.4380i	0.830139	+	1.43784i	0.897928	+	0.440143i	$0.145072\pi$
$313$	14.6867	+	25.4380i	0.830139	+	1.43784i	−0.0677887	+	0.997700i	$0.521594\pi$
$314$	−37.1632	−	46.6011i	−2.09724	−	2.62985i
$315$	−17.0109	+	5.53271i	−0.958458	+	0.311733i
$316$	36.9766	−	46.3672i	2.08010	−	2.60836i
$317$	−4.77463	−	0.719660i	−0.268170	−	0.0404201i	0.0135806	−	0.999908i	$-0.495677\pi$
$317$	−4.77463	−	0.719660i	−0.268170	−	0.0404201i	−0.281751	+	0.959488i	$0.590915\pi$
$318$	26.4329	−	18.0217i	1.48229	−	1.01061i
$319$	3.70047	−	2.52294i	0.207187	−	0.141257i
$320$	−116.412	−	17.5462i	−6.50761	−	0.980864i
$321$	16.1624	−	20.2670i	0.902098	−	1.13120i
$322$	22.8769	−	21.8854i	1.27488	−	1.21963i
$323$	6.95421	+	8.72031i	0.386943	+	0.485211i
$324$	30.6463	+	53.0809i	1.70257	+	2.94894i
$325$	−2.95523	+	5.11862i	−0.163927	+	0.283930i
$326$	−30.7224	+	4.63065i	−1.70156	+	0.256468i
$327$	−10.9713	+	10.1799i	−0.606716	+	0.562951i
$328$	11.1023	+	5.34658i	0.613022	+	0.295216i
$329$	9.96510	−	12.8945i	0.549394	−	0.710897i
$330$	−60.7195	+	29.2410i	−3.34250	+	1.60966i
$331$	3.57810	−	9.11684i	0.196670	−	0.501107i	−0.798185	−	0.602412i	$-0.794207\pi$
$331$	3.57810	−	9.11684i	0.196670	−	0.501107i	0.994855	+	0.101305i	$0.0323018\pi$
$332$	4.48694	−	59.8740i	0.246253	−	3.28601i
$333$	−14.0730	−	4.34095i	−0.771197	−	0.237883i
$334$	3.75328	+	50.0840i	0.205370	+	2.74047i
$335$	8.15061	−	35.7102i	0.445316	−	1.95106i
$336$	−5.70643	+	95.7182i	−0.311311	+	5.22186i
$337$	−4.72877	−	20.7181i	−0.257592	−	1.12859i	−0.923817	−	0.382835i	$-0.874948\pi$
$337$	−4.72877	−	20.7181i	−0.257592	−	1.12859i	0.666225	−	0.745751i	$-0.267909\pi$
$338$	2.63382	−	0.812425i	0.143261	−	0.0441901i
$339$	−10.9291	−	27.8469i	−0.593587	−	1.51244i
$340$	52.6590	+	48.8604i	2.85583	+	2.64983i
$341$	−27.3676	−	18.6589i	−1.48204	−	1.01044i
$342$	−16.1947			−0.875711
$343$	3.29088	−	18.2255i	0.177691	−	0.984086i
$344$	30.8248			1.66196
$345$	26.6178	+	18.1477i	1.43306	+	0.977041i
$346$	−17.0887	−	15.8560i	−0.918695	−	0.852424i
$347$	8.24066	+	20.9969i	0.442382	+	1.12717i	0.962067	+	0.272813i	$0.0879539\pi$
$347$	8.24066	+	20.9969i	0.442382	+	1.12717i	−0.519685	+	0.854358i	$0.673951\pi$
$348$	16.3313	−	5.03753i	0.875448	−	0.270040i
$349$	−1.61907	−	7.09363i	−0.0866670	−	0.379713i	0.912929	−	0.408117i	$-0.133815\pi$
$349$	−1.61907	−	7.09363i	−0.0866670	−	0.379713i	−0.999597	+	0.0284042i	$0.990957\pi$
$350$	−2.56503	+	43.0251i	−0.137107	+	2.29979i
$351$	0.476463	−	2.08752i	0.0254317	−	0.111424i
$352$	6.06664	+	80.9537i	0.323353	+	4.31485i
$353$	14.1289	+	4.35818i	0.752004	+	0.231963i	0.646980	−	0.762507i	$-0.276032\pi$
$353$	14.1289	+	4.35818i	0.752004	+	0.231963i	0.105024	+	0.994470i	$0.466508\pi$
$354$	−3.20797	+	42.8074i	−0.170502	+	2.27519i
$355$	−14.4400	+	36.7926i	−0.766398	+	1.95275i
$356$	61.8333	−	29.7774i	3.27716	−	1.57820i
$357$	14.1225	−	18.2740i	0.747440	−	0.967162i
$358$	−11.6871	−	5.62823i	−0.617685	−	0.297461i
$359$	1.67771	−	1.55669i	0.0885462	−	0.0821588i	−0.634658	−	0.772793i	$-0.718859\pi$
$359$	1.67771	−	1.55669i	0.0885462	−	0.0821588i	0.723204	+	0.690634i	$0.242669\pi$
$360$	−66.2828	+	9.99053i	−3.49341	+	0.526547i
$361$	5.38007	−	9.31856i	0.283162	−	0.490451i
$362$	7.77104	+	13.4598i	0.408437	+	0.707433i
$363$	−0.199678	−	0.250388i	−0.0104804	−	0.0131420i
$364$	10.7004	−	10.2366i	0.560852	−	0.536545i
$365$	1.73162	−	2.17138i	0.0906369	−	0.113655i
$366$	−76.0036	−	11.4557i	−3.97277	−	0.598799i
$367$	6.26751	−	4.27312i	0.327161	−	0.223055i	−0.388589	−	0.921411i	$-0.627037\pi$
$367$	6.26751	−	4.27312i	0.327161	−	0.223055i	0.715750	+	0.698356i	$0.246085\pi$
$368$	57.8687	−	39.4542i	3.01662	−	2.05669i
$369$	2.51567	+	0.379176i	0.130960	+	0.0197391i
$370$	−40.8417	+	51.2138i	−2.12326	+	2.66248i
$371$	−12.9993	+	4.22795i	−0.674891	+	0.219504i
$372$	−78.8070	−	98.8208i	−4.08595	−	5.12362i
$373$	−9.66643	−	16.7427i	−0.500509	−	0.866907i	−1.00000		0.000587627i	$-0.999813\pi$
$373$	−9.66643	−	16.7427i	−0.500509	−	0.866907i	0.499491	−	0.866319i	$-0.333520\pi$
$374$	17.6447	−	30.5615i	0.912386	−	1.58030i
$375$	−6.68068	+	1.00695i	−0.344989	+	0.0519987i
$376$	44.7653	−	41.5361i	2.30859	−	2.14206i
$377$	−1.22461	−	0.589741i	−0.0630706	−	0.0303732i
$378$	−3.70635	−	15.1683i	−0.190634	−	0.780173i
$379$	15.0673	−	7.25601i	0.773953	−	0.372716i	−0.00484719	−	0.999988i	$-0.501543\pi$
$379$	15.0673	−	7.25601i	0.773953	−	0.372716i	0.778800	+	0.627272i	$0.215829\pi$
$380$	−19.3882	+	49.4003i	−0.994592	+	2.53418i
$381$	−1.03547	+	13.8173i	−0.0530486	+	0.707884i
$382$	−63.2617	−	19.5136i	−3.23675	−	0.998405i
$383$	0.133073	+	1.77574i	0.00679971	+	0.0907358i	0.999571	−	0.0292848i	$-0.00932297\pi$
$383$	0.133073	+	1.77574i	0.00679971	+	0.0907358i	−0.992771	+	0.120021i	$0.961704\pi$
$384$	−24.4764	+	107.238i	−1.24906	+	5.47247i
$385$	28.4058	−	4.72566i	1.44769	−	0.240842i
$386$	11.4765	+	50.2819i	0.584139	+	2.55928i
$387$	6.08124	−	1.87581i	0.309127	−	0.0953530i
$388$	−6.53778	−	16.6580i	−0.331906	−	0.845682i
$389$	−23.4060	−	21.7176i	−1.18673	−	1.10113i	−0.992759	−	0.120120i	$-0.961672\pi$
$389$	−23.4060	−	21.7176i	−1.18673	−	1.10113i	−0.193973	−	0.981007i	$-0.562137\pi$
$390$	16.8990	+	11.5215i	0.855713	+	0.583415i
$391$	−16.8691			−0.853109
$392$	23.3725	−	65.3464i	1.18049	−	3.30049i
$393$	5.17126			0.260856
$394$	36.4361	+	24.8417i	1.83562	+	1.25151i
$395$	−25.6565	−	23.8057i	−1.29092	−	1.19780i
$396$	13.7915	+	35.1402i	0.693049	+	1.76586i
$397$	−7.61417	+	2.34866i	−0.382144	+	0.117876i	−0.479875	−	0.877337i	$-0.659318\pi$
$397$	−7.61417	+	2.34866i	−0.382144	+	0.117876i	0.0977306	+	0.995213i	$0.468842\pi$
$398$	5.74092	+	25.1526i	0.287766	+	1.26079i
$399$	16.3784	+	4.77974i	0.819947	+	0.239286i
$400$	−21.2177	+	92.9606i	−1.06088	+	4.64803i
$401$	−0.100066	−	1.33529i	−0.00499708	−	0.0666814i	0.994148	−	0.108029i	$-0.0344539\pi$
$401$	−0.100066	−	1.33529i	−0.00499708	−	0.0666814i	−0.999145	+	0.0413476i	$0.986835\pi$
$402$	−65.6137	−	20.2392i	−3.27251	−	1.00944i
$403$	−0.751212	+	10.0242i	−0.0374205	+	0.499342i
$404$	6.06596	−	15.4558i	0.301793	−	0.768956i
$405$	32.5898	−	15.6944i	1.61940	−	0.779863i
$406$	−9.91078	+	0.151184i	−0.491864	+	0.00750314i
$407$	21.3602	+	10.2865i	1.05878	+	0.509883i
$408$	63.4410	−	58.8646i	3.14080	−	2.91423i
$409$	21.7967	−	3.28532i	1.07778	−	0.162449i	0.413923	−	0.910312i	$-0.364158\pi$
$409$	21.7967	−	3.28532i	1.07778	−	0.162449i	0.663853	+	0.747863i	$0.268920\pi$
$410$	5.65785	−	9.79969i	0.279422	−	0.483972i
$411$	0.850250	+	1.47268i	0.0419397	+	0.0726417i
$412$	21.7753	+	27.3053i	1.07279	+	1.34524i
$413$	6.43994	−	17.1745i	0.316889	−	0.845100i
$414$	15.2714	−	19.1497i	0.750546	−	0.941155i
$415$	−35.0382	−	5.28115i	−1.71996	−	0.259242i
$416$	20.3561	−	13.8786i	0.998040	−	0.680452i
$417$	−2.52129	+	1.71899i	−0.123468	+	0.0841791i
$418$	25.7791	+	3.88557i	1.26090	+	0.190049i
$419$	−0.0611198	+	0.0766419i	−0.00298590	+	0.00374420i	−0.783322	−	0.621616i	$-0.786476\pi$
$419$	−0.0611198	+	0.0766419i	−0.00298590	+	0.00374420i	0.780336	+	0.625360i	$0.215048\pi$
$420$	108.895	+	14.7183i	5.31353	+	0.718180i
$421$	12.4497	+	15.6114i	0.606761	+	0.760854i	0.986415	−	0.164275i	$-0.0525283\pi$
$421$	12.4497	+	15.6114i	0.606761	+	0.760854i	−0.379654	+	0.925129i	$0.623957\pi$
$422$	2.25162	+	3.89991i	0.109607	+	0.189845i
$423$	6.30383	−	10.9186i	0.306503	−	0.530878i
$424$	−50.6516	+	7.63450i	−2.45986	+	0.370764i
$425$	16.8351	−	15.6207i	0.816622	−	0.757715i
$426$	66.7562	+	32.1481i	3.23435	+	1.55758i
$427$	29.8034	+	13.7966i	1.44229	+	0.667663i
$428$	−58.1878	+	28.0218i	−2.81262	+	1.35448i
$429$	2.70442	−	6.89074i	0.130571	−	0.332688i
$430$	2.11531	−	28.2269i	0.102009	−	1.36122i
$431$	−13.4960	−	4.16296i	−0.650078	−	0.200523i	−0.0478600	−	0.998854i	$-0.515240\pi$
$431$	−13.4960	−	4.16296i	−0.650078	−	0.200523i	−0.602218	+	0.798331i	$0.705716\pi$
$432$	−2.58142	−	34.4467i	−0.124199	−	1.65732i
$433$	0.645797	−	2.82942i	0.0310350	−	0.135973i	−0.957037	−	0.289966i	$-0.906356\pi$
$433$	0.645797	−	2.82942i	0.0310350	−	0.135973i	0.988072	+	0.153993i	$0.0492132\pi$
$434$	27.8193	+	67.8219i	1.33537	+	3.25555i
$435$	−2.24436	−	9.83317i	−0.107609	−	0.471464i
$436$	35.6315	−	10.9909i	1.70644	−	0.526367i
$437$	−4.55294	−	11.6007i	−0.217797	−	0.554937i
$438$	−3.81653	−	3.54122i	−0.182361	−	0.169206i
$439$	17.5432	+	11.9607i	0.837289	+	0.570854i	0.904300	−	0.426898i	$-0.140394\pi$
$439$	17.5432	+	11.9607i	0.837289	+	0.570854i	−0.0670104	+	0.997752i	$0.521346\pi$
$440$	107.907			5.14427
$441$	0.634432	−	14.3141i	0.0302111	−	0.681624i
$442$	−10.7098			−0.509412
$443$	21.6843	+	14.7841i	1.03025	+	0.702415i	0.955562	−	0.294792i	$-0.0952503\pi$
$443$	21.6843	+	14.7841i	1.03025	+	0.702415i	0.0746918	+	0.997207i	$0.476203\pi$
$444$	66.3184	+	61.5345i	3.14733	+	2.92030i
$445$	−14.7971	−	37.7023i	−0.701449	−	1.78726i
$446$	10.8937	−	3.36025i	0.515830	−	0.159113i
$447$	−4.28020	−	18.7528i	−0.202447	−	0.886976i
$448$	45.8978	−	82.3740i	2.16847	−	3.89180i
$449$	−4.57570	+	20.0475i	−0.215941	+	0.946098i	0.744502	+	0.667620i	$0.232687\pi$
$449$	−4.57570	+	20.0475i	−0.215941	+	0.946098i	−0.960443	+	0.278478i	$0.910170\pi$
$450$	2.49191	+	33.2522i	0.117470	+	1.56752i
$451$	−3.91351	−	1.20716i	−0.184280	−	0.0568428i
$452$	−5.56964	+	74.3216i	−0.261974	+	3.49580i
$453$	13.3925	−	34.1235i	0.629235	−	1.60326i
$454$	−56.6792	+	27.2952i	−2.66008	+	1.28103i
$455$	−5.55237	−	6.74866i	−0.260299	−	0.316382i
$456$	57.6031	+	27.7402i	2.69751	+	1.29905i
$457$	−15.0647	+	13.9780i	−0.704699	+	0.653865i	−0.948797	−	0.315886i	$-0.897698\pi$
$457$	−15.0647	+	13.9780i	−0.704699	+	0.653865i	0.244099	+	0.969750i	$0.421508\pi$
$458$	−31.3744	+	4.72894i	−1.46603	+	0.220969i
$459$	−4.15995	+	7.20524i	−0.194170	+	0.336312i
$460$	−40.1312	−	69.5093i	−1.87113	−	3.24089i
$461$	−6.32636	−	7.93300i	−0.294648	−	0.369477i	0.612368	−	0.790573i	$-0.290217\pi$
$461$	−6.32636	−	7.93300i	−0.294648	−	0.369477i	−0.907016	+	0.421096i	$0.861646\pi$
$462$	−4.85465	−	53.7629i	−0.225859	−	2.50128i
$463$	0.358626	−	0.449703i	0.0166668	−	0.0208995i	−0.773428	−	0.633884i	$-0.781460\pi$
$463$	0.358626	−	0.449703i	0.0166668	−	0.0208995i	0.790095	+	0.612984i	$0.210031\pi$
$464$	−21.6827	−	3.26815i	−1.00660	−	0.151720i
$465$	−61.6319	+	42.0199i	−2.85811	+	1.94863i
$466$	31.9497	−	21.7829i	1.48004	−	1.00907i
$467$	26.4695	+	3.98963i	1.22486	+	0.184618i	0.729447	−	0.684038i	$-0.239778\pi$
$467$	26.4695	+	3.98963i	1.22486	+	0.184618i	0.495416	+	0.868656i	$0.335016\pi$
$468$	7.14297	−	8.95700i	0.330184	−	0.414038i
$469$	24.4904	+	16.1556i	1.13086	+	0.745998i
$470$	−34.9635	−	43.8428i	−1.61275	−	2.02232i
$471$	24.2909	+	42.0730i	1.11926	+	1.93862i
$472$	34.3666	−	59.5246i	1.58185	−	2.73984i
$473$	−10.1303	+	1.52689i	−0.465791	+	0.0702067i
$474$	−48.0960	+	44.6265i	−2.20912	+	2.04976i
$475$	15.2859	+	7.36131i	0.701366	+	0.337760i
$476$	−51.4543	+	25.7532i	−2.35841	+	1.18040i
$477$	−9.52816	+	4.58852i	−0.436264	+	0.210094i
$478$	−19.6394	+	50.0404i	−0.898285	+	2.28879i
$479$	2.89664	−	38.6530i	0.132351	−	1.76610i	−0.397115	−	0.917769i	$-0.629989\pi$
$479$	2.89664	−	38.6530i	0.132351	−	1.76610i	0.529466	−	0.848331i	$-0.322392\pi$
$480$	174.697	+	53.8870i	7.97381	+	2.45959i
$481$	−0.537683	−	7.17488i	−0.0245162	−	0.327146i
$482$	−12.9200	+	56.6062i	−0.588489	+	2.57834i
$483$	−21.0964	+	14.8597i	−0.959921	+	0.676138i
$484$	0.177548	+	0.777890i	0.00807038	+	0.0353586i
$485$	−10.0916	+	3.11285i	−0.458237	+	0.141347i
$486$	−18.3048	−	46.6398i	−0.830321	−	2.11562i
$487$	13.7409	+	12.7496i	0.622657	+	0.577742i	0.927112	−	0.374785i	$-0.122284\pi$
$487$	13.7409	+	12.7496i	0.622657	+	0.577742i	−0.304454	+	0.952527i	$0.598474\pi$
$488$	101.683	+	69.3264i	4.60298	+	3.13826i
$489$	25.3234			1.14517
$490$	−58.2351	−	25.8870i	−2.63079	−	1.16946i
$491$	0.339127			0.0153046			0.00765230	−	0.999971i	$-0.497564\pi$
$491$	0.339127			0.0153046			0.00765230	+	0.999971i	$0.497564\pi$
$492$	−12.9126	−	8.80364i	−0.582143	−	0.396899i
$493$	3.87152	+	3.59224i	0.174364	+	0.161786i
$494$	−2.89055	−	7.36499i	−0.130052	−	0.331367i
$495$	21.2883	−	6.56658i	0.956840	−	0.295146i
$496$	36.0863	+	158.104i	1.62032	+	7.09909i
$497$	−23.5334	−	21.1771i	−1.05562	−	0.949923i
$498$	−14.7809	+	64.7595i	−0.662349	+	2.90194i
$499$	1.02884	+	13.7290i	0.0460574	+	0.614594i	0.971704	+	0.236203i	$0.0759032\pi$
$499$	1.02884	+	13.7290i	0.0460574	+	0.614594i	−0.925646	+	0.378390i	$0.876478\pi$
$500$	16.0845	+	4.96141i	0.719321	+	0.221881i
$501$	3.05915	−	40.8215i	0.136673	−	1.82377i
$502$	−9.85427	+	25.1083i	−0.439818	+	1.12064i
$503$	−17.4372	+	8.39731i	−0.777486	+	0.374418i	−0.780161	−	0.625579i	$-0.784863\pi$
$503$	−17.4372	+	8.39731i	−0.777486	+	0.374418i	0.00267490	+	0.999996i	$0.499149\pi$
$504$	11.1477	−	52.5216i	0.496558	−	2.33950i
$505$	−8.82828	−	4.25147i	−0.392853	−	0.189188i
$506$	−28.9037	+	26.8188i	−1.28493	+	1.19224i
$507$	−2.22143	+	0.334827i	−0.0986574	+	0.0148702i
$508$	17.2606	−	29.8962i	0.765815	−	1.32643i
$509$	−12.2870	−	21.2817i	−0.544611	−	0.943294i	−0.998631	−	0.0523029i	$-0.983344\pi$
$509$	−12.2870	−	21.2817i	−0.544611	−	0.943294i	0.454020	−	0.890992i	$-0.349989\pi$
$510$	−49.5499	−	62.1337i	−2.19411	−	2.75132i
$511$	1.14155	+	1.90936i	0.0504992	+	0.0844651i
$512$	48.3650	−	60.6478i	2.13745	−	2.68028i
$513$	−6.07772	−	0.916068i	−0.268338	−	0.0404454i
$514$	−12.4796	+	8.50842i	−0.550450	+	0.375290i
$515$	17.0296	−	11.6106i	0.750414	−	0.511623i
$516$	−38.6568	−	5.82658i	−1.70177	−	0.256501i
$517$	−12.6542	+	15.8679i	−0.556532	+	0.697868i
$518$	−26.9244	−	45.0339i	−1.18299	−	1.97868i
$519$	11.8466	+	14.8552i	0.520008	+	0.652070i
$520$	−16.3741	−	28.3607i	−0.718050	−	1.24370i
$521$	0.108157	−	0.187333i	0.00473844	−	0.00820722i	−0.863646	−	0.504098i	$-0.831825\pi$
$521$	0.108157	−	0.187333i	0.00473844	−	0.00820722i	0.868385	+	0.495891i	$0.165158\pi$
$522$	−7.58270	+	1.14291i	−0.331886	+	0.0500237i
$523$	25.7228	−	23.8673i	1.12478	−	1.04364i	0.126113	−	0.992016i	$-0.459750\pi$
$523$	25.7228	−	23.8673i	1.12478	−	1.04364i	0.998666	−	0.0516272i	$-0.0164408\pi$
$524$	−11.6078	−	5.59004i	−0.507091	−	0.244202i
$525$	7.29393	−	34.3648i	0.318333	−	1.49980i
$526$	73.0169	−	35.1631i	3.18369	−	1.53318i
$527$	14.2700	−	36.3594i	0.621611	−	1.58384i
$528$	8.92432	−	119.087i	0.388381	−	5.18259i
$529$	−3.96744	−	1.22379i	−0.172497	−	0.0532083i
$530$	3.51516	+	46.9066i	0.152689	+	2.03749i
$531$	3.15766	−	13.8346i	0.137031	−	0.600370i
$532$	−31.5976	−	28.4338i	−1.36993	−	1.23276i
$533$	0.276573	+	1.21174i	0.0119797	+	0.0524865i
$534$	−72.5526	+	22.3795i	−3.13966	+	0.968456i
$535$	13.9247	+	35.4795i	0.602017	+	1.53391i
$536$	80.5929	+	74.7793i	3.48109	+	3.22998i
$537$	8.73563	+	5.95585i	0.376970	+	0.257014i
$538$	2.71228			0.116935
$539$	−4.44425	+	22.6332i	−0.191428	+	0.974882i
$540$	−39.5856			−1.70349
$541$	−21.0506	−	14.3521i	−0.905036	−	0.617043i	0.0188032	−	0.999823i	$-0.494014\pi$
$541$	−21.0506	−	14.3521i	−0.905036	−	0.617043i	−0.923840	+	0.382780i	$0.874967\pi$
$542$	26.2896	+	24.3932i	1.12924	+	1.04778i
$543$	−4.62804	−	11.7921i	−0.198608	−	0.506046i
$544$	−91.4770	+	28.2169i	−3.92204	+	1.20979i
$545$	−4.89673	−	21.4540i	−0.209753	−	0.918987i
$546$	−13.3936	+	9.43402i	−0.573192	+	0.403739i
$547$	−4.44863	+	19.4907i	−0.190210	+	0.833362i	0.786293	+	0.617854i	$0.211998\pi$
$547$	−4.44863	+	19.4907i	−0.190210	+	0.833362i	−0.976502	+	0.215508i	$0.930859\pi$
$548$	−0.316605	−	4.22480i	−0.0135247	−	0.180474i
$549$	24.2792	+	7.48916i	1.03621	+	0.319629i
$550$	4.01146	−	53.5293i	0.171049	−	2.28250i
$551$	−1.42543	+	3.63194i	−0.0607253	+	0.154726i
$552$	−87.1204	+	41.9550i	−3.70809	+	1.78572i
$553$	25.0696	−	12.5475i	1.06607	−	0.533572i
$554$	6.71729	+	3.23487i	0.285390	+	0.137437i
$555$	39.1380	−	36.3148i	1.66132	−	1.54148i
$556$	7.51769	−	1.13311i	0.318821	−	0.0480545i
$557$	3.93455	−	6.81485i	0.166712	−	0.288754i	−0.770550	−	0.637380i	$-0.780018\pi$
$557$	3.93455	−	6.81485i	0.166712	−	0.288754i	0.937262	+	0.348626i	$0.113352\pi$
$558$	28.3564	+	49.1147i	1.20042	+	2.07919i
$559$	1.93850	+	2.43080i	0.0819897	+	0.102812i
$560$	−117.686	−	77.6341i	−4.97313	−	3.28064i
$561$	−17.9334	+	22.4878i	−0.757150	+	0.949436i
$562$	−18.1714	−	2.73890i	−0.766515	−	0.115534i
$563$	−13.4846	+	9.19363i	−0.568307	+	0.387465i	−0.813112	−	0.582107i	$-0.802228\pi$
$563$	−13.4846	+	9.19363i	−0.568307	+	0.387465i	0.244805	+	0.969572i	$0.421276\pi$
$564$	−63.9906	+	43.6280i	−2.69449	+	1.83707i
$565$	43.4929	+	6.55550i	1.82976	+	0.275792i
$566$	−16.9391	+	21.2410i	−0.712005	+	0.892825i
$567$	2.60562	+	28.8560i	0.109426	+	1.21184i
$568$	−73.9677	−	92.7526i	−3.10362	−	3.89181i
$569$	22.5810	+	39.1114i	0.946643	+	1.63963i	0.752428	+	0.658675i	$0.228883\pi$
$569$	22.5810	+	39.1114i	0.946643	+	1.63963i	0.194215	+	0.980959i	$0.437784\pi$
$570$	29.3552	−	50.8446i	1.22955	−	2.12965i
$571$	−18.3675	+	2.76846i	−0.768656	+	0.115856i	−0.521652	−	0.853158i	$-0.674684\pi$
$571$	−18.3675	+	2.76846i	−0.768656	+	0.115856i	−0.247004	+	0.969014i	$0.579446\pi$
$572$	−13.5193	+	12.5441i	−0.565272	+	0.524496i
$573$	48.6157	+	23.4121i	2.03095	+	0.978054i
$574$	5.75860	+	6.99932i	0.240359	+	0.292146i
$575$	−23.1188	+	11.1334i	−0.964121	+	0.464296i
$576$	26.6528	−	67.9103i	1.11054	−	2.82960i
$577$	−1.70231	+	22.7158i	−0.0708682	+	0.945670i	0.842542	+	0.538630i	$0.181058\pi$
$577$	−1.70231	+	22.7158i	−0.0708682	+	0.945670i	−0.913410	+	0.407040i	$0.866561\pi$
$578$	−5.00967	−	1.54528i	−0.208375	−	0.0642751i
$579$	−3.14141	−	41.9192i	−0.130552	−	1.74210i
$580$	−5.59161	+	24.4985i	−0.232179	+	1.01724i
$581$	13.8146	−	24.7933i	0.573125	−	1.02860i
$582$	4.40534	+	19.3010i	0.182607	+	0.800054i
$583$	16.2680	−	5.01801i	0.673752	−	0.207825i
$584$	3.04554	+	7.75990i	0.126025	+	0.321107i
$585$	−4.95620	−	4.59868i	−0.204914	−	0.190132i
$586$	−48.2702	−	32.9101i	−1.99402	−	1.35950i
$587$	−1.71697			−0.0708670			−0.0354335	−	0.999372i	$-0.511281\pi$
$587$	−1.71697			−0.0708670			−0.0354335	+	0.999372i	$0.511281\pi$
$588$	−41.6630	+	77.5318i	−1.71815	+	3.19736i
$589$	28.8554			1.18896
$590$	−52.1495	−	35.5550i	−2.14696	−	1.46377i
$591$	−26.3482	−	24.4475i	−1.08382	−	1.00564i
$592$	−42.4066	−	108.050i	−1.74290	−	4.44084i
$593$	−29.0439	+	8.95885i	−1.19269	+	0.367896i	−0.826657	−	0.562706i	$-0.809760\pi$
$593$	−29.0439	+	8.95885i	−1.19269	+	0.367896i	−0.366032	+	0.930602i	$0.619284\pi$
$594$	4.32728	+	18.9591i	0.177550	+	0.777899i
$595$	12.8866	+	31.4168i	0.528298	+	1.28796i
$596$	−10.6637	+	46.7209i	−0.436804	+	1.91376i
$597$	−1.57143	−	20.9693i	−0.0643145	−	0.858217i
$598$	11.4346	+	3.52709i	0.467594	+	0.144234i
$599$	0.0854946	−	1.14085i	0.00349321	−	0.0466137i	−0.995185	−	0.0980165i	$-0.968750\pi$
$599$	0.0854946	−	1.14085i	0.00349321	−	0.0466137i	0.998678	+	0.0514028i	$0.0163692\pi$
$600$	48.0946	−	122.543i	1.96346	−	5.00280i
$601$	−14.7105	+	7.08419i	−0.600052	+	0.288970i	−0.709146	−	0.705061i	$-0.750919\pi$
$601$	−14.7105	+	7.08419i	−0.600052	+	0.288970i	0.109094	+	0.994031i	$0.465205\pi$
$602$	20.5752	+	9.52467i	0.838583	+	0.388197i
$603$	20.4503	+	9.84835i	0.832801	+	0.401056i
$604$	−66.9489	+	62.1195i	−2.72411	+	2.52761i
$605$	0.465621	−	0.0701811i	0.0189302	−	0.00285327i
$606$	−9.18433	+	15.9077i	−0.373088	+	0.646207i
$607$	8.83393	+	15.3008i	0.358558	+	0.621041i	0.987720	−	0.156233i	$-0.0499351\pi$
$607$	8.83393	+	15.3008i	0.358558	+	0.621041i	−0.629162	+	0.777274i	$0.716602\pi$
$608$	−44.0939	−	55.2920i	−1.78824	−	2.24239i
$609$	8.00603	+	1.08210i	0.324421	+	0.0438488i
$610$	70.4615	−	88.3559i	2.85290	−	3.57742i
$611$	6.09065	+	0.918018i	0.246401	+	0.0371390i
$612$	−36.7802	+	25.0763i	−1.48675	+	1.01365i
$613$	0.943967	−	0.643586i	0.0381265	−	0.0259942i	−0.544107	−	0.839016i	$-0.683131\pi$
$613$	0.943967	−	0.643586i	0.0381265	−	0.0259942i	0.582233	+	0.813022i	$0.302179\pi$
$614$	41.5743	+	6.26632i	1.67780	+	0.252888i
$615$	−5.75044	+	7.21082i	−0.231880	+	0.290768i
$616$	−30.3465	+	80.9301i	−1.22269	+	3.26077i
$617$	28.5994	+	35.8625i	1.15137	+	1.44377i	0.875921	+	0.482454i	$0.160254\pi$
$617$	28.5994	+	35.8625i	1.15137	+	1.44377i	0.275447	+	0.961316i	$0.411174\pi$
$618$	−19.3188	−	33.4611i	−0.777116	−	1.34600i
$619$	10.1430	−	17.5683i	0.407684	−	0.706129i	−0.586946	−	0.809626i	$-0.699670\pi$
$619$	10.1430	−	17.5683i	0.407684	−	0.706129i	0.994630	+	0.103497i	$0.0330033\pi$
$620$	183.767	−	27.6984i	7.38026	−	1.11240i
$621$	6.81440	−	6.32284i	0.273452	−	0.253727i
$622$	−23.1058	−	11.1271i	−0.926457	−	0.446158i
$623$	32.4380	−	0.494826i	1.29960	−	0.0198248i
$624$	−32.6532	+	15.7250i	−1.30717	+	0.629502i
$625$	−7.16752	+	18.2625i	−0.286701	+	0.730501i
$626$	−6.05021	+	80.7344i	−0.241815	+	3.22679i
$627$	−20.3048	−	6.26320i	−0.810896	−	0.250128i
$628$	−9.04511	−	120.699i	−0.360939	−	4.81640i
$629$	−6.22101	+	27.2560i	−0.248048	+	1.08677i
$630$	−47.3300	−	13.8124i	−1.88567	−	0.550299i
$631$	−4.28557	−	18.7763i	−0.170606	−	0.747472i	−0.985750	−	0.168215i	$-0.946200\pi$
$631$	−4.28557	−	18.7763i	−0.170606	−	0.747472i	0.815145	−	0.579257i	$-0.196657\pi$
$632$	100.385	−	30.9647i	3.99310	−	1.23171i
$633$	−1.34095	−	3.41668i	−0.0532980	−	0.135801i
$634$	−9.75606	−	9.05230i	−0.387463	−	0.359513i
$635$	−16.8328	−	11.4764i	−0.667989	−	0.455427i
$636$	64.9643			2.57600
$637$	6.62296	−	2.26635i	0.262411	−	0.0897962i
$638$	12.3445			0.488723
$639$	−20.2370	−	13.7974i	−0.800564	−	0.545815i
$640$	−118.555	−	110.003i	−4.68631	−	4.34826i
$641$	−16.2856	−	41.4951i	−0.643243	−	1.63896i	−0.763188	−	0.646176i	$-0.776367\pi$
$641$	−16.2856	−	41.4951i	−0.643243	−	1.63896i	0.119945	−	0.992781i	$-0.461728\pi$
$642$	68.2751	−	21.0601i	2.69460	−	0.831175i
$643$	−2.47733	−	10.8539i	−0.0976964	−	0.428036i	0.902299	−	0.431111i	$-0.141878\pi$
$643$	−2.47733	−	10.8539i	−0.0976964	−	0.428036i	−0.999995	+	0.00307514i	$0.999021\pi$
$644$	63.4179	−	10.5504i	2.49901	−	0.415743i
$645$	−5.13381	+	22.4927i	−0.202144	+	0.885649i
$646$	2.29740	+	30.6566i	0.0903898	+	1.20617i
$647$	−16.0135	−	4.93952i	−0.629557	−	0.194193i	−0.0364748	−	0.999335i	$-0.511613\pi$
$647$	−16.0135	−	4.93952i	−0.629557	−	0.194193i	−0.593082	+	0.805142i	$0.702089\pi$
$648$	−8.11355	+	108.268i	−0.318730	+	4.25316i
$649$	−8.34572	+	21.2645i	−0.327598	+	0.834706i
$650$	−14.6775	+	7.06833i	−0.575701	+	0.277243i
$651$	−14.1822	−	58.0410i	−0.555846	−	2.27480i
$652$	−56.8431	−	27.3742i	−2.22615	−	1.07206i
$653$	−26.0651	+	24.1849i	−1.02001	+	0.946427i	−0.998576	−	0.0533431i	$-0.983012\pi$
$653$	−26.0651	+	24.1849i	−1.02001	+	0.946427i	−0.0214297	+	0.999770i	$0.506822\pi$
$654$	−40.7914	+	6.14831i	−1.59507	+	0.240418i
$655$	−3.80169	+	6.58472i	−0.148544	+	0.257286i
$656$	10.0257	+	17.3649i	0.391436	+	0.677987i
$657$	1.07306	+	1.34557i	0.0418639	+	0.0524957i
$658$	42.7147	−	13.8927i	1.66519	−	0.541594i
$659$	−8.98960	+	11.2726i	−0.350185	+	0.439118i	−0.925462	−	0.378840i	$-0.876323\pi$
$659$	−8.98960	+	11.2726i	−0.350185	+	0.439118i	0.575277	+	0.817959i	$0.304894\pi$
$660$	−135.324	−	20.3969i	−5.26749	−	0.793947i
$661$	−21.1038	+	14.3883i	−0.820842	+	0.559641i	−0.899328	−	0.437275i	$-0.855944\pi$
$661$	−21.1038	+	14.3883i	−0.820842	+	0.559641i	0.0784861	+	0.996915i	$0.474991\pi$
$662$	22.3039	−	15.2065i	0.866866	−	0.591019i
$663$	8.63162	+	1.30101i	0.335224	+	0.0505269i
$664$	66.3119	−	83.1525i	2.57340	−	3.22694i
$665$	−18.1269	+	17.3413i	−0.702931	+	0.672466i
$666$	−25.3090	−	31.7364i	−0.980703	−	1.22976i
$667$	−2.95047	−	5.11037i	−0.114243	−	0.197874i
$668$	−50.9941	+	88.3245i	−1.97302	+	3.41738i
$669$	−9.18803	+	1.38487i	−0.355230	+	0.0535423i
$670$	74.0075	−	68.6689i	2.85916	−	2.65291i
$671$	−36.8513	−	17.7466i	−1.42263	−	0.685101i
$672$	−89.5449	+	115.868i	−3.45427	+	4.46971i
$673$	6.42071	−	3.09205i	0.247500	−	0.119190i	−0.306022	−	0.952025i	$-0.598998\pi$
$673$	6.42071	−	3.09205i	0.247500	−	0.119190i	0.553522	+	0.832835i	$0.313284\pi$
$674$	21.3992	−	54.5242i	0.824266	−	2.10019i
$675$	−0.945750	+	12.6202i	−0.0364019	+	0.485750i
$676$	5.34836	+	1.64975i	0.205706	+	0.0634520i
$677$	−0.953755	−	12.7270i	−0.0366558	−	0.489137i	−0.985076	−	0.172121i	$-0.944938\pi$
$677$	−0.953755	−	12.7270i	−0.0366558	−	0.489137i	0.948420	−	0.317016i	$-0.102681\pi$
$678$	18.3476	−	80.3859i	0.704634	−	3.08720i
$679$	0.503412	−	8.44411i	0.0193192	−	0.324055i
$680$	28.3150	+	124.056i	1.08583	+	4.75733i
$681$	48.9967	−	15.1135i	1.87756	−	0.579150i
$682$	−33.3542	−	84.9852i	−1.27720	−	3.25425i
$683$	27.2641	+	25.2974i	1.04323	+	0.967977i	0.999517	−	0.0310668i	$-0.00989047\pi$
$683$	27.2641	+	25.2974i	1.04323	+	0.967977i	0.0437141	+	0.999044i	$0.486081\pi$
$684$	−27.1716	−	18.5253i	−1.03893	−	0.708331i
$685$	−2.50027			−0.0955304
$686$	35.7925	−	36.3961i	1.36657	−	1.38961i
$687$	25.8609			0.986656
$688$	41.4425	+	28.2550i	1.57998	+	1.07721i
$689$	−3.78740	−	3.51419i	−0.144288	−	0.133880i
$690$	32.4405	+	82.6570i	1.23499	+	3.14670i
$691$	6.07543	−	1.87402i	0.231120	−	0.0712912i	−0.177032	−	0.984205i	$-0.556650\pi$
$691$	6.07543	−	1.87402i	0.231120	−	0.0712912i	0.408152	+	0.912914i	$0.366173\pi$
$692$	−10.5337	−	46.1511i	−0.400431	−	1.75440i
$693$	−1.06195	+	17.8129i	−0.0403402	+	0.676657i
$694$	−13.8343	+	60.6119i	−0.525141	+	2.30080i
$695$	−0.335292	−	4.47416i	−0.0127183	−	0.169714i
$696$	28.9286	+	8.92329i	1.09654	+	0.338237i
$697$	0.360905	−	4.81594i	0.0136702	−	0.182417i
$698$	7.32683	−	18.6684i	0.277324	−	0.706611i
$699$	−28.3962	+	13.6749i	−1.07404	+	0.517233i
$700$	−53.5203	+	69.2535i	−2.02288	+	2.61754i
$701$	17.8261	+	8.58461i	0.673284	+	0.324236i	0.739100	−	0.673595i	$-0.235251\pi$
$701$	17.8261	+	8.58461i	0.673284	+	0.324236i	−0.0658166	+	0.997832i	$0.520965\pi$
$702$	4.32628	−	4.01421i	0.163285	−	0.151506i
$703$	−20.4227	+	3.07822i	−0.770256	+	0.116097i
$704$	−58.7201	+	101.706i	−2.21310	+	3.83319i
$705$	22.8531	+	39.5827i	0.860698	+	1.49077i
$706$	25.4094	+	31.8624i	0.956296	+	1.19916i
$707$	5.67135	−	5.42555i	0.213293	−	0.204049i
$708$	−54.3500	+	68.1527i	−2.04260	+	2.56134i
$709$	−29.2373	−	4.40682i	−1.09803	−	0.165502i	−0.425056	−	0.905167i	$-0.639746\pi$
$709$	−29.2373	−	4.40682i	−1.09803	−	0.165502i	−0.672975	+	0.739665i	$0.734984\pi$
$710$	−90.0114	+	61.3687i	−3.37807	+	2.30313i
$711$	17.9200	−	12.2177i	0.672054	−	0.458198i
$712$	120.211	+	18.1188i	4.50508	+	0.679032i
$713$	−27.2101	+	34.1204i	−1.01903	+	1.27782i
$714$	60.5349	−	19.6886i	2.26546	−	0.736828i
$715$	6.78602	+	8.50939i	0.253783	+	0.318233i
$716$	−13.1706	−	22.8121i	−0.492207	−	0.852527i
$717$	21.9073	−	37.9446i	0.818145	−	1.41707i
$718$	6.23772	−	0.940185i	0.232790	−	0.0350874i
$719$	−29.4606	+	27.3354i	−1.09869	+	1.01944i	−0.0989900	+	0.995088i	$0.531561\pi$
$719$	−29.4606	+	27.3354i	−1.09869	+	1.01944i	−0.999703	+	0.0243501i	$0.992248\pi$
$720$	−98.2717	−	47.3252i	−3.66237	−	1.76370i
$721$	3.91871	+	16.0374i	0.145940	+	0.597263i
$722$	26.7208	−	12.8681i	0.994446	−	0.478900i
$723$	17.2894	−	44.0526i	0.642999	−	1.63833i
$724$	−2.35852	+	31.4723i	−0.0876538	+	1.16966i
$725$	7.67668	+	2.36794i	0.285105	+	0.0879432i
$726$	−0.0659656	−	0.880250i	−0.00244821	−	0.0326691i
$727$	4.42139	−	19.3714i	0.163980	−	0.718444i	−0.824345	−	0.566087i	$-0.808457\pi$
$727$	4.42139	−	19.3714i	0.163980	−	0.718444i	0.988326	−	0.152357i	$-0.0486863\pi$
$728$	25.8753	−	4.30469i	0.959003	−	0.159542i
$729$	1.77669	+	7.78421i	0.0658035	+	0.288304i
$730$	7.31489	−	2.25634i	0.270736	−	0.0835111i
$731$	−4.41360	−	11.2457i	−0.163243	−	0.415936i
$732$	−114.415	−	106.161i	−4.22889	−	3.92384i
$733$	−33.8422	−	23.0732i	−1.24999	−	0.852230i	−0.256546	−	0.966532i	$-0.582584\pi$
$733$	−33.8422	−	23.0732i	−1.24999	−	0.852230i	−0.993446	+	0.114302i	$0.963537\pi$
$734$	20.9079			0.771726
$735$	43.7903	+	27.9381i	1.61523	+	1.03051i
$736$	106.960			3.94261
$737$	−30.1903	−	20.5834i	−1.11207	−	0.758199i
$738$	5.14029	+	4.76949i	0.189217	+	0.175567i
$739$	−12.3547	−	31.4793i	−0.454475	−	1.15798i	−0.956137	−	0.292920i	$-0.905373\pi$
$739$	−12.3547	−	31.4793i	−0.454475	−	1.15798i	0.501662	−	0.865064i	$-0.332722\pi$
$740$	−127.108	+	39.2077i	−4.67259	+	1.44130i
$741$	1.43497	+	6.28700i	0.0527149	+	0.230959i
$742$	−36.1684	−	10.5551i	−1.32778	−	0.387489i
$743$	−1.72716	+	7.56719i	−0.0633634	+	0.277613i	−0.996678	−	0.0814474i	$-0.974046\pi$
$743$	−1.72716	+	7.56719i	−0.0633634	+	0.277613i	0.933314	+	0.359061i	$0.116903\pi$
$744$	−16.7316	−	223.268i	−0.613412	−	8.18541i
$745$	27.0251	+	8.33614i	0.990123	+	0.305412i
$746$	3.98211	−	53.1376i	0.145795	−	1.94550i
$747$	8.02211	−	20.4400i	0.293514	−	0.747861i
$748$	64.5638	−	31.0923i	2.36069	−	1.13685i
$749$	−30.5256	+	0.465653i	−1.11538	+	0.0170146i
$750$	−16.7776	−	8.07967i	−0.612632	−	0.295028i
$751$	34.5188	−	32.0288i	1.25961	−	1.16875i	0.281749	−	0.959488i	$-0.409085\pi$
$751$	34.5188	−	32.0288i	1.25961	−	1.16875i	0.977860	−	0.209259i	$-0.0671051\pi$
$752$	98.2581	−	14.8100i	3.58310	−	0.540066i
$753$	10.9922	−	19.0391i	0.400579	−	0.693823i
$754$	−1.87318	−	3.24444i	−0.0682172	−	0.118156i
$755$	33.6049	+	42.1392i	1.22301	+	1.53360i
$756$	11.1326	−	29.6891i	0.404888	−	1.07978i
$757$	12.5447	−	15.7305i	0.455943	−	0.571735i	−0.499723	−	0.866185i	$-0.666565\pi$
$757$	12.5447	−	15.7305i	0.455943	−	0.571735i	0.955667	+	0.294450i	$0.0951365\pi$
$758$	45.5793	+	6.86998i	1.65552	+	0.249529i
$759$	26.5531	−	18.1036i	0.963815	−	0.657118i
$760$	−77.6697	+	52.9543i	−2.81738	+	1.92085i
$761$	−34.3345	−	5.17509i	−1.24462	−	0.187597i	−0.506487	−	0.862248i	$-0.669056\pi$
$761$	−34.3345	−	5.17509i	−1.24462	−	0.187597i	−0.738137	+	0.674651i	$0.764294\pi$
$762$	−23.8118	+	29.8590i	−0.862609	+	1.08168i
$763$	17.4675	+	2.36092i	0.632367	+	0.0854710i
$764$	−83.8188	−	105.105i	−3.03246	−	3.80258i
$765$	13.1354	+	22.7512i	0.474911	+	0.822570i
$766$	−2.45406	+	4.25056i	−0.0886690	+	0.153579i
$767$	6.85525	−	1.03326i	0.247529	−	0.0373090i
$768$	−104.856	+	97.2922i	−3.78367	+	3.51073i
$769$	−5.06430	−	2.43884i	−0.182623	−	0.0879467i	0.340338	−	0.940303i	$-0.389458\pi$
$769$	−5.06430	−	2.43884i	−0.182623	−	0.0879467i	−0.522961	+	0.852356i	$0.675173\pi$
$770$	72.0268	+	33.3426i	2.59567	+	1.20158i
$771$	11.0916	−	5.34142i	0.399453	−	0.192367i
$772$	−38.2624	+	97.4911i	−1.37709	+	3.50878i
$773$	0.495173	−	6.60763i	0.0178101	−	0.237660i	−0.981193	−	0.193028i	$-0.938169\pi$
$773$	0.495173	−	6.60763i	0.0178101	−	0.237660i	0.999003	−	0.0446323i	$-0.0142116\pi$
$774$	16.7615	+	5.17025i	0.602481	+	0.185841i
$775$	−4.44001	−	59.2479i	−0.159490	−	2.12825i
$776$	7.05360	−	30.9038i	0.253209	−	1.10938i
$777$	16.2293	+	39.5661i	0.582223	+	1.41943i
$778$	−19.5833	−	85.7999i	−0.702094	−	3.07608i
$779$	3.40927	−	1.05162i	0.122150	−	0.0376783i
$780$	15.1736	+	38.6617i	0.543302	+	1.38431i
$781$	28.9033	+	26.8183i	1.03424	+	0.959635i
$782$	−38.4167	−	26.1921i	−1.37378	−	0.936626i
$783$	−2.91036			−0.104008
$784$	91.3219	−	66.4311i	3.26150	−	2.37254i
$785$	−71.4304			−2.54946
$786$	11.7767	+	8.02922i	0.420061	+	0.286393i
$787$	−27.8947	−	25.8825i	−0.994338	−	0.922611i	0.00266291	−	0.999996i	$-0.499152\pi$
$787$	−27.8947	−	25.8825i	−0.994338	−	0.922611i	−0.997001	+	0.0773853i	$0.975343\pi$
$788$	32.7160	+	83.3589i	1.16546	+	2.96954i
$789$	−63.1200	+	19.4699i	−2.24713	+	0.693149i
$790$	−21.4662	−	94.0495i	−0.763733	−	3.34613i
$791$	−17.1480	+	30.7760i	−0.609713	+	1.09427i
$792$	−14.8796	+	65.1919i	−0.528724	+	2.31649i
$793$	0.927629	+	12.3784i	0.0329411	+	0.439568i
$794$	−20.9867	−	6.47354i	−0.744790	−	0.229737i
$795$	2.86507	−	38.2317i	0.101614	−	1.35594i
$796$	−19.1401	+	48.7682i	−0.678403	+	1.72854i
$797$	−0.955402	+	0.460098i	−0.0338421	+	0.0162975i	−0.450728	−	0.892661i	$-0.648836\pi$
$797$	−0.955402	+	0.460098i	−0.0338421	+	0.0162975i	0.416886	+	0.908959i	$0.363121\pi$
$798$	29.8779	+	36.3152i	1.05767	+	1.28555i
$799$	−21.5631	−	10.3842i	−0.762847	−	0.367368i
$800$	−106.745	+	99.0445i	−3.77399	+	3.50175i
$801$	24.8182	−	3.74074i	0.876908	−	0.132173i
$802$	1.84537	−	3.19628i	0.0651625	−	0.112865i
$803$	−1.38527	−	2.39936i	−0.0488851	−	0.0846715i
$804$	−86.9352	−	109.013i	−3.06597	−	3.84460i
$805$	−3.41206	−	37.7869i	−0.120259	−	1.33181i
$806$	−17.2750	+	21.6622i	−0.608486	+	0.763017i
$807$	−2.18598	−	0.329484i	−0.0769503	−	0.0115984i
$808$	24.3005	−	16.5678i	0.854888	−	0.582852i
$809$	−7.92323	+	5.40197i	−0.278566	+	0.189923i	−0.694541	−	0.719453i	$-0.744393\pi$
$809$	−7.92323	+	5.40197i	−0.278566	+	0.189923i	0.415975	+	0.909376i	$0.363440\pi$
$810$	98.5862	+	14.8595i	3.46397	+	0.522109i
$811$	25.9798	−	32.5777i	0.912276	−	1.14396i	−0.0768732	−	0.997041i	$-0.524494\pi$
$811$	25.9798	−	32.5777i	0.912276	−	1.14396i	0.989149	−	0.146917i	$-0.0469349\pi$
$812$	−16.8013	−	11.0833i	−0.589609	−	0.388949i
$813$	−18.2251	−	22.8535i	−0.639181	−	0.801507i
$814$	32.6728	+	56.5909i	1.14518	+	1.98351i
$815$	−18.6167	+	32.2451i	−0.652115	+	1.12950i
$816$	139.251	−	20.9886i	4.87474	−	0.734749i
$817$	6.54230	−	6.07036i	0.228886	−	0.212375i
$818$	54.7394	+	26.3611i	1.91392	+	0.921694i
$819$	4.84282	−	2.42386i	0.169222	−	0.0846966i
$820$	20.7027	−	9.96989i	0.722969	−	0.348164i
$821$	17.8992	−	45.6063i	0.624685	−	1.59167i	−0.170535	−	0.985352i	$-0.554550\pi$
$821$	17.8992	−	45.6063i	0.624685	−	1.59167i	0.795221	−	0.606320i	$-0.207355\pi$
$822$	−0.350263	+	4.67393i	−0.0122168	+	0.163022i
$823$	42.7469	+	13.1857i	1.49006	+	0.459624i	0.929605	−	0.368558i	$-0.120148\pi$
$823$	42.7469	+	13.1857i	1.49006	+	0.459624i	0.560459	+	0.828182i	$0.310625\pi$
$824$	4.62314	+	61.6915i	0.161055	+	2.14913i
$825$	−9.73572	+	42.6550i	−0.338954	+	1.48506i
$826$	41.3320	−	29.1130i	1.43813	−	1.01297i
$827$	−8.04313	−	35.2393i	−0.279687	−	1.22539i	−0.898190	−	0.439607i	$-0.855118\pi$
$827$	−8.04313	−	35.2393i	−0.279687	−	1.22539i	0.618503	−	0.785782i	$-0.287739\pi$
$828$	47.5277	−	14.6604i	1.65170	−	0.509483i
$829$	3.19583	+	8.14284i	0.110996	+	0.282813i	0.975569	−	0.219695i	$-0.0705062\pi$
$829$	3.19583	+	8.14284i	0.110996	+	0.282813i	−0.864573	+	0.502507i	$0.832411\pi$
$830$	−71.5939	−	66.4294i	−2.48506	−	2.30580i
$831$	−5.02088	−	3.42317i	−0.174172	−	0.118749i
$832$	35.6412			1.23564
$833$	−27.1866	+	0.829629i	−0.941960	+	0.0287449i
$834$	−8.41083			−0.291243
$835$	49.7303	+	33.9055i	1.72099	+	1.17335i
$836$	38.8075	+	36.0081i	1.34218	+	1.24536i
$837$	7.86365	+	20.0362i	0.271807	+	0.692554i
$838$	−0.258189	+	0.0796409i	−0.00891900	+	0.00275115i
$839$	−6.01670	−	26.3609i	−0.207719	−	0.910078i	−0.966080	−	0.258243i	$-0.916856\pi$
$839$	−6.01670	−	26.3609i	−0.207719	−	0.910078i	0.758361	−	0.651835i	$-0.226001\pi$
$840$	144.689	+	130.202i	4.99224	+	4.49238i
$841$	6.04201	−	26.4718i	0.208345	−	0.912820i
$842$	4.11288	+	54.8826i	0.141739	+	1.89138i
$843$	14.3127	+	4.41487i	0.492954	+	0.152056i
$844$	−0.683369	+	9.11892i	−0.0235225	+	0.313886i
$845$	1.20676	−	3.07477i	0.0415137	−	0.105775i
$846$	31.3088	−	15.0775i	1.07642	−	0.518375i
$847$	−0.0783099	+	0.368951i	−0.00269076	+	0.0126773i
$848$	−75.0967	−	36.1647i	−2.57883	−	1.24190i
$849$	16.2325	−	15.0616i	0.557099	−	0.516912i
$850$	62.5928	−	9.43435i	2.14692	−	0.323596i
$851$	15.6183	−	27.0518i	0.535390	−	0.927322i
$852$	75.2293	+	130.301i	2.57731	+	4.46404i
$853$	11.4029	+	14.2988i	0.390429	+	0.489583i	0.937736	−	0.347349i	$-0.112918\pi$
$853$	11.4029	+	14.2988i	0.390429	+	0.489583i	−0.547306	+	0.836932i	$0.684347\pi$
$854$	46.4510	+	77.6941i	1.58952	+	2.65864i
$855$	−12.1005	+	15.1735i	−0.413828	+	0.518924i
$856$	−113.123	−	17.0506i	−3.86648	−	0.582778i
$857$	21.5188	−	14.6712i	0.735067	−	0.501160i	−0.136985	−	0.990573i	$-0.543741\pi$
$857$	21.5188	−	14.6712i	0.735067	−	0.501160i	0.872052	+	0.489413i	$0.162789\pi$
$858$	16.8579	−	11.4935i	0.575518	−	0.392382i
$859$	−15.3985	−	2.32094i	−0.525389	−	0.0791896i	−0.119008	−	0.992893i	$-0.537971\pi$
$859$	−15.3985	−	2.32094i	−0.525389	−	0.0791896i	−0.406381	+	0.913704i	$0.633209\pi$
$860$	35.8380	−	44.9394i	1.22207	−	1.53242i
$861$	−3.79092	−	6.34070i	−0.129194	−	0.216090i
$862$	−24.2712	−	30.4351i	−0.826681	−	1.03662i
$863$	−5.44859	−	9.43724i	−0.185472	−	0.321247i	0.758263	−	0.651948i	$-0.226048\pi$
$863$	−5.44859	−	9.43724i	−0.185472	−	0.321247i	−0.943736	+	0.330701i	$0.892715\pi$
$864$	26.3766	−	45.6855i	0.897348	−	1.55425i
$865$	−27.6246	+	4.16374i	−0.939266	+	0.141572i
$866$	5.86383	−	5.44084i	0.199261	−	0.184887i
$867$	3.84986	+	1.85400i	0.130748	+	0.0629650i
$868$	−30.9066	+	145.614i	−1.04904	+	4.94247i
$869$	−31.4568	+	15.1488i	−1.06710	+	0.513887i
$870$	10.1564	−	25.8782i	0.344335	−	0.877352i
$871$	−0.828692	+	11.0581i	−0.0280792	+	0.374690i
$872$	63.1163	+	19.4688i	2.13739	+	0.659297i
$873$	−0.489061	−	6.52607i	−0.0165522	−	0.220874i
$874$	7.64339	−	33.4879i	0.258542	−	1.13274i
$875$	5.91459	+	5.32238i	0.199949	+	0.179929i
$876$	−2.35256	−	10.3072i	−0.0794855	−	0.348249i
$877$	−7.93318	+	2.44706i	−0.267884	+	0.0826314i	−0.425787	−	0.904823i	$-0.640003\pi$
$877$	−7.93318	+	2.44706i	−0.267884	+	0.0826314i	0.157903	+	0.987455i	$0.449527\pi$
$878$	21.3807	+	54.4772i	0.721564	+	1.83852i
$879$	34.9058	+	32.3879i	1.17734	+	1.09242i
$880$	145.076	+	98.9111i	4.89051	+	3.33429i
$881$	−13.7807			−0.464283			−0.232142	−	0.972682i	$-0.574573\pi$
$881$	−13.7807			−0.464283			−0.232142	+	0.972682i	$0.574573\pi$
$882$	23.6698	−	31.6130i	0.797003	−	1.06446i
$883$	−13.4740			−0.453437			−0.226718	−	0.973960i	$-0.572800\pi$
$883$	−13.4740			−0.453437			−0.226718	+	0.973960i	$0.572800\pi$
$884$	−17.9689	−	12.2510i	−0.604359	−	0.412045i
$885$	37.7111	+	34.9908i	1.26765	+	1.17620i
$886$	26.4278	+	67.3368i	0.887858	+	2.26223i
$887$	14.5412	−	4.48536i	0.488245	−	0.150604i	−0.0408517	−	0.999165i	$-0.513007\pi$
$887$	14.5412	−	4.48536i	0.488245	−	0.150604i	0.529097	+	0.848562i	$0.322531\pi$
$888$	35.6597	+	156.235i	1.19666	+	5.24292i
$889$	13.3411	−	9.39707i	0.447447	−	0.315168i
$890$	24.8411	−	108.836i	0.832674	−	3.64818i
$891$	−2.69656	−	35.9831i	−0.0903381	−	1.20548i
$892$	22.1212	+	6.82350i	0.740674	+	0.228468i
$893$	1.32129	−	17.6313i	0.0442152	−	0.590011i
$894$	19.3693	−	49.3521i	0.647805	−	1.65058i
$895$	−14.0058	+	6.74485i	−0.468163	+	0.225455i
$896$	115.843	−	57.9803i	3.87005	−	1.93699i
$897$	−8.78729	−	4.23174i	−0.293399	−	0.141294i
$898$	−41.5473	+	38.5503i	−1.38645	+	1.28644i
$899$	13.5107	−	2.03640i	0.450606	−	0.0679179i
$900$	−33.8565	+	58.6411i	−1.12855	+	1.95470i
$901$	10.0377	+	17.3859i	0.334405	+	0.579207i
$902$	−7.03806	−	8.82545i	−0.234342	−	0.293855i
$903$	−15.4257	−	10.1759i	−0.513335	−	0.338633i
$904$	−82.3130	+	103.217i	−2.73769	+	3.43295i
$905$	18.4175	+	2.77600i	0.612219	+	0.0922772i
$906$	83.4816	−	56.9168i	2.77349	−	1.89093i
$907$	−1.95356	+	1.33191i	−0.0648668	+	0.0442254i	−0.595319	−	0.803489i	$-0.702974\pi$
$907$	−1.95356	+	1.33191i	−0.0648668	+	0.0442254i	0.530452	+	0.847715i	$0.322022\pi$
$908$	−126.320	−	19.0396i	−4.19206	−	0.631852i
$909$	3.78588	−	4.74734i	0.125570	−	0.157459i
$910$	−2.16623	−	23.9899i	−0.0718098	−	0.795259i
$911$	−23.7575	−	29.7909i	−0.787120	−	0.987018i	−0.999951	−	0.00992865i	$-0.996840\pi$
$911$	−23.7575	−	29.7909i	−0.787120	−	0.987018i	0.212830	−	0.977089i	$-0.431732\pi$
$912$	52.0170	+	90.0962i	1.72246	+	2.98338i
$913$	−17.6739	+	30.6120i	−0.584919	+	1.01311i
$914$	−56.0106	+	8.44225i	−1.85267	+	0.279245i
$915$	−67.5222	+	62.6515i	−2.23222	+	2.07119i
$916$	−58.0496	−	27.9552i	−1.91801	−	0.923666i
$917$	−3.86938	−	4.70306i	−0.127778	−	0.155309i
$918$	−20.6609	+	9.94976i	−0.681911	+	0.328391i
$919$	3.12627	−	7.96560i	0.103126	−	0.262761i	−0.869993	−	0.493064i	$-0.835877\pi$
$919$	3.12627	−	7.96560i	0.103126	−	0.262761i	0.973119	+	0.230304i	$0.0739719\pi$
$920$	10.6247	−	141.776i	0.350285	−	4.67423i
$921$	−32.7459	−	10.1008i	−1.07901	−	0.332831i
$922$	−2.08998	−	27.8888i	−0.0688297	−	0.918469i
$923$	2.66268	−	11.6660i	0.0876432	−	0.383990i
$924$	53.3546	−	95.7568i	1.75524	−	3.15017i
$925$	9.46289	+	41.4596i	0.311138	+	1.36318i
$926$	1.51495	−	0.467300i	0.0497844	−	0.0153564i
$927$	4.66625	+	11.8894i	0.153260	+	0.390499i
$928$	−24.5477	−	22.7770i	−0.805819	−	0.747691i
$929$	17.6635	+	12.0427i	0.579519	+	0.395110i	0.817303	−	0.576209i	$-0.195468\pi$
$929$	17.6635	+	12.0427i	0.579519	+	0.395110i	−0.237783	+	0.971318i	$0.576421\pi$
$930$	−205.599			−6.74187
$931$	−7.90813	−	18.4720i	−0.259178	−	0.605395i
$932$	78.5229			2.57210
$933$	17.2705	+	11.7749i	0.565412	+	0.385491i
$934$	54.0854	+	50.1839i	1.76973	+	1.64207i
$935$	−15.4505	−	39.3673i	−0.505286	−	1.28745i
$936$	19.3919	−	5.98162i	0.633845	−	0.195515i
$937$	−4.68159	−	20.5114i	−0.152941	−	0.670077i	−0.992021	−	0.126070i	$-0.959764\pi$
$937$	−4.68159	−	20.5114i	−0.152941	−	0.670077i	0.839081	−	0.544007i	$-0.183094\pi$
$938$	30.6886	+	74.8171i	1.00202	+	2.44286i
$939$	14.6837	−	64.3335i	0.479184	−	2.09944i
$940$	−8.50974	−	113.555i	−0.277557	−	3.70374i
$941$	7.74011	+	2.38751i	0.252320	+	0.0778305i	0.418335	−	0.908293i	$-0.362614\pi$
$941$	7.74011	+	2.38751i	0.252320	+	0.0778305i	−0.166015	+	0.986123i	$0.553090\pi$
$942$	−10.0067	+	133.530i	−0.326035	+	4.35064i
$943$	−1.97138	+	5.02300i	−0.0641970	+	0.163571i
$944$	100.766	−	48.5265i	3.27967	−	1.57940i
$945$	−16.9812	−	7.86091i	−0.552397	−	0.255715i
$946$	−25.4408	−	12.2517i	−0.827152	−	0.398336i
$947$	−23.6245	+	21.9204i	−0.767694	+	0.712316i	−0.963318	−	0.268363i	$-0.913517\pi$
$947$	−23.6245	+	21.9204i	−0.767694	+	0.712316i	0.195624	+	0.980679i	$0.437327\pi$
$948$	−131.744	+	19.8572i	−4.27885	+	0.644933i
$949$	−0.420408	+	0.728167i	−0.0136470	+	0.0236373i
$950$	23.3816	+	40.4980i	0.758598	+	1.31393i
$951$	6.76330	+	8.48091i	0.219315	+	0.275012i
$952$	−101.005	−	13.6518i	−3.27358	−	0.442459i
$953$	−18.6378	+	23.3711i	−0.603739	+	0.757064i	−0.985955	−	0.167008i	$-0.946589\pi$
$953$	−18.6378	+	23.3711i	−0.603739	+	0.757064i	0.382217	+	0.924073i	$0.375161\pi$
$954$	−28.8232	−	4.34440i	−0.933187	−	0.140655i
$955$	−65.5515	+	44.6923i	−2.12120	+	1.44621i
$956$	−90.1925	+	61.4922i	−2.91703	+	1.98880i
$957$	−9.94913	−	1.49959i	−0.321610	−	0.0484748i
$958$	66.6117	−	83.5284i	2.15212	−	2.69868i
$959$	0.703145	−	1.87520i	0.0227057	−	0.0605532i
$960$	164.898	+	206.775i	5.32206	+	6.67365i
$961$	−35.0247	−	60.6646i	−1.12983	−	1.95692i
$962$	9.91568	−	17.1745i	0.319694	−	0.553727i
$963$	−23.3550	+	3.52020i	−0.752605	+	0.113437i
$964$	−86.4293	+	80.1947i	−2.78370	+	2.58290i
$965$	55.6863	+	26.8171i	1.79261	+	0.863274i
$966$	−71.1157	+	1.08484i	−2.28811	+	0.0349040i
$967$	−13.8880	+	6.68812i	−0.446609	+	0.215076i	−0.643650	−	0.765320i	$-0.722581\pi$
$967$	−13.8880	+	6.68812i	−0.446609	+	0.215076i	0.197041	+	0.980395i	$0.436867\pi$
$968$	−0.516359	+	1.31566i	−0.0165964	+	0.0422870i
$969$	1.87252	−	24.9870i	0.0601539	−	0.802698i
$970$	−27.8152	−	8.57986i	−0.893093	−	0.275483i
$971$	1.59061	+	21.2253i	0.0510452	+	0.681151i	0.962765	+	0.270339i	$0.0871358\pi$
$971$	1.59061	+	21.2253i	0.0510452	+	0.681151i	−0.911720	+	0.410812i	$0.865245\pi$
$972$	22.6398	−	99.1913i	0.726171	−	3.18156i
$973$	3.44990	+	1.00679i	0.110599	+	0.0322762i
$974$	11.4967	+	50.3701i	0.368377	+	1.61396i
$975$	12.6881	−	3.91377i	0.406345	−	0.125341i
$976$	73.1614	+	186.412i	2.34184	+	5.96691i
$977$	37.7773	+	35.0522i	1.20860	+	1.12142i	0.989320	+	0.145758i	$0.0465622\pi$
$977$	37.7773	+	35.0522i	1.20860	+	1.12142i	0.219283	+	0.975661i	$0.429628\pi$
$978$	57.6700	+	39.3187i	1.84408	+	1.25727i
$979$	−40.4036			−1.29130
$980$	−68.0947	−	110.049i	−2.17521	−	3.51538i
$981$	13.6366			0.435383
$982$	0.772307	+	0.526550i	0.0246453	+	0.0168029i
$983$	−7.99992	−	7.42284i	−0.255158	−	0.236752i	0.542214	−	0.840241i	$-0.317586\pi$
$983$	−7.99992	−	7.42284i	−0.255158	−	0.236752i	−0.797371	+	0.603489i	$0.793777\pi$
$984$	−10.1138	−	25.7695i	−0.322415	−	0.821500i
$985$	50.4998	−	15.5771i	1.60906	−	0.496329i
$986$	3.23921	+	14.1919i	0.103157	+	0.451962i
$987$	−36.1139	+	6.00801i	−1.14952	+	0.191237i
$988$	3.57509	−	15.6635i	0.113739	−	0.498323i
$989$	1.00871	+	13.4603i	0.0320750	+	0.428011i
$990$	58.6764	+	18.0993i	1.86486	+	0.575233i
$991$	−0.0754033	+	1.00619i	−0.00239527	+	0.0319626i	−0.998273	−	0.0587392i	$-0.981292\pi$
$991$	−0.0754033	+	1.00619i	−0.00239527	+	0.0319626i	0.995878	+	0.0907018i	$0.0289110\pi$
$992$	−90.4804	+	230.540i	−2.87276	+	7.31966i
$993$	−19.8232	+	9.54637i	−0.629072	+	0.302945i
$994$	−20.7127	−	84.7669i	−0.656967	−	2.68864i
$995$	27.8561	+	13.4148i	0.883098	+	0.425278i
$996$	−98.8783	+	91.7456i	−3.13308	+	2.90707i
$997$	−50.4419	+	7.60290i	−1.59751	+	0.240786i	−0.886615	−	0.462509i	$-0.846949\pi$
$997$	−50.4419	+	7.60290i	−1.59751	+	0.240786i	−0.710898	+	0.703295i	$0.751711\pi$
$998$	−18.9734	+	32.8630i	−0.600594	+	1.04026i
$999$	−7.70300	−	13.3420i	−0.243712	−	0.422122i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bl.b.53.28	✓	348
49.37	even	21	inner	637.2.bl.b.625.28	yes	348

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.bl.b.53.28	✓	348	1.1	even	1	trivial
637.2.bl.b.625.28	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)

\(f(q)\)	\(=\)	\(q+(2.27734 + 1.55266i) q^{2} +(-1.64682 - 1.52803i) q^{3} +(2.04482 + 5.21012i) q^{4} +(3.15635 - 0.973606i) q^{5} +(-1.37786 - 6.03678i) q^{6} +(-0.157452 + 2.64106i) q^{7} +(-2.20615 + 9.66579i) q^{8} +(0.152964 + 2.04116i) q^{9} +O(q^{10})\)	\(q+(2.27734 + 1.55266i) q^{2} +(-1.64682 - 1.52803i) q^{3} +(2.04482 + 5.21012i) q^{4} +(3.15635 - 0.973606i) q^{5} +(-1.37786 - 6.03678i) q^{6} +(-0.157452 + 2.64106i) q^{7} +(-2.20615 + 9.66579i) q^{8} +(0.152964 + 2.04116i) q^{9} +(8.69976 + 2.68352i) q^{10} +(0.246240 - 3.28585i) q^{11} +(4.59375 - 11.7047i) q^{12} +(-0.900969 + 0.433884i) q^{13} +(-4.45925 + 5.77012i) q^{14} +(-6.68564 - 3.21963i) q^{15} +(-11.8260 + 10.9730i) q^{16} +(3.84221 - 0.579120i) q^{17} +(-2.82088 + 4.88590i) q^{18} +(1.43526 + 2.48594i) q^{19} +(11.5268 + 14.4541i) q^{20} +(4.29491 - 4.10876i) q^{21} +(5.66259 - 7.10066i) q^{22} +(-4.29295 - 0.647058i) q^{23} +(18.4027 - 12.5468i) q^{24} +(4.88346 - 3.32949i) q^{25} +(-2.72548 - 0.410801i) q^{26} +(-1.33502 + 1.67406i) q^{27} +(-14.0822 + 4.58016i) q^{28} +(0.847456 + 1.06268i) q^{29} +(-10.2265 - 17.7127i) q^{30} +(5.02617 - 8.70558i) q^{31} +(-24.3619 + 3.67197i) q^{32} +(-5.42638 + 5.03494i) q^{33} +(9.64918 + 4.64680i) q^{34} +(2.07438 + 8.48942i) q^{35} +(-10.3219 + 4.97076i) q^{36} +(-2.62863 + 6.69764i) q^{37} +(-0.591258 + 7.88979i) q^{38} +(2.14672 + 0.662175i) q^{39} +(2.44727 + 32.6565i) q^{40} +(0.276573 - 1.21174i) q^{41} +(16.1605 - 2.68850i) q^{42} +(-0.691842 - 3.03116i) q^{43} +(17.6232 - 5.43603i) q^{44} +(2.47009 + 6.29369i) q^{45} +(-8.77183 - 8.13907i) q^{46} +(-5.08918 - 3.46974i) q^{47} +36.2423 q^{48} +(-6.95042 - 0.831682i) q^{49} +16.2908 q^{50} +(-7.21234 - 4.91729i) q^{51} +(-4.10291 - 3.80694i) q^{52} +(1.88758 + 4.80947i) q^{53} +(-5.63955 + 1.73957i) q^{54} +(-2.42190 - 10.6110i) q^{55} +(-25.1806 - 7.34848i) q^{56} +(1.43497 - 6.28700i) q^{57} +(0.279966 + 3.73588i) q^{58} +(-6.62469 - 2.04345i) q^{59} +(3.10374 - 41.4166i) q^{60} +(4.53500 - 11.5550i) q^{61} +(24.9631 - 12.0216i) q^{62} +(-5.41491 + 0.0826017i) q^{63} +(-32.1116 - 15.4641i) q^{64} +(-2.42134 + 2.24668i) q^{65} +(-20.1753 + 3.04093i) q^{66} +(5.54457 - 9.60347i) q^{67} +(10.8739 + 18.8342i) q^{68} +(6.08100 + 7.62533i) q^{69} +(-8.45714 + 22.5541i) q^{70} +(-7.46067 + 9.35538i) q^{71} +(-20.0668 - 3.02459i) q^{72} +(0.694714 - 0.473648i) q^{73} +(-16.3854 + 11.1714i) q^{74} +(-13.1297 - 1.97899i) q^{75} +(-10.0172 + 12.5612i) q^{76} +(8.63936 + 1.16770i) q^{77} +(3.86067 + 4.84113i) q^{78} +(-5.29798 - 9.17638i) q^{79} +(-26.6438 + 46.1484i) q^{80} +(10.8286 - 1.63215i) q^{81} +(2.51128 - 2.33013i) q^{82} +(-9.66512 - 4.65448i) q^{83} +(30.1895 + 13.9753i) q^{84} +(11.5635 - 5.56870i) q^{85} +(3.13080 - 7.97716i) q^{86} +(0.228189 - 3.04497i) q^{87} +(31.2171 + 9.62919i) q^{88} +(-0.916329 - 12.2276i) q^{89} +(-4.14674 + 18.1681i) q^{90} +(-1.00405 - 2.44783i) q^{91} +(-5.40707 - 23.6899i) q^{92} +(-21.5795 + 6.65641i) q^{93} +(-6.20243 - 15.8035i) q^{94} +(6.95050 + 6.44912i) q^{95} +(45.7305 + 31.1786i) q^{96} -3.19724 q^{97} +(-14.5371 - 12.6857i) q^{98} +6.74460 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

Modular forms

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