LMFDB - Embedded newform 392.2.p.e.373.3

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			373.3
Root			$0.630783 - 1.26575i$ of defining polynomial
Character	$\chi$	$=$	392.373
Dual form			392.2.p.e.165.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.630783 + 1.26575i) q^{2} +(-2.61578 + 1.51022i) q^{3} +(-1.20422 + 1.59682i) q^{4} +(-1.46890 - 0.848071i) q^{5} +(-3.56155 - 2.35829i) q^{6} +(-2.78078 - 0.516994i) q^{8} +(3.06155 - 5.30277i) q^{9} +O(q^{10})$	\(q+(0.630783 + 1.26575i) q^{2} +(-2.61578 + 1.51022i) q^{3} +(-1.20422 + 1.59682i) 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} +(0.146883 - 2.39420i) q^{10} +(-1.14688 + 0.662153i) q^{11} +(0.738433 - 5.99559i) q^{12} -1.69614i q^{13} +5.12311 q^{15} +(-1.09968 - 3.84587i) q^{16} +(1.00000 + 1.73205i) q^{17} +(8.64313 + 0.530252i) 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} +(8.05469 - 2.84725i) q^{24} +(-1.06155 - 1.83866i) q^{25} +(2.14688 - 1.06990i) q^{26} +9.43318i q^{27} -6.04090i q^{29} +(3.23157 + 6.48455i) q^{30} +(-5.12311 - 8.87348i) q^{31} +(4.17423 - 3.81783i) 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} +(-0.261567 + 4.26354i) q^{38} +(2.56155 + 4.43674i) q^{39} +(3.64624 + 3.11771i) q^{40} -4.24621 q^{41} -1.32431i q^{43} +(0.323764 - 2.62875i) q^{44} +(-8.99424 + 5.19283i) q^{45} +(-7.23157 - 0.443654i) q^{46} +(8.68466 + 8.39919i) q^{48} +(1.65767 - 2.50345i) q^{50} +(-5.23157 - 3.02045i) q^{51} +(2.70844 + 2.04254i) q^{52} +(-2.29377 + 1.32431i) q^{53} +(-11.9400 + 5.95029i) q^{54} +2.24621 q^{55} -9.12311 q^{57} +(7.64624 - 3.81050i) q^{58} +(0.322018 - 0.185917i) q^{59} +(-6.16937 + 8.18069i) 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} +(5.64624 + 0.346394i) q^{66} +(-9.96029 + 5.75058i) q^{67} +(-3.97000 - 0.488956i) q^{68} -15.4741i q^{69} -8.00000 q^{71} +(-11.2550 + 13.1630i) q^{72} +(-3.00000 - 5.19615i) q^{73} +(0.523133 - 8.52708i) q^{74} +(5.55359 + 3.20636i) q^{75} +(-5.56155 + 2.35829i) q^{76} +(-4.00000 + 6.04090i) q^{78} +(-1.64624 + 6.58181i) q^{80} +(-5.06155 - 8.76687i) q^{81} +(-2.67844 - 5.37462i) q^{82} +5.66906i q^{83} -3.39228i q^{85} +(1.67624 - 0.835351i) q^{86} +(9.12311 + 15.8017i) q^{87} +(3.53156 - 1.24837i) 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} +(-5.15310 + 16.2906i) 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 $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.630783	+	1.26575i	0.446031	+	0.895017i
$2$	0.630783	+	1.26575i	0.446031	+	0.895017i
$3$	−2.61578	+	1.51022i	−1.51022	+	0.871928i	−0.510295	+	0.859999i	$0.670464\pi$
$3$	−2.61578	+	1.51022i	−1.51022	+	0.871928i	−0.999929	+	0.0119288i	$0.996203\pi$
$4$	−1.20422	+	1.59682i	−0.602112	+	0.798411i
$5$	−1.46890	−	0.848071i	−0.656913	−	0.379269i	0.134187	−	0.990956i	$-0.457158\pi$
$5$	−1.46890	−	0.848071i	−0.656913	−	0.379269i	−0.791100	+	0.611687i	$0.790491\pi$
$6$	−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
$10$	0.146883	−	2.39420i	0.0464486	−	0.757114i
$11$	−1.14688	+	0.662153i	−0.345798	+	0.199647i	−0.662833	−	0.748767i	$-0.730646\pi$
$11$	−1.14688	+	0.662153i	−0.345798	+	0.199647i	0.317035	+	0.948414i	$0.397313\pi$
$12$	0.738433	−	5.99559i	0.213167	−	1.73078i
$13$		−	1.69614i		−	0.470425i	−0.971944	−	0.235212i	$-0.924421\pi$
$13$		−	1.69614i		−	0.470425i	0.971944	−	0.235212i	$-0.0755786\pi$
$14$		0			0
$15$	5.12311			1.32278
$16$	−1.09968	−	3.84587i	−0.274921	−	0.961467i
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	0.961436	−	0.275029i	$-0.0886875\pi$
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	−0.718900	+	0.695113i	$0.755354\pi$
$18$	8.64313	+	0.530252i	2.03721	+	0.124982i
$19$	2.61578	+	1.51022i	0.600102	+	0.346469i	0.769082	−	0.639150i	$-0.220714\pi$
$19$	2.61578	+	1.51022i	0.600102	+	0.346469i	−0.168980	+	0.985620i	$0.554047\pi$
$20$	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	0.465085	+	0.885266i	$0.346024\pi$
$23$	−2.56155	+	4.43674i	−0.534121	+	0.925124i	−0.999205	+	0.0398580i	$0.987309\pi$
$24$	8.05469	−	2.84725i	1.64416	−	0.581193i
$25$	−1.06155	−	1.83866i	−0.212311	−	0.367733i
$26$	2.14688	−	1.06990i	0.421038	−	0.209824i
$27$			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	$-0.189538\pi$
$30$	3.23157	+	6.48455i	0.590001	+	1.18391i
$31$	−5.12311	−	8.87348i	−0.920137	−	1.59372i	−0.799201	−	0.601064i	$-0.794744\pi$
$31$	−5.12311	−	8.87348i	−0.920137	−	1.59372i	−0.120936	−	0.992660i	$-0.538589\pi$
$32$	4.17423	−	3.81783i	0.737906	−	0.674903i
$33$	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	$-0.498737\pi$
$37$	−5.23157	−	3.02045i	−0.860065	−	0.496559i	−0.864034	+	0.503434i	$0.832070\pi$
$38$	−0.261567	+	4.26354i	−0.0424317	+	0.691638i
$39$	2.56155	+	4.43674i	0.410177	+	0.710447i
$40$	3.64624	+	3.11771i	0.576521	+	0.492953i
$41$	−4.24621			−0.663147			−0.331573	−	0.943429i	$-0.607579\pi$
$41$	−4.24621			−0.663147			−0.331573	+	0.943429i	$0.607579\pi$
$42$		0			0
$43$		−	1.32431i		−	0.201955i	−0.994889	−	0.100977i	$-0.967803\pi$
$43$		−	1.32431i		−	0.201955i	0.994889	−	0.100977i	$-0.0321970\pi$
$44$	0.323764	−	2.62875i	0.0488093	−	0.396299i
$45$	−8.99424	+	5.19283i	−1.34078	+	0.774101i
$46$	−7.23157	−	0.443654i	−1.06624	−	0.0654132i
$47$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$47$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$48$	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
$52$	2.70844	+	2.04254i	0.375593	+	0.283249i
$53$	−2.29377	+	1.32431i	−0.315073	+	0.181908i	−0.649194	−	0.760623i	$-0.724894\pi$
$53$	−2.29377	+	1.32431i	−0.315073	+	0.181908i	0.334121	+	0.942530i	$0.391560\pi$
$54$	−11.9400	+	5.95029i	−1.62483	+	0.809732i
$55$	2.24621			0.302879
$56$		0			0
$57$	−9.12311			−1.20838
$58$	7.64624	−	3.81050i	1.00400	−	0.500343i
$59$	0.322018	−	0.185917i	0.0419231	−	0.0242043i	−0.478892	−	0.877874i	$-0.658961\pi$
$59$	0.322018	−	0.185917i	0.0419231	−	0.0242043i	0.520815	+	0.853670i	$0.325628\pi$
$60$	−6.16937	+	8.18069i	−0.796462	+	1.05612i
$61$	1.46890	+	0.848071i	0.188074	+	0.108584i	0.591080	−	0.806613i	$-0.298702\pi$
$61$	1.46890	+	0.848071i	0.188074	+	0.108584i	−0.403007	+	0.915197i	$0.632035\pi$
$62$	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
$66$	5.64624	+	0.346394i	0.695004	+	0.0426382i
$67$	−9.96029	+	5.75058i	−1.21684	+	0.702545i	−0.964241	−	0.265026i	$-0.914620\pi$
$67$	−9.96029	+	5.75058i	−1.21684	+	0.702545i	−0.252602	+	0.967570i	$0.581286\pi$
$68$	−3.97000	−	0.488956i	−0.481434	−	0.0592947i
$69$		−	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	$0.657448\pi$
$72$	−11.2550	+	13.1630i	−1.32641	+	1.55127i
$73$	−3.00000	−	5.19615i	−0.351123	−	0.608164i	0.635323	−	0.772246i	$-0.280867\pi$
$73$	−3.00000	−	5.19615i	−0.351123	−	0.608164i	−0.986447	+	0.164083i	$0.947534\pi$
$74$	0.523133	−	8.52708i	0.0608130	−	0.991253i
$75$	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	$-0.833333\pi$
$79$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$80$	−1.64624	+	6.58181i	−0.184055	+	0.735869i
$81$	−5.06155	−	8.76687i	−0.562395	−	0.974096i
$82$	−2.67844	−	5.37462i	−0.295784	−	0.593528i
$83$			5.66906i			0.622260i	0.950367	+	0.311130i	$0.100708\pi$
$83$			5.66906i			0.622260i	−0.950367	+	0.311130i	$0.899292\pi$
$84$		0			0
$85$		−	3.39228i		−	0.367945i
$86$	1.67624	−	0.835351i	0.180753	−	0.0900782i
$87$	9.12311	+	15.8017i	0.978100	+	1.69412i
$88$	3.53156	−	1.24837i	0.376465	−	0.133077i
$89$	−8.12311	+	14.0696i	−0.861047	+	1.49138i	0.00987147	+	0.999951i	$0.496858\pi$
$89$	−8.12311	+	14.0696i	−0.861047	+	1.49138i	−0.870919	+	0.491427i	$0.836476\pi$
$90$	−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
$96$	−5.15310	+	16.2906i	−0.525936	+	1.66266i
$97$	−12.2462			−1.24341			−0.621707	−	0.783250i	$-0.713561\pi$
$97$	−12.2462			−1.24341			−0.621707	+	0.783250i	$0.713561\pi$
$98$		0			0
$99$			8.10887i			0.814972i
$100$	4.21437	+	0.519053i	0.421437	+	0.0519053i
$101$	8.99424	−	5.19283i	0.894960	−	0.516705i	0.0193984	−	0.999812i	$-0.493825\pi$
$101$	8.99424	−	5.19283i	0.894960	−	0.516705i	0.875562	+	0.483106i	$0.160492\pi$
$102$	0.523133	−	8.52708i	0.0517979	−	0.844307i
$103$	1.12311	−	1.94528i	0.110663	−	0.191674i	−0.805375	−	0.592766i	$-0.798036\pi$
$103$	1.12311	−	1.94528i	0.110663	−	0.191674i	0.916038	+	0.401092i	$0.131369\pi$
$104$	−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	$-0.573075\pi$
$107$	−12.2541	−	7.07488i	−1.18464	−	0.683955i	−0.957084	+	0.289809i	$0.906408\pi$
$108$	−15.0631	−	11.3597i	−1.44945	−	1.09308i
$109$	15.6947	−	9.06134i	1.50328	−	0.867919i	0.503288	−	0.864119i	$-0.332124\pi$
$109$	15.6947	−	9.06134i	1.50328	−	0.867919i	0.999993	−	0.00380035i	$-0.00120969\pi$
$110$	1.41687	+	2.84313i	0.135093	+	0.271082i
$111$	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	$0.426327\pi$
$114$	−5.75470	−	11.5475i	−0.538977	−	1.08153i
$115$	7.52534	−	4.34475i	0.701741	−	0.405150i
$116$	9.64624	+	7.27460i	0.895631	+	0.675429i
$117$	−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
$122$	−0.146883	+	2.39420i	−0.0132982	+	0.216761i
$123$	11.1072	−	6.41273i	1.00150	−	0.578216i
$124$	20.3387	+	2.50497i	1.82647	+	0.224953i
$125$			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	$0.302175\pi$
$128$	1.06969	+	11.2630i	0.0945479	+	0.995520i
$129$	2.00000	+	3.46410i	0.176090	+	0.304997i
$130$	−4.06091	−	0.249135i	−0.356165	−	0.0218506i
$131$	−10.7852	−	6.22681i	−0.942303	−	0.544039i	−0.0516218	−	0.998667i	$-0.516439\pi$
$131$	−10.7852	−	6.22681i	−0.942303	−	0.544039i	−0.890682	+	0.454628i	$0.849772\pi$
$132$	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
$136$	−1.88532	−	5.33344i	−0.161665	−	0.457339i
$137$	8.12311	+	14.0696i	0.694004	+	1.20205i	0.970515	+	0.241039i	$0.0774882\pi$
$137$	8.12311	+	14.0696i	0.694004	+	1.20205i	−0.276512	+	0.961011i	$0.589178\pi$
$138$	19.5862	−	9.76079i	1.66729	−	0.830893i
$139$		−	8.31768i		−	0.705496i	−0.935718	−	0.352748i	$-0.885247\pi$
$139$		−	8.31768i		−	0.705496i	0.935718	−	0.352748i	$-0.114753\pi$
$140$		0			0
$141$		0			0
$142$	−5.04627	−	10.1260i	−0.423473	−	0.849752i
$143$	1.12311	+	1.94528i	0.0939188	+	0.162672i
$144$	−23.7605	−	5.94296i	−1.98004	−	0.495246i
$145$	−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	$-0.539513\pi$
$149$	−12.7569	−	7.36520i	−1.04509	−	0.603381i	−0.921270	+	0.388924i	$0.872847\pi$
$150$	−0.555333	+	9.05195i	−0.0453428	+	0.739089i
$151$	−5.43845	−	9.41967i	−0.442575	−	0.766562i	0.555305	−	0.831647i	$-0.312601\pi$
$151$	−5.43845	−	9.41967i	−0.442575	−	0.766562i	−0.997880	+	0.0650850i	$0.979268\pi$
$152$	−6.49314	−	5.55194i	−0.526663	−	0.450322i
$153$	12.2462			0.990048
$154$		0			0
$155$			17.3790i			1.39592i
$156$	−10.1694	−	1.25249i	−0.814201	−	0.100279i
$157$	−7.34451	+	4.24035i	−0.586155	+	0.338417i	−0.763576	−	0.645718i	$-0.776558\pi$
$157$	−7.34451	+	4.24035i	−0.586155	+	0.338417i	0.177420	+	0.984135i	$0.443225\pi$
$158$		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	$-0.157390\pi$
$163$	11.6100	+	6.70305i	0.909367	+	0.525023i	0.0291396	+	0.999575i	$0.490723\pi$
$164$	5.11339	−	6.78045i	0.399289	−	0.529464i
$165$	−5.87560	+	3.39228i	−0.457415	+	0.264089i
$166$	−7.17559	+	3.57595i	−0.556934	+	0.277547i
$167$	−8.00000			−0.619059			−0.309529	−	0.950890i	$-0.600171\pi$
$167$	−8.00000			−0.619059			−0.309529	+	0.950890i	$0.600171\pi$
$168$		0			0
$169$	10.1231			0.778700
$170$	4.29377	−	2.13979i	0.329317	−	0.164115i
$171$	16.0167	−	9.24726i	1.22483	−	0.707156i
$172$	2.11468	+	1.59476i	0.161243	+	0.121600i
$173$	16.5196	+	9.53758i	1.25596	+	0.725129i	0.972287	−	0.233792i	$-0.0751135\pi$
$173$	16.5196	+	9.53758i	1.25596	+	0.725129i	0.283673	+	0.958921i	$0.408447\pi$
$174$	−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
$178$	−22.9325	−	1.40690i	−1.71886	−	0.105452i
$179$	−4.08469	+	2.35829i	−0.305304	+	0.176267i	−0.644823	−	0.764332i	$-0.723069\pi$
$179$	−4.08469	+	2.35829i	−0.305304	+	0.176267i	0.339519	+	0.940599i	$0.389736\pi$
$180$	2.53906	−	20.6155i	0.189251	−	1.53659i
$181$		−	6.99337i		−	0.519813i	−0.965634	−	0.259906i	$-0.916308\pi$
$181$		−	6.99337i		−	0.519813i	0.965634	−	0.259906i	$-0.0836917\pi$
$182$		0			0
$183$	−5.12311			−0.378711
$184$	9.41687	−	11.0133i	0.694221	−	0.811909i
$185$	5.12311	+	8.87348i	0.376658	+	0.652391i
$186$	−2.68007	+	43.6852i	−0.196512	+	3.20315i
$187$	−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	0.416751	+	0.909021i	$0.363169\pi$
$191$	−8.00000	+	13.8564i	−0.578860	+	1.00261i	−0.995610	+	0.0935936i	$0.970165\pi$
$192$	−23.8703	+	3.75334i	−1.72269	+	0.270874i
$193$	5.56155	+	9.63289i	0.400329	+	0.693391i	0.993766	−	0.111490i	$-0.0355624\pi$
$193$	5.56155	+	9.63289i	0.400329	+	0.693391i	−0.593436	+	0.804881i	$0.702229\pi$
$194$	−7.72471	−	15.5006i	−0.554601	−	1.11288i
$195$		−	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	$0.722027\pi$
$198$	−10.2638	+	5.11494i	−0.729414	+	0.363503i
$199$	−9.12311	−	15.8017i	−0.646720	−	1.12015i	−0.983901	−	0.178712i	$-0.942807\pi$
$199$	−9.12311	−	15.8017i	−0.646720	−	1.12015i	0.337182	−	0.941440i	$-0.390526\pi$
$200$	2.00136	+	5.66173i	0.141518	+	0.400345i
$201$	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
$206$	3.17066	+	0.194519i	0.220910	+	0.0135528i
$207$	15.6847	+	27.1666i	1.09016	+	1.88821i
$208$	−6.52313	+	1.86522i	−0.452298	+	0.129330i
$209$	−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	$-0.0519079\pi$
$212$	0.647528	−	5.25750i	0.0444724	−	0.361087i
$213$	20.9263	−	12.0818i	1.43384	−	0.827831i
$214$	1.22535	−	19.9732i	0.0837632	−	1.36534i
$215$	−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
$220$	−2.70494	+	3.58680i	−0.182367	+	0.241822i
$221$	2.93780	−	1.69614i	0.197618	−	0.114095i
$222$	11.5094	+	23.0951i	0.772461	+	1.55004i
$223$	5.75379			0.385302			0.192651	−	0.981267i	$-0.438291\pi$
$223$	5.75379			0.385302			0.192651	+	0.981267i	$0.438291\pi$
$224$		0			0
$225$	−13.0000			−0.866667
$226$	3.07626	+	6.17291i	0.204630	+	0.410616i
$227$	−8.49139	+	4.90251i	−0.563593	+	0.325391i	−0.754586	−	0.656201i	$-0.772163\pi$
$227$	−8.49139	+	4.90251i	−0.563593	+	0.325391i	0.190993	+	0.981591i	$0.438829\pi$
$228$	10.9863	−	14.5680i	0.727584	−	0.964788i
$229$	−22.3952	−	12.9299i	−1.47992	−	0.854429i	−0.480174	−	0.877173i	$-0.659426\pi$
$229$	−22.3952	−	12.9299i	−1.47992	−	0.854429i	−0.999741	+	0.0227441i	$0.992760\pi$
$230$	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	−0.467133	−	0.884187i	$-0.654713\pi$
$233$	8.12311	−	14.0696i	0.532162	−	0.921732i	0.999295	−	0.0375449i	$-0.0119537\pi$
$234$	0.899383	−	14.6600i	0.0587945	−	0.958352i
$235$		0			0
$236$	−0.0909053	+	0.738091i	−0.00591743	+	0.0480456i
$237$		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	$0.692951\pi$
$240$	−5.63380	−	19.7028i	−0.363660	−	1.27181i
$241$	−1.87689	−	3.25088i	−0.120901	−	0.209407i	0.799222	−	0.601036i	$-0.205245\pi$
$241$	−1.87689	−	3.25088i	−0.120901	−	0.209407i	−0.920123	+	0.391629i	$0.871912\pi$
$242$	−13.0516	−	0.800709i	−0.838987	−	0.0514715i
$243$	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
$248$	9.65868	+	27.3238i	0.613327	+	1.73506i
$249$	−8.56155	−	14.8290i	−0.542566	−	0.939753i
$250$	−15.2925	+	7.62099i	−0.967181	+	0.481994i
$251$			10.9663i			0.692186i	0.938200	+	0.346093i	$0.112492\pi$
$251$			10.9663i			0.692186i	−0.938200	+	0.346093i	$0.887508\pi$
$252$		0			0
$253$		−	6.78456i		−	0.426542i
$254$	8.27784	+	16.6105i	0.519398	+	1.04224i
$255$	5.12311	+	8.87348i	0.320821	+	0.555679i
$256$	−13.5814	+	8.45848i	−0.848837	+	0.528655i
$257$	11.2462	−	19.4790i	0.701519	−	1.21507i	−0.266414	−	0.963859i	$-0.585839\pi$
$257$	11.2462	−	19.4790i	0.701519	−	1.21507i	0.967933	−	0.251208i	$-0.0808280\pi$
$258$	−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
$262$	1.07847	−	17.5790i	0.0666279	−	1.08604i
$263$	−6.24621	−	10.8188i	−0.385158	−	0.667113i	0.606633	−	0.794982i	$-0.292520\pi$
$263$	−6.24621	−	10.8188i	−0.385158	−	0.667113i	−0.991791	+	0.127869i	$0.959186\pi$
$264$	−7.35247	+	8.59890i	−0.452513	+	0.529226i
$265$	4.49242			0.275967
$266$		0			0
$267$		−	49.0708i		−	3.00309i
$268$	2.81178	−	22.8298i	0.171757	−	1.39455i
$269$	10.2823	−	5.93649i	0.626923	−	0.361954i	−0.152636	−	0.988282i	$-0.548776\pi$
$269$	10.2823	−	5.93649i	0.626923	−	0.361954i	0.779560	+	0.626328i	$0.215443\pi$
$270$	22.5850	+	1.38558i	1.37448	+	0.0843236i
$271$	5.12311	−	8.87348i	0.311207	−	0.539025i	−0.667417	−	0.744684i	$-0.732600\pi$
$271$	5.12311	−	8.87348i	0.311207	−	0.539025i	0.978624	+	0.205658i	$0.0659336\pi$
$272$	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
$276$	24.7093	+	18.6343i	1.48733	+	1.12165i
$277$	−2.29377	+	1.32431i	−0.137819	+	0.0795699i	−0.567324	−	0.823495i	$-0.692021\pi$
$277$	−2.29377	+	1.32431i	−0.137819	+	0.0795699i	0.429505	+	0.903064i	$0.358688\pi$
$278$	10.5281	−	5.24665i	0.631431	−	0.314673i
$279$	−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	−0.943110	−	0.332480i	$-0.892115\pi$
$283$	−18.9545	+	10.9434i	−1.12673	+	0.650518i	−0.183619	+	0.982997i	$0.558781\pi$
$284$	9.63380	−	12.7746i	0.571661	−	0.758032i
$285$	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
$290$	−14.4631	−	0.887307i	−0.849305	−	0.0521045i
$291$	32.0335	−	18.4945i	1.87783	−	1.08417i
$292$	11.9100	+	1.46687i	0.696981	+	0.0858420i
$293$			10.3857i			0.606736i	0.952873	+	0.303368i	$0.0981112\pi$
$293$			10.3857i			0.606736i	−0.952873	+	0.303368i	$0.901889\pi$
$294$		0			0
$295$	−0.630683			−0.0367198
$296$	12.9863	+	11.1039i	0.754812	+	0.645400i
$297$	−6.24621	−	10.8188i	−0.362442	−	0.627768i
$298$	1.27563	−	20.7928i	0.0738954	−	1.20450i
$299$	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
$304$	2.93158	−	11.7207i	0.168138	−	0.672230i
$305$	−1.43845	−	2.49146i	−0.0823652	−	0.142661i
$306$	7.72471	+	15.5006i	0.441592	+	0.886110i
$307$		−	25.2791i		−	1.44275i	−0.692543	−	0.721377i	$-0.743510\pi$
$307$		−	25.2791i		−	1.44275i	0.692543	−	0.721377i	$-0.256490\pi$
$308$		0			0
$309$			6.78456i			0.385960i
$310$	−21.9974	+	10.9624i	−1.24937	+	0.622622i
$311$	−6.24621	−	10.8188i	−0.354190	−	0.613475i	0.632789	−	0.774324i	$-0.281910\pi$
$311$	−6.24621	−	10.8188i	−0.354190	−	0.613475i	−0.986979	+	0.160849i	$0.948577\pi$
$312$	−4.82934	−	13.6619i	−0.273407	−	0.773452i
$313$	−10.3693	+	17.9602i	−0.586108	+	1.01517i	0.408628	+	0.912701i	$0.366007\pi$
$313$	−10.3693	+	17.9602i	−0.586108	+	1.01517i	−0.994736	+	0.102468i	$0.967326\pi$
$314$	−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	$-0.296278\pi$
$317$	3.58184	+	2.06798i	0.201176	+	0.116149i	−0.396028	+	0.918238i	$0.629612\pi$
$318$	11.2925	+	0.692789i	0.633251	+	0.0388497i
$319$	4.00000	+	6.92820i	0.223957	+	0.387905i
$320$	−8.52754	−	10.5547i	−0.476704	−	0.590027i
$321$	42.7386			2.38544
$322$		0			0
$323$			6.04090i			0.336124i
$324$	20.0944	+	2.47488i	1.11635	+	0.137493i
$325$	−3.11863	+	1.80054i	−0.172991	+	0.0998762i
$326$	−1.16095	+	18.9235i	−0.0642990	+	1.04808i
$327$	−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	$-0.199103\pi$
$331$	12.8981	+	7.44672i	0.708943	+	0.409309i	−0.101726	+	0.994812i	$0.532437\pi$
$332$	−9.05249	−	6.82683i	−0.496820	−	0.374671i
$333$	−32.0335	+	18.4945i	−1.75542	+	1.01349i
$334$	−5.04627	−	10.1260i	−0.276119	−	0.554068i
$335$	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	$0.507603\pi$
$338$	6.38549	+	12.8133i	0.347325	+	0.696950i
$339$	−12.7569	+	7.36520i	−0.692860	+	0.400023i
$340$	5.41687	+	4.08507i	0.293771	+	0.221544i
$341$	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
$346$	−1.65188	+	26.9257i	−0.0888057	+	1.44754i
$347$	−7.02249	+	4.05444i	−0.376987	+	0.217654i	−0.676507	−	0.736437i	$-0.736507\pi$
$347$	−7.02249	+	4.05444i	−0.376987	+	0.217654i	0.299520	+	0.954090i	$0.403174\pi$
$348$	−36.2188	−	4.46080i	−1.94153	−	0.239124i
$349$			27.3471i			1.46385i	0.681383	+	0.731927i	$0.261379\pi$
$349$			27.3471i			1.46385i	−0.681383	+	0.731927i	$0.738621\pi$
$350$		0			0
$351$	16.0000			0.854017
$352$	−2.25936	+	7.14258i	−0.120424	+	0.380701i
$353$	3.87689	+	6.71498i	0.206346	+	0.357402i	0.950561	−	0.310538i	$-0.100509\pi$
$353$	3.87689	+	6.71498i	0.206346	+	0.357402i	−0.744215	+	0.667941i	$0.767176\pi$
$354$	−1.58533	−	0.0972594i	−0.0842594	−	0.00516928i
$355$	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	−0.0719522	−	0.997408i	$-0.522923\pi$
$359$	15.6847	−	27.1666i	0.827805	−	1.43380i	0.899757	−	0.436392i	$-0.143744\pi$
$360$	27.6956	−	9.79012i	1.45969	−	0.515985i
$361$	−4.93845	−	8.55364i	−0.259918	−	0.450192i
$362$	8.85183	−	4.41130i	0.465242	−	0.231853i
$363$		−	27.9277i		−	1.46582i
$364$		0			0
$365$			10.1768i			0.532680i
$366$	−3.23157	−	6.48455i	−0.168917	−	0.338953i
$367$	5.12311	+	8.87348i	0.267424	+	0.463192i	0.968196	−	0.250194i	$-0.0804943\pi$
$367$	5.12311	+	8.87348i	0.267424	+	0.463192i	−0.700772	+	0.713385i	$0.747161\pi$
$368$	19.8800	+	4.97238i	1.03632	+	0.259203i
$369$	−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	$-0.457876\pi$
$373$	−12.7569	−	7.36520i	−0.660528	−	0.381356i	−0.792478	+	0.609901i	$0.791209\pi$
$374$	0.229366	−	3.73868i	0.0118602	−	0.193322i
$375$	−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	$0.615321\pi$
$380$	10.1694	+	1.25249i	0.521678	+	0.0642512i
$381$	−34.3272	+	19.8188i	−1.75864	+	1.01535i
$382$	−22.5850	−	1.38558i	−1.15555	−	0.0708923i
$383$	−2.24621	+	3.89055i	−0.114776	+	0.198798i	−0.917690	−	0.397297i	$-0.869948\pi$
$383$	−2.24621	+	3.89055i	−0.114776	+	0.198798i	0.802914	+	0.596095i	$0.203282\pi$
$384$	−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
$388$	14.7472	−	19.5550i	0.748675	−	0.992756i
$389$	−21.5703	+	12.4536i	−1.09366	+	0.631424i	−0.934548	−	0.355837i	$-0.884196\pi$
$389$	−21.5703	+	12.4536i	−1.09366	+	0.631424i	−0.159110	+	0.987261i	$0.550863\pi$
$390$	10.9987	−	5.48120i	0.556941	−	0.277551i
$391$	−10.2462			−0.518173
$392$		0			0
$393$	37.6155			1.89745
$394$	−27.2325	+	13.5713i	−1.37195	+	0.683711i
$395$		0			0
$396$	−12.9484	−	9.76490i	−0.650683	−	0.490705i
$397$	−17.8076	−	10.2812i	−0.893740	−	0.516001i	−0.0185761	−	0.999827i	$-0.505913\pi$
$397$	−17.8076	−	10.2812i	−0.893740	−	0.516001i	−0.875164	+	0.483826i	$0.839247\pi$
$398$	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	−0.854870	−	0.518842i	$-0.826363\pi$
$401$	0.438447	−	0.759413i	0.0218950	−	0.0379233i	0.876765	+	0.480919i	$0.159697\pi$
$402$	49.0357	+	3.00832i	2.44568	+	0.150041i
$403$	−15.0507	+	8.68951i	−0.749727	+	0.432855i
$404$	−2.53906	+	20.6155i	−0.126323	+	1.02566i
$405$			17.1702i			0.853195i
$406$		0			0
$407$	8.00000			0.396545
$408$	12.9863	+	11.1039i	0.642916	+	0.549724i
$409$	13.0000	+	22.5167i	0.642809	+	1.11338i	0.984803	+	0.173675i	$0.0555643\pi$
$409$	13.0000	+	22.5167i	0.642809	+	1.11338i	−0.341994	+	0.939702i	$0.611102\pi$
$410$	−0.623698	+	10.1663i	−0.0308022	+	0.502078i
$411$	−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
$416$	−6.47558	−	7.08008i	−0.317491	−	0.347129i
$417$	12.5616	+	21.7572i	0.615142	+	1.06546i
$418$	−2.52313	−	5.06298i	−0.123410	−	0.247639i
$419$			27.9277i			1.36436i	0.731185	+	0.682179i	$0.238967\pi$
$419$			27.9277i			1.36436i	−0.731185	+	0.682179i	$0.761033\pi$
$420$		0			0
$421$		−	26.8122i		−	1.30675i	−0.757036	−	0.653373i	$-0.773353\pi$
$421$		−	26.8122i		−	1.30675i	0.757036	−	0.653373i	$-0.226647\pi$
$422$	5.97000	−	2.97515i	0.290615	−	0.144828i
$423$		0			0
$424$	7.06311	−	2.49674i	0.343015	−	0.121252i
$425$	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
$430$	−3.17066	−	0.194519i	−0.152903	−	0.00938053i
$431$	−8.80776	−	15.2555i	−0.424255	−	0.734831i	0.572095	−	0.820187i	$-0.306131\pi$
$431$	−8.80776	−	15.2555i	−0.424255	−	0.734831i	−0.996351	+	0.0853557i	$0.972797\pi$
$432$	36.2787	−	10.3735i	1.74546	−	0.499096i
$433$	18.4924			0.888689			0.444345	−	0.895856i	$-0.353437\pi$
$433$	18.4924			0.888689			0.444345	+	0.895856i	$0.353437\pi$
$434$		0			0
$435$		−	30.9481i		−	1.48385i
$436$	−4.43060	+	35.9736i	−0.212187	+	1.72282i
$437$	−13.4009	+	7.73704i	−0.641054	+	0.370113i
$438$	−1.56940	+	25.5813i	−0.0749888	+	1.22232i
$439$	11.3693	−	19.6922i	0.542628	−	0.939859i	−0.456124	−	0.889916i	$-0.650763\pi$
$439$	11.3693	−	19.6922i	0.542628	−	0.939859i	0.998752	−	0.0499429i	$-0.0159039\pi$
$440$	−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	$-0.389315\pi$
$443$	−6.37845	−	3.68260i	−0.303049	−	0.174966i	−0.643812	+	0.765184i	$0.722648\pi$
$444$	−21.9725	+	29.1360i	−1.04277	+	1.38273i
$445$	23.8641	−	13.7779i	1.13127	−	0.653137i
$446$	3.62939	+	7.28283i	0.171857	+	0.344852i
$447$	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	$0.370754\pi$
$450$	−8.20018	−	16.4547i	−0.386560	−	0.775682i
$451$	4.86991	−	2.81164i	0.229315	−	0.132395i
$452$	−5.87288	+	7.78753i	−0.276237	+	0.366295i
$453$	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	−0.994466	−	0.105057i	$-0.966498\pi$
$457$	−8.68466	+	15.0423i	−0.406251	+	0.703648i	0.588215	+	0.808705i	$0.299831\pi$
$458$	2.23942	−	36.5025i	0.104641	−	1.70565i
$459$	−16.3387	+	9.43318i	−0.762627	+	0.440303i
$460$	−2.12440	+	17.2487i	−0.0990504	+	0.804224i
$461$			24.3724i			1.13514i	0.823327	+	0.567568i	$0.192115\pi$
$461$			24.3724i			1.13514i	−0.823327	+	0.567568i	$0.807885\pi$
$462$		0			0
$463$		0			0			−	1.00000i	$-0.5\pi$
$463$		0			0				1.00000i	$0.5\pi$
$464$	−23.2325	+	6.64308i	−1.07854	+	0.308397i
$465$	−26.2462	−	45.4598i	−1.21714	−	2.10815i
$466$	22.9325	+	1.40690i	1.06233	+	0.0651733i
$467$	2.61578	+	1.51022i	0.121044	+	0.0698848i	0.559300	−	0.828966i	$-0.311070\pi$
$467$	2.61578	+	1.51022i	0.121044	+	0.0698848i	−0.438255	+	0.898850i	$0.644403\pi$
$468$	19.1231	−	8.10887i	0.883966	−	0.374833i
$469$		0			0
$470$		0			0
$471$	12.8078	−	22.1837i	0.590151	−	1.02217i
$472$	−0.991577	+	0.350513i	−0.0456411	+	0.0161336i
$473$	0.876894	+	1.51883i	0.0403196	+	0.0698357i
$474$		0			0
$475$		−	6.41273i		−	0.294236i
$476$		0			0
$477$			16.2177i			0.742559i
$478$	−11.1116	−	22.2968i	−0.508232	−	1.01983i
$479$	5.12311	+	8.87348i	0.234081	+	0.405440i	0.959005	−	0.283389i	$-0.0914587\pi$
$479$	5.12311	+	8.87348i	0.234081	+	0.405440i	−0.724924	+	0.688828i	$0.758125\pi$
$480$	21.3850	−	19.5591i	0.976088	−	0.892749i
$481$	−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
$486$	−0.197166	+	3.21381i	−0.00894363	+	0.145781i
$487$	−0.315342	−	0.546188i	−0.0142895	−	0.0247501i	0.858792	−	0.512324i	$-0.171215\pi$
$487$	−0.315342	−	0.546188i	−0.0142895	−	0.0247501i	−0.873082	+	0.487574i	$0.837882\pi$
$488$	−3.64624	−	3.11771i	−0.165057	−	0.141132i
$489$	−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	$-0.280344\pi$
$492$	−3.13554	+	25.4586i	−0.141361	+	1.14776i
$493$	10.4631	−	6.04090i	0.471236	−	0.272068i
$494$	7.23157	+	0.443654i	0.325364	+	0.0199609i
$495$	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	$-0.396826\pi$
$499$	−7.66652	−	4.42627i	−0.343201	−	0.198147i	−0.661687	+	0.749781i	$0.730159\pi$
$500$	−19.2925	−	14.5492i	−0.862786	−	0.650660i
$501$	20.9263	−	12.0818i	0.934917	−	0.539775i
$502$	−13.8805	+	6.91735i	−0.619519	+	0.308737i
$503$	−13.7538			−0.613251			−0.306626	−	0.951830i	$-0.599200\pi$
$503$	−13.7538			−0.613251			−0.306626	+	0.951830i	$0.599200\pi$
$504$		0			0
$505$	−17.6155			−0.783881
$506$	8.58753	−	4.27959i	0.381762	−	0.190251i
$507$	−26.4799	+	15.2882i	−1.17601	+	0.678971i
$508$	−15.8032	+	20.9553i	−0.701152	+	0.929740i
$509$	26.6211	+	15.3697i	1.17996	+	0.681249i	0.956005	−	0.293351i	$-0.0947706\pi$
$509$	26.6211	+	15.3697i	1.17996	+	0.681249i	0.223953	+	0.974600i	$0.428104\pi$
$510$	−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
$514$	31.7494	+	1.94781i	1.40041	+	0.0859143i
$515$	−3.29946	+	1.90495i	−0.145392	+	0.0839419i
$516$	−7.94001	−	0.977913i	−0.349539	−	0.0430502i
$517$		0			0
$518$		0			0
$519$	−57.6155			−2.52904
$520$	5.28807	−	6.18453i	0.231897	−	0.271210i
$521$	−11.0000	−	19.0526i	−0.481919	−	0.834708i	0.517866	−	0.855462i	$-0.326727\pi$
$521$	−11.0000	−	19.0526i	−0.481919	−	0.834708i	−0.999785	+	0.0207541i	$0.993393\pi$
$522$	3.20320	−	52.2122i	0.140200	−	2.28527i
$523$	35.6549	+	20.5854i	1.55908	+	0.900136i	0.997345	+	0.0728196i	$0.0231997\pi$
$523$	35.6549	+	20.5854i	1.55908	+	0.900136i	0.561736	+	0.827316i	$0.310134\pi$
$524$	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
$528$	−15.5218	−	3.88232i	−0.675502	−	0.168956i
$529$	−1.62311	−	2.81130i	−0.0705698	−	0.122230i
$530$	2.83374	+	5.68627i	0.123090	+	0.246996i
$531$		−	2.27678i		−	0.0988038i
$532$		0			0
$533$			7.20217i			0.311961i
$534$	62.1112	−	30.9531i	2.68781	−	1.33947i
$535$	12.0000	+	20.7846i	0.518805	+	0.898597i
$536$	30.6704	−	10.8417i	1.32476	−	0.468288i
$537$	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	$-0.425221\pi$
$541$	−11.4688	−	6.62153i	−0.493084	−	0.284682i	−0.725853	+	0.687850i	$0.758555\pi$
$542$	14.4631	+	0.887307i	0.621245	+	0.0381131i
$543$	10.5616	+	18.2931i	0.453240	+	0.785034i
$544$	10.7869	+	3.41214i	0.462485	+	0.146295i
$545$	−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	$-0.0657689\pi$
$548$	−32.2488	−	3.97184i	−1.37760	−	0.169669i
$549$	8.99424	−	5.19283i	0.383865	−	0.221624i
$550$	−0.243484	+	3.96880i	−0.0103822	+	0.169230i
$551$	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
$556$	13.2819	+	10.0164i	0.563276	+	0.424788i
$557$	2.29377	−	1.32431i	0.0971900	−	0.0561127i	−0.450617	−	0.892717i	$-0.648796\pi$
$557$	2.29377	−	1.32431i	0.0971900	−	0.0561127i	0.547807	+	0.836605i	$0.315463\pi$
$558$	−39.5745	−	79.4112i	−1.67532	−	3.36174i
$559$	−2.24621			−0.0950046
$560$		0			0
$561$	8.00000			0.337760
$562$	−3.78470	−	7.59447i	−0.159648	−	0.320354i
$563$	25.8358	−	14.9163i	1.08885	−	0.628648i	0.155580	−	0.987823i	$-0.450275\pi$
$563$	25.8358	−	14.9163i	1.08885	−	0.628648i	0.933270	+	0.359175i	$0.116942\pi$
$564$		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	−0.691207	−	0.722657i	$-0.742921\pi$
$569$	6.68466	−	11.5782i	0.280235	−	0.485382i	0.971443	+	0.237275i	$0.0762541\pi$
$570$	−1.34003	+	21.8426i	−0.0561278	+	0.914885i
$571$	8.02818	−	4.63507i	0.335969	−	0.193972i	−0.322519	−	0.946563i	$-0.604530\pi$
$571$	8.02818	−	4.63507i	0.335969	−	0.193972i	0.658488	+	0.752591i	$0.271196\pi$
$572$	−4.45873	−	0.549150i	−0.186429	−	0.0229611i
$573$		−	48.3272i		−	2.01890i
$574$		0			0
$575$	10.8769			0.453598
$576$	38.1028	−	30.7846i	1.58762	−	1.28269i
$577$	3.87689	+	6.71498i	0.161397	+	0.279548i	0.935370	−	0.353671i	$-0.115067\pi$
$577$	3.87689	+	6.71498i	0.161397	+	0.279548i	−0.773973	+	0.633219i	$0.781733\pi$
$578$	18.3503	+	1.12578i	0.763271	+	0.0468263i
$579$	−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
$584$	5.65595	+	16.0003i	0.234045	+	0.662098i
$585$	8.80776	+	15.2555i	0.364156	+	0.630737i
$586$	−13.1456	+	6.55109i	−0.543039	+	0.270623i
$587$		−	21.8868i		−	0.903365i	−0.892179	−	0.451683i	$-0.850824\pi$
$587$		−	21.8868i		−	0.903365i	0.892179	−	0.451683i	$-0.149176\pi$
$588$		0			0
$589$		−	30.9481i		−	1.27520i
$590$	−0.397824	−	0.798285i	−0.0163782	−	0.0328649i
$591$	−32.4924	−	56.2785i	−1.33656	−	2.31499i
$592$	−5.86317	+	23.4415i	−0.240975	+	0.963438i
$593$	9.00000	−	15.5885i	0.369586	−	0.640141i	−0.619915	−	0.784669i	$-0.712833\pi$
$593$	9.00000	−	15.5885i	0.369586	−	0.640141i	0.989501	+	0.144528i	$0.0461663\pi$
$594$	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
$598$	−0.752499	+	12.2658i	−0.0307720	+	0.501584i
$599$	6.24621	+	10.8188i	0.255213	+	0.442042i	0.964953	−	0.262421i	$-0.0845210\pi$
$599$	6.24621	+	10.8188i	0.255213	+	0.442042i	−0.709740	+	0.704464i	$0.751188\pi$
$600$	−13.7856	−	11.7874i	−0.562795	−	0.481217i
$601$	16.2462			0.662697			0.331348	−	0.943508i	$-0.392496\pi$
$601$	16.2462			0.662697			0.331348	+	0.943508i	$0.392496\pi$
$602$		0			0
$603$			70.4228i			2.86784i
$604$	21.5907	+	2.65916i	0.878511	+	0.108200i
$605$	13.5818	−	7.84144i	0.552178	−	0.318800i
$606$	−44.2797	−	2.71654i	−1.79874	−	0.110352i
$607$	20.4924	−	35.4939i	0.831762	−	1.44065i	−0.0648782	−	0.997893i	$-0.520666\pi$
$607$	20.4924	−	35.4939i	0.831762	−	1.44065i	0.896640	−	0.442760i	$-0.146001\pi$
$608$	16.6847	−	3.68260i	0.676652	−	0.149349i
$609$		0			0
$610$	2.24621	−	3.39228i	0.0909464	−	0.137349i
$611$		0			0
$612$	−14.7472	+	19.5550i	−0.596120	+	0.790465i
$613$	1.93211	−	1.11550i	0.0780371	−	0.0450547i	−0.460474	−	0.887673i	$-0.652320\pi$
$613$	1.93211	−	1.11550i	0.0780371	−	0.0450547i	0.538511	+	0.842619i	$0.318987\pi$
$614$	31.9969	−	15.9456i	1.29129	−	0.643513i
$615$	−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	$0.701339\pi$
$618$	−8.58753	+	4.27959i	−0.345441	+	0.172150i
$619$	17.0224	−	9.82790i	0.684189	−	0.395017i	−0.117243	−	0.993103i	$-0.537405\pi$
$619$	17.0224	−	9.82790i	0.684189	−	0.395017i	0.801431	+	0.598087i	$0.204072\pi$
$620$	−27.7512	−	20.9282i	−1.11452	−	0.840499i
$621$	−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
$626$	−29.2738	−	1.79594i	−1.17002	−	0.0717801i
$627$	10.4631	−	6.04090i	0.417858	−	0.241250i
$628$	2.07335	−	16.8342i	0.0827356	−	0.671758i
$629$		−	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
$634$	−0.358167	+	5.83814i	−0.0142246	+	0.231862i
$635$	−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
$640$	7.98058	−	17.4514i	0.315460	−	0.689829i
$641$	2.68466	+	4.64996i	0.106038	+	0.183663i	0.914162	−	0.405350i	$-0.132850\pi$
$641$	2.68466	+	4.64996i	0.106038	+	0.183663i	−0.808124	+	0.589012i	$0.799517\pi$
$642$	26.9588	+	54.0962i	1.06398	+	2.13501i
$643$			5.66906i			0.223566i	0.993733	+	0.111783i	$0.0356562\pi$
$643$			5.66906i			0.223566i	−0.993733	+	0.111783i	$0.964344\pi$
$644$		0			0
$645$		−	6.78456i		−	0.267142i
$646$	−7.64624	+	3.81050i	−0.300837	+	0.149922i
$647$	21.6155	+	37.4392i	0.849794	+	1.47189i	0.881392	+	0.472386i	$0.156607\pi$
$647$	21.6155	+	37.4392i	0.849794	+	1.47189i	−0.0315977	+	0.999501i	$0.510060\pi$
$648$	9.54263	+	26.9955i	0.374870	+	1.06048i
$649$	−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	$-0.546241\pi$
$653$	−27.4459	−	15.8459i	−1.07404	−	0.620098i	−0.929283	+	0.369369i	$0.879574\pi$
$654$	−77.2668	−	4.74029i	−3.02137	−	0.185360i
$655$	10.5616	+	18.2931i	0.412674	+	0.714772i
$656$	4.66949	+	16.3304i	0.182313	+	0.637594i
$657$	−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	$-0.0411668\pi$
$660$	1.65868	−	13.4674i	0.0645639	−	0.524217i
$661$	−38.7339	+	22.3630i	−1.50657	+	0.869821i	−0.506604	+	0.862179i	$0.669099\pi$
$661$	−38.7339	+	22.3630i	−1.50657	+	0.869821i	−0.999971	+	0.00764267i	$0.997567\pi$
$662$	−1.28975	+	21.0230i	−0.0501276	+	0.817081i
$663$	−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
$668$	9.63380	−	12.7746i	0.372743	−	0.494263i
$669$	−15.0507	+	8.68951i	−0.581893	+	0.335956i
$670$	12.3051	+	24.6916i	0.475386	+	0.953921i
$671$	−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	$0.770610\pi$
$674$	−0.553130	−	1.10993i	−0.0213058	−	0.0427527i
$675$	17.3444	−	10.0138i	0.667588	−	0.385432i
$676$	−12.1905	+	16.1648i	−0.468865	+	0.621723i
$677$	−14.8698	−	8.58511i	−0.571494	−	0.329952i	0.186252	−	0.982502i	$-0.440366\pi$
$677$	−14.8698	−	8.58511i	−0.571494	−	0.329952i	−0.757746	+	0.652550i	$0.773699\pi$
$678$	−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
$682$	−1.17507	+	19.1536i	−0.0449957	+	0.733431i
$683$	0.502848	−	0.290319i	0.0192409	−	0.0111088i	−0.490349	−	0.871526i	$-0.663131\pi$
$683$	0.502848	−	0.290319i	0.0192409	−	0.0111088i	0.509590	+	0.860418i	$0.329797\pi$
$684$	−4.52151	+	36.7117i	−0.172884	+	1.40371i
$685$		−	27.5559i		−	1.05286i
$686$		0			0
$687$	78.1080			2.98000
$688$	−5.09311	+	1.45632i	−0.194173	+	0.0555217i
$689$	2.24621	+	3.89055i	0.0855738	+	0.148218i
$690$	−37.0481	−	2.27288i	−1.41040	−	0.0865272i
$691$	33.6435	+	19.4241i	1.27986	+	0.738928i	0.976823	−	0.214051i	$-0.0686657\pi$
$691$	33.6435	+	19.4241i	1.27986	+	0.738928i	0.303038	+	0.952978i	$0.401999\pi$
$692$	−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
$696$	−17.1999	−	48.6575i	−0.651962	−	1.84436i
$697$	−4.24621	−	7.35465i	−0.160837	−	0.278577i
$698$	−34.6144	+	17.2501i	−1.31018	+	0.652925i
$699$			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	$-0.0134150\pi$
$702$	10.0925	+	20.2519i	0.380918	+	0.764360i
$703$	−9.12311	−	15.8017i	−0.344084	−	0.595972i
$704$	−10.4659	+	1.64564i	−0.394447	+	0.0620225i
$705$		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	$-0.152042\pi$
$709$	24.8698	+	14.3586i	0.934004	+	0.539247i	0.0459283	+	0.998945i	$0.485375\pi$
$710$	−1.17507	+	19.1536i	−0.0440995	+	0.718823i
$711$		0			0
$712$	29.8625	−	34.9249i	1.11914	−	1.30887i
$713$	52.4924			1.96586
$714$		0			0
$715$		−	3.80989i		−	0.142482i
$716$	1.15310	−	9.36244i	0.0430935	−	0.349891i
$717$	46.0784	−	26.6034i	1.72083	−	0.993522i
$718$	44.2797	+	2.71654i	1.65250	+	0.101380i
$719$	−26.2462	+	45.4598i	−0.978819	+	1.69536i	−0.312108	+	0.950047i	$0.601035\pi$
$719$	−26.2462	+	45.4598i	−0.978819	+	1.69536i	−0.666711	+	0.745317i	$0.732298\pi$
$720$	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
$724$	11.1672	+	8.42159i	0.415025	+	0.312986i
$725$	−11.1072	+	6.41273i	−0.412510	+	0.238163i
$726$	35.3494	−	17.6163i	1.31194	−	0.653803i
$727$	16.9848			0.629933			0.314967	−	0.949103i	$-0.398007\pi$
$727$	16.9848			0.629933			0.314967	+	0.949103i	$0.398007\pi$
$728$		0			0
$729$	23.4924			0.870090
$730$	−12.8813	+	6.41938i	−0.476758	+	0.237592i
$731$	2.29377	−	1.32431i	0.0848380	−	0.0489813i
$732$	6.16937	−	8.18069i	0.228027	−	0.302367i
$733$	−25.3330	−	14.6260i	−0.935695	−	0.540224i	−0.0470868	−	0.998891i	$-0.514994\pi$
$733$	−25.3330	−	14.6260i	−0.935695	−	0.540224i	−0.888608	+	0.458667i	$0.848327\pi$
$734$	−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
$738$	−36.7006	−	2.25156i	−1.35097	−	0.0828812i
$739$	18.4913	−	10.6760i	0.680214	−	0.392722i	−0.119721	−	0.992808i	$-0.538200\pi$
$739$	18.4913	−	10.6760i	0.680214	−	0.392722i	0.799936	+	0.600086i	$0.204867\pi$
$740$	−20.3387	−	2.50497i	−0.747667	−	0.0920847i
$741$			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	$0.496317\pi$
$744$	−66.5300	−	56.8863i	−2.43911	−	2.08555i
$745$	12.4924	+	21.6375i	0.457687	+	0.792737i
$746$	1.27563	−	20.7928i	0.0467042	−	0.761280i
$747$	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	−0.933955	−	0.357390i	$-0.883667\pi$
$751$	−4.31534	+	7.47439i	−0.157469	+	0.272744i	0.776486	+	0.630134i	$0.217000\pi$
$752$		0			0
$753$	−16.5616	−	28.6855i	−0.603537	−	1.04536i
$754$	−6.46314	−	12.9691i	−0.235374	−	0.472307i
$755$			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	$0.840759\pi$
$758$	−46.0838	+	22.9658i	−1.67384	+	0.834156i
$759$	10.2462	+	17.7470i	0.371914	+	0.644174i
$760$	4.82934	+	13.6619i	0.175179	+	0.495569i
$761$	4.36932	−	7.56788i	0.158388	−	0.274335i	−0.775900	−	0.630856i	$-0.782704\pi$
$761$	4.36932	−	7.56788i	0.158388	−	0.274335i	0.934287	+	0.356521i	$0.116037\pi$
$762$	−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
$766$	−6.34132	−	0.389037i	−0.229121	−	0.0140565i
$767$	−0.315342	−	0.546188i	−0.0113863	−	0.0197217i
$768$	22.7518	−	42.6365i	0.820984	−	1.53851i
$769$	40.2462			1.45132			0.725658	−	0.688056i	$-0.241536\pi$
$769$	40.2462			1.45132			0.725658	+	0.688056i	$0.241536\pi$
$770$		0			0
$771$			67.9372i			2.44670i
$772$	−22.0794	−	2.71936i	−0.794654	−	0.0978718i
$773$	1.46890	−	0.848071i	0.0528327	−	0.0305030i	−0.473351	−	0.880874i	$-0.656956\pi$
$773$	1.46890	−	0.848071i	0.0528327	−	0.0305030i	0.526184	+	0.850371i	$0.323622\pi$
$774$	0.702217	−	11.4462i	0.0252407	−	0.411424i
$775$	−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
$780$	13.8756	+	10.4641i	0.496826	+	0.374676i
$781$	9.17507	−	5.29723i	0.328310	−	0.189550i
$782$	−6.46314	−	12.9691i	−0.231121	−	0.463774i
$783$	56.9848			2.03647
$784$		0			0
$785$	14.3845			0.513404
$786$	23.7272	+	47.6117i	0.846323	+	1.69825i
$787$	9.13543	−	5.27434i	0.325643	−	0.188010i	−0.328262	−	0.944587i	$-0.606463\pi$
$787$	9.13543	−	5.27434i	0.325643	−	0.188010i	0.653905	+	0.756577i	$0.273130\pi$
$788$	−34.3556	−	25.9089i	−1.22387	−	0.922965i
$789$	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
$794$	1.78068	−	29.0252i	0.0631941	−	1.03007i
$795$	−11.7512	+	6.78456i	−0.416772	+	0.240624i
$796$	36.2188	+	4.46080i	1.28374	+	0.158109i
$797$		−	25.8597i		−	0.915998i	−0.888953	−	0.457999i	$-0.848566\pi$
$797$		−	25.8597i		−	0.915998i	0.888953	−	0.457999i	$-0.151434\pi$
$798$		0			0
$799$		0			0
$800$	−11.4509	−	3.62217i	−0.404849	−	0.128063i
$801$	49.7386	+	86.1498i	1.75743	+	3.04395i
$802$	1.23779	+	0.0759378i	0.0437078	+	0.00268146i
$803$	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
$808$	−27.6956	+	9.79012i	−0.974329	+	0.344415i
$809$	−18.9309	−	32.7892i	−0.665574	−	1.15281i	−0.979129	−	0.203238i	$-0.934853\pi$
$809$	−18.9309	−	32.7892i	−0.665574	−	1.15281i	0.313555	−	0.949570i	$-0.398480\pi$
$810$	−21.7331	+	10.8307i	−0.763624	+	0.380551i
$811$			15.8459i			0.556425i	0.960520	+	0.278213i	$0.0897420\pi$
$811$			15.8459i			0.556425i	−0.960520	+	0.278213i	$0.910258\pi$
$812$		0			0
$813$			30.9481i			1.08540i
$814$	5.04627	+	10.1260i	0.176872	+	0.354915i
$815$	−11.3693	−	19.6922i	−0.398250	−	0.689789i
$816$	−5.86317	+	23.4415i	−0.205252	+	0.820615i
$817$	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	$-0.133930\pi$
$821$	29.0956	+	16.7984i	1.01545	+	0.586268i	0.102664	+	0.994716i	$0.467263\pi$
$822$	4.24946	−	69.2664i	0.148217	−	2.41594i
$823$	16.4924	+	28.5657i	0.574890	+	0.995738i	0.996054	+	0.0887536i	$0.0282884\pi$
$823$	16.4924	+	28.5657i	0.574890	+	0.995738i	−0.421164	+	0.906985i	$0.638378\pi$
$824$	−4.12880	+	4.82874i	−0.143834	+	0.168217i
$825$	−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	$-0.0344017\pi$
$828$	−62.2681	−	7.66911i	−2.16397	−	0.266520i
$829$	40.3837	−	23.3155i	1.40258	−	0.809781i	0.407925	−	0.913015i	$-0.366252\pi$
$829$	40.3837	−	23.3155i	1.40258	−	0.809781i	0.994657	+	0.103234i	$0.0329191\pi$
$830$	13.5729	+	0.832691i	0.471122	+	0.0289031i
$831$	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
$836$	4.81690	−	6.38729i	0.166596	−	0.220909i
$837$	83.7051	−	48.3272i	2.89327	−	1.67043i
$838$	−35.3494	+	17.6163i	−1.22112	+	0.608546i
$839$	6.73863			0.232643			0.116322	−	0.993212i	$-0.462890\pi$
$839$	6.73863			0.232643			0.116322	+	0.993212i	$0.462890\pi$
$840$		0			0
$841$	−7.49242			−0.258359
$842$	33.9374	−	16.9127i	1.16956	−	0.582850i
$843$	15.6947	−	9.06134i	0.540554	−	0.312089i
$844$	7.53156	+	5.67983i	0.259247	+	0.195508i
$845$	−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
$850$	5.99378	+	0.367716i	0.205585	+	0.0126126i
$851$	26.8019	−	15.4741i	0.918757	−	0.530444i
$852$	−5.90747	+	47.9647i	−0.202387	+	1.64325i
$853$		−	25.4421i		−	0.871121i	−0.900159	−	0.435561i	$-0.856550\pi$
$853$		−	25.4421i		−	0.871121i	0.900159	−	0.435561i	$-0.143450\pi$
$854$		0			0
$855$	−31.3693			−1.07281
$856$	30.4181	+	26.0089i	1.03967	+	0.888967i
$857$	−23.4924	−	40.6901i	−0.802486	−	1.38995i	−0.917975	−	0.396638i	$-0.870177\pi$
$857$	−23.4924	−	40.6901i	−0.802486	−	1.38995i	0.115489	−	0.993309i	$-0.463156\pi$
$858$	0.587534	−	9.57682i	0.0200581	−	0.326947i
$859$	−24.5478	−	14.1727i	−0.837559	−	0.483565i	0.0188750	−	0.999822i	$-0.493992\pi$
$859$	−24.5478	−	14.1727i	−0.837559	−	0.483565i	−0.856434	+	0.516257i	$0.827325\pi$
$860$	−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	0.368171	+	0.929758i	$0.379984\pi$
$863$	−18.2462	+	31.6034i	−0.621108	+	1.07579i	−0.989280	+	0.146033i	$0.953349\pi$
$864$	36.0143	+	39.3762i	1.22523	+	1.33961i
$865$	−16.1771	−	28.0195i	−0.550037	−	0.952692i
$866$	11.6647	+	23.4067i	0.396383	+	0.795392i
$867$			39.2658i			1.33354i
$868$		0			0
$869$		0			0
$870$	39.1725	−	19.5216i	1.32807	−	0.661843i
$871$	9.75379	+	16.8941i	0.330495	+	0.572433i
$872$	−48.3281	+	17.0835i	−1.63660	+	0.578520i
$873$	−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	$-0.537929\pi$
$877$	−30.7454	−	17.7509i	−1.03820	−	0.599404i	−0.919322	+	0.393505i	$0.871262\pi$
$878$	32.0969	+	1.96913i	1.08322	+	0.0664550i
$879$	−15.6847	−	27.1666i	−0.529030	−	0.916308i
$880$	−2.47012	−	8.63863i	−0.0832679	−	0.291208i
$881$	−44.2462			−1.49069			−0.745346	−	0.666677i	$-0.767716\pi$
$881$	−44.2462			−1.49069			−0.745346	+	0.666677i	$0.767716\pi$
$882$		0			0
$883$		−	4.71659i		−	0.158726i	−0.996846	−	0.0793629i	$-0.974711\pi$
$883$		−	4.71659i		−	0.158726i	0.996846	−	0.0793629i	$-0.0252886\pi$
$884$	−0.829339	+	6.73368i	−0.0278937	+	0.226478i
$885$	1.64973	−	0.952473i	0.0554551	−	0.0320170i
$886$	0.637816	−	10.3964i	0.0214279	−	0.349275i
$887$	−14.2462	+	24.6752i	−0.478341	+	0.828511i	−0.999692	−	0.0248317i	$-0.992095\pi$
$887$	−14.2462	+	24.6752i	−0.478341	+	0.828511i	0.521351	+	0.853343i	$0.325428\pi$
$888$	−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
$892$	−6.92886	+	9.18778i	−0.231995	+	0.307630i
$893$		0			0
$894$	28.0651	+	56.3161i	0.938637	+	1.88349i
$895$	8.00000			0.267411
$896$		0			0
$897$	−26.2462			−0.876335
$898$	10.5584	+	21.1869i	0.352340	+	0.707015i
$899$	−53.6038	+	30.9481i	−1.78779	+	1.03218i
$900$	15.6549	−	20.7587i	0.521831	−	0.691956i
$901$	−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
$906$	−2.84503	+	46.3741i	−0.0945198	+	1.54068i
$907$	−44.6492	+	25.7782i	−1.48255	+	0.855951i	−0.999804	−	0.0198082i	$-0.993694\pi$
$907$	−44.6492	+	25.7782i	−1.48255	+	0.855951i	−0.482748	+	0.875760i	$0.660361\pi$
$908$	2.39711	−	19.4630i	0.0795509	−	0.645901i
$909$		−	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	$0.437043\pi$
$912$	10.0325	+	35.0863i	0.332211	+	1.16182i
$913$	−3.75379	−	6.50175i	−0.124232	−	0.215177i
$914$	−24.5178	−	1.50416i	−0.810978	−	0.0497531i
$915$	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	−0.924427	−	0.381358i	$-0.875456\pi$
$919$	−4.00000	+	6.92820i	−0.131948	+	0.228540i	0.792480	+	0.609898i	$0.208790\pi$
$920$	−23.1725	+	8.19124i	−0.763974	+	0.270057i
$921$	38.1771	+	66.1246i	1.25798	+	2.17888i
$922$	−30.8492	+	15.3737i	−1.01597	+	0.506306i
$923$			13.5691i			0.446633i
$924$		0			0
$925$			12.8255i			0.421699i
$926$		0			0
$927$	−6.87689	−	11.9111i	−0.225867	−	0.391213i
$928$	−23.0631	−	25.2161i	−0.757084	−	0.827758i
$929$	−1.24621	+	2.15850i	−0.0408869	+	0.0708181i	−0.885745	−	0.464173i	$-0.846352\pi$
$929$	−1.24621	+	2.15850i	−0.0408869	+	0.0708181i	0.844858	+	0.534991i	$0.179685\pi$
$930$	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
$934$	−0.261567	+	4.26354i	−0.00855872	+	0.139507i
$935$	2.24621	+	3.89055i	0.0734590	+	0.127235i
$936$	22.3263	+	19.0901i	0.729758	+	0.623978i
$937$	−34.9848			−1.14291			−0.571453	−	0.820635i	$-0.693620\pi$
$937$	−34.9848			−1.14291			−0.571453	+	0.820635i	$0.693620\pi$
$938$		0			0
$939$		−	62.6400i		−	2.04418i
$940$		0			0
$941$	−26.6211	+	15.3697i	−0.867821	+	0.501037i	−0.866624	−	0.498962i	$-0.833715\pi$
$941$	−26.6211	+	15.3697i	−0.867821	+	0.501037i	−0.00119780	+	0.999999i	$0.500381\pi$
$942$	36.1578	+	2.21827i	1.17809	+	0.0722751i
$943$	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	$-0.570324\pi$
$947$	−36.1181	−	20.8528i	−1.17368	−	0.677625i	−0.954544	+	0.298069i	$0.903658\pi$
$948$		0			0
$949$	−8.81341	+	5.08842i	−0.286095	+	0.165177i
$950$	8.11689	−	4.04504i	0.263347	−	0.131239i
$951$	−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	$0.591517\pi$
$954$	−20.5275	+	10.2299i	−0.664604	+	0.331205i
$955$	23.5024	−	13.5691i	0.760520	−	0.439087i
$956$	21.2131	−	28.1289i	0.686079	−	0.909753i
$957$	−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
$962$	−14.4631	−	0.887307i	−0.466310	−	0.0286079i
$963$	−75.0329	+	43.3203i	−2.41790	+	1.39598i
$964$	7.45128	+	0.917719i	0.239989	+	0.0295577i
$965$		−	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	$0.555957\pi$
$968$	16.9956	−	19.8768i	0.546260	−	0.638865i
$969$	−9.12311	−	15.8017i	−0.293076	−	0.507623i
$970$	−1.79877	+	29.3199i	−0.0577549	+	0.941406i
$971$	−9.49709	−	5.48314i	−0.304776	−	0.175962i	0.339810	−	0.940494i	$-0.389637\pi$
$971$	−9.49709	−	5.48314i	−0.304776	−	0.175962i	−0.644586	+	0.764531i	$0.722970\pi$
$972$	−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
$976$	1.64624	−	6.58181i	0.0526948	−	0.210679i
$977$	−11.8769	−	20.5714i	−0.379976	−	0.658137i	0.611083	−	0.791567i	$-0.290734\pi$
$977$	−11.8769	−	20.5714i	−0.379976	−	0.658137i	−0.991058	+	0.133430i	$0.957401\pi$
$978$	−25.5419	−	51.2531i	−0.816741	−	1.63889i
$979$		−	21.5150i		−	0.687621i
$980$		0			0
$981$		−	110.967i		−	3.54291i
$982$	43.2599	−	21.5585i	1.38048	−	0.687960i
$983$	−17.1231	−	29.6581i	−0.546142	−	0.945946i	−0.998534	−	0.0541268i	$-0.982762\pi$
$983$	−17.1231	−	29.6581i	−0.546142	−	0.945946i	0.452392	−	0.891819i	$-0.350571\pi$
$984$	−34.2019	+	12.0900i	−1.09032	+	0.385416i
$985$	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
$990$	19.4143	+	1.19106i	0.617027	+	0.0378543i
$991$	18.2462	+	31.6034i	0.579610	+	1.00391i	0.995524	+	0.0945100i	$0.0301284\pi$
$991$	18.2462	+	31.6034i	0.579610	+	1.00391i	−0.415914	+	0.909404i	$0.636538\pi$
$992$	−55.2624	−	17.4808i	−1.75458	−	0.555015i
$993$	−44.9848			−1.42755
$994$		0			0
$995$			30.9481i			0.981122i
$996$	33.9894	+	4.18622i	1.07699	+	0.132646i
$997$	−28.6324	+	16.5309i	−0.906799	+	0.523540i	−0.879400	−	0.476084i	$-0.842056\pi$
$997$	−28.6324	+	16.5309i	−0.906799	+	0.523540i	−0.0273989	+	0.999625i	$0.508722\pi$
$998$	0.766617	−	12.4959i	0.0242668	−	0.395550i
$999$	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.e.373.3		8
4.3	odd	2		1568.2.t.e.177.4		8
7.2	even	3		392.2.b.c.197.3		4
7.3	odd	6		392.2.p.f.165.1		8
7.4	even	3	inner	392.2.p.e.165.1		8
7.5	odd	6		56.2.b.b.29.3	✓	4
7.6	odd	2		392.2.p.f.373.3		8
8.3	odd	2		1568.2.t.e.177.1		8
8.5	even	2	inner	392.2.p.e.373.1		8
21.5	even	6		504.2.c.d.253.2		4
28.3	even	6		1568.2.t.d.753.4		8
28.11	odd	6		1568.2.t.e.753.1		8
28.19	even	6		224.2.b.b.113.1		4
28.23	odd	6		1568.2.b.d.785.4		4
28.27	even	2		1568.2.t.d.177.1		8
56.3	even	6		1568.2.t.d.753.1		8
56.5	odd	6		56.2.b.b.29.4	yes	4
56.11	odd	6		1568.2.t.e.753.4		8
56.13	odd	2		392.2.p.f.373.1		8
56.19	even	6		224.2.b.b.113.4		4
56.27	even	2		1568.2.t.d.177.4		8
56.37	even	6		392.2.b.c.197.4		4
56.45	odd	6		392.2.p.f.165.3		8
56.51	odd	6		1568.2.b.d.785.1		4
56.53	even	6	inner	392.2.p.e.165.3		8
84.47	odd	6		2016.2.c.c.1009.3		4
112.5	odd	12		1792.2.a.x.1.4		4
112.19	even	12		1792.2.a.v.1.4		4
112.61	odd	12		1792.2.a.x.1.1		4
112.75	even	12		1792.2.a.v.1.1		4
168.5	even	6		504.2.c.d.253.1		4
168.131	odd	6		2016.2.c.c.1009.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.2.b.b.29.3	✓	4	7.5	odd	6
56.2.b.b.29.4	yes	4	56.5	odd	6
224.2.b.b.113.1		4	28.19	even	6
224.2.b.b.113.4		4	56.19	even	6
392.2.b.c.197.3		4	7.2	even	3
392.2.b.c.197.4		4	56.37	even	6
392.2.p.e.165.1		8	7.4	even	3	inner
392.2.p.e.165.3		8	56.53	even	6	inner
392.2.p.e.373.1		8	8.5	even	2	inner
392.2.p.e.373.3		8	1.1	even	1	trivial
392.2.p.f.165.1		8	7.3	odd	6
392.2.p.f.165.3		8	56.45	odd	6
392.2.p.f.373.1		8	56.13	odd	2
392.2.p.f.373.3		8	7.6	odd	2
504.2.c.d.253.1		4	168.5	even	6
504.2.c.d.253.2		4	21.5	even	6
1568.2.b.d.785.1		4	56.51	odd	6
1568.2.b.d.785.4		4	28.23	odd	6
1568.2.t.d.177.1		8	28.27	even	2
1568.2.t.d.177.4		8	56.27	even	2
1568.2.t.d.753.1		8	56.3	even	6
1568.2.t.d.753.4		8	28.3	even	6
1568.2.t.e.177.1		8	8.3	odd	2
1568.2.t.e.177.4		8	4.3	odd	2
1568.2.t.e.753.1		8	28.11	odd	6
1568.2.t.e.753.4		8	56.11	odd	6
1792.2.a.v.1.1		4	112.75	even	12
1792.2.a.v.1.4		4	112.19	even	12
1792.2.a.x.1.1		4	112.61	odd	12
1792.2.a.x.1.4		4	112.5	odd	12
2016.2.c.c.1009.2		4	168.131	odd	6
2016.2.c.c.1009.3		4	84.47	odd	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)

\(f(q)\)	\(=\)	\(q+(0.630783 + 1.26575i) q^{2} +(-2.61578 + 1.51022i) q^{3} +(-1.20422 + 1.59682i) q^{4} +(-1.46890 - 0.848071i) q^{5} +(-3.56155 - 2.35829i) q^{6} +(-2.78078 - 0.516994i) q^{8} +(3.06155 - 5.30277i) q^{9} +O(q^{10})\)	\(q+(0.630783 + 1.26575i) q^{2} +(-2.61578 + 1.51022i) q^{3} +(-1.20422 + 1.59682i) 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} +(0.146883 - 2.39420i) q^{10} +(-1.14688 + 0.662153i) q^{11} +(0.738433 - 5.99559i) q^{12} -1.69614i q^{13} +5.12311 q^{15} +(-1.09968 - 3.84587i) q^{16} +(1.00000 + 1.73205i) q^{17} +(8.64313 + 0.530252i) 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} +(8.05469 - 2.84725i) q^{24} +(-1.06155 - 1.83866i) q^{25} +(2.14688 - 1.06990i) q^{26} +9.43318i q^{27} -6.04090i q^{29} +(3.23157 + 6.48455i) q^{30} +(-5.12311 - 8.87348i) q^{31} +(4.17423 - 3.81783i) 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} +(-0.261567 + 4.26354i) q^{38} +(2.56155 + 4.43674i) q^{39} +(3.64624 + 3.11771i) q^{40} -4.24621 q^{41} -1.32431i q^{43} +(0.323764 - 2.62875i) q^{44} +(-8.99424 + 5.19283i) q^{45} +(-7.23157 - 0.443654i) q^{46} +(8.68466 + 8.39919i) q^{48} +(1.65767 - 2.50345i) q^{50} +(-5.23157 - 3.02045i) q^{51} +(2.70844 + 2.04254i) q^{52} +(-2.29377 + 1.32431i) q^{53} +(-11.9400 + 5.95029i) q^{54} +2.24621 q^{55} -9.12311 q^{57} +(7.64624 - 3.81050i) q^{58} +(0.322018 - 0.185917i) q^{59} +(-6.16937 + 8.18069i) 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} +(5.64624 + 0.346394i) q^{66} +(-9.96029 + 5.75058i) q^{67} +(-3.97000 - 0.488956i) q^{68} -15.4741i q^{69} -8.00000 q^{71} +(-11.2550 + 13.1630i) q^{72} +(-3.00000 - 5.19615i) q^{73} +(0.523133 - 8.52708i) q^{74} +(5.55359 + 3.20636i) q^{75} +(-5.56155 + 2.35829i) q^{76} +(-4.00000 + 6.04090i) q^{78} +(-1.64624 + 6.58181i) q^{80} +(-5.06155 - 8.76687i) q^{81} +(-2.67844 - 5.37462i) q^{82} +5.66906i q^{83} -3.39228i q^{85} +(1.67624 - 0.835351i) q^{86} +(9.12311 + 15.8017i) q^{87} +(3.53156 - 1.24837i) 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} +(-5.15310 + 16.2906i) 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

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