LMFDB - Embedded newform 504.2.ch.b.269.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(269,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 3, 1]))

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

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

chi := DirichletCharacter("504.269");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.ch (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			269.20
Character	$\chi$	$=$	504.269
Dual form			504.2.ch.b.341.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.722843 - 1.21552i) q^{2} +(-0.954995 - 1.75727i) q^{4} +(-0.785247 + 0.453362i) q^{5} +(-2.47043 - 0.947077i) q^{7} +(-2.82631 - 0.109409i) q^{8} +O(q^{10})$	\(q+(0.722843 - 1.21552i) q^{2} +(-0.954995 - 1.75727i) q^{4} +(-0.785247 + 0.453362i) q^{5} +(-2.47043 - 0.947077i) q^{7} +(-2.82631 - 0.109409i) q^{8} +(-0.0165377 + 1.28220i) q^{10} +(-0.0729337 + 0.126325i) q^{11} -6.12830 q^{13} +(-2.93693 + 2.31828i) q^{14} +(-2.17597 + 3.35636i) q^{16} +(3.00430 - 5.20361i) q^{17} +(-2.10516 - 3.64625i) q^{19} +(1.54658 + 0.946928i) q^{20} +(0.100831 + 0.179966i) q^{22} +(-3.20566 + 1.85079i) q^{23} +(-2.08893 + 3.61812i) q^{25} +(-4.42980 + 7.44909i) q^{26} +(0.694985 + 5.24566i) q^{28} +10.2484 q^{29} +(-3.54741 - 2.04810i) q^{31} +(2.50685 + 5.07106i) q^{32} +(-4.15347 - 7.41320i) q^{34} +(2.36927 - 0.376312i) q^{35} +(2.51971 - 1.45475i) q^{37} +(-5.95380 - 0.0767918i) q^{38} +(2.26895 - 1.19543i) q^{40} -2.26244 q^{41} -8.73882i q^{43} +(0.291638 + 0.00752431i) q^{44} +(-0.0675128 + 5.23438i) q^{46} +(-3.58285 - 6.20567i) q^{47} +(5.20609 + 4.67938i) q^{49} +(2.88795 + 5.15448i) q^{50} +(5.85250 + 10.7691i) q^{52} +(-1.86849 + 3.23632i) q^{53} -0.132262i q^{55} +(6.87859 + 2.94702i) q^{56} +(7.40801 - 12.4572i) q^{58} +(6.35100 + 3.66675i) q^{59} +(-3.41070 - 5.90751i) q^{61} +(-5.05374 + 2.83151i) q^{62} +(7.97606 + 0.618449i) q^{64} +(4.81223 - 2.77834i) q^{65} +(2.66978 + 1.54140i) q^{67} +(-12.0132 - 0.309943i) q^{68} +(1.25519 - 3.15192i) q^{70} +4.91850i q^{71} +(2.67843 + 1.54639i) q^{73} +(0.0530663 - 4.11432i) q^{74} +(-4.39701 + 7.18148i) q^{76} +(0.299817 - 0.243004i) q^{77} +(-5.41731 - 9.38305i) q^{79} +(0.187025 - 3.62207i) q^{80} +(-1.63539 + 2.75005i) q^{82} -12.8534i q^{83} +5.44815i q^{85} +(-10.6222 - 6.31680i) q^{86} +(0.219954 - 0.349054i) q^{88} +(-1.55708 - 2.69694i) q^{89} +(15.1396 + 5.80397i) q^{91} +(6.31372 + 3.86570i) q^{92} +(-10.1330 - 0.130695i) q^{94} +(3.30614 + 1.90880i) q^{95} -0.593803i q^{97} +(9.45109 - 2.94566i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{4} - 20 q^{7}+O(q^{10}) $ 56 * q - 8 * q^4 - 20 * q^7	$ 56 q - 8 q^{4} - 20 q^{7} + 20 q^{16} - 16 q^{22} + 8 q^{25} + 36 q^{28} - 36 q^{31} + 60 q^{40} - 8 q^{46} - 28 q^{49} + 36 q^{52} - 44 q^{58} + 40 q^{64} - 60 q^{70} + 72 q^{73} - 12 q^{79} - 36 q^{82} + 4 q^{88} - 180 q^{94}+O(q^{100}) $ 56 * q - 8 * q^4 - 20 * q^7 + 20 * q^16 - 16 * q^22 + 8 * q^25 + 36 * q^28 - 36 * q^31 + 60 * q^40 - 8 * q^46 - 28 * q^49 + 36 * q^52 - 44 * q^58 + 40 * q^64 - 60 * q^70 + 72 * q^73 - 12 * q^79 - 36 * q^82 + 4 * q^88 - 180 * q^94

Display 100 coefficients 10 coefficients

Character values

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

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$	$-1$

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 $

$2$	0.722843	−	1.21552i	0.511127	−	0.859505i
$2$	0.722843	−	1.21552i	0.511127	−	0.859505i
$3$		0			0
$3$		0			0
$4$	−0.954995	−	1.75727i	−0.477497	−	0.878633i
$5$	−0.785247	+	0.453362i	−0.351173	+	0.202750i	−0.665202	−	0.746664i	$-0.731654\pi$
$5$	−0.785247	+	0.453362i	−0.351173	+	0.202750i	0.314029	+	0.949413i	$0.398321\pi$
$6$		0			0
$7$	−2.47043	−	0.947077i	−0.933736	−	0.357962i
$7$	−2.47043	−	0.947077i	−0.933736	−	0.357962i
$8$	−2.82631	−	0.109409i	−0.999252	−	0.0386820i
$9$		0			0
$10$	−0.0165377	+	1.28220i	−0.00522967	+	0.405466i
$11$	−0.0729337	+	0.126325i	−0.0219903	+	0.0380884i	−0.876811	−	0.480835i	$-0.840334\pi$
$11$	−0.0729337	+	0.126325i	−0.0219903	+	0.0380884i	0.854821	+	0.518923i	$0.173667\pi$
$12$		0			0
$13$	−6.12830			−1.69968			−0.849842	−	0.527037i	$-0.823303\pi$
$13$	−6.12830			−1.69968			−0.849842	+	0.527037i	$0.823303\pi$
$14$	−2.93693	+	2.31828i	−0.784928	+	0.619587i
$15$		0			0
$16$	−2.17597	+	3.35636i	−0.543992	+	0.839090i
$17$	3.00430	−	5.20361i	0.728651	−	1.26206i	−0.228803	−	0.973473i	$-0.573481\pi$
$17$	3.00430	−	5.20361i	0.728651	−	1.26206i	0.957454	−	0.288587i	$-0.0931856\pi$
$18$		0			0
$19$	−2.10516	−	3.64625i	−0.482957	−	0.836506i	0.516851	−	0.856075i	$-0.327104\pi$
$19$	−2.10516	−	3.64625i	−0.482957	−	0.836506i	−0.999809	+	0.0195688i	$0.993771\pi$
$20$	1.54658	+	0.946928i	0.345827	+	0.211740i
$21$		0			0
$22$	0.100831	+	0.179966i	0.0214973	+	0.0383688i
$23$	−3.20566	+	1.85079i	−0.668426	+	0.385916i	−0.795480	−	0.605980i	$-0.792781\pi$
$23$	−3.20566	+	1.85079i	−0.668426	+	0.385916i	0.127054	+	0.991896i	$0.459448\pi$
$24$		0			0
$25$	−2.08893	+	3.61812i	−0.417785	+	0.723625i
$26$	−4.42980	+	7.44909i	−0.868755	+	1.46089i
$27$		0			0
$28$	0.694985	+	5.24566i	0.131340	+	0.991337i
$29$	10.2484			1.90309			0.951543	−	0.307515i	$-0.0994973\pi$
$29$	10.2484			1.90309			0.951543	+	0.307515i	$0.0994973\pi$
$30$		0			0
$31$	−3.54741	−	2.04810i	−0.637134	−	0.367849i	0.146376	−	0.989229i	$-0.453239\pi$
$31$	−3.54741	−	2.04810i	−0.637134	−	0.367849i	−0.783510	+	0.621380i	$0.786572\pi$
$32$	2.50685	+	5.07106i	0.443153	+	0.896446i
$33$		0			0
$34$	−4.15347	−	7.41320i	−0.712314	−	1.27135i
$35$	2.36927	−	0.376312i	0.400480	−	0.0636084i
$36$		0			0
$37$	2.51971	−	1.45475i	0.414238	−	0.239160i	−0.278371	−	0.960474i	$-0.589795\pi$
$37$	2.51971	−	1.45475i	0.414238	−	0.239160i	0.692609	+	0.721313i	$0.256461\pi$
$38$	−5.95380	−	0.0767918i	−0.965834	−	0.0124573i
$39$		0			0
$40$	2.26895	−	1.19543i	0.358753	−	0.189014i
$41$	−2.26244			−0.353334			−0.176667	−	0.984271i	$-0.556532\pi$
$41$	−2.26244			−0.353334			−0.176667	+	0.984271i	$0.556532\pi$
$42$		0			0
$43$		−	8.73882i		−	1.33266i	−0.745658	−	0.666329i	$-0.767865\pi$
$43$		−	8.73882i		−	1.33266i	0.745658	−	0.666329i	$-0.232135\pi$
$44$	0.291638	+	0.00752431i	0.0439661	+	0.00113433i
$45$		0			0
$46$	−0.0675128	+	5.23438i	−0.00995422	+	0.771768i
$47$	−3.58285	−	6.20567i	−0.522612	−	0.905190i	−0.999654	−	0.0263098i	$-0.991624\pi$
$47$	−3.58285	−	6.20567i	−0.522612	−	0.905190i	0.477042	−	0.878881i	$-0.341709\pi$
$48$		0			0
$49$	5.20609	+	4.67938i	0.743727	+	0.668483i
$50$	2.88795	+	5.15448i	0.408418	+	0.728953i
$51$		0			0
$52$	5.85250	+	10.7691i	0.811595	+	1.49340i
$53$	−1.86849	+	3.23632i	−0.256657	+	0.444543i	−0.965344	−	0.260980i	$-0.915954\pi$
$53$	−1.86849	+	3.23632i	−0.256657	+	0.444543i	0.708687	+	0.705523i	$0.249288\pi$
$54$		0			0
$55$		−	0.132262i		−	0.0178342i
$56$	6.87859	+	2.94702i	0.919191	+	0.393812i
$57$		0			0
$58$	7.40801	−	12.4572i	0.972720	−	1.63571i
$59$	6.35100	+	3.66675i	0.826829	+	0.477370i	0.852766	−	0.522293i	$-0.174923\pi$
$59$	6.35100	+	3.66675i	0.826829	+	0.477370i	−0.0259364	+	0.999664i	$0.508257\pi$
$60$		0			0
$61$	−3.41070	−	5.90751i	−0.436696	−	0.756379i	0.560737	−	0.827994i	$-0.310518\pi$
$61$	−3.41070	−	5.90751i	−0.436696	−	0.756379i	−0.997432	+	0.0716150i	$0.977185\pi$
$62$	−5.05374	+	2.83151i	−0.641825	+	0.359602i
$63$		0			0
$64$	7.97606	+	0.618449i	0.997007	+	0.0773061i
$65$	4.81223	−	2.77834i	0.596883	−	0.344611i
$66$		0			0
$67$	2.66978	+	1.54140i	0.326166	+	0.188312i	0.654138	−	0.756376i	$-0.273032\pi$
$67$	2.66978	+	1.54140i	0.326166	+	0.188312i	−0.327972	+	0.944688i	$0.606365\pi$
$68$	−12.0132	−	0.309943i	−1.45682	−	0.0375861i
$69$		0			0
$70$	1.25519	−	3.15192i	0.150024	−	0.376726i
$71$			4.91850i			0.583719i	0.956461	+	0.291859i	$0.0942739\pi$
$71$			4.91850i			0.583719i	−0.956461	+	0.291859i	$0.905726\pi$
$72$		0			0
$73$	2.67843	+	1.54639i	0.313486	+	0.180991i	0.648485	−	0.761227i	$-0.275403\pi$
$73$	2.67843	+	1.54639i	0.313486	+	0.180991i	−0.334999	+	0.942218i	$0.608736\pi$
$74$	0.0530663	−	4.11432i	0.00616883	−	0.478281i
$75$		0			0
$76$	−4.39701	+	7.18148i	−0.504371	+	0.823772i
$77$	0.299817	−	0.243004i	0.0341674	−	0.0276928i
$78$		0			0
$79$	−5.41731	−	9.38305i	−0.609495	−	1.05568i	−0.991324	−	0.131443i	$-0.958039\pi$
$79$	−5.41731	−	9.38305i	−0.609495	−	1.05568i	0.381829	−	0.924233i	$-0.375294\pi$
$80$	0.187025	−	3.62207i	0.0209100	−	0.404960i
$81$		0			0
$82$	−1.63539	+	2.75005i	−0.180599	+	0.303693i
$83$		−	12.8534i		−	1.41085i	−0.708785	−	0.705424i	$-0.750756\pi$
$83$		−	12.8534i		−	1.41085i	0.708785	−	0.705424i	$-0.249244\pi$
$84$		0			0
$85$			5.44815i			0.590935i
$86$	−10.6222	−	6.31680i	−1.14543	−	0.681158i
$87$		0			0
$88$	0.219954	−	0.349054i	0.0234472	−	0.0372093i
$89$	−1.55708	−	2.69694i	−0.165050	−	0.285875i	0.771623	−	0.636080i	$-0.219445\pi$
$89$	−1.55708	−	2.69694i	−0.165050	−	0.285875i	−0.936673	+	0.350205i	$0.886112\pi$
$90$		0			0
$91$	15.1396	+	5.80397i	1.58706	+	0.608422i
$92$	6.31372	+	3.86570i	0.658250	+	0.403027i
$93$		0			0
$94$	−10.1330	−	0.130695i	−1.04514	−	0.0134801i
$95$	3.30614	+	1.90880i	0.339203	+	0.195839i
$96$		0			0
$97$		−	0.593803i		−	0.0602915i	−0.999546	−	0.0301458i	$-0.990403\pi$
$97$		−	0.593803i		−	0.0602915i	0.999546	−	0.0301458i	$-0.00959715\pi$
$98$	9.45109	−	2.94566i	0.954704	−	0.297557i
$99$		0			0
$100$	8.35292	+	0.215507i	0.835292	+	0.0215507i
$101$	9.65297	+	5.57314i	0.960506	+	0.554549i	0.896329	−	0.443390i	$-0.146224\pi$
$101$	9.65297	+	5.57314i	0.960506	+	0.554549i	0.0641776	+	0.997938i	$0.479558\pi$
$102$		0			0
$103$	−1.41603	+	0.817548i	−0.139526	+	0.0805554i	−0.568138	−	0.822933i	$-0.692336\pi$
$103$	−1.41603	+	0.817548i	−0.139526	+	0.0805554i	0.428612	+	0.903489i	$0.359003\pi$
$104$	17.3205	+	0.670493i	1.69841	+	0.0657472i
$105$		0			0
$106$	2.58320	+	4.61055i	0.250903	+	0.447816i
$107$	−7.12074	−	12.3335i	−0.688387	−	1.19232i	−0.972359	−	0.233489i	$-0.924986\pi$
$107$	−7.12074	−	12.3335i	−0.688387	−	1.19232i	0.283972	−	0.958833i	$-0.408348\pi$
$108$		0			0
$109$	5.88150	+	3.39568i	0.563345	+	0.325247i	0.754487	−	0.656315i	$-0.227886\pi$
$109$	5.88150	+	3.39568i	0.563345	+	0.325247i	−0.191142	+	0.981562i	$0.561219\pi$
$110$	−0.160767	−	0.0956044i	−0.0153285	−	0.00911552i
$111$		0			0
$112$	8.55432	−	6.23086i	0.808307	−	0.588761i
$113$		−	8.54183i		−	0.803548i	−0.915739	−	0.401774i	$-0.868394\pi$
$113$		−	8.54183i		−	0.803548i	0.915739	−	0.401774i	$-0.131606\pi$
$114$		0			0
$115$	1.67816	−	2.90665i	0.156489	−	0.271046i
$116$	−9.78720	−	18.0092i	−0.908719	−	1.67211i
$117$		0			0
$118$	9.04780	−	5.06930i	0.832917	−	0.466667i
$119$	−12.3502	+	10.0099i	−1.13214	+	0.917602i
$120$		0			0
$121$	5.48936	+	9.50785i	0.499033	+	0.864350i
$122$	−9.64612	−	0.124415i	−0.873319	−	0.0112640i
$123$		0			0
$124$	−0.211295	+	8.18967i	−0.0189748	+	0.735454i
$125$		−	8.32178i		−	0.744323i
$126$		0			0
$127$	−18.0974			−1.60589			−0.802944	−	0.596054i	$-0.796734\pi$
$127$	−18.0974			−1.60589			−0.802944	+	0.596054i	$0.796734\pi$
$128$	6.51718	−	9.24805i	0.576043	−	0.817419i
$129$		0			0
$130$	0.101348	−	7.85768i	0.00888880	−	0.689164i
$131$	−8.38458	+	4.84084i	−0.732564	+	0.422946i	−0.819359	−	0.573280i	$-0.805671\pi$
$131$	−8.38458	+	4.84084i	−0.732564	+	0.422946i	0.0867954	+	0.996226i	$0.472337\pi$
$132$		0			0
$133$	1.74739	+	11.0016i	0.151518	+	0.953957i
$134$	3.80344	−	2.13099i	0.328568	−	0.184090i
$135$		0			0
$136$	−9.06042	+	14.3783i	−0.776925	+	1.23293i
$137$	9.11532	+	5.26273i	0.778774	+	0.449625i	0.835996	−	0.548736i	$-0.184891\pi$
$137$	9.11532	+	5.26273i	0.778774	+	0.449625i	−0.0572215	+	0.998362i	$0.518224\pi$
$138$		0			0
$139$	−15.8152			−1.34143			−0.670715	−	0.741715i	$-0.734013\pi$
$139$	−15.8152			−1.34143			−0.670715	+	0.741715i	$0.734013\pi$
$140$	−2.92392	−	3.80406i	−0.247116	−	0.321502i
$141$		0			0
$142$	5.97855	+	3.55531i	0.501709	+	0.298355i
$143$	0.446960	−	0.774157i	0.0373767	−	0.0647383i
$144$		0			0
$145$	−8.04755	+	4.64625i	−0.668312	+	0.385850i
$146$	3.81576	−	2.13789i	0.315794	−	0.176933i
$147$		0			0
$148$	−4.96270	−	3.03852i	−0.407931	−	0.249764i
$149$	−5.79849	−	10.0433i	−0.475031	−	0.822777i	0.524560	−	0.851373i	$-0.324230\pi$
$149$	−5.79849	−	10.0433i	−0.475031	−	0.822777i	−0.999591	+	0.0285960i	$0.990896\pi$
$150$		0			0
$151$	7.79321	−	13.4982i	0.634202	−	1.09847i	−0.352481	−	0.935819i	$-0.614662\pi$
$151$	7.79321	−	13.4982i	0.634202	−	1.09847i	0.986684	−	0.162652i	$-0.0520047\pi$
$152$	5.55091	+	10.5357i	0.450238	+	0.854562i
$153$		0			0
$154$	−0.0786555	−	0.540089i	−0.00633824	−	0.0435216i
$155$	3.71412			0.298326
$156$		0			0
$157$	−6.66733	+	11.5482i	−0.532111	+	0.921643i	0.467186	+	0.884159i	$0.345268\pi$
$157$	−6.66733	+	11.5482i	−0.532111	+	0.921643i	−0.999297	+	0.0374841i	$0.988066\pi$
$158$	−15.3212	−	0.197612i	−1.21889	−	0.0157211i
$159$		0			0
$160$	−4.26753	−	2.84552i	−0.337378	−	0.224958i
$161$	9.67221	−	1.53624i	0.762277	−	0.121073i
$162$		0			0
$163$	14.7888	−	8.53830i	1.15835	−	0.668771i	0.207439	−	0.978248i	$-0.433487\pi$
$163$	14.7888	−	8.53830i	1.15835	−	0.668771i	0.950907	+	0.309477i	$0.100154\pi$
$164$	2.16062	+	3.97572i	0.168716	+	0.310451i
$165$		0			0
$166$	−15.6237	−	9.29103i	−1.21263	−	0.721124i
$167$	1.64523			0.127312			0.0636558	−	0.997972i	$-0.479724\pi$
$167$	1.64523			0.127312			0.0636558	+	0.997972i	$0.479724\pi$
$168$		0			0
$169$	24.5561			1.88893
$170$	6.62236	+	3.93816i	0.507912	+	0.302043i
$171$		0			0
$172$	−15.3564	+	8.34553i	−1.17092	+	0.636341i
$173$	−7.80851	+	4.50825i	−0.593670	+	0.342756i	−0.766547	−	0.642188i	$-0.778027\pi$
$173$	−7.80851	+	4.50825i	−0.593670	+	0.342756i	0.172877	+	0.984943i	$0.444694\pi$
$174$		0			0
$175$	8.58720	−	6.95996i	0.649131	−	0.526124i
$176$	−0.265290	−	0.519671i	−0.0199970	−	0.0391717i
$177$		0			0
$178$	−4.40372	−	0.0567989i	−0.330073	−	0.00425726i
$179$	−7.30700	+	12.6561i	−0.546151	+	0.945961i	0.452383	+	0.891824i	$0.350574\pi$
$179$	−7.30700	+	12.6561i	−0.546151	+	0.945961i	−0.998534	+	0.0541368i	$0.982759\pi$
$180$		0			0
$181$	−0.198456			−0.0147511			−0.00737556	−	0.999973i	$-0.502348\pi$
$181$	−0.198456			−0.0147511			−0.00737556	+	0.999973i	$0.502348\pi$
$182$	17.9984	−	14.2071i	1.33413	−	1.05310i
$183$		0			0
$184$	9.26268	−	4.88017i	0.682854	−	0.359771i
$185$	−1.31906	+	2.28468i	−0.0969793	+	0.167973i
$186$		0			0
$187$	0.438230	+	0.759037i	0.0320466	+	0.0555063i
$188$	−7.48342	+	12.2224i	−0.545784	+	0.891410i
$189$		0			0
$190$	4.71002	−	2.63893i	0.341700	−	0.191448i
$191$	0.169619	−	0.0979296i	0.0122732	−	0.00708594i	−0.493851	−	0.869547i	$-0.664411\pi$
$191$	0.169619	−	0.0979296i	0.0122732	−	0.00708594i	0.506124	+	0.862461i	$0.331078\pi$
$192$		0			0
$193$	5.03614	−	8.72285i	0.362509	−	0.627884i	−0.625864	−	0.779932i	$-0.715254\pi$
$193$	5.03614	−	8.72285i	0.362509	−	0.627884i	0.988373	+	0.152048i	$0.0485868\pi$
$194$	−0.721781	−	0.429226i	−0.0518209	−	0.0308167i
$195$		0			0
$196$	3.25113	−	13.6173i	0.232224	−	0.972662i
$197$	−0.981430			−0.0699240			−0.0349620	−	0.999389i	$-0.511131\pi$
$197$	−0.981430			−0.0699240			−0.0349620	+	0.999389i	$0.511131\pi$
$198$		0			0
$199$	−1.90703	−	1.10102i	−0.135185	−	0.0780494i	0.430882	−	0.902408i	$-0.358203\pi$
$199$	−1.90703	−	1.10102i	−0.135185	−	0.0780494i	−0.566067	+	0.824359i	$0.691536\pi$
$200$	6.29981	−	9.99740i	0.445464	−	0.706923i
$201$		0			0
$202$	13.7519	−	7.70490i	0.967578	−	0.542115i
$203$	−25.3181	−	9.70606i	−1.77698	−	0.681232i
$204$		0			0
$205$	1.77658	−	1.02571i	0.124081	−	0.0716385i
$206$	−0.0298224	+	2.31218i	−0.00207783	+	0.161097i
$207$		0			0
$208$	13.3350	−	20.5688i	0.924615	−	1.42619i
$209$	0.614149			0.0424816
$210$		0			0
$211$			17.7696i			1.22331i	0.791125	+	0.611654i	$0.209496\pi$
$211$			17.7696i			1.22331i	−0.791125	+	0.611654i	$0.790504\pi$
$212$	7.47148	+	0.192766i	0.513144	+	0.0132392i
$213$		0			0
$214$	−20.1388	−	0.259749i	−1.37666	−	0.0177561i
$215$	3.96185	+	6.86213i	0.270196	+	0.467993i
$216$		0			0
$217$	6.82394	+	8.41937i	0.463239	+	0.571544i
$218$	8.37893	−	4.69455i	0.567493	−	0.317955i
$219$		0			0
$220$	−0.232419	+	0.126309i	−0.0156697	+	0.00851576i
$221$	−18.4113	+	31.8893i	−1.23848	+	2.14510i
$222$		0			0
$223$			20.7181i			1.38738i	0.720271	+	0.693692i	$0.244017\pi$
$223$			20.7181i			1.38738i	−0.720271	+	0.693692i	$0.755983\pi$
$224$	−1.39032	−	14.9019i	−0.0928946	−	0.995676i
$225$		0			0
$226$	−10.3828	−	6.17441i	−0.690653	−	0.410715i
$227$	17.3954	+	10.0432i	1.15457	+	0.666593i	0.949997	−	0.312258i	$-0.101085\pi$
$227$	17.3954	+	10.0432i	1.15457	+	0.666593i	0.204575	+	0.978851i	$0.434419\pi$
$228$		0			0
$229$	−9.68640	−	16.7773i	−0.640095	−	1.10868i	−0.985411	−	0.170191i	$-0.945562\pi$
$229$	−9.68640	−	16.7773i	−0.640095	−	1.10868i	0.345316	−	0.938487i	$-0.387772\pi$
$230$	−2.32006	−	4.14089i	−0.152980	−	0.273042i
$231$		0			0
$232$	−28.9653	−	1.12127i	−1.90166	−	0.0736152i
$233$	−22.4100	+	12.9384i	−1.46813	+	0.847625i	−0.999363	−	0.0356961i	$-0.988635\pi$
$233$	−22.4100	+	12.9384i	−1.46813	+	0.847625i	−0.468768	+	0.883322i	$0.655302\pi$
$234$		0			0
$235$	5.62684	+	3.24866i	0.367054	+	0.211919i
$236$	0.378285	−	14.6621i	0.0246243	−	0.954423i
$237$		0			0
$238$	3.24000	+	22.2475i	0.210018	+	1.44209i
$239$			11.2007i			0.724512i	0.932079	+	0.362256i	$0.117993\pi$
$239$			11.2007i			0.724512i	−0.932079	+	0.362256i	$0.882007\pi$
$240$		0			0
$241$	−23.6842	−	13.6741i	−1.52563	−	0.880825i	−0.999538	−	0.0303997i	$-0.990322\pi$
$241$	−23.6842	−	13.6741i	−1.52563	−	0.880825i	−0.526096	−	0.850425i	$-0.676345\pi$
$242$	15.5250	+	0.200240i	0.997983	+	0.0128719i
$243$		0			0
$244$	−7.12386	+	11.6352i	−0.456059	+	0.744865i
$245$	−6.20952	−	1.31423i	−0.396712	−	0.0839628i
$246$		0			0
$247$	12.9011	+	22.3453i	0.820875	+	1.42180i
$248$	9.80200	+	6.17668i	0.622428	+	0.392220i
$249$		0			0
$250$	−10.1153	−	6.01535i	−0.639749	−	0.380444i
$251$			29.0073i			1.83092i	0.402407	+	0.915461i	$0.368174\pi$
$251$			29.0073i			1.83092i	−0.402407	+	0.915461i	$0.631826\pi$
$252$		0			0
$253$		−	0.539939i		−	0.0339457i
$254$	−13.0816	+	21.9979i	−0.820814	+	1.38027i
$255$		0			0
$256$	−6.53032	−	14.6067i	−0.408145	−	0.912917i
$257$	6.02554	+	10.4365i	0.375863	+	0.651014i	0.990456	−	0.137831i	$-0.0440130\pi$
$257$	6.02554	+	10.4365i	0.375863	+	0.651014i	−0.614593	+	0.788845i	$0.710680\pi$
$258$		0			0
$259$	−7.60254	+	1.20752i	−0.472399	+	0.0750314i
$260$	−9.47794	−	5.80306i	−0.587797	−	0.359891i
$261$		0			0
$262$	−0.176583	+	13.6908i	−0.0109094	+	0.845822i
$263$	−2.36800	−	1.36716i	−0.146017	−	0.0843029i	0.425212	−	0.905094i	$-0.360200\pi$
$263$	−2.36800	−	1.36716i	−0.146017	−	0.0843029i	−0.571229	+	0.820791i	$0.693533\pi$
$264$		0			0
$265$		−	3.38842i		−	0.208149i
$266$	14.6357	+	5.82842i	0.897375	+	0.357363i
$267$		0			0
$268$	0.159021	−	6.16355i	0.00971373	−	0.376499i
$269$	4.45879	+	2.57428i	0.271857	+	0.156957i	0.629731	−	0.776813i	$-0.283165\pi$
$269$	4.45879	+	2.57428i	0.271857	+	0.156957i	−0.357874	+	0.933770i	$0.616498\pi$
$270$		0			0
$271$	21.0489	−	12.1526i	1.27863	−	0.738216i	0.302031	−	0.953298i	$-0.402335\pi$
$271$	21.0489	−	12.1526i	1.27863	−	0.738216i	0.976596	+	0.215082i	$0.0690020\pi$
$272$	10.9279	+	21.4064i	0.662602	+	1.29795i
$273$		0			0
$274$	12.9859	−	7.27575i	0.784508	−	0.439544i
$275$	−0.304706	−	0.527767i	−0.0183745	−	0.0318255i
$276$		0			0
$277$	−0.705869	−	0.407533i	−0.0424115	−	0.0244863i	0.478644	−	0.878009i	$-0.341128\pi$
$277$	−0.705869	−	0.407533i	−0.0424115	−	0.0244863i	−0.521056	+	0.853523i	$0.674462\pi$
$278$	−11.4319	+	19.2238i	−0.685641	+	1.15297i
$279$		0			0
$280$	−6.73746	+	0.804356i	−0.402640	+	0.0480695i
$281$		−	1.06599i		−	0.0635918i	−0.999494	−	0.0317959i	$-0.989877\pi$
$281$		−	1.06599i		−	0.0635918i	0.999494	−	0.0317959i	$-0.0101227\pi$
$282$		0			0
$283$	−3.14663	+	5.45012i	−0.187048	+	0.323976i	−0.944265	−	0.329187i	$-0.893225\pi$
$283$	−3.14663	+	5.45012i	−0.187048	+	0.323976i	0.757217	+	0.653164i	$0.226559\pi$
$284$	8.64312	−	4.69714i	0.512875	−	0.278724i
$285$		0			0
$286$	−0.617924	−	1.10288i	−0.0365386	−	0.0652149i
$287$	5.58922	+	2.14271i	0.329921	+	0.126480i
$288$		0			0
$289$	−9.55169	−	16.5440i	−0.561864	−	0.973177i
$290$	−0.169485	+	13.1405i	−0.00995252	+	0.771637i
$291$		0			0
$292$	0.159536	−	6.18351i	0.00933611	−	0.361862i
$293$		−	17.9687i		−	1.04974i	−0.851181	−	0.524872i	$-0.824113\pi$
$293$		−	17.9687i		−	1.04974i	0.851181	−	0.524872i	$-0.175887\pi$
$294$		0			0
$295$	−6.64946			−0.387147
$296$	−7.28064	+	3.83591i	−0.423179	+	0.222958i
$297$		0			0
$298$	−16.3992	−	0.211516i	−0.949982	−	0.0122528i
$299$	19.6452	−	11.3422i	1.13611	−	0.655936i
$300$		0			0
$301$	−8.27634	+	21.5887i	−0.477040	+	1.24435i
$302$	−10.7742	−	19.2299i	−0.619983	−	1.10656i
$303$		0			0
$304$	16.8189	+	0.868438i	0.964629	+	0.0498084i
$305$	5.35648	+	3.09257i	0.306711	+	0.177080i
$306$		0			0
$307$	−27.7008			−1.58097			−0.790485	−	0.612481i	$-0.790171\pi$
$307$	−27.7008			−1.58097			−0.790485	+	0.612481i	$0.790171\pi$
$308$	−0.713346	−	0.294792i	−0.0406467	−	0.0167973i
$309$		0			0
$310$	2.68473	−	4.51460i	0.152482	−	0.256412i
$311$	12.7971	−	22.1653i	0.725658	−	1.25688i	−0.233045	−	0.972466i	$-0.574869\pi$
$311$	12.7971	−	22.1653i	0.725658	−	1.25688i	0.958703	−	0.284410i	$-0.0917977\pi$
$312$		0			0
$313$	−14.9541	+	8.63375i	−0.845255	+	0.488008i	−0.859047	−	0.511897i	$-0.828943\pi$
$313$	−14.9541	+	8.63375i	−0.845255	+	0.488008i	0.0137920	+	0.999905i	$0.495610\pi$
$314$	9.21762	+	16.4518i	0.520180	+	0.928429i
$315$		0			0
$316$	−11.3150	+	18.4804i	−0.636520	+	1.03961i
$317$	−2.17346	−	3.76454i	−0.122074	−	0.211438i	0.798512	−	0.601979i	$-0.205621\pi$
$317$	−2.17346	−	3.76454i	−0.122074	−	0.211438i	−0.920585	+	0.390542i	$0.872288\pi$
$318$		0			0
$319$	−0.747457	+	1.29463i	−0.0418495	+	0.0724855i
$320$	−6.54355	+	3.13041i	−0.365796	+	0.174995i
$321$		0			0
$322$	5.12415	−	12.8673i	0.285558	−	0.717064i
$323$	−25.2982			−1.40763
$324$		0			0
$325$	12.8016	−	22.1730i	0.710103	−	1.22993i
$326$	0.311459	−	24.1479i	0.0172501	−	1.33743i
$327$		0			0
$328$	6.39437	+	0.247532i	0.353070	+	0.0136677i
$329$	2.97393	+	18.7239i	0.163958	+	1.03228i
$330$		0			0
$331$	−15.0111	+	8.66665i	−0.825084	+	0.476362i	−0.852166	−	0.523271i	$-0.824712\pi$
$331$	−15.0111	+	8.66665i	−0.825084	+	0.476362i	0.0270828	+	0.999633i	$0.491378\pi$
$332$	−22.5869	+	12.2750i	−1.23962	+	0.673677i
$333$		0			0
$334$	1.18924	−	1.99981i	0.0650725	−	0.109425i
$335$	−2.79525			−0.152721
$336$		0			0
$337$	−0.659592			−0.0359303			−0.0179651	−	0.999839i	$-0.505719\pi$
$337$	−0.659592			−0.0359303			−0.0179651	+	0.999839i	$0.505719\pi$
$338$	17.7502	−	29.8485i	0.965483	−	1.62354i
$339$		0			0
$340$	9.57386	−	5.20296i	0.519215	−	0.282170i
$341$	0.517452	−	0.298751i	0.0280216	−	0.0161783i
$342$		0			0
$343$	−8.42956	−	16.4907i	−0.455154	−	0.890413i
$344$	−0.956108	+	24.6986i	−0.0515499	+	1.33166i
$345$		0			0
$346$	−0.164451	+	12.7502i	−0.00884095	+	0.685454i
$347$	−3.49897	+	6.06039i	−0.187834	+	0.325339i	−0.944528	−	0.328431i	$-0.893480\pi$
$347$	−3.49897	+	6.06039i	−0.187834	+	0.325339i	0.756694	+	0.653770i	$0.226813\pi$
$348$		0			0
$349$	20.2632			1.08467			0.542333	−	0.840164i	$-0.317541\pi$
$349$	20.2632			1.08467			0.542333	+	0.840164i	$0.317541\pi$
$350$	−2.25280	−	15.4689i	−0.120417	−	0.826848i
$351$		0			0
$352$	−0.823436	−	0.0531739i	−0.0438893	−	0.00283418i
$353$	5.18465	−	8.98008i	0.275951	−	0.477962i	−0.694423	−	0.719567i	$-0.744341\pi$
$353$	5.18465	−	8.98008i	0.275951	−	0.477962i	0.970375	+	0.241605i	$0.0776738\pi$
$354$		0			0
$355$	−2.22986	−	3.86224i	−0.118349	−	0.204986i
$356$	−3.25224	+	5.31177i	−0.172368	+	0.281523i
$357$		0			0
$358$	10.1020	+	18.0302i	0.533905	+	0.952926i
$359$	17.5691	−	10.1436i	0.927264	−	0.535356i	0.0413188	−	0.999146i	$-0.486844\pi$
$359$	17.5691	−	10.1436i	0.927264	−	0.535356i	0.885945	+	0.463790i	$0.153511\pi$
$360$		0			0
$361$	0.636589	−	1.10261i	0.0335047	−	0.0580319i
$362$	−0.143453	+	0.241228i	−0.00753970	+	0.0126787i
$363$		0			0
$364$	−4.25908	−	32.1470i	−0.223236	−	1.68496i
$365$	−2.80430			−0.146784
$366$		0			0
$367$	21.6024	+	12.4722i	1.12764	+	0.651042i	0.943340	−	0.331829i	$-0.107666\pi$
$367$	21.6024	+	12.4722i	1.12764	+	0.651042i	0.184298	+	0.982870i	$0.440999\pi$
$368$	0.763502	−	14.7866i	0.0398003	−	0.770805i
$369$		0			0
$370$	1.82361	+	3.25482i	0.0948050	+	0.169210i
$371$	7.68104	−	6.22552i	0.398780	−	0.323213i
$372$		0			0
$373$	4.26886	−	2.46463i	0.221033	−	0.127614i	−0.385395	−	0.922752i	$-0.625935\pi$
$373$	4.26886	−	2.46463i	0.221033	−	0.127614i	0.606429	+	0.795138i	$0.292602\pi$
$374$	1.23940	+	0.0159857i	0.0640878	+	0.000826601i
$375$		0			0
$376$	9.44728	+	17.9312i	0.487206	+	0.924729i
$377$	−62.8055			−3.23465
$378$		0			0
$379$		−	25.1007i		−	1.28934i	−0.764462	−	0.644669i	$-0.776995\pi$
$379$		−	25.1007i		−	1.28934i	0.764462	−	0.644669i	$-0.223005\pi$
$380$	0.196924	−	7.63267i	0.0101020	−	0.391548i
$381$		0			0
$382$	0.00357226	−	0.276964i	0.000182773	−	0.0141707i
$383$	−14.0619	−	24.3560i	−0.718531	−	1.24453i	−0.961582	−	0.274519i	$-0.911482\pi$
$383$	−14.0619	−	24.3560i	−0.718531	−	1.24453i	0.243051	−	0.970014i	$-0.421852\pi$
$384$		0			0
$385$	−0.125262	+	0.326744i	−0.00638394	+	0.0166524i
$386$	−6.96249	−	12.4268i	−0.354381	−	0.632507i
$387$		0			0
$388$	−1.04347	+	0.567079i	−0.0529741	+	0.0287891i
$389$	3.82681	−	6.62822i	0.194027	−	0.336064i	−0.752554	−	0.658530i	$-0.771178\pi$
$389$	3.82681	−	6.62822i	0.194027	−	0.336064i	0.946581	+	0.322466i	$0.104512\pi$
$390$		0			0
$391$			22.2413i			1.12479i
$392$	−14.2021	−	13.7950i	−0.717312	−	0.696752i
$393$		0			0
$394$	−0.709420	+	1.19295i	−0.0357401	+	0.0601000i
$395$	8.50785	+	4.91201i	0.428076	+	0.247150i
$396$		0			0
$397$	−6.22748	−	10.7863i	−0.312548	−	0.541350i	0.666365	−	0.745626i	$-0.267849\pi$
$397$	−6.22748	−	10.7863i	−0.312548	−	0.541350i	−0.978913	+	0.204276i	$0.934516\pi$
$398$	−2.71680	+	1.52217i	−0.136181	+	0.0762994i
$399$		0			0
$400$	−7.59830	−	14.8841i	−0.379915	−	0.744206i
$401$	18.1682	−	10.4894i	0.907279	−	0.523818i	0.0277241	−	0.999616i	$-0.491174\pi$
$401$	18.1682	−	10.4894i	0.907279	−	0.523818i	0.879555	+	0.475798i	$0.157841\pi$
$402$		0			0
$403$	21.7396	+	12.5514i	1.08293	+	0.625228i
$404$	0.574961	−	22.2852i	0.0286054	−	1.10873i
$405$		0			0
$406$	−30.0990	+	23.7588i	−1.49379	+	1.17913i
$407$			0.424403i			0.0210369i
$408$		0			0
$409$	0.456865	+	0.263771i	0.0225905	+	0.0130426i	0.511253	−	0.859430i	$-0.329182\pi$
$409$	0.456865	+	0.263771i	0.0225905	+	0.0130426i	−0.488662	+	0.872473i	$0.662515\pi$
$410$	0.0374156	−	2.90090i	0.00184782	−	0.143265i
$411$		0			0
$412$	2.78896	+	1.70760i	0.137402	+	0.0841272i
$413$	−12.2170	−	15.0733i	−0.601160	−	0.741711i
$414$		0			0
$415$	5.82727	+	10.0931i	0.286049	+	0.495452i
$416$	−15.3627	−	31.0770i	−0.753220	−	1.52368i
$417$		0			0
$418$	0.443934	−	0.746513i	0.0217135	−	0.0365131i
$419$		−	22.0482i		−	1.07713i	−0.842585	−	0.538564i	$-0.818967\pi$
$419$		−	22.0482i		−	1.07713i	0.842585	−	0.538564i	$-0.181033\pi$
$420$		0			0
$421$			18.2360i			0.888771i	0.895836	+	0.444385i	$0.146578\pi$
$421$			18.2360i			0.888771i	−0.895836	+	0.444385i	$0.853422\pi$
$422$	21.5993	+	12.8446i	1.05144	+	0.625267i
$423$		0			0
$424$	5.63502	−	8.94242i	0.273661	−	0.434283i
$425$	12.5515	+	21.7399i	0.608839	+	1.05454i
$426$		0			0
$427$	2.83105	+	17.8243i	0.137004	+	0.862579i
$428$	−14.8729	+	24.2914i	−0.718910	+	1.17417i
$429$		0			0
$430$	11.2049	+	0.144520i	0.540347	+	0.00696937i
$431$	24.8419	+	14.3425i	1.19659	+	0.690854i	0.959794	−	0.280705i	$-0.0905683\pi$
$431$	24.8419	+	14.3425i	1.19659	+	0.690854i	0.236799	+	0.971559i	$0.423902\pi$
$432$		0			0
$433$		−	37.7023i		−	1.81186i	−0.423429	−	0.905929i	$-0.639174\pi$
$433$		−	37.7023i		−	1.81186i	0.423429	−	0.905929i	$-0.360826\pi$
$434$	15.1666	−	2.20877i	0.728019	−	0.106025i
$435$		0			0
$436$	0.350320	−	13.5782i	0.0167773	−	0.650278i
$437$	13.4969	+	7.79242i	0.645642	+	0.372762i
$438$		0			0
$439$	−7.68790	+	4.43861i	−0.366924	+	0.211843i	−0.672114	−	0.740448i	$-0.734613\pi$
$439$	−7.68790	+	4.43861i	−0.366924	+	0.211843i	0.305190	+	0.952291i	$0.401280\pi$
$440$	−0.0144706	+	0.373812i	−0.000689861	+	0.0178208i
$441$		0			0
$442$	25.4537	+	45.4303i	1.21071	+	2.16090i
$443$	0.209480	+	0.362830i	0.00995270	+	0.0172386i	0.870959	−	0.491356i	$-0.163499\pi$
$443$	0.209480	+	0.362830i	0.00995270	+	0.0172386i	−0.861006	+	0.508595i	$0.830165\pi$
$444$		0			0
$445$	2.44538	+	1.41184i	0.115922	+	0.0669278i
$446$	25.1833	+	14.9759i	1.19246	+	0.709130i
$447$		0			0
$448$	−19.1186	−	9.08178i	−0.903269	−	0.429074i
$449$		−	39.4411i		−	1.86134i	−0.365861	−	0.930670i	$-0.619225\pi$
$449$		−	39.4411i		−	1.86134i	0.365861	−	0.930670i	$-0.380775\pi$
$450$		0			0
$451$	0.165008	−	0.285803i	0.00776994	−	0.0134579i
$452$	−15.0103	+	8.15741i	−0.706024	+	0.383692i
$453$		0			0
$454$	24.7819	−	13.8848i	1.16307	−	0.651647i
$455$	−14.5196	+	2.30616i	−0.680689	+	0.108114i
$456$		0			0
$457$	−5.94479	−	10.2967i	−0.278085	−	0.481658i	0.692823	−	0.721107i	$-0.256367\pi$
$457$	−5.94479	−	10.2967i	−0.278085	−	0.481658i	−0.970909	+	0.239449i	$0.923033\pi$
$458$	−27.3950	−	0.353339i	−1.28008	−	0.0165104i
$459$		0			0
$460$	−6.71039	−	0.173129i	−0.312873	−	0.00807219i
$461$		−	0.217896i		−	0.0101484i	−0.999987	−	0.00507422i	$-0.998385\pi$
$461$		−	0.217896i		−	0.0101484i	0.999987	−	0.00507422i	$-0.00161518\pi$
$462$		0			0
$463$	−9.13271			−0.424433			−0.212216	−	0.977223i	$-0.568068\pi$
$463$	−9.13271			−0.424433			−0.212216	+	0.977223i	$0.568068\pi$
$464$	−22.3003	+	34.3974i	−1.03526	+	1.59686i
$465$		0			0
$466$	−0.471967	+	36.5924i	−0.0218634	+	1.69511i
$467$	23.4188	−	13.5208i	1.08369	−	0.625670i	0.151802	−	0.988411i	$-0.451492\pi$
$467$	23.4188	−	13.5208i	1.08369	−	0.625670i	0.931890	+	0.362741i	$0.118159\pi$
$468$		0			0
$469$	−5.13570	−	6.33642i	−0.237145	−	0.292589i
$470$	8.01614	−	4.49128i	0.369757	−	0.207167i
$471$		0			0
$472$	−17.5487	−	11.0582i	−0.807745	−	0.508996i
$473$	1.10393	+	0.637355i	0.0507588	+	0.0293056i
$474$		0			0
$475$	17.5901			0.807089
$476$	29.3843	+	12.1431i	1.34683	+	0.556580i
$477$		0			0
$478$	13.6147	+	8.09634i	0.622722	+	0.370318i
$479$	5.06539	−	8.77352i	0.231444	−	0.400872i	−0.726789	−	0.686860i	$-0.758988\pi$
$479$	5.06539	−	8.77352i	0.231444	−	0.400872i	0.958233	+	0.285988i	$0.0923218\pi$
$480$		0			0
$481$	−15.4415	+	8.91517i	−0.704073	+	0.406497i
$482$	−33.7411	+	18.9045i	−1.53687	+	0.861076i
$483$		0			0
$484$	11.4655	−	18.7262i	0.521160	−	0.851192i
$485$	0.269208	+	0.466281i	0.0122241	+	0.0211728i
$486$		0			0
$487$	5.08735	−	8.81155i	0.230530	−	0.399290i	−0.727434	−	0.686177i	$-0.759287\pi$
$487$	5.08735	−	8.81155i	0.230530	−	0.399290i	0.957964	+	0.286888i	$0.0926207\pi$
$488$	8.99337	+	17.0696i	0.407111	+	0.772705i
$489$		0			0
$490$	−6.08598	+	6.59784i	−0.274937	+	0.298060i
$491$	24.6642			1.11308			0.556540	−	0.830821i	$-0.312129\pi$
$491$	24.6642			1.11308			0.556540	+	0.830821i	$0.312129\pi$
$492$		0			0
$493$	30.7894	−	53.3288i	1.38669	−	2.40181i
$494$	36.4867	+	0.470603i	1.64161	+	0.0211734i
$495$		0			0
$496$	14.5932	−	7.44979i	0.655255	−	0.334506i
$497$	4.65820	−	12.1508i	0.208949	−	0.545039i
$498$		0			0
$499$	−12.8103	+	7.39603i	−0.573468	+	0.331092i	−0.758533	−	0.651634i	$-0.774084\pi$
$499$	−12.8103	+	7.39603i	−0.573468	+	0.331092i	0.185065	+	0.982726i	$0.440750\pi$
$500$	−14.6236	+	7.94726i	−0.653987	+	0.355412i
$501$		0			0
$502$	35.2590	+	20.9677i	1.57369	+	0.935834i
$503$	34.7978			1.55156			0.775778	−	0.631006i	$-0.217358\pi$
$503$	34.7978			1.55156			0.775778	+	0.631006i	$0.217358\pi$
$504$		0			0
$505$	−10.1066			−0.449738
$506$	−0.656309	−	0.390292i	−0.0291765	−	0.0173506i
$507$		0			0
$508$	17.2830	+	31.8020i	0.766808	+	1.41099i
$509$	30.0509	−	17.3499i	1.33198	−	0.769021i	0.346381	−	0.938094i	$-0.387411\pi$
$509$	30.0509	−	17.3499i	1.33198	−	0.769021i	0.985604	+	0.169073i	$0.0540772\pi$
$510$		0			0
$511$	−5.15233	−	6.35693i	−0.227926	−	0.281214i
$512$	−22.4752	−	2.62058i	−0.993271	−	0.115815i
$513$		0			0
$514$	17.0414	+	0.219799i	0.751664	+	0.00969491i
$515$	0.741291	−	1.28395i	0.0326652	−	0.0565778i
$516$		0			0
$517$	1.04524			0.0459697
$518$	−4.02768	+	10.1139i	−0.176966	+	0.444380i
$519$		0			0
$520$	−13.9048	+	7.32595i	−0.609767	+	0.321264i
$521$	−19.9658	+	34.5818i	−0.874718	+	1.51506i	−0.0176549	+	0.999844i	$0.505620\pi$
$521$	−19.9658	+	34.5818i	−0.874718	+	1.51506i	−0.857063	+	0.515212i	$0.827713\pi$
$522$		0			0
$523$	3.77245	+	6.53407i	0.164958	+	0.285715i	0.936640	−	0.350293i	$-0.113918\pi$
$523$	3.77245	+	6.53407i	0.164958	+	0.285715i	−0.771683	+	0.636008i	$0.780585\pi$
$524$	16.5139	+	10.1110i	0.721412	+	0.441699i
$525$		0			0
$526$	−3.37351	+	1.89011i	−0.147092	+	0.0824127i
$527$	−21.3150	+	12.3062i	−0.928496	+	0.536068i
$528$		0			0
$529$	−4.64917	+	8.05259i	−0.202138	+	0.350113i
$530$	−4.11870	−	2.44929i	−0.178905	−	0.106391i
$531$		0			0
$532$	17.6639	−	13.5771i	0.765829	−	0.588640i
$533$	13.8649			0.600557
$534$		0			0
$535$	11.1831	+	6.45655i	0.483486	+	0.279141i
$536$	−7.37699	−	4.64858i	−0.318638	−	0.200788i
$537$		0			0
$538$	6.35210	−	3.55896i	0.273859	−	0.153438i
$539$	−0.970822	+	0.316374i	−0.0418163	+	0.0136272i
$540$		0			0
$541$	14.8073	−	8.54900i	0.636616	−	0.367550i	−0.146694	−	0.989182i	$-0.546863\pi$
$541$	14.8073	−	8.54900i	0.636616	−	0.367550i	0.783310	+	0.621632i	$0.213530\pi$
$542$	0.443299	−	34.3698i	0.0190413	−	1.47631i
$543$		0			0
$544$	33.9192	+	2.19035i	1.45427	+	0.0939106i
$545$	−6.15790			−0.263775
$546$		0			0
$547$		−	26.4723i		−	1.13187i	−0.824449	−	0.565936i	$-0.808515\pi$
$547$		−	26.4723i		−	1.13187i	0.824449	−	0.565936i	$-0.191485\pi$
$548$	0.542937	−	21.0439i	0.0231931	−	0.898952i
$549$		0			0
$550$	−0.861768	−	0.0111150i	−0.0367459	−	0.000473946i
$551$	−21.5746	−	37.3683i	−0.919109	−	1.59194i
$552$		0			0
$553$	4.49663	+	28.3108i	0.191216	+	1.20390i
$554$	−1.00560	+	0.563417i	−0.0427238	+	0.0239373i
$555$		0			0
$556$	15.1035	+	27.7916i	0.640529	+	1.17862i
$557$	21.9010	−	37.9337i	0.927976	−	1.60730i	0.141273	−	0.989971i	$-0.454881\pi$
$557$	21.9010	−	37.9337i	0.927976	−	1.60730i	0.786703	−	0.617331i	$-0.211786\pi$
$558$		0			0
$559$			53.5541i			2.26510i
$560$	−3.89242	+	8.77097i	−0.164485	+	0.370641i
$561$		0			0
$562$	−1.29574	−	0.770546i	−0.0546575	−	0.0325035i
$563$	30.7646	+	17.7620i	1.29657	+	0.748578i	0.979811	−	0.199927i	$-0.0640705\pi$
$563$	30.7646	+	17.7620i	1.29657	+	0.748578i	0.316764	+	0.948505i	$0.397404\pi$
$564$		0			0
$565$	3.87254	+	6.70744i	0.162919	+	0.282184i
$566$	4.35023	+	7.76439i	0.182854	+	0.326362i
$567$		0			0
$568$	0.538130	−	13.9012i	0.0225794	−	0.583282i
$569$	−22.4782	+	12.9778i	−0.942334	+	0.544057i	−0.890691	−	0.454609i	$-0.849779\pi$
$569$	−22.4782	+	12.9778i	−0.942334	+	0.544057i	−0.0516428	+	0.998666i	$0.516446\pi$
$570$		0			0
$571$	−13.6202	−	7.86364i	−0.569989	−	0.329083i	0.187156	−	0.982330i	$-0.440073\pi$
$571$	−13.6202	−	7.86364i	−0.569989	−	0.329083i	−0.757145	+	0.653247i	$0.773406\pi$
$572$	−1.78724	−	0.0461112i	−0.0747284	−	0.00192801i
$573$		0			0
$574$	6.64464	−	5.24498i	0.277342	−	0.218921i
$575$		−	15.4646i		−	0.644920i
$576$		0			0
$577$	−31.0772	−	17.9424i	−1.29376	−	0.746953i	−0.314441	−	0.949277i	$-0.601817\pi$
$577$	−31.0772	−	17.9424i	−1.29376	−	0.746953i	−0.979319	+	0.202324i	$0.935150\pi$
$578$	−27.0140	−	0.348425i	−1.12363	−	0.0144926i
$579$		0			0
$580$	15.8501	+	9.70453i	0.658138	+	0.402959i
$581$	−12.1732	+	31.7536i	−0.505030	+	1.31736i
$582$		0			0
$583$	−0.272552	−	0.472074i	−0.0112880	−	0.0195513i
$584$	−7.40088	−	4.66363i	−0.306251	−	0.192982i
$585$		0			0
$586$	−21.8414	−	12.9886i	−0.902259	−	0.536552i
$587$			3.78446i			0.156201i	0.996945	+	0.0781007i	$0.0248856\pi$
$587$			3.78446i			0.156201i	−0.996945	+	0.0781007i	$0.975114\pi$
$588$		0			0
$589$			17.2463i			0.710622i
$590$	−4.80652	+	8.08258i	−0.197881	+	0.332755i
$591$		0			0
$592$	−0.600127	+	11.6226i	−0.0246651	+	0.477684i
$593$	−11.6115	−	20.1117i	−0.476826	−	0.825887i	0.522821	−	0.852442i	$-0.324880\pi$
$593$	−11.6115	−	20.1117i	−0.476826	−	0.825887i	−0.999647	+	0.0265552i	$0.991546\pi$
$594$		0			0
$595$	5.15982	−	13.4593i	0.211532	−	0.551778i
$596$	−12.1112	+	19.7808i	−0.496093	+	0.810252i
$597$		0			0
$598$	0.413739	−	32.0779i	0.0169190	−	1.31176i
$599$	−13.4585	−	7.77024i	−0.549898	−	0.317484i	0.199183	−	0.979962i	$-0.436171\pi$
$599$	−13.4585	−	7.77024i	−0.549898	−	0.317484i	−0.749081	+	0.662479i	$0.769504\pi$
$600$		0			0
$601$		−	23.5188i		−	0.959354i	−0.877445	−	0.479677i	$-0.840754\pi$
$601$		−	23.5188i		−	0.959354i	0.877445	−	0.479677i	$-0.159246\pi$
$602$	20.2591	+	25.6653i	0.825697	+	1.04604i
$603$		0			0
$604$	−31.1625	−	0.803997i	−1.26798	−	0.0327142i
$605$	−8.62100	−	4.97734i	−0.350494	−	0.202358i
$606$		0			0
$607$	29.9332	−	17.2819i	1.21495	−	0.701452i	0.251117	−	0.967957i	$-0.419202\pi$
$607$	29.9332	−	17.2819i	1.21495	−	0.701452i	0.963834	+	0.266505i	$0.0858687\pi$
$608$	13.2130	−	19.8160i	0.535859	−	0.803645i
$609$		0			0
$610$	7.63099	−	4.27549i	0.308970	−	0.173110i
$611$	21.9568	+	38.0302i	0.888275	+	1.53854i
$612$		0			0
$613$	7.20869	+	4.16194i	0.291156	+	0.168099i	0.638463	−	0.769652i	$-0.279570\pi$
$613$	7.20869	+	4.16194i	0.291156	+	0.168099i	−0.347307	+	0.937752i	$0.612904\pi$
$614$	−20.0234	+	33.6710i	−0.808077	+	1.35885i
$615$		0			0
$616$	−0.873964	+	0.654000i	−0.0352130	+	0.0263504i
$617$			9.28453i			0.373781i	0.982381	+	0.186891i	$0.0598410\pi$
$617$			9.28453i			0.373781i	−0.982381	+	0.186891i	$0.940159\pi$
$618$		0			0
$619$	12.0804	−	20.9238i	0.485551	−	0.840999i	−0.514311	−	0.857604i	$-0.671952\pi$
$619$	12.0804	−	20.9238i	0.485551	−	0.840999i	0.999862	+	0.0166047i	$0.00528567\pi$
$620$	−3.54697	−	6.52670i	−0.142450	−	0.262119i
$621$		0			0
$622$	−17.6921	−	31.5772i	−0.709388	−	1.26613i
$623$	1.29245	+	8.13729i	0.0517810	+	0.326014i
$624$		0			0
$625$	−6.67184	−	11.5560i	−0.266874	−	0.462239i
$626$	−0.314941	+	24.4179i	−0.0125876	+	0.975935i
$627$		0			0
$628$	26.6604	+	0.687844i	1.06387	+	0.0274480i
$629$		−	17.4821i		−	0.697057i
$630$		0			0
$631$	−10.8391			−0.431498			−0.215749	−	0.976449i	$-0.569219\pi$
$631$	−10.8391			−0.431498			−0.215749	+	0.976449i	$0.569219\pi$
$632$	14.2844	+	27.1121i	0.568203	+	1.07846i
$633$		0			0
$634$	−6.14696	−	0.0792831i	−0.244127	−	0.00314873i
$635$	14.2110	−	8.20470i	0.563944	−	0.325593i
$636$		0			0
$637$	−31.9045	−	28.6767i	−1.26410	−	1.13621i
$638$	1.03336	+	1.84437i	0.0409112	+	0.0730192i
$639$		0			0
$640$	−0.924878	+	10.2166i	−0.0365590	+	0.403848i
$641$	32.0492	+	18.5036i	1.26587	+	0.730849i	0.974203	−	0.225672i	$-0.0724576\pi$
$641$	32.0492	+	18.5036i	1.26587	+	0.730849i	0.291664	+	0.956521i	$0.405791\pi$
$642$		0			0
$643$	−24.9620			−0.984405			−0.492203	−	0.870481i	$-0.663808\pi$
$643$	−24.9620			−0.984405			−0.492203	+	0.870481i	$0.663808\pi$
$644$	−11.9365	−	15.5295i	−0.470364	−	0.611950i
$645$		0			0
$646$	−18.2866	+	30.7505i	−0.719478	+	1.20986i
$647$	15.6875	−	27.1715i	0.616738	−	1.06822i	−0.373339	−	0.927695i	$-0.621787\pi$
$647$	15.6875	−	27.1715i	0.616738	−	1.06822i	0.990077	−	0.140527i	$-0.0448797\pi$
$648$		0			0
$649$	−0.926404	+	0.534859i	−0.0363645	+	0.0209951i
$650$	−17.6982	−	31.5882i	−0.694182	−	1.23899i
$651$		0			0
$652$	−29.1273	−	17.8338i	−1.14071	−	0.698424i
$653$	−3.95300	−	6.84679i	−0.154693	−	0.267936i	0.778254	−	0.627949i	$-0.216105\pi$
$653$	−3.95300	−	6.84679i	−0.154693	−	0.267936i	−0.932947	+	0.360014i	$0.882772\pi$
$654$		0			0
$655$	4.38931	−	7.60250i	0.171504	−	0.297054i
$656$	4.92301	−	7.59358i	0.192211	−	0.296479i
$657$		0			0
$658$	24.9091	+	9.91959i	0.971057	+	0.386706i
$659$	−32.9121			−1.28207			−0.641036	−	0.767510i	$-0.721495\pi$
$659$	−32.9121			−1.28207			−0.641036	+	0.767510i	$0.721495\pi$
$660$		0			0
$661$	−2.37104	+	4.10677i	−0.0922230	+	0.159735i	−0.908446	−	0.418002i	$-0.862731\pi$
$661$	−2.37104	+	4.10677i	−0.0922230	+	0.159735i	0.816223	+	0.577737i	$0.196064\pi$
$662$	−0.316141	+	24.5110i	−0.0122872	+	0.952645i
$663$		0			0
$664$	−1.40629	+	36.3278i	−0.0545745	+	1.40979i
$665$	−6.35982	−	7.84674i	−0.246623	−	0.304284i
$666$		0			0
$667$	−32.8530	+	18.9677i	−1.27207	+	0.734432i
$668$	−1.57119	−	2.89111i	−0.0607910	−	0.111860i
$669$		0			0
$670$	−2.02053	+	3.39769i	−0.0780598	+	0.131264i
$671$	0.995021			0.0384124
$672$		0			0
$673$	12.7891			0.492983			0.246492	−	0.969145i	$-0.420722\pi$
$673$	12.7891			0.492983			0.246492	+	0.969145i	$0.420722\pi$
$674$	−0.476782	+	0.801750i	−0.0183650	+	0.0308823i
$675$		0			0
$676$	−23.4509	−	43.1515i	−0.901958	−	1.65967i
$677$	−19.9765	+	11.5334i	−0.767759	+	0.443266i	−0.832075	−	0.554664i	$-0.812847\pi$
$677$	−19.9765	+	11.5334i	−0.767759	+	0.443266i	0.0643155	+	0.997930i	$0.479514\pi$
$678$		0			0
$679$	−0.562377	+	1.46695i	−0.0215820	+	0.0562964i
$680$	0.596079	−	15.3982i	0.0228586	−	0.590493i
$681$		0			0
$682$	0.0108978	−	0.844925i	0.000417298	−	0.0323539i
$683$	−3.40643	+	5.90011i	−0.130343	+	0.225761i	−0.923809	−	0.382854i	$-0.874941\pi$
$683$	−3.40643	+	5.90011i	−0.130343	+	0.225761i	0.793466	+	0.608615i	$0.208275\pi$
$684$		0			0
$685$	−9.54370			−0.364646
$686$	−26.1381	−	1.67385i	−0.997956	−	0.0639078i
$687$		0			0
$688$	29.3306	+	19.0154i	1.11822	+	0.724955i
$689$	11.4507	−	19.8332i	0.436236	−	0.755583i
$690$		0			0
$691$	14.9637	+	25.9178i	0.569245	+	0.985961i	0.996641	+	0.0818962i	$0.0260976\pi$
$691$	14.9637	+	25.9178i	0.569245	+	0.985961i	−0.427396	+	0.904064i	$0.640569\pi$
$692$	15.3793	+	9.41628i	0.584633	+	0.357953i
$693$		0			0
$694$	4.83734	+	8.63379i	0.183623	+	0.327734i
$695$	12.4188	−	7.17002i	0.471074	−	0.271975i
$696$		0			0
$697$	−6.79707	+	11.7729i	−0.257457	+	0.445929i
$698$	14.6471	−	24.6304i	0.554402	−	0.932275i
$699$		0			0
$700$	−20.4312	−	8.44326i	−0.772228	−	0.319125i
$701$	18.0414			0.681415			0.340707	−	0.940169i	$-0.389333\pi$
$701$	18.0414			0.681415			0.340707	+	0.940169i	$0.389333\pi$
$702$		0			0
$703$	−10.6088	−	6.12499i	−0.400118	−	0.231008i
$704$	−0.659849	+	0.962469i	−0.0248690	+	0.0362744i
$705$		0			0
$706$	−7.16781	−	12.7933i	−0.269764	−	0.481481i
$707$	−18.5688	−	22.9102i	−0.698353	−	0.861627i
$708$		0			0
$709$	−29.1885	+	16.8520i	−1.09620	+	0.632889i	−0.935219	−	0.354069i	$-0.884798\pi$
$709$	−29.1885	+	16.8520i	−1.09620	+	0.632889i	−0.160977	+	0.986958i	$0.551464\pi$
$710$	−6.30648	−	0.0813406i	−0.236678	−	0.00305266i
$711$		0			0
$712$	4.10572	+	7.79275i	0.153868	+	0.292046i
$713$	15.1624			0.567836
$714$		0			0
$715$			0.810539i			0.0303124i
$716$	29.2183	+	0.753836i	1.09194	+	0.0281722i
$717$		0			0
$718$	0.370015	−	28.6879i	0.0138088	−	1.07062i
$719$	24.8458	+	43.0342i	0.926592	+	1.60490i	0.788981	+	0.614418i	$0.210609\pi$
$719$	24.8458	+	43.0342i	0.926592	+	1.60490i	0.137611	+	0.990486i	$0.456058\pi$
$720$		0			0
$721$	4.27250	−	0.678604i	0.159116	−	0.0252725i
$722$	−0.880088	−	1.57080i	−0.0327535	−	0.0584591i
$723$		0			0
$724$	0.189525	+	0.348740i	0.00704362	+	0.0129608i
$725$	−21.4082	+	37.0801i	−0.795081	+	1.37712i
$726$		0			0
$727$		−	5.49208i		−	0.203690i	−0.994800	−	0.101845i	$-0.967525\pi$
$727$		−	5.49208i		−	0.203690i	0.994800	−	0.101845i	$-0.0324746\pi$
$728$	−42.1541	−	18.0602i	−1.56233	−	0.669357i
$729$		0			0
$730$	−2.02707	+	3.40869i	−0.0750252	+	0.126161i
$731$	−45.4734	−	26.2541i	−1.68189	−	0.971042i
$732$		0			0
$733$	−0.176068	−	0.304959i	−0.00650322	−	0.0112639i	0.862755	−	0.505621i	$-0.168737\pi$
$733$	−0.176068	−	0.304959i	−0.00650322	−	0.0112639i	−0.869259	+	0.494357i	$0.835403\pi$
$734$	30.7754	−	17.2428i	1.13594	−	0.636445i
$735$		0			0
$736$	−17.4216	−	11.6165i	−0.642168	−	0.428188i
$737$	−0.389435	+	0.224840i	−0.0143450	+	0.00828209i
$738$		0			0
$739$	13.2521	+	7.65108i	0.487485	+	0.281450i	0.723531	−	0.690292i	$-0.242518\pi$
$739$	13.2521	+	7.65108i	0.487485	+	0.281450i	−0.236045	+	0.971742i	$0.575851\pi$
$740$	5.27449	+	0.136083i	0.193894	+	0.00500250i
$741$		0			0
$742$	−2.01508	−	13.8366i	−0.0739758	−	0.507956i
$743$			41.8196i			1.53421i	0.641520	+	0.767106i	$0.278304\pi$
$743$			41.8196i			1.53421i	−0.641520	+	0.767106i	$0.721696\pi$
$744$		0			0
$745$	9.10648	+	5.25763i	0.333636	+	0.192625i
$746$	0.0899043	−	6.97044i	0.00329163	−	0.255206i
$747$		0			0
$748$	0.915322	−	1.49496i	0.0334675	−	0.0546613i
$749$	5.91055	+	37.2129i	0.215967	+	1.35973i
$750$		0			0
$751$	0.457654	+	0.792680i	0.0167000	+	0.0289253i	0.874255	−	0.485468i	$-0.161351\pi$
$751$	0.457654	+	0.792680i	0.0167000	+	0.0289253i	−0.857555	+	0.514393i	$0.828017\pi$
$752$	28.6246	+	1.47803i	1.04383	+	0.0538980i
$753$		0			0
$754$	−45.3985	+	76.3415i	−1.65332	+	2.78020i
$755$			14.1326i			0.514338i
$756$		0			0
$757$		−	20.2296i		−	0.735257i	−0.929973	−	0.367628i	$-0.880170\pi$
$757$		−	20.2296i		−	0.735257i	0.929973	−	0.367628i	$-0.119830\pi$
$758$	−30.5105	−	18.1439i	−1.10819	−	0.659016i
$759$		0			0
$760$	−9.13534	−	5.75659i	−0.331374	−	0.208813i
$761$	5.53329	+	9.58394i	0.200582	+	0.347417i	0.948716	−	0.316130i	$-0.102384\pi$
$761$	5.53329	+	9.58394i	0.200582	+	0.347417i	−0.748134	+	0.663547i	$0.769050\pi$
$762$		0			0
$763$	−11.3139	−	13.9590i	−0.409590	−	0.505351i
$764$	−0.334074	−	0.204544i	−0.0120864	−	0.00740012i
$765$		0			0
$766$	−39.7698	−	0.512949i	−1.43694	−	0.0185336i
$767$	−38.9208	−	22.4709i	−1.40535	−	0.811379i
$768$		0			0
$769$		−	20.8715i		−	0.752646i	−0.926489	−	0.376323i	$-0.877188\pi$
$769$		−	20.8715i		−	0.752646i	0.926489	−	0.376323i	$-0.122812\pi$
$770$	0.306620	+	0.388443i	0.0110498	+	0.0139985i
$771$		0			0
$772$	−20.1378	−	0.519560i	−0.724777	−	0.0186994i
$773$	−25.3570	−	14.6399i	−0.912030	−	0.526561i	−0.0309460	−	0.999521i	$-0.509852\pi$
$773$	−25.3570	−	14.6399i	−0.912030	−	0.526561i	−0.881084	+	0.472961i	$0.843185\pi$
$774$		0			0
$775$	14.8206	−	8.55665i	0.532370	−	0.307364i
$776$	−0.0649675	+	1.67827i	−0.00233220	+	0.0602464i
$777$		0			0
$778$	−5.29058	−	9.44274i	−0.189676	−	0.338539i
$779$	4.76281	+	8.24943i	0.170645	+	0.295566i
$780$		0			0
$781$	−0.621329	−	0.358725i	−0.0222329	−	0.0128362i
$782$	27.0349	+	16.0770i	0.966764	+	0.574912i
$783$		0			0
$784$	−27.0340	+	7.29132i	−0.965500	+	0.260404i
$785$		−	12.0909i		−	0.431541i
$786$		0			0
$787$	−10.4134	+	18.0366i	−0.371199	+	0.642935i	−0.989750	−	0.142809i	$-0.954387\pi$
$787$	−10.4134	+	18.0366i	−0.371199	+	0.642935i	0.618551	+	0.785744i	$0.287720\pi$
$788$	0.937260	+	1.72463i	0.0333885	+	0.0614375i
$789$		0			0
$790$	12.1205	−	6.79088i	0.431228	−	0.241608i
$791$	−8.08977	+	21.1020i	−0.287639	+	0.750302i
$792$		0			0
$793$	20.9018	+	36.2030i	0.742245	+	1.28561i
$794$	−17.6125	−	0.227165i	−0.625045	−	0.00806179i
$795$		0			0
$796$	−0.113588	+	4.40262i	−0.00402603	+	0.156047i
$797$		−	28.8543i		−	1.02207i	−0.859559	−	0.511036i	$-0.829262\pi$
$797$		−	28.8543i		−	1.02207i	0.859559	−	0.511036i	$-0.170738\pi$
$798$		0			0
$799$	−43.0558			−1.52321
$800$	−23.5844	−	1.52298i	−0.833833	−	0.0538453i
$801$		0			0
$802$	0.382632	−	29.6661i	0.0135112	−	1.04755i
$803$	−0.390695	+	0.225568i	−0.0137873	+	0.00796013i
$804$		0			0
$805$	−6.89859	+	5.59134i	−0.243143	+	0.197069i
$806$	30.9708	−	17.3523i	1.09090	−	0.611210i
$807$		0			0
$808$	−26.6725	−	16.8076i	−0.938336	−	0.591288i
$809$	−32.6025	−	18.8231i	−1.14624	−	0.661784i	−0.198275	−	0.980146i	$-0.563534\pi$
$809$	−32.6025	−	18.8231i	−1.14624	−	0.661784i	−0.947969	+	0.318362i	$0.896867\pi$
$810$		0			0
$811$	11.3863			0.399827			0.199913	−	0.979814i	$-0.435934\pi$
$811$	11.3863			0.399827			0.199913	+	0.979814i	$0.435934\pi$
$812$	7.12251	+	53.7599i	0.249951	+	1.88660i
$813$		0			0
$814$	0.515871	+	0.306777i	0.0180813	+	0.0107525i
$815$	−7.74189	+	13.4093i	−0.271186	+	0.469709i
$816$		0			0
$817$	−31.8639	+	18.3966i	−1.11478	+	0.643617i
$818$	0.650862	−	0.364665i	0.0227568	−	0.0127502i
$819$		0			0
$820$	−3.49906	−	2.14237i	−0.122192	−	0.0748149i
$821$	6.92169	+	11.9887i	0.241569	+	0.418409i	0.961161	−	0.275987i	$-0.0890048\pi$
$821$	6.92169	+	11.9887i	0.241569	+	0.418409i	−0.719593	+	0.694396i	$0.755671\pi$
$822$		0			0
$823$	−6.60648	+	11.4428i	−0.230287	+	0.398869i	−0.957893	−	0.287127i	$-0.907300\pi$
$823$	−6.60648	+	11.4428i	−0.230287	+	0.398869i	0.727605	+	0.685996i	$0.240633\pi$
$824$	4.09160	−	2.15572i	0.142538	−	0.0750980i
$825$		0			0
$826$	−27.1530	+	3.95441i	−0.944774	+	0.137592i
$827$	12.2445			0.425784			0.212892	−	0.977076i	$-0.431712\pi$
$827$	12.2445			0.425784			0.212892	+	0.977076i	$0.431712\pi$
$828$		0			0
$829$	−21.1084	+	36.5609i	−0.733126	+	1.26981i	0.222415	+	0.974952i	$0.428606\pi$
$829$	−21.1084	+	36.5609i	−0.733126	+	1.26981i	−0.955541	+	0.294859i	$0.904727\pi$
$830$	16.4806	+	0.212566i	0.572051	+	0.00737828i
$831$		0			0
$832$	−48.8797	−	3.79004i	−1.69460	−	0.131396i
$833$	39.9904	−	13.0322i	1.38558	−	0.451537i
$834$		0			0
$835$	−1.29191	+	0.745885i	−0.0447084	+	0.0258124i
$836$	−0.586509	−	1.07922i	−0.0202848	−	0.0373257i
$837$		0			0
$838$	−26.8002	−	15.9374i	−0.925796	−	0.550549i
$839$	4.30094			0.148485			0.0742424	−	0.997240i	$-0.476346\pi$
$839$	4.30094			0.148485			0.0742424	+	0.997240i	$0.476346\pi$
$840$		0			0
$841$	76.0304			2.62174
$842$	22.1663	+	13.1818i	0.763903	+	0.454275i
$843$		0			0
$844$	31.2259	−	16.9699i	1.07484	−	0.584127i
$845$	−19.2826	+	11.1328i	−0.663340	+	0.382980i
$846$		0			0
$847$	−4.55643	−	28.6874i	−0.156561	−	0.985710i
$848$	−6.79649	−	13.3135i	−0.233392	−	0.457187i
$849$		0			0
$850$	35.4981	+	0.457853i	1.21758	+	0.0157042i
$851$	−5.38488	+	9.32689i	−0.184591	+	0.319722i
$852$		0			0
$853$	28.0209			0.959416			0.479708	−	0.877428i	$-0.340743\pi$
$853$	28.0209			0.959416			0.479708	+	0.877428i	$0.340743\pi$
$854$	23.7123	+	9.44298i	0.811417	+	0.323132i
$855$		0			0
$856$	18.7760	+	35.6373i	0.641751	+	1.21806i
$857$	−6.76275	+	11.7134i	−0.231011	+	0.400123i	−0.958106	−	0.286414i	$-0.907537\pi$
$857$	−6.76275	+	11.7134i	−0.231011	+	0.400123i	0.727095	+	0.686537i	$0.240870\pi$
$858$		0			0
$859$	9.51823	+	16.4861i	0.324758	+	0.562497i	0.981463	−	0.191650i	$-0.0613838\pi$
$859$	9.51823	+	16.4861i	0.324758	+	0.562497i	−0.656705	+	0.754147i	$0.728050\pi$
$860$	8.27504	−	13.5153i	0.282176	−	0.460869i
$861$		0			0
$862$	35.3905	−	19.8286i	1.20540	−	0.675364i
$863$	14.7548	−	8.51871i	0.502260	−	0.289980i	−0.227386	−	0.973805i	$-0.573018\pi$
$863$	14.7548	−	8.51871i	0.502260	−	0.289980i	0.729646	+	0.683825i	$0.239685\pi$
$864$		0			0
$865$	4.08774	−	7.08017i	0.138987	−	0.240733i
$866$	−45.8281	−	27.2529i	−1.55730	−	0.926091i
$867$		0			0
$868$	8.27824	−	20.0319i	0.280982	−	0.679928i
$869$	1.58042			0.0536120
$870$		0			0
$871$	−16.3612	−	9.44617i	−0.554379	−	0.320071i
$872$	−16.2514	−	10.2407i	−0.550342	−	0.346795i
$873$		0			0
$874$	19.2280	−	10.7731i	0.650396	−	0.364404i
$875$	−7.88137	+	20.5584i	−0.266439	+	0.695001i
$876$		0			0
$877$	−39.7587	+	22.9547i	−1.34255	+	0.775124i	−0.987182	−	0.159600i	$-0.948980\pi$
$877$	−39.7587	+	22.9547i	−1.34255	+	0.775124i	−0.355373	+	0.934725i	$0.615646\pi$
$878$	−0.161911	+	12.5533i	−0.00546423	+	0.423652i
$879$		0			0
$880$	0.443918	+	0.287797i	0.0149645	+	0.00970164i
$881$	12.9601			0.436638			0.218319	−	0.975877i	$-0.429943\pi$
$881$	12.9601			0.436638			0.218319	+	0.975877i	$0.429943\pi$
$882$		0			0
$883$		−	53.9117i		−	1.81427i	−0.420835	−	0.907137i	$-0.638263\pi$
$883$		−	53.9117i		−	1.81427i	0.420835	−	0.907137i	$-0.361737\pi$
$884$	73.6206	+	1.89942i	2.47613	+	0.0638846i
$885$		0			0
$886$	0.592450	+	0.00764138i	0.0199037	+	0.000256717i
$887$	−8.11124	−	14.0491i	−0.272349	−	0.471722i	0.697114	−	0.716960i	$-0.254467\pi$
$887$	−8.11124	−	14.0491i	−0.272349	−	0.471722i	−0.969463	+	0.245238i	$0.921134\pi$
$888$		0			0
$889$	44.7085	+	17.1397i	1.49948	+	0.574846i
$890$	3.48376	−	1.95188i	0.116776	−	0.0654272i
$891$		0			0
$892$	36.4072	−	19.7857i	1.21900	−	0.662473i
$893$	−15.0849	+	26.1279i	−0.504798	+	0.874336i
$894$		0			0
$895$		−	13.2509i		−	0.442928i
$896$	−24.8589	+	16.6744i	−0.830477	+	0.557053i
$897$		0			0
$898$	−47.9415	−	28.5097i	−1.59983	−	0.951381i
$899$	−36.3554	−	20.9898i	−1.21252	−	0.700049i
$900$		0			0
$901$	11.2270	+	19.4458i	0.374027	+	0.647834i
$902$	−0.228125	−	0.407162i	−0.00759573	−	0.0135570i
$903$		0			0
$904$	−0.934556	+	24.1419i	−0.0310829	+	0.802946i
$905$	0.155837	−	0.0899725i	0.00518019	−	0.00299079i
$906$		0			0
$907$	−6.60352	−	3.81255i	−0.219266	−	0.126594i	0.386344	−	0.922355i	$-0.373738\pi$
$907$	−6.60352	−	3.81255i	−0.219266	−	0.126594i	−0.605611	+	0.795761i	$0.707071\pi$
$908$	1.03612	−	40.1596i	0.0343850	−	1.33274i
$909$		0			0
$910$	−7.69220	+	19.3159i	−0.254994	+	0.640316i
$911$			33.1109i			1.09701i	0.836146	+	0.548507i	$0.184804\pi$
$911$			33.1109i			1.09701i	−0.836146	+	0.548507i	$0.815196\pi$
$912$		0			0
$913$	1.62371	+	0.937450i	0.0537370	+	0.0310251i
$914$	−16.8130	−	0.216853i	−0.556125	−	0.00717286i
$915$		0			0
$916$	−20.2318	+	33.0439i	−0.668477	+	1.09180i
$917$	25.2982	−	4.01813i	0.835420	−	0.132690i
$918$		0			0
$919$	−16.2880	−	28.2116i	−0.537291	−	0.930616i	−0.999049	−	0.0436094i	$-0.986114\pi$
$919$	−16.2880	−	28.2116i	−0.537291	−	0.930616i	0.461758	−	0.887006i	$-0.347219\pi$
$920$	−5.06100	+	8.03149i	−0.166856	+	0.264790i
$921$		0			0
$922$	−0.264858	−	0.157505i	−0.00872264	−	0.00518715i
$923$		−	30.1421i		−	0.992138i
$924$		0			0
$925$			12.1555i			0.399670i
$926$	−6.60152	+	11.1010i	−0.216939	+	0.364802i
$927$		0			0
$928$	25.6913	+	51.9705i	0.843358	+	1.70601i
$929$	7.81822	+	13.5416i	0.256507	+	0.444284i	0.965304	−	0.261129i	$-0.0840948\pi$
$929$	7.81822	+	13.5416i	0.256507	+	0.444284i	−0.708796	+	0.705413i	$0.750762\pi$
$930$		0			0
$931$	6.10253	−	28.8335i	0.200002	−	0.944981i
$932$	44.1378	+	27.0243i	1.44578	+	0.885209i
$933$		0			0
$934$	0.493211	−	38.2395i	0.0161384	−	1.25124i
$935$	−0.688237	−	0.397354i	−0.0225078	−	0.0129949i
$936$		0			0
$937$			49.5708i			1.61941i	0.586839	+	0.809704i	$0.300372\pi$
$937$			49.5708i			1.61941i	−0.586839	+	0.809704i	$0.699628\pi$
$938$	−11.4144	+	1.66232i	−0.372693	+	0.0542768i
$939$		0			0
$940$	0.335152	−	12.9903i	0.0109315	−	0.423697i
$941$	10.5801	+	6.10840i	0.344900	+	0.199128i	0.662437	−	0.749118i	$-0.269522\pi$
$941$	10.5801	+	6.10840i	0.344900	+	0.199128i	−0.317537	+	0.948246i	$0.602856\pi$
$942$		0			0
$943$	7.25262	−	4.18730i	0.236178	−	0.136357i
$944$	−26.1265	+	13.3375i	−0.850345	+	0.434099i
$945$		0			0
$946$	1.57269	−	0.881146i	0.0511325	−	0.0286485i
$947$	−11.4761	−	19.8772i	−0.372923	−	0.645921i	0.617091	−	0.786892i	$-0.288311\pi$
$947$	−11.4761	−	19.8772i	−0.372923	−	0.645921i	−0.990014	+	0.140971i	$0.954978\pi$
$948$		0			0
$949$	−16.4142	−	9.47675i	−0.532828	−	0.307628i
$950$	12.7149	−	21.3812i	0.412525	−	0.693697i
$951$		0			0
$952$	36.0005	−	26.9398i	1.16678	−	0.873122i
$953$			10.7450i			0.348063i	0.984740	+	0.174032i	$0.0556795\pi$
$953$			10.7450i			0.348063i	−0.984740	+	0.174032i	$0.944321\pi$
$954$		0			0
$955$	−0.0887952	+	0.153798i	−0.00287334	+	0.00497678i
$956$	19.6826	−	10.6966i	0.636580	−	0.345953i
$957$		0			0
$958$	−7.00293	−	12.4990i	−0.226254	−	0.403824i
$959$	−17.5346	−	21.6341i	−0.566221	−	0.698603i
$960$		0			0
$961$	−7.11058	−	12.3159i	−0.229374	−	0.397287i
$962$	−0.325206	+	25.2138i	−0.0104851	+	0.812926i
$963$		0			0
$964$	−1.41071	+	54.6781i	−0.0454358	+	1.76106i
$965$			9.13278i			0.293995i
$966$		0			0
$967$	−7.48832			−0.240808			−0.120404	−	0.992725i	$-0.538419\pi$
$967$	−7.48832			−0.240808			−0.120404	+	0.992725i	$0.538419\pi$
$968$	−14.4744	−	27.4727i	−0.465225	−	0.883007i
$969$		0			0
$970$	0.761371	+	0.00982012i	0.0244462	+	0.000315305i
$971$	−45.0252	+	25.9953i	−1.44493	+	0.834229i	−0.998173	−	0.0604275i	$-0.980754\pi$
$971$	−45.0252	+	25.9953i	−1.44493	+	0.834229i	−0.446755	+	0.894657i	$0.647420\pi$
$972$		0			0
$973$	39.0705	+	14.9782i	1.25254	+	0.480180i
$974$	−7.03329	−	12.5532i	−0.225361	−	0.402229i
$975$		0			0
$976$	27.2493	+	1.40701i	0.872230	+	0.0450373i
$977$	17.3850	+	10.0372i	0.556196	+	0.321120i	0.751617	−	0.659600i	$-0.229274\pi$
$977$	17.3850	+	10.0372i	0.556196	+	0.321120i	−0.195421	+	0.980719i	$0.562607\pi$
$978$		0			0
$979$	0.454255			0.0145180
$980$	3.62062	+	12.1669i	0.115656	+	0.388656i
$981$		0			0
$982$	17.8284	−	29.9799i	0.568926	−	0.956698i
$983$	−30.7294	+	53.2249i	−0.980115	+	1.69761i	−0.318214	+	0.948019i	$0.603083\pi$
$983$	−30.7294	+	53.2249i	−0.980115	+	1.69761i	−0.661902	+	0.749591i	$0.730250\pi$
$984$		0			0
$985$	0.770664	−	0.444943i	0.0245554	−	0.0141771i
$986$	−42.5665	−	75.9737i	−1.35559	−	2.41949i
$987$		0			0
$988$	26.9462	−	44.0102i	0.857272	−	1.40015i
$989$	16.1737	+	28.0137i	0.514294	+	0.890783i
$990$		0			0
$991$	9.87483	−	17.1037i	0.313684	−	0.543317i	−0.665473	−	0.746422i	$-0.731770\pi$
$991$	9.87483	−	17.1037i	0.313684	−	0.543317i	0.979157	+	0.203105i	$0.0651033\pi$
$992$	1.49321	−	23.1234i	0.0474095	−	0.734170i
$993$		0			0
$994$	−11.4025	−	14.4453i	−0.361665	−	0.458177i
$995$	1.99665			0.0632980
$996$		0			0
$997$	−1.94579	+	3.37021i	−0.0616239	+	0.106736i	−0.895191	−	0.445682i	$-0.852961\pi$
$997$	−1.94579	+	3.37021i	−0.0616239	+	0.106736i	0.833568	+	0.552418i	$0.186295\pi$
$998$	−0.269791	+	20.9174i	−0.00854009	+	0.662128i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.ch.b.269.20	yes	56
3.2	odd	2	inner	504.2.ch.b.269.9	yes	56
4.3	odd	2		2016.2.cp.b.17.12		56
7.5	odd	6	inner	504.2.ch.b.341.1	yes	56
8.3	odd	2		2016.2.cp.b.17.17		56
8.5	even	2	inner	504.2.ch.b.269.28	yes	56
12.11	even	2		2016.2.cp.b.17.18		56
21.5	even	6	inner	504.2.ch.b.341.28	yes	56
24.5	odd	2	inner	504.2.ch.b.269.1	✓	56
24.11	even	2		2016.2.cp.b.17.11		56
28.19	even	6		2016.2.cp.b.593.11		56
56.5	odd	6	inner	504.2.ch.b.341.9	yes	56
56.19	even	6		2016.2.cp.b.593.18		56
84.47	odd	6		2016.2.cp.b.593.17		56
168.5	even	6	inner	504.2.ch.b.341.20	yes	56
168.131	odd	6		2016.2.cp.b.593.12		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.ch.b.269.1	✓	56	24.5	odd	2	inner
504.2.ch.b.269.9	yes	56	3.2	odd	2	inner
504.2.ch.b.269.20	yes	56	1.1	even	1	trivial
504.2.ch.b.269.28	yes	56	8.5	even	2	inner
504.2.ch.b.341.1	yes	56	7.5	odd	6	inner
504.2.ch.b.341.9	yes	56	56.5	odd	6	inner
504.2.ch.b.341.20	yes	56	168.5	even	6	inner
504.2.ch.b.341.28	yes	56	21.5	even	6	inner
2016.2.cp.b.17.11		56	24.11	even	2
2016.2.cp.b.17.12		56	4.3	odd	2
2016.2.cp.b.17.17		56	8.3	odd	2
2016.2.cp.b.17.18		56	12.11	even	2
2016.2.cp.b.593.11		56	28.19	even	6
2016.2.cp.b.593.12		56	168.131	odd	6
2016.2.cp.b.593.17		56	84.47	odd	6
2016.2.cp.b.593.18		56	56.19	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.ch (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.722843 - 1.21552i) q^{2} +(-0.954995 - 1.75727i) q^{4} +(-0.785247 + 0.453362i) q^{5} +(-2.47043 - 0.947077i) q^{7} +(-2.82631 - 0.109409i) q^{8} +O(q^{10})\)	\(q+(0.722843 - 1.21552i) q^{2} +(-0.954995 - 1.75727i) q^{4} +(-0.785247 + 0.453362i) q^{5} +(-2.47043 - 0.947077i) q^{7} +(-2.82631 - 0.109409i) q^{8} +(-0.0165377 + 1.28220i) q^{10} +(-0.0729337 + 0.126325i) q^{11} -6.12830 q^{13} +(-2.93693 + 2.31828i) q^{14} +(-2.17597 + 3.35636i) q^{16} +(3.00430 - 5.20361i) q^{17} +(-2.10516 - 3.64625i) q^{19} +(1.54658 + 0.946928i) q^{20} +(0.100831 + 0.179966i) q^{22} +(-3.20566 + 1.85079i) q^{23} +(-2.08893 + 3.61812i) q^{25} +(-4.42980 + 7.44909i) q^{26} +(0.694985 + 5.24566i) q^{28} +10.2484 q^{29} +(-3.54741 - 2.04810i) q^{31} +(2.50685 + 5.07106i) q^{32} +(-4.15347 - 7.41320i) q^{34} +(2.36927 - 0.376312i) q^{35} +(2.51971 - 1.45475i) q^{37} +(-5.95380 - 0.0767918i) q^{38} +(2.26895 - 1.19543i) q^{40} -2.26244 q^{41} -8.73882i q^{43} +(0.291638 + 0.00752431i) q^{44} +(-0.0675128 + 5.23438i) q^{46} +(-3.58285 - 6.20567i) q^{47} +(5.20609 + 4.67938i) q^{49} +(2.88795 + 5.15448i) q^{50} +(5.85250 + 10.7691i) q^{52} +(-1.86849 + 3.23632i) q^{53} -0.132262i q^{55} +(6.87859 + 2.94702i) q^{56} +(7.40801 - 12.4572i) q^{58} +(6.35100 + 3.66675i) q^{59} +(-3.41070 - 5.90751i) q^{61} +(-5.05374 + 2.83151i) q^{62} +(7.97606 + 0.618449i) q^{64} +(4.81223 - 2.77834i) q^{65} +(2.66978 + 1.54140i) q^{67} +(-12.0132 - 0.309943i) q^{68} +(1.25519 - 3.15192i) q^{70} +4.91850i q^{71} +(2.67843 + 1.54639i) q^{73} +(0.0530663 - 4.11432i) q^{74} +(-4.39701 + 7.18148i) q^{76} +(0.299817 - 0.243004i) q^{77} +(-5.41731 - 9.38305i) q^{79} +(0.187025 - 3.62207i) q^{80} +(-1.63539 + 2.75005i) q^{82} -12.8534i q^{83} +5.44815i q^{85} +(-10.6222 - 6.31680i) q^{86} +(0.219954 - 0.349054i) q^{88} +(-1.55708 - 2.69694i) q^{89} +(15.1396 + 5.80397i) q^{91} +(6.31372 + 3.86570i) q^{92} +(-10.1330 - 0.130695i) q^{94} +(3.30614 + 1.90880i) q^{95} -0.593803i q^{97} +(9.45109 - 2.94566i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{4} - 20 q^{7}+O(q^{10}) \) 56 * q - 8 * q^4 - 20 * q^7	\( 56 q - 8 q^{4} - 20 q^{7} + 20 q^{16} - 16 q^{22} + 8 q^{25} + 36 q^{28} - 36 q^{31} + 60 q^{40} - 8 q^{46} - 28 q^{49} + 36 q^{52} - 44 q^{58} + 40 q^{64} - 60 q^{70} + 72 q^{73} - 12 q^{79} - 36 q^{82} + 4 q^{88} - 180 q^{94}+O(q^{100}) \) 56 * q - 8 * q^4 - 20 * q^7 + 20 * q^16 - 16 * q^22 + 8 * q^25 + 36 * q^28 - 36 * q^31 + 60 * q^40 - 8 * q^46 - 28 * q^49 + 36 * q^52 - 44 * q^58 + 40 * q^64 - 60 * q^70 + 72 * q^73 - 12 * q^79 - 36 * q^82 + 4 * q^88 - 180 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more