LMFDB - Embedded newform 25.3.f.a.2.4

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			2.4
Character	$\chi$	$=$	25.2
Dual form			25.3.f.a.13.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.80600 + 0.286042i) q^{2} +(-0.665351 - 1.30583i) q^{3} +(-0.624420 - 0.202886i) q^{4} +(-3.20727 + 3.83580i) q^{5} +(-0.828102 - 2.54863i) q^{6} +(3.62927 + 3.62927i) q^{7} +(-7.58652 - 3.86553i) q^{8} +(4.02758 - 5.54349i) q^{9} +O(q^{10})$	\(q+(1.80600 + 0.286042i) q^{2} +(-0.665351 - 1.30583i) q^{3} +(-0.624420 - 0.202886i) q^{4} +(-3.20727 + 3.83580i) q^{5} +(-0.828102 - 2.54863i) q^{6} +(3.62927 + 3.62927i) q^{7} +(-7.58652 - 3.86553i) q^{8} +(4.02758 - 5.54349i) q^{9} +(-6.88953 + 6.01004i) q^{10} +(5.24977 - 3.81418i) q^{11} +(0.150524 + 0.950373i) q^{12} +(-4.11948 + 0.652461i) q^{13} +(5.51633 + 7.59258i) q^{14} +(7.14285 + 1.63598i) q^{15} +(-10.4709 - 7.60754i) q^{16} +(-6.15907 + 12.0879i) q^{17} +(8.85947 - 8.85947i) q^{18} +(25.5969 - 8.31693i) q^{19} +(2.78092 - 1.74444i) q^{20} +(2.32445 - 7.15393i) q^{21} +(10.5721 - 5.38675i) q^{22} +(-5.03647 + 31.7990i) q^{23} +12.4786i q^{24} +(-4.42679 - 24.6050i) q^{25} -7.62639 q^{26} +(-22.9462 - 3.63433i) q^{27} +(-1.52986 - 3.00252i) q^{28} +(-52.2931 - 16.9911i) q^{29} +(12.4320 + 4.99773i) q^{30} +(8.09752 + 24.9216i) q^{31} +(7.34848 + 7.34848i) q^{32} +(-8.47360 - 4.31751i) q^{33} +(-14.5809 + 20.0689i) q^{34} +(-25.5612 + 2.28111i) q^{35} +(-3.63960 + 2.64432i) q^{36} +(-6.89764 - 43.5500i) q^{37} +(48.6069 - 7.69857i) q^{38} +(3.59290 + 4.94520i) q^{39} +(39.1595 - 16.7026i) q^{40} +(29.6072 + 21.5109i) q^{41} +(6.24428 - 12.2551i) q^{42} +(28.0309 - 28.0309i) q^{43} +(-4.05190 + 1.31654i) q^{44} +(8.34618 + 33.2285i) q^{45} +(-18.1917 + 55.9883i) q^{46} +(9.78846 - 4.98747i) q^{47} +(-2.96731 + 18.7348i) q^{48} -22.6568i q^{49} +(-0.956716 - 45.7027i) q^{50} +19.8826 q^{51} +(2.70466 + 0.428376i) q^{52} +(17.0182 + 33.4001i) q^{53} +(-40.4013 - 13.1272i) q^{54} +(-2.20700 + 32.3702i) q^{55} +(-13.5045 - 41.5626i) q^{56} +(-27.8914 - 27.8914i) q^{57} +(-89.5811 - 45.6438i) q^{58} +(-14.1810 + 19.5185i) q^{59} +(-4.12822 - 2.47073i) q^{60} +(-34.1559 + 24.8157i) q^{61} +(7.49548 + 47.3246i) q^{62} +(34.7360 - 5.50164i) q^{63} +(41.5995 + 57.2568i) q^{64} +(10.7096 - 17.8941i) q^{65} +(-14.0683 - 10.2212i) q^{66} +(-2.47613 + 4.85968i) q^{67} +(6.29831 - 6.29831i) q^{68} +(44.8749 - 14.5808i) q^{69} +(-46.8160 - 3.19191i) q^{70} +(33.2596 - 102.362i) q^{71} +(-51.9838 + 26.4871i) q^{72} +(-14.9176 + 94.1859i) q^{73} -80.6242i q^{74} +(-29.1844 + 22.1515i) q^{75} -17.6706 q^{76} +(32.8955 + 5.21014i) q^{77} +(5.07423 + 9.95874i) q^{78} +(106.211 + 34.5101i) q^{79} +(62.7640 - 15.7648i) q^{80} +(-8.53531 - 26.2690i) q^{81} +(47.3174 + 47.3174i) q^{82} +(-54.8539 - 27.9495i) q^{83} +(-2.90287 + 3.99546i) q^{84} +(-26.6128 - 62.3941i) q^{85} +(58.6417 - 42.6057i) q^{86} +(12.6059 + 79.5907i) q^{87} +(-54.5713 + 8.64325i) q^{88} +(-6.88788 - 9.48035i) q^{89} +(5.56844 + 62.3979i) q^{90} +(-17.3187 - 12.5827i) q^{91} +(9.59645 - 18.8341i) q^{92} +(27.1556 - 27.1556i) q^{93} +(19.1046 - 6.20745i) q^{94} +(-50.1941 + 124.859i) q^{95} +(4.70651 - 14.4851i) q^{96} +(46.3527 - 23.6179i) q^{97} +(6.48079 - 40.9181i) q^{98} -44.4640i 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 $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{20}\right)$

Coefficient data

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

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

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

$2$	1.80600	+	0.286042i	0.902999	+	0.143021i	0.590632	−	0.806941i	$-0.298878\pi$
$2$	1.80600	+	0.286042i	0.902999	+	0.143021i	0.312366	+	0.949962i	$0.398878\pi$
$3$	−0.665351	−	1.30583i	−0.221784	−	0.435275i	0.753126	−	0.657877i	$-0.228545\pi$
$3$	−0.665351	−	1.30583i	−0.221784	−	0.435275i	−0.974910	+	0.222601i	$0.928545\pi$
$4$	−0.624420	−	0.202886i	−0.156105	−	0.0507216i
$5$	−3.20727	+	3.83580i	−0.641455	+	0.767161i
$5$	−3.20727	+	3.83580i	−0.641455	+	0.767161i
$6$	−0.828102	−	2.54863i	−0.138017	−	0.424772i
$7$	3.62927	+	3.62927i	0.518467	+	0.518467i	0.917107	−	0.398640i	$-0.130518\pi$
$7$	3.62927	+	3.62927i	0.518467	+	0.518467i	−0.398640	+	0.917107i	$0.630518\pi$
$8$	−7.58652	−	3.86553i	−0.948315	−	0.483191i
$9$	4.02758	−	5.54349i	0.447509	−	0.615943i
$10$	−6.88953	+	6.01004i	−0.688953	+	0.601004i
$11$	5.24977	−	3.81418i	0.477252	−	0.346744i	−0.323009	−	0.946396i	$-0.604694\pi$
$11$	5.24977	−	3.81418i	0.477252	−	0.346744i	0.800261	+	0.599652i	$0.204694\pi$
$12$	0.150524	+	0.950373i	0.0125437	+	0.0791978i
$13$	−4.11948	+	0.652461i	−0.316883	+	0.0501893i	−0.312850	−	0.949803i	$-0.601284\pi$
$13$	−4.11948	+	0.652461i	−0.316883	+	0.0501893i	−0.00403283	+	0.999992i	$0.501284\pi$
$14$	5.51633	+	7.59258i	0.394024	+	0.542327i
$15$	7.14285	+	1.63598i	0.476190	+	0.109065i
$16$	−10.4709	−	7.60754i	−0.654430	−	0.475471i
$17$	−6.15907	+	12.0879i	−0.362298	+	0.711051i	−0.998152	−	0.0607586i	$-0.980648\pi$
$17$	−6.15907	+	12.0879i	−0.362298	+	0.711051i	0.635854	+	0.771809i	$0.280648\pi$
$18$	8.85947	−	8.85947i	0.492193	−	0.492193i
$19$	25.5969	−	8.31693i	1.34720	−	0.437733i	0.455453	−	0.890260i	$-0.349477\pi$
$19$	25.5969	−	8.31693i	1.34720	−	0.437733i	0.891751	+	0.452527i	$0.149477\pi$
$20$	2.78092	−	1.74444i	0.139046	−	0.0872220i
$21$	2.32445	−	7.15393i	0.110688	−	0.340663i
$22$	10.5721	−	5.38675i	0.480550	−	0.244852i
$23$	−5.03647	+	31.7990i	−0.218977	+	1.38256i	0.595960	+	0.803014i	$0.296772\pi$
$23$	−5.03647	+	31.7990i	−0.218977	+	1.38256i	−0.814936	+	0.579551i	$0.803228\pi$
$24$			12.4786i			0.519942i
$25$	−4.42679	−	24.6050i	−0.177071	−	0.984198i
$26$	−7.62639			−0.293323
$27$	−22.9462	−	3.63433i	−0.849861	−	0.134605i
$28$	−1.52986	−	3.00252i	−0.0546378	−	0.107233i
$29$	−52.2931	−	16.9911i	−1.80321	−	0.585899i	−0.803258	−	0.595631i	$-0.796902\pi$
$29$	−52.2931	−	16.9911i	−1.80321	−	0.585899i	−0.999953	+	0.00973242i	$0.996902\pi$
$30$	12.4320	+	4.99773i	0.414400	+	0.166591i
$31$	8.09752	+	24.9216i	0.261210	+	0.803923i	0.992542	+	0.121901i	$0.0388991\pi$
$31$	8.09752	+	24.9216i	0.261210	+	0.803923i	−0.731332	+	0.682022i	$0.761101\pi$
$32$	7.34848	+	7.34848i	0.229640	+	0.229640i
$33$	−8.47360	−	4.31751i	−0.256776	−	0.130834i
$34$	−14.5809	+	20.0689i	−0.428850	+	0.590262i
$35$	−25.5612	+	2.28111i	−0.730321	+	0.0651744i
$36$	−3.63960	+	2.64432i	−0.101100	+	0.0734534i
$37$	−6.89764	−	43.5500i	−0.186423	−	1.17703i	−0.886420	−	0.462882i	$-0.846816\pi$
$37$	−6.89764	−	43.5500i	−0.186423	−	1.17703i	0.699997	−	0.714145i	$-0.253184\pi$
$38$	48.6069	−	7.69857i	1.27913	−	0.202594i
$39$	3.59290	+	4.94520i	0.0921256	+	0.126800i
$40$	39.1595	−	16.7026i	0.978986	−	0.417565i
$41$	29.6072	+	21.5109i	0.722126	+	0.524655i	0.887063	−	0.461649i	$-0.152742\pi$
$41$	29.6072	+	21.5109i	0.722126	+	0.524655i	−0.164937	+	0.986304i	$0.552742\pi$
$42$	6.24428	−	12.2551i	0.148673	−	0.291788i
$43$	28.0309	−	28.0309i	0.651881	−	0.651881i	−0.301565	−	0.953446i	$-0.597509\pi$
$43$	28.0309	−	28.0309i	0.651881	−	0.651881i	0.953446	+	0.301565i	$0.0975090\pi$
$44$	−4.05190	+	1.31654i	−0.0920887	+	0.0299214i
$45$	8.34618	+	33.2285i	0.185471	+	0.738411i
$46$	−18.1917	+	55.9883i	−0.395471	+	1.21714i
$47$	9.78846	−	4.98747i	0.208265	−	0.106116i	−0.346747	−	0.937959i	$-0.612714\pi$
$47$	9.78846	−	4.98747i	0.208265	−	0.106116i	0.555012	+	0.831842i	$0.312714\pi$
$48$	−2.96731	+	18.7348i	−0.0618189	+	0.390309i
$49$		−	22.6568i		−	0.462383i
$50$	−0.956716	−	45.7027i	−0.0191343	−	0.914054i
$51$	19.8826			0.389855
$52$	2.70466	+	0.428376i	0.0520126	+	0.00823799i
$53$	17.0182	+	33.4001i	0.321098	+	0.630190i	0.993980	−	0.109560i	$-0.0349441\pi$
$53$	17.0182	+	33.4001i	0.321098	+	0.630190i	−0.672883	+	0.739749i	$0.734944\pi$
$54$	−40.4013	−	13.1272i	−0.748172	−	0.243096i
$55$	−2.20700	+	32.3702i	−0.0401273	+	0.588549i
$56$	−13.5045	−	41.5626i	−0.241152	−	0.742189i
$57$	−27.8914	−	27.8914i	−0.489322	−	0.489322i
$58$	−89.5811	−	45.6438i	−1.54450	−	0.786963i
$59$	−14.1810	+	19.5185i	−0.240356	+	0.330821i	−0.912105	−	0.409958i	$-0.865543\pi$
$59$	−14.1810	+	19.5185i	−0.240356	+	0.330821i	0.671749	+	0.740779i	$0.265543\pi$
$60$	−4.12822	−	2.47073i	−0.0688036	−	0.0411788i
$61$	−34.1559	+	24.8157i	−0.559933	+	0.406815i	−0.831434	−	0.555623i	$-0.812480\pi$
$61$	−34.1559	+	24.8157i	−0.559933	+	0.406815i	0.271502	+	0.962438i	$0.412480\pi$
$62$	7.49548	+	47.3246i	0.120895	+	0.763300i
$63$	34.7360	−	5.50164i	0.551365	−	0.0873276i
$64$	41.5995	+	57.2568i	0.649993	+	0.894638i
$65$	10.7096	−	17.8941i	0.164763	−	0.275294i
$66$	−14.0683	−	10.2212i	−0.213156	−	0.154867i
$67$	−2.47613	+	4.85968i	−0.0369572	+	0.0725326i	−0.908747	−	0.417348i	$-0.862960\pi$
$67$	−2.47613	+	4.85968i	−0.0369572	+	0.0725326i	0.871790	+	0.489881i	$0.162960\pi$
$68$	6.29831	−	6.29831i	0.0926222	−	0.0926222i
$69$	44.8749	−	14.5808i	0.650361	−	0.211315i
$70$	−46.8160	−	3.19191i	−0.668800	−	0.0455988i
$71$	33.2596	−	102.362i	0.468445	−	1.44172i	−0.386153	−	0.922435i	$-0.626196\pi$
$71$	33.2596	−	102.362i	0.468445	−	1.44172i	0.854598	−	0.519290i	$-0.173804\pi$
$72$	−51.9838	+	26.4871i	−0.721998	+	0.367876i
$73$	−14.9176	+	94.1859i	−0.204350	+	1.29022i	0.645730	+	0.763565i	$0.276553\pi$
$73$	−14.9176	+	94.1859i	−0.204350	+	1.29022i	−0.850081	+	0.526652i	$0.823447\pi$
$74$		−	80.6242i		−	1.08952i
$75$	−29.1844	+	22.1515i	−0.389125	+	0.295354i
$76$	−17.6706			−0.232508
$77$	32.8955	+	5.21014i	0.427215	+	0.0676642i
$78$	5.07423	+	9.95874i	0.0650542	+	0.127676i
$79$	106.211	+	34.5101i	1.34445	+	0.436837i	0.890821	−	0.454355i	$-0.150130\pi$
$79$	106.211	+	34.5101i	1.34445	+	0.436837i	0.453626	+	0.891192i	$0.350130\pi$
$80$	62.7640	−	15.7648i	0.784550	−	0.197060i
$81$	−8.53531	−	26.2690i	−0.105374	−	0.324308i
$82$	47.3174	+	47.3174i	0.577042	+	0.577042i
$83$	−54.8539	−	27.9495i	−0.660891	−	0.336741i	0.0911693	−	0.995835i	$-0.470940\pi$
$83$	−54.8539	−	27.9495i	−0.660891	−	0.336741i	−0.752060	+	0.659095i	$0.770940\pi$
$84$	−2.90287	+	3.99546i	−0.0345580	+	0.0475649i
$85$	−26.6128	−	62.3941i	−0.313092	−	0.734048i
$86$	58.6417	−	42.6057i	0.681880	−	0.495415i
$87$	12.6059	+	79.5907i	0.144896	+	0.914835i
$88$	−54.5713	+	8.64325i	−0.620129	+	0.0982187i
$89$	−6.88788	−	9.48035i	−0.0773919	−	0.106521i	0.768566	−	0.639771i	$-0.220971\pi$
$89$	−6.88788	−	9.48035i	−0.0773919	−	0.106521i	−0.845958	+	0.533250i	$0.820971\pi$
$90$	5.56844	+	62.3979i	0.0618716	+	0.693310i
$91$	−17.3187	−	12.5827i	−0.190315	−	0.138272i
$92$	9.59645	−	18.8341i	0.104309	−	0.204718i
$93$	27.1556	−	27.1556i	0.291995	−	0.291995i
$94$	19.1046	−	6.20745i	0.203240	−	0.0660367i
$95$	−50.1941	+	124.859i	−0.528359	+	1.31431i
$96$	4.70651	−	14.4851i	0.0490261	−	0.150887i
$97$	46.3527	−	23.6179i	0.477863	−	0.243483i	−0.198431	−	0.980115i	$-0.563585\pi$
$97$	46.3527	−	23.6179i	0.477863	−	0.243483i	0.676295	+	0.736631i	$0.263585\pi$
$98$	6.48079	−	40.9181i	0.0661305	−	0.417532i
$99$		−	44.4640i		−	0.449131i
$100$	−2.22783	+	16.2619i	−0.0222783	+	0.162619i
$101$	−22.2710			−0.220505			−0.110252	−	0.993904i	$-0.535166\pi$
$101$	−22.2710			−0.220505			−0.110252	+	0.993904i	$0.535166\pi$
$102$	35.9079	+	5.68725i	0.352038	+	0.0557574i
$103$	−57.8159	−	113.470i	−0.561319	−	1.10165i	−0.981005	−	0.193982i	$-0.937860\pi$
$103$	−57.8159	−	113.470i	−0.561319	−	1.10165i	0.419686	−	0.907669i	$-0.362140\pi$
$104$	33.7746	+	10.9740i	0.324756	+	0.105520i
$105$	19.9859	+	31.8608i	0.190342	+	0.303436i
$106$	21.1810	+	65.1883i	0.199820	+	0.614984i
$107$	−59.7030	−	59.7030i	−0.557972	−	0.557972i	0.370758	−	0.928730i	$-0.379098\pi$
$107$	−59.7030	−	59.7030i	−0.557972	−	0.557972i	−0.928730	+	0.370758i	$0.879098\pi$
$108$	13.5907	+	6.92482i	0.125840	+	0.0641187i
$109$	−55.1483	+	75.9051i	−0.505947	+	0.696377i	−0.983229	−	0.182373i	$-0.941622\pi$
$109$	−55.1483	+	75.9051i	−0.505947	+	0.696377i	0.477282	+	0.878750i	$0.341622\pi$
$110$	−13.2451	+	57.8292i	−0.120410	+	0.525720i
$111$	−52.2793	+	37.9832i	−0.470985	+	0.342191i
$112$	−10.3918	−	65.6115i	−0.0927843	−	0.585817i
$113$	10.7406	−	1.70114i	0.0950495	−	0.0150544i	−0.108728	−	0.994071i	$-0.534678\pi$
$113$	10.7406	−	1.70114i	0.0950495	−	0.0150544i	0.203778	+	0.979017i	$0.434678\pi$
$114$	−42.3936	−	58.3498i	−0.371874	−	0.511840i
$115$	−105.821	−	121.307i	−0.920186	−	1.05484i
$116$	29.2056	+	21.2191i	0.251772	+	0.182923i
$117$	−12.9746	+	25.4641i	−0.110894	+	0.217642i
$118$	−31.1939	+	31.1939i	−0.264355	+	0.264355i
$119$	−66.2231	+	21.5172i	−0.556496	+	0.180817i
$120$	−47.8655	−	40.0223i	−0.398879	−	0.333519i
$121$	−24.3789	+	75.0307i	−0.201479	+	0.620088i
$122$	−68.7838	+	35.0471i	−0.563802	+	0.287271i
$123$	8.39026	−	52.9740i	0.0682135	−	0.430683i
$124$		−	17.2044i		−	0.138745i
$125$	108.578	+	61.9345i	0.868621	+	0.495476i
$126$	64.3068			0.510372
$127$	95.2024	+	15.0786i	0.749625	+	0.118729i	0.519546	−	0.854443i	$-0.326101\pi$
$127$	95.2024	+	15.0786i	0.749625	+	0.118729i	0.230080	+	0.973172i	$0.426101\pi$
$128$	39.8787	+	78.2664i	0.311553	+	0.611456i
$129$	−55.2538	−	17.9530i	−0.428324	−	0.139171i
$130$	24.4599	−	29.2534i	0.188153	−	0.225026i
$131$	−3.98398	−	12.2614i	−0.0304121	−	0.0935987i	0.934698	−	0.355442i	$-0.115670\pi$
$131$	−3.98398	−	12.2614i	−0.0304121	−	0.0935987i	−0.965110	+	0.261843i	$0.915670\pi$
$132$	4.41512	+	4.41512i	0.0334478	+	0.0334478i
$133$	123.082	+	62.7136i	0.925431	+	0.471531i
$134$	−5.86196	+	8.06830i	−0.0437460	+	0.0602112i
$135$	87.5355	−	76.3610i	0.648411	−	0.565637i
$136$	93.4519	−	67.8968i	0.687146	−	0.499241i
$137$	−1.74431	−	11.0131i	−0.0127322	−	0.0803878i	0.980504	−	0.196499i	$-0.0629572\pi$
$137$	−1.74431	−	11.0131i	−0.0127322	−	0.0803878i	−0.993236	+	0.116111i	$0.962957\pi$
$138$	85.2147	−	13.4967i	0.617498	−	0.0978021i
$139$	16.7074	+	22.9958i	0.120197	+	0.165437i	0.864876	−	0.501986i	$-0.167397\pi$
$139$	16.7074	+	22.9958i	0.120197	+	0.165437i	−0.744678	+	0.667423i	$0.767397\pi$
$140$	16.4237	+	3.76166i	0.117312	+	0.0268690i
$141$	−13.0255	−	9.46360i	−0.0923796	−	0.0671177i
$142$	89.3467	−	175.353i	0.629202	−	1.23488i
$143$	−19.1377	+	19.1377i	−0.133830	+	0.133830i
$144$	−84.3446	+	27.4052i	−0.585727	+	0.190314i
$145$	232.893	−	146.091i	1.60616	−	1.00753i
$146$	−53.8822	+	165.832i	−0.369056	+	1.13584i
$147$	−29.5858	+	15.0747i	−0.201264	+	0.102549i
$148$	−4.52867	+	28.5929i	−0.0305991	+	0.193195i
$149$			46.6140i			0.312845i	0.987690	+	0.156423i	$0.0499962\pi$
$149$			46.6140i			0.312845i	−0.987690	+	0.156423i	$0.950004\pi$
$150$	−59.0432	+	31.6577i	−0.393621	+	0.211051i
$151$	−5.00531			−0.0331477			−0.0165739	−	0.999863i	$-0.505276\pi$
$151$	−5.00531			−0.0331477			−0.0165739	+	0.999863i	$0.505276\pi$
$152$	−226.340	−	35.8488i	−1.48908	−	0.235847i
$153$	42.2028	+	82.8276i	0.275835	+	0.541357i
$154$	57.9189	+	18.8190i	0.376097	+	0.122201i
$155$	−121.565	−	48.8699i	−0.784293	−	0.315290i
$156$	−1.24016	−	3.81683i	−0.00794976	−	0.0244668i
$157$	−57.4113	−	57.4113i	−0.365677	−	0.365677i	0.500221	−	0.865898i	$-0.333252\pi$
$157$	−57.4113	−	57.4113i	−0.365677	−	0.365677i	−0.865898	+	0.500221i	$0.833252\pi$
$158$	181.946	+	92.7061i	1.15156	+	0.586747i
$159$	32.2916	−	44.4455i	0.203092	−	0.279532i
$160$	−51.7559	+	4.61874i	−0.323474	+	0.0288671i
$161$	−133.686	+	97.1285i	−0.830347	+	0.603282i
$162$	−7.90071	−	49.8831i	−0.0487698	−	0.307921i
$163$	−191.803	+	30.3786i	−1.17671	+	0.186372i	−0.714004	−	0.700142i	$-0.753120\pi$
$163$	−191.803	+	30.3786i	−1.17671	+	0.186372i	−0.462703	+	0.886514i	$0.653120\pi$
$164$	−14.1230	−	19.4387i	−0.0861160	−	0.118529i
$165$	43.7383	−	18.6556i	0.265080	−	0.113064i
$166$	−91.0713	−	66.1672i	−0.548622	−	0.398597i
$167$	−106.874	+	209.753i	−0.639966	+	1.25600i	0.312082	+	0.950055i	$0.398974\pi$
$167$	−106.874	+	209.753i	−0.639966	+	1.25600i	−0.952048	+	0.305948i	$0.901026\pi$
$168$	−45.2882	+	45.2882i	−0.269573	+	0.269573i
$169$	−144.184	+	46.8483i	−0.853161	+	0.277209i
$170$	−30.2154	−	120.296i	−0.177738	−	0.707623i
$171$	56.9886	−	175.393i	0.333267	−	1.02569i
$172$	−23.1901	+	11.8159i	−0.134826	+	0.0686974i
$173$	27.5428	−	173.898i	0.159207	−	1.00519i	−0.770646	−	0.637263i	$-0.780067\pi$
$173$	27.5428	−	173.898i	0.159207	−	1.00519i	0.929853	−	0.367930i	$-0.119933\pi$
$174$			147.346i			0.846818i
$175$	73.2320	−	105.364i	0.418469	−	0.602080i
$176$	−83.9863			−0.477195
$177$	34.9230	+	5.53126i	0.197305	+	0.0312501i
$178$	−9.72771	−	19.0917i	−0.0546501	−	0.107257i
$179$	43.5329	+	14.1447i	0.243200	+	0.0790206i	0.428081	−	0.903740i	$-0.359190\pi$
$179$	43.5329	+	14.1447i	0.243200	+	0.0790206i	−0.184881	+	0.982761i	$0.559190\pi$
$180$	1.53008	−	22.4418i	0.00850047	−	0.124677i
$181$	62.2354	+	191.541i	0.343842	+	1.05824i	0.962201	+	0.272341i	$0.0877979\pi$
$181$	62.2354	+	191.541i	0.343842	+	1.05824i	−0.618359	+	0.785896i	$0.712202\pi$
$182$	−27.6782	−	27.6782i	−0.152078	−	0.152078i
$183$	55.1307	+	28.0905i	0.301260	+	0.153500i
$184$	161.129	−	221.775i	0.875702	−	1.20530i
$185$	189.172	+	113.219i	1.02255	+	0.611993i
$186$	56.8105	−	41.2753i	0.305433	−	0.221910i
$187$	13.7716	+	86.9503i	0.0736448	+	0.464975i
$188$	−7.12399	+	1.12833i	−0.0378936	+	0.00600175i
$189$	−70.0882	−	96.4681i	−0.370837	−	0.510413i
$190$	−126.365	+	211.138i	−0.665081	+	1.11125i
$191$	60.1244	+	43.6829i	0.314787	+	0.228706i	0.733948	−	0.679206i	$-0.237676\pi$
$191$	60.1244	+	43.6829i	0.314787	+	0.228706i	−0.419161	+	0.907912i	$0.637676\pi$
$192$	47.0891	−	92.4176i	0.245256	−	0.481342i
$193$	−8.10479	+	8.10479i	−0.0419937	+	0.0419937i	−0.727792	−	0.685798i	$-0.759453\pi$
$193$	−8.10479	+	8.10479i	−0.0419937	+	0.0419937i	0.685798	+	0.727792i	$0.259453\pi$
$194$	90.4686	−	29.3950i	0.466333	−	0.151521i
$195$	−30.4922	−	2.07896i	−0.156370	−	0.0106613i
$196$	−4.59675	+	14.1473i	−0.0234528	+	0.0721803i
$197$	326.552	−	166.387i	1.65763	−	0.844603i	0.662173	−	0.749351i	$-0.269634\pi$
$197$	326.552	−	166.387i	1.65763	−	0.844603i	0.995453	−	0.0952522i	$-0.0303658\pi$
$198$	12.7186	−	80.3018i	0.0642351	−	0.405565i
$199$			277.973i			1.39685i	0.715683	+	0.698426i	$0.246116\pi$
$199$			277.973i			1.39685i	−0.715683	+	0.698426i	$0.753884\pi$
$200$	−61.5272	+	203.778i	−0.307636	+	1.01889i
$201$	7.99339			0.0397681
$202$	−40.2213	−	6.37043i	−0.199115	−	0.0315368i
$203$	−128.121	−	251.451i	−0.631136	−	1.23867i
$204$	−12.4151	−	4.03390i	−0.0608582	−	0.0197740i
$205$	−177.470	+	44.5760i	−0.865706	+	0.217444i
$206$	−71.9582	−	221.464i	−0.349311	−	1.07507i
$207$	155.993	+	155.993i	0.753587	+	0.753587i
$208$	48.0982	+	24.5072i	0.231241	+	0.117823i
$209$	102.655	−	141.293i	0.491174	−	0.676043i
$210$	26.9810	+	63.2573i	0.128481	+	0.301225i
$211$	133.828	−	97.2318i	0.634257	−	0.460814i	−0.223616	−	0.974677i	$-0.571786\pi$
$211$	133.828	−	97.2318i	0.634257	−	0.460814i	0.857872	+	0.513863i	$0.171786\pi$
$212$	−3.85007	−	24.3084i	−0.0181607	−	0.114662i
$213$	−155.797	+	24.6758i	−0.731440	+	0.115849i
$214$	−90.7459	−	124.901i	−0.424046	−	0.583650i
$215$	17.6182	+	197.424i	0.0819453	+	0.918249i
$216$	160.034	+	116.271i	0.740896	+	0.538293i
$217$	−61.0592	+	119.835i	−0.281379	+	0.552237i
$218$	−121.310	+	121.310i	−0.556466	+	0.556466i
$219$	132.916	−	43.1869i	0.606921	−	0.197201i
$220$	7.94557	−	19.7648i	0.0361162	−	0.0898401i
$221$	17.4853	−	53.8142i	0.0791190	−	0.243503i
$222$	−105.281	+	53.6434i	−0.474239	+	0.241637i
$223$	32.3723	−	204.391i	0.145167	−	0.916550i	−0.802352	−	0.596851i	$-0.796418\pi$
$223$	32.3723	−	204.391i	0.145167	−	0.916550i	0.947519	−	0.319699i	$-0.103582\pi$
$224$			53.3392i			0.238122i
$225$	−154.226	−	74.5586i	−0.685451	−	0.331371i
$226$	19.8841			0.0879827
$227$	101.575	+	16.0878i	0.447465	+	0.0708716i	0.376101	−	0.926579i	$-0.377265\pi$
$227$	101.575	+	16.0878i	0.447465	+	0.0708716i	0.0713646	+	0.997450i	$0.477265\pi$
$228$	11.7571	+	23.0747i	0.0515664	+	0.101205i
$229$	−155.888	−	50.6512i	−0.680736	−	0.221184i	−0.0518182	−	0.998657i	$-0.516502\pi$
$229$	−155.888	−	50.6512i	−0.680736	−	0.221184i	−0.628917	+	0.777472i	$0.716502\pi$
$230$	−156.414	−	249.349i	−0.680062	−	1.08413i
$231$	−15.0836	−	46.4224i	−0.0652968	−	0.200963i
$232$	331.043	+	331.043i	1.42691	+	1.42691i
$233$	−8.91169	−	4.54073i	−0.0382476	−	0.0194881i	0.434762	−	0.900545i	$-0.356832\pi$
$233$	−8.91169	−	4.54073i	−0.0382476	−	0.0194881i	−0.473010	+	0.881057i	$0.656832\pi$
$234$	−30.7159	+	42.2768i	−0.131265	+	0.180670i
$235$	−12.2633	+	53.5428i	−0.0521843	+	0.227842i
$236$	12.8149	−	9.31058i	0.0543005	−	0.0394516i
$237$	−25.6036	−	161.655i	−0.108032	−	0.682087i
$238$	−125.754	+	19.9174i	−0.528376	+	0.0836865i
$239$	18.5330	+	25.5085i	0.0775440	+	0.106730i	0.846027	−	0.533140i	$-0.178988\pi$
$239$	18.5330	+	25.5085i	0.0775440	+	0.106730i	−0.768483	+	0.639870i	$0.778988\pi$
$240$	−62.3462	−	71.4697i	−0.259776	−	0.297791i
$241$	−243.401	−	176.841i	−1.00996	−	0.733780i	−0.0457606	−	0.998952i	$-0.514571\pi$
$241$	−243.401	−	176.841i	−1.00996	−	0.733780i	−0.964201	+	0.265172i	$0.914571\pi$
$242$	−65.4902	+	128.532i	−0.270621	+	0.531123i
$243$	−176.473	+	176.473i	−0.726226	+	0.726226i
$244$	26.3624	−	8.56566i	0.108043	−	0.0351052i
$245$	86.9070	+	72.6665i	0.354722	+	0.296598i
$246$	30.3056	−	93.2710i	0.123193	−	0.379150i
$247$	−100.019	+	50.9623i	−0.404936	+	0.206325i
$248$	34.9031	−	220.370i	0.140738	−	0.888587i
$249$			90.2258i			0.362353i
$250$	178.375	+	142.911i	0.713501	+	0.571646i
$251$	69.8662			0.278352			0.139176	−	0.990268i	$-0.455555\pi$
$251$	69.8662			0.278352			0.139176	+	0.990268i	$0.455555\pi$
$252$	−22.8060	−	3.61212i	−0.0905002	−	0.0143338i
$253$	94.8469	+	186.147i	0.374889	+	0.735761i
$254$	167.622	+	54.4638i	0.659930	+	0.214424i
$255$	−63.7689	+	76.2657i	−0.250074	+	0.299081i
$256$	−37.8473	−	116.482i	−0.147841	−	0.455007i
$257$	−255.557	−	255.557i	−0.994385	−	0.994385i	0.00559938	−	0.999984i	$-0.498218\pi$
$257$	−255.557	−	255.557i	−0.994385	−	0.994385i	−0.999984	+	0.00559938i	$0.998218\pi$
$258$	−94.6529	−	48.2280i	−0.366872	−	0.186930i
$259$	133.021	−	183.088i	0.513596	−	0.706904i
$260$	−10.3177	+	9.00062i	−0.0396836	+	0.0346178i
$261$	−304.804	+	221.453i	−1.16783	+	0.848480i
$262$	−3.68778	−	23.2837i	−0.0140755	−	0.0888691i
$263$	78.3156	−	12.4040i	0.297778	−	0.0471634i	−0.00575796	−	0.999983i	$-0.501833\pi$
$263$	78.3156	−	12.4040i	0.297778	−	0.0471634i	0.303536	+	0.952820i	$0.401833\pi$
$264$	47.5957	+	65.5098i	0.180287	+	0.248143i
$265$	−182.698	−	41.8447i	−0.689427	−	0.157905i
$266$	204.348	+	148.467i	0.768224	+	0.558148i
$267$	−7.79682	+	15.3021i	−0.0292016	+	0.0573113i
$268$	2.53211	−	2.53211i	0.00944816	−	0.00944816i
$269$	−16.7285	+	5.43543i	−0.0621879	+	0.0202061i	−0.339946	−	0.940445i	$-0.610409\pi$
$269$	−16.7285	+	5.43543i	−0.0621879	+	0.0202061i	0.277758	+	0.960651i	$0.410409\pi$
$270$	179.931	−	112.869i	0.666412	−	0.418033i
$271$	34.1637	−	105.145i	0.126065	−	0.387990i	−0.868028	−	0.496515i	$-0.834613\pi$
$271$	34.1637	−	105.145i	0.126065	−	0.387990i	0.994094	+	0.108525i	$0.0346128\pi$
$272$	156.450	−	79.7152i	0.575183	−	0.293071i
$273$	−4.90787	+	30.9871i	−0.0179775	+	0.113506i
$274$		−	20.3886i		−	0.0744110i
$275$	−117.087	−	112.286i	−0.425772	−	0.408312i
$276$	−30.9790			−0.112243
$277$	−147.138	−	23.3044i	−0.531185	−	0.0841315i	−0.114920	−	0.993375i	$-0.536661\pi$
$277$	−147.138	−	23.3044i	−0.531185	−	0.0841315i	−0.416265	+	0.909243i	$0.636661\pi$
$278$	23.5958	+	46.3093i	0.0848769	+	0.166580i
$279$	170.766	+	55.4853i	0.612065	+	0.198872i
$280$	202.739	+	81.5020i	0.724066	+	0.291078i
$281$	−34.2189	−	105.315i	−0.121775	−	0.374786i	0.871524	−	0.490352i	$-0.163132\pi$
$281$	−34.2189	−	105.315i	−0.121775	−	0.374786i	−0.993300	+	0.115566i	$0.963132\pi$
$282$	−20.8171	−	20.8171i	−0.0738194	−	0.0738194i
$283$	381.180	+	194.221i	1.34692	+	0.686292i	0.970713	−	0.240241i	$-0.0772266\pi$
$283$	381.180	+	194.221i	1.34692	+	0.686292i	0.376212	+	0.926534i	$0.377227\pi$
$284$	−41.5359	+	57.1692i	−0.146253	+	0.201300i
$285$	196.441	−	17.5306i	0.689267	−	0.0615107i
$286$	−40.0368	+	29.0885i	−0.139989	+	0.101708i
$287$	29.3837	+	185.521i	0.102382	+	0.646415i
$288$	70.3328	−	11.1396i	0.244211	−	0.0386792i
$289$	61.6877	+	84.9058i	0.213452	+	0.293792i
$290$	462.392	−	197.223i	1.59445	−	0.680080i
$291$	−61.6817	−	44.8144i	−0.211965	−	0.154001i
$292$	28.4238	−	55.7849i	0.0973419	−	0.191044i
$293$	11.2170	−	11.2170i	0.0382834	−	0.0382834i	−0.687706	−	0.725989i	$-0.741382\pi$
$293$	11.2170	−	11.2170i	0.0382834	−	0.0382834i	0.725989	+	0.687706i	$0.241382\pi$
$294$	−57.7439	+	18.7621i	−0.196408	+	0.0638168i
$295$	−29.3867	−	116.997i	−0.0996158	−	0.396598i
$296$	−116.015	+	357.056i	−0.391941	+	1.20627i
$297$	−134.325	+	68.4418i	−0.452271	+	0.230444i
$298$	−13.3335	+	84.1847i	−0.0447434	+	0.282499i
$299$		−	134.281i		−	0.449101i
$300$	22.7175	−	7.91074i	0.0757252	−	0.0263691i
$301$	203.463			0.675958
$302$	−9.03957	−	1.43173i	−0.0299324	−	0.00474082i
$303$	14.8180	+	29.0820i	0.0489043	+	0.0959802i
$304$	−331.293	−	107.644i	−1.08978	−	0.354091i
$305$	14.3591	−	210.606i	0.0470791	−	0.690512i
$306$	52.5259	+	161.658i	0.171653	+	0.528295i
$307$	−314.231	−	314.231i	−1.02355	−	1.02355i	−0.999716	−	0.0238366i	$-0.992412\pi$
$307$	−314.231	−	314.231i	−1.02355	−	1.02355i	−0.0238366	−	0.999716i	$-0.507588\pi$
$308$	−19.4836	−	9.92737i	−0.0632583	−	0.0322317i
$309$	−109.704	+	150.995i	−0.355030	+	0.488657i
$310$	−205.568	−	123.032i	−0.663123	−	0.396877i
$311$	145.002	−	105.350i	0.466244	−	0.338746i	−0.329732	−	0.944075i	$-0.606958\pi$
$311$	145.002	−	105.350i	0.466244	−	0.338746i	0.795976	+	0.605329i	$0.206958\pi$
$312$	−8.14180	−	51.4053i	−0.0260955	−	0.164761i
$313$	398.978	−	63.1919i	1.27469	−	0.201891i	0.517839	−	0.855478i	$-0.326737\pi$
$313$	398.978	−	63.1919i	1.27469	−	0.201891i	0.756852	+	0.653587i	$0.226737\pi$
$314$	−87.2626	−	120.107i	−0.277906	−	0.382505i
$315$	−90.3047	+	150.886i	−0.286681	+	0.479002i
$316$	−59.3188	−	43.0976i	−0.187718	−	0.136385i
$317$	122.836	−	241.080i	0.387497	−	0.760505i	−0.612044	−	0.790824i	$-0.709652\pi$
$317$	122.836	−	241.080i	0.387497	−	0.760505i	0.999540	+	0.0303190i	$0.00965233\pi$
$318$	71.0318	−	71.0318i	0.223370	−	0.223370i
$319$	−339.334	+	110.256i	−1.06374	+	0.345631i
$320$	−353.047	−	24.0707i	−1.10327	−	0.0752211i
$321$	−38.2382	+	117.685i	−0.119122	+	0.366620i
$322$	−269.219	+	137.174i	−0.836084	+	0.426006i
$323$	−57.1191	+	360.636i	−0.176839	+	1.11652i
$324$			18.1346i			0.0559708i
$325$	34.2898	+	98.4712i	0.105507	+	0.302988i
$326$	−355.086			−1.08922
$327$	135.812	+	21.5105i	0.415326	+	0.0657812i
$328$	−141.465	−	277.640i	−0.431294	−	0.846463i
$329$	53.6258	+	17.4241i	0.162996	+	0.0529608i
$330$	84.3275	−	21.1810i	0.255538	−	0.0641848i
$331$	191.695	+	589.977i	0.579140	+	1.78241i	0.621629	+	0.783312i	$0.286471\pi$
$331$	191.695	+	589.977i	0.579140	+	1.78241i	−0.0424888	+	0.999097i	$0.513529\pi$
$332$	28.5813	+	28.5813i	0.0860882	+	0.0860882i
$333$	−269.200	−	137.164i	−0.808408	−	0.411904i
$334$	−253.013	+	348.242i	−0.757523	+	1.04264i
$335$	−10.6992	−	25.0843i	−0.0319378	−	0.0748785i
$336$	−78.7629	+	57.2246i	−0.234413	+	0.170311i
$337$	−26.9235	−	169.988i	−0.0798917	−	0.504416i	−0.994891	−	0.100960i	$-0.967809\pi$
$337$	−26.9235	−	169.988i	−0.0798917	−	0.504416i	0.914999	−	0.403456i	$-0.132191\pi$
$338$	−273.797	+	43.3652i	−0.810050	+	0.128299i
$339$	−9.36766	−	12.8935i	−0.0276332	−	0.0380339i
$340$	3.95867	+	44.3595i	0.0116432	+	0.130469i
$341$	137.566	+	99.9474i	0.403419	+	0.293101i
$342$	153.091	−	300.458i	0.447635	−	0.878533i
$343$	260.062	−	260.062i	0.758198	−	0.758198i
$344$	−321.011	+	104.303i	−0.933171	+	0.303206i
$345$	−87.9973	+	218.896i	−0.255065	+	0.634481i
$346$	99.4844	−	306.182i	0.287527	−	0.884918i
$347$	370.185	−	188.619i	1.06682	−	0.543570i	0.169759	−	0.985486i	$-0.445701\pi$
$347$	370.185	−	188.619i	1.06682	−	0.543570i	0.897056	+	0.441916i	$0.145701\pi$
$348$	8.27646	−	52.2555i	0.0237829	−	0.150160i
$349$		−	677.633i		−	1.94164i	−0.239808	−	0.970820i	$-0.577084\pi$
$349$		−	677.633i		−	1.94164i	0.239808	−	0.970820i	$-0.422916\pi$
$350$	162.395	−	169.340i	0.463987	−	0.483828i
$351$	96.8978			0.276062
$352$	66.6063	+	10.5494i	0.189222	+	0.0299699i
$353$	189.176	+	371.279i	0.535910	+	1.05178i	0.987212	+	0.159412i	$0.0509597\pi$
$353$	189.176	+	371.279i	0.535910	+	1.05178i	−0.451302	+	0.892371i	$0.649040\pi$
$354$	61.4887	+	19.9789i	0.173697	+	0.0564375i
$355$	285.970	+	455.882i	0.805549	+	1.28417i
$356$	2.37749	+	7.31717i	0.00667835	+	0.0205539i
$357$	72.1593	+	72.1593i	0.202127	+	0.202127i
$358$	74.5743	+	37.9975i	0.208308	+	0.106138i
$359$	−99.0885	+	136.384i	−0.276012	+	0.379899i	−0.924408	−	0.381405i	$-0.875440\pi$
$359$	−99.0885	+	136.384i	−0.276012	+	0.379899i	0.648396	+	0.761304i	$0.275440\pi$
$360$	65.1271	−	284.351i	0.180909	−	0.789864i
$361$	293.973	−	213.584i	0.814330	−	0.591645i
$362$	57.6083	+	363.724i	0.159139	+	1.00476i
$363$	114.197	−	18.0871i	0.314594	−	0.0498267i
$364$	8.26124	+	11.3706i	0.0226957	+	0.0312380i
$365$	−313.434	−	359.301i	−0.858723	−	0.984386i
$366$	91.5308	+	66.5010i	0.250084	+	0.181697i
$367$	−91.6947	+	179.961i	−0.249849	+	0.490357i	−0.981534	−	0.191286i	$-0.938734\pi$
$367$	−91.6947	+	179.961i	−0.249849	+	0.490357i	0.731685	+	0.681643i	$0.238734\pi$
$368$	294.648	−	294.648i	0.800675	−	0.800675i
$369$	238.490	−	77.4902i	0.646315	−	0.210001i
$370$	309.259	+	258.584i	0.835834	+	0.698875i
$371$	−59.4543	+	182.981i	−0.160254	+	0.493211i
$372$	−22.4660	+	11.4470i	−0.0603924	+	0.0307715i
$373$	−42.9307	+	271.054i	−0.115096	+	0.726686i	0.860880	+	0.508808i	$0.169914\pi$
$373$	−42.9307	+	271.054i	−0.115096	+	0.726686i	−0.975976	+	0.217878i	$0.930086\pi$
$374$			160.971i			0.430405i
$375$	8.63339	−	182.992i	0.0230224	−	0.487978i
$376$	−93.5395			−0.248775
$377$	226.506	+	35.8751i	0.600812	+	0.0951593i
$378$	−98.9851	−	194.269i	−0.261865	−	0.513940i
$379$	223.313	+	72.5589i	0.589217	+	0.191448i	0.588425	−	0.808552i	$-0.299748\pi$
$379$	223.313	+	72.5589i	0.589217	+	0.191448i	0.000791498		1.00000i	$0.499748\pi$
$380$	56.6744	−	67.7809i	0.149143	−	0.178371i
$381$	−43.6530	−	134.350i	−0.114575	−	0.352625i
$382$	96.0894	+	96.0894i	0.251543	+	0.251543i
$383$	−497.316	−	253.395i	−1.29848	−	0.661607i	−0.338310	−	0.941035i	$-0.609855\pi$
$383$	−497.316	−	253.395i	−1.29848	−	0.661607i	−0.960167	+	0.279428i	$0.909855\pi$
$384$	75.6689	−	104.149i	0.197054	−	0.271222i
$385$	−125.490	+	109.470i	−0.325948	+	0.284339i
$386$	−16.9555	+	12.3189i	−0.0439262	+	0.0319143i
$387$	−42.4922	−	268.285i	−0.109799	−	0.693244i
$388$	−33.7353	+	5.34315i	−0.0869466	+	0.0137710i
$389$	85.3645	+	117.494i	0.219446	+	0.302042i	0.904519	−	0.426433i	$-0.140230\pi$
$389$	85.3645	+	117.494i	0.219446	+	0.302042i	−0.685073	+	0.728474i	$0.740230\pi$
$390$	−54.4742	−	12.4766i	−0.139677	−	0.0319914i
$391$	−353.362	−	256.732i	−0.903739	−	0.656605i
$392$	−87.5804	+	171.886i	−0.223419	+	0.438485i
$393$	−13.3605	+	13.3605i	−0.0339963	+	0.0339963i
$394$	637.346	−	207.086i	1.61763	−	0.525600i
$395$	−473.023	+	296.722i	−1.19753	+	0.751195i
$396$	−9.02113	+	27.7642i	−0.0227806	+	0.0701116i
$397$	−649.716	+	331.047i	−1.63657	+	0.833872i	−0.638639	+	0.769507i	$0.720502\pi$
$397$	−649.716	+	331.047i	−1.63657	+	0.833872i	−0.997926	+	0.0643647i	$0.979498\pi$
$398$	−79.5120	+	502.019i	−0.199779	+	1.26136i
$399$		−	202.451i		−	0.507395i
$400$	−140.831	+	291.313i	−0.352077	+	0.728281i
$401$	213.430			0.532245			0.266123	−	0.963939i	$-0.414257\pi$
$401$	213.430			0.532245			0.266123	+	0.963939i	$0.414257\pi$
$402$	14.4360	+	2.28645i	0.0359106	+	0.00568767i
$403$	−49.6179	−	97.3807i	−0.123121	−	0.241639i
$404$	13.9064	+	4.51847i	0.0344219	+	0.0111843i
$405$	128.138	+	51.5120i	0.316389	+	0.127190i
$406$	−159.460	−	490.768i	−0.392759	−	1.20879i
$407$	−202.319	−	202.319i	−0.497097	−	0.497097i
$408$	−150.840	−	76.8566i	−0.369705	−	0.188374i
$409$	−168.244	+	231.568i	−0.411355	+	0.566182i	−0.963548	−	0.267534i	$-0.913791\pi$
$409$	−168.244	+	231.568i	−0.411355	+	0.566182i	0.552193	+	0.833716i	$0.313791\pi$
$410$	−333.260	+	29.7404i	−0.812830	+	0.0725376i
$411$	−13.2206	+	9.60536i	−0.0321670	+	0.0233707i
$412$	13.0799	+	82.5830i	0.0317472	+	0.200444i
$413$	−122.304	+	19.3711i	−0.296137	+	0.0469034i
$414$	237.102	+	326.343i	0.572710	+	0.788267i
$415$	283.140	−	120.767i	0.682266	−	0.291005i
$416$	−35.0665	−	25.4773i	−0.0842944	−	0.0612435i
$417$	18.9122	−	37.1172i	0.0453529	−	0.0890101i
$418$	225.811	−	225.811i	0.540218	−	0.540218i
$419$	370.064	−	120.241i	0.883209	−	0.286972i	0.167920	−	0.985801i	$-0.446295\pi$
$419$	370.064	−	120.241i	0.883209	−	0.286972i	0.715289	+	0.698829i	$0.246295\pi$
$420$	−6.01549	−	23.9494i	−0.0143226	−	0.0570223i
$421$	−5.96539	+	18.3596i	−0.0141696	+	0.0436094i	−0.957891	−	0.287131i	$-0.907298\pi$
$421$	−5.96539	+	18.3596i	−0.0141696	+	0.0436094i	0.943722	+	0.330740i	$0.107298\pi$
$422$	269.506	−	137.320i	0.638639	−	0.325403i
$423$	11.7758	−	74.3496i	0.0278388	−	0.175767i
$424$		−	319.174i		−	0.752770i
$425$	324.686	+	98.0333i	0.763967	+	0.230667i
$426$	−288.427			−0.677058
$427$	−214.024	−	33.8981i	−0.501227	−	0.0793866i
$428$	25.1668	+	49.3926i	0.0588009	+	0.115403i
$429$	37.7238	+	12.2572i	0.0879342	+	0.0285716i
$430$	−24.6529	+	361.586i	−0.0573324	+	0.840898i
$431$	−158.150	−	486.736i	−0.366938	−	1.12932i	−0.948759	−	0.316002i	$-0.897659\pi$
$431$	−158.150	−	486.736i	−0.366938	−	1.12932i	0.581821	−	0.813317i	$-0.302341\pi$
$432$	212.619	+	212.619i	0.492174	+	0.492174i
$433$	−491.655	−	250.511i	−1.13546	−	0.578546i	−0.217833	−	0.975986i	$-0.569899\pi$
$433$	−491.655	−	250.511i	−1.13546	−	0.578546i	−0.917628	+	0.397440i	$0.869899\pi$
$434$	−144.551	+	198.957i	−0.333066	+	0.458426i
$435$	−345.725	−	206.915i	−0.794770	−	0.475667i
$436$	49.8357	−	36.2078i	0.114302	−	0.0830454i
$437$	135.552	+	855.843i	0.310188	+	1.95845i
$438$	252.399	−	39.9760i	0.576253	−	0.0912695i
$439$	−156.461	−	215.349i	−0.356402	−	0.490545i	0.592740	−	0.805394i	$-0.298046\pi$
$439$	−156.461	−	215.349i	−0.356402	−	0.490545i	−0.949142	+	0.314849i	$0.898046\pi$
$440$	141.871	−	237.046i	0.322435	−	0.538741i
$441$	−125.598	−	91.2520i	−0.284802	−	0.206921i
$442$	46.9715	−	92.1868i	0.106270	−	0.208567i
$443$	−602.533	+	602.533i	−1.36012	+	1.36012i	−0.486364	+	0.873756i	$0.661677\pi$
$443$	−602.533	+	602.533i	−1.36012	+	1.36012i	−0.873756	+	0.486364i	$0.838323\pi$
$444$	40.3505	−	13.1107i	0.0908795	−	0.0295285i
$445$	58.4561	+	3.98553i	0.131362	+	0.00895625i
$446$	116.929	−	359.869i	0.262172	−	0.806881i
$447$	60.8697	−	31.0147i	0.136174	−	0.0693840i
$448$	−56.8246	+	358.776i	−0.126841	+	0.800840i
$449$		−	128.073i		−	0.285240i	−0.989778	−	0.142620i	$-0.954447\pi$
$449$		−	128.073i		−	0.285240i	0.989778	−	0.142620i	$-0.0455527\pi$
$450$	−257.206	−	178.768i	−0.571568	−	0.397262i
$451$	237.477			0.526557
$452$	−7.05178	−	1.11689i	−0.0156013	−	0.00247100i
$453$	3.33029	+	6.53606i	0.00735163	+	0.0144284i
$454$	178.842	+	58.1092i	0.393925	+	0.127994i
$455$	103.811	−	26.0747i	0.228155	−	0.0573070i
$456$	103.784	+	319.413i	0.227596	+	0.700467i
$457$	246.412	+	246.412i	0.539196	+	0.539196i	0.923293	−	0.384097i	$-0.125487\pi$
$457$	246.412	+	246.412i	0.539196	+	0.539196i	−0.384097	+	0.923293i	$0.625487\pi$
$458$	−267.046	−	136.067i	−0.583069	−	0.297089i
$459$	185.259	−	254.987i	0.403614	−	0.555527i
$460$	41.4654	+	97.2162i	0.0901422	+	0.211339i
$461$	250.643	−	182.103i	0.543694	−	0.395017i	−0.281761	−	0.959485i	$-0.590919\pi$
$461$	250.643	−	182.103i	0.543694	−	0.395017i	0.825455	+	0.564468i	$0.190919\pi$
$462$	−13.9621	−	88.1532i	−0.0302210	−	0.190808i
$463$	372.239	−	58.9568i	0.803971	−	0.127337i	0.259094	−	0.965852i	$-0.416576\pi$
$463$	372.239	−	58.9568i	0.803971	−	0.127337i	0.544878	+	0.838516i	$0.316576\pi$
$464$	418.295	+	575.733i	0.901497	+	1.24080i
$465$	17.0681	+	191.259i	0.0367056	+	0.411309i
$466$	−14.7956	−	10.7497i	−0.0317503	−	0.0230680i
$467$	−86.5405	+	169.845i	−0.185312	+	0.363695i	−0.964908	−	0.262587i	$-0.915424\pi$
$467$	−86.5405	+	169.845i	−0.185312	+	0.363695i	0.779597	+	0.626282i	$0.215424\pi$
$468$	13.2679	−	13.2679i	0.0283502	−	0.0283502i
$469$	−26.6237	+	8.65055i	−0.0567669	+	0.0184447i
$470$	−37.4630	+	93.1903i	−0.0797085	+	0.198277i
$471$	−36.7704	+	113.168i	−0.0780688	+	0.240271i
$472$	183.033	−	93.2602i	0.387783	−	0.197585i
$473$	40.2408	−	254.071i	0.0850757	−	0.537147i
$474$		−	299.272i		−	0.631375i
$475$	−317.949	−	592.992i	−0.669367	−	1.24841i
$476$	45.7165			0.0960431
$477$	253.695	+	40.1813i	0.531855	+	0.0842376i
$478$	26.1741	+	51.3695i	0.0547575	+	0.107468i
$479$	−744.274	−	241.829i	−1.55381	−	0.504863i	−0.598663	−	0.801001i	$-0.704301\pi$
$479$	−744.274	−	241.829i	−1.55381	−	0.504863i	−0.955145	+	0.296139i	$0.904301\pi$
$480$	40.4671	+	64.5111i	0.0843065	+	0.134398i
$481$	56.8293	+	174.903i	0.118148	+	0.363623i
$482$	−388.997	−	388.997i	−0.807048	−	0.807048i
$483$	215.781	+	109.946i	0.446751	+	0.227631i
$484$	30.4454	−	41.9045i	0.0629037	−	0.0865795i
$485$	−58.0723	+	253.549i	−0.119737	+	0.522782i
$486$	−369.188	+	268.231i	−0.759647	+	0.551916i
$487$	−61.8159	−	390.290i	−0.126932	−	0.801417i	−0.966218	−	0.257727i	$-0.917027\pi$
$487$	−61.8159	−	390.290i	−0.126932	−	0.801417i	0.839286	−	0.543690i	$-0.182973\pi$
$488$	355.050	−	56.2344i	0.727562	−	0.115235i
$489$	167.286	+	230.249i	0.342097	+	0.470857i
$490$	136.168	+	156.095i	0.277894	+	0.318560i
$491$	356.707	+	259.163i	0.726490	+	0.527826i	0.888451	−	0.458971i	$-0.151782\pi$
$491$	356.707	+	259.163i	0.726490	+	0.527826i	−0.161961	+	0.986797i	$0.551782\pi$
$492$	−15.9867	+	31.3758i	−0.0324934	+	0.0637719i
$493$	527.463	−	527.463i	1.06990	−	1.06990i
$494$	−195.212	+	63.4282i	−0.395166	+	0.128397i
$495$	170.555	+	142.608i	0.344556	+	0.288097i
$496$	104.804	−	322.554i	0.211298	−	0.650310i
$497$	492.209	−	250.793i	0.990360	−	0.504614i
$498$	−25.8084	+	162.948i	−0.0518240	+	0.327204i
$499$			553.396i			1.10901i	0.832180	+	0.554505i	$0.187092\pi$
$499$			553.396i			1.10901i	−0.832180	+	0.554505i	$0.812908\pi$
$500$	−55.2324	−	60.7021i	−0.110465	−	0.121404i
$501$	345.009			0.688641
$502$	126.178	+	19.9847i	0.251351	+	0.0398101i
$503$	−117.168	−	229.955i	−0.232938	−	0.457167i	0.744718	−	0.667380i	$-0.232584\pi$
$503$	−117.168	−	229.955i	−0.232938	−	0.457167i	−0.977656	+	0.210213i	$0.932584\pi$
$504$	−284.792	−	92.5346i	−0.565064	−	0.183600i
$505$	71.4291	−	85.4271i	0.141444	−	0.169163i
$506$	118.047	+	363.312i	0.233295	+	0.718008i
$507$	157.109	+	157.109i	0.309879	+	0.309879i
$508$	−56.3870	−	28.7306i	−0.110998	−	0.0565563i
$509$	−91.2224	+	125.557i	−0.179219	+	0.246674i	−0.889170	−	0.457578i	$-0.848717\pi$
$509$	−91.2224	+	125.557i	−0.179219	+	0.246674i	0.709951	+	0.704251i	$0.248717\pi$
$510$	−136.982	+	119.495i	−0.268591	+	0.234304i
$511$	−395.966	+	287.686i	−0.774885	+	0.562987i
$512$	−89.9984	−	568.228i	−0.175778	−	1.10982i
$513$	−617.578	+	97.8148i	−1.20386	+	0.190672i
$514$	−388.435	−	534.635i	−0.755710	−	1.04015i
$515$	620.680	+	142.159i	1.20520	+	0.276037i
$516$	30.8591	+	22.4205i	0.0598045	+	0.0434505i
$517$	32.3641	−	63.5180i	0.0625997	−	0.122859i
$518$	292.607	−	292.607i	0.564878	−	0.564878i
$519$	−245.407	+	79.7374i	−0.472845	+	0.153637i
$520$	−150.419	+	94.3560i	−0.289267	+	0.181454i
$521$	−128.145	+	394.388i	−0.245959	+	0.756983i	0.749519	+	0.661983i	$0.230285\pi$
$521$	−128.145	+	394.388i	−0.245959	+	0.756983i	−0.995477	+	0.0949999i	$0.969715\pi$
$522$	−613.821	+	312.757i	−1.17590	+	0.599152i
$523$	−32.5786	+	205.693i	−0.0622918	+	0.393295i	0.936768	+	0.349950i	$0.113801\pi$
$523$	−32.5786	+	205.693i	−0.0622918	+	0.393295i	−0.999060	+	0.0433450i	$0.986199\pi$
$524$			8.46458i			0.0161538i
$525$	−186.312	−	25.5241i	−0.354880	−	0.0486174i
$526$	144.986			0.275638
$527$	−351.122	−	55.6123i	−0.666266	−	0.105526i
$528$	55.8804	+	109.671i	0.105834	+	0.207711i
$529$	−482.701	−	156.839i	−0.912479	−	0.296482i
$530$	−317.983	−	127.831i	−0.599968	−	0.241190i
$531$	51.0853	+	157.224i	0.0962058	+	0.296091i
$532$	−64.1313	−	64.1313i	−0.120548	−	0.120548i
$533$	−136.001	−	69.2959i	−0.255161	−	0.130011i
$534$	−18.4581	+	25.4054i	−0.0345657	+	0.0475756i
$535$	420.493	−	37.5251i	0.785968	−	0.0701404i
$536$	37.5705	−	27.2965i	0.0700941	−	0.0509264i
$537$	−10.4942	−	66.2575i	−0.0195422	−	0.123385i
$538$	−31.7665	+	5.03132i	−0.0590455	+	0.00935189i
$539$	−86.4171	−	118.943i	−0.160329	−	0.220673i
$540$	−70.1515	+	29.9216i	−0.129910	+	0.0554103i
$541$	141.270	+	102.638i	0.261127	+	0.189720i	0.710644	−	0.703552i	$-0.248404\pi$
$541$	141.270	+	102.638i	0.261127	+	0.189720i	−0.449517	+	0.893272i	$0.648404\pi$
$542$	91.7755	−	180.120i	0.169328	−	0.332324i
$543$	208.711	−	208.711i	0.384366	−	0.384366i
$544$	−134.087	+	43.5676i	−0.246484	+	0.0800875i
$545$	−114.281	−	454.986i	−0.209691	−	0.834837i
$546$	−17.7272	+	54.5587i	−0.0324674	+	0.0999244i
$547$	41.4187	−	21.1039i	0.0757197	−	0.0385811i	−0.415721	−	0.909492i	$-0.636471\pi$
$547$	41.4187	−	21.1039i	0.0757197	−	0.0385811i	0.491440	+	0.870911i	$0.336471\pi$
$548$	−1.14523	+	7.23071i	−0.00208984	+	0.0131947i
$549$			289.290i			0.526940i
$550$	−179.341	−	236.280i	−0.326075	−	0.429600i
$551$	−1479.85			−2.68576
$552$	−396.807	−	62.8480i	−0.718853	−	0.113855i
$553$	260.223	+	510.716i	0.470566	+	0.923537i
$554$	−259.065	−	84.1755i	−0.467627	−	0.151941i
$555$	21.9782	−	322.356i	0.0396003	−	0.580821i
$556$	−5.76691	−	17.7487i	−0.0103721	−	0.0319222i
$557$	3.64987	+	3.64987i	0.00655272	+	0.00655272i	0.710376	−	0.703823i	$-0.248525\pi$
$557$	3.64987	+	3.64987i	0.00655272	+	0.00655272i	−0.703823	+	0.710376i	$0.748525\pi$
$558$	292.532	+	149.053i	0.524251	+	0.267119i
$559$	−97.1835	+	133.762i	−0.173852	+	0.239287i
$560$	285.002	+	170.573i	0.508933	+	0.304595i
$561$	104.379	−	75.8358i	0.186059	−	0.135180i
$562$	−31.6747	−	199.986i	−0.0563607	−	0.355848i
$563$	908.523	−	143.896i	1.61372	−	0.255588i	0.716635	−	0.697449i	$-0.245682\pi$
$563$	908.523	−	143.896i	1.61372	−	0.255588i	0.897084	+	0.441861i	$0.145682\pi$
$564$	6.21336	+	8.55195i	0.0110166	+	0.0151630i
$565$	−27.9228	+	46.6549i	−0.0494209	+	0.0825750i
$566$	632.854	+	459.796i	1.11812	+	0.812360i
$567$	64.3603	−	126.314i	0.113510	−	0.222776i
$568$	−648.009	+	648.009i	−1.14086	+	1.14086i
$569$	1000.14	−	324.965i	1.75772	−	0.571116i	0.760756	−	0.649038i	$-0.224828\pi$
$569$	1000.14	−	324.965i	1.75772	−	0.571116i	0.996959	+	0.0779216i	$0.0248284\pi$
$570$	359.786	+	24.5302i	0.631204	+	0.0430355i
$571$	−91.2802	+	280.932i	−0.159860	+	0.491999i	−0.998621	−	0.0525011i	$-0.983281\pi$
$571$	−91.2802	+	280.932i	−0.159860	+	0.491999i	0.838761	+	0.544500i	$0.183281\pi$
$572$	15.8327	−	8.06718i	0.0276796	−	0.0141035i
$573$	17.0384	−	107.576i	0.0297355	−	0.187742i
$574$			343.456i			0.598355i
$575$	804.708	−	16.8453i	1.39949	−	0.0292962i
$576$	484.948			0.841924
$577$	−431.463	−	68.3370i	−0.747769	−	0.118435i	−0.229092	−	0.973405i	$-0.573576\pi$
$577$	−431.463	−	68.3370i	−0.747769	−	0.118435i	−0.518678	+	0.854970i	$0.673576\pi$
$578$	87.1212	+	170.985i	0.150729	+	0.295822i
$579$	15.9760	+	5.19090i	0.0275923	+	0.00896529i
$580$	−175.063	+	43.9714i	−0.301832	+	0.0758128i
$581$	−97.6435	−	300.516i	−0.168061	−	0.517239i
$582$	−98.5782	−	98.5782i	−0.169378	−	0.169378i
$583$	216.735	+	110.432i	0.371759	+	0.189421i
$584$	477.251	−	656.879i	0.817210	−	1.12479i
$585$	−56.0622	−	131.438i	−0.0958328	−	0.224681i
$586$	23.4665	−	17.0494i	0.0400452	−	0.0290945i
$587$	−72.7149	−	459.104i	−0.123876	−	0.782119i	−0.968911	−	0.247409i	$-0.920421\pi$
$587$	−72.7149	−	459.104i	−0.123876	−	0.782119i	0.845036	−	0.534710i	$-0.179579\pi$
$588$	21.5324	−	3.41040i	0.0366197	−	0.00580000i
$589$	414.542	+	570.569i	0.703807	+	0.968708i
$590$	−19.6063	−	219.701i	−0.0332310	−	0.372375i
$591$	−434.544	−	315.715i	−0.735269	−	0.534204i
$592$	−259.084	+	508.481i	−0.437642	+	0.858921i
$593$	292.352	−	292.352i	0.493006	−	0.493006i	−0.416246	−	0.909252i	$-0.636655\pi$
$593$	292.352	−	292.352i	0.493006	−	0.493006i	0.909252	+	0.416246i	$0.136655\pi$
$594$	−262.167	+	85.1832i	−0.441359	+	0.143406i
$595$	129.860	−	323.030i	0.218252	−	0.542908i
$596$	9.45733	−	29.1067i	0.0158680	−	0.0488367i
$597$	362.985	−	184.950i	0.608015	−	0.309799i
$598$	38.4101	−	242.512i	0.0642309	−	0.405538i
$599$			747.602i			1.24808i	0.781391	+	0.624042i	$0.214511\pi$
$599$			747.602i			1.24808i	−0.781391	+	0.624042i	$0.785489\pi$
$600$	307.035	−	55.2401i	0.511726	−	0.0920668i
$601$	96.7209			0.160933			0.0804666	−	0.996757i	$-0.474359\pi$
$601$	96.7209			0.160933			0.0804666	+	0.996757i	$0.474359\pi$
$602$	367.454	+	58.1990i	0.610389	+	0.0966761i
$603$	16.9668	+	33.2992i	0.0281373	+	0.0552225i
$604$	3.12541	+	1.01551i	0.00517452	+	0.00168130i
$605$	−209.613	−	334.157i	−0.346468	−	0.552325i
$606$	18.4426	+	56.7606i	0.0304334	+	0.0936643i
$607$	664.195	+	664.195i	1.09423	+	1.09423i	0.995072	+	0.0991528i	$0.0316133\pi$
$607$	664.195	+	664.195i	1.09423	+	1.09423i	0.0991528	+	0.995072i	$0.468387\pi$
$608$	249.215	+	126.981i	0.409893	+	0.208851i
$609$	−243.106	+	334.606i	−0.399188	+	0.549436i
$610$	86.1747	−	376.247i	0.141270	−	0.616798i
$611$	−37.0692	+	26.9323i	−0.0606697	+	0.0440791i
$612$	−9.54766	−	60.2815i	−0.0156007	−	0.0984992i
$613$	−348.721	+	55.2320i	−0.568876	+	0.0901011i	−0.434245	−	0.900795i	$-0.642985\pi$
$613$	−348.721	+	55.2320i	−0.568876	+	0.0901011i	−0.134631	+	0.990896i	$0.542985\pi$
$614$	−477.617	−	657.383i	−0.777877	−	1.07066i
$615$	176.288	+	202.086i	0.286647	+	0.328595i
$616$	−229.423	−	166.685i	−0.372440	−	0.270593i
$617$	−455.572	+	894.111i	−0.738366	+	1.44913i	0.149374	+	0.988781i	$0.452274\pi$
$617$	−455.572	+	894.111i	−0.738366	+	1.44913i	−0.887740	+	0.460345i	$0.847726\pi$
$618$	−241.316	+	241.316i	−0.390480	+	0.390480i
$619$	−398.451	+	129.464i	−0.643700	+	0.209151i	−0.612634	−	0.790366i	$-0.709890\pi$
$619$	−398.451	+	129.464i	−0.643700	+	0.209151i	−0.0310659	+	0.999517i	$0.509890\pi$
$620$	65.9928	+	55.1793i	0.106440	+	0.0889989i
$621$	231.136	−	711.363i	0.372200	−	1.14551i
$622$	292.007	−	148.785i	0.469465	−	0.239204i
$623$	9.40878	−	59.4047i	0.0151024	−	0.0953527i
$624$		−	79.1137i		−	0.126785i
$625$	−585.807	+	217.842i	−0.937291	+	0.348547i
$626$	738.629			1.17992
$627$	−252.806	−	40.0405i	−0.403199	−	0.0638605i
$628$	24.2008	+	47.4967i	0.0385362	+	0.0756316i
$629$	568.909	+	184.850i	0.904467	+	0.293879i
$630$	−206.250	+	246.668i	−0.327380	+	0.391537i
$631$	−76.6332	−	235.853i	−0.121447	−	0.373776i	0.871790	−	0.489880i	$-0.162959\pi$
$631$	−76.6332	−	235.853i	−0.121447	−	0.373776i	−0.993237	+	0.116104i	$0.962959\pi$
$632$	−672.374	−	672.374i	−1.06388	−	1.06388i
$633$	−216.010	−	110.063i	−0.341249	−	0.173875i
$634$	290.801	−	400.254i	0.458677	−	0.631315i
$635$	−363.179	+	316.817i	−0.571935	+	0.498924i
$636$	−29.1809	+	21.2011i	−0.0458819	+	0.0333351i
$637$	14.7827	+	93.3341i	0.0232067	+	0.146521i
$638$	−644.374	+	102.059i	−1.00999	+	0.159967i
$639$	−433.489	−	596.647i	−0.678387	−	0.933720i
$640$	−428.117	−	98.0548i	−0.668932	−	0.153211i
$641$	−466.730	−	339.099i	−0.728128	−	0.529016i	0.160843	−	0.986980i	$-0.448579\pi$
$641$	−466.730	−	339.099i	−0.728128	−	0.529016i	−0.888971	+	0.457964i	$0.848579\pi$
$642$	−102.721	+	201.601i	−0.160002	+	0.314021i
$643$	−796.206	+	796.206i	−1.23827	+	1.23827i	−0.277558	+	0.960709i	$0.589525\pi$
$643$	−796.206	+	796.206i	−1.23827	+	1.23827i	−0.960709	+	0.277558i	$0.910475\pi$
$644$	103.182	−	33.5259i	0.160221	−	0.0520588i
$645$	246.078	−	154.362i	0.381517	−	0.239322i
$646$	−206.314	+	634.969i	−0.319371	+	0.982924i
$647$	−237.470	+	120.997i	−0.367033	+	0.187013i	−0.627773	−	0.778396i	$-0.716033\pi$
$647$	−237.470	+	120.997i	−0.367033	+	0.187013i	0.260740	+	0.965409i	$0.416033\pi$
$648$	−36.7901	+	232.284i	−0.0567748	+	0.358462i
$649$			156.556i			0.241227i
$650$	33.7604	+	187.647i	0.0519391	+	0.288688i
$651$	197.110			0.302780
$652$	125.929	+	19.9452i	0.193143	+	0.0305908i
$653$	−295.181	−	579.325i	−0.452038	−	0.887174i	−0.998756	−	0.0498579i	$-0.984123\pi$
$653$	−295.181	−	579.325i	−0.452038	−	0.887174i	0.546718	−	0.837317i	$-0.315877\pi$
$654$	239.123	+	77.6957i	0.365631	+	0.118801i
$655$	59.8102	+	24.0440i	0.0913133	+	0.0367084i
$656$	−146.368	−	450.475i	−0.223122	−	0.686700i
$657$	462.037	+	462.037i	0.703252	+	0.703252i
$658$	91.8641	+	46.8071i	0.139611	+	0.0711354i
$659$	366.844	−	504.918i	0.556668	−	0.766188i	−0.434230	−	0.900802i	$-0.642979\pi$
$659$	366.844	−	504.918i	0.556668	−	0.766188i	0.990898	+	0.134614i	$0.0429795\pi$
$660$	−31.0960	+	2.77503i	−0.0471152	+	0.00420459i
$661$	−232.940	+	169.241i	−0.352405	+	0.256037i	−0.749877	−	0.661577i	$-0.769887\pi$
$661$	−232.940	+	169.241i	−0.352405	+	0.256037i	0.397472	+	0.917614i	$0.369887\pi$
$662$	177.443	+	1120.33i	0.268041	+	1.69234i
$663$	−81.9058	+	12.9726i	−0.123538	+	0.0195665i
$664$	308.111	+	424.078i	0.464023	+	0.638672i
$665$	−635.316	+	270.980i	−0.955362	+	0.407489i
$666$	−446.939	−	324.720i	−0.671080	−	0.487568i
$667$	803.671	−	1577.29i	1.20490	−	2.36476i
$668$	109.290	−	109.290i	0.163608	−	0.163608i
$669$	−288.437	+	93.7190i	−0.431147	+	0.140088i
$670$	−12.1475	−	48.3626i	−0.0181306	−	0.0721830i
$671$	−84.6590	+	260.554i	−0.126168	+	0.388307i
$672$	69.6517	−	35.4893i	0.103648	−	0.0528115i
$673$	196.643	−	1241.55i	0.292189	−	1.84481i	−0.207036	−	0.978333i	$-0.566382\pi$
$673$	196.643	−	1241.55i	0.292189	−	1.84481i	0.499225	−	0.866472i	$-0.333618\pi$
$674$		−	314.700i		−	0.466913i
$675$	12.1556	+	580.680i	0.0180084	+	0.860266i
$676$	99.5363			0.147243
$677$	−20.8211	−	3.29774i	−0.0307549	−	0.00487110i	0.141038	−	0.990004i	$-0.454956\pi$
$677$	−20.8211	−	3.29774i	−0.0307549	−	0.00487110i	−0.171793	+	0.985133i	$0.554956\pi$
$678$	−13.2299	−	25.9651i	−0.0195131	−	0.0382967i
$679$	253.942	+	82.5109i	0.373995	+	0.121518i
$680$	−39.2871	+	576.227i	−0.0577752	+	0.847392i
$681$	−46.5749	−	143.343i	−0.0683919	−	0.210489i
$682$	219.854	+	219.854i	0.322367	+	0.322367i
$683$	930.248	+	473.985i	1.36200	+	0.693975i	0.973759	−	0.227582i	$-0.0730819\pi$
$683$	930.248	+	473.985i	1.36200	+	0.693975i	0.388244	+	0.921557i	$0.373082\pi$
$684$	−71.1697	+	97.9566i	−0.104049	+	0.143211i
$685$	47.8387	+	28.6313i	0.0698375	+	0.0417975i
$686$	544.060	−	395.282i	0.793090	−	0.576214i
$687$	37.5789	+	237.264i	0.0547000	+	0.345362i
$688$	−506.754	+	80.2620i	−0.736561	+	0.116660i
$689$	−91.8982	−	126.487i	−0.133379	−	0.183581i
$690$	−221.536	+	370.155i	−0.321067	+	0.536456i
$691$	813.904	+	591.336i	1.17786	+	0.855768i	0.991929	−	0.126794i	$-0.0404686\pi$
$691$	813.904	+	591.336i	1.17786	+	0.855768i	0.185935	+	0.982562i	$0.440469\pi$
$692$	−52.4799	+	102.998i	−0.0758379	+	0.148840i
$693$	161.372	−	161.372i	0.232860	−	0.232860i
$694$	722.506	−	234.756i	1.04107	−	0.338266i
$695$	−141.793	−	9.66741i	−0.204018	−	0.0139099i
$696$	212.025	−	652.545i	0.304633	−	0.937564i
$697$	−442.373	+	225.400i	−0.634681	+	0.323386i
$698$	193.831	−	1223.80i	0.277695	−	1.75330i
$699$			14.6583i			0.0209704i
$700$	−67.1044	+	50.9336i	−0.0958634	+	0.0727623i
$701$	−1006.63			−1.43599			−0.717994	−	0.696049i	$-0.754940\pi$
$701$	−1006.63			−1.43599			−0.717994	+	0.696049i	$0.754940\pi$
$702$	174.997	+	27.7168i	0.249284	+	0.0394826i
$703$	−538.760	−	1057.38i	−0.766373	−	1.50409i
$704$	436.776	+	141.917i	0.620420	+	0.201587i
$705$	78.0769	−	19.6110i	0.110747	−	0.0278170i
$706$	235.450	+	724.642i	0.333499	+	1.02640i
$707$	−80.8274	−	80.8274i	−0.114324	−	0.114324i
$708$	−20.6844	−	10.5392i	−0.0292153	−	0.0148859i
$709$	201.533	−	277.387i	0.284250	−	0.391236i	−0.642886	−	0.765962i	$-0.722263\pi$
$709$	201.533	−	277.387i	0.284250	−	0.391236i	0.927136	+	0.374726i	$0.122263\pi$
$710$	386.059	+	905.120i	0.543746	+	1.27482i
$711$	619.081	−	449.789i	0.870718	−	0.632614i
$712$	15.6085	+	98.5481i	0.0219220	+	0.138410i
$713$	−833.265	+	131.976i	−1.16867	+	0.185100i
$714$	109.679	+	150.960i	0.153612	+	0.211429i
$715$	−12.0286	−	134.788i	−0.0168232	−	0.188515i
$716$	−24.3130	−	17.6644i	−0.0339567	−	0.0246710i
$717$	20.9787	−	41.1730i	0.0292590	−	0.0574240i
$718$	−217.965	+	217.965i	−0.303572	+	0.303572i
$719$	−1038.19	+	337.329i	−1.44394	+	0.469164i	−0.923123	−	0.384506i	$-0.874372\pi$
$719$	−1038.19	+	337.329i	−1.44394	+	0.469164i	−0.520815	+	0.853669i	$0.674372\pi$
$720$	165.395	−	411.426i	0.229716	−	0.571424i
$721$	201.984	−	621.643i	0.280144	−	0.862196i
$722$	592.009	−	301.644i	0.819957	−	0.417789i
$723$	−68.9764	+	435.500i	−0.0954031	+	0.602352i
$724$		−	132.229i		−	0.182636i
$725$	−186.574	+	1361.89i	−0.257343	+	1.87846i
$726$	211.414			0.291204
$727$	1260.13	+	199.586i	1.73333	+	0.274533i	0.941698	−	0.336460i	$-0.109230\pi$
$727$	1260.13	+	199.586i	1.73333	+	0.274533i	0.791636	+	0.610993i	$0.209230\pi$
$728$	82.7494	+	162.405i	0.113667	+	0.223084i
$729$	111.439	+	36.2086i	0.152865	+	0.0496689i
$730$	−463.286	−	738.552i	−0.634638	−	1.01171i
$731$	166.189	+	511.478i	0.227345	+	0.699696i
$732$	−28.7255	−	28.7255i	−0.0392425	−	0.0392425i
$733$	2.09264	+	1.06625i	0.00285490	+	0.00145464i	0.455417	−	0.890278i	$-0.349490\pi$
$733$	2.09264	+	1.06625i	0.00285490	+	0.00145464i	−0.452562	+	0.891733i	$0.649490\pi$
$734$	−217.077	+	298.781i	−0.295745	+	0.407058i
$735$	37.0661	−	161.834i	0.0504301	−	0.220182i
$736$	−270.685	+	196.664i	−0.367778	+	0.267206i
$737$	5.53659	+	34.9566i	0.00751233	+	0.0474310i
$738$	452.878	−	71.7289i	0.613656	−	0.0971936i
$739$	−104.284	−	143.535i	−0.141116	−	0.194229i	0.732609	−	0.680649i	$-0.238302\pi$
$739$	−104.284	−	143.535i	−0.141116	−	0.194229i	−0.873725	+	0.486421i	$0.838302\pi$
$740$	−95.1521	−	109.076i	−0.128584	−	0.147401i
$741$	133.096	+	96.6997i	0.179616	+	0.130499i
$742$	−159.715	+	313.458i	−0.215249	+	0.422450i
$743$	−157.030	+	157.030i	−0.211346	+	0.211346i	−0.804839	−	0.593493i	$-0.797749\pi$
$743$	−157.030	+	157.030i	−0.211346	+	0.211346i	0.593493	+	0.804839i	$0.297749\pi$
$744$	−310.987	+	101.046i	−0.417993	+	0.135814i
$745$	−178.802	−	149.504i	−0.240003	−	0.200676i
$746$	−155.065	+	477.243i	−0.207863	+	0.639735i
$747$	−375.866	+	191.513i	−0.503167	+	0.256377i
$748$	9.04178	−	57.0876i	0.0120879	−	0.0763203i
$749$		−	433.357i		−	0.578580i
$750$	67.9352	−	328.013i	0.0905802	−	0.437351i
$751$	23.4284			0.0311963			0.0155982	−	0.999878i	$-0.495035\pi$
$751$	23.4284			0.0311963			0.0155982	+	0.999878i	$0.495035\pi$
$752$	−140.436	−	22.2429i	−0.186750	−	0.0295783i
$753$	−46.4856	−	91.2331i	−0.0617338	−	0.121159i
$754$	398.808	+	129.581i	0.528923	+	0.171857i
$755$	16.0534	−	19.1994i	0.0212628	−	0.0254296i
$756$	24.1924	+	74.4565i	0.0320005	+	0.0984874i
$757$	−292.199	−	292.199i	−0.385995	−	0.385995i	0.487261	−	0.873256i	$-0.337996\pi$
$757$	−292.199	−	292.199i	−0.385995	−	0.385995i	−0.873256	+	0.487261i	$0.837996\pi$
$758$	382.548	+	194.918i	0.504681	+	0.257148i
$759$	179.970	−	247.707i	0.237114	−	0.326359i
$760$	863.445	−	753.221i	1.13611	−	0.991080i
$761$	514.474	−	373.787i	0.676050	−	0.491179i	−0.195995	−	0.980605i	$-0.562794\pi$
$761$	514.474	−	373.787i	0.676050	−	0.491179i	0.872045	+	0.489426i	$0.162794\pi$
$762$	−40.4075	−	255.123i	−0.0530282	−	0.334807i
$763$	−475.628	+	75.3321i	−0.623366	+	0.0987314i
$764$	−28.6802	−	39.4749i	−0.0375395	−	0.0516687i
$765$	−453.066	−	103.769i	−0.592243	−	0.135646i
$766$	−825.670	−	599.885i	−1.07790	−	0.783139i
$767$	45.6832	−	89.6583i	0.0595609	−	0.116895i
$768$	−126.923	+	126.923i	−0.165265	+	0.165265i
$769$	30.7819	−	10.0017i	0.0400285	−	0.0130061i	−0.288934	−	0.957349i	$-0.593301\pi$
$769$	30.7819	−	10.0017i	0.0400285	−	0.0130061i	0.328963	+	0.944343i	$0.393301\pi$
$770$	−257.948	+	161.808i	−0.334997	+	0.210140i
$771$	−163.678	+	503.748i	−0.212293	+	0.653369i
$772$	6.70514	−	3.41644i	0.00868541	−	0.00442544i
$773$	−76.6551	+	483.981i	−0.0991657	+	0.626107i	0.887181	+	0.461422i	$0.152661\pi$
$773$	−76.6551	+	483.981i	−0.0991657	+	0.626107i	−0.986346	+	0.164685i	$0.947339\pi$
$774$		−	496.677i		−	0.641702i
$775$	577.349	−	309.562i	0.744967	−	0.399435i
$776$	−442.952			−0.570814
$777$	−327.587	−	51.8847i	−0.421605	−	0.0667756i
$778$	120.560	+	236.612i	0.154961	+	0.304128i
$779$	936.755	+	304.370i	1.20251	+	0.390719i
$780$	18.6181	+	7.48459i	0.0238694	+	0.00959563i
$781$	−215.824	−	664.238i	−0.276343	−	0.850496i
$782$	−564.734	−	564.734i	−0.722167	−	0.722167i
$783$	1138.18	+	579.931i	1.45361	+	0.740653i
$784$	−172.362	+	237.237i	−0.219850	+	0.302598i
$785$	404.352	−	36.0847i	0.515098	−	0.0459678i
$786$	−27.9508	+	20.3074i	−0.0355608	+	0.0258364i
$787$	35.7839	+	225.931i	0.0454687	+	0.287078i	0.999937	−	0.0112346i	$-0.00357614\pi$
$787$	35.7839	+	225.931i	0.0454687	+	0.287078i	−0.954468	+	0.298313i	$0.903576\pi$
$788$	−237.663	+	37.6422i	−0.301603	+	0.0477693i
$789$	−68.3047	−	94.0134i	−0.0865713	−	0.119155i
$790$	−939.153	+	400.575i	−1.18880	+	0.507057i
$791$	45.1544	+	32.8066i	0.0570853	+	0.0414749i
$792$	−171.877	+	337.327i	−0.217016	+	0.425918i
$793$	124.513	−	124.513i	0.157015	−	0.157015i
$794$	−1268.08	+	412.024i	−1.59708	+	0.518922i
$795$	66.9164	+	266.413i	0.0841716	+	0.335111i
$796$	56.3970	−	173.572i	0.0708505	−	0.218055i
$797$	−1028.03	+	523.809i	−1.28988	+	0.657226i	−0.958182	−	0.286161i	$-0.907621\pi$
$797$	−1028.03	+	523.809i	−1.28988	+	0.657226i	−0.331696	+	0.943386i	$0.607621\pi$
$798$	57.9093	−	365.625i	0.0725681	−	0.458177i
$799$			149.040i			0.186533i
$800$	148.279	−	213.339i	0.185348	−	0.266674i
$801$	−80.2957			−0.100244
$802$	385.455	+	61.0500i	0.480617	+	0.0761222i
$803$	280.928	+	551.353i	0.349848	+	0.686616i
$804$	−4.99123	−	1.62175i	−0.00620800	−	0.00201710i
$805$	56.2014	−	824.310i	0.0698155	−	1.02399i
$806$	−61.7549	−	190.062i	−0.0766190	−	0.235809i
$807$	18.2281	+	18.2281i	0.0225875	+	0.0225875i
$808$	168.959	+	86.0890i	0.209108	+	0.106546i
$809$	−355.996	+	489.987i	−0.440045	+	0.605670i	−0.970222	−	0.242217i	$-0.922125\pi$
$809$	−355.996	+	489.987i	−0.440045	+	0.605670i	0.530177	+	0.847887i	$0.322125\pi$
$810$	216.682	+	129.683i	0.267508	+	0.160103i
$811$	−870.243	+	632.269i	−1.07305	+	0.779616i	−0.976458	−	0.215708i	$-0.930794\pi$
$811$	−870.243	+	632.269i	−1.07305	+	0.779616i	−0.0965917	+	0.995324i	$0.530794\pi$
$812$	28.9851	+	183.005i	0.0356960	+	0.225375i
$813$	−160.032	+	25.3466i	−0.196841	+	0.0311766i
$814$	−307.515	−	423.259i	−0.377783	−	0.519974i
$815$	498.639	−	833.152i	0.611827	−	1.02227i
$816$	−208.188	−	151.258i	−0.255133	−	0.185365i
$817$	484.372	−	950.633i	0.592866	−	1.16357i
$818$	−370.087	+	370.087i	−0.452429	+	0.452429i
$819$	−139.505	+	45.3278i	−0.170335	+	0.0553453i
$820$	119.859	+	8.17201i	0.146170	+	0.00996587i
$821$	−97.0397	+	298.658i	−0.118197	+	0.363773i	−0.992600	−	0.121427i	$-0.961253\pi$
$821$	−97.0397	+	298.658i	−0.118197	+	0.363773i	0.874403	+	0.485200i	$0.161253\pi$
$822$	−26.6240	+	13.5656i	−0.0323893	+	0.0165032i
$823$	1.67889	−	10.6001i	0.00203996	−	0.0128798i	−0.986647	−	0.162871i	$-0.947925\pi$
$823$	1.67889	−	10.6001i	0.00203996	−	0.0128798i	0.988687	+	0.149991i	$0.0479245\pi$
$824$			1084.33i			1.31594i
$825$	−68.7214	+	227.605i	−0.0832987	+	0.275885i
$826$	−226.422			−0.274119
$827$	−1043.28	−	165.240i	−1.26153	−	0.199806i	−0.510384	−	0.859947i	$-0.670497\pi$
$827$	−1043.28	−	165.240i	−1.26153	−	0.199806i	−0.751142	+	0.660141i	$0.770497\pi$
$828$	−65.7561	−	129.054i	−0.0794156	−	0.155862i
$829$	631.029	+	205.034i	0.761193	+	0.247327i	0.663791	−	0.747918i	$-0.268947\pi$
$829$	631.029	+	205.034i	0.761193	+	0.247327i	0.0974024	+	0.995245i	$0.468947\pi$
$830$	545.895	−	137.115i	0.657705	−	0.165199i
$831$	67.4672	+	207.643i	0.0811879	+	0.249871i
$832$	−208.726	−	208.726i	−0.250873	−	0.250873i
$833$	273.872	+	139.545i	0.328778	+	0.167521i
$834$	44.7724	−	61.6239i	0.0536839	−	0.0738896i
$835$	−461.795	−	1082.68i	−0.553048	−	1.29663i
$836$	−92.7665	+	67.3988i	−0.110965	+	0.0806206i
$837$	−95.2344	−	601.287i	−0.113781	−	0.718383i
$838$	702.729	−	111.301i	0.838579	−	0.132818i
$839$	−574.315	−	790.477i	−0.684523	−	0.942166i	0.315454	−	0.948941i	$-0.397843\pi$
$839$	−574.315	−	790.477i	−0.684523	−	0.942166i	−0.999977	+	0.00677528i	$0.997843\pi$
$840$	−28.4650	−	318.968i	−0.0338869	−	0.379724i
$841$	1765.49	+	1282.70i	2.09927	+	1.52521i
$842$	−16.0251	+	31.4510i	−0.0190322	+	0.0373527i
$843$	−114.755	+	114.755i	−0.136127	+	0.136127i
$844$	−103.292	+	33.5616i	−0.122384	+	0.0397649i
$845$	282.737	−	703.318i	0.334600	−	0.832328i
$846$	42.5342	−	130.907i	0.0502769	−	0.154736i
$847$	−360.784	+	183.829i	−0.425956	+	0.217035i
$848$	75.8970	−	479.195i	0.0895011	−	0.565088i
$849$		−	626.979i		−	0.738491i
$850$	558.341	+	269.922i	0.656871	+	0.317555i
$851$	1419.59			1.66814
$852$	102.289	+	16.2010i	0.120057	+	0.0190152i
$853$	748.198	+	1468.42i	0.877137	+	1.72148i	0.668830	+	0.743415i	$0.266795\pi$
$853$	748.198	+	1468.42i	0.877137	+	1.72148i	0.208307	+	0.978064i	$0.433205\pi$
$854$	−376.830	−	122.440i	−0.441253	−	0.143372i
$855$	489.995	+	781.131i	0.573094	+	0.913603i
$856$	222.155	+	683.721i	0.259526	+	0.798740i
$857$	426.293	+	426.293i	0.497425	+	0.497425i	0.910636	−	0.413210i	$-0.135593\pi$
$857$	426.293	+	426.293i	0.497425	+	0.497425i	−0.413210	+	0.910636i	$0.635593\pi$
$858$	64.6230	+	32.9271i	0.0753182	+	0.0383765i
$859$	23.9279	−	32.9339i	0.0278555	−	0.0383398i	−0.794862	−	0.606790i	$-0.792457\pi$
$859$	23.9279	−	32.9339i	0.0278555	−	0.0383398i	0.822718	+	0.568450i	$0.192457\pi$
$860$	29.0534	−	126.850i	0.0337830	−	0.147500i
$861$	222.708	−	161.807i	0.258662	−	0.187929i
$862$	−146.392	−	924.282i	−0.169828	−	1.07225i
$863$	858.454	−	135.966i	0.994732	−	0.157550i	0.362213	−	0.932095i	$-0.382021\pi$
$863$	858.454	−	135.966i	0.994732	−	0.157550i	0.632519	+	0.774545i	$0.282021\pi$
$864$	−141.913	−	195.327i	−0.164251	−	0.226073i
$865$	578.703	+	663.389i	0.669021	+	0.766923i
$866$	−816.271	−	593.055i	−0.942576	−	0.684821i
$867$	69.8282	−	137.046i	0.0805400	−	0.158069i
$868$	62.4395	−	62.4395i	0.0719349	−	0.0719349i
$869$	689.213	−	223.939i	0.793110	−	0.257697i
$870$	−565.192	−	472.580i	−0.649646	−	0.543196i
$871$	7.02961	−	21.6349i	0.00807074	−	0.0248392i
$872$	711.796	−	362.678i	0.816280	−	0.415916i
$873$	55.7638	−	352.079i	0.0638761	−	0.403298i
$874$			1584.42i			1.81284i
$875$	169.281	+	618.835i	0.193464	+	0.707240i
$876$	−91.7572			−0.104746
$877$	177.591	+	28.1277i	0.202499	+	0.0320726i	0.256860	−	0.966449i	$-0.417312\pi$
$877$	177.591	+	28.1277i	0.202499	+	0.0320726i	−0.0543610	+	0.998521i	$0.517312\pi$
$878$	−220.968	−	433.675i	−0.251672	−	0.493935i
$879$	−22.1108	−	7.18422i	−0.0251544	−	0.00817317i
$880$	269.367	−	322.155i	0.306099	−	0.366085i
$881$	−75.2021	−	231.448i	−0.0853599	−	0.262711i	0.899262	−	0.437411i	$-0.144104\pi$
$881$	−75.2021	−	231.448i	−0.0853599	−	0.262711i	−0.984622	+	0.174700i	$0.944104\pi$
$882$	−200.727	−	200.727i	−0.227582	−	0.227582i
$883$	−859.392	−	437.882i	−0.973264	−	0.495903i	−0.106333	−	0.994331i	$-0.533911\pi$
$883$	−859.392	−	437.882i	−0.973264	−	0.495903i	−0.866931	+	0.498428i	$0.833911\pi$
$884$	−21.8363	+	30.0551i	−0.0247017	+	0.0339990i
$885$	−133.225	+	116.218i	−0.150536	+	0.131319i
$886$	−1260.52	+	915.824i	−1.42271	+	1.03366i
$887$	42.2734	+	266.904i	0.0476589	+	0.300906i	0.999991	−	0.00415563i	$-0.00132278\pi$
$887$	42.2734	+	266.904i	0.0476589	+	0.300906i	−0.952332	+	0.305062i	$0.901323\pi$
$888$	543.443	−	86.0729i	0.611985	−	0.0969290i
$889$	290.791	+	400.240i	0.327099	+	0.450213i
$890$	104.431	+	23.9187i	0.117339	+	0.0268750i
$891$	−145.003	−	105.351i	−0.162742	−	0.118239i
$892$	−61.6819	+	121.058i	−0.0691501	+	0.135715i
$893$	209.073	−	209.073i	0.234125	−	0.234125i
$894$	118.802	−	38.6011i	0.132888	−	0.0431780i
$895$	−193.878	+	121.618i	−0.216624	+	0.135886i
$896$	−139.319	+	428.781i	−0.155490	+	0.478550i
$897$	−175.348	+	89.3442i	−0.195483	+	0.0996033i
$898$	36.6342	−	231.299i	0.0407953	−	0.257571i
$899$		−	1440.81i		−	1.60269i
$900$	81.1751	+	77.8463i	0.0901946	+	0.0864958i
$901$	−508.551			−0.564430
$902$	428.883	+	67.9284i	0.475480	+	0.0753086i
$903$	−135.374	−	265.687i	−0.149916	−	0.294227i
$904$	−88.0596	−	28.6123i	−0.0974110	−	0.0316508i
$905$	−934.320	−	375.601i	−1.03240	−	0.415029i
$906$	4.14490	+	12.7567i	0.00457495	+	0.0140802i
$907$	−612.661	−	612.661i	−0.675481	−	0.675481i	0.283494	−	0.958974i	$-0.408507\pi$
$907$	−612.661	−	612.661i	−0.675481	−	0.675481i	−0.958974	+	0.283494i	$0.908507\pi$
$908$	−60.1612	−	30.6537i	−0.0662568	−	0.0337595i
$909$	−89.6981	+	123.459i	−0.0986778	+	0.135818i
$910$	194.940	−	17.3966i	0.214220	−	0.0191171i
$911$	−75.9892	+	55.2094i	−0.0834130	+	0.0606031i	−0.628710	−	0.777640i	$-0.716417\pi$
$911$	−75.9892	+	55.2094i	−0.0834130	+	0.0606031i	0.545297	+	0.838243i	$0.316417\pi$
$912$	79.8625	+	504.232i	0.0875685	+	0.552886i
$913$	−394.575	+	62.4945i	−0.432174	+	0.0684496i
$914$	374.536	+	515.504i	0.409777	+	0.564009i
$915$	−284.569	+	121.377i	−0.311004	+	0.132652i
$916$	87.0634	+	63.2552i	0.0950473	+	0.0690559i
$917$	30.0411	−	58.9590i	0.0327602	−	0.0642955i
$918$	407.514	−	407.514i	0.443915	−	0.443915i
$919$	−991.884	+	322.283i	−1.07931	+	0.350688i	−0.794106	−	0.607779i	$-0.792061\pi$
$919$	−991.884	+	322.283i	−1.07931	+	0.350688i	−0.285202	+	0.958467i	$0.592061\pi$
$920$	333.901	+	1329.35i	0.362936	+	1.44495i
$921$	−201.257	+	619.404i	−0.218520	+	0.672534i
$922$	504.750	−	257.183i	0.547451	−	0.278940i
$923$	−70.2245	+	443.380i	−0.0760829	+	0.480369i
$924$			32.0473i			0.0346832i
$925$	−1041.01	+	362.503i	−1.12542	+	0.391895i
$926$	689.126			0.744197
$927$	−861.878	−	136.508i	−0.929750	−	0.147258i
$928$	−259.416	−	509.133i	−0.279543	−	0.548635i
$929$	−1624.18	−	527.728i	−1.74831	−	0.568060i	−0.752424	−	0.658679i	$-0.771116\pi$
$929$	−1624.18	−	527.728i	−1.74831	−	0.568060i	−0.995886	+	0.0906186i	$0.971116\pi$
$930$	−23.8831	+	350.295i	−0.0256808	+	0.376661i
$931$	−188.435	−	579.943i	−0.202400	−	0.622925i
$932$	4.64338	+	4.64338i	0.00498217	+	0.00498217i
$933$	−234.046	−	119.252i	−0.250853	−	0.127816i
$934$	−204.875	+	281.986i	−0.219352	+	0.301912i
$935$	−377.694	−	226.049i	−0.403951	−	0.241763i
$936$	196.864	−	143.030i	0.210325	−	0.152810i
$937$	46.8861	+	296.027i	0.0500385	+	0.315931i	0.999994	+	0.00354453i	$0.00112826\pi$
$937$	46.8861	+	296.027i	0.0500385	+	0.315931i	−0.949955	+	0.312386i	$0.898872\pi$
$938$	−50.5567	+	8.00739i	−0.0538984	+	0.00853666i
$939$	−347.978	−	478.951i	−0.370584	−	0.510065i
$940$	18.5205	−	30.9451i	0.0197027	−	0.0329203i
$941$	354.729	+	257.725i	0.376970	+	0.273885i	0.760095	−	0.649812i	$-0.225152\pi$
$941$	354.729	+	257.725i	0.376970	+	0.273885i	−0.383125	+	0.923696i	$0.625152\pi$
$942$	−98.7780	+	193.863i	−0.104860	+	0.205799i
$943$	−833.139	+	833.139i	−0.883498	+	0.883498i
$944$	296.975	−	96.4930i	0.314592	−	0.102217i
$945$	594.825	+	40.5551i	0.629444	+	0.0429155i
$946$	145.350	−	447.340i	0.153647	−	0.472875i
$947$	869.096	−	442.827i	0.917736	−	0.467610i	0.0697120	−	0.997567i	$-0.477792\pi$
$947$	869.096	−	442.827i	0.917736	−	0.467610i	0.848024	+	0.529957i	$0.177792\pi$
$948$	−16.8101	+	106.135i	−0.0177322	+	0.111957i
$949$		−	397.730i		−	0.419104i
$950$	−404.595	−	1161.89i	−0.425890	−	1.22304i
$951$	−396.538			−0.416969
$952$	585.578	+	92.7464i	0.615103	+	0.0974227i
$953$	−189.159	−	371.246i	−0.198488	−	0.389555i	0.770212	−	0.637788i	$-0.220150\pi$
$953$	−189.159	−	371.246i	−0.198488	−	0.389555i	−0.968700	+	0.248233i	$0.920150\pi$
$954$	446.679	+	145.135i	0.468217	+	0.152133i
$955$	−360.395	+	90.5223i	−0.377377	+	0.0947877i
$956$	−6.39706	−	19.6881i	−0.00669148	−	0.0205943i
$957$	369.752	+	369.752i	0.386365	+	0.386365i
$958$	−1274.98	−	649.636i	−1.33088	−	0.678117i
$959$	33.6390	−	46.3002i	0.0350772	−	0.0482796i
$960$	203.468	+	477.033i	0.211946	+	0.496910i
$961$	221.948	−	161.255i	0.230956	−	0.167799i
$962$	52.6041	+	332.129i	0.0546820	+	0.345249i
$963$	−571.421	+	90.5043i	−0.593376	+	0.0939816i
$964$	116.106	+	159.806i	0.120441	+	0.165773i
$965$	−5.09410	−	57.0826i	−0.00527886	−	0.0591530i
$966$	358.250	+	260.284i	0.370860	+	0.269445i
$967$	−183.296	+	359.738i	−0.189551	+	0.372015i	−0.966150	−	0.257980i	$-0.916943\pi$
$967$	−183.296	+	359.738i	−0.189551	+	0.372015i	0.776599	+	0.629995i	$0.216943\pi$
$968$	474.984	−	474.984i	0.490686	−	0.490686i
$969$	508.932	−	165.362i	0.525213	−	0.170652i
$970$	−177.404	+	441.298i	−0.182891	+	0.454946i
$971$	511.600	−	1574.54i	0.526879	−	1.62157i	−0.233690	−	0.972311i	$-0.575080\pi$
$971$	511.600	−	1574.54i	0.526879	−	1.62157i	0.760569	−	0.649257i	$-0.224920\pi$
$972$	145.997	−	74.3892i	0.150203	−	0.0765321i
$973$	−22.8222	+	144.094i	−0.0234555	+	0.148092i
$974$		−	722.545i		−	0.741832i
$975$	105.771	−	110.294i	0.108483	−	0.113122i
$976$	546.429			0.559866
$977$	91.0619	+	14.4228i	0.0932056	+	0.0147623i	0.202863	−	0.979207i	$-0.434975\pi$
$977$	91.0619	+	14.4228i	0.0932056	+	0.0147623i	−0.109657	+	0.993969i	$0.534975\pi$
$978$	236.257	+	463.680i	0.241571	+	0.474110i
$979$	−72.3196	−	23.4981i	−0.0738709	−	0.0240021i
$980$	−39.5234	−	63.0066i	−0.0403300	−	0.0642925i
$981$	198.665	+	611.428i	0.202513	+	0.623270i
$982$	570.080	+	570.080i	0.580530	+	0.580530i
$983$	557.209	+	283.912i	0.566845	+	0.288822i	0.713833	−	0.700316i	$-0.246958\pi$
$983$	557.209	+	283.912i	0.566845	+	0.288822i	−0.146987	+	0.989138i	$0.546958\pi$
$984$	−268.425	+	369.456i	−0.272790	+	0.375463i
$985$	−409.116	+	1786.24i	−0.415346	+	1.81344i
$986$	1103.47	−	801.720i	1.11914	−	0.813103i
$987$	−12.9272	−	81.6191i	−0.0130975	−	0.0826941i
$988$	72.7935	−	11.5294i	0.0736776	−	0.0116694i
$989$	750.177	+	1032.53i	0.758521	+	1.04401i
$990$	267.230	+	306.336i	0.269929	+	0.309430i
$991$	100.361	+	72.9162i	0.101272	+	0.0735784i	0.637269	−	0.770642i	$-0.280064\pi$
$991$	100.361	+	72.9162i	0.101272	+	0.0735784i	−0.535997	+	0.844220i	$0.680064\pi$
$992$	−123.631	+	242.640i	−0.124628	+	0.244597i
$993$	642.863	−	642.863i	0.647394	−	0.647394i
$994$	960.666	−	312.139i	0.966464	−	0.314023i
$995$	−1066.25	−	891.537i	−1.07161	−	0.896017i
$996$	18.3056	−	56.3388i	0.0183791	−	0.0565650i
$997$	−227.413	+	115.873i	−0.228097	+	0.116221i	−0.564305	−	0.825567i	$-0.690856\pi$
$997$	−227.413	+	115.873i	−0.228097	+	0.116221i	0.336207	+	0.941788i	$0.390856\pi$
$998$	−158.295	+	999.432i	−0.158612	+	1.00144i
$999$			1024.38i			1.02540i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.3.f.a.2.4	✓	32
3.2	odd	2		225.3.r.a.127.1		32
4.3	odd	2		400.3.bg.c.177.3		32
5.2	odd	4		125.3.f.b.93.1		32
5.3	odd	4		125.3.f.a.93.4		32
5.4	even	2		125.3.f.c.32.1		32
25.9	even	10		125.3.f.b.82.1		32
25.12	odd	20		125.3.f.c.43.1		32
25.13	odd	20	inner	25.3.f.a.13.4	yes	32
25.16	even	5		125.3.f.a.82.4		32
75.38	even	20		225.3.r.a.163.1		32
100.63	even	20		400.3.bg.c.113.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.3.f.a.2.4	✓	32	1.1	even	1	trivial
25.3.f.a.13.4	yes	32	25.13	odd	20	inner
125.3.f.a.82.4		32	25.16	even	5
125.3.f.a.93.4		32	5.3	odd	4
125.3.f.b.82.1		32	25.9	even	10
125.3.f.b.93.1		32	5.2	odd	4
125.3.f.c.32.1		32	5.4	even	2
125.3.f.c.43.1		32	25.12	odd	20
225.3.r.a.127.1		32	3.2	odd	2
225.3.r.a.163.1		32	75.38	even	20
400.3.bg.c.113.3		32	100.63	even	20
400.3.bg.c.177.3		32	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	25.f (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.80600 + 0.286042i) q^{2} +(-0.665351 - 1.30583i) q^{3} +(-0.624420 - 0.202886i) q^{4} +(-3.20727 + 3.83580i) q^{5} +(-0.828102 - 2.54863i) q^{6} +(3.62927 + 3.62927i) q^{7} +(-7.58652 - 3.86553i) q^{8} +(4.02758 - 5.54349i) q^{9} +O(q^{10})\)	\(q+(1.80600 + 0.286042i) q^{2} +(-0.665351 - 1.30583i) q^{3} +(-0.624420 - 0.202886i) q^{4} +(-3.20727 + 3.83580i) q^{5} +(-0.828102 - 2.54863i) q^{6} +(3.62927 + 3.62927i) q^{7} +(-7.58652 - 3.86553i) q^{8} +(4.02758 - 5.54349i) q^{9} +(-6.88953 + 6.01004i) q^{10} +(5.24977 - 3.81418i) q^{11} +(0.150524 + 0.950373i) q^{12} +(-4.11948 + 0.652461i) q^{13} +(5.51633 + 7.59258i) q^{14} +(7.14285 + 1.63598i) q^{15} +(-10.4709 - 7.60754i) q^{16} +(-6.15907 + 12.0879i) q^{17} +(8.85947 - 8.85947i) q^{18} +(25.5969 - 8.31693i) q^{19} +(2.78092 - 1.74444i) q^{20} +(2.32445 - 7.15393i) q^{21} +(10.5721 - 5.38675i) q^{22} +(-5.03647 + 31.7990i) q^{23} +12.4786i q^{24} +(-4.42679 - 24.6050i) q^{25} -7.62639 q^{26} +(-22.9462 - 3.63433i) q^{27} +(-1.52986 - 3.00252i) q^{28} +(-52.2931 - 16.9911i) q^{29} +(12.4320 + 4.99773i) q^{30} +(8.09752 + 24.9216i) q^{31} +(7.34848 + 7.34848i) q^{32} +(-8.47360 - 4.31751i) q^{33} +(-14.5809 + 20.0689i) q^{34} +(-25.5612 + 2.28111i) q^{35} +(-3.63960 + 2.64432i) q^{36} +(-6.89764 - 43.5500i) q^{37} +(48.6069 - 7.69857i) q^{38} +(3.59290 + 4.94520i) q^{39} +(39.1595 - 16.7026i) q^{40} +(29.6072 + 21.5109i) q^{41} +(6.24428 - 12.2551i) q^{42} +(28.0309 - 28.0309i) q^{43} +(-4.05190 + 1.31654i) q^{44} +(8.34618 + 33.2285i) q^{45} +(-18.1917 + 55.9883i) q^{46} +(9.78846 - 4.98747i) q^{47} +(-2.96731 + 18.7348i) q^{48} -22.6568i q^{49} +(-0.956716 - 45.7027i) q^{50} +19.8826 q^{51} +(2.70466 + 0.428376i) q^{52} +(17.0182 + 33.4001i) q^{53} +(-40.4013 - 13.1272i) q^{54} +(-2.20700 + 32.3702i) q^{55} +(-13.5045 - 41.5626i) q^{56} +(-27.8914 - 27.8914i) q^{57} +(-89.5811 - 45.6438i) q^{58} +(-14.1810 + 19.5185i) q^{59} +(-4.12822 - 2.47073i) q^{60} +(-34.1559 + 24.8157i) q^{61} +(7.49548 + 47.3246i) q^{62} +(34.7360 - 5.50164i) q^{63} +(41.5995 + 57.2568i) q^{64} +(10.7096 - 17.8941i) q^{65} +(-14.0683 - 10.2212i) q^{66} +(-2.47613 + 4.85968i) q^{67} +(6.29831 - 6.29831i) q^{68} +(44.8749 - 14.5808i) q^{69} +(-46.8160 - 3.19191i) q^{70} +(33.2596 - 102.362i) q^{71} +(-51.9838 + 26.4871i) q^{72} +(-14.9176 + 94.1859i) q^{73} -80.6242i q^{74} +(-29.1844 + 22.1515i) q^{75} -17.6706 q^{76} +(32.8955 + 5.21014i) q^{77} +(5.07423 + 9.95874i) q^{78} +(106.211 + 34.5101i) q^{79} +(62.7640 - 15.7648i) q^{80} +(-8.53531 - 26.2690i) q^{81} +(47.3174 + 47.3174i) q^{82} +(-54.8539 - 27.9495i) q^{83} +(-2.90287 + 3.99546i) q^{84} +(-26.6128 - 62.3941i) q^{85} +(58.6417 - 42.6057i) q^{86} +(12.6059 + 79.5907i) q^{87} +(-54.5713 + 8.64325i) q^{88} +(-6.88788 - 9.48035i) q^{89} +(5.56844 + 62.3979i) q^{90} +(-17.3187 - 12.5827i) q^{91} +(9.59645 - 18.8341i) q^{92} +(27.1556 - 27.1556i) q^{93} +(19.1046 - 6.20745i) q^{94} +(-50.1941 + 124.859i) q^{95} +(4.70651 - 14.4851i) q^{96} +(46.3527 - 23.6179i) q^{97} +(6.48079 - 40.9181i) q^{98} -44.4640i 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

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