LMFDB - Embedded newform 637.2.w.b.92.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(92,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("637.92");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.w (of order $7$, degree $6$, 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:	$174$
Relative dimension:	$29$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			92.15
Character	$\chi$	$=$	637.92
Dual form			637.2.w.b.547.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.153433 - 0.192399i) q^{2} +(-1.67003 - 0.804242i) q^{3} +(0.431566 + 1.89082i) q^{4} +(0.217813 + 0.104893i) q^{5} +(-0.410972 + 0.197914i) q^{6} +(-2.59813 - 0.499745i) q^{7} +(0.873441 + 0.420627i) q^{8} +(0.271713 + 0.340717i) q^{9} +O(q^{10})$	\(q+(0.153433 - 0.192399i) q^{2} +(-1.67003 - 0.804242i) q^{3} +(0.431566 + 1.89082i) q^{4} +(0.217813 + 0.104893i) q^{5} +(-0.410972 + 0.197914i) q^{6} +(-2.59813 - 0.499745i) q^{7} +(0.873441 + 0.420627i) q^{8} +(0.271713 + 0.340717i) q^{9} +(0.0536009 - 0.0258129i) q^{10} +(-0.00113574 + 0.00142418i) q^{11} +(0.799947 - 3.50480i) q^{12} +(0.623490 - 0.781831i) q^{13} +(-0.494788 + 0.423199i) q^{14} +(-0.279393 - 0.350348i) q^{15} +(-3.27981 + 1.57947i) q^{16} +(1.38330 - 6.06065i) q^{17} +0.107243 q^{18} +7.36841 q^{19} +(-0.104333 + 0.457112i) q^{20} +(3.93702 + 2.92411i) q^{21} +(9.97495e-5 + 0.000437031i) q^{22} +(-1.18833 - 5.20643i) q^{23} +(-1.12038 - 1.40492i) q^{24} +(-3.08101 - 3.86346i) q^{25} +(-0.0547596 - 0.239917i) q^{26} +(1.05764 + 4.63382i) q^{27} +(-0.176338 - 5.12825i) q^{28} +(-0.125700 + 0.550728i) q^{29} -0.110275 q^{30} +9.65003 q^{31} +(-0.630786 + 2.76366i) q^{32} +(0.00304210 - 0.00146500i) q^{33} +(-0.953818 - 1.19605i) q^{34} +(-0.513485 - 0.381376i) q^{35} +(-0.526971 + 0.660801i) q^{36} +(1.63503 - 7.16355i) q^{37} +(1.13056 - 1.41767i) q^{38} +(-1.67003 + 0.804242i) q^{39} +(0.146126 + 0.183236i) q^{40} +(-9.56342 - 4.60550i) q^{41} +(1.16666 - 0.308824i) q^{42} +(-3.15791 + 1.52077i) q^{43} +(-0.00318300 - 0.00153285i) q^{44} +(0.0234436 + 0.102713i) q^{45} +(-1.18404 - 0.570204i) q^{46} +(5.99487 - 7.51734i) q^{47} +6.74765 q^{48} +(6.50051 + 2.59680i) q^{49} -1.21605 q^{50} +(-7.18439 + 9.00893i) q^{51} +(1.74738 + 0.841492i) q^{52} +(-0.930574 - 4.07711i) q^{53} +(1.05382 + 0.507492i) q^{54} +(-0.000396765 + 0.000191072i) q^{55} +(-2.05910 - 1.52934i) q^{56} +(-12.3054 - 5.92598i) q^{57} +(0.0866729 + 0.108684i) q^{58} +(-2.09108 + 1.00701i) q^{59} +(0.541867 - 0.679480i) q^{60} +(0.251447 - 1.10166i) q^{61} +(1.48063 - 1.85665i) q^{62} +(-0.535673 - 1.02101i) q^{63} +(-4.10446 - 5.14682i) q^{64} +(0.217813 - 0.104893i) q^{65} +(0.000184895 - 0.000810077i) q^{66} -5.22001 q^{67} +12.0566 q^{68} +(-2.20268 + 9.65058i) q^{69} +(-0.152162 + 0.0402782i) q^{70} +(0.583921 + 2.55832i) q^{71} +(0.0940104 + 0.411887i) q^{72} +(-4.06927 - 5.10271i) q^{73} +(-1.12739 - 1.41370i) q^{74} +(2.03821 + 8.92996i) q^{75} +(3.17995 + 13.9323i) q^{76} +(0.00366253 - 0.00313261i) q^{77} +(-0.101502 + 0.444708i) q^{78} +0.670602 q^{79} -0.880059 q^{80} +(2.25135 - 9.86380i) q^{81} +(-2.35344 + 1.13336i) q^{82} +(7.51906 + 9.42860i) q^{83} +(-3.82986 + 8.70613i) q^{84} +(0.937021 - 1.17499i) q^{85} +(-0.191933 + 0.840915i) q^{86} +(0.652841 - 0.818637i) q^{87} +(-0.00159105 + 0.000766210i) q^{88} +(-9.78147 - 12.2656i) q^{89} +(0.0233590 + 0.0112491i) q^{90} +(-2.01062 + 1.71971i) q^{91} +(9.33155 - 4.49384i) q^{92} +(-16.1158 - 7.76096i) q^{93} +(-0.526515 - 2.30681i) q^{94} +(1.60493 + 0.772894i) q^{95} +(3.27608 - 4.10807i) q^{96} -12.5101 q^{97} +(1.49701 - 0.852256i) q^{98} -0.000793838 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 174 q - 3 q^{2} - 31 q^{4} - 4 q^{5} - 2 q^{6} + 9 q^{7} - 15 q^{8} - 31 q^{9}+O(q^{10}) $ 174 * q - 3 * q^2 - 31 * q^4 - 4 * q^5 - 2 * q^6 + 9 * q^7 - 15 * q^8 - 31 * q^9	\( 174 q - 3 q^{2} - 31 q^{4} - 4 q^{5} - 2 q^{6} + 9 q^{7} - 15 q^{8} - 31 q^{9} - 10 q^{10} - 5 q^{11} + 25 q^{12} - 29 q^{13} + 15 q^{14} - 10 q^{15} - 51 q^{16} - 9 q^{17} + 44 q^{18} + 24 q^{19} + 63 q^{20} - 28 q^{21} - 8 q^{22} - 13 q^{23} - 48 q^{24} - 49 q^{25} - 3 q^{26} - 9 q^{27} - 44 q^{28} + 2 q^{29} - 22 q^{30} + 10 q^{31} + 24 q^{32} - 26 q^{33} + 118 q^{34} + 5 q^{35} - 55 q^{36} - 32 q^{37} + 16 q^{38} + 42 q^{40} - 14 q^{41} + 4 q^{42} - 50 q^{43} + 35 q^{44} - q^{45} + 4 q^{46} - 24 q^{47} - 116 q^{48} - 25 q^{49} + 156 q^{50} + 12 q^{51} - 31 q^{52} - 30 q^{53} - 78 q^{54} + 25 q^{55} + 3 q^{56} - 63 q^{57} - 12 q^{58} - 4 q^{59} + 128 q^{60} - 42 q^{61} - 38 q^{62} - 85 q^{63} - 105 q^{64} - 4 q^{65} + 15 q^{66} + 94 q^{67} + 214 q^{68} + 32 q^{69} - 57 q^{70} - 29 q^{71} - 64 q^{72} - 66 q^{73} - 90 q^{74} + 131 q^{75} - 21 q^{76} - 82 q^{77} + 19 q^{78} + 6 q^{79} + 22 q^{80} + 49 q^{81} - 50 q^{82} + 25 q^{83} + 89 q^{84} - 86 q^{85} - 28 q^{86} + 24 q^{87} + 48 q^{88} - 50 q^{89} - 155 q^{90} - 5 q^{91} - 98 q^{92} + 89 q^{93} - 28 q^{94} - 130 q^{95} - 105 q^{96} - 42 q^{97} + 195 q^{98} + 438 q^{99}+O(q^{100}) \) 174 * q - 3 * q^2 - 31 * q^4 - 4 * q^5 - 2 * q^6 + 9 * q^7 - 15 * q^8 - 31 * q^9 - 10 * q^10 - 5 * q^11 + 25 * q^12 - 29 * q^13 + 15 * q^14 - 10 * q^15 - 51 * q^16 - 9 * q^17 + 44 * q^18 + 24 * q^19 + 63 * q^20 - 28 * q^21 - 8 * q^22 - 13 * q^23 - 48 * q^24 - 49 * q^25 - 3 * q^26 - 9 * q^27 - 44 * q^28 + 2 * q^29 - 22 * q^30 + 10 * q^31 + 24 * q^32 - 26 * q^33 + 118 * q^34 + 5 * q^35 - 55 * q^36 - 32 * q^37 + 16 * q^38 + 42 * q^40 - 14 * q^41 + 4 * q^42 - 50 * q^43 + 35 * q^44 - q^45 + 4 * q^46 - 24 * q^47 - 116 * q^48 - 25 * q^49 + 156 * q^50 + 12 * q^51 - 31 * q^52 - 30 * q^53 - 78 * q^54 + 25 * q^55 + 3 * q^56 - 63 * q^57 - 12 * q^58 - 4 * q^59 + 128 * q^60 - 42 * q^61 - 38 * q^62 - 85 * q^63 - 105 * q^64 - 4 * q^65 + 15 * q^66 + 94 * q^67 + 214 * q^68 + 32 * q^69 - 57 * q^70 - 29 * q^71 - 64 * q^72 - 66 * q^73 - 90 * q^74 + 131 * q^75 - 21 * q^76 - 82 * q^77 + 19 * q^78 + 6 * q^79 + 22 * q^80 + 49 * q^81 - 50 * q^82 + 25 * q^83 + 89 * q^84 - 86 * q^85 - 28 * q^86 + 24 * q^87 + 48 * q^88 - 50 * q^89 - 155 * q^90 - 5 * q^91 - 98 * q^92 + 89 * q^93 - 28 * q^94 - 130 * q^95 - 105 * q^96 - 42 * q^97 + 195 * q^98 + 438 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$248$
$\chi(n)$	$1$	$e\left(\frac{1}{7}\right)$

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 $

$2$	0.153433	−	0.192399i	0.108493	−	0.136047i	−0.724620	−	0.689149i	$-0.757985\pi$
$2$	0.153433	−	0.192399i	0.108493	−	0.136047i	0.833113	+	0.553102i	$0.186556\pi$
$3$	−1.67003	−	0.804242i	−0.964190	−	0.464330i	−0.115551	−	0.993302i	$-0.536863\pi$
$3$	−1.67003	−	0.804242i	−0.964190	−	0.464330i	−0.848639	+	0.528972i	$0.822578\pi$
$4$	0.431566	+	1.89082i	0.215783	+	0.945408i
$5$	0.217813	+	0.104893i	0.0974088	+	0.0469096i	0.481954	−	0.876197i	$-0.339927\pi$
$5$	0.217813	+	0.104893i	0.0974088	+	0.0469096i	−0.384545	+	0.923106i	$0.625642\pi$
$6$	−0.410972	+	0.197914i	−0.167779	+	0.0807980i
$7$	−2.59813	−	0.499745i	−0.981999	−	0.188886i
$7$	−2.59813	−	0.499745i	−0.981999	−	0.188886i
$8$	0.873441	+	0.420627i	0.308808	+	0.148714i
$9$	0.271713	+	0.340717i	0.0905710	+	0.113572i
$10$	0.0536009	−	0.0258129i	0.0169501	−	0.00816274i
$11$	−0.00113574	+	0.00142418i	−0.000342439	+	0.000429405i	−0.782003	−	0.623275i	$-0.785802\pi$
$11$	−0.00113574	+	0.00142418i	−0.000342439	+	0.000429405i	0.781660	+	0.623704i	$0.214373\pi$
$12$	0.799947	−	3.50480i	0.230925	−	1.01175i
$13$	0.623490	−	0.781831i	0.172925	−	0.216841i
$13$	0.623490	−	0.781831i	0.172925	−	0.216841i
$14$	−0.494788	+	0.423199i	−0.132238	+	0.113105i
$15$	−0.279393	−	0.350348i	−0.0721391	−	0.0904595i
$16$	−3.27981	+	1.57947i	−0.819952	+	0.394868i
$17$	1.38330	−	6.06065i	0.335500	−	1.46992i	−0.472809	−	0.881165i	$-0.656760\pi$
$17$	1.38330	−	6.06065i	0.335500	−	1.46992i	0.808309	−	0.588758i	$-0.200383\pi$
$18$	0.107243			0.0252775
$19$	7.36841			1.69043			0.845214	−	0.534428i	$-0.179473\pi$
$19$	7.36841			1.69043			0.845214	+	0.534428i	$0.179473\pi$
$20$	−0.104333	+	0.457112i	−0.0233295	+	0.102213i
$21$	3.93702	+	2.92411i	0.859129	+	0.638093i
$22$	9.97495e−5	0	0.000437031i	2.12667e−5	0	9.31754e-5i
$23$	−1.18833	−	5.20643i	−0.247785	−	1.08562i	−0.933734	−	0.357967i	$-0.883470\pi$
$23$	−1.18833	−	5.20643i	−0.247785	−	1.08562i	0.685950	−	0.727649i	$-0.259387\pi$
$24$	−1.12038	−	1.40492i	−0.228697	−	0.286777i
$25$	−3.08101	−	3.86346i	−0.616202	−	0.772693i
$26$	−0.0547596	−	0.239917i	−0.0107392	−	0.0470517i
$27$	1.05764	+	4.63382i	0.203543	+	0.891779i
$28$	−0.176338	−	5.12825i	−0.0333248	−	0.969148i
$29$	−0.125700	+	0.550728i	−0.0233419	+	0.102268i	−0.985257	−	0.171081i	$-0.945274\pi$
$29$	−0.125700	+	0.550728i	−0.0233419	+	0.102268i	0.961915	+	0.273348i	$0.0881312\pi$
$30$	−0.110275			−0.0201333
$31$	9.65003			1.73320			0.866598	−	0.499007i	$-0.166302\pi$
$31$	9.65003			1.73320			0.866598	+	0.499007i	$0.166302\pi$
$32$	−0.630786	+	2.76366i	−0.111508	+	0.488550i
$33$	0.00304210	−	0.00146500i	0.000529562	−	0.000255024i
$34$	−0.953818	−	1.19605i	−0.163578	−	0.205121i
$35$	−0.513485	−	0.381376i	−0.0867948	−	0.0644643i
$36$	−0.526971	+	0.660801i	−0.0878286	+	0.110134i
$37$	1.63503	−	7.16355i	0.268798	−	1.17768i	−0.642615	−	0.766189i	$-0.722151\pi$
$37$	1.63503	−	7.16355i	0.268798	−	1.17768i	0.911413	−	0.411492i	$-0.134992\pi$
$38$	1.13056	−	1.41767i	0.183400	−	0.229977i
$39$	−1.67003	+	0.804242i	−0.267418	+	0.128782i
$40$	0.146126	+	0.183236i	0.0231045	+	0.0289721i
$41$	−9.56342	−	4.60550i	−1.49356	−	0.719258i	−0.504039	−	0.863681i	$-0.668153\pi$
$41$	−9.56342	−	4.60550i	−1.49356	−	0.719258i	−0.989516	+	0.144422i	$0.953868\pi$
$42$	1.16666	−	0.308824i	0.180020	−	0.0476525i
$43$	−3.15791	+	1.52077i	−0.481577	+	0.231915i	−0.658890	−	0.752239i	$-0.728974\pi$
$43$	−3.15791	+	1.52077i	−0.481577	+	0.231915i	0.177313	+	0.984155i	$0.443260\pi$
$44$	−0.00318300	−	0.00153285i	−0.000479856	−	0.000231086i
$45$	0.0234436	+	0.102713i	0.00349477	+	0.0153116i
$46$	−1.18404	−	0.570204i	−0.174577	−	0.0840720i
$47$	5.99487	−	7.51734i	0.874442	−	1.09652i	−0.120160	−	0.992755i	$-0.538341\pi$
$47$	5.99487	−	7.51734i	0.874442	−	1.09652i	0.994602	−	0.103761i	$-0.0330879\pi$
$48$	6.74765			0.973939
$49$	6.50051	+	2.59680i	0.928644	+	0.370971i
$50$	−1.21605			−0.171976
$51$	−7.18439	+	9.00893i	−1.00602	+	1.26150i
$52$	1.74738	+	0.841492i	0.242317	+	0.116694i
$53$	−0.930574	−	4.07711i	−0.127824	−	0.560034i	−0.997762	−	0.0668722i	$-0.978698\pi$
$53$	−0.930574	−	4.07711i	−0.127824	−	0.560034i	0.869937	−	0.493162i	$-0.164159\pi$
$54$	1.05382	+	0.507492i	0.143406	+	0.0690609i
$55$	−0.000396765	0	0.000191072i	−5.34998e−5	0	2.57642e-5i
$56$	−2.05910	−	1.52934i	−0.275159	−	0.204367i
$57$	−12.3054	−	5.92598i	−1.62989	−	0.784916i
$58$	0.0866729	+	0.108684i	0.0113807	+	0.0142710i
$59$	−2.09108	+	1.00701i	−0.272236	+	0.131102i	−0.565021	−	0.825076i	$-0.691132\pi$
$59$	−2.09108	+	1.00701i	−0.272236	+	0.131102i	0.292785	+	0.956178i	$0.405418\pi$
$60$	0.541867	−	0.679480i	0.0699547	−	0.0877205i
$61$	0.251447	−	1.10166i	0.0321945	−	0.141054i	−0.956276	−	0.292465i	$-0.905525\pi$
$61$	0.251447	−	1.10166i	0.0321945	−	0.141054i	0.988471	+	0.151411i	$0.0483817\pi$
$62$	1.48063	−	1.85665i	0.188041	−	0.235795i
$63$	−0.535673	−	1.02101i	−0.0674884	−	0.128636i
$64$	−4.10446	−	5.14682i	−0.513057	−	0.643353i
$65$	0.217813	−	0.104893i	0.0270163	−	0.0130104i
$66$	0.000184895	0	0.000810077i	2.27590e−5	0	9.97135e-5i
$67$	−5.22001			−0.637726			−0.318863	−	0.947801i	$-0.603301\pi$
$67$	−5.22001			−0.637726			−0.318863	+	0.947801i	$0.603301\pi$
$68$	12.0566			1.46207
$69$	−2.20268	+	9.65058i	−0.265172	+	1.16179i
$70$	−0.152162	+	0.0402782i	−0.0181868	+	0.00481417i
$71$	0.583921	+	2.55832i	0.0692987	+	0.303617i	0.997685	−	0.0679981i	$-0.0216612\pi$
$71$	0.583921	+	2.55832i	0.0692987	+	0.303617i	−0.928387	+	0.371615i	$0.878804\pi$
$72$	0.0940104	+	0.411887i	0.0110792	+	0.0485413i
$73$	−4.06927	−	5.10271i	−0.476272	−	0.597227i	0.484422	−	0.874834i	$-0.339030\pi$
$73$	−4.06927	−	5.10271i	−0.476272	−	0.597227i	−0.960695	+	0.277608i	$0.910458\pi$
$74$	−1.12739	−	1.41370i	−0.131057	−	0.164340i
$75$	2.03821	+	8.92996i	0.235352	+	1.03114i
$76$	3.17995	+	13.9323i	0.364766	+	1.59814i
$77$	0.00366253	−	0.00313261i	0.000417384	−	0.000356994i
$78$	−0.101502	+	0.444708i	−0.0114928	+	0.0503533i
$79$	0.670602			0.0754487			0.0377243	−	0.999288i	$-0.487989\pi$
$79$	0.670602			0.0754487			0.0377243	+	0.999288i	$0.487989\pi$
$80$	−0.880059			−0.0983936
$81$	2.25135	−	9.86380i	0.250150	−	1.09598i
$82$	−2.35344	+	1.13336i	−0.259894	+	0.125158i
$83$	7.51906	+	9.42860i	0.825324	+	1.03492i	0.998745	+	0.0500755i	$0.0159462\pi$
$83$	7.51906	+	9.42860i	0.825324	+	1.03492i	−0.173422	+	0.984848i	$0.555482\pi$
$84$	−3.82986	+	8.70613i	−0.417872	+	0.949916i
$85$	0.937021	−	1.17499i	0.101634	−	0.127445i
$86$	−0.191933	+	0.840915i	−0.0206967	+	0.0906782i
$87$	0.652841	−	0.818637i	0.0699919	−	0.0877671i
$88$	−0.00159105		0.000766210i	−0.000169607		8.16783e-5i
$89$	−9.78147	−	12.2656i	−1.03683	−	1.30015i	−0.952772	−	0.303688i	$-0.901782\pi$
$89$	−9.78147	−	12.2656i	−1.03683	−	1.30015i	−0.0840621	−	0.996461i	$-0.526789\pi$
$90$	0.0233590	+	0.0112491i	0.00246225	+	0.00118576i
$91$	−2.01062	+	1.71971i	−0.210770	+	0.180275i
$92$	9.33155	−	4.49384i	0.972881	−	0.468515i
$93$	−16.1158	−	7.76096i	−1.67113	−	0.804774i
$94$	−0.526515	−	2.30681i	−0.0543059	−	0.237930i
$95$	1.60493	+	0.772894i	0.164663	+	0.0792973i
$96$	3.27608	−	4.10807i	0.334363	−	0.419278i
$97$	−12.5101			−1.27021			−0.635106	−	0.772425i	$-0.719044\pi$
$97$	−12.5101			−1.27021			−0.635106	+	0.772425i	$0.719044\pi$
$98$	1.49701	−	0.852256i	0.151221	−	0.0860909i
$99$	−0.000793838	0		−7.97837e−5	0
$100$	5.97544	−	7.49296i	0.597544	−	0.749296i
$101$	8.79037	+	4.23322i	0.874675	+	0.421221i	0.816677	−	0.577096i	$-0.195814\pi$
$101$	8.79037	+	4.23322i	0.874675	+	0.421221i	0.0579981	+	0.998317i	$0.481528\pi$
$102$	0.630987	+	2.76454i	0.0624770	+	0.273730i
$103$	1.49912	+	0.721936i	0.147712	+	0.0711345i	0.506280	−	0.862369i	$-0.331020\pi$
$103$	1.49912	+	0.721936i	0.147712	+	0.0711345i	−0.358567	+	0.933504i	$0.616735\pi$
$104$	0.873441	−	0.420627i	0.0856480	−	0.0412459i
$105$	0.550814	+	1.04987i	0.0537540	+	0.102457i
$106$	−0.927213	−	0.446522i	−0.0900589	−	0.0433701i
$107$	−1.96575	−	2.46497i	−0.190036	−	0.238297i	0.677681	−	0.735356i	$-0.262985\pi$
$107$	−1.96575	−	2.46497i	−0.190036	−	0.238297i	−0.867717	+	0.497058i	$0.834414\pi$
$108$	−8.30525	+	3.99960i	−0.799173	+	0.384862i
$109$	−5.39802	+	6.76891i	−0.517037	+	0.648344i	−0.969977	−	0.243197i	$-0.921804\pi$
$109$	−5.39802	+	6.76891i	−0.517037	+	0.648344i	0.452940	+	0.891541i	$0.350375\pi$
$110$	−2.41148e−5	0	0.000105654i	−2.29926e−6	0	1.00737e-5i
$111$	−8.49178	+	10.6484i	−0.806004	+	1.01070i
$112$	9.31069	−	2.46460i	0.879777	−	0.232883i
$113$	11.6161	+	14.5662i	1.09275	+	1.37027i	0.923008	+	0.384781i	$0.125723\pi$
$113$	11.6161	+	14.5662i	1.09275	+	1.37027i	0.169745	+	0.985488i	$0.445705\pi$
$114$	−3.02821	+	1.45831i	−0.283618	+	0.136583i
$115$	0.287284	−	1.25867i	0.0267894	−	0.117372i
$116$	−1.09557			−0.101721
$117$	0.435794			0.0402892
$118$	−0.127093	+	0.556831i	−0.0116999	+	0.0512605i
$119$	−6.62278	+	15.0550i	−0.607109	+	1.38009i
$120$	−0.0966678	−	0.423529i	−0.00882452	−	0.0386627i
$121$	2.44773	+	10.7242i	0.222521	+	0.974928i
$122$	−0.173378	−	0.217410i	−0.0156969	−	0.0196833i
$123$	12.2672	+	15.3826i	1.10610	+	1.38700i
$124$	4.16463	+	18.2464i	0.373994	+	1.63858i
$125$	−0.534809	−	2.34315i	−0.0478347	−	0.209578i
$126$	−0.278632	−	0.0535943i	−0.0248225	−	0.00477456i
$127$	−4.18219	+	18.3234i	−0.371109	+	1.62594i	0.352560	+	0.935789i	$0.385311\pi$
$127$	−4.18219	+	18.3234i	−0.371109	+	1.62594i	−0.723670	+	0.690147i	$0.757546\pi$
$128$	−7.28946			−0.644303
$129$	6.49687			0.572017
$130$	0.0132383	−	0.0580009i	0.00116108	−	0.00508702i
$131$	11.5439	−	5.55925i	1.00860	−	0.485714i	0.144749	−	0.989468i	$-0.453763\pi$
$131$	11.5439	−	5.55925i	1.00860	−	0.485714i	0.863847	+	0.503754i	$0.168048\pi$
$132$	0.00408291	+	0.00511981i	0.000355372	+	0.000445622i
$133$	−19.1440	−	3.68232i	−1.66000	−	0.319298i
$134$	−0.800922	+	1.00432i	−0.0691891	+	0.0867604i
$135$	−0.255688	+	1.12024i	−0.0220061	+	0.0964152i
$136$	3.75751	−	4.71177i	0.322204	−	0.404031i
$137$	13.1265	−	6.32140i	1.12147	−	0.540074i	0.221127	−	0.975245i	$-0.429026\pi$
$137$	13.1265	−	6.32140i	1.12147	−	0.540074i	0.900348	+	0.435171i	$0.143312\pi$
$138$	1.51880	+	1.90451i	0.129289	+	0.162123i
$139$	12.5649	+	6.05094i	1.06574	+	0.513234i	0.882732	−	0.469877i	$-0.155702\pi$
$139$	12.5649	+	6.05094i	1.06574	+	0.513234i	0.183010	+	0.983111i	$0.441416\pi$
$140$	0.499509	−	1.13549i	0.0422162	−	0.0959667i
$141$	−16.0574	+	7.73282i	−1.35227	+	0.651221i
$142$	0.581812	+	0.280186i	0.0488245	+	0.0235127i
$143$	0.000405342		0.00177592i	3.38964e−5		0.000148510i
$144$	−1.42932	−	0.688325i	−0.119110	−	0.0573604i
$145$	−0.0851466	+	0.106770i	−0.00707104	+	0.00886680i
$146$	−1.60612			−0.132923
$147$	−8.76757	−	9.56471i	−0.723137	−	0.788884i
$148$	14.2506			1.17139
$149$	1.29488	−	1.62373i	0.106081	−	0.133021i	−0.725957	−	0.687740i	$-0.758603\pi$
$149$	1.29488	−	1.62373i	0.106081	−	0.133021i	0.832038	+	0.554719i	$0.187174\pi$
$150$	2.03084	+	0.978002i	0.165818	+	0.0798536i
$151$	0.788617	+	3.45516i	0.0641768	+	0.281177i	0.996826	−	0.0796068i	$-0.0253665\pi$
$151$	0.788617	+	3.45516i	0.0641768	+	0.281177i	−0.932650	+	0.360784i	$0.882509\pi$
$152$	6.43587	+	3.09935i	0.522018	+	0.251391i
$153$	2.44083	−	1.17544i	0.197329	−	0.0950289i
$154$	−4.07577e−5	−	0.00118531i	−3.28435e−6	−	9.55151e-5i
$155$	2.10190	+	1.01222i	0.168828	+	0.0813035i
$156$	−2.24140	−	2.81063i	−0.179456	−	0.225030i
$157$	−6.23964	+	3.00485i	−0.497978	+	0.239813i	−0.665975	−	0.745974i	$-0.731984\pi$
$157$	−6.23964	+	3.00485i	−0.497978	+	0.239813i	0.167997	+	0.985787i	$0.446270\pi$
$158$	0.102893	−	0.129023i	0.00818569	−	0.0102645i
$159$	−1.72490	+	7.55729i	−0.136794	+	0.599332i
$160$	−0.427282	+	0.535794i	−0.0337796	+	0.0423582i
$161$	0.485554	+	14.1208i	0.0382670	+	1.11288i
$162$	−1.55235	−	1.94659i	−0.121964	−	0.152938i
$163$	−8.98089	+	4.32497i	−0.703437	+	0.338758i	−0.751176	−	0.660102i	$-0.770513\pi$
$163$	−8.98089	+	4.32497i	−0.703437	+	0.338758i	0.0477384	+	0.998860i	$0.484799\pi$
$164$	4.58090	−	20.0702i	0.357708	−	1.56722i
$165$	0.000816277	0		6.35471e−5	0
$166$	2.96772			0.230340
$167$	3.12296	−	13.6826i	0.241662	−	1.05879i	−0.697842	−	0.716251i	$-0.745856\pi$
$167$	3.12296	−	13.6826i	0.241662	−	1.05879i	0.939504	−	0.342538i	$-0.111286\pi$
$168$	2.20880	+	4.21006i	0.170412	+	0.324813i
$169$	−0.222521	−	0.974928i	−0.0171170	−	0.0749945i
$170$	−0.0822963	−	0.360564i	−0.00631184	−	0.0276540i
$171$	2.00209	+	2.51054i	0.153104	+	0.191986i
$172$	−4.23835	−	5.31472i	−0.323171	−	0.405243i
$173$	−4.14494	−	18.1602i	−0.315134	−	1.38069i	−0.845976	−	0.533222i	$-0.820981\pi$
$173$	−4.14494	−	18.1602i	−0.315134	−	1.38069i	0.530841	−	0.847471i	$-0.321876\pi$
$174$	−0.0573375	−	0.251212i	−0.00434674	−	0.0190443i
$175$	6.07410	+	11.5775i	0.459159	+	0.875175i
$176$	0.00147557	−	0.00646490i	0.000111225	−	0.000487310i
$177$	4.30205			0.323362
$178$	−3.86068			−0.289370
$179$	3.26102	−	14.2875i	0.243740	−	1.06790i	−0.693841	−	0.720129i	$-0.744083\pi$
$179$	3.26102	−	14.2875i	0.243740	−	1.06790i	0.937581	−	0.347767i	$-0.113060\pi$
$180$	−0.184094	+	0.0886552i	−0.0137216	+	0.00660797i
$181$	7.34270	+	9.20746i	0.545779	+	0.684385i	0.975858	−	0.218406i	$-0.0700858\pi$
$181$	7.34270	+	9.20746i	0.545779	+	0.684385i	−0.430079	+	0.902791i	$0.641514\pi$
$182$	0.0223748	+	0.650701i	0.00165853	+	0.0482332i
$183$	−1.30593	+	1.63758i	−0.0965370	+	0.121054i
$184$	1.15203	−	5.04736i	0.0849285	−	0.372096i
$185$	1.10754	−	1.38881i	0.0814278	−	0.102107i
$186$	−3.96590	+	1.90987i	−0.290794	+	0.140039i
$187$	0.00706036	+	0.00885341i	0.000516305	+	0.000647425i
$188$	16.8011	+	8.09097i	1.22534	+	0.590095i
$189$	−0.432152	−	12.5678i	−0.0314344	−	0.914172i
$190$	0.394953	−	0.190200i	0.0286529	−	0.0137985i
$191$	−4.38948	−	2.11386i	−0.317612	−	0.152954i	0.268285	−	0.963340i	$-0.413543\pi$
$191$	−4.38948	−	2.11386i	−0.317612	−	0.152954i	−0.585896	+	0.810386i	$0.699257\pi$
$192$	2.71526	+	11.8963i	0.195957	+	0.858542i
$193$	16.1542	+	7.77948i	1.16281	+	0.559979i	0.912857	−	0.408279i	$-0.133871\pi$
$193$	16.1542	+	7.77948i	1.16281	+	0.559979i	0.249951	+	0.968258i	$0.419585\pi$
$194$	−1.91947	+	2.40694i	−0.137810	+	0.172808i
$195$	−0.448112			−0.0320900
$196$	−2.10467	+	13.4120i	−0.150333	+	0.957997i
$197$	−21.2007			−1.51049			−0.755243	−	0.655445i	$-0.772481\pi$
$197$	−21.2007			−1.51049			−0.755243	+	0.655445i	$0.772481\pi$
$198$	−0.000121801	0	0.000152734i	−8.65601e−6	0	1.08543e-5i
$199$	−20.6426	−	9.94094i	−1.46331	−	0.704695i	−0.478465	−	0.878107i	$-0.658807\pi$
$199$	−20.6426	−	9.94094i	−1.46331	−	0.704695i	−0.984849	+	0.173412i	$0.944521\pi$
$200$	−1.06600	−	4.67046i	−0.0753778	−	0.330252i
$201$	8.71755	+	4.19815i	0.614889	+	0.296115i
$202$	2.16320	−	1.04174i	0.152202	−	0.0732967i
$203$	0.601808	−	1.36804i	0.0422386	−	0.0960177i
$204$	−20.1348	−	9.69639i	−1.40972	−	0.678883i
$205$	−1.59995	−	2.00627i	−0.111745	−	0.140124i
$206$	0.368914	−	0.177659i	0.0257034	−	0.0123781i
$207$	1.45104	−	1.81954i	0.100854	−	0.126467i
$208$	−0.810046	+	3.54904i	−0.0561666	+	0.246082i
$209$	−0.00836861	+	0.0104939i	−0.000578869	+	0.000725879i
$210$	0.286508	+	0.0551092i	0.0197709	+	0.00380290i
$211$	−7.12832	−	8.93863i	−0.490734	−	0.615360i	0.473378	−	0.880860i	$-0.343035\pi$
$211$	−7.12832	−	8.93863i	−0.490734	−	0.615360i	−0.964111	+	0.265499i	$0.914463\pi$
$212$	7.30746	−	3.51909i	0.501879	−	0.241692i
$213$	1.08235	−	4.74208i	0.0741614	−	0.324922i
$214$	−0.775867			−0.0530372
$215$	−0.847352			−0.0577889
$216$	−1.02532	+	4.49224i	−0.0697645	+	0.305658i
$217$	−25.0720	−	4.82255i	−1.70200	−	0.327376i
$218$	0.474095	+	2.07715i	0.0321098	+	0.140682i
$219$	2.69198	+	11.7943i	0.181907	+	0.796988i
$220$	−0.000532513	0	0.000667750i	−3.59020e−5	0	4.50197e-5i
$221$	−3.87593	−	4.86026i	−0.260723	−	0.326937i
$222$	0.745813	+	3.26762i	0.0500557	+	0.219308i
$223$	−4.77141	−	20.9049i	−0.319518	−	1.39990i	−0.838401	−	0.545053i	$-0.816509\pi$
$223$	−4.77141	−	20.9049i	−0.319518	−	1.39990i	0.518884	−	0.854845i	$-0.326348\pi$
$224$	3.01998	−	6.86509i	0.201781	−	0.458693i
$225$	0.479199	−	2.09951i	0.0319466	−	0.139967i
$226$	4.58481			0.304977
$227$	−5.21607			−0.346203			−0.173101	−	0.984904i	$-0.555379\pi$
$227$	−5.21607			−0.346203			−0.173101	+	0.984904i	$0.555379\pi$
$228$	5.89433	−	25.8248i	0.390362	−	1.71029i
$229$	−22.0835	+	10.6348i	−1.45932	+	0.702770i	−0.984185	−	0.177144i	$-0.943314\pi$
$229$	−22.0835	+	10.6348i	−1.45932	+	0.702770i	−0.475132	+	0.879914i	$0.657600\pi$
$230$	−0.198089	−	0.248395i	−0.0130616	−	0.0163787i
$231$	−0.00863589	+	0.00228598i	−0.000568200	+	0.000150406i
$232$	−0.341443	+	0.428156i	−0.0224168	+	0.0281098i
$233$	5.34548	−	23.4201i	0.350194	−	1.53430i	−0.426538	−	0.904470i	$-0.640267\pi$
$233$	5.34548	−	23.4201i	0.350194	−	1.53430i	0.776732	−	0.629831i	$-0.216876\pi$
$234$	0.0668652	−	0.0838462i	0.00437111	−	0.00548120i
$235$	2.09428	−	1.00855i	0.136615	−	0.0657905i
$236$	−2.80652	−	3.51926i	−0.182689	−	0.229084i
$237$	−1.11992	−	0.539327i	−0.0727469	−	0.0350330i
$238$	1.88042	+	3.58415i	0.121889	+	0.232326i
$239$	−11.0816	+	5.33660i	−0.716806	+	0.345196i	−0.756480	−	0.654017i	$-0.773083\pi$
$239$	−11.0816	+	5.33660i	−0.716806	+	0.345196i	0.0396735	+	0.999213i	$0.487368\pi$
$240$	1.46972	+	0.707781i	0.0948702	+	0.0456871i
$241$	−4.86967	−	21.3354i	−0.313683	−	1.37433i	−0.848423	−	0.529318i	$-0.822448\pi$
$241$	−4.86967	−	21.3354i	−0.313683	−	1.37433i	0.534740	−	0.845016i	$-0.320409\pi$
$242$	2.43889	+	1.17451i	0.156778	+	0.0755001i
$243$	−2.80238	+	3.51408i	−0.179773	+	0.225428i
$244$	2.19156			0.140300
$245$	1.14351	+	1.24747i	0.0730560	+	0.0796982i
$246$	4.84180			0.308702
$247$	4.59413	−	5.76085i	0.292317	−	0.366554i
$248$	8.42873	+	4.05906i	0.535225	+	0.257751i
$249$	−4.97414	−	21.7932i	−0.315224	−	1.38108i
$250$	−0.532877	−	0.256620i	−0.0337021	−	0.0162301i
$251$	18.9949	−	9.14748i	1.19895	−	0.577384i	0.275574	−	0.961280i	$-0.411132\pi$
$251$	18.9949	−	9.14748i	1.19895	−	0.577384i	0.923376	+	0.383896i	$0.125418\pi$
$252$	1.69937	−	1.45349i	0.107050	−	0.0915615i
$253$	0.00876452	+	0.00422077i	0.000551020	+	0.000265357i
$254$	2.88371	+	3.61606i	0.180940	+	0.226892i
$255$	−2.50982	+	1.20867i	−0.157171	+	0.0756897i
$256$	7.09047	−	8.89117i	0.443154	−	0.555698i
$257$	−6.35112	+	27.8261i	−0.396172	+	1.73574i	0.246079	+	0.969250i	$0.420858\pi$
$257$	−6.35112	+	27.8261i	−0.396172	+	1.73574i	−0.642251	+	0.766494i	$0.722000\pi$
$258$	0.996834	−	1.24999i	0.0620602	−	0.0778210i
$259$	−7.82797	+	17.7947i	−0.486407	+	1.10571i
$260$	0.292334	+	0.366575i	0.0181298	+	0.0227340i
$261$	−0.221797	+	0.106812i	−0.0137289	+	0.00661148i
$262$	0.701622	−	3.07401i	0.0433464	−	0.189913i
$263$	7.44202			0.458894			0.229447	−	0.973321i	$-0.426308\pi$
$263$	7.44202			0.458894			0.229447	+	0.973321i	$0.426308\pi$
$264$	0.00327332			0.000201459
$265$	0.224970	−	0.985657i	0.0138198	−	0.0605484i
$266$	−3.64580	+	3.11830i	−0.223538	+	0.191195i
$267$	6.47082	+	28.3505i	0.396008	+	1.73502i
$268$	−2.25278	−	9.87007i	−0.137610	−	0.602911i
$269$	7.45388	+	9.34687i	0.454471	+	0.569888i	0.955293	−	0.295662i	$-0.0955402\pi$
$269$	7.45388	+	9.34687i	0.454471	+	0.569888i	−0.500822	+	0.865550i	$0.666969\pi$
$270$	0.176302	+	0.221076i	0.0107294	+	0.0134543i
$271$	−0.906308	−	3.97079i	−0.0550543	−	0.241209i	0.939912	−	0.341416i	$-0.110906\pi$
$271$	−0.906308	−	3.97079i	−0.0550543	−	0.241209i	−0.994967	+	0.100207i	$0.968049\pi$
$272$	5.03566	+	22.0627i	0.305332	+	1.33775i
$273$	4.74085	−	1.25494i	0.286930	−	0.0759521i
$274$	0.797811	−	3.49544i	0.0481975	−	0.211167i
$275$	0.00900149			0.000542810
$276$	−19.1981			−1.15559
$277$	2.61748	−	11.4679i	0.157269	−	0.689042i	−0.833390	−	0.552685i	$-0.813603\pi$
$277$	2.61748	−	11.4679i	0.157269	−	0.689042i	0.990660	−	0.136357i	$-0.0435395\pi$
$278$	3.09206	−	1.48906i	0.185450	−	0.0893079i
$279$	2.62204	+	3.28793i	0.156977	+	0.196843i
$280$	−0.288082	−	0.549095i	−0.0172162	−	0.0328147i
$281$	−5.61102	+	7.03600i	−0.334726	+	0.419733i	−0.920501	−	0.390741i	$-0.872219\pi$
$281$	−5.61102	+	7.03600i	−0.334726	+	0.419733i	0.585775	+	0.810474i	$0.300790\pi$
$282$	−0.975943	+	4.27589i	−0.0581166	+	0.254625i
$283$	8.33018	−	10.4457i	0.495178	−	0.620933i	−0.469956	−	0.882690i	$-0.655730\pi$
$283$	8.33018	−	10.4457i	0.495178	−	0.620933i	0.965134	+	0.261756i	$0.0843017\pi$
$284$	−4.58532	+	2.20817i	−0.272089	+	0.131031i
$285$	−2.05868	−	2.58151i	−0.121946	−	0.152915i
$286$	0.000403878	0	0.000194497i	2.38818e−5	0	1.15009e-5i
$287$	22.5454	+	16.7449i	1.33081	+	0.988422i
$288$	−1.11302	+	0.536001i	−0.0655852	+	0.0315842i
$289$	−19.5015	−	9.39142i	−1.14715	−	0.552436i
$290$	0.00747822	+	0.0327642i	0.000439136	+	0.00192398i
$291$	20.8923	+	10.0612i	1.22473	+	0.589797i
$292$	7.89212	−	9.89640i	0.461851	−	0.579143i
$293$	31.6295			1.84782			0.923909	−	0.382613i	$-0.124976\pi$
$293$	31.6295			1.84782			0.923909	+	0.382613i	$0.124976\pi$
$294$	−3.18547	+	0.219329i	−0.185781	+	0.0127915i
$295$	−0.561093			−0.0326681
$296$	4.44129	−	5.56920i	0.258145	−	0.323703i
$297$	−0.00780058	−	0.00375656i	−0.000452636	−	0.000217978i
$298$	−0.113726	−	0.498267i	−0.00658798	−	0.0288638i
$299$	−4.81146	−	2.31708i	−0.278254	−	0.134000i
$300$	−16.0053	+	7.70774i	−0.924066	+	0.445007i
$301$	8.96465	−	2.37300i	0.516714	−	0.136778i
$302$	0.785768	+	0.378406i	0.0452159	+	0.0217748i
$303$	−11.2756	−	14.1392i	−0.647767	−	0.812275i
$304$	−24.1670	+	11.6382i	−1.38607	+	0.667496i
$305$	0.170325	−	0.213581i	0.00975279	−	0.0122296i
$306$	0.148350	−	0.649965i	0.00848062	−	0.0371560i
$307$	−9.01771	+	11.3079i	−0.514668	+	0.645373i	−0.969467	−	0.245221i	$-0.921140\pi$
$307$	−9.01771	+	11.3079i	−0.514668	+	0.645373i	0.454799	+	0.890594i	$0.349711\pi$
$308$	0.00750381	+	0.00557323i	0.000427569	+	0.000317564i
$309$	−1.92295	−	2.41131i	−0.109393	−	0.137174i
$310$	0.517251	−	0.249095i	0.0293779	−	0.0141476i
$311$	−5.19501	+	22.7608i	−0.294582	+	1.29065i	0.583490	+	0.812120i	$0.301687\pi$
$311$	−5.19501	+	22.7608i	−0.294582	+	1.29065i	−0.878072	+	0.478528i	$0.841171\pi$
$312$	−1.79696			−0.101733
$313$	26.1614			1.47873			0.739364	−	0.673306i	$-0.235126\pi$
$313$	26.1614			1.47873			0.739364	+	0.673306i	$0.235126\pi$
$314$	−0.379236	+	1.66154i	−0.0214016	+	0.0937663i
$315$	−0.00957909	−	0.278578i	−0.000539720	−	0.0156961i
$316$	0.289409	+	1.26799i	0.0162805	+	0.0713297i
$317$	−4.43272	−	19.4210i	−0.248966	−	1.09079i	−0.932584	−	0.360953i	$-0.882451\pi$
$317$	−4.43272	−	19.4210i	−0.248966	−	1.09079i	0.683618	−	0.729840i	$-0.260406\pi$
$318$	1.18936	+	1.49141i	0.0666959	+	0.0836340i
$319$	−0.000641571	0	0.000804504i	−3.59211e−5	0	4.50436e-5i
$320$	−0.354136	−	1.55157i	−0.0197968	−	0.0867355i
$321$	1.30042	+	5.69750i	0.0725822	+	0.318003i
$322$	2.79133	+	2.07318i	0.155555	+	0.115534i
$323$	10.1927	−	44.6573i	0.567139	−	2.48480i
$324$	19.6222			1.09012
$325$	−4.94156			−0.274108
$326$	−0.545845	+	2.39150i	−0.0302316	+	0.132453i
$327$	14.4587	−	6.96294i	0.799567	−	0.385051i
$328$	−6.41589	−	8.04527i	−0.354258	−	0.444226i
$329$	−19.3322	+	16.5351i	−1.06582	+	0.911608i
$330$	0.000125244	0	0.000157051i	6.89444e−6	0	8.64536e-6i
$331$	−7.24259	+	31.7319i	−0.398089	+	1.74414i	0.236820	+	0.971554i	$0.423895\pi$
$331$	−7.24259	+	31.7319i	−0.398089	+	1.74414i	−0.634909	+	0.772587i	$0.718962\pi$
$332$	−14.5828	+	18.2862i	−0.800333	+	1.00359i
$333$	2.88501	−	1.38935i	0.158097	−	0.0761357i
$334$	−2.15335	−	2.70021i	−0.117826	−	0.147749i
$335$	−1.13698	−	0.547543i	−0.0621201	−	0.0299154i
$336$	−17.5312	−	3.37210i	−0.956407	−	0.183963i
$337$	−9.77228	+	4.70608i	−0.532330	+	0.256357i	−0.680683	−	0.732578i	$-0.738317\pi$
$337$	−9.77228	+	4.70608i	−0.532330	+	0.256357i	0.148353	+	0.988934i	$0.452603\pi$
$338$	−0.221717	−	0.106773i	−0.0120598	−	0.00580770i
$339$	−7.68451	−	33.6681i	−0.417365	−	1.82860i
$340$	2.62607	+	1.26465i	0.142419	+	0.0685852i
$341$	−0.0109600	+	0.0137433i	−0.000593515	+	0.000744244i
$342$	0.790213			0.0427298
$343$	−15.5914	−	9.99540i	−0.841857	−	0.539701i
$344$	−3.39793			−0.183204
$345$	−1.49205	+	1.87097i	−0.0803293	+	0.100730i
$346$	−4.12997	−	1.98889i	−0.222029	−	0.106923i
$347$	−2.00309	−	8.77610i	−0.107531	−	0.471126i	−0.999807	−	0.0196350i	$-0.993750\pi$
$347$	−2.00309	−	8.77610i	−0.107531	−	0.471126i	0.892276	−	0.451491i	$-0.149108\pi$
$348$	1.82964	+	0.881106i	0.0980787	+	0.0472322i
$349$	1.10417	−	0.531741i	0.0591049	−	0.0284634i	−0.404098	−	0.914716i	$-0.632414\pi$
$349$	1.10417	−	0.531741i	0.0591049	−	0.0284634i	0.463203	+	0.886252i	$0.346700\pi$
$350$	3.15946	+	0.607717i	0.168880	+	0.0324838i
$351$	4.28229	+	2.06224i	0.228572	+	0.110074i
$352$	−0.00321952	−	0.00403715i	−0.000171601	−	0.000215181i
$353$	8.67171	−	4.17607i	0.461548	−	0.222270i	−0.188635	−	0.982047i	$-0.560406\pi$
$353$	8.67171	−	4.17607i	0.461548	−	0.222270i	0.650183	+	0.759777i	$0.274692\pi$
$354$	0.660076	−	0.827709i	0.0350826	−	0.0439922i
$355$	−0.141165	+	0.618485i	−0.00749226	+	0.0328258i
$356$	18.9706	−	23.7884i	1.00544	−	1.26078i
$357$	23.1681	−	19.8160i	1.22619	−	1.04877i
$358$	−2.24855	−	2.81959i	−0.118839	−	0.149020i
$359$	−18.0813	+	8.70748i	−0.954292	+	0.459563i	−0.845189	−	0.534467i	$-0.820512\pi$
$359$	−18.0813	+	8.70748i	−0.954292	+	0.459563i	−0.109103	+	0.994030i	$0.534798\pi$
$360$	−0.0227274	+	0.0995751i	−0.00119784	+	0.00524807i
$361$	35.2934			1.85755
$362$	2.89812			0.152322
$363$	4.53709	−	19.8783i	0.238135	−	1.04334i
$364$	−4.11937	−	3.05954i	−0.215914	−	0.160364i
$365$	−0.351101	−	1.53827i	−0.0183774	−	0.0805169i
$366$	0.114697	+	0.502518i	0.00599528	+	0.0262670i
$367$	20.5709	+	25.7951i	1.07379	+	1.34649i	0.934389	+	0.356256i	$0.115947\pi$
$367$	20.5709	+	25.7951i	1.07379	+	1.34649i	0.139402	+	0.990236i	$0.455482\pi$
$368$	12.1209	+	15.1992i	0.631847	+	0.792311i
$369$	−1.02933	−	4.50980i	−0.0535849	−	0.234771i
$370$	−0.0972724	−	0.426178i	−0.00505695	−	0.0221559i
$371$	0.380233	+	11.0579i	0.0197407	+	0.574097i
$372$	7.71951	−	33.8214i	0.400238	−	1.75356i
$373$	11.3830			0.589392			0.294696	−	0.955591i	$-0.404782\pi$
$373$	11.3830			0.589392			0.294696	+	0.955591i	$0.404782\pi$
$374$	0.00278668			0.000144096
$375$	−0.991316	+	4.34324i	−0.0511913	+	0.224284i
$376$	8.39817	−	4.04434i	0.433102	−	0.208571i
$377$	0.352204	+	0.441650i	0.0181394	+	0.0227461i
$378$	−2.48433	−	1.84517i	−0.127780	−	0.0949052i
$379$	5.47128	−	6.86076i	0.281041	−	0.352414i	−0.621196	−	0.783655i	$-0.713353\pi$
$379$	5.47128	−	6.86076i	0.281041	−	0.352414i	0.902237	+	0.431242i	$0.141924\pi$
$380$	−0.768766	+	3.36818i	−0.0394369	+	0.172784i
$381$	21.7208	−	27.2370i	1.11279	−	1.39539i
$382$	−1.08020	+	0.520195i	−0.0552676	+	0.0266155i
$383$	−2.13957	−	2.68293i	−0.109327	−	0.137091i	0.724158	−	0.689635i	$-0.242229\pi$
$383$	−2.13957	−	2.68293i	−0.109327	−	0.137091i	−0.833484	+	0.552543i	$0.813657\pi$
$384$	12.1736	+	5.86249i	0.621231	+	0.299169i
$385$	0.00112633		0.000298148i	5.74033e−5		1.51950e-5i
$386$	3.97536	−	1.91443i	0.202340	−	0.0974420i
$387$	−1.37620	−	0.662743i	−0.0699561	−	0.0336891i
$388$	−5.39896	−	23.6544i	−0.274090	−	1.20087i
$389$	15.8958	+	7.65503i	0.805951	+	0.388125i	0.791041	−	0.611764i	$-0.209540\pi$
$389$	15.8958	+	7.65503i	0.805951	+	0.388125i	0.0149098	+	0.999889i	$0.495254\pi$
$390$	−0.0687552	+	0.0862163i	−0.00348155	+	0.00436573i
$391$	−33.1982			−1.67890
$392$	4.58553	+	5.00244i	0.231604	+	0.252662i
$393$	−23.7496			−1.19801
$394$	−3.25288	+	4.07899i	−0.163878	+	0.205496i
$395$	0.146066	+	0.0703415i	0.00734936	+	0.00353927i
$396$	−0.000342594	−	0.00150100i	−1.72160e−5	−	7.54281e-5i
$397$	−6.97648	−	3.35970i	−0.350140	−	0.168618i	0.250544	−	0.968105i	$-0.419391\pi$
$397$	−6.97648	−	3.35970i	−0.350140	−	0.168618i	−0.600684	+	0.799487i	$0.705105\pi$
$398$	−5.07988	+	2.44634i	−0.254631	+	0.122624i
$399$	29.0096	+	21.5460i	1.45230	+	1.07865i
$400$	16.2074	+	7.80505i	0.810368	+	0.390253i
$401$	3.13916	+	3.93638i	0.156762	+	0.196573i	0.854010	−	0.520257i	$-0.174164\pi$
$401$	3.13916	+	3.93638i	0.156762	+	0.196573i	−0.697248	+	0.716830i	$0.745592\pi$
$402$	2.14528	−	1.03311i	0.106997	−	0.0515270i
$403$	6.01669	−	7.54470i	0.299713	−	0.375828i
$404$	−4.21061	+	18.4479i	−0.209486	+	0.917817i
$405$	1.52502	−	1.91231i	0.0757786	−	0.0950234i
$406$	−0.170873	−	0.325690i	−0.00848026	−	0.0161637i
$407$	0.00834519	+	0.0104645i	0.000413656	+	0.000518708i
$408$	−10.0645	+	4.84683i	−0.498269	+	0.239954i
$409$	0.205695	−	0.901208i	0.0101710	−	0.0445619i	−0.969588	−	0.244744i	$-0.921296\pi$
$409$	0.205695	−	0.901208i	0.0101710	−	0.0445619i	0.979759	+	0.200182i	$0.0641533\pi$
$410$	−0.631489			−0.0311870
$411$	−27.0056			−1.33209
$412$	−0.718080	+	3.14611i	−0.0353773	+	0.154998i
$413$	5.93615	−	1.57134i	0.292099	−	0.0773205i
$414$	−0.127441	−	0.558355i	−0.00626338	−	0.0274417i
$415$	0.648751	+	2.84236i	0.0318459	+	0.139526i
$416$	1.76742	+	2.21628i	0.0866551	+	0.108662i
$417$	−16.1173	−	20.2105i	−0.789268	−	0.989710i
$418$	0.000734995		0.00322022i	3.59498e−5		0.000157506i
$419$	−3.29624	−	14.4418i	−0.161032	−	0.705526i	−0.989385	−	0.145320i	$-0.953579\pi$
$419$	−3.29624	−	14.4418i	−0.161032	−	0.705526i	0.828353	−	0.560206i	$-0.189278\pi$
$420$	−1.74740	+	1.49458i	−0.0852646	+	0.0729280i
$421$	−2.83714	+	12.4303i	−0.138274	+	0.605817i	0.857540	+	0.514417i	$0.171992\pi$
$421$	−2.83714	+	12.4303i	−0.138274	+	0.605817i	−0.995814	+	0.0914007i	$0.970866\pi$
$422$	−2.81350			−0.136959
$423$	4.19017			0.203733
$424$	0.902142	−	3.95254i	0.0438119	−	0.191952i
$425$	−27.6771	+	13.3286i	−1.34254	+	0.646531i
$426$	−0.746303	−	0.935835i	−0.0361585	−	0.0453413i
$427$	−1.20384	+	2.73660i	−0.0582580	+	0.132433i
$428$	3.81245	−	4.78066i	0.184282	−	0.231082i
$429$	0.000751338	−	0.00329183i	3.62749e−5	−	0.000158931i
$430$	−0.130012	+	0.163030i	−0.00626972	+	0.00786198i
$431$	−15.4892	+	7.45918i	−0.746086	+	0.359296i	−0.767988	−	0.640464i	$-0.778742\pi$
$431$	−15.4892	+	7.45918i	−0.746086	+	0.359296i	0.0219021	+	0.999760i	$0.493028\pi$
$432$	−10.7878	−	13.5275i	−0.519030	−	0.650843i
$433$	9.27204	+	4.46518i	0.445586	+	0.214583i	0.643202	−	0.765697i	$-0.277606\pi$
$433$	9.27204	+	4.46518i	0.445586	+	0.214583i	−0.197616	+	0.980280i	$0.563320\pi$
$434$	−4.77472	+	4.08388i	−0.229194	+	0.196033i
$435$	0.228066	−	0.109831i	0.0109349	−	0.00526599i
$436$	−15.1284	−	7.28543i	−0.724517	−	0.348909i
$437$	−8.75612	−	38.3631i	−0.418862	−	1.83516i
$438$	2.68226	+	1.29171i	0.128163	+	0.0617201i
$439$	0.242266	−	0.303792i	0.0115627	−	0.0144992i	−0.776017	−	0.630713i	$-0.782763\pi$
$439$	0.242266	−	0.303792i	0.0115627	−	0.0144992i	0.787579	+	0.616213i	$0.211334\pi$
$440$	−0.000426921	0		−2.03527e−5	0
$441$	0.881499	+	2.92042i	0.0419761	+	0.139068i
$442$	−1.52981			−0.0727654
$443$	12.4234	−	15.5785i	0.590254	−	0.740155i	−0.393570	−	0.919295i	$-0.628760\pi$
$443$	12.4234	−	15.5785i	0.590254	−	0.740155i	0.983824	+	0.179140i	$0.0573314\pi$
$444$	−23.7988	−	11.4609i	−1.12944	−	0.543911i
$445$	−0.843954	−	3.69760i	−0.0400073	−	0.175283i
$446$	−4.75418	−	2.28949i	−0.225117	−	0.108411i
$447$	−3.46835	+	1.67027i	−0.164047	+	0.0790011i
$448$	8.09179	+	15.4233i	0.382301	+	0.728681i
$449$	4.37925	+	2.10893i	0.206669	+	0.0995267i	0.534355	−	0.845260i	$-0.320554\pi$
$449$	4.37925	+	2.10893i	0.206669	+	0.0995267i	−0.327686	+	0.944787i	$0.606269\pi$
$450$	−0.330418	−	0.414331i	−0.0155760	−	0.0195317i
$451$	0.0174206	−	0.00838934i	0.000820306	−	0.000395038i
$452$	−22.5288	+	28.2502i	−1.05967	+	1.32878i
$453$	1.46177	−	6.40444i	0.0686801	−	0.300907i
$454$	−0.800317	+	1.00357i	−0.0375608	+	0.0470997i
$455$	−0.618324	+	0.163675i	−0.0289875	+	0.00767318i
$456$	−8.25544	−	10.3520i	−0.386597	−	0.484777i
$457$	5.56640	−	2.68064i	0.260385	−	0.125395i	−0.299137	−	0.954210i	$-0.596699\pi$
$457$	5.56640	−	2.68064i	0.260385	−	0.125395i	0.559523	+	0.828815i	$0.310985\pi$
$458$	−1.34220	+	5.88057i	−0.0627170	+	0.274781i
$459$	29.5470			1.37914
$460$	2.50390			0.116745
$461$	4.11810	−	18.0426i	0.191799	−	0.840326i	−0.783843	−	0.620959i	$-0.786743\pi$
$461$	4.11810	−	18.0426i	0.191799	−	0.840326i	0.975642	−	0.219368i	$-0.0703994\pi$
$462$	−0.000885211		0.00201228i	−4.11837e−5		9.36198e-5i
$463$	2.30678	+	10.1067i	0.107205	+	0.469696i	0.999822	+	0.0188798i	$0.00600999\pi$
$463$	2.30678	+	10.1067i	0.107205	+	0.469696i	−0.892617	+	0.450817i	$0.851133\pi$
$464$	−0.457588	−	2.00482i	−0.0212430	−	0.0930715i
$465$	−2.69615	−	3.38087i	−0.125031	−	0.156784i
$466$	−3.68582	−	4.62188i	−0.170743	−	0.214104i
$467$	5.35910	+	23.4797i	0.247989	+	1.08651i	0.933536	+	0.358484i	$0.116706\pi$
$467$	5.35910	+	23.4797i	0.247989	+	1.08651i	−0.685547	+	0.728029i	$0.740437\pi$
$468$	0.188074	+	0.824006i	0.00869372	+	0.0380897i
$469$	13.5622	+	2.60867i	0.626246	+	0.120457i
$470$	0.127287	−	0.557681i	0.00587131	−	0.0257239i
$471$	12.8370			0.591498
$472$	−2.25002			−0.103565
$473$	0.00142073	−	0.00622463i	6.53253e−5	−	0.000286209i
$474$	−0.275599	+	0.132722i	−0.0126587	+	0.00609610i
$475$	−22.7021	−	28.4676i	−1.04164	−	1.30618i
$476$	−31.3244	−	6.02520i	−1.43575	−	0.276165i
$477$	1.13629	−	1.42487i	0.0520273	−	0.0652402i
$478$	−0.673521	+	2.95089i	−0.0308061	+	0.134971i
$479$	2.47002	−	3.09731i	0.112858	−	0.141520i	−0.722194	−	0.691691i	$-0.756866\pi$
$479$	2.47002	−	3.09731i	0.112858	−	0.141520i	0.835052	+	0.550171i	$0.185438\pi$
$480$	1.14448	−	0.551152i	0.0522381	−	0.0251565i
$481$	−4.58126	−	5.74472i	−0.208888	−	0.261937i
$482$	−4.85208	−	2.33664i	−0.221006	−	0.106431i
$483$	10.5457	−	23.9726i	0.479845	−	1.09079i
$484$	−19.2211	+	9.25641i	−0.873688	+	0.420746i
$485$	−2.72487	−	1.31223i	−0.123730	−	0.0595852i
$486$	0.246126	+	1.07835i	0.0111645	+	0.0489149i
$487$	20.8449	+	10.0384i	0.944573	+	0.454883i	0.841780	−	0.539820i	$-0.181508\pi$
$487$	20.8449	+	10.0384i	0.944573	+	0.454883i	0.102793	+	0.994703i	$0.467222\pi$
$488$	0.683014	−	0.856473i	0.0309186	−	0.0387707i
$489$	18.4766			0.835542
$490$	0.415464	−	0.0286058i	0.0187688	−	0.00129228i
$491$	23.4088			1.05643			0.528213	−	0.849112i	$-0.322862\pi$
$491$	23.4088			1.05643			0.528213	+	0.849112i	$0.322862\pi$
$492$	−23.7916	+	29.8337i	−1.07261	+	1.34501i
$493$	3.16389	+	1.52365i	0.142494	+	0.0686217i
$494$	−0.403491	−	1.76781i	−0.0181539	−	0.0795375i
$495$	−0.000172908	0	8.32681e-5i	−7.77163e−6	0	3.74262e-6i
$496$	−31.6502	+	15.2420i	−1.42114	+	0.684384i
$497$	−0.238590	−	6.93866i	−0.0107022	−	0.311241i
$498$	−4.95618	−	2.38677i	−0.222092	−	0.106954i
$499$	9.29278	+	11.6528i	0.416002	+	0.521650i	0.945043	−	0.326946i	$-0.106020\pi$
$499$	9.29278	+	11.6528i	0.416002	+	0.521650i	−0.529041	+	0.848596i	$0.677448\pi$
$500$	4.19966	−	2.02245i	0.187814	−	0.0904467i
$501$	−16.2195	+	20.3386i	−0.724635	+	0.908664i
$502$	1.15449	−	5.05813i	0.0515272	−	0.225755i
$503$	−1.83518	+	2.30124i	−0.0818266	+	0.102607i	−0.821060	−	0.570842i	$-0.806617\pi$
$503$	−1.83518	+	2.30124i	−0.0818266	+	0.102607i	0.739233	+	0.673450i	$0.235188\pi$
$504$	−0.0384127	−	1.11711i	−0.00171104	−	0.0497602i
$505$	1.47062	+	1.84410i	0.0654417	+	0.0820613i
$506$	0.00215684	−	0.00103868i	9.58831e−5	−	4.61749e-5i
$507$	−0.412462	+	1.80712i	−0.0183181	+	0.0802568i
$508$	−36.4510			−1.61725
$509$	35.9029			1.59137			0.795684	−	0.605712i	$-0.207112\pi$
$509$	35.9029			1.59137			0.795684	+	0.605712i	$0.207112\pi$
$510$	−0.152544	+	0.668337i	−0.00675474	+	0.0295945i
$511$	8.02243	+	15.2911i	0.354891	+	0.676437i
$512$	−3.86685	−	16.9418i	−0.170892	−	0.748728i
$513$	7.79311	+	34.1439i	0.344074	+	1.50749i
$514$	4.37924	+	5.49139i	0.193160	+	0.242215i
$515$	0.250800	+	0.314494i	0.0110516	+	0.0138582i
$516$	2.80383	+	12.2844i	0.123432	+	0.540789i
$517$	0.00389738	+	0.0170755i	0.000171406	+	0.000750981i
$518$	2.22261	+	4.23639i	0.0976560	+	0.186136i
$519$	−7.68302	+	33.6615i	−0.337247	+	1.47758i
$520$	0.234367			0.0102777
$521$	14.3227			0.627489			0.313745	−	0.949507i	$-0.398416\pi$
$521$	14.3227			0.627489			0.313745	+	0.949507i	$0.398416\pi$
$522$	−0.0134805	+	0.0590619i	−0.000590025	+	0.00258507i
$523$	16.8137	−	8.09707i	0.735214	−	0.354060i	−0.0285187	−	0.999593i	$-0.509079\pi$
$523$	16.8137	−	8.09707i	0.735214	−	0.354060i	0.763732	+	0.645533i	$0.223365\pi$
$524$	15.4935	+	19.4282i	0.676836	+	0.848726i
$525$	−0.832812	−	24.2197i	−0.0363469	−	1.05704i
$526$	1.14185	−	1.43184i	0.0497871	−	0.0624310i
$527$	13.3489	−	58.4854i	0.581488	−	2.54767i
$528$	−0.00766359	+	0.00960984i	−0.000333515	+	0.000418215i
$529$	−4.97249	+	2.39462i	−0.216195	+	0.104114i
$530$	−0.155122	−	0.194516i	−0.00673805	−	0.00844925i
$531$	−0.911282	−	0.438850i	−0.0395463	−	0.0190445i
$532$	−1.29933	−	37.7870i	−0.0563332	−	1.63827i
$533$	−9.56342	+	4.60550i	−0.414238	+	0.199486i
$534$	6.44744	+	3.10492i	0.279008	+	0.134363i
$535$	−0.169606	−	0.743094i	−0.00733272	−	0.0321268i
$536$	−4.55937	−	2.19568i	−0.196935	−	0.0948388i
$537$	−16.9366	+	21.2378i	−0.730868	+	0.916479i
$538$	2.94200			0.126838
$539$	−0.0110812	+	0.00630858i	−0.000477301	+	0.000271730i
$540$	−2.22852			−0.0959002
$541$	4.25129	−	5.33095i	0.182777	−	0.229196i	−0.681999	−	0.731354i	$-0.738889\pi$
$541$	4.25129	−	5.33095i	0.182777	−	0.229196i	0.864776	+	0.502158i	$0.167460\pi$
$542$	−0.903034	−	0.434878i	−0.0387886	−	0.0186796i
$543$	−4.85748	−	21.2820i	−0.208454	−	0.913298i
$544$	15.8770	+	7.64595i	0.680720	+	0.327818i
$545$	−1.88577	+	0.908139i	−0.0807775	+	0.0389004i
$546$	0.485955	−	1.10468i	0.0207970	−	0.0472761i
$547$	−28.4187	−	13.6857i	−1.21509	−	0.585159i	−0.287153	−	0.957885i	$-0.592709\pi$
$547$	−28.4187	−	13.6857i	−1.21509	−	0.585159i	−0.927941	+	0.372726i	$0.878423\pi$
$548$	17.6176	+	22.0917i	0.752585	+	0.943712i
$549$	0.443677	−	0.213664i	0.0189357	−	0.00911895i
$550$	0.00138113	−	0.00173188i	5.88914e−5	−	7.38474e-5i
$551$	−0.926209	+	4.05799i	−0.0394578	+	0.172876i
$552$	−5.98321	+	7.50271i	−0.254662	+	0.319337i
$553$	−1.74231	−	0.335130i	−0.0740905	−	0.0142512i
$554$	−1.80481	−	2.26316i	−0.0766791	−	0.0961525i
$555$	−2.96656	+	1.42862i	−0.125923	+	0.0606415i
$556$	−6.01862	+	26.3693i	−0.255246	+	1.11831i
$557$	−21.1284			−0.895237			−0.447619	−	0.894225i	$-0.647728\pi$
$557$	−21.1284			−0.895237			−0.447619	+	0.894225i	$0.647728\pi$
$558$	1.03490			0.0438109
$559$	−0.779940	+	3.41714i	−0.0329880	+	0.144530i
$560$	2.28650	+	0.439805i	0.0966225	+	0.0185852i
$561$	−0.00467070	−	0.0204637i	−0.000197197	−	0.000863977i
$562$	0.492802	+	2.15911i	0.0207876	+	0.0910765i
$563$	25.8484	+	32.4128i	1.08938	+	1.36604i	0.925144	+	0.379616i	$0.123944\pi$
$563$	25.8484	+	32.4128i	1.08938	+	1.36604i	0.164234	+	0.986421i	$0.447485\pi$
$564$	−21.5511	−	27.0243i	−0.907467	−	1.13793i
$565$	1.00225	+	4.39114i	0.0421650	+	0.184737i
$566$	−0.731620	−	3.20543i	−0.0307523	−	0.134734i
$567$	−10.7787	+	24.5023i	−0.452661	+	1.02900i
$568$	−0.566080	+	2.48016i	−0.0237522	+	0.104065i
$569$	11.4186			0.478691			0.239345	−	0.970934i	$-0.423067\pi$
$569$	11.4186			0.478691			0.239345	+	0.970934i	$0.423067\pi$
$570$	−0.812549			−0.0340339
$571$	0.253718	−	1.11161i	0.0106178	−	0.0465195i	−0.969342	−	0.245717i	$-0.920976\pi$
$571$	0.253718	−	1.11161i	0.0106178	−	0.0465195i	0.979959	+	0.199198i	$0.0638336\pi$
$572$	−0.00318300	+	0.00153285i	−0.000133088	+	6.40918e-5i
$573$	5.63049	+	7.06041i	0.235217	+	0.294953i
$574$	6.68091	−	1.76848i	0.278856	−	0.0738150i
$575$	−16.4536	+	20.6321i	−0.686162	+	0.860420i
$576$	0.638378	−	2.79692i	0.0265991	−	0.116538i
$577$	−20.2795	+	25.4297i	−0.844247	+	1.05865i	0.153267	+	0.988185i	$0.451020\pi$
$577$	−20.2795	+	25.4297i	−0.844247	+	1.05865i	−0.997514	+	0.0704671i	$0.977551\pi$
$578$	−4.79907	+	2.31111i	−0.199615	+	0.0961295i
$579$	−20.7214	−	25.9839i	−0.861154	−	1.07985i
$580$	−0.238630	−	0.114918i	−0.00990855	−	0.00477171i
$581$	−14.8236	−	28.2543i	−0.614985	−	1.17219i
$582$	5.14132	−	2.47593i	0.213115	−	0.102631i
$583$	0.00686342	+	0.00330525i	0.000284254	+	0.000136889i
$584$	−1.40793	−	6.16856i	−0.0582607	−	0.255257i
$585$	0.0949214	+	0.0457117i	0.00392452	+	0.00188995i
$586$	4.85301	−	6.08549i	0.200476	−	0.251389i
$587$	−17.2126			−0.710440			−0.355220	−	0.934783i	$-0.615594\pi$
$587$	−17.2126			−0.710440			−0.355220	+	0.934783i	$0.615594\pi$
$588$	14.3013	−	20.7057i	0.589776	−	0.853887i
$589$	71.1053			2.92984
$590$	−0.0860902	+	0.107954i	−0.00354428	+	0.00444438i
$591$	35.4057	+	17.0505i	1.45640	+	0.701363i
$592$	5.95204	+	26.0776i	0.244627	+	1.07178i
$593$	10.5133	+	5.06294i	0.431730	+	0.207910i	0.637111	−	0.770772i	$-0.280129\pi$
$593$	10.5133	+	5.06294i	0.431730	+	0.207910i	−0.205381	+	0.978682i	$0.565843\pi$
$594$	−0.00191962		0.000924443i	−7.87632e−5		3.79303e-5i
$595$	−3.02169	+	2.58449i	−0.123877	+	0.105954i
$596$	3.62899	+	1.74763i	0.148649	+	0.0715858i
$597$	26.4787	+	33.2033i	1.08370	+	1.35892i
$598$	−1.18404	+	0.570204i	−0.0484190	+	0.0233174i
$599$	−25.8617	+	32.4296i	−1.05668	+	1.32504i	−0.113213	+	0.993571i	$0.536114\pi$
$599$	−25.8617	+	32.4296i	−1.05668	+	1.32504i	−0.943468	+	0.331465i	$0.892457\pi$
$600$	−1.97593	+	8.65712i	−0.0806671	+	0.353426i
$601$	2.99165	−	3.75141i	0.122032	−	0.153023i	−0.717063	−	0.697009i	$-0.754514\pi$
$601$	2.99165	−	3.75141i	0.122032	−	0.153023i	0.839095	+	0.543985i	$0.183085\pi$
$602$	0.918910	−	2.08889i	0.0374520	−	0.0851366i
$603$	−1.41834	−	1.77855i	−0.0577595	−	0.0724281i
$604$	−6.19272	+	2.98226i	−0.251978	+	0.121346i
$605$	−0.591748	+	2.59262i	−0.0240580	+	0.105405i
$606$	−4.45041			−0.180786
$607$	12.1058			0.491359			0.245679	−	0.969351i	$-0.420989\pi$
$607$	12.1058			0.491359			0.245679	+	0.969351i	$0.420989\pi$
$608$	−4.64789	+	20.3637i	−0.188497	+	0.825859i
$609$	−2.10527	+	1.80067i	−0.0853099	+	0.0729667i
$610$	−0.0149593	−	0.0655408i	−0.000605682	−	0.00265367i
$611$	−2.13955	−	9.37396i	−0.0865568	−	0.379230i
$612$	3.27592	+	4.10788i	0.132421	+	0.166051i
$613$	18.9234	+	23.7292i	0.764308	+	0.958412i	0.999910	−	0.0134377i	$-0.00427747\pi$
$613$	18.9234	+	23.7292i	0.764308	+	0.958412i	−0.235602	+	0.971850i	$0.575706\pi$
$614$	0.792004	+	3.47000i	0.0319627	+	0.140038i
$615$	1.05843	+	4.63727i	0.0426799	+	0.186993i
$616$	0.00451666	−	0.00119559i	0.000181982	−	4.81717e-5i
$617$	3.86493	−	16.9334i	0.155596	−	0.681711i	−0.835603	−	0.549333i	$-0.814882\pi$
$617$	3.86493	−	16.9334i	0.155596	−	0.681711i	0.991199	−	0.132378i	$-0.0422612\pi$
$618$	−0.758977			−0.0305305
$619$	5.77000			0.231916			0.115958	−	0.993254i	$-0.463006\pi$
$619$	5.77000			0.231916			0.115958	+	0.993254i	$0.463006\pi$
$620$	−1.00681	+	4.41114i	−0.0404346	+	0.177156i
$621$	22.8688	−	11.0130i	0.917694	−	0.441938i
$622$	3.58207	+	4.49177i	0.143628	+	0.180104i
$623$	19.2838	+	36.7557i	0.772590	+	1.47259i
$624$	4.20709	−	5.27552i	0.168418	−	0.211190i
$625$	−5.36871	+	23.5218i	−0.214748	+	0.940873i
$626$	4.01402	−	5.03342i	0.160432	−	0.201176i
$627$	0.0224155	−	0.0107947i	0.000895187	−	0.000431099i
$628$	−8.37444	−	10.5012i	−0.334177	−	0.419044i
$629$	−41.1540	−	19.8187i	−1.64092	−	0.790225i
$630$	−0.0550678	−	0.0409000i	−0.00219396	−	0.00162950i
$631$	−0.896837	+	0.431894i	−0.0357025	+	0.0171934i	−0.451650	−	0.892195i	$-0.649164\pi$
$631$	−0.896837	+	0.431894i	−0.0357025	+	0.0171934i	0.415947	+	0.909389i	$0.363450\pi$
$632$	0.585732	+	0.282074i	0.0232992	+	0.0112203i
$633$	4.71566	+	20.6606i	0.187430	+	0.821187i
$634$	−4.41671	−	2.12697i	−0.175410	−	0.0844730i
$635$	−2.83293	+	3.55238i	−0.112421	+	0.140972i
$636$	−15.0339			−0.596131
$637$	6.08326	−	3.46323i	0.241028	−	0.137218i
$638$	−0.000253224	0		−1.00252e−5	0
$639$	−0.713007	+	0.894082i	−0.0282061	+	0.0353693i
$640$	−1.58774	−	0.764613i	−0.0627608	−	0.0302240i
$641$	−4.76128	−	20.8605i	−0.188059	−	0.823942i	−0.977638	−	0.210293i	$-0.932558\pi$
$641$	−4.76128	−	20.8605i	−0.188059	−	0.823942i	0.789579	−	0.613649i	$-0.210299\pi$
$642$	1.29572	+	0.623985i	0.0511380	+	0.0246267i
$643$	−3.25140	+	1.56579i	−0.128223	+	0.0617488i	−0.496895	−	0.867811i	$-0.665527\pi$
$643$	−3.25140	+	1.56579i	−0.128223	+	0.0617488i	0.368672	+	0.929559i	$0.379812\pi$
$644$	−26.4903	+	7.01216i	−1.04386	+	0.276318i
$645$	1.41510	+	0.681476i	0.0557195	+	0.0268331i
$646$	−7.02812	−	8.81298i	−0.276518	−	0.346742i
$647$	−41.4926	+	19.9818i	−1.63124	+	0.785565i	−0.631293	+	0.775544i	$0.717476\pi$
$647$	−41.4926	+	19.9818i	−1.63124	+	0.785565i	−0.999950	+	0.0100211i	$0.996810\pi$
$648$	6.11540	−	7.66847i	0.240236	−	0.301246i
$649$	0.000940770	−	0.00412178i	3.69284e−5	−	0.000161794i
$650$	−0.758198	+	0.950750i	−0.0297390	+	0.0372915i
$651$	37.9924	+	28.2177i	1.48904	+	1.10594i
$652$	−12.0536	−	15.1147i	−0.472054	−	0.591937i
$653$	−27.1411	+	13.0705i	−1.06211	+	0.511487i	−0.881557	−	0.472078i	$-0.843504\pi$
$653$	−27.1411	+	13.0705i	−1.06211	+	0.511487i	−0.180556	+	0.983565i	$0.557790\pi$
$654$	0.878778	−	3.85018i	0.0343629	−	0.150554i
$655$	3.09754			0.121031
$656$	38.6405			1.50866
$657$	0.632906	−	2.77294i	0.0246920	−	0.108183i
$658$	0.215134	+	6.25652i	0.00838681	+	0.243904i
$659$	7.45621	+	32.6678i	0.290453	+	1.27256i	0.883897	+	0.467682i	$0.154911\pi$
$659$	7.45621	+	32.6678i	0.290453	+	1.27256i	−0.593444	+	0.804875i	$0.702232\pi$
$660$	0.000352278		0.00154343i	1.37124e−5		6.00779e-5i
$661$	−20.9337	−	26.2500i	−0.814227	−	1.02101i	−0.999267	−	0.0382769i	$-0.987813\pi$
$661$	−20.9337	−	26.2500i	−0.814227	−	1.02101i	0.185041	−	0.982731i	$-0.440758\pi$
$662$	4.99392	+	6.26218i	0.194094	+	0.243387i
$663$	2.56408	+	11.2340i	0.0995805	+	0.436291i
$664$	2.60153	+	11.3980i	0.100959	+	0.442330i
$665$	−3.78356	−	2.81013i	−0.146720	−	0.108972i
$666$	0.175347	−	0.768244i	0.00679454	−	0.0297688i
$667$	3.01670			0.116807
$668$	27.2190			1.05313
$669$	−8.84424	+	38.7492i	−0.341938	+	1.49813i
$670$	−0.279797	+	0.134743i	−0.0108095	+	0.00520559i
$671$	0.00128338	+	0.00160931i	4.95445e−5	+	6.21268e-5i
$672$	−10.5647	+	9.03609i	−0.407540	+	0.348575i
$673$	−26.5867	+	33.3386i	−1.02484	+	1.28511i	−0.0670176	+	0.997752i	$0.521348\pi$
$673$	−26.5867	+	33.3386i	−1.02484	+	1.28511i	−0.957823	+	0.287358i	$0.907223\pi$
$674$	−0.593945	+	2.60224i	−0.0228779	+	0.100235i
$675$	14.6440	−	18.3630i	0.563648	−	0.706792i
$676$	1.74738	−	0.841492i	0.0672068	−	0.0323651i
$677$	−15.9078	−	19.9478i	−0.611387	−	0.766656i	0.375717	−	0.926735i	$-0.377397\pi$
$677$	−15.9078	−	19.9478i	−0.611387	−	0.766656i	−0.987104	+	0.160079i	$0.948825\pi$
$678$	−7.65675	−	3.68730i	−0.294056	−	0.141610i
$679$	32.5029	+	6.25188i	1.24735	+	0.239925i
$680$	1.31266	−	0.632146i	0.0503384	−	0.0242417i
$681$	8.71098	+	4.19499i	0.333805	+	0.160752i
$682$	0.000962586		0.00421736i	3.68593e−5		0.000161491i
$683$	22.3121	+	10.7450i	0.853750	+	0.411144i	0.808968	−	0.587853i	$-0.200027\pi$
$683$	22.3121	+	10.7450i	0.853750	+	0.411144i	0.0447816	+	0.998997i	$0.485741\pi$
$684$	−3.88294	+	4.86905i	−0.148468	+	0.186173i
$685$	3.52219			0.134576
$686$	−4.31534	+	1.46614i	−0.164760	+	0.0559776i
$687$	45.4330			1.73338
$688$	7.95534	−	9.97568i	0.303294	−	0.380319i
$689$	−3.76782	−	1.81449i	−0.143542	−	0.0691264i
$690$	0.131043	+	0.574138i	0.00498873	+	0.0218571i
$691$	−1.47635	−	0.710971i	−0.0561629	−	0.0270466i	0.405591	−	0.914054i	$-0.367066\pi$
$691$	−1.47635	−	0.710971i	−0.0561629	−	0.0270466i	−0.461754	+	0.887008i	$0.652780\pi$
$692$	32.5487	−	15.6746i	1.23732	−	0.595860i
$693$	0.00206249		0.000396716i	7.83475e−5		1.50700e-5i
$694$	−1.99585	−	0.961151i	−0.0757614	−	0.0364848i
$695$	2.10209	+	2.63594i	0.0797370	+	0.0999870i
$696$	0.914559	−	0.440429i	0.0346663	−	0.0166944i
$697$	−41.1414	+	51.5897i	−1.55834	+	1.95410i
$698$	0.0671099	−	0.294028i	0.00254015	−	0.0111291i
$699$	−27.7625	+	34.8131i	−1.05007	+	1.31675i
$700$	−19.2695	+	16.4815i	−0.728319	+	0.622940i
$701$	10.5481	+	13.2268i	0.398395	+	0.499571i	0.940053	−	0.341027i	$-0.110775\pi$
$701$	10.5481	+	13.2268i	0.398395	+	0.499571i	−0.541659	+	0.840599i	$0.682203\pi$
$702$	1.05382	−	0.507492i	0.0397738	−	0.0191541i
$703$	12.0476	−	52.7840i	0.454384	−	1.99079i
$704$	0.0119916			0.000451950
$705$	−4.30861			−0.162272
$706$	0.527054	−	2.30917i	0.0198359	−	0.0869069i
$707$	−20.7230	−	15.3914i	−0.779367	−	0.578852i
$708$	1.85662	+	8.13438i	0.0697760	+	0.305709i
$709$	−5.19654	−	22.7675i	−0.195160	−	0.855052i	−0.973768	−	0.227542i	$-0.926931\pi$
$709$	−5.19654	−	22.7675i	−0.195160	−	0.855052i	0.778608	−	0.627510i	$-0.215926\pi$
$710$	0.0973364	+	0.122056i	0.00365297	+	0.00458068i
$711$	0.182211	+	0.228486i	0.00683346	+	0.00856889i
$712$	−3.38431	−	14.8276i	−0.126832	−	0.555688i
$713$	−11.4675	−	50.2422i	−0.429459	−	1.88158i
$714$	−0.257822	−	7.49794i	−0.00964873	−	0.280603i
$715$	−9.79929e−5	0	0.000429335i	−3.66473e−6	0	1.60562e-5i
$716$	28.4223			1.06219
$717$	22.7984			0.851422
$718$	−1.09895	+	4.81483i	−0.0410126	+	0.179688i
$719$	−22.0161	+	10.6024i	−0.821061	+	0.395402i	−0.796755	−	0.604303i	$-0.793452\pi$
$719$	−22.0161	+	10.6024i	−0.821061	+	0.395402i	−0.0243057	+	0.999705i	$0.507738\pi$
$720$	−0.239124	−	0.299852i	−0.00891161	−	0.0111748i
$721$	−3.53411	−	2.62486i	−0.131617	−	0.0977548i
$722$	5.41517	−	6.79041i	0.201532	−	0.252713i
$723$	−9.02637	+	39.5471i	−0.335694	+	1.47077i
$724$	−14.2407	+	17.8573i	−0.529253	+	0.663662i
$725$	2.51500	−	1.21116i	0.0934048	−	0.0449814i
$726$	−3.12842	−	3.92291i	−0.116106	−	0.145593i
$727$	−3.46947	−	1.67081i	−0.128676	−	0.0619669i	0.368438	−	0.929652i	$-0.379893\pi$
$727$	−3.46947	−	1.67081i	−0.128676	−	0.0619669i	−0.497114	+	0.867685i	$0.665607\pi$
$728$	−2.47952	+	0.656344i	−0.0918970	+	0.0243257i
$729$	−19.8403	+	9.55461i	−0.734828	+	0.353874i
$730$	−0.349832	−	0.168470i	−0.0129479	−	0.00623537i
$731$	4.84851	+	21.2427i	0.179329	+	0.785690i
$732$	−3.65996	−	1.76254i	−0.135276	−	0.0651455i
$733$	0.234755	−	0.294374i	0.00867089	−	0.0108729i	−0.777477	−	0.628911i	$-0.783501\pi$
$733$	0.234755	−	0.294374i	0.00867089	−	0.0108729i	0.786148	+	0.618038i	$0.212072\pi$
$734$	8.11919			0.299685
$735$	−0.906416	−	3.00297i	−0.0334336	−	0.110766i
$736$	15.1384			0.558008
$737$	0.00592859	−	0.00743422i	0.000218382	−	0.000273843i
$738$	−1.02561	−	0.493909i	−0.0377534	−	0.0181811i
$739$	2.64571	+	11.5916i	0.0973242	+	0.426405i	0.999992	−	0.00393240i	$-0.00125172\pi$
$739$	2.64571	+	11.5916i	0.0973242	+	0.426405i	−0.902668	+	0.430337i	$0.858395\pi$
$740$	3.10396	+	1.49479i	0.114104	+	0.0549495i
$741$	−12.3054	+	5.92598i	−0.452051	+	0.217696i
$742$	2.18587	+	1.62349i	0.0802457	+	0.0596002i
$743$	13.7451	+	6.61927i	0.504257	+	0.242837i	0.668677	−	0.743553i	$-0.266861\pi$
$743$	13.7451	+	6.61927i	0.504257	+	0.242837i	−0.164420	+	0.986390i	$0.552575\pi$
$744$	−10.8117	−	13.5575i	−0.396377	−	0.497042i
$745$	0.452359	−	0.217844i	0.0165731	−	0.00798120i
$746$	1.74653	−	2.19008i	0.0639452	−	0.0801847i
$747$	−1.16946	+	5.12375i	−0.0427884	+	0.187468i
$748$	−0.0136931	+	0.0171707i	−0.000500671	+	0.000627822i
$749$	3.87540	+	7.38667i	0.141604	+	0.269903i
$750$	0.683534	+	0.857124i	0.0249591	+	0.0312977i
$751$	12.8756	−	6.20056i	0.469837	−	0.226262i	−0.183957	−	0.982934i	$-0.558891\pi$
$751$	12.8756	−	6.20056i	0.469837	−	0.226262i	0.653794	+	0.756673i	$0.273176\pi$
$752$	−7.78862	+	34.1242i	−0.284022	+	1.24438i
$753$	−39.0789			−1.42411
$754$	0.139013			0.00506254
$755$	−0.190651	+	0.835297i	−0.00693851	+	0.0303996i
$756$	23.5769	−	6.24095i	0.857482	−	0.226981i
$757$	−1.71114	−	7.49698i	−0.0621923	−	0.272482i	0.934265	−	0.356579i	$-0.116057\pi$
$757$	−1.71114	−	7.49698i	−0.0621923	−	0.272482i	−0.996458	+	0.0840963i	$0.973200\pi$
$758$	−0.480529	−	2.10533i	−0.0174536	−	0.0764692i
$759$	−0.0112425	−	0.0140976i	−0.000408075	−	0.000511710i
$760$	1.07671	+	1.35016i	0.0390565	+	0.0489753i
$761$	−6.73799	−	29.5211i	−0.244252	−	1.07014i	−0.937102	−	0.349056i	$-0.886502\pi$
$761$	−6.73799	−	29.5211i	−0.244252	−	1.07014i	0.692850	−	0.721082i	$-0.256355\pi$
$762$	−1.90768	−	8.35811i	−0.0691081	−	0.302782i
$763$	17.4075	−	14.8888i	0.630193	−	0.539012i
$764$	2.10257	−	9.21196i	0.0760683	−	0.333277i
$765$	0.654939			0.0236794
$766$	−0.844473			−0.0305120
$767$	−0.516455	+	2.26274i	−0.0186481	+	0.0817027i
$768$	−18.9919	+	9.14603i	−0.685312	+	0.330029i
$769$	−6.10660	−	7.65743i	−0.220210	−	0.276134i	0.659439	−	0.751758i	$-0.270794\pi$
$769$	−6.10660	−	7.65743i	−0.220210	−	0.276134i	−0.879649	+	0.475624i	$0.842222\pi$
$770$	0.000115453	0	0.000262451i	4.16065e−6	0	9.45808e-6i
$771$	32.9855	−	41.3625i	1.18794	−	1.48963i
$772$	−7.73792	+	33.9021i	−0.278494	+	1.22016i
$773$	19.6307	−	24.6161i	0.706068	−	0.885381i	−0.291393	−	0.956603i	$-0.594119\pi$
$773$	19.6307	−	24.6161i	0.706068	−	0.885381i	0.997460	+	0.0712227i	$0.0226901\pi$
$774$	−0.338665	+	0.163093i	−0.0121731	+	0.00586224i
$775$	−29.7318	−	37.2825i	−1.06800	−	1.33923i
$776$	−10.9269	−	5.26211i	−0.392252	−	0.188899i
$777$	27.3842	−	23.4221i	0.982402	−	0.840261i
$778$	3.91176	−	1.88381i	0.140243	−	0.0675377i
$779$	−70.4672	−	33.9352i	−2.52475	−	1.21585i
$780$	−0.193390	−	0.847297i	−0.00692448	−	0.0303381i
$781$	−0.00430669	−	0.00207399i	−0.000154105	−	7.42133e-5i
$782$	−5.09369	+	6.38729i	−0.182150	+	0.228409i
$783$	−2.68492			−0.0959512
$784$	−25.4220	+	1.75037i	−0.907929	+	0.0625134i
$785$	−1.67426			−0.0597569
$786$	−3.64398	+	4.56940i	−0.129976	+	0.162985i
$787$	18.6682	+	8.99012i	0.665449	+	0.320463i	0.735938	−	0.677049i	$-0.236742\pi$
$787$	18.6682	+	8.99012i	0.665449	+	0.320463i	−0.0704887	+	0.997513i	$0.522456\pi$
$788$	−9.14950	−	40.0866i	−0.325937	−	1.42803i
$789$	−12.4284	−	5.98518i	−0.442461	−	0.213078i
$790$	0.0359449	−	0.0173102i	0.00127886	−	0.000615868i
$791$	−22.9008	−	43.6498i	−0.814258	−	1.55201i
$792$	−0.000693371	0	0.000333910i	−2.46379e−5	0	1.18650e-5i
$793$	−0.704540	−	0.883465i	−0.0250190	−	0.0313728i
$794$	−1.71682	+	0.826779i	−0.0609278	+	0.0293413i
$795$	−1.16841	+	1.46514i	−0.0414393	+	0.0519633i
$796$	9.88785	−	43.3215i	0.350465	−	1.53549i
$797$	22.0888	−	27.6985i	0.782425	−	0.981130i	−0.217562	−	0.976046i	$-0.569810\pi$
$797$	22.0888	−	27.6985i	0.782425	−	0.981130i	0.999987	−	0.00508338i	$-0.00161810\pi$
$798$	8.59646	−	2.27554i	0.304311	−	0.0805532i
$799$	−37.2672	−	46.7316i	−1.31842	−	1.65325i
$800$	12.6207	−	6.07783i	0.446211	−	0.214884i
$801$	1.52134	−	6.66543i	0.0537540	−	0.235511i
$802$	1.23900			0.0437508
$803$	0.0118888			0.000419547
$804$	−4.17573	+	18.2951i	−0.147267	+	0.645217i
$805$	−1.37542	+	3.12662i	−0.0484770	+	0.110199i
$806$	−0.528432	−	2.31521i	−0.0186132	−	0.0815498i
$807$	−4.93103	−	21.6042i	−0.173580	−	0.760505i
$808$	5.89727	+	7.39494i	0.207465	+	0.260153i
$809$	20.0303	+	25.1173i	0.704230	+	0.883076i	0.997332	−	0.0730052i	$-0.0232590\pi$
$809$	20.0303	+	25.1173i	0.704230	+	0.883076i	−0.293102	+	0.956081i	$0.594688\pi$
$810$	−0.133938	−	0.586823i	−0.00470612	−	0.0206188i
$811$	3.44670	+	15.1010i	0.121030	+	0.530268i	0.998699	+	0.0509996i	$0.0162407\pi$
$811$	3.44670	+	15.1010i	0.121030	+	0.530268i	−0.877669	+	0.479268i	$0.840902\pi$
$812$	2.84643	+	0.547507i	0.0998903	+	0.0192137i
$813$	−1.67992	+	7.36022i	−0.0589175	+	0.258134i
$814$	0.00329379			0.000115447
$815$	−2.40981			−0.0844119
$816$	9.33405	−	40.8951i	0.326757	−	1.43162i
$817$	−23.2688	+	11.2057i	−0.814072	+	0.392036i
$818$	−0.141831	−	0.177851i	−0.00495901	−	0.00621840i
$819$	−1.13225	−	0.217786i	−0.0395639	−	0.00761005i
$820$	3.10301	−	3.89105i	0.108362	−	0.135881i
$821$	2.35094	−	10.3001i	0.0820484	−	0.359477i	−0.917192	−	0.398445i	$-0.869550\pi$
$821$	2.35094	−	10.3001i	0.0820484	−	0.359477i	0.999240	+	0.0389679i	$0.0124070\pi$
$822$	−4.14355	+	5.19584i	−0.144523	+	0.181226i
$823$	−31.0443	+	14.9501i	−1.08214	+	0.521129i	−0.887999	−	0.459846i	$-0.847905\pi$
$823$	−31.0443	+	14.9501i	−1.08214	+	0.521129i	−0.194136	+	0.980975i	$0.562190\pi$
$824$	1.00572	+	1.26114i	0.0350361	+	0.0439338i
$825$	−0.0150327	−	0.00723938i	−0.000523372	−	0.000252043i
$826$	0.608477	−	1.38320i	0.0211716	−	0.0481278i
$827$	22.2912	−	10.7349i	0.775141	−	0.373288i	−0.00411669	−	0.999992i	$-0.501310\pi$
$827$	22.2912	−	10.7349i	0.775141	−	0.373288i	0.779258	+	0.626703i	$0.215596\pi$
$828$	4.06663	+	1.95839i	0.141325	+	0.0680587i
$829$	9.24426	+	40.5018i	0.321066	+	1.40668i	0.835659	+	0.549249i	$0.185086\pi$
$829$	9.24426	+	40.5018i	0.321066	+	1.40668i	−0.514592	+	0.857435i	$0.672057\pi$
$830$	0.646407	+	0.311293i	0.0224371	+	0.0108052i
$831$	−13.5943	+	17.0467i	−0.471580	+	0.591343i
$832$	−6.58304			−0.228226
$833$	24.7305	−	35.8052i	0.856860	−	1.24058i
$834$	−6.36139			−0.220277
$835$	2.11543	−	2.65266i	0.0732073	−	0.0917991i
$836$	−0.0234537	−	0.0112947i	−0.000811162	−	0.000390635i
$837$	10.2062	+	44.7165i	0.352779	+	1.54563i
$838$	−3.28433	−	1.58165i	−0.113455	−	0.0546372i
$839$	5.05877	−	2.43617i	0.174648	−	0.0841060i	−0.344517	−	0.938780i	$-0.611957\pi$
$839$	5.05877	−	2.43617i	0.174648	−	0.0841060i	0.519165	+	0.854674i	$0.326243\pi$
$840$	0.0394985	+	1.14869i	0.00136283	+	0.0396336i
$841$	25.8406	+	12.4442i	0.891055	+	0.429109i
$842$	1.95627	+	2.45309i	0.0674176	+	0.0845389i
$843$	15.0292	−	7.23768i	0.517633	−	0.249279i
$844$	13.8249	−	17.3359i	0.475874	−	0.596728i
$845$	0.0537953	−	0.235692i	0.00185061	−	0.00810807i
$846$	0.642911	−	0.806184i	0.0221037	−	0.0277172i
$847$	−1.00014	−	29.0861i	−0.0343653	−	0.999409i
$848$	9.49179	+	11.9023i	0.325950	+	0.408728i
$849$	−22.3125	+	10.7451i	−0.765763	+	0.368772i
$850$	−1.68217	+	7.37008i	−0.0576981	+	0.252792i
$851$	−39.2395			−1.34511
$852$	9.43351			0.323187
$853$	−5.84308	+	25.6002i	−0.200063	+	0.876534i	0.770834	+	0.637036i	$0.219840\pi$
$853$	−5.84308	+	25.6002i	−0.200063	+	0.876534i	−0.970897	+	0.239498i	$0.923017\pi$
$854$	0.341810	+	0.651503i	0.0116965	+	0.0222940i
$855$	0.172742	+	0.756834i	0.00590766	+	0.0258832i
$856$	−0.680132	−	2.97985i	−0.0232464	−	0.101849i
$857$	−11.1798	−	14.0190i	−0.381894	−	0.478880i	0.553317	−	0.832971i	$-0.313362\pi$
$857$	−11.1798	−	14.0190i	−0.381894	−	0.478880i	−0.935211	+	0.354090i	$0.884790\pi$
$858$	−0.000518063	0	0.000649631i	−1.76864e−5	0	2.21780e-5i
$859$	−1.55368	−	6.80712i	−0.0530109	−	0.232256i	0.941481	−	0.337065i	$-0.109434\pi$
$859$	−1.55368	−	6.80712i	−0.0530109	−	0.232256i	−0.994492	+	0.104809i	$0.966577\pi$
$860$	−0.365688	−	1.60219i	−0.0124699	−	0.0546341i
$861$	−24.1844	−	46.0964i	−0.824203	−	1.57096i
$862$	−0.941408	+	4.12458i	−0.0320645	+	0.140484i
$863$	−57.9630			−1.97308			−0.986542	−	0.163510i	$-0.947719\pi$
$863$	−57.9630			−1.97308			−0.986542	+	0.163510i	$0.947719\pi$
$864$	−13.4734			−0.458375
$865$	1.00206	−	4.39029i	0.0340709	−	0.149274i
$866$	2.28173	−	1.09882i	0.0775364	−	0.0373396i
$867$	25.0150	+	31.3678i	0.849554	+	1.06531i
$868$	−1.70167	−	49.4877i	−0.0577584	−	1.67972i
$869$	−0.000761632	0	0.000955056i	−2.58366e−5	0	3.23981e-5i
$870$	0.0138615	−	0.0607314i	0.000469950	−	0.00205899i
$871$	−3.25462	+	4.08117i	−0.110279	+	0.138285i
$872$	−7.56204	+	3.64169i	−0.256083	+	0.123323i
$873$	−3.39917	−	4.26242i	−0.115044	−	0.144261i
$874$	−8.72449	−	4.20149i	−0.295110	−	0.142118i
$875$	0.218523	+	6.35506i	0.00738743	+	0.214840i
$876$	−21.1391	+	10.1801i	−0.714226	+	0.343953i
$877$	13.5748	+	6.53730i	0.458390	+	0.220749i	0.648805	−	0.760955i	$-0.275269\pi$
$877$	13.5748	+	6.53730i	0.458390	+	0.220749i	−0.190415	+	0.981704i	$0.560983\pi$
$878$	−0.0212777	−	0.0932235i	−0.000718086	−	0.00314614i
$879$	−52.8222	−	25.4378i	−1.78165	−	0.857996i
$880$	0.000999521	−	0.00125336i	3.36939e−5	−	4.22508e-5i
$881$	43.3999			1.46218			0.731089	−	0.682282i	$-0.239012\pi$
$881$	43.3999			1.46218			0.731089	+	0.682282i	$0.239012\pi$
$882$	0.697137	+	0.278489i	0.0234738	+	0.00937723i
$883$	57.4511			1.93338			0.966691	−	0.255945i	$-0.0823867\pi$
$883$	57.4511			1.93338			0.966691	+	0.255945i	$0.0823867\pi$
$884$	7.51714	−	9.42620i	0.252829	−	0.317037i
$885$	0.937040	+	0.451255i	0.0314983	+	0.0151688i
$886$	−1.09112	−	4.78050i	−0.0366568	−	0.160604i
$887$	11.4741	+	5.52563i	0.385262	+	0.185532i	0.616482	−	0.787369i	$-0.288557\pi$
$887$	11.4741	+	5.52563i	0.385262	+	0.185532i	−0.231220	+	0.972902i	$0.574272\pi$
$888$	−11.8961	+	5.72884i	−0.399206	+	0.192247i
$889$	20.0229	−	45.5164i	0.671545	−	1.52657i
$890$	−0.840905	−	0.404959i	−0.0281872	−	0.0135742i
$891$	0.0114908	+	0.0144091i	0.000384958	+	0.000482722i
$892$	37.4682	−	18.0437i	1.25453	−	0.604149i
$893$	44.1727	−	55.3908i	1.47818	−	1.85358i
$894$	−0.210802	+	0.923582i	−0.00705026	+	0.0308892i
$895$	2.20895	−	2.76993i	0.0738370	−	0.0925887i
$896$	18.9389	+	3.64287i	0.632705	+	0.121700i
$897$	6.17178	+	7.73917i	0.206070	+	0.258403i
$898$	1.07768	−	0.518982i	0.0359626	−	0.0173187i
$899$	−1.21301	+	5.31454i	−0.0404561	+	0.177250i
$900$	4.17659			0.139220
$901$	−25.9972			−0.866093
$902$	0.00105880	−	0.00463891i	3.52542e−5	−	0.000154459i
$903$	−16.8797	−	3.24678i	−0.561720	−	0.108046i
$904$	4.01908	+	17.6087i	0.133673	+	0.585658i
$905$	0.633535	+	2.77570i	0.0210594	+	0.0922673i
$906$	−1.00792	−	1.26390i	−0.0334860	−	0.0419901i
$907$	14.3399	+	17.9817i	0.476149	+	0.597072i	0.960665	−	0.277711i	$-0.0895756\pi$
$907$	14.3399	+	17.9817i	0.476149	+	0.597072i	−0.484516	+	0.874782i	$0.661004\pi$
$908$	−2.25108	−	9.86263i	−0.0747047	−	0.327303i
$909$	0.946127	+	4.14525i	0.0313811	+	0.137489i
$910$	−0.0633805	+	0.144078i	−0.00210104	+	0.00477614i
$911$	−3.68972	+	16.1657i	−0.122246	+	0.535594i	0.876304	+	0.481759i	$0.160002\pi$
$911$	−3.68972	+	16.1657i	−0.122246	+	0.535594i	−0.998550	+	0.0538356i	$0.982855\pi$
$912$	49.7194			1.64637
$913$	−0.0219677			−0.000727025
$914$	0.338318	−	1.48227i	0.0111906	−	0.0490291i
$915$	−0.456219	+	0.219703i	−0.0150821	+	0.00726317i
$916$	−29.6390	−	37.1661i	−0.979300	−	1.22800i
$917$	−32.7707	+	8.67463i	−1.08219	+	0.286462i
$918$	4.53348	−	5.68481i	0.149627	−	0.187627i
$919$	1.95320	−	8.55753i	0.0644301	−	0.282287i	−0.932442	−	0.361320i	$-0.882326\pi$
$919$	1.95320	−	8.55753i	0.0644301	−	0.282287i	0.996872	+	0.0790333i	$0.0251833\pi$
$920$	0.780358	−	0.978538i	0.0257277	−	0.0322615i
$921$	24.1541	−	11.6320i	0.795904	−	0.383287i
$922$	−2.83952	−	3.56064i	−0.0935145	−	0.117264i
$923$	2.36425	+	1.13856i	0.0778202	+	0.0374762i
$924$	−0.00804932	−	0.0153423i	−0.000264803	−	0.000504725i
$925$	−32.7137	+	15.7541i	−1.07562	+	0.517991i
$926$	2.29845	+	1.10687i	0.0755316	+	0.0363741i
$927$	0.161353	+	0.706934i	0.00529953	+	0.0232188i
$928$	−1.44273	−	0.694783i	−0.0473600	−	0.0228074i
$929$	13.7029	−	17.1829i	0.449578	−	0.563753i	−0.504461	−	0.863434i	$-0.668309\pi$
$929$	13.7029	−	17.1829i	0.449578	−	0.563753i	0.954039	+	0.299681i	$0.0968803\pi$
$930$	−1.06415			−0.0348950
$931$	47.8984	+	19.1343i	1.56981	+	0.627100i
$932$	46.5900			1.52611
$933$	26.9810	−	33.8331i	0.883319	−	1.10765i
$934$	5.33974	+	2.57148i	0.174722	+	0.0841414i
$935$	0.000609174		0.00266897i	1.99221e−5		8.72845e-5i
$936$	0.380640	+	0.183307i	0.0124416	+	0.00599157i
$937$	−5.84060	+	2.81268i	−0.190804	+	0.0918864i	−0.526847	−	0.849960i	$-0.676626\pi$
$937$	−5.84060	+	2.81268i	−0.190804	+	0.0918864i	0.336042	+	0.941847i	$0.390911\pi$
$938$	2.58280	−	2.20910i	0.0843314	−	0.0721298i
$939$	−43.6902	−	21.0401i	−1.42578	−	0.686617i
$940$	2.81080	+	3.52463i	0.0916782	+	0.114961i
$941$	15.5507	−	7.48881i	0.506938	−	0.244128i	−0.162891	−	0.986644i	$-0.552082\pi$
$941$	15.5507	−	7.48881i	0.506938	−	0.244128i	0.669829	+	0.742516i	$0.266368\pi$
$942$	1.96962	−	2.46982i	0.0641736	−	0.0804712i
$943$	−12.6137	+	55.2641i	−0.410758	+	1.79965i
$944$	5.26781	−	6.60562i	0.171453	−	0.214995i
$945$	1.22415	−	2.78275i	0.0398215	−	0.0905230i
$946$	−0.000979625	−	0.00122841i	−3.18504e−5	−	3.99391e-5i
$947$	−19.2934	+	9.29120i	−0.626950	+	0.301923i	−0.720250	−	0.693715i	$-0.755973\pi$
$947$	−19.2934	+	9.29120i	−0.626950	+	0.301923i	0.0932995	+	0.995638i	$0.470259\pi$
$948$	0.536446	−	2.35032i	0.0174230	−	0.0763350i
$949$	−6.52661			−0.211863
$950$	−8.96038			−0.290713
$951$	−8.21645	+	35.9986i	−0.266437	+	1.16733i
$952$	−12.1172	+	10.3640i	−0.392719	+	0.335898i
$953$	10.8590	+	47.5763i	0.351757	+	1.54115i	0.773123	+	0.634256i	$0.218693\pi$
$953$	10.8590	+	47.5763i	0.351757	+	1.54115i	−0.421367	+	0.906890i	$0.638449\pi$
$954$	−0.0997979	−	0.437243i	−0.00323108	−	0.0141563i
$955$	−0.734355	−	0.920851i	−0.0237632	−	0.0297981i
$956$	−14.8729	−	18.6501i	−0.481025	−	0.603187i
$957$	0.000424424		0.00185952i	1.37197e−5		6.01098e-5i
$958$	−0.216936	−	0.950459i	−0.00700889	−	0.0307079i
$959$	−37.2634	+	9.86388i	−1.20330	+	0.318521i
$960$	−0.656423	+	2.87598i	−0.0211860	+	0.0928218i
$961$	62.1230			2.00397
$962$	−1.80820			−0.0582986
$963$	0.305739	−	1.33953i	0.00985229	−	0.0431657i
$964$	38.2397	−	18.4153i	1.23162	−	0.593116i
$965$	2.70259	+	3.38894i	0.0869993	+	0.109094i
$966$	−2.99426	−	5.70717i	−0.0963386	−	0.183625i
$967$	24.8696	−	31.1855i	0.799753	−	1.00286i	−0.199981	−	0.979800i	$-0.564088\pi$
$967$	24.8696	−	31.1855i	0.799753	−	1.00286i	0.999734	−	0.0230586i	$-0.00734043\pi$
$968$	−2.37294	+	10.3965i	−0.0762693	+	0.334158i
$969$	−52.9375	+	66.3815i	−1.70060	+	2.13248i
$970$	−0.670555	+	0.322922i	−0.0215302	+	0.0103684i
$971$	−26.1048	−	32.7343i	−0.837741	−	1.05049i	−0.997987	−	0.0634173i	$-0.979800\pi$
$971$	−26.1048	−	32.7343i	−0.837741	−	1.05049i	0.160246	−	0.987077i	$-0.448771\pi$
$972$	−7.85388	−	3.78223i	−0.251913	−	0.121315i
$973$	−29.6213	−	22.0003i	−0.949614	−	0.705299i
$974$	5.12967	−	2.47032i	0.164365	−	0.0791541i
$975$	8.25253	+	3.97421i	0.264292	+	0.127277i
$976$	0.915348	+	4.01040i	0.0292996	+	0.128370i
$977$	−47.8360	−	23.0366i	−1.53041	−	0.737006i	−0.536161	−	0.844116i	$-0.680126\pi$
$977$	−47.8360	−	23.0366i	−1.53041	−	0.737006i	−0.994247	+	0.107110i	$0.965840\pi$
$978$	2.83493	−	3.55488i	0.0906509	−	0.113673i
$979$	0.0285776			0.000913343
$980$	−1.86524	+	2.70053i	−0.0595830	+	0.0862652i
$981$	−3.77300			−0.120463
$982$	3.59169	−	4.50383i	0.114615	−	0.143723i
$983$	8.27708	+	3.98603i	0.263998	+	0.127135i	0.561201	−	0.827680i	$-0.310340\pi$
$983$	8.27708	+	3.98603i	0.263998	+	0.127135i	−0.297203	+	0.954814i	$0.596054\pi$
$984$	4.24436	+	18.5957i	0.135305	+	0.592811i
$985$	−4.61778	−	2.22380i	−0.147135	−	0.0708563i
$986$	0.778593	−	0.374951i	0.0247955	−	0.0119409i
$987$	45.5835	−	12.0662i	1.45094	−	0.384073i
$988$	12.8754	+	6.20045i	0.409620	+	0.197263i
$989$	11.6704	+	14.6343i	0.371098	+	0.465343i
$990$	−4.25505e−5	0	2.04912e-5i	−1.35234e−6	0	6.51254e-7i
$991$	0.634556	−	0.795708i	0.0201573	−	0.0252765i	−0.771651	−	0.636047i	$-0.780569\pi$
$991$	0.634556	−	0.795708i	0.0201573	−	0.0252765i	0.791808	+	0.610770i	$0.209140\pi$
$992$	−6.08711	+	26.6694i	−0.193266	+	0.846753i
$993$	37.6154	−	47.1682i	1.19369	−	1.49684i
$994$	−1.37160	−	1.01871i	−0.0435044	−	0.0323117i
$995$	−3.45348	−	4.33053i	−0.109483	−	0.137287i
$996$	39.0601	−	18.8104i	1.23767	−	0.596030i
$997$	−0.133942	+	0.586838i	−0.00424198	+	0.0185853i	−0.977005	−	0.213218i	$-0.931605\pi$
$997$	−0.133942	+	0.586838i	−0.00424198	+	0.0185853i	0.972763	+	0.231803i	$0.0744626\pi$
$998$	3.66780			0.116102
$999$	34.9239			1.10494

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.w.b.92.15	✓	174
49.8	even	7	inner	637.2.w.b.547.15	yes	174

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.w.b.92.15	✓	174	1.1	even	1	trivial
637.2.w.b.547.15	yes	174	49.8	even	7	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.w (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.153433 - 0.192399i) q^{2} +(-1.67003 - 0.804242i) q^{3} +(0.431566 + 1.89082i) q^{4} +(0.217813 + 0.104893i) q^{5} +(-0.410972 + 0.197914i) q^{6} +(-2.59813 - 0.499745i) q^{7} +(0.873441 + 0.420627i) q^{8} +(0.271713 + 0.340717i) q^{9} +O(q^{10})\)	\(q+(0.153433 - 0.192399i) q^{2} +(-1.67003 - 0.804242i) q^{3} +(0.431566 + 1.89082i) q^{4} +(0.217813 + 0.104893i) q^{5} +(-0.410972 + 0.197914i) q^{6} +(-2.59813 - 0.499745i) q^{7} +(0.873441 + 0.420627i) q^{8} +(0.271713 + 0.340717i) q^{9} +(0.0536009 - 0.0258129i) q^{10} +(-0.00113574 + 0.00142418i) q^{11} +(0.799947 - 3.50480i) q^{12} +(0.623490 - 0.781831i) q^{13} +(-0.494788 + 0.423199i) q^{14} +(-0.279393 - 0.350348i) q^{15} +(-3.27981 + 1.57947i) q^{16} +(1.38330 - 6.06065i) q^{17} +0.107243 q^{18} +7.36841 q^{19} +(-0.104333 + 0.457112i) q^{20} +(3.93702 + 2.92411i) q^{21} +(9.97495e-5 + 0.000437031i) q^{22} +(-1.18833 - 5.20643i) q^{23} +(-1.12038 - 1.40492i) q^{24} +(-3.08101 - 3.86346i) q^{25} +(-0.0547596 - 0.239917i) q^{26} +(1.05764 + 4.63382i) q^{27} +(-0.176338 - 5.12825i) q^{28} +(-0.125700 + 0.550728i) q^{29} -0.110275 q^{30} +9.65003 q^{31} +(-0.630786 + 2.76366i) q^{32} +(0.00304210 - 0.00146500i) q^{33} +(-0.953818 - 1.19605i) q^{34} +(-0.513485 - 0.381376i) q^{35} +(-0.526971 + 0.660801i) q^{36} +(1.63503 - 7.16355i) q^{37} +(1.13056 - 1.41767i) q^{38} +(-1.67003 + 0.804242i) q^{39} +(0.146126 + 0.183236i) q^{40} +(-9.56342 - 4.60550i) q^{41} +(1.16666 - 0.308824i) q^{42} +(-3.15791 + 1.52077i) q^{43} +(-0.00318300 - 0.00153285i) q^{44} +(0.0234436 + 0.102713i) q^{45} +(-1.18404 - 0.570204i) q^{46} +(5.99487 - 7.51734i) q^{47} +6.74765 q^{48} +(6.50051 + 2.59680i) q^{49} -1.21605 q^{50} +(-7.18439 + 9.00893i) q^{51} +(1.74738 + 0.841492i) q^{52} +(-0.930574 - 4.07711i) q^{53} +(1.05382 + 0.507492i) q^{54} +(-0.000396765 + 0.000191072i) q^{55} +(-2.05910 - 1.52934i) q^{56} +(-12.3054 - 5.92598i) q^{57} +(0.0866729 + 0.108684i) q^{58} +(-2.09108 + 1.00701i) q^{59} +(0.541867 - 0.679480i) q^{60} +(0.251447 - 1.10166i) q^{61} +(1.48063 - 1.85665i) q^{62} +(-0.535673 - 1.02101i) q^{63} +(-4.10446 - 5.14682i) q^{64} +(0.217813 - 0.104893i) q^{65} +(0.000184895 - 0.000810077i) q^{66} -5.22001 q^{67} +12.0566 q^{68} +(-2.20268 + 9.65058i) q^{69} +(-0.152162 + 0.0402782i) q^{70} +(0.583921 + 2.55832i) q^{71} +(0.0940104 + 0.411887i) q^{72} +(-4.06927 - 5.10271i) q^{73} +(-1.12739 - 1.41370i) q^{74} +(2.03821 + 8.92996i) q^{75} +(3.17995 + 13.9323i) q^{76} +(0.00366253 - 0.00313261i) q^{77} +(-0.101502 + 0.444708i) q^{78} +0.670602 q^{79} -0.880059 q^{80} +(2.25135 - 9.86380i) q^{81} +(-2.35344 + 1.13336i) q^{82} +(7.51906 + 9.42860i) q^{83} +(-3.82986 + 8.70613i) q^{84} +(0.937021 - 1.17499i) q^{85} +(-0.191933 + 0.840915i) q^{86} +(0.652841 - 0.818637i) q^{87} +(-0.00159105 + 0.000766210i) q^{88} +(-9.78147 - 12.2656i) q^{89} +(0.0233590 + 0.0112491i) q^{90} +(-2.01062 + 1.71971i) q^{91} +(9.33155 - 4.49384i) q^{92} +(-16.1158 - 7.76096i) q^{93} +(-0.526515 - 2.30681i) q^{94} +(1.60493 + 0.772894i) q^{95} +(3.27608 - 4.10807i) q^{96} -12.5101 q^{97} +(1.49701 - 0.852256i) q^{98} -0.000793838 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 174 q - 3 q^{2} - 31 q^{4} - 4 q^{5} - 2 q^{6} + 9 q^{7} - 15 q^{8} - 31 q^{9}+O(q^{10}) \) 174 * q - 3 * q^2 - 31 * q^4 - 4 * q^5 - 2 * q^6 + 9 * q^7 - 15 * q^8 - 31 * q^9	\( 174 q - 3 q^{2} - 31 q^{4} - 4 q^{5} - 2 q^{6} + 9 q^{7} - 15 q^{8} - 31 q^{9} - 10 q^{10} - 5 q^{11} + 25 q^{12} - 29 q^{13} + 15 q^{14} - 10 q^{15} - 51 q^{16} - 9 q^{17} + 44 q^{18} + 24 q^{19} + 63 q^{20} - 28 q^{21} - 8 q^{22} - 13 q^{23} - 48 q^{24} - 49 q^{25} - 3 q^{26} - 9 q^{27} - 44 q^{28} + 2 q^{29} - 22 q^{30} + 10 q^{31} + 24 q^{32} - 26 q^{33} + 118 q^{34} + 5 q^{35} - 55 q^{36} - 32 q^{37} + 16 q^{38} + 42 q^{40} - 14 q^{41} + 4 q^{42} - 50 q^{43} + 35 q^{44} - q^{45} + 4 q^{46} - 24 q^{47} - 116 q^{48} - 25 q^{49} + 156 q^{50} + 12 q^{51} - 31 q^{52} - 30 q^{53} - 78 q^{54} + 25 q^{55} + 3 q^{56} - 63 q^{57} - 12 q^{58} - 4 q^{59} + 128 q^{60} - 42 q^{61} - 38 q^{62} - 85 q^{63} - 105 q^{64} - 4 q^{65} + 15 q^{66} + 94 q^{67} + 214 q^{68} + 32 q^{69} - 57 q^{70} - 29 q^{71} - 64 q^{72} - 66 q^{73} - 90 q^{74} + 131 q^{75} - 21 q^{76} - 82 q^{77} + 19 q^{78} + 6 q^{79} + 22 q^{80} + 49 q^{81} - 50 q^{82} + 25 q^{83} + 89 q^{84} - 86 q^{85} - 28 q^{86} + 24 q^{87} + 48 q^{88} - 50 q^{89} - 155 q^{90} - 5 q^{91} - 98 q^{92} + 89 q^{93} - 28 q^{94} - 130 q^{95} - 105 q^{96} - 42 q^{97} + 195 q^{98} + 438 q^{99}+O(q^{100}) \) 174 * q - 3 * q^2 - 31 * q^4 - 4 * q^5 - 2 * q^6 + 9 * q^7 - 15 * q^8 - 31 * q^9 - 10 * q^10 - 5 * q^11 + 25 * q^12 - 29 * q^13 + 15 * q^14 - 10 * q^15 - 51 * q^16 - 9 * q^17 + 44 * q^18 + 24 * q^19 + 63 * q^20 - 28 * q^21 - 8 * q^22 - 13 * q^23 - 48 * q^24 - 49 * q^25 - 3 * q^26 - 9 * q^27 - 44 * q^28 + 2 * q^29 - 22 * q^30 + 10 * q^31 + 24 * q^32 - 26 * q^33 + 118 * q^34 + 5 * q^35 - 55 * q^36 - 32 * q^37 + 16 * q^38 + 42 * q^40 - 14 * q^41 + 4 * q^42 - 50 * q^43 + 35 * q^44 - q^45 + 4 * q^46 - 24 * q^47 - 116 * q^48 - 25 * q^49 + 156 * q^50 + 12 * q^51 - 31 * q^52 - 30 * q^53 - 78 * q^54 + 25 * q^55 + 3 * q^56 - 63 * q^57 - 12 * q^58 - 4 * q^59 + 128 * q^60 - 42 * q^61 - 38 * q^62 - 85 * q^63 - 105 * q^64 - 4 * q^65 + 15 * q^66 + 94 * q^67 + 214 * q^68 + 32 * q^69 - 57 * q^70 - 29 * q^71 - 64 * q^72 - 66 * q^73 - 90 * q^74 + 131 * q^75 - 21 * q^76 - 82 * q^77 + 19 * q^78 + 6 * q^79 + 22 * q^80 + 49 * q^81 - 50 * q^82 + 25 * q^83 + 89 * q^84 - 86 * q^85 - 28 * q^86 + 24 * q^87 + 48 * q^88 - 50 * q^89 - 155 * q^90 - 5 * q^91 - 98 * q^92 + 89 * q^93 - 28 * q^94 - 130 * q^95 - 105 * q^96 - 42 * q^97 + 195 * q^98 + 438 * q^99

Introduction

L-functions

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