LMFDB - Embedded newform 585.2.j.i.406.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(406,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("585.406");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.j (of order $3$, 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:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 10x^{8} - 8x^{7} + 50x^{6} - 42x^{5} + 124x^{4} - 12x^{3} + 96x^{2} - 36x + 36 $ x^10 - 2x^9 + 10x^8 - 8x^7 + 50x^6 - 42x^5 + 124x^4 - 12x^3 + 96x^2 - 36*x + 36
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			406.1
Root			$-1.06141 + 1.83842i$ of defining polynomial
Character	$\chi$	$=$	585.406
Dual form			585.2.j.i.451.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.06141 - 1.83842i) q^{2} +(-1.25320 + 2.17061i) q^{4} -1.00000 q^{5} +(-0.733534 + 1.27052i) q^{7} +1.07500 q^{8} +O(q^{10})$	\(q+(-1.06141 - 1.83842i) q^{2} +(-1.25320 + 2.17061i) q^{4} -1.00000 q^{5} +(-0.733534 + 1.27052i) q^{7} +1.07500 q^{8} +(1.06141 + 1.83842i) q^{10} +(0.172120 + 0.298120i) q^{11} +(1.76679 + 3.14300i) q^{13} +3.11433 q^{14} +(1.36538 + 2.36491i) q^{16} +(2.56781 - 4.44758i) q^{17} +(-0.253200 + 0.438555i) q^{19} +(1.25320 - 2.17061i) q^{20} +(0.365380 - 0.632857i) q^{22} +(0.537500 + 0.930977i) q^{23} +1.00000 q^{25} +(3.90288 - 6.58413i) q^{26} +(-1.83853 - 3.18442i) q^{28} +(4.02423 + 6.97018i) q^{29} +9.17129 q^{31} +(3.97347 - 6.88225i) q^{32} -10.9021 q^{34} +(0.733534 - 1.27052i) q^{35} +(-1.36538 - 2.36491i) q^{37} +1.07500 q^{38} -1.07500 q^{40} +(3.06357 + 5.30625i) q^{41} +(2.93744 - 5.08780i) q^{43} -0.862801 q^{44} +(1.14102 - 1.97630i) q^{46} -4.26369 q^{47} +(2.42386 + 4.19824i) q^{49} +(-1.06141 - 1.83842i) q^{50} +(-9.03636 - 0.103818i) q^{52} +4.07866 q^{53} +(-0.172120 - 0.298120i) q^{55} +(-0.788548 + 1.36581i) q^{56} +(8.54276 - 14.7965i) q^{58} +(-2.53063 + 4.38318i) q^{59} +(2.58565 - 4.47847i) q^{61} +(-9.73454 - 16.8607i) q^{62} -11.4085 q^{64} +(-1.76679 - 3.14300i) q^{65} +(-0.598595 - 1.03680i) q^{67} +(6.43597 + 11.1474i) q^{68} -3.11433 q^{70} +(0.222886 - 0.386049i) q^{71} -7.52634 q^{73} +(-2.89847 + 5.02029i) q^{74} +(-0.634620 - 1.09919i) q^{76} -0.505022 q^{77} +0.834915 q^{79} +(-1.36538 - 2.36491i) q^{80} +(6.50342 - 11.2643i) q^{82} -15.2506 q^{83} +(-2.56781 + 4.44758i) q^{85} -12.4714 q^{86} +(0.185028 + 0.320479i) q^{88} +(5.97494 + 10.3489i) q^{89} +(-5.28924 - 0.0607674i) q^{91} -2.69438 q^{92} +(4.52554 + 7.83847i) q^{94} +(0.253200 - 0.438555i) q^{95} +(0.700282 - 1.21292i) q^{97} +(5.14543 - 8.91215i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 2 q^{2} - 6 q^{4} - 10 q^{5} - q^{7} - 12 q^{8}+O(q^{10}) $ 10 * q + 2 * q^2 - 6 * q^4 - 10 * q^5 - q^7 - 12 * q^8	$ 10 q + 2 q^{2} - 6 q^{4} - 10 q^{5} - q^{7} - 12 q^{8} - 2 q^{10} + 8 q^{11} + q^{13} + 8 q^{14} - 4 q^{16} + 4 q^{19} + 6 q^{20} - 14 q^{22} - 6 q^{23} + 10 q^{25} + 10 q^{26} + 2 q^{28} + 16 q^{29} + 18 q^{31} + 14 q^{32} + q^{35} + 4 q^{37} - 12 q^{38} + 12 q^{40} + 6 q^{41} - 15 q^{43} - 28 q^{44} + 16 q^{46} - 20 q^{47} - 10 q^{49} + 2 q^{50} - 22 q^{52} + 40 q^{53} - 8 q^{55} - 2 q^{56} + 4 q^{58} + 12 q^{59} - 11 q^{61} - 22 q^{62} + 8 q^{64} - q^{65} - 5 q^{67} + 50 q^{68} - 8 q^{70} + 10 q^{71} + 2 q^{73} - 26 q^{74} - 24 q^{76} - 84 q^{77} - 34 q^{79} + 4 q^{80} - 16 q^{82} - 32 q^{83} - 88 q^{86} - 20 q^{88} + 4 q^{89} - q^{91} + 68 q^{92} + 16 q^{94} - 4 q^{95} + 11 q^{97} + 30 q^{98}+O(q^{100}) $ 10 * q + 2 * q^2 - 6 * q^4 - 10 * q^5 - q^7 - 12 * q^8 - 2 * q^10 + 8 * q^11 + q^13 + 8 * q^14 - 4 * q^16 + 4 * q^19 + 6 * q^20 - 14 * q^22 - 6 * q^23 + 10 * q^25 + 10 * q^26 + 2 * q^28 + 16 * q^29 + 18 * q^31 + 14 * q^32 + q^35 + 4 * q^37 - 12 * q^38 + 12 * q^40 + 6 * q^41 - 15 * q^43 - 28 * q^44 + 16 * q^46 - 20 * q^47 - 10 * q^49 + 2 * q^50 - 22 * q^52 + 40 * q^53 - 8 * q^55 - 2 * q^56 + 4 * q^58 + 12 * q^59 - 11 * q^61 - 22 * q^62 + 8 * q^64 - q^65 - 5 * q^67 + 50 * q^68 - 8 * q^70 + 10 * q^71 + 2 * q^73 - 26 * q^74 - 24 * q^76 - 84 * q^77 - 34 * q^79 + 4 * q^80 - 16 * q^82 - 32 * q^83 - 88 * q^86 - 20 * q^88 + 4 * q^89 - q^91 + 68 * q^92 + 16 * q^94 - 4 * q^95 + 11 * q^97 + 30 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.06141	−	1.83842i	−0.750533	−	1.29996i	−0.947565	−	0.319564i	$-0.896463\pi$
$2$	−1.06141	−	1.83842i	−0.750533	−	1.29996i	0.197031	−	0.980397i	$-0.436870\pi$
$3$		0			0
$3$		0			0
$4$	−1.25320	+	2.17061i	−0.626600	+	1.08530i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$		0			0
$7$	−0.733534	+	1.27052i	−0.277250	+	0.480210i	−0.970700	−	0.240294i	$-0.922756\pi$
$7$	−0.733534	+	1.27052i	−0.277250	+	0.480210i	0.693451	+	0.720504i	$0.256090\pi$
$8$	1.07500			0.380070
$9$		0			0
$10$	1.06141	+	1.83842i	0.335649	+	0.581360i
$11$	0.172120	+	0.298120i	0.0518960	+	0.0898865i	0.890806	−	0.454383i	$-0.150140\pi$
$11$	0.172120	+	0.298120i	0.0518960	+	0.0898865i	−0.838910	+	0.544269i	$0.816807\pi$
$12$		0			0
$13$	1.76679	+	3.14300i	0.490018	+	0.871712i
$13$	1.76679	+	3.14300i	0.490018	+	0.871712i
$14$	3.11433			0.832340
$15$		0			0
$16$	1.36538	+	2.36491i	0.341345	+	0.591227i
$17$	2.56781	−	4.44758i	0.622786	−	1.07870i	−0.366178	−	0.930545i	$-0.619334\pi$
$17$	2.56781	−	4.44758i	0.622786	−	1.07870i	0.988964	−	0.148153i	$-0.0473327\pi$
$18$		0			0
$19$	−0.253200	+	0.438555i	−0.0580880	+	0.100611i	−0.893607	−	0.448850i	$-0.851834\pi$
$19$	−0.253200	+	0.438555i	−0.0580880	+	0.100611i	0.835519	+	0.549461i	$0.185167\pi$
$20$	1.25320	−	2.17061i	0.280224	−	0.485362i
$21$		0			0
$22$	0.365380	−	0.632857i	0.0778993	−	0.134926i
$23$	0.537500	+	0.930977i	0.112076	+	0.194122i	0.916607	−	0.399789i	$-0.130917\pi$
$23$	0.537500	+	0.930977i	0.112076	+	0.194122i	−0.804531	+	0.593911i	$0.797583\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$	3.90288	−	6.58413i	0.765418	−	1.29125i
$27$		0			0
$28$	−1.83853	−	3.18442i	−0.347449	−	0.601800i
$29$	4.02423	+	6.97018i	0.747281	+	1.29433i	0.949121	+	0.314911i	$0.101975\pi$
$29$	4.02423	+	6.97018i	0.747281	+	1.29433i	−0.201840	+	0.979419i	$0.564692\pi$
$30$		0			0
$31$	9.17129			1.64721			0.823607	−	0.567162i	$-0.191959\pi$
$31$	9.17129			1.64721			0.823607	+	0.567162i	$0.191959\pi$
$32$	3.97347	−	6.88225i	0.702416	−	1.21662i
$33$		0			0
$34$	−10.9021			−1.86969
$35$	0.733534	−	1.27052i	0.123990	−	0.214757i
$36$		0			0
$37$	−1.36538	−	2.36491i	−0.224467	−	0.388788i	0.731692	−	0.681635i	$-0.238731\pi$
$37$	−1.36538	−	2.36491i	−0.224467	−	0.388788i	−0.956159	+	0.292847i	$0.905397\pi$
$38$	1.07500			0.174388
$39$		0			0
$40$	−1.07500			−0.169972
$41$	3.06357	+	5.30625i	0.478449	+	0.828697i	0.999695	−	0.0247092i	$-0.00786599\pi$
$41$	3.06357	+	5.30625i	0.478449	+	0.828697i	−0.521246	+	0.853406i	$0.674533\pi$
$42$		0			0
$43$	2.93744	−	5.08780i	0.447956	−	0.775882i	−0.550297	−	0.834969i	$-0.685486\pi$
$43$	2.93744	−	5.08780i	0.447956	−	0.775882i	0.998253	+	0.0590868i	$0.0188189\pi$
$44$	−0.862801			−0.130072
$45$		0			0
$46$	1.14102	−	1.97630i	0.168234	−	0.291390i
$47$	−4.26369			−0.621924			−0.310962	−	0.950422i	$-0.600651\pi$
$47$	−4.26369			−0.621924			−0.310962	+	0.950422i	$0.600651\pi$
$48$		0			0
$49$	2.42386	+	4.19824i	0.346265	+	0.599749i
$50$	−1.06141	−	1.83842i	−0.150107	−	0.259992i
$51$		0			0
$52$	−9.03636	−	0.103818i	−1.25312	−	0.0143969i
$53$	4.07866			0.560248			0.280124	−	0.959964i	$-0.409624\pi$
$53$	4.07866			0.560248			0.280124	+	0.959964i	$0.409624\pi$
$54$		0			0
$55$	−0.172120	−	0.298120i	−0.0232086	−	0.0401985i
$56$	−0.788548	+	1.36581i	−0.105374	+	0.182513i
$57$		0			0
$58$	8.54276	−	14.7965i	1.12172	−	1.94287i
$59$	−2.53063	+	4.38318i	−0.329460	+	0.570642i	−0.982405	−	0.186764i	$-0.940200\pi$
$59$	−2.53063	+	4.38318i	−0.329460	+	0.570642i	0.652945	+	0.757406i	$0.273533\pi$
$60$		0			0
$61$	2.58565	−	4.47847i	0.331058	−	0.573410i	−0.651661	−	0.758510i	$-0.725928\pi$
$61$	2.58565	−	4.47847i	0.331058	−	0.573410i	0.982720	+	0.185100i	$0.0592610\pi$
$62$	−9.73454	−	16.8607i	−1.23629	−	2.14131i
$63$		0			0
$64$	−11.4085			−1.42606
$65$	−1.76679	−	3.14300i	−0.219143	−	0.389842i
$66$		0			0
$67$	−0.598595	−	1.03680i	−0.0731300	−	0.126665i	0.827142	−	0.561994i	$-0.189965\pi$
$67$	−0.598595	−	1.03680i	−0.0731300	−	0.126665i	−0.900272	+	0.435329i	$0.856632\pi$
$68$	6.43597	+	11.1474i	0.780476	+	1.35182i
$69$		0			0
$70$	−3.11433			−0.372234
$71$	0.222886	−	0.386049i	0.0264517	−	0.0458156i	−0.852497	−	0.522733i	$-0.824913\pi$
$71$	0.222886	−	0.386049i	0.0264517	−	0.0458156i	0.878948	+	0.476917i	$0.158246\pi$
$72$		0			0
$73$	−7.52634			−0.880892			−0.440446	−	0.897779i	$-0.645180\pi$
$73$	−7.52634			−0.880892			−0.440446	+	0.897779i	$0.645180\pi$
$74$	−2.89847	+	5.02029i	−0.336940	+	0.583597i
$75$		0			0
$76$	−0.634620	−	1.09919i	−0.0727959	−	0.126086i
$77$	−0.505022			−0.0575526
$78$		0			0
$79$	0.834915			0.0939352			0.0469676	−	0.998896i	$-0.485044\pi$
$79$	0.834915			0.0939352			0.0469676	+	0.998896i	$0.485044\pi$
$80$	−1.36538	−	2.36491i	−0.152654	−	0.264405i
$81$		0			0
$82$	6.50342	−	11.2643i	0.718183	−	1.24393i
$83$	−15.2506			−1.67397			−0.836985	−	0.547226i	$-0.815684\pi$
$83$	−15.2506			−1.67397			−0.836985	+	0.547226i	$0.815684\pi$
$84$		0			0
$85$	−2.56781	+	4.44758i	−0.278518	+	0.482408i
$86$	−12.4714			−1.34482
$87$		0			0
$88$	0.185028	+	0.320479i	0.0197241	+	0.0341631i
$89$	5.97494	+	10.3489i	0.633343	+	1.09698i	0.986864	+	0.161555i	$0.0516509\pi$
$89$	5.97494	+	10.3489i	0.633343	+	1.09698i	−0.353521	+	0.935427i	$0.615016\pi$
$90$		0			0
$91$	−5.28924	−	0.0607674i	−0.554463	−	0.00637016i
$92$	−2.69438			−0.280908
$93$		0			0
$94$	4.52554	+	7.83847i	0.466774	+	0.808477i
$95$	0.253200	−	0.438555i	0.0259778	−	0.0449948i
$96$		0			0
$97$	0.700282	−	1.21292i	0.0711029	−	0.123154i	−0.828282	−	0.560311i	$-0.810681\pi$
$97$	0.700282	−	1.21292i	0.0711029	−	0.123154i	0.899385	+	0.437158i	$0.144015\pi$
$98$	5.14543	−	8.91215i	0.519767	−	0.900263i
$99$		0			0
$100$	−1.25320	+	2.17061i	−0.125320	+	0.217061i
$101$	5.04700	+	8.74167i	0.502196	+	0.869828i	0.999997	+	0.00253716i	$0.000807605\pi$
$101$	5.04700	+	8.74167i	0.502196	+	0.869828i	−0.497801	+	0.867291i	$0.665859\pi$
$102$		0			0
$103$	15.5592			1.53309			0.766545	−	0.642190i	$-0.221974\pi$
$103$	15.5592			1.53309			0.766545	+	0.642190i	$0.221974\pi$
$104$	1.89929	+	3.37873i	0.186241	+	0.331311i
$105$		0			0
$106$	−4.32915	−	7.49831i	−0.420484	−	0.728300i
$107$	1.05685	+	1.83051i	0.102169	+	0.176962i	0.912578	−	0.408902i	$-0.134088\pi$
$107$	1.05685	+	1.83051i	0.102169	+	0.176962i	−0.810409	+	0.585865i	$0.800755\pi$
$108$		0			0
$109$	4.12514			0.395117			0.197558	−	0.980291i	$-0.436699\pi$
$109$	4.12514			0.395117			0.197558	+	0.980291i	$0.436699\pi$
$110$	−0.365380	+	0.632857i	−0.0348376	+	0.0603405i
$111$		0			0
$112$	−4.00621			−0.378551
$113$	−5.69573	+	9.86529i	−0.535809	+	0.928049i	0.463314	+	0.886194i	$0.346660\pi$
$113$	−5.69573	+	9.86529i	−0.535809	+	0.928049i	−0.999124	+	0.0418549i	$0.986673\pi$
$114$		0			0
$115$	−0.537500	−	0.930977i	−0.0501221	−	0.0868140i
$116$	−20.1727			−1.87299
$117$		0			0
$118$	10.7442			0.989083
$119$	3.76716	+	6.52490i	0.345335	+	0.598137i
$120$		0			0
$121$	5.44075	−	9.42365i	0.494614	−	0.856696i
$122$	−10.9778			−0.993881
$123$		0			0
$124$	−11.4935	+	19.9073i	−1.03214	+	1.78773i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	10.5067	+	18.1982i	0.932322	+	1.61483i	0.779342	+	0.626599i	$0.215554\pi$
$127$	10.5067	+	18.1982i	0.932322	+	1.61483i	0.152980	+	0.988229i	$0.451113\pi$
$128$	4.16216	+	7.20907i	0.367886	+	0.637198i
$129$		0			0
$130$	−3.90288	+	6.58413i	−0.342305	+	0.577466i
$131$	13.4726			1.17711			0.588555	−	0.808457i	$-0.299697\pi$
$131$	13.4726			1.17711			0.588555	+	0.808457i	$0.299697\pi$
$132$		0			0
$133$	−0.371461	−	0.643390i	−0.0322098	−	0.0557889i
$134$	−1.27071	+	2.20094i	−0.109773	+	0.190132i
$135$		0			0
$136$	2.76040	−	4.78115i	0.236702	−	0.409980i
$137$	5.10101	−	8.83521i	0.435809	−	0.754843i	−0.561553	−	0.827441i	$-0.689796\pi$
$137$	5.10101	−	8.83521i	0.435809	−	0.754843i	0.997361	+	0.0725982i	$0.0231291\pi$
$138$		0			0
$139$	−6.07601	+	10.5240i	−0.515360	+	0.892630i	0.484481	+	0.874802i	$0.339009\pi$
$139$	−6.07601	+	10.5240i	−0.515360	+	0.892630i	−0.999841	+	0.0178282i	$0.994325\pi$
$140$	1.83853	+	3.18442i	0.155384	+	0.269133i
$141$		0			0
$142$	−0.946296			−0.0794114
$143$	−0.632893	+	1.06769i	−0.0529252	+	0.0892844i
$144$		0			0
$145$	−4.02423	−	6.97018i	−0.334194	−	0.578842i
$146$	7.98857	+	13.8366i	0.661138	+	1.14513i
$147$		0			0
$148$	6.84438			0.562604
$149$	0.333643	−	0.577886i	0.0273331	−	0.0473423i	−0.852035	−	0.523484i	$-0.824632\pi$
$149$	0.333643	−	0.577886i	0.0273331	−	0.0473423i	0.879368	+	0.476142i	$0.157965\pi$
$150$		0			0
$151$	−15.9198			−1.29553			−0.647767	−	0.761839i	$-0.724297\pi$
$151$	−15.9198			−1.29553			−0.647767	+	0.761839i	$0.724297\pi$
$152$	−0.272190	+	0.471446i	−0.0220775	+	0.0382393i
$153$		0			0
$154$	0.536037	+	0.928444i	0.0431951	+	0.0748161i
$155$	−9.17129			−0.736656
$156$		0			0
$157$	17.4611			1.39355			0.696774	−	0.717290i	$-0.254618\pi$
$157$	17.4611			1.39355			0.696774	+	0.717290i	$0.254618\pi$
$158$	−0.886190	−	1.53493i	−0.0705015	−	0.122112i
$159$		0			0
$160$	−3.97347	+	6.88225i	−0.314130	+	0.544089i
$161$	−1.57710			−0.124293
$162$		0			0
$163$	−7.27927	+	12.6081i	−0.570156	+	0.987539i	0.426393	+	0.904538i	$0.359784\pi$
$163$	−7.27927	+	12.6081i	−0.570156	+	0.987539i	−0.996549	+	0.0830015i	$0.973549\pi$
$164$	−15.3570			−1.19918
$165$		0			0
$166$	16.1872	+	28.0370i	1.25637	+	2.17610i
$167$	7.76055	+	13.4417i	0.600530	+	1.04015i	0.992741	+	0.120273i	$0.0383769\pi$
$167$	7.76055	+	13.4417i	0.600530	+	1.04015i	−0.392211	+	0.919875i	$0.628290\pi$
$168$		0			0
$169$	−6.75694	+	11.1060i	−0.519765	+	0.854309i
$170$	10.9021			0.836149
$171$		0			0
$172$	7.36240	+	12.7521i	0.561378	+	0.972335i
$173$	−4.16295	+	7.21044i	−0.316503	+	0.548199i	−0.979756	−	0.200196i	$-0.935842\pi$
$173$	−4.16295	+	7.21044i	−0.316503	+	0.548199i	0.663253	+	0.748395i	$0.269175\pi$
$174$		0			0
$175$	−0.733534	+	1.27052i	−0.0554499	+	0.0960421i
$176$	−0.470017	+	0.814094i	−0.0354289	+	0.0613646i
$177$		0			0
$178$	12.6838	−	21.9689i	0.950689	−	1.64664i
$179$	−12.6313	−	21.8781i	−0.944111	−	1.63525i	−0.757522	−	0.652810i	$-0.773590\pi$
$179$	−12.6313	−	21.8781i	−0.944111	−	1.63525i	−0.186589	−	0.982438i	$-0.559743\pi$
$180$		0			0
$181$	−21.6041			−1.60582			−0.802909	−	0.596102i	$-0.796716\pi$
$181$	−21.6041			−1.60582			−0.802909	+	0.596102i	$0.796716\pi$
$182$	5.50235	+	9.78836i	0.407862	+	0.725561i
$183$		0			0
$184$	0.577812	+	1.00080i	0.0425968	+	0.0737799i
$185$	1.36538	+	2.36491i	0.100385	+	0.173871i
$186$		0			0
$187$	1.76788			0.129280
$188$	5.34326	−	9.25480i	0.389697	−	0.674975i
$189$		0			0
$190$	−1.07500			−0.0779886
$191$	4.65724	−	8.06657i	0.336986	−	0.583676i	−0.646878	−	0.762593i	$-0.723926\pi$
$191$	4.65724	−	8.06657i	0.336986	−	0.583676i	0.983864	+	0.178917i	$0.0572592\pi$
$192$		0			0
$193$	3.80004	+	6.58186i	0.273533	+	0.473772i	0.969764	−	0.244045i	$-0.0784745\pi$
$193$	3.80004	+	6.58186i	0.273533	+	0.473772i	−0.696231	+	0.717818i	$0.745141\pi$
$194$	−2.97316			−0.213460
$195$		0			0
$196$	−12.1503			−0.867879
$197$	5.47163	+	9.47715i	0.389838	+	0.675219i	0.992427	−	0.122832i	$-0.0391977\pi$
$197$	5.47163	+	9.47715i	0.389838	+	0.675219i	−0.602590	+	0.798051i	$0.705864\pi$
$198$		0			0
$199$	7.09839	−	12.2948i	0.503192	−	0.871554i	−0.496802	−	0.867864i	$-0.665492\pi$
$199$	7.09839	−	12.2948i	0.503192	−	0.871554i	0.999993	−	0.00368935i	$-0.00117436\pi$
$200$	1.07500			0.0760139
$201$		0			0
$202$	10.7139	−	18.5571i	0.753829	−	1.30567i
$203$	−11.8076			−0.828734
$204$		0			0
$205$	−3.06357	−	5.30625i	−0.213969	−	0.370605i
$206$	−16.5147	−	28.6043i	−1.15064	−	1.99296i
$207$		0			0
$208$	−5.02058	+	8.46968i	−0.348115	+	0.587267i
$209$	−0.174322			−0.0120581
$210$		0			0
$211$	−5.16489	−	8.94586i	−0.355566	−	0.615858i	0.631649	−	0.775255i	$-0.282379\pi$
$211$	−5.16489	−	8.94586i	−0.355566	−	0.615858i	−0.987215	+	0.159396i	$0.949045\pi$
$212$	−5.11138	+	8.85317i	−0.351051	+	0.608038i
$213$		0			0
$214$	2.24351	−	3.88586i	0.153363	−	0.265632i
$215$	−2.93744	+	5.08780i	−0.200332	+	0.346985i
$216$		0			0
$217$	−6.72745	+	11.6523i	−0.456689	+	0.791009i
$218$	−4.37848	−	7.58375i	−0.296548	−	0.513637i
$219$		0			0
$220$	0.862801			0.0581700
$221$	18.5155	+	0.212723i	1.24549	+	0.0143093i
$222$		0			0
$223$	−12.2531	−	21.2229i	−0.820526	−	1.42119i	−0.905291	−	0.424791i	$-0.860347\pi$
$223$	−12.2531	−	21.2229i	−0.820526	−	1.42119i	0.0847654	−	0.996401i	$-0.472986\pi$
$224$	5.82934	+	10.0967i	0.389489	+	0.674615i
$225$		0			0
$226$	24.1821			1.60857
$227$	1.50262	−	2.60261i	0.0997323	−	0.172741i	−0.811842	−	0.583878i	$-0.801535\pi$
$227$	1.50262	−	2.60261i	0.0997323	−	0.172741i	0.911574	+	0.411136i	$0.134868\pi$
$228$		0			0
$229$	−21.9741			−1.45209			−0.726046	−	0.687646i	$-0.758644\pi$
$229$	−21.9741			−1.45209			−0.726046	+	0.687646i	$0.758644\pi$
$230$	−1.14102	+	1.97630i	−0.0752366	+	0.130314i
$231$		0			0
$232$	4.32605	+	7.49293i	0.284019	+	0.491935i
$233$	−7.22372			−0.473242			−0.236621	−	0.971602i	$-0.576040\pi$
$233$	−7.22372			−0.473242			−0.236621	+	0.971602i	$0.576040\pi$
$234$		0			0
$235$	4.26369			0.278133
$236$	−6.34278	−	10.9860i	−0.412880	−	0.715128i
$237$		0			0
$238$	7.99702	−	13.8513i	0.518370	−	0.897843i
$239$	−0.492963			−0.0318871			−0.0159436	−	0.999873i	$-0.505075\pi$
$239$	−0.492963			−0.0318871			−0.0159436	+	0.999873i	$0.505075\pi$
$240$		0			0
$241$	13.1384	−	22.7564i	0.846320	−	1.46587i	−0.0381504	−	0.999272i	$-0.512147\pi$
$241$	13.1384	−	22.7564i	0.846320	−	1.46587i	0.884470	−	0.466597i	$-0.154520\pi$
$242$	−23.0996			−1.48490
$243$		0			0
$244$	6.48066	+	11.2248i	0.414882	+	0.718597i
$245$	−2.42386	−	4.19824i	−0.154855	−	0.268216i
$246$		0			0
$247$	−1.82573	−	0.0209756i	−0.116168	−	0.00133465i
$248$	9.85914			0.626056
$249$		0			0
$250$	1.06141	+	1.83842i	0.0671297	+	0.116272i
$251$	−10.7771	+	18.6665i	−0.680246	+	1.17822i	0.294659	+	0.955602i	$0.404794\pi$
$251$	−10.7771	+	18.6665i	−0.680246	+	1.17822i	−0.974906	+	0.222619i	$0.928540\pi$
$252$		0			0
$253$	−0.185028	+	0.320479i	−0.0116326	+	0.0201483i
$254$	22.3040	−	38.6316i	1.39948	−	2.42396i
$255$		0			0
$256$	−2.57290	+	4.45640i	−0.160806	+	0.278525i
$257$	6.40603	+	11.0956i	0.399597	+	0.692122i	0.993676	−	0.112284i	$-0.0358168\pi$
$257$	6.40603	+	11.0956i	0.399597	+	0.692122i	−0.594079	+	0.804407i	$0.702483\pi$
$258$		0			0
$259$	4.00621			0.248934
$260$	9.03636	+	0.103818i	0.560411	+	0.00643850i
$261$		0			0
$262$	−14.3000	−	24.7684i	−0.883460	−	1.53020i
$263$	−12.2190	−	21.1639i	−0.753454	−	1.30502i	−0.946139	−	0.323760i	$-0.895053\pi$
$263$	−12.2190	−	21.1639i	−0.753454	−	1.30502i	0.192685	−	0.981261i	$-0.438280\pi$
$264$		0			0
$265$	−4.07866			−0.250550
$266$	−0.788548	+	1.36581i	−0.0483490	+	0.0837429i
$267$		0			0
$268$	3.00064			0.183293
$269$	11.9134	−	20.6346i	0.726372	−	1.25811i	−0.232035	−	0.972707i	$-0.574539\pi$
$269$	11.9134	−	20.6346i	0.726372	−	1.25811i	0.958407	−	0.285405i	$-0.0921281\pi$
$270$		0			0
$271$	−10.3877	−	17.9920i	−0.631007	−	1.09294i	−0.987346	−	0.158579i	$-0.949309\pi$
$271$	−10.3877	−	17.9920i	−0.631007	−	1.09294i	0.356339	−	0.934357i	$-0.384025\pi$
$272$	14.0242			0.850340
$273$		0			0
$274$	−21.6571			−1.30836
$275$	0.172120	+	0.298120i	0.0103792	+	0.0179773i
$276$		0			0
$277$	−0.234055	+	0.405396i	−0.0140630	+	0.0243579i	−0.872971	−	0.487772i	$-0.837810\pi$
$277$	−0.234055	+	0.405396i	−0.0140630	+	0.0243579i	0.858908	+	0.512129i	$0.171143\pi$
$278$	25.7966			1.54718
$279$		0			0
$280$	0.788548	−	1.36581i	0.0471248	−	0.0816225i
$281$	24.5123			1.46228			0.731141	−	0.682226i	$-0.238988\pi$
$281$	24.5123			1.46228			0.731141	+	0.682226i	$0.238988\pi$
$282$		0			0
$283$	−11.4475	−	19.8276i	−0.680481	−	1.17863i	−0.974834	−	0.222930i	$-0.928438\pi$
$283$	−11.4475	−	19.8276i	−0.680481	−	1.17863i	0.294354	−	0.955697i	$-0.404896\pi$
$284$	0.558641	+	0.967594i	0.0331492	+	0.0574162i
$285$		0			0
$286$	2.63462	+	0.0302688i	0.155788	+	0.00178983i
$287$	−8.98891			−0.530599
$288$		0			0
$289$	−4.68733	−	8.11870i	−0.275726	−	0.477571i
$290$	−8.54276	+	14.7965i	−0.501648	+	0.868880i
$291$		0			0
$292$	9.43201	−	16.3367i	0.551967	−	0.956034i
$293$	9.62021	−	16.6627i	0.562019	−	0.973445i	−0.435302	−	0.900285i	$-0.643358\pi$
$293$	9.62021	−	16.6627i	0.562019	−	0.973445i	0.997320	−	0.0731601i	$-0.0233084\pi$
$294$		0			0
$295$	2.53063	−	4.38318i	0.147339	−	0.255199i
$296$	−1.46778	−	2.54227i	−0.0853131	−	0.147767i
$297$		0			0
$298$	−1.41653			−0.0820575
$299$	−1.97642	+	3.33420i	−0.114299	+	0.192822i
$300$		0			0
$301$	4.30943	+	7.46414i	0.248391	+	0.430226i
$302$	16.8975	+	29.2673i	0.972341	+	1.68414i
$303$		0			0
$304$	−1.38286			−0.0793122
$305$	−2.58565	+	4.47847i	−0.148054	+	0.256437i
$306$		0			0
$307$	−16.4739			−0.940216			−0.470108	−	0.882609i	$-0.655785\pi$
$307$	−16.4739			−0.940216			−0.470108	+	0.882609i	$0.655785\pi$
$308$	0.632893	−	1.09620i	0.0360624	−	0.0624620i
$309$		0			0
$310$	9.73454	+	16.8607i	0.552885	+	0.957625i
$311$	−9.54562			−0.541283			−0.270641	−	0.962680i	$-0.587236\pi$
$311$	−9.54562			−0.541283			−0.270641	+	0.962680i	$0.587236\pi$
$312$		0			0
$313$	21.9067			1.23824			0.619120	−	0.785297i	$-0.287490\pi$
$313$	21.9067			1.23824			0.619120	+	0.785297i	$0.287490\pi$
$314$	−18.5335	−	32.1009i	−1.04590	−	1.81156i
$315$		0			0
$316$	−1.04631	+	1.81227i	−0.0588598	+	0.101948i
$317$	27.1321			1.52389			0.761945	−	0.647642i	$-0.224245\pi$
$317$	27.1321			1.52389			0.761945	+	0.647642i	$0.224245\pi$
$318$		0			0
$319$	−1.38530	+	2.39941i	−0.0775618	+	0.134341i
$320$	11.4085			0.637752
$321$		0			0
$322$	1.67395	+	2.89937i	0.0932857	+	0.161576i
$323$	1.30034	+	2.25225i	0.0723528	+	0.125319i
$324$		0			0
$325$	1.76679	+	3.14300i	0.0980036	+	0.174342i
$326$	30.9053			1.71168
$327$		0			0
$328$	3.29333	+	5.70422i	0.181844	+	0.314963i
$329$	3.12756	−	5.41710i	0.172428	−	0.298654i
$330$		0			0
$331$	−0.568970	+	0.985485i	−0.0312734	+	0.0541672i	−0.881239	−	0.472672i	$-0.843290\pi$
$331$	−0.568970	+	0.985485i	−0.0312734	+	0.0541672i	0.849965	+	0.526839i	$0.176623\pi$
$332$	19.1120	−	33.1030i	1.04891	−	1.81676i
$333$		0			0
$334$	16.4743	−	28.5344i	0.901435	−	1.56133i
$335$	0.598595	+	1.03680i	0.0327047	+	0.0566463i
$336$		0			0
$337$	−26.9676			−1.46902			−0.734510	−	0.678598i	$-0.762588\pi$
$337$	−26.9676			−1.46902			−0.734510	+	0.678598i	$0.762588\pi$
$338$	27.5895	+	0.634028i	1.50067	+	0.0344866i
$339$		0			0
$340$	−6.43597	−	11.1474i	−0.349039	−	0.604554i
$341$	1.57856	+	2.73414i	0.0854837	+	0.148062i
$342$		0			0
$343$	−17.3814			−0.938507
$344$	3.15775	−	5.46938i	0.170254	−	0.294889i
$345$		0			0
$346$	17.6744			0.950184
$347$	−3.26695	+	5.65853i	−0.175379	+	0.303766i	−0.940292	−	0.340368i	$-0.889448\pi$
$347$	−3.26695	+	5.65853i	−0.175379	+	0.303766i	0.764913	+	0.644133i	$0.222782\pi$
$348$		0			0
$349$	0.528839	+	0.915976i	0.0283081	+	0.0490311i	0.879832	−	0.475284i	$-0.157655\pi$
$349$	0.528839	+	0.915976i	0.0283081	+	0.0490311i	−0.851524	+	0.524315i	$0.824321\pi$
$350$	3.11433			0.166468
$351$		0			0
$352$	2.73564			0.145810
$353$	−12.2843	−	21.2771i	−0.653828	−	1.13246i	−0.982186	−	0.187910i	$-0.939829\pi$
$353$	−12.2843	−	21.2771i	−0.653828	−	1.13246i	0.328358	−	0.944553i	$-0.393505\pi$
$354$		0			0
$355$	−0.222886	+	0.386049i	−0.0118295	+	0.0204894i
$356$	−29.9512			−1.58741
$357$		0			0
$358$	−26.8142	+	46.4435i	−1.41717	+	2.45462i
$359$	−7.44704			−0.393040			−0.196520	−	0.980500i	$-0.562964\pi$
$359$	−7.44704			−0.393040			−0.196520	+	0.980500i	$0.562964\pi$
$360$		0			0
$361$	9.37178	+	16.2324i	0.493252	+	0.854337i
$362$	22.9309	+	39.7174i	1.20522	+	2.08750i
$363$		0			0
$364$	6.76037	−	11.4047i	0.354340	−	0.597768i
$365$	7.52634			0.393947
$366$		0			0
$367$	0.0222907	+	0.0386086i	0.00116356	+	0.00201535i	0.866607	−	0.498992i	$-0.166296\pi$
$367$	0.0222907	+	0.0386086i	0.00116356	+	0.00201535i	−0.865443	+	0.501007i	$0.832963\pi$
$368$	−1.46778	+	2.54227i	−0.0765135	+	0.132525i
$369$		0			0
$370$	2.89847	−	5.02029i	0.150684	−	0.260993i
$371$	−2.99184	+	5.18201i	−0.155328	+	0.269037i
$372$		0			0
$373$	1.67118	−	2.89457i	0.0865304	−	0.149875i	−0.819512	−	0.573062i	$-0.805755\pi$
$373$	1.67118	−	2.89457i	0.0865304	−	0.149875i	0.906042	+	0.423187i	$0.139089\pi$
$374$	−1.87646	−	3.25012i	−0.0970292	−	0.168060i
$375$		0			0
$376$	−4.58347			−0.236374
$377$	−14.7973	+	24.9630i	−0.762101	+	1.28566i
$378$		0			0
$379$	13.1095	+	22.7064i	0.673391	+	1.16635i	0.976936	+	0.213530i	$0.0684962\pi$
$379$	13.1095	+	22.7064i	0.673391	+	1.16635i	−0.303545	+	0.952817i	$0.598170\pi$
$380$	0.634620	+	1.09919i	0.0325553	+	0.0563875i
$381$		0			0
$382$	−19.7730			−1.01168
$383$	6.44955	−	11.1710i	0.329557	−	0.570809i	−0.652867	−	0.757472i	$-0.726434\pi$
$383$	6.44955	−	11.1710i	0.329557	−	0.570809i	0.982424	+	0.186663i	$0.0597674\pi$
$384$		0			0
$385$	0.505022			0.0257383
$386$	8.06682	−	13.9721i	0.410591	−	0.711164i
$387$		0			0
$388$	1.75519	+	3.04007i	0.0891061	+	0.154336i
$389$	−5.08578			−0.257859			−0.128930	−	0.991654i	$-0.541154\pi$
$389$	−5.08578			−0.257859			−0.128930	+	0.991654i	$0.541154\pi$
$390$		0			0
$391$	5.52080			0.279199
$392$	2.60564	+	4.51311i	0.131605	+	0.227946i
$393$		0			0
$394$	11.6153	−	20.1184i	0.585172	−	1.01355i
$395$	−0.834915			−0.0420091
$396$		0			0
$397$	5.53209	−	9.58187i	0.277648	−	0.480900i	−0.693152	−	0.720791i	$-0.743779\pi$
$397$	5.53209	−	9.58187i	0.277648	−	0.480900i	0.970800	+	0.239891i	$0.0771119\pi$
$398$	−30.1373			−1.51065
$399$		0			0
$400$	1.36538	+	2.36491i	0.0682690	+	0.118245i
$401$	−11.5476	−	20.0011i	−0.576662	−	0.998807i	−0.995859	−	0.0909120i	$-0.971022\pi$
$401$	−11.5476	−	20.0011i	−0.576662	−	0.998807i	0.419197	−	0.907895i	$-0.362312\pi$
$402$		0			0
$403$	16.2037	+	28.8254i	0.807164	+	1.43590i
$404$	−25.2996			−1.25870
$405$		0			0
$406$	12.5328	+	21.7074i	0.621992	+	1.07732i
$407$	0.470017	−	0.814094i	0.0232979	−	0.0403531i
$408$		0			0
$409$	−7.21057	+	12.4891i	−0.356540	+	0.617545i	−0.987380	−	0.158367i	$-0.949377\pi$
$409$	−7.21057	+	12.4891i	−0.356540	+	0.617545i	0.630840	+	0.775913i	$0.282710\pi$
$410$	−6.50342	+	11.2643i	−0.321181	+	0.556302i
$411$		0			0
$412$	−19.4987	+	33.7728i	−0.960634	+	1.66387i
$413$	−3.71261	−	6.43043i	−0.182686	−	0.316421i
$414$		0			0
$415$	15.2506			0.748622
$416$	28.6512	+	0.329170i	1.40474	+	0.0161389i
$417$		0			0
$418$	0.185028	+	0.320479i	0.00905003	+	0.0156751i
$419$	−7.58423	−	13.1363i	−0.370514	−	0.641749i	0.619131	−	0.785288i	$-0.287485\pi$
$419$	−7.58423	−	13.1363i	−0.370514	−	0.641749i	−0.989645	+	0.143539i	$0.954152\pi$
$420$		0			0
$421$	10.7707			0.524932			0.262466	−	0.964941i	$-0.415464\pi$
$421$	10.7707			0.524932			0.262466	+	0.964941i	$0.415464\pi$
$422$	−10.9642	+	18.9905i	−0.533728	+	0.924444i
$423$		0			0
$424$	4.38456			0.212933
$425$	2.56781	−	4.44758i	0.124557	−	0.215740i
$426$		0			0
$427$	3.79332	+	6.57022i	0.183572	+	0.317955i
$428$	−5.29776			−0.256077
$429$		0			0
$430$	12.4714			0.601423
$431$	−20.6570	−	35.7789i	−0.995010	−	1.72341i	−0.583910	−	0.811818i	$-0.698478\pi$
$431$	−20.6570	−	35.7789i	−0.995010	−	1.72341i	−0.411100	−	0.911590i	$-0.634855\pi$
$432$		0			0
$433$	−9.22620	+	15.9802i	−0.443383	+	0.767962i	−0.997938	−	0.0641854i	$-0.979555\pi$
$433$	−9.22620	+	15.9802i	−0.443383	+	0.767962i	0.554555	+	0.832147i	$0.312888\pi$
$434$	28.5625			1.37104
$435$		0			0
$436$	−5.16963	+	8.95405i	−0.247580	+	0.428821i
$437$	−0.544379			−0.0260412
$438$		0			0
$439$	−3.94070	−	6.82548i	−0.188079	−	0.325763i	0.756531	−	0.653958i	$-0.226893\pi$
$439$	−3.94070	−	6.82548i	−0.188079	−	0.325763i	−0.944610	+	0.328196i	$0.893559\pi$
$440$	−0.185028	−	0.320479i	−0.00882088	−	0.0152782i
$441$		0			0
$442$	−19.2616	−	34.2652i	−0.916180	−	1.62983i
$443$	−38.2769			−1.81859			−0.909294	−	0.416154i	$-0.863378\pi$
$443$	−38.2769			−1.81859			−0.909294	+	0.416154i	$0.863378\pi$
$444$		0			0
$445$	−5.97494	−	10.3489i	−0.283239	−	0.490585i
$446$	−26.0111	+	45.0526i	−1.23166	+	2.13330i
$447$		0			0
$448$	8.36848	−	14.4946i	0.395374	−	0.684807i
$449$	6.27219	−	10.8638i	0.296003	−	0.512692i	−0.679215	−	0.733940i	$-0.737680\pi$
$449$	6.27219	−	10.8638i	0.296003	−	0.512692i	0.975218	+	0.221247i	$0.0710128\pi$
$450$		0			0
$451$	−1.05460	+	1.82662i	−0.0496591	+	0.0860121i
$452$	−14.2758	−	24.7264i	−0.671476	−	1.16303i
$453$		0			0
$454$	−6.37960			−0.299410
$455$	5.28924	+	0.0607674i	0.247963	+	0.00284882i
$456$		0			0
$457$	10.1343	+	17.5532i	0.474064	+	0.821103i	0.999559	−	0.0296935i	$-0.00945313\pi$
$457$	10.1343	+	17.5532i	0.474064	+	0.821103i	−0.525495	+	0.850797i	$0.676120\pi$
$458$	23.3237	+	40.3977i	1.08984	+	1.88766i
$459$		0			0
$460$	2.69438			0.125626
$461$	6.25006	−	10.8254i	0.291094	−	0.504190i	−0.682975	−	0.730442i	$-0.739314\pi$
$461$	6.25006	−	10.8254i	0.291094	−	0.504190i	0.974069	+	0.226252i	$0.0726474\pi$
$462$		0			0
$463$	−15.0923			−0.701400			−0.350700	−	0.936488i	$-0.614056\pi$
$463$	−15.0923			−0.701400			−0.350700	+	0.936488i	$0.614056\pi$
$464$	−10.9892	+	19.0339i	−0.510162	+	0.883626i
$465$		0			0
$466$	7.66736	+	13.2803i	0.355184	+	0.615196i
$467$	−14.8821			−0.688662			−0.344331	−	0.938848i	$-0.611894\pi$
$467$	−14.8821			−0.688662			−0.344331	+	0.938848i	$0.611894\pi$
$468$		0			0
$469$	1.75636			0.0811011
$470$	−4.52554	−	7.83847i	−0.208748	−	0.361562i
$471$		0			0
$472$	−2.72043	+	4.71192i	−0.125218	+	0.216884i
$473$	2.02236			0.0929884
$474$		0			0
$475$	−0.253200	+	0.438555i	−0.0116176	+	0.0201223i
$476$	−18.8840			−0.865546
$477$		0			0
$478$	0.523238	+	0.906275i	0.0239324	+	0.0414521i
$479$	0.152080	+	0.263411i	0.00694873	+	0.0120355i	0.869479	−	0.493970i	$-0.164455\pi$
$479$	0.152080	+	0.263411i	0.00694873	+	0.0120355i	−0.862530	+	0.506006i	$0.831121\pi$
$480$		0			0
$481$	5.02058	−	8.46968i	0.228919	−	0.386184i
$482$	−55.7812			−2.54076
$483$		0			0
$484$	13.6367	+	23.6194i	0.619850	+	1.07361i
$485$	−0.700282	+	1.21292i	−0.0317982	+	0.0550761i
$486$		0			0
$487$	−20.8582	+	36.1274i	−0.945174	+	1.63709i	−0.189772	+	0.981828i	$0.560775\pi$
$487$	−20.8582	+	36.1274i	−0.945174	+	1.63709i	−0.755402	+	0.655261i	$0.772559\pi$
$488$	2.77957	−	4.81435i	0.125825	−	0.217936i
$489$		0			0
$490$	−5.14543	+	8.91215i	−0.232447	+	0.402610i
$491$	20.2798	+	35.1256i	0.915213	+	1.58520i	0.806589	+	0.591112i	$0.201311\pi$
$491$	20.2798	+	35.1256i	0.915213	+	1.58520i	0.108624	+	0.994083i	$0.465356\pi$
$492$		0			0
$493$	41.3339			1.86159
$494$	1.89929	+	3.37873i	0.0854532	+	0.152016i
$495$		0			0
$496$	12.5223	+	21.6893i	0.562268	+	0.973877i
$497$	0.326988	+	0.566361i	0.0146674	+	0.0254047i
$498$		0			0
$499$	21.7238			0.972493			0.486246	−	0.873822i	$-0.338366\pi$
$499$	21.7238			0.972493			0.486246	+	0.873822i	$0.338366\pi$
$500$	1.25320	−	2.17061i	0.0560448	−	0.0970724i
$501$		0			0
$502$	45.7560			2.04219
$503$	12.2136	−	21.1545i	0.544575	−	0.943232i	−0.454058	−	0.890972i	$-0.650024\pi$
$503$	12.2136	−	21.1545i	0.544575	−	0.943232i	0.998634	−	0.0522601i	$-0.0166425\pi$
$504$		0			0
$505$	−5.04700	−	8.74167i	−0.224589	−	0.388999i
$506$	0.785567			0.0349227
$507$		0			0
$508$	−52.6681			−2.33677
$509$	15.7512	+	27.2819i	0.698161	+	1.20925i	0.969103	+	0.246655i	$0.0793314\pi$
$509$	15.7512	+	27.2819i	0.698161	+	1.20925i	−0.270942	+	0.962596i	$0.587335\pi$
$510$		0			0
$511$	5.52083	−	9.56235i	0.244227	−	0.423013i
$512$	27.5723			1.21854
$513$		0			0
$514$	13.5989	−	23.5540i	0.599821	−	1.03892i
$515$	−15.5592			−0.685619
$516$		0			0
$517$	−0.733865	−	1.27109i	−0.0322753	−	0.0559025i
$518$	−4.25225	−	7.36511i	−0.186833	−	0.323604i
$519$		0			0
$520$	−1.89929	−	3.37873i	−0.0832895	−	0.148167i
$521$	38.2684			1.67657			0.838284	−	0.545235i	$-0.183559\pi$
$521$	38.2684			1.67657			0.838284	+	0.545235i	$0.183559\pi$
$522$		0			0
$523$	−7.50085	−	12.9919i	−0.327989	−	0.568094i	0.654123	−	0.756388i	$-0.273038\pi$
$523$	−7.50085	−	12.9919i	−0.327989	−	0.568094i	−0.982113	+	0.188294i	$0.939704\pi$
$524$	−16.8839	+	29.2438i	−0.737577	+	1.27752i
$525$		0			0
$526$	−25.9388	+	44.9273i	−1.13098	+	1.95892i
$527$	23.5502	−	40.7901i	1.02586	−	1.77684i
$528$		0			0
$529$	10.9222	−	18.9178i	0.474878	−	0.822512i
$530$	4.32915	+	7.49831i	0.188046	+	0.325706i
$531$		0			0
$532$	1.86206			0.0807305
$533$	−11.2649	+	19.0038i	−0.487937	+	0.823146i
$534$		0			0
$535$	−1.05685	−	1.83051i	−0.0456915	−	0.0791400i
$536$	−0.643489	−	1.11456i	−0.0277945	−	0.0481415i
$537$		0			0
$538$	−50.5801			−2.18066
$539$	−0.834386	+	1.44520i	−0.0359396	+	0.0622491i
$540$		0			0
$541$	−11.9341			−0.513089			−0.256544	−	0.966532i	$-0.582584\pi$
$541$	−11.9341			−0.513089			−0.256544	+	0.966532i	$0.582584\pi$
$542$	−22.0513	+	38.1939i	−0.947183	+	1.64057i
$543$		0			0
$544$	−20.4062	−	35.3447i	−0.874911	−	1.51539i
$545$	−4.12514			−0.176702
$546$		0			0
$547$	23.5978			1.00897			0.504484	−	0.863421i	$-0.331683\pi$
$547$	23.5978			1.00897			0.504484	+	0.863421i	$0.331683\pi$
$548$	12.7852	+	22.1446i	0.546155	+	0.945969i
$549$		0			0
$550$	0.365380	−	0.632857i	0.0155799	−	0.0269851i
$551$	−4.07574			−0.173632
$552$		0			0
$553$	−0.612438	+	1.06077i	−0.0260435	+	0.0451087i
$554$	0.993719			0.0422191
$555$		0			0
$556$	−15.2289	−	26.3772i	−0.645849	−	1.11864i
$557$	7.33970	+	12.7127i	0.310993	+	0.538656i	0.978578	−	0.205878i	$-0.0660051\pi$
$557$	7.33970	+	12.7127i	0.310993	+	0.538656i	−0.667585	+	0.744534i	$0.732672\pi$
$558$		0			0
$559$	21.1808	+	0.243344i	0.895852	+	0.0102923i
$560$	4.00621			0.169293
$561$		0			0
$562$	−26.0177	−	45.0640i	−1.09749	−	1.90091i
$563$	−15.2670	+	26.4431i	−0.643425	+	1.11445i	0.341237	+	0.939977i	$0.389154\pi$
$563$	−15.2670	+	26.4431i	−0.643425	+	1.11445i	−0.984663	+	0.174468i	$0.944179\pi$
$564$		0			0
$565$	5.69573	−	9.86529i	0.239621	−	0.415036i
$566$	−24.3010	+	42.0905i	−1.02145	+	1.76920i
$567$		0			0
$568$	0.239602	−	0.415003i	0.0100535	−	0.0174131i
$569$	−9.56420	−	16.5657i	−0.400952	−	0.694469i	0.592889	−	0.805284i	$-0.297987\pi$
$569$	−9.56420	−	16.5657i	−0.400952	−	0.694469i	−0.993841	+	0.110815i	$0.964654\pi$
$570$		0			0
$571$	−25.5461			−1.06907			−0.534535	−	0.845146i	$-0.679513\pi$
$571$	−25.5461			−1.06907			−0.534535	+	0.845146i	$0.679513\pi$
$572$	−1.52438	−	2.71179i	−0.0637377	−	0.113385i
$573$		0			0
$574$	9.54096	+	16.5254i	0.398232	+	0.689758i
$575$	0.537500	+	0.930977i	0.0224153	+	0.0388244i
$576$		0			0
$577$	28.2497			1.17605			0.588025	−	0.808843i	$-0.299906\pi$
$577$	28.2497			1.17605			0.588025	+	0.808843i	$0.299906\pi$
$578$	−9.95041	+	17.2346i	−0.413882	+	0.716865i
$579$		0			0
$580$	20.1727			0.837625
$581$	11.1868	−	19.3761i	0.464108	−	0.803858i
$582$		0			0
$583$	0.702018	+	1.21593i	0.0290746	+	0.0503587i
$584$	−8.09081			−0.334800
$585$		0			0
$586$	−40.8441			−1.68725
$587$	0.397524	+	0.688532i	0.0164076	+	0.0284188i	0.874113	−	0.485723i	$-0.161444\pi$
$587$	0.397524	+	0.688532i	0.0164076	+	0.0284188i	−0.857705	+	0.514142i	$0.828110\pi$
$588$		0			0
$589$	−2.32217	+	4.02212i	−0.0956833	+	0.165728i
$590$	−10.7442			−0.442332
$591$		0			0
$592$	3.72853	−	6.45800i	0.153241	−	0.265422i
$593$	36.0924			1.48214			0.741068	−	0.671430i	$-0.234320\pi$
$593$	36.0924			1.48214			0.741068	+	0.671430i	$0.234320\pi$
$594$		0			0
$595$	−3.76716	−	6.52490i	−0.154438	−	0.267495i
$596$	0.836242	+	1.44841i	0.0342538	+	0.0593294i
$597$		0			0
$598$	8.22747	+	0.0945244i	0.336446	+	0.00386539i
$599$	2.37758			0.0971454			0.0485727	−	0.998820i	$-0.484533\pi$
$599$	2.37758			0.0971454			0.0485727	+	0.998820i	$0.484533\pi$
$600$		0			0
$601$	−14.0688	−	24.3679i	−0.573880	−	0.993989i	−0.996162	−	0.0875246i	$-0.972104\pi$
$601$	−14.0688	−	24.3679i	−0.573880	−	0.993989i	0.422283	−	0.906464i	$-0.361229\pi$
$602$	9.14817	−	15.8451i	0.372852	−	0.645798i
$603$		0			0
$604$	19.9507	−	34.5556i	0.811781	−	1.40605i
$605$	−5.44075	+	9.42365i	−0.221198	+	0.383126i
$606$		0			0
$607$	−4.57022	+	7.91586i	−0.185500	+	0.321295i	−0.943745	−	0.330675i	$-0.892724\pi$
$607$	−4.57022	+	7.91586i	−0.185500	+	0.321295i	0.758245	+	0.651970i	$0.226057\pi$
$608$	2.01216	+	3.48517i	0.0816039	+	0.141342i
$609$		0			0
$610$	10.9778			0.444477
$611$	−7.53303	−	13.4008i	−0.304754	−	0.542138i
$612$		0			0
$613$	19.3652	+	33.5415i	0.782153	+	1.35473i	0.930685	+	0.365821i	$0.119212\pi$
$613$	19.3652	+	33.5415i	0.782153	+	1.35473i	−0.148532	+	0.988908i	$0.547455\pi$
$614$	17.4856	+	30.2860i	0.705663	+	1.22224i
$615$		0			0
$616$	−0.542898			−0.0218740
$617$	18.8173	−	32.5924i	0.757554	−	1.31212i	−0.186541	−	0.982447i	$-0.559728\pi$
$617$	18.8173	−	32.5924i	0.757554	−	1.31212i	0.944095	−	0.329675i	$-0.106939\pi$
$618$		0			0
$619$	33.3469			1.34033			0.670163	−	0.742214i	$-0.266224\pi$
$619$	33.3469			1.34033			0.670163	+	0.742214i	$0.266224\pi$
$620$	11.4935	−	19.9073i	0.461589	−	0.799495i
$621$		0			0
$622$	10.1319	+	17.5489i	0.406251	+	0.703647i
$623$	−17.5313			−0.702376
$624$		0			0
$625$	1.00000			0.0400000
$626$	−23.2521	−	40.2738i	−0.929340	−	1.60966i
$627$		0			0
$628$	−21.8823	+	37.9012i	−0.873197	+	1.51242i
$629$	−14.0242			−0.559180
$630$		0			0
$631$	18.5301	−	32.0951i	0.737673	−	1.27769i	−0.215867	−	0.976423i	$-0.569258\pi$
$631$	18.5301	−	32.0951i	0.737673	−	1.27769i	0.953541	−	0.301265i	$-0.0974088\pi$
$632$	0.897533			0.0357019
$633$		0			0
$634$	−28.7984	−	49.8803i	−1.14373	−	1.98100i
$635$	−10.5067	−	18.1982i	−0.416947	−	0.722173i
$636$		0			0
$637$	−8.91266	+	15.0356i	−0.353132	+	0.595732i
$638$	5.88150			0.232851
$639$		0			0
$640$	−4.16216	−	7.20907i	−0.164524	−	0.284964i
$641$	−17.0532	+	29.5370i	−0.673561	+	1.16664i	0.303326	+	0.952887i	$0.401903\pi$
$641$	−17.0532	+	29.5370i	−0.673561	+	1.16664i	−0.976887	+	0.213756i	$0.931430\pi$
$642$		0			0
$643$	−3.63742	+	6.30019i	−0.143446	+	0.248455i	−0.928792	−	0.370601i	$-0.879152\pi$
$643$	−3.63742	+	6.30019i	−0.143446	+	0.248455i	0.785346	+	0.619057i	$0.212485\pi$
$644$	1.97642	−	3.42325i	0.0778817	−	0.134895i
$645$		0			0
$646$	2.76040	−	4.78115i	0.108606	−	0.188112i
$647$	−23.3891	−	40.5111i	−0.919521	−	1.59266i	−0.800144	−	0.599808i	$-0.795244\pi$
$647$	−23.3891	−	40.5111i	−0.919521	−	1.59266i	−0.119377	−	0.992849i	$-0.538090\pi$
$648$		0			0
$649$	−1.74228			−0.0683907
$650$	3.90288	−	6.58413i	0.153084	−	0.258251i
$651$		0			0
$652$	−18.2447	−	31.6008i	−0.714519	−	1.23758i
$653$	0.899891	+	1.55866i	0.0352154	+	0.0609949i	0.883096	−	0.469192i	$-0.155455\pi$
$653$	0.899891	+	1.55866i	0.0352154	+	0.0609949i	−0.847881	+	0.530187i	$0.822122\pi$
$654$		0			0
$655$	−13.4726			−0.526420
$656$	−8.36586	+	14.4901i	−0.326632	+	0.565743i
$657$		0			0
$658$	−13.2786			−0.517652
$659$	−13.6361	+	23.6184i	−0.531186	+	0.920041i	0.468152	+	0.883648i	$0.344920\pi$
$659$	−13.6361	+	23.6184i	−0.531186	+	0.920041i	−0.999338	+	0.0363930i	$0.988413\pi$
$660$		0			0
$661$	−12.0632	−	20.8941i	−0.469204	−	0.812686i	0.530176	−	0.847888i	$-0.322126\pi$
$661$	−12.0632	−	20.8941i	−0.469204	−	0.812686i	−0.999380	+	0.0352019i	$0.988793\pi$
$662$	2.41565			0.0938870
$663$		0			0
$664$	−16.3944			−0.636225
$665$	0.371461	+	0.643390i	0.0144046	+	0.0249496i
$666$		0			0
$667$	−4.32605	+	7.49293i	−0.167505	+	0.290128i
$668$	−38.9021			−1.50517
$669$		0			0
$670$	1.27071	−	2.20094i	0.0490920	−	0.0850298i
$671$	1.78016			0.0687224
$672$		0			0
$673$	−19.4433	−	33.6768i	−0.749485	−	1.29815i	−0.948070	−	0.318063i	$-0.896968\pi$
$673$	−19.4433	−	33.6768i	−0.749485	−	1.29815i	0.198584	−	0.980084i	$-0.436366\pi$
$674$	28.6238	+	49.5779i	1.10255	+	1.90967i
$675$		0			0
$676$	−15.6390	−	28.5847i	−0.601500	−	1.09941i
$677$	−23.0788			−0.886991			−0.443495	−	0.896277i	$-0.646262\pi$
$677$	−23.0788			−0.886991			−0.443495	+	0.896277i	$0.646262\pi$
$678$		0			0
$679$	1.02736	+	1.77944i	0.0394265	+	0.0682887i
$680$	−2.76040	+	4.78115i	−0.105856	+	0.183349i
$681$		0			0
$682$	3.35101	−	5.80412i	0.128317	−	0.222251i
$683$	−0.457785	+	0.792906i	−0.0175166	+	0.0303397i	−0.874651	−	0.484753i	$-0.838909\pi$
$683$	−0.457785	+	0.792906i	−0.0175166	+	0.0303397i	0.857134	+	0.515093i	$0.172243\pi$
$684$		0			0
$685$	−5.10101	+	8.83521i	−0.194900	+	0.337576i
$686$	18.4489	+	31.9544i	0.704381	+	1.22002i
$687$		0			0
$688$	16.0429			0.611630
$689$	7.20612	+	12.8193i	0.274531	+	0.488375i
$690$		0			0
$691$	−3.58980	−	6.21771i	−0.136562	−	0.236533i	0.789631	−	0.613582i	$-0.210272\pi$
$691$	−3.58980	−	6.21771i	−0.136562	−	0.236533i	−0.926193	+	0.377049i	$0.876939\pi$
$692$	−10.4340	−	18.0722i	−0.396641	−	0.687003i
$693$		0			0
$694$	13.8704			0.526512
$695$	6.07601	−	10.5240i	0.230476	−	0.399196i
$696$		0			0
$697$	31.4667			1.19188
$698$	1.12263	−	1.94446i	0.0424923	−	0.0735989i
$699$		0			0
$700$	−1.83853	−	3.18442i	−0.0694898	−	0.120360i
$701$	−32.6040			−1.23143			−0.615717	−	0.787967i	$-0.711134\pi$
$701$	−32.6040			−1.23143			−0.615717	+	0.787967i	$0.711134\pi$
$702$		0			0
$703$	1.38286			0.0521554
$704$	−1.96362	−	3.40109i	−0.0740066	−	0.128183i
$705$		0			0
$706$	−26.0775	+	45.1675i	−0.981440	+	1.69990i
$707$	−14.8086			−0.556934
$708$		0			0
$709$	−1.75954	+	3.04762i	−0.0660811	+	0.114456i	−0.897173	−	0.441679i	$-0.854383\pi$
$709$	−1.75954	+	3.04762i	−0.0660811	+	0.114456i	0.831092	+	0.556135i	$0.187716\pi$
$710$	0.946296			0.0355139
$711$		0			0
$712$	6.42306	+	11.1251i	0.240714	+	0.416929i
$713$	4.92957	+	8.53826i	0.184614	+	0.319760i
$714$		0			0
$715$	0.632893	−	1.06769i	0.0236689	−	0.0399292i
$716$	63.3184			2.36632
$717$		0			0
$718$	7.90439	+	13.6908i	0.294989	+	0.510937i
$719$	10.7649	−	18.6453i	0.401462	−	0.695352i	−0.592441	−	0.805614i	$-0.701836\pi$
$719$	10.7649	−	18.6453i	0.401462	−	0.695352i	0.993903	+	0.110262i	$0.0351689\pi$
$720$		0			0
$721$	−11.4132	+	19.7682i	−0.425049	+	0.736206i
$722$	19.8947	−	34.4586i	0.740403	−	1.28242i
$723$		0			0
$724$	27.0742	−	46.8939i	1.00621	−	1.74280i
$725$	4.02423	+	6.97018i	0.149456	+	0.258866i
$726$		0			0
$727$	51.8935			1.92462			0.962312	−	0.271948i	$-0.0876679\pi$
$727$	51.8935			1.92462			0.962312	+	0.271948i	$0.0876679\pi$
$728$	−5.68593	−	0.0653250i	−0.210734	−	0.00242110i
$729$		0			0
$730$	−7.98857	−	13.8366i	−0.295670	−	0.512116i
$731$	−15.0856	−	26.1290i	−0.557961	−	0.966417i
$732$		0			0
$733$	−22.8890			−0.845423			−0.422711	−	0.906264i	$-0.638922\pi$
$733$	−22.8890			−0.845423			−0.422711	+	0.906264i	$0.638922\pi$
$734$	0.0473193	−	0.0819594i	0.00174659	−	0.00302518i
$735$		0			0
$736$	8.54295			0.314897
$737$	0.206060	−	0.356906i	0.00759031	−	0.0131468i
$738$		0			0
$739$	−12.7987	−	22.1680i	−0.470807	−	0.815462i	0.528635	−	0.848849i	$-0.322704\pi$
$739$	−12.7987	−	22.1680i	−0.470807	−	0.815462i	−0.999443	+	0.0333870i	$0.989371\pi$
$740$	−6.84438			−0.251604
$741$		0			0
$742$	12.7023			0.466317
$743$	14.0506	+	24.3364i	0.515467	+	0.892815i	0.999839	+	0.0179525i	$0.00571475\pi$
$743$	14.0506	+	24.3364i	0.515467	+	0.892815i	−0.484372	+	0.874862i	$0.660952\pi$
$744$		0			0
$745$	−0.333643	+	0.577886i	−0.0122237	+	0.0211721i
$746$	−7.09525			−0.259776
$747$		0			0
$748$	−2.21551	+	3.83738i	−0.0810071	+	0.140308i
$749$	−3.10093			−0.113306
$750$		0			0
$751$	−4.93493	−	8.54755i	−0.180078	−	0.311905i	0.761829	−	0.647778i	$-0.224302\pi$
$751$	−4.93493	−	8.54755i	−0.180078	−	0.311905i	−0.941907	+	0.335874i	$0.890968\pi$
$752$	−5.82156	−	10.0832i	−0.212291	−	0.367698i
$753$		0			0
$754$	61.5986	+	0.707699i	2.24329	+	0.0257729i
$755$	15.9198			0.579380
$756$		0			0
$757$	−0.930521	−	1.61171i	−0.0338204	−	0.0585786i	0.848620	−	0.529003i	$-0.177434\pi$
$757$	−0.930521	−	1.61171i	−0.0338204	−	0.0585786i	−0.882440	+	0.470425i	$0.844101\pi$
$758$	27.8293	−	48.2017i	1.01080	−	1.75076i
$759$		0			0
$760$	0.272190	−	0.471446i	0.00987335	−	0.0171012i
$761$	−15.8963	+	27.5332i	−0.576240	+	0.998077i	0.419666	+	0.907679i	$0.362147\pi$
$761$	−15.8963	+	27.5332i	−0.576240	+	0.998077i	−0.995906	+	0.0903983i	$0.971186\pi$
$762$		0			0
$763$	−3.02593	+	5.24106i	−0.109546	+	0.189739i
$764$	11.6729	+	20.2180i	0.422310	+	0.731463i
$765$		0			0
$766$	−27.3826			−0.989373
$767$	−18.2474	−	0.209643i	−0.658877	−	0.00756976i
$768$		0			0
$769$	9.66750	+	16.7446i	0.348619	+	0.603826i	0.986004	−	0.166719i	$-0.0533174\pi$
$769$	9.66750	+	16.7446i	0.348619	+	0.603826i	−0.637385	+	0.770545i	$0.719984\pi$
$770$	−0.536037	−	0.928444i	−0.0193174	−	0.0334588i
$771$		0			0
$772$	−19.0488			−0.685582
$773$	−0.820176	+	1.42059i	−0.0294997	+	0.0510949i	−0.880398	−	0.474235i	$-0.842725\pi$
$773$	−0.820176	+	1.42059i	−0.0294997	+	0.0510949i	0.850899	+	0.525330i	$0.176058\pi$
$774$		0			0
$775$	9.17129			0.329443
$776$	0.752803	−	1.30389i	0.0270240	−	0.0468070i
$777$		0			0
$778$	5.39812	+	9.34982i	0.193532	+	0.335207i
$779$	−3.10278			−0.111169
$780$		0			0
$781$	0.153452			0.00549094
$782$	−5.85985	−	10.1496i	−0.209548	−	0.362947i
$783$		0			0
$784$	−6.61897	+	11.4644i	−0.236392	+	0.409443i
$785$	−17.4611			−0.623214
$786$		0			0
$787$	16.1460	−	27.9657i	0.575544	−	0.996871i	−0.420439	−	0.907321i	$-0.638124\pi$
$787$	16.1460	−	27.9657i	0.575544	−	0.996871i	0.995982	−	0.0895500i	$-0.0285429\pi$
$788$	−27.4282			−0.977089
$789$		0			0
$790$	0.886190	+	1.53493i	0.0315292	+	0.0546102i
$791$	−8.35602	−	14.4731i	−0.297106	−	0.514602i
$792$		0			0
$793$	18.6441	+	0.214200i	0.662073	+	0.00760648i
$794$	−23.4874			−0.833535
$795$		0			0
$796$	17.7914	+	30.8156i	0.630600	+	1.09223i
$797$	20.5207	−	35.5429i	0.726880	−	1.25899i	−0.231315	−	0.972879i	$-0.574303\pi$
$797$	20.5207	−	35.5429i	0.726880	−	1.25899i	0.958195	−	0.286115i	$-0.0923638\pi$
$798$		0			0
$799$	−10.9484	+	18.9631i	−0.387325	+	0.670867i
$800$	3.97347	−	6.88225i	0.140483	−	0.243324i
$801$		0			0
$802$	−24.5137	+	42.4589i	−0.865607	+	1.49928i
$803$	−1.29543	−	2.24375i	−0.0457147	−	0.0791803i
$804$		0			0
$805$	1.57710			0.0555853
$806$	35.7945	−	60.3850i	1.26081	−	2.12697i
$807$		0			0
$808$	5.42553	+	9.39729i	0.190869	+	0.330595i
$809$	11.3191	+	19.6052i	0.397958	+	0.689283i	0.993474	−	0.114060i	$-0.0363857\pi$
$809$	11.3191	+	19.6052i	0.397958	+	0.689283i	−0.595516	+	0.803343i	$0.703052\pi$
$810$		0			0
$811$	−6.81520			−0.239314			−0.119657	−	0.992815i	$-0.538180\pi$
$811$	−6.81520			−0.239314			−0.119657	+	0.992815i	$0.538180\pi$
$812$	14.7973	−	25.6297i	0.519285	−	0.899427i
$813$		0			0
$814$	−1.99553			−0.0699433
$815$	7.27927	−	12.6081i	0.254982	−	0.441641i
$816$		0			0
$817$	1.48752	+	2.57646i	0.0520417	+	0.0901389i
$818$	30.6136			1.07038
$819$		0			0
$820$	15.3570			0.536291
$821$	21.0056	+	36.3827i	0.733100	+	1.26977i	0.955552	+	0.294822i	$0.0952605\pi$
$821$	21.0056	+	36.3827i	0.733100	+	1.26977i	−0.222452	+	0.974944i	$0.571406\pi$
$822$		0			0
$823$	−16.9766	+	29.4043i	−0.591766	+	1.02497i	0.402228	+	0.915539i	$0.368236\pi$
$823$	−16.9766	+	29.4043i	−0.591766	+	1.02497i	−0.993995	+	0.109430i	$0.965098\pi$
$824$	16.7261			0.582681
$825$		0			0
$826$	−7.88123	+	13.6507i	−0.274223	+	0.474968i
$827$	−24.6063			−0.855644			−0.427822	−	0.903863i	$-0.640719\pi$
$827$	−24.6063			−0.855644			−0.427822	+	0.903863i	$0.640719\pi$
$828$		0			0
$829$	7.42428	+	12.8592i	0.257856	+	0.446619i	0.965667	−	0.259782i	$-0.0836507\pi$
$829$	7.42428	+	12.8592i	0.257856	+	0.446619i	−0.707811	+	0.706401i	$0.750317\pi$
$830$	−16.1872	−	28.0370i	−0.561866	−	0.973180i
$831$		0			0
$832$	−20.1563	−	35.8568i	−0.698793	−	1.24311i
$833$	24.8961			0.862597
$834$		0			0
$835$	−7.76055	−	13.4417i	−0.268565	−	0.465168i
$836$	0.218461	−	0.378385i	0.00755563	−	0.0130867i
$837$		0			0
$838$	−16.1000	+	27.8860i	−0.556166	+	0.963307i
$839$	3.61789	−	6.26637i	0.124903	−	0.216339i	−0.796792	−	0.604254i	$-0.793471\pi$
$839$	3.61789	−	6.26637i	0.124903	−	0.216339i	0.921695	+	0.387915i	$0.126805\pi$
$840$		0			0
$841$	−17.8889	+	30.9845i	−0.616859	+	1.06843i
$842$	−11.4322	−	19.8011i	−0.393979	−	0.682391i
$843$		0			0
$844$	25.8906			0.891191
$845$	6.75694	−	11.1060i	0.232446	−	0.382059i
$846$		0			0
$847$	7.98195	+	13.8251i	0.274263	+	0.475037i
$848$	5.56893	+	9.64567i	0.191238	+	0.331234i
$849$		0			0
$850$	−10.9021			−0.373937
$851$	1.46778	−	2.54227i	0.0503149	−	0.0871480i
$852$		0			0
$853$	36.9206			1.26414			0.632068	−	0.774913i	$-0.282206\pi$
$853$	36.9206			1.26414			0.632068	+	0.774913i	$0.282206\pi$
$854$	8.05256	−	13.9474i	0.275553	−	0.477272i
$855$		0			0
$856$	1.13611	+	1.96780i	0.0388314	+	0.0672580i
$857$	16.2642			0.555573			0.277786	−	0.960643i	$-0.410399\pi$
$857$	16.2642			0.555573			0.277786	+	0.960643i	$0.410399\pi$
$858$		0			0
$859$	25.2975			0.863141			0.431571	−	0.902079i	$-0.357960\pi$
$859$	25.2975			0.863141			0.431571	+	0.902079i	$0.357960\pi$
$860$	−7.36240	−	12.7521i	−0.251056	−	0.434842i
$861$		0			0
$862$	−43.8512	+	75.9524i	−1.49358	+	2.58695i
$863$	55.7647			1.89825			0.949127	−	0.314894i	$-0.101969\pi$
$863$	55.7647			1.89825			0.949127	+	0.314894i	$0.101969\pi$
$864$		0			0
$865$	4.16295	−	7.21044i	0.141544	−	0.245162i
$866$	39.1713			1.33109
$867$		0			0
$868$	−16.8617	−	29.2053i	−0.572323	−	0.991292i
$869$	0.143705	+	0.248905i	0.00487486	+	0.00844351i
$870$		0			0
$871$	2.20107	−	3.71318i	0.0745804	−	0.125816i
$872$	4.43452			0.150172
$873$		0			0
$874$	0.577812	+	1.00080i	0.0195448	+	0.0338525i
$875$	0.733534	−	1.27052i	0.0247980	−	0.0429513i
$876$		0			0
$877$	−15.7171	+	27.2227i	−0.530727	+	0.919246i	0.468630	+	0.883395i	$0.344748\pi$
$877$	−15.7171	+	27.2227i	−0.530727	+	0.919246i	−0.999357	+	0.0358518i	$0.988586\pi$
$878$	−8.36542	+	14.4893i	−0.282319	+	0.488991i
$879$		0			0
$880$	0.470017	−	0.814094i	0.0158443	−	0.0274431i
$881$	−15.5090	−	26.8624i	−0.522512	−	0.905018i	−0.999657	−	0.0261932i	$-0.991662\pi$
$881$	−15.5090	−	26.8624i	−0.522512	−	0.905018i	0.477145	−	0.878825i	$-0.341672\pi$
$882$		0			0
$883$	−43.7232			−1.47140			−0.735701	−	0.677307i	$-0.763147\pi$
$883$	−43.7232			−1.47140			−0.735701	+	0.677307i	$0.763147\pi$
$884$	−23.6654	+	39.9234i	−0.795954	+	1.34277i
$885$		0			0
$886$	40.6276	+	70.3691i	1.36491	+	2.36409i
$887$	−9.12624	−	15.8071i	−0.306429	−	0.530751i	0.671149	−	0.741322i	$-0.265801\pi$
$887$	−9.12624	−	15.8071i	−0.306429	−	0.530751i	−0.977578	+	0.210571i	$0.932468\pi$
$888$		0			0
$889$	−30.8282			−1.03394
$890$	−12.6838	+	21.9689i	−0.425161	+	0.736401i
$891$		0			0
$892$	61.4221			2.05657
$893$	1.07957	−	1.86986i	0.0361263	−	0.0625726i
$894$		0			0
$895$	12.6313	+	21.8781i	0.422219	+	0.731305i
$896$	−12.2123			−0.407986
$897$		0			0
$898$	−26.6296			−0.888640
$899$	36.9074	+	63.9255i	1.23093	+	2.13204i
$900$		0			0
$901$	10.4733	−	18.1402i	0.348915	−	0.604338i
$902$	4.47746			0.149083
$903$		0			0
$904$	−6.12291	+	10.6052i	−0.203645	+	0.352723i
$905$	21.6041			0.718144
$906$		0			0
$907$	−9.08126	−	15.7292i	−0.301538	−	0.522280i	0.674946	−	0.737867i	$-0.264167\pi$
$907$	−9.08126	−	15.7292i	−0.301538	−	0.522280i	−0.976485	+	0.215587i	$0.930833\pi$
$908$	3.76616	+	6.52319i	0.124985	+	0.216480i
$909$		0			0
$910$	−5.50235	−	9.78836i	−0.182401	−	0.324481i
$911$	43.3147			1.43508			0.717541	−	0.696517i	$-0.245268\pi$
$911$	43.3147			1.43508			0.717541	+	0.696517i	$0.245268\pi$
$912$		0			0
$913$	−2.62493	−	4.54650i	−0.0868723	−	0.150467i
$914$	21.5135	−	37.2624i	0.711602	−	1.23253i
$915$		0			0
$916$	27.5380	−	47.6972i	0.909880	−	1.57596i
$917$	−9.88263	+	17.1172i	−0.326353	+	0.565261i
$918$		0			0
$919$	−2.05975	+	3.56759i	−0.0679449	+	0.117684i	−0.897997	−	0.440003i	$-0.854978\pi$
$919$	−2.05975	+	3.56759i	−0.0679449	+	0.117684i	0.830052	+	0.557687i	$0.188311\pi$
$920$	−0.577812	−	1.00080i	−0.0190499	−	0.0329954i
$921$		0			0
$922$	−26.5356			−0.873903
$923$	1.60715	+	0.0184643i	0.0528999	+	0.000607760i
$924$		0			0
$925$	−1.36538	−	2.36491i	−0.0448934	−	0.0777577i
$926$	16.0192	+	27.7461i	0.526424	+	0.911793i
$927$		0			0
$928$	63.9606			2.09961
$929$	24.1733	−	41.8694i	0.793101	−	1.37369i	−0.130938	−	0.991391i	$-0.541799\pi$
$929$	24.1733	−	41.8694i	0.793101	−	1.37369i	0.924038	−	0.382300i	$-0.124868\pi$
$930$		0			0
$931$	−2.45488			−0.0804554
$932$	9.05277	−	15.6799i	0.296533	−	0.513611i
$933$		0			0
$934$	15.7961	+	27.3596i	0.516864	+	0.895234i
$935$	−1.76788			−0.0578160
$936$		0			0
$937$	−17.7174			−0.578801			−0.289401	−	0.957208i	$-0.593456\pi$
$937$	−17.7174			−0.578801			−0.289401	+	0.957208i	$0.593456\pi$
$938$	−1.86422	−	3.22893i	−0.0608691	−	0.105428i
$939$		0			0
$940$	−5.34326	+	9.25480i	−0.174278	+	0.301858i
$941$	−25.7342			−0.838912			−0.419456	−	0.907776i	$-0.637779\pi$
$941$	−25.7342			−0.838912			−0.419456	+	0.907776i	$0.637779\pi$
$942$		0			0
$943$	−3.29333	+	5.70422i	−0.107246	+	0.185755i
$944$	−13.8211			−0.449839
$945$		0			0
$946$	−2.14657	−	3.71796i	−0.0697909	−	0.120881i
$947$	24.1941	+	41.9054i	0.786203	+	1.36174i	0.928278	+	0.371888i	$0.121289\pi$
$947$	24.1941	+	41.9054i	0.786203	+	1.36174i	−0.142075	+	0.989856i	$0.545377\pi$
$948$		0			0
$949$	−13.2974	−	23.6553i	−0.431653	−	0.767884i
$950$	1.07500			0.0348776
$951$		0			0
$952$	4.04969	+	7.01427i	0.131251	+	0.227334i
$953$	−6.91281	+	11.9733i	−0.223928	+	0.387854i	−0.955997	−	0.293376i	$-0.905221\pi$
$953$	−6.91281	+	11.9733i	−0.223928	+	0.387854i	0.732069	+	0.681230i	$0.238555\pi$
$954$		0			0
$955$	−4.65724	+	8.06657i	−0.150705	+	0.261028i
$956$	0.617781	−	1.07003i	0.0199805	−	0.0346072i
$957$		0			0
$958$	0.322840	−	0.559176i	0.0104305	−	0.0180662i
$959$	7.48353	+	12.9618i	0.241656	+	0.418560i
$960$		0			0
$961$	53.1126			1.71331
$962$	−20.8998	−	0.240115i	−0.673836	−	0.00774162i
$963$		0			0
$964$	32.9301	+	57.0366i	1.06061	+	1.83703i
$965$	−3.80004	−	6.58186i	−0.122327	−	0.211877i
$966$		0			0
$967$	−34.8289			−1.12002			−0.560010	−	0.828486i	$-0.689203\pi$
$967$	−34.8289			−1.12002			−0.560010	+	0.828486i	$0.689203\pi$
$968$	5.84880	−	10.1304i	0.187988	−	0.325604i
$969$		0			0
$970$	2.97316			0.0954623
$971$	−3.90970	+	6.77180i	−0.125468	+	0.217317i	−0.921916	−	0.387390i	$-0.873377\pi$
$971$	−3.90970	+	6.77180i	−0.125468	+	0.217317i	0.796448	+	0.604708i	$0.206710\pi$
$972$		0			0
$973$	−8.91391	−	15.4393i	−0.285767	−	0.494963i
$974$	88.5566			2.83754
$975$		0			0
$976$	14.1216			0.452020
$977$	2.45793	+	4.25727i	0.0786363	+	0.136202i	0.902662	−	0.430351i	$-0.141610\pi$
$977$	2.45793	+	4.25727i	0.0786363	+	0.136202i	−0.824026	+	0.566553i	$0.808277\pi$
$978$		0			0
$979$	−2.05681	+	3.56250i	−0.0657359	+	0.113858i
$980$	12.1503			0.388127
$981$		0			0
$982$	43.0505	−	74.5656i	1.37380	−	2.37948i
$983$	5.23823			0.167074			0.0835368	−	0.996505i	$-0.473378\pi$
$983$	5.23823			0.167074			0.0835368	+	0.996505i	$0.473378\pi$
$984$		0			0
$985$	−5.47163	−	9.47715i	−0.174341	−	0.301967i
$986$	−43.8724	−	75.9892i	−1.39718	−	2.41999i
$987$		0			0
$988$	2.33353	−	3.93665i	0.0742396	−	0.125242i
$989$	6.31550			0.200821
$990$		0			0
$991$	0.889392	+	1.54047i	0.0282525	+	0.0489347i	0.879806	−	0.475333i	$-0.157672\pi$
$991$	0.889392	+	1.54047i	0.0282525	+	0.0489347i	−0.851553	+	0.524268i	$0.824339\pi$
$992$	36.4418	−	63.1191i	1.15703	−	2.00403i
$993$		0			0
$994$	0.694140	−	1.20229i	0.0220168	−	0.0381342i
$995$	−7.09839	+	12.2948i	−0.225034	+	0.389771i
$996$		0			0
$997$	−21.9585	+	38.0333i	−0.695434	+	1.20453i	0.274601	+	0.961558i	$0.411454\pi$
$997$	−21.9585	+	38.0333i	−0.695434	+	1.20453i	−0.970034	+	0.242968i	$0.921879\pi$
$998$	−23.0580	−	39.9376i	−0.729888	−	1.26420i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.j.i.406.1	yes	10
3.2	odd	2		585.2.j.h.406.5	✓	10
13.3	even	3		7605.2.a.cm.1.5		5
13.9	even	3	inner	585.2.j.i.451.1	yes	10
13.10	even	6		7605.2.a.cn.1.1		5
39.23	odd	6		7605.2.a.cl.1.5		5
39.29	odd	6		7605.2.a.co.1.1		5
39.35	odd	6		585.2.j.h.451.5	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.j.h.406.5	✓	10	3.2	odd	2
585.2.j.h.451.5	yes	10	39.35	odd	6
585.2.j.i.406.1	yes	10	1.1	even	1	trivial
585.2.j.i.451.1	yes	10	13.9	even	3	inner
7605.2.a.cl.1.5		5	39.23	odd	6
7605.2.a.cm.1.5		5	13.3	even	3
7605.2.a.cn.1.1		5	13.10	even	6
7605.2.a.co.1.1		5	39.29	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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.06141 - 1.83842i) q^{2} +(-1.25320 + 2.17061i) q^{4} -1.00000 q^{5} +(-0.733534 + 1.27052i) q^{7} +1.07500 q^{8} +O(q^{10})\)	\(q+(-1.06141 - 1.83842i) q^{2} +(-1.25320 + 2.17061i) q^{4} -1.00000 q^{5} +(-0.733534 + 1.27052i) q^{7} +1.07500 q^{8} +(1.06141 + 1.83842i) q^{10} +(0.172120 + 0.298120i) q^{11} +(1.76679 + 3.14300i) q^{13} +3.11433 q^{14} +(1.36538 + 2.36491i) q^{16} +(2.56781 - 4.44758i) q^{17} +(-0.253200 + 0.438555i) q^{19} +(1.25320 - 2.17061i) q^{20} +(0.365380 - 0.632857i) q^{22} +(0.537500 + 0.930977i) q^{23} +1.00000 q^{25} +(3.90288 - 6.58413i) q^{26} +(-1.83853 - 3.18442i) q^{28} +(4.02423 + 6.97018i) q^{29} +9.17129 q^{31} +(3.97347 - 6.88225i) q^{32} -10.9021 q^{34} +(0.733534 - 1.27052i) q^{35} +(-1.36538 - 2.36491i) q^{37} +1.07500 q^{38} -1.07500 q^{40} +(3.06357 + 5.30625i) q^{41} +(2.93744 - 5.08780i) q^{43} -0.862801 q^{44} +(1.14102 - 1.97630i) q^{46} -4.26369 q^{47} +(2.42386 + 4.19824i) q^{49} +(-1.06141 - 1.83842i) q^{50} +(-9.03636 - 0.103818i) q^{52} +4.07866 q^{53} +(-0.172120 - 0.298120i) q^{55} +(-0.788548 + 1.36581i) q^{56} +(8.54276 - 14.7965i) q^{58} +(-2.53063 + 4.38318i) q^{59} +(2.58565 - 4.47847i) q^{61} +(-9.73454 - 16.8607i) q^{62} -11.4085 q^{64} +(-1.76679 - 3.14300i) q^{65} +(-0.598595 - 1.03680i) q^{67} +(6.43597 + 11.1474i) q^{68} -3.11433 q^{70} +(0.222886 - 0.386049i) q^{71} -7.52634 q^{73} +(-2.89847 + 5.02029i) q^{74} +(-0.634620 - 1.09919i) q^{76} -0.505022 q^{77} +0.834915 q^{79} +(-1.36538 - 2.36491i) q^{80} +(6.50342 - 11.2643i) q^{82} -15.2506 q^{83} +(-2.56781 + 4.44758i) q^{85} -12.4714 q^{86} +(0.185028 + 0.320479i) q^{88} +(5.97494 + 10.3489i) q^{89} +(-5.28924 - 0.0607674i) q^{91} -2.69438 q^{92} +(4.52554 + 7.83847i) q^{94} +(0.253200 - 0.438555i) q^{95} +(0.700282 - 1.21292i) q^{97} +(5.14543 - 8.91215i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{2} - 6 q^{4} - 10 q^{5} - q^{7} - 12 q^{8}+O(q^{10}) \) 10 * q + 2 * q^2 - 6 * q^4 - 10 * q^5 - q^7 - 12 * q^8	\( 10 q + 2 q^{2} - 6 q^{4} - 10 q^{5} - q^{7} - 12 q^{8} - 2 q^{10} + 8 q^{11} + q^{13} + 8 q^{14} - 4 q^{16} + 4 q^{19} + 6 q^{20} - 14 q^{22} - 6 q^{23} + 10 q^{25} + 10 q^{26} + 2 q^{28} + 16 q^{29} + 18 q^{31} + 14 q^{32} + q^{35} + 4 q^{37} - 12 q^{38} + 12 q^{40} + 6 q^{41} - 15 q^{43} - 28 q^{44} + 16 q^{46} - 20 q^{47} - 10 q^{49} + 2 q^{50} - 22 q^{52} + 40 q^{53} - 8 q^{55} - 2 q^{56} + 4 q^{58} + 12 q^{59} - 11 q^{61} - 22 q^{62} + 8 q^{64} - q^{65} - 5 q^{67} + 50 q^{68} - 8 q^{70} + 10 q^{71} + 2 q^{73} - 26 q^{74} - 24 q^{76} - 84 q^{77} - 34 q^{79} + 4 q^{80} - 16 q^{82} - 32 q^{83} - 88 q^{86} - 20 q^{88} + 4 q^{89} - q^{91} + 68 q^{92} + 16 q^{94} - 4 q^{95} + 11 q^{97} + 30 q^{98}+O(q^{100}) \) 10 * q + 2 * q^2 - 6 * q^4 - 10 * q^5 - q^7 - 12 * q^8 - 2 * q^10 + 8 * q^11 + q^13 + 8 * q^14 - 4 * q^16 + 4 * q^19 + 6 * q^20 - 14 * q^22 - 6 * q^23 + 10 * q^25 + 10 * q^26 + 2 * q^28 + 16 * q^29 + 18 * q^31 + 14 * q^32 + q^35 + 4 * q^37 - 12 * q^38 + 12 * q^40 + 6 * q^41 - 15 * q^43 - 28 * q^44 + 16 * q^46 - 20 * q^47 - 10 * q^49 + 2 * q^50 - 22 * q^52 + 40 * q^53 - 8 * q^55 - 2 * q^56 + 4 * q^58 + 12 * q^59 - 11 * q^61 - 22 * q^62 + 8 * q^64 - q^65 - 5 * q^67 + 50 * q^68 - 8 * q^70 + 10 * q^71 + 2 * q^73 - 26 * q^74 - 24 * q^76 - 84 * q^77 - 34 * q^79 + 4 * q^80 - 16 * q^82 - 32 * q^83 - 88 * q^86 - 20 * q^88 + 4 * q^89 - q^91 + 68 * q^92 + 16 * q^94 - 4 * q^95 + 11 * q^97 + 30 * q^98

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