LMFDB - Embedded newform 637.2.bl.a.625.5

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:	$324$
Relative dimension:	$27$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			625.5
Character	$\chi$	$=$	637.625
Dual form			637.2.bl.a.53.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.79391 + 1.22307i) q^{2} +(1.34252 - 1.24567i) q^{3} +(0.991536 - 2.52639i) q^{4} +(1.96924 + 0.607429i) q^{5} +(-0.884812 + 3.87661i) q^{6} +(1.60270 - 2.10508i) q^{7} +(0.344956 + 1.51135i) q^{8} +(0.0264586 - 0.353066i) q^{9} +O(q^{10})$	\(q+(-1.79391 + 1.22307i) q^{2} +(1.34252 - 1.24567i) q^{3} +(0.991536 - 2.52639i) q^{4} +(1.96924 + 0.607429i) q^{5} +(-0.884812 + 3.87661i) q^{6} +(1.60270 - 2.10508i) q^{7} +(0.344956 + 1.51135i) q^{8} +(0.0264586 - 0.353066i) q^{9} +(-4.27556 + 1.31883i) q^{10} +(0.146375 + 1.95324i) q^{11} +(-1.81591 - 4.62685i) q^{12} +(0.900969 + 0.433884i) q^{13} +(-0.300439 + 5.73653i) q^{14} +(3.40039 - 1.63754i) q^{15} +(1.51170 + 1.40265i) q^{16} +(4.13378 + 0.623068i) q^{17} +(0.384358 + 0.665728i) q^{18} +(-2.88397 + 4.99518i) q^{19} +(3.48717 - 4.37277i) q^{20} +(-0.470596 - 4.82254i) q^{21} +(-2.65153 - 3.32492i) q^{22} +(1.19838 - 0.180626i) q^{23} +(2.34576 + 1.59931i) q^{24} +(-0.622274 - 0.424259i) q^{25} +(-2.14692 + 0.323597i) q^{26} +(3.02131 + 3.78860i) q^{27} +(-3.72913 - 6.13630i) q^{28} +(4.84425 - 6.07450i) q^{29} +(-4.09717 + 7.09650i) q^{30} +(-5.35291 - 9.27151i) q^{31} +(-7.49320 - 1.12942i) q^{32} +(2.62962 + 2.43993i) q^{33} +(-8.17768 + 3.93817i) q^{34} +(4.43477 - 3.17188i) q^{35} +(-0.865747 - 0.416922i) q^{36} +(0.147931 + 0.376923i) q^{37} +(-0.935859 - 12.4882i) q^{38} +(1.75004 - 0.539817i) q^{39} +(-0.238739 + 3.18575i) q^{40} +(2.35981 + 10.3390i) q^{41} +(6.74250 + 8.07563i) q^{42} +(0.267062 - 1.17008i) q^{43} +(5.07980 + 1.56691i) q^{44} +(0.266565 - 0.679198i) q^{45} +(-1.92886 + 1.78972i) q^{46} +(10.7816 - 7.35075i) q^{47} +3.77674 q^{48} +(-1.86273 - 6.74761i) q^{49} +1.63520 q^{50} +(6.32581 - 4.31287i) q^{51} +(1.98950 - 1.84599i) q^{52} +(1.56040 - 3.97584i) q^{53} +(-10.0537 - 3.10115i) q^{54} +(-0.898209 + 3.93531i) q^{55} +(3.73438 + 1.69608i) q^{56} +(2.35059 + 10.2986i) q^{57} +(-1.26063 + 16.8219i) q^{58} +(-8.61113 + 2.65618i) q^{59} +(-0.765463 - 10.2144i) q^{60} +(-2.15148 - 5.48189i) q^{61} +(20.9423 + 10.0853i) q^{62} +(-0.700826 - 0.621554i) q^{63} +(11.1075 - 5.34910i) q^{64} +(1.51067 + 1.40169i) q^{65} +(-7.70149 - 1.16081i) q^{66} +(3.49131 + 6.04712i) q^{67} +(5.67291 - 9.82576i) q^{68} +(1.38384 - 1.73528i) q^{69} +(-4.07617 + 11.1141i) q^{70} +(2.28057 + 2.85974i) q^{71} +(0.542733 - 0.0818039i) q^{72} +(0.0413083 + 0.0281635i) q^{73} +(-0.726377 - 0.495236i) q^{74} +(-1.36390 + 0.205575i) q^{75} +(9.76022 + 12.2389i) q^{76} +(4.34633 + 2.82233i) q^{77} +(-2.47919 + 3.10880i) q^{78} +(-6.04972 + 10.4784i) q^{79} +(2.12488 + 3.68041i) q^{80} +(9.82583 + 1.48100i) q^{81} +(-16.8786 - 15.6611i) q^{82} +(-8.62083 + 4.15157i) q^{83} +(-12.6502 - 3.59281i) q^{84} +(7.76193 + 3.73795i) q^{85} +(0.951995 + 2.42564i) q^{86} +(-1.06335 - 14.1895i) q^{87} +(-2.90155 + 0.895009i) q^{88} +(-0.575740 + 7.68272i) q^{89} +(0.352510 + 1.54445i) q^{90} +(2.35734 - 1.20123i) q^{91} +(0.731902 - 3.20667i) q^{92} +(-18.7357 - 5.77918i) q^{93} +(-10.3507 + 26.3731i) q^{94} +(-8.71342 + 8.08488i) q^{95} +(-11.4666 + 7.81782i) q^{96} +0.774155 q^{97} +(11.5943 + 9.82636i) q^{98} +0.693496 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9}+O(q^{10}) $ 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9	\( 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9} - 5 q^{10} - 18 q^{11} - 40 q^{12} + 54 q^{13} - 15 q^{14} + 6 q^{15} + 29 q^{16} - 6 q^{17} + 49 q^{18} - 24 q^{19} + 11 q^{20} - 6 q^{22} - 42 q^{23} + 20 q^{24} + 14 q^{25} + 3 q^{26} - 33 q^{27} + 7 q^{28} - 22 q^{29} + 57 q^{30} - 31 q^{31} - 139 q^{32} + 6 q^{33} + 50 q^{34} + 42 q^{35} - 78 q^{36} - 4 q^{37} - 90 q^{38} + 40 q^{40} + 8 q^{41} + 20 q^{42} + 34 q^{43} - 256 q^{44} + 19 q^{45} + 85 q^{46} + 34 q^{47} - 10 q^{48} + 51 q^{49} - 54 q^{50} + 74 q^{51} - 25 q^{52} + 10 q^{53} + 111 q^{54} - 10 q^{55} - 196 q^{56} - 5 q^{57} - 21 q^{58} + 65 q^{59} + 87 q^{60} + 3 q^{61} - 54 q^{62} - 35 q^{63} - 28 q^{64} - q^{65} - 110 q^{66} + 135 q^{67} - 158 q^{68} + 42 q^{69} + 44 q^{70} + 9 q^{71} - 133 q^{72} + 31 q^{73} - 97 q^{74} - 315 q^{75} - 177 q^{76} + 6 q^{77} - 25 q^{78} + 43 q^{79} - 20 q^{80} - 259 q^{81} + 96 q^{82} + 59 q^{83} + 285 q^{84} + 6 q^{85} + 95 q^{86} - 206 q^{87} + 228 q^{88} + 43 q^{89} - 61 q^{90} - 7 q^{91} + 53 q^{92} - 10 q^{93} - 36 q^{94} - 17 q^{95} + 277 q^{96} + 66 q^{97} + 260 q^{98} - 206 q^{99}+O(q^{100}) \) 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9 - 5 * q^10 - 18 * q^11 - 40 * q^12 + 54 * q^13 - 15 * q^14 + 6 * q^15 + 29 * q^16 - 6 * q^17 + 49 * q^18 - 24 * q^19 + 11 * q^20 - 6 * q^22 - 42 * q^23 + 20 * q^24 + 14 * q^25 + 3 * q^26 - 33 * q^27 + 7 * q^28 - 22 * q^29 + 57 * q^30 - 31 * q^31 - 139 * q^32 + 6 * q^33 + 50 * q^34 + 42 * q^35 - 78 * q^36 - 4 * q^37 - 90 * q^38 + 40 * q^40 + 8 * q^41 + 20 * q^42 + 34 * q^43 - 256 * q^44 + 19 * q^45 + 85 * q^46 + 34 * q^47 - 10 * q^48 + 51 * q^49 - 54 * q^50 + 74 * q^51 - 25 * q^52 + 10 * q^53 + 111 * q^54 - 10 * q^55 - 196 * q^56 - 5 * q^57 - 21 * q^58 + 65 * q^59 + 87 * q^60 + 3 * q^61 - 54 * q^62 - 35 * q^63 - 28 * q^64 - q^65 - 110 * q^66 + 135 * q^67 - 158 * q^68 + 42 * q^69 + 44 * q^70 + 9 * q^71 - 133 * q^72 + 31 * q^73 - 97 * q^74 - 315 * q^75 - 177 * q^76 + 6 * q^77 - 25 * q^78 + 43 * q^79 - 20 * q^80 - 259 * q^81 + 96 * q^82 + 59 * q^83 + 285 * q^84 + 6 * q^85 + 95 * q^86 - 206 * q^87 + 228 * q^88 + 43 * q^89 - 61 * q^90 - 7 * q^91 + 53 * q^92 - 10 * q^93 - 36 * q^94 - 17 * q^95 + 277 * q^96 + 66 * q^97 + 260 * q^98 - 206 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$248$
$\chi(n)$	$1$	$e\left(\frac{16}{21}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.79391	+	1.22307i	−1.26849	+	0.864839i	−0.995273	−	0.0971153i	$-0.969038\pi$
$2$	−1.79391	+	1.22307i	−1.26849	+	0.864839i	−0.273212	+	0.961954i	$0.588086\pi$
$3$	1.34252	−	1.24567i	0.775103	−	0.719190i	−0.189793	−	0.981824i	$-0.560782\pi$
$3$	1.34252	−	1.24567i	0.775103	−	0.719190i	0.964896	+	0.262634i	$0.0845912\pi$
$4$	0.991536	−	2.52639i	0.495768	−	1.26320i
$5$	1.96924	+	0.607429i	0.880669	+	0.271650i	0.701930	−	0.712246i	$-0.252322\pi$
$5$	1.96924	+	0.607429i	0.880669	+	0.271650i	0.178739	+	0.983896i	$0.442798\pi$
$6$	−0.884812	+	3.87661i	−0.361223	+	1.58262i
$7$	1.60270	−	2.10508i	0.605762	−	0.795646i
$7$	1.60270	−	2.10508i	0.605762	−	0.795646i
$8$	0.344956	+	1.51135i	0.121960	+	0.534344i
$9$	0.0264586	−	0.353066i	0.00881954	−	0.117689i
$10$	−4.27556	+	1.31883i	−1.35205	+	0.417052i
$11$	0.146375	+	1.95324i	0.0441339	+	0.588925i	0.974804	+	0.223065i	$0.0716062\pi$
$11$	0.146375	+	1.95324i	0.0441339	+	0.588925i	−0.930670	+	0.365860i	$0.880775\pi$
$12$	−1.81591	−	4.62685i	−0.524207	−	1.33566i
$13$	0.900969	+	0.433884i	0.249884	+	0.120338i
$13$	0.900969	+	0.433884i	0.249884	+	0.120338i
$14$	−0.300439	+	5.73653i	−0.0802956	+	1.53315i
$15$	3.40039	−	1.63754i	0.877977	−	0.422812i
$16$	1.51170	+	1.40265i	0.377925	+	0.350664i
$17$	4.13378	+	0.623068i	1.00259	+	0.151116i	0.629765	−	0.776786i	$-0.283151\pi$
$17$	4.13378	+	0.623068i	1.00259	+	0.151116i	0.372825	+	0.927902i	$0.378389\pi$
$18$	0.384358	+	0.665728i	0.0905941	+	0.156914i
$19$	−2.88397	+	4.99518i	−0.661627	+	1.14597i	0.318561	+	0.947902i	$0.396801\pi$
$19$	−2.88397	+	4.99518i	−0.661627	+	1.14597i	−0.980188	+	0.198070i	$0.936533\pi$
$20$	3.48717	−	4.37277i	0.779755	−	0.977782i
$21$	−0.470596	−	4.82254i	−0.102692	−	1.05237i
$22$	−2.65153	−	3.32492i	−0.565309	−	0.708874i
$23$	1.19838	−	0.180626i	0.249879	−	0.0376632i	−0.0229082	−	0.999738i	$-0.507293\pi$
$23$	1.19838	−	0.180626i	0.249879	−	0.0376632i	0.272787	+	0.962074i	$0.412054\pi$
$24$	2.34576	+	1.59931i	0.478827	+	0.326458i
$25$	−0.622274	−	0.424259i	−0.124455	−	0.0848519i
$26$	−2.14692	+	0.323597i	−0.421047	+	0.0634626i
$27$	3.02131	+	3.78860i	0.581451	+	0.729117i
$28$	−3.72913	−	6.13630i	−0.704739	−	1.15965i
$29$	4.84425	−	6.07450i	0.899555	−	1.12801i	−0.0916661	−	0.995790i	$-0.529219\pi$
$29$	4.84425	−	6.07450i	0.899555	−	1.12801i	0.991221	−	0.132216i	$-0.0422093\pi$
$30$	−4.09717	+	7.09650i	−0.748037	+	1.29564i
$31$	−5.35291	−	9.27151i	−0.961411	−	1.66521i	−0.718963	−	0.695048i	$-0.755383\pi$
$31$	−5.35291	−	9.27151i	−0.961411	−	1.66521i	−0.242447	−	0.970165i	$-0.577950\pi$
$32$	−7.49320	−	1.12942i	−1.32462	−	0.199655i
$33$	2.62962	+	2.43993i	0.457758	+	0.424737i
$34$	−8.17768	+	3.93817i	−1.40246	+	0.675390i
$35$	4.43477	−	3.17188i	0.749614	−	0.536145i
$36$	−0.865747	−	0.416922i	−0.144291	−	0.0694870i
$37$	0.147931	+	0.376923i	0.0243198	+	0.0619658i	0.942518	−	0.334156i	$-0.108451\pi$
$37$	0.147931	+	0.376923i	0.0243198	+	0.0619658i	−0.918198	+	0.396121i	$0.870356\pi$
$38$	−0.935859	−	12.4882i	−0.151816	−	2.02585i
$39$	1.75004	−	0.539817i	0.280231	−	0.0864399i
$40$	−0.238739	+	3.18575i	−0.0377479	+	0.503711i
$41$	2.35981	+	10.3390i	0.368541	+	1.61468i	0.730790	+	0.682602i	$0.239152\pi$
$41$	2.35981	+	10.3390i	0.368541	+	1.61468i	−0.362249	+	0.932081i	$0.617991\pi$
$42$	6.74250	+	8.07563i	1.04039	+	1.24610i
$43$	0.267062	−	1.17008i	0.0407266	−	0.178435i	−0.950474	−	0.310805i	$-0.899401\pi$
$43$	0.267062	−	1.17008i	0.0407266	−	0.178435i	0.991200	+	0.132370i	$0.0422586\pi$
$44$	5.07980	+	1.56691i	0.765808	+	0.236221i
$45$	0.266565	−	0.679198i	0.0397372	−	0.101249i
$46$	−1.92886	+	1.78972i	−0.284395	+	0.263880i
$47$	10.7816	−	7.35075i	1.57265	−	1.07222i	0.613360	−	0.789803i	$-0.289817\pi$
$47$	10.7816	−	7.35075i	1.57265	−	1.07222i	0.959293	−	0.282414i	$-0.0911351\pi$
$48$	3.77674			0.545125
$49$	−1.86273	−	6.74761i	−0.266104	−	0.963944i
$50$	1.63520			0.231252
$51$	6.32581	−	4.31287i	0.885791	−	0.603922i
$52$	1.98950	−	1.84599i	0.275894	−	0.255993i
$53$	1.56040	−	3.97584i	0.214338	−	0.546124i	−0.782754	−	0.622331i	$-0.786186\pi$
$53$	1.56040	−	3.97584i	0.214338	−	0.546124i	0.997092	+	0.0762072i	$0.0242811\pi$
$54$	−10.0537	−	3.10115i	−1.36813	−	0.422012i
$55$	−0.898209	+	3.93531i	−0.121115	+	0.530637i
$56$	3.73438	+	1.69608i	0.499027	+	0.226648i
$57$	2.35059	+	10.2986i	0.311343	+	1.36408i
$58$	−1.26063	+	16.8219i	−0.165529	+	2.20883i
$59$	−8.61113	+	2.65618i	−1.12107	+	0.345806i	−0.799253	−	0.600995i	$-0.794771\pi$
$59$	−8.61113	+	2.65618i	−1.12107	+	0.345806i	−0.321821	+	0.946800i	$0.604295\pi$
$60$	−0.765463	−	10.2144i	−0.0988209	−	1.31867i
$61$	−2.15148	−	5.48189i	−0.275469	−	0.701884i	−0.999921	−	0.0125587i	$-0.996002\pi$
$61$	−2.15148	−	5.48189i	−0.275469	−	0.701884i	0.724452	−	0.689325i	$-0.242093\pi$
$62$	20.9423	+	10.0853i	2.65968	+	1.28083i
$63$	−0.700826	−	0.621554i	−0.0882958	−	0.0783085i
$64$	11.1075	−	5.34910i	1.38844	−	0.668637i
$65$	1.51067	+	1.40169i	0.187375	+	0.173859i
$66$	−7.70149	−	1.16081i	−0.947988	−	0.142886i
$67$	3.49131	+	6.04712i	0.426531	+	0.738774i	0.996562	−	0.0828495i	$-0.0264021\pi$
$67$	3.49131	+	6.04712i	0.426531	+	0.738774i	−0.570031	+	0.821623i	$0.693069\pi$
$68$	5.67291	−	9.82576i	0.687941	−	1.19155i
$69$	1.38384	−	1.73528i	0.166595	−	0.208903i
$70$	−4.07617	+	11.1141i	−0.487195	+	1.32839i
$71$	2.28057	+	2.85974i	0.270653	+	0.339388i	0.898520	−	0.438932i	$-0.144643\pi$
$71$	2.28057	+	2.85974i	0.270653	+	0.339388i	−0.627867	+	0.778321i	$0.716072\pi$
$72$	0.542733	−	0.0818039i	0.0639618	−	0.00964068i
$73$	0.0413083	+	0.0281635i	0.00483477	+	0.00329629i	0.565735	−	0.824587i	$-0.308593\pi$
$73$	0.0413083	+	0.0281635i	0.00483477	+	0.00329629i	−0.560900	+	0.827883i	$0.689545\pi$
$74$	−0.726377	−	0.495236i	−0.0844396	−	0.0575700i
$75$	−1.36390	+	0.205575i	−0.157490	+	0.0237378i
$76$	9.76022	+	12.2389i	1.11957	+	1.40390i
$77$	4.34633	+	2.82233i	0.495311	+	0.321634i
$78$	−2.47919	+	3.10880i	−0.280713	+	0.352003i
$79$	−6.04972	+	10.4784i	−0.680646	+	1.17891i	0.294138	+	0.955763i	$0.404968\pi$
$79$	−6.04972	+	10.4784i	−0.680646	+	1.17891i	−0.974784	+	0.223151i	$0.928366\pi$
$80$	2.12488	+	3.68041i	0.237569	+	0.411482i
$81$	9.82583	+	1.48100i	1.09176	+	0.164556i
$82$	−16.8786	−	15.6611i	−1.86393	−	1.72947i
$83$	−8.62083	+	4.15157i	−0.946259	+	0.455694i	−0.842373	−	0.538895i	$-0.818842\pi$
$83$	−8.62083	+	4.15157i	−0.946259	+	0.455694i	−0.103886	+	0.994589i	$0.533128\pi$
$84$	−12.6502	−	3.59281i	−1.38026	−	0.392008i
$85$	7.76193	+	3.73795i	0.841899	+	0.405437i
$86$	0.951995	+	2.42564i	0.102656	+	0.261564i
$87$	−1.06335	−	14.1895i	−0.114004	−	1.52127i
$88$	−2.90155	+	0.895009i	−0.309306	+	0.0954083i
$89$	−0.575740	+	7.68272i	−0.0610283	+	0.814367i	0.879770	+	0.475400i	$0.157697\pi$
$89$	−0.575740	+	7.68272i	−0.0610283	+	0.814367i	−0.940798	+	0.338967i	$0.889923\pi$
$90$	0.352510	+	1.54445i	0.0371578	+	0.162799i
$91$	2.35734	−	1.20123i	0.247116	−	0.125923i
$92$	0.731902	−	3.20667i	0.0763060	−	0.334318i
$93$	−18.7357	−	5.77918i	−1.94280	−	0.599273i
$94$	−10.3507	+	26.3731i	−1.06759	+	2.72018i
$95$	−8.71342	+	8.08488i	−0.893978	+	0.829491i
$96$	−11.4666	+	7.81782i	−1.17031	+	0.797903i
$97$	0.774155			0.0786035			0.0393017	−	0.999227i	$-0.487487\pi$
$97$	0.774155			0.0786035			0.0393017	+	0.999227i	$0.487487\pi$
$98$	11.5943	+	9.82636i	1.17120	+	0.992612i
$99$	0.693496			0.0696990
$100$	−1.68885	+	1.15144i	−0.168885	+	0.115144i
$101$	11.9297	−	11.0691i	1.18705	−	1.10142i	0.194330	−	0.980936i	$-0.437747\pi$
$101$	11.9297	−	11.0691i	1.18705	−	1.10142i	0.992716	−	0.120481i	$-0.0384437\pi$
$102$	−6.07301	+	15.4738i	−0.601318	+	1.53213i
$103$	−13.4332	−	4.14359i	−1.32361	−	0.408280i	−0.449184	−	0.893439i	$-0.648285\pi$
$103$	−13.4332	−	4.14359i	−1.32361	−	0.408280i	−0.874426	+	0.485160i	$0.838762\pi$
$104$	−0.344956	+	1.51135i	−0.0338257	+	0.148200i
$105$	2.00264	−	9.78258i	0.195437	−	0.954682i
$106$	2.06350	+	9.04077i	0.200425	+	0.878117i
$107$	−0.492456	+	6.57137i	−0.0476076	+	0.635279i	0.921458	+	0.388477i	$0.126999\pi$
$107$	−0.492456	+	6.57137i	−0.0476076	+	0.635279i	−0.969066	+	0.246802i	$0.920620\pi$
$108$	12.5672	−	3.87648i	1.20928	−	0.373014i
$109$	−0.0625692	−	0.834928i	−0.00599304	−	0.0799716i	0.993405	−	0.114656i	$-0.0365765\pi$
$109$	−0.0625692	−	0.834928i	−0.00599304	−	0.0799716i	−0.999398	+	0.0346842i	$0.988957\pi$
$110$	−3.20184	−	8.15816i	−0.305284	−	0.777850i
$111$	0.668123	+	0.321751i	0.0634155	+	0.0305393i
$112$	5.37550	−	0.934224i	0.507937	−	0.0882759i
$113$	11.0322	−	5.31284i	1.03783	−	0.499790i	0.164219	−	0.986424i	$-0.447490\pi$
$113$	11.0322	−	5.31284i	1.03783	−	0.499790i	0.873606	+	0.486634i	$0.161775\pi$
$114$	−16.8126	−	15.5998i	−1.57464	−	1.46106i
$115$	2.46961	+	0.372233i	0.230292	+	0.0347109i
$116$	−10.5433	−	18.2616i	−0.978922	−	1.69554i
$117$	0.177028	−	0.306621i	0.0163662	−	0.0283471i
$118$	12.1989	−	15.2969i	1.12300	−	1.40820i
$119$	7.93681	−	7.70336i	0.727566	−	0.706166i
$120$	3.64789	+	4.57431i	0.333005	+	0.417575i
$121$	7.08340	−	1.06765i	0.643945	−	0.0970592i
$122$	10.5643	+	7.20260i	0.956445	+	0.652093i
$123$	16.0471	+	10.9408i	1.44692	+	0.986495i
$124$	−28.7311	+	4.33051i	−2.58013	+	0.388891i
$125$	−7.39211	−	9.26941i	−0.661170	−	0.829081i
$126$	2.01742	+	0.257855i	0.179726	+	0.0229716i
$127$	−8.63340	+	10.8259i	−0.766091	+	0.960647i	−0.999932	−	0.0116275i	$-0.996299\pi$
$127$	−8.63340	+	10.8259i	−0.766091	+	0.960647i	0.233842	+	0.972275i	$0.424870\pi$
$128$	−5.80573	+	10.0558i	−0.513159	+	0.888817i
$129$	−1.09900	−	1.90352i	−0.0967613	−	0.167596i
$130$	−4.42436	−	0.666865i	−0.388042	−	0.0584880i
$131$	−4.82406	−	4.47608i	−0.421480	−	0.391077i	0.440719	−	0.897645i	$-0.354723\pi$
$131$	−4.82406	−	4.47608i	−0.421480	−	0.391077i	−0.862200	+	0.506568i	$0.830914\pi$
$132$	8.77157	−	4.22417i	0.763467	−	0.367667i
$133$	5.89313	+	14.0767i	0.510999	+	1.22061i
$134$	−13.6591	−	6.57789i	−1.17997	−	0.568243i
$135$	3.64836	+	9.29588i	0.314001	+	0.800062i
$136$	0.484300	+	6.46254i	0.0415284	+	0.554158i
$137$	−10.1703	+	3.13711i	−0.868905	+	0.268022i	−0.696982	−	0.717089i	$-0.745474\pi$
$137$	−10.1703	+	3.13711i	−0.868905	+	0.268022i	−0.171923	+	0.985110i	$0.554998\pi$
$138$	−0.360120	+	4.80547i	−0.0306555	+	0.409069i
$139$	−1.99178	−	8.72655i	−0.168940	−	0.740177i	−0.986423	−	0.164223i	$-0.947488\pi$
$139$	−1.99178	−	8.72655i	−0.168940	−	0.740177i	0.817483	−	0.575953i	$-0.195369\pi$
$140$	−3.61616	−	14.3490i	−0.305622	−	1.21271i
$141$	5.31780	−	23.2988i	0.447840	−	1.96211i
$142$	−7.58878	−	2.34083i	−0.636836	−	0.196438i
$143$	−0.715601	+	1.82332i	−0.0598416	+	0.152474i
$144$	0.535226	−	0.496618i	0.0446022	−	0.0413848i
$145$	13.2293	−	9.01958i	1.09863	−	0.749036i
$146$	−0.108549			−0.00898359
$147$	−10.9061	−	6.73843i	−0.899517	−	0.555777i
$148$	1.09893			0.0903318
$149$	2.93125	−	1.99849i	0.240137	−	0.163723i	−0.437272	−	0.899330i	$-0.644055\pi$
$149$	2.93125	−	1.99849i	0.240137	−	0.163723i	0.677409	+	0.735607i	$0.263103\pi$
$150$	2.19529	−	2.03693i	0.179244	−	0.166314i
$151$	−2.60416	+	6.63528i	−0.211923	+	0.539972i	−0.996823	−	0.0796514i	$-0.974619\pi$
$151$	−2.60416	+	6.63528i	−0.211923	+	0.539972i	0.784900	+	0.619623i	$0.212715\pi$
$152$	−8.54431	−	2.63557i	−0.693035	−	0.213773i
$153$	0.329358	−	1.44301i	0.0266270	−	0.116661i
$154$	−11.2488	+	0.252856i	−0.906455	+	0.0203757i
$155$	−4.90936	−	21.5093i	−0.394329	−	1.72767i
$156$	0.371442	−	4.95654i	0.0297391	−	0.396841i
$157$	−15.3195	+	4.72543i	−1.22263	+	0.377130i	−0.837861	−	0.545884i	$-0.816194\pi$
$157$	−15.3195	+	4.72543i	−1.22263	+	0.377130i	−0.384766	+	0.923014i	$0.625718\pi$
$158$	−1.96316	−	26.1965i	−0.156181	−	2.08408i
$159$	−2.85773	−	7.28139i	−0.226633	−	0.577452i
$160$	−14.0698	−	6.77568i	−1.11232	−	0.535664i
$161$	1.54040	−	2.81217i	0.121401	−	0.221630i
$162$	−19.4380	+	9.36085i	−1.52719	+	0.735458i
$163$	−17.3804	−	16.1266i	−1.36133	−	1.26313i	−0.933171	−	0.359432i	$-0.882970\pi$
$163$	−17.3804	−	16.1266i	−1.36133	−	1.26313i	−0.428163	−	0.903701i	$-0.640839\pi$
$164$	28.4603	+	4.28969i	2.22237	+	0.334969i
$165$	3.69625	+	6.40210i	0.287753	+	0.498403i
$166$	10.3873	−	17.9914i	0.806213	−	1.39640i
$167$	3.31198	−	4.15310i	0.256289	−	0.321376i	−0.636996	−	0.770867i	$-0.719823\pi$
$167$	3.31198	−	4.15310i	0.256289	−	0.321376i	0.893285	+	0.449491i	$0.148395\pi$
$168$	7.12623	−	2.37480i	0.549800	−	0.183220i
$169$	0.623490	+	0.781831i	0.0479608	+	0.0601409i
$170$	−18.4959	+	2.78782i	−1.41857	+	0.213816i
$171$	1.68732	+	1.15039i	0.129033	+	0.0879729i
$172$	−2.69127	−	1.83488i	−0.205207	−	0.139908i
$173$	−0.640727	+	0.0965741i	−0.0487136	+	0.00734239i	−0.173354	−	0.984860i	$-0.555460\pi$
$173$	−0.640727	+	0.0965741i	−0.0487136	+	0.00734239i	0.124640	+	0.992202i	$0.460222\pi$
$174$	19.2622	+	24.1541i	1.46027	+	1.83112i
$175$	−1.89042	+	0.629978i	−0.142902	+	0.0476219i
$176$	−2.51845	+	3.15804i	−0.189835	+	0.238046i
$177$	−8.25186	+	14.2926i	−0.620248	+	1.07430i
$178$	−8.36365	−	14.4863i	−0.626882	−	1.08579i
$179$	−25.2028	−	3.79872i	−1.88375	−	0.283929i	−0.896491	−	0.443062i	$-0.853892\pi$
$179$	−25.2028	−	3.79872i	−1.88375	−	0.283929i	−0.987257	+	0.159133i	$0.949130\pi$
$180$	−1.45161	−	1.34690i	−0.108197	−	0.100392i
$181$	10.5256	−	5.06888i	0.782365	−	0.376767i	0.000328569	−	1.00000i	$-0.499895\pi$
$181$	10.5256	−	5.06888i	0.782365	−	0.376767i	0.782036	+	0.623233i	$0.214181\pi$
$182$	−2.75967	+	5.03808i	−0.204560	+	0.373447i
$183$	−9.71705	−	4.67948i	−0.718305	−	0.345917i
$184$	0.686378	+	1.74886i	0.0506005	+	0.128928i
$185$	0.0623579	+	0.832108i	0.00458464	+	0.0611778i
$186$	40.6784	−	12.5476i	2.98268	−	0.920036i
$187$	−0.611919	+	8.16549i	−0.0447480	+	0.597120i
$188$	−7.88056	−	34.5270i	−0.574749	−	2.51814i
$189$	12.8176	−	0.288119i	0.932340	−	0.0209576i
$190$	5.74275	−	25.1606i	0.416623	−	1.82534i
$191$	−2.22001	−	0.684782i	−0.160634	−	0.0495491i	0.213395	−	0.976966i	$-0.431548\pi$
$191$	−2.22001	−	0.684782i	−0.160634	−	0.0495491i	−0.374029	+	0.927417i	$0.622024\pi$
$192$	8.24880	−	21.0176i	0.595306	−	1.51681i
$193$	−1.91425	+	1.77616i	−0.137791	+	0.127851i	−0.746057	−	0.665882i	$-0.768056\pi$
$193$	−1.91425	+	1.77616i	−0.137791	+	0.127851i	0.608267	+	0.793733i	$0.291865\pi$
$194$	−1.38876	+	0.946842i	−0.0997074	+	0.0679793i
$195$	3.77415			0.270272
$196$	−18.8941	−	1.98452i	−1.34958	−	0.141751i
$197$	−18.8436			−1.34255			−0.671274	−	0.741209i	$-0.734253\pi$
$197$	−18.8436			−1.34255			−0.671274	+	0.741209i	$0.734253\pi$
$198$	−1.24407	+	0.848192i	−0.0884121	+	0.0602784i
$199$	7.61269	−	7.06355i	0.539649	−	0.500721i	−0.362595	−	0.931947i	$-0.618109\pi$
$199$	7.61269	−	7.06355i	0.539649	−	0.500721i	0.902244	+	0.431225i	$0.141919\pi$
$200$	0.426548	−	1.08683i	0.0301615	−	0.0768503i
$201$	12.2199	+	3.76934i	0.861924	+	0.265868i
$202$	−7.86247	+	34.4477i	−0.553201	+	2.42373i
$203$	−5.02344	−	19.9331i	−0.352577	−	1.39903i
$204$	−4.62372	−	20.2578i	−0.323725	−	1.41833i
$205$	−1.63319	+	21.7934i	−0.114067	+	1.52212i
$206$	29.1658	−	8.99645i	2.03208	−	0.626812i
$207$	−0.0320656	−	0.427885i	−0.00222871	−	0.0297401i
$208$	0.753407	+	1.91965i	0.0522394	+	0.133104i
$209$	−10.1789	−	4.90192i	−0.704092	−	0.339073i
$210$	8.37219	+	19.9984i	0.577736	+	1.38002i
$211$	−4.35614	+	2.09781i	−0.299889	+	0.144419i	−0.577777	−	0.816194i	$-0.696080\pi$
$211$	−4.35614	+	2.09781i	−0.299889	+	0.144419i	0.277888	+	0.960613i	$0.410366\pi$
$212$	−8.49734	−	7.88438i	−0.583599	−	0.541501i
$213$	6.62400	+	0.998407i	0.453869	+	0.0684097i
$214$	−7.15380	−	12.3908i	−0.489024	−	0.847014i
$215$	1.23665	−	2.14193i	0.0843386	−	0.146079i
$216$	−4.68369	+	5.87317i	−0.318685	+	0.399618i
$217$	−28.0964	−	3.59111i	−1.90731	−	0.243781i
$218$	1.13342	+	1.42126i	0.0767646	+	0.0962598i
$219$	0.0905396	−	0.0136466i	0.00611810	−	0.000922155i
$220$	9.05153	+	6.17123i	0.610254	+	0.416064i
$221$	3.45407	+	2.35495i	0.232346	+	0.158411i
$222$	−1.59208	+	0.239967i	−0.106853	+	0.0161055i
$223$	8.34680	+	10.4666i	0.558943	+	0.700892i	0.978362	−	0.206900i	$-0.0663376\pi$
$223$	8.34680	+	10.4666i	0.558943	+	0.700892i	−0.419419	+	0.907793i	$0.637766\pi$
$224$	−14.3869	+	13.9637i	−0.961262	+	0.932988i
$225$	−0.166256	+	0.208478i	−0.0110837	+	0.0138986i
$226$	−13.2929	+	23.0239i	−0.884228	+	1.53153i
$227$	14.1883	+	24.5748i	0.941709	+	1.63109i	0.762211	+	0.647329i	$0.224114\pi$
$227$	14.1883	+	24.5748i	0.941709	+	1.63109i	0.179498	+	0.983758i	$0.442553\pi$
$228$	28.3490	+	4.27292i	1.87746	+	0.282981i
$229$	−7.57760	−	7.03098i	−0.500742	−	0.464621i	0.388900	−	0.921280i	$-0.372855\pi$
$229$	−7.57760	−	7.03098i	−0.500742	−	0.464621i	−0.889642	+	0.456660i	$0.849046\pi$
$230$	−4.88552	+	2.35274i	−0.322141	+	0.155135i
$231$	9.35072	−	1.62509i	0.615232	−	0.106923i
$232$	10.8518	+	5.22593i	0.712453	+	0.343099i
$233$	−0.144745	−	0.368805i	−0.00948257	−	0.0241612i	0.926054	−	0.377391i	$-0.123179\pi$
$233$	−0.144745	−	0.368805i	−0.00948257	−	0.0241612i	−0.935537	+	0.353230i	$0.885083\pi$
$234$	0.0574463	+	0.766567i	0.00375538	+	0.0501121i
$235$	25.6965	−	7.92632i	1.67625	−	0.517056i
$236$	−1.82769	+	24.3888i	−0.118972	+	1.58758i
$237$	4.93084	+	21.6034i	0.320293	+	1.40329i
$238$	−4.81619	+	23.5264i	−0.312187	+	1.52499i
$239$	0.604746	−	2.64956i	0.0391177	−	0.171386i	−0.951596	−	0.307353i	$-0.900557\pi$
$239$	0.604746	−	2.64956i	0.0391177	−	0.171386i	0.990713	+	0.135967i	$0.0434140\pi$
$240$	7.43728	+	2.29410i	0.480074	+	0.148083i
$241$	−7.81494	+	19.9122i	−0.503405	+	1.28265i	0.423001	+	0.906129i	$0.360977\pi$
$241$	−7.81494	+	19.9122i	−0.503405	+	1.28265i	−0.926406	+	0.376526i	$0.877119\pi$
$242$	−11.4012	+	10.5787i	−0.732895	+	0.680027i
$243$	3.02481	−	2.06228i	0.194042	−	0.132296i
$244$	−15.9827			−1.02319
$245$	0.430544	−	14.4191i	0.0275065	−	0.921203i
$246$	−42.1684			−2.68856
$247$	−4.76569	+	3.24919i	−0.303234	+	0.206741i
$248$	12.1660	−	11.2884i	0.772542	−	0.716814i
$249$	−6.40210	+	16.3123i	−0.405717	+	1.03375i
$250$	24.5979	+	7.58744i	1.55571	+	0.479872i
$251$	4.70262	−	20.6035i	0.296827	−	1.30048i	−0.577995	−	0.816040i	$-0.696165\pi$
$251$	4.70262	−	20.6035i	0.296827	−	1.30048i	0.874822	−	0.484444i	$-0.160978\pi$
$252$	−2.26518	+	1.15427i	−0.142693	+	0.0727121i
$253$	0.528221	+	2.31429i	0.0332090	+	0.145498i
$254$	2.24669	−	29.9800i	0.140970	−	1.88111i
$255$	15.0768	−	4.65057i	0.944145	−	0.291230i
$256$	−0.0413766	−	0.552132i	−0.00258604	−	0.0345082i
$257$	10.7232	+	27.3223i	0.668896	+	1.70432i	0.709081	+	0.705127i	$0.249110\pi$
$257$	10.7232	+	27.3223i	0.668896	+	1.70432i	−0.0401846	+	0.999192i	$0.512795\pi$
$258$	4.29963	+	2.07059i	0.267683	+	0.128910i
$259$	1.03054	+	0.292686i	0.0640348	+	0.0181866i
$260$	5.03911	−	2.42671i	0.312512	−	0.150498i
$261$	−2.01652	−	1.87106i	−0.124820	−	0.115816i
$262$	14.1285	+	2.12952i	0.872860	+	0.131562i
$263$	12.8964	+	22.3372i	0.795226	+	1.37737i	0.922696	+	0.385529i	$0.125981\pi$
$263$	12.8964	+	22.3372i	0.795226	+	1.37737i	−0.127470	+	0.991842i	$0.540686\pi$
$264$	−2.78049	+	4.81595i	−0.171127	+	0.296401i
$265$	5.48784	−	6.88153i	0.337115	−	0.422729i
$266$	−27.7885	−	18.0447i	−1.70382	−	1.10639i
$267$	8.79722	+	11.0314i	0.538381	+	0.675109i
$268$	18.7392	−	2.82447i	1.14468	−	0.172532i
$269$	8.67642	+	5.91548i	0.529011	+	0.360673i	0.798180	−	0.602420i	$-0.205797\pi$
$269$	8.67642	+	5.91548i	0.529011	+	0.360673i	−0.269169	+	0.963093i	$0.586749\pi$
$270$	−17.9143	−	12.2138i	−1.09023	−	0.743306i
$271$	−25.8236	+	3.89228i	−1.56867	+	0.236439i	−0.875098	−	0.483946i	$-0.839203\pi$
$271$	−25.8236	+	3.89228i	−1.56867	+	0.236439i	−0.693574	+	0.720386i	$0.743965\pi$
$272$	5.37510	+	6.74016i	0.325913	+	0.408682i
$273$	1.66843	−	4.54915i	0.100978	−	0.275327i
$274$	14.4076	−	18.0666i	0.870397	−	1.09144i
$275$	0.737597	−	1.27756i	0.0444788	−	0.0770395i
$276$	−3.01187	−	5.21672i	−0.181294	−	0.314010i
$277$	1.42708	+	0.215098i	0.0857451	+	0.0129240i	0.191775	−	0.981439i	$-0.438576\pi$
$277$	1.42708	+	0.215098i	0.0857451	+	0.0129240i	−0.106030	+	0.994363i	$0.533814\pi$
$278$	14.2462	+	13.2186i	0.854432	+	0.792797i
$279$	−3.41508	+	1.64462i	−0.204456	+	0.0984606i
$280$	6.32362	+	5.60835i	0.377909	+	0.335163i
$281$	2.80745	+	1.35199i	0.167478	+	0.0806532i	0.515745	−	0.856742i	$-0.327515\pi$
$281$	2.80745	+	1.35199i	0.167478	+	0.0806532i	−0.348267	+	0.937396i	$0.613230\pi$
$282$	18.9563	+	48.3000i	1.12883	+	2.87622i
$283$	0.164940	+	2.20097i	0.00980468	+	0.130834i	0.999958	−	0.00915195i	$-0.00291320\pi$
$283$	0.164940	+	2.20097i	0.00980468	+	0.130834i	−0.990153	+	0.139986i	$0.955294\pi$
$284$	9.48608	−	2.92607i	0.562895	−	0.173630i
$285$	−1.62680	+	21.7082i	−0.0963635	+	1.28588i
$286$	−0.946321	−	4.14610i	−0.0559571	−	0.245164i
$287$	25.5465	+	11.6027i	1.50796	+	0.684887i
$288$	−0.597019	+	2.61571i	−0.0351797	+	0.154132i
$289$	0.455219	+	0.140416i	0.0267776	+	0.00825979i
$290$	−12.7006	+	32.3606i	−0.745805	+	1.90028i
$291$	1.03932	−	0.964344i	0.0609258	−	0.0565309i
$292$	0.112111	−	0.0764357i	0.00656078	−	0.00447306i
$293$	−25.4482			−1.48670			−0.743350	−	0.668903i	$-0.766764\pi$
$293$	−25.4482			−1.48670			−0.743350	+	0.668903i	$0.766764\pi$
$294$	27.8060	−	1.25071i	1.62168	−	0.0729427i
$295$	−18.5708			−1.08123
$296$	−0.518634	+	0.353598i	−0.0301450	+	0.0205525i
$297$	−6.95782	+	6.45591i	−0.403734	+	0.374610i
$298$	−2.81411	+	7.17023i	−0.163017	+	0.415360i
$299$	1.15807	+	0.357218i	0.0669730	+	0.0206584i
$300$	−0.832995	+	3.64959i	−0.0480930	+	0.210709i
$301$	−2.03508	−	2.43746i	−0.117300	−	0.140493i
$302$	−3.44377	−	15.0881i	−0.198167	−	0.868225i
$303$	2.22728	−	29.7209i	0.127954	−	1.70742i
$304$	−11.3662	+	3.50601i	−0.651896	+	0.201083i
$305$	−0.906920	−	12.1020i	−0.0519301	−	0.692959i
$306$	1.17406	+	2.99146i	0.0671166	+	0.171010i
$307$	−15.2969	−	7.36660i	−0.873040	−	0.420434i	−0.0569623	−	0.998376i	$-0.518141\pi$
$307$	−15.2969	−	7.36660i	−0.873040	−	0.420434i	−0.816077	+	0.577943i	$0.803856\pi$
$308$	11.4398	−	8.18210i	0.651846	−	0.466218i
$309$	−23.1958	+	11.1705i	−1.31956	+	0.635469i
$310$	35.1142	+	32.5813i	1.99435	+	1.85049i
$311$	−28.6360	−	4.31619i	−1.62380	−	0.244748i	−0.726823	−	0.686825i	$-0.759004\pi$
$311$	−28.6360	−	4.31619i	−1.62380	−	0.244748i	−0.896977	+	0.442077i	$0.854242\pi$
$312$	1.41954	+	2.45872i	0.0803658	+	0.139198i
$313$	6.69180	−	11.5905i	0.378243	−	0.655136i	−0.612564	−	0.790421i	$-0.709862\pi$
$313$	6.69180	−	11.5905i	0.378243	−	0.655136i	0.990807	+	0.135285i	$0.0431952\pi$
$314$	21.7022	−	27.2137i	1.22473	−	1.53576i
$315$	−1.00254	−	1.64969i	−0.0564868	−	0.0929495i
$316$	20.4741	+	25.6737i	1.15176	+	1.44426i
$317$	−2.56308	+	0.386322i	−0.143957	+	0.0216980i	−0.220625	−	0.975359i	$-0.570810\pi$
$317$	−2.56308	+	0.386322i	−0.143957	+	0.0216980i	0.0766684	+	0.997057i	$0.475572\pi$
$318$	14.0321	+	9.56695i	0.786883	+	0.536488i
$319$	12.5741	+	8.57285i	0.704012	+	0.479987i
$320$	25.1225	−	3.78661i	1.40439	−	0.211678i
$321$	7.52466	+	9.43562i	0.419985	+	0.526645i
$322$	0.676129	+	6.92880i	0.0376792	+	0.386127i
$323$	−15.0340	+	18.8521i	−0.836516	+	1.04896i
$324$	13.4843	−	23.3554i	0.749125	−	1.29752i
$325$	−0.376571	−	0.652239i	−0.0208884	−	0.0361797i
$326$	50.9027	+	7.67235i	2.81924	+	0.424932i
$327$	−1.12405	−	1.04296i	−0.0621600	−	0.0576761i
$328$	−14.8119	+	7.13302i	−0.817849	+	0.393855i
$329$	1.80567	−	34.4771i	0.0995496	−	1.90078i
$330$	−14.4609	−	6.96402i	−0.796048	−	0.383357i
$331$	−10.7922	−	27.4981i	−0.593194	−	1.51143i	−0.840121	−	0.542399i	$-0.817516\pi$
$331$	−10.7922	−	27.4981i	−0.593194	−	1.51143i	0.246927	−	0.969034i	$-0.420579\pi$
$332$	1.94064	+	25.8960i	0.106506	+	1.42123i
$333$	0.136993	−	0.0422566i	0.00750715	−	0.00231565i
$334$	−0.861885	+	11.5011i	−0.0471602	+	0.629309i
$335$	3.20201	+	14.0289i	0.174945	+	0.766483i
$336$	6.05296	−	7.95033i	0.330216	−	0.433726i
$337$	2.79968	−	12.2662i	0.152508	−	0.668182i	−0.839643	−	0.543139i	$-0.817236\pi$
$337$	2.79968	−	12.2662i	0.152508	−	0.668182i	0.992151	−	0.125043i	$-0.0399070\pi$
$338$	−2.07472	−	0.639965i	−0.112850	−	0.0348095i
$339$	8.19289	−	20.8752i	0.444977	−	1.13378i
$340$	17.1397	−	15.9034i	0.929533	−	0.862481i
$341$	17.3260	−	11.8127i	0.938255	−	0.639692i
$342$	−4.43391			−0.239758
$343$	−17.1896	−	6.89318i	−0.928154	−	0.372197i
$344$	1.86052			0.100313
$345$	3.77917	−	2.57659i	0.203464	−	0.138719i
$346$	1.03129	−	0.956897i	0.0554425	−	0.0514431i
$347$	−1.07017	+	2.72675i	−0.0574499	+	0.146380i	−0.956717	−	0.291020i	$-0.906005\pi$
$347$	−1.07017	+	2.72675i	−0.0574499	+	0.146380i	0.899267	+	0.437400i	$0.144101\pi$
$348$	−36.9025	−	11.3829i	−1.97818	−	0.610189i
$349$	−3.30762	+	14.4916i	−0.177053	+	0.775720i	0.805928	+	0.592013i	$0.201667\pi$
$349$	−3.30762	+	14.4916i	−0.177053	+	0.775720i	−0.982981	+	0.183706i	$0.941190\pi$
$350$	2.62073	−	3.44223i	0.140084	−	0.183995i
$351$	1.07829	+	4.72431i	0.0575550	+	0.252165i
$352$	1.10921	−	14.8014i	0.0591211	−	0.788916i
$353$	1.33347	−	0.411320i	0.0709732	−	0.0218923i	−0.259065	−	0.965860i	$-0.583414\pi$
$353$	1.33347	−	0.411320i	0.0709732	−	0.0218923i	0.330038	+	0.943967i	$0.392938\pi$
$354$	−2.67776	−	35.7323i	−0.142321	−	1.89915i
$355$	2.75388	+	7.01678i	0.146161	+	0.372412i
$356$	18.8387	+	9.07223i	0.998449	+	0.480827i
$357$	1.05943	−	20.2286i	0.0560709	−	1.07061i
$358$	49.8577	−	24.0102i	2.63506	−	1.26898i
$359$	1.11016	+	1.03008i	0.0585922	+	0.0543656i	0.708925	−	0.705283i	$-0.249180\pi$
$359$	1.11016	+	1.03008i	0.0585922	+	0.0543656i	−0.650333	+	0.759649i	$0.725371\pi$
$360$	1.11846	+	0.168581i	0.0589480	+	0.00888499i
$361$	−7.13453	−	12.3574i	−0.375501	−	0.650388i
$362$	−12.6825	+	21.9667i	−0.666576	+	1.15454i
$363$	8.17964	−	10.2569i	0.429320	−	0.538350i
$364$	−0.697386	−	7.14662i	−0.0365529	−	0.374585i
$365$	0.0642384	+	0.0805524i	0.00336239	+	0.00421631i
$366$	23.1548	−	3.49003i	1.21032	−	0.182427i
$367$	−0.734050	−	0.500467i	−0.0383171	−	0.0261242i	0.544010	−	0.839079i	$-0.316905\pi$
$367$	−0.734050	−	0.500467i	−0.0383171	−	0.0261242i	−0.582327	+	0.812955i	$0.697858\pi$
$368$	2.06495	+	1.40786i	0.107643	+	0.0733896i
$369$	3.71279	−	0.559613i	0.193280	−	0.0291323i
$370$	−1.12959	−	1.41646i	−0.0587245	−	0.0736381i
$371$	−5.86861	−	9.65684i	−0.304683	−	0.501358i
$372$	−33.1775	+	41.6033i	−1.72018	+	2.15703i
$373$	−5.09265	+	8.82073i	−0.263687	+	0.456720i	−0.967219	−	0.253944i	$-0.918272\pi$
$373$	−5.09265	+	8.82073i	−0.263687	+	0.456720i	0.703531	+	0.710664i	$0.251605\pi$
$374$	−8.88921	−	15.3966i	−0.459650	−	0.796138i
$375$	−21.4707	−	3.23619i	−1.10874	−	0.167116i
$376$	14.8287	+	13.7591i	0.764734	+	0.709569i
$377$	7.00015	−	3.37109i	0.360526	−	0.173620i
$378$	−22.6411	+	16.1936i	−1.16453	+	0.832908i
$379$	18.5792	+	8.94728i	0.954350	+	0.459591i	0.845209	−	0.534435i	$-0.179476\pi$
$379$	18.5792	+	8.94728i	0.954350	+	0.459591i	0.109141	+	0.994026i	$0.465190\pi$
$380$	11.7859	+	30.0300i	0.604604	+	1.54050i
$381$	1.89510	+	25.2884i	0.0970892	+	1.29556i
$382$	4.82003	−	1.48678i	0.246614	−	0.0760704i
$383$	0.151124	−	2.01660i	0.00772205	−	0.103044i	−0.992011	−	0.126152i	$-0.959737\pi$
$383$	0.151124	−	2.01660i	0.00772205	−	0.103044i	0.999733	+	0.0231085i	$0.00735631\pi$
$384$	4.73198	+	20.7322i	0.241478	+	1.05798i
$385$	6.84459	+	8.19791i	0.348833	+	0.417804i
$386$	1.26162	−	5.52753i	0.0642149	−	0.281344i
$387$	−0.406047	−	0.125249i	−0.0206406	−	0.00636677i
$388$	0.767602	−	1.95582i	0.0389691	−	0.0992916i
$389$	−8.75448	+	8.12297i	−0.443870	+	0.411851i	−0.870186	−	0.492723i	$-0.836002\pi$
$389$	−8.75448	+	8.12297i	−0.443870	+	0.411851i	0.426316	+	0.904574i	$0.359811\pi$
$390$	−6.77048	+	4.61603i	−0.342837	+	0.233742i
$391$	5.06638			0.256218
$392$	9.55546	−	5.14287i	0.482623	−	0.259754i
$393$	−12.0521			−0.607949
$394$	33.8036	−	23.0469i	1.70300	−	1.16109i
$395$	−18.2782	+	16.9597i	−0.919677	+	0.853335i
$396$	0.687626	−	1.75204i	0.0345545	−	0.0880435i
$397$	6.56279	+	2.02435i	0.329377	+	0.101599i	0.455033	−	0.890474i	$-0.349627\pi$
$397$	6.56279	+	2.02435i	0.329377	+	0.101599i	−0.125656	+	0.992074i	$0.540104\pi$
$398$	−5.01729	+	21.9822i	−0.251494	+	1.10187i
$399$	25.4466	+	11.5573i	1.27393	+	0.578591i
$400$	−0.345604	−	1.51419i	−0.0172802	−	0.0757095i
$401$	0.00120659	−	0.0161008i	6.02542e−5	−	0.000804037i	−0.997174	−	0.0751321i	$-0.976062\pi$
$401$	0.00120659	−	0.0161008i	6.02542e−5	−	0.000804037i	0.997234	+	0.0743281i	$0.0236812\pi$
$402$	−26.5315	+	8.18389i	−1.32327	+	0.408175i
$403$	−0.800047	−	10.6759i	−0.0398532	−	0.531804i
$404$	−16.1362	−	41.1144i	−0.802807	−	2.04552i
$405$	18.4498	+	8.88494i	0.916776	+	0.441496i
$406$	33.3911	+	29.6142i	1.65717	+	1.46973i
$407$	−0.714569	+	0.344118i	−0.0354199	+	0.0170573i
$408$	8.70039	+	8.07278i	0.430734	+	0.399662i
$409$	25.5647	+	3.85326i	1.26409	+	0.190532i	0.746669	−	0.665196i	$-0.231652\pi$
$409$	25.5647	+	3.85326i	1.26409	+	0.190532i	0.517426	+	0.855728i	$0.326890\pi$
$410$	−23.7250	−	41.0929i	−1.17169	−	2.02943i
$411$	−9.74594	+	16.8805i	−0.480732	+	0.832652i
$412$	−23.7878	+	29.8289i	−1.17194	+	1.46957i
$413$	−8.20956	+	22.3842i	−0.403966	+	1.10145i
$414$	0.580855	+	0.728369i	0.0285474	+	0.0357974i
$415$	−19.4982	+	2.93888i	−0.957130	+	0.144264i
$416$	−6.26111	−	4.26875i	−0.306976	−	0.209293i
$417$	−13.5444	−	9.23444i	−0.663274	−	0.452213i
$418$	24.2555	−	3.65592i	1.18637	−	0.178817i
$419$	−2.92130	−	3.66319i	−0.142715	−	0.178959i	0.705337	−	0.708872i	$-0.250796\pi$
$419$	−2.92130	−	3.66319i	−0.142715	−	0.178959i	−0.848052	+	0.529914i	$0.822224\pi$
$420$	−22.7289	−	14.7592i	−1.10906	−	0.720176i
$421$	1.98378	−	2.48758i	0.0966834	−	0.121237i	−0.731136	−	0.682231i	$-0.761010\pi$
$421$	1.98378	−	2.48758i	0.0966834	−	0.121237i	0.827820	+	0.560994i	$0.189581\pi$
$422$	5.24876	−	9.09112i	0.255506	−	0.442549i
$423$	−2.31003	−	4.00109i	−0.112318	−	0.194540i
$424$	6.54717	+	0.986827i	0.317959	+	0.0479245i
$425$	−2.30801	−	2.14152i	−0.111955	−	0.103879i
$426$	−13.1040	+	6.31054i	−0.634889	+	0.305747i
$427$	−14.9880	−	4.25676i	−0.725320	−	0.205999i
$428$	16.1136	+	7.75989i	0.778879	+	0.375088i
$429$	1.31056	+	3.33925i	0.0632743	+	0.161220i
$430$	0.401297	+	5.35494i	0.0193523	+	0.258238i
$431$	−11.5289	+	3.55618i	−0.555325	+	0.171295i	−0.559700	−	0.828695i	$-0.689084\pi$
$431$	−11.5289	+	3.55618i	−0.555325	+	0.171295i	0.00437467	+	0.999990i	$0.498607\pi$
$432$	−0.746780	+	9.96509i	−0.0359295	+	0.479446i
$433$	1.22630	+	5.37278i	0.0589323	+	0.258199i	0.995809	−	0.0914616i	$-0.0291539\pi$
$433$	1.22630	+	5.37278i	0.0589323	+	0.258199i	−0.936876	+	0.349661i	$0.886297\pi$
$434$	54.7945	−	27.9216i	2.63022	−	1.34028i
$435$	6.52510	−	28.5883i	0.312855	−	1.37071i
$436$	−2.17139	−	0.669787i	−0.103991	−	0.0320770i
$437$	−2.55382	+	6.50703i	−0.122166	+	0.311274i
$438$	−0.145729	+	0.135217i	−0.00696320	+	0.00646091i
$439$	24.3276	−	16.5863i	1.16109	−	0.791619i	0.179717	−	0.983718i	$-0.442482\pi$
$439$	24.3276	−	16.5863i	1.16109	−	0.791619i	0.981376	+	0.192099i	$0.0615294\pi$
$440$	−6.25749			−0.298314
$441$	−2.43163	+	0.479132i	−0.115792	+	0.0228158i
$442$	−9.07655			−0.431727
$443$	−25.9600	+	17.6992i	−1.23340	+	0.840915i	−0.991591	−	0.129411i	$-0.958691\pi$
$443$	−25.9600	+	17.6992i	−1.23340	+	0.840915i	−0.241804	+	0.970325i	$0.577739\pi$
$444$	1.47534	−	1.36891i	0.0700164	−	0.0649658i
$445$	−5.80047	+	14.7794i	−0.274969	+	0.700609i
$446$	−27.7747	−	8.56736i	−1.31517	−	0.405676i
$447$	1.44578	−	6.33439i	0.0683832	−	0.299607i
$448$	6.54170	−	31.9552i	0.309066	−	1.50974i
$449$	−1.88058	−	8.23937i	−0.0887502	−	0.388840i	0.910971	−	0.412471i	$-0.135334\pi$
$449$	−1.88058	−	8.23937i	−0.0887502	−	0.388840i	−0.999721	+	0.0236315i	$0.992477\pi$
$450$	0.0432651	−	0.577333i	0.00203954	−	0.0272157i
$451$	−19.8492	+	6.12267i	−0.934663	+	0.288305i
$452$	−2.48347	−	33.1396i	−0.116813	−	1.55876i
$453$	4.76927	+	12.1519i	0.224080	+	0.570947i
$454$	−55.5091	−	26.7318i	−2.60517	−	1.25458i
$455$	5.37182	−	0.933585i	0.251835	−	0.0437671i
$456$	−14.7540	+	7.10513i	−0.690917	+	0.332728i
$457$	6.35986	+	5.90109i	0.297502	+	0.276041i	0.814773	−	0.579780i	$-0.196862\pi$
$457$	6.35986	+	5.90109i	0.297502	+	0.276041i	−0.517271	+	0.855822i	$0.673052\pi$
$458$	22.1929	+	3.34504i	1.03701	+	0.156303i
$459$	10.1289	+	17.5437i	0.472776	+	0.818872i
$460$	3.38911	−	5.87011i	0.158018	−	0.273695i
$461$	−13.4558	+	16.8730i	−0.626698	+	0.785855i	−0.989270	−	0.146101i	$-0.953327\pi$
$461$	−13.4558	+	16.8730i	−0.626698	+	0.785855i	0.362571	+	0.931956i	$0.381899\pi$
$462$	−14.7868	+	14.3518i	−0.687942	+	0.667707i
$463$	−16.1913	−	20.3033i	−0.752475	−	0.943574i	0.247202	−	0.968964i	$-0.420489\pi$
$463$	−16.1913	−	20.3033i	−0.752475	−	0.943574i	−0.999678	+	0.0253896i	$0.991917\pi$
$464$	15.8435	−	2.38802i	0.735515	−	0.110861i
$465$	−33.3845	−	22.7611i	−1.54817	−	1.05552i
$466$	0.710732	+	0.484569i	0.0329240	+	0.0224472i
$467$	17.2259	−	2.59638i	0.797118	−	0.120146i	0.262160	−	0.965025i	$-0.415565\pi$
$467$	17.2259	−	2.59638i	0.797118	−	0.120146i	0.534959	+	0.844878i	$0.320327\pi$
$468$	−0.599116	−	0.751267i	−0.0276941	−	0.0347273i
$469$	18.3252	+	2.34222i	0.846179	+	0.108154i
$470$	−36.4028	+	45.6476i	−1.67913	+	2.10557i
$471$	−14.6803	+	25.4270i	−0.676432	+	1.17162i
$472$	−6.98489	−	12.0982i	−0.321506	−	0.556864i
$473$	2.32454	+	0.350367i	0.106882	+	0.0161099i
$474$	−35.2679	−	32.7238i	−1.61991	−	1.50306i
$475$	3.91387	−	1.88482i	0.179581	−	0.0864815i
$476$	−11.5921	−	27.6896i	−0.531322	−	1.26915i
$477$	−1.36245	−	0.656120i	−0.0623821	−	0.0300416i
$478$	2.15573	+	5.49272i	0.0986010	+	0.251231i
$479$	1.29967	+	17.3430i	0.0593836	+	0.792420i	0.944806	+	0.327632i	$0.106250\pi$
$479$	1.29967	+	17.3430i	0.0593836	+	0.792420i	−0.885422	+	0.464788i	$0.846130\pi$
$480$	−27.3293	+	8.42997i	−1.24741	+	0.384774i
$481$	−0.0302592	+	0.403781i	−0.00137970	+	0.0184108i
$482$	−10.3346	−	45.2788i	−0.470728	−	2.06239i
$483$	−1.43503	−	5.69423i	−0.0652962	−	0.259096i
$484$	4.32614	−	18.9541i	0.196643	−	0.861548i
$485$	1.52449	+	0.470244i	0.0692237	+	0.0213527i
$486$	−2.90393	+	7.39910i	−0.131725	+	0.335630i
$487$	24.5591	−	22.7875i	1.11288	−	1.03260i	0.113642	−	0.993522i	$-0.463748\pi$
$487$	24.5591	−	22.7875i	1.11288	−	1.03260i	0.999236	−	0.0390779i	$-0.0124421\pi$
$488$	7.54290	−	5.14266i	0.341451	−	0.232797i
$489$	−43.4219			−1.96361
$490$	16.8632	+	26.3932i	0.761800	+	1.19232i
$491$	23.2421			1.04890			0.524451	−	0.851441i	$-0.324271\pi$
$491$	23.2421			1.04890			0.524451	+	0.851441i	$0.324271\pi$
$492$	43.5519	−	29.6932i	1.96347	−	1.33867i
$493$	23.8099	−	22.0924i	1.07234	−	0.994990i
$494$	4.57524	−	11.6575i	0.205850	−	0.524496i
$495$	1.36566	+	0.421250i	0.0613817	+	0.0189338i
$496$	4.91272	−	21.5240i	0.220588	−	0.966458i
$497$	9.67503	−	0.217480i	0.433985	−	0.00975532i
$498$	−8.46623	−	37.0930i	−0.379381	−	1.66218i
$499$	3.15983	−	42.1650i	0.141453	−	1.88757i	−0.251282	−	0.967914i	$-0.580852\pi$
$499$	3.15983	−	42.1650i	0.141453	−	1.88757i	0.392736	−	0.919651i	$-0.371529\pi$
$500$	−30.7477	+	9.48441i	−1.37508	+	0.424156i
$501$	−0.727008	−	9.70125i	−0.0324803	−	0.433420i
$502$	16.7634	+	42.7125i	0.748188	+	1.90635i
$503$	−13.1356	−	6.32579i	−0.585690	−	0.282053i	0.117480	−	0.993075i	$-0.462518\pi$
$503$	−13.1356	−	6.32579i	−0.585690	−	0.282053i	−0.703170	+	0.711022i	$0.748233\pi$
$504$	0.697633	−	1.27360i	0.0310751	−	0.0567309i
$505$	30.2160	−	14.5513i	1.34459	−	0.647523i
$506$	−3.77811	−	3.50557i	−0.167957	−	0.155842i
$507$	1.81095	+	0.272957i	0.0804272	+	0.0121225i
$508$	18.7902	+	32.5457i	0.833682	+	1.44398i
$509$	6.46543	−	11.1985i	0.286575	−	0.496363i	−0.686415	−	0.727210i	$-0.740817\pi$
$509$	6.46543	−	11.1985i	0.286575	−	0.496363i	0.972990	+	0.230848i	$0.0741499\pi$
$510$	−21.3584	+	26.7826i	−0.945766	+	1.18595i
$511$	0.125491	−	0.0418197i	0.00555140	−	0.00184999i
$512$	−13.7297	−	17.2165i	−0.606774	−	0.760871i
$513$	−27.6381	+	4.16577i	−1.22025	+	0.183923i
$514$	−52.6535	−	35.8985i	−2.32245	−	1.58342i
$515$	−23.9362	−	16.3194i	−1.05475	−	0.719118i
$516$	−5.89873	+	0.889091i	−0.259677	+	0.0391400i
$517$	15.9360	+	19.9831i	0.700863	+	0.878854i
$518$	−2.20667	+	0.735370i	−0.0969556	+	0.0323103i
$519$	−0.739888	+	0.927790i	−0.0324775	+	0.0407254i
$520$	−1.59734	+	2.76667i	−0.0700480	+	0.121327i
$521$	10.6379	+	18.4254i	0.466055	+	0.807231i	0.999248	−	0.0387625i	$-0.0123416\pi$
$521$	10.6379	+	18.4254i	0.466055	+	0.807231i	−0.533193	+	0.845993i	$0.679008\pi$
$522$	5.90589	+	0.890170i	0.258494	+	0.0389617i
$523$	6.48945	+	6.02133i	0.283764	+	0.263294i	0.809193	−	0.587543i	$-0.199905\pi$
$523$	6.48945	+	6.02133i	0.283764	+	0.263294i	−0.525429	+	0.850837i	$0.676095\pi$
$524$	−16.0916	+	7.74928i	−0.702963	+	0.338529i
$525$	−1.75317	+	3.20060i	−0.0765146	+	0.139686i
$526$	−50.4549	−	24.2978i	−2.19994	−	1.05943i
$527$	−16.3510	−	41.6616i	−0.712260	−	1.81481i
$528$	0.552821	+	7.37689i	0.0240585	+	0.321038i
$529$	−20.5747	+	6.34645i	−0.894552	+	0.275933i
$530$	−1.42811	+	19.0568i	−0.0620332	+	0.827776i
$531$	0.709968	+	3.11057i	0.0308100	+	0.134987i
$532$	41.4066	−	0.930758i	1.79520	−	0.0403535i
$533$	−2.35981	+	10.3390i	−0.102215	+	0.447833i
$534$	−29.2735	−	9.02968i	−1.26679	−	0.390752i
$535$	−4.96140	+	12.6415i	−0.214500	+	0.546538i
$536$	−7.93499	+	7.36259i	−0.342739	+	0.318015i
$537$	−38.5672	+	26.2947i	−1.66430	+	1.13470i
$538$	−22.7997			−0.982966
$539$	12.9071	−	4.62605i	0.555947	−	0.199258i
$540$	27.1025			1.16631
$541$	5.62518	−	3.83518i	0.241845	−	0.164887i	−0.436332	−	0.899786i	$-0.643723\pi$
$541$	5.62518	−	3.83518i	0.241845	−	0.164887i	0.678177	+	0.734899i	$0.262770\pi$
$542$	41.5647	−	38.5664i	1.78535	−	1.65657i
$543$	7.81668	−	19.9166i	0.335446	−	0.854702i
$544$	−30.2716	−	9.33755i	−1.29788	−	0.400344i
$545$	0.383946	−	1.68218i	0.0164464	−	0.0720565i
$546$	2.57089	+	10.2014i	0.110024	+	0.436578i
$547$	7.63449	+	33.4489i	0.326427	+	1.43017i	0.825888	+	0.563834i	$0.190674\pi$
$547$	7.63449	+	33.4489i	0.326427	+	1.43017i	−0.499461	+	0.866337i	$0.666469\pi$
$548$	−2.15861	+	28.8046i	−0.0922112	+	1.23047i
$549$	−1.99239	+	0.614571i	−0.0850332	+	0.0262293i
$550$	0.239353	+	3.19395i	0.0102061	+	0.136190i
$551$	16.3725	+	41.7165i	0.697493	+	1.77718i
$552$	3.09999	+	1.49288i	0.131944	+	0.0635410i
$553$	12.3620	+	29.5289i	0.525688	+	1.25570i
$554$	−2.82314	+	1.35955i	−0.119944	+	0.0577618i
$555$	1.12025	+	1.03944i	0.0475520	+	0.0441218i
$556$	−24.0216	−	3.62068i	−1.01874	−	0.153551i
$557$	5.99680	+	10.3868i	0.254092	+	0.440101i	0.964649	−	0.263539i	$-0.0848899\pi$
$557$	5.99680	+	10.3868i	0.254092	+	0.440101i	−0.710556	+	0.703640i	$0.751557\pi$
$558$	4.11487	−	7.12716i	0.174196	−	0.301717i
$559$	0.748292	−	0.938328i	0.0316494	−	0.0396871i
$560$	11.1531	+	1.42552i	0.471304	+	0.0602394i
$561$	9.35003	+	11.7246i	0.394759	+	0.495012i
$562$	−6.68988	+	1.00834i	−0.282196	+	0.0425341i
$563$	15.5954	+	10.6328i	0.657269	+	0.448118i	0.845478	−	0.534011i	$-0.179316\pi$
$563$	15.5954	+	10.6328i	0.657269	+	0.448118i	−0.188209	+	0.982129i	$0.560268\pi$
$564$	−53.5892	−	36.5365i	−2.25651	−	1.53846i
$565$	24.9522	−	3.76095i	1.04975	−	0.158224i
$566$	−2.98783	−	3.74661i	−0.125588	−	0.157482i
$567$	18.8655	−	18.3106i	0.792274	−	0.768971i
$568$	−3.53538	+	4.43322i	−0.148341	+	0.186014i
$569$	−1.18125	+	2.04599i	−0.0495206	+	0.0857722i	−0.889723	−	0.456500i	$-0.849103\pi$
$569$	−1.18125	+	2.04599i	−0.0495206	+	0.0857722i	0.840203	+	0.542273i	$0.182436\pi$
$570$	−23.6322	−	40.9322i	−0.989844	−	1.71446i
$571$	−12.9009	−	1.94449i	−0.539885	−	0.0813746i	−0.126561	−	0.991959i	$-0.540394\pi$
$571$	−12.9009	−	1.94449i	−0.539885	−	0.0813746i	−0.413324	+	0.910584i	$0.635632\pi$
$572$	3.89688	+	3.61578i	0.162937	+	0.151183i
$573$	−3.83342	+	1.84608i	−0.160143	+	0.0771209i
$574$	−60.0190	+	10.4309i	−2.50515	+	0.435377i
$575$	−0.822352	−	0.396024i	−0.0342945	−	0.0165153i
$576$	−1.59469	−	4.06321i	−0.0664455	−	0.169300i
$577$	−1.26183	−	16.8380i	−0.0525308	−	0.700975i	−0.959847	−	0.280525i	$-0.909491\pi$
$577$	−1.26183	−	16.8380i	−0.0525308	−	0.700975i	0.907316	−	0.420450i	$-0.138128\pi$
$578$	−0.988360	+	0.304869i	−0.0411104	+	0.0126809i
$579$	−0.357392	+	4.76906i	−0.0148527	+	0.198195i
$580$	−9.66968	−	42.3656i	−0.401511	−	1.75914i
$581$	−5.07718	+	24.8012i	−0.210637	+	1.02893i
$582$	−0.684981	+	3.00110i	−0.0283934	+	0.124400i
$583$	7.99419	+	2.46588i	0.331086	+	0.102126i
$584$	−0.0283154	+	0.0721465i	−0.00117170	+	0.00298544i
$585$	0.534860	−	0.496277i	0.0221137	−	0.0205185i
$586$	45.6518	−	31.1248i	1.88586	−	1.28576i
$587$	21.2659			0.877739			0.438869	−	0.898551i	$-0.355379\pi$
$587$	21.2659			0.877739			0.438869	+	0.898551i	$0.355379\pi$
$588$	−27.8377	+	20.8716i	−1.14801	+	0.860730i
$589$	61.7504			2.54438
$590$	33.3143	−	22.7133i	1.37153	−	0.935092i
$591$	−25.2978	+	23.4729i	−1.04061	+	0.965548i
$592$	−0.305064	+	0.777292i	−0.0125381	+	0.0319465i
$593$	12.5824	+	3.88115i	0.516696	+	0.159380i	0.542127	−	0.840297i	$-0.317619\pi$
$593$	12.5824	+	3.88115i	0.516696	+	0.159380i	−0.0254302	+	0.999677i	$0.508096\pi$
$594$	4.58569	−	20.0912i	0.188153	−	0.824352i
$595$	20.3087	−	10.3487i	0.832575	−	0.424255i
$596$	−2.14254	−	9.38707i	−0.0877617	−	0.384509i
$597$	1.42129	−	18.9659i	0.0581697	−	0.776221i
$598$	−2.51438	+	0.775583i	−0.102821	+	0.0317159i
$599$	−0.276807	−	3.69374i	−0.0113100	−	0.150922i	−1.00000		0.000945177i	$-0.999699\pi$
$599$	−0.276807	−	3.69374i	−0.0113100	−	0.150922i	0.988690	−	0.149977i	$-0.0479199\pi$
$600$	−0.781184	−	1.99042i	−0.0318917	−	0.0812587i
$601$	−20.3785	−	9.81375i	−0.831255	−	0.400311i	−0.0306690	−	0.999530i	$-0.509764\pi$
$601$	−20.3785	−	9.81375i	−0.831255	−	0.400311i	−0.800586	+	0.599218i	$0.795478\pi$
$602$	6.63194	+	1.88355i	0.270298	+	0.0767676i
$603$	2.22741	−	1.07266i	0.0907070	−	0.0436822i
$604$	14.1812	+	13.1582i	0.577025	+	0.535401i
$605$	14.5974	+	2.20021i	0.593469	+	0.0894511i
$606$	32.3551	+	56.0407i	1.31434	+	2.27650i
$607$	1.45824	−	2.52574i	0.0591879	−	0.102517i	−0.834913	−	0.550382i	$-0.814482\pi$
$607$	1.45824	−	2.52574i	0.0591879	−	0.102517i	0.894101	+	0.447865i	$0.147816\pi$
$608$	27.2518	−	34.1727i	1.10521	−	1.38588i
$609$	−31.5742	−	20.5030i	−1.27945	−	0.830823i
$610$	16.4285	+	20.6007i	0.665170	+	0.834097i
$611$	12.9032	−	1.94485i	0.522009	−	0.0786801i
$612$	−3.31904	−	2.26288i	−0.134164	−	0.0914717i
$613$	−9.79850	−	6.68051i	−0.395758	−	0.269823i	0.349047	−	0.937105i	$-0.386505\pi$
$613$	−9.79850	−	6.68051i	−0.395758	−	0.269823i	−0.744805	+	0.667282i	$0.767458\pi$
$614$	36.4511	−	5.49411i	1.47105	−	0.221724i
$615$	24.9549	+	31.2924i	1.00628	+	1.26183i
$616$	−2.76623	+	7.54242i	−0.111455	+	0.303893i
$617$	−23.9963	+	30.0905i	−0.966056	+	1.21140i	0.0113306	+	0.999936i	$0.496393\pi$
$617$	−23.9963	+	30.0905i	−0.966056	+	1.21140i	−0.977387	+	0.211460i	$0.932178\pi$
$618$	27.9489	−	48.4089i	1.12427	−	1.94729i
$619$	−2.28285	−	3.95402i	−0.0917556	−	0.158925i	0.816494	−	0.577353i	$-0.195915\pi$
$619$	−2.28285	−	3.95402i	−0.0917556	−	0.158925i	−0.908250	+	0.418428i	$0.862581\pi$
$620$	−59.2087	−	8.92428i	−2.37788	−	0.358408i
$621$	4.30499	+	3.99445i	0.172753	+	0.160292i
$622$	56.6494	−	27.2809i	2.27143	−	1.09386i
$623$	15.2500	+	13.5250i	0.610978	+	0.541870i
$624$	3.40272	+	1.63866i	0.136218	+	0.0655991i
$625$	−7.55053	−	19.2384i	−0.302021	−	0.769537i
$626$	2.17152	+	28.9769i	0.0867912	+	1.15815i
$627$	−19.7716	+	6.09873i	−0.789602	+	0.243560i
$628$	−3.25151	+	43.3884i	−0.129749	+	1.73139i
$629$	0.376668	+	1.65029i	0.0150187	+	0.0658013i
$630$	3.81615	+	1.73322i	0.152039	+	0.0690530i
$631$	3.41378	−	14.9567i	0.135900	−	0.595419i	−0.860410	−	0.509602i	$-0.829793\pi$
$631$	3.41378	−	14.9567i	0.135900	−	0.595419i	0.996311	−	0.0858171i	$-0.0273501\pi$
$632$	−17.9235	−	5.52866i	−0.712957	−	0.219918i
$633$	−3.23501	+	8.24267i	−0.128580	+	0.327617i
$634$	4.12544	−	3.82785i	0.163842	−	0.152023i
$635$	−23.5772	+	16.0747i	−0.935632	+	0.637903i
$636$	−21.2292			−0.841792
$637$	1.24942	−	6.88759i	0.0495038	−	0.272896i
$638$	−33.0419			−1.30814
$639$	1.07002	−	0.729524i	0.0423292	−	0.0288595i
$640$	−17.5410	+	16.2757i	−0.693371	+	0.643354i
$641$	−4.07464	+	10.3820i	−0.160939	+	0.410065i	−0.988482	−	0.151336i	$-0.951642\pi$
$641$	−4.07464	+	10.3820i	−0.160939	+	0.410065i	0.827544	+	0.561402i	$0.189738\pi$
$642$	−25.0389	−	7.72349i	−0.988208	−	0.304822i
$643$	8.45017	−	37.0226i	0.333242	−	1.46003i	−0.479570	−	0.877504i	$-0.659207\pi$
$643$	8.45017	−	37.0226i	0.333242	−	1.46003i	0.812812	−	0.582526i	$-0.197936\pi$
$644$	−5.57728	−	6.68003i	−0.219776	−	0.263230i
$645$	−1.00793	−	4.41604i	−0.0396873	−	0.173881i
$646$	3.91234	−	52.2065i	0.153929	−	2.05404i
$647$	31.6552	−	9.76432i	1.24449	−	0.383875i	0.398549	−	0.917147i	$-0.369514\pi$
$647$	31.6552	−	9.76432i	1.24449	−	0.383875i	0.845944	+	0.533272i	$0.179038\pi$
$648$	1.15116	+	15.3612i	0.0452218	+	0.603444i
$649$	−6.44863	−	16.4308i	−0.253131	−	0.644967i
$650$	1.47327	+	0.709487i	0.0577862	+	0.0278284i
$651$	−42.1932	+	30.1778i	−1.65368	+	1.18276i
$652$	−57.9754	+	27.9195i	−2.27049	+	1.09341i
$653$	−18.3249	−	17.0030i	−0.717110	−	0.665381i	0.234701	−	0.972068i	$-0.424589\pi$
$653$	−18.3249	−	17.0030i	−0.717110	−	0.665381i	−0.951810	+	0.306687i	$0.900780\pi$
$654$	3.29205	+	0.496197i	0.128730	+	0.0194029i
$655$	−6.78082	−	11.7447i	−0.264949	−	0.458904i
$656$	−10.9347	+	18.9395i	−0.426930	+	0.739464i
$657$	0.0110365	−	0.0138394i	0.000430576	−	0.000539925i
$658$	38.9286	+	64.0572i	1.51759	+	2.49721i
$659$	12.2377	+	15.3455i	0.476711	+	0.597777i	0.960800	−	0.277242i	$-0.0894203\pi$
$659$	12.2377	+	15.3455i	0.476711	+	0.597777i	−0.484089	+	0.875019i	$0.660849\pi$
$660$	19.8392	−	2.99027i	0.772239	−	0.116396i
$661$	6.41406	+	4.37303i	0.249478	+	0.170091i	0.681602	−	0.731723i	$-0.261283\pi$
$661$	6.41406	+	4.37303i	0.249478	+	0.170091i	−0.432124	+	0.901814i	$0.642236\pi$
$662$	52.9923	+	36.1295i	2.05960	+	1.40421i
$663$	7.57065	−	1.14109i	0.294020	−	0.0443163i
$664$	−9.24829	−	11.5970i	−0.358903	−	0.450051i
$665$	3.05434	+	31.3001i	0.118442	+	1.21376i
$666$	−0.194070	+	0.243356i	−0.00752004	+	0.00942983i
$667$	4.70803	−	8.15455i	0.182296	−	0.315745i
$668$	−7.20840	−	12.4853i	−0.278901	−	0.483071i
$669$	24.2436	+	3.65414i	0.937313	+	0.141277i
$670$	−22.9024	−	21.2504i	−0.884798	−	0.820973i
$671$	10.3925	−	5.00479i	0.401200	−	0.193208i
$672$	−1.92040	+	36.6678i	−0.0740810	+	1.41449i
$673$	−28.4937	−	13.7219i	−1.09835	−	0.528939i	−0.205213	−	0.978717i	$-0.565789\pi$
$673$	−28.4937	−	13.7219i	−1.09835	−	0.528939i	−0.893140	+	0.449778i	$0.851503\pi$
$674$	9.98000	+	25.4286i	0.384415	+	0.979474i
$675$	−0.272733	−	3.63937i	−0.0104975	−	0.140079i
$676$	2.59342	−	0.799966i	0.0997471	−	0.0307679i
$677$	−1.30273	+	17.3837i	−0.0500680	+	0.668111i	0.914552	+	0.404468i	$0.132543\pi$
$677$	−1.30273	+	17.3837i	−0.0500680	+	0.668111i	−0.964620	+	0.263643i	$0.915076\pi$
$678$	10.8344	+	47.4686i	0.416092	+	1.82302i
$679$	1.24073	−	1.62966i	0.0476150	−	0.0625405i
$680$	−2.97183	+	13.0204i	−0.113964	+	0.499311i
$681$	49.6602	+	15.3181i	1.90298	+	0.586993i
$682$	−16.6336	+	42.3817i	−0.636933	+	1.62288i
$683$	26.4450	−	24.5374i	1.01189	−	0.938896i	0.0137520	−	0.999905i	$-0.495622\pi$
$683$	26.4450	−	24.5374i	1.01189	−	0.938896i	0.998137	+	0.0610095i	$0.0194320\pi$
$684$	4.57938	−	3.12217i	0.175097	−	0.119379i
$685$	−21.9332			−0.838025
$686$	39.2675	−	8.65834i	1.49924	−	0.330577i
$687$	−18.9314			−0.722277
$688$	2.04493	−	1.39421i	0.0779623	−	0.0531538i
$689$	3.13093	−	2.90508i	0.119279	−	0.110675i
$690$	−3.62814	+	9.24435i	−0.138121	+	0.351927i
$691$	−15.5646	−	4.80105i	−0.592107	−	0.182641i	−0.0158012	−	0.999875i	$-0.505030\pi$
$691$	−15.5646	−	4.80105i	−0.592107	−	0.182641i	−0.576305	+	0.817234i	$0.695506\pi$
$692$	−0.391320	+	1.71448i	−0.0148758	+	0.0651749i
$693$	1.11146	−	1.45987i	0.0422210	−	0.0554557i
$694$	−1.41521	−	6.20044i	−0.0537206	−	0.235366i
$695$	1.37848	−	18.3945i	0.0522886	−	0.697743i
$696$	21.0785	−	6.50185i	0.798978	−	0.246452i
$697$	3.31305	+	44.2096i	0.125491	+	1.67456i
$698$	−11.7907	−	30.0421i	−0.446283	−	1.13711i
$699$	−0.653733	−	0.314821i	−0.0247265	−	0.0119076i
$700$	−0.282844	+	5.40058i	−0.0106905	+	0.204123i
$701$	−40.9822	+	19.7360i	−1.54788	+	0.745419i	−0.996071	−	0.0885538i	$-0.971775\pi$
$701$	−40.9822	+	19.7360i	−1.54788	+	0.745419i	−0.551806	+	0.833972i	$0.686061\pi$
$702$	−7.71250	−	7.15616i	−0.291090	−	0.270092i
$703$	−2.30943	−	0.348090i	−0.0871017	−	0.0131285i
$704$	12.0740	+	20.9127i	0.455055	+	0.788178i
$705$	24.6244	−	42.6507i	0.927408	−	1.60632i
$706$	−1.88904	+	2.36879i	−0.0710951	+	0.0891504i
$707$	−4.18173	−	42.8533i	−0.157270	−	1.61166i
$708$	27.9268	+	35.0191i	1.04955	+	1.31610i
$709$	−12.9752	+	1.95569i	−0.487292	+	0.0734475i	−0.388093	−	0.921620i	$-0.626866\pi$
$709$	−12.9752	+	1.95569i	−0.487292	+	0.0734475i	−0.0991989	+	0.995068i	$0.531628\pi$
$710$	−13.5222	−	9.21928i	−0.507479	−	0.345993i
$711$	3.53950	+	2.41319i	0.132742	+	0.0905017i
$712$	−11.8099	+	1.78006i	−0.442595	+	0.0667104i
$713$	−8.08949	−	10.1439i	−0.302954	−	0.379892i
$714$	22.8404	+	37.5840i	0.854779	+	1.40654i
$715$	−2.51673	+	3.15587i	−0.0941202	+	0.118023i
$716$	−34.5865	+	59.9057i	−1.29256	+	2.23878i
$717$	−2.48861	−	4.31040i	−0.0929389	−	0.160975i
$718$	−3.25139	−	0.490068i	−0.121341	−	0.0182892i
$719$	−0.789396	−	0.732452i	−0.0294395	−	0.0273159i	0.665316	−	0.746562i	$-0.268297\pi$
$719$	−0.789396	−	0.732452i	−0.0294395	−	0.0273159i	−0.694755	+	0.719246i	$0.744487\pi$
$720$	1.35565	−	0.652845i	0.0505220	−	0.0243301i
$721$	−30.2519	+	21.6370i	−1.12664	+	0.805804i
$722$	27.9126	+	13.4420i	1.03880	+	0.500259i
$723$	14.3124	+	36.4673i	0.532282	+	1.35623i
$724$	−2.36943	−	31.6179i	−0.0880592	−	1.17507i
$725$	−5.59162	+	1.72479i	−0.207667	+	0.0640569i
$726$	−2.12861	+	28.4043i	−0.0790000	+	1.05418i
$727$	9.78794	+	42.8838i	0.363015	+	1.59047i	0.745497	+	0.666509i	$0.232212\pi$
$727$	9.78794	+	42.8838i	0.363015	+	1.59047i	−0.382482	+	0.923963i	$0.624931\pi$
$728$	2.62866	+	3.14840i	0.0974245	+	0.116687i
$729$	−5.14151	+	22.5264i	−0.190426	+	0.834313i
$730$	−0.213759	−	0.0659358i	−0.00791157	−	0.00244039i
$731$	1.83301	−	4.67044i	0.0677965	−	0.172743i
$732$	−21.4570	+	19.9092i	−0.793074	+	0.735865i
$733$	27.8975	−	19.0202i	1.03042	−	0.702527i	0.0748183	−	0.997197i	$-0.476162\pi$
$733$	27.8975	−	19.0202i	1.03042	−	0.702527i	0.955599	+	0.294671i	$0.0952099\pi$
$734$	1.92892			0.0711979
$735$	−17.3835	−	19.8942i	−0.641200	−	0.733809i
$736$	−9.18369			−0.338515
$737$	−11.3005	+	7.70453i	−0.416258	+	0.283800i
$738$	−5.97596	+	5.54488i	−0.219978	+	0.204110i
$739$	−5.17424	+	13.1837i	−0.190337	+	0.484972i	−0.993905	−	0.110242i	$-0.964837\pi$
$739$	−5.17424	+	13.1837i	−0.190337	+	0.484972i	0.803567	+	0.595214i	$0.202933\pi$
$740$	2.16406	+	0.667524i	0.0795524	+	0.0245387i
$741$	−2.35059	+	10.2986i	−0.0863510	+	0.378328i
$742$	22.3387	+	10.1458i	0.820080	+	0.372464i
$743$	0.448761	+	1.96615i	0.0164634	+	0.0721311i	0.982492	−	0.186303i	$-0.0596506\pi$
$743$	0.448761	+	1.96615i	0.0164634	+	0.0721311i	−0.966029	+	0.258434i	$0.916793\pi$
$744$	2.27140	−	30.3097i	0.0832736	−	1.11121i
$745$	6.98627	−	2.15498i	0.255957	−	0.0789523i
$746$	−1.65259	−	22.0522i	−0.0605055	−	0.807390i
$747$	1.23768	+	3.15356i	0.0452844	+	0.115383i
$748$	20.0225	+	9.64232i	0.732095	+	0.352558i
$749$	13.0440	+	11.5686i	0.476618	+	0.422707i
$750$	42.4745	−	20.4547i	1.55095	−	0.746899i
$751$	−32.8740	−	30.5026i	−1.19959	−	1.11305i	−0.990834	−	0.135087i	$-0.956869\pi$
$751$	−32.8740	−	30.5026i	−1.19959	−	1.11305i	−0.208754	−	0.977968i	$-0.566941\pi$
$752$	26.6091	+	4.01067i	0.970333	+	0.146254i
$753$	−19.3519	−	33.5185i	−0.705224	−	1.22148i
$754$	−8.43455	+	14.6091i	−0.307168	+	0.532031i
$755$	−9.15866	+	11.4846i	−0.333318	+	0.417967i
$756$	11.9812	−	32.6678i	0.435751	−	1.18812i
$757$	19.5100	+	24.4648i	0.709103	+	0.889186i	0.997667	−	0.0682741i	$-0.0217492\pi$
$757$	19.5100	+	24.4648i	0.709103	+	0.889186i	−0.288564	+	0.957461i	$0.593178\pi$
$758$	−44.2725	+	6.67301i	−1.60805	+	0.242375i
$759$	3.59199	+	2.44898i	0.130381	+	0.0888923i
$760$	−15.2248	−	10.3801i	−0.552263	−	0.376527i
$761$	−15.4558	+	2.32959i	−0.560273	+	0.0844475i	−0.423072	−	0.906096i	$-0.639048\pi$
$761$	−15.4558	+	2.32959i	−0.560273	+	0.0844475i	−0.137200	+	0.990543i	$0.543810\pi$
$762$	−34.3291	−	43.0473i	−1.24361	−	1.55944i
$763$	−1.85787	−	1.20642i	−0.0672594	−	0.0436754i
$764$	−3.93125	+	4.92963i	−0.142228	+	0.178348i
$765$	1.52511	−	2.64157i	0.0551405	−	0.0955061i
$766$	2.19534	+	3.80244i	0.0793208	+	0.137388i
$767$	−8.91084	−	1.34309i	−0.321752	−	0.0484963i
$768$	−0.743325	−	0.689705i	−0.0268224	−	0.0248876i
$769$	43.2001	−	20.8041i	1.55784	−	0.750214i	0.560859	−	0.827912i	$-0.310471\pi$
$769$	43.2001	−	20.8041i	1.55784	−	0.750214i	0.996977	+	0.0776974i	$0.0247568\pi$
$770$	−22.3052	−	6.33492i	−0.803822	−	0.228295i
$771$	48.4308	+	23.3230i	1.74419	+	0.839959i
$772$	2.58924	+	6.59727i	0.0931887	+	0.237441i
$773$	0.870644	+	11.6179i	0.0313149	+	0.417868i	0.990728	+	0.135863i	$0.0433806\pi$
$773$	0.870644	+	11.6179i	0.0313149	+	0.417868i	−0.959413	+	0.282005i	$0.909000\pi$
$774$	0.881600	−	0.271938i	0.0316885	−	0.00977460i
$775$	−0.602548	+	8.04045i	−0.0216442	+	0.288821i
$776$	0.267050	+	1.17002i	0.00958652	+	0.0420013i
$777$	1.74811	−	0.890784i	0.0627132	−	0.0319567i
$778$	5.76981	−	25.2792i	0.206858	−	0.906303i
$779$	−58.4509	−	18.0297i	−2.09422	−	0.645981i
$780$	3.74220	−	9.53498i	0.133992	−	0.341407i
$781$	−5.25195	+	4.87310i	−0.187930	+	0.174373i
$782$	−9.08862	+	6.19652i	−0.325008	+	0.221587i
$783$	37.6498			1.34550
$784$	6.64868	−	12.8131i	0.237453	−	0.457612i
$785$	−33.0380			−1.17918
$786$	21.6204	−	14.7405i	0.771174	−	0.525778i
$787$	−8.76008	+	8.12817i	−0.312263	+	0.289738i	−0.820698	−	0.571363i	$-0.806415\pi$
$787$	−8.76008	+	8.12817i	−0.312263	+	0.289738i	0.508434	+	0.861101i	$0.330224\pi$
$788$	−18.6841	+	47.6062i	−0.665592	+	1.69590i
$789$	45.1385	+	13.9234i	1.60697	+	0.495686i
$790$	12.0466	−	52.7796i	0.428599	−	1.87781i
$791$	6.49736	−	31.7386i	0.231020	−	1.12850i
$792$	0.239226	+	1.04812i	0.00850052	+	0.0372432i
$793$	0.440083	−	5.87251i	0.0156278	−	0.208539i
$794$	−14.2490	+	4.39523i	−0.505677	+	0.155981i
$795$	−1.20463	−	16.0746i	−0.0427237	−	0.570109i
$796$	−10.2970	−	26.2364i	−0.364968	−	0.929925i
$797$	25.8878	+	12.4669i	0.916994	+	0.441601i	0.831997	−	0.554780i	$-0.187198\pi$
$797$	25.8878	+	12.4669i	0.916994	+	0.441601i	0.0849968	+	0.996381i	$0.472912\pi$
$798$	−59.7844	+	10.3901i	−2.11634	+	0.367806i
$799$	49.1487	−	23.6688i	1.73876	−	0.837340i
$800$	4.18366	+	3.88187i	0.147915	+	0.137245i
$801$	2.69727	+	0.406548i	0.0953033	+	0.0143647i
$802$	0.0175279	+	0.0303592i	0.000618930	+	0.00107202i
$803$	−0.0489637	+	0.0848076i	−0.00172789	+	0.00299279i
$804$	21.6393	−	27.1348i	0.763158	−	0.956970i
$805$	4.74161	−	4.60214i	0.167120	−	0.162204i
$806$	14.4925	+	18.1731i	0.510477	+	0.640118i
$807$	19.0170	−	2.86635i	0.669430	−	0.100900i
$808$	20.8445	+	14.2116i	0.733308	+	0.499961i
$809$	−23.2165	−	15.8287i	−0.816248	−	0.556508i	0.0816762	−	0.996659i	$-0.473973\pi$
$809$	−23.2165	−	15.8287i	−0.816248	−	0.556508i	−0.897924	+	0.440151i	$0.854925\pi$
$810$	−43.9641	+	6.62652i	−1.54474	+	0.232832i
$811$	−0.720845	−	0.903911i	−0.0253123	−	0.0317406i	0.769014	−	0.639232i	$-0.220747\pi$
$811$	−0.720845	−	0.903911i	−0.0253123	−	0.0317406i	−0.794327	+	0.607491i	$0.792176\pi$
$812$	−55.3398	−	7.07321i	−1.94205	−	0.248221i
$813$	−29.8201	+	37.3932i	−1.04584	+	1.31144i
$814$	0.860992	−	1.49128i	0.0301778	−	0.0522694i
$815$	−24.4302	−	42.3144i	−0.855754	−	1.48221i
$816$	15.6122	+	2.35316i	0.546537	+	0.0823771i
$817$	5.07454	+	4.70848i	0.177536	+	0.164729i
$818$	−50.5736	+	24.3550i	−1.76826	+	0.851551i
$819$	−0.361740	−	0.864078i	−0.0126402	−	0.0301933i
$820$	53.4393	+	25.7350i	1.86618	+	0.898705i
$821$	0.649115	+	1.65392i	0.0226543	+	0.0577222i	0.941753	−	0.336304i	$-0.109177\pi$
$821$	0.649115	+	1.65392i	0.0226543	+	0.0577222i	−0.919099	+	0.394026i	$0.871082\pi$
$822$	−3.16260	−	42.2019i	−0.110308	−	1.47196i
$823$	−6.65369	+	2.05239i	−0.231933	+	0.0715419i	−0.408543	−	0.912739i	$-0.633963\pi$
$823$	−6.65369	+	2.05239i	−0.231933	+	0.0715419i	0.176610	+	0.984281i	$0.443487\pi$
$824$	1.62856	−	21.7316i	0.0567335	−	0.757057i
$825$	−0.601181	−	2.63394i	−0.0209304	−	0.0917022i
$826$	−12.6501	−	50.1960i	−0.440155	−	1.74654i
$827$	−1.84738	+	8.09391i	−0.0642397	+	0.281453i	−0.996838	−	0.0794642i	$-0.974679\pi$
$827$	−1.84738	+	8.09391i	−0.0642397	+	0.281453i	0.932598	+	0.360917i	$0.117536\pi$
$828$	−1.11280	−	0.343253i	−0.0386725	−	0.0119289i
$829$	−2.62811	+	6.69631i	−0.0912780	+	0.232573i	−0.969221	−	0.246193i	$-0.920820\pi$
$829$	−2.62811	+	6.69631i	−0.0912780	+	0.232573i	0.877943	+	0.478765i	$0.158916\pi$
$830$	31.3836	−	29.1197i	1.08934	−	1.01076i
$831$	2.18383	−	1.48891i	0.0757561	−	0.0516496i
$832$	12.3284			0.427411
$833$	−3.49589	−	29.0538i	−0.121126	−	1.00665i
$834$	35.5918			1.23244
$835$	9.04479	−	6.16663i	0.313008	−	0.213405i
$836$	−22.4770	+	20.8556i	−0.777382	+	0.721305i
$837$	18.9533	−	48.2921i	0.655121	−	1.66922i
$838$	9.72087	+	2.99849i	0.335802	+	0.103581i
$839$	3.59731	−	15.7608i	0.124193	−	0.544125i	−0.874101	−	0.485743i	$-0.838549\pi$
$839$	3.59731	−	15.7608i	0.124193	−	0.544125i	0.998294	−	0.0583812i	$-0.0185939\pi$
$840$	15.4757	−	0.347871i	0.533964	−	0.0120027i
$841$	−6.97966	−	30.5799i	−0.240678	−	1.05448i
$842$	−0.516242	+	6.88878i	−0.0177909	+	0.237403i
$843$	5.45319	−	1.68209i	0.187818	−	0.0579341i
$844$	0.980613	+	13.0854i	0.0337541	+	0.450417i
$845$	0.752891	+	1.91834i	0.0259003	+	0.0659928i
$846$	9.03758	+	4.35227i	0.310719	+	0.149634i
$847$	9.10505	−	16.6222i	0.312853	−	0.571147i
$848$	7.93559	−	3.82158i	0.272509	−	0.131234i
$849$	2.96313	+	2.74938i	0.101694	+	0.0943586i
$850$	6.75957	+	1.01884i	0.231851	+	0.0349460i
$851$	0.245360	+	0.424976i	0.00841083	+	0.0145680i
$852$	9.09030	−	15.7449i	0.311428	−	0.539410i
$853$	9.80270	−	12.2922i	0.335638	−	0.420877i	−0.585159	−	0.810918i	$-0.698968\pi$
$853$	9.80270	−	12.2922i	0.335638	−	0.420877i	0.920797	+	0.390042i	$0.127539\pi$
$854$	32.0934	−	10.6951i	1.09821	−	0.365978i
$855$	2.62395	+	3.29032i	0.0897371	+	0.112527i
$856$	−10.1015	+	1.52256i	−0.345263	+	0.0520401i
$857$	21.2400	+	14.4812i	0.725545	+	0.494669i	0.868891	−	0.495004i	$-0.164834\pi$
$857$	21.2400	+	14.4812i	0.725545	+	0.494669i	−0.143345	+	0.989673i	$0.545786\pi$
$858$	−6.43514	−	4.38741i	−0.219692	−	0.149784i
$859$	−26.4907	+	3.99284i	−0.903852	+	0.136234i	−0.584492	−	0.811399i	$-0.698706\pi$
$859$	−26.4907	+	3.99284i	−0.903852	+	0.136234i	−0.319360	+	0.947633i	$0.603468\pi$
$860$	−4.18519	−	5.24806i	−0.142714	−	0.178957i
$861$	48.7499	−	16.2458i	1.66139	−	0.553656i
$862$	16.3323	−	20.4800i	0.556279	−	0.697552i
$863$	−0.120386	+	0.208515i	−0.00409799	+	0.00709793i	−0.868067	−	0.496447i	$-0.834638\pi$
$863$	−0.120386	+	0.208515i	−0.00409799	+	0.00709793i	0.863969	+	0.503545i	$0.167971\pi$
$864$	−18.3604	−	31.8011i	−0.624632	−	1.08190i
$865$	−1.32041	−	0.199019i	−0.0448951	−	0.00676685i
$866$	−8.77115	−	8.13843i	−0.298056	−	0.276555i
$867$	0.786053	−	0.378543i	0.0266957	−	0.0128560i
$868$	−36.9311	+	67.4217i	−1.25352	+	2.28844i
$869$	−21.3524	−	10.2828i	−0.724332	−	0.348820i
$870$	23.2600	+	59.2655i	0.788588	+	2.00929i
$871$	0.521812	+	6.96309i	0.0176809	+	0.235935i
$872$	1.24029	−	0.382578i	0.0420014	−	0.0129557i
$873$	0.0204831	−	0.273327i	0.000693246	−	0.00925073i
$874$	−3.37721	−	14.7965i	−0.114236	−	0.500500i
$875$	−31.3602	+	0.704929i	−1.06017	+	0.0238310i
$876$	0.0552965	−	0.242270i	0.00186829	−	0.00818553i
$877$	20.7077	+	6.38748i	0.699249	+	0.215690i	0.623942	−	0.781471i	$-0.285530\pi$
$877$	20.7077	+	6.38748i	0.699249	+	0.215690i	0.0753072	+	0.997160i	$0.476006\pi$
$878$	−23.3554	+	59.5085i	−0.788206	+	2.00831i
$879$	−34.1647	+	31.7002i	−1.15235	+	1.06922i
$880$	−6.87771	+	4.68914i	−0.231847	+	0.158071i
$881$	40.1685			1.35331			0.676655	−	0.736300i	$-0.263429\pi$
$881$	40.1685			1.35331			0.676655	+	0.736300i	$0.263429\pi$
$882$	3.77612	−	3.83357i	0.127149	−	0.129083i
$883$	27.6613			0.930878			0.465439	−	0.885080i	$-0.345896\pi$
$883$	27.6613			0.930878			0.465439	+	0.885080i	$0.345896\pi$
$884$	9.37435	−	6.39132i	0.315294	−	0.214964i
$885$	−24.9316	+	23.1332i	−0.838067	+	0.777612i
$886$	24.9225	−	63.5015i	0.837288	−	2.13338i
$887$	−29.3854	−	9.06421i	−0.986667	−	0.304346i	−0.240897	−	0.970551i	$-0.577442\pi$
$887$	−29.3854	−	9.06421i	−0.986667	−	0.304346i	−0.745769	+	0.666204i	$0.767918\pi$
$888$	−0.255806	+	1.12076i	−0.00858429	+	0.0376102i
$889$	8.95276	+	35.5247i	0.300266	+	1.19146i
$890$	−7.67062	−	33.6072i	−0.257120	−	1.12652i
$891$	−1.45451	+	19.4090i	−0.0487278	+	0.650227i
$892$	34.7188	−	10.7093i	1.16247	−	0.358575i
$893$	5.62461	+	75.0551i	0.188220	+	2.51162i
$894$	5.15378	+	13.1316i	0.172368	+	0.439187i
$895$	−47.3229	−	22.7895i	−1.58183	−	0.761769i
$896$	11.8635	+	28.3380i	0.396331	+	0.946705i
$897$	1.99971	−	0.963009i	0.0667683	−	0.0321539i
$898$	13.4509	+	12.4806i	0.448862	+	0.416483i
$899$	−82.2506	−	12.3973i	−2.74321	−	0.413473i
$900$	0.361849	+	0.626741i	0.0120616	+	0.0208914i
$901$	8.92758	−	15.4630i	0.297421	−	0.515148i
$902$	28.1193	−	35.2604i	0.936269	−	1.17404i
$903$	−5.76842	−	0.737286i	−0.191961	−	0.0245354i
$904$	11.8352	+	14.8409i	0.393634	+	0.493601i
$905$	23.8065	−	3.58825i	0.791353	−	0.119277i
$906$	−23.4182	−	15.9663i	−0.778019	−	0.530444i
$907$	−3.59839	−	2.45334i	−0.119483	−	0.0814619i	0.502104	−	0.864807i	$-0.332559\pi$
$907$	−3.59839	−	2.45334i	−0.119483	−	0.0814619i	−0.621587	+	0.783345i	$0.713512\pi$
$908$	76.1538	−	11.4783i	2.52725	−	0.380922i
$909$	−3.59248	−	4.50482i	−0.119155	−	0.149416i
$910$	−8.49472	+	8.24486i	−0.281597	+	0.273314i
$911$	−33.7486	+	42.3194i	−1.11814	+	1.40210i	−0.212968	+	0.977059i	$0.568313\pi$
$911$	−33.7486	+	42.3194i	−1.11814	+	1.40210i	−0.905172	+	0.425045i	$0.860258\pi$
$912$	−10.8920	+	18.8655i	−0.360669	+	0.624698i
$913$	−9.37091	−	16.2309i	−0.310132	−	0.537164i
$914$	−18.6264	−	2.80748i	−0.616108	−	0.0928633i
$915$	−16.2927	−	15.1174i	−0.538620	−	0.499767i
$916$	−25.2765	+	12.1725i	−0.835158	+	0.402191i
$917$	−17.1540	+	2.98125i	−0.566475	+	0.0984495i
$918$	−39.6275	−	19.0836i	−1.30790	−	0.629852i
$919$	−15.2599	−	38.8817i	−0.503379	−	1.28259i	−0.926425	−	0.376480i	$-0.877134\pi$
$919$	−15.2599	−	38.8817i	−0.503379	−	1.28259i	0.423046	−	0.906108i	$-0.360961\pi$
$920$	0.289331	+	3.86085i	0.00953895	+	0.127288i
$921$	−29.7127	+	9.16516i	−0.979067	+	0.302002i
$922$	3.50163	−	46.7260i	0.115320	−	1.53884i
$923$	0.813924	+	3.56604i	0.0267906	+	0.117377i
$924$	5.16596	−	25.2349i	0.169948	−	0.830168i
$925$	0.0678592	−	0.297311i	0.00223120	−	0.00977552i
$926$	53.8781	+	16.6192i	1.77054	+	0.546140i
$927$	−1.81838	+	4.63316i	−0.0597234	+	0.152173i
$928$	−43.1596	+	40.0463i	−1.41678	+	1.31458i
$929$	24.7438	−	16.8701i	0.811819	−	0.553489i	−0.0847452	−	0.996403i	$-0.527008\pi$
$929$	24.7438	−	16.8701i	0.811819	−	0.553489i	0.896564	+	0.442914i	$0.146055\pi$
$930$	87.7271			2.87668
$931$	39.0776	+	10.1552i	1.28072	+	0.332824i
$932$	−1.07526			−0.0352215
$933$	−43.8209	+	29.8766i	−1.43463	+	0.978116i
$934$	−27.7261	+	25.7261i	−0.907226	+	0.841782i
$935$	−6.16497	+	15.7081i	−0.201616	+	0.513709i
$936$	0.524479	+	0.161780i	0.0171431	+	0.00528796i
$937$	4.99083	−	21.8662i	0.163043	−	0.714339i	−0.825625	−	0.564220i	$-0.809177\pi$
$937$	4.99083	−	21.8662i	0.163043	−	0.714339i	0.988668	−	0.150119i	$-0.0479657\pi$
$938$	−35.7384	+	18.2112i	−1.16690	+	0.594617i
$939$	−5.45417	−	23.8963i	−0.177990	−	0.779826i
$940$	5.45401	−	72.7787i	0.177890	−	2.37378i
$941$	23.0676	−	7.11542i	0.751983	−	0.231956i	0.105012	−	0.994471i	$-0.466512\pi$
$941$	23.0676	−	7.11542i	0.751983	−	0.231956i	0.646971	+	0.762515i	$0.276036\pi$
$942$	−4.76382	−	63.5687i	−0.155214	−	2.07118i
$943$	4.69545	+	11.9638i	0.152905	+	0.389595i
$944$	−16.7432	−	8.06309i	−0.544944	−	0.262431i
$945$	25.4158	+	7.21838i	0.826776	+	0.234814i
$946$	−4.59853	+	2.21453i	−0.149511	+	0.0720007i
$947$	−1.87804	−	1.74257i	−0.0610282	−	0.0566259i	0.649069	−	0.760729i	$-0.275159\pi$
$947$	−1.87804	−	1.74257i	−0.0610282	−	0.0566259i	−0.710097	+	0.704104i	$0.751349\pi$
$948$	59.4678	+	8.96333i	1.93143	+	0.291116i
$949$	0.0249978	+	0.0432974i	0.000811462	+	0.00140549i
$950$	−4.71586	+	8.16812i	−0.153003	+	0.265009i
$951$	−2.95975	+	3.71141i	−0.0959764	+	0.120351i
$952$	14.3803	+	9.33799i	0.466070	+	0.302646i
$953$	7.60587	+	9.53745i	0.246378	+	0.308948i	0.889608	−	0.456725i	$-0.150978\pi$
$953$	7.60587	+	9.53745i	0.246378	+	0.308948i	−0.643230	+	0.765673i	$0.722406\pi$
$954$	3.24658	−	0.489344i	0.105112	−	0.0158431i
$955$	−3.95577	−	2.69700i	−0.128006	−	0.0872727i
$956$	−6.09421	−	4.15496i	−0.197101	−	0.134381i
$957$	27.5599	−	4.15398i	0.890884	−	0.134279i
$958$	−23.5431	−	29.5221i	−0.760642	−	0.953815i
$959$	−9.69598	+	26.4371i	−0.313100	+	0.853697i
$960$	29.0105	−	36.3781i	0.936311	−	1.17410i
$961$	−41.8073	+	72.4123i	−1.34862	+	2.33588i
$962$	−0.439569	−	0.761355i	−0.0141723	−	0.0245471i
$963$	2.30710	+	0.347739i	0.0743451	+	0.0112057i
$964$	42.5571	+	39.4872i	1.37067	+	1.27180i
$965$	−4.84850	+	2.33491i	−0.156079	+	0.0751636i
$966$	9.53873	+	8.45979i	0.306904	+	0.272189i
$967$	43.6933	+	21.0416i	1.40508	+	0.676652i	0.974185	−	0.225750i	$-0.0724832\pi$
$967$	43.6933	+	21.0416i	1.40508	+	0.676652i	0.430896	+	0.902402i	$0.358198\pi$
$968$	4.05706	+	10.3372i	0.130399	+	0.332251i
$969$	3.30010	+	44.0367i	0.106014	+	1.41466i
$970$	−3.30994	+	1.02098i	−0.106276	+	0.0327817i
$971$	2.73037	−	36.4342i	0.0876217	−	1.16923i	−0.764051	−	0.645156i	$-0.776792\pi$
$971$	2.73037	−	36.4342i	0.0876217	−	1.16923i	0.851673	−	0.524074i	$-0.175588\pi$
$972$	−2.21092	−	9.68669i	−0.0709154	−	0.310701i
$973$	−21.5623	−	9.79316i	−0.691256	−	0.313954i
$974$	−16.1861	+	70.9161i	−0.518637	+	2.27230i
$975$	−1.31803	−	0.406558i	−0.0422107	−	0.0130203i
$976$	4.43679	−	11.3048i	0.142018	−	0.361857i
$977$	17.4088	−	16.1530i	0.556957	−	0.516781i	−0.350703	−	0.936487i	$-0.614057\pi$
$977$	17.4088	−	16.1530i	0.556957	−	0.516781i	0.907660	+	0.419706i	$0.137867\pi$
$978$	77.8950	−	53.1079i	2.49081	−	1.69820i
$979$	−15.0905			−0.482295
$980$	−36.0014	−	15.3848i	−1.15002	−	0.491449i
$981$	−0.296440			−0.00946459
$982$	−41.6942	+	28.4266i	−1.33052	+	0.907131i
$983$	39.3113	−	36.4756i	1.25384	−	1.16339i	0.274406	−	0.961614i	$-0.411519\pi$
$983$	39.3113	−	36.4756i	1.25384	−	1.16339i	0.979431	−	0.201777i	$-0.0646716\pi$
$984$	−10.9998	+	28.0270i	−0.350660	+	0.893467i
$985$	−37.1074	−	11.4461i	−1.18234	−	0.364704i
$986$	−15.6924	+	68.7528i	−0.499747	+	2.18954i
$987$	−40.5231	−	48.5353i	−1.28986	−	1.54490i
$988$	3.48338	+	15.2617i	0.110821	+	0.485539i
$989$	0.108695	−	1.45043i	0.00345630	−	0.0461211i
$990$	−2.96508	+	0.914607i	−0.0942365	+	0.0290681i
$991$	−1.53787	−	20.5214i	−0.0488519	−	0.651884i	−0.966858	−	0.255316i	$-0.917820\pi$
$991$	−1.53787	−	20.5214i	−0.0488519	−	0.651884i	0.918006	−	0.396567i	$-0.129799\pi$
$992$	29.6390	+	75.5190i	0.941040	+	2.39773i
$993$	−48.7424	−	23.4731i	−1.54679	−	0.744897i
$994$	−17.0901	+	12.2233i	−0.542066	+	0.387701i
$995$	19.2818	−	9.28562i	0.611274	−	0.294374i
$996$	34.8633	+	32.3484i	1.10469	+	1.02500i
$997$	4.87423	+	0.734673i	0.154369	+	0.0232673i	0.225772	−	0.974180i	$-0.427510\pi$
$997$	4.87423	+	0.734673i	0.154369	+	0.0232673i	−0.0714033	+	0.997448i	$0.522748\pi$
$998$	45.9022	+	79.5049i	1.45301	+	2.51668i
$999$	−0.981065	+	1.69925i	−0.0310395	+	0.0537620i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bl.a.625.5	yes	324
49.4	even	21	inner	637.2.bl.a.53.5	✓	324

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.bl.a.53.5	✓	324	49.4	even	21	inner
637.2.bl.a.625.5	yes	324	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(-1.79391 + 1.22307i) q^{2} +(1.34252 - 1.24567i) q^{3} +(0.991536 - 2.52639i) q^{4} +(1.96924 + 0.607429i) q^{5} +(-0.884812 + 3.87661i) q^{6} +(1.60270 - 2.10508i) q^{7} +(0.344956 + 1.51135i) q^{8} +(0.0264586 - 0.353066i) q^{9} +O(q^{10})\)	\(q+(-1.79391 + 1.22307i) q^{2} +(1.34252 - 1.24567i) q^{3} +(0.991536 - 2.52639i) q^{4} +(1.96924 + 0.607429i) q^{5} +(-0.884812 + 3.87661i) q^{6} +(1.60270 - 2.10508i) q^{7} +(0.344956 + 1.51135i) q^{8} +(0.0264586 - 0.353066i) q^{9} +(-4.27556 + 1.31883i) q^{10} +(0.146375 + 1.95324i) q^{11} +(-1.81591 - 4.62685i) q^{12} +(0.900969 + 0.433884i) q^{13} +(-0.300439 + 5.73653i) q^{14} +(3.40039 - 1.63754i) q^{15} +(1.51170 + 1.40265i) q^{16} +(4.13378 + 0.623068i) q^{17} +(0.384358 + 0.665728i) q^{18} +(-2.88397 + 4.99518i) q^{19} +(3.48717 - 4.37277i) q^{20} +(-0.470596 - 4.82254i) q^{21} +(-2.65153 - 3.32492i) q^{22} +(1.19838 - 0.180626i) q^{23} +(2.34576 + 1.59931i) q^{24} +(-0.622274 - 0.424259i) q^{25} +(-2.14692 + 0.323597i) q^{26} +(3.02131 + 3.78860i) q^{27} +(-3.72913 - 6.13630i) q^{28} +(4.84425 - 6.07450i) q^{29} +(-4.09717 + 7.09650i) q^{30} +(-5.35291 - 9.27151i) q^{31} +(-7.49320 - 1.12942i) q^{32} +(2.62962 + 2.43993i) q^{33} +(-8.17768 + 3.93817i) q^{34} +(4.43477 - 3.17188i) q^{35} +(-0.865747 - 0.416922i) q^{36} +(0.147931 + 0.376923i) q^{37} +(-0.935859 - 12.4882i) q^{38} +(1.75004 - 0.539817i) q^{39} +(-0.238739 + 3.18575i) q^{40} +(2.35981 + 10.3390i) q^{41} +(6.74250 + 8.07563i) q^{42} +(0.267062 - 1.17008i) q^{43} +(5.07980 + 1.56691i) q^{44} +(0.266565 - 0.679198i) q^{45} +(-1.92886 + 1.78972i) q^{46} +(10.7816 - 7.35075i) q^{47} +3.77674 q^{48} +(-1.86273 - 6.74761i) q^{49} +1.63520 q^{50} +(6.32581 - 4.31287i) q^{51} +(1.98950 - 1.84599i) q^{52} +(1.56040 - 3.97584i) q^{53} +(-10.0537 - 3.10115i) q^{54} +(-0.898209 + 3.93531i) q^{55} +(3.73438 + 1.69608i) q^{56} +(2.35059 + 10.2986i) q^{57} +(-1.26063 + 16.8219i) q^{58} +(-8.61113 + 2.65618i) q^{59} +(-0.765463 - 10.2144i) q^{60} +(-2.15148 - 5.48189i) q^{61} +(20.9423 + 10.0853i) q^{62} +(-0.700826 - 0.621554i) q^{63} +(11.1075 - 5.34910i) q^{64} +(1.51067 + 1.40169i) q^{65} +(-7.70149 - 1.16081i) q^{66} +(3.49131 + 6.04712i) q^{67} +(5.67291 - 9.82576i) q^{68} +(1.38384 - 1.73528i) q^{69} +(-4.07617 + 11.1141i) q^{70} +(2.28057 + 2.85974i) q^{71} +(0.542733 - 0.0818039i) q^{72} +(0.0413083 + 0.0281635i) q^{73} +(-0.726377 - 0.495236i) q^{74} +(-1.36390 + 0.205575i) q^{75} +(9.76022 + 12.2389i) q^{76} +(4.34633 + 2.82233i) q^{77} +(-2.47919 + 3.10880i) q^{78} +(-6.04972 + 10.4784i) q^{79} +(2.12488 + 3.68041i) q^{80} +(9.82583 + 1.48100i) q^{81} +(-16.8786 - 15.6611i) q^{82} +(-8.62083 + 4.15157i) q^{83} +(-12.6502 - 3.59281i) q^{84} +(7.76193 + 3.73795i) q^{85} +(0.951995 + 2.42564i) q^{86} +(-1.06335 - 14.1895i) q^{87} +(-2.90155 + 0.895009i) q^{88} +(-0.575740 + 7.68272i) q^{89} +(0.352510 + 1.54445i) q^{90} +(2.35734 - 1.20123i) q^{91} +(0.731902 - 3.20667i) q^{92} +(-18.7357 - 5.77918i) q^{93} +(-10.3507 + 26.3731i) q^{94} +(-8.71342 + 8.08488i) q^{95} +(-11.4666 + 7.81782i) q^{96} +0.774155 q^{97} +(11.5943 + 9.82636i) q^{98} +0.693496 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9}+O(q^{10}) \) 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9	\( 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9} - 5 q^{10} - 18 q^{11} - 40 q^{12} + 54 q^{13} - 15 q^{14} + 6 q^{15} + 29 q^{16} - 6 q^{17} + 49 q^{18} - 24 q^{19} + 11 q^{20} - 6 q^{22} - 42 q^{23} + 20 q^{24} + 14 q^{25} + 3 q^{26} - 33 q^{27} + 7 q^{28} - 22 q^{29} + 57 q^{30} - 31 q^{31} - 139 q^{32} + 6 q^{33} + 50 q^{34} + 42 q^{35} - 78 q^{36} - 4 q^{37} - 90 q^{38} + 40 q^{40} + 8 q^{41} + 20 q^{42} + 34 q^{43} - 256 q^{44} + 19 q^{45} + 85 q^{46} + 34 q^{47} - 10 q^{48} + 51 q^{49} - 54 q^{50} + 74 q^{51} - 25 q^{52} + 10 q^{53} + 111 q^{54} - 10 q^{55} - 196 q^{56} - 5 q^{57} - 21 q^{58} + 65 q^{59} + 87 q^{60} + 3 q^{61} - 54 q^{62} - 35 q^{63} - 28 q^{64} - q^{65} - 110 q^{66} + 135 q^{67} - 158 q^{68} + 42 q^{69} + 44 q^{70} + 9 q^{71} - 133 q^{72} + 31 q^{73} - 97 q^{74} - 315 q^{75} - 177 q^{76} + 6 q^{77} - 25 q^{78} + 43 q^{79} - 20 q^{80} - 259 q^{81} + 96 q^{82} + 59 q^{83} + 285 q^{84} + 6 q^{85} + 95 q^{86} - 206 q^{87} + 228 q^{88} + 43 q^{89} - 61 q^{90} - 7 q^{91} + 53 q^{92} - 10 q^{93} - 36 q^{94} - 17 q^{95} + 277 q^{96} + 66 q^{97} + 260 q^{98} - 206 q^{99}+O(q^{100}) \) 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9 - 5 * q^10 - 18 * q^11 - 40 * q^12 + 54 * q^13 - 15 * q^14 + 6 * q^15 + 29 * q^16 - 6 * q^17 + 49 * q^18 - 24 * q^19 + 11 * q^20 - 6 * q^22 - 42 * q^23 + 20 * q^24 + 14 * q^25 + 3 * q^26 - 33 * q^27 + 7 * q^28 - 22 * q^29 + 57 * q^30 - 31 * q^31 - 139 * q^32 + 6 * q^33 + 50 * q^34 + 42 * q^35 - 78 * q^36 - 4 * q^37 - 90 * q^38 + 40 * q^40 + 8 * q^41 + 20 * q^42 + 34 * q^43 - 256 * q^44 + 19 * q^45 + 85 * q^46 + 34 * q^47 - 10 * q^48 + 51 * q^49 - 54 * q^50 + 74 * q^51 - 25 * q^52 + 10 * q^53 + 111 * q^54 - 10 * q^55 - 196 * q^56 - 5 * q^57 - 21 * q^58 + 65 * q^59 + 87 * q^60 + 3 * q^61 - 54 * q^62 - 35 * q^63 - 28 * q^64 - q^65 - 110 * q^66 + 135 * q^67 - 158 * q^68 + 42 * q^69 + 44 * q^70 + 9 * q^71 - 133 * q^72 + 31 * q^73 - 97 * q^74 - 315 * q^75 - 177 * q^76 + 6 * q^77 - 25 * q^78 + 43 * q^79 - 20 * q^80 - 259 * q^81 + 96 * q^82 + 59 * q^83 + 285 * q^84 + 6 * q^85 + 95 * q^86 - 206 * q^87 + 228 * q^88 + 43 * q^89 - 61 * q^90 - 7 * q^91 + 53 * q^92 - 10 * q^93 - 36 * q^94 - 17 * q^95 + 277 * q^96 + 66 * q^97 + 260 * q^98 - 206 * q^99

Introduction

L-functions

Modular forms

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