LMFDB - Embedded newform 847.2.f.x.729.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(148,847)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 14 x^{14} - 32 x^{13} + 86 x^{12} - 145 x^{11} + 245 x^{10} - 245 x^{9} + 640 x^{8} + \cdots + 25 $ x^16 - 3x^15 + 14x^14 - 32x^13 + 86x^12 - 145x^11 + 245x^10 - 245x^9 + 640x^8 - 1175x^7 + 2135x^6 - 2300x^5 + 1850x^4 - 925x^3 + 700x^2 - 200*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			729.4
Root			$1.60551 - 1.16647i$ of defining polynomial
Character	$\chi$	$=$	847.729
Dual form			847.2.f.x.323.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.60551 - 1.16647i) q^{2} +(0.861043 + 2.65002i) q^{3} +(0.598967 - 1.84343i) q^{4} +(0.0217822 + 0.0158257i) q^{5} +(4.47357 + 3.25024i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(0.0378378 + 0.116453i) q^{8} +(-3.85415 + 2.80020i) q^{9} +O(q^{10})$	\(q+(1.60551 - 1.16647i) q^{2} +(0.861043 + 2.65002i) q^{3} +(0.598967 - 1.84343i) q^{4} +(0.0217822 + 0.0158257i) q^{5} +(4.47357 + 3.25024i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(0.0378378 + 0.116453i) q^{8} +(-3.85415 + 2.80020i) q^{9} +0.0534317 q^{10} +5.40087 q^{12} +(-3.94891 + 2.86905i) q^{13} +(0.613249 + 1.88739i) q^{14} +(-0.0231830 + 0.0713500i) q^{15} +(3.33282 + 2.42144i) q^{16} +(1.35816 + 0.986762i) q^{17} +(-2.92151 + 8.99149i) q^{18} +(-0.424571 - 1.30670i) q^{19} +(0.0422205 - 0.0306750i) q^{20} -2.78639 q^{21} +8.06246 q^{23} +(-0.276022 + 0.200542i) q^{24} +(-1.54486 - 4.75459i) q^{25} +(-2.99334 + 9.21255i) q^{26} +(-3.97645 - 2.88906i) q^{27} +(1.56812 + 1.13930i) q^{28} +(1.97560 - 6.08026i) q^{29} +(0.0460070 + 0.141595i) q^{30} +(-3.24460 + 2.35734i) q^{31} +7.93050 q^{32} +3.33156 q^{34} +(-0.0217822 + 0.0158257i) q^{35} +(2.85347 + 8.78209i) q^{36} +(0.161010 - 0.495536i) q^{37} +(-2.20587 - 1.60266i) q^{38} +(-11.0032 - 7.99430i) q^{39} +(-0.00101876 + 0.00313541i) q^{40} +(3.27519 + 10.0800i) q^{41} +(-4.47357 + 3.25024i) q^{42} -3.73968 q^{43} -0.128267 q^{45} +(12.9443 - 9.40461i) q^{46} +(-2.76850 - 8.52058i) q^{47} +(-3.54715 + 10.9170i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(-8.02637 - 5.83150i) q^{50} +(-1.44550 + 4.44879i) q^{51} +(2.92363 + 8.99801i) q^{52} +(3.20417 - 2.32797i) q^{53} -9.75422 q^{54} -0.122446 q^{56} +(3.09719 - 2.25024i) q^{57} +(-3.92060 - 12.0664i) q^{58} +(3.00680 - 9.25399i) q^{59} +(0.117643 + 0.0854726i) q^{60} +(6.85013 + 4.97691i) q^{61} +(-2.45946 + 7.56944i) q^{62} +(-1.47215 - 4.53082i) q^{63} +(6.06683 - 4.40781i) q^{64} -0.131421 q^{65} +2.81285 q^{67} +(2.63252 - 1.91264i) q^{68} +(6.94213 + 21.3657i) q^{69} +(-0.0165113 + 0.0508166i) q^{70} +(-1.65485 - 1.20232i) q^{71} +(-0.471924 - 0.342873i) q^{72} +(3.23520 - 9.95693i) q^{73} +(-0.319526 - 0.983399i) q^{74} +(11.2696 - 8.18782i) q^{75} -2.66311 q^{76} -26.9908 q^{78} +(4.73697 - 3.44161i) q^{79} +(0.0342753 + 0.105489i) q^{80} +(-0.184290 + 0.567186i) q^{81} +(17.0163 + 12.3631i) q^{82} +(2.10787 + 1.53146i) q^{83} +(-1.66896 + 5.13653i) q^{84} +(0.0139676 + 0.0429878i) q^{85} +(-6.00409 + 4.36222i) q^{86} +17.8139 q^{87} +1.21791 q^{89} +(-0.205934 + 0.149620i) q^{90} +(-1.50835 - 4.64222i) q^{91} +(4.82915 - 14.8626i) q^{92} +(-9.04072 - 6.56847i) q^{93} +(-14.3838 - 10.4505i) q^{94} +(0.0114313 - 0.0351819i) q^{95} +(6.82851 + 21.0160i) q^{96} +(-2.74799 + 1.99653i) q^{97} -1.98451 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 3 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} - 3 q^{6} + 4 q^{7} + 5 q^{8} - 12 q^{9}+O(q^{10}) $ 16 * q + 3 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 - 3 * q^6 + 4 * q^7 + 5 * q^8 - 12 * q^9	$ 16 q + 3 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} - 3 q^{6} + 4 q^{7} + 5 q^{8} - 12 q^{9} - 12 q^{10} + 18 q^{12} + 7 q^{13} + 2 q^{14} - 18 q^{15} + 17 q^{16} + 5 q^{17} - 11 q^{18} - 19 q^{19} + q^{20} - 8 q^{21} + 32 q^{23} + 35 q^{24} + 7 q^{25} - 27 q^{26} + 10 q^{27} - 4 q^{28} - 3 q^{29} + 2 q^{30} - 7 q^{31} - 32 q^{32} - 24 q^{34} + 5 q^{35} + 52 q^{36} + 4 q^{37} - 5 q^{38} - 11 q^{39} + 10 q^{40} + 10 q^{41} + 3 q^{42} + 8 q^{43} + 70 q^{45} + 42 q^{46} - 23 q^{47} - 36 q^{48} - 4 q^{49} - 52 q^{50} + 29 q^{51} - 33 q^{52} + 4 q^{53} - 60 q^{54} + 11 q^{57} + 20 q^{58} + 17 q^{59} - 30 q^{60} + 7 q^{61} - 79 q^{62} + 2 q^{63} + 7 q^{64} + 8 q^{65} - 38 q^{67} + 2 q^{68} + 10 q^{69} - 18 q^{70} - 14 q^{71} + 35 q^{73} + 29 q^{74} + 9 q^{75} - 52 q^{76} - 58 q^{78} - 15 q^{79} - 87 q^{80} - 14 q^{81} + 19 q^{82} - 5 q^{83} - 8 q^{84} - 6 q^{85} - 52 q^{86} + 72 q^{87} + 74 q^{89} + 14 q^{90} + 13 q^{91} - 55 q^{92} + 32 q^{93} + 24 q^{94} - 32 q^{95} + 42 q^{96} + 20 q^{97} - 2 q^{98}+O(q^{100}) $ 16 * q + 3 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 - 3 * q^6 + 4 * q^7 + 5 * q^8 - 12 * q^9 - 12 * q^10 + 18 * q^12 + 7 * q^13 + 2 * q^14 - 18 * q^15 + 17 * q^16 + 5 * q^17 - 11 * q^18 - 19 * q^19 + q^20 - 8 * q^21 + 32 * q^23 + 35 * q^24 + 7 * q^25 - 27 * q^26 + 10 * q^27 - 4 * q^28 - 3 * q^29 + 2 * q^30 - 7 * q^31 - 32 * q^32 - 24 * q^34 + 5 * q^35 + 52 * q^36 + 4 * q^37 - 5 * q^38 - 11 * q^39 + 10 * q^40 + 10 * q^41 + 3 * q^42 + 8 * q^43 + 70 * q^45 + 42 * q^46 - 23 * q^47 - 36 * q^48 - 4 * q^49 - 52 * q^50 + 29 * q^51 - 33 * q^52 + 4 * q^53 - 60 * q^54 + 11 * q^57 + 20 * q^58 + 17 * q^59 - 30 * q^60 + 7 * q^61 - 79 * q^62 + 2 * q^63 + 7 * q^64 + 8 * q^65 - 38 * q^67 + 2 * q^68 + 10 * q^69 - 18 * q^70 - 14 * q^71 + 35 * q^73 + 29 * q^74 + 9 * q^75 - 52 * q^76 - 58 * q^78 - 15 * q^79 - 87 * q^80 - 14 * q^81 + 19 * q^82 - 5 * q^83 - 8 * q^84 - 6 * q^85 - 52 * q^86 + 72 * q^87 + 74 * q^89 + 14 * q^90 + 13 * q^91 - 55 * q^92 + 32 * q^93 + 24 * q^94 - 32 * q^95 + 42 * q^96 + 20 * q^97 - 2 * q^98

Display 100 coefficients 10 coefficients

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 $

$2$	1.60551	−	1.16647i	1.13526	−	0.824818i	0.148812	−	0.988866i	$-0.452455\pi$
$2$	1.60551	−	1.16647i	1.13526	−	0.824818i	0.986452	+	0.164048i	$0.0524551\pi$
$3$	0.861043	+	2.65002i	0.497123	+	1.52999i	0.813621	+	0.581395i	$0.197493\pi$
$3$	0.861043	+	2.65002i	0.497123	+	1.52999i	−0.316498	+	0.948593i	$0.602507\pi$
$4$	0.598967	−	1.84343i	0.299484	−	0.921716i
$5$	0.0217822	+	0.0158257i	0.00974131	+	0.00707748i	0.592645	−	0.805464i	$-0.298084\pi$
$5$	0.0217822	+	0.0158257i	0.00974131	+	0.00707748i	−0.582904	+	0.812541i	$0.698084\pi$
$6$	4.47357	+	3.25024i	1.82633	+	1.32691i
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i
$8$	0.0378378	+	0.116453i	0.0133777	+	0.0411723i
$9$	−3.85415	+	2.80020i	−1.28472	+	0.933401i
$10$	0.0534317			0.0168966
$11$		0			0
$11$		0			0
$12$	5.40087			1.55910
$13$	−3.94891	+	2.86905i	−1.09523	+	0.795731i	−0.980275	−	0.197639i	$-0.936672\pi$
$13$	−3.94891	+	2.86905i	−1.09523	+	0.795731i	−0.114955	+	0.993371i	$0.536672\pi$
$14$	0.613249	+	1.88739i	0.163898	+	0.504425i
$15$	−0.0231830	+	0.0713500i	−0.00598583	+	0.0184225i
$16$	3.33282	+	2.42144i	0.833205	+	0.605359i
$17$	1.35816	+	0.986762i	0.329402	+	0.239325i	0.740177	−	0.672412i	$-0.234742\pi$
$17$	1.35816	+	0.986762i	0.329402	+	0.239325i	−0.410775	+	0.911737i	$0.634742\pi$
$18$	−2.92151	+	8.99149i	−0.688607	+	2.11931i
$19$	−0.424571	−	1.30670i	−0.0974033	−	0.299776i	0.890469	−	0.455043i	$-0.150376\pi$
$19$	−0.424571	−	1.30670i	−0.0974033	−	0.299776i	−0.987873	+	0.155267i	$0.950376\pi$
$20$	0.0422205	−	0.0306750i	0.00944079	−	0.00685914i
$21$	−2.78639			−0.608041
$22$		0			0
$23$	8.06246			1.68114			0.840570	−	0.541703i	$-0.182220\pi$
$23$	8.06246			1.68114			0.840570	+	0.541703i	$0.182220\pi$
$24$	−0.276022	+	0.200542i	−0.0563428	+	0.0409354i
$25$	−1.54486	−	4.75459i	−0.308972	−	0.950919i
$26$	−2.99334	+	9.21255i	−0.587042	+	1.80673i
$27$	−3.97645	−	2.88906i	−0.765269	−	0.556000i
$28$	1.56812	+	1.13930i	0.296346	+	0.215308i
$29$	1.97560	−	6.08026i	0.366859	−	1.12908i	−0.581950	−	0.813225i	$-0.697710\pi$
$29$	1.97560	−	6.08026i	0.366859	−	1.12908i	0.948809	−	0.315851i	$-0.102290\pi$
$30$	0.0460070	+	0.141595i	0.00839969	+	0.0258516i
$31$	−3.24460	+	2.35734i	−0.582747	+	0.423390i	−0.839713	−	0.543030i	$-0.817277\pi$
$31$	−3.24460	+	2.35734i	−0.582747	+	0.423390i	0.256967	+	0.966420i	$0.417277\pi$
$32$	7.93050			1.40193
$33$		0			0
$34$	3.33156			0.571358
$35$	−0.0217822	+	0.0158257i	−0.00368187	+	0.00267504i
$36$	2.85347	+	8.78209i	0.475579	+	1.46368i
$37$	0.161010	−	0.495536i	0.0264698	−	0.0814657i	−0.936949	−	0.349466i	$-0.886363\pi$
$37$	0.161010	−	0.495536i	0.0264698	−	0.0814657i	0.963419	+	0.268001i	$0.0863629\pi$
$38$	−2.20587	−	1.60266i	−0.357839	−	0.259986i
$39$	−11.0032	−	7.99430i	−1.76192	−	1.28011i
$40$	−0.00101876	+	0.00313541i	−0.000161080	+	0.000495752i
$41$	3.27519	+	10.0800i	0.511499	+	1.57423i	0.789563	+	0.613669i	$0.210307\pi$
$41$	3.27519	+	10.0800i	0.511499	+	1.57423i	−0.278064	+	0.960563i	$0.589693\pi$
$42$	−4.47357	+	3.25024i	−0.690287	+	0.501523i
$43$	−3.73968			−0.570296			−0.285148	−	0.958483i	$-0.592043\pi$
$43$	−3.73968			−0.570296			−0.285148	+	0.958483i	$0.592043\pi$
$44$		0			0
$45$	−0.128267			−0.0191209
$46$	12.9443	−	9.40461i	1.90854	−	1.38663i
$47$	−2.76850	−	8.52058i	−0.403828	−	1.24285i	−0.921870	−	0.387499i	$-0.873339\pi$
$47$	−2.76850	−	8.52058i	−0.403828	−	1.24285i	0.518042	−	0.855355i	$-0.326661\pi$
$48$	−3.54715	+	10.9170i	−0.511987	+	1.57573i
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$	−8.02637	−	5.83150i	−1.13510	−	0.824698i
$51$	−1.44550	+	4.44879i	−0.202411	+	0.622956i
$52$	2.92363	+	8.99801i	0.405435	+	1.24780i
$53$	3.20417	−	2.32797i	0.440127	−	0.319771i	−0.345558	−	0.938397i	$-0.612311\pi$
$53$	3.20417	−	2.32797i	0.440127	−	0.319771i	0.785685	+	0.618626i	$0.212311\pi$
$54$	−9.75422			−1.32738
$55$		0			0
$56$	−0.122446			−0.0163625
$57$	3.09719	−	2.25024i	0.410233	−	0.298052i
$58$	−3.92060	−	12.0664i	−0.514800	−	1.58439i
$59$	3.00680	−	9.25399i	0.391452	−	1.20477i	−0.540238	−	0.841512i	$-0.681666\pi$
$59$	3.00680	−	9.25399i	0.391452	−	1.20477i	0.931690	−	0.363254i	$-0.118334\pi$
$60$	0.117643	+	0.0854726i	0.0151876	+	0.0110345i
$61$	6.85013	+	4.97691i	0.877069	+	0.637228i	0.932474	−	0.361236i	$-0.117645\pi$
$61$	6.85013	+	4.97691i	0.877069	+	0.637228i	−0.0554053	+	0.998464i	$0.517645\pi$
$62$	−2.45946	+	7.56944i	−0.312352	+	0.961320i
$63$	−1.47215	−	4.53082i	−0.185474	−	0.570830i
$64$	6.06683	−	4.40781i	0.758354	−	0.550976i
$65$	−0.131421			−0.0163008
$66$		0			0
$67$	2.81285			0.343644			0.171822	−	0.985128i	$-0.445035\pi$
$67$	2.81285			0.343644			0.171822	+	0.985128i	$0.445035\pi$
$68$	2.63252	−	1.91264i	0.319240	−	0.231942i
$69$	6.94213	+	21.3657i	0.835734	+	2.57212i
$70$	−0.0165113	+	0.0508166i	−0.00197348	+	0.00607375i
$71$	−1.65485	−	1.20232i	−0.196395	−	0.142689i	0.485242	−	0.874380i	$-0.338732\pi$
$71$	−1.65485	−	1.20232i	−0.196395	−	0.142689i	−0.681637	+	0.731691i	$0.738732\pi$
$72$	−0.471924	−	0.342873i	−0.0556168	−	0.0404079i
$73$	3.23520	−	9.95693i	0.378652	−	1.16537i	−0.562330	−	0.826913i	$-0.690095\pi$
$73$	3.23520	−	9.95693i	0.378652	−	1.16537i	0.940982	−	0.338457i	$-0.109905\pi$
$74$	−0.319526	−	0.983399i	−0.0371441	−	0.114318i
$75$	11.2696	−	8.18782i	1.30130	−	0.945448i
$76$	−2.66311			−0.305479
$77$		0			0
$78$	−26.9908			−3.05611
$79$	4.73697	−	3.44161i	0.532950	−	0.387211i	−0.288510	−	0.957477i	$-0.593160\pi$
$79$	4.73697	−	3.44161i	0.532950	−	0.387211i	0.821460	+	0.570266i	$0.193160\pi$
$80$	0.0342753	+	0.105489i	0.00383210	+	0.0117940i
$81$	−0.184290	+	0.567186i	−0.0204767	+	0.0630207i
$82$	17.0163	+	12.3631i	1.87914	+	1.36528i
$83$	2.10787	+	1.53146i	0.231369	+	0.168100i	0.697430	−	0.716653i	$-0.254327\pi$
$83$	2.10787	+	1.53146i	0.231369	+	0.168100i	−0.466060	+	0.884753i	$0.654327\pi$
$84$	−1.66896	+	5.13653i	−0.182098	+	0.560441i
$85$	0.0139676	+	0.0429878i	0.00151500	+	0.00466268i
$86$	−6.00409	+	4.36222i	−0.647437	+	0.470391i
$87$	17.8139			1.90985
$88$		0			0
$89$	1.21791			0.129099			0.0645493	−	0.997915i	$-0.479439\pi$
$89$	1.21791			0.129099			0.0645493	+	0.997915i	$0.479439\pi$
$90$	−0.205934	+	0.149620i	−0.0217073	+	0.0157713i
$91$	−1.50835	−	4.64222i	−0.158118	−	0.486637i
$92$	4.82915	−	14.8626i	0.503474	−	1.54953i
$93$	−9.04072	−	6.56847i	−0.937479	−	0.681119i
$94$	−14.3838	−	10.4505i	−1.48358	−	1.07788i
$95$	0.0114313	−	0.0351819i	0.00117283	−	0.00360959i
$96$	6.82851	+	21.0160i	0.696931	+	2.14493i
$97$	−2.74799	+	1.99653i	−0.279016	+	0.202717i	−0.718488	−	0.695539i	$-0.755166\pi$
$97$	−2.74799	+	1.99653i	−0.279016	+	0.202717i	0.439472	+	0.898256i	$0.355166\pi$
$98$	−1.98451			−0.200466
$99$		0			0
$100$	−9.69009			−0.969009
$101$	−3.27519	+	2.37956i	−0.325893	+	0.236775i	−0.738686	−	0.674050i	$-0.764553\pi$
$101$	−3.27519	+	2.37956i	−0.325893	+	0.236775i	0.412793	+	0.910825i	$0.364553\pi$
$102$	2.86862	+	8.82870i	0.284036	+	0.874171i
$103$	−1.22153	+	3.75950i	−0.120361	+	0.370434i	−0.993027	−	0.117883i	$-0.962389\pi$
$103$	−1.22153	+	3.75950i	−0.120361	+	0.370434i	0.872666	+	0.488317i	$0.162389\pi$
$104$	−0.483527	−	0.351303i	−0.0474137	−	0.0344481i
$105$	−0.0606939	−	0.0440967i	−0.00592312	−	0.00430340i
$106$	2.42882	−	7.47513i	0.235908	−	0.726049i
$107$	−3.21335	−	9.88966i	−0.310646	−	0.956070i	−0.977510	−	0.210890i	$-0.932364\pi$
$107$	−3.21335	−	9.88966i	−0.310646	−	0.956070i	0.666864	−	0.745179i	$-0.267636\pi$
$108$	−7.70756	+	5.59987i	−0.741660	+	0.538848i
$109$	3.77697			0.361768			0.180884	−	0.983504i	$-0.442104\pi$
$109$	3.77697			0.361768			0.180884	+	0.983504i	$0.442104\pi$
$110$		0			0
$111$	1.45182			0.137800
$112$	−3.33282	+	2.42144i	−0.314922	+	0.228804i
$113$	1.96185	+	6.03796i	0.184555	+	0.568003i	0.999940	−	0.0109158i	$-0.00347467\pi$
$113$	1.96185	+	6.03796i	0.184555	+	0.568003i	−0.815385	+	0.578919i	$0.803475\pi$
$114$	2.34772	−	7.22555i	0.219885	−	0.676735i
$115$	0.175619	+	0.127594i	0.0163765	+	0.0118982i
$116$	−10.0252	−	7.28375i	−0.930819	−	0.676279i
$117$	7.18576	−	22.1155i	0.664323	−	2.04458i
$118$	−5.96704	−	18.3647i	−0.549311	−	1.69061i
$119$	−1.35816	+	0.986762i	−0.124502	+	0.0904563i
$120$	−0.00918610			−0.000838572
$121$		0			0
$122$	16.8033			1.52130
$123$	−23.8921	+	17.3586i	−2.15428	+	1.56518i
$124$	2.40218	+	7.39316i	0.215722	+	0.663926i
$125$	0.0831947	−	0.256047i	0.00744116	−	0.0229015i
$126$	−7.64861	−	5.55704i	−0.681393	−	0.495061i
$127$	−4.07039	−	2.95731i	−0.361189	−	0.262419i	0.392359	−	0.919812i	$-0.371659\pi$
$127$	−4.07039	−	2.95731i	−0.361189	−	0.262419i	−0.753548	+	0.657393i	$0.771659\pi$
$128$	−0.302558	+	0.931179i	−0.0267426	+	0.0823054i
$129$	−3.22003	−	9.91023i	−0.283508	−	0.872547i
$130$	−0.210997	+	0.153298i	−0.0185057	+	0.0134452i
$131$	3.76357			0.328825			0.164412	−	0.986392i	$-0.447427\pi$
$131$	3.76357			0.328825			0.164412	+	0.986392i	$0.447427\pi$
$132$		0			0
$133$	1.37394			0.119136
$134$	4.51604	−	3.28110i	0.390127	−	0.283444i
$135$	−0.0408946	−	0.125861i	−0.00351964	−	0.0108324i
$136$	−0.0635213	+	0.195499i	−0.00544691	+	0.0167639i
$137$	−15.4829	−	11.2490i	−1.32279	−	0.961063i	−0.999893	−	0.0146288i	$-0.995343\pi$
$137$	−15.4829	−	11.2490i	−1.32279	−	0.961063i	−0.322897	−	0.946434i	$-0.604657\pi$
$138$	36.0680	+	26.2049i	3.07031	+	2.23071i
$139$	−1.08498	+	3.33924i	−0.0920272	+	0.283231i	−0.986468	−	0.163957i	$-0.947574\pi$
$139$	−1.08498	+	3.33924i	−0.0920272	+	0.283231i	0.894440	+	0.447187i	$0.147574\pi$
$140$	0.0161268	+	0.0496332i	0.00136296	+	0.00419477i
$141$	20.1959	−	14.6732i	1.70080	−	1.23570i
$142$	−4.05934			−0.340652
$143$		0			0
$144$	−19.6257			−1.63548
$145$	0.139257	−	0.101176i	0.0115647	−	0.00840224i
$146$	−6.42031	−	19.7597i	−0.531348	−	1.63532i
$147$	0.861043	−	2.65002i	0.0710176	−	0.218570i
$148$	−0.817048	−	0.593620i	−0.0671610	−	0.0487953i
$149$	−2.52933	−	1.83767i	−0.207211	−	0.150548i	0.479340	−	0.877629i	$-0.340876\pi$
$149$	−2.52933	−	1.83767i	−0.207211	−	0.150548i	−0.686551	+	0.727082i	$0.740876\pi$
$150$	8.54252	−	26.2912i	0.697494	−	2.14667i
$151$	−6.09427	−	18.7562i	−0.495945	−	1.52636i	−0.815479	−	0.578787i	$-0.803526\pi$
$151$	−6.09427	−	18.7562i	−0.495945	−	1.52636i	0.319534	−	0.947575i	$-0.396474\pi$
$152$	0.136103	−	0.0988850i	0.0110395	−	0.00802063i
$153$	−7.99769			−0.646575
$154$		0			0
$155$	−0.107981			−0.00867326
$156$	−21.3275	+	15.4953i	−1.70757	+	1.24062i
$157$	−7.09335	−	21.8311i	−0.566111	−	1.74231i	−0.664626	−	0.747176i	$-0.731409\pi$
$157$	−7.09335	−	21.8311i	−0.566111	−	1.74231i	0.0985151	−	0.995136i	$-0.468591\pi$
$158$	3.59070	−	11.0510i	0.285661	−	0.879174i
$159$	8.92808	+	6.48663i	0.708043	+	0.514423i
$160$	0.172744	+	0.125506i	0.0136566	+	0.00992212i
$161$	−2.49144	+	7.66786i	−0.196353	+	0.604312i
$162$	0.365726	+	1.12559i	0.0287342	+	0.0884346i
$163$	−15.3625	+	11.1615i	−1.20328	+	0.874236i	−0.994604	−	0.103748i	$-0.966917\pi$
$163$	−15.3625	+	11.1615i	−1.20328	+	0.874236i	−0.208679	+	0.977984i	$0.566917\pi$
$164$	20.5435			1.60418
$165$		0			0
$166$	5.17061			0.401317
$167$	−2.44358	+	1.77537i	−0.189090	+	0.137382i	−0.678303	−	0.734783i	$-0.737284\pi$
$167$	−2.44358	+	1.77537i	−0.189090	+	0.137382i	0.489213	+	0.872165i	$0.337284\pi$
$168$	−0.105431	−	0.324483i	−0.00813418	−	0.0250344i
$169$	3.34521	−	10.2955i	0.257324	−	0.791961i
$170$	0.0725689	+	0.0527244i	0.00556578	+	0.00404378i
$171$	5.29537	+	3.84731i	0.404947	+	0.294211i
$172$	−2.23995	+	6.89385i	−0.170794	+	0.525651i
$173$	−2.73056	−	8.40381i	−0.207601	−	0.638930i	−0.999597	−	0.0284032i	$-0.990958\pi$
$173$	−2.73056	−	8.40381i	−0.207601	−	0.638930i	0.791996	−	0.610527i	$-0.209042\pi$
$174$	28.6003	−	20.7793i	2.16818	−	1.57528i
$175$	4.99928			0.377910
$176$		0			0
$177$	27.1122			2.03788
$178$	1.95537	−	1.42066i	0.146561	−	0.106483i
$179$	2.61562	+	8.05006i	0.195501	+	0.601690i	0.999970	+	0.00769596i	$0.00244972\pi$
$179$	2.61562	+	8.05006i	0.195501	+	0.601690i	−0.804469	+	0.593994i	$0.797550\pi$
$180$	−0.0768279	+	0.236452i	−0.00572641	+	0.0176241i
$181$	19.5789	+	14.2249i	1.45528	+	1.05733i	0.984560	+	0.175046i	$0.0560073\pi$
$181$	19.5789	+	14.2249i	1.45528	+	1.05733i	0.470724	+	0.882280i	$0.343993\pi$
$182$	−7.83667	−	5.69367i	−0.580892	−	0.422043i
$183$	−7.29064	+	22.4383i	−0.538940	+	1.65869i
$184$	0.305066	+	0.938896i	0.0224898	+	0.0692164i
$185$	0.0113494	−	0.00824580i	0.000834422	−	0.000606243i
$186$	−22.1769			−1.62609
$187$		0			0
$188$	−17.3653			−1.26650
$189$	3.97645	−	2.88906i	0.289245	−	0.210148i
$190$	−0.0226856	−	0.0698190i	−0.00164578	−	0.00506520i
$191$	−2.40637	+	7.40605i	−0.174119	+	0.535883i	−0.999592	−	0.0285585i	$-0.990908\pi$
$191$	−2.40637	+	7.40605i	−0.174119	+	0.535883i	0.825473	+	0.564441i	$0.190908\pi$
$192$	16.9046	+	12.2819i	1.21998	+	0.886370i
$193$	13.8048	+	10.0298i	0.993690	+	0.721958i	0.960726	−	0.277498i	$-0.0895052\pi$
$193$	13.8048	+	10.0298i	0.993690	+	0.721958i	0.0329643	+	0.999457i	$0.489505\pi$
$194$	−2.08302	+	6.41089i	−0.149552	+	0.460275i
$195$	−0.113159	−	0.348268i	−0.00810349	−	0.0249400i
$196$	−1.56812	+	1.13930i	−0.112008	+	0.0813788i
$197$	6.05536			0.431426			0.215713	−	0.976457i	$-0.430792\pi$
$197$	6.05536			0.431426			0.215713	+	0.976457i	$0.430792\pi$
$198$		0			0
$199$	−13.7181			−0.972451			−0.486226	−	0.873833i	$-0.661627\pi$
$199$	−13.7181			−0.972451			−0.486226	+	0.873833i	$0.661627\pi$
$200$	0.495232	−	0.359807i	0.0350182	−	0.0254422i
$201$	2.42198	+	7.45410i	0.170833	+	0.525771i
$202$	−2.48265	+	7.64081i	−0.174679	+	0.537605i
$203$	5.17218	+	3.75781i	0.363016	+	0.263746i
$204$	7.33524	+	5.32937i	0.513570	+	0.373130i
$205$	−0.0881823	+	0.271397i	−0.00615892	+	0.0189552i
$206$	2.42415	+	7.46078i	0.168899	+	0.519817i
$207$	−31.0739	+	22.5765i	−2.15979	+	1.56918i
$208$	−20.1082			−1.39425
$209$		0			0
$210$	−0.148882			−0.0102738
$211$	14.5908	−	10.6009i	1.00447	−	0.729793i	0.0414309	−	0.999141i	$-0.486808\pi$
$211$	14.5908	−	10.6009i	1.00447	−	0.729793i	0.963043	+	0.269349i	$0.0868083\pi$
$212$	−2.37226	−	7.30105i	−0.162927	−	0.501438i
$213$	1.76127	−	5.42063i	0.120680	−	0.371416i
$214$	−16.6950	−	12.1296i	−1.14125	−	0.829165i
$215$	−0.0814587	−	0.0591832i	−0.00555544	−	0.00403626i
$216$	0.185979	−	0.572385i	0.0126543	−	0.0389459i
$217$	−1.23933	−	3.81425i	−0.0841309	−	0.258928i
$218$	6.06395	−	4.40572i	0.410703	−	0.298393i
$219$	29.1717			1.97124
$220$		0			0
$221$	−8.19432			−0.551210
$222$	2.33090	−	1.69350i	0.156440	−	0.113660i
$223$	−2.01885	−	6.21338i	−0.135192	−	0.416079i	0.860428	−	0.509573i	$-0.170197\pi$
$223$	−2.01885	−	6.21338i	−0.135192	−	0.416079i	−0.995620	+	0.0934937i	$0.970197\pi$
$224$	−2.45066	+	7.54236i	−0.163742	+	0.503945i
$225$	19.2679	+	13.9990i	1.28453	+	0.933266i
$226$	10.1929	+	7.40554i	0.678019	+	0.492609i
$227$	−4.20501	+	12.9417i	−0.279097	+	0.858971i	0.709010	+	0.705199i	$0.249142\pi$
$227$	−4.20501	+	12.9417i	−0.279097	+	0.858971i	−0.988106	+	0.153772i	$0.950858\pi$
$228$	−2.29305	−	7.05728i	−0.151861	−	0.467380i
$229$	15.7120	−	11.4154i	1.03828	−	0.754352i	0.0683285	−	0.997663i	$-0.478233\pi$
$229$	15.7120	−	11.4154i	1.03828	−	0.754352i	0.969948	+	0.243311i	$0.0782334\pi$
$230$	0.430791			0.0284055
$231$		0			0
$232$	0.782815			0.0513943
$233$	3.52853	−	2.56363i	0.231162	−	0.167949i	−0.466175	−	0.884693i	$-0.654368\pi$
$233$	3.52853	−	2.56363i	0.231162	−	0.167949i	0.697337	+	0.716744i	$0.254368\pi$
$234$	−14.2602	−	43.8885i	−0.932221	−	2.86908i
$235$	0.0745401	−	0.229411i	0.00486246	−	0.0149651i
$236$	−15.2581	−	11.0857i	−0.993219	−	0.721616i
$237$	13.1991	+	9.58967i	0.857371	+	0.622916i
$238$	−1.02951	+	3.16850i	−0.0667332	+	0.205384i
$239$	−3.27253	−	10.0718i	−0.211682	−	0.651491i	−0.999373	−	0.0354193i	$-0.988723\pi$
$239$	−3.27253	−	10.0718i	−0.211682	−	0.651491i	0.787690	−	0.616071i	$-0.211277\pi$
$240$	−0.250034	+	0.181661i	−0.0161396	+	0.0117261i
$241$	−18.6887			−1.20384			−0.601921	−	0.798555i	$-0.705598\pi$
$241$	−18.6887			−1.20384			−0.601921	+	0.798555i	$0.705598\pi$
$242$		0			0
$243$	−16.4072			−1.05252
$244$	13.2776	−	9.64674i	0.850011	−	0.617569i
$245$	−0.00832008	−	0.0256066i	−0.000531550	−	0.00163594i
$246$	−18.1106	+	55.7388i	−1.15469	+	3.55377i
$247$	5.42557	+	3.94190i	0.345220	+	0.250817i
$248$	−0.397287	−	0.288646i	−0.0252277	−	0.0183290i
$249$	−2.24343	+	6.90456i	−0.142171	+	0.437559i
$250$	−0.165101	−	0.508129i	−0.0104419	−	0.0321369i
$251$	−15.3577	+	11.1580i	−0.969369	+	0.704288i	−0.955308	−	0.295613i	$-0.904476\pi$
$251$	−15.3577	+	11.1580i	−0.969369	+	0.704288i	−0.0140616	+	0.999901i	$0.504476\pi$
$252$	−9.23404			−0.581690
$253$		0			0
$254$	−9.98465			−0.626493
$255$	−0.101892	+	0.0740286i	−0.00638070	+	0.00463585i
$256$	5.23508	+	16.1119i	0.327192	+	1.00699i
$257$	−4.23633	+	13.0381i	−0.264255	+	0.813293i	0.727609	+	0.685992i	$0.240631\pi$
$257$	−4.23633	+	13.0381i	−0.264255	+	0.813293i	−0.991864	+	0.127301i	$0.959369\pi$
$258$	−16.7297	−	12.1549i	−1.04155	−	0.756729i
$259$	0.421528	+	0.306258i	0.0261925	+	0.0190300i
$260$	−0.0787168	+	0.242265i	−0.00488181	+	0.0150247i
$261$	9.41171	+	28.9663i	0.582571	+	1.79297i
$262$	6.04244	−	4.39009i	0.373303	−	0.271221i
$263$	−16.5767			−1.02217			−0.511083	−	0.859531i	$-0.670756\pi$
$263$	−16.5767			−1.02217			−0.511083	+	0.859531i	$0.670756\pi$
$264$		0			0
$265$	0.106636			0.00655059
$266$	2.20587	−	1.60266i	0.135251	−	0.0982653i
$267$	1.04868	+	3.22749i	0.0641779	+	0.197519i
$268$	1.68480	−	5.18529i	0.102916	−	0.316742i
$269$	6.91193	+	5.02181i	0.421428	+	0.306185i	0.778212	−	0.628002i	$-0.216127\pi$
$269$	6.91193	+	5.02181i	0.421428	+	0.306185i	−0.356784	+	0.934187i	$0.616127\pi$
$270$	−0.212469	−	0.154368i	−0.0129304	−	0.00939452i
$271$	1.96088	−	6.03496i	0.119115	−	0.366597i	−0.873668	−	0.486522i	$-0.838265\pi$
$271$	1.96088	−	6.03496i	0.119115	−	0.366597i	0.992783	+	0.119925i	$0.0382653\pi$
$272$	2.13713	+	6.57740i	0.129582	+	0.398814i
$273$	11.0032	−	7.99430i	0.665945	−	0.483837i
$274$	−37.9794			−2.29442
$275$		0			0
$276$	43.5443			2.62106
$277$	−19.4200	+	14.1094i	−1.16683	+	0.847753i	−0.990626	−	0.136600i	$-0.956382\pi$
$277$	−19.4200	+	14.1094i	−1.16683	+	0.847753i	−0.176206	+	0.984353i	$0.556382\pi$
$278$	2.15317	+	6.62677i	0.129138	+	0.397447i
$279$	5.90413	−	18.1711i	0.353471	−	1.08787i
$280$	−0.00266714	−	0.00193779i	−0.000159392	−	0.000115805i
$281$	−2.59811	−	1.88764i	−0.154990	−	0.112607i	0.507587	−	0.861600i	$-0.330537\pi$
$281$	−2.59811	−	1.88764i	−0.154990	−	0.112607i	−0.662577	+	0.748993i	$0.730537\pi$
$282$	15.3088	−	47.1157i	0.911627	−	2.80570i
$283$	6.42860	+	19.7852i	0.382141	+	1.17611i	0.938533	+	0.345188i	$0.112185\pi$
$283$	6.42860	+	19.7852i	0.382141	+	1.17611i	−0.556393	+	0.830919i	$0.687815\pi$
$284$	−3.20760	+	2.33046i	−0.190336	+	0.138287i
$285$	0.103075			0.00610567
$286$		0			0
$287$	−10.5987			−0.625624
$288$	−30.5653	+	22.2070i	−1.80108	+	1.30856i
$289$	−4.38239	−	13.4876i	−0.257787	−	0.793388i
$290$	0.105559	−	0.324879i	0.00619867	−	0.0190775i
$291$	−7.65698	−	5.56312i	−0.448860	−	0.326116i
$292$	−16.4171	−	11.9278i	−0.960741	−	0.698019i
$293$	−1.70498	+	5.24740i	−0.0996062	+	0.306556i	−0.988427	−	0.151699i	$-0.951526\pi$
$293$	−1.70498	+	5.24740i	−0.0996062	+	0.306556i	0.888821	+	0.458255i	$0.151526\pi$
$294$	−1.70875	−	5.25900i	−0.0996565	−	0.306711i
$295$	0.211946	−	0.153988i	0.0123400	−	0.00896551i
$296$	0.0637988			0.00370823
$297$		0			0
$298$	−6.20444			−0.359414
$299$	−31.8379	+	23.1316i	−1.84123	+	1.33774i
$300$	−8.34359	−	25.6789i	−0.481717	−	1.48257i
$301$	1.15563	−	3.55665i	0.0666092	−	0.205002i
$302$	−31.6630	−	23.0045i	−1.82200	−	1.32376i
$303$	−9.12596	−	6.63040i	−0.524273	−	0.380907i
$304$	1.74906	−	5.38305i	0.100315	−	0.308739i
$305$	0.0704480	+	0.216817i	0.00403384	+	0.0124149i
$306$	−12.8403	+	9.32905i	−0.734033	+	0.533306i
$307$	−8.60991			−0.491394			−0.245697	−	0.969347i	$-0.579017\pi$
$307$	−8.60991			−0.491394			−0.245697	+	0.969347i	$0.579017\pi$
$308$		0			0
$309$	−11.0145			−0.626594
$310$	−0.173364	+	0.125957i	−0.00984644	+	0.00715386i
$311$	5.91021	+	18.1897i	0.335137	+	1.03145i	0.966654	+	0.256084i	$0.0824325\pi$
$311$	5.91021	+	18.1897i	0.335137	+	1.03145i	−0.631517	+	0.775362i	$0.717568\pi$
$312$	0.514621	−	1.58384i	0.0291347	−	0.0896674i
$313$	0.490875	+	0.356642i	0.0277459	+	0.0201586i	0.601572	−	0.798819i	$-0.294541\pi$
$313$	0.490875	+	0.356642i	0.0277459	+	0.0201586i	−0.573826	+	0.818977i	$0.694541\pi$
$314$	−36.8537	−	26.7758i	−2.07978	−	1.51105i
$315$	0.0396368	−	0.121989i	0.00223328	−	0.00687332i
$316$	−3.50708	−	10.7937i	−0.197289	−	0.607192i
$317$	4.21727	−	3.06402i	0.236865	−	0.172093i	−0.463020	−	0.886348i	$-0.653234\pi$
$317$	4.21727	−	3.06402i	0.236865	−	0.172093i	0.699886	+	0.714255i	$0.253234\pi$
$318$	21.9005			1.22812
$319$		0			0
$320$	0.201906			0.0112869
$321$	23.4409	−	17.0308i	1.30835	−	0.950569i
$322$	4.94430	+	15.2170i	0.275535	+	0.848009i
$323$	0.712761	−	2.19365i	0.0396591	−	0.122058i
$324$	0.935185	+	0.679452i	0.0519547	+	0.0377473i
$325$	19.7417	+	14.3432i	1.09507	+	0.795616i
$326$	−11.6450	+	35.8397i	−0.644959	+	1.98498i
$327$	3.25213	+	10.0090i	0.179843	+	0.553501i
$328$	−1.04992	+	0.762810i	−0.0579720	+	0.0421192i
$329$	8.95906			0.493929
$330$		0			0
$331$	0.669012			0.0367722			0.0183861	−	0.999831i	$-0.494147\pi$
$331$	0.669012			0.0367722			0.0183861	+	0.999831i	$0.494147\pi$
$332$	4.08569	−	2.96843i	0.224231	−	0.162914i
$333$	0.767048	+	2.36073i	0.0420340	+	0.129367i
$334$	−1.85228	+	5.70073i	−0.101352	+	0.311930i
$335$	0.0612701	+	0.0445154i	0.00334754	+	0.00243213i
$336$	−9.28655	−	6.74708i	−0.506623	−	0.368083i
$337$	2.04018	−	6.27902i	0.111136	−	0.342040i	−0.879986	−	0.475000i	$-0.842448\pi$
$337$	2.04018	−	6.27902i	0.111136	−	0.342040i	0.991121	+	0.132960i	$0.0424481\pi$
$338$	−6.63862	−	20.4316i	−0.361093	−	1.11133i
$339$	−14.3115	+	10.3979i	−0.777292	+	0.564736i
$340$	0.0876111			0.00475138
$341$		0			0
$342$	12.9895			0.702393
$343$	0.809017	−	0.587785i	0.0436828	−	0.0317374i
$344$	−0.141501	−	0.435497i	−0.00762925	−	0.0234804i
$345$	−0.186912	+	0.575256i	−0.0100630	+	0.0309708i
$346$	−14.1867	−	10.3073i	−0.762683	−	0.554122i
$347$	9.87011	+	7.17106i	0.529855	+	0.384963i	0.820304	−	0.571928i	$-0.193804\pi$
$347$	9.87011	+	7.17106i	0.529855	+	0.384963i	−0.290448	+	0.956891i	$0.593804\pi$
$348$	10.6699	−	32.8386i	0.571968	−	1.76034i
$349$	0.273727	+	0.842446i	0.0146523	+	0.0450951i	0.958115	−	0.286383i	$-0.0924528\pi$
$349$	0.273727	+	0.842446i	0.0146523	+	0.0450951i	−0.943463	+	0.331478i	$0.892453\pi$
$350$	8.02637	−	5.83150i	0.429027	−	0.311707i
$351$	23.9915			1.28057
$352$		0			0
$353$	5.36012			0.285291			0.142645	−	0.989774i	$-0.454439\pi$
$353$	5.36012			0.285291			0.142645	+	0.989774i	$0.454439\pi$
$354$	43.5288	−	31.6255i	2.31353	−	1.68088i
$355$	−0.0170188	−	0.0523784i	−0.000903263	−	0.00277996i
$356$	0.729491	−	2.24514i	0.0386629	−	0.118992i
$357$	−3.78437	−	2.74951i	−0.200290	−	0.145519i
$358$	13.5895	+	9.87338i	0.718230	+	0.521825i
$359$	−7.98654	+	24.5801i	−0.421514	+	1.29729i	0.484780	+	0.874636i	$0.338900\pi$
$359$	−7.98654	+	24.5801i	−0.421514	+	1.29729i	−0.906293	+	0.422649i	$0.861100\pi$
$360$	−0.00485335	−	0.0149371i	−0.000255794	−	0.000787253i
$361$	13.8441	−	10.0583i	0.728638	−	0.529387i
$362$	48.0268			2.52423
$363$		0			0
$364$	−9.46107			−0.495895
$365$	0.228046	−	0.165685i	0.0119365	−	0.00867234i
$366$	14.4684	+	44.5291i	0.756275	+	2.32758i
$367$	−6.31953	+	19.4495i	−0.329877	+	1.01526i	0.639314	+	0.768946i	$0.279218\pi$
$367$	−6.31953	+	19.4495i	−0.329877	+	1.01526i	−0.969191	+	0.246311i	$0.920782\pi$
$368$	26.8708	+	19.5227i	1.40073	+	1.01769i
$369$	−40.8491	−	29.6786i	−2.12652	−	1.54501i
$370$	0.00860302	−	0.0264774i	0.000447250	−	0.00137649i
$371$	1.22388	+	3.76673i	0.0635409	+	0.195559i
$372$	−17.5236	+	12.7317i	−0.908558	+	0.660106i
$373$	−9.39109			−0.486252			−0.243126	−	0.969995i	$-0.578173\pi$
$373$	−9.39109			−0.486252			−0.243126	+	0.969995i	$0.578173\pi$
$374$		0			0
$375$	0.750163			0.0387383
$376$	0.887491	−	0.644800i	0.0457688	−	0.0332530i
$377$	9.64312	+	29.6785i	0.496646	+	1.52852i
$378$	3.01422	−	9.27682i	0.155035	−	0.477148i
$379$	4.55956	+	3.31272i	0.234209	+	0.170163i	0.698699	−	0.715415i	$-0.253762\pi$
$379$	4.55956	+	3.31272i	0.234209	+	0.170163i	−0.464490	+	0.885578i	$0.653762\pi$
$380$	−0.0580085	−	0.0421456i	−0.00297577	−	0.00216202i
$381$	4.33215	−	13.3330i	0.221943	−	0.683069i
$382$	4.77548	+	14.6974i	0.244335	+	0.751985i
$383$	1.01891	−	0.740281i	0.0520638	−	0.0378266i	−0.561449	−	0.827511i	$-0.689756\pi$
$383$	1.01891	−	0.740281i	0.0520638	−	0.0378266i	0.613513	+	0.789685i	$0.289756\pi$
$384$	−2.72816			−0.139221
$385$		0			0
$386$	33.8631			1.72359
$387$	14.4133	−	10.4719i	0.732669	−	0.532315i
$388$	2.03451	+	6.26159i	0.103287	+	0.317884i
$389$	−1.81828	+	5.59610i	−0.0921906	+	0.283734i	−0.986511	−	0.163693i	$-0.947659\pi$
$389$	−1.81828	+	5.59610i	−0.0921906	+	0.283734i	0.894321	+	0.447427i	$0.147659\pi$
$390$	−0.587921	−	0.427149i	−0.0297705	−	0.0216296i
$391$	10.9501	+	7.95573i	0.553771	+	0.402339i
$392$	0.0378378	−	0.116453i	0.00191110	−	0.00588175i
$393$	3.24060	+	9.97354i	0.163467	+	0.503098i
$394$	9.72191	−	7.06338i	0.489783	−	0.355848i
$395$	0.157648			0.00793212
$396$		0			0
$397$	4.86018			0.243925			0.121963	−	0.992535i	$-0.461081\pi$
$397$	4.86018			0.243925			0.121963	+	0.992535i	$0.461081\pi$
$398$	−22.0245	+	16.0017i	−1.10399	+	0.802095i
$399$	1.18302	+	3.64097i	0.0592252	+	0.182276i
$400$	6.36420	−	19.5870i	0.318210	−	0.979350i
$401$	20.6560	+	15.0074i	1.03151	+	0.749435i	0.968610	−	0.248585i	$-0.0799654\pi$
$401$	20.6560	+	15.0074i	1.03151	+	0.749435i	0.0628990	+	0.998020i	$0.479965\pi$
$402$	12.5835	+	9.14243i	0.627607	+	0.455983i
$403$	6.04930	−	18.6178i	0.301337	−	0.927420i
$404$	2.42483	+	7.46287i	0.120640	+	0.371292i
$405$	−0.0129904	+	0.00943806i	−0.000645497	+	0.000468981i
$406$	12.6873			0.629661
$407$		0			0
$408$	−0.572769			−0.0283563
$409$	17.0109	−	12.3592i	0.841136	−	0.611121i	−0.0815517	−	0.996669i	$-0.525988\pi$
$409$	17.0109	−	12.3592i	0.841136	−	0.611121i	0.922688	+	0.385548i	$0.125988\pi$
$410$	0.174999	+	0.538592i	0.00864259	+	0.0265992i
$411$	16.4785	−	50.7157i	0.812826	−	2.50162i
$412$	6.19872	+	4.50363i	0.305389	+	0.221878i
$413$	7.87191	+	5.71928i	0.387351	+	0.281427i
$414$	−23.5546	+	72.4935i	−1.15764	+	3.56286i
$415$	0.0216778	+	0.0667173i	0.00106412	+	0.00327502i
$416$	−31.3168	+	22.7530i	−1.53543	+	1.11556i
$417$	−9.78326			−0.479088
$418$		0			0
$419$	−31.3141			−1.52980			−0.764898	−	0.644151i	$-0.777211\pi$
$419$	−31.3141			−1.52980			−0.764898	+	0.644151i	$0.777211\pi$
$420$	−0.117643	+	0.0854726i	−0.00574039	+	0.00417064i
$421$	3.95191	+	12.1627i	0.192604	+	0.592775i	0.999996	+	0.00275943i	$0.000878355\pi$
$421$	3.95191	+	12.1627i	0.192604	+	0.592775i	−0.807392	+	0.590015i	$0.799122\pi$
$422$	11.0601	−	34.0395i	0.538397	−	1.65702i
$423$	34.5296	+	25.0872i	1.67888	+	1.21978i
$424$	0.392337	+	0.285050i	0.0190536	+	0.0138432i
$425$	2.59348	−	7.98191i	0.125802	−	0.387180i
$426$	−3.49527	−	10.7573i	−0.169346	−	0.521194i
$427$	−6.85013	+	4.97691i	−0.331501	+	0.240850i
$428$	−20.1556			−0.974258
$429$		0			0
$430$	−0.199818			−0.00963607
$431$	17.0443	−	12.3834i	0.820994	−	0.596487i	−0.0960031	−	0.995381i	$-0.530606\pi$
$431$	17.0443	−	12.3834i	0.820994	−	0.596487i	0.916997	+	0.398894i	$0.130606\pi$
$432$	−6.25713	−	19.2575i	−0.301046	−	0.926525i
$433$	11.7436	−	36.1430i	0.564361	−	1.73692i	−0.105483	−	0.994421i	$-0.533639\pi$
$433$	11.7436	−	36.1430i	0.564361	−	1.73692i	0.669844	−	0.742502i	$-0.266361\pi$
$434$	−6.43895	−	4.67817i	−0.309079	−	0.224559i
$435$	0.388026	+	0.281917i	0.0186044	+	0.0135169i
$436$	2.26228	−	6.96259i	0.108344	−	0.333448i
$437$	−3.42309	−	10.5352i	−0.163749	−	0.503966i
$438$	46.8353	−	34.0279i	2.23788	−	1.62591i
$439$	37.7677			1.80256			0.901278	−	0.433241i	$-0.142630\pi$
$439$	37.7677			1.80256			0.901278	+	0.433241i	$0.142630\pi$
$440$		0			0
$441$	4.76399			0.226857
$442$	−13.1560	+	9.55842i	−0.625769	+	0.454648i
$443$	−0.317646	−	0.977613i	−0.0150918	−	0.0464478i	0.943227	−	0.332149i	$-0.107774\pi$
$443$	−0.317646	−	0.977613i	−0.0150918	−	0.0464478i	−0.958319	+	0.285701i	$0.907774\pi$
$444$	0.869591	−	2.67633i	0.0412689	−	0.127013i
$445$	0.0265289	+	0.0192744i	0.00125759	+	0.000913693i
$446$	−10.4890	−	7.62070i	−0.496668	−	0.360851i
$447$	2.69199	−	8.28509i	0.127327	−	0.391871i
$448$	2.31732	+	7.13199i	0.109483	+	0.336955i
$449$	−16.2882	+	11.8341i	−0.768687	+	0.558483i	−0.901562	−	0.432649i	$-0.857579\pi$
$449$	−16.2882	+	11.8341i	−0.768687	+	0.558483i	0.132876	+	0.991133i	$0.457579\pi$
$450$	47.2642			2.22806
$451$		0			0
$452$	12.3057			0.578809
$453$	44.4570	−	32.2999i	2.08877	−	1.51758i
$454$	8.34491	+	25.6830i	0.391646	+	1.20536i
$455$	0.0406113	−	0.124989i	0.00190389	−	0.00585956i
$456$	0.379238	+	0.275532i	0.0177594	+	0.0129030i
$457$	−19.5342	−	14.1924i	−0.913771	−	0.663894i	0.0281947	−	0.999602i	$-0.491024\pi$
$457$	−19.5342	−	14.1924i	−0.913771	−	0.663894i	−0.941966	+	0.335709i	$0.891024\pi$
$458$	11.9100	−	36.6551i	0.556516	−	1.71278i
$459$	−2.54985	−	7.84763i	−0.119017	−	0.366296i
$460$	0.340401	−	0.247316i	0.0158713	−	0.0115312i
$461$	−11.5885			−0.539731			−0.269865	−	0.962898i	$-0.586979\pi$
$461$	−11.5885			−0.539731			−0.269865	+	0.962898i	$0.586979\pi$
$462$		0			0
$463$	21.6077			1.00419			0.502097	−	0.864811i	$-0.332562\pi$
$463$	21.6077			1.00419			0.502097	+	0.864811i	$0.332562\pi$
$464$	21.3073	−	15.4806i	0.989165	−	0.718670i
$465$	−0.0929764	−	0.286152i	−0.00431168	−	0.0132700i
$466$	2.67469	−	8.23184i	0.123902	−	0.381332i
$467$	−12.8755	−	9.35457i	−0.595805	−	0.432878i	0.248582	−	0.968611i	$-0.420035\pi$
$467$	−12.8755	−	9.35457i	−0.595805	−	0.432878i	−0.844388	+	0.535733i	$0.820035\pi$
$468$	−36.4644	−	26.4929i	−1.68557	−	1.22464i
$469$	−0.869218	+	2.67518i	−0.0401367	+	0.123528i
$470$	−0.147926	−	0.455269i	−0.00682331	−	0.0210000i
$471$	51.7451	−	37.5950i	2.38429	−	1.73229i
$472$	1.19142			0.0548397
$473$		0			0
$474$	32.3772			1.48713
$475$	−5.55690	+	4.03733i	−0.254968	+	0.185245i
$476$	1.00553	+	3.09472i	0.0460886	+	0.141846i
$477$	−5.83057	+	17.9447i	−0.266964	+	0.821630i
$478$	−17.0025	−	12.3530i	−0.777676	−	0.565015i
$479$	4.27462	+	3.10569i	0.195312	+	0.141903i	0.681143	−	0.732150i	$-0.261483\pi$
$479$	4.27462	+	3.10569i	0.195312	+	0.141903i	−0.485831	+	0.874053i	$0.661483\pi$
$480$	−0.183853	+	0.565841i	−0.00839170	+	0.0258270i
$481$	0.785907	+	2.41877i	0.0358343	+	0.110287i
$482$	−30.0048	+	21.7997i	−1.36668	+	0.992951i
$483$	−22.4652			−1.02220
$484$		0			0
$485$	−0.0914540			−0.00415271
$486$	−26.3419	+	19.1385i	−1.19489	+	0.868141i
$487$	−8.36372	−	25.7409i	−0.378996	−	1.16643i	−0.940743	−	0.339121i	$-0.889870\pi$
$487$	−8.36372	−	25.7409i	−0.378996	−	1.16643i	0.561747	−	0.827309i	$-0.310130\pi$
$488$	−0.320381	+	0.986032i	−0.0145030	+	0.0446356i
$489$	−42.8059	−	31.1003i	−1.93575	−	1.40641i
$490$	−0.0432272	−	0.0314064i	−0.00195281	−	0.00141880i
$491$	−5.80951	+	17.8798i	−0.262179	+	0.806905i	0.730150	+	0.683287i	$0.239450\pi$
$491$	−5.80951	+	17.8798i	−0.262179	+	0.806905i	−0.992330	+	0.123619i	$0.960550\pi$
$492$	17.6889	+	54.4407i	0.797476	+	2.45438i
$493$	8.68294	−	6.30853i	0.391060	−	0.284122i
$494$	13.3089			0.598795
$495$		0			0
$496$	−16.5218			−0.741851
$497$	1.65485	−	1.20232i	0.0742302	−	0.0539314i
$498$	4.45211	+	13.7022i	0.199504	+	0.614010i
$499$	−12.2886	+	37.8203i	−0.550112	+	1.69307i	0.158402	+	0.987375i	$0.449366\pi$
$499$	−12.2886	+	37.8203i	−0.550112	+	1.69307i	−0.708514	+	0.705696i	$0.750634\pi$
$500$	−0.422174	−	0.306728i	−0.0188802	−	0.0137173i
$501$	−6.80879	−	4.94687i	−0.304194	−	0.221010i
$502$	−11.6414	+	35.8285i	−0.519581	+	1.59911i
$503$	−12.5345	−	38.5771i	−0.558885	−	1.72007i	−0.685458	−	0.728113i	$-0.740398\pi$
$503$	−12.5345	−	38.5771i	−0.558885	−	1.72007i	0.126573	−	0.991957i	$-0.459602\pi$
$504$	0.471924	−	0.342873i	0.0210212	−	0.0152728i
$505$	−0.108999			−0.00485040
$506$		0			0
$507$	30.1636			1.33961
$508$	−7.88964	+	5.73216i	−0.350046	+	0.254323i
$509$	−4.78386	−	14.7232i	−0.212041	−	0.652595i	−0.999350	−	0.0360372i	$-0.988527\pi$
$509$	−4.78386	−	14.7232i	−0.212041	−	0.652595i	0.787309	−	0.616558i	$-0.211473\pi$
$510$	−0.0772356	+	0.237707i	−0.00342005	+	0.0105258i
$511$	8.46987	+	6.15372i	0.374685	+	0.272225i
$512$	25.6148	+	18.6102i	1.13202	+	0.822464i
$513$	−2.08684	+	6.42263i	−0.0921361	+	0.283566i
$514$	8.40705	+	25.8743i	0.370819	+	1.14126i
$515$	−0.0861045	+	0.0625586i	−0.00379422	+	0.00275666i
$516$	−20.1975			−0.889147
$517$		0			0
$518$	1.03401			0.0454317
$519$	19.9191	−	14.4721i	0.874352	−	0.635254i
$520$	−0.00497268	−	0.0153043i	−0.000218066	−	0.000671139i
$521$	11.5800	−	35.6397i	0.507331	−	1.56140i	−0.289486	−	0.957182i	$-0.593484\pi$
$521$	11.5800	−	35.6397i	0.507331	−	1.56140i	0.796817	−	0.604221i	$-0.206516\pi$
$522$	48.8988	+	35.5271i	2.14024	+	1.55498i
$523$	−16.8369	−	12.2327i	−0.736225	−	0.534899i	0.155302	−	0.987867i	$-0.450365\pi$
$523$	−16.8369	−	12.2327i	−0.736225	−	0.534899i	−0.891527	+	0.452968i	$0.850365\pi$
$524$	2.25426	−	6.93789i	0.0984777	−	0.303083i
$525$	4.30459	+	13.2482i	0.187868	+	0.578197i
$526$	−26.6141	+	19.3363i	−1.16043	+	0.843101i
$527$	−6.73281			−0.293286
$528$		0			0
$529$	42.0033			1.82623
$530$	0.171204	−	0.124387i	0.00743665	−	0.00540304i
$531$	14.3244	+	44.0859i	0.621625	+	1.91316i
$532$	0.822946	−	2.53277i	0.0356792	−	0.109809i
$533$	−41.8535	−	30.4083i	−1.81287	−	1.31713i
$534$	5.44843	+	3.95851i	0.235776	+	0.171302i
$535$	0.0865172	−	0.266272i	0.00374046	−	0.0115120i
$536$	0.106432	+	0.327564i	0.00459716	+	0.0141486i
$537$	−19.0806	+	13.8629i	−0.823391	+	0.598228i
$538$	16.9549			0.730979
$539$		0			0
$540$	−0.256510			−0.0110384
$541$	−14.0978	+	10.2427i	−0.606112	+	0.440366i	−0.848043	−	0.529927i	$-0.822219\pi$
$541$	−14.0978	+	10.2427i	−0.606112	+	0.440366i	0.241931	+	0.970293i	$0.422219\pi$
$542$	−3.89139	−	11.9765i	−0.167149	−	0.514433i
$543$	−20.8379	+	64.1325i	−0.894241	+	2.75219i
$544$	10.7709	+	7.82552i	0.461799	+	0.335516i
$545$	0.0822709	+	0.0597733i	0.00352410	+	0.00256041i
$546$	8.34062	−	25.6698i	0.356946	−	1.09857i
$547$	4.88122	+	15.0228i	0.208706	+	0.642331i	0.999541	+	0.0303011i	$0.00964663\pi$
$547$	4.88122	+	15.0228i	0.208706	+	0.642331i	−0.790835	+	0.612029i	$0.790353\pi$
$548$	−30.0104	+	21.8038i	−1.28198	+	0.931414i
$549$	−40.3378			−1.72157
$550$		0			0
$551$	−8.78382			−0.374203
$552$	−2.22542	+	1.61686i	−0.0947201	+	0.0688181i
$553$	1.80936	+	5.56864i	0.0769418	+	0.236803i
$554$	−14.7207	+	45.3055i	−0.625421	+	1.92485i
$555$	0.0316238	+	0.0229760i	0.00134236	+	0.000975279i
$556$	5.50579	+	4.00019i	0.233498	+	0.169646i
$557$	5.20233	−	16.0111i	0.220430	−	0.678413i	−0.778294	−	0.627900i	$-0.783915\pi$
$557$	5.20233	−	16.0111i	0.220430	−	0.678413i	0.998723	−	0.0505123i	$-0.0160854\pi$
$558$	−11.7168	−	36.0607i	−0.496013	−	1.52657i
$559$	14.7677	−	10.7293i	0.624606	−	0.453803i
$560$	−0.110917			−0.00468711
$561$		0			0
$562$	−6.37315			−0.268835
$563$	−30.2818	+	22.0010i	−1.27623	+	0.927233i	−0.999432	−	0.0336966i	$-0.989272\pi$
$563$	−30.2818	+	22.0010i	−1.27623	+	0.927233i	−0.276794	+	0.960929i	$0.589272\pi$
$564$	−14.9523	−	46.0185i	−0.629606	−	1.93773i
$565$	−0.0528215	+	0.162568i	−0.00222222	+	0.00683929i
$566$	33.4000	+	24.2665i	1.40391	+	1.02000i
$567$	−0.482477	−	0.350540i	−0.0202621	−	0.0147213i
$568$	0.0773976	−	0.238205i	0.00324753	−	0.00999487i
$569$	0.855698	+	2.63357i	0.0358727	+	0.110405i	0.967389	−	0.253294i	$-0.0815139\pi$
$569$	0.855698	+	2.63357i	0.0358727	+	0.110405i	−0.931517	+	0.363698i	$0.881514\pi$
$570$	0.165488	−	0.120234i	0.00693154	−	0.00503606i
$571$	8.85289			0.370482			0.185241	−	0.982693i	$-0.440693\pi$
$571$	8.85289			0.370482			0.185241	+	0.982693i	$0.440693\pi$
$572$		0			0
$573$	−21.6981			−0.906453
$574$	−17.0163	+	12.3631i	−0.710249	+	0.516026i
$575$	−12.4554	−	38.3337i	−0.519425	−	1.59863i
$576$	−11.0397	+	33.9767i	−0.459988	+	1.41570i
$577$	−30.0697	−	21.8469i	−1.25182	−	0.909500i	−0.253493	−	0.967337i	$-0.581580\pi$
$577$	−30.0697	−	21.8469i	−1.25182	−	0.909500i	−0.998326	+	0.0578373i	$0.981580\pi$
$578$	−22.7688	−	16.5425i	−0.947058	−	0.688078i
$579$	−14.6925	+	45.2190i	−0.610601	+	1.87924i
$580$	−0.103101	−	0.317313i	−0.00428105	−	0.0131757i
$581$	−2.10787	+	1.53146i	−0.0874494	+	0.0635357i
$582$	−18.7825			−0.778562
$583$		0			0
$584$	1.28193			0.0530464
$585$	0.506515	−	0.368005i	0.0209418	−	0.0152151i
$586$	3.38356	+	10.4135i	0.139774	+	0.430179i
$587$	−10.9141	+	33.5903i	−0.450475	+	1.38642i	0.425892	+	0.904774i	$0.359960\pi$
$587$	−10.9141	+	33.5903i	−0.450475	+	1.38642i	−0.876367	+	0.481645i	$0.840040\pi$
$588$	−4.36939	−	3.17455i	−0.180191	−	0.130916i
$589$	4.45788	+	3.23884i	0.183684	+	0.133454i
$590$	0.160659	−	0.494457i	0.00661421	−	0.0203565i
$591$	5.21392	+	16.0468i	0.214472	+	0.660077i
$592$	1.73653	−	1.26166i	0.0713708	−	0.0518539i
$593$	8.09224			0.332308			0.166154	−	0.986100i	$-0.446865\pi$
$593$	8.09224			0.332308			0.166154	+	0.986100i	$0.446865\pi$
$594$		0			0
$595$	−0.0452000			−0.00185302
$596$	−4.90260	+	3.56195i	−0.200818	+	0.145903i
$597$	−11.8119	−	36.3532i	−0.483428	−	1.48784i
$598$	−24.1337	+	74.2759i	−0.986900	+	3.03737i
$599$	−3.10352	−	2.25484i	−0.126806	−	0.0921302i	0.522574	−	0.852594i	$-0.324972\pi$
$599$	−3.10352	−	2.25484i	−0.126806	−	0.0921302i	−0.649381	+	0.760464i	$0.724972\pi$
$600$	1.37991	+	1.00256i	0.0563346	+	0.0409295i
$601$	4.43027	−	13.6350i	0.180714	−	0.556182i	−0.819134	−	0.573602i	$-0.805545\pi$
$601$	4.43027	−	13.6350i	0.180714	−	0.556182i	0.999848	+	0.0174208i	$0.00554549\pi$
$602$	−2.29336	−	7.05823i	−0.0934702	−	0.287672i
$603$	−10.8411	+	7.87654i	−0.441485	+	0.320758i
$604$	−38.2261			−1.55540
$605$		0			0
$606$	−22.3859			−0.909367
$607$	11.1471	−	8.09883i	0.452446	−	0.328722i	−0.338114	−	0.941105i	$-0.609789\pi$
$607$	11.1471	−	8.09883i	0.452446	−	0.328722i	0.790561	+	0.612383i	$0.209789\pi$
$608$	−3.36706	−	10.3628i	−0.136552	−	0.420265i
$609$	−5.50479	+	16.9420i	−0.223065	+	0.686524i
$610$	0.366014	+	0.265925i	0.0148195	+	0.0107670i
$611$	35.3785	+	25.7040i	1.43126	+	1.03987i
$612$	−4.79035	+	14.7432i	−0.193639	+	0.595958i
$613$	2.94937	+	9.07722i	0.119124	+	0.366625i	0.992785	−	0.119910i	$-0.0382605\pi$
$613$	2.94937	+	9.07722i	0.119124	+	0.366625i	−0.873661	+	0.486535i	$0.838261\pi$
$614$	−13.8233	+	10.0432i	−0.557862	+	0.405310i
$615$	−0.795137			−0.0320630
$616$		0			0
$617$	−31.5153			−1.26876			−0.634379	−	0.773023i	$-0.718744\pi$
$617$	−31.5153			−1.26876			−0.634379	+	0.773023i	$0.718744\pi$
$618$	−17.6839	+	12.8481i	−0.711350	+	0.516826i
$619$	6.34403	+	19.5249i	0.254988	+	0.784773i	0.993832	+	0.110896i	$0.0353721\pi$
$619$	6.34403	+	19.5249i	0.254988	+	0.784773i	−0.738844	+	0.673877i	$0.764628\pi$
$620$	−0.0646772	+	0.199056i	−0.00259750	+	0.00799428i
$621$	−32.0600	−	23.2930i	−1.28652	−	0.934715i
$622$	30.7066	+	22.3097i	1.23122	+	0.894537i
$623$	−0.376356	+	1.15831i	−0.0150784	+	0.0464065i
$624$	−17.3140	−	53.2872i	−0.693117	−	2.13319i
$625$	−20.2166	+	14.6882i	−0.808665	+	0.587530i
$626$	1.20411			0.0481261
$627$		0			0
$628$	−44.4928			−1.77546
$629$	0.707653	−	0.514140i	0.0282160	−	0.0205001i
$630$	−0.0786597	−	0.242090i	−0.00313388	−	0.00964509i
$631$	11.1141	−	34.2055i	0.442444	−	1.36170i	−0.442819	−	0.896611i	$-0.646022\pi$
$631$	11.1141	−	34.2055i	0.442444	−	1.36170i	0.885263	−	0.465091i	$-0.153978\pi$
$632$	0.580021	+	0.421410i	0.0230720	+	0.0167628i
$633$	40.6558	+	29.5382i	1.61592	+	1.17404i
$634$	3.19676	−	9.83862i	0.126960	−	0.390741i
$635$	−0.0418606	−	0.128834i	−0.00166119	−	0.00511261i
$636$	17.3053	−	12.5730i	0.686200	−	0.498553i
$637$	4.88112			0.193397
$638$		0			0
$639$	9.74478			0.385498
$640$	−0.0213270	+	0.0154950i	−0.000843023	+	0.000612492i
$641$	4.20895	+	12.9538i	0.166244	+	0.511645i	0.999126	−	0.0418050i	$-0.0133108\pi$
$641$	4.20895	+	12.9538i	0.166244	+	0.511645i	−0.832882	+	0.553450i	$0.813311\pi$
$642$	17.7686	−	54.6863i	0.701272	−	2.15829i
$643$	−17.7896	−	12.9249i	−0.701552	−	0.509707i	0.178885	−	0.983870i	$-0.442751\pi$
$643$	−17.7896	−	12.9249i	−0.701552	−	0.509707i	−0.880437	+	0.474163i	$0.842751\pi$
$644$	12.6429	+	9.18560i	0.498200	+	0.361963i
$645$	0.0866971	−	0.266826i	0.00341370	−	0.0105063i
$646$	−1.41448	−	4.35334i	−0.0556522	−	0.171280i
$647$	11.9898	−	8.71112i	0.471369	−	0.342470i	−0.326606	−	0.945161i	$-0.605905\pi$
$647$	11.9898	−	8.71112i	0.471369	−	0.342470i	0.797975	+	0.602691i	$0.205905\pi$
$648$	−0.0730235			−0.00286863
$649$		0			0
$650$	48.4262			1.89943
$651$	9.04072	−	6.56847i	0.354334	−	0.257439i
$652$	11.3738	+	35.0051i	0.445434	+	1.37090i
$653$	13.4044	−	41.2545i	0.524555	−	1.61441i	−0.240639	−	0.970615i	$-0.577357\pi$
$653$	13.4044	−	41.2545i	0.524555	−	1.61441i	0.765194	−	0.643800i	$-0.222643\pi$
$654$	16.8966	+	12.2761i	0.660707	+	0.480032i
$655$	0.0819791	+	0.0595613i	0.00320319	+	0.00232725i
$656$	−13.4925	+	41.5255i	−0.526792	+	1.62130i
$657$	15.4125	+	47.4347i	0.601298	+	1.85060i
$658$	14.3838	−	10.4505i	0.560740	−	0.407402i
$659$	−42.2093			−1.64424			−0.822121	−	0.569313i	$-0.807209\pi$
$659$	−42.2093			−1.64424			−0.822121	+	0.569313i	$0.807209\pi$
$660$		0			0
$661$	16.2794			0.633197			0.316599	−	0.948560i	$-0.397459\pi$
$661$	16.2794			0.633197			0.316599	+	0.948560i	$0.397459\pi$
$662$	1.07410	−	0.780382i	0.0417462	−	0.0303304i
$663$	−7.05566	−	21.7151i	−0.274019	−	0.843344i
$664$	−0.0985855	+	0.303415i	−0.00382586	+	0.0117748i
$665$	0.0299275	+	0.0217436i	0.00116054	+	0.000843181i
$666$	3.98522	+	2.89543i	0.154424	+	0.112196i
$667$	15.9282	−	49.0219i	0.616741	−	1.89813i
$668$	1.80914	+	5.56797i	0.0699978	+	0.215431i
$669$	14.7273	−	10.7000i	0.569389	−	0.413685i
$670$	0.150295			0.00580642
$671$		0			0
$672$	−22.0975			−0.852430
$673$	−4.29626	+	3.12142i	−0.165609	+	0.120322i	−0.667503	−	0.744607i	$-0.732637\pi$
$673$	−4.29626	+	3.12142i	−0.165609	+	0.120322i	0.501894	+	0.864929i	$0.332637\pi$
$674$	−4.04876	−	12.4608i	−0.155952	−	0.479972i
$675$	−7.59325	+	23.3696i	−0.292264	+	0.899497i
$676$	−16.9754	−	12.3333i	−0.652899	−	0.474359i
$677$	−27.3405	−	19.8640i	−1.05078	−	0.763437i	−0.0784205	−	0.996920i	$-0.524988\pi$
$677$	−27.3405	−	19.8640i	−1.05078	−	0.763437i	−0.972361	+	0.233483i	$0.924988\pi$
$678$	−10.8483	+	33.3877i	−0.416628	+	1.28225i
$679$	−1.04964	−	3.23046i	−0.0402815	−	0.123974i
$680$	−0.00447754	+	0.00325313i	−0.000171706	+	0.000124752i
$681$	−37.9164			−1.45296
$682$		0			0
$683$	−15.8834			−0.607761			−0.303880	−	0.952710i	$-0.598282\pi$
$683$	−15.8834			−0.607761			−0.303880	+	0.952710i	$0.598282\pi$
$684$	10.2640	−	7.45724i	0.392454	−	0.285135i
$685$	−0.159228	−	0.490055i	−0.00608381	−	0.0187240i
$686$	0.613249	−	1.88739i	0.0234139	−	0.0720607i
$687$	43.7798	+	31.8079i	1.67030	+	1.21355i
$688$	−12.4637	−	9.05541i	−0.475174	−	0.345234i
$689$	−5.97393	+	18.3859i	−0.227589	+	0.700445i
$690$	0.370930	+	1.14160i	0.0141211	+	0.0434602i
$691$	−20.6602	+	15.0105i	−0.785952	+	0.571028i	−0.906759	−	0.421648i	$-0.861452\pi$
$691$	−20.6602	+	15.0105i	−0.785952	+	0.571028i	0.120807	+	0.992676i	$0.461452\pi$
$692$	−17.1274			−0.651085
$693$		0			0
$694$	24.2113			0.919050
$695$	−0.0764793	+	0.0555655i	−0.00290103	+	0.00210772i
$696$	0.674037	+	2.07447i	0.0255493	+	0.0786327i
$697$	−5.49832	+	16.9221i	−0.208264	+	0.640970i
$698$	1.42216	+	1.03326i	0.0538295	+	0.0391094i
$699$	9.83187	+	7.14327i	0.371876	+	0.270183i
$700$	2.99440	−	9.21583i	0.113178	−	0.348325i
$701$	1.01832	+	3.13407i	0.0384614	+	0.118372i	0.968444	−	0.249232i	$-0.0801782\pi$
$701$	1.01832	+	3.13407i	0.0384614	+	0.118372i	−0.929982	+	0.367604i	$0.880178\pi$
$702$	38.5185	−	27.9854i	1.45379	−	1.05624i
$703$	−0.715875			−0.0269997
$704$		0			0
$705$	0.672125			0.0253137
$706$	8.60571	−	6.25242i	0.323880	−	0.235313i
$707$	−1.25101	−	3.85021i	−0.0470491	−	0.144802i
$708$	16.2393	−	49.9795i	0.610312	−	1.87835i
$709$	36.3269	+	26.3931i	1.36429	+	0.991213i	0.998159	+	0.0606480i	$0.0193167\pi$
$709$	36.3269	+	26.3931i	1.36429	+	0.991213i	0.366128	+	0.930565i	$0.380683\pi$
$710$	−0.0884216	−	0.0642420i	−0.00331840	−	0.00241096i
$711$	−8.61977	+	26.5289i	−0.323267	+	0.994913i
$712$	0.0460832	+	0.141829i	0.00172704	+	0.00531528i
$713$	−26.1594	+	19.0059i	−0.979679	+	0.711778i
$714$	−9.28304			−0.347409
$715$		0			0
$716$	16.4064			0.613137
$717$	23.8727	−	17.3445i	0.891541	−	0.647742i
$718$	15.8494	+	48.7795i	0.591495	+	1.82043i
$719$	0.986580	−	3.03638i	0.0367932	−	0.113238i	−0.930973	−	0.365088i	$-0.881039\pi$
$719$	0.986580	−	3.03638i	0.0367932	−	0.113238i	0.967766	+	0.251850i	$0.0810389\pi$
$720$	−0.427492	−	0.310591i	−0.0159317	−	0.0115750i
$721$	−3.19802	−	2.32350i	−0.119100	−	0.0865315i
$722$	10.4941	−	32.2975i	0.390550	−	1.20199i
$723$	−16.0917	−	49.5253i	−0.598458	−	1.84187i
$724$	37.9497	−	27.5721i	1.41039	−	1.02471i
$725$	−31.9612			−1.18701
$726$		0			0
$727$	20.1654			0.747891			0.373946	−	0.927451i	$-0.378005\pi$
$727$	20.1654			0.747891			0.373946	+	0.927451i	$0.378005\pi$
$728$	0.483527	−	0.351303i	0.0179207	−	0.0130201i
$729$	−13.5745	−	41.7779i	−0.502758	−	1.54733i
$730$	0.172862	−	0.532016i	0.00639793	−	0.0196908i
$731$	−5.07909	−	3.69018i	−0.187857	−	0.136486i
$732$	36.9966	+	26.8796i	1.36743	+	0.993499i
$733$	6.09055	−	18.7448i	0.224960	−	0.692355i	−0.773336	−	0.633996i	$-0.781413\pi$
$733$	6.09055	−	18.7448i	0.224960	−	0.692355i	0.998296	−	0.0583583i	$-0.0185866\pi$
$734$	12.5412	+	38.5979i	0.462904	+	1.42467i
$735$	0.0606939	−	0.0440967i	0.00223873	−	0.00162653i
$736$	63.9394			2.35684
$737$		0			0
$738$	−100.203			−3.68851
$739$	−27.9576	+	20.3124i	−1.02844	+	0.747204i	−0.967996	−	0.250967i	$-0.919251\pi$
$739$	−27.9576	+	20.3124i	−1.02844	+	0.747204i	−0.0604429	+	0.998172i	$0.519251\pi$
$740$	−0.00840267	−	0.0258608i	−0.000308888	−	0.000950661i
$741$	−5.77447	+	17.7720i	−0.212130	+	0.652871i
$742$	6.35873	+	4.61989i	0.233436	+	0.169601i
$743$	−20.9035	−	15.1873i	−0.766875	−	0.557167i	0.134136	−	0.990963i	$-0.457174\pi$
$743$	−20.9035	−	15.1873i	−0.766875	−	0.557167i	−0.901011	+	0.433796i	$0.857174\pi$
$744$	0.422836	−	1.30135i	0.0155019	−	0.0477100i
$745$	−0.0260121	−	0.0800570i	−0.000953010	−	0.00293306i
$746$	−15.0775	+	10.9544i	−0.552025	+	0.401069i
$747$	−12.4125			−0.454148
$748$		0			0
$749$	10.3986			0.379957
$750$	1.20439	−	0.875042i	0.0439782	−	0.0319520i
$751$	−11.0381	−	33.9717i	−0.402785	−	1.23964i	−0.922731	−	0.385445i	$-0.874048\pi$
$751$	−11.0381	−	33.9717i	−0.402785	−	1.23964i	0.519946	−	0.854199i	$-0.325952\pi$
$752$	11.4051	−	35.1013i	0.415902	−	1.28001i
$753$	−42.7926	−	31.0906i	−1.55945	−	1.13301i
$754$	50.1011	+	36.4006i	1.82457	+	1.32563i
$755$	0.164084	−	0.504999i	0.00597164	−	0.0183788i
$756$	−2.94403	−	9.06078i	−0.107073	−	0.329537i
$757$	11.9893	−	8.71077i	0.435760	−	0.316598i	−0.348188	−	0.937425i	$-0.613203\pi$
$757$	11.9893	−	8.71077i	0.435760	−	0.316598i	0.783948	+	0.620826i	$0.213203\pi$
$758$	11.1846			0.406242
$759$		0			0
$760$	0.00452957			0.000164305
$761$	−17.6171	+	12.7996i	−0.638619	+	0.463984i	−0.859376	−	0.511345i	$-0.829148\pi$
$761$	−17.6171	+	12.7996i	−0.638619	+	0.463984i	0.220756	+	0.975329i	$0.429148\pi$
$762$	−8.59721	−	26.4595i	−0.311444	−	0.958527i
$763$	−1.16715	+	3.59211i	−0.0422536	+	0.130043i
$764$	12.2112	+	8.87196i	0.441786	+	0.320976i
$765$	−0.174208	−	0.126569i	−0.00629849	−	0.00457612i
$766$	0.772350	−	2.37705i	0.0279062	−	0.0858863i
$767$	14.6766	+	45.1698i	0.529940	+	1.63099i
$768$	−38.1892	+	27.7461i	−1.37804	+	1.00120i
$769$	35.6991			1.28734			0.643672	−	0.765302i	$-0.277410\pi$
$769$	35.6991			1.28734			0.643672	+	0.765302i	$0.277410\pi$
$770$		0			0
$771$	−38.1988			−1.37570
$772$	26.7578	−	19.4407i	0.963035	−	0.699686i
$773$	13.1712	+	40.5368i	0.473735	+	1.45801i	0.847656	+	0.530547i	$0.178013\pi$
$773$	13.1712	+	40.5368i	0.473735	+	1.45801i	−0.373920	+	0.927461i	$0.621987\pi$
$774$	10.9255	−	33.6253i	0.392710	−	1.20864i
$775$	16.2206	+	11.7850i	0.582662	+	0.423329i
$776$	−0.336480	−	0.244467i	−0.0120789	−	0.00877585i
$777$	−0.448636	+	1.38076i	−0.0160947	+	0.0495345i
$778$	3.60841	+	11.1055i	0.129368	+	0.398153i
$779$	11.7809	−	8.55935i	0.422096	−	0.306671i
$780$	−0.709786			−0.0254144
$781$		0			0
$782$	26.8606			0.960533
$783$	−25.4221	+	18.4702i	−0.908512	+	0.660073i
$784$	−1.27302	−	3.91797i	−0.0454652	−	0.139927i
$785$	0.190984	−	0.587788i	0.00681650	−	0.0209790i
$786$	16.8366	+	12.2325i	0.600542	+	0.436320i
$787$	−38.0939	−	27.6769i	−1.35790	−	0.986574i	−0.998575	−	0.0533617i	$-0.983006\pi$
$787$	−38.0939	−	27.6769i	−1.35790	−	0.986574i	−0.359327	−	0.933212i	$-0.616994\pi$
$788$	3.62696	−	11.1626i	0.129205	−	0.397653i
$789$	−14.2733	−	43.9287i	−0.508143	−	1.56390i
$790$	0.253104	−	0.183891i	0.00900505	−	0.00654255i
$791$	−6.34869			−0.225733
$792$		0			0
$793$	−41.3295			−1.46765
$794$	7.80304	−	5.66924i	0.276920	−	0.201194i
$795$	0.0918180	+	0.282587i	0.00325645	+	0.0100223i
$796$	−8.21670	+	25.2884i	−0.291233	+	0.896324i
$797$	6.05358	+	4.39818i	0.214429	+	0.155792i	0.689815	−	0.723985i	$-0.257692\pi$
$797$	6.05358	+	4.39818i	0.214429	+	0.155792i	−0.475386	+	0.879777i	$0.657692\pi$
$798$	6.14642	+	4.46564i	0.217581	+	0.158082i
$799$	4.64771	−	14.3042i	0.164424	−	0.506045i
$800$	−12.2515	−	37.7063i	−0.433157	−	1.33312i
$801$	−4.69402	+	3.41041i	−0.165855	+	0.120501i
$802$	50.6690			1.78918
$803$		0			0
$804$	15.1918			0.535774
$805$	−0.175619	+	0.127594i	−0.00618974	+	0.00449711i
$806$	−12.0049	−	36.9473i	−0.422855	−	1.30141i
$807$	−7.35642	+	22.6407i	−0.258958	+	0.796991i
$808$	−0.401033	−	0.291367i	−0.0141083	−	0.0102503i
$809$	28.1125	+	20.4249i	0.988384	+	0.718103i	0.959567	−	0.281482i	$-0.0908259\pi$
$809$	28.1125	+	20.4249i	0.988384	+	0.718103i	0.0288171	+	0.999585i	$0.490826\pi$
$810$	−0.00984693	+	0.0303057i	−0.000345986	+	0.00106483i
$811$	−3.95952	−	12.1862i	−0.139038	−	0.427914i	0.857159	−	0.515053i	$-0.172228\pi$
$811$	−3.95952	−	12.1862i	−0.139038	−	0.427914i	−0.996196	+	0.0871388i	$0.972228\pi$
$812$	10.0252	−	7.28375i	0.351816	−	0.255610i
$813$	17.6811			0.620105
$814$		0			0
$815$	−0.511268			−0.0179089
$816$	−15.5901	+	11.3268i	−0.545762	+	0.396519i
$817$	1.58776	+	4.88663i	0.0555487	+	0.170961i
$818$	12.8946	−	39.6854i	0.450848	−	1.38757i
$819$	18.8126	+	13.6681i	0.657364	+	0.477603i
$820$	0.447484	+	0.325116i	0.0156268	+	0.0113536i
$821$	16.7866	−	51.6638i	0.585856	−	1.80308i	−0.00995123	−	0.999950i	$-0.503168\pi$
$821$	16.7866	−	51.6638i	0.585856	−	1.80308i	0.595807	−	0.803128i	$-0.296832\pi$
$822$	−32.7019	−	100.646i	−1.14061	−	3.51043i
$823$	15.9940	−	11.6203i	0.557517	−	0.405060i	−0.273032	−	0.962005i	$-0.588027\pi$
$823$	15.9940	−	11.6203i	0.557517	−	0.405060i	0.830549	+	0.556945i	$0.188027\pi$
$824$	−0.484024			−0.0168618
$825$		0			0
$826$	19.3098			0.671873
$827$	9.95887	−	7.23554i	0.346304	−	0.251605i	−0.401013	−	0.916072i	$-0.631342\pi$
$827$	9.95887	−	7.23554i	0.346304	−	0.251605i	0.747317	+	0.664468i	$0.231342\pi$
$828$	23.0060	+	70.8053i	0.799515	+	2.46065i
$829$	−7.94973	+	24.4668i	−0.276106	+	0.849765i	0.712819	+	0.701348i	$0.247418\pi$
$829$	−7.94973	+	24.4668i	−0.276106	+	0.849765i	−0.988925	+	0.148418i	$0.952582\pi$
$830$	0.112627	+	0.0818286i	0.00390935	+	0.00284031i
$831$	−54.1116	−	39.3144i	−1.87711	−	1.36380i
$832$	−11.3111	+	34.8121i	−0.392143	+	1.20689i
$833$	−0.518771	−	1.59661i	−0.0179744	−	0.0553194i
$834$	−15.7071	+	11.4119i	−0.543892	+	0.395161i
$835$	−0.0813232			−0.00281431
$836$		0			0
$837$	19.7125			0.681363
$838$	−50.2751	+	36.5270i	−1.73672	+	1.26180i
$839$	−14.4044	−	44.3322i	−0.497295	−	1.53052i	−0.813349	−	0.581776i	$-0.802358\pi$
$839$	−14.4044	−	44.3322i	−0.497295	−	1.53052i	0.316054	−	0.948741i	$-0.397642\pi$
$840$	0.00283866	−	0.00873650i	9.79431e−5	−	0.000301438i
$841$	−9.60506	−	6.97848i	−0.331209	−	0.240637i
$842$	20.5322	+	14.9176i	0.707588	+	0.514093i
$843$	2.76519	−	8.51037i	0.0952380	−	0.293113i
$844$	−10.8025	−	33.2468i	−0.371838	−	1.14440i
$845$	0.235800	−	0.171319i	0.00811176	−	0.00589354i
$846$	84.7009			2.91208
$847$		0			0
$848$	16.3160			0.560292
$849$	−46.8958	+	34.0718i	−1.60946	+	1.16934i
$850$	−5.14680	−	15.8402i	−0.176534	−	0.543315i
$851$	1.29813	−	3.99524i	0.0444994	−	0.136955i
$852$	−8.93763	−	6.49357i	−0.306198	−	0.222466i
$853$	−7.93549	−	5.76547i	−0.271706	−	0.197406i	0.443586	−	0.896232i	$-0.353706\pi$
$853$	−7.93549	−	5.76547i	−0.271706	−	0.197406i	−0.715292	+	0.698826i	$0.753706\pi$
$854$	−5.19252	+	15.9809i	−0.177684	+	0.546856i
$855$	0.0544585	+	0.167606i	0.00186244	+	0.00573201i
$856$	1.03009	−	0.748406i	0.0352078	−	0.0255800i
$857$	32.9168			1.12442			0.562208	−	0.826996i	$-0.309952\pi$
$857$	32.9168			1.12442			0.562208	+	0.826996i	$0.309952\pi$
$858$		0			0
$859$	−28.4747			−0.971543			−0.485772	−	0.874086i	$-0.661461\pi$
$859$	−28.4747			−0.971543			−0.485772	+	0.874086i	$0.661461\pi$
$860$	−0.157891	+	0.114715i	−0.00538405	+	0.00391174i
$861$	−9.12597	−	28.0869i	−0.311012	−	0.957197i
$862$	12.9199	−	39.7632i	0.440052	−	1.35434i
$863$	−23.6856	−	17.2086i	−0.806267	−	0.585787i	0.106479	−	0.994315i	$-0.466042\pi$
$863$	−23.6856	−	17.2086i	−0.806267	−	0.585787i	−0.912746	+	0.408528i	$0.866042\pi$
$864$	−31.5353	−	22.9117i	−1.07285	−	0.779473i
$865$	0.0735186	−	0.226267i	0.00249971	−	0.00769331i
$866$	−23.3053	−	71.7264i	−0.791947	−	2.43736i
$867$	31.9690	−	23.2268i	1.08572	−	0.788824i
$868$	−7.77363			−0.263854
$869$		0			0
$870$	0.951826			0.0322699
$871$	−11.1077	+	8.07020i	−0.376369	+	0.273448i
$872$	0.142912	+	0.439839i	0.00483962	+	0.0148948i
$873$	5.00047	−	15.3899i	0.169240	−	0.520868i
$874$	−17.7848	−	12.9214i	−0.601578	−	0.437072i
$875$	0.217807	+	0.158246i	0.00736321	+	0.00534968i
$876$	17.4729	−	53.7760i	0.590354	−	1.81692i
$877$	6.98456	+	21.4963i	0.235852	+	0.725877i	0.997007	+	0.0773079i	$0.0246324\pi$
$877$	6.98456	+	21.4963i	0.235852	+	0.725877i	−0.761155	+	0.648570i	$0.775368\pi$
$878$	60.6363	−	44.0549i	2.04638	−	1.48678i
$879$	−15.3738			−0.518544
$880$		0			0
$881$	−35.1102			−1.18289			−0.591447	−	0.806344i	$-0.701443\pi$
$881$	−35.1102			−1.18289			−0.591447	+	0.806344i	$0.701443\pi$
$882$	7.64861	−	5.55704i	0.257542	−	0.187115i
$883$	4.69804	+	14.4591i	0.158102	+	0.486587i	0.998462	−	0.0554413i	$-0.0176566\pi$
$883$	4.69804	+	14.4591i	0.158102	+	0.486587i	−0.840360	+	0.542028i	$0.817657\pi$
$884$	−4.90813	+	15.1057i	−0.165078	+	0.508059i
$885$	0.590565	+	0.429070i	0.0198516	+	0.0144230i
$886$	−1.65034	−	1.19904i	−0.0554441	−	0.0402825i
$887$	11.9069	−	36.6458i	0.399796	−	1.23044i	−0.525368	−	0.850875i	$-0.676072\pi$
$887$	11.9069	−	36.6458i	0.399796	−	1.23044i	0.925163	−	0.379569i	$-0.123928\pi$
$888$	0.0549335	+	0.169068i	0.00184345	+	0.00567355i
$889$	4.07039	−	2.95731i	0.136517	−	0.0991851i
$890$	0.0650753			0.00218133
$891$		0			0
$892$	−12.6632			−0.423995
$893$	−9.95837	+	7.23518i	−0.333244	+	0.242116i
$894$	−5.34229	−	16.4419i	−0.178673	−	0.549899i
$895$	−0.0704239	+	0.216743i	−0.00235401	+	0.00724491i
$896$	−0.792108	−	0.575500i	−0.0264625	−	0.0192261i
$897$	−88.7130	−	64.4538i	−2.96204	−	2.15205i
$898$	−12.3467	+	37.9993i	−0.412015	+	1.26805i
$899$	7.92321	+	24.3851i	0.264254	+	0.813289i
$900$	37.3471	−	27.1342i	1.24490	−	0.904474i
$901$	6.64893			0.221508
$902$		0			0
$903$	10.4202			0.346764
$904$	−0.628905	+	0.456926i	−0.0209171	+	0.0151971i
$905$	0.201352	+	0.619699i	0.00669318	+	0.0205995i
$906$	33.6991	−	103.715i	1.11958	−	3.44571i
$907$	45.6459	+	33.1637i	1.51565	+	1.10118i	0.963593	+	0.267374i	$0.0861559\pi$
$907$	45.6459	+	33.1637i	1.51565	+	1.10118i	0.552054	+	0.833808i	$0.313844\pi$
$908$	21.3385	+	15.5033i	0.708143	+	0.514496i
$909$	5.95980	−	18.3424i	0.197674	−	0.608378i
$910$	−0.0805937	−	0.248042i	−0.00267165	−	0.00822251i
$911$	24.7481	−	17.9806i	0.819942	−	0.595723i	−0.0967538	−	0.995308i	$-0.530846\pi$
$911$	24.7481	−	17.9806i	0.819942	−	0.595723i	0.916696	+	0.399585i	$0.130846\pi$
$912$	15.7712			0.522237
$913$		0			0
$914$	−47.9173			−1.58496
$915$	−0.513909	+	0.373377i	−0.0169893	+	0.0123435i
$916$	−11.6326	−	35.8014i	−0.384352	−	1.18291i
$917$	−1.16301	+	3.57937i	−0.0384059	+	0.118201i
$918$	−13.2478	−	9.62509i	−0.437243	−	0.317675i
$919$	26.6089	+	19.3325i	0.877745	+	0.637719i	0.932654	−	0.360772i	$-0.117487\pi$
$919$	26.6089	+	19.3325i	0.877745	+	0.637719i	−0.0549086	+	0.998491i	$0.517487\pi$
$920$	−0.00821370	+	0.0252792i	−0.000270798	+	0.000833429i
$921$	−7.41350	−	22.8164i	−0.244283	−	0.751827i
$922$	−18.6054	+	13.5176i	−0.612737	+	0.445180i
$923$	9.98437			0.328640
$924$		0			0
$925$	−2.60481			−0.0856457
$926$	34.6913	−	25.2047i	1.14003	−	0.828277i
$927$	−5.81938	−	17.9102i	−0.191133	−	0.588248i
$928$	15.6675	−	48.2195i	0.514310	−	1.58288i
$929$	−17.6630	−	12.8329i	−0.579503	−	0.421033i	0.259042	−	0.965866i	$-0.416593\pi$
$929$	−17.6630	−	12.8329i	−0.579503	−	0.421033i	−0.838545	+	0.544833i	$0.816593\pi$
$930$	−0.483062	−	0.350965i	−0.0158402	−	0.0115086i
$931$	−0.424571	+	1.30670i	−0.0139148	+	0.0428252i
$932$	−2.61240	−	8.04013i	−0.0855719	−	0.263363i
$933$	−43.1142	+	31.3243i	−1.41150	+	1.02551i
$934$	−31.5835			−1.03344
$935$		0			0
$936$	2.84730			0.0930670
$937$	−28.2770	+	20.5444i	−0.923769	+	0.671157i	−0.944459	−	0.328628i	$-0.893414\pi$
$937$	−28.2770	+	20.5444i	−0.923769	+	0.671157i	0.0206903	+	0.999786i	$0.493414\pi$
$938$	1.72498	+	5.30893i	0.0563224	+	0.173343i
$939$	−0.522442	+	1.60791i	−0.0170493	+	0.0524722i
$940$	−0.378256	−	0.274819i	−0.0123374	−	0.00896362i
$941$	−16.5205	−	12.0029i	−0.538554	−	0.391282i	0.284994	−	0.958529i	$-0.408008\pi$
$941$	−16.5205	−	12.0029i	−0.538554	−	0.391282i	−0.823548	+	0.567247i	$0.808008\pi$
$942$	39.2237	−	120.718i	1.27798	−	3.93321i
$943$	26.4061	+	81.2697i	0.859901	+	2.64650i
$944$	32.4291	−	23.5611i	1.05548	−	0.766849i
$945$	0.132338			0.00430494
$946$		0			0
$947$	−11.3122			−0.367597			−0.183799	−	0.982964i	$-0.558839\pi$
$947$	−11.3122			−0.367597			−0.183799	+	0.982964i	$0.558839\pi$
$948$	25.5837	−	18.5877i	0.830921	−	0.603699i
$949$	15.7914	+	48.6010i	0.512611	+	1.57765i
$950$	−4.21223	+	12.9639i	−0.136663	+	0.420605i
$951$	11.7510	+	8.53757i	0.381051	+	0.276850i
$952$	−0.166301	−	0.120825i	−0.00538985	−	0.00391595i
$953$	1.40887	−	4.33605i	0.0456377	−	0.140458i	−0.925641	−	0.378403i	$-0.876474\pi$
$953$	1.40887	−	4.33605i	0.0456377	−	0.140458i	0.971279	+	0.237944i	$0.0764735\pi$
$954$	11.5709	+	35.6114i	0.374620	+	1.15296i
$955$	−0.169622	+	0.123238i	−0.00548885	+	0.00398788i
$956$	−20.5268			−0.663885
$957$		0			0
$958$	10.4856			0.338775
$959$	15.4829	−	11.2490i	0.499968	−	0.363248i
$960$	0.173850	+	0.535055i	0.00561098	+	0.0172688i
$961$	−4.60916	+	14.1855i	−0.148683	+	0.457598i
$962$	4.08320	+	2.96662i	0.131648	+	0.0956476i
$963$	40.0778	+	29.1182i	1.29149	+	0.938321i
$964$	−11.1939	+	34.4513i	−0.360531	+	1.10960i
$965$	0.141971	+	0.436942i	0.00457021	+	0.0140656i
$966$	−36.0680	+	26.2049i	−1.16047	+	0.843130i
$967$	38.9153			1.25143			0.625715	−	0.780052i	$-0.284807\pi$
$967$	38.9153			1.25143			0.625715	+	0.780052i	$0.284807\pi$
$968$		0			0
$969$	6.42694			0.206463
$970$	−0.146830	+	0.106678i	−0.00471442	+	0.00342523i
$971$	13.0841	+	40.2686i	0.419888	+	1.29228i	0.907805	+	0.419392i	$0.137757\pi$
$971$	13.0841	+	40.2686i	0.419888	+	1.29228i	−0.487918	+	0.872890i	$0.662243\pi$
$972$	−9.82740	+	30.2456i	−0.315214	+	0.970129i
$973$	−2.84053	−	2.06376i	−0.0910631	−	0.0661612i
$974$	−43.4539	−	31.5711i	−1.39235	−	1.01160i
$975$	−21.0112	+	64.6659i	−0.672898	+	2.07097i
$976$	10.7790	+	33.1743i	0.345027	+	1.06188i
$977$	−28.8475	+	20.9590i	−0.922914	+	0.670536i	−0.944248	−	0.329236i	$-0.893209\pi$
$977$	−28.8475	+	20.9590i	−0.922914	+	0.670536i	0.0213336	+	0.999772i	$0.493209\pi$
$978$	−105.003			−3.35762
$979$		0			0
$980$	−0.0521874			−0.00166707
$981$	−14.5570	+	10.5763i	−0.464769	+	0.337675i
$982$	11.5291	+	35.4828i	0.367907	+	1.13230i
$983$	−9.12258	+	28.0764i	−0.290965	+	0.895498i	0.693582	+	0.720378i	$0.256032\pi$
$983$	−9.12258	+	28.0764i	−0.290965	+	0.895498i	−0.984547	+	0.175121i	$0.943968\pi$
$984$	−2.92549	−	2.12549i	−0.0932611	−	0.0677581i
$985$	0.131899	+	0.0958304i	0.00420266	+	0.00305341i
$986$	6.58182	−	20.2568i	0.209608	−	0.645107i
$987$	7.71414	+	23.7417i	0.245544	+	0.755706i
$988$	10.5164	−	7.64059i	0.334570	−	0.243080i
$989$	−30.1511			−0.958748
$990$		0			0
$991$	−30.7292			−0.976145			−0.488072	−	0.872803i	$-0.662300\pi$
$991$	−30.7292			−0.976145			−0.488072	+	0.872803i	$0.662300\pi$
$992$	−25.7313	+	18.6949i	−0.816969	+	0.593563i
$993$	0.576048	+	1.77289i	0.0182803	+	0.0562611i
$994$	1.25441	−	3.86066i	0.0397873	−	0.122453i
$995$	−0.298811	−	0.217099i	−0.00947295	−	0.00688250i
$996$	11.3843	+	8.27121i	0.360727	+	0.262083i
$997$	−15.4495	+	47.5488i	−0.489292	+	1.50589i	0.336375	+	0.941728i	$0.390799\pi$
$997$	−15.4495	+	47.5488i	−0.489292	+	1.50589i	−0.825667	+	0.564158i	$0.809201\pi$
$998$	24.3869	+	75.0550i	0.771952	+	2.37583i
$999$	−2.07188	+	1.50531i	−0.0655515	+	0.0476259i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.f.x.729.4		16
11.2	odd	10		847.2.a.p.1.7		8
11.3	even	5		847.2.f.v.148.1		16
11.4	even	5	inner	847.2.f.x.323.4		16
11.5	even	5		847.2.f.v.372.1		16
11.6	odd	10		847.2.f.w.372.4		16
11.7	odd	10		77.2.f.b.15.1	✓	16
11.8	odd	10		847.2.f.w.148.4		16
11.9	even	5		847.2.a.o.1.2		8
11.10	odd	2		77.2.f.b.36.1	yes	16
33.2	even	10		7623.2.a.ct.1.2		8
33.20	odd	10		7623.2.a.cw.1.7		8
33.29	even	10		693.2.m.i.631.4		16
33.32	even	2		693.2.m.i.190.4		16
77.10	even	6		539.2.q.f.520.1		32
77.13	even	10		5929.2.a.bt.1.7		8
77.18	odd	30		539.2.q.g.422.4		32
77.20	odd	10		5929.2.a.bs.1.2		8
77.32	odd	6		539.2.q.g.520.1		32
77.40	even	30		539.2.q.f.312.1		32
77.51	odd	30		539.2.q.g.312.1		32
77.54	even	6		539.2.q.f.410.4		32
77.62	even	10		539.2.f.e.246.1		16
77.65	odd	6		539.2.q.g.410.4		32
77.73	even	30		539.2.q.f.422.4		32
77.76	even	2		539.2.f.e.344.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.b.15.1	✓	16	11.7	odd	10
77.2.f.b.36.1	yes	16	11.10	odd	2
539.2.f.e.246.1		16	77.62	even	10
539.2.f.e.344.1		16	77.76	even	2
539.2.q.f.312.1		32	77.40	even	30
539.2.q.f.410.4		32	77.54	even	6
539.2.q.f.422.4		32	77.73	even	30
539.2.q.f.520.1		32	77.10	even	6
539.2.q.g.312.1		32	77.51	odd	30
539.2.q.g.410.4		32	77.65	odd	6
539.2.q.g.422.4		32	77.18	odd	30
539.2.q.g.520.1		32	77.32	odd	6
693.2.m.i.190.4		16	33.32	even	2
693.2.m.i.631.4		16	33.29	even	10
847.2.a.o.1.2		8	11.9	even	5
847.2.a.p.1.7		8	11.2	odd	10
847.2.f.v.148.1		16	11.3	even	5
847.2.f.v.372.1		16	11.5	even	5
847.2.f.w.148.4		16	11.8	odd	10
847.2.f.w.372.4		16	11.6	odd	10
847.2.f.x.323.4		16	11.4	even	5	inner
847.2.f.x.729.4		16	1.1	even	1	trivial
5929.2.a.bs.1.2		8	77.20	odd	10
5929.2.a.bt.1.7		8	77.13	even	10
7623.2.a.ct.1.2		8	33.2	even	10
7623.2.a.cw.1.7		8	33.20	odd	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(1.60551 - 1.16647i) q^{2} +(0.861043 + 2.65002i) q^{3} +(0.598967 - 1.84343i) q^{4} +(0.0217822 + 0.0158257i) q^{5} +(4.47357 + 3.25024i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(0.0378378 + 0.116453i) q^{8} +(-3.85415 + 2.80020i) q^{9} +O(q^{10})\)	\(q+(1.60551 - 1.16647i) q^{2} +(0.861043 + 2.65002i) q^{3} +(0.598967 - 1.84343i) q^{4} +(0.0217822 + 0.0158257i) q^{5} +(4.47357 + 3.25024i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(0.0378378 + 0.116453i) q^{8} +(-3.85415 + 2.80020i) q^{9} +0.0534317 q^{10} +5.40087 q^{12} +(-3.94891 + 2.86905i) q^{13} +(0.613249 + 1.88739i) q^{14} +(-0.0231830 + 0.0713500i) q^{15} +(3.33282 + 2.42144i) q^{16} +(1.35816 + 0.986762i) q^{17} +(-2.92151 + 8.99149i) q^{18} +(-0.424571 - 1.30670i) q^{19} +(0.0422205 - 0.0306750i) q^{20} -2.78639 q^{21} +8.06246 q^{23} +(-0.276022 + 0.200542i) q^{24} +(-1.54486 - 4.75459i) q^{25} +(-2.99334 + 9.21255i) q^{26} +(-3.97645 - 2.88906i) q^{27} +(1.56812 + 1.13930i) q^{28} +(1.97560 - 6.08026i) q^{29} +(0.0460070 + 0.141595i) q^{30} +(-3.24460 + 2.35734i) q^{31} +7.93050 q^{32} +3.33156 q^{34} +(-0.0217822 + 0.0158257i) q^{35} +(2.85347 + 8.78209i) q^{36} +(0.161010 - 0.495536i) q^{37} +(-2.20587 - 1.60266i) q^{38} +(-11.0032 - 7.99430i) q^{39} +(-0.00101876 + 0.00313541i) q^{40} +(3.27519 + 10.0800i) q^{41} +(-4.47357 + 3.25024i) q^{42} -3.73968 q^{43} -0.128267 q^{45} +(12.9443 - 9.40461i) q^{46} +(-2.76850 - 8.52058i) q^{47} +(-3.54715 + 10.9170i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(-8.02637 - 5.83150i) q^{50} +(-1.44550 + 4.44879i) q^{51} +(2.92363 + 8.99801i) q^{52} +(3.20417 - 2.32797i) q^{53} -9.75422 q^{54} -0.122446 q^{56} +(3.09719 - 2.25024i) q^{57} +(-3.92060 - 12.0664i) q^{58} +(3.00680 - 9.25399i) q^{59} +(0.117643 + 0.0854726i) q^{60} +(6.85013 + 4.97691i) q^{61} +(-2.45946 + 7.56944i) q^{62} +(-1.47215 - 4.53082i) q^{63} +(6.06683 - 4.40781i) q^{64} -0.131421 q^{65} +2.81285 q^{67} +(2.63252 - 1.91264i) q^{68} +(6.94213 + 21.3657i) q^{69} +(-0.0165113 + 0.0508166i) q^{70} +(-1.65485 - 1.20232i) q^{71} +(-0.471924 - 0.342873i) q^{72} +(3.23520 - 9.95693i) q^{73} +(-0.319526 - 0.983399i) q^{74} +(11.2696 - 8.18782i) q^{75} -2.66311 q^{76} -26.9908 q^{78} +(4.73697 - 3.44161i) q^{79} +(0.0342753 + 0.105489i) q^{80} +(-0.184290 + 0.567186i) q^{81} +(17.0163 + 12.3631i) q^{82} +(2.10787 + 1.53146i) q^{83} +(-1.66896 + 5.13653i) q^{84} +(0.0139676 + 0.0429878i) q^{85} +(-6.00409 + 4.36222i) q^{86} +17.8139 q^{87} +1.21791 q^{89} +(-0.205934 + 0.149620i) q^{90} +(-1.50835 - 4.64222i) q^{91} +(4.82915 - 14.8626i) q^{92} +(-9.04072 - 6.56847i) q^{93} +(-14.3838 - 10.4505i) q^{94} +(0.0114313 - 0.0351819i) q^{95} +(6.82851 + 21.0160i) q^{96} +(-2.74799 + 1.99653i) q^{97} -1.98451 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 3 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} - 3 q^{6} + 4 q^{7} + 5 q^{8} - 12 q^{9}+O(q^{10}) \) 16 * q + 3 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 - 3 * q^6 + 4 * q^7 + 5 * q^8 - 12 * q^9	\( 16 q + 3 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} - 3 q^{6} + 4 q^{7} + 5 q^{8} - 12 q^{9} - 12 q^{10} + 18 q^{12} + 7 q^{13} + 2 q^{14} - 18 q^{15} + 17 q^{16} + 5 q^{17} - 11 q^{18} - 19 q^{19} + q^{20} - 8 q^{21} + 32 q^{23} + 35 q^{24} + 7 q^{25} - 27 q^{26} + 10 q^{27} - 4 q^{28} - 3 q^{29} + 2 q^{30} - 7 q^{31} - 32 q^{32} - 24 q^{34} + 5 q^{35} + 52 q^{36} + 4 q^{37} - 5 q^{38} - 11 q^{39} + 10 q^{40} + 10 q^{41} + 3 q^{42} + 8 q^{43} + 70 q^{45} + 42 q^{46} - 23 q^{47} - 36 q^{48} - 4 q^{49} - 52 q^{50} + 29 q^{51} - 33 q^{52} + 4 q^{53} - 60 q^{54} + 11 q^{57} + 20 q^{58} + 17 q^{59} - 30 q^{60} + 7 q^{61} - 79 q^{62} + 2 q^{63} + 7 q^{64} + 8 q^{65} - 38 q^{67} + 2 q^{68} + 10 q^{69} - 18 q^{70} - 14 q^{71} + 35 q^{73} + 29 q^{74} + 9 q^{75} - 52 q^{76} - 58 q^{78} - 15 q^{79} - 87 q^{80} - 14 q^{81} + 19 q^{82} - 5 q^{83} - 8 q^{84} - 6 q^{85} - 52 q^{86} + 72 q^{87} + 74 q^{89} + 14 q^{90} + 13 q^{91} - 55 q^{92} + 32 q^{93} + 24 q^{94} - 32 q^{95} + 42 q^{96} + 20 q^{97} - 2 q^{98}+O(q^{100}) \) 16 * q + 3 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 - 3 * q^6 + 4 * q^7 + 5 * q^8 - 12 * q^9 - 12 * q^10 + 18 * q^12 + 7 * q^13 + 2 * q^14 - 18 * q^15 + 17 * q^16 + 5 * q^17 - 11 * q^18 - 19 * q^19 + q^20 - 8 * q^21 + 32 * q^23 + 35 * q^24 + 7 * q^25 - 27 * q^26 + 10 * q^27 - 4 * q^28 - 3 * q^29 + 2 * q^30 - 7 * q^31 - 32 * q^32 - 24 * q^34 + 5 * q^35 + 52 * q^36 + 4 * q^37 - 5 * q^38 - 11 * q^39 + 10 * q^40 + 10 * q^41 + 3 * q^42 + 8 * q^43 + 70 * q^45 + 42 * q^46 - 23 * q^47 - 36 * q^48 - 4 * q^49 - 52 * q^50 + 29 * q^51 - 33 * q^52 + 4 * q^53 - 60 * q^54 + 11 * q^57 + 20 * q^58 + 17 * q^59 - 30 * q^60 + 7 * q^61 - 79 * q^62 + 2 * q^63 + 7 * q^64 + 8 * q^65 - 38 * q^67 + 2 * q^68 + 10 * q^69 - 18 * q^70 - 14 * q^71 + 35 * q^73 + 29 * q^74 + 9 * q^75 - 52 * q^76 - 58 * q^78 - 15 * q^79 - 87 * q^80 - 14 * q^81 + 19 * q^82 - 5 * q^83 - 8 * q^84 - 6 * q^85 - 52 * q^86 + 72 * q^87 + 74 * q^89 + 14 * q^90 + 13 * q^91 - 55 * q^92 + 32 * q^93 + 24 * q^94 - 32 * q^95 + 42 * q^96 + 20 * q^97 - 2 * q^98

Introduction

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