LMFDB - Embedded newform 800.2.ba.f.549.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [800,2,Mod(149,800)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(800, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 5, 4]))

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

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

chi := DirichletCharacter("800.149");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 800 = 2^{5} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	800.ba (of order $8$, degree $4$, 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:	$6.38803216170$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			549.16
Character	$\chi$	$=$	800.549
Dual form			800.2.ba.f.749.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.37027 - 0.349813i) q^{2} +(-2.56208 + 1.06125i) q^{3} +(1.75526 - 0.958675i) q^{4} +(-3.13949 + 2.35044i) q^{6} +(-2.94098 + 2.94098i) q^{7} +(2.06982 - 1.92765i) q^{8} +(3.31668 - 3.31668i) q^{9} +O(q^{10})$	\(q+(1.37027 - 0.349813i) q^{2} +(-2.56208 + 1.06125i) q^{3} +(1.75526 - 0.958675i) q^{4} +(-3.13949 + 2.35044i) q^{6} +(-2.94098 + 2.94098i) q^{7} +(2.06982 - 1.92765i) q^{8} +(3.31668 - 3.31668i) q^{9} +(-0.569137 + 1.37402i) q^{11} +(-3.47973 + 4.31897i) q^{12} +(-1.87795 - 4.53377i) q^{13} +(-3.00114 + 5.05872i) q^{14} +(2.16189 - 3.36545i) q^{16} -2.78896 q^{17} +(3.38452 - 5.70495i) q^{18} +(-2.08461 + 0.863472i) q^{19} +(4.41392 - 10.6561i) q^{21} +(-0.299220 + 2.08186i) q^{22} +(-3.26157 - 3.26157i) q^{23} +(-3.25732 + 7.13539i) q^{24} +(-4.15927 - 5.55555i) q^{26} +(-1.79403 + 4.33117i) q^{27} +(-2.34275 + 7.98164i) q^{28} +(-2.85519 - 6.89303i) q^{29} -0.800126 q^{31} +(1.78508 - 5.36782i) q^{32} -4.12434i q^{33} +(-3.82162 + 0.975616i) q^{34} +(2.64202 - 9.00125i) q^{36} +(-3.53070 + 8.52386i) q^{37} +(-2.55441 + 1.91241i) q^{38} +(9.62291 + 9.62291i) q^{39} +(-8.87560 + 8.87560i) q^{41} +(2.32059 - 16.1458i) q^{42} +(-4.67600 - 1.93686i) q^{43} +(0.318252 + 2.95738i) q^{44} +(-5.61017 - 3.32828i) q^{46} +2.86075 q^{47} +(-1.96735 + 10.9168i) q^{48} -10.2987i q^{49} +(7.14554 - 2.95978i) q^{51} +(-7.64271 - 6.15762i) q^{52} +(5.42935 + 2.24891i) q^{53} +(-0.943199 + 6.56244i) q^{54} +(-0.418107 + 11.7565i) q^{56} +(4.42457 - 4.42457i) q^{57} +(-6.32364 - 8.44650i) q^{58} +(-13.6375 - 5.64885i) q^{59} +(-4.72380 - 11.4043i) q^{61} +(-1.09639 + 0.279895i) q^{62} +19.5086i q^{63} +(0.568304 - 7.97979i) q^{64} +(-1.44275 - 5.65144i) q^{66} +(12.6341 - 5.23321i) q^{67} +(-4.89536 + 2.67371i) q^{68} +(11.8177 + 4.89507i) q^{69} +(2.90308 + 2.90308i) q^{71} +(0.471518 - 13.2583i) q^{72} +(-1.13529 - 1.13529i) q^{73} +(-1.85624 + 12.9151i) q^{74} +(-2.83124 + 3.51408i) q^{76} +(-2.36714 - 5.71478i) q^{77} +(16.5522 + 9.81974i) q^{78} +6.06396i q^{79} +1.07076i q^{81} +(-9.05714 + 15.2667i) q^{82} +(-0.121076 - 0.292304i) q^{83} +(-2.46819 - 22.9358i) q^{84} +(-7.08491 - 1.01829i) q^{86} +(14.6304 + 14.6304i) q^{87} +(1.47062 + 3.94107i) q^{88} +(8.97315 + 8.97315i) q^{89} +(18.8568 + 7.81073i) q^{91} +(-8.85170 - 2.59813i) q^{92} +(2.04999 - 0.849132i) q^{93} +(3.91999 - 1.00073i) q^{94} +(1.12307 + 15.6472i) q^{96} +13.5255i q^{97} +(-3.60264 - 14.1120i) q^{98} +(2.66953 + 6.44482i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q+O(q^{10}) $ 64 * q	$ 64 q - 24 q^{12} + 16 q^{14} + 20 q^{16} + 40 q^{18} + 24 q^{22} - 8 q^{23} + 28 q^{24} - 48 q^{28} - 20 q^{32} + 20 q^{34} + 12 q^{36} + 16 q^{37} - 24 q^{39} - 40 q^{44} + 32 q^{46} + 80 q^{47} + 40 q^{48} + 16 q^{51} - 76 q^{54} + 48 q^{56} - 8 q^{58} - 32 q^{59} - 32 q^{61} - 44 q^{62} - 48 q^{64} + 16 q^{66} - 32 q^{68} + 32 q^{69} + 32 q^{71} + 96 q^{72} - 8 q^{74} + 52 q^{78} - 116 q^{82} - 56 q^{84} - 84 q^{86} + 20 q^{88} + 48 q^{91} + 88 q^{92} - 48 q^{93} - 32 q^{94} - 100 q^{96} - 72 q^{98} + 64 q^{99}+O(q^{100}) $ 64 * q - 24 * q^12 + 16 * q^14 + 20 * q^16 + 40 * q^18 + 24 * q^22 - 8 * q^23 + 28 * q^24 - 48 * q^28 - 20 * q^32 + 20 * q^34 + 12 * q^36 + 16 * q^37 - 24 * q^39 - 40 * q^44 + 32 * q^46 + 80 * q^47 + 40 * q^48 + 16 * q^51 - 76 * q^54 + 48 * q^56 - 8 * q^58 - 32 * q^59 - 32 * q^61 - 44 * q^62 - 48 * q^64 + 16 * q^66 - 32 * q^68 + 32 * q^69 + 32 * q^71 + 96 * q^72 - 8 * q^74 + 52 * q^78 - 116 * q^82 - 56 * q^84 - 84 * q^86 + 20 * q^88 + 48 * q^91 + 88 * q^92 - 48 * q^93 - 32 * q^94 - 100 * q^96 - 72 * q^98 + 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/800\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$577$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	1.37027	−	0.349813i	0.968925	−	0.247355i
$2$	1.37027	−	0.349813i	0.968925	−	0.247355i
$3$	−2.56208	+	1.06125i	−1.47922	+	0.612712i	−0.968939	−	0.247298i	$-0.920457\pi$
$3$	−2.56208	+	1.06125i	−1.47922	+	0.612712i	−0.510277	+	0.860010i	$0.670457\pi$
$4$	1.75526	−	0.958675i	0.877631	−	0.479337i
$5$		0			0
$5$		0			0
$6$	−3.13949	+	2.35044i	−1.28169	+	0.959564i
$7$	−2.94098	+	2.94098i	−1.11159	+	1.11159i	−0.118651	+	0.992936i	$0.537857\pi$
$7$	−2.94098	+	2.94098i	−1.11159	+	1.11159i	−0.992936	+	0.118651i	$0.962143\pi$
$8$	2.06982	−	1.92765i	0.731792	−	0.681528i
$9$	3.31668	−	3.31668i	1.10556	−	1.10556i
$10$		0			0
$11$	−0.569137	+	1.37402i	−0.171601	+	0.414282i	−0.986159	−	0.165800i	$-0.946979\pi$
$11$	−0.569137	+	1.37402i	−0.171601	+	0.414282i	0.814558	+	0.580082i	$0.196979\pi$
$12$	−3.47973	+	4.31897i	−1.00451	+	1.24678i
$13$	−1.87795	−	4.53377i	−0.520850	−	1.25744i	−0.937376	−	0.348319i	$-0.886753\pi$
$13$	−1.87795	−	4.53377i	−0.520850	−	1.25744i	0.416526	−	0.909124i	$-0.363247\pi$
$14$	−3.00114	+	5.05872i	−0.802087	+	1.35200i
$15$		0			0
$16$	2.16189	−	3.36545i	0.540471	−	0.841362i
$17$	−2.78896			−0.676423			−0.338211	−	0.941070i	$-0.609822\pi$
$17$	−2.78896			−0.676423			−0.338211	+	0.941070i	$0.609822\pi$
$18$	3.38452	−	5.70495i	0.797738	−	1.34467i
$19$	−2.08461	+	0.863472i	−0.478242	+	0.198094i	−0.608764	−	0.793351i	$-0.708334\pi$
$19$	−2.08461	+	0.863472i	−0.478242	+	0.198094i	0.130523	+	0.991445i	$0.458334\pi$
$20$		0			0
$21$	4.41392	−	10.6561i	0.963195	−	2.32536i
$22$	−0.299220	+	2.08186i	−0.0637939	+	0.443855i
$23$	−3.26157	−	3.26157i	−0.680085	−	0.680085i	0.279934	−	0.960019i	$-0.409687\pi$
$23$	−3.26157	−	3.26157i	−0.680085	−	0.680085i	−0.960019	+	0.279934i	$0.909687\pi$
$24$	−3.25732	+	7.13539i	−0.664898	+	1.45651i
$25$		0			0
$26$	−4.15927	−	5.55555i	−0.815699	−	1.08953i
$27$	−1.79403	+	4.33117i	−0.345261	+	0.833535i
$28$	−2.34275	+	7.98164i	−0.442738	+	1.50839i
$29$	−2.85519	−	6.89303i	−0.530195	−	1.28000i	−0.931394	−	0.364012i	$-0.881407\pi$
$29$	−2.85519	−	6.89303i	−0.530195	−	1.28000i	0.401200	−	0.915991i	$-0.368593\pi$
$30$		0			0
$31$	−0.800126			−0.143707			−0.0718535	−	0.997415i	$-0.522891\pi$
$31$	−0.800126			−0.143707			−0.0718535	+	0.997415i	$0.522891\pi$
$32$	1.78508	−	5.36782i	0.315561	−	0.948905i
$33$		−	4.12434i		−	0.717955i
$34$	−3.82162	+	0.975616i	−0.655403	+	0.167317i
$35$		0			0
$36$	2.64202	−	9.00125i	0.440337	−	1.50021i
$37$	−3.53070	+	8.52386i	−0.580443	+	1.40131i	0.311968	+	0.950093i	$0.399012\pi$
$37$	−3.53070	+	8.52386i	−0.580443	+	1.40131i	−0.892412	+	0.451222i	$0.850988\pi$
$38$	−2.55441	+	1.91241i	−0.414380	+	0.310234i
$39$	9.62291	+	9.62291i	1.54090	+	1.54090i
$40$		0			0
$41$	−8.87560	+	8.87560i	−1.38614	+	1.38614i	−0.552864	+	0.833271i	$0.686465\pi$
$41$	−8.87560	+	8.87560i	−1.38614	+	1.38614i	−0.833271	+	0.552864i	$0.813535\pi$
$42$	2.32059	−	16.1458i	0.358074	−	2.49135i
$43$	−4.67600	−	1.93686i	−0.713083	−	0.295369i	−0.00350351	−	0.999994i	$-0.501115\pi$
$43$	−4.67600	−	1.93686i	−0.713083	−	0.295369i	−0.709580	+	0.704625i	$0.751115\pi$
$44$	0.318252	+	2.95738i	0.0479783	+	0.445842i
$45$		0			0
$46$	−5.61017	−	3.32828i	−0.827174	−	0.490729i
$47$	2.86075			0.417284			0.208642	−	0.977992i	$-0.433096\pi$
$47$	2.86075			0.417284			0.208642	+	0.977992i	$0.433096\pi$
$48$	−1.96735	+	10.9168i	−0.283962	+	1.57571i
$49$		−	10.2987i		−	1.47125i
$50$		0			0
$51$	7.14554	−	2.95978i	1.00058	−	0.414452i
$52$	−7.64271	−	6.15762i	−1.05985	−	0.853908i
$53$	5.42935	+	2.24891i	0.745779	+	0.308912i	0.723018	−	0.690829i	$-0.242754\pi$
$53$	5.42935	+	2.24891i	0.745779	+	0.308912i	0.0227609	+	0.999741i	$0.492754\pi$
$54$	−0.943199	+	6.56244i	−0.128353	+	0.893035i
$55$		0			0
$56$	−0.418107	+	11.7565i	−0.0558719	+	1.57103i
$57$	4.42457	−	4.42457i	0.586048	−	0.586048i
$58$	−6.32364	−	8.44650i	−0.830334	−	1.10908i
$59$	−13.6375	−	5.64885i	−1.77545	−	0.735417i	−0.993732	−	0.111790i	$-0.964342\pi$
$59$	−13.6375	−	5.64885i	−1.77545	−	0.735417i	−0.781722	−	0.623627i	$-0.785658\pi$
$60$		0			0
$61$	−4.72380	−	11.4043i	−0.604820	−	1.46016i	−0.868567	−	0.495573i	$-0.834958\pi$
$61$	−4.72380	−	11.4043i	−0.604820	−	1.46016i	0.263747	−	0.964592i	$-0.415042\pi$
$62$	−1.09639	+	0.279895i	−0.139241	+	0.0355467i
$63$			19.5086i			2.45785i
$64$	0.568304	−	7.97979i	0.0710380	−	0.997474i
$65$		0			0
$66$	−1.44275	−	5.65144i	−0.177590	−	0.695645i
$67$	12.6341	−	5.23321i	1.54350	−	0.639338i	0.561373	−	0.827563i	$-0.310273\pi$
$67$	12.6341	−	5.23321i	1.54350	−	0.639338i	0.982126	+	0.188225i	$0.0602733\pi$
$68$	−4.89536	+	2.67371i	−0.593649	+	0.324235i
$69$	11.8177	+	4.89507i	1.42269	+	0.589297i
$70$		0			0
$71$	2.90308	+	2.90308i	0.344532	+	0.344532i	0.858068	−	0.513536i	$-0.171665\pi$
$71$	2.90308	+	2.90308i	0.344532	+	0.344532i	−0.513536	+	0.858068i	$0.671665\pi$
$72$	0.471518	−	13.2583i	0.0555690	−	1.56251i
$73$	−1.13529	−	1.13529i	−0.132876	−	0.132876i	0.637541	−	0.770417i	$-0.279952\pi$
$73$	−1.13529	−	1.13529i	−0.132876	−	0.132876i	−0.770417	+	0.637541i	$0.779952\pi$
$74$	−1.85624	+	12.9151i	−0.215784	+	1.50134i
$75$		0			0
$76$	−2.83124	+	3.51408i	−0.324766	+	0.403093i
$77$	−2.36714	−	5.71478i	−0.269761	−	0.651260i
$78$	16.5522	+	9.81974i	1.87417	+	1.11187i
$79$			6.06396i			0.682249i	0.940018	+	0.341124i	$0.110808\pi$
$79$			6.06396i			0.682249i	−0.940018	+	0.341124i	$0.889192\pi$
$80$		0			0
$81$			1.07076i			0.118973i
$82$	−9.05714	+	15.2667i	−1.00019	+	1.68593i
$83$	−0.121076	−	0.292304i	−0.0132899	−	0.0320846i	0.917095	−	0.398668i	$-0.130527\pi$
$83$	−0.121076	−	0.292304i	−0.0132899	−	0.0320846i	−0.930385	+	0.366583i	$0.880527\pi$
$84$	−2.46819	−	22.9358i	−0.269302	−	2.50250i
$85$		0			0
$86$	−7.08491	−	1.01829i	−0.763985	−	0.109805i
$87$	14.6304	+	14.6304i	1.56855	+	1.56855i
$88$	1.47062	+	3.94107i	0.156769	+	0.420119i
$89$	8.97315	+	8.97315i	0.951152	+	0.951152i	0.998861	−	0.0477088i	$-0.0151920\pi$
$89$	8.97315	+	8.97315i	0.951152	+	0.951152i	−0.0477088	+	0.998861i	$0.515192\pi$
$90$		0			0
$91$	18.8568	+	7.81073i	1.97673	+	0.818787i
$92$	−8.85170	−	2.59813i	−0.922854	−	0.270873i
$93$	2.04999	−	0.849132i	0.212574	−	0.0880509i
$94$	3.91999	−	1.00073i	0.404316	−	0.103217i
$95$		0			0
$96$	1.12307	+	15.6472i	0.114622	+	1.59698i
$97$			13.5255i			1.37330i	0.726987	+	0.686651i	$0.240920\pi$
$97$			13.5255i			1.37330i	−0.726987	+	0.686651i	$0.759080\pi$
$98$	−3.60264	−	14.1120i	−0.363921	−	1.42553i
$99$	2.66953	+	6.44482i	0.268298	+	0.647729i
$100$		0			0
$101$	8.14849	+	3.37522i	0.810805	+	0.335846i	0.749275	−	0.662259i	$-0.230402\pi$
$101$	8.14849	+	3.37522i	0.810805	+	0.335846i	0.0615299	+	0.998105i	$0.480402\pi$
$102$	8.75592	−	6.55529i	0.866966	−	0.649070i
$103$	−6.88114	+	6.88114i	−0.678019	+	0.678019i	−0.959552	−	0.281532i	$-0.909157\pi$
$103$	−6.88114	+	6.88114i	−0.678019	+	0.678019i	0.281532	+	0.959552i	$0.409157\pi$
$104$	−12.6266	−	5.76406i	−1.23814	−	0.565212i
$105$		0			0
$106$	8.22636	+	1.18235i	0.799015	+	0.114840i
$107$	−2.26206	−	0.936975i	−0.218681	−	0.0905807i	0.270653	−	0.962677i	$-0.412760\pi$
$107$	−2.26206	−	0.936975i	−0.218681	−	0.0905807i	−0.489335	+	0.872096i	$0.662760\pi$
$108$	1.00319	+	9.32223i	0.0965323	+	0.897032i
$109$	4.31645	−	1.78793i	0.413441	−	0.171253i	−0.166260	−	0.986082i	$-0.553169\pi$
$109$	4.31645	−	1.78793i	0.413441	−	0.171253i	0.579702	+	0.814829i	$0.303169\pi$
$110$		0			0
$111$		−	25.5858i		−	2.42849i
$112$	3.53966	+	16.2558i	0.334466	+	1.53603i
$113$	0.592560			0.0557433			0.0278717	−	0.999612i	$-0.491127\pi$
$113$	0.592560			0.0557433			0.0278717	+	0.999612i	$0.491127\pi$
$114$	4.51507	−	7.61061i	0.422875	−	0.712799i
$115$		0			0
$116$	−11.6198	−	9.36187i	−1.07887	−	0.869228i
$117$	−21.2656	−	8.80851i	−1.96601	−	0.814347i
$118$	−20.6631	−	2.96984i	−1.90219	−	0.273396i
$119$	8.20229	−	8.20229i	0.751902	−	0.751902i
$120$		0			0
$121$	6.21416	+	6.21416i	0.564924	+	0.564924i
$122$	−10.4622	−	13.9744i	−0.947205	−	1.26518i
$123$	13.3208	−	32.1592i	1.20109	−	2.89970i
$124$	−1.40443	+	0.767061i	−0.126122	+	0.0688841i
$125$		0			0
$126$	6.82436	+	26.7320i	0.607962	+	2.38147i
$127$		−	3.21186i		−	0.285006i	−0.989794	−	0.142503i	$-0.954485\pi$
$127$		−	3.21186i		−	0.285006i	0.989794	−	0.142503i	$-0.0455151\pi$
$128$	−2.01271	−	11.1332i	−0.177900	−	0.984049i
$129$	14.0358			1.23578
$130$		0			0
$131$	−3.16454	−	7.63987i	−0.276487	−	0.667499i	0.723246	−	0.690590i	$-0.242649\pi$
$131$	−3.16454	−	7.63987i	−0.276487	−	0.667499i	−0.999733	+	0.0230915i	$0.992649\pi$
$132$	−3.95390	−	7.23929i	−0.344143	−	0.630100i
$133$	3.59133	−	8.67025i	0.311408	−	0.751806i
$134$	15.4814	−	11.5905i	1.33739	−	1.00126i
$135$		0			0
$136$	−5.77265	+	5.37615i	−0.495000	+	0.461001i
$137$	−3.47339	−	3.47339i	−0.296751	−	0.296751i	0.542989	−	0.839740i	$-0.317293\pi$
$137$	−3.47339	−	3.47339i	−0.296751	−	0.296751i	−0.839740	+	0.542989i	$0.817293\pi$
$138$	17.9058	+	2.57355i	1.52424	+	0.219075i
$139$	−7.36134	+	17.7718i	−0.624380	+	1.50739i	0.222131	+	0.975017i	$0.428699\pi$
$139$	−7.36134	+	17.7718i	−0.624380	+	1.50739i	−0.846511	+	0.532371i	$0.821301\pi$
$140$		0			0
$141$	−7.32947	+	3.03597i	−0.617253	+	0.255674i
$142$	4.99352	+	2.96245i	0.419047	+	0.248604i
$143$	7.29830			0.610315
$144$	−3.99183	−	18.3324i	−0.332653	−	1.52770i
$145$		0			0
$146$	−1.95279	−	1.15851i	−0.161614	−	0.0958791i
$147$	10.9295	+	26.3862i	0.901452	+	2.17630i
$148$	1.97431	+	18.3464i	0.162287	+	1.50806i
$149$	0.649458	−	1.56793i	0.0532056	−	0.128450i	−0.895042	−	0.445983i	$-0.852854\pi$
$149$	0.649458	−	1.56793i	0.0532056	−	0.128450i	0.948247	+	0.317533i	$0.102854\pi$
$150$		0			0
$151$	−6.11339	+	6.11339i	−0.497501	+	0.497501i	−0.910659	−	0.413158i	$-0.864426\pi$
$151$	−6.11339	+	6.11339i	−0.497501	+	0.497501i	0.413158	+	0.910659i	$0.364426\pi$
$152$	−2.65028	+	5.80563i	−0.214966	+	0.470899i
$153$	−9.25009	+	9.25009i	−0.747826	+	0.747826i
$154$	−5.24272	−	7.00272i	−0.422471	−	0.564295i
$155$		0			0
$156$	26.1160	+	7.66549i	2.09095	+	0.613730i
$157$	11.5402	−	4.78009i	0.921005	−	0.381493i	0.128746	−	0.991678i	$-0.458905\pi$
$157$	11.5402	−	4.78009i	0.921005	−	0.381493i	0.792259	+	0.610185i	$0.208905\pi$
$158$	2.12125	+	8.30924i	0.168758	+	0.661048i
$159$	−16.2971			−1.29244
$160$		0			0
$161$	19.1845			1.51195
$162$	0.374566	+	1.46723i	0.0294287	+	0.115276i
$163$	−1.10939	+	0.459523i	−0.0868938	+	0.0359926i	−0.425707	−	0.904861i	$-0.639975\pi$
$163$	−1.10939	+	0.459523i	−0.0868938	+	0.0359926i	0.338813	+	0.940854i	$0.389975\pi$
$164$	−7.07019	+	24.0878i	−0.552089	+	1.88094i
$165$		0			0
$166$	−0.268159	−	0.358181i	−0.0208132	−	0.0278002i
$167$	−3.35519	+	3.35519i	−0.259632	+	0.259632i	−0.824904	−	0.565272i	$-0.808771\pi$
$167$	−3.35519	+	3.35519i	−0.259632	+	0.259632i	0.565272	+	0.824904i	$0.308771\pi$
$168$	−11.4053	−	30.5648i	−0.879940	−	2.35812i
$169$	−7.83602	+	7.83602i	−0.602771	+	0.602771i
$170$		0			0
$171$	−4.05011	+	9.77783i	−0.309720	+	0.747729i
$172$	−10.0644	+	1.08306i	−0.767405	+	0.0825827i
$173$	−4.28956	−	10.3559i	−0.326129	−	0.787345i	−0.998873	−	0.0474697i	$-0.984884\pi$
$173$	−4.28956	−	10.3559i	−0.326129	−	0.787345i	0.672744	−	0.739876i	$-0.265116\pi$
$174$	25.1655	+	14.9297i	1.90779	+	1.13181i
$175$		0			0
$176$	3.39378	+	4.88587i	0.255816	+	0.368287i
$177$	40.9352			3.07688
$178$	15.4345	+	9.15669i	1.15687	+	0.686323i
$179$	−4.10991	+	1.70238i	−0.307189	+	0.127242i	−0.530952	−	0.847402i	$-0.678166\pi$
$179$	−4.10991	+	1.70238i	−0.307189	+	0.127242i	0.223763	+	0.974643i	$0.428166\pi$
$180$		0			0
$181$	−0.0541726	+	0.130784i	−0.00402662	+	0.00972112i	−0.925880	−	0.377818i	$-0.876675\pi$
$181$	−0.0541726	+	0.130784i	−0.00402662	+	0.00972112i	0.921853	+	0.387539i	$0.126675\pi$
$182$	28.5711	+	4.10644i	2.11783	+	0.304389i
$183$	24.2055	+	24.2055i	1.78932	+	1.78932i
$184$	−13.0380	−	0.463684i	−0.961178	−	0.0341833i
$185$		0			0
$186$	2.51199	−	1.88065i	0.184188	−	0.137896i
$187$	1.58730	−	3.83209i	0.116075	−	0.280230i
$188$	5.02137	−	2.74253i	0.366221	−	0.200020i
$189$	−7.46169	−	18.0141i	−0.542758	−	1.31033i
$190$		0			0
$191$	−0.866006			−0.0626620			−0.0313310	−	0.999509i	$-0.509975\pi$
$191$	−0.866006			−0.0626620			−0.0313310	+	0.999509i	$0.509975\pi$
$192$	7.01249	+	21.0480i	0.506083	+	1.51901i
$193$		−	16.6416i		−	1.19789i	−0.800790	−	0.598946i	$-0.795586\pi$
$193$		−	16.6416i		−	1.19789i	0.800790	−	0.598946i	$-0.204414\pi$
$194$	4.73138	+	18.5335i	0.339694	+	1.33063i
$195$		0			0
$196$	−9.87315	−	18.0770i	−0.705225	−	1.29121i
$197$	−2.14835	+	5.18658i	−0.153064	+	0.369529i	−0.981748	−	0.190188i	$-0.939090\pi$
$197$	−2.14835	+	5.18658i	−0.153064	+	0.369529i	0.828684	+	0.559717i	$0.189090\pi$
$198$	5.91246	+	7.89729i	0.420180	+	0.561236i
$199$	−10.7219	−	10.7219i	−0.760055	−	0.760055i	0.216277	−	0.976332i	$-0.430608\pi$
$199$	−10.7219	−	10.7219i	−0.760055	−	0.760055i	−0.976332	+	0.216277i	$0.930608\pi$
$200$		0			0
$201$	−26.8158	+	26.8158i	−1.89144	+	1.89144i
$202$	12.3463	+	1.77450i	0.868683	+	0.124853i
$203$	28.6693	+	11.8752i	2.01219	+	0.833477i
$204$	9.70482	−	12.0454i	0.679474	−	0.843349i
$205$		0			0
$206$	−7.02189	+	11.8361i	−0.489238	+	0.824661i
$207$	−21.6352			−1.50375
$208$	−19.3181	−	3.48135i	−1.33947	−	0.241388i
$209$		−	3.35572i		−	0.232120i
$210$		0			0
$211$	−13.5357	+	5.60666i	−0.931835	+	0.385979i	−0.796374	−	0.604804i	$-0.793251\pi$
$211$	−13.5357	+	5.60666i	−0.931835	+	0.385979i	−0.135461	+	0.990783i	$0.543251\pi$
$212$	11.6859	−	1.25755i	0.802591	−	0.0863692i
$213$	−10.5188	−	4.35702i	−0.720736	−	0.298538i
$214$	−3.42739	−	0.492608i	−0.234291	−	0.0336740i
$215$		0			0
$216$	4.63568	+	12.4230i	0.315418	+	0.845279i
$217$	2.35316	−	2.35316i	0.159743	−	0.159743i
$218$	5.28925	−	3.95990i	0.358233	−	0.268198i
$219$	4.11353	+	1.70388i	0.277967	+	0.115138i
$220$		0			0
$221$	5.23753	+	12.6445i	0.352315	+	0.850563i
$222$	−8.95023	−	35.0593i	−0.600700	−	2.35303i
$223$			10.8919i			0.729378i	0.931129	+	0.364689i	$0.118825\pi$
$223$			10.8919i			0.729378i	−0.931129	+	0.364689i	$0.881175\pi$
$224$	10.5368	+	21.0366i	0.704017	+	1.40556i
$225$		0			0
$226$	0.811965	−	0.207285i	0.0540111	−	0.0137884i
$227$	1.13308	−	0.469337i	0.0752051	−	0.0311510i	−0.344764	−	0.938689i	$-0.612041\pi$
$227$	1.13308	−	0.469337i	0.0752051	−	0.0311510i	0.419969	+	0.907539i	$0.362041\pi$
$228$	3.52455	−	12.0080i	0.233419	−	0.795249i
$229$	2.28178	+	0.945143i	0.150784	+	0.0624568i	0.456799	−	0.889570i	$-0.348996\pi$
$229$	2.28178	+	0.945143i	0.150784	+	0.0624568i	−0.306015	+	0.952027i	$0.598996\pi$
$230$		0			0
$231$	12.1296	+	12.1296i	0.798069	+	0.798069i
$232$	−19.1971	−	8.76351i	−1.26035	−	0.575353i
$233$	3.16863	+	3.16863i	0.207584	+	0.207584i	0.803240	−	0.595656i	$-0.203108\pi$
$233$	3.16863	+	3.16863i	0.207584	+	0.207584i	−0.595656	+	0.803240i	$0.703108\pi$
$234$	−32.2209	−	4.63101i	−2.10635	−	0.302739i
$235$		0			0
$236$	−29.3528	+	3.15874i	−1.91071	+	0.205617i
$237$	−6.43536	−	15.5363i	−0.418022	−	1.00919i
$238$	8.37005	−	14.1086i	0.542550	−	0.914524i
$239$		−	8.68507i		−	0.561790i	−0.959738	−	0.280895i	$-0.909369\pi$
$239$		−	8.68507i		−	0.561790i	0.959738	−	0.280895i	$-0.0906313\pi$
$240$		0			0
$241$			7.76968i			0.500489i	0.968183	+	0.250244i	$0.0805110\pi$
$241$			7.76968i			0.500489i	−0.968183	+	0.250244i	$0.919489\pi$
$242$	10.6889	+	6.34127i	0.687106	+	0.407632i
$243$	−6.51843	−	15.7369i	−0.418158	−	1.00952i
$244$	−19.2245	−	15.4889i	−1.23072	−	0.991573i
$245$		0			0
$246$	7.00330	−	48.7264i	0.446514	−	3.10668i
$247$	7.82958	+	7.82958i	0.498184	+	0.498184i
$248$	−1.65612	+	1.54237i	−0.105164	+	0.0979404i
$249$	0.620414	+	0.620414i	0.0393172	+	0.0393172i
$250$		0			0
$251$	−17.3540	−	7.18827i	−1.09538	−	0.453720i	−0.239498	−	0.970897i	$-0.576983\pi$
$251$	−17.3540	−	7.18827i	−1.09538	−	0.453720i	−0.855878	+	0.517177i	$0.826983\pi$
$252$	18.7024	+	34.2427i	1.17814	+	2.15709i
$253$	6.33774	−	2.62518i	0.398451	−	0.165044i
$254$	−1.12355	−	4.40110i	−0.0704978	−	0.276150i
$255$		0			0
$256$	−6.65250	−	14.5514i	−0.415781	−	0.909465i
$257$		−	15.7332i		−	0.981413i	−0.871325	−	0.490707i	$-0.836739\pi$
$257$		−	15.7332i		−	0.981413i	0.871325	−	0.490707i	$-0.163261\pi$
$258$	19.2327	−	4.90990i	1.19738	−	0.305677i
$259$	−14.6848	−	35.4523i	−0.912469	−	2.20290i
$260$		0			0
$261$	−32.3317	−	13.3922i	−2.00128	−	0.828958i
$262$	−7.00879	−	9.36166i	−0.433004	−	0.578365i
$263$	5.45192	−	5.45192i	0.336180	−	0.336180i	−0.518748	−	0.854927i	$-0.673602\pi$
$263$	5.45192	−	5.45192i	0.336180	−	0.336180i	0.854927	+	0.518748i	$0.173602\pi$
$264$	−7.95030	−	8.53664i	−0.489307	−	0.525394i
$265$		0			0
$266$	1.88812	−	13.1368i	0.115768	−	0.805472i
$267$	−32.5127	−	13.4672i	−1.98974	−	0.824178i
$268$	17.1592	−	21.2976i	1.04816	−	1.30096i
$269$	7.58007	−	3.13977i	0.462165	−	0.191435i	−0.139437	−	0.990231i	$-0.544529\pi$
$269$	7.58007	−	3.13977i	0.462165	−	0.191435i	0.601602	+	0.798796i	$0.294529\pi$
$270$		0			0
$271$			20.7286i			1.25918i	0.776929	+	0.629588i	$0.216776\pi$
$271$			20.7286i			1.25918i	−0.776929	+	0.629588i	$0.783224\pi$
$272$	−6.02942	+	9.38611i	−0.365587	+	0.569117i
$273$	−56.6016			−3.42569
$274$	−5.97450	−	3.54443i	−0.360933	−	0.214127i
$275$		0			0
$276$	25.4360	−	2.73724i	1.53107	−	0.164763i
$277$	−21.7769	−	9.02027i	−1.30844	−	0.541975i	−0.384014	−	0.923327i	$-0.625459\pi$
$277$	−21.7769	−	9.02027i	−1.30844	−	0.541975i	−0.924430	+	0.381352i	$0.875459\pi$
$278$	−3.87017	+	26.9273i	−0.232117	+	1.61499i
$279$	−2.65376	+	2.65376i	−0.158877	+	0.158877i
$280$		0			0
$281$	1.41047	+	1.41047i	0.0841416	+	0.0841416i	0.747925	−	0.663783i	$-0.231050\pi$
$281$	1.41047	+	1.41047i	0.0841416	+	0.0841416i	−0.663783	+	0.747925i	$0.731050\pi$
$282$	−8.98131	+	6.72403i	−0.534829	+	0.400410i
$283$	−0.763298	+	1.84276i	−0.0453733	+	0.109541i	−0.944941	−	0.327240i	$-0.893881\pi$
$283$	−0.763298	+	1.84276i	−0.0453733	+	0.109541i	0.899568	+	0.436781i	$0.143881\pi$
$284$	7.87876	+	2.31255i	0.467518	+	0.137225i
$285$		0			0
$286$	10.0006	−	2.55304i	0.591349	−	0.150965i
$287$		−	52.2059i		−	3.08162i
$288$	−11.8828	−	23.7239i	−0.700200	−	1.39794i
$289$	−9.22169			−0.542452
$290$		0			0
$291$	−14.3539	−	34.6533i	−0.841438	−	2.03141i
$292$	−3.08111	−	0.904358i	−0.180308	−	0.0529236i
$293$	−4.04309	+	9.76088i	−0.236200	+	0.570236i	−0.996884	−	0.0788860i	$-0.974864\pi$
$293$	−4.04309	+	9.76088i	−0.236200	+	0.570236i	0.760684	+	0.649122i	$0.224864\pi$
$294$	24.2066	+	32.3328i	1.41176	+	1.88569i
$295$		0			0
$296$	9.12314	+	24.4488i	0.530272	+	1.42106i
$297$	−4.93006	−	4.93006i	−0.286071	−	0.286071i
$298$	0.341448	−	2.37567i	0.0197795	−	0.137619i
$299$	−8.66216	+	20.9123i	−0.500946	+	1.20939i
$300$		0			0
$301$	19.4483	−	8.05575i	1.12098	−	0.464326i
$302$	−6.23843	+	10.5155i	−0.358981	+	0.605100i
$303$	−24.4590			−1.40513
$304$	−1.60071	+	8.88237i	−0.0918070	+	0.509439i
$305$		0			0
$306$	−9.43929	+	15.9109i	−0.539608	+	0.909565i
$307$	−1.73871	−	4.19762i	−0.0992336	−	0.239571i	0.866464	−	0.499239i	$-0.166387\pi$
$307$	−1.73871	−	4.19762i	−0.0992336	−	0.239571i	−0.965698	+	0.259668i	$0.916387\pi$
$308$	−9.63357	−	7.76162i	−0.548924	−	0.442260i
$309$	10.3274	−	24.9326i	0.587507	−	1.41837i
$310$		0			0
$311$	22.5777	−	22.5777i	1.28026	−	1.28026i	0.339745	−	0.940518i	$-0.389659\pi$
$311$	22.5777	−	22.5777i	1.28026	−	1.28026i	0.940518	−	0.339745i	$-0.110341\pi$
$312$	38.4673	+	1.36805i	2.17778	+	0.0774506i
$313$	−18.6877	+	18.6877i	−1.05629	+	1.05629i	−0.0579726	+	0.998318i	$0.518464\pi$
$313$	−18.6877	+	18.6877i	−1.05629	+	1.05629i	−0.998318	+	0.0579726i	$0.981536\pi$
$314$	14.1410	−	10.5869i	0.798020	−	0.597453i
$315$		0			0
$316$	5.81336	+	10.6438i	0.327027	+	0.598763i
$317$	24.8116	−	10.2773i	1.39356	−	0.577231i	0.445488	−	0.895288i	$-0.353030\pi$
$317$	24.8116	−	10.2773i	1.39356	−	0.577231i	0.948072	+	0.318057i	$0.103030\pi$
$318$	−22.3313	+	5.70093i	−1.25228	+	0.319692i
$319$	11.0961			0.621264
$320$		0			0
$321$	6.78993			0.378977
$322$	26.2878	−	6.71097i	1.46496	−	0.373988i
$323$	5.81389	−	2.40819i	0.323493	−	0.133995i
$324$	1.02651	+	1.87946i	0.0570283	+	0.104415i
$325$		0			0
$326$	−1.35941	+	1.01775i	−0.0752906	+	0.0563678i
$327$	−9.16165	+	9.16165i	−0.506641	+	0.506641i
$328$	−1.26181	+	35.4800i	−0.0696716	+	1.95905i
$329$	−8.41342	+	8.41342i	−0.463847	+	0.463847i
$330$		0			0
$331$	−4.97531	+	12.0115i	−0.273468	+	0.660210i	−0.999627	−	0.0273171i	$-0.991304\pi$
$331$	−4.97531	+	12.0115i	−0.273468	+	0.660210i	0.726159	+	0.687527i	$0.241304\pi$
$332$	−0.492745	−	0.396997i	−0.0270429	−	0.0217881i
$333$	16.5607	+	39.9811i	0.907522	+	2.19095i
$334$	−3.42381	+	5.77119i	−0.187343	+	0.315786i
$335$		0			0
$336$	−26.3203	−	37.8922i	−1.43589	−	2.06719i
$337$	−30.1871			−1.64440			−0.822199	−	0.569200i	$-0.807253\pi$
$337$	−30.1871			−1.64440			−0.822199	+	0.569200i	$0.807253\pi$
$338$	−7.99630	+	13.4786i	−0.434941	+	0.733138i
$339$	−1.51818	+	0.628852i	−0.0824564	+	0.0341546i
$340$		0			0
$341$	0.455382	−	1.09939i	0.0246603	−	0.0595352i
$342$	−2.12932	+	14.8150i	−0.115140	+	0.801104i
$343$	9.70156	+	9.70156i	0.523835	+	0.523835i
$344$	−13.4121	+	5.00475i	−0.723131	+	0.269838i
$345$		0			0
$346$	−9.50047	−	12.6898i	−0.510749	−	0.682209i
$347$	0.981507	−	2.36957i	0.0526900	−	0.127205i	−0.895343	−	0.445378i	$-0.853069\pi$
$347$	0.981507	−	2.36957i	0.0526900	−	0.127205i	0.948033	+	0.318173i	$0.103069\pi$
$348$	39.7060	+	11.6544i	2.12847	+	0.624741i
$349$	−5.45739	−	13.1753i	−0.292127	−	0.705258i	0.707872	−	0.706341i	$-0.249655\pi$
$349$	−5.45739	−	13.1753i	−0.292127	−	0.705258i	−0.999999	+	0.00108291i	$0.999655\pi$
$350$		0			0
$351$	23.0057			1.22795
$352$	6.35953	+	5.50776i	0.338964	+	0.293565i
$353$		−	3.26004i		−	0.173514i	−0.996229	−	0.0867571i	$-0.972350\pi$
$353$		−	3.26004i		−	0.173514i	0.996229	−	0.0867571i	$-0.0276504\pi$
$354$	56.0922	−	14.3197i	2.98126	−	0.761082i
$355$		0			0
$356$	24.3526	+	7.14790i	1.29068	+	0.378838i
$357$	−12.3102	+	29.7196i	−0.651527	+	1.57293i
$358$	−5.03616	+	3.77041i	−0.266169	+	0.199273i
$359$	5.76463	+	5.76463i	0.304245	+	0.304245i	0.842672	−	0.538427i	$-0.180981\pi$
$359$	5.76463	+	5.76463i	0.304245	+	0.304245i	−0.538427	+	0.842672i	$0.680981\pi$
$360$		0			0
$361$	−9.83503	+	9.83503i	−0.517633	+	0.517633i
$362$	−0.0284809	+	0.198160i	−0.00149692	+	0.0104150i
$363$	−22.5159	−	9.32641i	−1.18178	−	0.489510i
$364$	40.5865	−	4.36763i	2.12731	−	0.228926i
$365$		0			0
$366$	41.6353	+	24.7006i	2.17631	+	1.29112i
$367$	3.11540			0.162622			0.0813112	−	0.996689i	$-0.474089\pi$
$367$	3.11540			0.162622			0.0813112	+	0.996689i	$0.474089\pi$
$368$	−18.0278	+	3.92551i	−0.939764	+	0.204631i
$369$			58.8750i			3.06491i
$370$		0			0
$371$	−22.5816	+	9.35362i	−1.17238	+	0.485616i
$372$	2.78422	−	3.45572i	0.144355	−	0.179171i
$373$	−7.70139	−	3.19002i	−0.398763	−	0.165173i	0.174284	−	0.984695i	$-0.444239\pi$
$373$	−7.70139	−	3.19002i	−0.398763	−	0.165173i	−0.573047	+	0.819522i	$0.694239\pi$
$374$	0.834513	−	5.80624i	0.0431516	−	0.300233i
$375$		0			0
$376$	5.92124	−	5.51454i	0.305365	−	0.284391i
$377$	−25.8895	+	25.8895i	−1.33338	+	1.33338i
$378$	−16.5261	−	22.0739i	−0.850010	−	1.13536i
$379$	−13.1426	−	5.44383i	−0.675089	−	0.279631i	0.0186833	−	0.999825i	$-0.494053\pi$
$379$	−13.1426	−	5.44383i	−0.675089	−	0.279631i	−0.693772	+	0.720194i	$0.744053\pi$
$380$		0			0
$381$	3.40858	+	8.22903i	0.174627	+	0.421586i
$382$	−1.18666	+	0.302940i	−0.0607148	+	0.0154998i
$383$		−	23.2837i		−	1.18974i	−0.803822	−	0.594870i	$-0.797203\pi$
$383$		−	23.2837i		−	1.18974i	0.803822	−	0.594870i	$-0.202797\pi$
$384$	16.9718	+	26.3883i	0.866090	+	1.34662i
$385$		0			0
$386$	−5.82147	−	22.8035i	−0.296305	−	1.16067i
$387$	−21.9327	+	9.08484i	−1.11490	+	0.461808i
$388$	12.9665	+	23.7407i	0.658275	+	1.20525i
$389$	10.0350	+	4.15664i	0.508796	+	0.210750i	0.622287	−	0.782789i	$-0.286204\pi$
$389$	10.0350	+	4.15664i	0.508796	+	0.210750i	−0.113492	+	0.993539i	$0.536204\pi$
$390$		0			0
$391$	9.09640	+	9.09640i	0.460025	+	0.460025i
$392$	−19.8524	−	21.3165i	−1.00270	−	1.07665i
$393$	16.2156	+	16.2156i	0.817968	+	0.817968i
$394$	−1.12948	+	7.85852i	−0.0569025	+	0.395907i
$395$		0			0
$396$	10.8642	+	8.75314i	0.545947	+	0.439862i
$397$	6.34955	+	15.3292i	0.318675	+	0.769349i	0.999325	+	0.0367406i	$0.0116975\pi$
$397$	6.34955	+	15.3292i	0.318675	+	0.769349i	−0.680650	+	0.732609i	$0.738302\pi$
$398$	−18.4425	−	10.9412i	−0.924439	−	0.548432i
$399$			26.0251i			1.30289i
$400$		0			0
$401$		−	24.7249i		−	1.23470i	−0.786687	−	0.617352i	$-0.788206\pi$
$401$		−	24.7249i		−	1.23470i	0.786687	−	0.617352i	$-0.211794\pi$
$402$	−27.3643	+	46.1253i	−1.36481	+	2.30052i
$403$	1.50260	+	3.62759i	0.0748497	+	0.180703i
$404$	17.5385	−	1.88737i	0.872571	−	0.0939000i
$405$		0			0
$406$	43.4387	+	6.24331i	2.15583	+	0.309850i
$407$	−9.70249	−	9.70249i	−0.480935	−	0.480935i
$408$	9.08455	−	19.9003i	0.449752	−	0.985213i
$409$	−13.2241	−	13.2241i	−0.653888	−	0.653888i	0.300039	−	0.953927i	$-0.403000\pi$
$409$	−13.2241	−	13.2241i	−0.653888	−	0.653888i	−0.953927	+	0.300039i	$0.903000\pi$
$410$		0			0
$411$	12.5852	+	5.21296i	0.620782	+	0.257137i
$412$	−5.48143	+	18.6750i	−0.270051	+	0.920051i
$413$	56.7208	−	23.4945i	2.79105	−	1.15609i
$414$	−29.6460	+	7.56827i	−1.45702	+	0.371960i
$415$		0			0
$416$	−27.6888	+	1.98734i	−1.35755	+	0.0974375i
$417$		−	53.3451i		−	2.61232i
$418$	−1.17388	−	4.59823i	−0.0574161	−	0.224907i
$419$	1.44829	+	3.49648i	0.0707536	+	0.170814i	0.955300	−	0.295638i	$-0.0955321\pi$
$419$	1.44829	+	3.49648i	0.0707536	+	0.170814i	−0.884547	+	0.466452i	$0.845532\pi$
$420$		0			0
$421$	−2.95627	−	1.22453i	−0.144080	−	0.0596797i	0.309478	−	0.950906i	$-0.399846\pi$
$421$	−2.95627	−	1.22453i	−0.144080	−	0.0596797i	−0.453558	+	0.891227i	$0.649846\pi$
$422$	−16.5862	+	12.4176i	−0.807404	+	0.604479i
$423$	9.48819	−	9.48819i	0.461332	−	0.461332i
$424$	15.5729	−	5.81107i	0.756287	−	0.282211i
$425$		0			0
$426$	−15.9377	−	2.29068i	−0.772184	−	0.110984i
$427$	47.4323	+	19.6471i	2.29541	+	0.950790i
$428$	−4.86875	+	0.523941i	−0.235340	+	0.0253256i
$429$	−18.6988	+	7.74530i	−0.902788	+	0.373947i
$430$		0			0
$431$		−	32.8098i		−	1.58039i	−0.612855	−	0.790195i	$-0.709979\pi$
$431$		−	32.8098i		−	1.58039i	0.612855	−	0.790195i	$-0.290021\pi$
$432$	10.6979	+	15.4012i	0.514701	+	0.740992i
$433$	−2.17672			−0.104606			−0.0523032	−	0.998631i	$-0.516656\pi$
$433$	−2.17672			−0.104606			−0.0523032	+	0.998631i	$0.516656\pi$
$434$	2.40129	−	4.04762i	0.115265	−	0.194292i
$435$		0			0
$436$	5.86246	−	7.27637i	0.280761	−	0.348475i
$437$	9.61537	+	3.98282i	0.459966	+	0.190524i
$438$	6.23267	+	0.895803i	0.297809	+	0.0428031i
$439$	17.7331	−	17.7331i	0.846357	−	0.846357i	−0.143319	−	0.989676i	$-0.545778\pi$
$439$	17.7331	−	17.7331i	0.846357	−	0.846357i	0.989676	+	0.143319i	$0.0457776\pi$
$440$		0			0
$441$	−34.1576	−	34.1576i	−1.62655	−	1.62655i
$442$	11.6000	+	15.4942i	0.551758	+	0.736985i
$443$	−11.3716	+	27.4536i	−0.540283	+	1.30436i	0.384240	+	0.923233i	$0.374464\pi$
$443$	−11.3716	+	27.4536i	−0.540283	+	1.30436i	−0.924523	+	0.381126i	$0.875536\pi$
$444$	−24.5284	−	44.9097i	−1.16407	−	2.13132i
$445$		0			0
$446$	3.81014	+	14.9249i	0.180415	+	0.706712i
$447$			4.70639i			0.222605i
$448$	21.7970	+	25.1398i	1.02981	+	1.18774i
$449$	27.1341			1.28054			0.640268	−	0.768152i	$-0.278823\pi$
$449$	27.1341			1.28054			0.640268	+	0.768152i	$0.278823\pi$
$450$		0			0
$451$	−7.14380	−	17.2467i	−0.336389	−	0.812114i
$452$	1.04010	−	0.568072i	0.0489220	−	0.0267199i
$453$	9.17516	−	22.1508i	0.431087	−	1.04074i
$454$	1.38844	−	1.03948i	0.0651627	−	0.0487853i
$455$		0			0
$456$	0.629022	−	17.6871i	0.0294567	−	0.828274i
$457$	−11.5359	−	11.5359i	−0.539627	−	0.539627i	0.383793	−	0.923419i	$-0.374618\pi$
$457$	−11.5359	−	11.5359i	−0.539627	−	0.539627i	−0.923419	+	0.383793i	$0.874618\pi$
$458$	3.45727	+	0.496902i	0.161547	+	0.0232187i
$459$	5.00348	−	12.0795i	0.233543	−	0.563822i
$460$		0			0
$461$	−31.7669	+	13.1583i	−1.47953	+	0.612843i	−0.969010	−	0.247022i	$-0.920548\pi$
$461$	−31.7669	+	13.1583i	−1.47953	+	0.612843i	−0.510523	+	0.859864i	$0.670548\pi$
$462$	20.8639	+	12.3777i	0.970676	+	0.575863i
$463$	−9.22961			−0.428937			−0.214468	−	0.976731i	$-0.568802\pi$
$463$	−9.22961			−0.428937			−0.214468	+	0.976731i	$0.568802\pi$
$464$	−29.3707	−	5.29296i	−1.36350	−	0.245719i
$465$		0			0
$466$	5.45029	+	3.23344i	0.252480	+	0.149786i
$467$	5.67749	+	13.7067i	0.262723	+	0.634270i	0.999105	−	0.0422963i	$-0.0134674\pi$
$467$	5.67749	+	13.7067i	0.262723	+	0.634270i	−0.736382	+	0.676566i	$0.763467\pi$
$468$	−45.7712	+	4.92558i	−2.11578	+	0.227685i
$469$	−21.7658	+	52.5474i	−1.00505	+	2.42641i
$470$		0			0
$471$	−24.4939	+	24.4939i	−1.12862	+	1.12862i
$472$	−39.1162	+	14.5963i	−1.80047	+	0.671850i
$473$	5.32257	−	5.32257i	0.244732	−	0.244732i
$474$	−14.2530	−	19.0378i	−0.654661	−	0.874433i
$475$		0			0
$476$	6.53383	−	22.2605i	0.299478	−	1.02031i
$477$	25.4663	−	10.5485i	1.16602	−	0.482983i
$478$	−3.03815	−	11.9009i	−0.138962	−	0.544333i
$479$	−1.86348			−0.0851446			−0.0425723	−	0.999093i	$-0.513555\pi$
$479$	−1.86348			−0.0851446			−0.0425723	+	0.999093i	$0.513555\pi$
$480$		0			0
$481$	45.2758			2.06440
$482$	2.71793	+	10.6465i	0.123799	+	0.484936i
$483$	−49.1521	+	20.3595i	−2.23650	+	0.926387i
$484$	16.8648	+	4.95012i	0.766584	+	0.225006i
$485$		0			0
$486$	−14.4370	−	19.2835i	−0.654874	−	0.874717i
$487$	25.1963	−	25.1963i	1.14175	−	1.14175i	0.153624	−	0.988129i	$-0.450905\pi$
$487$	25.1963	−	25.1963i	1.14175	−	1.14175i	0.988129	−	0.153624i	$-0.0490946\pi$
$488$	−31.7608	−	14.4989i	−1.43775	−	0.656334i
$489$	2.35467	−	2.35467i	0.106482	−	0.106482i
$490$		0			0
$491$	3.62967	−	8.76279i	0.163805	−	0.395459i	−0.820570	−	0.571546i	$-0.806344\pi$
$491$	3.62967	−	8.76279i	0.163805	−	0.395459i	0.984375	+	0.176087i	$0.0563439\pi$
$492$	−7.44876	−	69.2181i	−0.335816	−	3.12059i
$493$	7.96300	+	19.2244i	0.358636	+	0.865823i
$494$	13.4675	+	7.98972i	0.605931	+	0.359474i
$495$		0			0
$496$	−1.72978	+	2.69279i	−0.0776695	+	0.120910i
$497$	−17.0758			−0.765954
$498$	1.06716	+	0.633104i	0.0478207	+	0.0283701i
$499$	−6.90859	+	2.86163i	−0.309271	+	0.128104i	−0.531921	−	0.846794i	$-0.678529\pi$
$499$	−6.90859	+	2.86163i	−0.309271	+	0.128104i	0.222649	+	0.974899i	$0.428529\pi$
$500$		0			0
$501$	5.03557	−	12.1569i	0.224973	−	0.543132i
$502$	−26.2942	−	3.77918i	−1.17357	−	0.168673i
$503$	22.1549	+	22.1549i	0.987836	+	0.987836i	0.999927	−	0.0120907i	$-0.00384868\pi$
$503$	22.1549	+	22.1549i	0.987836	+	0.987836i	−0.0120907	+	0.999927i	$0.503849\pi$
$504$	37.6058	+	40.3792i	1.67510	+	1.79863i
$505$		0			0
$506$	7.76608	−	5.81422i	0.345244	−	0.258474i
$507$	11.7605	−	28.3925i	0.522304	−	1.26095i
$508$	−3.07913	−	5.63765i	−0.136614	−	0.250130i
$509$	2.19097	+	5.28948i	0.0971132	+	0.234452i	0.964969	−	0.262364i	$-0.0845022\pi$
$509$	2.19097	+	5.28948i	0.0971132	+	0.234452i	−0.867856	+	0.496816i	$0.834502\pi$
$510$		0			0
$511$	6.67774			0.295406
$512$	−14.2060	−	17.6122i	−0.627822	−	0.778357i
$513$		−	10.5779i		−	0.467025i
$514$	−5.50370	−	21.5587i	−0.242758	−	0.950916i
$515$		0			0
$516$	24.6364	−	13.4557i	1.08456	−	0.592356i
$517$	−1.62816	+	3.93073i	−0.0716064	+	0.172873i
$518$	−32.5238	−	43.4421i	−1.42901	−	1.90874i
$519$	21.9804	+	21.9804i	0.964831	+	0.964831i
$520$		0			0
$521$	28.8673	−	28.8673i	1.26470	−	1.26470i	0.315912	−	0.948789i	$-0.397690\pi$
$521$	28.8673	−	28.8673i	1.26470	−	1.26470i	0.948789	−	0.315912i	$-0.102310\pi$
$522$	−48.9878	−	7.04087i	−2.14414	−	0.308170i
$523$	−24.1124	−	9.98767i	−1.05436	−	0.436731i	−0.212914	−	0.977071i	$-0.568295\pi$
$523$	−24.1124	−	9.98767i	−1.05436	−	0.436731i	−0.841447	+	0.540340i	$0.818295\pi$
$524$	−12.8787	−	10.3762i	−0.562610	−	0.453287i
$525$		0			0
$526$	5.56343	−	9.37774i	0.242577	−	0.408889i
$527$	2.23152			0.0972066
$528$	−13.8803	−	8.91635i	−0.604060	−	0.388034i
$529$		−	1.72428i		−	0.0749688i
$530$		0			0
$531$	−63.9667	+	26.4959i	−2.77592	+	1.14982i
$532$	−2.00822	−	18.6615i	−0.0870672	−	0.809077i
$533$	56.9079	+	23.5720i	2.46495	+	1.02102i
$534$	−49.2620	−	7.08028i	−2.13178	−	0.306394i
$535$		0			0
$536$	16.0625	−	35.1859i	0.693793	−	1.51980i
$537$	8.72326	−	8.72326i	0.376437	−	0.376437i
$538$	9.28839	−	6.95393i	0.400451	−	0.299805i
$539$	14.1507	+	5.86140i	0.609512	+	0.252468i
$540$		0			0
$541$	7.97446	+	19.2520i	0.342849	+	0.827710i	0.997425	+	0.0717144i	$0.0228470\pi$
$541$	7.97446	+	19.2520i	0.342849	+	0.827710i	−0.654576	+	0.755996i	$0.727153\pi$
$542$	7.25115	+	28.4038i	0.311464	+	1.22005i
$543$		−	0.392570i		−	0.0168468i
$544$	−4.97852	+	14.9706i	−0.213452	+	0.641861i
$545$		0			0
$546$	−77.5593	+	19.8000i	−3.31923	+	0.847362i
$547$	−26.5343	+	10.9909i	−1.13452	+	0.469935i	−0.869316	−	0.494256i	$-0.835440\pi$
$547$	−26.5343	+	10.9909i	−1.13452	+	0.469935i	−0.265207	+	0.964191i	$0.585440\pi$
$548$	−9.42655	−	2.76685i	−0.402682	−	0.118194i
$549$	−53.4915	−	22.1569i	−2.28296	−	0.945634i
$550$		0			0
$551$	11.9039	+	11.9039i	0.507122	+	0.507122i
$552$	33.8966	−	12.6486i	1.44273	−	0.538360i
$553$	−17.8340	−	17.8340i	−0.758379	−	0.758379i
$554$	−32.9955	−	4.74234i	−1.40184	−	0.201483i
$555$		0			0
$556$	4.11634	+	38.2514i	0.174572	+	1.62222i
$557$	−1.47853	−	3.56948i	−0.0626472	−	0.151244i	0.889456	−	0.457021i	$-0.151084\pi$
$557$	−1.47853	−	3.56948i	−0.0626472	−	0.151244i	−0.952103	+	0.305777i	$0.901084\pi$
$558$	−2.70804	+	4.56468i	−0.114641	+	0.193238i
$559$			24.8373i			1.05050i
$560$		0			0
$561$			11.5026i			0.485641i
$562$	2.42612	+	1.43932i	0.102340	+	0.0607140i
$563$	8.65287	+	20.8899i	0.364675	+	0.880404i	0.994603	+	0.103750i	$0.0330843\pi$
$563$	8.65287	+	20.8899i	0.364675	+	0.880404i	−0.629928	+	0.776653i	$0.716916\pi$
$564$	−9.95463	+	12.3555i	−0.419166	+	0.520260i
$565$		0			0
$566$	−0.401298	+	2.79209i	−0.0168678	+	0.117360i
$567$	−3.14908	−	3.14908i	−0.132249	−	0.132249i
$568$	11.6050	+	0.412718i	0.486934	+	0.0173173i
$569$	3.66437	+	3.66437i	0.153618	+	0.153618i	0.779732	−	0.626114i	$-0.215355\pi$
$569$	3.66437	+	3.66437i	0.153618	+	0.153618i	−0.626114	+	0.779732i	$0.715355\pi$
$570$		0			0
$571$	28.9785	+	12.0033i	1.21271	+	0.502321i	0.895085	−	0.445895i	$-0.147114\pi$
$571$	28.9785	+	12.0033i	1.21271	+	0.502321i	0.317626	+	0.948216i	$0.397114\pi$
$572$	12.8104	−	6.99670i	0.535631	−	0.292547i
$573$	2.21878	−	0.919047i	0.0926907	−	0.0383937i
$574$	−18.2623	−	71.5361i	−0.762255	−	2.98586i
$575$		0			0
$576$	−24.5815	−	28.3513i	−1.02423	−	1.18130i
$577$			39.1035i			1.62790i	0.580935	+	0.813950i	$0.302687\pi$
$577$			39.1035i			1.62790i	−0.580935	+	0.813950i	$0.697313\pi$
$578$	−12.6362	+	3.22587i	−0.525596	+	0.134178i
$579$	17.6609	+	42.6372i	0.733962	+	1.77194i
$580$		0			0
$581$	1.21574	+	0.503578i	0.0504376	+	0.0208919i
$582$	−31.7908	−	42.4631i	−1.31777	−	1.76015i
$583$	−6.18009	+	6.18009i	−0.255953	+	0.255953i
$584$	−4.53830	−	0.161400i	−0.187796	−	0.00667876i
$585$		0			0
$586$	−2.12562	+	14.7893i	−0.0878087	+	0.610941i
$587$	−16.2558	−	6.73339i	−0.670950	−	0.277917i	0.0210878	−	0.999778i	$-0.493287\pi$
$587$	−16.2558	−	6.73339i	−0.670950	−	0.277917i	−0.692038	+	0.721861i	$0.743287\pi$
$588$	44.4799	+	35.8368i	1.83432	+	1.47789i
$589$	1.66795	−	0.690887i	0.0687266	−	0.0284675i
$590$		0			0
$591$		−	15.5684i		−	0.640397i
$592$	21.0537	+	30.3100i	0.865300	+	1.24573i
$593$	−6.43191			−0.264127			−0.132063	−	0.991241i	$-0.542160\pi$
$593$	−6.43191			−0.264127			−0.132063	+	0.991241i	$0.542160\pi$
$594$	−8.48010	−	5.03090i	−0.347943	−	0.206420i
$595$		0			0
$596$	−0.363166	−	3.37475i	−0.0148759	−	0.138235i
$597$	38.8489	+	16.0917i	1.58998	+	0.658591i
$598$	−4.55407	+	31.6856i	−0.186230	+	1.29572i
$599$	18.1680	−	18.1680i	0.742322	−	0.742322i	−0.230702	−	0.973024i	$-0.574102\pi$
$599$	18.1680	−	18.1680i	0.742322	−	0.742322i	0.973024	+	0.230702i	$0.0741023\pi$
$600$		0			0
$601$	−10.2457	−	10.2457i	−0.417933	−	0.417933i	0.466558	−	0.884491i	$-0.345494\pi$
$601$	−10.2457	−	10.2457i	−0.417933	−	0.417933i	−0.884491	+	0.466558i	$0.845494\pi$
$602$	23.8314	−	17.8418i	0.971294	−	0.727178i
$603$	24.5463	−	59.2601i	0.999604	−	2.41326i
$604$	−4.86985	+	16.5914i	−0.198151	+	0.675092i
$605$		0			0
$606$	−33.5154	+	8.55608i	−1.36147	+	0.347567i
$607$		−	28.5016i		−	1.15684i	−0.815738	−	0.578422i	$-0.803669\pi$
$607$		−	28.5016i		−	1.15684i	0.815738	−	0.578422i	$-0.196331\pi$
$608$	0.913770	+	12.7312i	0.0370583	+	0.516317i
$609$	−86.0556			−3.48715
$610$		0			0
$611$	−5.37235	−	12.9700i	−0.217342	−	0.524710i
$612$	−7.36850	+	25.1042i	−0.297854	+	1.01478i
$613$	−4.94365	+	11.9350i	−0.199672	+	0.482051i	−0.991722	−	0.128406i	$-0.959014\pi$
$613$	−4.94365	+	11.9350i	−0.199672	+	0.482051i	0.792050	+	0.610457i	$0.209014\pi$
$614$	−3.85088	−	5.14364i	−0.155409	−	0.207580i
$615$		0			0
$616$	−15.9157	−	7.26554i	−0.641261	−	0.292737i
$617$	34.4226	+	34.4226i	1.38580	+	1.38580i	0.833930	+	0.551870i	$0.186085\pi$
$617$	34.4226	+	34.4226i	1.38580	+	1.38580i	0.551870	+	0.833930i	$0.313915\pi$
$618$	5.42958	−	37.7770i	0.218410	−	1.51961i
$619$	13.3861	−	32.3170i	0.538034	−	1.29893i	−0.388059	−	0.921635i	$-0.626854\pi$
$619$	13.3861	−	32.3170i	0.538034	−	1.29893i	0.926093	−	0.377295i	$-0.123146\pi$
$620$		0			0
$621$	19.9778	−	8.27508i	0.801682	−	0.332067i
$622$	23.0395	−	38.8354i	0.923799	−	1.55716i
$623$	−52.7798			−2.11458
$624$	53.1891	−	11.5818i	2.12927	−	0.463643i
$625$		0			0
$626$	−19.0699	+	32.1443i	−0.762187	+	1.28475i
$627$	3.56125	+	8.59762i	0.142223	+	0.343356i
$628$	15.6734	−	19.4536i	0.625439	−	0.776282i
$629$	9.84699	−	23.7727i	0.392625	−	0.947881i
$630$		0			0
$631$	−30.3075	+	30.3075i	−1.20652	+	1.20652i	−0.234377	+	0.972146i	$0.575305\pi$
$631$	−30.3075	+	30.3075i	−1.20652	+	1.20652i	−0.972146	+	0.234377i	$0.924695\pi$
$632$	11.6892	+	12.5513i	0.464972	+	0.499264i
$633$	28.7294	−	28.7294i	1.14189	−	1.14189i
$634$	30.4034	−	22.7621i	1.20747	−	0.903998i
$635$		0			0
$636$	−28.6056	+	15.6236i	−1.13429	+	0.619516i
$637$	−46.6922	+	19.3405i	−1.85001	+	0.766300i
$638$	15.2047	−	3.88157i	0.601959	−	0.153673i
$639$	19.2571			0.761801
$640$		0			0
$641$	−27.6617			−1.09257			−0.546286	−	0.837599i	$-0.683959\pi$
$641$	−27.6617			−1.09257			−0.546286	+	0.837599i	$0.683959\pi$
$642$	9.30401	−	2.37521i	0.367200	−	0.0937419i
$643$	28.2623	−	11.7066i	1.11455	−	0.461664i	0.252051	−	0.967714i	$-0.418895\pi$
$643$	28.2623	−	11.7066i	1.11455	−	0.461664i	0.862504	+	0.506050i	$0.168895\pi$
$644$	33.6737	−	18.3916i	1.32693	−	0.724732i
$645$		0			0
$646$	7.12416	−	5.33364i	0.280296	−	0.209849i
$647$	33.6047	−	33.6047i	1.32114	−	1.32114i	0.408284	−	0.912855i	$-0.366127\pi$
$647$	33.6047	−	33.6047i	1.32114	−	1.32114i	0.912855	−	0.408284i	$-0.133873\pi$
$648$	2.06405	+	2.21628i	0.0810836	+	0.0870636i
$649$	15.5232	−	15.5232i	0.609340	−	0.609340i
$650$		0			0
$651$	−3.53169	+	8.52626i	−0.138418	+	0.334170i
$652$	−1.50673	+	1.87012i	−0.0590081	+	0.0732397i
$653$	5.91232	+	14.2736i	0.231367	+	0.558570i	0.996339	−	0.0854945i	$-0.0272470\pi$
$653$	5.91232	+	14.2736i	0.231367	+	0.558570i	−0.764972	+	0.644064i	$0.777247\pi$
$654$	−9.34904	+	15.7588i	−0.365577	+	0.616217i
$655$		0			0
$656$	10.6823	+	49.0584i	0.417076	+	1.91541i
$657$	−7.53079			−0.293804
$658$	−8.58550	+	14.4718i	−0.334698	+	0.564168i
$659$	3.69353	−	1.52991i	0.143880	−	0.0595969i	−0.309582	−	0.950873i	$-0.600189\pi$
$659$	3.69353	−	1.52991i	0.143880	−	0.0595969i	0.453461	+	0.891276i	$0.350189\pi$
$660$		0			0
$661$	9.19176	−	22.1909i	0.357518	−	0.863125i	−0.638130	−	0.769929i	$-0.720292\pi$
$661$	9.19176	−	22.1909i	0.357518	−	0.863125i	0.995648	−	0.0931960i	$-0.0297083\pi$
$662$	−2.61573	+	18.1993i	−0.101663	+	0.707337i
$663$	−26.8379	−	26.8379i	−1.04230	−	1.04230i
$664$	−0.814067	−	0.371624i	−0.0315919	−	0.0144218i
$665$		0			0
$666$	36.6785	+	48.9916i	1.42126	+	1.89839i
$667$	−13.1697	+	31.7945i	−0.509933	+	1.23109i
$668$	−2.67270	+	9.10577i	−0.103410	+	0.352313i
$669$	−11.5590	−	27.9060i	−0.446898	−	1.07891i
$670$		0			0
$671$	18.3581			0.708708
$672$	−49.3210	−	42.7152i	−1.90260	−	1.64777i
$673$			4.29624i			0.165608i	0.996566	+	0.0828040i	$0.0263875\pi$
$673$			4.29624i			0.165608i	−0.996566	+	0.0828040i	$0.973612\pi$
$674$	−41.3644	+	10.5599i	−1.59330	+	0.406751i
$675$		0			0
$676$	−6.24207	+	21.2665i	−0.240080	+	0.817941i
$677$	9.87475	−	23.8398i	0.379518	−	0.916236i	−0.612539	−	0.790441i	$-0.709852\pi$
$677$	9.87475	−	23.8398i	0.379518	−	0.916236i	0.992056	−	0.125796i	$-0.0401484\pi$
$678$	−1.86034	+	1.39278i	−0.0714458	+	0.0534893i
$679$	−39.7781	−	39.7781i	−1.52654	−	1.52654i
$680$		0			0
$681$	−2.40495	+	2.40495i	−0.0921581	+	0.0921581i
$682$	0.239414	−	1.66575i	0.00916762	−	0.0637850i
$683$	−6.14467	−	2.54520i	−0.235119	−	0.0973895i	0.262013	−	0.965064i	$-0.415614\pi$
$683$	−6.14467	−	2.54520i	−0.235119	−	0.0973895i	−0.497132	+	0.867675i	$0.665614\pi$
$684$	2.26476	+	21.0454i	0.0865951	+	0.804690i
$685$		0			0
$686$	16.6874	+	9.89999i	0.637130	+	0.377983i
$687$	−6.84912			−0.261310
$688$	−16.6274	+	11.5496i	−0.633913	+	0.440323i
$689$		−	28.8388i		−	1.09867i
$690$		0			0
$691$	−7.14914	+	2.96127i	−0.271966	+	0.112652i	−0.514498	−	0.857491i	$-0.672022\pi$
$691$	−7.14914	+	2.96127i	−0.271966	+	0.112652i	0.242533	+	0.970143i	$0.422022\pi$
$692$	−17.4572	−	14.0650i	−0.663625	−	0.534673i
$693$	−26.8052	−	11.1031i	−1.01824	−	0.421770i
$694$	0.516020	−	3.59028i	0.0195879	−	0.136285i
$695$		0			0
$696$	58.4847	+	2.07995i	2.21686	+	0.0788401i
$697$	24.7537	−	24.7537i	0.937614	−	0.937614i
$698$	−12.0870	−	16.1446i	−0.457499	−	0.611083i
$699$	−11.4810	−	4.75557i	−0.434250	−	0.179872i
$700$		0			0
$701$	−1.82186	−	4.39835i	−0.0688106	−	0.166124i	0.885733	−	0.464195i	$-0.153656\pi$
$701$	−1.82186	−	4.39835i	−0.0688106	−	0.166124i	−0.954543	+	0.298072i	$0.903656\pi$
$702$	31.5239	−	8.04769i	1.18979	−	0.303740i
$703$		−	20.8176i		−	0.785149i
$704$	10.6409	+	5.32245i	0.401045	+	0.200598i
$705$		0			0
$706$	−1.14040	−	4.46712i	−0.0429196	−	0.168122i
$707$	−33.8910	+	14.0381i	−1.27460	+	0.527958i
$708$	71.8520	−	39.2436i	2.70036	−	1.47486i
$709$	35.5634	+	14.7309i	1.33561	+	0.553229i	0.932251	−	0.361812i	$-0.117842\pi$
$709$	35.5634	+	14.7309i	1.33561	+	0.553229i	0.403361	+	0.915041i	$0.367842\pi$
$710$		0			0
$711$	20.1122	+	20.1122i	0.754267	+	0.754267i
$712$	35.8699	+	1.27568i	1.34428	+	0.0478080i
$713$	2.60967	+	2.60967i	0.0977329	+	0.0977329i
$714$	−6.47202	+	45.0300i	−0.242209	+	1.68521i
$715$		0			0
$716$	−5.58194	+	6.92819i	−0.208607	+	0.258919i
$717$	9.21701	+	22.2518i	0.344215	+	0.831010i
$718$	9.91562	+	5.88253i	0.370048	+	0.219534i
$719$		−	43.7997i		−	1.63345i	−0.577026	−	0.816726i	$-0.695787\pi$
$719$		−	43.7997i		−	1.63345i	0.577026	−	0.816726i	$-0.304213\pi$
$720$		0			0
$721$		−	40.4746i		−	1.50735i
$722$	−10.0362	+	16.9170i	−0.373508	+	0.629587i
$723$	−8.24555	−	19.9065i	−0.306655	−	0.740331i
$724$	0.0302924	+	0.281494i	0.00112581	+	0.0104617i
$725$		0			0
$726$	−34.1154	−	4.90329i	−1.26614	−	0.181978i
$727$	−10.7411	−	10.7411i	−0.398366	−	0.398366i	0.479290	−	0.877656i	$-0.340894\pi$
$727$	−10.7411	−	10.7411i	−0.398366	−	0.398366i	−0.877656	+	0.479290i	$0.840894\pi$
$728$	54.0865	−	20.1825i	2.00458	−	0.748014i
$729$	31.1301	+	31.1301i	1.15296	+	1.15296i
$730$		0			0
$731$	13.0412	+	5.40184i	0.482346	+	0.199794i
$732$	65.6921	+	19.2818i	2.42805	+	0.712674i
$733$	2.43961	−	1.01052i	0.0901091	−	0.0373244i	−0.337174	−	0.941443i	$-0.609471\pi$
$733$	2.43961	−	1.01052i	0.0901091	−	0.0373244i	0.427283	+	0.904118i	$0.359471\pi$
$734$	4.26892	−	1.08981i	0.157569	−	0.0402255i
$735$		0			0
$736$	−23.3297	+	11.6854i	−0.859944	+	0.430728i
$737$			20.3379i			0.749155i
$738$	20.5953	+	80.6745i	0.758122	+	2.96967i
$739$	13.5424	+	32.6942i	0.498165	+	1.20268i	0.950471	+	0.310813i	$0.100601\pi$
$739$	13.5424	+	32.6942i	0.498165	+	1.20268i	−0.452306	+	0.891863i	$0.649399\pi$
$740$		0			0
$741$	−28.3691	−	11.7509i	−1.04217	−	0.431679i
$742$	−27.6708	+	20.7163i	−1.01583	+	0.760520i
$743$	16.8110	−	16.8110i	0.616735	−	0.616735i	−0.327958	−	0.944692i	$-0.606360\pi$
$743$	16.8110	−	16.8110i	0.616735	−	0.616735i	0.944692	+	0.327958i	$0.106360\pi$
$744$	2.60627	−	5.70921i	0.0955505	−	0.209310i
$745$		0			0
$746$	−11.6689	−	1.67713i	−0.427228	−	0.0614041i
$747$	−1.37105	−	0.567908i	−0.0501641	−	0.0207787i
$748$	−0.887593	−	8.24802i	−0.0324536	−	0.301577i
$749$	9.40829	−	3.89704i	0.343772	−	0.142395i
$750$		0			0
$751$			22.4107i			0.817778i	0.912584	+	0.408889i	$0.134084\pi$
$751$			22.4107i			0.817778i	−0.912584	+	0.408889i	$0.865916\pi$
$752$	6.18462	−	9.62771i	0.225530	−	0.351087i
$753$	52.0909			1.89830
$754$	−26.4191	+	44.5321i	−0.962126	+	1.62176i
$755$		0			0
$756$	−30.3669	−	24.4661i	−1.10443	−	0.889825i
$757$	−30.1022	−	12.4687i	−1.09408	−	0.453184i	−0.238654	−	0.971105i	$-0.576706\pi$
$757$	−30.1022	−	12.4687i	−1.09408	−	0.453184i	−0.855429	+	0.517921i	$0.826706\pi$
$758$	−19.9132	−	2.86206i	−0.723279	−	0.103955i
$759$	−13.4518	+	13.4518i	−0.488271	+	0.488271i
$760$		0			0
$761$	30.4349	+	30.4349i	1.10326	+	1.10326i	0.994014	+	0.109249i	$0.0348445\pi$
$761$	30.4349	+	30.4349i	1.10326	+	1.10326i	0.109249	+	0.994014i	$0.465155\pi$
$762$	7.54928	+	10.0836i	0.273482	+	0.365290i
$763$	−7.43633	+	17.9529i	−0.269213	+	0.649938i
$764$	−1.52007	+	0.830218i	−0.0549941	+	0.0300362i
$765$		0			0
$766$	−8.14494	−	31.9049i	−0.294289	−	1.15277i
$767$			72.4377i			2.61557i
$768$	32.4869	+	30.2220i	1.17227	+	1.09054i
$769$	−7.75534			−0.279665			−0.139832	−	0.990175i	$-0.544656\pi$
$769$	−7.75534			−0.279665			−0.139832	+	0.990175i	$0.544656\pi$
$770$		0			0
$771$	16.6969	+	40.3098i	0.601323	+	1.45172i
$772$	−15.9539	−	29.2104i	−0.574194	−	1.05131i
$773$	−6.97787	+	16.8461i	−0.250976	+	0.605911i	−0.998283	−	0.0585684i	$-0.981346\pi$
$773$	−6.97787	+	16.8461i	−0.250976	+	0.605911i	0.747307	+	0.664479i	$0.231346\pi$
$774$	−26.8757	+	20.1210i	−0.966027	+	0.723235i
$775$		0			0
$776$	26.0724	+	27.9953i	0.935945	+	1.00497i
$777$	75.2472	+	75.2472i	2.69948	+	2.69948i
$778$	15.2047	+	2.18532i	0.545115	+	0.0783477i
$779$	10.8383	−	26.1660i	0.388322	−	0.937493i
$780$		0			0
$781$	−5.64113	+	2.33663i	−0.201855	+	0.0836112i
$782$	15.6465	+	9.28246i	0.559519	+	0.331940i
$783$	34.9772			1.24998
$784$	−34.6599	−	22.2647i	−1.23785	−	0.795168i
$785$		0			0
$786$	27.8921	+	16.5473i	0.994878	+	0.590221i
$787$	−6.24398	−	15.0743i	−0.222574	−	0.537341i	0.772664	−	0.634815i	$-0.218924\pi$
$787$	−6.24398	−	15.0743i	−0.222574	−	0.537341i	−0.995238	+	0.0974741i	$0.968924\pi$
$788$	1.20132	+	11.1634i	0.0427954	+	0.397679i
$789$	−8.18241	+	19.7541i	−0.291302	+	0.703264i
$790$		0			0
$791$	−1.74271	+	1.74271i	−0.0619635	+	0.0619635i
$792$	17.9488	+	8.19368i	0.637784	+	0.291150i
$793$	−42.8332	+	42.8332i	−1.52105	+	1.52105i
$794$	14.0629	+	18.7839i	0.499075	+	0.666616i
$795$		0			0
$796$	−29.0985	−	8.54092i	−1.03137	−	0.302725i
$797$	−0.220883	+	0.0914925i	−0.00782406	+	0.00324083i	−0.386592	−	0.922251i	$-0.626348\pi$
$797$	−0.220883	+	0.0914925i	−0.00782406	+	0.00324083i	0.378768	+	0.925492i	$0.376348\pi$
$798$	9.10394	+	35.6614i	0.322276	+	1.26240i
$799$	−7.97853			−0.282260
$800$		0			0
$801$	59.5221			2.10311
$802$	−8.64910	−	33.8797i	−0.305410	−	1.19633i
$803$	2.20605	−	0.913775i	0.0778497	−	0.0322464i
$804$	−21.3611	+	72.7763i	−0.753348	+	2.56662i
$805$		0			0
$806$	3.32794	+	4.44514i	0.117222	+	0.156573i
$807$	−16.0887	+	16.0887i	−0.566348	+	0.566348i
$808$	23.3721	−	8.72138i	0.822229	−	0.306817i
$809$	24.8428	−	24.8428i	0.873427	−	0.873427i	−0.119417	−	0.992844i	$-0.538103\pi$
$809$	24.8428	−	24.8428i	0.873427	−	0.873427i	0.992844	+	0.119417i	$0.0381027\pi$
$810$		0			0
$811$	4.55425	−	10.9949i	0.159921	−	0.386085i	−0.823526	−	0.567279i	$-0.807996\pi$
$811$	4.55425	−	10.9949i	0.159921	−	0.386085i	0.983447	+	0.181194i	$0.0579962\pi$
$812$	61.7066	−	6.64043i	2.16548	−	0.233033i
$813$	−21.9982	−	53.1084i	−0.771512	−	1.86259i
$814$	−16.6891	−	9.90094i	−0.584951	−	0.347028i
$815$		0			0
$816$	5.48685	−	30.4467i	0.192078	−	1.06585i
$817$	11.4200			0.399537
$818$	−22.7465	−	13.4945i	−0.795311	−	0.471826i
$819$	88.4475	−	36.6362i	3.09061	−	1.28017i
$820$		0			0
$821$	14.5757	−	35.1889i	0.508696	−	1.22810i	−0.435939	−	0.899976i	$-0.643584\pi$
$821$	14.5757	−	35.1889i	0.508696	−	1.22810i	0.944635	−	0.328124i	$-0.106416\pi$
$822$	19.0687	+	2.74068i	0.665096	+	0.0955922i
$823$	−20.9180	−	20.9180i	−0.729157	−	0.729157i	0.241295	−	0.970452i	$-0.422428\pi$
$823$	−20.9180	−	20.9180i	−0.729157	−	0.729157i	−0.970452	+	0.241295i	$0.922428\pi$
$824$	−0.978264	+	27.5072i	−0.0340794	+	0.958258i
$825$		0			0
$826$	69.5040	−	52.0355i	2.41835	−	1.81055i
$827$	17.9831	−	43.4150i	0.625333	−	1.50969i	−0.220029	−	0.975493i	$-0.570615\pi$
$827$	17.9831	−	43.4150i	0.625333	−	1.50969i	0.845362	−	0.534194i	$-0.179385\pi$
$828$	−37.9754	+	20.7411i	−1.31974	+	0.720803i
$829$	11.8059	+	28.5019i	0.410035	+	0.989911i	0.985128	+	0.171823i	$0.0549658\pi$
$829$	11.8059	+	28.5019i	0.410035	+	0.989911i	−0.575093	+	0.818088i	$0.695034\pi$
$830$		0			0
$831$	65.3667			2.26755
$832$	−37.2458	+	12.4091i	−1.29127	+	0.430208i
$833$			28.7228i			0.995187i
$834$	−18.6608	−	73.0969i	−0.646171	−	2.53114i
$835$		0			0
$836$	−3.21705	−	5.89017i	−0.111264	−	0.203716i
$837$	1.43545	−	3.46549i	0.0496165	−	0.119785i
$838$	3.20766	+	4.28448i	0.110807	+	0.148005i
$839$	8.76568	+	8.76568i	0.302625	+	0.302625i	0.842040	−	0.539415i	$-0.181355\pi$
$839$	8.76568	+	8.76568i	0.302625	+	0.302625i	−0.539415	+	0.842040i	$0.681355\pi$
$840$		0			0
$841$	−18.8556	+	18.8556i	−0.650194	+	0.650194i
$842$	−4.47923	−	0.643786i	−0.154364	−	0.0221863i
$843$	−5.11060	−	2.11688i	−0.176018	−	0.0729091i
$844$	−18.3837	+	22.8175i	−0.632793	+	0.785410i
$845$		0			0
$846$	9.68226	−	16.3205i	0.332883	−	0.561109i
$847$	−36.5515			−1.25592
$848$	19.3062	−	13.4103i	0.662979	−	0.460512i
$849$		−	5.53135i		−	0.189836i
$850$		0			0
$851$	39.3168	−	16.2856i	1.34776	−	0.558262i
$852$	−22.6402	+	2.43638i	−0.775640	+	0.0834689i
$853$	−27.0766	−	11.2155i	−0.927084	−	0.384011i	−0.132512	−	0.991181i	$-0.542304\pi$
$853$	−27.0766	−	11.2155i	−0.927084	−	0.384011i	−0.794571	+	0.607171i	$0.792304\pi$
$854$	71.8677	+	10.3293i	2.45926	+	0.353462i
$855$		0			0
$856$	−6.48821	+	2.42109i	−0.221762	+	0.0827513i
$857$	−37.4118	+	37.4118i	−1.27796	+	1.27796i	−0.336157	+	0.941806i	$0.609127\pi$
$857$	−37.4118	+	37.4118i	−1.27796	+	1.27796i	−0.941806	+	0.336157i	$0.890873\pi$
$858$	−22.9130	+	17.1542i	−0.782236	+	0.585636i
$859$	−13.0928	−	5.42323i	−0.446722	−	0.185038i	0.147970	−	0.988992i	$-0.452726\pi$
$859$	−13.0928	−	5.42323i	−0.446722	−	0.185038i	−0.594692	+	0.803954i	$0.702726\pi$
$860$		0			0
$861$	55.4034	+	133.756i	1.88814	+	4.55838i
$862$	−11.4773	−	44.9581i	−0.390918	−	1.53128i
$863$		−	10.9648i		−	0.373246i	−0.982432	−	0.186623i	$-0.940246\pi$
$863$		−	10.9648i		−	0.373246i	0.982432	−	0.186623i	$-0.0597543\pi$
$864$	20.0465	+	17.3615i	0.681995	+	0.590651i
$865$		0			0
$866$	−2.98268	+	0.761445i	−0.101356	+	0.0258749i
$867$	23.6267	−	9.78650i	0.802405	−	0.332367i
$868$	1.87449	−	6.38632i	0.0636245	−	0.216766i
$869$	−8.33199	−	3.45122i	−0.282643	−	0.117075i
$870$		0			0
$871$	−47.4524	−	47.4524i	−1.60786	−	1.60786i
$872$	5.48776	−	12.0213i	0.185839	−	0.407094i
$873$	44.8596	+	44.8596i	1.51827	+	1.51827i
$874$	14.5689	+	2.09394i	0.492799	+	0.0708285i
$875$		0			0
$876$	8.85379	−	0.952782i	0.299142	−	0.0321915i
$877$	8.33816	+	20.1301i	0.281560	+	0.679745i	0.999872	−	0.0159754i	$-0.00508535\pi$
$877$	8.33816	+	20.1301i	0.281560	+	0.679745i	−0.718313	+	0.695720i	$0.755085\pi$
$878$	18.0959	−	30.5024i	0.610706	−	1.02941i
$879$		−	29.2988i		−	0.988225i
$880$		0			0
$881$			31.0921i			1.04752i	0.851866	+	0.523760i	$0.175471\pi$
$881$			31.0921i			1.04752i	−0.851866	+	0.523760i	$0.824529\pi$
$882$	−58.7539	−	34.8563i	−1.97835	−	1.17367i
$883$	9.27074	+	22.3815i	0.311985	+	0.753199i	0.999631	+	0.0271529i	$0.00864410\pi$
$883$	9.27074	+	22.3815i	0.311985	+	0.753199i	−0.687646	+	0.726046i	$0.741356\pi$
$884$	21.3152	+	17.1734i	0.716909	+	0.577602i
$885$		0			0
$886$	−5.97857	+	41.5967i	−0.200854	+	1.39747i
$887$	0.745073	+	0.745073i	0.0250171	+	0.0250171i	0.719505	−	0.694488i	$-0.244369\pi$
$887$	0.745073	+	0.745073i	0.0250171	+	0.0250171i	−0.694488	+	0.719505i	$0.744369\pi$
$888$	−49.3205	−	52.9579i	−1.65509	−	1.77715i
$889$	9.44601	+	9.44601i	0.316809	+	0.316809i
$890$		0			0
$891$	−1.47124	−	0.609409i	−0.0492885	−	0.0204160i
$892$	10.4418	+	19.1182i	0.349618	+	0.640124i
$893$	−5.96354	+	2.47018i	−0.199562	+	0.0826614i
$894$	1.64636	+	6.44901i	0.0550625	+	0.215687i
$895$		0			0
$896$	38.6620	+	26.8233i	1.29161	+	0.896104i
$897$		−	62.7717i		−	2.09589i
$898$	37.1809	−	9.49186i	1.24074	−	0.316747i
$899$	2.28451	+	5.51529i	0.0761926	+	0.183945i
$900$		0			0
$901$	−15.1423	−	6.27213i	−0.504462	−	0.208955i
$902$	−15.8220	−	21.1335i	−0.526816	−	0.703670i
$903$	−41.2789	+	41.2789i	−1.37368	+	1.37368i
$904$	1.22649	−	1.14225i	0.0407925	−	0.0379907i
$905$		0			0
$906$	4.82378	−	33.5621i	0.160259	−	1.11503i
$907$	42.2276	+	17.4912i	1.40214	+	0.580787i	0.950307	−	0.311314i	$-0.100769\pi$
$907$	42.2276	+	17.4912i	1.40214	+	0.580787i	0.451836	+	0.892101i	$0.350769\pi$
$908$	1.53891	−	1.91006i	0.0510705	−	0.0633877i
$909$	38.2204	−	15.8314i	1.26769	−	0.525095i
$910$		0			0
$911$		−	32.5610i		−	1.07880i	−0.842051	−	0.539398i	$-0.818652\pi$
$911$		−	32.5610i		−	1.07880i	0.842051	−	0.539398i	$-0.181348\pi$
$912$	−5.32525	−	24.4561i	−0.176337	−	0.809821i
$913$	0.470540			0.0155726
$914$	−19.8427	−	11.7719i	−0.656337	−	0.389378i
$915$		0			0
$916$	4.91120	−	0.528509i	0.162271	−	0.0174624i
$917$	31.7756	+	13.1619i	1.04932	+	0.434643i
$918$	2.63055	−	18.3024i	0.0868210	−	0.604069i
$919$	30.1203	−	30.1203i	0.993576	−	0.993576i	−0.00640371	−	0.999979i	$-0.502038\pi$
$919$	30.1203	−	30.1203i	0.993576	−	0.993576i	0.999979	+	0.00640371i	$0.00203838\pi$
$920$		0			0
$921$	8.90943	+	8.90943i	0.293576	+	0.293576i
$922$	−38.9262	+	29.1428i	−1.28197	+	0.959769i
$923$	7.71006	−	18.6137i	0.253780	−	0.612678i
$924$	32.9190	+	9.66228i	1.08295	+	0.317866i
$925$		0			0
$926$	−12.6470	+	3.22864i	−0.415607	+	0.106100i
$927$			45.6451i			1.49918i
$928$	−42.0973	+	3.02150i	−1.38191	+	0.0991857i
$929$	−46.0639			−1.51131			−0.755654	−	0.654971i	$-0.772681\pi$
$929$	−46.0639			−1.51131			−0.755654	+	0.654971i	$0.772681\pi$
$930$		0			0
$931$	8.89268	+	21.4688i	0.291446	+	0.703613i
$932$	8.59945	+	2.52409i	0.281684	+	0.0826792i
$933$	−33.8853	+	81.8063i	−1.10935	+	2.67822i
$934$	12.5745	+	16.7957i	0.411449	+	0.549574i
$935$		0			0
$936$	−60.9958	+	22.7607i	−1.99371	+	0.743958i
$937$	8.50147	+	8.50147i	0.277731	+	0.277731i	0.832203	−	0.554472i	$-0.187080\pi$
$937$	8.50147	+	8.50147i	0.277731	+	0.277731i	−0.554472	+	0.832203i	$0.687080\pi$
$938$	−11.4432	+	79.6179i	−0.373635	+	2.59962i
$939$	28.0471	−	67.7116i	0.915281	−	2.20968i
$940$		0			0
$941$	21.7142	−	8.99431i	0.707862	−	0.293206i	0.000442416	−	1.00000i	$-0.499859\pi$
$941$	21.7142	−	8.99431i	0.707862	−	0.293206i	0.707420	+	0.706794i	$0.249859\pi$
$942$	−24.9949	+	42.1315i	−0.814379	+	1.37272i
$943$	57.8968			1.88538
$944$	−48.4937	+	33.6842i	−1.57833	+	1.09633i
$945$		0			0
$946$	5.43143	−	9.15524i	0.176591	−	0.297663i
$947$	−4.88093	−	11.7836i	−0.158609	−	0.382916i	0.824519	−	0.565834i	$-0.191446\pi$
$947$	−4.88093	−	11.7836i	−0.158609	−	0.382916i	−0.983128	+	0.182918i	$0.941446\pi$
$948$	−26.1900	−	21.1009i	−0.850613	−	0.685326i
$949$	−3.01513	+	7.27918i	−0.0978754	+	0.236292i
$950$		0			0
$951$	−52.6625	+	52.6625i	−1.70770	+	1.70770i
$952$	1.16608	−	32.7884i	0.0377930	−	1.06268i
$953$	−9.27815	+	9.27815i	−0.300549	+	0.300549i	−0.841228	−	0.540680i	$-0.818167\pi$
$953$	−9.27815	+	9.27815i	−0.300549	+	0.300549i	0.540680	+	0.841228i	$0.318167\pi$
$954$	31.2057	−	23.3627i	1.01032	−	0.756396i
$955$		0			0
$956$	−8.32615	−	15.2446i	−0.269287	−	0.493044i
$957$	−28.4292	+	11.7757i	−0.918985	+	0.380656i
$958$	−2.55346	+	0.651870i	−0.0824987	+	0.0210610i
$959$	20.4303			0.659730
$960$		0			0
$961$	−30.3598			−0.979348
$962$	62.0399	−	15.8381i	2.00025	−	0.510639i
$963$	−10.6102	+	4.39487i	−0.341908	+	0.141623i
$964$	7.44859	+	13.6378i	0.239903	+	0.439244i
$965$		0			0
$966$	−60.2294	+	45.0919i	−1.93785	+	1.45081i
$967$	14.0727	−	14.0727i	0.452549	−	0.452549i	−0.443651	−	0.896200i	$-0.646317\pi$
$967$	14.0727	−	14.0727i	0.452549	−	0.452549i	0.896200	+	0.443651i	$0.146317\pi$
$968$	24.8410	+	0.883442i	0.798419	+	0.0283949i
$969$	−12.3399	+	12.3399i	−0.396416	+	0.396416i
$970$		0			0
$971$	−1.57164	+	3.79427i	−0.0504363	+	0.121764i	−0.947089	−	0.320970i	$-0.895991\pi$
$971$	−1.57164	+	3.79427i	−0.0504363	+	0.121764i	0.896653	+	0.442734i	$0.145991\pi$
$972$	−26.5281	−	21.3733i	−0.850890	−	0.685549i
$973$	−30.6171	−	73.9162i	−0.981539	−	2.36965i
$974$	25.7117	−	43.3397i	0.823855	−	1.38869i
$975$		0			0
$976$	−48.5927	−	8.75699i	−1.55542	−	0.280305i
$977$	−45.4460			−1.45394			−0.726972	−	0.686667i	$-0.759073\pi$
$977$	−45.4460			−1.45394			−0.726972	+	0.686667i	$0.759073\pi$
$978$	2.40283	−	4.05021i	0.0768340	−	0.129512i
$979$	−17.4362	+	7.22232i	−0.557264	+	0.230827i
$980$		0			0
$981$	8.38629	−	20.2463i	0.267754	−	0.646415i
$982$	1.90827	−	13.2771i	0.0608954	−	0.423688i
$983$	14.0959	+	14.0959i	0.449588	+	0.449588i	0.895218	−	0.445629i	$-0.147020\pi$
$983$	14.0959	+	14.0959i	0.449588	+	0.449588i	−0.445629	+	0.895218i	$0.647020\pi$
$984$	−34.4202	−	92.2415i	−1.09728	−	2.94055i
$985$		0			0
$986$	17.6364	+	23.5570i	0.561657	+	0.750207i
$987$	12.6271	−	30.4846i	0.401926	−	0.970334i
$988$	21.2490	+	6.23694i	0.676020	+	0.198423i
$989$	8.93390	+	21.5683i	0.284081	+	0.685833i
$990$		0			0
$991$	−51.5618			−1.63792			−0.818958	−	0.573854i	$-0.805448\pi$
$991$	−51.5618			−1.63792			−0.818958	+	0.573854i	$0.805448\pi$
$992$	−1.42829	+	4.29493i	−0.0453483	+	0.136364i
$993$		−	36.0543i		−	1.14415i
$994$	−23.3984	+	5.97333i	−0.742151	+	0.189463i
$995$		0			0
$996$	1.68376	+	0.494214i	0.0533521	+	0.0156598i
$997$	7.89192	−	19.0528i	0.249939	−	0.603407i	−0.748259	−	0.663407i	$-0.769110\pi$
$997$	7.89192	−	19.0528i	0.249939	−	0.603407i	0.998198	+	0.0599995i	$0.0191099\pi$
$998$	−8.46558	+	6.33792i	−0.267973	+	0.200623i
$999$	−30.5841	−	30.5841i	−0.967640	−	0.967640i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	800.2.ba.f.549.16		64
5.2	odd	4		800.2.y.d.101.9	✓	64
5.3	odd	4		800.2.y.e.101.8	yes	64
5.4	even	2		800.2.ba.h.549.1		64
32.13	even	8		800.2.ba.h.749.1		64
160.13	odd	8		800.2.y.e.301.8	yes	64
160.77	odd	8		800.2.y.d.301.9	yes	64
160.109	even	8	inner	800.2.ba.f.749.16		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
800.2.y.d.101.9	✓	64	5.2	odd	4
800.2.y.d.301.9	yes	64	160.77	odd	8
800.2.y.e.101.8	yes	64	5.3	odd	4
800.2.y.e.301.8	yes	64	160.13	odd	8
800.2.ba.f.549.16		64	1.1	even	1	trivial
800.2.ba.f.749.16		64	160.109	even	8	inner
800.2.ba.h.549.1		64	5.4	even	2
800.2.ba.h.749.1		64	32.13	even	8

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:	\( N \)	\(=\)	\( 800 = 2^{5} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	800.ba (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.37027 - 0.349813i) q^{2} +(-2.56208 + 1.06125i) q^{3} +(1.75526 - 0.958675i) q^{4} +(-3.13949 + 2.35044i) q^{6} +(-2.94098 + 2.94098i) q^{7} +(2.06982 - 1.92765i) q^{8} +(3.31668 - 3.31668i) q^{9} +O(q^{10})\)	\(q+(1.37027 - 0.349813i) q^{2} +(-2.56208 + 1.06125i) q^{3} +(1.75526 - 0.958675i) q^{4} +(-3.13949 + 2.35044i) q^{6} +(-2.94098 + 2.94098i) q^{7} +(2.06982 - 1.92765i) q^{8} +(3.31668 - 3.31668i) q^{9} +(-0.569137 + 1.37402i) q^{11} +(-3.47973 + 4.31897i) q^{12} +(-1.87795 - 4.53377i) q^{13} +(-3.00114 + 5.05872i) q^{14} +(2.16189 - 3.36545i) q^{16} -2.78896 q^{17} +(3.38452 - 5.70495i) q^{18} +(-2.08461 + 0.863472i) q^{19} +(4.41392 - 10.6561i) q^{21} +(-0.299220 + 2.08186i) q^{22} +(-3.26157 - 3.26157i) q^{23} +(-3.25732 + 7.13539i) q^{24} +(-4.15927 - 5.55555i) q^{26} +(-1.79403 + 4.33117i) q^{27} +(-2.34275 + 7.98164i) q^{28} +(-2.85519 - 6.89303i) q^{29} -0.800126 q^{31} +(1.78508 - 5.36782i) q^{32} -4.12434i q^{33} +(-3.82162 + 0.975616i) q^{34} +(2.64202 - 9.00125i) q^{36} +(-3.53070 + 8.52386i) q^{37} +(-2.55441 + 1.91241i) q^{38} +(9.62291 + 9.62291i) q^{39} +(-8.87560 + 8.87560i) q^{41} +(2.32059 - 16.1458i) q^{42} +(-4.67600 - 1.93686i) q^{43} +(0.318252 + 2.95738i) q^{44} +(-5.61017 - 3.32828i) q^{46} +2.86075 q^{47} +(-1.96735 + 10.9168i) q^{48} -10.2987i q^{49} +(7.14554 - 2.95978i) q^{51} +(-7.64271 - 6.15762i) q^{52} +(5.42935 + 2.24891i) q^{53} +(-0.943199 + 6.56244i) q^{54} +(-0.418107 + 11.7565i) q^{56} +(4.42457 - 4.42457i) q^{57} +(-6.32364 - 8.44650i) q^{58} +(-13.6375 - 5.64885i) q^{59} +(-4.72380 - 11.4043i) q^{61} +(-1.09639 + 0.279895i) q^{62} +19.5086i q^{63} +(0.568304 - 7.97979i) q^{64} +(-1.44275 - 5.65144i) q^{66} +(12.6341 - 5.23321i) q^{67} +(-4.89536 + 2.67371i) q^{68} +(11.8177 + 4.89507i) q^{69} +(2.90308 + 2.90308i) q^{71} +(0.471518 - 13.2583i) q^{72} +(-1.13529 - 1.13529i) q^{73} +(-1.85624 + 12.9151i) q^{74} +(-2.83124 + 3.51408i) q^{76} +(-2.36714 - 5.71478i) q^{77} +(16.5522 + 9.81974i) q^{78} +6.06396i q^{79} +1.07076i q^{81} +(-9.05714 + 15.2667i) q^{82} +(-0.121076 - 0.292304i) q^{83} +(-2.46819 - 22.9358i) q^{84} +(-7.08491 - 1.01829i) q^{86} +(14.6304 + 14.6304i) q^{87} +(1.47062 + 3.94107i) q^{88} +(8.97315 + 8.97315i) q^{89} +(18.8568 + 7.81073i) q^{91} +(-8.85170 - 2.59813i) q^{92} +(2.04999 - 0.849132i) q^{93} +(3.91999 - 1.00073i) q^{94} +(1.12307 + 15.6472i) q^{96} +13.5255i q^{97} +(-3.60264 - 14.1120i) q^{98} +(2.66953 + 6.44482i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q+O(q^{10}) \) 64 * q	\( 64 q - 24 q^{12} + 16 q^{14} + 20 q^{16} + 40 q^{18} + 24 q^{22} - 8 q^{23} + 28 q^{24} - 48 q^{28} - 20 q^{32} + 20 q^{34} + 12 q^{36} + 16 q^{37} - 24 q^{39} - 40 q^{44} + 32 q^{46} + 80 q^{47} + 40 q^{48} + 16 q^{51} - 76 q^{54} + 48 q^{56} - 8 q^{58} - 32 q^{59} - 32 q^{61} - 44 q^{62} - 48 q^{64} + 16 q^{66} - 32 q^{68} + 32 q^{69} + 32 q^{71} + 96 q^{72} - 8 q^{74} + 52 q^{78} - 116 q^{82} - 56 q^{84} - 84 q^{86} + 20 q^{88} + 48 q^{91} + 88 q^{92} - 48 q^{93} - 32 q^{94} - 100 q^{96} - 72 q^{98} + 64 q^{99}+O(q^{100}) \) 64 * q - 24 * q^12 + 16 * q^14 + 20 * q^16 + 40 * q^18 + 24 * q^22 - 8 * q^23 + 28 * q^24 - 48 * q^28 - 20 * q^32 + 20 * q^34 + 12 * q^36 + 16 * q^37 - 24 * q^39 - 40 * q^44 + 32 * q^46 + 80 * q^47 + 40 * q^48 + 16 * q^51 - 76 * q^54 + 48 * q^56 - 8 * q^58 - 32 * q^59 - 32 * q^61 - 44 * q^62 - 48 * q^64 + 16 * q^66 - 32 * q^68 + 32 * q^69 + 32 * q^71 + 96 * q^72 - 8 * q^74 + 52 * q^78 - 116 * q^82 - 56 * q^84 - 84 * q^86 + 20 * q^88 + 48 * q^91 + 88 * q^92 - 48 * q^93 - 32 * q^94 - 100 * q^96 - 72 * q^98 + 64 * q^99

Introduction

L-functions

Modular forms

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