LMFDB - Embedded newform 124.6.f.a.33.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [124,6,Mod(33,124)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(124, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("124.33");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 124 = 2^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	124.f (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$19.8875936568$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			33.3
Character	$\chi$	$=$	124.33
Dual form			124.6.f.a.109.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-18.4148 + 13.3791i) q^{3} -27.4655 q^{5} +(63.1359 + 194.312i) q^{7} +(85.0116 - 261.639i) q^{9} +O(q^{10})$	\(q+(-18.4148 + 13.3791i) q^{3} -27.4655 q^{5} +(63.1359 + 194.312i) q^{7} +(85.0116 - 261.639i) q^{9} +(240.799 + 741.102i) q^{11} +(-638.445 + 463.857i) q^{13} +(505.769 - 367.463i) q^{15} +(87.0809 - 268.008i) q^{17} +(396.822 + 288.308i) q^{19} +(-3762.36 - 2733.51i) q^{21} +(398.519 - 1226.52i) q^{23} -2370.65 q^{25} +(225.810 + 694.970i) q^{27} +(1735.99 + 1261.27i) q^{29} +(-2439.73 - 4762.02i) q^{31} +(-14349.5 - 10425.5i) q^{33} +(-1734.06 - 5336.87i) q^{35} +14730.9 q^{37} +(5550.81 - 17083.6i) q^{39} +(-1109.56 - 806.141i) q^{41} +(-6879.20 - 4998.03i) q^{43} +(-2334.88 + 7186.03i) q^{45} +(-18755.0 + 13626.3i) q^{47} +(-20174.0 + 14657.3i) q^{49} +(1982.13 + 6100.36i) q^{51} +(-6500.48 + 20006.4i) q^{53} +(-6613.64 - 20354.7i) q^{55} -11164.7 q^{57} +(4904.68 - 3563.46i) q^{59} -2809.84 q^{61} +56206.9 q^{63} +(17535.2 - 12740.1i) q^{65} +49844.4 q^{67} +(9071.05 + 27917.8i) q^{69} +(-4696.28 + 14453.7i) q^{71} +(-21316.1 - 65604.1i) q^{73} +(43654.9 - 31717.2i) q^{75} +(-128802. + 93580.3i) q^{77} +(13498.3 - 41543.5i) q^{79} +(40626.6 + 29516.9i) q^{81} +(30909.6 + 22457.1i) q^{83} +(-2391.72 + 7360.95i) q^{85} -48842.4 q^{87} +(-5893.73 - 18139.0i) q^{89} +(-130442. - 94771.7i) q^{91} +(108639. + 55050.0i) q^{93} +(-10898.9 - 7918.51i) q^{95} +(45361.2 + 139608. i) q^{97} +214372. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 2 q^{3} - 58 q^{5} + 104 q^{7} - 1234 q^{9}+O(q^{10}) $ 56 * q + 2 * q^3 - 58 * q^5 + 104 * q^7 - 1234 * q^9	$ 56 q + 2 q^{3} - 58 q^{5} + 104 q^{7} - 1234 q^{9} - 509 q^{11} - 117 q^{13} + 89 q^{15} - 3504 q^{17} + 262 q^{19} + 352 q^{21} - 2448 q^{23} + 49618 q^{25} + 14324 q^{27} - 9888 q^{29} - 12771 q^{31} + 27699 q^{33} + 13840 q^{35} + 76096 q^{37} + 33520 q^{39} - 4843 q^{41} - 40778 q^{43} + 56692 q^{45} + 38922 q^{47} - 17126 q^{49} - 69292 q^{51} - 41728 q^{53} - 172096 q^{55} + 57066 q^{57} - 58198 q^{59} + 176328 q^{61} - 37444 q^{63} + 143863 q^{65} + 9812 q^{67} - 9250 q^{69} - 67356 q^{71} - 63512 q^{73} - 198012 q^{75} - 74257 q^{77} + 137651 q^{79} + 196077 q^{81} + 156427 q^{83} + 238828 q^{85} - 558144 q^{87} - 99292 q^{89} - 243609 q^{91} - 325925 q^{93} - 75077 q^{95} - 476340 q^{97} + 745812 q^{99}+O(q^{100}) $ 56 * q + 2 * q^3 - 58 * q^5 + 104 * q^7 - 1234 * q^9 - 509 * q^11 - 117 * q^13 + 89 * q^15 - 3504 * q^17 + 262 * q^19 + 352 * q^21 - 2448 * q^23 + 49618 * q^25 + 14324 * q^27 - 9888 * q^29 - 12771 * q^31 + 27699 * q^33 + 13840 * q^35 + 76096 * q^37 + 33520 * q^39 - 4843 * q^41 - 40778 * q^43 + 56692 * q^45 + 38922 * q^47 - 17126 * q^49 - 69292 * q^51 - 41728 * q^53 - 172096 * q^55 + 57066 * q^57 - 58198 * q^59 + 176328 * q^61 - 37444 * q^63 + 143863 * q^65 + 9812 * q^67 - 9250 * q^69 - 67356 * q^71 - 63512 * q^73 - 198012 * q^75 - 74257 * q^77 + 137651 * q^79 + 196077 * q^81 + 156427 * q^83 + 238828 * q^85 - 558144 * q^87 - 99292 * q^89 - 243609 * q^91 - 325925 * q^93 - 75077 * q^95 - 476340 * q^97 + 745812 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/124\mathbb{Z}\right)^\times$.

$n$	$63$	$65$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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
$3$	−18.4148	+	13.3791i	−1.18131	+	0.858270i	−0.992318	−	0.123710i	$-0.960521\pi$
$3$	−18.4148	+	13.3791i	−1.18131	+	0.858270i	−0.188988	+	0.981979i	$0.560521\pi$
$4$		0			0
$5$	−27.4655			−0.491317			−0.245658	−	0.969356i	$-0.579004\pi$
$5$	−27.4655			−0.491317			−0.245658	+	0.969356i	$0.579004\pi$
$6$		0			0
$7$	63.1359	+	194.312i	0.487003	+	1.49884i	0.829059	+	0.559160i	$0.188876\pi$
$7$	63.1359	+	194.312i	0.487003	+	1.49884i	−0.342057	+	0.939679i	$0.611124\pi$
$8$		0			0
$9$	85.0116	−	261.639i	0.349842	−	1.07670i
$10$		0			0
$11$	240.799	+	741.102i	0.600029	+	1.84670i	0.527904	+	0.849304i	$0.322978\pi$
$11$	240.799	+	741.102i	0.600029	+	1.84670i	0.0721246	+	0.997396i	$0.477022\pi$
$12$		0			0
$13$	−638.445	+	463.857i	−1.04777	+	0.761248i	−0.971787	−	0.235861i	$-0.924209\pi$
$13$	−638.445	+	463.857i	−1.04777	+	0.761248i	−0.0759813	+	0.997109i	$0.524209\pi$
$14$		0			0
$15$	505.769	−	367.463i	0.580396	−	0.421682i
$16$		0			0
$17$	87.0809	−	268.008i	0.0730804	−	0.224918i	−0.907844	−	0.419308i	$-0.862273\pi$
$17$	87.0809	−	268.008i	0.0730804	−	0.224918i	0.980924	+	0.194390i	$0.0622727\pi$
$18$		0			0
$19$	396.822	+	288.308i	0.252181	+	0.183220i	0.706693	−	0.707521i	$-0.250186\pi$
$19$	396.822	+	288.308i	0.252181	+	0.183220i	−0.454512	+	0.890741i	$0.650186\pi$
$20$		0			0
$21$	−3762.36	−	2733.51i	−1.86171	−	1.35261i
$22$		0			0
$23$	398.519	−	1226.52i	0.157083	−	0.483453i	−0.841283	−	0.540595i	$-0.818199\pi$
$23$	398.519	−	1226.52i	0.157083	−	0.483453i	0.998366	+	0.0571428i	$0.0181990\pi$
$24$		0			0
$25$	−2370.65			−0.758608
$26$		0			0
$27$	225.810	+	694.970i	0.0596119	+	0.183467i
$28$		0			0
$29$	1735.99	+	1261.27i	0.383311	+	0.278492i	0.762709	−	0.646742i	$-0.223869\pi$
$29$	1735.99	+	1261.27i	0.383311	+	0.278492i	−0.379398	+	0.925234i	$0.623869\pi$
$30$		0			0
$31$	−2439.73	−	4762.02i	−0.455972	−	0.889994i
$31$	−2439.73	−	4762.02i	−0.455972	−	0.889994i
$32$		0			0
$33$	−14349.5	−	10425.5i	−2.29378	−	1.66653i
$34$		0			0
$35$	−1734.06	−	5336.87i	−0.239273	−	0.736405i
$36$		0			0
$37$	14730.9			1.76899			0.884495	−	0.466549i	$-0.154503\pi$
$37$	14730.9			1.76899			0.884495	+	0.466549i	$0.154503\pi$
$38$		0			0
$39$	5550.81	−	17083.6i	0.584380	−	1.79854i
$40$		0			0
$41$	−1109.56	−	806.141i	−0.103084	−	0.0748947i	0.535049	−	0.844821i	$-0.320293\pi$
$41$	−1109.56	−	806.141i	−0.103084	−	0.0748947i	−0.638133	+	0.769926i	$0.720293\pi$
$42$		0			0
$43$	−6879.20	−	4998.03i	−0.567371	−	0.412219i	0.266779	−	0.963758i	$-0.414041\pi$
$43$	−6879.20	−	4998.03i	−0.567371	−	0.412219i	−0.834149	+	0.551539i	$0.814041\pi$
$44$		0			0
$45$	−2334.88	+	7186.03i	−0.171883	+	0.529003i
$46$		0			0
$47$	−18755.0	+	13626.3i	−1.23843	+	0.899775i	−0.997493	−	0.0707650i	$-0.977456\pi$
$47$	−18755.0	+	13626.3i	−1.23843	+	0.899775i	−0.240941	+	0.970540i	$0.577456\pi$
$48$		0			0
$49$	−20174.0	+	14657.3i	−1.20033	+	0.872092i
$50$		0			0
$51$	1982.13	+	6100.36i	0.106710	+	0.328420i
$52$		0			0
$53$	−6500.48	+	20006.4i	−0.317875	+	0.978317i	0.656681	+	0.754169i	$0.271960\pi$
$53$	−6500.48	+	20006.4i	−0.317875	+	0.978317i	−0.974555	+	0.224148i	$0.928040\pi$
$54$		0			0
$55$	−6613.64	−	20354.7i	−0.294804	−	0.907315i
$56$		0			0
$57$	−11164.7			−0.455155
$58$		0			0
$59$	4904.68	−	3563.46i	0.183434	−	0.133273i	−0.492279	−	0.870438i	$-0.663836\pi$
$59$	4904.68	−	3563.46i	0.183434	−	0.133273i	0.675713	+	0.737165i	$0.263836\pi$
$60$		0			0
$61$	−2809.84			−0.0966846			−0.0483423	−	0.998831i	$-0.515394\pi$
$61$	−2809.84			−0.0966846			−0.0483423	+	0.998831i	$0.515394\pi$
$62$		0			0
$63$	56206.9			1.78418
$64$		0			0
$65$	17535.2	−	12740.1i	0.514786	−	0.374014i
$66$		0			0
$67$	49844.4			1.35653			0.678265	−	0.734817i	$-0.262732\pi$
$67$	49844.4			1.35653			0.678265	+	0.734817i	$0.262732\pi$
$68$		0			0
$69$	9071.05	+	27917.8i	0.229369	+	0.705926i
$70$		0			0
$71$	−4696.28	+	14453.7i	−0.110563	+	0.340277i	−0.990996	−	0.133894i	$-0.957252\pi$
$71$	−4696.28	+	14453.7i	−0.110563	+	0.340277i	0.880433	+	0.474170i	$0.157252\pi$
$72$		0			0
$73$	−21316.1	−	65604.1i	−0.468166	−	1.44087i	−0.854957	−	0.518700i	$-0.826416\pi$
$73$	−21316.1	−	65604.1i	−0.468166	−	1.44087i	0.386790	−	0.922168i	$-0.373584\pi$
$74$		0			0
$75$	43654.9	−	31717.2i	0.896148	−	0.651090i
$76$		0			0
$77$	−128802.	+	93580.3i	−2.47569	+	1.79869i
$78$		0			0
$79$	13498.3	−	41543.5i	0.243339	−	0.748919i	−0.752567	−	0.658516i	$-0.771184\pi$
$79$	13498.3	−	41543.5i	0.243339	−	0.748919i	0.995905	−	0.0904033i	$-0.0288156\pi$
$80$		0			0
$81$	40626.6	+	29516.9i	0.688015	+	0.499872i
$82$		0			0
$83$	30909.6	+	22457.1i	0.492491	+	0.357816i	0.806141	−	0.591723i	$-0.201552\pi$
$83$	30909.6	+	22457.1i	0.492491	+	0.357816i	−0.313651	+	0.949538i	$0.601552\pi$
$84$		0			0
$85$	−2391.72	+	7360.95i	−0.0359056	+	0.110506i
$86$		0			0
$87$	−48842.4			−0.691829
$88$		0			0
$89$	−5893.73	−	18139.0i	−0.0788706	−	0.242739i	0.903845	−	0.427860i	$-0.140732\pi$
$89$	−5893.73	−	18139.0i	−0.0788706	−	0.242739i	−0.982716	+	0.185121i	$0.940732\pi$
$90$		0			0
$91$	−130442.	−	94771.7i	−1.65125	−	1.19971i
$92$		0			0
$93$	108639.	+	55050.0i	1.30250	+	0.660009i
$94$		0			0
$95$	−10898.9	−	7918.51i	−0.123901	−	0.0900191i
$96$		0			0
$97$	45361.2	+	139608.i	0.489503	+	1.50654i	0.825351	+	0.564620i	$0.190977\pi$
$97$	45361.2	+	139608.i	0.489503	+	1.50654i	−0.335848	+	0.941916i	$0.609023\pi$
$98$		0			0
$99$	214372.			2.19826
$100$		0			0
$101$	57350.5	−	176507.i	0.559414	−	1.72170i	−0.124577	−	0.992210i	$-0.539757\pi$
$101$	57350.5	−	176507.i	0.559414	−	1.72170i	0.683991	−	0.729490i	$-0.260243\pi$
$102$		0			0
$103$	131666.	+	95660.8i	1.22287	+	0.888466i	0.996335	−	0.0855376i	$-0.0272608\pi$
$103$	131666.	+	95660.8i	1.22287	+	0.888466i	0.226533	+	0.974003i	$0.427261\pi$
$104$		0			0
$105$	103335.	+	75077.1i	0.914689	+	0.664560i
$106$		0			0
$107$	−25969.7	+	79926.5i	−0.219284	+	0.674888i	0.779537	+	0.626356i	$0.215454\pi$
$107$	−25969.7	+	79926.5i	−0.219284	+	0.674888i	−0.998822	+	0.0485320i	$0.984546\pi$
$108$		0			0
$109$	78462.4	−	57006.2i	0.632550	−	0.459575i	−0.224732	−	0.974421i	$-0.572151\pi$
$109$	78462.4	−	57006.2i	0.632550	−	0.459575i	0.857283	+	0.514846i	$0.172151\pi$
$110$		0			0
$111$	−271266.	+	197086.i	−2.08972	+	1.51827i
$112$		0			0
$113$	−45723.0	−	140721.i	−0.336851	−	1.03672i	−0.965803	−	0.259277i	$-0.916516\pi$
$113$	−45723.0	−	140721.i	−0.336851	−	1.03672i	0.628952	−	0.777444i	$-0.283484\pi$
$114$		0			0
$115$	−10945.5	+	33686.8i	−0.0771777	+	0.237528i
$116$		0			0
$117$	67087.9	+	206475.i	0.453085	+	1.39445i
$118$		0			0
$119$	57575.1			0.372707
$120$		0			0
$121$	−360955.	+	262249.i	−2.24125	+	1.62836i
$122$		0			0
$123$	31217.7			0.186053
$124$		0			0
$125$	150940.			0.864034
$126$		0			0
$127$	−13396.9	+	9733.43i	−0.0737048	+	0.0535497i	−0.624027	−	0.781402i	$-0.714505\pi$
$127$	−13396.9	+	9733.43i	−0.0737048	+	0.0535497i	0.550323	+	0.834952i	$0.314505\pi$
$128$		0			0
$129$	193548.			1.02403
$130$		0			0
$131$	−37153.6	−	114347.i	−0.189157	−	0.582166i	0.810838	−	0.585271i	$-0.199012\pi$
$131$	−37153.6	−	114347.i	−0.189157	−	0.582166i	−0.999995	+	0.00310445i	$0.999012\pi$
$132$		0			0
$133$	−30968.1	+	95310.0i	−0.151805	+	0.467207i
$134$		0			0
$135$	−6201.96	−	19087.7i	−0.0292883	−	0.0901402i
$136$		0			0
$137$	−191277.	+	138971.i	−0.870687	+	0.632591i	−0.930771	−	0.365602i	$-0.880863\pi$
$137$	−191277.	+	138971.i	−0.870687	+	0.632591i	0.0600840	+	0.998193i	$0.480863\pi$
$138$		0			0
$139$	185971.	−	135116.i	0.816411	−	0.593157i	−0.0992714	−	0.995060i	$-0.531651\pi$
$139$	185971.	−	135116.i	0.816411	−	0.593157i	0.915682	+	0.401903i	$0.131651\pi$
$140$		0			0
$141$	163061.	−	501850.i	0.690721	−	2.12582i
$142$		0			0
$143$	−497502.	−	361457.i	−2.03449	−	1.47814i
$144$		0			0
$145$	−47679.6	−	34641.3i	−0.188327	−	0.136828i
$146$		0			0
$147$	175398.	−	539819.i	0.669470	−	2.06042i
$148$		0			0
$149$	−403722.			−1.48976			−0.744881	−	0.667198i	$-0.767494\pi$
$149$	−403722.			−1.48976			−0.744881	+	0.667198i	$0.767494\pi$
$150$		0			0
$151$	−21267.4	−	65454.3i	−0.0759053	−	0.233612i	0.905904	−	0.423484i	$-0.139193\pi$
$151$	−21267.4	−	65454.3i	−0.0759053	−	0.233612i	−0.981809	+	0.189871i	$0.939193\pi$
$152$		0			0
$153$	−62718.3	−	45567.5i	−0.216604	−	0.157372i
$154$		0			0
$155$	67008.4	+	130791.i	0.224027	+	0.437269i
$156$		0			0
$157$	−209194.	−	151989.i	−0.677331	−	0.492110i	0.195140	−	0.980775i	$-0.437484\pi$
$157$	−209194.	−	151989.i	−0.677331	−	0.492110i	−0.872471	+	0.488666i	$0.837484\pi$
$158$		0			0
$159$	−147963.	−	455384.i	−0.464153	−	1.42851i
$160$		0			0
$161$	263488.			0.801118
$162$		0			0
$163$	−151988.	+	467770.i	−0.448063	+	1.37900i	0.431026	+	0.902340i	$0.358152\pi$
$163$	−151988.	+	467770.i	−0.448063	+	1.37900i	−0.879089	+	0.476657i	$0.841848\pi$
$164$		0			0
$165$	394116.	+	286342.i	1.12698	+	0.818795i
$166$		0			0
$167$	−260960.	−	189598.i	−0.724073	−	0.526070i	0.163610	−	0.986525i	$-0.447686\pi$
$167$	−260960.	−	189598.i	−0.724073	−	0.526070i	−0.887683	+	0.460455i	$0.847686\pi$
$168$		0			0
$169$	77712.5	−	239174.i	0.209302	−	0.644166i
$170$		0			0
$171$	109167.	−	79314.6i	0.285497	−	0.207426i
$172$		0			0
$173$	−574269.	+	417231.i	−1.45882	+	1.05989i	−0.475146	+	0.879907i	$0.657605\pi$
$173$	−574269.	+	417231.i	−1.45882	+	1.05989i	−0.983669	+	0.179985i	$0.942395\pi$
$174$		0			0
$175$	−149673.	−	460646.i	−0.369444	−	1.13703i
$176$		0			0
$177$	−42642.6	+	131240.i	−0.102308	+	0.314872i
$178$		0			0
$179$	−14764.5	−	45440.4i	−0.0344418	−	0.106001i	0.932358	−	0.361537i	$-0.117748\pi$
$179$	−14764.5	−	45440.4i	−0.0344418	−	0.106001i	−0.966799	+	0.255536i	$0.917748\pi$
$180$		0			0
$181$	−106779.			−0.242264			−0.121132	−	0.992636i	$-0.538652\pi$
$181$	−106779.			−0.242264			−0.121132	+	0.992636i	$0.538652\pi$
$182$		0			0
$183$	51742.6	−	37593.2i	0.114214	−	0.0829815i
$184$		0			0
$185$	−404591.			−0.869135
$186$		0			0
$187$	219590.			0.459207
$188$		0			0
$189$	−120785.	+	87755.1i	−0.245956	+	0.178697i
$190$		0			0
$191$	935174.			1.85485			0.927426	−	0.374008i	$-0.122017\pi$
$191$	935174.			1.85485			0.927426	+	0.374008i	$0.122017\pi$
$192$		0			0
$193$	−62182.7	−	191379.i	−0.120164	−	0.369828i	0.872825	−	0.488034i	$-0.162286\pi$
$193$	−62182.7	−	191379.i	−0.120164	−	0.369828i	−0.992989	+	0.118206i	$0.962286\pi$
$194$		0			0
$195$	−152456.	+	469210.i	−0.287116	+	0.883651i
$196$		0			0
$197$	190425.	+	586068.i	0.349590	+	1.07593i	0.959080	+	0.283134i	$0.0913740\pi$
$197$	190425.	+	586068.i	0.349590	+	1.07593i	−0.609491	+	0.792793i	$0.708626\pi$
$198$		0			0
$199$	474281.	−	344585.i	0.848991	−	0.616828i	−0.0758769	−	0.997117i	$-0.524176\pi$
$199$	474281.	−	344585.i	0.848991	−	0.616828i	0.924868	+	0.380289i	$0.124176\pi$
$200$		0			0
$201$	−917873.	+	666874.i	−1.60248	+	1.16427i
$202$		0			0
$203$	−135477.	+	416955.i	−0.230741	+	0.710148i
$204$		0			0
$205$	30474.5	+	22141.0i	0.0506468	+	0.0367970i
$206$		0			0
$207$	−287026.	−	208536.i	−0.465581	−	0.338264i
$208$		0			0
$209$	−118112.	+	363510.i	−0.187037	+	0.575639i
$210$		0			0
$211$	405222.			0.626595			0.313297	−	0.949655i	$-0.398566\pi$
$211$	405222.			0.626595			0.313297	+	0.949655i	$0.398566\pi$
$212$		0			0
$213$	−106896.	−	328993.i	−0.161441	−	0.496864i
$214$		0			0
$215$	188940.	+	137273.i	0.278759	+	0.202530i
$216$		0			0
$217$	771285.	−	774725.i	1.11190	−	1.11686i
$218$		0			0
$219$	1.27025e6	+	922894.i	1.78970	+	1.30029i
$220$		0			0
$221$	68720.9	+	211501.i	0.0946473	+	0.291294i
$222$		0			0
$223$	−714742.			−0.962470			−0.481235	−	0.876592i	$-0.659812\pi$
$223$	−714742.			−0.962470			−0.481235	+	0.876592i	$0.659812\pi$
$224$		0			0
$225$	−201533.	+	620254.i	−0.265393	+	0.816795i
$226$		0			0
$227$	756358.	+	549526.i	0.974233	+	0.707822i	0.956412	−	0.292019i	$-0.0943272\pi$
$227$	756358.	+	549526.i	0.974233	+	0.707822i	0.0178207	+	0.999841i	$0.494327\pi$
$228$		0			0
$229$	−345857.	−	251280.i	−0.435821	−	0.316643i	0.348151	−	0.937438i	$-0.386810\pi$
$229$	−345857.	−	251280.i	−0.435821	−	0.316643i	−0.783972	+	0.620796i	$0.786810\pi$
$230$		0			0
$231$	1.11984e6	−	3.44651e6i	1.38079	−	4.24962i
$232$		0			0
$233$	−805433.	+	585182.i	−0.971941	+	0.706156i	−0.955893	−	0.293715i	$-0.905108\pi$
$233$	−805433.	+	585182.i	−0.971941	+	0.706156i	−0.0160478	+	0.999871i	$0.505108\pi$
$234$		0			0
$235$	515115.	−	374253.i	0.608463	−	0.442075i
$236$		0			0
$237$	307247.	+	945608.i	0.355317	+	1.09355i
$238$		0			0
$239$	−247816.	+	762698.i	−0.280630	+	0.863690i	0.707045	+	0.707169i	$0.250028\pi$
$239$	−247816.	+	762698.i	−0.280630	+	0.863690i	−0.987675	+	0.156521i	$0.949972\pi$
$240$		0			0
$241$	−105239.	−	323892.i	−0.116717	−	0.359217i	0.875584	−	0.483065i	$-0.160477\pi$
$241$	−105239.	−	323892.i	−0.116717	−	0.359217i	−0.992301	+	0.123848i	$0.960477\pi$
$242$		0			0
$243$	−1.32061e6			−1.43469
$244$		0			0
$245$	554087.	−	402568.i	0.589743	−	0.428474i
$246$		0			0
$247$	−387083.			−0.403703
$248$		0			0
$249$	−869649.			−0.888885
$250$		0			0
$251$	−614177.	+	446226.i	−0.615332	+	0.447065i	−0.851288	−	0.524699i	$-0.824178\pi$
$251$	−614177.	+	446226.i	−0.615332	+	0.447065i	0.235956	+	0.971764i	$0.424178\pi$
$252$		0			0
$253$	1.00494e6			0.987046
$254$		0			0
$255$	−54440.0	−	167549.i	−0.0524285	−	0.161358i
$256$		0			0
$257$	−224770.	+	691771.i	−0.212278	+	0.653326i	0.787057	+	0.616880i	$0.211604\pi$
$257$	−224770.	+	691771.i	−0.212278	+	0.653326i	−0.999336	+	0.0364456i	$0.988396\pi$
$258$		0			0
$259$	930050.	+	2.86240e6i	0.861503	+	2.65143i
$260$		0			0
$261$	477576.	−	346979.i	0.433951	−	0.315284i
$262$		0			0
$263$	967702.	−	703077.i	0.862685	−	0.626777i	−0.0659292	−	0.997824i	$-0.521001\pi$
$263$	967702.	−	703077.i	0.862685	−	0.626777i	0.928614	+	0.371047i	$0.121001\pi$
$264$		0			0
$265$	178539.	−	549485.i	0.156177	−	0.480664i
$266$		0			0
$267$	351216.	+	255173.i	0.301506	+	0.219057i
$268$		0			0
$269$	−517159.	−	375738.i	−0.435756	−	0.316595i	0.348190	−	0.937424i	$-0.386796\pi$
$269$	−517159.	−	375738.i	−0.435756	−	0.316595i	−0.783946	+	0.620829i	$0.786796\pi$
$270$		0			0
$271$	−823.054	+	2533.10i	−0.000680777	+	0.00209522i	−0.951396	−	0.307969i	$-0.900351\pi$
$271$	−823.054	+	2533.10i	−0.000680777	+	0.00209522i	0.950716	+	0.310064i	$0.100351\pi$
$272$		0			0
$273$	3.67002e6			2.98031
$274$		0			0
$275$	−570849.	−	1.75689e6i	−0.455187	−	1.40092i
$276$		0			0
$277$	1.53642e6	+	1.11627e6i	1.20312	+	0.874120i	0.994588	−	0.103896i	$-0.0331308\pi$
$277$	1.53642e6	+	1.11627e6i	1.20312	+	0.874120i	0.208534	+	0.978015i	$0.433131\pi$
$278$		0			0
$279$	−1.45334e6	+	233502.i	−1.11778	+	0.179589i
$280$		0			0
$281$	−1.20445e6	−	875086.i	−0.909963	−	0.661127i	0.0310426	−	0.999518i	$-0.490117\pi$
$281$	−1.20445e6	−	875086.i	−0.909963	−	0.661127i	−0.941005	+	0.338391i	$0.890117\pi$
$282$		0			0
$283$	306025.	+	941848.i	0.227139	+	0.699061i	0.998067	+	0.0621395i	$0.0197924\pi$
$283$	306025.	+	941848.i	0.227139	+	0.699061i	−0.770929	+	0.636921i	$0.780208\pi$
$284$		0			0
$285$	306643.			0.223625
$286$		0			0
$287$	86590.1	−	266497.i	0.0620531	−	0.190980i
$288$		0			0
$289$	1.08444e6	+	787894.i	0.763770	+	0.554911i
$290$		0			0
$291$	−2.70314e6	−	1.96395e6i	−1.87127	−	1.35956i
$292$		0			0
$293$	−680561.	+	2.09455e6i	−0.463125	+	1.42535i	0.398201	+	0.917298i	$0.369635\pi$
$293$	−680561.	+	2.09455e6i	−0.463125	+	1.42535i	−0.861326	+	0.508053i	$0.830365\pi$
$294$		0			0
$295$	−134709.	+	97872.0i	−0.0901244	+	0.0654792i
$296$		0			0
$297$	−460669.	+	334696.i	−0.303039	+	0.220170i
$298$		0			0
$299$	314496.	+	967920.i	0.203441	+	0.626125i
$300$		0			0
$301$	536855.	−	1.65227e6i	0.341539	−	1.05115i
$302$		0			0
$303$	1.30540e6	+	4.01762e6i	0.816843	+	2.51398i
$304$		0			0
$305$	77173.6			0.0475028
$306$		0			0
$307$	816007.	−	592864.i	0.494138	−	0.359012i	−0.312636	−	0.949873i	$-0.601212\pi$
$307$	816007.	−	592864.i	0.494138	−	0.359012i	0.806773	+	0.590861i	$0.201212\pi$
$308$		0			0
$309$	−3.70445e6			−2.20713
$310$		0			0
$311$	−2.17987e6			−1.27800			−0.638999	−	0.769208i	$-0.720651\pi$
$311$	−2.17987e6			−1.27800			−0.638999	+	0.769208i	$0.720651\pi$
$312$		0			0
$313$	1.41889e6	−	1.03089e6i	0.818633	−	0.594772i	−0.0976877	−	0.995217i	$-0.531145\pi$
$313$	1.41889e6	−	1.03089e6i	0.818633	−	0.594772i	0.916321	+	0.400446i	$0.131145\pi$
$314$		0			0
$315$	−1.54375e6			−0.876598
$316$		0			0
$317$	246503.	+	758657.i	0.137776	+	0.424031i	0.996011	−	0.0892253i	$-0.0284391\pi$
$317$	246503.	+	758657.i	0.137776	+	0.424031i	−0.858236	+	0.513256i	$0.828439\pi$
$318$		0			0
$319$	−516705.	+	1.59025e6i	−0.284293	+	0.874963i
$320$		0			0
$321$	−591120.	−	1.81928e6i	−0.320194	−	0.985455i
$322$		0			0
$323$	111824.	−	81245.2i	0.0596390	−	0.0433303i
$324$		0			0
$325$	1.51353e6	−	1.09964e6i	0.794845	−	0.577489i
$326$		0			0
$327$	−682173.	+	2.09951e6i	−0.352797	+	1.08580i
$328$		0			0
$329$	−3.83188e6	−	2.78402e6i	−1.95174	−	1.41802i
$330$		0			0
$331$	1.53253e6	+	1.11345e6i	0.768845	+	0.558599i	0.901610	−	0.432549i	$-0.142386\pi$
$331$	1.53253e6	+	1.11345e6i	0.768845	+	0.558599i	−0.132765	+	0.991147i	$0.542386\pi$
$332$		0			0
$333$	1.25230e6	−	3.85418e6i	0.618867	−	1.90468i
$334$		0			0
$335$	−1.36900e6			−0.666487
$336$		0			0
$337$	−556054.	−	1.71136e6i	−0.266712	−	0.820854i	−0.991294	−	0.131666i	$-0.957967\pi$
$337$	−556054.	−	1.71136e6i	−0.266712	−	0.820854i	0.724583	−	0.689188i	$-0.242033\pi$
$338$		0			0
$339$	2.72469e6	+	1.97961e6i	1.28771	+	0.935577i
$340$		0			0
$341$	2.94166e6	−	2.95478e6i	1.36996	−	1.37607i
$342$		0			0
$343$	−1.34373e6	−	976273.i	−0.616702	−	0.448060i
$344$		0			0
$345$	−249141.	−	766776.i	−0.112693	−	0.346833i
$346$		0			0
$347$	−2.92145e6			−1.30249			−0.651245	−	0.758867i	$-0.725753\pi$
$347$	−2.92145e6			−1.30249			−0.651245	+	0.758867i	$0.725753\pi$
$348$		0			0
$349$	104506.	−	321637.i	0.0459281	−	0.141352i	−0.925463	−	0.378839i	$-0.876324\pi$
$349$	104506.	−	321637.i	0.0459281	−	0.141352i	0.971391	+	0.237486i	$0.0763235\pi$
$350$		0			0
$351$	−466534.	−	338957.i	−0.202123	−	0.146851i
$352$		0			0
$353$	2.28455e6	+	1.65982e6i	0.975808	+	0.708966i	0.956768	−	0.290853i	$-0.0939390\pi$
$353$	2.28455e6	+	1.65982e6i	0.975808	+	0.708966i	0.0190402	+	0.999819i	$0.493939\pi$
$354$		0			0
$355$	128986.	−	396977.i	0.0543213	−	0.167184i
$356$		0			0
$357$	−1.06023e6	+	770303.i	−0.440281	+	0.319883i
$358$		0			0
$359$	−22076.0	+	16039.2i	−0.00904034	+	0.00656819i	−0.592296	−	0.805720i	$-0.701778\pi$
$359$	−22076.0	+	16039.2i	−0.00904034	+	0.00656819i	0.583256	+	0.812288i	$0.301778\pi$
$360$		0			0
$361$	−690810.	−	2.12610e6i	−0.278991	−	0.858647i
$362$		0			0
$363$	3.13824e6	−	9.65851e6i	1.25003	−	3.84719i
$364$		0			0
$365$	585456.	+	1.80185e6i	0.230018	+	0.707922i
$366$		0			0
$367$	−1.56492e6			−0.606496			−0.303248	−	0.952912i	$-0.598071\pi$
$367$	−1.56492e6			−0.606496			−0.303248	+	0.952912i	$0.598071\pi$
$368$		0			0
$369$	−305243.	+	221772.i	−0.116702	+	0.0847893i
$370$		0			0
$371$	−4.29791e6			−1.62115
$372$		0			0
$373$	−2.77553e6			−1.03294			−0.516469	−	0.856306i	$-0.672754\pi$
$373$	−2.77553e6			−1.03294			−0.516469	+	0.856306i	$0.672754\pi$
$374$		0			0
$375$	−2.77953e6	+	2.01945e6i	−1.02069	+	0.741574i
$376$		0			0
$377$	−1.69338e6			−0.613622
$378$		0			0
$379$	−142991.	−	440082.i	−0.0511342	−	0.157375i	0.922229	−	0.386645i	$-0.126366\pi$
$379$	−142991.	−	440082.i	−0.0511342	−	0.157375i	−0.973363	+	0.229270i	$0.926366\pi$
$380$		0			0
$381$	116476.	−	358477.i	0.0411079	−	0.126517i
$382$		0			0
$383$	−261191.	−	803865.i	−0.0909834	−	0.280018i	0.895203	−	0.445659i	$-0.147031\pi$
$383$	−261191.	−	803865.i	−0.0909834	−	0.280018i	−0.986186	+	0.165641i	$0.947031\pi$
$384$		0			0
$385$	3.53761e6	−	2.57022e6i	1.21635	−	0.883729i
$386$		0			0
$387$	−1.89249e6	+	1.37498e6i	−0.642328	+	0.466678i
$388$		0			0
$389$	−50399.9	+	155115.i	−0.0168871	+	0.0519732i	−0.959145	−	0.282915i	$-0.908699\pi$
$389$	−50399.9	+	155115.i	−0.0168871	+	0.0519732i	0.942258	+	0.334888i	$0.108699\pi$
$390$		0			0
$391$	−294012.	−	213612.i	−0.0972576	−	0.0706618i
$392$		0			0
$393$	2.21404e6	+	1.60859e6i	0.723109	+	0.525369i
$394$		0			0
$395$	−370737.	+	1.14101e6i	−0.119556	+	0.367957i
$396$		0			0
$397$	1.72294e6			0.548648			0.274324	−	0.961637i	$-0.411546\pi$
$397$	1.72294e6			0.548648			0.274324	+	0.961637i	$0.411546\pi$
$398$		0			0
$399$	−704892.	−	2.16944e6i	−0.221662	−	0.682204i
$400$		0			0
$401$	−428203.	−	311108.i	−0.132981	−	0.0966162i	0.519306	−	0.854588i	$-0.326190\pi$
$401$	−428203.	−	311108.i	−0.132981	−	0.0966162i	−0.652287	+	0.757972i	$0.726190\pi$
$402$		0			0
$403$	3.76654e6	+	1.90860e6i	1.15526	+	0.585400i
$404$		0			0
$405$	−1.11583e6	−	810696.i	−0.338033	−	0.245596i
$406$		0			0
$407$	3.54718e6	+	1.09171e7i	1.06145	+	3.26679i
$408$		0			0
$409$	−3.74727e6			−1.10766			−0.553830	−	0.832630i	$-0.686834\pi$
$409$	−3.74727e6			−1.10766			−0.553830	+	0.832630i	$0.686834\pi$
$410$		0			0
$411$	1.66302e6	−	5.11824e6i	0.485615	−	1.49457i
$412$		0			0
$413$	1.00209e6	+	728057.i	0.289088	+	0.210034i
$414$		0			0
$415$	−848946.	−	616795.i	−0.241969	−	0.175801i
$416$		0			0
$417$	−1.61688e6	+	4.97625e6i	−0.455343	+	1.40140i
$418$		0			0
$419$	−2.56718e6	+	1.86516e6i	−0.714366	+	0.519017i	−0.884579	−	0.466390i	$-0.845554\pi$
$419$	−2.56718e6	+	1.86516e6i	−0.714366	+	0.519017i	0.170213	+	0.985407i	$0.445554\pi$
$420$		0			0
$421$	−586116.	+	425838.i	−0.161168	+	0.117095i	−0.665446	−	0.746446i	$-0.731759\pi$
$421$	−586116.	+	425838.i	−0.161168	+	0.117095i	0.504278	+	0.863541i	$0.331759\pi$
$422$		0			0
$423$	1.97078e6	+	6.06544e6i	0.535534	+	1.64821i
$424$		0			0
$425$	−206438.	+	635352.i	−0.0554393	+	0.170625i
$426$		0			0
$427$	−177402.	−	545987.i	−0.0470857	−	0.144915i
$428$		0			0
$429$	1.39973e7			3.67200
$430$		0			0
$431$	−2.39451e6	+	1.73972e6i	−0.620903	+	0.451113i	−0.853237	−	0.521524i	$-0.825364\pi$
$431$	−2.39451e6	+	1.73972e6i	−0.620903	+	0.451113i	0.232334	+	0.972636i	$0.425364\pi$
$432$		0			0
$433$	−5.07473e6			−1.30075			−0.650374	−	0.759614i	$-0.725388\pi$
$433$	−5.07473e6			−1.30075			−0.650374	+	0.759614i	$0.725388\pi$
$434$		0			0
$435$	1.34148e6			0.339907
$436$		0			0
$437$	511756.	−	371813.i	0.128192	−	0.0931366i
$438$		0			0
$439$	3.05201e6			0.755832			0.377916	−	0.925840i	$-0.376641\pi$
$439$	3.05201e6			0.755832			0.377916	+	0.925840i	$0.376641\pi$
$440$		0			0
$441$	2.11988e6	+	6.52433e6i	0.519058	+	1.59750i
$442$		0			0
$443$	−286562.	+	881948.i	−0.0693761	+	0.213518i	−0.979734	−	0.200305i	$-0.935807\pi$
$443$	−286562.	+	881948.i	−0.0693761	+	0.213518i	0.910357	+	0.413823i	$0.135807\pi$
$444$		0			0
$445$	161874.	+	498197.i	0.0387505	+	0.119262i
$446$		0			0
$447$	7.43444e6	−	5.40144e6i	1.75987	−	1.27862i
$448$		0			0
$449$	−4.90355e6	+	3.56264e6i	−1.14788	+	0.833981i	−0.988197	−	0.153188i	$-0.951046\pi$
$449$	−4.90355e6	+	3.56264e6i	−1.14788	+	0.833981i	−0.159679	+	0.987169i	$0.551046\pi$
$450$		0			0
$451$	330252.	−	1.01641e6i	0.0764548	−	0.235304i
$452$		0			0
$453$	1.26735e6	+	920787.i	0.290170	+	0.210821i
$454$		0			0
$455$	3.58265e6	+	2.60295e6i	0.811289	+	0.589436i
$456$		0			0
$457$	1.91544e6	−	5.89512e6i	0.429020	−	1.32039i	−0.470071	−	0.882628i	$-0.655772\pi$
$457$	1.91544e6	−	5.89512e6i	0.429020	−	1.32039i	0.899092	−	0.437760i	$-0.144228\pi$
$458$		0			0
$459$	205921.			0.0456214
$460$		0			0
$461$	−1.98733e6	−	6.11639e6i	−0.435531	−	1.34043i	−0.892542	−	0.450965i	$-0.851080\pi$
$461$	−1.98733e6	−	6.11639e6i	−0.435531	−	1.34043i	0.457011	−	0.889461i	$-0.348920\pi$
$462$		0			0
$463$	−642468.	−	466780.i	−0.139283	−	0.101195i	0.515962	−	0.856612i	$-0.327435\pi$
$463$	−642468.	−	466780.i	−0.139283	−	0.101195i	−0.655245	+	0.755416i	$0.727435\pi$
$464$		0			0
$465$	−2.98381e6	−	1.51197e6i	−0.639939	−	0.324274i
$466$		0			0
$467$	−546932.	−	397370.i	−0.116049	−	0.0843145i	0.528247	−	0.849091i	$-0.322850\pi$
$467$	−546932.	−	397370.i	−0.116049	−	0.0843145i	−0.644296	+	0.764776i	$0.722850\pi$
$468$		0			0
$469$	3.14697e6	+	9.68539e6i	0.660634	+	2.03322i
$470$		0			0
$471$	5.88573e6			1.22250
$472$		0			0
$473$	2.04755e6	−	6.30171e6i	0.420806	−	1.29511i
$474$		0			0
$475$	−940726.	−	683477.i	−0.191306	−	0.138992i
$476$		0			0
$477$	4.68184e6	+	3.40156e6i	0.942152	+	0.684513i
$478$		0			0
$479$	−59741.7	+	183866.i	−0.0118970	+	0.0366153i	−0.956829	−	0.290652i	$-0.906128\pi$
$479$	−59741.7	+	183866.i	−0.0118970	+	0.0366153i	0.944932	+	0.327267i	$0.106128\pi$
$480$		0			0
$481$	−9.40488e6	+	6.83305e6i	−1.85349	+	1.34664i
$482$		0			0
$483$	−4.85207e6	+	3.52523e6i	−0.946366	+	0.687575i
$484$		0			0
$485$	−1.24587e6	−	3.83438e6i	−0.240501	−	0.740187i
$486$		0			0
$487$	673928.	−	2.07414e6i	0.128763	−	0.396292i	−0.865805	−	0.500382i	$-0.833193\pi$
$487$	673928.	−	2.07414e6i	0.128763	−	0.396292i	0.994568	+	0.104090i	$0.0331930\pi$
$488$		0			0
$489$	−3.45953e6	−	1.06473e7i	−0.654251	−	2.01358i
$490$		0			0
$491$	−4.51339e6			−0.844888			−0.422444	−	0.906389i	$-0.638828\pi$
$491$	−4.51339e6			−0.844888			−0.422444	+	0.906389i	$0.638828\pi$
$492$		0			0
$493$	489200.	−	355425.i	0.0906504	−	0.0658613i
$494$		0			0
$495$	−5.88782e6			−1.08004
$496$		0			0
$497$	−3.10503e6			−0.563865
$498$		0			0
$499$	316706.	−	230100.i	0.0569383	−	0.0413681i	−0.558952	−	0.829200i	$-0.688796\pi$
$499$	316706.	−	230100.i	0.0569383	−	0.0413681i	0.615890	+	0.787832i	$0.288796\pi$
$500$		0			0
$501$	7.34217e6			1.30686
$502$		0			0
$503$	3.30847e6	+	1.01824e7i	0.583052	+	1.79445i	0.606955	+	0.794736i	$0.292391\pi$
$503$	3.30847e6	+	1.01824e7i	0.583052	+	1.79445i	−0.0239033	+	0.999714i	$0.507609\pi$
$504$		0			0
$505$	−1.57516e6	+	4.84783e6i	−0.274850	+	0.845900i
$506$		0			0
$507$	1.76888e6	+	5.44406e6i	0.305618	+	0.940596i
$508$		0			0
$509$	2.46386e6	−	1.79010e6i	0.421523	−	0.306254i	−0.356727	−	0.934209i	$-0.616108\pi$
$509$	2.46386e6	−	1.79010e6i	0.421523	−	0.306254i	0.778250	+	0.627954i	$0.216108\pi$
$510$		0			0
$511$	1.14019e7	−	8.28395e6i	1.93163	−	1.40341i
$512$		0			0
$513$	−110759.	+	340882.i	−0.0185818	+	0.0571888i
$514$		0			0
$515$	−3.61626e6	−	2.62737e6i	−0.600816	−	0.436518i
$516$		0			0
$517$	−1.46147e7	−	1.06182e7i	−2.40471	−	1.74712i
$518$		0			0
$519$	4.99285e6	−	1.53664e7i	0.813636	−	2.50411i
$520$		0			0
$521$	−3.21482e6			−0.518875			−0.259437	−	0.965760i	$-0.583537\pi$
$521$	−3.21482e6			−0.518875			−0.259437	+	0.965760i	$0.583537\pi$
$522$		0			0
$523$	3.75449e6	+	1.15551e7i	0.600201	+	1.84723i	0.526917	+	0.849917i	$0.323348\pi$
$523$	3.75449e6	+	1.15551e7i	0.600201	+	1.84723i	0.0732839	+	0.997311i	$0.476652\pi$
$524$		0			0
$525$	8.91922e6	+	6.48020e6i	1.41231	+	1.02610i
$526$		0			0
$527$	−1.48871e6	+	239186.i	−0.233499	+	0.0375153i
$528$		0			0
$529$	3.86159e6	+	2.80561e6i	0.599966	+	0.435901i
$530$		0			0
$531$	−515385.	−	1.58619e6i	−0.0793223	−	0.244129i
$532$		0			0
$533$	1.08233e6			0.165021
$534$		0			0
$535$	713270.	−	2.19522e6i	0.107738	−	0.331584i
$536$		0			0
$537$	879837.	+	639239.i	0.131664	+	0.0956593i
$538$		0			0
$539$	−1.57204e7	−	1.14215e7i	−2.33073	−	1.69337i
$540$		0			0
$541$	1.60263e6	−	4.93238e6i	0.235418	−	0.724541i	−0.761648	−	0.647991i	$-0.775609\pi$
$541$	1.60263e6	−	4.93238e6i	0.235418	−	0.724541i	0.997066	−	0.0765501i	$-0.0243905\pi$
$542$		0			0
$543$	1.96630e6	−	1.42860e6i	0.286188	−	0.207928i
$544$		0			0
$545$	−2.15500e6	+	1.56570e6i	−0.310783	+	0.225797i
$546$		0			0
$547$	2.14720e6	+	6.60839e6i	0.306834	+	0.944338i	0.978986	+	0.203925i	$0.0653700\pi$
$547$	2.14720e6	+	6.60839e6i	0.306834	+	0.944338i	−0.672152	+	0.740413i	$0.734630\pi$
$548$		0			0
$549$	−238869.	+	735164.i	−0.0338244	+	0.104101i
$550$		0			0
$551$	325244.	+	1.00100e6i	0.0456384	+	0.140460i
$552$		0			0
$553$	8.92464e6			1.24102
$554$		0			0
$555$	7.45045e6	−	5.41307e6i	1.02672	−	0.745952i
$556$		0			0
$557$	5.06951e6			0.692353			0.346177	−	0.938169i	$-0.387480\pi$
$557$	5.06951e6			0.692353			0.346177	+	0.938169i	$0.387480\pi$
$558$		0			0
$559$	6.71037e6			0.908274
$560$		0			0
$561$	−4.04369e6	+	2.93791e6i	−0.542464	+	0.394123i
$562$		0			0
$563$	−797252.			−0.106005			−0.0530023	−	0.998594i	$-0.516879\pi$
$563$	−797252.			−0.106005			−0.0530023	+	0.998594i	$0.516879\pi$
$564$		0			0
$565$	1.25580e6	+	3.86496e6i	0.165501	+	0.509359i
$566$		0			0
$567$	−3.17051e6	+	9.75782e6i	−0.414163	+	1.27466i
$568$		0			0
$569$	2.72501e6	+	8.38672e6i	0.352848	+	1.08595i	0.957247	+	0.289272i	$0.0934132\pi$
$569$	2.72501e6	+	8.38672e6i	0.352848	+	1.08595i	−0.604399	+	0.796682i	$0.706587\pi$
$570$		0			0
$571$	−8.61276e6	+	6.25754e6i	−1.10548	+	0.803180i	−0.981946	−	0.189160i	$-0.939424\pi$
$571$	−8.61276e6	+	6.25754e6i	−1.10548	+	0.803180i	−0.123537	+	0.992340i	$0.539424\pi$
$572$		0			0
$573$	−1.72210e7	+	1.25118e7i	−2.19115	+	1.59196i
$574$		0			0
$575$	−944750.	+	2.90764e6i	−0.119165	+	0.366751i
$576$		0			0
$577$	−1.25722e7	−	9.13425e6i	−1.57207	−	1.14218i	−0.925139	−	0.379629i	$-0.876052\pi$
$577$	−1.25722e7	−	9.13425e6i	−1.57207	−	1.14218i	−0.646933	−	0.762547i	$-0.723948\pi$
$578$		0			0
$579$	3.70555e6	+	2.69224e6i	0.459364	+	0.333747i
$580$		0			0
$581$	−2.41219e6	+	7.42397e6i	−0.296464	+	0.912422i
$582$		0			0
$583$	−1.63921e7			−1.99739
$584$		0			0
$585$	−1.84260e6	−	5.67094e6i	−0.222608	−	0.685118i
$586$		0			0
$587$	−1.19693e7	−	8.69624e6i	−1.43376	−	1.04168i	−0.989302	−	0.145883i	$-0.953398\pi$
$587$	−1.19693e7	−	8.69624e6i	−1.43376	−	1.04168i	−0.444454	−	0.895802i	$-0.646602\pi$
$588$		0			0
$589$	404790.	−	2.59307e6i	0.0480774	−	0.307983i
$590$		0			0
$591$	−1.13477e7	−	8.24459e6i	−1.33641	−	0.970958i
$592$		0			0
$593$	229029.	+	704878.i	0.0267457	+	0.0823147i	0.963538	−	0.267570i	$-0.0862207\pi$
$593$	229029.	+	704878.i	0.0267457	+	0.0823147i	−0.936793	+	0.349885i	$0.886221\pi$
$594$		0			0
$595$	−1.58133e6			−0.183117
$596$		0			0
$597$	−4.12352e6	+	1.26909e7i	−0.473514	+	1.45733i
$598$		0			0
$599$	1.02740e7	+	7.46448e6i	1.16996	+	0.850026i	0.991004	−	0.133831i	$-0.0427279\pi$
$599$	1.02740e7	+	7.46448e6i	1.16996	+	0.850026i	0.178957	+	0.983857i	$0.442728\pi$
$600$		0			0
$601$	−2.93745e6	−	2.13419e6i	−0.331730	−	0.241016i	0.409434	−	0.912340i	$-0.365726\pi$
$601$	−2.93745e6	−	2.13419e6i	−0.331730	−	0.241016i	−0.741164	+	0.671324i	$0.765726\pi$
$602$		0			0
$603$	4.23736e6	−	1.30412e7i	0.474572	−	1.46058i
$604$		0			0
$605$	9.91379e6	−	7.20279e6i	1.10116	−	0.800041i
$606$		0			0
$607$	6.07038e6	−	4.41039e6i	0.668720	−	0.485854i	−0.200876	−	0.979617i	$-0.564379\pi$
$607$	6.07038e6	−	4.41039e6i	0.668720	−	0.485854i	0.869597	+	0.493763i	$0.164379\pi$
$608$		0			0
$609$	−3.08371e6	−	9.49067e6i	−0.336922	−	1.03694i
$610$		0			0
$611$	5.65338e6	−	1.73993e7i	0.612640	−	1.88551i
$612$		0			0
$613$	1.34245e6	+	4.13163e6i	0.144293	+	0.444089i	0.996919	−	0.0784325i	$-0.0249915\pi$
$613$	1.34245e6	+	4.13163e6i	0.144293	+	0.444089i	−0.852626	+	0.522521i	$0.824992\pi$
$614$		0			0
$615$	−857407.			−0.0914112
$616$		0			0
$617$	1.06033e7	−	7.70376e6i	1.12132	−	0.814685i	0.136910	−	0.990583i	$-0.456283\pi$
$617$	1.06033e7	−	7.70376e6i	1.12132	−	0.814685i	0.984408	+	0.175898i	$0.0562829\pi$
$618$		0			0
$619$	97702.2			0.0102489			0.00512446	−	0.999987i	$-0.498369\pi$
$619$	97702.2			0.0102489			0.00512446	+	0.999987i	$0.498369\pi$
$620$		0			0
$621$	942382.			0.0980614
$622$		0			0
$623$	3.15253e6	−	2.29045e6i	0.325416	−	0.236429i
$624$		0			0
$625$	3.26263e6			0.334093
$626$		0			0
$627$	−2.68844e6	−	8.27417e6i	−0.273106	−	0.840534i
$628$		0			0
$629$	1.28278e6	−	3.94800e6i	0.129278	−	0.397878i
$630$		0			0
$631$	−4.25430e6	−	1.30934e7i	−0.425358	−	1.30912i	−0.902651	−	0.430373i	$-0.858382\pi$
$631$	−4.25430e6	−	1.30934e7i	−0.425358	−	1.30912i	0.477294	−	0.878744i	$-0.341618\pi$
$632$		0			0
$633$	−7.46206e6	+	5.42150e6i	−0.740201	+	0.537787i
$634$		0			0
$635$	367952.	−	267333.i	0.0362124	−	0.0263099i
$636$		0			0
$637$	6.08110e6	−	1.87157e7i	0.593791	−	1.82750i
$638$		0			0
$639$	3.38241e6	+	2.45746e6i	0.327698	+	0.238086i
$640$		0			0
$641$	−4.25673e6	−	3.09269e6i	−0.409195	−	0.297298i	0.364081	−	0.931367i	$-0.381383\pi$
$641$	−4.25673e6	−	3.09269e6i	−0.409195	−	0.297298i	−0.773276	+	0.634070i	$0.781383\pi$
$642$		0			0
$643$	2.01400e6	−	6.19847e6i	0.192102	−	0.591231i	−0.807896	−	0.589325i	$-0.799394\pi$
$643$	2.01400e6	−	6.19847e6i	0.192102	−	0.591231i	0.999998	−	0.00190510i	$-0.000606414\pi$
$644$		0			0
$645$	−5.31588e6			−0.503125
$646$		0			0
$647$	−4.92433e6	−	1.51555e7i	−0.462473	−	1.42335i	−0.862133	−	0.506683i	$-0.830872\pi$
$647$	−4.92433e6	−	1.51555e7i	−0.462473	−	1.42335i	0.399659	−	0.916664i	$-0.369128\pi$
$648$		0			0
$649$	3.82193e6	+	2.77679e6i	0.356181	+	0.258781i
$650$		0			0
$651$	−3.83790e6	+	2.45855e7i	−0.354929	+	2.27366i
$652$		0			0
$653$	1.13274e7	+	8.22983e6i	1.03955	+	0.755280i	0.970198	−	0.242312i	$-0.0779059\pi$
$653$	1.13274e7	+	8.22983e6i	1.03955	+	0.755280i	0.0693550	+	0.997592i	$0.477906\pi$
$654$		0			0
$655$	1.02044e6	+	3.14060e6i	0.0929362	+	0.286028i
$656$		0			0
$657$	−1.89767e7			−1.71517
$658$		0			0
$659$	−6.24876e6	+	1.92317e7i	−0.560506	+	1.72506i	0.120434	+	0.992721i	$0.461571\pi$
$659$	−6.24876e6	+	1.92317e7i	−0.560506	+	1.72506i	−0.680940	+	0.732339i	$0.738429\pi$
$660$		0			0
$661$	1.18181e7	+	8.58633e6i	1.05207	+	0.764371i	0.972604	−	0.232467i	$-0.0746799\pi$
$661$	1.18181e7	+	8.58633e6i	1.05207	+	0.764371i	0.0794617	+	0.996838i	$0.474680\pi$
$662$		0			0
$663$	−4.09517e6	−	2.97532e6i	−0.361817	−	0.262875i
$664$		0			0
$665$	850553.	−	2.61773e6i	0.0745843	−	0.229547i
$666$		0			0
$667$	2.23879e6	−	1.62658e6i	0.194849	−	0.141566i
$668$		0			0
$669$	1.31618e7	−	9.56260e6i	1.13697	−	0.826059i
$670$		0			0
$671$	−676606.	−	2.08238e6i	−0.0580136	−	0.178547i
$672$		0			0
$673$	−2.74187e6	+	8.43862e6i	−0.233351	+	0.718181i	0.763985	+	0.645234i	$0.223240\pi$
$673$	−2.74187e6	+	8.43862e6i	−0.233351	+	0.718181i	−0.997336	+	0.0729464i	$0.976760\pi$
$674$		0			0
$675$	−535315.	−	1.64753e6i	−0.0452220	−	0.139179i
$676$		0			0
$677$	5.38882e6			0.451879			0.225939	−	0.974141i	$-0.427455\pi$
$677$	5.38882e6			0.451879			0.225939	+	0.974141i	$0.427455\pi$
$678$		0			0
$679$	−2.42635e7	+	1.76285e7i	−2.01967	+	1.46737i
$680$		0			0
$681$	−2.12803e7			−1.75837
$682$		0			0
$683$	−1.08886e7			−0.893140			−0.446570	−	0.894749i	$-0.647355\pi$
$683$	−1.08886e7			−0.893140			−0.446570	+	0.894749i	$0.647355\pi$
$684$		0			0
$685$	5.25352e6	−	3.81691e6i	0.427783	−	0.310803i
$686$		0			0
$687$	9.73078e6			0.786603
$688$		0			0
$689$	−5.12993e6	−	1.57883e7i	−0.411683	−	1.26703i
$690$		0			0
$691$	4.07455e6	−	1.25402e7i	0.324627	−	0.999100i	−0.646981	−	0.762506i	$-0.723969\pi$
$691$	4.07455e6	−	1.25402e7i	0.324627	−	0.999100i	0.971609	−	0.236594i	$-0.0760312\pi$
$692$		0			0
$693$	1.35346e7	+	4.16551e7i	1.07056	+	3.29484i
$694$		0			0
$695$	−5.10778e6	+	3.71102e6i	−0.401116	+	0.291428i
$696$		0			0
$697$	−312673.	+	227170.i	−0.0243786	+	0.0177121i
$698$		0			0
$699$	7.00265e6	−	2.15519e7i	0.542088	−	1.66837i
$700$		0			0
$701$	1.50874e7	+	1.09617e7i	1.15963	+	0.842522i	0.989731	−	0.142940i	$-0.0456555\pi$
$701$	1.50874e7	+	1.09617e7i	1.15963	+	0.842522i	0.169900	+	0.985461i	$0.445655\pi$
$702$		0			0
$703$	5.84555e6	+	4.24704e6i	0.446105	+	0.324114i
$704$		0			0
$705$	−4.47855e6	+	1.37836e7i	−0.339363	+	1.04445i
$706$		0			0
$707$	3.79183e7			2.85299
$708$		0			0
$709$	−176754.	−	543994.i	−0.0132055	−	0.0406423i	0.944237	−	0.329268i	$-0.106802\pi$
$709$	−176754.	−	543994.i	−0.0132055	−	0.0406423i	−0.957442	+	0.288625i	$0.906802\pi$
$710$		0			0
$711$	−9.72188e6	−	7.06336e6i	−0.721234	−	0.524007i
$712$		0			0
$713$	−6.81298e6	+	1.09461e6i	−0.501896	+	0.0806376i
$714$		0			0
$715$	1.36641e7	+	9.92757e6i	0.999578	+	0.726236i
$716$		0			0
$717$	−5.64075e6	−	1.73605e7i	−0.409769	−	1.26114i
$718$		0			0
$719$	1.45812e7			1.05189			0.525947	−	0.850518i	$-0.323711\pi$
$719$	1.45812e7			1.05189			0.525947	+	0.850518i	$0.323711\pi$
$720$		0			0
$721$	−1.02752e7	+	3.16239e7i	−0.736128	+	2.26557i
$722$		0			0
$723$	6.27133e6	+	4.55639e6i	0.446184	+	0.324171i
$724$		0			0
$725$	−4.11541e6	−	2.99002e6i	−0.290783	−	0.211266i
$726$		0			0
$727$	2.61281e6	−	8.04140e6i	0.183346	−	0.564282i	−0.816570	−	0.577247i	$-0.804127\pi$
$727$	2.61281e6	−	8.04140e6i	0.183346	−	0.564282i	0.999916	+	0.0129652i	$0.00412707\pi$
$728$		0			0
$729$	1.44464e7	−	1.04959e7i	1.00679	−	0.731479i
$730$		0			0
$731$	−1.93856e6	+	1.40844e6i	−0.134179	+	0.0974869i
$732$		0			0
$733$	−260999.	−	803272.i	−0.0179423	−	0.0552208i	0.941684	−	0.336497i	$-0.109242\pi$
$733$	−260999.	−	803272.i	−0.0179423	−	0.0552208i	−0.959627	+	0.281276i	$0.909242\pi$
$734$		0			0
$735$	−4.81738e6	+	1.48264e7i	−0.328922	+	1.01232i
$736$		0			0
$737$	1.20025e7	+	3.69398e7i	0.813958	+	2.50510i
$738$		0			0
$739$	−9.06833e6			−0.610824			−0.305412	−	0.952220i	$-0.598794\pi$
$739$	−9.06833e6			−0.610824			−0.305412	+	0.952220i	$0.598794\pi$
$740$		0			0
$741$	7.12804e6	−	5.17882e6i	0.476897	−	0.346486i
$742$		0			0
$743$	2.74546e7			1.82449			0.912247	−	0.409641i	$-0.134346\pi$
$743$	2.74546e7			1.82449			0.912247	+	0.409641i	$0.134346\pi$
$744$		0			0
$745$	1.10884e7			0.731945
$746$		0			0
$747$	8.50334e6	−	6.17804e6i	0.557555	−	0.405088i
$748$		0			0
$749$	−1.71703e7			−1.11834
$750$		0			0
$751$	8.28655e6	+	2.55034e7i	0.536134	+	1.65005i	0.741185	+	0.671301i	$0.234264\pi$
$751$	8.28655e6	+	2.55034e7i	0.536134	+	1.65005i	−0.205050	+	0.978751i	$0.565736\pi$
$752$		0			0
$753$	5.33982e6	−	1.64343e7i	0.343194	−	1.05624i
$754$		0			0
$755$	584119.	+	1.79773e6i	0.0372936	+	0.114778i
$756$		0			0
$757$	94120.5	−	68382.6i	0.00596959	−	0.00433716i	−0.584796	−	0.811180i	$-0.698826\pi$
$757$	94120.5	−	68382.6i	0.00596959	−	0.00433716i	0.590766	+	0.806843i	$0.298826\pi$
$758$		0			0
$759$	−1.85057e7	+	1.34452e7i	−1.16600	+	0.847152i
$760$		0			0
$761$	−4.25369e6	+	1.30915e7i	−0.266259	+	0.819461i	0.725142	+	0.688600i	$0.241774\pi$
$761$	−4.25369e6	+	1.30915e7i	−0.266259	+	0.819461i	−0.991401	+	0.130861i	$0.958226\pi$
$762$		0			0
$763$	1.60308e7	+	1.16471e7i	0.996882	+	0.724277i
$764$		0			0
$765$	1.72259e6	+	1.25153e6i	0.106421	+	0.0773194i
$766$		0			0
$767$	−1.47843e6	+	4.55015e6i	−0.0907429	+	0.279278i
$768$		0			0
$769$	−6.77471e6			−0.413118			−0.206559	−	0.978434i	$-0.566227\pi$
$769$	−6.77471e6			−0.413118			−0.206559	+	0.978434i	$0.566227\pi$
$770$		0			0
$771$	−5.11619e6	−	1.57460e7i	−0.309964	−	0.953970i
$772$		0			0
$773$	−1.13136e7	−	8.21982e6i	−0.681009	−	0.494782i	0.192683	−	0.981261i	$-0.438281\pi$
$773$	−1.13136e7	−	8.21982e6i	−0.681009	−	0.494782i	−0.873692	+	0.486479i	$0.838281\pi$
$774$		0			0
$775$	5.78375e6	+	1.12891e7i	0.345904	+	0.675156i
$776$		0			0
$777$	−5.54229e7	−	4.02671e7i	−3.29334	−	2.39275i
$778$		0			0
$779$	−207880.	−	639789.i	−0.0122735	−	0.0377740i
$780$		0			0
$781$	−1.18425e7			−0.694730
$782$		0			0
$783$	−484541.	+	1.49127e6i	−0.0282440	+	0.0869262i
$784$		0			0
$785$	5.74562e6	+	4.17444e6i	0.332784	+	0.241782i
$786$		0			0
$787$	−1.45175e6	−	1.05476e6i	−0.0835519	−	0.0607040i	0.545225	−	0.838290i	$-0.316444\pi$
$787$	−1.45175e6	−	1.05476e6i	−0.0835519	−	0.0607040i	−0.628777	+	0.777586i	$0.716444\pi$
$788$		0			0
$789$	−8.41346e6	+	2.58940e7i	−0.481152	+	1.48083i
$790$		0			0
$791$	2.44570e7	−	1.77691e7i	1.38983	−	1.00977i
$792$		0			0
$793$	1.79393e6	−	1.30337e6i	0.101303	−	0.0736010i
$794$		0			0
$795$	4.06388e6	+	1.25073e7i	0.228046	+	0.701854i
$796$		0			0
$797$	−4.48180e6	+	1.37936e7i	−0.249923	+	0.769184i	0.744864	+	0.667216i	$0.232514\pi$
$797$	−4.48180e6	+	1.37936e7i	−0.249923	+	0.769184i	−0.994788	+	0.101969i	$0.967486\pi$
$798$		0			0
$799$	2.01875e6	+	6.21308e6i	0.111871	+	0.344302i
$800$		0			0
$801$	−5.24692e6			−0.288950
$802$		0			0
$803$	4.34865e7	−	3.15948e7i	2.37994	−	1.72912i
$804$		0			0
$805$	−7.23682e6			−0.393603
$806$		0			0
$807$	1.45504e7			0.786485
$808$		0			0
$809$	1.69449e7	−	1.23112e7i	0.910266	−	0.661347i	−0.0308163	−	0.999525i	$-0.509811\pi$
$809$	1.69449e7	−	1.23112e7i	0.910266	−	0.661347i	0.941082	+	0.338178i	$0.109811\pi$
$810$		0			0
$811$	6.57641e6			0.351105			0.175552	−	0.984470i	$-0.443829\pi$
$811$	6.57641e6			0.351105			0.175552	+	0.984470i	$0.443829\pi$
$812$		0			0
$813$	−18734.3	−	57658.1i	−0.000994054	−	0.00305938i
$814$		0			0
$815$	4.17441e6	−	1.28475e7i	0.220141	−	0.677525i
$816$		0			0
$817$	−1.28885e6	−	3.96666e6i	−0.0675532	−	0.207907i
$818$		0			0
$819$	−3.58850e7	+	2.60720e7i	−1.86941	+	1.35820i
$820$		0			0
$821$	6.21962e6	−	4.51882e6i	0.322037	−	0.233974i	−0.415007	−	0.909818i	$-0.636221\pi$
$821$	6.21962e6	−	4.51882e6i	0.322037	−	0.233974i	0.737044	+	0.675844i	$0.236221\pi$
$822$		0			0
$823$	1.12027e7	−	3.44784e7i	0.576532	−	1.77438i	−0.0543689	−	0.998521i	$-0.517315\pi$
$823$	1.12027e7	−	3.44784e7i	0.576532	−	1.77438i	0.630901	−	0.775863i	$-0.282685\pi$
$824$		0			0
$825$	3.40177e7	+	2.47153e7i	1.74008	+	1.26424i
$826$		0			0
$827$	−2.43113e7	−	1.76632e7i	−1.23607	−	0.898060i	−0.238743	−	0.971083i	$-0.576736\pi$
$827$	−2.43113e7	−	1.76632e7i	−1.23607	−	0.898060i	−0.997330	+	0.0730225i	$0.976736\pi$
$828$		0			0
$829$	8.52228e6	−	2.62289e7i	0.430695	−	1.32554i	−0.466740	−	0.884395i	$-0.654572\pi$
$829$	8.52228e6	−	2.62289e7i	0.430695	−	1.32554i	0.897435	−	0.441148i	$-0.145428\pi$
$830$		0			0
$831$	−4.32275e7			−2.17149
$832$		0			0
$833$	2.17149e6	+	6.68314e6i	0.108429	+	0.333709i
$834$		0			0
$835$	7.16738e6	+	5.20741e6i	0.355749	+	0.258467i
$836$		0			0
$837$	2.75855e6	−	2.77085e6i	0.136103	−	0.136710i
$838$		0			0
$839$	−2.05202e7	−	1.49088e7i	−1.00642	−	0.731204i	−0.0429620	−	0.999077i	$-0.513679\pi$
$839$	−2.05202e7	−	1.49088e7i	−1.00642	−	0.731204i	−0.963454	+	0.267872i	$0.913679\pi$
$840$		0			0
$841$	−4.91544e6	−	1.51282e7i	−0.239647	−	0.737559i
$842$		0			0
$843$	3.38875e7			1.64237
$844$		0			0
$845$	−2.13441e6	+	6.56903e6i	−0.102834	+	0.316490i
$846$		0			0
$847$	−7.37475e7	−	5.35807e7i	−3.53215	−	2.56625i
$848$		0			0
$849$	−1.82365e7	−	1.32496e7i	−0.868303	−	0.630859i
$850$		0			0
$851$	5.87056e6	−	1.80677e7i	0.277879	−	0.855223i
$852$		0			0
$853$	−2.15045e7	+	1.56239e7i	−1.01194	+	0.735220i	−0.964616	−	0.263659i	$-0.915071\pi$
$853$	−2.15045e7	+	1.56239e7i	−1.01194	+	0.735220i	−0.0473280	+	0.998879i	$0.515071\pi$
$854$		0			0
$855$	−2.99832e6	+	2.17841e6i	−0.140270	+	0.101912i
$856$		0			0
$857$	5.25559e6	+	1.61750e7i	0.244438	+	0.752304i	0.995728	+	0.0923318i	$0.0294321\pi$
$857$	5.25559e6	+	1.61750e7i	0.244438	+	0.752304i	−0.751290	+	0.659972i	$0.770568\pi$
$858$		0			0
$859$	−4.85247e6	+	1.49344e7i	−0.224378	+	0.690565i	0.773976	+	0.633215i	$0.218265\pi$
$859$	−4.85247e6	+	1.49344e7i	−0.224378	+	0.690565i	−0.998354	+	0.0573497i	$0.981735\pi$
$860$		0			0
$861$	1.97095e6	+	6.06597e6i	0.0906085	+	0.278864i
$862$		0			0
$863$	3.44308e7			1.57370			0.786848	−	0.617147i	$-0.211712\pi$
$863$	3.44308e7			1.57370			0.786848	+	0.617147i	$0.211712\pi$
$864$		0			0
$865$	1.57726e7	−	1.14594e7i	0.716741	−	0.520743i
$866$		0			0
$867$	−3.05111e7			−1.37851
$868$		0			0
$869$	3.40383e7			1.52904
$870$		0			0
$871$	−3.18229e7	+	2.31207e7i	−1.42133	+	1.03266i
$872$		0			0
$873$	4.03830e7			1.79334
$874$		0			0
$875$	9.52976e6	+	2.93296e7i	0.420787	+	1.29505i
$876$		0			0
$877$	9.95678e6	−	3.06438e7i	0.437139	−	1.34538i	−0.453739	−	0.891135i	$-0.649910\pi$
$877$	9.95678e6	−	3.06438e7i	0.437139	−	1.34538i	0.890878	−	0.454242i	$-0.150090\pi$
$878$		0			0
$879$	−1.54909e7	−	4.76759e7i	−0.676243	−	2.08126i
$880$		0			0
$881$	−1.38117e7	+	1.00348e7i	−0.599525	+	0.435580i	−0.845710	−	0.533642i	$-0.820823\pi$
$881$	−1.38117e7	+	1.00348e7i	−0.599525	+	0.435580i	0.246185	+	0.969223i	$0.420823\pi$
$882$		0			0
$883$	−2.49086e6	+	1.80972e6i	−0.107510	+	0.0781104i	−0.640241	−	0.768174i	$-0.721166\pi$
$883$	−2.49086e6	+	1.80972e6i	−0.107510	+	0.0781104i	0.532731	+	0.846284i	$0.321166\pi$
$884$		0			0
$885$	1.17120e6	−	3.60458e6i	0.0502658	−	0.154702i
$886$		0			0
$887$	−6.54972e6	−	4.75865e6i	−0.279520	−	0.203083i	0.439188	−	0.898395i	$-0.355266\pi$
$887$	−6.54972e6	−	4.75865e6i	−0.279520	−	0.203083i	−0.718708	+	0.695312i	$0.755266\pi$
$888$		0			0
$889$	−2.73715e6	−	1.98866e6i	−0.116157	−	0.0843928i
$890$		0			0
$891$	−1.20922e7	+	3.72161e7i	−0.510285	+	1.57049i
$892$		0			0
$893$	−1.13710e7			−0.477166
$894$		0			0
$895$	405513.	+	1.24804e6i	0.0169218	+	0.0520801i
$896$		0			0
$897$	−1.87413e7	−	1.36163e7i	−0.777710	−	0.565040i
$898$		0			0
$899$	1.77084e6	−	1.13440e7i	0.0730770	−	0.468129i
$900$		0			0
$901$	4.79580e6	+	3.48435e6i	0.196811	+	0.142992i
$902$		0			0
$903$	1.22198e7	+	3.76087e7i	0.498707	+	1.53486i
$904$		0			0
$905$	2.93273e6			0.119028
$906$		0			0
$907$	−1.17523e7	+	3.61699e7i	−0.474357	+	1.45992i	0.372467	+	0.928045i	$0.378512\pi$
$907$	−1.17523e7	+	3.61699e7i	−0.474357	+	1.45992i	−0.846824	+	0.531874i	$0.821488\pi$
$908$		0			0
$909$	−4.13055e7	−	3.00102e7i	−1.65805	−	1.20465i
$910$		0			0
$911$	8.29827e6	+	6.02905e6i	0.331277	+	0.240687i	0.740972	−	0.671535i	$-0.234365\pi$
$911$	8.29827e6	+	6.02905e6i	0.331277	+	0.240687i	−0.409695	+	0.912223i	$0.634365\pi$
$912$		0			0
$913$	−9.20004e6	+	2.83148e7i	−0.365269	+	1.12418i
$914$		0			0
$915$	−1.42113e6	+	1.03251e6i	−0.0561154	+	0.0407702i
$916$		0			0
$917$	1.98733e7	−	1.44388e7i	0.780454	−	0.567033i
$918$		0			0
$919$	2.18470e6	+	6.72381e6i	0.0853302	+	0.262619i	0.984613	−	0.174748i	$-0.0559110\pi$
$919$	2.18470e6	+	6.72381e6i	0.0853302	+	0.262619i	−0.899283	+	0.437367i	$0.855911\pi$
$920$		0			0
$921$	−7.09459e6	+	2.18349e7i	−0.275599	+	0.848207i
$922$		0			0
$923$	−3.70613e6	−	1.14063e7i	−0.143191	−	0.440697i
$924$		0			0
$925$	−3.49218e7			−1.34197
$926$		0			0
$927$	3.62217e7	−	2.63166e7i	1.38443	−	1.00584i
$928$		0			0
$929$	−4.98695e6			−0.189582			−0.0947908	−	0.995497i	$-0.530218\pi$
$929$	−4.98695e6			−0.189582			−0.0947908	+	0.995497i	$0.530218\pi$
$930$		0			0
$931$	−1.22313e7			−0.462485
$932$		0			0
$933$	4.01418e7	−	2.91647e7i	1.50971	−	1.09687i
$934$		0			0
$935$	−6.03113e6			−0.225616
$936$		0			0
$937$	−3.88337e6	−	1.19518e7i	−0.144497	−	0.444717i	0.852449	−	0.522811i	$-0.175117\pi$
$937$	−3.88337e6	−	1.19518e7i	−0.144497	−	0.444717i	−0.996946	+	0.0780939i	$0.975117\pi$
$938$		0			0
$939$	−1.23362e7	+	3.79671e7i	−0.456582	+	1.40522i
$940$		0			0
$941$	−1.03476e7	−	3.18466e7i	−0.380948	−	1.17244i	−0.939378	−	0.342885i	$-0.888596\pi$
$941$	−1.03476e7	−	3.18466e7i	−0.380948	−	1.17244i	0.558430	−	0.829552i	$-0.311404\pi$
$942$		0			0
$943$	−1.43093e6	+	1.03963e6i	−0.0524008	+	0.0380714i
$944$		0			0
$945$	3.31740e6	−	2.41023e6i	0.120842	−	0.0877970i
$946$		0			0
$947$	−7.77887e6	+	2.39409e7i	−0.281865	+	0.867492i	0.705456	+	0.708754i	$0.250742\pi$
$947$	−7.77887e6	+	2.39409e7i	−0.281865	+	0.867492i	−0.987321	+	0.158738i	$0.949258\pi$
$948$		0			0
$949$	4.40401e7	+	3.19970e7i	1.58739	+	1.15330i
$950$		0			0
$951$	−1.46894e7	−	1.06725e7i	−0.526688	−	0.382662i
$952$		0			0
$953$	6.69446e6	−	2.06034e7i	0.238772	−	0.734865i	−0.757827	−	0.652456i	$-0.773739\pi$
$953$	6.69446e6	−	2.06034e7i	0.238772	−	0.734865i	0.996599	−	0.0824088i	$-0.0262613\pi$
$954$		0			0
$955$	−2.56850e7			−0.911320
$956$		0			0
$957$	−1.17612e7	−	3.61972e7i	−0.415117	−	1.27760i
$958$		0			0
$959$	−3.90803e7	−	2.83935e7i	−1.37218	−	0.996947i
$960$		0			0
$961$	−1.67246e7	+	2.32361e7i	−0.584179	+	0.811625i
$962$		0			0
$963$	1.87042e7	+	1.35894e7i	0.649939	+	0.472208i
$964$		0			0
$965$	1.70788e6	+	5.25630e6i	0.0590388	+	0.181703i
$966$		0			0
$967$	1.49392e7			0.513760			0.256880	−	0.966443i	$-0.417306\pi$
$967$	1.49392e7			0.513760			0.256880	+	0.966443i	$0.417306\pi$
$968$		0			0
$969$	−972231.	+	2.99222e6i	−0.0332629	+	0.102373i
$970$		0			0
$971$	−9.15061e6	−	6.64830e6i	−0.311460	−	0.226289i	0.421063	−	0.907031i	$-0.361657\pi$
$971$	−9.15061e6	−	6.64830e6i	−0.311460	−	0.226289i	−0.732523	+	0.680743i	$0.761657\pi$
$972$		0			0
$973$	3.79962e7	+	2.76058e7i	1.28664	+	0.934800i
$974$		0			0
$975$	−1.31590e7	+	4.04993e7i	−0.443315	+	1.36438i
$976$		0			0
$977$	−9.31242e6	+	6.76587e6i	−0.312123	+	0.226771i	−0.732807	−	0.680436i	$-0.761790\pi$
$977$	−9.31242e6	+	6.76587e6i	−0.312123	+	0.226771i	0.420684	+	0.907207i	$0.361790\pi$
$978$		0			0
$979$	1.20237e7	−	8.73571e6i	0.400941	−	0.291301i
$980$		0			0
$981$	−8.24484e6	−	2.53750e7i	−0.273533	−	0.841848i
$982$		0			0
$983$	−7.21052e6	+	2.21917e7i	−0.238003	+	0.732498i	0.758706	+	0.651433i	$0.225832\pi$
$983$	−7.21052e6	+	2.21917e7i	−0.238003	+	0.732498i	−0.996709	+	0.0810646i	$0.974168\pi$
$984$		0			0
$985$	−5.23011e6	−	1.60966e7i	−0.171759	−	0.528621i
$986$		0			0
$987$	1.07811e8			3.52265
$988$		0			0
$989$	−8.87166e6	+	6.44564e6i	−0.288413	+	0.209544i
$990$		0			0
$991$	−8.21115e6			−0.265595			−0.132798	−	0.991143i	$-0.542396\pi$
$991$	−8.21115e6			−0.265595			−0.132798	+	0.991143i	$0.542396\pi$
$992$		0			0
$993$	−4.31181e7			−1.38767
$994$		0			0
$995$	−1.30263e7	+	9.46419e6i	−0.417123	+	0.303058i
$996$		0			0
$997$	5.44919e6			0.173618			0.0868089	−	0.996225i	$-0.472333\pi$
$997$	5.44919e6			0.173618			0.0868089	+	0.996225i	$0.472333\pi$
$998$		0			0
$999$	3.32638e6	+	1.02376e7i	0.105453	+	0.324551i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	124.6.f.a.33.3	✓	56
31.16	even	5	inner	124.6.f.a.109.3	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
124.6.f.a.33.3	✓	56	1.1	even	1	trivial
124.6.f.a.109.3	yes	56	31.16	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 124 = 2^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	124.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-18.4148 + 13.3791i) q^{3} -27.4655 q^{5} +(63.1359 + 194.312i) q^{7} +(85.0116 - 261.639i) q^{9} +O(q^{10})\)	\(q+(-18.4148 + 13.3791i) q^{3} -27.4655 q^{5} +(63.1359 + 194.312i) q^{7} +(85.0116 - 261.639i) q^{9} +(240.799 + 741.102i) q^{11} +(-638.445 + 463.857i) q^{13} +(505.769 - 367.463i) q^{15} +(87.0809 - 268.008i) q^{17} +(396.822 + 288.308i) q^{19} +(-3762.36 - 2733.51i) q^{21} +(398.519 - 1226.52i) q^{23} -2370.65 q^{25} +(225.810 + 694.970i) q^{27} +(1735.99 + 1261.27i) q^{29} +(-2439.73 - 4762.02i) q^{31} +(-14349.5 - 10425.5i) q^{33} +(-1734.06 - 5336.87i) q^{35} +14730.9 q^{37} +(5550.81 - 17083.6i) q^{39} +(-1109.56 - 806.141i) q^{41} +(-6879.20 - 4998.03i) q^{43} +(-2334.88 + 7186.03i) q^{45} +(-18755.0 + 13626.3i) q^{47} +(-20174.0 + 14657.3i) q^{49} +(1982.13 + 6100.36i) q^{51} +(-6500.48 + 20006.4i) q^{53} +(-6613.64 - 20354.7i) q^{55} -11164.7 q^{57} +(4904.68 - 3563.46i) q^{59} -2809.84 q^{61} +56206.9 q^{63} +(17535.2 - 12740.1i) q^{65} +49844.4 q^{67} +(9071.05 + 27917.8i) q^{69} +(-4696.28 + 14453.7i) q^{71} +(-21316.1 - 65604.1i) q^{73} +(43654.9 - 31717.2i) q^{75} +(-128802. + 93580.3i) q^{77} +(13498.3 - 41543.5i) q^{79} +(40626.6 + 29516.9i) q^{81} +(30909.6 + 22457.1i) q^{83} +(-2391.72 + 7360.95i) q^{85} -48842.4 q^{87} +(-5893.73 - 18139.0i) q^{89} +(-130442. - 94771.7i) q^{91} +(108639. + 55050.0i) q^{93} +(-10898.9 - 7918.51i) q^{95} +(45361.2 + 139608. i) q^{97} +214372. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 2 q^{3} - 58 q^{5} + 104 q^{7} - 1234 q^{9}+O(q^{10}) \) 56 * q + 2 * q^3 - 58 * q^5 + 104 * q^7 - 1234 * q^9	\( 56 q + 2 q^{3} - 58 q^{5} + 104 q^{7} - 1234 q^{9} - 509 q^{11} - 117 q^{13} + 89 q^{15} - 3504 q^{17} + 262 q^{19} + 352 q^{21} - 2448 q^{23} + 49618 q^{25} + 14324 q^{27} - 9888 q^{29} - 12771 q^{31} + 27699 q^{33} + 13840 q^{35} + 76096 q^{37} + 33520 q^{39} - 4843 q^{41} - 40778 q^{43} + 56692 q^{45} + 38922 q^{47} - 17126 q^{49} - 69292 q^{51} - 41728 q^{53} - 172096 q^{55} + 57066 q^{57} - 58198 q^{59} + 176328 q^{61} - 37444 q^{63} + 143863 q^{65} + 9812 q^{67} - 9250 q^{69} - 67356 q^{71} - 63512 q^{73} - 198012 q^{75} - 74257 q^{77} + 137651 q^{79} + 196077 q^{81} + 156427 q^{83} + 238828 q^{85} - 558144 q^{87} - 99292 q^{89} - 243609 q^{91} - 325925 q^{93} - 75077 q^{95} - 476340 q^{97} + 745812 q^{99}+O(q^{100}) \) 56 * q + 2 * q^3 - 58 * q^5 + 104 * q^7 - 1234 * q^9 - 509 * q^11 - 117 * q^13 + 89 * q^15 - 3504 * q^17 + 262 * q^19 + 352 * q^21 - 2448 * q^23 + 49618 * q^25 + 14324 * q^27 - 9888 * q^29 - 12771 * q^31 + 27699 * q^33 + 13840 * q^35 + 76096 * q^37 + 33520 * q^39 - 4843 * q^41 - 40778 * q^43 + 56692 * q^45 + 38922 * q^47 - 17126 * q^49 - 69292 * q^51 - 41728 * q^53 - 172096 * q^55 + 57066 * q^57 - 58198 * q^59 + 176328 * q^61 - 37444 * q^63 + 143863 * q^65 + 9812 * q^67 - 9250 * q^69 - 67356 * q^71 - 63512 * q^73 - 198012 * q^75 - 74257 * q^77 + 137651 * q^79 + 196077 * q^81 + 156427 * q^83 + 238828 * q^85 - 558144 * q^87 - 99292 * q^89 - 243609 * q^91 - 325925 * q^93 - 75077 * q^95 - 476340 * q^97 + 745812 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more