LMFDB - Embedded newform 240.5.bg.c.193.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [240,5,Mod(97,240)] 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("240.97"); S:= CuspForms(chi, 5); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(240, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 0, 1])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	240.bg (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,0,-84] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$24.8087911401$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
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} - 60x^{5} + 1973x^{4} - 3300x^{3} + 1800x^{2} + 31560x + 276676 $ x^8 - 60x^5 + 1973x^4 - 3300x^3 + 1800x^2 + 31560*x + 276676
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 15)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			193.2
Root			$3.30519 - 3.30519i$ of defining polynomial
Character	$\chi$	$=$	240.193
Dual form			240.5.bg.c.97.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.67423 - 3.67423i) q^{3} +(-8.43390 + 23.5344i) q^{5} +(-65.1093 + 65.1093i) q^{7} +27.0000i q^{9} -56.3999 q^{11} +(0.983822 + 0.983822i) q^{13} +(117.459 - 55.4829i) q^{15} +(159.144 - 159.144i) q^{17} -265.552i q^{19} +478.454 q^{21} +(185.430 + 185.430i) q^{23} +(-482.739 - 396.974i) q^{25} +(99.2043 - 99.2043i) q^{27} -544.071i q^{29} +710.805 q^{31} +(207.227 + 207.227i) q^{33} +(-983.184 - 2081.43i) q^{35} +(-639.026 + 639.026i) q^{37} -7.22958i q^{39} -1325.70 q^{41} +(22.3358 + 22.3358i) q^{43} +(-635.430 - 227.715i) q^{45} +(-456.136 + 456.136i) q^{47} -6077.44i q^{49} -1169.47 q^{51} +(-424.212 - 424.212i) q^{53} +(475.672 - 1327.34i) q^{55} +(-975.701 + 975.701i) q^{57} -3460.30i q^{59} +4937.82 q^{61} +(-1757.95 - 1757.95i) q^{63} +(-31.4511 + 14.8562i) q^{65} +(3801.58 - 3801.58i) q^{67} -1362.62i q^{69} -7950.20 q^{71} +(-1940.65 - 1940.65i) q^{73} +(315.118 + 3232.27i) q^{75} +(3672.16 - 3672.16i) q^{77} -4083.83i q^{79} -729.000 q^{81} +(9103.10 + 9103.10i) q^{83} +(2403.16 + 5087.58i) q^{85} +(-1999.04 + 1999.04i) q^{87} +7016.23i q^{89} -128.112 q^{91} +(-2611.66 - 2611.66i) q^{93} +(6249.62 + 2239.64i) q^{95} +(2571.87 - 2571.87i) q^{97} -1522.80i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 84 q^{5} - 20 q^{7} + 288 q^{11} - 340 q^{13} - 144 q^{15} + 900 q^{17} + 792 q^{21} + 1560 q^{23} - 1204 q^{25} + 512 q^{31} + 2700 q^{33} - 6600 q^{35} - 3820 q^{37} - 2712 q^{41} + 1240 q^{43}+ \cdots + 58640 q^{97}+O(q^{100}) $ 8 * q - 84 * q^5 - 20 * q^7 + 288 * q^11 - 340 * q^13 - 144 * q^15 + 900 * q^17 + 792 * q^21 + 1560 * q^23 - 1204 * q^25 + 512 * q^31 + 2700 * q^33 - 6600 * q^35 - 3820 * q^37 - 2712 * q^41 + 1240 * q^43 - 1944 * q^45 - 4800 * q^47 - 6264 * q^51 + 1020 * q^53 + 3644 * q^55 - 5400 * q^57 - 4760 * q^61 - 540 * q^63 - 1212 * q^65 + 8920 * q^67 - 7536 * q^71 + 11600 * q^73 + 5976 * q^75 - 360 * q^77 - 5832 * q^81 + 32400 * q^83 - 15628 * q^85 - 10620 * q^87 - 16528 * q^91 + 14040 * q^93 - 18864 * q^95 + 58640 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$1$	$1$

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
$3$	−3.67423	−	3.67423i	−0.408248	−	0.408248i
$3$	−3.67423	−	3.67423i	−0.408248	−	0.408248i
$4$		0			0
$5$	−8.43390	+	23.5344i	−0.337356	+	0.941377i
$5$	−8.43390	+	23.5344i	−0.337356	+	0.941377i
$6$		0			0
$7$	−65.1093	+	65.1093i	−1.32876	+	1.32876i	−0.422309	+	0.906452i	$0.638780\pi$
$7$	−65.1093	+	65.1093i	−1.32876	+	1.32876i	−0.906452	+	0.422309i	$0.861220\pi$
$8$		0			0
$9$			27.0000i			0.333333i
$10$		0			0
$11$	−56.3999			−0.466115			−0.233058	−	0.972463i	$-0.574873\pi$
$11$	−56.3999			−0.466115			−0.233058	+	0.972463i	$0.574873\pi$
$12$		0			0
$13$	0.983822	+	0.983822i	0.00582143	+	0.00582143i	0.710012	−	0.704190i	$-0.248690\pi$
$13$	0.983822	+	0.983822i	0.00582143	+	0.00582143i	−0.704190	+	0.710012i	$0.748690\pi$
$14$		0			0
$15$	117.459	−	55.4829i	0.522041	−	0.246591i
$16$		0			0
$17$	159.144	−	159.144i	0.550673	−	0.550673i	−0.375962	−	0.926635i	$-0.622688\pi$
$17$	159.144	−	159.144i	0.550673	−	0.550673i	0.926635	+	0.375962i	$0.122688\pi$
$18$		0			0
$19$		−	265.552i		−	0.735602i	−0.929905	−	0.367801i	$-0.880111\pi$
$19$		−	265.552i		−	0.735602i	0.929905	−	0.367801i	$-0.119889\pi$
$20$		0			0
$21$	478.454			1.08493
$22$		0			0
$23$	185.430	+	185.430i	0.350529	+	0.350529i	0.860306	−	0.509778i	$-0.170272\pi$
$23$	185.430	+	185.430i	0.350529	+	0.350529i	−0.509778	+	0.860306i	$0.670272\pi$
$24$		0			0
$25$	−482.739	−	396.974i	−0.772382	−	0.635159i
$26$		0			0
$27$	99.2043	−	99.2043i	0.136083	−	0.136083i
$28$		0			0
$29$		−	544.071i		−	0.646933i	−0.946240	−	0.323467i	$-0.895152\pi$
$29$		−	544.071i		−	0.646933i	0.946240	−	0.323467i	$-0.104848\pi$
$30$		0			0
$31$	710.805			0.739651			0.369826	−	0.929101i	$-0.379417\pi$
$31$	710.805			0.739651			0.369826	+	0.929101i	$0.379417\pi$
$32$		0			0
$33$	207.227	+	207.227i	0.190291	+	0.190291i
$34$		0			0
$35$	−983.184	−	2081.43i	−0.802599	−	1.69913i
$36$		0			0
$37$	−639.026	+	639.026i	−0.466783	+	0.466783i	−0.900871	−	0.434088i	$-0.857071\pi$
$37$	−639.026	+	639.026i	−0.466783	+	0.466783i	0.434088	+	0.900871i	$0.357071\pi$
$38$		0			0
$39$		−	7.22958i		−	0.00475318i
$40$		0			0
$41$	−1325.70			−0.788638			−0.394319	−	0.918974i	$-0.629019\pi$
$41$	−1325.70			−0.788638			−0.394319	+	0.918974i	$0.629019\pi$
$42$		0			0
$43$	22.3358	+	22.3358i	0.0120799	+	0.0120799i	0.713121	−	0.701041i	$-0.247281\pi$
$43$	22.3358	+	22.3358i	0.0120799	+	0.0120799i	−0.701041	+	0.713121i	$0.747281\pi$
$44$		0			0
$45$	−635.430	−	227.715i	−0.313792	−	0.112452i
$46$		0			0
$47$	−456.136	+	456.136i	−0.206490	+	0.206490i	−0.802774	−	0.596284i	$-0.796643\pi$
$47$	−456.136	+	456.136i	−0.206490	+	0.206490i	0.596284	+	0.802774i	$0.296643\pi$
$48$		0			0
$49$		−	6077.44i		−	2.53121i
$50$		0			0
$51$	−1169.47			−0.449622
$52$		0			0
$53$	−424.212	−	424.212i	−0.151019	−	0.151019i	0.627554	−	0.778573i	$-0.284056\pi$
$53$	−424.212	−	424.212i	−0.151019	−	0.151019i	−0.778573	+	0.627554i	$0.784056\pi$
$54$		0			0
$55$	475.672	−	1327.34i	0.157247	−	0.438790i
$56$		0			0
$57$	−975.701	+	975.701i	−0.300308	+	0.300308i
$58$		0			0
$59$		−	3460.30i		−	0.994054i	−0.867735	−	0.497027i	$-0.834425\pi$
$59$		−	3460.30i		−	0.994054i	0.867735	−	0.497027i	$-0.165575\pi$
$60$		0			0
$61$	4937.82			1.32701			0.663507	−	0.748170i	$-0.269067\pi$
$61$	4937.82			1.32701			0.663507	+	0.748170i	$0.269067\pi$
$62$		0			0
$63$	−1757.95	−	1757.95i	−0.442920	−	0.442920i
$64$		0			0
$65$	−31.4511	+	14.8562i	−0.00744406	+	0.00351627i
$66$		0			0
$67$	3801.58	−	3801.58i	0.846866	−	0.846866i	−0.142874	−	0.989741i	$-0.545634\pi$
$67$	3801.58	−	3801.58i	0.846866	−	0.846866i	0.989741	+	0.142874i	$0.0456345\pi$
$68$		0			0
$69$		−	1362.62i		−	0.286206i
$70$		0			0
$71$	−7950.20			−1.57711			−0.788554	−	0.614966i	$-0.789170\pi$
$71$	−7950.20			−1.57711			−0.788554	+	0.614966i	$0.789170\pi$
$72$		0			0
$73$	−1940.65	−	1940.65i	−0.364168	−	0.364168i	0.501177	−	0.865345i	$-0.332901\pi$
$73$	−1940.65	−	1940.65i	−0.364168	−	0.364168i	−0.865345	+	0.501177i	$0.832901\pi$
$74$		0			0
$75$	315.118	+	3232.27i	0.0560211	+	0.574626i
$76$		0			0
$77$	3672.16	−	3672.16i	0.619355	−	0.619355i
$78$		0			0
$79$		−	4083.83i		−	0.654355i	−0.944963	−	0.327178i	$-0.893902\pi$
$79$		−	4083.83i		−	0.654355i	0.944963	−	0.327178i	$-0.106098\pi$
$80$		0			0
$81$	−729.000			−0.111111
$82$		0			0
$83$	9103.10	+	9103.10i	1.32140	+	1.32140i	0.912646	+	0.408750i	$0.134035\pi$
$83$	9103.10	+	9103.10i	1.32140	+	1.32140i	0.408750	+	0.912646i	$0.365965\pi$
$84$		0			0
$85$	2403.16	+	5087.58i	0.332618	+	0.704164i
$86$		0			0
$87$	−1999.04	+	1999.04i	−0.264109	+	0.264109i
$88$		0			0
$89$			7016.23i			0.885775i	0.896577	+	0.442888i	$0.146046\pi$
$89$			7016.23i			0.885775i	−0.896577	+	0.442888i	$0.853954\pi$
$90$		0			0
$91$	−128.112			−0.0154706
$92$		0			0
$93$	−2611.66	−	2611.66i	−0.301961	−	0.301961i
$94$		0			0
$95$	6249.62	+	2239.64i	0.692479	+	0.248160i
$96$		0			0
$97$	2571.87	−	2571.87i	0.273342	−	0.273342i	−0.557102	−	0.830444i	$-0.688087\pi$
$97$	2571.87	−	2571.87i	0.273342	−	0.273342i	0.830444	+	0.557102i	$0.188087\pi$
$98$		0			0
$99$		−	1522.80i		−	0.155372i
$100$		0			0
$101$	−7459.58			−0.731260			−0.365630	−	0.930760i	$-0.619146\pi$
$101$	−7459.58			−0.731260			−0.365630	+	0.930760i	$0.619146\pi$
$102$		0			0
$103$	−4637.29	−	4637.29i	−0.437109	−	0.437109i	0.453929	−	0.891038i	$-0.350022\pi$
$103$	−4637.29	−	4637.29i	−0.437109	−	0.437109i	−0.891038	+	0.453929i	$0.850022\pi$
$104$		0			0
$105$	−4035.23	+	11260.1i	−0.366007	+	1.02133i
$106$		0			0
$107$	8804.34	−	8804.34i	0.769005	−	0.769005i	−0.208926	−	0.977931i	$-0.566997\pi$
$107$	8804.34	−	8804.34i	0.769005	−	0.769005i	0.977931	+	0.208926i	$0.0669969\pi$
$108$		0			0
$109$		−	7981.01i		−	0.671746i	−0.941907	−	0.335873i	$-0.890969\pi$
$109$		−	7981.01i		−	0.671746i	0.941907	−	0.335873i	$-0.109031\pi$
$110$		0			0
$111$	4695.86			0.381126
$112$		0			0
$113$	1867.37	+	1867.37i	0.146242	+	0.146242i	0.776437	−	0.630195i	$-0.217025\pi$
$113$	1867.37	+	1867.37i	0.146242	+	0.146242i	−0.630195	+	0.776437i	$0.717025\pi$
$114$		0			0
$115$	−5927.88	+	2800.09i	−0.448233	+	0.211727i
$116$		0			0
$117$	−26.5632	+	26.5632i	−0.00194048	+	0.00194048i
$118$		0			0
$119$			20723.6i			1.46342i
$120$		0			0
$121$	−11460.0			−0.782737
$122$		0			0
$123$	4870.93	+	4870.93i	0.321960	+	0.321960i
$124$		0			0
$125$	13413.9	−	8012.93i	0.858492	−	0.512828i
$126$		0			0
$127$	−3139.44	+	3139.44i	−0.194646	+	0.194646i	−0.797700	−	0.603054i	$-0.793950\pi$
$127$	−3139.44	+	3139.44i	−0.194646	+	0.194646i	0.603054	+	0.797700i	$0.293950\pi$
$128$		0			0
$129$		−	164.134i		−	0.00986323i
$130$		0			0
$131$	−28716.4			−1.67335			−0.836676	−	0.547698i	$-0.815504\pi$
$131$	−28716.4			−1.67335			−0.836676	+	0.547698i	$0.815504\pi$
$132$		0			0
$133$	17289.9	+	17289.9i	0.977439	+	0.977439i
$134$		0			0
$135$	1498.04	+	3171.40i	0.0821968	+	0.174014i
$136$		0			0
$137$	−25626.6	+	25626.6i	−1.36537	+	1.36537i	−0.498453	+	0.866917i	$0.666098\pi$
$137$	−25626.6	+	25626.6i	−1.36537	+	1.36537i	−0.866917	+	0.498453i	$0.833902\pi$
$138$		0			0
$139$		−	16504.6i		−	0.854229i	−0.904197	−	0.427115i	$-0.859530\pi$
$139$		−	16504.6i		−	0.854229i	0.904197	−	0.427115i	$-0.140470\pi$
$140$		0			0
$141$	3351.90			0.168598
$142$		0			0
$143$	−55.4875	−	55.4875i	−0.00271346	−	0.00271346i
$144$		0			0
$145$	12804.4	+	4588.64i	0.609008	+	0.218247i
$146$		0			0
$147$	−22329.9	+	22329.9i	−1.03336	+	1.03336i
$148$		0			0
$149$			10599.1i			0.477413i	0.971092	+	0.238707i	$0.0767235\pi$
$149$			10599.1i			0.477413i	−0.971092	+	0.238707i	$0.923277\pi$
$150$		0			0
$151$	30610.3			1.34250			0.671248	−	0.741233i	$-0.265758\pi$
$151$	30610.3			1.34250			0.671248	+	0.741233i	$0.265758\pi$
$152$		0			0
$153$	4296.90	+	4296.90i	0.183558	+	0.183558i
$154$		0			0
$155$	−5994.86	+	16728.4i	−0.249526	+	0.696291i
$156$		0			0
$157$	17506.2	−	17506.2i	0.710220	−	0.710220i	−0.256361	−	0.966581i	$-0.582524\pi$
$157$	17506.2	−	17506.2i	0.710220	−	0.710220i	0.966581	+	0.256361i	$0.0825237\pi$
$158$		0			0
$159$			3117.31i			0.123306i
$160$		0			0
$161$	−24146.4			−0.931538
$162$		0			0
$163$	13776.0	+	13776.0i	0.518500	+	0.518500i	0.917117	−	0.398618i	$-0.130510\pi$
$163$	13776.0	+	13776.0i	0.518500	+	0.518500i	−0.398618	+	0.917117i	$0.630510\pi$
$164$		0			0
$165$	−6624.69	+	3129.23i	−0.243331	+	0.114940i
$166$		0			0
$167$	−22076.9	+	22076.9i	−0.791598	+	0.791598i	−0.981754	−	0.190156i	$-0.939101\pi$
$167$	−22076.9	+	22076.9i	−0.791598	+	0.791598i	0.190156	+	0.981754i	$0.439101\pi$
$168$		0			0
$169$		−	28559.1i		−	0.999932i
$170$		0			0
$171$	7169.91			0.245201
$172$		0			0
$173$	26956.5	+	26956.5i	0.900682	+	0.900682i	0.995495	−	0.0948128i	$-0.0302252\pi$
$173$	26956.5	+	26956.5i	0.900682	+	0.900682i	−0.0948128	+	0.995495i	$0.530225\pi$
$174$		0			0
$175$	57277.5	−	5584.06i	1.87028	−	0.182337i
$176$		0			0
$177$	−12714.0	+	12714.0i	−0.405821	+	0.405821i
$178$		0			0
$179$		−	43705.2i		−	1.36404i	−0.731333	−	0.682020i	$-0.761102\pi$
$179$		−	43705.2i		−	1.36404i	0.731333	−	0.682020i	$-0.238898\pi$
$180$		0			0
$181$	30384.4			0.927456			0.463728	−	0.885978i	$-0.346512\pi$
$181$	30384.4			0.927456			0.463728	+	0.885978i	$0.346512\pi$
$182$		0			0
$183$	−18142.7	−	18142.7i	−0.541751	−	0.541751i
$184$		0			0
$185$	−9649.62	−	20428.6i	−0.281947	−	0.596891i
$186$		0			0
$187$	−8975.73	+	8975.73i	−0.256677	+	0.256677i
$188$		0			0
$189$			12918.2i			0.361643i
$190$		0			0
$191$	−4369.57			−0.119777			−0.0598883	−	0.998205i	$-0.519074\pi$
$191$	−4369.57			−0.119777			−0.0598883	+	0.998205i	$0.519074\pi$
$192$		0			0
$193$	−5475.99	−	5475.99i	−0.147011	−	0.147011i	0.629771	−	0.776781i	$-0.283149\pi$
$193$	−5475.99	−	5475.99i	−0.147011	−	0.147011i	−0.776781	+	0.629771i	$0.783149\pi$
$194$		0			0
$195$	170.144	+	60.9736i	0.00447453	+	0.00160351i
$196$		0			0
$197$	−11188.4	+	11188.4i	−0.288295	+	0.288295i	−0.836406	−	0.548111i	$-0.815347\pi$
$197$	−11188.4	+	11188.4i	−0.288295	+	0.288295i	0.548111	+	0.836406i	$0.315347\pi$
$198$		0			0
$199$		−	17995.1i		−	0.454409i	−0.973847	−	0.227205i	$-0.927041\pi$
$199$		−	17995.1i		−	0.454409i	0.973847	−	0.227205i	$-0.0729586\pi$
$200$		0			0
$201$	−27935.8			−0.691464
$202$		0			0
$203$	35424.1	+	35424.1i	0.859620	+	0.859620i
$204$		0			0
$205$	11180.8	−	31199.6i	0.266052	−	0.742406i
$206$		0			0
$207$	−5006.60	+	5006.60i	−0.116843	+	0.116843i
$208$		0			0
$209$			14977.1i			0.342875i
$210$		0			0
$211$	12455.8			0.279774			0.139887	−	0.990167i	$-0.455326\pi$
$211$	12455.8			0.279774			0.139887	+	0.990167i	$0.455326\pi$
$212$		0			0
$213$	29210.9	+	29210.9i	0.643852	+	0.643852i
$214$		0			0
$215$	−714.039	+	337.282i	−0.0154470	+	0.00729654i
$216$		0			0
$217$	−46280.0	+	46280.0i	−0.982820	+	0.982820i
$218$		0			0
$219$			14260.8i			0.297342i
$220$		0			0
$221$	313.140			0.00641141
$222$		0			0
$223$	−26399.5	−	26399.5i	−0.530867	−	0.530867i	0.389963	−	0.920830i	$-0.372488\pi$
$223$	−26399.5	−	26399.5i	−0.530867	−	0.530867i	−0.920830	+	0.389963i	$0.872488\pi$
$224$		0			0
$225$	10718.3	−	13033.9i	0.211720	−	0.257461i
$226$		0			0
$227$	−32267.3	+	32267.3i	−0.626197	+	0.626197i	−0.947109	−	0.320912i	$-0.896011\pi$
$227$	−32267.3	+	32267.3i	−0.626197	+	0.626197i	0.320912	+	0.947109i	$0.396011\pi$
$228$		0			0
$229$		−	68117.5i		−	1.29894i	−0.760389	−	0.649468i	$-0.774992\pi$
$229$		−	68117.5i		−	1.29894i	0.760389	−	0.649468i	$-0.225008\pi$
$230$		0			0
$231$	−26984.7			−0.505702
$232$		0			0
$233$	−65936.0	−	65936.0i	−1.21454	−	1.21454i	−0.969518	−	0.245019i	$-0.921206\pi$
$233$	−65936.0	−	65936.0i	−1.21454	−	1.21454i	−0.245019	−	0.969518i	$-0.578794\pi$
$234$		0			0
$235$	−6887.90	−	14581.9i	−0.124724	−	0.264045i
$236$		0			0
$237$	−15005.0	+	15005.0i	−0.267139	+	0.267139i
$238$		0			0
$239$		−	64820.9i		−	1.13480i	−0.823443	−	0.567400i	$-0.807950\pi$
$239$		−	64820.9i		−	1.13480i	0.823443	−	0.567400i	$-0.192050\pi$
$240$		0			0
$241$	−59597.9			−1.02612			−0.513058	−	0.858354i	$-0.671488\pi$
$241$	−59597.9			−1.02612			−0.513058	+	0.858354i	$0.671488\pi$
$242$		0			0
$243$	2678.52	+	2678.52i	0.0453609	+	0.0453609i
$244$		0			0
$245$	143029.	+	51256.5i	2.38282	+	0.853919i
$246$		0			0
$247$	261.256	−	261.256i	0.00428226	−	0.00428226i
$248$		0			0
$249$		−	66893.9i		−	1.07892i
$250$		0			0
$251$	33922.6			0.538445			0.269223	−	0.963078i	$-0.413233\pi$
$251$	33922.6			0.538445			0.269223	+	0.963078i	$0.413233\pi$
$252$		0			0
$253$	−10458.2	−	10458.2i	−0.163387	−	0.163387i
$254$		0			0
$255$	9863.18	−	27522.8i	0.151683	−	0.423264i
$256$		0			0
$257$	26107.3	−	26107.3i	0.395272	−	0.395272i	−0.481290	−	0.876562i	$-0.659832\pi$
$257$	26107.3	−	26107.3i	0.395272	−	0.395272i	0.876562	+	0.481290i	$0.159832\pi$
$258$		0			0
$259$		−	83213.0i		−	1.24049i
$260$		0			0
$261$	14689.9			0.215644
$262$		0			0
$263$	−25675.0	−	25675.0i	−0.371192	−	0.371192i	0.496719	−	0.867911i	$-0.334538\pi$
$263$	−25675.0	−	25675.0i	−0.371192	−	0.371192i	−0.867911	+	0.496719i	$0.834538\pi$
$264$		0			0
$265$	13561.4	−	6405.83i	0.193113	−	0.0912186i
$266$		0			0
$267$	25779.3	−	25779.3i	0.361616	−	0.361616i
$268$		0			0
$269$		−	84488.9i		−	1.16760i	−0.811896	−	0.583801i	$-0.801565\pi$
$269$		−	84488.9i		−	1.16760i	0.811896	−	0.583801i	$-0.198435\pi$
$270$		0			0
$271$	−105918.			−1.44222			−0.721109	−	0.692821i	$-0.756367\pi$
$271$	−105918.			−1.44222			−0.721109	+	0.692821i	$0.756367\pi$
$272$		0			0
$273$	470.713	+	470.713i	0.00631584	+	0.00631584i
$274$		0			0
$275$	27226.4	+	22389.3i	0.360019	+	0.296057i
$276$		0			0
$277$	71448.5	−	71448.5i	0.931180	−	0.931180i	−0.0665996	−	0.997780i	$-0.521215\pi$
$277$	71448.5	−	71448.5i	0.931180	−	0.931180i	0.997780	+	0.0665996i	$0.0212150\pi$
$278$		0			0
$279$			19191.7i			0.246550i
$280$		0			0
$281$	6316.20			0.0799914			0.0399957	−	0.999200i	$-0.487266\pi$
$281$	6316.20			0.0799914			0.0399957	+	0.999200i	$0.487266\pi$
$282$		0			0
$283$	−51729.2	−	51729.2i	−0.645896	−	0.645896i	0.306102	−	0.951999i	$-0.400975\pi$
$283$	−51729.2	−	51729.2i	−0.645896	−	0.645896i	−0.951999	+	0.306102i	$0.900975\pi$
$284$		0			0
$285$	−14733.6	−	31191.5i	−0.181392	−	0.384014i
$286$		0			0
$287$	86315.4	−	86315.4i	1.04791	−	1.04791i
$288$		0			0
$289$			32867.1i			0.393519i
$290$		0			0
$291$	−18899.3			−0.223183
$292$		0			0
$293$	−71710.7	−	71710.7i	−0.835312	−	0.835312i	0.152926	−	0.988238i	$-0.451130\pi$
$293$	−71710.7	−	71710.7i	−0.835312	−	0.835312i	−0.988238	+	0.152926i	$0.951130\pi$
$294$		0			0
$295$	81436.3	+	29183.9i	0.935780	+	0.335350i
$296$		0			0
$297$	−5595.12	+	5595.12i	−0.0634302	+	0.0634302i
$298$		0			0
$299$			364.860i			0.00408116i
$300$		0			0
$301$	−2908.54			−0.0321027
$302$		0			0
$303$	27408.2	+	27408.2i	0.298535	+	0.298535i
$304$		0			0
$305$	−41645.1	+	116209.i	−0.447676	+	1.24922i
$306$		0			0
$307$	−22058.5	+	22058.5i	−0.234045	+	0.234045i	−0.814379	−	0.580334i	$-0.802922\pi$
$307$	−22058.5	+	22058.5i	−0.234045	+	0.234045i	0.580334	+	0.814379i	$0.302922\pi$
$308$		0			0
$309$			34076.9i			0.356898i
$310$		0			0
$311$	−100432.			−1.03837			−0.519184	−	0.854663i	$-0.673764\pi$
$311$	−100432.			−1.03837			−0.519184	+	0.854663i	$0.673764\pi$
$312$		0			0
$313$	32532.8	+	32532.8i	0.332072	+	0.332072i	0.853373	−	0.521301i	$-0.174553\pi$
$313$	32532.8	+	32532.8i	0.332072	+	0.332072i	−0.521301	+	0.853373i	$0.674553\pi$
$314$		0			0
$315$	56198.7	−	26546.0i	0.566377	−	0.267533i
$316$		0			0
$317$	−72670.5	+	72670.5i	−0.723169	+	0.723169i	−0.969249	−	0.246080i	$-0.920857\pi$
$317$	−72670.5	+	72670.5i	−0.723169	+	0.723169i	0.246080	+	0.969249i	$0.420857\pi$
$318$		0			0
$319$			30685.6i			0.301545i
$320$		0			0
$321$	−64698.4			−0.627890
$322$		0			0
$323$	−42261.2	−	42261.2i	−0.405076	−	0.405076i
$324$		0			0
$325$	−84.3769	−	865.481i	−0.000798834	−	0.00819390i
$326$		0			0
$327$	−29324.1	+	29324.1i	−0.274239	+	0.274239i
$328$		0			0
$329$		−	59397.4i		−	0.548751i
$330$		0			0
$331$	−114400.			−1.04417			−0.522085	−	0.852893i	$-0.674846\pi$
$331$	−114400.			−1.04417			−0.522085	+	0.852893i	$0.674846\pi$
$332$		0			0
$333$	−17253.7	−	17253.7i	−0.155594	−	0.155594i
$334$		0			0
$335$	57405.9	+	121530.i	0.511525	+	1.08292i
$336$		0			0
$337$	−75745.0	+	75745.0i	−0.666952	+	0.666952i	−0.957009	−	0.290058i	$-0.906326\pi$
$337$	−75745.0	+	75745.0i	−0.666952	+	0.666952i	0.290058	+	0.957009i	$0.406326\pi$
$338$		0			0
$339$		−	13722.3i		−	0.119406i
$340$		0			0
$341$	−40089.3			−0.344763
$342$		0			0
$343$	239370.	+	239370.i	2.03461	+	2.03461i
$344$		0			0
$345$	32068.6	+	11492.2i	0.269427	+	0.0965532i
$346$		0			0
$347$	−49964.9	+	49964.9i	−0.414960	+	0.414960i	−0.883462	−	0.468502i	$-0.844794\pi$
$347$	−49964.9	+	49964.9i	−0.414960	+	0.414960i	0.468502	+	0.883462i	$0.344794\pi$
$348$		0			0
$349$			74192.9i			0.609132i	0.952491	+	0.304566i	$0.0985115\pi$
$349$			74192.9i			0.609132i	−0.952491	+	0.304566i	$0.901489\pi$
$350$		0			0
$351$	195.199			0.00158439
$352$		0			0
$353$	−15476.1	−	15476.1i	−0.124198	−	0.124198i	0.642276	−	0.766473i	$-0.277990\pi$
$353$	−15476.1	−	15476.1i	−0.124198	−	0.124198i	−0.766473	+	0.642276i	$0.777990\pi$
$354$		0			0
$355$	67051.2	−	187103.i	0.532047	−	1.48465i
$356$		0			0
$357$	76143.2	−	76143.2i	0.597441	−	0.597441i
$358$		0			0
$359$		−	46469.2i		−	0.360559i	−0.983615	−	0.180279i	$-0.942300\pi$
$359$		−	46469.2i		−	0.360559i	0.983615	−	0.180279i	$-0.0577002\pi$
$360$		0			0
$361$	59803.0			0.458890
$362$		0			0
$363$	42106.9	+	42106.9i	0.319551	+	0.319551i
$364$		0			0
$365$	62039.4	−	29304.9i	0.465674	−	0.219965i
$366$		0			0
$367$	−57731.0	+	57731.0i	−0.428624	+	0.428624i	−0.888160	−	0.459535i	$-0.848016\pi$
$367$	−57731.0	+	57731.0i	−0.428624	+	0.428624i	0.459535	+	0.888160i	$0.348016\pi$
$368$		0			0
$369$		−	35793.9i		−	0.262879i
$370$		0			0
$371$	55240.3			0.401336
$372$		0			0
$373$	166181.	+	166181.i	1.19444	+	1.19444i	0.975807	+	0.218634i	$0.0701600\pi$
$373$	166181.	+	166181.i	1.19444	+	1.19444i	0.218634	+	0.975807i	$0.429840\pi$
$374$		0			0
$375$	−78727.3	−	19844.5i	−0.559839	−	0.141117i
$376$		0			0
$377$	535.269	−	535.269i	0.00376608	−	0.00376608i
$378$		0			0
$379$			41316.4i			0.287636i	0.989604	+	0.143818i	$0.0459380\pi$
$379$			41316.4i			0.287636i	−0.989604	+	0.143818i	$0.954062\pi$
$380$		0			0
$381$	23070.1			0.158928
$382$		0			0
$383$	−72155.3	−	72155.3i	−0.491893	−	0.491893i	0.417009	−	0.908902i	$-0.363078\pi$
$383$	−72155.3	−	72155.3i	−0.491893	−	0.491893i	−0.908902	+	0.417009i	$0.863078\pi$
$384$		0			0
$385$	55451.5	+	117393.i	0.374104	+	0.791990i
$386$		0			0
$387$	−603.067	+	603.067i	−0.00402665	+	0.00402665i
$388$		0			0
$389$		−	192183.i		−	1.27004i	−0.772497	−	0.635018i	$-0.780993\pi$
$389$		−	192183.i		−	1.27004i	0.772497	−	0.635018i	$-0.219007\pi$
$390$		0			0
$391$	59020.2			0.386053
$392$		0			0
$393$	105511.	+	105511.i	0.683143	+	0.683143i
$394$		0			0
$395$	96110.7	+	34442.6i	0.615995	+	0.220751i
$396$		0			0
$397$	−177091.	+	177091.i	−1.12361	+	1.12361i	−0.132416	+	0.991194i	$0.542274\pi$
$397$	−177091.	+	177091.i	−1.12361	+	1.12361i	−0.991194	+	0.132416i	$0.957726\pi$
$398$		0			0
$399$		−	127054.i		−	0.798076i
$400$		0			0
$401$	208300.			1.29539			0.647694	−	0.761900i	$-0.275733\pi$
$401$	208300.			1.29539			0.647694	+	0.761900i	$0.275733\pi$
$402$		0			0
$403$	699.305	+	699.305i	0.00430583	+	0.00430583i
$404$		0			0
$405$	6148.32	−	17156.6i	0.0374840	−	0.104597i
$406$		0			0
$407$	36041.0	−	36041.0i	0.217574	−	0.217574i
$408$		0			0
$409$		−	265733.i		−	1.58854i	−0.607563	−	0.794271i	$-0.707853\pi$
$409$		−	265733.i		−	1.58854i	0.607563	−	0.794271i	$-0.292147\pi$
$410$		0			0
$411$	188316.			1.11482
$412$		0			0
$413$	225298.	+	225298.i	1.32086	+	1.32086i
$414$		0			0
$415$	−291011.	+	137462.i	−1.68971	+	0.798151i
$416$		0			0
$417$	−60641.6	+	60641.6i	−0.348738	+	0.348738i
$418$		0			0
$419$			125608.i			0.715467i	0.933824	+	0.357734i	$0.116450\pi$
$419$			125608.i			0.715467i	−0.933824	+	0.357734i	$0.883550\pi$
$420$		0			0
$421$	−278634.			−1.57206			−0.786031	−	0.618187i	$-0.787868\pi$
$421$	−278634.			−1.57206			−0.786031	+	0.618187i	$0.787868\pi$
$422$		0			0
$423$	−12315.7	−	12315.7i	−0.0688300	−	0.0688300i
$424$		0			0
$425$	−140001.	+	13648.9i	−0.775094	+	0.0755650i
$426$		0			0
$427$	−321498.	+	321498.i	−1.76328	+	1.76328i
$428$		0			0
$429$			407.748i			0.00221553i
$430$		0			0
$431$	−100603.			−0.541575			−0.270787	−	0.962639i	$-0.587284\pi$
$431$	−100603.			−0.541575			−0.270787	+	0.962639i	$0.587284\pi$
$432$		0			0
$433$	−116014.	−	116014.i	−0.618777	−	0.618777i	0.326440	−	0.945218i	$-0.394151\pi$
$433$	−116014.	−	116014.i	−0.618777	−	0.618777i	−0.945218	+	0.326440i	$0.894151\pi$
$434$		0			0
$435$	−30186.6	−	63906.1i	−0.159528	−	0.337726i
$436$		0			0
$437$	49241.3	−	49241.3i	0.257850	−	0.257850i
$438$		0			0
$439$			163656.i			0.849184i	0.905385	+	0.424592i	$0.139582\pi$
$439$			163656.i			0.849184i	−0.905385	+	0.424592i	$0.860418\pi$
$440$		0			0
$441$	164091.			0.843737
$442$		0			0
$443$	117313.	+	117313.i	0.597775	+	0.597775i	0.939720	−	0.341945i	$-0.111086\pi$
$443$	117313.	+	117313.i	0.597775	+	0.597775i	−0.341945	+	0.939720i	$0.611086\pi$
$444$		0			0
$445$	−165123.	−	59174.2i	−0.833849	−	0.298822i
$446$		0			0
$447$	38943.4	−	38943.4i	0.194903	−	0.194903i
$448$		0			0
$449$			342550.i			1.69915i	0.527468	+	0.849575i	$0.323141\pi$
$449$			342550.i			1.69915i	−0.527468	+	0.849575i	$0.676859\pi$
$450$		0			0
$451$	74769.4			0.367596
$452$		0			0
$453$	−112469.	−	112469.i	−0.548072	−	0.548072i
$454$		0			0
$455$	1080.48	−	3015.04i	0.00521909	−	0.0145636i
$456$		0			0
$457$	−162804.	+	162804.i	−0.779530	+	0.779530i	−0.979751	−	0.200221i	$-0.935834\pi$
$457$	−162804.	+	162804.i	−0.779530	+	0.779530i	0.200221	+	0.979751i	$0.435834\pi$
$458$		0			0
$459$		−	31575.6i		−	0.149874i
$460$		0			0
$461$	−283688.			−1.33487			−0.667436	−	0.744667i	$-0.732608\pi$
$461$	−283688.			−1.33487			−0.667436	+	0.744667i	$0.732608\pi$
$462$		0			0
$463$	34085.9	+	34085.9i	0.159006	+	0.159006i	0.782126	−	0.623120i	$-0.214135\pi$
$463$	34085.9	+	34085.9i	0.159006	+	0.159006i	−0.623120	+	0.782126i	$0.714135\pi$
$464$		0			0
$465$	83490.5	−	39437.5i	0.386128	−	0.182391i
$466$		0			0
$467$	124988.	−	124988.i	0.573107	−	0.573107i	−0.359889	−	0.932995i	$-0.617185\pi$
$467$	124988.	−	124988.i	0.573107	−	0.573107i	0.932995	+	0.359889i	$0.117185\pi$
$468$		0			0
$469$			495037.i			2.25057i
$470$		0			0
$471$	−128644.			−0.579892
$472$		0			0
$473$	−1259.74	−	1259.74i	−0.00563064	−	0.00563064i
$474$		0			0
$475$	−105417.	+	128192.i	−0.467224	+	0.568165i
$476$		0			0
$477$	11453.7	−	11453.7i	0.0503396	−	0.0503396i
$478$		0			0
$479$		−	248368.i		−	1.08249i	−0.840864	−	0.541247i	$-0.817953\pi$
$479$		−	248368.i		−	1.08249i	0.840864	−	0.541247i	$-0.182047\pi$
$480$		0			0
$481$	−1257.37			−0.00543469
$482$		0			0
$483$	88719.5	+	88719.5i	0.380299	+	0.380299i
$484$		0			0
$485$	38836.6	+	82218.5i	0.165104	+	0.349531i
$486$		0			0
$487$	159374.	−	159374.i	0.671983	−	0.671983i	−0.286190	−	0.958173i	$-0.592389\pi$
$487$	159374.	−	159374.i	0.671983	−	0.671983i	0.958173	+	0.286190i	$0.0923888\pi$
$488$		0			0
$489$		−	101233.i		−	0.423353i
$490$		0			0
$491$	16577.9			0.0687647			0.0343823	−	0.999409i	$-0.489054\pi$
$491$	16577.9			0.0687647			0.0343823	+	0.999409i	$0.489054\pi$
$492$		0			0
$493$	−86585.9	−	86585.9i	−0.356249	−	0.356249i
$494$		0			0
$495$	35838.2	+	12843.1i	0.146263	+	0.0524156i
$496$		0			0
$497$	517632.	−	517632.i	2.09560	−	2.09560i
$498$		0			0
$499$		−	202437.i		−	0.812998i	−0.913651	−	0.406499i	$-0.866750\pi$
$499$		−	202437.i		−	0.812998i	0.913651	−	0.406499i	$-0.133250\pi$
$500$		0			0
$501$	162231.			0.646337
$502$		0			0
$503$	33478.6	+	33478.6i	0.132322	+	0.132322i	0.770166	−	0.637844i	$-0.220173\pi$
$503$	33478.6	+	33478.6i	0.132322	+	0.132322i	−0.637844	+	0.770166i	$0.720173\pi$
$504$		0			0
$505$	62913.4	−	175557.i	0.246695	−	0.688391i
$506$		0			0
$507$	−104933.	+	104933.i	−0.408221	+	0.408221i
$508$		0			0
$509$		−	57834.5i		−	0.223229i	−0.993752	−	0.111615i	$-0.964398\pi$
$509$		−	57834.5i		−	0.223229i	0.993752	−	0.111615i	$-0.0356022\pi$
$510$		0			0
$511$	252709.			0.967784
$512$		0			0
$513$	−26343.9	−	26343.9i	−0.100103	−	0.100103i
$514$		0			0
$515$	148246.	−	70025.4i	0.558945	−	0.264023i
$516$		0			0
$517$	25726.0	−	25726.0i	0.0962481	−	0.0962481i
$518$		0			0
$519$		−	198089.i		−	0.735404i
$520$		0			0
$521$	−56237.4			−0.207181			−0.103591	−	0.994620i	$-0.533033\pi$
$521$	−56237.4			−0.207181			−0.103591	+	0.994620i	$0.533033\pi$
$522$		0			0
$523$	−210047.	−	210047.i	−0.767914	−	0.767914i	0.209825	−	0.977739i	$-0.432711\pi$
$523$	−210047.	−	210047.i	−0.767914	−	0.767914i	−0.977739	+	0.209825i	$0.932711\pi$
$524$		0			0
$525$	−230968.	−	189934.i	−0.837979	−	0.689102i
$526$		0			0
$527$	113121.	−	113121.i	0.407306	−	0.407306i
$528$		0			0
$529$		−	211073.i		−	0.754259i
$530$		0			0
$531$	93428.2			0.331351
$532$		0			0
$533$	−1304.25	−	1304.25i	−0.00459100	−	0.00459100i
$534$		0			0
$535$	132950.	+	281460.i	0.464495	+	0.983352i
$536$		0			0
$537$	−160583.	+	160583.i	−0.556867	+	0.556867i
$538$		0			0
$539$			342767.i			1.17984i
$540$		0			0
$541$	263561.			0.900505			0.450252	−	0.892901i	$-0.351334\pi$
$541$	263561.			0.900505			0.450252	+	0.892901i	$0.351334\pi$
$542$		0			0
$543$	−111639.	−	111639.i	−0.378632	−	0.378632i
$544$		0			0
$545$	187829.	+	67311.1i	0.632366	+	0.226618i
$546$		0			0
$547$	155327.	−	155327.i	0.519125	−	0.519125i	−0.398182	−	0.917306i	$-0.630359\pi$
$547$	155327.	−	155327.i	0.519125	−	0.519125i	0.917306	+	0.398182i	$0.130359\pi$
$548$		0			0
$549$			133321.i			0.442338i
$550$		0			0
$551$	−144479.			−0.475885
$552$		0			0
$553$	265895.	+	265895.i	0.869482	+	0.869482i
$554$		0			0
$555$	−39604.4	+	110514.i	−0.128575	+	0.358784i
$556$		0			0
$557$	144074.	−	144074.i	0.464381	−	0.464381i	−0.435707	−	0.900088i	$-0.643502\pi$
$557$	144074.	−	144074.i	0.464381	−	0.464381i	0.900088	+	0.435707i	$0.143502\pi$
$558$		0			0
$559$			43.9489i			0.000140645i
$560$		0			0
$561$	65957.9			0.209576
$562$		0			0
$563$	−348774.	−	348774.i	−1.10034	−	1.10034i	−0.994369	−	0.105970i	$-0.966205\pi$
$563$	−348774.	−	348774.i	−1.10034	−	1.10034i	−0.105970	−	0.994369i	$-0.533795\pi$
$564$		0			0
$565$	−59696.6	+	28198.2i	−0.187005	+	0.0883334i
$566$		0			0
$567$	47464.7	−	47464.7i	0.147640	−	0.147640i
$568$		0			0
$569$			183209.i			0.565878i	0.959138	+	0.282939i	$0.0913095\pi$
$569$			183209.i			0.565878i	−0.959138	+	0.282939i	$0.908691\pi$
$570$		0			0
$571$	−363497.			−1.11488			−0.557440	−	0.830217i	$-0.688216\pi$
$571$	−363497.			−1.11488			−0.557440	+	0.830217i	$0.688216\pi$
$572$		0			0
$573$	16054.8	+	16054.8i	0.0488986	+	0.0488986i
$574$		0			0
$575$	−15903.3	−	163125.i	−0.0481006	−	0.493383i
$576$		0			0
$577$	168516.	−	168516.i	0.506161	−	0.506161i	−0.407184	−	0.913346i	$-0.633489\pi$
$577$	168516.	−	168516.i	0.506161	−	0.506161i	0.913346	+	0.407184i	$0.133489\pi$
$578$		0			0
$579$			40240.2i			0.120034i
$580$		0			0
$581$	−1.18539e6			−3.51164
$582$		0			0
$583$	23925.5	+	23925.5i	0.0703922	+	0.0703922i
$584$		0			0
$585$	−401.118	−	849.181i	−0.00117209	−	0.00248135i
$586$		0			0
$587$	129891.	−	129891.i	0.376966	−	0.376966i	−0.493040	−	0.870007i	$-0.664114\pi$
$587$	129891.	−	129891.i	0.376966	−	0.376966i	0.870007	+	0.493040i	$0.164114\pi$
$588$		0			0
$589$		−	188756.i		−	0.544089i
$590$		0			0
$591$	82217.9			0.235392
$592$		0			0
$593$	−299982.	−	299982.i	−0.853072	−	0.853072i	0.137438	−	0.990510i	$-0.456113\pi$
$593$	−299982.	−	299982.i	−0.853072	−	0.853072i	−0.990510	+	0.137438i	$0.956113\pi$
$594$		0			0
$595$	−487717.	−	174780.i	−1.37763	−	0.493695i
$596$		0			0
$597$	−66118.1	+	66118.1i	−0.185512	+	0.185512i
$598$		0			0
$599$			642365.i			1.79031i	0.445754	+	0.895155i	$0.352935\pi$
$599$			642365.i			1.79031i	−0.445754	+	0.895155i	$0.647065\pi$
$600$		0			0
$601$	624794.			1.72977			0.864884	−	0.501971i	$-0.167392\pi$
$601$	624794.			1.72977			0.864884	+	0.501971i	$0.167392\pi$
$602$		0			0
$603$	102643.	+	102643.i	0.282289	+	0.282289i
$604$		0			0
$605$	96652.9	−	269706.i	0.264061	−	0.736850i
$606$		0			0
$607$	133169.	−	133169.i	0.361431	−	0.361431i	−0.502909	−	0.864340i	$-0.667737\pi$
$607$	133169.	−	133169.i	0.361431	−	0.361431i	0.864340	+	0.502909i	$0.167737\pi$
$608$		0			0
$609$		−	260313.i		−	0.701877i
$610$		0			0
$611$	−897.513			−0.00240413
$612$		0			0
$613$	−394586.	−	394586.i	−1.05008	−	1.05008i	−0.998678	−	0.0513978i	$-0.983632\pi$
$613$	−394586.	−	394586.i	−1.05008	−	1.05008i	−0.0513978	−	0.998678i	$-0.516368\pi$
$614$		0			0
$615$	−155716.	+	73553.7i	−0.411701	+	0.194471i
$616$		0			0
$617$	246284.	−	246284.i	0.646942	−	0.646942i	−0.305311	−	0.952253i	$-0.598760\pi$
$617$	246284.	−	246284.i	0.646942	−	0.646942i	0.952253	+	0.305311i	$0.0987603\pi$
$618$		0			0
$619$		−	135789.i		−	0.354391i	−0.984176	−	0.177195i	$-0.943298\pi$
$619$		−	135789.i		−	0.354391i	0.984176	−	0.177195i	$-0.0567025\pi$
$620$		0			0
$621$	36790.9			0.0954018
$622$		0			0
$623$	−456821.	−	456821.i	−1.17698	−	1.17698i
$624$		0			0
$625$	75448.0	+	383269.i	0.193147	+	0.981170i
$626$		0			0
$627$	55029.5	−	55029.5i	0.139978	−	0.139978i
$628$		0			0
$629$			203395.i			0.514089i
$630$		0			0
$631$	566102.			1.42179			0.710896	−	0.703297i	$-0.248290\pi$
$631$	566102.			1.42179			0.710896	+	0.703297i	$0.248290\pi$
$632$		0			0
$633$	−45765.6	−	45765.6i	−0.114217	−	0.114217i
$634$		0			0
$635$	−47407.2	−	100363.i	−0.117570	−	0.248900i
$636$		0			0
$637$	5979.11	−	5979.11i	0.0147353	−	0.0147353i
$638$		0			0
$639$		−	214655.i		−	0.525703i
$640$		0			0
$641$	398483.			0.969826			0.484913	−	0.874562i	$-0.338851\pi$
$641$	398483.			0.969826			0.484913	+	0.874562i	$0.338851\pi$
$642$		0			0
$643$	−270770.	−	270770.i	−0.654905	−	0.654905i	0.299265	−	0.954170i	$-0.403259\pi$
$643$	−270770.	−	270770.i	−0.654905	−	0.654905i	−0.954170	+	0.299265i	$0.903259\pi$
$644$		0			0
$645$	3862.80	+	1384.29i	0.00928502	+	0.00332742i
$646$		0			0
$647$	−22129.0	+	22129.0i	−0.0528632	+	0.0528632i	−0.733044	−	0.680181i	$-0.761901\pi$
$647$	−22129.0	+	22129.0i	−0.0528632	+	0.0528632i	0.680181	+	0.733044i	$0.261901\pi$
$648$		0			0
$649$			195161.i			0.463344i
$650$		0			0
$651$	340087.			0.802469
$652$		0			0
$653$	−168610.	−	168610.i	−0.395418	−	0.395418i	0.481195	−	0.876613i	$-0.340203\pi$
$653$	−168610.	−	168610.i	−0.395418	−	0.395418i	−0.876613	+	0.481195i	$0.840203\pi$
$654$		0			0
$655$	242191.	−	675824.i	0.564516	−	1.57526i
$656$		0			0
$657$	52397.6	−	52397.6i	0.121389	−	0.121389i
$658$		0			0
$659$		−	106032.i		−	0.244155i	−0.992521	−	0.122078i	$-0.961044\pi$
$659$		−	106032.i		−	0.244155i	0.992521	−	0.122078i	$-0.0389557\pi$
$660$		0			0
$661$	−360211.			−0.824432			−0.412216	−	0.911086i	$-0.635245\pi$
$661$	−360211.			−0.824432			−0.412216	+	0.911086i	$0.635245\pi$
$662$		0			0
$663$	−1150.55	−	1150.55i	−0.00261745	−	0.00261745i
$664$		0			0
$665$	−552730.	+	261087.i	−1.24988	+	0.590394i
$666$		0			0
$667$	100887.	−	100887.i	0.226769	−	0.226769i
$668$		0			0
$669$			193996.i			0.433451i
$670$		0			0
$671$	−278492.			−0.618541
$672$		0			0
$673$	−174418.	−	174418.i	−0.385090	−	0.385090i	0.487842	−	0.872932i	$-0.337784\pi$
$673$	−174418.	−	174418.i	−0.385090	−	0.385090i	−0.872932	+	0.487842i	$0.837784\pi$
$674$		0			0
$675$	−87271.3	+	8508.20i	−0.191542	+	0.0186737i
$676$		0			0
$677$	118882.	−	118882.i	0.259382	−	0.259382i	−0.565421	−	0.824803i	$-0.691286\pi$
$677$	118882.	−	118882.i	0.259382	−	0.259382i	0.824803	+	0.565421i	$0.191286\pi$
$678$		0			0
$679$			334906.i			0.726412i
$680$		0			0
$681$	237115.			0.511288
$682$		0			0
$683$	464368.	+	464368.i	0.995453	+	0.995453i	0.999990	−	0.00453640i	$-0.00144399\pi$
$683$	464368.	+	464368.i	0.995453	+	0.995453i	−0.00453640	+	0.999990i	$0.501444\pi$
$684$		0			0
$685$	−386975.	−	819240.i	−0.824712	−	1.74594i
$686$		0			0
$687$	−250280.	+	250280.i	−0.530288	+	0.530288i
$688$		0			0
$689$		−	834.698i		−	0.00175829i
$690$		0			0
$691$	−112733.			−0.236099			−0.118050	−	0.993008i	$-0.537664\pi$
$691$	−112733.			−0.236099			−0.118050	+	0.993008i	$0.537664\pi$
$692$		0			0
$693$	99148.3	+	99148.3i	0.206452	+	0.206452i
$694$		0			0
$695$	388425.	+	139198.i	0.804152	+	0.288179i
$696$		0			0
$697$	−210978.	+	210978.i	−0.434282	+	0.434282i
$698$		0			0
$699$			484529.i			0.991665i
$700$		0			0
$701$	540863.			1.10065			0.550327	−	0.834949i	$-0.314503\pi$
$701$	540863.			1.10065			0.550327	+	0.834949i	$0.314503\pi$
$702$		0			0
$703$	169695.	+	169695.i	0.343366	+	0.343366i
$704$		0			0
$705$	−28269.6	+	78885.1i	−0.0568777	+	0.158715i
$706$		0			0
$707$	485688.	−	485688.i	0.971669	−	0.971669i
$708$		0			0
$709$			209535.i			0.416835i	0.978040	+	0.208418i	$0.0668313\pi$
$709$			209535.i			0.416835i	−0.978040	+	0.208418i	$0.933169\pi$
$710$		0			0
$711$	110263.			0.218118
$712$		0			0
$713$	131804.	+	131804.i	0.259269	+	0.259269i
$714$		0			0
$715$	1773.84	−	837.890i	0.00346979	−	0.00163898i
$716$		0			0
$717$	−238167.	+	238167.i	−0.463280	+	0.463280i
$718$		0			0
$719$			579641.i			1.12125i	0.828071	+	0.560623i	$0.189438\pi$
$719$			579641.i			1.12125i	−0.828071	+	0.560623i	$0.810562\pi$
$720$		0			0
$721$	603861.			1.16163
$722$		0			0
$723$	218977.	+	218977.i	0.418910	+	0.418910i
$724$		0			0
$725$	−215982.	+	262644.i	−0.410905	+	0.499680i
$726$		0			0
$727$	−666638.	+	666638.i	−1.26131	+	1.26131i	−0.310848	+	0.950460i	$0.600613\pi$
$727$	−666638.	+	666638.i	−1.26131	+	1.26131i	−0.950460	+	0.310848i	$0.899387\pi$
$728$		0			0
$729$		−	19683.0i		−	0.0370370i
$730$		0			0
$731$	7109.24			0.0133042
$732$		0			0
$733$	184382.	+	184382.i	0.343171	+	0.343171i	0.857558	−	0.514387i	$-0.171981\pi$
$733$	184382.	+	184382.i	0.343171	+	0.343171i	−0.514387	+	0.857558i	$0.671981\pi$
$734$		0			0
$735$	−337194.	−	713850.i	−0.624172	−	1.32139i
$736$		0			0
$737$	−214409.	+	214409.i	−0.394737	+	0.394737i
$738$		0			0
$739$		−	175164.i		−	0.320742i	−0.987057	−	0.160371i	$-0.948731\pi$
$739$		−	175164.i		−	0.320742i	0.987057	−	0.160371i	$-0.0512691\pi$
$740$		0			0
$741$	−1919.83			−0.00349645
$742$		0			0
$743$	−540487.	−	540487.i	−0.979057	−	0.979057i	0.0207283	−	0.999785i	$-0.493402\pi$
$743$	−540487.	−	540487.i	−0.979057	−	0.979057i	−0.999785	+	0.0207283i	$0.993402\pi$
$744$		0			0
$745$	−249443.	−	89391.4i	−0.449426	−	0.161058i
$746$		0			0
$747$	−245784.	+	245784.i	−0.440465	+	0.440465i
$748$		0			0
$749$			1.14649e6i			2.04365i
$750$		0			0
$751$	588360.			1.04319			0.521595	−	0.853193i	$-0.325337\pi$
$751$	588360.			1.04319			0.521595	+	0.853193i	$0.325337\pi$
$752$		0			0
$753$	−124640.	−	124640.i	−0.219819	−	0.219819i
$754$		0			0
$755$	−258164.	+	720395.i	−0.452899	+	1.26380i
$756$		0			0
$757$	497479.	−	497479.i	0.868126	−	0.868126i	−0.124139	−	0.992265i	$-0.539617\pi$
$757$	497479.	−	497479.i	0.868126	−	0.868126i	0.992265	+	0.124139i	$0.0396168\pi$
$758$		0			0
$759$			76851.9i			0.133405i
$760$		0			0
$761$	968464.			1.67230			0.836150	−	0.548501i	$-0.184801\pi$
$761$	968464.			1.67230			0.836150	+	0.548501i	$0.184801\pi$
$762$		0			0
$763$	519638.	+	519638.i	0.892589	+	0.892589i
$764$		0			0
$765$	−137365.	+	64885.4i	−0.234721	+	0.110873i
$766$		0			0
$767$	3404.32	−	3404.32i	0.00578682	−	0.00578682i
$768$		0			0
$769$		−	63796.8i		−	0.107881i	−0.998544	−	0.0539406i	$-0.982822\pi$
$769$		−	63796.8i		−	0.107881i	0.998544	−	0.0539406i	$-0.0171782\pi$
$770$		0			0
$771$	−191849.			−0.322738
$772$		0			0
$773$	142221.	+	142221.i	0.238015	+	0.238015i	0.816028	−	0.578013i	$-0.196172\pi$
$773$	142221.	+	142221.i	0.238015	+	0.238015i	−0.578013	+	0.816028i	$0.696172\pi$
$774$		0			0
$775$	−343133.	−	282171.i	−0.571293	−	0.469796i
$776$		0			0
$777$	−305744.	+	305744.i	−0.506426	+	0.506426i
$778$		0			0
$779$			352043.i			0.580124i
$780$		0			0
$781$	448391.			0.735114
$782$		0			0
$783$	−53974.2	−	53974.2i	−0.0880365	−	0.0880365i
$784$		0			0
$785$	264353.	+	559644.i	0.428988	+	0.908181i
$786$		0			0
$787$	171318.	−	171318.i	0.276601	−	0.276601i	−0.555150	−	0.831751i	$-0.687339\pi$
$787$	171318.	−	171318.i	0.276601	−	0.276601i	0.831751	+	0.555150i	$0.187339\pi$
$788$		0			0
$789$			188672.i			0.303077i
$790$		0			0
$791$	−243166.			−0.388642
$792$		0			0
$793$	4857.93	+	4857.93i	0.00772512	+	0.00772512i
$794$		0			0
$795$	−73364.1	−	26291.1i	−0.116078	−	0.0415982i
$796$		0			0
$797$	−396832.	+	396832.i	−0.624727	+	0.624727i	−0.946736	−	0.322010i	$-0.895642\pi$
$797$	−396832.	+	396832.i	−0.624727	+	0.624727i	0.322010	+	0.946736i	$0.395642\pi$
$798$		0			0
$799$			145183.i			0.227417i
$800$		0			0
$801$	−189438.			−0.295258
$802$		0			0
$803$	109453.	+	109453.i	0.169744	+	0.169744i
$804$		0			0
$805$	203648.	−	568271.i	0.314260	−	0.876928i
$806$		0			0
$807$	−310432.	+	310432.i	−0.476672	+	0.476672i
$808$		0			0
$809$		−	571851.i		−	0.873748i	−0.899523	−	0.436874i	$-0.856086\pi$
$809$		−	571851.i		−	0.873748i	0.899523	−	0.436874i	$-0.143914\pi$
$810$		0			0
$811$	851039.			1.29392			0.646960	−	0.762524i	$-0.276040\pi$
$811$	851039.			1.29392			0.646960	+	0.762524i	$0.276040\pi$
$812$		0			0
$813$	389167.	+	389167.i	0.588783	+	0.588783i
$814$		0			0
$815$	−440396.	+	208025.i	−0.663023	+	0.313185i
$816$		0			0
$817$	5931.33	−	5931.33i	0.00888603	−	0.00888603i
$818$		0			0
$819$		−	3459.02i		−	0.00515686i
$820$		0			0
$821$	−422213.			−0.626391			−0.313195	−	0.949689i	$-0.601399\pi$
$821$	−422213.			−0.626391			−0.313195	+	0.949689i	$0.601399\pi$
$822$		0			0
$823$	742417.	+	742417.i	1.09609	+	1.09609i	0.994863	+	0.101231i	$0.0322783\pi$
$823$	742417.	+	742417.i	1.09609	+	1.09609i	0.101231	+	0.994863i	$0.467722\pi$
$824$		0			0
$825$	−17772.7	−	182300.i	−0.0261123	−	0.267842i
$826$		0			0
$827$	422050.	−	422050.i	0.617097	−	0.617097i	−0.327689	−	0.944786i	$-0.606270\pi$
$827$	422050.	−	422050.i	0.617097	−	0.617097i	0.944786	+	0.327689i	$0.106270\pi$
$828$		0			0
$829$			310239.i			0.451427i	0.974194	+	0.225713i	$0.0724712\pi$
$829$			310239.i			0.451427i	−0.974194	+	0.225713i	$0.927529\pi$
$830$		0			0
$831$	−525037.			−0.760305
$832$		0			0
$833$	−967190.	−	967190.i	−1.39387	−	1.39387i
$834$		0			0
$835$	−333372.	−	705761.i	−0.478142	−	1.01224i
$836$		0			0
$837$	70514.9	−	70514.9i	0.100654	−	0.100654i
$838$		0			0
$839$			1.20455e6i			1.71120i	0.517636	+	0.855601i	$0.326812\pi$
$839$			1.20455e6i			1.71120i	−0.517636	+	0.855601i	$0.673188\pi$
$840$		0			0
$841$	411268.			0.581477
$842$		0			0
$843$	−23207.2	−	23207.2i	−0.0326563	−	0.0326563i
$844$		0			0
$845$	672121.	+	240864.i	0.941313	+	0.337333i
$846$		0			0
$847$	746155.	−	746155.i	1.04007	−	1.04007i
$848$		0			0
$849$			380130.i			0.527372i
$850$		0			0
$851$	−236989.			−0.327242
$852$		0			0
$853$	460012.	+	460012.i	0.632224	+	0.632224i	0.948625	−	0.316402i	$-0.102475\pi$
$853$	460012.	+	460012.i	0.632224	+	0.632224i	−0.316402	+	0.948625i	$0.602475\pi$
$854$		0			0
$855$	−60470.3	+	168740.i	−0.0827199	+	0.230826i
$856$		0			0
$857$	−398341.	+	398341.i	−0.542367	+	0.542367i	−0.924222	−	0.381855i	$-0.875285\pi$
$857$	−398341.	+	398341.i	−0.542367	+	0.542367i	0.381855	+	0.924222i	$0.375285\pi$
$858$		0			0
$859$		−	323065.i		−	0.437828i	−0.975744	−	0.218914i	$-0.929749\pi$
$859$		−	323065.i		−	0.437828i	0.975744	−	0.218914i	$-0.0702514\pi$
$860$		0			0
$861$	−634286.			−0.855616
$862$		0			0
$863$	−414986.	−	414986.i	−0.557200	−	0.557200i	0.371309	−	0.928509i	$-0.378909\pi$
$863$	−414986.	−	414986.i	−0.557200	−	0.557200i	−0.928509	+	0.371309i	$0.878909\pi$
$864$		0			0
$865$	−861755.	+	407058.i	−1.15173	+	0.544031i
$866$		0			0
$867$	120761.	−	120761.i	0.160653	−	0.160653i
$868$		0			0
$869$			230328.i			0.305005i
$870$		0			0
$871$	7480.16			0.00985995
$872$		0			0
$873$	69440.6	+	69440.6i	0.0911139	+	0.0911139i
$874$		0			0
$875$	−351655.	+	1.39509e6i	−0.459304	+	1.82216i
$876$		0			0
$877$	−257142.	+	257142.i	−0.334328	+	0.334328i	−0.854228	−	0.519899i	$-0.825969\pi$
$877$	−257142.	+	257142.i	−0.334328	+	0.334328i	0.519899	+	0.854228i	$0.325969\pi$
$878$		0			0
$879$			526964.i			0.682029i
$880$		0			0
$881$	−831152.			−1.07085			−0.535425	−	0.844583i	$-0.679848\pi$
$881$	−831152.			−1.07085			−0.535425	+	0.844583i	$0.679848\pi$
$882$		0			0
$883$	−908952.	−	908952.i	−1.16579	−	1.16579i	−0.983187	−	0.182601i	$-0.941548\pi$
$883$	−908952.	−	908952.i	−1.16579	−	1.16579i	−0.182601	−	0.983187i	$-0.558452\pi$
$884$		0			0
$885$	−191988.	−	406444.i	−0.245124	−	0.518937i
$886$		0			0
$887$	93115.5	−	93115.5i	0.118352	−	0.118352i	−0.645450	−	0.763802i	$-0.723330\pi$
$887$	93115.5	−	93115.5i	0.118352	−	0.118352i	0.763802	+	0.645450i	$0.223330\pi$
$888$		0			0
$889$		−	408814.i		−	0.517276i
$890$		0			0
$891$	41115.5			0.0517906
$892$		0			0
$893$	121128.	+	121128.i	0.151894	+	0.151894i
$894$		0			0
$895$	1.02858e6	+	368606.i	1.28408	+	0.460167i
$896$		0			0
$897$	1340.58	−	1340.58i	0.00166613	−	0.00166613i
$898$		0			0
$899$		−	386728.i		−	0.478505i
$900$		0			0
$901$	−135022.			−0.166324
$902$		0			0
$903$	10686.6	+	10686.6i	0.0131059	+	0.0131059i
$904$		0			0
$905$	−256259.	+	715079.i	−0.312883	+	0.873086i
$906$		0			0
$907$	62370.3	−	62370.3i	0.0758164	−	0.0758164i	−0.668182	−	0.743998i	$-0.732927\pi$
$907$	62370.3	−	62370.3i	0.0758164	−	0.0758164i	0.743998	+	0.668182i	$0.232927\pi$
$908$		0			0
$909$		−	201409.i		−	0.243753i
$910$		0			0
$911$	1.18436e6			1.42708			0.713540	−	0.700615i	$-0.247091\pi$
$911$	1.18436e6			1.42708			0.713540	+	0.700615i	$0.247091\pi$
$912$		0			0
$913$	−513414.	−	513414.i	−0.615923	−	0.615923i
$914$		0			0
$915$	579992.	−	273964.i	0.692755	−	0.327229i
$916$		0			0
$917$	1.86970e6	−	1.86970e6i	2.22349	−	2.22349i
$918$		0			0
$919$			773358.i			0.915692i	0.889031	+	0.457846i	$0.151379\pi$
$919$			773358.i			0.915692i	−0.889031	+	0.457846i	$0.848621\pi$
$920$		0			0
$921$	162096.			0.191097
$922$		0			0
$923$	−7821.58	−	7821.58i	−0.00918103	−	0.00918103i
$924$		0			0
$925$	562159.	−	54805.6i	0.657016	−	0.0640533i
$926$		0			0
$927$	125207.	−	125207.i	0.145703	−	0.145703i
$928$		0			0
$929$			881163.i			1.02100i	0.859878	+	0.510499i	$0.170539\pi$
$929$			881163.i			1.02100i	−0.859878	+	0.510499i	$0.829461\pi$
$930$		0			0
$931$	−1.61388e6			−1.86196
$932$		0			0
$933$	369010.	+	369010.i	0.423912	+	0.423912i
$934$		0			0
$935$	−135538.	−	286939.i	−0.155038	−	0.328221i
$936$		0			0
$937$	992967.	−	992967.i	1.13098	−	1.13098i	0.140967	−	0.990014i	$-0.454979\pi$
$937$	992967.	−	992967.i	1.13098	−	1.13098i	0.990014	−	0.140967i	$-0.0450212\pi$
$938$		0			0
$939$		−	239066.i		−	0.271136i
$940$		0			0
$941$	−1.13615e6			−1.28309			−0.641545	−	0.767085i	$-0.721706\pi$
$941$	−1.13615e6			−1.28309			−0.641545	+	0.767085i	$0.721706\pi$
$942$		0			0
$943$	−245824.	−	245824.i	−0.276440	−	0.276440i
$944$		0			0
$945$	−304023.	−	108951.i	−0.340442	−	0.122002i
$946$		0			0
$947$	208361.	−	208361.i	0.232336	−	0.232336i	−0.581331	−	0.813667i	$-0.697468\pi$
$947$	208361.	−	208361.i	0.232336	−	0.232336i	0.813667	+	0.581331i	$0.197468\pi$
$948$		0			0
$949$		−	3818.51i		−	0.00423996i
$950$		0			0
$951$	534017.			0.590465
$952$		0			0
$953$	−761064.	−	761064.i	−0.837983	−	0.837983i	0.150610	−	0.988593i	$-0.451876\pi$
$953$	−761064.	−	761064.i	−0.837983	−	0.837983i	−0.988593	+	0.150610i	$0.951876\pi$
$954$		0			0
$955$	36852.6	−	102835.i	0.0404074	−	0.112755i
$956$		0			0
$957$	112746.	−	112746.i	0.123105	−	0.123105i
$958$		0			0
$959$		−	3.33706e6i		−	3.62850i
$960$		0			0
$961$	−418277.			−0.452916
$962$		0			0
$963$	237717.	+	237717.i	0.256335	+	0.256335i
$964$		0			0
$965$	175058.	−	82690.4i	0.187987	−	0.0887974i
$966$		0			0
$967$	−456976.	+	456976.i	−0.488698	+	0.488698i	−0.907895	−	0.419197i	$-0.862312\pi$
$967$	−456976.	+	456976.i	−0.488698	+	0.488698i	0.419197	+	0.907895i	$0.362312\pi$
$968$		0			0
$969$			310555.i			0.330743i
$970$		0			0
$971$	−1.23029e6			−1.30488			−0.652439	−	0.757841i	$-0.726254\pi$
$971$	−1.23029e6			−1.30488			−0.652439	+	0.757841i	$0.726254\pi$
$972$		0			0
$973$	1.07460e6	+	1.07460e6i	1.13507	+	1.13507i
$974$		0			0
$975$	−2869.96	+	3490.00i	−0.00301902	+	0.00367127i
$976$		0			0
$977$	120924.	−	120924.i	0.126684	−	0.126684i	−0.640922	−	0.767606i	$-0.721448\pi$
$977$	120924.	−	120924.i	0.126684	−	0.126684i	0.767606	+	0.640922i	$0.221448\pi$
$978$		0			0
$979$		−	395715.i		−	0.412873i
$980$		0			0
$981$	215487.			0.223915
$982$		0			0
$983$	607621.	+	607621.i	0.628819	+	0.628819i	0.947771	−	0.318952i	$-0.103331\pi$
$983$	607621.	+	607621.i	0.628819	+	0.628819i	−0.318952	+	0.947771i	$0.603331\pi$
$984$		0			0
$985$	−168951.	−	357676.i	−0.174136	−	0.368652i
$986$		0			0
$987$	−218240.	+	218240.i	−0.224027	+	0.224027i
$988$		0			0
$989$			8283.45i			0.00846873i
$990$		0			0
$991$	32696.1			0.0332927			0.0166464	−	0.999861i	$-0.494701\pi$
$991$	32696.1			0.0332927			0.0166464	+	0.999861i	$0.494701\pi$
$992$		0			0
$993$	420334.	+	420334.i	0.426281	+	0.426281i
$994$		0			0
$995$	423504.	+	151769.i	0.427771	+	0.153298i
$996$		0			0
$997$	196213.	−	196213.i	0.197395	−	0.197395i	−0.601487	−	0.798882i	$-0.705425\pi$
$997$	196213.	−	196213.i	0.197395	−	0.197395i	0.798882	+	0.601487i	$0.205425\pi$
$998$		0			0
$999$			126788.i			0.127042i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.5.bg.c.193.2		8
4.3	odd	2		15.5.f.a.13.2	yes	8
5.2	odd	4	inner	240.5.bg.c.97.2		8
12.11	even	2		45.5.g.e.28.3		8
20.3	even	4		75.5.f.e.7.3		8
20.7	even	4		15.5.f.a.7.2	✓	8
20.19	odd	2		75.5.f.e.43.3		8
60.23	odd	4		225.5.g.m.82.2		8
60.47	odd	4		45.5.g.e.37.3		8
60.59	even	2		225.5.g.m.118.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.5.f.a.7.2	✓	8	20.7	even	4
15.5.f.a.13.2	yes	8	4.3	odd	2
45.5.g.e.28.3		8	12.11	even	2
45.5.g.e.37.3		8	60.47	odd	4
75.5.f.e.7.3		8	20.3	even	4
75.5.f.e.43.3		8	20.19	odd	2
225.5.g.m.82.2		8	60.23	odd	4
225.5.g.m.118.2		8	60.59	even	2
240.5.bg.c.97.2		8	5.2	odd	4	inner
240.5.bg.c.193.2		8	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	240.bg (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-3.67423 - 3.67423i) q^{3} +(-8.43390 + 23.5344i) q^{5} +(-65.1093 + 65.1093i) q^{7} +27.0000i q^{9} -56.3999 q^{11} +(0.983822 + 0.983822i) q^{13} +(117.459 - 55.4829i) q^{15} +(159.144 - 159.144i) q^{17} -265.552i q^{19} +478.454 q^{21} +(185.430 + 185.430i) q^{23} +(-482.739 - 396.974i) q^{25} +(99.2043 - 99.2043i) q^{27} -544.071i q^{29} +710.805 q^{31} +(207.227 + 207.227i) q^{33} +(-983.184 - 2081.43i) q^{35} +(-639.026 + 639.026i) q^{37} -7.22958i q^{39} -1325.70 q^{41} +(22.3358 + 22.3358i) q^{43} +(-635.430 - 227.715i) q^{45} +(-456.136 + 456.136i) q^{47} -6077.44i q^{49} -1169.47 q^{51} +(-424.212 - 424.212i) q^{53} +(475.672 - 1327.34i) q^{55} +(-975.701 + 975.701i) q^{57} -3460.30i q^{59} +4937.82 q^{61} +(-1757.95 - 1757.95i) q^{63} +(-31.4511 + 14.8562i) q^{65} +(3801.58 - 3801.58i) q^{67} -1362.62i q^{69} -7950.20 q^{71} +(-1940.65 - 1940.65i) q^{73} +(315.118 + 3232.27i) q^{75} +(3672.16 - 3672.16i) q^{77} -4083.83i q^{79} -729.000 q^{81} +(9103.10 + 9103.10i) q^{83} +(2403.16 + 5087.58i) q^{85} +(-1999.04 + 1999.04i) q^{87} +7016.23i q^{89} -128.112 q^{91} +(-2611.66 - 2611.66i) q^{93} +(6249.62 + 2239.64i) q^{95} +(2571.87 - 2571.87i) q^{97} -1522.80i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 84 q^{5} - 20 q^{7} + 288 q^{11} - 340 q^{13} - 144 q^{15} + 900 q^{17} + 792 q^{21} + 1560 q^{23} - 1204 q^{25} + 512 q^{31} + 2700 q^{33} - 6600 q^{35} - 3820 q^{37} - 2712 q^{41} + 1240 q^{43}+ \cdots + 58640 q^{97}+O(q^{100}) \) 8 * q - 84 * q^5 - 20 * q^7 + 288 * q^11 - 340 * q^13 - 144 * q^15 + 900 * q^17 + 792 * q^21 + 1560 * q^23 - 1204 * q^25 + 512 * q^31 + 2700 * q^33 - 6600 * q^35 - 3820 * q^37 - 2712 * q^41 + 1240 * q^43 - 1944 * q^45 - 4800 * q^47 - 6264 * q^51 + 1020 * q^53 + 3644 * q^55 - 5400 * q^57 - 4760 * q^61 - 540 * q^63 - 1212 * q^65 + 8920 * q^67 - 7536 * q^71 + 11600 * q^73 + 5976 * q^75 - 360 * q^77 - 5832 * q^81 + 32400 * q^83 - 15628 * q^85 - 10620 * q^87 - 16528 * q^91 + 14040 * q^93 - 18864 * q^95 + 58640 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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