LMFDB - Embedded newform 124.6.f.a.33.6

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			33.6
Character	$\chi$	$=$	124.33
Dual form			124.6.f.a.109.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.61067 + 5.52948i) q^{3} -0.875792 q^{5} +(42.6014 + 131.114i) q^{7} +(-47.7439 + 146.941i) q^{9} +O(q^{10})$	\(q+(-7.61067 + 5.52948i) q^{3} -0.875792 q^{5} +(42.6014 + 131.114i) q^{7} +(-47.7439 + 146.941i) q^{9} +(-121.647 - 374.392i) q^{11} +(441.224 - 320.568i) q^{13} +(6.66536 - 4.84267i) q^{15} +(-329.547 + 1014.24i) q^{17} +(-218.175 - 158.513i) q^{19} +(-1049.22 - 762.300i) q^{21} +(-1043.84 + 3212.61i) q^{23} -3124.23 q^{25} +(-1155.55 - 3556.41i) q^{27} +(-5680.16 - 4126.88i) q^{29} +(530.807 - 5324.23i) q^{31} +(2996.01 + 2176.73i) q^{33} +(-37.3100 - 114.828i) q^{35} -14774.2 q^{37} +(-1585.44 + 4879.48i) q^{39} +(4129.91 + 3000.55i) q^{41} +(-15903.2 - 11554.3i) q^{43} +(41.8137 - 128.689i) q^{45} +(-3629.54 + 2637.02i) q^{47} +(-1778.77 + 1292.36i) q^{49} +(-3100.15 - 9541.28i) q^{51} +(-10179.1 + 31327.9i) q^{53} +(106.538 + 327.890i) q^{55} +2536.95 q^{57} +(26385.1 - 19169.9i) q^{59} +18315.5 q^{61} -21299.9 q^{63} +(-386.421 + 280.751i) q^{65} -5063.95 q^{67} +(-9819.74 - 30222.0i) q^{69} +(-4579.20 + 14093.3i) q^{71} +(21782.0 + 67038.1i) q^{73} +(23777.5 - 17275.4i) q^{75} +(43905.6 - 31899.3i) q^{77} +(2559.91 - 7878.59i) q^{79} +(-1914.27 - 1390.80i) q^{81} +(-45618.8 - 33144.0i) q^{83} +(288.615 - 888.264i) q^{85} +66049.3 q^{87} +(7689.18 + 23664.8i) q^{89} +(60827.7 + 44193.9i) q^{91} +(25400.4 + 43456.0i) q^{93} +(191.076 + 138.825i) q^{95} +(-35519.8 - 109319. i) q^{97} +60821.4 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−7.61067	+	5.52948i	−0.488225	+	0.354716i	−0.804501	−	0.593951i	$-0.797567\pi$
$3$	−7.61067	+	5.52948i	−0.488225	+	0.354716i	0.316276	+	0.948667i	$0.397567\pi$
$4$		0			0
$5$	−0.875792			−0.0156666			−0.00783332	−	0.999969i	$-0.502493\pi$
$5$	−0.875792			−0.0156666			−0.00783332	+	0.999969i	$0.502493\pi$
$6$		0			0
$7$	42.6014	+	131.114i	0.328609	+	1.01135i	0.969785	+	0.243960i	$0.0784466\pi$
$7$	42.6014	+	131.114i	0.328609	+	1.01135i	−0.641177	+	0.767393i	$0.721553\pi$
$8$		0			0
$9$	−47.7439	+	146.941i	−0.196477	+	0.604694i
$10$		0			0
$11$	−121.647	−	374.392i	−0.303125	−	0.932921i	−0.980370	−	0.197165i	$-0.936827\pi$
$11$	−121.647	−	374.392i	−0.303125	−	0.932921i	0.677246	−	0.735757i	$-0.263173\pi$
$12$		0			0
$13$	441.224	−	320.568i	0.724104	−	0.526093i	−0.163589	−	0.986529i	$-0.552307\pi$
$13$	441.224	−	320.568i	0.724104	−	0.526093i	0.887693	+	0.460436i	$0.152307\pi$
$14$		0			0
$15$	6.66536	−	4.84267i	0.00764884	−	0.00555721i
$16$		0			0
$17$	−329.547	+	1014.24i	−0.276564	+	0.851175i	0.712238	+	0.701938i	$0.247682\pi$
$17$	−329.547	+	1014.24i	−0.276564	+	0.851175i	−0.988801	+	0.149237i	$0.952318\pi$
$18$		0			0
$19$	−218.175	−	158.513i	−0.138650	−	0.100735i	0.516298	−	0.856409i	$-0.327310\pi$
$19$	−218.175	−	158.513i	−0.138650	−	0.100735i	−0.654948	+	0.755674i	$0.727310\pi$
$20$		0			0
$21$	−1049.22	−	762.300i	−0.519178	−	0.377205i
$22$		0			0
$23$	−1043.84	+	3212.61i	−0.411448	+	1.26631i	0.503942	+	0.863738i	$0.331883\pi$
$23$	−1043.84	+	3212.61i	−0.411448	+	1.26631i	−0.915390	+	0.402569i	$0.868117\pi$
$24$		0			0
$25$	−3124.23			−0.999755
$26$		0			0
$27$	−1155.55	−	3556.41i	−0.305055	−	0.938863i
$28$		0			0
$29$	−5680.16	−	4126.88i	−1.25420	−	0.911227i	−0.255739	−	0.966746i	$-0.582319\pi$
$29$	−5680.16	−	4126.88i	−1.25420	−	0.911227i	−0.998458	+	0.0555183i	$0.982319\pi$
$30$		0			0
$31$	530.807	−	5324.23i	0.0992048	−	0.995067i
$31$	530.807	−	5324.23i	0.0992048	−	0.995067i
$32$		0			0
$33$	2996.01	+	2176.73i	0.478915	+	0.347952i
$34$		0			0
$35$	−37.3100	−	114.828i	−0.00514819	−	0.0158445i
$36$		0			0
$37$	−14774.2			−1.77419			−0.887094	−	0.461590i	$-0.847279\pi$
$37$	−14774.2			−1.77419			−0.887094	+	0.461590i	$0.847279\pi$
$38$		0			0
$39$	−1585.44	+	4879.48i	−0.166912	+	0.513703i
$40$		0			0
$41$	4129.91	+	3000.55i	0.383690	+	0.278767i	0.762865	−	0.646558i	$-0.223792\pi$
$41$	4129.91	+	3000.55i	0.383690	+	0.278767i	−0.379175	+	0.925325i	$0.623792\pi$
$42$		0			0
$43$	−15903.2	−	11554.3i	−1.31163	−	0.952958i	−0.999996	−	0.00275698i	$-0.999122\pi$
$43$	−15903.2	−	11554.3i	−1.31163	−	0.952958i	−0.311638	−	0.950201i	$-0.600878\pi$
$44$		0			0
$45$	41.8137	−	128.689i	0.00307814	−	0.00947353i
$46$		0			0
$47$	−3629.54	+	2637.02i	−0.239666	+	0.174128i	−0.701135	−	0.713029i	$-0.747323\pi$
$47$	−3629.54	+	2637.02i	−0.239666	+	0.174128i	0.461468	+	0.887157i	$0.347323\pi$
$48$		0			0
$49$	−1778.77	+	1292.36i	−0.105835	+	0.0768939i
$50$		0			0
$51$	−3100.15	−	9541.28i	−0.166900	−	0.513666i
$52$		0			0
$53$	−10179.1	+	31327.9i	−0.497758	+	1.53194i	0.314857	+	0.949139i	$0.398044\pi$
$53$	−10179.1	+	31327.9i	−0.497758	+	1.53194i	−0.812614	+	0.582802i	$0.801956\pi$
$54$		0			0
$55$	106.538	+	327.890i	0.00474894	+	0.0146157i
$56$		0			0
$57$	2536.95			0.103425
$58$		0			0
$59$	26385.1	−	19169.9i	0.986799	−	0.716952i	0.0275814	−	0.999620i	$-0.491219\pi$
$59$	26385.1	−	19169.9i	0.986799	−	0.716952i	0.959218	+	0.282668i	$0.0912195\pi$
$60$		0			0
$61$	18315.5			0.630224			0.315112	−	0.949054i	$-0.397958\pi$
$61$	18315.5			0.630224			0.315112	+	0.949054i	$0.397958\pi$
$62$		0			0
$63$	−21299.9			−0.676124
$64$		0			0
$65$	−386.421	+	280.751i	−0.0113443	+	0.00824210i
$66$		0			0
$67$	−5063.95			−0.137817			−0.0689084	−	0.997623i	$-0.521952\pi$
$67$	−5063.95			−0.137817			−0.0689084	+	0.997623i	$0.521952\pi$
$68$		0			0
$69$	−9819.74	−	30222.0i	−0.248300	−	0.764189i
$70$		0			0
$71$	−4579.20	+	14093.3i	−0.107806	+	0.331793i	−0.990379	−	0.138383i	$-0.955810\pi$
$71$	−4579.20	+	14093.3i	−0.107806	+	0.331793i	0.882573	+	0.470176i	$0.155810\pi$
$72$		0			0
$73$	21782.0	+	67038.1i	0.478400	+	1.47236i	0.841318	+	0.540541i	$0.181780\pi$
$73$	21782.0	+	67038.1i	0.478400	+	1.47236i	−0.362918	+	0.931821i	$0.618220\pi$
$74$		0			0
$75$	23777.5	−	17275.4i	0.488105	−	0.354629i
$76$		0			0
$77$	43905.6	−	31899.3i	0.843904	−	0.613132i
$78$		0			0
$79$	2559.91	−	7878.59i	0.0461484	−	0.142030i	−0.925327	−	0.379169i	$-0.876210\pi$
$79$	2559.91	−	7878.59i	0.0461484	−	0.142030i	0.971476	+	0.237139i	$0.0762098\pi$
$80$		0			0
$81$	−1914.27	−	1390.80i	−0.0324184	−	0.0235533i
$82$		0			0
$83$	−45618.8	−	33144.0i	−0.726856	−	0.528092i	0.161711	−	0.986838i	$-0.448299\pi$
$83$	−45618.8	−	33144.0i	−0.726856	−	0.528092i	−0.888567	+	0.458746i	$0.848299\pi$
$84$		0			0
$85$	288.615	−	888.264i	0.00433282	−	0.0133351i
$86$		0			0
$87$	66049.3			0.935557
$88$		0			0
$89$	7689.18	+	23664.8i	0.102897	+	0.316686i	0.989231	−	0.146361i	$-0.0467561\pi$
$89$	7689.18	+	23664.8i	0.102897	+	0.316686i	−0.886334	+	0.463047i	$0.846756\pi$
$90$		0			0
$91$	60827.7	+	44193.9i	0.770013	+	0.559447i
$92$		0			0
$93$	25400.4	+	43456.0i	0.304532	+	0.521006i
$94$		0			0
$95$	191.076	+	138.825i	0.00217218	+	0.00157818i
$96$		0			0
$97$	−35519.8	−	109319.i	−0.383302	−	1.17968i	−0.937704	−	0.347434i	$-0.887053\pi$
$97$	−35519.8	−	109319.i	−0.383302	−	1.17968i	0.554402	−	0.832249i	$-0.312947\pi$
$98$		0			0
$99$	60821.4			0.623689
$100$		0			0
$101$	−62945.3	+	193726.i	−0.613988	+	1.88966i	−0.198350	+	0.980131i	$0.563558\pi$
$101$	−62945.3	+	193726.i	−0.613988	+	1.88966i	−0.415638	+	0.909530i	$0.636442\pi$
$102$		0			0
$103$	83900.1	+	60957.0i	0.779236	+	0.566148i	0.904750	−	0.425943i	$-0.140058\pi$
$103$	83900.1	+	60957.0i	0.779236	+	0.566148i	−0.125513	+	0.992092i	$0.540058\pi$
$104$		0			0
$105$	918.894	+	667.616i	0.00813378	+	0.00590954i
$106$		0			0
$107$	62534.3	−	192461.i	0.528030	−	1.62511i	−0.230215	−	0.973140i	$-0.573943\pi$
$107$	62534.3	−	192461.i	0.528030	−	1.62511i	0.758245	−	0.651970i	$-0.226057\pi$
$108$		0			0
$109$	117739.	−	85542.1i	0.949189	−	0.689626i	−0.00142586	−	0.999999i	$-0.500454\pi$
$109$	117739.	−	85542.1i	0.949189	−	0.689626i	0.950615	+	0.310373i	$0.100454\pi$
$110$		0			0
$111$	112442.	−	81693.5i	0.866202	−	0.629333i
$112$		0			0
$113$	54894.8	+	168949.i	0.404422	+	1.24468i	0.921377	+	0.388671i	$0.127066\pi$
$113$	54894.8	+	168949.i	0.404422	+	1.24468i	−0.516955	+	0.856013i	$0.672934\pi$
$114$		0			0
$115$	914.188	−	2813.58i	0.00644601	−	0.0198388i
$116$		0			0
$117$	26038.7	+	80139.0i	0.175855	+	0.541227i
$118$		0			0
$119$	−147020.			−0.951720
$120$		0			0
$121$	4921.56	−	3575.72i	0.0305590	−	0.0222024i
$122$		0			0
$123$	−48022.9			−0.286210
$124$		0			0
$125$	5473.03			0.0313294
$126$		0			0
$127$	−206891.	+	150315.i	−1.13824	+	0.826978i	−0.986873	−	0.161500i	$-0.948367\pi$
$127$	−206891.	+	150315.i	−1.13824	+	0.826978i	−0.151364	+	0.988478i	$0.548367\pi$
$128$		0			0
$129$	184923.			0.978402
$130$		0			0
$131$	−37998.3	−	116947.i	−0.193458	−	0.595402i	−0.999991	−	0.00421305i	$-0.998659\pi$
$131$	−37998.3	−	116947.i	−0.193458	−	0.595402i	0.806533	−	0.591188i	$-0.201341\pi$
$132$		0			0
$133$	11488.7	−	35358.6i	0.0563173	−	0.173327i
$134$		0			0
$135$	1012.02	+	3114.67i	0.00477919	+	0.0147088i
$136$		0			0
$137$	−153844.	+	111774.i	−0.700293	+	0.508793i	−0.880028	−	0.474923i	$-0.842476\pi$
$137$	−153844.	+	111774.i	−0.700293	+	0.508793i	0.179735	+	0.983715i	$0.442476\pi$
$138$		0			0
$139$	−240520.	+	174748.i	−1.05588	+	0.767140i	−0.973321	−	0.229446i	$-0.926308\pi$
$139$	−240520.	+	174748.i	−1.05588	+	0.767140i	−0.0825564	+	0.996586i	$0.526308\pi$
$140$		0			0
$141$	13041.9	−	40138.9i	0.0552451	−	0.170027i
$142$		0			0
$143$	−173692.	−	126195.i	−0.710297	−	0.516061i
$144$		0			0
$145$	4974.64	+	3614.29i	0.0196491	+	0.0142759i
$146$		0			0
$147$	6391.62	−	19671.4i	0.0243959	−	0.0750830i
$148$		0			0
$149$	187878.			0.693282			0.346641	−	0.937998i	$-0.387322\pi$
$149$	187878.			0.693282			0.346641	+	0.937998i	$0.387322\pi$
$150$		0			0
$151$	−149906.	−	461364.i	−0.535030	−	1.64665i	−0.743585	−	0.668641i	$-0.766876\pi$
$151$	−149906.	−	461364.i	−0.535030	−	1.64665i	0.208556	−	0.978010i	$-0.433124\pi$
$152$		0			0
$153$	−133299.	−	96847.7i	−0.460362	−	0.334473i
$154$		0			0
$155$	−464.877	+	4662.91i	−0.00155421	+	0.0155894i
$156$		0			0
$157$	64818.7	+	47093.5i	0.209870	+	0.152480i	0.687755	−	0.725943i	$-0.258596\pi$
$157$	64818.7	+	47093.5i	0.209870	+	0.152480i	−0.477885	+	0.878423i	$0.658596\pi$
$158$		0			0
$159$	−95757.6	−	294711.i	−0.300386	−	0.924494i
$160$		0			0
$161$	−465687.			−1.41589
$162$		0			0
$163$	19462.9	−	59900.6i	0.0573770	−	0.176588i	−0.918261	−	0.395977i	$-0.870406\pi$
$163$	19462.9	−	59900.6i	0.0573770	−	0.176588i	0.975638	+	0.219388i	$0.0704061\pi$
$164$		0			0
$165$	−2623.88	−	1906.36i	−0.00750299	−	0.00545124i
$166$		0			0
$167$	−78517.0	−	57045.9i	−0.217857	−	0.158283i	0.473504	−	0.880792i	$-0.342989\pi$
$167$	−78517.0	−	57045.9i	−0.217857	−	0.158283i	−0.691362	+	0.722509i	$0.742989\pi$
$168$		0			0
$169$	−22820.9	+	70235.5i	−0.0614633	+	0.189165i
$170$		0			0
$171$	33708.6	−	24490.7i	0.0881557	−	0.0640488i
$172$		0			0
$173$	−410702.	+	298393.i	−1.04331	+	0.758006i	−0.970928	−	0.239371i	$-0.923059\pi$
$173$	−410702.	+	298393.i	−1.04331	+	0.758006i	−0.0723777	+	0.997377i	$0.523059\pi$
$174$		0			0
$175$	−133097.	−	409630.i	−0.328528	−	1.01111i
$176$		0			0
$177$	−94808.8	+	291792.i	−0.227466	+	0.700067i
$178$		0			0
$179$	167155.	+	514449.i	0.389929	+	1.20008i	0.932841	+	0.360289i	$0.117322\pi$
$179$	167155.	+	514449.i	0.389929	+	1.20008i	−0.542912	+	0.839790i	$0.682678\pi$
$180$		0			0
$181$	−665867.			−1.51075			−0.755373	−	0.655296i	$-0.772544\pi$
$181$	−665867.			−1.51075			−0.755373	+	0.655296i	$0.772544\pi$
$182$		0			0
$183$	−139394.	+	101275.i	−0.307691	+	0.223551i
$184$		0			0
$185$	12939.1			0.0277956
$186$		0			0
$187$	419813.			0.877913
$188$		0			0
$189$	417066.	−	303016.i	0.849279	−	0.617037i
$190$		0			0
$191$	−11281.3			−0.0223757			−0.0111879	−	0.999937i	$-0.503561\pi$
$191$	−11281.3			−0.0223757			−0.0111879	+	0.999937i	$0.503561\pi$
$192$		0			0
$193$	139949.	+	430719.i	0.270444	+	0.832340i	0.990389	+	0.138309i	$0.0441668\pi$
$193$	139949.	+	430719.i	0.270444	+	0.832340i	−0.719945	+	0.694031i	$0.755833\pi$
$194$		0			0
$195$	1388.51	−	4273.41i	0.00261495	−	0.00804800i
$196$		0			0
$197$	240295.	+	739552.i	0.441143	+	1.35770i	0.886659	+	0.462424i	$0.153020\pi$
$197$	240295.	+	739552.i	0.441143	+	1.35770i	−0.445516	+	0.895274i	$0.646980\pi$
$198$		0			0
$199$	165921.	−	120549.i	0.297008	−	0.215789i	−0.429294	−	0.903165i	$-0.641237\pi$
$199$	165921.	−	120549.i	0.297008	−	0.215789i	0.726302	+	0.687376i	$0.241237\pi$
$200$		0			0
$201$	38540.0	−	28001.0i	0.0672856	−	0.0488858i
$202$		0			0
$203$	299107.	−	920558.i	0.509433	−	1.56787i
$204$		0			0
$205$	−3616.94	−	2627.86i	−0.00601114	−	0.00436735i
$206$		0			0
$207$	−422226.	−	306765.i	−0.684888	−	0.497600i
$208$		0			0
$209$	−32805.8	+	100966.i	−0.0519498	+	0.159885i
$210$		0			0
$211$	−62119.8			−0.0960559			−0.0480280	−	0.998846i	$-0.515294\pi$
$211$	−62119.8			−0.0960559			−0.0480280	+	0.998846i	$0.515294\pi$
$212$		0			0
$213$	−43077.9	−	132580.i	−0.0650587	−	0.200230i
$214$		0			0
$215$	13927.9	+	10119.2i	0.0205489	+	0.0149296i
$216$		0			0
$217$	720692.	−	157224.i	1.03896	−	0.226657i
$218$		0			0
$219$	−536461.	−	389762.i	−0.755837	−	0.549148i
$220$		0			0
$221$	179729.	+	553150.i	0.247536	+	0.761838i
$222$		0			0
$223$	1.13978e6			1.53483			0.767414	−	0.641151i	$-0.221543\pi$
$223$	1.13978e6			1.53483			0.767414	+	0.641151i	$0.221543\pi$
$224$		0			0
$225$	149163.	−	459077.i	0.196429	−	0.604546i
$226$		0			0
$227$	821659.	+	596970.i	1.05834	+	0.768932i	0.973781	−	0.227486i	$-0.0730507\pi$
$227$	821659.	+	596970.i	1.05834	+	0.768932i	0.0845625	+	0.996418i	$0.473051\pi$
$228$		0			0
$229$	−322306.	−	234169.i	−0.406144	−	0.295081i	0.365895	−	0.930656i	$-0.380763\pi$
$229$	−322306.	−	234169.i	−0.406144	−	0.295081i	−0.772039	+	0.635575i	$0.780763\pi$
$230$		0			0
$231$	−157765.	+	485550.i	−0.194527	+	0.598693i
$232$		0			0
$233$	−624731.	+	453893.i	−0.753881	+	0.547727i	−0.897027	−	0.441975i	$-0.854278\pi$
$233$	−624731.	+	453893.i	−0.753881	+	0.547727i	0.143146	+	0.989702i	$0.454278\pi$
$234$		0			0
$235$	3178.72	−	2309.48i	0.00375477	−	0.00272800i
$236$		0			0
$237$	24081.8	+	74116.3i	0.0278496	+	0.0857122i
$238$		0			0
$239$	−98999.4	+	304689.i	−0.112108	+	0.345034i	−0.991333	−	0.131374i	$-0.958061\pi$
$239$	−98999.4	+	304689.i	−0.112108	+	0.345034i	0.879225	+	0.476407i	$0.158061\pi$
$240$		0			0
$241$	81987.9	+	252333.i	0.0909300	+	0.279854i	0.986172	−	0.165727i	$-0.0529971\pi$
$241$	81987.9	+	252333.i	0.0909300	+	0.279854i	−0.895242	+	0.445581i	$0.852997\pi$
$242$		0			0
$243$	930940.			1.01136
$244$		0			0
$245$	1557.84	−	1131.83i	0.00165808	−	0.00120467i
$246$		0			0
$247$	−147078.			−0.153393
$248$		0			0
$249$	530458.			0.542192
$250$		0			0
$251$	−542775.	+	394349.i	−0.543796	+	0.395091i	−0.825493	−	0.564413i	$-0.809103\pi$
$251$	−542775.	+	394349.i	−0.543796	+	0.395091i	0.281697	+	0.959503i	$0.409103\pi$
$252$		0			0
$253$	1.32976e6			1.30608
$254$		0			0
$255$	2715.09	+	8356.17i	0.00261477	+	0.00804743i
$256$		0			0
$257$	−27413.3	+	84369.4i	−0.0258898	+	0.0796805i	−0.963167	−	0.268905i	$-0.913338\pi$
$257$	−27413.3	+	84369.4i	−0.0258898	+	0.0796805i	0.937277	+	0.348586i	$0.113338\pi$
$258$		0			0
$259$	−629402.	−	1.93710e6i	−0.583013	−	1.79433i
$260$		0			0
$261$	877600.	−	637613.i	0.797435	−	0.579370i
$262$		0			0
$263$	−225458.	+	163805.i	−0.200991	+	0.146029i	−0.683728	−	0.729737i	$-0.739643\pi$
$263$	−225458.	+	163805.i	−0.200991	+	0.146029i	0.482737	+	0.875765i	$0.339643\pi$
$264$		0			0
$265$	8914.74	−	27436.7i	0.00779819	−	0.0240004i
$266$		0			0
$267$	−189374.	−	137588.i	−0.162571	−	0.118115i
$268$		0			0
$269$	738983.	+	536903.i	0.622664	+	0.452392i	0.853851	−	0.520517i	$-0.174261\pi$
$269$	738983.	+	536903.i	0.622664	+	0.452392i	−0.231187	+	0.972909i	$0.574261\pi$
$270$		0			0
$271$	380868.	−	1.17219e6i	0.315030	−	0.969562i	−0.660712	−	0.750639i	$-0.729746\pi$
$271$	380868.	−	1.17219e6i	0.315030	−	0.969562i	0.975742	−	0.218923i	$-0.0702543\pi$
$272$		0			0
$273$	−707309.			−0.574384
$274$		0			0
$275$	380055.	+	1.16969e6i	0.303050	+	0.932692i
$276$		0			0
$277$	136364.	+	99074.3i	0.106783	+	0.0775821i	0.639895	−	0.768462i	$-0.278978\pi$
$277$	136364.	+	99074.3i	0.106783	+	0.0775821i	−0.533113	+	0.846044i	$0.678978\pi$
$278$		0			0
$279$	757003.	+	332197.i	0.582220	+	0.255496i
$280$		0			0
$281$	−533439.	−	387566.i	−0.403013	−	0.292806i	0.367754	−	0.929923i	$-0.380127\pi$
$281$	−533439.	−	387566.i	−0.403013	−	0.292806i	−0.770767	+	0.637117i	$0.780127\pi$
$282$		0			0
$283$	363859.	+	1.11984e6i	0.270064	+	0.831173i	0.990483	+	0.137634i	$0.0439496\pi$
$283$	363859.	+	1.11984e6i	0.270064	+	0.831173i	−0.720419	+	0.693539i	$0.756050\pi$
$284$		0			0
$285$	−2221.84			−0.00162032
$286$		0			0
$287$	−217474.	+	669316.i	−0.155848	+	0.479652i
$288$		0			0
$289$	228604.	+	166091.i	0.161005	+	0.116977i
$290$		0			0
$291$	874805.	+	635583.i	0.605590	+	0.439987i
$292$		0			0
$293$	287698.	−	885444.i	0.195780	−	0.602549i	−0.804187	−	0.594377i	$-0.797399\pi$
$293$	287698.	−	885444.i	0.195780	−	0.602549i	0.999967	−	0.00817183i	$-0.00260120\pi$
$294$		0			0
$295$	−23107.9	+	16788.8i	−0.0154598	+	0.0112322i
$296$		0			0
$297$	−1.19092e6	+	865256.i	−0.783416	+	0.569185i
$298$		0			0
$299$	569294.	+	1.75211e6i	0.368263	+	1.13340i
$300$		0			0
$301$	837433.	−	2.57736e6i	0.532763	−	1.63968i
$302$		0			0
$303$	−592146.	−	1.82244e6i	−0.370529	−	1.14037i
$304$		0			0
$305$	−16040.6			−0.00987350
$306$		0			0
$307$	−201294.	+	146249.i	−0.121895	+	0.0885618i	−0.647062	−	0.762437i	$-0.724003\pi$
$307$	−201294.	+	146249.i	−0.121895	+	0.0885618i	0.525167	+	0.850999i	$0.324003\pi$
$308$		0			0
$309$	−975596.			−0.581265
$310$		0			0
$311$	−2.08337e6			−1.22142			−0.610711	−	0.791854i	$-0.709116\pi$
$311$	−2.08337e6			−1.22142			−0.610711	+	0.791854i	$0.709116\pi$
$312$		0			0
$313$	−43925.0	+	31913.4i	−0.0253426	+	0.0184125i	−0.600384	−	0.799712i	$-0.704986\pi$
$313$	−43925.0	+	31913.4i	−0.0253426	+	0.0184125i	0.575042	+	0.818124i	$0.304986\pi$
$314$		0			0
$315$	18654.3			0.0105926
$316$		0			0
$317$	−265301.	−	816513.i	−0.148283	−	0.456368i	0.849136	−	0.528175i	$-0.177123\pi$
$317$	−265301.	−	816513.i	−0.148283	−	0.456368i	−0.997419	+	0.0718069i	$0.977123\pi$
$318$		0			0
$319$	−854095.	+	2.62863e6i	−0.469926	+	1.44628i
$320$		0			0
$321$	588279.	+	1.81054e6i	0.318655	+	0.980720i
$322$		0			0
$323$	232670.	−	169044.i	0.124089	−	0.0901560i
$324$		0			0
$325$	−1.37849e6	+	1.00153e6i	−0.723927	+	0.525963i
$326$		0			0
$327$	−423067.	+	1.30207e6i	−0.218796	+	0.673385i
$328$		0			0
$329$	−500373.	−	363542.i	−0.254861	−	0.185168i
$330$		0			0
$331$	−532578.	−	386940.i	−0.267186	−	0.194122i	0.446123	−	0.894972i	$-0.352804\pi$
$331$	−532578.	−	386940.i	−0.267186	−	0.194122i	−0.713309	+	0.700850i	$0.752804\pi$
$332$		0			0
$333$	705378.	−	2.17093e6i	0.348587	−	1.07284i
$334$		0			0
$335$	4434.97			0.00215913
$336$		0			0
$337$	−886118.	−	2.72719e6i	−0.425027	−	1.30810i	−0.902968	−	0.429707i	$-0.858617\pi$
$337$	−886118.	−	2.72719e6i	−0.425027	−	1.30810i	0.477941	−	0.878392i	$-0.341383\pi$
$338$		0			0
$339$	−1.35198e6	−	982274.i	−0.638958	−	0.464230i
$340$		0			0
$341$	−2.05792e6	+	448948.i	−0.958391	+	0.209079i
$342$		0			0
$343$	1.62929e6	+	1.18375e6i	0.747763	+	0.543282i
$344$		0			0
$345$	8600.04	+	26468.2i	0.00389003	+	0.0119723i
$346$		0			0
$347$	−332774.			−0.148363			−0.0741815	−	0.997245i	$-0.523634\pi$
$347$	−332774.			−0.148363			−0.0741815	+	0.997245i	$0.523634\pi$
$348$		0			0
$349$	573942.	−	1.76641e6i	0.252235	−	0.776298i	−0.742127	−	0.670259i	$-0.766183\pi$
$349$	573942.	−	1.76641e6i	0.252235	−	0.776298i	0.994362	−	0.106039i	$-0.0338169\pi$
$350$		0			0
$351$	−1.64993e6	−	1.19874e6i	−0.714820	−	0.519347i
$352$		0			0
$353$	−2.19929e6	−	1.59788e6i	−0.939391	−	0.682508i	0.00888274	−	0.999961i	$-0.497172\pi$
$353$	−2.19929e6	−	1.59788e6i	−0.939391	−	0.682508i	−0.948274	+	0.317453i	$0.897172\pi$
$354$		0			0
$355$	4010.42	−	12342.8i	0.00168896	−	0.00519808i
$356$		0			0
$357$	1.11892e6	−	812944.i	0.464653	−	0.337590i
$358$		0			0
$359$	−1.35630e6	+	985408.i	−0.555417	+	0.403534i	−0.829779	−	0.558093i	$-0.811533\pi$
$359$	−1.35630e6	+	985408.i	−0.555417	+	0.403534i	0.274362	+	0.961627i	$0.411533\pi$
$360$		0			0
$361$	−742683.	−	2.28574e6i	−0.299941	−	0.923123i
$362$		0			0
$363$	−17684.5	+	54427.3i	−0.00704412	+	0.0216796i
$364$		0			0
$365$	−19076.5	−	58711.4i	−0.00749491	−	0.0230670i
$366$		0			0
$367$	4.23316e6			1.64059			0.820295	−	0.571941i	$-0.193809\pi$
$367$	4.23316e6			1.64059			0.820295	+	0.571941i	$0.193809\pi$
$368$		0			0
$369$	−638082.	+	463593.i	−0.243955	+	0.177244i
$370$		0			0
$371$	−4.54116e6			−1.71290
$372$		0			0
$373$	−874682.			−0.325520			−0.162760	−	0.986666i	$-0.552040\pi$
$373$	−874682.			−0.325520			−0.162760	+	0.986666i	$0.552040\pi$
$374$		0			0
$375$	−41653.4	+	30263.0i	−0.0152958	+	0.0111131i
$376$		0			0
$377$	−3.82917e6			−1.38756
$378$		0			0
$379$	1.17938e6	+	3.62976e6i	0.421751	+	1.29802i	0.906071	+	0.423126i	$0.139067\pi$
$379$	1.17938e6	+	3.62976e6i	0.421751	+	1.29802i	−0.484320	+	0.874891i	$0.660933\pi$
$380$		0			0
$381$	743416.	−	2.28800e6i	0.262373	−	0.807502i
$382$		0			0
$383$	958718.	+	2.95063e6i	0.333960	+	1.02782i	0.967232	+	0.253893i	$0.0817112\pi$
$383$	958718.	+	2.95063e6i	0.333960	+	1.02782i	−0.633273	+	0.773929i	$0.718289\pi$
$384$		0			0
$385$	−38452.2	+	27937.1i	−0.0132211	+	0.00960572i
$386$		0			0
$387$	2.45708e6	−	1.78517e6i	0.833954	−	0.605903i
$388$		0			0
$389$	−788775.	+	2.42760e6i	−0.264289	+	0.813398i	0.727567	+	0.686036i	$0.240651\pi$
$389$	−788775.	+	2.42760e6i	−0.264289	+	0.813398i	−0.991856	+	0.127362i	$0.959349\pi$
$390$		0			0
$391$	−2.91437e6	−	2.11741e6i	−0.964057	−	0.700429i
$392$		0			0
$393$	935847.	+	679933.i	0.305649	+	0.222067i
$394$		0			0
$395$	−2241.95	+	6900.00i	−0.000722990	+	0.00222514i
$396$		0			0
$397$	−201945.			−0.0643067			−0.0321534	−	0.999483i	$-0.510236\pi$
$397$	−201945.			−0.0643067			−0.0321534	+	0.999483i	$0.510236\pi$
$398$		0			0
$399$	108078.	+	332629.i	0.0339863	+	0.104599i
$400$		0			0
$401$	4.36282e6	+	3.16977e6i	1.35490	+	0.984390i	0.998751	+	0.0499593i	$0.0159092\pi$
$401$	4.36282e6	+	3.16977e6i	1.35490	+	0.984390i	0.356145	+	0.934431i	$0.384091\pi$
$402$		0			0
$403$	−1.47257e6	−	2.51934e6i	−0.451663	−	0.772723i
$404$		0			0
$405$	1676.50	+	1218.05i	0.000507887	+	0.000369001i
$406$		0			0
$407$	1.79724e6	+	5.53134e6i	0.537800	+	1.65518i
$408$		0			0
$409$	−4.44612e6			−1.31423			−0.657117	−	0.753788i	$-0.728224\pi$
$409$	−4.44612e6			−1.31423			−0.657117	+	0.753788i	$0.728224\pi$
$410$		0			0
$411$	552804.	−	1.70136e6i	0.161423	−	0.496810i
$412$		0			0
$413$	3.63748e6	+	2.64278e6i	1.04936	+	0.762406i
$414$		0			0
$415$	39952.6	+	29027.2i	0.0113874	+	0.00827343i
$416$		0			0
$417$	864253.	−	2.65990e6i	0.243389	−	0.749074i
$418$		0			0
$419$	−2.70330e6	+	1.96406e6i	−0.752244	+	0.546537i	−0.896522	−	0.443000i	$-0.853914\pi$
$419$	−2.70330e6	+	1.96406e6i	−0.752244	+	0.546537i	0.144278	+	0.989537i	$0.453914\pi$
$420$		0			0
$421$	5.11481e6	−	3.71613e6i	1.40645	−	1.02185i	0.412623	−	0.910902i	$-0.364613\pi$
$421$	5.11481e6	−	3.71613e6i	1.40645	−	1.02185i	0.993827	−	0.110944i	$-0.0353873\pi$
$422$		0			0
$423$	−214196.	−	659229.i	−0.0582051	−	0.179137i
$424$		0			0
$425$	1.02958e6	−	3.16873e6i	0.276496	−	0.850966i
$426$		0			0
$427$	780268.	+	2.40142e6i	0.207097	+	0.637380i
$428$		0			0
$429$	2.01970e6			0.529840
$430$		0			0
$431$	2.42663e6	−	1.76305e6i	0.629232	−	0.457163i	−0.226902	−	0.973918i	$-0.572860\pi$
$431$	2.42663e6	−	1.76305e6i	0.629232	−	0.457163i	0.856134	+	0.516754i	$0.172860\pi$
$432$		0			0
$433$	−382962.			−0.0981603			−0.0490802	−	0.998795i	$-0.515629\pi$
$433$	−382962.			−0.0981603			−0.0490802	+	0.998795i	$0.515629\pi$
$434$		0			0
$435$	−57845.5			−0.0146570
$436$		0			0
$437$	736982.	−	535449.i	0.184609	−	0.134126i
$438$		0			0
$439$	4.96131e6			1.22867			0.614335	−	0.789045i	$-0.289424\pi$
$439$	4.96131e6			1.22867			0.614335	+	0.789045i	$0.289424\pi$
$440$		0			0
$441$	−104974.	−	323076.i	−0.0257031	−	0.0791059i
$442$		0			0
$443$	−1.03704e6	+	3.19167e6i	−0.251064	+	0.772696i	0.743515	+	0.668719i	$0.233157\pi$
$443$	−1.03704e6	+	3.19167e6i	−0.251064	+	0.772696i	−0.994580	+	0.103978i	$0.966843\pi$
$444$		0			0
$445$	−6734.12	−	20725.5i	−0.00161206	−	0.00496140i
$446$		0			0
$447$	−1.42988e6	+	1.03887e6i	−0.338478	+	0.245918i
$448$		0			0
$449$	3.19741e6	−	2.32306e6i	0.748485	−	0.543806i	−0.146872	−	0.989155i	$-0.546921\pi$
$449$	3.19741e6	−	2.32306e6i	0.748485	−	0.543806i	0.895357	+	0.445349i	$0.146921\pi$
$450$		0			0
$451$	620992.	−	1.91122e6i	0.143762	−	0.442454i
$452$		0			0
$453$	3.69199e6	+	2.68239e6i	0.845308	+	0.614153i
$454$		0			0
$455$	−53272.4	−	38704.7i	−0.0120635	−	0.00876465i
$456$		0			0
$457$	−1.05600e6	+	3.25005e6i	−0.236524	+	0.727946i	0.760392	+	0.649465i	$0.225007\pi$
$457$	−1.05600e6	+	3.25005e6i	−0.236524	+	0.727946i	−0.996916	+	0.0784811i	$0.974993\pi$
$458$		0			0
$459$	3.98786e6			0.883504
$460$		0			0
$461$	142147.	+	437484.i	0.0311520	+	0.0958759i	0.965424	−	0.260686i	$-0.0839488\pi$
$461$	142147.	+	437484.i	0.0311520	+	0.0958759i	−0.934272	+	0.356562i	$0.883949\pi$
$462$		0			0
$463$	3.06579e6	+	2.22743e6i	0.664645	+	0.482893i	0.868228	−	0.496165i	$-0.165259\pi$
$463$	3.06579e6	+	2.22743e6i	0.664645	+	0.482893i	−0.203583	+	0.979058i	$0.565259\pi$
$464$		0			0
$465$	−22245.5	−	38058.4i	−0.00477099	−	0.00816241i
$466$		0			0
$467$	436107.	+	316850.i	0.0925339	+	0.0672298i	0.633090	−	0.774078i	$-0.281786\pi$
$467$	436107.	+	316850.i	0.0925339	+	0.0672298i	−0.540556	+	0.841308i	$0.681786\pi$
$468$		0			0
$469$	−215731.	−	663953.i	−0.0452878	−	0.139382i
$470$		0			0
$471$	−753716.			−0.156551
$472$		0			0
$473$	−2.39127e6	+	7.35958e6i	−0.491446	+	1.51252i
$474$		0			0
$475$	681629.	+	495233.i	0.138616	+	0.100711i
$476$		0			0
$477$	−4.11736e6	−	2.99144e6i	−0.828558	−	0.601982i
$478$		0			0
$479$	218011.	−	670970.i	0.0434151	−	0.133618i	−0.927000	−	0.375063i	$-0.877621\pi$
$479$	218011.	−	670970.i	0.0434151	−	0.133618i	0.970415	+	0.241445i	$0.0776212\pi$
$480$		0			0
$481$	−6.51873e6	+	4.73614e6i	−1.28470	+	0.933387i
$482$		0			0
$483$	3.54419e6	−	2.57500e6i	0.691272	−	0.502239i
$484$		0			0
$485$	31108.0	+	95740.5i	0.00600506	+	0.0184817i
$486$		0			0
$487$	2.65694e6	−	8.17723e6i	0.507644	−	1.56237i	−0.288635	−	0.957439i	$-0.593201\pi$
$487$	2.65694e6	−	8.17723e6i	0.507644	−	1.56237i	0.796279	−	0.604929i	$-0.206799\pi$
$488$		0			0
$489$	183093.	+	563503.i	0.0346258	+	0.106567i
$490$		0			0
$491$	−4.61485e6			−0.863880			−0.431940	−	0.901902i	$-0.642171\pi$
$491$	−4.61485e6			−0.863880			−0.431940	+	0.901902i	$0.642171\pi$
$492$		0			0
$493$	6.05753e6	−	4.40105e6i	1.12248	−	0.815529i
$494$		0			0
$495$	−53266.9			−0.00977111
$496$		0			0
$497$	−2.04291e6			−0.370986
$498$		0			0
$499$	3.64045e6	−	2.64494e6i	0.654491	−	0.475515i	−0.210307	−	0.977635i	$-0.567446\pi$
$499$	3.64045e6	−	2.64494e6i	0.654491	−	0.475515i	0.864798	+	0.502120i	$0.167446\pi$
$500$		0			0
$501$	913001.			0.162509
$502$		0			0
$503$	1.46469e6	+	4.50786e6i	0.258123	+	0.794420i	0.993198	+	0.116435i	$0.0371466\pi$
$503$	1.46469e6	+	4.50786e6i	0.258123	+	0.794420i	−0.735076	+	0.677985i	$0.762853\pi$
$504$		0			0
$505$	55127.0	−	169663.i	0.00961913	−	0.0296046i
$506$		0			0
$507$	−214683.	−	660727.i	−0.0370918	−	0.114157i
$508$		0			0
$509$	6.39084e6	−	4.64322e6i	1.09336	−	0.794374i	0.113398	−	0.993550i	$-0.463827\pi$
$509$	6.39084e6	−	4.64322e6i	1.09336	−	0.794374i	0.979964	+	0.199176i	$0.0638265\pi$
$510$		0			0
$511$	−7.86167e6	+	5.71184e6i	−1.33187	+	0.967662i
$512$		0			0
$513$	−311627.	+	959089.i	−0.0522807	+	0.160903i
$514$		0			0
$515$	−73479.0	−	53385.6i	−0.0122080	−	0.00886964i
$516$		0			0
$517$	1.42880e6	+	1.03809e6i	0.235096	+	0.170808i
$518$		0			0
$519$	1.47576e6	−	4.54193e6i	0.240491	−	0.740155i
$520$		0			0
$521$	−7.70621e6			−1.24379			−0.621895	−	0.783101i	$-0.713637\pi$
$521$	−7.70621e6			−1.24379			−0.621895	+	0.783101i	$0.713637\pi$
$522$		0			0
$523$	−2.76167e6	−	8.49955e6i	−0.441487	−	1.35876i	−0.886291	−	0.463129i	$-0.846727\pi$
$523$	−2.76167e6	−	8.49955e6i	−0.441487	−	1.35876i	0.444804	−	0.895628i	$-0.353273\pi$
$524$		0			0
$525$	3.27799e6	+	2.38160e6i	0.519051	+	0.377113i
$526$		0			0
$527$	5.22512e6	+	2.29295e6i	0.819540	+	0.359640i
$528$		0			0
$529$	−4.02417e6	−	2.92373e6i	−0.625226	−	0.454253i
$530$		0			0
$531$	1.55711e6	+	4.79229e6i	0.239653	+	0.737576i
$532$		0			0
$533$	2.78410e6			0.424489
$534$		0			0
$535$	−54767.0	+	168556.i	−0.00827246	+	0.0254600i
$536$		0			0
$537$	−4.11679e6	−	2.99102e6i	−0.616060	−	0.447594i
$538$		0			0
$539$	700231.	+	508748.i	0.103817	+	0.0754276i
$540$		0			0
$541$	−862445.	+	2.65433e6i	−0.126689	+	0.389908i	−0.994205	−	0.107501i	$-0.965715\pi$
$541$	−862445.	+	2.65433e6i	−0.126689	+	0.389908i	0.867516	+	0.497409i	$0.165715\pi$
$542$		0			0
$543$	5.06770e6	−	3.68190e6i	0.737583	−	0.535886i
$544$		0			0
$545$	−103115.	+	74917.1i	−0.0148706	+	0.0108041i
$546$		0			0
$547$	2.11765e6	+	6.51746e6i	0.302612	+	0.931343i	0.980558	+	0.196231i	$0.0628704\pi$
$547$	2.11765e6	+	6.51746e6i	0.302612	+	0.931343i	−0.677946	+	0.735112i	$0.737130\pi$
$548$		0			0
$549$	−874456.	+	2.69130e6i	−0.123825	+	0.381093i
$550$		0			0
$551$	585103.	+	1.80076e6i	0.0821020	+	0.252684i
$552$		0			0
$553$	1.14205e6			0.158807
$554$		0			0
$555$	−98475.4	+	71546.5i	−0.0135705	+	0.00985953i
$556$		0			0
$557$	−1.01216e7			−1.38233			−0.691165	−	0.722697i	$-0.742902\pi$
$557$	−1.01216e7			−1.38233			−0.691165	+	0.722697i	$0.742902\pi$
$558$		0			0
$559$	−1.07208e7			−1.45110
$560$		0			0
$561$	−3.19506e6	+	2.32134e6i	−0.428619	+	0.311410i
$562$		0			0
$563$	−5.76297e6			−0.766259			−0.383130	−	0.923695i	$-0.625154\pi$
$563$	−5.76297e6			−0.766259			−0.383130	+	0.923695i	$0.625154\pi$
$564$		0			0
$565$	−48076.4	−	147964.i	−0.00633594	−	0.0195000i
$566$		0			0
$567$	100802.	−	310237.i	0.0131678	−	0.0405262i
$568$		0			0
$569$	2.08013e6	+	6.40199e6i	0.269346	+	0.828961i	0.990660	+	0.136353i	$0.0435382\pi$
$569$	2.08013e6	+	6.40199e6i	0.269346	+	0.828961i	−0.721315	+	0.692608i	$0.756462\pi$
$570$		0			0
$571$	−7.27941e6	+	5.28880e6i	−0.934341	+	0.678839i	−0.947052	−	0.321080i	$-0.895954\pi$
$571$	−7.27941e6	+	5.28880e6i	−0.934341	+	0.678839i	0.0127105	+	0.999919i	$0.495954\pi$
$572$		0			0
$573$	85858.6	−	62379.9i	0.0109244	−	0.00793704i
$574$		0			0
$575$	3.26120e6	−	1.00370e7i	0.411347	−	1.26600i
$576$		0			0
$577$	3.22360e6	+	2.34209e6i	0.403090	+	0.292862i	0.770798	−	0.637079i	$-0.219858\pi$
$577$	3.22360e6	+	2.34209e6i	0.403090	+	0.292862i	−0.367708	+	0.929941i	$0.619858\pi$
$578$		0			0
$579$	−3.44676e6	−	2.50422e6i	−0.427282	−	0.310438i
$580$		0			0
$581$	2.40221e6	−	7.39323e6i	0.295236	−	0.908644i
$582$		0			0
$583$	1.29672e7			1.58006
$584$		0			0
$585$	−22804.5	−	70185.1i	−0.00275506	−	0.00847921i
$586$		0			0
$587$	−1.02107e7	−	7.41852e6i	−1.22310	−	0.888633i	−0.226744	−	0.973954i	$-0.572808\pi$
$587$	−1.02107e7	−	7.41852e6i	−1.22310	−	0.888633i	−0.996353	+	0.0853217i	$0.972808\pi$
$588$		0			0
$589$	−959770.	+	1.07747e6i	−0.113993	+	0.127973i
$590$		0			0
$591$	−5.91814e6	−	4.29978e6i	−0.696974	−	0.506381i
$592$		0			0
$593$	1.16875e6	+	3.59703e6i	0.136484	+	0.420056i	0.995818	−	0.0913596i	$-0.0291213\pi$
$593$	1.16875e6	+	3.59703e6i	0.136484	+	0.420056i	−0.859334	+	0.511416i	$0.829121\pi$
$594$		0			0
$595$	128759.			0.0149103
$596$		0			0
$597$	−596199.	+	1.83491e6i	−0.0684629	+	0.210707i
$598$		0			0
$599$	−8.68847e6	−	6.31254e6i	−0.989409	−	0.718848i	−0.0296178	−	0.999561i	$-0.509429\pi$
$599$	−8.68847e6	−	6.31254e6i	−0.989409	−	0.718848i	−0.959792	+	0.280713i	$0.909429\pi$
$600$		0			0
$601$	−4.35407e6	−	3.16342e6i	−0.491710	−	0.357249i	0.314131	−	0.949380i	$-0.398287\pi$
$601$	−4.35407e6	−	3.16342e6i	−0.491710	−	0.357249i	−0.805842	+	0.592131i	$0.798287\pi$
$602$		0			0
$603$	241773.	−	744100.i	0.0270778	−	0.0833370i
$604$		0			0
$605$	−4310.26	+	3131.59i	−0.000478757	+	0.000347838i
$606$		0			0
$607$	−1.03373e7	+	7.51045e6i	−1.13876	+	0.827360i	−0.986946	−	0.161049i	$-0.948512\pi$
$607$	−1.03373e7	+	7.51045e6i	−1.13876	+	0.827360i	−0.151817	+	0.988409i	$0.548512\pi$
$608$		0			0
$609$	2.81380e6	+	8.65997e6i	0.307432	+	0.946179i
$610$		0			0
$611$	−756099.	+	2.32703e6i	−0.0819361	+	0.252173i
$612$		0			0
$613$	1.87740e6	+	5.77804e6i	0.201793	+	0.621054i	0.999830	+	0.0184455i	$0.00587172\pi$
$613$	1.87740e6	+	5.77804e6i	0.201793	+	0.621054i	−0.798037	+	0.602608i	$0.794128\pi$
$614$		0			0
$615$	42058.0			0.00448396
$616$		0			0
$617$	−6.03688e6	+	4.38605e6i	−0.638410	+	0.463832i	−0.859304	−	0.511466i	$-0.829103\pi$
$617$	−6.03688e6	+	4.38605e6i	−0.638410	+	0.463832i	0.220894	+	0.975298i	$0.429103\pi$
$618$		0			0
$619$	−7.61033e6			−0.798319			−0.399160	−	0.916881i	$-0.630698\pi$
$619$	−7.61033e6			−0.798319			−0.399160	+	0.916881i	$0.630698\pi$
$620$		0			0
$621$	1.26316e7			1.31440
$622$		0			0
$623$	−2.77522e6	+	2.01631e6i	−0.286468	+	0.208131i
$624$		0			0
$625$	9.75843e6			0.999264
$626$		0			0
$627$	−308614.	−	949816.i	−0.0313506	−	0.0964874i
$628$		0			0
$629$	4.86879e6	−	1.49846e7i	0.490676	−	1.51014i
$630$		0			0
$631$	−1.85543e6	−	5.71042e6i	−0.185512	−	0.570946i	0.814445	−	0.580240i	$-0.197041\pi$
$631$	−1.85543e6	−	5.71042e6i	−0.185512	−	0.570946i	−0.999957	+	0.00929451i	$0.997041\pi$
$632$		0			0
$633$	472774.	−	343490.i	0.0468969	−	0.0340726i
$634$		0			0
$635$	181194.	−	131645.i	0.0178324	−	0.0129560i
$636$		0			0
$637$	−370551.	+	1.14044e6i	−0.0361825	+	0.111358i
$638$		0			0
$639$	−1.85225e6	−	1.34574e6i	−0.179452	−	0.130379i
$640$		0			0
$641$	−6.70003e6	−	4.86785e6i	−0.644068	−	0.467943i	0.217178	−	0.976132i	$-0.430315\pi$
$641$	−6.70003e6	−	4.86785e6i	−0.644068	−	0.467943i	−0.861245	+	0.508190i	$0.830315\pi$
$642$		0			0
$643$	1.28246e6	−	3.94700e6i	0.122325	−	0.376478i	−0.871079	−	0.491143i	$-0.836579\pi$
$643$	1.28246e6	−	3.94700e6i	0.122325	−	0.376478i	0.993404	+	0.114664i	$0.0365793\pi$
$644$		0			0
$645$	−161954.			−0.0153283
$646$		0			0
$647$	−1.97695e6	−	6.08441e6i	−0.185667	−	0.571424i	0.814292	−	0.580455i	$-0.197125\pi$
$647$	−1.97695e6	−	6.08441e6i	−0.185667	−	0.571424i	−0.999959	+	0.00903130i	$0.997125\pi$
$648$		0			0
$649$	−1.03867e7	−	7.54641e6i	−0.967983	−	0.703281i
$650$		0			0
$651$	−4.61559e6	+	5.18163e6i	−0.426849	+	0.479197i
$652$		0			0
$653$	−9.78447e6	−	7.10883e6i	−0.897954	−	0.652402i	0.0399854	−	0.999200i	$-0.487269\pi$
$653$	−9.78447e6	−	7.10883e6i	−0.897954	−	0.652402i	−0.937940	+	0.346798i	$0.887269\pi$
$654$		0			0
$655$	33278.6	+	102421.i	0.00303083	+	0.00932794i
$656$		0			0
$657$	−1.08906e7			−0.984323
$658$		0			0
$659$	−313285.	+	964191.i	−0.0281012	+	0.0864867i	−0.964124	−	0.265454i	$-0.914478\pi$
$659$	−313285.	+	964191.i	−0.0281012	+	0.0864867i	0.936022	+	0.351941i	$0.114478\pi$
$660$		0			0
$661$	1.44938e7	+	1.05303e7i	1.29026	+	0.937429i	0.999811	−	0.0194613i	$-0.00619513\pi$
$661$	1.44938e7	+	1.05303e7i	1.29026	+	0.937429i	0.290450	+	0.956890i	$0.406195\pi$
$662$		0			0
$663$	−4.42649e6	−	3.21604e6i	−0.391089	−	0.284143i
$664$		0			0
$665$	−10061.7	+	30966.8i	−0.000882304	+	0.00271545i
$666$		0			0
$667$	1.91873e7	−	1.39404e7i	1.66993	−	1.21328i
$668$		0			0
$669$	−8.67451e6	+	6.30240e6i	−0.749341	+	0.544428i
$670$		0			0
$671$	−2.22804e6	−	6.85720e6i	−0.191036	−	0.587950i
$672$		0			0
$673$	−4.45488e6	+	1.37107e7i	−0.379139	+	1.16687i	0.561504	+	0.827474i	$0.310223\pi$
$673$	−4.45488e6	+	1.37107e7i	−0.379139	+	1.16687i	−0.940644	+	0.339396i	$0.889777\pi$
$674$		0			0
$675$	3.61020e6	+	1.11110e7i	0.304980	+	0.938632i
$676$		0			0
$677$	2.01211e7			1.68725			0.843627	−	0.536930i	$-0.180416\pi$
$677$	2.01211e7			1.68725			0.843627	+	0.536930i	$0.180416\pi$
$678$		0			0
$679$	1.28200e7	−	9.31427e6i	1.06712	−	0.775308i
$680$		0			0
$681$	−9.55430e6			−0.789462
$682$		0			0
$683$	1.79683e7			1.47386			0.736930	−	0.675969i	$-0.236275\pi$
$683$	1.79683e7			1.47386			0.736930	+	0.675969i	$0.236275\pi$
$684$		0			0
$685$	134736.	−	97891.1i	0.0109712	−	0.00797107i
$686$		0			0
$687$	3.74780e6			0.302959
$688$		0			0
$689$	5.55149e6	+	1.70857e7i	0.445514	+	1.37115i
$690$		0			0
$691$	−3.17539e6	+	9.77284e6i	−0.252989	+	0.778620i	0.741230	+	0.671251i	$0.234243\pi$
$691$	−3.17539e6	+	9.77284e6i	−0.252989	+	0.778620i	−0.994219	+	0.107369i	$0.965757\pi$
$692$		0			0
$693$	2.59108e6	+	7.97452e6i	0.204950	+	0.630770i
$694$		0			0
$695$	210645.	−	153043.i	0.0165421	−	0.0120185i
$696$		0			0
$697$	−4.40429e6	+	3.19990e6i	−0.343395	+	0.249491i
$698$		0			0
$699$	2.24483e6	−	6.90887e6i	0.173776	−	0.534828i
$700$		0			0
$701$	880309.	+	639582.i	0.0676613	+	0.0491588i	0.621102	−	0.783730i	$-0.286685\pi$
$701$	880309.	+	639582.i	0.0676613	+	0.0491588i	−0.553440	+	0.832889i	$0.686685\pi$
$702$		0			0
$703$	3.22336e6	+	2.34191e6i	0.245992	+	0.178723i
$704$		0			0
$705$	−11422.0	+	35153.4i	−0.000865506	+	0.00266375i
$706$		0			0
$707$	−2.80817e7			−2.11288
$708$		0			0
$709$	−5.22861e6	−	1.60920e7i	−0.390635	−	1.20225i	−0.932309	−	0.361662i	$-0.882210\pi$
$709$	−5.22861e6	−	1.60920e7i	−0.390635	−	1.20225i	0.541675	−	0.840588i	$-0.317790\pi$
$710$		0			0
$711$	1.03546e6	+	752309.i	0.0768177	+	0.0558113i
$712$		0			0
$713$	1.65506e7	+	7.26293e6i	1.21924	+	0.535042i
$714$		0			0
$715$	152118.	+	110520.i	0.0111280	+	0.00808494i
$716$		0			0
$717$	−931318.	−	2.86630e6i	−0.0676550	−	0.208221i
$718$		0			0
$719$	2.33584e7			1.68508			0.842539	−	0.538635i	$-0.181060\pi$
$719$	2.33584e7			1.68508			0.842539	+	0.538635i	$0.181060\pi$
$720$		0			0
$721$	−4.41803e6	+	1.35973e7i	−0.316512	+	0.974125i
$722$		0			0
$723$	−2.01925e6	−	1.46707e6i	−0.143663	−	0.104377i
$724$		0			0
$725$	1.77462e7	+	1.28933e7i	1.25389	+	0.911004i
$726$		0			0
$727$	−3.12399e6	+	9.61465e6i	−0.219217	+	0.674679i	0.779611	+	0.626264i	$0.215417\pi$
$727$	−3.12399e6	+	9.61465e6i	−0.219217	+	0.674679i	−0.998827	+	0.0484148i	$0.984583\pi$
$728$		0			0
$729$	−6.61991e6	+	4.80965e6i	−0.461353	+	0.335193i
$730$		0			0
$731$	1.69597e7	−	1.23220e7i	1.17388	−	0.852877i
$732$		0			0
$733$	−3.93550e6	−	1.21122e7i	−0.270545	−	0.832653i	−0.990364	−	0.138491i	$-0.955775\pi$
$733$	−3.93550e6	−	1.21122e7i	−0.270545	−	0.832653i	0.719818	−	0.694163i	$-0.244225\pi$
$734$		0			0
$735$	−5597.73	+	17228.0i	−0.000382202	+	0.00117630i
$736$		0			0
$737$	616016.	+	1.89590e6i	0.0417757	+	0.128572i
$738$		0			0
$739$	1.70403e7			1.14780			0.573902	−	0.818924i	$-0.305429\pi$
$739$	1.70403e7			1.14780			0.573902	+	0.818924i	$0.305429\pi$
$740$		0			0
$741$	1.11937e6	−	813267.i	0.0748905	−	0.0544111i
$742$		0			0
$743$	1.10410e7			0.733729			0.366864	−	0.930274i	$-0.380431\pi$
$743$	1.10410e7			0.733729			0.366864	+	0.930274i	$0.380431\pi$
$744$		0			0
$745$	−164542.			−0.0108614
$746$		0			0
$747$	7.04822e6	−	5.12083e6i	0.462145	−	0.335768i
$748$		0			0
$749$	2.78983e7			1.81708
$750$		0			0
$751$	−1.98388e6	−	6.10575e6i	−0.128356	−	0.395038i	0.866142	−	0.499798i	$-0.166593\pi$
$751$	−1.98388e6	−	6.10575e6i	−0.128356	−	0.395038i	−0.994498	+	0.104760i	$0.966593\pi$
$752$		0			0
$753$	1.95034e6	−	6.00252e6i	0.125349	−	0.385786i
$754$		0			0
$755$	131287.	+	404059.i	0.00838212	+	0.0257975i
$756$		0			0
$757$	−7.68271e6	+	5.58182e6i	−0.487276	+	0.354027i	−0.804136	−	0.594446i	$-0.797372\pi$
$757$	−7.68271e6	+	5.58182e6i	−0.487276	+	0.354027i	0.316860	+	0.948472i	$0.397372\pi$
$758$		0			0
$759$	−1.01204e7	+	7.35286e6i	−0.637663	+	0.463289i
$760$		0			0
$761$	6.88578e6	−	2.11922e7i	0.431014	−	1.32652i	−0.466102	−	0.884731i	$-0.654342\pi$
$761$	6.88578e6	−	2.11922e7i	0.431014	−	1.32652i	0.897116	−	0.441794i	$-0.145658\pi$
$762$		0			0
$763$	1.62316e7	+	1.17929e7i	1.00937	+	0.733349i
$764$		0			0
$765$	116743.	+	84818.4i	0.00721233	+	0.00524006i
$766$		0			0
$767$	5.49649e6	−	1.69165e7i	0.337363	−	1.03830i
$768$		0			0
$769$	−2.66597e7			−1.62570			−0.812848	−	0.582476i	$-0.802084\pi$
$769$	−2.66597e7			−1.62570			−0.812848	+	0.582476i	$0.802084\pi$
$770$		0			0
$771$	−257885.	−	793689.i	−0.0156239	−	0.0480855i
$772$		0			0
$773$	3.32093e6	+	2.41280e6i	0.199899	+	0.145235i	0.683232	−	0.730202i	$-0.260574\pi$
$773$	3.32093e6	+	2.41280e6i	0.199899	+	0.145235i	−0.483333	+	0.875437i	$0.660574\pi$
$774$		0			0
$775$	−1.65837e6	+	1.66341e7i	−0.0991804	+	0.994823i
$776$		0			0
$777$	1.55013e7	+	1.12624e7i	0.921119	+	0.669232i
$778$		0			0
$779$	−425415.	−	1.30929e6i	−0.0251171	−	0.0773024i
$780$		0			0
$781$	5.83348e6			0.342216
$782$		0			0
$783$	−8.11317e6	+	2.49698e7i	−0.472919	+	1.45549i
$784$		0			0
$785$	−56767.7	−	41244.1i	−0.00328796	−	0.00238885i
$786$		0			0
$787$	−2.26782e7	−	1.64767e7i	−1.30518	−	0.948271i	−0.305191	−	0.952291i	$-0.598720\pi$
$787$	−2.26782e7	−	1.64767e7i	−1.30518	−	0.948271i	−0.999992	+	0.00402067i	$0.998720\pi$
$788$		0			0
$789$	810133.	−	2.49333e6i	0.0463302	−	0.142590i
$790$		0			0
$791$	−1.98129e7	+	1.43949e7i	−1.12592	+	0.818028i
$792$		0			0
$793$	8.08126e6	−	5.87138e6i	0.456348	−	0.331556i
$794$		0			0
$795$	83863.7	+	258106.i	0.00470605	+	0.0144837i
$796$		0			0
$797$	1.05301e6	−	3.24083e6i	0.0587201	−	0.180722i	−0.917394	−	0.397980i	$-0.869711\pi$
$797$	1.05301e6	−	3.24083e6i	0.0587201	−	0.180722i	0.976114	+	0.217258i	$0.0697113\pi$
$798$		0			0
$799$	−1.47847e6	−	4.55025e6i	−0.0819303	−	0.252156i
$800$		0			0
$801$	−3.84444e6			−0.211715
$802$		0			0
$803$	2.24488e7	−	1.63100e7i	1.22858	−	0.892618i
$804$		0			0
$805$	407845.			0.0221822
$806$		0			0
$807$	−8.59295e6			−0.464471
$808$		0			0
$809$	8.79815e6	−	6.39223e6i	0.472629	−	0.343385i	−0.325836	−	0.945426i	$-0.605646\pi$
$809$	8.79815e6	−	6.39223e6i	0.472629	−	0.343385i	0.798465	+	0.602041i	$0.205646\pi$
$810$		0			0
$811$	−9.61923e6			−0.513557			−0.256778	−	0.966470i	$-0.582661\pi$
$811$	−9.61923e6			−0.513557			−0.256778	+	0.966470i	$0.582661\pi$
$812$		0			0
$813$	3.58295e6	+	1.10272e7i	0.190114	+	0.585110i
$814$		0			0
$815$	−17045.4	+	52460.5i	−0.000898906	+	0.00276655i
$816$		0			0
$817$	1.63816e6	+	5.04173e6i	0.0858619	+	0.264256i
$818$		0			0
$819$	−9.39803e6	+	6.82807e6i	−0.489584	+	0.355704i
$820$		0			0
$821$	−1.63506e7	+	1.18794e7i	−0.846597	+	0.615089i	−0.924206	−	0.381895i	$-0.875272\pi$
$821$	−1.63506e7	+	1.18794e7i	−0.846597	+	0.615089i	0.0776087	+	0.996984i	$0.475272\pi$
$822$		0			0
$823$	4.61876e6	−	1.42151e7i	0.237698	−	0.731559i	−0.759054	−	0.651027i	$-0.774338\pi$
$823$	4.61876e6	−	1.42151e7i	0.237698	−	0.731559i	0.996752	−	0.0805315i	$-0.0256617\pi$
$824$		0			0
$825$	−9.36024e6	−	6.80061e6i	−0.478798	−	0.347867i
$826$		0			0
$827$	−1.00356e7	−	7.29126e6i	−0.510244	−	0.370714i	0.302672	−	0.953095i	$-0.402121\pi$
$827$	−1.00356e7	−	7.29126e6i	−0.510244	−	0.370714i	−0.812916	+	0.582381i	$0.802121\pi$
$828$		0			0
$829$	−6.44735e6	+	1.98429e7i	−0.325833	+	1.00281i	0.645230	+	0.763988i	$0.276761\pi$
$829$	−6.44735e6	+	1.98429e7i	−0.325833	+	1.00281i	−0.971063	+	0.238823i	$0.923239\pi$
$830$		0			0
$831$	−1.58565e6			−0.0796536
$832$		0			0
$833$	−724570.	−	2.23000e6i	−0.0361800	−	0.111350i
$834$		0			0
$835$	68764.5	+	49960.3i	0.00341309	+	0.00247976i
$836$		0			0
$837$	−1.95485e7	+	4.26463e6i	−0.964494	+	0.210411i
$838$		0			0
$839$	−1.56490e7	−	1.13697e7i	−0.767507	−	0.557626i	0.133697	−	0.991022i	$-0.457315\pi$
$839$	−1.56490e7	−	1.13697e7i	−0.767507	−	0.557626i	−0.901204	+	0.433396i	$0.857315\pi$
$840$		0			0
$841$	8.89482e6	+	2.73754e7i	0.433658	+	1.33466i
$842$		0			0
$843$	6.20286e6			0.300624
$844$		0			0
$845$	19986.4	−	61511.7i	0.000962924	−	0.00296358i
$846$		0			0
$847$	678492.	+	492953.i	0.0324965	+	0.0236101i
$848$		0			0
$849$	−8.96136e6	−	6.51081e6i	−0.426683	−	0.310003i
$850$		0			0
$851$	1.54219e7	−	4.74638e7i	0.729986	−	2.24666i
$852$		0			0
$853$	2.01586e7	−	1.46461e7i	0.948609	−	0.689204i	−0.00186879	−	0.999998i	$-0.500595\pi$
$853$	2.01586e7	−	1.46461e7i	0.948609	−	0.689204i	0.950477	+	0.310794i	$0.100595\pi$
$854$		0			0
$855$	−29521.7	+	21448.8i	−0.00138110	+	0.00100343i
$856$		0			0
$857$	−1.17441e7	−	3.61447e7i	−0.546221	−	1.68110i	−0.718068	−	0.695973i	$-0.754973\pi$
$857$	−1.17441e7	−	3.61447e7i	−0.546221	−	1.68110i	0.171847	−	0.985124i	$-0.445027\pi$
$858$		0			0
$859$	−6.12247e6	+	1.88430e7i	−0.283103	+	0.871300i	0.703858	+	0.710340i	$0.251459\pi$
$859$	−6.12247e6	+	1.88430e7i	−0.283103	+	0.871300i	−0.986961	+	0.160960i	$0.948541\pi$
$860$		0			0
$861$	−2.04584e6	−	6.29646e6i	−0.0940512	−	0.289460i
$862$		0			0
$863$	678276.			0.0310013			0.0155006	−	0.999880i	$-0.495066\pi$
$863$	678276.			0.0310013			0.0155006	+	0.999880i	$0.495066\pi$
$864$		0			0
$865$	359690.	−	261330.i	0.0163451	−	0.0118754i
$866$		0			0
$867$	−2.65823e6			−0.120100
$868$		0			0
$869$	−3.26109e6			−0.146492
$870$		0			0
$871$	−2.23434e6	+	1.62334e6i	−0.0997938	+	0.0725044i
$872$		0			0
$873$	1.77592e7			0.788658
$874$		0			0
$875$	233159.	+	717589.i	0.0102951	+	0.0316851i
$876$		0			0
$877$	6.49351e6	−	1.99850e7i	0.285089	−	0.877414i	−0.701283	−	0.712883i	$-0.747389\pi$
$877$	6.49351e6	−	1.99850e7i	0.285089	−	0.877414i	0.986372	−	0.164531i	$-0.0526109\pi$
$878$		0			0
$879$	2.70647e6	+	8.32964e6i	0.118149	+	0.363625i
$880$		0			0
$881$	−3.49423e7	+	2.53870e7i	−1.51674	+	1.10198i	−0.553667	+	0.832738i	$0.686772\pi$
$881$	−3.49423e7	+	2.53870e7i	−1.51674	+	1.10198i	−0.963074	+	0.269238i	$0.913228\pi$
$882$		0			0
$883$	6.23461e6	−	4.52971e6i	0.269096	−	0.195510i	−0.445051	−	0.895505i	$-0.646815\pi$
$883$	6.23461e6	−	4.52971e6i	0.269096	−	0.195510i	0.714147	+	0.699995i	$0.246815\pi$
$884$		0			0
$885$	83032.8	−	255549.i	0.00356362	−	0.0109677i
$886$		0			0
$887$	9.94867e6	+	7.22813e6i	0.424576	+	0.308473i	0.779477	−	0.626431i	$-0.215485\pi$
$887$	9.94867e6	+	7.22813e6i	0.424576	+	0.308473i	−0.354900	+	0.934904i	$0.615485\pi$
$888$		0			0
$889$	−2.85223e7	−	2.07226e7i	−1.21040	−	0.879408i
$890$		0			0
$891$	−287838.	+	885876.i	−0.0121466	+	0.0373834i
$892$		0			0
$893$	1.20988e6			0.0507706
$894$		0			0
$895$	−146393.	−	450550.i	−0.00610888	−	0.0188012i
$896$		0			0
$897$	−1.40209e7	−	1.01868e7i	−0.581830	−	0.422724i
$898$		0			0
$899$	−2.49875e7	+	2.80519e7i	−1.03115	+	1.15761i
$900$		0			0
$901$	−2.84196e7	−	2.06480e7i	−1.16629	−	0.847358i
$902$		0			0
$903$	7.87799e6	+	2.42460e7i	0.321511	+	0.989510i
$904$		0			0
$905$	583161.			0.0236683
$906$		0			0
$907$	−1.15396e7	+	3.55153e7i	−0.465771	+	1.43350i	0.392238	+	0.919864i	$0.371701\pi$
$907$	−1.15396e7	+	3.55153e7i	−0.465771	+	1.43350i	−0.858010	+	0.513633i	$0.828299\pi$
$908$		0			0
$909$	−2.54609e7	−	1.84985e7i	−1.02203	−	0.742550i
$910$		0			0
$911$	−1.25527e7	−	9.12008e6i	−0.501120	−	0.364085i	0.308325	−	0.951281i	$-0.400232\pi$
$911$	−1.25527e7	−	9.12008e6i	−0.501120	−	0.364085i	−0.809445	+	0.587196i	$0.800232\pi$
$912$		0			0
$913$	−6.85944e6	+	2.11112e7i	−0.272340	+	0.838177i
$914$		0			0
$915$	122080.	−	88696.1i	0.00482049	−	0.00350229i
$916$		0			0
$917$	1.37145e7	−	9.96420e6i	0.538590	−	0.391308i
$918$		0			0
$919$	7.97536e6	+	2.45456e7i	0.311502	+	0.958706i	0.977170	+	0.212458i	$0.0681468\pi$
$919$	7.97536e6	+	2.45456e7i	0.311502	+	0.958706i	−0.665668	+	0.746248i	$0.731853\pi$
$920$		0			0
$921$	723305.	−	2.22610e6i	0.0280978	−	0.0864762i
$922$		0			0
$923$	2.49742e6	+	7.68626e6i	0.0964910	+	0.296969i
$924$		0			0
$925$	4.61580e7			1.77375
$926$		0			0
$927$	−1.29628e7	+	9.41801e6i	−0.495449	+	0.359965i
$928$		0			0
$929$	−2.85128e7			−1.08393			−0.541964	−	0.840401i	$-0.682319\pi$
$929$	−2.85128e7			−1.08393			−0.541964	+	0.840401i	$0.682319\pi$
$930$		0			0
$931$	592939.			0.0224200
$932$		0			0
$933$	1.58558e7	−	1.15199e7i	0.596328	−	0.433258i
$934$		0			0
$935$	−367668.			−0.0137539
$936$		0			0
$937$	7.53232e6	+	2.31821e7i	0.280272	+	0.862589i	0.987776	+	0.155879i	$0.0498211\pi$
$937$	7.53232e6	+	2.31821e7i	0.280272	+	0.862589i	−0.707504	+	0.706709i	$0.750179\pi$
$938$		0			0
$939$	157834.	−	485765.i	0.00584168	−	0.0179788i
$940$		0			0
$941$	−2.63295e6	−	8.10339e6i	−0.0969324	−	0.298327i	0.890820	−	0.454356i	$-0.150131\pi$
$941$	−2.63295e6	−	8.10339e6i	−0.0969324	−	0.298327i	−0.987752	+	0.156029i	$0.950131\pi$
$942$		0			0
$943$	−1.39506e7	+	1.01357e7i	−0.510873	+	0.371171i
$944$		0			0
$945$	−365263.	+	265379.i	−0.0133053	+	0.00966690i
$946$		0			0
$947$	−4.58910e6	+	1.41238e7i	−0.166285	+	0.511772i	−0.999129	−	0.0417359i	$-0.986711\pi$
$947$	−4.58910e6	+	1.41238e7i	−0.166285	+	0.511772i	0.832844	+	0.553508i	$0.186711\pi$
$948$		0			0
$949$	3.11010e7	+	2.25962e7i	1.12101	+	0.814461i
$950$		0			0
$951$	6.53401e6	+	4.74724e6i	0.234276	+	0.170212i
$952$		0			0
$953$	8.43575e6	−	2.59626e7i	0.300879	−	0.926010i	−0.680304	−	0.732930i	$-0.738152\pi$
$953$	8.43575e6	−	2.59626e7i	0.300879	−	0.926010i	0.981183	−	0.193080i	$-0.0618477\pi$
$954$		0			0
$955$	9880.11			0.000350553
$956$		0			0
$957$	−8.03473e6	−	2.47284e7i	−0.283590	−	0.872801i
$958$		0			0
$959$	−2.12091e7	−	1.54093e7i	−0.744692	−	0.541050i
$960$		0			0
$961$	−2.80656e7	−	5.65228e6i	−0.980317	−	0.197431i
$962$		0			0
$963$	2.52947e7	+	1.83777e7i	0.878949	+	0.638593i
$964$		0			0
$965$	−122566.	−	377220.i	−0.00423694	−	0.0130400i
$966$		0			0
$967$	2.08195e6			0.0715984			0.0357992	−	0.999359i	$-0.488602\pi$
$967$	2.08195e6			0.0715984			0.0357992	+	0.999359i	$0.488602\pi$
$968$		0			0
$969$	−836045.	+	2.57308e6i	−0.0286036	+	0.0880328i
$970$		0			0
$971$	−2.34075e7	−	1.70066e7i	−0.796723	−	0.578853i	0.113228	−	0.993569i	$-0.463881\pi$
$971$	−2.34075e7	−	1.70066e7i	−0.796723	−	0.578853i	−0.909951	+	0.414716i	$0.863881\pi$
$972$		0			0
$973$	−3.31583e7	−	2.40909e7i	−1.12282	−	0.815777i
$974$		0			0
$975$	4.95328e6	−	1.52446e7i	0.166871	−	0.513577i
$976$		0			0
$977$	2.94541e7	−	2.13996e7i	0.987209	−	0.717249i	0.0279009	−	0.999611i	$-0.491118\pi$
$977$	2.94541e7	−	2.13996e7i	0.987209	−	0.717249i	0.959308	+	0.282361i	$0.0911177\pi$
$978$		0			0
$979$	7.92457e6	−	5.75753e6i	0.264252	−	0.191991i
$980$		0			0
$981$	6.94831e6	+	2.13847e7i	0.230519	+	0.709465i
$982$		0			0
$983$	1.59766e7	−	4.91710e7i	0.527353	−	1.62303i	−0.232263	−	0.972653i	$-0.574613\pi$
$983$	1.59766e7	−	4.91710e7i	0.527353	−	1.62303i	0.759616	−	0.650372i	$-0.225387\pi$
$984$		0			0
$985$	−210448.	−	647694.i	−0.00691123	−	0.0212706i
$986$		0			0
$987$	5.81837e6			0.190112
$988$		0			0
$989$	5.37200e7	−	3.90299e7i	1.74641	−	1.26884i
$990$		0			0
$991$	−5.74601e7			−1.85858			−0.929292	−	0.369345i	$-0.879582\pi$
$991$	−5.74601e7			−1.85858			−0.929292	+	0.369345i	$0.879582\pi$
$992$		0			0
$993$	6.19285e6			0.199305
$994$		0			0
$995$	−145312.	+	105576.i	−0.00465312	+	0.00338069i
$996$		0			0
$997$	−4.11257e7			−1.31031			−0.655157	−	0.755493i	$-0.727398\pi$
$997$	−4.11257e7			−1.31031			−0.655157	+	0.755493i	$0.727398\pi$
$998$		0			0
$999$	1.70723e7	+	5.25431e7i	0.541225	+	1.66572i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	124.6.f.a.33.6	✓	56
31.16	even	5	inner	124.6.f.a.109.6	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
124.6.f.a.33.6	✓	56	1.1	even	1	trivial
124.6.f.a.109.6	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)

\(f(q)\)	\(=\)	\(q+(-7.61067 + 5.52948i) q^{3} -0.875792 q^{5} +(42.6014 + 131.114i) q^{7} +(-47.7439 + 146.941i) q^{9} +O(q^{10})\)	\(q+(-7.61067 + 5.52948i) q^{3} -0.875792 q^{5} +(42.6014 + 131.114i) q^{7} +(-47.7439 + 146.941i) q^{9} +(-121.647 - 374.392i) q^{11} +(441.224 - 320.568i) q^{13} +(6.66536 - 4.84267i) q^{15} +(-329.547 + 1014.24i) q^{17} +(-218.175 - 158.513i) q^{19} +(-1049.22 - 762.300i) q^{21} +(-1043.84 + 3212.61i) q^{23} -3124.23 q^{25} +(-1155.55 - 3556.41i) q^{27} +(-5680.16 - 4126.88i) q^{29} +(530.807 - 5324.23i) q^{31} +(2996.01 + 2176.73i) q^{33} +(-37.3100 - 114.828i) q^{35} -14774.2 q^{37} +(-1585.44 + 4879.48i) q^{39} +(4129.91 + 3000.55i) q^{41} +(-15903.2 - 11554.3i) q^{43} +(41.8137 - 128.689i) q^{45} +(-3629.54 + 2637.02i) q^{47} +(-1778.77 + 1292.36i) q^{49} +(-3100.15 - 9541.28i) q^{51} +(-10179.1 + 31327.9i) q^{53} +(106.538 + 327.890i) q^{55} +2536.95 q^{57} +(26385.1 - 19169.9i) q^{59} +18315.5 q^{61} -21299.9 q^{63} +(-386.421 + 280.751i) q^{65} -5063.95 q^{67} +(-9819.74 - 30222.0i) q^{69} +(-4579.20 + 14093.3i) q^{71} +(21782.0 + 67038.1i) q^{73} +(23777.5 - 17275.4i) q^{75} +(43905.6 - 31899.3i) q^{77} +(2559.91 - 7878.59i) q^{79} +(-1914.27 - 1390.80i) q^{81} +(-45618.8 - 33144.0i) q^{83} +(288.615 - 888.264i) q^{85} +66049.3 q^{87} +(7689.18 + 23664.8i) q^{89} +(60827.7 + 44193.9i) q^{91} +(25400.4 + 43456.0i) q^{93} +(191.076 + 138.825i) q^{95} +(-35519.8 - 109319. i) q^{97} +60821.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 2 q^{3} - 58 q^{5} + 104 q^{7} - 1234 q^{9}+O(q^{10}) \) 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

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