LMFDB - Embedded newform 504.2.ch.b.341.20

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			341.20
Character	$\chi$	$=$	504.341
Dual form			504.2.ch.b.269.20

$q$-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 $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$	$-1$

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	0.314029	−	0.949413i	$-0.398321\pi$
$5$	−0.785247	−	0.453362i	−0.351173	−	0.202750i	−0.665202	+	0.746664i	$0.731654\pi$
$6$		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	0.854821	−	0.518923i	$-0.173667\pi$
$11$	−0.0729337	−	0.126325i	−0.0219903	−	0.0380884i	−0.876811	+	0.480835i	$0.840334\pi$
$12$		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	0.957454	+	0.288587i	$0.0931856\pi$
$17$	3.00430	+	5.20361i	0.728651	+	1.26206i	−0.228803	+	0.973473i	$0.573481\pi$
$18$		0			0
$19$	−2.10516	+	3.64625i	−0.482957	+	0.836506i	−0.999809	−	0.0195688i	$-0.993771\pi$
$19$	−2.10516	+	3.64625i	−0.482957	+	0.836506i	0.516851	+	0.856075i	$0.327104\pi$
$20$	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	0.127054	−	0.991896i	$-0.459448\pi$
$23$	−3.20566	−	1.85079i	−0.668426	−	0.385916i	−0.795480	+	0.605980i	$0.792781\pi$
$24$		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	−0.783510	−	0.621380i	$-0.786572\pi$
$31$	−3.54741	+	2.04810i	−0.637134	+	0.367849i	0.146376	+	0.989229i	$0.453239\pi$
$32$	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	0.692609	−	0.721313i	$-0.256461\pi$
$37$	2.51971	+	1.45475i	0.414238	+	0.239160i	−0.278371	+	0.960474i	$0.589795\pi$
$38$	−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	$0.232135\pi$
$43$			8.73882i			1.33266i	−0.745658	+	0.666329i	$0.767865\pi$
$44$	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	0.477042	+	0.878881i	$0.341709\pi$
$47$	−3.58285	+	6.20567i	−0.522612	+	0.905190i	−0.999654	+	0.0263098i	$0.991624\pi$
$48$		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	0.708687	−	0.705523i	$-0.249288\pi$
$53$	−1.86849	−	3.23632i	−0.256657	−	0.444543i	−0.965344	+	0.260980i	$0.915954\pi$
$54$		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	−0.0259364	−	0.999664i	$-0.508257\pi$
$59$	6.35100	−	3.66675i	0.826829	−	0.477370i	0.852766	+	0.522293i	$0.174923\pi$
$60$		0			0
$61$	−3.41070	+	5.90751i	−0.436696	+	0.756379i	−0.997432	−	0.0716150i	$-0.977185\pi$
$61$	−3.41070	+	5.90751i	−0.436696	+	0.756379i	0.560737	+	0.827994i	$0.310518\pi$
$62$	−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	−0.327972	−	0.944688i	$-0.606365\pi$
$67$	2.66978	−	1.54140i	0.326166	−	0.188312i	0.654138	+	0.756376i	$0.273032\pi$
$68$	−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	$-0.905726\pi$
$71$		−	4.91850i		−	0.583719i	0.956461	−	0.291859i	$-0.0942739\pi$
$72$		0			0
$73$	2.67843	−	1.54639i	0.313486	−	0.180991i	−0.334999	−	0.942218i	$-0.608736\pi$
$73$	2.67843	−	1.54639i	0.313486	−	0.180991i	0.648485	+	0.761227i	$0.275403\pi$
$74$	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	0.381829	+	0.924233i	$0.375294\pi$
$79$	−5.41731	+	9.38305i	−0.609495	+	1.05568i	−0.991324	+	0.131443i	$0.958039\pi$
$80$	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	$0.249244\pi$
$83$			12.8534i			1.41085i	−0.708785	+	0.705424i	$0.750756\pi$
$84$		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	−0.936673	−	0.350205i	$-0.886112\pi$
$89$	−1.55708	+	2.69694i	−0.165050	+	0.285875i	0.771623	+	0.636080i	$0.219445\pi$
$90$		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	$0.00959715\pi$
$97$			0.593803i			0.0602915i	−0.999546	+	0.0301458i	$0.990403\pi$
$98$	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	0.0641776	−	0.997938i	$-0.479558\pi$
$101$	9.65297	−	5.57314i	0.960506	−	0.554549i	0.896329	+	0.443390i	$0.146224\pi$
$102$		0			0
$103$	−1.41603	−	0.817548i	−0.139526	−	0.0805554i	0.428612	−	0.903489i	$-0.359003\pi$
$103$	−1.41603	−	0.817548i	−0.139526	−	0.0805554i	−0.568138	+	0.822933i	$0.692336\pi$
$104$	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	0.283972	+	0.958833i	$0.408348\pi$
$107$	−7.12074	+	12.3335i	−0.688387	+	1.19232i	−0.972359	+	0.233489i	$0.924986\pi$
$108$		0			0
$109$	5.88150	−	3.39568i	0.563345	−	0.325247i	−0.191142	−	0.981562i	$-0.561219\pi$
$109$	5.88150	−	3.39568i	0.563345	−	0.325247i	0.754487	+	0.656315i	$0.227886\pi$
$110$	−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	$0.131606\pi$
$113$			8.54183i			0.803548i	−0.915739	+	0.401774i	$0.868394\pi$
$114$		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	0.0867954	−	0.996226i	$-0.472337\pi$
$131$	−8.38458	−	4.84084i	−0.732564	−	0.422946i	−0.819359	+	0.573280i	$0.805671\pi$
$132$		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	−0.0572215	−	0.998362i	$-0.518224\pi$
$137$	9.11532	−	5.26273i	0.778774	−	0.449625i	0.835996	+	0.548736i	$0.184891\pi$
$138$		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	−0.999591	−	0.0285960i	$-0.990896\pi$
$149$	−5.79849	+	10.0433i	−0.475031	+	0.822777i	0.524560	+	0.851373i	$0.324230\pi$
$150$		0			0
$151$	7.79321	+	13.4982i	0.634202	+	1.09847i	0.986684	+	0.162652i	$0.0520047\pi$
$151$	7.79321	+	13.4982i	0.634202	+	1.09847i	−0.352481	+	0.935819i	$0.614662\pi$
$152$	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	−0.999297	−	0.0374841i	$-0.988066\pi$
$157$	−6.66733	−	11.5482i	−0.532111	−	0.921643i	0.467186	−	0.884159i	$-0.345268\pi$
$158$	−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	0.950907	−	0.309477i	$-0.100154\pi$
$163$	14.7888	+	8.53830i	1.15835	+	0.668771i	0.207439	+	0.978248i	$0.433487\pi$
$164$	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	0.172877	−	0.984943i	$-0.444694\pi$
$173$	−7.80851	−	4.50825i	−0.593670	−	0.342756i	−0.766547	+	0.642188i	$0.778027\pi$
$174$		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	−0.998534	−	0.0541368i	$-0.982759\pi$
$179$	−7.30700	−	12.6561i	−0.546151	−	0.945961i	0.452383	−	0.891824i	$-0.350574\pi$
$180$		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	0.506124	−	0.862461i	$-0.331078\pi$
$191$	0.169619	+	0.0979296i	0.0122732	+	0.00708594i	−0.493851	+	0.869547i	$0.664411\pi$
$192$		0			0
$193$	5.03614	+	8.72285i	0.362509	+	0.627884i	0.988373	−	0.152048i	$-0.0485868\pi$
$193$	5.03614	+	8.72285i	0.362509	+	0.627884i	−0.625864	+	0.779932i	$0.715254\pi$
$194$	−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	−0.566067	−	0.824359i	$-0.691536\pi$
$199$	−1.90703	+	1.10102i	−0.135185	+	0.0780494i	0.430882	+	0.902408i	$0.358203\pi$
$200$	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	$-0.790504\pi$
$211$		−	17.7696i		−	1.22331i	0.791125	−	0.611654i	$-0.209496\pi$
$212$	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	$-0.755983\pi$
$223$		−	20.7181i		−	1.38738i	0.720271	−	0.693692i	$-0.244017\pi$
$224$	−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	0.204575	−	0.978851i	$-0.434419\pi$
$227$	17.3954	−	10.0432i	1.15457	−	0.666593i	0.949997	+	0.312258i	$0.101085\pi$
$228$		0			0
$229$	−9.68640	+	16.7773i	−0.640095	+	1.10868i	0.345316	+	0.938487i	$0.387772\pi$
$229$	−9.68640	+	16.7773i	−0.640095	+	1.10868i	−0.985411	+	0.170191i	$0.945562\pi$
$230$	−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	−0.468768	−	0.883322i	$-0.655302\pi$
$233$	−22.4100	−	12.9384i	−1.46813	−	0.847625i	−0.999363	+	0.0356961i	$0.988635\pi$
$234$		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	$-0.882007\pi$
$239$		−	11.2007i		−	0.724512i	0.932079	−	0.362256i	$-0.117993\pi$
$240$		0			0
$241$	−23.6842	+	13.6741i	−1.52563	+	0.880825i	−0.526096	+	0.850425i	$0.676345\pi$
$241$	−23.6842	+	13.6741i	−1.52563	+	0.880825i	−0.999538	+	0.0303997i	$0.990322\pi$
$242$	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	$-0.631826\pi$
$251$		−	29.0073i		−	1.83092i	0.402407	−	0.915461i	$-0.368174\pi$
$252$		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	−0.614593	−	0.788845i	$-0.710680\pi$
$257$	6.02554	−	10.4365i	0.375863	−	0.651014i	0.990456	+	0.137831i	$0.0440130\pi$
$258$		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	−0.571229	−	0.820791i	$-0.693533\pi$
$263$	−2.36800	+	1.36716i	−0.146017	+	0.0843029i	0.425212	+	0.905094i	$0.360200\pi$
$264$		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	−0.357874	−	0.933770i	$-0.616498\pi$
$269$	4.45879	−	2.57428i	0.271857	−	0.156957i	0.629731	+	0.776813i	$0.283165\pi$
$270$		0			0
$271$	21.0489	+	12.1526i	1.27863	+	0.738216i	0.976596	−	0.215082i	$-0.0690020\pi$
$271$	21.0489	+	12.1526i	1.27863	+	0.738216i	0.302031	+	0.953298i	$0.402335\pi$
$272$	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	−0.521056	−	0.853523i	$-0.674462\pi$
$277$	−0.705869	+	0.407533i	−0.0424115	+	0.0244863i	0.478644	+	0.878009i	$0.341128\pi$
$278$	−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	$0.0101227\pi$
$281$			1.06599i			0.0635918i	−0.999494	+	0.0317959i	$0.989877\pi$
$282$		0			0
$283$	−3.14663	−	5.45012i	−0.187048	−	0.323976i	0.757217	−	0.653164i	$-0.226559\pi$
$283$	−3.14663	−	5.45012i	−0.187048	−	0.323976i	−0.944265	+	0.329187i	$0.893225\pi$
$284$	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	$0.175887\pi$
$293$			17.9687i			1.04974i	−0.851181	+	0.524872i	$0.824113\pi$
$294$		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	0.958703	+	0.284410i	$0.0917977\pi$
$311$	12.7971	+	22.1653i	0.725658	+	1.25688i	−0.233045	+	0.972466i	$0.574869\pi$
$312$		0			0
$313$	−14.9541	−	8.63375i	−0.845255	−	0.488008i	0.0137920	−	0.999905i	$-0.495610\pi$
$313$	−14.9541	−	8.63375i	−0.845255	−	0.488008i	−0.859047	+	0.511897i	$0.828943\pi$
$314$	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	−0.920585	−	0.390542i	$-0.872288\pi$
$317$	−2.17346	+	3.76454i	−0.122074	+	0.211438i	0.798512	+	0.601979i	$0.205621\pi$
$318$		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	0.0270828	−	0.999633i	$-0.491378\pi$
$331$	−15.0111	−	8.66665i	−0.825084	−	0.476362i	−0.852166	+	0.523271i	$0.824712\pi$
$332$	−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	0.756694	−	0.653770i	$-0.226813\pi$
$347$	−3.49897	−	6.06039i	−0.187834	−	0.325339i	−0.944528	+	0.328431i	$0.893480\pi$
$348$		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	0.970375	−	0.241605i	$-0.0776738\pi$
$353$	5.18465	+	8.98008i	0.275951	+	0.477962i	−0.694423	+	0.719567i	$0.744341\pi$
$354$		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	0.885945	−	0.463790i	$-0.153511\pi$
$359$	17.5691	+	10.1436i	0.927264	+	0.535356i	0.0413188	+	0.999146i	$0.486844\pi$
$360$		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	0.184298	−	0.982870i	$-0.440999\pi$
$367$	21.6024	−	12.4722i	1.12764	−	0.651042i	0.943340	+	0.331829i	$0.107666\pi$
$368$	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	0.606429	−	0.795138i	$-0.292602\pi$
$373$	4.26886	+	2.46463i	0.221033	+	0.127614i	−0.385395	+	0.922752i	$0.625935\pi$
$374$	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	$0.223005\pi$
$379$			25.1007i			1.28934i	−0.764462	+	0.644669i	$0.776995\pi$
$380$	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	0.243051	+	0.970014i	$0.421852\pi$
$383$	−14.0619	+	24.3560i	−0.718531	+	1.24453i	−0.961582	+	0.274519i	$0.911482\pi$
$384$		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	0.946581	−	0.322466i	$-0.104512\pi$
$389$	3.82681	+	6.62822i	0.194027	+	0.336064i	−0.752554	+	0.658530i	$0.771178\pi$
$390$		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	−0.978913	−	0.204276i	$-0.934516\pi$
$397$	−6.22748	+	10.7863i	−0.312548	+	0.541350i	0.666365	+	0.745626i	$0.267849\pi$
$398$	−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	0.879555	−	0.475798i	$-0.157841\pi$
$401$	18.1682	+	10.4894i	0.907279	+	0.523818i	0.0277241	+	0.999616i	$0.491174\pi$
$402$		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	−0.488662	−	0.872473i	$-0.662515\pi$
$409$	0.456865	−	0.263771i	0.0225905	−	0.0130426i	0.511253	+	0.859430i	$0.329182\pi$
$410$	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	$0.181033\pi$
$419$			22.0482i			1.07713i	−0.842585	+	0.538564i	$0.818967\pi$
$420$		0			0
$421$		−	18.2360i		−	0.888771i	−0.895836	−	0.444385i	$-0.853422\pi$
$421$		−	18.2360i		−	0.888771i	0.895836	−	0.444385i	$-0.146578\pi$
$422$	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	0.236799	−	0.971559i	$-0.423902\pi$
$431$	24.8419	−	14.3425i	1.19659	−	0.690854i	0.959794	+	0.280705i	$0.0905683\pi$
$432$		0			0
$433$			37.7023i			1.81186i	0.423429	+	0.905929i	$0.360826\pi$
$433$			37.7023i			1.81186i	−0.423429	+	0.905929i	$0.639174\pi$
$434$	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	0.305190	−	0.952291i	$-0.401280\pi$
$439$	−7.68790	−	4.43861i	−0.366924	−	0.211843i	−0.672114	+	0.740448i	$0.734613\pi$
$440$	−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	−0.861006	−	0.508595i	$-0.830165\pi$
$443$	0.209480	−	0.362830i	0.00995270	−	0.0172386i	0.870959	+	0.491356i	$0.163499\pi$
$444$		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	$0.380775\pi$
$449$			39.4411i			1.86134i	−0.365861	+	0.930670i	$0.619225\pi$
$450$		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	−0.970909	−	0.239449i	$-0.923033\pi$
$457$	−5.94479	+	10.2967i	−0.278085	+	0.481658i	0.692823	+	0.721107i	$0.256367\pi$
$458$	−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	$0.00161518\pi$
$461$			0.217896i			0.0101484i	−0.999987	+	0.00507422i	$0.998385\pi$
$462$		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	0.931890	−	0.362741i	$-0.118159\pi$
$467$	23.4188	+	13.5208i	1.08369	+	0.625670i	0.151802	+	0.988411i	$0.451492\pi$
$468$		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	0.958233	−	0.285988i	$-0.0923218\pi$
$479$	5.06539	+	8.77352i	0.231444	+	0.400872i	−0.726789	+	0.686860i	$0.758988\pi$
$480$		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	0.957964	−	0.286888i	$-0.0926207\pi$
$487$	5.08735	+	8.81155i	0.230530	+	0.399290i	−0.727434	+	0.686177i	$0.759287\pi$
$488$	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	0.185065	−	0.982726i	$-0.440750\pi$
$499$	−12.8103	−	7.39603i	−0.573468	−	0.331092i	−0.758533	+	0.651634i	$0.774084\pi$
$500$	−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	0.985604	−	0.169073i	$-0.0540772\pi$
$509$	30.0509	+	17.3499i	1.33198	+	0.769021i	0.346381	+	0.938094i	$0.387411\pi$
$510$		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	−0.857063	−	0.515212i	$-0.827713\pi$
$521$	−19.9658	−	34.5818i	−0.874718	−	1.51506i	−0.0176549	−	0.999844i	$-0.505620\pi$
$522$		0			0
$523$	3.77245	−	6.53407i	0.164958	−	0.285715i	−0.771683	−	0.636008i	$-0.780585\pi$
$523$	3.77245	−	6.53407i	0.164958	−	0.285715i	0.936640	+	0.350293i	$0.113918\pi$
$524$	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	0.783310	−	0.621632i	$-0.213530\pi$
$541$	14.8073	+	8.54900i	0.636616	+	0.367550i	−0.146694	+	0.989182i	$0.546863\pi$
$542$	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	$0.191485\pi$
$547$			26.4723i			1.13187i	−0.824449	+	0.565936i	$0.808515\pi$
$548$	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	0.786703	+	0.617331i	$0.211786\pi$
$557$	21.9010	+	37.9337i	0.927976	+	1.60730i	0.141273	+	0.989971i	$0.454881\pi$
$558$		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	0.316764	−	0.948505i	$-0.397404\pi$
$563$	30.7646	−	17.7620i	1.29657	−	0.748578i	0.979811	+	0.199927i	$0.0640705\pi$
$564$		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	−0.0516428	−	0.998666i	$-0.516446\pi$
$569$	−22.4782	−	12.9778i	−0.942334	−	0.544057i	−0.890691	+	0.454609i	$0.849779\pi$
$570$		0			0
$571$	−13.6202	+	7.86364i	−0.569989	+	0.329083i	−0.757145	−	0.653247i	$-0.773406\pi$
$571$	−13.6202	+	7.86364i	−0.569989	+	0.329083i	0.187156	+	0.982330i	$0.440073\pi$
$572$	−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	−0.979319	−	0.202324i	$-0.935150\pi$
$577$	−31.0772	+	17.9424i	−1.29376	+	0.746953i	−0.314441	+	0.949277i	$0.601817\pi$
$578$	−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	$-0.975114\pi$
$587$		−	3.78446i		−	0.156201i	0.996945	−	0.0781007i	$-0.0248856\pi$
$588$		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	−0.999647	−	0.0265552i	$-0.991546\pi$
$593$	−11.6115	+	20.1117i	−0.476826	+	0.825887i	0.522821	+	0.852442i	$0.324880\pi$
$594$		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	−0.749081	−	0.662479i	$-0.769504\pi$
$599$	−13.4585	+	7.77024i	−0.549898	+	0.317484i	0.199183	+	0.979962i	$0.436171\pi$
$600$		0			0
$601$			23.5188i			0.959354i	0.877445	+	0.479677i	$0.159246\pi$
$601$			23.5188i			0.959354i	−0.877445	+	0.479677i	$0.840754\pi$
$602$	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	0.963834	−	0.266505i	$-0.0858687\pi$
$607$	29.9332	+	17.2819i	1.21495	+	0.701452i	0.251117	+	0.967957i	$0.419202\pi$
$608$	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	−0.347307	−	0.937752i	$-0.612904\pi$
$613$	7.20869	−	4.16194i	0.291156	−	0.168099i	0.638463	+	0.769652i	$0.279570\pi$
$614$	−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	$-0.940159\pi$
$617$		−	9.28453i		−	0.373781i	0.982381	−	0.186891i	$-0.0598410\pi$
$618$		0			0
$619$	12.0804	+	20.9238i	0.485551	+	0.840999i	0.999862	−	0.0166047i	$-0.00528567\pi$
$619$	12.0804	+	20.9238i	0.485551	+	0.840999i	−0.514311	+	0.857604i	$0.671952\pi$
$620$	−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	0.291664	−	0.956521i	$-0.405791\pi$
$641$	32.0492	−	18.5036i	1.26587	−	0.730849i	0.974203	+	0.225672i	$0.0724576\pi$
$642$		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	0.990077	+	0.140527i	$0.0448797\pi$
$647$	15.6875	+	27.1715i	0.616738	+	1.06822i	−0.373339	+	0.927695i	$0.621787\pi$
$648$		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	−0.932947	−	0.360014i	$-0.882772\pi$
$653$	−3.95300	+	6.84679i	−0.154693	+	0.267936i	0.778254	+	0.627949i	$0.216105\pi$
$654$		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	0.816223	−	0.577737i	$-0.196064\pi$
$661$	−2.37104	−	4.10677i	−0.0922230	−	0.159735i	−0.908446	+	0.418002i	$0.862731\pi$
$662$	−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	0.0643155	−	0.997930i	$-0.479514\pi$
$677$	−19.9765	−	11.5334i	−0.767759	−	0.443266i	−0.832075	+	0.554664i	$0.812847\pi$
$678$		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	0.793466	−	0.608615i	$-0.208275\pi$
$683$	−3.40643	−	5.90011i	−0.130343	−	0.225761i	−0.923809	+	0.382854i	$0.874941\pi$
$684$		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	−0.427396	−	0.904064i	$-0.640569\pi$
$691$	14.9637	−	25.9178i	0.569245	−	0.985961i	0.996641	−	0.0818962i	$-0.0260976\pi$
$692$	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	−0.160977	−	0.986958i	$-0.551464\pi$
$709$	−29.1885	−	16.8520i	−1.09620	−	0.632889i	−0.935219	+	0.354069i	$0.884798\pi$
$710$	−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	0.137611	−	0.990486i	$-0.456058\pi$
$719$	24.8458	−	43.0342i	0.926592	−	1.60490i	0.788981	−	0.614418i	$-0.210609\pi$
$720$		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	$0.0324746\pi$
$727$			5.49208i			0.203690i	−0.994800	+	0.101845i	$0.967525\pi$
$728$	−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	−0.869259	−	0.494357i	$-0.835403\pi$
$733$	−0.176068	+	0.304959i	−0.00650322	+	0.0112639i	0.862755	+	0.505621i	$0.168737\pi$
$734$	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	−0.236045	−	0.971742i	$-0.575851\pi$
$739$	13.2521	−	7.65108i	0.487485	−	0.281450i	0.723531	+	0.690292i	$0.242518\pi$
$740$	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	$-0.721696\pi$
$743$		−	41.8196i		−	1.53421i	0.641520	−	0.767106i	$-0.278304\pi$
$744$		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	−0.857555	−	0.514393i	$-0.828017\pi$
$751$	0.457654	−	0.792680i	0.0167000	−	0.0289253i	0.874255	+	0.485468i	$0.161351\pi$
$752$	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	$0.119830\pi$
$757$			20.2296i			0.735257i	−0.929973	+	0.367628i	$0.880170\pi$
$758$	−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	−0.748134	−	0.663547i	$-0.769050\pi$
$761$	5.53329	−	9.58394i	0.200582	−	0.347417i	0.948716	+	0.316130i	$0.102384\pi$
$762$		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	$0.122812\pi$
$769$			20.8715i			0.752646i	−0.926489	+	0.376323i	$0.877188\pi$
$770$	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	−0.881084	−	0.472961i	$-0.843185\pi$
$773$	−25.3570	+	14.6399i	−0.912030	+	0.526561i	−0.0309460	+	0.999521i	$0.509852\pi$
$774$		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	0.618551	−	0.785744i	$-0.287720\pi$
$787$	−10.4134	−	18.0366i	−0.371199	−	0.642935i	−0.989750	+	0.142809i	$0.954387\pi$
$788$	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	$0.170738\pi$
$797$			28.8543i			1.02207i	−0.859559	+	0.511036i	$0.829262\pi$
$798$		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	−0.947969	−	0.318362i	$-0.896867\pi$
$809$	−32.6025	+	18.8231i	−1.14624	+	0.661784i	−0.198275	+	0.980146i	$0.563534\pi$
$810$		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	−0.719593	−	0.694396i	$-0.755671\pi$
$821$	6.92169	−	11.9887i	0.241569	−	0.418409i	0.961161	+	0.275987i	$0.0890048\pi$
$822$		0			0
$823$	−6.60648	−	11.4428i	−0.230287	−	0.398869i	0.727605	−	0.685996i	$-0.240633\pi$
$823$	−6.60648	−	11.4428i	−0.230287	−	0.398869i	−0.957893	+	0.287127i	$0.907300\pi$
$824$	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	−0.955541	−	0.294859i	$-0.904727\pi$
$829$	−21.1084	−	36.5609i	−0.733126	−	1.26981i	0.222415	−	0.974952i	$-0.428606\pi$
$830$	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	0.727095	−	0.686537i	$-0.240870\pi$
$857$	−6.76275	−	11.7134i	−0.231011	−	0.400123i	−0.958106	+	0.286414i	$0.907537\pi$
$858$		0			0
$859$	9.51823	−	16.4861i	0.324758	−	0.562497i	−0.656705	−	0.754147i	$-0.728050\pi$
$859$	9.51823	−	16.4861i	0.324758	−	0.562497i	0.981463	+	0.191650i	$0.0613838\pi$
$860$	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	0.729646	−	0.683825i	$-0.239685\pi$
$863$	14.7548	+	8.51871i	0.502260	+	0.289980i	−0.227386	+	0.973805i	$0.573018\pi$
$864$		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	−0.355373	−	0.934725i	$-0.615646\pi$
$877$	−39.7587	−	22.9547i	−1.34255	−	0.775124i	−0.987182	+	0.159600i	$0.948980\pi$
$878$	−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	$0.361737\pi$
$883$			53.9117i			1.81427i	−0.420835	+	0.907137i	$0.638263\pi$
$884$	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	−0.969463	−	0.245238i	$-0.921134\pi$
$887$	−8.11124	+	14.0491i	−0.272349	+	0.471722i	0.697114	+	0.716960i	$0.254467\pi$
$888$		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	−0.605611	−	0.795761i	$-0.707071\pi$
$907$	−6.60352	+	3.81255i	−0.219266	+	0.126594i	0.386344	+	0.922355i	$0.373738\pi$
$908$	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	$-0.815196\pi$
$911$		−	33.1109i		−	1.09701i	0.836146	−	0.548507i	$-0.184804\pi$
$912$		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	0.461758	+	0.887006i	$0.347219\pi$
$919$	−16.2880	+	28.2116i	−0.537291	+	0.930616i	−0.999049	+	0.0436094i	$0.986114\pi$
$920$	−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	−0.708796	−	0.705413i	$-0.750762\pi$
$929$	7.81822	−	13.5416i	0.256507	−	0.444284i	0.965304	+	0.261129i	$0.0840948\pi$
$930$		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	$-0.699628\pi$
$937$		−	49.5708i		−	1.61941i	0.586839	−	0.809704i	$-0.300372\pi$
$938$	−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	−0.317537	−	0.948246i	$-0.602856\pi$
$941$	10.5801	−	6.10840i	0.344900	−	0.199128i	0.662437	+	0.749118i	$0.269522\pi$
$942$		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	−0.990014	−	0.140971i	$-0.954978\pi$
$947$	−11.4761	+	19.8772i	−0.372923	+	0.645921i	0.617091	+	0.786892i	$0.288311\pi$
$948$		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	$-0.944321\pi$
$953$		−	10.7450i		−	0.348063i	0.984740	−	0.174032i	$-0.0556795\pi$
$954$		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	−0.446755	−	0.894657i	$-0.647420\pi$
$971$	−45.0252	−	25.9953i	−1.44493	−	0.834229i	−0.998173	+	0.0604275i	$0.980754\pi$
$972$		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	−0.195421	−	0.980719i	$-0.562607\pi$
$977$	17.3850	−	10.0372i	0.556196	−	0.321120i	0.751617	+	0.659600i	$0.229274\pi$
$978$		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	−0.661902	−	0.749591i	$-0.730250\pi$
$983$	−30.7294	−	53.2249i	−0.980115	−	1.69761i	−0.318214	−	0.948019i	$-0.603083\pi$
$984$		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	0.979157	−	0.203105i	$-0.0651033\pi$
$991$	9.87483	+	17.1037i	0.313684	+	0.543317i	−0.665473	+	0.746422i	$0.731770\pi$
$992$	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	0.833568	−	0.552418i	$-0.186295\pi$
$997$	−1.94579	−	3.37021i	−0.0616239	−	0.106736i	−0.895191	+	0.445682i	$0.852961\pi$
$998$	−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.341.20	yes	56
3.2	odd	2	inner	504.2.ch.b.341.9	yes	56
4.3	odd	2		2016.2.cp.b.593.12		56
7.3	odd	6	inner	504.2.ch.b.269.1	✓	56
8.3	odd	2		2016.2.cp.b.593.17		56
8.5	even	2	inner	504.2.ch.b.341.28	yes	56
12.11	even	2		2016.2.cp.b.593.18		56
21.17	even	6	inner	504.2.ch.b.269.28	yes	56
24.5	odd	2	inner	504.2.ch.b.341.1	yes	56
24.11	even	2		2016.2.cp.b.593.11		56
28.3	even	6		2016.2.cp.b.17.11		56
56.3	even	6		2016.2.cp.b.17.18		56
56.45	odd	6	inner	504.2.ch.b.269.9	yes	56
84.59	odd	6		2016.2.cp.b.17.17		56
168.59	odd	6		2016.2.cp.b.17.12		56
168.101	even	6	inner	504.2.ch.b.269.20	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.ch.b.269.1	✓	56	7.3	odd	6	inner
504.2.ch.b.269.9	yes	56	56.45	odd	6	inner
504.2.ch.b.269.20	yes	56	168.101	even	6	inner
504.2.ch.b.269.28	yes	56	21.17	even	6	inner
504.2.ch.b.341.1	yes	56	24.5	odd	2	inner
504.2.ch.b.341.9	yes	56	3.2	odd	2	inner
504.2.ch.b.341.20	yes	56	1.1	even	1	trivial
504.2.ch.b.341.28	yes	56	8.5	even	2	inner
2016.2.cp.b.17.11		56	28.3	even	6
2016.2.cp.b.17.12		56	168.59	odd	6
2016.2.cp.b.17.17		56	84.59	odd	6
2016.2.cp.b.17.18		56	56.3	even	6
2016.2.cp.b.593.11		56	24.11	even	2
2016.2.cp.b.593.12		56	4.3	odd	2
2016.2.cp.b.593.17		56	8.3	odd	2
2016.2.cp.b.593.18		56	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
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

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