LMFDB - Embedded newform 441.4.p.c.215.3

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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 48 x^{14} + 1647 x^{12} - 27620 x^{10} + 336765 x^{8} - 1200006 x^{6} + 3242464 x^{4} + \cdots + 810000 $ x^16 - 48x^14 + 1647x^12 - 27620x^10 + 336765x^8 - 1200006x^6 + 3242464x^4 - 1762200*x^2 + 810000
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{8} $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			215.3
Root			$-1.57646 - 0.910170i$ of defining polynomial
Character	$\chi$	$=$	441.215
Dual form			441.4.p.c.80.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.57646 - 0.910170i) q^{2} +(-2.34318 - 4.05851i) q^{4} +(7.54372 - 13.0661i) q^{5} +23.0935i q^{8} +O(q^{10})$	\(q+(-1.57646 - 0.910170i) q^{2} +(-2.34318 - 4.05851i) q^{4} +(7.54372 - 13.0661i) q^{5} +23.0935i q^{8} +(-23.7848 + 13.7321i) q^{10} +(-8.56529 + 4.94517i) q^{11} -67.8891i q^{13} +(2.27356 - 3.93792i) q^{16} +(-35.0687 - 60.7407i) q^{17} +(53.2242 + 30.7290i) q^{19} -70.7052 q^{20} +18.0038 q^{22} +(-113.895 - 65.7575i) q^{23} +(-51.3154 - 88.8809i) q^{25} +(-61.7906 + 107.025i) q^{26} -158.738i q^{29} +(66.2349 - 38.2407i) q^{31} +(152.828 - 88.2353i) q^{32} +127.674i q^{34} +(-174.341 + 301.967i) q^{37} +(-55.9372 - 96.8861i) q^{38} +(301.742 + 174.211i) q^{40} -138.909 q^{41} +539.651 q^{43} +(40.1400 + 23.1749i) q^{44} +(119.701 + 207.328i) q^{46} +(-111.821 + 193.680i) q^{47} +186.823i q^{50} +(-275.529 + 159.076i) q^{52} +(-459.003 + 265.005i) q^{53} +149.220i q^{55} +(-144.479 + 250.245i) q^{58} +(-271.438 - 470.145i) q^{59} +(116.218 + 67.0983i) q^{61} -139.222 q^{62} -357.614 q^{64} +(-887.046 - 512.136i) q^{65} +(-160.290 - 277.630i) q^{67} +(-164.344 + 284.653i) q^{68} +416.958i q^{71} +(-472.510 + 272.804i) q^{73} +(549.683 - 317.360i) q^{74} -288.014i q^{76} +(161.369 - 279.499i) q^{79} +(-34.3022 - 59.4132i) q^{80} +(218.984 + 126.431i) q^{82} -885.170 q^{83} -1058.19 q^{85} +(-850.739 - 491.174i) q^{86} +(-114.201 - 197.802i) q^{88} +(-812.312 + 1406.97i) q^{89} +616.327i q^{92} +(352.564 - 203.553i) q^{94} +(803.017 - 463.622i) q^{95} +739.155i q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 32 q^{4}+O(q^{10}) $ 16 * q + 32 * q^4	$ 16 q + 32 q^{4} + 72 q^{10} - 188 q^{16} + 612 q^{19} + 528 q^{22} - 20 q^{25} - 1128 q^{31} - 1196 q^{37} + 3204 q^{40} + 328 q^{43} - 1392 q^{46} - 4452 q^{52} - 3372 q^{58} + 1632 q^{61} + 5432 q^{64} + 308 q^{67} - 4068 q^{73} - 2176 q^{79} + 10188 q^{82} - 4608 q^{85} + 708 q^{88} + 2916 q^{94}+O(q^{100}) $ 16 * q + 32 * q^4 + 72 * q^10 - 188 * q^16 + 612 * q^19 + 528 * q^22 - 20 * q^25 - 1128 * q^31 - 1196 * q^37 + 3204 * q^40 + 328 * q^43 - 1392 * q^46 - 4452 * q^52 - 3372 * q^58 + 1632 * q^61 + 5432 * q^64 + 308 * q^67 - 4068 * q^73 - 2176 * q^79 + 10188 * q^82 - 4608 * q^85 + 708 * q^88 + 2916 * q^94

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 $

$2$	−1.57646	−	0.910170i	−0.557363	−	0.321794i	0.194723	−	0.980858i	$-0.437619\pi$
$2$	−1.57646	−	0.910170i	−0.557363	−	0.321794i	−0.752086	+	0.659064i	$0.770952\pi$
$3$		0			0
$3$		0			0
$4$	−2.34318	−	4.05851i	−0.292898	−	0.507314i
$5$	7.54372	−	13.0661i	0.674731	−	1.16867i	−0.301817	−	0.953366i	$-0.597593\pi$
$5$	7.54372	−	13.0661i	0.674731	−	1.16867i	0.976547	−	0.215302i	$-0.0690736\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$			23.0935i			1.02060i
$9$		0			0
$10$	−23.7848	+	13.7321i	−0.752140	+	0.434248i
$11$	−8.56529	+	4.94517i	−0.234776	+	0.135548i	−0.612773	−	0.790259i	$-0.709946\pi$
$11$	−8.56529	+	4.94517i	−0.234776	+	0.135548i	0.377998	+	0.925807i	$0.376613\pi$
$12$		0			0
$13$		−	67.8891i		−	1.44839i	−0.689596	−	0.724194i	$-0.742212\pi$
$13$		−	67.8891i		−	1.44839i	0.689596	−	0.724194i	$-0.257788\pi$
$14$		0			0
$15$		0			0
$16$	2.27356	−	3.93792i	0.0355244	−	0.0615300i
$17$	−35.0687	−	60.7407i	−0.500318	−	0.866575i	−1.00000		0.000366661i	$-0.999883\pi$
$17$	−35.0687	−	60.7407i	−0.500318	−	0.866575i	0.499682	−	0.866209i	$-0.333450\pi$
$18$		0			0
$19$	53.2242	+	30.7290i	0.642656	+	0.371038i	0.785637	−	0.618688i	$-0.212335\pi$
$19$	53.2242	+	30.7290i	0.642656	+	0.371038i	−0.142981	+	0.989725i	$0.545669\pi$
$20$	−70.7052			−0.790508
$21$		0			0
$22$	18.0038			0.174474
$23$	−113.895	−	65.7575i	−1.03256	−	0.596147i	−0.114841	−	0.993384i	$-0.536636\pi$
$23$	−113.895	−	65.7575i	−1.03256	−	0.596147i	−0.917716	+	0.397236i	$0.869969\pi$
$24$		0			0
$25$	−51.3154	−	88.8809i	−0.410523	−	0.711047i
$26$	−61.7906	+	107.025i	−0.466082	+	0.807278i
$27$		0			0
$28$		0			0
$29$		−	158.738i		−	1.01645i	−0.861225	−	0.508223i	$-0.830302\pi$
$29$		−	158.738i		−	1.01645i	0.861225	−	0.508223i	$-0.169698\pi$
$30$		0			0
$31$	66.2349	−	38.2407i	0.383746	−	0.221556i	−0.295701	−	0.955281i	$-0.595553\pi$
$31$	66.2349	−	38.2407i	0.383746	−	0.221556i	0.679447	+	0.733725i	$0.262220\pi$
$32$	152.828	−	88.2353i	0.844264	−	0.487436i
$33$		0			0
$34$			127.674i			0.643996i
$35$		0			0
$36$		0			0
$37$	−174.341	+	301.967i	−0.774634	+	1.34171i	0.160366	+	0.987058i	$0.448733\pi$
$37$	−174.341	+	301.967i	−0.774634	+	1.34171i	−0.935000	+	0.354648i	$0.884601\pi$
$38$	−55.9372	−	96.8861i	−0.238795	−	0.413605i
$39$		0			0
$40$	301.742	+	174.211i	1.19274	+	0.688629i
$41$	−138.909			−0.529120			−0.264560	−	0.964369i	$-0.585227\pi$
$41$	−138.909			−0.529120			−0.264560	+	0.964369i	$0.585227\pi$
$42$		0			0
$43$	539.651			1.91386			0.956931	−	0.290316i	$-0.0937604\pi$
$43$	539.651			1.91386			0.956931	+	0.290316i	$0.0937604\pi$
$44$	40.1400	+	23.1749i	0.137530	+	0.0794032i
$45$		0			0
$46$	119.701	+	207.328i	0.383673	+	0.664541i
$47$	−111.821	+	193.680i	−0.347039	+	0.601089i	−0.985722	−	0.168381i	$-0.946146\pi$
$47$	−111.821	+	193.680i	−0.347039	+	0.601089i	0.638683	+	0.769470i	$0.279480\pi$
$48$		0			0
$49$		0			0
$50$			186.823i			0.528415i
$51$		0			0
$52$	−275.529	+	159.076i	−0.734787	+	0.424230i
$53$	−459.003	+	265.005i	−1.18960	+	0.686817i	−0.958216	−	0.286045i	$-0.907659\pi$
$53$	−459.003	+	265.005i	−1.18960	+	0.686817i	−0.231386	+	0.972862i	$0.574326\pi$
$54$		0			0
$55$			149.220i			0.365833i
$56$		0			0
$57$		0			0
$58$	−144.479	+	250.245i	−0.327086	+	0.566530i
$59$	−271.438	−	470.145i	−0.598953	−	1.03742i	−0.992976	−	0.118317i	$-0.962250\pi$
$59$	−271.438	−	470.145i	−0.598953	−	1.03742i	0.394023	−	0.919101i	$-0.371083\pi$
$60$		0			0
$61$	116.218	+	67.0983i	0.243937	+	0.140837i	0.616985	−	0.786975i	$-0.288354\pi$
$61$	116.218	+	67.0983i	0.243937	+	0.140837i	−0.373048	+	0.927812i	$0.621687\pi$
$62$	−139.222			−0.285181
$63$		0			0
$64$	−357.614			−0.698464
$65$	−887.046	−	512.136i	−1.69269	−	0.977272i
$66$		0			0
$67$	−160.290	−	277.630i	−0.292276	−	0.506238i	0.682071	−	0.731286i	$-0.261079\pi$
$67$	−160.290	−	277.630i	−0.292276	−	0.506238i	−0.974348	+	0.225048i	$0.927746\pi$
$68$	−164.344	+	284.653i	−0.293084	+	0.507636i
$69$		0			0
$70$		0			0
$71$			416.958i			0.696955i	0.937317	+	0.348478i	$0.113301\pi$
$71$			416.958i			0.696955i	−0.937317	+	0.348478i	$0.886699\pi$
$72$		0			0
$73$	−472.510	+	272.804i	−0.757577	+	0.437387i	−0.828425	−	0.560100i	$-0.810763\pi$
$73$	−472.510	+	272.804i	−0.757577	+	0.437387i	0.0708484	+	0.997487i	$0.477429\pi$
$74$	549.683	−	317.360i	0.863505	−	0.498545i
$75$		0			0
$76$		−	288.014i		−	0.434704i
$77$		0			0
$78$		0			0
$79$	161.369	−	279.499i	0.229815	−	0.398052i	−0.727938	−	0.685643i	$-0.759521\pi$
$79$	161.369	−	279.499i	0.229815	−	0.398052i	0.957753	+	0.287591i	$0.0928545\pi$
$80$	−34.3022	−	59.4132i	−0.0479388	−	0.0830324i
$81$		0			0
$82$	218.984	+	126.431i	0.294912	+	0.170267i
$83$	−885.170			−1.17060			−0.585301	−	0.810816i	$-0.699024\pi$
$83$	−885.170			−1.17060			−0.585301	+	0.810816i	$0.699024\pi$
$84$		0			0
$85$	−1058.19			−1.35032
$86$	−850.739	−	491.174i	−1.06672	−	0.615869i
$87$		0			0
$88$	−114.201	−	197.802i	−0.138340	−	0.239612i
$89$	−812.312	+	1406.97i	−0.967471	+	1.67571i	−0.264645	+	0.964346i	$0.585255\pi$
$89$	−812.312	+	1406.97i	−0.967471	+	1.67571i	−0.702826	+	0.711362i	$0.748079\pi$
$90$		0			0
$91$		0			0
$92$			616.327i			0.698441i
$93$		0			0
$94$	352.564	−	203.553i	0.386853	−	0.223350i
$95$	803.017	−	463.622i	0.867240	−	0.500701i
$96$		0			0
$97$			739.155i			0.773710i	0.922141	+	0.386855i	$0.126439\pi$
$97$			739.155i			0.773710i	−0.922141	+	0.386855i	$0.873561\pi$
$98$		0			0
$99$		0			0
$100$	−240.483	+	416.528i	−0.240483	+	0.416528i
$101$	−119.758	−	207.427i	−0.117984	−	0.204354i	0.800985	−	0.598685i	$-0.204310\pi$
$101$	−119.758	−	207.427i	−0.117984	−	0.204354i	−0.918969	+	0.394331i	$0.870976\pi$
$102$		0			0
$103$	44.2852	+	25.5681i	0.0423645	+	0.0244592i	0.521033	−	0.853537i	$-0.325547\pi$
$103$	44.2852	+	25.5681i	0.0423645	+	0.0244592i	−0.478668	+	0.877996i	$0.658880\pi$
$104$	1567.80			1.47822
$105$		0			0
$106$	964.800			0.884054
$107$	1031.43	+	595.495i	0.931886	+	0.538025i	0.887408	−	0.460986i	$-0.152504\pi$
$107$	1031.43	+	595.495i	0.931886	+	0.538025i	0.0444785	+	0.999010i	$0.485837\pi$
$108$		0			0
$109$	−194.585	−	337.031i	−0.170989	−	0.296162i	0.767777	−	0.640718i	$-0.221363\pi$
$109$	−194.585	−	337.031i	−0.170989	−	0.296162i	−0.938766	+	0.344555i	$0.888030\pi$
$110$	135.816	−	235.239i	0.117723	−	0.203902i
$111$		0			0
$112$		0			0
$113$		−	718.545i		−	0.598186i	−0.954224	−	0.299093i	$-0.903316\pi$
$113$		−	718.545i		−	0.598186i	0.954224	−	0.299093i	$-0.0966841\pi$
$114$		0			0
$115$	−1718.39	+	992.113i	−1.39340	+	0.804478i
$116$	−644.240	+	371.952i	−0.515657	+	0.297715i
$117$		0			0
$118$			988.220i			0.770958i
$119$		0			0
$120$		0			0
$121$	−616.591	+	1067.97i	−0.463254	+	0.802379i
$122$	−122.142	−	211.556i	−0.0906409	−	0.156995i
$123$		0			0
$124$	−310.401	−	179.210i	−0.224797	−	0.129786i
$125$	337.493			0.241490
$126$		0			0
$127$	−179.456			−0.125387			−0.0626934	−	0.998033i	$-0.519969\pi$
$127$	−179.456			−0.125387			−0.0626934	+	0.998033i	$0.519969\pi$
$128$	−658.861	−	380.393i	−0.454966	−	0.262675i
$129$		0			0
$130$	932.263	+	1614.73i	0.628960	+	1.08939i
$131$	1223.43	−	2119.05i	0.815968	−	1.41330i	−0.0926619	−	0.995698i	$-0.529538\pi$
$131$	1223.43	−	2119.05i	0.815968	−	1.41330i	0.908630	−	0.417601i	$-0.137129\pi$
$132$		0			0
$133$		0			0
$134$			583.564i			0.376211i
$135$		0			0
$136$	1402.71	−	809.858i	0.884425	−	0.510623i
$137$	−443.021	+	255.778i	−0.276276	+	0.159508i	−0.631736	−	0.775183i	$-0.717658\pi$
$137$	−443.021	+	255.778i	−0.276276	+	0.159508i	0.355460	+	0.934691i	$0.384324\pi$
$138$		0			0
$139$			599.427i			0.365775i	0.983134	+	0.182888i	$0.0585444\pi$
$139$			599.427i			0.365775i	−0.983134	+	0.182888i	$0.941456\pi$
$140$		0			0
$141$		0			0
$142$	379.503	−	657.318i	0.224276	−	0.388457i
$143$	335.723	+	581.490i	0.196326	+	0.340046i
$144$		0			0
$145$	−2074.09	−	1197.48i	−1.18789	−	0.685828i
$146$	993.191			0.562994
$147$		0			0
$148$	1634.05			0.907554
$149$	1899.63	+	1096.75i	1.04445	+	0.603016i	0.921092	−	0.389346i	$-0.127299\pi$
$149$	1899.63	+	1096.75i	1.04445	+	0.603016i	0.123362	+	0.992362i	$0.460632\pi$
$150$		0			0
$151$	358.683	+	621.257i	0.193306	+	0.334816i	0.946344	−	0.323161i	$-0.104746\pi$
$151$	358.683	+	621.257i	0.193306	+	0.334816i	−0.753038	+	0.657977i	$0.771412\pi$
$152$	−709.640	+	1229.13i	−0.378680	+	0.655893i
$153$		0			0
$154$		0			0
$155$		−	1153.91i		−	0.597963i
$156$		0			0
$157$	1561.39	−	901.471i	0.793712	−	0.458250i	−0.0475556	−	0.998869i	$-0.515143\pi$
$157$	1561.39	−	901.471i	0.793712	−	0.458250i	0.841268	+	0.540619i	$0.181810\pi$
$158$	−508.783	+	293.746i	−0.256181	+	0.147906i
$159$		0			0
$160$		−	2662.49i		−	1.31555i
$161$		0			0
$162$		0			0
$163$	1453.90	−	2518.24i	0.698642	−	1.21008i	−0.270296	−	0.962777i	$-0.587122\pi$
$163$	1453.90	−	2518.24i	0.698642	−	1.21008i	0.968938	−	0.247305i	$-0.0795451\pi$
$164$	325.489	+	563.763i	0.154978	+	0.268430i
$165$		0			0
$166$	1395.44	+	805.655i	0.652451	+	0.376693i
$167$	−3491.37			−1.61779			−0.808893	−	0.587956i	$-0.799933\pi$
$167$	−3491.37			−1.61779			−0.808893	+	0.587956i	$0.799933\pi$
$168$		0			0
$169$	−2411.93			−1.09783
$170$	1668.20	+	963.135i	0.752618	+	0.434524i
$171$		0			0
$172$	−1264.50	−	2190.18i	−0.560566	−	0.970928i
$173$	877.377	−	1519.66i	0.385583	−	0.667848i	−0.606267	−	0.795261i	$-0.707334\pi$
$173$	877.377	−	1519.66i	0.385583	−	0.667848i	0.991850	+	0.127412i	$0.0406672\pi$
$174$		0			0
$175$		0			0
$176$			44.9726i			0.0192610i
$177$		0			0
$178$	2561.16	−	1478.68i	1.07846	−	0.622652i
$179$	−685.639	+	395.854i	−0.286296	+	0.165293i	−0.636270	−	0.771466i	$-0.719524\pi$
$179$	−685.639	+	395.854i	−0.286296	+	0.165293i	0.349974	+	0.936759i	$0.386190\pi$
$180$		0			0
$181$		−	2522.19i		−	1.03576i	−0.855452	−	0.517882i	$-0.826721\pi$
$181$		−	2522.19i		−	1.03576i	0.855452	−	0.517882i	$-0.173279\pi$
$182$		0			0
$183$		0			0
$184$	1518.57	−	2630.24i	0.608427	−	1.05383i
$185$	2630.36	+	4555.91i	1.04534	+	1.81058i
$186$		0			0
$187$	600.746	+	346.841i	0.234925	+	0.135634i
$188$	1048.07			0.406588
$189$		0			0
$190$	−1687.90			−0.644490
$191$	−782.266	−	451.642i	−0.296350	−	0.171098i	0.344452	−	0.938804i	$-0.388065\pi$
$191$	−782.266	−	451.642i	−0.296350	−	0.171098i	−0.640802	+	0.767706i	$0.721398\pi$
$192$		0			0
$193$	99.4374	+	172.231i	0.0370863	+	0.0642354i	0.883973	−	0.467538i	$-0.154859\pi$
$193$	99.4374	+	172.231i	0.0370863	+	0.0642354i	−0.846886	+	0.531774i	$0.821526\pi$
$194$	672.757	−	1165.25i	0.248975	−	0.431237i
$195$		0			0
$196$		0			0
$197$		−	3220.69i		−	1.16480i	−0.812904	−	0.582398i	$-0.802114\pi$
$197$		−	3220.69i		−	1.16480i	0.812904	−	0.582398i	$-0.197886\pi$
$198$		0			0
$199$	−2468.10	+	1424.96i	−0.879191	+	0.507601i	−0.870392	−	0.492360i	$-0.836134\pi$
$199$	−2468.10	+	1424.96i	−0.879191	+	0.507601i	−0.00879944	+	0.999961i	$0.502801\pi$
$200$	2052.57	−	1185.05i	0.725694	−	0.418979i
$201$		0			0
$202$			436.000i			0.151866i
$203$		0			0
$204$		0			0
$205$	−1047.89	+	1815.00i	−0.357014	+	0.618366i
$206$	−46.5426	−	80.6141i	−0.0157416	−	0.0272653i
$207$		0			0
$208$	−267.342	−	154.350i	−0.0891194	−	0.0514531i
$209$	−607.841			−0.201173
$210$		0			0
$211$	1204.50			0.392993			0.196496	−	0.980505i	$-0.437044\pi$
$211$	1204.50			0.392993			0.196496	+	0.980505i	$0.437044\pi$
$212$	2151.05	+	1241.91i	0.696863	+	0.402334i
$213$		0			0
$214$	−1084.00	−	1877.55i	−0.346266	−	0.599750i
$215$	4070.98	−	7051.14i	1.29134	−	2.23667i
$216$		0			0
$217$		0			0
$218$			708.421i			0.220093i
$219$		0			0
$220$	605.611	−	349.649i	0.185592	−	0.107152i
$221$	−4123.63	+	2380.78i	−1.25514	+	0.724654i
$222$		0			0
$223$		−	3377.73i		−	1.01430i	−0.861857	−	0.507151i	$-0.830699\pi$
$223$		−	3377.73i		−	1.01430i	0.861857	−	0.507151i	$-0.169301\pi$
$224$		0			0
$225$		0			0
$226$	−653.998	+	1132.76i	−0.192493	+	0.333407i
$227$	−2261.98	−	3917.86i	−0.661378	−	1.14554i	−0.980254	−	0.197744i	$-0.936638\pi$
$227$	−2261.98	−	3917.86i	−0.661378	−	1.14554i	0.318875	−	0.947797i	$-0.396695\pi$
$228$		0			0
$229$	−3389.61	−	1956.99i	−0.978131	−	0.564724i	−0.0764258	−	0.997075i	$-0.524351\pi$
$229$	−3389.61	−	1956.99i	−0.978131	−	0.564724i	−0.901705	+	0.432351i	$0.857684\pi$
$230$	3611.96			1.03550
$231$		0			0
$232$	3665.82			1.03738
$233$	3783.80	+	2184.58i	1.06388	+	0.614234i	0.926504	−	0.376284i	$-0.122798\pi$
$233$	3783.80	+	2184.58i	1.06388	+	0.614234i	0.137381	+	0.990518i	$0.456132\pi$
$234$		0			0
$235$	1687.10	+	2922.14i	0.468316	+	0.811147i
$236$	−1272.06	+	2203.27i	−0.350864	+	0.607714i
$237$		0			0
$238$		0			0
$239$		−	1945.23i		−	0.526471i	−0.964732	−	0.263235i	$-0.915210\pi$
$239$		−	1945.23i		−	0.526471i	0.964732	−	0.263235i	$-0.0847896\pi$
$240$		0			0
$241$	3499.81	−	2020.61i	0.935446	−	0.540080i	0.0469158	−	0.998899i	$-0.485061\pi$
$241$	3499.81	−	2020.61i	0.935446	−	0.540080i	0.888530	+	0.458819i	$0.151727\pi$
$242$	1944.06	−	1122.40i	0.516401	−	0.298144i
$243$		0			0
$244$		−	628.894i		−	0.165003i
$245$		0			0
$246$		0			0
$247$	2086.16	−	3613.34i	0.537407	−	0.930816i
$248$	883.112	+	1529.59i	0.226120	+	0.391651i
$249$		0			0
$250$	−532.045	−	307.176i	−0.134598	−	0.0777101i
$251$	4415.70			1.11042			0.555212	−	0.831709i	$-0.312637\pi$
$251$	4415.70			1.11042			0.555212	+	0.831709i	$0.312637\pi$
$252$		0			0
$253$	1300.73			0.323226
$254$	282.905	+	163.335i	0.0698860	+	0.0403487i
$255$		0			0
$256$	2122.90	+	3676.97i	0.518286	+	0.897698i
$257$	348.800	−	604.139i	0.0846597	−	0.146635i	−0.820586	−	0.571522i	$-0.806353\pi$
$257$	348.800	−	604.139i	0.0846597	−	0.146635i	0.905246	+	0.424888i	$0.139686\pi$
$258$		0			0
$259$		0			0
$260$			4800.11i			1.14496i
$261$		0			0
$262$	−3857.39	+	2227.06i	−0.909581	+	0.525147i
$263$	690.664	−	398.755i	0.161932	−	0.0934915i	−0.416844	−	0.908978i	$-0.636864\pi$
$263$	690.664	−	398.755i	0.161932	−	0.0934915i	0.578776	+	0.815487i	$0.303531\pi$
$264$		0			0
$265$			7996.51i			1.85367i
$266$		0			0
$267$		0			0
$268$	−751.176	+	1301.08i	−0.171214	+	0.296552i
$269$	−205.351	−	355.679i	−0.0465446	−	0.0806176i	0.841815	−	0.539767i	$-0.181488\pi$
$269$	−205.351	−	355.679i	−0.0465446	−	0.0806176i	−0.888359	+	0.459149i	$0.848154\pi$
$270$		0			0
$271$	−3283.42	−	1895.69i	−0.735992	−	0.424925i	0.0846182	−	0.996413i	$-0.473033\pi$
$271$	−3283.42	−	1895.69i	−0.735992	−	0.424925i	−0.820610	+	0.571488i	$0.806366\pi$
$272$	−318.923			−0.0710939
$273$		0			0
$274$	931.207			0.205315
$275$	879.063	+	507.527i	0.192762	+	0.111291i
$276$		0			0
$277$	−1623.31	−	2811.66i	−0.352113	−	0.609877i	0.634507	−	0.772917i	$-0.281203\pi$
$277$	−1623.31	−	2811.66i	−0.352113	−	0.609877i	−0.986619	+	0.163040i	$0.947870\pi$
$278$	545.581	−	944.973i	0.117704	−	0.203870i
$279$		0			0
$280$		0			0
$281$		−	1599.58i		−	0.339583i	−0.985480	−	0.169791i	$-0.945691\pi$
$281$		−	1599.58i		−	0.339583i	0.985480	−	0.169791i	$-0.0543094\pi$
$282$		0			0
$283$	3694.70	−	2133.13i	0.776067	−	0.448062i	−0.0589678	−	0.998260i	$-0.518781\pi$
$283$	3694.70	−	2133.13i	0.776067	−	0.448062i	0.835034	+	0.550198i	$0.185448\pi$
$284$	1692.23	−	977.008i	0.353575	−	0.204137i
$285$		0			0
$286$		−	1222.26i		−	0.252706i
$287$		0			0
$288$		0			0
$289$	−3.12079	+	5.40536i	−0.000635210	+	0.00110022i
$290$	2179.82	+	3775.55i	0.441390	+	0.764510i
$291$		0			0
$292$	2214.35	+	1278.46i	0.443785	+	0.256219i
$293$	−2926.77			−0.583562			−0.291781	−	0.956485i	$-0.594248\pi$
$293$	−2926.77			−0.583562			−0.291781	+	0.956485i	$0.594248\pi$
$294$		0			0
$295$	−8190.62			−1.61653
$296$	−6973.48	−	4026.14i	−1.36934	−	0.790590i
$297$		0			0
$298$	−1996.46	−	3457.97i	−0.388093	−	0.672198i
$299$	−4464.22	+	7732.25i	−0.863453	+	1.49554i
$300$		0			0
$301$		0			0
$302$		−	1305.85i		−	0.248819i
$303$		0			0
$304$	242.017	−	139.728i	0.0456599	−	0.0263618i
$305$	1753.43	−	1012.34i	0.329183	−	0.190054i
$306$		0			0
$307$			3571.36i			0.663935i	0.943291	+	0.331968i	$0.107712\pi$
$307$			3571.36i			0.663935i	−0.943291	+	0.331968i	$0.892288\pi$
$308$		0			0
$309$		0			0
$310$	−1050.25	+	1819.09i	−0.192421	+	0.333282i
$311$	−1286.71	−	2228.64i	−0.234606	−	0.406349i	0.724552	−	0.689220i	$-0.242047\pi$
$311$	−1286.71	−	2228.64i	−0.234606	−	0.406349i	−0.959158	+	0.282871i	$0.908713\pi$
$312$		0			0
$313$	1278.56	+	738.176i	0.230889	+	0.133304i	0.610982	−	0.791644i	$-0.290775\pi$
$313$	1278.56	+	738.176i	0.230889	+	0.133304i	−0.380093	+	0.924948i	$0.624108\pi$
$314$	−3281.97			−0.589848
$315$		0			0
$316$	−1512.46			−0.269249
$317$	−2188.36	−	1263.45i	−0.387730	−	0.223856i	0.293446	−	0.955976i	$-0.405198\pi$
$317$	−2188.36	−	1263.45i	−0.387730	−	0.223856i	−0.681176	+	0.732120i	$0.738531\pi$
$318$		0			0
$319$	784.988	+	1359.64i	0.137777	+	0.238637i
$320$	−2697.74	+	4672.62i	−0.471275	+	0.816273i
$321$		0			0
$322$		0			0
$323$		−	4310.50i		−	0.742546i
$324$		0			0
$325$	−6034.05	+	3483.76i	−1.02987	+	0.594597i
$326$	−4584.05	+	2646.60i	−0.778794	+	0.449637i
$327$		0			0
$328$		−	3207.89i		−	0.540019i
$329$		0			0
$330$		0			0
$331$	−737.778	+	1277.87i	−0.122513	+	0.212200i	−0.920758	−	0.390134i	$-0.872429\pi$
$331$	−737.778	+	1277.87i	−0.122513	+	0.212200i	0.798245	+	0.602333i	$0.205762\pi$
$332$	2074.11	+	3592.47i	0.342867	+	0.593863i
$333$		0			0
$334$	5504.01	+	3177.74i	0.901694	+	0.520593i
$335$	−4836.73			−0.788832
$336$		0			0
$337$	−6727.28			−1.08741			−0.543706	−	0.839275i	$-0.682979\pi$
$337$	−6727.28			−1.08741			−0.543706	+	0.839275i	$0.682979\pi$
$338$	3802.32	+	2195.27i	0.611890	+	0.353275i
$339$		0			0
$340$	2479.54	+	4294.68i	0.395505	+	0.685035i
$341$	−378.214	+	655.086i	−0.0600629	+	0.104032i
$342$		0			0
$343$		0			0
$344$			12462.4i			1.95328i
$345$		0			0
$346$	−2766.30	+	1597.13i	−0.429819	+	0.248156i
$347$	466.060	−	269.080i	0.0721021	−	0.0416281i	−0.463516	−	0.886089i	$-0.653412\pi$
$347$	466.060	−	269.080i	0.0721021	−	0.0416281i	0.535618	+	0.844461i	$0.320079\pi$
$348$		0			0
$349$			6975.93i			1.06995i	0.844867	+	0.534976i	$0.179679\pi$
$349$			6975.93i			1.06995i	−0.844867	+	0.534976i	$0.820321\pi$
$350$		0			0
$351$		0			0
$352$	−872.678	+	1511.52i	−0.132142	+	0.228876i
$353$	−4438.40	−	7687.53i	−0.669213	−	1.15911i	−0.978125	−	0.208020i	$-0.933298\pi$
$353$	−4438.40	−	7687.53i	−0.669213	−	1.15911i	0.308912	−	0.951091i	$-0.400035\pi$
$354$		0			0
$355$	5448.02	+	3145.42i	0.814509	+	0.470257i
$356$	7613.57			1.13348
$357$		0			0
$358$	1441.18			0.212761
$359$	−9565.96	−	5522.91i	−1.40633	−	0.811944i	−0.411297	−	0.911502i	$-0.634924\pi$
$359$	−9565.96	−	5522.91i	−1.40633	−	0.811944i	−0.995032	+	0.0995575i	$0.968257\pi$
$360$		0			0
$361$	−1540.96	−	2669.02i	−0.224662	−	0.389126i
$362$	−2295.62	+	3976.14i	−0.333302	+	0.577296i
$363$		0			0
$364$		0			0
$365$			8231.82i			1.18047i
$366$		0			0
$367$	−7210.59	+	4163.04i	−1.02559	+	0.592122i	−0.915717	−	0.401824i	$-0.868376\pi$
$367$	−7210.59	+	4163.04i	−1.02559	+	0.592122i	−0.109868	+	0.993946i	$0.535043\pi$
$368$	−517.896	+	299.007i	−0.0733619	+	0.0423555i
$369$		0			0
$370$		−	9576.29i		−	1.34553i
$371$		0			0
$372$		0			0
$373$	2272.66	−	3936.36i	0.315479	−	0.546426i	−0.664060	−	0.747679i	$-0.731168\pi$
$373$	2272.66	−	3936.36i	0.315479	−	0.546426i	0.979539	+	0.201253i	$0.0645014\pi$
$374$	−631.369	−	1093.56i	−0.0872922	−	0.151195i
$375$		0			0
$376$	−4472.76	−	2582.35i	−0.613470	−	0.354187i
$377$	−10776.6			−1.47221
$378$		0			0
$379$	11527.2			1.56230			0.781151	−	0.624343i	$-0.214633\pi$
$379$	11527.2			1.56230			0.781151	+	0.624343i	$0.214633\pi$
$380$	−3763.23	−	2172.70i	−0.508025	−	0.293308i
$381$		0			0
$382$	822.141	+	1423.99i	0.110116	+	0.190727i
$383$	1960.23	−	3395.22i	0.261522	−	0.452970i	−0.705124	−	0.709084i	$-0.749109\pi$
$383$	1960.23	−	3395.22i	0.261522	−	0.452970i	0.966647	+	0.256114i	$0.0824422\pi$
$384$		0			0
$385$		0			0
$386$		−	362.020i		−	0.0477366i
$387$		0			0
$388$	2999.87	−	1731.97i	0.392513	−	0.226618i
$389$	−689.734	+	398.218i	−0.0898995	+	0.0519035i	−0.544276	−	0.838906i	$-0.683195\pi$
$389$	−689.734	+	398.218i	−0.0898995	+	0.0519035i	0.454376	+	0.890810i	$0.349862\pi$
$390$		0			0
$391$			9224.11i			1.19305i
$392$		0			0
$393$		0			0
$394$	−2931.38	+	5077.30i	−0.374824	+	0.649214i
$395$	−2434.64	−	4216.92i	−0.310127	−	0.537155i
$396$		0			0
$397$	−3338.59	−	1927.54i	−0.422063	−	0.243678i	0.273896	−	0.961759i	$-0.411687\pi$
$397$	−3338.59	−	1927.54i	−0.422063	−	0.243678i	−0.695960	+	0.718081i	$0.745021\pi$
$398$	5187.82			0.653371
$399$		0			0
$400$	−466.675			−0.0583344
$401$	−4031.65	−	2327.68i	−0.502073	−	0.289872i	0.227496	−	0.973779i	$-0.426946\pi$
$401$	−4031.65	−	2327.68i	−0.502073	−	0.289872i	−0.729569	+	0.683907i	$0.760279\pi$
$402$		0			0
$403$	−2596.13	−	4496.63i	−0.320899	−	0.555814i
$404$	−561.229	+	972.077i	−0.0691143	+	0.119709i
$405$		0			0
$406$		0			0
$407$		−	3448.58i		−	0.420000i
$408$		0			0
$409$	8478.82	−	4895.25i	1.02506	−	0.591821i	0.109497	−	0.993987i	$-0.465076\pi$
$409$	8478.82	−	4895.25i	1.02506	−	0.591821i	0.915566	+	0.402167i	$0.131743\pi$
$410$	3303.91	−	1907.52i	0.397972	−	0.229769i
$411$		0			0
$412$		−	239.642i		−	0.0286561i
$413$		0			0
$414$		0			0
$415$	−6677.47	+	11565.7i	−0.789842	+	1.36805i
$416$	−5990.22	−	10375.4i	−0.705997	−	1.22282i
$417$		0			0
$418$	958.237	+	553.238i	0.112127	+	0.0647363i
$419$	3007.46			0.350654			0.175327	−	0.984510i	$-0.443902\pi$
$419$	3007.46			0.350654			0.175327	+	0.984510i	$0.443902\pi$
$420$		0			0
$421$	7646.06			0.885145			0.442573	−	0.896733i	$-0.354066\pi$
$421$	7646.06			0.885145			0.442573	+	0.896733i	$0.354066\pi$
$422$	−1898.85	−	1096.30i	−0.219040	−	0.126463i
$423$		0			0
$424$	−6119.90	−	10600.0i	−0.700964	−	1.21411i
$425$	−3599.13	+	6233.87i	−0.410784	+	0.711499i
$426$		0			0
$427$		0			0
$428$		−	5581.41i		−	0.630345i
$429$		0			0
$430$	−12835.5	+	7410.57i	−1.43949	+	0.831091i
$431$	12983.1	−	7495.81i	1.45099	−	0.837727i	0.452448	−	0.891791i	$-0.350551\pi$
$431$	12983.1	−	7495.81i	1.45099	−	0.837727i	0.998537	+	0.0540641i	$0.0172175\pi$
$432$		0			0
$433$		−	5666.63i		−	0.628916i	−0.949271	−	0.314458i	$-0.898177\pi$
$433$		−	5666.63i		−	0.628916i	0.949271	−	0.314458i	$-0.101823\pi$
$434$		0			0
$435$		0			0
$436$	−911.895	+	1579.45i	−0.100165	+	0.173491i
$437$	−4041.32	−	6999.78i	−0.442386	−	0.766235i
$438$		0			0
$439$	4790.07	+	2765.55i	0.520769	+	0.300666i	0.737249	−	0.675621i	$-0.236124\pi$
$439$	4790.07	+	2765.55i	0.520769	+	0.300666i	−0.216480	+	0.976287i	$0.569458\pi$
$440$	−3446.01			−0.373368
$441$		0			0
$442$	8667.66			0.932757
$443$	349.200	+	201.611i	0.0374515	+	0.0216226i	0.518609	−	0.855012i	$-0.326450\pi$
$443$	349.200	+	201.611i	0.0374515	+	0.0216226i	−0.481157	+	0.876634i	$0.659783\pi$
$444$		0			0
$445$	12255.7	+	21227.5i	1.30556	+	2.26130i
$446$	−3074.31	+	5324.85i	−0.326396	+	0.565334i
$447$		0			0
$448$		0			0
$449$		−	8429.03i		−	0.885948i	−0.896534	−	0.442974i	$-0.853923\pi$
$449$		−	8429.03i		−	0.885948i	0.896534	−	0.442974i	$-0.146077\pi$
$450$		0			0
$451$	1189.79	−	686.928i	0.124224	−	0.0717210i
$452$	−2916.22	+	1683.68i	−0.303468	+	0.175207i
$453$		0			0
$454$			8235.15i			0.851310i
$455$		0			0
$456$		0			0
$457$	−342.830	+	593.799i	−0.0350917	+	0.0607807i	−0.883038	−	0.469302i	$-0.844506\pi$
$457$	−342.830	+	593.799i	−0.0350917	+	0.0607807i	0.847946	+	0.530082i	$0.177839\pi$
$458$	3562.40	+	6170.25i	0.363449	+	0.629513i
$459$		0			0
$460$	8052.99	+	4649.40i	0.816245	+	0.471259i
$461$	−4864.48			−0.491456			−0.245728	−	0.969339i	$-0.579027\pi$
$461$	−4864.48			−0.491456			−0.245728	+	0.969339i	$0.579027\pi$
$462$		0			0
$463$	−8354.23			−0.838562			−0.419281	−	0.907857i	$-0.637718\pi$
$463$	−8354.23			−0.838562			−0.419281	+	0.907857i	$0.637718\pi$
$464$	−625.099	−	360.901i	−0.0625420	−	0.0361086i
$465$		0			0
$466$	−3976.68	−	6887.81i	−0.395313	−	0.684703i
$467$	−501.469	+	868.570i	−0.0496900	+	0.0860656i	−0.889801	−	0.456350i	$-0.849157\pi$
$467$	−501.469	+	868.570i	−0.0496900	+	0.0860656i	0.840111	+	0.542415i	$0.182490\pi$
$468$		0			0
$469$		0			0
$470$		−	6142.19i		−	0.602804i
$471$		0			0
$472$	10857.3	−	6268.46i	1.05879	−	0.611290i
$473$	−4622.27	+	2668.67i	−0.449328	+	0.259420i
$474$		0			0
$475$		−	6307.49i		−	0.609279i
$476$		0			0
$477$		0			0
$478$	−1770.49	+	3066.58i	−0.169415	+	0.293435i
$479$	3026.38	+	5241.84i	0.288682	+	0.500012i	0.973495	−	0.228706i	$-0.0734496\pi$
$479$	3026.38	+	5241.84i	0.288682	+	0.500012i	−0.684813	+	0.728719i	$0.740116\pi$
$480$		0			0
$481$	20500.3	+	11835.8i	1.94331	+	1.12197i
$482$	−7356.41			−0.695177
$483$		0			0
$484$	5779.13			0.542743
$485$	9657.88	+	5575.98i	0.904210	+	0.522046i
$486$		0			0
$487$	−7654.72	−	13258.4i	−0.712255	−	1.23366i	−0.964009	−	0.265871i	$-0.914340\pi$
$487$	−7654.72	−	13258.4i	−0.712255	−	1.23366i	0.251753	−	0.967791i	$-0.418993\pi$
$488$	−1549.53	+	2683.87i	−0.143738	+	0.248961i
$489$		0			0
$490$		0			0
$491$			4291.01i			0.394400i	0.980363	+	0.197200i	$0.0631848\pi$
$491$			4291.01i			0.394400i	−0.980363	+	0.197200i	$0.936815\pi$
$492$		0			0
$493$	−9641.87	+	5566.74i	−0.880828	+	0.508546i
$494$	−6577.51	+	3797.53i	−0.599061	+	0.345868i
$495$		0			0
$496$		−	347.770i		−	0.0314826i
$497$		0			0
$498$		0			0
$499$	−3445.77	+	5968.24i	−0.309126	+	0.535421i	−0.978171	−	0.207800i	$-0.933370\pi$
$499$	−3445.77	+	5968.24i	−0.309126	+	0.535421i	0.669046	+	0.743221i	$0.266703\pi$
$500$	−790.807	−	1369.72i	−0.0707319	−	0.122511i
$501$		0			0
$502$	−6961.17	−	4019.03i	−0.618909	−	0.357327i
$503$	13534.6			1.19975			0.599877	−	0.800092i	$-0.295216\pi$
$503$	13534.6			1.19975			0.599877	+	0.800092i	$0.295216\pi$
$504$		0			0
$505$	−3613.68			−0.318429
$506$	−2050.55	−	1183.88i	−0.180154	−	0.104012i
$507$		0			0
$508$	420.498	+	728.323i	0.0367255	+	0.0636105i
$509$	6043.91	−	10468.4i	0.526310	−	0.911595i	−0.473221	−	0.880944i	$-0.656909\pi$
$509$	6043.91	−	10468.4i	0.526310	−	0.911595i	0.999530	−	0.0306510i	$-0.00975805\pi$
$510$		0			0
$511$		0			0
$512$		−	1642.50i		−	0.141776i
$513$		0			0
$514$	−1099.74	+	634.934i	−0.0943724	+	0.0544859i
$515$	668.150	−	385.757i	0.0571693	−	0.0330067i
$516$		0			0
$517$		−	2211.91i		−	0.188161i
$518$		0			0
$519$		0			0
$520$	11827.0	−	20485.0i	0.997402	−	1.72755i
$521$	3812.94	+	6604.20i	0.320629	+	0.555346i	0.980618	−	0.195930i	$-0.0627724\pi$
$521$	3812.94	+	6604.20i	0.320629	+	0.555346i	−0.659989	+	0.751275i	$0.729439\pi$
$522$		0			0
$523$	−13328.7	−	7695.34i	−1.11439	−	0.643392i	−0.174425	−	0.984670i	$-0.555807\pi$
$523$	−13328.7	−	7695.34i	−1.11439	−	0.643392i	−0.939962	+	0.341279i	$0.889140\pi$
$524$	−11466.9			−0.955981
$525$		0			0
$526$	−1451.74			−0.120340
$527$	−4645.54	−	2682.10i	−0.383990	−	0.221697i
$528$		0			0
$529$	2564.60	+	4442.02i	0.210783	+	0.365088i
$530$	7278.18	−	12606.2i	0.596498	−	1.03317i
$531$		0			0
$532$		0			0
$533$			9430.40i			0.766371i
$534$		0			0
$535$	15561.6	−	8984.49i	1.25754	−	0.726044i
$536$	6411.45	−	3701.65i	0.516665	−	0.298297i
$537$		0			0
$538$			747.619i			0.0599110i
$539$		0			0
$540$		0			0
$541$	6850.44	−	11865.3i	0.544406	−	0.942939i	−0.454238	−	0.890880i	$-0.650088\pi$
$541$	6850.44	−	11865.3i	0.544406	−	0.942939i	0.998644	−	0.0520584i	$-0.0165782\pi$
$542$	3450.79	+	5976.95i	0.273477	+	0.473675i
$543$		0			0
$544$	−10718.9	−	6188.59i	−0.844800	−	0.487745i
$545$	−5871.58			−0.461487
$546$		0			0
$547$	−6139.00			−0.479863			−0.239931	−	0.970790i	$-0.577125\pi$
$547$	−6139.00			−0.479863			−0.239931	+	0.970790i	$0.577125\pi$
$548$	2076.16	+	1198.67i	0.161841	+	0.0934391i
$549$		0			0
$550$	−923.872	−	1600.19i	−0.0716255	−	0.124059i
$551$	4877.87	−	8448.71i	0.377140	−	0.653226i
$552$		0			0
$553$		0			0
$554$			5909.95i			0.453231i
$555$		0			0
$556$	2432.78	−	1404.57i	0.185563	−	0.107135i
$557$	−19687.1	+	11366.4i	−1.49761	+	0.864646i	−0.999996	−	0.00275234i	$-0.999124\pi$
$557$	−19687.1	+	11366.4i	−1.49761	+	0.864646i	−0.497615	+	0.867398i	$0.665791\pi$
$558$		0			0
$559$		−	36636.4i		−	2.77202i
$560$		0			0
$561$		0			0
$562$	−1455.89	+	2521.67i	−0.109276	+	0.189271i
$563$	4958.81	+	8588.90i	0.371206	+	0.642947i	0.989751	−	0.142802i	$-0.0456112\pi$
$563$	4958.81	+	8588.90i	0.371206	+	0.642947i	−0.618546	+	0.785749i	$0.712278\pi$
$564$		0			0
$565$	−9388.59	−	5420.51i	−0.699081	−	0.403615i
$566$	−7766.06			−0.576735
$567$		0			0
$568$	−9629.02			−0.711311
$569$	4448.79	+	2568.51i	0.327773	+	0.189240i	0.654852	−	0.755757i	$-0.272731\pi$
$569$	4448.79	+	2568.51i	0.327773	+	0.189240i	−0.327079	+	0.944997i	$0.606064\pi$
$570$		0			0
$571$	9093.02	+	15749.6i	0.666429	+	1.15429i	0.978896	+	0.204360i	$0.0655114\pi$
$571$	9093.02	+	15749.6i	0.666429	+	1.15429i	−0.312467	+	0.949929i	$0.601155\pi$
$572$	1573.32	−	2725.07i	0.115007	−	0.199198i
$573$		0			0
$574$		0			0
$575$			13497.5i			0.978930i
$576$		0			0
$577$	−10737.5	+	6199.32i	−0.774713	+	0.447281i	−0.834553	−	0.550927i	$-0.814274\pi$
$577$	−10737.5	+	6199.32i	−0.774713	+	0.447281i	0.0598401	+	0.998208i	$0.480941\pi$
$578$	9.83959	−	5.68089i	0.000708085	−	0.000408813i
$579$		0			0
$580$			11223.6i			0.803509i
$581$		0			0
$582$		0			0
$583$	2621.00	−	4539.70i	0.186193	−	0.322496i
$584$	−6299.99	−	10911.9i	−0.446396	−	0.773181i
$585$		0			0
$586$	4613.94	+	2663.86i	0.325256	+	0.187787i
$587$	18977.6			1.33439			0.667195	−	0.744883i	$-0.267495\pi$
$587$	18977.6			1.33439			0.667195	+	0.744883i	$0.267495\pi$
$588$		0			0
$589$	4700.40			0.328822
$590$	12912.2	+	7454.85i	0.900994	+	0.520189i
$591$		0			0
$592$	792.749	+	1373.08i	0.0550368	+	0.0953265i
$593$	−5364.44	+	9291.48i	−0.371486	+	0.643432i	−0.989794	−	0.142503i	$-0.954485\pi$
$593$	−5364.44	+	9291.48i	−0.371486	+	0.643432i	0.618308	+	0.785936i	$0.287818\pi$
$594$		0			0
$595$		0			0
$596$		−	10279.5i		−	0.706488i
$597$		0			0
$598$	14075.3	−	8126.40i	0.962514	−	0.555708i
$599$	−1577.36	+	910.687i	−0.107594	+	0.0621196i	−0.552832	−	0.833293i	$-0.686453\pi$
$599$	−1577.36	+	910.687i	−0.107594	+	0.0621196i	0.445237	+	0.895413i	$0.353119\pi$
$600$		0			0
$601$			18933.3i			1.28503i	0.766273	+	0.642516i	$0.222109\pi$
$601$			18933.3i			1.28503i	−0.766273	+	0.642516i	$0.777891\pi$
$602$		0			0
$603$		0			0
$604$	1680.92	−	2911.43i	0.113238	−	0.196133i
$605$	9302.77	+	16112.9i	0.625143	+	1.08278i
$606$		0			0
$607$	−13323.3	−	7692.20i	−0.890898	−	0.514360i	−0.0166621	−	0.999861i	$-0.505304\pi$
$607$	−13323.3	−	7692.20i	−0.890898	−	0.514360i	−0.874236	+	0.485501i	$0.838637\pi$
$608$	10845.5			0.723428
$609$		0			0
$610$	−3685.61			−0.244633
$611$	13148.8	+	7591.46i	0.870611	+	0.502647i
$612$		0			0
$613$	2753.60	+	4769.38i	0.181431	+	0.314247i	0.942368	−	0.334578i	$-0.108594\pi$
$613$	2753.60	+	4769.38i	0.181431	+	0.314247i	−0.760937	+	0.648825i	$0.775261\pi$
$614$	3250.54	−	5630.10i	0.213650	−	0.370053i
$615$		0			0
$616$		0			0
$617$		−	18134.0i		−	1.18322i	−0.806224	−	0.591610i	$-0.798493\pi$
$617$		−	18134.0i		−	1.18322i	0.806224	−	0.591610i	$-0.201507\pi$
$618$		0			0
$619$	−3148.73	+	1817.92i	−0.204456	+	0.118043i	−0.598732	−	0.800949i	$-0.704329\pi$
$619$	−3148.73	+	1817.92i	−0.204456	+	0.118043i	0.394276	+	0.918992i	$0.370995\pi$
$620$	−4683.15	+	2703.82i	−0.303355	+	0.175142i
$621$		0			0
$622$			4684.49i			0.301979i
$623$		0			0
$624$		0			0
$625$	8960.38	−	15519.8i	0.573464	−	0.993270i
$626$	−1343.73	−	2327.41i	−0.0857928	−	0.148597i
$627$		0			0
$628$	−7317.26	−	4224.62i	−0.464953	−	0.268441i
$629$	24455.6			1.55025
$630$		0			0
$631$	−5912.59			−0.373021			−0.186511	−	0.982453i	$-0.559718\pi$
$631$	−5912.59			−0.373021			−0.186511	+	0.982453i	$0.559718\pi$
$632$	6454.60	+	3726.57i	0.406251	+	0.234549i
$633$		0			0
$634$	2299.90	+	3983.55i	0.144071	+	0.249538i
$635$	−1353.76	+	2344.79i	−0.0846024	+	0.146536i
$636$		0			0
$637$		0			0
$638$		−	2857.89i		−	0.177343i
$639$		0			0
$640$	−9940.52	+	5739.16i	−0.613959	+	0.354469i
$641$	23786.7	−	13733.3i	1.46571	−	0.846227i	0.466443	−	0.884551i	$-0.345535\pi$
$641$	23786.7	−	13733.3i	1.46571	−	0.846227i	0.999265	+	0.0383236i	$0.0122018\pi$
$642$		0			0
$643$			28474.0i			1.74635i	0.487403	+	0.873177i	$0.337944\pi$
$643$			28474.0i			1.74635i	−0.487403	+	0.873177i	$0.662056\pi$
$644$		0			0
$645$		0			0
$646$	−3923.29	+	6795.33i	−0.238947	+	0.413868i
$647$	−661.681	−	1146.06i	−0.0402061	−	0.0696390i	0.845222	−	0.534415i	$-0.179468\pi$
$647$	−661.681	−	1146.06i	−0.0402061	−	0.0696390i	−0.885428	+	0.464776i	$0.846135\pi$
$648$		0			0
$649$	4649.89	+	2684.62i	0.281239	+	0.162374i
$650$	12683.3			0.765351
$651$		0			0
$652$	−13627.0			−0.818522
$653$	−3331.38	−	1923.37i	−0.199643	−	0.115264i	0.396846	−	0.917885i	$-0.370105\pi$
$653$	−3331.38	−	1923.37i	−0.199643	−	0.115264i	−0.596489	+	0.802621i	$0.703438\pi$
$654$		0			0
$655$	−18458.5	−	31971.0i	−1.10112	−	1.90719i
$656$	−315.818	+	547.012i	−0.0187967	+	0.0325568i
$657$		0			0
$658$		0			0
$659$		−	6796.84i		−	0.401771i	−0.979615	−	0.200886i	$-0.935618\pi$
$659$		−	6796.84i		−	0.401771i	0.979615	−	0.200886i	$-0.0643819\pi$
$660$		0			0
$661$	26902.5	−	15532.2i	1.58304	−	0.913966i	0.588623	−	0.808408i	$-0.299670\pi$
$661$	26902.5	−	15532.2i	1.58304	−	0.913966i	0.994413	−	0.105559i	$-0.0336631\pi$
$662$	2326.16	−	1343.01i	0.136569	−	0.0788481i
$663$		0			0
$664$		−	20441.7i		−	1.19471i
$665$		0			0
$666$		0			0
$667$	−10438.2	+	18079.5i	−0.605952	+	1.04954i
$668$	8180.91	+	14169.7i	0.473846	+	0.820725i
$669$		0			0
$670$	7624.91	+	4402.24i	0.439666	+	0.253841i
$671$	−1327.25			−0.0763605
$672$		0			0
$673$	15508.2			0.888259			0.444129	−	0.895963i	$-0.353513\pi$
$673$	15508.2			0.888259			0.444129	+	0.895963i	$0.353513\pi$
$674$	10605.3	+	6122.97i	0.606084	+	0.349923i
$675$		0			0
$676$	5651.59	+	9788.84i	0.321552	+	0.556944i
$677$	15337.4	−	26565.2i	0.870701	−	1.50810i	0.00942744	−	0.999956i	$-0.496999\pi$
$677$	15337.4	−	26565.2i	0.870701	−	1.50810i	0.861273	−	0.508142i	$-0.169668\pi$
$678$		0			0
$679$		0			0
$680$		−	24437.4i		−	1.37813i
$681$		0			0
$682$	1192.48	−	688.478i	0.0669536	−	0.0386557i
$683$	15292.8	−	8829.33i	0.856756	−	0.494648i	−0.00616869	−	0.999981i	$-0.501964\pi$
$683$	15292.8	−	8829.33i	0.856756	−	0.494648i	0.862925	+	0.505333i	$0.168630\pi$
$684$		0			0
$685$			7718.08i			0.430500i
$686$		0			0
$687$		0			0
$688$	1226.93	−	2125.10i	0.0679887	−	0.117760i
$689$	17991.0	+	31161.3i	0.994778	+	1.72301i
$690$		0			0
$691$	−11402.3	−	6583.11i	−0.627733	−	0.362422i	0.152141	−	0.988359i	$-0.451383\pi$
$691$	−11402.3	−	6583.11i	−0.627733	−	0.362422i	−0.779874	+	0.625937i	$0.784717\pi$
$692$	−8223.42			−0.451745
$693$		0			0
$694$	−979.634			−0.0535827
$695$	7832.18	+	4521.91i	0.427470	+	0.246800i
$696$		0			0
$697$	4871.35	+	8437.42i	0.264728	+	0.458522i
$698$	6349.29	−	10997.3i	0.344304	−	0.596352i
$699$		0			0
$700$		0			0
$701$			25910.0i			1.39602i	0.716090	+	0.698008i	$0.245930\pi$
$701$			25910.0i			1.39602i	−0.716090	+	0.698008i	$0.754070\pi$
$702$		0			0
$703$	−18558.3	+	10714.6i	−0.995646	+	0.574837i
$704$	3063.06	−	1768.46i	0.163982	−	0.0946752i
$705$		0			0
$706$			16158.8i			0.861394i
$707$		0			0
$708$		0			0
$709$	−3104.25	+	5376.71i	−0.164432	+	0.284805i	−0.936454	−	0.350792i	$-0.885913\pi$
$709$	−3104.25	+	5376.71i	−0.164432	+	0.284805i	0.772021	+	0.635597i	$0.219246\pi$
$710$	−5725.73	−	9917.25i	−0.302652	−	0.524208i
$711$		0			0
$712$	−32491.7	−	18759.1i	−1.71022	−	0.987398i
$713$	−10058.5			−0.528320
$714$		0			0
$715$	10130.4			0.529868
$716$	3213.15	+	1855.11i	0.167711	+	0.0968280i
$717$		0			0
$718$	10053.6	+	17413.3i	0.522557	+	0.905095i
$719$	−14379.4	+	24905.9i	−0.745843	+	1.29184i	0.203957	+	0.978980i	$0.434620\pi$
$719$	−14379.4	+	24905.9i	−0.745843	+	1.29184i	−0.949800	+	0.312858i	$0.898713\pi$
$720$		0			0
$721$		0			0
$722$			5610.13i			0.289180i
$723$		0			0
$724$	−10236.3	+	5909.95i	−0.525457	+	0.303373i
$725$	−14108.8	+	8145.72i	−0.722742	+	0.417275i
$726$		0			0
$727$		−	35275.7i		−	1.79959i	−0.436312	−	0.899795i	$-0.643716\pi$
$727$		−	35275.7i		−	1.79959i	0.436312	−	0.899795i	$-0.356284\pi$
$728$		0			0
$729$		0			0
$730$	7492.35	−	12977.1i	0.379869	−	0.657953i
$731$	−18924.8	−	32778.8i	−0.957539	−	1.65851i
$732$		0			0
$733$	6885.15	+	3975.14i	0.346942	+	0.200307i	0.663338	−	0.748320i	$-0.269139\pi$
$733$	6885.15	+	3975.14i	0.346942	+	0.200307i	−0.316395	+	0.948627i	$0.602473\pi$
$734$	15156.3			0.762164
$735$		0			0
$736$	−23208.5			−1.16233
$737$	2745.86	+	1585.32i	0.137239	+	0.0792348i
$738$		0			0
$739$	−16676.8	−	28885.1i	−0.830130	−	1.43783i	−0.897935	−	0.440129i	$-0.854933\pi$
$739$	−16676.8	−	28885.1i	−0.830130	−	1.43783i	0.0678046	−	0.997699i	$-0.478401\pi$
$740$	12326.8	−	21350.6i	0.612354	−	1.06063i
$741$		0			0
$742$		0			0
$743$			32933.6i			1.62613i	0.582171	+	0.813066i	$0.302203\pi$
$743$			32933.6i			1.62613i	−0.582171	+	0.813066i	$0.697797\pi$
$744$		0			0
$745$	28660.5	−	16547.2i	1.40945	−	0.813747i
$746$	−7165.51	+	4137.01i	−0.351673	+	0.203039i
$747$		0			0
$748$		−	3250.85i		−	0.158907i
$749$		0			0
$750$		0			0
$751$	19818.3	−	34326.3i	0.962956	−	1.66789i	0.247945	−	0.968774i	$-0.420245\pi$
$751$	19818.3	−	34326.3i	0.962956	−	1.66789i	0.715010	−	0.699114i	$-0.246422\pi$
$752$	508.466	+	880.688i	0.0246567	+	0.0427066i
$753$		0			0
$754$	16988.9	+	9808.54i	0.820555	+	0.473748i
$755$	10823.2			0.521718
$756$		0			0
$757$	−3996.51			−0.191883			−0.0959417	−	0.995387i	$-0.530586\pi$
$757$	−3996.51			−0.191883			−0.0959417	+	0.995387i	$0.530586\pi$
$758$	−18172.2	−	10491.7i	−0.870769	−	0.502739i
$759$		0			0
$760$	10706.6	+	18544.5i	0.511014	+	0.885103i
$761$	−13117.8	+	22720.8i	−0.624863	+	1.08230i	0.363704	+	0.931515i	$0.381512\pi$
$761$	−13117.8	+	22720.8i	−0.624863	+	1.08230i	−0.988567	+	0.150781i	$0.951821\pi$
$762$		0			0
$763$		0			0
$764$			4233.11i			0.200456i
$765$		0			0
$766$	−6180.45	+	3568.28i	−0.291526	+	0.168312i
$767$	−31917.7	+	18427.7i	−1.50258	+	0.867517i
$768$		0			0
$769$		−	36456.9i		−	1.70958i	−0.518971	−	0.854792i	$-0.673685\pi$
$769$		−	36456.9i		−	1.70958i	0.518971	−	0.854792i	$-0.326315\pi$
$770$		0			0
$771$		0			0
$772$	466.000	−	807.135i	0.0217250	−	0.0376288i
$773$	4732.74	+	8197.34i	0.220213	+	0.381420i	0.954873	−	0.297016i	$-0.0959914\pi$
$773$	4732.74	+	8197.34i	0.220213	+	0.381420i	−0.734660	+	0.678436i	$0.762658\pi$
$774$		0			0
$775$	−6797.74	−	3924.68i	−0.315074	−	0.181908i
$776$	−17069.7			−0.789646
$777$		0			0
$778$	1449.79			0.0668089
$779$	−7393.31	−	4268.53i	−0.340042	−	0.196323i
$780$		0			0
$781$	−2061.93	−	3571.37i	−0.0944707	−	0.163628i
$782$	8395.51	−	14541.4i	0.383917	−	0.664963i
$783$		0			0
$784$		0			0
$785$		−	27201.8i		−	1.23678i
$786$		0			0
$787$	−21665.9	+	12508.8i	−0.981330	+	0.566571i	−0.902671	−	0.430331i	$-0.858397\pi$
$787$	−21665.9	+	12508.8i	−0.981330	+	0.566571i	−0.0786582	+	0.996902i	$0.525064\pi$
$788$	−13071.2	+	7546.67i	−0.590917	+	0.341166i
$789$		0			0
$790$			8863.75i			0.399187i
$791$		0			0
$792$		0			0
$793$	4555.24	−	7889.91i	0.203987	−	0.353315i
$794$	3508.77	+	6077.37i	0.156828	+	0.271635i
$795$		0			0
$796$	11566.4	+	6677.87i	0.515026	+	0.297350i
$797$	−38893.5			−1.72858			−0.864290	−	0.502994i	$-0.832232\pi$
$797$	−38893.5			−1.72858			−0.864290	+	0.502994i	$0.832232\pi$
$798$		0			0
$799$	15685.7			0.694519
$800$	−15684.9	−	9055.67i	−0.693180	−	0.400208i
$801$		0			0
$802$	4237.16	+	7338.98i	0.186558	+	0.323128i
$803$	2698.12	−	4673.28i	0.118574	−	0.205376i
$804$		0			0
$805$		0			0
$806$			9451.67i			0.413053i
$807$		0			0
$808$	4790.21	−	2765.63i	0.208563	−	0.120414i
$809$	−6072.26	+	3505.82i	−0.263893	+	0.152359i	−0.626109	−	0.779735i	$-0.715354\pi$
$809$	−6072.26	+	3505.82i	−0.263893	+	0.152359i	0.362216	+	0.932094i	$0.382020\pi$
$810$		0			0
$811$			5013.82i			0.217089i	0.994092	+	0.108544i	$0.0346189\pi$
$811$			5013.82i			0.217089i	−0.994092	+	0.108544i	$0.965381\pi$
$812$		0			0
$813$		0			0
$814$	−3138.80	+	5436.55i	−0.135153	+	0.234092i
$815$	−21935.7	−	37993.7i	−0.942790	−	1.63296i
$816$		0			0
$817$	28722.5	+	16582.9i	1.22995	+	0.710115i
$818$	−17822.0			−0.761776
$819$		0			0
$820$	9821.58			0.418274
$821$	−603.281	−	348.304i	−0.0256451	−	0.0148062i	0.487123	−	0.873334i	$-0.338046\pi$
$821$	−603.281	−	348.304i	−0.0256451	−	0.0148062i	−0.512768	+	0.858527i	$0.671380\pi$
$822$		0			0
$823$	−3206.57	−	5553.95i	−0.135813	−	0.235235i	0.790095	−	0.612985i	$-0.210031\pi$
$823$	−3206.57	−	5553.95i	−0.135813	−	0.235235i	−0.925908	+	0.377750i	$0.876698\pi$
$824$	−590.456	+	1022.70i	−0.0249630	+	0.0432372i
$825$		0			0
$826$		0			0
$827$		−	16718.9i		−	0.702989i	−0.936190	−	0.351494i	$-0.885674\pi$
$827$		−	16718.9i		−	0.702989i	0.936190	−	0.351494i	$-0.114326\pi$
$828$		0			0
$829$	12606.9	−	7278.59i	0.528173	−	0.304941i	−0.212099	−	0.977248i	$-0.568030\pi$
$829$	12606.9	−	7278.59i	0.528173	−	0.304941i	0.740272	+	0.672307i	$0.234697\pi$
$830$	21053.6	−	12155.3i	0.880457	−	0.508332i
$831$		0			0
$832$			24278.1i			1.01165i
$833$		0			0
$834$		0			0
$835$	−26337.9	+	45618.6i	−1.09157	+	1.89065i
$836$	1424.28	+	2466.93i	0.0589232	+	0.102058i
$837$		0			0
$838$	−4741.15	−	2737.30i	−0.195442	−	0.112838i
$839$	19467.0			0.801045			0.400523	−	0.916287i	$-0.368829\pi$
$839$	19467.0			0.801045			0.400523	+	0.916287i	$0.368829\pi$
$840$		0			0
$841$	−808.829			−0.0331637
$842$	−12053.7	−	6959.22i	−0.493347	−	0.284834i
$843$		0			0
$844$	−2822.37	−	4888.49i	−0.115107	−	0.199371i
$845$	−18194.9	+	31514.6i	−0.740740	+	1.28300i
$846$		0			0
$847$		0			0
$848$			2410.02i			0.0975950i
$849$		0			0
$850$	11347.8	−	6551.63i	0.457912	−	0.264376i
$851$	39713.2	−	22928.4i	1.59971	−	0.923592i
$852$		0			0
$853$		−	22345.3i		−	0.896938i	−0.893798	−	0.448469i	$-0.851969\pi$
$853$		−	22345.3i		−	0.896938i	0.893798	−	0.448469i	$-0.148031\pi$
$854$		0			0
$855$		0			0
$856$	−13752.1	+	23819.3i	−0.549107	+	0.951081i
$857$	24039.8	+	41638.2i	0.958209	+	1.65967i	0.726847	+	0.686800i	$0.240985\pi$
$857$	24039.8	+	41638.2i	0.958209	+	1.65967i	0.231363	+	0.972868i	$0.425682\pi$
$858$		0			0
$859$	22612.6	+	13055.4i	0.898173	+	0.518560i	0.876607	−	0.481207i	$-0.159801\pi$
$859$	22612.6	+	13055.4i	0.898173	+	0.518560i	0.0215659	+	0.999767i	$0.493135\pi$
$860$	−38156.2			−1.51292
$861$		0			0
$862$	−27289.8			−1.07830
$863$	2536.20	+	1464.27i	0.100038	+	0.0577572i	0.549185	−	0.835701i	$-0.314938\pi$
$863$	2536.20	+	1464.27i	0.100038	+	0.0577572i	−0.449146	+	0.893458i	$0.648272\pi$
$864$		0			0
$865$	−13237.4	−	22927.8i	−0.520329	−	0.901236i
$866$	−5157.59	+	8933.22i	−0.202381	+	0.350535i
$867$		0			0
$868$		0			0
$869$			3191.98i			0.124604i
$870$		0			0
$871$	−18848.1	+	10881.9i	−0.733229	+	0.423330i
$872$	7783.22	−	4493.64i	0.302263	−	0.174511i
$873$		0			0
$874$			14713.2i			0.569428i
$875$		0			0
$876$		0			0
$877$	−6545.28	+	11336.8i	−0.252016	+	0.436505i	−0.964081	−	0.265609i	$-0.914427\pi$
$877$	−6545.28	+	11336.8i	−0.252016	+	0.436505i	0.712064	+	0.702114i	$0.247760\pi$
$878$	−5034.24	−	8719.56i	−0.193505	−	0.335160i
$879$		0			0
$880$	587.617	+	339.261i	0.0225097	+	0.0129960i
$881$	7888.79			0.301680			0.150840	−	0.988558i	$-0.451802\pi$
$881$	7888.79			0.301680			0.150840	+	0.988558i	$0.451802\pi$
$882$		0			0
$883$	45061.9			1.71739			0.858694	−	0.512489i	$-0.171276\pi$
$883$	45061.9			1.71739			0.858694	+	0.512489i	$0.171276\pi$
$884$	19324.8	+	11157.2i	0.735254	+	0.424499i
$885$		0			0
$886$	−367.000	−	635.663i	−0.0139160	−	0.0241033i
$887$	−1773.29	+	3071.43i	−0.0671266	+	0.116267i	−0.897635	−	0.440739i	$-0.854716\pi$
$887$	−1773.29	+	3071.43i	−0.0671266	+	0.116267i	0.830509	+	0.557006i	$0.188050\pi$
$888$		0			0
$889$		0			0
$890$		−	44619.1i		−	1.68049i
$891$		0			0
$892$	−13708.5	+	7914.62i	−0.514569	+	0.297087i
$893$	−11903.2	+	6872.32i	−0.446053	+	0.257529i
$894$		0			0
$895$			11944.8i			0.446114i
$896$		0			0
$897$		0			0
$898$	−7671.85	+	13288.0i	−0.285092	+	0.493795i
$899$	−6070.26	−	10514.0i	−0.225200	−	0.390058i
$900$		0			0
$901$	32193.2	+	18586.8i	1.19036	+	0.687253i
$902$	−2500.89			−0.0923175
$903$		0			0
$904$	16593.7			0.610508
$905$	−32955.2	−	19026.7i	−1.21046	−	0.698861i
$906$		0			0
$907$	7339.77	+	12712.9i	0.268703	+	0.465406i	0.968527	−	0.248908i	$-0.0800718\pi$
$907$	7339.77	+	12712.9i	0.268703	+	0.465406i	−0.699825	+	0.714315i	$0.746738\pi$
$908$	−10600.5	+	18360.5i	−0.387432	+	0.671052i
$909$		0			0
$910$		0			0
$911$			12355.2i			0.449336i	0.974435	+	0.224668i	$0.0721297\pi$
$911$			12355.2i			0.449336i	−0.974435	+	0.224668i	$0.927870\pi$
$912$		0			0
$913$	7581.74	−	4377.32i	0.274829	−	0.158673i
$914$	1080.92	−	624.068i	0.0391177	−	0.0225846i
$915$		0			0
$916$			18342.4i			0.661626i
$917$		0			0
$918$		0			0
$919$	1535.18	−	2659.01i	0.0551044	−	0.0954437i	−0.837157	−	0.546962i	$-0.815784\pi$
$919$	1535.18	−	2659.01i	0.0551044	−	0.0954437i	0.892262	+	0.451518i	$0.149117\pi$
$920$	−22911.3	−	39683.6i	−0.821049	−	1.42210i
$921$		0			0
$922$	7668.66	+	4427.50i	0.273920	+	0.158148i
$923$	28306.9			1.00946
$924$		0			0
$925$	35785.5			1.27202
$926$	13170.1	+	7603.77i	0.467383	+	0.269844i
$927$		0			0
$928$	−14006.3	−	24259.7i	−0.495453	−	0.858149i
$929$	−15264.3	+	26438.6i	−0.539082	+	0.933717i	0.459872	+	0.887985i	$0.347895\pi$
$929$	−15264.3	+	26438.6i	−0.539082	+	0.933717i	−0.998954	+	0.0457316i	$0.985438\pi$
$930$		0			0
$931$		0			0
$932$		−	20475.5i		−	0.719631i
$933$		0			0
$934$	1581.09	−	912.844i	0.0553907	−	0.0319798i
$935$	9063.72	−	5232.94i	0.317022	−	0.183033i
$936$		0			0
$937$			18235.1i			0.635769i	0.948129	+	0.317885i	$0.102972\pi$
$937$			18235.1i			0.635769i	−0.948129	+	0.317885i	$0.897028\pi$
$938$		0			0
$939$		0			0
$940$	7906.36	−	13694.2i	0.274337	−	0.475166i
$941$	−6686.17	−	11580.8i	−0.231629	−	0.401193i	0.726659	−	0.686999i	$-0.241072\pi$
$941$	−6686.17	−	11580.8i	−0.231629	−	0.401193i	−0.958288	+	0.285806i	$0.907739\pi$
$942$		0			0
$943$	15821.1	+	9134.30i	0.546347	+	0.315433i
$944$	−2468.52			−0.0851098
$945$		0			0
$946$	9715.77			0.333919
$947$	−4431.54	−	2558.55i	−0.152065	−	0.0877948i	0.422037	−	0.906579i	$-0.361315\pi$
$947$	−4431.54	−	2558.55i	−0.152065	−	0.0877948i	−0.574102	+	0.818784i	$0.694649\pi$
$948$		0			0
$949$	18520.4	+	32078.3i	0.633506	+	1.09727i
$950$	−5740.89	+	9943.50i	−0.196062	+	0.339589i
$951$		0			0
$952$		0			0
$953$			35456.7i			1.20520i	0.798044	+	0.602599i	$0.205868\pi$
$953$			35456.7i			1.20520i	−0.798044	+	0.602599i	$0.794132\pi$
$954$		0			0
$955$	−11802.4	+	6814.12i	−0.399913	+	0.230890i
$956$	−7894.73	+	4558.03i	−0.267086	+	0.154202i
$957$		0			0
$958$		−	11018.1i		−	0.371584i
$959$		0			0
$960$		0			0
$961$	−11970.8	+	20734.0i	−0.401826	+	0.695983i
$962$	−21545.3	−	37317.5i	−0.722086	−	1.25069i
$963$		0			0
$964$	−16401.4	−	9469.33i	−0.547980	−	0.316376i
$965$	3000.51			0.100093
$966$		0			0
$967$	−2804.92			−0.0932784			−0.0466392	−	0.998912i	$-0.514851\pi$
$967$	−2804.92			−0.0932784			−0.0466392	+	0.998912i	$0.514851\pi$
$968$	−24663.1	−	14239.2i	−0.818906	−	0.472796i
$969$		0			0
$970$	−10150.2	−	17580.6i	−0.335982	−	0.581938i
$971$	13683.8	−	23701.0i	0.452248	−	0.783316i	−0.546278	−	0.837604i	$-0.683956\pi$
$971$	13683.8	−	23701.0i	0.452248	−	0.783316i	0.998525	+	0.0542881i	$0.0172889\pi$
$972$		0			0
$973$		0			0
$974$			27868.4i			0.916797i
$975$		0			0
$976$	528.455	−	305.104i	0.0173314	−	0.0100063i
$977$	−20868.5	+	12048.4i	−0.683359	+	0.394537i	−0.801119	−	0.598505i	$-0.795762\pi$
$977$	−20868.5	+	12048.4i	−0.683359	+	0.394537i	0.117761	+	0.993042i	$0.462428\pi$
$978$		0			0
$979$		−	16068.1i		−	0.524554i
$980$		0			0
$981$		0			0
$982$	3905.55	−	6764.60i	0.126915	−	0.219824i
$983$	−4655.36	−	8063.32i	−0.151051	−	0.261628i	0.780563	−	0.625077i	$-0.214932\pi$
$983$	−4655.36	−	8063.32i	−0.151051	−	0.261628i	−0.931614	+	0.363449i	$0.881599\pi$
$984$		0			0
$985$	−42081.9	−	24296.0i	−1.36126	−	0.785924i
$986$	20266.7			0.654588
$987$		0			0
$988$	−19553.0			−0.629621
$989$	−61463.8	−	35486.1i	−1.97617	−	1.14094i
$990$		0			0
$991$	12095.2	+	20949.6i	0.387707	+	0.671528i	0.992141	−	0.125127i	$-0.0399339\pi$
$991$	12095.2	+	20949.6i	0.387707	+	0.671528i	−0.604434	+	0.796655i	$0.706601\pi$
$992$	6748.36	−	11688.5i	0.215989	−	0.374103i
$993$		0			0
$994$		0			0
$995$			42998.0i			1.36998i
$996$		0			0
$997$	−42319.8	+	24433.4i	−1.34431	+	0.776140i	−0.987437	−	0.158011i	$-0.949492\pi$
$997$	−42319.8	+	24433.4i	−1.34431	+	0.776140i	−0.356877	+	0.934151i	$0.616159\pi$
$998$	10864.2	−	6272.47i	0.344590	−	0.198949i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.4.p.c.215.3		16
3.2	odd	2	inner	441.4.p.c.215.6		16
7.2	even	3		441.4.c.a.440.11		16
7.3	odd	6	inner	441.4.p.c.80.6		16
7.4	even	3		63.4.p.a.17.6	yes	16
7.5	odd	6		441.4.c.a.440.12		16
7.6	odd	2		63.4.p.a.26.3	yes	16
21.2	odd	6		441.4.c.a.440.6		16
21.5	even	6		441.4.c.a.440.5		16
21.11	odd	6		63.4.p.a.17.3	✓	16
21.17	even	6	inner	441.4.p.c.80.3		16
21.20	even	2		63.4.p.a.26.6	yes	16
28.11	odd	6		1008.4.bt.a.17.8		16
28.27	even	2		1008.4.bt.a.593.1		16
84.11	even	6		1008.4.bt.a.17.1		16
84.83	odd	2		1008.4.bt.a.593.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.p.a.17.3	✓	16	21.11	odd	6
63.4.p.a.17.6	yes	16	7.4	even	3
63.4.p.a.26.3	yes	16	7.6	odd	2
63.4.p.a.26.6	yes	16	21.20	even	2
441.4.c.a.440.5		16	21.5	even	6
441.4.c.a.440.6		16	21.2	odd	6
441.4.c.a.440.11		16	7.2	even	3
441.4.c.a.440.12		16	7.5	odd	6
441.4.p.c.80.3		16	21.17	even	6	inner
441.4.p.c.80.6		16	7.3	odd	6	inner
441.4.p.c.215.3		16	1.1	even	1	trivial
441.4.p.c.215.6		16	3.2	odd	2	inner
1008.4.bt.a.17.1		16	84.11	even	6
1008.4.bt.a.17.8		16	28.11	odd	6
1008.4.bt.a.593.1		16	28.27	even	2
1008.4.bt.a.593.8		16	84.83	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.57646 - 0.910170i) q^{2} +(-2.34318 - 4.05851i) q^{4} +(7.54372 - 13.0661i) q^{5} +23.0935i q^{8} +O(q^{10})\)	\(q+(-1.57646 - 0.910170i) q^{2} +(-2.34318 - 4.05851i) q^{4} +(7.54372 - 13.0661i) q^{5} +23.0935i q^{8} +(-23.7848 + 13.7321i) q^{10} +(-8.56529 + 4.94517i) q^{11} -67.8891i q^{13} +(2.27356 - 3.93792i) q^{16} +(-35.0687 - 60.7407i) q^{17} +(53.2242 + 30.7290i) q^{19} -70.7052 q^{20} +18.0038 q^{22} +(-113.895 - 65.7575i) q^{23} +(-51.3154 - 88.8809i) q^{25} +(-61.7906 + 107.025i) q^{26} -158.738i q^{29} +(66.2349 - 38.2407i) q^{31} +(152.828 - 88.2353i) q^{32} +127.674i q^{34} +(-174.341 + 301.967i) q^{37} +(-55.9372 - 96.8861i) q^{38} +(301.742 + 174.211i) q^{40} -138.909 q^{41} +539.651 q^{43} +(40.1400 + 23.1749i) q^{44} +(119.701 + 207.328i) q^{46} +(-111.821 + 193.680i) q^{47} +186.823i q^{50} +(-275.529 + 159.076i) q^{52} +(-459.003 + 265.005i) q^{53} +149.220i q^{55} +(-144.479 + 250.245i) q^{58} +(-271.438 - 470.145i) q^{59} +(116.218 + 67.0983i) q^{61} -139.222 q^{62} -357.614 q^{64} +(-887.046 - 512.136i) q^{65} +(-160.290 - 277.630i) q^{67} +(-164.344 + 284.653i) q^{68} +416.958i q^{71} +(-472.510 + 272.804i) q^{73} +(549.683 - 317.360i) q^{74} -288.014i q^{76} +(161.369 - 279.499i) q^{79} +(-34.3022 - 59.4132i) q^{80} +(218.984 + 126.431i) q^{82} -885.170 q^{83} -1058.19 q^{85} +(-850.739 - 491.174i) q^{86} +(-114.201 - 197.802i) q^{88} +(-812.312 + 1406.97i) q^{89} +616.327i q^{92} +(352.564 - 203.553i) q^{94} +(803.017 - 463.622i) q^{95} +739.155i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 32 q^{4}+O(q^{10}) \) 16 * q + 32 * q^4	\( 16 q + 32 q^{4} + 72 q^{10} - 188 q^{16} + 612 q^{19} + 528 q^{22} - 20 q^{25} - 1128 q^{31} - 1196 q^{37} + 3204 q^{40} + 328 q^{43} - 1392 q^{46} - 4452 q^{52} - 3372 q^{58} + 1632 q^{61} + 5432 q^{64} + 308 q^{67} - 4068 q^{73} - 2176 q^{79} + 10188 q^{82} - 4608 q^{85} + 708 q^{88} + 2916 q^{94}+O(q^{100}) \) 16 * q + 32 * q^4 + 72 * q^10 - 188 * q^16 + 612 * q^19 + 528 * q^22 - 20 * q^25 - 1128 * q^31 - 1196 * q^37 + 3204 * q^40 + 328 * q^43 - 1392 * q^46 - 4452 * q^52 - 3372 * q^58 + 1632 * q^61 + 5432 * q^64 + 308 * q^67 - 4068 * q^73 - 2176 * q^79 + 10188 * q^82 - 4608 * q^85 + 708 * q^88 + 2916 * q^94

Introduction

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