LMFDB - Embedded newform 800.2.y.d.301.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [800,2,Mod(101,800)]

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, 1, 0]))

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

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

chi := DirichletCharacter("800.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 800 = 2^{5} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	800.y (of order $8$, degree $4$, 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			301.9
Character	$\chi$	$=$	800.301
Dual form			800.2.y.d.101.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$351$	$577$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$	$1$

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 $

$2$	0.349813	−	1.37027i	0.247355	−	0.968925i
$2$	0.349813	−	1.37027i	0.247355	−	0.968925i
$3$	1.06125	−	2.56208i	0.612712	−	1.47922i	−0.247298	−	0.968939i	$-0.579543\pi$
$3$	1.06125	−	2.56208i	0.612712	−	1.47922i	0.860010	−	0.510277i	$-0.170457\pi$
$4$	−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	$0.962143\pi$
$8$	−1.92765	+	2.06982i	−0.681528	+	0.731792i
$9$	−3.31668	−	3.31668i	−1.10556	−	1.10556i
$10$		0			0
$11$	−0.569137	−	1.37402i	−0.171601	−	0.414282i	0.814558	−	0.580082i	$-0.196979\pi$
$11$	−0.569137	−	1.37402i	−0.171601	−	0.414282i	−0.986159	+	0.165800i	$0.946979\pi$
$12$	−4.31897	+	3.47973i	−1.24678	+	1.00451i
$13$	−4.53377	−	1.87795i	−1.25744	−	0.520850i	−0.348319	−	0.937376i	$-0.613247\pi$
$13$	−4.53377	−	1.87795i	−1.25744	−	0.520850i	−0.909124	+	0.416526i	$0.863247\pi$
$14$	3.00114	+	5.05872i	0.802087	+	1.35200i
$15$		0			0
$16$	2.16189	+	3.36545i	0.540471	+	0.841362i
$17$			2.78896i			0.676423i	0.941070	+	0.338211i	$0.109822\pi$
$17$			2.78896i			0.676423i	−0.941070	+	0.338211i	$0.890178\pi$
$18$	−5.70495	+	3.38452i	−1.34467	+	0.797738i
$19$	2.08461	+	0.863472i	0.478242	+	0.198094i	0.608764	−	0.793351i	$-0.291666\pi$
$19$	2.08461	+	0.863472i	0.478242	+	0.198094i	−0.130523	+	0.991445i	$0.541666\pi$
$20$		0			0
$21$	4.41392	+	10.6561i	0.963195	+	2.32536i
$22$	−2.08186	+	0.299220i	−0.443855	+	0.0637939i
$23$	−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
$27$	−4.33117	+	1.79403i	−0.833535	+	0.345261i
$28$	7.98164	−	2.34275i	1.50839	−	0.442738i
$29$	2.85519	−	6.89303i	0.530195	−	1.28000i	−0.401200	−	0.915991i	$-0.631407\pi$
$29$	2.85519	−	6.89303i	0.530195	−	1.28000i	0.931394	−	0.364012i	$-0.118593\pi$
$30$		0			0
$31$	−0.800126			−0.143707			−0.0718535	−	0.997415i	$-0.522891\pi$
$31$	−0.800126			−0.143707			−0.0718535	+	0.997415i	$0.522891\pi$
$32$	5.36782	−	1.78508i	0.948905	−	0.315561i
$33$	−4.12434			−0.717955
$34$	3.82162	+	0.975616i	0.655403	+	0.167317i
$35$		0			0
$36$	2.64202	+	9.00125i	0.440337	+	1.50021i
$37$	−8.52386	+	3.53070i	−1.40131	+	0.580443i	−0.950093	−	0.311968i	$-0.899012\pi$
$37$	−8.52386	+	3.53070i	−1.40131	+	0.580443i	−0.451222	+	0.892412i	$0.649012\pi$
$38$	1.91241	−	2.55441i	0.310234	−	0.414380i
$39$	−9.62291	+	9.62291i	−1.54090	+	1.54090i
$40$		0			0
$41$	−8.87560	−	8.87560i	−1.38614	−	1.38614i	−0.833271	−	0.552864i	$-0.813535\pi$
$41$	−8.87560	−	8.87560i	−1.38614	−	1.38614i	−0.552864	−	0.833271i	$-0.686465\pi$
$42$	16.1458	−	2.32059i	2.49135	−	0.358074i
$43$	−1.93686	−	4.67600i	−0.295369	−	0.713083i	−0.999994	−	0.00350351i	$-0.998885\pi$
$43$	−1.93686	−	4.67600i	−0.295369	−	0.713083i	0.704625	−	0.709580i	$-0.251115\pi$
$44$	−0.318252	+	2.95738i	−0.0479783	+	0.445842i
$45$		0			0
$46$	−5.61017	+	3.32828i	−0.827174	+	0.490729i
$47$		−	2.86075i		−	0.417284i	−0.977992	−	0.208642i	$-0.933096\pi$
$47$		−	2.86075i		−	0.417284i	0.977992	−	0.208642i	$-0.0669043\pi$
$48$	10.9168	−	1.96735i	1.57571	−	0.283962i
$49$		−	10.2987i		−	1.47125i
$50$		0			0
$51$	7.14554	+	2.95978i	1.00058	+	0.414452i
$52$	6.15762	+	7.64271i	0.853908	+	1.05985i
$53$	2.24891	+	5.42935i	0.308912	+	0.745779i	0.999741	+	0.0227609i	$0.00724566\pi$
$53$	2.24891	+	5.42935i	0.308912	+	0.745779i	−0.690829	+	0.723018i	$0.742754\pi$
$54$	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
$58$	−8.44650	−	6.32364i	−1.10908	−	0.830334i
$59$	13.6375	−	5.64885i	1.77545	−	0.735417i	0.781722	−	0.623627i	$-0.214342\pi$
$59$	13.6375	−	5.64885i	1.77545	−	0.735417i	0.993732	−	0.111790i	$-0.0356583\pi$
$60$		0			0
$61$	−4.72380	+	11.4043i	−0.604820	+	1.46016i	0.263747	+	0.964592i	$0.415042\pi$
$61$	−4.72380	+	11.4043i	−0.604820	+	1.46016i	−0.868567	+	0.495573i	$0.834958\pi$
$62$	−0.279895	+	1.09639i	−0.0355467	+	0.139241i
$63$	19.5086			2.45785
$64$	−0.568304	−	7.97979i	−0.0710380	−	0.997474i
$65$		0			0
$66$	−1.44275	+	5.65144i	−0.177590	+	0.695645i
$67$	5.23321	−	12.6341i	0.639338	−	1.54350i	−0.188225	−	0.982126i	$-0.560273\pi$
$67$	5.23321	−	12.6341i	0.639338	−	1.54350i	0.827563	−	0.561373i	$-0.189727\pi$
$68$	2.67371	−	4.89536i	0.324235	−	0.593649i
$69$	−11.8177	+	4.89507i	−1.42269	+	0.589297i
$70$		0			0
$71$	2.90308	−	2.90308i	0.344532	−	0.344532i	−0.513536	−	0.858068i	$-0.671665\pi$
$71$	2.90308	−	2.90308i	0.344532	−	0.344532i	0.858068	+	0.513536i	$0.171665\pi$
$72$	13.2583	−	0.471518i	1.56251	−	0.0555690i
$73$	−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
$77$	5.71478	+	2.36714i	0.651260	+	0.269761i
$78$	9.81974	+	16.5522i	1.11187	+	1.87417i
$79$			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
$82$	−15.2667	+	9.05714i	−1.68593	+	1.00019i
$83$	−0.292304	−	0.121076i	−0.0320846	−	0.0132899i	0.366583	−	0.930385i	$-0.380527\pi$
$83$	−0.292304	−	0.121076i	−0.0320846	−	0.0132899i	−0.398668	+	0.917095i	$0.630527\pi$
$84$	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
$88$	3.94107	+	1.47062i	0.420119	+	0.156769i
$89$	−8.97315	+	8.97315i	−0.951152	+	0.951152i	−0.998861	−	0.0477088i	$-0.984808\pi$
$89$	−8.97315	+	8.97315i	−0.951152	+	0.951152i	0.0477088	+	0.998861i	$0.484808\pi$
$90$		0			0
$91$	18.8568	−	7.81073i	1.97673	−	0.818787i
$92$	2.59813	+	8.85170i	0.270873	+	0.922854i
$93$	−0.849132	+	2.04999i	−0.0880509	+	0.212574i
$94$	−3.91999	−	1.00073i	−0.404316	−	0.103217i
$95$		0			0
$96$	1.12307	−	15.6472i	0.114622	−	1.59698i
$97$	−13.5255			−1.37330			−0.686651	−	0.726987i	$-0.740920\pi$
$97$	−13.5255			−1.37330			−0.686651	+	0.726987i	$0.740920\pi$
$98$	−14.1120	−	3.60264i	−1.42553	−	0.363921i
$99$	−2.66953	+	6.44482i	−0.268298	+	0.647729i
$100$		0			0
$101$	8.14849	−	3.37522i	0.810805	−	0.335846i	0.0615299	−	0.998105i	$-0.480402\pi$
$101$	8.14849	−	3.37522i	0.810805	−	0.335846i	0.749275	+	0.662259i	$0.230402\pi$
$102$	6.55529	−	8.75592i	0.649070	−	0.866966i
$103$	6.88114	−	6.88114i	0.678019	−	0.678019i	−0.281532	−	0.959552i	$-0.590843\pi$
$103$	6.88114	−	6.88114i	0.678019	−	0.678019i	0.959552	+	0.281532i	$0.0908427\pi$
$104$	12.6266	−	5.76406i	1.23814	−	0.565212i
$105$		0			0
$106$	8.22636	−	1.18235i	0.799015	−	0.114840i
$107$	0.936975	+	2.26206i	0.0905807	+	0.218681i	0.962677	−	0.270653i	$-0.0872397\pi$
$107$	0.936975	+	2.26206i	0.0905807	+	0.218681i	−0.872096	+	0.489335i	$0.837240\pi$
$108$	9.32223	+	1.00319i	0.897032	+	0.0965323i
$109$	−4.31645	−	1.78793i	−0.413441	−	0.171253i	0.166260	−	0.986082i	$-0.446831\pi$
$109$	−4.31645	−	1.78793i	−0.413441	−	0.171253i	−0.579702	+	0.814829i	$0.696831\pi$
$110$		0			0
$111$			25.5858i			2.42849i
$112$	−16.2558	−	3.53966i	−1.53603	−	0.334466i
$113$			0.592560i			0.0557433i	0.999612	+	0.0278717i	$0.00887297\pi$
$113$			0.592560i			0.0557433i	−0.999612	+	0.0278717i	$0.991127\pi$
$114$	−4.51507	−	7.61061i	−0.422875	−	0.712799i
$115$		0			0
$116$	−11.6198	+	9.36187i	−1.07887	+	0.869228i
$117$	8.80851	+	21.2656i	0.814347	+	1.96601i
$118$	−2.96984	−	20.6631i	−0.273396	−	1.90219i
$119$	−8.20229	−	8.20229i	−0.751902	−	0.751902i
$120$		0			0
$121$	6.21416	−	6.21416i	0.564924	−	0.564924i
$122$	13.9744	+	10.4622i	1.26518	+	0.947205i
$123$	−32.1592	+	13.3208i	−2.89970	+	1.20109i
$124$	1.40443	+	0.767061i	0.126122	+	0.0688841i
$125$		0			0
$126$	6.82436	−	26.7320i	0.607962	−	2.38147i
$127$	3.21186			0.285006			0.142503	−	0.989794i	$-0.454485\pi$
$127$	3.21186			0.285006			0.142503	+	0.989794i	$0.454485\pi$
$128$	−11.1332	−	2.01271i	−0.984049	−	0.177900i
$129$	−14.0358			−1.23578
$130$		0			0
$131$	−3.16454	+	7.63987i	−0.276487	+	0.667499i	−0.999733	−	0.0230915i	$-0.992649\pi$
$131$	−3.16454	+	7.63987i	−0.276487	+	0.667499i	0.723246	+	0.690590i	$0.242649\pi$
$132$	7.23929	+	3.95390i	0.630100	+	0.344143i
$133$	−8.67025	+	3.59133i	−0.751806	+	0.311408i
$134$	−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	0.839740	−	0.542989i	$-0.182707\pi$
$137$	3.47339	+	3.47339i	0.296751	+	0.296751i	−0.542989	+	0.839740i	$0.682707\pi$
$138$	2.57355	+	17.9058i	0.219075	+	1.52424i
$139$	7.36134	+	17.7718i	0.624380	+	1.50739i	0.846511	+	0.532371i	$0.178699\pi$
$139$	7.36134	+	17.7718i	0.624380	+	1.50739i	−0.222131	+	0.975017i	$0.571301\pi$
$140$		0			0
$141$	−7.32947	−	3.03597i	−0.617253	−	0.255674i
$142$	−2.96245	−	4.99352i	−0.248604	−	0.419047i
$143$			7.29830i			0.610315i
$144$	3.99183	−	18.3324i	0.332653	−	1.52770i
$145$		0			0
$146$	−1.95279	+	1.15851i	−0.161614	+	0.0958791i
$147$	−26.3862	−	10.9295i	−2.17630	−	0.901452i
$148$	18.3464	+	1.97431i	1.50806	+	0.162287i
$149$	−0.649458	−	1.56793i	−0.0532056	−	0.128450i	0.895042	−	0.445983i	$-0.147146\pi$
$149$	−0.649458	−	1.56793i	−0.0532056	−	0.128450i	−0.948247	+	0.317533i	$0.897146\pi$
$150$		0			0
$151$	−6.11339	−	6.11339i	−0.497501	−	0.497501i	0.413158	−	0.910659i	$-0.364426\pi$
$151$	−6.11339	−	6.11339i	−0.497501	−	0.497501i	−0.910659	+	0.413158i	$0.864426\pi$
$152$	−5.80563	+	2.65028i	−0.470899	+	0.214966i
$153$	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
$157$	4.78009	−	11.5402i	0.381493	−	0.921005i	−0.610185	−	0.792259i	$-0.708905\pi$
$157$	4.78009	−	11.5402i	0.381493	−	0.921005i	0.991678	−	0.128746i	$-0.0410952\pi$
$158$	8.30924	+	2.12125i	0.661048	+	0.168758i
$159$	16.2971			1.29244
$160$		0			0
$161$	19.1845			1.51195
$162$	−1.46723	−	0.374566i	−0.115276	−	0.0294287i
$163$	0.459523	−	1.10939i	0.0359926	−	0.0868938i	−0.904861	−	0.425707i	$-0.860025\pi$
$163$	0.459523	−	1.10939i	0.0359926	−	0.0868938i	0.940854	+	0.338813i	$0.110025\pi$
$164$	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	$0.308771\pi$
$168$	−30.5648	−	11.4053i	−2.35812	−	0.879940i
$169$	7.83602	+	7.83602i	0.602771	+	0.602771i
$170$		0			0
$171$	−4.05011	−	9.77783i	−0.309720	−	0.747729i
$172$	−1.08306	+	10.0644i	−0.0825827	+	0.767405i
$173$	−10.3559	−	4.28956i	−0.787345	−	0.326129i	−0.0474697	−	0.998873i	$-0.515116\pi$
$173$	−10.3559	−	4.28956i	−0.787345	−	0.326129i	−0.739876	+	0.672744i	$0.765116\pi$
$174$	−25.1655	+	14.9297i	−1.90779	+	1.13181i
$175$		0			0
$176$	3.39378	−	4.88587i	0.255816	−	0.368287i
$177$		−	40.9352i		−	3.07688i
$178$	9.15669	+	15.4345i	0.686323	+	1.15687i
$179$	4.10991	+	1.70238i	0.307189	+	0.127242i	0.530952	−	0.847402i	$-0.321834\pi$
$179$	4.10991	+	1.70238i	0.307189	+	0.127242i	−0.223763	+	0.974643i	$0.571834\pi$
$180$		0			0
$181$	−0.0541726	−	0.130784i	−0.00402662	−	0.00972112i	0.921853	−	0.387539i	$-0.126675\pi$
$181$	−0.0541726	−	0.130784i	−0.00402662	−	0.00972112i	−0.925880	+	0.377818i	$0.876675\pi$
$182$	−4.10644	−	28.5711i	−0.304389	−	2.11783i
$183$	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
$187$	3.83209	−	1.58730i	0.280230	−	0.116075i
$188$	−2.74253	+	5.02137i	−0.200020	+	0.366221i
$189$	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	$0.509975\pi$
$192$	−21.0480	−	7.01249i	−1.51901	−	0.506083i
$193$	−16.6416			−1.19789			−0.598946	−	0.800790i	$-0.704414\pi$
$193$	−16.6416			−1.19789			−0.598946	+	0.800790i	$0.704414\pi$
$194$	−4.73138	+	18.5335i	−0.339694	+	1.33063i
$195$		0			0
$196$	−9.87315	+	18.0770i	−0.705225	+	1.29121i
$197$	−5.18658	+	2.14835i	−0.369529	+	0.153064i	−0.559717	−	0.828684i	$-0.689090\pi$
$197$	−5.18658	+	2.14835i	−0.369529	+	0.153064i	0.190188	+	0.981748i	$0.439090\pi$
$198$	7.89729	+	5.91246i	0.561236	+	0.420180i
$199$	10.7219	−	10.7219i	0.760055	−	0.760055i	−0.216277	−	0.976332i	$-0.569392\pi$
$199$	10.7219	−	10.7219i	0.760055	−	0.760055i	0.976332	+	0.216277i	$0.0693916\pi$
$200$		0			0
$201$	−26.8158	−	26.8158i	−1.89144	−	1.89144i
$202$	−1.77450	−	12.3463i	−0.124853	−	0.868683i
$203$	11.8752	+	28.6693i	0.833477	+	2.01219i
$204$	−9.70482	−	12.0454i	−0.679474	−	0.843349i
$205$		0			0
$206$	−7.02189	−	11.8361i	−0.489238	−	0.824661i
$207$			21.6352i			1.50375i
$208$	−3.48135	−	19.3181i	−0.241388	−	1.33947i
$209$		−	3.35572i		−	0.232120i
$210$		0			0
$211$	−13.5357	−	5.60666i	−0.931835	−	0.385979i	−0.135461	−	0.990783i	$-0.543251\pi$
$211$	−13.5357	−	5.60666i	−0.931835	−	0.385979i	−0.796374	+	0.604804i	$0.793251\pi$
$212$	1.25755	−	11.6859i	0.0863692	−	0.802591i
$213$	−4.35702	−	10.5188i	−0.298538	−	0.720736i
$214$	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
$218$	−3.95990	+	5.28925i	−0.268198	+	0.358233i
$219$	−4.11353	+	1.70388i	−0.277967	+	0.115138i
$220$		0			0
$221$	5.23753	−	12.6445i	0.352315	−	0.850563i
$222$	35.0593	+	8.95023i	2.35303	+	0.600700i
$223$	10.8919			0.729378			0.364689	−	0.931129i	$-0.381175\pi$
$223$	10.8919			0.729378			0.364689	+	0.931129i	$0.381175\pi$
$224$	−10.5368	+	21.0366i	−0.704017	+	1.40556i
$225$		0			0
$226$	0.811965	+	0.207285i	0.0540111	+	0.0137884i
$227$	0.469337	−	1.13308i	0.0311510	−	0.0752051i	−0.907539	−	0.419969i	$-0.862041\pi$
$227$	0.469337	−	1.13308i	0.0311510	−	0.0752051i	0.938689	+	0.344764i	$0.112041\pi$
$228$	−12.0080	+	3.52455i	−0.795249	+	0.233419i
$229$	−2.28178	+	0.945143i	−0.150784	+	0.0624568i	−0.456799	−	0.889570i	$-0.651004\pi$
$229$	−2.28178	+	0.945143i	−0.150784	+	0.0624568i	0.306015	+	0.952027i	$0.401004\pi$
$230$		0			0
$231$	12.1296	−	12.1296i	0.798069	−	0.798069i
$232$	8.76351	+	19.1971i	0.575353	+	1.26035i
$233$	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
$237$	15.5363	+	6.43536i	1.00919	+	0.418022i
$238$	−14.1086	+	8.37005i	−0.914524	+	0.542550i
$239$		−	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	$-0.919489\pi$
$241$		−	7.76968i		−	0.500489i	0.968183	−	0.250244i	$-0.0805110\pi$
$242$	−6.34127	−	10.6889i	−0.407632	−	0.687106i
$243$	−15.7369	−	6.51843i	−1.00952	−	0.418158i
$244$	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
$248$	1.54237	−	1.65612i	0.0979404	−	0.105164i
$249$	−0.620414	+	0.620414i	−0.0393172	+	0.0393172i
$250$		0			0
$251$	−17.3540	+	7.18827i	−1.09538	+	0.453720i	−0.855878	−	0.517177i	$-0.826983\pi$
$251$	−17.3540	+	7.18827i	−1.09538	+	0.453720i	−0.239498	+	0.970897i	$0.576983\pi$
$252$	−34.2427	−	18.7024i	−2.15709	−	1.17814i
$253$	−2.62518	+	6.33774i	−0.165044	+	0.398451i
$254$	1.12355	−	4.40110i	0.0704978	−	0.276150i
$255$		0			0
$256$	−6.65250	+	14.5514i	−0.415781	+	0.909465i
$257$	15.7332			0.981413			0.490707	−	0.871325i	$-0.336739\pi$
$257$	15.7332			0.981413			0.490707	+	0.871325i	$0.336739\pi$
$258$	−4.90990	+	19.2327i	−0.305677	+	1.19738i
$259$	14.6848	−	35.4523i	0.912469	−	2.20290i
$260$		0			0
$261$	−32.3317	+	13.3922i	−2.00128	+	0.828958i
$262$	9.36166	+	7.00879i	0.578365	+	0.433004i
$263$	−5.45192	+	5.45192i	−0.336180	+	0.336180i	−0.854927	−	0.518748i	$-0.826398\pi$
$263$	−5.45192	+	5.45192i	−0.336180	+	0.336180i	0.518748	+	0.854927i	$0.326398\pi$
$264$	7.95030	−	8.53664i	0.489307	−	0.525394i
$265$		0			0
$266$	1.88812	+	13.1368i	0.115768	+	0.805472i
$267$	13.4672	+	32.5127i	0.824178	+	1.98974i
$268$	−21.2976	+	17.1592i	−1.30096	+	1.04816i
$269$	−7.58007	−	3.13977i	−0.462165	−	0.191435i	0.139437	−	0.990231i	$-0.455471\pi$
$269$	−7.58007	−	3.13977i	−0.462165	−	0.191435i	−0.601602	+	0.798796i	$0.705471\pi$
$270$		0			0
$271$		−	20.7286i		−	1.25918i	−0.776929	−	0.629588i	$-0.783224\pi$
$271$		−	20.7286i		−	1.25918i	0.776929	−	0.629588i	$-0.216776\pi$
$272$	−9.38611	+	6.02942i	−0.569117	+	0.365587i
$273$		−	56.6016i		−	3.42569i
$274$	5.97450	−	3.54443i	0.360933	−	0.214127i
$275$		0			0
$276$	25.4360	+	2.73724i	1.53107	+	0.164763i
$277$	9.02027	+	21.7769i	0.541975	+	1.30844i	0.923327	+	0.384014i	$0.125459\pi$
$277$	9.02027	+	21.7769i	0.541975	+	1.30844i	−0.381352	+	0.924430i	$0.624541\pi$
$278$	26.9273	−	3.87017i	1.61499	−	0.232117i
$279$	2.65376	+	2.65376i	0.158877	+	0.158877i
$280$		0			0
$281$	1.41047	−	1.41047i	0.0841416	−	0.0841416i	−0.663783	−	0.747925i	$-0.731050\pi$
$281$	1.41047	−	1.41047i	0.0841416	−	0.0841416i	0.747925	+	0.663783i	$0.231050\pi$
$282$	−6.72403	+	8.98131i	−0.400410	+	0.534829i
$283$	1.84276	−	0.763298i	0.109541	−	0.0453733i	−0.327240	−	0.944941i	$-0.606119\pi$
$283$	1.84276	−	0.763298i	0.109541	−	0.0453733i	0.436781	+	0.899568i	$0.356119\pi$
$284$	−7.87876	+	2.31255i	−0.467518	+	0.137225i
$285$		0			0
$286$	10.0006	+	2.55304i	0.591349	+	0.150965i
$287$	52.2059			3.08162
$288$	−23.7239	−	11.8828i	−1.39794	−	0.700200i
$289$	9.22169			0.542452
$290$		0			0
$291$	−14.3539	+	34.6533i	−0.841438	+	2.03141i
$292$	0.904358	+	3.08111i	0.0529236	+	0.180308i
$293$	9.76088	−	4.04309i	0.570236	−	0.236200i	−0.0788860	−	0.996884i	$-0.525136\pi$
$293$	9.76088	−	4.04309i	0.570236	−	0.236200i	0.649122	+	0.760684i	$0.275136\pi$
$294$	−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
$298$	−2.37567	+	0.341448i	−0.137619	+	0.0197795i
$299$	8.66216	+	20.9123i	0.500946	+	1.20939i
$300$		0			0
$301$	19.4483	+	8.05575i	1.12098	+	0.464326i
$302$	−10.5155	+	6.23843i	−0.605100	+	0.358981i
$303$		−	24.4590i		−	1.40513i
$304$	1.60071	+	8.88237i	0.0918070	+	0.509439i
$305$		0			0
$306$	−9.43929	−	15.9109i	−0.539608	−	0.909565i
$307$	4.19762	+	1.73871i	0.239571	+	0.0992336i	0.499239	−	0.866464i	$-0.333613\pi$
$307$	4.19762	+	1.73871i	0.239571	+	0.0992336i	−0.259668	+	0.965698i	$0.583613\pi$
$308$	−7.76162	−	9.63357i	−0.442260	−	0.548924i
$309$	−10.3274	−	24.9326i	−0.587507	−	1.41837i
$310$		0			0
$311$	22.5777	+	22.5777i	1.28026	+	1.28026i	0.940518	+	0.339745i	$0.110341\pi$
$311$	22.5777	+	22.5777i	1.28026	+	1.28026i	0.339745	+	0.940518i	$0.389659\pi$
$312$	−1.36805	−	38.4673i	−0.0774506	−	2.17778i
$313$	18.6877	−	18.6877i	1.05629	−	1.05629i	0.0579726	−	0.998318i	$-0.481536\pi$
$313$	18.6877	−	18.6877i	1.05629	−	1.05629i	0.998318	−	0.0579726i	$-0.0184636\pi$
$314$	−14.1410	−	10.5869i	−0.798020	−	0.597453i
$315$		0			0
$316$	5.81336	−	10.6438i	0.327027	−	0.598763i
$317$	10.2773	−	24.8116i	0.577231	−	1.39356i	−0.318057	−	0.948072i	$-0.603030\pi$
$317$	10.2773	−	24.8116i	0.577231	−	1.39356i	0.895288	−	0.445488i	$-0.146970\pi$
$318$	5.70093	−	22.3313i	0.319692	−	1.25228i
$319$	−11.0961			−0.621264
$320$		0			0
$321$	6.78993			0.378977
$322$	6.71097	−	26.2878i	0.373988	−	1.46496i
$323$	−2.40819	+	5.81389i	−0.133995	+	0.323493i
$324$	−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
$328$	35.4800	−	1.26181i	1.95905	−	0.0696716i
$329$	8.41342	+	8.41342i	0.463847	+	0.463847i
$330$		0			0
$331$	−4.97531	−	12.0115i	−0.273468	−	0.660210i	0.726159	−	0.687527i	$-0.241304\pi$
$331$	−4.97531	−	12.0115i	−0.273468	−	0.660210i	−0.999627	+	0.0273171i	$0.991304\pi$
$332$	0.396997	+	0.492745i	0.0217881	+	0.0270429i
$333$	39.9811	+	16.5607i	2.19095	+	0.907522i
$334$	3.42381	+	5.77119i	0.187343	+	0.315786i
$335$		0			0
$336$	−26.3203	+	37.8922i	−1.43589	+	2.06719i
$337$			30.1871i			1.64440i	0.569200	+	0.822199i	$0.307253\pi$
$337$			30.1871i			1.64440i	−0.569200	+	0.822199i	$0.692747\pi$
$338$	13.4786	−	7.99630i	0.733138	−	0.434941i
$339$	1.51818	+	0.628852i	0.0824564	+	0.0341546i
$340$		0			0
$341$	0.455382	+	1.09939i	0.0246603	+	0.0595352i
$342$	−14.8150	+	2.12932i	−0.801104	+	0.115140i
$343$	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
$347$	2.36957	−	0.981507i	0.127205	−	0.0526900i	−0.318173	−	0.948033i	$-0.603069\pi$
$347$	2.36957	−	0.981507i	0.127205	−	0.0526900i	0.445378	+	0.895343i	$0.353069\pi$
$348$	11.6544	+	39.7060i	0.624741	+	2.12847i
$349$	5.45739	−	13.1753i	0.292127	−	0.705258i	−0.707872	−	0.706341i	$-0.750345\pi$
$349$	5.45739	−	13.1753i	0.292127	−	0.705258i	0.999999	+	0.00108291i	$0.000344701\pi$
$350$		0			0
$351$	23.0057			1.22795
$352$	−5.50776	−	6.35953i	−0.293565	−	0.338964i
$353$	−3.26004			−0.173514			−0.0867571	−	0.996229i	$-0.527650\pi$
$353$	−3.26004			−0.173514			−0.0867571	+	0.996229i	$0.527650\pi$
$354$	−56.0922	−	14.3197i	−2.98126	−	0.761082i
$355$		0			0
$356$	24.3526	−	7.14790i	1.29068	−	0.378838i
$357$	−29.7196	+	12.3102i	−1.57293	+	0.651527i
$358$	3.77041	−	5.03616i	0.199273	−	0.266169i
$359$	−5.76463	+	5.76463i	−0.304245	+	0.304245i	−0.842672	−	0.538427i	$-0.819019\pi$
$359$	−5.76463	+	5.76463i	−0.304245	+	0.304245i	0.538427	+	0.842672i	$0.319019\pi$
$360$		0			0
$361$	−9.83503	−	9.83503i	−0.517633	−	0.517633i
$362$	−0.198160	+	0.0284809i	−0.0104150	+	0.00149692i
$363$	−9.32641	−	22.5159i	−0.489510	−	1.18178i
$364$	−40.5865	−	4.36763i	−2.12731	−	0.228926i
$365$		0			0
$366$	41.6353	−	24.7006i	2.17631	−	1.29112i
$367$		−	3.11540i		−	0.162622i	−0.996689	−	0.0813112i	$-0.974089\pi$
$367$		−	3.11540i		−	0.162622i	0.996689	−	0.0813112i	$-0.0259108\pi$
$368$	3.92551	−	18.0278i	0.204631	−	0.939764i
$369$			58.8750i			3.06491i
$370$		0			0
$371$	−22.5816	−	9.35362i	−1.17238	−	0.485616i
$372$	3.45572	−	2.78422i	0.179171	−	0.144355i
$373$	−3.19002	−	7.70139i	−0.165173	−	0.398763i	0.819522	−	0.573047i	$-0.194239\pi$
$373$	−3.19002	−	7.70139i	−0.165173	−	0.398763i	−0.984695	+	0.174284i	$0.944239\pi$
$374$	−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
$378$	−22.0739	−	16.5261i	−1.13536	−	0.850010i
$379$	13.1426	−	5.44383i	0.675089	−	0.279631i	−0.0186833	−	0.999825i	$-0.505947\pi$
$379$	13.1426	−	5.44383i	0.675089	−	0.279631i	0.693772	+	0.720194i	$0.255947\pi$
$380$		0			0
$381$	3.40858	−	8.22903i	0.174627	−	0.421586i
$382$	−0.302940	+	1.18666i	−0.0154998	+	0.0607148i
$383$	−23.2837			−1.18974			−0.594870	−	0.803822i	$-0.702797\pi$
$383$	−23.2837			−1.18974			−0.594870	+	0.803822i	$0.702797\pi$
$384$	−16.9718	+	26.3883i	−0.866090	+	1.34662i
$385$		0			0
$386$	−5.82147	+	22.8035i	−0.296305	+	1.16067i
$387$	−9.08484	+	21.9327i	−0.461808	+	1.11490i
$388$	23.7407	+	12.9665i	1.20525	+	0.658275i
$389$	−10.0350	+	4.15664i	−0.508796	+	0.210750i	−0.622287	−	0.782789i	$-0.713796\pi$
$389$	−10.0350	+	4.15664i	−0.508796	+	0.210750i	0.113492	+	0.993539i	$0.463796\pi$
$390$		0			0
$391$	9.09640	−	9.09640i	0.460025	−	0.460025i
$392$	21.3165	+	19.8524i	1.07665	+	1.00270i
$393$	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
$397$	−15.3292	−	6.34955i	−0.769349	−	0.318675i	−0.0367406	−	0.999325i	$-0.511698\pi$
$397$	−15.3292	−	6.34955i	−0.769349	−	0.318675i	−0.732609	+	0.680650i	$0.761698\pi$
$398$	−10.9412	−	18.4425i	−0.548432	−	0.924439i
$399$			26.0251i			1.30289i
$400$		0			0
$401$			24.7249i			1.23470i	0.786687	+	0.617352i	$0.211794\pi$
$401$			24.7249i			1.23470i	−0.786687	+	0.617352i	$0.788206\pi$
$402$	−46.1253	+	27.3643i	−2.30052	+	1.36481i
$403$	3.62759	+	1.50260i	0.180703	+	0.0748497i
$404$	−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
$408$	−19.9003	+	9.08455i	−0.985213	+	0.449752i
$409$	13.2241	−	13.2241i	0.653888	−	0.653888i	−0.300039	−	0.953927i	$-0.597000\pi$
$409$	13.2241	−	13.2241i	0.653888	−	0.653888i	0.953927	+	0.300039i	$0.0969996\pi$
$410$		0			0
$411$	12.5852	−	5.21296i	0.620782	−	0.257137i
$412$	−18.6750	+	5.48143i	−0.920051	+	0.270051i
$413$	−23.4945	+	56.7208i	−1.15609	+	2.79105i
$414$	29.6460	+	7.56827i	1.45702	+	0.371960i
$415$		0			0
$416$	−27.6888	−	1.98734i	−1.35755	−	0.0974375i
$417$	53.3451			2.61232
$418$	−4.59823	−	1.17388i	−0.224907	−	0.0574161i
$419$	−1.44829	+	3.49648i	−0.0707536	+	0.170814i	−0.955300	−	0.295638i	$-0.904468\pi$
$419$	−1.44829	+	3.49648i	−0.0707536	+	0.170814i	0.884547	+	0.466452i	$0.154468\pi$
$420$		0			0
$421$	−2.95627	+	1.22453i	−0.144080	+	0.0596797i	−0.453558	−	0.891227i	$-0.649846\pi$
$421$	−2.95627	+	1.22453i	−0.144080	+	0.0596797i	0.309478	+	0.950906i	$0.399846\pi$
$422$	−12.4176	+	16.5862i	−0.604479	+	0.807404i
$423$	−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
$427$	−19.6471	−	47.4323i	−0.950790	−	2.29541i
$428$	0.523941	−	4.86875i	0.0253256	−	0.235340i
$429$	18.6988	+	7.74530i	0.902788	+	0.373947i
$430$		0			0
$431$			32.8098i			1.58039i	0.612855	+	0.790195i	$0.290021\pi$
$431$			32.8098i			1.58039i	−0.612855	+	0.790195i	$0.709979\pi$
$432$	−15.4012	−	10.6979i	−0.740992	−	0.514701i
$433$		−	2.17672i		−	0.104606i	−0.998631	−	0.0523032i	$-0.983344\pi$
$433$		−	2.17672i		−	0.104606i	0.998631	−	0.0523032i	$-0.0166562\pi$
$434$	−2.40129	−	4.04762i	−0.115265	−	0.194292i
$435$		0			0
$436$	5.86246	+	7.27637i	0.280761	+	0.348475i
$437$	−3.98282	−	9.61537i	−0.190524	−	0.459966i
$438$	0.895803	+	6.23267i	0.0428031	+	0.297809i
$439$	−17.7331	−	17.7331i	−0.846357	−	0.846357i	0.143319	−	0.989676i	$-0.454222\pi$
$439$	−17.7331	−	17.7331i	−0.846357	−	0.846357i	−0.989676	+	0.143319i	$0.954222\pi$
$440$		0			0
$441$	−34.1576	+	34.1576i	−1.62655	+	1.62655i
$442$	−15.4942	−	11.6000i	−0.736985	−	0.551758i
$443$	27.4536	−	11.3716i	1.30436	−	0.540283i	0.381126	−	0.924523i	$-0.375536\pi$
$443$	27.4536	−	11.3716i	1.30436	−	0.540283i	0.923233	+	0.384240i	$0.125536\pi$
$444$	24.5284	−	44.9097i	1.16407	−	2.13132i
$445$		0			0
$446$	3.81014	−	14.9249i	0.180415	−	0.706712i
$447$	−4.70639			−0.222605
$448$	25.1398	+	21.7970i	1.18774	+	1.02981i
$449$	−27.1341			−1.28054			−0.640268	−	0.768152i	$-0.721177\pi$
$449$	−27.1341			−1.28054			−0.640268	+	0.768152i	$0.721177\pi$
$450$		0			0
$451$	−7.14380	+	17.2467i	−0.336389	+	0.812114i
$452$	0.568072	−	1.04010i	0.0267199	−	0.0489220i
$453$	−22.1508	+	9.17516i	−1.04074	+	0.431087i
$454$	−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	0.923419	−	0.383793i	$-0.125382\pi$
$457$	11.5359	+	11.5359i	0.539627	+	0.539627i	−0.383793	+	0.923419i	$0.625382\pi$
$458$	0.496902	+	3.45727i	0.0232187	+	0.161547i
$459$	−5.00348	−	12.0795i	−0.233543	−	0.563822i
$460$		0			0
$461$	−31.7669	−	13.1583i	−1.47953	−	0.612843i	−0.510523	−	0.859864i	$-0.670548\pi$
$461$	−31.7669	−	13.1583i	−1.47953	−	0.612843i	−0.969010	+	0.247022i	$0.920548\pi$
$462$	−12.3777	−	20.8639i	−0.575863	−	0.970676i
$463$		−	9.22961i		−	0.428937i	−0.976731	−	0.214468i	$-0.931198\pi$
$463$		−	9.22961i		−	0.428937i	0.976731	−	0.214468i	$-0.0688019\pi$
$464$	29.3707	−	5.29296i	1.36350	−	0.245719i
$465$		0			0
$466$	5.45029	−	3.23344i	0.252480	−	0.149786i
$467$	−13.7067	−	5.67749i	−0.634270	−	0.262723i	0.0422963	−	0.999105i	$-0.486533\pi$
$467$	−13.7067	−	5.67749i	−0.634270	−	0.262723i	−0.676566	+	0.736382i	$0.736533\pi$
$468$	4.92558	−	45.7712i	0.227685	−	2.11578i
$469$	21.7658	+	52.5474i	1.00505	+	2.42641i
$470$		0			0
$471$	−24.4939	−	24.4939i	−1.12862	−	1.12862i
$472$	−14.5963	+	39.1162i	−0.671850	+	1.80047i
$473$	−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
$477$	10.5485	−	25.4663i	0.482983	−	1.16602i
$478$	−11.9009	−	3.03815i	−0.544333	−	0.138962i
$479$	1.86348			0.0851446			0.0425723	−	0.999093i	$-0.486445\pi$
$479$	1.86348			0.0851446			0.0425723	+	0.999093i	$0.486445\pi$
$480$		0			0
$481$	45.2758			2.06440
$482$	−10.6465	−	2.71793i	−0.484936	−	0.123799i
$483$	20.3595	−	49.1521i	0.926387	−	2.23650i
$484$	−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	$-0.0490946\pi$
$488$	−14.4989	−	31.7608i	−0.656334	−	1.43775i
$489$	−2.35467	−	2.35467i	−0.106482	−	0.106482i
$490$		0			0
$491$	3.62967	+	8.76279i	0.163805	+	0.395459i	0.984375	−	0.176087i	$-0.0563439\pi$
$491$	3.62967	+	8.76279i	0.163805	+	0.395459i	−0.820570	+	0.571546i	$0.806344\pi$
$492$	69.2181	+	7.44876i	3.12059	+	0.335816i
$493$	19.2244	+	7.96300i	0.865823	+	0.358636i
$494$	−13.4675	+	7.98972i	−0.605931	+	0.359474i
$495$		0			0
$496$	−1.72978	−	2.69279i	−0.0776695	−	0.120910i
$497$			17.0758i			0.765954i
$498$	0.633104	+	1.06716i	0.0283701	+	0.0478207i
$499$	6.90859	+	2.86163i	0.309271	+	0.128104i	0.531921	−	0.846794i	$-0.321471\pi$
$499$	6.90859	+	2.86163i	0.309271	+	0.128104i	−0.222649	+	0.974899i	$0.571471\pi$
$500$		0			0
$501$	5.03557	+	12.1569i	0.224973	+	0.543132i
$502$	3.77918	+	26.2942i	0.168673	+	1.17357i
$503$	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
$507$	28.3925	−	11.7605i	1.26095	−	0.522304i
$508$	−5.63765	−	3.07913i	−0.250130	−	0.136614i
$509$	−2.19097	+	5.28948i	−0.0971132	+	0.234452i	−0.964969	−	0.262364i	$-0.915498\pi$
$509$	−2.19097	+	5.28948i	−0.0971132	+	0.234452i	0.867856	+	0.496816i	$0.165498\pi$
$510$		0			0
$511$	6.67774			0.295406
$512$	17.6122	+	14.2060i	0.778357	+	0.627822i
$513$	−10.5779			−0.467025
$514$	5.50370	−	21.5587i	0.242758	−	0.950916i
$515$		0			0
$516$	24.6364	+	13.4557i	1.08456	+	0.592356i
$517$	−3.93073	+	1.62816i	−0.172873	+	0.0716064i
$518$	−43.4421	−	32.5238i	−1.90874	−	1.42901i
$519$	−21.9804	+	21.9804i	−0.964831	+	0.964831i
$520$		0			0
$521$	28.8673	+	28.8673i	1.26470	+	1.26470i	0.948789	+	0.315912i	$0.102310\pi$
$521$	28.8673	+	28.8673i	1.26470	+	1.26470i	0.315912	+	0.948789i	$0.397690\pi$
$522$	7.04087	+	48.9878i	0.308170	+	2.14414i
$523$	−9.98767	−	24.1124i	−0.436731	−	1.05436i	−0.977071	−	0.212914i	$-0.931705\pi$
$523$	−9.98767	−	24.1124i	−0.436731	−	1.05436i	0.540340	−	0.841447i	$-0.318295\pi$
$524$	12.8787	−	10.3762i	0.562610	−	0.453287i
$525$		0			0
$526$	5.56343	+	9.37774i	0.242577	+	0.408889i
$527$		−	2.23152i		−	0.0972066i
$528$	−8.91635	−	13.8803i	−0.388034	−	0.604060i
$529$		−	1.72428i		−	0.0749688i
$530$		0			0
$531$	−63.9667	−	26.4959i	−2.77592	−	1.14982i
$532$	18.6615	+	2.00822i	0.809077	+	0.0870672i
$533$	23.5720	+	56.9079i	1.02102	+	2.46495i
$534$	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
$538$	−6.95393	+	9.28839i	−0.299805	+	0.400451i
$539$	−14.1507	+	5.86140i	−0.609512	+	0.252468i
$540$		0			0
$541$	7.97446	−	19.2520i	0.342849	−	0.827710i	−0.654576	−	0.755996i	$-0.727153\pi$
$541$	7.97446	−	19.2520i	0.342849	−	0.827710i	0.997425	−	0.0717144i	$-0.0228470\pi$
$542$	−28.4038	−	7.25115i	−1.22005	−	0.311464i
$543$	−0.392570			−0.0168468
$544$	4.97852	+	14.9706i	0.213452	+	0.641861i
$545$		0			0
$546$	−77.5593	−	19.8000i	−3.31923	−	0.847362i
$547$	−10.9909	+	26.5343i	−0.469935	+	1.13452i	0.494256	+	0.869316i	$0.335440\pi$
$547$	−10.9909	+	26.5343i	−0.469935	+	1.13452i	−0.964191	+	0.265207i	$0.914560\pi$
$548$	−2.76685	−	9.42655i	−0.118194	−	0.402682i
$549$	53.4915	−	22.1569i	2.28296	−	0.945634i
$550$		0			0
$551$	11.9039	−	11.9039i	0.507122	−	0.507122i
$552$	12.6486	−	33.8966i	0.538360	−	1.44273i
$553$	−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
$557$	3.56948	+	1.47853i	0.151244	+	0.0626472i	0.457021	−	0.889456i	$-0.348916\pi$
$557$	3.56948	+	1.47853i	0.151244	+	0.0626472i	−0.305777	+	0.952103i	$0.598916\pi$
$558$	4.56468	−	2.70804i	0.193238	−	0.114641i
$559$			24.8373i			1.05050i
$560$		0			0
$561$		−	11.5026i		−	0.485641i
$562$	−1.43932	−	2.42612i	−0.0607140	−	0.102340i
$563$	20.8899	+	8.65287i	0.880404	+	0.364675i	0.776653	−	0.629928i	$-0.216916\pi$
$563$	20.8899	+	8.65287i	0.880404	+	0.364675i	0.103750	+	0.994603i	$0.466916\pi$
$564$	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
$568$	0.412718	+	11.6050i	0.0173173	+	0.486934i
$569$	−3.66437	+	3.66437i	−0.153618	+	0.153618i	−0.779732	−	0.626114i	$-0.784645\pi$
$569$	−3.66437	+	3.66437i	−0.153618	+	0.153618i	0.626114	+	0.779732i	$0.284645\pi$
$570$		0			0
$571$	28.9785	−	12.0033i	1.21271	−	0.502321i	0.317626	−	0.948216i	$-0.397114\pi$
$571$	28.9785	−	12.0033i	1.21271	−	0.502321i	0.895085	+	0.445895i	$0.147114\pi$
$572$	6.99670	−	12.8104i	0.292547	−	0.535631i
$573$	−0.919047	+	2.21878i	−0.0383937	+	0.0926907i
$574$	18.2623	−	71.5361i	0.762255	−	2.98586i
$575$		0			0
$576$	−24.5815	+	28.3513i	−1.02423	+	1.18130i
$577$	−39.1035			−1.62790			−0.813950	−	0.580935i	$-0.802687\pi$
$577$	−39.1035			−1.62790			−0.813950	+	0.580935i	$0.802687\pi$
$578$	3.22587	−	12.6362i	0.134178	−	0.525596i
$579$	−17.6609	+	42.6372i	−0.733962	+	1.77194i
$580$		0			0
$581$	1.21574	−	0.503578i	0.0504376	−	0.0208919i
$582$	42.4631	+	31.7908i	1.76015	+	1.31777i
$583$	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
$587$	6.73339	+	16.2558i	0.277917	+	0.670950i	0.999778	−	0.0210878i	$-0.00671295\pi$
$587$	6.73339	+	16.2558i	0.277917	+	0.670950i	−0.721861	+	0.692038i	$0.756713\pi$
$588$	35.8368	+	44.4799i	1.47789	+	1.83432i
$589$	−1.66795	−	0.690887i	−0.0687266	−	0.0284675i
$590$		0			0
$591$			15.5684i			0.640397i
$592$	−30.3100	−	21.0537i	−1.24573	−	0.865300i
$593$		−	6.43191i		−	0.264127i	−0.991241	−	0.132063i	$-0.957840\pi$
$593$		−	6.43191i		−	0.264127i	0.991241	−	0.132063i	$-0.0421603\pi$
$594$	8.48010	−	5.03090i	0.347943	−	0.206420i
$595$		0			0
$596$	−0.363166	+	3.37475i	−0.0148759	+	0.138235i
$597$	−16.0917	−	38.8489i	−0.658591	−	1.58998i
$598$	31.6856	−	4.55407i	1.29572	−	0.186230i
$599$	−18.1680	−	18.1680i	−0.742322	−	0.742322i	0.230702	−	0.973024i	$-0.425898\pi$
$599$	−18.1680	−	18.1680i	−0.742322	−	0.742322i	−0.973024	+	0.230702i	$0.925898\pi$
$600$		0			0
$601$	−10.2457	+	10.2457i	−0.417933	+	0.417933i	−0.884491	−	0.466558i	$-0.845494\pi$
$601$	−10.2457	+	10.2457i	−0.417933	+	0.417933i	0.466558	+	0.884491i	$0.345494\pi$
$602$	17.8418	−	23.8314i	0.727178	−	0.971294i
$603$	−59.2601	+	24.5463i	−2.41326	+	0.999604i
$604$	4.86985	+	16.5914i	0.198151	+	0.675092i
$605$		0			0
$606$	−33.5154	−	8.55608i	−1.36147	−	0.347567i
$607$	28.5016			1.15684			0.578422	−	0.815738i	$-0.303669\pi$
$607$	28.5016			1.15684			0.578422	+	0.815738i	$0.303669\pi$
$608$	12.7312	+	0.913770i	0.516317	+	0.0370583i
$609$	86.0556			3.48715
$610$		0			0
$611$	−5.37235	+	12.9700i	−0.217342	+	0.524710i
$612$	−25.1042	+	7.36850i	−1.01478	+	0.297854i
$613$	11.9350	−	4.94365i	0.482051	−	0.199672i	−0.128406	−	0.991722i	$-0.540986\pi$
$613$	11.9350	−	4.94365i	0.482051	−	0.199672i	0.610457	+	0.792050i	$0.290986\pi$
$614$	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	$-0.813915\pi$
$617$	−34.4226	−	34.4226i	−1.38580	−	1.38580i	−0.551870	−	0.833930i	$-0.686085\pi$
$618$	−37.7770	+	5.42958i	−1.51961	+	0.218410i
$619$	−13.3861	−	32.3170i	−0.538034	−	1.29893i	−0.926093	−	0.377295i	$-0.876854\pi$
$619$	−13.3861	−	32.3170i	−0.538034	−	1.29893i	0.388059	−	0.921635i	$-0.373146\pi$
$620$		0			0
$621$	19.9778	+	8.27508i	0.801682	+	0.332067i
$622$	38.8354	−	23.0395i	1.55716	−	0.923799i
$623$		−	52.7798i		−	2.11458i
$624$	−53.1891	−	11.5818i	−2.12927	−	0.463643i
$625$		0			0
$626$	−19.0699	−	32.1443i	−0.762187	−	1.28475i
$627$	−8.59762	−	3.56125i	−0.343356	−	0.142223i
$628$	−19.4536	+	15.6734i	−0.776282	+	0.625439i
$629$	−9.84699	−	23.7727i	−0.392625	−	0.947881i
$630$		0			0
$631$	−30.3075	−	30.3075i	−1.20652	−	1.20652i	−0.972146	−	0.234377i	$-0.924695\pi$
$631$	−30.3075	−	30.3075i	−1.20652	−	1.20652i	−0.234377	−	0.972146i	$-0.575305\pi$
$632$	−12.5513	−	11.6892i	−0.499264	−	0.464972i
$633$	−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
$637$	−19.3405	+	46.6922i	−0.766300	+	1.85001i
$638$	−3.88157	+	15.2047i	−0.153673	+	0.601959i
$639$	−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	$0.683959\pi$
$642$	2.37521	−	9.30401i	0.0937419	−	0.367200i
$643$	−11.7066	+	28.2623i	−0.461664	+	1.11455i	0.506050	+	0.862504i	$0.331105\pi$
$643$	−11.7066	+	28.2623i	−0.461664	+	1.11455i	−0.967714	+	0.252051i	$0.918895\pi$
$644$	−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	$-0.133873\pi$
$648$	2.21628	+	2.06405i	0.0870636	+	0.0810836i
$649$	−15.5232	−	15.5232i	−0.609340	−	0.609340i
$650$		0			0
$651$	−3.53169	−	8.52626i	−0.138418	−	0.334170i
$652$	−1.87012	+	1.50673i	−0.0732397	+	0.0590081i
$653$	14.2736	+	5.91232i	0.558570	+	0.231367i	0.644064	−	0.764972i	$-0.277247\pi$
$653$	14.2736	+	5.91232i	0.558570	+	0.231367i	−0.0854945	+	0.996339i	$0.527247\pi$
$654$	9.34904	+	15.7588i	0.365577	+	0.616217i
$655$		0			0
$656$	10.6823	−	49.0584i	0.417076	−	1.91541i
$657$			7.53079i			0.293804i
$658$	14.4718	−	8.58550i	0.564168	−	0.334698i
$659$	−3.69353	−	1.52991i	−0.143880	−	0.0595969i	0.309582	−	0.950873i	$-0.399811\pi$
$659$	−3.69353	−	1.52991i	−0.143880	−	0.0595969i	−0.453461	+	0.891276i	$0.649811\pi$
$660$		0			0
$661$	9.19176	+	22.1909i	0.357518	+	0.863125i	0.995648	+	0.0931960i	$0.0297083\pi$
$661$	9.19176	+	22.1909i	0.357518	+	0.863125i	−0.638130	+	0.769929i	$0.720292\pi$
$662$	−18.1993	+	2.61573i	−0.707337	+	0.101663i
$663$	−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
$667$	−31.7945	+	13.1697i	−1.23109	+	0.509933i
$668$	9.10577	−	2.67270i	0.352313	−	0.103410i
$669$	11.5590	−	27.9060i	0.446898	−	1.07891i
$670$		0			0
$671$	18.3581			0.708708
$672$	42.7152	+	49.3210i	1.64777	+	1.90260i
$673$	4.29624			0.165608			0.0828040	−	0.996566i	$-0.473612\pi$
$673$	4.29624			0.165608			0.0828040	+	0.996566i	$0.473612\pi$
$674$	41.3644	+	10.5599i	1.59330	+	0.406751i
$675$		0			0
$676$	−6.24207	−	21.2665i	−0.240080	−	0.817941i
$677$	23.8398	−	9.87475i	0.916236	−	0.379518i	0.125796	−	0.992056i	$-0.459852\pi$
$677$	23.8398	−	9.87475i	0.916236	−	0.379518i	0.790441	+	0.612539i	$0.209852\pi$
$678$	1.39278	−	1.86034i	0.0534893	−	0.0714458i
$679$	39.7781	−	39.7781i	1.52654	−	1.52654i
$680$		0			0
$681$	−2.40495	−	2.40495i	−0.0921581	−	0.0921581i
$682$	1.66575	−	0.239414i	0.0637850	−	0.00916762i
$683$	−2.54520	−	6.14467i	−0.0973895	−	0.235119i	0.867675	−	0.497132i	$-0.165614\pi$
$683$	−2.54520	−	6.14467i	−0.0973895	−	0.235119i	−0.965064	+	0.262013i	$0.915614\pi$
$684$	−2.26476	+	21.0454i	−0.0865951	+	0.804690i
$685$		0			0
$686$	16.6874	−	9.89999i	0.637130	−	0.377983i
$687$			6.84912i			0.261310i
$688$	11.5496	−	16.6274i	0.440323	−	0.633913i
$689$		−	28.8388i		−	1.09867i
$690$		0			0
$691$	−7.14914	−	2.96127i	−0.271966	−	0.112652i	0.242533	−	0.970143i	$-0.422022\pi$
$691$	−7.14914	−	2.96127i	−0.271966	−	0.112652i	−0.514498	+	0.857491i	$0.672022\pi$
$692$	14.0650	+	17.4572i	0.534673	+	0.663625i
$693$	−11.1031	−	26.8052i	−0.421770	−	1.01824i
$694$	−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
$698$	−16.1446	−	12.0870i	−0.611083	−	0.457499i
$699$	11.4810	−	4.75557i	0.434250	−	0.179872i
$700$		0			0
$701$	−1.82186	+	4.39835i	−0.0688106	+	0.166124i	−0.954543	−	0.298072i	$-0.903656\pi$
$701$	−1.82186	+	4.39835i	−0.0688106	+	0.166124i	0.885733	+	0.464195i	$0.153656\pi$
$702$	8.04769	−	31.5239i	0.303740	−	1.18979i
$703$	−20.8176			−0.785149
$704$	−10.6409	+	5.32245i	−0.401045	+	0.200598i
$705$		0			0
$706$	−1.14040	+	4.46712i	−0.0429196	+	0.168122i
$707$	−14.0381	+	33.8910i	−0.527958	+	1.27460i
$708$	−39.2436	+	71.8520i	−1.47486	+	2.70036i
$709$	−35.5634	+	14.7309i	−1.33561	+	0.553229i	−0.932251	−	0.361812i	$-0.882158\pi$
$709$	−35.5634	+	14.7309i	−1.33561	+	0.553229i	−0.403361	+	0.915041i	$0.632158\pi$
$710$		0			0
$711$	20.1122	−	20.1122i	0.754267	−	0.754267i
$712$	−1.27568	−	35.8699i	−0.0478080	−	1.34428i
$713$	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
$717$	−22.2518	−	9.21701i	−0.831010	−	0.344215i
$718$	5.88253	+	9.91562i	0.219534	+	0.370048i
$719$		−	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
$722$	−16.9170	+	10.0362i	−0.629587	+	0.373508i
$723$	−19.9065	−	8.24555i	−0.740331	−	0.306655i
$724$	−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	0.877656	−	0.479290i	$-0.159106\pi$
$727$	10.7411	+	10.7411i	0.398366	+	0.398366i	−0.479290	+	0.877656i	$0.659106\pi$
$728$	−20.1825	+	54.0865i	−0.748014	+	2.00458i
$729$	−31.1301	+	31.1301i	−1.15296	+	1.15296i
$730$		0			0
$731$	13.0412	−	5.40184i	0.482346	−	0.199794i
$732$	−19.2818	−	65.6921i	−0.712674	−	2.42805i
$733$	−1.01052	+	2.43961i	−0.0373244	+	0.0901091i	−0.941443	−	0.337174i	$-0.890529\pi$
$733$	−1.01052	+	2.43961i	−0.0373244	+	0.0901091i	0.904118	+	0.427283i	$0.140529\pi$
$734$	−4.26892	−	1.08981i	−0.157569	−	0.0402255i
$735$		0			0
$736$	−23.3297	−	11.6854i	−0.859944	−	0.430728i
$737$	−20.3379			−0.749155
$738$	80.6745	+	20.5953i	2.96967	+	0.758122i
$739$	−13.5424	+	32.6942i	−0.498165	+	1.20268i	0.452306	+	0.891863i	$0.350601\pi$
$739$	−13.5424	+	32.6942i	−0.498165	+	1.20268i	−0.950471	+	0.310813i	$0.899399\pi$
$740$		0			0
$741$	−28.3691	+	11.7509i	−1.04217	+	0.431679i
$742$	−20.7163	+	27.6708i	−0.760520	+	1.01583i
$743$	−16.8110	+	16.8110i	−0.616735	+	0.616735i	−0.944692	−	0.327958i	$-0.893640\pi$
$743$	−16.8110	+	16.8110i	−0.616735	+	0.616735i	0.327958	+	0.944692i	$0.393640\pi$
$744$	−2.60627	−	5.70921i	−0.0955505	−	0.209310i
$745$		0			0
$746$	−11.6689	+	1.67713i	−0.427228	+	0.0614041i
$747$	0.567908	+	1.37105i	0.0207787	+	0.0501641i
$748$	−8.24802	−	0.887593i	−0.301577	−	0.0324536i
$749$	−9.40829	−	3.89704i	−0.343772	−	0.142395i
$750$		0			0
$751$		−	22.4107i		−	0.817778i	−0.912584	−	0.408889i	$-0.865916\pi$
$751$		−	22.4107i		−	0.817778i	0.912584	−	0.408889i	$-0.134084\pi$
$752$	9.62771	−	6.18462i	0.351087	−	0.225530i
$753$			52.0909i			1.89830i
$754$	26.4191	+	44.5321i	0.962126	+	1.62176i
$755$		0			0
$756$	−30.3669	+	24.4661i	−1.10443	+	0.889825i
$757$	12.4687	+	30.1022i	0.453184	+	1.09408i	0.971105	+	0.238654i	$0.0767062\pi$
$757$	12.4687	+	30.1022i	0.453184	+	1.09408i	−0.517921	+	0.855429i	$0.673294\pi$
$758$	−2.86206	−	19.9132i	−0.103955	−	0.723279i
$759$	13.4518	+	13.4518i	0.488271	+	0.488271i
$760$		0			0
$761$	30.4349	−	30.4349i	1.10326	−	1.10326i	0.109249	−	0.994014i	$-0.465155\pi$
$761$	30.4349	−	30.4349i	1.10326	−	1.10326i	0.994014	−	0.109249i	$-0.0348445\pi$
$762$	−10.0836	−	7.54928i	−0.365290	−	0.273482i
$763$	17.9529	−	7.43633i	0.649938	−	0.269213i
$764$	1.52007	+	0.830218i	0.0549941	+	0.0300362i
$765$		0			0
$766$	−8.14494	+	31.9049i	−0.294289	+	1.15277i
$767$	−72.4377			−2.61557
$768$	30.2220	+	32.4869i	1.09054	+	1.17227i
$769$	7.75534			0.279665			0.139832	−	0.990175i	$-0.455344\pi$
$769$	7.75534			0.279665			0.139832	+	0.990175i	$0.455344\pi$
$770$		0			0
$771$	16.6969	−	40.3098i	0.601323	−	1.45172i
$772$	29.2104	+	15.9539i	1.05131	+	0.574194i
$773$	16.8461	−	6.97787i	0.605911	−	0.250976i	−0.0585684	−	0.998283i	$-0.518654\pi$
$773$	16.8461	−	6.97787i	0.605911	−	0.250976i	0.664479	+	0.747307i	$0.268654\pi$
$774$	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
$778$	2.18532	+	15.2047i	0.0783477	+	0.545115i
$779$	−10.8383	−	26.1660i	−0.388322	−	0.937493i
$780$		0			0
$781$	−5.64113	−	2.33663i	−0.201855	−	0.0836112i
$782$	−9.28246	−	15.6465i	−0.331940	−	0.559519i
$783$			34.9772i			1.24998i
$784$	34.6599	−	22.2647i	1.23785	−	0.795168i
$785$		0			0
$786$	27.8921	−	16.5473i	0.994878	−	0.590221i
$787$	15.0743	+	6.24398i	0.537341	+	0.222574i	0.634815	−	0.772664i	$-0.281076\pi$
$787$	15.0743	+	6.24398i	0.537341	+	0.222574i	−0.0974741	+	0.995238i	$0.531076\pi$
$788$	11.1634	+	1.20132i	0.397679	+	0.0427954i
$789$	8.18241	+	19.7541i	0.291302	+	0.703264i
$790$		0			0
$791$	−1.74271	−	1.74271i	−0.0619635	−	0.0619635i
$792$	−8.19368	−	17.9488i	−0.291150	−	0.637784i
$793$	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
$797$	−0.0914925	+	0.220883i	−0.00324083	+	0.00782406i	−0.925492	−	0.378768i	$-0.876348\pi$
$797$	−0.0914925	+	0.220883i	−0.00324083	+	0.00782406i	0.922251	+	0.386592i	$0.126348\pi$
$798$	35.6614	+	9.10394i	1.26240	+	0.322276i
$799$	7.97853			0.282260
$800$		0			0
$801$	59.5221			2.10311
$802$	33.8797	+	8.64910i	1.19633	+	0.305410i
$803$	−0.913775	+	2.20605i	−0.0322464	+	0.0778497i
$804$	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
$808$	−8.72138	+	23.3721i	−0.306817	+	0.822229i
$809$	−24.8428	−	24.8428i	−0.873427	−	0.873427i	0.119417	−	0.992844i	$-0.461897\pi$
$809$	−24.8428	−	24.8428i	−0.873427	−	0.873427i	−0.992844	+	0.119417i	$0.961897\pi$
$810$		0			0
$811$	4.55425	+	10.9949i	0.159921	+	0.386085i	0.983447	−	0.181194i	$-0.0579962\pi$
$811$	4.55425	+	10.9949i	0.159921	+	0.386085i	−0.823526	+	0.567279i	$0.807996\pi$
$812$	6.64043	−	61.7066i	0.233033	−	2.16548i
$813$	−53.1084	−	21.9982i	−1.86259	−	0.771512i
$814$	16.6891	−	9.90094i	0.584951	−	0.347028i
$815$		0			0
$816$	5.48685	+	30.4467i	0.192078	+	1.06585i
$817$		−	11.4200i		−	0.399537i
$818$	−13.4945	−	22.7465i	−0.471826	−	0.795311i
$819$	−88.4475	−	36.6362i	−3.09061	−	1.28017i
$820$		0			0
$821$	14.5757	+	35.1889i	0.508696	+	1.22810i	0.944635	+	0.328124i	$0.106416\pi$
$821$	14.5757	+	35.1889i	0.508696	+	1.22810i	−0.435939	+	0.899976i	$0.643584\pi$
$822$	−2.74068	−	19.0687i	−0.0955922	−	0.665096i
$823$	−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
$827$	43.4150	−	17.9831i	1.50969	−	0.625333i	0.534194	−	0.845362i	$-0.320615\pi$
$827$	43.4150	−	17.9831i	1.50969	−	0.625333i	0.975493	+	0.220029i	$0.0706153\pi$
$828$	20.7411	−	37.9754i	0.720803	−	1.31974i
$829$	−11.8059	+	28.5019i	−0.410035	+	0.989911i	0.575093	+	0.818088i	$0.304966\pi$
$829$	−11.8059	+	28.5019i	−0.410035	+	0.989911i	−0.985128	+	0.171823i	$0.945034\pi$
$830$		0			0
$831$	65.3667			2.26755
$832$	−12.4091	+	37.2458i	−0.430208	+	1.29127i
$833$	28.7228			0.995187
$834$	18.6608	−	73.0969i	0.646171	−	2.53114i
$835$		0			0
$836$	−3.21705	+	5.89017i	−0.111264	+	0.203716i
$837$	3.46549	−	1.43545i	0.119785	−	0.0496165i
$838$	4.28448	+	3.20766i	0.148005	+	0.110807i
$839$	−8.76568	+	8.76568i	−0.302625	+	0.302625i	−0.842040	−	0.539415i	$-0.818645\pi$
$839$	−8.76568	+	8.76568i	−0.302625	+	0.302625i	0.539415	+	0.842040i	$0.318645\pi$
$840$		0			0
$841$	−18.8556	−	18.8556i	−0.650194	−	0.650194i
$842$	0.643786	+	4.47923i	0.0221863	+	0.154364i
$843$	−2.11688	−	5.11060i	−0.0729091	−	0.176018i
$844$	18.3837	+	22.8175i	0.632793	+	0.785410i
$845$		0			0
$846$	9.68226	+	16.3205i	0.332883	+	0.561109i
$847$			36.5515i			1.25592i
$848$	−13.4103	+	19.3062i	−0.460512	+	0.662979i
$849$		−	5.53135i		−	0.189836i
$850$		0			0
$851$	39.3168	+	16.2856i	1.34776	+	0.558262i
$852$	−2.43638	+	22.6402i	−0.0834689	+	0.775640i
$853$	−11.2155	−	27.0766i	−0.384011	−	0.927084i	−0.991181	−	0.132512i	$-0.957696\pi$
$853$	−11.2155	−	27.0766i	−0.384011	−	0.927084i	0.607171	−	0.794571i	$-0.292304\pi$
$854$	−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	$0.890873\pi$
$858$	17.1542	−	22.9130i	0.585636	−	0.782236i
$859$	13.0928	−	5.42323i	0.446722	−	0.185038i	−0.147970	−	0.988992i	$-0.547274\pi$
$859$	13.0928	−	5.42323i	0.446722	−	0.185038i	0.594692	+	0.803954i	$0.297274\pi$
$860$		0			0
$861$	55.4034	−	133.756i	1.88814	−	4.55838i
$862$	44.9581	+	11.4773i	1.53128	+	0.390918i
$863$	−10.9648			−0.373246			−0.186623	−	0.982432i	$-0.559754\pi$
$863$	−10.9648			−0.373246			−0.186623	+	0.982432i	$0.559754\pi$
$864$	−20.0465	+	17.3615i	−0.681995	+	0.590651i
$865$		0			0
$866$	−2.98268	−	0.761445i	−0.101356	−	0.0258749i
$867$	9.78650	−	23.6267i	0.332367	−	0.802405i
$868$	−6.38632	+	1.87449i	−0.216766	+	0.0636245i
$869$	8.33199	−	3.45122i	0.282643	−	0.117075i
$870$		0			0
$871$	−47.4524	+	47.4524i	−1.60786	+	1.60786i
$872$	12.0213	−	5.48776i	0.407094	−	0.185839i
$873$	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
$877$	−20.1301	−	8.33816i	−0.679745	−	0.281560i	0.0159754	−	0.999872i	$-0.494915\pi$
$877$	−20.1301	−	8.33816i	−0.679745	−	0.281560i	−0.695720	+	0.718313i	$0.744915\pi$
$878$	−30.5024	+	18.0959i	−1.02941	+	0.610706i
$879$		−	29.2988i		−	0.988225i
$880$		0			0
$881$		−	31.0921i		−	1.04752i	−0.851866	−	0.523760i	$-0.824529\pi$
$881$		−	31.0921i		−	1.04752i	0.851866	−	0.523760i	$-0.175471\pi$
$882$	34.8563	+	58.7539i	1.17367	+	1.97835i
$883$	22.3815	+	9.27074i	0.753199	+	0.311985i	0.726046	−	0.687646i	$-0.241356\pi$
$883$	22.3815	+	9.27074i	0.753199	+	0.311985i	0.0271529	+	0.999631i	$0.491356\pi$
$884$	−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	0.694488	−	0.719505i	$-0.255631\pi$
$887$	−0.745073	−	0.745073i	−0.0250171	−	0.0250171i	−0.719505	+	0.694488i	$0.755631\pi$
$888$	−52.9579	−	49.3205i	−1.77715	−	1.65509i
$889$	−9.44601	+	9.44601i	−0.316809	+	0.316809i
$890$		0			0
$891$	−1.47124	+	0.609409i	−0.0492885	+	0.0204160i
$892$	−19.1182	−	10.4418i	−0.640124	−	0.349618i
$893$	2.47018	−	5.96354i	0.0826614	−	0.199562i
$894$	−1.64636	+	6.44901i	−0.0550625	+	0.215687i
$895$		0			0
$896$	38.6620	−	26.8233i	1.29161	−	0.896104i
$897$	62.7717			2.09589
$898$	−9.49186	+	37.1809i	−0.316747	+	1.24074i
$899$	−2.28451	+	5.51529i	−0.0761926	+	0.183945i
$900$		0			0
$901$	−15.1423	+	6.27213i	−0.504462	+	0.208955i
$902$	21.1335	+	15.8220i	0.703670	+	0.526816i
$903$	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
$907$	−17.4912	−	42.2276i	−0.580787	−	1.40214i	−0.892101	−	0.451836i	$-0.850769\pi$
$907$	−17.4912	−	42.2276i	−0.580787	−	1.40214i	0.311314	−	0.950307i	$-0.399231\pi$
$908$	−1.91006	+	1.53891i	−0.0633877	+	0.0510705i
$909$	−38.2204	−	15.8314i	−1.26769	−	0.525095i
$910$		0			0
$911$			32.5610i			1.07880i	0.842051	+	0.539398i	$0.181348\pi$
$911$			32.5610i			1.07880i	−0.842051	+	0.539398i	$0.818652\pi$
$912$	24.4561	+	5.32525i	0.809821	+	0.176337i
$913$			0.470540i			0.0155726i
$914$	19.8427	−	11.7719i	0.656337	−	0.389378i
$915$		0			0
$916$	4.91120	+	0.528509i	0.162271	+	0.0174624i
$917$	−13.1619	−	31.7756i	−0.434643	−	1.04932i
$918$	−18.3024	+	2.63055i	−0.604069	+	0.0868210i
$919$	−30.1203	−	30.1203i	−0.993576	−	0.993576i	0.00640371	−	0.999979i	$-0.497962\pi$
$919$	−30.1203	−	30.1203i	−0.993576	−	0.993576i	−0.999979	+	0.00640371i	$0.997962\pi$
$920$		0			0
$921$	8.90943	−	8.90943i	0.293576	−	0.293576i
$922$	−29.1428	+	38.9262i	−0.959769	+	1.28197i
$923$	−18.6137	+	7.71006i	−0.612678	+	0.253780i
$924$	−32.9190	+	9.66228i	−1.08295	+	0.317866i
$925$		0			0
$926$	−12.6470	−	3.22864i	−0.415607	−	0.106100i
$927$	−45.6451			−1.49918
$928$	3.02150	−	42.0973i	0.0991857	−	1.38191i
$929$	46.0639			1.51131			0.755654	−	0.654971i	$-0.227319\pi$
$929$	46.0639			1.51131			0.755654	+	0.654971i	$0.227319\pi$
$930$		0			0
$931$	8.89268	−	21.4688i	0.291446	−	0.703613i
$932$	−2.52409	−	8.59945i	−0.0826792	−	0.281684i
$933$	81.8063	−	33.8853i	2.67822	−	1.10935i
$934$	−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	0.554472	−	0.832203i	$-0.312920\pi$
$937$	−8.50147	−	8.50147i	−0.277731	−	0.277731i	−0.832203	+	0.554472i	$0.812920\pi$
$938$	79.6179	−	11.4432i	2.59962	−	0.373635i
$939$	−28.0471	−	67.7116i	−0.915281	−	2.20968i
$940$		0			0
$941$	21.7142	+	8.99431i	0.707862	+	0.293206i	0.707420	−	0.706794i	$-0.249859\pi$
$941$	21.7142	+	8.99431i	0.707862	+	0.293206i	0.000442416		1.00000i	$0.499859\pi$
$942$	−42.1315	+	24.9949i	−1.37272	+	0.814379i
$943$			57.8968i			1.88538i
$944$	48.4937	+	33.6842i	1.57833	+	1.09633i
$945$		0			0
$946$	5.43143	+	9.15524i	0.176591	+	0.297663i
$947$	11.7836	+	4.88093i	0.382916	+	0.158609i	0.565834	−	0.824519i	$-0.308554\pi$
$947$	11.7836	+	4.88093i	0.382916	+	0.158609i	−0.182918	+	0.983128i	$0.558554\pi$
$948$	−21.1009	−	26.1900i	−0.685326	−	0.850613i
$949$	3.01513	+	7.27918i	0.0978754	+	0.236292i
$950$		0			0
$951$	−52.6625	−	52.6625i	−1.70770	−	1.70770i
$952$	32.7884	−	1.16608i	1.06268	−	0.0377930i
$953$	9.27815	−	9.27815i	0.300549	−	0.300549i	−0.540680	−	0.841228i	$-0.681833\pi$
$953$	9.27815	−	9.27815i	0.300549	−	0.300549i	0.841228	+	0.540680i	$0.181833\pi$
$954$	−31.2057	−	23.3627i	−1.01032	−	0.756396i
$955$		0			0
$956$	−8.32615	+	15.2446i	−0.269287	+	0.493044i
$957$	−11.7757	+	28.4292i	−0.380656	+	0.918985i
$958$	0.651870	−	2.55346i	0.0210610	−	0.0824987i
$959$	−20.4303			−0.659730
$960$		0			0
$961$	−30.3598			−0.979348
$962$	15.8381	−	62.0399i	0.510639	−	2.00025i
$963$	4.39487	−	10.6102i	0.141623	−	0.341908i
$964$	−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	$0.146317\pi$
$968$	0.883442	+	24.8410i	0.0283949	+	0.798419i
$969$	12.3399	+	12.3399i	0.396416	+	0.396416i
$970$		0			0
$971$	−1.57164	−	3.79427i	−0.0504363	−	0.121764i	0.896653	−	0.442734i	$-0.145991\pi$
$971$	−1.57164	−	3.79427i	−0.0504363	−	0.121764i	−0.947089	+	0.320970i	$0.895991\pi$
$972$	21.3733	+	26.5281i	0.685549	+	0.850890i
$973$	−73.9162	−	30.6171i	−2.36965	−	0.981539i
$974$	−25.7117	−	43.3397i	−0.823855	−	1.38869i
$975$		0			0
$976$	−48.5927	+	8.75699i	−1.55542	+	0.280305i
$977$			45.4460i			1.45394i	0.686667	+	0.726972i	$0.259073\pi$
$977$			45.4460i			1.45394i	−0.686667	+	0.726972i	$0.740927\pi$
$978$	−4.05021	+	2.40283i	−0.129512	+	0.0768340i
$979$	17.4362	+	7.22232i	0.557264	+	0.230827i
$980$		0			0
$981$	8.38629	+	20.2463i	0.267754	+	0.646415i
$982$	13.2771	−	1.90827i	0.423688	−	0.0608954i
$983$	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
$987$	30.4846	−	12.6271i	0.970334	−	0.401926i
$988$	6.23694	+	21.2490i	0.198423	+	0.676020i
$989$	−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	$0.805448\pi$
$992$	−4.29493	+	1.42829i	−0.136364	+	0.0453483i
$993$	−36.0543			−1.14415
$994$	23.3984	+	5.97333i	0.742151	+	0.189463i
$995$		0			0
$996$	1.68376	−	0.494214i	0.0533521	−	0.0156598i
$997$	19.0528	−	7.89192i	0.603407	−	0.249939i	−0.0599995	−	0.998198i	$-0.519110\pi$
$997$	19.0528	−	7.89192i	0.603407	−	0.249939i	0.663407	+	0.748259i	$0.269110\pi$
$998$	6.33792	−	8.46558i	0.200623	−	0.267973i
$999$	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.y.d.301.9	yes	64
5.2	odd	4		800.2.ba.f.749.16		64
5.3	odd	4		800.2.ba.h.749.1		64
5.4	even	2		800.2.y.e.301.8	yes	64
32.5	even	8	inner	800.2.y.d.101.9	✓	64
160.37	odd	8		800.2.ba.h.549.1		64
160.69	even	8		800.2.y.e.101.8	yes	64
160.133	odd	8		800.2.ba.f.549.16		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
800.2.y.d.101.9	✓	64	32.5	even	8	inner
800.2.y.d.301.9	yes	64	1.1	even	1	trivial
800.2.y.e.101.8	yes	64	160.69	even	8
800.2.y.e.301.8	yes	64	5.4	even	2
800.2.ba.f.549.16		64	160.133	odd	8
800.2.ba.f.749.16		64	5.2	odd	4
800.2.ba.h.549.1		64	160.37	odd	8
800.2.ba.h.749.1		64	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 800 = 2^{5} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	800.y (of order \(8\), degree \(4\), minimal)

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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