LMFDB - Embedded newform 25.3.f.a.23.2

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			23.2
Character	$\chi$	$=$	25.23
Dual form			25.3.f.a.12.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.312579 + 1.97355i) q^{2} +(-4.02069 + 2.04864i) q^{3} +(0.00704800 + 0.00229003i) q^{4} +(4.93389 - 0.810386i) q^{5} +(-2.78631 - 8.57538i) q^{6} +(3.91191 - 3.91191i) q^{7} +(-3.63528 + 7.13464i) q^{8} +(6.67894 - 9.19277i) q^{9} +O(q^{10})$	\(q+(-0.312579 + 1.97355i) q^{2} +(-4.02069 + 2.04864i) q^{3} +(0.00704800 + 0.00229003i) q^{4} +(4.93389 - 0.810386i) q^{5} +(-2.78631 - 8.57538i) q^{6} +(3.91191 - 3.91191i) q^{7} +(-3.63528 + 7.13464i) q^{8} +(6.67894 - 9.19277i) q^{9} +(0.0571038 + 9.99057i) q^{10} +(-2.73590 + 1.98775i) q^{11} +(-0.0330293 + 0.00523133i) q^{12} +(-3.13886 - 19.8180i) q^{13} +(6.49755 + 8.94311i) q^{14} +(-18.1775 + 13.3661i) q^{15} +(-12.9202 - 9.38711i) q^{16} +(17.7107 + 9.02407i) q^{17} +(16.0547 + 16.0547i) q^{18} +(-5.87938 + 1.91032i) q^{19} +(0.0366299 + 0.00558718i) q^{20} +(-7.71446 + 23.7427i) q^{21} +(-3.06773 - 6.02076i) q^{22} +(-13.6608 - 2.16366i) q^{23} -36.1336i q^{24} +(23.6865 - 7.99671i) q^{25} +40.0928 q^{26} +(-1.66800 + 10.5313i) q^{27} +(0.0365295 - 0.0186127i) q^{28} +(-29.3129 - 9.52435i) q^{29} +(-20.6967 - 40.0520i) q^{30} +(-0.774840 - 2.38471i) q^{31} +(-0.0838425 + 0.0838425i) q^{32} +(6.92803 - 13.5970i) q^{33} +(-23.3454 + 32.1322i) q^{34} +(16.1308 - 22.4711i) q^{35} +(0.0681249 - 0.0494957i) q^{36} +(-33.6313 + 5.32667i) q^{37} +(-1.93234 - 12.2003i) q^{38} +(53.2204 + 73.2515i) q^{39} +(-12.1543 + 38.1475i) q^{40} +(29.0354 + 21.0954i) q^{41} +(-44.4459 - 22.6463i) q^{42} +(23.3347 + 23.3347i) q^{43} +(-0.0238347 + 0.00774436i) q^{44} +(25.5035 - 50.7686i) q^{45} +(8.54016 - 26.2839i) q^{46} +(-19.2067 - 37.6953i) q^{47} +(71.1791 + 11.2737i) q^{48} +18.3940i q^{49} +(8.37796 + 49.2461i) q^{50} -89.6965 q^{51} +(0.0232612 - 0.146865i) q^{52} +(-73.4897 + 37.4449i) q^{53} +(-20.2627 - 6.58375i) q^{54} +(-11.8878 + 12.0245i) q^{55} +(13.6892 + 42.1309i) q^{56} +(19.7256 - 19.7256i) q^{57} +(27.9594 - 54.8733i) q^{58} +(1.53534 - 2.11322i) q^{59} +(-0.158724 + 0.0525773i) q^{60} +(21.8447 - 15.8711i) q^{61} +(4.94854 - 0.783771i) q^{62} +(-9.83388 - 62.0887i) q^{63} +(-37.6877 - 51.8727i) q^{64} +(-31.5470 - 95.2360i) q^{65} +(24.6688 + 17.9229i) q^{66} +(67.8430 + 34.5677i) q^{67} +(0.104160 + 0.104160i) q^{68} +(59.3584 - 19.2867i) q^{69} +(39.3056 + 38.8588i) q^{70} +(22.6659 - 69.7586i) q^{71} +(41.3073 + 81.0701i) q^{72} +(51.6598 + 8.18211i) q^{73} -68.0379i q^{74} +(-78.8539 + 80.6776i) q^{75} -0.0458126 q^{76} +(-2.92671 + 18.4785i) q^{77} +(-161.201 + 82.1359i) q^{78} +(-37.4103 - 12.1554i) q^{79} +(-71.3543 - 35.8446i) q^{80} +(16.7335 + 51.5004i) q^{81} +(-50.7087 + 50.7087i) q^{82} +(-22.8152 + 44.7773i) q^{83} +(-0.108743 + 0.149672i) q^{84} +(94.6958 + 30.1712i) q^{85} +(-53.3460 + 38.7581i) q^{86} +(137.370 - 21.7573i) q^{87} +(-4.23611 - 26.7457i) q^{88} +(-41.7155 - 57.4164i) q^{89} +(92.2224 + 66.2015i) q^{90} +(-89.8050 - 65.2472i) q^{91} +(-0.0913265 - 0.0465332i) q^{92} +(8.00082 + 8.00082i) q^{93} +(80.3971 - 26.1226i) q^{94} +(-27.4601 + 14.1899i) q^{95} +(0.165341 - 0.508868i) q^{96} +(-1.26842 - 2.48942i) q^{97} +(-36.3014 - 5.74957i) q^{98} +38.4266i 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 $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{11}{20}\right)$

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 $

$2$	−0.312579	+	1.97355i	−0.156289	+	0.986773i	0.777483	+	0.628905i	$0.216496\pi$
$2$	−0.312579	+	1.97355i	−0.156289	+	0.986773i	−0.933772	+	0.357868i	$0.883504\pi$
$3$	−4.02069	+	2.04864i	−1.34023	+	0.682881i	−0.969323	−	0.245789i	$-0.920953\pi$
$3$	−4.02069	+	2.04864i	−1.34023	+	0.682881i	−0.370907	+	0.928670i	$0.620953\pi$
$4$	0.00704800	+	0.00229003i	0.00176200	+	0.000572509i
$5$	4.93389	−	0.810386i	0.986778	−	0.162077i
$5$	4.93389	−	0.810386i	0.986778	−	0.162077i
$6$	−2.78631	−	8.57538i	−0.464385	−	1.42923i
$7$	3.91191	−	3.91191i	0.558844	−	0.558844i	−0.370134	−	0.928978i	$-0.620688\pi$
$7$	3.91191	−	3.91191i	0.558844	−	0.558844i	0.928978	+	0.370134i	$0.120688\pi$
$8$	−3.63528	+	7.13464i	−0.454410	+	0.891830i
$9$	6.67894	−	9.19277i	0.742104	−	1.02142i
$10$	0.0571038	+	9.99057i	0.00571038	+	0.999057i
$11$	−2.73590	+	1.98775i	−0.248719	+	0.180705i	−0.705159	−	0.709049i	$-0.749124\pi$
$11$	−2.73590	+	1.98775i	−0.248719	+	0.180705i	0.456440	+	0.889754i	$0.349124\pi$
$12$	−0.0330293	+	0.00523133i	−0.00275244	+	0.000435944i
$13$	−3.13886	−	19.8180i	−0.241451	−	1.52446i	−0.748845	−	0.662746i	$-0.769391\pi$
$13$	−3.13886	−	19.8180i	−0.241451	−	1.52446i	0.507394	−	0.861714i	$-0.330609\pi$
$14$	6.49755	+	8.94311i	0.464111	+	0.638793i
$15$	−18.1775	+	13.3661i	−1.21183	+	0.891073i
$16$	−12.9202	−	9.38711i	−0.807515	−	0.586694i
$17$	17.7107	+	9.02407i	1.04181	+	0.530828i	0.889228	−	0.457464i	$-0.151242\pi$
$17$	17.7107	+	9.02407i	1.04181	+	0.530828i	0.152579	+	0.988291i	$0.451242\pi$
$18$	16.0547	+	16.0547i	0.891926	+	0.891926i
$19$	−5.87938	+	1.91032i	−0.309441	+	0.100543i	−0.459621	−	0.888115i	$-0.652015\pi$
$19$	−5.87938	+	1.91032i	−0.309441	+	0.100543i	0.150180	+	0.988659i	$0.452015\pi$
$20$	0.0366299	+	0.00558718i	0.00183149	+	0.000279359i
$21$	−7.71446	+	23.7427i	−0.367355	+	1.13060i
$22$	−3.06773	−	6.02076i	−0.139442	−	0.273671i
$23$	−13.6608	−	2.16366i	−0.593948	−	0.0940721i	−0.147778	−	0.989021i	$-0.547212\pi$
$23$	−13.6608	−	2.16366i	−0.593948	−	0.0940721i	−0.446170	+	0.894948i	$0.647212\pi$
$24$		−	36.1336i		−	1.50557i
$25$	23.6865	−	7.99671i	0.947462	−	0.319868i
$26$	40.0928			1.54203
$27$	−1.66800	+	10.5313i	−0.0617777	+	0.390049i
$28$	0.0365295	−	0.0186127i	0.00130463	−	0.000664740i
$29$	−29.3129	−	9.52435i	−1.01079	−	0.328426i	−0.243622	−	0.969870i	$-0.578336\pi$
$29$	−29.3129	−	9.52435i	−1.01079	−	0.328426i	−0.767170	+	0.641444i	$0.778336\pi$
$30$	−20.6967	−	40.0520i	−0.689891	−	1.33507i
$31$	−0.774840	−	2.38471i	−0.0249948	−	0.0769262i	0.937781	−	0.347227i	$-0.112877\pi$
$31$	−0.774840	−	2.38471i	−0.0249948	−	0.0769262i	−0.962776	+	0.270301i	$0.912877\pi$
$32$	−0.0838425	+	0.0838425i	−0.00262008	+	0.00262008i
$33$	6.92803	−	13.5970i	0.209940	−	0.412031i
$34$	−23.3454	+	32.1322i	−0.686630	+	0.945065i
$35$	16.1308	−	22.4711i	0.460879	−	0.642031i
$36$	0.0681249	−	0.0494957i	0.00189236	−	0.00137488i
$37$	−33.6313	+	5.32667i	−0.908954	+	0.143964i	−0.593367	−	0.804932i	$-0.702202\pi$
$37$	−33.6313	+	5.32667i	−0.908954	+	0.143964i	−0.315587	+	0.948897i	$0.602202\pi$
$38$	−1.93234	−	12.2003i	−0.0508512	−	0.321062i
$39$	53.2204	+	73.2515i	1.36462	+	1.87824i
$40$	−12.1543	+	38.1475i	−0.303857	+	0.953688i
$41$	29.0354	+	21.0954i	0.708180	+	0.514523i	0.882586	−	0.470151i	$-0.155800\pi$
$41$	29.0354	+	21.0954i	0.708180	+	0.514523i	−0.174406	+	0.984674i	$0.555800\pi$
$42$	−44.4459	−	22.6463i	−1.05823	−	0.539198i
$43$	23.3347	+	23.3347i	0.542667	+	0.542667i	0.924310	−	0.381643i	$-0.124642\pi$
$43$	23.3347	+	23.3347i	0.542667	+	0.542667i	−0.381643	+	0.924310i	$0.624642\pi$
$44$	−0.0238347	+	0.00774436i	−0.000541697	+	0.000176008i
$45$	25.5035	−	50.7686i	0.566744	−	1.12819i
$46$	8.54016	−	26.2839i	0.185656	−	0.571389i
$47$	−19.2067	−	37.6953i	−0.408654	−	0.802029i	0.591336	−	0.806425i	$-0.298601\pi$
$47$	−19.2067	−	37.6953i	−0.408654	−	0.802029i	−0.999990	+	0.00439647i	$0.998601\pi$
$48$	71.1791	+	11.2737i	1.48290	+	0.234868i
$49$			18.3940i			0.375387i
$50$	8.37796	+	49.2461i	0.167559	+	0.984922i
$51$	−89.6965			−1.75875
$52$	0.0232612	−	0.146865i	0.000447330	−	0.00282433i
$53$	−73.4897	+	37.4449i	−1.38660	+	0.706507i	−0.978465	−	0.206415i	$-0.933820\pi$
$53$	−73.4897	+	37.4449i	−1.38660	+	0.706507i	−0.408134	+	0.912922i	$0.633820\pi$
$54$	−20.2627	−	6.58375i	−0.375235	−	0.121921i
$55$	−11.8878	+	12.0245i	−0.216142	+	0.218627i
$56$	13.6892	+	42.1309i	0.244449	+	0.752338i
$57$	19.7256	−	19.7256i	0.346063	−	0.346063i
$58$	27.9594	−	54.8733i	0.482058	−	0.946092i
$59$	1.53534	−	2.11322i	0.0260228	−	0.0358173i	−0.795807	−	0.605550i	$-0.792953\pi$
$59$	1.53534	−	2.11322i	0.0260228	−	0.0358173i	0.821830	+	0.569733i	$0.192953\pi$
$60$	−0.158724	+	0.0525773i	−0.00264539	+	0.000876288i
$61$	21.8447	−	15.8711i	0.358110	−	0.260182i	−0.394153	−	0.919045i	$-0.628962\pi$
$61$	21.8447	−	15.8711i	0.358110	−	0.260182i	0.752264	+	0.658862i	$0.228962\pi$
$62$	4.94854	−	0.783771i	0.0798151	−	0.0126415i
$63$	−9.83388	−	62.0887i	−0.156093	−	0.985534i
$64$	−37.6877	−	51.8727i	−0.588870	−	0.810510i
$65$	−31.5470	−	95.2360i	−0.485338	−	1.46517i
$66$	24.6688	+	17.9229i	0.373770	+	0.271560i
$67$	67.8430	+	34.5677i	1.01258	+	0.515936i	0.879868	−	0.475218i	$-0.157631\pi$
$67$	67.8430	+	34.5677i	1.01258	+	0.515936i	0.132714	+	0.991154i	$0.457631\pi$
$68$	0.104160	+	0.104160i	0.00153176	+	0.00153176i
$69$	59.3584	−	19.2867i	0.860267	−	0.279518i
$70$	39.3056	+	38.8588i	0.561508	+	0.555126i
$71$	22.6659	−	69.7586i	0.319239	−	0.982516i	−0.654736	−	0.755858i	$-0.727220\pi$
$71$	22.6659	−	69.7586i	0.319239	−	0.982516i	0.973974	−	0.226658i	$-0.0727799\pi$
$72$	41.3073	+	81.0701i	0.573712	+	1.12597i
$73$	51.6598	+	8.18211i	0.707669	+	0.112084i	0.499886	−	0.866091i	$-0.333375\pi$
$73$	51.6598	+	8.18211i	0.707669	+	0.112084i	0.207783	+	0.978175i	$0.433375\pi$
$74$		−	68.0379i		−	0.919431i
$75$	−78.8539	+	80.6776i	−1.05138	+	1.07570i
$76$	−0.0458126			−0.000602797
$77$	−2.92671	+	18.4785i	−0.0380092	+	0.239981i
$78$	−161.201	+	82.1359i	−2.06668	+	1.05302i
$79$	−37.4103	−	12.1554i	−0.473548	−	0.153865i	0.0625131	−	0.998044i	$-0.480088\pi$
$79$	−37.4103	−	12.1554i	−0.473548	−	0.153865i	−0.536061	+	0.844179i	$0.680088\pi$
$80$	−71.3543	−	35.8446i	−0.891928	−	0.448057i
$81$	16.7335	+	51.5004i	0.206586	+	0.635807i
$82$	−50.7087	+	50.7087i	−0.618399	+	0.618399i
$83$	−22.8152	+	44.7773i	−0.274881	+	0.539485i	−0.986635	−	0.162944i	$-0.947901\pi$
$83$	−22.8152	+	44.7773i	−0.274881	+	0.539485i	0.711754	+	0.702429i	$0.247901\pi$
$84$	−0.108743	+	0.149672i	−0.00129456	+	0.00178181i
$85$	94.6958	+	30.1712i	1.11407	+	0.354956i
$86$	−53.3460	+	38.7581i	−0.620302	+	0.450676i
$87$	137.370	−	21.7573i	1.57897	−	0.250084i
$88$	−4.23611	−	26.7457i	−0.0481376	−	0.303929i
$89$	−41.7155	−	57.4164i	−0.468713	−	0.645128i	0.507574	−	0.861608i	$-0.330542\pi$
$89$	−41.7155	−	57.4164i	−0.468713	−	0.645128i	−0.976287	+	0.216480i	$0.930542\pi$
$90$	92.2224	+	66.2015i	1.02469	+	0.735572i
$91$	−89.8050	−	65.2472i	−0.986868	−	0.717002i
$92$	−0.0913265	−	0.0465332i	−0.000992679	−	0.000505795i
$93$	8.00082	+	8.00082i	0.0860303	+	0.0860303i
$94$	80.3971	−	26.1226i	0.855288	−	0.277900i
$95$	−27.4601	+	14.1899i	−0.289054	+	0.149367i
$96$	0.165341	−	0.508868i	0.00172230	−	0.00530071i
$97$	−1.26842	−	2.48942i	−0.0130765	−	0.0256642i	0.884376	−	0.466775i	$-0.154584\pi$
$97$	−1.26842	−	2.48942i	−0.0130765	−	0.0256642i	−0.897452	+	0.441111i	$0.854584\pi$
$98$	−36.3014	−	5.74957i	−0.370422	−	0.0586691i
$99$			38.4266i			0.388148i
$100$	0.185256	−	0.00211783i	0.00185256	−	2.11783e-5i
$101$	−53.7631			−0.532308			−0.266154	−	0.963931i	$-0.585753\pi$
$101$	−53.7631			−0.532308			−0.266154	+	0.963931i	$0.585753\pi$
$102$	28.0372	−	177.020i	0.274875	−	1.73549i
$103$	104.783	−	53.3894i	1.01731	−	0.518344i	0.135911	−	0.990721i	$-0.456604\pi$
$103$	104.783	−	53.3894i	1.01731	−	0.518344i	0.881397	+	0.472377i	$0.156604\pi$
$104$	152.805	+	49.6493i	1.46928	+	0.477397i
$105$	−18.8216	+	123.395i	−0.179253	+	1.17519i
$106$	−50.9278	−	156.740i	−0.480451	−	1.47868i
$107$	1.86245	−	1.86245i	0.0174060	−	0.0174060i	−0.698350	−	0.715756i	$-0.746082\pi$
$107$	1.86245	−	1.86245i	0.0174060	−	0.0174060i	0.715756	+	0.698350i	$0.246082\pi$
$108$	−0.0358732	+	0.0704051i	−0.000332159	+	0.000651899i
$109$	−77.7078	+	106.956i	−0.712915	+	0.981244i	0.286814	+	0.957986i	$0.407404\pi$
$109$	−77.7078	+	106.956i	−0.712915	+	0.981244i	−0.999730	+	0.0232574i	$0.992596\pi$
$110$	−20.0150	−	27.2197i	−0.181954	−	0.247452i
$111$	124.309	−	90.3154i	1.11990	−	0.813653i
$112$	−87.2643	+	13.8213i	−0.779145	+	0.123405i
$113$	6.99224	+	44.1473i	0.0618782	+	0.390684i	0.999118	+	0.0419974i	$0.0133721\pi$
$113$	6.99224	+	44.1473i	0.0618782	+	0.390684i	−0.937239	+	0.348686i	$0.886628\pi$
$114$	32.7635	+	45.0951i	0.287399	+	0.395571i
$115$	−69.1543	+	0.395270i	−0.601342	+	0.00343713i
$116$	−0.184787	−	0.134255i	−0.00159299	−	0.00115737i
$117$	−203.146	−	103.508i	−1.73629	−	0.884686i
$118$	3.69062	+	3.69062i	0.0312765	+	0.0312765i
$119$	104.584	−	33.9814i	0.878858	−	0.285558i
$120$	−29.2821	−	178.279i	−0.244018	−	1.48566i
$121$	−33.8570	+	104.201i	−0.279810	+	0.861167i
$122$	24.4942	+	48.0726i	0.200772	+	0.394037i
$123$	−159.959	−	25.3351i	−1.30048	−	0.205976i
$124$		−	0.0185819i		−	0.000149854i
$125$	110.386	−	58.6502i	0.883091	−	0.469201i
$126$	125.609			0.996894
$127$	−26.6349	+	168.166i	−0.209724	+	1.32415i	0.628069	+	0.778158i	$0.283845\pi$
$127$	−26.6349	+	168.166i	−0.209724	+	1.32415i	−0.837793	+	0.545988i	$0.816155\pi$
$128$	113.731	−	57.9488i	0.888522	−	0.452725i
$129$	−141.626	−	46.0171i	−1.09788	−	0.356722i
$130$	197.814	−	32.4907i	1.52164	−	0.249928i
$131$	16.2028	+	49.8672i	0.123686	+	0.380665i	0.993659	−	0.112433i	$-0.0358643\pi$
$131$	16.2028	+	49.8672i	0.123686	+	0.380665i	−0.869974	+	0.493098i	$0.835864\pi$
$132$	0.0799664	−	0.0799664i	0.000605806	−	0.000605806i
$133$	−15.5266	+	30.4726i	−0.116741	+	0.229117i
$134$	−89.4273	+	123.086i	−0.667368	+	0.918553i
$135$	0.304720	+	53.3122i	0.00225718	+	0.394905i
$136$	−128.767	+	93.5547i	−0.946816	+	0.687902i
$137$	50.3103	−	7.96837i	0.367228	−	0.0581633i	0.0299067	−	0.999553i	$-0.490479\pi$
$137$	50.3103	−	7.96837i	0.367228	−	0.0581633i	0.337322	+	0.941389i	$0.390479\pi$
$138$	19.5090	+	123.175i	0.141370	+	0.892574i
$139$	−69.7880	−	96.0549i	−0.502072	−	0.691043i	0.480485	−	0.877003i	$-0.340461\pi$
$139$	−69.7880	−	96.0549i	−0.502072	−	0.691043i	−0.982557	+	0.185960i	$0.940461\pi$
$140$	0.165149	−	0.121436i	0.00117964	−	0.000867401i
$141$	154.449	+	112.214i	1.09538	+	0.795841i
$142$	130.587	+	66.5374i	0.919626	+	0.468573i
$143$	47.9808	+	47.9808i	0.335530	+	0.335530i
$144$	−172.587	+	56.0769i	−1.19852	+	0.389423i
$145$	−152.345	−	23.2373i	−1.05066	−	0.160257i
$146$	−32.2955	+	99.3955i	−0.221202	+	0.680791i
$147$	−37.6827	−	73.9565i	−0.256345	−	0.503105i
$148$	−0.249232	−	0.0394744i	−0.00168400	−	0.000266719i
$149$			64.0597i			0.429931i	0.976622	+	0.214965i	$0.0689639\pi$
$149$			64.0597i			0.429931i	−0.976622	+	0.214965i	$0.931036\pi$
$150$	−134.573	−	180.840i	−0.897153	−	1.20560i
$151$	227.547			1.50693			0.753467	−	0.657486i	$-0.228380\pi$
$151$	227.547			1.50693			0.753467	+	0.657486i	$0.228380\pi$
$152$	7.74370	−	48.8918i	0.0509454	−	0.321657i
$153$	201.245	−	102.540i	1.31533	−	0.670193i
$154$	−35.5533	−	11.5520i	−0.230866	−	0.0750129i
$155$	−5.75551	−	11.1380i	−0.0371323	−	0.0718580i
$156$	0.207349	+	0.638153i	0.00132916	+	0.00409073i
$157$	−65.7370	+	65.7370i	−0.418707	+	0.418707i	−0.884758	−	0.466051i	$-0.845676\pi$
$157$	−65.7370	+	65.7370i	−0.418707	+	0.418707i	0.466051	+	0.884758i	$0.345676\pi$
$158$	35.6828	−	70.0315i	0.225841	−	0.443237i
$159$	218.768	−	301.108i	1.37590	−	1.89376i
$160$	−0.345725	+	0.481614i	−0.00216078	+	0.00301009i
$161$	−61.9038	+	44.9757i	−0.384496	+	0.279352i
$162$	−106.869	+	16.9264i	−0.659685	+	0.104484i
$163$	−19.9218	−	125.781i	−0.122220	−	0.771664i	−0.970319	−	0.241827i	$-0.922253\pi$
$163$	−19.9218	−	125.781i	−0.122220	−	0.771664i	0.848100	−	0.529837i	$-0.177747\pi$
$164$	0.156332	+	0.215173i	0.000953245	+	0.00131203i
$165$	23.1633	−	72.7006i	0.140384	−	0.440610i
$166$	−81.2384	−	59.0232i	−0.489388	−	0.355561i
$167$	−71.6764	−	36.5209i	−0.429200	−	0.218688i	0.226026	−	0.974121i	$-0.427427\pi$
$167$	−71.6764	−	36.5209i	−0.429200	−	0.218688i	−0.655226	+	0.755433i	$0.727427\pi$
$168$	−141.351	−	141.351i	−0.841376	−	0.841376i
$169$	−222.171	+	72.1878i	−1.31462	+	0.427147i
$170$	−89.1442	+	177.456i	−0.524378	+	1.04386i
$171$	−21.7068	+	66.8067i	−0.126940	+	0.390682i
$172$	0.111026	+	0.217900i	0.000645498	+	0.00126686i
$173$	168.729	+	26.7241i	0.975314	+	0.154474i	0.623694	−	0.781669i	$-0.285631\pi$
$173$	168.729	+	26.7241i	0.975314	+	0.154474i	0.351619	+	0.936143i	$0.385631\pi$
$174$			277.907i			1.59717i
$175$	61.3772	−	123.942i	0.350727	−	0.708240i
$176$	54.0078			0.306862
$177$	−1.84391	+	11.6420i	−0.0104176	+	0.0657739i
$178$	126.353	−	64.3802i	0.709850	−	0.361687i
$179$	250.316	+	81.3326i	1.39841	+	0.454372i	0.908677	−	0.417499i	$-0.137093\pi$
$179$	250.316	+	81.3326i	1.39841	+	0.454372i	0.489736	+	0.871871i	$0.337093\pi$
$180$	0.296010	−	0.299414i	0.00164450	−	0.00166341i
$181$	−42.4512	−	130.651i	−0.234537	−	0.721830i	−0.997183	−	0.0750137i	$-0.976100\pi$
$181$	−42.4512	−	130.651i	−0.234537	−	0.721830i	0.762646	−	0.646817i	$-0.223900\pi$
$182$	156.839	−	156.839i	0.861755	−	0.861755i
$183$	−55.3166	+	108.565i	−0.302277	+	0.593251i
$184$	65.0978	−	89.5994i	0.353792	−	0.486953i
$185$	−161.616	+	53.5356i	−0.873602	+	0.289381i
$186$	−18.2909	+	13.2891i	−0.0983380	+	0.0714467i
$187$	−66.3925	+	10.5155i	−0.355040	+	0.0562328i
$188$	−0.0490455	−	0.309661i	−0.000260880	−	0.00164713i
$189$	34.6725	+	47.7226i	0.183453	+	0.252501i
$190$	−19.4210	−	58.6292i	−0.102216	−	0.308575i
$191$	−153.497	−	111.522i	−0.803651	−	0.583886i	0.108332	−	0.994115i	$-0.465449\pi$
$191$	−153.497	−	111.522i	−0.803651	−	0.583886i	−0.911983	+	0.410228i	$0.865449\pi$
$192$	257.799	+	131.355i	1.34270	+	0.684142i
$193$	46.3256	+	46.3256i	0.240029	+	0.240029i	0.816862	−	0.576833i	$-0.195712\pi$
$193$	46.3256	+	46.3256i	0.240029	+	0.240029i	−0.576833	+	0.816862i	$0.695712\pi$
$194$	5.30947	−	1.72515i	0.0273684	−	0.00889254i
$195$	321.945	+	318.286i	1.65100	+	1.63224i
$196$	−0.0421228	+	0.129641i	−0.000214912	+	0.000661433i
$197$	−124.210	−	243.776i	−0.630508	−	1.23744i	−0.956407	−	0.292038i	$-0.905667\pi$
$197$	−124.210	−	243.776i	−0.630508	−	1.23744i	0.325899	−	0.945405i	$-0.394333\pi$
$198$	−75.8367	−	12.0114i	−0.383014	−	0.0606634i
$199$		−	198.243i		−	0.996197i	−0.867120	−	0.498099i	$-0.834032\pi$
$199$		−	198.243i		−	0.996197i	0.867120	−	0.498099i	$-0.165968\pi$
$200$	−29.0536	+	198.065i	−0.145268	+	0.990326i
$201$	−343.593			−1.70942
$202$	16.8052	−	106.104i	0.0831941	−	0.525267i
$203$	−151.928	+	77.4111i	−0.748413	+	0.381336i
$204$	−0.632181	−	0.205408i	−0.00309893	−	0.00100690i
$205$	160.353	+	80.5527i	0.782209	+	0.392940i
$206$	72.6137	+	223.482i	0.352494	+	1.08486i
$207$	−111.130	+	111.130i	−0.536858	+	0.536858i
$208$	−145.479	+	285.518i	−0.699417	+	1.37268i
$209$	12.2882	−	16.9132i	0.0587950	−	0.0809244i
$210$	−237.643	−	75.7161i	−1.13163	−	0.360553i
$211$	304.272	−	221.067i	1.44205	−	1.04771i	0.454440	−	0.890777i	$-0.349839\pi$
$211$	304.272	−	221.067i	1.44205	−	1.04771i	0.987609	−	0.156933i	$-0.0501605\pi$
$212$	−0.603706	+	0.0956176i	−0.00284767	+	0.000451026i
$213$	51.7778	+	326.912i	0.243088	+	1.53480i
$214$	3.09346	+	4.25778i	0.0144554	+	0.0198962i
$215$	134.041	+	96.2207i	0.623446	+	0.447538i
$216$	−69.0736	−	50.1849i	−0.319785	−	0.232338i
$217$	−12.3599	−	6.29767i	−0.0569579	−	0.0290215i
$218$	−186.792	−	186.792i	−0.856844	−	0.856844i
$219$	−224.470	+	72.9348i	−1.02498	+	0.333036i
$220$	−0.111322	+	0.0575251i	−0.000506008	+	0.000261478i
$221$	123.247	−	379.316i	0.557680	−	1.71636i
$222$	139.385	+	273.559i	0.627862	+	1.23225i
$223$	−385.310	−	61.0271i	−1.72785	−	0.273664i	−0.788104	−	0.615542i	$-0.788937\pi$
$223$	−385.310	−	61.0271i	−1.72785	−	0.273664i	−0.939744	+	0.341878i	$0.888937\pi$
$224$			0.655968i			0.00292843i
$225$	84.6891	−	271.155i	0.376396	−	1.20513i
$226$	−89.3123			−0.395187
$227$	−65.9806	+	416.585i	−0.290663	+	1.83518i	0.220127	+	0.975471i	$0.429353\pi$
$227$	−65.9806	+	416.585i	−0.290663	+	1.83518i	−0.510790	+	0.859706i	$0.670647\pi$
$228$	0.184198	−	0.0938536i	0.000807886	−	0.000411639i
$229$	272.802	+	88.6388i	1.19128	+	0.387069i	0.836544	−	0.547899i	$-0.184572\pi$
$229$	272.802	+	88.6388i	1.19128	+	0.387069i	0.354731	+	0.934968i	$0.384572\pi$
$230$	20.8361	−	136.603i	0.0905917	−	0.593925i
$231$	−26.0885	−	80.2921i	−0.112937	−	0.347585i
$232$	174.514	−	174.514i	0.752214	−	0.752214i
$233$	87.8729	−	172.460i	0.377137	−	0.740173i	−0.621943	−	0.783063i	$-0.713656\pi$
$233$	87.8729	−	172.460i	0.377137	−	0.740173i	0.999080	+	0.0428897i	$0.0136564\pi$
$234$	267.778	−	368.564i	1.14435	−	1.57506i
$235$	−125.312	−	170.420i	−0.533241	−	0.725191i
$236$	0.0156605	−	0.0113780i	6.63579e−5	−	4.82118e-5i
$237$	175.317	−	27.7675i	0.739735	−	0.117163i
$238$	34.3731	+	217.023i	0.144425	+	0.911863i
$239$	−34.9983	−	48.1710i	−0.146436	−	0.201552i	0.729498	−	0.683983i	$-0.239754\pi$
$239$	−34.9983	−	48.1710i	−0.146436	−	0.201552i	−0.875934	+	0.482431i	$0.839754\pi$
$240$	360.326	−	2.05954i	1.50136	−	0.00858142i
$241$	361.028	+	262.302i	1.49804	+	1.08839i	0.971153	+	0.238457i	$0.0766416\pi$
$241$	361.028	+	262.302i	1.49804	+	1.08839i	0.526889	+	0.849934i	$0.323358\pi$
$242$	−195.063	−	99.3895i	−0.806045	−	0.410701i
$243$	−240.643	−	240.643i	−0.990299	−	0.990299i
$244$	0.190307	−	0.0618346i	0.000779948	−	0.000253420i
$245$	14.9062	+	90.7539i	0.0608417	+	0.370424i
$246$	99.9999	−	307.768i	0.406504	−	1.25109i
$247$	56.3133	+	110.521i	0.227989	+	0.447454i
$248$	19.8308	+	3.14089i	0.0799630	+	0.0126649i
$249$		−	226.776i		−	0.910745i
$250$	81.2443	+	236.185i	0.324977	+	0.944742i
$251$	−274.930			−1.09534			−0.547669	−	0.836695i	$-0.684485\pi$
$251$	−274.930			−1.09534			−0.547669	+	0.836695i	$0.684485\pi$
$252$	0.0728760	−	0.460121i	0.000289190	−	0.00182588i
$253$	41.6755	−	21.2347i	0.164725	−	0.0839316i
$254$	−323.559	−	105.131i	−1.27385	−	0.413900i
$255$	−442.553	+	72.6888i	−1.73550	+	0.285054i
$256$	−0.439685	−	1.35321i	−0.00171752	−	0.00528598i
$257$	160.142	−	160.142i	0.623121	−	0.623121i	−0.323207	−	0.946328i	$-0.604761\pi$
$257$	160.142	−	160.142i	0.623121	−	0.623121i	0.946328	+	0.323207i	$0.104761\pi$
$258$	135.086	−	265.121i	0.523590	−	1.02760i
$259$	−110.725	+	152.400i	−0.427510	+	0.588417i
$260$	−0.00424949	−	0.743468i	−1.63442e−5	−	0.00285949i
$261$	−283.335	+	205.855i	−1.08557	+	0.788715i
$262$	−103.480	+	16.3896i	−0.394961	+	0.0625557i
$263$	65.5157	+	413.650i	0.249109	+	1.57281i	0.722127	+	0.691760i	$0.243164\pi$
$263$	65.5157	+	413.650i	0.249109	+	1.57281i	−0.473018	+	0.881053i	$0.656836\pi$
$264$	71.8245	+	98.8580i	0.272063	+	0.374462i
$265$	−332.245	+	244.304i	−1.25376	+	0.921902i
$266$	−55.2858	−	40.1675i	−0.207841	−	0.151005i
$267$	285.351	+	145.394i	1.06873	+	0.544545i
$268$	0.398996	+	0.398996i	0.00148879	+	0.00148879i
$269$	−11.6319	+	3.77942i	−0.0432412	+	0.0140499i	−0.330558	−	0.943786i	$-0.607237\pi$
$269$	−11.6319	+	3.77942i	−0.0432412	+	0.0140499i	0.287317	+	0.957836i	$0.407237\pi$
$270$	−105.309	−	16.0629i	−0.390034	−	0.0594922i
$271$	−161.855	+	498.138i	−0.597250	+	1.83815i	−0.0540612	+	0.998538i	$0.517217\pi$
$271$	−161.855	+	498.138i	−0.597250	+	1.83815i	−0.543189	+	0.839610i	$0.682783\pi$
$272$	−144.117	−	282.846i	−0.529842	−	1.03987i
$273$	494.746	+	78.3601i	1.81226	+	0.287033i
$274$			101.780i			0.371461i
$275$	−48.9087	+	68.9612i	−0.177850	+	0.250768i
$276$	0.462525			0.00167582
$277$	68.2890	−	431.160i	0.246531	−	1.55653i	−0.484871	−	0.874586i	$-0.661133\pi$
$277$	68.2890	−	431.160i	0.246531	−	1.55653i	0.731402	−	0.681947i	$-0.238867\pi$
$278$	211.383	−	107.705i	0.760371	−	0.387428i
$279$	−27.0972	−	8.80442i	−0.0971227	−	0.0315571i
$280$	101.683	+	196.776i	0.363154	+	0.702771i
$281$	31.8261	+	97.9506i	0.113260	+	0.348579i	0.991580	−	0.129494i	$-0.0413354\pi$
$281$	31.8261	+	97.9506i	0.113260	+	0.348579i	−0.878320	+	0.478073i	$0.841335\pi$
$282$	−269.736	+	269.736i	−0.956510	+	0.956510i
$283$	96.0529	−	188.514i	0.339409	−	0.666129i	−0.656710	−	0.754143i	$-0.728052\pi$
$283$	96.0529	−	188.514i	0.339409	−	0.666129i	0.996119	+	0.0880149i	$0.0280523\pi$
$284$	0.319499	−	0.439753i	0.00112500	−	0.00154843i
$285$	81.3385	−	113.309i	0.285398	−	0.397576i
$286$	−109.690	+	79.6946i	−0.383532	+	0.278652i
$287$	196.107	−	31.0603i	0.683300	−	0.108224i
$288$	0.210766	+	1.33072i	0.000731826	+	0.00462057i
$289$	62.3663	+	85.8398i	0.215800	+	0.297024i
$290$	93.4798	−	293.397i	0.322344	−	1.01171i
$291$	10.1999	+	7.41065i	0.0350512	+	0.0254662i
$292$	0.345361	+	0.175970i	0.00118274	+	0.000602638i
$293$	−192.127	−	192.127i	−0.655724	−	0.655724i	0.298642	−	0.954365i	$-0.403466\pi$
$293$	−192.127	−	192.127i	−0.655724	−	0.655724i	−0.954365	+	0.298642i	$0.903466\pi$
$294$	157.735	−	51.2513i	0.536515	−	0.174324i
$295$	5.86270	−	11.6706i	0.0198736	−	0.0395614i
$296$	84.2553	−	259.311i	0.284646	−	0.876051i
$297$	−16.3702	−	32.1283i	−0.0551184	−	0.108176i
$298$	−126.425	−	20.0237i	−0.424244	−	0.0671937i
$299$			277.521i			0.928163i
$300$	−0.740517	+	0.388038i	−0.00246839	+	0.00129346i
$301$	182.566			0.606532
$302$	−71.1264	+	449.075i	−0.235518	+	1.48700i
$303$	216.165	−	110.141i	0.713415	−	0.363503i
$304$	93.8954	+	30.5085i	0.308866	+	0.100357i
$305$	94.9178	−	96.0091i	0.311206	−	0.314784i
$306$	139.461	+	429.218i	0.455756	+	1.40267i
$307$	−37.7886	+	37.7886i	−0.123090	+	0.123090i	−0.765968	−	0.642878i	$-0.777740\pi$
$307$	−37.7886	+	37.7886i	−0.123090	+	0.123090i	0.642878	+	0.765968i	$0.277740\pi$
$308$	−0.0629438	+	0.123534i	−0.000204363	+	0.000401085i
$309$	−311.923	+	429.325i	−1.00946	+	1.38940i
$310$	23.7804	−	7.87727i	0.0767109	−	0.0254105i
$311$	208.182	−	151.253i	0.669396	−	0.486345i	−0.200427	−	0.979709i	$-0.564233\pi$
$311$	208.182	−	151.253i	0.669396	−	0.486345i	0.869823	+	0.493364i	$0.164233\pi$
$312$	−716.094	+	113.418i	−2.29517	+	0.363520i
$313$	−75.0087	−	473.586i	−0.239644	−	1.51306i	−0.754798	−	0.655957i	$-0.772265\pi$
$313$	−75.0087	−	473.586i	−0.239644	−	1.51306i	0.515154	−	0.857098i	$-0.327735\pi$
$314$	−109.187	−	150.283i	−0.347729	−	0.478608i
$315$	−98.8350	−	298.369i	−0.313762	−	0.947204i
$316$	−0.235832	−	0.171342i	−0.000746303	−	0.000542221i
$317$	−175.952	−	89.6519i	−0.555053	−	0.282814i	0.153880	−	0.988090i	$-0.450823\pi$
$317$	−175.952	−	89.6519i	−0.555053	−	0.282814i	−0.708933	+	0.705276i	$0.750823\pi$
$318$	525.869	+	525.869i	1.65368	+	1.65368i
$319$	99.1295	−	32.2091i	0.310751	−	0.100969i
$320$	−227.984	−	225.392i	−0.712449	−	0.704351i
$321$	−3.67283	+	11.3038i	−0.0114418	+	0.0352143i
$322$	−69.4119	−	136.228i	−0.215565	−	0.423070i
$323$	−121.367	−	19.2226i	−0.375749	−	0.0595128i
$324$			0.401295i			0.00123857i
$325$	−232.827	−	444.319i	−0.716392	−	1.36714i
$326$	254.462			0.780559
$327$	93.3250	−	589.231i	0.285397	−	1.80193i
$328$	−256.060	+	130.469i	−0.780671	+	0.397772i
$329$	−222.596	−	72.3257i	−0.676582	−	0.219835i
$330$	136.238	+	68.4385i	0.412841	+	0.207389i
$331$	−91.8385	−	282.650i	−0.277458	−	0.853927i	−0.988559	−	0.150837i	$-0.951803\pi$
$331$	−91.8385	−	282.650i	−0.277458	−	0.853927i	0.711101	−	0.703090i	$-0.248197\pi$
$332$	−0.263343	+	0.263343i	−0.000793201	+	0.000793201i
$333$	−175.654	+	344.741i	−0.527491	+	1.03526i
$334$	94.4803	−	130.041i	0.282875	−	0.389344i
$335$	362.743	+	115.574i	1.08282	+	0.344998i
$336$	322.548	−	234.345i	0.959963	−	0.697454i
$337$	316.947	−	50.1994i	0.940495	−	0.148960i	0.332681	−	0.943039i	$-0.392047\pi$
$337$	316.947	−	50.1994i	0.940495	−	0.148960i	0.607814	+	0.794080i	$0.292047\pi$
$338$	−73.0199	−	461.030i	−0.216035	−	1.36399i
$339$	−118.556	−	163.178i	−0.349722	−	0.481351i
$340$	0.598323	+	0.429504i	0.00175977	+	0.00126325i
$341$	6.86010	+	4.98416i	0.0201176	+	0.0146163i
$342$	−125.061	−	63.7218i	−0.365675	−	0.186321i
$343$	263.639	+	263.639i	0.768627	+	0.768627i
$344$	−251.313	+	81.6564i	−0.730560	+	0.237373i
$345$	277.238	−	143.262i	0.803589	−	0.415251i
$346$	−105.482	+	324.642i	−0.304863	+	0.938270i
$347$	207.859	+	407.947i	0.599019	+	1.17564i	0.969106	+	0.246643i	$0.0793276\pi$
$347$	207.859	+	407.947i	0.599019	+	1.17564i	−0.370088	+	0.928997i	$0.620672\pi$
$348$	1.01801	+	0.161237i	0.00292532	+	0.000463325i
$349$			275.249i			0.788680i	0.918965	+	0.394340i	$0.129027\pi$
$349$			275.249i			0.788680i	−0.918965	+	0.394340i	$0.870973\pi$
$350$	225.420	+	159.872i	0.644057	+	0.456778i
$351$	213.945			0.609531
$352$	0.0627271	−	0.396043i	0.000178202	−	0.00112512i
$353$	−365.927	+	186.449i	−1.03662	+	0.528184i	−0.887583	−	0.460648i	$-0.847617\pi$
$353$	−365.927	+	186.449i	−1.03662	+	0.528184i	−0.149036	+	0.988832i	$0.547617\pi$
$354$	−22.3996	−	7.27808i	−0.0632758	−	0.0205595i
$355$	55.2999	−	362.549i	0.155774	−	1.02127i
$356$	−0.162525	−	0.500201i	−0.000456531	−	0.00140506i
$357$	−350.884	+	350.884i	−0.982869	+	0.982869i
$358$	−238.757	+	468.587i	−0.666919	+	1.30890i
$359$	−80.6575	+	111.015i	−0.224673	+	0.309235i	−0.906441	−	0.422333i	$-0.861211\pi$
$359$	−80.6575	+	111.015i	−0.224673	+	0.309235i	0.681768	+	0.731568i	$0.261211\pi$
$360$	269.504	+	366.516i	0.748622	+	1.01810i
$361$	−261.137	+	189.727i	−0.723372	+	0.525561i
$362$	271.116	−	42.9405i	0.748938	−	0.118620i
$363$	−77.3426	−	488.322i	−0.213065	−	1.34524i
$364$	−0.483528	−	0.665519i	−0.00132837	−	0.00182835i
$365$	261.515	−	1.49476i	0.716478	−	0.00409522i
$366$	−196.967	−	143.105i	−0.538162	−	0.390997i
$367$	−468.126	−	238.522i	−1.27555	−	0.649924i	−0.320745	−	0.947166i	$-0.603933\pi$
$367$	−468.126	−	238.522i	−1.27555	−	0.649924i	−0.954802	+	0.297242i	$0.903933\pi$
$368$	156.190	+	156.190i	0.424430	+	0.424430i
$369$	387.851	−	126.021i	1.05109	−	0.341519i
$370$	−55.1370	−	335.692i	−0.149019	−	0.907274i
$371$	−141.004	+	433.966i	−0.380065	+	1.16972i
$372$	0.0380676	+	0.0747119i	0.000102332	+	0.000200839i
$373$	171.238	+	27.1214i	0.459083	+	0.0727116i	0.381693	−	0.924289i	$-0.375341\pi$
$373$	171.238	+	27.1214i	0.459083	+	0.0727116i	0.0773903	+	0.997001i	$0.475341\pi$
$374$		−	134.316i		−	0.359132i
$375$	−323.676	+	461.957i	−0.863137	+	1.23188i
$376$	338.765			0.900970
$377$	−96.7442	+	610.819i	−0.256616	+	1.62021i
$378$	−105.021	+	53.5107i	−0.277833	+	0.141563i
$379$	474.193	+	154.074i	1.25117	+	0.406529i	0.858339	−	0.513083i	$-0.171497\pi$
$379$	474.193	+	154.074i	1.25117	+	0.406529i	0.392829	+	0.919612i	$0.371497\pi$
$380$	−0.226034	+	0.0371259i	−0.000594827	+	9.76996e-5i
$381$	−237.422	−	730.711i	−0.623156	−	1.91788i
$382$	268.074	−	268.074i	0.701765	−	0.701765i
$383$	46.0664	−	90.4105i	0.120278	−	0.236059i	−0.823015	−	0.568019i	$-0.807710\pi$
$383$	46.0664	−	90.4105i	0.120278	−	0.236059i	0.943293	+	0.331960i	$0.107710\pi$
$384$	−338.560	+	465.988i	−0.881667	+	1.21351i
$385$	0.534668	+	93.5427i	0.00138875	+	0.242968i
$386$	−105.906	+	76.9453i	−0.274368	+	0.199340i
$387$	370.361	−	58.6595i	0.957006	−	0.151575i
$388$	−0.00323899	−	0.0204502i	−8.34792e−6	−	5.27067e-5i
$389$	−40.2289	−	55.3703i	−0.103416	−	0.142340i	0.754172	−	0.656676i	$-0.228038\pi$
$389$	−40.2289	−	55.3703i	−0.103416	−	0.142340i	−0.857589	+	0.514336i	$0.828038\pi$
$390$	−728.785	+	535.885i	−1.86868	+	1.37406i
$391$	−222.418	−	161.596i	−0.568843	−	0.413289i
$392$	−131.234	−	66.8673i	−0.334782	−	0.170580i
$393$	−167.307	−	167.307i	−0.425716	−	0.425716i
$394$	519.929	−	168.935i	1.31962	−	0.428769i
$395$	−194.429	−	29.6564i	−0.492225	−	0.0750794i
$396$	−0.0879983	+	0.270831i	−0.000222218	+	0.000683916i
$397$	−44.2700	−	86.8847i	−0.111511	−	0.218853i	0.828506	−	0.559980i	$-0.189191\pi$
$397$	−44.2700	−	86.8847i	−0.111511	−	0.218853i	−0.940017	+	0.341127i	$0.889191\pi$
$398$	391.242	+	61.9667i	0.983021	+	0.155695i
$399$		−	154.329i		−	0.386790i
$400$	−381.102	−	119.029i	−0.952755	−	0.297572i
$401$	145.737			0.363435			0.181717	−	0.983351i	$-0.441834\pi$
$401$	145.737			0.363435			0.181717	+	0.983351i	$0.441834\pi$
$402$	107.400	−	678.096i	0.267164	−	1.68681i
$403$	−44.8281	+	22.8410i	−0.111236	+	0.0566775i
$404$	−0.378922	−	0.123119i	−0.000937927	−	0.000304751i
$405$	124.296	+	240.537i	0.306905	+	0.593918i
$406$	−105.285	−	324.034i	−0.259323	−	0.798113i
$407$	81.4239	−	81.4239i	0.200059	−	0.200059i
$408$	326.072	−	639.952i	0.799196	−	1.56851i
$409$	59.1584	−	81.4246i	0.144642	−	0.199082i	−0.730549	−	0.682860i	$-0.760736\pi$
$409$	59.1584	−	81.4246i	0.144642	−	0.199082i	0.875191	+	0.483778i	$0.160736\pi$
$410$	−209.098	+	291.285i	−0.509994	+	0.710451i
$411$	−185.958	+	135.106i	−0.452452	+	0.328726i
$412$	0.860772	−	0.136333i	0.00208925	−	0.000330905i
$413$	−2.26060	−	14.2728i	−0.00547360	−	0.0345590i
$414$	−184.583	−	254.056i	−0.445852	−	0.613663i
$415$	−76.2806	+	239.415i	−0.183809	+	0.576904i
$416$	1.92476	+	1.39842i	0.00462682	+	0.00336158i
$417$	477.378	+	243.236i	1.14479	+	0.583301i
$418$	29.5380	+	29.5380i	0.0706650	+	0.0706650i
$419$	330.195	−	107.287i	0.788054	−	0.256054i	0.112779	−	0.993620i	$-0.464025\pi$
$419$	330.195	−	107.287i	0.788054	−	0.256054i	0.675275	+	0.737566i	$0.264025\pi$
$420$	−0.415234	+	0.826589i	−0.000988653	+	0.00196807i
$421$	−78.9442	+	242.965i	−0.187516	+	0.577115i	−0.999983	−	0.00589274i	$-0.998124\pi$
$421$	−78.9442	+	242.965i	−0.187516	+	0.577115i	0.812467	+	0.583008i	$0.198124\pi$
$422$	341.176	+	669.596i	0.808475	+	1.58672i
$423$	−474.805	−	75.2018i	−1.12247	−	0.177782i
$424$		−	660.445i		−	1.55765i
$425$	491.669	+	72.1214i	1.15687	+	0.169697i
$426$	−661.361			−1.55249
$427$	23.3682	−	147.541i	0.0547264	−	0.345529i
$428$	0.0173916	−	0.00886145i	4.06345e−5	−	2.07043e-5i
$429$	−291.212	−	94.6204i	−0.678815	−	0.220560i
$430$	−231.794	+	234.459i	−0.539056	+	0.545254i
$431$	69.5257	+	213.978i	0.161312	+	0.496469i	0.998746	−	0.0500709i	$-0.0159447\pi$
$431$	69.5257	+	213.978i	0.161312	+	0.496469i	−0.837433	+	0.546540i	$0.815945\pi$
$432$	120.410	−	120.410i	0.278726	−	0.278726i
$433$	17.7029	−	34.7439i	0.0408843	−	0.0802399i	−0.869661	−	0.493650i	$-0.835662\pi$
$433$	17.7029	−	34.7439i	0.0408843	−	0.0802399i	0.910545	+	0.413410i	$0.135662\pi$
$434$	16.2922	−	22.4243i	0.0375396	−	0.0516688i
$435$	660.138	−	218.671i	1.51756	−	0.502692i
$436$	−0.792616	+	0.575870i	−0.00181793	+	0.00132080i
$437$	84.4503	−	13.3756i	0.193250	−	0.0306078i
$438$	−73.7755	−	465.800i	−0.168437	−	1.06347i
$439$	134.972	+	185.773i	0.307454	+	0.423174i	0.934585	−	0.355740i	$-0.115771\pi$
$439$	134.972	+	185.773i	0.307454	+	0.423174i	−0.627131	+	0.778914i	$0.715771\pi$
$440$	−42.5749	−	128.528i	−0.0967610	−	0.292108i
$441$	169.092	+	122.852i	0.383428	+	0.278577i
$442$	710.073	+	361.800i	1.60650	+	0.818553i
$443$	514.933	+	514.933i	1.16238	+	1.16238i	0.983954	+	0.178423i	$0.0570995\pi$
$443$	514.933	+	514.933i	1.16238	+	1.16238i	0.178423	+	0.983954i	$0.442900\pi$
$444$	1.08295	−	0.351873i	0.00243908	−	0.000792506i
$445$	−252.349	−	249.481i	−0.567077	−	0.560631i
$446$	240.880	−	741.351i	0.540089	−	1.66222i
$447$	−131.236	−	257.564i	−0.293592	−	0.576206i
$448$	−350.352	−	55.4903i	−0.782035	−	0.123862i
$449$		−	747.530i		−	1.66488i	−0.554117	−	0.832439i	$-0.686944\pi$
$449$		−	747.530i		−	1.66488i	0.554117	−	0.832439i	$-0.313056\pi$
$450$	508.664	+	251.895i	1.13036	+	0.559767i
$451$	−121.371			−0.269114
$452$	−0.0518174	+	0.327162i	−0.000114640	+	0.000723811i
$453$	−914.896	+	466.163i	−2.01964	+	1.02906i
$454$	−801.526	−	260.432i	−1.76548	−	0.573638i
$455$	−495.963	−	249.146i	−1.09003	−	0.547573i
$456$	69.0269	+	212.443i	0.151375	+	0.465883i
$457$	−131.867	+	131.867i	−0.288549	+	0.288549i	−0.836506	−	0.547957i	$-0.815406\pi$
$457$	−131.867	+	131.867i	−0.288549	+	0.288549i	0.547957	+	0.836506i	$0.315406\pi$
$458$	−260.205	+	510.681i	−0.568133	+	1.11502i
$459$	−124.577	+	171.465i	−0.271409	+	0.373563i
$460$	−0.488305	−	0.155580i	−0.00106153	−	0.000338217i
$461$	−146.995	+	106.798i	−0.318861	+	0.231666i	−0.735689	−	0.677319i	$-0.763142\pi$
$461$	−146.995	+	106.798i	−0.318861	+	0.231666i	0.416828	+	0.908985i	$0.363142\pi$
$462$	166.615	−	26.3892i	0.360638	−	0.0571195i
$463$	70.5369	+	445.353i	0.152348	+	0.961885i	0.938857	+	0.344307i	$0.111886\pi$
$463$	70.5369	+	445.353i	0.152348	+	0.961885i	−0.786510	+	0.617578i	$0.788114\pi$
$464$	289.324	+	398.221i	0.623544	+	0.858234i
$465$	45.9589	+	32.9914i	0.0988364	+	0.0709493i
$466$	312.891	+	227.329i	0.671440	+	0.487830i
$467$	−340.453	−	173.469i	−0.729021	−	0.371455i	0.0497511	−	0.998762i	$-0.484157\pi$
$467$	−340.453	−	173.469i	−0.729021	−	0.371455i	−0.778772	+	0.627307i	$0.784157\pi$
$468$	−1.19474	−	1.19474i	−0.00255286	−	0.00255286i
$469$	400.621	−	130.170i	0.854203	−	0.277547i
$470$	375.501	−	194.039i	0.798939	−	0.412848i
$471$	129.636	−	398.980i	0.275236	−	0.847091i
$472$	9.49566	+	18.6363i	0.0201179	+	0.0394837i
$473$	−110.225	−	17.4579i	−0.233034	−	0.0369089i
$474$			354.676i			0.748262i
$475$	−123.986	+	92.2647i	−0.261023	+	0.194241i
$476$	0.814927			0.00171203
$477$	−146.611	+	925.666i	−0.307361	+	1.94060i
$478$	106.007	−	54.0135i	0.221773	−	0.112999i
$479$	−333.071	−	108.221i	−0.695347	−	0.225932i	−0.0600450	−	0.998196i	$-0.519124\pi$
$479$	−333.071	−	108.221i	−0.695347	−	0.225932i	−0.635302	+	0.772264i	$0.719124\pi$
$480$	0.403396	−	2.64469i	0.000840408	−	0.00550977i
$481$	211.128	+	649.784i	0.438935	+	1.35090i
$482$	−630.515	+	630.515i	−1.30812	+	1.30812i
$483$	156.757	−	307.652i	0.324548	−	0.636961i
$484$	−0.477249	+	0.656877i	−0.000986052	+	0.00135718i
$485$	−8.27566	−	11.2546i	−0.0170632	−	0.0232054i
$486$	550.139	−	399.699i	1.13197	−	0.822427i
$487$	−798.213	+	126.425i	−1.63904	+	0.259599i	−0.906835	−	0.421485i	$-0.861509\pi$
$487$	−798.213	+	126.425i	−1.63904	+	0.259599i	−0.732206	+	0.681084i	$0.761509\pi$
$488$	33.8231	+	213.550i	0.0693095	+	0.437603i
$489$	337.780	+	464.915i	0.690757	+	0.950746i
$490$	−183.766	+	1.05037i	−0.375033	+	0.00214360i
$491$	−426.270	−	309.703i	−0.868166	−	0.630760i	0.0619282	−	0.998081i	$-0.480275\pi$
$491$	−426.270	−	309.703i	−0.868166	−	0.630760i	−0.930094	+	0.367321i	$0.880275\pi$
$492$	−1.06938	−	0.544874i	−0.00217353	−	0.00110747i
$493$	−433.205	−	433.205i	−0.878713	−	0.878713i
$494$	−235.721	+	76.5903i	−0.477168	+	0.155041i
$495$	31.1404	+	189.593i	0.0629099	+	0.383016i
$496$	−12.3744	+	38.0846i	−0.0249484	+	0.0767834i
$497$	−184.222	−	361.556i	−0.370668	−	0.727477i
$498$	447.552	+	70.8853i	0.898699	+	0.142340i
$499$			568.734i			1.13975i	0.821732	+	0.569874i	$0.193008\pi$
$499$			568.734i			1.13975i	−0.821732	+	0.569874i	$0.806992\pi$
$500$	0.912315	−	0.160578i	0.00182463	−	0.000321155i
$501$	363.007			0.724565
$502$	85.9373	−	542.587i	0.171190	−	1.08085i
$503$	165.934	−	84.5473i	0.329888	−	0.168086i	−0.281200	−	0.959649i	$-0.590732\pi$
$503$	165.934	−	84.5473i	0.329888	−	0.168086i	0.611087	+	0.791563i	$0.290732\pi$
$504$	478.729	+	155.549i	0.949859	+	0.308628i
$505$	−265.261	+	43.5689i	−0.525270	+	0.0862750i
$506$	28.8808	+	88.8860i	0.0570767	+	0.175664i
$507$	745.395	−	745.395i	1.47021	−	1.47021i
$508$	−0.572830	+	1.12424i	−0.00112762	+	0.00221308i
$509$	321.853	−	442.992i	0.632324	−	0.870319i	−0.365854	−	0.930672i	$-0.619223\pi$
$509$	321.853	−	442.992i	0.632324	−	0.870319i	0.998177	+	0.0603538i	$0.0192229\pi$
$510$	−5.12201	−	896.119i	−0.0100432	−	1.75710i
$511$	234.096	−	170.081i	0.458114	−	0.332839i
$512$	507.095	−	80.3159i	0.990419	−	0.156867i
$513$	−10.3115	−	65.1041i	−0.0201003	−	0.126909i
$514$	265.991	+	366.105i	0.517492	+	0.712266i
$515$	473.720	−	348.332i	0.919845	−	0.676373i
$516$	−0.892800	−	0.648657i	−0.00173023	−	0.00125709i
$517$	127.477	+	64.9526i	0.246570	+	0.125634i
$518$	−266.158	−	266.158i	−0.513818	−	0.513818i
$519$	−733.156	+	238.217i	−1.41263	+	0.458992i
$520$	794.157	+	121.133i	1.52723	+	0.232949i
$521$	140.714	−	433.072i	0.270084	−	0.831233i	−0.720395	−	0.693564i	$-0.756039\pi$
$521$	140.714	−	433.072i	0.270084	−	0.831233i	0.990478	−	0.137668i	$-0.0439607\pi$
$522$	−317.699	−	623.520i	−0.608619	−	1.19448i
$523$	946.845	+	149.965i	1.81041	+	0.286741i	0.967788	−	0.251765i	$-0.0810109\pi$
$523$	946.845	+	149.965i	1.81041	+	0.286741i	0.842622	+	0.538506i	$0.181011\pi$
$524$			0.388569i			0.000741544i
$525$	7.13434	+	624.072i	0.0135892	+	1.18871i
$526$	−836.836			−1.59094
$527$	7.79682	−	49.2272i	0.0147947	−	0.0934103i
$528$	−217.149	+	110.643i	−0.411266	+	0.209551i
$529$	−321.173	−	104.355i	−0.607132	−	0.197269i
$530$	−378.292	−	732.066i	−0.713759	−	1.38126i
$531$	−9.17188	−	28.2281i	−0.0172728	−	0.0531604i
$532$	−0.179214	+	0.179214i	−0.000336869	+	0.000336869i
$533$	326.931	−	641.638i	0.613379	−	1.20382i
$534$	−376.135	+	517.706i	−0.704373	+	0.969487i
$535$	7.67980	−	10.6984i	0.0143548	−	0.0199970i
$536$	−493.257	+	358.372i	−0.920255	+	0.668604i
$537$	−1173.06	+	185.795i	−2.18448	+	0.345987i
$538$	−3.82299	−	24.1374i	−0.00710593	−	0.0448651i
$539$	−36.5626	−	50.3242i	−0.0678342	−	0.0933658i
$540$	−0.119939	+	0.376442i	−0.000222109	+	0.000697115i
$541$	134.635	+	97.8182i	0.248864	+	0.180810i	0.705223	−	0.708986i	$-0.250847\pi$
$541$	134.635	+	97.8182i	0.248864	+	0.180810i	−0.456359	+	0.889796i	$0.650847\pi$
$542$	−932.506	−	475.136i	−1.72049	−	0.876634i
$543$	438.341	+	438.341i	0.807258	+	0.807258i
$544$	−2.24151	+	0.728311i	−0.00412043	+	0.00133881i
$545$	−296.726	+	590.680i	−0.544452	+	1.08382i
$546$	−309.295	+	951.911i	−0.566474	+	1.74343i
$547$	−107.533	−	211.046i	−0.196587	−	0.385824i	0.771579	−	0.636134i	$-0.219467\pi$
$547$	−107.533	−	211.046i	−0.196587	−	0.385824i	−0.968166	+	0.250310i	$0.919467\pi$
$548$	0.372835	+	0.0590513i	0.000680356	+	0.000107758i
$549$		−	306.816i		−	0.558863i
$550$	−120.810	−	118.079i	−0.219655	−	0.214690i
$551$	190.536			0.345801
$552$	−78.1807	+	493.613i	−0.141632	+	0.894227i
$553$	−193.896	+	98.7951i	−0.350626	+	0.178653i
$554$	829.567	+	269.543i	1.49741	+	0.486539i
$555$	540.134	−	546.344i	0.973215	−	0.984404i
$556$	−0.271897	−	0.836812i	−0.000489023	−	0.00150506i
$557$	443.386	−	443.386i	0.796026	−	0.796026i	−0.186441	−	0.982466i	$-0.559695\pi$
$557$	443.386	−	443.386i	0.796026	−	0.796026i	0.982466	+	0.186441i	$0.0596952\pi$
$558$	25.8460	−	50.7255i	0.0463189	−	0.0909060i
$559$	389.202	−	535.691i	0.696247	−	0.958302i
$560$	−419.352	+	138.911i	−0.748843	+	0.248055i
$561$	245.401	−	178.294i	0.437435	−	0.317815i
$562$	−203.258	+	32.1929i	−0.361669	+	0.0572828i
$563$	−78.6829	−	496.784i	−0.139757	−	0.882388i	−0.953550	−	0.301234i	$-0.902601\pi$
$563$	−78.6829	−	496.784i	−0.139757	−	0.882388i	0.813794	−	0.581154i	$-0.197399\pi$
$564$	0.831582	+	1.14457i	0.00147444	+	0.00202939i
$565$	70.2753	+	212.151i	0.124381	+	0.375489i
$566$	342.018	+	248.490i	0.604272	+	0.439029i
$567$	266.925	+	136.005i	0.470767	+	0.239868i
$568$	415.305	+	415.305i	0.731172	+	0.731172i
$569$	−780.470	+	253.590i	−1.37165	+	0.445677i	−0.899916	−	0.436063i	$-0.856373\pi$
$569$	−780.470	+	253.590i	−1.37165	+	0.445677i	−0.471736	+	0.881740i	$0.656373\pi$
$570$	198.196	+	195.943i	0.347712	+	0.343760i
$571$	119.477	−	367.712i	0.209241	−	0.643979i	−0.790271	−	0.612757i	$-0.790060\pi$
$571$	119.477	−	367.712i	0.209241	−	0.643979i	0.999512	−	0.0312214i	$-0.00993968\pi$
$572$	0.228291	+	0.448047i	0.000399110	+	0.000783298i
$573$	845.634	+	133.935i	1.47580	+	0.233744i
$574$			396.735i			0.691176i
$575$	−340.879	+	57.9919i	−0.592834	+	0.100855i
$576$	−728.567			−1.26487
$577$	24.2091	−	152.850i	0.0419568	−	0.264905i	−0.957788	−	0.287474i	$-0.907185\pi$
$577$	24.2091	−	152.850i	0.0419568	−	0.264905i	0.999745	+	0.0225689i	$0.00718452\pi$
$578$	−188.903	+	96.2510i	−0.326822	+	0.166524i
$579$	−281.165	−	91.3562i	−0.485605	−	0.157783i
$580$	−1.02052	−	0.512653i	−0.00175951	−	0.000883884i
$581$	85.9137	+	264.415i	0.147872	+	0.455104i
$582$	−17.8135	+	17.8135i	−0.0306074	+	0.0306074i
$583$	126.630	−	248.525i	0.217204	−	0.426286i
$584$	−246.174	+	338.830i	−0.421531	+	0.580188i
$585$	−1086.18	−	346.071i	−1.85672	−	0.591575i
$586$	439.226	−	319.117i	0.749533	−	0.544568i
$587$	587.344	−	93.0261i	1.00059	−	0.158477i	0.365412	−	0.930846i	$-0.380928\pi$
$587$	587.344	−	93.0261i	1.00059	−	0.158477i	0.635174	+	0.772369i	$0.280928\pi$
$588$	−0.0962249	−	0.607540i	−0.000163648	−	0.00103323i
$589$	9.11115	+	12.5404i	0.0154688	+	0.0212910i
$590$	21.2000	+	15.2183i	0.0359321	+	0.0257937i
$591$	998.821	+	725.686i	1.69005	+	1.22789i
$592$	484.527	+	246.879i	0.818457	+	0.417025i
$593$	−151.299	−	151.299i	−0.255142	−	0.255142i	0.567933	−	0.823075i	$-0.307743\pi$
$593$	−151.299	−	151.299i	−0.255142	−	0.255142i	−0.823075	+	0.567933i	$0.807743\pi$
$594$	68.5236	−	22.2647i	0.115360	−	0.0374826i
$595$	488.468	−	252.414i	0.820955	−	0.424225i
$596$	−0.146699	+	0.451493i	−0.000246139	+	0.000757539i
$597$	406.130	+	797.075i	0.680285	+	1.33513i
$598$	−547.700	−	86.7472i	−0.915886	−	0.145062i
$599$			471.606i			0.787322i	0.919256	+	0.393661i	$0.128792\pi$
$599$			471.606i			0.787322i	−0.919256	+	0.393661i	$0.871208\pi$
$600$	−288.950	−	855.880i	−0.481583	−	1.42647i
$601$	12.2283			0.0203466			0.0101733	−	0.999948i	$-0.496762\pi$
$601$	12.2283			0.0203466			0.0101733	+	0.999948i	$0.496762\pi$
$602$	−57.0664	+	360.303i	−0.0947946	+	0.598510i
$603$	770.893	−	392.789i	1.27843	−	0.651392i
$604$	1.60375	+	0.521091i	0.00265522	+	0.000862733i
$605$	−82.6037	+	541.555i	−0.136535	+	0.895132i
$606$	149.801	+	461.039i	0.247196	+	0.760790i
$607$	−786.089	+	786.089i	−1.29504	+	1.29504i	−0.363411	+	0.931629i	$0.618388\pi$
$607$	−786.089	+	786.089i	−1.29504	+	1.29504i	−0.931629	+	0.363411i	$0.881612\pi$
$608$	0.332775	−	0.653108i	0.000547327	−	0.00107419i
$609$	452.267	−	622.492i	0.742639	−	1.02215i
$610$	159.809	+	217.335i	0.261982	+	0.356287i
$611$	−686.758	+	498.959i	−1.12399	+	0.816627i
$612$	1.65320	−	0.261840i	0.00270130	−	0.000427844i
$613$	−9.63893	−	60.8578i	−0.0157242	−	0.0992786i	0.978578	−	0.205876i	$-0.0660044\pi$
$613$	−9.63893	−	60.8578i	−0.0157242	−	0.0992786i	−0.994302	+	0.106597i	$0.966004\pi$
$614$	−62.7656	−	86.3895i	−0.102224	−	0.140700i
$615$	−809.753	+	4.62836i	−1.31667	+	0.00752579i
$616$	−121.198	−	88.0555i	−0.196750	−	0.142947i
$617$	139.850	+	71.2571i	0.226661	+	0.115490i	0.563634	−	0.826025i	$-0.309403\pi$
$617$	139.850	+	71.2571i	0.226661	+	0.115490i	−0.336973	+	0.941514i	$0.609403\pi$
$618$	−749.792	−	749.792i	−1.21326	−	1.21326i
$619$	−972.585	+	316.012i	−1.57122	+	0.510520i	−0.959776	−	0.280767i	$-0.909411\pi$
$619$	−972.585	+	316.012i	−1.57122	+	0.510520i	−0.611444	+	0.791287i	$0.709411\pi$
$620$	−0.0150585	−	0.0916809i	−2.42879e−5	−	0.000147872i
$621$	45.5724	−	140.257i	0.0733855	−	0.225857i
$622$	233.432	+	458.136i	0.375292	+	0.736552i
$623$	−387.795	−	61.4207i	−0.622463	−	0.0985885i
$624$		−	1446.01i		−	2.31733i
$625$	497.105	−	378.829i	0.795368	−	0.606126i
$626$	958.090			1.53050
$627$	−14.7578	+	93.1768i	−0.0235371	+	0.148607i
$628$	−0.613854	+	0.312774i	−0.000977475	+	0.000498048i
$629$	−643.703	−	209.152i	−1.02338	−	0.332515i
$630$	619.739	−	101.792i	0.983713	−	0.161574i
$631$	80.5107	+	247.786i	0.127592	+	0.392688i	0.994364	−	0.106016i	$-0.0338094\pi$
$631$	80.5107	+	247.786i	0.127592	+	0.392688i	−0.866772	+	0.498704i	$0.833809\pi$
$632$	222.721	−	222.721i	0.352407	−	0.352407i
$633$	−770.498	+	1512.19i	−1.21722	+	2.38892i
$634$	231.931	−	319.226i	0.365822	−	0.503510i
$635$	4.86583	+	851.299i	0.00766272	+	1.34063i
$636$	2.23143	−	1.62123i	0.00350853	−	0.00254910i
$637$	364.531	−	57.7361i	0.572263	−	0.0906375i
$638$	32.5804	+	205.704i	0.0510664	+	0.322421i
$639$	−489.890	−	674.276i	−0.766652	−	1.05521i
$640$	514.175	−	378.079i	0.803398	−	0.590748i
$641$	−947.896	−	688.686i	−1.47878	−	1.07439i	−0.977948	−	0.208847i	$-0.933029\pi$
$641$	−947.896	−	688.686i	−1.47878	−	1.07439i	−0.500828	−	0.865547i	$-0.666971\pi$
$642$	−21.1605	−	10.7818i	−0.0329603	−	0.0167941i
$643$	−268.108	−	268.108i	−0.416965	−	0.416965i	0.467191	−	0.884156i	$-0.345266\pi$
$643$	−268.108	−	268.108i	−0.416965	−	0.416965i	−0.884156	+	0.467191i	$0.845266\pi$
$644$	−0.539294	+	0.175227i	−0.000837413	+	0.000272092i
$645$	−736.059	−	112.271i	−1.14118	−	0.174064i
$646$	75.8735	−	233.515i	0.117451	−	0.361478i
$647$	−540.483	−	1060.76i	−0.835368	−	1.63950i	−0.766828	−	0.641853i	$-0.778166\pi$
$647$	−540.483	−	1060.76i	−0.835368	−	1.63950i	−0.0685400	−	0.997648i	$-0.521834\pi$
$648$	−428.268	−	67.8310i	−0.660907	−	0.104677i
$649$			8.83345i			0.0136109i
$650$	949.661	−	320.611i	1.46102	−	0.493247i
$651$	62.5969			0.0961550
$652$	0.147635	−	0.932128i	0.000226433	−	0.00142964i
$653$	402.175	−	204.918i	0.615888	−	0.313810i	−0.118070	−	0.993005i	$-0.537671\pi$
$653$	402.175	−	204.918i	0.615888	−	0.313810i	0.733958	+	0.679195i	$0.237671\pi$
$654$	1133.70	+	368.362i	1.73349	+	0.563245i
$655$	120.355	+	232.909i	0.183747	+	0.355586i
$656$	−177.119	−	545.117i	−0.269999	−	0.830971i
$657$	420.249	−	420.249i	0.639648	−	0.639648i
$658$	212.317	−	416.695i	0.322670	−	0.633275i
$659$	190.013	−	261.531i	0.288336	−	0.396860i	−0.640137	−	0.768261i	$-0.721122\pi$
$659$	190.013	−	261.531i	0.288336	−	0.396860i	0.928473	+	0.371401i	$0.121122\pi$
$660$	0.329742	−	0.459349i	0.000499609	−	0.000695984i
$661$	346.646	−	251.853i	0.524427	−	0.381018i	−0.293842	−	0.955854i	$-0.594934\pi$
$661$	346.646	−	251.853i	0.524427	−	0.381018i	0.818269	+	0.574836i	$0.194934\pi$
$662$	586.529	−	92.8971i	0.885996	−	0.140328i
$663$	281.545	+	1777.60i	0.424652	+	2.68115i
$664$	−236.530	−	325.556i	−0.356220	−	0.490295i
$665$	−51.9118	+	162.931i	−0.0780628	+	0.245009i
$666$	−625.457	−	454.421i	−0.939124	−	0.682314i
$667$	379.831	+	193.533i	0.569462	+	0.290155i
$668$	−0.421541	−	0.421541i	−0.000631049	−	0.000631049i
$669$	1674.24	−	543.992i	2.50259	−	0.813142i
$670$	−341.477	+	679.764i	−0.509668	+	1.01457i
$671$	−28.2173	+	86.8438i	−0.0420525	+	0.129424i
$672$	−1.34384	−	2.63744i	−0.00199977	−	0.00392477i
$673$	−326.867	−	51.7706i	−0.485686	−	0.0769252i	−0.0912108	−	0.995832i	$-0.529074\pi$
$673$	−326.867	−	51.7706i	−0.485686	−	0.0769252i	−0.394476	+	0.918906i	$0.629074\pi$
$674$			641.200i			0.951336i
$675$	44.7069	+	262.789i	0.0662324	+	0.389318i
$676$	−1.73118			−0.00256091
$677$	163.559	−	1032.67i	0.241593	−	1.52536i	−0.506776	−	0.862078i	$-0.669163\pi$
$677$	163.559	−	1032.67i	0.241593	−	1.52536i	0.748369	−	0.663282i	$-0.230837\pi$
$678$	359.097	−	182.969i	0.529642	−	0.269866i
$679$	−14.7004	−	4.77643i	−0.0216500	−	0.00703451i
$680$	−559.507	+	565.939i	−0.822804	+	0.832264i
$681$	−588.147	−	1810.13i	−0.863652	−	2.65805i
$682$	−11.9808	+	11.9808i	−0.0175671	+	0.0175671i
$683$	−76.1595	+	149.471i	−0.111507	+	0.218845i	−0.940016	−	0.341131i	$-0.889190\pi$
$683$	−76.1595	+	149.471i	−0.111507	+	0.218845i	0.828508	+	0.559977i	$0.189190\pi$
$684$	−0.305979	+	0.421144i	−0.000447338	+	0.000615708i
$685$	241.768	−	80.0858i	0.352946	−	0.116914i
$686$	−602.712	+	437.896i	−0.878588	+	0.638332i
$687$	−1278.44	+	202.485i	−1.86091	+	0.294738i
$688$	−82.4447	−	520.535i	−0.119832	−	0.756592i
$689$	972.756	+	1338.88i	1.41184	+	1.94323i
$690$	196.075	+	591.923i	0.284166	+	0.857859i
$691$	−159.959	−	116.217i	−0.231489	−	0.168187i	0.465994	−	0.884788i	$-0.345697\pi$
$691$	−159.959	−	116.217i	−0.231489	−	0.168187i	−0.697483	+	0.716601i	$0.745697\pi$
$692$	1.12801	+	0.574747i	0.00163007	+	0.000830560i
$693$	150.321	+	150.321i	0.216914	+	0.216914i
$694$	−870.075	+	282.704i	−1.25371	+	0.407355i
$695$	−422.168	−	417.369i	−0.607436	−	0.600531i
$696$	−344.149	+	1059.18i	−0.494467	+	1.52181i
$697$	323.871	+	635.633i	0.464665	+	0.911956i
$698$	−543.217	−	86.0371i	−0.778248	−	0.123262i
$699$			873.430i			1.24954i
$700$	0.716418	−	0.732987i	0.00102345	−	0.00104712i
$701$	317.355			0.452718			0.226359	−	0.974044i	$-0.427318\pi$
$701$	317.355			0.452718			0.226359	+	0.974044i	$0.427318\pi$
$702$	−66.8748	+	422.231i	−0.0952633	+	0.601468i
$703$	187.555	−	95.5642i	0.266793	−	0.135938i
$704$	206.220	+	67.0049i	0.292926	+	0.0951774i
$705$	852.969	+	428.486i	1.20989	+	0.607782i
$706$	−253.584	−	780.453i	−0.359185	−	1.10546i
$707$	−210.316	+	210.316i	−0.297477	+	0.297477i
$708$	−0.0396564	+	0.0778301i	−5.60119e−5	+	0.000109930i
$709$	−600.695	+	826.785i	−0.847242	+	1.16613i	0.137221	+	0.990540i	$0.456183\pi$
$709$	−600.695	+	826.785i	−0.847242	+	1.16613i	−0.984464	+	0.175588i	$0.943817\pi$
$710$	698.222	+	222.462i	0.983412	+	0.313327i
$711$	−361.603	+	262.720i	−0.508583	+	0.369507i
$712$	561.293	−	88.9001i	0.788333	−	0.124860i
$713$	5.42523	+	34.2536i	0.00760902	+	0.0480415i
$714$	−582.807	−	802.165i	−0.816256	−	1.12348i
$715$	275.615	+	197.849i	0.385476	+	0.276712i
$716$	1.57797	+	1.14646i	0.00220387	+	0.00160121i
$717$	239.403	+	121.982i	0.333895	+	0.170128i
$718$	−193.882	−	193.882i	−0.270031	−	0.270031i
$719$	1129.58	−	367.024i	1.57105	−	0.510464i	0.611316	−	0.791387i	$-0.290640\pi$
$719$	1129.58	−	367.024i	1.57105	−	0.510464i	0.959730	+	0.280923i	$0.0906405\pi$
$720$	−806.082	+	416.540i	−1.11956	+	0.578527i
$721$	201.046	−	618.755i	0.278843	−	0.858190i
$722$	−292.810	−	574.672i	−0.405554	−	0.795944i
$723$	−1988.95	−	315.018i	−2.75096	−	0.435710i
$724$		−	1.01805i		−	0.00140614i
$725$	−770.486	+	8.80813i	−1.06274	+	0.0121491i
$726$	987.901			1.36075
$727$	39.2430	−	247.771i	0.0539794	−	0.340813i	−0.945887	−	0.324495i	$-0.894806\pi$
$727$	39.2430	−	247.771i	0.0539794	−	0.340813i	0.999867	−	0.0163178i	$-0.00519433\pi$
$728$	791.981	−	403.535i	1.08789	−	0.554306i
$729$	997.037	+	323.957i	1.36768	+	0.444385i
$730$	−78.7940	+	516.578i	−0.107937	+	0.707641i
$731$	202.701	+	623.848i	0.277292	+	0.853417i
$732$	−0.638489	+	0.638489i	−0.000872253	+	0.000872253i
$733$	−119.145	+	233.835i	−0.162544	+	0.319011i	−0.957885	−	0.287151i	$-0.907292\pi$
$733$	−119.145	+	233.835i	−0.162544	+	0.319011i	0.795341	+	0.606162i	$0.207292\pi$
$734$	617.060	−	849.311i	0.840682	−	1.15710i
$735$	−245.856	−	334.356i	−0.334497	−	0.454906i
$736$	1.32676	−	0.963949i	0.00180267	−	0.00130971i
$737$	−254.324	+	40.2810i	−0.345080	+	0.0546553i
$738$	127.473	+	804.834i	0.172728	+	1.09056i
$739$	−419.335	−	577.165i	−0.567435	−	0.781008i	0.424813	−	0.905281i	$-0.360340\pi$
$739$	−419.335	−	577.165i	−0.567435	−	0.781008i	−0.992248	+	0.124273i	$0.960340\pi$
$740$	−1.26167	+	0.00721142i	−0.00170496	+	9.74516e-6i
$741$	−452.837	−	329.005i	−0.611116	−	0.444002i
$742$	−812.376	−	413.926i	−1.09485	−	0.557852i
$743$	−9.34501	−	9.34501i	−0.0125774	−	0.0125774i	0.700790	−	0.713368i	$-0.252831\pi$
$743$	−9.34501	−	9.34501i	−0.0125774	−	0.0125774i	−0.713368	+	0.700790i	$0.752831\pi$
$744$	−86.1682	+	27.9977i	−0.115817	+	0.0376314i
$745$	51.9131	+	316.064i	0.0696820	+	0.424246i
$746$	−107.051	+	329.468i	−0.143500	+	0.441647i
$747$	259.246	+	508.799i	0.347050	+	0.681123i
$748$	−0.492015	−	0.0779276i	−0.000657774	−	0.000104181i
$749$		−	14.5714i		−	0.0194545i
$750$	−810.518	−	783.188i	−1.08069	−	1.04425i
$751$	−175.040			−0.233076			−0.116538	−	0.993186i	$-0.537180\pi$
$751$	−175.040			−0.233076			−0.116538	+	0.993186i	$0.537180\pi$
$752$	−105.694	+	667.329i	−0.140551	+	0.887405i
$753$	1105.41	−	563.234i	1.46801	−	0.747986i
$754$	−1175.24	−	381.858i	−1.55867	−	0.506443i
$755$	1122.69	−	184.401i	1.48701	−	0.244240i
$756$	0.135086	+	0.415751i	0.000178685	+	0.000549935i
$757$	−331.826	+	331.826i	−0.438343	+	0.438343i	−0.891454	−	0.453111i	$-0.850314\pi$
$757$	−331.826	+	331.826i	−0.438343	+	0.438343i	0.453111	+	0.891454i	$0.350314\pi$
$758$	−452.296	+	887.680i	−0.596696	+	1.17108i
$759$	−124.062	+	170.756i	−0.163454	+	0.224975i
$760$	−1.41466	−	247.502i	−0.00186140	−	0.325661i
$761$	854.871	−	621.100i	1.12335	−	0.816163i	0.138638	−	0.990343i	$-0.455727\pi$
$761$	854.871	−	621.100i	1.12335	−	0.816163i	0.984714	+	0.174180i	$0.0557274\pi$
$762$	1516.30	−	240.159i	1.98990	−	0.315169i
$763$	114.415	+	722.386i	0.149954	+	0.946770i
$764$	−0.826459	−	1.13752i	−0.00108175	−	0.00148891i
$765$	909.825	−	669.005i	1.18931	−	0.874516i
$766$	164.030	+	119.175i	0.214138	+	0.155581i
$767$	−46.6990	−	23.7943i	−0.0608853	−	0.0310226i
$768$	4.54009	+	4.54009i	0.00591157	+	0.00591157i
$769$	−407.934	+	132.546i	−0.530474	+	0.172361i	−0.561993	−	0.827142i	$-0.689965\pi$
$769$	−407.934	+	132.546i	−0.530474	+	0.172361i	0.0315195	+	0.999503i	$0.489965\pi$
$770$	−184.778	−	28.1843i	−0.239971	−	0.0366030i
$771$	−315.808	+	971.956i	−0.409608	+	1.26064i
$772$	0.220416	+	0.432590i	0.000285512	+	0.000560350i
$773$	209.109	+	33.1196i	0.270516	+	0.0428456i	0.290219	−	0.956960i	$-0.406272\pi$
$773$	209.109	+	33.1196i	0.270516	+	0.0428456i	−0.0197025	+	0.999806i	$0.506272\pi$
$774$			749.261i			0.968037i
$775$	−37.4231	−	50.2894i	−0.0482879	−	0.0648896i
$776$	22.3722			0.0288302
$777$	132.978	−	839.589i	0.171143	−	1.08055i
$778$	121.851	−	62.0859i	0.156620	−	0.0798020i
$779$	−211.009	−	68.5610i	−0.270872	−	0.0880116i
$780$	1.54019	+	2.98055i	0.00197460	+	0.00382121i
$781$	76.6509	+	235.907i	0.0981445	+	0.302058i
$782$	388.440	−	388.440i	0.496727	−	0.496727i
$783$	149.198	−	292.818i	0.190547	−	0.373969i
$784$	172.666	−	237.655i	0.220238	−	0.303131i
$785$	−271.067	+	377.611i	−0.345308	+	0.481034i
$786$	382.484	−	277.891i	0.486620	−	0.353550i
$787$	−506.378	+	80.2023i	−0.643428	+	0.101909i	−0.469617	−	0.882870i	$-0.655608\pi$
$787$	−506.378	+	80.2023i	−0.643428	+	0.101909i	−0.173811	+	0.984779i	$0.555608\pi$
$788$	−0.317178	−	2.00258i	−0.000402510	−	0.00254135i
$789$	−1110.84	−	1528.94i	−1.40791	−	1.93782i
$790$	119.303	−	374.445i	0.151016	−	0.473980i
$791$	200.053	+	145.347i	0.252911	+	0.183751i
$792$	−274.160	−	139.692i	−0.346162	−	0.176378i
$793$	−383.101	−	383.101i	−0.483104	−	0.483104i
$794$	185.309	−	60.2105i	0.233386	−	0.0758318i
$795$	835.364	−	1662.92i	1.05077	−	2.09173i
$796$	0.453984	−	1.39722i	0.000570332	−	0.00175530i
$797$	607.216	+	1191.73i	0.761878	+	1.49527i	0.865640	+	0.500667i	$0.166912\pi$
$797$	607.216	+	1191.73i	0.761878	+	1.49527i	−0.103762	+	0.994602i	$0.533088\pi$
$798$	304.576	+	48.2401i	0.381674	+	0.0604512i
$799$		−	840.935i		−	1.05248i
$800$	−1.31547	+	2.65640i	−0.00164434	+	0.00332050i
$801$	−806.431			−1.00678
$802$	−45.5544	+	287.619i	−0.0568010	+	0.358628i
$803$	−157.600	+	80.3014i	−0.196264	+	0.100002i
$804$	−2.42164	−	0.786839i	−0.00301199	−	0.000978656i
$805$	−268.979	+	272.071i	−0.334135	+	0.337977i
$806$	−31.0655	−	95.6099i	−0.0385428	−	0.118623i
$807$	39.0255	−	39.0255i	0.0483587	−	0.0483587i
$808$	195.444	−	383.580i	0.241886	−	0.474728i
$809$	−82.9765	+	114.207i	−0.102567	+	0.141171i	−0.857215	−	0.514958i	$-0.827807\pi$
$809$	−82.9765	+	114.207i	−0.102567	+	0.141171i	0.754649	+	0.656129i	$0.227807\pi$
$810$	−513.563	+	170.118i	−0.634028	+	0.210022i
$811$	105.885	−	76.9299i	0.130561	−	0.0948581i	−0.520588	−	0.853808i	$-0.674287\pi$
$811$	105.885	−	76.9299i	0.130561	−	0.0948581i	0.651149	+	0.758950i	$0.274287\pi$
$812$	−1.24806	+	0.197674i	−0.00153702	+	0.000243440i
$813$	−369.739	−	2334.44i	−0.454784	−	2.87139i
$814$	135.242	+	186.145i	0.166145	+	0.228680i
$815$	−200.223	−	604.447i	−0.245673	−	0.741652i
$816$	1158.90	+	841.990i	1.42022	+	1.03185i
$817$	−181.770	−	92.6165i	−0.222485	−	0.113362i
$818$	142.203	+	142.203i	0.173843	+	0.173843i
$819$	−1199.60	+	389.775i	−1.46472	+	0.475916i
$820$	0.945699	+	0.934950i	0.00115329	+	0.00114018i
$821$	−223.412	+	687.591i	−0.272122	+	0.837504i	0.717845	+	0.696203i	$0.245129\pi$
$821$	−223.412	+	687.591i	−0.272122	+	0.837504i	−0.989967	+	0.141301i	$0.954871\pi$
$822$	−208.512	−	409.228i	−0.253664	−	0.497844i
$823$	1267.47	+	200.748i	1.54006	+	0.243922i	0.867996	−	0.496571i	$-0.165408\pi$
$823$	1267.47	+	200.748i	1.54006	+	0.243922i	0.672065	+	0.740492i	$0.265408\pi$
$824$			941.672i			1.14281i
$825$	55.3696	−	377.468i	0.0671147	−	0.457537i
$826$	28.8747			0.0349573
$827$	−26.4921	+	167.265i	−0.0320340	+	0.202255i	−0.998515	−	0.0544850i	$-0.982648\pi$
$827$	−26.4921	+	167.265i	−0.0320340	+	0.202255i	0.966481	+	0.256740i	$0.0826483\pi$
$828$	−1.03773	+	0.528751i	−0.00125330	+	0.000638589i
$829$	1291.17	+	419.527i	1.55751	+	0.506064i	0.956140	−	0.292910i	$-0.0946235\pi$
$829$	1291.17	+	419.527i	1.55751	+	0.506064i	0.601366	+	0.798974i	$0.294624\pi$
$830$	−448.653	−	225.379i	−0.540546	−	0.271541i
$831$	608.724	+	1873.46i	0.732519	+	2.25446i
$832$	−909.715	+	909.715i	−1.09341	+	1.09341i
$833$	−165.988	+	325.771i	−0.199266	+	0.391081i
$834$	−629.257	+	866.097i	−0.754504	+	1.03849i
$835$	−383.239	−	122.105i	−0.458969	−	0.146233i
$836$	0.125339	−	0.0910640i	0.000149927	−	0.000108928i
$837$	26.4066	−	4.18240i	0.0315491	−	0.00499689i
$838$	108.523	+	685.190i	0.129503	+	0.817649i
$839$	−678.477	−	933.843i	−0.808673	−	1.11304i	−0.991527	−	0.129903i	$-0.958533\pi$
$839$	−678.477	−	933.843i	−0.808673	−	1.11304i	0.182853	−	0.983140i	$-0.441467\pi$
$840$	−811.960	−	582.862i	−0.966619	−	0.693883i
$841$	88.1522	+	64.0464i	0.104818	+	0.0761550i
$842$	−454.827	−	231.746i	−0.540175	−	0.275233i
$843$	−328.629	−	328.629i	−0.389833	−	0.389833i
$844$	2.65076	−	0.861285i	0.00314071	−	0.00102048i
$845$	−1037.67	+	536.211i	−1.22801	+	0.634569i
$846$	296.828	−	913.544i	0.350861	−	1.07984i
$847$	275.180	+	540.071i	0.324888	+	0.637628i
$848$	1301.00	+	206.059i	1.53420	+	0.242994i
$849$			954.736i			1.12454i
$850$	−296.020	+	947.788i	−0.348259	+	1.11504i
$851$	470.955			0.553414
$852$	−0.383710	+	2.42265i	−0.000450364	+	0.00284349i
$853$	83.5286	−	42.5599i	0.0979233	−	0.0498944i	−0.404343	−	0.914607i	$-0.632500\pi$
$853$	83.5286	−	42.5599i	0.0979233	−	0.0498944i	0.502266	+	0.864713i	$0.332500\pi$
$854$	283.874	+	92.2364i	0.332406	+	0.108005i
$855$	−52.9598	+	347.208i	−0.0619413	+	0.406091i
$856$	6.51737	+	20.0584i	0.00761374	+	0.0234327i
$857$	178.447	−	178.447i	0.208223	−	0.208223i	−0.595289	−	0.803512i	$-0.702962\pi$
$857$	178.447	−	178.447i	0.208223	−	0.208223i	0.803512	+	0.595289i	$0.202962\pi$
$858$	277.764	−	545.143i	0.323735	−	0.635365i
$859$	−192.730	+	265.270i	−0.224366	+	0.308813i	−0.906328	−	0.422574i	$-0.861127\pi$
$859$	−192.730	+	265.270i	−0.224366	+	0.308813i	0.681963	+	0.731387i	$0.261127\pi$
$860$	0.724372	+	0.985122i	0.000842293	+	0.00114549i
$861$	−724.855	+	526.638i	−0.841875	+	0.611658i
$862$	−444.028	+	70.3271i	−0.515113	+	0.0815860i
$863$	18.8095	+	118.758i	0.0217954	+	0.137611i	0.996187	−	0.0872489i	$-0.0278075\pi$
$863$	18.8095	+	118.758i	0.0217954	+	0.137611i	−0.974391	+	0.224860i	$0.927808\pi$
$864$	−0.743124	−	1.02282i	−0.000860097	−	0.00118382i
$865$	854.148	−	4.88211i	0.987455	−	0.00564406i
$866$	63.0351	+	45.7977i	0.0727888	+	0.0528842i
$867$	−426.611	−	217.369i	−0.492054	−	0.250714i
$868$	−0.0726905	−	0.0726905i	−8.37449e−5	−	8.37449e-5i
$869$	126.513	−	41.1065i	0.145584	−	0.0473033i
$870$	225.212	+	1371.16i	0.258865	+	1.57605i
$871$	472.113	−	1453.01i	0.542036	−	1.66821i
$872$	−480.600	−	943.230i	−0.551147	−	1.08169i
$873$	−31.3564	−	4.96637i	−0.0359180	−	0.00568886i
$874$			170.847i			0.195478i
$875$	202.387	−	661.255i	0.231300	−	0.755720i
$876$	−1.74909			−0.00199668
$877$	142.712	−	901.047i	0.162727	−	1.02742i	−0.762218	−	0.647320i	$-0.775890\pi$
$877$	142.712	−	901.047i	0.162727	−	1.02742i	0.924945	−	0.380100i	$-0.124110\pi$
$878$	−408.822	+	208.305i	−0.465628	+	0.237249i
$879$	1166.08	+	378.883i	1.32660	+	0.431039i
$880$	266.469	−	43.7672i	0.302805	−	0.0497354i
$881$	422.625	+	1300.71i	0.479710	+	1.47640i	0.839498	+	0.543363i	$0.182849\pi$
$881$	422.625	+	1300.71i	0.479710	+	1.47640i	−0.359788	+	0.933034i	$0.617151\pi$
$882$	−295.309	+	295.309i	−0.334817	+	0.334817i
$883$	700.304	−	1374.42i	0.793096	−	1.55654i	−0.0372608	−	0.999306i	$-0.511863\pi$
$883$	700.304	−	1374.42i	0.793096	−	1.55654i	0.830357	−	0.557232i	$-0.188137\pi$
$884$	1.73729	−	2.39118i	0.00196527	−	0.00270496i
$885$	0.336856	+	58.9345i	0.000380628	+	0.0665927i
$886$	−1177.20	+	855.287i	−1.32867	+	0.965335i
$887$	359.608	−	56.9563i	0.405421	−	0.0642123i	0.0496060	−	0.998769i	$-0.484203\pi$
$887$	359.608	−	56.9563i	0.405421	−	0.0642123i	0.355815	+	0.934557i	$0.384203\pi$
$888$	192.472	+	1215.22i	0.216747	+	1.36849i
$889$	553.658	+	762.045i	0.622787	+	0.857193i
$890$	571.241	−	420.040i	0.641843	−	0.471955i
$891$	−148.151	−	107.638i	−0.166275	−	0.120806i
$892$	−2.57591	−	1.31249i	−0.00288779	−	0.00147140i
$893$	184.934	+	184.934i	0.207093	+	0.207093i
$894$	549.336	−	178.490i	0.614470	−	0.199653i
$895$	1300.94	+	198.434i	1.45357	+	0.221713i
$896$	218.214	−	671.595i	0.243543	−	0.749548i
$897$	−568.541	−	1115.83i	−0.633825	−	1.24395i
$898$	1475.29	+	233.662i	1.64286	+	0.260203i
$899$			77.2828i			0.0859653i
$900$	1.21784	−	1.71716i	0.00135316	−	0.00190795i
$901$	−1639.46			−1.81960
$902$	37.9379	−	239.530i	0.0420597	−	0.265555i
$903$	−734.042	+	374.013i	−0.812893	+	0.414190i
$904$	−340.394	−	110.601i	−0.376542	−	0.122346i
$905$	−315.327	−	610.217i	−0.348428	−	0.674273i
$906$	−634.017	−	1951.30i	−0.699798	−	2.15376i
$907$	45.1187	−	45.1187i	0.0497450	−	0.0497450i	−0.681797	−	0.731542i	$-0.738801\pi$
$907$	45.1187	−	45.1187i	0.0497450	−	0.0497450i	0.731542	+	0.681797i	$0.238801\pi$
$908$	−1.41903	+	2.78500i	−0.00156280	+	0.00306718i
$909$	−359.080	+	494.232i	−0.395028	+	0.543709i
$910$	646.728	−	900.929i	0.710690	−	0.990032i
$911$	−274.452	+	199.401i	−0.301265	+	0.218882i	−0.728139	−	0.685429i	$-0.759615\pi$
$911$	−274.452	+	199.401i	−0.301265	+	0.218882i	0.426874	+	0.904311i	$0.359615\pi$
$912$	−440.025	+	69.6932i	−0.482484	+	0.0764179i
$913$	−26.5860	−	167.857i	−0.0291193	−	0.183852i
$914$	−219.027	−	301.465i	−0.239636	−	0.329830i
$915$	−184.947	+	580.476i	−0.202127	+	0.634400i
$916$	1.71972	+	1.24945i	0.00187743	+	0.00136403i
$917$	258.460	+	131.692i	0.281853	+	0.143611i
$918$	−299.455	−	299.455i	−0.326204	−	0.326204i
$919$	−240.689	+	78.2047i	−0.261903	+	0.0850976i	−0.437025	−	0.899449i	$-0.643968\pi$
$919$	−240.689	+	78.2047i	−0.261903	+	0.0850976i	0.175122	+	0.984547i	$0.443968\pi$
$920$	248.575	−	494.828i	0.270190	−	0.537856i
$921$	74.5209	−	229.352i	0.0809130	−	0.249025i
$922$	−164.823	−	323.484i	−0.178767	−	0.350851i
$923$	−1453.62	−	230.231i	−1.57489	−	0.249437i
$924$		−	0.625642i		−	0.000677102i
$925$	−754.013	+	395.110i	−0.815150	+	0.427146i
$926$	−900.972			−0.972972
$927$	209.040	−	1319.83i	0.225502	−	1.42376i
$928$	3.25622	−	1.65912i	0.00350885	−	0.00178785i
$929$	−658.494	−	213.958i	−0.708820	−	0.230310i	−0.0676508	−	0.997709i	$-0.521550\pi$
$929$	−658.494	−	213.958i	−0.708820	−	0.230310i	−0.641169	+	0.767399i	$0.721550\pi$
$930$	−79.4759	+	80.3896i	−0.0854579	+	0.0864404i
$931$	−35.1385	−	108.145i	−0.0377427	−	0.116160i
$932$	1.01427	−	1.01427i	0.00108827	−	0.00108827i
$933$	−527.172	+	1034.63i	−0.565029	+	1.10893i
$934$	448.768	−	617.676i	0.480480	−	0.661324i
$935$	−319.052	+	105.686i	−0.341232	+	0.113033i
$936$	1476.99	−	1073.09i	1.57798	−	1.14647i
$937$	218.653	−	34.6312i	0.233354	−	0.0369596i	−0.0386622	−	0.999252i	$-0.512310\pi$
$937$	218.653	−	34.6312i	0.233354	−	0.0369596i	0.272016	+	0.962293i	$0.412310\pi$
$938$	131.670	+	831.333i	0.140373	+	0.886282i
$939$	1271.80	+	1750.48i	1.35442	+	1.86419i
$940$	−0.492930	−	1.48809i	−0.000524394	−	0.00158307i
$941$	164.559	+	119.559i	0.174876	+	0.127055i	0.671780	−	0.740750i	$-0.265530\pi$
$941$	164.559	+	119.559i	0.174876	+	0.127055i	−0.496904	+	0.867805i	$0.665530\pi$
$942$	746.883	+	380.556i	0.792869	+	0.403987i
$943$	−351.003	−	351.003i	−0.372220	−	0.372220i
$944$	−39.6741	+	12.8909i	−0.0420276	+	0.0136556i
$945$	209.744	+	207.360i	0.221952	+	0.219429i
$946$	68.9080	−	212.077i	0.0728415	−	0.224183i
$947$	544.018	+	1067.69i	0.574464	+	1.12745i	0.977237	+	0.212150i	$0.0680464\pi$
$947$	544.018	+	1067.69i	0.574464	+	1.12745i	−0.402773	+	0.915300i	$0.631954\pi$
$948$	1.29923	+	0.205777i	0.00137049	+	0.000217064i
$949$		−	1049.48i		−	1.10588i
$950$	−143.333	−	273.532i	−0.150877	−	0.287928i
$951$	891.112			0.937026
$952$	−137.747	+	869.701i	−0.144692	+	0.913552i
$953$	−863.782	+	440.119i	−0.906382	+	0.461825i	−0.844071	−	0.536232i	$-0.819847\pi$
$953$	−863.782	+	440.119i	−0.906382	+	0.461825i	−0.0623115	+	0.998057i	$0.519847\pi$
$954$	−1781.02	−	578.688i	−1.86689	−	0.606591i
$955$	−847.715	−	425.847i	−0.887660	−	0.445913i
$956$	−0.136355	−	0.419657i	−0.000142631	−	0.000438972i
$957$	−332.584	+	332.584i	−0.347528	+	0.347528i
$958$	317.691	−	623.504i	0.331619	−	0.650839i
$959$	165.638	−	227.981i	0.172719	−	0.237728i
$960$	1378.40	+	439.175i	1.43583	+	0.457474i
$961$	772.379	−	561.166i	0.803724	−	0.583940i
$962$	−1348.37	+	213.561i	−1.40164	+	0.221997i
$963$	−4.68187	−	29.5602i	−0.00486176	−	0.0306959i
$964$	1.94385	+	2.67547i	0.00201644	+	0.00277539i
$965$	266.107	+	191.024i	0.275758	+	0.197952i
$966$	558.167	+	405.532i	0.577813	+	0.419806i
$967$	394.896	+	201.209i	0.408372	+	0.208076i	0.646095	−	0.763257i	$-0.276401\pi$
$967$	394.896	+	201.209i	0.408372	+	0.208076i	−0.237723	+	0.971333i	$0.576401\pi$
$968$	−620.359	−	620.359i	−0.640866	−	0.640866i
$969$	527.359	−	171.349i	0.544230	−	0.176831i
$970$	24.7983	−	12.8144i	0.0255653	−	0.0132108i
$971$	53.8408	−	165.705i	0.0554488	−	0.170654i	−0.919497	−	0.393098i	$-0.871403\pi$
$971$	53.8408	−	165.705i	0.0554488	−	0.170654i	0.974946	+	0.222444i	$0.0714034\pi$
$972$	−1.14497	−	2.24713i	−0.00117795	−	0.00231186i
$973$	−648.762	−	102.754i	−0.666765	−	0.105605i
$974$		−	1614.83i		−	1.65793i
$975$	1846.38	+	1309.49i	1.89372	+	1.34306i
$976$	−431.223			−0.441827
$977$	−257.214	+	1623.99i	−0.263269	+	1.66222i	0.402020	+	0.915631i	$0.368308\pi$
$977$	−257.214	+	1623.99i	−0.263269	+	1.66222i	−0.665289	+	0.746586i	$0.731692\pi$
$978$	−1023.11	+	521.302i	−1.04613	+	0.533029i
$979$	228.259	+	74.1659i	0.233155	+	0.0757568i
$980$	−0.102770	+	0.673769i	−0.000104868	+	0.000687520i
$981$	464.213	+	1428.70i	0.473203	+	1.45637i
$982$	744.456	−	744.456i	0.758102	−	0.758102i
$983$	378.134	−	742.129i	0.384673	−	0.754964i	−0.614757	−	0.788717i	$-0.710746\pi$
$983$	378.134	−	742.129i	0.384673	−	0.754964i	0.999430	+	0.0337529i	$0.0107459\pi$
$984$	762.254	−	1049.15i	0.774648	−	1.06621i
$985$	−810.392	−	1102.11i	−0.822733	−	1.11889i
$986$	990.361	−	719.540i	1.00442	−	0.729756i
$987$	1043.16	−	165.220i	1.05690	−	0.167396i
$988$	0.143799	+	0.907912i	0.000145546	+	0.000918940i
$989$	−268.282	−	369.259i	−0.271266	−	0.373366i
$990$	−383.904	+	2.19430i	−0.387782	+	0.00221647i
$991$	−238.832	−	173.522i	−0.241001	−	0.175098i	0.460728	−	0.887541i	$-0.347588\pi$
$991$	−238.832	−	173.522i	−0.241001	−	0.175098i	−0.701729	+	0.712444i	$0.747588\pi$
$992$	0.264905	+	0.134976i	0.000267041	+	0.000136064i
$993$	948.303	+	948.303i	0.954988	+	0.954988i
$994$	771.132	−	250.556i	0.775786	−	0.252068i
$995$	−160.654	−	978.111i	−0.161461	−	0.983026i
$996$	0.519324	−	1.59831i	0.000521410	−	0.00160473i
$997$	410.202	+	805.068i	0.411437	+	0.807490i	1.00000		0.000961470i	$-0.000306045\pi$
$997$	410.202	+	805.068i	0.411437	+	0.807490i	−0.588563	+	0.808451i	$0.700306\pi$
$998$	−1122.42	−	177.774i	−1.12467	−	0.178131i
$999$		−	363.067i		−	0.363431i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.3.f.a.23.2	yes	32
3.2	odd	2		225.3.r.a.73.3		32
4.3	odd	2		400.3.bg.c.273.4		32
5.2	odd	4		125.3.f.a.32.2		32
5.3	odd	4		125.3.f.b.32.3		32
5.4	even	2		125.3.f.c.93.3		32
25.9	even	10		125.3.f.b.43.3		32
25.12	odd	20	inner	25.3.f.a.12.2	✓	32
25.13	odd	20		125.3.f.c.82.3		32
25.16	even	5		125.3.f.a.43.2		32
75.62	even	20		225.3.r.a.37.3		32
100.87	even	20		400.3.bg.c.337.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.3.f.a.12.2	✓	32	25.12	odd	20	inner
25.3.f.a.23.2	yes	32	1.1	even	1	trivial
125.3.f.a.32.2		32	5.2	odd	4
125.3.f.a.43.2		32	25.16	even	5
125.3.f.b.32.3		32	5.3	odd	4
125.3.f.b.43.3		32	25.9	even	10
125.3.f.c.82.3		32	25.13	odd	20
125.3.f.c.93.3		32	5.4	even	2
225.3.r.a.37.3		32	75.62	even	20
225.3.r.a.73.3		32	3.2	odd	2
400.3.bg.c.273.4		32	4.3	odd	2
400.3.bg.c.337.4		32	100.87	even	20

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)

\(f(q)\)	\(=\)	\(q+(-0.312579 + 1.97355i) q^{2} +(-4.02069 + 2.04864i) q^{3} +(0.00704800 + 0.00229003i) q^{4} +(4.93389 - 0.810386i) q^{5} +(-2.78631 - 8.57538i) q^{6} +(3.91191 - 3.91191i) q^{7} +(-3.63528 + 7.13464i) q^{8} +(6.67894 - 9.19277i) q^{9} +O(q^{10})\)	\(q+(-0.312579 + 1.97355i) q^{2} +(-4.02069 + 2.04864i) q^{3} +(0.00704800 + 0.00229003i) q^{4} +(4.93389 - 0.810386i) q^{5} +(-2.78631 - 8.57538i) q^{6} +(3.91191 - 3.91191i) q^{7} +(-3.63528 + 7.13464i) q^{8} +(6.67894 - 9.19277i) q^{9} +(0.0571038 + 9.99057i) q^{10} +(-2.73590 + 1.98775i) q^{11} +(-0.0330293 + 0.00523133i) q^{12} +(-3.13886 - 19.8180i) q^{13} +(6.49755 + 8.94311i) q^{14} +(-18.1775 + 13.3661i) q^{15} +(-12.9202 - 9.38711i) q^{16} +(17.7107 + 9.02407i) q^{17} +(16.0547 + 16.0547i) q^{18} +(-5.87938 + 1.91032i) q^{19} +(0.0366299 + 0.00558718i) q^{20} +(-7.71446 + 23.7427i) q^{21} +(-3.06773 - 6.02076i) q^{22} +(-13.6608 - 2.16366i) q^{23} -36.1336i q^{24} +(23.6865 - 7.99671i) q^{25} +40.0928 q^{26} +(-1.66800 + 10.5313i) q^{27} +(0.0365295 - 0.0186127i) q^{28} +(-29.3129 - 9.52435i) q^{29} +(-20.6967 - 40.0520i) q^{30} +(-0.774840 - 2.38471i) q^{31} +(-0.0838425 + 0.0838425i) q^{32} +(6.92803 - 13.5970i) q^{33} +(-23.3454 + 32.1322i) q^{34} +(16.1308 - 22.4711i) q^{35} +(0.0681249 - 0.0494957i) q^{36} +(-33.6313 + 5.32667i) q^{37} +(-1.93234 - 12.2003i) q^{38} +(53.2204 + 73.2515i) q^{39} +(-12.1543 + 38.1475i) q^{40} +(29.0354 + 21.0954i) q^{41} +(-44.4459 - 22.6463i) q^{42} +(23.3347 + 23.3347i) q^{43} +(-0.0238347 + 0.00774436i) q^{44} +(25.5035 - 50.7686i) q^{45} +(8.54016 - 26.2839i) q^{46} +(-19.2067 - 37.6953i) q^{47} +(71.1791 + 11.2737i) q^{48} +18.3940i q^{49} +(8.37796 + 49.2461i) q^{50} -89.6965 q^{51} +(0.0232612 - 0.146865i) q^{52} +(-73.4897 + 37.4449i) q^{53} +(-20.2627 - 6.58375i) q^{54} +(-11.8878 + 12.0245i) q^{55} +(13.6892 + 42.1309i) q^{56} +(19.7256 - 19.7256i) q^{57} +(27.9594 - 54.8733i) q^{58} +(1.53534 - 2.11322i) q^{59} +(-0.158724 + 0.0525773i) q^{60} +(21.8447 - 15.8711i) q^{61} +(4.94854 - 0.783771i) q^{62} +(-9.83388 - 62.0887i) q^{63} +(-37.6877 - 51.8727i) q^{64} +(-31.5470 - 95.2360i) q^{65} +(24.6688 + 17.9229i) q^{66} +(67.8430 + 34.5677i) q^{67} +(0.104160 + 0.104160i) q^{68} +(59.3584 - 19.2867i) q^{69} +(39.3056 + 38.8588i) q^{70} +(22.6659 - 69.7586i) q^{71} +(41.3073 + 81.0701i) q^{72} +(51.6598 + 8.18211i) q^{73} -68.0379i q^{74} +(-78.8539 + 80.6776i) q^{75} -0.0458126 q^{76} +(-2.92671 + 18.4785i) q^{77} +(-161.201 + 82.1359i) q^{78} +(-37.4103 - 12.1554i) q^{79} +(-71.3543 - 35.8446i) q^{80} +(16.7335 + 51.5004i) q^{81} +(-50.7087 + 50.7087i) q^{82} +(-22.8152 + 44.7773i) q^{83} +(-0.108743 + 0.149672i) q^{84} +(94.6958 + 30.1712i) q^{85} +(-53.3460 + 38.7581i) q^{86} +(137.370 - 21.7573i) q^{87} +(-4.23611 - 26.7457i) q^{88} +(-41.7155 - 57.4164i) q^{89} +(92.2224 + 66.2015i) q^{90} +(-89.8050 - 65.2472i) q^{91} +(-0.0913265 - 0.0465332i) q^{92} +(8.00082 + 8.00082i) q^{93} +(80.3971 - 26.1226i) q^{94} +(-27.4601 + 14.1899i) q^{95} +(0.165341 - 0.508868i) q^{96} +(-1.26842 - 2.48942i) q^{97} +(-36.3014 - 5.74957i) q^{98} +38.4266i 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

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