LMFDB - Embedded newform 624.2.cn.f.353.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [624,2,Mod(305,624)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(624, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 0, 6, 5]))

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

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

chi := DirichletCharacter("624.305");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 624 = 2^{4} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	624.cn (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.98266508613$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 312)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			353.2
Character	$\chi$	$=$	624.353
Dual form			624.2.cn.f.449.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.55814 - 0.756439i) q^{3} +(-3.14772 - 3.14772i) q^{5} +(-2.26593 + 0.607154i) q^{7} +(1.85560 + 2.35728i) q^{9} +O(q^{10})$	\(q+(-1.55814 - 0.756439i) q^{3} +(-3.14772 - 3.14772i) q^{5} +(-2.26593 + 0.607154i) q^{7} +(1.85560 + 2.35728i) q^{9} +(-3.54906 - 0.950969i) q^{11} +(2.62122 - 2.47572i) q^{13} +(2.52353 + 7.28565i) q^{15} +(0.814572 - 1.41088i) q^{17} +(1.43802 + 5.36676i) q^{19} +(3.98991 + 0.768007i) q^{21} +(0.495519 + 0.858264i) q^{23} +14.8163i q^{25} +(-1.10815 - 5.07661i) q^{27} +(-3.01980 + 1.74348i) q^{29} +(4.72615 - 4.72615i) q^{31} +(4.81059 + 4.16639i) q^{33} +(9.04366 + 5.22136i) q^{35} +(0.485423 - 1.81162i) q^{37} +(-5.95697 + 1.87472i) q^{39} +(-1.42485 + 5.31761i) q^{41} +(2.75816 + 1.59242i) q^{43} +(1.57914 - 13.2610i) q^{45} +(1.43015 - 1.43015i) q^{47} +(-1.29638 + 0.748468i) q^{49} +(-2.33646 + 1.58217i) q^{51} +9.03162i q^{53} +(8.17808 + 14.1648i) q^{55} +(1.81899 - 9.44994i) q^{57} +(-0.206728 - 0.771519i) q^{59} +(-0.868812 + 1.50483i) q^{61} +(-5.63588 - 4.21478i) q^{63} +(-16.0438 - 0.458014i) q^{65} +(-12.5951 - 3.37485i) q^{67} +(-0.122863 - 1.71213i) q^{69} +(-4.81283 + 1.28959i) q^{71} +(-5.36519 - 5.36519i) q^{73} +(11.2076 - 23.0859i) q^{75} +8.61930 q^{77} -4.28909 q^{79} +(-2.11350 + 8.74832i) q^{81} +(5.71245 + 5.71245i) q^{83} +(-7.00511 + 1.87701i) q^{85} +(6.02411 - 0.432294i) q^{87} +(-5.12406 - 1.37299i) q^{89} +(-4.43637 + 7.20128i) q^{91} +(-10.9390 + 3.78895i) q^{93} +(12.3666 - 21.4196i) q^{95} +(1.80454 + 6.73465i) q^{97} +(-4.34394 - 10.1307i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 4 q^{7}+O(q^{10}) $ 56 * q - 4 * q^7	$ 56 q - 4 q^{7} + 8 q^{13} + 8 q^{15} - 4 q^{19} + 16 q^{21} - 24 q^{27} + 36 q^{31} + 28 q^{33} + 20 q^{37} - 16 q^{39} + 84 q^{43} + 12 q^{45} - 12 q^{49} + 24 q^{55} - 36 q^{57} - 24 q^{61} + 12 q^{63} + 32 q^{67} - 36 q^{69} - 20 q^{73} + 60 q^{75} + 32 q^{79} - 88 q^{85} + 16 q^{87} - 28 q^{91} - 88 q^{93} - 36 q^{97} - 44 q^{99}+O(q^{100}) $ 56 * q - 4 * q^7 + 8 * q^13 + 8 * q^15 - 4 * q^19 + 16 * q^21 - 24 * q^27 + 36 * q^31 + 28 * q^33 + 20 * q^37 - 16 * q^39 + 84 * q^43 + 12 * q^45 - 12 * q^49 + 24 * q^55 - 36 * q^57 - 24 * q^61 + 12 * q^63 + 32 * q^67 - 36 * q^69 - 20 * q^73 + 60 * q^75 + 32 * q^79 - 88 * q^85 + 16 * q^87 - 28 * q^91 - 88 * q^93 - 36 * q^97 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/624\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$209$	$469$
$\chi(n)$	$1$	$e\left(\frac{1}{12}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.55814	−	0.756439i	−0.899592	−	0.436730i
$3$	−1.55814	−	0.756439i	−0.899592	−	0.436730i
$4$		0			0
$5$	−3.14772	−	3.14772i	−1.40770	−	1.40770i	−0.771619	−	0.636085i	$-0.780553\pi$
$5$	−3.14772	−	3.14772i	−1.40770	−	1.40770i	−0.636085	−	0.771619i	$-0.719447\pi$
$6$		0			0
$7$	−2.26593	+	0.607154i	−0.856440	+	0.229482i	−0.660215	−	0.751076i	$-0.729535\pi$
$7$	−2.26593	+	0.607154i	−0.856440	+	0.229482i	−0.196225	+	0.980559i	$0.562868\pi$
$8$		0			0
$9$	1.85560	+	2.35728i	0.618533	+	0.785759i
$10$		0			0
$11$	−3.54906	−	0.950969i	−1.07008	−	0.286728i	−0.319556	−	0.947567i	$-0.603534\pi$
$11$	−3.54906	−	0.950969i	−1.07008	−	0.286728i	−0.750527	+	0.660840i	$0.770200\pi$
$12$		0			0
$13$	2.62122	−	2.47572i	0.726997	−	0.686641i
$13$	2.62122	−	2.47572i	0.726997	−	0.686641i
$14$		0			0
$15$	2.52353	+	7.28565i	0.651573	+	1.88115i
$16$		0			0
$17$	0.814572	−	1.41088i	0.197563	−	0.342189i	−0.750175	−	0.661240i	$-0.770031\pi$
$17$	0.814572	−	1.41088i	0.197563	−	0.342189i	0.947738	+	0.319051i	$0.103364\pi$
$18$		0			0
$19$	1.43802	+	5.36676i	0.329904	+	1.23122i	0.909289	+	0.416165i	$0.136626\pi$
$19$	1.43802	+	5.36676i	0.329904	+	1.23122i	−0.579385	+	0.815054i	$0.696707\pi$
$20$		0			0
$21$	3.98991	+	0.768007i	0.870669	+	0.167593i
$22$		0			0
$23$	0.495519	+	0.858264i	0.103323	+	0.178961i	0.913052	−	0.407844i	$-0.133719\pi$
$23$	0.495519	+	0.858264i	0.103323	+	0.178961i	−0.809729	+	0.586804i	$0.800386\pi$
$24$		0			0
$25$			14.8163i			2.96326i
$26$		0			0
$27$	−1.10815	−	5.07661i	−0.213263	−	0.976995i
$28$		0			0
$29$	−3.01980	+	1.74348i	−0.560763	+	0.323757i	−0.753452	−	0.657503i	$-0.771613\pi$
$29$	−3.01980	+	1.74348i	−0.560763	+	0.323757i	0.192689	+	0.981260i	$0.438279\pi$
$30$		0			0
$31$	4.72615	−	4.72615i	0.848841	−	0.848841i	−0.141148	−	0.989989i	$-0.545079\pi$
$31$	4.72615	−	4.72615i	0.848841	−	0.848841i	0.989989	+	0.141148i	$0.0450793\pi$
$32$		0			0
$33$	4.81059	+	4.16639i	0.837416	+	0.725276i
$34$		0			0
$35$	9.04366	+	5.22136i	1.52866	+	0.882571i
$36$		0			0
$37$	0.485423	−	1.81162i	0.0798031	−	0.297829i	−0.914476	−	0.404639i	$-0.867397\pi$
$37$	0.485423	−	1.81162i	0.0798031	−	0.297829i	0.994279	+	0.106810i	$0.0340637\pi$
$38$		0			0
$39$	−5.95697	+	1.87472i	−0.953878	+	0.300195i
$40$		0			0
$41$	−1.42485	+	5.31761i	−0.222524	+	0.830471i	0.760857	+	0.648919i	$0.224779\pi$
$41$	−1.42485	+	5.31761i	−0.222524	+	0.830471i	−0.983381	+	0.181552i	$0.941888\pi$
$42$		0			0
$43$	2.75816	+	1.59242i	0.420615	+	0.242842i	0.695341	−	0.718680i	$-0.255254\pi$
$43$	2.75816	+	1.59242i	0.420615	+	0.242842i	−0.274725	+	0.961523i	$0.588587\pi$
$44$		0			0
$45$	1.57914	−	13.2610i	0.235404	−	1.97683i
$46$		0			0
$47$	1.43015	−	1.43015i	0.208609	−	0.208609i	−0.595067	−	0.803676i	$-0.702875\pi$
$47$	1.43015	−	1.43015i	0.208609	−	0.208609i	0.803676	+	0.595067i	$0.202875\pi$
$48$		0			0
$49$	−1.29638	+	0.748468i	−0.185198	+	0.106924i
$50$		0			0
$51$	−2.33646	+	1.58217i	−0.327170	+	0.221549i
$52$		0			0
$53$			9.03162i			1.24059i	0.784369	+	0.620294i	$0.212987\pi$
$53$			9.03162i			1.24059i	−0.784369	+	0.620294i	$0.787013\pi$
$54$		0			0
$55$	8.17808	+	14.1648i	1.10273	+	1.90999i
$56$		0			0
$57$	1.81899	−	9.44994i	0.240932	−	1.25168i
$58$		0			0
$59$	−0.206728	−	0.771519i	−0.0269137	−	0.100443i	0.951163	−	0.308691i	$-0.0998907\pi$
$59$	−0.206728	−	0.771519i	−0.0269137	−	0.100443i	−0.978076	+	0.208247i	$0.933224\pi$
$60$		0			0
$61$	−0.868812	+	1.50483i	−0.111240	+	0.192673i	−0.916270	−	0.400560i	$-0.868816\pi$
$61$	−0.868812	+	1.50483i	−0.111240	+	0.192673i	0.805030	+	0.593233i	$0.202149\pi$
$62$		0			0
$63$	−5.63588	−	4.21478i	−0.710055	−	0.531013i
$64$		0			0
$65$	−16.0438	−	0.458014i	−1.98998	−	0.0568096i
$66$		0			0
$67$	−12.5951	−	3.37485i	−1.53874	−	0.412303i	−0.612879	−	0.790176i	$-0.709989\pi$
$67$	−12.5951	−	3.37485i	−1.53874	−	0.412303i	−0.925857	+	0.377873i	$0.876656\pi$
$68$		0			0
$69$	−0.122863	−	1.71213i	−0.0147910	−	0.206116i
$70$		0			0
$71$	−4.81283	+	1.28959i	−0.571178	+	0.153047i	−0.532837	−	0.846218i	$-0.678874\pi$
$71$	−4.81283	+	1.28959i	−0.571178	+	0.153047i	−0.0383409	+	0.999265i	$0.512207\pi$
$72$		0			0
$73$	−5.36519	−	5.36519i	−0.627948	−	0.627948i	0.319604	−	0.947551i	$-0.396450\pi$
$73$	−5.36519	−	5.36519i	−0.627948	−	0.627948i	−0.947551	+	0.319604i	$0.896450\pi$
$74$		0			0
$75$	11.2076	−	23.0859i	1.29415	−	2.66573i
$76$		0			0
$77$	8.61930			0.982261
$78$		0			0
$79$	−4.28909			−0.482561			−0.241280	−	0.970455i	$-0.577567\pi$
$79$	−4.28909			−0.482561			−0.241280	+	0.970455i	$0.577567\pi$
$80$		0			0
$81$	−2.11350	+	8.74832i	−0.234834	+	0.972036i
$82$		0			0
$83$	5.71245	+	5.71245i	0.627023	+	0.627023i	0.947318	−	0.320295i	$-0.103782\pi$
$83$	5.71245	+	5.71245i	0.627023	+	0.627023i	−0.320295	+	0.947318i	$0.603782\pi$
$84$		0			0
$85$	−7.00511	+	1.87701i	−0.759811	+	0.203591i
$86$		0			0
$87$	6.02411	−	0.432294i	0.645853	−	0.0463468i
$88$		0			0
$89$	−5.12406	−	1.37299i	−0.543150	−	0.145536i	−0.0231959	−	0.999731i	$-0.507384\pi$
$89$	−5.12406	−	1.37299i	−0.543150	−	0.145536i	−0.519954	+	0.854194i	$0.674051\pi$
$90$		0			0
$91$	−4.43637	+	7.20128i	−0.465057	+	0.754900i
$92$		0			0
$93$	−10.9390	+	3.78895i	−1.13433	+	0.392896i
$94$		0			0
$95$	12.3666	−	21.4196i	1.26879	−	2.19760i
$96$		0			0
$97$	1.80454	+	6.73465i	0.183224	+	0.683800i	0.995004	+	0.0998369i	$0.0318321\pi$
$97$	1.80454	+	6.73465i	0.183224	+	0.683800i	−0.811780	+	0.583963i	$0.801501\pi$
$98$		0			0
$99$	−4.34394	−	10.1307i	−0.436583	−	1.01818i
$100$		0			0
$101$	2.74059	+	4.74684i	0.272699	+	0.472328i	0.969552	−	0.244886i	$-0.0787504\pi$
$101$	2.74059	+	4.74684i	0.272699	+	0.472328i	−0.696853	+	0.717214i	$0.745417\pi$
$102$		0			0
$103$			1.08980i			0.107381i	0.998558	+	0.0536906i	$0.0170985\pi$
$103$			1.08980i			0.107381i	−0.998558	+	0.0536906i	$0.982902\pi$
$104$		0			0
$105$	−10.1416	−	14.9766i	−0.989723	−	1.46157i
$106$		0			0
$107$	3.10085	−	1.79028i	0.299771	−	0.173073i	−0.342569	−	0.939493i	$-0.611297\pi$
$107$	3.10085	−	1.79028i	0.299771	−	0.173073i	0.642340	+	0.766420i	$0.277964\pi$
$108$		0			0
$109$	0.882554	−	0.882554i	0.0845333	−	0.0845333i	−0.663576	−	0.748109i	$-0.730962\pi$
$109$	0.882554	−	0.882554i	0.0845333	−	0.0845333i	0.748109	+	0.663576i	$0.230962\pi$
$110$		0			0
$111$	−2.12674	+	2.45557i	−0.201861	+	0.233073i
$112$		0			0
$113$	10.0012	+	5.77419i	0.940832	+	0.543190i	0.890221	−	0.455529i	$-0.150550\pi$
$113$	10.0012	+	5.77419i	0.940832	+	0.543190i	0.0506112	+	0.998718i	$0.483883\pi$
$114$		0			0
$115$	1.14182	−	4.26133i	0.106475	−	0.397371i
$116$		0			0
$117$	10.6999	+	1.58501i	0.989206	+	0.146534i
$118$		0			0
$119$	−0.989141	+	3.69152i	−0.0906744	+	0.338401i
$120$		0			0
$121$	2.16523	+	1.25010i	0.196839	+	0.113645i
$122$		0			0
$123$	6.24256	−	7.20776i	0.562873	−	0.649902i
$124$		0			0
$125$	30.8990	−	30.8990i	2.76369	−	2.76369i
$126$		0			0
$127$	6.03332	−	3.48334i	0.535371	−	0.309096i	−0.207830	−	0.978165i	$-0.566640\pi$
$127$	6.03332	−	3.48334i	0.535371	−	0.309096i	0.743201	+	0.669069i	$0.233307\pi$
$128$		0			0
$129$	−3.09303	−	4.56760i	−0.272326	−	0.402155i
$130$		0			0
$131$			3.81151i			0.333013i	0.986040	+	0.166507i	$0.0532487\pi$
$131$			3.81151i			0.333013i	−0.986040	+	0.166507i	$0.946751\pi$
$132$		0			0
$133$	−6.51690	−	11.2876i	−0.565087	−	0.978759i
$134$		0			0
$135$	−12.4916	+	19.4679i	−1.07511	+	1.67553i
$136$		0			0
$137$	−1.45242	−	5.42052i	−0.124089	−	0.463106i	0.875717	−	0.482825i	$-0.160389\pi$
$137$	−1.45242	−	5.42052i	−0.124089	−	0.463106i	−0.999806	+	0.0197193i	$0.993723\pi$
$138$		0			0
$139$	−9.44568	+	16.3604i	−0.801172	+	1.38767i	0.117672	+	0.993052i	$0.462457\pi$
$139$	−9.44568	+	16.3604i	−0.801172	+	1.38767i	−0.918845	+	0.394619i	$0.870877\pi$
$140$		0			0
$141$	−3.31020	+	1.14655i	−0.278769	+	0.0965571i
$142$		0			0
$143$	−11.6572	+	6.29378i	−0.974826	+	0.526312i
$144$		0			0
$145$	14.9935	+	4.01750i	1.24514	+	0.333635i
$146$		0			0
$147$	2.58612	−	0.185582i	0.213299	−	0.0153065i
$148$		0			0
$149$	−8.75010	+	2.34458i	−0.716836	+	0.192076i	−0.598760	−	0.800929i	$-0.704339\pi$
$149$	−8.75010	+	2.34458i	−0.716836	+	0.192076i	−0.118077	+	0.993004i	$0.537673\pi$
$150$		0			0
$151$	−15.1312	−	15.1312i	−1.23136	−	1.23136i	−0.963441	−	0.267919i	$-0.913664\pi$
$151$	−15.1312	−	15.1312i	−1.23136	−	1.23136i	−0.267919	−	0.963441i	$-0.586336\pi$
$152$		0			0
$153$	4.83736	−	0.697857i	0.391077	−	0.0564184i
$154$		0			0
$155$	−29.7532			−2.38983
$156$		0			0
$157$	−14.0150			−1.11852			−0.559258	−	0.828994i	$-0.688914\pi$
$157$	−14.0150			−1.11852			−0.559258	+	0.828994i	$0.688914\pi$
$158$		0			0
$159$	6.83187	−	14.0725i	0.541803	−	1.11602i
$160$		0			0
$161$	−1.64391	−	1.64391i	−0.129558	−	0.129558i
$162$		0			0
$163$	9.97023	−	2.67152i	0.780929	−	0.209249i	0.153735	−	0.988112i	$-0.450870\pi$
$163$	9.97023	−	2.67152i	0.780929	−	0.209249i	0.627194	+	0.778863i	$0.284203\pi$
$164$		0			0
$165$	−2.02774	−	28.2570i	−0.157860	−	2.19981i
$166$		0			0
$167$	7.72646	+	2.07030i	0.597891	+	0.160204i	0.545057	−	0.838399i	$-0.316508\pi$
$167$	7.72646	+	2.07030i	0.597891	+	0.160204i	0.0528340	+	0.998603i	$0.483175\pi$
$168$		0			0
$169$	0.741638	−	12.9788i	0.0570491	−	0.998371i
$170$		0			0
$171$	−9.98255	+	13.3484i	−0.763385	+	1.02078i
$172$		0			0
$173$	0.913430	−	1.58211i	0.0694468	−	0.120285i	−0.829211	−	0.558936i	$-0.811210\pi$
$173$	0.913430	−	1.58211i	0.0694468	−	0.120285i	0.898658	+	0.438650i	$0.144543\pi$
$174$		0			0
$175$	−8.99577	−	33.5727i	−0.680016	−	2.53786i
$176$		0			0
$177$	−0.261496	+	1.35851i	−0.0196553	+	0.102112i
$178$		0			0
$179$	6.73189	+	11.6600i	0.503165	+	0.871508i	0.999993	+	0.00365865i	$0.00116459\pi$
$179$	6.73189	+	11.6600i	0.503165	+	0.871508i	−0.496828	+	0.867849i	$0.665502\pi$
$180$		0			0
$181$			7.13395i			0.530262i	0.964212	+	0.265131i	$0.0854153\pi$
$181$			7.13395i			0.530262i	−0.964212	+	0.265131i	$0.914585\pi$
$182$		0			0
$183$	2.49204	−	1.68753i	0.184217	−	0.124746i
$184$		0			0
$185$	−7.23047	+	4.17451i	−0.531595	+	0.306916i
$186$		0			0
$187$	−4.23267	+	4.23267i	−0.309524	+	0.309524i
$188$		0			0
$189$	5.59327	+	10.8304i	0.406850	+	0.787798i
$190$		0			0
$191$	−14.4696	−	8.35404i	−1.04699	−	0.604477i	−0.125182	−	0.992134i	$-0.539951\pi$
$191$	−14.4696	−	8.35404i	−1.04699	−	0.604477i	−0.921804	+	0.387656i	$0.873285\pi$
$192$		0			0
$193$	−5.47749	+	20.4423i	−0.394278	+	1.47147i	0.428728	+	0.903434i	$0.358962\pi$
$193$	−5.47749	+	20.4423i	−0.394278	+	1.47147i	−0.823006	+	0.568033i	$0.807705\pi$
$194$		0			0
$195$	24.6520	+	12.8498i	1.76536	+	0.920192i
$196$		0			0
$197$	−2.43576	+	9.09039i	−0.173541	+	0.647664i	0.823255	+	0.567672i	$0.192156\pi$
$197$	−2.43576	+	9.09039i	−0.173541	+	0.647664i	−0.996796	+	0.0799913i	$0.974511\pi$
$198$		0			0
$199$	3.91265	+	2.25897i	0.277360	+	0.160134i	0.632228	−	0.774783i	$-0.282141\pi$
$199$	3.91265	+	2.25897i	0.277360	+	0.160134i	−0.354867	+	0.934917i	$0.615474\pi$
$200$		0			0
$201$	17.0721	+	14.7859i	1.20417	+	1.04292i
$202$		0			0
$203$	5.78409	−	5.78409i	0.405964	−	0.405964i
$204$		0			0
$205$	21.2234	−	12.2533i	1.48230	−	0.855809i
$206$		0			0
$207$	−1.10368	+	2.76067i	−0.0767111	+	0.191880i
$208$		0			0
$209$		−	20.4145i		−	1.41210i
$210$		0			0
$211$	2.80684	+	4.86160i	0.193231	+	0.334686i	0.946319	−	0.323234i	$-0.104770\pi$
$211$	2.80684	+	4.86160i	0.193231	+	0.334686i	−0.753088	+	0.657920i	$0.771437\pi$
$212$		0			0
$213$	8.47456	+	1.63124i	0.580667	+	0.111771i
$214$		0			0
$215$	−3.66941	−	13.6944i	−0.250252	−	0.933952i
$216$		0			0
$217$	−7.83961	+	13.5786i	−0.532187	+	0.921775i
$218$		0			0
$219$	4.30127	+	12.4181i	0.290653	+	0.839141i
$220$		0			0
$221$	−1.35777	−	5.71489i	−0.0913332	−	0.384425i
$222$		0			0
$223$	20.3206	+	5.44489i	1.36077	+	0.364617i	0.864099	−	0.503322i	$-0.167889\pi$
$223$	20.3206	+	5.44489i	1.36077	+	0.364617i	0.496671	+	0.867939i	$0.334556\pi$
$224$		0			0
$225$	−34.9261	+	27.4931i	−2.32841	+	1.83288i
$226$		0			0
$227$	−21.0863	+	5.65005i	−1.39954	+	0.375007i	−0.878181	−	0.478328i	$-0.841243\pi$
$227$	−21.0863	+	5.65005i	−1.39954	+	0.375007i	−0.521363	+	0.853335i	$0.674576\pi$
$228$		0			0
$229$	−2.87926	−	2.87926i	−0.190267	−	0.190267i	0.605545	−	0.795811i	$-0.292955\pi$
$229$	−2.87926	−	2.87926i	−0.190267	−	0.190267i	−0.795811	+	0.605545i	$0.792955\pi$
$230$		0			0
$231$	−13.4301	−	6.51998i	−0.883635	−	0.428983i
$232$		0			0
$233$	23.3765			1.53145			0.765724	−	0.643169i	$-0.222381\pi$
$233$	23.3765			1.53145			0.765724	+	0.643169i	$0.222381\pi$
$234$		0			0
$235$	−9.00343			−0.587319
$236$		0			0
$237$	6.68301	+	3.24444i	0.434108	+	0.210749i
$238$		0			0
$239$	16.6210	+	16.6210i	1.07512	+	1.07512i	0.996939	+	0.0781813i	$0.0249113\pi$
$239$	16.6210	+	16.6210i	1.07512	+	1.07512i	0.0781813	+	0.996939i	$0.475089\pi$
$240$		0			0
$241$	−20.0852	+	5.38182i	−1.29380	+	0.346673i	−0.839103	−	0.543972i	$-0.816920\pi$
$241$	−20.0852	+	5.38182i	−1.29380	+	0.346673i	−0.454699	+	0.890645i	$0.650253\pi$
$242$		0			0
$243$	9.91070	−	12.0324i	0.635772	−	0.771877i
$244$		0			0
$245$	6.43662	+	1.72469i	0.411221	+	0.110186i
$246$		0			0
$247$	17.0560	+	10.5074i	1.08524	+	0.668567i
$248$		0			0
$249$	−4.57968	−	13.2219i	−0.290225	−	0.837906i
$250$		0			0
$251$	−4.45550	+	7.71715i	−0.281228	+	0.487102i	−0.971688	−	0.236269i	$-0.924075\pi$
$251$	−4.45550	+	7.71715i	−0.281228	+	0.487102i	0.690459	+	0.723371i	$0.257409\pi$
$252$		0			0
$253$	−0.942446	−	3.51726i	−0.0592511	−	0.221128i
$254$		0			0
$255$	12.3348	+	2.37429i	0.772434	+	0.148684i
$256$		0			0
$257$	14.4003	+	24.9421i	0.898269	+	1.55585i	0.829706	+	0.558201i	$0.188508\pi$
$257$	14.4003	+	24.9421i	0.898269	+	1.55585i	0.0685631	+	0.997647i	$0.478159\pi$
$258$		0			0
$259$			4.39974i			0.273386i
$260$		0			0
$261$	−9.71342	−	3.88330i	−0.601245	−	0.240370i
$262$		0			0
$263$	−9.48931	+	5.47865i	−0.585136	+	0.337828i	−0.763172	−	0.646196i	$-0.776359\pi$
$263$	−9.48931	+	5.47865i	−0.585136	+	0.337828i	0.178036	+	0.984024i	$0.443026\pi$
$264$		0			0
$265$	28.4290	−	28.4290i	1.74638	−	1.74638i
$266$		0			0
$267$	6.94542	+	6.01535i	0.425053	+	0.368133i
$268$		0			0
$269$	−18.8477	−	10.8817i	−1.14917	−	0.663472i	−0.200483	−	0.979697i	$-0.564251\pi$
$269$	−18.8477	−	10.8817i	−1.14917	−	0.663472i	−0.948684	+	0.316225i	$0.897584\pi$
$270$		0			0
$271$	−5.65767	+	21.1147i	−0.343679	+	1.28263i	0.550469	+	0.834855i	$0.314449\pi$
$271$	−5.65767	+	21.1147i	−0.343679	+	1.28263i	−0.894148	+	0.447771i	$0.852218\pi$
$272$		0			0
$273$	12.3598	−	7.86477i	0.748050	−	0.475997i
$274$		0			0
$275$	14.0898	−	52.5840i	0.849649	−	3.17093i
$276$		0			0
$277$	−18.0419	−	10.4165i	−1.08403	−	0.625867i	−0.152051	−	0.988373i	$-0.548588\pi$
$277$	−18.0419	−	10.4165i	−1.08403	−	0.625867i	−0.931981	+	0.362506i	$0.881921\pi$
$278$		0			0
$279$	19.9107	+	2.37100i	1.19202	+	0.141948i
$280$		0			0
$281$	−12.8134	+	12.8134i	−0.764385	+	0.764385i	−0.977112	−	0.212727i	$-0.931766\pi$
$281$	−12.8134	+	12.8134i	−0.764385	+	0.764385i	0.212727	+	0.977112i	$0.431766\pi$
$282$		0			0
$283$	−4.75138	+	2.74321i	−0.282440	+	0.163067i	−0.634528	−	0.772900i	$-0.718805\pi$
$283$	−4.75138	+	2.74321i	−0.282440	+	0.163067i	0.352087	+	0.935967i	$0.385472\pi$
$284$		0			0
$285$	−35.4715	+	24.0201i	−2.10115	+	1.42283i
$286$		0			0
$287$		−	12.9144i		−	0.762314i
$288$		0			0
$289$	7.17294	+	12.4239i	0.421938	+	0.730818i
$290$		0			0
$291$	2.28262	−	11.8586i	0.133810	−	0.695161i
$292$		0			0
$293$	3.84609	+	14.3538i	0.224691	+	0.838557i	0.982528	+	0.186114i	$0.0595893\pi$
$293$	3.84609	+	14.3538i	0.224691	+	0.838557i	−0.757837	+	0.652443i	$0.773744\pi$
$294$		0			0
$295$	−1.77780	+	3.07925i	−0.103508	+	0.179281i
$296$		0			0
$297$	−0.894816	+	19.0710i	−0.0519225	+	1.10661i
$298$		0			0
$299$	3.42369	+	1.02294i	0.197997	+	0.0591580i
$300$		0			0
$301$	−7.21664	−	1.93369i	−0.415960	−	0.111456i
$302$		0			0
$303$	−0.679526	−	9.46933i	−0.0390377	−	0.543999i
$304$		0			0
$305$	7.47155	−	2.00200i	0.427820	−	0.114634i
$306$		0			0
$307$	−13.9068	−	13.9068i	−0.793705	−	0.793705i	0.188390	−	0.982094i	$-0.439673\pi$
$307$	−13.9068	−	13.9068i	−0.793705	−	0.793705i	−0.982094	+	0.188390i	$0.939673\pi$
$308$		0			0
$309$	0.824368	−	1.69806i	0.0468967	−	0.0965994i
$310$		0			0
$311$	−14.2047			−0.805475			−0.402737	−	0.915316i	$-0.631941\pi$
$311$	−14.2047			−0.805475			−0.402737	+	0.915316i	$0.631941\pi$
$312$		0			0
$313$	15.6942			0.887091			0.443546	−	0.896252i	$-0.353720\pi$
$313$	15.6942			0.887091			0.443546	+	0.896252i	$0.353720\pi$
$314$		0			0
$315$	4.47322	+	31.0072i	0.252038	+	1.74706i
$316$		0			0
$317$	−7.57231	−	7.57231i	−0.425304	−	0.425304i	0.461721	−	0.887025i	$-0.347232\pi$
$317$	−7.57231	−	7.57231i	−0.425304	−	0.425304i	−0.887025	+	0.461721i	$0.847232\pi$
$318$		0			0
$319$	12.3755	−	3.31600i	0.692893	−	0.185660i
$320$		0			0
$321$	−6.18580	+	0.443897i	−0.345258	+	0.0247759i
$322$		0			0
$323$	8.74323	+	2.34274i	0.486486	+	0.130354i
$324$		0			0
$325$	36.6810	+	38.8369i	2.03470	+	2.15428i
$326$		0			0
$327$	−2.04274	+	0.707544i	−0.112964	+	0.0391273i
$328$		0			0
$329$	−2.37230	+	4.10894i	−0.130789	+	0.226533i
$330$		0			0
$331$	2.39175	+	8.92612i	0.131462	+	0.490624i	0.999987	−	0.00502131i	$-0.00159834\pi$
$331$	2.39175	+	8.92612i	0.131462	+	0.490624i	−0.868525	+	0.495645i	$0.834932\pi$
$332$		0			0
$333$	5.17125	−	2.21737i	0.283383	−	0.121511i
$334$		0			0
$335$	29.0228	+	50.2690i	1.58569	+	2.74649i
$336$		0			0
$337$		−	28.4642i		−	1.55054i	−0.631629	−	0.775271i	$-0.717613\pi$
$337$		−	28.4642i		−	1.55054i	0.631629	−	0.775271i	$-0.282387\pi$
$338$		0			0
$339$	−11.2154	−	16.5623i	−0.609138	−	0.899539i
$340$		0			0
$341$	−21.2678	+	12.2790i	−1.15172	+	0.664944i
$342$		0			0
$343$	14.0945	−	14.0945i	0.761031	−	0.761031i
$344$		0			0
$345$	−5.00256	+	5.77604i	−0.269329	+	0.310971i
$346$		0			0
$347$	−2.09837	−	1.21149i	−0.112646	−	0.0650363i	0.442618	−	0.896710i	$-0.354050\pi$
$347$	−2.09837	−	1.21149i	−0.112646	−	0.0650363i	−0.555265	+	0.831674i	$0.687383\pi$
$348$		0			0
$349$	3.83210	−	14.3016i	0.205128	−	0.765547i	−0.784283	−	0.620404i	$-0.786969\pi$
$349$	3.83210	−	14.3016i	0.205128	−	0.765547i	0.989411	−	0.145144i	$-0.0463645\pi$
$350$		0			0
$351$	−15.4730	−	10.5635i	−0.825886	−	0.563837i
$352$		0			0
$353$	4.21638	−	15.7357i	0.224415	−	0.837529i	−0.758223	−	0.651996i	$-0.773932\pi$
$353$	4.21638	−	15.7357i	0.224415	−	0.837529i	0.982638	−	0.185533i	$-0.0594013\pi$
$354$		0			0
$355$	19.2087	+	11.0902i	1.01949	+	0.588605i
$356$		0			0
$357$	4.33363	−	5.00369i	0.229360	−	0.264823i
$358$		0			0
$359$	−23.4805	+	23.4805i	−1.23926	+	1.23926i	−0.278950	+	0.960306i	$0.589986\pi$
$359$	−23.4805	+	23.4805i	−1.23926	+	1.23926i	−0.960306	+	0.278950i	$0.910014\pi$
$360$		0			0
$361$	−10.2798	+	5.93502i	−0.541040	+	0.312369i
$362$		0			0
$363$	−2.42811	−	3.58569i	−0.127443	−	0.188200i
$364$		0			0
$365$			33.7762i			1.76793i
$366$		0			0
$367$	−9.40635	−	16.2923i	−0.491007	−	0.850450i	0.508939	−	0.860803i	$-0.330038\pi$
$367$	−9.40635	−	16.2923i	−0.491007	−	0.850450i	−0.999946	+	0.0103530i	$0.996704\pi$
$368$		0			0
$369$	−15.1790	+	6.50859i	−0.790188	+	0.338823i
$370$		0			0
$371$	−5.48358	−	20.4650i	−0.284693	−	1.06249i
$372$		0			0
$373$	2.40324	−	4.16253i	0.124435	−	0.215528i	−0.797077	−	0.603878i	$-0.793622\pi$
$373$	2.40324	−	4.16253i	0.124435	−	0.215528i	0.921512	+	0.388350i	$0.126955\pi$
$374$		0			0
$375$	−71.5182	+	24.7717i	−3.69318	+	1.27921i
$376$		0			0
$377$	−3.59921	+	12.0462i	−0.185369	+	0.620413i
$378$		0			0
$379$	21.9656	+	5.88567i	1.12830	+	0.302326i	0.774237	−	0.632896i	$-0.218134\pi$
$379$	21.9656	+	5.88567i	1.12830	+	0.302326i	0.354061	+	0.935222i	$0.384801\pi$
$380$		0			0
$381$	−12.0357	+	0.863689i	−0.616607	+	0.0442481i
$382$		0			0
$383$	1.79837	−	0.481871i	0.0918923	−	0.0246225i	−0.212580	−	0.977144i	$-0.568187\pi$
$383$	1.79837	−	0.481871i	0.0918923	−	0.0246225i	0.304472	+	0.952521i	$0.401520\pi$
$384$		0			0
$385$	−27.1312	−	27.1312i	−1.38273	−	1.38273i
$386$		0			0
$387$	1.36426	+	9.45665i	0.0693490	+	0.480708i
$388$		0			0
$389$	−7.43410			−0.376924			−0.188462	−	0.982081i	$-0.560350\pi$
$389$	−7.43410			−0.376924			−0.188462	+	0.982081i	$0.560350\pi$
$390$		0			0
$391$	1.61455			0.0816511
$392$		0			0
$393$	2.88318	−	5.93887i	0.145437	−	0.299576i
$394$		0			0
$395$	13.5009	+	13.5009i	0.679303	+	0.679303i
$396$		0			0
$397$	−2.45026	+	0.656546i	−0.122975	+	0.0329511i	−0.319782	−	0.947491i	$-0.603610\pi$
$397$	−2.45026	+	0.656546i	−0.122975	+	0.0329511i	0.196806	+	0.980442i	$0.436943\pi$
$398$		0			0
$399$	1.61586	+	22.5173i	0.0808940	+	1.12727i
$400$		0			0
$401$	−19.8434	−	5.31703i	−0.990933	−	0.265520i	−0.273291	−	0.961931i	$-0.588112\pi$
$401$	−19.8434	−	5.31703i	−0.990933	−	0.265520i	−0.717643	+	0.696412i	$0.754779\pi$
$402$		0			0
$403$	0.687685	−	24.0889i	0.0342560	−	1.19995i
$404$		0			0
$405$	34.1900	−	20.8846i	1.69891	−	1.03776i
$406$		0			0
$407$	−3.44560	+	5.96795i	−0.170792	+	0.295820i
$408$		0			0
$409$	−2.36833	−	8.83872i	−0.117106	−	0.437047i	0.882330	−	0.470632i	$-0.155974\pi$
$409$	−2.36833	−	8.83872i	−0.117106	−	0.437047i	−0.999436	+	0.0335855i	$0.989307\pi$
$410$		0			0
$411$	−1.83721	+	9.54459i	−0.0906231	+	0.470800i
$412$		0			0
$413$	0.936860	+	1.62269i	0.0460999	+	0.0798473i
$414$		0			0
$415$		−	35.9624i		−	1.76533i
$416$		0			0
$417$	27.0933	−	18.3467i	1.32677	−	0.898442i
$418$		0			0
$419$	−5.18334	+	2.99260i	−0.253223	+	0.146198i	−0.621239	−	0.783621i	$-0.713370\pi$
$419$	−5.18334	+	2.99260i	−0.253223	+	0.146198i	0.368016	+	0.929819i	$0.380037\pi$
$420$		0			0
$421$	−18.8397	+	18.8397i	−0.918191	+	0.918191i	−0.996898	−	0.0787065i	$-0.974921\pi$
$421$	−18.8397	+	18.8397i	−0.918191	+	0.918191i	0.0787065	+	0.996898i	$0.474921\pi$
$422$		0			0
$423$	6.02505	+	0.717473i	0.292948	+	0.0348847i
$424$		0			0
$425$	20.9040	+	12.0690i	1.01399	+	0.585430i
$426$		0			0
$427$	1.05500	−	3.93733i	0.0510553	−	0.190541i
$428$		0			0
$429$	22.9244	−	0.988606i	1.10680	−	0.0477303i
$430$		0			0
$431$	−5.32426	+	19.8704i	−0.256461	+	0.957124i	0.710811	+	0.703383i	$0.248328\pi$
$431$	−5.32426	+	19.8704i	−0.256461	+	0.957124i	−0.967272	+	0.253742i	$0.918339\pi$
$432$		0			0
$433$	12.9674	+	7.48671i	0.623172	+	0.359788i	0.778103	−	0.628137i	$-0.216182\pi$
$433$	12.9674	+	7.48671i	0.623172	+	0.359788i	−0.154931	+	0.987925i	$0.549516\pi$
$434$		0			0
$435$	−20.3230	−	17.6015i	−0.974412	−	0.843927i
$436$		0			0
$437$	−3.89353	+	3.89353i	−0.186253	+	0.186253i
$438$		0			0
$439$	25.4738	−	14.7073i	1.21580	−	0.701941i	0.251781	−	0.967784i	$-0.418984\pi$
$439$	25.4738	−	14.7073i	1.21580	−	0.701941i	0.964016	+	0.265843i	$0.0856504\pi$
$440$		0			0
$441$	−4.16991	−	1.66708i	−0.198567	−	0.0793847i
$442$		0			0
$443$		−	13.4346i		−	0.638296i	−0.947705	−	0.319148i	$-0.896603\pi$
$443$		−	13.4346i		−	0.638296i	0.947705	−	0.319148i	$-0.103397\pi$
$444$		0			0
$445$	11.8073	+	20.4509i	0.559722	+	0.969466i
$446$		0			0
$447$	15.4074	+	2.96573i	0.728746	+	0.140274i
$448$		0			0
$449$	−9.13607	−	34.0963i	−0.431158	−	1.60910i	−0.750097	−	0.661328i	$-0.769993\pi$
$449$	−9.13607	−	34.0963i	−0.431158	−	1.60910i	0.318939	−	0.947775i	$-0.396673\pi$
$450$		0			0
$451$	10.1138	−	17.5175i	0.476238	−	0.824869i
$452$		0			0
$453$	12.1307	+	35.0224i	0.569950	+	1.64550i
$454$		0			0
$455$	36.6321	−	8.70320i	1.71734	−	0.408012i
$456$		0			0
$457$	−5.37186	−	1.43938i	−0.251285	−	0.0673316i	0.130978	−	0.991385i	$-0.458188\pi$
$457$	−5.37186	−	1.43938i	−0.251285	−	0.0673316i	−0.382263	+	0.924054i	$0.624855\pi$
$458$		0			0
$459$	−8.06516	−	2.57181i	−0.376450	−	0.120042i
$460$		0			0
$461$	15.4331	−	4.13530i	0.718793	−	0.192600i	0.119160	−	0.992875i	$-0.461980\pi$
$461$	15.4331	−	4.13530i	0.718793	−	0.192600i	0.599633	+	0.800275i	$0.295313\pi$
$462$		0			0
$463$	−19.1882	−	19.1882i	−0.891750	−	0.891750i	0.102938	−	0.994688i	$-0.467176\pi$
$463$	−19.1882	−	19.1882i	−0.891750	−	0.891750i	−0.994688	+	0.102938i	$0.967176\pi$
$464$		0			0
$465$	46.3596	+	22.5065i	2.14988	+	1.04371i
$466$		0			0
$467$	13.2438			0.612849			0.306425	−	0.951895i	$-0.400867\pi$
$467$	13.2438			0.612849			0.306425	+	0.951895i	$0.400867\pi$
$468$		0			0
$469$	30.5886			1.41245
$470$		0			0
$471$	21.8373	+	10.6015i	1.00621	+	0.488490i
$472$		0			0
$473$	−8.27454	−	8.27454i	−0.380464	−	0.380464i
$474$		0			0
$475$	−79.5156	+	21.3061i	−3.64843	+	0.977593i
$476$		0			0
$477$	−21.2900	+	16.7591i	−0.974803	+	0.767345i
$478$		0			0
$479$	35.0689	+	9.39667i	1.60234	+	0.429345i	0.945747	−	0.324903i	$-0.105332\pi$
$479$	35.0689	+	9.39667i	1.60234	+	0.429345i	0.656590	+	0.754248i	$0.271998\pi$
$480$		0			0
$481$	−3.21267	−	5.95045i	−0.146485	−	0.271317i
$482$		0			0
$483$	1.31792	+	3.80496i	0.0599676	+	0.173132i
$484$		0			0
$485$	15.5186	−	26.8790i	0.704663	−	1.22051i
$486$		0			0
$487$	7.12944	+	26.6074i	0.323066	+	1.20570i	0.916242	+	0.400625i	$0.131207\pi$
$487$	7.12944	+	26.6074i	0.323066	+	1.20570i	−0.593176	+	0.805073i	$0.702126\pi$
$488$		0			0
$489$	−17.5559	−	3.37928i	−0.793903	−	0.152816i
$490$		0			0
$491$	5.49069	+	9.51015i	0.247791	+	0.429187i	0.962913	−	0.269813i	$-0.0869620\pi$
$491$	5.49069	+	9.51015i	0.247791	+	0.429187i	−0.715121	+	0.699000i	$0.753629\pi$
$492$		0			0
$493$			5.68077i			0.255849i
$494$		0			0
$495$	−18.2152	+	45.5623i	−0.818713	+	2.04787i
$496$		0			0
$497$	10.1225	−	5.84425i	0.454058	−	0.262150i
$498$		0			0
$499$	−15.2819	+	15.2819i	−0.684112	+	0.684112i	−0.960924	−	0.276812i	$-0.910722\pi$
$499$	−15.2819	+	15.2819i	−0.684112	+	0.684112i	0.276812	+	0.960924i	$0.410722\pi$
$500$		0			0
$501$	−10.4728	−	9.07041i	−0.467892	−	0.405236i
$502$		0			0
$503$	−27.8209	−	16.0624i	−1.24047	−	0.716186i	−0.271281	−	0.962500i	$-0.587447\pi$
$503$	−27.8209	−	16.0624i	−1.24047	−	0.716186i	−0.969190	+	0.246314i	$0.920781\pi$
$504$		0			0
$505$	6.31512	−	23.5684i	0.281019	−	1.04878i
$506$		0			0
$507$	−10.9733	+	19.6618i	−0.487340	+	0.873212i
$508$		0			0
$509$	0.274449	−	1.02426i	0.0121647	−	0.0453994i	−0.959577	−	0.281447i	$-0.909186\pi$
$509$	0.274449	−	1.02426i	0.0121647	−	0.0453994i	0.971741	+	0.236048i	$0.0758522\pi$
$510$		0			0
$511$	15.4146	+	8.89963i	0.681903	+	0.393697i
$512$		0			0
$513$	25.6514	−	13.2474i	1.13254	−	0.584888i
$514$		0			0
$515$	3.43039	−	3.43039i	0.151161	−	0.151161i
$516$		0			0
$517$	−6.43572	+	3.71567i	−0.283043	+	0.163415i
$518$		0			0
$519$	−2.62002	+	1.77419i	−0.115006	+	0.0778783i
$520$		0			0
$521$		−	14.8230i		−	0.649407i	−0.945816	−	0.324704i	$-0.894735\pi$
$521$		−	14.8230i		−	0.649407i	0.945816	−	0.324704i	$-0.105265\pi$
$522$		0			0
$523$	0.156423	+	0.270933i	0.00683991	+	0.0118471i	0.869425	−	0.494065i	$-0.164489\pi$
$523$	0.156423	+	0.270933i	0.00683991	+	0.0118471i	−0.862585	+	0.505912i	$0.831156\pi$
$524$		0			0
$525$	−11.3790	+	59.1157i	−0.496621	+	2.58002i
$526$		0			0
$527$	−2.81824	−	10.5178i	−0.122764	−	0.458163i
$528$		0			0
$529$	11.0089	−	19.0680i	0.478649	−	0.829044i
$530$		0			0
$531$	1.43508	−	1.91894i	0.0622771	−	0.0832751i
$532$		0			0
$533$	9.43005	+	17.4662i	0.408461	+	0.756544i
$534$		0			0
$535$	−15.3959	−	4.12533i	−0.665624	−	0.178353i
$536$		0			0
$537$	−1.66916	−	23.2601i	−0.0720297	−	1.00375i
$538$		0			0
$539$	5.31272	−	1.42354i	0.228835	−	0.0613161i
$540$		0			0
$541$	1.64054	+	1.64054i	0.0705322	+	0.0705322i	0.741493	−	0.670961i	$-0.234118\pi$
$541$	1.64054	+	1.64054i	0.0705322	+	0.0705322i	−0.670961	+	0.741493i	$0.734118\pi$
$542$		0			0
$543$	5.39640	−	11.1157i	0.231582	−	0.477020i
$544$		0			0
$545$	−5.55607			−0.237996
$546$		0			0
$547$	−2.92991			−0.125274			−0.0626369	−	0.998036i	$-0.519951\pi$
$547$	−2.92991			−0.125274			−0.0626369	+	0.998036i	$0.519951\pi$
$548$		0			0
$549$	−5.15946	+	0.744325i	−0.220200	+	0.0317670i
$550$		0			0
$551$	−13.6994	−	13.6994i	−0.583614	−	0.583614i
$552$		0			0
$553$	9.71878	−	2.60414i	0.413285	−	0.110739i
$554$		0			0
$555$	14.4238	−	1.03506i	0.612258	−	0.0439361i
$556$		0			0
$557$	−37.5546	−	10.0627i	−1.59124	−	0.426371i	−0.648857	−	0.760910i	$-0.724753\pi$
$557$	−37.5546	−	10.0627i	−1.59124	−	0.426371i	−0.942382	+	0.334539i	$0.891419\pi$
$558$		0			0
$559$	11.1722	−	2.65432i	0.472532	−	0.112266i
$560$		0			0
$561$	9.79685	−	3.39334i	0.413623	−	0.143267i
$562$		0			0
$563$	−8.43667	+	14.6127i	−0.355563	+	0.615854i	−0.987214	−	0.159399i	$-0.949044\pi$
$563$	−8.43667	+	14.6127i	−0.355563	+	0.615854i	0.631651	+	0.775253i	$0.282378\pi$
$564$		0			0
$565$	−13.3054	−	49.6565i	−0.559763	−	2.08906i
$566$		0			0
$567$	−0.522531	−	21.1063i	−0.0219443	−	0.886381i
$568$		0			0
$569$	−9.07218	−	15.7135i	−0.380326	−	0.658743i	0.610783	−	0.791798i	$-0.290855\pi$
$569$	−9.07218	−	15.7135i	−0.380326	−	0.658743i	−0.991109	+	0.133055i	$0.957521\pi$
$570$		0			0
$571$			32.6819i			1.36769i	0.729626	+	0.683847i	$0.239694\pi$
$571$			32.6819i			1.36769i	−0.729626	+	0.683847i	$0.760306\pi$
$572$		0			0
$573$	16.2264	+	23.9622i	0.677867	+	1.00103i
$574$		0			0
$575$	−12.7163	+	7.34176i	−0.530307	+	0.306173i
$576$		0			0
$577$	20.9504	−	20.9504i	0.872178	−	0.872178i	−0.120531	−	0.992710i	$-0.538460\pi$
$577$	20.9504	−	20.9504i	0.872178	−	0.872178i	0.992710	+	0.120531i	$0.0384597\pi$
$578$		0			0
$579$	23.9980	−	27.7085i	0.997324	−	1.15153i
$580$		0			0
$581$	−16.4123	−	9.47567i	−0.680899	−	0.393117i
$582$		0			0
$583$	8.58879	−	32.0538i	0.355711	−	1.32753i
$584$		0			0
$585$	−28.6911	−	38.6695i	−1.18623	−	1.59879i
$586$		0			0
$587$	10.2200	−	38.1416i	0.421825	−	1.57427i	−0.348935	−	0.937147i	$-0.613457\pi$
$587$	10.2200	−	38.1416i	0.421825	−	1.57427i	0.770760	−	0.637126i	$-0.219877\pi$
$588$		0			0
$589$	32.1604	+	18.5678i	1.32515	+	0.765073i
$590$		0			0
$591$	10.6716	−	12.3216i	0.438971	−	0.506843i
$592$		0			0
$593$	9.44894	−	9.44894i	0.388022	−	0.388022i	−0.485960	−	0.873981i	$-0.661530\pi$
$593$	9.44894	−	9.44894i	0.388022	−	0.388022i	0.873981	+	0.485960i	$0.161530\pi$
$594$		0			0
$595$	14.7334	−	8.50635i	0.604012	−	0.348726i
$596$		0			0
$597$	−4.38768	−	6.47947i	−0.179576	−	0.265187i
$598$		0			0
$599$		−	32.9682i		−	1.34704i	−0.739167	−	0.673522i	$-0.764780\pi$
$599$		−	32.9682i		−	1.34704i	0.739167	−	0.673522i	$-0.235220\pi$
$600$		0			0
$601$	0.969322	+	1.67891i	0.0395395	+	0.0684844i	0.885118	−	0.465367i	$-0.154078\pi$
$601$	0.969322	+	1.67891i	0.0395395	+	0.0684844i	−0.845578	+	0.533851i	$0.820744\pi$
$602$		0			0
$603$	−15.4160	−	35.9525i	−0.627789	−	1.46410i
$604$		0			0
$605$	−2.88058	−	10.7505i	−0.117112	−	0.437069i
$606$		0			0
$607$	−4.67064	+	8.08978i	−0.189575	+	0.328354i	−0.945109	−	0.326756i	$-0.894044\pi$
$607$	−4.67064	+	8.08978i	−0.189575	+	0.328354i	0.755533	+	0.655110i	$0.227378\pi$
$608$		0			0
$609$	−13.3877	+	4.63711i	−0.542498	+	0.187905i
$610$		0			0
$611$	0.208096	−	7.28940i	0.00841867	−	0.294897i
$612$		0			0
$613$	−31.7571	−	8.50929i	−1.28266	−	0.343687i	−0.447790	−	0.894139i	$-0.647789\pi$
$613$	−31.7571	−	8.50929i	−1.28266	−	0.343687i	−0.834867	+	0.550452i	$0.814455\pi$
$614$		0			0
$615$	−42.3379	+	3.03819i	−1.70723	+	0.122512i
$616$		0			0
$617$	−24.1659	+	6.47523i	−0.972881	+	0.260683i	−0.710044	−	0.704157i	$-0.751325\pi$
$617$	−24.1659	+	6.47523i	−0.972881	+	0.260683i	−0.262837	+	0.964840i	$0.584658\pi$
$618$		0			0
$619$	−12.3512	−	12.3512i	−0.496437	−	0.496437i	0.413890	−	0.910327i	$-0.364170\pi$
$619$	−12.3512	−	12.3512i	−0.496437	−	0.496437i	−0.910327	+	0.413890i	$0.864170\pi$
$620$		0			0
$621$	3.80797	−	3.46664i	0.152809	−	0.139112i
$622$		0			0
$623$	12.4444			0.498573
$624$		0			0
$625$	−120.441			−4.81766
$626$		0			0
$627$	−15.4423	+	31.8086i	−0.616707	+	1.27031i
$628$		0			0
$629$	−2.16057	−	2.16057i	−0.0861477	−	0.0861477i
$630$		0			0
$631$	−32.6451	+	8.74723i	−1.29958	+	0.348222i	−0.841292	−	0.540581i	$-0.818204\pi$
$631$	−32.6451	+	8.74723i	−1.29958	+	0.348222i	−0.458289	+	0.888803i	$0.651538\pi$
$632$		0			0
$633$	−0.695953	−	9.69825i	−0.0276616	−	0.385471i
$634$		0			0
$635$	−29.9558	−	8.02663i	−1.18876	−	0.318527i
$636$		0			0
$637$	−1.54512	+	5.17138i	−0.0612198	+	0.204898i
$638$		0			0
$639$	−11.9706	−	8.95219i	−0.473550	−	0.354143i
$640$		0			0
$641$	11.3280	−	19.6207i	0.447430	−	0.774971i	−0.550788	−	0.834645i	$-0.685673\pi$
$641$	11.3280	−	19.6207i	0.447430	−	0.774971i	0.998218	+	0.0596740i	$0.0190061\pi$
$642$		0			0
$643$	−11.8724	−	44.3085i	−0.468203	−	1.74736i	−0.646046	−	0.763299i	$-0.723579\pi$
$643$	−11.8724	−	44.3085i	−0.468203	−	1.74736i	0.177843	−	0.984059i	$-0.443088\pi$
$644$		0			0
$645$	−4.64155	+	24.1135i	−0.182761	+	0.949469i
$646$		0			0
$647$	−23.7381	−	41.1155i	−0.933239	−	1.61642i	−0.777744	−	0.628581i	$-0.783636\pi$
$647$	−23.7381	−	41.1155i	−0.933239	−	1.61642i	−0.155495	−	0.987837i	$-0.549697\pi$
$648$		0			0
$649$			2.93476i			0.115199i
$650$		0			0
$651$	22.4866	−	15.2272i	0.881319	−	0.596800i
$652$		0			0
$653$	−28.5462	+	16.4812i	−1.11710	+	0.644958i	−0.940659	−	0.339353i	$-0.889792\pi$
$653$	−28.5462	+	16.4812i	−1.11710	+	0.644958i	−0.176441	+	0.984311i	$0.556458\pi$
$654$		0			0
$655$	11.9976	−	11.9976i	0.468784	−	0.468784i
$656$		0			0
$657$	2.69159	−	22.6029i	0.105009	−	0.881822i
$658$		0			0
$659$	14.6160	+	8.43857i	0.569360	+	0.328720i	0.756894	−	0.653538i	$-0.226716\pi$
$659$	14.6160	+	8.43857i	0.569360	+	0.328720i	−0.187534	+	0.982258i	$0.560049\pi$
$660$		0			0
$661$	−3.30272	+	12.3259i	−0.128461	+	0.479423i	−0.999939	−	0.0110108i	$-0.996495\pi$
$661$	−3.30272	+	12.3259i	−0.128461	+	0.479423i	0.871478	+	0.490434i	$0.163162\pi$
$662$		0			0
$663$	−2.20738	+	9.93166i	−0.0857274	+	0.385714i
$664$		0			0
$665$	−15.0168	+	56.0436i	−0.582328	+	2.17328i
$666$		0			0
$667$	−2.99274	−	1.72786i	−0.115879	−	0.0669030i
$668$		0			0
$669$	−27.5436	−	23.8552i	−1.06490	−	0.922296i
$670$		0			0
$671$	4.51451	−	4.51451i	0.174281	−	0.174281i
$672$		0			0
$673$	−13.3091	+	7.68401i	−0.513028	+	0.296197i	−0.734077	−	0.679066i	$-0.762385\pi$
$673$	−13.3091	+	7.68401i	−0.513028	+	0.296197i	0.221049	+	0.975263i	$0.429052\pi$
$674$		0			0
$675$	75.2167	−	16.4186i	2.89509	−	0.631954i
$676$		0			0
$677$			4.08973i			0.157181i	0.996907	+	0.0785906i	$0.0250420\pi$
$677$			4.08973i			0.157181i	−0.996907	+	0.0785906i	$0.974958\pi$
$678$		0			0
$679$	−8.17793	−	14.1646i	−0.313840	−	0.543587i
$680$		0			0
$681$	37.1293	+	7.14691i	1.42280	+	0.273870i
$682$		0			0
$683$	9.15575	+	34.1697i	0.350335	+	1.30747i	0.886254	+	0.463199i	$0.153299\pi$
$683$	9.15575	+	34.1697i	0.350335	+	1.30747i	−0.535919	+	0.844269i	$0.680035\pi$
$684$		0			0
$685$	−12.4905	+	21.6341i	−0.477236	+	0.826597i
$686$		0			0
$687$	2.30830	+	6.66427i	0.0880672	+	0.254258i
$688$		0			0
$689$	22.3597	+	23.6739i	0.851838	+	0.901904i
$690$		0			0
$691$	2.30242	+	0.616931i	0.0875881	+	0.0234692i	0.302347	−	0.953198i	$-0.402230\pi$
$691$	2.30242	+	0.616931i	0.0875881	+	0.0234692i	−0.214759	+	0.976667i	$0.568897\pi$
$692$		0			0
$693$	15.9940	+	20.3181i	0.607561	+	0.771820i
$694$		0			0
$695$	81.2304	−	21.7656i	3.08124	−	0.825617i
$696$		0			0
$697$	6.34187	+	6.34187i	0.240215	+	0.240215i
$698$		0			0
$699$	−36.4239	−	17.6829i	−1.37768	−	0.668830i
$700$		0			0
$701$	44.9525			1.69783			0.848916	−	0.528528i	$-0.177256\pi$
$701$	44.9525			1.69783			0.848916	+	0.528528i	$0.177256\pi$
$702$		0			0
$703$	10.4206			0.393021
$704$		0			0
$705$	14.0286	+	6.81055i	0.528348	+	0.256500i
$706$		0			0
$707$	−9.09204	−	9.09204i	−0.341941	−	0.341941i
$708$		0			0
$709$	−26.4355	+	7.08337i	−0.992807	+	0.266022i	−0.718429	−	0.695600i	$-0.755138\pi$
$709$	−26.4355	+	7.08337i	−0.992807	+	0.266022i	−0.274378	+	0.961622i	$0.588472\pi$
$710$		0			0
$711$	−7.95884	−	10.1106i	−0.298480	−	0.379176i
$712$		0			0
$713$	6.39818	+	1.71439i	0.239614	+	0.0642043i
$714$		0			0
$715$	56.5048	+	16.8826i	2.11316	+	0.631375i
$716$		0			0
$717$	−13.3250	−	38.4705i	−0.497632	−	1.43671i
$718$		0			0
$719$	5.57711	−	9.65984i	0.207991	−	0.360251i	−0.743090	−	0.669191i	$-0.766641\pi$
$719$	5.57711	−	9.65984i	0.207991	−	0.360251i	0.951082	+	0.308940i	$0.0999741\pi$
$720$		0			0
$721$	−0.661676	−	2.46941i	−0.0246421	−	0.0919656i
$722$		0			0
$723$	35.3666	+	6.80762i	1.31530	+	0.253178i
$724$		0			0
$725$	−25.8320	−	44.7423i	−0.959376	−	1.66169i
$726$		0			0
$727$			29.1867i			1.08247i	0.840870	+	0.541237i	$0.182044\pi$
$727$			29.1867i			1.08247i	−0.840870	+	0.541237i	$0.817956\pi$
$728$		0			0
$729$	−24.5440	+	11.2513i	−0.909038	+	0.416714i
$730$		0			0
$731$	4.49344	−	2.59429i	0.166196	−	0.0959533i
$732$		0			0
$733$	30.3088	−	30.3088i	1.11948	−	1.11948i	0.127663	−	0.991818i	$-0.459252\pi$
$733$	30.3088	−	30.3088i	1.11948	−	1.11948i	0.991818	−	0.127663i	$-0.0407476\pi$
$734$		0			0
$735$	−8.72454	−	7.55622i	−0.321809	−	0.278715i
$736$		0			0
$737$	41.4914	+	23.9551i	1.52836	+	0.882397i
$738$		0			0
$739$	−6.82020	+	25.4533i	−0.250885	+	0.936316i	0.719448	+	0.694546i	$0.244395\pi$
$739$	−6.82020	+	25.4533i	−0.250885	+	0.936316i	−0.970334	+	0.241770i	$0.922272\pi$
$740$		0			0
$741$	−18.6274	−	29.2737i	−0.684295	−	1.07540i
$742$		0			0
$743$	−6.56318	+	24.4941i	−0.240780	+	0.898602i	0.734678	+	0.678416i	$0.237333\pi$
$743$	−6.56318	+	24.4941i	−0.240780	+	0.898602i	−0.975458	+	0.220186i	$0.929333\pi$
$744$		0			0
$745$	34.9230	+	20.1628i	1.27948	+	0.738707i
$746$		0			0
$747$	−2.86581	+	24.0659i	−0.104854	+	0.880524i
$748$		0			0
$749$	−5.93934	+	5.93934i	−0.217019	+	0.217019i
$750$		0			0
$751$	−16.1198	+	9.30675i	−0.588219	+	0.339608i	−0.764393	−	0.644751i	$-0.776961\pi$
$751$	−16.1198	+	9.30675i	−0.588219	+	0.339608i	0.176174	+	0.984359i	$0.443628\pi$
$752$		0			0
$753$	12.7798	−	8.65408i	0.465723	−	0.315372i
$754$		0			0
$755$			95.2577i			3.46678i
$756$		0			0
$757$	−1.20008	−	2.07859i	−0.0436175	−	0.0755478i	0.843392	−	0.537298i	$-0.180555\pi$
$757$	−1.20008	−	2.07859i	−0.0436175	−	0.0755478i	−0.887010	+	0.461750i	$0.847222\pi$
$758$		0			0
$759$	−1.19213	+	6.19328i	−0.0432715	+	0.224802i
$760$		0			0
$761$	−2.70569	−	10.0978i	−0.0980811	−	0.366044i	0.899387	−	0.437152i	$-0.144013\pi$
$761$	−2.70569	−	10.0978i	−0.0980811	−	0.366044i	−0.997469	+	0.0711086i	$0.977346\pi$
$762$		0			0
$763$	−1.46396	+	2.53565i	−0.0529988	+	0.0917967i
$764$		0			0
$765$	−17.4233	−	13.0300i	−0.629941	−	0.471100i
$766$		0			0
$767$	−2.45194	−	1.51052i	−0.0885345	−	0.0545419i
$768$		0			0
$769$	31.6831	+	8.48946i	1.14252	+	0.306138i	0.779964	−	0.625824i	$-0.215237\pi$
$769$	31.6831	+	8.48946i	1.14252	+	0.306138i	0.362557	+	0.931962i	$0.381904\pi$
$770$		0			0
$771$	−3.57055	−	49.7563i	−0.128590	−	1.79193i
$772$		0			0
$773$	30.9596	−	8.29561i	1.11354	−	0.298372i	0.345274	−	0.938502i	$-0.387786\pi$
$773$	30.9596	−	8.29561i	1.11354	−	0.298372i	0.768267	+	0.640130i	$0.221119\pi$
$774$		0			0
$775$	70.0240	+	70.0240i	2.51534	+	2.51534i
$776$		0			0
$777$	3.32813	−	6.85541i	0.119396	−	0.245936i
$778$		0			0
$779$	−30.5873			−1.09590
$780$		0			0
$781$	18.3074			0.655090
$782$		0			0
$783$	12.1974	+	13.3983i	0.435899	+	0.478817i
$784$		0			0
$785$	44.1152	+	44.1152i	1.57454	+	1.57454i
$786$		0			0
$787$	−0.821024	+	0.219993i	−0.0292663	+	0.00784189i	−0.273423	−	0.961894i	$-0.588156\pi$
$787$	−0.821024	+	0.219993i	−0.0292663	+	0.00784189i	0.244156	+	0.969736i	$0.421489\pi$
$788$		0			0
$789$	18.9299	−	1.35842i	0.673923	−	0.0483612i
$790$		0			0
$791$	−26.1678	−	7.01164i	−0.930419	−	0.249305i
$792$		0			0
$793$	1.44817	+	6.09542i	0.0514262	+	0.216455i
$794$		0			0
$795$	−65.8012	+	22.7916i	−2.33373	+	0.808333i
$796$		0			0
$797$	−10.3419	+	17.9126i	−0.366328	+	0.634498i	−0.988988	−	0.147994i	$-0.952718\pi$
$797$	−10.3419	+	17.9126i	−0.366328	+	0.634498i	0.622661	+	0.782492i	$0.286052\pi$
$798$		0			0
$799$	−0.852811	−	3.18273i	−0.0301703	−	0.112597i
$800$		0			0
$801$	−6.27170	−	14.6265i	−0.221599	−	0.516804i
$802$		0			0
$803$	13.9393	+	24.1435i	0.491906	+	0.852006i
$804$		0			0
$805$			10.3491i			0.364759i
$806$		0			0
$807$	21.1360	+	31.2125i	0.744024	+	1.09873i
$808$		0			0
$809$	29.9570	−	17.2957i	1.05323	−	0.608084i	0.129680	−	0.991556i	$-0.458605\pi$
$809$	29.9570	−	17.2957i	1.05323	−	0.608084i	0.923553	+	0.383472i	$0.125272\pi$
$810$		0			0
$811$	15.3840	−	15.3840i	0.540206	−	0.540206i	−0.383383	−	0.923589i	$-0.625241\pi$
$811$	15.3840	−	15.3840i	0.540206	−	0.540206i	0.923589	+	0.383383i	$0.125241\pi$
$812$		0			0
$813$	24.7874	−	28.6200i	0.869333	−	1.00375i
$814$		0			0
$815$	−39.7927	−	22.9743i	−1.39388	−	0.804755i
$816$		0			0
$817$	−4.57988	+	17.0923i	−0.160230	+	0.597985i
$818$		0			0
$819$	−25.2075	+	2.90496i	−0.880823	+	0.101508i
$820$		0			0
$821$	−3.50244	+	13.0713i	−0.122236	+	0.456191i	−0.999726	−	0.0234035i	$-0.992550\pi$
$821$	−3.50244	+	13.0713i	−0.122236	+	0.456191i	0.877490	+	0.479595i	$0.159216\pi$
$822$		0			0
$823$	−46.1779	−	26.6608i	−1.60966	−	0.929339i	−0.989445	−	0.144908i	$-0.953711\pi$
$823$	−46.1779	−	26.6608i	−1.60966	−	0.929339i	−0.620217	−	0.784431i	$-0.712955\pi$
$824$		0			0
$825$	−61.7305	+	71.2751i	−2.14918	+	2.48148i
$826$		0			0
$827$	37.8390	−	37.8390i	1.31579	−	1.31579i	0.398716	−	0.917075i	$-0.369456\pi$
$827$	37.8390	−	37.8390i	1.31579	−	1.31579i	0.917075	−	0.398716i	$-0.130544\pi$
$828$		0			0
$829$	12.8736	−	7.43259i	0.447119	−	0.258144i	−0.259493	−	0.965745i	$-0.583556\pi$
$829$	12.8736	−	7.43259i	0.447119	−	0.258144i	0.706613	+	0.707600i	$0.250222\pi$
$830$		0			0
$831$	20.2324	+	29.8780i	0.701853	+	1.03645i
$832$		0			0
$833$			2.43872i			0.0844968i
$834$		0			0
$835$	−17.8040	−	30.8375i	−0.616133	−	1.06717i
$836$		0			0
$837$	−29.2301	−	18.7556i	−1.01034	−	0.648287i
$838$		0			0
$839$	9.79042	+	36.5383i	0.338003	+	1.26144i	0.900577	+	0.434696i	$0.143144\pi$
$839$	9.79042	+	36.5383i	0.338003	+	1.26144i	−0.562574	+	0.826747i	$0.690189\pi$
$840$		0			0
$841$	−8.42053	+	14.5848i	−0.290363	+	0.502924i
$842$		0			0
$843$	29.6577	−	10.2725i	1.02146	−	0.353805i
$844$		0			0
$845$	−43.1882	+	38.5193i	−1.48572	+	1.32510i
$846$		0			0
$847$	−5.66525	−	1.51800i	−0.194660	−	0.0521591i
$848$		0			0
$849$	9.47839	−	0.680176i	0.325298	−	0.0233436i
$850$		0			0
$851$	1.79539	−	0.481073i	0.0615452	−	0.0164910i
$852$		0			0
$853$	9.33060	+	9.33060i	0.319474	+	0.319474i	0.848565	−	0.529091i	$-0.177467\pi$
$853$	9.33060	+	9.33060i	0.319474	+	0.319474i	−0.529091	+	0.848565i	$0.677467\pi$
$854$		0			0
$855$	73.4393	−	10.5947i	2.51157	−	0.362330i
$856$		0			0
$857$	10.8514			0.370677			0.185338	−	0.982675i	$-0.440662\pi$
$857$	10.8514			0.370677			0.185338	+	0.982675i	$0.440662\pi$
$858$		0			0
$859$	21.8093			0.744125			0.372063	−	0.928208i	$-0.378651\pi$
$859$	21.8093			0.744125			0.372063	+	0.928208i	$0.378651\pi$
$860$		0			0
$861$	−9.76897	+	20.1225i	−0.332926	+	0.685772i
$862$		0			0
$863$	−28.0435	−	28.0435i	−0.954612	−	0.954612i	0.0444016	−	0.999014i	$-0.485862\pi$
$863$	−28.0435	−	28.0435i	−0.954612	−	0.954612i	−0.999014	+	0.0444016i	$0.985862\pi$
$864$		0			0
$865$	−7.85525	+	2.10481i	−0.267087	+	0.0715657i
$866$		0			0
$867$	−1.77852	−	24.7841i	−0.0604018	−	0.841711i
$868$		0			0
$869$	15.2223	+	4.07879i	0.516380	+	0.138364i
$870$		0			0
$871$	−41.3698	+	22.3357i	−1.40176	+	0.756816i
$872$		0			0
$873$	−12.5269	+	16.7506i	−0.423972	+	0.566923i
$874$		0			0
$875$	−51.2545	+	88.7753i	−1.73272	+	3.00115i
$876$		0			0
$877$	7.49875	+	27.9857i	0.253215	+	0.945011i	0.969075	+	0.246767i	$0.0793682\pi$
$877$	7.49875	+	27.9857i	0.253215	+	0.945011i	−0.715860	+	0.698244i	$0.753965\pi$
$878$		0			0
$879$	4.86503	−	25.2745i	0.164093	−	0.852489i
$880$		0			0
$881$	−25.2594	−	43.7505i	−0.851010	−	1.47399i	−0.880298	−	0.474421i	$-0.842658\pi$
$881$	−25.2594	−	43.7505i	−0.851010	−	1.47399i	0.0292886	−	0.999571i	$-0.490676\pi$
$882$		0			0
$883$			37.9550i			1.27729i	0.769503	+	0.638643i	$0.220504\pi$
$883$			37.9550i			1.27729i	−0.769503	+	0.638643i	$0.779496\pi$
$884$		0			0
$885$	5.09933	−	3.45310i	0.171412	−	0.116075i
$886$		0			0
$887$	−27.7408	+	16.0162i	−0.931445	+	0.537770i	−0.887268	−	0.461254i	$-0.847400\pi$
$887$	−27.7408	+	16.0162i	−0.931445	+	0.537770i	−0.0441764	+	0.999024i	$0.514066\pi$
$888$		0			0
$889$	−11.5561	+	11.5561i	−0.387581	+	0.387581i
$890$		0			0
$891$	15.8203	−	29.0385i	0.530001	−	0.972825i
$892$		0			0
$893$	9.73186	+	5.61869i	0.325664	+	0.188022i
$894$		0			0
$895$	15.5122	−	57.8925i	0.518517	−	1.93513i
$896$		0			0
$897$	−4.56079	−	4.18369i	−0.152280	−	0.139689i
$898$		0			0
$899$	−6.03207	+	22.5120i	−0.201181	+	0.750817i
$900$		0			0
$901$	12.7425	+	7.35691i	0.424515	+	0.245094i
$902$		0			0
$903$	9.78181	+	8.47191i	0.325518	+	0.281928i
$904$		0			0
$905$	22.4557	−	22.4557i	0.746452	−	0.746452i
$906$		0			0
$907$	9.90121	−	5.71647i	0.328764	−	0.189812i	−0.326528	−	0.945187i	$-0.605879\pi$
$907$	9.90121	−	5.71647i	0.328764	−	0.189812i	0.655292	+	0.755375i	$0.272545\pi$
$908$		0			0
$909$	−6.10418	+	15.2686i	−0.202463	+	0.506426i
$910$		0			0
$911$		−	57.2998i		−	1.89843i	−0.314633	−	0.949213i	$-0.601881\pi$
$911$		−	57.2998i		−	1.89843i	0.314633	−	0.949213i	$-0.398119\pi$
$912$		0			0
$913$	−14.8415	−	25.7062i	−0.491182	−	0.850752i
$914$		0			0
$915$	−13.1561	−	2.53239i	−0.434928	−	0.0837181i
$916$		0			0
$917$	−2.31417	−	8.63661i	−0.0764207	−	0.285206i
$918$		0			0
$919$	−18.0716	+	31.3010i	−0.596128	+	1.03252i	0.397259	+	0.917707i	$0.369962\pi$
$919$	−18.0716	+	31.3010i	−0.596128	+	1.03252i	−0.993387	+	0.114817i	$0.963372\pi$
$920$		0			0
$921$	11.1491	+	32.1885i	0.367376	+	1.06065i
$922$		0			0
$923$	−9.42283	+	15.2955i	−0.310156	+	0.503458i
$924$		0			0
$925$	26.8416	+	7.19218i	0.882546	+	0.236477i
$926$		0			0
$927$	−2.56896	+	2.02223i	−0.0843758	+	0.0664189i
$928$		0			0
$929$	−24.0945	+	6.45609i	−0.790514	+	0.211818i	−0.631415	−	0.775445i	$-0.717526\pi$
$929$	−24.0945	+	6.45609i	−0.790514	+	0.211818i	−0.159099	+	0.987263i	$0.550859\pi$
$930$		0			0
$931$	−5.88107	−	5.88107i	−0.192744	−	0.192744i
$932$		0			0
$933$	22.1329	+	10.7450i	0.724599	+	0.351775i
$934$		0			0
$935$	26.6465			0.871435
$936$		0			0
$937$	30.1453			0.984804			0.492402	−	0.870368i	$-0.336119\pi$
$937$	30.1453			0.984804			0.492402	+	0.870368i	$0.336119\pi$
$938$		0			0
$939$	−24.4538	−	11.8717i	−0.798021	−	0.387420i
$940$		0			0
$941$	7.18440	+	7.18440i	0.234205	+	0.234205i	0.814445	−	0.580241i	$-0.197041\pi$
$941$	7.18440	+	7.18440i	0.234205	+	0.234205i	−0.580241	+	0.814445i	$0.697041\pi$
$942$		0			0
$943$	−5.26995	+	1.41208i	−0.171613	+	0.0459836i
$944$		0			0
$945$	16.4851	−	51.6972i	0.536261	−	1.68171i
$946$		0			0
$947$	−24.1863	−	6.48071i	−0.785950	−	0.210595i	−0.156544	−	0.987671i	$-0.550035\pi$
$947$	−24.1863	−	6.48071i	−0.785950	−	0.210595i	−0.629406	+	0.777076i	$0.716702\pi$
$948$		0			0
$949$	−27.3461	−	0.780670i	−0.887690	−	0.0253416i
$950$		0			0
$951$	6.07073	+	17.5267i	0.196857	+	0.568343i
$952$		0			0
$953$	−4.31518	+	7.47410i	−0.139782	+	0.242110i	−0.927414	−	0.374036i	$-0.877974\pi$
$953$	−4.31518	+	7.47410i	−0.139782	+	0.242110i	0.787632	+	0.616146i	$0.211307\pi$
$954$		0			0
$955$	19.2502	+	71.8426i	0.622921	+	2.32477i
$956$		0			0
$957$	−21.7911	−	4.19450i	−0.704405	−	0.135589i
$958$		0			0
$959$	6.58217	+	11.4007i	0.212549	+	0.368146i
$960$		0			0
$961$		−	13.6729i		−	0.441061i
$962$		0			0
$963$	9.97412	+	3.98753i	0.321412	+	0.128496i
$964$		0			0
$965$	81.5882	−	47.1050i	2.62642	−	1.51636i
$966$		0			0
$967$	4.49854	−	4.49854i	0.144663	−	0.144663i	−0.631066	−	0.775729i	$-0.717382\pi$
$967$	4.49854	−	4.49854i	0.144663	−	0.144663i	0.775729	+	0.631066i	$0.217382\pi$
$968$		0			0
$969$	−11.8510	−	10.2640i	−0.380710	−	0.329729i
$970$		0			0
$971$	21.3486	+	12.3256i	0.685109	+	0.395548i	0.801777	−	0.597623i	$-0.203888\pi$
$971$	21.3486	+	12.3256i	0.685109	+	0.395548i	−0.116668	+	0.993171i	$0.537221\pi$
$972$		0			0
$973$	11.4700	−	42.8065i	0.367710	−	1.37231i
$974$		0			0
$975$	−27.7764	−	88.2602i	−0.889557	−	2.82659i
$976$		0			0
$977$	−6.75059	+	25.1936i	−0.215971	+	0.806013i	0.769852	+	0.638222i	$0.220330\pi$
$977$	−6.75059	+	25.1936i	−0.215971	+	0.806013i	−0.985823	+	0.167791i	$0.946337\pi$
$978$		0			0
$979$	16.8800	+	9.74565i	0.539486	+	0.311472i
$980$		0			0
$981$	3.71809	+	0.442757i	0.118709	+	0.0141361i
$982$		0			0
$983$	−29.1826	+	29.1826i	−0.930781	+	0.930781i	−0.997755	−	0.0669741i	$-0.978666\pi$
$983$	−29.1826	+	29.1826i	−0.930781	+	0.930781i	0.0669741	+	0.997755i	$0.478666\pi$
$984$		0			0
$985$	36.2811	−	20.9469i	1.15601	−	0.667424i
$986$		0			0
$987$	6.80453	−	4.60780i	0.216591	−	0.146668i
$988$		0			0
$989$			3.15631i			0.100365i
$990$		0			0
$991$	5.88803	+	10.1984i	0.187040	+	0.323962i	0.944262	−	0.329195i	$-0.106777\pi$
$991$	5.88803	+	10.1984i	0.187040	+	0.323962i	−0.757222	+	0.653157i	$0.773444\pi$
$992$		0			0
$993$	3.02539	−	15.7173i	0.0960079	−	0.498775i
$994$		0			0
$995$	−5.20532	−	19.4265i	−0.165020	−	0.615863i
$996$		0			0
$997$	−26.6958	+	46.2385i	−0.845466	+	1.46439i	0.0397507	+	0.999210i	$0.487344\pi$
$997$	−26.6958	+	46.2385i	−0.845466	+	1.46439i	−0.885216	+	0.465180i	$0.845990\pi$
$998$		0			0
$999$	−9.73484	−	0.456760i	−0.307997	−	0.0144513i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	624.2.cn.f.353.2		56
3.2	odd	2	inner	624.2.cn.f.353.8		56
4.3	odd	2		312.2.bp.a.41.13	yes	56
12.11	even	2		312.2.bp.a.41.7	✓	56
13.7	odd	12	inner	624.2.cn.f.449.8		56
39.20	even	12	inner	624.2.cn.f.449.2		56
52.7	even	12		312.2.bp.a.137.7	yes	56
156.59	odd	12		312.2.bp.a.137.13	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.bp.a.41.7	✓	56	12.11	even	2
312.2.bp.a.41.13	yes	56	4.3	odd	2
312.2.bp.a.137.7	yes	56	52.7	even	12
312.2.bp.a.137.13	yes	56	156.59	odd	12
624.2.cn.f.353.2		56	1.1	even	1	trivial
624.2.cn.f.353.8		56	3.2	odd	2	inner
624.2.cn.f.449.2		56	39.20	even	12	inner
624.2.cn.f.449.8		56	13.7	odd	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	624.cn (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.55814 - 0.756439i) q^{3} +(-3.14772 - 3.14772i) q^{5} +(-2.26593 + 0.607154i) q^{7} +(1.85560 + 2.35728i) q^{9} +O(q^{10})\)	\(q+(-1.55814 - 0.756439i) q^{3} +(-3.14772 - 3.14772i) q^{5} +(-2.26593 + 0.607154i) q^{7} +(1.85560 + 2.35728i) q^{9} +(-3.54906 - 0.950969i) q^{11} +(2.62122 - 2.47572i) q^{13} +(2.52353 + 7.28565i) q^{15} +(0.814572 - 1.41088i) q^{17} +(1.43802 + 5.36676i) q^{19} +(3.98991 + 0.768007i) q^{21} +(0.495519 + 0.858264i) q^{23} +14.8163i q^{25} +(-1.10815 - 5.07661i) q^{27} +(-3.01980 + 1.74348i) q^{29} +(4.72615 - 4.72615i) q^{31} +(4.81059 + 4.16639i) q^{33} +(9.04366 + 5.22136i) q^{35} +(0.485423 - 1.81162i) q^{37} +(-5.95697 + 1.87472i) q^{39} +(-1.42485 + 5.31761i) q^{41} +(2.75816 + 1.59242i) q^{43} +(1.57914 - 13.2610i) q^{45} +(1.43015 - 1.43015i) q^{47} +(-1.29638 + 0.748468i) q^{49} +(-2.33646 + 1.58217i) q^{51} +9.03162i q^{53} +(8.17808 + 14.1648i) q^{55} +(1.81899 - 9.44994i) q^{57} +(-0.206728 - 0.771519i) q^{59} +(-0.868812 + 1.50483i) q^{61} +(-5.63588 - 4.21478i) q^{63} +(-16.0438 - 0.458014i) q^{65} +(-12.5951 - 3.37485i) q^{67} +(-0.122863 - 1.71213i) q^{69} +(-4.81283 + 1.28959i) q^{71} +(-5.36519 - 5.36519i) q^{73} +(11.2076 - 23.0859i) q^{75} +8.61930 q^{77} -4.28909 q^{79} +(-2.11350 + 8.74832i) q^{81} +(5.71245 + 5.71245i) q^{83} +(-7.00511 + 1.87701i) q^{85} +(6.02411 - 0.432294i) q^{87} +(-5.12406 - 1.37299i) q^{89} +(-4.43637 + 7.20128i) q^{91} +(-10.9390 + 3.78895i) q^{93} +(12.3666 - 21.4196i) q^{95} +(1.80454 + 6.73465i) q^{97} +(-4.34394 - 10.1307i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 4 q^{7}+O(q^{10}) \) 56 * q - 4 * q^7	\( 56 q - 4 q^{7} + 8 q^{13} + 8 q^{15} - 4 q^{19} + 16 q^{21} - 24 q^{27} + 36 q^{31} + 28 q^{33} + 20 q^{37} - 16 q^{39} + 84 q^{43} + 12 q^{45} - 12 q^{49} + 24 q^{55} - 36 q^{57} - 24 q^{61} + 12 q^{63} + 32 q^{67} - 36 q^{69} - 20 q^{73} + 60 q^{75} + 32 q^{79} - 88 q^{85} + 16 q^{87} - 28 q^{91} - 88 q^{93} - 36 q^{97} - 44 q^{99}+O(q^{100}) \) 56 * q - 4 * q^7 + 8 * q^13 + 8 * q^15 - 4 * q^19 + 16 * q^21 - 24 * q^27 + 36 * q^31 + 28 * q^33 + 20 * q^37 - 16 * q^39 + 84 * q^43 + 12 * q^45 - 12 * q^49 + 24 * q^55 - 36 * q^57 - 24 * q^61 + 12 * q^63 + 32 * q^67 - 36 * q^69 - 20 * q^73 + 60 * q^75 + 32 * q^79 - 88 * q^85 + 16 * q^87 - 28 * q^91 - 88 * q^93 - 36 * q^97 - 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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