LMFDB - Embedded newform 441.4.p.c.80.6

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			80.6
Root			$1.57646 - 0.910170i$ of defining polynomial
Character	$\chi$	$=$	441.80
Dual form			441.4.p.c.215.6

$q$-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 $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.57646	−	0.910170i	0.557363	−	0.321794i	−0.194723	−	0.980858i	$-0.562381\pi$
$2$	1.57646	−	0.910170i	0.557363	−	0.321794i	0.752086	+	0.659064i	$0.229048\pi$
$3$		0			0
$3$		0			0
$4$	−2.34318	+	4.05851i	−0.292898	+	0.507314i
$5$	−7.54372	−	13.0661i	−0.674731	−	1.16867i	−0.976547	−	0.215302i	$-0.930926\pi$
$5$	−7.54372	−	13.0661i	−0.674731	−	1.16867i	0.301817	−	0.953366i	$-0.402407\pi$
$6$		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	$-0.290054\pi$
$11$	8.56529	+	4.94517i	0.234776	+	0.135548i	−0.377998	+	0.925807i	$0.623387\pi$
$12$		0			0
$13$			67.8891i			1.44839i	0.689596	+	0.724194i	$0.257788\pi$
$13$			67.8891i			1.44839i	−0.689596	+	0.724194i	$0.742212\pi$
$14$		0			0
$15$		0			0
$16$	2.27356	+	3.93792i	0.0355244	+	0.0615300i
$17$	35.0687	−	60.7407i	0.500318	−	0.866575i	−0.499682	−	0.866209i	$-0.666550\pi$
$17$	35.0687	−	60.7407i	0.500318	−	0.866575i	1.00000		0.000366661i	$-0.000116712\pi$
$18$		0			0
$19$	53.2242	−	30.7290i	0.642656	−	0.371038i	−0.142981	−	0.989725i	$-0.545669\pi$
$19$	53.2242	−	30.7290i	0.642656	−	0.371038i	0.785637	+	0.618688i	$0.212335\pi$
$20$	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	$-0.463364\pi$
$23$	113.895	−	65.7575i	1.03256	−	0.596147i	0.917716	+	0.397236i	$0.130031\pi$
$24$		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	0.679447	−	0.733725i	$-0.262220\pi$
$31$	66.2349	+	38.2407i	0.383746	+	0.221556i	−0.295701	+	0.955281i	$0.595553\pi$
$32$	−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	−0.935000	−	0.354648i	$-0.884601\pi$
$37$	−174.341	−	301.967i	−0.774634	−	1.34171i	0.160366	−	0.987058i	$-0.448733\pi$
$38$	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	$-0.414773\pi$
$41$	138.909			0.529120			0.264560	+	0.964369i	$0.414773\pi$
$42$		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	$-0.0538538\pi$
$47$	111.821	+	193.680i	0.347039	+	0.601089i	−0.638683	+	0.769470i	$0.720520\pi$
$48$		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	$-0.0923407\pi$
$53$	459.003	+	265.005i	1.18960	+	0.686817i	0.231386	+	0.972862i	$0.425674\pi$
$54$		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	−0.394023	−	0.919101i	$-0.628917\pi$
$59$	271.438	−	470.145i	0.598953	−	1.03742i	0.992976	−	0.118317i	$-0.0377498\pi$
$60$		0			0
$61$	116.218	−	67.0983i	0.243937	−	0.140837i	−0.373048	−	0.927812i	$-0.621687\pi$
$61$	116.218	−	67.0983i	0.243937	−	0.140837i	0.616985	+	0.786975i	$0.288354\pi$
$62$	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	−0.974348	−	0.225048i	$-0.927746\pi$
$67$	−160.290	+	277.630i	−0.292276	+	0.506238i	0.682071	+	0.731286i	$0.261079\pi$
$68$	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	0.0708484	−	0.997487i	$-0.477429\pi$
$73$	−472.510	−	272.804i	−0.757577	−	0.437387i	−0.828425	+	0.560100i	$0.810763\pi$
$74$	−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	0.957753	−	0.287591i	$-0.0928545\pi$
$79$	161.369	+	279.499i	0.229815	+	0.398052i	−0.727938	+	0.685643i	$0.759521\pi$
$80$	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	$-0.300976\pi$
$83$	885.170			1.17060			0.585301	+	0.810816i	$0.300976\pi$
$84$		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	0.702826	+	0.711362i	$0.251921\pi$
$89$	812.312	+	1406.97i	0.967471	+	1.67571i	0.264645	+	0.964346i	$0.414745\pi$
$90$		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	$-0.873561\pi$
$97$		−	739.155i		−	0.773710i	0.922141	−	0.386855i	$-0.126439\pi$
$98$		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	$-0.795690\pi$
$101$	119.758	−	207.427i	0.117984	−	0.204354i	0.918969	+	0.394331i	$0.129024\pi$
$102$		0			0
$103$	44.2852	−	25.5681i	0.0423645	−	0.0244592i	−0.478668	−	0.877996i	$-0.658880\pi$
$103$	44.2852	−	25.5681i	0.0423645	−	0.0244592i	0.521033	+	0.853537i	$0.325547\pi$
$104$	−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	$-0.847496\pi$
$107$	−1031.43	+	595.495i	−0.931886	+	0.538025i	−0.0444785	+	0.999010i	$0.514163\pi$
$108$		0			0
$109$	−194.585	+	337.031i	−0.170989	+	0.296162i	−0.938766	−	0.344555i	$-0.888030\pi$
$109$	−194.585	+	337.031i	−0.170989	+	0.296162i	0.767777	+	0.640718i	$0.221363\pi$
$110$	−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	−0.908630	−	0.417601i	$-0.862871\pi$
$131$	−1223.43	−	2119.05i	−0.815968	−	1.41330i	0.0926619	−	0.995698i	$-0.470462\pi$
$132$		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	$-0.282342\pi$
$137$	443.021	+	255.778i	0.276276	+	0.159508i	−0.355460	+	0.934691i	$0.615676\pi$
$138$		0			0
$139$		−	599.427i		−	0.365775i	−0.983134	−	0.182888i	$-0.941456\pi$
$139$		−	599.427i		−	0.365775i	0.983134	−	0.182888i	$-0.0585444\pi$
$140$		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	$-0.872701\pi$
$149$	−1899.63	+	1096.75i	−1.04445	+	0.603016i	−0.123362	+	0.992362i	$0.539368\pi$
$150$		0			0
$151$	358.683	−	621.257i	0.193306	−	0.334816i	−0.753038	−	0.657977i	$-0.771412\pi$
$151$	358.683	−	621.257i	0.193306	−	0.334816i	0.946344	+	0.323161i	$0.104746\pi$
$152$	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	0.841268	−	0.540619i	$-0.181810\pi$
$157$	1561.39	+	901.471i	0.793712	+	0.458250i	−0.0475556	+	0.998869i	$0.515143\pi$
$158$	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	0.968938	+	0.247305i	$0.0795451\pi$
$163$	1453.90	+	2518.24i	0.698642	+	1.21008i	−0.270296	+	0.962777i	$0.587122\pi$
$164$	−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	$-0.200067\pi$
$167$	3491.37			1.61779			0.808893	+	0.587956i	$0.200067\pi$
$168$		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	$-0.292666\pi$
$173$	−877.377	−	1519.66i	−0.385583	−	0.667848i	−0.991850	+	0.127412i	$0.959333\pi$
$174$		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	$-0.280476\pi$
$179$	685.639	+	395.854i	0.286296	+	0.165293i	−0.349974	+	0.936759i	$0.613810\pi$
$180$		0			0
$181$			2522.19i			1.03576i	0.855452	+	0.517882i	$0.173279\pi$
$181$			2522.19i			1.03576i	−0.855452	+	0.517882i	$0.826721\pi$
$182$		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	$-0.611935\pi$
$191$	782.266	−	451.642i	0.296350	−	0.171098i	0.640802	+	0.767706i	$0.278602\pi$
$192$		0			0
$193$	99.4374	−	172.231i	0.0370863	−	0.0642354i	−0.846886	−	0.531774i	$-0.821526\pi$
$193$	99.4374	−	172.231i	0.0370863	−	0.0642354i	0.883973	+	0.467538i	$0.154859\pi$
$194$	−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	−0.00879944	−	0.999961i	$-0.502801\pi$
$199$	−2468.10	−	1424.96i	−0.879191	−	0.507601i	−0.870392	+	0.492360i	$0.836134\pi$
$200$	−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	$0.169301\pi$
$223$			3377.73i			1.01430i	−0.861857	+	0.507151i	$0.830699\pi$
$224$		0			0
$225$		0			0
$226$	−653.998	−	1132.76i	−0.192493	−	0.333407i
$227$	2261.98	−	3917.86i	0.661378	−	1.14554i	−0.318875	−	0.947797i	$-0.603305\pi$
$227$	2261.98	−	3917.86i	0.661378	−	1.14554i	0.980254	−	0.197744i	$-0.0633615\pi$
$228$		0			0
$229$	−3389.61	+	1956.99i	−0.978131	+	0.564724i	−0.901705	−	0.432351i	$-0.857684\pi$
$229$	−3389.61	+	1956.99i	−0.978131	+	0.564724i	−0.0764258	+	0.997075i	$0.524351\pi$
$230$	−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	$-0.877202\pi$
$233$	−3783.80	+	2184.58i	−1.06388	+	0.614234i	−0.137381	+	0.990518i	$0.543868\pi$
$234$		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	0.888530	−	0.458819i	$-0.151727\pi$
$241$	3499.81	+	2020.61i	0.935446	+	0.540080i	0.0469158	+	0.998899i	$0.485061\pi$
$242$	−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	$-0.687363\pi$
$251$	−4415.70			−1.11042			−0.555212	+	0.831709i	$0.687363\pi$
$252$		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	$-0.193647\pi$
$257$	−348.800	−	604.139i	−0.0846597	−	0.146635i	−0.905246	+	0.424888i	$0.860314\pi$
$258$		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	$-0.363136\pi$
$263$	−690.664	−	398.755i	−0.161932	−	0.0934915i	−0.578776	+	0.815487i	$0.696469\pi$
$264$		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	$-0.818512\pi$
$269$	205.351	−	355.679i	0.0465446	−	0.0806176i	0.888359	+	0.459149i	$0.151846\pi$
$270$		0			0
$271$	−3283.42	+	1895.69i	−0.735992	+	0.424925i	−0.820610	−	0.571488i	$-0.806366\pi$
$271$	−3283.42	+	1895.69i	−0.735992	+	0.424925i	0.0846182	+	0.996413i	$0.473033\pi$
$272$	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	−0.986619	−	0.163040i	$-0.947870\pi$
$277$	−1623.31	+	2811.66i	−0.352113	+	0.609877i	0.634507	+	0.772917i	$0.281203\pi$
$278$	−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	0.835034	−	0.550198i	$-0.185448\pi$
$283$	3694.70	+	2133.13i	0.776067	+	0.448062i	−0.0589678	+	0.998260i	$0.518781\pi$
$284$	−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	$-0.405752\pi$
$293$	2926.77			0.583562			0.291781	+	0.956485i	$0.405752\pi$
$294$		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	$-0.892288\pi$
$307$		−	3571.36i		−	0.663935i	0.943291	−	0.331968i	$-0.107712\pi$
$308$		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	$-0.757953\pi$
$311$	1286.71	−	2228.64i	0.234606	−	0.406349i	0.959158	+	0.282871i	$0.0912867\pi$
$312$		0			0
$313$	1278.56	−	738.176i	0.230889	−	0.133304i	−0.380093	−	0.924948i	$-0.624108\pi$
$313$	1278.56	−	738.176i	0.230889	−	0.133304i	0.610982	+	0.791644i	$0.290775\pi$
$314$	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	$-0.594802\pi$
$317$	2188.36	−	1263.45i	0.387730	−	0.223856i	0.681176	+	0.732120i	$0.261469\pi$
$318$		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	0.798245	−	0.602333i	$-0.205762\pi$
$331$	−737.778	−	1277.87i	−0.122513	−	0.212200i	−0.920758	+	0.390134i	$0.872429\pi$
$332$	−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	$-0.346588\pi$
$347$	−466.060	−	269.080i	−0.0721021	−	0.0416281i	−0.535618	+	0.844461i	$0.679921\pi$
$348$		0			0
$349$		−	6975.93i		−	1.06995i	−0.844867	−	0.534976i	$-0.820321\pi$
$349$		−	6975.93i		−	1.06995i	0.844867	−	0.534976i	$-0.179679\pi$
$350$		0			0
$351$		0			0
$352$	−872.678	−	1511.52i	−0.132142	−	0.228876i
$353$	4438.40	−	7687.53i	0.669213	−	1.15911i	−0.308912	−	0.951091i	$-0.599965\pi$
$353$	4438.40	−	7687.53i	0.669213	−	1.15911i	0.978125	−	0.208020i	$-0.0667019\pi$
$354$		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	$-0.365076\pi$
$359$	9565.96	−	5522.91i	1.40633	−	0.811944i	0.995032	+	0.0995575i	$0.0317427\pi$
$360$		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	−0.109868	−	0.993946i	$-0.535043\pi$
$367$	−7210.59	−	4163.04i	−1.02559	−	0.592122i	−0.915717	+	0.401824i	$0.868376\pi$
$368$	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	0.979539	−	0.201253i	$-0.0645014\pi$
$373$	2272.66	+	3936.36i	0.315479	+	0.546426i	−0.664060	+	0.747679i	$0.731168\pi$
$374$	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	$-0.250891\pi$
$383$	−1960.23	−	3395.22i	−0.261522	−	0.452970i	−0.966647	+	0.256114i	$0.917558\pi$
$384$		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	$-0.316805\pi$
$389$	689.734	+	398.218i	0.0898995	+	0.0519035i	−0.454376	+	0.890810i	$0.650138\pi$
$390$		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	−0.695960	−	0.718081i	$-0.745021\pi$
$397$	−3338.59	+	1927.54i	−0.422063	+	0.243678i	0.273896	+	0.961759i	$0.411687\pi$
$398$	−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	$-0.573054\pi$
$401$	4031.65	−	2327.68i	0.502073	−	0.289872i	0.729569	+	0.683907i	$0.239721\pi$
$402$		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	0.915566	−	0.402167i	$-0.131743\pi$
$409$	8478.82	+	4895.25i	1.02506	+	0.591821i	0.109497	+	0.993987i	$0.465076\pi$
$410$	−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	$-0.556098\pi$
$419$	−3007.46			−0.350654			−0.175327	+	0.984510i	$0.556098\pi$
$420$		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	$-0.649449\pi$
$431$	−12983.1	−	7495.81i	−1.45099	−	0.837727i	−0.998537	+	0.0540641i	$0.982782\pi$
$432$		0			0
$433$			5666.63i			0.628916i	0.949271	+	0.314458i	$0.101823\pi$
$433$			5666.63i			0.628916i	−0.949271	+	0.314458i	$0.898177\pi$
$434$		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	−0.216480	−	0.976287i	$-0.569458\pi$
$439$	4790.07	−	2765.55i	0.520769	−	0.300666i	0.737249	+	0.675621i	$0.236124\pi$
$440$	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	$-0.673550\pi$
$443$	−349.200	+	201.611i	−0.0374515	+	0.0216226i	0.481157	+	0.876634i	$0.340217\pi$
$444$		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	0.847946	−	0.530082i	$-0.177839\pi$
$457$	−342.830	−	593.799i	−0.0350917	−	0.0607807i	−0.883038	+	0.469302i	$0.844506\pi$
$458$	−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	$-0.420973\pi$
$461$	4864.48			0.491456			0.245728	+	0.969339i	$0.420973\pi$
$462$		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	$-0.150843\pi$
$467$	501.469	+	868.570i	0.0496900	+	0.0860656i	−0.840111	+	0.542415i	$0.817510\pi$
$468$		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	$-0.926550\pi$
$479$	−3026.38	+	5241.84i	−0.288682	+	0.500012i	0.684813	+	0.728719i	$0.259884\pi$
$480$		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	0.251753	+	0.967791i	$0.418993\pi$
$487$	−7654.72	+	13258.4i	−0.712255	+	1.23366i	−0.964009	+	0.265871i	$0.914340\pi$
$488$	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	0.669046	−	0.743221i	$-0.266703\pi$
$499$	−3445.77	−	5968.24i	−0.309126	−	0.535421i	−0.978171	+	0.207800i	$0.933370\pi$
$500$	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	$-0.704784\pi$
$503$	−13534.6			−1.19975			−0.599877	+	0.800092i	$0.704784\pi$
$504$		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	−0.999530	−	0.0306510i	$-0.990242\pi$
$509$	−6043.91	−	10468.4i	−0.526310	−	0.911595i	0.473221	−	0.880944i	$-0.343091\pi$
$510$		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	$-0.937228\pi$
$521$	−3812.94	+	6604.20i	−0.320629	+	0.555346i	0.659989	+	0.751275i	$0.270561\pi$
$522$		0			0
$523$	−13328.7	+	7695.34i	−1.11439	+	0.643392i	−0.939962	−	0.341279i	$-0.889140\pi$
$523$	−13328.7	+	7695.34i	−1.11439	+	0.643392i	−0.174425	+	0.984670i	$0.555807\pi$
$524$	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	0.998644	+	0.0520584i	$0.0165782\pi$
$541$	6850.44	+	11865.3i	0.544406	+	0.942939i	−0.454238	+	0.890880i	$0.650088\pi$
$542$	−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	$-0.000876098\pi$
$557$	19687.1	+	11366.4i	1.49761	+	0.864646i	0.497615	+	0.867398i	$0.334209\pi$
$558$		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	$-0.954389\pi$
$563$	−4958.81	+	8588.90i	−0.371206	+	0.642947i	0.618546	+	0.785749i	$0.287722\pi$
$564$		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	$-0.727269\pi$
$569$	−4448.79	+	2568.51i	−0.327773	+	0.189240i	0.327079	+	0.944997i	$0.393936\pi$
$570$		0			0
$571$	9093.02	−	15749.6i	0.666429	−	1.15429i	−0.312467	−	0.949929i	$-0.601155\pi$
$571$	9093.02	−	15749.6i	0.666429	−	1.15429i	0.978896	−	0.204360i	$-0.0655114\pi$
$572$	−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	0.0598401	−	0.998208i	$-0.480941\pi$
$577$	−10737.5	−	6199.32i	−0.774713	−	0.447281i	−0.834553	+	0.550927i	$0.814274\pi$
$578$	−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	$-0.732505\pi$
$587$	−18977.6			−1.33439			−0.667195	+	0.744883i	$0.732505\pi$
$588$		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	$-0.0455151\pi$
$593$	5364.44	+	9291.48i	0.371486	+	0.643432i	−0.618308	+	0.785936i	$0.712182\pi$
$594$		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	$-0.313547\pi$
$599$	1577.36	+	910.687i	0.107594	+	0.0621196i	−0.445237	+	0.895413i	$0.646881\pi$
$600$		0			0
$601$		−	18933.3i		−	1.28503i	−0.766273	−	0.642516i	$-0.777891\pi$
$601$		−	18933.3i		−	1.28503i	0.766273	−	0.642516i	$-0.222109\pi$
$602$		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	−0.874236	−	0.485501i	$-0.838637\pi$
$607$	−13323.3	+	7692.20i	−0.890898	+	0.514360i	−0.0166621	+	0.999861i	$0.505304\pi$
$608$	−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	−0.760937	−	0.648825i	$-0.775261\pi$
$613$	2753.60	−	4769.38i	0.181431	−	0.314247i	0.942368	+	0.334578i	$0.108594\pi$
$614$	−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	0.394276	−	0.918992i	$-0.370995\pi$
$619$	−3148.73	−	1817.92i	−0.204456	−	0.118043i	−0.598732	+	0.800949i	$0.704329\pi$
$620$	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	$-0.654465\pi$
$641$	−23786.7	−	13733.3i	−1.46571	−	0.846227i	−0.999265	+	0.0383236i	$0.987798\pi$
$642$		0			0
$643$		−	28474.0i		−	1.74635i	−0.487403	−	0.873177i	$-0.662056\pi$
$643$		−	28474.0i		−	1.74635i	0.487403	−	0.873177i	$-0.337944\pi$
$644$		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	$-0.820532\pi$
$647$	661.681	−	1146.06i	0.0402061	−	0.0696390i	0.885428	+	0.464776i	$0.153865\pi$
$648$		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	$-0.629895\pi$
$653$	3331.38	−	1923.37i	0.199643	−	0.115264i	0.596489	+	0.802621i	$0.296562\pi$
$654$		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	0.994413	+	0.105559i	$0.0336631\pi$
$661$	26902.5	+	15532.2i	1.58304	+	0.913966i	0.588623	+	0.808408i	$0.299670\pi$
$662$	−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	−0.861273	−	0.508142i	$-0.830332\pi$
$677$	−15337.4	−	26565.2i	−0.870701	−	1.50810i	−0.00942744	−	0.999956i	$-0.503001\pi$
$678$		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	$-0.498036\pi$
$683$	−15292.8	−	8829.33i	−0.856756	−	0.494648i	−0.862925	+	0.505333i	$0.831370\pi$
$684$		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	−0.779874	−	0.625937i	$-0.784717\pi$
$691$	−11402.3	+	6583.11i	−0.627733	+	0.362422i	0.152141	+	0.988359i	$0.451383\pi$
$692$	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	0.772021	−	0.635597i	$-0.219246\pi$
$709$	−3104.25	−	5376.71i	−0.164432	−	0.284805i	−0.936454	+	0.350792i	$0.885913\pi$
$710$	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	0.949800	+	0.312858i	$0.101287\pi$
$719$	14379.4	+	24905.9i	0.745843	+	1.29184i	−0.203957	+	0.978980i	$0.565380\pi$
$720$		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	$0.356284\pi$
$727$			35275.7i			1.79959i	−0.436312	+	0.899795i	$0.643716\pi$
$728$		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	−0.316395	−	0.948627i	$-0.602473\pi$
$733$	6885.15	−	3975.14i	0.346942	−	0.200307i	0.663338	+	0.748320i	$0.269139\pi$
$734$	−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	0.0678046	+	0.997699i	$0.478401\pi$
$739$	−16676.8	+	28885.1i	−0.830130	+	1.43783i	−0.897935	+	0.440129i	$0.854933\pi$
$740$	−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	0.715010	+	0.699114i	$0.246422\pi$
$751$	19818.3	+	34326.3i	0.962956	+	1.66789i	0.247945	+	0.968774i	$0.420245\pi$
$752$	−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	0.988567	+	0.150781i	$0.0481787\pi$
$761$	13117.8	+	22720.8i	0.624863	+	1.08230i	−0.363704	+	0.931515i	$0.618488\pi$
$762$		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	$0.326315\pi$
$769$			36456.9i			1.70958i	−0.518971	+	0.854792i	$0.673685\pi$
$770$		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	$-0.904009\pi$
$773$	−4732.74	+	8197.34i	−0.220213	+	0.381420i	0.734660	+	0.678436i	$0.237342\pi$
$774$		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	−0.0786582	−	0.996902i	$-0.525064\pi$
$787$	−21665.9	−	12508.8i	−0.981330	−	0.566571i	−0.902671	+	0.430331i	$0.858397\pi$
$788$	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	$-0.167768\pi$
$797$	38893.5			1.72858			0.864290	+	0.502994i	$0.167768\pi$
$798$		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	$-0.284646\pi$
$809$	6072.26	+	3505.82i	0.263893	+	0.152359i	−0.362216	+	0.932094i	$0.617980\pi$
$810$		0			0
$811$		−	5013.82i		−	0.217089i	−0.994092	−	0.108544i	$-0.965381\pi$
$811$		−	5013.82i		−	0.217089i	0.994092	−	0.108544i	$-0.0346189\pi$
$812$		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	$-0.661954\pi$
$821$	603.281	−	348.304i	0.0256451	−	0.0148062i	0.512768	+	0.858527i	$0.328620\pi$
$822$		0			0
$823$	−3206.57	+	5553.95i	−0.135813	+	0.235235i	−0.925908	−	0.377750i	$-0.876698\pi$
$823$	−3206.57	+	5553.95i	−0.135813	+	0.235235i	0.790095	+	0.612985i	$0.210031\pi$
$824$	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	0.740272	−	0.672307i	$-0.234697\pi$
$829$	12606.9	+	7278.59i	0.528173	+	0.304941i	−0.212099	+	0.977248i	$0.568030\pi$
$830$	−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	$-0.631171\pi$
$839$	−19467.0			−0.801045			−0.400523	+	0.916287i	$0.631171\pi$
$840$		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	$0.148031\pi$
$853$			22345.3i			0.896938i	−0.893798	+	0.448469i	$0.851969\pi$
$854$		0			0
$855$		0			0
$856$	−13752.1	−	23819.3i	−0.549107	−	0.951081i
$857$	−24039.8	+	41638.2i	−0.958209	+	1.65967i	−0.231363	+	0.972868i	$0.574318\pi$
$857$	−24039.8	+	41638.2i	−0.958209	+	1.65967i	−0.726847	+	0.686800i	$0.759015\pi$
$858$		0			0
$859$	22612.6	−	13055.4i	0.898173	−	0.518560i	0.0215659	−	0.999767i	$-0.493135\pi$
$859$	22612.6	−	13055.4i	0.898173	−	0.518560i	0.876607	+	0.481207i	$0.159801\pi$
$860$	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	$-0.685062\pi$
$863$	−2536.20	+	1464.27i	−0.100038	+	0.0577572i	0.449146	+	0.893458i	$0.351728\pi$
$864$		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	0.712064	−	0.702114i	$-0.247760\pi$
$877$	−6545.28	−	11336.8i	−0.252016	−	0.436505i	−0.964081	+	0.265609i	$0.914427\pi$
$878$	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	$-0.548198\pi$
$881$	−7888.79			−0.301680			−0.150840	+	0.988558i	$0.548198\pi$
$882$		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	$-0.145284\pi$
$887$	1773.29	+	3071.43i	0.0671266	+	0.116267i	−0.830509	+	0.557006i	$0.811950\pi$
$888$		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	−0.699825	−	0.714315i	$-0.746738\pi$
$907$	7339.77	−	12712.9i	0.268703	−	0.465406i	0.968527	+	0.248908i	$0.0800718\pi$
$908$	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	0.892262	−	0.451518i	$-0.149117\pi$
$919$	1535.18	+	2659.01i	0.0551044	+	0.0954437i	−0.837157	+	0.546962i	$0.815784\pi$
$920$	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	0.998954	+	0.0457316i	$0.0145619\pi$
$929$	15264.3	+	26438.6i	0.539082	+	0.933717i	−0.459872	+	0.887985i	$0.652105\pi$
$930$		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	$-0.897028\pi$
$937$		−	18235.1i		−	0.635769i	0.948129	−	0.317885i	$-0.102972\pi$
$938$		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	$-0.758928\pi$
$941$	6686.17	−	11580.8i	0.231629	−	0.401193i	0.958288	+	0.285806i	$0.0922611\pi$
$942$		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	$-0.638685\pi$
$947$	4431.54	−	2558.55i	0.152065	−	0.0877948i	0.574102	+	0.818784i	$0.305351\pi$
$948$		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	$-0.316044\pi$
$971$	−13683.8	−	23701.0i	−0.452248	−	0.783316i	−0.998525	+	0.0542881i	$0.982711\pi$
$972$		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	$-0.204238\pi$
$977$	20868.5	+	12048.4i	0.683359	+	0.394537i	−0.117761	+	0.993042i	$0.537572\pi$
$978$		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	$-0.785068\pi$
$983$	4655.36	−	8063.32i	0.151051	−	0.261628i	0.931614	+	0.363449i	$0.118401\pi$
$984$		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	−0.604434	−	0.796655i	$-0.706601\pi$
$991$	12095.2	−	20949.6i	0.387707	−	0.671528i	0.992141	+	0.125127i	$0.0399339\pi$
$992$	−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	−0.356877	−	0.934151i	$-0.616159\pi$
$997$	−42319.8	−	24433.4i	−1.34431	−	0.776140i	−0.987437	+	0.158011i	$0.949492\pi$
$998$	−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.80.6		16
3.2	odd	2	inner	441.4.p.c.80.3		16
7.2	even	3		63.4.p.a.26.3	yes	16
7.3	odd	6		441.4.c.a.440.11		16
7.4	even	3		441.4.c.a.440.12		16
7.5	odd	6	inner	441.4.p.c.215.3		16
7.6	odd	2		63.4.p.a.17.6	yes	16
21.2	odd	6		63.4.p.a.26.6	yes	16
21.5	even	6	inner	441.4.p.c.215.6		16
21.11	odd	6		441.4.c.a.440.5		16
21.17	even	6		441.4.c.a.440.6		16
21.20	even	2		63.4.p.a.17.3	✓	16
28.23	odd	6		1008.4.bt.a.593.1		16
28.27	even	2		1008.4.bt.a.17.8		16
84.23	even	6		1008.4.bt.a.593.8		16
84.83	odd	2		1008.4.bt.a.17.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.p.a.17.3	✓	16	21.20	even	2
63.4.p.a.17.6	yes	16	7.6	odd	2
63.4.p.a.26.3	yes	16	7.2	even	3
63.4.p.a.26.6	yes	16	21.2	odd	6
441.4.c.a.440.5		16	21.11	odd	6
441.4.c.a.440.6		16	21.17	even	6
441.4.c.a.440.11		16	7.3	odd	6
441.4.c.a.440.12		16	7.4	even	3
441.4.p.c.80.3		16	3.2	odd	2	inner
441.4.p.c.80.6		16	1.1	even	1	trivial
441.4.p.c.215.3		16	7.5	odd	6	inner
441.4.p.c.215.6		16	21.5	even	6	inner
1008.4.bt.a.17.1		16	84.83	odd	2
1008.4.bt.a.17.8		16	28.27	even	2
1008.4.bt.a.593.1		16	28.23	odd	6
1008.4.bt.a.593.8		16	84.23	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
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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