LMFDB - Embedded newform 504.2.ch.b.269.9

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			269.9
Character	$\chi$	$=$	504.269
Dual form			504.2.ch.b.341.9

$q$-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	−0.314029	−	0.949413i	$-0.601679\pi$
$5$	0.785247	−	0.453362i	0.351173	−	0.202750i	0.665202	+	0.746664i	$0.268346\pi$
$6$		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	$-0.826333\pi$
$11$	0.0729337	−	0.126325i	0.0219903	−	0.0380884i	0.876811	+	0.480835i	$0.159666\pi$
$12$		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	$0.426519\pi$
$17$	−3.00430	+	5.20361i	−0.728651	+	1.26206i	−0.957454	+	0.288587i	$0.906814\pi$
$18$		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	−0.127054	−	0.991896i	$-0.540552\pi$
$23$	3.20566	−	1.85079i	0.668426	−	0.385916i	0.795480	+	0.605980i	$0.207219\pi$
$24$		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	$-0.900503\pi$
$29$	−10.2484			−1.90309			−0.951543	+	0.307515i	$0.900503\pi$
$30$		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	$-0.443468\pi$
$41$	2.26244			0.353334			0.176667	+	0.984271i	$0.443468\pi$
$42$		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	$0.00837564\pi$
$47$	3.58285	+	6.20567i	0.522612	+	0.905190i	−0.477042	+	0.878881i	$0.658291\pi$
$48$		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	$-0.750712\pi$
$53$	1.86849	−	3.23632i	0.256657	−	0.444543i	0.965344	+	0.260980i	$0.0840455\pi$
$54$		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	$-0.491743\pi$
$59$	−6.35100	−	3.66675i	−0.826829	−	0.477370i	−0.852766	+	0.522293i	$0.825077\pi$
$60$		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	$-0.905726\pi$
$71$		−	4.91850i		−	0.583719i	0.956461	−	0.291859i	$-0.0942739\pi$
$72$		0			0
$73$	2.67843	+	1.54639i	0.313486	+	0.180991i	0.648485	−	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	$0.249244\pi$
$83$			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	$-0.113888\pi$
$89$	1.55708	+	2.69694i	0.165050	+	0.285875i	−0.771623	+	0.636080i	$0.780555\pi$
$90$		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	−0.0641776	−	0.997938i	$-0.520442\pi$
$101$	−9.65297	−	5.57314i	−0.960506	−	0.554549i	−0.896329	+	0.443390i	$0.853776\pi$
$102$		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	$0.0750144\pi$
$107$	7.12074	+	12.3335i	0.688387	+	1.19232i	−0.283972	+	0.958833i	$0.591652\pi$
$108$		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	$0.131606\pi$
$113$			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	$-0.527663\pi$
$131$	8.38458	−	4.84084i	0.732564	−	0.422946i	0.819359	+	0.573280i	$0.194329\pi$
$132$		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	$-0.481776\pi$
$137$	−9.11532	−	5.26273i	−0.778774	−	0.449625i	−0.835996	+	0.548736i	$0.815109\pi$
$138$		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	$-0.00910364\pi$
$149$	5.79849	+	10.0433i	0.475031	+	0.822777i	−0.524560	+	0.851373i	$0.675770\pi$
$150$		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	$-0.520276\pi$
$167$	−1.64523			−0.127312			−0.0636558	+	0.997972i	$0.520276\pi$
$168$		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	$-0.555306\pi$
$173$	7.80851	−	4.50825i	0.593670	−	0.342756i	0.766547	+	0.642188i	$0.221973\pi$
$174$		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	$-0.649426\pi$
$179$	7.30700	−	12.6561i	0.546151	−	0.945961i	0.998534	−	0.0541368i	$-0.0172407\pi$
$180$		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	$-0.668922\pi$
$191$	−0.169619	+	0.0979296i	−0.0122732	+	0.00708594i	0.493851	+	0.869547i	$0.335589\pi$
$192$		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	$-0.488869\pi$
$197$	0.981430			0.0699240			0.0349620	+	0.999389i	$0.488869\pi$
$198$		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	−0.204575	−	0.978851i	$-0.565581\pi$
$227$	−17.3954	−	10.0432i	−1.15457	−	0.666593i	−0.949997	+	0.312258i	$0.898915\pi$
$228$		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	0.468768	−	0.883322i	$-0.344698\pi$
$233$	22.4100	−	12.9384i	1.46813	−	0.847625i	0.999363	+	0.0356961i	$0.0113649\pi$
$234$		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	−0.999538	−	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	$-0.631826\pi$
$251$		−	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	$-0.289320\pi$
$257$	−6.02554	−	10.4365i	−0.375863	−	0.651014i	−0.990456	+	0.137831i	$0.955987\pi$
$258$		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	$-0.306467\pi$
$263$	2.36800	+	1.36716i	0.146017	+	0.0843029i	−0.425212	+	0.905094i	$0.639800\pi$
$264$		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	$-0.383502\pi$
$269$	−4.45879	−	2.57428i	−0.271857	−	0.156957i	−0.629731	+	0.776813i	$0.716835\pi$
$270$		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	$0.0101227\pi$
$281$			1.06599i			0.0635918i	−0.999494	+	0.0317959i	$0.989877\pi$
$282$		0			0
$283$	−3.14663	+	5.45012i	−0.187048	+	0.323976i	−0.944265	−	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	$0.175887\pi$
$293$			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	0.233045	+	0.972466i	$0.425131\pi$
$311$	−12.7971	+	22.1653i	−0.725658	+	1.25688i	−0.958703	+	0.284410i	$0.908202\pi$
$312$		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	0.920585	−	0.390542i	$-0.127712\pi$
$317$	2.17346	+	3.76454i	0.122074	+	0.211438i	−0.798512	+	0.601979i	$0.794379\pi$
$318$		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	−0.756694	−	0.653770i	$-0.773187\pi$
$347$	3.49897	−	6.06039i	0.187834	−	0.325339i	0.944528	+	0.328431i	$0.106520\pi$
$348$		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	$-0.922326\pi$
$353$	−5.18465	+	8.98008i	−0.275951	+	0.477962i	0.694423	+	0.719567i	$0.255659\pi$
$354$		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	$-0.846489\pi$
$359$	−17.5691	+	10.1436i	−0.927264	+	0.535356i	−0.0413188	+	0.999146i	$0.513156\pi$
$360$		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	$0.0885185\pi$
$383$	14.0619	+	24.3560i	0.718531	+	1.24453i	−0.243051	+	0.970014i	$0.578148\pi$
$384$		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	$-0.895488\pi$
$389$	−3.82681	+	6.62822i	−0.194027	+	0.336064i	0.752554	+	0.658530i	$0.228822\pi$
$390$		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	−0.879555	−	0.475798i	$-0.842159\pi$
$401$	−18.1682	+	10.4894i	−0.907279	+	0.523818i	−0.0277241	+	0.999616i	$0.508826\pi$
$402$		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	$0.181033\pi$
$419$			22.0482i			1.07713i	−0.842585	+	0.538564i	$0.818967\pi$
$420$		0			0
$421$			18.2360i			0.888771i	0.895836	+	0.444385i	$0.146578\pi$
$421$			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	−0.236799	−	0.971559i	$-0.576098\pi$
$431$	−24.8419	−	14.3425i	−1.19659	−	0.690854i	−0.959794	+	0.280705i	$0.909432\pi$
$432$		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	0.861006	−	0.508595i	$-0.169835\pi$
$443$	−0.209480	−	0.362830i	−0.00995270	−	0.0172386i	−0.870959	+	0.491356i	$0.836501\pi$
$444$		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	0.692823	−	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	$0.00161518\pi$
$461$			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	$-0.881841\pi$
$467$	−23.4188	+	13.5208i	−1.08369	+	0.625670i	−0.151802	+	0.988411i	$0.548508\pi$
$468$		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	$-0.907678\pi$
$479$	−5.06539	+	8.77352i	−0.231444	+	0.400872i	0.726789	+	0.686860i	$0.241012\pi$
$480$		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	$-0.687871\pi$
$491$	−24.6642			−1.11308			−0.556540	+	0.830821i	$0.687871\pi$
$492$		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	$-0.782642\pi$
$503$	−34.7978			−1.55156			−0.775778	+	0.631006i	$0.782642\pi$
$504$		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	$-0.945923\pi$
$509$	−30.0509	+	17.3499i	−1.33198	+	0.769021i	−0.346381	+	0.938094i	$0.612589\pi$
$510$		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	$-0.494380\pi$
$521$	19.9658	−	34.5818i	0.874718	−	1.51506i	0.857063	−	0.515212i	$-0.172287\pi$
$522$		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	$0.545119\pi$
$557$	−21.9010	+	37.9337i	−0.927976	+	1.60730i	−0.786703	+	0.617331i	$0.788214\pi$
$558$		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	$-0.602596\pi$
$563$	−30.7646	−	17.7620i	−1.29657	−	0.748578i	−0.979811	+	0.199927i	$0.935930\pi$
$564$		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	$-0.483554\pi$
$569$	22.4782	−	12.9778i	0.942334	−	0.544057i	0.890691	+	0.454609i	$0.150221\pi$
$570$		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	$-0.975114\pi$
$587$		−	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	$-0.00845376\pi$
$593$	11.6115	+	20.1117i	0.476826	+	0.825887i	−0.522821	+	0.852442i	$0.675120\pi$
$594$		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	$-0.230496\pi$
$599$	13.4585	+	7.77024i	0.549898	+	0.317484i	−0.199183	+	0.979962i	$0.563829\pi$
$600$		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	$-0.940159\pi$
$617$		−	9.28453i		−	0.373781i	0.982381	−	0.186891i	$-0.0598410\pi$
$618$		0			0
$619$	12.0804	−	20.9238i	0.485551	−	0.840999i	−0.514311	−	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	−0.291664	−	0.956521i	$-0.594209\pi$
$641$	−32.0492	−	18.5036i	−1.26587	−	0.730849i	−0.974203	+	0.225672i	$0.927542\pi$
$642$		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	$0.378213\pi$
$647$	−15.6875	+	27.1715i	−0.616738	+	1.06822i	−0.990077	+	0.140527i	$0.955120\pi$
$648$		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	$-0.117228\pi$
$653$	3.95300	+	6.84679i	0.154693	+	0.267936i	−0.778254	+	0.627949i	$0.783895\pi$
$654$		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	$-0.278505\pi$
$659$	32.9121			1.28207			0.641036	+	0.767510i	$0.278505\pi$
$660$		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	−0.0643155	−	0.997930i	$-0.520486\pi$
$677$	19.9765	−	11.5334i	0.767759	−	0.443266i	0.832075	+	0.554664i	$0.187153\pi$
$678$		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	$-0.791725\pi$
$683$	3.40643	−	5.90011i	0.130343	−	0.225761i	0.923809	+	0.382854i	$0.125059\pi$
$684$		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	$-0.610667\pi$
$701$	−18.0414			−0.681415			−0.340707	+	0.940169i	$0.610667\pi$
$702$		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	$-0.789391\pi$
$719$	−24.8458	−	43.0342i	−0.926592	−	1.60490i	−0.137611	−	0.990486i	$-0.543942\pi$
$720$		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	$-0.721696\pi$
$743$		−	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	0.874255	−	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	0.748134	−	0.663547i	$-0.230950\pi$
$761$	−5.53329	−	9.58394i	−0.200582	−	0.347417i	−0.948716	+	0.316130i	$0.897616\pi$
$762$		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	0.881084	−	0.472961i	$-0.156815\pi$
$773$	25.3570	+	14.6399i	0.912030	+	0.526561i	0.0309460	+	0.999521i	$0.490148\pi$
$774$		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	$0.170738\pi$
$797$			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	$-0.103133\pi$
$809$	32.6025	+	18.8231i	1.14624	+	0.661784i	0.198275	+	0.980146i	$0.436466\pi$
$810$		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	$-0.244329\pi$
$821$	−6.92169	−	11.9887i	−0.241569	−	0.418409i	−0.961161	+	0.275987i	$0.910995\pi$
$822$		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	$-0.568288\pi$
$827$	−12.2445			−0.425784			−0.212892	+	0.977076i	$0.568288\pi$
$828$		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	$-0.523654\pi$
$839$	−4.30094			−0.148485			−0.0742424	+	0.997240i	$0.523654\pi$
$840$		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	$-0.759130\pi$
$857$	6.76275	−	11.7134i	0.231011	−	0.400123i	0.958106	+	0.286414i	$0.0924632\pi$
$858$		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	−0.729646	−	0.683825i	$-0.760315\pi$
$863$	−14.7548	+	8.51871i	−0.502260	+	0.289980i	0.227386	+	0.973805i	$0.426982\pi$
$864$		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	$-0.570057\pi$
$881$	−12.9601			−0.436638			−0.218319	+	0.975877i	$0.570057\pi$
$882$		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	0.969463	−	0.245238i	$-0.0788662\pi$
$887$	8.11124	+	14.0491i	0.272349	+	0.471722i	−0.697114	+	0.716960i	$0.745533\pi$
$888$		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	$-0.815196\pi$
$911$		−	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	−0.999049	−	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	0.708796	−	0.705413i	$-0.249238\pi$
$929$	−7.81822	−	13.5416i	−0.256507	−	0.444284i	−0.965304	+	0.261129i	$0.915905\pi$
$930$		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	0.317537	−	0.948246i	$-0.397144\pi$
$941$	−10.5801	−	6.10840i	−0.344900	−	0.199128i	−0.662437	+	0.749118i	$0.730478\pi$
$942$		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	$-0.0450223\pi$
$947$	11.4761	+	19.8772i	0.372923	+	0.645921i	−0.617091	+	0.786892i	$0.711689\pi$
$948$		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	$-0.352580\pi$
$971$	45.0252	−	25.9953i	1.44493	−	0.834229i	0.998173	+	0.0604275i	$0.0192464\pi$
$972$		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	$-0.437393\pi$
$977$	−17.3850	−	10.0372i	−0.556196	−	0.321120i	−0.751617	+	0.659600i	$0.770726\pi$
$978$		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	$-0.396917\pi$
$983$	30.7294	−	53.2249i	0.980115	−	1.69761i	0.661902	−	0.749591i	$-0.269750\pi$
$984$		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.269.9	yes	56
3.2	odd	2	inner	504.2.ch.b.269.20	yes	56
4.3	odd	2		2016.2.cp.b.17.18		56
7.5	odd	6	inner	504.2.ch.b.341.28	yes	56
8.3	odd	2		2016.2.cp.b.17.11		56
8.5	even	2	inner	504.2.ch.b.269.1	✓	56
12.11	even	2		2016.2.cp.b.17.12		56
21.5	even	6	inner	504.2.ch.b.341.1	yes	56
24.5	odd	2	inner	504.2.ch.b.269.28	yes	56
24.11	even	2		2016.2.cp.b.17.17		56
28.19	even	6		2016.2.cp.b.593.17		56
56.5	odd	6	inner	504.2.ch.b.341.20	yes	56
56.19	even	6		2016.2.cp.b.593.12		56
84.47	odd	6		2016.2.cp.b.593.11		56
168.5	even	6	inner	504.2.ch.b.341.9	yes	56
168.131	odd	6		2016.2.cp.b.593.18		56

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