LMFDB - Embedded newform 50.3.f.a.27.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [50,3,Mod(3,50)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(50, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([7]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("50.3");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 50 = 2 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	50.f (of order $20$, degree $8$, 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:	$1.36240132180$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{20})$
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} + 30x^{14} + 351x^{12} + 2130x^{10} + 7341x^{8} + 14480x^{6} + 15196x^{4} + 6560x^{2} + 16 $ x^16 + 30x^14 + 351x^12 + 2130x^10 + 7341x^8 + 14480x^6 + 15196x^4 + 6560*x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			27.1
Root			$-1.78563i$ of defining polynomial
Character	$\chi$	$=$	50.27
Dual form			50.3.f.a.13.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39680 - 0.221232i) q^{2} +(-1.14941 - 2.25584i) q^{3} +(1.90211 + 0.618034i) q^{4} +(-4.68874 - 1.73657i) q^{5} +(1.10643 + 3.40526i) q^{6} +(-6.58346 - 6.58346i) q^{7} +(-2.52015 - 1.28408i) q^{8} +(1.52238 - 2.09537i) q^{9} +O(q^{10})$	\(q+(-1.39680 - 0.221232i) q^{2} +(-1.14941 - 2.25584i) q^{3} +(1.90211 + 0.618034i) q^{4} +(-4.68874 - 1.73657i) q^{5} +(1.10643 + 3.40526i) q^{6} +(-6.58346 - 6.58346i) q^{7} +(-2.52015 - 1.28408i) q^{8} +(1.52238 - 2.09537i) q^{9} +(6.16506 + 3.46295i) q^{10} +(-3.81477 + 2.77159i) q^{11} +(-0.792120 - 5.00125i) q^{12} +(17.5244 - 2.77559i) q^{13} +(7.73932 + 10.6523i) q^{14} +(1.47185 + 12.5731i) q^{15} +(3.23607 + 2.35114i) q^{16} +(-7.44532 + 14.6123i) q^{17} +(-2.59002 + 2.59002i) q^{18} +(16.0908 - 5.22822i) q^{19} +(-7.84526 - 6.20096i) q^{20} +(-7.28417 + 22.4184i) q^{21} +(5.94165 - 3.02742i) q^{22} +(5.91002 - 37.3144i) q^{23} +7.16099i q^{24} +(18.9686 + 16.2847i) q^{25} -25.0922 q^{26} +(-28.9823 - 4.59034i) q^{27} +(-8.45369 - 16.5913i) q^{28} +(-1.46851 - 0.477149i) q^{29} +(0.725684 - 17.8878i) q^{30} +(-9.29144 - 28.5961i) q^{31} +(-4.00000 - 4.00000i) q^{32} +(10.6370 + 5.41983i) q^{33} +(13.6323 - 18.7633i) q^{34} +(19.4355 + 42.3008i) q^{35} +(4.19074 - 3.04475i) q^{36} +(1.26903 + 8.01234i) q^{37} +(-23.6323 + 3.74300i) q^{38} +(-26.4040 - 36.3420i) q^{39} +(9.58643 + 10.3971i) q^{40} +(-30.0830 - 21.8566i) q^{41} +(15.1342 - 29.7025i) q^{42} +(-25.9880 + 25.9880i) q^{43} +(-8.96907 + 2.91423i) q^{44} +(-10.7768 + 7.18094i) q^{45} +(-16.5103 + 50.8134i) q^{46} +(41.1918 - 20.9883i) q^{47} +(1.58424 - 10.0025i) q^{48} +37.6840i q^{49} +(-22.8927 - 26.9429i) q^{50} +41.5207 q^{51} +(35.0488 + 5.55119i) q^{52} +(37.0947 + 72.8025i) q^{53} +(39.4670 + 12.8236i) q^{54} +(22.6996 - 6.37067i) q^{55} +(8.13761 + 25.0450i) q^{56} +(-30.2890 - 30.2890i) q^{57} +(1.94566 + 0.991364i) q^{58} +(24.7807 - 34.1077i) q^{59} +(-4.97098 + 24.8251i) q^{60} +(96.0793 - 69.8057i) q^{61} +(6.65194 + 41.9987i) q^{62} +(-23.8173 + 3.77229i) q^{63} +(4.70228 + 6.47214i) q^{64} +(-86.9875 - 17.4184i) q^{65} +(-13.6588 - 9.92368i) q^{66} +(-39.7150 + 77.9450i) q^{67} +(-23.1927 + 23.1927i) q^{68} +(-90.9685 + 29.5575i) q^{69} +(-17.7893 - 63.3856i) q^{70} +(-5.14879 + 15.8463i) q^{71} +(-6.52723 + 3.32579i) q^{72} +(9.91177 - 62.5804i) q^{73} -11.4724i q^{74} +(14.9330 - 61.5081i) q^{75} +33.8378 q^{76} +(43.3611 + 6.86772i) q^{77} +(28.8412 + 56.6041i) q^{78} +(-19.2036 - 6.23964i) q^{79} +(-11.0902 - 16.6436i) q^{80} +(15.7542 + 48.4864i) q^{81} +(37.1847 + 37.1847i) q^{82} +(22.1438 + 11.2828i) q^{83} +(-27.7106 + 38.1404i) q^{84} +(60.2844 - 55.5838i) q^{85} +(42.0494 - 30.5507i) q^{86} +(0.611550 + 3.86118i) q^{87} +(13.1727 - 2.08636i) q^{88} +(-39.7082 - 54.6536i) q^{89} +(16.6417 - 7.64618i) q^{90} +(-133.644 - 97.0982i) q^{91} +(34.3031 - 67.3236i) q^{92} +(-53.8287 + 53.8287i) q^{93} +(-62.1801 + 20.2035i) q^{94} +(-84.5249 - 3.42907i) q^{95} +(-4.42574 + 13.6210i) q^{96} +(-26.2088 + 13.3540i) q^{97} +(8.33689 - 52.6370i) q^{98} +12.2128i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} + 2 q^{3} + 4 q^{6} - 2 q^{7} + 8 q^{8} - 40 q^{9}+O(q^{10}) $ 16 * q - 4 * q^2 + 2 * q^3 + 4 * q^6 - 2 * q^7 + 8 * q^8 - 40 * q^9	\( 16 q - 4 q^{2} + 2 q^{3} + 4 q^{6} - 2 q^{7} + 8 q^{8} - 40 q^{9} + 10 q^{10} + 32 q^{11} + 4 q^{12} - 8 q^{13} - 30 q^{14} + 16 q^{16} - 62 q^{17} - 16 q^{18} + 30 q^{19} - 20 q^{20} - 68 q^{21} - 48 q^{22} - 18 q^{23} + 70 q^{25} - 56 q^{26} - 40 q^{27} + 44 q^{28} + 100 q^{29} + 120 q^{30} + 132 q^{31} - 64 q^{32} - 36 q^{33} + 100 q^{34} + 150 q^{35} + 48 q^{36} + 138 q^{37} + 20 q^{38} - 320 q^{39} - 88 q^{41} - 8 q^{42} - 78 q^{43} + 40 q^{44} - 20 q^{45} - 26 q^{46} - 22 q^{47} - 8 q^{48} - 20 q^{50} - 168 q^{51} - 16 q^{52} + 182 q^{53} + 80 q^{54} + 280 q^{55} + 48 q^{56} + 280 q^{57} - 120 q^{58} - 350 q^{59} - 140 q^{60} + 372 q^{61} - 158 q^{62} + 22 q^{63} - 910 q^{65} - 202 q^{66} - 112 q^{67} - 196 q^{68} - 30 q^{69} - 20 q^{70} + 122 q^{71} - 132 q^{72} - 248 q^{73} - 80 q^{75} + 40 q^{76} + 16 q^{77} + 438 q^{78} + 760 q^{79} + 80 q^{80} - 144 q^{81} + 352 q^{82} + 132 q^{83} - 20 q^{84} - 30 q^{85} + 264 q^{86} + 770 q^{87} + 116 q^{88} + 550 q^{89} - 140 q^{90} - 798 q^{91} + 384 q^{92} + 54 q^{93} + 190 q^{94} + 40 q^{95} - 16 q^{96} - 292 q^{97} - 24 q^{98}+O(q^{100}) \) 16 * q - 4 * q^2 + 2 * q^3 + 4 * q^6 - 2 * q^7 + 8 * q^8 - 40 * q^9 + 10 * q^10 + 32 * q^11 + 4 * q^12 - 8 * q^13 - 30 * q^14 + 16 * q^16 - 62 * q^17 - 16 * q^18 + 30 * q^19 - 20 * q^20 - 68 * q^21 - 48 * q^22 - 18 * q^23 + 70 * q^25 - 56 * q^26 - 40 * q^27 + 44 * q^28 + 100 * q^29 + 120 * q^30 + 132 * q^31 - 64 * q^32 - 36 * q^33 + 100 * q^34 + 150 * q^35 + 48 * q^36 + 138 * q^37 + 20 * q^38 - 320 * q^39 - 88 * q^41 - 8 * q^42 - 78 * q^43 + 40 * q^44 - 20 * q^45 - 26 * q^46 - 22 * q^47 - 8 * q^48 - 20 * q^50 - 168 * q^51 - 16 * q^52 + 182 * q^53 + 80 * q^54 + 280 * q^55 + 48 * q^56 + 280 * q^57 - 120 * q^58 - 350 * q^59 - 140 * q^60 + 372 * q^61 - 158 * q^62 + 22 * q^63 - 910 * q^65 - 202 * q^66 - 112 * q^67 - 196 * q^68 - 30 * q^69 - 20 * q^70 + 122 * q^71 - 132 * q^72 - 248 * q^73 - 80 * q^75 + 40 * q^76 + 16 * q^77 + 438 * q^78 + 760 * q^79 + 80 * q^80 - 144 * q^81 + 352 * q^82 + 132 * q^83 - 20 * q^84 - 30 * q^85 + 264 * q^86 + 770 * q^87 + 116 * q^88 + 550 * q^89 - 140 * q^90 - 798 * q^91 + 384 * q^92 + 54 * q^93 + 190 * q^94 + 40 * q^95 - 16 * q^96 - 292 * q^97 - 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/50\mathbb{Z}\right)^\times$.

$n$	$27$
$\chi(n)$	$e\left(\frac{1}{20}\right)$

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 $

$2$	−1.39680	−	0.221232i	−0.698401	−	0.110616i
$2$	−1.39680	−	0.221232i	−0.698401	−	0.110616i
$3$	−1.14941	−	2.25584i	−0.383137	−	0.751948i	0.616229	−	0.787567i	$-0.288660\pi$
$3$	−1.14941	−	2.25584i	−0.383137	−	0.751948i	−0.999365	+	0.0356190i	$0.988660\pi$
$4$	1.90211	+	0.618034i	0.475528	+	0.154508i
$5$	−4.68874	−	1.73657i	−0.937749	−	0.347314i
$5$	−4.68874	−	1.73657i	−0.937749	−	0.347314i
$6$	1.10643	+	3.40526i	0.184406	+	0.567543i
$7$	−6.58346	−	6.58346i	−0.940495	−	0.940495i	0.0578317	−	0.998326i	$-0.481581\pi$
$7$	−6.58346	−	6.58346i	−0.940495	−	0.940495i	−0.998326	+	0.0578317i	$0.981581\pi$
$8$	−2.52015	−	1.28408i	−0.315018	−	0.160510i
$9$	1.52238	−	2.09537i	0.169153	−	0.232819i
$10$	6.16506	+	3.46295i	0.616506	+	0.346295i
$11$	−3.81477	+	2.77159i	−0.346797	+	0.251963i	−0.747524	−	0.664235i	$-0.768758\pi$
$11$	−3.81477	+	2.77159i	−0.346797	+	0.251963i	0.400727	+	0.916198i	$0.368758\pi$
$12$	−0.792120	−	5.00125i	−0.0660100	−	0.416771i
$13$	17.5244	−	2.77559i	1.34803	−	0.213507i	0.559668	−	0.828717i	$-0.310929\pi$
$13$	17.5244	−	2.77559i	1.34803	−	0.213507i	0.788363	+	0.615210i	$0.210929\pi$
$14$	7.73932	+	10.6523i	0.552809	+	0.760876i
$15$	1.47185	+	12.5731i	0.0981235	+	0.838208i
$16$	3.23607	+	2.35114i	0.202254	+	0.146946i
$17$	−7.44532	+	14.6123i	−0.437960	+	0.859545i	0.561525	+	0.827460i	$0.310215\pi$
$17$	−7.44532	+	14.6123i	−0.437960	+	0.859545i	−0.999485	+	0.0320852i	$0.989785\pi$
$18$	−2.59002	+	2.59002i	−0.143890	+	0.143890i
$19$	16.0908	−	5.22822i	0.846885	−	0.275170i	0.146744	−	0.989174i	$-0.453121\pi$
$19$	16.0908	−	5.22822i	0.846885	−	0.275170i	0.700141	+	0.714005i	$0.253121\pi$
$20$	−7.84526	−	6.20096i	−0.392263	−	0.310048i
$21$	−7.28417	+	22.4184i	−0.346865	+	1.06754i
$22$	5.94165	−	3.02742i	0.270075	−	0.137610i
$23$	5.91002	−	37.3144i	0.256957	−	1.62237i	−0.435003	−	0.900429i	$-0.643253\pi$
$23$	5.91002	−	37.3144i	0.256957	−	1.62237i	0.691960	−	0.721936i	$-0.256747\pi$
$24$			7.16099i			0.298375i
$25$	18.9686	+	16.2847i	0.758745	+	0.651387i
$26$	−25.0922			−0.965084
$27$	−28.9823	−	4.59034i	−1.07342	−	0.170013i
$28$	−8.45369	−	16.5913i	−0.301917	−	0.592546i
$29$	−1.46851	−	0.477149i	−0.0506384	−	0.0164534i	0.283588	−	0.958946i	$-0.408475\pi$
$29$	−1.46851	−	0.477149i	−0.0506384	−	0.0164534i	−0.334227	+	0.942493i	$0.608475\pi$
$30$	0.725684	−	17.8878i	0.0241895	−	0.596259i
$31$	−9.29144	−	28.5961i	−0.299724	−	0.922456i	−0.981594	−	0.190982i	$-0.938833\pi$
$31$	−9.29144	−	28.5961i	−0.299724	−	0.922456i	0.681870	−	0.731474i	$-0.261167\pi$
$32$	−4.00000	−	4.00000i	−0.125000	−	0.125000i
$33$	10.6370	+	5.41983i	0.322334	+	0.164237i
$34$	13.6323	−	18.7633i	0.400951	−	0.551862i
$35$	19.4355	+	42.3008i	0.555300	+	1.20859i
$36$	4.19074	−	3.04475i	0.116409	−	0.0845764i
$37$	1.26903	+	8.01234i	0.0342981	+	0.216550i	0.998885	−	0.0472168i	$-0.0150352\pi$
$37$	1.26903	+	8.01234i	0.0342981	+	0.216550i	−0.964587	+	0.263766i	$0.915035\pi$
$38$	−23.6323	+	3.74300i	−0.621904	+	0.0984999i
$39$	−26.4040	−	36.3420i	−0.677027	−	0.931847i
$40$	9.58643	+	10.3971i	0.239661	+	0.259928i
$41$	−30.0830	−	21.8566i	−0.733733	−	0.533088i	0.157009	−	0.987597i	$-0.449815\pi$
$41$	−30.0830	−	21.8566i	−0.733733	−	0.533088i	−0.890742	+	0.454509i	$0.849815\pi$
$42$	15.1342	−	29.7025i	0.360338	−	0.707203i
$43$	−25.9880	+	25.9880i	−0.604371	+	0.604371i	−0.941470	−	0.337098i	$-0.890555\pi$
$43$	−25.9880	+	25.9880i	−0.604371	+	0.604371i	0.337098	+	0.941470i	$0.390555\pi$
$44$	−8.96907	+	2.91423i	−0.203842	+	0.0662324i
$45$	−10.7768	+	7.18094i	−0.239484	+	0.159576i
$46$	−16.5103	+	50.8134i	−0.358919	+	1.10464i
$47$	41.1918	−	20.9883i	0.876421	−	0.446559i	0.0429212	−	0.999078i	$-0.486334\pi$
$47$	41.1918	−	20.9883i	0.876421	−	0.446559i	0.833500	+	0.552520i	$0.186334\pi$
$48$	1.58424	−	10.0025i	0.0330050	−	0.208385i
$49$			37.6840i			0.769060i
$50$	−22.8927	−	26.9429i	−0.457855	−	0.538859i
$51$	41.5207			0.814132
$52$	35.0488	+	5.55119i	0.674016	+	0.106754i
$53$	37.0947	+	72.8025i	0.699900	+	1.37363i	0.917556	+	0.397606i	$0.130159\pi$
$53$	37.0947	+	72.8025i	0.699900	+	1.37363i	−0.217656	+	0.976026i	$0.569841\pi$
$54$	39.4670	+	12.8236i	0.730870	+	0.237474i
$55$	22.6996	−	6.37067i	0.412719	−	0.115830i
$56$	8.13761	+	25.0450i	0.145314	+	0.447232i
$57$	−30.2890	−	30.2890i	−0.531386	−	0.531386i
$58$	1.94566	+	0.991364i	0.0335459	+	0.0170925i
$59$	24.7807	−	34.1077i	0.420012	−	0.578097i	−0.545612	−	0.838038i	$-0.683703\pi$
$59$	24.7807	−	34.1077i	0.420012	−	0.578097i	0.965625	+	0.259940i	$0.0837029\pi$
$60$	−4.97098	+	24.8251i	−0.0828497	+	0.413752i
$61$	96.0793	−	69.8057i	1.57507	−	1.14436i	0.652983	−	0.757372i	$-0.273517\pi$
$61$	96.0793	−	69.8057i	1.57507	−	1.14436i	0.922087	−	0.386983i	$-0.126483\pi$
$62$	6.65194	+	41.9987i	0.107289	+	0.677398i
$63$	−23.8173	+	3.77229i	−0.378052	+	0.0598776i
$64$	4.70228	+	6.47214i	0.0734732	+	0.101127i
$65$	−86.9875	−	17.4184i	−1.33827	−	0.267975i
$66$	−13.6588	−	9.92368i	−0.206951	−	0.150359i
$67$	−39.7150	+	77.9450i	−0.592761	+	1.16336i	0.378558	+	0.925577i	$0.376420\pi$
$67$	−39.7150	+	77.9450i	−0.592761	+	1.16336i	−0.971319	+	0.237781i	$0.923580\pi$
$68$	−23.1927	+	23.1927i	−0.341069	+	0.341069i
$69$	−90.9685	+	29.5575i	−1.31838	+	0.428369i
$70$	−17.7893	−	63.3856i	−0.254133	−	0.905509i
$71$	−5.14879	+	15.8463i	−0.0725181	+	0.223188i	−0.980746	−	0.195288i	$-0.937436\pi$
$71$	−5.14879	+	15.8463i	−0.0725181	+	0.223188i	0.908228	+	0.418476i	$0.137436\pi$
$72$	−6.52723	+	3.32579i	−0.0906560	+	0.0461915i
$73$	9.91177	−	62.5804i	0.135778	−	0.857266i	−0.821944	−	0.569569i	$-0.807110\pi$
$73$	9.91177	−	62.5804i	0.135778	−	0.857266i	0.957721	−	0.287697i	$-0.0928898\pi$
$74$		−	11.4724i		−	0.155032i
$75$	14.9330	−	61.5081i	0.199106	−	0.820108i
$76$	33.8378			0.445234
$77$	43.3611	+	6.86772i	0.563131	+	0.0891912i
$78$	28.8412	+	56.6041i	0.369759	+	0.725693i
$79$	−19.2036	−	6.23964i	−0.243084	−	0.0789827i	0.184941	−	0.982750i	$-0.440791\pi$
$79$	−19.2036	−	6.23964i	−0.243084	−	0.0789827i	−0.428025	+	0.903767i	$0.640791\pi$
$80$	−11.0902	−	16.6436i	−0.138627	−	0.208045i
$81$	15.7542	+	48.4864i	0.194496	+	0.598598i
$82$	37.1847	+	37.1847i	0.453472	+	0.453472i
$83$	22.1438	+	11.2828i	0.266793	+	0.135938i	0.582270	−	0.812995i	$-0.302165\pi$
$83$	22.1438	+	11.2828i	0.266793	+	0.135938i	−0.315477	+	0.948933i	$0.602165\pi$
$84$	−27.7106	+	38.1404i	−0.329888	+	0.454052i
$85$	60.2844	−	55.5838i	0.709229	−	0.653927i
$86$	42.0494	−	30.5507i	0.488947	−	0.355241i
$87$	0.611550	+	3.86118i	0.00702931	+	0.0443813i
$88$	13.1727	−	2.08636i	0.149690	−	0.0237086i
$89$	−39.7082	−	54.6536i	−0.446159	−	0.614085i	0.525408	−	0.850851i	$-0.323913\pi$
$89$	−39.7082	−	54.6536i	−0.446159	−	0.614085i	−0.971567	+	0.236765i	$0.923913\pi$
$90$	16.6417	−	7.64618i	0.184908	−	0.0849576i
$91$	−133.644	−	97.0982i	−1.46862	−	1.06701i
$92$	34.3031	−	67.3236i	0.372860	−	0.731778i
$93$	−53.8287	+	53.8287i	−0.578804	+	0.578804i
$94$	−62.1801	+	20.2035i	−0.661490	+	0.214931i
$95$	−84.5249	−	3.42907i	−0.889736	−	0.0360955i
$96$	−4.42574	+	13.6210i	−0.0461014	+	0.141886i
$97$	−26.2088	+	13.3540i	−0.270194	+	0.137671i	−0.583839	−	0.811870i	$-0.698450\pi$
$97$	−26.2088	+	13.3540i	−0.270194	+	0.137671i	0.313645	+	0.949540i	$0.398450\pi$
$98$	8.33689	−	52.6370i	0.0850703	−	0.537113i
$99$			12.2128i			0.123361i
$100$	26.0160	+	42.6986i	0.260160	+	0.426986i
$101$	140.710			1.39317			0.696586	−	0.717474i	$-0.254702\pi$
$101$	140.710			1.39317			0.696586	+	0.717474i	$0.254702\pi$
$102$	−57.9962	−	9.18570i	−0.568591	−	0.0900559i
$103$	−16.8755	−	33.1201i	−0.163840	−	0.321554i	0.794461	−	0.607316i	$-0.207754\pi$
$103$	−16.8755	−	33.1201i	−0.163840	−	0.321554i	−0.958301	+	0.285761i	$0.907754\pi$
$104$	−47.7282	−	15.5078i	−0.458925	−	0.149114i
$105$	73.0847	−	92.4645i	0.696045	−	0.880614i
$106$	−35.7078	−	109.897i	−0.336866	−	1.03677i
$107$	93.0390	+	93.0390i	0.869523	+	0.869523i	0.992420	−	0.122896i	$-0.0392183\pi$
$107$	93.0390	+	93.0390i	0.869523	+	0.869523i	−0.122896	+	0.992420i	$0.539218\pi$
$108$	−52.2906	−	26.6434i	−0.484172	−	0.246698i
$109$	−110.706	+	152.374i	−1.01565	+	1.39793i	−0.100448	+	0.994942i	$0.532028\pi$
$109$	−110.706	+	152.374i	−1.01565	+	1.39793i	−0.915206	+	0.402986i	$0.867972\pi$
$110$	−33.1162	+	3.87670i	−0.301056	+	0.0352427i
$111$	16.6160	−	12.0722i	0.149693	−	0.108759i
$112$	−5.82588	−	36.7832i	−0.0520168	−	0.328421i
$113$	158.222	−	25.0599i	1.40020	−	0.221769i	0.589752	−	0.807585i	$-0.299226\pi$
$113$	158.222	−	25.0599i	1.40020	−	0.221769i	0.810445	+	0.585815i	$0.199226\pi$
$114$	35.6069	+	49.0087i	0.312341	+	0.429901i
$115$	−92.5097	+	164.694i	−0.804432	+	1.43213i
$116$	−2.49838	−	1.81518i	−0.0215378	−	0.0156481i
$117$	20.8628	−	40.9456i	0.178315	−	0.349962i
$118$	−42.1595	+	42.1595i	−0.357284	+	0.357284i
$119$	145.215	−	47.1833i	1.22030	−	0.396498i
$120$	12.4356	−	33.5761i	0.103630	−	0.279801i
$121$	−30.5203	+	93.9318i	−0.252234	+	0.776296i
$122$	−149.647	+	76.2489i	−1.22661	+	0.624991i
$123$	−14.7274	+	92.9849i	−0.119735	+	0.755975i
$124$		−	60.1355i		−	0.484964i
$125$	−60.6595	−	109.295i	−0.485276	−	0.874361i
$126$	34.1026			0.270655
$127$	115.861	+	18.3506i	0.912294	+	0.144493i	0.594899	−	0.803800i	$-0.297192\pi$
$127$	115.861	+	18.3506i	0.912294	+	0.144493i	0.317395	+	0.948293i	$0.397192\pi$
$128$	−5.13632	−	10.0806i	−0.0401275	−	0.0787546i
$129$	88.4957	+	28.7540i	0.686013	+	0.222899i
$130$	117.651	+	43.5744i	0.905006	+	0.335188i
$131$	54.0155	+	166.243i	0.412332	+	1.26903i	0.914615	+	0.404325i	$0.132494\pi$
$131$	54.0155	+	166.243i	0.412332	+	1.26903i	−0.502283	+	0.864703i	$0.667506\pi$
$132$	16.8832	+	16.8832i	0.127903	+	0.127903i
$133$	−140.353	−	71.5135i	−1.05529	−	0.537695i
$134$	72.7178	−	100.088i	0.542671	−	0.746922i
$135$	127.919	+	71.8527i	0.947548	+	0.532243i
$136$	37.5266	−	27.2647i	0.275931	−	0.200476i
$137$	−9.54211	−	60.2465i	−0.0696505	−	0.439756i	−0.997728	−	0.0673690i	$-0.978540\pi$
$137$	−9.54211	−	60.2465i	−0.0696505	−	0.439756i	0.928078	−	0.372387i	$-0.121460\pi$
$138$	133.604	−	21.1608i	0.968146	−	0.153339i
$139$	45.5691	+	62.7205i	0.327835	+	0.451227i	0.940839	−	0.338853i	$-0.110039\pi$
$139$	45.5691	+	62.7205i	0.327835	+	0.451227i	−0.613004	+	0.790080i	$0.710039\pi$
$140$	10.8252	+	92.4728i	0.0773228	+	0.660520i
$141$	−94.6925	−	68.7982i	−0.671578	−	0.487930i
$142$	10.6976	−	20.9951i	0.0753349	−	0.147853i
$143$	−59.1588	+	59.1588i	−0.413698	+	0.413698i
$144$	9.85302	−	3.20144i	0.0684237	−	0.0222322i
$145$	6.05688	+	4.78741i	0.0417716	+	0.0330166i
$146$	−27.6896	+	85.2197i	−0.189654	+	0.583697i
$147$	85.0092	−	43.3143i	0.578294	−	0.294655i
$148$	−2.53806	+	16.0247i	−0.0171490	+	0.108275i
$149$		−	146.792i		−	0.985181i	−0.870261	−	0.492590i	$-0.836050\pi$
$149$		−	146.792i		−	0.985181i	0.870261	−	0.492590i	$-0.163950\pi$
$150$	−34.4660	+	82.6110i	−0.229773	+	0.550740i
$151$	−81.4983			−0.539724			−0.269862	−	0.962899i	$-0.586978\pi$
$151$	−81.4983			−0.539724			−0.269862	+	0.962899i	$0.586978\pi$
$152$	−47.2647	−	7.48599i	−0.310952	−	0.0492499i
$153$	19.2835	+	37.8460i	0.126036	+	0.247360i
$154$	−59.0475	−	19.1857i	−0.383425	−	0.124582i
$155$	−6.09404	+	150.215i	−0.0393164	+	0.969130i
$156$	−27.7629	−	85.4453i	−0.177967	−	0.547726i
$157$	−211.160	−	211.160i	−1.34497	−	1.34497i	−0.891033	−	0.453938i	$-0.850019\pi$
$157$	−211.160	−	211.160i	−1.34497	−	1.34497i	−0.453938	−	0.891033i	$-0.649981\pi$
$158$	25.4433	+	12.9640i	0.161033	+	0.0820506i
$159$	121.594	−	167.360i	0.764742	−	1.05258i
$160$	11.8087	+	25.7013i	0.0738043	+	0.160633i
$161$	−284.566	+	206.750i	−1.76749	+	1.28416i
$162$	−11.2788	−	71.2113i	−0.0696219	−	0.439576i
$163$	−84.8146	+	13.4333i	−0.520335	+	0.0824129i	−0.411077	−	0.911601i	$-0.634847\pi$
$163$	−84.8146	+	13.4333i	−0.520335	+	0.0824129i	−0.109258	+	0.994013i	$0.534847\pi$
$164$	−43.7132	−	60.1661i	−0.266544	−	0.366866i
$165$	−40.4623	−	43.8842i	−0.245226	−	0.265965i
$166$	−28.4344	−	20.6588i	−0.171291	−	0.124451i
$167$	17.8505	−	35.0337i	0.106889	−	0.209782i	−0.831366	−	0.555725i	$-0.812441\pi$
$167$	17.8505	−	35.0337i	0.106889	−	0.209782i	0.938256	+	0.345943i	$0.112441\pi$
$168$	47.1441	−	47.1441i	0.280620	−	0.280620i
$169$	138.672	−	45.0574i	0.820546	−	0.266612i
$170$	−96.5023	+	64.3028i	−0.567661	+	0.378252i
$171$	13.5412	−	41.6755i	0.0791883	−	0.243717i
$172$	−65.4935	+	33.3706i	−0.380776	+	0.194015i
$173$	35.6189	−	224.889i	0.205889	−	1.29993i	−0.640742	−	0.767756i	$-0.721373\pi$
$173$	35.6189	−	224.889i	0.205889	−	1.29993i	0.846632	−	0.532179i	$-0.178627\pi$
$174$		−	5.52860i		−	0.0317735i
$175$	−17.6697	−	232.089i	−0.100970	−	1.32622i
$176$	−18.8613			−0.107166
$177$	−105.425	−	16.6977i	−0.595622	−	0.0943372i
$178$	43.3733	+	85.1250i	0.243670	+	0.478230i
$179$	−7.90838	−	2.56959i	−0.0441809	−	0.0143552i	0.286843	−	0.957978i	$-0.407394\pi$
$179$	−7.90838	−	2.56959i	−0.0441809	−	0.0143552i	−0.331024	+	0.943622i	$0.607394\pi$
$180$	−24.9367	+	6.99853i	−0.138537	+	0.0388807i
$181$	33.4318	+	102.892i	0.184706	+	0.568466i	0.999943	−	0.0106608i	$-0.00339351\pi$
$181$	33.4318	+	102.892i	0.184706	+	0.568466i	−0.815237	+	0.579127i	$0.803394\pi$
$182$	165.193	+	165.193i	0.907656	+	0.907656i
$183$	−267.905	−	136.505i	−1.46396	−	0.745927i
$184$	−62.8088	+	86.4488i	−0.341352	+	0.469831i
$185$	7.96385	−	39.7716i	0.0430478	−	0.214981i
$186$	87.0967	−	63.2795i	0.468262	−	0.340212i
$187$	−12.0971	−	76.3778i	−0.0646902	−	0.408438i
$188$	91.3229	−	14.4641i	0.485760	−	0.0769368i
$189$	160.583	+	221.024i	0.849647	+	1.16944i
$190$	117.306	+	23.4893i	0.617400	+	0.123628i
$191$	−185.233	−	134.580i	−0.969808	−	0.704607i	−0.0144000	−	0.999896i	$-0.504584\pi$
$191$	−185.233	−	134.580i	−0.969808	−	0.704607i	−0.955408	+	0.295290i	$0.904584\pi$
$192$	9.19528	−	18.0468i	0.0478921	−	0.0939935i
$193$	176.707	−	176.707i	0.915582	−	0.915582i	−0.0811226	−	0.996704i	$-0.525851\pi$
$193$	176.707	−	176.707i	0.915582	−	0.915582i	0.996704	+	0.0811226i	$0.0258505\pi$
$194$	39.5628	−	12.8547i	0.203932	−	0.0662616i
$195$	60.6912	+	216.251i	0.311237	+	1.10898i
$196$	−23.2900	+	71.6791i	−0.118826	+	0.365710i
$197$	−15.3892	+	7.84117i	−0.0781175	+	0.0398029i	−0.492613	−	0.870249i	$-0.663958\pi$
$197$	−15.3892	+	7.84117i	−0.0781175	+	0.0398029i	0.414495	+	0.910051i	$0.363958\pi$
$198$	2.70185	−	17.0588i	0.0136457	−	0.0861556i
$199$			266.747i			1.34044i	0.742164	+	0.670218i	$0.233800\pi$
$199$			266.747i			1.34044i	−0.742164	+	0.670218i	$0.766200\pi$
$200$	−26.8929	−	65.3970i	−0.134465	−	0.326985i
$201$	221.481			1.10189
$202$	−196.544	−	31.1296i	−0.972992	−	0.154107i
$203$	6.52661	+	12.8092i	0.0321508	+	0.0630995i
$204$	78.9771	+	25.6612i	0.387143	+	0.125790i
$205$	103.096	+	154.721i	0.502908	+	0.754739i
$206$	16.2446	+	49.9956i	0.0788571	+	0.242697i
$207$	−69.1902	−	69.1902i	−0.334252	−	0.334252i
$208$	63.2360	+	32.2203i	0.304019	+	0.154905i
$209$	−46.8923	+	64.5417i	−0.224365	+	0.308812i
$210$	−122.541	+	112.986i	−0.583529	+	0.538028i
$211$	200.960	−	146.006i	0.952419	−	0.691973i	0.00104087	−	0.999999i	$-0.499669\pi$
$211$	200.960	−	146.006i	0.952419	−	0.691973i	0.951378	+	0.308027i	$0.0996687\pi$
$212$	25.5639	+	161.404i	0.120585	+	0.761341i
$213$	41.6650	−	6.59908i	0.195610	−	0.0309816i
$214$	−109.374	−	150.540i	−0.511093	−	0.703459i
$215$	166.981	−	76.7209i	0.776655	−	0.356842i
$216$	67.1452	+	48.7839i	0.310858	+	0.225851i
$217$	−127.092	+	249.431i	−0.585676	+	1.14945i
$218$	188.345	−	188.345i	0.863967	−	0.863967i
$219$	−152.564	+	49.5712i	−0.696641	+	0.226352i
$220$	47.1144	+	1.91137i	0.214156	+	0.00868805i
$221$	−89.9171	+	276.736i	−0.406865	+	1.25220i
$222$	−25.8800	+	13.1865i	−0.116576	+	0.0593986i
$223$	−8.86348	+	55.9618i	−0.0397466	+	0.250950i	−0.999559	−	0.0296920i	$-0.990547\pi$
$223$	−8.86348	+	55.9618i	−0.0397466	+	0.250950i	0.959813	+	0.280642i	$0.0905474\pi$
$224$			52.6677i			0.235124i
$225$	62.9998	−	14.9549i	0.279999	−	0.0664662i
$226$	−226.549			−1.00243
$227$	152.356	+	24.1307i	0.671170	+	0.106303i	0.482713	−	0.875779i	$-0.339651\pi$
$227$	152.356	+	24.1307i	0.671170	+	0.106303i	0.188457	+	0.982081i	$0.439651\pi$
$228$	−38.8935	−	76.3328i	−0.170586	−	0.334793i
$229$	−80.9675	−	26.3079i	−0.353570	−	0.114882i	0.126847	−	0.991922i	$-0.459514\pi$
$229$	−80.9675	−	26.3079i	−0.353570	−	0.114882i	−0.480416	+	0.877041i	$0.659514\pi$
$230$	165.653	−	209.580i	0.720232	−	0.911215i
$231$	−34.3472	−	105.710i	−0.148689	−	0.457618i
$232$	3.08817	+	3.08817i	0.0133111	+	0.0133111i
$233$	49.0406	+	24.9874i	0.210475	+	0.107242i	0.556050	−	0.831149i	$-0.312316\pi$
$233$	49.0406	+	24.9874i	0.210475	+	0.107242i	−0.345575	+	0.938391i	$0.612316\pi$
$234$	−38.1997	+	52.5774i	−0.163247	+	0.224690i
$235$	−229.585	+	26.8761i	−0.976959	+	0.114366i
$236$	68.2155	−	49.5615i	0.289049	−	0.210006i
$237$	7.99719	+	50.4923i	0.0337434	+	0.213048i
$238$	−213.275	+	33.7795i	−0.896115	+	0.141931i
$239$	−8.97514	−	12.3532i	−0.0375529	−	0.0516871i	0.789828	−	0.613329i	$-0.210170\pi$
$239$	−8.97514	−	12.3532i	−0.0375529	−	0.0516871i	−0.827381	+	0.561642i	$0.810170\pi$
$240$	−24.7981	+	44.1480i	−0.103326	+	0.183950i
$241$	191.342	+	139.018i	0.793950	+	0.576839i	0.909133	−	0.416506i	$-0.136745\pi$
$241$	191.342	+	139.018i	0.793950	+	0.576839i	−0.115183	+	0.993344i	$0.536745\pi$
$242$	63.4115	−	124.452i	0.262031	−	0.514265i
$243$	−95.4714	+	95.4714i	−0.392886	+	0.392886i
$244$	225.896	−	73.3980i	0.925803	−	0.300812i
$245$	65.4409	−	176.690i	0.267106	−	0.721185i
$246$	41.1424	−	126.623i	0.167246	−	0.514729i
$247$	267.471	−	136.283i	1.08288	−	0.551753i
$248$	−13.3039	+	83.9974i	−0.0536447	+	0.338699i
$249$		−	62.9216i		−	0.252697i
$250$	60.5498	+	166.083i	0.242199	+	0.664334i
$251$	−68.4984			−0.272902			−0.136451	−	0.990647i	$-0.543570\pi$
$251$	−68.4984			−0.272902			−0.136451	+	0.990647i	$0.543570\pi$
$252$	−47.6346	−	7.54458i	−0.189026	−	0.0299388i
$253$	80.8750	+	158.726i	0.319664	+	0.627376i
$254$	−157.776	−	51.2644i	−0.621164	−	0.201828i
$255$	−194.680	−	72.1037i	−0.763451	−	0.282760i
$256$	4.94427	+	15.2169i	0.0193136	+	0.0594410i
$257$	8.28497	+	8.28497i	0.0322372	+	0.0322372i	0.723042	−	0.690804i	$-0.242743\pi$
$257$	8.28497	+	8.28497i	0.0322372	+	0.0322372i	−0.690804	+	0.723042i	$0.742743\pi$
$258$	−117.250	−	59.7417i	−0.454456	−	0.231557i
$259$	44.3943	−	61.1035i	0.171407	−	0.235921i
$260$	−154.695	−	86.8929i	−0.594980	−	0.334203i
$261$	−3.23543	+	2.35068i	−0.0123963	+	0.00900643i
$262$	−38.6708	−	244.158i	−0.147599	−	0.931901i
$263$	91.2822	−	14.4577i	0.347081	−	0.0549722i	0.0195395	−	0.999809i	$-0.493780\pi$
$263$	91.2822	−	14.4577i	0.347081	−	0.0549722i	0.327541	+	0.944837i	$0.393780\pi$
$264$	−19.8474	−	27.3176i	−0.0751794	−	0.103476i
$265$	−47.5008	−	405.770i	−0.179248	−	1.53121i
$266$	180.225	+	130.941i	0.677536	+	0.492259i
$267$	−77.6491	+	152.395i	−0.290820	+	0.570767i
$268$	−123.715	+	123.715i	−0.461623	+	0.461623i
$269$	−203.293	+	66.0538i	−0.755735	+	0.245553i	−0.661447	−	0.749992i	$-0.730057\pi$
$269$	−203.293	+	66.0538i	−0.755735	+	0.245553i	−0.0942877	+	0.995545i	$0.530057\pi$
$270$	−162.781	−	128.664i	−0.602894	−	0.476533i
$271$	119.535	−	367.892i	0.441090	−	1.35754i	−0.445625	−	0.895220i	$-0.647019\pi$
$271$	119.535	−	367.892i	0.441090	−	1.35754i	0.886715	−	0.462316i	$-0.152981\pi$
$272$	−58.4490	+	29.7813i	−0.214886	+	0.109490i
$273$	−65.4265	+	413.086i	−0.239657	+	1.51314i
$274$			86.2635i			0.314830i
$275$	−117.496	−	9.54900i	−0.427256	−	0.0347237i
$276$	−191.300			−0.693116
$277$	35.9094	+	5.68749i	0.129637	+	0.0205324i	0.220916	−	0.975293i	$-0.429095\pi$
$277$	35.9094	+	5.68749i	0.129637	+	0.0205324i	−0.0912789	+	0.995825i	$0.529095\pi$
$278$	−49.7753	−	97.6895i	−0.179048	−	0.351401i
$279$	−74.0645	−	24.0650i	−0.265464	−	0.0862545i
$280$	5.33726	−	131.561i	0.0190617	−	0.469861i
$281$	−53.3063	−	164.060i	−0.189702	−	0.583843i	0.810295	−	0.586022i	$-0.199307\pi$
$281$	−53.3063	−	164.060i	−0.189702	−	0.583843i	−0.999998	+	0.00217821i	$0.999307\pi$
$282$	117.046	+	117.046i	0.415058	+	0.415058i
$283$	290.318	+	147.924i	1.02586	+	0.522701i	0.884148	−	0.467207i	$-0.154740\pi$
$283$	290.318	+	147.924i	1.02586	+	0.522701i	0.141710	+	0.989908i	$0.454740\pi$
$284$	−19.5872	+	26.9594i	−0.0689688	+	0.0949275i
$285$	89.4184	+	194.617i	0.313749	+	0.682865i
$286$	95.7209	−	69.5453i	0.334689	−	0.243165i
$287$	54.1584	+	341.943i	0.188705	+	1.19144i
$288$	−14.4710	+	2.29198i	−0.0502465	+	0.00795826i
$289$	11.7845	+	16.2200i	0.0407769	+	0.0561246i
$290$	−7.40113	−	8.02703i	−0.0255211	−	0.0276794i
$291$	60.2493	+	43.7737i	0.207042	+	0.150425i
$292$	57.5301	−	112.909i	0.197021	−	0.386676i
$293$	68.8337	−	68.8337i	0.234927	−	0.234927i	−0.579818	−	0.814746i	$-0.696877\pi$
$293$	68.8337	−	68.8337i	0.234927	−	0.234927i	0.814746	+	0.579818i	$0.196877\pi$
$294$	−128.323	+	41.6948i	−0.436474	+	0.141819i
$295$	−175.421	+	116.889i	−0.594648	+	0.396234i
$296$	7.09033	−	21.8218i	0.0239538	−	0.0737223i
$297$	123.283	−	62.8160i	0.415095	−	0.211502i
$298$	−32.4750	+	205.039i	−0.108977	+	0.688051i
$299$		−	670.316i		−	2.24186i
$300$	66.4183	−	107.766i	0.221394	−	0.359221i
$301$	342.182			1.13682
$302$	113.837	+	18.0300i	0.376944	+	0.0597021i
$303$	−161.734	−	317.421i	−0.533775	−	1.04759i
$304$	64.3633	+	20.9129i	0.211721	+	0.0687924i
$305$	−571.714	+	160.452i	−1.87447	+	0.526073i
$306$	−18.5625	−	57.1296i	−0.0606618	−	0.186698i
$307$	−196.445	−	196.445i	−0.639887	−	0.639887i	0.310641	−	0.950527i	$-0.399456\pi$
$307$	−196.445	−	196.445i	−0.639887	−	0.639887i	−0.950527	+	0.310641i	$0.899456\pi$
$308$	78.2332	+	39.8618i	0.254004	+	0.129421i
$309$	−55.3169	+	76.1372i	−0.179019	+	0.246399i
$310$	41.7445	−	208.473i	0.134660	−	0.672492i
$311$	−194.521	+	141.328i	−0.625470	+	0.454431i	−0.854828	−	0.518911i	$-0.826337\pi$
$311$	−194.521	+	141.328i	−0.625470	+	0.454431i	0.229358	+	0.973342i	$0.426337\pi$
$312$	19.8760	+	125.492i	0.0637052	+	0.402218i
$313$	−203.623	+	32.2507i	−0.650552	+	0.103037i	−0.472984	−	0.881071i	$-0.656823\pi$
$313$	−203.623	+	32.2507i	−0.650552	+	0.103037i	−0.177568	+	0.984108i	$0.556823\pi$
$314$	248.234	+	341.665i	0.790554	+	1.08810i
$315$	118.224	+	23.6731i	0.375314	+	0.0751529i
$316$	−32.6712	−	23.7370i	−0.103390	−	0.0751170i
$317$	−15.7136	+	30.8396i	−0.0495696	+	0.0972858i	−0.914463	−	0.404671i	$-0.867386\pi$
$317$	−15.7136	+	30.8396i	−0.0495696	+	0.0972858i	0.864893	+	0.501956i	$0.167386\pi$
$318$	−206.868	+	206.868i	−0.650529	+	0.650529i
$319$	6.92450	−	2.24991i	0.0217069	−	0.00705300i
$320$	−10.8085	−	38.5120i	−0.0337764	−	0.120350i
$321$	102.942	−	316.822i	0.320690	−	0.986983i
$322$	443.222	−	225.833i	1.37647	−	0.701345i
$323$	−43.4051	+	274.049i	−0.134381	+	0.848449i
$324$			101.963i			0.314701i
$325$	377.614	+	232.730i	1.16189	+	0.716093i
$326$	121.441			0.372519
$327$	470.979	+	74.5958i	1.44030	+	0.228122i
$328$	47.7481	+	93.7109i	0.145573	+	0.285704i
$329$	−409.360	−	133.009i	−1.24426	−	0.404283i
$330$	46.8093	+	70.2491i	0.141846	+	0.212876i
$331$	7.67891	+	23.6332i	0.0231991	+	0.0713995i	0.961986	−	0.273099i	$-0.0880488\pi$
$331$	7.67891	+	23.6332i	0.0231991	+	0.0713995i	−0.938787	+	0.344499i	$0.888049\pi$
$332$	35.1468	+	35.1468i	0.105864	+	0.105864i
$333$	18.7207	+	9.53870i	0.0562185	+	0.0286447i
$334$	−32.6842	+	44.9860i	−0.0978570	+	0.134689i
$335$	321.570	−	296.496i	0.959912	−	0.885063i
$336$	−76.2808	+	55.4213i	−0.227026	+	0.164944i
$337$	39.5913	+	249.970i	0.117482	+	0.741750i	0.974153	+	0.225888i	$0.0725284\pi$
$337$	39.5913	+	249.970i	0.117482	+	0.741750i	−0.856672	+	0.515862i	$0.827472\pi$
$338$	−203.666	+	32.2575i	−0.602562	+	0.0954364i
$339$	−238.394	−	328.121i	−0.703226	−	0.967907i
$340$	149.021	−	68.4689i	0.438296	−	0.201379i
$341$	114.702	+	83.3356i	0.336368	+	0.244386i
$342$	−28.1343	+	55.2167i	−0.0822641	+	0.161452i
$343$	−74.4988	+	74.4988i	−0.217198	+	0.217198i
$344$	98.8641	−	32.1229i	0.287396	−	0.0933805i
$345$	477.857	+	19.3860i	1.38509	+	0.0561914i
$346$	−99.5050	+	306.245i	−0.287587	+	0.885101i
$347$	−185.879	+	94.7100i	−0.535674	+	0.272939i	−0.700830	−	0.713328i	$-0.747187\pi$
$347$	−185.879	+	94.7100i	−0.535674	+	0.272939i	0.165157	+	0.986267i	$0.447187\pi$
$348$	−1.22310	+	7.72235i	−0.00351466	+	0.0221907i
$349$			198.448i			0.568620i	0.958732	+	0.284310i	$0.0917645\pi$
$349$			198.448i			0.568620i	−0.958732	+	0.284310i	$0.908235\pi$
$350$	−26.6644	+	328.091i	−0.0761840	+	0.937404i
$351$	−520.638			−1.48330
$352$	26.3455	+	4.17271i	0.0748451	+	0.0118543i
$353$	82.9237	+	162.747i	0.234911	+	0.461039i	0.978126	−	0.208014i	$-0.0666999\pi$
$353$	82.9237	+	162.747i	0.234911	+	0.461039i	−0.743215	+	0.669053i	$0.766700\pi$
$354$	143.564	+	46.6467i	0.405548	+	0.131770i
$355$	51.6597	−	65.3582i	0.145520	−	0.184108i
$356$	−41.7516	−	128.498i	−0.117280	−	0.360950i
$357$	−273.350	−	273.350i	−0.765687	−	0.765687i
$358$	10.4780	+	5.33879i	0.0292681	+	0.0149128i
$359$	−114.552	+	157.667i	−0.319086	+	0.439184i	−0.938188	−	0.346127i	$-0.887497\pi$
$359$	−114.552	+	157.667i	−0.319086	+	0.439184i	0.619102	+	0.785310i	$0.287497\pi$
$360$	36.3800	−	4.25877i	0.101055	−	0.0118299i
$361$	−60.4750	+	43.9376i	−0.167521	+	0.121711i
$362$	−23.9345	−	151.116i	−0.0661174	−	0.417449i
$363$	246.976	−	39.1172i	0.680375	−	0.107761i
$364$	−194.196	−	267.289i	−0.533507	−	0.734309i
$365$	−155.149	+	276.211i	−0.425066	+	0.756743i
$366$	344.012	+	249.939i	0.939922	+	0.682894i
$367$	−62.4163	+	122.499i	−0.170072	+	0.333785i	−0.960273	−	0.279063i	$-0.909976\pi$
$367$	−62.4163	+	122.499i	−0.170072	+	0.333785i	0.790201	+	0.612848i	$0.209976\pi$
$368$	106.857	−	106.857i	0.290371	−	0.290371i
$369$	−91.5954	+	29.7611i	−0.248226	+	0.0806535i
$370$	−19.9227	+	53.7911i	−0.0538450	+	0.145381i
$371$	235.081	−	723.504i	0.633641	−	1.95015i
$372$	−135.656	+	69.1204i	−0.364668	+	0.185807i
$373$	62.8520	−	396.832i	0.168504	−	1.06389i	−0.747951	−	0.663754i	$-0.768962\pi$
$373$	62.8520	−	396.832i	0.168504	−	1.06389i	0.916455	−	0.400139i	$-0.131038\pi$
$374$			109.361i			0.292409i
$375$	−176.830	+	262.463i	−0.471547	+	0.699902i
$376$	−130.760			−0.347766
$377$	−27.0592	−	4.28575i	−0.0717750	−	0.0113680i
$378$	−175.406	−	344.253i	−0.464036	−	0.910722i
$379$	509.120	+	165.423i	1.34332	+	0.436473i	0.890442	−	0.455097i	$-0.150396\pi$
$379$	509.120	+	165.423i	1.34332	+	0.436473i	0.452883	+	0.891570i	$0.350396\pi$
$380$	−158.657	−	58.7618i	−0.417518	−	0.154636i
$381$	−91.7760	−	282.458i	−0.240882	−	0.741359i
$382$	228.961	+	228.961i	0.599374	+	0.599374i
$383$	412.878	+	210.372i	1.07801	+	0.549274i	0.900505	−	0.434846i	$-0.143197\pi$
$383$	412.878	+	210.372i	1.07801	+	0.549274i	0.177505	+	0.984120i	$0.443197\pi$
$384$	−16.8365	+	23.1735i	−0.0438451	+	0.0603476i
$385$	−191.383	−	107.501i	−0.497098	−	0.279222i
$386$	−285.918	+	207.732i	−0.740721	+	0.538165i
$387$	14.8910	+	94.0178i	0.0384779	+	0.242940i
$388$	−58.1053	+	9.20298i	−0.149756	+	0.0237190i
$389$	−19.0616	−	26.2360i	−0.0490015	−	0.0674448i	0.783813	−	0.620997i	$-0.213272\pi$
$389$	−19.0616	−	26.2360i	−0.0490015	−	0.0674448i	−0.832815	+	0.553552i	$0.813272\pi$
$390$	−36.9320	−	315.487i	−0.0946974	−	0.808940i
$391$	501.246	+	364.176i	1.28196	+	0.931397i
$392$	48.3892	−	94.9691i	0.123442	−	0.242268i
$393$	312.932	−	312.932i	0.796264	−	0.796264i
$394$	23.2303	−	7.54799i	0.0589602	−	0.0191573i
$395$	79.2053	+	62.6045i	0.200520	+	0.158492i
$396$	−7.54790	+	23.2301i	−0.0190604	+	0.0586618i
$397$	−145.742	+	74.2593i	−0.367109	+	0.187051i	−0.627807	−	0.778369i	$-0.716047\pi$
$397$	−145.742	+	74.2593i	−0.367109	+	0.187051i	0.260698	+	0.965420i	$0.416047\pi$
$398$	59.0129	−	372.593i	0.148274	−	0.936163i
$399$			398.813i			0.999532i
$400$	23.0962	+	97.2963i	0.0577405	+	0.243241i
$401$	−461.933			−1.15195			−0.575977	−	0.817466i	$-0.695378\pi$
$401$	−461.933			−1.15195			−0.575977	+	0.817466i	$0.695378\pi$
$402$	−309.365	−	48.9985i	−0.769564	−	0.121887i
$403$	−242.198	−	475.341i	−0.600988	−	1.17951i
$404$	267.647	+	86.9637i	0.662492	+	0.215257i
$405$	10.3328	−	254.699i	0.0255131	−	0.628885i
$406$	−6.28258	−	19.3358i	−0.0154743	−	0.0476251i
$407$	−27.0480	−	27.0480i	−0.0664570	−	0.0664570i
$408$	−104.638	−	53.3159i	−0.256466	−	0.130676i
$409$	152.579	−	210.007i	0.373054	−	0.513465i	−0.580674	−	0.814136i	$-0.697211\pi$
$409$	152.579	−	210.007i	0.373054	−	0.513465i	0.953728	+	0.300672i	$0.0972108\pi$
$410$	−109.776	−	238.923i	−0.267745	−	0.582740i
$411$	−124.939	+	90.7735i	−0.303988	+	0.220860i
$412$	−11.6298	−	73.4278i	−0.0282277	−	0.178223i
$413$	−387.690	+	61.4041i	−0.938717	+	0.148678i
$414$	81.3379	+	111.952i	0.196468	+	0.270416i
$415$	−84.2331	−	91.3566i	−0.202971	−	0.220136i
$416$	−81.2000	−	58.9952i	−0.195192	−	0.141815i
$417$	89.1101	−	174.888i	0.213693	−	0.419397i
$418$	79.7779	−	79.7779i	0.190856	−	0.190856i
$419$	−374.972	+	121.836i	−0.894922	+	0.290778i	−0.720139	−	0.693829i	$-0.755922\pi$
$419$	−374.972	+	121.836i	−0.894922	+	0.290778i	−0.174782	+	0.984607i	$0.555922\pi$
$420$	196.162	−	130.709i	0.467051	−	0.311212i
$421$	96.2390	−	296.193i	0.228596	−	0.703547i	−0.769310	−	0.638875i	$-0.779400\pi$
$421$	96.2390	−	296.193i	0.228596	−	0.703547i	0.997907	−	0.0646716i	$-0.0206000\pi$
$422$	−313.003	+	159.483i	−0.741713	+	0.377922i
$423$	18.7312	−	118.264i	0.0442818	−	0.279584i
$424$		−	231.105i		−	0.545060i
$425$	−379.184	+	155.930i	−0.892197	+	0.366894i
$426$	−59.6576			−0.140041
$427$	−1092.10	−	172.971i	−2.55760	−	0.405085i
$428$	119.469	+	234.472i	0.279134	+	0.547832i
$429$	201.451	+	65.4553i	0.469582	+	0.152577i
$430$	−250.212	+	70.2225i	−0.581889	+	0.163308i
$431$	223.411	+	687.587i	0.518354	+	1.59533i	0.777095	+	0.629383i	$0.216692\pi$
$431$	223.411	+	687.587i	0.518354	+	1.59533i	−0.258741	+	0.965947i	$0.583308\pi$
$432$	−82.9961	−	82.9961i	−0.192121	−	0.192121i
$433$	213.481	+	108.774i	0.493027	+	0.251210i	0.682783	−	0.730621i	$-0.260770\pi$
$433$	213.481	+	108.774i	0.493027	+	0.251210i	−0.189755	+	0.981831i	$0.560770\pi$
$434$	232.704	−	320.290i	0.536184	−	0.737994i
$435$	3.83781	−	19.1661i	0.00882255	−	0.0440599i
$436$	−304.748	+	221.413i	−0.698964	+	0.507827i
$437$	−99.9910	−	631.318i	−0.228812	−	1.44466i
$438$	224.069	−	35.4891i	0.511573	−	0.0810252i
$439$	43.7867	+	60.2673i	0.0997420	+	0.137283i	0.855971	−	0.517024i	$-0.172960\pi$
$439$	43.7867	+	60.2673i	0.0997420	+	0.137283i	−0.756229	+	0.654307i	$0.772960\pi$
$440$	−65.3867	−	13.0930i	−0.148606	−	0.0297568i
$441$	78.9618	+	57.3691i	0.179052	+	0.130089i
$442$	186.819	−	366.653i	0.422668	−	0.829533i
$443$	144.493	−	144.493i	0.326170	−	0.326170i	−0.524958	−	0.851128i	$-0.675919\pi$
$443$	144.493	−	144.493i	0.326170	−	0.326170i	0.851128	+	0.524958i	$0.175919\pi$
$444$	39.0664	−	12.6935i	0.0879875	−	0.0285889i
$445$	91.2715	+	325.213i	0.205104	+	0.730815i
$446$	24.7611	−	76.2067i	0.0555181	−	0.170867i
$447$	−331.140	+	168.724i	−0.740805	+	0.377459i
$448$	11.6518	−	73.5664i	0.0260084	−	0.164211i
$449$			63.0893i			0.140511i	0.997529	+	0.0702554i	$0.0223814\pi$
$449$			63.0893i			0.140511i	−0.997529	+	0.0702554i	$0.977619\pi$
$450$	−91.3068	+	6.95148i	−0.202904	+	0.0154477i
$451$	175.338			0.388775
$452$	316.444	+	50.1199i	0.700098	+	0.110885i
$453$	93.6750	+	183.848i	0.206788	+	0.405845i
$454$	−207.472	−	67.4118i	−0.456987	−	0.148484i
$455$	458.006	+	687.352i	1.00661	+	1.51066i
$456$	37.4393	+	115.226i	0.0821037	+	0.252689i
$457$	456.270	+	456.270i	0.998403	+	0.998403i	0.999999	−	0.00159596i	$-0.000508011\pi$
$457$	456.270	+	456.270i	0.998403	+	0.998403i	−0.00159596	+	0.999999i	$0.500508\pi$
$458$	107.275	+	54.6596i	0.234226	+	0.119344i
$459$	282.858	−	389.320i	0.616247	−	0.848192i
$460$	−277.751	+	256.093i	−0.603806	+	0.556725i
$461$	−279.602	+	203.143i	−0.606512	+	0.440656i	−0.848184	−	0.529701i	$-0.822304\pi$
$461$	−279.602	+	203.143i	−0.606512	+	0.440656i	0.241673	+	0.970358i	$0.422304\pi$
$462$	24.5899	+	155.254i	0.0532248	+	0.336048i
$463$	−704.232	+	111.539i	−1.52102	+	0.240906i	−0.860324	−	0.509748i	$-0.829739\pi$
$463$	−704.232	+	111.539i	−1.52102	+	0.240906i	−0.660696	+	0.750654i	$0.729739\pi$
$464$	−3.63036	−	4.99677i	−0.00782406	−	0.0107689i
$465$	345.867	−	158.912i	0.743799	−	0.341745i
$466$	−62.9720	−	45.7518i	−0.135133	−	0.0981799i
$467$	45.3195	−	88.9445i	0.0970438	−	0.190459i	−0.837381	−	0.546620i	$-0.815914\pi$
$467$	45.3195	−	88.9445i	0.0970438	−	0.190459i	0.934425	+	0.356160i	$0.115914\pi$
$468$	64.9892	−	64.9892i	0.138866	−	0.138866i
$469$	774.610	−	251.686i	1.65162	−	0.536644i
$470$	326.631	+	13.2510i	0.694960	+	0.0281936i
$471$	−233.635	+	719.055i	−0.496041	+	1.52666i
$472$	−106.248	+	54.1361i	−0.225102	+	0.114695i
$473$	27.1101	−	171.166i	0.0573152	−	0.361874i
$474$		−	72.2970i		−	0.152525i
$475$	390.361	+	162.862i	0.821812	+	0.342867i
$476$	305.377			0.641548
$477$	209.020	+	33.1055i	0.438197	+	0.0694037i
$478$	9.80358	+	19.2406i	0.0205096	+	0.0402523i
$479$	828.170	+	269.089i	1.72896	+	0.561772i	0.993298	−	0.115581i	$-0.0368731\pi$
$479$	828.170	+	269.089i	1.72896	+	0.561772i	0.735658	+	0.677353i	$0.236873\pi$
$480$	44.4050	−	56.1799i	0.0925105	−	0.117041i
$481$	44.4780	+	136.889i	0.0924698	+	0.284593i
$482$	−236.512	−	236.512i	−0.490688	−	0.490688i
$483$	793.478	+	404.297i	1.64281	+	0.837055i
$484$	−116.106	+	159.806i	−0.239889	+	0.330179i
$485$	146.077	−	17.1002i	0.301189	−	0.0352582i
$486$	154.476	−	112.233i	0.317852	−	0.230933i
$487$	−77.6661	−	490.364i	−0.159479	−	1.00691i	−0.929482	−	0.368868i	$-0.879745\pi$
$487$	−77.6661	−	490.364i	−0.159479	−	1.00691i	0.770003	−	0.638040i	$-0.220255\pi$
$488$	−331.770	+	52.5472i	−0.679856	+	0.107679i
$489$	127.790	+	175.888i	0.261330	+	0.359689i
$490$	−130.498	+	232.324i	−0.266321	+	0.474130i
$491$	135.584	+	98.5073i	0.276138	+	0.200626i	0.717231	−	0.696835i	$-0.245409\pi$
$491$	135.584	+	98.5073i	0.276138	+	0.200626i	−0.441093	+	0.897461i	$0.645409\pi$
$492$	−85.4809	+	167.766i	−0.173742	+	0.340987i
$493$	17.9058	−	17.9058i	0.0363200	−	0.0363200i
$494$	−403.754	+	131.188i	−0.817315	+	0.265562i
$495$	21.2083	−	57.2625i	0.0428451	−	0.115682i
$496$	37.1658	−	114.384i	0.0749310	−	0.230614i
$497$	138.221	−	70.4269i	0.278110	−	0.141704i
$498$	−13.9202	+	87.8890i	−0.0279523	+	0.176484i
$499$			199.265i			0.399328i	0.979864	+	0.199664i	$0.0639851\pi$
$499$			199.265i			0.399328i	−0.979864	+	0.199664i	$0.936015\pi$
$500$	−47.8332	−	245.381i	−0.0956664	−	0.490763i
$501$	−99.5481			−0.198699
$502$	95.6787	+	15.1540i	0.190595	+	0.0301873i
$503$	−361.401	−	709.290i	−0.718492	−	1.41012i	−0.904024	−	0.427481i	$-0.859401\pi$
$503$	−361.401	−	709.290i	−0.718492	−	1.41012i	0.185532	−	0.982638i	$-0.440599\pi$
$504$	64.8670	+	21.0766i	0.128704	+	0.0418186i
$505$	−659.754	−	244.354i	−1.30644	−	0.483868i
$506$	−77.8511	−	239.601i	−0.153856	−	0.473520i
$507$	−261.034	−	261.034i	−0.514860	−	0.514860i
$508$	209.040	+	106.511i	0.411496	+	0.209668i
$509$	99.1120	−	136.416i	0.194719	−	0.268008i	−0.700482	−	0.713670i	$-0.747032\pi$
$509$	99.1120	−	136.416i	0.194719	−	0.268008i	0.895201	+	0.445662i	$0.147032\pi$
$510$	255.978	+	143.784i	0.501917	+	0.281930i
$511$	−477.250	+	346.742i	−0.933952	+	0.678556i
$512$	−3.53971	−	22.3488i	−0.00691349	−	0.0436501i
$513$	−490.348	+	77.6635i	−0.955844	+	0.151391i
$514$	−9.73956	−	13.4054i	−0.0189486	−	0.0260805i
$515$	21.6096	+	184.597i	0.0419604	+	0.358441i
$516$	150.558	+	109.387i	0.291779	+	0.211990i
$517$	−98.9663	+	194.232i	−0.191424	+	0.375691i
$518$	−75.5281	+	75.5281i	−0.145807	+	0.145807i
$519$	−548.255	+	178.139i	−1.05637	+	0.343235i
$520$	196.855	+	155.596i	0.378567	+	0.299222i
$521$	279.151	−	859.137i	0.535798	−	1.64902i	−0.206121	−	0.978526i	$-0.566084\pi$
$521$	279.151	−	859.137i	0.535798	−	1.64902i	0.741919	−	0.670490i	$-0.233916\pi$
$522$	5.03930	−	2.56765i	0.00965383	−	0.00491887i
$523$	0.893732	−	5.64280i	0.00170886	−	0.0107893i	−0.986819	−	0.161827i	$-0.948261\pi$
$523$	0.893732	−	5.64280i	0.00170886	−	0.0107893i	0.988528	+	0.151037i	$0.0482614\pi$
$524$			349.596i			0.667168i
$525$	−503.247	+	306.625i	−0.958565	+	0.584048i
$526$	−130.702			−0.248482
$527$	487.032	+	77.1383i	0.924159	+	0.146372i
$528$	21.6793	+	42.5481i	0.0410594	+	0.0805835i
$529$	−854.327	−	277.588i	−1.61499	−	0.524740i
$530$	−23.4199	+	577.289i	−0.0441884	+	1.08922i
$531$	−33.7428	−	103.850i	−0.0635457	−	0.195574i
$532$	−222.770	−	222.770i	−0.418740	−	0.418740i
$533$	−587.853	−	299.526i	−1.10291	−	0.561962i
$534$	142.175	−	195.687i	0.266245	−	0.366455i
$535$	−274.667	−	597.805i	−0.513396	−	1.11739i
$536$	200.175	−	145.436i	0.373461	−	0.271335i
$537$	3.29338	+	20.7936i	0.00613293	+	0.0387218i
$538$	298.573	−	47.2893i	0.554968	−	0.0878983i
$539$	−104.445	−	143.756i	−0.193775	−	0.266708i
$540$	198.909	+	215.730i	0.368350	+	0.399501i
$541$	−568.079	−	412.734i	−1.05005	−	0.762909i	−0.0778309	−	0.996967i	$-0.524799\pi$
$541$	−568.079	−	412.734i	−1.05005	−	0.762909i	−0.972223	+	0.234058i	$0.924799\pi$
$542$	−248.357	+	487.428i	−0.458223	+	0.899313i
$543$	193.682	−	193.682i	0.356690	−	0.356690i
$544$	88.2303	−	28.6678i	0.162188	−	0.0526981i
$545$	783.682	−	522.194i	1.43795	−	0.958154i
$546$	182.776	−	562.526i	0.334754	−	1.03027i
$547$	102.294	−	52.1216i	0.187010	−	0.0952862i	−0.357979	−	0.933730i	$-0.616534\pi$
$547$	102.294	−	52.1216i	0.187010	−	0.0952862i	0.544989	+	0.838443i	$0.316534\pi$
$548$	19.0842	−	120.493i	0.0348252	−	0.219878i
$549$		−	307.592i		−	0.560277i
$550$	162.005	+	39.3318i	0.294555	+	0.0715124i
$551$	−26.1242			−0.0474124
$552$	267.208	+	42.3216i	0.484073	+	0.0766696i
$553$	85.3479	+	167.505i	0.154336	+	0.302902i
$554$	−48.9001	−	15.8886i	−0.0882672	−	0.0286798i
$555$	−98.8722	+	27.7486i	−0.178148	+	0.0499975i
$556$	47.9142	+	147.465i	0.0861766	+	0.265224i
$557$	719.095	+	719.095i	1.29101	+	1.29101i	0.934160	+	0.356853i	$0.116150\pi$
$557$	719.095	+	719.095i	1.29101	+	1.29101i	0.356853	+	0.934160i	$0.383850\pi$
$558$	98.1295	+	49.9995i	0.175859	+	0.0896048i
$559$	−383.292	+	527.556i	−0.685674	+	0.943749i
$560$	−36.5606	+	182.584i	−0.0652867	+	0.326043i
$561$	−158.392	+	115.079i	−0.282339	+	0.205131i
$562$	38.1631	+	240.952i	0.0679059	+	0.428741i
$563$	370.346	−	58.6570i	0.657808	−	0.104187i	0.181398	−	0.983410i	$-0.441938\pi$
$563$	370.346	−	58.6570i	0.657808	−	0.104187i	0.476410	+	0.879223i	$0.341938\pi$
$564$	−137.596	−	189.385i	−0.243965	−	0.335789i
$565$	−785.382	−	157.265i	−1.39006	−	0.278345i
$566$	−372.791	−	270.849i	−0.658641	−	0.478531i
$567$	215.491	−	422.926i	0.380055	−	0.745900i
$568$	33.3237	−	33.3237i	0.0586684	−	0.0586684i
$569$	648.640	−	210.756i	1.13997	−	0.370397i	0.322610	−	0.946532i	$-0.395440\pi$
$569$	648.640	−	210.756i	1.13997	−	0.370397i	0.817355	+	0.576135i	$0.195440\pi$
$570$	−81.8444	−	291.623i	−0.143587	−	0.511619i
$571$	−42.9687	+	132.244i	−0.0752517	+	0.231601i	−0.981606	−	0.190917i	$-0.938854\pi$
$571$	−42.9687	+	132.244i	−0.0752517	+	0.231601i	0.906354	+	0.422518i	$0.138854\pi$
$572$	−149.089	+	75.9646i	−0.260645	+	0.132805i
$573$	−90.6822	+	572.545i	−0.158259	+	0.999206i
$574$		−	489.608i		−	0.852976i
$575$	719.758	−	611.560i	1.25175	−	1.06358i
$576$	20.7202			0.0359725
$577$	−69.5115	−	11.0095i	−0.120471	−	0.0190807i	0.0959080	−	0.995390i	$-0.469425\pi$
$577$	−69.5115	−	11.0095i	−0.120471	−	0.0190807i	−0.216379	+	0.976310i	$0.569425\pi$
$578$	−12.8723	−	25.2632i	−0.0222704	−	0.0437080i
$579$	−601.733	−	195.515i	−1.03926	−	0.337677i
$580$	8.56208	+	12.8495i	0.0147622	+	0.0221544i
$581$	−71.5028	−	220.063i	−0.123068	−	0.378766i
$582$	−74.4722	−	74.4722i	−0.127959	−	0.127959i
$583$	−343.287	−	174.913i	−0.588828	−	0.300023i
$584$	−105.337	+	144.984i	−0.180372	+	0.248261i
$585$	−168.925	+	155.754i	−0.288761	+	0.266245i
$586$	−111.375	+	80.9189i	−0.190060	+	0.138087i
$587$	−34.3351	−	216.783i	−0.0584924	−	0.369307i	−0.999520	−	0.0309770i	$-0.990138\pi$
$587$	−34.3351	−	216.783i	−0.0584924	−	0.369307i	0.941028	−	0.338330i	$-0.109862\pi$
$588$	188.467	−	29.8502i	0.320522	−	0.0507656i
$589$	−299.014	−	411.557i	−0.507664	−	0.698739i
$590$	270.888	−	124.462i	0.459132	−	0.210953i
$591$	35.3769	+	25.7028i	0.0598594	+	0.0434904i
$592$	−14.7315	+	28.9121i	−0.0248842	+	0.0488381i
$593$	−597.816	+	597.816i	−1.00812	+	1.00812i	−0.00815551	+	0.999967i	$0.502596\pi$
$593$	−597.816	+	597.816i	−1.00812	+	1.00812i	−0.999967	+	0.00815551i	$0.997404\pi$
$594$	−186.099	+	60.4673i	−0.313298	+	0.101797i
$595$	−762.814	−	30.9464i	−1.28204	−	0.0520108i
$596$	90.7224	−	279.215i	0.152219	−	0.468481i
$597$	601.740	−	306.602i	1.00794	−	0.513571i
$598$	−148.295	+	936.299i	−0.247985	+	1.56572i
$599$			658.191i			1.09882i	0.835554	+	0.549408i	$0.185147\pi$
$599$			658.191i			1.09882i	−0.835554	+	0.549408i	$0.814853\pi$
$600$	−116.615	+	135.834i	−0.194358	+	0.226390i
$601$	−350.388			−0.583009			−0.291504	−	0.956570i	$-0.594156\pi$
$601$	−350.388			−0.583009			−0.291504	+	0.956570i	$0.594156\pi$
$602$	−477.960	−	75.7014i	−0.793954	−	0.125750i
$603$	102.863	+	201.879i	0.170585	+	0.334791i
$604$	−155.019	−	50.3687i	−0.256654	−	0.0833920i
$605$	306.221	−	387.422i	0.506151	−	0.640366i
$606$	155.687	+	479.154i	0.256909	+	0.790684i
$607$	814.998	+	814.998i	1.34266	+	1.34266i	0.893397	+	0.449268i	$0.148315\pi$
$607$	814.998	+	814.998i	1.34266	+	1.34266i	0.449268	+	0.893397i	$0.351685\pi$
$608$	−85.2762	−	43.4504i	−0.140257	−	0.0714644i
$609$	21.3938	−	29.4460i	0.0351294	−	0.0483514i
$610$	834.068	−	97.6390i	1.36732	−	0.160064i
$611$	663.607	−	482.139i	1.08610	−	0.789097i
$612$	13.2893	+	83.9053i	0.0217145	+	0.137100i
$613$	633.098	−	100.273i	1.03279	−	0.163577i	0.383043	−	0.923731i	$-0.374876\pi$
$613$	633.098	−	100.273i	1.03279	−	0.163577i	0.649744	+	0.760153i	$0.274876\pi$
$614$	230.935	+	317.855i	0.376116	+	0.517679i
$615$	230.528	−	410.407i	0.374842	−	0.667329i
$616$	−100.458	−	72.9867i	−0.163081	−	0.118485i
$617$	177.567	−	348.494i	0.287790	−	0.564820i	−0.701171	−	0.712993i	$-0.747339\pi$
$617$	177.567	−	348.494i	0.287790	−	0.564820i	0.988962	+	0.148173i	$0.0473391\pi$
$618$	94.1107	−	94.1107i	0.152283	−	0.152283i
$619$	506.694	−	164.635i	0.818569	−	0.265969i	0.130346	−	0.991469i	$-0.458391\pi$
$619$	506.694	−	164.635i	0.818569	−	0.265969i	0.688223	+	0.725499i	$0.258391\pi$
$620$	−104.430	+	281.960i	−0.168435	+	0.454774i
$621$	−342.572	+	1054.33i	−0.551645	+	1.69779i
$622$	302.974	−	154.373i	0.487097	−	0.248188i
$623$	−98.3927	+	621.227i	−0.157934	+	0.997154i
$624$		−	179.685i		−	0.287957i
$625$	94.6181	+	617.796i	0.151389	+	0.988474i
$626$	291.556			0.465744
$627$	199.495	+	31.5968i	0.318173	+	0.0503937i
$628$	−271.147	−	532.155i	−0.431762	−	0.847381i
$629$	−126.527	−	41.1110i	−0.201155	−	0.0653593i
$630$	−159.898	−	59.2216i	−0.253807	−	0.0940026i
$631$	−69.5221	−	213.967i	−0.110178	−	0.339092i	0.880733	−	0.473613i	$-0.157050\pi$
$631$	−69.5221	−	213.967i	−0.110178	−	0.339092i	−0.990911	+	0.134521i	$0.957050\pi$
$632$	40.3838	+	40.3838i	0.0638984	+	0.0638984i
$633$	−560.353	−	285.514i	−0.885234	−	0.451049i
$634$	28.7714	−	39.6005i	0.0453808	−	0.0624613i
$635$	−511.377	−	287.243i	−0.805318	−	0.452351i
$636$	334.720	−	243.188i	0.526289	−	0.382371i
$637$	104.595	+	660.389i	0.164200	+	1.03672i
$638$	−10.1699	+	1.61076i	−0.0159403	+	0.00252470i
$639$	25.3656	+	34.9127i	0.0396957	+	0.0546364i
$640$	6.57720	+	56.1849i	0.0102769	+	0.0877889i
$641$	635.805	+	461.939i	0.991896	+	0.720654i	0.960335	−	0.278848i	$-0.0899524\pi$
$641$	635.805	+	461.939i	0.991896	+	0.720654i	0.0315601	+	0.999502i	$0.489952\pi$
$642$	−213.880	+	419.763i	−0.333146	+	0.653837i
$643$	−408.621	+	408.621i	−0.635491	+	0.635491i	−0.949440	−	0.313949i	$-0.898348\pi$
$643$	−408.621	+	408.621i	−0.635491	+	0.635491i	0.313949	+	0.949440i	$0.398348\pi$
$644$	−669.056	+	217.389i	−1.03891	+	0.337561i
$645$	−365.000	−	288.499i	−0.565892	−	0.447286i
$646$	121.257	−	373.190i	0.187704	−	0.577693i
$647$	−730.065	+	371.987i	−1.12839	+	0.574941i	−0.915573	−	0.402152i	$-0.868262\pi$
$647$	−730.065	+	371.987i	−1.12839	+	0.574941i	−0.212812	+	0.977093i	$0.568262\pi$
$648$	22.5575	−	142.423i	0.0348110	−	0.219788i
$649$			198.795i			0.306310i
$650$	−475.964	−	408.618i	−0.732253	−	0.628643i
$651$	708.759			1.08872
$652$	−169.629	−	26.8666i	−0.260167	−	0.0412065i
$653$	247.278	+	485.310i	0.378679	+	0.743200i	0.999158	−	0.0410232i	$-0.0130617\pi$
$653$	247.278	+	485.310i	0.378679	+	0.743200i	−0.620479	+	0.784223i	$0.713062\pi$
$654$	−641.362	−	208.391i	−0.980676	−	0.318641i
$655$	35.4275	−	873.271i	0.0540878	−	1.33324i
$656$	−45.9628	−	141.459i	−0.0700653	−	0.215639i
$657$	−116.040	−	116.040i	−0.176621	−	0.176621i
$658$	542.369	+	276.351i	0.824269	+	0.419986i
$659$	−223.989	+	308.295i	−0.339893	+	0.467822i	−0.944410	−	0.328770i	$-0.893366\pi$
$659$	−223.989	+	308.295i	−0.339893	+	0.467822i	0.604517	+	0.796592i	$0.293366\pi$
$660$	−49.8420	−	108.480i	−0.0755182	−	0.164363i
$661$	807.083	−	586.380i	1.22100	−	0.887110i	0.224820	−	0.974400i	$-0.427821\pi$
$661$	807.083	−	586.380i	1.22100	−	0.887110i	0.996183	+	0.0872901i	$0.0278207\pi$
$662$	−5.49749	−	34.7098i	−0.00830437	−	0.0524317i
$663$	727.626	−	115.245i	1.09748	−	0.173823i
$664$	−41.3176	−	56.8688i	−0.0622253	−	0.0856457i
$665$	533.891	+	579.042i	0.802844	+	0.870740i
$666$	−24.0389	−	17.4653i	−0.0360945	−	0.0262242i
$667$	−26.4835	+	51.9767i	−0.0397053	+	0.0779261i
$668$	55.6057	−	55.6057i	0.0832421	−	0.0832421i
$669$	136.429	−	44.3285i	0.203930	−	0.0662608i
$670$	−514.765	+	343.005i	−0.768305	+	0.511948i
$671$	−173.047	+	532.585i	−0.257895	+	0.793719i
$672$	118.810	−	60.5368i	0.176801	−	0.0900845i
$673$	51.8013	−	327.061i	0.0769708	−	0.485974i	−0.918847	−	0.394614i	$-0.870878\pi$
$673$	51.8013	−	327.061i	0.0769708	−	0.485974i	0.995818	−	0.0913606i	$-0.0291216\pi$
$674$		−	357.917i		−	0.531035i
$675$	−475.002	−	559.040i	−0.703706	−	0.828207i
$676$	291.617			0.431387
$677$	−95.1245	−	15.0662i	−0.140509	−	0.0222544i	0.0857838	−	0.996314i	$-0.472661\pi$
$677$	−95.1245	−	15.0662i	−0.140509	−	0.0222544i	−0.226293	+	0.974059i	$0.572661\pi$
$678$	260.398	+	511.060i	0.384068	+	0.753776i
$679$	260.460	+	84.6287i	0.383594	+	0.124637i
$680$	−223.300	+	62.6694i	−0.328382	+	0.0921609i
$681$	−120.684	−	371.427i	−0.177216	−	0.545414i
$682$	−141.779	−	141.779i	−0.207887	−	0.207887i
$683$	−53.9401	−	27.4839i	−0.0789753	−	0.0402399i	0.414057	−	0.910251i	$-0.364111\pi$
$683$	−53.9401	−	27.4839i	−0.0789753	−	0.0402399i	−0.493032	+	0.870011i	$0.664111\pi$
$684$	51.5138	−	70.9027i	0.0753126	−	0.103659i
$685$	−59.8819	+	299.051i	−0.0874189	+	0.436571i
$686$	120.542	−	87.5786i	0.175717	−	0.127666i
$687$	33.7183	+	212.889i	0.0490804	+	0.309882i
$688$	−145.200	+	22.9975i	−0.211047	+	0.0334265i
$689$	852.133	+	1172.86i	1.23677	+	1.70226i
$690$	−663.183	−	132.796i	−0.961134	−	0.192457i
$691$	816.866	+	593.488i	1.18215	+	0.858883i	0.992413	−	0.122952i	$-0.0392362\pi$
$691$	816.866	+	593.488i	1.18215	+	0.858883i	0.189738	+	0.981835i	$0.439236\pi$
$692$	206.740	−	405.750i	0.298757	−	0.586344i
$693$	80.4023	−	80.4023i	0.116021	−	0.116021i
$694$	280.589	−	91.1688i	0.404307	−	0.131367i
$695$	−104.743	−	373.214i	−0.150710	−	0.536999i
$696$	3.41686	−	10.5160i	0.00490928	−	0.0151092i
$697$	543.352	−	276.852i	0.779559	−	0.397205i
$698$	43.9031	−	277.193i	0.0628984	−	0.397125i
$699$		−	139.349i		−	0.199354i
$700$	109.829	−	452.380i	0.156899	−	0.646257i
$701$	290.914			0.414998			0.207499	−	0.978235i	$-0.433468\pi$
$701$	290.914			0.414998			0.207499	+	0.978235i	$0.433468\pi$
$702$	727.228	+	115.182i	1.03594	+	0.164076i
$703$	62.3100	+	122.290i	0.0886345	+	0.173955i
$704$	−35.8763	−	11.6569i	−0.0509606	−	0.0165581i
$705$	324.516	+	487.017i	0.460307	+	0.690805i
$706$	−79.8232	−	245.671i	−0.113064	−	0.347975i
$707$	−926.361	−	926.361i	−1.31027	−	1.31027i
$708$	−190.211	−	96.9171i	−0.268659	−	0.136889i
$709$	−710.682	+	978.170i	−1.00237	+	1.37965i	−0.0785145	+	0.996913i	$0.525018\pi$
$709$	−710.682	+	978.170i	−1.00237	+	1.37965i	−0.923858	+	0.382735i	$0.874982\pi$
$710$	−86.6176	+	79.8637i	−0.121997	+	0.112484i
$711$	−42.3095	+	30.7396i	−0.0595070	+	0.0432343i
$712$	29.8909	+	188.724i	0.0419816	+	0.265061i
$713$	−1121.96	+	177.701i	−1.57358	+	0.249230i
$714$	321.342	+	442.290i	0.450059	+	0.619453i
$715$	380.114	−	174.647i	0.531628	−	0.244261i
$716$	−13.4545	−	9.77530i	−0.0187913	−	0.0136527i
$717$	−17.5508	+	34.4455i	−0.0244782	+	0.0480411i
$718$	194.887	−	194.887i	0.271430	−	0.271430i
$719$	−746.586	+	242.581i	−1.03837	+	0.337386i	−0.778093	−	0.628149i	$-0.783813\pi$
$719$	−746.586	+	242.581i	−1.03837	+	0.337386i	−0.260274	+	0.965535i	$0.583813\pi$
$720$	−51.7578	−	2.09975i	−0.0718858	−	0.00291632i
$721$	−106.946	+	329.144i	−0.148329	+	0.456511i
$722$	94.1920	−	47.9932i	0.130460	−	0.0664726i
$723$	93.6728	−	591.427i	0.129561	−	0.818017i
$724$			216.375i			0.298860i
$725$	−20.0855	−	32.9651i	−0.0277041	−	0.0454691i
$726$	−353.631			−0.487095
$727$	−554.000	−	87.7449i	−0.762035	−	0.120695i	−0.236692	−	0.971585i	$-0.576063\pi$
$727$	−554.000	−	87.7449i	−0.762035	−	0.120695i	−0.525344	+	0.850890i	$0.676063\pi$
$728$	212.121	+	416.312i	0.291376	+	0.571857i
$729$	761.482	+	247.421i	1.04456	+	0.339397i
$730$	277.819	−	351.488i	0.380574	−	0.481491i
$731$	−186.254	−	573.232i	−0.254794	−	0.784175i
$732$	−425.222	−	425.222i	−0.580904	−	0.580904i
$733$	−821.470	−	418.560i	−1.12070	−	0.571023i	−0.207374	−	0.978262i	$-0.566492\pi$
$733$	−821.470	−	418.560i	−1.12070	−	0.571023i	−0.913322	+	0.407238i	$0.866492\pi$
$734$	114.284	−	157.298i	0.155700	−	0.214303i
$735$	−473.805	+	55.4652i	−0.644632	+	0.0754629i
$736$	−172.898	+	125.618i	−0.234915	+	0.170676i
$737$	−64.5284	−	407.416i	−0.0875554	−	0.552803i
$738$	134.525	−	21.3066i	0.182283	−	0.0288708i
$739$	−767.079	−	1055.79i	−1.03800	−	1.42868i	−0.898771	−	0.438418i	$-0.855539\pi$
$739$	−767.079	−	1055.79i	−1.03800	−	1.42868i	−0.139225	−	0.990261i	$-0.544461\pi$
$740$	39.7283	−	70.7281i	0.0536869	−	0.0955785i
$741$	−614.867	−	446.727i	−0.829780	−	0.602871i
$742$	−488.423	+	958.585i	−0.658252	+	1.29189i
$743$	−519.059	+	519.059i	−0.698599	+	0.698599i	−0.964108	−	0.265510i	$-0.914460\pi$
$743$	−519.059	+	519.059i	−0.698599	+	0.698599i	0.265510	+	0.964108i	$0.414460\pi$
$744$	204.777	−	66.5360i	0.275237	−	0.0894301i
$745$	−254.915	+	688.270i	−0.342167	+	0.923852i
$746$	−175.584	+	540.391i	−0.235367	+	0.724385i
$747$	57.3528	−	29.2227i	0.0767776	−	0.0391201i
$748$	24.1941	−	152.756i	0.0323451	−	0.204219i
$749$		−	1225.04i		−	1.63556i
$750$	305.062	−	327.489i	0.406749	−	0.436652i
$751$	−404.740			−0.538934			−0.269467	−	0.963010i	$-0.586848\pi$
$751$	−404.740			−0.538934			−0.269467	+	0.963010i	$0.586848\pi$
$752$	182.646	+	28.9283i	0.242880	+	0.0384684i
$753$	78.7327	+	154.522i	0.104559	+	0.205208i
$754$	36.8482	+	11.9727i	0.0488703	+	0.0158789i
$755$	382.125	+	141.528i	0.506126	+	0.187454i
$756$	168.847	+	519.659i	0.223343	+	0.687379i
$757$	167.278	+	167.278i	0.220975	+	0.220975i	0.808909	−	0.587934i	$-0.200059\pi$
$757$	167.278	+	167.278i	0.220975	+	0.220975i	−0.587934	+	0.808909i	$0.700059\pi$
$758$	−674.543	−	343.697i	−0.889899	−	0.453426i
$759$	265.103	−	364.883i	0.349279	−	0.480742i
$760$	208.612	+	117.178i	0.274490	+	0.154182i
$761$	278.142	−	202.082i	0.365496	−	0.265548i	−0.389845	−	0.920881i	$-0.627471\pi$
$761$	278.142	−	202.082i	0.365496	−	0.265548i	0.755341	+	0.655332i	$0.227471\pi$
$762$	65.7044	+	414.841i	0.0862262	+	0.544411i
$763$	1731.98	−	274.319i	2.26996	−	0.359526i
$764$	−269.160	−	370.467i	−0.352303	−	0.484904i
$765$	−24.6931	−	210.938i	−0.0322786	−	0.275735i
$766$	−530.168	−	385.189i	−0.692125	−	0.502858i
$767$	339.598	−	666.499i	0.442762	−	0.868969i
$768$	28.6440	−	28.6440i	0.0372968	−	0.0372968i
$769$	162.525	−	52.8077i	0.211346	−	0.0686706i	−0.201430	−	0.979503i	$-0.564559\pi$
$769$	162.525	−	52.8077i	0.211346	−	0.0686706i	0.412777	+	0.910832i	$0.364559\pi$
$770$	243.541	+	192.497i	0.316287	+	0.249996i
$771$	9.16678	−	28.2124i	0.0118895	−	0.0365920i
$772$	445.328	−	226.906i	0.576850	−	0.293920i
$773$	−83.1560	+	525.026i	−0.107576	+	0.679206i	0.873681	+	0.486500i	$0.161727\pi$
$773$	−83.1560	+	525.026i	−0.107576	+	0.679206i	−0.981256	+	0.192706i	$0.938273\pi$
$774$		−	134.619i		−	0.173926i
$775$	289.433	−	693.738i	0.373462	−	0.895145i
$776$	83.1976			0.107213
$777$	−188.867	−	29.9136i	−0.243073	−	0.0384989i
$778$	20.8210	+	40.8635i	0.0267622	+	0.0525238i
$779$	−598.332	−	194.410i	−0.768077	−	0.249563i
$780$	−18.2090	+	448.843i	−0.0233449	+	0.575440i
$781$	−24.2782	−	74.7205i	−0.0310860	−	0.0956729i
$782$	−619.574	−	619.574i	−0.792294	−	0.792294i
$783$	40.3706	+	20.5698i	0.0515588	+	0.0262705i
$784$	−88.6003	+	121.948i	−0.113011	+	0.155546i
$785$	623.382	+	1356.77i	0.794117	+	1.72837i
$786$	−506.334	+	367.873i	−0.644191	+	0.468032i
$787$	59.2289	+	373.957i	0.0752591	+	0.475167i	0.996317	+	0.0857424i	$0.0273262\pi$
$787$	59.2289	+	373.957i	0.0752591	+	0.475167i	−0.921058	+	0.389425i	$0.872674\pi$
$788$	−34.1180	+	5.40376i	−0.0432970	+	0.00685757i
$789$	−137.535	−	189.301i	−0.174316	−	0.239925i
$790$	−96.7840	−	104.969i	−0.122511	−	0.132872i
$791$	−1206.63	−	876.669i	−1.52545	−	1.10830i
$792$	15.6822	−	30.7780i	0.0198007	−	0.0388611i
$793$	1489.98	−	1489.98i	1.87892	−	1.87892i
$794$	220.001	−	71.4828i	0.277080	−	0.0900287i
$795$	−860.756	+	573.551i	−1.08271	+	0.721447i
$796$	−164.859	+	507.383i	−0.207109	+	0.637416i
$797$	−848.786	+	432.478i	−1.06498	+	0.542633i	−0.896487	−	0.443071i	$-0.853889\pi$
$797$	−848.786	+	432.478i	−1.06498	+	0.542633i	−0.168490	+	0.985703i	$0.553889\pi$
$798$	88.2301	−	557.063i	0.110564	−	0.698074i
$799$			758.170i			0.948898i
$800$	−10.7358	−	141.013i	−0.0134197	−	0.176267i
$801$	−174.970			−0.218440
$802$	645.229	+	102.194i	0.804525	+	0.127424i
$803$	135.636	+	266.201i	0.168912	+	0.331509i
$804$	421.281	+	136.883i	0.523982	+	0.170252i
$805$	1693.29	−	475.226i	2.10347	−	0.590342i
$806$	233.143	+	717.539i	0.289259	+	0.890247i
$807$	382.674	+	382.674i	0.474193	+	0.474193i
$808$	−354.611	−	180.683i	−0.438874	−	0.223618i
$809$	427.150	−	587.922i	0.527998	−	0.726727i	−0.458826	−	0.888526i	$-0.651730\pi$
$809$	427.150	−	587.922i	0.527998	−	0.726727i	0.986824	+	0.161799i	$0.0517297\pi$
$810$	−70.7803	+	353.478i	−0.0873831	+	0.436392i
$811$	−121.097	+	87.9821i	−0.149318	+	0.108486i	−0.659936	−	0.751322i	$-0.729417\pi$
$811$	−121.097	+	87.9821i	−0.149318	+	0.108486i	0.510618	+	0.859808i	$0.329417\pi$
$812$	4.49783	+	28.3982i	0.00553920	+	0.0349731i
$813$	−967.303	+	153.206i	−1.18979	+	0.188445i
$814$	31.7968	+	43.7646i	0.0390624	+	0.0537648i
$815$	421.002	+	84.3013i	0.516567	+	0.103437i
$816$	134.364	+	97.6211i	0.164662	+	0.119634i
$817$	−282.297	+	554.039i	−0.345529	+	0.678138i
$818$	−259.583	+	259.583i	−0.317339	+	0.317339i
$819$	−406.913	+	132.214i	−0.496842	+	0.161434i
$820$	100.477	+	358.015i	0.122533	+	0.436603i
$821$	−197.621	+	608.214i	−0.240707	+	0.740821i	0.755605	+	0.655027i	$0.227343\pi$
$821$	−197.621	+	608.214i	−0.240707	+	0.740821i	−0.996313	+	0.0857943i	$0.972657\pi$
$822$	194.597	−	99.1522i	0.236736	−	0.120623i
$823$	194.429	−	1227.58i	0.236245	−	1.49159i	−0.529425	−	0.848357i	$-0.677592\pi$
$823$	194.429	−	1227.58i	0.236245	−	1.49159i	0.765670	−	0.643234i	$-0.222408\pi$
$824$			105.137i			0.127594i
$825$	113.510	+	276.027i	0.137587	+	0.334579i
$826$	555.111			0.672047
$827$	−1115.18	−	176.628i	−1.34847	−	0.213576i	−0.559918	−	0.828548i	$-0.689168\pi$
$827$	−1115.18	−	176.628i	−1.34847	−	0.213576i	−0.788549	+	0.614971i	$0.789168\pi$
$828$	−88.8457	−	174.369i	−0.107302	−	0.210591i
$829$	655.807	+	213.085i	0.791082	+	0.257038i	0.676565	−	0.736383i	$-0.263468\pi$
$829$	655.807	+	213.085i	0.791082	+	0.257038i	0.114517	+	0.993421i	$0.463468\pi$
$830$	97.4460	+	146.242i	0.117405	+	0.176195i
$831$	−28.4445	−	87.5433i	−0.0342293	−	0.105347i
$832$	100.369	+	100.369i	0.120635	+	0.120635i
$833$	−550.648	−	280.569i	−0.661042	−	0.336818i
$834$	−163.160	+	224.571i	−0.195636	+	0.269269i
$835$	−144.535	+	133.265i	−0.173096	+	0.159599i
$836$	−129.083	+	93.7846i	−0.154406	+	0.112183i
$837$	138.021	+	871.432i	0.164900	+	1.04114i
$838$	550.716	−	87.2248i	0.657179	−	0.104087i
$839$	896.187	+	1233.50i	1.06816	+	1.47020i	0.871924	+	0.489642i	$0.162872\pi$
$839$	896.187	+	1233.50i	1.06816	+	1.47020i	0.196238	+	0.980556i	$0.437128\pi$
$840$	−302.916	+	139.178i	−0.360614	+	0.165688i
$841$	−678.454	−	492.926i	−0.806723	−	0.586119i
$842$	−199.954	+	392.432i	−0.237475	+	0.466072i
$843$	−308.823	+	308.823i	−0.366338	+	0.366338i
$844$	472.486	−	153.520i	0.559818	−	0.181896i
$845$	−728.444	−	29.5521i	−0.862064	−	0.0349728i
$846$	−52.3275	+	161.048i	−0.0618529	+	0.190364i
$847$	819.326	−	417.467i	0.967327	−	0.492878i
$848$	−51.1279	+	322.809i	−0.0602923	+	0.380671i
$849$		−	824.938i		−	0.971658i
$850$	564.141	−	133.916i	0.663695	−	0.157548i
$851$	306.476			0.360136
$852$	83.3299	+	13.1982i	0.0978051	+	0.0154908i
$853$	405.910	+	796.644i	0.475862	+	0.933932i	0.996769	+	0.0803183i	$0.0255937\pi$
$853$	405.910	+	796.644i	0.475862	+	0.933932i	−0.520907	+	0.853613i	$0.674406\pi$
$854$	1487.18	+	483.213i	1.74143	+	0.565823i
$855$	−135.864	+	171.891i	−0.158905	+	0.201042i
$856$	−115.003	−	353.941i	−0.134349	−	0.413483i
$857$	−302.090	−	302.090i	−0.352497	−	0.352497i	0.508541	−	0.861038i	$-0.330185\pi$
$857$	−302.090	−	302.090i	−0.352497	−	0.352497i	−0.861038	+	0.508541i	$0.830185\pi$
$858$	−266.906	−	135.995i	−0.311079	−	0.158503i
$859$	623.184	−	857.740i	0.725477	−	0.998533i	−0.273847	−	0.961773i	$-0.588296\pi$
$859$	623.184	−	857.740i	0.725477	−	0.998533i	0.999324	−	0.0367598i	$-0.0117037\pi$
$860$	365.033	−	42.7320i	0.424457	−	0.0496884i
$861$	709.120	−	515.206i	0.823600	−	0.598380i
$862$	−159.944	−	1009.85i	−0.185550	−	1.17152i
$863$	1102.02	−	174.542i	1.27696	−	0.202251i	0.519126	−	0.854698i	$-0.326258\pi$
$863$	1102.02	−	174.542i	1.27696	−	0.202251i	0.757834	+	0.652447i	$0.226258\pi$
$864$	97.5677	+	134.290i	0.112926	+	0.155429i
$865$	−557.543	+	992.591i	−0.644559	+	1.14750i
$866$	−274.126	−	199.164i	−0.316543	−	0.229982i
$867$	23.0446	−	45.2275i	0.0265796	−	0.0521655i
$868$	−395.900	+	395.900i	−0.456106	+	0.456106i
$869$	90.5512	−	29.4219i	0.104202	−	0.0338571i
$870$	−9.60081	+	25.9222i	−0.0110354	+	0.0297956i
$871$	−479.637	+	1476.17i	−0.550674	+	1.69480i
$872$	474.657	−	241.850i	0.544331	−	0.277350i
$873$	−11.9179	+	75.2470i	−0.0136517	+	0.0861935i
$874$			903.948i			1.03427i
$875$	−320.191	+	1118.89i	−0.365932	+	1.27873i
$876$	−320.831			−0.366246
$877$	512.451	+	81.1642i	0.584322	+	0.0925476i	0.441595	−	0.897214i	$-0.354413\pi$
$877$	512.451	+	81.1642i	0.584322	+	0.0925476i	0.142727	+	0.989762i	$0.454413\pi$
$878$	−47.8284	−	93.8685i	−0.0544742	−	0.106912i
$879$	−234.396	−	76.1600i	−0.266663	−	0.0866439i
$880$	88.4356	+	32.7540i	0.100495	+	0.0372204i
$881$	116.262	+	357.816i	0.131965	+	0.406148i	0.995106	−	0.0988164i	$-0.0315056\pi$
$881$	116.262	+	357.816i	0.131965	+	0.406148i	−0.863140	+	0.504964i	$0.831506\pi$
$882$	−97.6022	−	97.6022i	−0.110660	−	0.110660i
$883$	364.916	+	185.934i	0.413268	+	0.210571i	0.648247	−	0.761430i	$-0.275502\pi$
$883$	364.916	+	185.934i	0.413268	+	0.210571i	−0.234979	+	0.972000i	$0.575502\pi$
$884$	−342.065	+	470.812i	−0.386951	+	0.532593i
$885$	465.314	+	261.369i	0.525779	+	0.295333i
$886$	−233.795	+	169.862i	−0.263877	+	0.191718i
$887$	−159.924	−	1009.72i	−0.180298	−	1.13835i	−0.897345	−	0.441330i	$-0.854507\pi$
$887$	−159.924	−	1009.72i	−0.180298	−	1.13835i	0.717047	−	0.697025i	$-0.245493\pi$
$888$	−57.3763	+	9.08751i	−0.0646129	+	0.0102337i
$889$	−641.958	−	883.579i	−0.722113	−	0.993903i
$890$	−55.5408	−	474.450i	−0.0624054	−	0.533090i
$891$	−194.483	−	141.300i	−0.218275	−	0.158586i
$892$	−51.4457	+	100.968i	−0.0576745	+	0.113193i
$893$	553.078	−	553.078i	0.619349	−	0.619349i
$894$	499.864	−	162.416i	0.559132	−	0.181673i
$895$	32.6181	+	25.7816i	0.0364448	+	0.0288063i
$896$	−32.5504	+	100.180i	−0.0363286	+	0.111808i
$897$	−1512.13	+	770.469i	−1.68576	+	0.858939i
$898$	13.9574	−	88.1233i	0.0155427	−	0.0981328i
$899$			46.4272i			0.0516431i
$900$	129.075	+	10.4901i	0.143417	+	0.0116557i
$901$	−1339.99			−1.48723
$902$	−244.912	−	38.7902i	−0.271521	−	0.0430047i
$903$	−393.307	−	771.909i	−0.435556	−	0.854827i
$904$	−430.922	−	140.015i	−0.476684	−	0.154884i
$905$	21.9271	−	540.493i	0.0242288	−	0.597230i
$906$	−90.1726	−	277.523i	−0.0995282	−	0.306316i
$907$	113.458	+	113.458i	0.125092	+	0.125092i	0.766881	−	0.641789i	$-0.221808\pi$
$907$	113.458	+	113.458i	0.125092	+	0.125092i	−0.641789	+	0.766881i	$0.721808\pi$
$908$	274.884	+	140.060i	0.302736	+	0.154251i
$909$	214.214	−	294.840i	0.235659	−	0.324356i
$910$	−487.679	−	1061.42i	−0.535911	−	1.16640i
$911$	1420.57	−	1032.11i	1.55936	−	1.13294i	0.622820	−	0.782365i	$-0.285987\pi$
$911$	1420.57	−	1032.11i	1.55936	−	1.13294i	0.936535	−	0.350573i	$-0.114013\pi$
$912$	−26.8036	−	169.231i	−0.0293899	−	0.185560i
$913$	−115.745	+	18.3322i	−0.126774	+	0.0200791i
$914$	−536.378	−	738.260i	−0.586846	−	0.807725i
$915$	1019.09	+	1105.27i	1.11376	+	1.20795i
$916$	−137.750	−	100.081i	−0.150382	−	0.109259i
$917$	738.843	−	1450.06i	0.805718	−	1.58131i
$918$	−481.226	+	481.226i	−0.524211	+	0.524211i
$919$	416.300	−	135.264i	0.452993	−	0.147186i	−0.0736296	−	0.997286i	$-0.523458\pi$
$919$	416.300	−	135.264i	0.452993	−	0.147186i	0.526622	+	0.850099i	$0.323458\pi$
$920$	444.619	−	296.264i	0.483281	−	0.322027i
$921$	−217.354	+	668.946i	−0.235998	+	0.726326i
$922$	435.490	−	221.893i	0.472332	−	0.240665i
$923$	−46.2464	+	291.989i	−0.0501045	+	0.316347i
$924$		−	222.300i		−	0.240584i
$925$	−106.407	+	172.649i	−0.115034	+	0.186647i
$926$	1008.35			1.08893
$927$	−95.0898	−	15.0607i	−0.102578	−	0.0162468i
$928$	3.96546	+	7.78265i	0.00427312	+	0.00838647i
$929$	−1302.45	−	423.191i	−1.40199	−	0.455534i	−0.492155	−	0.870507i	$-0.663791\pi$
$929$	−1302.45	−	423.191i	−1.40199	−	0.455534i	−0.909833	+	0.414974i	$0.863791\pi$
$930$	−518.264	+	145.451i	−0.557273	+	0.156399i
$931$	197.020	+	606.366i	0.211622	+	0.651306i
$932$	77.8377	+	77.8377i	0.0835168	+	0.0835168i
$933$	542.399	+	276.366i	0.581349	+	0.296212i
$934$	−82.9797	+	114.212i	−0.0888433	+	0.122282i
$935$	−75.9156	+	379.124i	−0.0811932	+	0.405480i
$936$	−105.155	+	76.3994i	−0.112345	+	0.0816233i
$937$	−197.372	−	1246.16i	−0.210642	−	1.32994i	−0.835623	−	0.549303i	$-0.814893\pi$
$937$	−197.372	−	1246.16i	−0.210642	−	1.32994i	0.624981	−	0.780640i	$-0.285107\pi$
$938$	−1137.66	+	180.187i	−1.21285	+	0.192097i
$939$	306.799	+	422.272i	0.326729	+	0.449704i
$940$	−453.308	−	90.7702i	−0.482242	−	0.0965641i
$941$	37.6478	+	27.3527i	0.0400083	+	0.0290677i	0.607610	−	0.794236i	$-0.292129\pi$
$941$	37.6478	+	27.3527i	0.0400083	+	0.0290677i	−0.567601	+	0.823303i	$0.692129\pi$
$942$	485.420	−	952.691i	0.515308	−	1.01135i
$943$	−993.358	+	993.358i	−1.05340	+	1.05340i
$944$	160.384	−	52.1120i	0.169899	−	0.0552034i
$945$	−369.110	−	1315.19i	−0.390593	−	1.39174i
$946$	−75.7348	+	233.088i	−0.0800580	+	0.246393i
$947$	−1144.07	+	582.931i	−1.20809	+	0.615555i	−0.937784	−	0.347218i	$-0.887126\pi$
$947$	−1144.07	+	582.931i	−1.20809	+	0.615555i	−0.270310	+	0.962773i	$0.587126\pi$
$948$	−15.9944	+	100.985i	−0.0168717	+	0.106524i
$949$		−	1124.20i		−	1.18461i
$950$	−509.227	−	313.846i	−0.536028	−	0.330364i
$951$	87.6306			0.0921458
$952$	−426.551	−	67.5590i	−0.448058	−	0.0709654i
$953$	−210.075	−	412.296i	−0.220436	−	0.432630i	0.754132	−	0.656723i	$-0.228058\pi$
$953$	−210.075	−	412.296i	−0.220436	−	0.432630i	−0.974568	+	0.224093i	$0.928058\pi$
$954$	−284.636	−	92.4838i	−0.298360	−	0.0969432i
$955$	634.804	+	952.681i	0.664716	+	0.997572i
$956$	−9.43702	−	29.0442i	−0.00987136	−	0.0303809i
$957$	−13.0345	−	13.0345i	−0.0136202	−	0.0136202i
$958$	−1097.26	−	559.081i	−1.14536	−	0.583592i
$959$	−333.811	+	459.451i	−0.348082	+	0.479094i
$960$	−74.4538	+	68.6484i	−0.0775561	+	0.0715087i
$961$	46.0580	−	33.4631i	0.0479272	−	0.0348211i
$962$	−31.8427	−	201.047i	−0.0331005	−	0.208989i
$963$	336.591	−	53.3108i	0.349524	−	0.0553591i
$964$	278.036	+	382.684i	0.288419	+	0.396975i
$965$	−1135.40	+	521.670i	−1.17658	+	0.540591i
$966$	−1018.89	−	740.266i	−1.05475	−	0.766321i
$967$	−331.668	+	650.934i	−0.342986	+	0.673148i	−0.996484	−	0.0837799i	$-0.973301\pi$
$967$	−331.668	+	650.934i	−0.342986	+	0.673148i	0.653498	+	0.756928i	$0.273301\pi$
$968$	197.532	−	197.532i	0.204062	−	0.204062i
$969$	668.103	−	217.080i	0.689476	−	0.224024i
$970$	−207.823	−	8.43112i	−0.214251	−	0.00869188i
$971$	48.6355	−	149.685i	0.0500880	−	0.154155i	−0.922884	−	0.385078i	$-0.874175\pi$
$971$	48.6355	−	149.685i	0.0500880	−	0.154155i	0.972972	+	0.230923i	$0.0741745\pi$
$972$	−240.602	+	122.593i	−0.247533	+	0.126124i
$973$	112.916	−	712.921i	0.116049	−	0.732704i
$974$			702.124i			0.720867i
$975$	90.9702	−	1119.34i	0.0933027	−	1.14804i
$976$	475.042			0.486723
$977$	82.4828	+	13.0640i	0.0844245	+	0.0133715i	0.198504	−	0.980100i	$-0.436392\pi$
$977$	82.4828	+	13.0640i	0.0844245	+	0.0133715i	−0.114079	+	0.993472i	$0.536392\pi$
$978$	−139.586	−	273.952i	−0.142726	−	0.280115i
$979$	302.955	+	98.4361i	0.309454	+	0.100548i
$980$	233.677	−	295.640i	0.238446	−	0.301674i
$981$	150.744	+	463.941i	0.153663	+	0.472927i
$982$	−167.591	−	167.591i	−0.170663	−	0.170663i
$983$	−150.200	−	76.5307i	−0.152798	−	0.0778543i	0.375920	−	0.926652i	$-0.377327\pi$
$983$	−150.200	−	76.5307i	−0.152798	−	0.0778543i	−0.528717	+	0.848798i	$0.677327\pi$
$984$	156.515	−	215.425i	0.159060	−	0.218927i
$985$	85.7725	−	10.0408i	0.0870787	−	0.0101937i
$986$	−28.9721	+	21.0495i	−0.0293835	+	0.0213484i
$987$	170.475	+	1076.33i	0.172720	+	1.09051i
$988$	592.987	−	93.9199i	0.600189	−	0.0950606i
$989$	816.136	+	1123.31i	0.825213	+	1.13581i
$990$	−42.2921	+	75.2924i	−0.0427193	+	0.0760530i
$991$	269.381	+	195.717i	0.271827	+	0.197494i	0.715345	−	0.698772i	$-0.246270\pi$
$991$	269.381	+	195.717i	0.271827	+	0.197494i	−0.443517	+	0.896266i	$0.646270\pi$
$992$	−77.2187	+	151.550i	−0.0778414	+	0.152772i
$993$	44.4867	−	44.4867i	0.0448003	−	0.0448003i
$994$	−208.648	+	67.7937i	−0.209907	+	0.0682029i
$995$	463.225	−	1250.71i	0.465553	−	1.25699i
$996$	38.8877	−	119.684i	0.0390438	−	0.120165i
$997$	−817.923	+	416.752i	−0.820384	+	0.418006i	−0.813212	−	0.581968i	$-0.802283\pi$
$997$	−817.923	+	416.752i	−0.820384	+	0.418006i	−0.00717202	+	0.999974i	$0.502283\pi$
$998$	44.0837	−	278.333i	0.0441720	−	0.278891i
$999$		−	238.041i		−	0.238279i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.3.f.a.27.1	yes	16
4.3	odd	2		400.3.bg.a.177.2		16
5.2	odd	4		250.3.f.c.93.1		16
5.3	odd	4		250.3.f.a.93.2		16
5.4	even	2		250.3.f.b.157.2		16
25.9	even	10		250.3.f.c.207.1		16
25.12	odd	20		250.3.f.b.43.2		16
25.13	odd	20	inner	50.3.f.a.13.1	✓	16
25.16	even	5		250.3.f.a.207.2		16
100.63	even	20		400.3.bg.a.113.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.3.f.a.13.1	✓	16	25.13	odd	20	inner
50.3.f.a.27.1	yes	16	1.1	even	1	trivial
250.3.f.a.93.2		16	5.3	odd	4
250.3.f.a.207.2		16	25.16	even	5
250.3.f.b.43.2		16	25.12	odd	20
250.3.f.b.157.2		16	5.4	even	2
250.3.f.c.93.1		16	5.2	odd	4
250.3.f.c.207.1		16	25.9	even	10
400.3.bg.a.113.2		16	100.63	even	20
400.3.bg.a.177.2		16	4.3	odd	2

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:	\( N \)	\(=\)	\( 50 = 2 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	50.f (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39680 - 0.221232i) q^{2} +(-1.14941 - 2.25584i) q^{3} +(1.90211 + 0.618034i) q^{4} +(-4.68874 - 1.73657i) q^{5} +(1.10643 + 3.40526i) q^{6} +(-6.58346 - 6.58346i) q^{7} +(-2.52015 - 1.28408i) q^{8} +(1.52238 - 2.09537i) q^{9} +O(q^{10})\)	\(q+(-1.39680 - 0.221232i) q^{2} +(-1.14941 - 2.25584i) q^{3} +(1.90211 + 0.618034i) q^{4} +(-4.68874 - 1.73657i) q^{5} +(1.10643 + 3.40526i) q^{6} +(-6.58346 - 6.58346i) q^{7} +(-2.52015 - 1.28408i) q^{8} +(1.52238 - 2.09537i) q^{9} +(6.16506 + 3.46295i) q^{10} +(-3.81477 + 2.77159i) q^{11} +(-0.792120 - 5.00125i) q^{12} +(17.5244 - 2.77559i) q^{13} +(7.73932 + 10.6523i) q^{14} +(1.47185 + 12.5731i) q^{15} +(3.23607 + 2.35114i) q^{16} +(-7.44532 + 14.6123i) q^{17} +(-2.59002 + 2.59002i) q^{18} +(16.0908 - 5.22822i) q^{19} +(-7.84526 - 6.20096i) q^{20} +(-7.28417 + 22.4184i) q^{21} +(5.94165 - 3.02742i) q^{22} +(5.91002 - 37.3144i) q^{23} +7.16099i q^{24} +(18.9686 + 16.2847i) q^{25} -25.0922 q^{26} +(-28.9823 - 4.59034i) q^{27} +(-8.45369 - 16.5913i) q^{28} +(-1.46851 - 0.477149i) q^{29} +(0.725684 - 17.8878i) q^{30} +(-9.29144 - 28.5961i) q^{31} +(-4.00000 - 4.00000i) q^{32} +(10.6370 + 5.41983i) q^{33} +(13.6323 - 18.7633i) q^{34} +(19.4355 + 42.3008i) q^{35} +(4.19074 - 3.04475i) q^{36} +(1.26903 + 8.01234i) q^{37} +(-23.6323 + 3.74300i) q^{38} +(-26.4040 - 36.3420i) q^{39} +(9.58643 + 10.3971i) q^{40} +(-30.0830 - 21.8566i) q^{41} +(15.1342 - 29.7025i) q^{42} +(-25.9880 + 25.9880i) q^{43} +(-8.96907 + 2.91423i) q^{44} +(-10.7768 + 7.18094i) q^{45} +(-16.5103 + 50.8134i) q^{46} +(41.1918 - 20.9883i) q^{47} +(1.58424 - 10.0025i) q^{48} +37.6840i q^{49} +(-22.8927 - 26.9429i) q^{50} +41.5207 q^{51} +(35.0488 + 5.55119i) q^{52} +(37.0947 + 72.8025i) q^{53} +(39.4670 + 12.8236i) q^{54} +(22.6996 - 6.37067i) q^{55} +(8.13761 + 25.0450i) q^{56} +(-30.2890 - 30.2890i) q^{57} +(1.94566 + 0.991364i) q^{58} +(24.7807 - 34.1077i) q^{59} +(-4.97098 + 24.8251i) q^{60} +(96.0793 - 69.8057i) q^{61} +(6.65194 + 41.9987i) q^{62} +(-23.8173 + 3.77229i) q^{63} +(4.70228 + 6.47214i) q^{64} +(-86.9875 - 17.4184i) q^{65} +(-13.6588 - 9.92368i) q^{66} +(-39.7150 + 77.9450i) q^{67} +(-23.1927 + 23.1927i) q^{68} +(-90.9685 + 29.5575i) q^{69} +(-17.7893 - 63.3856i) q^{70} +(-5.14879 + 15.8463i) q^{71} +(-6.52723 + 3.32579i) q^{72} +(9.91177 - 62.5804i) q^{73} -11.4724i q^{74} +(14.9330 - 61.5081i) q^{75} +33.8378 q^{76} +(43.3611 + 6.86772i) q^{77} +(28.8412 + 56.6041i) q^{78} +(-19.2036 - 6.23964i) q^{79} +(-11.0902 - 16.6436i) q^{80} +(15.7542 + 48.4864i) q^{81} +(37.1847 + 37.1847i) q^{82} +(22.1438 + 11.2828i) q^{83} +(-27.7106 + 38.1404i) q^{84} +(60.2844 - 55.5838i) q^{85} +(42.0494 - 30.5507i) q^{86} +(0.611550 + 3.86118i) q^{87} +(13.1727 - 2.08636i) q^{88} +(-39.7082 - 54.6536i) q^{89} +(16.6417 - 7.64618i) q^{90} +(-133.644 - 97.0982i) q^{91} +(34.3031 - 67.3236i) q^{92} +(-53.8287 + 53.8287i) q^{93} +(-62.1801 + 20.2035i) q^{94} +(-84.5249 - 3.42907i) q^{95} +(-4.42574 + 13.6210i) q^{96} +(-26.2088 + 13.3540i) q^{97} +(8.33689 - 52.6370i) q^{98} +12.2128i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} + 2 q^{3} + 4 q^{6} - 2 q^{7} + 8 q^{8} - 40 q^{9}+O(q^{10}) \) 16 * q - 4 * q^2 + 2 * q^3 + 4 * q^6 - 2 * q^7 + 8 * q^8 - 40 * q^9	\( 16 q - 4 q^{2} + 2 q^{3} + 4 q^{6} - 2 q^{7} + 8 q^{8} - 40 q^{9} + 10 q^{10} + 32 q^{11} + 4 q^{12} - 8 q^{13} - 30 q^{14} + 16 q^{16} - 62 q^{17} - 16 q^{18} + 30 q^{19} - 20 q^{20} - 68 q^{21} - 48 q^{22} - 18 q^{23} + 70 q^{25} - 56 q^{26} - 40 q^{27} + 44 q^{28} + 100 q^{29} + 120 q^{30} + 132 q^{31} - 64 q^{32} - 36 q^{33} + 100 q^{34} + 150 q^{35} + 48 q^{36} + 138 q^{37} + 20 q^{38} - 320 q^{39} - 88 q^{41} - 8 q^{42} - 78 q^{43} + 40 q^{44} - 20 q^{45} - 26 q^{46} - 22 q^{47} - 8 q^{48} - 20 q^{50} - 168 q^{51} - 16 q^{52} + 182 q^{53} + 80 q^{54} + 280 q^{55} + 48 q^{56} + 280 q^{57} - 120 q^{58} - 350 q^{59} - 140 q^{60} + 372 q^{61} - 158 q^{62} + 22 q^{63} - 910 q^{65} - 202 q^{66} - 112 q^{67} - 196 q^{68} - 30 q^{69} - 20 q^{70} + 122 q^{71} - 132 q^{72} - 248 q^{73} - 80 q^{75} + 40 q^{76} + 16 q^{77} + 438 q^{78} + 760 q^{79} + 80 q^{80} - 144 q^{81} + 352 q^{82} + 132 q^{83} - 20 q^{84} - 30 q^{85} + 264 q^{86} + 770 q^{87} + 116 q^{88} + 550 q^{89} - 140 q^{90} - 798 q^{91} + 384 q^{92} + 54 q^{93} + 190 q^{94} + 40 q^{95} - 16 q^{96} - 292 q^{97} - 24 q^{98}+O(q^{100}) \) 16 * q - 4 * q^2 + 2 * q^3 + 4 * q^6 - 2 * q^7 + 8 * q^8 - 40 * q^9 + 10 * q^10 + 32 * q^11 + 4 * q^12 - 8 * q^13 - 30 * q^14 + 16 * q^16 - 62 * q^17 - 16 * q^18 + 30 * q^19 - 20 * q^20 - 68 * q^21 - 48 * q^22 - 18 * q^23 + 70 * q^25 - 56 * q^26 - 40 * q^27 + 44 * q^28 + 100 * q^29 + 120 * q^30 + 132 * q^31 - 64 * q^32 - 36 * q^33 + 100 * q^34 + 150 * q^35 + 48 * q^36 + 138 * q^37 + 20 * q^38 - 320 * q^39 - 88 * q^41 - 8 * q^42 - 78 * q^43 + 40 * q^44 - 20 * q^45 - 26 * q^46 - 22 * q^47 - 8 * q^48 - 20 * q^50 - 168 * q^51 - 16 * q^52 + 182 * q^53 + 80 * q^54 + 280 * q^55 + 48 * q^56 + 280 * q^57 - 120 * q^58 - 350 * q^59 - 140 * q^60 + 372 * q^61 - 158 * q^62 + 22 * q^63 - 910 * q^65 - 202 * q^66 - 112 * q^67 - 196 * q^68 - 30 * q^69 - 20 * q^70 + 122 * q^71 - 132 * q^72 - 248 * q^73 - 80 * q^75 + 40 * q^76 + 16 * q^77 + 438 * q^78 + 760 * q^79 + 80 * q^80 - 144 * q^81 + 352 * q^82 + 132 * q^83 - 20 * q^84 - 30 * q^85 + 264 * q^86 + 770 * q^87 + 116 * q^88 + 550 * q^89 - 140 * q^90 - 798 * q^91 + 384 * q^92 + 54 * q^93 + 190 * q^94 + 40 * q^95 - 16 * q^96 - 292 * q^97 - 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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