LMFDB - Embedded newform 441.4.p.c.215.4

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			215.4
Root			$-0.648633 - 0.374489i$ of defining polynomial
Character	$\chi$	$=$	441.215
Dual form			441.4.p.c.80.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.648633 - 0.374489i) q^{2} +(-3.71952 - 6.44239i) q^{4} +(5.42768 - 9.40102i) q^{5} +11.5635i q^{8} +O(q^{10})$	\(q+(-0.648633 - 0.374489i) q^{2} +(-3.71952 - 6.44239i) q^{4} +(5.42768 - 9.40102i) q^{5} +11.5635i q^{8} +(-7.04115 + 4.06521i) q^{10} +(-44.9131 + 25.9306i) q^{11} +32.1880i q^{13} +(-25.4257 + 44.0387i) q^{16} +(40.7324 + 70.5506i) q^{17} +(0.0420661 + 0.0242869i) q^{19} -80.7534 q^{20} +38.8428 q^{22} +(77.3322 + 44.6478i) q^{23} +(3.58060 + 6.20178i) q^{25} +(12.0540 - 20.8782i) q^{26} -175.246i q^{29} +(-186.238 + 107.524i) q^{31} +(113.098 - 65.2972i) q^{32} -61.0153i q^{34} +(-32.2729 + 55.8983i) q^{37} +(-0.0181903 - 0.0315065i) q^{38} +(108.708 + 62.7629i) q^{40} +411.485 q^{41} -234.771 q^{43} +(334.110 + 192.898i) q^{44} +(-33.4402 - 57.9201i) q^{46} +(316.076 - 547.460i) q^{47} -5.36357i q^{50} +(207.368 - 119.724i) q^{52} +(-230.049 + 132.819i) q^{53} +562.971i q^{55} +(-65.6275 + 113.670i) q^{58} +(175.530 + 304.026i) q^{59} +(673.827 + 389.034i) q^{61} +161.067 q^{62} +309.000 q^{64} +(302.600 + 174.706i) q^{65} +(98.0043 + 169.748i) q^{67} +(303.010 - 524.828i) q^{68} +142.632i q^{71} +(-676.261 + 390.439i) q^{73} +(41.8665 - 24.1716i) q^{74} -0.361341i q^{76} +(-644.525 + 1116.35i) q^{79} +(276.006 + 478.056i) q^{80} +(-266.903 - 154.097i) q^{82} -235.123 q^{83} +884.330 q^{85} +(152.280 + 87.9191i) q^{86} +(-299.848 - 519.351i) q^{88} +(-335.390 + 580.913i) q^{89} -664.273i q^{92} +(-410.035 + 236.734i) q^{94} +(0.456642 - 0.263642i) q^{95} -655.891i q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.648633	−	0.374489i	−0.229326	−	0.132402i	0.380935	−	0.924602i	$-0.375602\pi$
$2$	−0.648633	−	0.374489i	−0.229326	−	0.132402i	−0.610261	+	0.792200i	$0.708936\pi$
$3$		0			0
$3$		0			0
$4$	−3.71952	−	6.44239i	−0.464940	−	0.805299i
$5$	5.42768	−	9.40102i	0.485466	−	0.840852i	−0.514394	−	0.857554i	$-0.671983\pi$
$5$	5.42768	−	9.40102i	0.485466	−	0.840852i	0.999861	+	0.0167014i	$0.00531648\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$			11.5635i			0.511039i
$9$		0			0
$10$	−7.04115	+	4.06521i	−0.222661	+	0.128553i
$11$	−44.9131	+	25.9306i	−1.23107	+	0.710760i	−0.967254	−	0.253812i	$-0.918315\pi$
$11$	−44.9131	+	25.9306i	−1.23107	+	0.710760i	−0.263819	+	0.964572i	$0.584982\pi$
$12$		0			0
$13$			32.1880i			0.686719i	0.939204	+	0.343360i	$0.111565\pi$
$13$			32.1880i			0.686719i	−0.939204	+	0.343360i	$0.888435\pi$
$14$		0			0
$15$		0			0
$16$	−25.4257	+	44.0387i	−0.397277	+	0.688104i
$17$	40.7324	+	70.5506i	0.581121	+	1.00653i	0.995347	+	0.0963575i	$0.0307192\pi$
$17$	40.7324	+	70.5506i	0.581121	+	1.00653i	−0.414225	+	0.910174i	$0.635947\pi$
$18$		0			0
$19$	0.0420661	+	0.0242869i	0.000507927	+	0.000293252i	0.500254	−	0.865879i	$-0.333240\pi$
$19$	0.0420661	+	0.0242869i	0.000507927	+	0.000293252i	−0.499746	+	0.866172i	$0.666573\pi$
$20$	−80.7534			−0.902850
$21$		0			0
$22$	38.8428			0.376423
$23$	77.3322	+	44.6478i	0.701082	+	0.404770i	0.807750	−	0.589525i	$-0.200685\pi$
$23$	77.3322	+	44.6478i	0.701082	+	0.404770i	−0.106668	+	0.994295i	$0.534018\pi$
$24$		0			0
$25$	3.58060	+	6.20178i	0.0286448	+	0.0496142i
$26$	12.0540	−	20.8782i	0.0909228	−	0.157483i
$27$		0			0
$28$		0			0
$29$		−	175.246i		−	1.12215i	−0.827766	−	0.561074i	$-0.810388\pi$
$29$		−	175.246i		−	1.12215i	0.827766	−	0.561074i	$-0.189612\pi$
$30$		0			0
$31$	−186.238	+	107.524i	−1.07901	+	0.622966i	−0.930629	−	0.365964i	$-0.880739\pi$
$31$	−186.238	+	107.524i	−1.07901	+	0.622966i	−0.148380	+	0.988930i	$0.547406\pi$
$32$	113.098	−	65.2972i	0.624785	−	0.360720i
$33$		0			0
$34$		−	61.0153i		−	0.307766i
$35$		0			0
$36$		0			0
$37$	−32.2729	+	55.8983i	−0.143395	+	0.248368i	−0.928773	−	0.370649i	$-0.879135\pi$
$37$	−32.2729	+	55.8983i	−0.143395	+	0.248368i	0.785378	+	0.619017i	$0.212469\pi$
$38$	−0.0181903	−	0.0315065i	−7.76541e−5	−	0.000134501i
$39$		0			0
$40$	108.708	+	62.7629i	0.429708	+	0.248092i
$41$	411.485			1.56740			0.783698	−	0.621142i	$-0.213331\pi$
$41$	411.485			1.56740			0.783698	+	0.621142i	$0.213331\pi$
$42$		0			0
$43$	−234.771			−0.832611			−0.416305	−	0.909225i	$-0.636675\pi$
$43$	−234.771			−0.832611			−0.416305	+	0.909225i	$0.636675\pi$
$44$	334.110	+	192.898i	1.14475	+	0.660921i
$45$		0			0
$46$	−33.4402	−	57.9201i	−0.107184	−	0.185649i
$47$	316.076	−	547.460i	0.980946	−	1.69905i	0.322219	−	0.946665i	$-0.395571\pi$
$47$	316.076	−	547.460i	0.980946	−	1.69905i	0.658726	−	0.752382i	$-0.271095\pi$
$48$		0			0
$49$		0			0
$50$		−	5.36357i		−	0.0151705i
$51$		0			0
$52$	207.368	−	119.724i	0.553014	−	0.319283i
$53$	−230.049	+	132.819i	−0.596220	+	0.344228i	−0.767553	−	0.640985i	$-0.778526\pi$
$53$	−230.049	+	132.819i	−0.596220	+	0.344228i	0.171333	+	0.985213i	$0.445193\pi$
$54$		0			0
$55$			562.971i			1.38020i
$56$		0			0
$57$		0			0
$58$	−65.6275	+	113.670i	−0.148574	+	0.257338i
$59$	175.530	+	304.026i	0.387322	+	0.670862i	0.992088	−	0.125541i	$-0.0400667\pi$
$59$	175.530	+	304.026i	0.387322	+	0.670862i	−0.604766	+	0.796403i	$0.706733\pi$
$60$		0			0
$61$	673.827	+	389.034i	1.41434	+	0.816569i	0.995793	−	0.0916261i	$-0.0292065\pi$
$61$	673.827	+	389.034i	1.41434	+	0.816569i	0.418546	+	0.908196i	$0.362540\pi$
$62$	161.067			0.329927
$63$		0			0
$64$	309.000			0.603515
$65$	302.600	+	174.706i	0.577430	+	0.333379i
$66$		0			0
$67$	98.0043	+	169.748i	0.178703	+	0.309523i	0.941437	−	0.337190i	$-0.109476\pi$
$67$	98.0043	+	169.748i	0.178703	+	0.309523i	−0.762733	+	0.646713i	$0.776143\pi$
$68$	303.010	−	524.828i	0.540373	−	0.935953i
$69$		0			0
$70$		0			0
$71$			142.632i			0.238412i	0.992870	+	0.119206i	$0.0380349\pi$
$71$			142.632i			0.238412i	−0.992870	+	0.119206i	$0.961965\pi$
$72$		0			0
$73$	−676.261	+	390.439i	−1.08425	+	0.625993i	−0.932040	−	0.362355i	$-0.881973\pi$
$73$	−676.261	+	390.439i	−1.08425	+	0.625993i	−0.152211	+	0.988348i	$0.548639\pi$
$74$	41.8665	−	24.1716i	0.0657687	−	0.0379716i
$75$		0			0
$76$		−	0.361341i		−	0.000545378i
$77$		0			0
$78$		0			0
$79$	−644.525	+	1116.35i	−0.917908	+	1.58986i	−0.115320	+	0.993328i	$0.536789\pi$
$79$	−644.525	+	1116.35i	−0.917908	+	1.58986i	−0.802588	+	0.596534i	$0.796544\pi$
$80$	276.006	+	478.056i	0.385729	+	0.668103i
$81$		0			0
$82$	−266.903	−	154.097i	−0.359445	−	0.207526i
$83$	−235.123			−0.310940			−0.155470	−	0.987841i	$-0.549689\pi$
$83$	−235.123			−0.310940			−0.155470	+	0.987841i	$0.549689\pi$
$84$		0			0
$85$	884.330			1.12846
$86$	152.280	+	87.9191i	0.190940	+	0.110239i
$87$		0			0
$88$	−299.848	−	519.351i	−0.363226	−	0.629125i
$89$	−335.390	+	580.913i	−0.399453	+	0.691872i	−0.993658	−	0.112441i	$-0.964133\pi$
$89$	−335.390	+	580.913i	−0.399453	+	0.691872i	0.594206	+	0.804313i	$0.297466\pi$
$90$		0			0
$91$		0			0
$92$		−	664.273i		−	0.752774i
$93$		0			0
$94$	−410.035	+	236.734i	−0.449914	+	0.259758i
$95$	0.456642	−	0.263642i	0.000493163	−	0.000284728i
$96$		0			0
$97$		−	655.891i		−	0.686553i	−0.939234	−	0.343276i	$-0.888463\pi$
$97$		−	655.891i		−	0.686553i	0.939234	−	0.343276i	$-0.111537\pi$
$98$		0			0
$99$		0			0
$100$	26.6362	−	46.1352i	0.0266362	−	0.0461352i
$101$	581.618	+	1007.39i	0.573002	+	0.992468i	0.996256	+	0.0864572i	$0.0275546\pi$
$101$	581.618	+	1007.39i	0.573002	+	0.992468i	−0.423254	+	0.906011i	$0.639112\pi$
$102$		0			0
$103$	−22.8802	−	13.2099i	−0.0218879	−	0.0126370i	0.489016	−	0.872275i	$-0.337356\pi$
$103$	−22.8802	−	13.2099i	−0.0218879	−	0.0126370i	−0.510904	+	0.859638i	$0.670689\pi$
$104$	−372.206			−0.350940
$105$		0			0
$106$	198.957			0.182305
$107$	1270.53	+	733.538i	1.14791	+	0.662746i	0.948377	−	0.317145i	$-0.102724\pi$
$107$	1270.53	+	733.538i	1.14791	+	0.662746i	0.199532	+	0.979891i	$0.436058\pi$
$108$		0			0
$109$	67.5343	+	116.973i	0.0593450	+	0.102789i	0.894172	−	0.447724i	$-0.147765\pi$
$109$	67.5343	+	116.973i	0.0593450	+	0.102789i	−0.834827	+	0.550513i	$0.814432\pi$
$110$	210.826	−	365.162i	0.182741	−	0.316516i
$111$		0			0
$112$		0			0
$113$			288.471i			0.240151i	0.992765	+	0.120076i	$0.0383137\pi$
$113$			288.471i			0.240151i	−0.992765	+	0.120076i	$0.961686\pi$
$114$		0			0
$115$	839.469	−	484.668i	0.680703	−	0.393004i
$116$	−1129.00	+	651.829i	−0.903665	+	0.521731i
$117$		0			0
$118$		−	262.935i		−	0.205129i
$119$		0			0
$120$		0			0
$121$	679.288	−	1176.56i	0.510359	−	0.883969i
$122$	−291.378	−	504.681i	−0.216230	−	0.374522i
$123$		0			0
$124$	1385.43	+	799.877i	1.00335	+	0.579283i
$125$	1434.66			1.02656
$126$		0			0
$127$	−2269.80			−1.58592			−0.792961	−	0.609273i	$-0.791461\pi$
$127$	−2269.80			−1.58592			−0.792961	+	0.609273i	$0.791461\pi$
$128$	−1105.21	−	638.095i	−0.763187	−	0.440626i
$129$		0			0
$130$	−130.851	−	226.641i	−0.0882799	−	0.152905i
$131$	194.846	−	337.483i	0.129952	−	0.225084i	−0.793706	−	0.608302i	$-0.791851\pi$
$131$	194.846	−	337.483i	0.129952	−	0.225084i	0.923658	+	0.383218i	$0.125184\pi$
$132$		0			0
$133$		0			0
$134$		−	146.806i		−	0.0946425i
$135$		0			0
$136$	−815.811	+	471.009i	−0.514377	+	0.296975i
$137$	1271.93	−	734.347i	0.793197	−	0.457953i	−0.0478898	−	0.998853i	$-0.515250\pi$
$137$	1271.93	−	734.347i	0.793197	−	0.457953i	0.841087	+	0.540900i	$0.181916\pi$
$138$		0			0
$139$			624.712i			0.381204i	0.981667	+	0.190602i	$0.0610440\pi$
$139$			624.712i			0.381204i	−0.981667	+	0.190602i	$0.938956\pi$
$140$		0			0
$141$		0			0
$142$	53.4139	−	92.5156i	0.0315662	−	0.0546742i
$143$	−834.654	−	1445.66i	−0.488093	−	0.845401i
$144$		0			0
$145$	−1647.49	−	951.177i	−0.943561	−	0.544765i
$146$	584.860			0.331530
$147$		0			0
$148$	480.158			0.266681
$149$	−1387.25	−	800.930i	−0.762739	−	0.440367i	0.0675396	−	0.997717i	$-0.478485\pi$
$149$	−1387.25	−	800.930i	−0.762739	−	0.440367i	−0.830278	+	0.557349i	$0.811818\pi$
$150$		0			0
$151$	−202.188	−	350.200i	−0.108966	−	0.188734i	0.806386	−	0.591390i	$-0.201421\pi$
$151$	−202.188	−	350.200i	−0.108966	−	0.188734i	−0.915351	+	0.402656i	$0.868087\pi$
$152$	−0.280841	+	0.486430i	−0.000149863	+	0.000259570i
$153$		0			0
$154$		0			0
$155$			2334.43i			1.20972i
$156$		0			0
$157$	2088.91	−	1206.04i	1.06187	−	0.613071i	0.135921	−	0.990720i	$-0.456601\pi$
$157$	2088.91	−	1206.04i	1.06187	−	0.613071i	0.925949	+	0.377649i	$0.123267\pi$
$158$	836.120	−	482.734i	0.421001	−	0.243065i
$159$		0			0
$160$		−	1417.65i		−	0.700469i
$161$		0			0
$162$		0			0
$163$	472.684	−	818.712i	0.227138	−	0.393414i	−0.729821	−	0.683638i	$-0.760397\pi$
$163$	472.684	−	818.712i	0.227138	−	0.393414i	0.956959	+	0.290224i	$0.0937299\pi$
$164$	−1530.53	−	2650.95i	−0.728744	−	1.26222i
$165$		0			0
$166$	152.508	+	88.0507i	0.0713069	+	0.0411690i
$167$	−1271.18			−0.589022			−0.294511	−	0.955648i	$-0.595157\pi$
$167$	−1271.18			−0.589022			−0.294511	+	0.955648i	$0.595157\pi$
$168$		0			0
$169$	1160.93			0.528417
$170$	−573.606	−	331.172i	−0.258786	−	0.149410i
$171$		0			0
$172$	873.235	+	1512.49i	0.387114	+	0.670501i
$173$	−2217.49	+	3840.81i	−0.974525	+	1.68793i	−0.293032	+	0.956103i	$0.594664\pi$
$173$	−2217.49	+	3840.81i	−0.974525	+	1.68793i	−0.681493	+	0.731825i	$0.738669\pi$
$174$		0			0
$175$		0			0
$176$		−	2637.22i		−	1.12947i
$177$		0			0
$178$	435.090	−	251.200i	0.183210	−	0.105776i
$179$	941.835	−	543.769i	0.393274	−	0.227057i	−0.290304	−	0.956935i	$-0.593756\pi$
$179$	941.835	−	543.769i	0.393274	−	0.227057i	0.683578	+	0.729878i	$0.260423\pi$
$180$		0			0
$181$			2916.08i			1.19752i	0.800930	+	0.598758i	$0.204339\pi$
$181$			2916.08i			1.19752i	−0.800930	+	0.598758i	$0.795661\pi$
$182$		0			0
$183$		0			0
$184$	−516.284	+	894.230i	−0.206853	+	0.358280i
$185$	350.334	+	606.796i	0.139227	+	0.241149i
$186$		0			0
$187$	−3658.84	−	2112.43i	−1.43081	−	0.826076i
$188$	−4702.60			−1.82432
$189$		0			0
$190$	−0.394924			−0.000150794
$191$	−3948.97	−	2279.94i	−1.49601	−	0.863719i	−0.496017	−	0.868313i	$-0.665204\pi$
$191$	−3948.97	−	2279.94i	−1.49601	−	0.863719i	−0.999989	+	0.00459364i	$0.998538\pi$
$192$		0			0
$193$	1878.60	+	3253.83i	0.700645	+	1.21355i	0.968240	+	0.250022i	$0.0804378\pi$
$193$	1878.60	+	3253.83i	0.700645	+	1.21355i	−0.267595	+	0.963531i	$0.586229\pi$
$194$	−245.624	+	425.433i	−0.0909008	+	0.157445i
$195$		0			0
$196$		0			0
$197$			2014.34i			0.728507i	0.931300	+	0.364253i	$0.118676\pi$
$197$			2014.34i			0.728507i	−0.931300	+	0.364253i	$0.881324\pi$
$198$		0			0
$199$	−10.8355	+	6.25590i	−0.00385986	+	0.00222849i	−0.501929	−	0.864909i	$-0.667376\pi$
$199$	−10.8355	+	6.25590i	−0.00385986	+	0.00222849i	0.498069	+	0.867137i	$0.334043\pi$
$200$	−71.7141	+	41.4042i	−0.0253548	+	0.0146386i
$201$		0			0
$202$		−	871.238i		−	0.303466i
$203$		0			0
$204$		0			0
$205$	2233.41	−	3868.38i	0.760918	−	1.31795i
$206$	9.89391	+	17.1367i	0.00334632	+	0.00579599i
$207$		0			0
$208$	−1417.52	−	818.404i	−0.472534	−	0.272818i
$209$	−2.51909			−0.000833727
$210$		0			0
$211$	−2915.84			−0.951349			−0.475675	−	0.879621i	$-0.657796\pi$
$211$	−2915.84			−0.951349			−0.475675	+	0.879621i	$0.657796\pi$
$212$	1711.34	+	988.044i	0.554413	+	0.320090i
$213$		0			0
$214$	−549.403	−	951.594i	−0.175497	−	0.303970i
$215$	−1274.26	+	2207.09i	−0.404205	+	0.700103i
$216$		0			0
$217$		0			0
$218$		−	101.163i		−	0.0314295i
$219$		0			0
$220$	3626.88	−	2093.98i	1.11147	−	0.641710i
$221$	−2270.88	+	1311.10i	−0.691205	+	0.399067i
$222$		0			0
$223$		−	1097.87i		−	0.329681i	−0.986320	−	0.164841i	$-0.947289\pi$
$223$		−	1097.87i		−	0.329681i	0.986320	−	0.164841i	$-0.0527110\pi$
$224$		0			0
$225$		0			0
$226$	108.029	−	187.112i	0.0317964	−	0.0550731i
$227$	−250.297	−	433.527i	−0.0731841	−	0.126759i	0.827111	−	0.562039i	$-0.189983\pi$
$227$	−250.297	−	433.527i	−0.0731841	−	0.126759i	−0.900295	+	0.435280i	$0.856649\pi$
$228$		0			0
$229$	981.664	+	566.764i	0.283276	+	0.163549i	0.634906	−	0.772590i	$-0.281039\pi$
$229$	981.664	+	566.764i	0.283276	+	0.163549i	−0.351630	+	0.936139i	$0.614372\pi$
$230$	−726.010			−0.208138
$231$		0			0
$232$	2026.45			0.573461
$233$	−2975.12	−	1717.68i	−0.836508	−	0.482958i	0.0195676	−	0.999809i	$-0.493771\pi$
$233$	−2975.12	−	1717.68i	−0.836508	−	0.482958i	−0.856076	+	0.516850i	$0.827104\pi$
$234$		0			0
$235$	−3431.12	−	5942.87i	−0.952432	−	1.64966i
$236$	1305.77	−	2261.66i	0.360163	−	0.623821i
$237$		0			0
$238$		0			0
$239$			2213.97i			0.599203i	0.954064	+	0.299602i	$0.0968537\pi$
$239$			2213.97i			0.599203i	−0.954064	+	0.299602i	$0.903146\pi$
$240$		0			0
$241$	−5154.55	+	2975.98i	−1.37773	+	0.795435i	−0.991886	−	0.127128i	$-0.959424\pi$
$241$	−5154.55	+	2975.98i	−1.37773	+	0.795435i	−0.385847	+	0.922563i	$0.626091\pi$
$242$	−881.218	+	508.772i	−0.234078	+	0.135145i
$243$		0			0
$244$		−	5788.08i		−	1.51862i
$245$		0			0
$246$		0			0
$247$	−0.781746	+	1.35402i	−0.000201382	+	0.000348803i
$248$	−1243.36	−	2153.56i	−0.318360	−	0.551415i
$249$		0			0
$250$	−930.566	−	537.263i	−0.235417	−	0.135918i
$251$	4889.86			1.22966			0.614831	−	0.788659i	$-0.289224\pi$
$251$	4889.86			1.22966			0.614831	+	0.788659i	$0.289224\pi$
$252$		0			0
$253$	−4630.97			−1.15078
$254$	1472.27	+	850.013i	0.363694	+	0.209979i
$255$		0			0
$256$	−758.080	−	1313.03i	−0.185078	−	0.320565i
$257$	−1598.21	+	2768.18i	−0.387913	+	0.671884i	−0.992169	−	0.124906i	$-0.960137\pi$
$257$	−1598.21	+	2768.18i	−0.387913	+	0.671884i	0.604256	+	0.796790i	$0.293470\pi$
$258$		0			0
$259$		0			0
$260$		−	2599.29i		−	0.620005i
$261$		0			0
$262$	−252.767	+	145.935i	−0.0596030	+	0.0344118i
$263$	−648.189	+	374.232i	−0.151973	+	0.0877419i	−0.574058	−	0.818814i	$-0.694632\pi$
$263$	−648.189	+	374.232i	−0.151973	+	0.0877419i	0.422085	+	0.906556i	$0.361298\pi$
$264$		0			0
$265$			2883.59i			0.668444i
$266$		0			0
$267$		0			0
$268$	729.057	−	1262.76i	0.166173	−	0.287819i
$269$	−649.628	−	1125.19i	−0.147244	−	0.255033i	0.782964	−	0.622067i	$-0.213707\pi$
$269$	−649.628	−	1125.19i	−0.147244	−	0.255033i	−0.930208	+	0.367033i	$0.880373\pi$
$270$		0			0
$271$	−72.3660	−	41.7806i	−0.0162211	−	0.00936527i	0.491868	−	0.870670i	$-0.336314\pi$
$271$	−72.3660	−	41.7806i	−0.0162211	−	0.00936527i	−0.508089	+	0.861305i	$0.669648\pi$
$272$	−4142.61			−0.923465
$273$		0			0
$274$	−1100.02			−0.242535
$275$	−321.631	−	185.694i	−0.0705276	−	0.0407191i
$276$		0			0
$277$	2320.93	+	4019.97i	0.503434	+	0.871973i	0.999992	+	0.00396948i	$0.00126353\pi$
$277$	2320.93	+	4019.97i	0.503434	+	0.871973i	−0.496558	+	0.868003i	$0.665403\pi$
$278$	233.948	−	405.209i	0.0504721	−	0.0874202i
$279$		0			0
$280$		0			0
$281$		−	179.289i		−	0.0380622i	−0.999819	−	0.0190311i	$-0.993942\pi$
$281$		−	179.289i		−	0.0380622i	0.999819	−	0.0190311i	$-0.00605816\pi$
$282$		0			0
$283$	3506.14	−	2024.27i	0.736461	−	0.425196i	−0.0843205	−	0.996439i	$-0.526872\pi$
$283$	3506.14	−	2024.27i	0.736461	−	0.425196i	0.820781	+	0.571243i	$0.193539\pi$
$284$	918.889	−	530.521i	0.191993	−	0.110847i
$285$		0			0
$286$			1250.27i			0.258497i
$287$		0			0
$288$		0			0
$289$	−861.761	+	1492.61i	−0.175404	+	0.303809i
$290$	712.410	+	1233.93i	0.144256	+	0.249858i
$291$		0			0
$292$	5030.73	+	2904.49i	1.00822	+	0.582098i
$293$	3389.52			0.675828			0.337914	−	0.941177i	$-0.390279\pi$
$293$	3389.52			0.675828			0.337914	+	0.941177i	$0.390279\pi$
$294$		0			0
$295$	3810.88			0.752128
$296$	−646.379	−	373.187i	−0.126926	−	0.0732806i
$297$		0			0
$298$	599.878	+	1039.02i	0.116611	+	0.201976i
$299$	−1437.12	+	2489.17i	−0.277963	+	0.481446i
$300$		0			0
$301$		0			0
$302$			302.868i			0.0577089i
$303$		0			0
$304$	−2.13912	+	1.23502i	−0.000403576	+	0.000233005i
$305$	7314.63	−	4223.11i	1.37323	−	0.792834i
$306$		0			0
$307$		−	2014.64i		−	0.374534i	−0.982309	−	0.187267i	$-0.940037\pi$
$307$		−	2014.64i		−	0.374534i	0.982309	−	0.187267i	$-0.0599629\pi$
$308$		0			0
$309$		0			0
$310$	874.218	−	1514.19i	0.160169	−	0.277420i
$311$	2922.01	+	5061.07i	0.532772	+	0.922788i	0.999268	+	0.0382648i	$0.0121830\pi$
$311$	2922.01	+	5061.07i	0.532772	+	0.922788i	−0.466496	+	0.884524i	$0.654484\pi$
$312$		0			0
$313$	−2121.29	−	1224.73i	−0.383074	−	0.221168i	0.296081	−	0.955163i	$-0.404320\pi$
$313$	−2121.29	−	1224.73i	−0.383074	−	0.221168i	−0.679155	+	0.733995i	$0.737654\pi$
$314$	−1806.59			−0.324686
$315$		0			0
$316$	9589.28			1.70709
$317$	5303.24	+	3061.83i	0.939621	+	0.542490i	0.889842	−	0.456270i	$-0.150815\pi$
$317$	5303.24	+	3061.83i	0.939621	+	0.542490i	0.0497796	+	0.998760i	$0.484148\pi$
$318$		0			0
$319$	4544.22	+	7870.82i	0.797578	+	1.38145i
$320$	1677.15	−	2904.91i	0.292986	−	0.507467i
$321$		0			0
$322$		0			0
$323$			3.95705i			0.000681660i
$324$		0			0
$325$	−199.623	+	115.252i	−0.0340710	+	0.0196709i
$326$	−613.197	+	354.029i	−0.104177	+	0.0601468i
$327$		0			0
$328$			4758.20i			0.801000i
$329$		0			0
$330$		0			0
$331$	−3798.52	+	6579.23i	−0.630772	+	1.09253i	0.356622	+	0.934249i	$0.383928\pi$
$331$	−3798.52	+	6579.23i	−0.630772	+	1.09253i	−0.987394	+	0.158280i	$0.949405\pi$
$332$	874.542	+	1514.75i	0.144568	+	0.250400i
$333$		0			0
$334$	824.528	+	476.042i	0.135078	+	0.0779875i
$335$	2127.74			0.347018
$336$		0			0
$337$	−3863.22			−0.624460			−0.312230	−	0.950007i	$-0.601076\pi$
$337$	−3863.22			−0.624460			−0.312230	+	0.950007i	$0.601076\pi$
$338$	−753.019	−	434.756i	−0.121180	−	0.0699633i
$339$		0			0
$340$	−3289.28	−	5697.20i	−0.524666	−	0.908747i
$341$	5576.34	−	9658.50i	0.885559	−	1.53383i
$342$		0			0
$343$		0			0
$344$		−	2714.77i		−	0.425496i
$345$		0			0
$346$	2876.68	−	1660.85i	0.446969	−	0.258058i
$347$	−1579.98	+	912.204i	−0.244432	+	0.141123i	−0.617212	−	0.786797i	$-0.711738\pi$
$347$	−1579.98	+	912.204i	−0.244432	+	0.141123i	0.372780	+	0.927920i	$0.378405\pi$
$348$		0			0
$349$			1537.52i			0.235822i	0.993024	+	0.117911i	$0.0376197\pi$
$349$			1537.52i			0.235822i	−0.993024	+	0.117911i	$0.962380\pi$
$350$		0			0
$351$		0			0
$352$	−3386.39	+	5865.40i	−0.512770	+	0.888144i
$353$	−2963.66	−	5133.22i	−0.446855	−	0.773976i	0.551324	−	0.834291i	$-0.314123\pi$
$353$	−2963.66	−	5133.22i	−0.446855	−	0.773976i	−0.998179	+	0.0603149i	$0.980789\pi$
$354$		0			0
$355$	1340.88	+	774.159i	0.200469	+	0.115741i
$356$	4989.96			0.742885
$357$		0			0
$358$	−814.541			−0.120251
$359$	4191.12	+	2419.74i	0.616153	+	0.355736i	0.775370	−	0.631508i	$-0.217564\pi$
$359$	4191.12	+	2419.74i	0.616153	+	0.355736i	−0.159217	+	0.987244i	$0.550897\pi$
$360$		0			0
$361$	−3429.50	−	5940.07i	−0.500000	−	0.866025i
$362$	1092.04	−	1891.46i	0.158553	−	0.274622i
$363$		0			0
$364$		0			0
$365$			8476.72i			1.21559i
$366$		0			0
$367$	−9967.21	+	5754.57i	−1.41767	+	0.818491i	−0.996094	−	0.0883026i	$-0.971856\pi$
$367$	−9967.21	+	5754.57i	−1.41767	+	0.818491i	−0.421575	+	0.906794i	$0.638522\pi$
$368$	−3932.46	+	2270.41i	−0.557048	+	0.321612i
$369$		0			0
$370$		−	524.784i		−	0.0737357i
$371$		0			0
$372$		0			0
$373$	−93.7487	+	162.378i	−0.0130137	+	0.0225405i	−0.872459	−	0.488687i	$-0.837476\pi$
$373$	−93.7487	+	162.378i	−0.0130137	+	0.0225405i	0.859445	+	0.511228i	$0.170809\pi$
$374$	1582.16	+	2740.38i	0.218748	+	0.378882i
$375$		0			0
$376$	6330.54	+	3654.94i	0.868279	+	0.501301i
$377$	5640.81			0.770601
$378$		0			0
$379$	3515.82			0.476506			0.238253	−	0.971203i	$-0.423425\pi$
$379$	3515.82			0.476506			0.238253	+	0.971203i	$0.423425\pi$
$380$	−3.39698	−	1.96125i	−0.000458582	−	0.000264763i
$381$		0			0
$382$	1707.62	+	2957.69i	0.228716	+	0.396147i
$383$	1014.69	−	1757.49i	0.135374	−	0.234474i	−0.790366	−	0.612634i	$-0.790110\pi$
$383$	1014.69	−	1757.49i	0.135374	−	0.234474i	0.925740	+	0.378160i	$0.123443\pi$
$384$		0			0
$385$		0			0
$386$		−	2814.06i		−	0.371067i
$387$		0			0
$388$	−4225.51	+	2439.60i	−0.552880	+	0.319206i
$389$	−5577.15	+	3219.97i	−0.726923	+	0.419689i	−0.817295	−	0.576219i	$-0.804528\pi$
$389$	−5577.15	+	3219.97i	−0.726923	+	0.419689i	0.0903727	+	0.995908i	$0.471194\pi$
$390$		0			0
$391$			7274.45i			0.940882i
$392$		0			0
$393$		0			0
$394$	754.348	−	1306.57i	0.0964555	−	0.167066i
$395$	6996.55	+	12118.4i	0.891227	+	1.54365i
$396$		0			0
$397$	8369.80	+	4832.31i	1.05811	+	0.610898i	0.924908	−	0.380191i	$-0.124142\pi$
$397$	8369.80	+	4832.31i	1.05811	+	0.610898i	0.133199	+	0.991089i	$0.457475\pi$
$398$	9.37106			0.00118022
$399$		0			0
$400$	−364.157			−0.0455197
$401$	10186.9	+	5881.40i	1.26860	+	0.732426i	0.974723	−	0.223417i	$-0.0717212\pi$
$401$	10186.9	+	5881.40i	1.26860	+	0.732426i	0.293876	+	0.955843i	$0.405055\pi$
$402$		0			0
$403$	−3461.00	−	5994.62i	−0.427803	−	0.740976i
$404$	4326.68	−	7494.03i	0.532823	−	0.922876i
$405$		0			0
$406$		0			0
$407$		−	3347.42i		−	0.407679i
$408$		0			0
$409$	4565.71	−	2636.01i	0.551980	−	0.318686i	−0.197940	−	0.980214i	$-0.563425\pi$
$409$	4565.71	−	2636.01i	0.551980	−	0.318686i	0.749920	+	0.661528i	$0.230092\pi$
$410$	−2897.33	+	1672.77i	−0.348997	+	0.201494i
$411$		0			0
$412$			196.538i			0.0235017i
$413$		0			0
$414$		0			0
$415$	−1276.17	+	2210.39i	−0.150951	+	0.261455i
$416$	2101.79	+	3640.40i	0.247713	+	0.429052i
$417$		0			0
$418$	1.63396	+	0.943369i	0.000191196	+	0.000110387i
$419$	−5103.18			−0.595003			−0.297502	−	0.954721i	$-0.596153\pi$
$419$	−5103.18			−0.595003			−0.297502	+	0.954721i	$0.596153\pi$
$420$		0			0
$421$	−8395.31			−0.971882			−0.485941	−	0.873992i	$-0.661523\pi$
$421$	−8395.31			−0.971882			−0.485941	+	0.873992i	$0.661523\pi$
$422$	1891.31	+	1091.95i	0.218170	+	0.125960i
$423$		0			0
$424$	−1535.85	−	2660.17i	−0.175914	−	0.304691i
$425$	−291.693	+	505.227i	−0.0332922	+	0.0576638i
$426$		0			0
$427$		0			0
$428$		−	10913.6i		−	1.23255i
$429$		0			0
$430$	1653.06	−	954.394i	0.185390	−	0.107035i
$431$	−1808.68	+	1044.24i	−0.202137	+	0.116704i	−0.597652	−	0.801756i	$-0.703900\pi$
$431$	−1808.68	+	1044.24i	−0.202137	+	0.116704i	0.395515	+	0.918460i	$0.370566\pi$
$432$		0			0
$433$		−	11495.3i		−	1.27582i	−0.770111	−	0.637910i	$-0.779799\pi$
$433$		−	11495.3i		−	1.27582i	0.770111	−	0.637910i	$-0.220201\pi$
$434$		0			0
$435$		0			0
$436$	502.390	−	870.164i	0.0551837	−	0.0955810i
$437$	2.16871	+	3.75631i	0.000237399	+	0.000411187i
$438$		0			0
$439$	−3682.95	−	2126.35i	−0.400404	−	0.231173i	0.286254	−	0.958154i	$-0.407590\pi$
$439$	−3682.95	−	2126.35i	−0.400404	−	0.231173i	−0.686658	+	0.726980i	$0.740923\pi$
$440$	−6509.91			−0.705336
$441$		0			0
$442$	1963.96			0.211349
$443$	2862.03	+	1652.40i	0.306951	+	0.177218i	0.645561	−	0.763708i	$-0.276623\pi$
$443$	2862.03	+	1652.40i	0.306951	+	0.177218i	−0.338610	+	0.940927i	$0.609957\pi$
$444$		0			0
$445$	3640.78	+	6306.02i	0.387842	+	0.671761i
$446$	−411.140	+	712.116i	−0.0436503	+	0.0756046i
$447$		0			0
$448$		0			0
$449$		−	6952.63i		−	0.730768i	−0.930857	−	0.365384i	$-0.880938\pi$
$449$		−	6952.63i		−	0.730768i	0.930857	−	0.365384i	$-0.119062\pi$
$450$		0			0
$451$	−18481.1	+	10670.0i	−1.92958	+	1.11404i
$452$	1858.45	−	1072.97i	0.193394	−	0.111656i
$453$		0			0
$454$			374.933i			0.0387588i
$455$		0			0
$456$		0			0
$457$	−4870.57	+	8436.08i	−0.498546	+	0.863508i	−0.999999	−	0.00167767i	$-0.999466\pi$
$457$	−4870.57	+	8436.08i	−0.498546	+	0.863508i	0.501452	+	0.865185i	$0.332799\pi$
$458$	−424.493	−	735.244i	−0.0433085	−	0.0750124i
$459$		0			0
$460$	−6244.84	−	3605.46i	−0.632972	−	0.365447i
$461$	5563.15			0.562043			0.281021	−	0.959702i	$-0.409327\pi$
$461$	5563.15			0.562043			0.281021	+	0.959702i	$0.409327\pi$
$462$		0			0
$463$	4114.02			0.412948			0.206474	−	0.978452i	$-0.433801\pi$
$463$	4114.02			0.412948			0.206474	+	0.978452i	$0.433801\pi$
$464$	7717.59	+	4455.75i	0.772155	+	0.445804i
$465$		0			0
$466$	1286.51	+	2228.29i	0.127889	+	0.221510i
$467$	−3030.79	+	5249.49i	−0.300318	+	0.520166i	−0.976208	−	0.216837i	$-0.930426\pi$
$467$	−3030.79	+	5249.49i	−0.300318	+	0.520166i	0.675890	+	0.737002i	$0.263759\pi$
$468$		0			0
$469$		0			0
$470$			5139.66i			0.504415i
$471$		0			0
$472$	−3515.60	+	2029.73i	−0.342836	+	0.197937i
$473$	10544.3	−	6087.75i	1.02500	−	0.591787i
$474$		0			0
$475$			0.347846i			3.36005e-5i
$476$		0			0
$477$		0			0
$478$	829.105	−	1436.05i	0.0793355	−	0.137413i
$479$	4123.33	+	7141.82i	0.393319	+	0.681248i	0.992885	−	0.119077i	$-0.0379935\pi$
$479$	4123.33	+	7141.82i	0.393319	+	0.681248i	−0.599566	+	0.800325i	$0.704660\pi$
$480$		0			0
$481$	−1799.25	−	1038.80i	−0.170559	−	0.0984724i
$482$	4457.88			0.421268
$483$		0			0
$484$	−10106.5			−0.949145
$485$	−6166.04	−	3559.96i	−0.577290	−	0.333298i
$486$		0			0
$487$	−5872.08	−	10170.7i	−0.546385	−	0.946366i	−0.998518	−	0.0544159i	$-0.982670\pi$
$487$	−5872.08	−	10170.7i	−0.546385	−	0.946366i	0.452134	−	0.891950i	$-0.350663\pi$
$488$	−4498.59	+	7791.79i	−0.417298	+	0.722782i
$489$		0			0
$490$		0			0
$491$		−	6008.34i		−	0.552246i	−0.961122	−	0.276123i	$-0.910950\pi$
$491$		−	6008.34i		−	0.552246i	0.961122	−	0.276123i	$-0.0890497\pi$
$492$		0			0
$493$	12363.7	−	7138.18i	1.12948	−	0.652104i
$494$	1.01413	−	0.585510i	9.23643e−5	−	5.33266e-5i
$495$		0			0
$496$		−	10935.5i		−	0.989961i
$497$		0			0
$498$		0			0
$499$	6824.93	−	11821.1i	0.612276	−	1.06049i	−0.378580	−	0.925569i	$-0.623587\pi$
$499$	6824.93	−	11821.1i	0.612276	−	1.06049i	0.990856	−	0.134925i	$-0.0430792\pi$
$500$	−5336.23	−	9242.62i	−0.477287	−	0.826685i
$501$		0			0
$502$	−3171.72	−	1831.20i	−0.281994	−	0.162809i
$503$	−4862.69			−0.431047			−0.215524	−	0.976499i	$-0.569146\pi$
$503$	−4862.69			−0.431047			−0.215524	+	0.976499i	$0.569146\pi$
$504$		0			0
$505$	12627.4			1.11269
$506$	3003.80	+	1734.25i	0.263904	+	0.152365i
$507$		0			0
$508$	8442.55	+	14622.9i	0.737358	+	1.27714i
$509$	8861.33	−	15348.3i	0.771653	−	1.33654i	−0.165003	−	0.986293i	$-0.552763\pi$
$509$	8861.33	−	15348.3i	0.771653	−	1.33654i	0.936656	−	0.350250i	$-0.113903\pi$
$510$		0			0
$511$		0			0
$512$			11345.1i			0.979271i
$513$		0			0
$514$	2073.30	−	1197.02i	0.177917	−	0.102721i
$515$	−248.373	+	143.398i	−0.0212517	+	0.0122697i
$516$		0			0
$517$			32784.1i			2.78887i
$518$		0			0
$519$		0			0
$520$	−2020.21	+	3499.11i	−0.170370	+	0.295089i
$521$	−6877.95	−	11913.0i	−0.578366	−	1.00176i	−0.995667	−	0.0929909i	$-0.970357\pi$
$521$	−6877.95	−	11913.0i	−0.578366	−	1.00176i	0.417301	−	0.908768i	$-0.362976\pi$
$522$		0			0
$523$	−1136.17	−	655.971i	−0.0949932	−	0.0548443i	0.451751	−	0.892144i	$-0.350800\pi$
$523$	−1136.17	−	655.971i	−0.0949932	−	0.0548443i	−0.546744	+	0.837300i	$0.684133\pi$
$524$	−2898.93			−0.241680
$525$		0			0
$526$	560.582			0.0464687
$527$	−15171.8	−	8759.46i	−1.25407	−	0.724038i
$528$		0			0
$529$	−2096.65	−	3631.50i	−0.172323	−	0.298472i
$530$	1079.87	−	1870.39i	0.0885031	−	0.153292i
$531$		0			0
$532$		0			0
$533$			13244.9i			1.07636i
$534$		0			0
$535$	13792.0	−	7962.82i	1.11454	−	0.643482i
$536$	−1962.88	+	1133.27i	−0.158178	+	0.0913243i
$537$		0			0
$538$			973.114i			0.0779812i
$539$		0			0
$540$		0			0
$541$	−597.954	+	1035.69i	−0.0475195	+	0.0823061i	−0.888807	−	0.458282i	$-0.848465\pi$
$541$	−597.954	+	1035.69i	−0.0475195	+	0.0823061i	0.841287	+	0.540588i	$0.181798\pi$
$542$	31.2927	+	54.2005i	0.00247996	+	0.00429541i
$543$		0			0
$544$	9213.52	+	5319.43i	0.726152	+	0.419244i
$545$	1466.22			0.115240
$546$		0			0
$547$	−6178.59			−0.482957			−0.241478	−	0.970406i	$-0.577632\pi$
$547$	−6178.59			−0.482957			−0.241478	+	0.970406i	$0.577632\pi$
$548$	−9461.90	−	5462.83i	−0.737577	−	0.425841i
$549$		0			0
$550$	139.080	+	240.894i	0.0107826	+	0.0186759i
$551$	4.25617	−	7.37189i	0.000329072	−	0.000569970i
$552$		0			0
$553$		0			0
$554$		−	3476.65i		−	0.266622i
$555$		0			0
$556$	4024.64	−	2323.63i	0.306983	−	0.177237i
$557$	−2906.56	+	1678.10i	−0.221104	+	0.127654i	−0.606461	−	0.795113i	$-0.707411\pi$
$557$	−2906.56	+	1678.10i	−0.221104	+	0.127654i	0.385357	+	0.922767i	$0.374078\pi$
$558$		0			0
$559$		−	7556.82i		−	0.571770i
$560$		0			0
$561$		0			0
$562$	−67.1417	+	116.293i	−0.00503950	+	0.00872868i
$563$	−1792.64	−	3104.94i	−0.134193	−	0.232429i	0.791096	−	0.611692i	$-0.209511\pi$
$563$	−1792.64	−	3104.94i	−0.134193	−	0.232429i	−0.925289	+	0.379263i	$0.876178\pi$
$564$		0			0
$565$	2711.92	+	1565.73i	0.201932	+	0.116585i
$566$	−3032.26			−0.225187
$567$		0			0
$568$	−1649.32			−0.121838
$569$	−15835.9	−	9142.84i	−1.16674	−	0.673617i	−0.213829	−	0.976871i	$-0.568593\pi$
$569$	−15835.9	−	9142.84i	−1.16674	−	0.673617i	−0.952910	+	0.303254i	$0.901927\pi$
$570$		0			0
$571$	8181.51	+	14170.8i	0.599624	+	1.03858i	0.992876	+	0.119149i	$0.0380165\pi$
$571$	8181.51	+	14170.8i	0.599624	+	1.03858i	−0.393252	+	0.919431i	$0.628650\pi$
$572$	−6209.02	+	10754.3i	−0.453867	+	0.786121i
$573$		0			0
$574$		0			0
$575$			639.463i			0.0463782i
$576$		0			0
$577$	6678.26	−	3855.69i	0.481836	−	0.278188i	−0.239345	−	0.970935i	$-0.576933\pi$
$577$	6678.26	−	3855.69i	0.481836	−	0.278188i	0.721181	+	0.692746i	$0.243599\pi$
$578$	1117.93	−	645.439i	0.0804497	−	0.0464476i
$579$		0			0
$580$			14151.7i			1.01313i
$581$		0			0
$582$		0			0
$583$	6888.14	−	11930.6i	0.489327	−	0.847539i
$584$	−4514.84	−	7819.93i	−0.319906	−	0.554094i
$585$		0			0
$586$	−2198.55	−	1269.34i	−0.154985	−	0.0894808i
$587$	4182.21			0.294069			0.147034	−	0.989131i	$-0.453027\pi$
$587$	4182.21			0.294069			0.147034	+	0.989131i	$0.453027\pi$
$588$		0			0
$589$	−10.4457			−0.000730744
$590$	−2471.86	−	1427.13i	−0.172483	−	0.0995830i
$591$		0			0
$592$	−1641.12	−	2842.51i	−0.113935	−	0.197342i
$593$	−8094.65	+	14020.4i	−0.560552	+	0.970905i	0.436896	+	0.899512i	$0.356078\pi$
$593$	−8094.65	+	14020.4i	−0.560552	+	0.970905i	−0.997448	+	0.0713932i	$0.977256\pi$
$594$		0			0
$595$		0			0
$596$			11916.3i			0.818977i
$597$		0			0
$598$	1864.33	−	1076.37i	0.127489	−	0.0736056i
$599$	−11065.5	+	6388.67i	−0.754798	+	0.435783i	−0.827425	−	0.561576i	$-0.810195\pi$
$599$	−11065.5	+	6388.67i	−0.754798	+	0.435783i	0.0726267	+	0.997359i	$0.476862\pi$
$600$		0			0
$601$		−	24022.7i		−	1.63046i	−0.579137	−	0.815231i	$-0.696610\pi$
$601$		−	24022.7i		−	1.63046i	0.579137	−	0.815231i	$-0.303390\pi$
$602$		0			0
$603$		0			0
$604$	−1504.08	+	2605.15i	−0.101325	+	0.175500i
$605$	−7373.92	−	12772.0i	−0.495525	−	0.858274i
$606$		0			0
$607$	−8371.72	−	4833.42i	−0.559798	−	0.323200i	0.193266	−	0.981146i	$-0.438092\pi$
$607$	−8371.72	−	4833.42i	−0.559798	−	0.323200i	−0.753065	+	0.657947i	$0.771425\pi$
$608$	6.34346			0.000423127
$609$		0			0
$610$	−6326.02			−0.419890
$611$	17621.7	+	10173.9i	1.16677	+	0.673634i
$612$		0			0
$613$	−7192.73	−	12458.2i	−0.473918	−	0.820850i	0.525636	−	0.850710i	$-0.323827\pi$
$613$	−7192.73	−	12458.2i	−0.473918	−	0.820850i	−0.999554	+	0.0298593i	$0.990494\pi$
$614$	−754.461	+	1306.77i	−0.0495889	+	0.0858905i
$615$		0			0
$616$		0			0
$617$			7712.69i			0.503244i	0.967826	+	0.251622i	$0.0809639\pi$
$617$			7712.69i			0.503244i	−0.967826	+	0.251622i	$0.919036\pi$
$618$		0			0
$619$	−12398.9	+	7158.52i	−0.805096	+	0.464822i	−0.845250	−	0.534371i	$-0.820549\pi$
$619$	−12398.9	+	7158.52i	−0.805096	+	0.464822i	0.0401539	+	0.999194i	$0.487215\pi$
$620$	15039.3	−	8682.96i	0.974183	−	0.562445i
$621$		0			0
$622$		−	4377.04i		−	0.282160i
$623$		0			0
$624$		0			0
$625$	7339.28	−	12712.0i	0.469714	−	0.813569i
$626$	917.292	+	1588.80i	0.0585661	+	0.101439i
$627$		0			0
$628$	−15539.5	−	8971.73i	−0.987410	−	0.570082i
$629$	−5258.21			−0.333320
$630$		0			0
$631$	4971.96			0.313678			0.156839	−	0.987624i	$-0.449870\pi$
$631$	4971.96			0.313678			0.156839	+	0.987624i	$0.449870\pi$
$632$	−12908.9	−	7452.95i	−0.812481	−	0.469086i
$633$		0			0
$634$	−2293.24	−	3972.01i	−0.143653	−	0.248815i
$635$	−12319.7	+	21338.4i	−0.769911	+	1.33353i
$636$		0			0
$637$		0			0
$638$		−	6807.03i		−	0.422403i
$639$		0			0
$640$	−11997.5	+	6926.75i	−0.741003	+	0.427818i
$641$	25481.7	−	14711.9i	1.57015	−	0.906529i	0.574004	−	0.818852i	$-0.305389\pi$
$641$	25481.7	−	14711.9i	1.57015	−	0.906529i	0.996149	−	0.0876763i	$-0.0279441\pi$
$642$		0			0
$643$		−	31273.9i		−	1.91807i	−0.283283	−	0.959036i	$-0.591424\pi$
$643$		−	31273.9i		−	1.91807i	0.283283	−	0.959036i	$-0.408576\pi$
$644$		0			0
$645$		0			0
$646$	1.48187	−	2.56667i	9.02529e−5	−	0.000156323i
$647$	4005.82	+	6938.29i	0.243408	+	0.421595i	0.961683	−	0.274164i	$-0.0884012\pi$
$647$	4005.82	+	6938.29i	0.243408	+	0.421595i	−0.718275	+	0.695760i	$0.755068\pi$
$648$		0			0
$649$	−15767.2	−	9103.17i	−0.953644	−	0.550586i
$650$	172.643			0.0104179
$651$		0			0
$652$	−7032.62			−0.422421
$653$	−13372.0	−	7720.32i	−0.801357	−	0.462664i	0.0425886	−	0.999093i	$-0.486440\pi$
$653$	−13372.0	−	7720.32i	−0.801357	−	0.462664i	−0.843945	+	0.536429i	$0.819773\pi$
$654$		0			0
$655$	−2115.12	−	3663.50i	−0.126175	−	0.218542i
$656$	−10462.3	+	18121.3i	−0.622691	+	1.07853i
$657$		0			0
$658$		0			0
$659$		−	31288.9i		−	1.84953i	−0.380537	−	0.924766i	$-0.624261\pi$
$659$		−	31288.9i		−	1.84953i	0.380537	−	0.924766i	$-0.375739\pi$
$660$		0			0
$661$	26263.2	−	15163.1i	1.54541	−	0.892246i	0.546932	−	0.837177i	$-0.315795\pi$
$661$	26263.2	−	15163.1i	1.54541	−	0.892246i	0.998483	−	0.0550690i	$-0.0175379\pi$
$662$	4927.69	−	2845.00i	0.289305	−	0.167031i
$663$		0			0
$664$		−	2718.84i		−	0.158903i
$665$		0			0
$666$		0			0
$667$	7824.33	−	13552.1i	0.454212	−	0.786718i
$668$	4728.17	+	8189.42i	0.273860	+	0.474339i
$669$		0			0
$670$	−1380.12	−	796.815i	−0.0795804	−	0.0459458i
$671$	−40351.5			−2.32154
$672$		0			0
$673$	12067.9			0.691207			0.345604	−	0.938381i	$-0.387674\pi$
$673$	12067.9			0.691207			0.345604	+	0.938381i	$0.387674\pi$
$674$	2505.81	+	1446.73i	0.143205	+	0.0826795i
$675$		0			0
$676$	−4318.10	−	7479.18i	−0.245682	−	0.425533i
$677$	3272.41	−	5667.98i	0.185774	−	0.321770i	−0.758063	−	0.652181i	$-0.773854\pi$
$677$	3272.41	−	5667.98i	0.185774	−	0.321770i	0.943837	+	0.330411i	$0.107187\pi$
$678$		0			0
$679$		0			0
$680$			10225.9i			0.576686i
$681$		0			0
$682$	−7233.99	+	4176.55i	−0.406164	+	0.234499i
$683$	−27267.1	+	15742.7i	−1.52759	+	0.881956i	−0.528130	+	0.849163i	$0.677107\pi$
$683$	−27267.1	+	15742.7i	−1.52759	+	0.881956i	−0.999462	+	0.0327927i	$0.989560\pi$
$684$		0			0
$685$		−	15943.2i		−	0.889282i
$686$		0			0
$687$		0			0
$688$	5969.23	−	10339.0i	0.330777	−	0.572923i
$689$	−4275.18	−	7404.82i	−0.236388	−	0.409436i
$690$		0			0
$691$	8690.83	+	5017.66i	0.478459	+	0.276238i	0.719774	−	0.694209i	$-0.244245\pi$
$691$	8690.83	+	5017.66i	0.478459	+	0.276238i	−0.241315	+	0.970447i	$0.577579\pi$
$692$	32992.0			1.81238
$693$		0			0
$694$	1366.44			0.0747397
$695$	5872.93	+	3390.74i	0.320537	+	0.185062i
$696$		0			0
$697$	16760.8	+	29030.6i	0.910847	+	1.57763i
$698$	575.785	−	997.290i	0.0312232	−	0.0540802i
$699$		0			0
$700$		0			0
$701$		−	768.196i		−	0.0413900i	−0.999786	−	0.0206950i	$-0.993412\pi$
$701$		−	768.196i		−	0.0413900i	0.999786	−	0.0206950i	$-0.00658789\pi$
$702$		0			0
$703$	−2.71519	+	1.56761i	−0.000145669	+	8.41019e-5i
$704$	−13878.1	+	8012.53i	−0.742970	+	0.428954i
$705$		0			0
$706$			4439.43i			0.236658i
$707$		0			0
$708$		0			0
$709$	−6984.30	+	12097.2i	−0.369959	+	0.640787i	−0.989559	−	0.144130i	$-0.953962\pi$
$709$	−6984.30	+	12097.2i	−0.369959	+	0.640787i	0.619600	+	0.784918i	$0.287295\pi$
$710$	−579.827	−	1004.29i	−0.0306486	−	0.0530850i
$711$		0			0
$712$	−6717.38	−	3878.28i	−0.353573	−	0.204136i
$713$	−19202.9			−1.00863
$714$		0			0
$715$	−18120.9			−0.947810
$716$	−7006.34	−	4045.11i	−0.365697	−	0.211135i
$717$		0			0
$718$	−1812.33	−	3139.05i	−0.0942001	−	0.163159i
$719$	−5984.78	+	10365.9i	−0.310424	+	0.537669i	−0.978454	−	0.206465i	$-0.933804\pi$
$719$	−5984.78	+	10365.9i	−0.310424	+	0.537669i	0.668031	+	0.744134i	$0.267138\pi$
$720$		0			0
$721$		0			0
$722$			5137.23i			0.264803i
$723$		0			0
$724$	18786.5	−	10846.4i	0.964358	−	0.556772i
$725$	1086.83	−	627.484i	0.0556745	−	0.0321437i
$726$		0			0
$727$			12223.3i			0.623575i	0.950152	+	0.311787i	$0.100928\pi$
$727$			12223.3i			0.623575i	−0.950152	+	0.311787i	$0.899072\pi$
$728$		0			0
$729$		0			0
$730$	3174.43	−	5498.28i	0.160947	−	0.278768i
$731$	−9562.80	−	16563.3i	−0.483848	−	0.838049i
$732$		0			0
$733$	20598.5	+	11892.5i	1.03796	+	0.599264i	0.919253	−	0.393666i	$-0.128793\pi$
$733$	20598.5	+	11892.5i	1.03796	+	0.599264i	0.118702	+	0.992930i	$0.462127\pi$
$734$	8620.09			0.433478
$735$		0			0
$736$	11661.5			0.584034
$737$	−8803.34	−	5082.61i	−0.439994	−	0.254030i
$738$		0			0
$739$	−5739.04	−	9940.31i	−0.285675	−	0.494804i	0.687097	−	0.726565i	$-0.258885\pi$
$739$	−5739.04	−	9940.31i	−0.285675	−	0.494804i	−0.972773	+	0.231761i	$0.925551\pi$
$740$	2606.14	−	4513.97i	0.129465	−	0.224239i
$741$		0			0
$742$		0			0
$743$			18604.0i			0.918593i	0.888283	+	0.459297i	$0.151899\pi$
$743$			18604.0i			0.918593i	−0.888283	+	0.459297i	$0.848101\pi$
$744$		0			0
$745$	−15059.1	+	8694.38i	−0.740568	+	0.427567i
$746$	121.617	−	70.2157i	0.00596879	−	0.00344608i
$747$		0			0
$748$			31428.9i			1.53630i
$749$		0			0
$750$		0			0
$751$	−15506.2	+	26857.6i	−0.753436	+	1.30499i	0.192713	+	0.981255i	$0.438272\pi$
$751$	−15506.2	+	26857.6i	−0.753436	+	1.30499i	−0.946148	+	0.323734i	$0.895062\pi$
$752$	16072.9	+	27839.1i	0.779415	+	1.34999i
$753$		0			0
$754$	−3658.82	−	2112.42i	−0.176719	−	0.102029i
$755$	−4389.64			−0.211597
$756$		0			0
$757$	−19065.9			−0.915407			−0.457703	−	0.889105i	$-0.651328\pi$
$757$	−19065.9			−0.915407			−0.457703	+	0.889105i	$0.651328\pi$
$758$	−2280.48	−	1316.63i	−0.109275	−	0.0630901i
$759$		0			0
$760$	3.04863	+	5.28037i	0.000145507	+	0.000252025i
$761$	7339.58	−	12712.5i	0.349618	−	0.605556i	−0.636563	−	0.771224i	$-0.719645\pi$
$761$	7339.58	−	12712.5i	0.349618	−	0.605556i	0.986182	+	0.165668i	$0.0529780\pi$
$762$		0			0
$763$		0			0
$764$			33921.0i			1.60631i
$765$		0			0
$766$	−1316.32	+	759.979i	−0.0620896	+	0.0358475i
$767$	−9786.01	+	5649.95i	−0.460694	+	0.265982i
$768$		0			0
$769$			29972.5i			1.40551i	0.711434	+	0.702753i	$0.248046\pi$
$769$			29972.5i			1.40551i	−0.711434	+	0.702753i	$0.751954\pi$
$770$		0			0
$771$		0			0
$772$	13975.0	−	24205.3i	0.651515	−	1.12846i
$773$	−11343.9	−	19648.2i	−0.527828	−	0.914225i	−0.999474	−	0.0324367i	$-0.989673\pi$
$773$	−11343.9	−	19648.2i	−0.527828	−	0.914225i	0.471646	−	0.881788i	$-0.343660\pi$
$774$		0			0
$775$	−1333.68	−	770.003i	−0.0618159	−	0.0356894i
$776$	7584.38			0.350855
$777$		0			0
$778$	4823.37			0.222270
$779$	17.3096	+	9.99369i	0.000796123	+	0.000459642i
$780$		0			0
$781$	−3698.52	−	6406.02i	−0.169454	−	0.293503i
$782$	2724.20	−	4718.45i	0.124574	−	0.215769i
$783$		0			0
$784$		0			0
$785$		−	26183.9i		−	1.19050i
$786$		0			0
$787$	18132.8	−	10469.0i	0.821301	−	0.474178i	−0.0295639	−	0.999563i	$-0.509412\pi$
$787$	18132.8	−	10469.0i	0.821301	−	0.474178i	0.850865	+	0.525385i	$0.176079\pi$
$788$	12977.2	−	7492.37i	0.586666	−	0.338712i
$789$		0			0
$790$		−	10480.5i		−	0.472000i
$791$		0			0
$792$		0			0
$793$	−12522.2	+	21689.2i	−0.560754	+	0.971254i
$794$	−3619.29	−	6268.79i	−0.161768	−	0.280190i
$795$		0			0
$796$	80.6060	+	46.5379i	0.00358920	+	0.00207223i
$797$	27393.4			1.21747			0.608735	−	0.793373i	$-0.291677\pi$
$797$	27393.4			1.21747			0.608735	+	0.793373i	$0.291677\pi$
$798$		0			0
$799$	51498.2			2.28019
$800$	809.918	+	467.606i	0.0357936	+	0.0206655i
$801$		0			0
$802$	−4405.03	−	7629.74i	−0.193949	−	0.335929i
$803$	20248.6	−	35071.7i	0.889861	−	1.54128i
$804$		0			0
$805$		0			0
$806$			5184.41i			0.226567i
$807$		0			0
$808$	−11649.0	+	6725.53i	−0.507190	+	0.292826i
$809$	23214.2	−	13402.7i	1.00886	−	0.582465i	0.0980012	−	0.995186i	$-0.468755\pi$
$809$	23214.2	−	13402.7i	1.00886	−	0.582465i	0.910857	+	0.412722i	$0.135422\pi$
$810$		0			0
$811$		−	17139.6i		−	0.742113i	−0.928610	−	0.371056i	$-0.878996\pi$
$811$		−	17139.6i		−	0.742113i	0.928610	−	0.371056i	$-0.121004\pi$
$812$		0			0
$813$		0			0
$814$	−1253.57	+	2171.25i	−0.0539774	+	0.0934915i
$815$	−5131.15	−	8887.41i	−0.220535	−	0.381979i
$816$		0			0
$817$	−9.87590	−	5.70185i	−0.000422906	−	0.000244165i
$818$	−3948.63			−0.168778
$819$		0			0
$820$	−33228.8			−1.41512
$821$	7473.17	+	4314.64i	0.317680	+	0.183413i	0.650358	−	0.759628i	$-0.274619\pi$
$821$	7473.17	+	4314.64i	0.317680	+	0.183413i	−0.332678	+	0.943041i	$0.607952\pi$
$822$		0			0
$823$	2642.48	+	4576.91i	0.111921	+	0.193853i	0.916545	−	0.399932i	$-0.130966\pi$
$823$	2642.48	+	4576.91i	0.111921	+	0.193853i	−0.804624	+	0.593785i	$0.797633\pi$
$824$	152.752	−	264.575i	0.00645798	−	0.0111856i
$825$		0			0
$826$		0			0
$827$			1845.35i			0.0775926i	0.999247	+	0.0387963i	$0.0123523\pi$
$827$			1845.35i			0.0775926i	−0.999247	+	0.0387963i	$0.987648\pi$
$828$		0			0
$829$	−16881.6	+	9746.58i	−0.707263	+	0.408339i	−0.810047	−	0.586365i	$-0.800558\pi$
$829$	−16881.6	+	9746.58i	−0.707263	+	0.408339i	0.102784	+	0.994704i	$0.467225\pi$
$830$	1655.53	−	955.822i	0.0692342	−	0.0399724i
$831$		0			0
$832$			9946.08i			0.414445i
$833$		0			0
$834$		0			0
$835$	−6899.54	+	11950.4i	−0.285950	+	0.495281i
$836$	9.36979	+	16.2289i	0.000387633	+	0.000671399i
$837$		0			0
$838$	3310.09	+	1911.08i	0.136450	+	0.0787795i
$839$	−27816.7			−1.14462			−0.572312	−	0.820036i	$-0.693953\pi$
$839$	−27816.7			−1.14462			−0.572312	+	0.820036i	$0.693953\pi$
$840$		0			0
$841$	−6322.03			−0.259217
$842$	5445.48	+	3143.95i	0.222878	+	0.128679i
$843$		0			0
$844$	10845.5	+	18785.0i	0.442320	+	0.766121i
$845$	6301.16	−	10913.9i	0.256529	−	0.444320i
$846$		0			0
$847$		0			0
$848$		−	13508.1i		−	0.547015i
$849$		0			0
$850$	378.403	−	218.471i	0.0152696	−	0.00881588i
$851$	−4991.47	+	2881.83i	−0.201064	+	0.116084i
$852$		0			0
$853$			9210.41i			0.369705i	0.982766	+	0.184852i	$0.0591807\pi$
$853$			9210.41i			0.369705i	−0.982766	+	0.184852i	$0.940819\pi$
$854$		0			0
$855$		0			0
$856$	−8482.25	+	14691.7i	−0.338689	+	0.586626i
$857$	17250.5	+	29878.7i	0.687589	+	1.19094i	0.972615	+	0.232420i	$0.0746644\pi$
$857$	17250.5	+	29878.7i	0.687589	+	1.19094i	−0.285026	+	0.958520i	$0.592002\pi$
$858$		0			0
$859$	37843.6	+	21849.0i	1.50315	+	0.867845i	0.999993	+	0.00365004i	$0.00116185\pi$
$859$	37843.6	+	21849.0i	1.50315	+	0.867845i	0.503158	+	0.864195i	$0.332171\pi$
$860$	18958.6			0.751723
$861$		0			0
$862$	1564.23			0.0618072
$863$	24537.6	+	14166.8i	0.967869	+	0.558800i	0.898586	−	0.438797i	$-0.144595\pi$
$863$	24537.6	+	14166.8i	0.967869	+	0.558800i	0.0692834	+	0.997597i	$0.477929\pi$
$864$		0			0
$865$	24071.7	+	41693.4i	0.946199	+	1.63886i
$866$	−4304.86	+	7456.24i	−0.168921	+	0.292579i
$867$		0			0
$868$		0			0
$869$		−	66851.6i		−	2.60965i
$870$		0			0
$871$	−5463.86	+	3154.56i	−0.212556	+	0.122719i
$872$	−1352.61	+	780.931i	−0.0525290	+	0.0303276i
$873$		0			0
$874$		−	3.24863i		−	0.000125728i
$875$		0			0
$876$		0			0
$877$	22562.9	−	39080.1i	0.868751	−	1.50472i	0.00547715	−	0.999985i	$-0.498257\pi$
$877$	22562.9	−	39080.1i	0.868751	−	1.50472i	0.863274	−	0.504736i	$-0.168410\pi$
$878$	1592.59	+	2758.44i	0.0612155	+	0.106028i
$879$		0			0
$880$	−24792.5	−	14314.0i	−0.949722	−	0.548322i
$881$	4244.09			0.162301			0.0811504	−	0.996702i	$-0.474141\pi$
$881$	4244.09			0.162301			0.0811504	+	0.996702i	$0.474141\pi$
$882$		0			0
$883$	−21.9077			−0.000834939			−0.000417470	−	1.00000i	$-0.500133\pi$
$883$	−21.9077			−0.000834939			−0.000417470		1.00000i	$0.500133\pi$
$884$	16893.2	+	9753.29i	0.642737	+	0.371084i
$885$		0			0
$886$	−1237.61	−	2143.60i	−0.0469280	−	0.0812817i
$887$	−3750.82	+	6496.61i	−0.141984	+	0.245924i	−0.928244	−	0.371972i	$-0.878682\pi$
$887$	−3750.82	+	6496.61i	−0.141984	+	0.245924i	0.786259	+	0.617896i	$0.212015\pi$
$888$		0			0
$889$		0			0
$890$		−	5453.72i		−	0.205404i
$891$		0			0
$892$	−7072.92	+	4083.55i	−0.265492	+	0.153282i
$893$	26.5922	−	15.3530i	0.000996498	−	0.000575328i
$894$		0			0
$895$		−	11805.6i		−	0.440914i
$896$		0			0
$897$		0			0
$898$	−2603.68	+	4509.71i	−0.0967550	+	0.167584i
$899$	18843.2	+	32637.3i	0.699060	+	1.21081i
$900$		0			0
$901$	−18740.9	−	10820.1i	−0.692952	−	0.400076i
$902$	15983.2			0.590004
$903$		0			0
$904$	−3335.73			−0.122727
$905$	27414.1	+	15827.5i	1.00693	+	0.581354i
$906$		0			0
$907$	−20568.7	−	35626.0i	−0.753001	−	1.30424i	−0.946362	−	0.323108i	$-0.895272\pi$
$907$	−20568.7	−	35626.0i	−0.753001	−	1.30424i	0.193362	−	0.981128i	$-0.438061\pi$
$908$	−1861.97	+	3225.02i	−0.0680524	+	0.117870i
$909$		0			0
$910$		0			0
$911$			14080.6i			0.512086i	0.966665	+	0.256043i	$0.0824189\pi$
$911$			14080.6i			0.512086i	−0.966665	+	0.256043i	$0.917581\pi$
$912$		0			0
$913$	10560.1	−	6096.86i	0.382790	−	0.221004i
$914$	6318.43	−	3647.95i	0.228660	−	0.132017i
$915$		0			0
$916$		−	8432.35i		−	0.304162i
$917$		0			0
$918$		0			0
$919$	−6311.58	+	10932.0i	−0.226550	+	0.392397i	−0.956783	−	0.290801i	$-0.906078\pi$
$919$	−6311.58	+	10932.0i	−0.226550	+	0.392397i	0.730233	+	0.683198i	$0.239411\pi$
$920$	5604.45	+	9707.19i	0.200840	+	0.347866i
$921$		0			0
$922$	−3608.44	−	2083.34i	−0.128891	−	0.0744154i
$923$	−4591.03			−0.163722
$924$		0			0
$925$	−462.225			−0.0164301
$926$	−2668.49	−	1540.65i	−0.0946998	−	0.0546750i
$927$		0			0
$928$	−11443.1	−	19820.0i	−0.404781	−	0.701101i
$929$	16736.8	−	28989.1i	0.591085	−	1.02379i	−0.403002	−	0.915199i	$-0.632033\pi$
$929$	16736.8	−	28989.1i	0.591085	−	1.02379i	0.994087	−	0.108590i	$-0.0346336\pi$
$930$		0			0
$931$		0			0
$932$			25555.8i			0.898186i
$933$		0			0
$934$	3931.75	−	2270.00i	0.137742	−	0.0795252i
$935$	−39718.0	+	22931.2i	−1.38922	+	0.802064i
$936$		0			0
$937$			25652.3i			0.894371i	0.894441	+	0.447185i	$0.147574\pi$
$937$			25652.3i			0.894371i	−0.894441	+	0.447185i	$0.852426\pi$
$938$		0			0
$939$		0			0
$940$	−25524.2	+	44209.2i	−0.885647	+	1.53399i
$941$	−1301.48	−	2254.23i	−0.0450872	−	0.0780933i	0.842601	−	0.538538i	$-0.181023\pi$
$941$	−1301.48	−	2254.23i	−0.0450872	−	0.0780933i	−0.887688	+	0.460445i	$0.847690\pi$
$942$		0			0
$943$	31821.1	+	18371.9i	1.09887	+	0.634435i
$944$	−17851.9			−0.615497
$945$		0			0
$946$	−9119.17			−0.313414
$947$	32577.1	+	18808.4i	1.11786	+	0.645397i	0.940854	−	0.338813i	$-0.110025\pi$
$947$	32577.1	+	18808.4i	1.11786	+	0.645397i	0.177006	+	0.984210i	$0.443359\pi$
$948$		0			0
$949$	−12567.5	−	21767.5i	−0.429881	−	0.744576i
$950$	0.130264	−	0.225624i	4.44877e−6	−	7.70549e-6i
$951$		0			0
$952$		0			0
$953$		−	23444.5i		−	0.796896i	−0.917191	−	0.398448i	$-0.869549\pi$
$953$		−	23444.5i		−	0.796896i	0.917191	−	0.398448i	$-0.130451\pi$
$954$		0			0
$955$	−42867.4	+	24749.5i	−1.45252	+	0.838614i
$956$	14263.2	−	8234.88i	0.482538	−	0.278593i
$957$		0			0
$958$		−	6176.56i		−	0.208304i
$959$		0			0
$960$		0			0
$961$	8227.49	−	14250.4i	0.276174	−	0.478347i
$962$	778.037	+	1347.60i	0.0260758	+	0.0451646i
$963$		0			0
$964$	38344.9	+	22138.4i	1.28113	+	0.739658i
$965$	40785.7			1.36056
$966$		0			0
$967$	4312.24			0.143405			0.0717023	−	0.997426i	$-0.477157\pi$
$967$	4312.24			0.143405			0.0717023	+	0.997426i	$0.477157\pi$
$968$	13605.2	+	7854.94i	0.451742	+	0.260813i
$969$		0			0
$970$	2666.33	+	4618.22i	0.0882585	+	0.152868i
$971$	23526.3	−	40748.8i	0.777545	−	1.34675i	−0.155808	−	0.987787i	$-0.549798\pi$
$971$	23526.3	−	40748.8i	0.777545	−	1.34675i	0.933353	−	0.358960i	$-0.116869\pi$
$972$		0			0
$973$		0			0
$974$			8796.11i			0.289369i
$975$		0			0
$976$	−34265.1	+	19783.0i	−1.12377	+	0.648809i
$977$	−17721.5	+	10231.5i	−0.580308	+	0.335041i	−0.761256	−	0.648452i	$-0.775417\pi$
$977$	−17721.5	+	10231.5i	−0.580308	+	0.335041i	0.180948	+	0.983493i	$0.442084\pi$
$978$		0			0
$979$		−	34787.4i		−	1.13566i
$980$		0			0
$981$		0			0
$982$	−2250.06	+	3897.21i	−0.0731183	+	0.126645i
$983$	22314.5	+	38649.9i	0.724031	+	1.25406i	0.959372	+	0.282146i	$0.0910462\pi$
$983$	22314.5	+	38649.9i	0.724031	+	1.25406i	−0.235340	+	0.971913i	$0.575620\pi$
$984$		0			0
$985$	18936.9	+	10933.2i	0.612567	+	0.353666i
$986$	−10692.7			−0.345359
$987$		0			0
$988$	11.6309			0.000374521
$989$	−18155.4	−	10482.0i	−0.583729	−	0.337016i
$990$		0			0
$991$	−21565.5	−	37352.5i	−0.691272	−	1.19732i	−0.971421	−	0.237362i	$-0.923717\pi$
$991$	−21565.5	−	37352.5i	−0.691272	−	1.19732i	0.280149	−	0.959957i	$-0.409616\pi$
$992$	−14042.1	+	24321.6i	−0.449432	+	0.778439i
$993$		0			0
$994$		0			0
$995$			135.820i			0.00432743i
$996$		0			0
$997$	−3136.96	+	1811.13i	−0.0996475	+	0.0575315i	−0.548996	−	0.835825i	$-0.684990\pi$
$997$	−3136.96	+	1811.13i	−0.0996475	+	0.0575315i	0.449348	+	0.893357i	$0.351656\pi$
$998$	−8853.75	+	5111.72i	−0.280822	+	0.162133i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.4.p.c.215.4		16
3.2	odd	2	inner	441.4.p.c.215.5		16
7.2	even	3		441.4.c.a.440.9		16
7.3	odd	6	inner	441.4.p.c.80.5		16
7.4	even	3		63.4.p.a.17.5	yes	16
7.5	odd	6		441.4.c.a.440.10		16
7.6	odd	2		63.4.p.a.26.4	yes	16
21.2	odd	6		441.4.c.a.440.8		16
21.5	even	6		441.4.c.a.440.7		16
21.11	odd	6		63.4.p.a.17.4	✓	16
21.17	even	6	inner	441.4.p.c.80.4		16
21.20	even	2		63.4.p.a.26.5	yes	16
28.11	odd	6		1008.4.bt.a.17.6		16
28.27	even	2		1008.4.bt.a.593.3		16
84.11	even	6		1008.4.bt.a.17.3		16
84.83	odd	2		1008.4.bt.a.593.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.p.a.17.4	✓	16	21.11	odd	6
63.4.p.a.17.5	yes	16	7.4	even	3
63.4.p.a.26.4	yes	16	7.6	odd	2
63.4.p.a.26.5	yes	16	21.20	even	2
441.4.c.a.440.7		16	21.5	even	6
441.4.c.a.440.8		16	21.2	odd	6
441.4.c.a.440.9		16	7.2	even	3
441.4.c.a.440.10		16	7.5	odd	6
441.4.p.c.80.4		16	21.17	even	6	inner
441.4.p.c.80.5		16	7.3	odd	6	inner
441.4.p.c.215.4		16	1.1	even	1	trivial
441.4.p.c.215.5		16	3.2	odd	2	inner
1008.4.bt.a.17.3		16	84.11	even	6
1008.4.bt.a.17.6		16	28.11	odd	6
1008.4.bt.a.593.3		16	28.27	even	2
1008.4.bt.a.593.6		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)

\(f(q)\)	\(=\)	\(q+(-0.648633 - 0.374489i) q^{2} +(-3.71952 - 6.44239i) q^{4} +(5.42768 - 9.40102i) q^{5} +11.5635i q^{8} +O(q^{10})\)	\(q+(-0.648633 - 0.374489i) q^{2} +(-3.71952 - 6.44239i) q^{4} +(5.42768 - 9.40102i) q^{5} +11.5635i q^{8} +(-7.04115 + 4.06521i) q^{10} +(-44.9131 + 25.9306i) q^{11} +32.1880i q^{13} +(-25.4257 + 44.0387i) q^{16} +(40.7324 + 70.5506i) q^{17} +(0.0420661 + 0.0242869i) q^{19} -80.7534 q^{20} +38.8428 q^{22} +(77.3322 + 44.6478i) q^{23} +(3.58060 + 6.20178i) q^{25} +(12.0540 - 20.8782i) q^{26} -175.246i q^{29} +(-186.238 + 107.524i) q^{31} +(113.098 - 65.2972i) q^{32} -61.0153i q^{34} +(-32.2729 + 55.8983i) q^{37} +(-0.0181903 - 0.0315065i) q^{38} +(108.708 + 62.7629i) q^{40} +411.485 q^{41} -234.771 q^{43} +(334.110 + 192.898i) q^{44} +(-33.4402 - 57.9201i) q^{46} +(316.076 - 547.460i) q^{47} -5.36357i q^{50} +(207.368 - 119.724i) q^{52} +(-230.049 + 132.819i) q^{53} +562.971i q^{55} +(-65.6275 + 113.670i) q^{58} +(175.530 + 304.026i) q^{59} +(673.827 + 389.034i) q^{61} +161.067 q^{62} +309.000 q^{64} +(302.600 + 174.706i) q^{65} +(98.0043 + 169.748i) q^{67} +(303.010 - 524.828i) q^{68} +142.632i q^{71} +(-676.261 + 390.439i) q^{73} +(41.8665 - 24.1716i) q^{74} -0.361341i q^{76} +(-644.525 + 1116.35i) q^{79} +(276.006 + 478.056i) q^{80} +(-266.903 - 154.097i) q^{82} -235.123 q^{83} +884.330 q^{85} +(152.280 + 87.9191i) q^{86} +(-299.848 - 519.351i) q^{88} +(-335.390 + 580.913i) q^{89} -664.273i q^{92} +(-410.035 + 236.734i) q^{94} +(0.456642 - 0.263642i) q^{95} -655.891i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 32 q^{4}+O(q^{10}) \) 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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