LMFDB - Embedded newform 279.3.v.a.46.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [279,3,Mod(46,279)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(279, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 7])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("279.46"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 279 = 3^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	279.v (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [20,3,0,-11,14,0,-1,19] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(8)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.60219937565$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} + 20 x^{18} - 33 x^{17} + 250 x^{16} - 510 x^{15} + 2908 x^{14} - 6447 x^{13} + \cdots + 731025 $ x^20 - 2x^19 + 20x^18 - 33x^17 + 250x^16 - 510x^15 + 2908x^14 - 6447x^13 + 39842x^12 - 79034x^11 + 199542x^10 - 173039x^9 + 688988x^8 - 636120x^7 + 3401146x^6 - 2156427x^5 + 7116556x^4 - 6139950x^3 + 6454710x^2 - 3116475*x + 731025
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			46.2
Root			$-0.453363 - 1.39531i$ of defining polynomial
Character	$\chi$	$=$	279.46
Dual form			279.3.v.a.91.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.18692 + 0.862348i) q^{2} +(-0.570933 + 1.75715i) q^{4} +4.14776 q^{5} +(1.06697 - 3.28380i) q^{7} +(-2.65108 - 8.15917i) q^{8} +(-4.92306 + 3.57681i) q^{10} +(13.6300 + 4.42864i) q^{11} +(5.41722 - 7.45616i) q^{13} +(1.56537 + 4.81771i) q^{14} +(4.20377 + 3.05422i) q^{16} +(1.46101 - 0.474711i) q^{17} +(16.5438 - 12.0198i) q^{19} +(-2.36809 + 7.28825i) q^{20} +(-19.9967 + 6.49732i) q^{22} +(-17.2964 + 5.61995i) q^{23} -7.79606 q^{25} +13.5214i q^{26} +(5.16097 + 3.74966i) q^{28} +(23.9358 + 32.9448i) q^{29} +(20.1838 + 23.5290i) q^{31} +26.6929 q^{32} +(-1.32474 + 1.82334i) q^{34} +(4.42555 - 13.6204i) q^{35} +42.0983i q^{37} +(-9.27096 + 28.5331i) q^{38} +(-10.9960 - 33.8423i) q^{40} +(61.3917 - 44.6037i) q^{41} +(15.1894 + 20.9064i) q^{43} +(-15.5636 + 21.4214i) q^{44} +(15.6831 - 21.5860i) q^{46} +(3.99548 + 2.90289i) q^{47} +(29.9969 + 21.7940i) q^{49} +(9.25330 - 6.72292i) q^{50} +(10.0087 + 13.7758i) q^{52} +(-38.5605 + 12.5291i) q^{53} +(56.5338 + 18.3689i) q^{55} -29.6217 q^{56} +(-56.8198 - 18.4619i) q^{58} +(-36.1430 - 26.2594i) q^{59} -84.8005i q^{61} +(-44.2468 - 10.5215i) q^{62} +(-48.4974 + 35.2354i) q^{64} +(22.4693 - 30.9264i) q^{65} -109.556 q^{67} +2.83825i q^{68} +(6.49278 + 19.9827i) q^{70} +(19.6220 + 60.3903i) q^{71} +(-85.9266 - 27.9192i) q^{73} +(-36.3034 - 49.9674i) q^{74} +(11.6752 + 35.9325i) q^{76} +(29.0856 - 40.0328i) q^{77} +(142.262 - 46.2236i) q^{79} +(17.4362 + 12.6682i) q^{80} +(-34.4032 + 105.882i) q^{82} +(-25.0530 - 34.4824i) q^{83} +(6.05993 - 1.96899i) q^{85} +(-36.0572 - 11.7157i) q^{86} -122.950i q^{88} +(-46.3352 - 15.0552i) q^{89} +(-18.7045 - 25.7446i) q^{91} -33.6011i q^{92} -7.24561 q^{94} +(68.6199 - 49.8553i) q^{95} +(15.1554 - 46.6434i) q^{97} -54.3979 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 3 q^{2} - 11 q^{4} + 14 q^{5} - q^{7} + 19 q^{8} + 12 q^{10} + 10 q^{11} + 10 q^{13} - 103 q^{16} - 35 q^{17} + 47 q^{19} + 125 q^{20} + 150 q^{22} - 75 q^{23} + 82 q^{25} + 88 q^{28} - 5 q^{29}+ \cdots + 1000 q^{98}+O(q^{100}) $ 20 * q + 3 * q^2 - 11 * q^4 + 14 * q^5 - q^7 + 19 * q^8 + 12 * q^10 + 10 * q^11 + 10 * q^13 - 103 * q^16 - 35 * q^17 + 47 * q^19 + 125 * q^20 + 150 * q^22 - 75 * q^23 + 82 * q^25 + 88 * q^28 - 5 * q^29 + 73 * q^31 - 226 * q^32 - 265 * q^34 + 50 * q^35 - 8 * q^38 - 466 * q^40 + 98 * q^41 + 245 * q^43 - 380 * q^44 - 445 * q^46 + 187 * q^47 + 328 * q^49 + 44 * q^50 - 15 * q^52 - 25 * q^53 + 190 * q^55 - 64 * q^56 - 85 * q^58 + 173 * q^59 + 40 * q^62 - 469 * q^64 + 345 * q^65 + 76 * q^67 - 11 * q^70 + 467 * q^71 - 15 * q^73 - 45 * q^74 + 55 * q^76 + 320 * q^77 + 500 * q^79 - 1030 * q^80 + 178 * q^82 + 50 * q^83 + 20 * q^85 - 1125 * q^86 - 55 * q^89 + 300 * q^91 + 62 * q^94 + 559 * q^95 - 405 * q^97 + 1000 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/279\mathbb{Z}\right)^\times$.

$n$	$127$	$218$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$1$

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 $

$2$	−1.18692	+	0.862348i	−0.593460	+	0.431174i	−0.843551	−	0.537048i	$-0.819539\pi$
$2$	−1.18692	+	0.862348i	−0.593460	+	0.431174i	0.250092	+	0.968222i	$0.419539\pi$
$3$		0			0
$3$		0			0
$4$	−0.570933	+	1.75715i	−0.142733	+	0.439288i
$5$	4.14776			0.829553			0.414776	−	0.909923i	$-0.363860\pi$
$5$	4.14776			0.829553			0.414776	+	0.909923i	$0.363860\pi$
$6$		0			0
$7$	1.06697	−	3.28380i	0.152425	−	0.469115i	−0.845466	−	0.534029i	$-0.820677\pi$
$7$	1.06697	−	3.28380i	0.152425	−	0.469115i	0.997891	+	0.0649142i	$0.0206774\pi$
$8$	−2.65108	−	8.15917i	−0.331384	−	1.01990i
$9$		0			0
$10$	−4.92306	+	3.57681i	−0.492306	+	0.357681i
$11$	13.6300	+	4.42864i	1.23909	+	0.402604i	0.853998	−	0.520276i	$-0.174171\pi$
$11$	13.6300	+	4.42864i	1.23909	+	0.402604i	0.385088	+	0.922880i	$0.374171\pi$
$12$		0			0
$13$	5.41722	−	7.45616i	0.416709	−	0.573551i	−0.548130	−	0.836393i	$-0.684660\pi$
$13$	5.41722	−	7.45616i	0.416709	−	0.573551i	0.964839	+	0.262842i	$0.0846599\pi$
$14$	1.56537	+	4.81771i	0.111812	+	0.344122i
$15$		0			0
$16$	4.20377	+	3.05422i	0.262735	+	0.190888i
$17$	1.46101	−	0.474711i	0.0859418	−	0.0279242i	−0.265730	−	0.964047i	$-0.585613\pi$
$17$	1.46101	−	0.474711i	0.0859418	−	0.0279242i	0.351672	+	0.936123i	$0.385613\pi$
$18$		0			0
$19$	16.5438	−	12.0198i	0.870728	−	0.632621i	−0.0600541	−	0.998195i	$-0.519127\pi$
$19$	16.5438	−	12.0198i	0.870728	−	0.632621i	0.930782	+	0.365574i	$0.119127\pi$
$20$	−2.36809	+	7.28825i	−0.118405	+	0.364412i
$21$		0			0
$22$	−19.9967	+	6.49732i	−0.908940	+	0.295333i
$23$	−17.2964	+	5.61995i	−0.752019	+	0.244346i	−0.659850	−	0.751397i	$-0.729380\pi$
$23$	−17.2964	+	5.61995i	−0.752019	+	0.244346i	−0.0921694	+	0.995743i	$0.529380\pi$
$24$		0			0
$25$	−7.79606			−0.311843
$26$			13.5214i			0.520054i
$27$		0			0
$28$	5.16097	+	3.74966i	0.184320	+	0.133917i
$29$	23.9358	+	32.9448i	0.825373	+	1.13603i	0.988767	+	0.149468i	$0.0477560\pi$
$29$	23.9358	+	32.9448i	0.825373	+	1.13603i	−0.163393	+	0.986561i	$0.552244\pi$
$30$		0			0
$31$	20.1838	+	23.5290i	0.651092	+	0.758999i
$31$	20.1838	+	23.5290i	0.651092	+	0.758999i
$32$	26.6929			0.834154
$33$		0			0
$34$	−1.32474	+	1.82334i	−0.0389629	+	0.0536278i
$35$	4.42555	−	13.6204i	0.126444	−	0.389155i
$36$		0			0
$37$			42.0983i			1.13779i	0.822409	+	0.568897i	$0.192630\pi$
$37$			42.0983i			1.13779i	−0.822409	+	0.568897i	$0.807370\pi$
$38$	−9.27096	+	28.5331i	−0.243973	+	0.750870i
$39$		0			0
$40$	−10.9960	−	33.8423i	−0.274901	−	0.846058i
$41$	61.3917	−	44.6037i	1.49736	−	1.08790i	0.525941	−	0.850521i	$-0.323713\pi$
$41$	61.3917	−	44.6037i	1.49736	−	1.08790i	0.971418	−	0.237374i	$-0.0762866\pi$
$42$		0			0
$43$	15.1894	+	20.9064i	0.353242	+	0.486196i	0.948250	−	0.317523i	$-0.102851\pi$
$43$	15.1894	+	20.9064i	0.353242	+	0.486196i	−0.595008	+	0.803720i	$0.702851\pi$
$44$	−15.5636	+	21.4214i	−0.353718	+	0.486851i
$45$		0			0
$46$	15.6831	−	21.5860i	0.340938	−	0.469260i
$47$	3.99548	+	2.90289i	0.0850102	+	0.0617635i	0.629479	−	0.777018i	$-0.283269\pi$
$47$	3.99548	+	2.90289i	0.0850102	+	0.0617635i	−0.544468	+	0.838781i	$0.683269\pi$
$48$		0			0
$49$	29.9969	+	21.7940i	0.612182	+	0.444776i
$50$	9.25330	−	6.72292i	0.185066	−	0.134458i
$51$		0			0
$52$	10.0087	+	13.7758i	0.192476	+	0.264920i
$53$	−38.5605	+	12.5291i	−0.727557	+	0.236398i	−0.649296	−	0.760535i	$-0.724937\pi$
$53$	−38.5605	+	12.5291i	−0.727557	+	0.236398i	−0.0782603	+	0.996933i	$0.524937\pi$
$54$		0			0
$55$	56.5338	+	18.3689i	1.02789	+	0.333981i
$56$	−29.6217			−0.528959
$57$		0			0
$58$	−56.8198	−	18.4619i	−0.979652	−	0.318308i
$59$	−36.1430	−	26.2594i	−0.612592	−	0.445074i	0.237734	−	0.971330i	$-0.423595\pi$
$59$	−36.1430	−	26.2594i	−0.612592	−	0.445074i	−0.850326	+	0.526256i	$0.823595\pi$
$60$		0			0
$61$		−	84.8005i		−	1.39017i	−0.718927	−	0.695086i	$-0.755366\pi$
$61$		−	84.8005i		−	1.39017i	0.718927	−	0.695086i	$-0.244634\pi$
$62$	−44.2468	−	10.5215i	−0.713657	−	0.169702i
$63$		0			0
$64$	−48.4974	+	35.2354i	−0.757772	+	0.550554i
$65$	22.4693	−	30.9264i	0.345682	−	0.475791i
$66$		0			0
$67$	−109.556			−1.63517			−0.817583	−	0.575811i	$-0.804686\pi$
$67$	−109.556			−1.63517			−0.817583	+	0.575811i	$0.804686\pi$
$68$			2.83825i			0.0417389i
$69$		0			0
$70$	6.49278	+	19.9827i	0.0927540	+	0.285467i
$71$	19.6220	+	60.3903i	0.276366	+	0.850568i	0.988855	+	0.148884i	$0.0475682\pi$
$71$	19.6220	+	60.3903i	0.276366	+	0.850568i	−0.712488	+	0.701684i	$0.752432\pi$
$72$		0			0
$73$	−85.9266	−	27.9192i	−1.17708	−	0.382455i	−0.345796	−	0.938310i	$-0.612391\pi$
$73$	−85.9266	−	27.9192i	−1.17708	−	0.382455i	−0.831280	+	0.555854i	$0.812391\pi$
$74$	−36.3034	−	49.9674i	−0.490587	−	0.675235i
$75$		0			0
$76$	11.6752	+	35.9325i	0.153621	+	0.472796i
$77$	29.0856	−	40.0328i	0.377735	−	0.519907i
$78$		0			0
$79$	142.262	−	46.2236i	1.80078	−	0.585108i	0.800873	−	0.598834i	$-0.204369\pi$
$79$	142.262	−	46.2236i	1.80078	−	0.585108i	0.999906	+	0.0137258i	$0.00436918\pi$
$80$	17.4362	+	12.6682i	0.217953	+	0.158352i
$81$		0			0
$82$	−34.4032	+	105.882i	−0.419551	+	1.29124i
$83$	−25.0530	−	34.4824i	−0.301843	−	0.415451i	0.630973	−	0.775805i	$-0.282656\pi$
$83$	−25.0530	−	34.4824i	−0.301843	−	0.415451i	−0.932816	+	0.360354i	$0.882656\pi$
$84$		0			0
$85$	6.05993	−	1.96899i	0.0712933	−	0.0231646i
$86$	−36.0572	−	11.7157i	−0.419270	−	0.136229i
$87$		0			0
$88$		−	122.950i		−	1.39716i
$89$	−46.3352	−	15.0552i	−0.520620	−	0.169160i	0.0369067	−	0.999319i	$-0.488250\pi$
$89$	−46.3352	−	15.0552i	−0.520620	−	0.169160i	−0.557527	+	0.830159i	$0.688250\pi$
$90$		0			0
$91$	−18.7045	−	25.7446i	−0.205544	−	0.282908i
$92$		−	33.6011i		−	0.365229i
$93$		0			0
$94$	−7.24561			−0.0770810
$95$	68.6199	−	49.8553i	0.722315	−	0.524792i
$96$		0			0
$97$	15.1554	−	46.6434i	0.156241	−	0.480860i	−0.842044	−	0.539409i	$-0.818648\pi$
$97$	15.1554	−	46.6434i	0.156241	−	0.480860i	0.998284	+	0.0585497i	$0.0186476\pi$
$98$	−54.3979			−0.555081
$99$		0			0
$100$	4.45103	−	13.6989i	0.0445103	−	0.136989i
$101$	−17.7682	−	54.6850i	−0.175923	−	0.541435i	0.823751	−	0.566951i	$-0.191877\pi$
$101$	−17.7682	−	54.6850i	−0.175923	−	0.541435i	−0.999674	+	0.0255158i	$0.991877\pi$
$102$		0			0
$103$	51.9380	−	37.7352i	0.504253	−	0.366361i	−0.306386	−	0.951907i	$-0.599120\pi$
$103$	51.9380	−	37.7352i	0.504253	−	0.366361i	0.810639	+	0.585546i	$0.199120\pi$
$104$	−75.1976	−	24.4332i	−0.723054	−	0.234934i
$105$		0			0
$106$	34.9638	−	48.1236i	0.329847	−	0.453996i
$107$	40.4335	+	124.442i	0.377883	+	1.16300i	0.941513	+	0.336977i	$0.109405\pi$
$107$	40.4335	+	124.442i	0.377883	+	1.16300i	−0.563630	+	0.826028i	$0.690595\pi$
$108$		0			0
$109$	−123.474	−	89.7092i	−1.13279	−	0.823020i	−0.146692	−	0.989182i	$-0.546863\pi$
$109$	−123.474	−	89.7092i	−1.13279	−	0.823020i	−0.986099	+	0.166162i	$0.946863\pi$
$110$	−82.9415	+	26.9493i	−0.754014	+	0.244994i
$111$		0			0
$112$	14.5147	−	10.5456i	0.129596	−	0.0941570i
$113$	37.7786	−	116.270i	0.334324	−	1.02894i	−0.632731	−	0.774372i	$-0.718066\pi$
$113$	37.7786	−	116.270i	0.334324	−	1.02894i	0.967054	−	0.254570i	$-0.0819340\pi$
$114$		0			0
$115$	−71.7415	+	23.3102i	−0.623839	+	0.202698i
$116$	−71.5548	+	23.2496i	−0.616852	+	0.200427i
$117$		0			0
$118$	65.5435			0.555453
$119$		−	5.30418i		−	0.0445729i
$120$		0			0
$121$	68.2717	+	49.6023i	0.564229	+	0.409936i
$122$	73.1275	+	100.651i	0.599406	+	0.825011i
$123$		0			0
$124$	−52.8676	+	22.0326i	−0.426351	+	0.177682i
$125$	−136.030			−1.08824
$126$		0			0
$127$	−86.5000	+	119.057i	−0.681102	+	0.937457i	−0.999946	−	0.0103505i	$-0.996705\pi$
$127$	−86.5000	+	119.057i	−0.681102	+	0.937457i	0.318844	+	0.947807i	$0.396705\pi$
$128$	−5.81691	+	17.9026i	−0.0454446	+	0.139864i
$129$		0			0
$130$			56.0835i			0.431412i
$131$	−19.6729	+	60.5470i	−0.150175	+	0.462191i	−0.997640	−	0.0686600i	$-0.978128\pi$
$131$	−19.6729	+	60.5470i	−0.150175	+	0.462191i	0.847465	+	0.530851i	$0.178128\pi$
$132$		0			0
$133$	−21.8188	−	67.1515i	−0.164051	−	0.504898i
$134$	130.034	−	94.4754i	0.970405	−	0.705040i
$135$		0			0
$136$	−7.74650	−	10.6621i	−0.0569596	−	0.0783981i
$137$	56.0236	−	77.1098i	0.408931	−	0.562846i	−0.554026	−	0.832499i	$-0.686909\pi$
$137$	56.0236	−	77.1098i	0.408931	−	0.562846i	0.962957	+	0.269654i	$0.0869092\pi$
$138$		0			0
$139$	43.4725	−	59.8347i	0.312752	−	0.430466i	−0.623485	−	0.781835i	$-0.714284\pi$
$139$	43.4725	−	59.8347i	0.312752	−	0.430466i	0.936237	+	0.351369i	$0.114284\pi$
$140$	21.4065	+	15.5527i	0.152903	+	0.111091i
$141$		0			0
$142$	−75.3672	−	54.7575i	−0.530755	−	0.385616i
$143$	106.857	−	77.6362i	0.747252	−	0.542911i
$144$		0			0
$145$	99.2801	+	136.647i	0.684690	+	0.942396i
$146$	126.064	−	40.9607i	0.863452	−	0.280553i
$147$		0			0
$148$	−73.9732	−	24.0353i	−0.499819	−	0.162401i
$149$	41.6680			0.279651			0.139826	−	0.990176i	$-0.455346\pi$
$149$	41.6680			0.279651			0.139826	+	0.990176i	$0.455346\pi$
$150$		0			0
$151$	−18.9900	−	6.17023i	−0.125762	−	0.0408624i	0.245460	−	0.969407i	$-0.421061\pi$
$151$	−18.9900	−	6.17023i	−0.125762	−	0.0408624i	−0.371222	+	0.928544i	$0.621061\pi$
$152$	−141.931	−	103.119i	−0.933754	−	0.678412i
$153$		0			0
$154$			72.5976i			0.471413i
$155$	83.7178	+	97.5926i	0.540115	+	0.629630i
$156$		0			0
$157$	80.3853	−	58.4034i	0.512009	−	0.371996i	−0.301576	−	0.953442i	$-0.597513\pi$
$157$	80.3853	−	58.4034i	0.512009	−	0.371996i	0.813585	+	0.581446i	$0.197513\pi$
$158$	−128.992	+	177.543i	−0.816406	+	1.12369i
$159$		0			0
$160$	110.716			0.691974
$161$			62.7944i			0.390028i
$162$		0			0
$163$	51.9446	+	159.869i	0.318679	+	0.980792i	0.974214	+	0.225627i	$0.0724431\pi$
$163$	51.9446	+	159.869i	0.318679	+	0.980792i	−0.655535	+	0.755165i	$0.727557\pi$
$164$	43.3249	+	133.340i	0.264176	+	0.813050i
$165$		0			0
$166$	59.4717	+	19.3235i	0.358263	+	0.116407i
$167$	41.7004	+	57.3956i	0.249703	+	0.343686i	0.915407	−	0.402529i	$-0.131869\pi$
$167$	41.7004	+	57.3956i	0.249703	+	0.343686i	−0.665704	+	0.746216i	$0.731869\pi$
$168$		0			0
$169$	25.9758	+	79.9452i	0.153703	+	0.473049i
$170$	−5.49469	+	7.56280i	−0.0323217	+	0.0444870i
$171$		0			0
$172$	−45.4079	+	14.7539i	−0.263999	+	0.0857786i
$173$	−166.025	−	120.624i	−0.959684	−	0.697251i	−0.00660682	−	0.999978i	$-0.502103\pi$
$173$	−166.025	−	120.624i	−0.959684	−	0.697251i	−0.953077	+	0.302727i	$0.902103\pi$
$174$		0			0
$175$	−8.31818	+	25.6007i	−0.0475325	+	0.146290i
$176$	43.7711	+	60.2458i	0.248700	+	0.342306i
$177$		0			0
$178$	67.9790	−	22.0877i	0.381904	−	0.124088i
$179$	101.179	+	32.8752i	0.565248	+	0.183660i	0.577681	−	0.816263i	$-0.303958\pi$
$179$	101.179	+	32.8752i	0.565248	+	0.183660i	−0.0124333	+	0.999923i	$0.503958\pi$
$180$		0			0
$181$		−	137.906i		−	0.761913i	−0.924593	−	0.380957i	$-0.875595\pi$
$181$		−	137.906i		−	0.761913i	0.924593	−	0.380957i	$-0.124405\pi$
$182$	44.4016	+	14.4269i	0.243965	+	0.0792690i
$183$		0			0
$184$	91.7083	+	126.226i	0.498415	+	0.686009i
$185$			174.614i			0.943859i
$186$		0			0
$187$	22.0158			0.117732
$188$	−7.38196	+	5.36331i	−0.0392657	+	0.0285282i
$189$		0			0
$190$	−38.4537	+	118.348i	−0.202388	+	0.622886i
$191$	30.5286			0.159836			0.0799178	−	0.996801i	$-0.474534\pi$
$191$	30.5286			0.159836			0.0799178	+	0.996801i	$0.474534\pi$
$192$		0			0
$193$	−55.8889	+	172.008i	−0.289580	+	0.891236i	0.695408	+	0.718615i	$0.255224\pi$
$193$	−55.8889	+	172.008i	−0.289580	+	0.891236i	−0.984988	+	0.172621i	$0.944776\pi$
$194$	22.2346	+	68.4311i	0.114611	+	0.352738i
$195$		0			0
$196$	−55.4216	+	40.2662i	−0.282763	+	0.205440i
$197$	54.3265	+	17.6518i	0.275769	+	0.0896028i	0.443637	−	0.896207i	$-0.353688\pi$
$197$	54.3265	+	17.6518i	0.275769	+	0.0896028i	−0.167868	+	0.985810i	$0.553688\pi$
$198$		0			0
$199$	−138.187	+	190.199i	−0.694409	+	0.955773i	0.305584	+	0.952165i	$0.401148\pi$
$199$	−138.187	+	190.199i	−0.694409	+	0.955773i	−0.999993	+	0.00360755i	$0.998852\pi$
$200$	20.6680	+	63.6094i	0.103340	+	0.318047i
$201$		0			0
$202$	68.2469	+	49.5843i	0.337856	+	0.245467i
$203$	133.723	−	43.4493i	0.658735	−	0.214036i
$204$		0			0
$205$	254.638	−	185.006i	1.24214	−	0.902466i
$206$	−29.1054	+	89.5773i	−0.141288	+	0.434841i
$207$		0			0
$208$	45.5455	−	14.7986i	0.218969	−	0.0711472i
$209$	278.723	−	90.5626i	1.33360	−	0.433314i
$210$		0			0
$211$	−122.713			−0.581578			−0.290789	−	0.956787i	$-0.593918\pi$
$211$	−122.713			−0.581578			−0.290789	+	0.956787i	$0.593918\pi$
$212$		−	74.9099i		−	0.353349i
$213$		0			0
$214$	−155.303	−	112.834i	−0.725716	−	0.527263i
$215$	63.0021	+	86.7149i	0.293033	+	0.403325i
$216$		0			0
$217$	98.8001	−	41.1750i	0.455300	−	0.189747i
$218$	223.914			1.02713
$219$		0			0
$220$	−64.5540	+	88.8510i	−0.293427	+	0.403868i
$221$	4.37509	−	13.4652i	0.0197968	−	0.0609283i
$222$		0			0
$223$		−	310.445i		−	1.39213i	−0.717980	−	0.696064i	$-0.754933\pi$
$223$		−	310.445i		−	1.39213i	0.717980	−	0.696064i	$-0.245067\pi$
$224$	28.4806	−	87.6543i	0.127146	−	0.391314i
$225$		0			0
$226$	55.4254	+	170.582i	0.245245	+	0.754787i
$227$	−344.688	+	250.430i	−1.51845	+	1.10322i	−0.556198	+	0.831050i	$0.687740\pi$
$227$	−344.688	+	250.430i	−1.51845	+	1.10322i	−0.962250	+	0.272167i	$0.912260\pi$
$228$		0			0
$229$	0.576116	+	0.792956i	0.00251579	+	0.00346269i	0.810273	−	0.586053i	$-0.199319\pi$
$229$	0.576116	+	0.792956i	0.00251579	+	0.00346269i	−0.807757	+	0.589515i	$0.799319\pi$
$230$	65.0499	−	89.5335i	0.282826	−	0.389276i
$231$		0			0
$232$	205.347	−	282.636i	0.885116	−	1.21826i
$233$	−287.434	−	208.833i	−1.23362	−	0.896280i	−0.236468	−	0.971639i	$-0.575990\pi$
$233$	−287.434	−	208.833i	−1.23362	−	0.896280i	−0.997156	+	0.0753591i	$0.975990\pi$
$234$		0			0
$235$	16.5723	+	12.0405i	0.0705204	+	0.0512361i
$236$	66.7769	−	48.5163i	0.282953	−	0.205577i
$237$		0			0
$238$	4.57404	+	6.29563i	0.0192187	+	0.0264522i
$239$	−226.754	+	73.6767i	−0.948760	+	0.308271i	−0.742212	−	0.670166i	$-0.766223\pi$
$239$	−226.754	+	73.6767i	−0.948760	+	0.308271i	−0.206548	+	0.978436i	$0.566223\pi$
$240$		0			0
$241$	−309.669	−	100.617i	−1.28493	−	0.417500i	−0.414617	−	0.909996i	$-0.636085\pi$
$241$	−309.669	−	100.617i	−1.28493	−	0.417500i	−0.870315	+	0.492496i	$0.836085\pi$
$242$	−123.807			−0.511601
$243$		0			0
$244$	149.007	+	48.4154i	0.610686	+	0.198424i
$245$	124.420	+	90.3964i	0.507837	+	0.368965i
$246$		0			0
$247$		−	188.467i		−	0.763026i
$248$	138.468	−	227.061i	0.558339	−	0.915567i
$249$		0			0
$250$	161.457	−	117.305i	0.645828	−	0.469222i
$251$	−107.602	+	148.101i	−0.428692	+	0.590044i	−0.967652	−	0.252287i	$-0.918817\pi$
$251$	−107.602	+	148.101i	−0.428692	+	0.590044i	0.538960	+	0.842331i	$0.318817\pi$
$252$		0			0
$253$	−260.638			−1.03019
$254$		−	215.904i		−	0.850016i
$255$		0			0
$256$	−82.6315	−	254.314i	−0.322779	−	0.993413i
$257$	−58.6764	−	180.587i	−0.228313	−	0.702675i	−0.997938	−	0.0641793i	$-0.979557\pi$
$257$	−58.6764	−	180.587i	−0.228313	−	0.702675i	0.769625	−	0.638496i	$-0.220443\pi$
$258$		0			0
$259$	138.243	+	44.9178i	0.533755	+	0.173428i
$260$	41.5139	+	57.1389i	0.159669	+	0.219765i
$261$		0			0
$262$	−28.8624	−	88.8294i	−0.110162	−	0.339043i
$263$	16.6417	−	22.9053i	0.0632762	−	0.0870923i	−0.776206	−	0.630479i	$-0.782858\pi$
$263$	16.6417	−	22.9053i	0.0632762	−	0.0870923i	0.839482	+	0.543387i	$0.182858\pi$
$264$		0			0
$265$	−159.940	+	51.9676i	−0.603547	+	0.196104i
$266$	83.8051	+	60.8880i	0.315057	+	0.228902i
$267$		0			0
$268$	62.5492	−	192.507i	0.233392	−	0.718308i
$269$	166.176	+	228.722i	0.617756	+	0.850268i	0.997187	−	0.0749520i	$-0.0238804\pi$
$269$	166.176	+	228.722i	0.617756	+	0.850268i	−0.379431	+	0.925220i	$0.623880\pi$
$270$		0			0
$271$	−70.9562	+	23.0551i	−0.261831	+	0.0850740i	−0.436991	−	0.899466i	$-0.643956\pi$
$271$	−70.9562	+	23.0551i	−0.261831	+	0.0850740i	0.175160	+	0.984540i	$0.443956\pi$
$272$	7.59162	+	2.46667i	0.0279104	+	0.00906863i
$273$		0			0
$274$			139.835i			0.510347i
$275$	−106.260	−	34.5260i	−0.386400	−	0.125549i
$276$		0			0
$277$	253.022	+	348.255i	0.913437	+	1.25724i	0.965979	+	0.258620i	$0.0832678\pi$
$277$	253.022	+	348.255i	0.913437	+	1.25724i	−0.0525416	+	0.998619i	$0.516732\pi$
$278$			108.507i			0.390314i
$279$		0			0
$280$	−122.864			−0.438800
$281$	−111.187	+	80.7824i	−0.395685	+	0.287482i	−0.767781	−	0.640712i	$-0.778639\pi$
$281$	−111.187	+	80.7824i	−0.395685	+	0.287482i	0.372096	+	0.928194i	$0.378639\pi$
$282$		0			0
$283$	15.0593	−	46.3479i	0.0532132	−	0.163773i	−0.920918	−	0.389756i	$-0.872559\pi$
$283$	15.0593	−	46.3479i	0.0532132	−	0.163773i	0.974131	+	0.225983i	$0.0725593\pi$
$284$	−117.318			−0.413091
$285$		0			0
$286$	−59.8814	+	184.296i	−0.209375	+	0.644391i
$287$	−80.9665	−	249.189i	−0.282113	−	0.868255i
$288$		0			0
$289$	−231.897	+	168.483i	−0.802411	+	0.582986i
$290$	−235.675	−	76.5755i	−0.812673	−	0.264053i
$291$		0			0
$292$	98.1166	−	135.046i	0.336016	−	0.462486i
$293$	−126.593	−	389.613i	−0.432058	−	1.32974i	−0.896072	−	0.443909i	$-0.853591\pi$
$293$	−126.593	−	389.613i	−0.432058	−	1.32974i	0.464014	−	0.885828i	$-0.346409\pi$
$294$		0			0
$295$	−149.912	−	108.918i	−0.508178	−	0.369213i
$296$	343.488	−	111.606i	1.16043	−	0.377047i
$297$		0			0
$298$	−49.4566	+	35.9323i	−0.165962	+	0.120578i
$299$	−51.7953	+	159.410i	−0.173229	+	0.533143i
$300$		0			0
$301$	84.8593	−	27.5725i	0.281925	−	0.0916028i
$302$	27.8605	−	9.05242i	0.0922533	−	0.0299749i
$303$		0			0
$304$	106.257			0.349531
$305$		−	351.732i		−	1.15322i
$306$		0			0
$307$	45.5020	+	33.0591i	0.148215	+	0.107684i	0.659421	−	0.751773i	$-0.270801\pi$
$307$	45.5020	+	33.0591i	0.148215	+	0.107684i	−0.511207	+	0.859458i	$0.670801\pi$
$308$	53.7378	+	73.9638i	0.174474	+	0.240142i
$309$		0			0
$310$	−183.525	−	43.6407i	−0.592016	−	0.140776i
$311$	151.616			0.487511			0.243756	−	0.969837i	$-0.421620\pi$
$311$	151.616			0.487511			0.243756	+	0.969837i	$0.421620\pi$
$312$		0			0
$313$	50.3435	−	69.2919i	0.160842	−	0.221380i	−0.720988	−	0.692948i	$-0.756312\pi$
$313$	50.3435	−	69.2919i	0.160842	−	0.221380i	0.881830	+	0.471568i	$0.156312\pi$
$314$	−45.0469	+	138.640i	−0.143462	+	0.441529i
$315$		0			0
$316$			276.366i			0.874575i
$317$	−51.1637	+	157.466i	−0.161400	+	0.496737i	−0.998753	−	0.0499250i	$-0.984102\pi$
$317$	−51.1637	+	157.466i	−0.161400	+	0.496737i	0.837353	+	0.546662i	$0.184102\pi$
$318$		0			0
$319$	180.343	+	555.040i	0.565340	+	1.73994i
$320$	−201.156	+	146.148i	−0.628612	+	0.456713i
$321$		0			0
$322$	−54.1506	−	74.5320i	−0.168170	−	0.231466i
$323$	18.4648	−	25.4146i	0.0571665	−	0.0786830i
$324$		0			0
$325$	−42.2330	+	58.1287i	−0.129948	+	0.178858i
$326$	−199.517	−	144.957i	−0.612015	−	0.444655i
$327$		0			0
$328$	−526.683	−	382.658i	−1.60574	−	1.16664i
$329$	13.7956	−	10.0231i	0.0419318	−	0.0304652i
$330$		0			0
$331$	−200.957	−	276.593i	−0.607120	−	0.835630i	0.389216	−	0.921146i	$-0.372746\pi$
$331$	−200.957	−	276.593i	−0.607120	−	0.835630i	−0.996337	+	0.0855168i	$0.972746\pi$
$332$	74.8944	−	24.3347i	0.225586	−	0.0732972i
$333$		0			0
$334$	−98.9900	−	32.1638i	−0.296377	−	0.0962988i
$335$	−454.413			−1.35646
$336$		0			0
$337$	444.678	+	144.485i	1.31952	+	0.428738i	0.882330	−	0.470632i	$-0.155974\pi$
$337$	444.678	+	144.485i	1.31952	+	0.428738i	0.437189	+	0.899369i	$0.355974\pi$
$338$	−99.7717	−	72.4884i	−0.295183	−	0.214463i
$339$		0			0
$340$			11.7724i			0.0346246i
$341$	170.904	+	410.086i	0.501183	+	1.20260i
$342$		0			0
$343$	240.448	−	174.696i	0.701015	−	0.509317i
$344$	130.311	−	179.358i	0.378811	−	0.521388i
$345$		0			0
$346$	301.079			0.870171
$347$			279.411i			0.805218i	0.915372	+	0.402609i	$0.131897\pi$
$347$			279.411i			0.805218i	−0.915372	+	0.402609i	$0.868103\pi$
$348$		0			0
$349$	−95.5019	−	293.925i	−0.273644	−	0.842191i	−0.989575	−	0.144019i	$-0.953997\pi$
$349$	−95.5019	−	293.925i	−0.273644	−	0.842191i	0.715930	−	0.698172i	$-0.246003\pi$
$350$	−12.2037	−	37.5592i	−0.0348678	−	0.107312i
$351$		0			0
$352$	363.823	+	118.213i	1.03359	+	0.335833i
$353$	−345.083	−	474.966i	−0.977572	−	1.34551i	−0.938127	−	0.346291i	$-0.887441\pi$
$353$	−345.083	−	474.966i	−0.977572	−	1.34551i	−0.0394454	−	0.999222i	$-0.512559\pi$
$354$		0			0
$355$	81.3875	+	250.485i	0.229260	+	0.705591i
$356$	52.9086	−	72.8224i	0.148620	−	0.204557i
$357$		0			0
$358$	−148.442	+	48.2316i	−0.414641	+	0.134725i
$359$	−208.797	−	151.700i	−0.581609	−	0.422563i	0.257695	−	0.966226i	$-0.417037\pi$
$359$	−208.797	−	151.700i	−0.581609	−	0.422563i	−0.839304	+	0.543663i	$0.817037\pi$
$360$		0			0
$361$	17.6678	−	54.3758i	0.0489412	−	0.150625i
$362$	118.923	+	163.684i	0.328517	+	0.452165i
$363$		0			0
$364$	55.9162	−	18.1683i	0.153616	−	0.0499128i
$365$	−356.403	−	115.802i	−0.976447	−	0.317267i
$366$		0			0
$367$			79.9018i			0.217716i	0.994057	+	0.108858i	$0.0347194\pi$
$367$			79.9018i			0.217716i	−0.994057	+	0.108858i	$0.965281\pi$
$368$	−89.8748	−	29.2021i	−0.244225	−	0.0793535i
$369$		0			0
$370$	−150.578	−	207.253i	−0.406967	−	0.560143i
$371$			139.993i			0.377340i
$372$		0			0
$373$	−381.373			−1.02245			−0.511224	−	0.859447i	$-0.670808\pi$
$373$	−381.373			−1.02245			−0.511224	+	0.859447i	$0.670808\pi$
$374$	−26.1310	+	18.9853i	−0.0698691	+	0.0507629i
$375$		0			0
$376$	13.0928	−	40.2956i	0.0348213	−	0.107169i
$377$	375.308			0.995511
$378$		0			0
$379$	−111.049	+	341.775i	−0.293006	+	0.901781i	0.690877	+	0.722972i	$0.257224\pi$
$379$	−111.049	+	341.775i	−0.293006	+	0.901781i	−0.983884	+	0.178809i	$0.942776\pi$
$380$	48.4259	+	149.040i	0.127437	+	0.392209i
$381$		0			0
$382$	−36.2350	+	26.3263i	−0.0948560	+	0.0689169i
$383$	−11.2735	−	3.66299i	−0.0294348	−	0.00956395i	0.294263	−	0.955725i	$-0.404926\pi$
$383$	−11.2735	−	3.66299i	−0.0294348	−	0.00956395i	−0.323697	+	0.946161i	$0.604926\pi$
$384$		0			0
$385$	120.640	−	166.047i	0.313351	−	0.431290i
$386$	−81.9954	−	252.356i	−0.212423	−	0.653772i
$387$		0			0
$388$	73.3068	+	53.2605i	0.188935	+	0.137269i
$389$	195.309	−	63.4597i	0.502079	−	0.163135i	−0.0470179	−	0.998894i	$-0.514972\pi$
$389$	195.309	−	63.4597i	0.502079	−	0.163135i	0.549097	+	0.835759i	$0.314972\pi$
$390$		0			0
$391$	−22.6024	+	16.4216i	−0.0578068	+	0.0419991i
$392$	98.2971	−	302.527i	0.250758	−	0.771754i
$393$		0			0
$394$	−79.7031	+	25.8971i	−0.202292	+	0.0657287i
$395$	590.067	−	191.724i	1.49384	−	0.485378i
$396$		0			0
$397$	−710.602			−1.78993			−0.894964	−	0.446137i	$-0.852799\pi$
$397$	−710.602			−1.78993			−0.894964	+	0.446137i	$0.852799\pi$
$398$		−	344.916i		−	0.866624i
$399$		0			0
$400$	−32.7728	−	23.8109i	−0.0819321	−	0.0595272i
$401$	46.2384	+	63.6417i	0.115308	+	0.158708i	0.862770	−	0.505597i	$-0.168728\pi$
$401$	46.2384	+	63.6417i	0.115308	+	0.158708i	−0.747462	+	0.664305i	$0.768728\pi$
$402$		0			0
$403$	284.776	−	23.0324i	0.706641	−	0.0571525i
$404$	106.234			0.262956
$405$		0			0
$406$	−121.250	+	166.887i	−0.298646	+	0.411051i
$407$	−186.438	+	573.798i	−0.458080	+	1.40982i
$408$		0			0
$409$		−	480.633i		−	1.17514i	−0.809173	−	0.587571i	$-0.800084\pi$
$409$		−	480.633i		−	1.17514i	0.809173	−	0.587571i	$-0.199916\pi$
$410$	−142.696	+	439.173i	−0.348039	+	1.07115i
$411$		0			0
$412$	36.6533	+	112.807i	0.0889643	+	0.273804i
$413$	−124.794	+	90.6683i	−0.302165	+	0.219536i
$414$		0			0
$415$	−103.914	−	143.025i	−0.250395	−	0.344639i
$416$	144.601	−	199.027i	0.347599	−	0.478430i
$417$		0			0
$418$	−252.725	+	347.847i	−0.604606	+	0.832169i
$419$	69.0155	+	50.1427i	0.164715	+	0.119672i	0.667089	−	0.744978i	$-0.267540\pi$
$419$	69.0155	+	50.1427i	0.164715	+	0.119672i	−0.502374	+	0.864650i	$0.667540\pi$
$420$		0			0
$421$	248.970	+	180.888i	0.591379	+	0.429662i	0.842808	−	0.538214i	$-0.180901\pi$
$421$	248.970	+	180.888i	0.591379	+	0.429662i	−0.251430	+	0.967876i	$0.580901\pi$
$422$	145.651	−	105.821i	0.345143	−	0.250761i
$423$		0			0
$424$	204.454	+	281.406i	0.482202	+	0.663694i
$425$	−11.3901	+	3.70088i	−0.0268003	+	0.00870795i
$426$		0			0
$427$	−278.468	−	90.4798i	−0.652150	−	0.211896i
$428$	−241.747			−0.564830
$429$		0			0
$430$	−149.557	−	48.5940i	−0.347807	−	0.113009i
$431$	11.4520	+	8.32036i	0.0265707	+	0.0193048i	0.600991	−	0.799256i	$-0.294773\pi$
$431$	11.4520	+	8.32036i	0.0265707	+	0.0193048i	−0.574421	+	0.818560i	$0.694773\pi$
$432$		0			0
$433$		−	414.463i		−	0.957190i	−0.878036	−	0.478595i	$-0.841146\pi$
$433$		−	414.463i		−	0.957190i	0.878036	−	0.478595i	$-0.158854\pi$
$434$	−81.7606	+	134.071i	−0.188388	+	0.308920i
$435$		0			0
$436$	228.128	−	165.745i	0.523230	−	0.380149i
$437$	−218.599	+	300.875i	−0.500226	+	0.688502i
$438$		0			0
$439$	354.356			0.807190			0.403595	−	0.914938i	$-0.367760\pi$
$439$	354.356			0.807190			0.403595	+	0.914938i	$0.367760\pi$
$440$		−	509.967i		−	1.15901i
$441$		0			0
$442$	6.41876	+	19.7549i	0.0145221	+	0.0446944i
$443$	−22.0099	−	67.7395i	−0.0496837	−	0.152911i	0.923137	−	0.384472i	$-0.125617\pi$
$443$	−22.0099	−	67.7395i	−0.0496837	−	0.152911i	−0.972820	+	0.231561i	$0.925617\pi$
$444$		0			0
$445$	−192.187	−	62.4455i	−0.431882	−	0.140327i
$446$	267.711	+	368.473i	0.600249	+	0.826172i
$447$		0			0
$448$	63.9608	+	196.851i	0.142770	+	0.439400i
$449$	−388.723	+	535.031i	−0.865752	+	1.19161i	0.114415	+	0.993433i	$0.463500\pi$
$449$	−388.723	+	535.031i	−0.865752	+	1.19161i	−0.980167	+	0.198172i	$0.936500\pi$
$450$		0			0
$451$	1034.30	−	336.064i	2.29335	−	0.745154i
$452$	182.736	+	132.765i	0.404283	+	0.293729i
$453$		0			0
$454$	193.159	−	594.481i	0.425460	−	1.30943i
$455$	−77.5820	−	106.782i	−0.170510	−	0.234687i
$456$		0			0
$457$	78.2123	−	25.4127i	0.171143	−	0.0556077i	−0.222192	−	0.975003i	$-0.571321\pi$
$457$	78.2123	−	25.4127i	0.171143	−	0.0556077i	0.393335	+	0.919395i	$0.371321\pi$
$458$	−1.36761	−	0.444363i	−0.00298604	−	0.000970224i
$459$		0			0
$460$		−	139.369i		−	0.302977i
$461$	−26.7061	−	8.67734i	−0.0579308	−	0.0188229i	0.279908	−	0.960027i	$-0.409696\pi$
$461$	−26.7061	−	8.67734i	−0.0579308	−	0.0188229i	−0.337839	+	0.941204i	$0.609696\pi$
$462$		0			0
$463$	213.250	+	293.513i	0.460583	+	0.633938i	0.974630	−	0.223824i	$-0.0718542\pi$
$463$	213.250	+	293.513i	0.460583	+	0.633938i	−0.514047	+	0.857762i	$0.671854\pi$
$464$			211.598i			0.456029i
$465$		0			0
$466$	521.248			1.11856
$467$	576.186	−	418.624i	1.23380	−	0.896411i	0.236634	−	0.971599i	$-0.423956\pi$
$467$	576.186	−	418.624i	1.23380	−	0.896411i	0.997169	+	0.0751878i	$0.0239556\pi$
$468$		0			0
$469$	−116.893	+	359.760i	−0.249239	+	0.767080i
$470$	−30.0531			−0.0639427
$471$		0			0
$472$	−118.437	+	364.512i	−0.250926	+	0.772272i
$473$	114.444	+	352.222i	0.241953	+	0.744656i
$474$		0			0
$475$	−128.977	+	93.7071i	−0.271530	+	0.197278i
$476$	9.32024	+	3.02833i	0.0195803	+	0.00636204i
$477$		0			0
$478$	205.603	−	282.989i	0.430133	−	0.592027i
$479$	200.415	+	616.813i	0.418402	+	1.28771i	0.909172	+	0.416420i	$0.136715\pi$
$479$	200.415	+	616.813i	0.418402	+	1.28771i	−0.490770	+	0.871289i	$0.663285\pi$
$480$		0			0
$481$	313.892	+	228.056i	0.652582	+	0.474129i
$482$	454.319	−	147.617i	0.942570	−	0.306260i
$483$		0			0
$484$	−126.137	+	91.6441i	−0.260614	+	0.189347i
$485$	62.8608	−	193.466i	0.129610	−	0.398898i
$486$		0			0
$487$	−684.840	+	222.518i	−1.40624	+	0.456916i	−0.911204	−	0.411955i	$-0.864846\pi$
$487$	−684.840	+	222.518i	−1.40624	+	0.456916i	−0.495038	+	0.868871i	$0.664846\pi$
$488$	−691.902	+	224.813i	−1.41783	+	0.460681i
$489$		0			0
$490$	−225.630			−0.460469
$491$			201.155i			0.409684i	0.978795	+	0.204842i	$0.0656681\pi$
$491$			201.155i			0.409684i	−0.978795	+	0.204842i	$0.934332\pi$
$492$		0			0
$493$	50.6098	+	36.7702i	0.102657	+	0.0745845i
$494$	162.524	+	223.696i	0.328997	+	0.452825i
$495$		0			0
$496$	12.9856	+	160.556i	0.0261807	+	0.323702i
$497$	219.246			0.441139
$498$		0			0
$499$	−43.0223	+	59.2151i	−0.0862170	+	0.118668i	−0.849947	−	0.526869i	$-0.823366\pi$
$499$	−43.0223	+	59.2151i	−0.0862170	+	0.118668i	0.763730	+	0.645536i	$0.223366\pi$
$500$	77.6642	−	239.026i	0.155328	−	0.478052i
$501$		0			0
$502$		−	268.574i		−	0.535008i
$503$	−9.73355	+	29.9568i	−0.0193510	+	0.0595562i	−0.960266	−	0.279087i	$-0.909968\pi$
$503$	−9.73355	+	29.9568i	−0.0193510	+	0.0595562i	0.940915	+	0.338644i	$0.109968\pi$
$504$		0			0
$505$	−73.6984	−	226.820i	−0.145937	−	0.449149i
$506$	309.357	−	224.761i	0.611377	−	0.444192i
$507$		0			0
$508$	−159.815	−	219.967i	−0.314597	−	0.433006i
$509$	526.782	−	725.053i	1.03494	−	1.42447i	0.133759	−	0.991014i	$-0.457295\pi$
$509$	526.782	−	725.053i	1.03494	−	1.42447i	0.901177	−	0.433452i	$-0.142705\pi$
$510$		0			0
$511$	−183.362	+	252.377i	−0.358831	+	0.493888i
$512$	256.468	+	186.335i	0.500915	+	0.363936i
$513$		0			0
$514$	225.373	+	163.743i	0.438470	+	0.318567i
$515$	215.427	−	156.517i	0.418304	−	0.303916i
$516$		0			0
$517$	41.6024	+	57.2607i	0.0804688	+	0.110756i
$518$	−202.818	+	65.8994i	−0.391540	+	0.127219i
$519$		0			0
$520$	−311.902	−	101.343i	−0.599811	−	0.194890i
$521$	−854.877			−1.64084			−0.820420	−	0.571762i	$-0.806260\pi$
$521$	−854.877			−1.64084			−0.820420	+	0.571762i	$0.806260\pi$
$522$		0			0
$523$	−613.920	−	199.475i	−1.17384	−	0.381405i	−0.343768	−	0.939055i	$-0.611703\pi$
$523$	−613.920	−	199.475i	−1.17384	−	0.381405i	−0.830076	+	0.557650i	$0.811703\pi$
$524$	−95.1584	−	69.1366i	−0.181600	−	0.131940i
$525$		0			0
$526$			41.5376i			0.0789688i
$527$	40.6583	+	24.7946i	0.0771505	+	0.0470486i
$528$		0			0
$529$	−160.387	+	116.528i	−0.303189	+	0.220280i
$530$	145.022	−	199.605i	0.273626	−	0.376613i
$531$		0			0
$532$	130.452			0.245211
$533$		−	699.375i		−	1.31215i
$534$		0			0
$535$	167.709	+	516.154i	0.313474	+	0.964774i
$536$	290.441	+	893.887i	0.541868	+	1.66770i
$537$		0			0
$538$	−394.476	−	128.173i	−0.733227	−	0.238240i
$539$	312.338	+	429.897i	0.579478	+	0.797583i
$540$		0			0
$541$	−21.6931	−	66.7644i	−0.0400981	−	0.123409i	0.929004	−	0.370071i	$-0.120666\pi$
$541$	−21.6931	−	66.7644i	−0.0400981	−	0.123409i	−0.969102	+	0.246661i	$0.920666\pi$
$542$	64.3378	−	88.5534i	0.118704	−	0.163383i
$543$		0			0
$544$	38.9986	−	12.6714i	0.0716887	−	0.0232931i
$545$	−512.142	−	372.093i	−0.939709	−	0.682739i
$546$		0			0
$547$	−215.959	+	664.654i	−0.394807	+	1.21509i	0.534305	+	0.845292i	$0.320573\pi$
$547$	−215.959	+	664.654i	−0.394807	+	1.21509i	−0.929112	+	0.369799i	$0.879427\pi$
$548$	103.508	+	142.466i	0.188883	+	0.259975i
$549$		0			0
$550$	155.895	−	50.6535i	0.283446	−	0.0920973i
$551$	791.981	+	257.330i	1.43735	+	0.467024i
$552$		0			0
$553$		−	516.478i		−	0.933957i
$554$	−600.634	−	195.158i	−1.08418	−	0.352270i
$555$		0			0
$556$	80.3188	+	110.549i	0.144458	+	0.198830i
$557$		−	744.534i		−	1.33669i	−0.743853	−	0.668343i	$-0.767004\pi$
$557$		−	744.534i		−	1.33669i	0.743853	−	0.668343i	$-0.232996\pi$
$558$		0			0
$559$	238.166			0.426058
$560$	60.2037	−	43.7406i	0.107507	−	0.0781081i
$561$		0			0
$562$	62.3081	−	191.764i	0.110868	−	0.341218i
$563$	−672.379			−1.19428			−0.597140	−	0.802137i	$-0.703696\pi$
$563$	−672.379			−1.19428			−0.597140	+	0.802137i	$0.703696\pi$
$564$		0			0
$565$	156.697	−	482.262i	0.277339	−	0.853562i
$566$	22.0938	+	67.9976i	0.0390349	+	0.120137i
$567$		0			0
$568$	440.716	−	320.199i	0.775908	−	0.563730i
$569$	−81.1903	−	26.3803i	−0.142689	−	0.0463626i	0.236802	−	0.971558i	$-0.423901\pi$
$569$	−81.1903	−	26.3803i	−0.142689	−	0.0463626i	−0.379491	+	0.925195i	$0.623901\pi$
$570$		0			0
$571$	−16.3121	+	22.4517i	−0.0285676	+	0.0393199i	−0.823062	−	0.567952i	$-0.807736\pi$
$571$	−16.3121	+	22.4517i	−0.0285676	+	0.0393199i	0.794494	+	0.607272i	$0.207736\pi$
$572$	75.4104	+	232.089i	0.131836	+	0.405750i
$573$		0			0
$574$	310.988	+	225.946i	0.541792	+	0.393635i
$575$	134.844	−	43.8135i	0.234512	−	0.0761974i
$576$		0			0
$577$	632.893	−	459.823i	1.09687	−	0.796921i	0.116322	−	0.993212i	$-0.462890\pi$
$577$	632.893	−	459.823i	1.09687	−	0.796921i	0.980546	+	0.196291i	$0.0628896\pi$
$578$	129.952	−	399.951i	0.224830	−	0.691957i
$579$		0			0
$580$	−296.792	+	96.4337i	−0.511711	+	0.166265i
$581$	−139.964	+	45.4772i	−0.240902	+	0.0782740i
$582$		0			0
$583$	−581.065			−0.996680
$584$			775.106i			1.32724i
$585$		0			0
$586$	486.237	+	353.272i	0.829756	+	0.602853i
$587$	642.042	+	883.695i	1.09377	+	1.50544i	0.843395	+	0.537294i	$0.180553\pi$
$587$	642.042	+	883.695i	1.09377	+	1.50544i	0.250373	+	0.968149i	$0.419447\pi$
$588$		0			0
$589$	616.732	+	146.654i	1.04708	+	0.248987i
$590$	271.859			0.460778
$591$		0			0
$592$	−128.577	+	176.972i	−0.217192	+	0.298939i
$593$	−129.086	+	397.287i	−0.217684	+	0.669962i	0.781268	+	0.624195i	$0.214573\pi$
$593$	−129.086	+	397.287i	−0.217684	+	0.669962i	−0.998952	+	0.0457665i	$0.985427\pi$
$594$		0			0
$595$		−	22.0005i		−	0.0369756i
$596$	−23.7897	+	73.2170i	−0.0399155	+	0.122847i
$597$		0			0
$598$	−75.9896	−	233.872i	−0.127073	−	0.391090i
$599$	−478.000	+	347.288i	−0.797997	+	0.579779i	−0.910326	−	0.413892i	$-0.864169\pi$
$599$	−478.000	+	347.288i	−0.797997	+	0.579779i	0.112329	+	0.993671i	$0.464169\pi$
$600$		0			0
$601$	194.037	+	267.069i	0.322857	+	0.444375i	0.939337	−	0.342996i	$-0.111442\pi$
$601$	194.037	+	267.069i	0.322857	+	0.444375i	−0.616480	+	0.787371i	$0.711442\pi$
$602$	−76.9441	+	105.905i	−0.127814	+	0.175921i
$603$		0			0
$604$	21.6840	−	29.8455i	0.0359007	−	0.0494131i
$605$	283.175	+	205.739i	0.468058	+	0.340064i
$606$		0			0
$607$	439.177	+	319.081i	0.723520	+	0.525668i	0.887507	−	0.460794i	$-0.152435\pi$
$607$	439.177	+	319.081i	0.723520	+	0.525668i	−0.163987	+	0.986463i	$0.552435\pi$
$608$	441.603	−	320.843i	0.726321	−	0.527703i
$609$		0			0
$610$	303.316	+	417.478i	0.497239	+	0.684390i
$611$	43.2888	−	14.0654i	0.0708491	−	0.0230203i
$612$		0			0
$613$	523.889	+	170.222i	0.854631	+	0.277686i	0.703384	−	0.710810i	$-0.251671\pi$
$613$	523.889	+	170.222i	0.854631	+	0.277686i	0.151247	+	0.988496i	$0.451671\pi$
$614$	−82.5156			−0.134390
$615$		0			0
$616$	−403.743	−	131.184i	−0.655427	−	0.212961i
$617$	−432.605	−	314.306i	−0.701143	−	0.509410i	0.179161	−	0.983820i	$-0.442662\pi$
$617$	−432.605	−	314.306i	−0.701143	−	0.509410i	−0.880304	+	0.474409i	$0.842662\pi$
$618$		0			0
$619$			410.084i			0.662495i	0.943544	+	0.331247i	$0.107469\pi$
$619$			410.084i			0.662495i	−0.943544	+	0.331247i	$0.892531\pi$
$620$	−219.282	+	91.3860i	−0.353681	+	0.147397i
$621$		0			0
$622$	−179.956	+	130.746i	−0.289318	+	0.210202i
$623$	−98.8767	+	136.092i	−0.158711	+	0.218446i
$624$		0			0
$625$	−369.320			−0.590912
$626$			125.657i			0.200731i
$627$		0			0
$628$	56.7289	+	174.594i	0.0903326	+	0.278015i
$629$	19.9846	+	61.5062i	0.0317720	+	0.0977840i
$630$		0			0
$631$	−769.194	−	249.926i	−1.21901	−	0.396080i	−0.372288	−	0.928117i	$-0.621427\pi$
$631$	−769.194	−	249.926i	−1.21901	−	0.396080i	−0.846721	+	0.532037i	$0.821427\pi$
$632$	−754.292	−	1038.19i	−1.19350	−	1.64271i
$633$		0			0
$634$	−75.0629	−	231.020i	−0.118396	−	0.364385i
$635$	−358.781	+	493.820i	−0.565010	+	0.777669i
$636$		0			0
$637$	325.000	−	105.599i	0.510203	−	0.165775i
$638$	−692.690	−	503.269i	−1.08572	−	0.788823i
$639$		0			0
$640$	−24.1272	+	74.2558i	−0.0376987	+	0.116025i
$641$	455.154	+	626.465i	0.710068	+	0.977325i	0.999796	+	0.0202159i	$0.00643537\pi$
$641$	455.154	+	626.465i	0.710068	+	0.977325i	−0.289727	+	0.957109i	$0.593565\pi$
$642$		0			0
$643$	264.903	−	86.0723i	0.411980	−	0.133861i	−0.0956915	−	0.995411i	$-0.530506\pi$
$643$	264.903	−	86.0723i	0.411980	−	0.133861i	0.507672	+	0.861550i	$0.330506\pi$
$644$	−110.339	−	35.8514i	−0.171334	−	0.0556699i
$645$		0			0
$646$			46.0882i			0.0713439i
$647$	244.776	+	79.5325i	0.378324	+	0.122925i	0.492005	−	0.870592i	$-0.336264\pi$
$647$	244.776	+	79.5325i	0.378324	+	0.122925i	−0.113681	+	0.993517i	$0.536264\pi$
$648$		0			0
$649$	−376.333	−	517.978i	−0.579866	−	0.798118i
$650$		−	105.414i		−	0.162175i
$651$		0			0
$652$	−310.571			−0.476336
$653$	462.588	−	336.090i	0.708405	−	0.514686i	−0.174254	−	0.984701i	$-0.555751\pi$
$653$	462.588	−	336.090i	0.708405	−	0.514686i	0.882659	+	0.470015i	$0.155751\pi$
$654$		0			0
$655$	−81.5986	+	251.135i	−0.124578	+	0.383412i
$656$	394.306			0.601076
$657$		0			0
$658$	−7.73086	+	23.7932i	−0.0117490	+	0.0361598i
$659$	−234.466	−	721.613i	−0.355791	−	1.09501i	−0.955549	−	0.294831i	$-0.904737\pi$
$659$	−234.466	−	721.613i	−0.355791	−	1.09501i	0.599759	−	0.800181i	$-0.295263\pi$
$660$		0			0
$661$	−815.622	+	592.584i	−1.23392	+	0.896497i	−0.997178	−	0.0750752i	$-0.976080\pi$
$661$	−815.622	+	592.584i	−1.23392	+	0.896497i	−0.236744	+	0.971572i	$0.576080\pi$
$662$	477.039	+	154.999i	0.720603	+	0.234138i
$663$		0			0
$664$	−214.931	+	295.827i	−0.323691	+	0.445522i
$665$	−90.4994	−	278.528i	−0.136089	−	0.418840i
$666$		0			0
$667$	−599.153	−	435.310i	−0.898280	−	0.652639i
$668$	−124.661	+	40.5048i	−0.186618	+	0.0606359i
$669$		0			0
$670$	539.351	−	391.862i	0.805002	−	0.584868i
$671$	375.551	−	1155.83i	0.559688	−	1.72254i
$672$		0			0
$673$	−649.297	+	210.969i	−0.964780	+	0.313476i	−0.748707	−	0.662901i	$-0.769325\pi$
$673$	−649.297	+	210.969i	−0.964780	+	0.313476i	−0.216073	+	0.976377i	$0.569325\pi$
$674$	−652.393	+	211.975i	−0.967942	+	0.314503i
$675$		0			0
$676$	−155.306			−0.229743
$677$		−	149.853i		−	0.221349i	−0.993857	−	0.110675i	$-0.964699\pi$
$677$		−	149.853i		−	0.221349i	0.993857	−	0.110675i	$-0.0353011\pi$
$678$		0			0
$679$	−136.997	−	99.5344i	−0.201763	−	0.146590i
$680$	−32.1307	−	44.2241i	−0.0472510	−	0.0650354i
$681$		0			0
$682$	−556.485	−	339.361i	−0.815961	−	0.497596i
$683$	−619.114			−0.906462			−0.453231	−	0.891393i	$-0.649729\pi$
$683$	−619.114			−0.906462			−0.453231	+	0.891393i	$0.649729\pi$
$684$		0			0
$685$	232.373	−	319.833i	0.339230	−	0.466910i
$686$	−134.744	+	414.700i	−0.196420	+	0.604519i
$687$		0			0
$688$			134.278i			0.195171i
$689$	−115.472	+	355.386i	−0.167594	+	0.515800i
$690$		0			0
$691$	−154.326	−	474.965i	−0.223337	−	0.687359i	−0.998456	−	0.0555447i	$-0.982310\pi$
$691$	−154.326	−	474.965i	−0.223337	−	0.687359i	0.775120	−	0.631814i	$-0.217690\pi$
$692$	306.745	−	222.863i	0.443273	−	0.322057i
$693$		0			0
$694$	−240.949	−	331.638i	−0.347189	−	0.477865i
$695$	180.313	−	248.180i	0.259444	−	0.357094i
$696$		0			0
$697$	68.5201	−	94.3099i	0.0983072	−	0.135308i
$698$	366.818	+	266.509i	0.525528	+	0.381818i
$699$		0			0
$700$	−40.2352	−	29.2326i	−0.0574789	−	0.0417609i
$701$	327.624	−	238.033i	0.467367	−	0.339562i	−0.329047	−	0.944313i	$-0.606728\pi$
$701$	327.624	−	238.033i	0.467367	−	0.339562i	0.796414	+	0.604751i	$0.206728\pi$
$702$		0			0
$703$	506.014	+	696.468i	0.719792	+	0.990708i
$704$	−817.062	+	265.480i	−1.16060	+	0.377102i
$705$		0			0
$706$	819.172	+	266.165i	1.16030	+	0.377004i
$707$	−198.533			−0.280810
$708$		0			0
$709$	−132.389	−	43.0157i	−0.186726	−	0.0606709i	0.214161	−	0.976798i	$-0.431298\pi$
$709$	−132.389	−	43.0157i	−0.186726	−	0.0606709i	−0.400887	+	0.916127i	$0.631298\pi$
$710$	−312.605	−	227.121i	−0.440289	−	0.319889i
$711$		0			0
$712$			417.969i			0.587035i
$713$	−481.340	−	293.535i	−0.675092	−	0.411690i
$714$		0			0
$715$	443.218	−	322.017i	0.619885	−	0.450373i
$716$	−115.533	+	159.018i	−0.161359	+	0.222092i
$717$		0			0
$718$	378.644			0.527360
$719$		−	372.976i		−	0.518742i	−0.965778	−	0.259371i	$-0.916485\pi$
$719$		−	372.976i		−	0.518742i	0.965778	−	0.259371i	$-0.0835153\pi$
$720$		0			0
$721$	−68.4985	−	210.817i	−0.0950048	−	0.292395i
$722$	25.9206	+	79.7754i	0.0359011	+	0.110492i
$723$		0			0
$724$	242.322	+	78.7353i	0.334699	+	0.108750i
$725$	−186.605	−	256.840i	−0.257386	−	0.354262i
$726$		0			0
$727$	−94.1007	−	289.612i	−0.129437	−	0.398366i	0.865246	−	0.501347i	$-0.167162\pi$
$727$	−94.1007	−	289.612i	−0.129437	−	0.398366i	−0.994683	+	0.102981i	$0.967162\pi$
$728$	−160.467	+	220.864i	−0.220422	+	0.303385i
$729$		0			0
$730$	522.884	−	169.895i	0.716279	−	0.232733i
$731$	32.1164	+	23.3340i	0.0439349	+	0.0319206i
$732$		0			0
$733$	53.3882	−	164.312i	0.0728352	−	0.224164i	−0.908011	−	0.418945i	$-0.862400\pi$
$733$	53.3882	−	164.312i	0.0728352	−	0.224164i	0.980847	+	0.194782i	$0.0623998\pi$
$734$	−68.9032	−	94.8371i	−0.0938735	−	0.129206i
$735$		0			0
$736$	−461.692	+	150.013i	−0.627299	+	0.203822i
$737$	−1493.24	−	485.184i	−2.02611	−	0.658323i
$738$		0			0
$739$		−	709.952i		−	0.960693i	−0.877079	−	0.480346i	$-0.840511\pi$
$739$		−	709.952i		−	0.960693i	0.877079	−	0.480346i	$-0.159489\pi$
$740$	−306.823	−	99.6929i	−0.414626	−	0.134720i
$741$		0			0
$742$	−120.723	−	166.161i	−0.162699	−	0.223936i
$743$			782.674i			1.05340i	0.850052	+	0.526698i	$0.176570\pi$
$743$			782.674i			1.05340i	−0.850052	+	0.526698i	$0.823430\pi$
$744$		0			0
$745$	172.829			0.231985
$746$	452.659	−	328.876i	0.606782	−	0.440853i
$747$		0			0
$748$	−12.5696	+	38.6852i	−0.0168042	+	0.0517181i
$749$	451.783			0.603181
$750$		0			0
$751$	281.220	−	865.505i	0.374460	−	1.15247i	−0.569382	−	0.822073i	$-0.692817\pi$
$751$	281.220	−	865.505i	0.374460	−	1.15247i	0.943842	−	0.330397i	$-0.107183\pi$
$752$	7.93003	+	24.4061i	0.0105452	+	0.0324549i
$753$		0			0
$754$	−445.460	+	323.646i	−0.590796	+	0.429238i
$755$	−78.7660	−	25.5926i	−0.104326	−	0.0338975i
$756$		0			0
$757$	843.357	−	1160.78i	1.11408	−	1.53340i	0.298809	−	0.954313i	$-0.403411\pi$
$757$	843.357	−	1160.78i	1.11408	−	1.53340i	0.815268	−	0.579083i	$-0.196589\pi$
$758$	−162.922	−	501.423i	−0.214937	−	0.661508i
$759$		0			0
$760$	−588.694	−	427.711i	−0.774598	−	0.562778i
$761$	805.298	−	261.657i	1.05821	−	0.343834i	0.272325	−	0.962205i	$-0.412207\pi$
$761$	805.298	−	261.657i	1.05821	−	0.343834i	0.785886	+	0.618372i	$0.212207\pi$
$762$		0			0
$763$	−426.331	+	309.748i	−0.558756	+	0.405960i
$764$	−17.4298	+	53.6434i	−0.0228139	+	0.0702138i
$765$		0			0
$766$	16.5396	−	5.37403i	0.0215921	−	0.00701570i
$767$	−391.589	+	127.235i	−0.510546	+	0.165886i
$768$		0			0
$769$	−214.787			−0.279307			−0.139654	−	0.990200i	$-0.544599\pi$
$769$	−214.787			−0.279307			−0.139654	+	0.990200i	$0.544599\pi$
$770$			301.118i			0.391062i
$771$		0			0
$772$	−270.336	−	196.411i	−0.350176	−	0.254418i
$773$	432.607	+	595.433i	0.559647	+	0.770289i	0.991282	−	0.131760i	$-0.0420629\pi$
$773$	432.607	+	595.433i	0.559647	+	0.770289i	−0.431634	+	0.902049i	$0.642063\pi$
$774$		0			0
$775$	−157.355	−	183.433i	−0.203038	−	0.236688i
$776$	−420.749			−0.542203
$777$		0			0
$778$	−177.092	+	243.746i	−0.227624	+	0.313298i
$779$	479.527	−	1475.83i	0.615567	−	1.89452i
$780$		0			0
$781$			910.016i			1.16519i
$782$	12.6661	−	38.9823i	0.0161971	−	0.0498495i
$783$		0			0
$784$	59.5363	+	183.234i	0.0759392	+	0.233717i
$785$	333.419	−	242.243i	0.424738	−	0.308590i
$786$		0			0
$787$	124.783	+	171.749i	0.158555	+	0.218232i	0.880902	−	0.473298i	$-0.156937\pi$
$787$	124.783	+	171.749i	0.158555	+	0.218232i	−0.722347	+	0.691530i	$0.756937\pi$
$788$	−62.0336	+	85.3819i	−0.0787228	+	0.108353i
$789$		0			0
$790$	−535.029	+	736.404i	−0.677252	+	0.932157i
$791$	−341.501	−	248.115i	−0.431733	−	0.313672i
$792$		0			0
$793$	−632.286	−	459.383i	−0.797335	−	0.579298i
$794$	843.427	−	612.786i	1.06225	−	0.771770i
$795$		0			0
$796$	−255.312	−	351.407i	−0.320744	−	0.441466i
$797$	80.3901	−	26.1203i	0.100866	−	0.0327733i	−0.258149	−	0.966105i	$-0.583113\pi$
$797$	80.3901	−	26.1203i	0.100866	−	0.0327733i	0.359015	+	0.933332i	$0.383113\pi$
$798$		0			0
$799$	7.21547	+	2.34445i	0.00903063	+	0.00293423i
$800$	−208.100			−0.260125
$801$		0			0
$802$	−109.763	−	35.6640i	−0.136861	−	0.0444689i
$803$	−1047.53	−	761.076i	−1.30452	−	0.947790i
$804$		0			0
$805$			260.456i			0.323548i
$806$	−318.144	+	272.914i	−0.394720	+	0.338603i
$807$		0			0
$808$	−399.079	+	289.948i	−0.493910	+	0.358847i
$809$	531.248	−	731.201i	0.656673	−	0.903833i	−0.342693	−	0.939448i	$-0.611339\pi$
$809$	531.248	−	731.201i	0.656673	−	0.903833i	0.999366	+	0.0356150i	$0.0113390\pi$
$810$		0			0
$811$	−13.2753			−0.0163690			−0.00818450	−	0.999967i	$-0.502605\pi$
$811$	−13.2753			−0.0163690			−0.00818450	+	0.999967i	$0.502605\pi$
$812$			259.778i			0.319924i
$813$		0			0
$814$	−273.526	−	841.827i	−0.336027	−	1.03419i
$815$	215.454	+	663.099i	0.264361	+	0.813618i
$816$		0			0
$817$	502.582	+	163.299i	0.615156	+	0.199876i
$818$	414.472	+	570.472i	0.506690	+	0.697399i
$819$		0			0
$820$	179.701	+	553.064i	0.219148	+	0.674468i
$821$	290.078	−	399.258i	0.353323	−	0.486307i	−0.594950	−	0.803762i	$-0.702828\pi$
$821$	290.078	−	399.258i	0.353323	−	0.486307i	0.948273	+	0.317455i	$0.102828\pi$
$822$		0			0
$823$	920.846	−	299.201i	1.11889	−	0.363549i	0.309546	−	0.950885i	$-0.399823\pi$
$823$	920.846	−	299.201i	1.11889	−	0.363549i	0.809344	+	0.587335i	$0.199823\pi$
$824$	−445.580	−	323.732i	−0.540752	−	0.392879i
$825$		0			0
$826$	69.9331	−	215.232i	0.0846648	−	0.260571i
$827$	606.565	+	834.865i	0.733452	+	1.00951i	0.998969	+	0.0454043i	$0.0144576\pi$
$827$	606.565	+	834.865i	0.733452	+	1.00951i	−0.265516	+	0.964106i	$0.585542\pi$
$828$		0			0
$829$	−184.738	+	60.0251i	−0.222845	+	0.0724067i	−0.418311	−	0.908304i	$-0.637378\pi$
$829$	−184.738	+	60.0251i	−0.222845	+	0.0724067i	0.195467	+	0.980710i	$0.437378\pi$
$830$	246.675	+	80.1494i	0.297198	+	0.0965656i
$831$		0			0
$832$			552.483i			0.664042i
$833$	54.1717	+	17.6014i	0.0650320	+	0.0211302i
$834$		0			0
$835$	172.963	+	238.063i	0.207142	+	0.285106i
$836$			541.464i			0.647684i
$837$		0			0
$838$	−125.156			−0.149351
$839$	126.468	−	91.8842i	0.150736	−	0.109516i	−0.509861	−	0.860257i	$-0.670303\pi$
$839$	126.468	−	91.8842i	0.150736	−	0.109516i	0.660597	+	0.750740i	$0.270303\pi$
$840$		0			0
$841$	−252.555	+	777.285i	−0.300303	+	0.924239i
$842$	−451.496			−0.536218
$843$		0			0
$844$	70.0609	−	215.625i	0.0830106	−	0.255480i
$845$	107.741	+	331.594i	0.127505	+	0.392419i
$846$		0			0
$847$	235.728	−	171.267i	0.278310	−	0.202204i
$848$	−200.366	−	65.1028i	−0.236281	−	0.0767722i
$849$		0			0
$850$	10.3277	−	14.2149i	0.0121503	−	0.0167234i
$851$	−236.591	−	728.152i	−0.278015	−	0.855642i
$852$		0			0
$853$	262.545	+	190.750i	0.307790	+	0.223623i	0.730948	−	0.682433i	$-0.239078\pi$
$853$	262.545	+	190.750i	0.307790	+	0.223623i	−0.423158	+	0.906056i	$0.639078\pi$
$854$	408.544	−	132.744i	0.478389	−	0.155438i
$855$		0			0
$856$	908.147	−	659.808i	1.06092	−	0.770803i
$857$	−292.610	+	900.560i	−0.341435	+	1.05083i	0.622030	+	0.782993i	$0.286308\pi$
$857$	−292.610	+	900.560i	−0.341435	+	1.05083i	−0.963465	+	0.267835i	$0.913692\pi$
$858$		0			0
$859$	934.896	−	303.766i	1.08835	−	0.353628i	0.290744	−	0.956801i	$-0.406097\pi$
$859$	934.896	−	303.766i	1.08835	−	0.353628i	0.797610	+	0.603173i	$0.206097\pi$
$860$	−188.341	+	61.1958i	−0.219001	+	0.0711579i
$861$		0			0
$862$	−20.7676			−0.0240924
$863$		−	581.969i		−	0.674355i	−0.941441	−	0.337178i	$-0.890528\pi$
$863$		−	581.969i		−	0.674355i	0.941441	−	0.337178i	$-0.109472\pi$
$864$		0			0
$865$	−688.634	−	500.322i	−0.796108	−	0.578407i
$866$	357.411	+	491.935i	0.412715	+	0.568054i
$867$		0			0
$868$	15.9425	+	197.115i	0.0183669	+	0.227091i
$869$	2143.73			2.46689
$870$		0			0
$871$	−593.489	+	816.868i	−0.681388	+	0.937851i
$872$	−404.614	+	1245.27i	−0.464007	+	1.42807i
$873$		0			0
$874$		−	545.623i		−	0.624283i
$875$	−145.141	+	446.697i	−0.165875	+	0.510510i
$876$		0			0
$877$	443.166	+	1363.93i	0.505321	+	1.55522i	0.800230	+	0.599693i	$0.204711\pi$
$877$	443.166	+	1363.93i	0.505321	+	1.55522i	−0.294909	+	0.955525i	$0.595289\pi$
$878$	−420.593	+	305.578i	−0.479035	+	0.348039i
$879$		0			0
$880$	181.552	+	249.885i	0.206309	+	0.283960i
$881$	−594.355	+	818.060i	−0.674637	+	0.928559i	−0.999854	−	0.0170809i	$-0.994563\pi$
$881$	−594.355	+	818.060i	−0.674637	+	0.928559i	0.325217	+	0.945639i	$0.394563\pi$
$882$		0			0
$883$	253.066	−	348.316i	0.286598	−	0.394468i	−0.641307	−	0.767284i	$-0.721608\pi$
$883$	253.066	−	348.316i	0.286598	−	0.394468i	0.927905	+	0.372816i	$0.121608\pi$
$884$	21.1624	+	15.3754i	0.0239394	+	0.0173930i
$885$		0			0
$886$	84.5389	+	61.4211i	0.0954164	+	0.0693241i
$887$	637.301	−	463.026i	0.718490	−	0.522014i	−0.167411	−	0.985887i	$-0.553541\pi$
$887$	637.301	−	463.026i	0.718490	−	0.522014i	0.885901	+	0.463874i	$0.153541\pi$
$888$		0			0
$889$	298.667	+	411.079i	0.335958	+	0.462406i
$890$	281.961	−	91.6146i	0.316810	−	0.102938i
$891$		0			0
$892$	545.498	+	177.243i	0.611545	+	0.198703i
$893$	100.993			0.113094
$894$		0			0
$895$	419.668	+	136.358i	0.468903	+	0.152356i
$896$	52.5822	+	38.2032i	0.0586855	+	0.0426375i
$897$		0			0
$898$		−	970.252i		−	1.08046i
$899$	−292.041	+	1228.14i	−0.324851	+	1.36612i
$900$		0			0
$901$	−50.3897	+	36.6102i	−0.0559264	+	0.0406329i
$902$	−937.827	+	1290.81i	−1.03972	+	1.43105i
$903$		0			0
$904$	−1048.82			−1.16020
$905$		−	572.003i		−	0.632047i
$906$		0			0
$907$	300.044	+	923.442i	0.330810	+	1.01813i	0.968749	+	0.248042i	$0.0797869\pi$
$907$	300.044	+	923.442i	0.330810	+	1.01813i	−0.637940	+	0.770086i	$0.720213\pi$
$908$	−243.250	−	748.647i	−0.267897	−	0.824501i
$909$		0			0
$910$	184.167	+	59.8396i	0.202382	+	0.0657578i
$911$	−78.3571	−	107.849i	−0.0860122	−	0.118386i	0.763843	−	0.645403i	$-0.223310\pi$
$911$	−78.3571	−	107.849i	−0.0860122	−	0.118386i	−0.849855	+	0.527017i	$0.823310\pi$
$912$		0			0
$913$	−188.760	−	580.945i	−0.206747	−	0.636303i
$914$	−70.9171	+	97.6091i	−0.0775899	+	0.106793i
$915$		0			0
$916$	−1.72227	+	0.559599i	−0.00188020	+	0.000610916i
$917$	177.834	+	129.204i	0.193930	+	0.140899i
$918$		0			0
$919$	354.402	−	1090.74i	0.385638	−	1.18687i	−0.550378	−	0.834916i	$-0.685516\pi$
$919$	354.402	−	1090.74i	0.385638	−	1.18687i	0.936016	−	0.351957i	$-0.114484\pi$
$920$	380.384	+	523.554i	0.413461	+	0.569081i
$921$		0			0
$922$	39.1809	−	12.7306i	0.0424956	−	0.0138076i
$923$	556.577	+	180.843i	0.603009	+	0.195929i
$924$		0			0
$925$		−	328.201i		−	0.354812i
$926$	−506.221	−	164.481i	−0.546675	−	0.177625i
$927$		0			0
$928$	638.917	+	879.394i	0.688488	+	0.947622i
$929$			1665.59i			1.79288i	0.443162	+	0.896441i	$0.353857\pi$
$929$			1665.59i			1.79288i	−0.443162	+	0.896441i	$0.646143\pi$
$930$		0			0
$931$	758.224			0.814419
$932$	531.058	−	385.836i	0.569804	−	0.413987i
$933$		0			0
$934$	−322.888	+	993.746i	−0.345704	+	1.06397i
$935$	91.3165			0.0976647
$936$		0			0
$937$	173.875	−	535.132i	0.185566	−	0.571112i	−0.814392	−	0.580315i	$-0.802929\pi$
$937$	173.875	−	535.132i	0.185566	−	0.571112i	0.999958	+	0.00920275i	$0.00292937\pi$
$938$	−171.496	−	527.809i	−0.182831	−	0.562697i
$939$		0			0
$940$	−30.6186	+	22.2457i	−0.0325730	+	0.0236657i
$941$	567.485	+	184.387i	0.603066	+	0.195948i	0.594607	−	0.804016i	$-0.297308\pi$
$941$	567.485	+	184.387i	0.603066	+	0.195948i	0.00845860	+	0.999964i	$0.497308\pi$
$942$		0			0
$943$	−811.188	+	1116.50i	−0.860220	+	1.18399i
$944$	−71.7347	−	220.777i	−0.0759902	−	0.233874i
$945$		0			0
$946$	−439.574	−	319.369i	−0.464666	−	0.337599i
$947$	1296.15	−	421.143i	1.36869	−	0.444713i	0.469752	−	0.882798i	$-0.344343\pi$
$947$	1296.15	−	421.143i	1.36869	−	0.444713i	0.898933	+	0.438086i	$0.144343\pi$
$948$		0			0
$949$	−673.653	+	489.438i	−0.709856	+	0.515741i
$950$	72.2770	−	222.446i	0.0760810	−	0.234153i
$951$		0			0
$952$	−43.2777	+	14.0618i	−0.0454598	+	0.0147708i
$953$	603.483	−	196.083i	0.633245	−	0.205754i	0.0252332	−	0.999682i	$-0.491967\pi$
$953$	603.483	−	196.083i	0.633245	−	0.205754i	0.608012	+	0.793928i	$0.291967\pi$
$954$		0			0
$955$	126.625			0.132592
$956$		−	440.505i		−	0.460779i
$957$		0			0
$958$	−769.783	−	559.280i	−0.803531	−	0.583800i
$959$	−193.438	−	266.244i	−0.201708	−	0.277627i
$960$		0			0
$961$	−146.225	+	949.810i	−0.152159	+	0.988356i
$962$	−569.228			−0.591713
$963$		0			0
$964$	353.600	−	486.689i	0.366805	−	0.504864i
$965$	−231.814	+	713.450i	−0.240222	+	0.739327i
$966$		0			0
$967$		−	535.924i		−	0.554213i	−0.960839	−	0.277107i	$-0.910624\pi$
$967$		−	535.924i		−	0.554213i	0.960839	−	0.277107i	$-0.0893755\pi$
$968$	223.720	−	688.540i	0.231116	−	0.711302i
$969$		0			0
$970$	92.2239	+	283.836i	0.0950762	+	0.292614i
$971$	−842.284	+	611.955i	−0.867439	+	0.630232i	−0.929899	−	0.367816i	$-0.880106\pi$
$971$	−842.284	+	611.955i	−0.867439	+	0.630232i	0.0624592	+	0.998048i	$0.480106\pi$
$972$		0			0
$973$	−150.101	−	206.597i	−0.154267	−	0.212330i
$974$	620.962	−	854.681i	0.637538	−	0.877496i
$975$		0			0
$976$	258.999	−	356.482i	0.265368	−	0.365248i
$977$	504.334	+	366.420i	0.516207	+	0.375046i	0.815173	−	0.579218i	$-0.196642\pi$
$977$	504.334	+	366.420i	0.516207	+	0.375046i	−0.298966	+	0.954264i	$0.596642\pi$
$978$		0			0
$979$	−564.872	−	410.404i	−0.576989	−	0.419207i
$980$	−229.876	+	167.015i	−0.234567	+	0.170423i
$981$		0			0
$982$	−173.465	−	238.755i	−0.176645	−	0.243131i
$983$	478.127	−	155.353i	0.486395	−	0.158039i	−0.0555453	−	0.998456i	$-0.517690\pi$
$983$	478.127	−	155.353i	0.486395	−	0.158039i	0.541941	+	0.840417i	$0.317690\pi$
$984$		0			0
$985$	225.333	+	73.2153i	0.228765	+	0.0743302i
$986$	−91.7784			−0.0930816
$987$		0			0
$988$	331.166	+	107.602i	0.335188	+	0.108909i
$989$	−380.216	−	276.243i	−0.384445	−	0.279316i
$990$		0			0
$991$			1685.38i			1.70068i	0.526232	+	0.850341i	$0.323604\pi$
$991$			1685.38i			1.70068i	−0.526232	+	0.850341i	$0.676396\pi$
$992$	538.766	+	628.057i	0.543110	+	0.633122i
$993$		0			0
$994$	−260.228	+	189.066i	−0.261798	+	0.190208i
$995$	−573.169	+	788.899i	−0.576049	+	0.792864i
$996$		0			0
$997$	−368.804			−0.369913			−0.184957	−	0.982747i	$-0.559214\pi$
$997$	−368.804			−0.369913			−0.184957	+	0.982747i	$0.559214\pi$
$998$		−	107.384i		−	0.107599i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	279.3.v.a.46.2		20
3.2	odd	2		31.3.f.a.15.4	✓	20
31.29	odd	10	inner	279.3.v.a.91.2		20
93.29	even	10		31.3.f.a.29.4	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.3.f.a.15.4	✓	20	3.2	odd	2
31.3.f.a.29.4	yes	20	93.29	even	10
279.3.v.a.46.2		20	1.1	even	1	trivial
279.3.v.a.91.2		20	31.29	odd	10	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 279 = 3^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	279.v (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.18692 + 0.862348i) q^{2} +(-0.570933 + 1.75715i) q^{4} +4.14776 q^{5} +(1.06697 - 3.28380i) q^{7} +(-2.65108 - 8.15917i) q^{8} +(-4.92306 + 3.57681i) q^{10} +(13.6300 + 4.42864i) q^{11} +(5.41722 - 7.45616i) q^{13} +(1.56537 + 4.81771i) q^{14} +(4.20377 + 3.05422i) q^{16} +(1.46101 - 0.474711i) q^{17} +(16.5438 - 12.0198i) q^{19} +(-2.36809 + 7.28825i) q^{20} +(-19.9967 + 6.49732i) q^{22} +(-17.2964 + 5.61995i) q^{23} -7.79606 q^{25} +13.5214i q^{26} +(5.16097 + 3.74966i) q^{28} +(23.9358 + 32.9448i) q^{29} +(20.1838 + 23.5290i) q^{31} +26.6929 q^{32} +(-1.32474 + 1.82334i) q^{34} +(4.42555 - 13.6204i) q^{35} +42.0983i q^{37} +(-9.27096 + 28.5331i) q^{38} +(-10.9960 - 33.8423i) q^{40} +(61.3917 - 44.6037i) q^{41} +(15.1894 + 20.9064i) q^{43} +(-15.5636 + 21.4214i) q^{44} +(15.6831 - 21.5860i) q^{46} +(3.99548 + 2.90289i) q^{47} +(29.9969 + 21.7940i) q^{49} +(9.25330 - 6.72292i) q^{50} +(10.0087 + 13.7758i) q^{52} +(-38.5605 + 12.5291i) q^{53} +(56.5338 + 18.3689i) q^{55} -29.6217 q^{56} +(-56.8198 - 18.4619i) q^{58} +(-36.1430 - 26.2594i) q^{59} -84.8005i q^{61} +(-44.2468 - 10.5215i) q^{62} +(-48.4974 + 35.2354i) q^{64} +(22.4693 - 30.9264i) q^{65} -109.556 q^{67} +2.83825i q^{68} +(6.49278 + 19.9827i) q^{70} +(19.6220 + 60.3903i) q^{71} +(-85.9266 - 27.9192i) q^{73} +(-36.3034 - 49.9674i) q^{74} +(11.6752 + 35.9325i) q^{76} +(29.0856 - 40.0328i) q^{77} +(142.262 - 46.2236i) q^{79} +(17.4362 + 12.6682i) q^{80} +(-34.4032 + 105.882i) q^{82} +(-25.0530 - 34.4824i) q^{83} +(6.05993 - 1.96899i) q^{85} +(-36.0572 - 11.7157i) q^{86} -122.950i q^{88} +(-46.3352 - 15.0552i) q^{89} +(-18.7045 - 25.7446i) q^{91} -33.6011i q^{92} -7.24561 q^{94} +(68.6199 - 49.8553i) q^{95} +(15.1554 - 46.6434i) q^{97} -54.3979 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 3 q^{2} - 11 q^{4} + 14 q^{5} - q^{7} + 19 q^{8} + 12 q^{10} + 10 q^{11} + 10 q^{13} - 103 q^{16} - 35 q^{17} + 47 q^{19} + 125 q^{20} + 150 q^{22} - 75 q^{23} + 82 q^{25} + 88 q^{28} - 5 q^{29}+ \cdots + 1000 q^{98}+O(q^{100}) \) 20 * q + 3 * q^2 - 11 * q^4 + 14 * q^5 - q^7 + 19 * q^8 + 12 * q^10 + 10 * q^11 + 10 * q^13 - 103 * q^16 - 35 * q^17 + 47 * q^19 + 125 * q^20 + 150 * q^22 - 75 * q^23 + 82 * q^25 + 88 * q^28 - 5 * q^29 + 73 * q^31 - 226 * q^32 - 265 * q^34 + 50 * q^35 - 8 * q^38 - 466 * q^40 + 98 * q^41 + 245 * q^43 - 380 * q^44 - 445 * q^46 + 187 * q^47 + 328 * q^49 + 44 * q^50 - 15 * q^52 - 25 * q^53 + 190 * q^55 - 64 * q^56 - 85 * q^58 + 173 * q^59 + 40 * q^62 - 469 * q^64 + 345 * q^65 + 76 * q^67 - 11 * q^70 + 467 * q^71 - 15 * q^73 - 45 * q^74 + 55 * q^76 + 320 * q^77 + 500 * q^79 - 1030 * q^80 + 178 * q^82 + 50 * q^83 + 20 * q^85 - 1125 * q^86 - 55 * q^89 + 300 * q^91 + 62 * q^94 + 559 * q^95 - 405 * q^97 + 1000 * q^98

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