LMFDB - Embedded newform 441.4.p.d.80.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [441,4,Mod(80,441)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("441.80"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(441, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 1])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	441.p (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,96] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$26.0198423125$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			80.16
Character	$\chi$	$=$	441.80
Dual form			441.4.p.d.215.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.40358 - 0.810356i) q^{2} +(-2.68665 + 4.65341i) q^{4} +(2.35993 + 4.08752i) q^{5} +21.6743i q^{8} +(6.62469 + 3.82477i) q^{10} +(-25.9801 - 14.9996i) q^{11} +27.1586i q^{13} +(-3.92932 - 6.80578i) q^{16} +(8.92464 - 15.4579i) q^{17} +(-107.297 + 61.9477i) q^{19} -25.3612 q^{20} -48.6201 q^{22} +(71.0802 - 41.0382i) q^{23} +(51.3615 - 88.9606i) q^{25} +(22.0081 + 38.1191i) q^{26} +88.2194i q^{29} +(-220.389 - 127.242i) q^{31} +(-161.194 - 93.0653i) q^{32} -28.9285i q^{34} +(-107.695 - 186.533i) q^{37} +(-100.399 + 173.897i) q^{38} +(-88.5939 + 51.1497i) q^{40} -427.760 q^{41} +62.4602 q^{43} +(139.599 - 80.5974i) q^{44} +(66.5110 - 115.200i) q^{46} +(211.787 + 366.825i) q^{47} -166.484i q^{50} +(-126.380 - 72.9654i) q^{52} +(-587.234 - 339.039i) q^{53} -141.592i q^{55} +(71.4891 + 123.823i) q^{58} +(-383.719 + 664.621i) q^{59} +(-313.156 + 180.801i) q^{61} -412.444 q^{62} -238.795 q^{64} +(-111.011 + 64.0923i) q^{65} +(323.947 - 561.093i) q^{67} +(47.9547 + 83.0600i) q^{68} +536.663i q^{71} +(-547.293 - 315.980i) q^{73} +(-302.316 - 174.542i) q^{74} -665.726i q^{76} +(298.709 + 517.379i) q^{79} +(18.5458 - 32.1223i) q^{80} +(-600.395 + 346.638i) q^{82} +591.773 q^{83} +84.2461 q^{85} +(87.6677 - 50.6150i) q^{86} +(325.106 - 563.100i) q^{88} +(769.502 + 1332.82i) q^{89} +441.020i q^{92} +(594.517 + 343.245i) q^{94} +(-506.425 - 292.385i) q^{95} -654.102i q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 96 q^{4} - 144 q^{16} + 1248 q^{22} - 312 q^{25} + 864 q^{37} + 2496 q^{43} + 3888 q^{46} + 7440 q^{58} - 6720 q^{64} + 2688 q^{67} - 480 q^{79} + 26496 q^{85} + 7248 q^{88}+O(q^{100}) $ 48 * q + 96 * q^4 - 144 * q^16 + 1248 * q^22 - 312 * q^25 + 864 * q^37 + 2496 * q^43 + 3888 * q^46 + 7440 * q^58 - 6720 * q^64 + 2688 * q^67 - 480 * q^79 + 26496 * q^85 + 7248 * q^88

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	1.40358	−	0.810356i	0.496240	−	0.286504i	−0.230920	−	0.972973i	$-0.574173\pi$
$2$	1.40358	−	0.810356i	0.496240	−	0.286504i	0.727159	+	0.686469i	$0.240840\pi$
$3$		0			0
$3$		0			0
$4$	−2.68665	+	4.65341i	−0.335831	+	0.581676i
$5$	2.35993	+	4.08752i	0.211079	+	0.365599i	0.952052	−	0.305935i	$-0.0989691\pi$
$5$	2.35993	+	4.08752i	0.211079	+	0.365599i	−0.740974	+	0.671534i	$0.765636\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$			21.6743i			0.957876i
$9$		0			0
$10$	6.62469	+	3.82477i	0.209491	+	0.120950i
$11$	−25.9801	−	14.9996i	−0.712118	−	0.411142i	0.0997267	−	0.995015i	$-0.468203\pi$
$11$	−25.9801	−	14.9996i	−0.712118	−	0.411142i	−0.811845	+	0.583873i	$0.801536\pi$
$12$		0			0
$13$			27.1586i			0.579417i	0.957115	+	0.289709i	$0.0935584\pi$
$13$			27.1586i			0.579417i	−0.957115	+	0.289709i	$0.906442\pi$
$14$		0			0
$15$		0			0
$16$	−3.92932	−	6.80578i	−0.0613956	−	0.106340i
$17$	8.92464	−	15.4579i	0.127326	−	0.220535i	−0.795314	−	0.606198i	$-0.792694\pi$
$17$	8.92464	−	15.4579i	0.127326	−	0.220535i	0.922640	+	0.385663i	$0.126027\pi$
$18$		0			0
$19$	−107.297	+	61.9477i	−1.29555	+	0.747988i	−0.979633	−	0.200797i	$-0.935647\pi$
$19$	−107.297	+	61.9477i	−1.29555	+	0.747988i	−0.315921	+	0.948786i	$0.602313\pi$
$20$	−25.3612			−0.283547
$21$		0			0
$22$	−48.6201			−0.471175
$23$	71.0802	−	41.0382i	0.644402	−	0.372046i	−0.141906	−	0.989880i	$-0.545323\pi$
$23$	71.0802	−	41.0382i	0.644402	−	0.372046i	0.786308	+	0.617835i	$0.211990\pi$
$24$		0			0
$25$	51.3615	−	88.9606i	0.410892	−	0.711685i
$26$	22.0081	+	38.1191i	0.166005	+	0.287530i
$27$		0			0
$28$		0			0
$29$			88.2194i			0.564894i	0.959283	+	0.282447i	$0.0911462\pi$
$29$			88.2194i			0.564894i	−0.959283	+	0.282447i	$0.908854\pi$
$30$		0			0
$31$	−220.389	−	127.242i	−1.27687	−	0.737203i	−0.300600	−	0.953750i	$-0.597187\pi$
$31$	−220.389	−	127.242i	−1.27687	−	0.737203i	−0.976272	+	0.216548i	$0.930520\pi$
$32$	−161.194	−	93.0653i	−0.890479	−	0.514118i
$33$		0			0
$34$		−	28.9285i		−	0.145918i
$35$		0			0
$36$		0			0
$37$	−107.695	−	186.533i	−0.478511	−	0.828805i	0.521186	−	0.853443i	$-0.325490\pi$
$37$	−107.695	−	186.533i	−0.478511	−	0.828805i	−0.999696	+	0.0246385i	$0.992157\pi$
$38$	−100.399	+	173.897i	−0.428603	+	0.742363i
$39$		0			0
$40$	−88.5939	+	51.1497i	−0.350198	+	0.202187i
$41$	−427.760			−1.62939			−0.814695	−	0.579890i	$-0.803095\pi$
$41$	−427.760			−1.62939			−0.814695	+	0.579890i	$0.803095\pi$
$42$		0			0
$43$	62.4602			0.221514			0.110757	−	0.993848i	$-0.464673\pi$
$43$	62.4602			0.221514			0.110757	+	0.993848i	$0.464673\pi$
$44$	139.599	−	80.5974i	0.478303	−	0.276148i
$45$		0			0
$46$	66.5110	−	115.200i	0.213185	−	0.369247i
$47$	211.787	+	366.825i	0.657282	+	1.13845i	0.981317	+	0.192400i	$0.0616271\pi$
$47$	211.787	+	366.825i	0.657282	+	1.13845i	−0.324035	+	0.946045i	$0.605040\pi$
$48$		0			0
$49$		0			0
$50$		−	166.484i		−	0.470888i
$51$		0			0
$52$	−126.380	−	72.9654i	−0.337033	−	0.194586i
$53$	−587.234	−	339.039i	−1.52194	−	0.878692i	−0.999664	−	0.0259140i	$-0.991750\pi$
$53$	−587.234	−	339.039i	−1.52194	−	0.878692i	−0.522274	−	0.852778i	$-0.674916\pi$
$54$		0			0
$55$		−	141.592i		−	0.347133i
$56$		0			0
$57$		0			0
$58$	71.4891	+	123.823i	0.161844	+	0.280323i
$59$	−383.719	+	664.621i	−0.846711	+	1.46655i	0.0374163	+	0.999300i	$0.488087\pi$
$59$	−383.719	+	664.621i	−0.846711	+	1.46655i	−0.884127	+	0.467246i	$0.845246\pi$
$60$		0			0
$61$	−313.156	+	180.801i	−0.657303	+	0.379494i	−0.791249	−	0.611495i	$-0.790569\pi$
$61$	−313.156	+	180.801i	−0.657303	+	0.379494i	0.133946	+	0.990989i	$0.457235\pi$
$62$	−412.444			−0.844846
$63$		0			0
$64$	−238.795			−0.466396
$65$	−111.011	+	64.0923i	−0.211834	+	0.122303i
$66$		0			0
$67$	323.947	−	561.093i	0.590694	−	1.02311i	−0.403446	−	0.915004i	$-0.632188\pi$
$67$	323.947	−	561.093i	0.590694	−	1.02311i	0.994139	−	0.108108i	$-0.0344791\pi$
$68$	47.9547	+	83.0600i	0.0855200	+	0.148125i
$69$		0			0
$70$		0			0
$71$			536.663i			0.897045i	0.893772	+	0.448522i	$0.148050\pi$
$71$			536.663i			0.897045i	−0.893772	+	0.448522i	$0.851950\pi$
$72$		0			0
$73$	−547.293	−	315.980i	−0.877477	−	0.506612i	−0.00765130	−	0.999971i	$-0.502436\pi$
$73$	−547.293	−	315.980i	−0.877477	−	0.506612i	−0.869826	+	0.493359i	$0.835769\pi$
$74$	−302.316	−	174.542i	−0.474912	−	0.274190i
$75$		0			0
$76$		−	665.726i		−	1.00479i
$77$		0			0
$78$		0			0
$79$	298.709	+	517.379i	0.425410	+	0.736832i	0.996459	−	0.0840844i	$-0.0267965\pi$
$79$	298.709	+	517.379i	0.425410	+	0.736832i	−0.571049	+	0.820916i	$0.693463\pi$
$80$	18.5458	−	32.1223i	0.0259186	−	0.0448923i
$81$		0			0
$82$	−600.395	+	346.638i	−0.808567	+	0.466827i
$83$	591.773			0.782597			0.391299	−	0.920264i	$-0.372026\pi$
$83$	591.773			0.782597			0.391299	+	0.920264i	$0.372026\pi$
$84$		0			0
$85$	84.2461			0.107503
$86$	87.6677	−	50.6150i	0.109924	−	0.0634646i
$87$		0			0
$88$	325.106	−	563.100i	0.393823	−	0.682121i
$89$	769.502	+	1332.82i	0.916484	+	1.58740i	0.804714	+	0.593662i	$0.202318\pi$
$89$	769.502	+	1332.82i	0.916484	+	1.58740i	0.111769	+	0.993734i	$0.464348\pi$
$90$		0			0
$91$		0			0
$92$			441.020i			0.499778i
$93$		0			0
$94$	594.517	+	343.245i	0.652338	+	0.376628i
$95$	−506.425	−	292.385i	−0.546927	−	0.315769i
$96$		0			0
$97$		−	654.102i		−	0.684680i	−0.939576	−	0.342340i	$-0.888781\pi$
$97$		−	654.102i		−	0.684680i	0.939576	−	0.342340i	$-0.111219\pi$
$98$		0			0
$99$		0			0
$100$	275.980	+	478.012i	0.275980	+	0.478012i
$101$	−148.389	+	257.018i	−0.146191	+	0.253210i	−0.929817	−	0.368023i	$-0.880035\pi$
$101$	−148.389	+	257.018i	−0.146191	+	0.253210i	0.783626	+	0.621233i	$0.213368\pi$
$102$		0			0
$103$	387.255	−	223.582i	0.370460	−	0.213885i	−0.303199	−	0.952927i	$-0.598055\pi$
$103$	387.255	−	223.582i	0.370460	−	0.213885i	0.673660	+	0.739042i	$0.264721\pi$
$104$	−588.641			−0.555010
$105$		0			0
$106$	−1098.97			−1.00699
$107$	−655.418	+	378.406i	−0.592165	+	0.341887i	−0.765953	−	0.642896i	$-0.777733\pi$
$107$	−655.418	+	378.406i	−0.592165	+	0.341887i	0.173788	+	0.984783i	$0.444399\pi$
$108$		0			0
$109$	−59.2503	+	102.625i	−0.0520656	+	0.0901803i	−0.890884	−	0.454232i	$-0.849914\pi$
$109$	−59.2503	+	102.625i	−0.0520656	+	0.0901803i	0.838818	+	0.544412i	$0.183247\pi$
$110$	−114.740	−	198.736i	−0.0994550	−	0.172261i
$111$		0			0
$112$		0			0
$113$			90.4761i			0.0753210i	0.999291	+	0.0376605i	$0.0119905\pi$
$113$			90.4761i			0.0753210i	−0.999291	+	0.0376605i	$0.988009\pi$
$114$		0			0
$115$	335.489	+	193.694i	0.272039	+	0.157062i
$116$	−410.521	−	237.014i	−0.328586	−	0.189709i
$117$		0			0
$118$			1243.80i			0.970344i
$119$		0			0
$120$		0			0
$121$	−215.522	−	373.296i	−0.161925	−	0.280463i
$122$	−293.026	+	507.535i	−0.217453	+	0.376640i
$123$		0			0
$124$	1184.22	−	683.707i	0.857626	−	0.495151i
$125$	1074.82			0.769079
$126$		0			0
$127$	324.991			0.227073			0.113536	−	0.993534i	$-0.463782\pi$
$127$	324.991			0.227073			0.113536	+	0.993534i	$0.463782\pi$
$128$	954.384	−	551.014i	0.659034	−	0.380494i
$129$		0			0
$130$	−103.875	+	179.917i	−0.0700804	+	0.121383i
$131$	338.925	+	587.035i	0.226046	+	0.391523i	0.956633	−	0.291297i	$-0.0940868\pi$
$131$	338.925	+	587.035i	0.226046	+	0.391523i	−0.730587	+	0.682820i	$0.760753\pi$
$132$		0			0
$133$		0			0
$134$		−	1050.05i		−	0.676944i
$135$		0			0
$136$	335.039	+	193.435i	0.211245	+	0.121963i
$137$	1866.23	+	1077.47i	1.16381	+	0.671928i	0.952215	−	0.305429i	$-0.0987998\pi$
$137$	1866.23	+	1077.47i	1.16381	+	0.671928i	0.211598	+	0.977357i	$0.432133\pi$
$138$		0			0
$139$		−	719.518i		−	0.439055i	−0.975606	−	0.219528i	$-0.929548\pi$
$139$		−	719.518i		−	0.439055i	0.975606	−	0.219528i	$-0.0704516\pi$
$140$		0			0
$141$		0			0
$142$	434.888	+	753.248i	0.257007	+	0.445149i
$143$	407.368	−	705.582i	0.238223	−	0.412614i
$144$		0			0
$145$	−360.599	+	208.192i	−0.206525	+	0.119237i
$146$	−1024.22			−0.580585
$147$		0			0
$148$	1157.35			0.642795
$149$	−1034.65	+	597.357i	−0.568873	+	0.328439i	−0.756699	−	0.653763i	$-0.773189\pi$
$149$	−1034.65	+	597.357i	−0.568873	+	0.328439i	0.187826	+	0.982202i	$0.439856\pi$
$150$		0			0
$151$	−536.066	+	928.494i	−0.288904	+	0.500396i	−0.973548	−	0.228481i	$-0.926624\pi$
$151$	−536.066	+	928.494i	−0.288904	+	0.500396i	0.684645	+	0.728877i	$0.259957\pi$
$152$	−1342.67	−	2325.57i	−0.716480	−	1.24098i
$153$		0			0
$154$		0			0
$155$		−	1201.13i		−	0.622431i
$156$		0			0
$157$	−2022.12	−	1167.47i	−1.02792	−	0.593468i	−0.111530	−	0.993761i	$-0.535575\pi$
$157$	−2022.12	−	1167.47i	−1.02792	−	0.593468i	−0.916387	+	0.400293i	$0.868908\pi$
$158$	838.523	+	484.121i	0.422211	+	0.243763i
$159$		0			0
$160$		−	878.511i		−	0.434077i
$161$		0			0
$162$		0			0
$163$	−1803.42	−	3123.61i	−0.866592	−	1.50098i	−0.865458	−	0.500982i	$-0.832972\pi$
$163$	−1803.42	−	3123.61i	−0.866592	−	1.50098i	−0.00113428	−	0.999999i	$-0.500361\pi$
$164$	1149.24	−	1990.54i	0.547199	−	0.947777i
$165$		0			0
$166$	830.600	−	479.547i	0.388356	−	0.224217i
$167$	2249.44			1.04232			0.521159	−	0.853460i	$-0.325500\pi$
$167$	2249.44			1.04232			0.521159	+	0.853460i	$0.325500\pi$
$168$		0			0
$169$	1459.41			0.664275
$170$	118.246	−	68.2693i	0.0533473	−	0.0308001i
$171$		0			0
$172$	−167.809	+	290.653i	−0.0743912	+	0.128849i
$173$	−2022.40	−	3502.90i	−0.888788	−	1.53943i	−0.841310	−	0.540553i	$-0.818215\pi$
$173$	−2022.40	−	3502.90i	−0.888788	−	1.53943i	−0.0474778	−	0.998872i	$-0.515118\pi$
$174$		0			0
$175$		0			0
$176$			235.753i			0.100969i
$177$		0			0
$178$	2160.11	+	1247.14i	0.909591	+	0.525153i
$179$	1843.22	+	1064.18i	0.769658	+	0.444362i	0.832753	−	0.553645i	$-0.186764\pi$
$179$	1843.22	+	1064.18i	0.769658	+	0.444362i	−0.0630946	+	0.998008i	$0.520097\pi$
$180$		0			0
$181$			4272.10i			1.75438i	0.480143	+	0.877190i	$0.340585\pi$
$181$			4272.10i			1.75438i	−0.480143	+	0.877190i	$0.659415\pi$
$182$		0			0
$183$		0			0
$184$	889.472	+	1540.61i	0.356373	+	0.617257i
$185$	508.304	−	880.408i	0.202007	−	0.349886i
$186$		0			0
$187$	−463.726	+	267.732i	−0.181342	+	0.104698i
$188$	−2275.98			−0.882942
$189$		0			0
$190$	−947.742			−0.361876
$191$	−670.762	+	387.265i	−0.254108	+	0.146709i	−0.621644	−	0.783300i	$-0.713535\pi$
$191$	−670.762	+	387.265i	−0.254108	+	0.146709i	0.367536	+	0.930009i	$0.380202\pi$
$192$		0			0
$193$	−2456.61	+	4254.97i	−0.916221	+	1.58694i	−0.111117	+	0.993807i	$0.535443\pi$
$193$	−2456.61	+	4254.97i	−0.916221	+	1.58694i	−0.805104	+	0.593134i	$0.797890\pi$
$194$	−530.055	−	918.082i	−0.196164	−	0.339765i
$195$		0			0
$196$		0			0
$197$		−	1004.44i		−	0.363265i	−0.983366	−	0.181632i	$-0.941862\pi$
$197$		−	1004.44i		−	0.363265i	0.983366	−	0.181632i	$-0.0581381\pi$
$198$		0			0
$199$	1734.53	+	1001.43i	0.617878	+	0.356732i	0.776042	−	0.630681i	$-0.217224\pi$
$199$	1734.53	+	1001.43i	0.617878	+	0.356732i	−0.158164	+	0.987413i	$0.550558\pi$
$200$	1928.16	+	1113.22i	0.681706	+	0.393583i
$201$		0			0
$202$			480.992i			0.167537i
$203$		0			0
$204$		0			0
$205$	−1009.49	−	1748.48i	−0.343929	−	0.595703i
$206$	362.362	−	627.629i	0.122558	−	0.212277i
$207$		0			0
$208$	184.835	−	106.715i	0.0616154	−	0.0355737i
$209$	3716.77			1.23012
$210$		0			0
$211$	2630.90			0.858383			0.429191	−	0.903214i	$-0.358799\pi$
$211$	2630.90			0.858383			0.429191	+	0.903214i	$0.358799\pi$
$212$	3155.38	−	1821.76i	1.02223	−	0.590184i
$213$		0			0
$214$	−613.287	+	1062.24i	−0.195904	+	0.339315i
$215$	147.402	+	255.307i	0.0467568	+	0.0809852i
$216$		0			0
$217$		0			0
$218$			192.055i			0.0596680i
$219$		0			0
$220$	658.887	+	380.409i	0.201919	+	0.116578i
$221$	419.815	+	242.380i	0.127782	+	0.0737749i
$222$		0			0
$223$			4972.20i			1.49311i	0.665324	+	0.746555i	$0.268293\pi$
$223$			4972.20i			1.49311i	−0.665324	+	0.746555i	$0.731707\pi$
$224$		0			0
$225$		0			0
$226$	73.3178	+	126.990i	0.0215798	+	0.0373773i
$227$	1710.26	−	2962.26i	0.500062	−	0.866133i	−0.499938	−	0.866061i	$-0.666644\pi$
$227$	1710.26	−	2962.26i	0.500062	−	0.866133i	1.00000		7.18991e-5i	$-2.28862e-5\pi$
$228$		0			0
$229$	2770.81	−	1599.73i	0.799566	−	0.461629i	−0.0437537	−	0.999042i	$-0.513932\pi$
$229$	2770.81	−	1599.73i	0.799566	−	0.461629i	0.843319	+	0.537413i	$0.180598\pi$
$230$	627.846			0.179995
$231$		0			0
$232$	−1912.09			−0.541099
$233$	−1859.97	+	1073.85i	−0.522964	+	0.301933i	−0.738146	−	0.674641i	$-0.764299\pi$
$233$	−1859.97	+	1073.85i	−0.522964	+	0.301933i	0.215183	+	0.976574i	$0.430965\pi$
$234$		0			0
$235$	−999.603	+	1731.36i	−0.277476	+	0.480603i
$236$	−2061.83	−	3571.20i	−0.568703	−	0.985023i
$237$		0			0
$238$		0			0
$239$			2853.29i			0.772236i	0.922449	+	0.386118i	$0.126184\pi$
$239$			2853.29i			0.772236i	−0.922449	+	0.386118i	$0.873816\pi$
$240$		0			0
$241$	340.988	+	196.869i	0.0911409	+	0.0526202i	0.544878	−	0.838516i	$-0.316576\pi$
$241$	340.988	+	196.869i	0.0911409	+	0.0526202i	−0.453737	+	0.891136i	$0.649909\pi$
$242$	−605.005	−	349.300i	−0.160707	−	0.0927844i
$243$		0			0
$244$		−	1942.99i		−	0.509783i
$245$		0			0
$246$		0			0
$247$	−1682.41	−	2914.02i	−0.433397	−	0.750666i
$248$	2757.87	−	4776.77i	0.706149	−	1.22309i
$249$		0			0
$250$	1508.59	−	870.987i	0.381647	−	0.220344i
$251$	2520.34			0.633794			0.316897	−	0.948460i	$-0.397359\pi$
$251$	2520.34			0.633794			0.316897	+	0.948460i	$0.397359\pi$
$252$		0			0
$253$	−2462.23			−0.611854
$254$	456.150	−	263.358i	0.112683	−	0.0650573i
$255$		0			0
$256$	1848.21	−	3201.20i	0.451224	−	0.781543i
$257$	2125.96	+	3682.26i	0.516006	+	0.893748i	0.999827	+	0.0185815i	$0.00591500\pi$
$257$	2125.96	+	3682.26i	0.516006	+	0.893748i	−0.483822	+	0.875167i	$0.660752\pi$
$258$		0			0
$259$		0			0
$260$		−	688.774i		−	0.164292i
$261$		0			0
$262$	951.414	+	549.299i	0.224346	+	0.129526i
$263$	6145.87	+	3548.32i	1.44095	+	0.831935i	0.997913	−	0.0645666i	$-0.0205665\pi$
$263$	6145.87	+	3548.32i	1.44095	+	0.831935i	0.443040	+	0.896502i	$0.353900\pi$
$264$		0			0
$265$		−	3200.44i		−	0.741892i
$266$		0			0
$267$		0			0
$268$	1740.66	+	3014.92i	0.396746	+	0.687185i
$269$	−2180.43	+	3776.61i	−0.494212	+	0.856000i	−0.999978	−	0.00667106i	$-0.997877\pi$
$269$	−2180.43	+	3776.61i	−0.494212	+	0.856000i	0.505766	+	0.862671i	$0.331210\pi$
$270$		0			0
$271$	−3737.79	+	2158.02i	−0.837841	+	0.483727i	−0.856530	−	0.516098i	$-0.827384\pi$
$271$	−3737.79	+	2158.02i	−0.837841	+	0.483727i	0.0186891	+	0.999825i	$0.494051\pi$
$272$	−140.271			−0.0312690
$273$		0			0
$274$	3492.52			0.770040
$275$	−2668.75	+	1540.81i	−0.585207	+	0.337869i
$276$		0			0
$277$	1319.46	−	2285.38i	0.286205	−	0.495722i	−0.686696	−	0.726945i	$-0.740939\pi$
$277$	1319.46	−	2285.38i	0.286205	−	0.495722i	0.972901	+	0.231223i	$0.0742728\pi$
$278$	−583.065	−	1009.90i	−0.125791	−	0.217877i
$279$		0			0
$280$		0			0
$281$		−	5925.56i		−	1.25797i	−0.777417	−	0.628985i	$-0.783471\pi$
$281$		−	5925.56i		−	1.25797i	0.777417	−	0.628985i	$-0.216529\pi$
$282$		0			0
$283$	−2663.30	−	1537.65i	−0.559422	−	0.322983i	0.193491	−	0.981102i	$-0.438019\pi$
$283$	−2663.30	−	1537.65i	−0.559422	−	0.322983i	−0.752914	+	0.658119i	$0.771352\pi$
$284$	−2497.31	−	1441.82i	−0.521789	−	0.301255i
$285$		0			0
$286$		−	1320.45i		−	0.273007i
$287$		0			0
$288$		0			0
$289$	2297.20	+	3978.87i	0.467576	+	0.809866i
$290$	−337.419	+	584.426i	−0.0683238	+	0.118340i
$291$		0			0
$292$	2940.77	−	1697.85i	0.589368	−	0.340272i
$293$	−1557.31			−0.310509			−0.155254	−	0.987875i	$-0.549620\pi$
$293$	−1557.31			−0.310509			−0.155254	+	0.987875i	$0.549620\pi$
$294$		0			0
$295$	−3622.20			−0.714890
$296$	4042.96	−	2334.20i	0.793892	−	0.458354i
$297$		0			0
$298$	−968.144	+	1676.87i	−0.188198	+	0.325969i
$299$	1114.54	+	1930.43i	0.215570	+	0.373378i
$300$		0			0
$301$		0			0
$302$			1737.62i			0.331088i
$303$		0			0
$304$	843.205	+	486.825i	0.159083	+	0.0918464i
$305$	−1478.05	−	853.353i	−0.277485	−	0.160206i
$306$		0			0
$307$			1802.67i			0.335127i	0.985861	+	0.167563i	$0.0535898\pi$
$307$			1802.67i			0.335127i	−0.985861	+	0.167563i	$0.946410\pi$
$308$		0			0
$309$		0			0
$310$	−973.340	−	1685.87i	−0.178329	−	0.308875i
$311$	−4769.98	+	8261.85i	−0.869714	+	1.50639i	−0.00742422	+	0.999972i	$0.502363\pi$
$311$	−4769.98	+	8261.85i	−0.869714	+	1.50639i	−0.862289	+	0.506416i	$0.830970\pi$
$312$		0			0
$313$	−1095.23	+	632.332i	−0.197783	+	0.114190i	−0.595621	−	0.803266i	$-0.703094\pi$
$313$	−1095.23	+	632.332i	−0.197783	+	0.114190i	0.397838	+	0.917456i	$0.369761\pi$
$314$	−3784.27			−0.680124
$315$		0			0
$316$	−3210.10			−0.571463
$317$	−8265.68	+	4772.19i	−1.46450	+	0.845530i	−0.999214	−	0.0396301i	$-0.987382\pi$
$317$	−8265.68	+	4772.19i	−1.46450	+	0.845530i	−0.465287	+	0.885160i	$0.654049\pi$
$318$		0			0
$319$	1323.26	−	2291.95i	0.232252	−	0.402271i
$320$	−563.539	−	976.079i	−0.0984463	−	0.170514i
$321$		0			0
$322$		0			0
$323$			2211.44i			0.380954i
$324$		0			0
$325$	2416.04	+	1394.90i	0.412363	+	0.238078i
$326$	−5062.47	−	2922.82i	−0.860074	−	0.496564i
$327$		0			0
$328$		−	9271.39i		−	1.56075i
$329$		0			0
$330$		0			0
$331$	1353.22	+	2343.85i	0.224712	+	0.389213i	0.956233	−	0.292606i	$-0.0945225\pi$
$331$	1353.22	+	2343.85i	0.224712	+	0.389213i	−0.731521	+	0.681819i	$0.761189\pi$
$332$	−1589.89	+	2753.76i	−0.262820	+	0.455218i
$333$		0			0
$334$	3157.27	−	1822.85i	0.517239	−	0.298628i
$335$	3057.97			0.498731
$336$		0			0
$337$	10550.8			1.70545			0.852727	−	0.522357i	$-0.174947\pi$
$337$	10550.8			1.70545			0.852727	+	0.522357i	$0.174947\pi$
$338$	2048.40	−	1182.64i	0.329640	−	0.190318i
$339$		0			0
$340$	−226.340	+	392.032i	−0.0361029	+	0.0625321i
$341$	3817.16	+	6611.51i	0.606189	+	1.04995i
$342$		0			0
$343$		0			0
$344$			1353.78i			0.212183i
$345$		0			0
$346$	−5677.19	−	3277.73i	−0.882103	−	0.509283i
$347$	−8636.09	−	4986.05i	−1.33605	−	0.771369i	−0.349831	−	0.936813i	$-0.613761\pi$
$347$	−8636.09	−	4986.05i	−1.33605	−	0.771369i	−0.986219	+	0.165444i	$0.947094\pi$
$348$		0			0
$349$		−	1653.11i		−	0.253549i	−0.991932	−	0.126775i	$-0.959537\pi$
$349$		−	1653.11i		−	0.253549i	0.991932	−	0.126775i	$-0.0404625\pi$
$350$		0			0
$351$		0			0
$352$	2791.89	+	4835.69i	0.422751	+	0.732226i
$353$	−1677.25	+	2905.09i	−0.252893	+	0.438024i	−0.964321	−	0.264735i	$-0.914715\pi$
$353$	−1677.25	+	2905.09i	−0.252893	+	0.438024i	0.711428	+	0.702759i	$0.248049\pi$
$354$		0			0
$355$	−2193.62	+	1266.49i	−0.327959	+	0.189347i
$356$	−8269.52			−1.23113
$357$		0			0
$358$	3449.47			0.509246
$359$	937.988	−	541.548i	0.137897	−	0.0796150i	−0.429464	−	0.903084i	$-0.641298\pi$
$359$	937.988	−	541.548i	0.137897	−	0.0796150i	0.567361	+	0.823469i	$0.307964\pi$
$360$		0			0
$361$	4245.53	−	7353.48i	0.618973	−	1.07209i
$362$	3461.92	+	5996.23i	0.502637	+	0.870593i
$363$		0			0
$364$		0			0
$365$		−	2982.76i		−	0.427739i
$366$		0			0
$367$	−1823.53	−	1052.81i	−0.259366	−	0.149745i	0.364679	−	0.931133i	$-0.381179\pi$
$367$	−1823.53	−	1052.81i	−0.259366	−	0.149745i	−0.624045	+	0.781388i	$0.714512\pi$
$368$	−558.594	−	322.504i	−0.0791269	−	0.0456839i
$369$		0			0
$370$		−	1647.63i		−	0.231503i
$371$		0			0
$372$		0			0
$373$	−1867.35	−	3234.34i	−0.259216	−	0.448975i	0.706816	−	0.707397i	$-0.250131\pi$
$373$	−1867.35	−	3234.34i	−0.259216	−	0.448975i	−0.966032	+	0.258422i	$0.916797\pi$
$374$	−433.917	+	751.567i	−0.0599928	+	0.103911i
$375$		0			0
$376$	−7950.66	+	4590.31i	−1.09049	+	0.629594i
$377$	−2395.91			−0.327310
$378$		0			0
$379$	−13141.6			−1.78111			−0.890555	−	0.454876i	$-0.849684\pi$
$379$	−13141.6			−1.78111			−0.890555	+	0.454876i	$0.849684\pi$
$380$	2721.17	−	1571.07i	0.367350	−	0.212090i
$381$		0			0
$382$	−627.645	+	1087.11i	−0.0840657	+	0.145606i
$383$	2671.88	+	4627.84i	0.356467	+	0.617419i	0.987368	−	0.158444i	$-0.0506479\pi$
$383$	2671.88	+	4627.84i	0.356467	+	0.617419i	−0.630901	+	0.775863i	$0.717315\pi$
$384$		0			0
$385$		0			0
$386$			7962.91i			1.05000i
$387$		0			0
$388$	3043.80	+	1757.34i	0.398262	+	0.229937i
$389$	−1624.29	−	937.783i	−0.211709	−	0.122230i	0.390397	−	0.920647i	$-0.372338\pi$
$389$	−1624.29	−	937.783i	−0.211709	−	0.122230i	−0.602105	+	0.798417i	$0.705671\pi$
$390$		0			0
$391$		−	1465.00i		−	0.189484i
$392$		0			0
$393$		0			0
$394$	−813.951	−	1409.81i	−0.104077	−	0.180266i
$395$	−1409.87	+	2441.96i	−0.179590	+	0.311059i
$396$		0			0
$397$	−8327.97	+	4808.16i	−1.05282	+	0.607845i	−0.923437	−	0.383750i	$-0.874633\pi$
$397$	−8327.97	+	4808.16i	−1.05282	+	0.607845i	−0.129381	+	0.991595i	$0.541299\pi$
$398$	3246.07			0.408821
$399$		0			0
$400$	−807.262			−0.100908
$401$	−562.762	+	324.911i	−0.0700823	+	0.0404620i	−0.534632	−	0.845085i	$-0.679550\pi$
$401$	−562.762	+	324.911i	−0.0700823	+	0.0404620i	0.464549	+	0.885547i	$0.346216\pi$
$402$		0			0
$403$	3455.70	−	5985.45i	0.427148	−	0.739842i
$404$	−797.339	−	1381.03i	−0.0981908	−	0.170072i
$405$		0			0
$406$		0			0
$407$			6461.52i			0.786943i
$408$		0			0
$409$	−13491.6	−	7789.38i	−1.63109	−	0.941711i	−0.983757	−	0.179505i	$-0.942550\pi$
$409$	−13491.6	−	7789.38i	−1.63109	−	0.941711i	−0.647334	−	0.762206i	$-0.724116\pi$
$410$	−2833.78	−	1636.08i	−0.341343	−	0.197074i
$411$		0			0
$412$			2402.74i			0.287317i
$413$		0			0
$414$		0			0
$415$	1396.54	+	2418.89i	0.165190	+	0.286117i
$416$	2527.52	−	4377.79i	0.297889	−	0.515959i
$417$		0			0
$418$	5216.77	−	3011.91i	0.610432	−	0.352433i
$419$	−5391.59			−0.628631			−0.314315	−	0.949319i	$-0.601775\pi$
$419$	−5391.59			−0.628631			−0.314315	+	0.949319i	$0.601775\pi$
$420$		0			0
$421$	−12506.0			−1.44776			−0.723879	−	0.689927i	$-0.757642\pi$
$421$	−12506.0			−1.44776			−0.723879	+	0.689927i	$0.757642\pi$
$422$	3692.67	−	2131.97i	0.425963	−	0.245930i
$423$		0			0
$424$	7348.43	−	12727.8i	0.841677	−	1.45783i
$425$	−916.765	−	1587.88i	−0.104634	−	0.181232i
$426$		0			0
$427$		0			0
$428$		−	4066.57i		−	0.459264i
$429$		0			0
$430$	413.780	+	238.896i	0.0464052	+	0.0267920i
$431$	−7648.94	−	4416.12i	−0.854841	−	0.493543i	0.00744041	−	0.999972i	$-0.497632\pi$
$431$	−7648.94	−	4416.12i	−0.854841	−	0.493543i	−0.862281	+	0.506430i	$0.830965\pi$
$432$		0			0
$433$			5550.41i			0.616017i	0.951384	+	0.308009i	$0.0996626\pi$
$433$			5550.41i			0.616017i	−0.951384	+	0.308009i	$0.900337\pi$
$434$		0			0
$435$		0			0
$436$	−318.369	−	551.432i	−0.0349705	−	0.0605707i
$437$	−5084.44	+	8806.51i	−0.556571	+	0.964010i
$438$		0			0
$439$	−9848.19	+	5685.86i	−1.07068	+	0.618157i	−0.928367	−	0.371664i	$-0.878787\pi$
$439$	−9848.19	+	5685.86i	−1.07068	+	0.618157i	−0.142313	+	0.989822i	$0.545454\pi$
$440$	3068.91			0.332510
$441$		0			0
$442$	785.657			0.0845473
$443$	6944.93	−	4009.66i	0.744839	−	0.430033i	−0.0789873	−	0.996876i	$-0.525169\pi$
$443$	6944.93	−	4009.66i	0.744839	−	0.430033i	0.823826	+	0.566843i	$0.191835\pi$
$444$		0			0
$445$	−3631.94	+	6290.71i	−0.386900	+	0.670131i
$446$	4029.25	+	6978.87i	0.427782	+	0.740940i
$447$		0			0
$448$		0			0
$449$			1039.67i			0.109276i	0.998506	+	0.0546379i	$0.0174005\pi$
$449$			1039.67i			0.109276i	−0.998506	+	0.0546379i	$0.982600\pi$
$450$		0			0
$451$	11113.3	+	6416.25i	1.16032	+	0.669910i
$452$	−421.022	−	243.077i	−0.0438124	−	0.0252951i
$453$		0			0
$454$		−	5543.69i		−	0.573079i
$455$		0			0
$456$		0			0
$457$	−7151.36	−	12386.5i	−0.732005	−	1.26787i	−0.956025	−	0.293286i	$-0.905251\pi$
$457$	−7151.36	−	12386.5i	−0.732005	−	1.26787i	0.224019	−	0.974585i	$-0.428082\pi$
$458$	2592.70	−	4490.69i	0.264517	−	0.458158i
$459$		0			0
$460$	−1802.68	+	1040.78i	−0.182718	+	0.105492i
$461$	−12732.1			−1.28632			−0.643159	−	0.765733i	$-0.722377\pi$
$461$	−12732.1			−1.28632			−0.643159	+	0.765733i	$0.722377\pi$
$462$		0			0
$463$	12358.7			1.24051			0.620256	−	0.784400i	$-0.287029\pi$
$463$	12358.7			1.24051			0.620256	+	0.784400i	$0.287029\pi$
$464$	600.402	−	346.642i	0.0600711	−	0.0346820i
$465$		0			0
$466$	−1740.41	+	3014.47i	−0.173010	+	0.299662i
$467$	6288.06	+	10891.2i	0.623077	+	1.07920i	0.988909	+	0.148520i	$0.0474509\pi$
$467$	6288.06	+	10891.2i	0.623077	+	1.07920i	−0.365833	+	0.930681i	$0.619216\pi$
$468$		0			0
$469$		0			0
$470$			3240.14i			0.317992i
$471$		0			0
$472$	−14405.2	−	8316.82i	−1.40477	−	0.811044i
$473$	−1622.72	−	936.880i	−0.157744	−	0.0910735i
$474$		0			0
$475$			12726.9i			1.22937i
$476$		0			0
$477$		0			0
$478$	2312.18	+	4004.82i	0.221249	+	0.383214i
$479$	6137.19	−	10629.9i	0.585418	−	1.01397i	−0.409405	−	0.912353i	$-0.634264\pi$
$479$	6137.19	−	10629.9i	0.585418	−	1.01397i	0.994823	−	0.101621i	$-0.0324030\pi$
$480$		0			0
$481$	5065.96	−	2924.83i	0.480224	−	0.277257i
$482$	638.137			0.0603036
$483$		0			0
$484$	2316.13			0.217518
$485$	2673.65	−	1543.63i	0.250318	−	0.144521i
$486$		0			0
$487$	−3769.96	+	6529.76i	−0.350787	+	0.607581i	−0.986388	−	0.164437i	$-0.947419\pi$
$487$	−3769.96	+	6529.76i	−0.350787	+	0.607581i	0.635601	+	0.772018i	$0.280753\pi$
$488$	−3918.72	−	6787.42i	−0.363508	−	0.629614i
$489$		0			0
$490$		0			0
$491$		−	406.618i		−	0.0373735i	−0.999825	−	0.0186868i	$-0.994051\pi$
$491$		−	406.618i		−	0.0373735i	0.999825	−	0.0186868i	$-0.00594853\pi$
$492$		0			0
$493$	1363.69	+	787.326i	0.124579	+	0.0719258i
$494$	−4722.78	−	2726.70i	−0.430138	−	0.248340i
$495$		0			0
$496$			1999.89i			0.181044i
$497$		0			0
$498$		0			0
$499$	−2752.48	−	4767.44i	−0.246930	−	0.427695i	0.715742	−	0.698364i	$-0.246088\pi$
$499$	−2752.48	−	4767.44i	−0.246930	−	0.427695i	−0.962672	+	0.270669i	$0.912755\pi$
$500$	−2887.66	+	5001.58i	−0.258280	+	0.447355i
$501$		0			0
$502$	3537.49	−	2042.37i	0.314514	−	0.181585i
$503$	6535.76			0.579354			0.289677	−	0.957124i	$-0.406452\pi$
$503$	6535.76			0.579354			0.289677	+	0.957124i	$0.406452\pi$
$504$		0			0
$505$	−1400.75			−0.123431
$506$	−3455.93	+	1995.28i	−0.303626	+	0.175299i
$507$		0			0
$508$	−873.135	+	1512.31i	−0.0762581	+	0.132083i
$509$	−8953.46	−	15507.9i	−0.779677	−	1.35044i	−0.932128	−	0.362128i	$-0.882050\pi$
$509$	−8953.46	−	15507.9i	−0.779677	−	1.35044i	0.152452	−	0.988311i	$-0.451283\pi$
$510$		0			0
$511$		0			0
$512$			2825.37i			0.243877i
$513$		0			0
$514$	5967.89	+	3445.56i	0.512125	+	0.295675i
$515$	1827.79	+	1055.28i	0.156392	+	0.0902932i
$516$		0			0
$517$		−	12706.9i		−	1.08094i
$518$		0			0
$519$		0			0
$520$	−1389.15	−	2406.08i	−0.117151	−	0.202911i
$521$	−5445.98	+	9432.71i	−0.457951	+	0.793195i	−0.998853	−	0.0478914i	$-0.984750\pi$
$521$	−5445.98	+	9432.71i	−0.457951	+	0.793195i	0.540901	+	0.841086i	$0.318083\pi$
$522$		0			0
$523$	2311.20	−	1334.37i	0.193235	−	0.111564i	−0.400261	−	0.916401i	$-0.631081\pi$
$523$	2311.20	−	1334.37i	0.193235	−	0.111564i	0.593496	+	0.804837i	$0.297747\pi$
$524$	−3642.28			−0.303652
$525$		0			0
$526$	11501.6			0.953411
$527$	−3933.79	+	2271.17i	−0.325158	+	0.187730i
$528$		0			0
$529$	−2715.24	+	4702.93i	−0.223164	+	0.386532i
$530$	−2593.49	−	4492.06i	−0.212555	−	0.368156i
$531$		0			0
$532$		0			0
$533$		−	11617.4i		−	0.944097i
$534$		0			0
$535$	−3093.48	−	1786.02i	−0.249987	−	0.144330i
$536$	12161.3	+	7021.32i	0.980013	+	0.565811i
$537$		0			0
$538$			7067.68i			0.566374i
$539$		0			0
$540$		0			0
$541$	5388.29	+	9332.80i	0.428209	+	0.741679i	0.996714	−	0.0810005i	$-0.0258115\pi$
$541$	5388.29	+	9332.80i	0.428209	+	0.741679i	−0.568506	+	0.822679i	$0.692478\pi$
$542$	−3497.52	+	6057.89i	−0.277180	+	0.480089i
$543$		0			0
$544$	−2877.19	+	1661.15i	−0.226762	+	0.130921i
$545$	−559.307			−0.0439598
$546$		0			0
$547$	−6796.09			−0.531225			−0.265612	−	0.964080i	$-0.585574\pi$
$547$	−6796.09			−0.531225			−0.265612	+	0.964080i	$0.585574\pi$
$548$	−10027.8	+	5789.54i	−0.781689	+	0.451308i
$549$		0			0
$550$	−2497.20	+	4325.28i	−0.193602	+	0.335328i
$551$	−5464.99	−	9465.64i	−0.422534	−	0.731851i
$552$		0			0
$553$		0			0
$554$		−	4276.94i		−	0.327996i
$555$		0			0
$556$	3348.21	+	1933.09i	0.255388	+	0.147448i
$557$	15641.9	+	9030.85i	1.18989	+	0.686983i	0.958282	−	0.285826i	$-0.0922680\pi$
$557$	15641.9	+	9030.85i	1.18989	+	0.686983i	0.231608	+	0.972809i	$0.425601\pi$
$558$		0			0
$559$			1696.33i			0.128349i
$560$		0			0
$561$		0			0
$562$	−4801.82	−	8316.99i	−0.360413	−	0.624254i
$563$	10523.3	−	18227.0i	0.787755	−	1.36443i	−0.139585	−	0.990210i	$-0.544577\pi$
$563$	10523.3	−	18227.0i	0.787755	−	1.36443i	0.927339	−	0.374221i	$-0.122090\pi$
$564$		0			0
$565$	−369.823	+	213.517i	−0.0275373	+	0.0158986i
$566$	−4984.19			−0.370143
$567$		0			0
$568$	−11631.8			−0.859257
$569$	10497.9	−	6060.98i	0.773455	−	0.446554i	−0.0606509	−	0.998159i	$-0.519318\pi$
$569$	10497.9	−	6060.98i	0.773455	−	0.446554i	0.834106	+	0.551605i	$0.185984\pi$
$570$		0			0
$571$	1472.07	−	2549.70i	0.107888	−	0.186868i	−0.807026	−	0.590516i	$-0.798924\pi$
$571$	1472.07	−	2549.70i	0.107888	−	0.186868i	0.914915	+	0.403647i	$0.132258\pi$
$572$	2188.91	+	3791.30i	0.160005	+	0.277137i
$573$		0			0
$574$		0			0
$575$		−	8431.12i		−	0.611482i
$576$		0			0
$577$	4495.86	+	2595.69i	0.324376	+	0.187279i	0.653342	−	0.757063i	$-0.273367\pi$
$577$	4495.86	+	2595.69i	0.324376	+	0.187279i	−0.328965	+	0.944342i	$0.606700\pi$
$578$	6448.60	+	3723.10i	0.464060	+	0.267925i
$579$		0			0
$580$		−	2237.35i		−	0.160174i
$581$		0			0
$582$		0			0
$583$	10170.9	+	17616.6i	0.722533	+	1.25146i
$584$	6848.63	−	11862.2i	0.485271	−	0.840514i
$585$		0			0
$586$	−2185.81	+	1261.98i	−0.154087	+	0.0889620i
$587$	21918.4			1.54118			0.770588	−	0.637334i	$-0.219963\pi$
$587$	21918.4			1.54118			0.770588	+	0.637334i	$0.219963\pi$
$588$		0			0
$589$	31529.3			2.20568
$590$	−5084.04	+	2935.27i	−0.354757	+	0.204819i
$591$		0			0
$592$	−846.334	+	1465.89i	−0.0587569	+	0.101770i
$593$	−10119.7	−	17527.9i	−0.700788	−	1.21380i	−0.968190	−	0.250216i	$-0.919499\pi$
$593$	−10119.7	−	17527.9i	−0.700788	−	1.21380i	0.267402	−	0.963585i	$-0.413835\pi$
$594$		0			0
$595$		0			0
$596$		−	6419.55i		−	0.441200i
$597$		0			0
$598$	3128.68	+	1806.34i	0.213948	+	0.123523i
$599$	7376.06	+	4258.57i	0.503135	+	0.290485i	0.730007	−	0.683439i	$-0.239517\pi$
$599$	7376.06	+	4258.57i	0.503135	+	0.290485i	−0.226872	+	0.973925i	$0.572850\pi$
$600$		0			0
$601$		−	5040.33i		−	0.342096i	−0.985263	−	0.171048i	$-0.945285\pi$
$601$		−	5040.33i		−	0.342096i	0.985263	−	0.171048i	$-0.0547152\pi$
$602$		0			0
$603$		0			0
$604$	−2880.44	−	4989.07i	−0.194046	−	0.336097i
$605$	1017.24	−	1761.90i	0.0683579	−	0.118399i
$606$		0			0
$607$	23489.5	−	13561.6i	1.57069	−	0.906837i	0.574604	−	0.818432i	$-0.305156\pi$
$607$	23489.5	−	13561.6i	1.57069	−	0.906837i	0.996085	−	0.0884057i	$-0.0281772\pi$
$608$	23060.7			1.53822
$609$		0			0
$610$	−2766.08			−0.183599
$611$	−9962.44	+	5751.81i	−0.659635	+	0.380840i
$612$		0			0
$613$	−1467.22	+	2541.30i	−0.0966730	+	0.167443i	−0.910306	−	0.413937i	$-0.864153\pi$
$613$	−1467.22	+	2541.30i	−0.0966730	+	0.167443i	0.813633	+	0.581379i	$0.197487\pi$
$614$	1460.80	+	2530.19i	0.0960151	+	0.166303i
$615$		0			0
$616$		0			0
$617$			2908.86i			0.189799i	0.995487	+	0.0948996i	$0.0302530\pi$
$617$			2908.86i			0.189799i	−0.995487	+	0.0948996i	$0.969747\pi$
$618$		0			0
$619$	13814.4	+	7975.77i	0.897010	+	0.517889i	0.876229	−	0.481895i	$-0.160051\pi$
$619$	13814.4	+	7975.77i	0.897010	+	0.517889i	0.0207811	+	0.999784i	$0.493385\pi$
$620$	5589.33	+	3227.00i	0.362053	+	0.209032i
$621$		0			0
$622$			15461.5i			0.996706i
$623$		0			0
$624$		0			0
$625$	−3883.68	−	6726.73i	−0.248556	−	0.430511i
$626$	−1024.83	+	1775.05i	−0.0654319	+	0.113331i
$627$		0			0
$628$	10865.5	−	6273.18i	0.690412	−	0.398610i
$629$	−3844.54			−0.243707
$630$		0			0
$631$	−31218.8			−1.96957			−0.984786	−	0.173771i	$-0.944405\pi$
$631$	−31218.8			−1.96957			−0.984786	+	0.173771i	$0.944405\pi$
$632$	−11213.8	+	6474.30i	−0.705793	+	0.407490i
$633$		0			0
$634$	−7734.35	+	13396.3i	−0.484496	+	0.839171i
$635$	766.955	+	1328.41i	0.0479302	+	0.0830176i
$636$		0			0
$637$		0			0
$638$		−	4289.24i		−	0.266164i
$639$		0			0
$640$	4504.56	+	2600.71i	0.278216	+	0.160628i
$641$	4720.80	+	2725.55i	0.290890	+	0.167945i	0.638343	−	0.769752i	$-0.279620\pi$
$641$	4720.80	+	2725.55i	0.290890	+	0.167945i	−0.347453	+	0.937697i	$0.612953\pi$
$642$		0			0
$643$		−	15700.8i		−	0.962956i	−0.876458	−	0.481478i	$-0.840100\pi$
$643$		−	15700.8i		−	0.962956i	0.876458	−	0.481478i	$-0.159900\pi$
$644$		0			0
$645$		0			0
$646$	1792.06	+	3103.93i	0.109145	+	0.189044i
$647$	11372.0	−	19696.9i	0.691006	−	1.19686i	−0.280502	−	0.959853i	$-0.590501\pi$
$647$	11372.0	−	19696.9i	0.691006	−	1.19686i	0.971509	−	0.237004i	$-0.0761656\pi$
$648$		0			0
$649$	19938.1	−	11511.3i	1.20592	−	0.696236i
$650$	4521.47			0.272841
$651$		0			0
$652$	19380.6			1.16411
$653$	4984.17	−	2877.61i	0.298691	−	0.172450i	−0.343163	−	0.939276i	$-0.611498\pi$
$653$	4984.17	−	2877.61i	0.298691	−	0.172450i	0.641855	+	0.766826i	$0.278165\pi$
$654$		0			0
$655$	−1599.68	+	2770.72i	−0.0954268	+	0.165284i
$656$	1680.81	+	2911.24i	0.100037	+	0.173270i
$657$		0			0
$658$		0			0
$659$			24579.2i			1.45292i	0.687211	+	0.726458i	$0.258835\pi$
$659$			24579.2i			1.45292i	−0.687211	+	0.726458i	$0.741165\pi$
$660$		0			0
$661$	4251.57	+	2454.64i	0.250177	+	0.144440i	0.619845	−	0.784724i	$-0.287195\pi$
$661$	4251.57	+	2454.64i	0.250177	+	0.144440i	−0.369669	+	0.929164i	$0.620529\pi$
$662$	3798.70	+	2193.18i	0.223022	+	0.128762i
$663$		0			0
$664$			12826.2i			0.749631i
$665$		0			0
$666$		0			0
$667$	3620.36	+	6270.65i	0.210166	+	0.364019i
$668$	−6043.46	+	10467.6i	−0.350043	+	0.606291i
$669$		0			0
$670$	4292.10	−	2478.05i	0.247490	−	0.142888i
$671$	10847.8			0.624103
$672$		0			0
$673$	2635.70			0.150964			0.0754819	−	0.997147i	$-0.475950\pi$
$673$	2635.70			0.150964			0.0754819	+	0.997147i	$0.475950\pi$
$674$	14808.8	−	8549.89i	0.846314	−	0.488619i
$675$		0			0
$676$	−3920.93	+	6791.25i	−0.223084	+	0.386393i
$677$	3191.45	+	5527.76i	0.181178	+	0.313809i	0.942282	−	0.334821i	$-0.108676\pi$
$677$	3191.45	+	5527.76i	0.181178	+	0.313809i	−0.761104	+	0.648630i	$0.775342\pi$
$678$		0			0
$679$		0			0
$680$			1825.97i			0.102975i
$681$		0			0
$682$	10715.3	+	6186.51i	0.601630	+	0.347351i
$683$	11952.8	+	6900.95i	0.669636	+	0.386614i	0.795939	−	0.605377i	$-0.206978\pi$
$683$	11952.8	+	6900.95i	0.669636	+	0.386614i	−0.126303	+	0.991992i	$0.540311\pi$
$684$		0			0
$685$			10171.0i			0.567318i
$686$		0			0
$687$		0			0
$688$	−245.426	−	425.091i	−0.0136000	−	0.0235559i
$689$	9207.82	−	15948.4i	0.509129	−	0.881838i
$690$		0			0
$691$	−1516.12	+	875.333i	−0.0834674	+	0.0481899i	−0.541153	−	0.840924i	$-0.682012\pi$
$691$	−1516.12	+	875.333i	−0.0834674	+	0.0481899i	0.457685	+	0.889114i	$0.348679\pi$
$692$	21733.9			1.19393
$693$		0			0
$694$	−16161.9			−0.884001
$695$	2941.04	−	1698.01i	0.160518	−	0.0926752i
$696$		0			0
$697$	−3817.61	+	6612.29i	−0.207464	+	0.359338i
$698$	−1339.60	−	2320.26i	−0.0726429	−	0.125821i
$699$		0			0
$700$		0			0
$701$		−	26927.8i		−	1.45085i	−0.688300	−	0.725426i	$-0.741643\pi$
$701$		−	26927.8i		−	1.45085i	0.688300	−	0.725426i	$-0.258357\pi$
$702$		0			0
$703$	23110.5	+	13342.9i	1.23987	+	0.715841i
$704$	6203.92	+	3581.83i	0.332129	+	0.191755i
$705$		0			0
$706$			5436.69i			0.289819i
$707$		0			0
$708$		0			0
$709$	5801.80	+	10049.0i	0.307322	+	0.532297i	0.977776	−	0.209654i	$-0.0672338\pi$
$709$	5801.80	+	10049.0i	0.307322	+	0.532297i	−0.670454	+	0.741952i	$0.733900\pi$
$710$	−2052.61	+	3555.23i	−0.108497	+	0.187923i
$711$		0			0
$712$	−28887.8	+	16678.4i	−1.52053	+	0.877877i
$713$	−20887.1			−1.09709
$714$		0			0
$715$	3845.44			0.201135
$716$	−9904.17	+	5718.17i	−0.516950	+	0.298461i
$717$		0			0
$718$	877.693	−	1520.21i	0.0456201	−	0.0790163i
$719$	−6750.67	−	11692.5i	−0.350150	−	0.606477i	0.636126	−	0.771585i	$-0.280536\pi$
$719$	−6750.67	−	11692.5i	−0.350150	−	0.606477i	−0.986275	+	0.165108i	$0.947203\pi$
$720$		0			0
$721$		0			0
$722$		−	13761.6i		−	0.709353i
$723$		0			0
$724$	−19879.8	−	11477.6i	−1.02048	−	0.589175i
$725$	7848.06	+	4531.08i	0.402027	+	0.232110i
$726$		0			0
$727$			1116.75i			0.0569708i	0.999594	+	0.0284854i	$0.00906842\pi$
$727$			1116.75i			0.0569708i	−0.999594	+	0.0284854i	$0.990932\pi$
$728$		0			0
$729$		0			0
$730$	−2417.10	−	4186.54i	−0.122549	−	0.212261i
$731$	557.435	−	965.505i	0.0282045	−	0.0488516i
$732$		0			0
$733$	25019.4	−	14444.9i	1.26072	−	0.727879i	0.287510	−	0.957778i	$-0.407173\pi$
$733$	25019.4	−	14444.9i	1.26072	−	0.727879i	0.973215	+	0.229898i	$0.0738394\pi$
$734$	−3412.62			−0.171610
$735$		0			0
$736$	−15276.9			−0.765101
$737$	−16832.4	+	9718.18i	−0.841287	+	0.485717i
$738$		0			0
$739$	996.244	−	1725.55i	0.0495906	−	0.0858934i	−0.840165	−	0.542332i	$-0.817542\pi$
$739$	996.244	−	1725.55i	0.0495906	−	0.0858934i	0.889755	+	0.456438i	$0.150875\pi$
$740$	2731.27	+	4730.69i	0.135680	+	0.235005i
$741$		0			0
$742$		0			0
$743$			32395.7i			1.59957i	0.600284	+	0.799787i	$0.295054\pi$
$743$			32395.7i			1.59957i	−0.600284	+	0.799787i	$0.704946\pi$
$744$		0			0
$745$	−4883.42	−	2819.44i	−0.240154	−	0.138653i
$746$	−5241.93	−	3026.43i	−0.257266	−	0.148533i
$747$		0			0
$748$		−	2877.21i		−	0.140643i
$749$		0			0
$750$		0			0
$751$	3796.22	+	6575.24i	0.184455	+	0.319486i	0.943393	−	0.331677i	$-0.107615\pi$
$751$	3796.22	+	6575.24i	0.184455	+	0.319486i	−0.758937	+	0.651163i	$0.774281\pi$
$752$	1664.35	−	2882.75i	0.0807084	−	0.139791i
$753$		0			0
$754$	−3362.85	+	1941.54i	−0.162424	+	0.0937755i
$755$	−5060.32			−0.243926
$756$		0			0
$757$	29398.9			1.41152			0.705760	−	0.708451i	$-0.250605\pi$
$757$	29398.9			1.41152			0.705760	+	0.708451i	$0.250605\pi$
$758$	−18445.3	+	10649.4i	−0.883857	+	0.510295i
$759$		0			0
$760$	6337.22	−	10976.4i	0.302467	−	0.523888i
$761$	−16277.5	−	28193.4i	−0.775373	−	1.34299i	−0.934585	−	0.355741i	$-0.884229\pi$
$761$	−16277.5	−	28193.4i	−0.775373	−	1.34299i	0.159212	−	0.987244i	$-0.449105\pi$
$762$		0			0
$763$		0			0
$764$		−	4161.78i		−	0.197078i
$765$		0			0
$766$	7500.39	+	4330.35i	0.353786	+	0.204258i
$767$	−18050.1	−	10421.2i	−0.849742	−	0.490599i
$768$		0			0
$769$		−	34767.8i		−	1.63038i	−0.579195	−	0.815189i	$-0.696633\pi$
$769$		−	34767.8i		−	1.63038i	0.579195	−	0.815189i	$-0.303367\pi$
$770$		0			0
$771$		0			0
$772$	−13200.1	−	22863.2i	−0.615391	−	1.06589i
$773$	−2994.63	+	5186.85i	−0.139339	+	0.241343i	−0.927247	−	0.374451i	$-0.877831\pi$
$773$	−2994.63	+	5186.85i	−0.139339	+	0.241343i	0.787907	+	0.615794i	$0.211165\pi$
$774$		0			0
$775$	−22639.0	+	13070.6i	−1.04931	+	0.605821i
$776$	14177.2			0.655838
$777$		0			0
$778$	−3039.75			−0.140078
$779$	45897.2	−	26498.8i	2.11096	−	1.21876i
$780$		0			0
$781$	8049.74	−	13942.6i	0.368812	−	0.638802i
$782$	−1187.17	−	2056.25i	−0.0542880	−	0.0940296i
$783$		0			0
$784$		0			0
$785$		−	11020.6i		−	0.501074i
$786$		0			0
$787$	−36037.5	−	20806.3i	−1.63227	−	0.942393i	−0.983390	−	0.181504i	$-0.941903\pi$
$787$	−36037.5	−	20806.3i	−1.63227	−	0.942393i	−0.648882	−	0.760889i	$-0.724763\pi$
$788$	4674.06	+	2698.57i	0.211302	+	0.121996i
$789$		0			0
$790$			4569.97i			0.205813i
$791$		0			0
$792$		0			0
$793$	−4910.28	−	8504.86i	−0.219885	−	0.380853i
$794$	−7792.64	+	13497.2i	−0.348300	+	0.603274i
$795$		0			0
$796$	−9320.15	+	5380.99i	−0.415005	+	0.239603i
$797$	−2077.70			−0.0923412			−0.0461706	−	0.998934i	$-0.514702\pi$
$797$	−2077.70			−0.0923412			−0.0461706	+	0.998934i	$0.514702\pi$
$798$		0			0
$799$	7560.47			0.334756
$800$	−16558.3	+	9559.94i	−0.731780	+	0.422494i
$801$		0			0
$802$	−526.587	+	912.075i	−0.0231851	+	0.0401577i
$803$	9479.16	+	16418.4i	0.416578	+	0.721535i
$804$		0			0
$805$		0			0
$806$		−	11201.4i		−	0.489519i
$807$		0			0
$808$	−5570.67	−	3216.23i	−0.242544	−	0.140033i
$809$	−21392.6	−	12351.0i	−0.929697	−	0.536761i	−0.0429815	−	0.999076i	$-0.513686\pi$
$809$	−21392.6	−	12351.0i	−0.929697	−	0.536761i	−0.886716	+	0.462315i	$0.847019\pi$
$810$		0			0
$811$			30991.5i			1.34187i	0.741516	+	0.670936i	$0.234107\pi$
$811$			30991.5i			1.34187i	−0.741516	+	0.670936i	$0.765893\pi$
$812$		0			0
$813$		0			0
$814$	5236.13	+	9069.24i	0.225462	+	0.390512i
$815$	8511.88	−	14743.0i	0.365838	−	0.633650i
$816$		0			0
$817$	−6701.77	+	3869.27i	−0.286983	+	0.165690i
$818$	−25248.7			−1.07922
$819$		0			0
$820$	10848.5			0.462008
$821$	24401.5	−	14088.2i	1.03730	−	0.598883i	0.118230	−	0.992986i	$-0.462278\pi$
$821$	24401.5	−	14088.2i	1.03730	−	0.598883i	0.919066	+	0.394103i	$0.128945\pi$
$822$		0			0
$823$	−8539.10	+	14790.2i	−0.361670	+	0.626431i	−0.988236	−	0.152938i	$-0.951127\pi$
$823$	−8539.10	+	14790.2i	−0.361670	+	0.626431i	0.626566	+	0.779368i	$0.284460\pi$
$824$	4845.97	+	8393.47i	0.204876	+	0.354855i
$825$		0			0
$826$		0			0
$827$			19778.2i			0.831626i	0.909450	+	0.415813i	$0.136503\pi$
$827$			19778.2i			0.831626i	−0.909450	+	0.415813i	$0.863497\pi$
$828$		0			0
$829$	−10941.2	−	6316.89i	−0.458387	−	0.264650i	0.252979	−	0.967472i	$-0.418590\pi$
$829$	−10941.2	−	6316.89i	−0.458387	−	0.264650i	−0.711366	+	0.702822i	$0.751923\pi$
$830$	3920.32	+	2263.40i	0.163947	+	0.0946549i
$831$		0			0
$832$		−	6485.32i		−	0.270238i
$833$		0			0
$834$		0			0
$835$	5308.53	+	9194.64i	0.220011	+	0.381070i
$836$	−9985.65	+	17295.6i	−0.413111	+	0.715529i
$837$		0			0
$838$	−7567.51	+	4369.10i	−0.311951	+	0.180105i
$839$	−39650.4			−1.63157			−0.815784	−	0.578357i	$-0.803694\pi$
$839$	−39650.4			−1.63157			−0.815784	+	0.578357i	$0.803694\pi$
$840$		0			0
$841$	16606.3			0.680894
$842$	−17553.2	+	10134.3i	−0.718434	+	0.414788i
$843$		0			0
$844$	−7068.30	+	12242.7i	−0.288271	+	0.499301i
$845$	3444.11	+	5965.38i	0.140214	+	0.242858i
$846$		0			0
$847$		0			0
$848$			5328.78i			0.215791i
$849$		0			0
$850$	−2573.50	−	1485.81i	−0.103847	−	0.0599564i
$851$	−15309.9	−	8839.18i	−0.616706	−	0.356056i
$852$		0			0
$853$		−	27542.7i		−	1.10556i	−0.833327	−	0.552780i	$-0.813567\pi$
$853$		−	27542.7i		−	1.10556i	0.833327	−	0.552780i	$-0.186433\pi$
$854$		0			0
$855$		0			0
$856$	−8201.67	−	14205.7i	−0.327485	−	0.567221i
$857$	−20097.4	+	34809.8i	−0.801068	+	1.38749i	0.117846	+	0.993032i	$0.462401\pi$
$857$	−20097.4	+	34809.8i	−0.801068	+	1.38749i	−0.918914	+	0.394458i	$0.870932\pi$
$858$		0			0
$859$	10338.3	−	5968.81i	0.410638	−	0.237082i	−0.280426	−	0.959876i	$-0.590476\pi$
$859$	10338.3	−	5968.81i	0.410638	−	0.237082i	0.691064	+	0.722794i	$0.257142\pi$
$860$	−1584.07			−0.0628095
$861$		0			0
$862$	−14314.5			−0.565608
$863$	28785.5	−	16619.3i	1.13542	−	0.655536i	0.190129	−	0.981759i	$-0.439109\pi$
$863$	28785.5	−	16619.3i	1.13542	−	0.655536i	0.945293	+	0.326223i	$0.105776\pi$
$864$		0			0
$865$	9545.45	−	16533.2i	0.375208	−	0.649880i
$866$	4497.80	+	7790.43i	0.176491	+	0.305692i
$867$		0			0
$868$		0			0
$869$		−	17922.1i		−	0.699615i
$870$		0			0
$871$	15238.5	+	8797.94i	0.592809	+	0.342258i
$872$	−2224.31	−	1284.21i	−0.0863815	−	0.0498724i
$873$		0			0
$874$			16480.8i			0.637840i
$875$		0			0
$876$		0			0
$877$	−10709.6	−	18549.6i	−0.412358	−	0.714226i	0.582789	−	0.812624i	$-0.301961\pi$
$877$	−10709.6	−	18549.6i	−0.412358	−	0.714226i	−0.995147	+	0.0983981i	$0.968628\pi$
$878$	−9215.13	+	15961.1i	−0.354209	+	0.613508i
$879$		0			0
$880$	−963.646	+	556.362i	−0.0369142	+	0.0213124i
$881$	−31353.3			−1.19900			−0.599501	−	0.800374i	$-0.704634\pi$
$881$	−31353.3			−1.19900			−0.599501	+	0.800374i	$0.704634\pi$
$882$		0			0
$883$	−35483.7			−1.35235			−0.676173	−	0.736743i	$-0.736363\pi$
$883$	−35483.7			−1.35235			−0.676173	+	0.736743i	$0.736363\pi$
$884$	−2255.79	+	1302.38i	−0.0858262	+	0.0495518i
$885$		0			0
$886$	6498.50	−	11255.7i	0.246412	−	0.426799i
$887$	10127.6	+	17541.6i	0.383374	+	0.664024i	0.991542	−	0.129785i	$-0.0414286\pi$
$887$	10127.6	+	17541.6i	0.383374	+	0.664024i	−0.608168	+	0.793808i	$0.708095\pi$
$888$		0			0
$889$		0			0
$890$			11772.7i			0.443394i
$891$		0			0
$892$	−23137.7	−	13358.6i	−0.868506	−	0.501432i
$893$	−45447.9	−	26239.4i	−1.70309	−	0.983278i
$894$		0			0
$895$			10045.6i			0.375182i
$896$		0			0
$897$		0			0
$898$	842.499	+	1459.25i	0.0313080	+	0.0542270i
$899$	11225.2	−	19442.6i	0.416442	−	0.721298i
$900$		0			0
$901$	−10481.7	+	6051.61i	−0.387565	+	0.223761i
$902$	20797.8			0.767727
$903$		0			0
$904$	−1961.00			−0.0721481
$905$	−17462.3	+	10081.9i	−0.641400	+	0.370312i
$906$		0			0
$907$	12848.0	−	22253.5i	0.470355	−	0.814680i	−0.529070	−	0.848578i	$-0.677459\pi$
$907$	12848.0	−	22253.5i	0.470355	−	0.814680i	0.999425	+	0.0338987i	$0.0107924\pi$
$908$	9189.75	+	15917.1i	0.335873	+	0.581749i
$909$		0			0
$910$		0			0
$911$			33200.2i			1.20743i	0.797199	+	0.603716i	$0.206314\pi$
$911$			33200.2i			1.20743i	−0.797199	+	0.603716i	$0.793686\pi$
$912$		0			0
$913$	−15374.3	−	8876.38i	−0.557302	−	0.321758i
$914$	−20075.0	−	11590.3i	−0.726500	−	0.419445i
$915$		0			0
$916$			17191.6i			0.620118i
$917$		0			0
$918$		0			0
$919$	−1068.12	−	1850.03i	−0.0383394	−	0.0664058i	0.846219	−	0.532835i	$-0.178873\pi$
$919$	−1068.12	−	1850.03i	−0.0383394	−	0.0664058i	−0.884558	+	0.466429i	$0.845540\pi$
$920$	−4198.18	+	7271.46i	−0.150446	+	0.260579i
$921$		0			0
$922$	−17870.5	+	10317.5i	−0.638322	+	0.368535i
$923$	−14575.0			−0.519763
$924$		0			0
$925$	−22125.4			−0.786464
$926$	17346.4	−	10014.9i	0.615591	−	0.355412i
$927$		0			0
$928$	8210.17	−	14220.4i	0.290422	−	0.503026i
$929$	526.275	+	911.535i	0.0185861	+	0.0321921i	0.875169	−	0.483818i	$-0.160750\pi$
$929$	526.275	+	911.535i	0.0185861	+	0.0321921i	−0.856583	+	0.516010i	$0.827417\pi$
$930$		0			0
$931$		0			0
$932$		−	11540.3i		−	0.405594i
$933$		0			0
$934$	17651.6	+	10191.1i	0.618391	+	0.357028i
$935$	−2188.72	−	1263.66i	−0.0765550	−	0.0441990i
$936$		0			0
$937$		−	14333.0i		−	0.499721i	−0.968282	−	0.249861i	$-0.919615\pi$
$937$		−	14333.0i		−	0.499721i	0.968282	−	0.249861i	$-0.0803848\pi$
$938$		0			0
$939$		0			0
$940$	−5371.16	−	9303.12i	−0.186370	−	0.322803i
$941$	−6563.30	+	11368.0i	−0.227372	+	0.393821i	−0.957029	−	0.289994i	$-0.906347\pi$
$941$	−6563.30	+	11368.0i	−0.227372	+	0.393821i	0.729656	+	0.683814i	$0.239680\pi$
$942$		0			0
$943$	−30405.3	+	17554.5i	−1.04998	+	0.606207i
$944$	6031.02			0.207937
$945$		0			0
$946$	−3036.82			−0.104372
$947$	7602.28	−	4389.18i	0.260867	−	0.150611i	−0.363863	−	0.931452i	$-0.618542\pi$
$947$	7602.28	−	4389.18i	0.260867	−	0.150611i	0.624730	+	0.780841i	$0.285209\pi$
$948$		0			0
$949$	8581.56	−	14863.7i	0.293540	−	0.508425i
$950$	10313.3	+	17863.2i	0.352219	+	0.610061i
$951$		0			0
$952$		0			0
$953$			4130.75i			0.140407i	0.997533	+	0.0702036i	$0.0223649\pi$
$953$			4130.75i			0.140407i	−0.997533	+	0.0702036i	$0.977635\pi$
$954$		0			0
$955$	−3165.91	−	1827.84i	−0.107274	−	0.0619344i
$956$	−13277.5	−	7665.80i	−0.449191	−	0.259341i
$957$		0			0
$958$		−	19893.2i		−	0.670899i
$959$		0			0
$960$		0			0
$961$	17485.4	+	30285.6i	0.586936	+	1.01660i
$962$	4740.31	−	8210.45i	0.158871	−	0.275172i
$963$		0			0
$964$	−1832.23	+	1057.84i	−0.0612158	+	0.0353430i
$965$	−23189.7			−0.773579
$966$		0			0
$967$	2697.99			0.0897222			0.0448611	−	0.998993i	$-0.485715\pi$
$967$	2697.99			0.0897222			0.0448611	+	0.998993i	$0.485715\pi$
$968$	8090.91	−	4671.29i	0.268648	−	0.155104i
$969$		0			0
$970$	2501.79	−	4333.22i	0.0828119	−	0.143434i
$971$	8411.94	+	14569.9i	0.278014	+	0.481535i	0.970891	−	0.239521i	$-0.0769904\pi$
$971$	8411.94	+	14569.9i	0.278014	+	0.481535i	−0.692877	+	0.721056i	$0.743657\pi$
$972$		0			0
$973$		0			0
$974$			12220.0i			0.402007i
$975$		0			0
$976$	2460.98	+	1420.85i	0.0807110	+	0.0465985i
$977$	33352.8	+	19256.3i	1.09217	+	0.630565i	0.934154	−	0.356871i	$-0.116157\pi$
$977$	33352.8	+	19256.3i	1.09217	+	0.630565i	0.158017	+	0.987436i	$0.449490\pi$
$978$		0			0
$979$		−	46169.0i		−	1.50722i
$980$		0			0
$981$		0			0
$982$	−329.505	−	570.719i	−0.0107077	−	0.0185462i
$983$	13465.4	−	23322.7i	0.436905	−	0.756742i	−0.560544	−	0.828125i	$-0.689408\pi$
$983$	13465.4	−	23322.7i	0.436905	−	0.756742i	0.997449	+	0.0713826i	$0.0227411\pi$
$984$		0			0
$985$	4105.66	−	2370.40i	0.132809	−	0.0766774i
$986$	2552.06			0.0824281
$987$		0			0
$988$	18080.2			0.582193
$989$	4439.68	−	2563.25i	0.142744	−	0.0824132i
$990$		0			0
$991$	5796.70	−	10040.2i	0.185810	−	0.321833i	−0.758039	−	0.652209i	$-0.773842\pi$
$991$	5796.70	−	10040.2i	0.185810	−	0.321833i	0.943849	+	0.330376i	$0.107176\pi$
$992$	23683.6	+	41021.2i	0.758018	+	1.31293i
$993$		0			0
$994$		0			0
$995$			9453.25i			0.301194i
$996$		0			0
$997$	−43168.7	−	24923.4i	−1.37128	−	0.791708i	−0.380190	−	0.924908i	$-0.624141\pi$
$997$	−43168.7	−	24923.4i	−1.37128	−	0.791708i	−0.991089	+	0.133200i	$0.957475\pi$
$998$	−7726.65	−	4460.98i	−0.245073	−	0.141493i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.4.p.d.80.16		48
3.2	odd	2	inner	441.4.p.d.80.9		48
7.2	even	3	inner	441.4.p.d.215.10		48
7.3	odd	6		441.4.c.b.440.10	yes	24
7.4	even	3		441.4.c.b.440.16	yes	24
7.5	odd	6	inner	441.4.p.d.215.9		48
7.6	odd	2	inner	441.4.p.d.80.15		48
21.2	odd	6	inner	441.4.p.d.215.15		48
21.5	even	6	inner	441.4.p.d.215.16		48
21.11	odd	6		441.4.c.b.440.9	✓	24
21.17	even	6		441.4.c.b.440.15	yes	24
21.20	even	2	inner	441.4.p.d.80.10		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.4.c.b.440.9	✓	24	21.11	odd	6
441.4.c.b.440.10	yes	24	7.3	odd	6
441.4.c.b.440.15	yes	24	21.17	even	6
441.4.c.b.440.16	yes	24	7.4	even	3
441.4.p.d.80.9		48	3.2	odd	2	inner
441.4.p.d.80.10		48	21.20	even	2	inner
441.4.p.d.80.15		48	7.6	odd	2	inner
441.4.p.d.80.16		48	1.1	even	1	trivial
441.4.p.d.215.9		48	7.5	odd	6	inner
441.4.p.d.215.10		48	7.2	even	3	inner
441.4.p.d.215.15		48	21.2	odd	6	inner
441.4.p.d.215.16		48	21.5	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	441.p (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.40358 - 0.810356i) q^{2} +(-2.68665 + 4.65341i) q^{4} +(2.35993 + 4.08752i) q^{5} +21.6743i q^{8} +(6.62469 + 3.82477i) q^{10} +(-25.9801 - 14.9996i) q^{11} +27.1586i q^{13} +(-3.92932 - 6.80578i) q^{16} +(8.92464 - 15.4579i) q^{17} +(-107.297 + 61.9477i) q^{19} -25.3612 q^{20} -48.6201 q^{22} +(71.0802 - 41.0382i) q^{23} +(51.3615 - 88.9606i) q^{25} +(22.0081 + 38.1191i) q^{26} +88.2194i q^{29} +(-220.389 - 127.242i) q^{31} +(-161.194 - 93.0653i) q^{32} -28.9285i q^{34} +(-107.695 - 186.533i) q^{37} +(-100.399 + 173.897i) q^{38} +(-88.5939 + 51.1497i) q^{40} -427.760 q^{41} +62.4602 q^{43} +(139.599 - 80.5974i) q^{44} +(66.5110 - 115.200i) q^{46} +(211.787 + 366.825i) q^{47} -166.484i q^{50} +(-126.380 - 72.9654i) q^{52} +(-587.234 - 339.039i) q^{53} -141.592i q^{55} +(71.4891 + 123.823i) q^{58} +(-383.719 + 664.621i) q^{59} +(-313.156 + 180.801i) q^{61} -412.444 q^{62} -238.795 q^{64} +(-111.011 + 64.0923i) q^{65} +(323.947 - 561.093i) q^{67} +(47.9547 + 83.0600i) q^{68} +536.663i q^{71} +(-547.293 - 315.980i) q^{73} +(-302.316 - 174.542i) q^{74} -665.726i q^{76} +(298.709 + 517.379i) q^{79} +(18.5458 - 32.1223i) q^{80} +(-600.395 + 346.638i) q^{82} +591.773 q^{83} +84.2461 q^{85} +(87.6677 - 50.6150i) q^{86} +(325.106 - 563.100i) q^{88} +(769.502 + 1332.82i) q^{89} +441.020i q^{92} +(594.517 + 343.245i) q^{94} +(-506.425 - 292.385i) q^{95} -654.102i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 96 q^{4} - 144 q^{16} + 1248 q^{22} - 312 q^{25} + 864 q^{37} + 2496 q^{43} + 3888 q^{46} + 7440 q^{58} - 6720 q^{64} + 2688 q^{67} - 480 q^{79} + 26496 q^{85} + 7248 q^{88}+O(q^{100}) \) 48 * q + 96 * q^4 - 144 * q^16 + 1248 * q^22 - 312 * q^25 + 864 * q^37 + 2496 * q^43 + 3888 * q^46 + 7440 * q^58 - 6720 * q^64 + 2688 * q^67 - 480 * q^79 + 26496 * q^85 + 7248 * q^88

Introduction

L-functions

Modular forms

Varieties

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Database

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