LMFDB - Embedded newform 799.2.k.a.256.29

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [799,2,Mod(18,799)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(799, base_ring=CyclotomicField(46))

chi = DirichletCharacter(H, H._module([0, 12]))

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

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

chi := DirichletCharacter("799.18");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 799 = 17 \cdot 47 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	799.k (of order $23$, degree $22$, 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:	$6.38004712150$
Analytic rank:	$0$
Dimension:	$704$
Relative dimension:	$32$ over $\Q(\zeta_{23})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{23}]$

Embedding invariants

Embedding label			256.29
Character	$\chi$	$=$	799.256
Dual form			799.2.k.a.103.29

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.08830 + 2.10033i) q^{2} +(-1.11163 + 3.12782i) q^{3} +(-2.07363 + 2.93766i) q^{4} +(-0.863380 - 0.375019i) q^{5} +(-7.77926 + 1.06923i) q^{6} +(-2.24078 - 1.36265i) q^{7} +(-3.73977 - 0.514020i) q^{8} +(-6.22043 - 5.06070i) q^{9} +O(q^{10})$	\(q+(1.08830 + 2.10033i) q^{2} +(-1.11163 + 3.12782i) q^{3} +(-2.07363 + 2.93766i) q^{4} +(-0.863380 - 0.375019i) q^{5} +(-7.77926 + 1.06923i) q^{6} +(-2.24078 - 1.36265i) q^{7} +(-3.73977 - 0.514020i) q^{8} +(-6.22043 - 5.06070i) q^{9} +(-0.151956 - 2.22152i) q^{10} +(2.29419 - 0.642803i) q^{11} +(-6.88338 - 9.75153i) q^{12} +(1.36296 + 6.55893i) q^{13} +(0.423363 - 6.18936i) q^{14} +(2.13275 - 2.28362i) q^{15} +(-0.582077 - 1.63781i) q^{16} +(0.962917 + 0.269797i) q^{17} +(3.85942 - 18.5726i) q^{18} +(-0.293217 + 0.127362i) q^{19} +(2.89201 - 1.75867i) q^{20} +(6.75304 - 5.49401i) q^{21} +(3.84688 + 4.11900i) q^{22} +(-2.13228 + 4.11510i) q^{23} +(5.76500 - 11.1259i) q^{24} +(-2.80798 - 3.00661i) q^{25} +(-12.2926 + 10.0008i) q^{26} +(14.2351 - 8.65655i) q^{27} +(8.64953 - 3.75702i) q^{28} +(-0.518744 + 2.49633i) q^{29} +(7.11744 + 1.99421i) q^{30} +(-1.93658 - 5.44902i) q^{31} +(-2.34672 + 2.51272i) q^{32} +(-0.539718 + 7.89039i) q^{33} +(0.481284 + 2.31607i) q^{34} +(1.42363 + 2.01682i) q^{35} +(27.7655 - 7.77952i) q^{36} +(-0.675541 - 9.87606i) q^{37} +(-0.586613 - 0.477245i) q^{38} +(-22.0303 - 3.02799i) q^{39} +(3.03608 + 1.84628i) q^{40} +(3.32078 - 0.456431i) q^{41} +(18.8886 + 8.20447i) q^{42} +(-4.62332 + 6.54975i) q^{43} +(-2.86896 + 8.07249i) q^{44} +(3.47274 + 6.70209i) q^{45} -10.9636 q^{46} +(-3.64611 + 5.80567i) q^{47} +5.76983 q^{48} +(-0.0561728 - 0.108409i) q^{49} +(3.25895 - 9.16980i) q^{50} +(-1.91428 + 2.71192i) q^{51} +(-22.0942 - 9.59685i) q^{52} +(2.21046 - 0.303821i) q^{53} +(33.6737 + 20.4774i) q^{54} +(-2.22182 - 0.305383i) q^{55} +(7.67957 + 6.24780i) q^{56} +(-0.0724179 - 1.05871i) q^{57} +(-5.80768 + 1.62723i) q^{58} +(0.0280069 + 0.0396767i) q^{59} +(2.28597 + 11.0007i) q^{60} +(-0.491021 + 7.17848i) q^{61} +(9.33717 - 9.99766i) q^{62} +(7.04267 + 19.8162i) q^{63} +(-11.1789 - 3.13219i) q^{64} +(1.28297 - 6.17398i) q^{65} +(-17.1598 + 7.45356i) q^{66} +(7.82939 - 4.76116i) q^{67} +(-2.78930 + 2.26926i) q^{68} +(-10.5010 - 11.2439i) q^{69} +(-2.68665 + 5.18500i) q^{70} +(-2.26213 + 4.36571i) q^{71} +(20.6617 + 22.1233i) q^{72} +(0.639080 - 0.519930i) q^{73} +(20.0078 - 12.1670i) q^{74} +(12.5256 - 5.44063i) q^{75} +(0.233876 - 1.12547i) q^{76} +(-6.01669 - 1.68580i) q^{77} +(-17.6159 - 49.5663i) q^{78} +(-6.21298 + 6.65248i) q^{79} +(-0.111655 + 1.63234i) q^{80} +(6.35748 + 30.5939i) q^{81} +(4.57267 + 6.47800i) q^{82} +(-10.3383 + 2.89664i) q^{83} +(2.13623 + 31.2306i) q^{84} +(-0.730185 - 0.594049i) q^{85} +(-18.7882 - 2.58238i) q^{86} +(-7.23144 - 4.39753i) q^{87} +(-8.91017 + 1.22467i) q^{88} +(9.34284 + 4.05817i) q^{89} +(-10.2972 + 14.5878i) q^{90} +(5.88341 - 16.5543i) q^{91} +(-7.66723 - 14.7971i) q^{92} +19.1964 q^{93} +(-16.1619 - 1.33971i) q^{94} +0.300921 q^{95} +(-5.25067 - 10.1333i) q^{96} +(1.42956 - 4.02241i) q^{97} +(0.166561 - 0.235963i) q^{98} +(-17.5239 - 7.61171i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 704 q - 2 q^{3} - 32 q^{4} - 6 q^{5} - 10 q^{6} + 21 q^{7} - 24 q^{8} - 42 q^{9}+O(q^{10}) $ 704 * q - 2 * q^3 - 32 * q^4 - 6 * q^5 - 10 * q^6 + 21 * q^7 - 24 * q^8 - 42 * q^9	\( 704 q - 2 q^{3} - 32 q^{4} - 6 q^{5} - 10 q^{6} + 21 q^{7} - 24 q^{8} - 42 q^{9} - 36 q^{10} - 12 q^{11} - 40 q^{12} - 12 q^{13} - 30 q^{14} - 34 q^{15} - 48 q^{16} - 32 q^{17} - 6 q^{18} - 12 q^{19} - 26 q^{20} - 32 q^{21} - 28 q^{22} - 30 q^{23} - 24 q^{24} - 42 q^{25} - 46 q^{26} - 56 q^{27} - 14 q^{28} - 44 q^{29} + 136 q^{30} - 44 q^{31} - 48 q^{32} - 28 q^{33} - 46 q^{35} - 42 q^{36} - 24 q^{37} + 520 q^{38} - 11 q^{39} + 50 q^{40} + 31 q^{41} - 94 q^{42} - 35 q^{43} - 68 q^{44} - 110 q^{45} + 280 q^{46} - 17 q^{47} - 128 q^{48} - 59 q^{49} + 20 q^{50} - 2 q^{51} - 84 q^{52} - 11 q^{53} + 415 q^{54} - 17 q^{55} - 18 q^{56} - 37 q^{57} - 40 q^{58} - 54 q^{59} - 128 q^{60} - 66 q^{61} + 96 q^{62} - 74 q^{63} - 124 q^{64} - 52 q^{65} - 68 q^{66} - 56 q^{67} - 32 q^{68} + 4 q^{69} + 514 q^{70} - 42 q^{71} - 130 q^{72} - 62 q^{73} - 110 q^{74} - 80 q^{75} - 186 q^{76} + 450 q^{77} - 82 q^{78} - 64 q^{79} - 164 q^{80} + 18 q^{81} + 57 q^{82} - 56 q^{83} - 38 q^{84} - 6 q^{85} + 72 q^{86} - 42 q^{87} - 178 q^{88} - 56 q^{89} + 94 q^{90} + 110 q^{91} + 31 q^{92} + 290 q^{93} - 136 q^{94} - 96 q^{95} - 188 q^{96} - 74 q^{97} - 11 q^{98} + 68 q^{99}+O(q^{100}) \) 704 * q - 2 * q^3 - 32 * q^4 - 6 * q^5 - 10 * q^6 + 21 * q^7 - 24 * q^8 - 42 * q^9 - 36 * q^10 - 12 * q^11 - 40 * q^12 - 12 * q^13 - 30 * q^14 - 34 * q^15 - 48 * q^16 - 32 * q^17 - 6 * q^18 - 12 * q^19 - 26 * q^20 - 32 * q^21 - 28 * q^22 - 30 * q^23 - 24 * q^24 - 42 * q^25 - 46 * q^26 - 56 * q^27 - 14 * q^28 - 44 * q^29 + 136 * q^30 - 44 * q^31 - 48 * q^32 - 28 * q^33 - 46 * q^35 - 42 * q^36 - 24 * q^37 + 520 * q^38 - 11 * q^39 + 50 * q^40 + 31 * q^41 - 94 * q^42 - 35 * q^43 - 68 * q^44 - 110 * q^45 + 280 * q^46 - 17 * q^47 - 128 * q^48 - 59 * q^49 + 20 * q^50 - 2 * q^51 - 84 * q^52 - 11 * q^53 + 415 * q^54 - 17 * q^55 - 18 * q^56 - 37 * q^57 - 40 * q^58 - 54 * q^59 - 128 * q^60 - 66 * q^61 + 96 * q^62 - 74 * q^63 - 124 * q^64 - 52 * q^65 - 68 * q^66 - 56 * q^67 - 32 * q^68 + 4 * q^69 + 514 * q^70 - 42 * q^71 - 130 * q^72 - 62 * q^73 - 110 * q^74 - 80 * q^75 - 186 * q^76 + 450 * q^77 - 82 * q^78 - 64 * q^79 - 164 * q^80 + 18 * q^81 + 57 * q^82 - 56 * q^83 - 38 * q^84 - 6 * q^85 + 72 * q^86 - 42 * q^87 - 178 * q^88 - 56 * q^89 + 94 * q^90 + 110 * q^91 + 31 * q^92 + 290 * q^93 - 136 * q^94 - 96 * q^95 - 188 * q^96 - 74 * q^97 - 11 * q^98 + 68 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/799\mathbb{Z}\right)^\times$.

$n$	$52$	$377$
$\chi(n)$	$e\left(\frac{3}{23}\right)$	$1$

Coefficient data

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

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

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

$2$	1.08830	+	2.10033i	0.769547	+	1.48516i	0.871514	+	0.490371i	$0.163139\pi$
$2$	1.08830	+	2.10033i	0.769547	+	1.48516i	−0.101967	+	0.994788i	$0.532514\pi$
$3$	−1.11163	+	3.12782i	−0.641799	+	1.80585i	−0.0514898	+	0.998674i	$0.516397\pi$
$3$	−1.11163	+	3.12782i	−0.641799	+	1.80585i	−0.590310	+	0.807177i	$0.700994\pi$
$4$	−2.07363	+	2.93766i	−1.03681	+	1.46883i
$5$	−0.863380	−	0.375019i	−0.386115	−	0.167714i	0.196418	−	0.980520i	$-0.437069\pi$
$5$	−0.863380	−	0.375019i	−0.386115	−	0.167714i	−0.582534	+	0.812807i	$0.697939\pi$
$6$	−7.77926	+	1.06923i	−3.17587	+	0.436513i
$7$	−2.24078	−	1.36265i	−0.846935	−	0.515033i	0.0278116	−	0.999613i	$-0.491146\pi$
$7$	−2.24078	−	1.36265i	−0.846935	−	0.515033i	−0.874747	+	0.484581i	$0.838972\pi$
$8$	−3.73977	−	0.514020i	−1.32221	−	0.181733i
$9$	−6.22043	−	5.06070i	−2.07348	−	1.68690i
$10$	−0.151956	−	2.22152i	−0.0480527	−	0.702506i
$11$	2.29419	−	0.642803i	0.691725	−	0.193812i	0.0940700	−	0.995566i	$-0.470012\pi$
$11$	2.29419	−	0.642803i	0.691725	−	0.193812i	0.597655	+	0.801753i	$0.296099\pi$
$12$	−6.88338	−	9.75153i	−1.98706	−	2.81502i
$13$	1.36296	+	6.55893i	0.378017	+	1.81912i	0.551372	+	0.834259i	$0.314104\pi$
$13$	1.36296	+	6.55893i	0.378017	+	1.81912i	−0.173355	+	0.984859i	$0.555461\pi$
$14$	0.423363	−	6.18936i	0.113149	−	1.65417i
$15$	2.13275	−	2.28362i	0.550674	−	0.589628i
$16$	−0.582077	−	1.63781i	−0.145519	−	0.409452i
$17$	0.962917	+	0.269797i	0.233542	+	0.0654353i
$17$	0.962917	+	0.269797i	0.233542	+	0.0654353i
$18$	3.85942	−	18.5726i	0.909674	−	4.37759i
$19$	−0.293217	+	0.127362i	−0.0672687	+	0.0292189i	−0.431767	−	0.901985i	$-0.642110\pi$
$19$	−0.293217	+	0.127362i	−0.0672687	+	0.0292189i	0.364499	+	0.931204i	$0.381240\pi$
$20$	2.89201	−	1.75867i	0.646672	−	0.393250i
$21$	6.75304	−	5.49401i	1.47363	−	1.19889i
$22$	3.84688	+	4.11900i	0.820157	+	0.878174i
$23$	−2.13228	+	4.11510i	−0.444610	+	0.858059i	0.555046	+	0.831820i	$0.312701\pi$
$23$	−2.13228	+	4.11510i	−0.444610	+	0.858059i	−0.999656	+	0.0262386i	$0.991647\pi$
$24$	5.76500	−	11.1259i	1.17678	−	2.27107i
$25$	−2.80798	−	3.00661i	−0.561596	−	0.601322i
$26$	−12.2926	+	10.0008i	−2.41078	+	1.96131i
$27$	14.2351	−	8.65655i	2.73954	−	1.66595i
$28$	8.64953	−	3.75702i	1.63461	−	0.710011i
$29$	−0.518744	+	2.49633i	−0.0963283	+	0.463557i	0.903090	+	0.429451i	$0.141293\pi$
$29$	−0.518744	+	2.49633i	−0.0963283	+	0.463557i	−0.999418	+	0.0341057i	$0.989142\pi$
$30$	7.11744	+	1.99421i	1.29946	+	0.364092i
$31$	−1.93658	−	5.44902i	−0.347821	−	0.978674i	−0.979146	−	0.203156i	$-0.934880\pi$
$31$	−1.93658	−	5.44902i	−0.347821	−	0.978674i	0.631326	−	0.775518i	$-0.282511\pi$
$32$	−2.34672	+	2.51272i	−0.414845	+	0.444191i
$33$	−0.539718	+	7.89039i	−0.0939528	+	1.37354i
$34$	0.481284	+	2.31607i	0.0825396	+	0.397202i
$35$	1.42363	+	2.01682i	0.240637	+	0.340904i
$36$	27.7655	−	7.77952i	4.62758	−	1.29659i
$37$	−0.675541	−	9.87606i	−0.111058	−	1.62361i	−0.635453	−	0.772139i	$-0.719187\pi$
$37$	−0.675541	−	9.87606i	−0.111058	−	1.62361i	0.524395	−	0.851475i	$-0.324292\pi$
$38$	−0.586613	−	0.477245i	−0.0951612	−	0.0774194i
$39$	−22.0303	−	3.02799i	−3.52767	−	0.484867i
$40$	3.03608	+	1.84628i	0.480046	+	0.291922i
$41$	3.32078	−	0.456431i	0.518619	−	0.0712825i	0.127890	−	0.991788i	$-0.459180\pi$
$41$	3.32078	−	0.456431i	0.518619	−	0.0712825i	0.390729	+	0.920506i	$0.372223\pi$
$42$	18.8886	+	8.20447i	2.91457	+	1.26598i
$43$	−4.62332	+	6.54975i	−0.705049	+	0.998827i	0.294025	+	0.955798i	$0.405005\pi$
$43$	−4.62332	+	6.54975i	−0.705049	+	0.998827i	−0.999074	+	0.0430293i	$0.986299\pi$
$44$	−2.86896	+	8.07249i	−0.432512	+	1.21697i
$45$	3.47274	+	6.70209i	0.517686	+	0.999088i
$46$	−10.9636			−1.61650
$47$	−3.64611	+	5.80567i	−0.531840	+	0.846845i
$47$	−3.64611	+	5.80567i	−0.531840	+	0.846845i
$48$	5.76983			0.832804
$49$	−0.0561728	−	0.108409i	−0.00802469	−	0.0154870i
$50$	3.25895	−	9.16980i	0.460885	−	1.29681i
$51$	−1.91428	+	2.71192i	−0.268053	+	0.379745i
$52$	−22.0942	−	9.59685i	−3.06391	−	1.33084i
$53$	2.21046	−	0.303821i	0.303630	−	0.0417330i	0.0172569	−	0.999851i	$-0.494507\pi$
$53$	2.21046	−	0.303821i	0.303630	−	0.0417330i	0.286374	+	0.958118i	$0.407550\pi$
$54$	33.6737	+	20.4774i	4.58241	+	2.78663i
$55$	−2.22182	−	0.305383i	−0.299591	−	0.0411778i
$56$	7.67957	+	6.24780i	1.02623	+	0.834897i
$57$	−0.0724179	−	1.05871i	−0.00959199	−	0.140230i
$58$	−5.80768	+	1.62723i	−0.762585	+	0.213666i
$59$	0.0280069	+	0.0396767i	0.00364618	+	0.00516546i	0.818789	−	0.574095i	$-0.194646\pi$
$59$	0.0280069	+	0.0396767i	0.00364618	+	0.00516546i	−0.815143	+	0.579260i	$0.803342\pi$
$60$	2.28597	+	11.0007i	0.295117	+	1.42018i
$61$	−0.491021	+	7.17848i	−0.0628688	+	0.919110i	0.854089	+	0.520126i	$0.174115\pi$
$61$	−0.491021	+	7.17848i	−0.0628688	+	0.919110i	−0.916958	+	0.398984i	$0.869363\pi$
$62$	9.33717	−	9.99766i	1.18582	−	1.26970i
$63$	7.04267	+	19.8162i	0.887293	+	2.49660i
$64$	−11.1789	−	3.13219i	−1.39736	−	0.391523i
$65$	1.28297	−	6.17398i	0.159133	−	0.765788i
$66$	−17.1598	+	7.45356i	−2.11223	+	0.917470i
$67$	7.82939	−	4.76116i	0.956512	−	0.581668i	0.0476947	−	0.998862i	$-0.484813\pi$
$67$	7.82939	−	4.76116i	0.956512	−	0.581668i	0.908817	+	0.417194i	$0.136986\pi$
$68$	−2.78930	+	2.26926i	−0.338252	+	0.275189i
$69$	−10.5010	−	11.2439i	−1.26417	−	1.35360i
$70$	−2.68665	+	5.18500i	−0.321116	+	0.619726i
$71$	−2.26213	+	4.36571i	−0.268466	+	0.518115i	−0.983485	−	0.180990i	$-0.942070\pi$
$71$	−2.26213	+	4.36571i	−0.268466	+	0.518115i	0.715019	+	0.699105i	$0.246418\pi$
$72$	20.6617	+	22.1233i	2.43500	+	2.60725i
$73$	0.639080	−	0.519930i	0.0747987	−	0.0608532i	−0.592955	−	0.805236i	$-0.702039\pi$
$73$	0.639080	−	0.519930i	0.0747987	−	0.0608532i	0.667753	+	0.744383i	$0.267256\pi$
$74$	20.0078	−	12.1670i	2.32586	−	1.41439i
$75$	12.5256	−	5.44063i	1.44633	−	0.628230i
$76$	0.233876	−	1.12547i	0.0268275	−	0.129101i
$77$	−6.01669	−	1.68580i	−0.685666	−	0.192115i
$78$	−17.6159	−	49.5663i	−1.99460	−	5.61227i
$79$	−6.21298	+	6.65248i	−0.699015	+	0.748462i	−0.977259	−	0.212048i	$-0.931987\pi$
$79$	−6.21298	+	6.65248i	−0.699015	+	0.748462i	0.278244	+	0.960510i	$0.410248\pi$
$80$	−0.111655	+	1.63234i	−0.0124834	+	0.182501i
$81$	6.35748	+	30.5939i	0.706387	+	3.39932i
$82$	4.57267	+	6.47800i	0.504967	+	0.715376i
$83$	−10.3383	+	2.89664i	−1.13477	+	0.317948i	−0.785371	−	0.619026i	$-0.787528\pi$
$83$	−10.3383	+	2.89664i	−1.13477	+	0.317948i	−0.349400	+	0.936974i	$0.613615\pi$
$84$	2.13623	+	31.2306i	0.233082	+	3.40754i
$85$	−0.730185	−	0.594049i	−0.0791997	−	0.0644337i
$86$	−18.7882	−	2.58238i	−2.02599	−	0.278465i
$87$	−7.23144	−	4.39753i	−0.775291	−	0.471465i
$88$	−8.91017	+	1.22467i	−0.949827	+	0.130551i
$89$	9.34284	+	4.05817i	0.990339	+	0.430165i	0.830524	−	0.556982i	$-0.188041\pi$
$89$	9.34284	+	4.05817i	0.990339	+	0.430165i	0.159815	+	0.987147i	$0.448910\pi$
$90$	−10.2972	+	14.5878i	−1.08542	+	1.53769i
$91$	5.88341	−	16.5543i	0.616749	−	1.73537i
$92$	−7.66723	−	14.7971i	−0.799364	−	1.54270i
$93$	19.1964			1.99057
$94$	−16.1619	−	1.33971i	−1.66697	−	0.138180i
$95$	0.300921			0.0308739
$96$	−5.25067	−	10.1333i	−0.535894	−	1.03423i
$97$	1.42956	−	4.02241i	0.145150	−	0.408414i	−0.847292	−	0.531128i	$-0.821768\pi$
$97$	1.42956	−	4.02241i	0.145150	−	0.408414i	0.992442	+	0.122714i	$0.0391598\pi$
$98$	0.166561	−	0.235963i	0.0168252	−	0.0238359i
$99$	−17.5239	−	7.61171i	−1.76122	−	0.765005i
$100$	14.6551	−	2.01430i	1.46551	−	0.201430i
$101$	−11.8575	−	7.21069i	−1.17986	−	0.717490i	−0.214073	−	0.976818i	$-0.568673\pi$
$101$	−11.8575	−	7.21069i	−1.17986	−	0.717490i	−0.965790	+	0.259327i	$0.916499\pi$
$102$	−7.77926	−	1.06923i	−0.770261	−	0.105870i
$103$	10.6149	+	8.63586i	1.04592	+	0.850917i	0.989067	−	0.147466i	$-0.0471116\pi$
$103$	10.6149	+	8.63586i	1.04592	+	0.850917i	0.0568503	+	0.998383i	$0.481894\pi$
$104$	−1.72574	−	25.2295i	−0.169223	−	2.47395i
$105$	−7.89080	+	2.21090i	−0.770063	+	0.215762i
$106$	3.04378	+	4.31206i	0.295638	+	0.418824i
$107$	−0.567308	−	2.73004i	−0.0548438	−	0.263923i	0.942729	−	0.333561i	$-0.108250\pi$
$107$	−0.567308	−	2.73004i	−0.0548438	−	0.263923i	−0.997572	+	0.0696382i	$0.977816\pi$
$108$	−4.08826	+	59.7683i	−0.393393	+	5.75120i
$109$	4.29823	−	4.60228i	0.411696	−	0.440818i	−0.490960	−	0.871182i	$-0.663354\pi$
$109$	4.29823	−	4.60228i	0.411696	−	0.440818i	0.902656	+	0.430364i	$0.141615\pi$
$110$	−1.77662	−	4.99892i	−0.169394	−	0.476628i
$111$	31.6415	+	8.86554i	3.00328	+	0.841480i
$112$	−0.927450	+	4.46313i	−0.0876358	+	0.421727i
$113$	11.7761	−	5.11510i	1.10781	−	0.481188i	0.236353	−	0.971667i	$-0.424048\pi$
$113$	11.7761	−	5.11510i	1.10781	−	0.481188i	0.871453	+	0.490480i	$0.163178\pi$
$114$	2.14483	−	1.30430i	0.200882	−	0.122159i
$115$	3.38421	−	2.75326i	0.315579	−	0.256742i
$116$	−6.25769	−	6.70035i	−0.581012	−	0.622112i
$117$	24.7145	−	47.6969i	2.28486	−	4.40958i
$118$	−0.0528542	+	0.102004i	−0.00486562	+	0.00939023i
$119$	−1.79005	−	1.91667i	−0.164093	−	0.175701i
$120$	−9.14983	+	7.44394i	−0.835261	+	0.679536i
$121$	−4.54849	+	2.76600i	−0.413499	+	0.251454i
$122$	−15.6116	+	6.78106i	−1.41340	+	0.613928i
$123$	−2.26384	+	10.8942i	−0.204124	+	0.982297i
$124$	20.0231	+	5.61022i	1.79813	+	0.503812i
$125$	2.87295	+	8.08369i	0.256964	+	0.723027i
$126$	−33.9560	+	36.3580i	−3.02504	+	3.23902i
$127$	−1.34604	+	19.6784i	−0.119442	+	1.74618i	0.423039	+	0.906112i	$0.360963\pi$
$127$	−1.34604	+	19.6784i	−0.119442	+	1.74618i	−0.542481	+	0.840068i	$0.682515\pi$
$128$	−4.18841	−	20.1557i	−0.370207	−	1.78153i
$129$	−15.3470	−	21.7418i	−1.35123	−	1.91426i
$130$	14.3637	−	4.02451i	1.25978	−	0.352973i
$131$	−0.658400	−	9.62547i	−0.0575247	−	0.840981i	−0.933489	−	0.358606i	$-0.883252\pi$
$131$	−0.658400	−	9.62547i	−0.0575247	−	0.840981i	0.875964	−	0.482376i	$-0.160226\pi$
$132$	−22.0601	−	17.9472i	−1.92009	−	1.56211i
$133$	0.830586	+	0.114161i	0.0720209	+	0.00989905i
$134$	18.5208	+	11.2627i	1.59995	+	0.972951i
$135$	−15.5367	+	2.13546i	−1.33718	+	0.183792i
$136$	−3.46241	−	1.50394i	−0.296899	−	0.128962i
$137$	−7.72447	+	10.9431i	−0.659946	+	0.934930i	−0.999985	−	0.00548124i	$-0.998255\pi$
$137$	−7.72447	+	10.9431i	−0.659946	+	0.934930i	0.340039	+	0.940411i	$0.389560\pi$
$138$	12.1875	−	34.2924i	1.03747	−	2.91916i
$139$	5.31662	+	10.2606i	0.450950	+	0.870293i	0.999418	+	0.0341218i	$0.0108634\pi$
$139$	5.31662	+	10.2606i	0.450950	+	0.870293i	−0.548468	+	0.836172i	$0.684789\pi$
$140$	−8.87679			−0.750226
$141$	−14.1060	−	17.8582i	−1.18794	−	1.50393i
$142$	−11.6313			−0.976080
$143$	7.34299	+	14.1713i	0.614052	+	1.18507i
$144$	−4.66768	+	13.1336i	−0.388974	+	1.09447i
$145$	1.38404	−	1.96074i	0.114939	−	0.162831i
$146$	1.78754	+	0.776438i	0.147938	+	0.0642585i
$147$	0.401527	−	0.0551886i	0.0331174	−	0.00455188i
$148$	30.4133	+	18.4948i	2.49996	+	1.52026i
$149$	−20.6855	−	2.84316i	−1.69462	−	0.232921i	−0.776755	−	0.629803i	$-0.783136\pi$
$149$	−20.6855	−	2.84316i	−1.69462	−	0.232921i	−0.917870	+	0.396882i	$0.870092\pi$
$150$	25.0588	+	20.3868i	2.04604	+	1.66458i
$151$	0.715770	+	10.4642i	0.0582485	+	0.851563i	0.931373	+	0.364066i	$0.118612\pi$
$151$	0.715770	+	10.4642i	0.0582485	+	0.851563i	−0.873125	+	0.487497i	$0.837910\pi$
$152$	1.16203	−	0.325586i	0.0942533	−	0.0264085i
$153$	−4.62440	−	6.55129i	−0.373861	−	0.529640i
$154$	−3.00726	−	14.4717i	−0.242332	−	1.16616i
$155$	−0.371479	+	5.43084i	−0.0298379	+	0.436215i
$156$	54.5778	−	58.4385i	4.36972	−	4.67883i
$157$	6.25796	+	17.6082i	0.499439	+	1.40529i	0.877531	+	0.479520i	$0.159189\pi$
$157$	6.25796	+	17.6082i	0.499439	+	1.40529i	−0.378092	+	0.925768i	$0.623420\pi$
$158$	−20.7340	−	5.80940i	−1.64951	−	0.462171i
$159$	−1.50692	+	7.25168i	−0.119506	+	0.575095i
$160$	2.96843	−	1.28937i	0.234675	−	0.101934i
$161$	10.3854	−	6.31550i	0.818484	−	0.497731i
$162$	−57.3384	+	46.6483i	−4.50493	+	3.66503i
$163$	1.39716	+	1.49599i	0.109434	+	0.117175i	0.783201	−	0.621769i	$-0.213586\pi$
$163$	1.39716	+	1.49599i	0.109434	+	0.117175i	−0.673767	+	0.738944i	$0.735325\pi$
$164$	−5.54522	+	10.7018i	−0.433009	+	0.835669i
$165$	3.42503	−	6.61000i	0.266638	−	0.514588i
$166$	−17.3351	−	18.5613i	−1.34546	−	1.44064i
$167$	−12.4529	+	10.1311i	−0.963631	+	0.783972i	−0.976405	−	0.215947i	$-0.930716\pi$
$167$	−12.4529	+	10.1311i	−0.963631	+	0.783972i	0.0127744	+	0.999918i	$0.495934\pi$
$168$	−28.0789	+	17.0751i	−2.16633	+	1.31737i
$169$	−29.2381	+	12.6999i	−2.24909	+	0.976916i
$170$	0.453038	−	2.18014i	0.0347464	−	0.167209i
$171$	2.46848	+	0.691636i	0.188770	+	0.0528907i
$172$	−9.65389	−	27.1635i	−0.736103	−	2.07119i
$173$	14.0861	−	15.0826i	1.07095	−	1.14671i	0.0822770	−	0.996609i	$-0.473781\pi$
$173$	14.0861	−	15.0826i	1.07095	−	1.14671i	0.988671	−	0.150096i	$-0.0479584\pi$
$174$	1.36628	−	19.9743i	0.103577	−	1.51425i
$175$	2.19511	+	10.5634i	0.165935	+	0.798521i
$176$	−2.38819	−	3.38329i	−0.180016	−	0.255025i
$177$	−0.155235	+	0.0434948i	−0.0116682	+	0.00326927i
$178$	1.64435	+	24.0396i	0.123249	+	1.80184i
$179$	−7.04378	−	5.73054i	−0.526477	−	0.428320i	0.330401	−	0.943841i	$-0.392816\pi$
$179$	−7.04378	−	5.73054i	−0.526477	−	0.428320i	−0.856877	+	0.515520i	$0.827599\pi$
$180$	−26.8896	−	3.69589i	−2.00423	−	0.275476i
$181$	−2.13791	−	1.30009i	−0.158910	−	0.0966351i	0.437878	−	0.899035i	$-0.355730\pi$
$181$	−2.13791	−	1.30009i	−0.158910	−	0.0966351i	−0.596787	+	0.802399i	$0.703556\pi$
$182$	41.1726	−	5.65904i	3.05191	−	0.419476i
$183$	−21.9072	−	9.51563i	−1.61943	−	0.703416i
$184$	10.0895	−	14.2935i	0.743805	−	1.05373i
$185$	−3.12046	+	8.78014i	−0.229421	+	0.645529i
$186$	20.8915	+	40.3187i	1.53184	+	2.95631i
$187$	2.38254			0.174229
$188$	−9.49442	−	22.7498i	−0.692452	−	1.65920i
$189$	−43.6935			−3.17824
$190$	0.327494	+	0.632035i	0.0237589	+	0.0458526i
$191$	−0.0378637	+	0.106538i	−0.00273972	+	0.00770884i	−0.943623	−	0.331022i	$-0.892606\pi$
$191$	−0.0378637	+	0.106538i	−0.00273972	+	0.00770884i	0.940883	+	0.338731i	$0.109998\pi$
$192$	22.2237	−	31.4839i	1.60386	−	2.27215i
$193$	−18.1959	−	7.90359i	−1.30977	−	0.568913i	−0.375943	−	0.926643i	$-0.622681\pi$
$193$	−18.1959	−	7.90359i	−1.30977	−	0.568913i	−0.933825	+	0.357730i	$0.883551\pi$
$194$	10.0042	−	1.37504i	0.718259	−	0.0987224i
$195$	17.8850	+	10.8761i	1.28077	+	0.778852i
$196$	0.434949	+	0.0597824i	0.0310678	+	0.00427017i
$197$	11.2927	+	9.18728i	0.804571	+	0.654567i	0.941876	−	0.335962i	$-0.109061\pi$
$197$	11.2927	+	9.18728i	0.804571	+	0.654567i	−0.137305	+	0.990529i	$0.543844\pi$
$198$	−3.08423	−	45.0899i	−0.219187	−	3.20440i
$199$	−5.61530	+	1.57333i	−0.398058	+	0.111531i	−0.463000	−	0.886358i	$-0.653227\pi$
$199$	−5.61530	+	1.57333i	−0.398058	+	0.111531i	0.0649415	+	0.997889i	$0.479314\pi$
$200$	8.95574	+	12.6874i	0.633267	+	0.897135i
$201$	6.18869	+	29.7816i	0.436516	+	2.10063i
$202$	2.24030	−	32.7520i	0.157627	−	2.30443i
$203$	4.56401	−	4.88686i	0.320331	−	0.342991i
$204$	−3.99719	−	11.2470i	−0.279860	−	0.787449i
$205$	−3.03827	−	0.851282i	−0.212202	−	0.0594561i
$206$	−6.58594	+	31.6933i	−0.458864	+	2.20817i
$207$	34.0890	−	14.8069i	2.36935	−	1.02915i
$208$	9.94892	−	6.05007i	0.689833	−	0.419497i
$209$	−0.590829	+	0.480675i	−0.0408685	+	0.0332490i
$210$	−13.2312	−	14.1672i	−0.913040	−	0.977627i
$211$	−8.82893	+	17.0391i	−0.607809	+	1.17302i	0.362690	+	0.931910i	$0.381859\pi$
$211$	−8.82893	+	17.0391i	−0.607809	+	1.17302i	−0.970498	+	0.241108i	$0.922489\pi$
$212$	−3.69115	+	7.12360i	−0.253509	+	0.489251i
$213$	−11.1405	−	11.9286i	−0.763337	−	0.817334i
$214$	5.11658	−	4.16265i	0.349762	−	0.284553i
$215$	6.44796	−	3.92109i	0.439747	−	0.267416i
$216$	−57.6856	+	25.0564i	−3.92501	+	1.70487i
$217$	−3.08565	+	14.8489i	−0.209467	+	1.00801i
$218$	14.3441	+	4.01903i	0.971504	+	0.272203i
$219$	0.915831	+	2.57690i	0.0618861	+	0.174131i
$220$	5.50434	−	5.89371i	0.371103	−	0.397354i
$221$	−0.457159	+	6.68343i	−0.0307518	+	0.449576i
$222$	15.8150	+	76.1061i	1.06144	+	5.10791i
$223$	8.58448	+	12.1614i	0.574859	+	0.814390i	0.995689	−	0.0927495i	$-0.0295656\pi$
$223$	8.58448	+	12.1614i	0.574859	+	0.814390i	−0.420830	+	0.907139i	$0.638261\pi$
$224$	8.68243	−	2.43270i	0.580119	−	0.162542i
$225$	2.25130	+	32.9128i	0.150086	+	2.19418i
$226$	23.5594	+	19.1670i	1.56715	+	1.27497i
$227$	15.6128	+	2.14594i	1.03626	+	0.142431i	0.634190	−	0.773177i	$-0.281334\pi$
$227$	15.6128	+	2.14594i	1.03626	+	0.142431i	0.402071	+	0.915608i	$0.368290\pi$
$228$	3.26030	+	1.98263i	0.215919	+	0.131303i
$229$	8.60003	−	1.18205i	0.568306	−	0.0781119i	0.153708	−	0.988116i	$-0.450879\pi$
$229$	8.60003	−	1.18205i	0.568306	−	0.0781119i	0.414598	+	0.910004i	$0.363922\pi$
$230$	9.46580	+	4.11158i	0.624156	+	0.271109i
$231$	11.9612	−	16.9452i	0.786990	−	1.11491i
$232$	3.22315	−	9.06907i	0.211610	−	0.595413i
$233$	−12.6699	−	24.4518i	−0.830034	−	1.60189i	−0.798194	−	0.602401i	$-0.794211\pi$
$233$	−12.6699	−	24.4518i	−0.830034	−	1.60189i	−0.0318407	−	0.999493i	$-0.510137\pi$
$234$	127.076			8.30723
$235$	5.32522	−	3.64514i	0.347379	−	0.237783i
$236$	−0.174632			−0.0113676
$237$	−13.9013	−	26.8282i	−0.902984	−	1.74268i
$238$	2.07753	−	5.84562i	0.134666	−	0.378915i
$239$	7.00772	−	9.92768i	0.453292	−	0.642168i	−0.524583	−	0.851359i	$-0.675779\pi$
$239$	7.00772	−	9.92768i	0.453292	−	0.642168i	0.977875	+	0.209191i	$0.0670831\pi$
$240$	−4.98156	−	2.16380i	−0.321558	−	0.139672i
$241$	−16.6532	+	2.28893i	−1.07273	+	0.147443i	−0.650847	−	0.759209i	$-0.725586\pi$
$241$	−16.6532	+	2.28893i	−1.07273	+	0.147443i	−0.421880	+	0.906652i	$0.638630\pi$
$242$	−10.7596	−	6.54309i	−0.691656	−	0.420606i
$243$	−53.2434	−	7.31813i	−3.41556	−	0.469458i
$244$	−20.0697	−	16.3279i	−1.28483	−	1.04529i
$245$	0.00784322	+	0.114664i	0.000501085	+	0.00732560i
$246$	−25.3452	+	7.10139i	−1.61595	+	0.452768i
$247$	−1.23500	−	1.74960i	−0.0785814	−	0.111325i
$248$	4.44147	+	21.3735i	0.282034	+	1.35722i
$249$	2.43211	−	35.5563i	0.154129	−	2.25329i
$250$	−13.8518	+	14.8317i	−0.876065	+	0.938036i
$251$	1.35630	+	3.81625i	0.0856086	+	0.240880i	0.977336	−	0.211693i	$-0.0678977\pi$
$251$	1.35630	+	3.81625i	0.0856086	+	0.240880i	−0.891728	+	0.452572i	$0.850506\pi$
$252$	−72.8170	−	20.4024i	−4.58704	−	1.28523i
$253$	−2.24665	+	10.8115i	−0.141246	+	0.679712i
$254$	−42.7962	+	18.5890i	−2.68527	+	1.16638i
$255$	2.66978	−	1.62353i	0.167188	−	0.101669i
$256$	19.7643	−	16.0795i	1.23527	−	1.00497i
$257$	−0.286882	−	0.307176i	−0.0178952	−	0.0191611i	0.721826	−	0.692075i	$-0.243303\pi$
$257$	−0.286882	−	0.307176i	−0.0178952	−	0.0191611i	−0.739721	+	0.672914i	$0.765042\pi$
$258$	28.9628	−	55.8956i	1.80314	−	3.47991i
$259$	−11.9439	+	23.0506i	−0.742155	+	1.43229i
$260$	15.4767	+	16.5715i	0.959822	+	1.02772i
$261$	15.8600	−	12.9031i	0.981709	−	0.798679i
$262$	19.5001	−	11.8583i	1.20472	−	0.732608i
$263$	11.1694	−	4.85154i	0.688733	−	0.299159i	−0.0248889	−	0.999690i	$-0.507923\pi$
$263$	11.1694	−	4.85154i	0.688733	−	0.299159i	0.713622	+	0.700531i	$0.247054\pi$
$264$	6.07424	−	29.2308i	0.373843	−	1.79903i
$265$	−2.02241	−	0.566652i	−0.124236	−	0.0348092i
$266$	0.664153	+	1.86875i	0.0407218	+	0.114580i
$267$	−23.0790	+	24.7116i	−1.41241	+	1.51232i
$268$	−2.24857	+	32.8729i	−0.137353	+	2.00803i
$269$	−1.27675	−	6.14404i	−0.0778446	−	0.374609i	0.922079	−	0.387003i	$-0.126490\pi$
$269$	−1.27675	−	6.14404i	−0.0778446	−	0.374609i	−0.999923	+	0.0123938i	$0.996055\pi$
$270$	−21.3938	−	30.3081i	−1.30198	−	1.84449i
$271$	22.3183	−	6.25330i	1.35574	−	0.379861i	0.486255	−	0.873817i	$-0.338363\pi$
$271$	22.3183	−	6.25330i	1.35574	−	0.379861i	0.869487	+	0.493956i	$0.164450\pi$
$272$	−0.118617	−	1.73412i	−0.00719220	−	0.105146i
$273$	45.2389	+	36.8046i	2.73798	+	2.22751i
$274$	−31.3907	−	4.31455i	−1.89638	−	0.260651i
$275$	−8.37471	−	5.09277i	−0.505014	−	0.307106i
$276$	54.8058	−	7.53288i	3.29892	−	0.453426i
$277$	11.2001	+	4.86490i	0.672949	+	0.292303i	0.707100	−	0.707113i	$-0.250003\pi$
$277$	11.2001	+	4.86490i	0.672949	+	0.292303i	−0.0341506	+	0.999417i	$0.510873\pi$
$278$	−15.7646	+	22.3333i	−0.945497	+	1.33946i
$279$	−15.5295	+	43.6958i	−0.929726	+	2.61600i
$280$	−4.28735	−	8.27421i	−0.256218	−	0.494479i
$281$	−9.39657			−0.560552			−0.280276	−	0.959919i	$-0.590426\pi$
$281$	−9.39657			−0.560552			−0.280276	+	0.959919i	$0.590426\pi$
$282$	22.1564	−	49.0624i	1.31940	−	2.92162i
$283$	−3.33018			−0.197958			−0.0989792	−	0.995090i	$-0.531558\pi$
$283$	−3.33018			−0.197958			−0.0989792	+	0.995090i	$0.531558\pi$
$284$	−8.13417	−	15.6982i	−0.482674	−	0.931518i
$285$	−0.334513	+	0.941230i	−0.0198148	+	0.0557536i
$286$	−21.7731	+	30.8454i	−1.28747	+	1.82393i
$287$	−8.06309	−	3.50229i	−0.475949	−	0.206734i
$288$	27.3137	−	3.75419i	1.60948	−	0.221218i
$289$	0.854419	+	0.519584i	0.0502600	+	0.0305638i
$290$	5.62448	+	0.773066i	0.330281	+	0.0453960i
$291$	10.9922	+	8.94285i	0.644376	+	0.524239i
$292$	0.202164	+	2.95554i	0.0118308	+	0.172960i
$293$	27.9948	−	7.84379i	1.63548	−	0.458239i	0.675279	−	0.737562i	$-0.264023\pi$
$293$	27.9948	−	7.84379i	1.63548	−	0.458239i	0.960197	+	0.279323i	$0.0901100\pi$
$294$	0.552897	+	0.783277i	0.0322456	+	0.0456817i
$295$	−0.00930106	−	0.0447592i	−0.000541529	−	0.00260598i
$296$	−2.55012	+	37.2815i	−0.148223	+	2.16694i
$297$	27.0936	−	29.0101i	1.57213	−	1.68334i
$298$	−16.5406	−	46.5407i	−0.958169	−	2.69603i
$299$	−29.8969	−	8.37671i	−1.72898	−	0.484438i
$300$	−9.99067	+	48.0777i	−0.576812	+	2.77577i
$301$	19.2848	−	8.37659i	1.11156	−	0.482818i
$302$	−21.1993	+	12.8916i	−1.21988	+	0.741827i
$303$	35.7349	−	29.0725i	2.05292	−	1.67017i
$304$	0.379270	+	0.406099i	0.0217526	+	0.0232914i
$305$	3.11600	−	6.01361i	0.178422	−	0.344339i
$306$	8.72712	−	16.8426i	0.498896	−	0.962826i
$307$	9.42564	+	10.0924i	0.537950	+	0.576004i	0.940671	−	0.339319i	$-0.110197\pi$
$307$	9.42564	+	10.0924i	0.537950	+	0.576004i	−0.402721	+	0.915323i	$0.631936\pi$
$308$	17.4287	−	14.1793i	0.993091	−	0.807939i
$309$	−38.8113	+	23.6017i	−2.20790	+	1.34265i
$310$	−11.8108	+	5.13017i	−0.670811	+	0.291374i
$311$	1.84994	−	8.90238i	0.104900	−	0.504808i	−0.893540	−	0.448983i	$-0.851786\pi$
$311$	1.84994	−	8.90238i	0.104900	−	0.504808i	0.998441	−	0.0558247i	$-0.0177788\pi$
$312$	80.8318	+	22.6480i	4.57620	+	1.28219i
$313$	−0.497849	−	1.40081i	−0.0281401	−	0.0791786i	0.927359	−	0.374173i	$-0.122073\pi$
$313$	−0.497849	−	1.40081i	−0.0281401	−	0.0791786i	−0.955499	+	0.294995i	$0.904682\pi$
$314$	−30.1725	+	32.3069i	−1.70273	+	1.82318i
$315$	1.35094	−	19.7500i	0.0761168	−	1.11279i
$316$	−6.65931	−	32.0464i	−0.374616	−	1.80275i
$317$	6.62046	+	9.37906i	0.371842	+	0.526781i	0.959268	−	0.282498i	$-0.0911629\pi$
$317$	6.62046	+	9.37906i	0.371842	+	0.526781i	−0.587426	+	0.809278i	$0.699859\pi$
$318$	−16.8709	+	4.72701i	−0.946074	+	0.265077i
$319$	0.414551	+	6.06052i	0.0232104	+	0.339324i
$320$	8.47703	+	6.89657i	0.473880	+	0.385530i
$321$	9.16972	+	1.26035i	0.511804	+	0.0703458i
$322$	24.5671	+	14.9396i	1.36907	+	0.832551i
$323$	−0.316706	+	0.0435303i	−0.0176220	+	0.00242209i
$324$	−103.057	−	44.7642i	−5.72541	−	2.48690i
$325$	15.8930	−	22.5152i	0.881584	−	1.24892i
$326$	−1.62154	+	4.56258i	−0.0898089	+	0.252698i
$327$	9.61708	+	18.5601i	0.531826	+	1.02638i
$328$	−12.6536			−0.698677
$329$	16.0812	−	8.04087i	0.886587	−	0.443307i
$330$	17.6107			0.969435
$331$	6.71029	+	12.9503i	0.368831	+	0.711812i	0.997847	−	0.0655806i	$-0.0208899\pi$
$331$	6.71029	+	12.9503i	0.368831	+	0.711812i	−0.629016	+	0.777392i	$0.716542\pi$
$332$	12.9283	−	36.3768i	0.709534	−	1.99644i
$333$	−45.7776	+	64.8521i	−2.50860	+	3.55387i
$334$	−34.8313	−	15.1294i	−1.90588	−	0.827841i
$335$	−8.54526	+	1.17452i	−0.466878	+	0.0641709i
$336$	−12.9289	−	7.86225i	−0.705331	−	0.428921i
$337$	0.0647527	+	0.00890006i	0.00352731	+	0.000484817i	0.137930	−	0.990442i	$-0.455955\pi$
$337$	0.0647527	+	0.00890006i	0.00352731	+	0.000484817i	−0.134403	+	0.990927i	$0.542912\pi$
$338$	−58.4940	−	47.5884i	−3.18165	−	2.58847i
$339$	2.90843	+	42.5198i	0.157964	+	2.30936i
$340$	3.25924	−	0.913198i	0.176757	−	0.0495251i
$341$	−7.94554	−	11.2563i	−0.430275	−	0.609561i
$342$	1.23379	+	5.93734i	0.0667159	+	0.321055i
$343$	−1.27465	+	18.6347i	−0.0688245	+	1.00618i
$344$	20.6568	−	22.1181i	1.11374	−	1.19253i
$345$	4.84972	+	13.6458i	0.261100	+	0.734665i
$346$	47.0084	+	13.1711i	2.52719	+	0.708084i
$347$	−5.54264	+	26.6726i	−0.297544	+	1.43186i	0.519097	+	0.854715i	$0.326268\pi$
$347$	−5.54264	+	26.6726i	−0.297544	+	1.43186i	−0.816641	+	0.577146i	$0.804166\pi$
$348$	27.9138	−	12.1247i	1.49633	−	0.649950i
$349$	3.98492	−	2.42328i	0.213308	−	0.129715i	−0.408866	−	0.912594i	$-0.634076\pi$
$349$	3.98492	−	2.42328i	0.213308	−	0.129715i	0.622174	+	0.782879i	$0.286250\pi$
$350$	−19.7978	+	16.1067i	−1.05824	+	0.860939i
$351$	76.1795	+	81.5683i	4.06616	+	4.35380i
$352$	−3.76864	+	7.27314i	−0.200869	+	0.387660i
$353$	3.99310	−	7.70632i	0.212531	−	0.410166i	−0.757610	−	0.652707i	$-0.773633\pi$
$353$	3.99310	−	7.70632i	0.212531	−	0.410166i	0.970141	+	0.242541i	$0.0779809\pi$
$354$	−0.260296	−	0.278709i	−0.0138346	−	0.0148132i
$355$	3.59030	−	2.92093i	0.190554	−	0.155027i
$356$	−31.2951	+	19.0310i	−1.65864	+	1.00864i
$357$	7.98488	−	3.46832i	0.422605	−	0.183563i
$358$	4.37026	−	21.0308i	0.230975	−	1.11151i
$359$	−7.02965	−	1.96962i	−0.371011	−	0.103952i	0.0792375	−	0.996856i	$-0.474751\pi$
$359$	−7.02965	−	1.96962i	−0.371011	−	0.103952i	−0.450248	+	0.892903i	$0.648664\pi$
$360$	−9.54225	−	26.8493i	−0.502921	−	1.41508i
$361$	−12.8988	+	13.8112i	−0.678882	+	0.726905i
$362$	0.403928	−	5.90522i	0.0212300	−	0.310371i
$363$	−3.59532	−	17.3016i	−0.188705	−	0.908100i
$364$	36.4310	+	51.6110i	1.90950	+	2.70515i
$365$	−0.746753	+	0.209230i	−0.0390868	+	0.0109516i
$366$	−3.85569	−	56.3683i	−0.201540	−	2.94642i
$367$	11.5225	+	9.37423i	0.601468	+	0.489331i	0.882465	−	0.470378i	$-0.155882\pi$
$367$	11.5225	+	9.37423i	0.601468	+	0.489331i	−0.280997	+	0.959709i	$0.590665\pi$
$368$	7.98090	+	1.09695i	0.416033	+	0.0571825i
$369$	−22.9665	−	13.9663i	−1.19559	−	0.727055i
$370$	−21.8372	+	3.00146i	−1.13526	+	0.156038i
$371$	−5.36716	−	2.33129i	−0.278649	−	0.121034i
$372$	−39.8061	+	56.3923i	−2.06385	+	2.92381i
$373$	8.22883	−	23.1537i	0.426073	−	1.19885i	−0.513973	−	0.857806i	$-0.671827\pi$
$373$	8.22883	−	23.1537i	0.426073	−	1.19885i	0.940046	−	0.341048i	$-0.110782\pi$
$374$	2.59293	+	5.00413i	0.134077	+	0.258758i
$375$	−28.4780			−1.47060
$376$	16.6199	−	19.8377i	0.857104	−	1.02305i
$377$	−17.0803			−0.879679
$378$	−47.5518	−	91.7709i	−2.44580	−	4.72018i
$379$	−6.66161	+	18.7440i	−0.342184	+	0.962813i	0.638910	+	0.769281i	$0.279385\pi$
$379$	−6.66161	+	18.7440i	−0.342184	+	0.962813i	−0.981094	+	0.193532i	$0.938006\pi$
$380$	−0.623999	+	0.884005i	−0.0320105	+	0.0453485i
$381$	−60.0544	−	26.0853i	−3.07668	−	1.33639i
$382$	−0.264973	+	0.0364197i	−0.0135572	+	0.00186339i
$383$	5.47176	+	3.32745i	0.279594	+	0.170025i	0.652379	−	0.757893i	$-0.273771\pi$
$383$	5.47176	+	3.32745i	0.279594	+	0.170025i	−0.372785	+	0.927918i	$0.621597\pi$
$384$	67.6996	+	9.30509i	3.45478	+	0.474848i
$385$	4.56249	+	3.71186i	0.232526	+	0.189174i
$386$	−3.20250	−	46.8189i	−0.163003	−	2.38302i
$387$	61.9053	−	17.3451i	3.14683	−	0.881699i
$388$	8.85208	+	12.5405i	0.449396	+	0.636649i
$389$	3.30277	+	15.8938i	0.167457	+	0.805848i	0.976061	+	0.217495i	$0.0697885\pi$
$389$	3.30277	+	15.8938i	0.167457	+	0.805848i	−0.808604	+	0.588353i	$0.799777\pi$
$390$	−3.37911	+	49.4008i	−0.171108	+	2.50151i
$391$	−3.16345	+	3.38722i	−0.159982	+	0.171299i
$392$	0.154349	+	0.434298i	0.00779582	+	0.0219353i
$393$	30.8387	+	8.64059i	1.55561	+	0.435860i
$394$	−7.00646	+	33.7169i	−0.352980	+	1.69864i
$395$	7.85897	−	3.41363i	0.395428	−	0.171759i
$396$	58.6986	−	35.6954i	2.94972	−	1.79376i
$397$	−0.0609192	+	0.0495614i	−0.00305745	+	0.00248742i	−0.632615	−	0.774466i	$-0.718019\pi$
$397$	−0.0609192	+	0.0495614i	−0.00305745	+	0.00248742i	0.629558	+	0.776953i	$0.283236\pi$
$398$	−9.41568	−	10.0817i	−0.471965	−	0.505352i
$399$	−1.28038	+	2.47102i	−0.0640992	+	0.123706i
$400$	−3.28979	+	6.34901i	−0.164490	+	0.317451i
$401$	0.398709	+	0.426913i	0.0199106	+	0.0213190i	0.740714	−	0.671821i	$-0.234488\pi$
$401$	0.398709	+	0.426913i	0.0199106	+	0.0213190i	−0.720803	+	0.693140i	$0.756227\pi$
$402$	−55.8161	+	45.4097i	−2.78385	+	2.26483i
$403$	33.1003	−	20.1287i	1.64884	−	1.00268i
$404$	45.7705	−	19.8809i	2.27717	−	0.989114i
$405$	5.98436	−	28.7983i	0.297365	−	1.43100i
$406$	15.2311	+	4.26754i	0.755905	+	0.211795i
$407$	−7.89818	−	22.2234i	−0.391498	−	1.10157i
$408$	8.55297	−	9.15799i	0.423435	−	0.453388i
$409$	0.888373	−	12.9876i	0.0439272	−	0.642193i	−0.922621	−	0.385708i	$-0.873957\pi$
$409$	0.888373	−	12.9876i	0.0439272	−	0.642193i	0.966548	−	0.256485i	$-0.0825645\pi$
$410$	−1.51858	−	7.30782i	−0.0749974	−	0.360907i
$411$	−25.6413	−	36.3254i	−1.26479	−	1.79180i
$412$	−47.3806	+	13.2754i	−2.33427	+	0.654033i
$413$	−0.00869184	−	0.127070i	−0.000427697	−	0.00625271i
$414$	68.1986	+	55.4837i	3.35178	+	2.72688i
$415$	10.0121	+	1.37614i	0.491477	+	0.0675519i
$416$	−19.6792	−	11.9672i	−0.964854	−	0.586741i
$417$	−38.0035	+	5.22346i	−1.86104	+	0.255794i
$418$	−1.65258	−	0.717816i	−0.0808302	−	0.0351095i
$419$	−2.56548	+	3.63446i	−0.125332	+	0.177555i	−0.874798	−	0.484488i	$-0.839006\pi$
$419$	−2.56548	+	3.63446i	−0.125332	+	0.177555i	0.749466	+	0.662043i	$0.230310\pi$
$420$	9.86770	−	27.7650i	0.481494	−	1.35480i
$421$	16.2341	+	31.3304i	0.791201	+	1.52695i	0.848863	+	0.528612i	$0.177287\pi$
$421$	16.2341	+	31.3304i	0.791201	+	1.52695i	−0.0576627	+	0.998336i	$0.518365\pi$
$422$	−45.3963			−2.20986
$423$	52.0612	−	17.6619i	2.53130	−	0.858753i
$424$	−8.42280			−0.409047
$425$	−1.89268	−	3.65270i	−0.0918084	−	0.177182i
$426$	12.9297	−	36.3808i	0.626447	−	1.76265i
$427$	10.8820	−	15.4163i	0.526617	−	0.746047i
$428$	9.19631	+	3.99452i	0.444520	+	0.193082i
$429$	−52.4881	+	7.21432i	−2.53415	+	0.348311i
$430$	15.2529	+	9.27551i	0.735562	+	0.447305i
$431$	4.53750	+	0.623665i	0.218564	+	0.0300409i	0.244617	−	0.969620i	$-0.421338\pi$
$431$	4.53750	+	0.623665i	0.218564	+	0.0300409i	−0.0260539	+	0.999661i	$0.508294\pi$
$432$	−22.4637	−	18.2756i	−1.08078	−	0.879284i
$433$	−0.884369	−	12.9290i	−0.0425001	−	0.621329i	−0.969317	−	0.245815i	$-0.920944\pi$
$433$	−0.884369	−	12.9290i	−0.0425001	−	0.621329i	0.926817	−	0.375514i	$-0.122534\pi$
$434$	−34.5458	+	9.67929i	−1.65825	+	0.464621i
$435$	4.59432	+	6.50867i	0.220281	+	0.312067i
$436$	4.60701	+	22.1701i	0.220636	+	1.06176i
$437$	0.101111	−	1.47819i	0.00483680	−	0.0707115i
$438$	−4.41564	+	4.72800i	−0.210988	+	0.225913i
$439$	−0.111483	−	0.313683i	−0.00532079	−	0.0149713i	0.939571	−	0.342355i	$-0.111224\pi$
$439$	−0.111483	−	0.313683i	−0.00532079	−	0.0149713i	−0.944892	+	0.327383i	$0.893833\pi$
$440$	8.15214	+	2.28412i	0.388638	+	0.108891i
$441$	−0.199204	+	0.958623i	−0.00948591	+	0.0456487i
$442$	−14.5349	+	6.31341i	−0.691357	+	0.300299i
$443$	34.5425	−	21.0058i	1.64116	−	0.998014i	0.675809	−	0.737077i	$-0.263794\pi$
$443$	34.5425	−	21.0058i	1.64116	−	0.998014i	0.965356	−	0.260938i	$-0.0840318\pi$
$444$	−91.6567	+	74.5682i	−4.34983	+	3.53885i
$445$	−6.54453	−	7.00748i	−0.310241	−	0.332187i
$446$	−16.2005	+	31.2656i	−0.767117	+	1.48047i
$447$	31.8875	−	61.5402i	1.50823	−	2.91075i
$448$	20.7814	+	22.2515i	0.981830	+	1.05128i
$449$	15.0293	−	12.2273i	0.709277	−	0.577040i	−0.206635	−	0.978418i	$-0.566251\pi$
$449$	15.0293	−	12.2273i	0.709277	−	0.577040i	0.915912	+	0.401378i	$0.131469\pi$
$450$	−66.6776	+	40.5476i	−3.14321	+	1.91143i
$451$	7.32511	−	3.18175i	0.344926	−	0.149823i
$452$	−9.39289	+	45.2011i	−0.441804	+	2.12608i
$453$	−33.5258	−	9.39349i	−1.57518	−	0.441345i
$454$	12.4843	+	35.1276i	0.585920	+	1.64862i
$455$	−11.2878	+	12.0863i	−0.529181	+	0.566614i
$456$	−0.273373	+	3.99657i	−0.0128018	+	0.187156i
$457$	5.82842	+	28.0479i	0.272642	+	1.31202i	0.863131	+	0.504979i	$0.168500\pi$
$457$	5.82842	+	28.0479i	0.272642	+	1.31202i	−0.590490	+	0.807045i	$0.701065\pi$
$458$	11.8421	+	16.7765i	0.553347	+	0.783914i
$459$	16.0427	−	4.49496i	0.748810	−	0.209807i
$460$	1.07055	+	15.6509i	0.0499146	+	0.729725i
$461$	5.87089	+	4.77632i	0.273435	+	0.222456i	0.757926	−	0.652340i	$-0.226213\pi$
$461$	5.87089	+	4.77632i	0.273435	+	0.222456i	−0.484491	+	0.874796i	$0.660995\pi$
$462$	48.6079	+	6.68101i	2.26145	+	0.310829i
$463$	13.0861	+	7.95782i	0.608162	+	0.369831i	0.789646	−	0.613562i	$-0.210264\pi$
$463$	13.0861	+	7.95782i	0.608162	+	0.369831i	−0.181484	+	0.983394i	$0.558090\pi$
$464$	4.39046	−	0.603455i	0.203822	−	0.0280147i
$465$	−16.5738	−	7.19900i	−0.768589	−	0.333846i
$466$	37.5683	−	53.2221i	1.74032	−	2.46547i
$467$	−3.75732	+	10.5721i	−0.173868	+	0.489218i	−0.996891	−	0.0787901i	$-0.974894\pi$
$467$	−3.75732	+	10.5721i	−0.173868	+	0.489218i	0.823023	+	0.568008i	$0.192286\pi$
$468$	88.8685	+	171.508i	4.10795	+	7.92798i
$469$	−24.0317			−1.10968
$470$	13.4515	+	7.21770i	0.620470	+	0.332928i
$471$	−62.0319			−2.85828
$472$	−0.0843446	−	0.162778i	−0.00388228	−	0.00749245i
$473$	−6.39659	+	17.9983i	−0.294115	+	0.827561i
$474$	41.2193	−	58.3945i	1.89327	−	2.68215i
$475$	1.20628	+	0.523960i	0.0553478	+	0.0240410i
$476$	9.34242	−	1.28409i	0.428209	−	0.0588560i
$477$	−15.2876	−	9.29659i	−0.699971	−	0.425662i
$478$	28.4779	+	3.91420i	1.30255	+	0.179032i
$479$	12.5926	+	10.2448i	0.575370	+	0.468098i	0.873768	−	0.486343i	$-0.161670\pi$
$479$	12.5926	+	10.2448i	0.575370	+	0.468098i	−0.298398	+	0.954442i	$0.596452\pi$
$480$	0.733133	+	10.7180i	0.0334628	+	0.489209i
$481$	63.8556	−	17.8915i	2.91157	−	0.815783i
$482$	−22.9313	−	32.4862i	−1.04449	−	1.47971i
$483$	8.20907	+	39.5042i	0.373525	+	1.79750i
$484$	1.30631	−	19.0975i	0.0593776	−	0.868070i
$485$	−2.74274	+	2.93675i	−0.124541	+	0.133351i
$486$	−42.5745	−	119.793i	−1.93122	−	5.43392i
$487$	25.4829	+	7.13997i	1.15474	+	0.323543i	0.793287	−	0.608847i	$-0.208368\pi$
$487$	25.4829	+	7.13997i	1.15474	+	0.323543i	0.361453	+	0.932390i	$0.382281\pi$
$488$	5.52619	−	26.5935i	0.250159	−	1.20383i
$489$	−6.23231	+	2.70707i	−0.281835	+	0.122418i
$490$	−0.232296	+	0.141262i	−0.0104941	+	0.00638159i
$491$	−3.56104	+	2.89712i	−0.160707	+	0.130745i	−0.708047	−	0.706166i	$-0.750423\pi$
$491$	−3.56104	+	2.89712i	−0.160707	+	0.130745i	0.547339	+	0.836911i	$0.315641\pi$
$492$	−27.3091	−	29.2409i	−1.23119	−	1.31828i
$493$	−1.17301	+	2.26381i	−0.0528297	+	0.101957i
$494$	2.33068	−	4.49802i	0.104862	−	0.202375i
$495$	12.2753	+	13.1436i	0.551732	+	0.590761i
$496$	−7.79722	+	6.34351i	−0.350105	+	0.284832i
$497$	11.0179	−	6.70011i	0.494219	−	0.300541i
$498$	77.3268	−	33.5878i	3.46510	−	1.50510i
$499$	1.89203	−	9.10494i	0.0846989	−	0.407593i	−0.915290	−	0.402796i	$-0.868038\pi$
$499$	1.89203	−	9.10494i	0.0846989	−	0.407593i	0.999988	−	0.00479697i	$-0.00152693\pi$
$500$	−29.7045	−	8.32282i	−1.32843	−	0.372208i
$501$	−17.8455	−	50.2124i	−0.797278	−	2.24333i
$502$	−6.53933	+	7.00191i	−0.291864	+	0.312511i
$503$	1.59467	−	23.3133i	0.0711029	−	1.03949i	−0.816041	−	0.577994i	$-0.803836\pi$
$503$	1.59467	−	23.3133i	0.0711029	−	1.03949i	0.887144	−	0.461493i	$-0.152686\pi$
$504$	−16.1521	−	77.7280i	−0.719470	−	3.46228i
$505$	7.53336	+	10.6723i	0.335230	+	0.474913i
$506$	−25.1527	+	7.04746i	−1.11817	+	0.313298i
$507$	−7.22113	−	105.569i	−0.320702	−	4.68850i
$508$	−55.0174	−	44.7600i	−2.44100	−	1.98590i
$509$	37.1151	+	5.10135i	1.64510	+	0.226113i	0.898440	−	0.439096i	$-0.144701\pi$
$509$	37.1151	+	5.10135i	1.64510	+	0.226113i	0.746657	+	0.665209i	$0.231658\pi$
$510$	6.31548	+	3.84053i	0.279654	+	0.170061i
$511$	−2.14052	+	0.294208i	−0.0946910	+	0.0130150i
$512$	17.5178	+	7.60907i	0.774186	+	0.336277i
$513$	−3.07146	+	4.35126i	−0.135608	+	0.192113i
$514$	0.332956	−	0.936848i	0.0146861	−	0.0413226i
$515$	−5.92608	−	11.4368i	−0.261134	−	0.503967i
$516$	95.6941			4.21270
$517$	−4.63298	+	15.6631i	−0.203758	+	0.688861i
$518$	−61.4125			−2.69831
$519$	31.5171	+	60.8251i	1.38345	+	2.66993i
$520$	−7.97156	+	22.4298i	−0.349576	+	0.983612i
$521$	10.2404	−	14.5074i	0.448642	−	0.635581i	−0.528307	−	0.849053i	$-0.677173\pi$
$521$	10.2404	−	14.5074i	0.448642	−	0.635581i	0.976949	+	0.213472i	$0.0684773\pi$
$522$	44.3612	+	19.2688i	1.94164	+	0.843372i
$523$	15.6938	−	2.15706i	0.686242	−	0.0943218i	0.215382	−	0.976530i	$-0.430900\pi$
$523$	15.6938	−	2.15706i	0.686242	−	0.0943218i	0.470860	+	0.882208i	$0.343944\pi$
$524$	29.6416	+	18.0255i	1.29490	+	0.787446i
$525$	−35.4807	−	4.87672i	−1.54851	−	0.212837i
$526$	22.3455	+	18.1794i	0.974311	+	0.792661i
$527$	−0.394641	−	5.76944i	−0.0171908	−	0.251321i
$528$	13.2371	−	3.70886i	0.576071	−	0.161408i
$529$	0.876163	+	1.24124i	0.0380941	+	0.0539670i
$530$	−1.01084	−	4.86442i	−0.0439080	−	0.211297i
$531$	0.0265769	−	0.388540i	0.00115334	−	0.0168612i
$532$	−2.05769	+	2.20325i	−0.0892122	+	0.0955230i
$533$	7.51979	+	21.1587i	0.325718	+	0.916483i
$534$	−77.0195	−	21.5799i	−3.33296	−	0.933852i
$535$	−0.534013	+	2.56981i	−0.0230874	+	0.111103i
$536$	−31.7275	+	13.7812i	−1.37042	+	0.595256i
$537$	25.7542	−	15.6615i	1.11138	−	0.675842i
$538$	11.5150	−	9.36818i	0.496449	−	0.403891i
$539$	−0.198557	−	0.212602i	−0.00855244	−	0.00915743i
$540$	25.9440	−	50.0696i	1.11645	−	2.15465i
$541$	8.69434	−	16.7793i	0.373799	−	0.721399i	−0.624418	−	0.781090i	$-0.714664\pi$
$541$	8.69434	−	16.7793i	0.373799	−	0.721399i	0.998217	+	0.0596914i	$0.0190117\pi$
$542$	37.4231	+	40.0704i	1.60746	+	1.72117i
$543$	6.44303	−	5.24179i	0.276497	−	0.224947i
$544$	−2.93762	+	1.78641i	−0.125949	+	0.0765915i
$545$	−5.43695	+	2.36160i	−0.232893	+	0.101160i
$546$	−28.0681	+	135.071i	−1.20121	+	5.78052i
$547$	−30.2372	−	8.47208i	−1.29285	−	0.362240i	−0.446461	−	0.894803i	$-0.647316\pi$
$547$	−30.2372	−	8.47208i	−1.29285	−	0.362240i	−0.846390	+	0.532563i	$0.821229\pi$
$548$	−16.1294	−	45.3837i	−0.689012	−	1.93870i
$549$	39.3825	−	42.1683i	1.68080	−	1.79970i
$550$	1.58228	−	23.1321i	0.0674687	−	0.986358i
$551$	−0.165834	−	0.798037i	−0.00706476	−	0.0339975i
$552$	33.4919	+	47.4472i	1.42551	+	2.01949i
$553$	22.9869	−	6.44063i	0.977503	−	0.273883i
$554$	1.97123	+	28.8184i	0.0837497	+	1.22438i
$555$	−23.9939	−	19.5205i	−1.01849	−	0.828600i
$556$	−41.1668	−	5.65825i	−1.74586	−	0.239963i
$557$	−29.9703	−	18.2254i	−1.26988	−	0.772233i	−0.287262	−	0.957852i	$-0.592745\pi$
$557$	−29.9703	−	18.2254i	−1.26988	−	0.772233i	−0.982622	+	0.185619i	$0.940571\pi$
$558$	−108.676	+	14.9372i	−4.60064	+	0.632343i
$559$	−49.2607	−	21.3969i	−2.08351	−	0.904994i
$560$	2.47450	−	3.50557i	0.104567	−	0.148137i
$561$	−2.64851	+	7.45218i	−0.111820	+	0.314631i
$562$	−10.2263	−	19.7359i	−0.431371	−	0.832509i
$563$	−38.9290			−1.64066			−0.820330	−	0.571890i	$-0.806210\pi$
$563$	−38.9290			−1.64066			−0.820330	+	0.571890i	$0.806210\pi$
$564$	81.7118	−	4.40749i	3.44069	−	0.185589i
$565$	−12.0855			−0.508442
$566$	−3.62424	−	6.99447i	−0.152338	−	0.294000i
$567$	27.4430	−	77.2171i	1.15250	−	3.24282i
$568$	10.7039	−	15.1640i	0.449126	−	0.636267i
$569$	17.9212	+	7.78426i	0.751295	+	0.326333i	0.739103	−	0.673592i	$-0.235250\pi$
$569$	17.9212	+	7.78426i	0.751295	+	0.326333i	0.0121917	+	0.999926i	$0.496119\pi$
$570$	−2.34095	+	0.321756i	−0.0980514	+	0.0134769i
$571$	−26.5361	−	16.1369i	−1.11050	−	0.675310i	−0.160336	−	0.987062i	$-0.551258\pi$
$571$	−26.5361	−	16.1369i	−1.11050	−	0.675310i	−0.950163	+	0.311753i	$0.899084\pi$
$572$	−56.8571	−	7.81483i	−2.37732	−	0.326755i
$573$	−0.291143	−	0.236862i	−0.0121627	−	0.00989506i
$574$	−1.41911	−	20.7467i	−0.0592327	−	0.865951i
$575$	18.3599	−	5.14420i	0.765661	−	0.214528i
$576$	53.6867	+	76.0567i	2.23694	+	3.16903i
$577$	−8.37695	−	40.3121i	−0.348737	−	1.67821i	−0.678853	−	0.734274i	$-0.737523\pi$
$577$	−8.37695	−	40.3121i	−0.348737	−	1.67821i	0.330116	−	0.943940i	$-0.392912\pi$
$578$	−0.161430	+	2.36003i	−0.00671462	+	0.0981643i
$579$	44.9481	−	48.1277i	1.86798	−	2.00012i
$580$	2.89001	+	8.13170i	0.120001	+	0.337651i
$581$	27.1129	+	7.59667i	1.12483	+	0.315163i
$582$	−6.82005	+	32.8199i	−0.282700	+	1.36043i
$583$	4.87593	−	2.11792i	0.201940	−	0.0877151i
$584$	−2.65727	+	1.61592i	−0.109959	+	0.0668673i
$585$	−39.2253	+	31.9121i	−1.62177	+	1.31940i
$586$	46.9415	+	50.2620i	1.93913	+	2.07631i
$587$	3.99406	−	7.70819i	0.164853	−	0.318151i	−0.791092	−	0.611697i	$-0.790487\pi$
$587$	3.99406	−	7.70819i	0.164853	−	0.318151i	0.955945	+	0.293545i	$0.0948352\pi$
$588$	−0.670491	+	1.29399i	−0.0276506	+	0.0533632i
$589$	1.26184	+	1.35110i	0.0519932	+	0.0556712i
$590$	0.0838867	−	0.0682469i	0.00345356	−	0.00280968i
$591$	−41.2895	+	25.1087i	−1.69842	+	1.03283i
$592$	−15.7819	+	6.85504i	−0.648631	+	0.281740i
$593$	−0.856834	+	4.12331i	−0.0351859	+	0.169324i	−0.993010	−	0.118032i	$-0.962341\pi$
$593$	−0.856834	+	4.12331i	−0.0351859	+	0.169324i	0.957824	+	0.287356i	$0.0927763\pi$
$594$	90.4170	+	25.3336i	3.70985	+	1.03945i
$595$	0.826703	+	2.32612i	0.0338915	+	0.0953616i
$596$	51.2463	−	54.8714i	2.09913	−	2.24762i
$597$	1.32102	−	19.3126i	0.0540658	−	0.790414i
$598$	−14.9430	−	71.9097i	−0.611065	−	2.94061i
$599$	−1.79994	−	2.54993i	−0.0735434	−	0.104187i	0.778536	−	0.627600i	$-0.215963\pi$
$599$	−1.79994	−	2.54993i	−0.0735434	−	0.104187i	−0.852079	+	0.523413i	$0.824658\pi$
$600$	−49.6394	+	13.9083i	−2.02652	+	0.567805i
$601$	−1.97716	−	28.9050i	−0.0806499	−	1.17906i	−0.845184	−	0.534476i	$-0.820509\pi$
$601$	−1.97716	−	28.9050i	−0.0806499	−	1.17906i	0.764534	−	0.644583i	$-0.222969\pi$
$602$	38.5814	+	31.3883i	1.57246	+	1.27929i
$603$	−72.7970	−	10.0057i	−2.96452	−	0.407464i
$604$	−32.2245	−	19.5961i	−1.31119	−	0.797355i
$605$	4.96438	−	0.682338i	0.201831	−	0.0277410i
$606$	99.9523	+	43.4154i	4.06028	+	1.76363i
$607$	−27.6712	+	39.2011i	−1.12314	+	1.59112i	−0.375769	+	0.926713i	$0.622621\pi$
$607$	−27.6712	+	39.2011i	−1.12314	+	1.59112i	−0.747368	+	0.664410i	$0.768683\pi$
$608$	0.368073	−	1.03566i	0.0149273	−	0.0420015i
$609$	10.2118	+	19.7078i	0.413802	+	0.798601i
$610$	16.0217			0.648701
$611$	−43.0485	−	16.0017i	−1.74156	−	0.647359i
$612$	28.8347			1.16557
$613$	8.60021	+	16.5977i	0.347359	+	0.670373i	0.995866	−	0.0908360i	$-0.0289539\pi$
$613$	8.60021	+	16.5977i	0.347359	+	0.670373i	−0.648507	+	0.761209i	$0.724606\pi$
$614$	−10.9394	+	30.7806i	−0.441479	+	1.24220i
$615$	6.04009	−	8.55685i	0.243560	−	0.345046i
$616$	21.6345	+	9.39720i	0.871680	+	0.378624i
$617$	−3.63764	+	0.499982i	−0.146446	+	0.0201285i	−0.209017	−	0.977912i	$-0.567026\pi$
$617$	−3.63764	+	0.499982i	−0.146446	+	0.0201285i	0.0625714	+	0.998040i	$0.480070\pi$
$618$	−91.8098	−	55.8308i	−3.69313	−	2.24584i
$619$	26.2748	+	3.61138i	1.05607	+	0.145154i	0.643249	−	0.765657i	$-0.277586\pi$
$619$	26.2748	+	3.61138i	1.05607	+	0.145154i	0.412823	+	0.910811i	$0.364543\pi$
$620$	−15.1836	−	12.3528i	−0.609789	−	0.496100i
$621$	5.26948	+	77.0370i	0.211457	+	3.09139i
$622$	20.7112	−	5.80302i	0.830445	−	0.232680i
$623$	−15.4054	−	21.8245i	−0.617204	−	0.874379i
$624$	7.86405	+	37.8439i	0.314814	+	1.51497i
$625$	−0.852630	+	12.4650i	−0.0341052	+	0.498601i
$626$	2.40036	−	2.57016i	0.0959377	−	0.102724i
$627$	−0.846684	−	2.38234i	−0.0338133	−	0.0951415i
$628$	−64.7036	−	18.1291i	−2.58195	−	0.723429i
$629$	2.01404	−	9.69209i	0.0803050	−	0.386449i
$630$	42.9518	−	18.6566i	1.71124	−	0.743297i
$631$	37.6696	−	22.9074i	1.49960	−	0.911929i	0.500675	−	0.865635i	$-0.333085\pi$
$631$	37.6696	−	22.9074i	1.49960	−	0.911929i	0.998928	−	0.0462935i	$-0.0147410\pi$
$632$	26.6546	−	21.6852i	1.06026	−	0.862589i
$633$	−43.4807	−	46.5565i	−1.72820	−	1.85045i
$634$	−12.4941	+	24.1124i	−0.496202	+	0.957627i
$635$	8.54194	−	16.4852i	0.338976	−	0.654195i
$636$	−18.1782	−	19.4641i	−0.720812	−	0.771801i
$637$	0.634483	−	0.516190i	0.0251391	−	0.0204522i
$638$	−12.2779	+	7.46638i	−0.486088	+	0.295597i
$639$	36.1650	−	15.7087i	1.43067	−	0.621426i
$640$	−3.94259	+	18.9728i	−0.155845	+	0.749965i
$641$	10.5422	+	2.95379i	0.416393	+	0.116668i	0.471611	−	0.881806i	$-0.343673\pi$
$641$	10.5422	+	2.95379i	0.416393	+	0.116668i	−0.0552185	+	0.998474i	$0.517586\pi$
$642$	7.33229	+	20.6311i	0.289382	+	0.814244i
$643$	−25.0337	+	26.8046i	−0.987233	+	1.05707i	0.0111334	+	0.999938i	$0.496456\pi$
$643$	−25.0337	+	26.8046i	−0.987233	+	1.05707i	−0.998367	+	0.0571308i	$0.981805\pi$
$644$	−2.98265	+	43.6047i	−0.117533	+	1.71827i
$645$	5.09675	+	24.5269i	0.200684	+	0.965745i
$646$	−0.436101	−	0.617814i	−0.0171581	−	0.0243076i
$647$	−28.0172	+	7.85006i	−1.10147	+	0.308618i	−0.772048	−	0.635565i	$-0.780767\pi$
$647$	−28.0172	+	7.85006i	−1.10147	+	0.308618i	−0.329423	+	0.944182i	$0.606854\pi$
$648$	−8.04967	−	117.682i	−0.316221	−	4.62298i
$649$	0.0897574	+	0.0730231i	0.00352329	+	0.00286641i
$650$	64.5858	+	8.87712i	2.53326	+	0.348189i
$651$	−43.0148	−	26.1579i	−1.68588	−	1.02521i
$652$	−7.29188	+	1.00225i	−0.285572	+	0.0392510i
$653$	27.7814	+	12.0672i	1.08717	+	0.472224i	0.864481	−	0.502665i	$-0.167647\pi$
$653$	27.7814	+	12.0672i	1.08717	+	0.472224i	0.222689	+	0.974890i	$0.428517\pi$
$654$	−28.5161	+	40.3981i	−1.11507	+	1.57969i
$655$	−3.04128	+	8.55735i	−0.118833	+	0.334363i
$656$	−2.68050	−	5.17312i	−0.104656	−	0.201977i
$657$	−6.60657			−0.257747
$658$	34.3898	+	25.0250i	1.34065	+	0.975576i
$659$	−47.6363			−1.85565			−0.927823	−	0.373021i	$-0.878322\pi$
$659$	−47.6363			−1.85565			−0.927823	+	0.373021i	$0.878322\pi$
$660$	12.3157	+	23.7682i	0.479388	+	0.925177i
$661$	4.49685	−	12.6529i	0.174907	−	0.492142i	−0.822109	−	0.569330i	$-0.807203\pi$
$661$	4.49685	−	12.6529i	0.174907	−	0.492142i	0.997017	+	0.0771879i	$0.0245941\pi$
$662$	−19.8970	+	28.1877i	−0.773320	+	1.09555i
$663$	−20.3964	−	8.85940i	−0.792130	−	0.344071i
$664$	40.1517	−	5.51872i	1.55819	−	0.214168i
$665$	−0.674299	−	0.410050i	−0.0261482	−	0.0159011i
$666$	−186.031	−	25.5694i	−7.20855	−	0.990792i
$667$	−9.16656	−	7.45755i	−0.354931	−	0.288757i
$668$	−3.93930	−	57.5905i	−0.152416	−	2.22824i
$669$	−47.5816	+	13.3317i	−1.83961	+	0.515435i
$670$	−11.7667	−	16.6697i	−0.454588	−	0.644005i
$671$	3.48785	+	16.7844i	0.134647	+	0.647956i
$672$	−2.04258	+	29.8614i	−0.0787940	+	1.15193i
$673$	−24.4630	+	26.1935i	−0.942979	+	1.00968i	0.0569566	+	0.998377i	$0.481860\pi$
$673$	−24.4630	+	26.1935i	−0.942979	+	1.00968i	−0.999936	+	0.0113078i	$0.996401\pi$
$674$	0.0517776	+	0.145688i	0.00199440	+	0.00561170i
$675$	−65.9987	−	18.4920i	−2.54029	−	0.711756i
$676$	23.3209	−	112.226i	0.896959	−	4.31640i
$677$	23.8776	−	10.3715i	0.917690	−	0.398609i	0.113880	−	0.993495i	$-0.463672\pi$
$677$	23.8776	−	10.3715i	0.917690	−	0.398609i	0.803810	+	0.594885i	$0.202803\pi$
$678$	−86.1404	+	52.3831i	−3.30820	+	2.01176i
$679$	−8.68446	+	7.06533i	−0.333279	+	0.271143i
$680$	2.42537	+	2.59694i	0.0930087	+	0.0995880i
$681$	−24.0678	+	46.4488i	−0.922281	+	1.77992i
$682$	14.9947	−	28.9385i	0.574178	−	1.10811i
$683$	−2.21885	−	2.37581i	−0.0849021	−	0.0909079i	0.686970	−	0.726686i	$-0.258940\pi$
$683$	−2.21885	−	2.37581i	−0.0849021	−	0.0909079i	−0.771872	+	0.635778i	$0.780679\pi$
$684$	−7.15050	+	5.81736i	−0.273406	+	0.222432i
$685$	10.7730	−	6.55121i	0.411616	−	0.250309i
$686$	−40.5262	+	17.6030i	−1.54730	+	0.672087i
$687$	−5.86281	+	28.2134i	−0.223680	+	1.07641i
$688$	13.4184	+	3.75965i	0.511570	+	0.143335i
$689$	5.00552	+	14.0842i	0.190695	+	0.536564i
$690$	−23.3827	+	25.0368i	−0.890166	+	0.953135i
$691$	0.893191	−	13.0580i	0.0339786	−	0.496749i	−0.949268	−	0.314468i	$-0.898174\pi$
$691$	0.893191	−	13.0580i	0.0339786	−	0.496749i	0.983247	−	0.182281i	$-0.0583480\pi$
$692$	15.0981	+	72.6558i	0.573942	+	2.76196i
$693$	28.8951	+	40.9351i	1.09764	+	1.55499i
$694$	−62.0534	+	17.3866i	−2.35552	+	0.659985i
$695$	−0.742341	−	10.8526i	−0.0281586	−	0.411664i
$696$	24.7835	+	20.1629i	0.939416	+	0.764272i
$697$	3.32078	+	0.456431i	0.125784	+	0.0172885i
$698$	9.42651	+	5.73239i	0.356799	+	0.216974i
$699$	90.5654	−	12.4479i	3.42550	−	0.470824i
$700$	−35.5836	−	15.4561i	−1.34493	−	0.584188i
$701$	−17.8180	+	25.2424i	−0.672977	+	0.953391i	0.326988	+	0.945028i	$0.393966\pi$
$701$	−17.8180	+	25.2424i	−0.672977	+	0.953391i	−0.999965	+	0.00836254i	$0.997338\pi$
$702$	−88.4141	+	248.773i	−3.33697	+	9.38935i
$703$	1.45592	+	2.80980i	0.0549110	+	0.105973i
$704$	−27.6600			−1.04247
$705$	5.48170	+	20.7084i	0.206453	+	0.779924i
$706$	20.5315			0.772715
$707$	16.7444	+	32.3151i	0.629736	+	1.21534i
$708$	0.194126	−	0.546219i	0.00729572	−	0.0205282i
$709$	−27.2545	+	38.6108i	−1.02356	+	1.45006i	−0.135254	+	0.990811i	$0.543185\pi$
$709$	−27.2545	+	38.6108i	−1.02356	+	1.45006i	−0.888309	+	0.459247i	$0.848119\pi$
$710$	10.0423	+	4.36197i	0.376879	+	0.163702i
$711$	72.3136	−	9.93928i	2.71197	−	0.372752i
$712$	−32.8541	−	19.9790i	−1.23126	−	0.748746i
$713$	26.5526	+	3.64958i	0.994404	+	0.136678i
$714$	15.9746	+	12.9963i	0.597835	+	0.486375i
$715$	−1.02528	−	14.9890i	−0.0383431	−	0.560557i
$716$	31.4405	−	8.80922i	1.17499	−	0.329216i
$717$	23.2621	+	32.9548i	0.868737	+	1.23072i
$718$	−3.51355	−	16.9081i	−0.131125	−	0.631006i
$719$	0.464503	−	6.79079i	0.0173230	−	0.253254i	−0.980939	−	0.194317i	$-0.937751\pi$
$719$	0.464503	−	6.79079i	0.0173230	−	0.253254i	0.998262	−	0.0589364i	$-0.0187709\pi$
$720$	8.95533	−	9.58882i	0.333746	−	0.357354i
$721$	−12.0180	−	33.8154i	−0.447574	−	1.25935i
$722$	−43.0459	−	12.0609i	−1.60200	−	0.448860i
$723$	11.3528	−	54.6327i	0.422216	−	2.03181i
$724$	8.25246	−	3.58455i	0.306700	−	0.133219i
$725$	8.96212	−	5.44999i	0.332845	−	0.202407i
$726$	32.4264	−	26.3808i	1.20346	−	0.979084i
$727$	29.5491	+	31.6394i	1.09592	+	1.17344i	0.983711	+	0.179756i	$0.0575308\pi$
$727$	29.5491	+	31.6394i	1.09592	+	1.17344i	0.112206	+	0.993685i	$0.464208\pi$
$728$	−30.5119	+	58.8853i	−1.13085	+	2.18243i
$729$	38.9491	−	75.1684i	1.44256	−	2.78402i
$730$	−1.25215	−	1.34072i	−0.0463440	−	0.0496224i
$731$	−6.21897	+	5.05951i	−0.230017	+	0.187133i
$732$	73.3810	−	44.6240i	2.71224	−	1.64935i
$733$	−30.4153	+	13.2112i	−1.12341	+	0.487967i	−0.876660	−	0.481111i	$-0.840233\pi$
$733$	−30.4153	+	13.2112i	−1.12341	+	0.487967i	−0.246754	+	0.969078i	$0.579364\pi$
$734$	−7.14903	+	34.4030i	−0.263876	+	1.26984i
$735$	−0.367367	−	0.102931i	−0.0135505	−	0.00379668i
$736$	−5.33626	−	15.0148i	−0.196697	−	0.553453i
$737$	14.9016	−	15.9558i	0.548909	−	0.587738i
$738$	4.33920	−	63.4369i	0.159728	−	2.33515i
$739$	−0.671776	−	3.23276i	−0.0247117	−	0.118919i	0.964921	−	0.262540i	$-0.0845602\pi$
$739$	−0.671776	−	3.23276i	−0.0247117	−	0.118919i	−0.989633	+	0.143621i	$0.954125\pi$
$740$	−19.3224	−	27.3736i	−0.710305	−	1.00627i
$741$	6.84531	−	1.91797i	0.251469	−	0.0704583i
$742$	−0.944628	−	13.8100i	−0.0346784	−	0.506980i
$743$	−1.57047	−	1.27767i	−0.0576150	−	0.0468733i	0.601845	−	0.798613i	$-0.294432\pi$
$743$	−1.57047	−	1.27767i	−0.0576150	−	0.0468733i	−0.659460	+	0.751740i	$0.729215\pi$
$744$	−71.7900	−	9.86731i	−2.63195	−	0.361753i
$745$	16.7932	+	10.2122i	0.615257	+	0.374146i
$746$	57.5860	−	7.91501i	2.10837	−	0.289789i
$747$	78.9675	+	34.3004i	2.88927	+	1.25499i
$748$	−4.94051	+	6.99910i	−0.180643	+	0.255913i
$749$	−2.44887	+	6.89046i	−0.0894797	+	0.251772i
$750$	−30.9927	−	59.8133i	−1.13170	−	2.18407i
$751$	17.4959			0.638435			0.319217	−	0.947682i	$-0.396580\pi$
$751$	17.4959			0.638435			0.319217	+	0.947682i	$0.396580\pi$
$752$	11.6309	+	2.59228i	0.424135	+	0.0945309i
$753$	−13.4443			−0.489936
$754$	−18.5885	−	35.8743i	−0.676955	−	1.30646i
$755$	3.30629	−	9.30300i	0.120328	−	0.338571i
$756$	90.6040	−	128.357i	3.29524	−	4.66829i
$757$	18.1506	+	7.88390i	0.659694	+	0.286545i	0.701595	−	0.712576i	$-0.252472\pi$
$757$	18.1506	+	7.88390i	0.659694	+	0.286545i	−0.0419009	+	0.999122i	$0.513341\pi$
$758$	−46.6184	+	6.40755i	−1.69326	+	0.232733i
$759$	−31.3190	−	19.0455i	−1.13681	−	0.691307i
$760$	−1.12538	−	0.154680i	−0.0408217	−	0.00561082i
$761$	20.6325	+	16.7858i	0.747928	+	0.608485i	0.926873	−	0.375374i	$-0.122486\pi$
$761$	20.6325	+	16.7858i	0.747928	+	0.608485i	−0.178945	+	0.983859i	$0.557268\pi$
$762$	−10.5697	−	154.523i	−0.382898	−	5.59778i
$763$	−15.9027	+	4.45572i	−0.575715	+	0.161308i
$764$	−0.234458	−	0.332151i	−0.00848240	−	0.0120168i
$765$	1.53576	+	7.39049i	0.0555256	+	0.267204i
$766$	−1.03381	+	15.1138i	−0.0373531	+	0.546083i
$767$	−0.222064	+	0.237773i	−0.00801827	+	0.00858547i
$768$	28.3232	+	79.6938i	1.02202	+	2.87570i
$769$	36.7326	+	10.2920i	1.32461	+	0.371138i	0.858148	−	0.513403i	$-0.171615\pi$
$769$	36.7326	+	10.2920i	1.32461	+	0.371138i	0.466462	+	0.884541i	$0.345528\pi$
$770$	−2.83076	+	13.6224i	−0.102014	+	0.490916i
$771$	1.27970	−	0.555851i	0.0460872	−	0.0200185i
$772$	60.9495	−	37.0642i	2.19362	−	1.33397i
$773$	−4.94864	+	4.02602i	−0.177990	+	0.144806i	−0.715916	−	0.698186i	$-0.753991\pi$
$773$	−4.94864	+	4.02602i	−0.177990	+	0.144806i	0.537926	+	0.842992i	$0.319208\pi$
$774$	103.802	+	111.145i	3.73109	+	3.99503i
$775$	−10.9452	+	21.1233i	−0.393164	+	0.758772i
$776$	−7.41384	+	14.3081i	−0.266141	+	0.513629i
$777$	−58.8211	−	62.9820i	−2.11020	−	2.25947i
$778$	−29.7878	+	24.2342i	−1.06795	+	0.868838i
$779$	−0.915579	+	0.556776i	−0.0328040	+	0.0199486i
$780$	−69.0369	+	29.9870i	−2.47192	+	1.07371i
$781$	−2.38347	+	11.4699i	−0.0852873	+	0.410425i
$782$	−10.5571	−	2.95796i	−0.377521	−	0.105776i
$783$	14.2253	+	40.0260i	0.508369	+	1.43041i
$784$	−0.144856	+	0.155103i	−0.00517342	+	0.00553938i
$785$	1.20041	−	17.5494i	0.0428446	−	0.626366i
$786$	15.4138	+	74.1750i	0.549790	+	2.64574i
$787$	17.2899	+	24.4943i	0.616320	+	0.873127i	0.998705	−	0.0508764i	$-0.0162015\pi$
$787$	17.2899	+	24.4943i	0.616320	+	0.873127i	−0.382385	+	0.924003i	$0.624897\pi$
$788$	−50.4059	+	14.1231i	−1.79564	+	0.503114i
$789$	2.75857	+	40.3289i	0.0982079	+	1.43575i
$790$	15.7227	+	12.7914i	0.559389	+	0.455097i
$791$	−33.3578	−	4.58492i	−1.18607	−	0.163021i
$792$	61.6228	+	37.4737i	2.18967	+	1.33157i
$793$	−47.7524	+	6.56341i	−1.69574	+	0.233074i
$794$	−0.170394	−	0.0740126i	−0.00604706	−	0.00262661i
$795$	4.02056	−	5.69583i	0.142595	−	0.202010i
$796$	7.02212	−	19.7584i	0.248892	−	0.700316i
$797$	−18.1464	−	35.0209i	−0.642777	−	1.24050i	−0.956706	−	0.291056i	$-0.905993\pi$
$797$	−18.1464	−	35.0209i	−0.642777	−	1.24050i	0.313929	−	0.949446i	$-0.398355\pi$
$798$	−6.58341			−0.233050
$799$	−5.07726	+	4.60668i	−0.179620	+	0.162972i
$800$	14.1443			0.500077
$801$	−37.5794	−	72.5249i	−1.32780	−	2.56254i
$802$	−0.462743	+	1.30203i	−0.0163400	+	0.0459764i
$803$	1.13196	−	1.60362i	0.0399460	−	0.0565906i
$804$	−100.321	−	43.5756i	−3.53806	−	1.53679i
$805$	−11.3350	+	1.55796i	−0.399505	+	0.0549108i
$806$	78.3001	+	47.6154i	2.75800	+	1.67718i
$807$	20.6368	+	2.83646i	0.726448	+	0.0998480i
$808$	40.6378	+	33.0613i	1.42963	+	1.16309i
$809$	−0.672727	−	9.83492i	−0.0236518	−	0.345777i	−0.994400	−	0.105679i	$-0.966298\pi$
$809$	−0.672727	−	9.83492i	−0.0236518	−	0.345777i	0.970748	−	0.240099i	$-0.0771798\pi$
$810$	66.9988	−	18.7722i	2.35410	−	0.659588i
$811$	−28.0549	−	39.7447i	−0.985141	−	1.39563i	−0.917419	−	0.397922i	$-0.869731\pi$
$811$	−28.0549	−	39.7447i	−0.985141	−	1.39563i	−0.0677213	−	0.997704i	$-0.521573\pi$
$812$	4.89188	+	23.5410i	0.171671	+	0.826129i
$813$	−5.25047	+	76.7592i	−0.184142	+	2.69206i
$814$	38.0808	−	40.7746i	1.33473	−	1.42915i
$815$	−0.645252	−	1.81557i	−0.0226022	−	0.0635965i
$816$	5.55587	+	1.55668i	0.194494	+	0.0544948i
$817$	0.521446	−	2.50934i	0.0182431	−	0.0877906i
$818$	28.2450	−	12.2685i	0.987563	−	0.428959i
$819$	−120.374	+	73.2010i	−4.20621	+	2.55785i
$820$	8.80100	−	7.16015i	0.307344	−	0.250043i
$821$	3.49823	+	3.74569i	0.122089	+	0.130725i	0.788952	−	0.614455i	$-0.210624\pi$
$821$	3.49823	+	3.74569i	0.122089	+	0.130725i	−0.666863	+	0.745181i	$0.732363\pi$
$822$	48.3899	−	93.3883i	1.68779	−	3.25729i
$823$	15.4425	−	29.8027i	0.538292	−	1.03886i	−0.450947	−	0.892551i	$-0.648914\pi$
$823$	15.4425	−	29.8027i	0.538292	−	1.03886i	0.989239	−	0.146306i	$-0.0467385\pi$
$824$	−35.2583	−	37.7524i	−1.22828	−	1.31517i
$825$	25.2389	−	20.5333i	0.878704	−	0.714879i
$826$	0.257430	−	0.156547i	0.00895714	−	0.00544696i
$827$	7.11221	−	3.08927i	0.247316	−	0.107424i	−0.271106	−	0.962550i	$-0.587389\pi$
$827$	7.11221	−	3.08927i	0.247316	−	0.107424i	0.518422	+	0.855125i	$0.326520\pi$
$828$	−27.1901	+	130.846i	−0.944920	+	4.54721i
$829$	36.5086	+	10.2292i	1.26799	+	0.355276i	0.837062	−	0.547108i	$-0.184271\pi$
$829$	36.5086	+	10.2292i	1.26799	+	0.355276i	0.430933	+	0.902384i	$0.358184\pi$
$830$	8.00591	+	22.5265i	0.277889	+	0.781905i
$831$	−27.6669	+	29.6240i	−0.959754	+	1.02765i
$832$	5.30735	−	77.5907i	0.183999	−	2.68997i
$833$	−0.0248415	−	0.119544i	−0.000860707	−	0.00414195i
$834$	−52.3303	−	74.1352i	−1.81205	−	2.56709i
$835$	14.5509	−	4.07698i	0.503555	−	0.141090i
$836$	−0.186901	−	2.73239i	−0.00646410	−	0.0945018i
$837$	−74.7372	−	60.8032i	−2.58329	−	2.10167i
$838$	−10.4256	−	1.43296i	−0.360146	−	0.0495009i
$839$	−19.3498	−	11.7669i	−0.668030	−	0.406238i	0.144222	−	0.989545i	$-0.453932\pi$
$839$	−19.3498	−	11.7669i	−0.668030	−	0.406238i	−0.812251	+	0.583307i	$0.801758\pi$
$840$	30.6462	−	4.21223i	1.05740	−	0.145336i
$841$	20.6366	+	8.96372i	0.711605	+	0.309094i
$842$	−48.1365	+	68.1939i	−1.65889	+	2.35012i
$843$	10.4455	−	29.3908i	0.359762	−	1.01227i
$844$	−31.7471	−	61.2691i	−1.09278	−	2.10897i
$845$	30.0063			1.03225
$846$	93.7543	+	90.1242i	3.22334	+	3.09853i
$847$	13.9612			0.479714
$848$	−1.78426	−	3.44347i	−0.0612718	−	0.118249i
$849$	3.70192	−	10.4162i	0.127050	−	0.357483i
$850$	5.61208	−	7.95050i	0.192493	−	0.272700i
$851$	42.0815	+	18.2786i	1.44253	+	0.626581i
$852$	58.1435	−	7.99164i	1.99196	−	0.273789i
$853$	−19.0949	−	11.6119i	−0.653799	−	0.397584i	0.153152	−	0.988203i	$-0.451058\pi$
$853$	−19.0949	−	11.6119i	−0.653799	−	0.397584i	−0.806951	+	0.590619i	$0.798884\pi$
$854$	44.2223	+	6.07821i	1.51325	+	0.207992i
$855$	−1.87186	−	1.52287i	−0.0640163	−	0.0520811i
$856$	0.718310	+	10.5013i	0.0245513	+	0.358928i
$857$	28.4586	−	7.97371i	0.972126	−	0.272377i	0.253162	−	0.967424i	$-0.418530\pi$
$857$	28.4586	−	7.97371i	0.972126	−	0.272377i	0.718964	+	0.695047i	$0.244617\pi$
$858$	−72.2755	−	102.391i	−2.46744	−	3.49557i
$859$	−6.42237	−	30.9062i	−0.219129	−	1.05450i	−0.934556	−	0.355817i	$-0.884203\pi$
$859$	−6.42237	−	30.9062i	−0.219129	−	1.05450i	0.715427	−	0.698687i	$-0.246232\pi$
$860$	−1.85183	+	27.0728i	−0.0631469	+	0.923174i
$861$	19.9177	−	21.3267i	0.678794	−	0.726811i
$862$	3.62827	+	10.2090i	0.123580	+	0.347719i
$863$	−22.1936	−	6.21834i	−0.755478	−	0.211675i	−0.129568	−	0.991571i	$-0.541359\pi$
$863$	−22.1936	−	6.21834i	−0.755478	−	0.211675i	−0.625910	+	0.779896i	$0.715272\pi$
$864$	−11.6542	+	56.0833i	−0.396485	+	1.90799i
$865$	−17.8179	+	7.73942i	−0.605828	+	0.263148i
$866$	26.1928	−	15.9282i	0.890067	−	0.541261i
$867$	−2.57497	+	2.09489i	−0.0874504	+	0.0711462i
$868$	−37.2227	−	39.8557i	−1.26342	−	1.35279i
$869$	−9.97755	+	19.2558i	−0.338465	+	0.653208i
$870$	−8.67035	+	16.7330i	−0.293952	+	0.567302i
$871$	41.8992	+	44.8631i	1.41970	+	1.52013i
$872$	−18.4401	+	15.0021i	−0.624459	+	0.508035i
$873$	−29.2487	+	17.7865i	−0.989918	+	0.601983i
$874$	3.21473	−	1.39636i	0.108740	−	0.0472324i
$875$	4.57759	−	22.0286i	0.154751	−	0.744702i
$876$	−9.46914	−	2.65313i	−0.319933	−	0.0896409i
$877$	−17.3507	−	48.8202i	−0.585892	−	1.64854i	−0.749491	−	0.662015i	$-0.769702\pi$
$877$	−17.3507	−	48.8202i	−0.585892	−	1.64854i	0.163599	−	0.986527i	$-0.447690\pi$
$878$	0.537511	−	0.575534i	0.0181401	−	0.0194233i
$879$	−6.58589	+	96.2824i	−0.222137	+	3.24752i
$880$	0.793115	+	3.81668i	0.0267359	+	0.128660i
$881$	16.1409	+	22.8665i	0.543801	+	0.770390i	0.992362	−	0.123362i	$-0.0393676\pi$
$881$	16.1409	+	22.8665i	0.543801	+	0.770390i	−0.448561	+	0.893752i	$0.648063\pi$
$882$	−2.23022	+	0.624878i	−0.0750954	+	0.0210408i
$883$	−1.23604	−	18.0703i	−0.0415961	−	0.608114i	−0.971005	−	0.239061i	$-0.923160\pi$
$883$	−1.23604	−	18.0703i	−0.0415961	−	0.608114i	0.929408	−	0.369053i	$-0.120318\pi$
$884$	−18.6856	−	15.2019i	−0.628466	−	0.511295i
$885$	0.150338	+	0.0206635i	0.00505356	+	0.000694596i
$886$	81.7119	+	49.6901i	2.74516	+	1.66937i
$887$	−34.2893	+	4.71295i	−1.15132	+	0.158245i	−0.686480	−	0.727149i	$-0.740845\pi$
$887$	−34.2893	+	4.71295i	−1.15132	+	0.158245i	−0.464841	+	0.885394i	$0.653889\pi$
$888$	−113.775	−	49.4195i	−3.81804	−	1.65841i
$889$	29.8310	−	42.2609i	1.00050	−	1.41738i
$890$	7.59560	−	21.3720i	0.254605	−	0.716390i
$891$	34.2511	+	66.1017i	1.14746	+	2.21449i
$892$	−53.5271			−1.79222
$893$	0.329680	−	2.16670i	0.0110323	−	0.0725059i
$894$	163.958			5.48358
$895$	3.93240	+	7.58918i	0.131446	+	0.253678i
$896$	−18.0799	+	50.8719i	−0.604006	+	1.69951i
$897$	59.4351	−	84.2004i	1.98448	−	2.81137i
$898$	42.0378	+	18.2596i	1.40282	+	0.609330i
$899$	14.6072	−	2.00771i	0.487176	−	0.0669608i
$900$	−101.355	−	61.6352i	−3.37849	−	2.05451i
$901$	2.21046	+	0.303821i	0.0736412	+	0.0101218i
$902$	14.6547	+	11.9225i	0.487947	+	0.396975i
$903$	4.76291	+	69.6312i	0.158500	+	2.31718i
$904$	−46.6693	+	13.0761i	−1.55220	+	0.434905i
$905$	1.35827	+	1.92423i	0.0451505	+	0.0639636i
$906$	−16.7568	−	80.6383i	−0.556708	−	2.67903i
$907$	0.0850614	−	1.24355i	0.00282442	−	0.0412915i	−0.996043	−	0.0888736i	$-0.971673\pi$
$907$	0.0850614	−	1.24355i	0.00282442	−	0.0412915i	0.998867	+	0.0475820i	$0.0151516\pi$
$908$	−38.6792	+	41.4154i	−1.28362	+	1.37442i
$909$	37.2675	+	104.861i	1.23609	+	3.47801i
$910$	−37.6698	−	10.5546i	−1.24874	−	0.349881i
$911$	−9.18710	+	44.2107i	−0.304382	+	1.46477i	0.497593	+	0.867410i	$0.334217\pi$
$911$	−9.18710	+	44.2107i	−0.304382	+	1.46477i	−0.801976	+	0.597357i	$0.796218\pi$
$912$	−1.69182	+	0.734859i	−0.0560216	+	0.0243336i
$913$	−21.8560	+	13.2909i	−0.723328	+	0.439865i
$914$	−52.5668	+	42.7662i	−1.73875	+	1.41458i
$915$	15.3457	+	16.4312i	0.507313	+	0.543199i
$916$	−14.3608	+	27.7151i	−0.474494	+	0.915732i
$917$	−11.6408	+	22.4657i	−0.384413	+	0.741884i
$918$	26.9003	+	28.8031i	0.887841	+	0.950645i
$919$	−31.1333	+	25.3288i	−1.02699	+	0.835520i	−0.986517	−	0.163660i	$-0.947670\pi$
$919$	−31.1333	+	25.3288i	−1.02699	+	0.835520i	−0.0404758	+	0.999181i	$0.512887\pi$
$920$	−14.0714	+	8.55700i	−0.463920	+	0.282116i
$921$	−42.0451	+	18.2628i	−1.38543	+	0.601778i
$922$	−3.64255	+	17.5289i	−0.119961	+	0.577284i
$923$	−31.7176	−	8.88685i	−1.04400	−	0.292514i
$924$	24.9761	+	70.2759i	0.821653	+	2.31191i
$925$	−27.7966	+	29.7629i	−0.913946	+	0.978597i
$926$	−2.47243	+	36.1456i	−0.0812491	+	1.18782i
$927$	−22.3258	−	107.438i	−0.733275	−	3.52872i
$928$	−5.05524	−	7.16165i	−0.165946	−	0.235093i
$929$	−4.98524	+	1.39680i	−0.163560	+	0.0458275i	−0.350602	−	0.936524i	$-0.614023\pi$
$929$	−4.98524	+	1.39680i	−0.163560	+	0.0458275i	0.187042	+	0.982352i	$0.440110\pi$
$930$	−2.91700	−	42.6451i	−0.0956523	−	1.39839i
$931$	0.0302780	+	0.0246330i	0.000992323	+	0.000807314i
$932$	98.1039	+	13.4841i	3.21350	+	0.441685i
$933$	25.7886	+	15.6824i	0.844282	+	0.513419i
$934$	−26.2940	+	3.61402i	−0.860365	+	0.118254i
$935$	−2.05704	−	0.893499i	−0.0672724	−	0.0292205i
$936$	−116.944	+	165.672i	−3.82243	+	5.41515i
$937$	−3.08593	+	8.68299i	−0.100813	+	0.283661i	−0.981932	−	0.189234i	$-0.939400\pi$
$937$	−3.08593	+	8.68299i	−0.100813	+	0.283661i	0.881119	+	0.472895i	$0.156791\pi$
$938$	−26.1538	−	50.4746i	−0.853952	−	1.64805i
$939$	4.93492			0.161045
$940$	−0.334327	+	23.2023i	−0.0109046	+	0.756777i
$941$	6.00627			0.195799			0.0978993	−	0.995196i	$-0.468788\pi$
$941$	6.00627			0.195799			0.0978993	+	0.995196i	$0.468788\pi$
$942$	−67.5096	−	130.288i	−2.19958	−	4.24500i
$943$	−5.20256	+	14.6386i	−0.169419	+	0.476698i
$944$	0.0486807	−	0.0689648i	0.00158442	−	0.00224461i
$945$	37.7241	+	16.3859i	1.22717	+	0.533033i
$946$	−44.7638	+	6.15264i	−1.45540	+	0.200039i
$947$	11.5485	+	7.02279i	0.375275	+	0.228210i	0.694538	−	0.719456i	$-0.255609\pi$
$947$	11.5485	+	7.02279i	0.375275	+	0.228210i	−0.319262	+	0.947666i	$0.603435\pi$
$948$	107.638	+	14.7945i	3.49592	+	0.480504i
$949$	4.28123	+	3.48303i	0.138974	+	0.113064i
$950$	0.212307	+	3.10381i	0.00688813	+	0.100701i
$951$	−36.6956	+	10.2816i	−1.18993	+	0.333404i
$952$	5.70916	+	8.08804i	0.185035	+	0.262135i
$953$	0.216713	+	1.04288i	0.00702001	+	0.0337821i	0.982448	−	0.186535i	$-0.0597257\pi$
$953$	0.216713	+	1.04288i	0.00702001	+	0.0337821i	−0.975428	+	0.220317i	$0.929291\pi$
$954$	2.88837	−	42.2265i	0.0935145	−	1.36713i
$955$	0.0726447	−	0.0777835i	0.00235073	−	0.00251701i
$956$	14.6327	+	41.1726i	0.473257	+	1.33162i
$957$	−19.4171	−	5.44041i	−0.627664	−	0.175863i
$958$	−7.81297	+	37.5981i	−0.252426	+	1.21474i
$959$	32.2204	−	13.9953i	1.04045	−	0.451931i
$960$	−30.9946	+	18.8482i	−1.00035	+	0.608324i
$961$	−1.89446	+	1.54126i	−0.0611117	+	0.0497180i
$962$	107.072	+	114.647i	3.45215	+	3.69635i
$963$	−10.2870	+	19.8530i	−0.331494	+	0.639754i
$964$	27.8084	−	53.6678i	0.895649	−	1.72852i
$965$	12.7460	+	13.6476i	0.410307	+	0.439332i
$966$	−74.0379	+	60.2343i	−2.38213	+	1.93801i
$967$	−41.9574	+	25.5149i	−1.34926	+	0.820503i	−0.993473	−	0.114064i	$-0.963613\pi$
$967$	−41.9574	+	25.5149i	−1.34926	+	0.820503i	−0.355787	+	0.934567i	$0.615787\pi$
$968$	18.4321	−	8.00618i	0.592430	−	0.257328i
$969$	0.215905	−	1.03899i	0.00693586	−	0.0333772i
$970$	−9.15309	−	2.56457i	−0.293888	−	0.0823435i
$971$	7.81503	+	21.9894i	0.250796	+	0.705673i	0.999104	+	0.0423214i	$0.0134753\pi$
$971$	7.81503	+	21.9894i	0.250796	+	0.705673i	−0.748308	+	0.663352i	$0.769133\pi$
$972$	131.905	−	141.236i	4.23086	−	4.53014i
$973$	2.06823	−	30.2364i	0.0663044	−	0.969336i
$974$	12.7368	+	61.2930i	0.408114	+	1.96395i
$975$	52.7566	+	74.7390i	1.68956	+	2.39356i
$976$	12.0428	−	3.37423i	0.385480	−	0.108006i
$977$	−4.03884	−	59.0458i	−0.129214	−	1.88904i	−0.385889	−	0.922545i	$-0.626105\pi$
$977$	−4.03884	−	59.0458i	−0.129214	−	1.88904i	0.256675	−	0.966498i	$-0.417373\pi$
$978$	−12.4684	−	10.1438i	−0.398695	−	0.324363i
$979$	24.0429	+	3.30462i	0.768414	+	0.105616i
$980$	−0.353107	−	0.214729i	−0.0112796	−	0.00685927i
$981$	−50.0276	+	6.87613i	−1.59726	+	0.219538i
$982$	−9.96040	−	4.32641i	−0.317849	−	0.138061i
$983$	0.494688	−	0.700814i	0.0157781	−	0.0223525i	−0.809004	−	0.587803i	$-0.799993\pi$
$983$	0.494688	−	0.700814i	0.0157781	−	0.0223525i	0.824782	+	0.565450i	$0.191298\pi$
$984$	14.0661	−	39.5782i	0.448410	−	1.26171i
$985$	−6.30448	−	12.1671i	−0.200877	−	0.387676i
$986$	−6.03133			−0.192077
$987$	7.27406	+	59.2377i	0.231536	+	1.88556i
$988$	7.70067			0.244991
$989$	−17.0947	−	32.9913i	−0.543580	−	1.04906i
$990$	−14.2467	+	40.0863i	−0.452789	+	1.27403i
$991$	−6.51720	+	9.23276i	−0.207026	+	0.293288i	−0.907214	−	0.420670i	$-0.861795\pi$
$991$	−6.51720	+	9.23276i	−0.207026	+	0.293288i	0.700188	+	0.713958i	$0.253099\pi$
$992$	18.2365	+	7.92123i	0.579009	+	0.251499i
$993$	−47.9656	+	6.59271i	−1.52214	+	0.209213i
$994$	26.0633	+	15.8494i	0.826676	+	0.502713i
$995$	5.43817	+	0.747460i	0.172402	+	0.0236961i
$996$	99.4088	+	80.8751i	3.14989	+	2.56263i
$997$	3.04147	+	44.4647i	0.0963243	+	1.40821i	0.754970	+	0.655759i	$0.227651\pi$
$997$	3.04147	+	44.4647i	0.0963243	+	1.40821i	−0.658646	+	0.752453i	$0.728871\pi$
$998$	21.1825	−	5.93506i	0.670521	−	0.187871i
$999$	−95.1090	−	134.739i	−3.00912	−	4.26295i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	799.2.k.a.256.29	yes	704
47.9	even	23	inner	799.2.k.a.103.29	✓	704

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
799.2.k.a.103.29	✓	704	47.9	even	23	inner
799.2.k.a.256.29	yes	704	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 799 = 17 \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	799.k (of order \(23\), degree \(22\), minimal)

\(f(q)\)	\(=\)	\(q+(1.08830 + 2.10033i) q^{2} +(-1.11163 + 3.12782i) q^{3} +(-2.07363 + 2.93766i) q^{4} +(-0.863380 - 0.375019i) q^{5} +(-7.77926 + 1.06923i) q^{6} +(-2.24078 - 1.36265i) q^{7} +(-3.73977 - 0.514020i) q^{8} +(-6.22043 - 5.06070i) q^{9} +O(q^{10})\)	\(q+(1.08830 + 2.10033i) q^{2} +(-1.11163 + 3.12782i) q^{3} +(-2.07363 + 2.93766i) q^{4} +(-0.863380 - 0.375019i) q^{5} +(-7.77926 + 1.06923i) q^{6} +(-2.24078 - 1.36265i) q^{7} +(-3.73977 - 0.514020i) q^{8} +(-6.22043 - 5.06070i) q^{9} +(-0.151956 - 2.22152i) q^{10} +(2.29419 - 0.642803i) q^{11} +(-6.88338 - 9.75153i) q^{12} +(1.36296 + 6.55893i) q^{13} +(0.423363 - 6.18936i) q^{14} +(2.13275 - 2.28362i) q^{15} +(-0.582077 - 1.63781i) q^{16} +(0.962917 + 0.269797i) q^{17} +(3.85942 - 18.5726i) q^{18} +(-0.293217 + 0.127362i) q^{19} +(2.89201 - 1.75867i) q^{20} +(6.75304 - 5.49401i) q^{21} +(3.84688 + 4.11900i) q^{22} +(-2.13228 + 4.11510i) q^{23} +(5.76500 - 11.1259i) q^{24} +(-2.80798 - 3.00661i) q^{25} +(-12.2926 + 10.0008i) q^{26} +(14.2351 - 8.65655i) q^{27} +(8.64953 - 3.75702i) q^{28} +(-0.518744 + 2.49633i) q^{29} +(7.11744 + 1.99421i) q^{30} +(-1.93658 - 5.44902i) q^{31} +(-2.34672 + 2.51272i) q^{32} +(-0.539718 + 7.89039i) q^{33} +(0.481284 + 2.31607i) q^{34} +(1.42363 + 2.01682i) q^{35} +(27.7655 - 7.77952i) q^{36} +(-0.675541 - 9.87606i) q^{37} +(-0.586613 - 0.477245i) q^{38} +(-22.0303 - 3.02799i) q^{39} +(3.03608 + 1.84628i) q^{40} +(3.32078 - 0.456431i) q^{41} +(18.8886 + 8.20447i) q^{42} +(-4.62332 + 6.54975i) q^{43} +(-2.86896 + 8.07249i) q^{44} +(3.47274 + 6.70209i) q^{45} -10.9636 q^{46} +(-3.64611 + 5.80567i) q^{47} +5.76983 q^{48} +(-0.0561728 - 0.108409i) q^{49} +(3.25895 - 9.16980i) q^{50} +(-1.91428 + 2.71192i) q^{51} +(-22.0942 - 9.59685i) q^{52} +(2.21046 - 0.303821i) q^{53} +(33.6737 + 20.4774i) q^{54} +(-2.22182 - 0.305383i) q^{55} +(7.67957 + 6.24780i) q^{56} +(-0.0724179 - 1.05871i) q^{57} +(-5.80768 + 1.62723i) q^{58} +(0.0280069 + 0.0396767i) q^{59} +(2.28597 + 11.0007i) q^{60} +(-0.491021 + 7.17848i) q^{61} +(9.33717 - 9.99766i) q^{62} +(7.04267 + 19.8162i) q^{63} +(-11.1789 - 3.13219i) q^{64} +(1.28297 - 6.17398i) q^{65} +(-17.1598 + 7.45356i) q^{66} +(7.82939 - 4.76116i) q^{67} +(-2.78930 + 2.26926i) q^{68} +(-10.5010 - 11.2439i) q^{69} +(-2.68665 + 5.18500i) q^{70} +(-2.26213 + 4.36571i) q^{71} +(20.6617 + 22.1233i) q^{72} +(0.639080 - 0.519930i) q^{73} +(20.0078 - 12.1670i) q^{74} +(12.5256 - 5.44063i) q^{75} +(0.233876 - 1.12547i) q^{76} +(-6.01669 - 1.68580i) q^{77} +(-17.6159 - 49.5663i) q^{78} +(-6.21298 + 6.65248i) q^{79} +(-0.111655 + 1.63234i) q^{80} +(6.35748 + 30.5939i) q^{81} +(4.57267 + 6.47800i) q^{82} +(-10.3383 + 2.89664i) q^{83} +(2.13623 + 31.2306i) q^{84} +(-0.730185 - 0.594049i) q^{85} +(-18.7882 - 2.58238i) q^{86} +(-7.23144 - 4.39753i) q^{87} +(-8.91017 + 1.22467i) q^{88} +(9.34284 + 4.05817i) q^{89} +(-10.2972 + 14.5878i) q^{90} +(5.88341 - 16.5543i) q^{91} +(-7.66723 - 14.7971i) q^{92} +19.1964 q^{93} +(-16.1619 - 1.33971i) q^{94} +0.300921 q^{95} +(-5.25067 - 10.1333i) q^{96} +(1.42956 - 4.02241i) q^{97} +(0.166561 - 0.235963i) q^{98} +(-17.5239 - 7.61171i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 704 q - 2 q^{3} - 32 q^{4} - 6 q^{5} - 10 q^{6} + 21 q^{7} - 24 q^{8} - 42 q^{9}+O(q^{10}) \) 704 * q - 2 * q^3 - 32 * q^4 - 6 * q^5 - 10 * q^6 + 21 * q^7 - 24 * q^8 - 42 * q^9	\( 704 q - 2 q^{3} - 32 q^{4} - 6 q^{5} - 10 q^{6} + 21 q^{7} - 24 q^{8} - 42 q^{9} - 36 q^{10} - 12 q^{11} - 40 q^{12} - 12 q^{13} - 30 q^{14} - 34 q^{15} - 48 q^{16} - 32 q^{17} - 6 q^{18} - 12 q^{19} - 26 q^{20} - 32 q^{21} - 28 q^{22} - 30 q^{23} - 24 q^{24} - 42 q^{25} - 46 q^{26} - 56 q^{27} - 14 q^{28} - 44 q^{29} + 136 q^{30} - 44 q^{31} - 48 q^{32} - 28 q^{33} - 46 q^{35} - 42 q^{36} - 24 q^{37} + 520 q^{38} - 11 q^{39} + 50 q^{40} + 31 q^{41} - 94 q^{42} - 35 q^{43} - 68 q^{44} - 110 q^{45} + 280 q^{46} - 17 q^{47} - 128 q^{48} - 59 q^{49} + 20 q^{50} - 2 q^{51} - 84 q^{52} - 11 q^{53} + 415 q^{54} - 17 q^{55} - 18 q^{56} - 37 q^{57} - 40 q^{58} - 54 q^{59} - 128 q^{60} - 66 q^{61} + 96 q^{62} - 74 q^{63} - 124 q^{64} - 52 q^{65} - 68 q^{66} - 56 q^{67} - 32 q^{68} + 4 q^{69} + 514 q^{70} - 42 q^{71} - 130 q^{72} - 62 q^{73} - 110 q^{74} - 80 q^{75} - 186 q^{76} + 450 q^{77} - 82 q^{78} - 64 q^{79} - 164 q^{80} + 18 q^{81} + 57 q^{82} - 56 q^{83} - 38 q^{84} - 6 q^{85} + 72 q^{86} - 42 q^{87} - 178 q^{88} - 56 q^{89} + 94 q^{90} + 110 q^{91} + 31 q^{92} + 290 q^{93} - 136 q^{94} - 96 q^{95} - 188 q^{96} - 74 q^{97} - 11 q^{98} + 68 q^{99}+O(q^{100}) \) 704 * q - 2 * q^3 - 32 * q^4 - 6 * q^5 - 10 * q^6 + 21 * q^7 - 24 * q^8 - 42 * q^9 - 36 * q^10 - 12 * q^11 - 40 * q^12 - 12 * q^13 - 30 * q^14 - 34 * q^15 - 48 * q^16 - 32 * q^17 - 6 * q^18 - 12 * q^19 - 26 * q^20 - 32 * q^21 - 28 * q^22 - 30 * q^23 - 24 * q^24 - 42 * q^25 - 46 * q^26 - 56 * q^27 - 14 * q^28 - 44 * q^29 + 136 * q^30 - 44 * q^31 - 48 * q^32 - 28 * q^33 - 46 * q^35 - 42 * q^36 - 24 * q^37 + 520 * q^38 - 11 * q^39 + 50 * q^40 + 31 * q^41 - 94 * q^42 - 35 * q^43 - 68 * q^44 - 110 * q^45 + 280 * q^46 - 17 * q^47 - 128 * q^48 - 59 * q^49 + 20 * q^50 - 2 * q^51 - 84 * q^52 - 11 * q^53 + 415 * q^54 - 17 * q^55 - 18 * q^56 - 37 * q^57 - 40 * q^58 - 54 * q^59 - 128 * q^60 - 66 * q^61 + 96 * q^62 - 74 * q^63 - 124 * q^64 - 52 * q^65 - 68 * q^66 - 56 * q^67 - 32 * q^68 + 4 * q^69 + 514 * q^70 - 42 * q^71 - 130 * q^72 - 62 * q^73 - 110 * q^74 - 80 * q^75 - 186 * q^76 + 450 * q^77 - 82 * q^78 - 64 * q^79 - 164 * q^80 + 18 * q^81 + 57 * q^82 - 56 * q^83 - 38 * q^84 - 6 * q^85 + 72 * q^86 - 42 * q^87 - 178 * q^88 - 56 * q^89 + 94 * q^90 + 110 * q^91 + 31 * q^92 + 290 * q^93 - 136 * q^94 - 96 * q^95 - 188 * q^96 - 74 * q^97 - 11 * q^98 + 68 * q^99

Introduction

L-functions

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