LMFDB - Embedded newform 504.2.j.a.323.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(323,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("504.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.j (of order $2$, degree $1$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.12
Character	$\chi$	$=$	504.323
Dual form			504.2.j.a.323.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.157273 + 1.40544i) q^{2} +(-1.95053 - 0.442076i) q^{4} +1.81873 q^{5} +1.00000i q^{7} +(0.928077 - 2.67183i) q^{8} +O(q^{10})$	\(q+(-0.157273 + 1.40544i) q^{2} +(-1.95053 - 0.442076i) q^{4} +1.81873 q^{5} +1.00000i q^{7} +(0.928077 - 2.67183i) q^{8} +(-0.286037 + 2.55612i) q^{10} -2.36894i q^{11} +6.99210i q^{13} +(-1.40544 - 0.157273i) q^{14} +(3.60914 + 1.72456i) q^{16} +3.69378i q^{17} +5.53035 q^{19} +(-3.54749 - 0.804017i) q^{20} +(3.32941 + 0.372570i) q^{22} +7.60875 q^{23} -1.69222 q^{25} +(-9.82698 - 1.09967i) q^{26} +(0.442076 - 1.95053i) q^{28} -5.87055 q^{29} +2.39191i q^{31} +(-2.99139 + 4.80120i) q^{32} +(-5.19139 - 0.580932i) q^{34} +1.81873i q^{35} +8.88054i q^{37} +(-0.869775 + 7.77259i) q^{38} +(1.68792 - 4.85934i) q^{40} -9.83200i q^{41} -2.88967 q^{43} +(-1.04725 + 4.62069i) q^{44} +(-1.19665 + 10.6937i) q^{46} -0.169907 q^{47} -1.00000 q^{49} +(0.266140 - 2.37831i) q^{50} +(3.09104 - 13.6383i) q^{52} +2.02343 q^{53} -4.30847i q^{55} +(2.67183 + 0.928077i) q^{56} +(0.923279 - 8.25072i) q^{58} +0.169907i q^{59} +0.420023i q^{61} +(-3.36169 - 0.376183i) q^{62} +(-6.27735 - 4.95933i) q^{64} +12.7167i q^{65} -9.76396 q^{67} +(1.63293 - 7.20483i) q^{68} +(-2.55612 - 0.286037i) q^{70} +12.0101 q^{71} +8.78003 q^{73} +(-12.4811 - 1.39667i) q^{74} +(-10.7871 - 2.44484i) q^{76} +2.36894 q^{77} -14.2845i q^{79} +(6.56405 + 3.13652i) q^{80} +(13.8183 + 1.54631i) q^{82} -10.2248i q^{83} +6.71799i q^{85} +(0.454467 - 4.06126i) q^{86} +(-6.32941 - 2.19856i) q^{88} -7.42827i q^{89} -6.99210 q^{91} +(-14.8411 - 3.36364i) q^{92} +(0.0267217 - 0.238794i) q^{94} +10.0582 q^{95} +4.84384 q^{97} +(0.157273 - 1.40544i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{4}+O(q^{10}) $ 24 * q - 8 * q^4	$ 24 q - 8 q^{4} + 24 q^{10} + 12 q^{16} + 32 q^{19} + 12 q^{22} + 24 q^{25} + 4 q^{28} - 8 q^{40} - 64 q^{43} - 12 q^{46} - 24 q^{49} - 16 q^{52} - 12 q^{58} + 16 q^{64} + 16 q^{67} + 24 q^{70} + 8 q^{76} + 24 q^{82} - 84 q^{88} - 72 q^{94}+O(q^{100}) $ 24 * q - 8 * q^4 + 24 * q^10 + 12 * q^16 + 32 * q^19 + 12 * q^22 + 24 * q^25 + 4 * q^28 - 8 * q^40 - 64 * q^43 - 12 * q^46 - 24 * q^49 - 16 * q^52 - 12 * q^58 + 16 * q^64 + 16 * q^67 + 24 * q^70 + 8 * q^76 + 24 * q^82 - 84 * q^88 - 72 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$1$	$-1$	$-1$	$-1$

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 $

$2$	−0.157273	+	1.40544i	−0.111209	+	0.993797i
$2$	−0.157273	+	1.40544i	−0.111209	+	0.993797i
$3$		0			0
$3$		0			0
$4$	−1.95053	−	0.442076i	−0.975265	−	0.221038i
$5$	1.81873			0.813361			0.406681	−	0.913570i	$-0.366686\pi$
$5$	1.81873			0.813361			0.406681	+	0.913570i	$0.366686\pi$
$6$		0			0
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	0.928077	−	2.67183i	0.328125	−	0.944634i
$9$		0			0
$10$	−0.286037	+	2.55612i	−0.0904529	+	0.808316i
$11$		−	2.36894i		−	0.714263i	−0.934054	−	0.357131i	$-0.883755\pi$
$11$		−	2.36894i		−	0.714263i	0.934054	−	0.357131i	$-0.116245\pi$
$12$		0			0
$13$			6.99210i			1.93926i	0.244579	+	0.969629i	$0.421350\pi$
$13$			6.99210i			1.93926i	−0.244579	+	0.969629i	$0.578650\pi$
$14$	−1.40544	−	0.157273i	−0.375620	−	0.0420330i
$15$		0			0
$16$	3.60914	+	1.72456i	0.902285	+	0.431141i
$17$			3.69378i			0.895873i	0.894065	+	0.447937i	$0.147841\pi$
$17$			3.69378i			0.895873i	−0.894065	+	0.447937i	$0.852159\pi$
$18$		0			0
$19$	5.53035			1.26875			0.634375	−	0.773025i	$-0.281258\pi$
$19$	5.53035			1.26875			0.634375	+	0.773025i	$0.281258\pi$
$20$	−3.54749	−	0.804017i	−0.793243	−	0.179784i
$21$		0			0
$22$	3.32941	+	0.372570i	0.709832	+	0.0794323i
$23$	7.60875			1.58653			0.793267	−	0.608874i	$-0.208378\pi$
$23$	7.60875			1.58653			0.793267	+	0.608874i	$0.208378\pi$
$24$		0			0
$25$	−1.69222			−0.338443
$26$	−9.82698	−	1.09967i	−1.92723	−	0.215663i
$27$		0			0
$28$	0.442076	−	1.95053i	0.0835445	−	0.368616i
$29$	−5.87055			−1.09013			−0.545067	−	0.838392i	$-0.683496\pi$
$29$	−5.87055			−1.09013			−0.545067	+	0.838392i	$0.683496\pi$
$30$		0			0
$31$			2.39191i			0.429600i	0.976658	+	0.214800i	$0.0689099\pi$
$31$			2.39191i			0.429600i	−0.976658	+	0.214800i	$0.931090\pi$
$32$	−2.99139	+	4.80120i	−0.528809	+	0.848741i
$33$		0			0
$34$	−5.19139	−	0.580932i	−0.890316	−	0.0996290i
$35$			1.81873i			0.307422i
$36$		0			0
$37$			8.88054i			1.45995i	0.683473	+	0.729976i	$0.260469\pi$
$37$			8.88054i			1.45995i	−0.683473	+	0.729976i	$0.739531\pi$
$38$	−0.869775	+	7.77259i	−0.141096	+	1.26088i
$39$		0			0
$40$	1.68792	−	4.85934i	0.266884	−	0.768329i
$41$		−	9.83200i		−	1.53550i	−0.640749	−	0.767750i	$-0.721376\pi$
$41$		−	9.83200i		−	1.53550i	0.640749	−	0.767750i	$-0.278624\pi$
$42$		0			0
$43$	−2.88967			−0.440671			−0.220335	−	0.975424i	$-0.570715\pi$
$43$	−2.88967			−0.440671			−0.220335	+	0.975424i	$0.570715\pi$
$44$	−1.04725	+	4.62069i	−0.157879	+	0.696596i
$45$		0			0
$46$	−1.19665	+	10.6937i	−0.176437	+	1.57669i
$47$	−0.169907			−0.0247835			−0.0123917	−	0.999923i	$-0.503945\pi$
$47$	−0.169907			−0.0247835			−0.0123917	+	0.999923i	$0.503945\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$	0.266140	−	2.37831i	0.0376379	−	0.336344i
$51$		0			0
$52$	3.09104	−	13.6383i	0.428650	−	1.89129i
$53$	2.02343			0.277939			0.138970	−	0.990297i	$-0.455621\pi$
$53$	2.02343			0.277939			0.138970	+	0.990297i	$0.455621\pi$
$54$		0			0
$55$		−	4.30847i		−	0.580954i
$56$	2.67183	+	0.928077i	0.357038	+	0.124020i
$57$		0			0
$58$	0.923279	−	8.25072i	0.121232	−	1.08337i
$59$			0.169907i			0.0221200i	0.999939	+	0.0110600i	$0.00352058\pi$
$59$			0.169907i			0.0221200i	−0.999939	+	0.0110600i	$0.996479\pi$
$60$		0			0
$61$			0.420023i			0.0537785i	0.999638	+	0.0268892i	$0.00856014\pi$
$61$			0.420023i			0.0537785i	−0.999638	+	0.0268892i	$0.991440\pi$
$62$	−3.36169	−	0.376183i	−0.426935	−	0.0477753i
$63$		0			0
$64$	−6.27735	−	4.95933i	−0.784668	−	0.619916i
$65$			12.7167i			1.57732i
$66$		0			0
$67$	−9.76396			−1.19286			−0.596429	−	0.802666i	$-0.703414\pi$
$67$	−9.76396			−1.19286			−0.596429	+	0.802666i	$0.703414\pi$
$68$	1.63293	−	7.20483i	0.198022	−	0.873714i
$69$		0			0
$70$	−2.55612	−	0.286037i	−0.305515	−	0.0341880i
$71$	12.0101			1.42534			0.712670	−	0.701500i	$-0.247486\pi$
$71$	12.0101			1.42534			0.712670	+	0.701500i	$0.247486\pi$
$72$		0			0
$73$	8.78003			1.02762			0.513812	−	0.857903i	$-0.328233\pi$
$73$	8.78003			1.02762			0.513812	+	0.857903i	$0.328233\pi$
$74$	−12.4811	−	1.39667i	−1.45090	−	0.162359i
$75$		0			0
$76$	−10.7871	−	2.44484i	−1.23737	−	0.280442i
$77$	2.36894			0.269966
$78$		0			0
$79$		−	14.2845i		−	1.60713i	−0.595216	−	0.803566i	$-0.702933\pi$
$79$		−	14.2845i		−	1.60713i	0.595216	−	0.803566i	$-0.297067\pi$
$80$	6.56405	+	3.13652i	0.733883	+	0.350674i
$81$		0			0
$82$	13.8183	+	1.54631i	1.52598	+	0.170761i
$83$		−	10.2248i		−	1.12232i	−0.827707	−	0.561161i	$-0.810355\pi$
$83$		−	10.2248i		−	1.12232i	0.827707	−	0.561161i	$-0.189645\pi$
$84$		0			0
$85$			6.71799i			0.728669i
$86$	0.454467	−	4.06126i	0.0490064	−	0.437937i
$87$		0			0
$88$	−6.32941	−	2.19856i	−0.674717	−	0.234367i
$89$		−	7.42827i		−	0.787395i	−0.919240	−	0.393698i	$-0.871196\pi$
$89$		−	7.42827i		−	0.787395i	0.919240	−	0.393698i	$-0.128804\pi$
$90$		0			0
$91$	−6.99210			−0.732971
$92$	−14.8411	−	3.36364i	−1.54729	−	0.350684i
$93$		0			0
$94$	0.0267217	−	0.238794i	0.00275614	−	0.0246297i
$95$	10.0582			1.03195
$96$		0			0
$97$	4.84384			0.491818			0.245909	−	0.969293i	$-0.420914\pi$
$97$	4.84384			0.491818			0.245909	+	0.969293i	$0.420914\pi$
$98$	0.157273	−	1.40544i	0.0158870	−	0.141971i
$99$		0			0
$100$	3.30072	+	0.748088i	0.330072	+	0.0748088i
$101$	−0.899761			−0.0895295			−0.0447648	−	0.998998i	$-0.514254\pi$
$101$	−0.899761			−0.0895295			−0.0447648	+	0.998998i	$0.514254\pi$
$102$		0			0
$103$		−	13.6119i		−	1.34122i	−0.741810	−	0.670611i	$-0.766032\pi$
$103$		−	13.6119i		−	1.34122i	0.741810	−	0.670611i	$-0.233968\pi$
$104$	18.6817	+	6.48921i	1.83189	+	0.636319i
$105$		0			0
$106$	−0.318230	+	2.84381i	−0.0309093	+	0.276215i
$107$			9.64387i			0.932308i	0.884704	+	0.466154i	$0.154361\pi$
$107$			9.64387i			0.932308i	−0.884704	+	0.466154i	$0.845639\pi$
$108$		0			0
$109$			1.13844i			0.109043i	0.998513	+	0.0545215i	$0.0173633\pi$
$109$			1.13844i			0.109043i	−0.998513	+	0.0545215i	$0.982637\pi$
$110$	6.05530	+	0.677605i	0.577350	+	0.0646071i
$111$		0			0
$112$	−1.72456	+	3.60914i	−0.162956	+	0.341031i
$113$		−	7.28073i		−	0.684914i	−0.939534	−	0.342457i	$-0.888741\pi$
$113$		−	7.28073i		−	0.684914i	0.939534	−	0.342457i	$-0.111259\pi$
$114$		0			0
$115$	13.8383			1.29043
$116$	11.4507	+	2.59523i	1.06317	+	0.240961i
$117$		0			0
$118$	−0.238794	−	0.0267217i	−0.0219828	−	0.00245994i
$119$	−3.69378			−0.338608
$120$		0			0
$121$	5.38811			0.489829
$122$	−0.590318	−	0.0660583i	−0.0534449	−	0.00598064i
$123$		0			0
$124$	1.05741	−	4.66549i	0.0949578	−	0.418974i
$125$	−12.1713			−1.08864
$126$		0			0
$127$			5.44445i			0.483117i	0.970386	+	0.241559i	$0.0776586\pi$
$127$			5.44445i			0.483117i	−0.970386	+	0.241559i	$0.922341\pi$
$128$	7.95730	−	8.04247i	0.703333	−	0.710861i
$129$		0			0
$130$	−17.8726	−	2.00000i	−1.56753	−	0.175412i
$131$			6.73222i			0.588197i	0.955775	+	0.294099i	$0.0950194\pi$
$131$			6.73222i			0.588197i	−0.955775	+	0.294099i	$0.904981\pi$
$132$		0			0
$133$			5.53035i			0.479542i
$134$	1.53561	−	13.7227i	0.132656	−	1.18546i
$135$		0			0
$136$	9.86915	+	3.42811i	0.846273	+	0.293958i
$137$		−	4.79689i		−	0.409826i	−0.978780	−	0.204913i	$-0.934309\pi$
$137$		−	4.79689i		−	0.409826i	0.978780	−	0.204913i	$-0.0656911\pi$
$138$		0			0
$139$	8.68075			0.736292			0.368146	−	0.929768i	$-0.379993\pi$
$139$	8.68075			0.736292			0.368146	+	0.929768i	$0.379993\pi$
$140$	0.804017	−	3.54749i	0.0679518	−	0.299818i
$141$		0			0
$142$	−1.88887	+	16.8795i	−0.158510	+	1.41650i
$143$	16.5639			1.38514
$144$		0			0
$145$	−10.6770			−0.886673
$146$	−1.38086	+	12.3398i	−0.114281	+	1.02125i
$147$		0			0
$148$	3.92587	−	17.3218i	0.322705	−	1.42384i
$149$	6.20706			0.508503			0.254251	−	0.967138i	$-0.418171\pi$
$149$	6.20706			0.508503			0.254251	+	0.967138i	$0.418171\pi$
$150$		0			0
$151$		−	4.68075i		−	0.380914i	−0.981695	−	0.190457i	$-0.939003\pi$
$151$		−	4.68075i		−	0.380914i	0.981695	−	0.190457i	$-0.0609970\pi$
$152$	5.13259	−	14.7762i	0.416308	−	1.19850i
$153$		0			0
$154$	−0.372570	+	3.32941i	−0.0300226	+	0.268291i
$155$			4.35024i			0.349420i
$156$		0			0
$157$		−	1.71964i		−	0.137243i	−0.997643	−	0.0686213i	$-0.978140\pi$
$157$		−	1.71964i		−	0.137243i	0.997643	−	0.0686213i	$-0.0218600\pi$
$158$	20.0760	+	2.24657i	1.59716	+	0.178727i
$159$		0			0
$160$	−5.44054	+	8.73210i	−0.430113	+	0.690333i
$161$			7.60875i			0.599654i
$162$		0			0
$163$	−18.2044			−1.42588			−0.712941	−	0.701225i	$-0.752637\pi$
$163$	−18.2044			−1.42588			−0.712941	+	0.701225i	$0.752637\pi$
$164$	−4.34649	+	19.1776i	−0.339404	+	1.49752i
$165$		0			0
$166$	14.3704	+	1.60809i	1.11536	+	0.124812i
$167$	−8.80889			−0.681652			−0.340826	−	0.940126i	$-0.610707\pi$
$167$	−8.80889			−0.681652			−0.340826	+	0.940126i	$0.610707\pi$
$168$		0			0
$169$	−35.8894			−2.76073
$170$	−9.44175	−	1.05656i	−0.724149	−	0.0810343i
$171$		0			0
$172$	5.63639	+	1.27745i	0.429771	+	0.0974049i
$173$	−3.74110			−0.284430			−0.142215	−	0.989836i	$-0.545422\pi$
$173$	−3.74110			−0.284430			−0.142215	+	0.989836i	$0.545422\pi$
$174$		0			0
$175$		−	1.69222i		−	0.127920i
$176$	4.08539	−	8.54984i	0.307948	−	0.644468i
$177$		0			0
$178$	10.4400	+	1.16827i	0.782511	+	0.0875652i
$179$		−	15.8375i		−	1.18375i	−0.806031	−	0.591873i	$-0.798389\pi$
$179$		−	15.8375i		−	1.18375i	0.806031	−	0.591873i	$-0.201611\pi$
$180$		0			0
$181$		−	8.14875i		−	0.605692i	−0.953040	−	0.302846i	$-0.902063\pi$
$181$		−	8.14875i		−	0.605692i	0.953040	−	0.302846i	$-0.0979368\pi$
$182$	1.09967	−	9.82698i	0.0815128	−	0.728424i
$183$		0			0
$184$	7.06151	−	20.3293i	0.520581	−	1.49870i
$185$			16.1513i			1.18747i
$186$		0			0
$187$	8.75035			0.639889
$188$	0.331408	+	0.0751117i	0.0241704	+	0.00547808i
$189$		0			0
$190$	−1.58189	+	14.1362i	−0.114762	+	1.02555i
$191$	−21.8014			−1.57750			−0.788748	−	0.614717i	$-0.789270\pi$
$191$	−21.8014			−1.57750			−0.788748	+	0.614717i	$0.789270\pi$
$192$		0			0
$193$	18.2130			1.31100			0.655501	−	0.755194i	$-0.272458\pi$
$193$	18.2130			1.31100			0.655501	+	0.755194i	$0.272458\pi$
$194$	−0.761805	+	6.80774i	−0.0546944	+	0.488767i
$195$		0			0
$196$	1.95053	+	0.442076i	0.139324	+	0.0315768i
$197$	−12.1692			−0.867022			−0.433511	−	0.901148i	$-0.642726\pi$
$197$	−12.1692			−0.867022			−0.433511	+	0.901148i	$0.642726\pi$
$198$		0			0
$199$		−	19.9646i		−	1.41525i	−0.706588	−	0.707625i	$-0.749766\pi$
$199$		−	19.9646i		−	1.41525i	0.706588	−	0.707625i	$-0.250234\pi$
$200$	−1.57051	+	4.52131i	−0.111052	+	0.319705i
$201$		0			0
$202$	0.141508	−	1.26456i	0.00995647	−	0.0889742i
$203$		−	5.87055i		−	0.412032i
$204$		0			0
$205$		−	17.8818i		−	1.24892i
$206$	19.1307	+	2.14078i	1.33290	+	0.149156i
$207$		0			0
$208$	−12.0583	+	25.2354i	−0.836094	+	1.74976i
$209$		−	13.1011i		−	0.906221i
$210$		0			0
$211$	−0.750003			−0.0516323			−0.0258162	−	0.999667i	$-0.508218\pi$
$211$	−0.750003			−0.0516323			−0.0258162	+	0.999667i	$0.508218\pi$
$212$	−3.94676	−	0.894508i	−0.271064	−	0.0614351i
$213$		0			0
$214$	−13.5539	−	1.51672i	−0.926525	−	0.103681i
$215$	−5.25553			−0.358424
$216$		0			0
$217$	−2.39191			−0.162373
$218$	−1.60001	−	0.179046i	−0.108367	−	0.0121265i
$219$		0			0
$220$	−1.90467	+	8.40380i	−0.128413	+	0.566584i
$221$	−25.8273			−1.73733
$222$		0			0
$223$		−	11.6042i		−	0.777078i	−0.921432	−	0.388539i	$-0.872980\pi$
$223$		−	11.6042i		−	0.777078i	0.921432	−	0.388539i	$-0.127020\pi$
$224$	−4.80120	−	2.99139i	−0.320794	−	0.199871i
$225$		0			0
$226$	10.2326	+	1.14506i	0.680665	+	0.0761684i
$227$			5.59958i			0.371657i	0.982582	+	0.185829i	$0.0594970\pi$
$227$			5.59958i			0.371657i	−0.982582	+	0.185829i	$0.940503\pi$
$228$		0			0
$229$			23.4718i			1.55106i	0.631310	+	0.775531i	$0.282518\pi$
$229$			23.4718i			1.55106i	−0.631310	+	0.775531i	$0.717482\pi$
$230$	−2.17639	+	19.4489i	−0.143507	+	1.28242i
$231$		0			0
$232$	−5.44833	+	15.6851i	−0.357700	+	1.02978i
$233$			16.9709i			1.11180i	0.831248	+	0.555901i	$0.187627\pi$
$233$			16.9709i			1.11180i	−0.831248	+	0.555901i	$0.812373\pi$
$234$		0			0
$235$	−0.309015			−0.0201579
$236$	0.0751117	−	0.331408i	0.00488936	−	0.0215729i
$237$		0			0
$238$	0.580932	−	5.19139i	0.0376562	−	0.336508i
$239$	−15.4661			−1.00042			−0.500211	−	0.865904i	$-0.666744\pi$
$239$	−15.4661			−1.00042			−0.500211	+	0.865904i	$0.666744\pi$
$240$		0			0
$241$	25.5683			1.64700			0.823500	−	0.567316i	$-0.192018\pi$
$241$	25.5683			1.64700			0.823500	+	0.567316i	$0.192018\pi$
$242$	−0.847405	+	7.57268i	−0.0544732	+	0.486790i
$243$		0			0
$244$	0.185682	−	0.819268i	0.0118871	−	0.0524483i
$245$	−1.81873			−0.116194
$246$		0			0
$247$			38.6688i			2.46043i
$248$	6.39078	+	2.21988i	0.405815	+	0.140962i
$249$		0			0
$250$	1.91422	−	17.1061i	0.121066	−	1.08189i
$251$		−	21.8041i		−	1.37626i	−0.725586	−	0.688131i	$-0.758431\pi$
$251$		−	21.8041i		−	1.37626i	0.725586	−	0.688131i	$-0.241569\pi$
$252$		0			0
$253$		−	18.0247i		−	1.13320i
$254$	−7.65186	−	0.856265i	−0.480120	−	0.0537269i
$255$		0			0
$256$	10.0518	+	12.4484i	0.628235	+	0.778024i
$257$			2.98714i			0.186333i	0.995651	+	0.0931664i	$0.0296989\pi$
$257$			2.98714i			0.186333i	−0.995651	+	0.0931664i	$0.970301\pi$
$258$		0			0
$259$	−8.88054			−0.551810
$260$	5.62177	−	24.8044i	0.348647	−	1.53830i
$261$		0			0
$262$	−9.46174	−	1.05880i	−0.584549	−	0.0654127i
$263$	−25.7673			−1.58888			−0.794441	−	0.607342i	$-0.792236\pi$
$263$	−25.7673			−1.58888			−0.794441	+	0.607342i	$0.792236\pi$
$264$		0			0
$265$	3.68007			0.226065
$266$	−7.77259	−	0.869775i	−0.476568	−	0.0533293i
$267$		0			0
$268$	19.0449	+	4.31641i	1.16335	+	0.263667i
$269$	−17.9674			−1.09549			−0.547744	−	0.836646i	$-0.684513\pi$
$269$	−17.9674			−1.09549			−0.547744	+	0.836646i	$0.684513\pi$
$270$		0			0
$271$			4.90908i			0.298205i	0.988822	+	0.149103i	$0.0476385\pi$
$271$			4.90908i			0.298205i	−0.988822	+	0.149103i	$0.952362\pi$
$272$	−6.37016	+	13.3314i	−0.386248	+	0.808333i
$273$		0			0
$274$	6.74174	+	0.754420i	0.407284	+	0.0455762i
$275$			4.00876i			0.241737i
$276$		0			0
$277$			3.72578i			0.223860i	0.993716	+	0.111930i	$0.0357033\pi$
$277$			3.72578i			0.223860i	−0.993716	+	0.111930i	$0.964297\pi$
$278$	−1.36525	+	12.2003i	−0.0818821	+	0.731725i
$279$		0			0
$280$	4.85934	+	1.68792i	0.290401	+	0.100873i
$281$			16.9316i			1.01006i	0.863103	+	0.505028i	$0.168518\pi$
$281$			16.9316i			1.01006i	−0.863103	+	0.505028i	$0.831482\pi$
$282$		0			0
$283$	−10.1986			−0.606244			−0.303122	−	0.952952i	$-0.598029\pi$
$283$	−10.1986			−0.606244			−0.303122	+	0.952952i	$0.598029\pi$
$284$	−23.4261	−	5.30938i	−1.39008	−	0.315054i
$285$		0			0
$286$	−2.60505	+	23.2796i	−0.154040	+	1.37655i
$287$	9.83200			0.580365
$288$		0			0
$289$	3.35598			0.197411
$290$	1.67920	−	15.0058i	0.0986058	−	0.881173i
$291$		0			0
$292$	−17.1257	−	3.88144i	−1.00221	−	0.227144i
$293$	30.0240			1.75402			0.877010	−	0.480472i	$-0.159535\pi$
$293$	30.0240			1.75402			0.877010	+	0.480472i	$0.159535\pi$
$294$		0			0
$295$			0.309015i			0.0179915i
$296$	23.7273	+	8.24183i	1.37912	+	0.479047i
$297$		0			0
$298$	−0.976203	+	8.72367i	−0.0565499	+	0.505348i
$299$			53.2011i			3.07670i
$300$		0			0
$301$		−	2.88967i		−	0.166558i
$302$	6.57853	+	0.736156i	0.378552	+	0.0423610i
$303$		0			0
$304$	19.9598	+	9.53745i	1.14477	+	0.547010i
$305$			0.763909i			0.0437413i
$306$		0			0
$307$	30.1978			1.72348			0.861738	−	0.507353i	$-0.169376\pi$
$307$	30.1978			1.72348			0.861738	+	0.507353i	$0.169376\pi$
$308$	−4.62069	−	1.04725i	−0.263288	−	0.0596727i
$309$		0			0
$310$	−6.11401	−	0.684175i	−0.347252	−	0.0388586i
$311$	−21.8076			−1.23659			−0.618297	−	0.785945i	$-0.712177\pi$
$311$	−21.8076			−1.23659			−0.618297	+	0.785945i	$0.712177\pi$
$312$		0			0
$313$	−31.6447			−1.78866			−0.894331	−	0.447406i	$-0.852348\pi$
$313$	−31.6447			−1.78866			−0.894331	+	0.447406i	$0.852348\pi$
$314$	2.41686	+	0.270453i	0.136391	+	0.0152626i
$315$		0			0
$316$	−6.31483	+	27.8624i	−0.355237	+	1.56738i
$317$	5.63931			0.316735			0.158368	−	0.987380i	$-0.449377\pi$
$317$	5.63931			0.316735			0.158368	+	0.987380i	$0.449377\pi$
$318$		0			0
$319$			13.9070i			0.778642i
$320$	−11.4168	−	9.01968i	−0.638219	−	0.504216i
$321$		0			0
$322$	−10.6937	−	1.19665i	−0.595934	−	0.0666867i
$323$			20.4279i			1.13664i
$324$		0			0
$325$		−	11.8321i		−	0.656329i
$326$	2.86306	−	25.5853i	0.158570	−	1.41704i
$327$		0			0
$328$	−26.2694	−	9.12486i	−1.45049	−	0.503836i
$329$		−	0.169907i		−	0.00936727i
$330$		0			0
$331$	−5.48698			−0.301592			−0.150796	−	0.988565i	$-0.548184\pi$
$331$	−5.48698			−0.301592			−0.150796	+	0.988565i	$0.548184\pi$
$332$	−4.52015	+	19.9438i	−0.248075	+	1.09456i
$333$		0			0
$334$	1.38540	−	12.3804i	0.0758057	−	0.677424i
$335$	−17.7580			−0.970224
$336$		0			0
$337$	−5.06316			−0.275808			−0.137904	−	0.990446i	$-0.544036\pi$
$337$	−5.06316			−0.275808			−0.137904	+	0.990446i	$0.544036\pi$
$338$	5.64444	−	50.4405i	0.307017	−	2.74360i
$339$		0			0
$340$	2.96986	−	13.1037i	0.161063	−	0.710645i
$341$	5.66630			0.306847
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$	−2.68184	+	7.72071i	−0.144595	+	0.416273i
$345$		0			0
$346$	0.588373	−	5.25789i	0.0316311	−	0.282666i
$347$		−	31.2066i		−	1.67526i	−0.546241	−	0.837628i	$-0.683942\pi$
$347$		−	31.2066i		−	1.67526i	0.546241	−	0.837628i	$-0.316058\pi$
$348$		0			0
$349$		−	10.6407i		−	0.569583i	−0.958590	−	0.284791i	$-0.908076\pi$
$349$		−	10.6407i		−	0.569583i	0.958590	−	0.284791i	$-0.0919243\pi$
$350$	2.37831	+	0.266140i	0.127126	+	0.0142258i
$351$		0			0
$352$	11.3738	+	7.08644i	0.606224	+	0.377708i
$353$		−	29.5238i		−	1.57139i	−0.618613	−	0.785696i	$-0.712305\pi$
$353$		−	29.5238i		−	1.57139i	0.618613	−	0.785696i	$-0.287695\pi$
$354$		0			0
$355$	21.8432			1.15932
$356$	−3.28386	+	14.4891i	−0.174044	+	0.767919i
$357$		0			0
$358$	22.2586	+	2.49080i	1.17640	+	0.131643i
$359$	21.6557			1.14294			0.571471	−	0.820622i	$-0.306373\pi$
$359$	21.6557			1.14294			0.571471	+	0.820622i	$0.306373\pi$
$360$		0			0
$361$	11.5848			0.609727
$362$	11.4526	+	1.28158i	0.601935	+	0.0673582i
$363$		0			0
$364$	13.6383	+	3.09104i	0.714841	+	0.162014i
$365$	15.9685			0.835830
$366$		0			0
$367$			13.2680i			0.692585i	0.938127	+	0.346292i	$0.112559\pi$
$367$			13.2680i			0.692585i	−0.938127	+	0.346292i	$0.887441\pi$
$368$	27.4610	+	13.1218i	1.43151	+	0.684020i
$369$		0			0
$370$	−22.6997	−	2.54017i	−1.18010	−	0.132057i
$371$			2.02343i			0.105051i
$372$		0			0
$373$		−	2.38377i		−	0.123427i	−0.998094	−	0.0617135i	$-0.980343\pi$
$373$		−	2.38377i		−	0.123427i	0.998094	−	0.0617135i	$-0.0196565\pi$
$374$	−1.37619	+	12.2981i	−0.0711613	+	0.635920i
$375$		0			0
$376$	−0.157687	+	0.453962i	−0.00813207	+	0.0234113i
$377$		−	41.0475i		−	2.11405i
$378$		0			0
$379$	−4.33792			−0.222824			−0.111412	−	0.993774i	$-0.535537\pi$
$379$	−4.33792			−0.222824			−0.111412	+	0.993774i	$0.535537\pi$
$380$	−19.6189	−	4.44650i	−1.00643	−	0.228101i
$381$		0			0
$382$	3.42877	−	30.6406i	0.175431	−	1.56771i
$383$	28.5614			1.45942			0.729709	−	0.683758i	$-0.239656\pi$
$383$	28.5614			1.45942			0.729709	+	0.683758i	$0.239656\pi$
$384$		0			0
$385$	4.30847			0.219580
$386$	−2.86441	+	25.5973i	−0.145795	+	1.30287i
$387$		0			0
$388$	−9.44806	−	2.14135i	−0.479653	−	0.108710i
$389$	25.5023			1.29302			0.646510	−	0.762906i	$-0.276228\pi$
$389$	25.5023			1.29302			0.646510	+	0.762906i	$0.276228\pi$
$390$		0			0
$391$			28.1051i			1.42133i
$392$	−0.928077	+	2.67183i	−0.0468750	+	0.134948i
$393$		0			0
$394$	1.91389	−	17.1031i	0.0964205	−	0.861644i
$395$		−	25.9797i		−	1.30718i
$396$		0			0
$397$		−	25.9062i		−	1.30020i	−0.759850	−	0.650099i	$-0.774728\pi$
$397$		−	25.9062i		−	1.30020i	0.759850	−	0.650099i	$-0.225272\pi$
$398$	28.0590	+	3.13989i	1.40647	+	0.157388i
$399$		0			0
$400$	−6.10744	−	2.91834i	−0.305372	−	0.145917i
$401$			4.65113i			0.232266i	0.993234	+	0.116133i	$0.0370499\pi$
$401$			4.65113i			0.232266i	−0.993234	+	0.116133i	$0.962950\pi$
$402$		0			0
$403$	−16.7245			−0.833105
$404$	1.75501	+	0.397762i	0.0873150	+	0.0197894i
$405$		0			0
$406$	8.25072	+	0.923279i	0.409476	+	0.0458216i
$407$	21.0375			1.04279
$408$		0			0
$409$	18.1415			0.897041			0.448521	−	0.893773i	$-0.351951\pi$
$409$	18.1415			0.897041			0.448521	+	0.893773i	$0.351951\pi$
$410$	25.1318	+	2.81232i	1.24117	+	0.138890i
$411$		0			0
$412$	−6.01749	+	26.5504i	−0.296461	+	1.30805i
$413$	−0.169907			−0.00836057
$414$		0			0
$415$		−	18.5962i		−	0.912853i
$416$	−33.5705	−	20.9161i	−1.64593	−	1.02550i
$417$		0			0
$418$	18.4128	+	2.06045i	0.900600	+	0.100780i
$419$			8.21628i			0.401392i	0.979654	+	0.200696i	$0.0643203\pi$
$419$			8.21628i			0.401392i	−0.979654	+	0.200696i	$0.935680\pi$
$420$		0			0
$421$			14.8382i			0.723171i	0.932339	+	0.361586i	$0.117765\pi$
$421$			14.8382i			0.723171i	−0.932339	+	0.361586i	$0.882235\pi$
$422$	0.117955	−	1.05408i	0.00574197	−	0.0513121i
$423$		0			0
$424$	1.87790	−	5.40625i	0.0911987	−	0.262551i
$425$		−	6.25068i		−	0.303202i
$426$		0			0
$427$	−0.420023			−0.0203264
$428$	4.26332	−	18.8107i	0.206075	−	0.909247i
$429$		0			0
$430$	0.826553	−	7.38634i	0.0398599	−	0.356201i
$431$	−13.1807			−0.634893			−0.317447	−	0.948276i	$-0.602825\pi$
$431$	−13.1807			−0.634893			−0.317447	+	0.948276i	$0.602825\pi$
$432$		0			0
$433$	−7.66377			−0.368297			−0.184149	−	0.982898i	$-0.558953\pi$
$433$	−7.66377			−0.368297			−0.184149	+	0.982898i	$0.558953\pi$
$434$	0.376183	−	3.36169i	0.0180574	−	0.161366i
$435$		0			0
$436$	0.503278	−	2.22057i	0.0241026	−	0.106346i
$437$	42.0791			2.01292
$438$		0			0
$439$			23.3466i			1.11427i	0.830422	+	0.557135i	$0.188099\pi$
$439$			23.3466i			1.11427i	−0.830422	+	0.557135i	$0.811901\pi$
$440$	−11.5115	−	3.99859i	−0.548789	−	0.190625i
$441$		0			0
$442$	4.06193	−	36.2987i	0.193206	−	1.72655i
$443$		−	14.8435i		−	0.705236i	−0.935767	−	0.352618i	$-0.885291\pi$
$443$		−	14.8435i		−	0.705236i	0.935767	−	0.352618i	$-0.114709\pi$
$444$		0			0
$445$		−	13.5100i		−	0.640437i
$446$	16.3091	+	1.82503i	0.772257	+	0.0864178i
$447$		0			0
$448$	4.95933	−	6.27735i	0.234306	−	0.296577i
$449$			4.06073i			0.191638i	0.995399	+	0.0958189i	$0.0305470\pi$
$449$			4.06073i			0.191638i	−0.995399	+	0.0958189i	$0.969453\pi$
$450$		0			0
$451$	−23.2914			−1.09675
$452$	−3.21863	+	14.2013i	−0.151392	+	0.667972i
$453$		0			0
$454$	−7.86989	−	0.880663i	−0.369352	−	0.0413316i
$455$	−12.7167			−0.596170
$456$		0			0
$457$	23.0425			1.07788			0.538940	−	0.842344i	$-0.318825\pi$
$457$	23.0425			1.07788			0.538940	+	0.842344i	$0.318825\pi$
$458$	−32.9883	−	3.69148i	−1.54144	−	0.172492i
$459$		0			0
$460$	−26.9920	−	6.11757i	−1.25851	−	0.285233i
$461$	−27.1646			−1.26518			−0.632592	−	0.774485i	$-0.718009\pi$
$461$	−27.1646			−1.26518			−0.632592	+	0.774485i	$0.718009\pi$
$462$		0			0
$463$			16.8894i			0.784917i	0.919770	+	0.392459i	$0.128375\pi$
$463$			16.8894i			0.784917i	−0.919770	+	0.392459i	$0.871625\pi$
$464$	−21.1876	−	10.1241i	−0.983611	−	0.470002i
$465$		0			0
$466$	−23.8516	−	2.66907i	−1.10491	−	0.123642i
$467$			12.0923i			0.559566i	0.960063	+	0.279783i	$0.0902625\pi$
$467$			12.0923i			0.559566i	−0.960063	+	0.279783i	$0.909737\pi$
$468$		0			0
$469$		−	9.76396i		−	0.450858i
$470$	0.0485997	−	0.434302i	0.00224174	−	0.0200329i
$471$		0			0
$472$	0.453962	+	0.157687i	0.0208953	+	0.00725812i
$473$			6.84546i			0.314755i
$474$		0			0
$475$	−9.35856			−0.429400
$476$	7.20483	+	1.63293i	0.330233	+	0.0748453i
$477$		0			0
$478$	2.43240	−	21.7367i	0.111256	−	0.994216i
$479$	−6.77258			−0.309447			−0.154724	−	0.987958i	$-0.549449\pi$
$479$	−6.77258			−0.309447			−0.154724	+	0.987958i	$0.549449\pi$
$480$		0			0
$481$	−62.0936			−2.83123
$482$	−4.02120	+	35.9348i	−0.183161	+	1.63678i
$483$		0			0
$484$	−10.5097	−	2.38195i	−0.477713	−	0.108271i
$485$	8.80965			0.400026
$486$		0			0
$487$			6.15599i			0.278955i	0.990225	+	0.139477i	$0.0445422\pi$
$487$			6.15599i			0.278955i	−0.990225	+	0.139477i	$0.955458\pi$
$488$	1.12223	+	0.389814i	0.0508010	+	0.0176461i
$489$		0			0
$490$	0.286037	−	2.55612i	0.0129218	−	0.115474i
$491$			29.4205i			1.32773i	0.747853	+	0.663864i	$0.231085\pi$
$491$			29.4205i			1.32773i	−0.747853	+	0.663864i	$0.768915\pi$
$492$		0			0
$493$		−	21.6845i		−	0.976622i
$494$	−54.3467	−	6.08155i	−2.44517	−	0.273622i
$495$		0			0
$496$	−4.12500	+	8.63274i	−0.185218	+	0.387621i
$497$			12.0101i			0.538728i
$498$		0			0
$499$	−15.1862			−0.679827			−0.339913	−	0.940457i	$-0.610398\pi$
$499$	−15.1862			−0.679827			−0.339913	+	0.940457i	$0.610398\pi$
$500$	23.7406	+	5.38066i	1.06171	+	0.240630i
$501$		0			0
$502$	30.6444	+	3.42919i	1.36773	+	0.153052i
$503$	38.0202			1.69524			0.847619	−	0.530605i	$-0.178035\pi$
$503$	38.0202			1.69524			0.847619	+	0.530605i	$0.178035\pi$
$504$		0			0
$505$	−1.63642			−0.0728199
$506$	25.3326	+	2.83480i	1.12617	+	0.126022i
$507$		0			0
$508$	2.40686	−	10.6196i	0.106787	−	0.471167i
$509$	−0.855999			−0.0379415			−0.0189707	−	0.999820i	$-0.506039\pi$
$509$	−0.855999			−0.0379415			−0.0189707	+	0.999820i	$0.506039\pi$
$510$		0			0
$511$			8.78003i			0.388405i
$512$	−19.0763	+	12.1694i	−0.843063	+	0.537815i
$513$		0			0
$514$	−4.19825	−	0.469797i	−0.185177	−	0.0207218i
$515$		−	24.7564i		−	1.09090i
$516$		0			0
$517$			0.402499i			0.0177019i
$518$	1.39667	−	12.4811i	0.0613661	−	0.548387i
$519$		0			0
$520$	33.9770	+	11.8021i	1.48999	+	0.517557i
$521$			8.80793i			0.385883i	0.981210	+	0.192941i	$0.0618027\pi$
$521$			8.80793i			0.385883i	−0.981210	+	0.192941i	$0.938197\pi$
$522$		0			0
$523$	29.4892			1.28947			0.644736	−	0.764405i	$-0.276967\pi$
$523$	29.4892			1.28947			0.644736	+	0.764405i	$0.276967\pi$
$524$	2.97615	−	13.1314i	0.130014	−	0.573648i
$525$		0			0
$526$	4.05250	−	36.2145i	0.176697	−	1.57903i
$527$	−8.83519			−0.384867
$528$		0			0
$529$	34.8931			1.51709
$530$	−0.578775	+	5.17212i	−0.0251404	+	0.224663i
$531$		0			0
$532$	2.44484	−	10.7871i	0.105997	−	0.467681i
$533$	68.7463			2.97773
$534$		0			0
$535$			17.5396i			0.758303i
$536$	−9.06171	+	26.0876i	−0.391406	+	1.12681i
$537$		0			0
$538$	2.82578	−	25.2521i	0.121828	−	1.08869i
$539$			2.36894i			0.102038i
$540$		0			0
$541$			9.02347i			0.387949i	0.981007	+	0.193975i	$0.0621379\pi$
$541$			9.02347i			0.387949i	−0.981007	+	0.193975i	$0.937862\pi$
$542$	−6.89942	−	0.772065i	−0.296356	−	0.0331631i
$543$		0			0
$544$	−17.7346	−	11.0496i	−0.760365	−	0.473746i
$545$			2.07052i			0.0886914i
$546$		0			0
$547$	23.0161			0.984097			0.492048	−	0.870568i	$-0.336248\pi$
$547$	23.0161			0.984097			0.492048	+	0.870568i	$0.336248\pi$
$548$	−2.12059	+	9.35647i	−0.0905870	+	0.399689i
$549$		0			0
$550$	−5.63408	−	0.630470i	−0.240238	−	0.0268833i
$551$	−32.4662			−1.38311
$552$		0			0
$553$	14.2845			0.607439
$554$	−5.23636	−	0.585964i	−0.222472	−	0.0248952i
$555$		0			0
$556$	−16.9321	−	3.83755i	−0.718080	−	0.162748i
$557$	14.6781			0.621930			0.310965	−	0.950421i	$-0.399348\pi$
$557$	14.6781			0.621930			0.310965	+	0.950421i	$0.399348\pi$
$558$		0			0
$559$		−	20.2049i		−	0.854574i
$560$	−3.13652	+	6.56405i	−0.132542	+	0.277382i
$561$		0			0
$562$	−23.7964	−	2.66289i	−1.00379	−	0.112327i
$563$		−	22.3172i		−	0.940556i	−0.882518	−	0.470278i	$-0.844154\pi$
$563$		−	22.3172i		−	0.940556i	0.882518	−	0.470278i	$-0.155846\pi$
$564$		0			0
$565$		−	13.2417i		−	0.557082i
$566$	1.60396	−	14.3335i	0.0674196	−	0.602484i
$567$		0			0
$568$	11.1463	−	32.0890i	0.467689	−	1.34642i
$569$			19.5564i			0.819847i	0.912120	+	0.409923i	$0.134445\pi$
$569$			19.5564i			0.819847i	−0.912120	+	0.409923i	$0.865555\pi$
$570$		0			0
$571$	22.2399			0.930709			0.465355	−	0.885124i	$-0.345927\pi$
$571$	22.2399			0.930709			0.465355	+	0.885124i	$0.345927\pi$
$572$	−32.3083	−	7.32249i	−1.35088	−	0.306169i
$573$		0			0
$574$	−1.54631	+	13.8183i	−0.0645416	+	0.576765i
$575$	−12.8757			−0.536952
$576$		0			0
$577$	−41.9160			−1.74499			−0.872493	−	0.488627i	$-0.837498\pi$
$577$	−41.9160			−1.74499			−0.872493	+	0.488627i	$0.837498\pi$
$578$	−0.527806	+	4.71664i	−0.0219538	+	0.196186i
$579$		0			0
$580$	20.8257	+	4.72002i	0.864741	+	0.195988i
$581$	10.2248			0.424197
$582$		0			0
$583$		−	4.79338i		−	0.198522i
$584$	8.14854	−	23.4587i	0.337189	−	0.970729i
$585$		0			0
$586$	−4.72196	+	42.1969i	−0.195062	+	1.74314i
$587$		−	9.70280i		−	0.400478i	−0.979747	−	0.200239i	$-0.935828\pi$
$587$		−	9.70280i		−	0.400478i	0.979747	−	0.200239i	$-0.0641718\pi$
$588$		0			0
$589$			13.2281i			0.545055i
$590$	−0.434302	−	0.0485997i	−0.0178799	−	0.00200082i
$591$		0			0
$592$	−15.3151	+	32.0511i	−0.629445	+	1.31729i
$593$		−	19.0205i		−	0.781077i	−0.920587	−	0.390538i	$-0.872289\pi$
$593$		−	19.0205i		−	0.781077i	0.920587	−	0.390538i	$-0.127711\pi$
$594$		0			0
$595$	−6.71799			−0.275411
$596$	−12.1071	−	2.74399i	−0.495925	−	0.112398i
$597$		0			0
$598$	−74.7711	−	8.36710i	−3.05762	−	0.342156i
$599$	22.2207			0.907914			0.453957	−	0.891024i	$-0.350012\pi$
$599$	22.2207			0.907914			0.453957	+	0.891024i	$0.350012\pi$
$600$		0			0
$601$	7.60754			0.310318			0.155159	−	0.987889i	$-0.450411\pi$
$601$	7.60754			0.310318			0.155159	+	0.987889i	$0.450411\pi$
$602$	4.06126	+	0.454467i	0.165525	+	0.0185227i
$603$		0			0
$604$	−2.06925	+	9.12995i	−0.0841965	+	0.371493i
$605$	9.79953			0.398408
$606$		0			0
$607$			14.1339i			0.573678i	0.957979	+	0.286839i	$0.0926045\pi$
$607$			14.1339i			0.573678i	−0.957979	+	0.286839i	$0.907396\pi$
$608$	−16.5435	+	26.5524i	−0.670926	+	1.07684i
$609$		0			0
$610$	−1.07363	−	0.120142i	−0.0434700	−	0.00486442i
$611$		−	1.18801i		−	0.0480615i
$612$		0			0
$613$		−	17.3711i		−	0.701611i	−0.936448	−	0.350806i	$-0.885908\pi$
$613$		−	17.3711i		−	0.701611i	0.936448	−	0.350806i	$-0.114092\pi$
$614$	−4.74929	+	42.4412i	−0.191666	+	1.71279i
$615$		0			0
$616$	2.19856	−	6.32941i	0.0885825	−	0.255019i
$617$		−	26.9441i		−	1.08473i	−0.840143	−	0.542365i	$-0.817529\pi$
$617$		−	26.9441i		−	1.08473i	0.840143	−	0.542365i	$-0.182471\pi$
$618$		0			0
$619$	11.4286			0.459355			0.229678	−	0.973267i	$-0.426233\pi$
$619$	11.4286			0.459355			0.229678	+	0.973267i	$0.426233\pi$
$620$	1.92314	−	8.48528i	0.0772350	−	0.340777i
$621$		0			0
$622$	3.42974	−	30.6493i	0.137520	−	1.22892i
$623$	7.42827			0.297607
$624$		0			0
$625$	−13.6753			−0.547013
$626$	4.97685	−	44.4747i	0.198915	−	1.77757i
$627$		0			0
$628$	−0.760213	+	3.35422i	−0.0303358	+	0.133848i
$629$	−32.8028			−1.30793
$630$		0			0
$631$		−	42.8774i		−	1.70692i	−0.521156	−	0.853462i	$-0.674499\pi$
$631$		−	42.8774i		−	1.70692i	0.521156	−	0.853462i	$-0.325501\pi$
$632$	−38.1658	−	13.2571i	−1.51815	−	0.527340i
$633$		0			0
$634$	−0.886911	+	7.92572i	−0.0352237	+	0.314771i
$635$			9.90200i			0.392949i
$636$		0			0
$637$		−	6.99210i		−	0.277037i
$638$	−19.5455	−	2.18719i	−0.773813	−	0.0865919i
$639$		0			0
$640$	14.4722	−	14.6271i	0.572064	−	0.578187i
$641$			6.41036i			0.253194i	0.991954	+	0.126597i	$0.0404055\pi$
$641$			6.41036i			0.253194i	−0.991954	+	0.126597i	$0.959594\pi$
$642$		0			0
$643$	23.5994			0.930668			0.465334	−	0.885135i	$-0.345934\pi$
$643$	23.5994			0.930668			0.465334	+	0.885135i	$0.345934\pi$
$644$	3.36364	−	14.8411i	0.132546	−	0.584821i
$645$		0			0
$646$	−28.7102	−	3.21276i	−1.12959	−	0.126404i
$647$	−5.87058			−0.230796			−0.115398	−	0.993319i	$-0.536814\pi$
$647$	−5.87058			−0.230796			−0.115398	+	0.993319i	$0.536814\pi$
$648$		0			0
$649$	0.402499			0.0157995
$650$	16.6294	+	1.86088i	0.652258	+	0.0729896i
$651$		0			0
$652$	35.5083	+	8.04774i	1.39061	+	0.315174i
$653$	−34.2268			−1.33940			−0.669699	−	0.742633i	$-0.733577\pi$
$653$	−34.2268			−1.33940			−0.669699	+	0.742633i	$0.733577\pi$
$654$		0			0
$655$			12.2441i			0.478417i
$656$	16.9559	−	35.4850i	0.662017	−	1.38546i
$657$		0			0
$658$	0.238794	+	0.0267217i	0.00930916	+	0.00104172i
$659$			11.1474i			0.434241i	0.976145	+	0.217120i	$0.0696664\pi$
$659$			11.1474i			0.434241i	−0.976145	+	0.217120i	$0.930334\pi$
$660$		0			0
$661$			49.2293i			1.91480i	0.288768	+	0.957399i	$0.406754\pi$
$661$			49.2293i			1.91480i	−0.288768	+	0.957399i	$0.593246\pi$
$662$	0.862954	−	7.71163i	0.0335397	−	0.299721i
$663$		0			0
$664$	−27.3190	−	9.48943i	−1.06018	−	0.368261i
$665$			10.0582i			0.390041i
$666$		0			0
$667$	−44.6676			−1.72954
$668$	17.1820	+	3.89419i	0.664792	+	0.150671i
$669$		0			0
$670$	2.79286	−	24.9579i	0.107897	−	0.964206i
$671$	0.995011			0.0384120
$672$		0			0
$673$	−16.3489			−0.630202			−0.315101	−	0.949058i	$-0.602038\pi$
$673$	−16.3489			−0.630202			−0.315101	+	0.949058i	$0.602038\pi$
$674$	0.796297	−	7.11597i	0.0306722	−	0.274097i
$675$		0			0
$676$	70.0034	+	15.8658i	2.69244	+	0.610225i
$677$	32.1693			1.23637			0.618184	−	0.786034i	$-0.287869\pi$
$677$	32.1693			1.23637			0.618184	+	0.786034i	$0.287869\pi$
$678$		0			0
$679$			4.84384i			0.185890i
$680$	17.9493	+	6.23482i	0.688326	+	0.239094i
$681$		0			0
$682$	−0.891155	+	7.96365i	−0.0341241	+	0.304944i
$683$			18.0796i			0.691798i	0.938272	+	0.345899i	$0.112426\pi$
$683$			18.0796i			0.691798i	−0.938272	+	0.345899i	$0.887574\pi$
$684$		0			0
$685$		−	8.72425i		−	0.333336i
$686$	1.40544	+	0.157273i	0.0536600	+	0.00600471i
$687$		0			0
$688$	−10.4292	−	4.98342i	−0.397610	−	0.189991i
$689$			14.1480i			0.538996i
$690$		0			0
$691$	10.8603			0.413146			0.206573	−	0.978431i	$-0.433769\pi$
$691$	10.8603			0.413146			0.206573	+	0.978431i	$0.433769\pi$
$692$	7.29712	+	1.65385i	0.277395	+	0.0628699i
$693$		0			0
$694$	43.8590	+	4.90795i	1.66486	+	0.186303i
$695$	15.7880			0.598871
$696$		0			0
$697$	36.3173			1.37561
$698$	14.9549	+	1.67349i	0.566050	+	0.0633426i
$699$		0			0
$700$	−0.748088	+	3.30072i	−0.0282751	+	0.124755i
$701$	−48.4528			−1.83004			−0.915018	−	0.403414i	$-0.867824\pi$
$701$	−48.4528			−1.83004			−0.915018	+	0.403414i	$0.867824\pi$
$702$		0			0
$703$			49.1125i			1.85231i
$704$	−11.7484	+	14.8707i	−0.442783	+	0.560459i
$705$		0			0
$706$	41.4939	+	4.64329i	1.56164	+	0.174752i
$707$		−	0.899761i		−	0.0338390i
$708$		0			0
$709$			24.1866i			0.908348i	0.890913	+	0.454174i	$0.150066\pi$
$709$			24.1866i			0.908348i	−0.890913	+	0.454174i	$0.849934\pi$
$710$	−3.43534	+	30.6993i	−0.128926	+	1.15212i
$711$		0			0
$712$	−19.8471	−	6.89401i	−0.743800	−	0.258364i
$713$			18.1995i			0.681575i
$714$		0			0
$715$	30.1252			1.12662
$716$	−7.00135	+	30.8914i	−0.261653	+	1.15447i
$717$		0			0
$718$	−3.40585	+	30.4358i	−0.127105	+	1.13585i
$719$	40.8996			1.52530			0.762650	−	0.646812i	$-0.223898\pi$
$719$	40.8996			1.52530			0.762650	+	0.646812i	$0.223898\pi$
$720$		0			0
$721$	13.6119			0.506934
$722$	−1.82198	+	16.2818i	−0.0678069	+	0.605945i
$723$		0			0
$724$	−3.60237	+	15.8944i	−0.133881	+	0.590710i
$725$	9.93425			0.368949
$726$		0			0
$727$			27.9812i			1.03777i	0.854845	+	0.518883i	$0.173652\pi$
$727$			27.9812i			1.03777i	−0.854845	+	0.518883i	$0.826348\pi$
$728$	−6.48921	+	18.6817i	−0.240506	+	0.692390i
$729$		0			0
$730$	−2.51141	+	22.4428i	−0.0929516	+	0.830645i
$731$		−	10.6738i		−	0.394785i
$732$		0			0
$733$			17.8163i			0.658062i	0.944319	+	0.329031i	$0.106722\pi$
$733$			17.8163i			0.658062i	−0.944319	+	0.329031i	$0.893278\pi$
$734$	−18.6474	−	2.08670i	−0.688288	−	0.0770215i
$735$		0			0
$736$	−22.7608	+	36.5312i	−0.838973	+	1.34656i
$737$			23.1303i			0.852014i
$738$		0			0
$739$	−39.6052			−1.45690			−0.728450	−	0.685099i	$-0.759759\pi$
$739$	−39.6052			−1.45690			−0.728450	+	0.685099i	$0.759759\pi$
$740$	7.14011	−	31.5036i	0.262476	−	1.15810i
$741$		0			0
$742$	−2.84381	−	0.318230i	−0.104399	−	0.0116826i
$743$	−37.2631			−1.36705			−0.683525	−	0.729927i	$-0.739554\pi$
$743$	−37.2631			−1.36705			−0.683525	+	0.729927i	$0.739554\pi$
$744$		0			0
$745$	11.2890			0.413596
$746$	3.35025	+	0.374903i	0.122661	+	0.0137262i
$747$		0			0
$748$	−17.0678	−	3.86832i	−0.624062	−	0.141440i
$749$	−9.64387			−0.352379
$750$		0			0
$751$			10.2637i			0.374529i	0.982310	+	0.187264i	$0.0599621\pi$
$751$			10.2637i			0.374529i	−0.982310	+	0.187264i	$0.940038\pi$
$752$	−0.613217	−	0.293015i	−0.0223617	−	0.0106852i
$753$		0			0
$754$	57.6898	+	6.45566i	2.10094	+	0.235101i
$755$		−	8.51303i		−	0.309821i
$756$		0			0
$757$			18.9330i			0.688132i	0.938945	+	0.344066i	$0.111804\pi$
$757$			18.9330i			0.688132i	−0.938945	+	0.344066i	$0.888196\pi$
$758$	0.682238	−	6.09669i	0.0247800	−	0.221442i
$759$		0			0
$760$	9.33481	−	26.8739i	0.338609	−	0.974818i
$761$		−	41.0983i		−	1.48981i	−0.667170	−	0.744905i	$-0.732495\pi$
$761$		−	41.0983i		−	1.48981i	0.667170	−	0.744905i	$-0.267505\pi$
$762$		0			0
$763$	−1.13844			−0.0412144
$764$	42.5243	+	9.63788i	1.53848	+	0.348686i
$765$		0			0
$766$	−4.49193	+	40.1413i	−0.162300	+	1.45037i
$767$	−1.18801			−0.0428964
$768$		0			0
$769$	24.3838			0.879301			0.439651	−	0.898169i	$-0.355102\pi$
$769$	24.3838			0.879301			0.439651	+	0.898169i	$0.355102\pi$
$770$	−0.677605	+	6.05530i	−0.0244192	+	0.218218i
$771$		0			0
$772$	−35.5250	−	8.05153i	−1.27857	−	0.289781i
$773$	−27.1940			−0.978102			−0.489051	−	0.872255i	$-0.662657\pi$
$773$	−27.1940			−0.978102			−0.489051	+	0.872255i	$0.662657\pi$
$774$		0			0
$775$		−	4.04763i		−	0.145395i
$776$	4.49546	−	12.9419i	0.161378	−	0.464588i
$777$		0			0
$778$	−4.01083	+	35.8420i	−0.143795	+	1.28500i
$779$		−	54.3744i		−	1.94817i
$780$		0			0
$781$		−	28.4513i		−	1.01807i
$782$	−39.5000	−	4.42017i	−1.41252	−	0.158065i
$783$		0			0
$784$	−3.60914	−	1.72456i	−0.128898	−	0.0615916i
$785$		−	3.12757i		−	0.111628i
$786$		0			0
$787$	−40.8769			−1.45710			−0.728552	−	0.684990i	$-0.759807\pi$
$787$	−40.8769			−1.45710			−0.728552	+	0.684990i	$0.759807\pi$
$788$	23.7365	+	5.37972i	0.845577	+	0.191645i
$789$		0			0
$790$	36.5129	+	4.08590i	1.29907	+	0.145370i
$791$	7.28073			0.258873
$792$		0			0
$793$	−2.93684			−0.104290
$794$	36.4097	+	4.07435i	1.29213	+	0.144593i
$795$		0			0
$796$	−8.82585	+	38.9415i	−0.312824	+	1.38024i
$797$	21.8622			0.774398			0.387199	−	0.921996i	$-0.373443\pi$
$797$	21.8622			0.774398			0.387199	+	0.921996i	$0.373443\pi$
$798$		0			0
$799$		−	0.627599i		−	0.0222028i
$800$	5.06209	−	8.12468i	0.178972	−	0.287251i
$801$		0			0
$802$	−6.53689	−	0.731496i	−0.230825	−	0.0258300i
$803$		−	20.7994i		−	0.733994i
$804$		0			0
$805$			13.8383i			0.487735i
$806$	2.63031	−	23.5053i	0.0926486	−	0.827938i
$807$		0			0
$808$	−0.835047	+	2.40401i	−0.0293769	+	0.0845727i
$809$			15.7533i			0.553855i	0.960891	+	0.276928i	$0.0893163\pi$
$809$			15.7533i			0.553855i	−0.960891	+	0.276928i	$0.910684\pi$
$810$		0			0
$811$	35.0976			1.23244			0.616221	−	0.787573i	$-0.288663\pi$
$811$	35.0976			1.23244			0.616221	+	0.787573i	$0.288663\pi$
$812$	−2.59523	+	11.4507i	−0.0910747	+	0.401841i
$813$		0			0
$814$	−3.30863	+	29.5670i	−0.115967	+	1.03632i
$815$	−33.1090			−1.15976
$816$		0			0
$817$	−15.9809			−0.559101
$818$	−2.85317	+	25.4969i	−0.0997588	+	0.891477i
$819$		0			0
$820$	−7.90510	+	34.8789i	−0.276058	+	1.21803i
$821$	13.6689			0.477047			0.238524	−	0.971137i	$-0.423337\pi$
$821$	13.6689			0.477047			0.238524	+	0.971137i	$0.423337\pi$
$822$		0			0
$823$		−	50.4577i		−	1.75885i	−0.476041	−	0.879423i	$-0.657929\pi$
$823$		−	50.4577i		−	1.75885i	0.476041	−	0.879423i	$-0.342071\pi$
$824$	−36.3687	−	12.6329i	−1.26696	−	0.440088i
$825$		0			0
$826$	0.0267217	−	0.238794i	0.000929769	−	0.00830871i
$827$			27.4214i			0.953535i	0.879029	+	0.476768i	$0.158192\pi$
$827$			27.4214i			0.953535i	−0.879029	+	0.476768i	$0.841808\pi$
$828$		0			0
$829$			0.0571961i			0.00198650i	1.00000		0.000993251i	$0.000316162\pi$
$829$			0.0571961i			0.00198650i	−1.00000		0.000993251i	$0.999684\pi$
$830$	26.1359	+	2.92468i	0.907190	+	0.101517i
$831$		0			0
$832$	34.6761	−	43.8918i	1.20218	−	1.52167i
$833$		−	3.69378i		−	0.127982i
$834$		0			0
$835$	−16.0210			−0.554429
$836$	−5.79167	+	25.5541i	−0.200309	+	0.883806i
$837$		0			0
$838$	−11.5475	−	1.29220i	−0.398902	−	0.0446383i
$839$	−24.4761			−0.845010			−0.422505	−	0.906361i	$-0.638849\pi$
$839$	−24.4761			−0.845010			−0.422505	+	0.906361i	$0.638849\pi$
$840$		0			0
$841$	5.46339			0.188393
$842$	−20.8543	−	2.33365i	−0.718686	−	0.0804230i
$843$		0			0
$844$	1.46290	+	0.331558i	0.0503552	+	0.0114127i
$845$	−65.2732			−2.24547
$846$		0			0
$847$			5.38811i			0.185138i
$848$	7.30283	+	3.48953i	0.250780	+	0.119831i
$849$		0			0
$850$	8.78496	+	0.983062i	0.301322	+	0.0337188i
$851$			67.5699i			2.31626i
$852$		0			0
$853$			38.5932i			1.32141i	0.750648	+	0.660703i	$0.229742\pi$
$853$			38.5932i			1.32141i	−0.750648	+	0.660703i	$0.770258\pi$
$854$	0.0660583	−	0.590318i	0.00226047	−	0.0202003i
$855$		0			0
$856$	25.7668	+	8.95025i	0.880690	+	0.305913i
$857$		−	9.45790i		−	0.323076i	−0.986867	−	0.161538i	$-0.948355\pi$
$857$		−	9.45790i		−	0.323076i	0.986867	−	0.161538i	$-0.0516454\pi$
$858$		0			0
$859$	−2.27620			−0.0776631			−0.0388315	−	0.999246i	$-0.512364\pi$
$859$	−2.27620			−0.0776631			−0.0388315	+	0.999246i	$0.512364\pi$
$860$	10.2511	+	2.32334i	0.349559	+	0.0792254i
$861$		0			0
$862$	2.07297	−	18.5247i	0.0706057	−	0.630955i
$863$	11.3263			0.385553			0.192776	−	0.981243i	$-0.438251\pi$
$863$	11.3263			0.385553			0.192776	+	0.981243i	$0.438251\pi$
$864$		0			0
$865$	−6.80405			−0.231345
$866$	1.20530	−	10.7710i	0.0409579	−	0.366013i
$867$		0			0
$868$	4.66549	+	1.05741i	0.158357	+	0.0358907i
$869$	−33.8392			−1.14791
$870$		0			0
$871$		−	68.2706i		−	2.31326i
$872$	3.04172	+	1.05656i	0.103006	+	0.0357797i
$873$		0			0
$874$	−6.61790	+	59.1397i	−0.223854	+	2.00043i
$875$		−	12.1713i		−	0.411467i
$876$		0			0
$877$		−	33.2328i		−	1.12219i	−0.827751	−	0.561096i	$-0.810380\pi$
$877$		−	33.2328i		−	1.12219i	0.827751	−	0.561096i	$-0.189620\pi$
$878$	−32.8122	−	3.67178i	−1.10736	−	0.123917i
$879$		0			0
$880$	7.43023	−	15.5499i	0.250473	−	0.524186i
$881$		−	3.87015i		−	0.130389i	−0.997873	−	0.0651943i	$-0.979233\pi$
$881$		−	3.87015i		−	0.130389i	0.997873	−	0.0651943i	$-0.0207667\pi$
$882$		0			0
$883$	44.6838			1.50373			0.751865	−	0.659317i	$-0.229154\pi$
$883$	44.6838			1.50373			0.751865	+	0.659317i	$0.229154\pi$
$884$	50.3769	+	11.4176i	1.69436	+	0.384016i
$885$		0			0
$886$	20.8617	+	2.33448i	0.700862	+	0.0784284i
$887$	−8.13586			−0.273176			−0.136588	−	0.990628i	$-0.543614\pi$
$887$	−8.13586			−0.273176			−0.136588	+	0.990628i	$0.543614\pi$
$888$		0			0
$889$	−5.44445			−0.182601
$890$	18.9876	+	2.12476i	0.636464	+	0.0712222i
$891$		0			0
$892$	−5.12995	+	22.6344i	−0.171764	+	0.757857i
$893$	−0.939645			−0.0314440
$894$		0			0
$895$		−	28.8041i		−	0.962814i
$896$	8.04247	+	7.95730i	0.268680	+	0.265835i
$897$		0			0
$898$	−5.70712	−	0.638643i	−0.190449	−	0.0213118i
$899$		−	14.0418i		−	0.468322i
$900$		0			0
$901$			7.47409i			0.248998i
$902$	3.66311	−	32.7348i	0.121968	−	1.08995i
$903$		0			0
$904$	−19.4529	−	6.75708i	−0.646993	−	0.224737i
$905$		−	14.8204i		−	0.492646i
$906$		0			0
$907$	−30.7597			−1.02136			−0.510679	−	0.859771i	$-0.670606\pi$
$907$	−30.7597			−1.02136			−0.510679	+	0.859771i	$0.670606\pi$
$908$	2.47544	−	10.9222i	0.0821504	−	0.362465i
$909$		0			0
$910$	2.00000	−	17.8726i	0.0662994	−	0.592472i
$911$	−11.5179			−0.381606			−0.190803	−	0.981628i	$-0.561109\pi$
$911$	−11.5179			−0.381606			−0.190803	+	0.981628i	$0.561109\pi$
$912$		0			0
$913$	−24.2220			−0.801632
$914$	−3.62395	+	32.3848i	−0.119870	+	1.07119i
$915$		0			0
$916$	10.3763	−	45.7825i	0.342843	−	1.51270i
$917$	−6.73222			−0.222318
$918$		0			0
$919$			16.5397i			0.545595i	0.962071	+	0.272797i	$0.0879489\pi$
$919$			16.5397i			0.545595i	−0.962071	+	0.272797i	$0.912051\pi$
$920$	12.8430	−	36.9735i	0.423421	−	1.21898i
$921$		0			0
$922$	4.27226	−	38.1783i	0.140699	−	1.25734i
$923$			83.9760i			2.76410i
$924$		0			0
$925$		−	15.0278i		−	0.494111i
$926$	−23.7371	−	2.65625i	−0.780048	−	0.0872897i
$927$		0			0
$928$	17.5611	−	28.1857i	0.576473	−	0.925242i
$929$		−	49.8949i		−	1.63700i	−0.574509	−	0.818499i	$-0.694807\pi$
$929$		−	49.8949i		−	1.63700i	0.574509	−	0.818499i	$-0.305193\pi$
$930$		0			0
$931$	−5.53035			−0.181250
$932$	7.50244	−	33.1023i	0.245750	−	1.08430i
$933$		0			0
$934$	−16.9950	−	1.90180i	−0.556095	−	0.0622286i
$935$	15.9145			0.520461
$936$		0			0
$937$	−11.6763			−0.381447			−0.190724	−	0.981644i	$-0.561083\pi$
$937$	−11.6763			−0.381447			−0.190724	+	0.981644i	$0.561083\pi$
$938$	13.7227	+	1.53561i	0.448061	+	0.0501393i
$939$		0			0
$940$	0.602743	+	0.136608i	0.0196593	+	0.00445566i
$941$	−38.1741			−1.24444			−0.622219	−	0.782843i	$-0.713769\pi$
$941$	−38.1741			−1.24444			−0.622219	+	0.782843i	$0.713769\pi$
$942$		0			0
$943$		−	74.8093i		−	2.43612i
$944$	−0.293015	+	0.613217i	−0.00953684	+	0.0199585i
$945$		0			0
$946$	−9.62089	−	1.07661i	−0.312802	−	0.0350035i
$947$			35.3693i			1.14935i	0.818382	+	0.574675i	$0.194871\pi$
$947$			35.3693i			1.14935i	−0.818382	+	0.574675i	$0.805129\pi$
$948$		0			0
$949$			61.3908i			1.99283i
$950$	1.47185	−	13.1529i	0.0477530	−	0.426736i
$951$		0			0
$952$	−3.42811	+	9.86915i	−0.111106	+	0.319861i
$953$		−	8.21631i		−	0.266152i	−0.991106	−	0.133076i	$-0.957514\pi$
$953$		−	8.21631i		−	0.266152i	0.991106	−	0.133076i	$-0.0424855\pi$
$954$		0			0
$955$	−39.6509			−1.28307
$956$	30.1672	+	6.83720i	0.975676	+	0.221131i
$957$		0			0
$958$	1.06514	−	9.51846i	0.0344132	−	0.307528i
$959$	4.79689			0.154900
$960$		0			0
$961$	25.2788			0.815444
$962$	9.76565	−	87.2689i	0.314857	−	2.81366i
$963$		0			0
$964$	−49.8718	−	11.3031i	−1.60626	−	0.364049i
$965$	33.1246			1.06632
$966$		0			0
$967$		−	17.5083i		−	0.563028i	−0.959557	−	0.281514i	$-0.909163\pi$
$967$		−	17.5083i		−	0.563028i	0.959557	−	0.281514i	$-0.0908366\pi$
$968$	5.00059	−	14.3961i	0.160725	−	0.462709i
$969$		0			0
$970$	−1.38552	+	12.3814i	−0.0444863	+	0.397544i
$971$			25.6587i			0.823428i	0.911313	+	0.411714i	$0.135070\pi$
$971$			25.6587i			0.823428i	−0.911313	+	0.411714i	$0.864930\pi$
$972$		0			0
$973$			8.68075i			0.278292i
$974$	−8.65189	−	0.968171i	−0.277224	−	0.0310222i
$975$		0			0
$976$	−0.724357	+	1.51592i	−0.0231861	+	0.0485235i
$977$			47.1792i			1.50940i	0.656072	+	0.754698i	$0.272217\pi$
$977$			47.1792i			1.50940i	−0.656072	+	0.754698i	$0.727783\pi$
$978$		0			0
$979$	−17.5971			−0.562407
$980$	3.54749	+	0.804017i	0.113320	+	0.0256834i
$981$		0			0
$982$	−41.3488	−	4.62705i	−1.31949	−	0.147655i
$983$	28.1932			0.899225			0.449612	−	0.893224i	$-0.351562\pi$
$983$	28.1932			0.899225			0.449612	+	0.893224i	$0.351562\pi$
$984$		0			0
$985$	−22.1326			−0.705202
$986$	30.4763	+	3.41039i	0.970564	+	0.108609i
$987$		0			0
$988$	17.0945	−	75.4246i	0.543849	−	2.39958i
$989$	−21.9868			−0.699139
$990$		0			0
$991$		−	23.1846i		−	0.736482i	−0.929730	−	0.368241i	$-0.879960\pi$
$991$		−	23.1846i		−	0.736482i	0.929730	−	0.368241i	$-0.120040\pi$
$992$	−11.4841	−	7.15515i	−0.364619	−	0.227176i
$993$		0			0
$994$	−16.8795	−	1.88887i	−0.535386	−	0.0599112i
$995$		−	36.3102i		−	1.15111i
$996$		0			0
$997$			9.32007i			0.295169i	0.989049	+	0.147585i	$0.0471499\pi$
$997$			9.32007i			0.295169i	−0.989049	+	0.147585i	$0.952850\pi$
$998$	2.38837	−	21.3433i	0.0756027	−	0.675610i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.j.a.323.12	yes	24
3.2	odd	2	inner	504.2.j.a.323.13	yes	24
4.3	odd	2		2016.2.j.a.1583.18		24
8.3	odd	2	inner	504.2.j.a.323.14	yes	24
8.5	even	2		2016.2.j.a.1583.8		24
12.11	even	2		2016.2.j.a.1583.7		24
24.5	odd	2		2016.2.j.a.1583.17		24
24.11	even	2	inner	504.2.j.a.323.11	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.j.a.323.11	✓	24	24.11	even	2	inner
504.2.j.a.323.12	yes	24	1.1	even	1	trivial
504.2.j.a.323.13	yes	24	3.2	odd	2	inner
504.2.j.a.323.14	yes	24	8.3	odd	2	inner
2016.2.j.a.1583.7		24	12.11	even	2
2016.2.j.a.1583.8		24	8.5	even	2
2016.2.j.a.1583.17		24	24.5	odd	2
2016.2.j.a.1583.18		24	4.3	odd	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.j (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.157273 + 1.40544i) q^{2} +(-1.95053 - 0.442076i) q^{4} +1.81873 q^{5} +1.00000i q^{7} +(0.928077 - 2.67183i) q^{8} +O(q^{10})\)	\(q+(-0.157273 + 1.40544i) q^{2} +(-1.95053 - 0.442076i) q^{4} +1.81873 q^{5} +1.00000i q^{7} +(0.928077 - 2.67183i) q^{8} +(-0.286037 + 2.55612i) q^{10} -2.36894i q^{11} +6.99210i q^{13} +(-1.40544 - 0.157273i) q^{14} +(3.60914 + 1.72456i) q^{16} +3.69378i q^{17} +5.53035 q^{19} +(-3.54749 - 0.804017i) q^{20} +(3.32941 + 0.372570i) q^{22} +7.60875 q^{23} -1.69222 q^{25} +(-9.82698 - 1.09967i) q^{26} +(0.442076 - 1.95053i) q^{28} -5.87055 q^{29} +2.39191i q^{31} +(-2.99139 + 4.80120i) q^{32} +(-5.19139 - 0.580932i) q^{34} +1.81873i q^{35} +8.88054i q^{37} +(-0.869775 + 7.77259i) q^{38} +(1.68792 - 4.85934i) q^{40} -9.83200i q^{41} -2.88967 q^{43} +(-1.04725 + 4.62069i) q^{44} +(-1.19665 + 10.6937i) q^{46} -0.169907 q^{47} -1.00000 q^{49} +(0.266140 - 2.37831i) q^{50} +(3.09104 - 13.6383i) q^{52} +2.02343 q^{53} -4.30847i q^{55} +(2.67183 + 0.928077i) q^{56} +(0.923279 - 8.25072i) q^{58} +0.169907i q^{59} +0.420023i q^{61} +(-3.36169 - 0.376183i) q^{62} +(-6.27735 - 4.95933i) q^{64} +12.7167i q^{65} -9.76396 q^{67} +(1.63293 - 7.20483i) q^{68} +(-2.55612 - 0.286037i) q^{70} +12.0101 q^{71} +8.78003 q^{73} +(-12.4811 - 1.39667i) q^{74} +(-10.7871 - 2.44484i) q^{76} +2.36894 q^{77} -14.2845i q^{79} +(6.56405 + 3.13652i) q^{80} +(13.8183 + 1.54631i) q^{82} -10.2248i q^{83} +6.71799i q^{85} +(0.454467 - 4.06126i) q^{86} +(-6.32941 - 2.19856i) q^{88} -7.42827i q^{89} -6.99210 q^{91} +(-14.8411 - 3.36364i) q^{92} +(0.0267217 - 0.238794i) q^{94} +10.0582 q^{95} +4.84384 q^{97} +(0.157273 - 1.40544i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{4}+O(q^{10}) \) 24 * q - 8 * q^4	\( 24 q - 8 q^{4} + 24 q^{10} + 12 q^{16} + 32 q^{19} + 12 q^{22} + 24 q^{25} + 4 q^{28} - 8 q^{40} - 64 q^{43} - 12 q^{46} - 24 q^{49} - 16 q^{52} - 12 q^{58} + 16 q^{64} + 16 q^{67} + 24 q^{70} + 8 q^{76} + 24 q^{82} - 84 q^{88} - 72 q^{94}+O(q^{100}) \) 24 * q - 8 * q^4 + 24 * q^10 + 12 * q^16 + 32 * q^19 + 12 * q^22 + 24 * q^25 + 4 * q^28 - 8 * q^40 - 64 * q^43 - 12 * q^46 - 24 * q^49 - 16 * q^52 - 12 * q^58 + 16 * q^64 + 16 * q^67 + 24 * q^70 + 8 * q^76 + 24 * q^82 - 84 * q^88 - 72 * q^94

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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