LMFDB - Embedded newform 684.3.s.a.445.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(445,684)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 1]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("684.445");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.s (of order $6$, degree $2$, 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:	$18.6376500822$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			445.2
Character	$\chi$	$=$	684.445
Dual form			684.3.s.a.601.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.99241 - 0.213197i) q^{3} +(2.77840 + 4.81232i) q^{5} +(0.506731 + 0.877684i) q^{7} +(8.90909 + 1.27595i) q^{9} +O(q^{10})$	\(q+(-2.99241 - 0.213197i) q^{3} +(2.77840 + 4.81232i) q^{5} +(0.506731 + 0.877684i) q^{7} +(8.90909 + 1.27595i) q^{9} +(-3.59027 - 6.21853i) q^{11} -21.0389i q^{13} +(-7.28814 - 14.9928i) q^{15} +(5.88580 - 10.1945i) q^{17} +(4.15216 + 18.5408i) q^{19} +(-1.32923 - 2.73443i) q^{21} -38.5635 q^{23} +(-2.93898 + 5.09046i) q^{25} +(-26.3877 - 5.71757i) q^{27} +(34.4637 + 19.8976i) q^{29} +(47.7320 + 27.5581i) q^{31} +(9.41780 + 19.3739i) q^{33} +(-2.81580 + 4.87711i) q^{35} -39.2580i q^{37} +(-4.48544 + 62.9572i) q^{39} +(1.00630 - 0.580990i) q^{41} +32.6087 q^{43} +(18.6127 + 46.4185i) q^{45} +(13.8579 - 24.0026i) q^{47} +(23.9864 - 41.5457i) q^{49} +(-19.7862 + 29.2514i) q^{51} +(32.1220 - 18.5456i) q^{53} +(19.9504 - 34.5551i) q^{55} +(-8.47215 - 56.3669i) q^{57} +(3.95707 - 2.28462i) q^{59} +(-15.6455 + 27.0989i) q^{61} +(3.39463 + 8.46593i) q^{63} +(101.246 - 58.4545i) q^{65} -41.2008i q^{67} +(115.398 + 8.22163i) q^{69} +(27.3414 + 15.7856i) q^{71} +(56.0237 - 97.0360i) q^{73} +(9.87992 - 14.6062i) q^{75} +(3.63860 - 6.30224i) q^{77} +1.05589i q^{79} +(77.7439 + 22.7351i) q^{81} +(76.0080 + 131.650i) q^{83} +65.4124 q^{85} +(-98.8875 - 66.8895i) q^{87} +(27.7627 - 16.0288i) q^{89} +(18.4655 - 10.6611i) q^{91} +(-136.959 - 92.6416i) q^{93} +(-77.6878 + 71.4951i) q^{95} +136.516i q^{97} +(-24.0515 - 59.9825i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - q^{7} + 4 q^{9}+O(q^{10}) $ 80 * q - q^7 + 4 * q^9	$ 80 q - q^{7} + 4 q^{9} - 6 q^{11} + 33 q^{15} - 21 q^{17} - 20 q^{19} - 48 q^{23} - 200 q^{25} - 63 q^{27} - 27 q^{29} - 24 q^{31} + 27 q^{33} - 54 q^{35} - 81 q^{39} - 18 q^{41} - 152 q^{43} + 188 q^{45} - 12 q^{47} - 267 q^{49} - 126 q^{51} - 36 q^{53} + 126 q^{57} - 135 q^{59} - 7 q^{61} - 190 q^{63} - 288 q^{65} + 48 q^{69} - 81 q^{71} + 55 q^{73} + 165 q^{75} + 30 q^{77} + 28 q^{81} - 93 q^{83} + 306 q^{87} + 216 q^{89} + 96 q^{91} + 24 q^{93} + 288 q^{95} - 241 q^{99}+O(q^{100}) $ 80 * q - q^7 + 4 * q^9 - 6 * q^11 + 33 * q^15 - 21 * q^17 - 20 * q^19 - 48 * q^23 - 200 * q^25 - 63 * q^27 - 27 * q^29 - 24 * q^31 + 27 * q^33 - 54 * q^35 - 81 * q^39 - 18 * q^41 - 152 * q^43 + 188 * q^45 - 12 * q^47 - 267 * q^49 - 126 * q^51 - 36 * q^53 + 126 * q^57 - 135 * q^59 - 7 * q^61 - 190 * q^63 - 288 * q^65 + 48 * q^69 - 81 * q^71 + 55 * q^73 + 165 * q^75 + 30 * q^77 + 28 * q^81 - 93 * q^83 + 306 * q^87 + 216 * q^89 + 96 * q^91 + 24 * q^93 + 288 * q^95 - 241 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.99241	−	0.213197i	−0.997472	−	0.0710658i
$3$	−2.99241	−	0.213197i	−0.997472	−	0.0710658i
$4$		0			0
$5$	2.77840	+	4.81232i	0.555679	+	0.962465i	0.997850	+	0.0655341i	$0.0208751\pi$
$5$	2.77840	+	4.81232i	0.555679	+	0.962465i	−0.442171	+	0.896931i	$0.645792\pi$
$6$		0			0
$7$	0.506731	+	0.877684i	0.0723901	+	0.125383i	0.899948	−	0.435996i	$-0.143604\pi$
$7$	0.506731	+	0.877684i	0.0723901	+	0.125383i	−0.827558	+	0.561380i	$0.810271\pi$
$8$		0			0
$9$	8.90909	+	1.27595i	0.989899	+	0.141772i
$10$		0			0
$11$	−3.59027	−	6.21853i	−0.326388	−	0.565321i	0.655404	−	0.755278i	$-0.272498\pi$
$11$	−3.59027	−	6.21853i	−0.326388	−	0.565321i	−0.981792	+	0.189958i	$0.939165\pi$
$12$		0			0
$13$		−	21.0389i		−	1.61838i	−0.587548	−	0.809189i	$-0.699907\pi$
$13$		−	21.0389i		−	1.61838i	0.587548	−	0.809189i	$-0.300093\pi$
$14$		0			0
$15$	−7.28814	−	14.9928i	−0.485876	−	0.999521i
$16$		0			0
$17$	5.88580	−	10.1945i	0.346224	−	0.599677i	−0.639352	−	0.768914i	$-0.720797\pi$
$17$	5.88580	−	10.1945i	0.346224	−	0.599677i	0.985575	+	0.169238i	$0.0541305\pi$
$18$		0			0
$19$	4.15216	+	18.5408i	0.218535	+	0.975829i
$19$	4.15216	+	18.5408i	0.218535	+	0.975829i
$20$		0			0
$21$	−1.32923	−	2.73443i	−0.0632966	−	0.130211i
$22$		0			0
$23$	−38.5635			−1.67667			−0.838336	−	0.545154i	$-0.816471\pi$
$23$	−38.5635			−1.67667			−0.838336	+	0.545154i	$0.816471\pi$
$24$		0			0
$25$	−2.93898	+	5.09046i	−0.117559	+	0.203618i
$26$		0			0
$27$	−26.3877	−	5.71757i	−0.977321	−	0.211762i
$28$		0			0
$29$	34.4637	+	19.8976i	1.18840	+	0.686124i	0.957943	−	0.286958i	$-0.0926439\pi$
$29$	34.4637	+	19.8976i	1.18840	+	0.686124i	0.230459	+	0.973082i	$0.425977\pi$
$30$		0			0
$31$	47.7320	+	27.5581i	1.53974	+	0.888971i	0.998853	+	0.0478768i	$0.0152455\pi$
$31$	47.7320	+	27.5581i	1.53974	+	0.888971i	0.540889	+	0.841094i	$0.318088\pi$
$32$		0			0
$33$	9.41780	+	19.3739i	0.285388	+	0.587086i
$34$		0			0
$35$	−2.81580	+	4.87711i	−0.0804514	+	0.139346i
$36$		0			0
$37$		−	39.2580i		−	1.06103i	−0.847677	−	0.530513i	$-0.821999\pi$
$37$		−	39.2580i		−	1.06103i	0.847677	−	0.530513i	$-0.178001\pi$
$38$		0			0
$39$	−4.48544	+	62.9572i	−0.115011	+	1.61429i
$40$		0			0
$41$	1.00630	−	0.580990i	0.0245440	−	0.0141705i	−0.487678	−	0.873024i	$-0.662156\pi$
$41$	1.00630	−	0.580990i	0.0245440	−	0.0141705i	0.512222	+	0.858853i	$0.328823\pi$
$42$		0			0
$43$	32.6087			0.758342			0.379171	−	0.925327i	$-0.376209\pi$
$43$	32.6087			0.758342			0.379171	+	0.925327i	$0.376209\pi$
$44$		0			0
$45$	18.6127	+	46.4185i	0.413616	+	1.03152i
$46$		0			0
$47$	13.8579	−	24.0026i	0.294850	−	0.510695i	−0.680100	−	0.733119i	$-0.738064\pi$
$47$	13.8579	−	24.0026i	0.294850	−	0.510695i	0.974950	+	0.222424i	$0.0713971\pi$
$48$		0			0
$49$	23.9864	−	41.5457i	0.489519	−	0.847872i
$50$		0			0
$51$	−19.7862	+	29.2514i	−0.387965	+	0.573556i
$52$		0			0
$53$	32.1220	−	18.5456i	0.606075	−	0.349918i	−0.165353	−	0.986235i	$-0.552876\pi$
$53$	32.1220	−	18.5456i	0.606075	−	0.349918i	0.771428	+	0.636317i	$0.219543\pi$
$54$		0			0
$55$	19.9504	−	34.5551i	0.362734	−	0.628274i
$56$		0			0
$57$	−8.47215	−	56.3669i	−0.148634	−	0.988892i
$58$		0			0
$59$	3.95707	−	2.28462i	0.0670691	−	0.0387223i	−0.466090	−	0.884737i	$-0.654338\pi$
$59$	3.95707	−	2.28462i	0.0670691	−	0.0387223i	0.533160	+	0.846015i	$0.321005\pi$
$60$		0			0
$61$	−15.6455	+	27.0989i	−0.256484	+	0.444244i	−0.965298	−	0.261152i	$-0.915897\pi$
$61$	−15.6455	+	27.0989i	−0.256484	+	0.444244i	0.708813	+	0.705396i	$0.249231\pi$
$62$		0			0
$63$	3.39463	+	8.46593i	0.0538831	+	0.134380i
$64$		0			0
$65$	101.246	−	58.4545i	1.55763	−	0.899300i
$66$		0			0
$67$		−	41.2008i		−	0.614937i	−0.951558	−	0.307469i	$-0.900518\pi$
$67$		−	41.2008i		−	0.614937i	0.951558	−	0.307469i	$-0.0994819\pi$
$68$		0			0
$69$	115.398	+	8.22163i	1.67243	+	0.119154i
$70$		0			0
$71$	27.3414	+	15.7856i	0.385090	+	0.222332i	0.680030	−	0.733184i	$-0.261967\pi$
$71$	27.3414	+	15.7856i	0.385090	+	0.222332i	−0.294941	+	0.955516i	$0.595300\pi$
$72$		0			0
$73$	56.0237	−	97.0360i	0.767448	−	1.32926i	−0.171494	−	0.985185i	$-0.554859\pi$
$73$	56.0237	−	97.0360i	0.767448	−	1.32926i	0.938942	−	0.344075i	$-0.111807\pi$
$74$		0			0
$75$	9.87992	−	14.6062i	0.131732	−	0.194749i
$76$		0			0
$77$	3.63860	−	6.30224i	0.0472546	−	0.0818473i
$78$		0			0
$79$			1.05589i			0.0133657i	0.999978	+	0.00668284i	$0.00212723\pi$
$79$			1.05589i			0.0133657i	−0.999978	+	0.00668284i	$0.997873\pi$
$80$		0			0
$81$	77.7439	+	22.7351i	0.959801	+	0.280681i
$82$		0			0
$83$	76.0080	+	131.650i	0.915759	+	1.58614i	0.805787	+	0.592206i	$0.201743\pi$
$83$	76.0080	+	131.650i	0.915759	+	1.58614i	0.109972	+	0.993935i	$0.464924\pi$
$84$		0			0
$85$	65.4124			0.769557
$86$		0			0
$87$	−98.8875	−	66.8895i	−1.13664	−	0.768844i
$88$		0			0
$89$	27.7627	−	16.0288i	0.311941	−	0.180099i	−0.335854	−	0.941914i	$-0.609025\pi$
$89$	27.7627	−	16.0288i	0.311941	−	0.180099i	0.647795	+	0.761815i	$0.275691\pi$
$90$		0			0
$91$	18.4655	−	10.6611i	0.202918	−	0.117155i
$92$		0			0
$93$	−136.959	−	92.6416i	−1.47267	−	0.996146i
$94$		0			0
$95$	−77.6878	+	71.4951i	−0.817766	+	0.752580i
$96$		0			0
$97$			136.516i			1.40738i	0.710505	+	0.703692i	$0.248466\pi$
$97$			136.516i			1.40738i	−0.710505	+	0.703692i	$0.751534\pi$
$98$		0			0
$99$	−24.0515	−	59.9825i	−0.242945	−	0.605883i
$100$		0			0
$101$	−51.4168	+	89.0564i	−0.509077	+	0.881747i	0.490868	+	0.871234i	$0.336680\pi$
$101$	−51.4168	+	89.0564i	−0.509077	+	0.881747i	−0.999945	+	0.0105129i	$0.996654\pi$
$102$		0			0
$103$	67.3695	+	38.8958i	0.654072	+	0.377629i	0.790015	−	0.613088i	$-0.210073\pi$
$103$	67.3695	+	38.8958i	0.654072	+	0.377629i	−0.135942	+	0.990717i	$0.543406\pi$
$104$		0			0
$105$	9.46583	−	13.9940i	0.0901507	−	0.133276i
$106$		0			0
$107$		−	109.565i		−	1.02397i	−0.858994	−	0.511986i	$-0.828910\pi$
$107$		−	109.565i		−	1.02397i	0.858994	−	0.511986i	$-0.171090\pi$
$108$		0			0
$109$	−9.20585	−	5.31500i	−0.0844574	−	0.0487615i	0.457177	−	0.889376i	$-0.348861\pi$
$109$	−9.20585	−	5.31500i	−0.0844574	−	0.0487615i	−0.541634	+	0.840614i	$0.682194\pi$
$110$		0			0
$111$	−8.36970	+	117.476i	−0.0754027	+	1.05834i
$112$		0			0
$113$	176.506	+	101.906i	1.56200	+	0.901823i	0.997054	+	0.0766977i	$0.0244376\pi$
$113$	176.506	+	101.906i	1.56200	+	0.901823i	0.564949	+	0.825126i	$0.308896\pi$
$114$		0			0
$115$	−107.145	−	185.580i	−0.931692	−	1.61374i
$116$		0			0
$117$	26.8446	−	187.438i	0.229441	−	1.60203i
$118$		0			0
$119$	11.9301			0.100253
$120$		0			0
$121$	34.7199	−	60.1367i	0.286942	−	0.496998i
$122$		0			0
$123$	−3.13515	+	1.52402i	−0.0254890	+	0.0123904i
$124$		0			0
$125$	106.257			0.850058
$126$		0			0
$127$	205.368	−	118.570i	1.61707	−	0.933618i	0.629403	−	0.777079i	$-0.283300\pi$
$127$	205.368	−	118.570i	1.61707	−	0.933618i	0.987672	−	0.156539i	$-0.0500336\pi$
$128$		0			0
$129$	−97.5788	−	6.95209i	−0.756424	−	0.0538922i
$130$		0			0
$131$	−11.8754	−	20.5688i	−0.0906521	−	0.157014i	0.817134	−	0.576448i	$-0.195562\pi$
$131$	−11.8754	−	20.5688i	−0.0906521	−	0.157014i	−0.907786	+	0.419434i	$0.862228\pi$
$132$		0			0
$133$	−14.1689	+	13.0395i	−0.106533	+	0.0980411i
$134$		0			0
$135$	−45.8006	−	142.872i	−0.339264	−	1.05831i
$136$		0			0
$137$	−85.3353	+	147.805i	−0.622886	+	1.07887i	0.366060	+	0.930591i	$0.380707\pi$
$137$	−85.3353	+	147.805i	−0.622886	+	1.07887i	−0.988946	+	0.148278i	$0.952627\pi$
$138$		0			0
$139$	−183.477			−1.31998			−0.659989	−	0.751276i	$-0.729439\pi$
$139$	−183.477			−1.31998			−0.659989	+	0.751276i	$0.729439\pi$
$140$		0			0
$141$	−46.5860	+	68.8714i	−0.330397	+	0.488450i
$142$		0			0
$143$	−130.831	+	75.5354i	−0.914903	+	0.528220i
$144$		0			0
$145$			221.134i			1.52506i
$146$		0			0
$147$	−80.6348	+	119.208i	−0.548536	+	0.810941i
$148$		0			0
$149$	41.3286	+	71.5832i	0.277373	+	0.480424i	0.970731	−	0.240169i	$-0.0772028\pi$
$149$	41.3286	+	71.5832i	0.277373	+	0.480424i	−0.693358	+	0.720593i	$0.743869\pi$
$150$		0			0
$151$	64.0926	−	37.0039i	0.424454	−	0.245059i	−0.272527	−	0.962148i	$-0.587859\pi$
$151$	64.0926	−	37.0039i	0.424454	−	0.245059i	0.696981	+	0.717089i	$0.254526\pi$
$152$		0			0
$153$	65.4448	−	83.3138i	0.427744	−	0.544535i
$154$		0			0
$155$			306.269i			1.97593i
$156$		0			0
$157$	−134.217	−	232.470i	−0.854882	−	1.48070i	−0.876754	−	0.480939i	$-0.840296\pi$
$157$	−134.217	−	232.470i	−0.854882	−	1.48070i	0.0218718	−	0.999761i	$-0.493037\pi$
$158$		0			0
$159$	−100.076	+	48.6479i	−0.629410	+	0.305962i
$160$		0			0
$161$	−19.5413	−	33.8465i	−0.121375	−	0.210227i
$162$		0			0
$163$	−303.332			−1.86093			−0.930467	−	0.366376i	$-0.880599\pi$
$163$	−303.332			−1.86093			−0.930467	+	0.366376i	$0.880599\pi$
$164$		0			0
$165$	−67.0669	+	99.1498i	−0.406466	+	0.600908i
$166$		0			0
$167$		−	42.9565i		−	0.257224i	−0.991695	−	0.128612i	$-0.958948\pi$
$167$		−	42.9565i		−	0.257224i	0.991695	−	0.128612i	$-0.0410522\pi$
$168$		0			0
$169$	−273.636			−1.61915
$170$		0			0
$171$	13.3349	+	170.479i	0.0779820	+	0.996955i
$172$		0			0
$173$			266.137i			1.53836i	0.639030	+	0.769182i	$0.279336\pi$
$173$			266.137i			1.53836i	−0.639030	+	0.769182i	$0.720664\pi$
$174$		0			0
$175$	−5.95709			−0.0340405
$176$		0			0
$177$	−12.3283	+	5.99289i	−0.0696513	+	0.0338581i
$178$		0			0
$179$		−	11.5293i		−	0.0644093i	−0.999481	−	0.0322046i	$-0.989747\pi$
$179$		−	11.5293i		−	0.0644093i	0.999481	−	0.0322046i	$-0.0102528\pi$
$180$		0			0
$181$	89.5762	−	51.7169i	0.494896	−	0.285729i	−0.231707	−	0.972786i	$-0.574431\pi$
$181$	89.5762	−	51.7169i	0.494896	−	0.285729i	0.726603	+	0.687057i	$0.241098\pi$
$182$		0			0
$183$	52.5953	−	77.7554i	0.287406	−	0.424893i
$184$		0			0
$185$	188.922	−	109.074i	1.02120	−	0.589590i
$186$		0			0
$187$	−84.5264			−0.452013
$188$		0			0
$189$	−8.35324	−	26.0573i	−0.0441970	−	0.137869i
$190$		0			0
$191$	−66.7070	−	115.540i	−0.349251	−	0.604921i	0.636865	−	0.770975i	$-0.280231\pi$
$191$	−66.7070	−	115.540i	−0.349251	−	0.604921i	−0.986117	+	0.166054i	$0.946897\pi$
$192$		0			0
$193$	148.126	−	85.5204i	0.767491	−	0.443111i	−0.0644881	−	0.997918i	$-0.520541\pi$
$193$	148.126	−	85.5204i	0.767491	−	0.443111i	0.831979	+	0.554808i	$0.187208\pi$
$194$		0			0
$195$	−315.433	+	153.335i	−1.61760	+	0.786331i
$196$		0			0
$197$	−78.2214			−0.397063			−0.198531	−	0.980095i	$-0.563617\pi$
$197$	−78.2214			−0.397063			−0.198531	+	0.980095i	$0.563617\pi$
$198$		0			0
$199$	−60.1557	−	104.193i	−0.302290	−	0.523582i	0.674364	−	0.738399i	$-0.264418\pi$
$199$	−60.1557	−	104.193i	−0.302290	−	0.523582i	−0.976654	+	0.214817i	$0.931084\pi$
$200$		0			0
$201$	−8.78390	+	123.290i	−0.0437010	+	0.613382i
$202$		0			0
$203$			40.3309i			0.198675i
$204$		0			0
$205$	5.59183	+	3.22844i	0.0272772	+	0.0157485i
$206$		0			0
$207$	−343.566	−	49.2051i	−1.65974	−	0.237706i
$208$		0			0
$209$	100.389	−	92.3866i	0.480329	−	0.442041i
$210$		0			0
$211$	−36.7654	+	21.2265i	−0.174243	+	0.100599i	−0.584585	−	0.811332i	$-0.698743\pi$
$211$	−36.7654	+	21.2265i	−0.174243	+	0.100599i	0.410342	+	0.911932i	$0.365409\pi$
$212$		0			0
$213$	−78.4513	−	53.0660i	−0.368316	−	0.249136i
$214$		0			0
$215$	90.5999	+	156.924i	0.421395	+	0.729877i
$216$		0			0
$217$			55.8582i			0.257411i
$218$		0			0
$219$	−188.334	+	278.428i	−0.859973	+	1.27136i
$220$		0			0
$221$	−214.481	−	123.831i	−0.970504	−	0.560321i
$222$		0			0
$223$		−	109.639i		−	0.491657i	−0.969313	−	0.245828i	$-0.920940\pi$
$223$		−	109.639i		−	0.491657i	0.969313	−	0.245828i	$-0.0790600\pi$
$224$		0			0
$225$	−32.6788	+	41.6014i	−0.145239	+	0.184895i
$226$		0			0
$227$	277.452	−	160.187i	1.22226	−	0.705671i	0.256859	−	0.966449i	$-0.417313\pi$
$227$	277.452	−	160.187i	1.22226	−	0.705671i	0.965399	+	0.260778i	$0.0839792\pi$
$228$		0			0
$229$	149.471	−	258.891i	0.652710	−	1.13053i	−0.329753	−	0.944067i	$-0.606965\pi$
$229$	149.471	−	258.891i	0.652710	−	1.13053i	0.982463	−	0.186459i	$-0.0597012\pi$
$230$		0			0
$231$	−12.2318	+	18.0832i	−0.0529516	+	0.0782822i
$232$		0			0
$233$	−171.378	+	296.835i	−0.735527	+	1.27397i	0.218965	+	0.975733i	$0.429732\pi$
$233$	−171.378	+	296.835i	−0.735527	+	1.27397i	−0.954492	+	0.298237i	$0.903601\pi$
$234$		0			0
$235$	154.011			0.655368
$236$		0			0
$237$	0.225113	−	3.15966i	0.000949843	−	0.0133319i
$238$		0			0
$239$	155.648	−	269.589i	0.651245	−	1.12799i	−0.331576	−	0.943428i	$-0.607580\pi$
$239$	155.648	−	269.589i	0.651245	−	1.12799i	0.982821	−	0.184561i	$-0.0590863\pi$
$240$		0			0
$241$	−61.0923	−	35.2717i	−0.253495	−	0.146355i	0.367868	−	0.929878i	$-0.380088\pi$
$241$	−61.0923	−	35.2717i	−0.253495	−	0.146355i	−0.621364	+	0.783522i	$0.713421\pi$
$242$		0			0
$243$	−227.795	−	84.6077i	−0.937428	−	0.348180i
$244$		0			0
$245$	266.575			1.08806
$246$		0			0
$247$	390.077	−	87.3570i	1.57926	−	0.353672i
$248$		0			0
$249$	−199.380	−	410.155i	−0.800723	−	1.64721i
$250$		0			0
$251$	−204.111	−	353.530i	−0.813190	−	1.40849i	−0.910620	−	0.413244i	$-0.864396\pi$
$251$	−204.111	−	353.530i	−0.813190	−	1.40849i	0.0974307	−	0.995242i	$-0.468938\pi$
$252$		0			0
$253$	138.453	+	239.808i	0.547246	+	0.947858i
$254$		0			0
$255$	−195.741	−	13.9458i	−0.767612	−	0.0546892i
$256$		0			0
$257$			334.530i			1.30167i	0.759217	+	0.650837i	$0.225582\pi$
$257$			334.530i			1.30167i	−0.759217	+	0.650837i	$0.774418\pi$
$258$		0			0
$259$	34.4561	−	19.8932i	0.133035	−	0.0768079i
$260$		0			0
$261$	281.652	+	221.244i	1.07913	+	0.847676i
$262$		0			0
$263$	−89.0859			−0.338730			−0.169365	−	0.985553i	$-0.554172\pi$
$263$	−89.0859			−0.338730			−0.169365	+	0.985553i	$0.554172\pi$
$264$		0			0
$265$	178.495	+	103.054i	0.673567	+	0.388884i
$266$		0			0
$267$	−86.4949	+	42.0460i	−0.323951	+	0.157475i
$268$		0			0
$269$	−253.828	−	146.548i	−0.943599	−	0.544787i	−0.0525125	−	0.998620i	$-0.516723\pi$
$269$	−253.828	−	146.548i	−0.943599	−	0.544787i	−0.891087	+	0.453833i	$0.850056\pi$
$270$		0			0
$271$	102.311	−	177.208i	0.377531	−	0.653903i	−0.613171	−	0.789950i	$-0.710106\pi$
$271$	102.311	−	177.208i	0.377531	−	0.653903i	0.990702	+	0.136047i	$0.0434398\pi$
$272$		0			0
$273$	−57.5294	+	27.9656i	−0.210730	+	0.102438i
$274$		0			0
$275$	42.2069			0.153480
$276$		0			0
$277$	−61.0472	−	105.737i	−0.220387	−	0.381721i	0.734539	−	0.678567i	$-0.237399\pi$
$277$	−61.0472	−	105.737i	−0.220387	−	0.381721i	−0.954925	+	0.296846i	$0.904065\pi$
$278$		0			0
$279$	390.086	+	306.421i	1.39816	+	1.09828i
$280$		0			0
$281$	19.8408	+	11.4551i	0.0706080	+	0.0407655i	0.534888	−	0.844923i	$-0.320354\pi$
$281$	19.8408	+	11.4551i	0.0706080	+	0.0407655i	−0.464280	+	0.885688i	$0.653687\pi$
$282$		0			0
$283$	−10.4229	−	18.0530i	−0.0368301	−	0.0637916i	0.847023	−	0.531557i	$-0.178393\pi$
$283$	−10.4229	−	18.0530i	−0.0368301	−	0.0637916i	−0.883853	+	0.467765i	$0.845059\pi$
$284$		0			0
$285$	247.717	−	197.380i	0.869181	−	0.692562i
$286$		0			0
$287$	1.01985	+	0.588812i	0.00355349	+	0.00205161i
$288$		0			0
$289$	75.2147	+	130.276i	0.260258	+	0.450781i
$290$		0			0
$291$	29.1049	−	408.513i	0.100017	−	1.40383i
$292$		0			0
$293$	−359.465	−	207.537i	−1.22684	−	0.708318i	−0.260475	−	0.965481i	$-0.583879\pi$
$293$	−359.465	−	207.537i	−1.22684	−	0.708318i	−0.966368	+	0.257162i	$0.917212\pi$
$294$		0			0
$295$	21.9886	+	12.6952i	0.0745378	+	0.0430344i
$296$		0			0
$297$	59.1840	+	184.620i	0.199273	+	0.621617i
$298$		0			0
$299$			811.334i			2.71349i
$300$		0			0
$301$	16.5238	+	28.6201i	0.0548965	+	0.0950835i
$302$		0			0
$303$	172.847	−	255.532i	0.570452	−	0.843340i
$304$		0			0
$305$	−173.878			−0.570092
$306$		0			0
$307$	20.0192	+	11.5581i	0.0652090	+	0.0376484i	0.532250	−	0.846587i	$-0.321347\pi$
$307$	20.0192	+	11.5581i	0.0652090	+	0.0376484i	−0.467041	+	0.884236i	$0.654680\pi$
$308$		0			0
$309$	−193.305	−	130.755i	−0.625582	−	0.423156i
$310$		0			0
$311$	−269.387	+	466.593i	−0.866197	+	1.50030i	−0.000344138		1.00000i	$0.500110\pi$
$311$	−269.387	+	466.593i	−0.866197	+	1.50030i	−0.865853	+	0.500298i	$0.833224\pi$
$312$		0			0
$313$	243.055	−	420.984i	0.776535	−	1.34500i	−0.157393	−	0.987536i	$-0.550309\pi$
$313$	243.055	−	420.984i	0.776535	−	1.34500i	0.933928	−	0.357462i	$-0.116358\pi$
$314$		0			0
$315$	−31.3092	+	39.8578i	−0.0993942	+	0.126533i
$316$		0			0
$317$	−202.411	−	116.862i	−0.638521	−	0.368650i	0.145524	−	0.989355i	$-0.453513\pi$
$317$	−202.411	−	116.862i	−0.638521	−	0.368650i	−0.784045	+	0.620704i	$0.786847\pi$
$318$		0			0
$319$		−	285.751i		−	0.895771i
$320$		0			0
$321$	−23.3590	+	327.864i	−0.0727694	+	1.02138i
$322$		0			0
$323$	213.453	+	66.7980i	0.660844	+	0.206805i
$324$		0			0
$325$	107.098	+	61.8330i	0.329532	+	0.190255i
$326$		0			0
$327$	26.4146	+	17.8674i	0.0807785	+	0.0546402i
$328$		0			0
$329$	28.0890			0.0853769
$330$		0			0
$331$	−424.338	+	244.992i	−1.28199	+	0.740156i	−0.977212	−	0.212267i	$-0.931915\pi$
$331$	−424.338	+	244.992i	−1.28199	+	0.740156i	−0.304777	+	0.952424i	$0.598582\pi$
$332$		0			0
$333$	50.0912	−	349.753i	0.150424	−	1.05031i
$334$		0			0
$335$	198.272	−	114.472i	0.591855	−	0.341708i
$336$		0			0
$337$	−269.298	+	155.479i	−0.799102	+	0.461362i	−0.843157	−	0.537667i	$-0.819306\pi$
$337$	−269.298	+	155.479i	−0.799102	+	0.461362i	0.0440548	+	0.999029i	$0.485972\pi$
$338$		0			0
$339$	−506.454	−	342.576i	−1.49397	−	1.01055i
$340$		0			0
$341$		−	395.764i		−	1.16060i
$342$		0			0
$343$	98.2783			0.286526
$344$		0			0
$345$	281.056	+	578.175i	0.814655	+	1.67587i
$346$		0			0
$347$	57.3941	+	99.4096i	0.165401	+	0.286483i	0.936798	−	0.349872i	$-0.113775\pi$
$347$	57.3941	+	99.4096i	0.165401	+	0.286483i	−0.771397	+	0.636355i	$0.780442\pi$
$348$		0			0
$349$	174.607	+	302.428i	0.500307	+	0.866557i	1.00000		0.000354398i	$0.000112809\pi$
$349$	174.607	+	302.428i	0.500307	+	0.866557i	−0.499693	+	0.866203i	$0.666554\pi$
$350$		0			0
$351$	−120.291	+	555.168i	−0.342711	+	1.58168i
$352$		0			0
$353$	2.50075	+	4.33142i	0.00708428	+	0.0122703i	0.869546	−	0.493852i	$-0.164412\pi$
$353$	2.50075	+	4.33142i	0.00708428	+	0.0122703i	−0.862462	+	0.506123i	$0.831078\pi$
$354$		0			0
$355$			175.434i			0.494181i
$356$		0			0
$357$	−35.6997	−	2.54346i	−0.0999992	−	0.00712454i
$358$		0			0
$359$	−285.463	+	494.437i	−0.795162	+	1.37726i	0.127574	+	0.991829i	$0.459281\pi$
$359$	−285.463	+	494.437i	−0.795162	+	1.37726i	−0.922736	+	0.385432i	$0.874052\pi$
$360$		0			0
$361$	−326.519	+	153.968i	−0.904485	+	0.426505i
$362$		0			0
$363$	−116.717	+	172.552i	−0.321536	+	0.475349i
$364$		0			0
$365$	622.625			1.70582
$366$		0			0
$367$	81.0373	−	140.361i	0.220810	−	0.382454i	−0.734244	−	0.678885i	$-0.762463\pi$
$367$	81.0373	−	140.361i	0.220810	−	0.382454i	0.955054	+	0.296431i	$0.0957966\pi$
$368$		0			0
$369$	9.70658	−	3.89210i	0.0263051	−	0.0105477i
$370$		0			0
$371$	32.5544	+	18.7953i	0.0877477	+	0.0506612i
$372$		0			0
$373$	−532.169	−	307.248i	−1.42673	−	0.823721i	−0.429865	−	0.902893i	$-0.641439\pi$
$373$	−532.169	−	307.248i	−1.42673	−	0.823721i	−0.996861	+	0.0791726i	$0.974772\pi$
$374$		0			0
$375$	−317.966	−	22.6538i	−0.847909	−	0.0604101i
$376$		0			0
$377$	418.624	−	725.078i	1.11041	−	1.92328i
$378$		0			0
$379$		−	286.091i		−	0.754856i	−0.926039	−	0.377428i	$-0.876809\pi$
$379$		−	286.091i		−	0.754856i	0.926039	−	0.377428i	$-0.123191\pi$
$380$		0			0
$381$	−639.826	+	311.025i	−1.67933	+	0.816339i
$382$		0			0
$383$	400.992	−	231.513i	1.04698	−	0.604473i	0.125176	−	0.992135i	$-0.460051\pi$
$383$	400.992	−	231.513i	1.04698	−	0.604473i	0.921802	+	0.387662i	$0.126717\pi$
$384$		0			0
$385$	40.4379			0.105034
$386$		0			0
$387$	290.514	+	41.6071i	0.750682	+	0.107512i
$388$		0			0
$389$	96.7327	−	167.546i	0.248670	−	0.430709i	−0.714487	−	0.699649i	$-0.753340\pi$
$389$	96.7327	−	167.546i	0.248670	−	0.430709i	0.963157	+	0.268939i	$0.0866732\pi$
$390$		0			0
$391$	−226.977	+	393.136i	−0.580504	+	1.00546i
$392$		0			0
$393$	31.1510	+	64.0823i	0.0792646	+	0.163059i
$394$		0			0
$395$	−5.08128	+	2.93368i	−0.0128640	+	0.00742703i
$396$		0			0
$397$	6.35868	−	11.0136i	0.0160168	−	0.0277420i	−0.857906	−	0.513807i	$-0.828235\pi$
$397$	6.35868	−	11.0136i	0.0160168	−	0.0277420i	0.873923	+	0.486065i	$0.161568\pi$
$398$		0			0
$399$	45.1792	−	35.9987i	0.113231	−	0.0902223i
$400$		0			0
$401$	−30.3215	+	17.5061i	−0.0756146	+	0.0436561i	−0.537331	−	0.843372i	$-0.680567\pi$
$401$	−30.3215	+	17.5061i	−0.0756146	+	0.0436561i	0.461716	+	0.887028i	$0.347234\pi$
$402$		0			0
$403$	579.793	−	1004.23i	1.43869	−	2.49189i
$404$		0			0
$405$	106.595	+	437.296i	0.263197	+	1.07974i
$406$		0			0
$407$	−244.127	+	140.947i	−0.599820	+	0.346306i
$408$		0			0
$409$		−	109.295i		−	0.267225i	−0.991034	−	0.133613i	$-0.957342\pi$
$409$		−	109.295i		−	0.267225i	0.991034	−	0.133613i	$-0.0426578\pi$
$410$		0			0
$411$	286.870	−	424.101i	0.697982	−	1.03188i
$412$		0			0
$413$	4.01035	+	2.31537i	0.00971028	+	0.00560623i
$414$		0			0
$415$	−422.361	+	731.550i	−1.01774	+	1.76277i
$416$		0			0
$417$	549.039	+	39.1168i	1.31664	+	0.0938053i
$418$		0			0
$419$	251.614	−	435.809i	0.600512	−	1.04012i	−0.392232	−	0.919866i	$-0.628297\pi$
$419$	251.614	−	435.809i	0.600512	−	1.04012i	0.992744	−	0.120250i	$-0.0383697\pi$
$420$		0			0
$421$			742.171i			1.76288i	0.472298	+	0.881439i	$0.343424\pi$
$421$			742.171i			1.76288i	−0.472298	+	0.881439i	$0.656576\pi$
$422$		0			0
$423$	154.088	−	196.160i	0.364274	−	0.463735i
$424$		0			0
$425$	34.5965	+	59.9229i	0.0814035	+	0.140995i
$426$		0			0
$427$	−31.7123			−0.0742677
$428$		0			0
$429$	407.605	−	198.140i	0.950128	−	0.461866i
$430$		0			0
$431$	112.449	−	64.9223i	0.260902	−	0.150632i	−0.363844	−	0.931460i	$-0.618536\pi$
$431$	112.449	−	64.9223i	0.260902	−	0.150632i	0.624746	+	0.780828i	$0.285203\pi$
$432$		0			0
$433$	476.929	−	275.355i	1.10145	−	0.635923i	0.164850	−	0.986319i	$-0.447286\pi$
$433$	476.929	−	275.355i	1.10145	−	0.635923i	0.936602	+	0.350395i	$0.113953\pi$
$434$		0			0
$435$	47.1452	−	661.724i	0.108380	−	1.52120i
$436$		0			0
$437$	−160.122	−	714.996i	−0.366411	−	1.63615i
$438$		0			0
$439$			419.239i			0.954987i	0.878635	+	0.477493i	$0.158455\pi$
$439$			419.239i			0.954987i	−0.878635	+	0.477493i	$0.841545\pi$
$440$		0			0
$441$	266.708	−	339.529i	0.604780	−	0.769908i
$442$		0			0
$443$	−254.848	+	441.409i	−0.575277	+	0.996409i	0.420734	+	0.907184i	$0.361772\pi$
$443$	−254.848	+	441.409i	−0.575277	+	0.996409i	−0.996011	+	0.0892254i	$0.971561\pi$
$444$		0			0
$445$	154.272	+	89.0689i	0.346678	+	0.200155i
$446$		0			0
$447$	−108.411	−	223.018i	−0.242530	−	0.498922i
$448$		0			0
$449$			580.640i			1.29318i	0.762836	+	0.646592i	$0.223806\pi$
$449$			580.640i			1.29318i	−0.762836	+	0.646592i	$0.776194\pi$
$450$		0			0
$451$	−7.22581	−	4.17182i	−0.0160218	−	0.00925016i
$452$		0			0
$453$	−199.681	+	97.0666i	−0.440796	+	0.214275i
$454$		0			0
$455$	102.609	+	59.2414i	0.225515	+	0.130201i
$456$		0			0
$457$	108.041	+	187.133i	0.236414	+	0.409481i	0.959683	−	0.281086i	$-0.0906946\pi$
$457$	108.041	+	187.133i	0.236414	+	0.409481i	−0.723269	+	0.690567i	$0.757361\pi$
$458$		0			0
$459$	−213.600	+	235.357i	−0.465360	+	0.512760i
$460$		0			0
$461$	259.030			0.561887			0.280943	−	0.959724i	$-0.409353\pi$
$461$	259.030			0.561887			0.280943	+	0.959724i	$0.409353\pi$
$462$		0			0
$463$	65.8203	−	114.004i	0.142161	−	0.246229i	−0.786149	−	0.618036i	$-0.787928\pi$
$463$	65.8203	−	114.004i	0.142161	−	0.246229i	0.928310	+	0.371807i	$0.121262\pi$
$464$		0			0
$465$	65.2958	−	916.485i	0.140421	−	1.97093i
$466$		0			0
$467$	−17.1989			−0.0368284			−0.0184142	−	0.999830i	$-0.505862\pi$
$467$	−17.1989			−0.0368284			−0.0184142	+	0.999830i	$0.505862\pi$
$468$		0			0
$469$	36.1613	−	20.8777i	0.0771029	−	0.0445154i
$470$		0			0
$471$	352.070	+	724.261i	0.747494	+	1.53771i
$472$		0			0
$473$	−117.074	−	202.778i	−0.247514	−	0.428706i
$474$		0			0
$475$	−106.584	−	33.3545i	−0.224388	−	0.0702199i
$476$		0			0
$477$	309.841	−	124.239i	0.649562	−	0.260459i
$478$		0			0
$479$	24.1287	−	41.7922i	0.0503731	−	0.0872488i	−0.839739	−	0.542990i	$-0.817292\pi$
$479$	24.1287	−	41.7922i	0.0503731	−	0.0872488i	0.890113	+	0.455741i	$0.150626\pi$
$480$		0			0
$481$	−825.946			−1.71714
$482$		0			0
$483$	51.2597	+	105.449i	0.106128	+	0.218321i
$484$		0			0
$485$	−656.960	+	379.296i	−1.35456	+	0.782054i
$486$		0			0
$487$			43.8696i			0.0900813i	0.998985	+	0.0450407i	$0.0143417\pi$
$487$			43.8696i			0.0900813i	−0.998985	+	0.0450407i	$0.985658\pi$
$488$		0			0
$489$	907.696	+	64.6697i	1.85623	+	0.132249i
$490$		0			0
$491$	108.425	+	187.797i	0.220824	+	0.382479i	0.955058	−	0.296417i	$-0.0957919\pi$
$491$	108.425	+	187.797i	0.220824	+	0.382479i	−0.734234	+	0.678896i	$0.762459\pi$
$492$		0			0
$493$	405.693	−	234.227i	0.822906	−	0.475105i
$494$		0			0
$495$	221.830	−	282.399i	0.448142	−	0.570502i
$496$		0			0
$497$			31.9961i			0.0643785i
$498$		0			0
$499$	−116.985	−	202.625i	−0.234440	−	0.406061i	0.724670	−	0.689096i	$-0.241992\pi$
$499$	−116.985	−	202.625i	−0.234440	−	0.406061i	−0.959110	+	0.283035i	$0.908659\pi$
$500$		0			0
$501$	−9.15821	+	128.544i	−0.0182799	+	0.256574i
$502$		0			0
$503$	−166.750	−	288.820i	−0.331511	−	0.574195i	0.651297	−	0.758823i	$-0.274225\pi$
$503$	−166.750	−	288.820i	−0.331511	−	0.574195i	−0.982808	+	0.184628i	$0.940892\pi$
$504$		0			0
$505$	−571.425			−1.13153
$506$		0			0
$507$	818.833	+	58.3386i	1.61506	+	0.115066i
$508$		0			0
$509$		−	289.196i		−	0.568165i	−0.958800	−	0.284082i	$-0.908311\pi$
$509$		−	289.196i		−	0.568165i	0.958800	−	0.284082i	$-0.0916889\pi$
$510$		0			0
$511$	113.556			0.222223
$512$		0			0
$513$	−3.55786	−	512.988i	−0.00693540	−	0.999976i
$514$		0			0
$515$			432.272i			0.839362i
$516$		0			0
$517$	−199.015			−0.384942
$518$		0			0
$519$	56.7397	−	796.392i	0.109325	−	1.53447i
$520$		0			0
$521$		−	188.549i		−	0.361898i	−0.983493	−	0.180949i	$-0.942083\pi$
$521$		−	188.549i		−	0.361898i	0.983493	−	0.180949i	$-0.0579169\pi$
$522$		0			0
$523$	−143.038	+	82.5829i	−0.273495	+	0.157902i	−0.630475	−	0.776210i	$-0.717140\pi$
$523$	−143.038	+	82.5829i	−0.273495	+	0.157902i	0.356980	+	0.934112i	$0.383806\pi$
$524$		0			0
$525$	17.8261	+	1.27004i	0.0339544	+	0.00241912i
$526$		0			0
$527$	561.882	−	324.403i	1.06619	−	0.615565i
$528$		0			0
$529$	958.141			1.81123
$530$		0			0
$531$	38.1690	−	15.3048i	0.0718814	−	0.0288227i
$532$		0			0
$533$	−12.2234	−	21.1716i	−0.0229332	−	0.0397215i
$534$		0			0
$535$	527.263	−	304.415i	0.985538	−	0.569000i
$536$		0			0
$537$	−2.45801	+	34.5003i	−0.00457730	+	0.0642464i
$538$		0			0
$539$	−344.471			−0.639093
$540$		0			0
$541$	−139.846	−	242.221i	−0.258496	−	0.447728i	0.707343	−	0.706870i	$-0.249894\pi$
$541$	−139.846	−	242.221i	−0.258496	−	0.447728i	−0.965839	+	0.259142i	$0.916560\pi$
$542$		0			0
$543$	−279.075	+	135.661i	−0.513951	+	0.249836i
$544$		0			0
$545$		−	59.0687i		−	0.108383i
$546$		0			0
$547$	196.738	+	113.587i	0.359667	+	0.207654i	0.668935	−	0.743321i	$-0.266751\pi$
$547$	196.738	+	113.587i	0.359667	+	0.207654i	−0.309268	+	0.950975i	$0.600084\pi$
$548$		0			0
$549$	−173.964	+	221.463i	−0.316875	+	0.403394i
$550$		0			0
$551$	−225.818	+	721.600i	−0.409833	+	1.30962i
$552$		0			0
$553$	−0.926736	+	0.535051i	−0.00167583	+	0.000967543i
$554$		0			0
$555$	−588.588	+	286.118i	−1.06052	+	0.515527i
$556$		0			0
$557$	16.6374	+	28.8168i	0.0298696	+	0.0517357i	0.880574	−	0.473909i	$-0.157157\pi$
$557$	16.6374	+	28.8168i	0.0298696	+	0.0517357i	−0.850704	+	0.525645i	$0.823824\pi$
$558$		0			0
$559$		−	686.052i		−	1.22728i
$560$		0			0
$561$	252.938	+	18.0208i	0.450870	+	0.0321227i
$562$		0			0
$563$	533.191	+	307.838i	0.947054	+	0.546782i	0.892165	−	0.451710i	$-0.149186\pi$
$563$	533.191	+	307.838i	0.947054	+	0.546782i	0.0548896	+	0.998492i	$0.482519\pi$
$564$		0			0
$565$			1132.54i			2.00450i
$566$		0			0
$567$	19.4410	+	79.7552i	0.0342875	+	0.140662i
$568$		0			0
$569$	759.702	−	438.614i	1.33515	−	0.770851i	0.349069	−	0.937097i	$-0.386498\pi$
$569$	759.702	−	438.614i	1.33515	−	0.770851i	0.986084	+	0.166246i	$0.0531646\pi$
$570$		0			0
$571$	−445.952	+	772.412i	−0.781002	+	1.35274i	0.150356	+	0.988632i	$0.451958\pi$
$571$	−445.952	+	772.412i	−0.781002	+	1.35274i	−0.931358	+	0.364104i	$0.881375\pi$
$572$		0			0
$573$	174.982	+	359.965i	0.305379	+	0.628211i
$574$		0			0
$575$	113.337	−	196.306i	0.197108	−	0.341401i
$576$		0			0
$577$	940.378			1.62977			0.814886	−	0.579622i	$-0.196800\pi$
$577$	940.378			1.62977			0.814886	+	0.579622i	$0.196800\pi$
$578$		0			0
$579$	−461.486	+	224.333i	−0.797040	+	0.387448i
$580$		0			0
$581$	−77.0312	+	133.422i	−0.132584	+	0.229642i
$582$		0			0
$583$	−230.653	−	133.168i	−0.395631	−	0.228418i
$584$		0			0
$585$	976.596	−	391.591i	1.66940	−	0.669387i
$586$		0			0
$587$	−220.328			−0.375346			−0.187673	−	0.982232i	$-0.560095\pi$
$587$	−220.328			−0.375346			−0.187673	+	0.982232i	$0.560095\pi$
$588$		0			0
$589$	−312.757	+	999.413i	−0.530996	+	1.69680i
$590$		0			0
$591$	234.071	+	16.6766i	0.396059	+	0.0282176i
$592$		0			0
$593$	−511.277	−	885.558i	−0.862188	−	1.49335i	−0.869813	−	0.493382i	$-0.835760\pi$
$593$	−511.277	−	885.558i	−0.862188	−	1.49335i	0.00762469	−	0.999971i	$-0.497573\pi$
$594$		0			0
$595$	33.1465	+	57.4114i	0.0557084	+	0.0964897i
$596$		0			0
$597$	157.797	+	324.613i	0.264317	+	0.543741i
$598$		0			0
$599$		−	1135.87i		−	1.89627i	−0.317867	−	0.948135i	$-0.602967\pi$
$599$		−	1135.87i		−	1.89627i	0.317867	−	0.948135i	$-0.397033\pi$
$600$		0			0
$601$	−33.2557	+	19.2002i	−0.0553339	+	0.0319470i	−0.527412	−	0.849610i	$-0.676837\pi$
$601$	−33.2557	+	19.2002i	−0.0553339	+	0.0319470i	0.472078	+	0.881557i	$0.343504\pi$
$602$		0			0
$603$	52.5702	−	367.062i	0.0871810	−	0.608726i
$604$		0			0
$605$	385.863			0.637790
$606$		0			0
$607$	418.741	+	241.760i	0.689854	+	0.398287i	0.803557	−	0.595227i	$-0.202938\pi$
$607$	418.741	+	241.760i	0.689854	+	0.398287i	−0.113703	+	0.993515i	$0.536271\pi$
$608$		0			0
$609$	8.59845	−	120.687i	0.0141190	−	0.198172i
$610$		0			0
$611$	−504.990	−	291.556i	−0.826497	−	0.477178i
$612$		0			0
$613$	−233.580	+	404.573i	−0.381044	+	0.659988i	−0.991212	−	0.132284i	$-0.957769\pi$
$613$	−233.580	+	404.573i	−0.381044	+	0.659988i	0.610167	+	0.792272i	$0.291102\pi$
$614$		0			0
$615$	−16.0448	−	10.8530i	−0.0260891	−	0.0176472i
$616$		0			0
$617$	−412.288			−0.668214			−0.334107	−	0.942535i	$-0.608435\pi$
$617$	−412.288			−0.668214			−0.334107	+	0.942535i	$0.608435\pi$
$618$		0			0
$619$	−72.2457	−	125.133i	−0.116714	−	0.202154i	0.801750	−	0.597660i	$-0.203903\pi$
$619$	−72.2457	−	125.133i	−0.116714	−	0.202154i	−0.918463	+	0.395506i	$0.870569\pi$
$620$		0			0
$621$	1017.60	+	220.489i	1.63865	+	0.355055i
$622$		0			0
$623$	28.1365	+	16.2446i	0.0451629	+	0.0260748i
$624$		0			0
$625$	368.699	+	638.606i	0.589919	+	1.02177i
$626$		0			0
$627$	−320.102	+	255.056i	−0.510529	+	0.406789i
$628$		0			0
$629$	−400.216	−	231.065i	−0.636273	−	0.367352i
$630$		0			0
$631$	201.659	+	349.283i	0.319586	+	0.553539i	0.980402	−	0.197009i	$-0.0631228\pi$
$631$	201.659	+	349.283i	0.319586	+	0.553539i	−0.660816	+	0.750548i	$0.729790\pi$
$632$		0			0
$633$	114.543	−	55.6802i	0.180952	−	0.0879624i
$634$		0			0
$635$	1141.19	+	658.866i	1.79715	+	1.03758i
$636$		0			0
$637$	−874.078	−	504.649i	−1.37218	−	0.792228i
$638$		0			0
$639$	223.445	+	175.521i	0.349680	+	0.274681i
$640$		0			0
$641$			522.043i			0.814420i	0.913335	+	0.407210i	$0.133498\pi$
$641$			522.043i			0.814420i	−0.913335	+	0.407210i	$0.866502\pi$
$642$		0			0
$643$	336.732	+	583.236i	0.523688	+	0.907055i	0.999620	+	0.0275725i	$0.00877770\pi$
$643$	336.732	+	583.236i	0.523688	+	0.907055i	−0.475931	+	0.879482i	$0.657889\pi$
$644$		0			0
$645$	−237.657	−	488.896i	−0.368460	−	0.757979i
$646$		0			0
$647$	−26.2000			−0.0404946			−0.0202473	−	0.999795i	$-0.506445\pi$
$647$	−26.2000			−0.0404946			−0.0202473	+	0.999795i	$0.506445\pi$
$648$		0			0
$649$	−28.4139	−	16.4048i	−0.0437811	−	0.0252770i
$650$		0			0
$651$	11.9088	−	167.151i	0.0182931	−	0.256760i
$652$		0			0
$653$	368.122	−	637.605i	0.563739	−	0.976424i	−0.433427	−	0.901189i	$-0.642696\pi$
$653$	368.122	−	637.605i	0.563739	−	0.976424i	0.997166	−	0.0752357i	$-0.0239709\pi$
$654$		0			0
$655$	65.9893	−	114.297i	0.100747	−	0.174499i
$656$		0			0
$657$	622.934	−	793.019i	0.948149	−	1.20703i
$658$		0			0
$659$	−265.997	−	153.573i	−0.403637	−	0.233040i	0.284415	−	0.958701i	$-0.408201\pi$
$659$	−265.997	−	153.573i	−0.403637	−	0.233040i	−0.688052	+	0.725661i	$0.741534\pi$
$660$		0			0
$661$			527.085i			0.797406i	0.917080	+	0.398703i	$0.130540\pi$
$661$			527.085i			0.797406i	−0.917080	+	0.398703i	$0.869460\pi$
$662$		0			0
$663$	615.417	+	416.280i	0.928231	+	0.627874i
$664$		0			0
$665$	−102.117	−	31.9565i	−0.153559	−	0.0480549i
$666$		0			0
$667$	−1329.04	−	767.321i	−1.99256	−	1.15041i
$668$		0			0
$669$	−23.3749	+	328.087i	−0.0349400	+	0.490414i
$670$		0			0
$671$	224.687			0.334853
$672$		0			0
$673$	−317.808	+	183.486i	−0.472226	+	0.272640i	−0.717171	−	0.696897i	$-0.754563\pi$
$673$	−317.808	+	183.486i	−0.472226	+	0.272640i	0.244945	+	0.969537i	$0.421230\pi$
$674$		0			0
$675$	106.658	−	117.522i	0.158012	−	0.174106i
$676$		0			0
$677$	−713.738	+	412.077i	−1.05427	+	0.608681i	−0.923841	−	0.382777i	$-0.874968\pi$
$677$	−713.738	+	412.077i	−1.05427	+	0.608681i	−0.130425	+	0.991458i	$0.541634\pi$
$678$		0			0
$679$	−119.818	+	69.1770i	−0.176463	+	0.101881i
$680$		0			0
$681$	−864.404	+	420.195i	−1.26932	+	0.617026i
$682$		0			0
$683$		−	21.9799i		−	0.0321813i	−0.999871	−	0.0160907i	$-0.994878\pi$
$683$		−	21.9799i		−	0.0321813i	0.999871	−	0.0160907i	$-0.00512204\pi$
$684$		0			0
$685$	−948.382			−1.38450
$686$		0			0
$687$	−502.473	+	742.841i	−0.731401	+	1.08128i
$688$		0			0
$689$	−390.180	−	675.812i	−0.566299	−	0.980859i
$690$		0			0
$691$	−435.220	−	753.824i	−0.629841	−	1.09092i	−0.987583	−	0.157097i	$-0.949787\pi$
$691$	−435.220	−	753.824i	−0.629841	−	1.09092i	0.357742	−	0.933821i	$-0.383547\pi$
$692$		0			0
$693$	40.4580	−	51.5046i	0.0583809	−	0.0743212i
$694$		0			0
$695$	−509.772	−	882.950i	−0.733484	−	1.27043i
$696$		0			0
$697$		−	13.6784i		−	0.0196246i
$698$		0			0
$699$	576.118	−	851.716i	0.824203	−	1.21848i
$700$		0			0
$701$	−319.482	+	553.359i	−0.455752	+	0.789385i	−0.998731	−	0.0503611i	$-0.983963\pi$
$701$	−319.482	+	553.359i	−0.455752	+	0.789385i	0.542980	+	0.839746i	$0.317296\pi$
$702$		0			0
$703$	727.872	−	163.005i	1.03538	−	0.231871i
$704$		0			0
$705$	−460.866	−	32.8348i	−0.653711	−	0.0465742i
$706$		0			0
$707$	−104.218			−0.147409
$708$		0			0
$709$	−76.8217	+	133.059i	−0.108352	+	0.187671i	−0.915103	−	0.403221i	$-0.867891\pi$
$709$	−76.8217	+	133.059i	−0.108352	+	0.187671i	0.806751	+	0.590892i	$0.201224\pi$
$710$		0			0
$711$	−1.34726	+	9.40701i	−0.00189488	+	0.0132307i
$712$		0			0
$713$	−1840.71	−	1062.74i	−2.58164	−	1.49051i
$714$		0			0
$715$	−727.002	−	419.735i	−1.01679	−	0.587041i
$716$		0			0
$717$	−523.238	+	773.540i	−0.729760	+	1.07886i
$718$		0			0
$719$	−233.565	+	404.547i	−0.324847	+	0.562652i	−0.981481	−	0.191557i	$-0.938646\pi$
$719$	−233.565	+	404.547i	−0.324847	+	0.562652i	0.656634	+	0.754209i	$0.271980\pi$
$720$		0			0
$721$			78.8388i			0.109346i
$722$		0			0
$723$	175.294	+	118.572i	0.242453	+	0.164000i
$724$		0			0
$725$	−202.576	+	116.957i	−0.279415	+	0.161320i
$726$		0			0
$727$	72.8160			0.100160			0.0500798	−	0.998745i	$-0.484052\pi$
$727$	72.8160			0.100160			0.0500798	+	0.998745i	$0.484052\pi$
$728$		0			0
$729$	663.619	+	301.747i	0.910314	+	0.413919i
$730$		0			0
$731$	191.928	−	332.430i	0.262556	−	0.454760i
$732$		0			0
$733$	290.253	−	502.733i	0.395980	−	0.685857i	−0.597246	−	0.802058i	$-0.703738\pi$
$733$	290.253	−	502.733i	0.395980	−	0.685857i	0.993226	+	0.116201i	$0.0370716\pi$
$734$		0			0
$735$	−797.704	−	56.8332i	−1.08531	−	0.0773241i
$736$		0			0
$737$	−256.208	+	147.922i	−0.347637	+	0.200708i
$738$		0			0
$739$	−264.128	+	457.483i	−0.357413	+	0.619058i	−0.987528	−	0.157444i	$-0.949674\pi$
$739$	−264.128	+	457.483i	−0.357413	+	0.619058i	0.630115	+	0.776502i	$0.283008\pi$
$740$		0			0
$741$	−1185.90	+	178.245i	−1.60040	+	0.240546i
$742$		0			0
$743$	1175.93	−	678.922i	1.58267	−	0.913757i	0.588207	−	0.808711i	$-0.299834\pi$
$743$	1175.93	−	678.922i	1.58267	−	0.913757i	0.994467	−	0.105046i	$-0.0334991\pi$
$744$		0			0
$745$	−229.655	+	397.773i	−0.308261	+	0.533924i
$746$		0			0
$747$	509.184	+	1269.86i	0.681638	+	1.69995i
$748$		0			0
$749$	96.1635	−	55.5200i	0.128389	−	0.0741255i
$750$		0			0
$751$			406.447i			0.541208i	0.962691	+	0.270604i	$0.0872235\pi$
$751$			406.447i			0.541208i	−0.962691	+	0.270604i	$0.912777\pi$
$752$		0			0
$753$	535.412	+	1101.42i	0.711039	+	1.46271i
$754$		0			0
$755$	356.149	+	205.623i	0.471721	+	0.272348i
$756$		0			0
$757$	−483.094	+	836.744i	−0.638169	+	1.10534i	0.347665	+	0.937619i	$0.386975\pi$
$757$	−483.094	+	836.744i	−0.638169	+	1.10534i	−0.985834	+	0.167723i	$0.946359\pi$
$758$		0			0
$759$	−363.183	−	747.123i	−0.478502	−	0.984352i
$760$		0			0
$761$	−283.140	+	490.413i	−0.372064	+	0.644433i	−0.989883	−	0.141887i	$-0.954683\pi$
$761$	−283.140	+	490.413i	−0.372064	+	0.644433i	0.617819	+	0.786320i	$0.288016\pi$
$762$		0			0
$763$		−	10.7731i		−	0.0141194i
$764$		0			0
$765$	582.765	+	83.4629i	0.761784	+	0.109102i
$766$		0			0
$767$	−48.0659	−	83.2526i	−0.0626674	−	0.108543i
$768$		0			0
$769$	667.484			0.867989			0.433995	−	0.900916i	$-0.357104\pi$
$769$	667.484			0.867989			0.433995	+	0.900916i	$0.357104\pi$
$770$		0			0
$771$	71.3210	−	1001.05i	0.0925046	−	1.29838i
$772$		0			0
$773$	−1071.10	+	618.401i	−1.38564	+	0.800002i	−0.992821	−	0.119613i	$-0.961835\pi$
$773$	−1071.10	+	618.401i	−1.38564	+	0.800002i	−0.392823	+	0.919614i	$0.628501\pi$
$774$		0			0
$775$	−280.567	+	161.985i	−0.362022	+	0.209013i
$776$		0			0
$777$	−107.348	+	52.1829i	−0.138157	+	0.0671594i
$778$		0			0
$779$	14.9503	+	16.2453i	0.0191917	+	0.0208540i
$780$		0			0
$781$		−	226.698i		−	0.290266i
$782$		0			0
$783$	−795.650	−	722.100i	−1.01616	−	0.922222i
$784$		0			0
$785$	745.814	−	1291.79i	0.950081	−	1.64559i
$786$		0			0
$787$	261.714	+	151.101i	0.332547	+	0.191996i	0.656971	−	0.753916i	$-0.271837\pi$
$787$	261.714	+	151.101i	0.332547	+	0.191996i	−0.324424	+	0.945912i	$0.605171\pi$
$788$		0			0
$789$	266.582	+	18.9929i	0.337873	+	0.0240721i
$790$		0			0
$791$			206.556i			0.261132i
$792$		0			0
$793$	570.131	+	329.165i	0.718954	+	0.415088i
$794$		0			0
$795$	−512.161	−	346.436i	−0.644227	−	0.435768i
$796$		0			0
$797$	−1026.26	−	592.512i	−1.28766	−	0.743428i	−0.309420	−	0.950925i	$-0.600135\pi$
$797$	−1026.26	−	592.512i	−1.28766	−	0.743428i	−0.978236	+	0.207497i	$0.933468\pi$
$798$		0			0
$799$	−163.130	−	282.550i	−0.204168	−	0.353629i
$800$		0			0
$801$	267.793	−	107.378i	0.334323	−	0.134055i
$802$		0			0
$803$	−804.561			−1.00194
$804$		0			0
$805$	108.587	−	188.078i	0.134891	−	0.233638i
$806$		0			0
$807$	728.316	+	492.647i	0.902498	+	0.610467i
$808$		0			0
$809$	−288.972			−0.357196			−0.178598	−	0.983922i	$-0.557156\pi$
$809$	−288.972			−0.357196			−0.178598	+	0.983922i	$0.557156\pi$
$810$		0			0
$811$	1210.21	−	698.716i	1.49225	−	0.861548i	0.492285	−	0.870434i	$-0.336162\pi$
$811$	1210.21	−	698.716i	1.49225	−	0.861548i	0.999961	+	0.00888554i	$0.00282839\pi$
$812$		0			0
$813$	−343.937	+	508.467i	−0.423047	+	0.625420i
$814$		0			0
$815$	−842.777	−	1459.73i	−1.03408	−	1.79108i
$816$		0			0
$817$	135.397	+	604.590i	0.165724	+	0.740012i
$818$		0			0
$819$	178.114	−	71.4194i	0.217478	−	0.0872032i
$820$		0			0
$821$	−455.668	+	789.240i	−0.555016	+	0.961316i	0.442886	+	0.896578i	$0.353955\pi$
$821$	−455.668	+	789.240i	−0.555016	+	0.961316i	−0.997902	+	0.0647382i	$0.979379\pi$
$822$		0			0
$823$	−352.717			−0.428575			−0.214287	−	0.976771i	$-0.568743\pi$
$823$	−352.717			−0.428575			−0.214287	+	0.976771i	$0.568743\pi$
$824$		0			0
$825$	−126.301	−	8.99840i	−0.153092	−	0.0109072i
$826$		0			0
$827$	−995.138	+	574.543i	−1.20331	+	0.694732i	−0.961290	−	0.275539i	$-0.911144\pi$
$827$	−995.138	+	574.543i	−1.20331	+	0.694732i	−0.242021	+	0.970271i	$0.577810\pi$
$828$		0			0
$829$		−	21.9296i		−	0.0264531i	−0.999913	−	0.0132266i	$-0.995790\pi$
$829$		−	21.9296i		−	0.0264531i	0.999913	−	0.0132266i	$-0.00421027\pi$
$830$		0			0
$831$	160.136	+	329.423i	0.192702	+	0.396418i
$832$		0			0
$833$	−282.359	−	489.060i	−0.338966	−	0.587107i
$834$		0			0
$835$	206.720	−	119.350i	0.247569	−	0.142934i
$836$		0			0
$837$	−1101.97	−	1000.11i	−1.31657	−	1.19487i
$838$		0			0
$839$			281.271i			0.335246i	0.985851	+	0.167623i	$0.0536091\pi$
$839$			281.271i			0.335246i	−0.985851	+	0.167623i	$0.946391\pi$
$840$		0			0
$841$	371.329	+	643.161i	0.441533	+	0.764758i
$842$		0			0
$843$	−56.9298	−	38.5085i	−0.0675324	−	0.0456803i
$844$		0			0
$845$	−760.270	−	1316.83i	−0.899728	−	1.55837i
$846$		0			0
$847$	70.3747			0.0830870
$848$		0			0
$849$	27.3408	+	56.2443i	0.0322036	+	0.0662477i
$850$		0			0
$851$			1513.92i			1.77899i
$852$		0			0
$853$	−555.466			−0.651191			−0.325596	−	0.945509i	$-0.605565\pi$
$853$	−555.466			−0.651191			−0.325596	+	0.945509i	$0.605565\pi$
$854$		0			0
$855$	−783.352	+	537.831i	−0.916201	+	0.629042i
$856$		0			0
$857$		−	942.067i		−	1.09926i	−0.835408	−	0.549631i	$-0.814768\pi$
$857$		−	942.067i		−	1.09926i	0.835408	−	0.549631i	$-0.185232\pi$
$858$		0			0
$859$	1681.66			1.95769			0.978845	−	0.204603i	$-0.0655904\pi$
$859$	1681.66			1.95769			0.978845	+	0.204603i	$0.0655904\pi$
$860$		0			0
$861$	−2.92629	−	1.97940i	−0.00339871	−	0.00229895i
$862$		0			0
$863$		−	1616.58i		−	1.87321i	−0.350381	−	0.936607i	$-0.613948\pi$
$863$		−	1616.58i		−	1.87321i	0.350381	−	0.936607i	$-0.386052\pi$
$864$		0			0
$865$	−1280.74	+	739.434i	−1.48062	+	0.854837i
$866$		0			0
$867$	−197.299	−	405.874i	−0.227565	−	0.468136i
$868$		0			0
$869$	6.56607	−	3.79092i	0.00755589	−	0.00436240i
$870$		0			0
$871$	−866.820			−0.995201
$872$		0			0
$873$	−174.188	+	1216.24i	−0.199528	+	1.39317i
$874$		0			0
$875$	53.8438	+	93.2603i	0.0615358	+	0.106583i
$876$		0			0
$877$	−1488.33	+	859.288i	−1.69707	+	0.979804i	−0.748554	+	0.663074i	$0.769252\pi$
$877$	−1488.33	+	859.288i	−1.69707	+	0.979804i	−0.948516	+	0.316730i	$0.897415\pi$
$878$		0			0
$879$	1031.42	+	697.675i	1.17340	+	0.793714i
$880$		0			0
$881$	278.729			0.316377			0.158189	−	0.987409i	$-0.449435\pi$
$881$	278.729			0.316377			0.158189	+	0.987409i	$0.449435\pi$
$882$		0			0
$883$	370.735	+	642.132i	0.419859	+	0.727217i	0.995925	−	0.0901863i	$-0.0287462\pi$
$883$	370.735	+	642.132i	0.419859	+	0.727217i	−0.576066	+	0.817403i	$0.695413\pi$
$884$		0			0
$885$	−63.0926	−	42.6771i	−0.0712911	−	0.0482227i
$886$		0			0
$887$			1028.63i			1.15967i	0.814734	+	0.579835i	$0.196883\pi$
$887$			1028.63i			1.15967i	−0.814734	+	0.579835i	$0.803117\pi$
$888$		0			0
$889$	208.133	+	120.166i	0.234120	+	0.135170i
$890$		0			0
$891$	−137.743	−	565.078i	−0.154593	−	0.634206i
$892$		0			0
$893$	502.568	+	157.274i	0.562786	+	0.176118i
$894$		0			0
$895$	55.4825	−	32.0329i	0.0619917	−	0.0357909i
$896$		0			0
$897$	172.974	−	2427.85i	0.192836	−	2.70663i
$898$		0			0
$899$	1096.68	+	1899.51i	1.21989	+	2.11291i
$900$		0			0
$901$		−	436.624i		−	0.484599i
$902$		0			0
$903$	−43.3444	−	89.1661i	−0.0480005	−	0.0987443i
$904$		0			0
$905$	497.757	+	287.380i	0.550007	+	0.317547i
$906$		0			0
$907$			1313.46i			1.44813i	0.689730	+	0.724067i	$0.257729\pi$
$907$			1313.46i			1.44813i	−0.689730	+	0.724067i	$0.742271\pi$
$908$		0			0
$909$	−571.708	+	727.807i	−0.628942	+	0.800668i
$910$		0			0
$911$	−848.119	+	489.662i	−0.930976	+	0.537499i	−0.887120	−	0.461539i	$-0.847297\pi$
$911$	−848.119	+	489.662i	−0.930976	+	0.537499i	−0.0438556	+	0.999038i	$0.513964\pi$
$912$		0			0
$913$	545.778	−	945.315i	0.597785	−	1.03539i
$914$		0			0
$915$	520.315	+	37.0703i	0.568650	+	0.0405140i
$916$		0			0
$917$	12.0353	−	20.8457i	0.0131246	−	0.0227325i
$918$		0			0
$919$	−1574.02			−1.71275			−0.856376	−	0.516353i	$-0.827289\pi$
$919$	−1574.02			−1.71275			−0.856376	+	0.516353i	$0.827289\pi$
$920$		0			0
$921$	−57.4415	−	38.8546i	−0.0623686	−	0.0421874i
$922$		0			0
$923$	332.111	−	575.233i	0.359817	−	0.623221i
$924$		0			0
$925$	199.841	+	115.378i	0.216045	+	0.124733i
$926$		0			0
$927$	550.572	+	432.486i	0.593929	+	0.466544i
$928$		0			0
$929$	203.007			0.218522			0.109261	−	0.994013i	$-0.465152\pi$
$929$	203.007			0.218522			0.109261	+	0.994013i	$0.465152\pi$
$930$		0			0
$931$	869.885	+	272.222i	0.934356	+	0.292398i
$932$		0			0
$933$	905.595	−	1338.81i	0.970627	−	1.43495i
$934$		0			0
$935$	−234.848	−	406.769i	−0.251174	−	0.435047i
$936$		0			0
$937$	−793.797	−	1374.90i	−0.847169	−	1.46734i	−0.883724	−	0.468008i	$-0.844972\pi$
$937$	−793.797	−	1374.90i	−0.847169	−	1.46734i	0.0365558	−	0.999332i	$-0.488361\pi$
$938$		0			0
$939$	−817.076	+	1207.94i	−0.870155	+	1.28641i
$940$		0			0
$941$			89.6514i			0.0952725i	0.998865	+	0.0476362i	$0.0151688\pi$
$941$			89.6514i			0.0952725i	−0.998865	+	0.0476362i	$0.984831\pi$
$942$		0			0
$943$	−38.8066	+	22.4050i	−0.0411523	+	0.0237593i
$944$		0			0
$945$	102.188	−	112.596i	0.108135	−	0.119149i
$946$		0			0
$947$	193.975			0.204831			0.102415	−	0.994742i	$-0.467343\pi$
$947$	193.975			0.204831			0.102415	+	0.994742i	$0.467343\pi$
$948$		0			0
$949$	−2041.53	−	1178.68i	−2.15125	−	1.24202i
$950$		0			0
$951$	580.784	+	392.854i	0.610708	+	0.413095i
$952$		0			0
$953$	−9.93498	−	5.73596i	−0.0104249	−	0.00601885i	0.494778	−	0.869019i	$-0.335249\pi$
$953$	−9.93498	−	5.73596i	−0.0104249	−	0.00601885i	−0.505203	+	0.863000i	$0.668583\pi$
$954$		0			0
$955$	370.677	−	642.031i	0.388143	−	0.672284i
$956$		0			0
$957$	−60.9214	+	855.086i	−0.0636587	+	0.893506i
$958$		0			0
$959$	−172.968			−0.180363
$960$		0			0
$961$	1038.40	+	1798.56i	1.08054	+	1.87155i
$962$		0			0
$963$	139.800	−	976.125i	0.145171	−	1.01363i
$964$		0			0
$965$	823.104	+	475.219i	0.852957	+	0.492455i
$966$		0			0
$967$	225.913	+	391.293i	0.233622	+	0.404646i	0.958871	−	0.283841i	$-0.0916087\pi$
$967$	225.913	+	391.293i	0.233622	+	0.404646i	−0.725249	+	0.688487i	$0.758275\pi$
$968$		0			0
$969$	−624.498	−	245.395i	−0.644477	−	0.253245i
$970$		0			0
$971$	1507.85	+	870.556i	1.55288	+	0.896556i	0.997905	+	0.0646895i	$0.0206057\pi$
$971$	1507.85	+	870.556i	1.55288	+	0.896556i	0.554975	+	0.831867i	$0.312728\pi$
$972$		0			0
$973$	−92.9734	−	161.035i	−0.0955534	−	0.165503i
$974$		0			0
$975$	−307.298	−	207.863i	−0.315178	−	0.213193i
$976$		0			0
$977$	1282.73	+	740.584i	1.31293	+	0.758018i	0.982580	−	0.185842i	$-0.0595011\pi$
$977$	1282.73	+	740.584i	1.31293	+	0.758018i	0.330346	+	0.943860i	$0.392834\pi$
$978$		0			0
$979$	−199.351	−	115.096i	−0.203628	−	0.117564i
$980$		0			0
$981$	−75.2341	−	59.0981i	−0.0766913	−	0.0602427i
$982$		0			0
$983$			1526.09i			1.55248i	0.630439	+	0.776239i	$0.282875\pi$
$983$			1526.09i			1.55248i	−0.630439	+	0.776239i	$0.717125\pi$
$984$		0			0
$985$	−217.330	−	376.427i	−0.220640	−	0.382159i
$986$		0			0
$987$	−84.0539	−	5.98850i	−0.0851610	−	0.00606738i
$988$		0			0
$989$	−1257.50			−1.27149
$990$		0			0
$991$	−86.2525	−	49.7979i	−0.0870358	−	0.0502502i	0.455850	−	0.890056i	$-0.349335\pi$
$991$	−86.2525	−	49.7979i	−0.0870358	−	0.0502502i	−0.542886	+	0.839806i	$0.682669\pi$
$992$		0			0
$993$	1322.03	−	642.649i	1.33135	−	0.647180i
$994$		0			0
$995$	334.273	−	578.978i	0.335953	−	0.581887i
$996$		0			0
$997$	111.900	−	193.816i	0.112236	−	0.194399i	−0.804435	−	0.594040i	$-0.797532\pi$
$997$	111.900	−	193.816i	0.112236	−	0.194399i	0.916672	+	0.399641i	$0.130865\pi$
$998$		0			0
$999$	−224.460	+	1035.93i	−0.224685	+	1.03696i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.s.a.445.2	✓	80
3.2	odd	2		2052.3.s.a.901.9		80
9.2	odd	6		2052.3.bl.a.1585.32		80
9.7	even	3		684.3.bl.a.673.13	yes	80
19.12	odd	6		684.3.bl.a.373.13	yes	80
57.50	even	6		2052.3.bl.a.145.32		80
171.88	odd	6	inner	684.3.s.a.601.2	yes	80
171.164	even	6		2052.3.s.a.829.9		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.s.a.445.2	✓	80	1.1	even	1	trivial
684.3.s.a.601.2	yes	80	171.88	odd	6	inner
684.3.bl.a.373.13	yes	80	19.12	odd	6
684.3.bl.a.673.13	yes	80	9.7	even	3
2052.3.s.a.829.9		80	171.164	even	6
2052.3.s.a.901.9		80	3.2	odd	2
2052.3.bl.a.145.32		80	57.50	even	6
2052.3.bl.a.1585.32		80	9.2	odd	6

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:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	684.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.99241 - 0.213197i) q^{3} +(2.77840 + 4.81232i) q^{5} +(0.506731 + 0.877684i) q^{7} +(8.90909 + 1.27595i) q^{9} +O(q^{10})\)	\(q+(-2.99241 - 0.213197i) q^{3} +(2.77840 + 4.81232i) q^{5} +(0.506731 + 0.877684i) q^{7} +(8.90909 + 1.27595i) q^{9} +(-3.59027 - 6.21853i) q^{11} -21.0389i q^{13} +(-7.28814 - 14.9928i) q^{15} +(5.88580 - 10.1945i) q^{17} +(4.15216 + 18.5408i) q^{19} +(-1.32923 - 2.73443i) q^{21} -38.5635 q^{23} +(-2.93898 + 5.09046i) q^{25} +(-26.3877 - 5.71757i) q^{27} +(34.4637 + 19.8976i) q^{29} +(47.7320 + 27.5581i) q^{31} +(9.41780 + 19.3739i) q^{33} +(-2.81580 + 4.87711i) q^{35} -39.2580i q^{37} +(-4.48544 + 62.9572i) q^{39} +(1.00630 - 0.580990i) q^{41} +32.6087 q^{43} +(18.6127 + 46.4185i) q^{45} +(13.8579 - 24.0026i) q^{47} +(23.9864 - 41.5457i) q^{49} +(-19.7862 + 29.2514i) q^{51} +(32.1220 - 18.5456i) q^{53} +(19.9504 - 34.5551i) q^{55} +(-8.47215 - 56.3669i) q^{57} +(3.95707 - 2.28462i) q^{59} +(-15.6455 + 27.0989i) q^{61} +(3.39463 + 8.46593i) q^{63} +(101.246 - 58.4545i) q^{65} -41.2008i q^{67} +(115.398 + 8.22163i) q^{69} +(27.3414 + 15.7856i) q^{71} +(56.0237 - 97.0360i) q^{73} +(9.87992 - 14.6062i) q^{75} +(3.63860 - 6.30224i) q^{77} +1.05589i q^{79} +(77.7439 + 22.7351i) q^{81} +(76.0080 + 131.650i) q^{83} +65.4124 q^{85} +(-98.8875 - 66.8895i) q^{87} +(27.7627 - 16.0288i) q^{89} +(18.4655 - 10.6611i) q^{91} +(-136.959 - 92.6416i) q^{93} +(-77.6878 + 71.4951i) q^{95} +136.516i q^{97} +(-24.0515 - 59.9825i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - q^{7} + 4 q^{9}+O(q^{10}) \) 80 * q - q^7 + 4 * q^9	\( 80 q - q^{7} + 4 q^{9} - 6 q^{11} + 33 q^{15} - 21 q^{17} - 20 q^{19} - 48 q^{23} - 200 q^{25} - 63 q^{27} - 27 q^{29} - 24 q^{31} + 27 q^{33} - 54 q^{35} - 81 q^{39} - 18 q^{41} - 152 q^{43} + 188 q^{45} - 12 q^{47} - 267 q^{49} - 126 q^{51} - 36 q^{53} + 126 q^{57} - 135 q^{59} - 7 q^{61} - 190 q^{63} - 288 q^{65} + 48 q^{69} - 81 q^{71} + 55 q^{73} + 165 q^{75} + 30 q^{77} + 28 q^{81} - 93 q^{83} + 306 q^{87} + 216 q^{89} + 96 q^{91} + 24 q^{93} + 288 q^{95} - 241 q^{99}+O(q^{100}) \) 80 * q - q^7 + 4 * q^9 - 6 * q^11 + 33 * q^15 - 21 * q^17 - 20 * q^19 - 48 * q^23 - 200 * q^25 - 63 * q^27 - 27 * q^29 - 24 * q^31 + 27 * q^33 - 54 * q^35 - 81 * q^39 - 18 * q^41 - 152 * q^43 + 188 * q^45 - 12 * q^47 - 267 * q^49 - 126 * q^51 - 36 * q^53 + 126 * q^57 - 135 * q^59 - 7 * q^61 - 190 * q^63 - 288 * q^65 + 48 * q^69 - 81 * q^71 + 55 * q^73 + 165 * q^75 + 30 * q^77 + 28 * q^81 - 93 * q^83 + 306 * q^87 + 216 * q^89 + 96 * q^91 + 24 * q^93 + 288 * q^95 - 241 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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