LMFDB - Embedded newform 60.6.i.a.53.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,6,Mod(17,60)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 1]))

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

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

chi := DirichletCharacter("60.17");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	60.i (of order $4$, degree $2$, 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:	$9.62302918878$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} + 2 x^{18} - 382 x^{17} + 117610 x^{16} - 661518 x^{15} + 1160778 x^{14} + \cdots + 48\!\cdots\!00 $ x^20 - 2x^19 + 2x^18 - 382x^17 + 117610x^16 - 661518x^15 + 1160778x^14 - 161859774x^13 + 12872525097x^12 - 60314430972x^11 + 238998177000x^10 - 23647959230160x^9 + 244333990200544x^8 + 369253960052800x^7 + 17753999958800000x^6 - 195554595639827200x^5 + 1195920778734496000x^4 - 5202205084237824000x^3 + 36839424090977280000x^2 - 600638984600463360000*x + 4896482487496796160000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{23}\cdot 3^{14}\cdot 5^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			53.1
Root			$14.4102 + 9.21685i$ of defining polynomial
Character	$\chi$	$=$	60.53
Dual form			60.6.i.a.17.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-15.0272 + 4.14525i) q^{3} +(29.4180 - 47.5351i) q^{5} +(-98.6056 + 98.6056i) q^{7} +(208.634 - 124.583i) q^{9} +O(q^{10})$	\(q+(-15.0272 + 4.14525i) q^{3} +(29.4180 - 47.5351i) q^{5} +(-98.6056 + 98.6056i) q^{7} +(208.634 - 124.583i) q^{9} -208.182i q^{11} +(823.732 + 823.732i) q^{13} +(-245.025 + 836.264i) q^{15} +(1335.24 + 1335.24i) q^{17} +2162.52i q^{19} +(1073.02 - 1890.51i) q^{21} +(2062.09 - 2062.09i) q^{23} +(-1394.16 - 2796.77i) q^{25} +(-2618.75 + 2736.98i) q^{27} -43.7465 q^{29} +1056.81 q^{31} +(862.967 + 3128.39i) q^{33} +(1786.44 + 7588.00i) q^{35} +(2198.97 - 2198.97i) q^{37} +(-15793.0 - 8963.81i) q^{39} -7326.11i q^{41} +(-5654.14 - 5654.14i) q^{43} +(215.515 - 13582.4i) q^{45} +(17023.3 + 17023.3i) q^{47} -2639.11i q^{49} +(-25599.8 - 14530.0i) q^{51} +(-16153.6 + 16153.6i) q^{53} +(-9895.94 - 6124.29i) q^{55} +(-8964.21 - 32496.7i) q^{57} +13460.4 q^{59} -1895.46 q^{61} +(-8287.85 + 32857.0i) q^{63} +(63388.7 - 14923.6i) q^{65} +(8179.25 - 8179.25i) q^{67} +(-22439.5 + 39535.3i) q^{69} -10066.0i q^{71} +(24469.5 + 24469.5i) q^{73} +(32543.7 + 36248.5i) q^{75} +(20527.9 + 20527.9i) q^{77} +85638.4i q^{79} +(28007.1 - 51984.5i) q^{81} +(-9108.14 + 9108.14i) q^{83} +(102751. - 24190.6i) q^{85} +(657.388 - 181.340i) q^{87} -34273.4 q^{89} -162449. q^{91} +(-15880.9 + 4380.74i) q^{93} +(102796. + 63617.1i) q^{95} +(-997.190 + 997.190i) q^{97} +(-25936.0 - 43433.8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{3} + 76 q^{7}+O(q^{10}) $ 20 * q + 2 * q^3 + 76 * q^7	$ 20 q + 2 q^{3} + 76 q^{7} + 1068 q^{13} - 130 q^{15} + 2180 q^{21} + 4060 q^{25} + 1454 q^{27} - 4720 q^{31} - 460 q^{33} - 612 q^{37} - 24012 q^{43} - 18860 q^{45} - 31700 q^{51} + 19200 q^{55} + 33476 q^{57} + 59880 q^{61} + 67208 q^{63} - 80804 q^{67} - 56956 q^{73} - 102470 q^{75} - 9980 q^{81} + 239260 q^{85} + 71540 q^{87} + 218520 q^{91} + 307928 q^{93} - 151164 q^{97}+O(q^{100}) $ 20 * q + 2 * q^3 + 76 * q^7 + 1068 * q^13 - 130 * q^15 + 2180 * q^21 + 4060 * q^25 + 1454 * q^27 - 4720 * q^31 - 460 * q^33 - 612 * q^37 - 24012 * q^43 - 18860 * q^45 - 31700 * q^51 + 19200 * q^55 + 33476 * q^57 + 59880 * q^61 + 67208 * q^63 - 80804 * q^67 - 56956 * q^73 - 102470 * q^75 - 9980 * q^81 + 239260 * q^85 + 71540 * q^87 + 218520 * q^91 + 307928 * q^93 - 151164 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$41$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−15.0272	+	4.14525i	−0.963996	+	0.265918i
$3$	−15.0272	+	4.14525i	−0.963996	+	0.265918i
$4$		0			0
$5$	29.4180	−	47.5351i	0.526245	−	0.850333i
$5$	29.4180	−	47.5351i	0.526245	−	0.850333i
$6$		0			0
$7$	−98.6056	+	98.6056i	−0.760600	+	0.760600i	−0.976431	−	0.215831i	$-0.930754\pi$
$7$	−98.6056	+	98.6056i	−0.760600	+	0.760600i	0.215831	+	0.976431i	$0.430754\pi$
$8$		0			0
$9$	208.634	−	124.583i	0.858575	−	0.512688i
$10$		0			0
$11$		−	208.182i		−	0.518754i	−0.965776	−	0.259377i	$-0.916483\pi$
$11$		−	208.182i		−	0.518754i	0.965776	−	0.259377i	$-0.0835172\pi$
$12$		0			0
$13$	823.732	+	823.732i	1.35185	+	1.35185i	0.883596	+	0.468251i	$0.155116\pi$
$13$	823.732	+	823.732i	1.35185	+	1.35185i	0.468251	+	0.883596i	$0.344884\pi$
$14$		0			0
$15$	−245.025	+	836.264i	−0.281179	+	0.959655i
$16$		0			0
$17$	1335.24	+	1335.24i	1.12056	+	1.12056i	0.991657	+	0.128907i	$0.0411469\pi$
$17$	1335.24	+	1335.24i	1.12056	+	1.12056i	0.128907	+	0.991657i	$0.458853\pi$
$18$		0			0
$19$			2162.52i			1.37428i	0.726523	+	0.687142i	$0.241135\pi$
$19$			2162.52i			1.37428i	−0.726523	+	0.687142i	$0.758865\pi$
$20$		0			0
$21$	1073.02	−	1890.51i	0.530958	−	0.935472i
$22$		0			0
$23$	2062.09	−	2062.09i	0.812807	−	0.812807i	−0.172247	−	0.985054i	$-0.555103\pi$
$23$	2062.09	−	2062.09i	0.812807	−	0.812807i	0.985054	+	0.172247i	$0.0551028\pi$
$24$		0			0
$25$	−1394.16	−	2796.77i	−0.446133	−	0.894967i
$26$		0			0
$27$	−2618.75	+	2736.98i	−0.691330	+	0.722540i
$28$		0			0
$29$	−43.7465			−0.00965936			−0.00482968	−	0.999988i	$-0.501537\pi$
$29$	−43.7465			−0.00965936			−0.00482968	+	0.999988i	$0.501537\pi$
$30$		0			0
$31$	1056.81			0.197511			0.0987556	−	0.995112i	$-0.468514\pi$
$31$	1056.81			0.197511			0.0987556	+	0.995112i	$0.468514\pi$
$32$		0			0
$33$	862.967	+	3128.39i	0.137946	+	0.500076i
$34$		0			0
$35$	1786.44	+	7588.00i	0.246501	+	1.04703i
$36$		0			0
$37$	2198.97	−	2198.97i	0.264067	−	0.264067i	−0.562637	−	0.826704i	$-0.690213\pi$
$37$	2198.97	−	2198.97i	0.264067	−	0.264067i	0.826704	+	0.562637i	$0.190213\pi$
$38$		0			0
$39$	−15793.0	−	8963.81i	−1.66265	−	0.943693i
$40$		0			0
$41$		−	7326.11i		−	0.680635i	−0.940311	−	0.340317i	$-0.889466\pi$
$41$		−	7326.11i		−	0.680635i	0.940311	−	0.340317i	$-0.110534\pi$
$42$		0			0
$43$	−5654.14	−	5654.14i	−0.466332	−	0.466332i	0.434392	−	0.900724i	$-0.356963\pi$
$43$	−5654.14	−	5654.14i	−0.466332	−	0.466332i	−0.900724	+	0.434392i	$0.856963\pi$
$44$		0			0
$45$	215.515	−	13582.4i	0.0158652	−	0.999874i
$46$		0			0
$47$	17023.3	+	17023.3i	1.12409	+	1.12409i	0.991121	+	0.132966i	$0.0424500\pi$
$47$	17023.3	+	17023.3i	1.12409	+	1.12409i	0.132966	+	0.991121i	$0.457550\pi$
$48$		0			0
$49$		−	2639.11i		−	0.157025i
$50$		0			0
$51$	−25599.8	−	14530.0i	−1.37820	−	0.782240i
$52$		0			0
$53$	−16153.6	+	16153.6i	−0.789915	+	0.789915i	−0.981480	−	0.191565i	$-0.938644\pi$
$53$	−16153.6	+	16153.6i	−0.789915	+	0.789915i	0.191565	+	0.981480i	$0.438644\pi$
$54$		0			0
$55$	−9895.94	−	6124.29i	−0.441113	−	0.272991i
$56$		0			0
$57$	−8964.21	−	32496.7i	−0.365447	−	1.32480i
$58$		0			0
$59$	13460.4			0.503417			0.251709	−	0.967803i	$-0.419008\pi$
$59$	13460.4			0.503417			0.251709	+	0.967803i	$0.419008\pi$
$60$		0			0
$61$	−1895.46			−0.0652213			−0.0326107	−	0.999468i	$-0.510382\pi$
$61$	−1895.46			−0.0652213			−0.0326107	+	0.999468i	$0.510382\pi$
$62$		0			0
$63$	−8287.85	+	32857.0i	−0.263082	+	1.04298i
$64$		0			0
$65$	63388.7	−	14923.6i	1.86092	−	0.438117i
$66$		0			0
$67$	8179.25	−	8179.25i	0.222601	−	0.222601i	−0.586992	−	0.809593i	$-0.699688\pi$
$67$	8179.25	−	8179.25i	0.222601	−	0.222601i	0.809593	+	0.586992i	$0.199688\pi$
$68$		0			0
$69$	−22439.5	+	39535.3i	−0.567402	+	0.999682i
$70$		0			0
$71$		−	10066.0i		−	0.236980i	−0.992955	−	0.118490i	$-0.962195\pi$
$71$		−	10066.0i		−	0.236980i	0.992955	−	0.118490i	$-0.0378054\pi$
$72$		0			0
$73$	24469.5	+	24469.5i	0.537426	+	0.537426i	0.922772	−	0.385346i	$-0.125918\pi$
$73$	24469.5	+	24469.5i	0.537426	+	0.537426i	−0.385346	+	0.922772i	$0.625918\pi$
$74$		0			0
$75$	32543.7	+	36248.5i	0.668058	+	0.744109i
$76$		0			0
$77$	20527.9	+	20527.9i	0.394564	+	0.394564i
$78$		0			0
$79$			85638.4i			1.54383i	0.635723	+	0.771917i	$0.280702\pi$
$79$			85638.4i			1.54383i	−0.635723	+	0.771917i	$0.719298\pi$
$80$		0			0
$81$	28007.1	−	51984.5i	0.474302	−	0.880362i
$82$		0			0
$83$	−9108.14	+	9108.14i	−0.145122	+	0.145122i	−0.775935	−	0.630813i	$-0.782722\pi$
$83$	−9108.14	+	9108.14i	−0.145122	+	0.145122i	0.630813	+	0.775935i	$0.282722\pi$
$84$		0			0
$85$	102751.	−	24190.6i	1.54254	−	0.363162i
$86$		0			0
$87$	657.388	−	181.340i	0.00931158	−	0.00256860i
$88$		0			0
$89$	−34273.4			−0.458651			−0.229325	−	0.973350i	$-0.573652\pi$
$89$	−34273.4			−0.458651			−0.229325	+	0.973350i	$0.573652\pi$
$90$		0			0
$91$	−162449.			−2.05643
$92$		0			0
$93$	−15880.9	+	4380.74i	−0.190400	+	0.0525218i
$94$		0			0
$95$	102796.	+	63617.1i	1.16860	+	0.723210i
$96$		0			0
$97$	−997.190	+	997.190i	−0.0107609	+	0.0107609i	−0.712467	−	0.701706i	$-0.752422\pi$
$97$	−997.190	+	997.190i	−0.0107609	+	0.0107609i	0.701706	+	0.712467i	$0.252422\pi$
$98$		0			0
$99$	−25936.0	−	43433.8i	−0.265959	−	0.445389i
$100$		0			0
$101$		−	152435.i		−	1.48690i	−0.668793	−	0.743449i	$-0.733189\pi$
$101$		−	152435.i		−	1.48690i	0.668793	−	0.743449i	$-0.266811\pi$
$102$		0			0
$103$	42872.6	+	42872.6i	0.398187	+	0.398187i	0.877593	−	0.479406i	$-0.159148\pi$
$103$	42872.6	+	42872.6i	0.398187	+	0.398187i	−0.479406	+	0.877593i	$0.659148\pi$
$104$		0			0
$105$	−58299.5	−	106621.i	−0.516049	−	0.943778i
$106$		0			0
$107$	−37956.8	−	37956.8i	−0.320502	−	0.320502i	0.528458	−	0.848959i	$-0.322770\pi$
$107$	−37956.8	−	37956.8i	−0.320502	−	0.320502i	−0.848959	+	0.528458i	$0.822770\pi$
$108$		0			0
$109$		−	65604.7i		−	0.528894i	−0.964400	−	0.264447i	$-0.914811\pi$
$109$		−	65604.7i		−	0.528894i	0.964400	−	0.264447i	$-0.0851894\pi$
$110$		0			0
$111$	−23929.0	+	42159.6i	−0.184339	+	0.324780i
$112$		0			0
$113$	−162953.	+	162953.i	−1.20051	+	1.20051i	−0.226504	+	0.974010i	$0.572730\pi$
$113$	−162953.	+	162953.i	−1.20051	+	1.20051i	−0.974010	+	0.226504i	$0.927270\pi$
$114$		0			0
$115$	−37359.0	−	158684.i	−0.263421	−	1.11889i
$116$		0			0
$117$	274481.	+	69235.1i	1.85374	+	0.467586i
$118$		0			0
$119$	−263324.			−1.70460
$120$		0			0
$121$	117711.			0.730895
$122$		0			0
$123$	30368.6	+	110091.i	0.180993	+	0.656129i
$124$		0			0
$125$	−173958.	−	16003.7i	−0.995795	−	0.0916103i
$126$		0			0
$127$	−37081.8	+	37081.8i	−0.204010	+	0.204010i	−0.801716	−	0.597706i	$-0.796079\pi$
$127$	−37081.8	+	37081.8i	−0.204010	+	0.204010i	0.597706	+	0.801716i	$0.296079\pi$
$128$		0			0
$129$	108404.	+	61528.1i	0.573548	+	0.325536i
$130$		0			0
$131$		−	281184.i		−	1.43157i	−0.698322	−	0.715784i	$-0.746070\pi$
$131$		−	281184.i		−	1.43157i	0.698322	−	0.715784i	$-0.253930\pi$
$132$		0			0
$133$	−213237.	−	213237.i	−1.04528	−	1.04528i
$134$		0			0
$135$	53063.9	+	204999.i	0.250591	+	0.968093i
$136$		0			0
$137$	103510.	+	103510.i	0.471175	+	0.471175i	0.902295	−	0.431120i	$-0.141881\pi$
$137$	103510.	+	103510.i	0.471175	+	0.471175i	−0.431120	+	0.902295i	$0.641881\pi$
$138$		0			0
$139$		−	75372.5i		−	0.330884i	−0.986220	−	0.165442i	$-0.947095\pi$
$139$		−	75372.5i		−	0.330884i	0.986220	−	0.165442i	$-0.0529051\pi$
$140$		0			0
$141$	−326379.	−	185247.i	−1.38253	−	0.784699i
$142$		0			0
$143$	171486.	−	171486.i	0.701275	−	0.701275i
$144$		0			0
$145$	−1286.93	+	2079.49i	−0.00508319	+	0.00821367i
$146$		0			0
$147$	10939.8	+	39658.5i	0.0417557	+	0.151371i
$148$		0			0
$149$	−222865.			−0.822388			−0.411194	−	0.911548i	$-0.634888\pi$
$149$	−222865.			−0.822388			−0.411194	+	0.911548i	$0.634888\pi$
$150$		0			0
$151$	261656.			0.933873			0.466937	−	0.884291i	$-0.345358\pi$
$151$	261656.			0.933873			0.466937	+	0.884291i	$0.345358\pi$
$152$		0			0
$153$	444924.	+	112228.i	1.53659	+	0.387589i
$154$		0			0
$155$	31089.2	−	50235.4i	0.103939	−	0.167950i
$156$		0			0
$157$	−231534.	+	231534.i	−0.749662	+	0.749662i	−0.974416	−	0.224754i	$-0.927842\pi$
$157$	−231534.	+	231534.i	−0.749662	+	0.749662i	0.224754	+	0.974416i	$0.427842\pi$
$158$		0			0
$159$	175783.	−	309705.i	0.551422	−	0.971527i
$160$		0			0
$161$			406666.i			1.23644i
$162$		0			0
$163$	130361.	+	130361.i	0.384308	+	0.384308i	0.872651	−	0.488344i	$-0.162399\pi$
$163$	130361.	+	130361.i	0.384308	+	0.384308i	−0.488344	+	0.872651i	$0.662399\pi$
$164$		0			0
$165$	174095.	+	51009.8i	0.497825	+	0.145862i
$166$		0			0
$167$	−302566.	−	302566.i	−0.839517	−	0.839517i	0.149278	−	0.988795i	$-0.452305\pi$
$167$	−302566.	−	302566.i	−0.839517	−	0.839517i	−0.988795	+	0.149278i	$0.952305\pi$
$168$		0			0
$169$			985774.i			2.65498i
$170$		0			0
$171$	269414.	+	451175.i	0.704579	+	1.17993i
$172$		0			0
$173$	−27432.5	+	27432.5i	−0.0696868	+	0.0696868i	−0.741091	−	0.671404i	$-0.765691\pi$
$173$	−27432.5	+	27432.5i	−0.0696868	+	0.0696868i	0.671404	+	0.741091i	$0.265691\pi$
$174$		0			0
$175$	413250.	+	138305.i	1.02004	+	0.341383i
$176$		0			0
$177$	−202272.	+	55796.8i	−0.485292	+	0.133868i
$178$		0			0
$179$	699192.			1.63104			0.815518	−	0.578731i	$-0.196452\pi$
$179$	699192.			1.63104			0.815518	+	0.578731i	$0.196452\pi$
$180$		0			0
$181$	53437.5			0.121241			0.0606206	−	0.998161i	$-0.480692\pi$
$181$	53437.5			0.121241			0.0606206	+	0.998161i	$0.480692\pi$
$182$		0			0
$183$	28483.4	−	7857.15i	0.0628731	−	0.0173435i
$184$		0			0
$185$	−39838.8	−	169217.i	−0.0855810	−	0.363509i
$186$		0			0
$187$	277972.	−	277972.i	0.581297	−	0.581297i
$188$		0			0
$189$	−11657.5	−	528105.i	−0.0237383	−	1.07539i
$190$		0			0
$191$		−	199891.i		−	0.396470i	−0.980155	−	0.198235i	$-0.936479\pi$
$191$		−	199891.i		−	0.396470i	0.980155	−	0.198235i	$-0.0635209\pi$
$192$		0			0
$193$	−649229.	−	649229.i	−1.25460	−	1.25460i	−0.953636	−	0.300962i	$-0.902692\pi$
$193$	−649229.	−	649229.i	−1.25460	−	1.25460i	−0.300962	−	0.953636i	$-0.597308\pi$
$194$		0			0
$195$	−890692.	+	487022.i	−1.67742	+	0.917196i
$196$		0			0
$197$	43021.0	+	43021.0i	0.0789796	+	0.0789796i	0.745493	−	0.666513i	$-0.232214\pi$
$197$	43021.0	+	43021.0i	0.0789796	+	0.0789796i	−0.666513	+	0.745493i	$0.732214\pi$
$198$		0			0
$199$		−	155958.i		−	0.279174i	−0.990210	−	0.139587i	$-0.955422\pi$
$199$		−	155958.i		−	0.279174i	0.990210	−	0.139587i	$-0.0445775\pi$
$200$		0			0
$201$	−89006.2	+	156816.i	−0.155392	+	0.273780i
$202$		0			0
$203$	4313.65	−	4313.65i	0.00734691	−	0.00734691i
$204$		0			0
$205$	−348247.	−	215519.i	−0.578766	−	0.358180i
$206$		0			0
$207$	173320.	−	687122.i	0.281139	−	1.11457i
$208$		0			0
$209$	450198.			0.712915
$210$		0			0
$211$	23276.7			0.0359928			0.0179964	−	0.999838i	$-0.494271\pi$
$211$	23276.7			0.0359928			0.0179964	+	0.999838i	$0.494271\pi$
$212$		0			0
$213$	41726.2	+	151264.i	0.0630173	+	0.228448i
$214$		0			0
$215$	−435103.	+	102437.i	−0.641943	+	0.151133i
$216$		0			0
$217$	−104207.	+	104207.i	−0.150227	+	0.150227i
$218$		0			0
$219$	−469141.	−	266276.i	−0.660988	−	0.375165i
$220$		0			0
$221$			2.19976e6i			3.02966i
$222$		0			0
$223$	−710151.	−	710151.i	−0.956288	−	0.956288i	0.0427958	−	0.999084i	$-0.486374\pi$
$223$	−710151.	−	710151.i	−0.956288	−	0.956288i	−0.999084	+	0.0427958i	$0.986374\pi$
$224$		0			0
$225$	−639300.	−	409811.i	−0.841877	−	0.539669i
$226$		0			0
$227$	−390981.	−	390981.i	−0.503606	−	0.503606i	0.408951	−	0.912557i	$-0.365895\pi$
$227$	−390981.	−	390981.i	−0.503606	−	0.503606i	−0.912557	+	0.408951i	$0.865895\pi$
$228$		0			0
$229$		−	1.01954e6i		−	1.28474i	−0.766393	−	0.642372i	$-0.777951\pi$
$229$		−	1.01954e6i		−	1.28474i	0.766393	−	0.642372i	$-0.222049\pi$
$230$		0			0
$231$	−393570.	−	223383.i	−0.485280	−	0.275436i
$232$		0			0
$233$	462104.	−	462104.i	0.557635	−	0.557635i	−0.370998	−	0.928633i	$-0.620984\pi$
$233$	462104.	−	462104.i	0.557635	−	0.557635i	0.928633	+	0.370998i	$0.120984\pi$
$234$		0			0
$235$	1.31000e6	−	308413.i	1.54739	−	0.364303i
$236$		0			0
$237$	−354993.	−	1.28691e6i	−0.410534	−	1.48825i
$238$		0			0
$239$	1.00447e6			1.13747			0.568737	−	0.822519i	$-0.307432\pi$
$239$	1.00447e6			1.13747			0.568737	+	0.822519i	$0.307432\pi$
$240$		0			0
$241$	1.33193e6			1.47720			0.738600	−	0.674144i	$-0.235487\pi$
$241$	1.33193e6			1.47720			0.738600	+	0.674144i	$0.235487\pi$
$242$		0			0
$243$	−205379.	+	897278.i	−0.223121	+	0.974791i
$244$		0			0
$245$	−125450.	−	77637.4i	−0.133523	−	0.0826334i
$246$		0			0
$247$	−1.78134e6	+	1.78134e6i	−1.85782	+	1.85782i
$248$		0			0
$249$	99114.4	−	174626.i	0.101307	−	0.178488i
$250$		0			0
$251$			196187.i			0.196556i	0.995159	+	0.0982781i	$0.0313335\pi$
$251$			196187.i			0.196556i	−0.995159	+	0.0982781i	$0.968667\pi$
$252$		0			0
$253$	−429289.	−	429289.i	−0.421646	−	0.421646i
$254$		0			0
$255$	−1.44378e6	+	789445.i	−1.39043	+	0.760276i
$256$		0			0
$257$	946428.	+	946428.i	0.893830	+	0.893830i	0.994881	−	0.101051i	$-0.0322206\pi$
$257$	946428.	+	946428.i	0.893830	+	0.893830i	−0.101051	+	0.994881i	$0.532221\pi$
$258$		0			0
$259$			433660.i			0.401699i
$260$		0			0
$261$	−9127.00	+	5450.08i	−0.00829329	+	0.00495224i
$262$		0			0
$263$	1.45489e6	−	1.45489e6i	1.29700	−	1.29700i	0.366637	−	0.930364i	$-0.380509\pi$
$263$	1.45489e6	−	1.45489e6i	1.29700	−	1.29700i	0.930364	−	0.366637i	$-0.119491\pi$
$264$		0			0
$265$	292656.	+	1.24307e6i	0.256002	+	1.08738i
$266$		0			0
$267$	515033.	−	142072.i	0.442137	−	0.121964i
$268$		0			0
$269$	−1.58867e6			−1.33861			−0.669303	−	0.742989i	$-0.733407\pi$
$269$	−1.58867e6			−1.33861			−0.669303	+	0.742989i	$0.733407\pi$
$270$		0			0
$271$	555550.			0.459516			0.229758	−	0.973248i	$-0.426207\pi$
$271$	555550.			0.459516			0.229758	+	0.973248i	$0.426207\pi$
$272$		0			0
$273$	2.44115e6	−	673392.i	1.98239	−	0.546842i
$274$		0			0
$275$	−582237.	+	290240.i	−0.464267	+	0.231433i
$276$		0			0
$277$	124826.	−	124826.i	0.0977478	−	0.0977478i	−0.656542	−	0.754290i	$-0.727981\pi$
$277$	124826.	−	124826.i	0.0977478	−	0.0977478i	0.754290	+	0.656542i	$0.227981\pi$
$278$		0			0
$279$	220486.	−	131660.i	0.169578	−	0.101262i
$280$		0			0
$281$		−	1.16333e6i		−	0.878897i	−0.898268	−	0.439448i	$-0.855174\pi$
$281$		−	1.16333e6i		−	0.878897i	0.898268	−	0.439448i	$-0.144826\pi$
$282$		0			0
$283$	−646581.	−	646581.i	−0.479907	−	0.479907i	0.425195	−	0.905102i	$-0.360205\pi$
$283$	−646581.	−	646581.i	−0.479907	−	0.479907i	−0.905102	+	0.425195i	$0.860205\pi$
$284$		0			0
$285$	−1.80844e6	−	529872.i	−1.31884	−	0.386420i
$286$		0			0
$287$	722396.	+	722396.i	0.517691	+	0.517691i
$288$		0			0
$289$			2.14587e6i			1.51133i
$290$		0			0
$291$	10851.4	−	19118.6i	0.00751194	−	0.0132350i
$292$		0			0
$293$	−327629.	+	327629.i	−0.222953	+	0.222953i	−0.809741	−	0.586788i	$-0.800392\pi$
$293$	−327629.	+	327629.i	−0.222953	+	0.222953i	0.586788	+	0.809741i	$0.300392\pi$
$294$		0			0
$295$	395978.	−	639841.i	0.264921	−	0.428072i
$296$		0			0
$297$	569789.	+	545177.i	0.374820	+	0.358630i
$298$		0			0
$299$	3.39721e6			2.19758
$300$		0			0
$301$	1.11506e6			0.709385
$302$		0			0
$303$	631881.	+	2.29067e6i	0.395393	+	1.43336i
$304$		0			0
$305$	−55760.5	+	90100.7i	−0.0343224	+	0.0554598i
$306$		0			0
$307$	−915551.	+	915551.i	−0.554417	+	0.554417i	−0.927712	−	0.373296i	$-0.878228\pi$
$307$	−915551.	+	915551.i	−0.554417	+	0.554417i	0.373296	+	0.927712i	$0.378228\pi$
$308$		0			0
$309$	−821973.	−	466537.i	−0.489735	−	0.277965i
$310$		0			0
$311$		−	893599.i		−	0.523892i	−0.965083	−	0.261946i	$-0.915636\pi$
$311$		−	893599.i		−	0.523892i	0.965083	−	0.261946i	$-0.0843642\pi$
$312$		0			0
$313$	807590.	+	807590.i	0.465940	+	0.465940i	0.900596	−	0.434656i	$-0.143130\pi$
$313$	807590.	+	807590.i	0.465940	+	0.465940i	−0.434656	+	0.900596i	$0.643130\pi$
$314$		0			0
$315$	1.31805e6	+	1.36055e6i	0.748437	+	0.772571i
$316$		0			0
$317$	−825216.	−	825216.i	−0.461232	−	0.461232i	0.437827	−	0.899059i	$-0.355748\pi$
$317$	−825216.	−	825216.i	−0.461232	−	0.461232i	−0.899059	+	0.437827i	$0.855748\pi$
$318$		0			0
$319$			9107.23i			0.00501083i
$320$		0			0
$321$	727725.	+	413044.i	0.394189	+	0.223735i
$322$		0			0
$323$	−2.88748e6	+	2.88748e6i	−1.53997	+	1.53997i
$324$		0			0
$325$	1.15537e6	−	3.45221e6i	0.606755	−	1.81296i
$326$		0			0
$327$	271948.	+	985855.i	0.140643	+	0.509852i
$328$		0			0
$329$	−3.35719e6			−1.70996
$330$		0			0
$331$	−2.16978e6			−1.08854			−0.544271	−	0.838910i	$-0.683194\pi$
$331$	−2.16978e6			−1.08854			−0.544271	+	0.838910i	$0.683194\pi$
$332$		0			0
$333$	184824.	−	732732.i	0.0913374	−	0.362105i
$334$		0			0
$335$	−148184.	−	629418.i	−0.0721422	−	0.306427i
$336$		0			0
$337$	1.48010e6	−	1.48010e6i	0.709931	−	0.709931i	−0.256589	−	0.966521i	$-0.582599\pi$
$337$	1.48010e6	−	1.48010e6i	0.709931	−	0.709931i	0.966521	+	0.256589i	$0.0825987\pi$
$338$		0			0
$339$	1.77325e6	−	3.12422e6i	0.838052	−	1.47653i
$340$		0			0
$341$		−	220008.i		−	0.102460i
$342$		0			0
$343$	−1.39703e6	−	1.39703e6i	−0.641167	−	0.641167i
$344$		0			0
$345$	1.21919e6	+	2.22971e6i	0.551470	+	1.00856i
$346$		0			0
$347$	−2.14143e6	−	2.14143e6i	−0.954729	−	0.954729i	0.0442899	−	0.999019i	$-0.485897\pi$
$347$	−2.14143e6	−	2.14143e6i	−0.954729	−	0.954729i	−0.999019	+	0.0442899i	$0.985897\pi$
$348$		0			0
$349$			1.13070e6i			0.496917i	0.968643	+	0.248458i	$0.0799239\pi$
$349$			1.13070e6i			0.496917i	−0.968643	+	0.248458i	$0.920076\pi$
$350$		0			0
$351$	−4.41168e6	+	97384.3i	−1.91133	+	0.0421911i
$352$		0			0
$353$	1.65417e6	−	1.65417e6i	0.706550	−	0.706550i	−0.259258	−	0.965808i	$-0.583478\pi$
$353$	1.65417e6	−	1.65417e6i	0.706550	−	0.706550i	0.965808	+	0.259258i	$0.0834781\pi$
$354$		0			0
$355$	−478489.	−	296122.i	−0.201512	−	0.124710i
$356$		0			0
$357$	3.95702e6	−	1.09154e6i	1.64323	−	0.453285i
$358$		0			0
$359$	−3.51467e6			−1.43929			−0.719644	−	0.694343i	$-0.755695\pi$
$359$	−3.51467e6			−1.43929			−0.719644	+	0.694343i	$0.755695\pi$
$360$		0			0
$361$	−2.20040e6			−0.888658
$362$		0			0
$363$	−1.76887e6	+	487943.i	−0.704579	+	0.194358i
$364$		0			0
$365$	1.88301e6	−	443317.i	0.739809	−	0.174173i
$366$		0			0
$367$	−162338.	+	162338.i	−0.0629152	+	0.0629152i	−0.737864	−	0.674949i	$-0.764166\pi$
$367$	−162338.	+	162338.i	−0.0629152	+	0.0629152i	0.674949	+	0.737864i	$0.264166\pi$
$368$		0			0
$369$	−912710.	−	1.52847e6i	−0.348953	−	0.584376i
$370$		0			0
$371$		−	3.18567e6i		−	1.20162i
$372$		0			0
$373$	−2.75008e6	−	2.75008e6i	−1.02347	−	1.02347i	−0.999718	−	0.0237481i	$-0.992440\pi$
$373$	−2.75008e6	−	2.75008e6i	−1.02347	−	1.02347i	−0.0237481	−	0.999718i	$-0.507560\pi$
$374$		0			0
$375$	2.68044e6	−	480611.i	0.984303	−	0.176488i
$376$		0			0
$377$	−36035.4	−	36035.4i	−0.0130580	−	0.0130580i
$378$		0			0
$379$			2.85204e6i			1.01990i	0.860204	+	0.509950i	$0.170336\pi$
$379$			2.85204e6i			1.01990i	−0.860204	+	0.509950i	$0.829664\pi$
$380$		0			0
$381$	403522.	−	710949.i	0.142415	−	0.250915i
$382$		0			0
$383$	−3.58384e6	+	3.58384e6i	−1.24839	+	1.24839i	−0.291964	+	0.956429i	$0.594309\pi$
$383$	−3.58384e6	+	3.58384e6i	−1.24839	+	1.24839i	−0.956429	+	0.291964i	$0.905691\pi$
$384$		0			0
$385$	1.57968e6	−	371905.i	0.543148	−	0.127874i
$386$		0			0
$387$	−1.88406e6	−	475234.i	−0.639464	−	0.161298i
$388$		0			0
$389$	−3.35177e6			−1.12305			−0.561526	−	0.827459i	$-0.689786\pi$
$389$	−3.35177e6			−1.12305			−0.561526	+	0.827459i	$0.689786\pi$
$390$		0			0
$391$	5.50675e6			1.82160
$392$		0			0
$393$	1.16558e6	+	4.22540e6i	0.380680	+	1.38002i
$394$		0			0
$395$	4.07083e6	+	2.51931e6i	1.31277	+	0.812435i
$396$		0			0
$397$	979362.	−	979362.i	0.311865	−	0.311865i	−0.533767	−	0.845632i	$-0.679224\pi$
$397$	979362.	−	979362.i	0.311865	−	0.311865i	0.845632	+	0.533767i	$0.179224\pi$
$398$		0			0
$399$	4.08827e6	+	2.32043e6i	1.28561	+	0.729687i
$400$		0			0
$401$			2.32513e6i			0.722082i	0.932550	+	0.361041i	$0.117579\pi$
$401$			2.32513e6i			0.722082i	−0.932550	+	0.361041i	$0.882421\pi$
$402$		0			0
$403$	870526.	+	870526.i	0.267005	+	0.267005i
$404$		0			0
$405$	−1.64717e6	−	2.86060e6i	−0.499002	−	0.866601i
$406$		0			0
$407$	−457785.	−	457785.i	−0.136986	−	0.136986i
$408$		0			0
$409$			3.54373e6i			1.04750i	0.851873	+	0.523748i	$0.175467\pi$
$409$			3.54373e6i			1.04750i	−0.851873	+	0.523748i	$0.824533\pi$
$410$		0			0
$411$	−1.98455e6	−	1.12639e6i	−0.579504	−	0.328917i
$412$		0			0
$413$	−1.32727e6	+	1.32727e6i	−0.382899	+	0.382899i
$414$		0			0
$415$	165013.	+	700899.i	0.0470325	+	0.199772i
$416$		0			0
$417$	312438.	+	1.13264e6i	0.0879881	+	0.318971i
$418$		0			0
$419$	1.37590e6			0.382869			0.191435	−	0.981505i	$-0.438686\pi$
$419$	1.37590e6			0.382869			0.191435	+	0.981505i	$0.438686\pi$
$420$		0			0
$421$	−4.61684e6			−1.26952			−0.634760	−	0.772709i	$-0.718901\pi$
$421$	−4.61684e6			−1.26952			−0.634760	+	0.772709i	$0.718901\pi$
$422$		0			0
$423$	5.67246e6	+	1.43082e6i	1.54142	+	0.388807i
$424$		0			0
$425$	1.87281e6	−	5.59590e6i	0.502947	−	1.50279i
$426$		0			0
$427$	186903.	−	186903.i	0.0496073	−	0.0496073i
$428$		0			0
$429$	−1.86610e6	+	3.28781e6i	−0.489544	+	0.862508i
$430$		0			0
$431$		−	5.92127e6i		−	1.53540i	−0.640809	−	0.767700i	$-0.721401\pi$
$431$		−	5.92127e6i		−	1.53540i	0.640809	−	0.767700i	$-0.278599\pi$
$432$		0			0
$433$	1.94617e6	+	1.94617e6i	0.498839	+	0.498839i	0.911076	−	0.412238i	$-0.135253\pi$
$433$	1.94617e6	+	1.94617e6i	0.498839	+	0.498839i	−0.412238	+	0.911076i	$0.635253\pi$
$434$		0			0
$435$	10719.0	−	36583.6i	0.00271601	−	0.00926966i
$436$		0			0
$437$	4.45931e6	+	4.45931e6i	1.11703	+	1.11703i
$438$		0			0
$439$		−	5.65182e6i		−	1.39967i	−0.714302	−	0.699837i	$-0.753256\pi$
$439$		−	5.65182e6i		−	1.39967i	0.714302	−	0.699837i	$-0.246744\pi$
$440$		0			0
$441$	−328789.	−	550608.i	−0.0805046	−	0.134817i
$442$		0			0
$443$	3.62907e6	−	3.62907e6i	0.878589	−	0.878589i	−0.114800	−	0.993389i	$-0.536623\pi$
$443$	3.62907e6	−	3.62907e6i	0.878589	−	0.878589i	0.993389	+	0.114800i	$0.0366227\pi$
$444$		0			0
$445$	−1.00825e6	+	1.62919e6i	−0.241363	+	0.390006i
$446$		0			0
$447$	3.34904e6	−	923833.i	0.792778	−	0.218688i
$448$		0			0
$449$	4.78413e6			1.11992			0.559960	−	0.828520i	$-0.310817\pi$
$449$	4.78413e6			1.11992			0.559960	+	0.828520i	$0.310817\pi$
$450$		0			0
$451$	−1.52516e6			−0.353082
$452$		0			0
$453$	−3.93196e6	+	1.08463e6i	−0.900250	+	0.248334i
$454$		0			0
$455$	−4.77892e6	+	7.72202e6i	−1.08218	+	1.74865i
$456$		0			0
$457$	−4.31444e6	+	4.31444e6i	−0.966350	+	0.966350i	−0.999452	−	0.0331021i	$-0.989461\pi$
$457$	−4.31444e6	+	4.31444e6i	−0.966350	+	0.966350i	0.0331021	+	0.999452i	$0.489461\pi$
$458$		0			0
$459$	−7.15118e6	+	157856.i	−1.58433	+	0.0349728i
$460$		0			0
$461$		−	5.42320e6i		−	1.18851i	−0.804277	−	0.594255i	$-0.797447\pi$
$461$		−	5.42320e6i		−	1.18851i	0.804277	−	0.594255i	$-0.202553\pi$
$462$		0			0
$463$	3.73081e6	+	3.73081e6i	0.808818	+	0.808818i	0.984455	−	0.175637i	$-0.0561985\pi$
$463$	3.73081e6	+	3.73081e6i	0.808818	+	0.808818i	−0.175637	+	0.984455i	$0.556198\pi$
$464$		0			0
$465$	−258945.	+	883771.i	−0.0555360	+	0.189543i
$466$		0			0
$467$	1.99079e6	+	1.99079e6i	0.422408	+	0.422408i	0.886032	−	0.463624i	$-0.153451\pi$
$467$	1.99079e6	+	1.99079e6i	0.422408	+	0.422408i	−0.463624	+	0.886032i	$0.653451\pi$
$468$		0			0
$469$			1.61304e6i			0.338620i
$470$		0			0
$471$	2.51954e6	−	4.43907e6i	0.523322	−	0.922020i
$472$		0			0
$473$	−1.17709e6	+	1.17709e6i	−0.241912	+	0.241912i
$474$		0			0
$475$	6.04808e6	−	3.01491e6i	1.22994	−	0.613113i
$476$		0			0
$477$	−1.35772e6	+	5.38266e6i	−0.273221	+	1.08318i
$478$		0			0
$479$	1.98299e6			0.394896			0.197448	−	0.980313i	$-0.436735\pi$
$479$	1.98299e6			0.394896			0.197448	+	0.980313i	$0.436735\pi$
$480$		0			0
$481$	3.62271e6			0.713956
$482$		0			0
$483$	−1.68574e6	−	6.11106e6i	−0.328792	−	1.19192i
$484$		0			0
$485$	18066.2	+	76736.8i	0.00348748	+	0.0148132i
$486$		0			0
$487$	−1.03480e6	+	1.03480e6i	−0.197712	+	0.197712i	−0.799018	−	0.601307i	$-0.794647\pi$
$487$	−1.03480e6	+	1.03480e6i	−0.197712	+	0.197712i	0.601307	+	0.799018i	$0.294647\pi$
$488$		0			0
$489$	−2.49934e6	−	1.41858e6i	−0.472665	−	0.268277i
$490$		0			0
$491$			7.04226e6i			1.31828i	0.752019	+	0.659141i	$0.229080\pi$
$491$			7.04226e6i			1.31828i	−0.752019	+	0.659141i	$0.770920\pi$
$492$		0			0
$493$	−58412.0	−	58412.0i	−0.0108239	−	0.0108239i
$494$		0			0
$495$	−2.82761e6	−	44866.4i	−0.518688	−	0.00823016i
$496$		0			0
$497$	992566.	+	992566.i	0.180247	+	0.180247i
$498$		0			0
$499$		−	3.72365e6i		−	0.669448i	−0.942316	−	0.334724i	$-0.891357\pi$
$499$		−	3.72365e6i		−	0.669448i	0.942316	−	0.334724i	$-0.108643\pi$
$500$		0			0
$501$	5.80094e6	+	3.29251e6i	1.03253	+	0.586048i
$502$		0			0
$503$	193077.	−	193077.i	0.0340260	−	0.0340260i	−0.689889	−	0.723915i	$-0.742341\pi$
$503$	193077.	−	193077.i	0.0340260	−	0.0340260i	0.723915	+	0.689889i	$0.242341\pi$
$504$		0			0
$505$	−7.24600e6	−	4.48433e6i	−1.26436	−	0.782472i
$506$		0			0
$507$	−4.08629e6	−	1.48134e7i	−0.706007	−	2.55939i
$508$		0			0
$509$	−2.85889e6			−0.489106			−0.244553	−	0.969636i	$-0.578641\pi$
$509$	−2.85889e6			−0.489106			−0.244553	+	0.969636i	$0.578641\pi$
$510$		0			0
$511$	−4.82567e6			−0.817533
$512$		0			0
$513$	−5.91877e6	−	5.66311e6i	−0.992975	−	0.950084i
$514$		0			0
$515$	3.29918e6	−	776726.i	0.548135	−	0.129048i
$516$		0			0
$517$	3.54395e6	−	3.54395e6i	0.583124	−	0.583124i
$518$		0			0
$519$	298519.	−	525949.i	0.0486468	−	0.0857088i
$520$		0			0
$521$			1.00713e7i			1.62551i	0.582604	+	0.812756i	$0.302034\pi$
$521$			1.00713e7i			1.62551i	−0.582604	+	0.812756i	$0.697966\pi$
$522$		0			0
$523$	1.23772e6	+	1.23772e6i	0.197865	+	0.197865i	0.799084	−	0.601219i	$-0.205318\pi$
$523$	1.23772e6	+	1.23772e6i	0.197865	+	0.197865i	−0.601219	+	0.799084i	$0.705318\pi$
$524$		0			0
$525$	−6.78329e6	−	365310.i	−1.07409	−	0.0578447i
$526$		0			0
$527$	1.41109e6	+	1.41109e6i	0.221324	+	0.221324i
$528$		0			0
$529$		−	2.06805e6i		−	0.321309i
$530$		0			0
$531$	2.80829e6	−	1.67694e6i	0.432221	−	0.258096i
$532$		0			0
$533$	6.03475e6	−	6.03475e6i	0.920113	−	0.920113i
$534$		0			0
$535$	−2.92089e6	+	687666.i	−0.441195	+	0.103871i
$536$		0			0
$537$	−1.05069e7	+	2.89833e6i	−1.57231	+	0.433722i
$538$		0			0
$539$	−549415.			−0.0814571
$540$		0			0
$541$	−900681.			−0.132305			−0.0661527	−	0.997810i	$-0.521072\pi$
$541$	−900681.			−0.132305			−0.0661527	+	0.997810i	$0.521072\pi$
$542$		0			0
$543$	−803017.	+	221512.i	−0.116876	+	0.0322402i
$544$		0			0
$545$	−3.11852e6	−	1.92996e6i	−0.449736	−	0.278328i
$546$		0			0
$547$	1.60062e6	−	1.60062e6i	0.228729	−	0.228729i	−0.583433	−	0.812162i	$-0.698291\pi$
$547$	1.60062e6	−	1.60062e6i	0.228729	−	0.228729i	0.812162	+	0.583433i	$0.198291\pi$
$548$		0			0
$549$	−395456.	+	236142.i	−0.0559974	+	0.0334382i
$550$		0			0
$551$		−	94602.8i		−	0.0132747i
$552$		0			0
$553$	−8.44442e6	−	8.44442e6i	−1.17424	−	1.17424i
$554$		0			0
$555$	1.30011e6	+	2.37772e6i	0.179163	+	0.327663i
$556$		0			0
$557$	−1.32883e6	−	1.32883e6i	−0.181481	−	0.181481i	0.610520	−	0.792001i	$-0.290960\pi$
$557$	−1.32883e6	−	1.32883e6i	−0.181481	−	0.181481i	−0.792001	+	0.610520i	$0.790960\pi$
$558$		0			0
$559$		−	9.31499e6i		−	1.26082i
$560$		0			0
$561$	−3.02488e6	+	5.32942e6i	−0.405790	+	0.714945i
$562$		0			0
$563$	−2.12575e6	+	2.12575e6i	−0.282645	+	0.282645i	−0.834163	−	0.551518i	$-0.814049\pi$
$563$	−2.12575e6	+	2.12575e6i	−0.282645	+	0.282645i	0.551518	+	0.834163i	$0.314049\pi$
$564$		0			0
$565$	2.95224e6	+	1.25398e7i	0.389073	+	1.65260i
$566$		0			0
$567$	2.36431e6	+	7.88761e6i	0.308849	+	1.03036i
$568$		0			0
$569$	1.15075e7			1.49005			0.745025	−	0.667037i	$-0.232438\pi$
$569$	1.15075e7			1.49005			0.745025	+	0.667037i	$0.232438\pi$
$570$		0			0
$571$	−281869.			−0.0361790			−0.0180895	−	0.999836i	$-0.505758\pi$
$571$	−281869.			−0.0361790			−0.0180895	+	0.999836i	$0.505758\pi$
$572$		0			0
$573$	828600.	+	3.00381e6i	0.105429	+	0.382195i
$574$		0			0
$575$	−8.64207e6	−	2.89230e6i	−1.09005	−	0.364815i
$576$		0			0
$577$	8.50758e6	−	8.50758e6i	1.06382	−	1.06382i	0.0659963	−	0.997820i	$-0.478977\pi$
$577$	8.50758e6	−	8.50758e6i	1.06382	−	1.06382i	0.997820	−	0.0659963i	$-0.0210226\pi$
$578$		0			0
$579$	1.24473e7	+	7.06488e6i	1.54305	+	0.875807i
$580$		0			0
$581$		−	1.79623e6i		−	0.220760i
$582$		0			0
$583$	3.36289e6	+	3.36289e6i	0.409771	+	0.409771i
$584$		0			0
$585$	1.13658e7	−	1.10107e7i	1.37312	−	1.33023i
$586$		0			0
$587$	−7.65918e6	−	7.65918e6i	−0.917460	−	0.917460i	0.0793840	−	0.996844i	$-0.474705\pi$
$587$	−7.65918e6	−	7.65918e6i	−0.917460	−	0.917460i	−0.996844	+	0.0793840i	$0.974705\pi$
$588$		0			0
$589$			2.28537e6i			0.271437i
$590$		0			0
$591$	−824818.	−	468152.i	−0.0971380	−	0.0551338i
$592$		0			0
$593$	1.60064e6	−	1.60064e6i	0.186921	−	0.186921i	−0.607443	−	0.794363i	$-0.707805\pi$
$593$	1.60064e6	−	1.60064e6i	0.186921	−	0.186921i	0.794363	+	0.607443i	$0.207805\pi$
$594$		0			0
$595$	−7.74646e6	+	1.25171e7i	−0.897038	+	1.44948i
$596$		0			0
$597$	646486.	+	2.34362e6i	0.0742375	+	0.269123i
$598$		0			0
$599$	2.83755e6			0.323129			0.161565	−	0.986862i	$-0.448346\pi$
$599$	2.83755e6			0.323129			0.161565	+	0.986862i	$0.448346\pi$
$600$		0			0
$601$	1.15589e7			1.30536			0.652680	−	0.757634i	$-0.273645\pi$
$601$	1.15589e7			1.30536			0.652680	+	0.757634i	$0.273645\pi$
$602$		0			0
$603$	687470.	−	2.72546e6i	0.0769947	−	0.305244i
$604$		0			0
$605$	3.46283e6	−	5.59541e6i	0.384630	−	0.621504i
$606$		0			0
$607$	−7.80631e6	+	7.80631e6i	−0.859952	+	0.859952i	−0.991332	−	0.131380i	$-0.958059\pi$
$607$	−7.80631e6	+	7.80631e6i	−0.859952	+	0.859952i	0.131380	+	0.991332i	$0.458059\pi$
$608$		0			0
$609$	−46940.9	+	82703.2i	−0.00512871	+	0.00903606i
$610$		0			0
$611$			2.80453e7i			3.03918i
$612$		0			0
$613$	8.92317e6	+	8.92317e6i	0.959109	+	0.959109i	0.999196	−	0.0400875i	$-0.0127637\pi$
$613$	8.92317e6	+	8.92317e6i	0.959109	+	0.959109i	−0.0400875	+	0.999196i	$0.512764\pi$
$614$		0			0
$615$	6.12657e6	+	1.79508e6i	0.653175	+	0.191380i
$616$		0			0
$617$	−3.99766e6	−	3.99766e6i	−0.422759	−	0.422759i	0.463394	−	0.886152i	$-0.346632\pi$
$617$	−3.99766e6	−	3.99766e6i	−0.422759	−	0.422759i	−0.886152	+	0.463394i	$0.846632\pi$
$618$		0			0
$619$			3.32337e6i			0.348620i	0.984691	+	0.174310i	$0.0557694\pi$
$619$			3.32337e6i			0.348620i	−0.984691	+	0.174310i	$0.944231\pi$
$620$		0			0
$621$	243787.	+	1.10440e7i	0.0253677	+	1.14920i
$622$		0			0
$623$	3.37955e6	−	3.37955e6i	0.348850	−	0.348850i
$624$		0			0
$625$	−5.87823e6	+	7.79832e6i	−0.601931	+	0.798548i
$626$		0			0
$627$	−6.76522e6	+	1.86618e6i	−0.687247	+	0.189577i
$628$		0			0
$629$	5.87229e6			0.591808
$630$		0			0
$631$	9.99889e6			0.999720			0.499860	−	0.866106i	$-0.333385\pi$
$631$	9.99889e6			0.999720			0.499860	+	0.866106i	$0.333385\pi$
$632$		0			0
$633$	−349784.	+	96487.9i	−0.0346969	+	0.00957114i
$634$		0			0
$635$	671814.	+	2.85356e6i	0.0661172	+	0.280836i
$636$		0			0
$637$	2.17392e6	−	2.17392e6i	0.212273	−	0.212273i
$638$		0			0
$639$	−1.25406e6	−	2.10011e6i	−0.121497	−	0.203465i
$640$		0			0
$641$		−	1.75514e7i		−	1.68720i	−0.536975	−	0.843598i	$-0.680433\pi$
$641$		−	1.75514e7i		−	1.68720i	0.536975	−	0.843598i	$-0.319567\pi$
$642$		0			0
$643$	3.09211e6	+	3.09211e6i	0.294936	+	0.294936i	0.839027	−	0.544090i	$-0.183125\pi$
$643$	3.09211e6	+	3.09211e6i	0.294936	+	0.294936i	−0.544090	+	0.839027i	$0.683125\pi$
$644$		0			0
$645$	6.11376e6	−	3.34295e6i	0.578641	−	0.316396i
$646$		0			0
$647$	−9.72315e6	−	9.72315e6i	−0.913159	−	0.913159i	0.0833606	−	0.996519i	$-0.473435\pi$
$647$	−9.72315e6	−	9.72315e6i	−0.913159	−	0.913159i	−0.996519	+	0.0833606i	$0.973435\pi$
$648$		0			0
$649$		−	2.80221e6i		−	0.261149i
$650$		0			0
$651$	1.13398e6	−	1.99791e6i	0.104870	−	0.184766i
$652$		0			0
$653$	985787.	−	985787.i	0.0904691	−	0.0904691i	−0.660424	−	0.750893i	$-0.729623\pi$
$653$	985787.	−	985787.i	0.0904691	−	0.0904691i	0.750893	+	0.660424i	$0.229623\pi$
$654$		0			0
$655$	−1.33661e7	−	8.27185e6i	−1.21731	−	0.753355i
$656$		0			0
$657$	8.15367e6	+	2.05668e6i	0.736953	+	0.185889i
$658$		0			0
$659$	804495.			0.0721622			0.0360811	−	0.999349i	$-0.488513\pi$
$659$	804495.			0.0721622			0.0360811	+	0.999349i	$0.488513\pi$
$660$		0			0
$661$	−1.24195e7			−1.10561			−0.552803	−	0.833312i	$-0.686442\pi$
$661$	−1.24195e7			−1.10561			−0.552803	+	0.833312i	$0.686442\pi$
$662$		0			0
$663$	−9.11855e6	−	3.30562e7i	−0.805642	−	2.92058i
$664$		0			0
$665$	−1.64092e7	+	3.86323e6i	−1.43891	+	0.338763i
$666$		0			0
$667$	−90209.0	+	90209.0i	−0.00785119	+	0.00785119i
$668$		0			0
$669$	1.36153e7	+	7.72783e6i	1.17615	+	0.667563i
$670$		0			0
$671$			394600.i			0.0338338i
$672$		0			0
$673$	−5.41526e6	−	5.41526e6i	−0.460873	−	0.460873i	0.438068	−	0.898942i	$-0.355663\pi$
$673$	−5.41526e6	−	5.41526e6i	−0.460873	−	0.460873i	−0.898942	+	0.438068i	$0.855663\pi$
$674$		0			0
$675$	1.13057e7	+	3.50826e6i	0.955074	+	0.296369i
$676$		0			0
$677$	−3.26339e6	−	3.26339e6i	−0.273651	−	0.273651i	0.556917	−	0.830568i	$-0.311984\pi$
$677$	−3.26339e6	−	3.26339e6i	−0.273651	−	0.273651i	−0.830568	+	0.556917i	$0.811984\pi$
$678$		0			0
$679$		−	196657.i		−	0.0163695i
$680$		0			0
$681$	7.49606e6	+	4.25463e6i	0.619392	+	0.351556i
$682$		0			0
$683$	−1.56392e6	+	1.56392e6i	−0.128281	+	0.128281i	−0.768332	−	0.640051i	$-0.778913\pi$
$683$	−1.56392e6	+	1.56392e6i	−0.128281	+	0.128281i	0.640051	+	0.768332i	$0.278913\pi$
$684$		0			0
$685$	7.96543e6	−	1.87530e6i	0.648609	−	0.152702i
$686$		0			0
$687$	4.22626e6	+	1.53209e7i	0.341637	+	1.23849i
$688$		0			0
$689$	−2.66125e7			−2.13569
$690$		0			0
$691$	−3.53262e6			−0.281450			−0.140725	−	0.990049i	$-0.544943\pi$
$691$	−3.53262e6			−0.281450			−0.140725	+	0.990049i	$0.544943\pi$
$692$		0			0
$693$	6.84024e6	+	1.72538e6i	0.541051	+	0.136475i
$694$		0			0
$695$	−3.58284e6	−	2.21731e6i	−0.281362	−	0.174126i
$696$		0			0
$697$	9.78211e6	−	9.78211e6i	0.762695	−	0.762695i
$698$		0			0
$699$	−5.02859e6	+	8.85967e6i	−0.389272	+	0.685843i
$700$		0			0
$701$		−	6.42784e6i		−	0.494049i	−0.969009	−	0.247024i	$-0.920547\pi$
$701$		−	6.42784e6i		−	0.494049i	0.969009	−	0.247024i	$-0.0794528\pi$
$702$		0			0
$703$	4.75531e6	+	4.75531e6i	0.362903	+	0.362903i
$704$		0			0
$705$	−1.84071e7	+	1.00649e7i	−1.39480	+	0.762666i
$706$		0			0
$707$	1.50309e7	+	1.50309e7i	1.13093	+	1.13093i
$708$		0			0
$709$		−	1.88206e7i		−	1.40610i	−0.711138	−	0.703052i	$-0.751820\pi$
$709$		−	1.88206e7i		−	1.40610i	0.711138	−	0.703052i	$-0.248180\pi$
$710$		0			0
$711$	1.06691e7	+	1.78671e7i	0.791505	+	1.32550i
$712$		0			0
$713$	2.17923e6	−	2.17923e6i	0.160538	−	0.160538i
$714$		0			0
$715$	−3.10683e6	−	1.31964e7i	−0.227275	−	0.965360i
$716$		0			0
$717$	−1.50944e7	+	4.16378e6i	−1.09652	+	0.302475i
$718$		0			0
$719$	−1.88543e7			−1.36015			−0.680077	−	0.733141i	$-0.738054\pi$
$719$	−1.88543e7			−1.36015			−0.680077	+	0.733141i	$0.738054\pi$
$720$		0			0
$721$	−8.45495e6			−0.605721
$722$		0			0
$723$	−2.00152e7	+	5.52120e6i	−1.42402	+	0.392815i
$724$		0			0
$725$	60989.8	+	122349.i	0.00430936	+	0.00864481i
$726$		0			0
$727$	1.11465e7	−	1.11465e7i	0.782170	−	0.782170i	−0.198027	−	0.980197i	$-0.563453\pi$
$727$	1.11465e7	−	1.11465e7i	0.782170	−	0.782170i	0.980197	+	0.198027i	$0.0634533\pi$
$728$		0			0
$729$	−633172.	−	1.43349e7i	−0.0441269	−	0.999026i
$730$		0			0
$731$		−	1.50993e7i		−	1.04511i
$732$		0			0
$733$	1.56320e7	+	1.56320e7i	1.07462	+	1.07462i	0.996981	+	0.0776406i	$0.0247387\pi$
$733$	1.56320e7	+	1.56320e7i	1.07462	+	1.07462i	0.0776406	+	0.996981i	$0.475261\pi$
$734$		0			0
$735$	2.20700e6	+	646649.i	0.150690	+	0.0441520i
$736$		0			0
$737$	−1.70277e6	−	1.70277e6i	−0.115475	−	0.115475i
$738$		0			0
$739$		−	1.95334e7i		−	1.31573i	−0.753136	−	0.657865i	$-0.771460\pi$
$739$		−	1.95334e7i		−	1.31573i	0.753136	−	0.657865i	$-0.228540\pi$
$740$		0			0
$741$	1.93844e7	−	3.41526e7i	1.29690	−	2.28496i
$742$		0			0
$743$	−1.17441e7	+	1.17441e7i	−0.780453	+	0.780453i	−0.979907	−	0.199454i	$-0.936083\pi$
$743$	−1.17441e7	+	1.17441e7i	−0.780453	+	0.780453i	0.199454	+	0.979907i	$0.436083\pi$
$744$		0			0
$745$	−6.55624e6	+	1.05939e7i	−0.432777	+	0.699303i
$746$		0			0
$747$	−765545.	+	3.03499e6i	−0.0501960	+	0.199001i
$748$		0			0
$749$	7.48550e6			0.487547
$750$		0			0
$751$	−2.69135e7			−1.74128			−0.870642	−	0.491917i	$-0.836296\pi$
$751$	−2.69135e7			−1.74128			−0.870642	+	0.491917i	$0.836296\pi$
$752$		0			0
$753$	−813246.	−	2.94815e6i	−0.0522679	−	0.189479i
$754$		0			0
$755$	7.69739e6	−	1.24378e7i	0.491446	−	0.794104i
$756$		0			0
$757$	−1.60633e7	+	1.60633e7i	−1.01882	+	1.01882i	−0.0189969	+	0.999820i	$0.506047\pi$
$757$	−1.60633e7	+	1.60633e7i	−1.01882	+	1.01882i	−0.999820	+	0.0189969i	$0.993953\pi$
$758$		0			0
$759$	8.23052e6	+	4.67150e6i	0.518589	+	0.294342i
$760$		0			0
$761$			1.77544e7i			1.11133i	0.831405	+	0.555666i	$0.187537\pi$
$761$			1.77544e7i			1.11133i	−0.831405	+	0.555666i	$0.812463\pi$
$762$		0			0
$763$	6.46899e6	+	6.46899e6i	0.402277	+	0.402277i
$764$		0			0
$765$	1.84235e7	−	1.78480e7i	1.13820	−	1.10264i
$766$		0			0
$767$	1.10878e7	+	1.10878e7i	0.680543	+	0.680543i
$768$		0			0
$769$		−	1.66161e7i		−	1.01324i	−0.862168	−	0.506622i	$-0.830894\pi$
$769$		−	1.66161e7i		−	1.01324i	0.862168	−	0.506622i	$-0.169106\pi$
$770$		0			0
$771$	−1.81454e7	−	1.02990e7i	−1.09933	−	0.623962i
$772$		0			0
$773$	−4.59367e6	+	4.59367e6i	−0.276510	+	0.276510i	−0.831714	−	0.555204i	$-0.812640\pi$
$773$	−4.59367e6	+	4.59367e6i	−0.276510	+	0.276510i	0.555204	+	0.831714i	$0.312640\pi$
$774$		0			0
$775$	−1.47336e6	−	2.95565e6i	−0.0881162	−	0.176766i
$776$		0			0
$777$	−1.79763e6	−	6.51670e6i	−0.106819	−	0.387236i
$778$		0			0
$779$	1.58429e7			0.935386
$780$		0			0
$781$	−2.09556e6			−0.122934
$782$		0			0
$783$	114561.	−	119733.i	0.00667780	−	0.00697927i
$784$		0			0
$785$	4.19472e6	+	1.78172e7i	0.242957	+	1.03197i
$786$		0			0
$787$	−272451.	+	272451.i	−0.0156802	+	0.0156802i	−0.714903	−	0.699223i	$-0.753529\pi$
$787$	−272451.	+	272451.i	−0.0156802	+	0.0156802i	0.699223	+	0.714903i	$0.253529\pi$
$788$		0			0
$789$	−1.58320e7	+	2.78938e7i	−0.905407	+	1.59520i
$790$		0			0
$791$		−	3.21362e7i		−	1.82622i
$792$		0			0
$793$	−1.56135e6	−	1.56135e6i	−0.0881692	−	0.0881692i
$794$		0			0
$795$	−9.55065e6	−	1.74667e7i	−0.535939	−	0.980153i
$796$		0			0
$797$	−3.98982e6	−	3.98982e6i	−0.222489	−	0.222489i	0.587057	−	0.809546i	$-0.300286\pi$
$797$	−3.98982e6	−	3.98982e6i	−0.222489	−	0.222489i	−0.809546	+	0.587057i	$0.800286\pi$
$798$		0			0
$799$			4.54604e7i			2.51922i
$800$		0			0
$801$	−7.15058e6	+	4.26989e6i	−0.393786	+	0.235145i
$802$		0			0
$803$	5.09412e6	−	5.09412e6i	0.278792	−	0.278792i
$804$		0			0
$805$	1.93309e7	+	1.19633e7i	1.05139	+	0.650671i
$806$		0			0
$807$	2.38733e7	−	6.58544e6i	1.29041	−	0.355960i
$808$		0			0
$809$	1.49611e7			0.803699			0.401849	−	0.915706i	$-0.368368\pi$
$809$	1.49611e7			0.803699			0.401849	+	0.915706i	$0.368368\pi$
$810$		0			0
$811$	3.03434e7			1.61999			0.809995	−	0.586436i	$-0.199470\pi$
$811$	3.03434e7			1.61999			0.809995	+	0.586436i	$0.199470\pi$
$812$		0			0
$813$	−8.34837e6	+	2.30290e6i	−0.442971	+	0.122194i
$814$		0			0
$815$	1.00317e7	−	2.36176e6i	0.529029	−	0.124550i
$816$		0			0
$817$	1.22272e7	−	1.22272e7i	0.640873	−	0.640873i
$818$		0			0
$819$	−3.38923e7	+	2.02384e7i	−1.76560	+	1.05431i
$820$		0			0
$821$			2.30832e6i			0.119519i	0.998213	+	0.0597597i	$0.0190334\pi$
$821$			2.30832e6i			0.119519i	−0.998213	+	0.0597597i	$0.980967\pi$
$822$		0			0
$823$	2.08400e7	+	2.08400e7i	1.07250	+	1.07250i	0.997157	+	0.0753457i	$0.0240060\pi$
$823$	2.08400e7	+	2.08400e7i	1.07250	+	1.07250i	0.0753457	+	0.997157i	$0.475994\pi$
$824$		0			0
$825$	7.54628e6	−	6.77501e6i	0.386009	−	0.346557i
$826$		0			0
$827$	2.14260e7	+	2.14260e7i	1.08937	+	1.08937i	0.995593	+	0.0937807i	$0.0298953\pi$
$827$	2.14260e7	+	2.14260e7i	1.08937	+	1.08937i	0.0937807	+	0.995593i	$0.470105\pi$
$828$		0			0
$829$			8.19636e6i			0.414223i	0.978317	+	0.207112i	$0.0664064\pi$
$829$			8.19636e6i			0.414223i	−0.978317	+	0.207112i	$0.933594\pi$
$830$		0			0
$831$	−1.35835e6	+	2.39323e6i	−0.0682355	+	0.120221i
$832$		0			0
$833$	3.52385e6	−	3.52385e6i	0.175956	−	0.175956i
$834$		0			0
$835$	−2.32834e7	+	5.48162e6i	−1.15566	+	0.272077i
$836$		0			0
$837$	−2.76752e6	+	2.89246e6i	−0.136545	+	0.142710i
$838$		0			0
$839$	−2.49281e7			−1.22260			−0.611299	−	0.791400i	$-0.709353\pi$
$839$	−2.49281e7			−1.22260			−0.611299	+	0.791400i	$0.709353\pi$
$840$		0			0
$841$	−2.05092e7			−0.999907
$842$		0			0
$843$	4.82231e6	+	1.74816e7i	0.233715	+	0.847253i
$844$		0			0
$845$	4.68588e7	+	2.89995e7i	2.25761	+	1.39717i
$846$		0			0
$847$	−1.16070e7	+	1.16070e7i	−0.555918	+	0.555918i
$848$		0			0
$849$	1.23965e7	+	7.03606e6i	0.590244	+	0.335012i
$850$		0			0
$851$		−	9.06891e6i		−	0.429271i
$852$		0			0
$853$	3.43432e6	+	3.43432e6i	0.161610	+	0.161610i	0.783280	−	0.621669i	$-0.213545\pi$
$853$	3.43432e6	+	3.43432e6i	0.161610	+	0.161610i	−0.621669	+	0.783280i	$0.713545\pi$
$854$		0			0
$855$	2.93723e7	+	466057.i	1.37411	+	0.0218034i
$856$		0			0
$857$	−1.20442e7	−	1.20442e7i	−0.560177	−	0.560177i	0.369181	−	0.929358i	$-0.379638\pi$
$857$	−1.20442e7	−	1.20442e7i	−0.560177	−	0.560177i	−0.929358	+	0.369181i	$0.879638\pi$
$858$		0			0
$859$		−	6.05636e6i		−	0.280046i	−0.990148	−	0.140023i	$-0.955282\pi$
$859$		−	6.05636e6i		−	0.280046i	0.990148	−	0.140023i	$-0.0447176\pi$
$860$		0			0
$861$	−1.38501e7	−	7.86107e6i	−0.636715	−	0.361388i
$862$		0			0
$863$	3.49696e6	−	3.49696e6i	0.159832	−	0.159832i	−0.622660	−	0.782492i	$-0.713948\pi$
$863$	3.49696e6	−	3.49696e6i	0.159832	−	0.159832i	0.782492	+	0.622660i	$0.213948\pi$
$864$		0			0
$865$	496997.	+	2.11102e6i	0.0225847	+	0.0959293i
$866$		0			0
$867$	−8.89517e6	−	3.22464e7i	−0.401889	−	1.45691i
$868$		0			0
$869$	1.78284e7			0.800870
$870$		0			0
$871$	1.34750e7			0.601844
$872$		0			0
$873$	−83814.4	+	332280.i	−0.00372206	+	0.0147560i
$874$		0			0
$875$	1.87313e7	−	1.55752e7i	0.827080	−	0.687723i
$876$		0			0
$877$	1.20703e7	−	1.20703e7i	0.529929	−	0.529929i	−0.390622	−	0.920551i	$-0.627740\pi$
$877$	1.20703e7	−	1.20703e7i	0.529929	−	0.529929i	0.920551	+	0.390622i	$0.127740\pi$
$878$		0			0
$879$	3.56525e6	−	6.28146e6i	0.155639	−	0.274213i
$880$		0			0
$881$			1.00926e6i			0.0438092i	0.999760	+	0.0219046i	$0.00697301\pi$
$881$			1.00926e6i			0.0438092i	−0.999760	+	0.0219046i	$0.993027\pi$
$882$		0			0
$883$	−2.57912e7	−	2.57912e7i	−1.11319	−	1.11319i	−0.992717	−	0.120473i	$-0.961559\pi$
$883$	−2.57912e7	−	2.57912e7i	−1.11319	−	1.11319i	−0.120473	−	0.992717i	$-0.538441\pi$
$884$		0			0
$885$	−3.29814e6	+	1.12565e7i	−0.141550	+	0.483107i
$886$		0			0
$887$	−1.69796e7	−	1.69796e7i	−0.724634	−	0.724634i	0.244912	−	0.969545i	$-0.421241\pi$
$887$	−1.69796e7	−	1.69796e7i	−0.724634	−	0.724634i	−0.969545	+	0.244912i	$0.921241\pi$
$888$		0			0
$889$		−	7.31294e6i		−	0.310340i
$890$		0			0
$891$	−1.08222e7	−	5.83056e6i	−0.456691	−	0.246046i
$892$		0			0
$893$	−3.68133e7	+	3.68133e7i	−1.54481	+	1.54481i
$894$		0			0
$895$	2.05688e7	−	3.32361e7i	0.858325	−	1.38692i
$896$		0			0
$897$	−5.10506e7	+	1.40823e7i	−2.11846	+	0.584376i
$898$		0			0
$899$	−46231.7			−0.00190783
$900$		0			0
$901$	−4.31379e7			−1.77030
$902$		0			0
$903$	−1.67562e7	+	4.62220e6i	−0.683844	+	0.188638i
$904$		0			0
$905$	1.57202e6	−	2.54016e6i	0.0638025	−	0.103095i
$906$		0			0
$907$	1.37950e7	−	1.37950e7i	0.556804	−	0.556804i	−0.371592	−	0.928396i	$-0.621188\pi$
$907$	1.37950e7	−	1.37950e7i	0.556804	−	0.556804i	0.928396	+	0.371592i	$0.121188\pi$
$908$		0			0
$909$	−1.89908e7	−	3.18031e7i	−0.762314	−	1.27661i
$910$		0			0
$911$			3.68392e7i			1.47067i	0.677706	+	0.735333i	$0.262974\pi$
$911$			3.68392e7i			1.47067i	−0.677706	+	0.735333i	$0.737026\pi$
$912$		0			0
$913$	1.89615e6	+	1.89615e6i	0.0752828	+	0.0752828i
$914$		0			0
$915$	464435.	−	1.58510e6i	0.0183388	−	0.0625900i
$916$		0			0
$917$	2.77263e7	+	2.77263e7i	1.08885	+	1.08885i
$918$		0			0
$919$		−	1.23698e7i		−	0.483139i	−0.970383	−	0.241570i	$-0.922338\pi$
$919$		−	1.23698e7i		−	0.483139i	0.970383	−	0.241570i	$-0.0776622\pi$
$920$		0			0
$921$	9.96298e6	−	1.75534e7i	0.387026	−	0.681885i
$922$		0			0
$923$	8.29170e6	−	8.29170e6i	0.320361	−	0.320361i
$924$		0			0
$925$	−9.21572e6	−	3.08428e6i	−0.354140	−	0.118522i
$926$		0			0
$927$	1.42859e7	+	3.60347e6i	0.546018	+	0.137728i
$928$		0			0
$929$	2.20679e6			0.0838921			0.0419460	−	0.999120i	$-0.486644\pi$
$929$	2.20679e6			0.0838921			0.0419460	+	0.999120i	$0.486644\pi$
$930$		0			0
$931$	5.70714e6			0.215796
$932$		0			0
$933$	3.70419e6	+	1.34283e7i	0.139312	+	0.505029i
$934$		0			0
$935$	−5.03605e6	−	2.13908e7i	−0.188391	−	0.800200i
$936$		0			0
$937$	4.22429e6	−	4.22429e6i	0.157183	−	0.157183i	−0.624134	−	0.781317i	$-0.714548\pi$
$937$	4.22429e6	−	4.22429e6i	0.157183	−	0.157183i	0.781317	+	0.624134i	$0.214548\pi$
$938$		0			0
$939$	−1.54835e7	−	8.78816e6i	−0.573066	−	0.325262i
$940$		0			0
$941$		−	2.76967e7i		−	1.01966i	−0.860276	−	0.509828i	$-0.829709\pi$
$941$		−	2.76967e7i		−	1.01966i	0.860276	−	0.509828i	$-0.170291\pi$
$942$		0			0
$943$	−1.51071e7	−	1.51071e7i	−0.553224	−	0.553224i
$944$		0			0
$945$	−2.54464e7	−	1.49816e7i	−0.926931	−	0.545732i
$946$		0			0
$947$	2.30040e7	+	2.30040e7i	0.833544	+	0.833544i	0.988000	−	0.154456i	$-0.0493625\pi$
$947$	2.30040e7	+	2.30040e7i	0.833544	+	0.833544i	−0.154456	+	0.988000i	$0.549363\pi$
$948$		0			0
$949$			4.03127e7i			1.45304i
$950$		0			0
$951$	1.58214e7	+	8.97996e6i	0.567276	+	0.321976i
$952$		0			0
$953$	−1.18544e7	+	1.18544e7i	−0.422814	+	0.422814i	−0.886171	−	0.463358i	$-0.846645\pi$
$953$	−1.18544e7	+	1.18544e7i	−0.422814	+	0.422814i	0.463358	+	0.886171i	$0.346645\pi$
$954$		0			0
$955$	−9.50184e6	−	5.88039e6i	−0.337131	−	0.208640i
$956$		0			0
$957$	−37751.8	−	136856.i	−0.00133247	−	0.00483042i
$958$		0			0
$959$	−2.04134e7			−0.716751
$960$		0			0
$961$	−2.75123e7			−0.960989
$962$		0			0
$963$	−1.26478e7	−	3.19029e6i	−0.439492	−	0.110857i
$964$		0			0
$965$	−4.99602e7	+	1.17621e7i	−1.72705	+	0.406601i
$966$		0			0
$967$	1.67798e7	−	1.67798e7i	0.577059	−	0.577059i	−0.357033	−	0.934092i	$-0.616212\pi$
$967$	1.67798e7	−	1.67798e7i	0.577059	−	0.577059i	0.934092	+	0.357033i	$0.116212\pi$
$968$		0			0
$969$	3.14215e7	−	5.53602e7i	1.07502	−	1.89403i
$970$		0			0
$971$		−	2.14564e7i		−	0.730312i	−0.930946	−	0.365156i	$-0.881016\pi$
$971$		−	2.14564e7i		−	0.730312i	0.930946	−	0.365156i	$-0.118984\pi$
$972$		0			0
$973$	7.43215e6	+	7.43215e6i	0.251670	+	0.251670i
$974$		0			0
$975$	−3.05173e6	+	5.66663e7i	−0.102810	+	1.90903i
$976$		0			0
$977$	−8.04251e6	−	8.04251e6i	−0.269560	−	0.269560i	0.559363	−	0.828923i	$-0.311046\pi$
$977$	−8.04251e6	−	8.04251e6i	−0.269560	−	0.269560i	−0.828923	+	0.559363i	$0.811046\pi$
$978$		0			0
$979$			7.13510e6i			0.237927i
$980$		0			0
$981$	−8.17324e6	−	1.36874e7i	−0.271158	−	0.454095i
$982$		0			0
$983$	2.43763e7	−	2.43763e7i	0.804607	−	0.804607i	−0.179205	−	0.983812i	$-0.557352\pi$
$983$	2.43763e7	−	2.43763e7i	0.804607	−	0.804607i	0.983812	+	0.179205i	$0.0573524\pi$
$984$		0			0
$985$	3.31060e6	−	779415.i	0.108722	−	0.0255963i
$986$		0			0
$987$	5.04492e7	−	1.39164e7i	1.64839	−	0.454709i
$988$		0			0
$989$	−2.33186e7			−0.758076
$990$		0			0
$991$	5.20983e7			1.68515			0.842576	−	0.538578i	$-0.181038\pi$
$991$	5.20983e7			1.68515			0.842576	+	0.538578i	$0.181038\pi$
$992$		0			0
$993$	3.26057e7	−	8.99427e6i	1.04935	−	0.289463i
$994$		0			0
$995$	−7.41348e6	−	4.58797e6i	−0.237391	−	0.146914i
$996$		0			0
$997$	2.69329e6	−	2.69329e6i	0.0858114	−	0.0858114i	−0.662898	−	0.748710i	$-0.730674\pi$
$997$	2.69329e6	−	2.69329e6i	0.0858114	−	0.0858114i	0.748710	+	0.662898i	$0.230674\pi$
$998$		0			0
$999$	259969.	+	1.17771e7i	0.00824153	+	0.373356i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.6.i.a.53.1	yes	20
3.2	odd	2	inner	60.6.i.a.53.6	yes	20
5.2	odd	4	inner	60.6.i.a.17.6	yes	20
5.3	odd	4		300.6.i.d.257.5		20
5.4	even	2		300.6.i.d.293.10		20
15.2	even	4	inner	60.6.i.a.17.1	✓	20
15.8	even	4		300.6.i.d.257.10		20
15.14	odd	2		300.6.i.d.293.5		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.6.i.a.17.1	✓	20	15.2	even	4	inner
60.6.i.a.17.6	yes	20	5.2	odd	4	inner
60.6.i.a.53.1	yes	20	1.1	even	1	trivial
60.6.i.a.53.6	yes	20	3.2	odd	2	inner
300.6.i.d.257.5		20	5.3	odd	4
300.6.i.d.257.10		20	15.8	even	4
300.6.i.d.293.5		20	15.14	odd	2
300.6.i.d.293.10		20	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	60.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-15.0272 + 4.14525i) q^{3} +(29.4180 - 47.5351i) q^{5} +(-98.6056 + 98.6056i) q^{7} +(208.634 - 124.583i) q^{9} +O(q^{10})\)	\(q+(-15.0272 + 4.14525i) q^{3} +(29.4180 - 47.5351i) q^{5} +(-98.6056 + 98.6056i) q^{7} +(208.634 - 124.583i) q^{9} -208.182i q^{11} +(823.732 + 823.732i) q^{13} +(-245.025 + 836.264i) q^{15} +(1335.24 + 1335.24i) q^{17} +2162.52i q^{19} +(1073.02 - 1890.51i) q^{21} +(2062.09 - 2062.09i) q^{23} +(-1394.16 - 2796.77i) q^{25} +(-2618.75 + 2736.98i) q^{27} -43.7465 q^{29} +1056.81 q^{31} +(862.967 + 3128.39i) q^{33} +(1786.44 + 7588.00i) q^{35} +(2198.97 - 2198.97i) q^{37} +(-15793.0 - 8963.81i) q^{39} -7326.11i q^{41} +(-5654.14 - 5654.14i) q^{43} +(215.515 - 13582.4i) q^{45} +(17023.3 + 17023.3i) q^{47} -2639.11i q^{49} +(-25599.8 - 14530.0i) q^{51} +(-16153.6 + 16153.6i) q^{53} +(-9895.94 - 6124.29i) q^{55} +(-8964.21 - 32496.7i) q^{57} +13460.4 q^{59} -1895.46 q^{61} +(-8287.85 + 32857.0i) q^{63} +(63388.7 - 14923.6i) q^{65} +(8179.25 - 8179.25i) q^{67} +(-22439.5 + 39535.3i) q^{69} -10066.0i q^{71} +(24469.5 + 24469.5i) q^{73} +(32543.7 + 36248.5i) q^{75} +(20527.9 + 20527.9i) q^{77} +85638.4i q^{79} +(28007.1 - 51984.5i) q^{81} +(-9108.14 + 9108.14i) q^{83} +(102751. - 24190.6i) q^{85} +(657.388 - 181.340i) q^{87} -34273.4 q^{89} -162449. q^{91} +(-15880.9 + 4380.74i) q^{93} +(102796. + 63617.1i) q^{95} +(-997.190 + 997.190i) q^{97} +(-25936.0 - 43433.8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{3} + 76 q^{7}+O(q^{10}) \) 20 * q + 2 * q^3 + 76 * q^7	\( 20 q + 2 q^{3} + 76 q^{7} + 1068 q^{13} - 130 q^{15} + 2180 q^{21} + 4060 q^{25} + 1454 q^{27} - 4720 q^{31} - 460 q^{33} - 612 q^{37} - 24012 q^{43} - 18860 q^{45} - 31700 q^{51} + 19200 q^{55} + 33476 q^{57} + 59880 q^{61} + 67208 q^{63} - 80804 q^{67} - 56956 q^{73} - 102470 q^{75} - 9980 q^{81} + 239260 q^{85} + 71540 q^{87} + 218520 q^{91} + 307928 q^{93} - 151164 q^{97}+O(q^{100}) \) 20 * q + 2 * q^3 + 76 * q^7 + 1068 * q^13 - 130 * q^15 + 2180 * q^21 + 4060 * q^25 + 1454 * q^27 - 4720 * q^31 - 460 * q^33 - 612 * q^37 - 24012 * q^43 - 18860 * q^45 - 31700 * q^51 + 19200 * q^55 + 33476 * q^57 + 59880 * q^61 + 67208 * q^63 - 80804 * q^67 - 56956 * q^73 - 102470 * q^75 - 9980 * q^81 + 239260 * q^85 + 71540 * q^87 + 218520 * q^91 + 307928 * q^93 - 151164 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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