LMFDB - Embedded newform 392.2.p.e.165.3

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			165.3
Root			$0.630783 + 1.26575i$ of defining polynomial
Character	$\chi$	$=$	392.165
Dual form			392.2.p.e.373.3

$q$-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 $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

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

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 $

$2$	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	−0.999929	−	0.0119288i	$-0.996203\pi$
$3$	−2.61578	−	1.51022i	−1.51022	−	0.871928i	−0.510295	−	0.859999i	$-0.670464\pi$
$4$	−1.20422	−	1.59682i	−0.602112	−	0.798411i
$5$	−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
$10$	0.146883	+	2.39420i	0.0464486	+	0.757114i
$11$	−1.14688	−	0.662153i	−0.345798	−	0.199647i	0.317035	−	0.948414i	$-0.397313\pi$
$11$	−1.14688	−	0.662153i	−0.345798	−	0.199647i	−0.662833	+	0.748767i	$0.730646\pi$
$12$	0.738433	+	5.99559i	0.213167	+	1.73078i
$13$			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
$16$	−1.09968	+	3.84587i	−0.274921	+	0.961467i
$17$	1.00000	−	1.73205i	0.242536	−	0.420084i	−0.718900	−	0.695113i	$-0.755354\pi$
$17$	1.00000	−	1.73205i	0.242536	−	0.420084i	0.961436	+	0.275029i	$0.0886875\pi$
$18$	8.64313	−	0.530252i	2.03721	−	0.124982i
$19$	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	$-0.346024\pi$
$24$	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	$0.189538\pi$
$29$			6.04090i			1.12177i	−0.827895	+	0.560883i	$0.810462\pi$
$30$	3.23157	−	6.48455i	0.590001	−	1.18391i
$31$	−5.12311	+	8.87348i	−0.920137	+	1.59372i	−0.120936	+	0.992660i	$0.538589\pi$
$31$	−5.12311	+	8.87348i	−0.920137	+	1.59372i	−0.799201	+	0.601064i	$0.794744\pi$
$32$	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	−0.864034	−	0.503434i	$-0.832070\pi$
$37$	−5.23157	+	3.02045i	−0.860065	+	0.496559i	0.00396926	+	0.999992i	$0.498737\pi$
$38$	−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	$0.0321970\pi$
$43$			1.32431i			0.201955i	−0.994889	+	0.100977i	$0.967803\pi$
$44$	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	$-0.166667\pi$
$47$		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
$52$	2.70844	−	2.04254i	0.375593	−	0.283249i
$53$	−2.29377	−	1.32431i	−0.315073	−	0.181908i	0.334121	−	0.942530i	$-0.391560\pi$
$53$	−2.29377	−	1.32431i	−0.315073	−	0.181908i	−0.649194	+	0.760623i	$0.724894\pi$
$54$	−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	0.520815	−	0.853670i	$-0.325628\pi$
$59$	0.322018	+	0.185917i	0.0419231	+	0.0242043i	−0.478892	+	0.877874i	$0.658961\pi$
$60$	−6.16937	−	8.18069i	−0.796462	−	1.05612i
$61$	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
$66$	5.64624	−	0.346394i	0.695004	−	0.0426382i
$67$	−9.96029	−	5.75058i	−1.21684	−	0.702545i	−0.252602	−	0.967570i	$-0.581286\pi$
$67$	−9.96029	−	5.75058i	−1.21684	−	0.702545i	−0.964241	+	0.265026i	$0.914620\pi$
$68$	−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	−0.986447	−	0.164083i	$-0.947534\pi$
$73$	−3.00000	+	5.19615i	−0.351123	+	0.608164i	0.635323	+	0.772246i	$0.280867\pi$
$74$	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	$-0.166667\pi$
$79$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$80$	−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	$-0.899292\pi$
$83$		−	5.66906i		−	0.622260i	0.950367	−	0.311130i	$-0.100708\pi$
$84$		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	−0.870919	−	0.491427i	$-0.836476\pi$
$89$	−8.12311	−	14.0696i	−0.861047	−	1.49138i	0.00987147	−	0.999951i	$-0.496858\pi$
$90$	−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	0.875562	−	0.483106i	$-0.160492\pi$
$101$	8.99424	+	5.19283i	0.894960	+	0.516705i	0.0193984	+	0.999812i	$0.493825\pi$
$102$	0.523133	+	8.52708i	0.0517979	+	0.844307i
$103$	1.12311	+	1.94528i	0.110663	+	0.191674i	0.916038	−	0.401092i	$-0.131369\pi$
$103$	1.12311	+	1.94528i	0.110663	+	0.191674i	−0.805375	+	0.592766i	$0.798036\pi$
$104$	−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	−0.957084	−	0.289809i	$-0.906408\pi$
$107$	−12.2541	+	7.07488i	−1.18464	+	0.683955i	−0.227560	+	0.973764i	$0.573075\pi$
$108$	−15.0631	+	11.3597i	−1.44945	+	1.09308i
$109$	15.6947	+	9.06134i	1.50328	+	0.867919i	0.999993	+	0.00380035i	$0.00120969\pi$
$109$	15.6947	+	9.06134i	1.50328	+	0.867919i	0.503288	+	0.864119i	$0.332124\pi$
$110$	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	−0.890682	−	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
$136$	−1.88532	+	5.33344i	−0.161665	+	0.457339i
$137$	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	$-0.0774882\pi$
$138$	19.5862	+	9.76079i	1.66729	+	0.830893i
$139$			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
$142$	−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	−0.921270	−	0.388924i	$-0.872847\pi$
$149$	−12.7569	+	7.36520i	−1.04509	+	0.603381i	−0.123817	+	0.992305i	$0.539513\pi$
$150$	−0.555333	−	9.05195i	−0.0453428	−	0.739089i
$151$	−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	$0.312601\pi$
$152$	−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	0.177420	−	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	0.0291396	−	0.999575i	$-0.490723\pi$
$163$	11.6100	−	6.70305i	0.909367	−	0.525023i	0.880227	+	0.474552i	$0.157390\pi$
$164$	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	0.283673	−	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
$178$	−22.9325	+	1.40690i	−1.71886	+	0.105452i
$179$	−4.08469	−	2.35829i	−0.305304	−	0.176267i	0.339519	−	0.940599i	$-0.389736\pi$
$179$	−4.08469	−	2.35829i	−0.305304	−	0.176267i	−0.644823	+	0.764332i	$0.723069\pi$
$180$	2.53906	+	20.6155i	0.189251	+	1.53659i
$181$			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
$184$	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	−0.995610	−	0.0935936i	$-0.970165\pi$
$191$	−8.00000	−	13.8564i	−0.578860	−	1.00261i	0.416751	−	0.909021i	$-0.363169\pi$
$192$	−23.8703	−	3.75334i	−1.72269	−	0.270874i
$193$	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	$0.0355624\pi$
$194$	−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	$-0.722027\pi$
$197$		−	21.5150i		−	1.53288i	0.642317	−	0.766439i	$-0.277973\pi$
$198$	−10.2638	−	5.11494i	−0.729414	−	0.363503i
$199$	−9.12311	+	15.8017i	−0.646720	+	1.12015i	0.337182	+	0.941440i	$0.390526\pi$
$199$	−9.12311	+	15.8017i	−0.646720	+	1.12015i	−0.983901	+	0.178712i	$0.942807\pi$
$200$	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	$0.0519079\pi$
$211$			4.71659i			0.324703i	−0.986733	+	0.162352i	$0.948092\pi$
$212$	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	0.190993	−	0.981591i	$-0.438829\pi$
$227$	−8.49139	−	4.90251i	−0.563593	−	0.325391i	−0.754586	+	0.656201i	$0.772163\pi$
$228$	10.9863	+	14.5680i	0.727584	+	0.964788i
$229$	−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	$0.654713\pi$
$234$	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	−0.920123	−	0.391629i	$-0.871912\pi$
$241$	−1.87689	+	3.25088i	−0.120901	+	0.209407i	0.799222	+	0.601036i	$0.205245\pi$
$242$	−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	$-0.887508\pi$
$251$		−	10.9663i		−	0.692186i	0.938200	−	0.346093i	$-0.112492\pi$
$252$		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	0.967933	+	0.251208i	$0.0808280\pi$
$257$	11.2462	+	19.4790i	0.701519	+	1.21507i	−0.266414	+	0.963859i	$0.585839\pi$
$258$	−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	−0.991791	−	0.127869i	$-0.959186\pi$
$263$	−6.24621	+	10.8188i	−0.385158	+	0.667113i	0.606633	+	0.794982i	$0.292520\pi$
$264$	−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	0.779560	−	0.626328i	$-0.215443\pi$
$269$	10.2823	+	5.93649i	0.626923	+	0.361954i	−0.152636	+	0.988282i	$0.548776\pi$
$270$	22.5850	−	1.38558i	1.37448	−	0.0843236i
$271$	5.12311	+	8.87348i	0.311207	+	0.539025i	0.978624	−	0.205658i	$-0.0659336\pi$
$271$	5.12311	+	8.87348i	0.311207	+	0.539025i	−0.667417	+	0.744684i	$0.732600\pi$
$272$	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	0.429505	−	0.903064i	$-0.358688\pi$
$277$	−2.29377	−	1.32431i	−0.137819	−	0.0795699i	−0.567324	+	0.823495i	$0.692021\pi$
$278$	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	−0.183619	−	0.982997i	$-0.558781\pi$
$283$	−18.9545	−	10.9434i	−1.12673	−	0.650518i	−0.943110	+	0.332480i	$0.892115\pi$
$284$	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	$-0.901889\pi$
$293$		−	10.3857i		−	0.606736i	0.952873	−	0.303368i	$-0.0981112\pi$
$294$		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	$0.256490\pi$
$307$			25.2791i			1.44275i	−0.692543	+	0.721377i	$0.743510\pi$
$308$		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	−0.986979	−	0.160849i	$-0.948577\pi$
$311$	−6.24621	+	10.8188i	−0.354190	+	0.613475i	0.632789	+	0.774324i	$0.281910\pi$
$312$	−4.82934	+	13.6619i	−0.273407	+	0.773452i
$313$	−10.3693	−	17.9602i	−0.586108	−	1.01517i	−0.994736	−	0.102468i	$-0.967326\pi$
$313$	−10.3693	−	17.9602i	−0.586108	−	1.01517i	0.408628	−	0.912701i	$-0.366007\pi$
$314$	−10.0000	+	6.62153i	−0.564333	+	0.373675i
$315$		0			0
$316$		0			0
$317$	3.58184	−	2.06798i	0.201176	−	0.116149i	−0.396028	−	0.918238i	$-0.629612\pi$
$317$	3.58184	−	2.06798i	0.201176	−	0.116149i	0.597204	+	0.802089i	$0.296278\pi$
$318$	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	−0.101726	−	0.994812i	$-0.532437\pi$
$331$	12.8981	−	7.44672i	0.708943	−	0.409309i	0.810670	+	0.585504i	$0.199103\pi$
$332$	−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	0.299520	−	0.954090i	$-0.403174\pi$
$347$	−7.02249	−	4.05444i	−0.376987	−	0.217654i	−0.676507	+	0.736437i	$0.736507\pi$
$348$	−36.2188	+	4.46080i	−1.94153	+	0.239124i
$349$		−	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
$352$	−2.25936	−	7.14258i	−0.120424	−	0.380701i
$353$	3.87689	−	6.71498i	0.206346	−	0.357402i	−0.744215	−	0.667941i	$-0.767176\pi$
$353$	3.87689	−	6.71498i	0.206346	−	0.357402i	0.950561	+	0.310538i	$0.100509\pi$
$354$	−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	0.899757	+	0.436392i	$0.143744\pi$
$359$	15.6847	+	27.1666i	0.827805	+	1.43380i	−0.0719522	+	0.997408i	$0.522923\pi$
$360$	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	−0.700772	−	0.713385i	$-0.747161\pi$
$367$	5.12311	−	8.87348i	0.267424	−	0.463192i	0.968196	+	0.250194i	$0.0804943\pi$
$368$	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	−0.792478	−	0.609901i	$-0.791209\pi$
$373$	−12.7569	+	7.36520i	−0.660528	+	0.381356i	0.131950	+	0.991256i	$0.457876\pi$
$374$	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	$-0.615321\pi$
$379$		−	36.4084i		−	1.87017i	0.354418	−	0.935087i	$-0.384679\pi$
$380$	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	0.802914	−	0.596095i	$-0.203282\pi$
$383$	−2.24621	−	3.89055i	−0.114776	−	0.198798i	−0.917690	+	0.397297i	$0.869948\pi$
$384$	−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	−0.159110	−	0.987261i	$-0.550863\pi$
$389$	−21.5703	−	12.4536i	−1.09366	−	0.631424i	−0.934548	+	0.355837i	$0.884196\pi$
$390$	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	−0.875164	−	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	$0.826363\pi$
$402$	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	−0.341994	−	0.939702i	$-0.611102\pi$
$409$	13.0000	−	22.5167i	0.642809	−	1.11338i	0.984803	−	0.173675i	$-0.0555643\pi$
$410$	−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	$-0.761033\pi$
$419$		−	27.9277i		−	1.36436i	0.731185	−	0.682179i	$-0.238967\pi$
$420$		0			0
$421$			26.8122i			1.30675i	0.757036	+	0.653373i	$0.226647\pi$
$421$			26.8122i			1.30675i	−0.757036	+	0.653373i	$0.773353\pi$
$422$	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	−0.996351	−	0.0853557i	$-0.972797\pi$
$431$	−8.80776	+	15.2555i	−0.424255	+	0.734831i	0.572095	+	0.820187i	$0.306131\pi$
$432$	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	0.998752	+	0.0499429i	$0.0159039\pi$
$439$	11.3693	+	19.6922i	0.542628	+	0.939859i	−0.456124	+	0.889916i	$0.650763\pi$
$440$	−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	−0.643812	−	0.765184i	$-0.722648\pi$
$443$	−6.37845	+	3.68260i	−0.303049	+	0.174966i	0.340763	+	0.940149i	$0.389315\pi$
$444$	−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	0.588215	−	0.808705i	$-0.299831\pi$
$457$	−8.68466	−	15.0423i	−0.406251	−	0.703648i	−0.994466	+	0.105057i	$0.966498\pi$
$458$	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	$-0.807885\pi$
$461$		−	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	$0.5\pi$
$464$	−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	−0.438255	−	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
$472$	−0.991577	−	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	−0.724924	−	0.688828i	$-0.758125\pi$
$479$	5.12311	−	8.87348i	0.234081	−	0.405440i	0.959005	+	0.283389i	$0.0914587\pi$
$480$	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	−0.873082	−	0.487574i	$-0.837882\pi$
$487$	−0.315342	+	0.546188i	−0.0142895	+	0.0247501i	0.858792	+	0.512324i	$0.171215\pi$
$488$	−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	$0.280344\pi$
$491$			34.1774i			1.54240i	−0.636590	+	0.771202i	$0.719656\pi$
$492$	−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	−0.661687	−	0.749781i	$-0.730159\pi$
$499$	−7.66652	+	4.42627i	−0.343201	+	0.198147i	0.318486	+	0.947928i	$0.396826\pi$
$500$	−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	0.223953	−	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
$514$	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	−0.999785	−	0.0207541i	$-0.993393\pi$
$521$	−11.0000	+	19.0526i	−0.481919	+	0.834708i	0.517866	+	0.855462i	$0.326727\pi$
$522$	3.20320	+	52.2122i	0.140200	+	2.28527i
$523$	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
$528$	−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	−0.725853	−	0.687850i	$-0.758555\pi$
$541$	−11.4688	+	6.62153i	−0.493084	+	0.284682i	0.232769	+	0.972532i	$0.425221\pi$
$542$	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	$0.0657689\pi$
$547$			9.59621i			0.410304i	−0.978730	+	0.205152i	$0.934231\pi$
$548$	−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	0.547807	−	0.836605i	$-0.315463\pi$
$557$	2.29377	+	1.32431i	0.0971900	+	0.0561127i	−0.450617	+	0.892717i	$0.648796\pi$
$558$	−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	0.933270	−	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	$0.742921\pi$
$570$	−1.34003	−	21.8426i	−0.0561278	−	0.914885i
$571$	8.02818	+	4.63507i	0.335969	+	0.193972i	0.658488	−	0.752591i	$-0.271196\pi$
$571$	8.02818	+	4.63507i	0.335969	+	0.193972i	−0.322519	+	0.946563i	$0.604530\pi$
$572$	−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	−0.773973	−	0.633219i	$-0.781733\pi$
$577$	3.87689	−	6.71498i	0.161397	−	0.279548i	0.935370	+	0.353671i	$0.115067\pi$
$578$	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	$0.149176\pi$
$587$			21.8868i			0.903365i	−0.892179	+	0.451683i	$0.850824\pi$
$588$		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	0.989501	−	0.144528i	$-0.0461663\pi$
$593$	9.00000	+	15.5885i	0.369586	+	0.640141i	−0.619915	+	0.784669i	$0.712833\pi$
$594$	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	−0.709740	−	0.704464i	$-0.751188\pi$
$599$	6.24621	−	10.8188i	0.255213	−	0.442042i	0.964953	+	0.262421i	$0.0845210\pi$
$600$	−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	0.896640	+	0.442760i	$0.146001\pi$
$607$	20.4924	+	35.4939i	0.831762	+	1.44065i	−0.0648782	+	0.997893i	$0.520666\pi$
$608$	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	0.538511	−	0.842619i	$-0.318987\pi$
$613$	1.93211	+	1.11550i	0.0780371	+	0.0450547i	−0.460474	+	0.887673i	$0.652320\pi$
$614$	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	0.801431	−	0.598087i	$-0.204072\pi$
$619$	17.0224	+	9.82790i	0.684189	+	0.395017i	−0.117243	+	0.993103i	$0.537405\pi$
$620$	−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	−0.808124	−	0.589012i	$-0.799517\pi$
$641$	2.68466	−	4.64996i	0.106038	−	0.183663i	0.914162	+	0.405350i	$0.132850\pi$
$642$	26.9588	−	54.0962i	1.06398	−	2.13501i
$643$		−	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
$646$	−7.64624	−	3.81050i	−0.300837	−	0.149922i
$647$	21.6155	−	37.4392i	0.849794	−	1.47189i	−0.0315977	−	0.999501i	$-0.510060\pi$
$647$	21.6155	−	37.4392i	0.849794	−	1.47189i	0.881392	−	0.472386i	$-0.156607\pi$
$648$	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	−0.929283	−	0.369369i	$-0.879574\pi$
$653$	−27.4459	+	15.8459i	−1.07404	+	0.620098i	−0.144759	+	0.989467i	$0.546241\pi$
$654$	−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	$0.0411668\pi$
$659$			6.62153i			0.257938i	−0.991649	+	0.128969i	$0.958833\pi$
$660$	1.65868	+	13.4674i	0.0645639	+	0.524217i
$661$	−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	$-0.669099\pi$
$662$	−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	−0.757746	−	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
$682$	−1.17507	−	19.1536i	−0.0449957	−	0.733431i
$683$	0.502848	+	0.290319i	0.0192409	+	0.0111088i	0.509590	−	0.860418i	$-0.329797\pi$
$683$	0.502848	+	0.290319i	0.0192409	+	0.0111088i	−0.490349	+	0.871526i	$0.663131\pi$
$684$	−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	0.303038	−	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
$696$	−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	$0.0134150\pi$
$701$			2.23100i			0.0842639i	−0.999112	+	0.0421319i	$0.986585\pi$
$702$	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	0.0459283	−	0.998945i	$-0.485375\pi$
$709$	24.8698	−	14.3586i	0.934004	−	0.539247i	0.888076	+	0.459697i	$0.152042\pi$
$710$	−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	−0.666711	−	0.745317i	$-0.732298\pi$
$719$	−26.2462	−	45.4598i	−0.978819	−	1.69536i	−0.312108	−	0.950047i	$-0.601035\pi$
$720$	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	−0.888608	−	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
$738$	−36.7006	+	2.25156i	−1.35097	+	0.0828812i
$739$	18.4913	+	10.6760i	0.680214	+	0.392722i	0.799936	−	0.600086i	$-0.204867\pi$
$739$	18.4913	+	10.6760i	0.680214	+	0.392722i	−0.119721	+	0.992808i	$0.538200\pi$
$740$	−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	0.776486	−	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
$754$	−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	$-0.840759\pi$
$757$		−	26.3946i		−	0.959328i	0.877452	−	0.479664i	$-0.159241\pi$
$758$	−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	0.934287	−	0.356521i	$-0.116037\pi$
$761$	4.36932	+	7.56788i	0.158388	+	0.274335i	−0.775900	+	0.630856i	$0.782704\pi$
$762$	−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	0.526184	−	0.850371i	$-0.323622\pi$
$773$	1.46890	+	0.848071i	0.0528327	+	0.0305030i	−0.473351	+	0.880874i	$0.656956\pi$
$774$	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	0.653905	−	0.756577i	$-0.273130\pi$
$787$	9.13543	+	5.27434i	0.325643	+	0.188010i	−0.328262	+	0.944587i	$0.606463\pi$
$788$	−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	$0.151434\pi$
$797$			25.8597i			0.915998i	−0.888953	+	0.457999i	$0.848566\pi$
$798$		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	0.313555	+	0.949570i	$0.398480\pi$
$809$	−18.9309	+	32.7892i	−0.665574	+	1.15281i	−0.979129	+	0.203238i	$0.934853\pi$
$810$	−21.7331	−	10.8307i	−0.763624	−	0.380551i
$811$		−	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
$814$	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	0.102664	−	0.994716i	$-0.467263\pi$
$821$	29.0956	−	16.7984i	1.01545	−	0.586268i	0.912781	+	0.408449i	$0.133930\pi$
$822$	4.24946	+	69.2664i	0.148217	+	2.41594i
$823$	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	$-0.0282884\pi$
$824$	−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	$0.0344017\pi$
$827$			6.20393i			0.215732i	−0.994165	+	0.107866i	$0.965598\pi$
$828$	−62.2681	+	7.66911i	−2.16397	+	0.266520i
$829$	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	$0.366252\pi$
$830$	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	$0.143450\pi$
$853$			25.4421i			0.871121i	−0.900159	+	0.435561i	$0.856550\pi$
$854$		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	0.115489	+	0.993309i	$0.463156\pi$
$857$	−23.4924	+	40.6901i	−0.802486	+	1.38995i	−0.917975	+	0.396638i	$0.870177\pi$
$858$	0.587534	+	9.57682i	0.0200581	+	0.326947i
$859$	−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	$-0.379984\pi$
$864$	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	−0.919322	−	0.393505i	$-0.871262\pi$
$877$	−30.7454	+	17.7509i	−1.03820	+	0.599404i	−0.118875	+	0.992909i	$0.537929\pi$
$878$	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	$0.0252886\pi$
$883$			4.71659i			0.158726i	−0.996846	+	0.0793629i	$0.974711\pi$
$884$	−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	0.521351	−	0.853343i	$-0.325428\pi$
$887$	−14.2462	−	24.6752i	−0.478341	−	0.828511i	−0.999692	+	0.0248317i	$0.992095\pi$
$888$	−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	−0.482748	−	0.875760i	$-0.660361\pi$
$907$	−44.6492	−	25.7782i	−1.48255	−	0.855951i	−0.999804	+	0.0198082i	$0.993694\pi$
$908$	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	0.792480	−	0.609898i	$-0.208790\pi$
$919$	−4.00000	−	6.92820i	−0.131948	−	0.228540i	−0.924427	+	0.381358i	$0.875456\pi$
$920$	−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	0.844858	−	0.534991i	$-0.179685\pi$
$929$	−1.24621	−	2.15850i	−0.0408869	−	0.0708181i	−0.885745	+	0.464173i	$0.846352\pi$
$930$	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	−0.00119780	−	0.999999i	$-0.500381\pi$
$941$	−26.6211	−	15.3697i	−0.867821	−	0.501037i	−0.866624	+	0.498962i	$0.833715\pi$
$942$	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	−0.954544	−	0.298069i	$-0.903658\pi$
$947$	−36.1181	+	20.8528i	−1.17368	+	0.677625i	−0.219137	+	0.975694i	$0.570324\pi$
$948$		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	−0.644586	−	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
$976$	1.64624	+	6.58181i	0.0526948	+	0.210679i
$977$	−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	$0.290734\pi$
$978$	−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	0.452392	+	0.891819i	$0.350571\pi$
$983$	−17.1231	+	29.6581i	−0.546142	+	0.945946i	−0.998534	+	0.0541268i	$0.982762\pi$
$984$	−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	−0.415914	−	0.909404i	$-0.636538\pi$
$991$	18.2462	−	31.6034i	0.579610	−	1.00391i	0.995524	−	0.0945100i	$-0.0301284\pi$
$992$	−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	−0.0273989	−	0.999625i	$-0.508722\pi$
$997$	−28.6324	−	16.5309i	−0.906799	−	0.523540i	−0.879400	+	0.476084i	$0.842056\pi$
$998$	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.165.3		8
4.3	odd	2		1568.2.t.e.753.4		8
7.2	even	3	inner	392.2.p.e.373.1		8
7.3	odd	6		56.2.b.b.29.4	yes	4
7.4	even	3		392.2.b.c.197.4		4
7.5	odd	6		392.2.p.f.373.1		8
7.6	odd	2		392.2.p.f.165.3		8
8.3	odd	2		1568.2.t.e.753.1		8
8.5	even	2	inner	392.2.p.e.165.1		8
21.17	even	6		504.2.c.d.253.1		4
28.3	even	6		224.2.b.b.113.4		4
28.11	odd	6		1568.2.b.d.785.1		4
28.19	even	6		1568.2.t.d.177.4		8
28.23	odd	6		1568.2.t.e.177.1		8
28.27	even	2		1568.2.t.d.753.1		8
56.3	even	6		224.2.b.b.113.1		4
56.5	odd	6		392.2.p.f.373.3		8
56.11	odd	6		1568.2.b.d.785.4		4
56.13	odd	2		392.2.p.f.165.1		8
56.19	even	6		1568.2.t.d.177.1		8
56.27	even	2		1568.2.t.d.753.4		8
56.37	even	6	inner	392.2.p.e.373.3		8
56.45	odd	6		56.2.b.b.29.3	✓	4
56.51	odd	6		1568.2.t.e.177.4		8
56.53	even	6		392.2.b.c.197.3		4
84.59	odd	6		2016.2.c.c.1009.2		4
112.3	even	12		1792.2.a.v.1.1		4
112.45	odd	12		1792.2.a.x.1.4		4
112.59	even	12		1792.2.a.v.1.4		4
112.101	odd	12		1792.2.a.x.1.1		4
168.59	odd	6		2016.2.c.c.1009.3		4
168.101	even	6		504.2.c.d.253.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.2.b.b.29.3	✓	4	56.45	odd	6
56.2.b.b.29.4	yes	4	7.3	odd	6
224.2.b.b.113.1		4	56.3	even	6
224.2.b.b.113.4		4	28.3	even	6
392.2.b.c.197.3		4	56.53	even	6
392.2.b.c.197.4		4	7.4	even	3
392.2.p.e.165.1		8	8.5	even	2	inner
392.2.p.e.165.3		8	1.1	even	1	trivial
392.2.p.e.373.1		8	7.2	even	3	inner
392.2.p.e.373.3		8	56.37	even	6	inner
392.2.p.f.165.1		8	56.13	odd	2
392.2.p.f.165.3		8	7.6	odd	2
392.2.p.f.373.1		8	7.5	odd	6
392.2.p.f.373.3		8	56.5	odd	6
504.2.c.d.253.1		4	21.17	even	6
504.2.c.d.253.2		4	168.101	even	6
1568.2.b.d.785.1		4	28.11	odd	6
1568.2.b.d.785.4		4	56.11	odd	6
1568.2.t.d.177.1		8	56.19	even	6
1568.2.t.d.177.4		8	28.19	even	6
1568.2.t.d.753.1		8	28.27	even	2
1568.2.t.d.753.4		8	56.27	even	2
1568.2.t.e.177.1		8	28.23	odd	6
1568.2.t.e.177.4		8	56.51	odd	6
1568.2.t.e.753.1		8	8.3	odd	2
1568.2.t.e.753.4		8	4.3	odd	2
1792.2.a.v.1.1		4	112.3	even	12
1792.2.a.v.1.4		4	112.59	even	12
1792.2.a.x.1.1		4	112.101	odd	12
1792.2.a.x.1.4		4	112.45	odd	12
2016.2.c.c.1009.2		4	84.59	odd	6
2016.2.c.c.1009.3		4	168.59	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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