LMFDB - Embedded newform 25.3.f.a.3.3

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			3.3
Character	$\chi$	$=$	25.3
Dual form			25.3.f.a.17.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.259330 - 0.508965i) q^{2} +(0.838638 + 5.29495i) q^{3} +(2.15935 - 2.97209i) q^{4} +(-3.73307 - 3.32629i) q^{5} +(2.47746 - 1.79998i) q^{6} +(1.66138 - 1.66138i) q^{7} +(-4.32944 - 0.685716i) q^{8} +(-18.7737 + 6.09994i) q^{9} +O(q^{10})$	\(q+(-0.259330 - 0.508965i) q^{2} +(0.838638 + 5.29495i) q^{3} +(2.15935 - 2.97209i) q^{4} +(-3.73307 - 3.32629i) q^{5} +(2.47746 - 1.79998i) q^{6} +(1.66138 - 1.66138i) q^{7} +(-4.32944 - 0.685716i) q^{8} +(-18.7737 + 6.09994i) q^{9} +(-0.724866 + 2.76261i) q^{10} +(0.984087 - 3.02871i) q^{11} +(17.5480 + 8.94114i) q^{12} +(1.52865 - 3.00014i) q^{13} +(-1.27643 - 0.414737i) q^{14} +(14.4819 - 22.5560i) q^{15} +(-3.76720 - 11.5942i) q^{16} +(-2.34094 + 14.7801i) q^{17} +(7.97324 + 7.97324i) q^{18} +(13.4919 + 18.5700i) q^{19} +(-17.9470 + 3.91238i) q^{20} +(10.1902 + 7.40363i) q^{21} +(-1.79671 + 0.284571i) q^{22} +(-13.8201 + 7.04168i) q^{23} -23.4992i q^{24} +(2.87158 + 24.8345i) q^{25} -1.92339 q^{26} +(-26.1388 - 51.3003i) q^{27} +(-1.35027 - 8.52527i) q^{28} +(10.2929 - 14.1670i) q^{29} +(-15.2358 - 1.52130i) q^{30} +(9.99041 - 7.25845i) q^{31} +(-17.3223 + 17.3223i) q^{32} +(16.8622 + 2.67070i) q^{33} +(8.12962 - 2.64147i) q^{34} +(-11.7283 + 0.675811i) q^{35} +(-22.4094 + 68.9689i) q^{36} +(0.734014 + 0.373999i) q^{37} +(5.95262 - 11.6827i) q^{38} +(17.1676 + 5.57808i) q^{39} +(13.8812 + 16.9608i) q^{40} +(-8.67834 - 26.7092i) q^{41} +(1.12555 - 7.10645i) q^{42} +(-42.9278 - 42.9278i) q^{43} +(-6.87660 - 9.46483i) q^{44} +(90.3736 + 39.6752i) q^{45} +(7.16793 + 5.20781i) q^{46} +(46.4052 - 7.34985i) q^{47} +(58.2316 - 29.6705i) q^{48} +43.4796i q^{49} +(11.8952 - 7.90189i) q^{50} -80.2230 q^{51} +(-5.61580 - 11.0216i) q^{52} +(-0.616814 - 3.89441i) q^{53} +(-19.3314 + 26.6074i) q^{54} +(-13.7480 + 8.03302i) q^{55} +(-8.33208 + 6.05361i) q^{56} +(-87.0125 + 87.0125i) q^{57} +(-9.87978 - 1.56480i) q^{58} +(77.9344 - 25.3224i) q^{59} +(-35.7669 - 91.7475i) q^{60} +(15.8508 - 48.7838i) q^{61} +(-6.28511 - 3.20243i) q^{62} +(-21.0559 + 41.3245i) q^{63} +(-33.0683 - 10.7446i) q^{64} +(-15.6859 + 6.11500i) q^{65} +(-3.01358 - 9.27484i) q^{66} +(11.9334 - 75.3444i) q^{67} +(38.8728 + 38.8728i) q^{68} +(-48.8754 - 67.2712i) q^{69} +(3.38546 + 5.79402i) q^{70} +(76.2237 + 55.3797i) q^{71} +(85.4623 - 13.5359i) q^{72} +(-101.086 + 51.5059i) q^{73} -0.470577i q^{74} +(-129.089 + 36.0321i) q^{75} +84.3254 q^{76} +(-3.39690 - 6.66678i) q^{77} +(-1.61303 - 10.1843i) q^{78} +(-47.6784 + 65.6237i) q^{79} +(-24.5026 + 55.8129i) q^{80} +(105.983 - 77.0010i) q^{81} +(-11.3435 + 11.3435i) q^{82} +(68.6020 + 10.8655i) q^{83} +(44.0085 - 14.2992i) q^{84} +(57.9017 - 47.3884i) q^{85} +(-10.7163 + 32.9812i) q^{86} +(83.6457 + 42.6196i) q^{87} +(-6.33738 + 12.4378i) q^{88} +(-33.4534 - 10.8697i) q^{89} +(-3.24333 - 56.2859i) q^{90} +(-2.44471 - 7.52404i) q^{91} +(-8.91386 + 56.2799i) q^{92} +(46.8115 + 46.8115i) q^{93} +(-15.7751 - 21.7125i) q^{94} +(11.4031 - 114.201i) q^{95} +(-106.248 - 77.1934i) q^{96} +(4.45480 - 0.705571i) q^{97} +(22.1296 - 11.2756i) q^{98} +62.8629i 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 $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{20}\right)$

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 $

$2$	−0.259330	−	0.508965i	−0.129665	−	0.254482i	0.817042	−	0.576579i	$-0.195613\pi$
$2$	−0.259330	−	0.508965i	−0.129665	−	0.254482i	−0.946707	+	0.322096i	$0.895613\pi$
$3$	0.838638	+	5.29495i	0.279546	+	1.76498i	0.583323	+	0.812240i	$0.301752\pi$
$3$	0.838638	+	5.29495i	0.279546	+	1.76498i	−0.303777	+	0.952743i	$0.598248\pi$
$4$	2.15935	−	2.97209i	0.539837	−	0.743022i
$5$	−3.73307	−	3.32629i	−0.746613	−	0.665258i
$5$	−3.73307	−	3.32629i	−0.746613	−	0.665258i
$6$	2.47746	−	1.79998i	0.412910	−	0.299996i
$7$	1.66138	−	1.66138i	0.237340	−	0.237340i	−0.578408	−	0.815748i	$-0.696326\pi$
$7$	1.66138	−	1.66138i	0.237340	−	0.237340i	0.815748	+	0.578408i	$0.196326\pi$
$8$	−4.32944	−	0.685716i	−0.541180	−	0.0857145i
$9$	−18.7737	+	6.09994i	−2.08596	+	0.677771i
$10$	−0.724866	+	2.76261i	−0.0724866	+	0.276261i
$11$	0.984087	−	3.02871i	0.0894625	−	0.275337i	−0.896309	−	0.443431i	$-0.853761\pi$
$11$	0.984087	−	3.02871i	0.0894625	−	0.275337i	0.985771	+	0.168094i	$0.0537611\pi$
$12$	17.5480	+	8.94114i	1.46233	+	0.745095i
$13$	1.52865	−	3.00014i	0.117588	−	0.230780i	−0.824709	−	0.565557i	$-0.808661\pi$
$13$	1.52865	−	3.00014i	0.117588	−	0.230780i	0.942297	+	0.334777i	$0.108661\pi$
$14$	−1.27643	−	0.414737i	−0.0911736	−	0.0296241i
$15$	14.4819	−	22.5560i	0.965457	−	1.50373i
$16$	−3.76720	−	11.5942i	−0.235450	−	0.724640i
$17$	−2.34094	+	14.7801i	−0.137702	+	0.869417i	0.818029	+	0.575176i	$0.195067\pi$
$17$	−2.34094	+	14.7801i	−0.137702	+	0.869417i	−0.955731	+	0.294240i	$0.904933\pi$
$18$	7.97324	+	7.97324i	0.442958	+	0.442958i
$19$	13.4919	+	18.5700i	0.710100	+	0.977369i	0.999795	+	0.0202499i	$0.00644618\pi$
$19$	13.4919	+	18.5700i	0.710100	+	0.977369i	−0.289695	+	0.957119i	$0.593554\pi$
$20$	−17.9470	+	3.91238i	−0.897351	+	0.195619i
$21$	10.1902	+	7.40363i	0.485249	+	0.352554i
$22$	−1.79671	+	0.284571i	−0.0816686	+	0.0129350i
$23$	−13.8201	+	7.04168i	−0.600873	+	0.306160i	−0.727840	−	0.685747i	$-0.759476\pi$
$23$	−13.8201	+	7.04168i	−0.600873	+	0.306160i	0.126967	+	0.991907i	$0.459476\pi$
$24$		−	23.4992i		−	0.979135i
$25$	2.87158	+	24.8345i	0.114863	+	0.993381i
$26$	−1.92339			−0.0739765
$27$	−26.1388	−	51.3003i	−0.968103	−	1.90001i
$28$	−1.35027	−	8.52527i	−0.0482239	−	0.304474i
$29$	10.2929	−	14.1670i	0.354929	−	0.488518i	−0.593798	−	0.804614i	$-0.702372\pi$
$29$	10.2929	−	14.1670i	0.354929	−	0.488518i	0.948727	+	0.316096i	$0.102372\pi$
$30$	−15.2358	−	1.52130i	−0.507859	−	0.0507101i
$31$	9.99041	−	7.25845i	0.322271	−	0.234144i	−0.414873	−	0.909879i	$-0.636174\pi$
$31$	9.99041	−	7.25845i	0.322271	−	0.234144i	0.737144	+	0.675736i	$0.236174\pi$
$32$	−17.3223	+	17.3223i	−0.541320	+	0.541320i
$33$	16.8622	+	2.67070i	0.510975	+	0.0809304i
$34$	8.12962	−	2.64147i	0.239106	−	0.0776904i
$35$	−11.7283	+	0.675811i	−0.335094	+	0.0193089i
$36$	−22.4094	+	68.9689i	−0.622482	+	1.91580i
$37$	0.734014	+	0.373999i	0.0198382	+	0.0101081i	0.463881	−	0.885897i	$-0.346456\pi$
$37$	0.734014	+	0.373999i	0.0198382	+	0.0101081i	−0.444043	+	0.896005i	$0.646456\pi$
$38$	5.95262	−	11.6827i	0.156648	−	0.307439i
$39$	17.1676	+	5.57808i	0.440194	+	0.143028i
$40$	13.8812	+	16.9608i	0.347030	+	0.424020i
$41$	−8.67834	−	26.7092i	−0.211667	−	0.651444i	−0.999373	−	0.0353932i	$-0.988732\pi$
$41$	−8.67834	−	26.7092i	−0.211667	−	0.651444i	0.787707	−	0.616051i	$-0.211268\pi$
$42$	1.12555	−	7.10645i	0.0267988	−	0.169201i
$43$	−42.9278	−	42.9278i	−0.998322	−	0.998322i	0.00167695	−	0.999999i	$-0.499466\pi$
$43$	−42.9278	−	42.9278i	−0.998322	−	0.998322i	−0.999999	+	0.00167695i	$0.999466\pi$
$44$	−6.87660	−	9.46483i	−0.156286	−	0.215110i
$45$	90.3736	+	39.6752i	2.00830	+	0.881672i
$46$	7.16793	+	5.20781i	0.155825	+	0.113213i
$47$	46.4052	−	7.34985i	0.987344	−	0.156380i	0.358180	−	0.933653i	$-0.383397\pi$
$47$	46.4052	−	7.34985i	0.987344	−	0.156380i	0.629164	+	0.777273i	$0.283397\pi$
$48$	58.2316	−	29.6705i	1.21316	−	0.618135i
$49$			43.4796i			0.887339i
$50$	11.8952	−	7.90189i	0.237904	−	0.158038i
$51$	−80.2230			−1.57300
$52$	−5.61580	−	11.0216i	−0.107996	−	0.211954i
$53$	−0.616814	−	3.89441i	−0.0116380	−	0.0734794i	0.981186	−	0.193066i	$-0.0618431\pi$
$53$	−0.616814	−	3.89441i	−0.0116380	−	0.0734794i	−0.992824	+	0.119586i	$0.961843\pi$
$54$	−19.3314	+	26.6074i	−0.357990	+	0.492730i
$55$	−13.7480	+	8.03302i	−0.249964	+	0.146055i
$56$	−8.33208	+	6.05361i	−0.148787	+	0.108100i
$57$	−87.0125	+	87.0125i	−1.52653	+	1.52653i
$58$	−9.87978	−	1.56480i	−0.170341	−	0.0269794i
$59$	77.9344	−	25.3224i	1.32092	−	0.429193i	0.438110	−	0.898921i	$-0.355648\pi$
$59$	77.9344	−	25.3224i	1.32092	−	0.429193i	0.882811	+	0.469728i	$0.155648\pi$
$60$	−35.7669	−	91.7475i	−0.596116	−	1.52913i
$61$	15.8508	−	48.7838i	0.259849	−	0.799734i	−0.732986	−	0.680244i	$-0.761874\pi$
$61$	15.8508	−	48.7838i	0.259849	−	0.799734i	0.992835	−	0.119490i	$-0.0381260\pi$
$62$	−6.28511	−	3.20243i	−0.101373	−	0.0516520i
$63$	−21.0559	+	41.3245i	−0.334221	+	0.655945i
$64$	−33.0683	−	10.7446i	−0.516693	−	0.167884i
$65$	−15.6859	+	6.11500i	−0.241321	+	0.0940769i
$66$	−3.01358	−	9.27484i	−0.0456603	−	0.140528i
$67$	11.9334	−	75.3444i	0.178110	−	1.12454i	−0.722966	−	0.690883i	$-0.757222\pi$
$67$	11.9334	−	75.3444i	0.178110	−	1.12454i	0.901077	−	0.433660i	$-0.142778\pi$
$68$	38.8728	+	38.8728i	0.571659	+	0.571659i
$69$	−48.8754	−	67.2712i	−0.708339	−	0.974945i
$70$	3.38546	+	5.79402i	0.0483638	+	0.0827717i
$71$	76.2237	+	55.3797i	1.07357	+	0.779996i	0.976551	−	0.215286i	$-0.0690684\pi$
$71$	76.2237	+	55.3797i	1.07357	+	0.779996i	0.0970218	+	0.995282i	$0.469068\pi$
$72$	85.4623	−	13.5359i	1.18698	−	0.187999i
$73$	−101.086	+	51.5059i	−1.38474	+	0.705560i	−0.978121	−	0.208038i	$-0.933292\pi$
$73$	−101.086	+	51.5059i	−1.38474	+	0.705560i	−0.406618	+	0.913598i	$0.633292\pi$
$74$		−	0.470577i		−	0.00635914i
$75$	−129.089	+	36.0321i	−1.72119	+	0.480428i
$76$	84.3254			1.10954
$77$	−3.39690	−	6.66678i	−0.0441155	−	0.0865816i
$78$	−1.61303	−	10.1843i	−0.0206798	−	0.130567i
$79$	−47.6784	+	65.6237i	−0.603525	+	0.830680i	−0.996025	−	0.0890714i	$-0.971610\pi$
$79$	−47.6784	+	65.6237i	−0.603525	+	0.830680i	0.392501	+	0.919752i	$0.371610\pi$
$80$	−24.5026	+	55.8129i	−0.306283	+	0.697661i
$81$	105.983	−	77.0010i	1.30843	−	0.950629i
$82$	−11.3435	+	11.3435i	−0.138335	+	0.138335i
$83$	68.6020	+	10.8655i	0.826530	+	0.130910i	0.555347	−	0.831618i	$-0.312585\pi$
$83$	68.6020	+	10.8655i	0.826530	+	0.130910i	0.271183	+	0.962528i	$0.412585\pi$
$84$	44.0085	−	14.2992i	0.523911	−	0.170229i
$85$	57.9017	−	47.3884i	0.681197	−	0.557511i
$86$	−10.7163	+	32.9812i	−0.124608	+	0.383503i
$87$	83.6457	+	42.6196i	0.961445	+	0.489880i
$88$	−6.33738	+	12.4378i	−0.0720157	+	0.141339i
$89$	−33.4534	−	10.8697i	−0.375881	−	0.122131i	0.114983	−	0.993368i	$-0.463319\pi$
$89$	−33.4534	−	10.8697i	−0.375881	−	0.122131i	−0.490864	+	0.871236i	$0.663319\pi$
$90$	−3.24333	−	56.2859i	−0.0360370	−	0.625399i
$91$	−2.44471	−	7.52404i	−0.0268649	−	0.0826818i
$92$	−8.91386	+	56.2799i	−0.0968898	+	0.611738i
$93$	46.8115	+	46.8115i	0.503349	+	0.503349i
$94$	−15.7751	−	21.7125i	−0.167820	−	0.230985i
$95$	11.4031	−	114.201i	0.120032	−	1.20212i
$96$	−106.248	−	77.1934i	−1.10675	−	0.804098i
$97$	4.45480	−	0.705571i	0.0459258	−	0.00727393i	−0.133429	−	0.991058i	$-0.542599\pi$
$97$	4.45480	−	0.705571i	0.0459258	−	0.00727393i	0.179355	+	0.983784i	$0.442599\pi$
$98$	22.1296	−	11.2756i	0.225812	−	0.115057i
$99$			62.8629i			0.634979i
$100$	80.0112	+	45.0918i	0.800112	+	0.450918i
$101$	−115.715			−1.14570			−0.572848	−	0.819662i	$-0.694161\pi$
$101$	−115.715			−1.14570			−0.572848	+	0.819662i	$0.694161\pi$
$102$	20.8043	+	40.8307i	0.203963	+	0.400301i
$103$	6.13718	+	38.7486i	0.0595843	+	0.376200i	0.999404	+	0.0345288i	$0.0109930\pi$
$103$	6.13718	+	38.7486i	0.0595843	+	0.376200i	−0.939819	+	0.341672i	$0.889007\pi$
$104$	−8.67543	+	11.9407i	−0.0834176	+	0.114814i
$105$	−13.4142	−	61.5339i	−0.127754	−	0.586037i
$106$	−1.82216	+	1.32388i	−0.0171902	+	0.0124894i
$107$	29.1432	−	29.1432i	0.272366	−	0.272366i	−0.557686	−	0.830052i	$-0.688311\pi$
$107$	29.1432	−	29.1432i	0.272366	−	0.272366i	0.830052	+	0.557686i	$0.188311\pi$
$108$	−208.912	−	33.0883i	−1.93437	−	0.306374i
$109$	−197.491	+	64.1688i	−1.81185	+	0.588705i	−0.811858	+	0.583855i	$0.801544\pi$
$109$	−197.491	+	64.1688i	−1.81185	+	0.588705i	−0.999988	+	0.00484956i	$0.998456\pi$
$110$	7.65380	+	4.91406i	0.0695800	+	0.0446732i
$111$	−1.36473	+	4.20022i	−0.0122949	+	0.0378398i
$112$	−25.5212	−	13.0037i	−0.227868	−	0.116104i
$113$	46.7730	−	91.7972i	0.413920	−	0.812364i	−0.586077	−	0.810255i	$-0.699329\pi$
$113$	46.7730	−	91.7972i	0.413920	−	0.812364i	0.999998	−	0.00210930i	$-0.000671413\pi$
$114$	66.8513	+	21.7213i	0.586414	+	0.190538i
$115$	75.0139	+	19.6825i	0.652295	+	0.171152i
$116$	−19.8796	−	61.1830i	−0.171376	−	0.527440i
$117$	−10.3977	+	65.6483i	−0.0888690	+	0.561097i
$118$	−33.0990	−	33.0990i	−0.280500	−	0.280500i
$119$	20.6662	+	28.4445i	0.173665	+	0.239030i
$120$	−78.1653	+	87.7242i	−0.651377	+	0.731035i
$121$	89.6864	+	65.1610i	0.741210	+	0.538521i
$122$	−28.9398	+	4.58361i	−0.237211	+	0.0375706i
$123$	134.146	−	68.3507i	1.09062	−	0.555697i
$124$		−	45.3659i		−	0.365854i
$125$	71.8871	−	102.261i	0.575096	−	0.818086i
$126$	26.4932			0.210263
$127$	−59.2292	−	116.244i	−0.466372	−	0.915306i	−0.997677	−	0.0681257i	$-0.978298\pi$
$127$	−59.2292	−	116.244i	−0.466372	−	0.915306i	0.531305	−	0.847181i	$-0.321702\pi$
$128$	18.4360	+	116.400i	0.144031	+	0.909375i
$129$	191.300	−	263.302i	1.48294	−	2.04110i
$130$	7.18014	+	6.39775i	0.0552319	+	0.0492135i
$131$	−138.994	+	100.985i	−1.06102	+	0.770879i	−0.974278	−	0.225351i	$-0.927647\pi$
$131$	−138.994	+	100.985i	−1.06102	+	0.770879i	−0.0867464	+	0.996230i	$0.527647\pi$
$132$	44.3488	−	44.3488i	0.335976	−	0.335976i
$133$	53.2670	+	8.43667i	0.400504	+	0.0634336i
$134$	−41.4423	+	13.4654i	−0.309271	+	0.100488i
$135$	−73.0617	+	278.453i	−0.541198	+	2.06261i
$136$	20.2699	−	62.3843i	0.149043	−	0.458708i
$137$	−43.4833	−	22.1558i	−0.317396	−	0.161721i	0.288033	−	0.957620i	$-0.406999\pi$
$137$	−43.4833	−	22.1558i	−0.317396	−	0.161721i	−0.605429	+	0.795899i	$0.706999\pi$
$138$	−21.5638	+	42.3213i	−0.156259	+	0.306676i
$139$	110.916	+	36.0389i	0.797960	+	0.259273i	0.679490	−	0.733685i	$-0.262201\pi$
$139$	110.916	+	36.0389i	0.797960	+	0.259273i	0.118470	+	0.992958i	$0.462201\pi$
$140$	−23.3169	+	36.3168i	−0.166549	+	0.259406i
$141$	77.8342	+	239.549i	0.552016	+	1.69893i
$142$	8.41921	−	53.1568i	0.0592902	−	0.374344i
$143$	−7.58223	−	7.58223i	−0.0530226	−	0.0530226i
$144$	141.448	+	194.687i	0.982279	+	1.35199i
$145$	−85.5478	+	18.6491i	−0.589985	+	0.128615i
$146$	52.4293	+	38.0921i	0.359105	+	0.260905i
$147$	−230.222	+	36.4637i	−1.56614	+	0.248052i
$148$	2.69655	−	1.37396i	0.0182199	−	0.00928352i
$149$		−	190.383i		−	1.27774i	−0.769315	−	0.638869i	$-0.779402\pi$
$149$		−	190.383i		−	1.27774i	0.769315	−	0.638869i	$-0.220598\pi$
$150$	51.8159	+	56.3577i	0.345439	+	0.375718i
$151$	45.3560			0.300371			0.150185	−	0.988658i	$-0.452013\pi$
$151$	45.3560			0.300371			0.150185	+	0.988658i	$0.452013\pi$
$152$	−45.6786	−	89.6493i	−0.300517	−	0.589798i
$153$	−46.2096	−	291.756i	−0.302024	−	1.90690i
$154$	−2.51224	+	3.45780i	−0.0163132	+	0.0224532i
$155$	−61.4386	−	6.13469i	−0.396378	−	0.0395787i
$156$	53.6493	−	38.9785i	0.343906	−	0.249862i
$157$	156.879	−	156.879i	0.999230	−	0.999230i	−0.000770113	−	1.00000i	$-0.500245\pi$
$157$	156.879	−	156.879i	0.999230	−	0.999230i	1.00000		0.000770113i	$0.000245135\pi$
$158$	45.7646	+	7.24841i	0.289650	+	0.0458760i
$159$	20.1034	−	6.53200i	0.126437	−	0.0410817i
$160$	122.284	−	7.04629i	0.764275	−	0.0440393i
$161$	−11.2615	+	34.6593i	−0.0699472	+	0.215275i
$162$	−66.6753	−	33.9728i	−0.411576	−	0.209709i
$163$	−0.0852138	+	0.167242i	−0.000522784	+	0.00102602i	−0.891268	−	0.453477i	$-0.850183\pi$
$163$	−0.0852138	+	0.167242i	−0.000522784	+	0.00102602i	0.890745	+	0.454503i	$0.150183\pi$
$164$	−98.1216	−	31.8817i	−0.598303	−	0.194400i
$165$	−54.0640	−	66.0584i	−0.327661	−	0.400354i
$166$	−12.2604	−	37.7337i	−0.0738581	−	0.227312i
$167$	−27.6815	+	174.774i	−0.165757	+	1.04655i	0.754803	+	0.655951i	$0.227732\pi$
$167$	−27.6815	+	174.774i	−0.165757	+	1.04655i	−0.920561	+	0.390599i	$0.872268\pi$
$168$	−39.0412	−	39.0412i	−0.232388	−	0.232388i
$169$	92.6716	+	127.552i	0.548353	+	0.754743i
$170$	−39.1347	−	17.1807i	−0.230204	−	0.101063i
$171$	−366.569	−	266.328i	−2.14368	−	1.55747i
$172$	−220.281	+	34.8891i	−1.28071	+	0.202844i
$173$	−221.143	+	112.678i	−1.27828	+	0.651317i	−0.955454	−	0.295141i	$-0.904633\pi$
$173$	−221.143	+	112.678i	−1.27828	+	0.651317i	−0.322828	+	0.946458i	$0.604633\pi$
$174$		−	53.6253i		−	0.308191i
$175$	46.0304	+	36.4888i	0.263031	+	0.208508i
$176$	−38.8228			−0.220584
$177$	199.440	+	391.422i	1.12678	+	2.21143i
$178$	3.14321	+	19.8455i	0.0176585	+	0.111491i
$179$	−99.4466	+	136.877i	−0.555568	+	0.764673i	−0.990755	−	0.135667i	$-0.956682\pi$
$179$	−99.4466	+	136.877i	−0.555568	+	0.764673i	0.435187	+	0.900340i	$0.356682\pi$
$180$	313.066	−	182.926i	1.73926	−	1.01625i
$181$	−187.870	+	136.495i	−1.03795	+	0.754117i	−0.969885	−	0.243563i	$-0.921684\pi$
$181$	−187.870	+	136.495i	−1.03795	+	0.754117i	−0.0680684	+	0.997681i	$0.521684\pi$
$182$	−3.19548	+	3.19548i	−0.0175576	+	0.0175576i
$183$	271.601	+	43.0173i	1.48416	+	0.235067i
$184$	64.6618	−	21.0099i	0.351423	−	0.114184i
$185$	−1.49610	−	3.83771i	−0.00808700	−	0.0207444i
$186$	11.6857	−	35.9650i	0.0628266	−	0.193360i
$187$	42.4609	+	21.6349i	0.227064	+	0.115695i
$188$	78.3605	−	153.791i	0.416811	−	0.818038i
$189$	−128.656	−	41.8028i	−0.680718	−	0.221179i
$190$	−61.0815	+	23.8121i	−0.321481	+	0.125327i
$191$	−25.6511	−	78.9459i	−0.134299	−	0.413329i	0.861181	−	0.508298i	$-0.169725\pi$
$191$	−25.6511	−	78.9459i	−0.134299	−	0.413329i	−0.995480	+	0.0949683i	$0.969725\pi$
$192$	29.1595	−	184.106i	0.151873	−	0.958886i
$193$	−69.4809	−	69.4809i	−0.360004	−	0.360004i	0.503810	−	0.863814i	$-0.331931\pi$
$193$	−69.4809	−	69.4809i	−0.360004	−	0.360004i	−0.863814	+	0.503810i	$0.831931\pi$
$194$	−1.51438	−	2.08436i	−0.00780606	−	0.0107441i
$195$	−45.5334	−	77.9277i	−0.233505	−	0.399629i
$196$	129.225	+	93.8877i	0.659313	+	0.479019i
$197$	176.475	−	27.9509i	0.895811	−	0.141883i	0.308481	−	0.951230i	$-0.400179\pi$
$197$	176.475	−	27.9509i	0.895811	−	0.141883i	0.587330	+	0.809348i	$0.300179\pi$
$198$	31.9950	−	16.3023i	0.161591	−	0.0823347i
$199$			109.756i			0.551538i	0.961224	+	0.275769i	$0.0889325\pi$
$199$			109.756i			0.551538i	−0.961224	+	0.275769i	$0.911068\pi$
$200$	4.59709	−	109.489i	0.0229854	−	0.547443i
$201$	408.953			2.03459
$202$	30.0085	+	58.8950i	0.148557	+	0.291559i
$203$	−6.43631	−	40.6373i	−0.0317060	−	0.200184i
$204$	−173.229	+	238.430i	−0.849164	+	1.16877i
$205$	−56.4457	+	128.574i	−0.275345	+	0.627190i
$206$	18.1301	−	13.1723i	0.0880103	−	0.0639432i
$207$	216.500	−	216.500i	1.04589	−	1.04589i
$208$	−40.5430	−	6.42139i	−0.194919	−	0.0308721i
$209$	69.5204	−	22.5885i	0.332633	−	0.108079i
$210$	−27.8399	+	22.7850i	−0.132571	+	0.108500i
$211$	54.9150	−	169.011i	0.260261	−	0.801000i	−0.732487	−	0.680781i	$-0.761640\pi$
$211$	54.9150	−	169.011i	0.260261	−	0.801000i	0.992747	−	0.120219i	$-0.0383597\pi$
$212$	−12.9064	−	6.57616i	−0.0608794	−	0.0310196i
$213$	−229.309	+	450.044i	−1.07657	+	2.11288i
$214$	−22.3906	−	7.27514i	−0.104629	−	0.0339960i
$215$	17.4620	+	303.043i	0.0812188	+	1.40950i
$216$	77.9889	+	240.025i	0.361060	+	1.11123i
$217$	4.53881	−	28.6569i	0.0209162	−	0.132060i
$218$	83.8751	+	83.8751i	0.384748	+	0.384748i
$219$	−357.495	−	492.050i	−1.63240	−	2.24681i
$220$	−5.81196	+	58.2064i	−0.0264180	+	0.264575i
$221$	40.7639	+	29.6167i	0.184452	+	0.134012i
$222$	2.49168	−	0.394643i	0.0112238	−	0.00177767i
$223$	136.370	−	69.4842i	0.611526	−	0.311588i	−0.120659	−	0.992694i	$-0.538501\pi$
$223$	136.370	−	69.4842i	0.611526	−	0.311588i	0.732185	+	0.681106i	$0.238501\pi$
$224$			57.5577i			0.256954i
$225$	−205.399	−	448.719i	−0.912886	−	1.99431i
$226$	−58.8512			−0.260403
$227$	111.701	+	219.225i	0.492074	+	0.965749i	0.994852	+	0.101334i	$0.0323111\pi$
$227$	111.701	+	219.225i	0.492074	+	0.965749i	−0.502779	+	0.864415i	$0.667689\pi$
$228$	70.7185	+	446.499i	0.310169	+	1.95833i
$229$	136.360	−	187.684i	0.595460	−	0.819580i	−0.399824	−	0.916592i	$-0.630929\pi$
$229$	136.360	−	187.684i	0.595460	−	0.819580i	0.995283	+	0.0970124i	$0.0309286\pi$
$230$	−9.43569	−	43.2837i	−0.0410248	−	0.188190i
$231$	32.4515	−	23.5774i	0.140483	−	0.102067i
$232$	−54.2772	+	54.2772i	−0.233953	+	0.233953i
$233$	−241.705	−	38.2824i	−1.03736	−	0.164302i	−0.385553	−	0.922686i	$-0.625989\pi$
$233$	−241.705	−	38.2824i	−1.03736	−	0.164302i	−0.651809	+	0.758383i	$0.725989\pi$
$234$	36.1091	−	11.7326i	0.154312	−	0.0501391i
$235$	−197.681	−	126.920i	−0.841197	−	0.540083i
$236$	93.0270	−	286.308i	0.394182	−	1.21317i
$237$	−387.459	−	197.420i	−1.63485	−	0.832998i
$238$	9.11790	−	17.8949i	0.0383105	−	0.0751886i
$239$	147.054	+	47.7809i	0.615290	+	0.199920i	0.600048	−	0.799964i	$-0.295148\pi$
$239$	147.054	+	47.7809i	0.615290	+	0.199920i	0.0152421	+	0.999884i	$0.495148\pi$
$240$	−316.075	−	82.9333i	−1.31698	−	0.345555i
$241$	−56.1968	−	172.956i	−0.233182	−	0.717660i	−0.997357	−	0.0726514i	$-0.976854\pi$
$241$	−56.1968	−	172.956i	−0.233182	−	0.717660i	0.764176	−	0.645008i	$-0.223146\pi$
$242$	9.90622	−	62.5454i	0.0409348	−	0.258452i
$243$	130.188	+	130.188i	0.535755	+	0.535755i
$244$	−110.762	−	152.451i	−0.453943	−	0.624800i
$245$	144.626	−	162.312i	0.590310	−	0.662500i
$246$	−69.5762	−	50.5501i	−0.282830	−	0.205488i
$247$	76.3370	−	12.0906i	0.309057	−	0.0489498i
$248$	−48.2301	+	24.5745i	−0.194476	+	0.0990906i
$249$			372.356i			1.49541i
$250$	−70.6896	−	10.0687i	−0.282758	−	0.0402746i
$251$	285.514			1.13751			0.568754	−	0.822508i	$-0.307426\pi$
$251$	285.514			1.13751			0.568754	+	0.822508i	$0.307426\pi$
$252$	77.3531	+	151.814i	0.306957	+	0.602437i
$253$	7.72704	+	48.7866i	0.0305417	+	0.192832i
$254$	−43.8041	+	60.2912i	−0.172457	+	0.237367i
$255$	299.478	+	266.845i	1.17442	+	1.04645i
$256$	−58.0559	+	42.1801i	−0.226781	+	0.164766i
$257$	−139.714	+	139.714i	−0.543634	+	0.543634i	−0.924592	−	0.380958i	$-0.875594\pi$
$257$	−139.714	+	139.714i	−0.543634	+	0.543634i	0.380958	+	0.924592i	$0.375594\pi$
$258$	−183.621	−	29.0827i	−0.711710	−	0.112724i
$259$	1.84083	−	0.598122i	0.00710746	−	0.00230935i
$260$	−15.6970	+	59.8242i	−0.0603730	+	0.230093i
$261$	−106.818	+	328.753i	−0.409266	+	1.25959i
$262$	87.4433	+	44.5546i	0.333753	+	0.170056i
$263$	154.454	−	303.133i	0.587278	−	1.15260i	−0.385899	−	0.922541i	$-0.626109\pi$
$263$	154.454	−	303.133i	0.587278	−	1.15260i	0.973177	−	0.230057i	$-0.0738912\pi$
$264$	−71.1723	−	23.1253i	−0.269592	−	0.0875958i
$265$	−10.6513	+	16.5898i	−0.0401937	+	0.0626030i
$266$	−9.51980	−	29.2989i	−0.0357887	−	0.110146i
$267$	29.4991	−	186.250i	0.110484	−	0.697565i
$268$	−198.162	−	198.162i	−0.739410	−	0.739410i
$269$	78.1444	+	107.557i	0.290500	+	0.399838i	0.929176	−	0.369637i	$-0.120518\pi$
$269$	78.1444	+	107.557i	0.290500	+	0.399838i	−0.638677	+	0.769475i	$0.720518\pi$
$270$	160.670	−	35.0254i	0.595073	−	0.129724i
$271$	−135.117	−	98.1681i	−0.498586	−	0.362244i	0.309891	−	0.950772i	$-0.399708\pi$
$271$	−135.117	−	98.1681i	−0.498586	−	0.362244i	−0.808477	+	0.588528i	$0.799708\pi$
$272$	180.183	−	28.5381i	0.662436	−	0.104920i
$273$	37.7892	−	19.2546i	0.138422	−	0.0705295i
$274$			27.8771i			0.101741i
$275$	78.0425	+	15.7422i	0.283791	+	0.0572442i
$276$	−305.475			−1.10679
$277$	91.4418	+	179.465i	0.330115	+	0.647887i	0.995090	−	0.0989790i	$-0.0315577\pi$
$277$	91.4418	+	179.465i	0.330115	+	0.647887i	−0.664975	+	0.746866i	$0.731558\pi$
$278$	−10.4215	−	65.7985i	−0.0374873	−	0.236685i
$279$	−143.281	+	197.209i	−0.513550	+	0.706841i
$280$	51.2403	+	5.11638i	0.183001	+	0.0182728i
$281$	68.9705	−	50.1100i	0.245447	−	0.178327i	−0.458260	−	0.888818i	$-0.651527\pi$
$281$	68.9705	−	50.1100i	0.245447	−	0.178327i	0.703706	+	0.710491i	$0.251527\pi$
$282$	101.737	−	101.737i	0.360770	−	0.360770i
$283$	268.552	+	42.5345i	0.948948	+	0.150299i	0.611676	−	0.791109i	$-0.290496\pi$
$283$	268.552	+	42.5345i	0.948948	+	0.150299i	0.337272	+	0.941407i	$0.390496\pi$
$284$	329.187	−	106.959i	1.15911	−	0.376617i
$285$	614.252	−	35.3947i	2.15527	−	0.124192i
$286$	−1.89278	+	5.82539i	−0.00661813	+	0.0203685i
$287$	−58.7922	−	29.9561i	−0.204851	−	0.104377i
$288$	219.538	−	430.867i	0.762284	−	1.49607i
$289$	61.8845	+	20.1075i	0.214133	+	0.0695761i
$290$	31.6769	+	38.7045i	0.109231	+	0.133464i
$291$	7.47192	+	22.9962i	0.0256767	+	0.0790248i
$292$	−65.1998	+	411.655i	−0.223287	+	1.40978i
$293$	80.2908	+	80.2908i	0.274030	+	0.274030i	0.830720	−	0.556690i	$-0.187929\pi$
$293$	80.2908	+	80.2908i	0.274030	+	0.274030i	−0.556690	+	0.830720i	$0.687929\pi$
$294$	78.2624	+	107.719i	0.266199	+	0.366391i
$295$	−375.164	−	164.702i	−1.27174	−	0.558312i
$296$	−2.92141	−	2.12253i	−0.00986964	−	0.00717071i
$297$	−181.096	+	28.6829i	−0.609752	+	0.0965753i
$298$	−96.8983	+	49.3721i	−0.325162	+	0.165678i
$299$			52.2264i			0.174670i
$300$	−171.658	+	461.471i	−0.572195	+	1.53824i
$301$	−142.639			−0.473884
$302$	−11.7622	−	23.0846i	−0.0389476	−	0.0764390i
$303$	−97.0432	−	612.706i	−0.320274	−	2.02213i
$304$	164.478	−	226.385i	0.541048	−	0.744688i
$305$	−221.441	+	129.389i	−0.726036	+	0.424225i
$306$	−136.510	+	99.1803i	−0.446111	+	0.324119i
$307$	−178.220	+	178.220i	−0.580520	+	0.580520i	−0.935046	−	0.354526i	$-0.884642\pi$
$307$	−178.220	+	178.220i	−0.580520	+	0.580520i	0.354526	+	0.935046i	$0.384642\pi$
$308$	−27.1493	−	4.30003i	−0.0881472	−	0.0139611i
$309$	−200.025	+	64.9921i	−0.647331	+	0.210331i
$310$	12.8106	+	32.8610i	0.0413244	+	0.106003i
$311$	−43.0769	+	132.577i	−0.138511	+	0.426293i	−0.996120	−	0.0880101i	$-0.971949\pi$
$311$	−43.0769	+	132.577i	−0.138511	+	0.426293i	0.857609	+	0.514303i	$0.171949\pi$
$312$	−70.5010	−	35.9220i	−0.225965	−	0.115135i
$313$	−128.557	+	252.306i	−0.410724	+	0.806091i	−0.999998	−	0.00184202i	$-0.999414\pi$
$313$	−128.557	+	252.306i	−0.410724	+	0.806091i	0.589274	+	0.807933i	$0.299414\pi$
$314$	−120.529	−	39.1624i	−0.383852	−	0.124721i
$315$	216.061	−	84.2292i	0.685907	−	0.267394i
$316$	92.0852	+	283.409i	0.291409	+	0.896864i
$317$	69.9874	−	441.883i	0.220780	−	1.39395i	−0.589433	−	0.807818i	$-0.700649\pi$
$317$	69.9874	−	441.883i	0.220780	−	1.39395i	0.810213	−	0.586135i	$-0.199351\pi$
$318$	−8.53798	−	8.53798i	−0.0268490	−	0.0268490i
$319$	−32.7786	−	45.1159i	−0.102754	−	0.141429i
$320$	87.7068	+	150.105i	0.274084	+	0.469078i
$321$	178.752	+	129.871i	0.556861	+	0.404583i
$322$	20.5608	−	3.25651i	0.0638535	−	0.0101134i
$323$	−306.050	+	155.940i	−0.947523	+	0.482787i
$324$		−	481.262i		−	1.48538i
$325$	78.8967	+	29.3481i	0.242759	+	0.0903018i
$326$	0.107219			0.000328891
$327$	−505.394	−	991.892i	−1.54555	−	3.03331i
$328$	19.2574	+	121.587i	0.0587117	+	0.370691i
$329$	64.8857	−	89.3075i	0.197221	−	0.271451i
$330$	−19.6009	+	44.6476i	−0.0593967	+	0.135296i
$331$	−16.6987	+	12.1323i	−0.0504491	+	0.0366534i	−0.612724	−	0.790297i	$-0.709926\pi$
$331$	−16.6987	+	12.1323i	−0.0504491	+	0.0366534i	0.562275	+	0.826950i	$0.309926\pi$
$332$	180.429	−	180.429i	0.543460	−	0.543460i
$333$	−16.0615	−	2.54389i	−0.0482328	−	0.00763932i
$334$	96.1324	−	31.2353i	0.287822	−	0.0935189i
$335$	−295.165	+	241.572i	−0.881091	+	0.721110i
$336$	47.4509	−	146.039i	0.141223	−	0.434639i
$337$	63.6484	+	32.4305i	0.188868	+	0.0962328i	0.545867	−	0.837872i	$-0.316200\pi$
$337$	63.6484	+	32.4305i	0.188868	+	0.0962328i	−0.357000	+	0.934104i	$0.616200\pi$
$338$	40.8867	−	80.2446i	0.120966	−	0.237410i
$339$	525.287	+	170.676i	1.54952	+	0.503469i
$340$	−15.8126	−	274.417i	−0.0465075	−	0.807109i
$341$	−12.1523	−	37.4010i	−0.0356373	−	0.109680i
$342$	−40.4890	+	255.637i	−0.118389	+	0.747477i
$343$	153.644	+	153.644i	0.447941	+	0.447941i
$344$	156.417	+	215.290i	0.454701	+	0.625842i
$345$	−41.3084	+	413.702i	−0.119735	+	1.19914i
$346$	114.698	+	83.3330i	0.331497	+	0.240847i
$347$	−620.587	+	98.2913i	−1.78843	+	0.283260i	−0.960645	−	0.277779i	$-0.910402\pi$
$347$	−620.587	+	98.2913i	−1.78843	+	0.283260i	−0.827789	+	0.561039i	$0.810402\pi$
$348$	307.289	−	156.572i	0.883015	−	0.449919i
$349$		−	276.312i		−	0.791726i	−0.918310	−	0.395863i	$-0.870445\pi$
$349$		−	276.312i		−	0.791726i	0.918310	−	0.395863i	$-0.129555\pi$
$350$	6.63443	−	32.8905i	0.0189555	−	0.0939729i
$351$	−193.865			−0.552322
$352$	35.4175	+	69.5107i	0.100618	+	0.197474i
$353$	32.0759	+	202.519i	0.0908666	+	0.573709i	0.990549	+	0.137163i	$0.0437984\pi$
$353$	32.0759	+	202.519i	0.0908666	+	0.573709i	−0.899682	+	0.436546i	$0.856202\pi$
$354$	147.499	−	203.015i	0.416665	−	0.573490i
$355$	−100.339	−	460.278i	−0.282645	−	1.29656i
$356$	−104.543	+	75.9551i	−0.293661	+	0.213357i
$357$	−133.281	+	133.281i	−0.373336	+	0.373336i
$358$	95.4548	+	15.1186i	0.266634	+	0.0422306i
$359$	−171.838	+	55.8337i	−0.478658	+	0.155526i	−0.538402	−	0.842688i	$-0.680972\pi$
$359$	−171.838	+	55.8337i	−0.478658	+	0.155526i	0.0597434	+	0.998214i	$0.480972\pi$
$360$	−364.061	−	233.742i	−1.01128	−	0.649284i
$361$	−51.2587	+	157.758i	−0.141991	+	0.437003i
$362$	118.192	+	60.2216i	0.326496	+	0.166358i
$363$	−269.810	+	529.532i	−0.743278	+	1.45876i
$364$	−27.6411	−	8.98113i	−0.0759371	−	0.0246734i
$365$	548.684	+	143.966i	1.50324	+	0.394428i
$366$	−48.5400	−	149.391i	−0.132623	−	0.408172i
$367$	−34.9328	+	220.557i	−0.0951848	+	0.600973i	0.893277	+	0.449506i	$0.148400\pi$
$367$	−34.9328	+	220.557i	−0.0951848	+	0.600973i	−0.988462	+	0.151467i	$0.951600\pi$
$368$	133.706	+	133.706i	0.363331	+	0.363331i
$369$	325.849	+	448.492i	0.883059	+	1.21543i
$370$	−1.56527	+	1.75669i	−0.00423047	+	0.00474782i
$371$	−7.49486	−	5.44533i	−0.0202018	−	0.0146774i
$372$	240.210	−	38.0456i	0.645726	−	0.102273i
$373$	618.966	−	315.379i	1.65943	−	0.845520i	0.664240	−	0.747520i	$-0.268755\pi$
$373$	618.966	−	315.379i	1.65943	−	0.845520i	0.995186	−	0.0980000i	$-0.0312445\pi$
$374$		−	27.2217i		−	0.0727853i
$375$	601.753	+	294.879i	1.60467	+	0.786343i
$376$	−205.948			−0.547735
$377$	−26.7687	−	52.5366i	−0.0710046	−	0.139354i
$378$	12.0882	+	76.3220i	0.0319794	+	0.201910i
$379$	101.685	−	139.958i	0.268299	−	0.369282i	−0.653516	−	0.756913i	$-0.726707\pi$
$379$	101.685	−	139.958i	0.268299	−	0.369282i	0.921814	+	0.387631i	$0.126707\pi$
$380$	−314.792	−	280.491i	−0.828401	−	0.738134i
$381$	565.834	−	411.102i	1.48513	−	1.07901i
$382$	−33.5286	+	33.5286i	−0.0877711	+	0.0877711i
$383$	−573.968	−	90.9075i	−1.49861	−	0.237356i	−0.647387	−	0.762161i	$-0.724138\pi$
$383$	−573.968	−	90.9075i	−1.49861	−	0.237356i	−0.851223	+	0.524805i	$0.824138\pi$
$384$	−600.871	+	195.235i	−1.56477	+	0.508424i
$385$	−9.49482	+	36.1866i	−0.0246619	+	0.0939912i
$386$	−17.3448	+	53.3818i	−0.0449347	+	0.138295i
$387$	1067.77	+	544.056i	2.75910	+	1.40583i
$388$	7.52244	−	14.7636i	0.0193877	−	0.0380506i
$389$	−582.686	−	189.326i	−1.49791	−	0.486700i	−0.558501	−	0.829504i	$-0.688623\pi$
$389$	−582.686	−	189.326i	−1.49791	−	0.486700i	−0.939407	+	0.342804i	$0.888623\pi$
$390$	−27.8543	+	43.3839i	−0.0714212	+	0.111241i
$391$	−71.7247	−	220.746i	−0.183439	−	0.564568i
$392$	29.8147	−	188.242i	0.0760578	−	0.480210i
$393$	−651.277	−	651.277i	−1.65719	−	1.65719i
$394$	−59.9913	−	82.5709i	−0.152262	−	0.209571i
$395$	396.270	−	86.3855i	1.00322	−	0.218698i
$396$	186.834	+	135.743i	0.471803	+	0.342785i
$397$	509.984	−	80.7736i	1.28460	−	0.203460i	0.523458	−	0.852051i	$-0.324642\pi$
$397$	509.984	−	80.7736i	1.28460	−	0.203460i	0.761137	+	0.648591i	$0.224642\pi$
$398$	55.8620	−	28.4631i	0.140357	−	0.0715153i
$399$			289.122i			0.724616i
$400$	277.120	−	126.850i	0.692799	−	0.317126i
$401$	−101.767			−0.253783			−0.126891	−	0.991917i	$-0.540500\pi$
$401$	−101.767			−0.253783			−0.126891	+	0.991917i	$0.540500\pi$
$402$	−106.054	−	208.142i	−0.263816	−	0.517767i
$403$	−6.50457	−	41.0682i	−0.0161404	−	0.101906i
$404$	−249.869	+	343.916i	−0.618489	+	0.851277i
$405$	−651.768	−	65.0796i	−1.60930	−	0.160690i
$406$	−19.0138	+	13.8143i	−0.0468321	+	0.0340255i
$407$	1.85507	−	1.85507i	0.00455791	−	0.00455791i
$408$	347.321	+	55.0102i	0.851276	+	0.134829i
$409$	−510.542	+	165.885i	−1.24827	+	0.405587i	−0.857300	−	0.514817i	$-0.827860\pi$
$409$	−510.542	+	165.885i	−1.24827	+	0.405587i	−0.390969	+	0.920404i	$0.627860\pi$
$410$	80.0777	−	4.61426i	0.195311	−	0.0112543i
$411$	80.8473	−	248.823i	0.196709	−	0.605408i
$412$	128.417	+	65.4315i	0.311691	+	0.158814i
$413$	87.4085	−	171.549i	0.211643	−	0.415372i
$414$	−166.336	−	54.0458i	−0.401777	−	0.130545i
$415$	−219.954	−	268.752i	−0.530010	−	0.647595i
$416$	25.4896	+	78.4488i	0.0612730	+	0.188579i
$417$	−97.8057	+	617.521i	−0.234546	+	1.48086i
$418$	−29.5255	−	29.5255i	−0.0706352	−	0.0706352i
$419$	76.6508	+	105.501i	0.182937	+	0.251792i	0.890630	−	0.454729i	$-0.150264\pi$
$419$	76.6508	+	105.501i	0.182937	+	0.251792i	−0.707693	+	0.706521i	$0.750264\pi$
$420$	−211.850	−	93.0050i	−0.504405	−	0.221441i
$421$	−204.504	−	148.581i	−0.485758	−	0.352924i	0.317793	−	0.948160i	$-0.397058\pi$
$421$	−204.504	−	148.581i	−0.485758	−	0.352924i	−0.803551	+	0.595236i	$0.797058\pi$
$422$	−100.262	+	15.8799i	−0.237587	+	0.0376301i
$423$	−826.362	+	421.052i	−1.95357	+	0.995396i
$424$			17.2836i			0.0407631i
$425$	−373.779	−	15.6938i	−0.879479	−	0.0369266i
$426$	288.523			0.677285
$427$	−54.7142	−	107.383i	−0.128136	−	0.251481i
$428$	−23.6858	−	149.547i	−0.0553408	−	0.349408i
$429$	33.7888	−	46.5063i	0.0787617	−	0.108406i
$430$	149.710	−	87.4758i	0.348162	−	0.203432i
$431$	233.732	−	169.816i	0.542302	−	0.394005i	−0.282637	−	0.959227i	$-0.591209\pi$
$431$	233.732	−	169.816i	0.542302	−	0.394005i	0.824939	+	0.565221i	$0.191209\pi$
$432$	−496.317	+	496.317i	−1.14888	+	1.14888i
$433$	682.311	+	108.067i	1.57578	+	0.249578i	0.882224	−	0.470829i	$-0.156045\pi$
$433$	682.311	+	108.067i	1.57578	+	0.249578i	0.693551	+	0.720408i	$0.256045\pi$
$434$	−15.7624	+	5.12152i	−0.0363189	+	0.0118007i
$435$	−170.490	−	437.332i	−0.391930	−	1.00536i
$436$	−235.737	+	725.524i	−0.540681	+	1.66405i
$437$	−317.223	−	161.633i	−0.725911	−	0.369870i
$438$	−157.727	+	309.556i	−0.360107	+	0.706749i
$439$	249.166	+	80.9589i	0.567576	+	0.184417i	0.578727	−	0.815521i	$-0.303550\pi$
$439$	249.166	+	80.9589i	0.567576	+	0.184417i	−0.0111511	+	0.999938i	$0.503550\pi$
$440$	65.0296	−	25.3512i	0.147795	−	0.0576164i
$441$	−265.223	−	816.273i	−0.601413	−	1.85096i
$442$	4.50253	−	28.4279i	0.0101867	−	0.0643164i
$443$	504.398	+	504.398i	1.13860	+	1.13860i	0.988702	+	0.149894i	$0.0478932\pi$
$443$	504.398	+	504.398i	1.13860	+	1.13860i	0.149894	+	0.988702i	$0.452107\pi$
$444$	9.53648	+	13.1258i	0.0214786	+	0.0295627i
$445$	88.7282	+	151.853i	0.199389	+	0.341243i
$446$	−70.7300	−	51.3883i	−0.158587	−	0.115221i
$447$	1008.07	−	159.662i	2.25519	−	0.357187i
$448$	−72.7899	+	37.0883i	−0.162477	+	0.0827864i
$449$		−	656.089i		−	1.46122i	−0.682793	−	0.730611i	$-0.739235\pi$
$449$		−	656.089i		−	1.46122i	0.682793	−	0.730611i	$-0.260765\pi$
$450$	−175.116	+	220.907i	−0.389146	+	0.490906i
$451$	−89.4346			−0.198303
$452$	−171.830	−	337.235i	−0.380155	−	0.746096i
$453$	38.0372	+	240.158i	0.0839674	+	0.530149i
$454$	82.6104	−	113.703i	0.181961	−	0.250448i
$455$	−15.9009	+	36.2196i	−0.0349470	+	0.0796034i
$456$	436.381	−	317.049i	0.956976	−	0.695284i
$457$	40.6292	−	40.6292i	0.0889042	−	0.0889042i	−0.661256	−	0.750160i	$-0.729976\pi$
$457$	40.6292	−	40.6292i	0.0889042	−	0.0889042i	0.750160	+	0.661256i	$0.229976\pi$
$458$	−130.887	−	20.7304i	−0.285779	−	0.0452629i
$459$	819.411	−	266.243i	1.78521	−	0.580050i
$460$	220.479	−	180.447i	0.479303	−	0.392275i
$461$	109.511	−	337.041i	0.237551	−	0.731108i	−0.759221	−	0.650833i	$-0.774420\pi$
$461$	109.511	−	337.041i	0.237551	−	0.731108i	0.996773	−	0.0802756i	$-0.0255800\pi$
$462$	−20.4157	−	10.4023i	−0.0441899	−	0.0225159i
$463$	−120.103	+	235.716i	−0.259402	+	0.509105i	−0.983572	−	0.180516i	$-0.942223\pi$
$463$	−120.103	+	235.716i	−0.259402	+	0.509105i	0.724170	+	0.689622i	$0.242223\pi$
$464$	−203.031	−	65.9688i	−0.437567	−	0.142174i
$465$	−19.0418	−	330.459i	−0.0409502	−	0.710665i
$466$	43.1972	+	132.947i	0.0926978	+	0.285295i
$467$	28.9178	−	182.580i	0.0619225	−	0.390963i	−0.937189	−	0.348821i	$-0.886582\pi$
$467$	28.9178	−	182.580i	0.0619225	−	0.390963i	0.999112	−	0.0421415i	$-0.0134180\pi$
$468$	172.660	+	172.660i	0.368932	+	0.368932i
$469$	−105.350	−	145.002i	−0.224627	−	0.309172i
$470$	−13.3328	+	133.527i	−0.0283676	+	0.284100i
$471$	962.231	+	699.102i	2.04295	+	1.48429i
$472$	−354.776	+	56.1910i	−0.751644	+	0.119049i
$473$	−172.261	+	87.7712i	−0.364187	+	0.185563i
$474$			248.400i			0.524051i
$475$	−422.434	+	388.390i	−0.889336	+	0.817664i
$476$	129.165			0.271355
$477$	35.3355	+	69.3498i	0.0740786	+	0.145388i
$478$	−13.8169	−	87.2365i	−0.0289057	−	0.182503i
$479$	−381.964	+	525.728i	−0.797419	+	1.09755i	0.195725	+	0.980659i	$0.437294\pi$
$479$	−381.964	+	525.728i	−0.797419	+	1.09755i	−0.993144	+	0.116895i	$0.962706\pi$
$480$	139.862	+	641.578i	0.291379	+	1.33662i
$481$	2.24410	−	1.63043i	0.00466549	−	0.00338967i
$482$	−73.4549	+	73.4549i	−0.152396	+	0.152396i
$483$	−192.964	−	30.5624i	−0.399511	−	0.0632763i
$484$	387.328	−	125.851i	0.800265	−	0.260022i
$485$	−18.9770	−	12.1840i	−0.0391278	−	0.0251217i
$486$	32.4995	−	100.023i	0.0668714	−	0.205809i
$487$	−307.201	−	156.527i	−0.630804	−	0.321411i	0.109193	−	0.994021i	$-0.465173\pi$
$487$	−307.201	−	156.527i	−0.630804	−	0.321411i	−0.739997	+	0.672610i	$0.765173\pi$
$488$	−102.077	+	200.337i	−0.209174	+	0.410527i
$489$	−0.956999	−	0.310948i	−0.00195705	−	0.000635885i
$490$	−120.117	−	31.5169i	−0.245137	−	0.0643202i
$491$	297.424	+	915.376i	0.605751	+	1.86431i	0.491544	+	0.870853i	$0.336433\pi$
$491$	297.424	+	915.376i	0.605751	+	1.86431i	0.114207	+	0.993457i	$0.463567\pi$
$492$	86.5233	−	546.286i	0.175860	−	1.11034i
$493$	185.295	+	185.295i	0.375851	+	0.375851i
$494$	−25.9502	−	35.7174i	−0.0525308	−	0.0723024i
$495$	209.100	−	234.671i	0.422425	−	0.474084i
$496$	−121.792	−	88.4871i	−0.245548	−	0.178401i
$497$	218.643	−	34.6297i	0.439926	−	0.0696775i
$498$	189.516	−	96.5634i	0.380555	−	0.193902i
$499$			211.715i			0.424279i	0.977239	+	0.212139i	$0.0680431\pi$
$499$			211.715i			0.424279i	−0.977239	+	0.212139i	$0.931957\pi$
$500$	−148.699	−	434.471i	−0.297397	−	0.868942i
$501$	−948.634			−1.89348
$502$	−74.0426	−	145.317i	−0.147495	−	0.289475i
$503$	−7.57422	−	47.8217i	−0.0150581	−	0.0950730i	0.979015	−	0.203790i	$-0.0653259\pi$
$503$	−7.57422	−	47.8217i	−0.0150581	−	0.0950730i	−0.994073	+	0.108717i	$0.965326\pi$
$504$	119.497	−	164.474i	0.237098	−	0.326337i
$505$	431.973	+	384.902i	0.855392	+	0.762183i
$506$	22.8268	−	16.5846i	0.0451123	−	0.0327760i
$507$	−597.661	+	597.661i	−1.17882	+	1.17882i
$508$	−473.384	−	74.9766i	−0.931858	−	0.147592i
$509$	474.985	−	154.332i	0.933173	−	0.303206i	0.197313	−	0.980341i	$-0.436778\pi$
$509$	474.985	−	154.332i	0.933173	−	0.303206i	0.735859	+	0.677134i	$0.236778\pi$
$510$	58.1510	−	221.625i	0.114021	−	0.434558i
$511$	−82.3714	+	253.513i	−0.161196	+	0.496112i
$512$	456.548	+	232.623i	0.891695	+	0.454341i
$513$	599.984	−	1177.54i	1.16956	−	2.29539i
$514$	107.342	+	34.8774i	0.208836	+	0.0678548i
$515$	105.979	−	165.065i	0.205784	−	0.320515i
$516$	−369.473	−	1137.12i	−0.716032	−	2.20372i
$517$	23.4062	−	147.781i	0.0452730	−	0.285843i
$518$	−0.781807	−	0.781807i	−0.00150928	−	0.00150928i
$519$	−782.082	−	1076.44i	−1.50690	−	2.07407i
$520$	72.1042	−	15.7185i	0.138662	−	0.0302278i
$521$	−153.828	−	111.763i	−0.295256	−	0.214516i	0.430288	−	0.902691i	$-0.358412\pi$
$521$	−153.828	−	111.763i	−0.295256	−	0.214516i	−0.725544	+	0.688176i	$0.758412\pi$
$522$	195.025	−	30.8889i	0.373611	−	0.0591742i
$523$	446.132	−	227.316i	0.853026	−	0.434638i	0.0279155	−	0.999610i	$-0.491113\pi$
$523$	446.132	−	227.316i	0.853026	−	0.434638i	0.825110	+	0.564972i	$0.191113\pi$
$524$			631.165i			1.20451i
$525$	−154.604	+	274.330i	−0.294483	+	0.522533i
$526$	−194.339			−0.369465
$527$	83.8937	+	164.651i	0.159191	+	0.312430i
$528$	−32.5583	−	205.565i	−0.0616634	−	0.389328i
$529$	−169.529	+	233.337i	−0.320471	+	0.441091i
$530$	11.2058	+	1.11891i	0.0211431	+	0.00211115i
$531$	−1308.65	+	950.789i	−2.46450	+	1.79056i
$532$	140.097	−	140.097i	0.263340	−	0.263340i
$533$	−93.3975	−	14.7927i	−0.175230	−	0.0277537i
$534$	−102.445	+	33.2863i	−0.191844	+	0.0623339i
$535$	−205.732	+	11.8548i	−0.384546	+	0.0221585i
$536$	−103.330	+	318.016i	−0.192779	+	0.593314i
$537$	−808.154	−	411.775i	−1.50494	−	0.766806i
$538$	34.4772	−	67.6654i	0.0640841	−	0.125772i
$539$	131.687	+	42.7878i	0.244318	+	0.0793836i
$540$	669.820	+	818.422i	1.24041	+	1.51560i
$541$	59.3734	+	182.733i	0.109748	+	0.337768i	0.990815	−	0.135222i	$-0.0431747\pi$
$541$	59.3734	+	182.733i	0.109748	+	0.337768i	−0.881068	+	0.472990i	$0.843175\pi$
$542$	−14.9242	+	94.2277i	−0.0275354	+	0.173852i
$543$	−880.290	−	880.290i	−1.62116	−	1.62116i
$544$	−215.474	−	296.575i	−0.396092	−	0.545174i
$545$	950.692	+	417.367i	1.74439	+	0.765811i
$546$	−19.5998	−	14.2401i	−0.0358970	−	0.0260807i
$547$	−128.505	+	20.3532i	−0.234926	+	0.0372087i	−0.272787	−	0.962074i	$-0.587946\pi$
$547$	−128.505	+	20.3532i	−0.234926	+	0.0372087i	0.0378610	+	0.999283i	$0.487946\pi$
$548$	−159.745	+	81.3940i	−0.291505	+	0.148529i
$549$			1012.54i			1.84433i
$550$	−12.2266	−	43.8033i	−0.0222302	−	0.0796423i
$551$	401.953			0.729497
$552$	165.474	+	324.761i	0.299772	+	0.588335i
$553$	29.8140	+	188.238i	0.0539132	+	0.340394i
$554$	67.6275	−	93.0813i	0.122071	−	0.168017i
$555$	19.0658	−	11.1402i	0.0343528	−	0.0200724i
$556$	346.618	−	251.833i	0.623414	−	0.452937i
$557$	−64.3334	+	64.3334i	−0.115500	+	0.115500i	−0.762494	−	0.646995i	$-0.776026\pi$
$557$	−64.3334	+	64.3334i	−0.115500	+	0.115500i	0.646995	+	0.762494i	$0.276026\pi$
$558$	137.529	+	21.7825i	0.246468	+	0.0390367i
$559$	−194.411	+	63.1680i	−0.347784	+	0.113002i
$560$	52.0182	+	133.435i	0.0928897	+	0.238276i
$561$	−78.9464	+	242.972i	−0.140724	+	0.433105i
$562$	−43.3904	−	22.1085i	−0.0772070	−	0.0393390i
$563$	478.198	−	938.516i	0.849375	−	1.66699i	0.109763	−	0.993958i	$-0.464991\pi$
$563$	478.198	−	938.516i	0.849375	−	1.66699i	0.739612	−	0.673034i	$-0.235009\pi$
$564$	880.032	+	285.940i	1.56034	+	0.506985i
$565$	−479.951	+	187.104i	−0.849470	+	0.331158i
$566$	−47.9952	−	147.714i	−0.0847972	−	0.260979i
$567$	48.1498	−	304.006i	0.0849202	−	0.536165i
$568$	−292.031	−	292.031i	−0.514139	−	0.514139i
$569$	72.2976	+	99.5091i	0.127061	+	0.174884i	0.867808	−	0.496900i	$-0.165528\pi$
$569$	72.2976	+	99.5091i	0.127061	+	0.174884i	−0.740747	+	0.671784i	$0.765528\pi$
$570$	−177.309	−	303.454i	−0.311068	−	0.532375i
$571$	−552.625	−	401.505i	−0.967819	−	0.703162i	−0.0128656	−	0.999917i	$-0.504095\pi$
$571$	−552.625	−	401.505i	−0.967819	−	0.703162i	−0.954953	+	0.296755i	$0.904095\pi$
$572$	−38.9077	+	6.16238i	−0.0680205	+	0.0107734i
$573$	396.503	−	202.028i	0.691977	−	0.352580i
$574$			37.6917i			0.0656649i
$575$	−214.562	−	322.994i	−0.373152	−	0.561729i
$576$	686.356			1.19159
$577$	−78.1886	−	153.454i	−0.135509	−	0.265951i	0.813273	−	0.581882i	$-0.197683\pi$
$577$	−78.1886	−	153.454i	−0.135509	−	0.265951i	−0.948782	+	0.315931i	$0.897683\pi$
$578$	−5.81453	−	36.7115i	−0.0100597	−	0.0635147i
$579$	309.628	−	426.167i	0.534764	−	0.736040i
$580$	−129.301	+	294.526i	−0.222932	+	0.507803i
$581$	132.026	−	95.9223i	0.227239	−	0.165099i
$582$	9.76657	−	9.76657i	0.0167810	−	0.0167810i
$583$	−12.4020	−	1.96429i	−0.0212728	−	0.00336928i
$584$	472.964	−	153.675i	0.809870	−	0.263143i
$585$	257.181	−	210.484i	0.439625	−	0.359802i
$586$	20.0433	−	61.6871i	0.0342036	−	0.105268i
$587$	458.117	+	233.422i	0.780438	+	0.397653i	0.798355	−	0.602187i	$-0.205704\pi$
$587$	458.117	+	233.422i	0.780438	+	0.397653i	−0.0179177	+	0.999839i	$0.505704\pi$
$588$	−388.757	+	762.979i	−0.661152	+	1.29758i
$589$	269.579	+	87.5916i	0.457690	+	0.148712i
$590$	13.4639	+	233.657i	0.0228202	+	0.396030i
$591$	295.997	+	910.984i	0.500841	+	1.54143i
$592$	1.57106	−	9.91926i	0.00265381	−	0.0167555i
$593$	747.054	+	747.054i	1.25979	+	1.25979i	0.951194	+	0.308594i	$0.0998585\pi$
$593$	747.054	+	747.054i	1.25979	+	1.25979i	0.308594	+	0.951194i	$0.400142\pi$
$594$	61.5624	+	84.7333i	0.103640	+	0.142649i
$595$	17.4666	−	174.927i	0.0293556	−	0.293995i
$596$	−565.835	−	411.103i	−0.949388	−	0.689771i
$597$	−581.153	+	92.0456i	−0.973455	+	0.154180i
$598$	26.5814	−	13.5439i	0.0444505	−	0.0226487i
$599$		−	1000.69i		−	1.67060i	−0.549791	−	0.835302i	$-0.685293\pi$
$599$		−	1000.69i		−	1.67060i	0.549791	−	0.835302i	$-0.314707\pi$
$600$	583.592	−	67.4800i	0.972654	−	0.112467i
$601$	145.582			0.242233			0.121116	−	0.992638i	$-0.461353\pi$
$601$	145.582			0.242233			0.121116	+	0.992638i	$0.461353\pi$
$602$	36.9906	+	72.5982i	0.0614462	+	0.120595i
$603$	235.563	+	1487.28i	0.390651	+	2.46647i
$604$	97.9393	−	134.802i	0.162151	−	0.223182i
$605$	−118.061	−	541.573i	−0.195142	−	0.895163i
$606$	−286.680	+	208.285i	−0.473069	+	0.343705i
$607$	−205.836	+	205.836i	−0.339104	+	0.339104i	−0.856030	−	0.516926i	$-0.827076\pi$
$607$	−205.836	+	205.836i	−0.339104	+	0.339104i	0.516926	+	0.856030i	$0.327076\pi$
$608$	−555.385	−	87.9643i	−0.913461	−	0.144678i
$609$	209.775	−	68.1599i	0.344458	−	0.111921i
$610$	123.281	+	79.1512i	0.202099	+	0.129756i
$611$	48.8865	−	150.457i	0.0800107	−	0.246248i
$612$	−966.907	−	492.664i	−1.57991	−	0.805006i
$613$	−209.603	+	411.369i	−0.341930	+	0.671075i	−0.996378	−	0.0850318i	$-0.972901\pi$
$613$	−209.603	+	411.369i	−0.341930	+	0.671075i	0.654449	+	0.756106i	$0.272901\pi$
$614$	136.925	+	44.4897i	0.223005	+	0.0724588i
$615$	−728.130	−	191.050i	−1.18395	−	0.310651i
$616$	10.1351	+	31.1927i	0.0164531	+	0.0506376i
$617$	−0.878358	+	5.54573i	−0.00142359	+	0.00898822i	−0.988390	−	0.151939i	$-0.951448\pi$
$617$	−0.878358	+	5.54573i	−0.00142359	+	0.00898822i	0.986966	+	0.160927i	$0.0514484\pi$
$618$	84.9513	+	84.9513i	0.137462	+	0.137462i
$619$	361.674	+	497.802i	0.584288	+	0.804203i	0.994157	−	0.107941i	$-0.0344259\pi$
$619$	361.674	+	497.802i	0.584288	+	0.804203i	−0.409870	+	0.912144i	$0.634426\pi$
$620$	−150.900	+	169.354i	−0.243387	+	0.273152i
$621$	722.480	+	524.912i	1.16341	+	0.845270i
$622$	78.6482	−	12.4566i	0.126444	−	0.0200268i
$623$	−73.6376	+	37.5202i	−0.118198	+	0.0602251i
$624$		−	220.059i		−	0.352658i
$625$	−608.508	+	142.629i	−0.973613	+	0.228206i
$626$	161.754			0.258392
$627$	177.908	+	349.163i	0.283744	+	0.556879i
$628$	−127.502	−	805.015i	−0.203028	−	1.28187i
$629$	−7.24601	+	9.97328i	−0.0115199	+	0.0158558i
$630$	−98.9008	−	88.1240i	−0.156985	−	0.139879i
$631$	887.761	−	644.996i	1.40691	−	1.02218i	0.413149	−	0.910664i	$-0.364429\pi$
$631$	887.761	−	644.996i	1.40691	−	1.02218i	0.993762	−	0.111517i	$-0.0355711\pi$
$632$	251.420	−	251.420i	0.397817	−	0.397817i
$633$	940.959	+	149.033i	1.48651	+	0.235440i
$634$	−243.053	+	78.9726i	−0.383364	+	0.124562i
$635$	−165.554	+	630.960i	−0.260715	+	0.993638i
$636$	23.9966	−	73.8540i	0.0377305	−	0.116123i
$637$	130.445	+	66.4650i	0.204780	+	0.104341i
$638$	−14.4619	+	28.3831i	−0.0226676	+	0.0444876i
$639$	−1768.81	−	574.722i	−2.76809	−	0.899408i
$640$	318.358	−	495.853i	0.497434	−	0.774770i
$641$	−167.885	−	516.698i	−0.261912	−	0.806082i	−0.992389	−	0.123144i	$-0.960702\pi$
$641$	−167.885	−	516.698i	−0.261912	−	0.806082i	0.730477	−	0.682937i	$-0.239298\pi$
$642$	19.7439	−	124.658i	0.0307538	−	0.194172i
$643$	−423.505	−	423.505i	−0.658639	−	0.658639i	0.296419	−	0.955058i	$-0.404208\pi$
$643$	−423.505	−	423.505i	−0.658639	−	0.658639i	−0.955058	+	0.296419i	$0.904208\pi$
$644$	78.6930	+	108.312i	0.122194	+	0.168186i
$645$	−1589.95	+	346.604i	−2.46504	+	0.537370i
$646$	158.736	+	115.329i	0.245722	+	0.178527i
$647$	−375.558	+	59.4826i	−0.580461	+	0.0919360i	−0.439759	−	0.898116i	$-0.644936\pi$
$647$	−375.558	+	59.4826i	−0.580461	+	0.0919360i	−0.140702	+	0.990052i	$0.544936\pi$
$648$	−511.647	+	260.697i	−0.789578	+	0.402310i
$649$		−	260.960i		−	0.402096i
$650$	−5.52317	−	47.7665i	−0.00849719	−	0.0734869i
$651$	155.543			0.238930
$652$	0.313050	+	0.614396i	0.000480138	+	0.000942325i
$653$	−169.537	−	1070.41i	−0.259628	−	1.63922i	−0.680962	−	0.732319i	$-0.738438\pi$
$653$	−169.537	−	1070.41i	−0.259628	−	1.63922i	0.421334	−	0.906905i	$-0.361562\pi$
$654$	−373.774	+	514.456i	−0.571520	+	0.786629i
$655$	854.780	+	85.3505i	1.30501	+	0.130306i
$656$	−276.980	+	201.238i	−0.422225	+	0.306765i
$657$	1583.57	−	1583.57i	2.41031	−	2.41031i
$658$	−62.2812	−	9.86438i	−0.0946523	−	0.0149915i
$659$	−180.050	+	58.5019i	−0.273217	+	0.0887737i	−0.442421	−	0.896807i	$-0.645880\pi$
$659$	−180.050	+	58.5019i	−0.273217	+	0.0887737i	0.169204	+	0.985581i	$0.445880\pi$
$660$	−313.074	+	18.0401i	−0.474355	+	0.0273335i
$661$	168.670	−	519.113i	0.255174	−	0.785345i	−0.738621	−	0.674120i	$-0.764523\pi$
$661$	168.670	−	519.113i	0.255174	−	0.785345i	0.993795	−	0.111224i	$-0.0354771\pi$
$662$	10.5054	+	5.35276i	0.0158691	+	0.00808573i
$663$	−122.633	+	240.680i	−0.184966	+	0.363017i
$664$	−289.558	−	94.0830i	−0.436081	−	0.141691i
$665$	−170.787	−	208.676i	−0.256822	−	0.313799i
$666$	2.87049	+	8.83445i	0.00431004	+	0.0132649i
$667$	−42.4896	+	268.269i	−0.0637025	+	0.402202i
$668$	459.670	+	459.670i	0.688128	+	0.688128i
$669$	482.281	+	663.802i	0.720898	+	0.992231i
$670$	199.497	+	87.5819i	0.297757	+	0.130719i
$671$	−132.153	−	96.0149i	−0.196950	−	0.143092i
$672$	−304.765	+	48.2701i	−0.453520	+	0.0718305i
$673$	−744.440	+	379.311i	−1.10615	+	0.563612i	−0.909015	−	0.416764i	$-0.863164\pi$
$673$	−744.440	+	379.311i	−1.10615	+	0.563612i	−0.197137	+	0.980376i	$0.563164\pi$
$674$		−	40.8050i		−	0.0605415i
$675$	1198.96	−	796.458i	1.77623	−	1.17994i
$676$	579.205			0.856812
$677$	442.466	+	868.388i	0.653569	+	1.28270i	0.945301	+	0.326201i	$0.105769\pi$
$677$	442.466	+	868.388i	0.653569	+	1.28270i	−0.291732	+	0.956500i	$0.594231\pi$
$678$	−49.3548	−	311.614i	−0.0727947	−	0.459608i
$679$	6.22889	−	8.57334i	0.00917363	−	0.0126264i
$680$	−283.177	+	165.461i	−0.416437	+	0.243325i
$681$	−1067.11	+	775.300i	−1.56697	+	1.13847i
$682$	−15.8843	+	15.8843i	−0.0232908	+	0.0232908i
$683$	151.632	+	24.0162i	0.222009	+	0.0351628i	0.266448	−	0.963849i	$-0.414150\pi$
$683$	151.632	+	24.0162i	0.222009	+	0.0351628i	−0.0444389	+	0.999012i	$0.514150\pi$
$684$	−1583.10	+	514.380i	−2.31447	+	0.752017i
$685$	88.6293	+	227.347i	0.129386	+	0.331894i
$686$	38.3548	−	118.044i	0.0559107	−	0.172076i
$687$	1108.13	+	564.622i	1.61300	+	0.821866i
$688$	−335.998	+	659.433i	−0.488369	+	0.958478i
$689$	−12.6267	−	4.10265i	−0.0183261	−	0.00595450i
$690$	221.272	−	86.2609i	0.320684	−	0.125016i
$691$	−9.78431	−	30.1130i	−0.0141596	−	0.0435789i	0.943727	−	0.330725i	$-0.107293\pi$
$691$	−9.78431	−	30.1130i	−0.0141596	−	0.0435789i	−0.957887	+	0.287146i	$0.907293\pi$
$692$	−142.636	+	900.566i	−0.206121	+	1.30140i
$693$	104.439	+	104.439i	0.150706	+	0.150706i
$694$	210.964	+	290.367i	0.303982	+	0.418396i
$695$	−294.183	−	503.476i	−0.423284	−	0.724426i
$696$	−332.914	−	241.876i	−0.478325	−	0.347523i
$697$	415.080	−	65.7421i	0.595523	−	0.0943216i
$698$	−140.633	+	71.6562i	−0.201480	+	0.102659i
$699$		−	1311.92i		−	1.87686i
$700$	207.844	−	58.0143i	0.296920	−	0.0828776i
$701$	−1176.90			−1.67889			−0.839445	−	0.543444i	$-0.817120\pi$
$701$	−1176.90			−1.67889			−0.839445	+	0.543444i	$0.817120\pi$
$702$	50.2751	+	98.6704i	0.0716169	+	0.140556i
$703$	2.95808	+	18.6766i	0.00420780	+	0.0265670i
$704$	−65.0843	+	89.5808i	−0.0924493	+	0.127245i
$705$	506.250	−	1153.15i	0.718084	−	1.63568i
$706$	94.7569	−	68.8449i	0.134217	−	0.0975140i
$707$	−192.247	+	192.247i	−0.271919	+	0.271919i
$708$	1594.00	+	252.465i	2.25141	+	0.356589i
$709$	−449.210	+	145.957i	−0.633583	+	0.205864i	−0.608162	−	0.793813i	$-0.708093\pi$
$709$	−449.210	+	145.957i	−0.633583	+	0.205864i	−0.0254215	+	0.999677i	$0.508093\pi$
$710$	−208.244	+	170.433i	−0.293302	+	0.240047i
$711$	494.799	−	1522.83i	0.695920	−	2.14182i
$712$	137.381	+	69.9992i	0.192951	+	0.0983134i
$713$	−86.9564	+	170.662i	−0.121959	+	0.239357i
$714$	102.399	+	33.2715i	0.143416	+	0.0465987i
$715$	3.08428	+	53.5257i	0.00431367	+	0.0748611i
$716$	192.069	+	591.128i	0.268253	+	0.825598i
$717$	−129.672	+	818.716i	−0.180853	+	1.14186i
$718$	72.9803	+	72.9803i	0.101644	+	0.101644i
$719$	558.015	+	768.042i	0.776099	+	1.06821i	0.995702	+	0.0926192i	$0.0295239\pi$
$719$	558.015	+	768.042i	0.776099	+	1.06821i	−0.219603	+	0.975589i	$0.570476\pi$
$720$	119.549	−	1197.28i	0.166040	−	1.66288i
$721$	74.5724	+	54.1800i	0.103429	+	0.0751457i
$722$	93.5862	−	14.8226i	0.129621	−	0.0205299i
$723$	868.664	−	442.607i	1.20147	−	0.612181i
$724$			853.106i			1.17832i
$725$	381.388	+	214.939i	0.526053	+	0.296467i
$726$	339.483			0.467607
$727$	92.0467	+	180.652i	0.126612	+	0.248489i	0.945607	−	0.325310i	$-0.105469\pi$
$727$	92.0467	+	180.652i	0.126612	+	0.248489i	−0.818996	+	0.573800i	$0.805469\pi$
$728$	5.42487	+	34.2513i	0.00745174	+	0.0470484i
$729$	112.848	−	155.322i	0.154799	−	0.213062i
$730$	−69.0167	−	316.596i	−0.0945434	−	0.433693i
$731$	734.968	−	533.986i	1.00543	−	0.730486i
$732$	714.332	−	714.332i	0.975863	−	0.975863i
$733$	−1334.72	−	211.399i	−1.82090	−	0.288402i	−0.849805	−	0.527097i	$-0.823280\pi$
$733$	−1334.72	−	211.399i	−1.82090	−	0.288402i	−0.971094	+	0.238695i	$0.923280\pi$
$734$	121.315	−	39.4176i	0.165279	−	0.0537025i
$735$	980.725	+	629.666i	1.33432	+	0.856688i
$736$	117.417	−	361.373i	0.159534	−	0.490995i
$737$	−216.453	−	110.288i	−0.293694	−	0.149645i
$738$	143.764	−	282.153i	0.194803	−	0.382322i
$739$	199.437	+	64.8011i	0.269875	+	0.0876876i	0.440828	−	0.897592i	$-0.354685\pi$
$739$	199.437	+	64.8011i	0.269875	+	0.0876876i	−0.170954	+	0.985279i	$0.554685\pi$
$740$	−14.6366	−	3.84042i	−0.0197792	−	0.00518976i
$741$	128.038	+	394.061i	0.172791	+	0.531796i
$742$	−0.827837	+	5.22676i	−0.00111568	+	0.00704415i
$743$	−410.177	−	410.177i	−0.552055	−	0.552055i	0.374979	−	0.927033i	$-0.377650\pi$
$743$	−410.177	−	410.177i	−0.552055	−	0.552055i	−0.927033	+	0.374979i	$0.877650\pi$
$744$	−170.568	−	234.767i	−0.229258	−	0.315547i
$745$	−633.269	+	710.713i	−0.850026	+	0.953977i
$746$	−321.033	−	233.244i	−0.430340	−	0.312660i
$747$	−1354.19	+	214.483i	−1.81284	+	0.287125i
$748$	155.989	−	79.4802i	0.208541	−	0.106257i
$749$		−	96.8359i		−	0.129287i
$750$	−5.96991	−	382.742i	−0.00795989	−	0.510322i
$751$	711.872			0.947898			0.473949	−	0.880552i	$-0.342828\pi$
$751$	711.872			0.947898			0.473949	+	0.880552i	$0.342828\pi$
$752$	−260.033	−	510.344i	−0.345789	−	0.678649i
$753$	239.443	+	1511.78i	0.317985	+	2.00768i
$754$	−19.7973	+	27.2487i	−0.0262564	+	0.0361389i
$755$	−169.317	−	150.867i	−0.224261	−	0.199824i
$756$	−402.054	+	292.109i	−0.531818	+	0.386388i
$757$	801.179	−	801.179i	1.05836	−	1.05836i	0.0601729	−	0.998188i	$-0.480835\pi$
$757$	801.179	−	801.179i	1.05836	−	1.05836i	0.998188	−	0.0601729i	$-0.0191652\pi$
$758$	−97.6036	−	15.4589i	−0.128765	−	0.0203943i
$759$	−251.843	+	81.8286i	−0.331808	+	0.107811i
$760$	−127.678	+	486.607i	−0.167998	+	0.640273i
$761$	−394.531	+	1214.24i	−0.518438	+	1.59559i	0.258501	+	0.966011i	$0.416772\pi$
$761$	−394.531	+	1214.24i	−0.518438	+	1.59559i	−0.776939	+	0.629576i	$0.783228\pi$
$762$	−355.975	−	181.378i	−0.467158	−	0.238029i
$763$	−221.499	+	434.717i	−0.290301	+	0.569747i
$764$	−290.024	−	94.2344i	−0.379612	−	0.123344i
$765$	−797.962	+	1242.85i	−1.04309	+	1.62464i
$766$	102.579	+	315.704i	0.133915	+	0.412147i
$767$	43.1634	−	272.523i	0.0562756	−	0.355310i
$768$	−272.029	−	272.029i	−0.354205	−	0.354205i
$769$	−446.629	−	614.732i	−0.580792	−	0.799392i	0.412990	−	0.910736i	$-0.364485\pi$
$769$	−446.629	−	614.732i	−0.580792	−	0.799392i	−0.993782	+	0.111344i	$0.964485\pi$
$770$	20.8800	−	4.55176i	0.0271169	−	0.00591138i
$771$	−856.948	−	622.609i	−1.11148	−	0.807534i
$772$	−356.537	+	56.4698i	−0.461835	+	0.0731475i
$773$	133.357	−	67.9490i	0.172519	−	0.0879030i	−0.365598	−	0.930773i	$-0.619136\pi$
$773$	133.357	−	67.9490i	0.172519	−	0.0879030i	0.538118	+	0.842870i	$0.319136\pi$
$774$		−	684.548i		−	0.884429i
$775$	208.949	+	227.264i	0.269611	+	0.293244i
$776$	−19.7706			−0.0254776
$777$	4.71082	+	9.24550i	0.00606283	+	0.0118990i
$778$	54.7479	+	345.665i	0.0703701	+	0.444299i
$779$	378.903	−	521.515i	0.486396	−	0.669467i
$780$	−329.930	−	32.9438i	−0.422988	−	0.0422357i
$781$	242.740	−	176.361i	0.310807	−	0.225814i
$782$	−93.7515	+	93.7515i	−0.119887	+	0.119887i
$783$	−995.816	−	157.722i	−1.27180	−	0.201433i
$784$	504.113	−	163.796i	0.643001	−	0.208924i
$785$	−1107.47	+	63.8148i	−1.41078	+	0.0812927i
$786$	−162.581	+	500.373i	−0.206846	+	0.636607i
$787$	−678.864	−	345.899i	−0.862597	−	0.439515i	−0.0340406	−	0.999420i	$-0.510838\pi$
$787$	−678.864	−	345.899i	−0.862597	−	0.439515i	−0.828557	+	0.559905i	$0.810838\pi$
$788$	297.998	−	584.854i	0.378170	−	0.742201i
$789$	1734.61	+	563.608i	2.19849	+	0.714332i
$790$	−146.732	−	179.285i	−0.185737	−	0.226943i
$791$	−74.8023	−	230.218i	−0.0945667	−	0.291047i
$792$	43.1061	−	272.161i	0.0544269	−	0.343638i
$793$	−122.128	−	122.128i	−0.154007	−	0.154007i
$794$	−173.365	−	238.617i	−0.218344	−	0.300525i
$795$	−96.7747	−	42.4854i	−0.121729	−	0.0534408i
$796$	326.205	+	237.002i	0.409805	+	0.297741i
$797$	−593.198	+	93.9533i	−0.744288	+	0.117884i	−0.517050	−	0.855955i	$-0.672970\pi$
$797$	−593.198	+	93.9533i	−0.744288	+	0.117884i	−0.227239	+	0.973839i	$0.572970\pi$
$798$	147.153	−	74.9780i	0.184402	−	0.0939575i
$799$			703.078i			0.879947i
$800$	−479.932	−	380.448i	−0.599915	−	0.475560i
$801$	694.348			0.866852
$802$	26.3913	+	51.7958i	0.0329068	+	0.0645833i
$803$	56.5189	+	356.846i	0.0703847	+	0.444391i
$804$	883.071	−	1215.44i	1.09835	−	1.51175i
$805$	157.327	−	91.9266i	0.195437	−	0.114194i
$806$	−19.2154	+	13.9608i	−0.0238405	+	0.0173211i
$807$	−503.972	+	503.972i	−0.624500	+	0.624500i
$808$	500.982	+	79.3478i	0.620027	+	0.0982027i
$809$	275.840	−	89.6257i	0.340964	−	0.110786i	−0.133530	−	0.991045i	$-0.542631\pi$
$809$	275.840	−	89.6257i	0.340964	−	0.110786i	0.474494	+	0.880259i	$0.342631\pi$
$810$	135.900	+	348.604i	0.167778	+	0.430376i
$811$	132.970	−	409.239i	0.163958	−	0.504610i	−0.835000	−	0.550250i	$-0.814533\pi$
$811$	132.970	−	409.239i	0.163958	−	0.504610i	0.998958	+	0.0456396i	$0.0145326\pi$
$812$	−134.676	−	68.6208i	−0.165857	−	0.0845083i
$813$	406.481	−	797.764i	0.499977	−	0.981260i
$814$	−1.42524	−	0.463089i	−0.00175091	−	0.000568905i
$815$	0.874403	−	0.340878i	0.00107289	−	0.000418255i
$816$	302.216	+	930.124i	0.370362	+	1.13986i
$817$	217.992	−	1376.35i	0.266820	−	1.68464i
$818$	216.829	+	216.829i	0.265072	+	0.265072i
$819$	91.7924	+	126.341i	0.112079	+	0.154263i
$820$	260.247	+	445.397i	0.317374	+	0.543168i
$821$	−13.0760	−	9.50029i	−0.0159269	−	0.0115716i	0.579793	−	0.814764i	$-0.303133\pi$
$821$	−13.0760	−	9.50029i	−0.0159269	−	0.0115716i	−0.595720	+	0.803192i	$0.703133\pi$
$822$	−147.608	+	23.3788i	−0.179572	+	0.0284414i
$823$	425.882	−	216.998i	0.517475	−	0.263667i	−0.175690	−	0.984445i	$-0.556216\pi$
$823$	425.882	−	216.998i	0.517475	−	0.263667i	0.693165	+	0.720779i	$0.256216\pi$
$824$		−	171.968i		−	0.208699i
$825$	−17.9046	+	426.433i	−0.0217025	+	0.516888i
$826$	−109.980			−0.133148
$827$	159.381	+	312.802i	0.192721	+	0.378237i	0.967066	−	0.254528i	$-0.0819200\pi$
$827$	159.381	+	312.802i	0.192721	+	0.378237i	−0.774344	+	0.632765i	$0.781920\pi$
$828$	−175.958	−	1110.96i	−0.212510	−	1.34173i
$829$	−512.333	+	705.166i	−0.618014	+	0.850623i	−0.997206	−	0.0746948i	$-0.976202\pi$
$829$	−512.333	+	705.166i	−0.618014	+	0.850623i	0.379193	+	0.925318i	$0.376202\pi$
$830$	−79.7444	+	181.644i	−0.0960775	+	0.218849i
$831$	−873.570	+	634.686i	−1.05123	+	0.763761i
$832$	−82.7850	+	82.7850i	−0.0995012	+	0.0995012i
$833$	−642.633	−	101.783i	−0.771468	−	0.122188i
$834$	339.660	−	110.362i	0.407266	−	0.132329i
$835$	684.686	−	560.366i	0.819983	−	0.671097i
$836$	82.9836	−	255.397i	0.0992626	−	0.305499i
$837$	−633.498	−	322.783i	−0.756867	−	0.385643i
$838$	33.8183	−	66.3721i	0.0403559	−	0.0792030i
$839$	−1064.20	−	345.780i	−1.26842	−	0.412134i	−0.403931	−	0.914789i	$-0.632356\pi$
$839$	−1064.20	−	345.780i	−1.26842	−	0.412134i	−0.864487	+	0.502655i	$0.832356\pi$
$840$	15.8810	+	275.606i	0.0189060	+	0.328102i
$841$	165.124	+	508.198i	0.196342	+	0.604278i
$842$	−22.5883	+	142.617i	−0.0268270	+	0.169379i
$843$	323.171	+	323.171i	0.383358	+	0.383358i
$844$	−383.735	−	528.166i	−0.454662	−	0.625789i
$845$	78.3241	−	784.411i	0.0926912	−	0.928297i
$846$	428.602	+	311.397i	0.506621	+	0.368082i
$847$	257.260	−	40.7461i	0.303731	−	0.0481063i
$848$	−42.8290	+	21.8225i	−0.0505059	+	0.0257341i
$849$			1457.64i			1.71689i
$850$	88.9446	+	194.310i	0.104641	+	0.228600i
$851$	−12.7777			−0.0150149
$852$	842.413	+	1653.33i	0.988747	+	1.94053i
$853$	−215.776	−	1362.36i	−0.252961	−	1.59713i	−0.707702	−	0.706511i	$-0.750268\pi$
$853$	−215.776	−	1362.36i	−0.252961	−	1.59713i	0.454741	−	0.890624i	$-0.349732\pi$
$854$	−40.4649	+	55.6952i	−0.0473828	+	0.0652168i
$855$	482.542	+	2213.53i	0.564377	+	2.58893i
$856$	−146.158	+	106.190i	−0.170745	+	0.124054i
$857$	475.070	−	475.070i	0.554341	−	0.554341i	−0.373350	−	0.927691i	$-0.621791\pi$
$857$	475.070	−	475.070i	0.554341	−	0.554341i	0.927691	+	0.373350i	$0.121791\pi$
$858$	−32.4325	−	5.13681i	−0.0378001	−	0.00598695i
$859$	138.172	−	44.8949i	0.160852	−	0.0522641i	−0.227484	−	0.973782i	$-0.573050\pi$
$859$	138.172	−	44.8949i	0.160852	−	0.0522641i	0.388336	+	0.921518i	$0.373050\pi$
$860$	938.377	+	602.476i	1.09114	+	0.700554i
$861$	109.311	−	336.424i	0.126958	−	0.390736i
$862$	−147.044	−	74.9228i	−0.170585	−	0.0869174i
$863$	154.551	−	303.324i	0.179086	−	0.351476i	−0.783961	−	0.620810i	$-0.786804\pi$
$863$	154.551	−	303.324i	0.179086	−	0.351476i	0.963047	+	0.269334i	$0.0868036\pi$
$864$	1341.42	+	435.853i	1.55257	+	0.504460i
$865$	1200.34	+	314.951i	1.38768	+	0.364105i
$866$	−121.941	−	375.297i	−0.140810	−	0.433369i
$867$	−54.5695	+	344.538i	−0.0629406	+	0.397391i
$868$	−75.3700	−	75.3700i	−0.0868318	−	0.0868318i
$869$	151.836	+	208.984i	0.174724	+	0.240488i
$870$	−178.373	+	200.187i	−0.205027	+	0.230100i
$871$	−207.802	−	150.977i	−0.238578	−	0.173337i
$872$	899.028	−	142.392i	1.03100	−	0.163294i
$873$	−79.3290	+	40.4201i	−0.0908694	+	0.0463003i
$874$			203.372i			0.232691i
$875$	−50.4622	−	289.326i	−0.0576711	−	0.330658i
$876$	−2234.37			−2.55066
$877$	−114.307	−	224.340i	−0.130339	−	0.255804i	0.816609	−	0.577191i	$-0.195851\pi$
$877$	−114.307	−	224.340i	−0.130339	−	0.255804i	−0.946948	+	0.321387i	$0.895851\pi$
$878$	−23.4111	−	147.812i	−0.0266641	−	0.168351i
$879$	−357.801	+	492.471i	−0.407055	+	0.560263i
$880$	144.928	+	129.136i	0.164691	+	0.146745i
$881$	−461.485	+	335.288i	−0.523819	+	0.380577i	−0.818041	−	0.575160i	$-0.804940\pi$
$881$	−461.485	+	335.288i	−0.523819	+	0.380577i	0.294221	+	0.955737i	$0.404940\pi$
$882$	−346.673	+	346.673i	−0.393054	+	0.393054i
$883$	−198.013	−	31.3622i	−0.224250	−	0.0355177i	0.0432981	−	0.999062i	$-0.486213\pi$
$883$	−198.013	−	31.3622i	−0.224250	−	0.0355177i	−0.267548	+	0.963544i	$0.586213\pi$
$884$	176.047	−	57.2010i	0.199148	−	0.0647071i
$885$	557.463	−	2124.60i	0.629901	−	2.40068i
$886$	125.915	−	387.527i	0.142116	−	0.437389i
$887$	−909.137	−	463.229i	−1.02496	−	0.522242i	−0.141099	−	0.989996i	$-0.545063\pi$
$887$	−909.137	−	463.229i	−1.02496	−	0.522242i	−0.883859	+	0.467754i	$0.845063\pi$
$888$	8.78869	−	17.2488i	0.00989717	−	0.0194243i
$889$	−291.528	−	94.7231i	−0.327928	−	0.106550i
$890$	54.2779	−	84.5396i	0.0609864	−	0.0949884i
$891$	−128.917	−	396.767i	−0.144688	−	0.445305i
$892$	87.9581	−	555.345i	0.0986077	−	0.622584i
$893$	762.581	+	762.581i	0.853954	+	0.853954i
$894$	−342.686	−	471.666i	−0.383317	−	0.527591i
$895$	826.532	−	180.181i	0.923499	−	0.201319i
$896$	224.014	+	162.756i	0.250016	+	0.181647i
$897$	−276.536	+	43.7990i	−0.308290	+	0.0488284i
$898$	−333.926	+	170.144i	−0.371855	+	0.189470i
$899$		−	216.245i		−	0.240540i
$900$	−1777.16	−	358.476i	−1.97462	−	0.398307i
$901$	59.0036			0.0654868
$902$	23.1931	+	45.5191i	0.0257130	+	0.0504646i
$903$	−119.622	−	755.266i	−0.132472	−	0.836397i
$904$	−265.448	+	365.357i	−0.293637	+	0.404156i
$905$	1155.35	+	115.363i	1.27663	+	0.127473i
$906$	112.368	−	81.6398i	0.124026	−	0.0901102i
$907$	−1016.91	+	1016.91i	−1.12119	+	1.12119i	−0.129622	+	0.991564i	$0.541376\pi$
$907$	−1016.91	+	1016.91i	−1.12119	+	1.12119i	−0.991564	+	0.129622i	$0.958624\pi$
$908$	892.757	+	141.399i	0.983213	+	0.155726i
$909$	2172.40	−	705.856i	2.38988	−	0.776519i
$910$	22.5581	−	1.29985i	0.0247891	−	0.00142841i
$911$	−310.425	+	955.390i	−0.340752	+	1.04873i	0.623067	+	0.782168i	$0.285886\pi$
$911$	−310.425	+	955.390i	−0.340752	+	1.04873i	−0.963819	+	0.266558i	$0.914114\pi$
$912$	1336.64	+	681.050i	1.46561	+	0.746765i
$913$	100.419	−	197.083i	0.109988	−	0.215863i
$914$	−31.2152	−	10.1424i	−0.0341523	−	0.0110968i
$915$	−870.815	−	1064.01i	−0.951711	−	1.16285i
$916$	−263.363	−	810.549i	−0.287515	−	0.884879i
$917$	−63.1474	+	398.697i	−0.0688630	+	0.434784i
$918$	−348.007	−	348.007i	−0.379092	−	0.379092i
$919$	313.698	+	431.768i	0.341347	+	0.469824i	0.944834	−	0.327549i	$-0.106223\pi$
$919$	313.698	+	431.768i	0.341347	+	0.469824i	−0.603487	+	0.797373i	$0.706223\pi$
$920$	−311.272	−	136.653i	−0.338339	−	0.148535i
$921$	−1093.13	−	794.202i	−1.18689	−	0.862326i
$922$	−199.942	+	31.6676i	−0.216856	+	0.0343467i
$923$	282.666	−	144.026i	0.306247	−	0.156041i
$924$		−	147.361i		−	0.159481i
$925$	−7.18031	+	19.3029i	−0.00776249	+	0.0208680i
$926$	151.117			0.163194
$927$	−351.582	−	690.018i	−0.379268	−	0.744356i
$928$	67.1077	+	423.701i	0.0723144	+	0.456575i
$929$	−545.396	+	750.673i	−0.587078	+	0.808044i	−0.994449	−	0.105219i	$-0.966446\pi$
$929$	−545.396	+	750.673i	−0.587078	+	0.808044i	0.407371	+	0.913263i	$0.366446\pi$
$930$	−163.254	+	95.3897i	−0.175542	+	0.102570i
$931$	−807.417	+	586.623i	−0.867258	+	0.630100i
$932$	−635.705	+	635.705i	−0.682087	+	0.682087i
$933$	−738.115	−	116.906i	−0.791120	−	0.125301i
$934$	−100.426	+	32.6304i	−0.107522	+	0.0349361i
$935$	−86.5454	−	222.002i	−0.0925619	−	0.237435i
$936$	90.0322	−	277.091i	0.0961882	−	0.296037i
$937$	−766.267	−	390.433i	−0.817788	−	0.416684i	−0.00553166	−	0.999985i	$-0.501761\pi$
$937$	−766.267	−	390.433i	−0.817788	−	0.416684i	−0.812256	+	0.583301i	$0.801761\pi$
$938$	−46.4803	+	91.2227i	−0.0495525	+	0.0972523i
$939$	−1443.76	−	469.107i	−1.53755	−	0.499581i
$940$	−804.079	+	313.463i	−0.855403	+	0.333471i
$941$	102.488	+	315.426i	0.108914	+	0.335203i	0.990629	−	0.136579i	$-0.0436109\pi$
$941$	102.488	+	315.426i	0.108914	+	0.335203i	−0.881715	+	0.471782i	$0.843611\pi$
$942$	106.282	−	671.040i	0.112826	−	0.712357i
$943$	308.013	+	308.013i	0.326631	+	0.326631i
$944$	−587.188	−	808.195i	−0.622021	−	0.856139i
$945$	341.232	+	583.999i	0.361092	+	0.617988i
$946$	89.3449	+	64.9128i	0.0944449	+	0.0686182i
$947$	1674.70	−	265.246i	1.76843	−	0.280091i	0.814506	−	0.580155i	$-0.197008\pi$
$947$	1674.70	−	265.246i	1.76843	−	0.280091i	0.953919	+	0.300064i	$0.0970079\pi$
$948$	−1423.41	+	725.264i	−1.50149	+	0.765046i
$949$			382.006i			0.402536i
$950$	307.227	+	114.283i	0.323397	+	0.120298i
$951$	2398.44			2.52202
$952$	−69.9680	−	137.320i	−0.0734958	−	0.144244i
$953$	248.853	+	1571.20i	0.261126	+	1.64868i	0.674611	+	0.738173i	$0.264311\pi$
$953$	248.853	+	1571.20i	0.261126	+	1.64868i	−0.413485	+	0.910511i	$0.635689\pi$
$954$	26.1330	−	35.9691i	0.0273931	−	0.0377034i
$955$	−166.840	+	380.033i	−0.174701	+	0.397941i
$956$	459.550	−	333.883i	0.480701	−	0.349250i
$957$	211.397	−	211.397i	0.220896	−	0.220896i
$958$	366.632	+	58.0688i	0.382706	+	0.0606146i
$959$	−109.052	+	35.4330i	−0.113714	+	0.0369479i
$960$	−721.245	+	590.287i	−0.751296	+	0.614882i
$961$	−249.842	+	768.936i	−0.259982	+	0.800141i
$962$	−1.41180	−	0.719346i	−0.00146756	−	0.000747761i
$963$	−369.354	+	724.897i	−0.383545	+	0.752749i
$964$	−635.389	−	206.450i	−0.659117	−	0.214160i
$965$	28.2632	+	490.490i	0.0292883	+	0.508280i
$966$	34.4862	+	106.137i	0.0357000	+	0.109873i
$967$	189.322	−	1195.33i	0.195783	−	1.23613i	−0.672515	−	0.740083i	$-0.734786\pi$
$967$	189.322	−	1195.33i	0.195783	−	1.23613i	0.868298	−	0.496043i	$-0.165214\pi$
$968$	−343.610	−	343.610i	−0.354969	−	0.354969i
$969$	−1082.36	−	1489.74i	−1.11699	−	1.53740i
$970$	−1.27992	+	12.8183i	−0.00131950	+	0.0132147i
$971$	847.746	+	615.924i	0.873065	+	0.634319i	0.931408	−	0.363978i	$-0.118582\pi$
$971$	847.746	+	615.924i	0.873065	+	0.634319i	−0.0583425	+	0.998297i	$0.518582\pi$
$972$	668.054	−	105.809i	0.687298	−	0.108857i
$973$	244.149	−	124.400i	0.250924	−	0.127852i
$974$			196.947i			0.202204i
$975$	−89.2310	+	442.367i	−0.0915189	+	0.453709i
$976$	−625.323			−0.640700
$977$	−315.774	−	619.741i	−0.323207	−	0.634330i	0.671042	−	0.741419i	$-0.265847\pi$
$977$	−315.774	−	619.741i	−0.323207	−	0.634330i	−0.994249	+	0.107089i	$0.965847\pi$
$978$	0.0899176	+	0.567717i	9.19402e−5	+	0.000580488i
$979$	−65.8422	+	90.6240i	−0.0672545	+	0.0925679i
$980$	−170.109	−	780.330i	−0.173581	−	0.796255i
$981$	3316.21	−	2409.37i	3.38044	−	2.45603i
$982$	388.763	−	388.763i	0.395889	−	0.395889i
$983$	299.178	+	47.3851i	0.304352	+	0.0482046i	0.306743	−	0.951793i	$-0.400761\pi$
$983$	299.178	+	47.3851i	0.304352	+	0.0482046i	−0.00239059	+	0.999997i	$0.500761\pi$
$984$	−627.646	+	203.934i	−0.637851	+	0.207250i
$985$	−751.765	−	482.664i	−0.763213	−	0.490014i
$986$	46.2559	−	142.361i	0.0469126	−	0.144382i
$987$	527.295	+	268.670i	0.534240	+	0.272209i
$988$	128.904	−	252.988i	0.130469	−	0.256061i
$989$	895.550	+	290.982i	0.905511	+	0.294218i
$990$	−173.665	−	45.5672i	−0.175420	−	0.0460275i
$991$	57.8216	+	177.956i	0.0583467	+	0.179573i	0.975982	−	0.217851i	$-0.0699045\pi$
$991$	57.8216	+	177.956i	0.0583467	+	0.179573i	−0.917635	+	0.397423i	$0.869905\pi$
$992$	−47.3235	+	298.789i	−0.0477052	+	0.301199i
$993$	−78.2440	−	78.2440i	−0.0787955	−	0.0787955i
$994$	−74.3262	−	102.301i	−0.0747748	−	0.102919i
$995$	365.081	−	409.727i	0.366915	−	0.411786i
$996$	1106.68	+	804.047i	1.11112	+	0.807276i
$997$	41.2167	−	6.52808i	0.0413407	−	0.00654773i	−0.135730	−	0.990746i	$-0.543338\pi$
$997$	41.2167	−	6.52808i	0.0413407	−	0.00654773i	0.177071	+	0.984198i	$0.443338\pi$
$998$	107.756	−	54.9042i	0.107971	−	0.0550142i
$999$		−	47.4310i		−	0.0474785i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.3.f.a.3.3	✓	32
3.2	odd	2		225.3.r.a.28.2		32
4.3	odd	2		400.3.bg.c.353.1		32
5.2	odd	4		125.3.f.a.7.2		32
5.3	odd	4		125.3.f.b.7.3		32
5.4	even	2		125.3.f.c.118.2		32
25.6	even	5		125.3.f.a.18.2		32
25.8	odd	20		125.3.f.c.107.2		32
25.17	odd	20	inner	25.3.f.a.17.3	yes	32
25.19	even	10		125.3.f.b.18.3		32
75.17	even	20		225.3.r.a.217.2		32
100.67	even	20		400.3.bg.c.17.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.3.f.a.3.3	✓	32	1.1	even	1	trivial
25.3.f.a.17.3	yes	32	25.17	odd	20	inner
125.3.f.a.7.2		32	5.2	odd	4
125.3.f.a.18.2		32	25.6	even	5
125.3.f.b.7.3		32	5.3	odd	4
125.3.f.b.18.3		32	25.19	even	10
125.3.f.c.107.2		32	25.8	odd	20
125.3.f.c.118.2		32	5.4	even	2
225.3.r.a.28.2		32	3.2	odd	2
225.3.r.a.217.2		32	75.17	even	20
400.3.bg.c.17.1		32	100.67	even	20
400.3.bg.c.353.1		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)

\(f(q)\)	\(=\)	\(q+(-0.259330 - 0.508965i) q^{2} +(0.838638 + 5.29495i) q^{3} +(2.15935 - 2.97209i) q^{4} +(-3.73307 - 3.32629i) q^{5} +(2.47746 - 1.79998i) q^{6} +(1.66138 - 1.66138i) q^{7} +(-4.32944 - 0.685716i) q^{8} +(-18.7737 + 6.09994i) q^{9} +O(q^{10})\)	\(q+(-0.259330 - 0.508965i) q^{2} +(0.838638 + 5.29495i) q^{3} +(2.15935 - 2.97209i) q^{4} +(-3.73307 - 3.32629i) q^{5} +(2.47746 - 1.79998i) q^{6} +(1.66138 - 1.66138i) q^{7} +(-4.32944 - 0.685716i) q^{8} +(-18.7737 + 6.09994i) q^{9} +(-0.724866 + 2.76261i) q^{10} +(0.984087 - 3.02871i) q^{11} +(17.5480 + 8.94114i) q^{12} +(1.52865 - 3.00014i) q^{13} +(-1.27643 - 0.414737i) q^{14} +(14.4819 - 22.5560i) q^{15} +(-3.76720 - 11.5942i) q^{16} +(-2.34094 + 14.7801i) q^{17} +(7.97324 + 7.97324i) q^{18} +(13.4919 + 18.5700i) q^{19} +(-17.9470 + 3.91238i) q^{20} +(10.1902 + 7.40363i) q^{21} +(-1.79671 + 0.284571i) q^{22} +(-13.8201 + 7.04168i) q^{23} -23.4992i q^{24} +(2.87158 + 24.8345i) q^{25} -1.92339 q^{26} +(-26.1388 - 51.3003i) q^{27} +(-1.35027 - 8.52527i) q^{28} +(10.2929 - 14.1670i) q^{29} +(-15.2358 - 1.52130i) q^{30} +(9.99041 - 7.25845i) q^{31} +(-17.3223 + 17.3223i) q^{32} +(16.8622 + 2.67070i) q^{33} +(8.12962 - 2.64147i) q^{34} +(-11.7283 + 0.675811i) q^{35} +(-22.4094 + 68.9689i) q^{36} +(0.734014 + 0.373999i) q^{37} +(5.95262 - 11.6827i) q^{38} +(17.1676 + 5.57808i) q^{39} +(13.8812 + 16.9608i) q^{40} +(-8.67834 - 26.7092i) q^{41} +(1.12555 - 7.10645i) q^{42} +(-42.9278 - 42.9278i) q^{43} +(-6.87660 - 9.46483i) q^{44} +(90.3736 + 39.6752i) q^{45} +(7.16793 + 5.20781i) q^{46} +(46.4052 - 7.34985i) q^{47} +(58.2316 - 29.6705i) q^{48} +43.4796i q^{49} +(11.8952 - 7.90189i) q^{50} -80.2230 q^{51} +(-5.61580 - 11.0216i) q^{52} +(-0.616814 - 3.89441i) q^{53} +(-19.3314 + 26.6074i) q^{54} +(-13.7480 + 8.03302i) q^{55} +(-8.33208 + 6.05361i) q^{56} +(-87.0125 + 87.0125i) q^{57} +(-9.87978 - 1.56480i) q^{58} +(77.9344 - 25.3224i) q^{59} +(-35.7669 - 91.7475i) q^{60} +(15.8508 - 48.7838i) q^{61} +(-6.28511 - 3.20243i) q^{62} +(-21.0559 + 41.3245i) q^{63} +(-33.0683 - 10.7446i) q^{64} +(-15.6859 + 6.11500i) q^{65} +(-3.01358 - 9.27484i) q^{66} +(11.9334 - 75.3444i) q^{67} +(38.8728 + 38.8728i) q^{68} +(-48.8754 - 67.2712i) q^{69} +(3.38546 + 5.79402i) q^{70} +(76.2237 + 55.3797i) q^{71} +(85.4623 - 13.5359i) q^{72} +(-101.086 + 51.5059i) q^{73} -0.470577i q^{74} +(-129.089 + 36.0321i) q^{75} +84.3254 q^{76} +(-3.39690 - 6.66678i) q^{77} +(-1.61303 - 10.1843i) q^{78} +(-47.6784 + 65.6237i) q^{79} +(-24.5026 + 55.8129i) q^{80} +(105.983 - 77.0010i) q^{81} +(-11.3435 + 11.3435i) q^{82} +(68.6020 + 10.8655i) q^{83} +(44.0085 - 14.2992i) q^{84} +(57.9017 - 47.3884i) q^{85} +(-10.7163 + 32.9812i) q^{86} +(83.6457 + 42.6196i) q^{87} +(-6.33738 + 12.4378i) q^{88} +(-33.4534 - 10.8697i) q^{89} +(-3.24333 - 56.2859i) q^{90} +(-2.44471 - 7.52404i) q^{91} +(-8.91386 + 56.2799i) q^{92} +(46.8115 + 46.8115i) q^{93} +(-15.7751 - 21.7125i) q^{94} +(11.4031 - 114.201i) q^{95} +(-106.248 - 77.1934i) q^{96} +(4.45480 - 0.705571i) q^{97} +(22.1296 - 11.2756i) q^{98} +62.8629i 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

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Database

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