LMFDB - Embedded newform 847.2.f.t.729.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [847,2,Mod(148,847)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("847.148"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(847, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.f (of order $5$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,-2,1,-8,-1,-12,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 7 x^{10} - 15 x^{9} + 59 x^{8} + 118 x^{7} + 266 x^{6} + 324 x^{5} + 1036 x^{4} + \cdots + 16 $ x^12 - x^11 + 7x^10 - 15x^9 + 59x^8 + 118x^7 + 266x^6 + 324x^5 + 1036x^4 + 376x^3 + 136x^2 + 48x + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			729.1
Root			$0.544351 - 1.67534i$ of defining polynomial
Character	$\chi$	$=$	847.729
Dual form			847.2.f.t.323.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.23415 + 1.62320i) q^{2} +(0.544351 + 1.67534i) q^{3} +(1.73859 - 5.35083i) q^{4} +(2.12464 + 1.54364i) q^{5} +(-3.93558 - 2.85936i) q^{6} +(0.309017 - 0.951057i) q^{7} +(3.09448 + 9.52384i) q^{8} +(-0.0833965 + 0.0605911i) q^{9} -7.25240 q^{10} +9.91087 q^{12} +(1.93173 - 1.40349i) q^{13} +(0.853368 + 2.62640i) q^{14} +(-1.42957 + 4.39978i) q^{15} +(-13.2693 - 9.64068i) q^{16} +(1.93173 + 1.40349i) q^{17} +(0.0879683 - 0.270739i) q^{18} +(-0.534377 - 1.64464i) q^{19} +(11.9536 - 8.68483i) q^{20} +1.76156 q^{21} -0.626198 q^{23} +(-14.2712 + 10.3686i) q^{24} +(0.586179 + 1.80407i) q^{25} +(-2.03763 + 6.27119i) q^{26} +(4.12848 + 2.99952i) q^{27} +(-4.55169 - 3.30700i) q^{28} +(0.534377 - 1.64464i) q^{29} +(-3.94785 - 12.1502i) q^{30} +(1.81094 - 1.31572i) q^{31} +25.2663 q^{32} -6.59392 q^{34} +(2.12464 - 1.54364i) q^{35} +(0.179220 + 0.551584i) q^{36} +(-2.13126 + 6.55936i) q^{37} +(3.86347 + 2.80697i) q^{38} +(3.40286 + 2.47232i) q^{39} +(-8.12672 + 25.0115i) q^{40} +(3.20999 + 9.87934i) q^{41} +(-3.93558 + 2.85936i) q^{42} +7.25240 q^{43} -0.270718 q^{45} +(1.39902 - 1.01645i) q^{46} +(1.97392 + 6.07512i) q^{47} +(8.92829 - 27.4784i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(-4.23799 - 3.07908i) q^{50} +(-1.29978 + 4.00030i) q^{51} +(-4.15133 - 12.7765i) q^{52} +(7.48535 - 5.43842i) q^{53} -14.0925 q^{54} +10.0140 q^{56} +(2.46445 - 1.79053i) q^{57} +(1.47571 + 4.54178i) q^{58} +(-0.544351 + 1.67534i) q^{59} +(21.0570 + 15.2988i) q^{60} +(8.40387 + 6.10577i) q^{61} +(-1.91022 + 5.87904i) q^{62} +(0.0318546 + 0.0980384i) q^{63} +(-29.9102 + 21.7310i) q^{64} +6.27072 q^{65} -6.42003 q^{67} +(10.8683 - 7.89630i) q^{68} +(-0.340872 - 1.04909i) q^{69} +(-2.24111 + 6.89744i) q^{70} +(-6.54071 - 4.75210i) q^{71} +(-0.835128 - 0.606756i) q^{72} +(3.20999 - 9.87934i) q^{73} +(-5.88561 - 18.1140i) q^{74} +(-2.70335 + 1.96410i) q^{75} -9.72928 q^{76} -11.6156 q^{78} +(-12.3394 + 8.96513i) q^{79} +(-13.3106 - 40.9659i) q^{80} +(-2.87343 + 8.84352i) q^{81} +(-23.2078 - 16.8614i) q^{82} +(-10.3356 - 7.50926i) q^{83} +(3.06263 - 9.42580i) q^{84} +(1.93776 + 5.96381i) q^{85} +(-16.2029 + 11.7721i) q^{86} +3.04623 q^{87} -14.1493 q^{89} +(0.604824 - 0.439431i) q^{90} +(-0.737857 - 2.27089i) q^{91} +(-1.08870 + 3.35068i) q^{92} +(3.19007 + 2.31772i) q^{93} +(-14.2712 - 10.3686i) q^{94} +(1.40338 - 4.31916i) q^{95} +(13.7538 + 42.3297i) q^{96} +(6.75973 - 4.91123i) q^{97} +2.76156 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} + q^{3} - 8 q^{4} - q^{5} - 12 q^{6} - 3 q^{7} - 6 q^{8} - 4 q^{9} - 16 q^{10} + 8 q^{12} - 8 q^{13} - 2 q^{14} + 5 q^{15} - 10 q^{16} - 8 q^{17} + 18 q^{18} + 14 q^{20} - 4 q^{21} + 28 q^{23}+ \cdots + 8 q^{98}+O(q^{100}) $ 12 * q - 2 * q^2 + q^3 - 8 * q^4 - q^5 - 12 * q^6 - 3 * q^7 - 6 * q^8 - 4 * q^9 - 16 * q^10 + 8 * q^12 - 8 * q^13 - 2 * q^14 + 5 * q^15 - 10 * q^16 - 8 * q^17 + 18 * q^18 + 14 * q^20 - 4 * q^21 + 28 * q^23 - 20 * q^24 - 2 * q^25 + 12 * q^26 + 19 * q^27 - 8 * q^28 + 8 * q^30 + 13 * q^31 + 136 * q^32 - 48 * q^34 - q^35 - 18 * q^36 + 17 * q^37 - 16 * q^38 + 20 * q^39 + 36 * q^40 - 16 * q^41 - 12 * q^42 + 16 * q^43 - 24 * q^45 - 4 * q^47 - 36 * q^48 - 3 * q^49 - 22 * q^50 + 20 * q^51 + 10 * q^53 + 32 * q^54 + 24 * q^56 - 16 * q^57 + 16 * q^58 - q^59 + 30 * q^60 + 16 * q^61 - 4 * q^62 - 4 * q^63 - 34 * q^64 + 96 * q^65 - 12 * q^67 + 7 * q^69 + 4 * q^70 - 5 * q^71 - 2 * q^72 - 16 * q^73 + 32 * q^74 - 20 * q^75 - 96 * q^76 + 112 * q^78 - 28 * q^79 + 56 * q^80 - 15 * q^81 - 28 * q^82 - 8 * q^83 - 2 * q^84 - 24 * q^85 - 12 * q^86 - 64 * q^87 - 84 * q^89 + 20 * q^90 - 8 * q^91 - 2 * q^92 - 17 * q^93 - 20 * q^94 - 24 * q^95 - 20 * q^96 + 11 * q^97 + 8 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	−2.23415	+	1.62320i	−1.57978	+	1.14778i	−0.662834	+	0.748766i	$0.730647\pi$
$2$	−2.23415	+	1.62320i	−1.57978	+	1.14778i	−0.916946	+	0.399011i	$0.869353\pi$
$3$	0.544351	+	1.67534i	0.314281	+	0.967258i	0.976049	+	0.217550i	$0.0698064\pi$
$3$	0.544351	+	1.67534i	0.314281	+	0.967258i	−0.661768	+	0.749709i	$0.730194\pi$
$4$	1.73859	−	5.35083i	0.869295	−	2.67542i
$5$	2.12464	+	1.54364i	0.950167	+	0.690337i	0.950846	−	0.309663i	$-0.100216\pi$
$5$	2.12464	+	1.54364i	0.950167	+	0.690337i	−0.000679067		1.00000i	$0.500216\pi$
$6$	−3.93558	−	2.85936i	−1.60669	−	1.16733i
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$8$	3.09448	+	9.52384i	1.09406	+	3.36718i
$9$	−0.0833965	+	0.0605911i	−0.0277988	+	0.0201970i
$10$	−7.25240			−2.29341
$11$		0			0
$11$		0			0
$12$	9.91087			2.86102
$13$	1.93173	−	1.40349i	0.535767	−	0.389257i	−0.286744	−	0.958007i	$-0.592573\pi$
$13$	1.93173	−	1.40349i	0.535767	−	0.389257i	0.822510	+	0.568750i	$0.192573\pi$
$14$	0.853368	+	2.62640i	0.228072	+	0.701934i
$15$	−1.42957	+	4.39978i	−0.369114	+	1.13602i
$16$	−13.2693	−	9.64068i	−3.31732	−	2.41017i
$17$	1.93173	+	1.40349i	0.468514	+	0.340396i	0.796862	−	0.604161i	$-0.206492\pi$
$17$	1.93173	+	1.40349i	0.468514	+	0.340396i	−0.328348	+	0.944557i	$0.606492\pi$
$18$	0.0879683	−	0.270739i	0.0207343	−	0.0638137i
$19$	−0.534377	−	1.64464i	−0.122595	−	0.377307i	0.870861	−	0.491530i	$-0.163562\pi$
$19$	−0.534377	−	1.64464i	−0.122595	−	0.377307i	−0.993455	+	0.114223i	$0.963562\pi$
$20$	11.9536	−	8.68483i	2.67291	−	1.94199i
$21$	1.76156			0.384403
$22$		0			0
$23$	−0.626198			−0.130571			−0.0652857	−	0.997867i	$-0.520796\pi$
$23$	−0.626198			−0.130571			−0.0652857	+	0.997867i	$0.520796\pi$
$24$	−14.2712	+	10.3686i	−2.91309	+	2.11649i
$25$	0.586179	+	1.80407i	0.117236	+	0.360815i
$26$	−2.03763	+	6.27119i	−0.399613	+	1.22988i
$27$	4.12848	+	2.99952i	0.794527	+	0.577257i
$28$	−4.55169	−	3.30700i	−0.860189	−	0.624964i
$29$	0.534377	−	1.64464i	0.0992314	−	0.305403i	−0.889102	−	0.457709i	$-0.848670\pi$
$29$	0.534377	−	1.64464i	0.0992314	−	0.305403i	0.988333	+	0.152306i	$0.0486701\pi$
$30$	−3.94785	−	12.1502i	−0.720775	−	2.21832i
$31$	1.81094	−	1.31572i	0.325254	−	0.236311i	−0.413160	−	0.910658i	$-0.635575\pi$
$31$	1.81094	−	1.31572i	0.325254	−	0.236311i	0.738414	+	0.674347i	$0.235575\pi$
$32$	25.2663			4.46650
$33$		0			0
$34$	−6.59392			−1.13085
$35$	2.12464	−	1.54364i	0.359130	−	0.260923i
$36$	0.179220	+	0.551584i	0.0298701	+	0.0919306i
$37$	−2.13126	+	6.55936i	−0.350378	+	1.07835i	0.608264	+	0.793735i	$0.291866\pi$
$37$	−2.13126	+	6.55936i	−0.350378	+	1.07835i	−0.958641	+	0.284617i	$0.908134\pi$
$38$	3.86347	+	2.80697i	0.626737	+	0.455351i
$39$	3.40286	+	2.47232i	0.544894	+	0.395889i
$40$	−8.12672	+	25.0115i	−1.28495	+	3.95466i
$41$	3.20999	+	9.87934i	0.501317	+	1.54289i	0.806876	+	0.590721i	$0.201157\pi$
$41$	3.20999	+	9.87934i	0.501317	+	1.54289i	−0.305559	+	0.952173i	$0.598843\pi$
$42$	−3.93558	+	2.85936i	−0.607273	+	0.441209i
$43$	7.25240			1.10598			0.552990	−	0.833188i	$-0.313487\pi$
$43$	7.25240			1.10598			0.552990	+	0.833188i	$0.313487\pi$
$44$		0			0
$45$	−0.270718			−0.0403563
$46$	1.39902	−	1.01645i	0.206274	−	0.149867i
$47$	1.97392	+	6.07512i	0.287927	+	0.886147i	0.985506	+	0.169640i	$0.0542603\pi$
$47$	1.97392	+	6.07512i	0.287927	+	0.886147i	−0.697580	+	0.716507i	$0.745740\pi$
$48$	8.92829	−	27.4784i	1.28869	−	3.96617i
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$	−4.23799	−	3.07908i	−0.599342	−	0.435448i
$51$	−1.29978	+	4.00030i	−0.182005	+	0.560154i
$52$	−4.15133	−	12.7765i	−0.575686	−	1.77178i
$53$	7.48535	−	5.43842i	1.02819	−	0.747025i	0.0602454	−	0.998184i	$-0.480812\pi$
$53$	7.48535	−	5.43842i	1.02819	−	0.747025i	0.967946	+	0.251159i	$0.0808117\pi$
$54$	−14.0925			−1.91774
$55$		0			0
$56$	10.0140			1.33817
$57$	2.46445	−	1.79053i	0.326424	−	0.237161i
$58$	1.47571	+	4.54178i	0.193771	+	0.596365i
$59$	−0.544351	+	1.67534i	−0.0708685	+	0.218111i	−0.980218	−	0.197923i	$-0.936580\pi$
$59$	−0.544351	+	1.67534i	−0.0708685	+	0.218111i	0.909349	+	0.416034i	$0.136580\pi$
$60$	21.0570	+	15.2988i	2.71845	+	1.97507i
$61$	8.40387	+	6.10577i	1.07601	+	0.781764i	0.976982	−	0.213321i	$-0.0684282\pi$
$61$	8.40387	+	6.10577i	1.07601	+	0.781764i	0.0990233	+	0.995085i	$0.468428\pi$
$62$	−1.91022	+	5.87904i	−0.242598	+	0.746639i
$63$	0.0318546	+	0.0980384i	0.00401330	+	0.0123517i
$64$	−29.9102	+	21.7310i	−3.73878	+	2.71638i
$65$	6.27072			0.777787
$66$		0			0
$67$	−6.42003			−0.784332			−0.392166	−	0.919895i	$-0.628274\pi$
$67$	−6.42003			−0.784332			−0.392166	+	0.919895i	$0.628274\pi$
$68$	10.8683	−	7.89630i	1.31798	−	0.957567i
$69$	−0.340872	−	1.04909i	−0.0410361	−	0.126296i
$70$	−2.24111	+	6.89744i	−0.267864	+	0.824402i
$71$	−6.54071	−	4.75210i	−0.776239	−	0.563971i	0.127609	−	0.991825i	$-0.459270\pi$
$71$	−6.54071	−	4.75210i	−0.776239	−	0.563971i	−0.903848	+	0.427854i	$0.859270\pi$
$72$	−0.835128	−	0.606756i	−0.0984208	−	0.0715069i
$73$	3.20999	−	9.87934i	0.375701	−	1.15629i	−0.567303	−	0.823509i	$-0.692013\pi$
$73$	3.20999	−	9.87934i	0.375701	−	1.15629i	0.943004	−	0.332780i	$-0.107987\pi$
$74$	−5.88561	−	18.1140i	−0.684188	−	2.10571i
$75$	−2.70335	+	1.96410i	−0.312156	+	0.226795i
$76$	−9.72928			−1.11603
$77$		0			0
$78$	−11.6156			−1.31520
$79$	−12.3394	+	8.96513i	−1.38830	+	1.00866i	−0.392247	+	0.919860i	$0.628302\pi$
$79$	−12.3394	+	8.96513i	−1.38830	+	1.00866i	−0.996050	+	0.0887962i	$0.971698\pi$
$80$	−13.3106	−	40.9659i	−1.48817	−	4.58013i
$81$	−2.87343	+	8.84352i	−0.319270	+	0.982613i
$82$	−23.2078	−	16.8614i	−2.56287	−	1.86203i
$83$	−10.3356	−	7.50926i	−1.13448	−	0.824248i	−0.148139	−	0.988966i	$-0.547328\pi$
$83$	−10.3356	−	7.50926i	−1.13448	−	0.824248i	−0.986341	+	0.164718i	$0.947328\pi$
$84$	3.06263	−	9.42580i	0.334160	−	1.02844i
$85$	1.93776	+	5.96381i	0.210179	+	0.646866i
$86$	−16.2029	+	11.7721i	−1.74721	+	1.26942i
$87$	3.04623			0.326590
$88$		0			0
$89$	−14.1493			−1.49982			−0.749912	−	0.661538i	$-0.769904\pi$
$89$	−14.1493			−1.49982			−0.749912	+	0.661538i	$0.769904\pi$
$90$	0.604824	−	0.439431i	0.0637541	−	0.0463200i
$91$	−0.737857	−	2.27089i	−0.0773484	−	0.238054i
$92$	−1.08870	+	3.35068i	−0.113505	+	0.349333i
$93$	3.19007	+	2.31772i	0.330795	+	0.240337i
$94$	−14.2712	−	10.3686i	−1.47196	−	1.06944i
$95$	1.40338	−	4.31916i	0.143984	−	0.443137i
$96$	13.7538	+	42.3297i	1.40374	+	4.32026i
$97$	6.75973	−	4.91123i	0.686346	−	0.498660i	−0.189111	−	0.981956i	$-0.560561\pi$
$97$	6.75973	−	4.91123i	0.686346	−	0.498660i	0.875457	+	0.483296i	$0.160561\pi$
$98$	2.76156			0.278959
$99$		0			0
$100$	10.6724			1.06724
$101$	11.2019	−	8.13866i	1.11463	−	0.809827i	0.131245	−	0.991350i	$-0.458103\pi$
$101$	11.2019	−	8.13866i	1.11463	−	0.809827i	0.983387	+	0.181523i	$0.0581026\pi$
$102$	−3.58941	−	11.0471i	−0.355404	−	1.09382i
$103$	−0.905170	+	2.78583i	−0.0891891	+	0.274496i	−0.985696	−	0.168534i	$-0.946097\pi$
$103$	−0.905170	+	2.78583i	−0.0891891	+	0.274496i	0.896507	+	0.443030i	$0.146097\pi$
$104$	19.3443	+	14.0545i	1.89686	+	1.37815i
$105$	3.74267	+	2.71921i	0.365247	+	0.265368i
$106$	−7.89570	+	24.3005i	−0.766898	+	2.36027i
$107$	1.06875	+	3.28929i	0.103320	+	0.317988i	0.989333	−	0.145674i	$-0.0465352\pi$
$107$	1.06875	+	3.28929i	0.103320	+	0.317988i	−0.886012	+	0.463662i	$0.846535\pi$
$108$	23.2277	−	16.8759i	2.23508	−	1.62388i
$109$	−16.2341			−1.55494			−0.777471	−	0.628919i	$-0.783498\pi$
$109$	−16.2341			−1.55494			−0.777471	+	0.628919i	$0.783498\pi$
$110$		0			0
$111$	−12.1493			−1.15316
$112$	−13.2693	+	9.64068i	−1.25383	+	0.910959i
$113$	2.19497	+	6.75543i	0.206486	+	0.635498i	0.999649	+	0.0264888i	$0.00843265\pi$
$113$	2.19497	+	6.75543i	0.206486	+	0.635498i	−0.793163	+	0.609009i	$0.791567\pi$
$114$	−2.59955	+	8.00061i	−0.243471	+	0.749325i
$115$	−1.33044	−	0.966625i	−0.124065	−	0.0901382i
$116$	−7.87115	−	5.71873i	−0.730818	−	0.530971i
$117$	−0.0760610	+	0.234092i	−0.00703184	+	0.0216418i
$118$	−1.50326	−	4.62655i	−0.138386	−	0.425908i
$119$	1.93173	−	1.40349i	0.177082	−	0.128657i
$120$	−46.3265			−4.22901
$121$		0			0
$122$	−28.6864			−2.59714
$123$	−14.8039	+	10.7557i	−1.33482	+	0.969805i
$124$	−3.89174	−	11.9775i	−0.349488	−	1.07561i
$125$	2.51828	−	7.75046i	0.225241	−	0.693222i
$126$	−0.230304	−	0.167326i	−0.0205171	−	0.0149066i
$127$	3.67410	+	2.66939i	0.326024	+	0.236870i	0.738741	−	0.673989i	$-0.235420\pi$
$127$	3.67410	+	2.66939i	0.326024	+	0.236870i	−0.412718	+	0.910859i	$0.635420\pi$
$128$	15.9345	−	49.0412i	1.40842	−	4.33467i
$129$	3.94785	+	12.1502i	0.347589	+	1.06977i
$130$	−14.0097	+	10.1786i	−1.22873	+	0.892726i
$131$	−6.27072			−0.547875			−0.273938	−	0.961747i	$-0.588326\pi$
$131$	−6.27072			−0.547875			−0.273938	+	0.961747i	$0.588326\pi$
$132$		0			0
$133$	−1.72928			−0.149948
$134$	14.3433	−	10.4210i	1.23907	−	0.900238i
$135$	4.14136	+	12.7458i	0.356431	+	1.09698i
$136$	−7.38887	+	22.7406i	−0.633590	+	1.94999i
$137$	−7.60614	−	5.52619i	−0.649837	−	0.472134i	0.213379	−	0.976970i	$-0.431553\pi$
$137$	−7.60614	−	5.52619i	−0.649837	−	0.472134i	−0.863216	+	0.504836i	$0.831553\pi$
$138$	2.46445	+	1.79053i	0.209788	+	0.152420i
$139$	4.88919	−	15.0474i	0.414695	−	1.27630i	−0.497828	−	0.867276i	$-0.665869\pi$
$139$	4.88919	−	15.0474i	0.414695	−	1.27630i	0.912523	−	0.409025i	$-0.134131\pi$
$140$	−4.56588	−	14.0523i	−0.385888	−	1.18764i
$141$	−9.10338	+	6.61399i	−0.766643	+	0.556999i
$142$	22.3265			1.87360
$143$		0			0
$144$	1.69075			0.140896
$145$	3.67410	−	2.66939i	0.305117	−	0.221681i
$146$	8.86458	+	27.2824i	0.733638	+	2.25790i
$147$	0.544351	−	1.67534i	0.0448973	−	0.138180i
$148$	31.3926	+	22.8081i	2.58046	+	1.87481i
$149$	−2.79804	−	2.03289i	−0.229224	−	0.166541i	0.467245	−	0.884128i	$-0.345247\pi$
$149$	−2.79804	−	2.03289i	−0.229224	−	0.166541i	−0.696469	+	0.717587i	$0.745247\pi$
$150$	2.85155	−	8.77618i	0.232828	−	0.716572i
$151$	−3.18245	−	9.79457i	−0.258984	−	0.797071i	−0.993018	−	0.117959i	$-0.962365\pi$
$151$	−3.18245	−	9.79457i	−0.258984	−	0.797071i	0.734034	−	0.679112i	$-0.237635\pi$
$152$	14.0097	−	10.1786i	1.13634	−	0.825597i
$153$	−0.246139			−0.0198991
$154$		0			0
$155$	5.87859			0.472180
$156$	19.1452	−	13.9098i	1.53284	−	1.11367i
$157$	3.50337	+	10.7823i	0.279600	+	0.860519i	0.987966	+	0.154674i	$0.0494327\pi$
$157$	3.50337	+	10.7823i	0.279600	+	0.860519i	−0.708366	+	0.705845i	$0.750567\pi$
$158$	13.0159	−	40.0588i	1.03549	−	3.18691i
$159$	13.1859	+	9.58009i	1.04571	+	0.759751i
$160$	53.6819	+	39.0022i	4.24392	+	3.08339i
$161$	−0.193506	+	0.595550i	−0.0152504	+	0.0469359i
$162$	−7.93515	−	24.4219i	−0.623444	−	1.91876i
$163$	7.87115	−	5.71873i	0.616516	−	0.447925i	−0.235187	−	0.971950i	$-0.575570\pi$
$163$	7.87115	−	5.71873i	0.616516	−	0.447925i	0.851703	+	0.524025i	$0.175570\pi$
$164$	58.4436			4.56368
$165$		0			0
$166$	35.2803			2.73828
$167$	−18.2068	+	13.2280i	−1.40888	+	1.02361i	−0.415397	+	0.909640i	$0.636357\pi$
$167$	−18.2068	+	13.2280i	−1.40888	+	1.02361i	−0.993484	+	0.113972i	$0.963643\pi$
$168$	5.45111	+	16.7768i	0.420562	+	1.29436i
$169$	−2.25540	+	6.94140i	−0.173492	+	0.533954i
$170$	−14.0097	−	10.1786i	−1.07450	−	0.780667i
$171$	0.144216	+	0.104779i	0.0110285	+	0.00801265i
$172$	12.6089	−	38.8064i	0.961423	−	2.95896i
$173$	2.14124	+	6.59005i	0.162795	+	0.501032i	0.998867	−	0.0475877i	$-0.0151533\pi$
$173$	2.14124	+	6.59005i	0.162795	+	0.501032i	−0.836072	+	0.548620i	$0.815153\pi$
$174$	−6.80572	+	4.94465i	−0.515940	+	0.374853i
$175$	1.89692			0.143393
$176$		0			0
$177$	−3.10308			−0.233242
$178$	31.6116	−	22.9672i	2.36939	−	1.72146i
$179$	4.30867	+	13.2607i	0.322045	+	0.991153i	0.972757	+	0.231828i	$0.0744706\pi$
$179$	4.30867	+	13.2607i	0.322045	+	0.991153i	−0.650712	+	0.759325i	$0.725529\pi$
$180$	−0.470668	+	1.44857i	−0.0350815	+	0.107970i
$181$	−2.56267	−	1.86189i	−0.190482	−	0.138393i	0.488457	−	0.872588i	$-0.337560\pi$
$181$	−2.56267	−	1.86189i	−0.190482	−	0.138393i	−0.678939	+	0.734195i	$0.737560\pi$
$182$	5.33460	+	3.87581i	0.395427	+	0.287294i
$183$	−5.65459	+	17.4030i	−0.417999	+	1.28647i
$184$	−1.93776	−	5.96381i	−0.142853	−	0.439658i
$185$	−14.6535	+	10.6464i	−1.07734	+	0.782736i
$186$	−10.8892			−0.798436
$187$		0			0
$188$	35.9388			2.62110
$189$	4.12848	−	2.99952i	0.300303	−	0.218183i
$190$	3.87552	+	11.9276i	0.281160	+	0.865320i
$191$	5.67216	−	17.4571i	0.410423	−	1.26315i	−0.505859	−	0.862616i	$-0.668824\pi$
$191$	5.67216	−	17.4571i	0.410423	−	1.26315i	0.916281	−	0.400535i	$-0.131176\pi$
$192$	−52.6885	−	38.2805i	−3.80247	−	2.76265i
$193$	2.46445	+	1.79053i	0.177395	+	0.128885i	0.672939	−	0.739698i	$-0.265031\pi$
$193$	2.46445	+	1.79053i	0.177395	+	0.128885i	−0.495544	+	0.868583i	$0.665031\pi$
$194$	−7.13030	+	21.9448i	−0.511926	+	1.57555i
$195$	3.41347	+	10.5056i	0.244444	+	0.752321i
$196$	−4.55169	+	3.30700i	−0.325121	+	0.236214i
$197$	4.95377			0.352942			0.176471	−	0.984306i	$-0.443532\pi$
$197$	4.95377			0.352942			0.176471	+	0.984306i	$0.443532\pi$
$198$		0			0
$199$	15.7047			1.11328			0.556638	−	0.830755i	$-0.312091\pi$
$199$	15.7047			1.11328			0.556638	+	0.830755i	$0.312091\pi$
$200$	−15.3678	+	11.1654i	−1.08667	+	0.789510i
$201$	−3.49475	−	10.7557i	−0.246501	−	0.758651i
$202$	−11.8160	+	36.3659i	−0.831371	+	2.55870i
$203$	−1.39902	−	1.01645i	−0.0981918	−	0.0713405i
$204$	19.1452	+	13.9098i	1.34043	+	0.973879i
$205$	−8.43008	+	25.9451i	−0.588782	+	1.81209i
$206$	−2.49968	−	7.69322i	−0.174161	−	0.536012i
$207$	0.0522227	−	0.0379420i	0.00362973	−	0.00263715i
$208$	−39.1633			−2.71548
$209$		0			0
$210$	−12.7755			−0.881594
$211$	−14.1991	+	10.3162i	−0.977505	+	0.710199i	−0.957150	−	0.289594i	$-0.906480\pi$
$211$	−14.1991	+	10.3162i	−0.977505	+	0.710199i	−0.0203551	+	0.999793i	$0.506480\pi$
$212$	−16.0861	−	49.5080i	−1.10480	−	3.40022i
$213$	4.40095	−	13.5447i	0.301548	−	0.928069i
$214$	−7.72694	−	5.61395i	−0.528203	−	0.383762i
$215$	15.4087	+	11.1951i	1.05087	+	0.763499i
$216$	−15.7914	+	48.6009i	−1.07447	+	3.30687i
$217$	−0.691717	−	2.12889i	−0.0469568	−	0.144518i
$218$	36.2693	−	26.3512i	2.45647	−	1.78473i
$219$	18.2986			1.23651
$220$		0			0
$221$	5.70138			0.383516
$222$	27.1433	−	19.7208i	1.82174	−	1.32357i
$223$	−6.88930	−	21.2031i	−0.461342	−	1.41986i	−0.863525	−	0.504305i	$-0.831749\pi$
$223$	−6.88930	−	21.2031i	−0.461342	−	1.41986i	0.402183	−	0.915559i	$-0.368251\pi$
$224$	7.80773	−	24.0297i	0.521676	−	1.60555i
$225$	−0.158196	−	0.114936i	−0.0105464	−	0.00766241i
$226$	−15.8693	−	11.5297i	−1.05561	−	0.766947i
$227$	4.40989	−	13.5723i	0.292695	−	0.900823i	−0.691291	−	0.722576i	$-0.742958\pi$
$227$	4.40989	−	13.5723i	0.292695	−	0.900823i	0.983986	−	0.178246i	$-0.0570423\pi$
$228$	−5.29615	−	16.2999i	−0.350746	−	1.07948i
$229$	3.13785	−	2.27978i	0.207355	−	0.150652i	−0.479261	−	0.877672i	$-0.659095\pi$
$229$	3.13785	−	2.27978i	0.207355	−	0.150652i	0.686616	+	0.727020i	$0.259095\pi$
$230$	4.54144			0.299453
$231$		0			0
$232$	17.3169			1.13691
$233$	−5.40670	+	3.92820i	−0.354205	+	0.257345i	−0.750631	−	0.660722i	$-0.770250\pi$
$233$	−5.40670	+	3.92820i	−0.354205	+	0.257345i	0.396426	+	0.918067i	$0.370250\pi$
$234$	−0.210047	−	0.646458i	−0.0137312	−	0.0422603i
$235$	−5.18392	+	15.9545i	−0.338162	+	1.04075i
$236$	8.01806	+	5.82546i	0.521931	+	0.379205i
$237$	−21.7366	−	15.7926i	−1.41195	−	1.02584i
$238$	−2.03763	+	6.27119i	−0.132080	+	0.406501i
$239$	−1.40338	−	4.31916i	−0.0907772	−	0.279383i	0.895353	−	0.445357i	$-0.146923\pi$
$239$	−1.40338	−	4.31916i	−0.0907772	−	0.279383i	−0.986130	+	0.165974i	$0.946923\pi$
$240$	61.3862	−	44.5997i	3.96246	−	2.87890i
$241$	−3.70470			−0.238641			−0.119320	−	0.992856i	$-0.538072\pi$
$241$	−3.70470			−0.238641			−0.119320	+	0.992856i	$0.538072\pi$
$242$		0			0
$243$	−1.07081			−0.0686924
$244$	47.2818	−	34.3523i	3.02691	−	2.19918i
$245$	−0.811540	−	2.49766i	−0.0518474	−	0.159570i
$246$	15.6155	−	48.0595i	0.995606	−	3.06416i
$247$	−3.34051	−	2.42703i	−0.212552	−	0.154428i
$248$	18.1347	+	13.1756i	1.15155	+	0.836651i
$249$	6.95436	−	21.4033i	0.440715	−	1.35638i
$250$	6.95436	+	21.4033i	0.439833	+	1.35367i
$251$	−6.88406	+	5.00156i	−0.434518	+	0.315696i	−0.783453	−	0.621451i	$-0.786543\pi$
$251$	−6.88406	+	5.00156i	−0.434518	+	0.315696i	0.348935	+	0.937147i	$0.386543\pi$
$252$	0.579969			0.0365346
$253$		0			0
$254$	−12.5414			−0.786920
$255$	−8.93659	+	6.49281i	−0.559631	+	0.406596i
$256$	21.1545	+	65.1070i	1.32216	+	4.06919i
$257$	−0.912766	+	2.80920i	−0.0569367	+	0.175233i	−0.975480	−	0.220086i	$-0.929366\pi$
$257$	−0.912766	+	2.80920i	−0.0569367	+	0.175233i	0.918544	+	0.395320i	$0.129366\pi$
$258$	−28.5424	−	20.7372i	−1.77697	−	1.29104i
$259$	5.57972	+	4.05391i	0.346707	+	0.251897i
$260$	10.9022	−	33.5536i	0.676127	−	2.08090i
$261$	0.0550856	+	0.169536i	0.00340971	+	0.0104940i
$262$	14.0097	−	10.1786i	0.865522	−	0.628839i
$263$	−16.0000			−0.986602			−0.493301	−	0.869859i	$-0.664210\pi$
$263$	−16.0000			−0.986602			−0.493301	+	0.869859i	$0.664210\pi$
$264$		0			0
$265$	24.2986			1.49265
$266$	3.86347	−	2.80697i	0.236884	−	0.172107i
$267$	−7.70219	−	23.7049i	−0.471367	−	1.45072i
$268$	−11.1618	+	34.3525i	−0.681816	+	2.09841i
$269$	5.48150	+	3.98255i	0.334213	+	0.242820i	0.742216	−	0.670160i	$-0.233775\pi$
$269$	5.48150	+	3.98255i	0.334213	+	0.242820i	−0.408003	+	0.912981i	$0.633775\pi$
$270$	−29.9414	−	21.7537i	−1.82217	−	1.32389i
$271$	1.06875	−	3.28929i	0.0649222	−	0.199810i	−0.913334	−	0.407212i	$-0.866501\pi$
$271$	1.06875	−	3.28929i	0.0649222	−	0.199810i	0.978256	+	0.207402i	$0.0665009\pi$
$272$	−12.1021	−	37.2465i	−0.733798	−	2.25840i
$273$	3.40286	−	2.47232i	0.205951	−	0.149632i
$274$	25.9634			1.56850
$275$		0			0
$276$	−6.20617			−0.373567
$277$	9.27017	−	6.73517i	0.556991	−	0.404677i	−0.273366	−	0.961910i	$-0.588137\pi$
$277$	9.27017	−	6.73517i	0.556991	−	0.404677i	0.830356	+	0.557233i	$0.188137\pi$
$278$	13.5018	+	41.5542i	0.809782	+	2.49225i
$279$	−0.0713047	+	0.219453i	−0.00426890	+	0.0131383i
$280$	21.2760	+	15.4579i	1.27149	+	0.923789i
$281$	18.0625	+	13.1232i	1.07752	+	0.782865i	0.977249	−	0.212095i	$-0.0680287\pi$
$281$	18.0625	+	13.1232i	1.07752	+	0.782865i	0.100272	+	0.994960i	$0.468029\pi$
$282$	9.60244	−	29.5533i	0.571817	−	1.75987i
$283$	−3.82043	−	11.7581i	−0.227101	−	0.698945i	−0.998072	−	0.0620743i	$-0.980228\pi$
$283$	−3.82043	−	11.7581i	−0.227101	−	0.698945i	0.770970	−	0.636871i	$-0.219772\pi$
$284$	−36.7993	+	26.7363i	−2.18364	+	1.58651i
$285$	8.00000			0.473879
$286$		0			0
$287$	10.3878			0.613170
$288$	−2.10712	+	1.53092i	−0.124163	+	0.0902101i
$289$	−3.49147	−	10.7456i	−0.205380	−	0.632096i
$290$	−3.87552	+	11.9276i	−0.227578	+	0.700414i
$291$	11.9076	+	8.65141i	0.698038	+	0.507155i
$292$	−47.2818	−	34.3523i	−2.76696	−	2.01031i
$293$	0.665524	−	2.04827i	0.0388803	−	0.119661i	−0.929733	−	0.368236i	$-0.879962\pi$
$293$	0.665524	−	2.04827i	0.0388803	−	0.119661i	0.968613	+	0.248574i	$0.0799620\pi$
$294$	1.50326	+	4.62655i	0.0876717	+	0.269826i
$295$	−3.74267	+	2.71921i	−0.217907	+	0.158319i
$296$	−69.0654			−4.01434
$297$		0			0
$298$	9.55102			0.553276
$299$	−1.20965	+	0.878861i	−0.0699558	+	0.0508258i
$300$	5.80955	+	17.8799i	0.335414	+	1.03230i
$301$	2.24111	−	6.89744i	0.129176	−	0.397562i
$302$	23.0086	+	16.7168i	1.32400	+	0.961941i
$303$	19.7328	+	14.3367i	1.13362	+	0.823623i
$304$	−8.76470	+	26.9750i	−0.502690	+	1.54712i
$305$	8.43008	+	25.9451i	0.482705	+	1.48561i
$306$	0.549910	−	0.399533i	0.0314363	−	0.0228398i
$307$	−31.8217			−1.81616			−0.908081	−	0.418794i	$-0.862453\pi$
$307$	−31.8217			−1.81616			−0.908081	+	0.418794i	$0.862453\pi$
$308$		0			0
$309$	−5.15994			−0.293539
$310$	−13.1336	+	9.54215i	−0.745941	+	0.541958i
$311$	−3.37731	−	10.3943i	−0.191509	−	0.589405i	−1.00000		0.000895774i	$-0.999715\pi$
$311$	−3.37731	−	10.3943i	−0.191509	−	0.589405i	0.808490	−	0.588510i	$-0.200285\pi$
$312$	−13.0159	+	40.0588i	−0.736881	+	2.26789i
$313$	−5.98811	−	4.35062i	−0.338468	−	0.245911i	0.405547	−	0.914074i	$-0.367081\pi$
$313$	−5.98811	−	4.35062i	−0.338468	−	0.245911i	−0.744015	+	0.668163i	$0.767081\pi$
$314$	−25.3289	−	18.4025i	−1.42939	−	1.03851i
$315$	−0.0836565	+	0.257468i	−0.00471351	+	0.0145067i
$316$	26.5177	+	81.6130i	1.49174	+	4.59109i
$317$	7.19776	−	5.22948i	0.404266	−	0.293717i	−0.367010	−	0.930217i	$-0.619619\pi$
$317$	7.19776	−	5.22948i	0.404266	−	0.293717i	0.771276	+	0.636500i	$0.219619\pi$
$318$	−45.0096			−2.52401
$319$		0			0
$320$	−97.0933			−5.42768
$321$	−4.92890	+	3.58106i	−0.275104	+	0.199875i
$322$	−0.534377	−	1.64464i	−0.0297797	−	0.0916525i
$323$	1.27596	−	3.92701i	0.0709965	−	0.218505i
$324$	42.3245	+	30.7505i	2.35136	+	1.70836i
$325$	3.66434	+	2.66230i	0.203261	+	0.147678i
$326$	−8.30266	+	25.5530i	−0.459842	+	1.41525i
$327$	−8.83704	−	27.1976i	−0.488689	−	1.50403i
$328$	−84.1560	+	61.1429i	−4.64674	+	3.37605i
$329$	6.38776			0.352168
$330$		0			0
$331$	8.56165			0.470591			0.235295	−	0.971924i	$-0.424394\pi$
$331$	8.56165			0.470591			0.235295	+	0.971924i	$0.424394\pi$
$332$	−58.1502	+	42.2486i	−3.19140	+	2.31869i
$333$	−0.219699	−	0.676163i	−0.0120394	−	0.0370535i
$334$	19.2049	−	59.1065i	1.05084	−	3.23416i
$335$	−13.6402	−	9.91022i	−0.745246	−	0.541453i
$336$	−23.3746	−	16.9826i	−1.27519	−	0.926478i
$337$	−3.00651	+	9.25310i	−0.163775	+	0.504048i	−0.998944	−	0.0459455i	$-0.985370\pi$
$337$	−3.00651	+	9.25310i	−0.163775	+	0.504048i	0.835169	+	0.549994i	$0.185370\pi$
$338$	−6.22841	−	19.1691i	−0.338781	−	1.04266i
$339$	−10.1228	+	7.35466i	−0.549796	+	0.399450i
$340$	35.2803			1.91334
$341$		0			0
$342$	−0.492277			−0.0266193
$343$	−0.809017	+	0.587785i	−0.0436828	+	0.0317374i
$344$	22.4424	+	69.0706i	1.21001	+	3.72404i
$345$	0.895196	−	2.75513i	0.0481958	−	0.148331i
$346$	−15.4808	−	11.2475i	−0.832255	−	0.604668i
$347$	−12.0059	−	8.72277i	−0.644508	−	0.468263i	0.216888	−	0.976197i	$-0.430409\pi$
$347$	−12.0059	−	8.72277i	−0.644508	−	0.468263i	−0.861396	+	0.507934i	$0.830409\pi$
$348$	5.29615	−	16.2999i	0.283903	−	0.873764i
$349$	5.02033	+	15.4510i	0.268732	+	0.827073i	0.990810	+	0.135261i	$0.0431873\pi$
$349$	5.02033	+	15.4510i	0.268732	+	0.827073i	−0.722078	+	0.691812i	$0.756813\pi$
$350$	−4.23799	+	3.07908i	−0.226530	+	0.164584i
$351$	12.1849			0.650383
$352$		0			0
$353$	30.8603			1.64253			0.821263	−	0.570549i	$-0.193270\pi$
$353$	30.8603			1.64253			0.821263	+	0.570549i	$0.193270\pi$
$354$	6.93274	−	5.03693i	0.368471	−	0.267710i
$355$	−6.56111	−	20.1930i	−0.348227	−	1.07173i
$356$	−24.5999	+	75.7106i	−1.30379	+	4.01265i
$357$	3.40286	+	2.47232i	0.180098	+	0.130849i
$358$	−31.1510	−	22.6325i	−1.64638	−	1.19617i
$359$	−3.64449	+	11.2166i	−0.192349	+	0.591990i	0.807648	+	0.589665i	$0.200740\pi$
$359$	−3.64449	+	11.2166i	−0.192349	+	0.591990i	−0.999997	+	0.00232497i	$0.999260\pi$
$360$	−0.837733	−	2.57828i	−0.0441524	−	0.135887i
$361$	12.9520	−	9.41020i	0.681686	−	0.495274i
$362$	8.74760			0.459764
$363$		0			0
$364$	−13.4340			−0.704132
$365$	22.0702	−	16.0350i	1.15521	−	0.839308i
$366$	−15.6155	−	48.0595i	−0.816233	−	2.51211i
$367$	−1.09868	+	3.38138i	−0.0573504	+	0.176506i	−0.975628	−	0.219430i	$-0.929580\pi$
$367$	−1.09868	+	3.38138i	−0.0573504	+	0.176506i	0.918278	+	0.395937i	$0.129580\pi$
$368$	8.30919	+	6.03698i	0.433146	+	0.314699i
$369$	−0.866302	−	0.629405i	−0.0450979	−	0.0327655i
$370$	15.4568	−	47.5711i	0.803559	−	2.47310i
$371$	−2.85915	−	8.79955i	−0.148440	−	0.456850i
$372$	17.9480	−	13.0400i	0.930559	−	0.676091i
$373$	22.5048			1.16525			0.582627	−	0.812740i	$-0.302025\pi$
$373$	22.5048			1.16525			0.582627	+	0.812740i	$0.302025\pi$
$374$		0			0
$375$	14.3555			0.741314
$376$	−51.7501	+	37.5987i	−2.66881	+	1.93900i
$377$	−1.27596	−	3.92701i	−0.0657154	−	0.202251i
$378$	−4.35481	+	13.4027i	−0.223987	+	0.689362i
$379$	−18.9550	−	13.7716i	−0.973651	−	0.707399i	−0.0173701	−	0.999849i	$-0.505529\pi$
$379$	−18.9550	−	13.7716i	−0.973651	−	0.707399i	−0.956281	+	0.292450i	$0.905529\pi$
$380$	−20.6712	−	15.0185i	−1.06041	−	0.770433i
$381$	−2.47214	+	7.60845i	−0.126651	+	0.389793i
$382$	15.6640	+	48.2088i	0.801439	+	2.46658i
$383$	2.77193	−	2.01392i	0.141639	−	0.102907i	−0.514709	−	0.857365i	$-0.672100\pi$
$383$	2.77193	−	2.01392i	0.141639	−	0.102907i	0.656348	+	0.754458i	$0.272100\pi$
$384$	90.8347			4.63539
$385$		0			0
$386$	−8.41233			−0.428177
$387$	−0.604824	+	0.439431i	−0.0307449	+	0.0223375i
$388$	−14.5268	−	44.7088i	−0.737485	−	2.26974i
$389$	2.48971	−	7.66252i	0.126233	−	0.388505i	−0.867891	−	0.496755i	$-0.834525\pi$
$389$	2.48971	−	7.66252i	0.126233	−	0.388505i	0.994124	+	0.108250i	$0.0345247\pi$
$390$	−24.6789	−	17.9303i	−1.24966	−	0.907934i
$391$	−1.20965	−	0.878861i	−0.0611746	−	0.0444459i
$392$	3.09448	−	9.52384i	0.156295	−	0.481026i
$393$	−3.41347	−	10.5056i	−0.172187	−	0.529937i
$394$	−11.0675	+	8.04097i	−0.557570	+	0.405098i
$395$	−40.0558			−2.01543
$396$		0			0
$397$	−26.3632			−1.32313			−0.661565	−	0.749888i	$-0.730107\pi$
$397$	−26.3632			−1.32313			−0.661565	+	0.749888i	$0.730107\pi$
$398$	−35.0866	+	25.4919i	−1.75873	+	1.27779i
$399$	−0.941336	−	2.89714i	−0.0471258	−	0.145038i
$400$	9.61434	−	29.5899i	0.480717	−	1.47950i
$401$	18.2816	+	13.2823i	0.912937	+	0.663288i	0.941756	−	0.336297i	$-0.109175\pi$
$401$	18.2816	+	13.2823i	0.912937	+	0.663288i	−0.0288186	+	0.999585i	$0.509175\pi$
$402$	25.2665	+	18.3572i	1.26018	+	0.915574i
$403$	1.65165	−	5.08326i	0.0822746	−	0.253215i
$404$	−24.0731	−	74.0893i	−1.19768	−	3.68608i
$405$	−19.7562	+	14.3537i	−0.981694	+	0.713243i
$406$	4.77551			0.237005
$407$		0			0
$408$	−42.1204			−2.08527
$409$	−7.52781	+	5.46927i	−0.372226	+	0.270438i	−0.758133	−	0.652099i	$-0.773888\pi$
$409$	−7.52781	+	5.46927i	−0.372226	+	0.270438i	0.385907	+	0.922538i	$0.373888\pi$
$410$	−23.2801	−	71.6489i	−1.14972	−	3.53849i
$411$	5.11783	−	15.7511i	0.252444	−	0.776943i
$412$	13.3328	+	9.68683i	0.656859	+	0.477236i
$413$	1.42513	+	1.03542i	0.0701260	+	0.0509496i
$414$	−0.0550856	+	0.169536i	−0.00270731	+	0.00833224i
$415$	−10.3678	−	31.9089i	−0.508937	−	1.56635i
$416$	48.8079	−	35.4610i	2.39300	−	1.73862i
$417$	27.8709			1.36484
$418$		0			0
$419$	−13.8463			−0.676437			−0.338218	−	0.941068i	$-0.609824\pi$
$419$	−13.8463			−0.676437			−0.338218	+	0.941068i	$0.609824\pi$
$420$	21.0570	−	15.2988i	1.02748	−	0.746506i
$421$	−11.0496	−	34.0071i	−0.538524	−	1.65740i	−0.735910	−	0.677079i	$-0.763245\pi$
$421$	−11.0496	−	34.0071i	−0.538524	−	1.65740i	0.197387	−	0.980326i	$-0.436755\pi$
$422$	14.9775	−	46.0959i	0.729092	−	2.24392i
$423$	−0.532716	−	0.387041i	−0.0259015	−	0.0188186i
$424$	74.9579	+	54.4601i	3.64028	+	2.64482i
$425$	−1.39965	+	4.30769i	−0.0678931	+	0.208954i
$426$	12.1535	+	37.4045i	0.588838	+	1.81226i
$427$	8.40387	−	6.10577i	0.406692	−	0.295479i
$428$	19.4586			0.940565
$429$		0			0
$430$	−52.5972			−2.53646
$431$	25.3289	−	18.4025i	1.22005	−	0.886417i	0.223945	−	0.974602i	$-0.428106\pi$
$431$	25.3289	−	18.4025i	1.22005	−	0.886417i	0.996104	+	0.0881844i	$0.0281065\pi$
$432$	−25.8645	−	79.6028i	−1.24441	−	3.82989i
$433$	6.67720	−	20.5503i	0.320886	−	0.987585i	−0.652378	−	0.757894i	$-0.726228\pi$
$433$	6.67720	−	20.5503i	0.320886	−	0.987585i	0.973264	−	0.229691i	$-0.0737716\pi$
$434$	5.00101	+	3.63345i	0.240056	+	0.174411i
$435$	6.47214	+	4.70228i	0.310315	+	0.225457i
$436$	−28.2244	+	86.8658i	−1.35170	+	4.16012i
$437$	0.334626	+	1.02987i	0.0160073	+	0.0492655i
$438$	−40.8818	+	29.7024i	−1.95341	+	1.41923i
$439$	15.5877			0.743959			0.371979	−	0.928241i	$-0.378679\pi$
$439$	15.5877			0.743959			0.371979	+	0.928241i	$0.378679\pi$
$440$		0			0
$441$	0.103084			0.00490875
$442$	−12.7377	+	9.25449i	−0.605871	+	0.440191i
$443$	7.26010	+	22.3443i	0.344938	+	1.06161i	0.961617	+	0.274395i	$0.0884774\pi$
$443$	7.26010	+	22.3443i	0.344938	+	1.06161i	−0.616680	+	0.787214i	$0.711523\pi$
$444$	−21.1227	+	65.0089i	−1.00244	+	3.08519i
$445$	−30.0622	−	21.8415i	−1.42508	−	1.03538i
$446$	49.8086	+	36.1881i	2.35851	+	1.71356i
$447$	1.88267	−	5.79427i	0.0890474	−	0.274060i
$448$	11.4247	+	35.1616i	0.539766	+	1.66123i
$449$	−18.4320	+	13.3916i	−0.869860	+	0.631990i	−0.930549	−	0.366166i	$-0.880670\pi$
$449$	−18.4320	+	13.3916i	−0.869860	+	0.631990i	0.0606894	+	0.998157i	$0.480670\pi$
$450$	0.539998			0.0254558
$451$		0			0
$452$	39.9634			1.87972
$453$	14.6769	−	10.6634i	0.689580	−	0.501009i
$454$	12.1782	+	37.4806i	0.571550	+	1.75905i
$455$	1.93776	−	5.96381i	0.0908435	−	0.279588i
$456$	24.6789	+	17.9303i	1.15570	+	0.839662i
$457$	11.7346	+	8.52570i	0.548923	+	0.398816i	0.827388	−	0.561631i	$-0.189826\pi$
$457$	11.7346	+	8.52570i	0.548923	+	0.398816i	−0.278466	+	0.960446i	$0.589826\pi$
$458$	−3.30987	+	10.1867i	−0.154660	+	0.475995i
$459$	3.76535	+	11.5885i	0.175751	+	0.540907i
$460$	−7.48535	+	5.43842i	−0.349006	+	0.253568i
$461$	−31.1633			−1.45142			−0.725709	−	0.688002i	$-0.758488\pi$
$461$	−31.1633			−1.45142			−0.725709	+	0.688002i	$0.758488\pi$
$462$		0			0
$463$	−5.87859			−0.273201			−0.136601	−	0.990626i	$-0.543618\pi$
$463$	−5.87859			−0.273201			−0.136601	+	0.990626i	$0.543618\pi$
$464$	−22.9463	+	16.6715i	−1.06525	+	0.773953i
$465$	3.20002	+	9.84865i	0.148397	+	0.456720i
$466$	5.70310	−	17.5524i	0.264191	−	0.813097i
$467$	19.1939	+	13.9452i	0.888186	+	0.645305i	0.935404	−	0.353580i	$-0.115036\pi$
$467$	19.1939	+	13.9452i	0.888186	+	0.645305i	−0.0472185	+	0.998885i	$0.515036\pi$
$468$	1.12035	+	0.813980i	0.0517881	+	0.0376262i
$469$	−1.98390	+	6.10581i	−0.0916079	+	0.281940i
$470$	−14.3157	−	44.0591i	−0.660333	−	2.03230i
$471$	−16.1569	+	11.7387i	−0.744472	+	0.540890i
$472$	−17.6402			−0.811954
$473$		0			0
$474$	74.1974			3.40800
$475$	2.65382	−	1.92811i	0.121766	−	0.0884679i
$476$	−4.15133	−	12.7765i	−0.190276	−	0.585609i
$477$	−0.294732	+	0.907090i	−0.0134948	+	0.0415328i
$478$	10.1462	+	7.37167i	0.464078	+	0.337172i
$479$	−6.80572	−	4.94465i	−0.310961	−	0.225927i	0.421348	−	0.906899i	$-0.361557\pi$
$479$	−6.80572	−	4.94465i	−0.310961	−	0.225927i	−0.732309	+	0.680973i	$0.761557\pi$
$480$	−36.1201	+	111.166i	−1.64865	+	5.07402i
$481$	5.08894	+	15.6621i	0.232036	+	0.714132i
$482$	8.27685	−	6.01348i	0.377000	−	0.273907i
$483$	−1.10308			−0.0501920
$484$		0			0
$485$	21.9431			0.996387
$486$	2.39234	−	1.73814i	0.108519	−	0.0788436i
$487$	7.66230	+	23.5821i	0.347212	+	1.06861i	0.960389	+	0.278663i	$0.0898912\pi$
$487$	7.66230	+	23.5821i	0.347212	+	1.06861i	−0.613177	+	0.789946i	$0.710109\pi$
$488$	−32.1447	+	98.9313i	−1.45512	+	4.47841i
$489$	13.8655	+	10.0739i	0.627019	+	0.455556i
$490$	5.86731	+	4.26285i	0.265058	+	0.192576i
$491$	3.77191	−	11.6088i	0.170224	−	0.523896i	−0.829159	−	0.559013i	$-0.811180\pi$
$491$	3.77191	−	11.6088i	0.170224	−	0.523896i	0.999383	+	0.0351168i	$0.0111803\pi$
$492$	31.8138	+	97.9129i	1.43428	+	4.41425i
$493$	3.34051	−	2.42703i	0.150449	−	0.109308i
$494$	11.4028			0.513034
$495$		0			0
$496$	−36.7143			−1.64852
$497$	−6.54071	+	4.75210i	−0.293391	+	0.213161i
$498$	19.2049	+	59.1065i	0.860591	+	2.64863i
$499$	6.89928	−	21.2338i	0.308854	−	0.950555i	−0.669357	−	0.742941i	$-0.733430\pi$
$499$	6.89928	−	21.2338i	0.308854	−	0.950555i	0.978211	−	0.207614i	$-0.0665698\pi$
$500$	−37.0931	−	26.9497i	−1.65886	−	1.20523i
$501$	−32.0722	−	23.3019i	−1.43288	−	1.04105i
$502$	7.26145	−	22.3484i	0.324094	−	0.997459i
$503$	−1.40338	−	4.31916i	−0.0625737	−	0.192582i	0.914883	−	0.403720i	$-0.132283\pi$
$503$	−1.40338	−	4.31916i	−0.0625737	−	0.192582i	−0.977456	+	0.211138i	$0.932283\pi$
$504$	−0.835128	+	0.606756i	−0.0371996	+	0.0270271i
$505$	36.3632			1.61814
$506$		0			0
$507$	−12.8569			−0.570997
$508$	20.6712	−	15.0185i	0.917137	−	0.666339i
$509$	1.27358	+	3.91969i	0.0564506	+	0.173737i	0.975306	−	0.220857i	$-0.0708853\pi$
$509$	1.27358	+	3.91969i	0.0564506	+	0.173737i	−0.918856	+	0.394594i	$0.870885\pi$
$510$	9.42650	−	29.0118i	0.417412	−	1.28466i
$511$	−8.40387	−	6.10577i	−0.371765	−	0.270103i
$512$	−69.5103	−	50.5022i	−3.07195	−	2.23190i
$513$	2.72697	−	8.39276i	0.120399	−	0.370549i
$514$	−2.52065	−	7.75778i	−0.111181	−	0.342181i
$515$	−6.22347	+	4.52162i	−0.274239	+	0.199246i
$516$	71.8776			3.16423
$517$		0			0
$518$	−19.0462			−0.836843
$519$	−9.87500	+	7.17461i	−0.433464	+	0.314930i
$520$	19.4046	+	59.7213i	0.850949	+	2.61895i
$521$	12.1407	−	37.3651i	0.531892	−	1.63700i	−0.218379	−	0.975864i	$-0.570077\pi$
$521$	12.1407	−	37.3651i	0.531892	−	1.63700i	0.750271	−	0.661131i	$-0.229923\pi$
$522$	−0.398261	−	0.289353i	−0.0174314	−	0.0126647i
$523$	1.73260	+	1.25881i	0.0757615	+	0.0550439i	0.625021	−	0.780608i	$-0.285090\pi$
$523$	1.73260	+	1.25881i	0.0757615	+	0.0550439i	−0.549260	+	0.835652i	$0.685090\pi$
$524$	−10.9022	+	33.5536i	−0.476265	+	1.46579i
$525$	1.03259	+	3.17798i	0.0450659	+	0.138698i
$526$	35.7463	−	25.9712i	1.55861	−	1.13240i
$527$	5.34485			0.232825
$528$		0			0
$529$	−22.6079			−0.982951
$530$	−54.2867	+	39.4416i	−2.35806	+	1.71323i
$531$	−0.0561137	−	0.172700i	−0.00243513	−	0.00749455i
$532$	−3.00651	+	9.25310i	−0.130349	+	0.401173i
$533$	20.0664	+	14.5791i	0.869172	+	0.631490i
$534$	55.6857	+	40.4580i	2.40976	+	1.75079i
$535$	−2.80676	+	8.63833i	−0.121347	+	0.373467i
$536$	−19.8667	−	61.1433i	−0.858109	−	2.64099i
$537$	−19.8708	+	14.4370i	−0.857488	+	0.623001i
$538$	−18.7110			−0.806687
$539$		0			0
$540$	75.4007			3.24473
$541$	34.8251	−	25.3019i	1.49725	−	1.08782i	0.525788	−	0.850615i	$-0.323770\pi$
$541$	34.8251	−	25.3019i	1.49725	−	1.08782i	0.971461	−	0.237200i	$-0.0762296\pi$
$542$	2.95143	+	9.08356i	0.126775	+	0.390172i
$543$	1.72431	−	5.30687i	0.0739970	−	0.227739i
$544$	48.8079	+	35.4610i	2.09262	+	1.52038i
$545$	−34.4915	−	25.0596i	−1.47746	−	1.07343i
$546$	−3.58941	+	11.0471i	−0.153613	+	0.472771i
$547$	−8.96445	−	27.5898i	−0.383292	−	1.17965i	−0.937711	−	0.347415i	$-0.887060\pi$
$547$	−8.96445	−	27.5898i	−0.383292	−	1.17965i	0.554419	−	0.832238i	$-0.312940\pi$
$548$	−42.7937	+	31.0914i	−1.82805	+	1.32816i
$549$	−1.07081			−0.0457010
$550$		0			0
$551$	−2.99042			−0.127396
$552$	8.93659	−	6.49281i	0.380366	−	0.276352i
$553$	4.71325	+	14.5059i	0.200428	+	0.616853i
$554$	−9.77837	+	30.0947i	−0.415443	+	1.27860i
$555$	−25.8129	−	18.7542i	−1.09570	−	0.796070i
$556$	−72.0156	−	52.3224i	−3.05414	−	2.21897i
$557$	−0.462045	+	1.42203i	−0.0195775	+	0.0602532i	−0.960368	−	0.278735i	$-0.910085\pi$
$557$	−0.462045	+	1.42203i	−0.0195775	+	0.0602532i	0.940791	+	0.338989i	$0.110085\pi$
$558$	−0.196912	−	0.606033i	−0.00833595	−	0.0256554i
$559$	14.0097	−	10.1786i	0.592547	−	0.430511i
$560$	−43.0741			−1.82021
$561$		0			0
$562$	−61.6560			−2.60080
$563$	−5.07312	+	3.68584i	−0.213806	+	0.155339i	−0.689534	−	0.724253i	$-0.742185\pi$
$563$	−5.07312	+	3.68584i	−0.213806	+	0.155339i	0.475728	+	0.879593i	$0.342185\pi$
$564$	19.5633	+	60.2097i	0.823764	+	2.53529i
$565$	−5.76444	+	17.7411i	−0.242512	+	0.746374i
$566$	27.6211	+	20.0679i	1.16100	+	0.843518i
$567$	7.52275	+	5.46559i	0.315926	+	0.229533i
$568$	25.0181	−	76.9979i	1.04974	−	3.23076i
$569$	2.41705	+	7.43892i	0.101328	+	0.311856i	0.988851	−	0.148908i	$-0.0475757\pi$
$569$	2.41705	+	7.43892i	0.101328	+	0.311856i	−0.887523	+	0.460763i	$0.847576\pi$
$570$	−17.8732	+	12.9856i	−0.748625	+	0.543908i
$571$	−15.1753			−0.635068			−0.317534	−	0.948247i	$-0.602855\pi$
$571$	−15.1753			−0.635068			−0.317534	+	0.948247i	$0.602855\pi$
$572$		0			0
$573$	32.3342			1.35078
$574$	−23.2078	+	16.8614i	−0.968674	+	0.703783i
$575$	−0.367064	−	1.12971i	−0.0153076	−	0.0471121i
$576$	1.17770	−	3.62458i	0.0490708	−	0.151024i
$577$	−19.1288	−	13.8979i	−0.796343	−	0.578577i	0.113496	−	0.993538i	$-0.463795\pi$
$577$	−19.1288	−	13.8979i	−0.796343	−	0.578577i	−0.909839	+	0.414961i	$0.863795\pi$
$578$	25.2428	+	18.3400i	1.04996	+	0.762842i
$579$	−1.65822	+	5.10347i	−0.0689132	+	0.212093i
$580$	−7.89570	−	24.3005i	−0.327851	−	1.00902i
$581$	−10.3356	+	7.50926i	−0.428793	+	0.311536i
$582$	−40.6464			−1.68485
$583$		0			0
$584$	104.022			4.30448
$585$	−0.522956	+	0.379950i	−0.0216216	+	0.0157090i
$586$	1.83788	+	5.65642i	0.0759222	+	0.233665i
$587$	−3.13766	+	9.65672i	−0.129505	+	0.398576i	−0.994695	−	0.102869i	$-0.967198\pi$
$587$	−3.13766	+	9.65672i	−0.129505	+	0.398576i	0.865190	+	0.501444i	$0.167198\pi$
$588$	−8.01806	−	5.82546i	−0.330659	−	0.240238i
$589$	−3.13162	−	2.27526i	−0.129036	−	0.0937503i
$590$	3.94785	−	12.1502i	0.162530	−	0.500217i
$591$	2.69659	+	8.29925i	0.110923	+	0.341386i
$592$	91.5170	−	66.4910i	3.76132	−	2.73276i
$593$	33.7972			1.38788			0.693942	−	0.720031i	$-0.255873\pi$
$593$	33.7972			1.38788			0.693942	+	0.720031i	$0.255873\pi$
$594$		0			0
$595$	6.27072			0.257074
$596$	−15.7423	+	11.4375i	−0.644830	+	0.468496i
$597$	8.54887	+	26.3107i	0.349882	+	1.07683i
$598$	1.27596	−	3.92701i	0.0521780	−	0.160587i
$599$	14.8265	+	10.7721i	0.605793	+	0.440135i	0.847931	−	0.530107i	$-0.177848\pi$
$599$	14.8265	+	10.7721i	0.605793	+	0.440135i	−0.242137	+	0.970242i	$0.577848\pi$
$600$	−27.0712	−	19.6684i	−1.10518	−	0.802959i
$601$	14.9812	−	46.1074i	0.611096	−	1.88076i	0.163446	−	0.986552i	$-0.447739\pi$
$601$	14.9812	−	46.1074i	0.611096	−	1.88076i	0.447650	−	0.894209i	$-0.352261\pi$
$602$	6.18896	+	19.0477i	0.252243	+	0.776325i
$603$	0.535408	−	0.388997i	0.0218035	−	0.0158412i
$604$	−57.9421			−2.35763
$605$		0			0
$606$	−67.3574			−2.73621
$607$	16.6635	−	12.1068i	0.676352	−	0.491398i	−0.195794	−	0.980645i	$-0.562728\pi$
$607$	16.6635	−	12.1068i	0.676352	−	0.491398i	0.872145	+	0.489247i	$0.162728\pi$
$608$	−13.5018	−	41.5542i	−0.547569	−	1.68524i
$609$	0.941336	−	2.89714i	0.0381449	−	0.117398i
$610$	−60.9482	−	44.2815i	−2.46772	−	1.79290i
$611$	12.3394	+	8.96513i	0.499201	+	0.362690i
$612$	−0.427934	+	1.31705i	−0.0172982	+	0.0532385i
$613$	5.81328	+	17.8914i	0.234796	+	0.722628i	0.997148	+	0.0754656i	$0.0240443\pi$
$613$	5.81328	+	17.8914i	0.234796	+	0.722628i	−0.762352	+	0.647162i	$0.775956\pi$
$614$	71.0944	−	51.6531i	2.86914	−	2.08455i
$615$	−48.0558			−1.93780
$616$		0			0
$617$	−14.2062			−0.571919			−0.285959	−	0.958242i	$-0.592312\pi$
$617$	−14.2062			−0.571919			−0.285959	+	0.958242i	$0.592312\pi$
$618$	11.5281	−	8.37563i	0.463727	−	0.336917i
$619$	−4.95155	−	15.2393i	−0.199019	−	0.612519i	−0.999906	−	0.0137029i	$-0.995638\pi$
$619$	−4.95155	−	15.2393i	−0.199019	−	0.612519i	0.800887	−	0.598816i	$-0.204362\pi$
$620$	10.2205	−	31.4554i	0.410464	−	1.26328i
$621$	−2.58525	−	1.87829i	−0.103742	−	0.0753733i
$622$	24.4174	+	17.7403i	0.979049	+	0.711321i
$623$	−4.37238	+	13.4568i	−0.175176	+	0.539135i
$624$	−21.3186	−	65.6118i	−0.853426	−	2.62657i
$625$	24.9875	−	18.1545i	0.999501	−	0.726180i
$626$	20.4402			0.816956
$627$		0			0
$628$	63.7851			2.54530
$629$	−13.3230	+	9.67973i	−0.531223	+	0.385956i
$630$	−0.231022	−	0.711014i	−0.00920415	−	0.0283275i
$631$	4.69568	−	14.4518i	0.186932	−	0.575318i	−0.813044	−	0.582202i	$-0.802191\pi$
$631$	4.69568	−	14.4518i	0.186932	−	0.575318i	0.999976	+	0.00688413i	$0.00219131\pi$
$632$	−123.567	−	89.7764i	−4.91522	−	3.57111i
$633$	−25.0125	−	18.1726i	−0.994157	−	0.722297i
$634$	−7.59234	+	23.3668i	−0.301531	+	0.928016i
$635$	3.68556	+	11.3430i	0.146257	+	0.450132i
$636$	74.1863	−	53.8995i	2.94168	−	2.13725i
$637$	−2.38776			−0.0946063
$638$		0			0
$639$	0.833407			0.0329691
$640$	109.557	−	79.5978i	4.33062	−	3.14638i
$641$	−3.16012	−	9.72586i	−0.124817	−	0.384149i	0.869050	−	0.494724i	$-0.164731\pi$
$641$	−3.16012	−	9.72586i	−0.124817	−	0.384149i	−0.993868	+	0.110575i	$0.964731\pi$
$642$	5.19911	−	16.0012i	0.205192	−	0.631517i
$643$	−16.6374	−	12.0878i	−0.656116	−	0.476696i	0.209233	−	0.977866i	$-0.432903\pi$
$643$	−16.6374	−	12.0878i	−0.656116	−	0.476696i	−0.865349	+	0.501170i	$0.832903\pi$
$644$	2.85026	+	2.07083i	0.112316	+	0.0816023i
$645$	−10.3678	+	31.9089i	−0.408233	+	1.25641i
$646$	3.52364	+	10.8447i	0.138636	+	0.426677i
$647$	20.5929	−	14.9616i	0.809590	−	0.588201i	−0.104122	−	0.994565i	$-0.533203\pi$
$647$	20.5929	−	14.9616i	0.809590	−	0.588201i	0.913712	+	0.406363i	$0.133203\pi$
$648$	−93.1160			−3.65794
$649$		0			0
$650$	−12.5081			−0.490609
$651$	3.19007	−	2.31772i	0.125029	−	0.0908387i
$652$	−16.9152	−	52.0598i	−0.662452	−	2.03882i
$653$	−13.9834	+	43.0366i	−0.547214	+	1.68415i	0.168452	+	0.985710i	$0.446123\pi$
$653$	−13.9834	+	43.0366i	−0.547214	+	1.68415i	−0.715666	+	0.698442i	$0.753877\pi$
$654$	63.8905	+	46.4191i	2.49831	+	1.81513i
$655$	−13.3230	−	9.67973i	−0.520573	−	0.378219i
$656$	52.6494	−	162.038i	2.05561	−	6.32652i
$657$	0.330898	+	1.01840i	0.0129096	+	0.0397315i
$658$	−14.2712	+	10.3686i	−0.556349	+	0.404211i
$659$	−50.3544			−1.96153			−0.980765	−	0.195191i	$-0.937467\pi$
$659$	−50.3544			−1.96153			−0.980765	+	0.195191i	$0.937467\pi$
$660$		0			0
$661$	−23.2234			−0.903287			−0.451644	−	0.892198i	$-0.649162\pi$
$661$	−23.2234			−0.903287			−0.451644	+	0.892198i	$0.649162\pi$
$662$	−19.1280	+	13.8973i	−0.743430	+	0.540133i
$663$	3.10355	+	9.55174i	0.120532	+	0.370959i
$664$	39.5336	−	121.672i	1.53420	−	4.72178i
$665$	−3.67410	−	2.66939i	−0.142475	−	0.103514i
$666$	1.58839	+	1.15403i	0.0615488	+	0.0447178i
$667$	−0.334626	+	1.02987i	−0.0129568	+	0.0398769i
$668$	39.1266	+	120.419i	1.51385	+	4.65917i
$669$	31.7722	−	23.0839i	1.22838	−	0.892474i
$670$	46.5606			1.79879
$671$		0			0
$672$	44.5081			1.71694
$673$	2.60867	−	1.89531i	0.100557	−	0.0730587i	−0.536371	−	0.843983i	$-0.680205\pi$
$673$	2.60867	−	1.89531i	0.100557	−	0.0730587i	0.636927	+	0.770924i	$0.280205\pi$
$674$	−8.30266	−	25.5530i	−0.319806	−	0.984263i
$675$	−2.99132	+	9.20634i	−0.115136	+	0.354352i
$676$	33.2211	+	24.1365i	1.27773	+	0.928328i
$677$	−34.4818	−	25.0525i	−1.32524	−	0.962845i	−0.999851	−	0.0172658i	$-0.994504\pi$
$677$	−34.4818	−	25.0525i	−1.32524	−	0.962845i	−0.325392	−	0.945579i	$-0.605496\pi$
$678$	10.6778	−	32.8628i	0.410077	−	1.26209i
$679$	−2.58199	−	7.94653i	−0.0990875	−	0.304960i
$680$	−50.8020	+	36.9098i	−1.94817	+	1.41543i
$681$	25.1387			0.963317
$682$		0			0
$683$	15.5877			0.596445			0.298223	−	0.954496i	$-0.403606\pi$
$683$	15.5877			0.596445			0.298223	+	0.954496i	$0.403606\pi$
$684$	0.811388	−	0.589508i	0.0310242	−	0.0225404i
$685$	−7.62986	−	23.4823i	−0.291522	−	0.897212i
$686$	0.853368	−	2.62640i	0.0325817	−	0.100276i
$687$	5.52750	+	4.01596i	0.210887	+	0.153219i
$688$	−96.2339	−	69.9180i	−3.66888	−	2.66560i
$689$	6.82694	−	21.0112i	0.260086	−	0.800462i
$690$	2.47214	+	7.60845i	0.0941126	+	0.289649i
$691$	−33.9230	+	24.6465i	−1.29049	+	0.937596i	−0.999815	−	0.0192259i	$-0.993880\pi$
$691$	−33.9230	+	24.6465i	−1.29049	+	0.937596i	−0.290675	+	0.956822i	$0.593880\pi$
$692$	38.9850			1.48199
$693$		0			0
$694$	40.9817			1.55564
$695$	33.6155	−	24.4231i	1.27511	−	0.926420i
$696$	9.42650	+	29.0118i	0.357311	+	1.09969i
$697$	−7.66468	+	23.5895i	−0.290320	+	0.893514i
$698$	−36.2963	−	26.3708i	−1.37383	−	0.998149i
$699$	−9.52422	−	6.91975i	−0.360239	−	0.261729i
$700$	3.29796	−	10.1501i	0.124651	−	0.383637i
$701$	−4.76177	−	14.6552i	−0.179849	−	0.553520i	0.819972	−	0.572403i	$-0.193989\pi$
$701$	−4.76177	−	14.6552i	−0.179849	−	0.553520i	−0.999822	+	0.0188835i	$0.993989\pi$
$702$	−27.2229	+	19.7786i	−1.02746	+	0.746495i
$703$	11.9267			0.449824
$704$		0			0
$705$	−29.5510			−1.11296
$706$	−68.9464	+	50.0925i	−2.59483	+	1.88526i
$707$	−4.27875	−	13.1686i	−0.160919	−	0.495257i
$708$	−5.39499	+	16.6041i	−0.202756	+	0.624020i
$709$	−2.31401	−	1.68123i	−0.0869044	−	0.0631398i	0.543485	−	0.839419i	$-0.317105\pi$
$709$	−2.31401	−	1.68123i	−0.0869044	−	0.0631398i	−0.630389	+	0.776279i	$0.717105\pi$
$710$	47.4358	+	34.4641i	1.78023	+	1.29342i
$711$	0.485859	−	1.49532i	0.0182211	−	0.0560789i
$712$	−43.7848	−	134.756i	−1.64090	−	5.05018i
$713$	−1.13401	+	0.823904i	−0.0424689	+	0.0308554i
$714$	−11.6156			−0.434702
$715$		0			0
$716$	78.4469			2.93170
$717$	6.47214	−	4.70228i	0.241706	−	0.175610i
$718$	−10.0645	−	30.9753i	−0.375603	−	1.15599i
$719$	−10.6526	+	32.7853i	−0.397275	+	1.22269i	0.529901	+	0.848059i	$0.322229\pi$
$719$	−10.6526	+	32.7853i	−0.397275	+	1.22269i	−0.927176	+	0.374626i	$0.877771\pi$
$720$	3.59223	+	2.60991i	0.133875	+	0.0972655i
$721$	2.36977	+	1.72174i	0.0882547	+	0.0641208i
$722$	−13.6621	+	42.0475i	−0.508450	+	1.56485i
$723$	−2.01666	−	6.20664i	−0.0750003	−	0.230827i
$724$	−14.4181	+	10.4754i	−0.535844	+	0.389314i
$725$	3.28030			0.121827
$726$		0			0
$727$	−40.3309			−1.49579			−0.747895	−	0.663817i	$-0.768935\pi$
$727$	−40.3309			−1.49579			−0.747895	+	0.663817i	$0.768935\pi$
$728$	19.3443	−	14.0545i	0.716947	−	0.520893i
$729$	8.03740	+	24.7366i	0.297682	+	0.916170i
$730$	−23.2801	+	71.6489i	−0.861637	+	2.65184i
$731$	14.0097	+	10.1786i	0.518168	+	0.376471i
$732$	83.2897	+	60.5135i	3.07847	+	2.23664i
$733$	−8.88839	+	27.3557i	−0.328300	+	1.01040i	0.641628	+	0.767016i	$0.278259\pi$
$733$	−8.88839	+	27.3557i	−0.328300	+	1.01040i	−0.969929	+	0.243389i	$0.921741\pi$
$734$	−3.03406	−	9.33786i	−0.111989	−	0.344667i
$735$	3.74267	−	2.71921i	0.138051	−	0.100300i
$736$	−15.8217			−0.583197
$737$		0			0
$738$	2.95710			0.108852
$739$	−28.3981	+	20.6325i	−1.04464	+	0.758977i	−0.971186	−	0.238321i	$-0.923403\pi$
$739$	−28.3981	+	20.6325i	−1.04464	+	0.758977i	−0.0734563	+	0.997298i	$0.523403\pi$
$740$	31.4905	+	96.9179i	1.15761	+	3.56277i
$741$	2.24768	−	6.91765i	0.0825706	−	0.254126i
$742$	20.6712	+	15.0185i	0.758864	+	0.551347i
$743$	26.2673	+	19.0843i	0.963653	+	0.700135i	0.953996	−	0.299818i	$-0.0969261\pi$
$743$	26.2673	+	19.0843i	0.963653	+	0.700135i	0.00965687	+	0.999953i	$0.496926\pi$
$744$	−12.2020	+	37.5539i	−0.447347	+	1.37679i
$745$	−2.80676	−	8.63833i	−0.102832	−	0.316484i
$746$	−50.2790	+	36.5298i	−1.84085	+	1.33745i
$747$	1.31695			0.0481846
$748$		0			0
$749$	3.45856			0.126373
$750$	−32.0722	+	23.3019i	−1.17111	+	0.850863i
$751$	−8.77095	−	26.9942i	−0.320056	−	0.985033i	−0.973623	−	0.228163i	$-0.926728\pi$
$751$	−8.77095	−	26.9942i	−0.320056	−	0.985033i	0.653566	−	0.756869i	$-0.273272\pi$
$752$	32.3757	−	99.6423i	1.18062	−	3.63358i
$753$	−12.1267	−	8.81053i	−0.441920	−	0.321074i
$754$	9.22502	+	6.70237i	0.335955	+	0.244086i
$755$	8.35774	−	25.7225i	0.304169	−	0.936137i
$756$	−8.87217	−	27.3057i	−0.322678	−	0.993100i
$757$	13.7907	−	10.0195i	0.501231	−	0.364166i	−0.308256	−	0.951303i	$-0.599745\pi$
$757$	13.7907	−	10.0195i	0.501231	−	0.364166i	0.809487	+	0.587138i	$0.199745\pi$
$758$	64.7022			2.35009
$759$		0			0
$760$	45.4777			1.64965
$761$	−22.6029	+	16.4220i	−0.819356	+	0.595297i	−0.916528	−	0.399971i	$-0.869020\pi$
$761$	−22.6029	+	16.4220i	−0.819356	+	0.595297i	0.0971719	+	0.995268i	$0.469020\pi$
$762$	−6.82694	−	21.0112i	−0.247314	−	0.761155i
$763$	−5.01660	+	15.4395i	−0.181613	+	0.558948i
$764$	−83.5485	−	60.7015i	−3.02268	−	2.19610i
$765$	−0.522956	−	0.379950i	−0.0189075	−	0.0137371i
$766$	−2.92388	+	8.99879i	−0.105644	+	0.325140i
$767$	1.29978	+	4.00030i	0.0469322	+	0.144443i
$768$	−97.5608	+	70.8821i	−3.52042	+	2.55774i
$769$	6.69512			0.241432			0.120716	−	0.992687i	$-0.461481\pi$
$769$	6.69512			0.241432			0.120716	+	0.992687i	$0.461481\pi$
$770$		0			0
$771$	−5.20324			−0.187390
$772$	13.8655	−	10.0739i	0.499030	−	0.362566i
$773$	8.62596	+	26.5480i	0.310254	+	0.954864i	0.977664	+	0.210174i	$0.0674030\pi$
$773$	8.62596	+	26.5480i	0.310254	+	0.954864i	−0.667410	+	0.744691i	$0.732597\pi$
$774$	0.637981	−	1.96350i	0.0229318	−	0.0705767i
$775$	3.43520	+	2.49582i	0.123396	+	0.0896524i
$776$	67.6916	+	49.1808i	2.42999	+	1.76549i
$777$	−3.75434	+	11.5547i	−0.134686	+	0.414522i
$778$	6.87546	+	21.1605i	0.246497	+	0.758641i
$779$	14.5327	−	10.5586i	0.520687	−	0.378301i
$780$	62.1483			2.22527
$781$		0			0
$782$	4.12910			0.147656
$783$	7.13931	−	5.18701i	0.255138	−	0.185369i
$784$	5.06841	+	15.5990i	0.181015	+	0.557105i
$785$	−9.20056	+	28.3164i	−0.328382	+	1.01066i
$786$	24.6789	+	17.9303i	0.880267	+	0.639551i
$787$	−17.6838	−	12.8480i	−0.630360	−	0.457983i	0.226165	−	0.974089i	$-0.427381\pi$
$787$	−17.6838	−	12.8480i	−0.630360	−	0.457983i	−0.856525	+	0.516106i	$0.827381\pi$
$788$	8.61258	−	26.5068i	0.306811	−	0.944266i
$789$	−8.70962	−	26.8054i	−0.310071	−	0.954299i
$790$	89.4906	−	65.0187i	3.18393	−	2.31326i
$791$	7.10308			0.252557
$792$		0			0
$793$	24.8034			0.880795
$794$	58.8992	−	42.7928i	2.09025	−	1.51866i
$795$	13.2270	+	40.7085i	0.469113	+	1.44378i
$796$	27.3041	−	84.0332i	0.967766	−	2.97848i
$797$	28.0132	+	20.3528i	0.992278	+	0.720932i	0.960419	−	0.278560i	$-0.0898572\pi$
$797$	28.0132	+	20.3528i	0.992278	+	0.720932i	0.0318591	+	0.999492i	$0.489857\pi$
$798$	6.80572	+	4.94465i	0.240920	+	0.175039i
$799$	−4.71325	+	14.5059i	−0.166743	+	0.513182i
$800$	14.8106	+	45.5824i	0.523634	+	1.61158i
$801$	1.18000	−	0.857322i	0.0416933	−	0.0302920i
$802$	−62.4036			−2.20355
$803$		0			0
$804$	−63.6281			−2.24399
$805$	−1.33044	+	0.966625i	−0.0468920	+	0.0340690i
$806$	4.56113	+	14.0377i	0.160659	+	0.494457i
$807$	−3.68826	+	11.3513i	−0.129833	+	0.399584i
$808$	112.175	+	81.5002i	3.94632	+	2.86717i
$809$	−28.3530	−	20.5997i	−0.996838	−	0.724245i	−0.0354303	−	0.999372i	$-0.511280\pi$
$809$	−28.3530	−	20.5997i	−0.996838	−	0.724245i	−0.961408	+	0.275127i	$0.911280\pi$
$810$	20.8393	−	64.1367i	0.732217	−	2.25353i
$811$	−5.60607	−	17.2537i	−0.196856	−	0.605859i	−0.999950	−	0.0100074i	$-0.996814\pi$
$811$	−5.60607	−	17.2537i	−0.196856	−	0.605859i	0.803094	−	0.595852i	$-0.203186\pi$
$812$	−7.87115	+	5.71873i	−0.276223	+	0.200688i
$813$	6.09246			0.213672
$814$		0			0
$815$	25.5510			0.895013
$816$	55.8127	−	40.5503i	1.95384	−	1.41955i
$817$	−3.87552	−	11.9276i	−0.135587	−	0.417294i
$818$	7.94049	−	24.4383i	0.277633	−	0.854466i
$819$	0.199130	+	0.144677i	0.00695818	+	0.00505541i
$820$	124.171	+	90.2159i	4.33626	+	3.15047i
$821$	−1.06875	+	3.28929i	−0.0372998	+	0.114797i	−0.967973	−	0.251055i	$-0.919222\pi$
$821$	−1.06875	+	3.28929i	−0.0372998	+	0.114797i	0.930673	+	0.365852i	$0.119222\pi$
$822$	14.1332	+	43.4975i	0.492951	+	1.51715i
$823$	27.1270	−	19.7089i	0.945588	−	0.687010i	−0.00417155	−	0.999991i	$-0.501328\pi$
$823$	27.1270	−	19.7089i	0.945588	−	0.687010i	0.949759	+	0.312982i	$0.101328\pi$
$824$	−29.3328			−1.02186
$825$		0			0
$826$	−4.86464			−0.169263
$827$	21.2760	−	15.4579i	0.739840	−	0.537525i	−0.152821	−	0.988254i	$-0.548836\pi$
$827$	21.2760	−	15.4579i	0.739840	−	0.537525i	0.892661	+	0.450729i	$0.148836\pi$
$828$	−0.112227	−	0.345401i	−0.00390017	−	0.0120035i
$829$	−8.96208	+	27.5824i	−0.311266	+	0.957978i	0.665999	+	0.745953i	$0.268006\pi$
$829$	−8.96208	+	27.5824i	−0.311266	+	0.957978i	−0.977264	+	0.212025i	$0.931994\pi$
$830$	74.9579	+	54.4601i	2.60183	+	1.89034i
$831$	16.3299	+	11.8644i	0.566479	+	0.411571i
$832$	−27.2793	+	83.9572i	−0.945741	+	2.91069i
$833$	−0.737857	−	2.27089i	−0.0255652	−	0.0786817i
$834$	−62.2677	+	45.2401i	−2.15615	+	1.56654i
$835$	−59.1020			−2.04531
$836$		0			0
$837$	11.4230			0.394835
$838$	30.9347	−	22.4754i	1.06862	−	0.776399i
$839$	9.01432	+	27.7432i	0.311209	+	0.957803i	0.977287	+	0.211921i	$0.0679718\pi$
$839$	9.01432	+	27.7432i	0.311209	+	0.957803i	−0.666078	+	0.745882i	$0.732028\pi$
$840$	−14.3157	+	44.0591i	−0.493938	+	1.52019i
$841$	21.0422	+	15.2881i	0.725593	+	0.527174i
$842$	79.8868	+	58.0412i	2.75308	+	2.00023i
$843$	−12.1535	+	37.4045i	−0.418588	+	1.28828i
$844$	30.5140	+	93.9126i	1.05034	+	3.23260i
$845$	−15.5069	+	11.2665i	−0.533455	+	0.387578i
$846$	1.81841			0.0625183
$847$		0			0
$848$	−151.755			−5.21129
$849$	17.6191	−	12.8010i	0.604687	−	0.439331i
$850$	−3.86522	−	11.8959i	−0.132576	−	0.408027i
$851$	1.33459	−	4.10746i	0.0457493	−	0.140802i
$852$	−64.8241	−	47.0975i	−2.22084	−	1.61353i
$853$	−8.59324	−	6.24335i	−0.294227	−	0.213768i	0.430872	−	0.902413i	$-0.358206\pi$
$853$	−8.59324	−	6.24335i	−0.294227	−	0.213768i	−0.725099	+	0.688645i	$0.758206\pi$
$854$	−8.86458	+	27.2824i	−0.303340	+	0.933583i
$855$	0.144666	+	0.445235i	0.00494746	+	0.0152267i
$856$	−28.0194	+	20.3573i	−0.957684	+	0.695798i
$857$	37.8463			1.29281			0.646403	−	0.762996i	$-0.276273\pi$
$857$	37.8463			1.29281			0.646403	+	0.762996i	$0.276273\pi$
$858$		0			0
$859$	−19.0785			−0.650950			−0.325475	−	0.945551i	$-0.605524\pi$
$859$	−19.0785			−0.650950			−0.325475	+	0.945551i	$0.605524\pi$
$860$	86.6925	−	62.9858i	2.95619	−	2.14780i
$861$	5.65459	+	17.4030i	0.192708	+	0.593094i
$862$	−26.7174	+	82.2278i	−0.909999	+	2.80069i
$863$	−9.04103	−	6.56869i	−0.307760	−	0.223601i	0.423175	−	0.906048i	$-0.360916\pi$
$863$	−9.04103	−	6.56869i	−0.307760	−	0.223601i	−0.730935	+	0.682447i	$0.760916\pi$
$864$	104.312	+	75.7869i	3.54875	+	2.57832i
$865$	−5.62332	+	17.3068i	−0.191198	+	0.588448i
$866$	18.4395	+	56.7509i	0.626599	+	1.92847i
$867$	16.1020	−	11.6988i	0.546853	−	0.397312i
$868$	−12.5939			−0.427466
$869$		0			0
$870$	−22.0925			−0.749004
$871$	−12.4018	+	9.01043i	−0.420219	+	0.305307i
$872$	−50.2360	−	154.611i	−1.70121	−	5.23578i
$873$	−0.266161	+	0.819158i	−0.00900817	+	0.0277243i
$874$	−2.41930	−	1.75772i	−0.0818339	−	0.0594558i
$875$	−6.59293	−	4.79005i	−0.222882	−	0.161933i
$876$	31.8138	−	97.9129i	1.07489	−	3.30817i
$877$	−1.81034	−	5.57165i	−0.0611308	−	0.188141i	0.915827	−	0.401572i	$-0.131536\pi$
$877$	−1.81034	−	5.57165i	−0.0611308	−	0.188141i	−0.976958	+	0.213431i	$0.931536\pi$
$878$	−34.8251	+	25.3019i	−1.17529	+	0.853899i
$879$	3.79383			0.127963
$880$		0			0
$881$	−25.9065			−0.872812			−0.436406	−	0.899750i	$-0.643749\pi$
$881$	−25.9065			−0.872812			−0.436406	+	0.899750i	$0.643749\pi$
$882$	−0.230304	+	0.167326i	−0.00775474	+	0.00563415i
$883$	4.14760	+	12.7650i	0.139578	+	0.429577i	0.996274	−	0.0862449i	$-0.0274868\pi$
$883$	4.14760	+	12.7650i	0.139578	+	0.429577i	−0.856696	+	0.515822i	$0.827487\pi$
$884$	9.91236	−	30.5071i	0.333389	−	1.02606i
$885$	−6.59293	−	4.79005i	−0.221619	−	0.161016i
$886$	−52.4894	−	38.1358i	−1.76342	−	1.28120i
$887$	−15.3294	+	47.1789i	−0.514709	+	1.58411i	0.269101	+	0.963112i	$0.413274\pi$
$887$	−15.3294	+	47.1789i	−0.514709	+	1.58411i	−0.783810	+	0.621001i	$0.786726\pi$
$888$	−37.5958	−	115.708i	−1.26163	−	3.88291i
$889$	3.67410	−	2.66939i	0.123225	−	0.0895284i
$890$	102.616			3.43971
$891$		0			0
$892$	−125.432			−4.19977
$893$	8.93659	−	6.49281i	0.299051	−	0.217274i
$894$	5.19911	+	16.0012i	0.173884	+	0.535161i
$895$	−11.3154	+	34.8253i	−0.378233	+	1.16408i
$896$	−41.7169	−	30.3091i	−1.39367	−	1.01256i
$897$	−2.13086	−	1.54816i	−0.0711475	−	0.0516917i
$898$	19.4425	−	59.8377i	0.648803	−	1.99681i
$899$	−1.19617	−	3.68144i	−0.0398946	−	0.122783i
$900$	−0.890043	+	0.646654i	−0.0296681	+	0.0215551i
$901$	22.0925			0.736006
$902$		0			0
$903$	12.7755			0.425142
$904$	−57.5453	+	41.8091i	−1.91393	+	1.39055i
$905$	−2.57066	−	7.91168i	−0.0854517	−	0.262993i
$906$	−15.4815	+	47.6471i	−0.514338	+	1.58297i
$907$	38.7338	+	28.1417i	1.28613	+	0.934430i	0.999720	−	0.0236757i	$-0.00753690\pi$
$907$	38.7338	+	28.1417i	1.28613	+	0.934430i	0.286413	+	0.958106i	$0.407537\pi$
$908$	−64.9559	−	47.1932i	−2.15564	−	1.56616i
$909$	−0.441069	+	1.35747i	−0.0146293	+	0.0450245i
$910$	5.35123	+	16.4694i	0.177392	+	0.545955i
$911$	−18.4554	+	13.4086i	−0.611455	+	0.444248i	−0.849927	−	0.526901i	$-0.823354\pi$
$911$	−18.4554	+	13.4086i	−0.611455	+	0.444248i	0.238471	+	0.971150i	$0.423354\pi$
$912$	−49.9634			−1.65445
$913$		0			0
$914$	−40.0558			−1.32493
$915$	−38.8780	+	28.2465i	−1.28527	+	0.933800i
$916$	−6.74329	−	20.7537i	−0.222805	−	0.685722i
$917$	−1.93776	+	5.96381i	−0.0639904	+	0.196942i
$918$	−27.2229	−	19.7786i	−0.898489	−	0.652791i
$919$	32.3607	+	23.5114i	1.06748	+	0.775570i	0.975458	−	0.220187i	$-0.0706668\pi$
$919$	32.3607	+	23.5114i	1.06748	+	0.775570i	0.0920227	+	0.995757i	$0.470667\pi$
$920$	5.08894	−	15.6621i	0.167777	−	0.516365i
$921$	−17.3222	−	53.3122i	−0.570786	−	1.75670i
$922$	69.6233	−	50.5843i	2.29292	−	1.66590i
$923$	−19.3044			−0.635413
$924$		0			0
$925$	−13.0829			−0.430162
$926$	13.1336	−	9.54215i	0.431598	−	0.313574i
$927$	−0.0933083	−	0.287173i	−0.00306465	−	0.00943201i
$928$	13.5018	−	41.5542i	0.443217	−	1.36408i
$929$	12.9739	+	9.42610i	0.425660	+	0.309260i	0.779911	−	0.625890i	$-0.215264\pi$
$929$	12.9739	+	9.42610i	0.425660	+	0.309260i	−0.354251	+	0.935150i	$0.615264\pi$
$930$	−23.1357	−	16.8090i	−0.758648	−	0.551190i
$931$	−0.534377	+	1.64464i	−0.0175135	+	0.0539011i
$932$	11.6191	+	35.7599i	0.380596	+	1.17135i
$933$	15.5755	−	11.3163i	0.509919	−	0.370478i
$934$	−65.5177			−2.14380
$935$		0			0
$936$	−2.46482			−0.0805652
$937$	20.4721	−	14.8738i	0.668794	−	0.485907i	−0.200827	−	0.979627i	$-0.564363\pi$
$937$	20.4721	−	14.8738i	0.668794	−	0.485907i	0.869621	+	0.493720i	$0.164363\pi$
$938$	−5.47865	−	16.8615i	−0.178884	−	0.550549i
$939$	4.02913	−	12.4004i	0.131486	−	0.404671i
$940$	76.3569	+	55.4766i	2.49049	+	1.80945i
$941$	−16.6086	−	12.0669i	−0.541425	−	0.393368i	0.283189	−	0.959064i	$-0.408608\pi$
$941$	−16.6086	−	12.0669i	−0.541425	−	0.393368i	−0.824614	+	0.565696i	$0.808608\pi$
$942$	17.0427	−	52.4519i	0.555280	−	1.70898i
$943$	−2.01009	−	6.18643i	−0.0654576	−	0.201458i
$944$	23.3746	−	16.9826i	0.760777	−	0.552737i
$945$	13.4017			0.435958
$946$		0			0
$947$	−16.6907			−0.542376			−0.271188	−	0.962526i	$-0.587417\pi$
$947$	−16.6907			−0.542376			−0.271188	+	0.962526i	$0.587417\pi$
$948$	−122.295	+	88.8523i	−3.97195	+	2.88579i
$949$	−7.66468	−	23.5895i	−0.248806	−	0.765746i
$950$	−2.79931	+	8.61538i	−0.0908215	+	0.279520i
$951$	12.6793	+	9.21202i	0.411153	+	0.298720i
$952$	19.3443	+	14.0545i	0.626952	+	0.455508i
$953$	17.4496	−	53.7044i	0.565249	−	1.73966i	−0.101963	−	0.994788i	$-0.532512\pi$
$953$	17.4496	−	53.7044i	0.565249	−	1.73966i	0.667212	−	0.744868i	$-0.267488\pi$
$954$	−0.813918	−	2.50498i	−0.0263516	−	0.0811018i
$955$	38.9988	−	28.3343i	1.26197	−	0.916875i
$956$	−25.5510			−0.826379
$957$		0			0
$958$	23.2311			0.750564
$959$	−7.60614	+	5.52619i	−0.245615	+	0.178450i
$960$	−52.8528	−	162.664i	−1.70582	−	5.24997i
$961$	−8.03116	+	24.7174i	−0.259070	+	0.797334i
$962$	−36.7923	−	26.7311i	−1.18623	−	0.861847i
$963$	−0.288432	−	0.209558i	−0.00929459	−	0.00675292i
$964$	−6.44096	+	19.8232i	−0.207449	+	0.638464i
$965$	2.47214	+	7.60845i	0.0795809	+	0.244925i
$966$	2.46445	−	1.79053i	0.0792924	−	0.0576093i
$967$	47.3082			1.52133			0.760665	−	0.649145i	$-0.224873\pi$
$967$	47.3082			1.52133			0.760665	+	0.649145i	$0.224873\pi$
$968$		0			0
$969$	7.27365			0.233663
$970$	−49.0242	+	35.6182i	−1.57407	+	1.14363i
$971$	−7.79820	−	24.0004i	−0.250256	−	0.770209i	−0.994727	−	0.102555i	$-0.967298\pi$
$971$	−7.79820	−	24.0004i	−0.250256	−	0.770209i	0.744471	−	0.667655i	$-0.232702\pi$
$972$	−1.86170	+	5.72972i	−0.0597140	+	0.183781i
$973$	−12.8001	−	9.29978i	−0.410351	−	0.298137i
$974$	−55.3973	−	40.2485i	−1.77504	−	1.28964i
$975$	−2.46557	+	7.58824i	−0.0789614	+	0.243018i
$976$	−52.6494	−	162.038i	−1.68527	−	5.18671i
$977$	−5.74652	+	4.17509i	−0.183847	+	0.133573i	−0.675902	−	0.736991i	$-0.736246\pi$
$977$	−5.74652	+	4.17509i	−0.183847	+	0.133573i	0.492055	+	0.870564i	$0.336246\pi$
$978$	−47.3295			−1.51343
$979$		0			0
$980$	−14.7755			−0.471986
$981$	1.35386	−	0.983640i	0.0432256	−	0.0314052i
$982$	10.4164	+	32.0582i	0.332399	+	1.02302i
$983$	−4.38473	+	13.4948i	−0.139851	+	0.430418i	−0.996313	−	0.0857927i	$-0.972658\pi$
$983$	−4.38473	+	13.4948i	−0.139851	+	0.430418i	0.856462	+	0.516210i	$0.172658\pi$
$984$	−148.246	−	107.707i	−4.72590	−	3.43356i
$985$	10.5250	+	7.64684i	0.335354	+	0.243649i
$986$	−3.52364	+	10.8447i	−0.112216	+	0.345364i
$987$	3.47718	+	10.7017i	0.110680	+	0.340638i
$988$	−18.7944	+	13.6549i	−0.597929	+	0.434421i
$989$	−4.54144			−0.144409
$990$		0			0
$991$	4.23407			0.134500			0.0672499	−	0.997736i	$-0.478578\pi$
$991$	4.23407			0.134500			0.0672499	+	0.997736i	$0.478578\pi$
$992$	45.7558	−	33.2435i	1.45275	−	1.05548i
$993$	4.66054	+	14.3437i	0.147898	+	0.455183i
$994$	6.89928	−	21.2338i	0.218832	−	0.673495i
$995$	33.3668	+	24.2424i	1.05780	+	0.768536i
$996$	−102.435	−	74.4233i	−3.24577	−	2.35819i
$997$	−8.56122	+	26.3487i	−0.271137	+	0.834473i	0.719079	+	0.694928i	$0.244564\pi$
$997$	−8.56122	+	26.3487i	−0.271137	+	0.834473i	−0.990216	+	0.139545i	$0.955436\pi$
$998$	19.0527	+	58.6383i	0.603104	+	1.85616i
$999$	−28.4738	+	20.6874i	−0.900871	+	0.654521i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.f.t.729.1		12
11.2	odd	10		847.2.a.i.1.1	✓	3
11.3	even	5	inner	847.2.f.t.148.3		12
11.4	even	5	inner	847.2.f.t.323.1		12
11.5	even	5	inner	847.2.f.t.372.3		12
11.6	odd	10		847.2.f.u.372.1		12
11.7	odd	10		847.2.f.u.323.3		12
11.8	odd	10		847.2.f.u.148.1		12
11.9	even	5		847.2.a.j.1.3	yes	3
11.10	odd	2		847.2.f.u.729.3		12
33.2	even	10		7623.2.a.ce.1.3		3
33.20	odd	10		7623.2.a.bz.1.1		3
77.13	even	10		5929.2.a.t.1.1		3
77.20	odd	10		5929.2.a.y.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
847.2.a.i.1.1	✓	3	11.2	odd	10
847.2.a.j.1.3	yes	3	11.9	even	5
847.2.f.t.148.3		12	11.3	even	5	inner
847.2.f.t.323.1		12	11.4	even	5	inner
847.2.f.t.372.3		12	11.5	even	5	inner
847.2.f.t.729.1		12	1.1	even	1	trivial
847.2.f.u.148.1		12	11.8	odd	10
847.2.f.u.323.3		12	11.7	odd	10
847.2.f.u.372.1		12	11.6	odd	10
847.2.f.u.729.3		12	11.10	odd	2
5929.2.a.t.1.1		3	77.13	even	10
5929.2.a.y.1.3		3	77.20	odd	10
7623.2.a.bz.1.1		3	33.20	odd	10
7623.2.a.ce.1.3		3	33.2	even	10

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.f (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.23415 + 1.62320i) q^{2} +(0.544351 + 1.67534i) q^{3} +(1.73859 - 5.35083i) q^{4} +(2.12464 + 1.54364i) q^{5} +(-3.93558 - 2.85936i) q^{6} +(0.309017 - 0.951057i) q^{7} +(3.09448 + 9.52384i) q^{8} +(-0.0833965 + 0.0605911i) q^{9} -7.25240 q^{10} +9.91087 q^{12} +(1.93173 - 1.40349i) q^{13} +(0.853368 + 2.62640i) q^{14} +(-1.42957 + 4.39978i) q^{15} +(-13.2693 - 9.64068i) q^{16} +(1.93173 + 1.40349i) q^{17} +(0.0879683 - 0.270739i) q^{18} +(-0.534377 - 1.64464i) q^{19} +(11.9536 - 8.68483i) q^{20} +1.76156 q^{21} -0.626198 q^{23} +(-14.2712 + 10.3686i) q^{24} +(0.586179 + 1.80407i) q^{25} +(-2.03763 + 6.27119i) q^{26} +(4.12848 + 2.99952i) q^{27} +(-4.55169 - 3.30700i) q^{28} +(0.534377 - 1.64464i) q^{29} +(-3.94785 - 12.1502i) q^{30} +(1.81094 - 1.31572i) q^{31} +25.2663 q^{32} -6.59392 q^{34} +(2.12464 - 1.54364i) q^{35} +(0.179220 + 0.551584i) q^{36} +(-2.13126 + 6.55936i) q^{37} +(3.86347 + 2.80697i) q^{38} +(3.40286 + 2.47232i) q^{39} +(-8.12672 + 25.0115i) q^{40} +(3.20999 + 9.87934i) q^{41} +(-3.93558 + 2.85936i) q^{42} +7.25240 q^{43} -0.270718 q^{45} +(1.39902 - 1.01645i) q^{46} +(1.97392 + 6.07512i) q^{47} +(8.92829 - 27.4784i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(-4.23799 - 3.07908i) q^{50} +(-1.29978 + 4.00030i) q^{51} +(-4.15133 - 12.7765i) q^{52} +(7.48535 - 5.43842i) q^{53} -14.0925 q^{54} +10.0140 q^{56} +(2.46445 - 1.79053i) q^{57} +(1.47571 + 4.54178i) q^{58} +(-0.544351 + 1.67534i) q^{59} +(21.0570 + 15.2988i) q^{60} +(8.40387 + 6.10577i) q^{61} +(-1.91022 + 5.87904i) q^{62} +(0.0318546 + 0.0980384i) q^{63} +(-29.9102 + 21.7310i) q^{64} +6.27072 q^{65} -6.42003 q^{67} +(10.8683 - 7.89630i) q^{68} +(-0.340872 - 1.04909i) q^{69} +(-2.24111 + 6.89744i) q^{70} +(-6.54071 - 4.75210i) q^{71} +(-0.835128 - 0.606756i) q^{72} +(3.20999 - 9.87934i) q^{73} +(-5.88561 - 18.1140i) q^{74} +(-2.70335 + 1.96410i) q^{75} -9.72928 q^{76} -11.6156 q^{78} +(-12.3394 + 8.96513i) q^{79} +(-13.3106 - 40.9659i) q^{80} +(-2.87343 + 8.84352i) q^{81} +(-23.2078 - 16.8614i) q^{82} +(-10.3356 - 7.50926i) q^{83} +(3.06263 - 9.42580i) q^{84} +(1.93776 + 5.96381i) q^{85} +(-16.2029 + 11.7721i) q^{86} +3.04623 q^{87} -14.1493 q^{89} +(0.604824 - 0.439431i) q^{90} +(-0.737857 - 2.27089i) q^{91} +(-1.08870 + 3.35068i) q^{92} +(3.19007 + 2.31772i) q^{93} +(-14.2712 - 10.3686i) q^{94} +(1.40338 - 4.31916i) q^{95} +(13.7538 + 42.3297i) q^{96} +(6.75973 - 4.91123i) q^{97} +2.76156 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} + q^{3} - 8 q^{4} - q^{5} - 12 q^{6} - 3 q^{7} - 6 q^{8} - 4 q^{9} - 16 q^{10} + 8 q^{12} - 8 q^{13} - 2 q^{14} + 5 q^{15} - 10 q^{16} - 8 q^{17} + 18 q^{18} + 14 q^{20} - 4 q^{21} + 28 q^{23}+ \cdots + 8 q^{98}+O(q^{100}) \) 12 * q - 2 * q^2 + q^3 - 8 * q^4 - q^5 - 12 * q^6 - 3 * q^7 - 6 * q^8 - 4 * q^9 - 16 * q^10 + 8 * q^12 - 8 * q^13 - 2 * q^14 + 5 * q^15 - 10 * q^16 - 8 * q^17 + 18 * q^18 + 14 * q^20 - 4 * q^21 + 28 * q^23 - 20 * q^24 - 2 * q^25 + 12 * q^26 + 19 * q^27 - 8 * q^28 + 8 * q^30 + 13 * q^31 + 136 * q^32 - 48 * q^34 - q^35 - 18 * q^36 + 17 * q^37 - 16 * q^38 + 20 * q^39 + 36 * q^40 - 16 * q^41 - 12 * q^42 + 16 * q^43 - 24 * q^45 - 4 * q^47 - 36 * q^48 - 3 * q^49 - 22 * q^50 + 20 * q^51 + 10 * q^53 + 32 * q^54 + 24 * q^56 - 16 * q^57 + 16 * q^58 - q^59 + 30 * q^60 + 16 * q^61 - 4 * q^62 - 4 * q^63 - 34 * q^64 + 96 * q^65 - 12 * q^67 + 7 * q^69 + 4 * q^70 - 5 * q^71 - 2 * q^72 - 16 * q^73 + 32 * q^74 - 20 * q^75 - 96 * q^76 + 112 * q^78 - 28 * q^79 + 56 * q^80 - 15 * q^81 - 28 * q^82 - 8 * q^83 - 2 * q^84 - 24 * q^85 - 12 * q^86 - 64 * q^87 - 84 * q^89 + 20 * q^90 - 8 * q^91 - 2 * q^92 - 17 * q^93 - 20 * q^94 - 24 * q^95 - 20 * q^96 + 11 * q^97 + 8 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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