LMFDB - Embedded newform 260.2.bk.c.197.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [260,2,Mod(33,260)]

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, 9, 11]))

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

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

chi := DirichletCharacter("260.33");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 260 = 2^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	260.bk (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:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			197.1
Root			$-1.49418i$ of defining polynomial
Character	$\chi$	$=$	260.197
Dual form			260.2.bk.c.33.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.51912 - 0.674996i) q^{3} +(2.14030 + 0.647383i) q^{5} +(-1.45437 - 0.839682i) q^{7} +(3.29226 + 1.90079i) q^{9} +O(q^{10})$	\(q+(-2.51912 - 0.674996i) q^{3} +(2.14030 + 0.647383i) q^{5} +(-1.45437 - 0.839682i) q^{7} +(3.29226 + 1.90079i) q^{9} +(0.758596 - 2.83112i) q^{11} +(0.727792 - 3.53133i) q^{13} +(-4.95470 - 3.07553i) q^{15} +(-2.11795 - 7.90430i) q^{17} +(-2.32093 + 0.621891i) q^{19} +(3.09695 + 3.09695i) q^{21} +(0.421590 - 1.57340i) q^{23} +(4.16179 + 2.77119i) q^{25} +(-1.47820 - 1.47820i) q^{27} +(-2.41580 + 1.39477i) q^{29} +(7.32419 - 7.32419i) q^{31} +(-3.82198 + 6.61987i) q^{33} +(-2.56920 - 2.73871i) q^{35} +(-3.60763 + 2.08286i) q^{37} +(-4.21703 + 8.40459i) q^{39} +(4.77856 + 1.28041i) q^{41} +(2.93456 - 0.786313i) q^{43} +(5.81590 + 6.19961i) q^{45} +10.5504i q^{47} +(-2.08987 - 3.61976i) q^{49} +21.3415i q^{51} +(-6.66320 + 6.66320i) q^{53} +(3.45644 - 5.56835i) q^{55} +6.26647 q^{57} +(1.16609 + 4.35192i) q^{59} +(-2.16875 + 3.75639i) q^{61} +(-3.19211 - 5.52891i) q^{63} +(3.84382 - 7.08696i) q^{65} +(-2.47460 - 4.28613i) q^{67} +(-2.12407 + 3.67900i) q^{69} +(1.63607 + 6.10591i) q^{71} +7.13327 q^{73} +(-8.61350 - 9.79014i) q^{75} +(-3.48052 + 3.48052i) q^{77} -9.73120i q^{79} +(-2.97638 - 5.15523i) q^{81} -6.67496i q^{83} +(0.584050 - 18.2887i) q^{85} +(7.02716 - 1.88292i) q^{87} +(-0.578139 - 0.154912i) q^{89} +(-4.02368 + 4.52476i) q^{91} +(-23.3943 + 13.5067i) q^{93} +(-5.37009 - 0.171494i) q^{95} +(6.03380 - 10.4508i) q^{97} +(7.87885 - 7.87885i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{3} + 12 q^{5} + 6 q^{7} - 12 q^{9}+O(q^{10}) $ 20 * q - 2 * q^3 + 12 * q^5 + 6 * q^7 - 12 * q^9	$ 20 q - 2 q^{3} + 12 q^{5} + 6 q^{7} - 12 q^{9} + 8 q^{13} - 20 q^{15} + 20 q^{19} - 12 q^{21} + 6 q^{23} + 2 q^{25} - 20 q^{27} + 24 q^{29} + 8 q^{31} - 10 q^{33} - 36 q^{35} + 4 q^{39} + 6 q^{41} + 38 q^{43} - 16 q^{45} + 14 q^{49} + 30 q^{53} + 2 q^{55} - 76 q^{57} - 24 q^{59} - 32 q^{61} - 24 q^{63} - 30 q^{65} + 22 q^{67} - 16 q^{69} - 44 q^{73} - 2 q^{75} - 12 q^{77} + 2 q^{81} + 50 q^{85} + 38 q^{87} - 30 q^{89} - 72 q^{91} - 48 q^{93} - 30 q^{95} + 46 q^{97} + 20 q^{99}+O(q^{100}) $ 20 * q - 2 * q^3 + 12 * q^5 + 6 * q^7 - 12 * q^9 + 8 * q^13 - 20 * q^15 + 20 * q^19 - 12 * q^21 + 6 * q^23 + 2 * q^25 - 20 * q^27 + 24 * q^29 + 8 * q^31 - 10 * q^33 - 36 * q^35 + 4 * q^39 + 6 * q^41 + 38 * q^43 - 16 * q^45 + 14 * q^49 + 30 * q^53 + 2 * q^55 - 76 * q^57 - 24 * q^59 - 32 * q^61 - 24 * q^63 - 30 * q^65 + 22 * q^67 - 16 * q^69 - 44 * q^73 - 2 * q^75 - 12 * q^77 + 2 * q^81 + 50 * q^85 + 38 * q^87 - 30 * q^89 - 72 * q^91 - 48 * q^93 - 30 * q^95 + 46 * q^97 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−2.51912	−	0.674996i	−1.45441	−	0.389709i	−0.556857	−	0.830608i	$-0.687993\pi$
$3$	−2.51912	−	0.674996i	−1.45441	−	0.389709i	−0.897557	+	0.440899i	$0.854660\pi$
$4$		0			0
$5$	2.14030	+	0.647383i	0.957172	+	0.289518i
$5$	2.14030	+	0.647383i	0.957172	+	0.289518i
$6$		0			0
$7$	−1.45437	−	0.839682i	−0.549701	−	0.317370i	0.199300	−	0.979938i	$-0.436133\pi$
$7$	−1.45437	−	0.839682i	−0.549701	−	0.317370i	−0.749001	+	0.662568i	$0.769466\pi$
$8$		0			0
$9$	3.29226	+	1.90079i	1.09742	+	0.633596i
$10$		0			0
$11$	0.758596	−	2.83112i	0.228725	−	0.853614i	−0.752153	−	0.658989i	$-0.770984\pi$
$11$	0.758596	−	2.83112i	0.228725	−	0.853614i	0.980878	−	0.194625i	$-0.0623490\pi$
$12$		0			0
$13$	0.727792	−	3.53133i	0.201853	−	0.979416i
$13$	0.727792	−	3.53133i	0.201853	−	0.979416i
$14$		0			0
$15$	−4.95470	−	3.07553i	−1.27930	−	0.794098i
$16$		0			0
$17$	−2.11795	−	7.90430i	−0.513679	−	1.91707i	−0.376082	−	0.926587i	$-0.622729\pi$
$17$	−2.11795	−	7.90430i	−0.513679	−	1.91707i	−0.137597	−	0.990488i	$-0.543938\pi$
$18$		0			0
$19$	−2.32093	+	0.621891i	−0.532458	+	0.142672i	−0.515023	−	0.857176i	$-0.672217\pi$
$19$	−2.32093	+	0.621891i	−0.532458	+	0.142672i	−0.0174347	+	0.999848i	$0.505550\pi$
$20$		0			0
$21$	3.09695	+	3.09695i	0.675811	+	0.675811i
$22$		0			0
$23$	0.421590	−	1.57340i	0.0879077	−	0.328076i	−0.907941	−	0.419098i	$-0.862347\pi$
$23$	0.421590	−	1.57340i	0.0879077	−	0.328076i	0.995849	+	0.0910215i	$0.0290132\pi$
$24$		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	$-0.750060\pi$
$29$	−2.41580	+	1.39477i	−0.448604	+	0.259001i	0.258637	+	0.965975i	$0.416727\pi$
$30$		0			0
$31$	7.32419	−	7.32419i	1.31546	−	1.31546i	0.398137	−	0.917326i	$-0.369657\pi$
$31$	7.32419	−	7.32419i	1.31546	−	1.31546i	0.917326	−	0.398137i	$-0.130343\pi$
$32$		0			0
$33$	−3.82198	+	6.61987i	−0.665322	+	1.15237i
$34$		0			0
$35$	−2.56920	−	2.73871i	−0.434274	−	0.462926i
$36$		0			0
$37$	−3.60763	+	2.08286i	−0.593090	+	0.342421i	−0.766318	−	0.642461i	$-0.777913\pi$
$37$	−3.60763	+	2.08286i	−0.593090	+	0.342421i	0.173228	+	0.984882i	$0.444580\pi$
$38$		0			0
$39$	−4.21703	+	8.40459i	−0.675265	+	1.34581i
$40$		0			0
$41$	4.77856	+	1.28041i	0.746286	+	0.199967i	0.611870	−	0.790958i	$-0.290418\pi$
$41$	4.77856	+	1.28041i	0.746286	+	0.199967i	0.134416	+	0.990925i	$0.457084\pi$
$42$		0			0
$43$	2.93456	−	0.786313i	0.447516	−	0.119912i	−0.0280207	−	0.999607i	$-0.508920\pi$
$43$	2.93456	−	0.786313i	0.447516	−	0.119912i	0.475537	+	0.879696i	$0.342254\pi$
$44$		0			0
$45$	5.81590	+	6.19961i	0.866983	+	0.924184i
$46$		0			0
$47$			10.5504i			1.53894i	0.638685	+	0.769469i	$0.279479\pi$
$47$			10.5504i			1.53894i	−0.638685	+	0.769469i	$0.720521\pi$
$48$		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
$55$	3.45644	−	5.56835i	0.466066	−	0.750836i
$56$		0			0
$57$	6.26647			0.830014
$58$		0			0
$59$	1.16609	+	4.35192i	0.151812	+	0.566572i	0.999357	+	0.0358480i	$0.0114132\pi$
$59$	1.16609	+	4.35192i	0.151812	+	0.566572i	−0.847545	+	0.530724i	$0.821920\pi$
$60$		0			0
$61$	−2.16875	+	3.75639i	−0.277680	+	0.480956i	−0.970808	−	0.239859i	$-0.922899\pi$
$61$	−2.16875	+	3.75639i	−0.277680	+	0.480956i	0.693128	+	0.720815i	$0.256232\pi$
$62$		0			0
$63$	−3.19211	−	5.52891i	−0.402169	−	0.696577i
$64$		0			0
$65$	3.84382	−	7.08696i	0.476767	−	0.879030i
$66$		0			0
$67$	−2.47460	−	4.28613i	−0.302320	−	0.523634i	0.674341	−	0.738420i	$-0.264428\pi$
$67$	−2.47460	−	4.28613i	−0.302320	−	0.523634i	−0.976661	+	0.214786i	$0.931095\pi$
$68$		0			0
$69$	−2.12407	+	3.67900i	−0.255708	+	0.442900i
$70$		0			0
$71$	1.63607	+	6.10591i	0.194166	+	0.724639i	0.992481	+	0.122398i	$0.0390585\pi$
$71$	1.63607	+	6.10591i	0.194166	+	0.724639i	−0.798315	+	0.602240i	$0.794275\pi$
$72$		0			0
$73$	7.13327			0.834886			0.417443	−	0.908703i	$-0.362926\pi$
$73$	7.13327			0.834886			0.417443	+	0.908703i	$0.362926\pi$
$74$		0			0
$75$	−8.61350	−	9.79014i	−0.994602	−	1.13047i
$76$		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
$83$		−	6.67496i		−	0.732672i	−0.930483	−	0.366336i	$-0.880612\pi$
$83$		−	6.67496i		−	0.732672i	0.930483	−	0.366336i	$-0.119388\pi$
$84$		0			0
$85$	0.584050	−	18.2887i	0.0633492	−	1.98369i
$86$		0			0
$87$	7.02716	−	1.88292i	0.753390	−	0.201870i
$88$		0			0
$89$	−0.578139	−	0.154912i	−0.0612826	−	0.0164206i	0.228047	−	0.973650i	$-0.426766\pi$
$89$	−0.578139	−	0.154912i	−0.0612826	−	0.0164206i	−0.289330	+	0.957229i	$0.593433\pi$
$90$		0			0
$91$	−4.02368	+	4.52476i	−0.421796	+	0.474324i
$92$		0			0
$93$	−23.3943	+	13.5067i	−2.42588	+	1.40058i
$94$		0			0
$95$	−5.37009	−	0.171494i	−0.550960	−	0.0175949i
$96$		0			0
$97$	6.03380	−	10.4508i	0.612639	−	1.06112i	−0.378155	−	0.925742i	$-0.623441\pi$
$97$	6.03380	−	10.4508i	0.612639	−	1.06112i	0.990794	−	0.135380i	$-0.0432254\pi$
$98$		0			0
$99$	7.87885	−	7.87885i	0.791854	−	0.791854i
$100$		0			0
$101$	1.73824	−	1.00357i	0.172961	−	0.0998590i	−0.411020	−	0.911626i	$-0.634827\pi$
$101$	1.73824	−	1.00357i	0.172961	−	0.0998590i	0.583981	+	0.811767i	$0.301494\pi$
$102$		0			0
$103$	6.87986	+	6.87986i	0.677892	+	0.677892i	0.959523	−	0.281631i	$-0.0908753\pi$
$103$	6.87986	+	6.87986i	0.677892	+	0.677892i	−0.281631	+	0.959523i	$0.590875\pi$
$104$		0			0
$105$	4.62350	+	8.63333i	0.451208	+	0.842527i
$106$		0			0
$107$	−0.716027	+	2.67225i	−0.0692209	+	0.258336i	−0.991861	−	0.127327i	$-0.959360\pi$
$107$	−0.716027	+	2.67225i	−0.0692209	+	0.258336i	0.922640	+	0.385662i	$0.126027\pi$
$108$		0			0
$109$	−1.04868	−	1.04868i	−0.100445	−	0.100445i	0.655098	−	0.755544i	$-0.272627\pi$
$109$	−1.04868	−	1.04868i	−0.100445	−	0.100445i	−0.755544	+	0.655098i	$0.772627\pi$
$110$		0			0
$111$	10.4940	−	2.81185i	0.996042	−	0.266889i
$112$		0			0
$113$	4.04332	+	15.0899i	0.380363	+	1.41953i	0.845348	+	0.534216i	$0.179393\pi$
$113$	4.04332	+	15.0899i	0.380363	+	1.41953i	−0.464985	+	0.885319i	$0.653940\pi$
$114$		0			0
$115$	1.92092	−	3.09462i	0.179127	−	0.288574i
$116$		0			0
$117$	9.10840	−	10.2427i	0.842072	−	0.946937i
$118$		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
$123$	−11.1735	−	6.45102i	−1.00748	−	0.581669i
$124$		0			0
$125$	7.11347	+	8.62546i	0.636248	+	0.771484i
$126$		0			0
$127$	16.4949	+	4.41981i	1.46369	+	0.392194i	0.900762	−	0.434312i	$-0.143009\pi$
$127$	16.4949	+	4.41981i	1.46369	+	0.392194i	0.562927	+	0.826507i	$0.309675\pi$
$128$		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
$133$	3.89768	+	1.04438i	0.337972	+	0.0905594i
$134$		0			0
$135$	−2.20684	−	4.12077i	−0.189935	−	0.354659i
$136$		0			0
$137$	−10.1199	−	5.84275i	−0.864605	−	0.499180i	0.000946524	−	1.00000i	$-0.499699\pi$
$137$	−10.1199	−	5.84275i	−0.864605	−	0.499180i	−0.865552	+	0.500819i	$0.833032\pi$
$138$		0			0
$139$	−2.95180	−	1.70422i	−0.250368	−	0.144550i	0.369565	−	0.929205i	$-0.379507\pi$
$139$	−2.95180	−	1.70422i	−0.250368	−	0.144550i	−0.619933	+	0.784655i	$0.712840\pi$
$140$		0			0
$141$	7.12149	−	26.5778i	0.599738	−	2.23825i
$142$		0			0
$143$	−9.44552	−	4.73932i	−0.789874	−	0.396322i
$144$		0			0
$145$	−6.07350	+	1.42127i	−0.504377	+	0.118030i
$146$		0			0
$147$	2.82130	+	10.5292i	0.232697	+	0.868438i
$148$		0			0
$149$	−8.18213	+	2.19240i	−0.670306	+	0.179608i	−0.577893	−	0.816113i	$-0.696125\pi$
$149$	−8.18213	+	2.19240i	−0.670306	+	0.179608i	−0.0924136	+	0.995721i	$0.529458\pi$
$150$		0			0
$151$	−8.28831	−	8.28831i	−0.674493	−	0.674493i	0.284255	−	0.958749i	$-0.408254\pi$
$151$	−8.28831	−	8.28831i	−0.674493	−	0.674493i	−0.958749	+	0.284255i	$0.908254\pi$
$152$		0			0
$153$	8.05155	−	30.0488i	0.650929	−	2.42930i
$154$		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
$163$	−7.22873	+	12.5205i	−0.566198	+	0.980683i	0.430739	+	0.902476i	$0.358253\pi$
$163$	−7.22873	+	12.5205i	−0.566198	+	0.980683i	−0.996937	+	0.0782070i	$0.975080\pi$
$164$		0			0
$165$	−12.4658	+	11.6942i	−0.970461	+	0.910396i
$166$		0			0
$167$	−6.61311	+	3.81808i	−0.511738	+	0.295452i	−0.733548	−	0.679638i	$-0.762137\pi$
$167$	−6.61311	+	3.81808i	−0.511738	+	0.295452i	0.221810	+	0.975090i	$0.428804\pi$
$168$		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
$173$	22.7032	−	6.08331i	1.72609	−	0.462505i	0.746816	−	0.665031i	$-0.231582\pi$
$173$	22.7032	−	6.08331i	1.72609	−	0.462505i	0.979277	+	0.202526i	$0.0649150\pi$
$174$		0			0
$175$	−3.72588	−	7.52492i	−0.281650	−	0.568831i
$176$		0			0
$177$		−	11.7501i		−	0.883193i
$178$		0			0
$179$	12.3426	+	21.3780i	0.922530	+	1.59787i	0.795486	+	0.605973i	$0.207216\pi$
$179$	12.3426	+	21.3780i	0.922530	+	1.59787i	0.127045	+	0.991897i	$0.459451\pi$
$180$		0			0
$181$			6.35761i			0.472557i	0.971685	+	0.236279i	$0.0759278\pi$
$181$			6.35761i			0.472557i	−0.971685	+	0.236279i	$0.924072\pi$
$182$		0			0
$183$	7.99888	−	7.99888i	0.591294	−	0.591294i
$184$		0			0
$185$	−9.06982	+	2.12244i	−0.666826	+	0.156045i
$186$		0			0
$187$	−23.9847			−1.75393
$188$		0			0
$189$	0.908637	+	3.39108i	0.0660936	+	0.246665i
$190$		0			0
$191$	5.43459	−	9.41299i	0.393233	−	0.681100i	−0.599641	−	0.800269i	$-0.704690\pi$
$191$	5.43459	−	9.41299i	0.393233	−	0.681100i	0.992874	+	0.119169i	$0.0380232\pi$
$192$		0			0
$193$	8.07014	+	13.9779i	0.580901	+	1.00615i	0.995373	+	0.0960884i	$0.0306332\pi$
$193$	8.07014	+	13.9779i	0.580901	+	1.00615i	−0.414471	+	0.910062i	$0.636034\pi$
$194$		0			0
$195$	−14.4667	+	15.2583i	−1.03598	+	1.09267i
$196$		0			0
$197$	−6.68699	−	11.5822i	−0.476428	−	0.825198i	0.523207	−	0.852206i	$-0.324736\pi$
$197$	−6.68699	−	11.5822i	−0.476428	−	0.825198i	−0.999635	+	0.0270075i	$0.991402\pi$
$198$		0			0
$199$	10.5547	−	18.2812i	0.748199	−	1.29592i	−0.200485	−	0.979697i	$-0.564252\pi$
$199$	10.5547	−	18.2812i	0.748199	−	1.29592i	0.948685	−	0.316223i	$-0.102415\pi$
$200$		0			0
$201$	3.34069	+	12.4676i	0.235634	+	0.879398i
$202$		0			0
$203$	4.68464			0.328797
$204$		0			0
$205$	9.39865	+	5.83403i	0.656430	+	0.407466i
$206$		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	0.995822	+	0.0913189i	$0.0291082\pi$
$211$	8.38134	+	14.5169i	0.576995	+	0.999385i	−0.418826	+	0.908066i	$0.637558\pi$
$212$		0			0
$213$		−	16.4859i		−	1.12959i
$214$		0			0
$215$	6.78989	+	0.216835i	0.463067	+	0.0147880i
$216$		0			0
$217$	−16.8021	+	4.50211i	−1.14060	+	0.305623i
$218$		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
$223$	3.13130	−	1.80786i	0.209688	−	0.121063i	−0.391479	−	0.920187i	$-0.628036\pi$
$223$	3.13130	−	1.80786i	0.209688	−	0.121063i	0.601166	+	0.799124i	$0.294703\pi$
$224$		0			0
$225$	8.43426	+	17.0342i	0.562284	+	1.13561i
$226$		0			0
$227$	−6.24896	+	10.8235i	−0.414758	+	0.718382i	−0.995403	−	0.0957751i	$-0.969467\pi$
$227$	−6.24896	+	10.8235i	−0.414758	+	0.718382i	0.580645	+	0.814157i	$0.302800\pi$
$228$		0			0
$229$	19.8049	−	19.8049i	1.30874	−	1.30874i	0.386417	−	0.922324i	$-0.373712\pi$
$229$	19.8049	−	19.8049i	1.30874	−	1.30874i	0.922324	−	0.386417i	$-0.126288\pi$
$230$		0			0
$231$	11.1172	−	6.41850i	0.731456	−	0.422307i
$232$		0			0
$233$	−8.31519	−	8.31519i	−0.544746	−	0.544746i	0.380170	−	0.924917i	$-0.375865\pi$
$233$	−8.31519	−	8.31519i	−0.544746	−	0.544746i	−0.924917	+	0.380170i	$0.875865\pi$
$234$		0			0
$235$	−6.83016	+	22.5811i	−0.445550	+	1.47303i
$236$		0			0
$237$	−6.56852	+	24.5140i	−0.426671	+	1.59236i
$238$		0			0
$239$	1.12430	+	1.12430i	0.0727249	+	0.0727249i	0.742534	−	0.669809i	$-0.233624\pi$
$239$	1.12430	+	1.12430i	0.0727249	+	0.0727249i	−0.669809	+	0.742534i	$0.733624\pi$
$240$		0			0
$241$	22.0900	−	5.91899i	1.42294	−	0.381275i	0.536414	−	0.843955i	$-0.319779\pi$
$241$	22.0900	−	5.91899i	1.42294	−	0.381275i	0.886525	+	0.462680i	$0.153112\pi$
$242$		0			0
$243$	5.64126	+	21.0535i	0.361887	+	1.35058i
$244$		0			0
$245$	−2.12958	−	9.10032i	−0.136054	−	0.581398i
$246$		0			0
$247$	0.506950	+	8.64858i	0.0322565	+	0.550296i
$248$		0			0
$249$	−4.50557	+	16.8150i	−0.285529	+	1.06561i
$250$		0			0
$251$	12.8530	+	7.42069i	0.811275	+	0.468390i	0.847398	−	0.530958i	$-0.178168\pi$
$251$	12.8530	+	7.42069i	0.811275	+	0.468390i	−0.0361238	+	0.999347i	$0.511501\pi$
$252$		0			0
$253$	−4.13466	−	2.38714i	−0.259944	−	0.150079i
$254$		0			0
$255$	−13.8161	+	45.6772i	−0.865198	+	2.86042i
$256$		0			0
$257$	−8.44452	−	2.26270i	−0.526754	−	0.141143i	−0.0143653	−	0.999897i	$-0.504573\pi$
$257$	−8.44452	−	2.26270i	−0.526754	−	0.141143i	−0.512389	+	0.858753i	$0.671239\pi$
$258$		0			0
$259$	6.99577			0.434696
$260$		0			0
$261$	−10.6046			−0.656409
$262$		0			0
$263$	17.7547	+	4.75737i	1.09480	+	0.293352i	0.760647	−	0.649166i	$-0.224882\pi$
$263$	17.7547	+	4.75737i	1.09480	+	0.293352i	0.334157	+	0.942517i	$0.391548\pi$
$264$		0			0
$265$	−18.5749	+	9.94763i	−1.14105	+	0.611078i
$266$		0			0
$267$	1.35184	+	0.780483i	0.0827310	+	0.0477648i
$268$		0			0
$269$	9.29173	+	5.36458i	0.566526	+	0.327084i	0.755761	−	0.654848i	$-0.227267\pi$
$269$	9.29173	+	5.36458i	0.566526	+	0.327084i	−0.189234	+	0.981932i	$0.560601\pi$
$270$		0			0
$271$	6.32705	−	23.6129i	0.384341	−	1.43438i	−0.454863	−	0.890562i	$-0.650312\pi$
$271$	6.32705	−	23.6129i	0.384341	−	1.43438i	0.839204	−	0.543817i	$-0.183022\pi$
$272$		0			0
$273$	13.1903	−	8.68244i	0.798314	−	0.525485i
$274$		0			0
$275$	11.0027	−	9.68031i	0.663487	−	0.583745i
$276$		0			0
$277$	6.99634	+	26.1107i	0.420369	+	1.56884i	0.773832	+	0.633390i	$0.218337\pi$
$277$	6.99634	+	26.1107i	0.420369	+	1.56884i	−0.353463	+	0.935448i	$0.614996\pi$
$278$		0			0
$279$	38.0349	−	10.1914i	2.27709	−	0.610144i
$280$		0			0
$281$	−20.7650	−	20.7650i	−1.23874	−	1.23874i	−0.960518	−	0.278218i	$-0.910256\pi$
$281$	−20.7650	−	20.7650i	−1.23874	−	1.23874i	−0.278218	−	0.960518i	$-0.589744\pi$
$282$		0			0
$283$	3.09550	−	11.5526i	0.184008	−	0.686729i	−0.810832	−	0.585279i	$-0.800985\pi$
$283$	3.09550	−	11.5526i	0.184008	−	0.686729i	0.994841	−	0.101450i	$-0.0323483\pi$
$284$		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
$293$	5.86338	−	10.1557i	0.342542	−	0.593301i	−0.642362	−	0.766402i	$-0.722045\pi$
$293$	5.86338	−	10.1557i	0.342542	−	0.593301i	0.984904	+	0.173101i	$0.0553786\pi$
$294$		0			0
$295$	−0.321564	+	10.0693i	−0.0187222	+	0.586260i
$296$		0			0
$297$	−5.30633	+	3.06361i	−0.307904	+	0.177769i
$298$		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
$303$	−5.05623	+	1.35481i	−0.290473	+	0.0778319i
$304$		0			0
$305$	−7.07360	+	6.63579i	−0.405033	+	0.379964i
$306$		0			0
$307$		−	17.5100i		−	0.999348i	−0.866214	−	0.499674i	$-0.833453\pi$
$307$		−	17.5100i		−	0.999348i	0.866214	−	0.499674i	$-0.166547\pi$
$308$		0			0
$309$	−12.6873	−	21.9750i	−0.721755	−	1.25012i
$310$		0			0
$311$			18.3218i			1.03893i	0.854491	+	0.519467i	$0.173869\pi$
$311$			18.3218i			1.03893i	−0.854491	+	0.519467i	$0.826131\pi$
$312$		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
$315$	−3.25278	−	13.9001i	−0.183273	−	0.783179i
$316$		0			0
$317$	28.5858			1.60554			0.802768	−	0.596291i	$-0.203359\pi$
$317$	28.5858			1.60554			0.802768	+	0.596291i	$0.203359\pi$
$318$		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
$323$	9.83123	+	17.0282i	0.547024	+	0.947474i
$324$		0			0
$325$	12.8149	−	12.6798i	0.710844	−	0.703350i
$326$		0			0
$327$	1.93390	+	3.34960i	0.106945	+	0.185234i
$328$		0			0
$329$	8.85900	−	15.3442i	0.488413	−	0.845955i
$330$		0			0
$331$	−5.56323	−	20.7622i	−0.305783	−	1.14120i	−0.932270	−	0.361764i	$-0.882175\pi$
$331$	−5.56323	−	20.7622i	−0.305783	−	1.14120i	0.626487	−	0.779432i	$-0.284492\pi$
$332$		0			0
$333$	−15.8363			−0.867825
$334$		0			0
$335$	−2.52162	−	10.7756i	−0.137771	−	0.588736i
$336$		0			0
$337$	12.5568	−	12.5568i	0.684010	−	0.684010i	−0.276891	−	0.960901i	$-0.589304\pi$
$337$	12.5568	−	12.5568i	0.684010	−	0.684010i	0.960901	+	0.276891i	$0.0893042\pi$
$338$		0			0
$339$		−	40.7424i		−	2.21282i
$340$		0			0
$341$	−15.1795	−	26.2917i	−0.822018	−	1.42378i
$342$		0			0
$343$			18.7748i			1.01375i
$344$		0			0
$345$	−6.92788	+	6.49909i	−0.372985	+	0.349899i
$346$		0			0
$347$	−3.96312	+	1.06192i	−0.212751	+	0.0570066i	−0.363620	−	0.931547i	$-0.618459\pi$
$347$	−3.96312	+	1.06192i	−0.212751	+	0.0570066i	0.150869	+	0.988554i	$0.451793\pi$
$348$		0			0
$349$	−1.89219	−	0.507011i	−0.101287	−	0.0271397i	0.207820	−	0.978167i	$-0.433363\pi$
$349$	−1.89219	−	0.507011i	−0.101287	−	0.0271397i	−0.309106	+	0.951027i	$0.600030\pi$
$350$		0			0
$351$	−6.29586	+	4.14420i	−0.336048	+	0.221201i
$352$		0			0
$353$	−2.69208	+	1.55427i	−0.143285	+	0.0827256i	−0.569929	−	0.821694i	$-0.693029\pi$
$353$	−2.69208	+	1.55427i	−0.143285	+	0.0827256i	0.426644	+	0.904420i	$0.359696\pi$
$354$		0			0
$355$	−0.451167	+	14.1277i	−0.0239455	+	0.749819i
$356$		0			0
$357$	17.9201	−	31.0385i	0.948430	−	1.64273i
$358$		0			0
$359$	6.98593	−	6.98593i	0.368703	−	0.368703i	−0.498301	−	0.867004i	$-0.666043\pi$
$359$	6.98593	−	6.98593i	0.368703	−	0.368703i	0.867004	+	0.498301i	$0.166043\pi$
$360$		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
$367$	0.336651	−	1.25640i	0.0175731	−	0.0655835i	−0.956583	−	0.291462i	$-0.905858\pi$
$367$	0.336651	−	1.25640i	0.0175731	−	0.0655835i	0.974156	+	0.225878i	$0.0725251\pi$
$368$		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
$373$	−0.233395	−	0.871043i	−0.0120847	−	0.0451009i	0.959620	−	0.281299i	$-0.0907653\pi$
$373$	−0.233395	−	0.871043i	−0.0120847	−	0.0451009i	−0.971705	+	0.236198i	$0.924099\pi$
$374$		0			0
$375$	−12.0975	−	26.5301i	−0.624714	−	1.37001i
$376$		0			0
$377$	3.16718	+	9.54611i	0.163118	+	0.491650i
$378$		0			0
$379$	3.97268	−	14.8263i	0.204063	−	0.761574i	−0.785670	−	0.618646i	$-0.787682\pi$
$379$	3.97268	−	14.8263i	0.204063	−	0.761574i	0.989733	−	0.142928i	$-0.0456517\pi$
$380$		0			0
$381$	−38.5694	−	22.2680i	−1.97597	−	1.14083i
$382$		0			0
$383$	−11.0835	−	6.39904i	−0.566339	−	0.326976i	0.189347	−	0.981910i	$-0.439363\pi$
$383$	−11.0835	−	6.39904i	−0.566339	−	0.326976i	−0.755686	+	0.654935i	$0.772696\pi$
$384$		0			0
$385$	−9.70259	+	5.19614i	−0.494490	+	0.264820i
$386$		0			0
$387$	11.1560	+	2.98923i	0.567089	+	0.151951i
$388$		0			0
$389$	−16.5057			−0.836870			−0.418435	−	0.908247i	$-0.637421\pi$
$389$	−16.5057			−0.836870			−0.418435	+	0.908247i	$0.637421\pi$
$390$		0			0
$391$	−13.3295			−0.674103
$392$		0			0
$393$	41.8730	+	11.2198i	2.11221	+	0.565966i
$394$		0			0
$395$	6.29981	−	20.8277i	0.316978	−	1.04796i
$396$		0			0
$397$	7.12829	+	4.11552i	0.357759	+	0.206552i	0.668097	−	0.744074i	$-0.267109\pi$
$397$	7.12829	+	4.11552i	0.357759	+	0.206552i	−0.310338	+	0.950626i	$0.600442\pi$
$398$		0			0
$399$	−9.11377	−	5.26184i	−0.456259	−	0.263422i
$400$		0			0
$401$	−7.17051	+	26.7607i	−0.358078	+	1.33637i	0.518488	+	0.855085i	$0.326495\pi$
$401$	−7.17051	+	26.7607i	−0.358078	+	1.33637i	−0.876566	+	0.481281i	$0.840172\pi$
$402$		0			0
$403$	−20.5337	−	31.1946i	−1.02285	−	1.55392i
$404$		0			0
$405$	−3.03294	−	12.9606i	−0.150708	−	0.644018i
$406$		0			0
$407$	3.16010	+	11.7937i	0.156640	+	0.584590i
$408$		0			0
$409$	−17.8703	+	4.78835i	−0.883632	+	0.236768i	−0.671973	−	0.740575i	$-0.734553\pi$
$409$	−17.8703	+	4.78835i	−0.883632	+	0.236768i	−0.211658	+	0.977344i	$0.567886\pi$
$410$		0			0
$411$	21.5495	+	21.5495i	1.06296	+	1.06296i
$412$		0			0
$413$	1.95830	−	7.30846i	0.0963615	−	0.359626i
$414$		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	$-0.633179\pi$
$419$	3.72308	−	2.14952i	0.181884	−	0.105011i	0.588178	+	0.808732i	$0.299846\pi$
$420$		0			0
$421$	6.99925	−	6.99925i	0.341123	−	0.341123i	−0.515667	−	0.856789i	$-0.672456\pi$
$421$	6.99925	−	6.99925i	0.341123	−	0.341123i	0.856789	+	0.515667i	$0.172456\pi$
$422$		0			0
$423$	−20.0541	+	34.7347i	−0.975064	+	1.68886i
$424$		0			0
$425$	13.0898	−	38.7653i	0.634951	−	1.88039i
$426$		0			0
$427$	6.30834	−	3.64212i	0.305282	−	0.176255i
$428$		0			0
$429$	20.5954	+	18.3146i	0.994354	+	0.884237i
$430$		0			0
$431$	1.26467	+	0.338868i	0.0609171	+	0.0163227i	0.289149	−	0.957284i	$-0.406628\pi$
$431$	1.26467	+	0.338868i	0.0609171	+	0.0163227i	−0.228232	+	0.973607i	$0.573294\pi$
$432$		0			0
$433$	−10.0767	+	2.70003i	−0.484253	+	0.129755i	−0.492682	−	0.870209i	$-0.663984\pi$
$433$	−10.0767	+	2.70003i	−0.484253	+	0.129755i	0.00842905	+	0.999964i	$0.497317\pi$
$434$		0			0
$435$	16.2592	+	0.519238i	0.779570	+	0.0248956i
$436$		0			0
$437$			3.91393i			0.187228i
$438$		0			0
$439$	13.6918	+	23.7150i	0.653476	+	1.13185i	0.982274	+	0.187453i	$0.0600232\pi$
$439$	13.6918	+	23.7150i	0.653476	+	1.13185i	−0.328798	+	0.944400i	$0.606643\pi$
$440$		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
$445$	−1.13711	−	0.705835i	−0.0539040	−	0.0334598i
$446$		0			0
$447$	22.0916			1.04490
$448$		0			0
$449$	1.73279	+	6.46685i	0.0817753	+	0.305190i	0.994684	−	0.102974i	$-0.0328359\pi$
$449$	1.73279	+	6.46685i	0.0817753	+	0.305190i	−0.912909	+	0.408164i	$0.866169\pi$
$450$		0			0
$451$	7.24999	−	12.5574i	0.341389	−	0.591303i
$452$		0			0
$453$	15.2847	+	26.4738i	0.718136	+	1.24385i
$454$		0			0
$455$	−11.5411	+	7.07949i	−0.541057	+	0.331892i
$456$		0			0
$457$	11.2163	+	19.4272i	0.524677	+	0.908768i	0.999587	+	0.0287333i	$0.00914734\pi$
$457$	11.2163	+	19.4272i	0.524677	+	0.908768i	−0.474910	+	0.880034i	$0.657519\pi$
$458$		0			0
$459$	−8.55340	+	14.8149i	−0.399239	+	0.691502i
$460$		0			0
$461$	6.83936	+	25.5248i	0.318541	+	1.18881i	0.920647	+	0.390395i	$0.127662\pi$
$461$	6.83936	+	25.5248i	0.318541	+	1.18881i	−0.602107	+	0.798416i	$0.705672\pi$
$462$		0			0
$463$	−19.6621			−0.913777			−0.456888	−	0.889524i	$-0.651036\pi$
$463$	−19.6621			−0.913777			−0.456888	+	0.889524i	$0.651036\pi$
$464$		0			0
$465$	−58.8149	+	13.7634i	−2.72747	+	0.638261i
$466$		0			0
$467$	0.598955	−	0.598955i	0.0277163	−	0.0277163i	−0.693113	−	0.720829i	$-0.743761\pi$
$467$	0.598955	−	0.598955i	0.0277163	−	0.0277163i	0.720829	+	0.693113i	$0.243761\pi$
$468$		0			0
$469$			8.31151i			0.383790i
$470$		0			0
$471$	−12.3696	−	21.4247i	−0.569960	−	0.987200i
$472$		0			0
$473$		−	8.90458i		−	0.409433i
$474$		0			0
$475$	−11.3826	−	3.84355i	−0.522269	−	0.176354i
$476$		0			0
$477$	−34.6023	+	9.27167i	−1.58433	+	0.424520i
$478$		0			0
$479$	15.1500	+	4.05942i	0.692220	+	0.185480i	0.587743	−	0.809048i	$-0.300017\pi$
$479$	15.1500	+	4.05942i	0.692220	+	0.185480i	0.104477	+	0.994527i	$0.466683\pi$
$480$		0			0
$481$	4.72968	+	14.2556i	0.215655	+	0.650000i
$482$		0			0
$483$	6.17838	−	3.56709i	0.281126	−	0.162308i
$484$		0			0
$485$	19.6798	−	18.4618i	0.893616	−	0.838307i
$486$		0			0
$487$	−11.5156	+	19.9455i	−0.521820	+	0.903818i	0.477858	+	0.878437i	$0.341413\pi$
$487$	−11.5156	+	19.9455i	−0.521820	+	0.903818i	−0.999678	+	0.0253810i	$0.991920\pi$
$488$		0			0
$489$	26.6613	−	26.6613i	1.20567	−	1.20567i
$490$		0			0
$491$	−25.0505	+	14.4629i	−1.13051	+	0.652702i	−0.944064	−	0.329762i	$-0.893031\pi$
$491$	−25.0505	+	14.4629i	−1.13051	+	0.652702i	−0.186449	+	0.982465i	$0.559698\pi$
$492$		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
$497$	2.74757	−	10.2541i	0.123245	−	0.459957i
$498$		0			0
$499$	−16.5783	−	16.5783i	−0.742147	−	0.742147i	0.230844	−	0.972991i	$-0.425851\pi$
$499$	−16.5783	−	16.5783i	−0.742147	−	0.742147i	−0.972991	+	0.230844i	$0.925851\pi$
$500$		0			0
$501$	19.2364	−	5.15438i	0.859419	−	0.230281i
$502$		0			0
$503$	−4.86494	−	18.1562i	−0.216917	−	0.809545i	−0.985483	−	0.169775i	$-0.945696\pi$
$503$	−4.86494	−	18.1562i	−0.216917	−	0.809545i	0.768566	−	0.639771i	$-0.220971\pi$
$504$		0			0
$505$	4.37005	−	1.02264i	0.194464	−	0.0455070i
$506$		0			0
$507$	26.6103	+	21.0085i	1.18180	+	0.933022i
$508$		0			0
$509$	7.12866	−	26.6045i	0.315972	−	1.17922i	−0.607109	−	0.794619i	$-0.707671\pi$
$509$	7.12866	−	26.6045i	0.315972	−	1.17922i	0.923081	−	0.384606i	$-0.125663\pi$
$510$		0			0
$511$	−10.3744	−	5.98968i	−0.458937	−	0.264968i
$512$		0			0
$513$	4.35009	+	2.51152i	0.192061	+	0.110886i
$514$		0			0
$515$	10.2711	+	19.1789i	0.452598	+	0.845122i
$516$		0			0
$517$	29.8695	+	8.00350i	1.31366	+	0.351994i
$518$		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
$523$	−12.3767	−	3.31632i	−0.541194	−	0.145012i	−0.0221413	−	0.999755i	$-0.507048\pi$
$523$	−12.3767	−	3.31632i	−0.541194	−	0.145012i	−0.519052	+	0.854742i	$0.673715\pi$
$524$		0			0
$525$	4.30663	+	21.4711i	0.187957	+	0.937076i
$526$		0			0
$527$	−73.4049	−	42.3803i	−3.19757	−	1.84612i
$528$		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
$533$	7.99936	−	15.9428i	0.346491	−	0.690560i
$534$		0			0
$535$	−3.26248	+	5.25588i	−0.141049	+	0.227231i
$536$		0			0
$537$	−16.6624	−	62.1850i	−0.719037	−	2.68348i
$538$		0			0
$539$	−11.8333	+	3.17073i	−0.509697	+	0.136573i
$540$		0			0
$541$	14.7555	+	14.7555i	0.634390	+	0.634390i	0.949166	−	0.314776i	$-0.101929\pi$
$541$	14.7555	+	14.7555i	0.634390	+	0.634390i	−0.314776	+	0.949166i	$0.601929\pi$
$542$		0			0
$543$	4.29136	−	16.0156i	0.184160	−	0.687294i
$544$		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
$553$	−8.17111	+	14.1528i	−0.347471	+	0.601837i
$554$		0			0
$555$	24.2806	+	0.775401i	1.03065	+	0.0329139i
$556$		0			0
$557$	0.635888	−	0.367130i	0.0269435	−	0.0155558i	−0.486468	−	0.873699i	$-0.661715\pi$
$557$	0.635888	−	0.367130i	0.0269435	−	0.0155558i	0.513411	+	0.858143i	$0.328382\pi$
$558$		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
$563$	−21.0579	+	5.64244i	−0.887483	+	0.237800i	−0.673633	−	0.739066i	$-0.735267\pi$
$563$	−21.0579	+	5.64244i	−0.887483	+	0.237800i	−0.213850	+	0.976866i	$0.568600\pi$
$564$		0			0
$565$	−1.11499	+	34.9144i	−0.0469081	+	1.46886i
$566$		0			0
$567$			9.99684i			0.419828i
$568$		0			0
$569$	12.9881	+	22.4960i	0.544487	+	0.943080i	0.998639	+	0.0521554i	$0.0166091\pi$
$569$	12.9881	+	22.4960i	0.544487	+	0.943080i	−0.454152	+	0.890924i	$0.650058\pi$
$570$		0			0
$571$		−	8.75018i		−	0.366184i	−0.983096	−	0.183092i	$-0.941389\pi$
$571$		−	8.75018i		−	0.366184i	0.983096	−	0.183092i	$-0.0586106\pi$
$572$		0			0
$573$	−20.0441	+	20.0441i	−0.837354	+	0.837354i
$574$		0			0
$575$	6.11475	−	5.37984i	0.255003	−	0.224355i
$576$		0			0
$577$	7.98223			0.332304			0.166152	−	0.986100i	$-0.446866\pi$
$577$	7.98223			0.332304			0.166152	+	0.986100i	$0.446866\pi$
$578$		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
$583$	13.8096	+	23.9190i	0.571937	+	0.990623i
$584$		0			0
$585$	26.1257	−	16.0258i	1.08016	−	0.662587i
$586$		0			0
$587$	−5.91804	−	10.2503i	−0.244264	−	0.423077i	0.717661	−	0.696393i	$-0.245213\pi$
$587$	−5.91804	−	10.2503i	−0.244264	−	0.423077i	−0.961924	+	0.273316i	$0.911880\pi$
$588$		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
$593$	−5.65756			−0.232328			−0.116164	−	0.993230i	$-0.537060\pi$
$593$	−5.65756			−0.232328			−0.116164	+	0.993230i	$0.537060\pi$
$594$		0			0
$595$	−16.2061	+	26.1082i	−0.664387	+	1.07033i
$596$		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	0.998838	−	0.0481961i	$-0.0153473\pi$
$601$	11.2202	+	19.4339i	0.457680	+	0.792725i	−0.541158	+	0.840921i	$0.682014\pi$
$602$		0			0
$603$		−	18.8148i		−	0.766196i
$604$		0			0
$605$	3.68591	+	3.92910i	0.149854	+	0.159741i
$606$		0			0
$607$	17.0372	−	4.56512i	0.691521	−	0.185292i	0.104091	−	0.994568i	$-0.466807\pi$
$607$	17.0372	−	4.56512i	0.691521	−	0.185292i	0.587429	+	0.809275i	$0.300140\pi$
$608$		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
$613$	−1.63937	+	0.946493i	−0.0662137	+	0.0382285i	−0.532741	−	0.846278i	$-0.678838\pi$
$613$	−1.63937	+	0.946493i	−0.0662137	+	0.0382285i	0.466528	+	0.884507i	$0.345505\pi$
$614$		0			0
$615$	−19.7384	−	21.0407i	−0.795928	−	0.848441i
$616$		0			0
$617$	2.77906	−	4.81348i	0.111881	−	0.193783i	−0.804648	−	0.593753i	$-0.797646\pi$
$617$	2.77906	−	4.81348i	0.111881	−	0.193783i	0.916529	+	0.399969i	$0.130979\pi$
$618$		0			0
$619$	−29.0772	+	29.0772i	−1.16871	+	1.16871i	−0.186200	+	0.982512i	$0.559617\pi$
$619$	−29.0772	+	29.0772i	−1.16871	+	1.16871i	−0.982512	+	0.186200i	$0.940383\pi$
$620$		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
$627$	4.75372	−	17.7411i	0.189845	−	0.708512i
$628$		0			0
$629$	24.1044	+	24.1044i	0.961104	+	0.961104i
$630$		0			0
$631$	1.87343	−	0.501983i	0.0745799	−	0.0199836i	−0.221336	−	0.975198i	$-0.571042\pi$
$631$	1.87343	−	0.501983i	0.0745799	−	0.0199836i	0.295916	+	0.955214i	$0.404375\pi$
$632$		0			0
$633$	−11.3147	−	42.2272i	−0.449720	−	1.67838i
$634$		0			0
$635$	32.4429	+	20.1383i	1.28746	+	0.799162i
$636$		0			0
$637$	−14.3036	+	4.74559i	−0.566728	+	0.188027i
$638$		0			0
$639$	−6.21966	+	23.2121i	−0.246046	+	0.918256i
$640$		0			0
$641$	−18.7660	−	10.8346i	−0.741213	−	0.427939i	0.0812974	−	0.996690i	$-0.474094\pi$
$641$	−18.7660	−	10.8346i	−0.741213	−	0.427939i	−0.822510	+	0.568751i	$0.807427\pi$
$642$		0			0
$643$	−37.2163	−	21.4869i	−1.46767	−	0.847359i	−0.468324	−	0.883557i	$-0.655142\pi$
$643$	−37.2163	−	21.4869i	−1.46767	−	0.847359i	−0.999345	+	0.0361975i	$0.988475\pi$
$644$		0			0
$645$	−16.9582	−	5.12938i	−0.667728	−	0.201969i
$646$		0			0
$647$	−9.70951	−	2.60165i	−0.381720	−	0.102282i	0.0628562	−	0.998023i	$-0.479979\pi$
$647$	−9.70951	−	2.60165i	−0.381720	−	0.102282i	−0.444576	+	0.895741i	$0.646646\pi$
$648$		0			0
$649$	13.2054			0.518357
$650$		0			0
$651$	45.3653			1.77801
$652$		0			0
$653$	4.62853	+	1.24021i	0.181128	+	0.0485332i	0.348243	−	0.937404i	$-0.386778\pi$
$653$	4.62853	+	1.24021i	0.181128	+	0.0485332i	−0.167115	+	0.985937i	$0.553445\pi$
$654$		0			0
$655$	−35.5763	−	10.7608i	−1.39008	−	0.420461i
$656$		0			0
$657$	23.4846	+	13.5588i	0.916220	+	0.528980i
$658$		0			0
$659$	30.9239	+	17.8539i	1.20462	+	0.695490i	0.961580	−	0.274525i	$-0.0885205\pi$
$659$	30.9239	+	17.8539i	1.20462	+	0.695490i	0.243045	+	0.970015i	$0.421854\pi$
$660$		0			0
$661$	−0.365777	+	1.36510i	−0.0142271	+	0.0530961i	−0.972674	−	0.232173i	$-0.925416\pi$
$661$	−0.365777	+	1.36510i	−0.0142271	+	0.0530961i	0.958447	+	0.285269i	$0.0920830\pi$
$662$		0			0
$663$	75.3639	+	15.5322i	2.92689	+	0.603219i
$664$		0			0
$665$	7.66611	+	4.75859i	0.297279	+	0.184530i
$666$		0			0
$667$	1.17604	+	4.38904i	0.0455364	+	0.169944i
$668$		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
$673$	−12.1843	+	45.4726i	−0.469672	+	1.75284i	0.171243	+	0.985229i	$0.445222\pi$
$673$	−12.1843	+	45.4726i	−0.469672	+	1.75284i	−0.640915	+	0.767611i	$0.721445\pi$
$674$		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
$683$	15.2209	−	26.3633i	0.582411	−	1.00877i	−0.412782	−	0.910830i	$-0.635443\pi$
$683$	15.2209	−	26.3633i	0.582411	−	1.00877i	0.995193	−	0.0979355i	$-0.0312239\pi$
$684$		0			0
$685$	−17.8772	−	19.0567i	−0.683055	−	0.728120i
$686$		0			0
$687$	−63.2589	+	36.5226i	−2.41348	+	1.39342i
$688$		0			0
$689$	18.6806	+	28.3794i	0.711673	+	1.08117i
$690$		0			0
$691$	6.23292	+	1.67011i	0.237111	+	0.0635338i	0.375418	−	0.926856i	$-0.377499\pi$
$691$	6.23292	+	1.67011i	0.237111	+	0.0635338i	−0.138306	+	0.990389i	$0.544166\pi$
$692$		0			0
$693$	−18.0745	+	4.84305i	−0.686594	+	0.183972i
$694$		0			0
$695$	−5.21445	−	5.55849i	−0.197795	−	0.210845i
$696$		0			0
$697$		−	40.4831i		−	1.53340i
$698$		0			0
$699$	15.3342	+	26.5597i	0.579994	+	1.00458i
$700$		0			0
$701$			13.4703i			0.508766i	0.967104	+	0.254383i	$0.0818724\pi$
$701$			13.4703i			0.508766i	−0.967104	+	0.254383i	$0.918128\pi$
$702$		0			0
$703$	7.07773	−	7.07773i	0.266942	−	0.266942i
$704$		0			0
$705$	32.4481	−	52.2741i	1.22207	−	1.96876i
$706$		0			0
$707$	−3.37072			−0.126769
$708$		0			0
$709$	−1.38408	−	5.16546i	−0.0519802	−	0.193993i	0.935053	−	0.354507i	$-0.115351\pi$
$709$	−1.38408	−	5.16546i	−0.0519802	−	0.193993i	−0.987034	+	0.160514i	$0.948685\pi$
$710$		0			0
$711$	18.4969	−	32.0376i	0.693689	−	1.20151i
$712$		0			0
$713$	−8.43605	−	14.6117i	−0.315933	−	0.547211i
$714$		0			0
$715$	−17.1481	−	16.2584i	−0.641303	−	0.608031i
$716$		0			0
$717$	−2.07335	−	3.59114i	−0.0774305	−	0.134114i
$718$		0			0
$719$	6.75667	−	11.7029i	0.251981	−	0.436444i	−0.712090	−	0.702088i	$-0.752251\pi$
$719$	6.75667	−	11.7029i	0.251981	−	0.436444i	0.964071	+	0.265644i	$0.0855845\pi$
$720$		0			0
$721$	−4.22898	−	15.7828i	−0.157495	−	0.587781i
$722$		0			0
$723$	−59.6425			−2.21813
$724$		0			0
$725$	−13.9192	−	0.889929i	−0.516947	−	0.0330511i
$726$		0			0
$727$	19.2005	−	19.2005i	0.712108	−	0.712108i	−0.254868	−	0.966976i	$-0.582032\pi$
$727$	19.2005	−	19.2005i	0.712108	−	0.712108i	0.966976	+	0.254868i	$0.0820319\pi$
$728$		0			0
$729$		−	38.9858i		−	1.44392i
$730$		0			0
$731$	−12.4305	−	21.5303i	−0.459759	−	0.796326i
$732$		0			0
$733$		−	14.0351i		−	0.518399i	−0.965824	−	0.259199i	$-0.916541\pi$
$733$		−	14.0351i		−	0.518399i	0.965824	−	0.259199i	$-0.0834587\pi$
$734$		0			0
$735$	−0.778008	+	24.3622i	−0.0286973	+	0.898615i
$736$		0			0
$737$	−14.0118	+	3.75444i	−0.516130	+	0.138297i
$738$		0			0
$739$	−20.2162	−	5.41692i	−0.743666	−	0.199265i	−0.132959	−	0.991122i	$-0.542448\pi$
$739$	−20.2162	−	5.41692i	−0.743666	−	0.199265i	−0.610707	+	0.791857i	$0.709115\pi$
$740$		0			0
$741$	4.56069	−	22.1290i	0.167541	−	0.812929i
$742$		0			0
$743$	16.2529	−	9.38363i	0.596262	−	0.344252i	−0.171308	−	0.985218i	$-0.554799\pi$
$743$	16.2529	−	9.38363i	0.596262	−	0.344252i	0.767570	+	0.640966i	$0.221466\pi$
$744$		0			0
$745$	−18.9316	−	0.604579i	−0.693599	−	0.0221501i
$746$		0			0
$747$	12.6877	−	21.9757i	0.464218	−	0.804049i
$748$		0			0
$749$	3.28521	−	3.28521i	0.120039	−	0.120039i
$750$		0			0
$751$	−23.6911	+	13.6781i	−0.864502	+	0.499121i	−0.865517	−	0.500879i	$-0.833010\pi$
$751$	−23.6911	+	13.6781i	−0.864502	+	0.499121i	0.00101517	+	0.999999i	$0.499677\pi$
$752$		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
$757$	3.85135	−	14.3734i	0.139980	−	0.522412i	−0.859948	−	0.510382i	$-0.829504\pi$
$757$	3.85135	−	14.3734i	0.139980	−	0.522412i	0.999928	−	0.0120297i	$-0.00382926\pi$
$758$		0			0
$759$	8.80437	+	8.80437i	0.319579	+	0.319579i
$760$		0			0
$761$	−39.9406	+	10.7020i	−1.44784	+	0.387949i	−0.895274	−	0.445517i	$-0.853020\pi$
$761$	−39.9406	+	10.7020i	−1.44784	+	0.387949i	−0.552571	+	0.833466i	$0.686353\pi$
$762$		0			0
$763$	0.644613	+	2.40573i	0.0233366	+	0.0870933i
$764$		0			0
$765$	36.6858	−	59.1011i	1.32638	−	2.13680i
$766$		0			0
$767$	16.2168	−	0.950571i	0.585553	−	0.0343231i
$768$		0			0
$769$	5.79043	−	21.6102i	0.208808	−	0.779283i	−0.779447	−	0.626469i	$-0.784500\pi$
$769$	5.79043	−	21.6102i	0.208808	−	0.779283i	0.988255	−	0.152815i	$-0.0488337\pi$
$770$		0			0
$771$	19.7454	+	11.4000i	0.711114	+	0.410562i
$772$		0			0
$773$	−17.2861	−	9.98015i	−0.621739	−	0.358961i	0.155807	−	0.987788i	$-0.450202\pi$
$773$	−17.2861	−	9.98015i	−0.621739	−	0.358961i	−0.777546	+	0.628827i	$0.783536\pi$
$774$		0			0
$775$	50.7785	−	10.1850i	1.82402	−	0.365857i
$776$		0			0
$777$	−17.6232	−	4.72212i	−0.632228	−	0.169405i
$778$		0			0
$779$	−11.8870			−0.425895
$780$		0			0
$781$	18.5277			0.662973
$782$		0			0
$783$	5.63280	+	1.50930i	0.201300	+	0.0539381i
$784$		0			0
$785$	10.0139	+	18.6986i	0.357410	+	0.667381i
$786$		0			0
$787$	29.4716	+	17.0155i	1.05055	+	0.606536i	0.922803	−	0.385271i	$-0.125892\pi$
$787$	29.4716	+	17.0155i	1.05055	+	0.606536i	0.127747	+	0.991807i	$0.459225\pi$
$788$		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
$793$	11.6867	+	10.3924i	0.415005	+	0.369047i
$794$		0			0
$795$	53.5070	−	12.5213i	1.89770	−	0.444084i
$796$		0			0
$797$	−4.34638	−	16.2209i	−0.153957	−	0.574574i	−0.999192	−	0.0401804i	$-0.987207\pi$
$797$	−4.34638	−	16.2209i	−0.153957	−	0.574574i	0.845236	−	0.534394i	$-0.179460\pi$
$798$		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
$803$	5.41127	−	20.1951i	0.190959	−	0.712670i
$804$		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	$-0.602779\pi$
$809$	9.82165	−	5.67053i	0.345311	−	0.199365i	0.662618	+	0.748957i	$0.269445\pi$
$810$		0			0
$811$	−28.6282	+	28.6282i	−1.00527	+	1.00527i	−0.00528760	+	0.999986i	$0.501683\pi$
$811$	−28.6282	+	28.6282i	−1.00527	+	1.00527i	−0.999986	+	0.00528760i	$0.998317\pi$
$812$		0			0
$813$	−31.8772	+	55.2129i	−1.11798	+	1.93640i
$814$		0			0
$815$	−23.5772	+	22.1180i	−0.825875	+	0.774759i
$816$		0			0
$817$	−6.32191	+	3.64995i	−0.221175	+	0.127696i
$818$		0			0
$819$	−21.8476	+	7.24853i	−0.763417	+	0.253284i
$820$		0			0
$821$	19.2420	+	5.15587i	0.671550	+	0.179941i	0.578453	−	0.815716i	$-0.303657\pi$
$821$	19.2420	+	5.15587i	0.671550	+	0.179941i	0.0930969	+	0.995657i	$0.470323\pi$
$822$		0			0
$823$	−5.55765	+	1.48917i	−0.193728	+	0.0519092i	−0.354378	−	0.935102i	$-0.615307\pi$
$823$	−5.55765	+	1.48917i	−0.193728	+	0.0519092i	0.160651	+	0.987011i	$0.448641\pi$
$824$		0			0
$825$	−34.2512	+	16.9591i	−1.19247	+	0.590439i
$826$		0			0
$827$		−	15.7588i		−	0.547985i	−0.961732	−	0.273993i	$-0.911656\pi$
$827$		−	15.7588i		−	0.547985i	0.961732	−	0.273993i	$-0.0883444\pi$
$828$		0			0
$829$	7.86690	+	13.6259i	0.273229	+	0.473246i	0.969687	−	0.244352i	$-0.0785751\pi$
$829$	7.86690	+	13.6259i	0.273229	+	0.473246i	−0.696458	+	0.717598i	$0.745242\pi$
$830$		0			0
$831$		−	70.4984i		−	2.44556i
$832$		0			0
$833$	−24.1854	+	24.1854i	−0.837975	+	0.837975i
$834$		0			0
$835$	−16.6258	+	3.89064i	−0.575360	+	0.134641i
$836$		0			0
$837$	−21.6533			−0.748447
$838$		0			0
$839$	0.629782	+	2.35038i	0.0217425	+	0.0811441i	0.975945	−	0.218019i	$-0.0699593\pi$
$839$	0.629782	+	2.35038i	0.0217425	+	0.0811441i	−0.954202	+	0.299163i	$0.903293\pi$
$840$		0			0
$841$	−10.6093	+	18.3758i	−0.365837	+	0.633648i
$842$		0			0
$843$	38.2932	+	66.3258i	1.31889	+	2.28438i
$844$		0			0
$845$	−22.2289	−	18.7316i	−0.764698	−	0.644388i
$846$		0			0
$847$	−2.02305	−	3.50403i	−0.0695128	−	0.120400i
$848$		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
$853$	−33.0234			−1.13070			−0.565350	−	0.824851i	$-0.691259\pi$
$853$	−33.0234			−1.13070			−0.565350	+	0.824851i	$0.691259\pi$
$854$		0			0
$855$	−17.3538	−	10.7720i	−0.593486	−	0.368395i
$856$		0			0
$857$	10.7686	−	10.7686i	0.367849	−	0.367849i	−0.498843	−	0.866692i	$-0.666242\pi$
$857$	10.7686	−	10.7686i	0.367849	−	0.367849i	0.866692	+	0.498843i	$0.166242\pi$
$858$		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
$863$			21.4239i			0.729278i	0.931149	+	0.364639i	$0.118808\pi$
$863$			21.4239i			0.729278i	−0.931149	+	0.364639i	$0.881192\pi$
$864$		0			0
$865$	52.5300	+	1.67754i	1.78607	+	0.0570382i
$866$		0			0
$867$	125.864	−	33.7253i	4.27458	−	1.14537i
$868$		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
$873$	39.7297	−	22.9379i	1.34465	−	0.776331i
$874$		0			0
$875$	−3.10300	−	18.5177i	−0.104900	−	0.626012i
$876$		0			0
$877$	−0.869538	+	1.50608i	−0.0293622	+	0.0508568i	−0.880333	−	0.474356i	$-0.842681\pi$
$877$	−0.869538	+	1.50608i	−0.0293622	+	0.0508568i	0.850971	+	0.525213i	$0.176014\pi$
$878$		0			0
$879$	−21.6256	+	21.6256i	−0.729413	+	0.729413i
$880$		0			0
$881$	−25.2860	+	14.5989i	−0.851908	+	0.491849i	−0.861294	−	0.508107i	$-0.830346\pi$
$881$	−25.2860	+	14.5989i	−0.851908	+	0.491849i	0.00938605	+	0.999956i	$0.497012\pi$
$882$		0			0
$883$	−11.5752	−	11.5752i	−0.389535	−	0.389535i	0.484986	−	0.874522i	$-0.338825\pi$
$883$	−11.5752	−	11.5752i	−0.389535	−	0.389535i	−0.874522	+	0.484986i	$0.838825\pi$
$884$		0			0
$885$	7.60682	−	25.1488i	0.255700	−	0.845368i
$886$		0			0
$887$	−12.3273	+	46.0060i	−0.413909	+	1.54473i	0.373102	+	0.927791i	$0.378294\pi$
$887$	−12.3273	+	46.0060i	−0.413909	+	1.54473i	−0.787011	+	0.616939i	$0.788372\pi$
$888$		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
$893$	−6.56121	−	24.4868i	−0.219563	−	0.819419i
$894$		0			0
$895$	12.5772	+	53.7459i	0.420408	+	1.79653i
$896$		0			0
$897$	11.4459	+	10.1784i	0.382167	+	0.339846i
$898$		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
$903$	11.5234	+	6.65302i	0.383474	+	0.221399i
$904$		0			0
$905$	−4.11581	+	13.6072i	−0.136814	+	0.452319i
$906$		0			0
$907$	27.8833	+	7.47130i	0.925848	+	0.248080i	0.690083	−	0.723730i	$-0.257574\pi$
$907$	27.8833	+	7.47130i	0.925848	+	0.248080i	0.235765	+	0.971810i	$0.424240\pi$
$908$		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
$913$	−18.8976	−	5.06359i	−0.625419	−	0.167581i
$914$		0			0
$915$	22.2984	−	11.9417i	0.737161	−	0.394780i
$916$		0			0
$917$	24.1747	+	13.9573i	0.798319	+	0.460909i
$918$		0			0
$919$	−45.7438	−	26.4102i	−1.50895	−	0.871193i	−0.999946	−	0.0104288i	$-0.996680\pi$
$919$	−45.7438	−	26.4102i	−1.50895	−	0.871193i	−0.509004	−	0.860764i	$-0.669986\pi$
$920$		0			0
$921$	−11.8192	+	44.1097i	−0.389455	+	1.45346i
$922$		0			0
$923$	22.7527	−	1.33369i	0.748916	−	0.0438989i
$924$		0			0
$925$	−20.7862	−	1.32897i	−0.683446	−	0.0436962i
$926$		0			0
$927$	9.57313	+	35.7274i	0.314423	+	1.17344i
$928$		0			0
$929$	1.13051	−	0.302919i	0.0370908	−	0.00993846i	−0.240226	−	0.970717i	$-0.577222\pi$
$929$	1.13051	−	0.302919i	0.0370908	−	0.00993846i	0.277317	+	0.960779i	$0.410555\pi$
$930$		0			0
$931$	7.10153	+	7.10153i	0.232743	+	0.232743i
$932$		0			0
$933$	12.3671	−	46.1548i	0.404882	−	1.51104i
$934$		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	−0.856208	−	0.516631i	$-0.827186\pi$
$941$	−10.4168	+	10.4168i	−0.339576	+	0.339576i	0.516631	+	0.856208i	$0.327186\pi$
$942$		0			0
$943$	4.02919	−	6.97877i	0.131209	−	0.227260i
$944$		0			0
$945$	−0.250567	+	7.84617i	−0.00815096	+	0.255236i
$946$		0			0
$947$	19.2039	−	11.0874i	0.624044	−	0.360292i	−0.154398	−	0.988009i	$-0.549344\pi$
$947$	19.2039	−	11.0874i	0.624044	−	0.360292i	0.778442	+	0.627717i	$0.216010\pi$
$948$		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
$953$	−0.0516447	+	0.0138381i	−0.00167293	+	0.000448262i	−0.259655	−	0.965701i	$-0.583609\pi$
$953$	−0.0516447	+	0.0138381i	−0.00167293	+	0.000448262i	0.257982	+	0.966150i	$0.416942\pi$
$954$		0			0
$955$	17.7255	−	16.6284i	0.573583	−	0.538082i
$956$		0			0
$957$		−	21.3231i		−	0.689277i
$958$		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
$965$	8.22350	+	35.1414i	0.264724	+	1.13124i
$966$		0			0
$967$	−24.7090			−0.794586			−0.397293	−	0.917692i	$-0.630050\pi$
$967$	−24.7090			−0.794586			−0.397293	+	0.917692i	$0.630050\pi$
$968$		0			0
$969$	−13.2721	−	49.5321i	−0.426360	−	1.59120i
$970$		0			0
$971$	−20.3866	+	35.3107i	−0.654238	+	1.13317i	0.327846	+	0.944731i	$0.393677\pi$
$971$	−20.3866	+	35.3107i	−0.654238	+	1.13317i	−0.982084	+	0.188442i	$0.939656\pi$
$972$		0			0
$973$	2.86201	+	4.95714i	0.0917517	+	0.158919i
$974$		0			0
$975$	−40.8411	+	23.2920i	−1.30796	+	0.745940i
$976$		0			0
$977$	13.3789	+	23.1729i	0.428029	+	0.741368i	0.996698	−	0.0811984i	$-0.0258747\pi$
$977$	13.3789	+	23.1729i	0.428029	+	0.741368i	−0.568669	+	0.822567i	$0.692541\pi$
$978$		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
$983$	−41.8407			−1.33451			−0.667256	−	0.744829i	$-0.732531\pi$
$983$	−41.8407			−1.33451			−0.667256	+	0.744829i	$0.732531\pi$
$984$		0			0
$985$	−6.81407	−	29.1185i	−0.217114	−	0.927792i
$986$		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	0.962717	−	0.270511i	$-0.0871927\pi$
$991$	7.77839	+	13.4726i	0.247089	+	0.427970i	−0.715628	+	0.698482i	$0.753859\pi$
$992$		0			0
$993$			56.0577i			1.77894i
$994$		0			0
$995$	34.4251	−	32.2944i	1.09135	−	1.02380i
$996$		0			0
$997$	−43.4062	+	11.6306i	−1.37469	+	0.368346i	−0.869188	−	0.494481i	$-0.835358\pi$
$997$	−43.4062	+	11.6306i	−1.37469	+	0.368346i	−0.505498	+	0.862828i	$0.668691\pi$
$998$		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.bk.c.197.1	yes	20
5.2	odd	4		1300.2.bn.d.93.1		20
5.3	odd	4		260.2.bf.c.93.5	✓	20
5.4	even	2		1300.2.bs.d.457.5		20
13.7	odd	12		260.2.bf.c.137.5	yes	20
65.7	even	12		1300.2.bs.d.293.5		20
65.33	even	12	inner	260.2.bk.c.33.1	yes	20
65.59	odd	12		1300.2.bn.d.657.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.bf.c.93.5	✓	20	5.3	odd	4
260.2.bf.c.137.5	yes	20	13.7	odd	12
260.2.bk.c.33.1	yes	20	65.33	even	12	inner
260.2.bk.c.197.1	yes	20	1.1	even	1	trivial
1300.2.bn.d.93.1		20	5.2	odd	4
1300.2.bn.d.657.1		20	65.59	odd	12
1300.2.bs.d.293.5		20	65.7	even	12
1300.2.bs.d.457.5		20	5.4	even	2

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.bk (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.51912 - 0.674996i) q^{3} +(2.14030 + 0.647383i) q^{5} +(-1.45437 - 0.839682i) q^{7} +(3.29226 + 1.90079i) q^{9} +O(q^{10})\)	\(q+(-2.51912 - 0.674996i) q^{3} +(2.14030 + 0.647383i) q^{5} +(-1.45437 - 0.839682i) q^{7} +(3.29226 + 1.90079i) q^{9} +(0.758596 - 2.83112i) q^{11} +(0.727792 - 3.53133i) q^{13} +(-4.95470 - 3.07553i) q^{15} +(-2.11795 - 7.90430i) q^{17} +(-2.32093 + 0.621891i) q^{19} +(3.09695 + 3.09695i) q^{21} +(0.421590 - 1.57340i) q^{23} +(4.16179 + 2.77119i) q^{25} +(-1.47820 - 1.47820i) q^{27} +(-2.41580 + 1.39477i) q^{29} +(7.32419 - 7.32419i) q^{31} +(-3.82198 + 6.61987i) q^{33} +(-2.56920 - 2.73871i) q^{35} +(-3.60763 + 2.08286i) q^{37} +(-4.21703 + 8.40459i) q^{39} +(4.77856 + 1.28041i) q^{41} +(2.93456 - 0.786313i) q^{43} +(5.81590 + 6.19961i) q^{45} +10.5504i q^{47} +(-2.08987 - 3.61976i) q^{49} +21.3415i q^{51} +(-6.66320 + 6.66320i) q^{53} +(3.45644 - 5.56835i) q^{55} +6.26647 q^{57} +(1.16609 + 4.35192i) q^{59} +(-2.16875 + 3.75639i) q^{61} +(-3.19211 - 5.52891i) q^{63} +(3.84382 - 7.08696i) q^{65} +(-2.47460 - 4.28613i) q^{67} +(-2.12407 + 3.67900i) q^{69} +(1.63607 + 6.10591i) q^{71} +7.13327 q^{73} +(-8.61350 - 9.79014i) q^{75} +(-3.48052 + 3.48052i) q^{77} -9.73120i q^{79} +(-2.97638 - 5.15523i) q^{81} -6.67496i q^{83} +(0.584050 - 18.2887i) q^{85} +(7.02716 - 1.88292i) q^{87} +(-0.578139 - 0.154912i) q^{89} +(-4.02368 + 4.52476i) q^{91} +(-23.3943 + 13.5067i) q^{93} +(-5.37009 - 0.171494i) q^{95} +(6.03380 - 10.4508i) q^{97} +(7.87885 - 7.87885i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{3} + 12 q^{5} + 6 q^{7} - 12 q^{9}+O(q^{10}) \) 20 * q - 2 * q^3 + 12 * q^5 + 6 * q^7 - 12 * q^9	\( 20 q - 2 q^{3} + 12 q^{5} + 6 q^{7} - 12 q^{9} + 8 q^{13} - 20 q^{15} + 20 q^{19} - 12 q^{21} + 6 q^{23} + 2 q^{25} - 20 q^{27} + 24 q^{29} + 8 q^{31} - 10 q^{33} - 36 q^{35} + 4 q^{39} + 6 q^{41} + 38 q^{43} - 16 q^{45} + 14 q^{49} + 30 q^{53} + 2 q^{55} - 76 q^{57} - 24 q^{59} - 32 q^{61} - 24 q^{63} - 30 q^{65} + 22 q^{67} - 16 q^{69} - 44 q^{73} - 2 q^{75} - 12 q^{77} + 2 q^{81} + 50 q^{85} + 38 q^{87} - 30 q^{89} - 72 q^{91} - 48 q^{93} - 30 q^{95} + 46 q^{97} + 20 q^{99}+O(q^{100}) \) 20 * q - 2 * q^3 + 12 * q^5 + 6 * q^7 - 12 * q^9 + 8 * q^13 - 20 * q^15 + 20 * q^19 - 12 * q^21 + 6 * q^23 + 2 * q^25 - 20 * q^27 + 24 * q^29 + 8 * q^31 - 10 * q^33 - 36 * q^35 + 4 * q^39 + 6 * q^41 + 38 * q^43 - 16 * q^45 + 14 * q^49 + 30 * q^53 + 2 * q^55 - 76 * q^57 - 24 * q^59 - 32 * q^61 - 24 * q^63 - 30 * q^65 + 22 * q^67 - 16 * q^69 - 44 * q^73 - 2 * q^75 - 12 * q^77 + 2 * q^81 + 50 * q^85 + 38 * q^87 - 30 * q^89 - 72 * q^91 - 48 * q^93 - 30 * q^95 + 46 * q^97 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more