LMFDB - Embedded newform 392.2.p.f.165.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [392,2,Mod(165,392)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(392, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("392.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 392 = 2^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	392.p (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.13013575923$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.432972864.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{6} + 4x^{5} - 6x^{4} + 8x^{3} + 4x^{2} - 8x + 16 $ x^8 - x^7 + x^6 + 4x^5 - 6x^4 + 8x^3 + 4x^2 - 8*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			165.1
Root			$-1.41156 + 0.0865986i$ of defining polynomial
Character	$\chi$	$=$	392.165
Dual form			392.2.p.f.373.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41156 - 0.0865986i) q^{2} +(-2.61578 - 1.51022i) q^{3} +(1.98500 + 0.244478i) q^{4} +(-1.46890 + 0.848071i) q^{5} +(3.56155 + 2.35829i) q^{6} +(-2.78078 - 0.516994i) q^{8} +(3.06155 + 5.30277i) q^{9} +O(q^{10})$	\(q+(-1.41156 - 0.0865986i) q^{2} +(-2.61578 - 1.51022i) q^{3} +(1.98500 + 0.244478i) q^{4} +(-1.46890 + 0.848071i) q^{5} +(3.56155 + 2.35829i) q^{6} +(-2.78078 - 0.516994i) q^{8} +(3.06155 + 5.30277i) q^{9} +(2.14688 - 1.06990i) q^{10} +(1.14688 + 0.662153i) q^{11} +(-4.82312 - 3.63730i) q^{12} +1.69614i q^{13} +5.12311 q^{15} +(3.88046 + 0.970579i) q^{16} +(-1.00000 + 1.73205i) q^{17} +(-3.86235 - 7.75030i) q^{18} +(2.61578 - 1.51022i) q^{19} +(-3.12311 + 1.32431i) q^{20} +(-1.56155 - 1.03399i) q^{22} +(-2.56155 - 4.43674i) q^{23} +(6.49314 + 5.55194i) q^{24} +(-1.06155 + 1.83866i) q^{25} +(0.146883 - 2.39420i) q^{26} -9.43318i q^{27} -6.04090i q^{29} +(-7.23157 - 0.443654i) q^{30} +(5.12311 - 8.87348i) q^{31} +(-5.39345 - 1.70607i) q^{32} +(-2.00000 - 3.46410i) q^{33} +(1.56155 - 2.35829i) q^{34} +(4.78078 + 11.2745i) q^{36} +(5.23157 - 3.02045i) q^{37} +(-3.82312 + 1.90525i) q^{38} +(2.56155 - 4.43674i) q^{39} +(4.52313 - 1.59888i) q^{40} +4.24621 q^{41} -1.32431i q^{43} +(2.11468 + 1.59476i) q^{44} +(-8.99424 - 5.19283i) q^{45} +(3.23157 + 6.48455i) q^{46} +(-8.68466 - 8.39919i) q^{48} +(1.65767 - 2.50345i) q^{50} +(5.23157 - 3.02045i) q^{51} +(-0.414669 + 3.36684i) q^{52} +(2.29377 + 1.32431i) q^{53} +(-0.816900 + 13.3155i) q^{54} -2.24621 q^{55} -9.12311 q^{57} +(-0.523133 + 8.52708i) q^{58} +(0.322018 + 0.185917i) q^{59} +(10.1694 + 1.25249i) q^{60} +(1.46890 - 0.848071i) q^{61} +(-8.00000 + 12.0818i) q^{62} +(7.46543 + 2.87529i) q^{64} +(-1.43845 - 2.49146i) q^{65} +(2.52313 + 5.06298i) q^{66} +(9.96029 + 5.75058i) q^{67} +(-2.40845 + 3.19365i) q^{68} +15.4741i q^{69} -8.00000 q^{71} +(-5.77200 - 16.3286i) q^{72} +(3.00000 - 5.19615i) q^{73} +(-7.64624 + 3.81050i) q^{74} +(5.55359 - 3.20636i) q^{75} +(5.56155 - 2.35829i) q^{76} +(-4.00000 + 6.04090i) q^{78} +(-6.52313 + 1.86522i) q^{80} +(-5.06155 + 8.76687i) q^{81} +(-5.99378 - 0.367716i) q^{82} -5.66906i q^{83} -3.39228i q^{85} +(-0.114683 + 1.86934i) q^{86} +(-9.12311 + 15.8017i) q^{87} +(-2.84690 - 2.43423i) q^{88} +(8.12311 + 14.0696i) q^{89} +(12.2462 + 8.10887i) q^{90} +(-4.00000 - 9.43318i) q^{92} +(-26.8019 + 15.4741i) q^{93} +(-2.56155 + 4.43674i) q^{95} +(11.5316 + 12.6080i) q^{96} +12.2462 q^{97} +8.10887i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} - q^{4} + 12 q^{6} - 14 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q + q^2 - q^4 + 12 * q^6 - 14 * q^8 + 8 * q^9	$ 8 q + q^{2} - q^{4} + 12 q^{6} - 14 q^{8} + 8 q^{9} + 8 q^{10} - 14 q^{12} + 8 q^{15} + 7 q^{16} - 8 q^{17} + 15 q^{18} + 8 q^{20} + 4 q^{22} - 4 q^{23} + 2 q^{24} + 8 q^{25} - 8 q^{26} - 16 q^{30} + 8 q^{31} - 9 q^{32} - 16 q^{33} - 4 q^{34} + 30 q^{36} - 6 q^{38} + 4 q^{39} + 20 q^{40} - 32 q^{41} + 18 q^{44} - 16 q^{46} - 20 q^{48} + 38 q^{50} + 4 q^{52} + 28 q^{54} + 48 q^{55} - 40 q^{57} + 12 q^{58} + 16 q^{60} - 64 q^{62} + 2 q^{64} - 28 q^{65} + 4 q^{66} - 2 q^{68} - 64 q^{71} - 31 q^{72} + 24 q^{73} - 12 q^{74} + 28 q^{76} - 32 q^{78} - 36 q^{80} - 24 q^{81} - 38 q^{82} - 2 q^{86} - 40 q^{87} - 22 q^{88} + 32 q^{89} + 32 q^{90} - 32 q^{92} - 4 q^{95} + 42 q^{96} + 32 q^{97}+O(q^{100}) $ 8 * q + q^2 - q^4 + 12 * q^6 - 14 * q^8 + 8 * q^9 + 8 * q^10 - 14 * q^12 + 8 * q^15 + 7 * q^16 - 8 * q^17 + 15 * q^18 + 8 * q^20 + 4 * q^22 - 4 * q^23 + 2 * q^24 + 8 * q^25 - 8 * q^26 - 16 * q^30 + 8 * q^31 - 9 * q^32 - 16 * q^33 - 4 * q^34 + 30 * q^36 - 6 * q^38 + 4 * q^39 + 20 * q^40 - 32 * q^41 + 18 * q^44 - 16 * q^46 - 20 * q^48 + 38 * q^50 + 4 * q^52 + 28 * q^54 + 48 * q^55 - 40 * q^57 + 12 * q^58 + 16 * q^60 - 64 * q^62 + 2 * q^64 - 28 * q^65 + 4 * q^66 - 2 * q^68 - 64 * q^71 - 31 * q^72 + 24 * q^73 - 12 * q^74 + 28 * q^76 - 32 * q^78 - 36 * q^80 - 24 * q^81 - 38 * q^82 - 2 * q^86 - 40 * q^87 - 22 * q^88 + 32 * q^89 + 32 * q^90 - 32 * q^92 - 4 * q^95 + 42 * q^96 + 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$297$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.41156	−	0.0865986i	−0.998123	−	0.0612344i
$2$	−1.41156	−	0.0865986i	−0.998123	−	0.0612344i
$3$	−2.61578	−	1.51022i	−1.51022	−	0.871928i	−0.999929	−	0.0119288i	$-0.996203\pi$
$3$	−2.61578	−	1.51022i	−1.51022	−	0.871928i	−0.510295	−	0.859999i	$-0.670464\pi$
$4$	1.98500	+	0.244478i	0.992501	+	0.122239i
$5$	−1.46890	+	0.848071i	−0.656913	+	0.379269i	−0.791100	−	0.611687i	$-0.790491\pi$
$5$	−1.46890	+	0.848071i	−0.656913	+	0.379269i	0.134187	+	0.990956i	$0.457158\pi$
$6$	3.56155	+	2.35829i	1.45400	+	0.962770i
$7$		0			0
$7$		0			0
$8$	−2.78078	−	0.516994i	−0.983153	−	0.182785i
$9$	3.06155	+	5.30277i	1.02052	+	1.76759i
$10$	2.14688	−	1.06990i	0.678904	−	0.338331i
$11$	1.14688	+	0.662153i	0.345798	+	0.199647i	0.662833	−	0.748767i	$-0.269354\pi$
$11$	1.14688	+	0.662153i	0.345798	+	0.199647i	−0.317035	+	0.948414i	$0.602687\pi$
$12$	−4.82312	−	3.63730i	−1.39231	−	1.05000i
$13$			1.69614i			0.470425i	0.971944	+	0.235212i	$0.0755786\pi$
$13$			1.69614i			0.470425i	−0.971944	+	0.235212i	$0.924421\pi$
$14$		0			0
$15$	5.12311			1.32278
$16$	3.88046	+	0.970579i	0.970115	+	0.242645i
$17$	−1.00000	+	1.73205i	−0.242536	+	0.420084i	−0.961436	−	0.275029i	$-0.911312\pi$
$17$	−1.00000	+	1.73205i	−0.242536	+	0.420084i	0.718900	+	0.695113i	$0.244646\pi$
$18$	−3.86235	−	7.75030i	−0.910365	−	1.82676i
$19$	2.61578	−	1.51022i	0.600102	−	0.346469i	−0.168980	−	0.985620i	$-0.554047\pi$
$19$	2.61578	−	1.51022i	0.600102	−	0.346469i	0.769082	+	0.639150i	$0.220714\pi$
$20$	−3.12311	+	1.32431i	−0.698348	+	0.296124i
$21$		0			0
$22$	−1.56155	−	1.03399i	−0.332924	−	0.220447i
$23$	−2.56155	−	4.43674i	−0.534121	−	0.925124i	−0.999205	−	0.0398580i	$-0.987309\pi$
$23$	−2.56155	−	4.43674i	−0.534121	−	0.925124i	0.465085	−	0.885266i	$-0.346024\pi$
$24$	6.49314	+	5.55194i	1.32541	+	1.13328i
$25$	−1.06155	+	1.83866i	−0.212311	+	0.367733i
$26$	0.146883	−	2.39420i	0.0288062	−	0.469542i
$27$		−	9.43318i		−	1.81542i
$28$		0			0
$29$		−	6.04090i		−	1.12177i	−0.827895	−	0.560883i	$-0.810462\pi$
$29$		−	6.04090i		−	1.12177i	0.827895	−	0.560883i	$-0.189538\pi$
$30$	−7.23157	−	0.443654i	−1.32030	−	0.0809997i
$31$	5.12311	−	8.87348i	0.920137	−	1.59372i	0.120936	−	0.992660i	$-0.461411\pi$
$31$	5.12311	−	8.87348i	0.920137	−	1.59372i	0.799201	−	0.601064i	$-0.205256\pi$
$32$	−5.39345	−	1.70607i	−0.953436	−	0.301594i
$33$	−2.00000	−	3.46410i	−0.348155	−	0.603023i
$34$	1.56155	−	2.35829i	0.267804	−	0.404444i
$35$		0			0
$36$	4.78078	+	11.2745i	0.796796	+	1.87908i
$37$	5.23157	−	3.02045i	0.860065	−	0.496559i	−0.00396926	−	0.999992i	$-0.501263\pi$
$37$	5.23157	−	3.02045i	0.860065	−	0.496559i	0.864034	+	0.503434i	$0.167930\pi$
$38$	−3.82312	+	1.90525i	−0.620192	+	0.309072i
$39$	2.56155	−	4.43674i	0.410177	−	0.710447i
$40$	4.52313	−	1.59888i	0.715170	−	0.252805i
$41$	4.24621			0.663147			0.331573	−	0.943429i	$-0.392421\pi$
$41$	4.24621			0.663147			0.331573	+	0.943429i	$0.392421\pi$
$42$		0			0
$43$		−	1.32431i		−	0.201955i	−0.994889	−	0.100977i	$-0.967803\pi$
$43$		−	1.32431i		−	0.201955i	0.994889	−	0.100977i	$-0.0321970\pi$
$44$	2.11468	+	1.59476i	0.318800	+	0.240420i
$45$	−8.99424	−	5.19283i	−1.34078	−	0.774101i
$46$	3.23157	+	6.48455i	0.476469	+	0.956095i
$47$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$47$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$48$	−8.68466	−	8.39919i	−1.25352	−	1.21232i
$49$		0			0
$50$	1.65767	−	2.50345i	0.234430	−	0.354042i
$51$	5.23157	−	3.02045i	0.732566	−	0.422947i
$52$	−0.414669	+	3.36684i	−0.0575043	+	0.466897i
$53$	2.29377	+	1.32431i	0.315073	+	0.181908i	0.649194	−	0.760623i	$-0.275106\pi$
$53$	2.29377	+	1.32431i	0.315073	+	0.181908i	−0.334121	+	0.942530i	$0.608440\pi$
$54$	−0.816900	+	13.3155i	−0.111166	+	1.81201i
$55$	−2.24621			−0.302879
$56$		0			0
$57$	−9.12311			−1.20838
$58$	−0.523133	+	8.52708i	−0.0686907	+	1.11966i
$59$	0.322018	+	0.185917i	0.0419231	+	0.0242043i	0.520815	−	0.853670i	$-0.325628\pi$
$59$	0.322018	+	0.185917i	0.0419231	+	0.0242043i	−0.478892	+	0.877874i	$0.658961\pi$
$60$	10.1694	+	1.25249i	1.31286	+	0.161695i
$61$	1.46890	−	0.848071i	0.188074	−	0.108584i	−0.403007	−	0.915197i	$-0.632035\pi$
$61$	1.46890	−	0.848071i	0.188074	−	0.108584i	0.591080	+	0.806613i	$0.298702\pi$
$62$	−8.00000	+	12.0818i	−1.01600	+	1.53439i
$63$		0			0
$64$	7.46543	+	2.87529i	0.933179	+	0.359411i
$65$	−1.43845	−	2.49146i	−0.178417	−	0.309028i
$66$	2.52313	+	5.06298i	0.310576	+	0.623210i
$67$	9.96029	+	5.75058i	1.21684	+	0.702545i	0.964241	−	0.265026i	$-0.0853804\pi$
$67$	9.96029	+	5.75058i	1.21684	+	0.702545i	0.252602	+	0.967570i	$0.418714\pi$
$68$	−2.40845	+	3.19365i	−0.292067	+	0.387286i
$69$			15.4741i			1.86286i
$70$		0			0
$71$	−8.00000			−0.949425			−0.474713	−	0.880141i	$-0.657448\pi$
$71$	−8.00000			−0.949425			−0.474713	+	0.880141i	$0.657448\pi$
$72$	−5.77200	−	16.3286i	−0.680236	−	1.92434i
$73$	3.00000	−	5.19615i	0.351123	−	0.608164i	−0.635323	−	0.772246i	$-0.719133\pi$
$73$	3.00000	−	5.19615i	0.351123	−	0.608164i	0.986447	+	0.164083i	$0.0524664\pi$
$74$	−7.64624	+	3.81050i	−0.888857	+	0.442961i
$75$	5.55359	−	3.20636i	0.641273	−	0.370239i
$76$	5.56155	−	2.35829i	0.637954	−	0.270515i
$77$		0			0
$78$	−4.00000	+	6.04090i	−0.452911	+	0.683997i
$79$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$79$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$80$	−6.52313	+	1.86522i	−0.729308	+	0.208538i
$81$	−5.06155	+	8.76687i	−0.562395	+	0.974096i
$82$	−5.99378	−	0.367716i	−0.661902	−	0.0406074i
$83$		−	5.66906i		−	0.622260i	−0.950367	−	0.311130i	$-0.899292\pi$
$83$		−	5.66906i		−	0.622260i	0.950367	−	0.311130i	$-0.100708\pi$
$84$		0			0
$85$		−	3.39228i		−	0.367945i
$86$	−0.114683	+	1.86934i	−0.0123666	+	0.201576i
$87$	−9.12311	+	15.8017i	−0.978100	+	1.69412i
$88$	−2.84690	−	2.43423i	−0.303480	−	0.259490i
$89$	8.12311	+	14.0696i	0.861047	+	1.49138i	0.870919	+	0.491427i	$0.163524\pi$
$89$	8.12311	+	14.0696i	0.861047	+	1.49138i	−0.00987147	+	0.999951i	$0.503142\pi$
$90$	12.2462	+	8.10887i	1.29086	+	0.854750i
$91$		0			0
$92$	−4.00000	−	9.43318i	−0.417029	−	0.983477i
$93$	−26.8019	+	15.4741i	−2.77923	+	1.60459i
$94$		0			0
$95$	−2.56155	+	4.43674i	−0.262810	+	0.455200i
$96$	11.5316	+	12.6080i	1.17693	+	1.28680i
$97$	12.2462			1.24341			0.621707	−	0.783250i	$-0.286439\pi$
$97$	12.2462			1.24341			0.621707	+	0.783250i	$0.286439\pi$
$98$		0			0
$99$			8.10887i			0.814972i
$100$	−2.55670	+	3.39022i	−0.255670	+	0.339022i
$101$	8.99424	+	5.19283i	0.894960	+	0.516705i	0.875562	−	0.483106i	$-0.160492\pi$
$101$	8.99424	+	5.19283i	0.894960	+	0.516705i	0.0193984	+	0.999812i	$0.493825\pi$
$102$	−7.64624	+	3.81050i	−0.757090	+	0.377295i
$103$	−1.12311	−	1.94528i	−0.110663	−	0.191674i	0.805375	−	0.592766i	$-0.201964\pi$
$103$	−1.12311	−	1.94528i	−0.110663	−	0.191674i	−0.916038	+	0.401092i	$0.868631\pi$
$104$	0.876894	−	4.71659i	0.0859866	−	0.462500i
$105$		0			0
$106$	−3.12311	−	2.06798i	−0.303343	−	0.200860i
$107$	12.2541	−	7.07488i	1.18464	−	0.683955i	0.227560	−	0.973764i	$-0.426925\pi$
$107$	12.2541	−	7.07488i	1.18464	−	0.683955i	0.957084	+	0.289809i	$0.0935919\pi$
$108$	2.30621	−	18.7249i	0.221915	−	1.80180i
$109$	−15.6947	−	9.06134i	−1.50328	−	0.867919i	−0.999993	−	0.00380035i	$-0.998790\pi$
$109$	−15.6947	−	9.06134i	−1.50328	−	0.867919i	−0.503288	−	0.864119i	$-0.667876\pi$
$110$	3.17066	+	0.194519i	0.302311	+	0.0185466i
$111$	−18.2462			−1.73185
$112$		0			0
$113$	4.87689			0.458780			0.229390	−	0.973335i	$-0.426327\pi$
$113$	4.87689			0.458780			0.229390	+	0.973335i	$0.426327\pi$
$114$	12.8778	+	0.790048i	1.20612	+	0.0739948i
$115$	7.52534	+	4.34475i	0.701741	+	0.405150i
$116$	1.47687	−	11.9912i	0.137124	−	1.11335i
$117$	−8.99424	+	5.19283i	−0.831518	+	0.480077i
$118$	−0.438447	−	0.290319i	−0.0403623	−	0.0267261i
$119$		0			0
$120$	−14.2462	−	2.64861i	−1.30050	−	0.241784i
$121$	−4.62311	−	8.00745i	−0.420282	−	0.727950i
$122$	−2.14688	+	1.06990i	−0.194370	+	0.0968640i
$123$	−11.1072	−	6.41273i	−1.00150	−	0.578216i
$124$	12.3387	−	16.3614i	1.10805	−	1.46930i
$125$		−	12.0818i		−	1.08063i
$126$		0			0
$127$	13.1231			1.16449			0.582244	−	0.813014i	$-0.302175\pi$
$127$	13.1231			1.16449			0.582244	+	0.813014i	$0.302175\pi$
$128$	−10.2889	−	4.70514i	−0.909420	−	0.415879i
$129$	−2.00000	+	3.46410i	−0.176090	+	0.304997i
$130$	1.81470	+	3.64142i	0.159159	+	0.319373i
$131$	−10.7852	+	6.22681i	−0.942303	+	0.544039i	−0.890682	−	0.454628i	$-0.849772\pi$
$131$	−10.7852	+	6.22681i	−0.942303	+	0.544039i	−0.0516218	+	0.998667i	$0.516439\pi$
$132$	−3.12311	−	7.36520i	−0.271831	−	0.641059i
$133$		0			0
$134$	−13.5616	−	8.97983i	−1.17154	−	0.775739i
$135$	8.00000	+	13.8564i	0.688530	+	1.19257i
$136$	3.67624	−	4.29945i	0.315235	−	0.368675i
$137$	8.12311	−	14.0696i	0.694004	−	1.20205i	−0.276512	−	0.961011i	$-0.589178\pi$
$137$	8.12311	−	14.0696i	0.694004	−	1.20205i	0.970515	−	0.241039i	$-0.0774882\pi$
$138$	1.34003	−	21.8426i	0.114071	−	1.85936i
$139$			8.31768i			0.705496i	0.935718	+	0.352748i	$0.114753\pi$
$139$			8.31768i			0.705496i	−0.935718	+	0.352748i	$0.885247\pi$
$140$		0			0
$141$		0			0
$142$	11.2925	+	0.692789i	0.947644	+	0.0581375i
$143$	−1.12311	+	1.94528i	−0.0939188	+	0.162672i
$144$	6.73348	+	23.5487i	0.561124	+	1.96239i
$145$	5.12311	+	8.87348i	0.425451	+	0.736902i
$146$	−4.68466	+	7.07488i	−0.387705	+	0.585522i
$147$		0			0
$148$	11.1231	−	4.71659i	0.914314	−	0.387701i
$149$	12.7569	−	7.36520i	1.04509	−	0.603381i	0.123817	−	0.992305i	$-0.460487\pi$
$149$	12.7569	−	7.36520i	1.04509	−	0.603381i	0.921270	+	0.388924i	$0.127153\pi$
$150$	−8.11689	+	4.04504i	−0.662741	+	0.330276i
$151$	−5.43845	+	9.41967i	−0.442575	+	0.766562i	−0.997880	−	0.0650850i	$-0.979268\pi$
$151$	−5.43845	+	9.41967i	−0.442575	+	0.766562i	0.555305	+	0.831647i	$0.312601\pi$
$152$	−8.05469	+	2.84725i	−0.653322	+	0.230943i
$153$	−12.2462			−0.990048
$154$		0			0
$155$			17.3790i			1.39592i
$156$	6.16937	−	8.18069i	0.493945	−	0.654979i
$157$	−7.34451	−	4.24035i	−0.586155	−	0.338417i	0.177420	−	0.984135i	$-0.443225\pi$
$157$	−7.34451	−	4.24035i	−0.586155	−	0.338417i	−0.763576	+	0.645718i	$0.776558\pi$
$158$		0			0
$159$	−4.00000	−	6.92820i	−0.317221	−	0.549442i
$160$	9.36932	−	2.06798i	0.740710	−	0.163488i
$161$		0			0
$162$	7.90388	−	11.9366i	0.620988	−	0.937830i
$163$	−11.6100	+	6.70305i	−0.909367	+	0.525023i	−0.880227	−	0.474552i	$-0.842610\pi$
$163$	−11.6100	+	6.70305i	−0.909367	+	0.525023i	−0.0291396	+	0.999575i	$0.509277\pi$
$164$	8.42874	+	1.03811i	0.658174	+	0.0810624i
$165$	5.87560	+	3.39228i	0.457415	+	0.264089i
$166$	−0.490933	+	8.00222i	−0.0381038	+	0.621093i
$167$	8.00000			0.619059			0.309529	−	0.950890i	$-0.399829\pi$
$167$	8.00000			0.619059			0.309529	+	0.950890i	$0.399829\pi$
$168$		0			0
$169$	10.1231			0.778700
$170$	−0.293767	+	4.78841i	−0.0225309	+	0.367254i
$171$	16.0167	+	9.24726i	1.22483	+	0.707156i
$172$	0.323764	−	2.62875i	0.0246868	−	0.200440i
$173$	16.5196	−	9.53758i	1.25596	−	0.725129i	0.283673	−	0.958921i	$-0.408447\pi$
$173$	16.5196	−	9.53758i	1.25596	−	0.725129i	0.972287	+	0.233792i	$0.0751135\pi$
$174$	14.2462	−	21.5150i	1.08000	−	1.63105i
$175$		0			0
$176$	3.80776	+	3.68260i	0.287021	+	0.277587i
$177$	−0.561553	−	0.972638i	−0.0422089	−	0.0731079i
$178$	−10.2478	−	20.5636i	−0.768108	−	1.54131i
$179$	4.08469	+	2.35829i	0.305304	+	0.176267i	0.644823	−	0.764332i	$-0.276931\pi$
$179$	4.08469	+	2.35829i	0.305304	+	0.176267i	−0.339519	+	0.940599i	$0.610264\pi$
$180$	−16.5840	−	12.5067i	−1.23610	−	0.932191i
$181$			6.99337i			0.519813i	0.965634	+	0.259906i	$0.0836917\pi$
$181$			6.99337i			0.519813i	−0.965634	+	0.259906i	$0.916308\pi$
$182$		0			0
$183$	−5.12311			−0.378711
$184$	4.82934	+	13.6619i	0.356024	+	1.00717i
$185$	−5.12311	+	8.87348i	−0.376658	+	0.652391i
$186$	39.1725	−	19.5216i	2.87227	−	1.43139i
$187$	−2.29377	+	1.32431i	−0.167737	+	0.0968429i
$188$		0			0
$189$		0			0
$190$	4.00000	−	6.04090i	0.290191	−	0.438253i
$191$	−8.00000	−	13.8564i	−0.578860	−	1.00261i	−0.995610	−	0.0935936i	$-0.970165\pi$
$191$	−8.00000	−	13.8564i	−0.578860	−	1.00261i	0.416751	−	0.909021i	$-0.363169\pi$
$192$	−15.1856	−	18.7956i	−1.09593	−	1.35646i
$193$	5.56155	−	9.63289i	0.400329	−	0.693391i	−0.593436	−	0.804881i	$-0.702229\pi$
$193$	5.56155	−	9.63289i	0.400329	−	0.693391i	0.993766	+	0.111490i	$0.0355624\pi$
$194$	−17.2863	−	1.06050i	−1.24108	−	0.0761398i
$195$			8.68951i			0.622269i
$196$		0			0
$197$			21.5150i			1.53288i	0.642317	+	0.766439i	$0.277973\pi$
$197$			21.5150i			1.53288i	−0.642317	+	0.766439i	$0.722027\pi$
$198$	0.702217	−	11.4462i	0.0499044	−	0.813443i
$199$	9.12311	−	15.8017i	0.646720	−	1.12015i	−0.337182	−	0.941440i	$-0.609474\pi$
$199$	9.12311	−	15.8017i	0.646720	−	1.12015i	0.983901	−	0.178712i	$-0.0571930\pi$
$200$	3.90252	−	4.56410i	0.275950	−	0.322730i
$201$	−17.3693	−	30.0845i	−1.22514	−	2.12200i
$202$	−12.2462	−	8.10887i	−0.861640	−	0.570538i
$203$		0			0
$204$	11.1231	−	4.71659i	0.778773	−	0.330227i
$205$	−6.23726	+	3.60109i	−0.435629	+	0.251511i
$206$	1.41687	+	2.84313i	0.0987182	+	0.198090i
$207$	15.6847	−	27.1666i	1.09016	−	1.88821i
$208$	−1.64624	+	6.58181i	−0.114146	+	0.456366i
$209$	4.00000			0.276686
$210$		0			0
$211$		−	4.71659i		−	0.324703i	−0.986733	−	0.162352i	$-0.948092\pi$
$211$		−	4.71659i		−	0.324703i	0.986733	−	0.162352i	$-0.0519079\pi$
$212$	4.22937	+	3.18953i	0.290474	+	0.219058i
$213$	20.9263	+	12.0818i	1.43384	+	0.827831i
$214$	−17.9100	+	8.92544i	−1.22430	+	0.610130i
$215$	1.12311	+	1.94528i	0.0765952	+	0.132667i
$216$	−4.87689	+	26.2316i	−0.331831	+	1.78483i
$217$		0			0
$218$	21.3693	+	14.1498i	1.44731	+	0.958343i
$219$	−15.6947	+	9.06134i	−1.06055	+	0.612309i
$220$	−4.45873	−	0.549150i	−0.300608	−	0.0370237i
$221$	−2.93780	−	1.69614i	−0.197618	−	0.114095i
$222$	25.7556	+	1.58010i	1.72860	+	0.106049i
$223$	−5.75379			−0.385302			−0.192651	−	0.981267i	$-0.561709\pi$
$223$	−5.75379			−0.385302			−0.192651	+	0.981267i	$0.561709\pi$
$224$		0			0
$225$	−13.0000			−0.866667
$226$	−6.88403	−	0.422332i	−0.457919	−	0.0280931i
$227$	−8.49139	−	4.90251i	−0.563593	−	0.325391i	0.190993	−	0.981591i	$-0.438829\pi$
$227$	−8.49139	−	4.90251i	−0.563593	−	0.325391i	−0.754586	+	0.656201i	$0.772163\pi$
$228$	−18.1094	−	2.23040i	−1.19932	−	0.147712i
$229$	−22.3952	+	12.9299i	−1.47992	+	0.854429i	−0.999741	−	0.0227441i	$-0.992760\pi$
$229$	−22.3952	+	12.9299i	−1.47992	+	0.854429i	−0.480174	+	0.877173i	$0.659426\pi$
$230$	−10.2462	−	6.78456i	−0.675615	−	0.447361i
$231$		0			0
$232$	−3.12311	+	16.7984i	−0.205042	+	1.10287i
$233$	8.12311	+	14.0696i	0.532162	+	0.921732i	0.999295	+	0.0375449i	$0.0119537\pi$
$233$	8.12311	+	14.0696i	0.532162	+	0.921732i	−0.467133	+	0.884187i	$0.654713\pi$
$234$	13.1456	−	6.55109i	0.859354	−	0.428258i
$235$		0			0
$236$	0.593753	+	0.447772i	0.0386500	+	0.0291475i
$237$		0			0
$238$		0			0
$239$	−17.6155			−1.13945			−0.569727	−	0.821834i	$-0.692951\pi$
$239$	−17.6155			−1.13945			−0.569727	+	0.821834i	$0.692951\pi$
$240$	19.8800	+	4.97238i	1.28325	+	0.320966i
$241$	1.87689	−	3.25088i	0.120901	−	0.209407i	−0.799222	−	0.601036i	$-0.794755\pi$
$241$	1.87689	−	3.25088i	0.120901	−	0.209407i	0.920123	+	0.391629i	$0.128088\pi$
$242$	5.83236	+	11.7034i	0.374918	+	0.752320i
$243$	1.97175	−	1.13839i	0.126488	−	0.0730277i
$244$	3.12311	−	1.32431i	0.199936	−	0.0847801i
$245$		0			0
$246$	15.1231	+	10.0138i	0.964214	+	0.638458i
$247$	2.56155	+	4.43674i	0.162988	+	0.282303i
$248$	−18.8337	+	22.0265i	−1.19594	+	1.39869i
$249$	−8.56155	+	14.8290i	−0.542566	+	0.939753i
$250$	−1.04627	+	17.0542i	−0.0661717	+	1.07860i
$251$		−	10.9663i		−	0.692186i	−0.938200	−	0.346093i	$-0.887508\pi$
$251$		−	10.9663i		−	0.692186i	0.938200	−	0.346093i	$-0.112492\pi$
$252$		0			0
$253$		−	6.78456i		−	0.426542i
$254$	−18.5240	−	1.13644i	−1.16230	−	0.0713067i
$255$	−5.12311	+	8.87348i	−0.320821	+	0.555679i
$256$	14.1160	+	7.53259i	0.882247	+	0.470787i
$257$	−11.2462	−	19.4790i	−0.701519	−	1.21507i	−0.967933	−	0.251208i	$-0.919172\pi$
$257$	−11.2462	−	19.4790i	−0.701519	−	1.21507i	0.266414	−	0.963859i	$-0.414161\pi$
$258$	3.12311	−	4.71659i	0.194436	−	0.293642i
$259$		0			0
$260$	−2.24621	−	5.29723i	−0.139304	−	0.328520i
$261$	32.0335	−	18.4945i	1.98282	−	1.14478i
$262$	15.7631	−	7.85554i	0.973849	−	0.485317i
$263$	−6.24621	+	10.8188i	−0.385158	+	0.667113i	−0.991791	−	0.127869i	$-0.959186\pi$
$263$	−6.24621	+	10.8188i	−0.385158	+	0.667113i	0.606633	+	0.794982i	$0.292520\pi$
$264$	3.77063	+	10.6669i	0.232066	+	0.656501i
$265$	−4.49242			−0.275967
$266$		0			0
$267$		−	49.0708i		−	3.00309i
$268$	18.3653	+	13.8500i	1.12184	+	0.846022i
$269$	10.2823	+	5.93649i	0.626923	+	0.361954i	0.779560	−	0.626328i	$-0.215443\pi$
$269$	10.2823	+	5.93649i	0.626923	+	0.361954i	−0.152636	+	0.988282i	$0.548776\pi$
$270$	−10.0925	−	20.2519i	−0.614212	−	1.23249i
$271$	−5.12311	−	8.87348i	−0.311207	−	0.539025i	0.667417	−	0.744684i	$-0.267400\pi$
$271$	−5.12311	−	8.87348i	−0.311207	−	0.539025i	−0.978624	+	0.205658i	$0.934066\pi$
$272$	−5.56155	+	5.75058i	−0.337219	+	0.348680i
$273$		0			0
$274$	−12.6847	+	19.1567i	−0.766308	+	1.15730i
$275$	−2.43495	+	1.40582i	−0.146833	+	0.0847742i
$276$	−3.78307	+	30.7161i	−0.227714	+	1.84889i
$277$	2.29377	+	1.32431i	0.137819	+	0.0795699i	0.567324	−	0.823495i	$-0.307979\pi$
$277$	2.29377	+	1.32431i	0.137819	+	0.0795699i	−0.429505	+	0.903064i	$0.641312\pi$
$278$	0.720299	−	11.7409i	0.0432007	−	0.704172i
$279$	62.7386			3.75606
$280$		0			0
$281$	−6.00000			−0.357930			−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000			−0.357930			−0.178965	+	0.983855i	$0.557275\pi$
$282$		0			0
$283$	−18.9545	−	10.9434i	−1.12673	−	0.650518i	−0.183619	−	0.982997i	$-0.558781\pi$
$283$	−18.9545	−	10.9434i	−1.12673	−	0.650518i	−0.943110	+	0.332480i	$0.892115\pi$
$284$	−15.8800	−	1.95583i	−0.942305	−	0.116057i
$285$	13.4009	−	7.73704i	0.793803	−	0.458303i
$286$	1.75379	−	2.64861i	0.103704	−	0.156616i
$287$		0			0
$288$	−7.46543	−	33.8234i	−0.439905	−	1.99307i
$289$	6.50000	+	11.2583i	0.382353	+	0.662255i
$290$	−6.46314	−	12.9691i	−0.379529	−	0.761572i
$291$	−32.0335	−	18.4945i	−1.87783	−	1.08417i
$292$	7.22535	−	9.58094i	0.422832	−	0.560682i
$293$		−	10.3857i		−	0.606736i	−0.952873	−	0.303368i	$-0.901889\pi$
$293$		−	10.3857i		−	0.606736i	0.952873	−	0.303368i	$-0.0981112\pi$
$294$		0			0
$295$	−0.630683			−0.0367198
$296$	−16.1094	+	5.69450i	−0.936339	+	0.330986i
$297$	6.24621	−	10.8188i	0.362442	−	0.627768i
$298$	−18.6449	+	9.29169i	−1.08007	+	0.538253i
$299$	7.52534	−	4.34475i	0.435201	−	0.251264i
$300$	11.8078	−	5.00691i	0.681722	−	0.289074i
$301$		0			0
$302$	8.49242	−	12.8255i	0.488684	−	0.738022i
$303$	−15.6847	−	27.1666i	−0.901060	−	1.56068i
$304$	11.6162	−	3.32154i	0.666237	−	0.190503i
$305$	−1.43845	+	2.49146i	−0.0823652	+	0.142661i
$306$	17.2863	+	1.06050i	0.988190	+	0.0606250i
$307$			25.2791i			1.44275i	0.692543	+	0.721377i	$0.256490\pi$
$307$			25.2791i			1.44275i	−0.692543	+	0.721377i	$0.743510\pi$
$308$		0			0
$309$			6.78456i			0.385960i
$310$	1.50500	−	24.5315i	0.0854782	−	1.39330i
$311$	6.24621	−	10.8188i	0.354190	−	0.613475i	−0.632789	−	0.774324i	$-0.718090\pi$
$311$	6.24621	−	10.8188i	0.354190	−	0.613475i	0.986979	+	0.160849i	$0.0514232\pi$
$312$	−9.41687	+	11.0133i	−0.533125	+	0.623504i
$313$	10.3693	+	17.9602i	0.586108	+	1.01517i	0.994736	+	0.102468i	$0.0326741\pi$
$313$	10.3693	+	17.9602i	0.586108	+	1.01517i	−0.408628	+	0.912701i	$0.633993\pi$
$314$	10.0000	+	6.62153i	0.564333	+	0.373675i
$315$		0			0
$316$		0			0
$317$	−3.58184	+	2.06798i	−0.201176	+	0.116149i	−0.597204	−	0.802089i	$-0.703722\pi$
$317$	−3.58184	+	2.06798i	−0.201176	+	0.116149i	0.396028	+	0.918238i	$0.370388\pi$
$318$	5.04627	+	10.1260i	0.282981	+	0.567836i
$319$	4.00000	−	6.92820i	0.223957	−	0.387905i
$320$	−13.4044	+	2.10770i	−0.749331	+	0.117824i
$321$	−42.7386			−2.38544
$322$		0			0
$323$			6.04090i			0.336124i
$324$	−12.1905	+	16.1648i	−0.677250	+	0.898045i
$325$	−3.11863	−	1.80054i	−0.172991	−	0.0998762i
$326$	16.9687	−	8.45634i	0.939810	−	0.468353i
$327$	27.3693	+	47.4050i	1.51353	+	2.62151i
$328$	−11.8078	−	2.19526i	−0.651975	−	0.121213i
$329$		0			0
$330$	−8.00000	−	5.29723i	−0.440386	−	0.291603i
$331$	−12.8981	+	7.44672i	−0.708943	+	0.409309i	−0.810670	−	0.585504i	$-0.800897\pi$
$331$	−12.8981	+	7.44672i	−0.708943	+	0.409309i	0.101726	+	0.994812i	$0.467563\pi$
$332$	1.38596	−	11.2531i	0.0760645	−	0.617594i
$333$	32.0335	+	18.4945i	1.75542	+	1.01349i
$334$	−11.2925	−	0.692789i	−0.617897	−	0.0379077i
$335$	−19.5076			−1.06581
$336$		0			0
$337$	−0.876894			−0.0477675			−0.0238837	−	0.999715i	$-0.507603\pi$
$337$	−0.876894			−0.0477675			−0.0238837	+	0.999715i	$0.507603\pi$
$338$	−14.2894	−	0.876647i	−0.777239	−	0.0476833i
$339$	−12.7569	−	7.36520i	−0.692860	−	0.400023i
$340$	0.829339	−	6.73368i	0.0449772	−	0.365185i
$341$	11.7512	−	6.78456i	0.636364	−	0.367405i
$342$	−21.8078	−	14.4401i	−1.17923	−	0.780830i
$343$		0			0
$344$	−0.684658	+	3.68260i	−0.0369143	+	0.198553i
$345$	−13.1231	−	22.7299i	−0.706524	−	1.22374i
$346$	−24.1443	+	12.0323i	−1.29801	+	0.646860i
$347$	7.02249	+	4.05444i	0.376987	+	0.217654i	0.676507	−	0.736437i	$-0.263493\pi$
$347$	7.02249	+	4.05444i	0.376987	+	0.217654i	−0.299520	+	0.954090i	$0.596826\pi$
$348$	−21.9725	+	29.1360i	−1.17785	+	1.56185i
$349$		−	27.3471i		−	1.46385i	−0.681383	−	0.731927i	$-0.738621\pi$
$349$		−	27.3471i		−	1.46385i	0.681383	−	0.731927i	$-0.261379\pi$
$350$		0			0
$351$	16.0000			0.854017
$352$	−5.05598	−	5.52796i	−0.269485	−	0.294641i
$353$	−3.87689	+	6.71498i	−0.206346	+	0.357402i	−0.950561	−	0.310538i	$-0.899491\pi$
$353$	−3.87689	+	6.71498i	−0.206346	+	0.357402i	0.744215	+	0.667941i	$0.232824\pi$
$354$	0.708436	+	1.42157i	0.0376530	+	0.0755554i
$355$	11.7512	−	6.78456i	0.623689	−	0.360087i
$356$	12.6847	+	29.9142i	0.672286	+	1.58545i
$357$		0			0
$358$	−5.56155	−	3.68260i	−0.293937	−	0.194632i
$359$	15.6847	+	27.1666i	0.827805	+	1.43380i	0.899757	+	0.436392i	$0.143744\pi$
$359$	15.6847	+	27.1666i	0.827805	+	1.43380i	−0.0719522	+	0.997408i	$0.522923\pi$
$360$	22.3263	+	19.0901i	1.17670	+	1.00613i
$361$	−4.93845	+	8.55364i	−0.259918	+	0.450192i
$362$	0.605616	−	9.87156i	0.0318305	−	0.518838i
$363$			27.9277i			1.46582i
$364$		0			0
$365$			10.1768i			0.532680i
$366$	7.23157	+	0.443654i	0.378000	+	0.0231902i
$367$	−5.12311	+	8.87348i	−0.267424	+	0.463192i	−0.968196	−	0.250194i	$-0.919506\pi$
$367$	−5.12311	+	8.87348i	−0.267424	+	0.463192i	0.700772	+	0.713385i	$0.252839\pi$
$368$	−5.63380	−	19.7028i	−0.293682	−	1.02708i
$369$	13.0000	+	22.5167i	0.676753	+	1.17217i
$370$	8.00000	−	12.0818i	0.415900	−	0.628102i
$371$		0			0
$372$	−56.9848	+	24.1636i	−2.95453	+	1.25282i
$373$	12.7569	−	7.36520i	0.660528	−	0.381356i	−0.131950	−	0.991256i	$-0.542124\pi$
$373$	12.7569	−	7.36520i	0.660528	−	0.381356i	0.792478	+	0.609901i	$0.208791\pi$
$374$	3.35247	−	1.67070i	0.173352	−	0.0863899i
$375$	−18.2462	+	31.6034i	−0.942230	+	1.63199i
$376$		0			0
$377$	10.2462			0.527707
$378$		0			0
$379$			36.4084i			1.87017i	0.354418	+	0.935087i	$0.384679\pi$
$379$			36.4084i			1.87017i	−0.354418	+	0.935087i	$0.615321\pi$
$380$	−6.16937	+	8.18069i	−0.316482	+	0.419661i
$381$	−34.3272	−	19.8188i	−1.75864	−	1.01535i
$382$	10.0925	+	20.2519i	0.516379	+	1.03618i
$383$	2.24621	+	3.89055i	0.114776	+	0.198798i	0.917690	−	0.397297i	$-0.130052\pi$
$383$	2.24621	+	3.89055i	0.114776	+	0.198798i	−0.802914	+	0.596095i	$0.796718\pi$
$384$	19.8078	+	27.8462i	1.01081	+	1.42102i
$385$		0			0
$386$	−8.68466	+	13.1158i	−0.442037	+	0.667576i
$387$	7.02249	−	4.05444i	0.356973	−	0.206099i
$388$	24.3087	+	2.99393i	1.23409	+	0.151994i
$389$	21.5703	+	12.4536i	1.09366	+	0.631424i	0.934548	−	0.355837i	$-0.115804\pi$
$389$	21.5703	+	12.4536i	1.09366	+	0.631424i	0.159110	+	0.987261i	$0.449137\pi$
$390$	0.752499	−	12.2658i	0.0381043	−	0.621101i
$391$	10.2462			0.518173
$392$		0			0
$393$	37.6155			1.89745
$394$	1.86317	−	30.3697i	0.0938649	−	1.53000i
$395$		0			0
$396$	−1.98244	+	16.0961i	−0.0996214	+	0.808860i
$397$	−17.8076	+	10.2812i	−0.893740	+	0.516001i	−0.875164	−	0.483826i	$-0.839247\pi$
$397$	−17.8076	+	10.2812i	−0.893740	+	0.516001i	−0.0185761	+	0.999827i	$0.505913\pi$
$398$	−14.2462	+	21.5150i	−0.714098	+	1.07845i
$399$		0			0
$400$	−5.90388	+	6.10454i	−0.295194	+	0.305227i
$401$	0.438447	+	0.759413i	0.0218950	+	0.0379233i	0.876765	−	0.480919i	$-0.159697\pi$
$401$	0.438447	+	0.759413i	0.0218950	+	0.0379233i	−0.854870	+	0.518842i	$0.826363\pi$
$402$	21.9125	+	43.9703i	1.09290	+	2.19304i
$403$	15.0507	+	8.68951i	0.749727	+	0.432855i
$404$	16.5840	+	12.5067i	0.825087	+	0.622230i
$405$		−	17.1702i		−	0.853195i
$406$		0			0
$407$	8.00000			0.396545
$408$	−16.1094	+	5.69450i	−0.797533	+	0.281920i
$409$	−13.0000	+	22.5167i	−0.642809	+	1.11338i	0.341994	+	0.939702i	$0.388898\pi$
$409$	−13.0000	+	22.5167i	−0.642809	+	1.11338i	−0.984803	+	0.173675i	$0.944436\pi$
$410$	9.11612	−	4.54301i	0.450213	−	0.224363i
$411$	−42.4966	+	24.5354i	−2.09620	+	1.21024i
$412$	−1.75379	−	4.13595i	−0.0864030	−	0.203764i
$413$		0			0
$414$	−24.4924	+	36.9890i	−1.20374	+	1.81791i
$415$	4.80776	+	8.32729i	0.236004	+	0.408771i
$416$	2.89374	−	9.14805i	0.141877	−	0.448520i
$417$	12.5616	−	21.7572i	0.615142	−	1.06546i
$418$	−5.64624	−	0.346394i	−0.276167	−	0.0169427i
$419$		−	27.9277i		−	1.36436i	−0.731185	−	0.682179i	$-0.761033\pi$
$419$		−	27.9277i		−	1.36436i	0.731185	−	0.682179i	$-0.238967\pi$
$420$		0			0
$421$		−	26.8122i		−	1.30675i	−0.757036	−	0.653373i	$-0.773353\pi$
$421$		−	26.8122i		−	1.30675i	0.757036	−	0.653373i	$-0.226647\pi$
$422$	−0.408450	+	6.65775i	−0.0198830	+	0.324094i
$423$		0			0
$424$	−5.69379	−	4.86846i	−0.276515	−	0.236434i
$425$	−2.12311	−	3.67733i	−0.102986	−	0.178377i
$426$	−28.4924	−	18.8664i	−1.38046	−	0.914078i
$427$		0			0
$428$	26.0540	−	11.0478i	1.25937	−	0.534016i
$429$	5.87560	−	3.39228i	0.283677	−	0.163781i
$430$	−1.41687	−	2.84313i	−0.0683277	−	0.137108i
$431$	−8.80776	+	15.2555i	−0.424255	+	0.734831i	−0.996351	−	0.0853557i	$-0.972797\pi$
$431$	−8.80776	+	15.2555i	−0.424255	+	0.734831i	0.572095	+	0.820187i	$0.306131\pi$
$432$	9.15564	−	36.6051i	0.440501	−	1.76116i
$433$	−18.4924			−0.888689			−0.444345	−	0.895856i	$-0.646563\pi$
$433$	−18.4924			−0.888689			−0.444345	+	0.895856i	$0.646563\pi$
$434$		0			0
$435$		−	30.9481i		−	1.48385i
$436$	−28.9387	−	21.8238i	−1.38591	−	1.04517i
$437$	−13.4009	−	7.73704i	−0.641054	−	0.370113i
$438$	22.9387	−	11.4315i	1.09605	−	0.546218i
$439$	−11.3693	−	19.6922i	−0.542628	−	0.939859i	−0.998752	−	0.0499429i	$-0.984096\pi$
$439$	−11.3693	−	19.6922i	−0.542628	−	0.939859i	0.456124	−	0.889916i	$-0.349237\pi$
$440$	6.24621	+	1.16128i	0.297776	+	0.0553617i
$441$		0			0
$442$	4.00000	+	2.64861i	0.190261	+	0.125982i
$443$	6.37845	−	3.68260i	0.303049	−	0.174966i	−0.340763	−	0.940149i	$-0.610685\pi$
$443$	6.37845	−	3.68260i	0.303049	−	0.174966i	0.643812	+	0.765184i	$0.277352\pi$
$444$	−36.2188	−	4.46080i	−1.71887	−	0.211700i
$445$	−23.8641	−	13.7779i	−1.13127	−	0.653137i
$446$	8.12182	+	0.498270i	0.384579	+	0.0235938i
$447$	−44.4924			−2.10442
$448$		0			0
$449$	16.7386			0.789945			0.394972	−	0.918693i	$-0.370754\pi$
$449$	16.7386			0.789945			0.394972	+	0.918693i	$0.370754\pi$
$450$	18.3503	+	1.12578i	0.865040	+	0.0530699i
$451$	4.86991	+	2.81164i	0.229315	+	0.132395i
$452$	9.68064	+	1.19229i	0.455339	+	0.0560808i
$453$	28.4516	−	16.4265i	1.33677	−	0.771786i
$454$	11.5616	+	7.65552i	0.542611	+	0.359291i
$455$		0			0
$456$	25.3693	+	4.71659i	1.18803	+	0.220875i
$457$	−8.68466	−	15.0423i	−0.406251	−	0.703648i	0.588215	−	0.808705i	$-0.299831\pi$
$457$	−8.68466	−	15.0423i	−0.406251	−	0.703648i	−0.994466	+	0.105057i	$0.966498\pi$
$458$	32.7318	−	16.3119i	1.52946	−	0.762204i
$459$	16.3387	+	9.43318i	0.762627	+	0.440303i
$460$	13.8756	+	10.4641i	0.646953	+	0.487892i
$461$		−	24.3724i		−	1.13514i	−0.823327	−	0.567568i	$-0.807885\pi$
$461$		−	24.3724i		−	1.13514i	0.823327	−	0.567568i	$-0.192115\pi$
$462$		0			0
$463$		0			0			−	1.00000i	$-0.5\pi$
$463$		0			0				1.00000i	$0.5\pi$
$464$	5.86317	−	23.4415i	0.272191	−	1.08824i
$465$	26.2462	−	45.4598i	1.21714	−	2.10815i
$466$	−10.2478	−	20.5636i	−0.474722	−	0.952589i
$467$	2.61578	−	1.51022i	0.121044	−	0.0698848i	−0.438255	−	0.898850i	$-0.644403\pi$
$467$	2.61578	−	1.51022i	0.121044	−	0.0698848i	0.559300	+	0.828966i	$0.311070\pi$
$468$	−19.1231	+	8.10887i	−0.883966	+	0.374833i
$469$		0			0
$470$		0			0
$471$	12.8078	+	22.1837i	0.590151	+	1.02217i
$472$	−0.799342	−	0.683475i	−0.0367927	−	0.0314595i
$473$	0.876894	−	1.51883i	0.0403196	−	0.0698357i
$474$		0			0
$475$			6.41273i			0.294236i
$476$		0			0
$477$			16.2177i			0.742559i
$478$	24.8654	+	1.52548i	1.13732	+	0.0697738i
$479$	−5.12311	+	8.87348i	−0.234081	+	0.405440i	−0.959005	−	0.283389i	$-0.908541\pi$
$479$	−5.12311	+	8.87348i	−0.234081	+	0.405440i	0.724924	+	0.688828i	$0.241875\pi$
$480$	−27.6312	−	8.74039i	−1.26119	−	0.398942i
$481$	5.12311	+	8.87348i	0.233594	+	0.404596i
$482$	−2.93087	+	4.42627i	−0.133497	+	0.201611i
$483$		0			0
$484$	−7.21922	−	17.0251i	−0.328147	−	0.773866i
$485$	−17.9885	+	10.3857i	−0.816815	+	0.471588i
$486$	−2.88182	+	1.43615i	−0.130722	+	0.0651453i
$487$	−0.315342	+	0.546188i	−0.0142895	+	0.0247501i	−0.873082	−	0.487574i	$-0.837882\pi$
$487$	−0.315342	+	0.546188i	−0.0142895	+	0.0247501i	0.858792	+	0.512324i	$0.171215\pi$
$488$	−4.52313	+	1.59888i	−0.204753	+	0.0723780i
$489$	40.4924			1.83113
$490$		0			0
$491$		−	34.1774i		−	1.54240i	−0.636590	−	0.771202i	$-0.719656\pi$
$491$		−	34.1774i		−	1.54240i	0.636590	−	0.771202i	$-0.280344\pi$
$492$	−20.4800	−	15.4447i	−0.923309	−	0.696303i
$493$	10.4631	+	6.04090i	0.471236	+	0.272068i
$494$	−3.23157	−	6.48455i	−0.145395	−	0.291754i
$495$	−6.87689	−	11.9111i	−0.309093	−	0.535366i
$496$	28.4924	−	29.4608i	1.27935	−	1.32283i
$497$		0			0
$498$	13.3693	−	20.1907i	0.599093	−	0.904765i
$499$	7.66652	−	4.42627i	0.343201	−	0.198147i	−0.318486	−	0.947928i	$-0.603174\pi$
$499$	7.66652	−	4.42627i	0.343201	−	0.198147i	0.661687	+	0.749781i	$0.269841\pi$
$500$	2.95373	−	23.9824i	0.132095	−	1.07252i
$501$	−20.9263	−	12.0818i	−0.934917	−	0.539775i
$502$	−0.949665	+	15.4796i	−0.0423856	+	0.690887i
$503$	13.7538			0.613251			0.306626	−	0.951830i	$-0.400800\pi$
$503$	13.7538			0.613251			0.306626	+	0.951830i	$0.400800\pi$
$504$		0			0
$505$	−17.6155			−0.783881
$506$	−0.587534	+	9.57682i	−0.0261191	+	0.425741i
$507$	−26.4799	−	15.2882i	−1.17601	−	0.678971i
$508$	26.0494	+	3.20831i	1.15575	+	0.142346i
$509$	26.6211	−	15.3697i	1.17996	−	0.681249i	0.223953	−	0.974600i	$-0.428104\pi$
$509$	26.6211	−	15.3697i	1.17996	−	0.681249i	0.956005	+	0.293351i	$0.0947706\pi$
$510$	8.00000	−	12.0818i	0.354246	−	0.534991i
$511$		0			0
$512$	−19.2732	−	11.8551i	−0.851763	−	0.523927i
$513$	−14.2462	−	24.6752i	−0.628986	−	1.08944i
$514$	14.1878	+	28.4697i	0.625799	+	1.25574i
$515$	3.29946	+	1.90495i	0.145392	+	0.0839419i
$516$	−4.81690	+	6.38729i	−0.212052	+	0.281185i
$517$		0			0
$518$		0			0
$519$	−57.6155			−2.52904
$520$	2.71193	+	7.67187i	0.118926	+	0.336434i
$521$	11.0000	−	19.0526i	0.481919	−	0.834708i	−0.517866	−	0.855462i	$-0.673273\pi$
$521$	11.0000	−	19.0526i	0.481919	−	0.834708i	0.999785	+	0.0207541i	$0.00660670\pi$
$522$	−46.8187	+	23.3321i	−2.04920	+	1.02122i
$523$	35.6549	−	20.5854i	1.55908	−	0.900136i	0.561736	−	0.827316i	$-0.310134\pi$
$523$	35.6549	−	20.5854i	1.55908	−	0.900136i	0.997345	−	0.0728196i	$-0.0231997\pi$
$524$	−22.9309	+	9.72350i	−1.00174	+	0.424773i
$525$		0			0
$526$	9.75379	−	14.7304i	0.425285	−	0.642276i
$527$	10.2462	+	17.7470i	0.446332	+	0.773070i
$528$	−4.39874	−	15.3835i	−0.191430	−	0.669480i
$529$	−1.62311	+	2.81130i	−0.0705698	+	0.122230i
$530$	6.34132	+	0.389037i	0.275449	+	0.0168987i
$531$			2.27678i			0.0988038i
$532$		0			0
$533$			7.20217i			0.311961i
$534$	−4.24946	+	69.2664i	−0.183892	+	2.99745i
$535$	−12.0000	+	20.7846i	−0.518805	+	0.898597i
$536$	−24.7243	−	21.1405i	−1.06793	−	0.913129i
$537$	−7.12311	−	12.3376i	−0.307385	−	0.532406i
$538$	−14.0000	−	9.27015i	−0.603583	−	0.399664i
$539$		0			0
$540$	12.4924	+	29.4608i	0.537588	+	1.26779i
$541$	11.4688	−	6.62153i	0.493084	−	0.284682i	−0.232769	−	0.972532i	$-0.574779\pi$
$541$	11.4688	−	6.62153i	0.493084	−	0.284682i	0.725853	+	0.687850i	$0.241445\pi$
$542$	6.46314	+	12.9691i	0.277616	+	0.557071i
$543$	10.5616	−	18.2931i	0.453240	−	0.785034i
$544$	8.34846	−	7.63566i	0.357937	−	0.327376i
$545$	30.7386			1.31670
$546$		0			0
$547$		−	9.59621i		−	0.410304i	−0.978730	−	0.205152i	$-0.934231\pi$
$547$		−	9.59621i		−	0.410304i	0.978730	−	0.205152i	$-0.0657689\pi$
$548$	19.5641	−	25.9423i	0.835737	−	1.10820i
$549$	8.99424	+	5.19283i	0.383865	+	0.221624i
$550$	3.55883	−	1.77354i	0.151749	−	0.0756239i
$551$	−9.12311	−	15.8017i	−0.388657	−	0.673174i
$552$	8.00000	−	43.0299i	0.340503	−	1.83148i
$553$		0			0
$554$	−3.12311	−	2.06798i	−0.132688	−	0.0878598i
$555$	26.8019	−	15.4741i	1.13768	−	0.656838i
$556$	−2.03349	+	16.5106i	−0.0862392	+	0.700205i
$557$	−2.29377	−	1.32431i	−0.0971900	−	0.0561127i	0.450617	−	0.892717i	$-0.351204\pi$
$557$	−2.29377	−	1.32431i	−0.0971900	−	0.0561127i	−0.547807	+	0.836605i	$0.684537\pi$
$558$	−88.5593	−	5.43308i	−3.74902	−	0.230000i
$559$	2.24621			0.0950046
$560$		0			0
$561$	8.00000			0.337760
$562$	8.46936	+	0.519592i	0.357258	+	0.0219176i
$563$	25.8358	+	14.9163i	1.08885	+	0.628648i	0.933270	−	0.359175i	$-0.116942\pi$
$563$	25.8358	+	14.9163i	1.08885	+	0.628648i	0.155580	+	0.987823i	$0.450275\pi$
$564$		0			0
$565$	−7.16368	+	4.13595i	−0.301378	+	0.174001i
$566$	25.8078	+	17.0887i	1.08478	+	0.718292i
$567$		0			0
$568$	22.2462	+	4.13595i	0.933430	+	0.173541i
$569$	6.68466	+	11.5782i	0.280235	+	0.485382i	0.971443	−	0.237275i	$-0.0762541\pi$
$569$	6.68466	+	11.5782i	0.280235	+	0.485382i	−0.691207	+	0.722657i	$0.742921\pi$
$570$	−19.5862	+	9.76079i	−0.820377	+	0.408834i
$571$	−8.02818	−	4.63507i	−0.335969	−	0.193972i	0.322519	−	0.946563i	$-0.395470\pi$
$571$	−8.02818	−	4.63507i	−0.335969	−	0.193972i	−0.658488	+	0.752591i	$0.728804\pi$
$572$	−2.70494	+	3.58680i	−0.113099	+	0.149972i
$573$			48.3272i			2.01890i
$574$		0			0
$575$	10.8769			0.453598
$576$	7.60885	+	48.3903i	0.317035	+	2.01626i
$577$	−3.87689	+	6.71498i	−0.161397	+	0.279548i	−0.935370	−	0.353671i	$-0.884933\pi$
$577$	−3.87689	+	6.71498i	−0.161397	+	0.279548i	0.773973	+	0.633219i	$0.218267\pi$
$578$	−8.20018	−	16.4547i	−0.341083	−	0.684425i
$579$	−29.0956	+	16.7984i	−1.20917	+	0.698117i
$580$	8.00000	+	18.8664i	0.332182	+	0.783383i
$581$		0			0
$582$	43.6155	+	28.8802i	1.80792	+	1.19712i
$583$	1.75379	+	3.03765i	0.0726345	+	0.125807i
$584$	−11.0287	+	12.8984i	−0.456371	+	0.533738i
$585$	8.80776	−	15.2555i	0.364156	−	0.630737i
$586$	−0.899383	+	14.6600i	−0.0371532	+	0.605598i
$587$			21.8868i			0.903365i	0.892179	+	0.451683i	$0.149176\pi$
$587$			21.8868i			0.903365i	−0.892179	+	0.451683i	$0.850824\pi$
$588$		0			0
$589$		−	30.9481i		−	1.27520i
$590$	0.890247	+	0.0546163i	0.0366509	+	0.00224852i
$591$	32.4924	−	56.2785i	1.33656	−	2.31499i
$592$	23.2325	−	6.64308i	0.954849	−	0.273029i
$593$	−9.00000	−	15.5885i	−0.369586	−	0.640141i	0.619915	−	0.784669i	$-0.287167\pi$
$593$	−9.00000	−	15.5885i	−0.369586	−	0.640141i	−0.989501	+	0.144528i	$0.953834\pi$
$594$	−9.75379	+	14.7304i	−0.400203	+	0.604396i
$595$		0			0
$596$	27.1231	−	11.5012i	1.11101	−	0.471106i
$597$	−47.7282	+	27.5559i	−1.95338	+	1.12779i
$598$	−10.9987	+	5.48120i	−0.449771	+	0.224143i
$599$	6.24621	−	10.8188i	0.255213	−	0.442042i	−0.709740	−	0.704464i	$-0.751188\pi$
$599$	6.24621	−	10.8188i	0.255213	−	0.442042i	0.964953	+	0.262421i	$0.0845210\pi$
$600$	−17.1010	+	6.04501i	−0.698144	+	0.246787i
$601$	−16.2462			−0.662697			−0.331348	−	0.943508i	$-0.607504\pi$
$601$	−16.2462			−0.662697			−0.331348	+	0.943508i	$0.607504\pi$
$602$		0			0
$603$			70.4228i			2.86784i
$604$	−13.0982	+	17.3685i	−0.532959	+	0.706713i
$605$	13.5818	+	7.84144i	0.552178	+	0.318800i
$606$	19.7872	+	39.7056i	0.803802	+	1.61293i
$607$	−20.4924	−	35.4939i	−0.831762	−	1.44065i	−0.896640	−	0.442760i	$-0.853999\pi$
$607$	−20.4924	−	35.4939i	−0.831762	−	1.44065i	0.0648782	−	0.997893i	$-0.479334\pi$
$608$	−16.6847	+	3.68260i	−0.676652	+	0.149349i
$609$		0			0
$610$	2.24621	−	3.39228i	0.0909464	−	0.137349i
$611$		0			0
$612$	−24.3087	−	2.99393i	−0.982623	−	0.121022i
$613$	−1.93211	−	1.11550i	−0.0780371	−	0.0450547i	0.460474	−	0.887673i	$-0.347680\pi$
$613$	−1.93211	−	1.11550i	−0.0780371	−	0.0450547i	−0.538511	+	0.842619i	$0.681013\pi$
$614$	2.18913	−	35.6829i	0.0883462	−	1.44005i
$615$	21.7538			0.877197
$616$		0			0
$617$	−29.3693			−1.18236			−0.591182	−	0.806538i	$-0.701339\pi$
$617$	−29.3693			−1.18236			−0.591182	+	0.806538i	$0.701339\pi$
$618$	0.587534	−	9.57682i	0.0236341	−	0.385236i
$619$	17.0224	+	9.82790i	0.684189	+	0.395017i	0.801431	−	0.598087i	$-0.204072\pi$
$619$	17.0224	+	9.82790i	0.684189	+	0.395017i	−0.117243	+	0.993103i	$0.537405\pi$
$620$	−4.24879	+	34.4974i	−0.170636	+	1.38545i
$621$	−41.8526	+	24.1636i	−1.67949	+	0.969651i
$622$	−9.75379	+	14.7304i	−0.391091	+	0.590635i
$623$		0			0
$624$	14.2462	−	14.7304i	0.570305	−	0.589688i
$625$	4.93845	+	8.55364i	0.197538	+	0.342146i
$626$	−13.0816	−	26.2498i	−0.522845	−	1.04915i
$627$	−10.4631	−	6.04090i	−0.417858	−	0.241250i
$628$	−13.5422	−	10.2127i	−0.540392	−	0.407530i
$629$			12.0818i			0.481733i
$630$		0			0
$631$	−3.50758			−0.139634			−0.0698172	−	0.997560i	$-0.522242\pi$
$631$	−3.50758			−0.139634			−0.0698172	+	0.997560i	$0.522242\pi$
$632$		0			0
$633$	−7.12311	+	12.3376i	−0.283118	+	0.490375i
$634$	5.23506	−	2.60889i	0.207911	−	0.103612i
$635$	−19.2765	+	11.1293i	−0.764966	+	0.441654i
$636$	−6.24621	−	14.7304i	−0.247678	−	0.584099i
$637$		0			0
$638$	−6.24621	+	9.43318i	−0.247290	+	0.373463i
$639$	−24.4924	−	42.4221i	−0.968905	−	1.67819i
$640$	19.1037	−	1.81434i	0.755139	−	0.0717181i
$641$	2.68466	−	4.64996i	0.106038	−	0.183663i	−0.808124	−	0.589012i	$-0.799517\pi$
$641$	2.68466	−	4.64996i	0.106038	−	0.183663i	0.914162	+	0.405350i	$0.132850\pi$
$642$	60.3281	+	3.70111i	2.38096	+	0.146071i
$643$		−	5.66906i		−	0.223566i	−0.993733	−	0.111783i	$-0.964344\pi$
$643$		−	5.66906i		−	0.223566i	0.993733	−	0.111783i	$-0.0356562\pi$
$644$		0			0
$645$		−	6.78456i		−	0.267142i
$646$	0.523133	−	8.52708i	0.0205824	−	0.335494i
$647$	−21.6155	+	37.4392i	−0.849794	+	1.47189i	0.0315977	+	0.999501i	$0.489940\pi$
$647$	−21.6155	+	37.4392i	−0.849794	+	1.47189i	−0.881392	+	0.472386i	$0.843393\pi$
$648$	18.6075	−	21.7619i	0.730970	−	0.854888i
$649$	0.246211	+	0.426450i	0.00966464	+	0.0167396i
$650$	4.24621	+	2.81164i	0.166550	+	0.110282i
$651$		0			0
$652$	−24.6847	+	10.4672i	−0.966726	+	0.409926i
$653$	27.4459	−	15.8459i	1.07404	−	0.620098i	0.144759	−	0.989467i	$-0.453759\pi$
$653$	27.4459	−	15.8459i	1.07404	−	0.620098i	0.929283	+	0.369369i	$0.120426\pi$
$654$	−34.5282	−	69.2852i	−1.35016	−	2.70927i
$655$	10.5616	−	18.2931i	0.412674	−	0.714772i
$656$	16.4773	+	4.12128i	0.643329	+	0.160909i
$657$	36.7386			1.43331
$658$		0			0
$659$		−	6.62153i		−	0.257938i	−0.991649	−	0.128969i	$-0.958833\pi$
$659$		−	6.62153i		−	0.257938i	0.991649	−	0.128969i	$-0.0411668\pi$
$660$	10.8337	+	8.17014i	0.421703	+	0.318022i
$661$	−38.7339	−	22.3630i	−1.50657	−	0.869821i	−0.999971	−	0.00764267i	$-0.997567\pi$
$661$	−38.7339	−	22.3630i	−1.50657	−	0.869821i	−0.506604	−	0.862179i	$-0.669099\pi$
$662$	18.8513	−	9.39453i	0.732677	−	0.365129i
$663$	5.12311	+	8.87348i	0.198965	+	0.344617i
$664$	−2.93087	+	15.7644i	−0.113740	+	0.611777i
$665$		0			0
$666$	−43.6155	−	28.8802i	−1.69007	−	1.11908i
$667$	−26.8019	+	15.4741i	−1.03777	+	0.599159i
$668$	15.8800	+	1.95583i	0.614416	+	0.0756731i
$669$	15.0507	+	8.68951i	0.581893	+	0.335956i
$670$	27.5361	+	1.68933i	1.06381	+	0.0652645i
$671$	2.24621			0.0867140
$672$		0			0
$673$	−38.9848			−1.50276			−0.751378	−	0.659872i	$-0.770610\pi$
$673$	−38.9848			−1.50276			−0.751378	+	0.659872i	$0.770610\pi$
$674$	1.23779	+	0.0759378i	0.0476778	+	0.00292502i
$675$	17.3444	+	10.0138i	0.667588	+	0.385432i
$676$	20.0944	+	2.47488i	0.772861	+	0.0951876i
$677$	−14.8698	+	8.58511i	−0.571494	+	0.329952i	−0.757746	−	0.652550i	$-0.773699\pi$
$677$	−14.8698	+	8.58511i	−0.571494	+	0.329952i	0.186252	+	0.982502i	$0.440366\pi$
$678$	17.3693	+	11.5012i	0.667065	+	0.441699i
$679$		0			0
$680$	−1.75379	+	9.43318i	−0.0672547	+	0.361746i
$681$	14.8078	+	25.6478i	0.567435	+	0.982826i
$682$	−17.1751	+	8.55918i	−0.657667	+	0.327748i
$683$	−0.502848	−	0.290319i	−0.0192409	−	0.0111088i	0.490349	−	0.871526i	$-0.336869\pi$
$683$	−0.502848	−	0.290319i	−0.0192409	−	0.0111088i	−0.509590	+	0.860418i	$0.670203\pi$
$684$	29.5325	+	22.2716i	1.12920	+	0.851575i
$685$			27.5559i			1.05286i
$686$		0			0
$687$	78.1080			2.98000
$688$	1.28534	−	5.13892i	0.0490033	−	0.195920i
$689$	−2.24621	+	3.89055i	−0.0855738	+	0.148218i
$690$	16.5557	+	33.2210i	0.630264	+	1.26470i
$691$	33.6435	−	19.4241i	1.27986	−	0.738928i	0.303038	−	0.952978i	$-0.401999\pi$
$691$	33.6435	−	19.4241i	1.27986	−	0.738928i	0.976823	+	0.214051i	$0.0686657\pi$
$692$	35.1231	−	14.8934i	1.33518	−	0.566163i
$693$		0			0
$694$	−9.56155	−	6.33122i	−0.362952	−	0.240330i
$695$	−7.05398	−	12.2178i	−0.267573	−	0.463449i
$696$	33.5387	−	39.2244i	1.27128	−	1.48680i
$697$	−4.24621	+	7.35465i	−0.160837	+	0.278577i
$698$	−2.36822	+	38.6020i	−0.0896383	+	1.46111i
$699$		−	49.0708i		−	1.85603i
$700$		0			0
$701$		−	2.23100i		−	0.0842639i	−0.999112	−	0.0421319i	$-0.986585\pi$
$701$		−	2.23100i		−	0.0842639i	0.999112	−	0.0421319i	$-0.0134150\pi$
$702$	−22.5850	−	1.38558i	−0.852414	−	0.0522952i
$703$	9.12311	−	15.8017i	0.344084	−	0.595972i
$704$	6.65810	+	8.24088i	0.250937	+	0.310590i
$705$		0			0
$706$	6.05398	−	9.14286i	0.227844	−	0.344096i
$707$		0			0
$708$	−0.876894	−	2.06798i	−0.0329557	−	0.0777193i
$709$	−24.8698	+	14.3586i	−0.934004	+	0.539247i	−0.888076	−	0.459697i	$-0.847958\pi$
$709$	−24.8698	+	14.3586i	−0.934004	+	0.539247i	−0.0459283	+	0.998945i	$0.514625\pi$
$710$	−17.1751	+	8.55918i	−0.644569	+	0.321220i
$711$		0			0
$712$	−15.3146	−	43.3241i	−0.573940	−	1.62364i
$713$	−52.4924			−1.96586
$714$		0			0
$715$		−	3.80989i		−	0.142482i
$716$	7.53156	+	5.67983i	0.281467	+	0.212265i
$717$	46.0784	+	26.6034i	1.72083	+	0.993522i
$718$	−19.7872	−	39.7056i	−0.738453	−	1.48180i
$719$	26.2462	+	45.4598i	0.978819	+	1.69536i	0.666711	+	0.745317i	$0.267702\pi$
$719$	26.2462	+	45.4598i	0.978819	+	1.69536i	0.312108	+	0.950047i	$0.398965\pi$
$720$	−29.8617	−	28.8802i	−1.11288	−	1.07630i
$721$		0			0
$722$	7.71165	−	11.6463i	0.286998	−	0.433431i
$723$	−9.81910	+	5.66906i	−0.365176	+	0.210835i
$724$	−1.70973	+	13.8818i	−0.0635415	+	0.515915i
$725$	11.1072	+	6.41273i	0.412510	+	0.238163i
$726$	2.41850	−	39.4216i	0.0897589	−	1.46307i
$727$	−16.9848			−0.629933			−0.314967	−	0.949103i	$-0.601993\pi$
$727$	−16.9848			−0.629933			−0.314967	+	0.949103i	$0.601993\pi$
$728$		0			0
$729$	23.4924			0.870090
$730$	0.881300	−	14.3652i	0.0326184	−	0.531681i
$731$	2.29377	+	1.32431i	0.0848380	+	0.0489813i
$732$	−10.1694	−	1.25249i	−0.375871	−	0.0462933i
$733$	−25.3330	+	14.6260i	−0.935695	+	0.540224i	−0.888608	−	0.458667i	$-0.848327\pi$
$733$	−25.3330	+	14.6260i	−0.935695	+	0.540224i	−0.0470868	+	0.998891i	$0.514994\pi$
$734$	8.00000	−	12.0818i	0.295285	−	0.445947i
$735$		0			0
$736$	6.24621	+	28.2995i	0.230238	+	1.04313i
$737$	7.61553	+	13.1905i	0.280522	+	0.485878i
$738$	−16.4004	−	32.9094i	−0.603706	−	1.21141i
$739$	−18.4913	−	10.6760i	−0.680214	−	0.392722i	0.119721	−	0.992808i	$-0.461800\pi$
$739$	−18.4913	−	10.6760i	−0.680214	−	0.392722i	−0.799936	+	0.600086i	$0.795133\pi$
$740$	−12.3387	+	16.3614i	−0.453581	+	0.601456i
$741$		−	15.4741i		−	0.568454i
$742$		0			0
$743$	0.630683			0.0231375			0.0115688	−	0.999933i	$-0.496317\pi$
$743$	0.630683			0.0231375			0.0115688	+	0.999933i	$0.496317\pi$
$744$	82.5300	−	29.1735i	3.02570	−	1.06955i
$745$	−12.4924	+	21.6375i	−0.457687	+	0.792737i
$746$	−18.6449	+	9.29169i	−0.682640	+	0.340193i
$747$	30.0617	−	17.3561i	1.09990	−	0.635028i
$748$	−4.87689	+	2.06798i	−0.178317	+	0.0756127i
$749$		0			0
$750$	28.4924	−	43.0299i	1.04040	−	1.57123i
$751$	−4.31534	−	7.47439i	−0.157469	−	0.272744i	0.776486	−	0.630134i	$-0.217000\pi$
$751$	−4.31534	−	7.47439i	−0.157469	−	0.272744i	−0.933955	+	0.357390i	$0.883667\pi$
$752$		0			0
$753$	−16.5616	+	28.6855i	−0.603537	+	1.04536i
$754$	−14.4631	−	0.887307i	−0.526716	−	0.0323138i
$755$		−	18.4487i		−	0.671419i
$756$		0			0
$757$			26.3946i			0.959328i	0.877452	+	0.479664i	$0.159241\pi$
$757$			26.3946i			0.959328i	−0.877452	+	0.479664i	$0.840759\pi$
$758$	3.15292	−	51.3926i	0.114519	−	1.86666i
$759$	−10.2462	+	17.7470i	−0.371914	+	0.644174i
$760$	9.41687	−	11.0133i	0.341586	−	0.399493i
$761$	−4.36932	−	7.56788i	−0.158388	−	0.274335i	0.775900	−	0.630856i	$-0.217296\pi$
$761$	−4.36932	−	7.56788i	−0.158388	−	0.274335i	−0.934287	+	0.356521i	$0.883963\pi$
$762$	46.7386	+	30.9481i	1.69316	+	1.12113i
$763$		0			0
$764$	−12.4924	−	29.4608i	−0.451960	−	1.06585i
$765$	17.9885	−	10.3857i	0.650375	−	0.375494i
$766$	−2.83374	−	5.68627i	−0.102387	−	0.205453i
$767$	−0.315342	+	0.546188i	−0.0113863	+	0.0197217i
$768$	−25.5484	−	41.0219i	−0.921898	−	1.48025i
$769$	−40.2462			−1.45132			−0.725658	−	0.688056i	$-0.758464\pi$
$769$	−40.2462			−1.45132			−0.725658	+	0.688056i	$0.758464\pi$
$770$		0			0
$771$			67.9372i			2.44670i
$772$	13.3947	−	17.7616i	0.482087	−	0.639255i
$773$	1.46890	+	0.848071i	0.0528327	+	0.0305030i	0.526184	−	0.850371i	$-0.323622\pi$
$773$	1.46890	+	0.848071i	0.0528327	+	0.0305030i	−0.473351	+	0.880874i	$0.656956\pi$
$774$	−10.2638	+	5.11494i	−0.368924	+	0.183853i
$775$	10.8769	+	18.8393i	0.390710	+	0.676729i
$776$	−34.0540	−	6.33122i	−1.22247	−	0.227277i
$777$		0			0
$778$	−29.3693	−	19.4470i	−1.05294	−	0.697209i
$779$	11.1072	−	6.41273i	0.397956	−	0.229760i
$780$	−2.12440	+	17.2487i	−0.0760655	+	0.617602i
$781$	−9.17507	−	5.29723i	−0.328310	−	0.189550i
$782$	−14.4631	−	0.887307i	−0.517201	−	0.0317300i
$783$	−56.9848			−2.03647
$784$		0			0
$785$	14.3845			0.513404
$786$	−53.0966	−	3.25745i	−1.89389	−	0.116189i
$787$	9.13543	+	5.27434i	0.325643	+	0.188010i	0.653905	−	0.756577i	$-0.273130\pi$
$787$	9.13543	+	5.27434i	0.325643	+	0.188010i	−0.328262	+	0.944587i	$0.606463\pi$
$788$	−5.25994	+	42.7072i	−0.187378	+	1.52138i
$789$	32.6775	−	18.8664i	1.16335	−	0.671660i
$790$		0			0
$791$		0			0
$792$	4.19224	−	22.5490i	0.148965	−	0.801242i
$793$	1.43845	+	2.49146i	0.0510808	+	0.0884745i
$794$	26.0269	−	12.9705i	0.923660	−	0.460305i
$795$	11.7512	+	6.78456i	0.416772	+	0.240624i
$796$	21.9725	−	29.1360i	0.778796	−	1.03270i
$797$			25.8597i			0.915998i	0.888953	+	0.457999i	$0.151434\pi$
$797$			25.8597i			0.915998i	−0.888953	+	0.457999i	$0.848566\pi$
$798$		0			0
$799$		0			0
$800$	8.86233	−	8.10566i	0.313331	−	0.286578i
$801$	−49.7386	+	86.1498i	−1.75743	+	3.04395i
$802$	−0.553130	−	1.10993i	−0.0195317	−	0.0391928i
$803$	6.88130	−	3.97292i	0.242836	−	0.140201i
$804$	−27.1231	−	63.9643i	−0.956558	−	2.25585i
$805$		0			0
$806$	−20.4924	−	13.5691i	−0.721815	−	0.477952i
$807$	−17.9309	−	31.0572i	−0.631197	−	1.09326i
$808$	−22.3263	−	19.0901i	−0.785437	−	0.671586i
$809$	−18.9309	+	32.7892i	−0.665574	+	1.15281i	0.313555	+	0.949570i	$0.398480\pi$
$809$	−18.9309	+	32.7892i	−0.665574	+	1.15281i	−0.979129	+	0.203238i	$0.934853\pi$
$810$	−1.48692	+	24.2368i	−0.0522449	+	0.851594i
$811$		−	15.8459i		−	0.556425i	−0.960520	−	0.278213i	$-0.910258\pi$
$811$		−	15.8459i		−	0.556425i	0.960520	−	0.278213i	$-0.0897420\pi$
$812$		0			0
$813$			30.9481i			1.08540i
$814$	−11.2925	−	0.692789i	−0.395801	−	0.0242822i
$815$	11.3693	−	19.6922i	0.398250	−	0.689789i
$816$	23.2325	−	6.64308i	0.813300	−	0.232554i
$817$	−2.00000	−	3.46410i	−0.0699711	−	0.121194i
$818$	20.3002	−	30.6578i	0.709779	−	1.07193i
$819$		0			0
$820$	−13.2614	+	5.62329i	−0.463107	+	0.196374i
$821$	−29.0956	+	16.7984i	−1.01545	+	0.586268i	−0.912781	−	0.408449i	$-0.866070\pi$
$821$	−29.0956	+	16.7984i	−1.01545	+	0.586268i	−0.102664	+	0.994716i	$0.532737\pi$
$822$	62.1112	−	30.9531i	2.16638	−	1.07961i
$823$	16.4924	−	28.5657i	0.574890	−	0.995738i	−0.421164	−	0.906985i	$-0.638378\pi$
$823$	16.4924	−	28.5657i	0.574890	−	0.995738i	0.996054	−	0.0887536i	$-0.0282884\pi$
$824$	2.11741	+	5.99002i	0.0737635	+	0.208672i
$825$	8.49242			0.295668
$826$		0			0
$827$		−	6.20393i		−	0.215732i	−0.994165	−	0.107866i	$-0.965598\pi$
$827$		−	6.20393i		−	0.215732i	0.994165	−	0.107866i	$-0.0344017\pi$
$828$	37.7757	−	50.0912i	1.31280	−	1.74079i
$829$	40.3837	+	23.3155i	1.40258	+	0.809781i	0.994657	−	0.103234i	$-0.0329191\pi$
$829$	40.3837	+	23.3155i	1.40258	+	0.809781i	0.407925	+	0.913015i	$0.366252\pi$
$830$	−6.06531	−	12.1708i	−0.210530	−	0.422455i
$831$	−4.00000	−	6.92820i	−0.138758	−	0.240337i
$832$	−4.87689	+	12.6624i	−0.169076	+	0.438991i
$833$		0			0
$834$	−19.6155	+	29.6238i	−0.679230	+	1.02579i
$835$	−11.7512	+	6.78456i	−0.406667	+	0.234790i
$836$	7.94001	+	0.977913i	0.274611	+	0.0338218i
$837$	−83.7051	−	48.3272i	−2.89327	−	1.67043i
$838$	−2.41850	+	39.4216i	−0.0835457	+	1.36180i
$839$	−6.73863			−0.232643			−0.116322	−	0.993212i	$-0.537110\pi$
$839$	−6.73863			−0.232643			−0.116322	+	0.993212i	$0.537110\pi$
$840$		0			0
$841$	−7.49242			−0.258359
$842$	−2.32190	+	37.8470i	−0.0800179	+	1.30429i
$843$	15.6947	+	9.06134i	0.540554	+	0.312089i
$844$	1.15310	−	9.36244i	0.0396914	−	0.322268i
$845$	−14.8698	+	8.58511i	−0.511538	+	0.295337i
$846$		0			0
$847$		0			0
$848$	7.61553	+	7.36520i	0.261518	+	0.252922i
$849$	33.0540	+	57.2512i	1.13441	+	1.96485i
$850$	2.67844	+	5.37462i	0.0918697	+	0.184348i
$851$	−26.8019	−	15.4741i	−0.918757	−	0.530444i
$852$	38.5850	+	29.0984i	1.32190	+	0.996894i
$853$			25.4421i			0.871121i	0.900159	+	0.435561i	$0.143450\pi$
$853$			25.4421i			0.871121i	−0.900159	+	0.435561i	$0.856550\pi$
$854$		0			0
$855$	−31.3693			−1.07281
$856$	−37.7335	+	13.3384i	−1.28970	+	0.455897i
$857$	23.4924	−	40.6901i	0.802486	−	1.38995i	−0.115489	−	0.993309i	$-0.536844\pi$
$857$	23.4924	−	40.6901i	0.802486	−	1.38995i	0.917975	−	0.396638i	$-0.129823\pi$
$858$	−8.58753	+	4.27959i	−0.293174	+	0.146103i
$859$	−24.5478	+	14.1727i	−0.837559	+	0.483565i	−0.856434	−	0.516257i	$-0.827325\pi$
$859$	−24.5478	+	14.1727i	−0.837559	+	0.483565i	0.0188750	+	0.999822i	$0.493992\pi$
$860$	1.75379	+	4.13595i	0.0598037	+	0.141035i
$861$		0			0
$862$	13.7538	−	20.7713i	0.468456	−	0.707473i
$863$	−18.2462	−	31.6034i	−0.621108	−	1.07579i	−0.989280	−	0.146033i	$-0.953349\pi$
$863$	−18.2462	−	31.6034i	−0.621108	−	1.07579i	0.368171	−	0.929758i	$-0.379984\pi$
$864$	−16.0937	+	50.8774i	−0.547518	+	1.73088i
$865$	−16.1771	+	28.0195i	−0.550037	+	0.952692i
$866$	26.1032	+	1.60142i	0.887021	+	0.0544184i
$867$		−	39.2658i		−	1.33354i
$868$		0			0
$869$		0			0
$870$	−2.68007	+	43.6852i	−0.0908627	+	1.48107i
$871$	−9.75379	+	16.8941i	−0.330495	+	0.572433i
$872$	38.9588	+	33.3116i	1.31931	+	1.12807i
$873$	37.4924	+	64.9388i	1.26893	+	2.19784i
$874$	18.2462	+	12.0818i	0.617187	+	0.408673i
$875$		0			0
$876$	−33.3693	+	14.1498i	−1.12744	+	0.478076i
$877$	30.7454	−	17.7509i	1.03820	−	0.599404i	0.118875	−	0.992909i	$-0.462071\pi$
$877$	30.7454	−	17.7509i	1.03820	−	0.599404i	0.919322	+	0.393505i	$0.128738\pi$
$878$	14.3431	+	28.7813i	0.484058	+	0.971323i
$879$	−15.6847	+	27.1666i	−0.529030	+	0.916308i
$880$	−8.71633	−	2.18013i	−0.293828	−	0.0734920i
$881$	44.2462			1.49069			0.745346	−	0.666677i	$-0.232284\pi$
$881$	44.2462			1.49069			0.745346	+	0.666677i	$0.232284\pi$
$882$		0			0
$883$		−	4.71659i		−	0.158726i	−0.996846	−	0.0793629i	$-0.974711\pi$
$883$		−	4.71659i		−	0.158726i	0.996846	−	0.0793629i	$-0.0252886\pi$
$884$	−5.41687	−	4.08507i	−0.182189	−	0.137396i
$885$	1.64973	+	0.952473i	0.0554551	+	0.0320170i
$886$	−9.32247	+	4.64585i	−0.313195	+	0.156080i
$887$	14.2462	+	24.6752i	0.478341	+	0.828511i	0.999692	−	0.0248317i	$-0.00790498\pi$
$887$	14.2462	+	24.6752i	0.478341	+	0.828511i	−0.521351	+	0.853343i	$0.674572\pi$
$888$	50.7386	+	9.43318i	1.70268	+	0.316557i
$889$		0			0
$890$	32.4924	+	21.5150i	1.08915	+	0.721183i
$891$	−11.6100	+	6.70305i	−0.388950	+	0.224561i
$892$	−11.4213	−	1.40668i	−0.382413	−	0.0470990i
$893$		0			0
$894$	62.8037	+	3.85298i	2.10047	+	0.128863i
$895$	−8.00000			−0.267411
$896$		0			0
$897$	−26.2462			−0.876335
$898$	−23.6276	−	1.44954i	−0.788463	−	0.0483718i
$899$	−53.6038	−	30.9481i	−1.78779	−	1.03218i
$900$	−25.8050	−	3.17822i	−0.860167	−	0.105941i
$901$	−4.58753	+	2.64861i	−0.152833	+	0.0882381i
$902$	−6.63068	−	4.39053i	−0.220778	−	0.146189i
$903$		0			0
$904$	−13.5616	−	2.52132i	−0.451051	−	0.0838580i
$905$	−5.93087	−	10.2726i	−0.197149	−	0.341472i
$906$	−41.5837	+	20.7232i	−1.38152	+	0.688482i
$907$	44.6492	+	25.7782i	1.48255	+	0.855951i	0.999804	−	0.0198082i	$-0.00630555\pi$
$907$	44.6492	+	25.7782i	1.48255	+	0.855951i	0.482748	+	0.875760i	$0.339639\pi$
$908$	−15.6569	−	11.8074i	−0.519591	−	0.391844i
$909$			63.5924i			2.10923i
$910$		0			0
$911$	11.8617			0.392997			0.196498	−	0.980504i	$-0.437043\pi$
$911$	11.8617			0.392997			0.196498	+	0.980504i	$0.437043\pi$
$912$	−35.4019	−	8.85469i	−1.17227	−	0.293208i
$913$	3.75379	−	6.50175i	0.124232	−	0.215177i
$914$	10.9563	+	21.9851i	0.362401	+	0.727204i
$915$	7.52534	−	4.34475i	0.248780	−	0.143633i
$916$	−47.6155	+	20.1907i	−1.57326	+	0.667118i
$917$		0			0
$918$	−22.2462	−	14.7304i	−0.734234	−	0.486176i
$919$	−4.00000	−	6.92820i	−0.131948	−	0.228540i	0.792480	−	0.609898i	$-0.208790\pi$
$919$	−4.00000	−	6.92820i	−0.131948	−	0.228540i	−0.924427	+	0.381358i	$0.875456\pi$
$920$	−18.6801	−	15.9723i	−0.615864	−	0.526593i
$921$	38.1771	−	66.1246i	1.25798	−	2.17888i
$922$	−2.11061	+	34.4031i	−0.0695094	+	1.13301i
$923$		−	13.5691i		−	0.446633i
$924$		0			0
$925$			12.8255i			0.421699i
$926$		0			0
$927$	6.87689	−	11.9111i	0.225867	−	0.391213i
$928$	−10.3062	+	32.5813i	−0.338318	+	1.06953i
$929$	1.24621	+	2.15850i	0.0408869	+	0.0708181i	0.885745	−	0.464173i	$-0.153648\pi$
$929$	1.24621	+	2.15850i	0.0408869	+	0.0708181i	−0.844858	+	0.534991i	$0.820315\pi$
$930$	−40.9848	+	61.8963i	−1.34395	+	2.02966i
$931$		0			0
$932$	12.6847	+	29.9142i	0.415500	+	0.979871i
$933$	−32.6775	+	18.8664i	−1.06981	+	0.617657i
$934$	−3.82312	+	1.90525i	−0.125096	+	0.0623416i
$935$	2.24621	−	3.89055i	0.0734590	−	0.127235i
$936$	27.6956	−	9.79012i	0.905260	−	0.320000i
$937$	34.9848			1.14291			0.571453	−	0.820635i	$-0.306380\pi$
$937$	34.9848			1.14291			0.571453	+	0.820635i	$0.306380\pi$
$938$		0			0
$939$		−	62.6400i		−	2.04418i
$940$		0			0
$941$	−26.6211	−	15.3697i	−0.867821	−	0.501037i	−0.00119780	−	0.999999i	$-0.500381\pi$
$941$	−26.6211	−	15.3697i	−0.867821	−	0.501037i	−0.866624	+	0.498962i	$0.833715\pi$
$942$	−16.1578	−	32.4227i	−0.526451	−	1.05639i
$943$	−10.8769	−	18.8393i	−0.354200	−	0.613493i
$944$	1.06913	+	1.03399i	0.0347972	+	0.0336534i
$945$		0			0
$946$	−1.36932	+	2.06798i	−0.0445203	+	0.0672357i
$947$	36.1181	−	20.8528i	1.17368	−	0.677625i	0.219137	−	0.975694i	$-0.429676\pi$
$947$	36.1181	−	20.8528i	1.17368	−	0.677625i	0.954544	+	0.298069i	$0.0963424\pi$
$948$		0			0
$949$	8.81341	+	5.08842i	0.286095	+	0.165177i
$950$	0.555333	−	9.05195i	0.0180174	−	0.293684i
$951$	12.4924			0.405095
$952$		0			0
$953$	−17.5076			−0.567126			−0.283563	−	0.958954i	$-0.591517\pi$
$953$	−17.5076			−0.567126			−0.283563	+	0.958954i	$0.591517\pi$
$954$	1.40443	−	22.8923i	0.0454702	−	0.741166i
$955$	23.5024	+	13.5691i	0.760520	+	0.439087i
$956$	−34.9668	−	4.30661i	−1.13091	−	0.139286i
$957$	−20.9263	+	12.0818i	−0.676450	+	0.390549i
$958$	8.00000	−	12.0818i	0.258468	−	0.390345i
$959$		0			0
$960$	38.2462	+	14.7304i	1.23439	+	0.475422i
$961$	−36.9924	−	64.0728i	−1.19330	−	2.06686i
$962$	−6.46314	−	12.9691i	−0.208380	−	0.418141i
$963$	75.0329	+	43.3203i	2.41790	+	1.39598i
$964$	4.52041	−	5.99413i	0.145592	−	0.193058i
$965$			18.8664i			0.607329i
$966$		0			0
$967$	−10.8769			−0.349777			−0.174889	−	0.984588i	$-0.555957\pi$
$967$	−10.8769			−0.349777			−0.174889	+	0.984588i	$0.555957\pi$
$968$	8.71602	+	24.6571i	0.280143	+	0.792508i
$969$	9.12311	−	15.8017i	0.293076	−	0.507623i
$970$	26.2912	−	13.1022i	0.844159	−	0.420686i
$971$	−9.49709	+	5.48314i	−0.304776	+	0.175962i	−0.644586	−	0.764531i	$-0.722970\pi$
$971$	−9.49709	+	5.48314i	−0.304776	+	0.175962i	0.339810	+	0.940494i	$0.389637\pi$
$972$	4.19224	−	1.77766i	0.134466	−	0.0570183i
$973$		0			0
$974$	0.492423	−	0.743668i	0.0157782	−	0.0238287i
$975$	5.43845	+	9.41967i	0.174170	+	0.301671i
$976$	6.52313	−	1.86522i	0.208800	−	0.0597042i
$977$	−11.8769	+	20.5714i	−0.379976	+	0.658137i	−0.991058	−	0.133430i	$-0.957401\pi$
$977$	−11.8769	+	20.5714i	−0.379976	+	0.658137i	0.611083	+	0.791567i	$0.290734\pi$
$978$	−57.1575	−	3.50659i	−1.82769	−	0.112128i
$979$			21.5150i			0.687621i
$980$		0			0
$981$		−	110.967i		−	3.54291i
$982$	−2.95971	+	48.2434i	−0.0944483	+	1.53951i
$983$	17.1231	−	29.6581i	0.546142	−	0.945946i	−0.452392	−	0.891819i	$-0.649429\pi$
$983$	17.1231	−	29.6581i	0.546142	−	0.945946i	0.998534	−	0.0541268i	$-0.0172375\pi$
$984$	27.5712	+	23.5747i	0.878939	+	0.751534i
$985$	−18.2462	−	31.6034i	−0.581373	−	1.00697i
$986$	−14.2462	−	9.43318i	−0.453692	−	0.300414i
$987$		0			0
$988$	4.00000	+	9.43318i	0.127257	+	0.300109i
$989$	−5.87560	+	3.39228i	−0.186833	+	0.107868i
$990$	8.67566	+	17.4088i	0.275731	+	0.553288i
$991$	18.2462	−	31.6034i	0.579610	−	1.00391i	−0.415914	−	0.909404i	$-0.636538\pi$
$991$	18.2462	−	31.6034i	0.579610	−	1.00391i	0.995524	−	0.0945100i	$-0.0301284\pi$
$992$	−42.7700	+	39.1183i	−1.35795	+	1.24201i
$993$	44.9848			1.42755
$994$		0			0
$995$			30.9481i			0.981122i
$996$	−20.6201	+	27.3426i	−0.653372	+	0.866382i
$997$	−28.6324	−	16.5309i	−0.906799	−	0.523540i	−0.0273989	−	0.999625i	$-0.508722\pi$
$997$	−28.6324	−	16.5309i	−0.906799	−	0.523540i	−0.879400	+	0.476084i	$0.842056\pi$
$998$	−11.2051	+	5.58403i	−0.354690	+	0.176759i
$999$	−28.4924	−	49.3503i	−0.901460	−	1.56138i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.2.p.f.165.1		8
4.3	odd	2		1568.2.t.d.753.4		8
7.2	even	3	inner	392.2.p.f.373.3		8
7.3	odd	6		392.2.b.c.197.3		4
7.4	even	3		56.2.b.b.29.3	✓	4
7.5	odd	6		392.2.p.e.373.3		8
7.6	odd	2		392.2.p.e.165.1		8
8.3	odd	2		1568.2.t.d.753.1		8
8.5	even	2	inner	392.2.p.f.165.3		8
21.11	odd	6		504.2.c.d.253.2		4
28.3	even	6		1568.2.b.d.785.4		4
28.11	odd	6		224.2.b.b.113.1		4
28.19	even	6		1568.2.t.e.177.4		8
28.23	odd	6		1568.2.t.d.177.1		8
28.27	even	2		1568.2.t.e.753.1		8
56.3	even	6		1568.2.b.d.785.1		4
56.5	odd	6		392.2.p.e.373.1		8
56.11	odd	6		224.2.b.b.113.4		4
56.13	odd	2		392.2.p.e.165.3		8
56.19	even	6		1568.2.t.e.177.1		8
56.27	even	2		1568.2.t.e.753.4		8
56.37	even	6	inner	392.2.p.f.373.1		8
56.45	odd	6		392.2.b.c.197.4		4
56.51	odd	6		1568.2.t.d.177.4		8
56.53	even	6		56.2.b.b.29.4	yes	4
84.11	even	6		2016.2.c.c.1009.3		4
112.11	odd	12		1792.2.a.v.1.1		4
112.53	even	12		1792.2.a.x.1.4		4
112.67	odd	12		1792.2.a.v.1.4		4
112.109	even	12		1792.2.a.x.1.1		4
168.11	even	6		2016.2.c.c.1009.2		4
168.53	odd	6		504.2.c.d.253.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.2.b.b.29.3	✓	4	7.4	even	3
56.2.b.b.29.4	yes	4	56.53	even	6
224.2.b.b.113.1		4	28.11	odd	6
224.2.b.b.113.4		4	56.11	odd	6
392.2.b.c.197.3		4	7.3	odd	6
392.2.b.c.197.4		4	56.45	odd	6
392.2.p.e.165.1		8	7.6	odd	2
392.2.p.e.165.3		8	56.13	odd	2
392.2.p.e.373.1		8	56.5	odd	6
392.2.p.e.373.3		8	7.5	odd	6
392.2.p.f.165.1		8	1.1	even	1	trivial
392.2.p.f.165.3		8	8.5	even	2	inner
392.2.p.f.373.1		8	56.37	even	6	inner
392.2.p.f.373.3		8	7.2	even	3	inner
504.2.c.d.253.1		4	168.53	odd	6
504.2.c.d.253.2		4	21.11	odd	6
1568.2.b.d.785.1		4	56.3	even	6
1568.2.b.d.785.4		4	28.3	even	6
1568.2.t.d.177.1		8	28.23	odd	6
1568.2.t.d.177.4		8	56.51	odd	6
1568.2.t.d.753.1		8	8.3	odd	2
1568.2.t.d.753.4		8	4.3	odd	2
1568.2.t.e.177.1		8	56.19	even	6
1568.2.t.e.177.4		8	28.19	even	6
1568.2.t.e.753.1		8	28.27	even	2
1568.2.t.e.753.4		8	56.27	even	2
1792.2.a.v.1.1		4	112.11	odd	12
1792.2.a.v.1.4		4	112.67	odd	12
1792.2.a.x.1.1		4	112.109	even	12
1792.2.a.x.1.4		4	112.53	even	12
2016.2.c.c.1009.2		4	168.11	even	6
2016.2.c.c.1009.3		4	84.11	even	6

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:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	392.p (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.41156 - 0.0865986i) q^{2} +(-2.61578 - 1.51022i) q^{3} +(1.98500 + 0.244478i) q^{4} +(-1.46890 + 0.848071i) q^{5} +(3.56155 + 2.35829i) q^{6} +(-2.78078 - 0.516994i) q^{8} +(3.06155 + 5.30277i) q^{9} +O(q^{10})\)	\(q+(-1.41156 - 0.0865986i) q^{2} +(-2.61578 - 1.51022i) q^{3} +(1.98500 + 0.244478i) q^{4} +(-1.46890 + 0.848071i) q^{5} +(3.56155 + 2.35829i) q^{6} +(-2.78078 - 0.516994i) q^{8} +(3.06155 + 5.30277i) q^{9} +(2.14688 - 1.06990i) q^{10} +(1.14688 + 0.662153i) q^{11} +(-4.82312 - 3.63730i) q^{12} +1.69614i q^{13} +5.12311 q^{15} +(3.88046 + 0.970579i) q^{16} +(-1.00000 + 1.73205i) q^{17} +(-3.86235 - 7.75030i) q^{18} +(2.61578 - 1.51022i) q^{19} +(-3.12311 + 1.32431i) q^{20} +(-1.56155 - 1.03399i) q^{22} +(-2.56155 - 4.43674i) q^{23} +(6.49314 + 5.55194i) q^{24} +(-1.06155 + 1.83866i) q^{25} +(0.146883 - 2.39420i) q^{26} -9.43318i q^{27} -6.04090i q^{29} +(-7.23157 - 0.443654i) q^{30} +(5.12311 - 8.87348i) q^{31} +(-5.39345 - 1.70607i) q^{32} +(-2.00000 - 3.46410i) q^{33} +(1.56155 - 2.35829i) q^{34} +(4.78078 + 11.2745i) q^{36} +(5.23157 - 3.02045i) q^{37} +(-3.82312 + 1.90525i) q^{38} +(2.56155 - 4.43674i) q^{39} +(4.52313 - 1.59888i) q^{40} +4.24621 q^{41} -1.32431i q^{43} +(2.11468 + 1.59476i) q^{44} +(-8.99424 - 5.19283i) q^{45} +(3.23157 + 6.48455i) q^{46} +(-8.68466 - 8.39919i) q^{48} +(1.65767 - 2.50345i) q^{50} +(5.23157 - 3.02045i) q^{51} +(-0.414669 + 3.36684i) q^{52} +(2.29377 + 1.32431i) q^{53} +(-0.816900 + 13.3155i) q^{54} -2.24621 q^{55} -9.12311 q^{57} +(-0.523133 + 8.52708i) q^{58} +(0.322018 + 0.185917i) q^{59} +(10.1694 + 1.25249i) q^{60} +(1.46890 - 0.848071i) q^{61} +(-8.00000 + 12.0818i) q^{62} +(7.46543 + 2.87529i) q^{64} +(-1.43845 - 2.49146i) q^{65} +(2.52313 + 5.06298i) q^{66} +(9.96029 + 5.75058i) q^{67} +(-2.40845 + 3.19365i) q^{68} +15.4741i q^{69} -8.00000 q^{71} +(-5.77200 - 16.3286i) q^{72} +(3.00000 - 5.19615i) q^{73} +(-7.64624 + 3.81050i) q^{74} +(5.55359 - 3.20636i) q^{75} +(5.56155 - 2.35829i) q^{76} +(-4.00000 + 6.04090i) q^{78} +(-6.52313 + 1.86522i) q^{80} +(-5.06155 + 8.76687i) q^{81} +(-5.99378 - 0.367716i) q^{82} -5.66906i q^{83} -3.39228i q^{85} +(-0.114683 + 1.86934i) q^{86} +(-9.12311 + 15.8017i) q^{87} +(-2.84690 - 2.43423i) q^{88} +(8.12311 + 14.0696i) q^{89} +(12.2462 + 8.10887i) q^{90} +(-4.00000 - 9.43318i) q^{92} +(-26.8019 + 15.4741i) q^{93} +(-2.56155 + 4.43674i) q^{95} +(11.5316 + 12.6080i) q^{96} +12.2462 q^{97} +8.10887i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} - q^{4} + 12 q^{6} - 14 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q + q^2 - q^4 + 12 * q^6 - 14 * q^8 + 8 * q^9	\( 8 q + q^{2} - q^{4} + 12 q^{6} - 14 q^{8} + 8 q^{9} + 8 q^{10} - 14 q^{12} + 8 q^{15} + 7 q^{16} - 8 q^{17} + 15 q^{18} + 8 q^{20} + 4 q^{22} - 4 q^{23} + 2 q^{24} + 8 q^{25} - 8 q^{26} - 16 q^{30} + 8 q^{31} - 9 q^{32} - 16 q^{33} - 4 q^{34} + 30 q^{36} - 6 q^{38} + 4 q^{39} + 20 q^{40} - 32 q^{41} + 18 q^{44} - 16 q^{46} - 20 q^{48} + 38 q^{50} + 4 q^{52} + 28 q^{54} + 48 q^{55} - 40 q^{57} + 12 q^{58} + 16 q^{60} - 64 q^{62} + 2 q^{64} - 28 q^{65} + 4 q^{66} - 2 q^{68} - 64 q^{71} - 31 q^{72} + 24 q^{73} - 12 q^{74} + 28 q^{76} - 32 q^{78} - 36 q^{80} - 24 q^{81} - 38 q^{82} - 2 q^{86} - 40 q^{87} - 22 q^{88} + 32 q^{89} + 32 q^{90} - 32 q^{92} - 4 q^{95} + 42 q^{96} + 32 q^{97}+O(q^{100}) \) 8 * q + q^2 - q^4 + 12 * q^6 - 14 * q^8 + 8 * q^9 + 8 * q^10 - 14 * q^12 + 8 * q^15 + 7 * q^16 - 8 * q^17 + 15 * q^18 + 8 * q^20 + 4 * q^22 - 4 * q^23 + 2 * q^24 + 8 * q^25 - 8 * q^26 - 16 * q^30 + 8 * q^31 - 9 * q^32 - 16 * q^33 - 4 * q^34 + 30 * q^36 - 6 * q^38 + 4 * q^39 + 20 * q^40 - 32 * q^41 + 18 * q^44 - 16 * q^46 - 20 * q^48 + 38 * q^50 + 4 * q^52 + 28 * q^54 + 48 * q^55 - 40 * q^57 + 12 * q^58 + 16 * q^60 - 64 * q^62 + 2 * q^64 - 28 * q^65 + 4 * q^66 - 2 * q^68 - 64 * q^71 - 31 * q^72 + 24 * q^73 - 12 * q^74 + 28 * q^76 - 32 * q^78 - 36 * q^80 - 24 * q^81 - 38 * q^82 - 2 * q^86 - 40 * q^87 - 22 * q^88 + 32 * q^89 + 32 * q^90 - 32 * q^92 - 4 * q^95 + 42 * q^96 + 32 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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