LMFDB - Embedded newform 260.2.bf.c.137.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [260,2,Mod(37,260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(260, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 7]))

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

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

chi := DirichletCharacter("260.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 260 = 2^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	260.bf (of order $12$, degree $4$, 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:	$2.07611045255$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 30 x^{18} + 371 x^{16} + 2460 x^{14} + 9517 x^{12} + 21870 x^{10} + 29001 x^{8} + 20400 x^{6} + \cdots + 9 $ x^20 + 30x^18 + 371x^16 + 2460x^14 + 9517x^12 + 21870x^10 + 29001x^8 + 20400x^6 + 6399x^4 + 666*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			137.5
Root			$1.49418i$ of defining polynomial
Character	$\chi$	$=$	260.137
Dual form			260.2.bf.c.93.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.674996 + 2.51912i) q^{3} +(-0.647383 + 2.14030i) q^{5} +(-0.839682 - 1.45437i) q^{7} +(-3.29226 + 1.90079i) q^{9} +O(q^{10})$	\(q+(0.674996 + 2.51912i) q^{3} +(-0.647383 + 2.14030i) q^{5} +(-0.839682 - 1.45437i) q^{7} +(-3.29226 + 1.90079i) q^{9} +(0.758596 + 2.83112i) q^{11} +(3.53133 - 0.727792i) q^{13} +(-5.82866 - 0.186138i) q^{15} +(-7.90430 - 2.11795i) q^{17} +(2.32093 + 0.621891i) q^{19} +(3.09695 - 3.09695i) q^{21} +(1.57340 - 0.421590i) q^{23} +(-4.16179 - 2.77119i) q^{25} +(-1.47820 - 1.47820i) q^{27} +(2.41580 + 1.39477i) q^{29} +(7.32419 + 7.32419i) q^{31} +(-6.61987 + 3.82198i) q^{33} +(3.65639 - 0.855639i) q^{35} +(2.08286 - 3.60763i) q^{37} +(4.21703 + 8.40459i) q^{39} +(4.77856 - 1.28041i) q^{41} +(0.786313 - 2.93456i) q^{43} +(-1.93691 - 8.27697i) q^{45} +10.5504 q^{47} +(2.08987 - 3.61976i) q^{49} -21.3415i q^{51} +(-6.66320 + 6.66320i) q^{53} +(-6.55055 - 0.209192i) q^{55} +6.26647i q^{57} +(-1.16609 + 4.35192i) q^{59} +(-2.16875 - 3.75639i) q^{61} +(5.52891 + 3.19211i) q^{63} +(-0.728428 + 8.02928i) q^{65} +(-4.28613 - 2.47460i) q^{67} +(2.12407 + 3.67900i) q^{69} +(1.63607 - 6.10591i) q^{71} -7.13327i q^{73} +(4.17176 - 12.3546i) q^{75} +(3.48052 - 3.48052i) q^{77} -9.73120i q^{79} +(-2.97638 + 5.15523i) q^{81} +6.67496 q^{83} +(9.65016 - 15.5465i) q^{85} +(-1.88292 + 7.02716i) q^{87} +(0.578139 - 0.154912i) q^{89} +(-4.02368 - 4.52476i) q^{91} +(-13.5067 + 23.3943i) q^{93} +(-2.83356 + 4.56489i) q^{95} +(-10.4508 + 6.03380i) q^{97} +(-7.87885 - 7.87885i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{3} - 6 q^{5} - 6 q^{7} + 12 q^{9}+O(q^{10}) $ 20 * q - 2 * q^3 - 6 * q^5 - 6 * q^7 + 12 * q^9	$ 20 q - 2 q^{3} - 6 q^{5} - 6 q^{7} + 12 q^{9} - 6 q^{13} + 20 q^{15} + 6 q^{17} - 20 q^{19} - 12 q^{21} + 30 q^{23} - 2 q^{25} - 20 q^{27} - 24 q^{29} + 8 q^{31} - 30 q^{33} + 30 q^{37} - 4 q^{39} + 6 q^{41} + 22 q^{43} + 36 q^{45} - 14 q^{49} + 30 q^{53} - 34 q^{55} + 24 q^{59} - 32 q^{61} - 84 q^{63} - 60 q^{65} - 54 q^{67} + 16 q^{69} + 26 q^{75} + 12 q^{77} + 2 q^{81} - 48 q^{83} + 74 q^{85} + 38 q^{87} + 30 q^{89} - 72 q^{91} - 16 q^{93} - 6 q^{95} - 6 q^{97} - 20 q^{99}+O(q^{100}) $ 20 * q - 2 * q^3 - 6 * q^5 - 6 * q^7 + 12 * q^9 - 6 * q^13 + 20 * q^15 + 6 * q^17 - 20 * q^19 - 12 * q^21 + 30 * q^23 - 2 * q^25 - 20 * q^27 - 24 * q^29 + 8 * q^31 - 30 * q^33 + 30 * q^37 - 4 * q^39 + 6 * q^41 + 22 * q^43 + 36 * q^45 - 14 * q^49 + 30 * q^53 - 34 * q^55 + 24 * q^59 - 32 * q^61 - 84 * q^63 - 60 * q^65 - 54 * q^67 + 16 * q^69 + 26 * q^75 + 12 * q^77 + 2 * q^81 - 48 * q^83 + 74 * q^85 + 38 * q^87 + 30 * q^89 - 72 * q^91 - 16 * q^93 - 6 * q^95 - 6 * q^97 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$.

$n$	$41$	$131$	$157$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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
$3$	0.674996	+	2.51912i	0.389709	+	1.45441i	0.830608	+	0.556857i	$0.187993\pi$
$3$	0.674996	+	2.51912i	0.389709	+	1.45441i	−0.440899	+	0.897557i	$0.645340\pi$
$4$		0			0
$5$	−0.647383	+	2.14030i	−0.289518	+	0.957172i
$5$	−0.647383	+	2.14030i	−0.289518	+	0.957172i
$6$		0			0
$7$	−0.839682	−	1.45437i	−0.317370	−	0.549701i	0.662568	−	0.749001i	$-0.269466\pi$
$7$	−0.839682	−	1.45437i	−0.317370	−	0.549701i	−0.979938	+	0.199300i	$0.936133\pi$
$8$		0			0
$9$	−3.29226	+	1.90079i	−1.09742	+	0.633596i
$10$		0			0
$11$	0.758596	+	2.83112i	0.228725	+	0.853614i	0.980878	+	0.194625i	$0.0623490\pi$
$11$	0.758596	+	2.83112i	0.228725	+	0.853614i	−0.752153	+	0.658989i	$0.770984\pi$
$12$		0			0
$13$	3.53133	−	0.727792i	0.979416	−	0.201853i
$13$	3.53133	−	0.727792i	0.979416	−	0.201853i
$14$		0			0
$15$	−5.82866	−	0.186138i	−1.50495	−	0.0480607i
$16$		0			0
$17$	−7.90430	−	2.11795i	−1.91707	−	0.513679i	−0.990488	−	0.137597i	$-0.956062\pi$
$17$	−7.90430	−	2.11795i	−1.91707	−	0.513679i	−0.926587	−	0.376082i	$-0.877271\pi$
$18$		0			0
$19$	2.32093	+	0.621891i	0.532458	+	0.142672i	0.515023	−	0.857176i	$-0.327783\pi$
$19$	2.32093	+	0.621891i	0.532458	+	0.142672i	0.0174347	+	0.999848i	$0.494450\pi$
$20$		0			0
$21$	3.09695	−	3.09695i	0.675811	−	0.675811i
$22$		0			0
$23$	1.57340	−	0.421590i	0.328076	−	0.0879077i	−0.0910215	−	0.995849i	$-0.529013\pi$
$23$	1.57340	−	0.421590i	0.328076	−	0.0879077i	0.419098	+	0.907941i	$0.362347\pi$
$24$		0			0
$25$	−4.16179	−	2.77119i	−0.832358	−	0.554238i
$26$		0			0
$27$	−1.47820	−	1.47820i	−0.284480	−	0.284480i
$28$		0			0
$29$	2.41580	+	1.39477i	0.448604	+	0.259001i	0.707240	−	0.706973i	$-0.249940\pi$
$29$	2.41580	+	1.39477i	0.448604	+	0.259001i	−0.258637	+	0.965975i	$0.583273\pi$
$30$		0			0
$31$	7.32419	+	7.32419i	1.31546	+	1.31546i	0.917326	+	0.398137i	$0.130343\pi$
$31$	7.32419	+	7.32419i	1.31546	+	1.31546i	0.398137	+	0.917326i	$0.369657\pi$
$32$		0			0
$33$	−6.61987	+	3.82198i	−1.15237	+	0.665322i
$34$		0			0
$35$	3.65639	−	0.855639i	0.618043	−	0.144629i
$36$		0			0
$37$	2.08286	−	3.60763i	0.342421	−	0.593090i	−0.642461	−	0.766318i	$-0.722087\pi$
$37$	2.08286	−	3.60763i	0.342421	−	0.593090i	0.984882	+	0.173228i	$0.0554199\pi$
$38$		0			0
$39$	4.21703	+	8.40459i	0.675265	+	1.34581i
$40$		0			0
$41$	4.77856	−	1.28041i	0.746286	−	0.199967i	0.134416	−	0.990925i	$-0.457084\pi$
$41$	4.77856	−	1.28041i	0.746286	−	0.199967i	0.611870	+	0.790958i	$0.290418\pi$
$42$		0			0
$43$	0.786313	−	2.93456i	0.119912	−	0.447516i	−0.879696	−	0.475537i	$-0.842254\pi$
$43$	0.786313	−	2.93456i	0.119912	−	0.447516i	0.999607	+	0.0280207i	$0.00892043\pi$
$44$		0			0
$45$	−1.93691	−	8.27697i	−0.288737	−	1.23386i
$46$		0			0
$47$	10.5504			1.53894			0.769469	−	0.638685i	$-0.220521\pi$
$47$	10.5504			1.53894			0.769469	+	0.638685i	$0.220521\pi$
$48$		0			0
$49$	2.08987	−	3.61976i	0.298553	−	0.517108i
$50$		0			0
$51$		−	21.3415i		−	2.98840i
$52$		0			0
$53$	−6.66320	+	6.66320i	−0.915261	+	0.915261i	−0.996680	−	0.0814188i	$-0.974055\pi$
$53$	−6.66320	+	6.66320i	−0.915261	+	0.915261i	0.0814188	+	0.996680i	$0.474055\pi$
$54$		0			0
$55$	−6.55055	−	0.209192i	−0.883276	−	0.0282074i
$56$		0			0
$57$			6.26647i			0.830014i
$58$		0			0
$59$	−1.16609	+	4.35192i	−0.151812	+	0.566572i	0.847545	+	0.530724i	$0.178080\pi$
$59$	−1.16609	+	4.35192i	−0.151812	+	0.566572i	−0.999357	+	0.0358480i	$0.988587\pi$
$60$		0			0
$61$	−2.16875	−	3.75639i	−0.277680	−	0.480956i	0.693128	−	0.720815i	$-0.256232\pi$
$61$	−2.16875	−	3.75639i	−0.277680	−	0.480956i	−0.970808	+	0.239859i	$0.922899\pi$
$62$		0			0
$63$	5.52891	+	3.19211i	0.696577	+	0.402169i
$64$		0			0
$65$	−0.728428	+	8.02928i	−0.0903504	+	0.995910i
$66$		0			0
$67$	−4.28613	−	2.47460i	−0.523634	−	0.302320i	0.214786	−	0.976661i	$-0.431095\pi$
$67$	−4.28613	−	2.47460i	−0.523634	−	0.302320i	−0.738420	+	0.674341i	$0.764428\pi$
$68$		0			0
$69$	2.12407	+	3.67900i	0.255708	+	0.442900i
$70$		0			0
$71$	1.63607	−	6.10591i	0.194166	−	0.724639i	−0.798315	−	0.602240i	$-0.794275\pi$
$71$	1.63607	−	6.10591i	0.194166	−	0.724639i	0.992481	−	0.122398i	$-0.0390585\pi$
$72$		0			0
$73$		−	7.13327i		−	0.834886i	−0.908703	−	0.417443i	$-0.862926\pi$
$73$		−	7.13327i		−	0.834886i	0.908703	−	0.417443i	$-0.137074\pi$
$74$		0			0
$75$	4.17176	−	12.3546i	0.481714	−	1.42658i
$76$		0			0
$77$	3.48052	−	3.48052i	0.396642	−	0.396642i
$78$		0			0
$79$		−	9.73120i		−	1.09485i	−0.836856	−	0.547423i	$-0.815609\pi$
$79$		−	9.73120i		−	1.09485i	0.836856	−	0.547423i	$-0.184391\pi$
$80$		0			0
$81$	−2.97638	+	5.15523i	−0.330708	+	0.572804i
$82$		0			0
$83$	6.67496			0.732672			0.366336	−	0.930483i	$-0.380612\pi$
$83$	6.67496			0.732672			0.366336	+	0.930483i	$0.380612\pi$
$84$		0			0
$85$	9.65016	−	15.5465i	1.04671	−	1.68625i
$86$		0			0
$87$	−1.88292	+	7.02716i	−0.201870	+	0.753390i
$88$		0			0
$89$	0.578139	−	0.154912i	0.0612826	−	0.0164206i	−0.228047	−	0.973650i	$-0.573234\pi$
$89$	0.578139	−	0.154912i	0.0612826	−	0.0164206i	0.289330	+	0.957229i	$0.406567\pi$
$90$		0			0
$91$	−4.02368	−	4.52476i	−0.421796	−	0.474324i
$92$		0			0
$93$	−13.5067	+	23.3943i	−1.40058	+	2.42588i
$94$		0			0
$95$	−2.83356	+	4.56489i	−0.290718	+	0.468348i
$96$		0			0
$97$	−10.4508	+	6.03380i	−1.06112	+	0.612639i	−0.925742	−	0.378155i	$-0.876559\pi$
$97$	−10.4508	+	6.03380i	−1.06112	+	0.612639i	−0.135380	+	0.990794i	$0.543225\pi$
$98$		0			0
$99$	−7.87885	−	7.87885i	−0.791854	−	0.791854i
$100$		0			0
$101$	1.73824	+	1.00357i	0.172961	+	0.0998590i	0.583981	−	0.811767i	$-0.301494\pi$
$101$	1.73824	+	1.00357i	0.172961	+	0.0998590i	−0.411020	+	0.911626i	$0.634827\pi$
$102$		0			0
$103$	−6.87986	−	6.87986i	−0.677892	−	0.677892i	0.281631	−	0.959523i	$-0.409125\pi$
$103$	−6.87986	−	6.87986i	−0.677892	−	0.677892i	−0.959523	+	0.281631i	$0.909125\pi$
$104$		0			0
$105$	4.62350	+	8.63333i	0.451208	+	0.842527i
$106$		0			0
$107$	2.67225	−	0.716027i	0.258336	−	0.0692209i	−0.127327	−	0.991861i	$-0.540640\pi$
$107$	2.67225	−	0.716027i	0.258336	−	0.0692209i	0.385662	+	0.922640i	$0.373973\pi$
$108$		0			0
$109$	1.04868	−	1.04868i	0.100445	−	0.100445i	−0.655098	−	0.755544i	$-0.727373\pi$
$109$	1.04868	−	1.04868i	0.100445	−	0.100445i	0.755544	+	0.655098i	$0.227373\pi$
$110$		0			0
$111$	10.4940	+	2.81185i	0.996042	+	0.266889i
$112$		0			0
$113$	−15.0899	−	4.04332i	−1.41953	−	0.380363i	−0.534216	−	0.845348i	$-0.679393\pi$
$113$	−15.0899	−	4.04332i	−1.41953	−	0.380363i	−0.885319	+	0.464985i	$0.846060\pi$
$114$		0			0
$115$	−0.116259	+	3.64048i	−0.0108412	+	0.339476i
$116$		0			0
$117$	−10.2427	+	9.10840i	−0.946937	+	0.842072i
$118$		0			0
$119$	3.55681	+	13.2742i	0.326052	+	1.21684i
$120$		0			0
$121$	2.08652	−	1.20465i	0.189684	−	0.109514i
$122$		0			0
$123$	6.45102	+	11.1735i	0.581669	+	1.00748i
$124$		0			0
$125$	8.62546	−	7.11347i	0.771484	−	0.636248i
$126$		0			0
$127$	4.41981	+	16.4949i	0.392194	+	1.46369i	0.826507	+	0.562927i	$0.190325\pi$
$127$	4.41981	+	16.4949i	0.392194	+	1.46369i	−0.434312	+	0.900762i	$0.643009\pi$
$128$		0			0
$129$	7.92326			0.697604
$130$		0			0
$131$	−16.6221			−1.45228			−0.726139	−	0.687548i	$-0.758687\pi$
$131$	−16.6221			−1.45228			−0.726139	+	0.687548i	$0.758687\pi$
$132$		0			0
$133$	−1.04438	−	3.89768i	−0.0905594	−	0.337972i
$134$		0			0
$135$	4.12077	−	2.20684i	0.354659	−	0.189935i
$136$		0			0
$137$	−5.84275	−	10.1199i	−0.499180	−	0.864605i	0.500819	−	0.865552i	$-0.333032\pi$
$137$	−5.84275	−	10.1199i	−0.499180	−	0.864605i	−1.00000		0.000946524i	$0.999699\pi$
$138$		0			0
$139$	2.95180	−	1.70422i	0.250368	−	0.144550i	−0.369565	−	0.929205i	$-0.620493\pi$
$139$	2.95180	−	1.70422i	0.250368	−	0.144550i	0.619933	+	0.784655i	$0.287160\pi$
$140$		0			0
$141$	7.12149	+	26.5778i	0.599738	+	2.23825i
$142$		0			0
$143$	4.73932	+	9.44552i	0.396322	+	0.789874i
$144$		0			0
$145$	−4.54917	+	4.26761i	−0.377788	+	0.354405i
$146$		0			0
$147$	10.5292	+	2.82130i	0.868438	+	0.232697i
$148$		0			0
$149$	8.18213	+	2.19240i	0.670306	+	0.179608i	0.577893	−	0.816113i	$-0.303875\pi$
$149$	8.18213	+	2.19240i	0.670306	+	0.179608i	0.0924136	+	0.995721i	$0.470542\pi$
$150$		0			0
$151$	−8.28831	+	8.28831i	−0.674493	+	0.674493i	−0.958749	−	0.284255i	$-0.908254\pi$
$151$	−8.28831	+	8.28831i	−0.674493	+	0.674493i	0.284255	+	0.958749i	$0.408254\pi$
$152$		0			0
$153$	30.0488	−	8.05155i	2.42930	−	0.650929i
$154$		0			0
$155$	−20.4175	+	10.9344i	−1.63998	+	0.878275i
$156$		0			0
$157$	6.70757	+	6.70757i	0.535322	+	0.535322i	0.922151	−	0.386829i	$-0.126430\pi$
$157$	6.70757	+	6.70757i	0.535322	+	0.535322i	−0.386829	+	0.922151i	$0.626430\pi$
$158$		0			0
$159$	−21.2830	−	12.2878i	−1.68785	−	0.974483i
$160$		0			0
$161$	−1.93430	−	1.93430i	−0.152444	−	0.152444i
$162$		0			0
$163$	−12.5205	+	7.22873i	−0.980683	+	0.566198i	−0.902476	−	0.430739i	$-0.858253\pi$
$163$	−12.5205	+	7.22873i	−0.980683	+	0.566198i	−0.0782070	+	0.996937i	$0.524920\pi$
$164$		0			0
$165$	−3.89461	−	16.6428i	−0.303195	−	1.29564i
$166$		0			0
$167$	3.81808	−	6.61311i	0.295452	−	0.511738i	−0.679638	−	0.733548i	$-0.737863\pi$
$167$	3.81808	−	6.61311i	0.295452	−	0.511738i	0.975090	+	0.221810i	$0.0711964\pi$
$168$		0			0
$169$	11.9406	−	5.14016i	0.918510	−	0.395397i
$170$		0			0
$171$	−8.82319	+	2.36417i	−0.674726	+	0.180792i
$172$		0			0
$173$	6.08331	−	22.7032i	0.462505	−	1.72609i	−0.202526	−	0.979277i	$-0.564915\pi$
$173$	6.08331	−	22.7032i	0.462505	−	1.72609i	0.665031	−	0.746816i	$-0.268418\pi$
$174$		0			0
$175$	−0.535759	+	8.37971i	−0.0404995	+	0.633447i
$176$		0			0
$177$	−11.7501			−0.883193
$178$		0			0
$179$	−12.3426	+	21.3780i	−0.922530	+	1.59787i	−0.127045	+	0.991897i	$0.540549\pi$
$179$	−12.3426	+	21.3780i	−0.922530	+	1.59787i	−0.795486	+	0.605973i	$0.792784\pi$
$180$		0			0
$181$		−	6.35761i		−	0.472557i	−0.971685	−	0.236279i	$-0.924072\pi$
$181$		−	6.35761i		−	0.472557i	0.971685	−	0.236279i	$-0.0759278\pi$
$182$		0			0
$183$	7.99888	−	7.99888i	0.591294	−	0.591294i
$184$		0			0
$185$	6.37300	+	6.79347i	0.468552	+	0.499466i
$186$		0			0
$187$		−	23.9847i		−	1.75393i
$188$		0			0
$189$	−0.908637	+	3.39108i	−0.0660936	+	0.246665i
$190$		0			0
$191$	5.43459	+	9.41299i	0.393233	+	0.681100i	0.992874	−	0.119169i	$-0.0380232\pi$
$191$	5.43459	+	9.41299i	0.393233	+	0.681100i	−0.599641	+	0.800269i	$0.704690\pi$
$192$		0			0
$193$	−13.9779	−	8.07014i	−1.00615	−	0.580901i	−0.0960884	−	0.995373i	$-0.530633\pi$
$193$	−13.9779	−	8.07014i	−1.00615	−	0.580901i	−0.910062	+	0.414471i	$0.863966\pi$
$194$		0			0
$195$	−20.7184	+	3.58474i	−1.48368	+	0.256708i
$196$		0			0
$197$	−11.5822	−	6.68699i	−0.825198	−	0.476428i	0.0270075	−	0.999635i	$-0.491402\pi$
$197$	−11.5822	−	6.68699i	−0.825198	−	0.476428i	−0.852206	+	0.523207i	$0.824736\pi$
$198$		0			0
$199$	−10.5547	−	18.2812i	−0.748199	−	1.29592i	−0.948685	−	0.316223i	$-0.897585\pi$
$199$	−10.5547	−	18.2812i	−0.748199	−	1.29592i	0.200485	−	0.979697i	$-0.435748\pi$
$200$		0			0
$201$	3.34069	−	12.4676i	0.235634	−	0.879398i
$202$		0			0
$203$		−	4.68464i		−	0.328797i
$204$		0			0
$205$	−0.353089	+	11.0565i	−0.0246608	+	0.772219i
$206$		0			0
$207$	−4.37868	+	4.37868i	−0.304339	+	0.304339i
$208$		0			0
$209$			7.04259i			0.487146i
$210$		0			0
$211$	8.38134	−	14.5169i	0.576995	−	0.999385i	−0.418826	−	0.908066i	$-0.637558\pi$
$211$	8.38134	−	14.5169i	0.576995	−	0.999385i	0.995822	−	0.0913189i	$-0.0291082\pi$
$212$		0			0
$213$	16.4859			1.12959
$214$		0			0
$215$	5.77180	+	3.58273i	0.393634	+	0.244340i
$216$		0			0
$217$	4.50211	−	16.8021i	0.305623	−	1.14060i
$218$		0			0
$219$	17.9695	−	4.81492i	1.21427	−	0.325362i
$220$		0			0
$221$	−29.4542	−	1.72650i	−1.98130	−	0.116137i
$222$		0			0
$223$	1.80786	−	3.13130i	0.121063	−	0.209688i	−0.799124	−	0.601166i	$-0.794703\pi$
$223$	1.80786	−	3.13130i	0.121063	−	0.209688i	0.920187	+	0.391479i	$0.128036\pi$
$224$		0			0
$225$	18.9691	+	1.21280i	1.26461	+	0.0808531i
$226$		0			0
$227$	10.8235	−	6.24896i	0.718382	−	0.414758i	−0.0957751	−	0.995403i	$-0.530533\pi$
$227$	10.8235	−	6.24896i	0.718382	−	0.414758i	0.814157	+	0.580645i	$0.197200\pi$
$228$		0			0
$229$	−19.8049	−	19.8049i	−1.30874	−	1.30874i	−0.922324	−	0.386417i	$-0.873712\pi$
$229$	−19.8049	−	19.8049i	−1.30874	−	1.30874i	−0.386417	−	0.922324i	$-0.626288\pi$
$230$		0			0
$231$	11.1172	+	6.41850i	0.731456	+	0.422307i
$232$		0			0
$233$	8.31519	+	8.31519i	0.544746	+	0.544746i	0.924917	−	0.380170i	$-0.124135\pi$
$233$	8.31519	+	8.31519i	0.544746	+	0.544746i	−0.380170	+	0.924917i	$0.624135\pi$
$234$		0			0
$235$	−6.83016	+	22.5811i	−0.445550	+	1.47303i
$236$		0			0
$237$	24.5140	−	6.56852i	1.59236	−	0.426671i
$238$		0			0
$239$	−1.12430	+	1.12430i	−0.0727249	+	0.0727249i	−0.742534	−	0.669809i	$-0.766376\pi$
$239$	−1.12430	+	1.12430i	−0.0727249	+	0.0727249i	0.669809	+	0.742534i	$0.266376\pi$
$240$		0			0
$241$	22.0900	+	5.91899i	1.42294	+	0.381275i	0.886525	−	0.462680i	$-0.153112\pi$
$241$	22.0900	+	5.91899i	1.42294	+	0.381275i	0.536414	+	0.843955i	$0.319779\pi$
$242$		0			0
$243$	−21.0535	−	5.64126i	−1.35058	−	0.361887i
$244$		0			0
$245$	6.39443	+	6.81632i	0.408525	+	0.435479i
$246$		0			0
$247$	8.64858	+	0.506950i	0.550296	+	0.0322565i
$248$		0			0
$249$	4.50557	+	16.8150i	0.285529	+	1.06561i
$250$		0			0
$251$	12.8530	−	7.42069i	0.811275	−	0.468390i	−0.0361238	−	0.999347i	$-0.511501\pi$
$251$	12.8530	−	7.42069i	0.811275	−	0.468390i	0.847398	+	0.530958i	$0.178168\pi$
$252$		0			0
$253$	2.38714	+	4.13466i	0.150079	+	0.259944i
$254$		0			0
$255$	45.6772	+	13.8161i	2.86042	+	0.865198i
$256$		0			0
$257$	−2.26270	−	8.44452i	−0.141143	−	0.526754i	−0.999897	−	0.0143653i	$-0.995427\pi$
$257$	−2.26270	−	8.44452i	−0.141143	−	0.526754i	0.858753	−	0.512389i	$-0.171239\pi$
$258$		0			0
$259$	−6.99577			−0.434696
$260$		0			0
$261$	−10.6046			−0.656409
$262$		0			0
$263$	−4.75737	−	17.7547i	−0.293352	−	1.09480i	−0.942517	−	0.334157i	$-0.891548\pi$
$263$	−4.75737	−	17.7547i	−0.293352	−	1.09480i	0.649166	−	0.760647i	$-0.275118\pi$
$264$		0			0
$265$	−9.94763	−	18.5749i	−0.611078	−	1.14105i
$266$		0			0
$267$	0.780483	+	1.35184i	0.0477648	+	0.0827310i
$268$		0			0
$269$	−9.29173	+	5.36458i	−0.566526	+	0.327084i	−0.755761	−	0.654848i	$-0.772733\pi$
$269$	−9.29173	+	5.36458i	−0.566526	+	0.327084i	0.189234	+	0.981932i	$0.439399\pi$
$270$		0			0
$271$	6.32705	+	23.6129i	0.384341	+	1.43438i	0.839204	+	0.543817i	$0.183022\pi$
$271$	6.32705	+	23.6129i	0.384341	+	1.43438i	−0.454863	+	0.890562i	$0.650312\pi$
$272$		0			0
$273$	8.68244	−	13.1903i	0.525485	−	0.798314i
$274$		0			0
$275$	4.68845	−	13.8847i	0.282724	−	0.837281i
$276$		0			0
$277$	26.1107	+	6.99634i	1.56884	+	0.420369i	0.935448	−	0.353463i	$-0.114996\pi$
$277$	26.1107	+	6.99634i	1.56884	+	0.420369i	0.633390	+	0.773832i	$0.281663\pi$
$278$		0			0
$279$	−38.0349	−	10.1914i	−2.27709	−	0.610144i
$280$		0			0
$281$	−20.7650	+	20.7650i	−1.23874	+	1.23874i	−0.278218	+	0.960518i	$0.589744\pi$
$281$	−20.7650	+	20.7650i	−1.23874	+	1.23874i	−0.960518	+	0.278218i	$0.910256\pi$
$282$		0			0
$283$	11.5526	−	3.09550i	0.686729	−	0.184008i	0.101450	−	0.994841i	$-0.467652\pi$
$283$	11.5526	−	3.09550i	0.686729	−	0.184008i	0.585279	+	0.810832i	$0.300985\pi$
$284$		0			0
$285$	−13.4121	−	4.05680i	−0.794466	−	0.240304i
$286$		0			0
$287$	−5.87467	−	5.87467i	−0.346771	−	0.346771i
$288$		0			0
$289$	43.2698	+	24.9819i	2.54528	+	1.46952i
$290$		0			0
$291$	−22.2541	−	22.2541i	−1.30456	−	1.30456i
$292$		0			0
$293$	10.1557	−	5.86338i	0.593301	−	0.342542i	−0.173101	−	0.984904i	$-0.555379\pi$
$293$	10.1557	−	5.86338i	0.593301	−	0.342542i	0.766402	+	0.642362i	$0.222045\pi$
$294$		0			0
$295$	−8.55952	−	5.31315i	−0.498355	−	0.309344i
$296$		0			0
$297$	3.06361	−	5.30633i	0.177769	−	0.307904i
$298$		0			0
$299$	5.24936	−	2.63388i	0.303578	−	0.152321i
$300$		0			0
$301$	−4.92820	+	1.32051i	−0.284057	+	0.0761127i
$302$		0			0
$303$	−1.35481	+	5.05623i	−0.0778319	+	0.290473i
$304$		0			0
$305$	9.44381	−	2.20996i	0.540751	−	0.126542i
$306$		0			0
$307$	−17.5100			−0.999348			−0.499674	−	0.866214i	$-0.666547\pi$
$307$	−17.5100			−0.999348			−0.499674	+	0.866214i	$0.666547\pi$
$308$		0			0
$309$	12.6873	−	21.9750i	0.721755	−	1.25012i
$310$		0			0
$311$		−	18.3218i		−	1.03893i	−0.854491	−	0.519467i	$-0.826131\pi$
$311$		−	18.3218i		−	1.03893i	0.854491	−	0.519467i	$-0.173869\pi$
$312$		0			0
$313$	4.75747	−	4.75747i	0.268908	−	0.268908i	−0.559752	−	0.828660i	$-0.689104\pi$
$313$	4.75747	−	4.75747i	0.268908	−	0.268908i	0.828660	+	0.559752i	$0.189104\pi$
$314$		0			0
$315$	−10.4114	+	9.76701i	−0.586616	+	0.550309i
$316$		0			0
$317$			28.5858i			1.60554i	0.596291	+	0.802768i	$0.296641\pi$
$317$			28.5858i			1.60554i	−0.596291	+	0.802768i	$0.703359\pi$
$318$		0			0
$319$	−2.11613	+	7.89749i	−0.118480	+	0.442174i
$320$		0			0
$321$	3.60751	+	6.24839i	0.201352	+	0.348751i
$322$		0			0
$323$	−17.0282	−	9.83123i	−0.947474	−	0.547024i
$324$		0			0
$325$	−16.7135	−	6.75707i	−0.927100	−	0.374815i
$326$		0			0
$327$	3.34960	+	1.93390i	0.185234	+	0.106945i
$328$		0			0
$329$	−8.85900	−	15.3442i	−0.488413	−	0.845955i
$330$		0			0
$331$	−5.56323	+	20.7622i	−0.305783	+	1.14120i	0.626487	+	0.779432i	$0.284492\pi$
$331$	−5.56323	+	20.7622i	−0.305783	+	1.14120i	−0.932270	+	0.361764i	$0.882175\pi$
$332$		0			0
$333$			15.8363i			0.867825i
$334$		0			0
$335$	8.07116	−	7.57161i	0.440974	−	0.413681i
$336$		0			0
$337$	−12.5568	+	12.5568i	−0.684010	+	0.684010i	−0.960901	−	0.276891i	$-0.910696\pi$
$337$	−12.5568	+	12.5568i	−0.684010	+	0.684010i	0.276891	+	0.960901i	$0.410696\pi$
$338$		0			0
$339$		−	40.7424i		−	2.21282i
$340$		0			0
$341$	−15.1795	+	26.2917i	−0.822018	+	1.42378i
$342$		0			0
$343$	−18.7748			−1.01375
$344$		0			0
$345$	−9.24926	+	2.16444i	−0.497964	+	0.116529i
$346$		0			0
$347$	1.06192	−	3.96312i	0.0570066	−	0.212751i	−0.931547	−	0.363620i	$-0.881541\pi$
$347$	1.06192	−	3.96312i	0.0570066	−	0.212751i	0.988554	+	0.150869i	$0.0482072\pi$
$348$		0			0
$349$	1.89219	−	0.507011i	0.101287	−	0.0271397i	−0.207820	−	0.978167i	$-0.566637\pi$
$349$	1.89219	−	0.507011i	0.101287	−	0.0271397i	0.309106	+	0.951027i	$0.399970\pi$
$350$		0			0
$351$	−6.29586	−	4.14420i	−0.336048	−	0.221201i
$352$		0			0
$353$	−1.55427	+	2.69208i	−0.0827256	+	0.143285i	−0.904420	−	0.426644i	$-0.859696\pi$
$353$	−1.55427	+	2.69208i	−0.0827256	+	0.143285i	0.821694	+	0.569929i	$0.193029\pi$
$354$		0			0
$355$	12.0093	+	7.45456i	0.637389	+	0.395647i
$356$		0			0
$357$	−31.0385	+	17.9201i	−1.64273	+	0.948430i
$358$		0			0
$359$	−6.98593	−	6.98593i	−0.368703	−	0.368703i	0.498301	−	0.867004i	$-0.333957\pi$
$359$	−6.98593	−	6.98593i	−0.368703	−	0.368703i	−0.867004	+	0.498301i	$0.833957\pi$
$360$		0			0
$361$	−11.4545	−	6.61327i	−0.602870	−	0.348067i
$362$		0			0
$363$	4.44305	+	4.44305i	0.233200	+	0.233200i
$364$		0			0
$365$	15.2673	+	4.61795i	0.799130	+	0.241715i
$366$		0			0
$367$	−1.25640	+	0.336651i	−0.0655835	+	0.0175731i	−0.291462	−	0.956583i	$-0.594142\pi$
$367$	−1.25640	+	0.336651i	−0.0655835	+	0.0175731i	0.225878	+	0.974156i	$0.427475\pi$
$368$		0			0
$369$	−13.2985	+	13.2985i	−0.692291	+	0.692291i
$370$		0			0
$371$	15.2857	+	4.09580i	0.793596	+	0.212644i
$372$		0			0
$373$	0.871043	+	0.233395i	0.0451009	+	0.0120847i	0.281299	−	0.959620i	$-0.409235\pi$
$373$	0.871043	+	0.233395i	0.0451009	+	0.0120847i	−0.236198	+	0.971705i	$0.575901\pi$
$374$		0			0
$375$	23.7418	+	16.9270i	1.22602	+	0.874105i
$376$		0			0
$377$	9.54611	+	3.16718i	0.491650	+	0.163118i
$378$		0			0
$379$	−3.97268	−	14.8263i	−0.204063	−	0.761574i	−0.989733	−	0.142928i	$-0.954348\pi$
$379$	−3.97268	−	14.8263i	−0.204063	−	0.761574i	0.785670	−	0.618646i	$-0.212318\pi$
$380$		0			0
$381$	−38.5694	+	22.2680i	−1.97597	+	1.14083i
$382$		0			0
$383$	6.39904	+	11.0835i	0.326976	+	0.566339i	0.981910	−	0.189347i	$-0.0606371\pi$
$383$	6.39904	+	11.0835i	0.326976	+	0.566339i	−0.654935	+	0.755686i	$0.727304\pi$
$384$		0			0
$385$	5.19614	+	9.70259i	0.264820	+	0.494490i
$386$		0			0
$387$	2.98923	+	11.1560i	0.151951	+	0.567089i
$388$		0			0
$389$	16.5057			0.836870			0.418435	−	0.908247i	$-0.362579\pi$
$389$	16.5057			0.836870			0.418435	+	0.908247i	$0.362579\pi$
$390$		0			0
$391$	−13.3295			−0.674103
$392$		0			0
$393$	−11.2198	−	41.8730i	−0.565966	−	2.11221i
$394$		0			0
$395$	20.8277	+	6.29981i	1.04796	+	0.316978i
$396$		0			0
$397$	4.11552	+	7.12829i	0.206552	+	0.357759i	0.950626	−	0.310338i	$-0.100442\pi$
$397$	4.11552	+	7.12829i	0.206552	+	0.357759i	−0.744074	+	0.668097i	$0.767109\pi$
$398$		0			0
$399$	9.11377	−	5.26184i	0.456259	−	0.263422i
$400$		0			0
$401$	−7.17051	−	26.7607i	−0.358078	−	1.33637i	−0.876566	−	0.481281i	$-0.840172\pi$
$401$	−7.17051	−	26.7607i	−0.358078	−	1.33637i	0.518488	−	0.855085i	$-0.326495\pi$
$402$		0			0
$403$	31.1946	+	20.5337i	1.55392	+	1.02285i
$404$		0			0
$405$	−9.10691	−	9.70775i	−0.452526	−	0.482382i
$406$		0			0
$407$	11.7937	+	3.16010i	0.584590	+	0.156640i
$408$		0			0
$409$	17.8703	+	4.78835i	0.883632	+	0.236768i	0.671973	−	0.740575i	$-0.265447\pi$
$409$	17.8703	+	4.78835i	0.883632	+	0.236768i	0.211658	+	0.977344i	$0.432114\pi$
$410$		0			0
$411$	21.5495	−	21.5495i	1.06296	−	1.06296i
$412$		0			0
$413$	7.30846	−	1.95830i	0.359626	−	0.0963615i
$414$		0			0
$415$	−4.32125	+	14.2864i	−0.212122	+	0.701293i
$416$		0			0
$417$	6.28558	+	6.28558i	0.307806	+	0.307806i
$418$		0			0
$419$	−3.72308	−	2.14952i	−0.181884	−	0.105011i	0.406293	−	0.913743i	$-0.366821\pi$
$419$	−3.72308	−	2.14952i	−0.181884	−	0.105011i	−0.588178	+	0.808732i	$0.700154\pi$
$420$		0			0
$421$	6.99925	+	6.99925i	0.341123	+	0.341123i	0.856789	−	0.515667i	$-0.172456\pi$
$421$	6.99925	+	6.99925i	0.341123	+	0.341123i	−0.515667	+	0.856789i	$0.672456\pi$
$422$		0			0
$423$	−34.7347	+	20.0541i	−1.68886	+	0.975064i
$424$		0			0
$425$	27.0268	+	30.7188i	1.31099	+	1.49008i
$426$		0			0
$427$	−3.64212	+	6.30834i	−0.176255	+	0.305282i
$428$		0			0
$429$	−20.5954	+	18.3146i	−0.994354	+	0.884237i
$430$		0			0
$431$	1.26467	−	0.338868i	0.0609171	−	0.0163227i	−0.228232	−	0.973607i	$-0.573294\pi$
$431$	1.26467	−	0.338868i	0.0609171	−	0.0163227i	0.289149	+	0.957284i	$0.406628\pi$
$432$		0			0
$433$	−2.70003	+	10.0767i	−0.129755	+	0.484253i	−0.999964	−	0.00842905i	$-0.997317\pi$
$433$	−2.70003	+	10.0767i	−0.129755	+	0.484253i	0.870209	+	0.492682i	$0.163984\pi$
$434$		0			0
$435$	−13.8213	−	8.57928i	−0.662679	−	0.411345i
$436$		0			0
$437$	3.91393			0.187228
$438$		0			0
$439$	−13.6918	+	23.7150i	−0.653476	+	1.13185i	0.328798	+	0.944400i	$0.393357\pi$
$439$	−13.6918	+	23.7150i	−0.653476	+	1.13185i	−0.982274	+	0.187453i	$0.939977\pi$
$440$		0			0
$441$			15.8896i			0.756647i
$442$		0			0
$443$	−2.05524	+	2.05524i	−0.0976474	+	0.0976474i	−0.754243	−	0.656595i	$-0.771996\pi$
$443$	−2.05524	+	2.05524i	−0.0976474	+	0.0976474i	0.656595	+	0.754243i	$0.271996\pi$
$444$		0			0
$445$	−0.0427188	+	1.33768i	−0.00202507	+	0.0634121i
$446$		0			0
$447$			22.0916i			1.04490i
$448$		0			0
$449$	−1.73279	+	6.46685i	−0.0817753	+	0.305190i	−0.994684	−	0.102974i	$-0.967164\pi$
$449$	−1.73279	+	6.46685i	−0.0817753	+	0.305190i	0.912909	+	0.408164i	$0.133831\pi$
$450$		0			0
$451$	7.24999	+	12.5574i	0.341389	+	0.591303i
$452$		0			0
$453$	−26.4738	−	15.2847i	−1.24385	−	0.718136i
$454$		0			0
$455$	12.2892	−	5.68264i	0.576127	−	0.266406i
$456$		0			0
$457$	19.4272	+	11.2163i	0.908768	+	0.524677i	0.880034	−	0.474910i	$-0.157519\pi$
$457$	19.4272	+	11.2163i	0.908768	+	0.524677i	0.0287333	+	0.999587i	$0.490853\pi$
$458$		0			0
$459$	8.55340	+	14.8149i	0.399239	+	0.691502i
$460$		0			0
$461$	6.83936	−	25.5248i	0.318541	−	1.18881i	−0.602107	−	0.798416i	$-0.705672\pi$
$461$	6.83936	−	25.5248i	0.318541	−	1.18881i	0.920647	−	0.390395i	$-0.127662\pi$
$462$		0			0
$463$			19.6621i			0.913777i	0.889524	+	0.456888i	$0.151036\pi$
$463$			19.6621i			0.913777i	−0.889524	+	0.456888i	$0.848964\pi$
$464$		0			0
$465$	−41.3269	−	44.0535i	−1.91649	−	2.04293i
$466$		0			0
$467$	−0.598955	+	0.598955i	−0.0277163	+	0.0277163i	−0.720829	−	0.693113i	$-0.756239\pi$
$467$	−0.598955	+	0.598955i	−0.0277163	+	0.0277163i	0.693113	+	0.720829i	$0.256239\pi$
$468$		0			0
$469$			8.31151i			0.383790i
$470$		0			0
$471$	−12.3696	+	21.4247i	−0.569960	+	0.987200i
$472$		0			0
$473$	8.90458			0.409433
$474$		0			0
$475$	−7.93584	−	9.01991i	−0.364121	−	0.413862i
$476$		0			0
$477$	9.27167	−	34.6023i	0.424520	−	1.58433i
$478$		0			0
$479$	−15.1500	+	4.05942i	−0.692220	+	0.185480i	−0.587743	−	0.809048i	$-0.699983\pi$
$479$	−15.1500	+	4.05942i	−0.692220	+	0.185480i	−0.104477	+	0.994527i	$0.533317\pi$
$480$		0			0
$481$	4.72968	−	14.2556i	0.215655	−	0.650000i
$482$		0			0
$483$	3.56709	−	6.17838i	0.162308	−	0.281126i
$484$		0			0
$485$	−6.14846	−	26.2741i	−0.279187	−	1.19305i
$486$		0			0
$487$	19.9455	−	11.5156i	0.903818	−	0.521820i	0.0253810	−	0.999678i	$-0.491920\pi$
$487$	19.9455	−	11.5156i	0.903818	−	0.521820i	0.878437	+	0.477858i	$0.158587\pi$
$488$		0			0
$489$	−26.6613	−	26.6613i	−1.20567	−	1.20567i
$490$		0			0
$491$	−25.0505	−	14.4629i	−1.13051	−	0.652702i	−0.186449	−	0.982465i	$-0.559698\pi$
$491$	−25.0505	−	14.4629i	−1.13051	−	0.652702i	−0.944064	+	0.329762i	$0.893031\pi$
$492$		0			0
$493$	−16.1412	−	16.1412i	−0.726963	−	0.726963i
$494$		0			0
$495$	21.9638	−	11.7625i	0.987197	−	0.528685i
$496$		0			0
$497$	−10.2541	+	2.74757i	−0.459957	+	0.123245i
$498$		0			0
$499$	16.5783	−	16.5783i	0.742147	−	0.742147i	−0.230844	−	0.972991i	$-0.574149\pi$
$499$	16.5783	−	16.5783i	0.742147	−	0.742147i	0.972991	+	0.230844i	$0.0741488\pi$
$500$		0			0
$501$	19.2364	+	5.15438i	0.859419	+	0.230281i
$502$		0			0
$503$	18.1562	+	4.86494i	0.809545	+	0.216917i	0.639771	−	0.768566i	$-0.279029\pi$
$503$	18.1562	+	4.86494i	0.809545	+	0.216917i	0.169775	+	0.985483i	$0.445696\pi$
$504$		0			0
$505$	−3.27325	+	3.07066i	−0.145658	+	0.136642i
$506$		0			0
$507$	21.0085	+	26.6103i	0.933022	+	1.18180i
$508$		0			0
$509$	−7.12866	−	26.6045i	−0.315972	−	1.17922i	−0.923081	−	0.384606i	$-0.874337\pi$
$509$	−7.12866	−	26.6045i	−0.315972	−	1.17922i	0.607109	−	0.794619i	$-0.292329\pi$
$510$		0			0
$511$	−10.3744	+	5.98968i	−0.458937	+	0.264968i
$512$		0			0
$513$	−2.51152	−	4.35009i	−0.110886	−	0.192061i
$514$		0			0
$515$	19.1789	−	10.2711i	0.845122	−	0.452598i
$516$		0			0
$517$	8.00350	+	29.8695i	0.351994	+	1.31366i
$518$		0			0
$519$	61.2983			2.69069
$520$		0			0
$521$	12.4504			0.545463			0.272731	−	0.962090i	$-0.412073\pi$
$521$	12.4504			0.545463			0.272731	+	0.962090i	$0.412073\pi$
$522$		0			0
$523$	3.31632	+	12.3767i	0.145012	+	0.541194i	0.999755	+	0.0221413i	$0.00704836\pi$
$523$	3.31632	+	12.3767i	0.145012	+	0.541194i	−0.854742	+	0.519052i	$0.826285\pi$
$524$		0			0
$525$	−21.4711	+	4.30663i	−0.937076	+	0.187957i
$526$		0			0
$527$	−42.3803	−	73.4049i	−1.84612	−	3.19757i
$528$		0			0
$529$	−17.6207	+	10.1733i	−0.766119	+	0.442319i
$530$		0			0
$531$	−4.43299	−	16.5442i	−0.192376	−	0.717955i
$532$		0			0
$533$	15.9428	−	7.99936i	0.690560	−	0.346491i
$534$		0			0
$535$	−0.197453	+	6.18296i	−0.00853663	+	0.267313i
$536$		0			0
$537$	−62.1850	−	16.6624i	−2.68348	−	0.719037i
$538$		0			0
$539$	11.8333	+	3.17073i	0.509697	+	0.136573i
$540$		0			0
$541$	14.7555	−	14.7555i	0.634390	−	0.634390i	−0.314776	−	0.949166i	$-0.601929\pi$
$541$	14.7555	−	14.7555i	0.634390	−	0.634390i	0.949166	+	0.314776i	$0.101929\pi$
$542$		0			0
$543$	16.0156	−	4.29136i	0.687294	−	0.184160i
$544$		0			0
$545$	1.56560	+	2.92339i	0.0670628	+	0.125224i
$546$		0			0
$547$	−12.8130	−	12.8130i	−0.547845	−	0.547845i	0.377972	−	0.925817i	$-0.376621\pi$
$547$	−12.8130	−	12.8130i	−0.547845	−	0.547845i	−0.925817	+	0.377972i	$0.876621\pi$
$548$		0			0
$549$	14.2802	+	8.24467i	0.609463	+	0.351874i
$550$		0			0
$551$	4.73952	+	4.73952i	0.201910	+	0.201910i
$552$		0			0
$553$	−14.1528	+	8.17111i	−0.601837	+	0.347471i
$554$		0			0
$555$	−12.8118	+	20.6399i	−0.543831	+	0.876115i
$556$		0			0
$557$	−0.367130	+	0.635888i	−0.0155558	+	0.0269435i	−0.873699	−	0.486468i	$-0.838285\pi$
$557$	−0.367130	+	0.635888i	−0.0155558	+	0.0269435i	0.858143	+	0.513411i	$0.171618\pi$
$558$		0			0
$559$	0.640983	−	10.9352i	0.0271107	−	0.462509i
$560$		0			0
$561$	60.4202	−	16.1896i	2.55094	−	0.683524i
$562$		0			0
$563$	−5.64244	+	21.0579i	−0.237800	+	0.887483i	0.739066	+	0.673633i	$0.235267\pi$
$563$	−5.64244	+	21.0579i	−0.237800	+	0.887483i	−0.976866	+	0.213850i	$0.931400\pi$
$564$		0			0
$565$	18.4228	−	29.6793i	0.775054	−	1.24862i
$566$		0			0
$567$	9.99684			0.419828
$568$		0			0
$569$	−12.9881	+	22.4960i	−0.544487	+	0.943080i	0.454152	+	0.890924i	$0.349942\pi$
$569$	−12.9881	+	22.4960i	−0.544487	+	0.943080i	−0.998639	+	0.0521554i	$0.983391\pi$
$570$		0			0
$571$			8.75018i			0.366184i	0.983096	+	0.183092i	$0.0586106\pi$
$571$			8.75018i			0.366184i	−0.983096	+	0.183092i	$0.941389\pi$
$572$		0			0
$573$	−20.0441	+	20.0441i	−0.837354	+	0.837354i
$574$		0			0
$575$	−7.71646	−	2.60561i	−0.321799	−	0.108661i
$576$		0			0
$577$			7.98223i			0.332304i	0.986100	+	0.166152i	$0.0531343\pi$
$577$			7.98223i			0.332304i	−0.986100	+	0.166152i	$0.946866\pi$
$578$		0			0
$579$	10.8946	−	40.6593i	0.452765	−	1.68974i
$580$		0			0
$581$	−5.60484	−	9.70787i	−0.232528	−	0.402750i
$582$		0			0
$583$	−23.9190	−	13.8096i	−0.990623	−	0.571937i
$584$		0			0
$585$	−12.8638	−	27.8191i	−0.531852	−	1.15018i
$586$		0			0
$587$	−10.2503	−	5.91804i	−0.423077	−	0.244264i	0.273316	−	0.961924i	$-0.411880\pi$
$587$	−10.2503	−	5.91804i	−0.423077	−	0.244264i	−0.696393	+	0.717661i	$0.745213\pi$
$588$		0			0
$589$	12.4441	+	21.5538i	0.512749	+	0.888108i
$590$		0			0
$591$	9.02738	−	33.6906i	0.371337	−	1.38585i
$592$		0			0
$593$			5.65756i			0.232328i	0.993230	+	0.116164i	$0.0370598\pi$
$593$			5.65756i			0.232328i	−0.993230	+	0.116164i	$0.962940\pi$
$594$		0			0
$595$	−30.7134	−	0.980833i	−1.25913	−	0.0402102i
$596$		0			0
$597$	38.9281	−	38.9281i	1.59322	−	1.59322i
$598$		0			0
$599$			21.5444i			0.880281i	0.897929	+	0.440141i	$0.145071\pi$
$599$			21.5444i			0.880281i	−0.897929	+	0.440141i	$0.854929\pi$
$600$		0			0
$601$	11.2202	−	19.4339i	0.457680	−	0.792725i	−0.541158	−	0.840921i	$-0.682014\pi$
$601$	11.2202	−	19.4339i	0.457680	−	0.792725i	0.998838	+	0.0481961i	$0.0153473\pi$
$602$		0			0
$603$	18.8148			0.766196
$604$		0			0
$605$	1.22754	+	5.24565i	0.0499068	+	0.213266i
$606$		0			0
$607$	−4.56512	+	17.0372i	−0.185292	+	0.691521i	0.809275	+	0.587429i	$0.199860\pi$
$607$	−4.56512	+	17.0372i	−0.185292	+	0.691521i	−0.994568	+	0.104091i	$0.966807\pi$
$608$		0			0
$609$	11.8012	−	3.16211i	0.478207	−	0.128135i
$610$		0			0
$611$	37.2571	−	7.67852i	1.50726	−	0.310640i
$612$		0			0
$613$	−0.946493	+	1.63937i	−0.0382285	+	0.0662137i	−0.884507	−	0.466528i	$-0.845505\pi$
$613$	−0.946493	+	1.63937i	−0.0382285	+	0.0662137i	0.846278	+	0.532741i	$0.178838\pi$
$614$		0			0
$615$	−28.0909	+	6.57361i	−1.13274	+	0.265073i
$616$		0			0
$617$	−4.81348	+	2.77906i	−0.193783	+	0.111881i	−0.593753	−	0.804648i	$-0.702354\pi$
$617$	−4.81348	+	2.77906i	−0.193783	+	0.111881i	0.399969	+	0.916529i	$0.369021\pi$
$618$		0			0
$619$	29.0772	+	29.0772i	1.16871	+	1.16871i	0.982512	+	0.186200i	$0.0596171\pi$
$619$	29.0772	+	29.0772i	1.16871	+	1.16871i	0.186200	+	0.982512i	$0.440383\pi$
$620$		0			0
$621$	−2.94900	−	1.70260i	−0.118339	−	0.0683232i
$622$		0			0
$623$	−0.710753	−	0.710753i	−0.0284757	−	0.0284757i
$624$		0			0
$625$	9.64102	+	23.0662i	0.385641	+	0.922649i
$626$		0			0
$627$	−17.7411	+	4.75372i	−0.708512	+	0.189845i
$628$		0			0
$629$	−24.1044	+	24.1044i	−0.961104	+	0.961104i
$630$		0			0
$631$	1.87343	+	0.501983i	0.0745799	+	0.0199836i	0.295916	−	0.955214i	$-0.404375\pi$
$631$	1.87343	+	0.501983i	0.0745799	+	0.0199836i	−0.221336	+	0.975198i	$0.571042\pi$
$632$		0			0
$633$	42.2272	+	11.3147i	1.67838	+	0.449720i
$634$		0			0
$635$	−38.1655	−	1.21881i	−1.51455	−	0.0483672i
$636$		0			0
$637$	4.74559	−	14.3036i	0.188027	−	0.566728i
$638$		0			0
$639$	6.21966	+	23.2121i	0.246046	+	0.918256i
$640$		0			0
$641$	−18.7660	+	10.8346i	−0.741213	+	0.427939i	−0.822510	−	0.568751i	$-0.807427\pi$
$641$	−18.7660	+	10.8346i	−0.741213	+	0.427939i	0.0812974	+	0.996690i	$0.474094\pi$
$642$		0			0
$643$	21.4869	+	37.2163i	0.847359	+	1.46767i	0.883557	+	0.468324i	$0.155142\pi$
$643$	21.4869	+	37.2163i	0.847359	+	1.46767i	−0.0361975	+	0.999345i	$0.511525\pi$
$644$		0			0
$645$	−5.12938	+	16.9582i	−0.201969	+	0.667728i
$646$		0			0
$647$	−2.60165	−	9.70951i	−0.102282	−	0.381720i	0.895741	−	0.444576i	$-0.146646\pi$
$647$	−2.60165	−	9.70951i	−0.102282	−	0.381720i	−0.998023	+	0.0628562i	$0.979979\pi$
$648$		0			0
$649$	−13.2054			−0.518357
$650$		0			0
$651$	45.3653			1.77801
$652$		0			0
$653$	−1.24021	−	4.62853i	−0.0485332	−	0.181128i	0.937404	−	0.348243i	$-0.113222\pi$
$653$	−1.24021	−	4.62853i	−0.0485332	−	0.181128i	−0.985937	+	0.167115i	$0.946555\pi$
$654$		0			0
$655$	10.7608	−	35.5763i	0.420461	−	1.39008i
$656$		0			0
$657$	13.5588	+	23.4846i	0.528980	+	0.916220i
$658$		0			0
$659$	−30.9239	+	17.8539i	−1.20462	+	0.695490i	−0.961580	−	0.274525i	$-0.911480\pi$
$659$	−30.9239	+	17.8539i	−1.20462	+	0.695490i	−0.243045	+	0.970015i	$0.578146\pi$
$660$		0			0
$661$	−0.365777	−	1.36510i	−0.0142271	−	0.0530961i	0.958447	−	0.285269i	$-0.0920830\pi$
$661$	−0.365777	−	1.36510i	−0.0142271	−	0.0530961i	−0.972674	+	0.232173i	$0.925416\pi$
$662$		0			0
$663$	−15.5322	−	75.3639i	−0.603219	−	2.92689i
$664$		0			0
$665$	9.01834	+	0.288001i	0.349716	+	0.0111682i
$666$		0			0
$667$	4.38904	+	1.17604i	0.169944	+	0.0455364i
$668$		0			0
$669$	9.10842	+	2.44059i	0.352152	+	0.0943588i
$670$		0			0
$671$	8.98956	−	8.98956i	0.347038	−	0.347038i
$672$		0			0
$673$	−45.4726	+	12.1843i	−1.75284	+	0.469672i	−0.985229	−	0.171243i	$-0.945222\pi$
$673$	−45.4726	+	12.1843i	−1.75284	+	0.469672i	−0.767611	+	0.640915i	$0.778555\pi$
$674$		0			0
$675$	2.05559	+	10.2484i	0.0791198	+	0.394459i
$676$		0			0
$677$	−8.45570	−	8.45570i	−0.324979	−	0.324979i	0.525695	−	0.850673i	$-0.323805\pi$
$677$	−8.45570	−	8.45570i	−0.324979	−	0.324979i	−0.850673	+	0.525695i	$0.823805\pi$
$678$		0			0
$679$	17.5508	+	10.1329i	0.673537	+	0.388867i
$680$		0			0
$681$	23.0477	+	23.0477i	0.883189	+	0.883189i
$682$		0			0
$683$	26.3633	−	15.2209i	1.00877	−	0.582411i	0.0979355	−	0.995193i	$-0.468776\pi$
$683$	26.3633	−	15.2209i	1.00877	−	0.582411i	0.910830	+	0.412782i	$0.135443\pi$
$684$		0			0
$685$	25.4422	−	5.95378i	0.972098	−	0.227482i
$686$		0			0
$687$	36.5226	−	63.2589i	1.39342	−	2.41348i
$688$		0			0
$689$	−18.6806	+	28.3794i	−0.711673	+	1.08117i
$690$		0			0
$691$	6.23292	−	1.67011i	0.237111	−	0.0635338i	−0.138306	−	0.990389i	$-0.544166\pi$
$691$	6.23292	−	1.67011i	0.237111	−	0.0635338i	0.375418	+	0.926856i	$0.377499\pi$
$692$		0			0
$693$	−4.84305	+	18.0745i	−0.183972	+	0.686594i
$694$		0			0
$695$	1.73661	+	7.42102i	0.0658732	+	0.281495i
$696$		0			0
$697$	−40.4831			−1.53340
$698$		0			0
$699$	−15.3342	+	26.5597i	−0.579994	+	1.00458i
$700$		0			0
$701$		−	13.4703i		−	0.508766i	−0.967104	−	0.254383i	$-0.918128\pi$
$701$		−	13.4703i		−	0.508766i	0.967104	−	0.254383i	$-0.0818724\pi$
$702$		0			0
$703$	7.07773	−	7.07773i	0.266942	−	0.266942i
$704$		0			0
$705$	−61.4948	−	1.96384i	−2.31603	−	0.0739623i
$706$		0			0
$707$		−	3.37072i		−	0.126769i
$708$		0			0
$709$	1.38408	−	5.16546i	0.0519802	−	0.193993i	−0.935053	−	0.354507i	$-0.884649\pi$
$709$	1.38408	−	5.16546i	0.0519802	−	0.193993i	0.987034	+	0.160514i	$0.0513153\pi$
$710$		0			0
$711$	18.4969	+	32.0376i	0.693689	+	1.20151i
$712$		0			0
$713$	14.6117	+	8.43605i	0.547211	+	0.315933i
$714$		0			0
$715$	−23.2844	+	4.02871i	−0.870788	+	0.150665i
$716$		0			0
$717$	−3.59114	−	2.07335i	−0.134114	−	0.0774305i
$718$		0			0
$719$	−6.75667	−	11.7029i	−0.251981	−	0.436444i	0.712090	−	0.702088i	$-0.247749\pi$
$719$	−6.75667	−	11.7029i	−0.251981	−	0.436444i	−0.964071	+	0.265644i	$0.914415\pi$
$720$		0			0
$721$	−4.22898	+	15.7828i	−0.157495	+	0.587781i
$722$		0			0
$723$			59.6425i			2.21813i
$724$		0			0
$725$	−6.18891	−	12.4994i	−0.229851	−	0.464215i
$726$		0			0
$727$	−19.2005	+	19.2005i	−0.712108	+	0.712108i	−0.966976	−	0.254868i	$-0.917968\pi$
$727$	−19.2005	+	19.2005i	−0.712108	+	0.712108i	0.254868	+	0.966976i	$0.417968\pi$
$728$		0			0
$729$		−	38.9858i		−	1.44392i
$730$		0			0
$731$	−12.4305	+	21.5303i	−0.459759	+	0.796326i
$732$		0			0
$733$	14.0351			0.518399			0.259199	−	0.965824i	$-0.416541\pi$
$733$	14.0351			0.518399			0.259199	+	0.965824i	$0.416541\pi$
$734$		0			0
$735$	−12.8549	+	20.7093i	−0.474160	+	0.763875i
$736$		0			0
$737$	3.75444	−	14.0118i	0.138297	−	0.516130i
$738$		0			0
$739$	20.2162	−	5.41692i	0.743666	−	0.199265i	0.132959	−	0.991122i	$-0.457552\pi$
$739$	20.2162	−	5.41692i	0.743666	−	0.199265i	0.610707	+	0.791857i	$0.290885\pi$
$740$		0			0
$741$	4.56069	+	22.1290i	0.167541	+	0.812929i
$742$		0			0
$743$	9.38363	−	16.2529i	0.344252	−	0.596262i	−0.640966	−	0.767570i	$-0.721466\pi$
$743$	9.38363	−	16.2529i	0.344252	−	0.596262i	0.985218	+	0.171308i	$0.0547992\pi$
$744$		0			0
$745$	−9.98936	+	16.0929i	−0.365982	+	0.589599i
$746$		0			0
$747$	−21.9757	+	12.6877i	−0.804049	+	0.464218i
$748$		0			0
$749$	−3.28521	−	3.28521i	−0.120039	−	0.120039i
$750$		0			0
$751$	−23.6911	−	13.6781i	−0.864502	−	0.499121i	0.00101517	−	0.999999i	$-0.499677\pi$
$751$	−23.6911	−	13.6781i	−0.864502	−	0.499121i	−0.865517	+	0.500879i	$0.833010\pi$
$752$		0			0
$753$	27.3693	+	27.3693i	0.997393	+	0.997393i
$754$		0			0
$755$	−12.3738	−	23.1052i	−0.450328	−	0.840884i
$756$		0			0
$757$	−14.3734	+	3.85135i	−0.522412	+	0.139980i	−0.510382	−	0.859948i	$-0.670496\pi$
$757$	−14.3734	+	3.85135i	−0.522412	+	0.139980i	−0.0120297	+	0.999928i	$0.503829\pi$
$758$		0			0
$759$	−8.80437	+	8.80437i	−0.319579	+	0.319579i
$760$		0			0
$761$	−39.9406	−	10.7020i	−1.44784	−	0.387949i	−0.552571	−	0.833466i	$-0.686353\pi$
$761$	−39.9406	−	10.7020i	−1.44784	−	0.387949i	−0.895274	+	0.445517i	$0.853020\pi$
$762$		0			0
$763$	−2.40573	−	0.644613i	−0.0870933	−	0.0233366i
$764$		0			0
$765$	−2.22031	+	69.5260i	−0.0802755	+	2.51372i
$766$		0			0
$767$	−0.950571	+	16.2168i	−0.0343231	+	0.585553i
$768$		0			0
$769$	−5.79043	−	21.6102i	−0.208808	−	0.779283i	−0.988255	−	0.152815i	$-0.951166\pi$
$769$	−5.79043	−	21.6102i	−0.208808	−	0.779283i	0.779447	−	0.626469i	$-0.215500\pi$
$770$		0			0
$771$	19.7454	−	11.4000i	0.711114	−	0.410562i
$772$		0			0
$773$	9.98015	+	17.2861i	0.358961	+	0.621739i	0.987788	−	0.155807i	$-0.0497978\pi$
$773$	9.98015	+	17.2861i	0.358961	+	0.621739i	−0.628827	+	0.777546i	$0.716464\pi$
$774$		0			0
$775$	−10.1850	−	50.7785i	−0.365857	−	1.82402i
$776$		0			0
$777$	−4.72212	−	17.6232i	−0.169405	−	0.632228i
$778$		0			0
$779$	11.8870			0.425895
$780$		0			0
$781$	18.5277			0.662973
$782$		0			0
$783$	−1.50930	−	5.63280i	−0.0539381	−	0.201300i
$784$		0			0
$785$	−18.6986	+	10.0139i	−0.667381	+	0.357410i
$786$		0			0
$787$	17.0155	+	29.4716i	0.606536	+	1.05055i	0.991807	+	0.127747i	$0.0407746\pi$
$787$	17.0155	+	29.4716i	0.606536	+	1.05055i	−0.385271	+	0.922803i	$0.625892\pi$
$788$		0			0
$789$	41.5151	−	23.9687i	1.47798	−	0.853310i
$790$		0			0
$791$	6.79020	+	25.3414i	0.241432	+	0.901036i
$792$		0			0
$793$	−10.3924	−	11.6867i	−0.369047	−	0.415005i
$794$		0			0
$795$	40.0778	−	37.5972i	1.42141	−	1.33344i
$796$		0			0
$797$	−16.2209	−	4.34638i	−0.574574	−	0.153957i	−0.0401804	−	0.999192i	$-0.512793\pi$
$797$	−16.2209	−	4.34638i	−0.574574	−	0.153957i	−0.534394	+	0.845236i	$0.679460\pi$
$798$		0			0
$799$	−83.3937	−	22.3453i	−2.95026	−	0.790519i
$800$		0			0
$801$	−1.60893	+	1.60893i	−0.0568487	+	0.0568487i
$802$		0			0
$803$	20.1951	−	5.41127i	0.712670	−	0.190959i
$804$		0			0
$805$	5.39223	−	2.88776i	0.190051	−	0.101780i
$806$		0			0
$807$	−19.7859	−	19.7859i	−0.696496	−	0.696496i
$808$		0			0
$809$	−9.82165	−	5.67053i	−0.345311	−	0.199365i	0.317307	−	0.948323i	$-0.397221\pi$
$809$	−9.82165	−	5.67053i	−0.345311	−	0.199365i	−0.662618	+	0.748957i	$0.730555\pi$
$810$		0			0
$811$	−28.6282	−	28.6282i	−1.00527	−	1.00527i	−0.999986	−	0.00528760i	$-0.998317\pi$
$811$	−28.6282	−	28.6282i	−1.00527	−	1.00527i	−0.00528760	−	0.999986i	$-0.501683\pi$
$812$		0			0
$813$	−55.2129	+	31.8772i	−1.93640	+	1.11798i
$814$		0			0
$815$	−7.36610	−	31.4775i	−0.258023	−	1.10261i
$816$		0			0
$817$	3.64995	−	6.32191i	0.127696	−	0.221175i
$818$		0			0
$819$	21.8476	+	7.24853i	0.763417	+	0.253284i
$820$		0			0
$821$	19.2420	−	5.15587i	0.671550	−	0.179941i	0.0930969	−	0.995657i	$-0.470323\pi$
$821$	19.2420	−	5.15587i	0.671550	−	0.179941i	0.578453	+	0.815716i	$0.303657\pi$
$822$		0			0
$823$	−1.48917	+	5.55765i	−0.0519092	+	0.193728i	−0.987011	−	0.160651i	$-0.948641\pi$
$823$	−1.48917	+	5.55765i	−0.0519092	+	0.193728i	0.935102	+	0.354378i	$0.115307\pi$
$824$		0			0
$825$	38.1420	+	2.43861i	1.32793	+	0.0849017i
$826$		0			0
$827$	−15.7588			−0.547985			−0.273993	−	0.961732i	$-0.588344\pi$
$827$	−15.7588			−0.547985			−0.273993	+	0.961732i	$0.588344\pi$
$828$		0			0
$829$	−7.86690	+	13.6259i	−0.273229	+	0.473246i	−0.969687	−	0.244352i	$-0.921425\pi$
$829$	−7.86690	+	13.6259i	−0.273229	+	0.473246i	0.696458	+	0.717598i	$0.254758\pi$
$830$		0			0
$831$			70.4984i			2.44556i
$832$		0			0
$833$	−24.1854	+	24.1854i	−0.837975	+	0.837975i
$834$		0			0
$835$	11.6823	+	12.4531i	0.404283	+	0.430956i
$836$		0			0
$837$		−	21.6533i		−	0.748447i
$838$		0			0
$839$	−0.629782	+	2.35038i	−0.0217425	+	0.0811441i	−0.975945	−	0.218019i	$-0.930041\pi$
$839$	−0.629782	+	2.35038i	−0.0217425	+	0.0811441i	0.954202	+	0.299163i	$0.0967073\pi$
$840$		0			0
$841$	−10.6093	−	18.3758i	−0.365837	−	0.633648i
$842$		0			0
$843$	−66.3258	−	38.2932i	−2.28438	−	1.31889i
$844$		0			0
$845$	3.27133	+	28.8842i	0.112537	+	0.993648i
$846$		0			0
$847$	−3.50403	−	2.02305i	−0.120400	−	0.0695128i
$848$		0			0
$849$	15.5959	+	27.0128i	0.535249	+	0.927078i
$850$		0			0
$851$	1.75623	−	6.55434i	0.0602028	−	0.224680i
$852$		0			0
$853$			33.0234i			1.13070i	0.824851	+	0.565350i	$0.191259\pi$
$853$			33.0234i			1.13070i	−0.824851	+	0.565350i	$0.808741\pi$
$854$		0			0
$855$	0.651947	−	20.4148i	0.0222961	−	0.698172i
$856$		0			0
$857$	−10.7686	+	10.7686i	−0.367849	+	0.367849i	−0.866692	−	0.498843i	$-0.833758\pi$
$857$	−10.7686	+	10.7686i	−0.367849	+	0.367849i	0.498843	+	0.866692i	$0.333758\pi$
$858$		0			0
$859$			15.3788i			0.524717i	0.964970	+	0.262359i	$0.0845003\pi$
$859$			15.3788i			0.524717i	−0.964970	+	0.262359i	$0.915500\pi$
$860$		0			0
$861$	10.8336	−	18.7644i	0.369208	−	0.639488i
$862$		0			0
$863$	−21.4239			−0.729278			−0.364639	−	0.931149i	$-0.618808\pi$
$863$	−21.4239			−0.729278			−0.364639	+	0.931149i	$0.618808\pi$
$864$		0			0
$865$	44.6535	+	27.7178i	1.51826	+	0.942433i
$866$		0			0
$867$	−33.7253	+	125.864i	−1.14537	+	4.27458i
$868$		0			0
$869$	27.5502	−	7.38204i	0.934575	−	0.250419i
$870$		0			0
$871$	−16.9368	−	5.61922i	−0.573880	−	0.190400i
$872$		0			0
$873$	22.9379	−	39.7297i	0.776331	−	1.34465i
$874$		0			0
$875$	−17.5883	−	6.57156i	−0.594592	−	0.222159i
$876$		0			0
$877$	1.50608	−	0.869538i	0.0508568	−	0.0293622i	−0.474356	−	0.880333i	$-0.657319\pi$
$877$	1.50608	−	0.869538i	0.0508568	−	0.0293622i	0.525213	+	0.850971i	$0.323986\pi$
$878$		0			0
$879$	21.6256	+	21.6256i	0.729413	+	0.729413i
$880$		0			0
$881$	−25.2860	−	14.5989i	−0.851908	−	0.491849i	0.00938605	−	0.999956i	$-0.497012\pi$
$881$	−25.2860	−	14.5989i	−0.851908	−	0.491849i	−0.861294	+	0.508107i	$0.830346\pi$
$882$		0			0
$883$	11.5752	+	11.5752i	0.389535	+	0.389535i	0.874522	−	0.484986i	$-0.161175\pi$
$883$	11.5752	+	11.5752i	0.389535	+	0.389535i	−0.484986	+	0.874522i	$0.661175\pi$
$884$		0			0
$885$	7.60682	−	25.1488i	0.255700	−	0.845368i
$886$		0			0
$887$	46.0060	−	12.3273i	1.54473	−	0.413909i	0.616939	−	0.787011i	$-0.288372\pi$
$887$	46.0060	−	12.3273i	1.54473	−	0.413909i	0.927791	+	0.373102i	$0.121706\pi$
$888$		0			0
$889$	20.2785	−	20.2785i	0.680121	−	0.680121i
$890$		0			0
$891$	−16.8529	−	4.51573i	−0.564595	−	0.151283i
$892$		0			0
$893$	24.4868	+	6.56121i	0.819419	+	0.219563i
$894$		0			0
$895$	−37.7651	−	40.2567i	−1.26235	−	1.34563i
$896$		0			0
$897$	10.1784	+	11.4459i	0.339846	+	0.382167i
$898$		0			0
$899$	7.47828	+	27.9093i	0.249415	+	0.930828i
$900$		0			0
$901$	66.7803	−	38.5556i	2.22477	−	1.28447i
$902$		0			0
$903$	−6.65302	−	11.5234i	−0.221399	−	0.383474i
$904$		0			0
$905$	13.6072	+	4.11581i	0.452319	+	0.136814i
$906$		0			0
$907$	7.47130	+	27.8833i	0.248080	+	0.925848i	0.971810	+	0.235765i	$0.0757595\pi$
$907$	7.47130	+	27.8833i	0.248080	+	0.925848i	−0.723730	+	0.690083i	$0.757574\pi$
$908$		0			0
$909$	−7.63030			−0.253081
$910$		0			0
$911$	20.5759			0.681711			0.340855	−	0.940116i	$-0.389283\pi$
$911$	20.5759			0.681711			0.340855	+	0.940116i	$0.389283\pi$
$912$		0			0
$913$	5.06359	+	18.8976i	0.167581	+	0.625419i
$914$		0			0
$915$	11.9417	+	22.2984i	0.394780	+	0.737161i
$916$		0			0
$917$	13.9573	+	24.1747i	0.460909	+	0.798319i
$918$		0			0
$919$	45.7438	−	26.4102i	1.50895	−	0.871193i	0.509004	−	0.860764i	$-0.330014\pi$
$919$	45.7438	−	26.4102i	1.50895	−	0.871193i	0.999946	−	0.0104288i	$-0.00331966\pi$
$920$		0			0
$921$	−11.8192	−	44.1097i	−0.389455	−	1.45346i
$922$		0			0
$923$	1.33369	−	22.7527i	0.0438989	−	0.748916i
$924$		0			0
$925$	−18.6659	+	9.24217i	−0.613730	+	0.303881i
$926$		0			0
$927$	35.7274	+	9.57313i	1.17344	+	0.314423i
$928$		0			0
$929$	−1.13051	−	0.302919i	−0.0370908	−	0.00993846i	0.240226	−	0.970717i	$-0.422778\pi$
$929$	−1.13051	−	0.302919i	−0.0370908	−	0.00993846i	−0.277317	+	0.960779i	$0.589445\pi$
$930$		0			0
$931$	7.10153	−	7.10153i	0.232743	−	0.232743i
$932$		0			0
$933$	46.1548	−	12.3671i	1.51104	−	0.404882i
$934$		0			0
$935$	51.3345	+	15.5273i	1.67882	+	0.507796i
$936$		0			0
$937$	19.3677	+	19.3677i	0.632716	+	0.632716i	0.948748	−	0.316033i	$-0.102351\pi$
$937$	19.3677	+	19.3677i	0.632716	+	0.632716i	−0.316033	+	0.948748i	$0.602351\pi$
$938$		0			0
$939$	15.1959	+	8.77336i	0.495900	+	0.286308i
$940$		0			0
$941$	−10.4168	−	10.4168i	−0.339576	−	0.339576i	0.516631	−	0.856208i	$-0.327186\pi$
$941$	−10.4168	−	10.4168i	−0.339576	−	0.339576i	−0.856208	+	0.516631i	$0.827186\pi$
$942$		0			0
$943$	6.97877	−	4.02919i	0.227260	−	0.131209i
$944$		0			0
$945$	−6.66970	−	4.14008i	−0.216965	−	0.134677i
$946$		0			0
$947$	−11.0874	+	19.2039i	−0.360292	+	0.624044i	−0.988009	−	0.154398i	$-0.950656\pi$
$947$	−11.0874	+	19.2039i	−0.360292	+	0.624044i	0.627717	+	0.778442i	$0.283990\pi$
$948$		0			0
$949$	−5.19154	−	25.1899i	−0.168524	−	0.817700i
$950$		0			0
$951$	−72.0109	+	19.2953i	−2.33511	+	0.625692i
$952$		0			0
$953$	−0.0138381	+	0.0516447i	−0.000448262	+	0.00167293i	−0.966150	−	0.257982i	$-0.916942\pi$
$953$	−0.0138381	+	0.0516447i	−0.000448262	+	0.00167293i	0.965701	+	0.259655i	$0.0836090\pi$
$954$		0			0
$955$	−23.6649	+	5.53787i	−0.765778	+	0.179201i
$956$		0			0
$957$	−21.3231			−0.689277
$958$		0			0
$959$	−9.81211	+	16.9951i	−0.316850	+	0.548800i
$960$		0			0
$961$			76.2875i			2.46089i
$962$		0			0
$963$	−7.43672	+	7.43672i	−0.239645	+	0.239645i
$964$		0			0
$965$	26.3216	−	24.6925i	0.847322	−	0.794878i
$966$		0			0
$967$		−	24.7090i		−	0.794586i	−0.917692	−	0.397293i	$-0.869950\pi$
$967$		−	24.7090i		−	0.794586i	0.917692	−	0.397293i	$-0.130050\pi$
$968$		0			0
$969$	13.2721	−	49.5321i	0.426360	−	1.59120i
$970$		0			0
$971$	−20.3866	−	35.3107i	−0.654238	−	1.13317i	−0.982084	−	0.188442i	$-0.939656\pi$
$971$	−20.3866	−	35.3107i	−0.654238	−	1.13317i	0.327846	−	0.944731i	$-0.393677\pi$
$972$		0			0
$973$	−4.95714	−	2.86201i	−0.158919	−	0.0917517i
$974$		0			0
$975$	5.74031	−	46.6643i	0.183837	−	1.49446i
$976$		0			0
$977$	23.1729	+	13.3789i	0.741368	+	0.428029i	0.822567	−	0.568669i	$-0.192541\pi$
$977$	23.1729	+	13.3789i	0.741368	+	0.428029i	−0.0811984	+	0.996698i	$0.525875\pi$
$978$		0			0
$979$	0.877148	+	1.51926i	0.0280338	+	0.0485559i
$980$		0			0
$981$	−1.45921	+	5.44585i	−0.0465890	+	0.173873i
$982$		0			0
$983$			41.8407i			1.33451i	0.744829	+	0.667256i	$0.232531\pi$
$983$			41.8407i			1.33451i	−0.744829	+	0.667256i	$0.767469\pi$
$984$		0			0
$985$	21.8103	−	20.4604i	0.694934	−	0.651922i
$986$		0			0
$987$	32.6742	−	32.6742i	1.04003	−	1.04003i
$988$		0			0
$989$		−	4.94873i		−	0.157361i
$990$		0			0
$991$	7.77839	−	13.4726i	0.247089	−	0.427970i	−0.715628	−	0.698482i	$-0.753859\pi$
$991$	7.77839	−	13.4726i	0.247089	−	0.427970i	0.962717	+	0.270511i	$0.0871927\pi$
$992$		0			0
$993$	−56.0577			−1.77894
$994$		0			0
$995$	45.9602	−	10.7552i	1.45704	−	0.340964i
$996$		0			0
$997$	11.6306	−	43.4062i	0.368346	−	1.37469i	−0.494481	−	0.869188i	$-0.664642\pi$
$997$	11.6306	−	43.4062i	0.368346	−	1.37469i	0.862828	−	0.505498i	$-0.168691\pi$
$998$		0			0
$999$	−8.41170	+	2.25391i	−0.266134	+	0.0713105i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	260.2.bf.c.137.5	yes	20
5.2	odd	4		1300.2.bs.d.293.5		20
5.3	odd	4		260.2.bk.c.33.1	yes	20
5.4	even	2		1300.2.bn.d.657.1		20
13.2	odd	12		260.2.bk.c.197.1	yes	20
65.2	even	12		1300.2.bn.d.93.1		20
65.28	even	12	inner	260.2.bf.c.93.5	✓	20
65.54	odd	12		1300.2.bs.d.457.5		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.bf.c.93.5	✓	20	65.28	even	12	inner
260.2.bf.c.137.5	yes	20	1.1	even	1	trivial
260.2.bk.c.33.1	yes	20	5.3	odd	4
260.2.bk.c.197.1	yes	20	13.2	odd	12
1300.2.bn.d.93.1		20	65.2	even	12
1300.2.bn.d.657.1		20	5.4	even	2
1300.2.bs.d.293.5		20	5.2	odd	4
1300.2.bs.d.457.5		20	65.54	odd	12

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:	\( N \)	\(=\)	\( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	260.bf (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.674996 + 2.51912i) q^{3} +(-0.647383 + 2.14030i) q^{5} +(-0.839682 - 1.45437i) q^{7} +(-3.29226 + 1.90079i) q^{9} +O(q^{10})\)	\(q+(0.674996 + 2.51912i) q^{3} +(-0.647383 + 2.14030i) q^{5} +(-0.839682 - 1.45437i) q^{7} +(-3.29226 + 1.90079i) q^{9} +(0.758596 + 2.83112i) q^{11} +(3.53133 - 0.727792i) q^{13} +(-5.82866 - 0.186138i) q^{15} +(-7.90430 - 2.11795i) q^{17} +(2.32093 + 0.621891i) q^{19} +(3.09695 - 3.09695i) q^{21} +(1.57340 - 0.421590i) q^{23} +(-4.16179 - 2.77119i) q^{25} +(-1.47820 - 1.47820i) q^{27} +(2.41580 + 1.39477i) q^{29} +(7.32419 + 7.32419i) q^{31} +(-6.61987 + 3.82198i) q^{33} +(3.65639 - 0.855639i) q^{35} +(2.08286 - 3.60763i) q^{37} +(4.21703 + 8.40459i) q^{39} +(4.77856 - 1.28041i) q^{41} +(0.786313 - 2.93456i) q^{43} +(-1.93691 - 8.27697i) q^{45} +10.5504 q^{47} +(2.08987 - 3.61976i) q^{49} -21.3415i q^{51} +(-6.66320 + 6.66320i) q^{53} +(-6.55055 - 0.209192i) q^{55} +6.26647i q^{57} +(-1.16609 + 4.35192i) q^{59} +(-2.16875 - 3.75639i) q^{61} +(5.52891 + 3.19211i) q^{63} +(-0.728428 + 8.02928i) q^{65} +(-4.28613 - 2.47460i) q^{67} +(2.12407 + 3.67900i) q^{69} +(1.63607 - 6.10591i) q^{71} -7.13327i q^{73} +(4.17176 - 12.3546i) q^{75} +(3.48052 - 3.48052i) q^{77} -9.73120i q^{79} +(-2.97638 + 5.15523i) q^{81} +6.67496 q^{83} +(9.65016 - 15.5465i) q^{85} +(-1.88292 + 7.02716i) q^{87} +(0.578139 - 0.154912i) q^{89} +(-4.02368 - 4.52476i) q^{91} +(-13.5067 + 23.3943i) q^{93} +(-2.83356 + 4.56489i) q^{95} +(-10.4508 + 6.03380i) q^{97} +(-7.87885 - 7.87885i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{3} - 6 q^{5} - 6 q^{7} + 12 q^{9}+O(q^{10}) \) 20 * q - 2 * q^3 - 6 * q^5 - 6 * q^7 + 12 * q^9	\( 20 q - 2 q^{3} - 6 q^{5} - 6 q^{7} + 12 q^{9} - 6 q^{13} + 20 q^{15} + 6 q^{17} - 20 q^{19} - 12 q^{21} + 30 q^{23} - 2 q^{25} - 20 q^{27} - 24 q^{29} + 8 q^{31} - 30 q^{33} + 30 q^{37} - 4 q^{39} + 6 q^{41} + 22 q^{43} + 36 q^{45} - 14 q^{49} + 30 q^{53} - 34 q^{55} + 24 q^{59} - 32 q^{61} - 84 q^{63} - 60 q^{65} - 54 q^{67} + 16 q^{69} + 26 q^{75} + 12 q^{77} + 2 q^{81} - 48 q^{83} + 74 q^{85} + 38 q^{87} + 30 q^{89} - 72 q^{91} - 16 q^{93} - 6 q^{95} - 6 q^{97} - 20 q^{99}+O(q^{100}) \) 20 * q - 2 * q^3 - 6 * q^5 - 6 * q^7 + 12 * q^9 - 6 * q^13 + 20 * q^15 + 6 * q^17 - 20 * q^19 - 12 * q^21 + 30 * q^23 - 2 * q^25 - 20 * q^27 - 24 * q^29 + 8 * q^31 - 30 * q^33 + 30 * q^37 - 4 * q^39 + 6 * q^41 + 22 * q^43 + 36 * q^45 - 14 * q^49 + 30 * q^53 - 34 * q^55 + 24 * q^59 - 32 * q^61 - 84 * q^63 - 60 * q^65 - 54 * q^67 + 16 * q^69 + 26 * q^75 + 12 * q^77 + 2 * q^81 - 48 * q^83 + 74 * q^85 + 38 * q^87 + 30 * q^89 - 72 * q^91 - 16 * q^93 - 6 * q^95 - 6 * q^97 - 20 * q^99

Introduction

L-functions

Modular forms

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Database

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