LMFDB - Embedded newform 80.2.j.b.43.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,2,Mod(43,80)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(80, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 3]))

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

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

chi := DirichletCharacter("80.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	80.j (of order $4$, degree $2$, 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:	$0.638803216170$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 2 x^{16} - 4 x^{15} - 5 x^{14} - 14 x^{13} - 10 x^{12} + 6 x^{11} + 37 x^{10} + 70 x^{9} + \cdots + 512 $ x^18 + 2x^16 - 4x^15 - 5x^14 - 14x^13 - 10x^12 + 6x^11 + 37x^10 + 70x^9 + 74x^8 + 24x^7 - 80x^6 - 224x^5 - 160x^4 - 256x^3 + 256*x^2 + 512
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.8
Root			$0.482716 - 1.32928i$ of defining polynomial
Character	$\chi$	$=$	80.43
Dual form			80.2.j.b.67.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.759419 - 1.19301i) q^{2} -1.39319i q^{3} +(-0.846564 - 1.81200i) q^{4} +(0.535339 + 2.17104i) q^{5} +(-1.66209 - 1.05801i) q^{6} +(-2.13436 + 2.13436i) q^{7} +(-2.80463 - 0.366101i) q^{8} +1.05903 q^{9} +O(q^{10})$	\(q+(0.759419 - 1.19301i) q^{2} -1.39319i q^{3} +(-0.846564 - 1.81200i) q^{4} +(0.535339 + 2.17104i) q^{5} +(-1.66209 - 1.05801i) q^{6} +(-2.13436 + 2.13436i) q^{7} +(-2.80463 - 0.366101i) q^{8} +1.05903 q^{9} +(2.99663 + 1.01006i) q^{10} +(2.17074 - 2.17074i) q^{11} +(-2.52445 + 1.17942i) q^{12} +1.54663 q^{13} +(0.925449 + 4.16720i) q^{14} +(3.02466 - 0.745827i) q^{15} +(-2.56666 + 3.06794i) q^{16} +(-3.86386 + 3.86386i) q^{17} +(0.804250 - 1.26344i) q^{18} +(-0.0136865 + 0.0136865i) q^{19} +(3.48071 - 2.80796i) q^{20} +(2.97357 + 2.97357i) q^{21} +(-0.941219 - 4.23822i) q^{22} +(-3.15240 - 3.15240i) q^{23} +(-0.510047 + 3.90738i) q^{24} +(-4.42682 + 2.32449i) q^{25} +(1.17454 - 1.84515i) q^{26} -5.65499i q^{27} +(5.67434 + 2.06058i) q^{28} +(-3.33787 - 3.33787i) q^{29} +(1.40720 - 4.17486i) q^{30} +8.92639i q^{31} +(1.71093 + 5.39191i) q^{32} +(-3.02424 - 3.02424i) q^{33} +(1.67535 + 7.54394i) q^{34} +(-5.77640 - 3.49118i) q^{35} +(-0.896540 - 1.91896i) q^{36} +7.24737 q^{37} +(0.00593441 + 0.0267220i) q^{38} -2.15475i q^{39} +(-0.706610 - 6.28496i) q^{40} -10.3771i q^{41} +(5.80569 - 1.28932i) q^{42} -2.02975 q^{43} +(-5.77103 - 2.09570i) q^{44} +(0.566942 + 2.29920i) q^{45} +(-6.15484 + 1.36686i) q^{46} +(-3.34313 - 3.34313i) q^{47} +(4.27421 + 3.57583i) q^{48} -2.11103i q^{49} +(-0.588672 + 7.04652i) q^{50} +(5.38308 + 5.38308i) q^{51} +(-1.30932 - 2.80249i) q^{52} -7.30702i q^{53} +(-6.74648 - 4.29451i) q^{54} +(5.87483 + 3.55067i) q^{55} +(6.76751 - 5.20472i) q^{56} +(0.0190679 + 0.0190679i) q^{57} +(-6.51696 + 1.44728i) q^{58} +(3.52732 + 3.52732i) q^{59} +(-3.91201 - 4.84928i) q^{60} +(1.41629 - 1.41629i) q^{61} +(10.6493 + 6.77887i) q^{62} +(-2.26036 + 2.26036i) q^{63} +(7.73194 + 2.05356i) q^{64} +(0.827973 + 3.35780i) q^{65} +(-5.90462 + 1.31129i) q^{66} +0.748197 q^{67} +(10.2723 + 3.73030i) q^{68} +(-4.39187 + 4.39187i) q^{69} +(-8.55174 + 4.24005i) q^{70} -0.269603 q^{71} +(-2.97020 - 0.387713i) q^{72} +(-0.811870 + 0.811870i) q^{73} +(5.50380 - 8.64622i) q^{74} +(3.23844 + 6.16739i) q^{75} +(0.0363865 + 0.0132134i) q^{76} +9.26628i q^{77} +(-2.57064 - 1.63636i) q^{78} +2.80567 q^{79} +(-8.03466 - 3.92992i) q^{80} -4.70135 q^{81} +(-12.3800 - 7.88056i) q^{82} +12.8279i q^{83} +(2.87077 - 7.90541i) q^{84} +(-10.4571 - 6.32012i) q^{85} +(-1.54143 + 2.42152i) q^{86} +(-4.65027 + 4.65027i) q^{87} +(-6.88283 + 5.29341i) q^{88} +13.3732 q^{89} +(3.17353 + 1.06969i) q^{90} +(-3.30108 + 3.30108i) q^{91} +(-3.04342 + 8.38083i) q^{92} +12.4361 q^{93} +(-6.52724 + 1.44956i) q^{94} +(-0.0370409 - 0.0223871i) q^{95} +(7.51194 - 2.38364i) q^{96} +(6.33466 - 6.33466i) q^{97} +(-2.51848 - 1.60315i) q^{98} +(2.29888 - 2.29888i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 4 q^{2} - 4 q^{4} - 4 q^{5} - 8 q^{6} + 2 q^{7} - 4 q^{8} - 10 q^{9}+O(q^{10}) $ 18 * q - 4 * q^2 - 4 * q^4 - 4 * q^5 - 8 * q^6 + 2 * q^7 - 4 * q^8 - 10 * q^9	$ 18 q - 4 q^{2} - 4 q^{4} - 4 q^{5} - 8 q^{6} + 2 q^{7} - 4 q^{8} - 10 q^{9} - 12 q^{10} - 2 q^{11} + 4 q^{12} + 12 q^{14} + 20 q^{15} - 6 q^{17} + 16 q^{18} + 2 q^{19} - 4 q^{20} - 16 q^{21} + 4 q^{22} - 2 q^{23} + 4 q^{24} + 6 q^{25} - 16 q^{26} - 4 q^{28} - 14 q^{29} + 20 q^{30} - 4 q^{32} - 8 q^{33} - 28 q^{34} - 6 q^{35} - 4 q^{36} + 8 q^{37} + 16 q^{38} + 20 q^{40} + 28 q^{42} - 44 q^{43} + 44 q^{44} - 4 q^{45} + 12 q^{46} - 38 q^{47} + 60 q^{48} + 20 q^{50} + 8 q^{51} - 40 q^{52} - 4 q^{54} - 6 q^{55} + 20 q^{56} + 24 q^{57} - 20 q^{58} - 10 q^{59} - 68 q^{60} + 14 q^{61} + 6 q^{63} - 16 q^{64} + 4 q^{66} + 12 q^{67} + 36 q^{68} + 32 q^{69} - 36 q^{70} + 24 q^{71} - 36 q^{72} + 14 q^{73} + 48 q^{74} + 64 q^{75} - 16 q^{76} - 84 q^{78} + 16 q^{79} - 20 q^{80} + 2 q^{81} - 28 q^{82} - 24 q^{84} - 10 q^{85} - 36 q^{86} + 24 q^{87} - 96 q^{88} - 12 q^{89} - 64 q^{90} + 52 q^{92} + 16 q^{93} + 28 q^{94} - 34 q^{95} - 40 q^{96} + 18 q^{97} + 32 q^{98} - 22 q^{99}+O(q^{100}) $ 18 * q - 4 * q^2 - 4 * q^4 - 4 * q^5 - 8 * q^6 + 2 * q^7 - 4 * q^8 - 10 * q^9 - 12 * q^10 - 2 * q^11 + 4 * q^12 + 12 * q^14 + 20 * q^15 - 6 * q^17 + 16 * q^18 + 2 * q^19 - 4 * q^20 - 16 * q^21 + 4 * q^22 - 2 * q^23 + 4 * q^24 + 6 * q^25 - 16 * q^26 - 4 * q^28 - 14 * q^29 + 20 * q^30 - 4 * q^32 - 8 * q^33 - 28 * q^34 - 6 * q^35 - 4 * q^36 + 8 * q^37 + 16 * q^38 + 20 * q^40 + 28 * q^42 - 44 * q^43 + 44 * q^44 - 4 * q^45 + 12 * q^46 - 38 * q^47 + 60 * q^48 + 20 * q^50 + 8 * q^51 - 40 * q^52 - 4 * q^54 - 6 * q^55 + 20 * q^56 + 24 * q^57 - 20 * q^58 - 10 * q^59 - 68 * q^60 + 14 * q^61 + 6 * q^63 - 16 * q^64 + 4 * q^66 + 12 * q^67 + 36 * q^68 + 32 * q^69 - 36 * q^70 + 24 * q^71 - 36 * q^72 + 14 * q^73 + 48 * q^74 + 64 * q^75 - 16 * q^76 - 84 * q^78 + 16 * q^79 - 20 * q^80 + 2 * q^81 - 28 * q^82 - 24 * q^84 - 10 * q^85 - 36 * q^86 + 24 * q^87 - 96 * q^88 - 12 * q^89 - 64 * q^90 + 52 * q^92 + 16 * q^93 + 28 * q^94 - 34 * q^95 - 40 * q^96 + 18 * q^97 + 32 * q^98 - 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	0.759419	−	1.19301i	0.536991	−	0.843588i
$2$	0.759419	−	1.19301i	0.536991	−	0.843588i
$3$		−	1.39319i		−	0.804356i	−0.915561	−	0.402178i	$-0.868253\pi$
$3$		−	1.39319i		−	0.804356i	0.915561	−	0.402178i	$-0.131747\pi$
$4$	−0.846564	−	1.81200i	−0.423282	−	0.905998i
$5$	0.535339	+	2.17104i	0.239411	+	0.970918i
$5$	0.535339	+	2.17104i	0.239411	+	0.970918i
$6$	−1.66209	−	1.05801i	−0.678546	−	0.431932i
$7$	−2.13436	+	2.13436i	−0.806714	+	0.806714i	−0.984135	−	0.177421i	$-0.943225\pi$
$7$	−2.13436	+	2.13436i	−0.806714	+	0.806714i	0.177421	+	0.984135i	$0.443225\pi$
$8$	−2.80463	−	0.366101i	−0.991588	−	0.129436i
$9$	1.05903			0.353011
$10$	2.99663	+	1.01006i	0.947617	+	0.319410i
$11$	2.17074	−	2.17074i	0.654501	−	0.654501i	−0.299572	−	0.954074i	$-0.596844\pi$
$11$	2.17074	−	2.17074i	0.654501	−	0.654501i	0.954074	+	0.299572i	$0.0968440\pi$
$12$	−2.52445	+	1.17942i	−0.728745	+	0.340470i
$13$	1.54663			0.428958			0.214479	−	0.976729i	$-0.431195\pi$
$13$	1.54663			0.428958			0.214479	+	0.976729i	$0.431195\pi$
$14$	0.925449	+	4.16720i	0.247337	+	1.11373i
$15$	3.02466	−	0.745827i	0.780964	−	0.192572i
$16$	−2.56666	+	3.06794i	−0.641664	+	0.766986i
$17$	−3.86386	+	3.86386i	−0.937125	+	0.937125i	−0.998137	−	0.0610123i	$-0.980567\pi$
$17$	−3.86386	+	3.86386i	−0.937125	+	0.937125i	0.0610123	+	0.998137i	$0.480567\pi$
$18$	0.804250	−	1.26344i	0.189564	−	0.297796i
$19$	−0.0136865	+	0.0136865i	−0.00313991	+	0.00313991i	−0.708675	−	0.705535i	$-0.750707\pi$
$19$	−0.0136865	+	0.0136865i	−0.00313991	+	0.00313991i	0.705535	+	0.708675i	$0.250707\pi$
$20$	3.48071	−	2.80796i	0.778311	−	0.627878i
$21$	2.97357	+	2.97357i	0.648886	+	0.648886i
$22$	−0.941219	−	4.23822i	−0.200669	−	0.903591i
$23$	−3.15240	−	3.15240i	−0.657320	−	0.657320i	0.297425	−	0.954745i	$-0.403872\pi$
$23$	−3.15240	−	3.15240i	−0.657320	−	0.657320i	−0.954745	+	0.297425i	$0.903872\pi$
$24$	−0.510047	+	3.90738i	−0.104113	+	0.797590i
$25$	−4.42682	+	2.32449i	−0.885365	+	0.464897i
$26$	1.17454	−	1.84515i	0.230347	−	0.361864i
$27$		−	5.65499i		−	1.08830i
$28$	5.67434	+	2.06058i	1.07235	+	0.389413i
$29$	−3.33787	−	3.33787i	−0.619826	−	0.619826i	0.325660	−	0.945487i	$-0.394413\pi$
$29$	−3.33787	−	3.33787i	−0.619826	−	0.619826i	−0.945487	+	0.325660i	$0.894413\pi$
$30$	1.40720	−	4.17486i	0.256919	−	0.762222i
$31$			8.92639i			1.60323i	0.597843	+	0.801613i	$0.296025\pi$
$31$			8.92639i			1.60323i	−0.597843	+	0.801613i	$0.703975\pi$
$32$	1.71093	+	5.39191i	0.302452	+	0.953164i
$33$	−3.02424	−	3.02424i	−0.526452	−	0.526452i
$34$	1.67535	+	7.54394i	0.287320	+	1.29377i
$35$	−5.77640	−	3.49118i	−0.976390	−	0.590117i
$36$	−0.896540	−	1.91896i	−0.149423	−	0.319827i
$37$	7.24737			1.19146			0.595730	−	0.803184i	$-0.296863\pi$
$37$	7.24737			1.19146			0.595730	+	0.803184i	$0.296863\pi$
$38$	0.00593441	+	0.0267220i	0.000962688	+	0.00433489i
$39$		−	2.15475i		−	0.345035i
$40$	−0.706610	−	6.28496i	−0.111725	−	0.993739i
$41$		−	10.3771i		−	1.62063i	−0.585996	−	0.810314i	$-0.699296\pi$
$41$		−	10.3771i		−	1.62063i	0.585996	−	0.810314i	$-0.300704\pi$
$42$	5.80569	−	1.28932i	0.895838	−	0.198947i
$43$	−2.02975			−0.309534			−0.154767	−	0.987951i	$-0.549463\pi$
$43$	−2.02975			−0.309534			−0.154767	+	0.987951i	$0.549463\pi$
$44$	−5.77103	−	2.09570i	−0.870015	−	0.315938i
$45$	0.566942	+	2.29920i	0.0845147	+	0.342745i
$46$	−6.15484	+	1.36686i	−0.907482	+	0.201533i
$47$	−3.34313	−	3.34313i	−0.487646	−	0.487646i	0.419917	−	0.907563i	$-0.362059\pi$
$47$	−3.34313	−	3.34313i	−0.487646	−	0.487646i	−0.907563	+	0.419917i	$0.862059\pi$
$48$	4.27421	+	3.57583i	0.616930	+	0.516127i
$49$		−	2.11103i		−	0.301575i
$50$	−0.588672	+	7.04652i	−0.0832508	+	0.996529i
$51$	5.38308	+	5.38308i	0.753782	+	0.753782i
$52$	−1.30932	−	2.80249i	−0.181570	−	0.388635i
$53$		−	7.30702i		−	1.00370i	−0.864956	−	0.501848i	$-0.832654\pi$
$53$		−	7.30702i		−	1.00370i	0.864956	−	0.501848i	$-0.167346\pi$
$54$	−6.74648	−	4.29451i	−0.918080	−	0.584408i
$55$	5.87483	+	3.55067i	0.792162	+	0.478772i
$56$	6.76751	−	5.20472i	0.904346	−	0.695510i
$57$	0.0190679	+	0.0190679i	0.00252560	+	0.00252560i
$58$	−6.51696	+	1.44728i	−0.855719	+	0.190037i
$59$	3.52732	+	3.52732i	0.459218	+	0.459218i	0.898399	−	0.439181i	$-0.144731\pi$
$59$	3.52732	+	3.52732i	0.459218	+	0.459218i	−0.439181	+	0.898399i	$0.644731\pi$
$60$	−3.91201	−	4.84928i	−0.505038	−	0.626040i
$61$	1.41629	−	1.41629i	0.181338	−	0.181338i	−0.610601	−	0.791939i	$-0.709072\pi$
$61$	1.41629	−	1.41629i	0.181338	−	0.181338i	0.791939	+	0.610601i	$0.209072\pi$
$62$	10.6493	+	6.77887i	1.35246	+	0.860918i
$63$	−2.26036	+	2.26036i	−0.284779	+	0.284779i
$64$	7.73194	+	2.05356i	0.966492	+	0.256695i
$65$	0.827973	+	3.35780i	0.102697	+	0.416484i
$66$	−5.90462	+	1.31129i	−0.726809	+	0.161409i
$67$	0.748197			0.0914068			0.0457034	−	0.998955i	$-0.485447\pi$
$67$	0.748197			0.0914068			0.0457034	+	0.998955i	$0.485447\pi$
$68$	10.2723	+	3.73030i	1.24570	+	0.452365i
$69$	−4.39187	+	4.39187i	−0.528719	+	0.528719i
$70$	−8.55174	+	4.24005i	−1.02213	+	0.506783i
$71$	−0.269603			−0.0319960			−0.0159980	−	0.999872i	$-0.505093\pi$
$71$	−0.269603			−0.0319960			−0.0159980	+	0.999872i	$0.505093\pi$
$72$	−2.97020	−	0.387713i	−0.350041	−	0.0456925i
$73$	−0.811870	+	0.811870i	−0.0950222	+	0.0950222i	−0.753020	−	0.657998i	$-0.771404\pi$
$73$	−0.811870	+	0.811870i	−0.0950222	+	0.0950222i	0.657998	+	0.753020i	$0.271404\pi$
$74$	5.50380	−	8.64622i	0.639803	−	1.00510i
$75$	3.23844	+	6.16739i	0.373943	+	0.712149i
$76$	0.0363865	+	0.0132134i	0.00417381	+	0.00151568i
$77$			9.26628i			1.05599i
$78$	−2.57064	−	1.63636i	−0.291068	−	0.185281i
$79$	2.80567			0.315662			0.157831	−	0.987466i	$-0.449550\pi$
$79$	2.80567			0.315662			0.157831	+	0.987466i	$0.449550\pi$
$80$	−8.03466	−	3.92992i	−0.898302	−	0.439379i
$81$	−4.70135			−0.522372
$82$	−12.3800	−	7.88056i	−1.36714	−	0.870262i
$83$			12.8279i			1.40804i	0.710178	+	0.704022i	$0.248614\pi$
$83$			12.8279i			1.40804i	−0.710178	+	0.704022i	$0.751386\pi$
$84$	2.87077	−	7.90541i	0.313227	−	0.862551i
$85$	−10.4571	−	6.32012i	−1.13423	−	0.685514i
$86$	−1.54143	+	2.42152i	−0.166217	+	0.261119i
$87$	−4.65027	+	4.65027i	−0.498561	+	0.498561i
$88$	−6.88283	+	5.29341i	−0.733712	+	0.564279i
$89$	13.3732			1.41755			0.708777	−	0.705432i	$-0.249247\pi$
$89$	13.3732			1.41755			0.708777	+	0.705432i	$0.249247\pi$
$90$	3.17353	+	1.06969i	0.334519	+	0.112755i
$91$	−3.30108	+	3.30108i	−0.346047	+	0.346047i
$92$	−3.04342	+	8.38083i	−0.317299	+	0.873762i
$93$	12.4361			1.28957
$94$	−6.52724	+	1.44956i	−0.673233	+	0.149511i
$95$	−0.0370409	−	0.0223871i	−0.00380032	−	0.00229686i
$96$	7.51194	−	2.38364i	0.766684	−	0.243279i
$97$	6.33466	−	6.33466i	0.643187	−	0.643187i	−0.308151	−	0.951338i	$-0.599710\pi$
$97$	6.33466	−	6.33466i	0.643187	−	0.643187i	0.951338	+	0.308151i	$0.0997101\pi$
$98$	−2.51848	−	1.60315i	−0.254405	−	0.161943i
$99$	2.29888	−	2.29888i	0.231046	−	0.231046i
$100$	7.95955	+	6.05356i	0.795955	+	0.605356i
$101$	−3.78129	−	3.78129i	−0.376252	−	0.376252i	0.493496	−	0.869748i	$-0.335719\pi$
$101$	−3.78129	−	3.78129i	−0.376252	−	0.376252i	−0.869748	+	0.493496i	$0.835719\pi$
$102$	10.5101	−	2.33407i	1.04066	−	0.231108i
$103$	10.7199	+	10.7199i	1.05626	+	1.05626i	0.998320	+	0.0579430i	$0.0184542\pi$
$103$	10.7199	+	10.7199i	1.05626	+	1.05626i	0.0579430	+	0.998320i	$0.481546\pi$
$104$	−4.33774	−	0.566224i	−0.425350	−	0.0555228i
$105$	−4.86386	+	8.04760i	−0.474665	+	0.785365i
$106$	−8.71737	−	5.54909i	−0.846706	−	0.538975i
$107$		−	10.9109i		−	1.05479i	−0.849619	−	0.527397i	$-0.823168\pi$
$107$		−	10.9109i		−	1.05479i	0.849619	−	0.527397i	$-0.176832\pi$
$108$	−10.2468	+	4.78731i	−0.986000	+	0.460659i
$109$	−9.12139	−	9.12139i	−0.873670	−	0.873670i	0.119200	−	0.992870i	$-0.461967\pi$
$109$	−9.12139	−	9.12139i	−0.873670	−	0.873670i	−0.992870	+	0.119200i	$0.961967\pi$
$110$	8.69746	−	4.31231i	0.829270	−	0.411162i
$111$		−	10.0969i		−	0.958359i
$112$	−1.06993	−	12.0263i	−0.101098	−	1.13638i
$113$	4.88810	+	4.88810i	0.459834	+	0.459834i	0.898601	−	0.438767i	$-0.144585\pi$
$113$	4.88810	+	4.88810i	0.459834	+	0.459834i	−0.438767	+	0.898601i	$0.644585\pi$
$114$	0.0372288	−	0.00826773i	0.00348679	−	0.000774344i
$115$	5.15637	−	8.53157i	0.480834	−	0.795573i
$116$	−3.22248	+	8.87392i	−0.299200	+	0.823923i
$117$	1.63793			0.151427
$118$	6.88685	−	1.52943i	0.633986	−	0.140795i
$119$		−	16.4938i		−	1.51198i
$120$	−8.75612	+	0.984439i	−0.799320	+	0.0898666i
$121$			1.57582i			0.143256i
$122$	−0.614097	−	2.76522i	−0.0555978	−	0.250351i
$123$	−14.4572			−1.30356
$124$	16.1746	−	7.55676i	1.45252	−	0.678617i
$125$	−7.41640	−	8.36642i	−0.663343	−	0.748315i
$126$	0.980081	+	4.41321i	0.0873125	+	0.393160i
$127$	−1.38586	−	1.38586i	−0.122975	−	0.122975i	0.642941	−	0.765916i	$-0.277714\pi$
$127$	−1.38586	−	1.38586i	−0.122975	−	0.122975i	−0.765916	+	0.642941i	$0.777714\pi$
$128$	8.32171	−	7.66480i	0.735542	−	0.677479i
$129$			2.82782i			0.248976i
$130$	4.63468	+	1.56219i	0.406488	+	0.137013i
$131$	−3.52096	−	3.52096i	−0.307627	−	0.307627i	0.536361	−	0.843989i	$-0.319798\pi$
$131$	−3.52096	−	3.52096i	−0.307627	−	0.307627i	−0.843989	+	0.536361i	$0.819798\pi$
$132$	−2.91969	+	8.04012i	−0.254127	+	0.699802i
$133$		−	0.0584241i		−	0.00506601i
$134$	0.568195	−	0.892609i	0.0490846	−	0.0771097i
$135$	12.2772	−	3.02734i	1.05665	−	0.260552i
$136$	12.2513	−	9.42216i	1.05054	−	0.807943i
$137$	5.62512	+	5.62512i	0.480587	+	0.480587i	0.905319	−	0.424732i	$-0.139632\pi$
$137$	5.62512	+	5.62512i	0.480587	+	0.480587i	−0.424732	+	0.905319i	$0.639632\pi$
$138$	1.90429	+	8.57484i	0.162104	+	0.729939i
$139$	12.1022	+	12.1022i	1.02650	+	1.02650i	0.999639	+	0.0268584i	$0.00855031\pi$
$139$	12.1022	+	12.1022i	1.02650	+	1.02650i	0.0268584	+	0.999639i	$0.491450\pi$
$140$	−1.43591	+	13.4223i	−0.121357	+	1.13439i
$141$	−4.65760	+	4.65760i	−0.392241	+	0.392241i
$142$	−0.204742	+	0.321641i	−0.0171816	+	0.0269915i
$143$	3.35733	−	3.35733i	0.280754	−	0.280754i
$144$	−2.71817	+	3.24905i	−0.226514	+	0.270754i
$145$	5.45975	−	9.03353i	0.453408	−	0.750194i
$146$	0.352023	+	1.58512i	0.0291336	+	0.131186i
$147$	−2.94105			−0.242574
$148$	−6.13537	−	13.1322i	−0.504324	−	1.07946i
$149$	−13.5590	+	13.5590i	−1.11080	+	1.11080i	−0.117757	+	0.993042i	$0.537570\pi$
$149$	−13.5590	+	13.5590i	−1.11080	+	1.11080i	−0.993042	+	0.117757i	$0.962430\pi$
$150$	9.81712	+	0.820130i	0.801564	+	0.0669633i
$151$	−20.7185			−1.68605			−0.843025	−	0.537874i	$-0.819228\pi$
$151$	−20.7185			−1.68605			−0.843025	+	0.537874i	$0.819228\pi$
$152$	0.0433964	−	0.0333751i	0.00351991	−	0.00270707i
$153$	−4.09196	+	4.09196i	−0.330815	+	0.330815i
$154$	11.0548	+	7.03699i	0.890821	+	0.567057i
$155$	−19.3795	+	4.77865i	−1.55660	+	0.383830i
$156$	−3.90439	+	1.82413i	−0.312601	+	0.146047i
$157$			5.72312i			0.456755i	0.973573	+	0.228377i	$0.0733420\pi$
$157$			5.72312i			0.456755i	−0.973573	+	0.228377i	$0.926658\pi$
$158$	2.13068	−	3.34720i	0.169508	−	0.266289i
$159$	−10.1800			−0.807329
$160$	−10.7901	+	6.60100i	−0.853034	+	0.521855i
$161$	13.4567			1.06054
$162$	−3.57030	+	5.60878i	−0.280509	+	0.440667i
$163$		−	17.9900i		−	1.40909i	−0.709662	−	0.704543i	$-0.751152\pi$
$163$		−	17.9900i		−	1.40909i	0.709662	−	0.704543i	$-0.248848\pi$
$164$	−18.8032	+	8.78487i	−1.46829	+	0.685983i
$165$	4.94675	−	8.18473i	0.385104	−	0.637181i
$166$	15.3039	+	9.74175i	1.18781	+	0.756106i
$167$	2.39642	−	2.39642i	0.185441	−	0.185441i	−0.608281	−	0.793722i	$-0.708141\pi$
$167$	2.39642	−	2.39642i	0.185441	−	0.185441i	0.793722	+	0.608281i	$0.208141\pi$
$168$	−7.25114	−	9.42839i	−0.559438	−	0.727416i
$169$	−10.6079			−0.815995
$170$	−15.4813	+	7.67582i	−1.18736	+	0.588708i
$171$	−0.0144945	+	0.0144945i	−0.00110842	+	0.00110842i
$172$	1.71832	+	3.67790i	0.131020	+	0.280437i
$173$	−9.45205			−0.718626			−0.359313	−	0.933217i	$-0.616989\pi$
$173$	−9.45205			−0.718626			−0.359313	+	0.933217i	$0.616989\pi$
$174$	2.01633	+	9.07934i	0.152858	+	0.688303i
$175$	4.48716	−	14.4098i	0.339197	−	1.08928i
$176$	1.08816	+	12.2312i	0.0820230	+	0.921963i
$177$	4.91421	−	4.91421i	0.369375	−	0.369375i
$178$	10.1559	−	15.9544i	0.761213	−	1.19583i
$179$	−11.7991	+	11.7991i	−0.881905	+	0.881905i	−0.993728	−	0.111824i	$-0.964331\pi$
$179$	−11.7991	+	11.7991i	−0.881905	+	0.881905i	0.111824	+	0.993728i	$0.464331\pi$
$180$	3.68619	−	2.97372i	0.274752	−	0.221648i
$181$	2.54155	+	2.54155i	0.188912	+	0.188912i	0.795225	−	0.606314i	$-0.207352\pi$
$181$	2.54155	+	2.54155i	0.188912	+	0.188912i	−0.606314	+	0.795225i	$0.707352\pi$
$182$	1.43133	+	6.44513i	0.106097	+	0.477745i
$183$	−1.97316	−	1.97316i	−0.145860	−	0.145860i
$184$	7.68722	+	9.99541i	0.566709	+	0.736871i
$185$	3.87980	+	15.7343i	0.285249	+	1.15681i
$186$	9.44423	−	14.8365i	0.692484	−	1.08786i
$187$			16.7748i			1.22670i
$188$	−3.22756	+	8.88791i	−0.235394	+	0.648217i
$189$	12.0698	+	12.0698i	0.877949	+	0.877949i
$190$	−0.0548377	+	0.0271892i	−0.00397834	+	0.00197251i
$191$		−	5.46421i		−	0.395376i	−0.980265	−	0.197688i	$-0.936657\pi$
$191$		−	5.46421i		−	0.395376i	0.980265	−	0.197688i	$-0.0633433\pi$
$192$	2.86099	−	10.7720i	0.206474	−	0.777404i
$193$	4.82485	+	4.82485i	0.347300	+	0.347300i	0.859103	−	0.511803i	$-0.171022\pi$
$193$	4.82485	+	4.82485i	0.347300	+	0.347300i	−0.511803	+	0.859103i	$0.671022\pi$
$194$	−2.74667	−	12.3680i	−0.197200	−	0.887970i
$195$	4.67804	−	1.15352i	0.335001	−	0.0826053i
$196$	−3.82517	+	1.78712i	−0.273226	+	0.127651i
$197$	2.94582			0.209881			0.104941	−	0.994478i	$-0.466535\pi$
$197$	2.94582			0.209881			0.104941	+	0.994478i	$0.466535\pi$
$198$	−0.996782	−	4.48841i	−0.0708382	−	0.318977i
$199$		−	2.14620i		−	0.152140i	−0.997102	−	0.0760700i	$-0.975763\pi$
$199$		−	2.14620i		−	0.152140i	0.997102	−	0.0760700i	$-0.0242372\pi$
$200$	13.2666	−	4.89866i	0.938091	−	0.346388i
$201$		−	1.04238i		−	0.0735236i
$202$	−7.38271	+	1.63955i	−0.519446	+	0.115358i
$203$	14.2485			1.00005
$204$	5.19699	−	14.3112i	0.363862	−	1.00199i
$205$	22.5291	−	5.55526i	1.57350	−	0.387996i
$206$	20.9299	−	4.64809i	1.45825	−	0.323848i
$207$	−3.33849	−	3.33849i	−0.232041	−	0.232041i
$208$	−3.96967	+	4.74498i	−0.275247	+	0.329005i
$209$			0.0594197i			0.00411014i
$210$	5.90719	+	11.9142i	0.407634	+	0.822155i
$211$	5.54427	+	5.54427i	0.381684	+	0.381684i	0.871708	−	0.490025i	$-0.163012\pi$
$211$	5.54427	+	5.54427i	0.381684	+	0.381684i	−0.490025	+	0.871708i	$0.663012\pi$
$212$	−13.2403	+	6.18586i	−0.909346	+	0.424847i
$213$			0.375608i			0.0257362i
$214$	−13.0168	−	8.28593i	−0.889812	−	0.566414i
$215$	−1.08661	−	4.40667i	−0.0741059	−	0.300532i
$216$	−2.07030	+	15.8602i	−0.140866	+	1.07915i
$217$	−19.0522	−	19.0522i	−1.29335	−	1.29335i
$218$	−17.8089	+	3.95498i	−1.20617	+	0.267865i
$219$	1.13109	+	1.13109i	0.0764317	+	0.0764317i
$220$	1.46038	−	13.6510i	0.0984587	−	0.920353i
$221$	−5.97597	+	5.97597i	−0.401988	+	0.401988i
$222$	−12.0458	−	7.66781i	−0.808461	−	0.514630i
$223$	−1.16163	+	1.16163i	−0.0777882	+	0.0777882i	−0.744930	−	0.667142i	$-0.767517\pi$
$223$	−1.16163	+	1.16163i	−0.0777882	+	0.0777882i	0.667142	+	0.744930i	$0.267517\pi$
$224$	−15.1601	−	7.85656i	−1.01292	−	0.524939i
$225$	−4.68815	+	2.46171i	−0.312543	+	0.164114i
$226$	9.54369	−	2.11945i	0.634837	−	0.140984i
$227$	12.8161			0.850632			0.425316	−	0.905045i	$-0.360163\pi$
$227$	12.8161			0.850632			0.425316	+	0.905045i	$0.360163\pi$
$228$	0.0184087	−	0.0506931i	0.00121915	−	0.00335723i
$229$	−0.976882	+	0.976882i	−0.0645542	+	0.0645542i	−0.738647	−	0.674093i	$-0.764535\pi$
$229$	−0.976882	+	0.976882i	−0.0645542	+	0.0645542i	0.674093	+	0.738647i	$0.264535\pi$
$230$	−6.26244	−	12.6307i	−0.412933	−	0.832842i
$231$	12.9097			0.849393
$232$	8.13950	+	10.5835i	0.534384	+	0.694840i
$233$	0.303870	−	0.303870i	0.0199072	−	0.0199072i	−0.697083	−	0.716990i	$-0.745519\pi$
$233$	0.303870	−	0.303870i	0.0199072	−	0.0199072i	0.716990	+	0.697083i	$0.245519\pi$
$234$	1.24388	−	1.95408i	0.0813149	−	0.127742i
$235$	5.46836	−	9.04777i	0.356716	−	0.590212i
$236$	3.40538	−	9.37758i	0.221671	−	0.610429i
$237$		−	3.90881i		−	0.253905i
$238$	−19.6773	−	12.5257i	−1.27549	−	0.811921i
$239$	12.5096			0.809178			0.404589	−	0.914499i	$-0.367415\pi$
$239$	12.5096			0.809178			0.404589	+	0.914499i	$0.367415\pi$
$240$	−5.47511	+	11.1938i	−0.353417	+	0.722555i
$241$	−19.5775			−1.26110			−0.630548	−	0.776150i	$-0.717170\pi$
$241$	−19.5775			−1.26110			−0.630548	+	0.776150i	$0.717170\pi$
$242$	1.87997	+	1.19671i	0.120849	+	0.0769273i
$243$		−	10.4151i		−	0.668129i
$244$	−3.76530	−	1.36733i	−0.241049	−	0.0875346i
$245$	4.58312	−	1.13012i	0.292805	−	0.0722004i
$246$	−10.9791	+	17.2477i	−0.700001	+	1.09967i
$247$	−0.0211680	+	0.0211680i	−0.00134689	+	0.00134689i
$248$	3.26796	−	25.0352i	0.207516	−	1.58974i
$249$	17.8716			1.13257
$250$	−15.6134	+	2.49425i	−0.987479	+	0.157750i
$251$	5.17763	−	5.17763i	0.326809	−	0.326809i	−0.524563	−	0.851372i	$-0.675771\pi$
$251$	5.17763	−	5.17763i	0.326809	−	0.326809i	0.851372	+	0.524563i	$0.175771\pi$
$252$	6.00931	+	2.18222i	0.378551	+	0.137467i
$253$	−13.6860			−0.860433
$254$	−2.70580	+	0.600902i	−0.169777	+	0.0377040i
$255$	−8.80511	+	14.5687i	−0.551397	+	0.912325i
$256$	−2.82454	−	15.7487i	−0.176534	−	0.984295i
$257$	−14.7989	+	14.7989i	−0.923131	+	0.923131i	−0.997249	−	0.0741183i	$-0.976386\pi$
$257$	−14.7989	+	14.7989i	−0.923131	+	0.923131i	0.0741183	+	0.997249i	$0.476386\pi$
$258$	3.37363	+	2.14750i	0.210033	+	0.133698i
$259$	−15.4685	+	15.4685i	−0.961168	+	0.961168i
$260$	5.38338	−	4.34288i	0.333863	−	0.269334i
$261$	−3.53491	−	3.53491i	−0.218805	−	0.218805i
$262$	−6.87443	+	1.52667i	−0.424704	+	0.0943178i
$263$	11.7906	+	11.7906i	0.727038	+	0.727038i	0.970029	−	0.242991i	$-0.0781285\pi$
$263$	11.7906	+	11.7906i	0.727038	+	0.727038i	−0.242991	+	0.970029i	$0.578129\pi$
$264$	7.37470	+	9.58906i	0.453881	+	0.590166i
$265$	15.8638	−	3.91173i	0.974507	−	0.240296i
$266$	−0.0697008	−	0.0443684i	−0.00427363	−	0.00272040i
$267$		−	18.6313i		−	1.14022i
$268$	−0.633397	−	1.35573i	−0.0386909	−	0.0828144i
$269$	−2.10121	−	2.10121i	−0.128113	−	0.128113i	0.640143	−	0.768256i	$-0.278875\pi$
$269$	−2.10121	−	2.10121i	−0.128113	−	0.128113i	−0.768256	+	0.640143i	$0.778875\pi$
$270$	5.71189	−	16.9459i	0.347614	−	1.03129i
$271$			18.8596i			1.14564i	0.819683	+	0.572818i	$0.194150\pi$
$271$			18.8596i			1.14564i	−0.819683	+	0.572818i	$0.805850\pi$
$272$	−1.93690	−	21.7713i	−0.117442	−	1.32008i
$273$	4.59901	+	4.59901i	0.278345	+	0.278345i
$274$	10.9827	−	2.43902i	0.663488	−	0.147347i
$275$	−4.56362	+	14.6553i	−0.275197	+	0.883748i
$276$	11.6761	+	4.24005i	0.702816	+	0.255221i
$277$	9.91909			0.595980			0.297990	−	0.954569i	$-0.403684\pi$
$277$	9.91909			0.595980			0.297990	+	0.954569i	$0.403684\pi$
$278$	23.6288	−	5.24746i	1.41716	−	0.314722i
$279$			9.45334i			0.565956i
$280$	14.9226	+	11.9062i	0.891793	+	0.711533i
$281$		−	9.31434i		−	0.555647i	−0.960632	−	0.277823i	$-0.910387\pi$
$281$		−	9.31434i		−	0.555647i	0.960632	−	0.277823i	$-0.0896130\pi$
$282$	2.01951	+	9.09366i	0.120260	+	0.541519i
$283$	−3.42364			−0.203514			−0.101757	−	0.994809i	$-0.532446\pi$
$283$	−3.42364			−0.203514			−0.101757	+	0.994809i	$0.532446\pi$
$284$	0.228237	+	0.488520i	0.0135434	+	0.0289883i
$285$	−0.0311893	+	0.0516049i	−0.00184750	+	0.00305681i
$286$	−1.45572	−	6.55496i	−0.0860785	−	0.387603i
$287$	22.1485	+	22.1485i	1.30738	+	1.30738i
$288$	1.81193	+	5.71021i	0.106769	+	0.336477i
$289$		−	12.8589i		−	0.756405i
$290$	−6.63089	−	13.3738i	−0.389379	−	0.785336i
$291$	−8.82535	−	8.82535i	−0.517351	−	0.517351i
$292$	2.15841	+	0.783805i	0.126311	+	0.0458687i
$293$			2.66471i			0.155674i	0.996966	+	0.0778369i	$0.0248013\pi$
$293$			2.66471i			0.155674i	−0.996966	+	0.0778369i	$0.975199\pi$
$294$	−2.23349	+	3.50872i	−0.130260	+	0.204633i
$295$	−5.76963	+	9.54626i	−0.335921	+	0.555804i
$296$	−20.3262	−	2.65327i	−1.18144	−	0.154218i
$297$	−12.2755	−	12.2755i	−0.712296	−	0.712296i
$298$	5.87912	+	26.4731i	0.340568	+	1.53355i
$299$	−4.87559	−	4.87559i	−0.281963	−	0.281963i
$300$	8.43373	−	11.0891i	0.486922	−	0.640231i
$301$	4.33223	−	4.33223i	0.249706	−	0.249706i
$302$	−15.7341	+	24.7175i	−0.905393	+	1.42233i
$303$	−5.26804	+	5.26804i	−0.302641	+	0.302641i
$304$	−0.00686086	−	0.0771181i	−0.000393497	−	0.00442303i
$305$	3.83303	+	2.31663i	0.219478	+	0.132650i
$306$	1.77425	+	7.98928i	0.101427	+	0.456717i
$307$	10.5554			0.602430			0.301215	−	0.953556i	$-0.402608\pi$
$307$	10.5554			0.602430			0.301215	+	0.953556i	$0.402608\pi$
$308$	16.7905	−	7.84450i	0.956725	−	0.446982i
$309$	14.9348	−	14.9348i	0.849612	−	0.849612i
$310$	−9.01621	+	26.7491i	−0.512086	+	1.51924i
$311$	−20.4762			−1.16110			−0.580550	−	0.814225i	$-0.697162\pi$
$311$	−20.4762			−1.16110			−0.580550	+	0.814225i	$0.697162\pi$
$312$	−0.788855	+	6.04327i	−0.0446601	+	0.342133i
$313$	2.82393	−	2.82393i	0.159618	−	0.159618i	−0.622780	−	0.782397i	$-0.713997\pi$
$313$	2.82393	−	2.82393i	0.159618	−	0.159618i	0.782397	+	0.622780i	$0.213997\pi$
$314$	6.82776	+	4.34625i	0.385313	+	0.245273i
$315$	−6.11740	−	3.69727i	−0.344676	−	0.208318i
$316$	−2.37518	−	5.08385i	−0.133614	−	0.285989i
$317$		−	20.2533i		−	1.13754i	−0.822497	−	0.568769i	$-0.807420\pi$
$317$		−	20.2533i		−	1.13754i	0.822497	−	0.568769i	$-0.192580\pi$
$318$	−7.73091	+	12.1449i	−0.433528	+	0.681053i
$319$	−14.4913			−0.811354
$320$	−0.319150	+	17.8857i	−0.0178410	+	0.999841i
$321$	−15.2009			−0.848430
$322$	10.2193	−	16.0541i	0.569499	−	0.894658i
$323$		−	0.105766i		−	0.00588497i
$324$	3.98000	+	8.51883i	0.221111	+	0.473268i
$325$	−6.84667	+	3.59512i	−0.379785	+	0.199422i
$326$	−21.4623	−	13.6620i	−1.18869	−	0.756666i
$327$	−12.7078	+	12.7078i	−0.702742	+	0.702742i
$328$	−3.79907	+	29.1039i	−0.209768	+	1.60700i
$329$	14.2709			0.786781
$330$	−6.00785	−	12.1172i	−0.330721	−	0.667029i
$331$	19.4930	−	19.4930i	1.07143	−	1.07143i	0.0741908	−	0.997244i	$-0.476363\pi$
$331$	19.4930	−	19.4930i	1.07143	−	1.07143i	0.997244	−	0.0741908i	$-0.0236374\pi$
$332$	23.2441	−	10.8596i	1.27569	−	0.596000i
$333$	7.67521			0.420599
$334$	−1.03908	−	4.67885i	−0.0568557	−	0.256016i
$335$	0.400539	+	1.62437i	0.0218838	+	0.0887485i
$336$	−16.7549	+	1.49061i	−0.914053	+	0.0813192i
$337$	−5.89449	+	5.89449i	−0.321093	+	0.321093i	−0.849186	−	0.528093i	$-0.822907\pi$
$337$	−5.89449	+	5.89449i	−0.321093	+	0.321093i	0.528093	+	0.849186i	$0.322907\pi$
$338$	−8.05587	+	12.6554i	−0.438181	+	0.688364i
$339$	6.81003	−	6.81003i	0.369870	−	0.369870i
$340$	−2.59944	+	24.2986i	−0.140975	+	1.31778i
$341$	19.3768	+	19.3768i	1.04931	+	1.04931i
$342$	0.00628473	+	0.0282995i	0.000339839	+	0.00153026i
$343$	−10.4349	−	10.4349i	−0.563429	−	0.563429i
$344$	5.69271	+	0.743095i	0.306930	+	0.0400650i
$345$	−11.8861	−	7.18379i	−0.639925	−	0.386762i
$346$	−7.17807	+	11.2764i	−0.385895	+	0.606225i
$347$			11.4626i			0.615346i	0.951492	+	0.307673i	$0.0995502\pi$
$347$			11.4626i			0.615346i	−0.951492	+	0.307673i	$0.900450\pi$
$348$	12.3630	+	4.48952i	0.662728	+	0.240663i
$349$	−0.317872	−	0.317872i	−0.0170153	−	0.0170153i	0.698548	−	0.715563i	$-0.253830\pi$
$349$	−0.317872	−	0.317872i	−0.0170153	−	0.0170153i	−0.715563	+	0.698548i	$0.753830\pi$
$350$	−13.7834	−	16.2963i	−0.736754	−	0.871073i
$351$		−	8.74618i		−	0.466837i
$352$	15.4184	+	7.99044i	0.821803	+	0.425892i
$353$	−18.4551	−	18.4551i	−0.982266	−	0.982266i	0.0175800	−	0.999845i	$-0.494404\pi$
$353$	−18.4551	−	18.4551i	−0.982266	−	0.982266i	−0.999845	+	0.0175800i	$0.994404\pi$
$354$	−2.13077	−	9.59466i	−0.113249	−	0.509951i
$355$	−0.144329	−	0.585320i	−0.00766020	−	0.0310655i
$356$	−11.3213	−	24.2321i	−0.600026	−	1.28430i
$357$	−22.9789			−1.21617
$358$	5.11602	+	23.0369i	0.270390	+	1.21754i
$359$		−	15.5802i		−	0.822292i	−0.911569	−	0.411146i	$-0.865129\pi$
$359$		−	15.5802i		−	0.822292i	0.911569	−	0.411146i	$-0.134871\pi$
$360$	−0.748323	−	6.65598i	−0.0394401	−	0.350801i
$361$			18.9996i			0.999980i
$362$	4.96220	−	1.10200i	0.260808	−	0.0579199i
$363$	2.19541			0.115229
$364$	8.77611	+	3.18696i	0.459993	+	0.167042i
$365$	−2.19723	−	1.32798i	−0.115008	−	0.0695095i
$366$	−3.85246	+	0.855552i	−0.201372	+	0.0447204i
$367$	5.37489	+	5.37489i	0.280567	+	0.280567i	0.833335	−	0.552768i	$-0.186428\pi$
$367$	5.37489	+	5.37489i	0.280567	+	0.280567i	−0.552768	+	0.833335i	$0.686428\pi$
$368$	17.7625	−	1.58025i	0.925933	−	0.0823762i
$369$		−	10.9897i		−	0.572100i
$370$	21.7177	+	7.32030i	1.12905	+	0.380564i
$371$	15.5958	+	15.5958i	0.809696	+	0.809696i
$372$	−10.5280	−	22.5342i	−0.545850	−	1.16834i
$373$			3.24424i			0.167980i	0.996467	+	0.0839902i	$0.0267664\pi$
$373$			3.24424i			0.167980i	−0.996467	+	0.0839902i	$0.973234\pi$
$374$	20.0126	+	12.7391i	1.03483	+	0.658726i
$375$	−11.6560	+	10.3324i	−0.601912	+	0.533564i
$376$	8.15233	+	10.6002i	0.420424	+	0.546662i
$377$	−5.16245	−	5.16245i	−0.265880	−	0.265880i
$378$	23.5655	−	5.23340i	1.21208	−	0.269177i
$379$	−25.7690	−	25.7690i	−1.32367	−	1.32367i	−0.910785	−	0.412882i	$-0.864522\pi$
$379$	−25.7690	−	25.7690i	−1.32367	−	1.32367i	−0.412882	−	0.910785i	$-0.635478\pi$
$380$	−0.00920772	+	0.0860701i	−0.000472346	+	0.00441530i
$381$	−1.93076	+	1.93076i	−0.0989160	+	0.0989160i
$382$	−6.51888	−	4.14962i	−0.333535	−	0.212313i
$383$	0.418091	−	0.418091i	0.0213634	−	0.0213634i	−0.696344	−	0.717708i	$-0.745191\pi$
$383$	0.418091	−	0.418091i	0.0213634	−	0.0213634i	0.717708	+	0.696344i	$0.245191\pi$
$384$	−10.6785	−	11.5937i	−0.544934	−	0.591638i
$385$	−20.1175	+	4.96060i	−1.02528	+	0.252816i
$386$	9.42019	−	2.09203i	0.479475	−	0.106481i
$387$	−2.14957			−0.109269
$388$	−16.8411	−	6.11568i	−0.854976	−	0.310476i
$389$	13.3626	−	13.3626i	0.677508	−	0.677508i	−0.281927	−	0.959436i	$-0.590974\pi$
$389$	13.3626	−	13.3626i	0.677508	−	0.677508i	0.959436	+	0.281927i	$0.0909737\pi$
$390$	2.17643	−	6.45697i	0.110208	−	0.326961i
$391$	24.3609			1.23198
$392$	−0.772850	+	5.92066i	−0.0390348	+	0.299038i
$393$	−4.90535	+	4.90535i	−0.247442	+	0.247442i
$394$	2.23712	−	3.51441i	0.112704	−	0.177053i
$395$	1.50198	+	6.09121i	0.0755730	+	0.306482i
$396$	−6.11171	−	2.21941i	−0.307125	−	0.111530i
$397$			13.8391i			0.694564i	0.937761	+	0.347282i	$0.112895\pi$
$397$			13.8391i			0.694564i	−0.937761	+	0.347282i	$0.887105\pi$
$398$	−2.56044	−	1.62986i	−0.128343	−	0.0816977i
$399$	−0.0813957			−0.00407488
$400$	4.23075	−	19.5474i	0.211538	−	0.977370i
$401$	20.3112			1.01430			0.507148	−	0.861859i	$-0.330700\pi$
$401$	20.3112			1.01430			0.507148	+	0.861859i	$0.330700\pi$
$402$	−1.24357	−	0.791602i	−0.0620237	−	0.0394815i
$403$			13.8058i			0.687718i
$404$	−3.65057	+	10.0528i	−0.181623	+	0.500144i
$405$	−2.51682	−	10.2068i	−0.125062	−	0.507181i
$406$	10.8206	−	16.9986i	0.537015	−	0.843626i
$407$	15.7321	−	15.7321i	0.779813	−	0.779813i
$408$	−13.1268	−	17.0683i	−0.649874	−	0.845008i
$409$	−18.2875			−0.904259			−0.452130	−	0.891952i	$-0.649336\pi$
$409$	−18.2875			−0.904259			−0.452130	+	0.891952i	$0.649336\pi$
$410$	10.4815	−	31.0963i	0.517644	−	1.53573i
$411$	7.83684	−	7.83684i	0.386563	−	0.386563i
$412$	10.3493	−	28.4995i	0.509875	−	1.40407i
$413$	−15.0572			−0.740915
$414$	−6.51818	+	1.44755i	−0.320351	+	0.0711433i
$415$	−27.8499	+	6.86728i	−1.36710	+	0.337101i
$416$	2.64618	+	8.33930i	0.129740	+	0.408868i
$417$	16.8607	−	16.8607i	0.825670	−	0.825670i
$418$	0.0708885	+	0.0451245i	0.00346727	+	0.00220711i
$419$	17.3188	−	17.3188i	0.846079	−	0.846079i	−0.143563	−	0.989641i	$-0.545856\pi$
$419$	17.3188	−	17.3188i	0.846079	−	0.846079i	0.989641	+	0.143563i	$0.0458558\pi$
$420$	18.6998	+	2.00049i	0.912456	+	0.0976139i
$421$	11.5457	+	11.5457i	0.562703	+	0.562703i	0.930074	−	0.367372i	$-0.119742\pi$
$421$	11.5457	+	11.5457i	0.562703	+	0.562703i	−0.367372	+	0.930074i	$0.619742\pi$
$422$	10.8248	−	2.40397i	0.526944	−	0.117023i
$423$	−3.54048	−	3.54048i	−0.172144	−	0.172144i
$424$	−2.67511	+	20.4935i	−0.129915	+	0.995252i
$425$	8.12315	−	26.0861i	0.394031	−	1.26536i
$426$	0.448105	+	0.285244i	0.0217108	+	0.0138201i
$427$			6.04577i			0.292576i
$428$	−19.7705	+	9.23676i	−0.955641	+	0.446475i
$429$	−4.67738	−	4.67738i	−0.225826	−	0.225826i
$430$	−6.08241	−	2.05018i	−0.293320	−	0.0988682i
$431$		−	15.9479i		−	0.768185i	−0.923295	−	0.384093i	$-0.874514\pi$
$431$		−	15.9479i		−	0.768185i	0.923295	−	0.384093i	$-0.125486\pi$
$432$	17.3492	+	14.5144i	0.834713	+	0.698325i
$433$	3.52109	+	3.52109i	0.169213	+	0.169213i	0.786633	−	0.617420i	$-0.211822\pi$
$433$	3.52109	+	3.52109i	0.169213	+	0.169213i	−0.617420	+	0.786633i	$0.711822\pi$
$434$	−37.1981	+	8.26092i	−1.78557	+	0.396537i
$435$	−12.5854	−	7.60645i	−0.603423	−	0.364701i
$436$	−8.80607	+	24.2498i	−0.421734	+	1.16135i
$437$	0.0862907			0.00412784
$438$	2.20837	−	0.490433i	0.105520	−	0.0234338i
$439$			6.45840i			0.308242i	0.988052	+	0.154121i	$0.0492546\pi$
$439$			6.45840i			0.308242i	−0.988052	+	0.154121i	$0.950745\pi$
$440$	−15.1768	−	12.1091i	−0.723528	−	0.577279i
$441$		−	2.23565i		−	0.106459i
$442$	2.59115	+	11.6677i	0.123248	+	0.554975i
$443$	27.0992			1.28752			0.643761	−	0.765226i	$-0.277373\pi$
$443$	27.0992			1.28752			0.643761	+	0.765226i	$0.277373\pi$
$444$	−18.2956	+	8.54771i	−0.868271	+	0.405656i
$445$	7.15919	+	29.0337i	0.339378	+	1.37633i
$446$	0.503675	+	2.26800i	0.0238497	+	0.107393i
$447$	18.8903	+	18.8903i	0.893478	+	0.893478i
$448$	−20.8858	+	12.1197i	−0.986763	+	0.572604i
$449$			41.0879i			1.93906i	0.244976	+	0.969529i	$0.421220\pi$
$449$			41.0879i			1.93906i	−0.244976	+	0.969529i	$0.578780\pi$
$450$	−0.623423	+	7.46250i	−0.0293884	+	0.351785i
$451$	−22.5259	−	22.5259i	−1.06070	−	1.06070i
$452$	4.71913	−	12.9953i	0.221969	−	0.611248i
$453$			28.8648i			1.35619i
$454$	9.73276	−	15.2897i	0.456781	−	0.717583i
$455$	−8.93396	−	5.39957i	−0.418831	−	0.253136i
$456$	−0.0464977	−	0.0604592i	−0.00217745	−	0.00283126i
$457$	18.2449	+	18.2449i	0.853462	+	0.853462i	0.990558	−	0.137096i	$-0.0437769\pi$
$457$	18.2449	+	18.2449i	0.853462	+	0.853462i	−0.137096	+	0.990558i	$0.543777\pi$
$458$	0.423571	+	1.90730i	0.0197922	+	0.0891221i
$459$	21.8501	+	21.8501i	1.01988	+	1.01988i
$460$	−19.8244	−	2.12080i	−0.924316	−	0.0988827i
$461$	6.68802	−	6.68802i	0.311492	−	0.311492i	−0.533995	−	0.845488i	$-0.679310\pi$
$461$	6.68802	−	6.68802i	0.311492	−	0.311492i	0.845488	+	0.533995i	$0.179310\pi$
$462$	9.80384	−	15.4014i	0.456116	−	0.716538i
$463$	28.6926	−	28.6926i	1.33346	−	1.33346i	0.431205	−	0.902254i	$-0.358089\pi$
$463$	28.6926	−	28.6926i	1.33346	−	1.33346i	0.902254	−	0.431205i	$-0.141911\pi$
$464$	18.8075	−	1.67322i	0.873118	−	0.0776775i
$465$	6.65754	+	26.9993i	0.308736	+	1.25206i
$466$	−0.131756	−	0.593286i	−0.00610349	−	0.0274834i
$467$	−32.4161			−1.50004			−0.750018	−	0.661417i	$-0.769955\pi$
$467$	−32.4161			−1.50004			−0.750018	+	0.661417i	$0.769955\pi$
$468$	−1.38662	−	2.96793i	−0.0640964	−	0.137193i
$469$	−1.59693	+	1.59693i	−0.0737392	+	0.0737392i
$470$	−6.64134	−	13.3949i	−0.306342	−	0.617860i
$471$	7.97337			0.367394
$472$	−8.60148	−	11.1842i	−0.395915	−	0.514794i
$473$	−4.40605	+	4.40605i	−0.202591	+	0.202591i
$474$	−4.66327	−	2.96843i	−0.214191	−	0.136344i
$475$	0.0287737	−	0.0924020i	0.00132023	−	0.00423970i
$476$	−29.8867	+	13.9631i	−1.36985	+	0.639996i
$477$		−	7.73837i		−	0.354316i
$478$	9.50003	−	14.9241i	0.434521	−	0.682613i
$479$	7.33117			0.334970			0.167485	−	0.985875i	$-0.446435\pi$
$479$	7.33117			0.334970			0.167485	+	0.985875i	$0.446435\pi$
$480$	9.19642	+	15.0327i	0.419757	+	0.686144i
$481$	11.2090			0.511087
$482$	−14.8675	+	23.3562i	−0.677197	+	1.06385i
$483$		−	18.7477i		−	0.853051i
$484$	2.85538	−	1.33403i	0.129790	−	0.0606378i
$485$	17.1440	+	10.3616i	0.778468	+	0.470496i
$486$	−12.4254	−	7.90943i	−0.563626	−	0.358779i
$487$	−11.7773	+	11.7773i	−0.533681	+	0.533681i	−0.921666	−	0.387985i	$-0.873171\pi$
$487$	−11.7773	+	11.7773i	−0.533681	+	0.533681i	0.387985	+	0.921666i	$0.373171\pi$
$488$	−4.49069	+	3.45368i	−0.203284	+	0.156341i
$489$	−25.0634			−1.13341
$490$	2.13227	−	6.32596i	0.0963260	−	0.285778i
$491$	−27.3556	+	27.3556i	−1.23454	+	1.23454i	−0.272343	+	0.962200i	$0.587798\pi$
$491$	−27.3556	+	27.3556i	−1.23454	+	1.23454i	−0.962200	+	0.272343i	$0.912202\pi$
$492$	12.2390	+	26.1964i	0.551775	+	1.18103i
$493$	25.7941			1.16171
$494$	0.00917834	+	0.0413292i	0.000412953	+	0.00185949i
$495$	6.22164	+	3.76028i	0.279642	+	0.169012i
$496$	−27.3856	−	22.9110i	−1.22965	−	1.02873i
$497$	0.575432	−	0.575432i	0.0258117	−	0.0258117i
$498$	13.5721	−	21.3211i	0.608179	−	0.955422i
$499$	12.1629	−	12.1629i	0.544488	−	0.544488i	−0.380353	−	0.924841i	$-0.624198\pi$
$499$	12.1629	−	12.1629i	0.544488	−	0.544488i	0.924841	+	0.380353i	$0.124198\pi$
$500$	−8.88145	+	20.5212i	−0.397191	+	0.917736i
$501$	−3.33866	−	3.33866i	−0.149160	−	0.149160i
$502$	−2.24499	−	10.1090i	−0.100199	−	0.451185i
$503$	−13.2748	−	13.2748i	−0.591892	−	0.591892i	0.346250	−	0.938142i	$-0.387455\pi$
$503$	−13.2748	−	13.2748i	−0.591892	−	0.591892i	−0.938142	+	0.346250i	$0.887455\pi$
$504$	7.16701	−	5.51197i	0.319244	−	0.245522i
$505$	6.18505	−	10.2336i	0.275231	−	0.455389i
$506$	−10.3934	+	16.3276i	−0.462045	+	0.725851i
$507$			14.7788i			0.656350i
$508$	−1.33795	+	3.68440i	−0.0593621	+	0.163469i
$509$	9.29995	+	9.29995i	0.412213	+	0.412213i	0.882509	−	0.470296i	$-0.155853\pi$
$509$	9.29995	+	9.29995i	0.412213	+	0.412213i	−0.470296	+	0.882509i	$0.655853\pi$
$510$	10.6938	+	21.5683i	0.473531	+	0.955062i
$511$		−	3.46565i		−	0.153312i
$512$	−20.9334	−	8.59016i	−0.925136	−	0.379635i
$513$	0.0773972	+	0.0773972i	0.00341717	+	0.00341717i
$514$	6.41673	+	28.8939i	0.283030	+	1.27446i
$515$	−17.5345	+	29.0121i	−0.772664	+	1.27843i
$516$	5.12400	−	2.39393i	0.225572	−	0.105387i
$517$	−14.5141			−0.638329
$518$	6.70708	+	30.2013i	0.294692	+	1.32697i
$519$			13.1685i			0.578031i
$520$	−1.09287	−	9.72052i	−0.0479253	−	0.426273i
$521$			33.5279i			1.46888i	0.678671	+	0.734442i	$0.262556\pi$
$521$			33.5279i			1.46888i	−0.678671	+	0.734442i	$0.737444\pi$
$522$	−6.90168	+	1.53272i	−0.302078	+	0.0670852i
$523$	−25.9463			−1.13455			−0.567276	−	0.823528i	$-0.692003\pi$
$523$	−25.9463			−1.13455			−0.567276	+	0.823528i	$0.692003\pi$
$524$	−3.39924	+	9.36067i	−0.148497	+	0.408923i
$525$	−20.0755	−	6.25144i	−0.876165	−	0.272835i
$526$	23.0203	−	5.11233i	1.00373	−	0.222908i
$527$	−34.4903	−	34.4903i	−1.50242	−	1.50242i
$528$	17.0404	−	1.51601i	0.741587	−	0.0659757i
$529$		−	3.12481i		−	0.135861i
$530$	7.38054	−	21.8964i	0.320590	−	0.951119i
$531$	3.73554	+	3.73554i	0.162109	+	0.162109i
$532$	−0.105864	+	0.0494598i	−0.00458980	+	0.00214435i
$533$		−	16.0495i		−	0.695182i
$534$	−22.2274	−	14.1490i	−0.961875	−	0.612287i
$535$	23.6879	−	5.84102i	1.02412	−	0.252529i
$536$	−2.09842	−	0.273916i	−0.0906379	−	0.0118314i
$537$	16.4383	+	16.4383i	0.709365	+	0.709365i
$538$	−4.10247	+	0.911073i	−0.176870	+	0.0392792i
$539$	−4.58248	−	4.58248i	−0.197381	−	0.197381i
$540$	−15.8790	−	19.6834i	−0.683322	−	0.847039i
$541$	4.47122	−	4.47122i	0.192233	−	0.192233i	−0.604428	−	0.796660i	$-0.706598\pi$
$541$	4.47122	−	4.47122i	0.192233	−	0.192233i	0.796660	+	0.604428i	$0.206598\pi$
$542$	22.4997	+	14.3223i	0.966445	+	0.615196i
$543$	3.54085	−	3.54085i	0.151952	−	0.151952i
$544$	−27.4444	−	14.2228i	−1.17667	−	0.609798i
$545$	14.9199	−	24.6859i	0.639096	−	1.05743i
$546$	8.97927	−	1.99411i	0.384277	−	0.0853399i
$547$	15.5964			0.666853			0.333426	−	0.942776i	$-0.391795\pi$
$547$	15.5964			0.666853			0.333426	+	0.942776i	$0.391795\pi$
$548$	5.43067	−	14.9547i	0.231987	−	0.638835i
$549$	1.49990	−	1.49990i	0.0640142	−	0.0640142i
$550$	14.0183	+	16.5740i	0.597741	+	0.706717i
$551$	0.0913677			0.00389239
$552$	13.9255	−	10.7097i	0.592707	−	0.455836i
$553$	−5.98831	+	5.98831i	−0.254649	+	0.254649i
$554$	7.53275	−	11.8336i	0.320036	−	0.502762i
$555$	21.9209	−	5.40529i	0.930488	−	0.229442i
$556$	11.6839	−	32.1745i	0.495506	−	1.36450i
$557$		−	15.5348i		−	0.658231i	−0.944290	−	0.329116i	$-0.893249\pi$
$557$		−	15.5348i		−	0.658231i	0.944290	−	0.329116i	$-0.106751\pi$
$558$	11.2780	+	7.17905i	0.477434	+	0.303913i
$559$	−3.13928			−0.132777
$560$	25.5368	−	8.76100i	1.07913	−	0.370220i
$561$	23.3705			0.986703
$562$	−11.1121	−	7.07349i	−0.468737	−	0.298377i
$563$			24.3087i			1.02449i	0.858839	+	0.512245i	$0.171186\pi$
$563$			24.3087i			1.02449i	−0.858839	+	0.512245i	$0.828814\pi$
$564$	12.3825	+	4.49659i	0.521398	+	0.189341i
$565$	−7.99547	+	13.2291i	−0.336372	+	0.556550i
$566$	−2.59998	+	4.08445i	−0.109285	+	0.171682i
$567$	10.0344	−	10.0344i	0.421405	−	0.421405i
$568$	0.756139	+	0.0987022i	0.0317269	+	0.00414145i
$569$	0.187259			0.00785029			0.00392515	−	0.999992i	$-0.498751\pi$
$569$	0.187259			0.00785029			0.00392515	+	0.999992i	$0.498751\pi$
$570$	0.0378796	+	0.0763991i	0.00158660	+	0.00320001i
$571$	−9.07187	+	9.07187i	−0.379646	+	0.379646i	−0.870974	−	0.491328i	$-0.836511\pi$
$571$	−9.07187	+	9.07187i	−0.379646	+	0.379646i	0.491328	+	0.870974i	$0.336511\pi$
$572$	−8.92566	−	3.24127i	−0.373200	−	0.135524i
$573$	−7.61266			−0.318023
$574$	43.2434	−	9.60346i	1.80495	−	0.400841i
$575$	21.2828	+	6.62740i	0.887554	+	0.276382i
$576$	8.18838	+	2.17479i	0.341182	+	0.0906162i
$577$	−1.53648	+	1.53648i	−0.0639645	+	0.0639645i	−0.738365	−	0.674401i	$-0.764402\pi$
$577$	−1.53648	+	1.53648i	−0.0639645	+	0.0639645i	0.674401	+	0.738365i	$0.264402\pi$
$578$	−15.3408	−	9.76529i	−0.638095	−	0.406183i
$579$	6.72191	−	6.72191i	0.279353	−	0.279353i
$580$	−20.9908	−	2.24557i	−0.871594	−	0.0932424i
$581$	−27.3794	−	27.3794i	−1.13589	−	1.13589i
$582$	−17.2309	+	3.82663i	−0.714244	+	0.158619i
$583$	−15.8616	−	15.8616i	−0.656920	−	0.656920i
$584$	2.57423	−	1.97977i	0.106522	−	0.0819235i
$585$	0.876850	+	3.55602i	0.0362533	+	0.147023i
$586$	3.17903	+	2.02363i	0.131325	+	0.0835954i
$587$			3.06150i			0.126362i	0.998002	+	0.0631808i	$0.0201245\pi$
$587$			3.06150i			0.126362i	−0.998002	+	0.0631808i	$0.979876\pi$
$588$	2.48979	+	5.32917i	0.102677	+	0.219771i
$589$	−0.122171	−	0.122171i	−0.00503398	−	0.00503398i
$590$	7.00724	+	14.1329i	0.288484	+	0.581841i
$591$		−	4.10408i		−	0.168819i
$592$	−18.6015	+	22.2345i	−0.764518	+	0.913833i
$593$	−20.8213	−	20.8213i	−0.855029	−	0.855029i	0.135718	−	0.990747i	$-0.456666\pi$
$593$	−20.8213	−	20.8213i	−0.855029	−	0.855029i	−0.990747	+	0.135718i	$0.956666\pi$
$594$	−23.9671	+	5.32258i	−0.983380	+	0.218388i
$595$	35.8087	−	8.82977i	1.46801	−	0.361985i
$596$	36.0475	+	13.0903i	1.47656	+	0.536200i
$597$	−2.99005			−0.122375
$598$	−9.51927	+	2.11403i	−0.389272	+	0.0864492i
$599$			27.8866i			1.13942i	0.821847	+	0.569709i	$0.192944\pi$
$599$			27.8866i			1.13942i	−0.821847	+	0.569709i	$0.807056\pi$
$600$	−6.82475	−	18.4829i	−0.278619	−	0.754560i
$601$			4.70260i			0.191823i	0.995390	+	0.0959115i	$0.0305766\pi$
$601$			4.70260i			0.191823i	−0.995390	+	0.0959115i	$0.969423\pi$
$602$	−1.87843	−	8.45839i	−0.0765592	−	0.344738i
$603$	0.792365			0.0322676
$604$	17.5396	+	37.5419i	0.713675	+	1.52756i
$605$	−3.42116	+	0.843598i	−0.139090	+	0.0342971i
$606$	2.28419	+	10.2855i	0.0927889	+	0.417819i
$607$	−28.8294	−	28.8294i	−1.17015	−	1.17015i	−0.982174	−	0.187975i	$-0.939807\pi$
$607$	−28.8294	−	28.8294i	−1.17015	−	1.17015i	−0.187975	−	0.982174i	$-0.560193\pi$
$608$	−0.0972133	−	0.0503799i	−0.00394252	−	0.00204317i
$609$		−	19.8507i		−	0.804393i
$610$	5.67465	−	2.81356i	0.229760	−	0.113918i
$611$	−5.17059	−	5.17059i	−0.209180	−	0.209180i
$612$	10.8787	+	3.95050i	0.439746	+	0.159690i
$613$		−	38.7980i		−	1.56704i	−0.621369	−	0.783518i	$-0.713423\pi$
$613$		−	38.7980i		−	1.56704i	0.621369	−	0.783518i	$-0.286577\pi$
$614$	8.01599	−	12.5928i	0.323499	−	0.508203i
$615$	−7.73951	−	31.3872i	−0.312087	−	1.26565i
$616$	3.39240	−	25.9885i	0.136684	−	1.04711i
$617$	−7.06723	−	7.06723i	−0.284516	−	0.284516i	0.550391	−	0.834907i	$-0.314479\pi$
$617$	−7.06723	−	7.06723i	−0.284516	−	0.284516i	−0.834907	+	0.550391i	$0.814479\pi$
$618$	−6.47565	−	29.1592i	−0.260489	−	1.17296i
$619$	−28.1001	−	28.1001i	−1.12944	−	1.12944i	−0.990268	−	0.139172i	$-0.955556\pi$
$619$	−28.1001	−	28.1001i	−1.12944	−	1.12944i	−0.139172	−	0.990268i	$-0.544444\pi$
$620$	25.0649	+	31.0702i	1.00663	+	1.24781i
$621$	−17.8268	+	17.8268i	−0.715363	+	0.715363i
$622$	−15.5500	+	24.4284i	−0.623500	+	0.979490i
$623$	−28.5432	+	28.5432i	−1.14356	+	1.14356i
$624$	6.61064	+	5.53049i	0.264637	+	0.221397i
$625$	14.1935	−	20.5802i	0.567741	−	0.823207i
$626$	−1.22444	−	5.51353i	−0.0489384	−	0.220365i
$627$	0.0827827			0.00330602
$628$	10.3703	−	4.84499i	0.413819	−	0.193336i
$629$	−28.0029	+	28.0029i	−1.11655	+	1.11655i
$630$	−9.05657	+	4.49036i	−0.360822	+	0.178900i
$631$	38.2613			1.52316			0.761580	−	0.648071i	$-0.224424\pi$
$631$	38.2613			1.52316			0.761580	+	0.648071i	$0.224424\pi$
$632$	−7.86886	−	1.02716i	−0.313007	−	0.0408582i
$633$	7.72420	−	7.72420i	0.307010	−	0.307010i
$634$	−24.1625	−	15.3807i	−0.959614	−	0.610847i
$635$	2.26685	−	3.75067i	0.0899574	−	0.148841i
$636$	8.61805	+	18.4462i	0.341728	+	0.731438i
$637$		−	3.26498i		−	0.129363i
$638$	−11.0049	+	17.2883i	−0.435690	+	0.684449i
$639$	−0.285519			−0.0112950
$640$	21.0955	+	13.9635i	0.833874	+	0.551956i
$641$	7.15922			0.282772			0.141386	−	0.989955i	$-0.454844\pi$
$641$	7.15922			0.282772			0.141386	+	0.989955i	$0.454844\pi$
$642$	−11.5438	+	18.1349i	−0.455599	+	0.715726i
$643$			8.74864i			0.345013i	0.985008	+	0.172506i	$0.0551866\pi$
$643$			8.74864i			0.345013i	−0.985008	+	0.172506i	$0.944813\pi$
$644$	−11.3920	−	24.3835i	−0.448907	−	0.960845i
$645$	−6.13931	+	1.51384i	−0.241735	+	0.0596076i
$646$	−0.126180	−	0.0803206i	−0.00496449	−	0.00316017i
$647$	8.84125	−	8.84125i	0.347585	−	0.347585i	−0.511624	−	0.859209i	$-0.670956\pi$
$647$	8.84125	−	8.84125i	0.347585	−	0.347585i	0.859209	+	0.511624i	$0.170956\pi$
$648$	13.1856	+	1.72117i	0.517978	+	0.0676140i
$649$	15.3137			0.601117
$650$	−0.910459	+	10.8984i	−0.0357111	+	0.427469i
$651$	−26.5432	+	26.5432i	−1.04031	+	1.04031i
$652$	−32.5978	+	15.2297i	−1.27663	+	0.596441i
$653$	−20.7854			−0.813396			−0.406698	−	0.913563i	$-0.633320\pi$
$653$	−20.7854			−0.813396			−0.406698	+	0.913563i	$0.633320\pi$
$654$	5.51003	+	24.8111i	0.215459	+	0.970191i
$655$	5.75923	−	9.52904i	0.225032	−	0.372330i
$656$	31.8363	+	26.6344i	1.24300	+	1.03990i
$657$	−0.859797	+	0.859797i	−0.0335439	+	0.0335439i
$658$	10.8376	−	17.0254i	0.422494	−	0.663719i
$659$	13.3330	−	13.3330i	0.519382	−	0.519382i	−0.398003	−	0.917384i	$-0.630297\pi$
$659$	13.3330	−	13.3330i	0.519382	−	0.519382i	0.917384	+	0.398003i	$0.130297\pi$
$660$	−19.0184	−	2.03458i	−0.740292	−	0.0791959i
$661$	−30.5831	−	30.5831i	−1.18954	−	1.18954i	−0.977194	−	0.212350i	$-0.931888\pi$
$661$	−30.5831	−	30.5831i	−1.18954	−	1.18954i	−0.212350	−	0.977194i	$-0.568112\pi$
$662$	−8.45208	−	38.0589i	−0.328499	−	1.47920i
$663$	8.32564	+	8.32564i	0.323341	+	0.323341i
$664$	4.69631	−	35.9775i	0.182252	−	1.39620i
$665$	0.126841	−	0.0312767i	0.00491868	−	0.00121286i
$666$	5.82870	−	9.15663i	0.225858	−	0.354812i
$667$			21.0446i			0.814848i
$668$	−6.37103	−	2.31358i	−0.246503	−	0.0895151i
$669$	1.61836	+	1.61836i	0.0625695	+	0.0625695i
$670$	2.24207	+	0.755725i	0.0866186	+	0.0291962i
$671$		−	6.14880i		−	0.237372i
$672$	−10.9457	+	21.1208i	−0.422238	+	0.814752i
$673$	29.9888	+	29.9888i	1.15598	+	1.15598i	0.985331	+	0.170652i	$0.0545873\pi$
$673$	29.9888	+	29.9888i	1.15598	+	1.15598i	0.170652	+	0.985331i	$0.445413\pi$
$674$	2.55582	+	11.5086i	0.0984464	+	0.443295i
$675$	13.1449	+	25.0336i	0.505949	+	0.963545i
$676$	8.98030	+	19.2215i	0.345396	+	0.739289i
$677$	−33.4274			−1.28472			−0.642360	−	0.766403i	$-0.722044\pi$
$677$	−33.4274			−1.28472			−0.642360	+	0.766403i	$0.722044\pi$
$678$	−2.95279	−	13.2961i	−0.113401	−	0.510635i
$679$			27.0409i			1.03774i
$680$	27.0145	+	21.5540i	1.03596	+	0.826557i
$681$		−	17.8551i		−	0.684211i
$682$	37.8320	−	8.40169i	1.44866	−	0.321717i
$683$	−4.07583			−0.155957			−0.0779787	−	0.996955i	$-0.524847\pi$
$683$	−4.07583			−0.155957			−0.0779787	+	0.996955i	$0.524847\pi$
$684$	0.0385345	+	0.0139934i	0.00147340	+	0.000535052i
$685$	−9.20102	+	15.2237i	−0.351553	+	0.581668i
$686$	−20.3734	+	4.52450i	−0.777858	+	0.172746i
$687$	1.36098	+	1.36098i	0.0519246	+	0.0519246i
$688$	5.20968	−	6.22716i	0.198617	−	0.237408i
$689$		−	11.3013i		−	0.430544i
$690$	−17.5969	+	8.72474i	−0.669901	+	0.332145i
$691$	−8.69768	−	8.69768i	−0.330875	−	0.330875i	0.522044	−	0.852919i	$-0.325170\pi$
$691$	−8.69768	−	8.69768i	−0.330875	−	0.330875i	−0.852919	+	0.522044i	$0.825170\pi$
$692$	8.00177	+	17.1271i	0.304182	+	0.651074i
$693$			9.81330i			0.372776i
$694$	13.6751	+	8.70494i	0.519098	+	0.330435i
$695$	−19.7956	+	32.7532i	−0.750890	+	1.24240i
$696$	14.7448	−	11.3398i	0.558899	−	0.429835i
$697$	40.0956	+	40.0956i	1.51873	+	1.51873i
$698$	−0.620624	+	0.137828i	−0.0234910	+	0.00521685i
$699$	−0.423347	−	0.423347i	−0.0160125	−	0.0160125i
$700$	−29.9091	+	4.06808i	−1.13046	+	0.153759i
$701$	11.8325	−	11.8325i	0.446908	−	0.446908i	−0.447418	−	0.894325i	$-0.647656\pi$
$701$	11.8325	−	11.8325i	0.446908	−	0.446908i	0.894325	+	0.447418i	$0.147656\pi$
$702$	−10.4343	−	6.64202i	−0.393818	−	0.250687i
$703$	−0.0991914	+	0.0991914i	−0.00374108	+	0.00374108i
$704$	21.2417	−	12.3263i	0.800578	−	0.464563i
$705$	−12.6052	−	7.61844i	−0.474740	−	0.286927i
$706$	−36.0323	+	8.00203i	−1.35609	+	0.301160i
$707$	16.1413			0.607056
$708$	−13.0647	−	4.74433i	−0.491002	−	0.178303i
$709$	32.3901	−	32.3901i	1.21643	−	1.21643i	0.247563	−	0.968872i	$-0.420370\pi$
$709$	32.3901	−	32.3901i	1.21643	−	1.21643i	0.968872	−	0.247563i	$-0.0796297\pi$
$710$	−0.807901	−	0.272316i	−0.0303200	−	0.0102198i
$711$	2.97129			0.111432
$712$	−37.5069	−	4.89594i	−1.40563	−	0.183483i
$713$	28.1395	−	28.1395i	1.05383	−	1.05383i
$714$	−17.4506	+	27.4142i	−0.653074	+	1.02595i
$715$	9.08620	+	5.49158i	0.339805	+	0.205373i
$716$	31.3686	+	11.3912i	1.17230	+	0.425709i
$717$		−	17.4282i		−	0.650868i
$718$	−18.5874	−	11.8319i	−0.693676	−	0.441563i
$719$	−4.16893			−0.155475			−0.0777374	−	0.996974i	$-0.524770\pi$
$719$	−4.16893			−0.155475			−0.0777374	+	0.996974i	$0.524770\pi$
$720$	−8.50896	−	4.16192i	−0.317110	−	0.155106i
$721$	−45.7603			−1.70420
$722$	22.6668	+	14.4287i	0.843572	+	0.536980i
$723$			27.2751i			1.01437i
$724$	2.45369	−	6.75686i	0.0911906	−	0.251117i
$725$	22.5350	+	7.01733i	0.836928	+	0.260617i
$726$	1.66724	−	2.61915i	0.0618769	−	0.0972059i
$727$	28.6014	−	28.6014i	1.06077	−	1.06077i	0.0627368	−	0.998030i	$-0.480017\pi$
$727$	28.6014	−	28.6014i	1.06077	−	1.06077i	0.998030	−	0.0627368i	$-0.0199829\pi$
$728$	10.4668	−	8.04978i	0.387927	−	0.298345i
$729$	−28.6142			−1.05979
$730$	−3.25291	+	1.61283i	−0.120396	+	0.0596936i
$731$	7.84269	−	7.84269i	0.290072	−	0.290072i
$732$	−1.90495	+	5.24577i	−0.0704090	+	0.193889i
$733$	18.7069			0.690956			0.345478	−	0.938427i	$-0.387717\pi$
$733$	18.7069			0.690956			0.345478	+	0.938427i	$0.387717\pi$
$734$	10.4941	−	2.33052i	0.387345	−	0.0860212i
$735$	−1.57446	−	6.38514i	−0.0580749	−	0.235519i
$736$	11.6039	−	22.3910i	0.427726	−	0.825342i
$737$	1.62414	−	1.62414i	0.0598259	−	0.0598259i
$738$	−13.1108	−	8.34577i	−0.482616	−	0.307212i
$739$	−34.6914	+	34.6914i	−1.27614	+	1.27614i	−0.333337	+	0.942808i	$0.608175\pi$
$739$	−34.6914	+	34.6914i	−1.27614	+	1.27614i	−0.942808	+	0.333337i	$0.891825\pi$
$740$	25.2260	−	20.3503i	0.927328	−	0.748093i
$741$	0.0294910	+	0.0294910i	0.00108338	+	0.00108338i
$742$	30.4498	−	6.76227i	1.11785	−	0.248251i
$743$	24.7660	+	24.7660i	0.908577	+	0.908577i	0.996157	−	0.0875803i	$-0.0279134\pi$
$743$	24.7660	+	24.7660i	0.908577	+	0.908577i	−0.0875803	+	0.996157i	$0.527913\pi$
$744$	−34.8788	−	4.55288i	−1.27872	−	0.166917i
$745$	−36.6959	−	22.1785i	−1.34443	−	0.812558i
$746$	3.87042	+	2.46374i	0.141706	+	0.0902039i
$747$			13.5852i			0.497055i
$748$	30.3960	−	14.2010i	1.11139	−	0.519240i
$749$	23.2878	+	23.2878i	0.850917	+	0.850917i
$750$	3.47495	+	21.7524i	0.126887	+	0.794285i
$751$			45.2370i			1.65072i	0.564606	+	0.825361i	$0.309028\pi$
$751$			45.2370i			1.65072i	−0.564606	+	0.825361i	$0.690972\pi$
$752$	18.8372	−	1.67586i	0.686922	−	0.0611124i
$753$	−7.21340	−	7.21340i	−0.262871	−	0.262871i
$754$	−10.0793	+	2.23841i	−0.367068	+	0.0815181i
$755$	−11.0914	−	44.9808i	−0.403659	−	1.63702i
$756$	11.6526	−	32.0883i	0.423800	−	1.16704i
$757$	6.44058			0.234087			0.117044	−	0.993127i	$-0.462658\pi$
$757$	6.44058			0.234087			0.117044	+	0.993127i	$0.462658\pi$
$758$	−50.3123	+	11.1733i	−1.82743	+	0.405833i
$759$			19.0672i			0.692095i
$760$	0.0956903	+	0.0763483i	0.00347105	+	0.00276944i
$761$		−	9.50571i		−	0.344582i	−0.985046	−	0.172291i	$-0.944883\pi$
$761$		−	9.50571i		−	0.344582i	0.985046	−	0.172291i	$-0.0551169\pi$
$762$	0.837169	+	3.76969i	0.0303274	+	0.136561i
$763$	38.9367			1.40960
$764$	−9.90112	+	4.62580i	−0.358210	+	0.167356i
$765$	−11.0744	−	6.69322i	−0.400395	−	0.241994i
$766$	−0.181282	−	0.816294i	−0.00654998	−	0.0294939i
$767$	5.45546	+	5.45546i	0.196985	+	0.196985i
$768$	−21.9409	+	3.93511i	−0.791724	+	0.141996i
$769$			46.8513i			1.68950i	0.535159	+	0.844751i	$0.320252\pi$
$769$			46.8513i			1.68950i	−0.535159	+	0.844751i	$0.679748\pi$
$770$	−9.35952	+	27.7676i	−0.337294	+	1.00067i
$771$	20.6176	+	20.6176i	0.742526	+	0.742526i
$772$	4.65806	−	12.8271i	0.167647	−	0.461659i
$773$			10.9964i			0.395513i	0.980251	+	0.197756i	$0.0633655\pi$
$773$			10.9964i			0.395513i	−0.980251	+	0.197756i	$0.936635\pi$
$774$	−1.63243	+	2.56447i	−0.0586764	+	0.0921780i
$775$	−20.7493	−	39.5155i	−0.745335	−	1.41944i
$776$	−20.0855	+	15.4473i	−0.721028	+	0.554524i
$777$	21.5506	+	21.5506i	0.773122	+	0.773122i
$778$	−5.79393	−	26.0895i	−0.207723	−	0.935354i
$779$	0.142026	+	0.142026i	0.00508862	+	0.00508862i
$780$	−6.05043	−	7.50005i	−0.216640	−	0.268545i
$781$	−0.585238	+	0.585238i	−0.0209414	+	0.0209414i
$782$	18.5001	−	29.0628i	0.661562	−	1.03928i
$783$	−18.8756	+	18.8756i	−0.674559	+	0.674559i
$784$	6.47651	+	5.41828i	0.231304	+	0.193510i
$785$	−12.4251	+	3.06381i	−0.443472	+	0.109352i
$786$	2.12693	+	9.57736i	0.0758651	+	0.341613i
$787$	−25.5190			−0.909653			−0.454826	−	0.890580i	$-0.650299\pi$
$787$	−25.5190			−0.909653			−0.454826	+	0.890580i	$0.650299\pi$
$788$	−2.49383	−	5.33782i	−0.0888390	−	0.190152i
$789$	16.4265	−	16.4265i	0.584797	−	0.584797i
$790$	8.40753	+	2.83390i	0.299127	+	0.100826i
$791$	−20.8660			−0.741909
$792$	−7.28914	+	5.60589i	−0.259008	+	0.199197i
$793$	2.19048	−	2.19048i	0.0777864	−	0.0777864i
$794$	16.5102	+	10.5097i	0.585926	+	0.372974i
$795$	−5.44977	−	22.1013i	−0.193283	−	0.783851i
$796$	−3.88890	+	1.81690i	−0.137838	+	0.0643981i
$797$			13.3808i			0.473972i	0.971513	+	0.236986i	$0.0761595\pi$
$797$			13.3808i			0.473972i	−0.971513	+	0.236986i	$0.923840\pi$
$798$	−0.0618134	+	0.0971061i	−0.00218817	+	0.00343752i
$799$	25.8348			0.913969
$800$	−20.1074	−	19.8920i	−0.710904	−	0.703289i
$801$	14.1626			0.500412
$802$	15.4248	−	24.2316i	0.544667	−	0.855648i
$803$			3.52471i			0.124384i
$804$	−1.88878	+	0.882440i	−0.0666123	+	0.0311213i
$805$	7.20391	+	29.2151i	0.253905	+	1.02970i
$806$	16.4706	+	10.4844i	0.580150	+	0.369298i
$807$	−2.92738	+	2.92738i	−0.103049	+	0.103049i
$808$	9.22079	+	11.9895i	0.324386	+	0.421788i
$809$	−52.7958			−1.85620			−0.928102	−	0.372327i	$-0.878560\pi$
$809$	−52.7958			−1.85620			−0.928102	+	0.372327i	$0.878560\pi$
$810$	−14.0882	−	4.74866i	−0.495009	−	0.166851i
$811$	1.57411	−	1.57411i	0.0552745	−	0.0552745i	−0.678929	−	0.734204i	$-0.737556\pi$
$811$	1.57411	−	1.57411i	0.0552745	−	0.0552745i	0.734204	+	0.678929i	$0.237556\pi$
$812$	−12.0622	−	25.8181i	−0.423301	−	0.906039i
$813$	26.2749			0.921500
$814$	−6.82137	−	30.7159i	−0.239089	−	1.07659i
$815$	39.0570	−	9.63075i	1.36811	−	0.337351i
$816$	−30.3315	+	2.69846i	−1.06182	+	0.0944650i
$817$	0.0277803	−	0.0277803i	0.000971909	−	0.000971909i
$818$	−13.8879	+	21.8173i	−0.485579	+	0.762822i
$819$	−3.49595	+	3.49595i	−0.122158	+	0.122158i
$820$	−29.1384	−	36.1197i	−1.01756	−	1.26135i
$821$	−25.7715	−	25.7715i	−0.899431	−	0.899431i	0.0959548	−	0.995386i	$-0.469410\pi$
$821$	−25.7715	−	25.7715i	−0.899431	−	0.899431i	−0.995386	+	0.0959548i	$0.969410\pi$
$822$	−3.39801	−	15.3009i	−0.118519	−	0.533681i
$823$	−17.5565	−	17.5565i	−0.611982	−	0.611982i	0.331480	−	0.943462i	$-0.392452\pi$
$823$	−17.5565	−	17.5565i	−0.611982	−	0.611982i	−0.943462	+	0.331480i	$0.892452\pi$
$824$	−26.1408	−	33.9900i	−0.910658	−	1.18410i
$825$	20.4176	+	6.35797i	0.710848	+	0.221356i
$826$	−11.4347	+	17.9634i	−0.397864	+	0.625027i
$827$		−	14.8548i		−	0.516551i	−0.966071	−	0.258276i	$-0.916846\pi$
$827$		−	14.8548i		−	0.516551i	0.966071	−	0.258276i	$-0.0831543\pi$
$828$	−3.22308	+	8.87558i	−0.112010	+	0.308448i
$829$	−9.71444	−	9.71444i	−0.337397	−	0.337397i	0.517990	−	0.855387i	$-0.326680\pi$
$829$	−9.71444	−	9.71444i	−0.337397	−	0.337397i	−0.855387	+	0.517990i	$0.826680\pi$
$830$	−12.9570	+	38.4404i	−0.449743	+	1.33429i
$831$		−	13.8191i		−	0.479380i
$832$	11.9585	+	3.17610i	0.414585	+	0.110112i
$833$	8.15672	+	8.15672i	0.282614	+	0.282614i
$834$	−7.31069	−	32.9193i	−0.253148	−	1.13990i
$835$	6.48563	+	3.91983i	0.224444	+	0.135651i
$836$	0.107668	−	0.0503026i	0.00372378	−	0.00173975i
$837$	50.4786			1.74480
$838$	−7.50934	−	33.8138i	−0.259406	−	1.16808i
$839$			4.54484i			0.156905i	0.996918	+	0.0784527i	$0.0249979\pi$
$839$			4.54484i			0.156905i	−0.996918	+	0.0784527i	$0.975002\pi$
$840$	16.5876	−	20.7899i	0.572326	−	0.717320i
$841$		−	6.71729i		−	0.231631i
$842$	22.5422	−	5.00615i	0.776855	−	0.172523i
$843$	−12.9766			−0.446938
$844$	5.35262	−	14.7398i	0.184245	−	0.507364i
$845$	−5.67884	−	23.0302i	−0.195358	−	0.792264i
$846$	−6.91256	+	1.53513i	−0.237659	+	0.0527790i
$847$	−3.36337	−	3.36337i	−0.115567	−	0.115567i
$848$	22.4175	+	18.7546i	0.769820	+	0.644036i
$849$			4.76977i			0.163698i
$850$	−24.9523	−	29.5013i	−0.855855	−	1.01189i
$851$	−22.8466	−	22.8466i	−0.783171	−	0.783171i
$852$	0.680600	−	0.317976i	0.0233170	−	0.0108937i
$853$			37.3745i			1.27968i	0.768509	+	0.639839i	$0.220999\pi$
$853$			37.3745i			1.27968i	−0.768509	+	0.639839i	$0.779001\pi$
$854$	7.21269	+	4.59128i	0.246813	+	0.157110i
$855$	−0.0392276	−	0.0237086i	−0.00134155	−	0.000810818i
$856$	−3.99449	+	30.6010i	−0.136529	+	1.04592i
$857$	−16.4541	−	16.4541i	−0.562062	−	0.562062i	0.367831	−	0.929893i	$-0.380101\pi$
$857$	−16.4541	−	16.4541i	−0.562062	−	0.562062i	−0.929893	+	0.367831i	$0.880101\pi$
$858$	−9.13228	+	2.02809i	−0.311771	+	0.0692378i
$859$	15.7662	+	15.7662i	0.537935	+	0.537935i	0.922922	−	0.384987i	$-0.125794\pi$
$859$	15.7662	+	15.7662i	0.537935	+	0.537935i	−0.384987	+	0.922922i	$0.625794\pi$
$860$	−7.06499	+	5.69946i	−0.240914	+	0.194350i
$861$	30.8570	−	30.8570i	1.05160	−	1.05160i
$862$	−19.0261	−	12.1112i	−0.648032	−	0.412508i
$863$	22.6395	−	22.6395i	0.770659	−	0.770659i	−0.207563	−	0.978222i	$-0.566553\pi$
$863$	22.6395	−	22.6395i	0.770659	−	0.770659i	0.978222	+	0.207563i	$0.0665532\pi$
$864$	30.4912	−	9.67528i	1.03733	−	0.329160i
$865$	−5.06005	−	20.5208i	−0.172047	−	0.697727i
$866$	6.87470	−	1.52673i	0.233612	−	0.0518803i
$867$	−17.9148			−0.608419
$868$	−18.3936	+	50.6513i	−0.624318	+	1.71922i
$869$	6.09036	−	6.09036i	0.206601	−	0.206601i
$870$	−18.6322	+	9.23806i	−0.631690	+	0.313200i
$871$	1.15719			0.0392097
$872$	22.2428	+	28.9215i	0.753236	+	0.979406i
$873$	6.70861	−	6.70861i	0.227052	−	0.227052i
$874$	0.0655308	−	0.102946i	0.00221661	−	0.00348220i
$875$	33.6863	+	2.02769i	1.13880	+	0.0685483i
$876$	1.09199	−	3.00706i	0.0368948	−	0.101599i
$877$			30.0542i			1.01486i	0.861694	+	0.507429i	$0.169404\pi$
$877$			30.0542i			1.01486i	−0.861694	+	0.507429i	$0.830596\pi$
$878$	7.70496	+	4.90463i	0.260030	+	0.165523i
$879$	3.71243			0.125217
$880$	−25.9719	+	8.91029i	−0.875514	+	0.300366i
$881$	−3.86747			−0.130298			−0.0651492	−	0.997876i	$-0.520752\pi$
$881$	−3.86747			−0.130298			−0.0651492	+	0.997876i	$0.520752\pi$
$882$	−2.66716	−	1.69779i	−0.0898078	−	0.0571677i
$883$		−	0.485919i		−	0.0163525i	−0.999967	−	0.00817624i	$-0.997397\pi$
$883$		−	0.485919i		−	0.0163525i	0.999967	−	0.00817624i	$-0.00260261\pi$
$884$	15.8875	+	5.76939i	0.534354	+	0.194046i
$885$	13.2997	+	8.03817i	0.447065	+	0.270200i
$886$	20.5797	−	32.3297i	0.691388	−	1.08614i
$887$	12.9762	−	12.9762i	0.435699	−	0.435699i	−0.454863	−	0.890561i	$-0.650312\pi$
$887$	12.9762	−	12.9762i	0.435699	−	0.435699i	0.890561	+	0.454863i	$0.150312\pi$
$888$	−3.69650	+	28.3182i	−0.124047	+	0.950297i
$889$	5.91587			0.198412
$890$	40.0744	+	13.5077i	1.34330	+	0.452781i
$891$	−10.2054	+	10.2054i	−0.341893	+	0.341893i
$892$	3.08825	+	1.12147i	0.103402	+	0.0375496i
$893$	0.0915117			0.00306232
$894$	36.8820	−	8.19071i	1.23352	−	0.273938i
$895$	−31.9328	−	19.2998i	−1.06739	−	0.645120i
$896$	−1.40209	+	34.1210i	−0.0468406	+	1.13990i
$897$	−6.79261	+	6.79261i	−0.226799	+	0.226799i
$898$	49.0184	+	31.2030i	1.63577	+	1.04126i
$899$	29.7951	−	29.7951i	0.993722	−	0.993722i
$900$	8.42942	+	6.41092i	0.280981	+	0.213697i
$901$	28.2333	+	28.2333i	0.940588	+	0.940588i
$902$	−43.9803	+	9.76711i	−1.46438	+	0.325209i
$903$	−6.03560	−	6.03560i	−0.200852	−	0.200852i
$904$	−11.9198	−	15.4989i	−0.396446	−	0.515485i
$905$	−4.15721	+	6.87839i	−0.138190	+	0.228645i
$906$	34.4361	+	21.9205i	1.14406	+	0.728259i
$907$		−	54.3645i		−	1.80514i	−0.430540	−	0.902571i	$-0.641677\pi$
$907$		−	54.3645i		−	1.80514i	0.430540	−	0.902571i	$-0.358323\pi$
$908$	−10.8496	−	23.2226i	−0.360057	−	0.770670i
$909$	−4.00451	−	4.00451i	−0.132821	−	0.132821i
$910$	−13.2264	+	6.55780i	−0.438450	+	0.217389i
$911$			40.0402i			1.32659i	0.748358	+	0.663295i	$0.230843\pi$
$911$			40.0402i			1.32659i	−0.748358	+	0.663295i	$0.769157\pi$
$912$	−0.107440	+	0.00955845i	−0.00355769	+	0.000316512i
$913$	27.8460	+	27.8460i	0.921567	+	0.921567i
$914$	35.6220	−	7.91090i	1.17827	−	0.261669i
$915$	3.22750	−	5.34012i	0.106698	−	0.176539i
$916$	2.59710	+	0.943112i	0.0858106	+	0.0311613i
$917$	15.0300			0.496335
$918$	42.6609	−	9.47409i	1.40802	−	0.312691i
$919$		−	8.81475i		−	0.290772i	−0.989375	−	0.145386i	$-0.953558\pi$
$919$		−	8.81475i		−	0.290772i	0.989375	−	0.145386i	$-0.0464423\pi$
$920$	−17.5852	+	22.0402i	−0.579765	+	0.726643i
$921$		−	14.7057i		−	0.484568i
$922$	−2.89989	−	13.0579i	−0.0955028	−	0.430040i
$923$	−0.416977			−0.0137250
$924$	−10.9289	−	23.3922i	−0.359533	−	0.769548i
$925$	−32.0828	+	16.8464i	−1.05488	+	0.553907i
$926$	−12.4410	−	56.0204i	−0.408835	−	1.84095i
$927$	11.3527	+	11.3527i	0.372872	+	0.372872i
$928$	12.2866	−	23.7083i	0.403329	−	0.778264i
$929$		−	47.9673i		−	1.57376i	−0.617109	−	0.786878i	$-0.711696\pi$
$929$		−	47.9673i		−	1.57376i	0.617109	−	0.786878i	$-0.288304\pi$
$930$	37.2664	+	12.5613i	1.22201	+	0.411900i
$931$	0.0288926	+	0.0288926i	0.000946918	+	0.000946918i
$932$	−0.807856	−	0.293365i	−0.0264622	−	0.00960951i
$933$			28.5272i			0.933938i
$934$	−24.6174	+	38.6728i	−0.805506	+	1.26541i
$935$	−36.4189	+	8.98024i	−1.19102	+	0.293685i
$936$	−4.59380	−	0.599650i	−0.150153	−	0.0196002i
$937$	−13.8299	−	13.8299i	−0.451803	−	0.451803i	0.444150	−	0.895953i	$-0.353506\pi$
$937$	−13.8299	−	13.8299i	−0.451803	−	0.451803i	−0.895953	+	0.444150i	$0.853506\pi$
$938$	0.692418	+	3.11789i	0.0226083	+	0.101803i
$939$	−3.93426	−	3.93426i	−0.128390	−	0.128390i
$940$	−21.0238	−	2.24912i	−0.685722	−	0.0733580i
$941$	−5.19108	+	5.19108i	−0.169224	+	0.169224i	−0.786638	−	0.617414i	$-0.788180\pi$
$941$	−5.19108	+	5.19108i	−0.169224	+	0.169224i	0.617414	+	0.786638i	$0.288180\pi$
$942$	6.05513	−	9.51234i	0.197287	−	0.309929i
$943$	−32.7127	+	32.7127i	−1.06527	+	1.06527i
$944$	−19.8750	+	1.76819i	−0.646877	+	0.0575498i
$945$	−19.7426	+	32.6655i	−0.642226	+	1.06261i
$946$	1.91044	+	8.60253i	0.0621138	+	0.279692i
$947$	−24.1342			−0.784255			−0.392128	−	0.919911i	$-0.628261\pi$
$947$	−24.1342			−0.784255			−0.392128	+	0.919911i	$0.628261\pi$
$948$	−7.08275	+	3.30906i	−0.230037	+	0.107473i
$949$	−1.25566	+	1.25566i	−0.0407606	+	0.0407606i
$950$	−0.0883856	−	0.104499i	−0.00286761	−	0.00339041i
$951$	−28.2166			−0.914986
$952$	−6.03840	+	46.2590i	−0.195706	+	1.49926i
$953$	−22.8500	+	22.8500i	−0.740183	+	0.740183i	−0.972613	−	0.232430i	$-0.925332\pi$
$953$	−22.8500	+	22.8500i	−0.740183	+	0.740183i	0.232430	+	0.972613i	$0.425332\pi$
$954$	−9.23198	−	5.87667i	−0.298896	−	0.190264i
$955$	11.8630	−	2.92521i	0.383878	−	0.0946574i
$956$	−10.5902	−	22.6673i	−0.342511	−	0.733114i
$957$			20.1890i			0.652618i
$958$	5.56743	−	8.74618i	0.179876	−	0.282576i
$959$	−24.0121			−0.775392
$960$	24.9181	+	0.444635i	0.804228	+	0.0143505i
$961$	−48.6804			−1.57034
$962$	8.51235	−	13.3725i	0.274449	−	0.431147i
$963$		−	11.5550i		−	0.372354i
$964$	16.5736	+	35.4743i	0.533799	+	1.14255i
$965$	−7.89200	+	13.0579i	−0.254052	+	0.420347i
$966$	−22.3663	−	14.2374i	−0.719624	−	0.458080i
$967$	−21.4211	+	21.4211i	−0.688855	+	0.688855i	−0.961979	−	0.273124i	$-0.911943\pi$
$967$	−21.4211	+	21.4211i	−0.688855	+	0.688855i	0.273124	+	0.961979i	$0.411943\pi$
$968$	0.576910	−	4.41959i	0.0185426	−	0.142051i
$969$	−0.147351			−0.00473361
$970$	25.3810	−	12.5842i	0.814935	−	0.404055i
$971$	−11.7978	+	11.7978i	−0.378609	+	0.378609i	−0.870600	−	0.491991i	$-0.836269\pi$
$971$	−11.7978	+	11.7978i	−0.378609	+	0.378609i	0.491991	+	0.870600i	$0.336269\pi$
$972$	−18.8721	+	8.81706i	−0.605324	+	0.282807i
$973$	−51.6611			−1.65618
$974$	5.10658	+	22.9944i	0.163625	+	0.736788i
$975$	5.00867	+	9.53868i	0.160406	+	0.305482i
$976$	0.709967	+	7.98025i	0.0227255	+	0.255442i
$977$	2.15703	−	2.15703i	0.0690096	−	0.0690096i	−0.671760	−	0.740769i	$-0.734461\pi$
$977$	2.15703	−	2.15703i	0.0690096	−	0.0690096i	0.740769	+	0.671760i	$0.234461\pi$
$978$	−19.0336	+	29.9010i	−0.608629	+	0.956129i
$979$	29.0296	−	29.0296i	0.927791	−	0.927791i
$980$	−5.92767	−	7.34788i	−0.189353	−	0.234719i
$981$	−9.65985	−	9.65985i	−0.308415	−	0.308415i
$982$	11.8613	+	53.4101i	0.378508	+	1.70438i
$983$	19.9712	+	19.9712i	0.636983	+	0.636983i	0.949810	−	0.312827i	$-0.101276\pi$
$983$	19.9712	+	19.9712i	0.636983	+	0.636983i	−0.312827	+	0.949810i	$0.601276\pi$
$984$	40.5472	+	5.29280i	1.29260	+	0.168728i
$985$	1.57702	+	6.39550i	0.0502479	+	0.203778i
$986$	19.5886	−	30.7728i	0.623827	−	0.980004i
$987$		−	19.8820i		−	0.632852i
$988$	0.0562765	+	0.0204363i	0.00179039	+	0.000650164i
$989$	6.39858	+	6.39858i	0.203463	+	0.203463i
$990$	9.21090	−	4.56687i	0.292741	−	0.145145i
$991$		−	19.2270i		−	0.610767i	−0.952230	−	0.305383i	$-0.901215\pi$
$991$		−	19.2270i		−	0.610767i	0.952230	−	0.305383i	$-0.0987846\pi$
$992$	−48.1303	+	15.2724i	−1.52814	+	0.484900i
$993$	−27.1574	−	27.1574i	−0.861815	−	0.861815i
$994$	−0.249504	−	1.12349i	−0.00791379	−	0.0356350i
$995$	4.65948	−	1.14894i	0.147715	−	0.0364240i
$996$	−15.1295	−	32.3833i	−0.479396	−	1.02611i
$997$	−2.01694			−0.0638771			−0.0319385	−	0.999490i	$-0.510168\pi$
$997$	−2.01694			−0.0638771			−0.0319385	+	0.999490i	$0.510168\pi$
$998$	−5.27379	−	23.7473i	−0.166939	−	0.751709i
$999$		−	40.9838i		−	1.29667i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.2.j.b.43.8	✓	18
3.2	odd	2		720.2.bd.g.523.2		18
4.3	odd	2		320.2.j.b.143.7		18
5.2	odd	4		80.2.s.b.27.8	yes	18
5.3	odd	4		400.2.s.d.107.2		18
5.4	even	2		400.2.j.d.43.2		18
8.3	odd	2		640.2.j.c.543.3		18
8.5	even	2		640.2.j.d.543.7		18
15.2	even	4		720.2.z.g.667.2		18
16.3	odd	4		80.2.s.b.3.8	yes	18
16.5	even	4		640.2.s.c.223.3		18
16.11	odd	4		640.2.s.d.223.7		18
16.13	even	4		320.2.s.b.303.7		18
20.3	even	4		1600.2.s.d.207.3		18
20.7	even	4		320.2.s.b.207.7		18
20.19	odd	2		1600.2.j.d.143.3		18
40.27	even	4		640.2.s.c.287.3		18
40.37	odd	4		640.2.s.d.287.7		18
48.35	even	4		720.2.z.g.163.2		18
80.3	even	4		400.2.j.d.307.2		18
80.13	odd	4		1600.2.j.d.1007.7		18
80.19	odd	4		400.2.s.d.243.2		18
80.27	even	4		640.2.j.d.607.3		18
80.29	even	4		1600.2.s.d.943.3		18
80.37	odd	4		640.2.j.c.607.7		18
80.67	even	4	inner	80.2.j.b.67.8	yes	18
80.77	odd	4		320.2.j.b.47.3		18
240.227	odd	4		720.2.bd.g.307.2		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.b.43.8	✓	18	1.1	even	1	trivial
80.2.j.b.67.8	yes	18	80.67	even	4	inner
80.2.s.b.3.8	yes	18	16.3	odd	4
80.2.s.b.27.8	yes	18	5.2	odd	4
320.2.j.b.47.3		18	80.77	odd	4
320.2.j.b.143.7		18	4.3	odd	2
320.2.s.b.207.7		18	20.7	even	4
320.2.s.b.303.7		18	16.13	even	4
400.2.j.d.43.2		18	5.4	even	2
400.2.j.d.307.2		18	80.3	even	4
400.2.s.d.107.2		18	5.3	odd	4
400.2.s.d.243.2		18	80.19	odd	4
640.2.j.c.543.3		18	8.3	odd	2
640.2.j.c.607.7		18	80.37	odd	4
640.2.j.d.543.7		18	8.5	even	2
640.2.j.d.607.3		18	80.27	even	4
640.2.s.c.223.3		18	16.5	even	4
640.2.s.c.287.3		18	40.27	even	4
640.2.s.d.223.7		18	16.11	odd	4
640.2.s.d.287.7		18	40.37	odd	4
720.2.z.g.163.2		18	48.35	even	4
720.2.z.g.667.2		18	15.2	even	4
720.2.bd.g.307.2		18	240.227	odd	4
720.2.bd.g.523.2		18	3.2	odd	2
1600.2.j.d.143.3		18	20.19	odd	2
1600.2.j.d.1007.7		18	80.13	odd	4
1600.2.s.d.207.3		18	20.3	even	4
1600.2.s.d.943.3		18	80.29	even	4

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:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	80.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.759419 - 1.19301i) q^{2} -1.39319i q^{3} +(-0.846564 - 1.81200i) q^{4} +(0.535339 + 2.17104i) q^{5} +(-1.66209 - 1.05801i) q^{6} +(-2.13436 + 2.13436i) q^{7} +(-2.80463 - 0.366101i) q^{8} +1.05903 q^{9} +O(q^{10})\)	\(q+(0.759419 - 1.19301i) q^{2} -1.39319i q^{3} +(-0.846564 - 1.81200i) q^{4} +(0.535339 + 2.17104i) q^{5} +(-1.66209 - 1.05801i) q^{6} +(-2.13436 + 2.13436i) q^{7} +(-2.80463 - 0.366101i) q^{8} +1.05903 q^{9} +(2.99663 + 1.01006i) q^{10} +(2.17074 - 2.17074i) q^{11} +(-2.52445 + 1.17942i) q^{12} +1.54663 q^{13} +(0.925449 + 4.16720i) q^{14} +(3.02466 - 0.745827i) q^{15} +(-2.56666 + 3.06794i) q^{16} +(-3.86386 + 3.86386i) q^{17} +(0.804250 - 1.26344i) q^{18} +(-0.0136865 + 0.0136865i) q^{19} +(3.48071 - 2.80796i) q^{20} +(2.97357 + 2.97357i) q^{21} +(-0.941219 - 4.23822i) q^{22} +(-3.15240 - 3.15240i) q^{23} +(-0.510047 + 3.90738i) q^{24} +(-4.42682 + 2.32449i) q^{25} +(1.17454 - 1.84515i) q^{26} -5.65499i q^{27} +(5.67434 + 2.06058i) q^{28} +(-3.33787 - 3.33787i) q^{29} +(1.40720 - 4.17486i) q^{30} +8.92639i q^{31} +(1.71093 + 5.39191i) q^{32} +(-3.02424 - 3.02424i) q^{33} +(1.67535 + 7.54394i) q^{34} +(-5.77640 - 3.49118i) q^{35} +(-0.896540 - 1.91896i) q^{36} +7.24737 q^{37} +(0.00593441 + 0.0267220i) q^{38} -2.15475i q^{39} +(-0.706610 - 6.28496i) q^{40} -10.3771i q^{41} +(5.80569 - 1.28932i) q^{42} -2.02975 q^{43} +(-5.77103 - 2.09570i) q^{44} +(0.566942 + 2.29920i) q^{45} +(-6.15484 + 1.36686i) q^{46} +(-3.34313 - 3.34313i) q^{47} +(4.27421 + 3.57583i) q^{48} -2.11103i q^{49} +(-0.588672 + 7.04652i) q^{50} +(5.38308 + 5.38308i) q^{51} +(-1.30932 - 2.80249i) q^{52} -7.30702i q^{53} +(-6.74648 - 4.29451i) q^{54} +(5.87483 + 3.55067i) q^{55} +(6.76751 - 5.20472i) q^{56} +(0.0190679 + 0.0190679i) q^{57} +(-6.51696 + 1.44728i) q^{58} +(3.52732 + 3.52732i) q^{59} +(-3.91201 - 4.84928i) q^{60} +(1.41629 - 1.41629i) q^{61} +(10.6493 + 6.77887i) q^{62} +(-2.26036 + 2.26036i) q^{63} +(7.73194 + 2.05356i) q^{64} +(0.827973 + 3.35780i) q^{65} +(-5.90462 + 1.31129i) q^{66} +0.748197 q^{67} +(10.2723 + 3.73030i) q^{68} +(-4.39187 + 4.39187i) q^{69} +(-8.55174 + 4.24005i) q^{70} -0.269603 q^{71} +(-2.97020 - 0.387713i) q^{72} +(-0.811870 + 0.811870i) q^{73} +(5.50380 - 8.64622i) q^{74} +(3.23844 + 6.16739i) q^{75} +(0.0363865 + 0.0132134i) q^{76} +9.26628i q^{77} +(-2.57064 - 1.63636i) q^{78} +2.80567 q^{79} +(-8.03466 - 3.92992i) q^{80} -4.70135 q^{81} +(-12.3800 - 7.88056i) q^{82} +12.8279i q^{83} +(2.87077 - 7.90541i) q^{84} +(-10.4571 - 6.32012i) q^{85} +(-1.54143 + 2.42152i) q^{86} +(-4.65027 + 4.65027i) q^{87} +(-6.88283 + 5.29341i) q^{88} +13.3732 q^{89} +(3.17353 + 1.06969i) q^{90} +(-3.30108 + 3.30108i) q^{91} +(-3.04342 + 8.38083i) q^{92} +12.4361 q^{93} +(-6.52724 + 1.44956i) q^{94} +(-0.0370409 - 0.0223871i) q^{95} +(7.51194 - 2.38364i) q^{96} +(6.33466 - 6.33466i) q^{97} +(-2.51848 - 1.60315i) q^{98} +(2.29888 - 2.29888i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 4 q^{2} - 4 q^{4} - 4 q^{5} - 8 q^{6} + 2 q^{7} - 4 q^{8} - 10 q^{9}+O(q^{10}) \) 18 * q - 4 * q^2 - 4 * q^4 - 4 * q^5 - 8 * q^6 + 2 * q^7 - 4 * q^8 - 10 * q^9	\( 18 q - 4 q^{2} - 4 q^{4} - 4 q^{5} - 8 q^{6} + 2 q^{7} - 4 q^{8} - 10 q^{9} - 12 q^{10} - 2 q^{11} + 4 q^{12} + 12 q^{14} + 20 q^{15} - 6 q^{17} + 16 q^{18} + 2 q^{19} - 4 q^{20} - 16 q^{21} + 4 q^{22} - 2 q^{23} + 4 q^{24} + 6 q^{25} - 16 q^{26} - 4 q^{28} - 14 q^{29} + 20 q^{30} - 4 q^{32} - 8 q^{33} - 28 q^{34} - 6 q^{35} - 4 q^{36} + 8 q^{37} + 16 q^{38} + 20 q^{40} + 28 q^{42} - 44 q^{43} + 44 q^{44} - 4 q^{45} + 12 q^{46} - 38 q^{47} + 60 q^{48} + 20 q^{50} + 8 q^{51} - 40 q^{52} - 4 q^{54} - 6 q^{55} + 20 q^{56} + 24 q^{57} - 20 q^{58} - 10 q^{59} - 68 q^{60} + 14 q^{61} + 6 q^{63} - 16 q^{64} + 4 q^{66} + 12 q^{67} + 36 q^{68} + 32 q^{69} - 36 q^{70} + 24 q^{71} - 36 q^{72} + 14 q^{73} + 48 q^{74} + 64 q^{75} - 16 q^{76} - 84 q^{78} + 16 q^{79} - 20 q^{80} + 2 q^{81} - 28 q^{82} - 24 q^{84} - 10 q^{85} - 36 q^{86} + 24 q^{87} - 96 q^{88} - 12 q^{89} - 64 q^{90} + 52 q^{92} + 16 q^{93} + 28 q^{94} - 34 q^{95} - 40 q^{96} + 18 q^{97} + 32 q^{98} - 22 q^{99}+O(q^{100}) \) 18 * q - 4 * q^2 - 4 * q^4 - 4 * q^5 - 8 * q^6 + 2 * q^7 - 4 * q^8 - 10 * q^9 - 12 * q^10 - 2 * q^11 + 4 * q^12 + 12 * q^14 + 20 * q^15 - 6 * q^17 + 16 * q^18 + 2 * q^19 - 4 * q^20 - 16 * q^21 + 4 * q^22 - 2 * q^23 + 4 * q^24 + 6 * q^25 - 16 * q^26 - 4 * q^28 - 14 * q^29 + 20 * q^30 - 4 * q^32 - 8 * q^33 - 28 * q^34 - 6 * q^35 - 4 * q^36 + 8 * q^37 + 16 * q^38 + 20 * q^40 + 28 * q^42 - 44 * q^43 + 44 * q^44 - 4 * q^45 + 12 * q^46 - 38 * q^47 + 60 * q^48 + 20 * q^50 + 8 * q^51 - 40 * q^52 - 4 * q^54 - 6 * q^55 + 20 * q^56 + 24 * q^57 - 20 * q^58 - 10 * q^59 - 68 * q^60 + 14 * q^61 + 6 * q^63 - 16 * q^64 + 4 * q^66 + 12 * q^67 + 36 * q^68 + 32 * q^69 - 36 * q^70 + 24 * q^71 - 36 * q^72 + 14 * q^73 + 48 * q^74 + 64 * q^75 - 16 * q^76 - 84 * q^78 + 16 * q^79 - 20 * q^80 + 2 * q^81 - 28 * q^82 - 24 * q^84 - 10 * q^85 - 36 * q^86 + 24 * q^87 - 96 * q^88 - 12 * q^89 - 64 * q^90 + 52 * q^92 + 16 * q^93 + 28 * q^94 - 34 * q^95 - 40 * q^96 + 18 * q^97 + 32 * q^98 - 22 * q^99

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