LMFDB - Embedded newform 44.3.f.a.17.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [44,3,Mod(13,44)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("44.13"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(44, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 44 = 2^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	44.f (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.19891316319$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 19x^{6} - 37x^{5} + 229x^{4} + 196x^{3} + 1496x^{2} + 2952x + 26896 $ x^8 - x^7 + 19x^6 - 37x^5 + 229x^4 + 196x^3 + 1496x^2 + 2952x + 26896
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			17.1
Root			$-1.37056 + 4.21816i$ of defining polynomial
Character	$\chi$	$=$	44.17
Dual form			44.3.f.a.13.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.08818 - 2.97024i) q^{3} +(1.46509 - 4.50908i) q^{5} +(-3.91877 - 5.39373i) q^{7} +(5.10976 + 15.7262i) q^{9} +(6.32112 + 9.00241i) q^{11} +(14.3229 - 4.65378i) q^{13} +(-19.3826 + 14.0823i) q^{15} +(-16.9976 - 5.52287i) q^{17} +(19.0249 - 26.1855i) q^{19} +33.6902i q^{21} -3.58879 q^{23} +(2.04012 + 1.48224i) q^{25} +(11.7671 - 36.2153i) q^{27} +(-7.50529 - 10.3301i) q^{29} +(6.76473 + 20.8197i) q^{31} +(0.897408 - 55.5787i) q^{33} +(-30.0621 + 9.76777i) q^{35} +(22.4250 - 16.2927i) q^{37} +(-72.3773 - 23.5168i) q^{39} +(-29.1270 + 40.0899i) q^{41} +16.8760i q^{43} +78.3970 q^{45} +(63.0835 + 45.8328i) q^{47} +(1.40631 - 4.32817i) q^{49} +(53.0852 + 73.0655i) q^{51} +(3.06043 + 9.41904i) q^{53} +(49.8536 - 15.3131i) q^{55} +(-155.554 + 50.5426i) q^{57} +(-29.6620 + 21.5507i) q^{59} +(-26.9171 - 8.74590i) q^{61} +(64.7990 - 89.1881i) q^{63} -71.4011i q^{65} -30.7234 q^{67} +(14.6716 + 10.6595i) q^{69} +(-12.6835 + 39.0359i) q^{71} +(-36.3001 - 49.9628i) q^{73} +(-3.93780 - 12.1193i) q^{75} +(23.7855 - 69.3728i) q^{77} +(118.204 - 38.4068i) q^{79} +(-35.2762 + 25.6296i) q^{81} +(-2.94344 - 0.956381i) q^{83} +(-49.8061 + 68.5522i) q^{85} +64.5240i q^{87} +60.4914 q^{89} +(-81.2293 - 59.0165i) q^{91} +(34.1840 - 105.207i) q^{93} +(-90.1993 - 124.149i) q^{95} +(14.8226 + 45.6193i) q^{97} +(-109.274 + 145.407i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 5 q^{3} - q^{5} + 15 q^{7} - q^{9} + 17 q^{11} - 15 q^{13} - 63 q^{15} - 75 q^{17} - 30 q^{19} + 100 q^{23} + 51 q^{25} + 100 q^{27} + 125 q^{29} + 73 q^{31} - 20 q^{33} - 155 q^{35} - 75 q^{37}+ \cdots - 419 q^{99}+O(q^{100}) $ 8 * q - 5 * q^3 - q^5 + 15 * q^7 - q^9 + 17 * q^11 - 15 * q^13 - 63 * q^15 - 75 * q^17 - 30 * q^19 + 100 * q^23 + 51 * q^25 + 100 * q^27 + 125 * q^29 + 73 * q^31 - 20 * q^33 - 155 * q^35 - 75 * q^37 - 185 * q^39 - 155 * q^41 + 332 * q^45 + 45 * q^47 + 87 * q^49 + 150 * q^51 - 85 * q^53 - 89 * q^55 - 310 * q^57 - 178 * q^59 - 145 * q^61 - 110 * q^63 + 10 * q^67 + 124 * q^69 + 207 * q^71 + 65 * q^73 + 192 * q^75 + 365 * q^77 + 235 * q^79 - 12 * q^81 + 210 * q^83 + 105 * q^85 + 18 * q^89 - 195 * q^91 - 335 * q^93 - 255 * q^95 - 90 * q^97 - 419 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/44\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$1$

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			0
$2$		0			0
$3$	−4.08818	−	2.97024i	−1.36273	−	0.990079i	−0.998266	−	0.0588599i	$-0.981253\pi$
$3$	−4.08818	−	2.97024i	−1.36273	−	0.990079i	−0.364460	−	0.931219i	$-0.618747\pi$
$4$		0			0
$5$	1.46509	−	4.50908i	0.293018	−	0.901816i	−0.690862	−	0.722986i	$-0.742769\pi$
$5$	1.46509	−	4.50908i	0.293018	−	0.901816i	0.983880	−	0.178829i	$-0.0572310\pi$
$6$		0			0
$7$	−3.91877	−	5.39373i	−0.559825	−	0.770533i	0.431479	−	0.902123i	$-0.357992\pi$
$7$	−3.91877	−	5.39373i	−0.559825	−	0.770533i	−0.991304	+	0.131590i	$0.957992\pi$
$8$		0			0
$9$	5.10976	+	15.7262i	0.567751	+	1.74736i
$10$		0			0
$11$	6.32112	+	9.00241i	0.574647	+	0.818401i
$11$	6.32112	+	9.00241i	0.574647	+	0.818401i
$12$		0			0
$13$	14.3229	−	4.65378i	1.10176	−	0.357983i	0.298980	−	0.954260i	$-0.403354\pi$
$13$	14.3229	−	4.65378i	1.10176	−	0.357983i	0.802779	+	0.596276i	$0.203354\pi$
$14$		0			0
$15$	−19.3826	+	14.0823i	−1.29217	+	0.938818i
$16$		0			0
$17$	−16.9976	−	5.52287i	−0.999861	−	0.324874i	−0.237051	−	0.971497i	$-0.576181\pi$
$17$	−16.9976	−	5.52287i	−0.999861	−	0.324874i	−0.762810	+	0.646623i	$0.776181\pi$
$18$		0			0
$19$	19.0249	−	26.1855i	1.00131	−	1.37818i	0.0767906	−	0.997047i	$-0.475533\pi$
$19$	19.0249	−	26.1855i	1.00131	−	1.37818i	0.924519	−	0.381137i	$-0.124467\pi$
$20$		0			0
$21$			33.6902i			1.60430i
$22$		0			0
$23$	−3.58879			−0.156034			−0.0780171	−	0.996952i	$-0.524859\pi$
$23$	−3.58879			−0.156034			−0.0780171	+	0.996952i	$0.524859\pi$
$24$		0			0
$25$	2.04012	+	1.48224i	0.0816049	+	0.0592894i
$26$		0			0
$27$	11.7671	−	36.2153i	0.435817	−	1.34131i
$28$		0			0
$29$	−7.50529	−	10.3301i	−0.258803	−	0.356212i	0.659767	−	0.751470i	$-0.270655\pi$
$29$	−7.50529	−	10.3301i	−0.258803	−	0.356212i	−0.918570	+	0.395258i	$0.870655\pi$
$30$		0			0
$31$	6.76473	+	20.8197i	0.218217	+	0.671603i	0.998910	+	0.0466876i	$0.0148665\pi$
$31$	6.76473	+	20.8197i	0.218217	+	0.671603i	−0.780692	+	0.624915i	$0.785133\pi$
$32$		0			0
$33$	0.897408	−	55.5787i	0.0271942	−	1.68420i
$34$		0			0
$35$	−30.0621	+	9.76777i	−0.858917	+	0.279079i
$36$		0			0
$37$	22.4250	−	16.2927i	0.606082	−	0.440345i	−0.241950	−	0.970289i	$-0.577787\pi$
$37$	22.4250	−	16.2927i	0.606082	−	0.440345i	0.848033	+	0.529944i	$0.177787\pi$
$38$		0			0
$39$	−72.3773	−	23.5168i	−1.85583	−	0.602995i
$40$		0			0
$41$	−29.1270	+	40.0899i	−0.710416	+	0.977803i	0.289372	+	0.957217i	$0.406553\pi$
$41$	−29.1270	+	40.0899i	−0.710416	+	0.977803i	−0.999788	+	0.0205868i	$0.993447\pi$
$42$		0			0
$43$			16.8760i			0.392466i	0.980557	+	0.196233i	$0.0628708\pi$
$43$			16.8760i			0.392466i	−0.980557	+	0.196233i	$0.937129\pi$
$44$		0			0
$45$	78.3970			1.74215
$46$		0			0
$47$	63.0835	+	45.8328i	1.34220	+	0.975166i	0.999360	+	0.0357732i	$0.0113894\pi$
$47$	63.0835	+	45.8328i	1.34220	+	0.975166i	0.342842	+	0.939393i	$0.388611\pi$
$48$		0			0
$49$	1.40631	−	4.32817i	0.0287001	−	0.0883299i
$50$		0			0
$51$	53.0852	+	73.0655i	1.04089	+	1.43266i
$52$		0			0
$53$	3.06043	+	9.41904i	0.0577440	+	0.177718i	0.975768	−	0.218806i	$-0.0702163\pi$
$53$	3.06043	+	9.41904i	0.0577440	+	0.177718i	−0.918024	+	0.396524i	$0.870216\pi$
$54$		0			0
$55$	49.8536	−	15.3131i	0.906429	−	0.278420i
$56$		0			0
$57$	−155.554	+	50.5426i	−2.72902	+	0.886713i
$58$		0			0
$59$	−29.6620	+	21.5507i	−0.502746	+	0.365267i	−0.810065	−	0.586340i	$-0.800568\pi$
$59$	−29.6620	+	21.5507i	−0.502746	+	0.365267i	0.307319	+	0.951607i	$0.400568\pi$
$60$		0			0
$61$	−26.9171	−	8.74590i	−0.441264	−	0.143375i	0.0799547	−	0.996799i	$-0.474522\pi$
$61$	−26.9171	−	8.74590i	−0.441264	−	0.143375i	−0.521219	+	0.853423i	$0.674522\pi$
$62$		0			0
$63$	64.7990	−	89.1881i	1.02855	−	1.41568i
$64$		0			0
$65$		−	71.4011i		−	1.09848i
$66$		0			0
$67$	−30.7234			−0.458558			−0.229279	−	0.973361i	$-0.573637\pi$
$67$	−30.7234			−0.458558			−0.229279	+	0.973361i	$0.573637\pi$
$68$		0			0
$69$	14.6716	+	10.6595i	0.212632	+	0.154486i
$70$		0			0
$71$	−12.6835	+	39.0359i	−0.178641	+	0.549802i	−0.999781	−	0.0209255i	$-0.993339\pi$
$71$	−12.6835	+	39.0359i	−0.178641	+	0.549802i	0.821140	+	0.570727i	$0.193339\pi$
$72$		0			0
$73$	−36.3001	−	49.9628i	−0.497261	−	0.684422i	0.484445	−	0.874822i	$-0.339021\pi$
$73$	−36.3001	−	49.9628i	−0.497261	−	0.684422i	−0.981707	+	0.190400i	$0.939021\pi$
$74$		0			0
$75$	−3.93780	−	12.1193i	−0.0525039	−	0.161591i
$76$		0			0
$77$	23.7855	−	69.3728i	0.308903	−	0.900946i
$78$		0			0
$79$	118.204	−	38.4068i	1.49625	−	0.486161i	0.557329	−	0.830292i	$-0.311826\pi$
$79$	118.204	−	38.4068i	1.49625	−	0.486161i	0.938922	+	0.344130i	$0.111826\pi$
$80$		0			0
$81$	−35.2762	+	25.6296i	−0.435508	+	0.316415i
$82$		0			0
$83$	−2.94344	−	0.956381i	−0.0354631	−	0.0115227i	0.291232	−	0.956653i	$-0.405935\pi$
$83$	−2.94344	−	0.956381i	−0.0354631	−	0.0115227i	−0.326695	+	0.945130i	$0.605935\pi$
$84$		0			0
$85$	−49.8061	+	68.5522i	−0.585954	+	0.806496i
$86$		0			0
$87$			64.5240i			0.741655i
$88$		0			0
$89$	60.4914			0.679678			0.339839	−	0.940484i	$-0.389627\pi$
$89$	60.4914			0.679678			0.339839	+	0.940484i	$0.389627\pi$
$90$		0			0
$91$	−81.2293	−	59.0165i	−0.892630	−	0.648533i
$92$		0			0
$93$	34.1840	−	105.207i	0.367570	−	1.13126i
$94$		0			0
$95$	−90.1993	−	124.149i	−0.949467	−	1.30683i
$96$		0			0
$97$	14.8226	+	45.6193i	0.152810	+	0.470302i	0.997932	−	0.0642712i	$-0.0204723\pi$
$97$	14.8226	+	45.6193i	0.152810	+	0.470302i	−0.845122	+	0.534574i	$0.820472\pi$
$98$		0			0
$99$	−109.274	+	145.407i	−1.10378	+	1.46876i
$100$		0			0
$101$	83.6741	−	27.1874i	0.828456	−	0.269182i	0.136061	−	0.990700i	$-0.456556\pi$
$101$	83.6741	−	27.1874i	0.828456	−	0.269182i	0.692395	+	0.721519i	$0.256556\pi$
$102$		0			0
$103$	10.0570	−	7.30685i	0.0976409	−	0.0709403i	−0.537894	−	0.843013i	$-0.680780\pi$
$103$	10.0570	−	7.30685i	0.0976409	−	0.0709403i	0.635535	+	0.772072i	$0.280780\pi$
$104$		0			0
$105$	151.912	+	49.3591i	1.44678	+	0.470087i
$106$		0			0
$107$	0.698862	−	0.961900i	0.00653142	−	0.00898972i	−0.805739	−	0.592271i	$-0.798231\pi$
$107$	0.698862	−	0.961900i	0.00653142	−	0.00898972i	0.812270	+	0.583281i	$0.198231\pi$
$108$		0			0
$109$			145.212i			1.33222i	0.745855	+	0.666108i	$0.232041\pi$
$109$			145.212i			1.33222i	−0.745855	+	0.666108i	$0.767959\pi$
$110$		0			0
$111$	−140.071			−1.26190
$112$		0			0
$113$	−47.0926	−	34.2148i	−0.416749	−	0.302786i	0.359580	−	0.933114i	$-0.382920\pi$
$113$	−47.0926	−	34.2148i	−0.416749	−	0.302786i	−0.776328	+	0.630329i	$0.782920\pi$
$114$		0			0
$115$	−5.25789	+	16.1821i	−0.0457208	+	0.140714i
$116$		0			0
$117$	146.373	+	201.465i	1.25105	+	1.72192i
$118$		0			0
$119$	36.8210	+	113.323i	0.309420	+	0.952298i
$120$		0			0
$121$	−41.0868	+	113.811i	−0.339561	+	0.940584i
$122$		0			0
$123$	238.153	−	77.3807i	1.93620	−	0.629111i
$124$		0			0
$125$	105.564	−	76.6966i	0.844510	−	0.613572i
$126$		0			0
$127$	−37.6191	−	12.2232i	−0.296213	−	0.0962455i	0.157140	−	0.987576i	$-0.449772\pi$
$127$	−37.6191	−	12.2232i	−0.296213	−	0.0962455i	−0.453353	+	0.891331i	$0.649772\pi$
$128$		0			0
$129$	50.1258	−	68.9922i	0.388572	−	0.534823i
$130$		0			0
$131$		−	130.281i		−	0.994510i	−0.867605	−	0.497255i	$-0.834341\pi$
$131$		−	130.281i		−	0.994510i	0.867605	−	0.497255i	$-0.165659\pi$
$132$		0			0
$133$	−215.792			−1.62249
$134$		0			0
$135$	−146.058	−	106.117i	−1.08191	−	0.786053i
$136$		0			0
$137$	−63.6741	+	195.969i	−0.464774	+	1.43043i	0.394492	+	0.918899i	$0.370921\pi$
$137$	−63.6741	+	195.969i	−0.464774	+	1.43043i	−0.859266	+	0.511528i	$0.829079\pi$
$138$		0			0
$139$	−125.901	−	173.288i	−0.905765	−	1.24668i	−0.968592	−	0.248655i	$-0.920012\pi$
$139$	−125.901	−	173.288i	−0.905765	−	1.24668i	0.0628270	−	0.998024i	$-0.479988\pi$
$140$		0			0
$141$	−121.762	−	374.746i	−0.863562	−	2.65777i
$142$		0			0
$143$	132.432	+	99.5232i	0.926097	+	0.695967i
$144$		0			0
$145$	−57.5753	+	18.7074i	−0.397071	+	0.129016i
$146$		0			0
$147$	−18.6049	+	13.5173i	−0.126564	+	0.0919542i
$148$		0			0
$149$	57.1220	+	18.5601i	0.383369	+	0.124564i	0.494360	−	0.869257i	$-0.335402\pi$
$149$	57.1220	+	18.5601i	0.383369	+	0.124564i	−0.110991	+	0.993821i	$0.535402\pi$
$150$		0			0
$151$	−75.8544	+	104.405i	−0.502347	+	0.691422i	−0.982605	−	0.185706i	$-0.940543\pi$
$151$	−75.8544	+	104.405i	−0.502347	+	0.691422i	0.480258	+	0.877127i	$0.340543\pi$
$152$		0			0
$153$		−	295.529i		−	1.93156i
$154$		0			0
$155$	103.789			0.669604
$156$		0			0
$157$	220.735	+	160.374i	1.40596	+	1.02149i	0.993895	+	0.110332i	$0.0351913\pi$
$157$	220.735	+	160.374i	1.40596	+	1.02149i	0.412062	+	0.911156i	$0.364809\pi$
$158$		0			0
$159$	15.4652	−	47.5969i	0.0972653	−	0.299352i
$160$		0			0
$161$	14.0636	+	19.3569i	0.0873518	+	0.120229i
$162$		0			0
$163$	−4.45141	−	13.7000i	−0.0273093	−	0.0840492i	0.936473	−	0.350740i	$-0.114070\pi$
$163$	−4.45141	−	13.7000i	−0.0273093	−	0.0840492i	−0.963782	+	0.266691i	$0.914070\pi$
$164$		0			0
$165$	−249.294	−	85.4742i	−1.51087	−	0.518025i
$166$		0			0
$167$	−154.632	+	50.2429i	−0.925938	+	0.300855i	−0.732900	−	0.680336i	$-0.761834\pi$
$167$	−154.632	+	50.2429i	−0.925938	+	0.300855i	−0.193037	+	0.981191i	$0.561834\pi$
$168$		0			0
$169$	46.7629	−	33.9752i	0.276704	−	0.201037i
$170$		0			0
$171$	509.011	+	165.388i	2.97667	+	0.967180i
$172$		0			0
$173$	−65.8448	+	90.6276i	−0.380606	+	0.523859i	−0.955745	−	0.294197i	$-0.904948\pi$
$173$	−65.8448	+	90.6276i	−0.380606	+	0.523859i	0.575139	+	0.818056i	$0.304948\pi$
$174$		0			0
$175$		−	16.8124i		−	0.0960709i
$176$		0			0
$177$	185.275			1.04675
$178$		0			0
$179$	−127.140	−	92.3729i	−0.710281	−	0.516050i	0.172983	−	0.984925i	$-0.444659\pi$
$179$	−127.140	−	92.3729i	−0.710281	−	0.516050i	−0.883264	+	0.468875i	$0.844659\pi$
$180$		0			0
$181$	−105.272	+	323.994i	−0.581614	+	1.79002i	0.0308474	+	0.999524i	$0.490179\pi$
$181$	−105.272	+	323.994i	−0.581614	+	1.79002i	−0.612462	+	0.790500i	$0.709821\pi$
$182$		0			0
$183$	84.0646	+	115.705i	0.459369	+	0.632268i
$184$		0			0
$185$	−40.6106	−	124.987i	−0.219517	−	0.675603i
$186$		0			0
$187$	−57.7250	−	187.930i	−0.308690	−	1.00498i
$188$		0			0
$189$	−241.448	+	78.4512i	−1.27750	+	0.415085i
$190$		0			0
$191$	−25.1761	+	18.2915i	−0.131812	+	0.0957671i	−0.651738	−	0.758444i	$-0.725960\pi$
$191$	−25.1761	+	18.2915i	−0.131812	+	0.0957671i	0.519926	+	0.854212i	$0.325960\pi$
$192$		0			0
$193$	−47.6999	−	15.4986i	−0.247150	−	0.0803038i	0.182822	−	0.983146i	$-0.441477\pi$
$193$	−47.6999	−	15.4986i	−0.247150	−	0.0803038i	−0.429972	+	0.902842i	$0.641477\pi$
$194$		0			0
$195$	−212.078	+	291.901i	−1.08758	+	1.49693i
$196$		0			0
$197$		−	225.831i		−	1.14635i	−0.819432	−	0.573176i	$-0.805711\pi$
$197$		−	225.831i		−	1.14635i	0.819432	−	0.573176i	$-0.194289\pi$
$198$		0			0
$199$	46.4242			0.233287			0.116644	−	0.993174i	$-0.462786\pi$
$199$	46.4242			0.233287			0.116644	+	0.993174i	$0.462786\pi$
$200$		0			0
$201$	125.603	+	91.2558i	0.624889	+	0.454009i
$202$		0			0
$203$	−26.3065	+	80.9630i	−0.129589	+	0.398832i
$204$		0			0
$205$	138.095	+	190.071i	0.673634	+	0.927178i
$206$		0			0
$207$	−18.3378	−	56.4380i	−0.0885885	−	0.272648i
$208$		0			0
$209$	355.991	+	5.74805i	1.70331	+	0.0275026i
$210$		0			0
$211$	101.556	−	32.9975i	0.481307	−	0.156386i	−0.0583069	−	0.998299i	$-0.518570\pi$
$211$	101.556	−	32.9975i	0.481307	−	0.156386i	0.539614	+	0.841913i	$0.318570\pi$
$212$		0			0
$213$	167.799	−	121.913i	0.787787	−	0.572361i
$214$		0			0
$215$	76.0953	+	24.7249i	0.353932	+	0.114999i
$216$		0			0
$217$	85.7863	−	118.075i	0.395329	−	0.544123i
$218$		0			0
$219$			312.077i			1.42501i
$220$		0			0
$221$	−269.157			−1.21791
$222$		0			0
$223$	108.118	+	78.5527i	0.484836	+	0.352254i	0.803195	−	0.595716i	$-0.203132\pi$
$223$	108.118	+	78.5527i	0.484836	+	0.352254i	−0.318359	+	0.947970i	$0.603132\pi$
$224$		0			0
$225$	−12.8854	+	39.6573i	−0.0572685	+	0.176254i
$226$		0			0
$227$	−106.721	−	146.889i	−0.470137	−	0.647088i	0.506436	−	0.862278i	$-0.330963\pi$
$227$	−106.721	−	146.889i	−0.470137	−	0.647088i	−0.976572	+	0.215190i	$0.930963\pi$
$228$		0			0
$229$	−81.2785	−	250.150i	−0.354928	−	1.09236i	−0.956051	−	0.293200i	$-0.905280\pi$
$229$	−81.2785	−	250.150i	−0.354928	−	1.09236i	0.601123	−	0.799156i	$-0.294720\pi$
$230$		0			0
$231$	−303.293	+	212.960i	−1.31296	+	0.921905i
$232$		0			0
$233$	−156.952	+	50.9968i	−0.673614	+	0.218870i	−0.625797	−	0.779986i	$-0.715226\pi$
$233$	−156.952	+	50.9968i	−0.673614	+	0.218870i	−0.0478167	+	0.998856i	$0.515226\pi$
$234$		0			0
$235$	299.087	−	217.299i	1.27271	−	0.924677i
$236$		0			0
$237$	−597.316	−	194.080i	−2.52032	−	0.818901i
$238$		0			0
$239$	178.104	−	245.140i	0.745207	−	1.02569i	−0.253096	−	0.967441i	$-0.581449\pi$
$239$	178.104	−	245.140i	0.745207	−	1.02569i	0.998302	−	0.0582476i	$-0.0185513\pi$
$240$		0			0
$241$		−	289.642i		−	1.20183i	−0.799311	−	0.600917i	$-0.794802\pi$
$241$		−	289.642i		−	1.20183i	0.799311	−	0.600917i	$-0.205198\pi$
$242$		0			0
$243$	−122.370			−0.503579
$244$		0			0
$245$	−17.4557	−	12.6823i	−0.0712477	−	0.0517645i
$246$		0			0
$247$	150.629	−	463.589i	0.609835	−	1.87688i
$248$		0			0
$249$	9.19263	+	12.6526i	0.0369182	+	0.0508135i
$250$		0			0
$251$	83.2179	+	256.118i	0.331545	+	1.02039i	0.968399	+	0.249407i	$0.0802356\pi$
$251$	83.2179	+	256.118i	0.331545	+	1.02039i	−0.636853	+	0.770985i	$0.719764\pi$
$252$		0			0
$253$	−22.6852	−	32.3077i	−0.0896647	−	0.127699i
$254$		0			0
$255$	407.232	−	132.318i	1.59699	−	0.518893i
$256$		0			0
$257$	−406.941	+	295.660i	−1.58343	+	1.15043i	−0.670795	+	0.741643i	$0.734047\pi$
$257$	−406.941	+	295.660i	−1.58343	+	1.15043i	−0.912631	+	0.408784i	$0.865953\pi$
$258$		0			0
$259$	−175.757	−	57.1070i	−0.678600	−	0.220490i
$260$		0			0
$261$	124.104	−	170.814i	0.475494	−	0.654461i
$262$		0			0
$263$			178.603i			0.679099i	0.940588	+	0.339550i	$0.110275\pi$
$263$			178.603i			0.679099i	−0.940588	+	0.339550i	$0.889725\pi$
$264$		0			0
$265$	46.9550			0.177189
$266$		0			0
$267$	−247.300	−	179.674i	−0.926215	−	0.672935i
$268$		0			0
$269$	32.5941	−	100.314i	0.121168	−	0.372916i	−0.872016	−	0.489478i	$-0.837187\pi$
$269$	32.5941	−	100.314i	0.121168	−	0.372916i	0.993183	+	0.116562i	$0.0371874\pi$
$270$		0			0
$271$	86.3298	+	118.823i	0.318560	+	0.438460i	0.938027	−	0.346563i	$-0.112651\pi$
$271$	86.3298	+	118.823i	0.318560	+	0.438460i	−0.619467	+	0.785023i	$0.712651\pi$
$272$		0			0
$273$	156.787	+	482.540i	0.574311	+	1.76755i
$274$		0			0
$275$	−0.447833	+	27.7354i	−0.00162848	+	0.100856i
$276$		0			0
$277$	247.480	−	80.4113i	0.893431	−	0.290293i	0.173908	−	0.984762i	$-0.444360\pi$
$277$	247.480	−	80.4113i	0.893431	−	0.290293i	0.719523	+	0.694469i	$0.244360\pi$
$278$		0			0
$279$	−292.849	+	212.767i	−1.04964	+	0.762606i
$280$		0			0
$281$	487.119	+	158.275i	1.73352	+	0.563255i	0.993951	−	0.109824i	$-0.0350288\pi$
$281$	487.119	+	158.275i	1.73352	+	0.563255i	0.739570	+	0.673080i	$0.235029\pi$
$282$		0			0
$283$	−105.155	+	144.733i	−0.371572	+	0.511425i	−0.953327	−	0.301939i	$-0.902366\pi$
$283$	−105.155	+	144.733i	−0.371572	+	0.511425i	0.581755	+	0.813364i	$0.302366\pi$
$284$		0			0
$285$			775.456i			2.72090i
$286$		0			0
$287$	330.377			1.15114
$288$		0			0
$289$	24.6116	+	17.8814i	0.0851613	+	0.0618733i
$290$		0			0
$291$	74.9027	−	230.527i	0.257397	−	0.792188i
$292$		0			0
$293$	−305.694	−	420.752i	−1.04332	−	1.43601i	−0.894456	−	0.447155i	$-0.852437\pi$
$293$	−305.694	−	420.752i	−1.04332	−	1.43601i	−0.148867	−	0.988857i	$-0.547563\pi$
$294$		0			0
$295$	53.7164	+	165.322i	0.182090	+	0.560414i
$296$		0			0
$297$	400.406	−	122.989i	1.34817	−	0.414105i
$298$		0			0
$299$	−51.4017	+	16.7014i	−0.171912	+	0.0558576i
$300$		0			0
$301$	91.0247	−	66.1333i	0.302408	−	0.219712i
$302$		0			0
$303$	−422.828	−	137.385i	−1.39547	−	0.453416i
$304$		0			0
$305$	−78.8719	+	108.558i	−0.258596	+	0.355927i
$306$		0			0
$307$			453.784i			1.47812i	0.673638	+	0.739061i	$0.264731\pi$
$307$			453.784i			1.47812i	−0.673638	+	0.739061i	$0.735269\pi$
$308$		0			0
$309$	−62.8180			−0.203294
$310$		0			0
$311$	−328.234	−	238.476i	−1.05541	−	0.766803i	−0.0821789	−	0.996618i	$-0.526188\pi$
$311$	−328.234	−	238.476i	−1.05541	−	0.766803i	−0.973234	+	0.229815i	$0.926188\pi$
$312$		0			0
$313$	5.16035	−	15.8819i	0.0164867	−	0.0507409i	−0.942475	−	0.334277i	$-0.891508\pi$
$313$	5.16035	−	15.8819i	0.0164867	−	0.0507409i	0.958961	+	0.283537i	$0.0915077\pi$
$314$		0			0
$315$	−307.220	−	422.852i	−0.975301	−	1.34239i
$316$		0			0
$317$	173.836	+	535.013i	0.548380	+	1.68774i	0.712815	+	0.701352i	$0.247420\pi$
$317$	173.836	+	535.013i	0.548380	+	1.68774i	−0.164436	+	0.986388i	$0.552580\pi$
$318$		0			0
$319$	45.5544	−	132.864i	0.142804	−	0.416501i
$320$		0			0
$321$	−5.71414	+	1.85664i	−0.0178011	+	0.00578392i
$322$		0			0
$323$	−467.997	+	340.020i	−1.44891	+	1.05269i
$324$		0			0
$325$	36.1184	+	11.7356i	0.111134	+	0.0361095i
$326$		0			0
$327$	431.313	−	593.651i	1.31900	−	1.81545i
$328$		0			0
$329$		−	519.864i		−	1.58013i
$330$		0			0
$331$	167.684			0.506597			0.253298	−	0.967388i	$-0.418485\pi$
$331$	167.684			0.506597			0.253298	+	0.967388i	$0.418485\pi$
$332$		0			0
$333$	370.810	+	269.409i	1.11354	+	0.809036i
$334$		0			0
$335$	−45.0125	+	138.534i	−0.134366	+	0.413535i
$336$		0			0
$337$	103.280	+	142.152i	0.306467	+	0.421816i	0.934276	−	0.356552i	$-0.116048\pi$
$337$	103.280	+	142.152i	0.306467	+	0.421816i	−0.627808	+	0.778368i	$0.716048\pi$
$338$		0			0
$339$	90.8971	+	279.752i	0.268133	+	0.825228i
$340$		0			0
$341$	−144.667	+	192.503i	−0.424243	+	0.564524i
$342$		0			0
$343$	−339.551	+	110.327i	−0.989944	+	0.321652i
$344$		0			0
$345$	69.5599	−	50.5382i	0.201623	−	0.146488i
$346$		0			0
$347$	−459.695	−	149.364i	−1.32477	−	0.430443i	−0.440639	−	0.897685i	$-0.645248\pi$
$347$	−459.695	−	149.364i	−1.32477	−	0.430443i	−0.884130	+	0.467241i	$0.845248\pi$
$348$		0			0
$349$	94.6593	−	130.287i	0.271230	−	0.373316i	−0.651574	−	0.758585i	$-0.725891\pi$
$349$	94.6593	−	130.287i	0.271230	−	0.373316i	0.922804	+	0.385269i	$0.125891\pi$
$350$		0			0
$351$		−	573.468i		−	1.63381i
$352$		0			0
$353$	522.647			1.48059			0.740294	−	0.672284i	$-0.234687\pi$
$353$	522.647			1.48059			0.740294	+	0.672284i	$0.234687\pi$
$354$		0			0
$355$	157.434	+	114.382i	0.443475	+	0.322203i
$356$		0			0
$357$	186.067	−	572.654i	0.521195	−	1.60407i
$358$		0			0
$359$	336.373	+	462.978i	0.936972	+	1.28963i	0.957077	+	0.289833i	$0.0935999\pi$
$359$	336.373	+	462.978i	0.936972	+	1.28963i	−0.0201051	+	0.999798i	$0.506400\pi$
$360$		0			0
$361$	−212.179	−	653.020i	−0.587754	−	1.80892i
$362$		0			0
$363$	506.015	−	343.241i	1.39398	−	0.945567i
$364$		0			0
$365$	−278.469	+	90.4800i	−0.762928	+	0.247890i
$366$		0			0
$367$	−136.244	+	98.9867i	−0.371236	+	0.269719i	−0.757723	−	0.652576i	$-0.773688\pi$
$367$	−136.244	+	98.9867i	−0.371236	+	0.269719i	0.386487	+	0.922295i	$0.373688\pi$
$368$		0			0
$369$	−779.295	−	253.208i	−2.11191	−	0.686201i
$370$		0			0
$371$	38.8106	−	53.4182i	0.104611	−	0.143984i
$372$		0			0
$373$			500.543i			1.34194i	0.741486	+	0.670969i	$0.234122\pi$
$373$			500.543i			1.34194i	−0.741486	+	0.670969i	$0.765878\pi$
$374$		0			0
$375$	−659.370			−1.75832
$376$		0			0
$377$	−155.571	−	113.029i	−0.412656	−	0.299812i
$378$		0			0
$379$	16.1149	−	49.5966i	0.0425195	−	0.130862i	−0.927543	−	0.373716i	$-0.878084\pi$
$379$	16.1149	−	49.5966i	0.0425195	−	0.130862i	0.970063	+	0.242854i	$0.0780836\pi$
$380$		0			0
$381$	117.488	+	161.708i	0.308367	+	0.424431i
$382$		0			0
$383$	−76.3632	−	235.022i	−0.199382	−	0.613634i	−0.999897	−	0.0143222i	$-0.995441\pi$
$383$	−76.3632	−	235.022i	−0.199382	−	0.613634i	0.800516	−	0.599312i	$-0.204559\pi$
$384$		0			0
$385$	−277.960	−	208.888i	−0.721973	−	0.542567i
$386$		0			0
$387$	−265.396	+	86.2324i	−0.685778	+	0.222823i
$388$		0			0
$389$	199.368	−	144.850i	0.512515	−	0.372364i	−0.301262	−	0.953542i	$-0.597408\pi$
$389$	199.368	−	144.850i	0.512515	−	0.372364i	0.813777	+	0.581177i	$0.197408\pi$
$390$		0			0
$391$	61.0009	+	19.8204i	0.156013	+	0.0506915i
$392$		0			0
$393$	−386.965	+	532.611i	−0.984643	+	1.35524i
$394$		0			0
$395$		−	589.260i		−	1.49180i
$396$		0			0
$397$	50.7517			0.127838			0.0639191	−	0.997955i	$-0.479640\pi$
$397$	50.7517			0.127838			0.0639191	+	0.997955i	$0.479640\pi$
$398$		0			0
$399$	882.195	+	640.952i	2.21102	+	1.60640i
$400$		0			0
$401$	14.8571	−	45.7254i	0.0370501	−	0.114028i	−0.930821	−	0.365475i	$-0.880906\pi$
$401$	14.8571	−	45.7254i	0.0370501	−	0.114028i	0.967871	+	0.251447i	$0.0809064\pi$
$402$		0			0
$403$	193.781	+	266.716i	0.480845	+	0.661827i
$404$		0			0
$405$	63.8833	+	196.613i	0.157737	+	0.485463i
$406$		0			0
$407$	288.425	+	98.8910i	0.708662	+	0.242976i
$408$		0			0
$409$	−486.442	+	158.055i	−1.18934	+	0.386441i	−0.835830	−	0.548988i	$-0.815013\pi$
$409$	−486.442	+	158.055i	−1.18934	+	0.386441i	−0.353514	+	0.935429i	$0.615013\pi$
$410$		0			0
$411$	842.384	−	612.028i	2.04960	−	1.48912i
$412$		0			0
$413$	232.478	+	75.5366i	0.562900	+	0.182897i
$414$		0			0
$415$	−8.62479	+	11.8710i	−0.0207826	+	0.0286048i
$416$		0			0
$417$			1082.39i			2.59566i
$418$		0			0
$419$	790.955			1.88772			0.943860	−	0.330345i	$-0.107165\pi$
$419$	790.955			1.88772			0.943860	+	0.330345i	$0.107165\pi$
$420$		0			0
$421$	−333.136	−	242.038i	−0.791297	−	0.574911i	0.117051	−	0.993126i	$-0.462656\pi$
$421$	−333.136	−	242.038i	−0.791297	−	0.574911i	−0.908348	+	0.418215i	$0.862656\pi$
$422$		0			0
$423$	−398.436	+	1226.26i	−0.941928	+	2.89896i
$424$		0			0
$425$	−26.4911	−	36.4618i	−0.0623319	−	0.0857925i
$426$		0			0
$427$	58.3090	+	179.457i	0.136555	+	0.420274i
$428$		0			0
$429$	−245.798	−	800.223i	−0.572955	−	1.86532i
$430$		0			0
$431$	−268.338	+	87.1884i	−0.622595	+	0.202293i	−0.603292	−	0.797520i	$-0.706145\pi$
$431$	−268.338	+	87.1884i	−0.622595	+	0.202293i	−0.0193028	+	0.999814i	$0.506145\pi$
$432$		0			0
$433$	44.9013	−	32.6227i	0.103698	−	0.0753411i	−0.534728	−	0.845024i	$-0.679586\pi$
$433$	44.9013	−	32.6227i	0.103698	−	0.0753411i	0.638426	+	0.769683i	$0.279586\pi$
$434$		0			0
$435$	290.944	+	94.5333i	0.668836	+	0.217318i
$436$		0			0
$437$	−68.2762	+	93.9742i	−0.156239	+	0.215044i
$438$		0			0
$439$			232.914i			0.530556i	0.964172	+	0.265278i	$0.0854638\pi$
$439$			232.914i			0.530556i	−0.964172	+	0.265278i	$0.914536\pi$
$440$		0			0
$441$	75.2516			0.170638
$442$		0			0
$443$	344.202	+	250.077i	0.776979	+	0.564508i	0.904071	−	0.427383i	$-0.140564\pi$
$443$	344.202	+	250.077i	0.776979	+	0.564508i	−0.127092	+	0.991891i	$0.540564\pi$
$444$		0			0
$445$	88.6252	−	272.760i	0.199158	−	0.612944i
$446$		0			0
$447$	−178.397	−	245.543i	−0.399099	−	0.549313i
$448$		0			0
$449$	14.2766	+	43.9388i	0.0317964	+	0.0978592i	0.965695	−	0.259678i	$-0.0836165\pi$
$449$	14.2766	+	43.9388i	0.0317964	+	0.0978592i	−0.933899	+	0.357537i	$0.883616\pi$
$450$		0			0
$451$	−545.022	−	8.80026i	−1.20847	−	0.0195128i
$452$		0			0
$453$	620.213	−	201.519i	1.36912	−	0.444855i
$454$		0			0
$455$	−385.118	+	279.805i	−0.846414	+	0.614956i
$456$		0			0
$457$	147.110	+	47.7990i	0.321904	+	0.104593i	0.465512	−	0.885042i	$-0.345870\pi$
$457$	147.110	+	47.7990i	0.321904	+	0.104593i	−0.143608	+	0.989635i	$0.545870\pi$
$458$		0			0
$459$	−400.024	+	550.586i	−0.871513	+	1.19953i
$460$		0			0
$461$		−	775.943i		−	1.68317i	−0.540123	−	0.841586i	$-0.681622\pi$
$461$		−	775.943i		−	1.68317i	0.540123	−	0.841586i	$-0.318378\pi$
$462$		0			0
$463$	−829.285			−1.79111			−0.895557	−	0.444948i	$-0.853222\pi$
$463$	−829.285			−1.79111			−0.895557	+	0.444948i	$0.853222\pi$
$464$		0			0
$465$	−424.306	−	308.277i	−0.912487	−	0.662960i
$466$		0			0
$467$	241.774	−	744.104i	0.517718	−	1.59337i	−0.260565	−	0.965456i	$-0.583909\pi$
$467$	241.774	−	744.104i	0.517718	−	1.59337i	0.778282	−	0.627914i	$-0.216091\pi$
$468$		0			0
$469$	120.398	+	165.714i	0.256712	+	0.353334i
$470$		0			0
$471$	−426.058	−	1311.27i	−0.904582	−	2.78402i
$472$		0			0
$473$	−151.925	+	106.675i	−0.321194	+	0.225529i
$474$		0			0
$475$	77.6261	−	25.2223i	0.163423	−	0.0530995i
$476$		0			0
$477$	−132.488	+	96.2580i	−0.277752	+	0.201799i
$478$		0			0
$479$	77.2103	+	25.0872i	0.161191	+	0.0523740i	0.388501	−	0.921448i	$-0.372993\pi$
$479$	77.2103	+	25.0872i	0.161191	+	0.0523740i	−0.227310	+	0.973822i	$0.572993\pi$
$480$		0			0
$481$	245.368	−	337.720i	0.510121	−	0.702121i
$482$		0			0
$483$		−	120.907i		−	0.250325i
$484$		0			0
$485$	227.418			0.468902
$486$		0			0
$487$	235.675	+	171.228i	0.483933	+	0.351598i	0.802846	−	0.596186i	$-0.203318\pi$
$487$	235.675	+	171.228i	0.483933	+	0.351598i	−0.318913	+	0.947784i	$0.603318\pi$
$488$		0			0
$489$	−22.4942	+	69.2299i	−0.0460003	+	0.141574i
$490$		0			0
$491$	176.504	+	242.937i	0.359479	+	0.494780i	0.950003	−	0.312239i	$-0.101079\pi$
$491$	176.504	+	242.937i	0.359479	+	0.494780i	−0.590524	+	0.807020i	$0.701079\pi$
$492$		0			0
$493$	70.5202	+	217.039i	0.143043	+	0.440241i
$494$		0			0
$495$	495.557	+	705.762i	1.00112	+	1.42578i
$496$		0			0
$497$	260.253	−	84.5614i	0.523648	−	0.170144i
$498$		0			0
$499$	−248.898	+	180.835i	−0.498794	+	0.362395i	−0.808556	−	0.588419i	$-0.799750\pi$
$499$	−248.898	+	180.835i	−0.498794	+	0.362395i	0.309762	+	0.950814i	$0.399750\pi$
$500$		0			0
$501$	781.395	+	253.891i	1.55967	+	0.506768i
$502$		0			0
$503$	470.986	−	648.257i	0.936354	−	1.28878i	−0.0209742	−	0.999780i	$-0.506677\pi$
$503$	470.986	−	648.257i	0.936354	−	1.28878i	0.957329	−	0.289001i	$-0.0933232\pi$
$504$		0			0
$505$		−	417.125i		−	0.825990i
$506$		0			0
$507$	−292.090			−0.576114
$508$		0			0
$509$	−438.219	−	318.385i	−0.860941	−	0.625510i	0.0671999	−	0.997740i	$-0.478593\pi$
$509$	−438.219	−	318.385i	−0.860941	−	0.625510i	−0.928141	+	0.372229i	$0.878593\pi$
$510$		0			0
$511$	−127.234	+	391.586i	−0.248990	+	0.766312i
$512$		0			0
$513$	−724.448	−	997.117i	−1.41218	−	1.94370i
$514$		0			0
$515$	−18.2127	−	56.0531i	−0.0353645	−	0.108841i
$516$		0			0
$517$	−13.8476	+	857.618i	−0.0267846	+	1.65884i
$518$		0			0
$519$	538.371	−	174.927i	1.03732	−	0.337047i
$520$		0			0
$521$	−577.263	+	419.406i	−1.10799	+	0.805002i	−0.982346	−	0.187073i	$-0.940100\pi$
$521$	−577.263	+	419.406i	−1.10799	+	0.805002i	−0.125644	+	0.992075i	$0.540100\pi$
$522$		0			0
$523$	−432.518	−	140.534i	−0.826994	−	0.268707i	−0.135215	−	0.990816i	$-0.543173\pi$
$523$	−432.518	−	140.534i	−0.826994	−	0.268707i	−0.691779	+	0.722110i	$0.743173\pi$
$524$		0			0
$525$	−49.9368	+	68.7321i	−0.0951178	+	0.130918i
$526$		0			0
$527$		−	391.246i		−	0.742403i
$528$		0			0
$529$	−516.121			−0.975653
$530$		0			0
$531$	−490.477	−	356.353i	−0.923686	−	0.671097i
$532$		0			0
$533$	−230.613	+	709.754i	−0.432670	+	1.33162i
$534$		0			0
$535$	−3.31339	−	4.56049i	−0.00619325	−	0.00852428i
$536$		0			0
$537$	245.403	+	755.274i	0.456989	+	1.40647i
$538$		0			0
$539$	47.8534	−	14.6987i	0.0887818	−	0.0272704i
$540$		0			0
$541$	768.411	−	249.672i	1.42035	−	0.461500i	0.504638	−	0.863331i	$-0.331626\pi$
$541$	768.411	−	249.672i	1.42035	−	0.461500i	0.915714	+	0.401830i	$0.131626\pi$
$542$		0			0
$543$	1392.71	−	1011.86i	2.56485	−	1.86347i
$544$		0			0
$545$	654.771	+	212.748i	1.20141	+	0.390363i
$546$		0			0
$547$	100.382	−	138.164i	0.183514	−	0.252585i	−0.707342	−	0.706872i	$-0.750106\pi$
$547$	100.382	−	138.164i	0.183514	−	0.252585i	0.890856	+	0.454287i	$0.150106\pi$
$548$		0			0
$549$		−	467.994i		−	0.852447i
$550$		0			0
$551$	−413.287			−0.750067
$552$		0			0
$553$	−670.370	−	487.052i	−1.21224	−	0.880745i
$554$		0			0
$555$	−205.216	+	631.591i	−0.369759	+	1.13800i
$556$		0			0
$557$	−13.9618	−	19.2168i	−0.0250661	−	0.0345005i	0.796300	−	0.604902i	$-0.206788\pi$
$557$	−13.9618	−	19.2168i	−0.0250661	−	0.0345005i	−0.821366	+	0.570401i	$0.806788\pi$
$558$		0			0
$559$	78.5373	+	241.713i	0.140496	+	0.432402i
$560$		0			0
$561$	−322.208	+	939.750i	−0.574345	+	1.67513i
$562$		0			0
$563$	−568.487	+	184.713i	−1.00975	+	0.328086i	−0.766753	−	0.641942i	$-0.778129\pi$
$563$	−568.487	+	184.713i	−1.00975	+	0.328086i	−0.242993	+	0.970028i	$0.578129\pi$
$564$		0			0
$565$	−223.272	+	162.217i	−0.395172	+	0.287109i
$566$		0			0
$567$	276.478	+	89.8333i	0.487616	+	0.158436i
$568$		0			0
$569$	−239.476	+	329.610i	−0.420871	+	0.579279i	−0.965828	−	0.259185i	$-0.916546\pi$
$569$	−239.476	+	329.610i	−0.420871	+	0.579279i	0.544957	+	0.838464i	$0.316546\pi$
$570$		0			0
$571$			1036.11i			1.81456i	0.420530	+	0.907279i	$0.361844\pi$
$571$			1036.11i			1.81456i	−0.420530	+	0.907279i	$0.638156\pi$
$572$		0			0
$573$	157.255			0.274441
$574$		0			0
$575$	−7.32156	−	5.31943i	−0.0127332	−	0.00925118i
$576$		0			0
$577$	212.646	−	654.458i	0.368538	−	1.13424i	−0.579198	−	0.815187i	$-0.696634\pi$
$577$	212.646	−	654.458i	0.368538	−	1.13424i	0.947736	−	0.319056i	$-0.103366\pi$
$578$		0			0
$579$	148.971	+	205.041i	0.257290	+	0.354130i
$580$		0			0
$581$	6.37621	+	19.6239i	0.0109745	+	0.0337762i
$582$		0			0
$583$	−65.4487	+	87.0902i	−0.112262	+	0.149383i
$584$		0			0
$585$	1122.87	−	364.842i	1.91943	−	0.623662i
$586$		0			0
$587$	−485.538	+	352.764i	−0.827152	+	0.600961i	−0.918752	−	0.394835i	$-0.870802\pi$
$587$	−485.538	+	352.764i	−0.827152	+	0.600961i	0.0915999	+	0.995796i	$0.470802\pi$
$588$		0			0
$589$	673.872	+	218.954i	1.14410	+	0.371739i
$590$		0			0
$591$	−670.773	+	923.239i	−1.13498	+	1.56216i
$592$		0			0
$593$			468.857i			0.790652i	0.918541	+	0.395326i	$0.129368\pi$
$593$			468.857i			0.790652i	−0.918541	+	0.395326i	$0.870632\pi$
$594$		0			0
$595$	564.931			0.949463
$596$		0			0
$597$	−189.790	−	137.891i	−0.317907	−	0.230973i
$598$		0			0
$599$	158.477	−	487.741i	0.264569	−	0.814259i	−0.727224	−	0.686400i	$-0.759190\pi$
$599$	158.477	−	487.741i	0.264569	−	0.814259i	0.991792	−	0.127858i	$-0.0408102\pi$
$600$		0			0
$601$	298.113	+	410.318i	0.496028	+	0.682725i	0.981486	−	0.191536i	$-0.0613468\pi$
$601$	298.113	+	410.318i	0.496028	+	0.682725i	−0.485457	+	0.874260i	$0.661347\pi$
$602$		0			0
$603$	−156.989	−	483.163i	−0.260347	−	0.801265i
$604$		0			0
$605$	452.985	+	352.006i	0.748736	+	0.581829i
$606$		0			0
$607$	320.774	−	104.226i	0.528458	−	0.171707i	−0.0326221	−	0.999468i	$-0.510386\pi$
$607$	320.774	−	104.226i	0.528458	−	0.171707i	0.561081	+	0.827761i	$0.310386\pi$
$608$		0			0
$609$	348.025	−	252.855i	0.571469	−	0.415197i
$610$		0			0
$611$	1116.83	+	362.881i	1.82788	+	0.593913i
$612$		0			0
$613$	−198.216	+	272.820i	−0.323353	+	0.445058i	−0.939487	−	0.342584i	$-0.888698\pi$
$613$	−198.216	+	272.820i	−0.323353	+	0.445058i	0.616134	+	0.787641i	$0.288698\pi$
$614$		0			0
$615$		−	1187.22i		−	1.93044i
$616$		0			0
$617$	−269.856			−0.437369			−0.218684	−	0.975796i	$-0.570177\pi$
$617$	−269.856			−0.437369			−0.218684	+	0.975796i	$0.570177\pi$
$618$		0			0
$619$	−439.905	−	319.610i	−0.710671	−	0.516333i	0.172719	−	0.984971i	$-0.444745\pi$
$619$	−439.905	−	319.610i	−0.710671	−	0.516333i	−0.883390	+	0.468639i	$0.844745\pi$
$620$		0			0
$621$	−42.2295	+	129.969i	−0.0680024	+	0.209290i
$622$		0			0
$623$	−237.052	−	326.274i	−0.380501	−	0.523714i
$624$		0			0
$625$	−171.689	−	528.405i	−0.274703	−	0.845448i
$626$		0			0
$627$	−1438.28	−	1080.88i	−2.29391	−	1.72389i
$628$		0			0
$629$	−471.155	+	153.088i	−0.749055	+	0.243383i
$630$		0			0
$631$	−91.5704	+	66.5298i	−0.145119	+	0.105435i	−0.657976	−	0.753039i	$-0.728587\pi$
$631$	−91.5704	+	66.5298i	−0.145119	+	0.105435i	0.512857	+	0.858474i	$0.328587\pi$
$632$		0			0
$633$	−513.189	−	166.745i	−0.810724	−	0.263420i
$634$		0			0
$635$	−110.230	+	151.719i	−0.173591	+	0.238928i
$636$		0			0
$637$		−	68.5364i		−	0.107592i
$638$		0			0
$639$	−678.697			−1.06212
$640$		0			0
$641$	426.791	+	310.082i	0.665821	+	0.483747i	0.868624	−	0.495472i	$-0.165005\pi$
$641$	426.791	+	310.082i	0.665821	+	0.483747i	−0.202803	+	0.979220i	$0.565005\pi$
$642$		0			0
$643$	90.5922	−	278.814i	0.140890	−	0.433614i	−0.855570	−	0.517688i	$-0.826793\pi$
$643$	90.5922	−	278.814i	0.140890	−	0.433614i	0.996460	+	0.0840733i	$0.0267930\pi$
$644$		0			0
$645$	−237.653	−	327.101i	−0.368454	−	0.507133i
$646$		0			0
$647$	−205.130	−	631.325i	−0.317048	−	0.975773i	−0.974903	−	0.222629i	$-0.928536\pi$
$647$	−205.130	−	631.325i	−0.317048	−	0.975773i	0.657855	−	0.753144i	$-0.271464\pi$
$648$		0			0
$649$	−381.506	−	130.805i	−0.587837	−	0.201549i
$650$		0			0
$651$	−701.420	+	227.905i	−1.07745	+	0.350085i
$652$		0			0
$653$	642.435	−	466.756i	0.983821	−	0.714788i	0.0252618	−	0.999681i	$-0.491958\pi$
$653$	642.435	−	466.756i	0.983821	−	0.714788i	0.958559	+	0.284893i	$0.0919581\pi$
$654$		0			0
$655$	−587.446	−	190.873i	−0.896864	−	0.291409i
$656$		0			0
$657$	600.241	−	826.160i	0.913608	−	1.25747i
$658$		0			0
$659$		−	187.489i		−	0.284505i	−0.989830	−	0.142253i	$-0.954565\pi$
$659$		−	187.489i		−	0.284505i	0.989830	−	0.142253i	$-0.0454346\pi$
$660$		0			0
$661$	74.1929			0.112243			0.0561217	−	0.998424i	$-0.482127\pi$
$661$	74.1929			0.112243			0.0561217	+	0.998424i	$0.482127\pi$
$662$		0			0
$663$	1100.36	+	799.460i	1.65967	+	1.20582i
$664$		0			0
$665$	−316.154	+	973.021i	−0.475419	+	1.46319i
$666$		0			0
$667$	26.9349	+	37.0727i	0.0403821	+	0.0555812i
$668$		0			0
$669$	−208.688	−	642.275i	−0.311940	−	0.960052i
$670$		0			0
$671$	−91.4122	−	297.603i	−0.136233	−	0.443521i
$672$		0			0
$673$	898.412	−	291.912i	1.33494	−	0.433747i	0.447338	−	0.894365i	$-0.352372\pi$
$673$	898.412	−	291.912i	1.33494	−	0.433747i	0.887598	+	0.460618i	$0.152372\pi$
$674$		0			0
$675$	77.6858	−	56.4420i	0.115090	−	0.0836178i
$676$		0			0
$677$	−688.441	−	223.688i	−1.01690	−	0.330411i	−0.247301	−	0.968939i	$-0.579544\pi$
$677$	−688.441	−	223.688i	−1.01690	−	0.330411i	−0.769599	+	0.638528i	$0.779544\pi$
$678$		0			0
$679$	187.972	−	258.721i	0.276836	−	0.381032i
$680$		0			0
$681$			917.495i			1.34728i
$682$		0			0
$683$	660.998			0.967787			0.483893	−	0.875127i	$-0.339222\pi$
$683$	660.998			0.967787			0.483893	+	0.875127i	$0.339222\pi$
$684$		0			0
$685$	790.350	+	574.223i	1.15380	+	0.838281i
$686$		0			0
$687$	−410.722	+	1264.07i	−0.597849	+	1.83999i
$688$		0			0
$689$	87.6683	+	120.665i	0.127240	+	0.175131i
$690$		0			0
$691$	−124.898	−	384.395i	−0.180749	−	0.556288i	0.819100	−	0.573650i	$-0.194473\pi$
$691$	−124.898	−	384.395i	−0.180749	−	0.556288i	−0.999849	+	0.0173622i	$0.994473\pi$
$692$		0			0
$693$	1212.51	+	19.5779i	1.74965	+	0.0282510i
$694$		0			0
$695$	−965.827	+	313.816i	−1.38968	+	0.451534i
$696$		0			0
$697$	716.502	−	520.569i	1.02798	−	0.746871i
$698$		0			0
$699$	793.121	+	257.701i	1.13465	+	0.368670i
$700$		0			0
$701$	233.239	−	321.027i	0.332724	−	0.457955i	−0.609575	−	0.792729i	$-0.708660\pi$
$701$	233.239	−	321.027i	0.332724	−	0.457955i	0.942299	+	0.334773i	$0.108660\pi$
$702$		0			0
$703$		−	897.178i		−	1.27621i
$704$		0			0
$705$	−1868.15			−2.64986
$706$		0			0
$707$	−474.541	−	344.774i	−0.671204	−	0.487658i
$708$		0			0
$709$	−4.25048	+	13.0816i	−0.00599503	+	0.0184508i	−0.954009	−	0.299777i	$-0.903088\pi$
$709$	−4.25048	+	13.0816i	−0.00599503	+	0.0184508i	0.948014	+	0.318228i	$0.103088\pi$
$710$		0			0
$711$	1207.99	+	1662.65i	1.69900	+	2.33847i
$712$		0			0
$713$	−24.2772	−	74.7174i	−0.0340493	−	0.104793i
$714$		0			0
$715$	642.782	−	451.335i	0.898996	−	0.631238i
$716$		0			0
$717$	−1456.25	+	473.163i	−2.03103	+	0.659920i
$718$		0			0
$719$	−84.0118	+	61.0381i	−0.116845	+	0.0848931i	−0.644673	−	0.764458i	$-0.723007\pi$
$719$	−84.0118	+	61.0381i	−0.116845	+	0.0848931i	0.527828	+	0.849351i	$0.323007\pi$
$720$		0			0
$721$	−78.8223	−	25.6109i	−0.109324	−	0.0355214i
$722$		0			0
$723$	−860.306	+	1184.11i	−1.18991	+	1.63777i
$724$		0			0
$725$		−	32.1994i		−	0.0444129i
$726$		0			0
$727$	1381.61			1.90043			0.950214	−	0.311599i	$-0.100864\pi$
$727$	1381.61			1.90043			0.950214	+	0.311599i	$0.100864\pi$
$728$		0			0
$729$	817.755	+	594.134i	1.12175	+	0.814998i
$730$		0			0
$731$	93.2040	−	286.852i	0.127502	−	0.392411i
$732$		0			0
$733$	−418.254	−	575.678i	−0.570606	−	0.785372i	0.422020	−	0.906586i	$-0.361321\pi$
$733$	−418.254	−	575.678i	−0.570606	−	0.785372i	−0.992626	+	0.121214i	$0.961321\pi$
$734$		0			0
$735$	33.6925	+	103.695i	0.0458402	+	0.141082i
$736$		0			0
$737$	−194.206	−	276.585i	−0.263509	−	0.375284i
$738$		0			0
$739$	−339.005	+	110.149i	−0.458734	+	0.149052i	−0.529263	−	0.848458i	$-0.677531\pi$
$739$	−339.005	+	110.149i	−0.458734	+	0.149052i	0.0705286	+	0.997510i	$0.477531\pi$
$740$		0			0
$741$	−1992.77	+	1447.83i	−2.68930	+	1.95389i
$742$		0			0
$743$	−204.751	−	66.5275i	−0.275573	−	0.0895391i	0.167970	−	0.985792i	$-0.446279\pi$
$743$	−204.751	−	66.5275i	−0.275573	−	0.0895391i	−0.443543	+	0.896253i	$0.646279\pi$
$744$		0			0
$745$	167.378	−	230.376i	0.224668	−	0.309229i
$746$		0			0
$747$		−	51.1760i		−	0.0685087i
$748$		0			0
$749$	−7.92691			−0.0105833
$750$		0			0
$751$	−15.0409	−	10.9279i	−0.0200279	−	0.0145511i	0.577726	−	0.816231i	$-0.303940\pi$
$751$	−15.0409	−	10.9279i	−0.0200279	−	0.0145511i	−0.597754	+	0.801679i	$0.703940\pi$
$752$		0			0
$753$	420.522	−	1294.23i	0.558463	−	1.71877i
$754$		0			0
$755$	359.635	+	494.996i	0.476338	+	0.655623i
$756$		0			0
$757$	99.0402	+	304.814i	0.130833	+	0.402661i	0.994919	−	0.100683i	$-0.0321028\pi$
$757$	99.0402	+	304.814i	0.130833	+	0.402661i	−0.864086	+	0.503344i	$0.832103\pi$
$758$		0			0
$759$	−3.22061	+	199.460i	−0.00424322	+	0.262793i
$760$		0			0
$761$	−7.81819	+	2.54029i	−0.0102736	+	0.00333809i	−0.314149	−	0.949374i	$-0.601719\pi$
$761$	−7.81819	+	2.54029i	−0.0102736	+	0.00333809i	0.303876	+	0.952712i	$0.401719\pi$
$762$		0			0
$763$	783.232	−	569.051i	1.02652	−	0.745808i
$764$		0			0
$765$	−1332.56	−	432.976i	−1.74191	−	0.565982i
$766$		0			0
$767$	−324.553	+	446.709i	−0.423146	+	0.582411i
$768$		0			0
$769$		−	32.0029i		−	0.0416162i	−0.999783	−	0.0208081i	$-0.993376\pi$
$769$		−	32.0029i		−	0.0416162i	0.999783	−	0.0208081i	$-0.00662391\pi$
$770$		0			0
$771$	2541.83			3.29679
$772$		0			0
$773$	−730.274	−	530.575i	−0.944728	−	0.686385i	0.00482645	−	0.999988i	$-0.498464\pi$
$773$	−730.274	−	530.575i	−0.944728	−	0.686385i	−0.949554	+	0.313604i	$0.898464\pi$
$774$		0			0
$775$	−17.0588	+	52.5016i	−0.0220114	+	0.0677440i
$776$		0			0
$777$	548.906	+	755.505i	0.706443	+	0.972335i
$778$		0			0
$779$	495.637	+	1525.41i	0.636247	+	1.95817i
$780$		0			0
$781$	−431.592	+	132.568i	−0.552614	+	0.169742i
$782$		0			0
$783$	−462.424	+	150.251i	−0.590580	+	0.191891i
$784$		0			0
$785$	1046.53	−	760.351i	1.33316	−	0.968600i
$786$		0			0
$787$	803.354	+	261.026i	1.02078	+	0.331672i	0.771139	−	0.636667i	$-0.219687\pi$
$787$	803.354	+	261.026i	1.02078	+	0.331672i	0.249641	+	0.968338i	$0.419687\pi$
$788$		0			0
$789$	530.493	−	730.161i	0.672362	−	0.925426i
$790$		0			0
$791$			388.085i			0.490626i
$792$		0			0
$793$	−426.232			−0.537493
$794$		0			0
$795$	−191.960	−	139.467i	−0.241460	−	0.175431i
$796$		0			0
$797$	−132.202	+	406.875i	−0.165874	+	0.510508i	−0.999100	−	0.0424253i	$-0.986492\pi$
$797$	−132.202	+	406.875i	−0.165874	+	0.510508i	0.833226	+	0.552933i	$0.186492\pi$
$798$		0			0
$799$	−819.141	−	1127.45i	−1.02521	−	1.41108i
$800$		0			0
$801$	309.096	+	951.300i	0.385888	+	1.18764i
$802$		0			0
$803$	220.328	−	642.609i	0.274381	−	0.800260i
$804$		0			0
$805$	107.886	−	35.0544i	0.134020	−	0.0435459i
$806$		0			0
$807$	−431.208	+	313.291i	−0.534334	+	0.388217i
$808$		0			0
$809$	−633.173	−	205.731i	−0.782662	−	0.254302i	−0.109686	−	0.993966i	$-0.534984\pi$
$809$	−633.173	−	205.731i	−0.782662	−	0.254302i	−0.672976	+	0.739664i	$0.734984\pi$
$810$		0			0
$811$	−382.500	+	526.466i	−0.471640	+	0.649156i	−0.976871	−	0.213828i	$-0.931407\pi$
$811$	−382.500	+	526.466i	−0.471640	+	0.649156i	0.505232	+	0.862984i	$0.331407\pi$
$812$		0			0
$813$		−	742.189i		−	0.912901i
$814$		0			0
$815$	−68.2962			−0.0837990
$816$		0			0
$817$	441.907	+	321.064i	0.540890	+	0.392979i
$818$		0			0
$819$	513.045	−	1578.99i	0.626428	−	1.92795i
$820$		0			0
$821$	−725.856	−	999.055i	−0.884112	−	1.21688i	−0.975265	−	0.221039i	$-0.929055\pi$
$821$	−725.856	−	999.055i	−0.884112	−	1.21688i	0.0911526	−	0.995837i	$-0.470945\pi$
$822$		0			0
$823$	210.770	+	648.683i	0.256100	+	0.788193i	0.993611	+	0.112859i	$0.0360008\pi$
$823$	210.770	+	648.683i	0.256100	+	0.788193i	−0.737512	+	0.675335i	$0.763999\pi$
$824$		0			0
$825$	84.2115	−	112.057i	0.102075	−	0.135827i
$826$		0			0
$827$	207.534	−	67.4319i	0.250948	−	0.0815379i	−0.180842	−	0.983512i	$-0.557882\pi$
$827$	207.534	−	67.4319i	0.250948	−	0.0815379i	0.431790	+	0.901974i	$0.357882\pi$
$828$		0			0
$829$	−1026.39	+	745.718i	−1.23811	+	0.899539i	−0.997471	−	0.0710752i	$-0.977357\pi$
$829$	−1026.39	+	745.718i	−1.23811	+	0.899539i	−0.240639	+	0.970615i	$0.577357\pi$
$830$		0			0
$831$	−1250.58	−	406.340i	−1.50492	−	0.488977i
$832$		0			0
$833$	−47.8078	+	65.8018i	−0.0573923	+	0.0789937i
$834$		0			0
$835$			770.856i			0.923181i
$836$		0			0
$837$	833.592			0.995928
$838$		0			0
$839$	−734.509	−	533.652i	−0.875458	−	0.636058i	0.0565879	−	0.998398i	$-0.481978\pi$
$839$	−734.509	−	533.652i	−0.875458	−	0.636058i	−0.932046	+	0.362340i	$0.881978\pi$
$840$		0			0
$841$	209.501	−	644.777i	0.249109	−	0.766679i
$842$		0			0
$843$	−1521.32	−	2093.92i	−1.80465	−	2.48389i
$844$		0			0
$845$	−84.6852	−	260.634i	−0.100219	−	0.308443i
$846$		0			0
$847$	774.874	−	224.387i	0.914845	−	0.264920i
$848$		0			0
$849$	859.784	−	279.361i	1.01270	−	0.329047i
$850$		0			0
$851$	−80.4787	+	58.4712i	−0.0945696	+	0.0687088i
$852$		0			0
$853$	18.1669	+	5.90278i	0.0212976	+	0.00692003i	0.319646	−	0.947537i	$-0.396436\pi$
$853$	18.1669	+	5.90278i	0.0212976	+	0.00692003i	−0.298349	+	0.954457i	$0.596436\pi$
$854$		0			0
$855$	1491.49	−	2052.86i	1.74444	−	2.40101i
$856$		0			0
$857$			488.737i			0.570289i	0.958485	+	0.285144i	$0.0920415\pi$
$857$			488.737i			0.570289i	−0.958485	+	0.285144i	$0.907958\pi$
$858$		0			0
$859$	−1449.51			−1.68744			−0.843721	−	0.536782i	$-0.819640\pi$
$859$	−1449.51			−1.68744			−0.843721	+	0.536782i	$0.819640\pi$
$860$		0			0
$861$	−1350.64	−	981.297i	−1.56869	−	1.13972i
$862$		0			0
$863$	10.0403	−	30.9007i	0.0116341	−	0.0358062i	−0.945071	−	0.326865i	$-0.894008\pi$
$863$	10.0403	−	30.9007i	0.0116341	−	0.0358062i	0.956705	+	0.291059i	$0.0940076\pi$
$864$		0			0
$865$	312.178	+	429.677i	0.360900	+	0.496736i
$866$		0			0
$867$	−47.5048	−	146.205i	−0.0547921	−	0.168633i
$868$		0			0
$869$	1092.93	+	821.346i	1.25769	+	0.945162i
$870$		0			0
$871$	−440.047	+	142.980i	−0.505221	+	0.164156i
$872$		0			0
$873$	−641.679	+	466.207i	−0.735028	+	0.534029i
$874$		0			0
$875$	−827.361	−	268.826i	−0.945555	−	0.307230i
$876$		0			0
$877$	−71.7460	+	98.7499i	−0.0818084	+	0.112600i	−0.847960	−	0.530060i	$-0.822169\pi$
$877$	−71.7460	+	98.7499i	−0.0818084	+	0.112600i	0.766151	+	0.642660i	$0.222169\pi$
$878$		0			0
$879$			2628.09i			2.98986i
$880$		0			0
$881$	−545.388			−0.619055			−0.309528	−	0.950890i	$-0.600171\pi$
$881$	−545.388			−0.619055			−0.309528	+	0.950890i	$0.600171\pi$
$882$		0			0
$883$	823.342	+	598.193i	0.932438	+	0.677456i	0.946588	−	0.322444i	$-0.104505\pi$
$883$	823.342	+	598.193i	0.932438	+	0.677456i	−0.0141509	+	0.999900i	$0.504505\pi$
$884$		0			0
$885$	271.444	−	835.417i	0.306716	−	0.943974i
$886$		0			0
$887$	894.768	+	1231.54i	1.00876	+	1.38844i	0.919794	+	0.392401i	$0.128355\pi$
$887$	894.768	+	1231.54i	1.00876	+	1.38844i	0.0889633	+	0.996035i	$0.471645\pi$
$888$		0			0
$889$	81.4921	+	250.807i	0.0916671	+	0.282122i
$890$		0			0
$891$	−453.713	−	155.562i	−0.509218	−	0.174593i
$892$		0			0
$893$	2400.31	−	779.908i	2.68792	−	0.873357i
$894$		0			0
$895$	−602.788	+	437.951i	−0.673507	+	0.489331i
$896$		0			0
$897$	259.747	+	84.3968i	0.289573	+	0.0940879i
$898$		0			0
$899$	164.299	−	226.138i	0.182758	−	0.251544i
$900$		0			0
$901$		−	177.004i		−	0.196453i
$902$		0			0
$903$	−568.557			−0.629631
$904$		0			0
$905$	1306.68	+	949.361i	1.44385	+	1.04902i
$906$		0			0
$907$	−193.968	+	596.971i	−0.213856	+	0.658182i	0.785377	+	0.619018i	$0.212469\pi$
$907$	−193.968	+	596.971i	−0.213856	+	0.658182i	−0.999233	+	0.0391635i	$0.987531\pi$
$908$		0			0
$909$	855.109	+	1176.96i	0.940713	+	1.29478i
$910$		0			0
$911$	221.708	+	682.348i	0.243368	+	0.749010i	0.995901	+	0.0904550i	$0.0288321\pi$
$911$	221.708	+	682.348i	0.243368	+	0.749010i	−0.752532	+	0.658555i	$0.771168\pi$
$912$		0			0
$913$	−9.99610	−	32.5434i	−0.0109486	−	0.0356445i
$914$		0			0
$915$	644.885	−	209.536i	0.704792	−	0.229001i
$916$		0			0
$917$	−702.699	+	510.541i	−0.766302	+	0.556751i
$918$		0			0
$919$	−847.124	−	275.247i	−0.921789	−	0.299507i	−0.190588	−	0.981670i	$-0.561040\pi$
$919$	−847.124	−	275.247i	−0.921789	−	0.299507i	−0.731200	+	0.682163i	$0.761040\pi$
$920$		0			0
$921$	1347.84	−	1855.15i	1.46346	−	2.01428i
$922$		0			0
$923$			618.133i			0.669700i
$924$		0			0
$925$	69.8995			0.0755670
$926$		0			0
$927$	166.298	+	120.823i	0.179394	+	0.130337i
$928$		0			0
$929$	−250.632	+	771.367i	−0.269787	+	0.830320i	0.720765	+	0.693180i	$0.243791\pi$
$929$	−250.632	+	771.367i	−0.269787	+	0.830320i	−0.990552	+	0.137140i	$0.956209\pi$
$930$		0			0
$931$	−86.5804	−	119.168i	−0.0929972	−	0.128000i
$932$		0			0
$933$	633.549	+	1949.86i	0.679045	+	2.08988i
$934$		0			0
$935$	−931.965	−	15.0481i	−0.996754	−	0.0160942i
$936$		0			0
$937$	−1399.40	+	454.693i	−1.49349	+	0.485265i	−0.938112	−	0.346331i	$-0.887427\pi$
$937$	−1399.40	+	454.693i	−1.49349	+	0.485265i	−0.555380	+	0.831596i	$0.687427\pi$
$938$		0			0
$939$	−68.2695	+	49.6007i	−0.0727044	+	0.0528229i
$940$		0			0
$941$	−130.287	−	42.3328i	−0.138456	−	0.0449871i	0.238969	−	0.971027i	$-0.423190\pi$
$941$	−130.287	−	42.3328i	−0.138456	−	0.0449871i	−0.377425	+	0.926040i	$0.623190\pi$
$942$		0			0
$943$	104.531	−	143.874i	0.110849	−	0.152571i
$944$		0			0
$945$			1203.65i			1.27370i
$946$		0			0
$947$	−862.357			−0.910620			−0.455310	−	0.890333i	$-0.650472\pi$
$947$	−862.357			−0.910620			−0.455310	+	0.890333i	$0.650472\pi$
$948$		0			0
$949$	−752.437	−	546.677i	−0.792873	−	0.576056i
$950$		0			0
$951$	878.442	−	2703.57i	0.923703	−	2.84287i
$952$		0			0
$953$	−875.727	−	1205.33i	−0.918916	−	1.26478i	−0.964029	−	0.265797i	$-0.914365\pi$
$953$	−875.727	−	1205.33i	−0.918916	−	1.26478i	0.0451134	−	0.998982i	$-0.485635\pi$
$954$		0			0
$955$	45.5926	+	140.320i	0.0477410	+	0.146932i
$956$		0			0
$957$	−580.871	+	407.864i	−0.606971	+	0.426190i
$958$		0			0
$959$	1306.53	−	424.516i	1.36238	−	0.442665i
$960$		0			0
$961$	389.767	−	283.183i	0.405585	−	0.294675i
$962$		0			0
$963$	18.6981	+	6.07537i	0.0194165	+	0.00630879i
$964$		0			0
$965$	−139.769	+	192.376i	−0.144838	+	0.199353i
$966$		0			0
$967$		−	961.962i		−	0.994790i	−0.867524	−	0.497395i	$-0.834290\pi$
$967$		−	961.962i		−	0.994790i	0.867524	−	0.497395i	$-0.165710\pi$
$968$		0			0
$969$	2923.19			3.01671
$970$		0			0
$971$	827.337	+	601.095i	0.852046	+	0.619048i	0.925709	−	0.378235i	$-0.123469\pi$
$971$	827.337	+	601.095i	0.852046	+	0.619048i	−0.0736633	+	0.997283i	$0.523469\pi$
$972$		0			0
$973$	−441.292	+	1358.16i	−0.453537	+	1.39584i
$974$		0			0
$975$	−112.801	−	155.257i	−0.115693	−	0.159238i
$976$		0			0
$977$	−363.804	−	1119.67i	−0.372368	−	1.14603i	−0.945237	−	0.326384i	$-0.894170\pi$
$977$	−363.804	−	1119.67i	−0.372368	−	1.14603i	0.572869	−	0.819647i	$-0.305830\pi$
$978$		0			0
$979$	382.373	+	544.568i	0.390575	+	0.556249i
$980$		0			0
$981$	−2283.63	+	741.996i	−2.32786	+	0.756367i
$982$		0			0
$983$	287.961	−	209.216i	0.292941	−	0.212834i	−0.431601	−	0.902065i	$-0.642051\pi$
$983$	287.961	−	209.216i	0.292941	−	0.212834i	0.724542	+	0.689230i	$0.242051\pi$
$984$		0			0
$985$	−1018.29	−	330.863i	−1.03380	−	0.335901i
$986$		0			0
$987$	−1544.12	+	2125.30i	−1.56446	+	2.15329i
$988$		0			0
$989$		−	60.5645i		−	0.0612381i
$990$		0			0
$991$	−370.283			−0.373646			−0.186823	−	0.982394i	$-0.559819\pi$
$991$	−370.283			−0.373646			−0.186823	+	0.982394i	$0.559819\pi$
$992$		0			0
$993$	−685.521	−	498.060i	−0.690353	−	0.501571i
$994$		0			0
$995$	68.0155	−	209.330i	0.0683573	−	0.210382i
$996$		0			0
$997$	16.4378	+	22.6247i	0.0164872	+	0.0226927i	0.817181	−	0.576381i	$-0.195536\pi$
$997$	16.4378	+	22.6247i	0.0164872	+	0.0226927i	−0.800694	+	0.599074i	$0.795536\pi$
$998$		0			0
$999$	−326.170	−	1003.85i	−0.326496	−	1.00485i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	44.3.f.a.17.1	yes	8
3.2	odd	2		396.3.t.a.325.1		8
4.3	odd	2		176.3.n.c.17.2		8
11.2	odd	10	inner	44.3.f.a.13.1	✓	8
11.3	even	5		484.3.d.c.241.8		8
11.4	even	5		484.3.f.e.481.2		8
11.5	even	5		484.3.f.d.161.2		8
11.6	odd	10		484.3.f.e.161.2		8
11.7	odd	10		484.3.f.d.481.2		8
11.8	odd	10		484.3.d.c.241.7		8
11.9	even	5		484.3.f.a.233.1		8
11.10	odd	2		484.3.f.a.457.1		8
33.2	even	10		396.3.t.a.145.1		8
33.8	even	10		4356.3.f.g.1693.3		8
33.14	odd	10		4356.3.f.g.1693.4		8
44.35	even	10		176.3.n.c.145.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
44.3.f.a.13.1	✓	8	11.2	odd	10	inner
44.3.f.a.17.1	yes	8	1.1	even	1	trivial
176.3.n.c.17.2		8	4.3	odd	2
176.3.n.c.145.2		8	44.35	even	10
396.3.t.a.145.1		8	33.2	even	10
396.3.t.a.325.1		8	3.2	odd	2
484.3.d.c.241.7		8	11.8	odd	10
484.3.d.c.241.8		8	11.3	even	5
484.3.f.a.233.1		8	11.9	even	5
484.3.f.a.457.1		8	11.10	odd	2
484.3.f.d.161.2		8	11.5	even	5
484.3.f.d.481.2		8	11.7	odd	10
484.3.f.e.161.2		8	11.6	odd	10
484.3.f.e.481.2		8	11.4	even	5
4356.3.f.g.1693.3		8	33.8	even	10
4356.3.f.g.1693.4		8	33.14	odd	10

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 44 = 2^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	44.f (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.08818 - 2.97024i) q^{3} +(1.46509 - 4.50908i) q^{5} +(-3.91877 - 5.39373i) q^{7} +(5.10976 + 15.7262i) q^{9} +(6.32112 + 9.00241i) q^{11} +(14.3229 - 4.65378i) q^{13} +(-19.3826 + 14.0823i) q^{15} +(-16.9976 - 5.52287i) q^{17} +(19.0249 - 26.1855i) q^{19} +33.6902i q^{21} -3.58879 q^{23} +(2.04012 + 1.48224i) q^{25} +(11.7671 - 36.2153i) q^{27} +(-7.50529 - 10.3301i) q^{29} +(6.76473 + 20.8197i) q^{31} +(0.897408 - 55.5787i) q^{33} +(-30.0621 + 9.76777i) q^{35} +(22.4250 - 16.2927i) q^{37} +(-72.3773 - 23.5168i) q^{39} +(-29.1270 + 40.0899i) q^{41} +16.8760i q^{43} +78.3970 q^{45} +(63.0835 + 45.8328i) q^{47} +(1.40631 - 4.32817i) q^{49} +(53.0852 + 73.0655i) q^{51} +(3.06043 + 9.41904i) q^{53} +(49.8536 - 15.3131i) q^{55} +(-155.554 + 50.5426i) q^{57} +(-29.6620 + 21.5507i) q^{59} +(-26.9171 - 8.74590i) q^{61} +(64.7990 - 89.1881i) q^{63} -71.4011i q^{65} -30.7234 q^{67} +(14.6716 + 10.6595i) q^{69} +(-12.6835 + 39.0359i) q^{71} +(-36.3001 - 49.9628i) q^{73} +(-3.93780 - 12.1193i) q^{75} +(23.7855 - 69.3728i) q^{77} +(118.204 - 38.4068i) q^{79} +(-35.2762 + 25.6296i) q^{81} +(-2.94344 - 0.956381i) q^{83} +(-49.8061 + 68.5522i) q^{85} +64.5240i q^{87} +60.4914 q^{89} +(-81.2293 - 59.0165i) q^{91} +(34.1840 - 105.207i) q^{93} +(-90.1993 - 124.149i) q^{95} +(14.8226 + 45.6193i) q^{97} +(-109.274 + 145.407i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 5 q^{3} - q^{5} + 15 q^{7} - q^{9} + 17 q^{11} - 15 q^{13} - 63 q^{15} - 75 q^{17} - 30 q^{19} + 100 q^{23} + 51 q^{25} + 100 q^{27} + 125 q^{29} + 73 q^{31} - 20 q^{33} - 155 q^{35} - 75 q^{37}+ \cdots - 419 q^{99}+O(q^{100}) \) 8 * q - 5 * q^3 - q^5 + 15 * q^7 - q^9 + 17 * q^11 - 15 * q^13 - 63 * q^15 - 75 * q^17 - 30 * q^19 + 100 * q^23 + 51 * q^25 + 100 * q^27 + 125 * q^29 + 73 * q^31 - 20 * q^33 - 155 * q^35 - 75 * q^37 - 185 * q^39 - 155 * q^41 + 332 * q^45 + 45 * q^47 + 87 * q^49 + 150 * q^51 - 85 * q^53 - 89 * q^55 - 310 * q^57 - 178 * q^59 - 145 * q^61 - 110 * q^63 + 10 * q^67 + 124 * q^69 + 207 * q^71 + 65 * q^73 + 192 * q^75 + 365 * q^77 + 235 * q^79 - 12 * q^81 + 210 * q^83 + 105 * q^85 + 18 * q^89 - 195 * q^91 - 335 * q^93 - 255 * q^95 - 90 * q^97 - 419 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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