LMFDB - Embedded newform 441.4.p.d.215.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,4,Mod(80,441)]

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

lf = mfeigenbasis(mf)

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")

//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);

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

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			215.16
Character	$\chi$	$=$	441.215
Dual form			441.4.p.d.80.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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	0.727159	−	0.686469i	$-0.240840\pi$
$2$	1.40358	+	0.810356i	0.496240	+	0.286504i	−0.230920	+	0.972973i	$0.574173\pi$
$3$		0			0
$3$		0			0
$4$	−2.68665	−	4.65341i	−0.335831	−	0.581676i
$5$	2.35993	−	4.08752i	0.211079	−	0.365599i	−0.740974	−	0.671534i	$-0.765636\pi$
$5$	2.35993	−	4.08752i	0.211079	−	0.365599i	0.952052	+	0.305935i	$0.0989691\pi$
$6$		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	−0.811845	−	0.583873i	$-0.801536\pi$
$11$	−25.9801	+	14.9996i	−0.712118	+	0.411142i	0.0997267	+	0.995015i	$0.468203\pi$
$12$		0			0
$13$		−	27.1586i		−	0.579417i	−0.957115	−	0.289709i	$-0.906442\pi$
$13$		−	27.1586i		−	0.579417i	0.957115	−	0.289709i	$-0.0935584\pi$
$14$		0			0
$15$		0			0
$16$	−3.92932	+	6.80578i	−0.0613956	+	0.106340i
$17$	8.92464	+	15.4579i	0.127326	+	0.220535i	0.922640	−	0.385663i	$-0.126027\pi$
$17$	8.92464	+	15.4579i	0.127326	+	0.220535i	−0.795314	+	0.606198i	$0.792694\pi$
$18$		0			0
$19$	−107.297	−	61.9477i	−1.29555	−	0.747988i	−0.315921	−	0.948786i	$-0.602313\pi$
$19$	−107.297	−	61.9477i	−1.29555	−	0.747988i	−0.979633	+	0.200797i	$0.935647\pi$
$20$	−25.3612			−0.283547
$21$		0			0
$22$	−48.6201			−0.471175
$23$	71.0802	+	41.0382i	0.644402	+	0.372046i	0.786308	−	0.617835i	$-0.211990\pi$
$23$	71.0802	+	41.0382i	0.644402	+	0.372046i	−0.141906	+	0.989880i	$0.545323\pi$
$24$		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	$-0.908854\pi$
$29$		−	88.2194i		−	0.564894i	0.959283	−	0.282447i	$-0.0911462\pi$
$30$		0			0
$31$	−220.389	+	127.242i	−1.27687	+	0.737203i	−0.976272	−	0.216548i	$-0.930520\pi$
$31$	−220.389	+	127.242i	−1.27687	+	0.737203i	−0.300600	+	0.953750i	$0.597187\pi$
$32$	−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	−0.999696	−	0.0246385i	$-0.992157\pi$
$37$	−107.695	+	186.533i	−0.478511	+	0.828805i	0.521186	+	0.853443i	$0.325490\pi$
$38$	−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	−0.324035	−	0.946045i	$-0.605040\pi$
$47$	211.787	−	366.825i	0.657282	−	1.13845i	0.981317	−	0.192400i	$-0.0616271\pi$
$48$		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	−0.522274	+	0.852778i	$0.674916\pi$
$53$	−587.234	+	339.039i	−1.52194	+	0.878692i	−0.999664	+	0.0259140i	$0.991750\pi$
$54$		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	−0.884127	−	0.467246i	$-0.845246\pi$
$59$	−383.719	−	664.621i	−0.846711	−	1.46655i	0.0374163	−	0.999300i	$-0.488087\pi$
$60$		0			0
$61$	−313.156	−	180.801i	−0.657303	−	0.379494i	0.133946	−	0.990989i	$-0.457235\pi$
$61$	−313.156	−	180.801i	−0.657303	−	0.379494i	−0.791249	+	0.611495i	$0.790569\pi$
$62$	−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	0.994139	+	0.108108i	$0.0344791\pi$
$67$	323.947	+	561.093i	0.590694	+	1.02311i	−0.403446	+	0.915004i	$0.632188\pi$
$68$	47.9547	−	83.0600i	0.0855200	−	0.148125i
$69$		0			0
$70$		0			0
$71$		−	536.663i		−	0.897045i	−0.893772	−	0.448522i	$-0.851950\pi$
$71$		−	536.663i		−	0.897045i	0.893772	−	0.448522i	$-0.148050\pi$
$72$		0			0
$73$	−547.293	+	315.980i	−0.877477	+	0.506612i	−0.869826	−	0.493359i	$-0.835769\pi$
$73$	−547.293	+	315.980i	−0.877477	+	0.506612i	−0.00765130	+	0.999971i	$0.502436\pi$
$74$	−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	−0.571049	−	0.820916i	$-0.693463\pi$
$79$	298.709	−	517.379i	0.425410	−	0.736832i	0.996459	+	0.0840844i	$0.0267965\pi$
$80$	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	0.111769	−	0.993734i	$-0.464348\pi$
$89$	769.502	−	1332.82i	0.916484	−	1.58740i	0.804714	−	0.593662i	$-0.202318\pi$
$90$		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	$0.111219\pi$
$97$			654.102i			0.684680i	−0.939576	+	0.342340i	$0.888781\pi$
$98$		0			0
$99$		0			0
$100$	275.980	−	478.012i	0.275980	−	0.478012i
$101$	−148.389	−	257.018i	−0.146191	−	0.253210i	0.783626	−	0.621233i	$-0.213368\pi$
$101$	−148.389	−	257.018i	−0.146191	−	0.253210i	−0.929817	+	0.368023i	$0.880035\pi$
$102$		0			0
$103$	387.255	+	223.582i	0.370460	+	0.213885i	0.673660	−	0.739042i	$-0.264721\pi$
$103$	387.255	+	223.582i	0.370460	+	0.213885i	−0.303199	+	0.952927i	$0.598055\pi$
$104$	−588.641			−0.555010
$105$		0			0
$106$	−1098.97			−1.00699
$107$	−655.418	−	378.406i	−0.592165	−	0.341887i	0.173788	−	0.984783i	$-0.444399\pi$
$107$	−655.418	−	378.406i	−0.592165	−	0.341887i	−0.765953	+	0.642896i	$0.777733\pi$
$108$		0			0
$109$	−59.2503	−	102.625i	−0.0520656	−	0.0901803i	0.838818	−	0.544412i	$-0.183247\pi$
$109$	−59.2503	−	102.625i	−0.0520656	−	0.0901803i	−0.890884	+	0.454232i	$0.849914\pi$
$110$	−114.740	+	198.736i	−0.0994550	+	0.172261i
$111$		0			0
$112$		0			0
$113$		−	90.4761i		−	0.0753210i	−0.999291	−	0.0376605i	$-0.988009\pi$
$113$		−	90.4761i		−	0.0753210i	0.999291	−	0.0376605i	$-0.0119905\pi$
$114$		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	−0.730587	−	0.682820i	$-0.760753\pi$
$131$	338.925	−	587.035i	0.226046	−	0.391523i	0.956633	+	0.291297i	$0.0940868\pi$
$132$		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	0.211598	−	0.977357i	$-0.432133\pi$
$137$	1866.23	−	1077.47i	1.16381	−	0.671928i	0.952215	+	0.305429i	$0.0987998\pi$
$138$		0			0
$139$			719.518i			0.439055i	0.975606	+	0.219528i	$0.0704516\pi$
$139$			719.518i			0.439055i	−0.975606	+	0.219528i	$0.929548\pi$
$140$		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	0.187826	−	0.982202i	$-0.439856\pi$
$149$	−1034.65	−	597.357i	−0.568873	−	0.328439i	−0.756699	+	0.653763i	$0.773189\pi$
$150$		0			0
$151$	−536.066	−	928.494i	−0.288904	−	0.500396i	0.684645	−	0.728877i	$-0.259957\pi$
$151$	−536.066	−	928.494i	−0.288904	−	0.500396i	−0.973548	+	0.228481i	$0.926624\pi$
$152$	−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	−0.916387	−	0.400293i	$-0.868908\pi$
$157$	−2022.12	+	1167.47i	−1.02792	+	0.593468i	−0.111530	+	0.993761i	$0.535575\pi$
$158$	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	−0.00113428	+	0.999999i	$0.500361\pi$
$163$	−1803.42	+	3123.61i	−0.866592	+	1.50098i	−0.865458	+	0.500982i	$0.832972\pi$
$164$	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	−0.0474778	+	0.998872i	$0.515118\pi$
$173$	−2022.40	+	3502.90i	−0.888788	+	1.53943i	−0.841310	+	0.540553i	$0.818215\pi$
$174$		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	−0.0630946	−	0.998008i	$-0.520097\pi$
$179$	1843.22	−	1064.18i	0.769658	−	0.444362i	0.832753	+	0.553645i	$0.186764\pi$
$180$		0			0
$181$		−	4272.10i		−	1.75438i	−0.480143	−	0.877190i	$-0.659415\pi$
$181$		−	4272.10i		−	1.75438i	0.480143	−	0.877190i	$-0.340585\pi$
$182$		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	0.367536	−	0.930009i	$-0.380202\pi$
$191$	−670.762	−	387.265i	−0.254108	−	0.146709i	−0.621644	+	0.783300i	$0.713535\pi$
$192$		0			0
$193$	−2456.61	−	4254.97i	−0.916221	−	1.58694i	−0.805104	−	0.593134i	$-0.797890\pi$
$193$	−2456.61	−	4254.97i	−0.916221	−	1.58694i	−0.111117	−	0.993807i	$-0.535443\pi$
$194$	−530.055	+	918.082i	−0.196164	+	0.339765i
$195$		0			0
$196$		0			0
$197$			1004.44i			0.363265i	0.983366	+	0.181632i	$0.0581381\pi$
$197$			1004.44i			0.363265i	−0.983366	+	0.181632i	$0.941862\pi$
$198$		0			0
$199$	1734.53	−	1001.43i	0.617878	−	0.356732i	−0.158164	−	0.987413i	$-0.550558\pi$
$199$	1734.53	−	1001.43i	0.617878	−	0.356732i	0.776042	+	0.630681i	$0.217224\pi$
$200$	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	$-0.731707\pi$
$223$		−	4972.20i		−	1.49311i	0.665324	−	0.746555i	$-0.268293\pi$
$224$		0			0
$225$		0			0
$226$	73.3178	−	126.990i	0.0215798	−	0.0373773i
$227$	1710.26	+	2962.26i	0.500062	+	0.866133i	1.00000		7.18991e-5i	$2.28862e-5\pi$
$227$	1710.26	+	2962.26i	0.500062	+	0.866133i	−0.499938	+	0.866061i	$0.666644\pi$
$228$		0			0
$229$	2770.81	+	1599.73i	0.799566	+	0.461629i	0.843319	−	0.537413i	$-0.180598\pi$
$229$	2770.81	+	1599.73i	0.799566	+	0.461629i	−0.0437537	+	0.999042i	$0.513932\pi$
$230$	627.846			0.179995
$231$		0			0
$232$	−1912.09			−0.541099
$233$	−1859.97	−	1073.85i	−0.522964	−	0.301933i	0.215183	−	0.976574i	$-0.430965\pi$
$233$	−1859.97	−	1073.85i	−0.522964	−	0.301933i	−0.738146	+	0.674641i	$0.764299\pi$
$234$		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	$-0.873816\pi$
$239$		−	2853.29i		−	0.772236i	0.922449	−	0.386118i	$-0.126184\pi$
$240$		0			0
$241$	340.988	−	196.869i	0.0911409	−	0.0526202i	−0.453737	−	0.891136i	$-0.649909\pi$
$241$	340.988	−	196.869i	0.0911409	−	0.0526202i	0.544878	+	0.838516i	$0.316576\pi$
$242$	−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	−0.483822	−	0.875167i	$-0.660752\pi$
$257$	2125.96	−	3682.26i	0.516006	−	0.893748i	0.999827	−	0.0185815i	$-0.00591500\pi$
$258$		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	0.443040	−	0.896502i	$-0.353900\pi$
$263$	6145.87	−	3548.32i	1.44095	−	0.831935i	0.997913	+	0.0645666i	$0.0205665\pi$
$264$		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	0.505766	−	0.862671i	$-0.331210\pi$
$269$	−2180.43	−	3776.61i	−0.494212	−	0.856000i	−0.999978	+	0.00667106i	$0.997877\pi$
$270$		0			0
$271$	−3737.79	−	2158.02i	−0.837841	−	0.483727i	0.0186891	−	0.999825i	$-0.494051\pi$
$271$	−3737.79	−	2158.02i	−0.837841	−	0.483727i	−0.856530	+	0.516098i	$0.827384\pi$
$272$	−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	0.972901	−	0.231223i	$-0.0742728\pi$
$277$	1319.46	+	2285.38i	0.286205	+	0.495722i	−0.686696	+	0.726945i	$0.740939\pi$
$278$	−583.065	+	1009.90i	−0.125791	+	0.217877i
$279$		0			0
$280$		0			0
$281$			5925.56i			1.25797i	0.777417	+	0.628985i	$0.216529\pi$
$281$			5925.56i			1.25797i	−0.777417	+	0.628985i	$0.783471\pi$
$282$		0			0
$283$	−2663.30	+	1537.65i	−0.559422	+	0.322983i	−0.752914	−	0.658119i	$-0.771352\pi$
$283$	−2663.30	+	1537.65i	−0.559422	+	0.322983i	0.193491	+	0.981102i	$0.438019\pi$
$284$	−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	$-0.946410\pi$
$307$		−	1802.67i		−	0.335127i	0.985861	−	0.167563i	$-0.0535898\pi$
$308$		0			0
$309$		0			0
$310$	−973.340	+	1685.87i	−0.178329	+	0.308875i
$311$	−4769.98	−	8261.85i	−0.869714	−	1.50639i	−0.862289	−	0.506416i	$-0.830970\pi$
$311$	−4769.98	−	8261.85i	−0.869714	−	1.50639i	−0.00742422	−	0.999972i	$-0.502363\pi$
$312$		0			0
$313$	−1095.23	−	632.332i	−0.197783	−	0.114190i	0.397838	−	0.917456i	$-0.369761\pi$
$313$	−1095.23	−	632.332i	−0.197783	−	0.114190i	−0.595621	+	0.803266i	$0.703094\pi$
$314$	−3784.27			−0.680124
$315$		0			0
$316$	−3210.10			−0.571463
$317$	−8265.68	−	4772.19i	−1.46450	−	0.845530i	−0.465287	−	0.885160i	$-0.654049\pi$
$317$	−8265.68	−	4772.19i	−1.46450	−	0.845530i	−0.999214	+	0.0396301i	$0.987382\pi$
$318$		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	−0.731521	−	0.681819i	$-0.761189\pi$
$331$	1353.22	−	2343.85i	0.224712	−	0.389213i	0.956233	+	0.292606i	$0.0945225\pi$
$332$	−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	−0.986219	−	0.165444i	$-0.947094\pi$
$347$	−8636.09	+	4986.05i	−1.33605	+	0.771369i	−0.349831	+	0.936813i	$0.613761\pi$
$348$		0			0
$349$			1653.11i			0.253549i	0.991932	+	0.126775i	$0.0404625\pi$
$349$			1653.11i			0.253549i	−0.991932	+	0.126775i	$0.959537\pi$
$350$		0			0
$351$		0			0
$352$	2791.89	−	4835.69i	0.422751	−	0.732226i
$353$	−1677.25	−	2905.09i	−0.252893	−	0.438024i	0.711428	−	0.702759i	$-0.248049\pi$
$353$	−1677.25	−	2905.09i	−0.252893	−	0.438024i	−0.964321	+	0.264735i	$0.914715\pi$
$354$		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	0.567361	−	0.823469i	$-0.307964\pi$
$359$	937.988	+	541.548i	0.137897	+	0.0796150i	−0.429464	+	0.903084i	$0.641298\pi$
$360$		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	−0.624045	−	0.781388i	$-0.714512\pi$
$367$	−1823.53	+	1052.81i	−0.259366	+	0.149745i	0.364679	+	0.931133i	$0.381179\pi$
$368$	−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	−0.966032	−	0.258422i	$-0.916797\pi$
$373$	−1867.35	+	3234.34i	−0.259216	+	0.448975i	0.706816	+	0.707397i	$0.250131\pi$
$374$	−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	−0.630901	−	0.775863i	$-0.717315\pi$
$383$	2671.88	−	4627.84i	0.356467	−	0.617419i	0.987368	+	0.158444i	$0.0506479\pi$
$384$		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	−0.602105	−	0.798417i	$-0.705671\pi$
$389$	−1624.29	+	937.783i	−0.211709	+	0.122230i	0.390397	+	0.920647i	$0.372338\pi$
$390$		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	−0.129381	−	0.991595i	$-0.541299\pi$
$397$	−8327.97	−	4808.16i	−1.05282	−	0.607845i	−0.923437	+	0.383750i	$0.874633\pi$
$398$	3246.07			0.408821
$399$		0			0
$400$	−807.262			−0.100908
$401$	−562.762	−	324.911i	−0.0700823	−	0.0404620i	0.464549	−	0.885547i	$-0.346216\pi$
$401$	−562.762	−	324.911i	−0.0700823	−	0.0404620i	−0.534632	+	0.845085i	$0.679550\pi$
$402$		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	−0.647334	+	0.762206i	$0.724116\pi$
$409$	−13491.6	+	7789.38i	−1.63109	+	0.941711i	−0.983757	+	0.179505i	$0.942550\pi$
$410$	−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	−0.862281	−	0.506430i	$-0.830965\pi$
$431$	−7648.94	+	4416.12i	−0.854841	+	0.493543i	0.00744041	+	0.999972i	$0.497632\pi$
$432$		0			0
$433$		−	5550.41i		−	0.616017i	−0.951384	−	0.308009i	$-0.900337\pi$
$433$		−	5550.41i		−	0.616017i	0.951384	−	0.308009i	$-0.0996626\pi$
$434$		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	−0.142313	−	0.989822i	$-0.545454\pi$
$439$	−9848.19	−	5685.86i	−1.07068	−	0.618157i	−0.928367	+	0.371664i	$0.878787\pi$
$440$	3068.91			0.332510
$441$		0			0
$442$	785.657			0.0845473
$443$	6944.93	+	4009.66i	0.744839	+	0.430033i	0.823826	−	0.566843i	$-0.191835\pi$
$443$	6944.93	+	4009.66i	0.744839	+	0.430033i	−0.0789873	+	0.996876i	$0.525169\pi$
$444$		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	$-0.982600\pi$
$449$		−	1039.67i		−	0.109276i	0.998506	−	0.0546379i	$-0.0174005\pi$
$450$		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	0.224019	+	0.974585i	$0.428082\pi$
$457$	−7151.36	+	12386.5i	−0.732005	+	1.26787i	−0.956025	+	0.293286i	$0.905251\pi$
$458$	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	−0.365833	−	0.930681i	$-0.619216\pi$
$467$	6288.06	−	10891.2i	0.623077	−	1.07920i	0.988909	−	0.148520i	$-0.0474509\pi$
$468$		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	0.994823	+	0.101621i	$0.0324030\pi$
$479$	6137.19	+	10629.9i	0.585418	+	1.01397i	−0.409405	+	0.912353i	$0.634264\pi$
$480$		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	0.635601	−	0.772018i	$-0.280753\pi$
$487$	−3769.96	−	6529.76i	−0.350787	−	0.607581i	−0.986388	+	0.164437i	$0.947419\pi$
$488$	−3918.72	+	6787.42i	−0.363508	+	0.629614i
$489$		0			0
$490$		0			0
$491$			406.618i			0.0373735i	0.999825	+	0.0186868i	$0.00594853\pi$
$491$			406.618i			0.0373735i	−0.999825	+	0.0186868i	$0.994051\pi$
$492$		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	−0.962672	−	0.270669i	$-0.912755\pi$
$499$	−2752.48	+	4767.44i	−0.246930	+	0.427695i	0.715742	+	0.698364i	$0.246088\pi$
$500$	−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	0.152452	+	0.988311i	$0.451283\pi$
$509$	−8953.46	+	15507.9i	−0.779677	+	1.35044i	−0.932128	+	0.362128i	$0.882050\pi$
$510$		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	0.540901	−	0.841086i	$-0.318083\pi$
$521$	−5445.98	−	9432.71i	−0.457951	−	0.793195i	−0.998853	+	0.0478914i	$0.984750\pi$
$522$		0			0
$523$	2311.20	+	1334.37i	0.193235	+	0.111564i	0.593496	−	0.804837i	$-0.297747\pi$
$523$	2311.20	+	1334.37i	0.193235	+	0.111564i	−0.400261	+	0.916401i	$0.631081\pi$
$524$	−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	−0.568506	−	0.822679i	$-0.692478\pi$
$541$	5388.29	−	9332.80i	0.428209	−	0.741679i	0.996714	+	0.0810005i	$0.0258115\pi$
$542$	−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	0.231608	−	0.972809i	$-0.425601\pi$
$557$	15641.9	−	9030.85i	1.18989	−	0.686983i	0.958282	+	0.285826i	$0.0922680\pi$
$558$		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	0.927339	+	0.374221i	$0.122090\pi$
$563$	10523.3	+	18227.0i	0.787755	+	1.36443i	−0.139585	+	0.990210i	$0.544577\pi$
$564$		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	0.834106	−	0.551605i	$-0.185984\pi$
$569$	10497.9	+	6060.98i	0.773455	+	0.446554i	−0.0606509	+	0.998159i	$0.519318\pi$
$570$		0			0
$571$	1472.07	+	2549.70i	0.107888	+	0.186868i	0.914915	−	0.403647i	$-0.132258\pi$
$571$	1472.07	+	2549.70i	0.107888	+	0.186868i	−0.807026	+	0.590516i	$0.798924\pi$
$572$	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	−0.328965	−	0.944342i	$-0.606700\pi$
$577$	4495.86	−	2595.69i	0.324376	−	0.187279i	0.653342	+	0.757063i	$0.273367\pi$
$578$	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	0.267402	+	0.963585i	$0.413835\pi$
$593$	−10119.7	+	17527.9i	−0.700788	+	1.21380i	−0.968190	+	0.250216i	$0.919499\pi$
$594$		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	−0.226872	−	0.973925i	$-0.572850\pi$
$599$	7376.06	−	4258.57i	0.503135	−	0.290485i	0.730007	+	0.683439i	$0.239517\pi$
$600$		0			0
$601$			5040.33i			0.342096i	0.985263	+	0.171048i	$0.0547152\pi$
$601$			5040.33i			0.342096i	−0.985263	+	0.171048i	$0.945285\pi$
$602$		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	0.996085	+	0.0884057i	$0.0281772\pi$
$607$	23489.5	+	13561.6i	1.57069	+	0.906837i	0.574604	+	0.818432i	$0.305156\pi$
$608$	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	0.813633	−	0.581379i	$-0.197487\pi$
$613$	−1467.22	−	2541.30i	−0.0966730	−	0.167443i	−0.910306	+	0.413937i	$0.864153\pi$
$614$	1460.80	−	2530.19i	0.0960151	−	0.166303i
$615$		0			0
$616$		0			0
$617$		−	2908.86i		−	0.189799i	−0.995487	−	0.0948996i	$-0.969747\pi$
$617$		−	2908.86i		−	0.189799i	0.995487	−	0.0948996i	$-0.0302530\pi$
$618$		0			0
$619$	13814.4	−	7975.77i	0.897010	−	0.517889i	0.0207811	−	0.999784i	$-0.493385\pi$
$619$	13814.4	−	7975.77i	0.897010	−	0.517889i	0.876229	+	0.481895i	$0.160051\pi$
$620$	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	−0.347453	−	0.937697i	$-0.612953\pi$
$641$	4720.80	−	2725.55i	0.290890	−	0.167945i	0.638343	+	0.769752i	$0.279620\pi$
$642$		0			0
$643$			15700.8i			0.962956i	0.876458	+	0.481478i	$0.159900\pi$
$643$			15700.8i			0.962956i	−0.876458	+	0.481478i	$0.840100\pi$
$644$		0			0
$645$		0			0
$646$	1792.06	−	3103.93i	0.109145	−	0.189044i
$647$	11372.0	+	19696.9i	0.691006	+	1.19686i	0.971509	+	0.237004i	$0.0761656\pi$
$647$	11372.0	+	19696.9i	0.691006	+	1.19686i	−0.280502	+	0.959853i	$0.590501\pi$
$648$		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	0.641855	−	0.766826i	$-0.278165\pi$
$653$	4984.17	+	2877.61i	0.298691	+	0.172450i	−0.343163	+	0.939276i	$0.611498\pi$
$654$		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	$-0.741165\pi$
$659$		−	24579.2i		−	1.45292i	0.687211	−	0.726458i	$-0.258835\pi$
$660$		0			0
$661$	4251.57	−	2454.64i	0.250177	−	0.144440i	−0.369669	−	0.929164i	$-0.620529\pi$
$661$	4251.57	−	2454.64i	0.250177	−	0.144440i	0.619845	+	0.784724i	$0.287195\pi$
$662$	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	−0.761104	−	0.648630i	$-0.775342\pi$
$677$	3191.45	−	5527.76i	0.181178	−	0.313809i	0.942282	+	0.334821i	$0.108676\pi$
$678$		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	−0.126303	−	0.991992i	$-0.540311\pi$
$683$	11952.8	−	6900.95i	0.669636	−	0.386614i	0.795939	+	0.605377i	$0.206978\pi$
$684$		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	0.457685	−	0.889114i	$-0.348679\pi$
$691$	−1516.12	−	875.333i	−0.0834674	−	0.0481899i	−0.541153	+	0.840924i	$0.682012\pi$
$692$	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	$0.258357\pi$
$701$			26927.8i			1.45085i	−0.688300	+	0.725426i	$0.741643\pi$
$702$		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	−0.670454	−	0.741952i	$-0.733900\pi$
$709$	5801.80	−	10049.0i	0.307322	−	0.532297i	0.977776	+	0.209654i	$0.0672338\pi$
$710$	−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	−0.986275	−	0.165108i	$-0.947203\pi$
$719$	−6750.67	+	11692.5i	−0.350150	+	0.606477i	0.636126	+	0.771585i	$0.280536\pi$
$720$		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	$-0.990932\pi$
$727$		−	1116.75i		−	0.0569708i	0.999594	−	0.0284854i	$-0.00906842\pi$
$728$		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	0.973215	−	0.229898i	$-0.0738394\pi$
$733$	25019.4	+	14444.9i	1.26072	+	0.727879i	0.287510	+	0.957778i	$0.407173\pi$
$734$	−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	0.889755	−	0.456438i	$-0.150875\pi$
$739$	996.244	+	1725.55i	0.0495906	+	0.0858934i	−0.840165	+	0.542332i	$0.817542\pi$
$740$	2731.27	−	4730.69i	0.135680	−	0.235005i
$741$		0			0
$742$		0			0
$743$		−	32395.7i		−	1.59957i	−0.600284	−	0.799787i	$-0.704946\pi$
$743$		−	32395.7i		−	1.59957i	0.600284	−	0.799787i	$-0.295054\pi$
$744$		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	−0.758937	−	0.651163i	$-0.774281\pi$
$751$	3796.22	−	6575.24i	0.184455	−	0.319486i	0.943393	+	0.331677i	$0.107615\pi$
$752$	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	0.159212	+	0.987244i	$0.449105\pi$
$761$	−16277.5	+	28193.4i	−0.775373	+	1.34299i	−0.934585	+	0.355741i	$0.884229\pi$
$762$		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	$0.303367\pi$
$769$			34767.8i			1.63038i	−0.579195	+	0.815189i	$0.696633\pi$
$770$		0			0
$771$		0			0
$772$	−13200.1	+	22863.2i	−0.615391	+	1.06589i
$773$	−2994.63	−	5186.85i	−0.139339	−	0.241343i	0.787907	−	0.615794i	$-0.211165\pi$
$773$	−2994.63	−	5186.85i	−0.139339	−	0.241343i	−0.927247	+	0.374451i	$0.877831\pi$
$774$		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	−0.648882	+	0.760889i	$0.724763\pi$
$787$	−36037.5	+	20806.3i	−1.63227	+	0.942393i	−0.983390	+	0.181504i	$0.941903\pi$
$788$	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	−0.886716	−	0.462315i	$-0.847019\pi$
$809$	−21392.6	+	12351.0i	−0.929697	+	0.536761i	−0.0429815	+	0.999076i	$0.513686\pi$
$810$		0			0
$811$		−	30991.5i		−	1.34187i	−0.741516	−	0.670936i	$-0.765893\pi$
$811$		−	30991.5i		−	1.34187i	0.741516	−	0.670936i	$-0.234107\pi$
$812$		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	0.919066	−	0.394103i	$-0.128945\pi$
$821$	24401.5	+	14088.2i	1.03730	+	0.598883i	0.118230	+	0.992986i	$0.462278\pi$
$822$		0			0
$823$	−8539.10	−	14790.2i	−0.361670	−	0.626431i	0.626566	−	0.779368i	$-0.284460\pi$
$823$	−8539.10	−	14790.2i	−0.361670	−	0.626431i	−0.988236	+	0.152938i	$0.951127\pi$
$824$	4845.97	−	8393.47i	0.204876	−	0.354855i
$825$		0			0
$826$		0			0
$827$		−	19778.2i		−	0.831626i	−0.909450	−	0.415813i	$-0.863497\pi$
$827$		−	19778.2i		−	0.831626i	0.909450	−	0.415813i	$-0.136503\pi$
$828$		0			0
$829$	−10941.2	+	6316.89i	−0.458387	+	0.264650i	−0.711366	−	0.702822i	$-0.751923\pi$
$829$	−10941.2	+	6316.89i	−0.458387	+	0.264650i	0.252979	+	0.967472i	$0.418590\pi$
$830$	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	$0.186433\pi$
$853$			27542.7i			1.10556i	−0.833327	+	0.552780i	$0.813567\pi$
$854$		0			0
$855$		0			0
$856$	−8201.67	+	14205.7i	−0.327485	+	0.567221i
$857$	−20097.4	−	34809.8i	−0.801068	−	1.38749i	−0.918914	−	0.394458i	$-0.870932\pi$
$857$	−20097.4	−	34809.8i	−0.801068	−	1.38749i	0.117846	−	0.993032i	$-0.462401\pi$
$858$		0			0
$859$	10338.3	+	5968.81i	0.410638	+	0.237082i	0.691064	−	0.722794i	$-0.257142\pi$
$859$	10338.3	+	5968.81i	0.410638	+	0.237082i	−0.280426	+	0.959876i	$0.590476\pi$
$860$	−1584.07			−0.0628095
$861$		0			0
$862$	−14314.5			−0.565608
$863$	28785.5	+	16619.3i	1.13542	+	0.655536i	0.945293	−	0.326223i	$-0.105776\pi$
$863$	28785.5	+	16619.3i	1.13542	+	0.655536i	0.190129	+	0.981759i	$0.439109\pi$
$864$		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	−0.995147	−	0.0983981i	$-0.968628\pi$
$877$	−10709.6	+	18549.6i	−0.412358	+	0.714226i	0.582789	+	0.812624i	$0.301961\pi$
$878$	−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	−0.608168	−	0.793808i	$-0.708095\pi$
$887$	10127.6	−	17541.6i	0.383374	−	0.664024i	0.991542	+	0.129785i	$0.0414286\pi$
$888$		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	0.999425	−	0.0338987i	$-0.0107924\pi$
$907$	12848.0	+	22253.5i	0.470355	+	0.814680i	−0.529070	+	0.848578i	$0.677459\pi$
$908$	9189.75	−	15917.1i	0.335873	−	0.581749i
$909$		0			0
$910$		0			0
$911$		−	33200.2i		−	1.20743i	−0.797199	−	0.603716i	$-0.793686\pi$
$911$		−	33200.2i		−	1.20743i	0.797199	−	0.603716i	$-0.206314\pi$
$912$		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	−0.884558	−	0.466429i	$-0.845540\pi$
$919$	−1068.12	+	1850.03i	−0.0383394	+	0.0664058i	0.846219	+	0.532835i	$0.178873\pi$
$920$	−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	−0.856583	−	0.516010i	$-0.827417\pi$
$929$	526.275	−	911.535i	0.0185861	−	0.0321921i	0.875169	+	0.483818i	$0.160750\pi$
$930$		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	$0.0803848\pi$
$937$			14333.0i			0.499721i	−0.968282	+	0.249861i	$0.919615\pi$
$938$		0			0
$939$		0			0
$940$	−5371.16	+	9303.12i	−0.186370	+	0.322803i
$941$	−6563.30	−	11368.0i	−0.227372	−	0.393821i	0.729656	−	0.683814i	$-0.239680\pi$
$941$	−6563.30	−	11368.0i	−0.227372	−	0.393821i	−0.957029	+	0.289994i	$0.906347\pi$
$942$		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	0.624730	−	0.780841i	$-0.285209\pi$
$947$	7602.28	+	4389.18i	0.260867	+	0.150611i	−0.363863	+	0.931452i	$0.618542\pi$
$948$		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	$-0.977635\pi$
$953$		−	4130.75i		−	0.140407i	0.997533	−	0.0702036i	$-0.0223649\pi$
$954$		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	−0.692877	−	0.721056i	$-0.743657\pi$
$971$	8411.94	−	14569.9i	0.278014	−	0.481535i	0.970891	+	0.239521i	$0.0769904\pi$
$972$		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	0.158017	−	0.987436i	$-0.449490\pi$
$977$	33352.8	−	19256.3i	1.09217	−	0.630565i	0.934154	+	0.356871i	$0.116157\pi$
$978$		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	0.997449	−	0.0713826i	$-0.0227411\pi$
$983$	13465.4	+	23322.7i	0.436905	+	0.756742i	−0.560544	+	0.828125i	$0.689408\pi$
$984$		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	0.943849	−	0.330376i	$-0.107176\pi$
$991$	5796.70	+	10040.2i	0.185810	+	0.321833i	−0.758039	+	0.652209i	$0.773842\pi$
$992$	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	−0.991089	−	0.133200i	$-0.957475\pi$
$997$	−43168.7	+	24923.4i	−1.37128	+	0.791708i	−0.380190	+	0.924908i	$0.624141\pi$
$998$	−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.215.16		48
3.2	odd	2	inner	441.4.p.d.215.9		48
7.2	even	3		441.4.c.b.440.15	yes	24
7.3	odd	6	inner	441.4.p.d.80.9		48
7.4	even	3	inner	441.4.p.d.80.10		48
7.5	odd	6		441.4.c.b.440.9	✓	24
7.6	odd	2	inner	441.4.p.d.215.15		48
21.2	odd	6		441.4.c.b.440.10	yes	24
21.5	even	6		441.4.c.b.440.16	yes	24
21.11	odd	6	inner	441.4.p.d.80.15		48
21.17	even	6	inner	441.4.p.d.80.16		48
21.20	even	2	inner	441.4.p.d.215.10		48

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

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

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

Fields

Representations

Groups

Database

Properties

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