LMFDB - Embedded newform 25.3.f.a.13.4

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			13.4
Character	$\chi$	$=$	25.13
Dual form			25.3.f.a.2.4

$q$-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 $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{19}{20}\right)$

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	0.312366	−	0.949962i	$-0.398878\pi$
$2$	1.80600	−	0.286042i	0.902999	−	0.143021i	0.590632	+	0.806941i	$0.298878\pi$
$3$	−0.665351	+	1.30583i	−0.221784	+	0.435275i	−0.974910	−	0.222601i	$-0.928545\pi$
$3$	−0.665351	+	1.30583i	−0.221784	+	0.435275i	0.753126	+	0.657877i	$0.228545\pi$
$4$	−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	−0.398640	−	0.917107i	$-0.630518\pi$
$7$	3.62927	−	3.62927i	0.518467	−	0.518467i	0.917107	+	0.398640i	$0.130518\pi$
$8$	−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	0.800261	−	0.599652i	$-0.204694\pi$
$11$	5.24977	+	3.81418i	0.477252	+	0.346744i	−0.323009	+	0.946396i	$0.604694\pi$
$12$	0.150524	−	0.950373i	0.0125437	−	0.0791978i
$13$	−4.11948	−	0.652461i	−0.316883	−	0.0501893i	−0.00403283	−	0.999992i	$-0.501284\pi$
$13$	−4.11948	−	0.652461i	−0.316883	−	0.0501893i	−0.312850	+	0.949803i	$0.601284\pi$
$14$	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	0.635854	−	0.771809i	$-0.280648\pi$
$17$	−6.15907	−	12.0879i	−0.362298	−	0.711051i	−0.998152	+	0.0607586i	$0.980648\pi$
$18$	8.85947	+	8.85947i	0.492193	+	0.492193i
$19$	25.5969	+	8.31693i	1.34720	+	0.437733i	0.891751	−	0.452527i	$-0.149477\pi$
$19$	25.5969	+	8.31693i	1.34720	+	0.437733i	0.455453	+	0.890260i	$0.349477\pi$
$20$	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	−0.814936	−	0.579551i	$-0.803228\pi$
$23$	−5.03647	−	31.7990i	−0.218977	−	1.38256i	0.595960	−	0.803014i	$-0.296772\pi$
$24$		−	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	−0.999953	−	0.00973242i	$-0.996902\pi$
$29$	−52.2931	+	16.9911i	−1.80321	+	0.585899i	−0.803258	+	0.595631i	$0.796902\pi$
$30$	12.4320	−	4.99773i	0.414400	−	0.166591i
$31$	8.09752	−	24.9216i	0.261210	−	0.803923i	−0.731332	−	0.682022i	$-0.761101\pi$
$31$	8.09752	−	24.9216i	0.261210	−	0.803923i	0.992542	−	0.121901i	$-0.0388991\pi$
$32$	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	0.699997	+	0.714145i	$0.253184\pi$
$37$	−6.89764	+	43.5500i	−0.186423	+	1.17703i	−0.886420	+	0.462882i	$0.846816\pi$
$38$	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	−0.164937	−	0.986304i	$-0.552742\pi$
$41$	29.6072	−	21.5109i	0.722126	−	0.524655i	0.887063	+	0.461649i	$0.152742\pi$
$42$	6.24428	+	12.2551i	0.148673	+	0.291788i
$43$	28.0309	+	28.0309i	0.651881	+	0.651881i	0.953446	−	0.301565i	$-0.0975090\pi$
$43$	28.0309	+	28.0309i	0.651881	+	0.651881i	−0.301565	+	0.953446i	$0.597509\pi$
$44$	−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	0.555012	−	0.831842i	$-0.312714\pi$
$47$	9.78846	+	4.98747i	0.208265	+	0.106116i	−0.346747	+	0.937959i	$0.612714\pi$
$48$	−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	−0.672883	−	0.739749i	$-0.734944\pi$
$53$	17.0182	−	33.4001i	0.321098	−	0.630190i	0.993980	+	0.109560i	$0.0349441\pi$
$54$	−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	0.671749	−	0.740779i	$-0.265543\pi$
$59$	−14.1810	−	19.5185i	−0.240356	−	0.330821i	−0.912105	+	0.409958i	$0.865543\pi$
$60$	−4.12822	+	2.47073i	−0.0688036	+	0.0411788i
$61$	−34.1559	−	24.8157i	−0.559933	−	0.406815i	0.271502	−	0.962438i	$-0.412480\pi$
$61$	−34.1559	−	24.8157i	−0.559933	−	0.406815i	−0.831434	+	0.555623i	$0.812480\pi$
$62$	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	0.871790	−	0.489881i	$-0.162960\pi$
$67$	−2.47613	−	4.85968i	−0.0369572	−	0.0725326i	−0.908747	+	0.417348i	$0.862960\pi$
$68$	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	0.854598	+	0.519290i	$0.173804\pi$
$71$	33.2596	+	102.362i	0.468445	+	1.44172i	−0.386153	+	0.922435i	$0.626196\pi$
$72$	−51.9838	−	26.4871i	−0.721998	−	0.367876i
$73$	−14.9176	−	94.1859i	−0.204350	−	1.29022i	−0.850081	−	0.526652i	$-0.823447\pi$
$73$	−14.9176	−	94.1859i	−0.204350	−	1.29022i	0.645730	−	0.763565i	$-0.276553\pi$
$74$			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	0.453626	−	0.891192i	$-0.350130\pi$
$79$	106.211	−	34.5101i	1.34445	−	0.436837i	0.890821	+	0.454355i	$0.150130\pi$
$80$	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	−0.752060	−	0.659095i	$-0.770940\pi$
$83$	−54.8539	+	27.9495i	−0.660891	+	0.336741i	0.0911693	+	0.995835i	$0.470940\pi$
$84$	−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	−0.845958	−	0.533250i	$-0.820971\pi$
$89$	−6.88788	+	9.48035i	−0.0773919	+	0.106521i	0.768566	+	0.639771i	$0.220971\pi$
$90$	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	0.676295	−	0.736631i	$-0.263585\pi$
$97$	46.3527	+	23.6179i	0.477863	+	0.243483i	−0.198431	+	0.980115i	$0.563585\pi$
$98$	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	0.419686	+	0.907669i	$0.362140\pi$
$103$	−57.8159	+	113.470i	−0.561319	+	1.10165i	−0.981005	+	0.193982i	$0.937860\pi$
$104$	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	−0.928730	−	0.370758i	$-0.879098\pi$
$107$	−59.7030	+	59.7030i	−0.557972	+	0.557972i	0.370758	+	0.928730i	$0.379098\pi$
$108$	13.5907	−	6.92482i	0.125840	−	0.0641187i
$109$	−55.1483	−	75.9051i	−0.505947	−	0.696377i	0.477282	−	0.878750i	$-0.341622\pi$
$109$	−55.1483	−	75.9051i	−0.505947	−	0.696377i	−0.983229	+	0.182373i	$0.941622\pi$
$110$	−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	0.203778	−	0.979017i	$-0.434678\pi$
$113$	10.7406	+	1.70114i	0.0950495	+	0.0150544i	−0.108728	+	0.994071i	$0.534678\pi$
$114$	−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	0.230080	−	0.973172i	$-0.426101\pi$
$127$	95.2024	−	15.0786i	0.749625	−	0.118729i	0.519546	+	0.854443i	$0.326101\pi$
$128$	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	−0.965110	−	0.261843i	$-0.915670\pi$
$131$	−3.98398	+	12.2614i	−0.0304121	+	0.0935987i	0.934698	+	0.355442i	$0.115670\pi$
$132$	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	−0.993236	−	0.116111i	$-0.962957\pi$
$137$	−1.74431	+	11.0131i	−0.0127322	+	0.0803878i	0.980504	+	0.196499i	$0.0629572\pi$
$138$	85.2147	+	13.4967i	0.617498	+	0.0978021i
$139$	16.7074	−	22.9958i	0.120197	−	0.165437i	−0.744678	−	0.667423i	$-0.767397\pi$
$139$	16.7074	−	22.9958i	0.120197	−	0.165437i	0.864876	+	0.501986i	$0.167397\pi$
$140$	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	$-0.950004\pi$
$149$		−	46.6140i		−	0.312845i	0.987690	−	0.156423i	$-0.0499962\pi$
$150$	−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	−0.865898	−	0.500221i	$-0.833252\pi$
$157$	−57.4113	+	57.4113i	−0.365677	+	0.365677i	0.500221	+	0.865898i	$0.333252\pi$
$158$	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	−0.462703	−	0.886514i	$-0.653120\pi$
$163$	−191.803	−	30.3786i	−1.17671	−	0.186372i	−0.714004	+	0.700142i	$0.753120\pi$
$164$	−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	−0.952048	−	0.305948i	$-0.901026\pi$
$167$	−106.874	−	209.753i	−0.639966	−	1.25600i	0.312082	−	0.950055i	$-0.398974\pi$
$168$	−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	0.929853	+	0.367930i	$0.119933\pi$
$173$	27.5428	+	173.898i	0.159207	+	1.00519i	−0.770646	+	0.637263i	$0.780067\pi$
$174$		−	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	−0.184881	−	0.982761i	$-0.559190\pi$
$179$	43.5329	−	14.1447i	0.243200	−	0.0790206i	0.428081	+	0.903740i	$0.359190\pi$
$180$	1.53008	+	22.4418i	0.00850047	+	0.124677i
$181$	62.2354	−	191.541i	0.343842	−	1.05824i	−0.618359	−	0.785896i	$-0.712202\pi$
$181$	62.2354	−	191.541i	0.343842	−	1.05824i	0.962201	−	0.272341i	$-0.0877979\pi$
$182$	−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	−0.419161	−	0.907912i	$-0.637676\pi$
$191$	60.1244	−	43.6829i	0.314787	−	0.228706i	0.733948	+	0.679206i	$0.237676\pi$
$192$	47.0891	+	92.4176i	0.245256	+	0.481342i
$193$	−8.10479	−	8.10479i	−0.0419937	−	0.0419937i	0.685798	−	0.727792i	$-0.259453\pi$
$193$	−8.10479	−	8.10479i	−0.0419937	−	0.0419937i	−0.727792	+	0.685798i	$0.759453\pi$
$194$	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	0.995453	+	0.0952522i	$0.0303658\pi$
$197$	326.552	+	166.387i	1.65763	+	0.844603i	0.662173	+	0.749351i	$0.269634\pi$
$198$	12.7186	+	80.3018i	0.0642351	+	0.405565i
$199$		−	277.973i		−	1.39685i	−0.715683	−	0.698426i	$-0.753884\pi$
$199$		−	277.973i		−	1.39685i	0.715683	−	0.698426i	$-0.246116\pi$
$200$	−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	0.857872	−	0.513863i	$-0.171786\pi$
$211$	133.828	+	97.2318i	0.634257	+	0.460814i	−0.223616	+	0.974677i	$0.571786\pi$
$212$	−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	0.947519	+	0.319699i	$0.103582\pi$
$223$	32.3723	+	204.391i	0.145167	+	0.916550i	−0.802352	+	0.596851i	$0.796418\pi$
$224$		−	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	0.0713646	−	0.997450i	$-0.477265\pi$
$227$	101.575	−	16.0878i	0.447465	−	0.0708716i	0.376101	+	0.926579i	$0.377265\pi$
$228$	11.7571	−	23.0747i	0.0515664	−	0.101205i
$229$	−155.888	+	50.6512i	−0.680736	+	0.221184i	−0.628917	−	0.777472i	$-0.716502\pi$
$229$	−155.888	+	50.6512i	−0.680736	+	0.221184i	−0.0518182	+	0.998657i	$0.516502\pi$
$230$	−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	−0.473010	−	0.881057i	$-0.656832\pi$
$233$	−8.91169	+	4.54073i	−0.0382476	+	0.0194881i	0.434762	+	0.900545i	$0.356832\pi$
$234$	−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	−0.768483	−	0.639870i	$-0.778988\pi$
$239$	18.5330	−	25.5085i	0.0775440	−	0.106730i	0.846027	+	0.533140i	$0.178988\pi$
$240$	−62.3462	+	71.4697i	−0.259776	+	0.297791i
$241$	−243.401	+	176.841i	−1.00996	+	0.733780i	−0.964201	−	0.265172i	$-0.914571\pi$
$241$	−243.401	+	176.841i	−1.00996	+	0.733780i	−0.0457606	+	0.998952i	$0.514571\pi$
$242$	−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	−0.999984	−	0.00559938i	$-0.998218\pi$
$257$	−255.557	+	255.557i	−0.994385	+	0.994385i	0.00559938	+	0.999984i	$0.498218\pi$
$258$	−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	0.303536	−	0.952820i	$-0.401833\pi$
$263$	78.3156	+	12.4040i	0.297778	+	0.0471634i	−0.00575796	+	0.999983i	$0.501833\pi$
$264$	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	0.277758	−	0.960651i	$-0.410409\pi$
$269$	−16.7285	−	5.43543i	−0.0621879	−	0.0202061i	−0.339946	+	0.940445i	$0.610409\pi$
$270$	179.931	+	112.869i	0.666412	+	0.418033i
$271$	34.1637	+	105.145i	0.126065	+	0.387990i	0.994094	−	0.108525i	$-0.0346128\pi$
$271$	34.1637	+	105.145i	0.126065	+	0.387990i	−0.868028	+	0.496515i	$0.834613\pi$
$272$	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	−0.416265	−	0.909243i	$-0.636661\pi$
$277$	−147.138	+	23.3044i	−0.531185	+	0.0841315i	−0.114920	+	0.993375i	$0.536661\pi$
$278$	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	−0.993300	−	0.115566i	$-0.963132\pi$
$281$	−34.2189	+	105.315i	−0.121775	+	0.374786i	0.871524	+	0.490352i	$0.163132\pi$
$282$	−20.8171	+	20.8171i	−0.0738194	+	0.0738194i
$283$	381.180	−	194.221i	1.34692	−	0.686292i	0.376212	−	0.926534i	$-0.377227\pi$
$283$	381.180	−	194.221i	1.34692	−	0.686292i	0.970713	+	0.240241i	$0.0772266\pi$
$284$	−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	0.725989	−	0.687706i	$-0.241382\pi$
$293$	11.2170	+	11.2170i	0.0382834	+	0.0382834i	−0.687706	+	0.725989i	$0.741382\pi$
$294$	−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	−0.0238366	+	0.999716i	$0.507588\pi$
$307$	−314.231	+	314.231i	−1.02355	+	1.02355i	−0.999716	+	0.0238366i	$0.992412\pi$
$308$	−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	0.795976	−	0.605329i	$-0.206958\pi$
$311$	145.002	+	105.350i	0.466244	+	0.338746i	−0.329732	+	0.944075i	$0.606958\pi$
$312$	−8.14180	+	51.4053i	−0.0260955	+	0.164761i
$313$	398.978	+	63.1919i	1.27469	+	0.201891i	0.756852	−	0.653587i	$-0.226737\pi$
$313$	398.978	+	63.1919i	1.27469	+	0.201891i	0.517839	+	0.855478i	$0.326737\pi$
$314$	−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	0.999540	−	0.0303190i	$-0.00965233\pi$
$317$	122.836	+	241.080i	0.387497	+	0.760505i	−0.612044	+	0.790824i	$0.709652\pi$
$318$	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	−0.0424888	−	0.999097i	$-0.513529\pi$
$331$	191.695	−	589.977i	0.579140	−	1.78241i	0.621629	−	0.783312i	$-0.286471\pi$
$332$	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	0.914999	+	0.403456i	$0.132191\pi$
$337$	−26.9235	+	169.988i	−0.0798917	+	0.504416i	−0.994891	+	0.100960i	$0.967809\pi$
$338$	−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	0.897056	−	0.441916i	$-0.145701\pi$
$347$	370.185	+	188.619i	1.06682	+	0.543570i	0.169759	+	0.985486i	$0.445701\pi$
$348$	8.27646	+	52.2555i	0.0237829	+	0.150160i
$349$			677.633i			1.94164i	0.239808	+	0.970820i	$0.422916\pi$
$349$			677.633i			1.94164i	−0.239808	+	0.970820i	$0.577084\pi$
$350$	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	−0.451302	−	0.892371i	$-0.649040\pi$
$353$	189.176	−	371.279i	0.535910	−	1.05178i	0.987212	−	0.159412i	$-0.0509597\pi$
$354$	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	0.648396	−	0.761304i	$-0.275440\pi$
$359$	−99.0885	−	136.384i	−0.276012	−	0.379899i	−0.924408	+	0.381405i	$0.875440\pi$
$360$	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	0.731685	−	0.681643i	$-0.238734\pi$
$367$	−91.6947	−	179.961i	−0.249849	−	0.490357i	−0.981534	+	0.191286i	$0.938734\pi$
$368$	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	−0.975976	−	0.217878i	$-0.930086\pi$
$373$	−42.9307	−	271.054i	−0.115096	−	0.726686i	0.860880	−	0.508808i	$-0.169914\pi$
$374$		−	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	0.000791498	−	1.00000i	$-0.499748\pi$
$379$	223.313	−	72.5589i	0.589217	−	0.191448i	0.588425	+	0.808552i	$0.299748\pi$
$380$	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	−0.960167	−	0.279428i	$-0.909855\pi$
$383$	−497.316	+	253.395i	−1.29848	+	0.661607i	−0.338310	+	0.941035i	$0.609855\pi$
$384$	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	−0.685073	−	0.728474i	$-0.740230\pi$
$389$	85.3645	−	117.494i	0.219446	−	0.302042i	0.904519	+	0.426433i	$0.140230\pi$
$390$	−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	−0.997926	−	0.0643647i	$-0.979498\pi$
$397$	−649.716	−	331.047i	−1.63657	−	0.833872i	−0.638639	−	0.769507i	$-0.720502\pi$
$398$	−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	0.552193	−	0.833716i	$-0.313791\pi$
$409$	−168.244	−	231.568i	−0.411355	−	0.566182i	−0.963548	+	0.267534i	$0.913791\pi$
$410$	−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	0.715289	−	0.698829i	$-0.246295\pi$
$419$	370.064	+	120.241i	0.883209	+	0.286972i	0.167920	+	0.985801i	$0.446295\pi$
$420$	−6.01549	+	23.9494i	−0.0143226	+	0.0570223i
$421$	−5.96539	−	18.3596i	−0.0141696	−	0.0436094i	0.943722	−	0.330740i	$-0.107298\pi$
$421$	−5.96539	−	18.3596i	−0.0141696	−	0.0436094i	−0.957891	+	0.287131i	$0.907298\pi$
$422$	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	0.581821	+	0.813317i	$0.302341\pi$
$431$	−158.150	+	486.736i	−0.366938	+	1.12932i	−0.948759	+	0.316002i	$0.897659\pi$
$432$	212.619	−	212.619i	0.492174	−	0.492174i
$433$	−491.655	+	250.511i	−1.13546	+	0.578546i	−0.917628	−	0.397440i	$-0.869899\pi$
$433$	−491.655	+	250.511i	−1.13546	+	0.578546i	−0.217833	+	0.975986i	$0.569899\pi$
$434$	−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	−0.949142	−	0.314849i	$-0.898046\pi$
$439$	−156.461	+	215.349i	−0.356402	+	0.490545i	0.592740	+	0.805394i	$0.298046\pi$
$440$	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	−0.873756	−	0.486364i	$-0.838323\pi$
$443$	−602.533	−	602.533i	−1.36012	−	1.36012i	−0.486364	−	0.873756i	$-0.661677\pi$
$444$	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	$0.0455527\pi$
$449$			128.073i			0.285240i	−0.989778	+	0.142620i	$0.954447\pi$
$450$	−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	−0.384097	−	0.923293i	$-0.625487\pi$
$457$	246.412	−	246.412i	0.539196	−	0.539196i	0.923293	+	0.384097i	$0.125487\pi$
$458$	−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	0.825455	−	0.564468i	$-0.190919\pi$
$461$	250.643	+	182.103i	0.543694	+	0.395017i	−0.281761	+	0.959485i	$0.590919\pi$
$462$	−13.9621	+	88.1532i	−0.0302210	+	0.190808i
$463$	372.239	+	58.9568i	0.803971	+	0.127337i	0.544878	−	0.838516i	$-0.316576\pi$
$463$	372.239	+	58.9568i	0.803971	+	0.127337i	0.259094	+	0.965852i	$0.416576\pi$
$464$	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	0.779597	−	0.626282i	$-0.215424\pi$
$467$	−86.5405	−	169.845i	−0.185312	−	0.363695i	−0.964908	+	0.262587i	$0.915424\pi$
$468$	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	−0.955145	−	0.296139i	$-0.904301\pi$
$479$	−744.274	+	241.829i	−1.55381	+	0.504863i	−0.598663	+	0.801001i	$0.704301\pi$
$480$	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	0.839286	+	0.543690i	$0.182973\pi$
$487$	−61.8159	+	390.290i	−0.126932	+	0.801417i	−0.966218	+	0.257727i	$0.917027\pi$
$488$	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	−0.161961	−	0.986797i	$-0.551782\pi$
$491$	356.707	−	259.163i	0.726490	−	0.527826i	0.888451	+	0.458971i	$0.151782\pi$
$492$	−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	$-0.812908\pi$
$499$		−	553.396i		−	1.10901i	0.832180	−	0.554505i	$-0.187092\pi$
$500$	−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	−0.977656	−	0.210213i	$-0.932584\pi$
$503$	−117.168	+	229.955i	−0.232938	+	0.457167i	0.744718	+	0.667380i	$0.232584\pi$
$504$	−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	0.709951	−	0.704251i	$-0.248717\pi$
$509$	−91.2224	−	125.557i	−0.179219	−	0.246674i	−0.889170	+	0.457578i	$0.848717\pi$
$510$	−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	−0.995477	−	0.0949999i	$-0.969715\pi$
$521$	−128.145	−	394.388i	−0.245959	−	0.756983i	0.749519	−	0.661983i	$-0.230285\pi$
$522$	−613.821	−	312.757i	−1.17590	−	0.599152i
$523$	−32.5786	−	205.693i	−0.0622918	−	0.393295i	−0.999060	−	0.0433450i	$-0.986199\pi$
$523$	−32.5786	−	205.693i	−0.0622918	−	0.393295i	0.936768	−	0.349950i	$-0.113801\pi$
$524$		−	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	−0.449517	−	0.893272i	$-0.648404\pi$
$541$	141.270	−	102.638i	0.261127	−	0.189720i	0.710644	+	0.703552i	$0.248404\pi$
$542$	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	0.491440	−	0.870911i	$-0.336471\pi$
$547$	41.4187	+	21.1039i	0.0757197	+	0.0385811i	−0.415721	+	0.909492i	$0.636471\pi$
$548$	−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	−0.703823	−	0.710376i	$-0.748525\pi$
$557$	3.64987	−	3.64987i	0.00655272	−	0.00655272i	0.710376	+	0.703823i	$0.248525\pi$
$558$	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	0.897084	−	0.441861i	$-0.145682\pi$
$563$	908.523	+	143.896i	1.61372	+	0.255588i	0.716635	+	0.697449i	$0.245682\pi$
$564$	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	0.996959	−	0.0779216i	$-0.0248284\pi$
$569$	1000.14	+	324.965i	1.75772	+	0.571116i	0.760756	+	0.649038i	$0.224828\pi$
$570$	359.786	−	24.5302i	0.631204	−	0.0430355i
$571$	−91.2802	−	280.932i	−0.159860	−	0.491999i	0.838761	−	0.544500i	$-0.183281\pi$
$571$	−91.2802	−	280.932i	−0.159860	−	0.491999i	−0.998621	+	0.0525011i	$0.983281\pi$
$572$	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	−0.518678	−	0.854970i	$-0.673576\pi$
$577$	−431.463	+	68.3370i	−0.747769	+	0.118435i	−0.229092	+	0.973405i	$0.573576\pi$
$578$	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	0.845036	+	0.534710i	$0.179579\pi$
$587$	−72.7149	+	459.104i	−0.123876	+	0.782119i	−0.968911	+	0.247409i	$0.920421\pi$
$588$	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	0.909252	−	0.416246i	$-0.136655\pi$
$593$	292.352	+	292.352i	0.493006	+	0.493006i	−0.416246	+	0.909252i	$0.636655\pi$
$594$	−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	$-0.785489\pi$
$599$		−	747.602i		−	1.24808i	0.781391	−	0.624042i	$-0.214511\pi$
$600$	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	0.0991528	−	0.995072i	$-0.468387\pi$
$607$	664.195	−	664.195i	1.09423	−	1.09423i	0.995072	−	0.0991528i	$-0.0316133\pi$
$608$	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	−0.134631	−	0.990896i	$-0.542985\pi$
$613$	−348.721	−	55.2320i	−0.568876	−	0.0901011i	−0.434245	+	0.900795i	$0.642985\pi$
$614$	−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	−0.887740	−	0.460345i	$-0.847726\pi$
$617$	−455.572	−	894.111i	−0.738366	−	1.44913i	0.149374	−	0.988781i	$-0.452274\pi$
$618$	−241.316	−	241.316i	−0.390480	−	0.390480i
$619$	−398.451	−	129.464i	−0.643700	−	0.209151i	−0.0310659	−	0.999517i	$-0.509890\pi$
$619$	−398.451	−	129.464i	−0.643700	−	0.209151i	−0.612634	+	0.790366i	$0.709890\pi$
$620$	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	−0.993237	−	0.116104i	$-0.962959\pi$
$631$	−76.6332	+	235.853i	−0.121447	+	0.373776i	0.871790	+	0.489880i	$0.162959\pi$
$632$	−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	−0.888971	−	0.457964i	$-0.848579\pi$
$641$	−466.730	+	339.099i	−0.728128	+	0.529016i	0.160843	+	0.986980i	$0.448579\pi$
$642$	−102.721	−	201.601i	−0.160002	−	0.314021i
$643$	−796.206	−	796.206i	−1.23827	−	1.23827i	−0.960709	−	0.277558i	$-0.910475\pi$
$643$	−796.206	−	796.206i	−1.23827	−	1.23827i	−0.277558	−	0.960709i	$-0.589525\pi$
$644$	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	0.260740	−	0.965409i	$-0.416033\pi$
$647$	−237.470	−	120.997i	−0.367033	−	0.187013i	−0.627773	+	0.778396i	$0.716033\pi$
$648$	−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	0.546718	+	0.837317i	$0.315877\pi$
$653$	−295.181	+	579.325i	−0.452038	+	0.887174i	−0.998756	+	0.0498579i	$0.984123\pi$
$654$	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	0.990898	−	0.134614i	$-0.0429795\pi$
$659$	366.844	+	504.918i	0.556668	+	0.766188i	−0.434230	+	0.900802i	$0.642979\pi$
$660$	−31.0960	−	2.77503i	−0.0471152	−	0.00420459i
$661$	−232.940	−	169.241i	−0.352405	−	0.256037i	0.397472	−	0.917614i	$-0.369887\pi$
$661$	−232.940	−	169.241i	−0.352405	−	0.256037i	−0.749877	+	0.661577i	$0.769887\pi$
$662$	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	0.499225	+	0.866472i	$0.333618\pi$
$673$	196.643	+	1241.55i	0.292189	+	1.84481i	−0.207036	+	0.978333i	$0.566382\pi$
$674$			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	−0.171793	−	0.985133i	$-0.554956\pi$
$677$	−20.8211	+	3.29774i	−0.0307549	+	0.00487110i	0.141038	+	0.990004i	$0.454956\pi$
$678$	−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	0.388244	−	0.921557i	$-0.373082\pi$
$683$	930.248	−	473.985i	1.36200	−	0.693975i	0.973759	+	0.227582i	$0.0730819\pi$
$684$	−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	0.185935	−	0.982562i	$-0.440469\pi$
$691$	813.904	−	591.336i	1.17786	−	0.855768i	0.991929	+	0.126794i	$0.0404686\pi$
$692$	−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	0.927136	−	0.374726i	$-0.122263\pi$
$709$	201.533	+	277.387i	0.284250	+	0.391236i	−0.642886	+	0.765962i	$0.722263\pi$
$710$	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	−0.520815	−	0.853669i	$-0.674372\pi$
$719$	−1038.19	−	337.329i	−1.44394	−	0.469164i	−0.923123	+	0.384506i	$0.874372\pi$
$720$	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	0.791636	−	0.610993i	$-0.209230\pi$
$727$	1260.13	−	199.586i	1.73333	−	0.274533i	0.941698	+	0.336460i	$0.109230\pi$
$728$	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	−0.452562	−	0.891733i	$-0.649490\pi$
$733$	2.09264	−	1.06625i	0.00285490	−	0.00145464i	0.455417	+	0.890278i	$0.349490\pi$
$734$	−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	−0.873725	−	0.486421i	$-0.838302\pi$
$739$	−104.284	+	143.535i	−0.141116	+	0.194229i	0.732609	+	0.680649i	$0.238302\pi$
$740$	−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	0.593493	−	0.804839i	$-0.297749\pi$
$743$	−157.030	−	157.030i	−0.211346	−	0.211346i	−0.804839	+	0.593493i	$0.797749\pi$
$744$	−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	−0.873256	−	0.487261i	$-0.837996\pi$
$757$	−292.199	+	292.199i	−0.385995	+	0.385995i	0.487261	+	0.873256i	$0.337996\pi$
$758$	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	0.872045	−	0.489426i	$-0.162794\pi$
$761$	514.474	+	373.787i	0.676050	+	0.491179i	−0.195995	+	0.980605i	$0.562794\pi$
$762$	−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	0.328963	−	0.944343i	$-0.393301\pi$
$769$	30.7819	+	10.0017i	0.0400285	+	0.0130061i	−0.288934	+	0.957349i	$0.593301\pi$
$770$	−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	−0.986346	−	0.164685i	$-0.947339\pi$
$773$	−76.6551	−	483.981i	−0.0991657	−	0.626107i	0.887181	−	0.461422i	$-0.152661\pi$
$774$			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	−0.954468	−	0.298313i	$-0.903576\pi$
$787$	35.7839	−	225.931i	0.0454687	−	0.287078i	0.999937	+	0.0112346i	$0.00357614\pi$
$788$	−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	−0.331696	−	0.943386i	$-0.607621\pi$
$797$	−1028.03	−	523.809i	−1.28988	−	0.657226i	−0.958182	+	0.286161i	$0.907621\pi$
$798$	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	0.530177	−	0.847887i	$-0.322125\pi$
$809$	−355.996	−	489.987i	−0.440045	−	0.605670i	−0.970222	+	0.242217i	$0.922125\pi$
$810$	216.682	−	129.683i	0.267508	−	0.160103i
$811$	−870.243	−	632.269i	−1.07305	−	0.779616i	−0.0965917	−	0.995324i	$-0.530794\pi$
$811$	−870.243	−	632.269i	−1.07305	−	0.779616i	−0.976458	+	0.215708i	$0.930794\pi$
$812$	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	0.874403	−	0.485200i	$-0.161253\pi$
$821$	−97.0397	−	298.658i	−0.118197	−	0.363773i	−0.992600	+	0.121427i	$0.961253\pi$
$822$	−26.6240	−	13.5656i	−0.0323893	−	0.0165032i
$823$	1.67889	+	10.6001i	0.00203996	+	0.0128798i	0.988687	−	0.149991i	$-0.0479245\pi$
$823$	1.67889	+	10.6001i	0.00203996	+	0.0128798i	−0.986647	+	0.162871i	$0.947925\pi$
$824$		−	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	−0.751142	−	0.660141i	$-0.770497\pi$
$827$	−1043.28	+	165.240i	−1.26153	+	0.199806i	−0.510384	+	0.859947i	$0.670497\pi$
$828$	−65.7561	+	129.054i	−0.0794156	+	0.155862i
$829$	631.029	−	205.034i	0.761193	−	0.247327i	0.0974024	−	0.995245i	$-0.468947\pi$
$829$	631.029	−	205.034i	0.761193	−	0.247327i	0.663791	+	0.747918i	$0.268947\pi$
$830$	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	−0.999977	−	0.00677528i	$-0.997843\pi$
$839$	−574.315	+	790.477i	−0.684523	+	0.942166i	0.315454	+	0.948941i	$0.397843\pi$
$840$	−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	0.208307	−	0.978064i	$-0.433205\pi$
$853$	748.198	−	1468.42i	0.877137	−	1.72148i	0.668830	−	0.743415i	$-0.266795\pi$
$854$	−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	−0.413210	−	0.910636i	$-0.635593\pi$
$857$	426.293	−	426.293i	0.497425	−	0.497425i	0.910636	+	0.413210i	$0.135593\pi$
$858$	64.6230	−	32.9271i	0.0753182	−	0.0383765i
$859$	23.9279	+	32.9339i	0.0278555	+	0.0383398i	0.822718	−	0.568450i	$-0.192457\pi$
$859$	23.9279	+	32.9339i	0.0278555	+	0.0383398i	−0.794862	+	0.606790i	$0.792457\pi$
$860$	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	0.632519	−	0.774545i	$-0.282021\pi$
$863$	858.454	+	135.966i	0.994732	+	0.157550i	0.362213	+	0.932095i	$0.382021\pi$
$864$	−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	−0.0543610	−	0.998521i	$-0.517312\pi$
$877$	177.591	−	28.1277i	0.202499	−	0.0320726i	0.256860	+	0.966449i	$0.417312\pi$
$878$	−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	−0.984622	−	0.174700i	$-0.944104\pi$
$881$	−75.2021	+	231.448i	−0.0853599	+	0.262711i	0.899262	+	0.437411i	$0.144104\pi$
$882$	−200.727	+	200.727i	−0.227582	+	0.227582i
$883$	−859.392	+	437.882i	−0.973264	+	0.495903i	−0.866931	−	0.498428i	$-0.833911\pi$
$883$	−859.392	+	437.882i	−0.973264	+	0.495903i	−0.106333	+	0.994331i	$0.533911\pi$
$884$	−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	−0.952332	−	0.305062i	$-0.901323\pi$
$887$	42.2734	−	266.904i	0.0476589	−	0.300906i	0.999991	+	0.00415563i	$0.00132278\pi$
$888$	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	−0.958974	−	0.283494i	$-0.908507\pi$
$907$	−612.661	+	612.661i	−0.675481	+	0.675481i	0.283494	+	0.958974i	$0.408507\pi$
$908$	−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	0.545297	−	0.838243i	$-0.316417\pi$
$911$	−75.9892	−	55.2094i	−0.0834130	−	0.0606031i	−0.628710	+	0.777640i	$0.716417\pi$
$912$	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	−0.285202	−	0.958467i	$-0.592061\pi$
$919$	−991.884	−	322.283i	−1.07931	−	0.350688i	−0.794106	+	0.607779i	$0.792061\pi$
$920$	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	−0.995886	−	0.0906186i	$-0.971116\pi$
$929$	−1624.18	+	527.728i	−1.74831	+	0.568060i	−0.752424	+	0.658679i	$0.771116\pi$
$930$	−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	−0.949955	−	0.312386i	$-0.898872\pi$
$937$	46.8861	−	296.027i	0.0500385	−	0.315931i	0.999994	−	0.00354453i	$-0.00112826\pi$
$938$	−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	−0.383125	−	0.923696i	$-0.625152\pi$
$941$	354.729	−	257.725i	0.376970	−	0.273885i	0.760095	+	0.649812i	$0.225152\pi$
$942$	−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	0.848024	−	0.529957i	$-0.177792\pi$
$947$	869.096	+	442.827i	0.917736	+	0.467610i	0.0697120	+	0.997567i	$0.477792\pi$
$948$	−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	−0.968700	−	0.248233i	$-0.920150\pi$
$953$	−189.159	+	371.246i	−0.198488	+	0.389555i	0.770212	+	0.637788i	$0.220150\pi$
$954$	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	0.776599	−	0.629995i	$-0.216943\pi$
$967$	−183.296	−	359.738i	−0.189551	−	0.372015i	−0.966150	+	0.257980i	$0.916943\pi$
$968$	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	0.760569	+	0.649257i	$0.224920\pi$
$971$	511.600	+	1574.54i	0.526879	+	1.62157i	−0.233690	+	0.972311i	$0.575080\pi$
$972$	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	−0.109657	−	0.993969i	$-0.534975\pi$
$977$	91.0619	−	14.4228i	0.0932056	−	0.0147623i	0.202863	+	0.979207i	$0.434975\pi$
$978$	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	−0.146987	−	0.989138i	$-0.546958\pi$
$983$	557.209	−	283.912i	0.566845	−	0.288822i	0.713833	+	0.700316i	$0.246958\pi$
$984$	−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	−0.535997	−	0.844220i	$-0.680064\pi$
$991$	100.361	−	72.9162i	0.101272	−	0.0735784i	0.637269	+	0.770642i	$0.280064\pi$
$992$	−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	0.336207	−	0.941788i	$-0.390856\pi$
$997$	−227.413	−	115.873i	−0.228097	−	0.116221i	−0.564305	+	0.825567i	$0.690856\pi$
$998$	−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.13.4	yes	32
3.2	odd	2		225.3.r.a.163.1		32
4.3	odd	2		400.3.bg.c.113.3		32
5.2	odd	4		125.3.f.a.82.4		32
5.3	odd	4		125.3.f.b.82.1		32
5.4	even	2		125.3.f.c.43.1		32
25.2	odd	20	inner	25.3.f.a.2.4	✓	32
25.11	even	5		125.3.f.a.93.4		32
25.14	even	10		125.3.f.b.93.1		32
25.23	odd	20		125.3.f.c.32.1		32
75.2	even	20		225.3.r.a.127.1		32
100.27	even	20		400.3.bg.c.177.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.3.f.a.2.4	✓	32	25.2	odd	20	inner
25.3.f.a.13.4	yes	32	1.1	even	1	trivial
125.3.f.a.82.4		32	5.2	odd	4
125.3.f.a.93.4		32	25.11	even	5
125.3.f.b.82.1		32	5.3	odd	4
125.3.f.b.93.1		32	25.14	even	10
125.3.f.c.32.1		32	25.23	odd	20
125.3.f.c.43.1		32	5.4	even	2
225.3.r.a.127.1		32	75.2	even	20
225.3.r.a.163.1		32	3.2	odd	2
400.3.bg.c.113.3		32	4.3	odd	2
400.3.bg.c.177.3		32	100.27	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)

\(f(q)\)	\(=\)	\(q+(1.80600 - 0.286042i) q^{2} +(-0.665351 + 1.30583i) q^{3} +(-0.624420 + 0.202886i) q^{4} +(-3.20727 - 3.83580i) q^{5} +(-0.828102 + 2.54863i) q^{6} +(3.62927 - 3.62927i) q^{7} +(-7.58652 + 3.86553i) q^{8} +(4.02758 + 5.54349i) q^{9} +O(q^{10})\)	\(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

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