LMFDB - Embedded newform 25.3.f.a.22.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,3,Mod(2,25)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("25.2");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	25.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:	$0.681200660901$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			22.2
Character	$\chi$	$=$	25.22
Dual form			25.3.f.a.8.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.61837 + 0.824603i) q^{2} +(3.42034 - 0.541729i) q^{3} +(-0.411975 + 0.567034i) q^{4} +(4.00059 + 2.99921i) q^{5} +(-5.08868 + 3.69715i) q^{6} +(-8.06323 - 8.06323i) q^{7} +(1.33571 - 8.43332i) q^{8} +(2.84577 - 0.924645i) q^{9} +O(q^{10})$	\(q+(-1.61837 + 0.824603i) q^{2} +(3.42034 - 0.541729i) q^{3} +(-0.411975 + 0.567034i) q^{4} +(4.00059 + 2.99921i) q^{5} +(-5.08868 + 3.69715i) q^{6} +(-8.06323 - 8.06323i) q^{7} +(1.33571 - 8.43332i) q^{8} +(2.84577 - 0.924645i) q^{9} +(-8.94762 - 1.55494i) q^{10} +(-1.43991 + 4.43160i) q^{11} +(-1.10192 + 2.16263i) q^{12} +(-7.37917 - 3.75988i) q^{13} +(19.6983 + 6.40037i) q^{14} +(15.3082 + 8.09108i) q^{15} +(3.92612 + 12.0833i) q^{16} +(16.4746 + 2.60932i) q^{17} +(-3.84305 + 3.84305i) q^{18} +(-2.60721 - 3.58851i) q^{19} +(-3.34880 + 1.03288i) q^{20} +(-31.9471 - 23.2109i) q^{21} +(-1.32399 - 8.35934i) q^{22} +(1.57553 + 3.09215i) q^{23} -29.5684i q^{24} +(7.00952 + 23.9972i) q^{25} +15.0427 q^{26} +(-18.5372 + 9.44519i) q^{27} +(7.89398 - 1.25028i) q^{28} +(-14.6125 + 20.1124i) q^{29} +(-31.4463 - 0.471235i) q^{30} +(39.2975 - 28.5513i) q^{31} +(7.83247 + 7.83247i) q^{32} +(-2.52427 + 15.9376i) q^{33} +(-28.8138 + 9.36216i) q^{34} +(-8.07443 - 56.4410i) q^{35} +(-0.648078 + 1.99458i) q^{36} +(-12.2064 + 23.9564i) q^{37} +(7.17853 + 3.65765i) q^{38} +(-27.2761 - 8.86255i) q^{39} +(30.6369 - 29.7322i) q^{40} +(10.7638 + 33.1275i) q^{41} +(70.8422 + 11.2203i) q^{42} +(-13.5798 + 13.5798i) q^{43} +(-1.91966 - 2.64219i) q^{44} +(14.1580 + 4.83591i) q^{45} +(-5.09959 - 3.70507i) q^{46} +(-8.94405 - 56.4705i) q^{47} +(19.9746 + 39.2023i) q^{48} +81.0315i q^{49} +(-31.1322 - 33.0564i) q^{50} +57.7624 q^{51} +(5.17201 - 2.63527i) q^{52} +(-15.9105 + 2.51997i) q^{53} +(22.2117 - 30.5717i) q^{54} +(-19.0518 + 13.4104i) q^{55} +(-78.7699 + 57.2297i) q^{56} +(-10.8615 - 10.8615i) q^{57} +(7.06378 - 44.5989i) q^{58} +(50.4257 - 16.3843i) q^{59} +(-10.8945 + 5.34694i) q^{60} +(25.1583 - 77.4292i) q^{61} +(-40.0545 + 78.6115i) q^{62} +(-30.4017 - 15.4904i) q^{63} +(-67.4679 - 21.9217i) q^{64} +(-18.2444 - 37.1734i) q^{65} +(-9.05700 - 27.8746i) q^{66} +(3.74472 + 0.593105i) q^{67} +(-8.26671 + 8.26671i) q^{68} +(7.06395 + 9.72269i) q^{69} +(59.6089 + 84.6845i) q^{70} +(-23.0210 - 16.7257i) q^{71} +(-3.99672 - 25.2343i) q^{72} +(-19.4330 - 38.1394i) q^{73} -48.8358i q^{74} +(36.9749 + 78.2815i) q^{75} +3.10891 q^{76} +(47.3434 - 24.1226i) q^{77} +(51.4511 - 8.14905i) q^{78} +(46.6168 - 64.1625i) q^{79} +(-20.5336 + 60.1158i) q^{80} +(-80.0737 + 58.1770i) q^{81} +(-44.7368 - 44.7368i) q^{82} +(-9.69615 + 61.2191i) q^{83} +(26.3228 - 8.55280i) q^{84} +(58.0824 + 59.8497i) q^{85} +(10.7792 - 33.1750i) q^{86} +(-39.0843 + 76.7073i) q^{87} +(35.4498 + 18.0626i) q^{88} +(91.0024 + 29.5685i) q^{89} +(-26.9006 + 3.84838i) q^{90} +(29.1832 + 89.8167i) q^{91} +(-2.40243 - 0.380508i) q^{92} +(118.944 - 118.944i) q^{93} +(61.0406 + 84.0152i) q^{94} +(0.332312 - 22.1757i) q^{95} +(31.0328 + 22.5467i) q^{96} +(-22.8066 - 143.995i) q^{97} +(-66.8188 - 131.139i) q^{98} +13.9427i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 10 q^{2} - 10 q^{3} - 10 q^{4} - 10 q^{5} - 6 q^{6} - 10 q^{7} - 10 q^{8} - 10 q^{9}+O(q^{10}) $ 32 * q - 10 * q^2 - 10 * q^3 - 10 * q^4 - 10 * q^5 - 6 * q^6 - 10 * q^7 - 10 * q^8 - 10 * q^9	\( 32 q - 10 q^{2} - 10 q^{3} - 10 q^{4} - 10 q^{5} - 6 q^{6} - 10 q^{7} - 10 q^{8} - 10 q^{9} - 10 q^{10} - 6 q^{11} - 10 q^{12} - 10 q^{13} - 10 q^{14} - 10 q^{15} + 2 q^{16} + 60 q^{17} + 140 q^{18} + 90 q^{19} + 130 q^{20} - 6 q^{21} + 70 q^{22} + 10 q^{23} - 40 q^{25} + 4 q^{26} - 100 q^{27} - 250 q^{28} - 110 q^{29} - 250 q^{30} - 6 q^{31} - 290 q^{32} - 190 q^{33} - 260 q^{34} - 120 q^{35} - 58 q^{36} + 50 q^{37} + 320 q^{38} + 390 q^{39} + 440 q^{40} - 86 q^{41} + 690 q^{42} + 230 q^{43} + 340 q^{44} + 310 q^{45} - 6 q^{46} + 70 q^{47} + 160 q^{48} - 100 q^{50} - 16 q^{51} - 320 q^{52} - 190 q^{53} - 660 q^{54} - 250 q^{55} - 70 q^{56} - 650 q^{57} - 640 q^{58} - 260 q^{59} - 550 q^{60} + 114 q^{61} + 60 q^{62} - 20 q^{63} + 340 q^{64} + 360 q^{65} + 138 q^{66} + 270 q^{67} + 710 q^{68} + 340 q^{69} + 310 q^{70} - 66 q^{71} + 360 q^{72} + 30 q^{73} - 90 q^{75} - 80 q^{76} - 250 q^{77} - 500 q^{78} - 210 q^{79} - 850 q^{80} + 62 q^{81} + 30 q^{82} - 10 q^{84} + 600 q^{85} - 6 q^{86} + 300 q^{87} + 190 q^{88} - 10 q^{89} + 380 q^{90} - 6 q^{91} - 30 q^{92} + 520 q^{93} + 790 q^{94} + 310 q^{95} + 174 q^{96} + 270 q^{97} + 170 q^{98}+O(q^{100}) \) 32 * q - 10 * q^2 - 10 * q^3 - 10 * q^4 - 10 * q^5 - 6 * q^6 - 10 * q^7 - 10 * q^8 - 10 * q^9 - 10 * q^10 - 6 * q^11 - 10 * q^12 - 10 * q^13 - 10 * q^14 - 10 * q^15 + 2 * q^16 + 60 * q^17 + 140 * q^18 + 90 * q^19 + 130 * q^20 - 6 * q^21 + 70 * q^22 + 10 * q^23 - 40 * q^25 + 4 * q^26 - 100 * q^27 - 250 * q^28 - 110 * q^29 - 250 * q^30 - 6 * q^31 - 290 * q^32 - 190 * q^33 - 260 * q^34 - 120 * q^35 - 58 * q^36 + 50 * q^37 + 320 * q^38 + 390 * q^39 + 440 * q^40 - 86 * q^41 + 690 * q^42 + 230 * q^43 + 340 * q^44 + 310 * q^45 - 6 * q^46 + 70 * q^47 + 160 * q^48 - 100 * q^50 - 16 * q^51 - 320 * q^52 - 190 * q^53 - 660 * q^54 - 250 * q^55 - 70 * q^56 - 650 * q^57 - 640 * q^58 - 260 * q^59 - 550 * q^60 + 114 * q^61 + 60 * q^62 - 20 * q^63 + 340 * q^64 + 360 * q^65 + 138 * q^66 + 270 * q^67 + 710 * q^68 + 340 * q^69 + 310 * q^70 - 66 * q^71 + 360 * q^72 + 30 * q^73 - 90 * q^75 - 80 * q^76 - 250 * q^77 - 500 * q^78 - 210 * q^79 - 850 * q^80 + 62 * q^81 + 30 * q^82 - 10 * q^84 + 600 * q^85 - 6 * q^86 + 300 * q^87 + 190 * q^88 - 10 * q^89 + 380 * q^90 - 6 * q^91 - 30 * q^92 + 520 * q^93 + 790 * q^94 + 310 * q^95 + 174 * q^96 + 270 * q^97 + 170 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{17}{20}\right)$

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 $

$2$	−1.61837	+	0.824603i	−0.809187	+	0.412302i	−0.809080	−	0.587698i	$-0.800034\pi$
$2$	−1.61837	+	0.824603i	−0.809187	+	0.412302i	−0.000107292		1.00000i	$0.500034\pi$
$3$	3.42034	−	0.541729i	1.14011	−	0.180576i	0.442308	−	0.896863i	$-0.354160\pi$
$3$	3.42034	−	0.541729i	1.14011	−	0.180576i	0.697806	+	0.716287i	$0.254160\pi$
$4$	−0.411975	+	0.567034i	−0.102994	+	0.141759i
$5$	4.00059	+	2.99921i	0.800119	+	0.599841i
$5$	4.00059	+	2.99921i	0.800119	+	0.599841i
$6$	−5.08868	+	3.69715i	−0.848114	+	0.616191i
$7$	−8.06323	−	8.06323i	−1.15189	−	1.15189i	−0.986173	−	0.165717i	$-0.947006\pi$
$7$	−8.06323	−	8.06323i	−1.15189	−	1.15189i	−0.165717	−	0.986173i	$-0.552994\pi$
$8$	1.33571	−	8.43332i	0.166963	−	1.05416i
$9$	2.84577	−	0.924645i	0.316196	−	0.102738i
$10$	−8.94762	−	1.55494i	−0.894762	−	0.155494i
$11$	−1.43991	+	4.43160i	−0.130901	+	0.402872i	−0.994930	−	0.100570i	$-0.967933\pi$
$11$	−1.43991	+	4.43160i	−0.130901	+	0.402872i	0.864029	+	0.503442i	$0.167933\pi$
$12$	−1.10192	+	2.16263i	−0.0918263	+	0.180219i
$13$	−7.37917	−	3.75988i	−0.567629	−	0.289221i	0.146529	−	0.989206i	$-0.453190\pi$
$13$	−7.37917	−	3.75988i	−0.567629	−	0.289221i	−0.714157	+	0.699985i	$0.753190\pi$
$14$	19.6983	+	6.40037i	1.40702	+	0.457169i
$15$	15.3082	+	8.09108i	1.02054	+	0.539405i
$16$	3.92612	+	12.0833i	0.245382	+	0.755209i
$17$	16.4746	+	2.60932i	0.969096	+	0.153490i	0.620864	−	0.783919i	$-0.286782\pi$
$17$	16.4746	+	2.60932i	0.969096	+	0.153490i	0.348232	+	0.937408i	$0.386782\pi$
$18$	−3.84305	+	3.84305i	−0.213503	+	0.213503i
$19$	−2.60721	−	3.58851i	−0.137221	−	0.188869i	0.734876	−	0.678202i	$-0.237240\pi$
$19$	−2.60721	−	3.58851i	−0.137221	−	0.188869i	−0.872097	+	0.489333i	$0.837240\pi$
$20$	−3.34880	+	1.03288i	−0.167440	+	0.0516439i
$21$	−31.9471	−	23.2109i	−1.52129	−	1.10528i
$22$	−1.32399	−	8.35934i	−0.0601813	−	0.379970i
$23$	1.57553	+	3.09215i	0.0685012	+	0.134441i	0.922718	−	0.385476i	$-0.125963\pi$
$23$	1.57553	+	3.09215i	0.0685012	+	0.134441i	−0.854217	+	0.519917i	$0.825963\pi$
$24$		−	29.5684i		−	1.23202i
$25$	7.00952	+	23.9972i	0.280381	+	0.959889i
$26$	15.0427			0.578564
$27$	−18.5372	+	9.44519i	−0.686564	+	0.349822i
$28$	7.89398	−	1.25028i	0.281928	−	0.0446530i
$29$	−14.6125	+	20.1124i	−0.503880	+	0.693531i	−0.982872	−	0.184288i	$-0.941002\pi$
$29$	−14.6125	+	20.1124i	−0.503880	+	0.693531i	0.478992	+	0.877819i	$0.341002\pi$
$30$	−31.4463	−	0.471235i	−1.04821	−	0.0157078i
$31$	39.2975	−	28.5513i	1.26766	−	0.921009i	0.268553	−	0.963265i	$-0.413454\pi$
$31$	39.2975	−	28.5513i	1.26766	−	0.921009i	0.999107	+	0.0422559i	$0.0134545\pi$
$32$	7.83247	+	7.83247i	0.244765	+	0.244765i
$33$	−2.52427	+	15.9376i	−0.0764931	+	0.482958i
$34$	−28.8138	+	9.36216i	−0.847464	+	0.275358i
$35$	−8.07443	−	56.4410i	−0.230698	−	1.61260i
$36$	−0.648078	+	1.99458i	−0.0180022	+	0.0554049i
$37$	−12.2064	+	23.9564i	−0.329902	+	0.647469i	−0.995065	−	0.0992294i	$-0.968362\pi$
$37$	−12.2064	+	23.9564i	−0.329902	+	0.647469i	0.665163	+	0.746699i	$0.268362\pi$
$38$	7.17853	+	3.65765i	0.188909	+	0.0962538i
$39$	−27.2761	−	8.86255i	−0.699388	−	0.227245i
$40$	30.6369	−	29.7322i	0.765922	−	0.743306i
$41$	10.7638	+	33.1275i	0.262531	+	0.807987i	0.992252	+	0.124242i	$0.0396500\pi$
$41$	10.7638	+	33.1275i	0.262531	+	0.807987i	−0.729721	+	0.683745i	$0.760350\pi$
$42$	70.8422	+	11.2203i	1.68672	+	0.267150i
$43$	−13.5798	+	13.5798i	−0.315808	+	0.315808i	−0.847155	−	0.531346i	$-0.821686\pi$
$43$	−13.5798	+	13.5798i	−0.315808	+	0.315808i	0.531346	+	0.847155i	$0.321686\pi$
$44$	−1.91966	−	2.64219i	−0.0436286	−	0.0600497i
$45$	14.1580	+	4.83591i	0.314621	+	0.107465i
$46$	−5.09959	−	3.70507i	−0.110861	−	0.0805449i
$47$	−8.94405	−	56.4705i	−0.190299	−	1.20150i	−0.879131	−	0.476580i	$-0.841876\pi$
$47$	−8.94405	−	56.4705i	−0.190299	−	1.20150i	0.688832	−	0.724921i	$-0.258124\pi$
$48$	19.9746	+	39.2023i	0.416137	+	0.816714i
$49$			81.0315i			1.65370i
$50$	−31.1322	−	33.0564i	−0.622644	−	0.661129i
$51$	57.7624			1.13260
$52$	5.17201	−	2.63527i	0.0994617	−	0.0506783i
$53$	−15.9105	+	2.51997i	−0.300198	+	0.0475466i	−0.304716	−	0.952443i	$-0.598562\pi$
$53$	−15.9105	+	2.51997i	−0.300198	+	0.0475466i	0.00451871	+	0.999990i	$0.498562\pi$
$54$	22.2117	−	30.5717i	0.411327	−	0.566143i
$55$	−19.0518	+	13.4104i	−0.346396	+	0.243826i
$56$	−78.7699	+	57.2297i	−1.40661	+	1.02196i
$57$	−10.8615	−	10.8615i	−0.190553	−	0.190553i
$58$	7.06378	−	44.5989i	0.121789	−	0.768947i
$59$	50.4257	−	16.3843i	0.854672	−	0.277700i	0.151270	−	0.988492i	$-0.451664\pi$
$59$	50.4257	−	16.3843i	0.854672	−	0.277700i	0.703402	+	0.710793i	$0.251664\pi$
$60$	−10.8945	+	5.34694i	−0.181575	+	0.0891156i
$61$	25.1583	−	77.4292i	0.412430	−	1.26933i	−0.502099	−	0.864810i	$-0.667439\pi$
$61$	25.1583	−	77.4292i	0.412430	−	1.26933i	0.914529	−	0.404520i	$-0.132561\pi$
$62$	−40.0545	+	78.6115i	−0.646041	+	1.26793i
$63$	−30.4017	−	15.4904i	−0.482567	−	0.245880i
$64$	−67.4679	−	21.9217i	−1.05419	−	0.342526i
$65$	−18.2444	−	37.1734i	−0.280684	−	0.571898i
$66$	−9.05700	−	27.8746i	−0.137227	−	0.422342i
$67$	3.74472	+	0.593105i	0.0558913	+	0.00885232i	0.184318	−	0.982867i	$-0.440993\pi$
$67$	3.74472	+	0.593105i	0.0558913	+	0.00885232i	−0.128426	+	0.991719i	$0.540993\pi$
$68$	−8.26671	+	8.26671i	−0.121569	+	0.121569i
$69$	7.06395	+	9.72269i	0.102376	+	0.140909i
$70$	59.6089	+	84.6845i	0.851556	+	1.20978i
$71$	−23.0210	−	16.7257i	−0.324239	−	0.235574i	0.413743	−	0.910394i	$-0.364221\pi$
$71$	−23.0210	−	16.7257i	−0.324239	−	0.235574i	−0.737982	+	0.674820i	$0.764221\pi$
$72$	−3.99672	−	25.2343i	−0.0555100	−	0.350476i
$73$	−19.4330	−	38.1394i	−0.266206	−	0.522458i	0.718749	−	0.695269i	$-0.244715\pi$
$73$	−19.4330	−	38.1394i	−0.266206	−	0.522458i	−0.984955	+	0.172811i	$0.944715\pi$
$74$		−	48.8358i		−	0.659943i
$75$	36.9749	+	78.2815i	0.492999	+	1.04375i
$76$	3.10891			0.0409067
$77$	47.3434	−	24.1226i	0.614849	−	0.313281i
$78$	51.4511	−	8.14905i	0.659629	−	0.104475i
$79$	46.6168	−	64.1625i	0.590086	−	0.812184i	−0.404669	−	0.914463i	$-0.632613\pi$
$79$	46.6168	−	64.1625i	0.590086	−	0.812184i	0.994756	+	0.102279i	$0.0326134\pi$
$80$	−20.5336	+	60.1158i	−0.256670	+	0.751447i
$81$	−80.0737	+	58.1770i	−0.988565	+	0.718234i
$82$	−44.7368	−	44.7368i	−0.545571	−	0.545571i
$83$	−9.69615	+	61.2191i	−0.116821	+	0.737579i	0.857844	+	0.513910i	$0.171803\pi$
$83$	−9.69615	+	61.2191i	−0.116821	+	0.737579i	−0.974665	+	0.223669i	$0.928197\pi$
$84$	26.3228	−	8.55280i	0.313367	−	0.101819i
$85$	58.0824	+	59.8497i	0.683322	+	0.704114i
$86$	10.7792	−	33.1750i	0.125340	−	0.385756i
$87$	−39.0843	+	76.7073i	−0.449245	+	0.881693i
$88$	35.4498	+	18.0626i	0.402838	+	0.205256i
$89$	91.0024	+	29.5685i	1.02250	+	0.332230i	0.771820	−	0.635841i	$-0.219346\pi$
$89$	91.0024	+	29.5685i	1.02250	+	0.332230i	0.250678	+	0.968070i	$0.419346\pi$
$90$	−26.9006	+	3.84838i	−0.298895	+	0.0427598i
$91$	29.1832	+	89.8167i	0.320695	+	0.986997i
$92$	−2.40243	−	0.380508i	−0.0261134	−	0.00413595i
$93$	118.944	−	118.944i	1.27896	−	1.27896i
$94$	61.0406	+	84.0152i	0.649368	+	0.893778i
$95$	0.332312	−	22.1757i	0.00349802	−	0.233429i
$96$	31.0328	+	22.5467i	0.323258	+	0.234861i
$97$	−22.8066	−	143.995i	−0.235119	−	1.48448i	−0.769177	−	0.639036i	$-0.779333\pi$
$97$	−22.8066	−	143.995i	−0.235119	−	1.48448i	0.534058	−	0.845448i	$-0.320667\pi$
$98$	−66.8188	−	131.139i	−0.681824	−	1.33816i
$99$			13.9427i			0.140835i
$100$	−16.4950	−	5.91161i	−0.164950	−	0.0591161i
$101$	−114.662			−1.13526			−0.567632	−	0.823282i	$-0.692140\pi$
$101$	−114.662			−1.13526			−0.567632	+	0.823282i	$0.692140\pi$
$102$	−93.4812	+	47.6311i	−0.916483	+	0.466971i
$103$	−157.550	+	24.9534i	−1.52961	+	0.242266i	−0.863792	−	0.503848i	$-0.831917\pi$
$103$	−157.550	+	24.9534i	−1.52961	+	0.242266i	−0.665818	+	0.746114i	$0.731917\pi$
$104$	−41.5646	+	57.2088i	−0.399660	+	0.550085i
$105$	−58.1931	−	188.674i	−0.554220	−	1.79689i
$106$	23.6711	−	17.1981i	0.223313	−	0.162246i
$107$	35.0684	+	35.0684i	0.327742	+	0.327742i	0.851727	−	0.523985i	$-0.175555\pi$
$107$	35.0684	+	35.0684i	0.327742	+	0.327742i	−0.523985	+	0.851727i	$0.675555\pi$
$108$	2.28112	−	14.4024i	0.0211215	−	0.133356i
$109$	−67.4721	+	21.9230i	−0.619010	+	0.201129i	−0.601701	−	0.798721i	$-0.705510\pi$
$109$	−67.4721	+	21.9230i	−0.619010	+	0.201129i	−0.0173095	+	0.999850i	$0.505510\pi$
$110$	19.7746	−	37.4133i	0.179770	−	0.340121i
$111$	−28.7721	+	88.5515i	−0.259208	+	0.797761i
$112$	65.7736	−	129.088i	0.587264	−	1.15257i
$113$	99.6694	+	50.7841i	0.882030	+	0.449417i	0.835494	−	0.549500i	$-0.185182\pi$
$113$	99.6694	+	50.7841i	0.882030	+	0.449417i	0.0465362	+	0.998917i	$0.485182\pi$
$114$	26.5345	+	8.62158i	0.232759	+	0.0756279i
$115$	−2.97094	+	17.0958i	−0.0258343	+	0.148659i
$116$	−5.38444	−	16.5716i	−0.0464176	−	0.142859i
$117$	−24.4759	−	3.87661i	−0.209196	−	0.0331334i
$118$	−68.0971	+	68.0971i	−0.577094	+	0.577094i
$119$	−111.799	−	153.878i	−0.939489	−	1.29310i
$120$	88.6818	−	118.291i	0.739015	−	0.985761i
$121$	80.3254	+	58.3598i	0.663846	+	0.482312i
$122$	23.1328	+	146.055i	0.189613	+	1.19717i
$123$	54.7619	+	107.476i	0.445219	+	0.873791i
$124$			34.0454i			0.274560i
$125$	−43.9304	+	117.026i	−0.351443	+	0.936209i
$126$	61.9748			0.491864
$127$	−3.65232	+	1.86095i	−0.0287584	+	0.0146531i	−0.468311	−	0.883564i	$-0.655137\pi$
$127$	−3.65232	+	1.86095i	−0.0287584	+	0.0146531i	0.439552	+	0.898217i	$0.355137\pi$
$128$	83.5034	−	13.2256i	0.652370	−	0.103325i
$129$	−39.0909	+	53.8040i	−0.303030	+	0.417085i
$130$	60.1796	+	45.1161i	0.462920	+	0.347047i
$131$	72.3111	−	52.5371i	0.551993	−	0.401047i	−0.276527	−	0.961006i	$-0.589183\pi$
$131$	72.3111	−	52.5371i	0.551993	−	0.401047i	0.828520	+	0.559960i	$0.189183\pi$
$132$	−7.99725	−	7.99725i	−0.0605852	−	0.0605852i
$133$	−7.91249	+	49.9575i	−0.0594924	+	0.375620i
$134$	−6.54944	+	2.12804i	−0.0488764	+	0.0158809i
$135$	−102.488	−	17.8106i	−0.759171	−	0.131930i
$136$	44.0105	−	135.450i	0.323607	−	0.995960i
$137$	36.3518	−	71.3445i	0.265342	−	0.520763i	−0.719441	−	0.694554i	$-0.755602\pi$
$137$	36.3518	−	71.3445i	0.265342	−	0.520763i	0.984783	+	0.173791i	$0.0556018\pi$
$138$	−19.4495	−	9.91001i	−0.140938	−	0.0718116i
$139$	−34.6269	−	11.2510i	−0.249115	−	0.0809422i	0.181798	−	0.983336i	$-0.441808\pi$
$139$	−34.6269	−	11.2510i	−0.249115	−	0.0809422i	−0.430913	+	0.902394i	$0.641808\pi$
$140$	35.3305	+	18.6738i	0.252360	+	0.133384i
$141$	−61.1834	−	188.303i	−0.433925	−	1.33548i
$142$	51.0487	+	8.08531i	0.359498	+	0.0569388i
$143$	27.2876	−	27.2876i	0.190823	−	0.190823i
$144$	22.3456	+	30.7561i	0.155178	+	0.213584i
$145$	−118.780	+	36.6356i	−0.819172	+	0.252659i
$146$	62.8998	+	45.6994i	0.430820	+	0.313009i
$147$	43.8971	+	277.155i	0.298620	+	1.88541i
$148$	−8.55536	−	16.7908i	−0.0578065	−	0.113452i
$149$		−	134.550i		−	0.903021i	−0.892266	−	0.451510i	$-0.850885\pi$
$149$		−	134.550i		−	0.903021i	0.892266	−	0.451510i	$-0.149115\pi$
$150$	−124.390	−	96.1991i	−0.829270	−	0.641327i
$151$	4.03813			0.0267426			0.0133713	−	0.999911i	$-0.495744\pi$
$151$	4.03813			0.0267426			0.0133713	+	0.999911i	$0.495744\pi$
$152$	−33.7455	+	17.1942i	−0.222010	+	0.113120i
$153$	49.2956	−	7.80766i	0.322194	−	0.0510305i
$154$	−56.7277	+	78.0790i	−0.368362	+	0.507006i
$155$	242.844	+	3.63912i	1.56674	+	0.0234782i
$156$	16.2624	−	11.8154i	0.104246	−	0.0757395i
$157$	110.437	+	110.437i	0.703420	+	0.703420i	0.965143	−	0.261723i	$-0.0842907\pi$
$157$	110.437	+	110.437i	0.703420	+	0.703420i	−0.261723	+	0.965143i	$0.584291\pi$
$158$	−22.5348	+	142.279i	−0.142626	+	0.900503i
$159$	−53.0541	+	17.2383i	−0.333674	+	0.108417i
$160$	7.84334	+	54.8257i	0.0490209	+	0.342661i
$161$	12.2289	−	37.6365i	0.0759556	−	0.233767i
$162$	81.6164	−	160.181i	0.503805	−	0.988773i
$163$	−159.166	−	81.0992i	−0.976480	−	0.497541i	−0.108476	−	0.994099i	$-0.534597\pi$
$163$	−159.166	−	81.0992i	−0.976480	−	0.497541i	−0.868004	+	0.496558i	$0.834597\pi$
$164$	−23.2188	−	7.54425i	−0.141578	−	0.0460015i
$165$	−57.8988	+	56.1892i	−0.350902	+	0.340540i
$166$	−34.7894	−	107.071i	−0.209575	−	0.645005i
$167$	31.9422	+	5.05914i	0.191270	+	0.0302943i	0.251335	−	0.967900i	$-0.419131\pi$
$167$	31.9422	+	5.05914i	0.191270	+	0.0302943i	−0.0600642	+	0.998195i	$0.519131\pi$
$168$	−238.417	+	238.417i	−1.41915	+	1.41915i
$169$	−59.0202	−	81.2343i	−0.349232	−	0.480677i
$170$	−143.351	−	48.9643i	−0.843243	−	0.288025i
$171$	−10.7376	−	7.80132i	−0.0627930	−	0.0456218i
$172$	−2.10567	−	13.2947i	−0.0122423	−	0.0772948i
$173$	71.4907	+	140.308i	0.413241	+	0.811031i	0.999999	+	0.00126870i	$0.000403840\pi$
$173$	71.4907	+	140.308i	0.413241	+	0.811031i	−0.586758	+	0.809762i	$0.699596\pi$
$174$		−	156.370i		−	0.898680i
$175$	136.976	−	250.015i	0.782719	−	1.42865i
$176$	−59.2018			−0.336374
$177$	163.597	−	83.3569i	0.924278	−	0.470943i
$178$	−171.658	+	27.1880i	−0.964372	+	0.152741i
$179$	18.5657	−	25.5534i	0.103719	−	0.142757i	−0.754003	−	0.656871i	$-0.771879\pi$
$179$	18.5657	−	25.5534i	0.103719	−	0.142757i	0.857721	+	0.514115i	$0.171879\pi$
$180$	−8.57485	+	6.03578i	−0.0476380	+	0.0335321i
$181$	−17.5232	+	12.7314i	−0.0968135	+	0.0703391i	−0.635139	−	0.772398i	$-0.719057\pi$
$181$	−17.5232	+	12.7314i	−0.0968135	+	0.0703391i	0.538325	+	0.842737i	$0.319057\pi$
$182$	−121.293	−	121.293i	−0.666443	−	0.666443i
$183$	44.1042	−	278.463i	0.241007	−	1.52166i
$184$	28.1815	−	9.15673i	0.153160	−	0.0497648i
$185$	−120.683	+	59.2303i	−0.652340	+	0.320164i
$186$	−94.4142	+	290.577i	−0.507603	+	1.56224i
$187$	−35.2855	+	69.2517i	−0.188693	+	0.370330i
$188$	35.7054	+	18.1928i	0.189923	+	0.0967704i
$189$	225.629	+	73.3113i	1.19380	+	0.387890i
$190$	17.7484	+	36.1627i	0.0934125	+	0.190330i
$191$	34.1484	+	105.098i	0.178788	+	0.550252i	0.999786	−	0.0206784i	$-0.00658262\pi$
$191$	34.1484	+	105.098i	0.178788	+	0.550252i	−0.820998	+	0.570930i	$0.806583\pi$
$192$	−242.639	−	38.4302i	−1.26374	−	0.200158i
$193$	202.877	−	202.877i	1.05118	−	1.05118i	0.0525601	−	0.998618i	$-0.483262\pi$
$193$	202.877	−	202.877i	1.05118	−	1.05118i	0.998618	−	0.0525601i	$-0.0167381\pi$
$194$	155.648	+	214.231i	0.802311	+	1.10429i
$195$	−82.5401	−	117.262i	−0.423283	−	0.601345i
$196$	−45.9476	−	33.3829i	−0.234427	−	0.170321i
$197$	18.4724	+	116.630i	0.0937684	+	0.592030i	0.989170	+	0.146772i	$0.0468882\pi$
$197$	18.4724	+	116.630i	0.0937684	+	0.592030i	−0.895402	+	0.445259i	$0.853112\pi$
$198$	−11.4972	−	22.5645i	−0.0580666	−	0.113962i
$199$			304.416i			1.52973i	0.644192	+	0.764864i	$0.277194\pi$
$199$			304.416i			1.52973i	−0.644192	+	0.764864i	$0.722806\pi$
$200$	211.739	−	27.0603i	1.05869	−	0.135301i
$201$	13.1295			0.0653210
$202$	185.566	−	94.5504i	0.918641	−	0.468071i
$203$	279.995	−	44.3469i	1.37929	−	0.218457i
$204$	−23.7967	+	32.7533i	−0.116650	+	0.160555i
$205$	−56.2947	+	164.812i	−0.274608	+	0.803963i
$206$	234.398	−	170.300i	1.13785	−	0.826700i
$207$	7.34272	+	7.34272i	0.0354721	+	0.0354721i
$208$	16.4604	−	103.927i	0.0791364	−	0.499648i
$209$	19.6570	−	6.38694i	0.0940526	−	0.0305595i
$210$	249.759	+	257.358i	1.18933	+	1.22552i
$211$	−100.154	+	308.242i	−0.474663	+	1.46086i	0.371748	+	0.928334i	$0.378759\pi$
$211$	−100.154	+	308.242i	−0.474663	+	1.46086i	−0.846411	+	0.532530i	$0.821241\pi$
$212$	5.12580	−	10.0599i	0.0241783	−	0.0474526i
$213$	−87.8005	−	44.7366i	−0.412209	−	0.210031i
$214$	−85.6714	−	27.8363i	−0.400334	−	0.130076i
$215$	−95.0556	+	13.5986i	−0.442119	+	0.0632493i
$216$	54.8940	+	168.946i	0.254139	+	0.782159i
$217$	−547.080	−	86.6490i	−2.52111	−	0.399304i
$218$	91.1174	−	91.1174i	0.417970	−	0.417970i
$219$	−87.1288	−	119.922i	−0.397848	−	0.547591i
$220$	0.244678	−	16.3278i	0.00111217	−	0.0742172i
$221$	−111.758	−	81.1972i	−0.505694	−	0.367408i
$222$	−26.4558	−	167.035i	−0.119170	−	0.752410i
$223$	17.0342	+	33.4316i	0.0763868	+	0.149917i	0.926041	−	0.377422i	$-0.123189\pi$
$223$	17.0342	+	33.4316i	0.0763868	+	0.149917i	−0.849654	+	0.527340i	$0.823189\pi$
$224$		−	126.310i		−	0.563884i
$225$	42.1364	+	61.8092i	0.187273	+	0.274707i
$226$	−203.179			−0.899023
$227$	−259.847	+	132.399i	−1.14470	+	0.583254i	−0.920289	−	0.391240i	$-0.872046\pi$
$227$	−259.847	+	132.399i	−1.14470	+	0.583254i	−0.224413	+	0.974494i	$0.572046\pi$
$228$	10.6335	−	1.68419i	0.0466384	−	0.00738679i
$229$	205.786	−	283.240i	0.898627	−	1.23685i	−0.0722771	−	0.997385i	$-0.523027\pi$
$229$	205.786	−	283.240i	0.898627	−	1.23685i	0.970904	−	0.239469i	$-0.0769734\pi$
$230$	−9.28912	−	30.1172i	−0.0403875	−	0.130944i
$231$	148.863	−	108.155i	0.644427	−	0.468203i
$232$	150.096	+	150.096i	0.646967	+	0.646967i
$233$	−12.3861	+	78.2025i	−0.0531590	+	0.335633i	0.946748	+	0.321976i	$0.104347\pi$
$233$	−12.3861	+	78.2025i	−0.0531590	+	0.335633i	−0.999907	+	0.0136566i	$0.995653\pi$
$234$	42.8079	−	13.9091i	0.182940	−	0.0594407i
$235$	133.585	−	252.741i	0.568448	−	1.07549i
$236$	−11.4836	+	35.3430i	−0.0486595	+	0.149758i
$237$	124.687	−	244.712i	0.526105	−	1.03254i
$238$	307.822	+	156.843i	1.29337	+	0.659004i
$239$	−375.540	−	122.021i	−1.57130	−	0.510546i	−0.611503	−	0.791242i	$-0.709435\pi$
$239$	−375.540	−	122.021i	−1.57130	−	0.510546i	−0.959797	+	0.280696i	$0.909435\pi$
$240$	−37.6656	+	216.740i	−0.156940	+	0.903084i
$241$	−9.67765	−	29.7847i	−0.0401562	−	0.123588i	0.928969	−	0.370158i	$-0.120696\pi$
$241$	−9.67765	−	29.7847i	−0.0401562	−	0.123588i	−0.969125	+	0.246570i	$0.920696\pi$
$242$	−178.120	−	28.2115i	−0.736034	−	0.116576i
$243$	−109.962	+	109.962i	−0.452520	+	0.452520i
$244$	33.5404	+	46.1644i	0.137461	+	0.189199i
$245$	−243.030	+	324.174i	−0.991960	+	1.32316i
$246$	−177.251	−	128.780i	−0.720531	−	0.523496i
$247$	5.74666	+	36.2830i	0.0232658	+	0.146895i
$248$	−188.292	−	369.544i	−0.759243	−	1.49010i
$249$			214.643i			0.862020i
$250$	−25.4043	−	225.617i	−0.101617	−	0.902469i
$251$	−155.694			−0.620295			−0.310147	−	0.950689i	$-0.600378\pi$
$251$	−155.694			−0.620295			−0.310147	+	0.950689i	$0.600378\pi$
$252$	21.3083	−	10.8571i	0.0845569	−	0.0430839i
$253$	−15.9718	+	2.52968i	−0.0631295	+	0.00999874i
$254$	4.37627	−	6.02342i	0.0172294	−	0.0237143i
$255$	231.084	+	173.241i	0.906212	+	0.679378i
$256$	105.333	−	76.5287i	0.411456	−	0.298940i
$257$	−49.8494	−	49.8494i	−0.193967	−	0.193967i	0.603441	−	0.797408i	$-0.293796\pi$
$257$	−49.8494	−	49.8494i	−0.193967	−	0.193967i	−0.797408	+	0.603441i	$0.793796\pi$
$258$	18.8968	−	119.309i	0.0732432	−	0.462440i
$259$	291.589	−	94.7429i	1.12582	−	0.365803i
$260$	28.5948	+	4.96928i	0.109980	+	0.0191126i
$261$	−22.9870	+	70.7466i	−0.0880726	+	0.271060i
$262$	−73.7042	+	144.653i	−0.281314	+	0.552109i
$263$	−419.056	−	213.520i	−1.59337	−	0.811863i	−0.999976	−	0.00695066i	$-0.997788\pi$
$263$	−419.056	−	213.520i	−1.59337	−	0.811863i	−0.593394	−	0.804912i	$-0.702212\pi$
$264$	131.035	+	42.5760i	0.496346	+	0.161273i
$265$	−71.2093	−	37.6374i	−0.268714	−	0.142028i
$266$	−28.3897	−	87.3747i	−0.106728	−	0.328476i
$267$	327.277	+	51.8356i	1.22576	+	0.194141i
$268$	−1.87904	+	1.87904i	−0.00701135	+	0.00701135i
$269$	219.028	+	301.467i	0.814232	+	1.12069i	0.990657	+	0.136380i	$0.0435467\pi$
$269$	219.028	+	301.467i	0.814232	+	1.12069i	−0.176425	+	0.984314i	$0.556453\pi$
$270$	180.551	−	55.6877i	0.668707	−	0.206251i
$271$	269.883	+	196.082i	0.995878	+	0.723548i	0.961201	−	0.275850i	$-0.0889595\pi$
$271$	269.883	+	196.082i	0.995878	+	0.723548i	0.0346779	+	0.999399i	$0.488959\pi$
$272$	33.1519	+	209.313i	0.121882	+	0.769533i
$273$	148.473	+	291.395i	0.543857	+	1.06738i
$274$			145.438i			0.530796i
$275$	−116.439	−	3.49056i	−0.423415	−	0.0126929i
$276$	−8.42327			−0.0305191
$277$	255.508	−	130.188i	0.922413	−	0.469993i	0.0727686	−	0.997349i	$-0.476817\pi$
$277$	255.508	−	130.188i	0.922413	−	0.469993i	0.849644	+	0.527356i	$0.176817\pi$
$278$	65.3169	−	10.3452i	0.234953	−	0.0372129i
$279$	85.4316	−	117.586i	0.306206	−	0.421457i
$280$	−486.770	−	7.29444i	−1.73847	−	0.0260516i
$281$	−162.496	+	118.060i	−0.578278	+	0.420143i	−0.838103	−	0.545512i	$-0.816335\pi$
$281$	−162.496	+	118.060i	−0.578278	+	0.420143i	0.259825	+	0.965656i	$0.416335\pi$
$282$	254.293	+	254.293i	0.901749	+	0.901749i
$283$	−25.4422	+	160.636i	−0.0899019	+	0.567618i	0.901083	+	0.433646i	$0.142773\pi$
$283$	−25.4422	+	160.636i	−0.0899019	+	0.567618i	−0.990985	+	0.133972i	$0.957227\pi$
$284$	18.9681	−	6.16312i	0.0667892	−	0.0217011i
$285$	−10.8766	−	76.0286i	−0.0381636	−	0.266767i
$286$	−21.6601	+	66.6630i	−0.0757347	+	0.233088i
$287$	180.324	−	353.905i	0.628306	−	1.23312i
$288$	29.5316	+	15.0471i	0.102540	+	0.0522469i
$289$	−10.2505	−	3.33060i	−0.0354690	−	0.0115246i
$290$	162.021	−	157.237i	0.558692	−	0.542195i
$291$	−156.013	−	480.157i	−0.536126	−	1.65002i
$292$	29.6323	+	4.69329i	0.101480	+	0.0160729i
$293$	−269.435	+	269.435i	−0.919573	+	0.919573i	−0.996998	−	0.0774250i	$-0.975330\pi$
$293$	−269.435	+	269.435i	−0.919573	+	0.919573i	0.0774250	+	0.996998i	$0.475330\pi$
$294$	−299.585	−	412.344i	−1.01900	−	1.40253i
$295$	250.872	+	85.6901i	0.850415	+	0.290475i
$296$	185.727	+	134.939i	0.627458	+	0.455875i
$297$	−15.1653	−	95.7498i	−0.0510616	−	0.322390i
$298$	110.950	+	217.752i	0.372317	+	0.730713i
$299$		−	28.7413i		−	0.0961246i
$300$	−59.6210	−	11.2839i	−0.198737	−	0.0376130i
$301$	218.993			0.727553
$302$	−6.53520	+	3.32985i	−0.0216397	+	0.0110260i
$303$	−392.182	+	62.1156i	−1.29433	+	0.205002i
$304$	33.1250	−	45.5927i	0.108964	−	0.149976i
$305$	332.874	−	234.308i	1.09139	−	0.768223i
$306$	−73.3406	+	53.2850i	−0.239675	+	0.174134i
$307$	15.5293	+	15.5293i	0.0505840	+	0.0505840i	0.731946	−	0.681362i	$-0.238612\pi$
$307$	15.5293	+	15.5293i	0.0505840	+	0.0505840i	−0.681362	+	0.731946i	$0.738612\pi$
$308$	−5.82589	+	36.7832i	−0.0189152	+	0.119426i
$309$	−525.357	+	170.699i	−1.70018	+	0.552423i
$310$	−396.014	+	194.361i	−1.27746	+	0.626970i
$311$	133.569	−	411.082i	0.429481	−	1.32181i	−0.469157	−	0.883115i	$-0.655442\pi$
$311$	133.569	−	411.082i	0.429481	−	1.32181i	0.898638	−	0.438691i	$-0.144558\pi$
$312$	−111.174	+	218.191i	−0.356326	+	0.699329i
$313$	83.8100	+	42.7034i	0.267764	+	0.136432i	0.582718	−	0.812674i	$-0.301989\pi$
$313$	83.8100	+	42.7034i	0.267764	+	0.136432i	−0.314954	+	0.949107i	$0.601989\pi$
$314$	−269.795	−	87.6617i	−0.859220	−	0.279177i
$315$	−75.1659	−	153.152i	−0.238622	−	0.486197i
$316$	17.1774	+	52.8667i	0.0543589	+	0.167300i
$317$	190.794	+	30.2188i	0.601874	+	0.0953274i	0.449933	−	0.893062i	$-0.351448\pi$
$317$	190.794	+	30.2188i	0.601874	+	0.0953274i	0.151940	+	0.988390i	$0.451448\pi$
$318$	71.6467	−	71.6467i	0.225304	−	0.225304i
$319$	−68.0893	−	93.7169i	−0.213446	−	0.293783i
$320$	−204.164	−	290.050i	−0.638013	−	0.906406i
$321$	138.944	+	100.948i	0.432846	+	0.314481i
$322$	11.2443	+	70.9940i	0.0349203	+	0.220478i
$323$	−33.5892	−	65.9224i	−0.103991	−	0.204094i
$324$		−	69.3720i		−	0.214111i
$325$	38.5021	−	203.435i	0.118468	−	0.625952i
$326$	324.465			0.995292
$327$	−218.902	+	111.536i	−0.669424	+	0.341088i
$328$	293.752	−	46.5257i	0.895585	−	0.141847i
$329$	−383.217	+	527.453i	−1.16479	+	1.60320i
$330$	47.3682	−	138.679i	0.143540	−	0.420238i
$331$	−220.979	+	160.551i	−0.667611	+	0.485048i	−0.869225	−	0.494417i	$-0.835382\pi$
$331$	−220.979	+	160.551i	−0.667611	+	0.485048i	0.201613	+	0.979465i	$0.435382\pi$
$332$	−30.7187	−	30.7187i	−0.0925264	−	0.0925264i
$333$	−12.5853	+	79.4608i	−0.0377938	+	0.238621i
$334$	−55.8662	+	18.1520i	−0.167264	+	0.0543474i
$335$	13.2023	+	13.6040i	0.0394097	+	0.0406089i
$336$	155.038	−	477.157i	0.461421	−	1.42011i
$337$	−258.565	+	507.462i	−0.767254	+	1.50582i	0.0928377	+	0.995681i	$0.470406\pi$
$337$	−258.565	+	507.462i	−0.767254	+	1.50582i	−0.860092	+	0.510140i	$0.829594\pi$
$338$	162.503	+	82.7994i	0.480778	+	0.244969i
$339$	368.415	+	119.705i	1.08677	+	0.353113i
$340$	−57.8653	+	8.27818i	−0.170192	+	0.0243476i
$341$	69.9428	+	215.262i	0.205111	+	0.631267i
$342$	23.8105	+	3.77121i	0.0696212	+	0.0110269i
$343$	258.277	−	258.277i	0.752995	−	0.752995i
$344$	96.3838	+	132.661i	0.280185	+	0.385642i
$345$	−0.900365	+	60.0828i	−0.00260975	+	0.174153i
$346$	−231.397	−	168.120i	−0.668778	−	0.485896i
$347$	−52.3196	−	330.333i	−0.150777	−	0.951968i	−0.940817	−	0.338914i	$-0.889941\pi$
$347$	−52.3196	−	330.333i	−0.150777	−	0.951968i	0.790040	−	0.613055i	$-0.210059\pi$
$348$	−27.3939	−	53.7636i	−0.0787182	−	0.154493i
$349$		−	502.965i		−	1.44116i	−0.693372	−	0.720580i	$-0.743876\pi$
$349$		−	502.965i		−	1.44116i	0.693372	−	0.720580i	$-0.256124\pi$
$350$	−15.5154	+	517.568i	−0.0443297	+	1.47877i
$351$	172.302			0.490889
$352$	−45.9884	+	23.4323i	−0.130649	+	0.0665690i
$353$	173.477	−	27.4761i	0.491437	−	0.0778360i	0.0942023	−	0.995553i	$-0.469970\pi$
$353$	173.477	−	27.4761i	0.491437	−	0.0778360i	0.397235	+	0.917717i	$0.369970\pi$
$354$	−196.025	+	269.805i	−0.553743	+	0.762162i
$355$	−41.9337	−	135.958i	−0.118123	−	0.382979i
$356$	−54.2570	+	39.4200i	−0.152407	+	0.110730i
$357$	−465.752	−	465.752i	−1.30463	−	1.30463i
$358$	−8.97475	+	56.6643i	−0.0250691	+	0.158280i
$359$	−129.730	+	42.1519i	−0.361366	+	0.117415i	−0.484072	−	0.875028i	$-0.660843\pi$
$359$	−129.730	+	42.1519i	−0.361366	+	0.117415i	0.122706	+	0.992443i	$0.460843\pi$
$360$	59.6936	−	112.939i	0.165816	−	0.313720i
$361$	105.475	−	324.619i	0.292175	−	0.899223i
$362$	17.8608	−	35.0539i	0.0493393	−	0.0968339i
$363$	306.355	+	156.096i	0.843954	+	0.430016i
$364$	−62.9519	−	20.4543i	−0.172945	−	0.0561932i
$365$	36.6444	−	210.864i	0.100396	−	0.577710i
$366$	158.244	+	487.026i	0.432362	+	1.33067i
$367$	330.443	+	52.3370i	0.900389	+	0.142608i	0.589433	−	0.807817i	$-0.299351\pi$
$367$	330.443	+	52.3370i	0.900389	+	0.142608i	0.310955	+	0.950425i	$0.399351\pi$
$368$	−31.1778	+	31.1778i	−0.0847222	+	0.0847222i
$369$	61.2623	+	84.3204i	0.166023	+	0.228510i
$370$	146.469	−	195.372i	0.395861	−	0.528033i
$371$	148.609	+	107.971i	0.400563	+	0.291026i
$372$	18.4434	+	116.447i	0.0495790	+	0.313030i
$373$	−83.7541	−	164.377i	−0.224542	−	0.440688i	0.751060	−	0.660233i	$-0.229543\pi$
$373$	−83.7541	−	164.377i	−0.224542	−	0.440688i	−0.975602	+	0.219545i	$0.929543\pi$
$374$		−	141.172i		−	0.377465i
$375$	−86.8605	+	424.068i	−0.231628	+	1.13085i
$376$	−488.180			−1.29835
$377$	183.448	−	93.4716i	0.486600	−	0.247935i
$378$	−425.605	+	67.4092i	−1.12594	+	0.178331i
$379$	143.236	−	197.147i	0.377931	−	0.520178i	−0.577104	−	0.816671i	$-0.695817\pi$
$379$	143.236	−	197.147i	0.377931	−	0.520178i	0.955035	+	0.296493i	$0.0958171\pi$
$380$	12.4375	+	9.32427i	0.0327303	+	0.0245376i
$381$	−11.4840	+	8.34365i	−0.0301418	+	0.0218993i
$382$	−141.929	−	141.929i	−0.371542	−	0.371542i
$383$	−101.123	+	638.468i	−0.264030	+	1.66702i	0.397882	+	0.917437i	$0.369745\pi$
$383$	−101.123	+	638.468i	−0.264030	+	1.66702i	−0.661912	+	0.749582i	$0.730255\pi$
$384$	278.445	−	90.4724i	0.725118	−	0.235605i
$385$	261.750	+	45.4876i	0.679871	+	0.118150i
$386$	−161.038	+	495.625i	−0.417198	+	1.28400i
$387$	−26.0883	+	51.2012i	−0.0674117	+	0.132303i
$388$	91.0458	+	46.3902i	0.234654	+	0.119562i
$389$	698.667	+	227.011i	1.79606	+	0.583575i	0.999772	−	0.0213423i	$-0.00679398\pi$
$389$	698.667	+	227.011i	1.79606	+	0.583575i	0.796288	+	0.604918i	$0.206794\pi$
$390$	230.276	+	121.711i	0.590450	+	0.312080i
$391$	17.8878	+	55.0530i	0.0457489	+	0.140801i
$392$	683.364	+	108.234i	1.74328	+	0.276108i
$393$	218.868	−	218.868i	0.556916	−	0.556916i
$394$	−126.069	−	173.519i	−0.319971	−	0.440402i
$395$	378.932	−	116.875i	0.959321	−	0.295886i
$396$	−7.90599	−	5.74404i	−0.0199646	−	0.0145051i
$397$	29.3710	+	185.441i	0.0739823	+	0.467106i	0.996669	+	0.0815548i	$0.0259886\pi$
$397$	29.3710	+	185.441i	0.0739823	+	0.467106i	−0.922687	+	0.385551i	$0.874011\pi$
$398$	−251.022	−	492.659i	−0.630709	−	1.23784i
$399$			175.158i			0.438993i
$400$	−262.446	+	178.914i	−0.656116	+	0.447286i
$401$	88.3502			0.220325			0.110162	−	0.993914i	$-0.464863\pi$
$401$	88.3502			0.220325			0.110162	+	0.993914i	$0.464863\pi$
$402$	−21.2485	+	10.8267i	−0.0528570	+	0.0269320i
$403$	−397.332	+	62.9312i	−0.985935	+	0.156157i
$404$	47.2377	−	65.0171i	0.116925	−	0.160933i
$405$	−494.827	−	7.41518i	−1.22180	−	0.0183091i
$406$	−416.568	+	302.655i	−1.02603	+	0.745455i
$407$	−88.5888	−	88.5888i	−0.217663	−	0.217663i
$408$	77.1536	−	487.129i	0.189102	−	1.19394i
$409$	−172.391	+	56.0134i	−0.421495	+	0.136952i	−0.512082	−	0.858936i	$-0.671126\pi$
$409$	−172.391	+	56.0134i	−0.421495	+	0.136952i	0.0905870	+	0.995889i	$0.471126\pi$
$410$	−44.7989	−	313.149i	−0.109266	−	0.763778i
$411$	85.6864	−	263.715i	0.208483	−	0.641644i
$412$	50.7571	−	99.6164i	0.123197	−	0.241787i
$413$	−538.704	−	274.483i	−1.30437	−	0.664609i
$414$	−17.9381	−	5.82844i	−0.0433288	−	0.0140784i
$415$	−222.399	+	215.832i	−0.535901	+	0.520077i
$416$	−28.3480	−	87.2463i	−0.0681443	−	0.209727i
$417$	−124.531	−	19.7238i	−0.298635	−	0.0472992i
$418$	−26.5457	+	26.5457i	−0.0635064	+	0.0635064i
$419$	113.418	+	156.106i	0.270687	+	0.372569i	0.922622	−	0.385706i	$-0.126042\pi$
$419$	113.418	+	156.106i	0.270687	+	0.372569i	−0.651934	+	0.758275i	$0.726042\pi$
$420$	130.958	+	44.7312i	0.311806	+	0.106503i
$421$	−659.764	−	479.346i	−1.56713	−	1.13859i	−0.929837	−	0.367972i	$-0.880052\pi$
$421$	−659.764	−	479.346i	−1.56713	−	1.13859i	−0.637298	−	0.770617i	$-0.719948\pi$
$422$	−92.0908	−	581.439i	−0.218225	−	1.37782i
$423$	−77.6679	−	152.432i	−0.183612	−	0.360359i
$424$			137.544i			0.324396i
$425$	52.8627	+	413.635i	0.124383	+	0.973260i
$426$	178.984			0.420150
$427$	−827.186	+	421.472i	−1.93720	+	0.987055i
$428$	−34.3323	+	5.43771i	−0.0802157	+	0.0127049i
$429$	78.5505	−	108.116i	0.183101	−	0.252017i
$430$	142.622	−	100.391i	0.331679	−	0.233467i
$431$	−199.776	+	145.146i	−0.463518	+	0.336765i	−0.794910	−	0.606728i	$-0.792482\pi$
$431$	−199.776	+	145.146i	−0.463518	+	0.336765i	0.331392	+	0.943493i	$0.392482\pi$
$432$	−186.909	−	186.909i	−0.432659	−	0.432659i
$433$	120.729	−	762.250i	0.278819	−	1.76039i	−0.308679	−	0.951166i	$-0.599887\pi$
$433$	120.729	−	762.250i	0.278819	−	1.76039i	0.587498	−	0.809226i	$-0.300113\pi$
$434$	956.832	−	310.894i	2.20468	−	0.716345i
$435$	−386.422	+	189.653i	−0.888326	+	0.435984i
$436$	15.3657	−	47.2908i	0.0352424	−	0.108465i
$437$	6.98848	−	13.7157i	0.0159919	−	0.0313860i
$438$	239.895	+	122.233i	0.547707	+	0.279070i
$439$	−16.9661	−	5.51263i	−0.0386472	−	0.0125572i	0.289630	−	0.957139i	$-0.406468\pi$
$439$	−16.9661	−	5.51263i	−0.0386472	−	0.0125572i	−0.328277	+	0.944582i	$0.606468\pi$
$440$	87.6468	+	178.582i	0.199197	+	0.405869i
$441$	74.9254	+	230.597i	0.169899	+	0.522895i
$442$	247.822	+	39.2512i	0.560684	+	0.0888036i
$443$	184.814	−	184.814i	0.417187	−	0.417187i	−0.467046	−	0.884233i	$-0.654682\pi$
$443$	184.814	−	184.814i	0.417187	−	0.417187i	0.884233	+	0.467046i	$0.154682\pi$
$444$	−38.3584	−	52.7958i	−0.0863927	−	0.118909i
$445$	275.382	+	391.226i	0.618835	+	0.879160i
$446$	−55.1356	−	40.0583i	−0.123622	−	0.0898169i
$447$	−72.8897	−	460.207i	−0.163064	−	1.02955i
$448$	367.250	+	720.769i	0.819755	+	1.60886i
$449$		−	266.342i		−	0.593189i	−0.955004	−	0.296594i	$-0.904149\pi$
$449$		−	266.342i		−	0.593189i	0.955004	−	0.296594i	$-0.0958509\pi$
$450$	−119.160	−	65.2846i	−0.264801	−	0.145077i
$451$	−162.307			−0.359881
$452$	−69.8576	+	35.5942i	−0.154552	+	0.0787483i
$453$	13.8118	−	2.18757i	0.0304896	−	0.00482907i
$454$	311.354	−	428.542i	0.685801	−	0.943924i
$455$	−152.629	+	446.847i	−0.335448	+	0.982081i
$456$	−106.107	+	77.0910i	−0.232690	+	0.169059i
$457$	473.310	+	473.310i	1.03569	+	1.03569i	0.999339	+	0.0363511i	$0.0115735\pi$
$457$	473.310	+	473.310i	1.03569	+	1.03569i	0.0363511	+	0.999339i	$0.488427\pi$
$458$	−99.4779	+	628.079i	−0.217201	+	1.37135i
$459$	−330.040	+	107.236i	−0.719041	+	0.233630i
$460$	−8.46993	−	8.72764i	−0.0184129	−	0.0189731i
$461$	14.4681	−	44.5284i	0.0313843	−	0.0965909i	−0.934137	−	0.356914i	$-0.883829\pi$
$461$	14.4681	−	44.5284i	0.0313843	−	0.0965909i	0.965522	+	0.260323i	$0.0838290\pi$
$462$	−151.730	+	297.788i	−0.328421	+	0.644562i
$463$	308.662	+	157.271i	0.666657	+	0.339679i	0.754354	−	0.656468i	$-0.227950\pi$
$463$	308.662	+	157.271i	0.666657	+	0.339679i	−0.0876962	+	0.996147i	$0.527950\pi$
$464$	−300.395	−	97.6044i	−0.647404	−	0.210354i
$465$	832.583	−	119.109i	1.79050	−	0.256148i
$466$	−44.4407	−	136.775i	−0.0953664	−	0.293508i
$467$	−106.477	−	16.8643i	−0.228002	−	0.0361120i	0.0413877	−	0.999143i	$-0.486822\pi$
$467$	−106.477	−	16.8643i	−0.228002	−	0.0361120i	−0.269390	+	0.963031i	$0.586822\pi$
$468$	12.2816	−	12.2816i	0.0262428	−	0.0262428i
$469$	−25.4122	−	34.9769i	−0.0541838	−	0.0745776i
$470$	−7.78018	+	519.184i	−0.0165536	+	1.10465i
$471$	437.559	+	317.905i	0.929000	+	0.674958i
$472$	−70.8201	−	447.140i	−0.150042	−	0.947331i
$473$	−40.6263	−	79.7337i	−0.0858908	−	0.168570i
$474$			498.852i			1.05243i
$475$	67.8391	−	87.7194i	0.142819	−	0.184673i
$476$	133.313			0.280069
$477$	−42.9474	+	21.8828i	−0.0900365	+	0.0458759i
$478$	708.384	−	112.197i	1.48197	−	0.234722i
$479$	−214.282	+	294.934i	−0.447353	+	0.615729i	−0.971826	−	0.235698i	$-0.924262\pi$
$479$	−214.282	+	294.934i	−0.447353	+	0.615729i	0.524473	+	0.851427i	$0.324262\pi$
$480$	56.5276	+	183.274i	0.117766	+	0.381821i
$481$	180.146	−	130.884i	0.374524	−	0.272107i
$482$	40.2227	+	40.2227i	0.0834495	+	0.0834495i
$483$	21.4381	−	135.355i	0.0443852	−	0.280237i
$484$	−66.1840	+	21.5045i	−0.136744	+	0.0444308i
$485$	340.631	−	644.467i	0.702332	−	1.32880i
$486$	87.2850	−	268.636i	0.179599	−	0.552748i
$487$	−171.861	+	337.296i	−0.352897	+	0.692599i	−0.997405	−	0.0719988i	$-0.977062\pi$
$487$	−171.861	+	337.296i	−0.352897	+	0.692599i	0.644508	+	0.764598i	$0.277062\pi$
$488$	−619.381	−	315.590i	−1.26922	−	0.646701i
$489$	−588.337	−	191.162i	−1.20314	−	0.390925i
$490$	125.999	−	725.039i	0.257141	−	1.47967i
$491$	−80.8943	−	248.967i	−0.164754	−	0.507061i	0.834264	−	0.551365i	$-0.185893\pi$
$491$	−80.8943	−	248.967i	−0.164754	−	0.507061i	−0.999018	+	0.0443043i	$0.985893\pi$
$492$	−83.5033	−	13.2256i	−0.169722	−	0.0268813i
$493$	−293.216	+	293.216i	−0.594758	+	0.594758i
$494$	−39.2193	−	53.9808i	−0.0793914	−	0.109273i
$495$	−41.8170	+	55.7791i	−0.0844788	+	0.112685i
$496$	499.281	+	362.749i	1.00662	+	0.731349i
$497$	50.7602	+	320.487i	0.102133	+	0.644843i
$498$	−176.995	−	347.373i	−0.355412	−	0.697535i
$499$			75.2156i			0.150733i	0.997156	+	0.0753664i	$0.0240126\pi$
$499$			75.2156i			0.150733i	−0.997156	+	0.0753664i	$0.975987\pi$
$500$	−48.2597	−	73.1218i	−0.0965193	−	0.146244i
$501$	111.994			0.223541
$502$	251.971	−	128.386i	0.501935	−	0.255748i
$503$	778.940	−	123.372i	1.54859	−	0.245272i	0.677175	−	0.735822i	$-0.263204\pi$
$503$	778.940	−	123.372i	1.54859	−	0.245272i	0.871413	+	0.490549i	$0.163204\pi$
$504$	−171.244	+	235.697i	−0.339769	+	0.467652i
$505$	−458.715	−	343.894i	−0.908346	−	0.680978i
$506$	23.7623	−	17.2643i	0.0469611	−	0.0341193i
$507$	−245.876	−	245.876i	−0.484963	−	0.484963i
$508$	0.449440	−	2.83765i	0.000884724	−	0.00558593i
$509$	−193.504	+	62.8734i	−0.380166	+	0.123523i	−0.492865	−	0.870106i	$-0.664050\pi$
$509$	−193.504	+	62.8734i	−0.380166	+	0.123523i	0.112699	+	0.993629i	$0.464050\pi$
$510$	−516.836	−	89.8169i	−1.01340	−	0.176112i
$511$	−150.834	+	464.220i	−0.295175	+	0.908454i
$512$	−260.891	+	512.028i	−0.509553	+	1.00005i
$513$	82.2246	+	41.8955i	0.160282	+	0.0816677i
$514$	121.781	+	39.5690i	0.236928	+	0.0769826i
$515$	−705.134	−	372.696i	−1.36919	−	0.723682i
$516$	−14.4043	−	44.3317i	−0.0279152	−	0.0859142i
$517$	263.133	+	41.6762i	0.508962	+	0.0806116i
$518$	−393.774	+	393.774i	−0.760182	+	0.760182i
$519$	320.532	+	441.174i	0.617595	+	0.850046i
$520$	−337.864	+	104.208i	−0.649739	+	0.200401i
$521$	−626.036	−	454.842i	−1.20160	−	0.873016i	−0.207163	−	0.978307i	$-0.566423\pi$
$521$	−626.036	−	454.842i	−1.20160	−	0.873016i	−0.994442	+	0.105290i	$0.966423\pi$
$522$	−21.1363	−	133.450i	−0.0404911	−	0.255651i
$523$	328.674	+	645.059i	0.628440	+	1.23338i	0.957325	+	0.289013i	$0.0933271\pi$
$523$	328.674	+	645.059i	0.628440	+	1.23338i	−0.328885	+	0.944370i	$0.606673\pi$
$524$			62.6468i			0.119555i
$525$	333.064	−	929.339i	0.634408	−	1.77017i
$526$	854.259			1.62407
$527$	721.911	−	367.832i	1.36985	−	0.697973i
$528$	−202.490	+	32.0713i	−0.383504	+	0.0607411i
$529$	303.859	−	418.226i	0.574403	−	0.790598i
$530$	146.279	+	2.19205i	0.275998	+	0.00413595i
$531$	128.350	−	93.2517i	0.241714	−	0.175615i
$532$	−25.0679	−	25.0679i	−0.0471201	−	0.0471201i
$533$	45.1275	−	284.924i	0.0846670	−	0.534566i
$534$	−572.401	+	185.984i	−1.07191	+	0.348286i
$535$	35.1171	+	245.472i	0.0656395	+	0.458826i
$536$	10.0037	−	30.7882i	0.0186636	−	0.0574407i
$537$	49.6579	−	97.4590i	0.0924727	−	0.181488i
$538$	−603.060	−	307.275i	−1.12093	−	0.571142i
$539$	−359.099	−	116.678i	−0.666232	−	0.216472i
$540$	52.3217	−	50.7767i	0.0968921	−	0.0940310i
$541$	283.746	+	873.280i	0.524484	+	1.61420i	0.765334	+	0.643633i	$0.222574\pi$
$541$	283.746	+	873.280i	0.524484	+	1.61420i	−0.240850	+	0.970562i	$0.577426\pi$
$542$	−598.461	−	94.7870i	−1.10417	−	0.174884i
$543$	−53.0385	+	53.0385i	−0.0976768	+	0.0976768i
$544$	108.600	+	149.475i	0.199632	+	0.274769i
$545$	−335.680	−	114.658i	−0.615927	−	0.210381i
$546$	−480.570	−	349.154i	−0.880164	−	0.639477i
$547$	−55.9587	−	353.309i	−0.102301	−	0.645903i	−0.984548	−	0.175116i	$-0.943970\pi$
$547$	−55.9587	−	353.309i	−0.102301	−	0.645903i	0.882247	−	0.470787i	$-0.156030\pi$
$548$	25.4788	+	50.0049i	0.0464941	+	0.0912498i
$549$		−	243.608i		−	0.443730i
$550$	191.320	−	90.3670i	0.347855	−	0.164304i
$551$	110.271			0.200130
$552$	91.4299	−	46.5859i	0.165634	−	0.0843947i
$553$	−893.240	+	141.475i	−1.61526	+	0.255832i
$554$	−306.155	+	421.386i	−0.552626	+	0.760625i
$555$	−380.690	+	267.965i	−0.685928	+	0.482820i
$556$	20.6451	−	14.9995i	0.0371315	−	0.0269776i
$557$	404.198	+	404.198i	0.725670	+	0.725670i	0.969754	−	0.244084i	$-0.0784872\pi$
$557$	404.198	+	404.198i	0.725670	+	0.725670i	−0.244084	+	0.969754i	$0.578487\pi$
$558$	−41.2981	+	260.746i	−0.0740110	+	0.467287i
$559$	151.265	−	49.1491i	0.270600	−	0.0879233i
$560$	650.295	−	319.160i	1.16124	−	0.569929i
$561$	−83.1729	+	255.980i	−0.148258	+	0.456292i
$562$	165.627	−	325.060i	0.294709	−	0.578399i
$563$	872.036	+	444.324i	1.54891	+	0.789208i	0.998942	−	0.0459785i	$-0.0146406\pi$
$563$	872.036	+	444.324i	1.54891	+	0.789208i	0.549966	+	0.835187i	$0.314641\pi$
$564$	131.980	+	42.8830i	0.234008	+	0.0760338i
$565$	246.425	+	502.096i	0.436150	+	0.888665i
$566$	−91.2859	−	280.949i	−0.161282	−	0.496376i
$567$	1114.75	+	176.559i	1.96605	+	0.311391i
$568$	−171.803	+	171.803i	−0.302469	+	0.302469i
$569$	−431.512	−	593.925i	−0.758369	−	1.04381i	−0.997348	−	0.0727807i	$-0.976813\pi$
$569$	−431.512	−	593.925i	−0.758369	−	1.04381i	0.238979	−	0.971025i	$-0.423187\pi$
$570$	80.2959	+	114.074i	0.140870	+	0.200130i
$571$	−612.726	−	445.171i	−1.07308	−	0.779635i	−0.0966128	−	0.995322i	$-0.530801\pi$
$571$	−612.726	−	445.171i	−1.07308	−	0.779635i	−0.976463	+	0.215687i	$0.930801\pi$
$572$	4.23121	+	26.7148i	0.00739723	+	0.0467042i
$573$	173.734	+	340.972i	0.303201	+	0.595065i
$574$			721.447i			1.25688i
$575$	−63.1592	+	59.4827i	−0.109842	+	0.103448i
$576$	−212.268			−0.368520
$577$	367.699	−	187.352i	0.637261	−	0.324700i	−0.105339	−	0.994436i	$-0.533593\pi$
$577$	367.699	−	187.352i	0.637261	−	0.324700i	0.742599	+	0.669736i	$0.233593\pi$
$578$	19.3356	−	3.06246i	0.0334527	−	0.00529838i
$579$	584.005	−	803.815i	1.00865	−	1.38828i
$580$	28.1607	−	82.4453i	0.0485529	−	0.142147i
$581$	571.806	−	415.441i	0.984175	−	0.715045i
$582$	648.426	+	648.426i	1.11413	+	1.11413i
$583$	11.7422	−	74.1373i	0.0201410	−	0.127165i
$584$	−347.599	+	112.942i	−0.595203	+	0.193393i
$585$	−86.2916	−	88.9172i	−0.147507	−	0.151995i
$586$	213.870	−	658.224i	0.364966	−	1.12325i
$587$	−199.151	+	390.856i	−0.339269	+	0.665853i	−0.996104	−	0.0881807i	$-0.971895\pi$
$587$	−199.151	+	390.856i	−0.339269	+	0.665853i	0.656835	+	0.754034i	$0.271895\pi$
$588$	−175.241	−	89.2898i	−0.298029	−	0.151853i
$589$	−204.913	−	66.5803i	−0.347900	−	0.113040i
$590$	−476.666	+	68.1916i	−0.807908	+	0.115579i
$591$	126.364	+	388.907i	0.213813	+	0.658050i
$592$	−337.397	−	53.4384i	−0.569927	−	0.0902675i
$593$	−279.182	+	279.182i	−0.470796	+	0.470796i	−0.902172	−	0.431376i	$-0.858028\pi$
$593$	−279.182	+	279.182i	−0.470796	+	0.470796i	0.431376	+	0.902172i	$0.358028\pi$
$594$	103.499	+	142.454i	0.174240	+	0.239821i
$595$	14.2498	−	950.914i	0.0239493	−	1.59817i
$596$	76.2945	+	55.4312i	0.128011	+	0.0930054i
$597$	164.911	+	1041.21i	0.276233	+	1.74406i
$598$	23.7001	+	46.5141i	0.0396323	+	0.0777828i
$599$		−	65.2707i		−	0.108966i	−0.998515	−	0.0544831i	$-0.982649\pi$
$599$		−	65.2707i		−	0.108966i	0.998515	−	0.0544831i	$-0.0173511\pi$
$600$	709.560	−	207.260i	1.18260	−	0.345434i
$601$	192.168			0.319747			0.159873	−	0.987138i	$-0.448891\pi$
$601$	192.168			0.319747			0.159873	+	0.987138i	$0.448891\pi$
$602$	−354.413	+	180.583i	−0.588727	+	0.299971i
$603$	11.2050	−	1.77470i	0.0185821	−	0.00294312i
$604$	−1.66361	+	2.28976i	−0.00275431	+	0.00379099i
$605$	146.316	+	474.386i	0.241845	+	0.784109i
$606$	583.477	−	423.921i	0.962833	−	0.699539i
$607$	−510.986	−	510.986i	−0.841822	−	0.841822i	0.147274	−	0.989096i	$-0.452950\pi$
$607$	−510.986	−	510.986i	−0.841822	−	0.841822i	−0.989096	+	0.147274i	$0.952950\pi$
$608$	7.68605	−	48.5278i	0.0126415	−	0.0798154i
$609$	933.655	−	303.363i	1.53310	−	0.498133i
$610$	−345.504	+	653.687i	−0.566400	+	1.07162i
$611$	−146.322	+	450.334i	−0.239480	+	0.737044i
$612$	−15.8813	+	31.1689i	−0.0259499	+	0.0509295i
$613$	−104.510	−	53.2504i	−0.170489	−	0.0868686i	0.366663	−	0.930354i	$-0.380500\pi$
$613$	−104.510	−	53.2504i	−0.170489	−	0.0868686i	−0.537153	+	0.843485i	$0.680500\pi$
$614$	−37.9377	−	12.3267i	−0.0617877	−	0.0200761i
$615$	−103.263	+	594.211i	−0.167908	+	0.966197i
$616$	−140.197	−	431.482i	−0.227593	−	0.700458i
$617$	−667.508	−	105.723i	−1.08186	−	0.171350i	−0.410043	−	0.912066i	$-0.634486\pi$
$617$	−667.508	−	105.723i	−1.08186	−	0.171350i	−0.671818	+	0.740716i	$0.734486\pi$
$618$	709.465	−	709.465i	1.14800	−	1.14800i
$619$	−239.653	−	329.853i	−0.387161	−	0.532881i	0.570303	−	0.821434i	$-0.306826\pi$
$619$	−239.653	−	329.853i	−0.387161	−	0.532881i	−0.957464	+	0.288553i	$0.906826\pi$
$620$	−102.109	+	136.202i	−0.164692	+	0.219681i
$621$	−58.4119	−	42.4387i	−0.0940610	−	0.0683393i
$622$	122.815	+	775.425i	0.197452	+	1.24666i
$623$	−495.356	−	972.191i	−0.795114	−	1.56050i
$624$		−	364.382i		−	0.583946i
$625$	−526.733	+	336.418i	−0.842773	+	0.538269i
$626$	−170.849			−0.272922
$627$	63.7736	−	32.4943i	0.101712	−	0.0518250i
$628$	−108.119	+	17.1243i	−0.172164	+	0.0272680i
$629$	−263.605	+	362.822i	−0.419087	+	0.576823i
$630$	247.936	+	185.875i	0.393549	+	0.295040i
$631$	620.336	−	450.700i	0.983099	−	0.714263i	0.0247001	−	0.999695i	$-0.492137\pi$
$631$	620.336	−	450.700i	0.983099	−	0.714263i	0.958399	+	0.285431i	$0.0921369\pi$
$632$	−478.837	−	478.837i	−0.757653	−	0.757653i
$633$	−175.577	+	1108.55i	−0.277373	+	1.75126i
$634$	−333.695	+	108.424i	−0.526332	+	0.171016i
$635$	−20.1928	−	3.50915i	−0.0317997	−	0.00552622i
$636$	12.0822	−	37.1853i	0.0189972	−	0.0584674i
$637$	304.668	−	597.945i	0.478286	−	0.938689i
$638$	187.473	+	95.5224i	0.293845	+	0.149722i
$639$	−80.9777	−	26.3112i	−0.126726	−	0.0411757i
$640$	373.730	+	197.533i	0.583953	+	0.308646i
$641$	8.23463	+	25.3436i	0.0128465	+	0.0395376i	0.957274	−	0.289181i	$-0.0933831\pi$
$641$	8.23463	+	25.3436i	0.0128465	+	0.0395376i	−0.944428	+	0.328719i	$0.893383\pi$
$642$	−308.105	−	48.7991i	−0.479915	−	0.0760111i
$643$	16.0826	−	16.0826i	0.0250118	−	0.0250118i	−0.694490	−	0.719502i	$-0.744370\pi$
$643$	16.0826	−	16.0826i	0.0250118	−	0.0250118i	0.719502	+	0.694490i	$0.244370\pi$
$644$	16.3032	+	22.4395i	0.0253156	+	0.0348439i
$645$	−317.756	+	98.0062i	−0.492645	+	0.151948i
$646$	108.720	+	78.9895i	0.168297	+	0.122275i
$647$	−79.1197	−	499.542i	−0.122287	−	0.772090i	−0.970263	−	0.242054i	$-0.922179\pi$
$647$	−79.1197	−	499.542i	−0.122287	−	0.772090i	0.847976	−	0.530035i	$-0.177821\pi$
$648$	383.670	+	752.995i	0.592083	+	1.16203i
$649$			247.058i			0.380675i
$650$	105.442	+	360.982i	0.162218	+	0.555357i
$651$	−1918.14			−2.94646
$652$	111.558	−	56.8419i	0.171102	−	0.0871808i
$653$	1110.46	−	175.880i	1.70055	−	0.269341i	0.770680	−	0.637222i	$-0.219917\pi$
$653$	1110.46	−	175.880i	1.70055	−	0.269341i	0.929873	+	0.367881i	$0.119917\pi$
$654$	262.292	−	361.014i	0.401058	−	0.552009i
$655$	446.857	+	6.69633i	0.682225	+	0.0102234i
$656$	−358.031	+	260.125i	−0.545779	+	0.396531i
$657$	−90.5672	−	90.5672i	−0.137850	−	0.137850i
$658$	185.249	−	1169.62i	0.281534	−	1.77754i
$659$	837.920	−	272.257i	1.27150	−	0.413136i	0.405923	−	0.913907i	$-0.366950\pi$
$659$	837.920	−	272.257i	1.27150	−	0.413136i	0.865580	+	0.500771i	$0.166950\pi$
$660$	−8.00835	−	55.9791i	−0.0121339	−	0.0848169i
$661$	−406.010	+	1249.57i	−0.614235	+	1.89042i	−0.201834	+	0.979420i	$0.564690\pi$
$661$	−406.010	+	1249.57i	−0.614235	+	1.89042i	−0.412401	+	0.911002i	$0.635310\pi$
$662$	225.237	−	442.052i	0.340237	−	0.667752i
$663$	−426.239	−	217.180i	−0.642894	−	0.327571i
$664$	503.329	+	163.541i	0.758025	+	0.246297i
$665$	−181.488	+	176.129i	−0.272914	+	0.264855i
$666$	−45.1558	−	138.975i	−0.0678015	−	0.208671i
$667$	−85.2129	−	13.4964i	−0.127756	−	0.0202345i
$668$	−16.0281	+	16.0281i	−0.0239941	+	0.0239941i
$669$	76.3738	+	105.120i	0.114161	+	0.157129i
$670$	−32.5841	−	11.1297i	−0.0486330	−	0.0166115i
$671$	306.909	+	222.983i	0.457391	+	0.332314i
$672$	−68.4258	−	432.024i	−0.101824	−	0.642893i
$673$	−533.613	−	1047.27i	−0.792887	−	1.55613i	−0.830620	−	0.556840i	$-0.812014\pi$
$673$	−533.613	−	1047.27i	−0.792887	−	1.55613i	0.0377336	−	0.999288i	$-0.487986\pi$
$674$		−	1034.48i		−	1.53483i
$675$	−356.595	−	378.636i	−0.528290	−	0.560942i
$676$	70.3775			0.104109
$677$	−1025.90	+	522.720i	−1.51536	+	0.772112i	−0.996567	−	0.0827899i	$-0.973617\pi$
$677$	−1025.90	+	522.720i	−1.51536	+	0.772112i	−0.518789	+	0.854902i	$0.673617\pi$
$678$	−694.942	+	110.068i	−1.02499	+	0.162342i
$679$	−977.170	+	1344.96i	−1.43913	+	1.98079i
$680$	582.312	−	409.886i	0.856342	−	0.602773i
$681$	−817.042	+	593.616i	−1.19977	+	0.871683i
$682$	−290.699	−	290.699i	−0.426245	−	0.426245i
$683$	99.8898	−	630.679i	0.146252	−	0.923396i	−0.800008	−	0.599989i	$-0.795172\pi$
$683$	99.8898	−	630.679i	0.146252	−	0.923396i	0.946260	−	0.323407i	$-0.104828\pi$
$684$	8.84724	−	2.87464i	0.0129346	−	0.00420269i
$685$	359.406	−	176.394i	0.524680	−	0.257509i
$686$	−205.013	+	630.965i	−0.298853	+	0.919775i
$687$	550.418	−	1080.26i	0.801191	−	1.57243i
$688$	−217.404	−	110.773i	−0.315995	−	0.161007i
$689$	126.881	+	41.2261i	0.184152	+	0.0598347i
$690$	−48.0873	−	97.9789i	−0.0696918	−	0.141998i
$691$	−230.779	−	710.264i	−0.333978	−	1.02788i	−0.967223	−	0.253928i	$-0.918277\pi$
$691$	−230.779	−	710.264i	−0.333978	−	1.02788i	0.633245	−	0.773951i	$-0.281723\pi$
$692$	−109.012	−	17.2658i	−0.157532	−	0.0249506i
$693$	112.423	−	112.423i	0.162227	−	0.162227i
$694$	357.066	+	491.460i	0.514505	+	0.708155i
$695$	−104.784	−	148.864i	−0.150769	−	0.214193i
$696$	594.692	+	432.069i	0.854443	+	0.620789i
$697$	90.8888	+	573.849i	0.130400	+	0.823313i
$698$	414.746	+	813.985i	0.594192	+	1.16617i
$699$			274.189i			0.392259i
$700$	85.3363	+	180.670i	0.121909	+	0.258100i
$701$	1200.51			1.71256			0.856282	−	0.516508i	$-0.172768\pi$
$701$	1200.51			1.71256			0.856282	+	0.516508i	$0.172768\pi$
$702$	−278.849	+	142.081i	−0.397222	+	0.202394i
$703$	117.792	−	18.6565i	0.167557	−	0.0265383i
$704$	194.296	−	267.425i	0.275988	−	0.379866i
$705$	319.990	−	936.827i	0.453887	−	1.32883i
$706$	−258.094	+	187.516i	−0.365573	+	0.265604i
$707$	924.544	+	924.544i	1.30770	+	1.30770i
$708$	−20.1316	+	127.106i	−0.0284345	+	0.179528i
$709$	−428.385	+	139.191i	−0.604210	+	0.196320i	−0.595117	−	0.803639i	$-0.702894\pi$
$709$	−428.385	+	139.191i	−0.604210	+	0.196320i	−0.00909262	+	0.999959i	$0.502894\pi$
$710$	179.976	+	185.452i	0.253487	+	0.261199i
$711$	73.3329	−	225.696i	0.103141	−	0.317434i
$712$	370.913	−	727.957i	0.520945	−	1.02241i
$713$	150.199	+	76.5302i	0.210658	+	0.107335i
$714$	1137.82	+	369.701i	1.59359	+	0.517788i
$715$	191.008	−	27.3255i	0.267144	−	0.0382175i
$716$	6.84110	+	21.0547i	0.00955460	+	0.0294060i
$717$	−1350.58	−	213.911i	−1.88365	−	0.298341i
$718$	175.194	−	175.194i	0.244002	−	0.244002i
$719$	571.568	+	786.696i	0.794949	+	1.09415i	0.993474	+	0.114057i	$0.0363847\pi$
$719$	571.568	+	786.696i	0.794949	+	1.09415i	−0.198526	+	0.980096i	$0.563615\pi$
$720$	−2.84815	+	190.062i	−0.00395576	+	0.263975i
$721$	1471.57	+	1069.16i	2.04101	+	1.48288i
$722$	96.9837	+	612.331i	0.134326	+	0.848104i
$723$	−49.2361	−	96.6314i	−0.0680998	−	0.133653i
$724$		−	15.1813i		−	0.0209686i
$725$	−585.068	−	209.682i	−0.806991	−	0.289216i
$726$	−624.515			−0.860214
$727$	−247.938	+	126.331i	−0.341043	+	0.173770i	−0.616120	−	0.787652i	$-0.711297\pi$
$727$	−247.938	+	126.331i	−0.341043	+	0.173770i	0.275077	+	0.961422i	$0.411297\pi$
$728$	796.433	−	126.143i	1.09400	−	0.173273i
$729$	207.054	−	284.985i	0.284024	−	0.390926i
$730$	114.575	+	371.474i	0.156952	+	0.508869i
$731$	−259.155	+	188.287i	−0.354522	+	0.257575i
$732$	139.728	+	139.728i	0.190886	+	0.190886i
$733$	17.0101	−	107.397i	0.0232061	−	0.146518i	−0.973365	−	0.229262i	$-0.926369\pi$
$733$	17.0101	−	107.397i	0.0232061	−	0.146518i	0.996571	+	0.0827448i	$0.0263686\pi$
$734$	−577.937	+	187.783i	−0.787380	+	0.255835i
$735$	−655.632	+	1240.44i	−0.892016	+	1.68768i
$736$	−11.8789	+	36.5594i	−0.0161398	+	0.0496731i
$737$	−8.02048	+	15.7411i	−0.0108826	+	0.0213583i
$738$	−168.676	−	85.9448i	−0.228559	−	0.116456i
$739$	1097.79	+	356.694i	1.48551	+	0.482671i	0.935754	−	0.352654i	$-0.114721\pi$
$739$	1097.79	+	356.694i	1.48551	+	0.482671i	0.549755	+	0.835326i	$0.314721\pi$
$740$	16.1327	−	92.8327i	0.0218009	−	0.125450i
$741$	39.3111	+	120.987i	0.0530515	+	0.163276i
$742$	−329.538	−	52.1937i	−0.444121	−	0.0703419i
$743$	−8.69864	+	8.69864i	−0.0117075	+	0.0117075i	−0.712936	−	0.701229i	$-0.752635\pi$
$743$	−8.69864	+	8.69864i	−0.0117075	+	0.0117075i	0.701229	+	0.712936i	$0.252635\pi$
$744$	−844.216	−	1161.96i	−1.13470	−	1.56178i
$745$	403.544	−	538.280i	0.541669	−	0.722524i
$746$	271.091	+	196.959i	0.363393	+	0.264020i
$747$	29.0130	+	183.181i	0.0388393	+	0.245222i
$748$	−24.7314	−	48.5380i	−0.0330633	−	0.0648904i
$749$		−	565.530i		−	0.755047i
$750$	−209.115	−	757.926i	−0.278820	−	1.01057i
$751$	−452.240			−0.602183			−0.301092	−	0.953595i	$-0.597351\pi$
$751$	−452.240			−0.602183			−0.301092	+	0.953595i	$0.597351\pi$
$752$	647.237	−	329.784i	0.860688	−	0.438542i
$753$	−532.527	+	84.3439i	−0.707207	+	0.112011i
$754$	−219.811	+	302.544i	−0.291527	+	0.401252i
$755$	16.1549	+	12.1112i	0.0213972	+	0.0160413i
$756$	−134.523	+	97.7370i	−0.177941	+	0.129282i
$757$	−706.820	−	706.820i	−0.933712	−	0.933712i	0.0642239	−	0.997936i	$-0.479543\pi$
$757$	−706.820	−	706.820i	−0.933712	−	0.933712i	−0.997936	+	0.0642239i	$0.979543\pi$
$758$	−69.2411	+	437.171i	−0.0913471	+	0.576743i
$759$	−53.2585	+	17.3047i	−0.0701693	+	0.0227994i
$760$	−186.571	−	32.4228i	−0.245488	−	0.0426615i
$761$	449.482	−	1383.36i	0.590646	−	1.81782i	0.0153439	−	0.999882i	$-0.495116\pi$
$761$	449.482	−	1383.36i	0.590646	−	1.81782i	0.575303	−	0.817941i	$-0.304884\pi$
$762$	11.7053	−	22.9729i	0.0153613	−	0.0301482i
$763$	720.814	+	367.273i	0.944710	+	0.481354i
$764$	−73.6625	−	23.9344i	−0.0964169	−	0.0313278i
$765$	220.629	+	116.612i	0.288403	+	0.152435i
$766$	−362.827	−	1116.67i	−0.473665	−	1.45779i
$767$	−433.702	−	68.6917i	−0.565453	−	0.0895590i
$768$	318.816	−	318.816i	0.415125	−	0.415125i
$769$	−181.101	−	249.264i	−0.235502	−	0.324141i	0.674866	−	0.737940i	$-0.264201\pi$
$769$	−181.101	−	249.264i	−0.235502	−	0.324141i	−0.910368	+	0.413800i	$0.864201\pi$
$770$	−461.119	+	142.224i	−0.598856	+	0.184707i
$771$	−197.507	−	143.497i	−0.256170	−	0.186118i
$772$	31.4581	+	198.619i	0.0407489	+	0.257278i
$773$	−1.75392	−	3.44225i	−0.00226897	−	0.00445311i	0.889869	−	0.456216i	$-0.150795\pi$
$773$	−1.75392	−	3.44225i	−0.00226897	−	0.00445311i	−0.892138	+	0.451763i	$0.850795\pi$
$774$		−	104.375i		−	0.134852i
$775$	960.608	+	742.899i	1.23949	+	0.958580i
$776$	−1244.82			−1.60415
$777$	946.008	−	482.015i	1.21751	−	0.620354i
$778$	−1317.90	+	208.735i	−1.69396	+	0.268297i
$779$	90.8150	−	124.996i	0.116579	−	0.160457i
$780$	100.496	+	1.50597i	0.128841	+	0.00193074i
$781$	107.270	−	77.9361i	0.137349	−	0.0997902i
$782$	−74.3461	−	74.3461i	−0.0950717	−	0.0950717i
$783$	80.9101	−	510.846i	0.103333	−	0.652422i
$784$	−979.131	+	318.139i	−1.24889	+	0.405789i
$785$	110.590	+	773.037i	0.140879	+	0.984760i
$786$	−173.731	+	534.689i	−0.221032	+	0.680266i
$787$	60.1800	−	118.110i	0.0764676	−	0.150076i	−0.849607	−	0.527416i	$-0.823161\pi$
$787$	60.1800	−	118.110i	0.0764676	−	0.150076i	0.926075	+	0.377340i	$0.123161\pi$
$788$	−73.7433	−	37.5741i	−0.0935829	−	0.0476829i
$789$	−1548.99	−	503.296i	−1.96323	−	0.637891i
$790$	−516.878	+	501.616i	−0.654276	+	0.634956i
$791$	−394.174	−	1213.14i	−0.498323	−	1.53368i
$792$	117.583	+	18.6233i	0.148464	+	0.0235143i
$793$	−476.771	+	476.771i	−0.601225	+	0.601225i
$794$	−200.448	−	275.894i	−0.252454	−	0.347473i
$795$	−263.949	−	90.1567i	−0.332012	−	0.113405i
$796$	−172.614	−	125.412i	−0.216852	−	0.157552i
$797$	149.295	+	942.614i	0.187322	+	1.18270i	0.884756	+	0.466054i	$0.154325\pi$
$797$	149.295	+	942.614i	0.187322	+	1.18270i	−0.697435	+	0.716648i	$0.745675\pi$
$798$	−144.436	−	283.472i	−0.180998	−	0.355228i
$799$		−	953.669i		−	1.19358i
$800$	−133.056	+	242.859i	−0.166320	+	0.303574i
$801$	286.312			0.357443
$802$	−142.984	+	72.8539i	−0.178284	+	0.0908402i
$803$	197.000	−	31.2018i	0.245331	−	0.0388565i
$804$	−5.40903	+	7.44490i	−0.00672765	+	0.00925982i
$805$	161.802	−	113.892i	0.200997	−	0.141480i
$806$	591.139	−	429.487i	0.733423	−	0.532863i
$807$	912.465	+	912.465i	1.13069	+	1.13069i
$808$	−153.154	+	966.978i	−0.189547	+	1.19676i
$809$	1278.62	−	415.449i	1.58049	−	0.513534i	0.618310	−	0.785934i	$-0.287818\pi$
$809$	1278.62	−	415.449i	1.58049	−	0.513534i	0.962184	+	0.272400i	$0.0878175\pi$
$810$	806.931	−	396.036i	0.996211	−	0.488933i
$811$	168.798	−	519.506i	0.208135	−	0.640574i	−0.791435	−	0.611253i	$-0.790666\pi$
$811$	168.798	−	519.506i	0.208135	−	0.640574i	0.999570	−	0.0293206i	$-0.00933438\pi$
$812$	−90.2047	+	177.037i	−0.111090	+	0.218025i
$813$	1029.32	+	524.463i	1.26607	+	0.645095i
$814$	216.421	+	70.3193i	0.265873	+	0.0863873i
$815$	−393.526	−	801.817i	−0.482854	−	0.983825i
$816$	226.782	+	697.963i	0.277919	+	0.855347i
$817$	84.1363	+	13.3259i	0.102982	+	0.0163108i
$818$	232.805	−	232.805i	0.284603	−	0.284603i
$819$	166.097	+	228.613i	0.202805	+	0.279137i
$820$	−70.2623	−	99.8195i	−0.0856857	−	0.121731i
$821$	124.274	+	90.2905i	0.151369	+	0.109976i	0.660892	−	0.750481i	$-0.270178\pi$
$821$	124.274	+	90.2905i	0.151369	+	0.109976i	−0.509523	+	0.860457i	$0.670178\pi$
$822$	78.7880	+	497.448i	0.0958491	+	0.605168i
$823$	−112.681	−	221.149i	−0.136915	−	0.268711i	0.812361	−	0.583155i	$-0.198182\pi$
$823$	−112.681	−	221.149i	−0.136915	−	0.268711i	−0.949276	+	0.314444i	$0.898182\pi$
$824$			1362.00i			1.65291i
$825$	−400.153	+	51.1396i	−0.485033	+	0.0619873i
$826$	1098.17			1.32950
$827$	8.58569	−	4.37463i	0.0103817	−	0.00528976i	−0.448792	−	0.893636i	$-0.648146\pi$
$827$	8.58569	−	4.37463i	0.0103817	−	0.00528976i	0.459174	+	0.888347i	$0.348146\pi$
$828$	−7.18859	+	1.13856i	−0.00868187	+	0.00137507i
$829$	−360.443	+	496.107i	−0.434792	+	0.598440i	−0.969045	−	0.246885i	$-0.920593\pi$
$829$	−360.443	+	496.107i	−0.434792	+	0.598440i	0.534253	+	0.845325i	$0.320593\pi$
$830$	181.949	−	532.688i	0.219216	−	0.641793i
$831$	803.400	−	583.704i	0.966787	−	0.702412i
$832$	415.435	+	415.435i	0.499320	+	0.499320i
$833$	−211.437	+	1334.96i	−0.253826	+	1.60260i
$834$	217.802	−	70.7682i	0.261153	−	0.0848539i
$835$	112.614	+	116.041i	0.134867	+	0.138971i
$836$	−4.47656	+	13.7774i	−0.00535474	+	0.0164802i
$837$	−458.794	+	900.434i	−0.548141	+	1.07579i
$838$	−312.279	−	159.114i	−0.372647	−	0.189873i
$839$	−1114.35	−	362.075i	−1.32819	−	0.431555i	−0.442890	−	0.896576i	$-0.646047\pi$
$839$	−1114.35	−	362.075i	−1.32819	−	0.431555i	−0.885300	+	0.465021i	$0.846047\pi$
$840$	−1668.87	+	238.748i	−1.98675	+	0.284224i
$841$	68.9002	+	212.053i	0.0819265	+	0.252144i
$842$	1463.02	+	231.719i	1.73755	+	0.275201i
$843$	−491.835	+	491.835i	−0.583435	+	0.583435i
$844$	−133.523	−	183.779i	−0.158203	−	0.217747i
$845$	7.52266	−	501.999i	0.00890256	−	0.594082i
$846$	251.391	+	182.647i	0.297153	+	0.215894i
$847$	−177.114	−	1118.25i	−0.209107	−	1.32025i
$848$	−92.9160	−	182.358i	−0.109571	−	0.215045i
$849$			563.213i			0.663384i
$850$	−426.637	−	625.826i	−0.501925	−	0.736266i
$851$	−93.3081			−0.109645
$852$	61.5387	−	31.3556i	0.0722286	−	0.0368023i
$853$	−488.140	+	77.3137i	−0.572262	+	0.0906374i	−0.435857	−	0.900016i	$-0.643555\pi$
$853$	−488.140	+	77.3137i	−0.572262	+	0.0906374i	−0.136405	+	0.990653i	$0.543555\pi$
$854$	991.150	−	1364.20i	1.16060	−	1.59742i
$855$	−19.5590	−	63.4142i	−0.0228760	−	0.0741687i
$856$	342.584	−	248.902i	0.400216	−	0.290774i
$857$	−127.840	−	127.840i	−0.149171	−	0.149171i	0.628577	−	0.777748i	$-0.283638\pi$
$857$	−127.840	−	127.840i	−0.149171	−	0.149171i	−0.777748	+	0.628577i	$0.783638\pi$
$858$	−37.9718	+	239.744i	−0.0442562	+	0.279422i
$859$	−242.766	+	78.8793i	−0.282614	+	0.0918269i	−0.446894	−	0.894587i	$-0.647470\pi$
$859$	−242.766	+	78.8793i	−0.282614	+	0.0918269i	0.164280	+	0.986414i	$0.447470\pi$
$860$	31.4496	−	59.5021i	0.0365693	−	0.0691884i
$861$	425.048	−	1308.16i	0.493668	−	1.51935i
$862$	203.625	−	399.636i	0.236224	−	0.463615i
$863$	−725.309	−	369.564i	−0.840451	−	0.428231i	−0.0198983	−	0.999802i	$-0.506334\pi$
$863$	−725.309	−	369.564i	−0.840451	−	0.428231i	−0.820553	+	0.571571i	$0.806334\pi$
$864$	−219.172	−	71.2132i	−0.253671	−	0.0824226i
$865$	−134.808	+	775.732i	−0.155848	+	0.896800i
$866$	433.170	+	1333.16i	0.500196	+	1.53944i
$867$	−36.8646	−	5.83878i	−0.0425198	−	0.00673447i
$868$	274.516	−	274.516i	0.316263	−	0.316263i
$869$	217.218	+	298.975i	0.249964	+	0.344045i
$870$	468.987	−	625.574i	0.539065	−	0.719051i
$871$	−25.4029	−	18.4563i	−0.0291652	−	0.0211898i
$872$	94.7609	+	598.297i	0.108671	+	0.686120i
$873$	−198.046	−	388.688i	−0.226857	−	0.445232i
$874$			27.9598i			0.0319906i
$875$	1297.83	−	589.388i	1.48323	−	0.673587i
$876$	103.895			0.118602
$877$	1141.28	−	581.509i	1.30134	−	0.663067i	0.340521	−	0.940237i	$-0.389397\pi$
$877$	1141.28	−	581.509i	1.30134	−	0.663067i	0.960821	+	0.277170i	$0.0893967\pi$
$878$	32.0033	−	5.06882i	0.0364502	−	0.00577315i
$879$	−775.599	+	1067.52i	−0.882365	+	1.21447i
$880$	−236.842	−	177.558i	−0.269139	−	0.201771i
$881$	−1038.70	+	754.660i	−1.17900	+	0.856595i	−0.992059	−	0.125776i	$-0.959858\pi$
$881$	−1038.70	+	754.660i	−1.17900	+	0.856595i	−0.186943	+	0.982371i	$0.559858\pi$
$882$	−311.408	−	311.408i	−0.353070	−	0.353070i
$883$	−101.079	+	638.190i	−0.114473	+	0.722752i	0.861968	+	0.506963i	$0.169232\pi$
$883$	−101.079	+	638.190i	−0.114473	+	0.722752i	−0.976440	+	0.215788i	$0.930768\pi$
$884$	92.0832	−	29.9197i	0.104167	−	0.0338458i
$885$	904.491	+	157.184i	1.02202	+	0.177610i
$886$	−146.700	+	451.497i	−0.165576	+	0.509590i
$887$	8.37810	−	16.4430i	0.00944544	−	0.0185377i	−0.886236	−	0.463235i	$-0.846689\pi$
$887$	8.37810	−	16.4430i	0.00944544	−	0.0185377i	0.895681	+	0.444697i	$0.146689\pi$
$888$	708.352	+	360.923i	0.797694	+	0.406445i
$889$	44.4547	+	14.4442i	0.0500053	+	0.0162477i
$890$	−768.277	−	406.070i	−0.863233	−	0.456259i
$891$	−142.518	−	438.624i	−0.159953	−	0.492283i
$892$	−25.9745	−	4.11396i	−0.0291194	−	0.00461207i
$893$	−179.326	+	179.326i	−0.200813	+	0.200813i
$894$	497.451	+	684.683i	0.556433	+	0.765865i
$895$	150.914	−	46.5467i	0.168619	−	0.0520075i
$896$	−779.949	−	566.666i	−0.870478	−	0.632440i
$897$	−15.5700	−	98.3050i	−0.0173578	−	0.109593i
$898$	219.626	+	431.041i	0.244573	+	0.480001i
$899$			1207.57i			1.34324i
$900$	−52.4070	−	1.57103i	−0.0582300	−	0.00174559i
$901$	−268.695			−0.298218
$902$	262.673	−	133.838i	0.291211	−	0.148380i
$903$	749.033	−	118.635i	0.829493	−	0.131379i
$904$	561.407	−	772.711i	0.621026	−	0.854769i
$905$	−108.287	−	1.62273i	−0.119655	−	0.00179307i
$906$	−20.5488	+	14.9295i	−0.0226807	+	0.0164785i
$907$	−17.1888	−	17.1888i	−0.0189512	−	0.0189512i	0.697568	−	0.716519i	$-0.254266\pi$
$907$	−17.1888	−	17.1888i	−0.0189512	−	0.0189512i	−0.716519	+	0.697568i	$0.754266\pi$
$908$	31.9758	−	201.887i	0.0352156	−	0.222343i
$909$	−326.300	+	106.021i	−0.358966	+	0.116635i
$910$	−121.461	−	849.024i	−0.133474	−	0.932993i
$911$	−541.240	+	1665.77i	−0.594116	+	1.82850i	−0.0350398	+	0.999386i	$0.511156\pi$
$911$	−541.240	+	1665.77i	−0.594116	+	1.82850i	−0.559077	+	0.829116i	$0.688844\pi$
$912$	88.6000	−	173.887i	0.0971492	−	0.190666i
$913$	−257.337	−	131.120i	−0.281858	−	0.143614i
$914$	−1156.29	−	375.700i	−1.26508	−	0.411051i
$915$	1011.61	−	981.741i	1.10559	−	1.07294i
$916$	75.8281	+	233.375i	0.0827818	+	0.254776i
$917$	−1006.68	−	159.442i	−1.09780	−	0.173874i
$918$	445.700	−	445.700i	0.485512	−	0.485512i
$919$	−374.893	−	515.995i	−0.407935	−	0.561475i	0.554778	−	0.831998i	$-0.312803\pi$
$919$	−374.893	−	515.995i	−0.407935	−	0.561475i	−0.962713	+	0.270524i	$0.912803\pi$
$920$	140.206	+	47.8898i	0.152397	+	0.0520541i
$921$	61.5281	+	44.7028i	0.0668058	+	0.0485372i
$922$	13.3034	+	83.9941i	0.0144288	+	0.0910999i
$923$	106.989	+	209.978i	0.115915	+	0.227495i
$924$			128.967i			0.139575i
$925$	−660.447	−	124.997i	−0.713997	−	0.135131i
$926$	−629.218			−0.679501
$927$	−425.277	+	216.689i	−0.458767	+	0.233753i
$928$	−271.982	+	43.0777i	−0.293084	+	0.0464199i
$929$	394.294	−	542.700i	0.424429	−	0.584176i	−0.542234	−	0.840227i	$-0.682422\pi$
$929$	394.294	−	542.700i	0.424429	−	0.584176i	0.966663	+	0.256051i	$0.0824215\pi$
$930$	−1249.21	+	879.313i	−1.34324	+	0.945498i
$931$	290.782	−	211.266i	0.312333	−	0.226923i
$932$	−39.2408	−	39.2408i	−0.0421038	−	0.0421038i
$933$	234.155	−	1478.40i	0.250970	−	1.58456i
$934$	186.226	−	60.5086i	0.199386	−	0.0647844i
$935$	−348.863	+	171.220i	−0.373116	+	0.183122i
$936$	−65.3853	+	201.235i	−0.0698561	+	0.214995i
$937$	58.1616	−	114.149i	0.0620721	−	0.121823i	−0.857886	−	0.513840i	$-0.828222\pi$
$937$	58.1616	−	114.149i	0.0620721	−	0.121823i	0.919958	+	0.392017i	$0.128222\pi$
$938$	69.9685	+	35.6507i	0.0745933	+	0.0380072i
$939$	309.793	+	100.658i	0.329918	+	0.107197i
$940$	88.2790	+	179.870i	0.0939138	+	0.191351i
$941$	−46.4634	−	143.000i	−0.0493766	−	0.151966i	0.923328	−	0.384012i	$-0.125458\pi$
$941$	−46.4634	−	143.000i	−0.0493766	−	0.151966i	−0.972705	+	0.232046i	$0.925458\pi$
$942$	−970.280	−	153.677i	−1.03002	−	0.163139i
$943$	−85.4764	+	85.4764i	−0.0906431	+	0.0906431i
$944$	395.954	+	544.984i	0.419443	+	0.577313i
$945$	682.774	+	969.996i	0.722512	+	1.02645i
$946$	131.497	+	95.5383i	0.139003	+	0.100992i
$947$	−238.481	−	1505.71i	−0.251828	−	1.58998i	−0.712019	−	0.702160i	$-0.752219\pi$
$947$	−238.481	−	1505.71i	−0.251828	−	1.58998i	0.460191	−	0.887820i	$-0.347781\pi$
$948$	87.3921	+	171.517i	0.0921858	+	0.180925i
$949$			354.503i			0.373554i
$950$	−37.4553	+	197.903i	−0.0394266	+	0.208319i
$951$	668.951			0.703419
$952$	−1447.04	+	737.302i	−1.52000	+	0.774477i
$953$	−608.849	+	96.4322i	−0.638876	+	0.101188i	−0.467465	−	0.884012i	$-0.654833\pi$
$953$	−608.849	+	96.4322i	−0.638876	+	0.101188i	−0.171411	+	0.985200i	$0.554833\pi$
$954$	51.4604	−	70.8291i	0.0539417	−	0.0742443i
$955$	−178.597	+	522.873i	−0.187012	+	0.547511i
$956$	223.903	−	162.675i	0.234208	−	0.170162i
$957$	−283.658	−	283.658i	−0.296403	−	0.296403i
$958$	103.585	−	654.012i	0.108127	−	0.682685i
$959$	−868.381	+	282.154i	−0.905506	+	0.294217i
$960$	−855.440	−	881.468i	−0.891083	−	0.918196i
$961$	432.150	−	1330.02i	0.449688	−	1.38400i
$962$	−183.616	+	360.368i	−0.190870	+	0.374603i
$963$	132.222	+	67.3707i	0.137303	+	0.0699592i
$964$	20.8759	+	6.78300i	0.0216555	+	0.00703630i
$965$	1420.10	−	203.159i	1.47161	−	0.210527i
$966$	76.9190	+	236.732i	0.0796263	+	0.245065i
$967$	−136.090	−	21.5545i	−0.140734	−	0.0222901i	0.0856700	−	0.996324i	$-0.472697\pi$
$967$	−136.090	−	21.5545i	−0.140734	−	0.0222901i	−0.226404	+	0.974033i	$0.572697\pi$
$968$	599.458	−	599.458i	0.619275	−	0.619275i
$969$	−150.599	−	207.281i	−0.155416	−	0.213912i
$970$	−19.8388	+	1323.87i	−0.0204524	+	1.36482i
$971$	596.601	+	433.456i	0.614419	+	0.446401i	0.850968	−	0.525218i	$-0.176016\pi$
$971$	596.601	+	433.456i	0.614419	+	0.446401i	−0.236549	+	0.971620i	$0.576016\pi$
$972$	−17.0507	−	107.654i	−0.0175419	−	0.110755i
$973$	188.486	+	369.924i	0.193716	+	0.380189i
$974$		−	687.587i		−	0.705942i
$975$	21.4841	−	716.674i	0.0220350	−	0.735050i
$976$	1034.38			1.05981
$977$	443.170	−	225.806i	0.453603	−	0.231122i	−0.212235	−	0.977219i	$-0.568074\pi$
$977$	443.170	−	225.806i	0.453603	−	0.231122i	0.665838	+	0.746096i	$0.268074\pi$
$978$	1109.78	−	175.772i	1.13475	−	0.179726i
$979$	−262.071	+	360.710i	−0.267693	+	0.368447i
$980$	−83.6956	−	271.358i	−0.0854037	−	0.276896i
$981$	−171.739	+	124.776i	−0.175065	+	0.127192i
$982$	336.216	+	336.216i	0.342379	+	0.342379i
$983$	117.421	−	741.369i	0.119452	−	0.754190i	−0.853142	−	0.521679i	$-0.825306\pi$
$983$	117.421	−	741.369i	0.119452	−	0.754190i	0.972594	−	0.232511i	$-0.0746942\pi$
$984$	979.527	−	318.268i	0.995455	−	0.323443i
$985$	−275.897	+	521.992i	−0.280098	+	0.529941i
$986$	232.746	−	716.319i	0.236051	−	0.726490i
$987$	−1025.00	+	2011.67i	−1.03850	+	2.03817i
$988$	−22.9412	−	11.6891i	−0.0232198	−	0.0118311i
$989$	−63.3859	−	20.5953i	−0.0640909	−	0.0208244i
$990$	21.6800	−	124.754i	0.0218990	−	0.126014i
$991$	−40.9055	−	125.894i	−0.0412770	−	0.127038i	0.928294	−	0.371846i	$-0.121275\pi$
$991$	−40.9055	−	125.894i	−0.0412770	−	0.127038i	−0.969572	+	0.244808i	$0.921275\pi$
$992$	531.423	+	84.1692i	0.535709	+	0.0848480i
$993$	−668.850	+	668.850i	−0.673565	+	0.673565i
$994$	−346.424	−	476.811i	−0.348515	−	0.479689i
$995$	−913.006	+	1217.84i	−0.917594	+	1.22396i
$996$	−121.710	−	88.4274i	−0.122199	−	0.0887825i
$997$	−78.2443	−	494.015i	−0.0784797	−	0.495501i	−0.995351	−	0.0963177i	$-0.969294\pi$
$997$	−78.2443	−	494.015i	−0.0784797	−	0.495501i	0.916871	−	0.399184i	$-0.130706\pi$
$998$	−62.0230	−	121.727i	−0.0621473	−	0.121971i
$999$		−	559.376i		−	0.559936i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.3.f.a.22.2	yes	32
3.2	odd	2		225.3.r.a.172.3		32
4.3	odd	2		400.3.bg.c.97.1		32
5.2	odd	4		125.3.f.b.118.2		32
5.3	odd	4		125.3.f.a.118.3		32
5.4	even	2		125.3.f.c.7.3		32
25.6	even	5		125.3.f.a.107.3		32
25.8	odd	20	inner	25.3.f.a.8.2	✓	32
25.17	odd	20		125.3.f.c.18.3		32
25.19	even	10		125.3.f.b.107.2		32
75.8	even	20		225.3.r.a.208.3		32
100.83	even	20		400.3.bg.c.33.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.3.f.a.8.2	✓	32	25.8	odd	20	inner
25.3.f.a.22.2	yes	32	1.1	even	1	trivial
125.3.f.a.107.3		32	25.6	even	5
125.3.f.a.118.3		32	5.3	odd	4
125.3.f.b.107.2		32	25.19	even	10
125.3.f.b.118.2		32	5.2	odd	4
125.3.f.c.7.3		32	5.4	even	2
125.3.f.c.18.3		32	25.17	odd	20
225.3.r.a.172.3		32	3.2	odd	2
225.3.r.a.208.3		32	75.8	even	20
400.3.bg.c.33.1		32	100.83	even	20
400.3.bg.c.97.1		32	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:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	25.f (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.61837 + 0.824603i) q^{2} +(3.42034 - 0.541729i) q^{3} +(-0.411975 + 0.567034i) q^{4} +(4.00059 + 2.99921i) q^{5} +(-5.08868 + 3.69715i) q^{6} +(-8.06323 - 8.06323i) q^{7} +(1.33571 - 8.43332i) q^{8} +(2.84577 - 0.924645i) q^{9} +O(q^{10})\)	\(q+(-1.61837 + 0.824603i) q^{2} +(3.42034 - 0.541729i) q^{3} +(-0.411975 + 0.567034i) q^{4} +(4.00059 + 2.99921i) q^{5} +(-5.08868 + 3.69715i) q^{6} +(-8.06323 - 8.06323i) q^{7} +(1.33571 - 8.43332i) q^{8} +(2.84577 - 0.924645i) q^{9} +(-8.94762 - 1.55494i) q^{10} +(-1.43991 + 4.43160i) q^{11} +(-1.10192 + 2.16263i) q^{12} +(-7.37917 - 3.75988i) q^{13} +(19.6983 + 6.40037i) q^{14} +(15.3082 + 8.09108i) q^{15} +(3.92612 + 12.0833i) q^{16} +(16.4746 + 2.60932i) q^{17} +(-3.84305 + 3.84305i) q^{18} +(-2.60721 - 3.58851i) q^{19} +(-3.34880 + 1.03288i) q^{20} +(-31.9471 - 23.2109i) q^{21} +(-1.32399 - 8.35934i) q^{22} +(1.57553 + 3.09215i) q^{23} -29.5684i q^{24} +(7.00952 + 23.9972i) q^{25} +15.0427 q^{26} +(-18.5372 + 9.44519i) q^{27} +(7.89398 - 1.25028i) q^{28} +(-14.6125 + 20.1124i) q^{29} +(-31.4463 - 0.471235i) q^{30} +(39.2975 - 28.5513i) q^{31} +(7.83247 + 7.83247i) q^{32} +(-2.52427 + 15.9376i) q^{33} +(-28.8138 + 9.36216i) q^{34} +(-8.07443 - 56.4410i) q^{35} +(-0.648078 + 1.99458i) q^{36} +(-12.2064 + 23.9564i) q^{37} +(7.17853 + 3.65765i) q^{38} +(-27.2761 - 8.86255i) q^{39} +(30.6369 - 29.7322i) q^{40} +(10.7638 + 33.1275i) q^{41} +(70.8422 + 11.2203i) q^{42} +(-13.5798 + 13.5798i) q^{43} +(-1.91966 - 2.64219i) q^{44} +(14.1580 + 4.83591i) q^{45} +(-5.09959 - 3.70507i) q^{46} +(-8.94405 - 56.4705i) q^{47} +(19.9746 + 39.2023i) q^{48} +81.0315i q^{49} +(-31.1322 - 33.0564i) q^{50} +57.7624 q^{51} +(5.17201 - 2.63527i) q^{52} +(-15.9105 + 2.51997i) q^{53} +(22.2117 - 30.5717i) q^{54} +(-19.0518 + 13.4104i) q^{55} +(-78.7699 + 57.2297i) q^{56} +(-10.8615 - 10.8615i) q^{57} +(7.06378 - 44.5989i) q^{58} +(50.4257 - 16.3843i) q^{59} +(-10.8945 + 5.34694i) q^{60} +(25.1583 - 77.4292i) q^{61} +(-40.0545 + 78.6115i) q^{62} +(-30.4017 - 15.4904i) q^{63} +(-67.4679 - 21.9217i) q^{64} +(-18.2444 - 37.1734i) q^{65} +(-9.05700 - 27.8746i) q^{66} +(3.74472 + 0.593105i) q^{67} +(-8.26671 + 8.26671i) q^{68} +(7.06395 + 9.72269i) q^{69} +(59.6089 + 84.6845i) q^{70} +(-23.0210 - 16.7257i) q^{71} +(-3.99672 - 25.2343i) q^{72} +(-19.4330 - 38.1394i) q^{73} -48.8358i q^{74} +(36.9749 + 78.2815i) q^{75} +3.10891 q^{76} +(47.3434 - 24.1226i) q^{77} +(51.4511 - 8.14905i) q^{78} +(46.6168 - 64.1625i) q^{79} +(-20.5336 + 60.1158i) q^{80} +(-80.0737 + 58.1770i) q^{81} +(-44.7368 - 44.7368i) q^{82} +(-9.69615 + 61.2191i) q^{83} +(26.3228 - 8.55280i) q^{84} +(58.0824 + 59.8497i) q^{85} +(10.7792 - 33.1750i) q^{86} +(-39.0843 + 76.7073i) q^{87} +(35.4498 + 18.0626i) q^{88} +(91.0024 + 29.5685i) q^{89} +(-26.9006 + 3.84838i) q^{90} +(29.1832 + 89.8167i) q^{91} +(-2.40243 - 0.380508i) q^{92} +(118.944 - 118.944i) q^{93} +(61.0406 + 84.0152i) q^{94} +(0.332312 - 22.1757i) q^{95} +(31.0328 + 22.5467i) q^{96} +(-22.8066 - 143.995i) q^{97} +(-66.8188 - 131.139i) q^{98} +13.9427i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 10 q^{2} - 10 q^{3} - 10 q^{4} - 10 q^{5} - 6 q^{6} - 10 q^{7} - 10 q^{8} - 10 q^{9}+O(q^{10}) \) 32 * q - 10 * q^2 - 10 * q^3 - 10 * q^4 - 10 * q^5 - 6 * q^6 - 10 * q^7 - 10 * q^8 - 10 * q^9	\( 32 q - 10 q^{2} - 10 q^{3} - 10 q^{4} - 10 q^{5} - 6 q^{6} - 10 q^{7} - 10 q^{8} - 10 q^{9} - 10 q^{10} - 6 q^{11} - 10 q^{12} - 10 q^{13} - 10 q^{14} - 10 q^{15} + 2 q^{16} + 60 q^{17} + 140 q^{18} + 90 q^{19} + 130 q^{20} - 6 q^{21} + 70 q^{22} + 10 q^{23} - 40 q^{25} + 4 q^{26} - 100 q^{27} - 250 q^{28} - 110 q^{29} - 250 q^{30} - 6 q^{31} - 290 q^{32} - 190 q^{33} - 260 q^{34} - 120 q^{35} - 58 q^{36} + 50 q^{37} + 320 q^{38} + 390 q^{39} + 440 q^{40} - 86 q^{41} + 690 q^{42} + 230 q^{43} + 340 q^{44} + 310 q^{45} - 6 q^{46} + 70 q^{47} + 160 q^{48} - 100 q^{50} - 16 q^{51} - 320 q^{52} - 190 q^{53} - 660 q^{54} - 250 q^{55} - 70 q^{56} - 650 q^{57} - 640 q^{58} - 260 q^{59} - 550 q^{60} + 114 q^{61} + 60 q^{62} - 20 q^{63} + 340 q^{64} + 360 q^{65} + 138 q^{66} + 270 q^{67} + 710 q^{68} + 340 q^{69} + 310 q^{70} - 66 q^{71} + 360 q^{72} + 30 q^{73} - 90 q^{75} - 80 q^{76} - 250 q^{77} - 500 q^{78} - 210 q^{79} - 850 q^{80} + 62 q^{81} + 30 q^{82} - 10 q^{84} + 600 q^{85} - 6 q^{86} + 300 q^{87} + 190 q^{88} - 10 q^{89} + 380 q^{90} - 6 q^{91} - 30 q^{92} + 520 q^{93} + 790 q^{94} + 310 q^{95} + 174 q^{96} + 270 q^{97} + 170 q^{98}+O(q^{100}) \) 32 * q - 10 * q^2 - 10 * q^3 - 10 * q^4 - 10 * q^5 - 6 * q^6 - 10 * q^7 - 10 * q^8 - 10 * q^9 - 10 * q^10 - 6 * q^11 - 10 * q^12 - 10 * q^13 - 10 * q^14 - 10 * q^15 + 2 * q^16 + 60 * q^17 + 140 * q^18 + 90 * q^19 + 130 * q^20 - 6 * q^21 + 70 * q^22 + 10 * q^23 - 40 * q^25 + 4 * q^26 - 100 * q^27 - 250 * q^28 - 110 * q^29 - 250 * q^30 - 6 * q^31 - 290 * q^32 - 190 * q^33 - 260 * q^34 - 120 * q^35 - 58 * q^36 + 50 * q^37 + 320 * q^38 + 390 * q^39 + 440 * q^40 - 86 * q^41 + 690 * q^42 + 230 * q^43 + 340 * q^44 + 310 * q^45 - 6 * q^46 + 70 * q^47 + 160 * q^48 - 100 * q^50 - 16 * q^51 - 320 * q^52 - 190 * q^53 - 660 * q^54 - 250 * q^55 - 70 * q^56 - 650 * q^57 - 640 * q^58 - 260 * q^59 - 550 * q^60 + 114 * q^61 + 60 * q^62 - 20 * q^63 + 340 * q^64 + 360 * q^65 + 138 * q^66 + 270 * q^67 + 710 * q^68 + 340 * q^69 + 310 * q^70 - 66 * q^71 + 360 * q^72 + 30 * q^73 - 90 * q^75 - 80 * q^76 - 250 * q^77 - 500 * q^78 - 210 * q^79 - 850 * q^80 + 62 * q^81 + 30 * q^82 - 10 * q^84 + 600 * q^85 - 6 * q^86 + 300 * q^87 + 190 * q^88 - 10 * q^89 + 380 * q^90 - 6 * q^91 - 30 * q^92 + 520 * q^93 + 790 * q^94 + 310 * q^95 + 174 * q^96 + 270 * q^97 + 170 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more