LMFDB - Embedded newform 441.3.q.e.116.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,3,Mod(116,441)]

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, 4]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("441.116");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	441.q (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:	$12.0163796583$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	16.0.6040479020157644046336.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 7x^{12} - 32x^{8} - 567x^{4} + 6561 $ x^16 - 7x^12 - 32x^8 - 567*x^4 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{12}\cdot 7^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			116.4
Root			$0.0537601 + 1.73122i$ of defining polynomial
Character	$\chi$	$=$	441.116
Dual form			441.3.q.e.422.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41864 + 0.819051i) q^{2} +(-0.658312 + 1.14023i) q^{4} +(1.45785 - 0.841688i) q^{5} -8.70917i q^{8} +O(q^{10})$	\(q+(-1.41864 + 0.819051i) q^{2} +(-0.658312 + 1.14023i) q^{4} +(1.45785 - 0.841688i) q^{5} -8.70917i q^{8} +(-1.37877 + 2.38810i) q^{10} +(7.28708 + 4.20720i) q^{11} -20.1759 q^{13} +(4.50000 + 7.79423i) q^{16} +(10.6665 + 6.15831i) q^{17} +(-16.2280 - 28.1077i) q^{19} +2.21637i q^{20} -13.7836 q^{22} +(-21.2084 + 12.2447i) q^{23} +(-11.0831 + 19.1965i) q^{25} +(28.6222 - 16.5251i) q^{26} -46.0795i q^{29} +(3.94786 - 6.83790i) q^{31} +(17.4017 + 10.0469i) q^{32} -20.1759 q^{34} +(-1.94987 - 3.37728i) q^{37} +(46.0433 + 26.5831i) q^{38} +(-7.33040 - 12.6966i) q^{40} -54.3166i q^{41} -24.6332 q^{43} +(-9.59435 + 5.53930i) q^{44} +(20.0581 - 34.7416i) q^{46} +(67.3763 - 38.8997i) q^{47} -36.3106i q^{50} +(13.2820 - 23.0052i) q^{52} +(-30.6186 - 17.6777i) q^{53} +14.1646 q^{55} +(37.7414 + 65.3701i) q^{58} +(-55.7136 - 32.1662i) q^{59} +(-23.5584 - 40.8044i) q^{61} +12.9340i q^{62} -68.9156 q^{64} +(-29.4133 + 16.9818i) q^{65} +(16.5831 - 28.7228i) q^{67} +(-14.0438 + 8.10819i) q^{68} +46.0795i q^{71} +(41.7305 - 72.2794i) q^{73} +(5.53233 + 3.19409i) q^{74} +42.7324 q^{76} +(-19.6332 - 34.0058i) q^{79} +(13.1206 + 7.57519i) q^{80} +(44.4881 + 77.0556i) q^{82} -138.765i q^{83} +20.7335 q^{85} +(34.9456 - 20.1759i) q^{86} +(36.6412 - 63.4644i) q^{88} +(-20.7984 + 12.0079i) q^{89} -32.2434i q^{92} +(-63.7217 + 110.369i) q^{94} +(-47.3159 - 27.3178i) q^{95} +32.0791 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{4}+O(q^{10}) $ 16 * q + 16 * q^4	$ 16 q + 16 q^{4} + 72 q^{16} - 592 q^{22} + 88 q^{25} + 128 q^{37} - 288 q^{43} - 24 q^{46} + 312 q^{58} + 224 q^{64} - 208 q^{79} + 544 q^{85} - 24 q^{88}+O(q^{100}) $ 16 * q + 16 * q^4 + 72 * q^16 - 592 * q^22 + 88 * q^25 + 128 * q^37 - 288 * q^43 - 24 * q^46 + 312 * q^58 + 224 * q^64 - 208 * q^79 + 544 * q^85 - 24 * q^88

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	−1.41864	+	0.819051i	−0.709319	+	0.409525i	−0.810809	−	0.585311i	$-0.800972\pi$
$2$	−1.41864	+	0.819051i	−0.709319	+	0.409525i	0.101490	+	0.994837i	$0.467639\pi$
$3$		0			0
$3$		0			0
$4$	−0.658312	+	1.14023i	−0.164578	+	0.285058i
$5$	1.45785	−	0.841688i	0.291569	−	0.168338i	−0.347080	−	0.937835i	$-0.612827\pi$
$5$	1.45785	−	0.841688i	0.291569	−	0.168338i	0.638649	+	0.769498i	$0.279493\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		−	8.70917i		−	1.08865i
$9$		0			0
$10$	−1.37877	+	2.38810i	−0.137877	+	0.238810i
$11$	7.28708	+	4.20720i	0.662462	+	0.382472i	0.793214	−	0.608943i	$-0.208406\pi$
$11$	7.28708	+	4.20720i	0.662462	+	0.382472i	−0.130753	+	0.991415i	$0.541739\pi$
$12$		0			0
$13$	−20.1759			−1.55199			−0.775995	−	0.630739i	$-0.782752\pi$
$13$	−20.1759			−1.55199			−0.775995	+	0.630739i	$0.782752\pi$
$14$		0			0
$15$		0			0
$16$	4.50000	+	7.79423i	0.281250	+	0.487139i
$17$	10.6665	+	6.15831i	0.627442	+	0.362254i	0.779761	−	0.626078i	$-0.215341\pi$
$17$	10.6665	+	6.15831i	0.627442	+	0.362254i	−0.152319	+	0.988331i	$0.548674\pi$
$18$		0			0
$19$	−16.2280	−	28.1077i	−0.854106	−	1.47935i	−0.877472	−	0.479628i	$-0.840772\pi$
$19$	−16.2280	−	28.1077i	−0.854106	−	1.47935i	0.0233661	−	0.999727i	$-0.492562\pi$
$20$			2.21637i			0.110819i
$21$		0			0
$22$	−13.7836			−0.626528
$23$	−21.2084	+	12.2447i	−0.922106	+	0.532378i	−0.884306	−	0.466907i	$-0.845368\pi$
$23$	−21.2084	+	12.2447i	−0.922106	+	0.532378i	−0.0378000	+	0.999285i	$0.512035\pi$
$24$		0			0
$25$	−11.0831	+	19.1965i	−0.443325	+	0.767861i
$26$	28.6222	−	16.5251i	1.10086	−	0.635579i
$27$		0			0
$28$		0			0
$29$		−	46.0795i		−	1.58895i	−0.607298	−	0.794474i	$-0.707747\pi$
$29$		−	46.0795i		−	1.58895i	0.607298	−	0.794474i	$-0.292253\pi$
$30$		0			0
$31$	3.94786	−	6.83790i	0.127350	−	0.220577i	−0.795299	−	0.606218i	$-0.792686\pi$
$31$	3.94786	−	6.83790i	0.127350	−	0.220577i	0.922649	+	0.385640i	$0.126019\pi$
$32$	17.4017	+	10.0469i	0.543803	+	0.313965i
$33$		0			0
$34$	−20.1759			−0.593408
$35$		0			0
$36$		0			0
$37$	−1.94987	−	3.37728i	−0.0526993	−	0.0912779i	0.838472	−	0.544944i	$-0.183449\pi$
$37$	−1.94987	−	3.37728i	−0.0526993	−	0.0912779i	−0.891172	+	0.453666i	$0.850116\pi$
$38$	46.0433	+	26.5831i	1.21167	+	0.699556i
$39$		0			0
$40$	−7.33040	−	12.6966i	−0.183260	−	0.317416i
$41$		−	54.3166i		−	1.32480i	−0.749152	−	0.662398i	$-0.769539\pi$
$41$		−	54.3166i		−	1.32480i	0.749152	−	0.662398i	$-0.230461\pi$
$42$		0			0
$43$	−24.6332			−0.572866			−0.286433	−	0.958100i	$-0.592470\pi$
$43$	−24.6332			−0.572866			−0.286433	+	0.958100i	$0.592470\pi$
$44$	−9.59435	+	5.53930i	−0.218053	+	0.125893i
$45$		0			0
$46$	20.0581	−	34.7416i	0.436045	−	0.755252i
$47$	67.3763	−	38.8997i	1.43354	−	0.827654i	0.436150	−	0.899874i	$-0.356342\pi$
$47$	67.3763	−	38.8997i	1.43354	−	0.827654i	0.997389	+	0.0722195i	$0.0230082\pi$
$48$		0			0
$49$		0			0
$50$		−	36.3106i		−	0.726211i
$51$		0			0
$52$	13.2820	−	23.0052i	0.255424	−	0.442407i
$53$	−30.6186	−	17.6777i	−0.577710	−	0.333541i	0.182513	−	0.983203i	$-0.441577\pi$
$53$	−30.6186	−	17.6777i	−0.577710	−	0.333541i	−0.760223	+	0.649663i	$0.774910\pi$
$54$		0			0
$55$	14.1646			0.257538
$56$		0			0
$57$		0			0
$58$	37.7414	+	65.3701i	0.650714	+	1.12707i
$59$	−55.7136	−	32.1662i	−0.944298	−	0.545191i	−0.0529929	−	0.998595i	$-0.516876\pi$
$59$	−55.7136	−	32.1662i	−0.944298	−	0.545191i	−0.891305	+	0.453404i	$0.850209\pi$
$60$		0			0
$61$	−23.5584	−	40.8044i	−0.386203	−	0.668924i	0.605732	−	0.795669i	$-0.292880\pi$
$61$	−23.5584	−	40.8044i	−0.386203	−	0.668924i	−0.991935	+	0.126745i	$0.959547\pi$
$62$			12.9340i			0.208613i
$63$		0			0
$64$	−68.9156			−1.07681
$65$	−29.4133	+	16.9818i	−0.452513	+	0.261258i
$66$		0			0
$67$	16.5831	−	28.7228i	0.247509	−	0.428699i	−0.715325	−	0.698792i	$-0.753721\pi$
$67$	16.5831	−	28.7228i	0.247509	−	0.428699i	0.962834	+	0.270093i	$0.0870546\pi$
$68$	−14.0438	+	8.10819i	−0.206526	+	0.119238i
$69$		0			0
$70$		0			0
$71$			46.0795i			0.649007i	0.945884	+	0.324503i	$0.105197\pi$
$71$			46.0795i			0.649007i	−0.945884	+	0.324503i	$0.894803\pi$
$72$		0			0
$73$	41.7305	−	72.2794i	0.571651	−	0.990129i	−0.424746	−	0.905313i	$-0.639636\pi$
$73$	41.7305	−	72.2794i	0.571651	−	0.990129i	0.996397	−	0.0848158i	$-0.0270302\pi$
$74$	5.53233	+	3.19409i	0.0747612	+	0.0431634i
$75$		0			0
$76$	42.7324			0.562268
$77$		0			0
$78$		0			0
$79$	−19.6332	−	34.0058i	−0.248522	−	0.430453i	0.714594	−	0.699540i	$-0.246612\pi$
$79$	−19.6332	−	34.0058i	−0.248522	−	0.430453i	−0.963116	+	0.269087i	$0.913278\pi$
$80$	13.1206	+	7.57519i	0.164008	+	0.0946899i
$81$		0			0
$82$	44.4881	+	77.0556i	0.542537	+	0.939702i
$83$		−	138.765i		−	1.67187i	−0.548828	−	0.835935i	$-0.684926\pi$
$83$		−	138.765i		−	1.67187i	0.548828	−	0.835935i	$-0.315074\pi$
$84$		0			0
$85$	20.7335			0.243924
$86$	34.9456	−	20.1759i	0.406345	−	0.234603i
$87$		0			0
$88$	36.6412	−	63.4644i	0.416377	−	0.721186i
$89$	−20.7984	+	12.0079i	−0.233689	+	0.134921i	−0.612273	−	0.790647i	$-0.709745\pi$
$89$	−20.7984	+	12.0079i	−0.233689	+	0.134921i	0.378584	+	0.925567i	$0.376411\pi$
$90$		0			0
$91$		0			0
$92$		−	32.2434i		−	0.350471i
$93$		0			0
$94$	−63.7217	+	110.369i	−0.677891	+	1.17414i
$95$	−47.3159	−	27.3178i	−0.498062	−	0.287556i
$96$		0			0
$97$	32.0791			0.330713			0.165356	−	0.986234i	$-0.447123\pi$
$97$	32.0791			0.330713			0.165356	+	0.986234i	$0.447123\pi$
$98$		0			0
$99$		0			0
$100$	−14.5923	−	25.2746i	−0.145923	−	0.252746i
$101$	−50.4169	−	29.1082i	−0.499177	−	0.288200i	0.229197	−	0.973380i	$-0.426390\pi$
$101$	−50.4169	−	29.1082i	−0.499177	−	0.288200i	−0.728374	+	0.685180i	$0.759723\pi$
$102$		0			0
$103$	35.2732	+	61.0950i	0.342459	+	0.593156i	0.984889	−	0.173189i	$-0.0554070\pi$
$103$	35.2732	+	61.0950i	0.342459	+	0.593156i	−0.642430	+	0.766344i	$0.722074\pi$
$104$			175.715i			1.68957i
$105$		0			0
$106$	57.9156			0.546374
$107$	30.7608	−	17.7598i	0.287485	−	0.165979i	−0.349322	−	0.937003i	$-0.613588\pi$
$107$	30.7608	−	17.7598i	0.287485	−	0.165979i	0.636807	+	0.771023i	$0.280255\pi$
$108$		0			0
$109$	−80.3668	+	139.199i	−0.737310	+	1.27706i	0.216393	+	0.976306i	$0.430571\pi$
$109$	−80.3668	+	139.199i	−0.737310	+	1.27706i	−0.953703	+	0.300751i	$0.902763\pi$
$110$	−20.0944	+	11.6015i	−0.182676	+	0.105468i
$111$		0			0
$112$		0			0
$113$			195.397i			1.72917i	0.502484	+	0.864587i	$0.332420\pi$
$113$			195.397i			1.72917i	−0.502484	+	0.864587i	$0.667580\pi$
$114$		0			0
$115$	−20.6124	+	35.7018i	−0.179239	+	0.310450i
$116$	52.5412	+	30.3347i	0.452942	+	0.261506i
$117$		0			0
$118$	105.383			0.893077
$119$		0			0
$120$		0			0
$121$	−25.0990	−	43.4727i	−0.207430	−	0.359279i
$122$	66.8417	+	38.5911i	0.547883	+	0.316320i
$123$		0			0
$124$	5.19786	+	9.00295i	0.0419182	+	0.0726045i
$125$			79.3985i			0.635188i
$126$		0			0
$127$	150.232			1.18293			0.591466	−	0.806330i	$-0.298550\pi$
$127$	150.232			1.18293			0.591466	+	0.806330i	$0.298550\pi$
$128$	28.1594	−	16.2578i	0.219995	−	0.127014i
$129$		0			0
$130$	27.8179	−	48.1820i	0.213984	−	0.370631i
$131$	−197.682	+	114.132i	−1.50903	+	0.871237i	−0.509081	+	0.860718i	$0.670015\pi$
$131$	−197.682	+	114.132i	−1.50903	+	0.871237i	−0.999945	+	0.0105182i	$0.996652\pi$
$132$		0			0
$133$		0			0
$134$			54.3297i			0.405445i
$135$		0			0
$136$	53.6338	−	92.8964i	0.394366	−	0.683062i
$137$	−36.1510	−	20.8718i	−0.263876	−	0.152349i	0.362226	−	0.932090i	$-0.382017\pi$
$137$	−36.1510	−	20.8718i	−0.263876	−	0.152349i	−0.626101	+	0.779742i	$0.715350\pi$
$138$		0			0
$139$	−234.334			−1.68586			−0.842928	−	0.538026i	$-0.819170\pi$
$139$	−234.334			−1.68586			−0.842928	+	0.538026i	$0.819170\pi$
$140$		0			0
$141$		0			0
$142$	−37.7414	−	65.3701i	−0.265785	−	0.460353i
$143$	−147.023	−	84.8839i	−1.02813	−	0.593594i
$144$		0			0
$145$	−38.7845	−	67.1768i	−0.267480	−	0.463288i
$146$			136.718i			0.936422i
$147$		0			0
$148$	5.13451			0.0346926
$149$	200.163	−	115.564i	1.34338	−	0.775600i	0.356077	−	0.934457i	$-0.384114\pi$
$149$	200.163	−	115.564i	1.34338	−	0.775600i	0.987302	+	0.158857i	$0.0507808\pi$
$150$		0			0
$151$	−112.449	+	194.767i	−0.744693	+	1.28985i	0.205645	+	0.978627i	$0.434071\pi$
$151$	−112.449	+	194.767i	−0.744693	+	1.28985i	−0.950338	+	0.311219i	$0.899263\pi$
$152$	−244.795	+	141.332i	−1.61049	+	0.929819i
$153$		0			0
$154$		0			0
$155$		−	13.2915i		−	0.0857515i
$156$		0			0
$157$	−134.337	+	232.679i	−0.855652	+	1.48203i	0.0203877	+	0.999792i	$0.493510\pi$
$157$	−134.337	+	232.679i	−0.855652	+	1.48203i	−0.876039	+	0.482240i	$0.839823\pi$
$158$	55.7049	+	32.1612i	0.352563	+	0.203552i
$159$		0			0
$160$	33.8253			0.211408
$161$		0			0
$162$		0			0
$163$	−62.6834	−	108.571i	−0.384561	−	0.666078i	0.607148	−	0.794589i	$-0.292314\pi$
$163$	−62.6834	−	108.571i	−0.384561	−	0.666078i	−0.991708	+	0.128511i	$0.958980\pi$
$164$	61.9335	+	35.7573i	0.377643	+	0.218032i
$165$		0			0
$166$	113.656	+	196.858i	0.684673	+	1.18589i
$167$			101.198i			0.605976i	0.952994	+	0.302988i	$0.0979842\pi$
$167$			101.198i			0.605976i	−0.952994	+	0.302988i	$0.902016\pi$
$168$		0			0
$169$	238.066			1.40867
$170$	−29.4133	+	16.9818i	−0.173019	+	0.0998929i
$171$		0			0
$172$	16.2164	−	28.0876i	0.0942812	−	0.163300i
$173$	144.350	−	83.3404i	0.834392	−	0.481737i	−0.0209619	−	0.999780i	$-0.506673\pi$
$173$	144.350	−	83.3404i	0.834392	−	0.481737i	0.855354	+	0.518044i	$0.173340\pi$
$174$		0			0
$175$		0			0
$176$			75.7295i			0.430281i
$177$		0			0
$178$	19.6702	−	34.0698i	0.110507	−	0.191403i
$179$	−47.6228	−	27.4951i	−0.266049	−	0.153604i	0.361042	−	0.932550i	$-0.382421\pi$
$179$	−47.6228	−	27.4951i	−0.266049	−	0.153604i	−0.627091	+	0.778946i	$0.715755\pi$
$180$		0			0
$181$	34.4598			0.190386			0.0951928	−	0.995459i	$-0.469653\pi$
$181$	34.4598			0.190386			0.0951928	+	0.995459i	$0.469653\pi$
$182$		0			0
$183$		0			0
$184$	106.641	+	184.708i	0.579572	+	1.00385i
$185$	−5.68523	−	3.28237i	−0.0307310	−	0.0177425i
$186$		0			0
$187$	51.8185	+	89.7522i	0.277104	+	0.479958i
$188$			102.433i			0.544855i
$189$		0			0
$190$	89.4987			0.471046
$191$	−178.137	+	102.848i	−0.932657	+	0.538470i	−0.887651	−	0.460517i	$-0.847664\pi$
$191$	−178.137	+	102.848i	−0.932657	+	0.538470i	−0.0450059	+	0.998987i	$0.514331\pi$
$192$		0			0
$193$	36.3325	−	62.9297i	0.188251	−	0.326061i	−0.756416	−	0.654091i	$-0.773051\pi$
$193$	36.3325	−	62.9297i	0.188251	−	0.326061i	0.944667	+	0.328030i	$0.106385\pi$
$194$	−45.5087	+	26.2744i	−0.234581	+	0.135435i
$195$		0			0
$196$		0			0
$197$			105.357i			0.534808i	0.963585	+	0.267404i	$0.0861658\pi$
$197$			105.357i			0.534808i	−0.963585	+	0.267404i	$0.913834\pi$
$198$		0			0
$199$	−38.3480	+	66.4207i	−0.192703	+	0.333772i	−0.946145	−	0.323742i	$-0.895059\pi$
$199$	−38.3480	+	66.4207i	−0.192703	+	0.333772i	0.753442	+	0.657515i	$0.228392\pi$
$200$	167.186	+	96.5248i	0.835929	+	0.482624i
$201$		0			0
$202$	95.3643			0.472101
$203$		0			0
$204$		0			0
$205$	−45.7176	−	79.1853i	−0.223013	−	0.386270i
$206$	−100.080	−	57.7811i	−0.485824	−	0.280491i
$207$		0			0
$208$	−90.7914	−	157.255i	−0.436497	−	0.756036i
$209$		−	273.098i		−	1.30669i
$210$		0			0
$211$	−132.201			−0.626543			−0.313271	−	0.949664i	$-0.601425\pi$
$211$	−132.201			−0.626543			−0.313271	+	0.949664i	$0.601425\pi$
$212$	40.3132	−	23.2749i	0.190157	−	0.109787i
$213$		0			0
$214$	−29.0923	+	50.3894i	−0.135945	+	0.235464i
$215$	−35.9115	+	20.7335i	−0.167030	+	0.0964349i
$216$		0			0
$217$		0			0
$218$		−	263.298i		−	1.20779i
$219$		0			0
$220$	−9.32472	+	16.1509i	−0.0423851	+	0.0734131i
$221$	−215.206	−	124.249i	−0.973784	−	0.562214i
$222$		0			0
$223$	−18.2914			−0.0820244			−0.0410122	−	0.999159i	$-0.513058\pi$
$223$	−18.2914			−0.0820244			−0.0410122	+	0.999159i	$0.513058\pi$
$224$		0			0
$225$		0			0
$226$	−160.040	−	277.197i	−0.708140	−	1.22653i
$227$	44.9740	+	25.9657i	0.198123	+	0.114387i	0.595780	−	0.803148i	$-0.296843\pi$
$227$	44.9740	+	25.9657i	0.198123	+	0.114387i	−0.397657	+	0.917534i	$0.630176\pi$
$228$		0			0
$229$	22.2488	+	38.5360i	0.0971561	+	0.168279i	0.910506	−	0.413495i	$-0.135692\pi$
$229$	22.2488	+	38.5360i	0.0971561	+	0.168279i	−0.813350	+	0.581774i	$0.802359\pi$
$230$		−	67.5305i		−	0.293611i
$231$		0			0
$232$	−401.314			−1.72980
$233$	172.056	−	99.3364i	0.738436	−	0.426336i	−0.0830641	−	0.996544i	$-0.526471\pi$
$233$	172.056	−	99.3364i	0.738436	−	0.426336i	0.821501	+	0.570208i	$0.193137\pi$
$234$		0			0
$235$	65.4829	−	113.420i	0.278651	−	0.482637i
$236$	73.3539	−	42.3509i	0.310822	−	0.179453i
$237$		0			0
$238$		0			0
$239$			178.165i			0.745460i	0.927940	+	0.372730i	$0.121578\pi$
$239$			178.165i			0.745460i	−0.927940	+	0.372730i	$0.878422\pi$
$240$		0			0
$241$	162.032	−	280.648i	0.672332	−	1.16451i	−0.304909	−	0.952381i	$-0.598626\pi$
$241$	162.032	−	280.648i	0.672332	−	1.16451i	0.977241	−	0.212132i	$-0.0680406\pi$
$242$	71.2127	+	41.1147i	0.294267	+	0.169895i
$243$		0			0
$244$	62.0352			0.254243
$245$		0			0
$246$		0			0
$247$	327.414	+	567.098i	1.32556	+	2.29594i
$248$	−59.5524	−	34.3826i	−0.240131	−	0.138640i
$249$		0			0
$250$	−65.0314	−	112.638i	−0.260126	−	0.450551i
$251$		−	289.567i		−	1.15365i	−0.816866	−	0.576827i	$-0.804291\pi$
$251$		−	289.567i		−	1.15365i	0.816866	−	0.576827i	$-0.195709\pi$
$252$		0			0
$253$	−206.063			−0.814480
$254$	−213.125	+	123.048i	−0.839075	+	0.484440i
$255$		0			0
$256$	111.199	−	192.603i	0.434372	−	0.752354i
$257$	255.462	−	147.491i	0.994014	−	0.573894i	0.0875422	−	0.996161i	$-0.472099\pi$
$257$	255.462	−	147.491i	0.994014	−	0.573894i	0.906472	+	0.422267i	$0.138765\pi$
$258$		0			0
$259$		0			0
$260$		−	44.7173i		−	0.171990i
$261$		0			0
$262$	186.960	−	323.824i	0.713587	−	1.23597i
$263$	−125.147	−	72.2537i	−0.475844	−	0.274729i	0.242839	−	0.970067i	$-0.421921\pi$
$263$	−125.147	−	72.2537i	−0.475844	−	0.274729i	−0.718683	+	0.695338i	$0.755255\pi$
$264$		0			0
$265$	−59.5163			−0.224590
$266$		0			0
$267$		0			0
$268$	21.8338	+	37.8172i	0.0814692	+	0.141109i
$269$	275.725	+	159.190i	1.02500	+	0.591785i	0.915549	−	0.402207i	$-0.131757\pi$
$269$	275.725	+	159.190i	1.02500	+	0.591785i	0.109452	+	0.993992i	$0.465090\pi$
$270$		0			0
$271$	−105.700	−	183.078i	−0.390038	−	0.675566i	0.602416	−	0.798182i	$-0.294205\pi$
$271$	−105.700	−	183.078i	−0.390038	−	0.675566i	−0.992454	+	0.122616i	$0.960872\pi$
$272$			110.850i			0.407535i
$273$		0			0
$274$	68.3801			0.249562
$275$	−161.527	+	93.2578i	−0.587372	+	0.339119i
$276$		0			0
$277$	121.565	−	210.556i	0.438862	−	0.760131i	−0.558740	−	0.829343i	$-0.688715\pi$
$277$	121.565	−	210.556i	0.438862	−	0.760131i	0.997602	+	0.0692117i	$0.0220484\pi$
$278$	332.435	−	191.931i	1.19581	−	0.690401i
$279$		0			0
$280$		0			0
$281$		−	257.174i		−	0.915211i	−0.889155	−	0.457605i	$-0.848707\pi$
$281$		−	257.174i		−	0.915211i	0.889155	−	0.457605i	$-0.151293\pi$
$282$		0			0
$283$	−226.875	+	392.959i	−0.801678	+	1.38855i	0.116833	+	0.993152i	$0.462726\pi$
$283$	−226.875	+	392.959i	−0.801678	+	1.38855i	−0.918511	+	0.395396i	$0.870607\pi$
$284$	−52.5412	−	30.3347i	−0.185004	−	0.106812i
$285$		0			0
$286$	278.097			0.972366
$287$		0			0
$288$		0			0
$289$	−68.6504	−	118.906i	−0.237545	−	0.411439i
$290$	110.042	+	63.5330i	0.379456	+	0.219079i
$291$		0			0
$292$	54.9434	+	95.1648i	0.188162	+	0.325907i
$293$		−	126.449i		−	0.431565i	−0.976441	−	0.215783i	$-0.930770\pi$
$293$		−	126.449i		−	0.431565i	0.976441	−	0.215783i	$-0.0692303\pi$
$294$		0			0
$295$	−108.296			−0.367104
$296$	−29.4133	+	16.9818i	−0.0993693	+	0.0573709i
$297$		0			0
$298$	−189.306	+	327.888i	−0.635256	+	1.10030i
$299$	427.899	−	247.048i	1.43110	−	0.826246i
$300$		0			0
$301$		0			0
$302$		−	368.404i		−	1.21988i
$303$		0			0
$304$	146.052	−	252.970i	0.480435	−	0.832137i
$305$	−68.6891	−	39.6576i	−0.225210	−	0.130025i
$306$		0			0
$307$	−72.5691			−0.236381			−0.118191	−	0.992991i	$-0.537709\pi$
$307$	−72.5691			−0.236381			−0.118191	+	0.992991i	$0.537709\pi$
$308$		0			0
$309$		0			0
$310$	10.8864	+	18.8558i	0.0351174	+	0.0608251i
$311$	−238.041	−	137.433i	−0.765404	−	0.441906i	0.0658289	−	0.997831i	$-0.479031\pi$
$311$	−238.041	−	137.433i	−0.765404	−	0.441906i	−0.831232	+	0.555925i	$0.812364\pi$
$312$		0			0
$313$	−97.1796	−	168.320i	−0.310478	−	0.537764i	0.667988	−	0.744172i	$-0.267156\pi$
$313$	−97.1796	−	168.320i	−0.310478	−	0.537764i	−0.978466	+	0.206408i	$0.933822\pi$
$314$		−	440.116i		−	1.40164i
$315$		0			0
$316$	51.6992			0.163605
$317$	113.042	−	65.2647i	0.356599	−	0.205882i	−0.310989	−	0.950414i	$-0.600660\pi$
$317$	113.042	−	65.2647i	0.356599	−	0.205882i	0.667588	+	0.744531i	$0.267327\pi$
$318$		0			0
$319$	193.865	−	335.785i	0.607729	−	1.05262i
$320$	−100.468	+	58.0054i	−0.313964	+	0.181267i
$321$		0			0
$322$		0			0
$323$		−	399.749i		−	1.23761i
$324$		0			0
$325$	223.612	−	387.307i	0.688036	−	1.19171i
$326$	177.850	+	102.682i	0.545552	+	0.314975i
$327$		0			0
$328$	−473.053			−1.44223
$329$		0			0
$330$		0			0
$331$	−19.4987	−	33.7728i	−0.0589086	−	0.102033i	0.835067	−	0.550148i	$-0.185429\pi$
$331$	−19.4987	−	33.7728i	−0.0589086	−	0.102033i	−0.893976	+	0.448115i	$0.852095\pi$
$332$	158.224	+	91.3509i	0.476579	+	0.275153i
$333$		0			0
$334$	−82.8863	−	143.563i	−0.248162	−	0.429830i
$335$		−	55.8312i		−	0.166660i
$336$		0			0
$337$	−333.166			−0.988624			−0.494312	−	0.869285i	$-0.664580\pi$
$337$	−333.166			−0.988624			−0.494312	+	0.869285i	$0.664580\pi$
$338$	−337.729	+	194.988i	−0.999199	+	0.576888i
$339$		0			0
$340$	−13.6491	+	23.6410i	−0.0401445	+	0.0695323i
$341$	57.5368	−	33.2189i	0.168730	−	0.0974161i
$342$		0			0
$343$		0			0
$344$			214.535i			0.623649i
$345$		0			0
$346$	−136.520	+	236.460i	−0.394567	+	0.683409i
$347$	464.812	+	268.359i	1.33951	+	0.773369i	0.986735	−	0.162337i	$-0.0519032\pi$
$347$	464.812	+	268.359i	1.33951	+	0.773369i	0.352780	+	0.935706i	$0.385237\pi$
$348$		0			0
$349$	−171.187			−0.490508			−0.245254	−	0.969459i	$-0.578871\pi$
$349$	−171.187			−0.490508			−0.245254	+	0.969459i	$0.578871\pi$
$350$		0			0
$351$		0			0
$352$	84.5384	+	146.425i	0.240166	+	0.415980i
$353$	373.328	+	215.541i	1.05759	+	0.610598i	0.924764	−	0.380542i	$-0.124263\pi$
$353$	373.328	+	215.541i	1.05759	+	0.610598i	0.132822	+	0.991140i	$0.457596\pi$
$354$		0			0
$355$	38.7845	+	67.1768i	0.109252	+	0.189230i
$356$		−	31.6199i		−	0.0888199i
$357$		0			0
$358$	90.0794			0.251618
$359$	−132.127	+	76.2836i	−0.368042	+	0.212489i	−0.672603	−	0.740004i	$-0.734824\pi$
$359$	−132.127	+	76.2836i	−0.368042	+	0.212489i	0.304561	+	0.952493i	$0.401490\pi$
$360$		0			0
$361$	−346.197	+	599.630i	−0.958994	+	1.66103i
$362$	−48.8859	+	28.2243i	−0.135044	+	0.0779677i
$363$		0			0
$364$		0			0
$365$		−	140.496i		−	0.384921i
$366$		0			0
$367$	−177.952	+	308.222i	−0.484884	+	0.839843i	−0.999849	−	0.0173679i	$-0.994471\pi$
$367$	−177.952	+	308.222i	−0.484884	+	0.839843i	0.514966	+	0.857211i	$0.327805\pi$
$368$	−190.876	−	110.202i	−0.518685	−	0.299463i
$369$		0			0
$370$	10.7537			0.0290641
$371$		0			0
$372$		0			0
$373$	198.631	+	344.039i	0.532522	+	0.922355i	0.999279	+	0.0379696i	$0.0120890\pi$
$373$	198.631	+	344.039i	0.532522	+	0.922355i	−0.466757	+	0.884386i	$0.654578\pi$
$374$	−147.023	−	84.8839i	−0.393110	−	0.226962i
$375$		0			0
$376$	−338.784	−	586.792i	−0.901023	−	1.56062i
$377$			929.694i			2.46603i
$378$		0			0
$379$	7.46198			0.0196886			0.00984430	−	0.999952i	$-0.496866\pi$
$379$	7.46198			0.0196886			0.00984430	+	0.999952i	$0.496866\pi$
$380$	62.2973	−	35.9673i	0.163940	−	0.0946509i
$381$		0			0
$382$	168.475	−	291.807i	0.441034	−	0.763893i
$383$	−222.223	+	128.301i	−0.580218	+	0.334989i	−0.761220	−	0.648494i	$-0.775399\pi$
$383$	−222.223	+	128.301i	−0.580218	+	0.334989i	0.181002	+	0.983483i	$0.442066\pi$
$384$		0			0
$385$		0			0
$386$			119.033i			0.308375i
$387$		0			0
$388$	−21.1181	+	36.5776i	−0.0544281	+	0.0942722i
$389$	−213.451	−	123.236i	−0.548718	−	0.316803i	0.199887	−	0.979819i	$-0.435943\pi$
$389$	−213.451	−	123.236i	−0.548718	−	0.316803i	−0.748605	+	0.663016i	$0.769276\pi$
$390$		0			0
$391$	−301.627			−0.771424
$392$		0			0
$393$		0			0
$394$	−86.2928	−	149.464i	−0.219017	−	0.379349i
$395$	−57.2445	−	33.0501i	−0.144923	−	0.0836712i
$396$		0			0
$397$	−24.3122	−	42.1099i	−0.0612398	−	0.106070i	0.833780	−	0.552097i	$-0.186172\pi$
$397$	−24.3122	−	42.1099i	−0.0612398	−	0.106070i	−0.895020	+	0.446026i	$0.852839\pi$
$398$		−	125.636i		−	0.315668i
$399$		0			0
$400$	−199.496			−0.498741
$401$	−56.6002	+	32.6781i	−0.141148	+	0.0814916i	−0.568911	−	0.822399i	$-0.692635\pi$
$401$	−56.6002	+	32.6781i	−0.141148	+	0.0814916i	0.427763	+	0.903891i	$0.359302\pi$
$402$		0			0
$403$	−79.6516	+	137.961i	−0.197647	+	0.342334i
$404$	66.3801	−	38.3246i	0.164307	−	0.0948628i
$405$		0			0
$406$		0			0
$407$		−	32.8140i		−	0.0806241i
$408$		0			0
$409$	−221.310	+	383.320i	−0.541099	+	0.937212i	0.457742	+	0.889085i	$0.348658\pi$
$409$	−221.310	+	383.320i	−0.541099	+	0.937212i	−0.998841	+	0.0481265i	$0.984675\pi$
$410$	129.713	+	74.8901i	0.316374	+	0.182659i
$411$		0			0
$412$	−92.8832			−0.225445
$413$		0			0
$414$		0			0
$415$	−116.797	−	202.298i	−0.281439	−	0.487466i
$416$	−351.095	−	202.705i	−0.843978	−	0.487271i
$417$		0			0
$418$	223.681	+	387.427i	0.535122	+	0.926858i
$419$		−	244.902i		−	0.584492i	−0.956343	−	0.292246i	$-0.905597\pi$
$419$		−	244.902i		−	0.584492i	0.956343	−	0.292246i	$-0.0944026\pi$
$420$		0			0
$421$	556.259			1.32128			0.660640	−	0.750703i	$-0.270285\pi$
$421$	556.259			1.32128			0.660640	+	0.750703i	$0.270285\pi$
$422$	187.545	−	108.279i	0.444418	−	0.256585i
$423$		0			0
$424$	−153.958	+	266.663i	−0.363108	+	0.628922i
$425$	−236.437	+	136.507i	−0.556321	+	0.321192i
$426$		0			0
$427$		0			0
$428$			46.7659i			0.109266i
$429$		0			0
$430$	33.9636	−	58.8266i	0.0789850	−	0.136806i
$431$	683.586	+	394.668i	1.58605	+	0.915704i	0.993950	+	0.109836i	$0.0350327\pi$
$431$	683.586	+	394.668i	1.58605	+	0.915704i	0.592096	+	0.805867i	$0.298301\pi$
$432$		0			0
$433$	113.656			0.262484			0.131242	−	0.991350i	$-0.458103\pi$
$433$	113.656			0.262484			0.131242	+	0.991350i	$0.458103\pi$
$434$		0			0
$435$		0			0
$436$	−105.813	−	183.273i	−0.242690	−	0.420351i
$437$	688.342	+	397.414i	1.57515	+	0.909415i
$438$		0			0
$439$	284.328	+	492.470i	0.647672	+	1.12180i	0.983678	+	0.179940i	$0.0575904\pi$
$439$	284.328	+	492.470i	0.647672	+	1.12180i	−0.336006	+	0.941860i	$0.609076\pi$
$440$		−	123.362i		−	0.280368i
$441$		0			0
$442$	407.066			0.920964
$443$	46.6017	−	26.9055i	0.105196	−	0.0607348i	−0.446479	−	0.894794i	$-0.647322\pi$
$443$	46.6017	−	26.9055i	0.105196	−	0.0607348i	0.551675	+	0.834059i	$0.313989\pi$
$444$		0			0
$445$	−20.2139	+	35.0114i	−0.0454244	+	0.0786774i
$446$	25.9489	−	14.9816i	0.0581814	−	0.0335911i
$447$		0			0
$448$		0			0
$449$			148.022i			0.329671i	0.986321	+	0.164835i	$0.0527093\pi$
$449$			148.022i			0.329671i	−0.986321	+	0.164835i	$0.947291\pi$
$450$		0			0
$451$	228.521	−	395.809i	0.506698	−	0.877626i
$452$	−222.797	−	128.632i	−0.492914	−	0.284584i
$453$		0			0
$454$	−85.0690			−0.187377
$455$		0			0
$456$		0			0
$457$	−283.900	−	491.729i	−0.621225	−	1.07599i	−0.989258	−	0.146180i	$-0.953302\pi$
$457$	−283.900	−	491.729i	−0.621225	−	1.07599i	0.368033	−	0.929813i	$-0.380031\pi$
$458$	−63.1258	−	36.4457i	−0.137829	−	0.0795758i
$459$		0			0
$460$	−27.1388	−	47.0058i	−0.0589975	−	0.102187i
$461$			449.150i			0.974296i	0.873319	+	0.487148i	$0.161963\pi$
$461$			449.150i			0.974296i	−0.873319	+	0.487148i	$0.838037\pi$
$462$		0			0
$463$	295.636			0.638522			0.319261	−	0.947667i	$-0.396565\pi$
$463$	295.636			0.638522			0.319261	+	0.947667i	$0.396565\pi$
$464$	359.154	−	207.358i	0.774039	−	0.446892i
$465$		0			0
$466$	−162.723	+	281.845i	−0.349191	+	0.604817i
$467$	−531.018	+	306.583i	−1.13708	+	0.656495i	−0.945706	−	0.325022i	$-0.894628\pi$
$467$	−531.018	+	306.583i	−1.13708	+	0.656495i	−0.191376	+	0.981517i	$0.561295\pi$
$468$		0			0
$469$		0			0
$470$			214.535i			0.456458i
$471$		0			0
$472$	−280.141	+	485.219i	−0.593520	+	1.02801i
$473$	−179.504	−	103.637i	−0.379502	−	0.219106i
$474$		0			0
$475$	719.428			1.51459
$476$		0			0
$477$		0			0
$478$	−145.926	−	252.751i	−0.305285	−	0.528769i
$479$	−787.014	−	454.383i	−1.64304	−	0.948607i	−0.979746	−	0.200243i	$-0.935827\pi$
$479$	−787.014	−	454.383i	−1.64304	−	0.948607i	−0.663289	−	0.748364i	$-0.730840\pi$
$480$		0			0
$481$	39.3404	+	68.1396i	0.0817888	+	0.141662i
$482$			530.850i			1.10135i
$483$		0			0
$484$	66.0919			0.136554
$485$	46.7664	−	27.0006i	0.0964256	−	0.0556714i
$486$		0			0
$487$	389.615	−	674.833i	0.800031	−	1.38569i	−0.119565	−	0.992826i	$-0.538150\pi$
$487$	389.615	−	674.833i	0.800031	−	1.38569i	0.919595	−	0.392867i	$-0.128517\pi$
$488$	−355.372	+	205.174i	−0.728222	+	0.420439i
$489$		0			0
$490$		0			0
$491$			207.815i			0.423248i	0.977351	+	0.211624i	$0.0678753\pi$
$491$			207.815i			0.423248i	−0.977351	+	0.211624i	$0.932125\pi$
$492$		0			0
$493$	283.772	−	491.507i	0.575602	−	0.996972i
$494$	−928.964	−	536.338i	−1.88049	−	1.08570i
$495$		0			0
$496$	71.0616			0.143269
$497$		0			0
$498$		0			0
$499$	437.282	+	757.395i	0.876317	+	1.51783i	0.855353	+	0.518046i	$0.173340\pi$
$499$	437.282	+	757.395i	0.876317	+	1.51783i	0.0209646	+	0.999780i	$0.493326\pi$
$500$	−90.5326	−	52.2690i	−0.181065	−	0.104538i
$501$		0			0
$502$	237.170	+	410.791i	0.472451	+	0.818308i
$503$			198.301i			0.394236i	0.980380	+	0.197118i	$0.0631582\pi$
$503$			198.301i			0.394236i	−0.980380	+	0.197118i	$0.936842\pi$
$504$		0			0
$505$	−98.0000			−0.194059
$506$	292.329	−	168.776i	0.577726	−	0.333550i
$507$		0			0
$508$	−98.8997	+	171.299i	−0.194685	+	0.337204i
$509$	218.481	−	126.140i	0.429235	−	0.247819i	−0.269786	−	0.962920i	$-0.586953\pi$
$509$	218.481	−	126.140i	0.429235	−	0.247819i	0.699021	+	0.715101i	$0.253619\pi$
$510$		0			0
$511$		0			0
$512$			494.374i			0.965574i
$513$		0			0
$514$	−241.605	+	418.472i	−0.470048	+	0.814148i
$515$	102.846	+	59.3781i	0.199701	+	0.115297i
$516$		0			0
$517$	654.636			1.26622
$518$		0			0
$519$		0			0
$520$	147.897	+	256.166i	0.284418	+	0.492626i
$521$	−120.878	−	69.7890i	−0.232012	−	0.133952i	0.379488	−	0.925197i	$-0.376100\pi$
$521$	−120.878	−	69.7890i	−0.232012	−	0.133952i	−0.611500	+	0.791245i	$0.709433\pi$
$522$		0			0
$523$	4.64197	+	8.04013i	0.00887566	+	0.0153731i	0.870429	−	0.492294i	$-0.163841\pi$
$523$	4.64197	+	8.04013i	0.00887566	+	0.0153731i	−0.861553	+	0.507667i	$0.830508\pi$
$524$		−	300.538i		−	0.573546i
$525$		0			0
$526$	236.718			0.450034
$527$	84.2199	−	48.6244i	0.159810	−	0.0922664i
$528$		0			0
$529$	35.3655	−	61.2548i	0.0668535	−	0.115794i
$530$	84.4320	−	48.7469i	0.159306	−	0.0919752i
$531$		0			0
$532$		0			0
$533$			1095.89i			2.05607i
$534$		0			0
$535$	29.8964	−	51.7820i	0.0558811	−	0.0967889i
$536$	−250.152	−	144.425i	−0.466701	−	0.269450i
$537$		0			0
$538$	−521.539			−0.969403
$539$		0			0
$540$		0			0
$541$	−503.264	−	871.679i	−0.930248	−	1.61124i	−0.782896	−	0.622152i	$-0.786259\pi$
$541$	−503.264	−	871.679i	−0.930248	−	1.61124i	−0.147351	−	0.989084i	$-0.547075\pi$
$542$	299.901	+	173.148i	0.553323	+	0.319461i
$543$		0			0
$544$	123.744	+	214.330i	0.227470	+	0.393990i
$545$			270.575i			0.496468i
$546$		0			0
$547$	−600.195			−1.09725			−0.548625	−	0.836069i	$-0.684848\pi$
$547$	−600.195			−1.09725			−0.548625	+	0.836069i	$0.684848\pi$
$548$	47.5972	−	27.4803i	0.0868563	−	0.0501465i
$549$		0			0
$550$	152.766	−	264.598i	0.277756	−	0.481087i
$551$	−1295.19	+	747.779i	−2.35062	+	1.35713i
$552$		0			0
$553$		0			0
$554$			398.271i			0.718900i
$555$		0			0
$556$	154.265	−	267.195i	0.277455	−	0.480566i
$557$	402.444	+	232.351i	0.722520	+	0.417147i	0.815680	−	0.578504i	$-0.196363\pi$
$557$	402.444	+	232.351i	0.722520	+	0.417147i	−0.0931593	+	0.995651i	$0.529697\pi$
$558$		0			0
$559$	496.997			0.889083
$560$		0			0
$561$		0			0
$562$	210.639	+	364.837i	0.374802	+	0.649176i
$563$	−395.534	−	228.362i	−0.702547	−	0.405616i	0.105748	−	0.994393i	$-0.466276\pi$
$563$	−395.534	−	228.362i	−0.702547	−	0.405616i	−0.808295	+	0.588777i	$0.799610\pi$
$564$		0			0
$565$	164.463	+	284.858i	0.291085	+	0.504174i
$566$		−	743.288i		−	1.31323i
$567$		0			0
$568$	401.314			0.706539
$569$	853.822	−	492.954i	1.50057	−	0.866352i	0.500566	−	0.865698i	$-0.333125\pi$
$569$	853.822	−	492.954i	1.50057	−	0.866352i	1.00000		0.000654059i	$-0.000208193\pi$
$570$		0			0
$571$	163.934	−	283.942i	0.287100	−	0.497271i	−0.686016	−	0.727586i	$-0.740642\pi$
$571$	163.934	−	283.942i	0.287100	−	0.497271i	0.973116	+	0.230315i	$0.0739755\pi$
$572$	193.574	−	111.760i	0.338417	−	0.195385i
$573$		0			0
$574$		0			0
$575$		−	542.838i		−	0.944066i
$576$		0			0
$577$	297.054	−	514.513i	0.514825	−	0.891703i	−0.485027	−	0.874499i	$-0.661190\pi$
$577$	297.054	−	514.513i	0.514825	−	0.891703i	0.999852	−	0.0172038i	$-0.00547639\pi$
$578$	194.780	+	112.456i	0.336990	+	0.194561i
$579$		0			0
$580$	102.129			0.176085
$581$		0			0
$582$		0			0
$583$	−148.747	−	257.637i	−0.255140	−	0.441916i
$584$	−629.493	−	363.438i	−1.07790	−	0.622326i
$585$		0			0
$586$	103.568	+	179.385i	0.176737	+	0.306117i
$587$			422.665i			0.720043i	0.932944	+	0.360021i	$0.117231\pi$
$587$			422.665i			0.720043i	−0.932944	+	0.360021i	$0.882769\pi$
$588$		0			0
$589$	−256.264			−0.435083
$590$	153.632	−	88.6997i	0.260394	−	0.150338i
$591$		0			0
$592$	17.5489	−	30.3955i	0.0296434	−	0.0513438i
$593$	148.627	−	85.8099i	0.250636	−	0.144705i	−0.369419	−	0.929263i	$-0.620443\pi$
$593$	148.627	−	85.8099i	0.250636	−	0.144705i	0.620055	+	0.784558i	$0.287110\pi$
$594$		0			0
$595$		0			0
$596$			304.310i			0.510587i
$597$		0			0
$598$	−404.689	+	700.942i	−0.676737	+	1.17214i
$599$	−516.044	−	297.938i	−0.861510	−	0.497393i	0.00300792	−	0.999995i	$-0.499043\pi$
$599$	−516.044	−	297.938i	−0.861510	−	0.497393i	−0.864518	+	0.502603i	$0.832376\pi$
$600$		0			0
$601$	940.213			1.56441			0.782207	−	0.623018i	$-0.214094\pi$
$601$	940.213			1.56441			0.782207	+	0.623018i	$0.214094\pi$
$602$		0			0
$603$		0			0
$604$	−148.053	−	256.435i	−0.245120	−	0.424561i
$605$	−73.1809	−	42.2510i	−0.120960	−	0.0698364i
$606$		0			0
$607$	357.651	+	619.469i	0.589210	+	1.02054i	0.994336	+	0.106281i	$0.0338944\pi$
$607$	357.651	+	619.469i	0.589210	+	1.02054i	−0.405126	+	0.914261i	$0.632772\pi$
$608$		−	652.164i		−	1.07264i
$609$		0			0
$610$	129.926			0.212994
$611$	−1359.38	+	784.837i	−2.22484	+	1.28451i
$612$		0			0
$613$	17.9156	−	31.0308i	0.0292261	−	0.0506211i	−0.851042	−	0.525097i	$-0.824029\pi$
$613$	17.9156	−	31.0308i	0.0292261	−	0.0506211i	0.880269	+	0.474476i	$0.157362\pi$
$614$	102.949	−	59.4378i	0.167670	−	0.0968042i
$615$		0			0
$616$		0			0
$617$		−	865.704i		−	1.40309i	−0.712627	−	0.701543i	$-0.752495\pi$
$617$		−	865.704i		−	1.40309i	0.712627	−	0.701543i	$-0.247505\pi$
$618$		0			0
$619$	−333.825	+	578.202i	−0.539298	+	0.934091i	0.459644	+	0.888103i	$0.347977\pi$
$619$	−333.825	+	578.202i	−0.539298	+	0.934091i	−0.998942	+	0.0459879i	$0.985356\pi$
$620$	15.1553	+	8.74994i	0.0244441	+	0.0141128i
$621$		0			0
$622$	450.257			0.723887
$623$		0			0
$624$		0			0
$625$	−210.249	−	364.163i	−0.336399	−	0.582660i
$626$	275.725	+	159.190i	0.440456	+	0.254297i
$627$		0			0
$628$	−176.872	−	306.351i	−0.281643	−	0.487820i
$629$		−	48.0317i		−	0.0763621i
$630$		0			0
$631$	48.8388			0.0773990			0.0386995	−	0.999251i	$-0.487678\pi$
$631$	48.8388			0.0773990			0.0386995	+	0.999251i	$0.487678\pi$
$632$	−296.162	+	170.989i	−0.468611	+	0.270553i
$633$		0			0
$634$	−106.910	+	185.174i	−0.168628	+	0.292072i
$635$	219.015	−	126.449i	0.344906	−	0.199132i
$636$		0			0
$637$		0			0
$638$			635.143i			0.995521i
$639$		0			0
$640$	27.3681	−	47.4029i	0.0427626	−	0.0740670i
$641$	−10.0660	−	5.81163i	−0.0157036	−	0.00906651i	0.492128	−	0.870523i	$-0.336219\pi$
$641$	−10.0660	−	5.81163i	−0.0157036	−	0.00906651i	−0.507831	+	0.861457i	$0.669553\pi$
$642$		0			0
$643$	−483.348			−0.751708			−0.375854	−	0.926679i	$-0.622651\pi$
$643$	−483.348			−0.751708			−0.375854	+	0.926679i	$0.622651\pi$
$644$		0			0
$645$		0			0
$646$	327.414	+	567.098i	0.506833	+	0.877861i
$647$	444.955	+	256.895i	0.687720	+	0.397055i	0.802757	−	0.596306i	$-0.203365\pi$
$647$	444.955	+	256.895i	0.687720	+	0.397055i	−0.115037	+	0.993361i	$0.536699\pi$
$648$		0			0
$649$	−270.659	−	468.796i	−0.417041	−	0.722336i
$650$			732.597i			1.12707i
$651$		0			0
$652$	165.061			0.253161
$653$	239.013	−	137.994i	0.366022	−	0.211323i	−0.305697	−	0.952129i	$-0.598889\pi$
$653$	239.013	−	137.994i	0.366022	−	0.211323i	0.671719	+	0.740806i	$0.265556\pi$
$654$		0			0
$655$	−192.127	+	332.774i	−0.293324	+	0.508051i
$656$	423.356	−	244.425i	0.645360	−	0.372599i
$657$		0			0
$658$		0			0
$659$			150.164i			0.227867i	0.993488	+	0.113933i	$0.0363450\pi$
$659$			150.164i			0.227867i	−0.993488	+	0.113933i	$0.963655\pi$
$660$		0			0
$661$	433.464	−	750.782i	0.655770	−	1.13583i	−0.325930	−	0.945394i	$-0.605677\pi$
$661$	433.464	−	750.782i	0.655770	−	1.13583i	0.981700	−	0.190433i	$-0.0609893\pi$
$662$	55.3233	+	31.9409i	0.0835699	+	0.0482491i
$663$		0			0
$664$	−1208.53			−1.82008
$665$		0			0
$666$		0			0
$667$	564.230	+	977.275i	0.845922	+	1.46518i
$668$	−115.389	−	66.6199i	−0.172738	−	0.0997304i
$669$		0			0
$670$	45.7286	+	79.2043i	0.0682517	+	0.118215i
$671$		−	396.459i		−	0.590849i
$672$		0			0
$673$	479.731			0.712825			0.356412	−	0.934329i	$-0.384000\pi$
$673$	479.731			0.712825			0.356412	+	0.934329i	$0.384000\pi$
$674$	472.642	−	272.880i	0.701249	−	0.404866i
$675$		0			0
$676$	−156.722	+	271.450i	−0.231837	+	0.401553i
$677$	−210.488	+	121.525i	−0.310912	+	0.179505i	−0.647335	−	0.762206i	$-0.724116\pi$
$677$	−210.488	+	121.525i	−0.310912	+	0.179505i	0.336422	+	0.941711i	$0.390783\pi$
$678$		0			0
$679$		0			0
$680$		−	180.572i		−	0.265546i
$681$		0			0
$682$	−54.4159	+	94.2511i	−0.0797887	+	0.138198i
$683$	584.830	+	337.652i	0.856267	+	0.494366i	0.862760	−	0.505613i	$-0.168734\pi$
$683$	584.830	+	337.652i	0.856267	+	0.494366i	−0.00649330	+	0.999979i	$0.502067\pi$
$684$		0			0
$685$	−70.2700			−0.102584
$686$		0			0
$687$		0			0
$688$	−110.850	−	191.997i	−0.161119	−	0.279066i
$689$	617.758	+	356.662i	0.896600	+	0.517652i
$690$		0			0
$691$	−270.817	−	469.068i	−0.391920	−	0.678825i	0.600783	−	0.799412i	$-0.294856\pi$
$691$	−270.817	−	469.068i	−0.391920	−	0.678825i	−0.992703	+	0.120587i	$0.961522\pi$
$692$			219.456i			0.317133i
$693$		0			0
$694$	−879.199			−1.26686
$695$	−341.623	+	197.236i	−0.491544	+	0.283793i
$696$		0			0
$697$	334.499	−	579.369i	0.479912	−	0.831232i
$698$	242.852	−	140.211i	0.347926	−	0.200875i
$699$		0			0
$700$		0			0
$701$		−	873.152i		−	1.24558i	−0.782389	−	0.622790i	$-0.785999\pi$
$701$		−	873.152i		−	1.24558i	0.782389	−	0.622790i	$-0.214001\pi$
$702$		0			0
$703$	−63.2852	+	109.613i	−0.0900216	+	0.155922i
$704$	−502.194	−	289.942i	−0.713343	−	0.411849i
$705$		0			0
$706$	−706.156			−1.00022
$707$		0			0
$708$		0			0
$709$	−244.129	−	422.845i	−0.344329	−	0.596396i	0.640902	−	0.767622i	$-0.278560\pi$
$709$	−244.129	−	422.845i	−0.344329	−	0.596396i	−0.985232	+	0.171227i	$0.945227\pi$
$710$	−110.042	−	63.5330i	−0.154989	−	0.0894831i
$711$		0			0
$712$	104.579	+	181.136i	0.146881	+	0.254405i
$713$			193.362i			0.271195i
$714$		0			0
$715$	−285.783			−0.399696
$716$	62.7014	−	36.2007i	0.0875718	−	0.0505596i
$717$		0			0
$718$	124.960	−	216.438i	0.174039	−	0.301445i
$719$	0.630878	−	0.364238i	0.000877439	−	0.000506589i	−0.499561	−	0.866279i	$-0.666505\pi$
$719$	0.630878	−	0.364238i	0.000877439	−	0.000506589i	0.500439	+	0.865772i	$0.333172\pi$
$720$		0			0
$721$		0			0
$722$		−	1134.21i		−	1.57093i
$723$		0			0
$724$	−22.6853	+	39.2921i	−0.0313333	+	0.0542709i
$725$	884.567	+	510.705i	1.22009	+	0.704420i
$726$		0			0
$727$	−342.255			−0.470777			−0.235389	−	0.971901i	$-0.575636\pi$
$727$	−342.255			−0.470777			−0.235389	+	0.971901i	$0.575636\pi$
$728$		0			0
$729$		0			0
$730$	115.074	+	199.313i	0.157635	+	0.273032i
$731$	−262.751	−	151.699i	−0.359440	−	0.207523i
$732$		0			0
$733$	−700.433	−	1213.19i	−0.955571	−	1.65510i	−0.733057	−	0.680167i	$-0.761907\pi$
$733$	−700.433	−	1213.19i	−0.955571	−	1.65510i	−0.222514	−	0.974930i	$-0.571426\pi$
$734$		−	583.008i		−	0.794288i
$735$		0			0
$736$	−492.084			−0.668593
$737$	241.685	−	139.537i	0.327931	−	0.189331i
$738$		0			0
$739$	−396.378	+	686.546i	−0.536370	+	0.929020i	0.462725	+	0.886502i	$0.346872\pi$
$739$	−396.378	+	686.546i	−0.536370	+	0.929020i	−0.999096	+	0.0425188i	$0.986462\pi$
$740$	7.48532	−	4.32165i	0.0101153	−	0.00584007i
$741$		0			0
$742$		0			0
$743$		−	586.406i		−	0.789241i	−0.918844	−	0.394620i	$-0.870876\pi$
$743$		−	586.406i		−	0.789241i	0.918844	−	0.394620i	$-0.129124\pi$
$744$		0			0
$745$	194.538	−	336.950i	0.261125	−	0.452282i
$746$	−563.570	−	325.377i	−0.755456	−	0.436163i
$747$		0			0
$748$	−136.451			−0.182421
$749$		0			0
$750$		0			0
$751$	−238.728	−	413.490i	−0.317881	−	0.550586i	0.662165	−	0.749358i	$-0.269638\pi$
$751$	−238.728	−	413.490i	−0.317881	−	0.550586i	−0.980046	+	0.198773i	$0.936305\pi$
$752$	606.387	+	350.098i	0.806366	+	0.465556i
$753$		0			0
$754$	−761.467	−	1318.90i	−1.00990	−	1.74920i
$755$			378.586i			0.501439i
$756$		0			0
$757$	−95.8680			−0.126642			−0.0633210	−	0.997993i	$-0.520169\pi$
$757$	−95.8680			−0.126642			−0.0633210	+	0.997993i	$0.520169\pi$
$758$	−10.5858	+	6.11174i	−0.0139655	+	0.00806298i
$759$		0			0
$760$	−237.916	+	412.082i	−0.313047	+	0.542213i
$761$	926.017	−	534.636i	1.21684	−	0.702544i	0.252601	−	0.967571i	$-0.418714\pi$
$761$	926.017	−	534.636i	1.21684	−	0.702544i	0.964241	+	0.265026i	$0.0853806\pi$
$762$		0			0
$763$		0			0
$764$		−	270.824i		−	0.354481i
$765$		0			0
$766$	210.170	−	364.024i	0.274373	−	0.475228i
$767$	1124.07	+	648.982i	1.46554	+	0.846131i
$768$		0			0
$769$	−931.960			−1.21191			−0.605956	−	0.795499i	$-0.707209\pi$
$769$	−931.960			−1.21191			−0.605956	+	0.795499i	$0.707209\pi$
$770$		0			0
$771$		0			0
$772$	47.8363	+	82.8548i	0.0619641	+	0.107325i
$773$	870.742	+	502.723i	1.12644	+	0.650353i	0.943038	−	0.332684i	$-0.107954\pi$
$773$	870.742	+	502.723i	1.12644	+	0.650353i	0.183406	+	0.983037i	$0.441288\pi$
$774$		0			0
$775$	87.5093	+	151.571i	0.112915	+	0.195575i
$776$		−	279.383i		−	0.360029i
$777$		0			0
$778$	403.747			0.518955
$779$	−1526.72	+	881.451i	−1.95984	+	1.13152i
$780$		0			0
$781$	−193.865	+	335.785i	−0.248227	+	0.429942i
$782$	427.899	−	247.048i	0.547185	−	0.315918i
$783$		0			0
$784$		0			0
$785$			452.280i			0.576153i
$786$		0			0
$787$	21.9221	−	37.9702i	0.0278553	−	0.0482467i	−0.851762	−	0.523929i	$-0.824466\pi$
$787$	21.9221	−	37.9702i	0.0278553	−	0.0482467i	0.879617	+	0.475683i	$0.157799\pi$
$788$	−120.131	−	69.3579i	−0.152451	−	0.0880176i
$789$		0			0
$790$	108.279			0.137062
$791$		0			0
$792$		0			0
$793$	475.312	+	823.264i	0.599384	+	1.03816i
$794$	68.9803	+	39.8258i	0.0868770	+	0.0501585i
$795$		0			0
$796$	−50.4899	−	87.4511i	−0.0634295	−	0.109863i
$797$			564.517i			0.708303i	0.935188	+	0.354151i	$0.115230\pi$
$797$			564.517i			0.708303i	−0.935188	+	0.354151i	$0.884770\pi$
$798$		0			0
$799$	958.227			1.19928
$800$	−385.731	+	222.702i	−0.482163	+	0.278377i
$801$		0			0
$802$	53.5301	−	92.7168i	0.0667457	−	0.115607i
$803$	608.187	−	351.137i	0.757394	−	0.437281i
$804$		0			0
$805$		0			0
$806$		−	260.955i		−	0.323765i
$807$		0			0
$808$	−253.508	+	439.089i	−0.313748	+	0.543427i
$809$	−576.480	−	332.831i	−0.712584	−	0.411410i	0.0994332	−	0.995044i	$-0.468297\pi$
$809$	−576.480	−	332.831i	−0.712584	−	0.411410i	−0.812017	+	0.583634i	$0.801630\pi$
$810$		0			0
$811$	−635.829			−0.784006			−0.392003	−	0.919964i	$-0.628218\pi$
$811$	−635.829			−0.784006			−0.392003	+	0.919964i	$0.628218\pi$
$812$		0			0
$813$		0			0
$814$	26.8763	+	46.5512i	0.0330176	+	0.0571882i
$815$	−182.765	−	105.520i	−0.224252	−	0.129472i
$816$		0			0
$817$	399.749	+	692.385i	0.489288	+	0.847472i
$818$		−	725.055i		−	0.886375i
$819$		0			0
$820$	120.386			0.146812
$821$	81.8574	−	47.2604i	0.0997045	−	0.0575644i	−0.449319	−	0.893372i	$-0.648333\pi$
$821$	81.8574	−	47.2604i	0.0997045	−	0.0575644i	0.549023	+	0.835807i	$0.315000\pi$
$822$		0			0
$823$	−21.1003	+	36.5467i	−0.0256382	+	0.0444067i	−0.878560	−	0.477632i	$-0.841495\pi$
$823$	−21.1003	+	36.5467i	−0.0256382	+	0.0444067i	0.852922	+	0.522039i	$0.174828\pi$
$824$	532.087	−	307.201i	0.645737	−	0.372816i
$825$		0			0
$826$		0			0
$827$		−	1105.74i		−	1.33705i	−0.743690	−	0.668525i	$-0.766926\pi$
$827$		−	1105.74i		−	1.33705i	0.743690	−	0.668525i	$-0.233074\pi$
$828$		0			0
$829$	−246.426	+	426.822i	−0.297257	+	0.514864i	−0.975507	−	0.219967i	$-0.929405\pi$
$829$	−246.426	+	426.822i	−0.297257	+	0.514864i	0.678251	+	0.734831i	$0.262738\pi$
$830$	331.385	+	191.325i	0.399259	+	0.230512i
$831$		0			0
$832$	1390.43			1.67119
$833$		0			0
$834$		0			0
$835$	85.1771	+	147.531i	0.102008	+	0.176684i
$836$	311.394	+	179.784i	0.372481	+	0.215052i
$837$		0			0
$838$	200.587	+	347.427i	0.239364	+	0.414591i
$839$		−	940.692i		−	1.12121i	−0.828085	−	0.560603i	$-0.810569\pi$
$839$		−	940.692i		−	1.12121i	0.828085	−	0.560603i	$-0.189431\pi$
$840$		0			0
$841$	−1282.32			−1.52476
$842$	−789.130	+	455.604i	−0.937209	+	0.541098i
$843$		0			0
$844$	87.0292	−	150.739i	0.103115	−	0.178601i
$845$	347.063	−	200.377i	0.410726	−	0.237133i
$846$		0			0
$847$		0			0
$848$		−	318.198i		−	0.375234i
$849$		0			0
$850$	223.612	−	387.307i	0.263073	−	0.455655i
$851$	82.7076	+	47.7513i	0.0971887	+	0.0561119i
$852$		0			0
$853$	338.071			0.396332			0.198166	−	0.980168i	$-0.436501\pi$
$853$	338.071			0.396332			0.198166	+	0.980168i	$0.436501\pi$
$854$		0			0
$855$		0			0
$856$	−154.673	−	267.901i	−0.180693	−	0.312969i
$857$	758.222	+	437.760i	0.884740	+	0.510805i	0.872218	−	0.489117i	$-0.162681\pi$
$857$	758.222	+	437.760i	0.884740	+	0.510805i	0.0125217	+	0.999922i	$0.496014\pi$
$858$		0			0
$859$	−438.772	−	759.975i	−0.510794	−	0.884721i	−0.999922	−	0.0125088i	$-0.996018\pi$
$859$	−438.772	−	759.975i	−0.510794	−	0.884721i	0.489128	−	0.872212i	$-0.337315\pi$
$860$		−	54.5965i		−	0.0634843i
$861$		0			0
$862$	−1293.01			−1.50002
$863$	927.100	−	535.262i	1.07428	−	0.620233i	0.144929	−	0.989442i	$-0.453705\pi$
$863$	927.100	−	535.262i	1.07428	−	0.620233i	0.929347	+	0.369209i	$0.120371\pi$
$864$		0			0
$865$	140.293	−	242.995i	0.162189	−	0.280919i
$866$	−161.236	+	93.0898i	−0.186185	+	0.107494i
$867$		0			0
$868$		0			0
$869$		−	330.404i		−	0.380211i
$870$		0			0
$871$	−334.579	+	579.508i	−0.384132	+	0.665336i
$872$	1212.31	+	699.928i	1.39026	+	0.802669i
$873$		0			0
$874$	−1302.01			−1.48971
$875$		0			0
$876$		0			0
$877$	95.0184	+	164.577i	0.108345	+	0.187659i	0.915100	−	0.403227i	$-0.132112\pi$
$877$	95.0184	+	164.577i	0.108345	+	0.187659i	−0.806755	+	0.590886i	$0.798778\pi$
$878$	−806.716	−	465.758i	−0.918811	−	0.530476i
$879$		0			0
$880$	63.7406	+	110.402i	0.0724325	+	0.125457i
$881$		−	382.322i		−	0.433963i	−0.976176	−	0.216982i	$-0.930379\pi$
$881$		−	382.322i		−	0.433963i	0.976176	−	0.216982i	$-0.0696212\pi$
$882$		0			0
$883$	−1507.96			−1.70777			−0.853883	−	0.520464i	$-0.825759\pi$
$883$	−1507.96			−1.70777			−0.853883	+	0.520464i	$0.825759\pi$
$884$	283.346	−	163.590i	0.320527	−	0.185056i
$885$		0			0
$886$	−44.0739	+	76.3383i	−0.0497448	+	0.0861606i
$887$	−700.612	+	404.499i	−0.789867	+	0.456030i	−0.839916	−	0.542717i	$-0.817396\pi$
$887$	−700.612	+	404.499i	−0.789867	+	0.456030i	0.0500485	+	0.998747i	$0.484062\pi$
$888$		0			0
$889$		0			0
$890$		−	66.2247i		−	0.0744098i
$891$		0			0
$892$	12.0415	−	20.8565i	0.0134994	−	0.0233817i
$893$	−2186.77	−	1262.53i	−2.44879	−	1.41381i
$894$		0			0
$895$	−92.5690			−0.103429
$896$		0			0
$897$		0			0
$898$	−121.238	−	209.990i	−0.135009	−	0.233842i
$899$	−315.087	−	181.916i	−0.350486	−	0.202353i
$900$		0			0
$901$	−217.729	−	377.118i	−0.241653	−	0.418555i
$902$			748.680i			0.830022i
$903$		0			0
$904$	1701.74			1.88246
$905$	50.2371	−	29.0044i	0.0555106	−	0.0320490i
$906$		0			0
$907$	799.541	−	1384.85i	0.881523	−	1.52684i	0.0318753	−	0.999492i	$-0.489852\pi$
$907$	799.541	−	1384.85i	0.881523	−	1.52684i	0.849648	−	0.527351i	$-0.176815\pi$
$908$	−59.2139	+	34.1871i	−0.0652135	+	0.0376510i
$909$		0			0
$910$		0			0
$911$			737.021i			0.809025i	0.914533	+	0.404512i	$0.132559\pi$
$911$			737.021i			0.809025i	−0.914533	+	0.404512i	$0.867441\pi$
$912$		0			0
$913$	583.813	−	1011.19i	0.639444	−	1.10755i
$914$	805.501	+	465.056i	0.881293	+	0.508815i
$915$		0			0
$916$	−58.5865			−0.0639591
$917$		0			0
$918$		0			0
$919$	175.715	+	304.348i	0.191203	+	0.331172i	0.945649	−	0.325189i	$-0.105428\pi$
$919$	175.715	+	304.348i	0.191203	+	0.331172i	−0.754447	+	0.656362i	$0.772095\pi$
$920$	310.933	+	179.517i	0.337970	+	0.195127i
$921$		0			0
$922$	−367.877	−	637.181i	−0.398999	−	0.691086i
$923$		−	929.694i		−	1.00725i
$924$		0			0
$925$	86.4428			0.0934517
$926$	−419.400	+	242.141i	−0.452916	+	0.261491i
$927$		0			0
$928$	462.955	−	801.862i	0.498874	−	0.864076i
$929$	530.652	−	306.372i	0.571208	−	0.329787i	−0.186424	−	0.982469i	$-0.559690\pi$
$929$	530.652	−	306.372i	0.571208	−	0.329787i	0.757632	+	0.652682i	$0.226356\pi$
$930$		0			0
$931$		0			0
$932$			261.578i			0.280663i
$933$		0			0
$934$	502.214	−	869.860i	0.537703	−	0.931328i
$935$	151.087	+	87.2299i	0.161590	+	0.0932940i
$936$		0			0
$937$	889.070			0.948848			0.474424	−	0.880297i	$-0.342656\pi$
$937$	889.070			0.948848			0.474424	+	0.880297i	$0.342656\pi$
$938$		0			0
$939$		0			0
$940$	86.2164	+	149.331i	0.0917195	+	0.158863i
$941$	−1061.21	−	612.689i	−1.12775	−	0.651104i	−0.184378	−	0.982855i	$-0.559027\pi$
$941$	−1061.21	−	612.689i	−1.12775	−	0.651104i	−0.943367	+	0.331751i	$0.892360\pi$
$942$		0			0
$943$	665.091	+	1151.97i	0.705293	+	1.22160i
$944$		−	578.992i		−	0.613339i
$945$		0			0
$946$	339.536			0.358917
$947$	54.8812	−	31.6857i	0.0579527	−	0.0334590i	−0.470744	−	0.882270i	$-0.656014\pi$
$947$	54.8812	−	31.6857i	0.0579527	−	0.0334590i	0.528696	+	0.848811i	$0.322681\pi$
$948$		0			0
$949$	−841.950	+	1458.30i	−0.887197	+	1.53667i
$950$	−1020.61	+	589.248i	−1.07432	+	0.620261i
$951$		0			0
$952$		0			0
$953$			1238.42i			1.29950i	0.760149	+	0.649749i	$0.225126\pi$
$953$			1238.42i			1.29950i	−0.760149	+	0.649749i	$0.774874\pi$
$954$		0			0
$955$	−173.131	+	299.872i	−0.181289	+	0.314002i
$956$	−203.149	−	117.288i	−0.212499	−	0.122686i
$957$		0			0
$958$	1488.65			1.55391
$959$		0			0
$960$		0			0
$961$	449.329	+	778.260i	0.467564	+	0.809844i
$962$	−111.620	−	64.4436i	−0.116029	−	0.0669892i
$963$		0			0
$964$	213.335	+	369.508i	0.221302	+	0.383307i
$965$		−	122.322i		−	0.126759i
$966$		0			0
$967$	−718.423			−0.742940			−0.371470	−	0.928445i	$-0.621146\pi$
$967$	−718.423			−0.742940			−0.371470	+	0.928445i	$0.621146\pi$
$968$	−378.611	+	218.591i	−0.391127	+	0.225818i
$969$		0			0
$970$	−44.2297	+	76.6081i	−0.0455977	+	0.0789775i
$971$	638.629	−	368.713i	0.657702	−	0.379725i	−0.133699	−	0.991022i	$-0.542685\pi$
$971$	638.629	−	368.713i	0.657702	−	0.379725i	0.791401	+	0.611297i	$0.209352\pi$
$972$		0			0
$973$		0			0
$974$			1276.46i			1.31053i
$975$		0			0
$976$	212.026	−	367.239i	0.217239	−	0.376270i
$977$	−288.152	−	166.364i	−0.294935	−	0.170281i	0.345230	−	0.938518i	$-0.387801\pi$
$977$	−288.152	−	166.364i	−0.294935	−	0.170281i	−0.640165	+	0.768237i	$0.721134\pi$
$978$		0			0
$979$	−202.079			−0.206414
$980$		0			0
$981$		0			0
$982$	−170.211	−	294.814i	−0.173331	−	0.300218i
$983$	−1379.89	−	796.681i	−1.40376	−	0.810459i	−0.408980	−	0.912543i	$-0.634115\pi$
$983$	−1379.89	−	796.681i	−1.40376	−	0.810459i	−0.994776	+	0.102085i	$0.967449\pi$
$984$		0			0
$985$	88.6778	+	153.594i	0.0900282	+	0.155933i
$986$			929.694i			0.942895i
$987$		0			0
$988$	−862.164			−0.872635
$989$	522.433	−	301.627i	0.528244	−	0.304982i
$990$		0			0
$991$	717.842	−	1243.34i	0.724361	−	1.25463i	−0.234875	−	0.972026i	$-0.575468\pi$
$991$	717.842	−	1243.34i	0.724361	−	1.25463i	0.959236	−	0.282605i	$-0.0911986\pi$
$992$	137.399	−	79.3275i	0.138507	−	0.0799672i
$993$		0			0
$994$		0			0
$995$			129.108i			0.129757i
$996$		0			0
$997$	−143.345	+	248.280i	−0.143776	+	0.249028i	−0.928916	−	0.370291i	$-0.879258\pi$
$997$	−143.345	+	248.280i	−0.143776	+	0.249028i	0.785140	+	0.619319i	$0.212591\pi$
$998$	−1240.69	−	716.313i	−1.24318	−	0.717748i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.3.q.e.116.4		16
3.2	odd	2	inner	441.3.q.e.116.5		16
7.2	even	3	inner	441.3.q.e.422.5		16
7.3	odd	6		441.3.b.e.197.3	✓	8
7.4	even	3		441.3.b.e.197.4	yes	8
7.5	odd	6	inner	441.3.q.e.422.6		16
7.6	odd	2	inner	441.3.q.e.116.3		16
21.2	odd	6	inner	441.3.q.e.422.4		16
21.5	even	6	inner	441.3.q.e.422.3		16
21.11	odd	6		441.3.b.e.197.5	yes	8
21.17	even	6		441.3.b.e.197.6	yes	8
21.20	even	2	inner	441.3.q.e.116.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.3.b.e.197.3	✓	8	7.3	odd	6
441.3.b.e.197.4	yes	8	7.4	even	3
441.3.b.e.197.5	yes	8	21.11	odd	6
441.3.b.e.197.6	yes	8	21.17	even	6
441.3.q.e.116.3		16	7.6	odd	2	inner
441.3.q.e.116.4		16	1.1	even	1	trivial
441.3.q.e.116.5		16	3.2	odd	2	inner
441.3.q.e.116.6		16	21.20	even	2	inner
441.3.q.e.422.3		16	21.5	even	6	inner
441.3.q.e.422.4		16	21.2	odd	6	inner
441.3.q.e.422.5		16	7.2	even	3	inner
441.3.q.e.422.6		16	7.5	odd	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.41864 + 0.819051i) q^{2} +(-0.658312 + 1.14023i) q^{4} +(1.45785 - 0.841688i) q^{5} -8.70917i q^{8} +O(q^{10})\)	\(q+(-1.41864 + 0.819051i) q^{2} +(-0.658312 + 1.14023i) q^{4} +(1.45785 - 0.841688i) q^{5} -8.70917i q^{8} +(-1.37877 + 2.38810i) q^{10} +(7.28708 + 4.20720i) q^{11} -20.1759 q^{13} +(4.50000 + 7.79423i) q^{16} +(10.6665 + 6.15831i) q^{17} +(-16.2280 - 28.1077i) q^{19} +2.21637i q^{20} -13.7836 q^{22} +(-21.2084 + 12.2447i) q^{23} +(-11.0831 + 19.1965i) q^{25} +(28.6222 - 16.5251i) q^{26} -46.0795i q^{29} +(3.94786 - 6.83790i) q^{31} +(17.4017 + 10.0469i) q^{32} -20.1759 q^{34} +(-1.94987 - 3.37728i) q^{37} +(46.0433 + 26.5831i) q^{38} +(-7.33040 - 12.6966i) q^{40} -54.3166i q^{41} -24.6332 q^{43} +(-9.59435 + 5.53930i) q^{44} +(20.0581 - 34.7416i) q^{46} +(67.3763 - 38.8997i) q^{47} -36.3106i q^{50} +(13.2820 - 23.0052i) q^{52} +(-30.6186 - 17.6777i) q^{53} +14.1646 q^{55} +(37.7414 + 65.3701i) q^{58} +(-55.7136 - 32.1662i) q^{59} +(-23.5584 - 40.8044i) q^{61} +12.9340i q^{62} -68.9156 q^{64} +(-29.4133 + 16.9818i) q^{65} +(16.5831 - 28.7228i) q^{67} +(-14.0438 + 8.10819i) q^{68} +46.0795i q^{71} +(41.7305 - 72.2794i) q^{73} +(5.53233 + 3.19409i) q^{74} +42.7324 q^{76} +(-19.6332 - 34.0058i) q^{79} +(13.1206 + 7.57519i) q^{80} +(44.4881 + 77.0556i) q^{82} -138.765i q^{83} +20.7335 q^{85} +(34.9456 - 20.1759i) q^{86} +(36.6412 - 63.4644i) q^{88} +(-20.7984 + 12.0079i) q^{89} -32.2434i q^{92} +(-63.7217 + 110.369i) q^{94} +(-47.3159 - 27.3178i) q^{95} +32.0791 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{4}+O(q^{10}) \) 16 * q + 16 * q^4	\( 16 q + 16 q^{4} + 72 q^{16} - 592 q^{22} + 88 q^{25} + 128 q^{37} - 288 q^{43} - 24 q^{46} + 312 q^{58} + 224 q^{64} - 208 q^{79} + 544 q^{85} - 24 q^{88}+O(q^{100}) \) 16 * q + 16 * q^4 + 72 * q^16 - 592 * q^22 + 88 * q^25 + 128 * q^37 - 288 * q^43 - 24 * q^46 + 312 * q^58 + 224 * q^64 - 208 * q^79 + 544 * q^85 - 24 * q^88

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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