LMFDB - Embedded newform 124.6.f.a.33.2

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			33.2
Character	$\chi$	$=$	124.33
Dual form			124.6.f.a.109.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-21.3000 + 15.4753i) q^{3} +92.0001 q^{5} +(26.8893 + 82.7567i) q^{7} +(139.112 - 428.142i) q^{9} +O(q^{10})$	\(q+(-21.3000 + 15.4753i) q^{3} +92.0001 q^{5} +(26.8893 + 82.7567i) q^{7} +(139.112 - 428.142i) q^{9} +(-196.836 - 605.799i) q^{11} +(225.634 - 163.933i) q^{13} +(-1959.60 + 1423.73i) q^{15} +(382.219 - 1176.35i) q^{17} +(1587.34 + 1153.27i) q^{19} +(-1853.43 - 1346.60i) q^{21} +(726.521 - 2236.00i) q^{23} +5339.02 q^{25} +(1685.54 + 5187.57i) q^{27} +(3261.85 + 2369.87i) q^{29} +(851.215 + 5282.48i) q^{31} +(13567.5 + 9857.39i) q^{33} +(2473.82 + 7613.63i) q^{35} +3614.50 q^{37} +(-2269.08 + 6983.52i) q^{39} +(-6762.45 - 4913.21i) q^{41} +(6386.36 + 4639.96i) q^{43} +(12798.3 - 39389.1i) q^{45} +(-12861.0 + 9344.07i) q^{47} +(7471.51 - 5428.37i) q^{49} +(10063.1 + 30971.1i) q^{51} +(5266.64 - 16209.1i) q^{53} +(-18108.9 - 55733.5i) q^{55} -51657.5 q^{57} +(-19214.1 + 13959.9i) q^{59} -746.505 q^{61} +39172.2 q^{63} +(20758.3 - 15081.8i) q^{65} +52388.5 q^{67} +(19128.0 + 58869.9i) q^{69} +(-2993.42 + 9212.79i) q^{71} +(22224.9 + 68401.1i) q^{73} +(-113721. + 82623.1i) q^{75} +(44841.1 - 32579.0i) q^{77} +(23898.1 - 73550.7i) q^{79} +(-27681.1 - 20111.5i) q^{81} +(-87903.8 - 63865.8i) q^{83} +(35164.2 - 108224. i) q^{85} -106152. q^{87} +(42405.2 + 130510. i) q^{89} +(19633.7 + 14264.7i) q^{91} +(-99879.0 - 99343.8i) q^{93} +(146035. + 106101. i) q^{95} +(-25537.7 - 78596.9i) q^{97} -286750. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−21.3000	+	15.4753i	−1.36639	+	0.992743i	−0.368385	+	0.929674i	$0.620089\pi$
$3$	−21.3000	+	15.4753i	−1.36639	+	0.992743i	−0.998009	+	0.0630696i	$0.979911\pi$
$4$		0			0
$5$	92.0001			1.64575			0.822874	−	0.568224i	$-0.192369\pi$
$5$	92.0001			1.64575			0.822874	+	0.568224i	$0.192369\pi$
$6$		0			0
$7$	26.8893	+	82.7567i	0.207412	+	0.638349i	0.999606	+	0.0280791i	$0.00893904\pi$
$7$	26.8893	+	82.7567i	0.207412	+	0.638349i	−0.792194	+	0.610270i	$0.791061\pi$
$8$		0			0
$9$	139.112	−	428.142i	0.572476	−	1.76190i
$10$		0			0
$11$	−196.836	−	605.799i	−0.490482	−	1.50955i	−0.823882	−	0.566762i	$-0.808196\pi$
$11$	−196.836	−	605.799i	−0.490482	−	1.50955i	0.333400	−	0.942785i	$-0.391804\pi$
$12$		0			0
$13$	225.634	−	163.933i	0.370293	−	0.269034i	−0.387039	−	0.922063i	$-0.626502\pi$
$13$	225.634	−	163.933i	0.370293	−	0.269034i	0.757333	+	0.653029i	$0.226502\pi$
$14$		0			0
$15$	−1959.60	+	1423.73i	−2.24874	+	1.63380i
$16$		0			0
$17$	382.219	−	1176.35i	0.320767	−	0.987219i	−0.652548	−	0.757747i	$-0.726300\pi$
$17$	382.219	−	1176.35i	0.320767	−	0.987219i	0.973315	−	0.229472i	$-0.0737000\pi$
$18$		0			0
$19$	1587.34	+	1153.27i	1.00876	+	0.732904i	0.963948	−	0.266092i	$-0.0857325\pi$
$19$	1587.34	+	1153.27i	1.00876	+	0.732904i	0.0448077	+	0.998996i	$0.485732\pi$
$20$		0			0
$21$	−1853.43	−	1346.60i	−0.917123	−	0.666329i
$22$		0			0
$23$	726.521	−	2236.00i	0.286371	−	0.881358i	−0.699614	−	0.714521i	$-0.746645\pi$
$23$	726.521	−	2236.00i	0.286371	−	0.881358i	0.985984	−	0.166837i	$-0.0533554\pi$
$24$		0			0
$25$	5339.02			1.70849
$26$		0			0
$27$	1685.54	+	5187.57i	0.444970	+	1.36948i
$28$		0			0
$29$	3261.85	+	2369.87i	0.720227	+	0.523275i	0.886457	−	0.462812i	$-0.153159\pi$
$29$	3261.85	+	2369.87i	0.720227	+	0.523275i	−0.166230	+	0.986087i	$0.553159\pi$
$30$		0			0
$31$	851.215	+	5282.48i	0.159087	+	0.987265i
$31$	851.215	+	5282.48i	0.159087	+	0.987265i
$32$		0			0
$33$	13567.5	+	9857.39i	2.16878	+	1.57571i
$34$		0			0
$35$	2473.82	+	7613.63i	0.341348	+	1.05056i
$36$		0			0
$37$	3614.50			0.434054			0.217027	−	0.976166i	$-0.430364\pi$
$37$	3614.50			0.434054			0.217027	+	0.976166i	$0.430364\pi$
$38$		0			0
$39$	−2269.08	+	6983.52i	−0.238885	+	0.735213i
$40$		0			0
$41$	−6762.45	−	4913.21i	−0.628267	−	0.456463i	0.227532	−	0.973771i	$-0.426934\pi$
$41$	−6762.45	−	4913.21i	−0.628267	−	0.456463i	−0.855800	+	0.517308i	$0.826934\pi$
$42$		0			0
$43$	6386.36	+	4639.96i	0.526723	+	0.382686i	0.819130	−	0.573607i	$-0.194456\pi$
$43$	6386.36	+	4639.96i	0.526723	+	0.382686i	−0.292408	+	0.956294i	$0.594456\pi$
$44$		0			0
$45$	12798.3	−	39389.1i	0.942151	−	2.89964i
$46$		0			0
$47$	−12861.0	+	9344.07i	−0.849240	+	0.617009i	−0.924936	−	0.380122i	$-0.875882\pi$
$47$	−12861.0	+	9344.07i	−0.849240	+	0.617009i	0.0756961	+	0.997131i	$0.475882\pi$
$48$		0			0
$49$	7471.51	−	5428.37i	0.444547	−	0.322982i
$50$		0			0
$51$	10063.1	+	30971.1i	0.541761	+	1.66737i
$52$		0			0
$53$	5266.64	−	16209.1i	0.257540	−	0.792625i	−0.735779	−	0.677222i	$-0.763184\pi$
$53$	5266.64	−	16209.1i	0.257540	−	0.792625i	0.993319	−	0.115404i	$-0.0368162\pi$
$54$		0			0
$55$	−18108.9	−	55733.5i	−0.807209	−	2.48433i
$56$		0			0
$57$	−51657.5			−2.10594
$58$		0			0
$59$	−19214.1	+	13959.9i	−0.718606	+	0.522098i	−0.885938	−	0.463803i	$-0.846485\pi$
$59$	−19214.1	+	13959.9i	−0.718606	+	0.522098i	0.167333	+	0.985900i	$0.446485\pi$
$60$		0			0
$61$	−746.505			−0.0256867			−0.0128433	−	0.999918i	$-0.504088\pi$
$61$	−746.505			−0.0256867			−0.0128433	+	0.999918i	$0.504088\pi$
$62$		0			0
$63$	39172.2			1.24345
$64$		0			0
$65$	20758.3	−	15081.8i	0.609410	−	0.442762i
$66$		0			0
$67$	52388.5			1.42577			0.712884	−	0.701282i	$-0.247389\pi$
$67$	52388.5			1.42577			0.712884	+	0.701282i	$0.247389\pi$
$68$		0			0
$69$	19128.0	+	58869.9i	0.483667	+	1.48858i
$70$		0			0
$71$	−2993.42	+	9212.79i	−0.0704727	+	0.216893i	−0.980090	−	0.198555i	$-0.936375\pi$
$71$	−2993.42	+	9212.79i	−0.0704727	+	0.216893i	0.909617	+	0.415448i	$0.136375\pi$
$72$		0			0
$73$	22224.9	+	68401.1i	0.488126	+	1.50230i	0.827402	+	0.561610i	$0.189818\pi$
$73$	22224.9	+	68401.1i	0.488126	+	1.50230i	−0.339276	+	0.940687i	$0.610182\pi$
$74$		0			0
$75$	−113721.	+	82623.1i	−2.33446	+	1.69609i
$76$		0			0
$77$	44841.1	−	32579.0i	0.861886	−	0.626197i
$78$		0			0
$79$	23898.1	−	73550.7i	0.430819	−	1.32592i	−0.466492	−	0.884526i	$-0.654482\pi$
$79$	23898.1	−	73550.7i	0.430819	−	1.32592i	0.897311	−	0.441399i	$-0.145518\pi$
$80$		0			0
$81$	−27681.1	−	20111.5i	−0.468783	−	0.340591i
$82$		0			0
$83$	−87903.8	−	63865.8i	−1.40059	−	1.01759i	−0.994607	−	0.103713i	$-0.966928\pi$
$83$	−87903.8	−	63865.8i	−1.40059	−	1.01759i	−0.405987	−	0.913879i	$-0.633072\pi$
$84$		0			0
$85$	35164.2	−	108224.i	0.527902	−	1.62471i
$86$		0			0
$87$	−106152.			−1.50359
$88$		0			0
$89$	42405.2	+	130510.i	0.567471	+	1.74650i	0.660493	+	0.750832i	$0.270347\pi$
$89$	42405.2	+	130510.i	0.567471	+	1.74650i	−0.0930219	+	0.995664i	$0.529653\pi$
$90$		0			0
$91$	19633.7	+	14264.7i	0.248541	+	0.180576i
$92$		0			0
$93$	−99879.0	−	99343.8i	−1.19748	−	1.19106i
$94$		0			0
$95$	146035.	+	106101.i	1.66016	+	1.20617i
$96$		0			0
$97$	−25537.7	−	78596.9i	−0.275583	−	0.848157i	−0.989065	−	0.147483i	$-0.952883\pi$
$97$	−25537.7	−	78596.9i	−0.275583	−	0.848157i	0.713482	−	0.700674i	$-0.247117\pi$
$98$		0			0
$99$	−286750.			−2.94046
$100$		0			0
$101$	−39449.7	+	121414.i	−0.384805	+	1.18431i	0.551817	+	0.833965i	$0.313935\pi$
$101$	−39449.7	+	121414.i	−0.384805	+	1.18431i	−0.936622	+	0.350342i	$0.886065\pi$
$102$		0			0
$103$	151684.	+	110205.i	1.40879	+	1.02354i	0.993497	+	0.113855i	$0.0363199\pi$
$103$	151684.	+	110205.i	1.40879	+	1.02354i	0.415290	+	0.909689i	$0.363680\pi$
$104$		0			0
$105$	−170516.	−	123887.i	−1.50935	−	1.09661i
$106$		0			0
$107$	59717.1	−	183790.i	0.504242	−	1.55190i	−0.297799	−	0.954628i	$-0.596253\pi$
$107$	59717.1	−	183790.i	0.504242	−	1.55190i	0.802041	−	0.597269i	$-0.203747\pi$
$108$		0			0
$109$	−35378.8	+	25704.2i	−0.285218	+	0.207223i	−0.721190	−	0.692737i	$-0.756405\pi$
$109$	−35378.8	+	25704.2i	−0.285218	+	0.207223i	0.435972	+	0.899960i	$0.356405\pi$
$110$		0			0
$111$	−76988.7	+	55935.5i	−0.593088	+	0.430904i
$112$		0			0
$113$	−60304.0	−	185597.i	−0.444273	−	1.36733i	−0.883279	−	0.468847i	$-0.844669\pi$
$113$	−60304.0	−	185597.i	−0.444273	−	1.36733i	0.439006	−	0.898484i	$-0.355331\pi$
$114$		0			0
$115$	66840.0	−	205712.i	0.471294	−	1.45049i
$116$		0			0
$117$	−38798.1	−	119408.i	−0.262027	−	0.806435i
$118$		0			0
$119$	107628.			0.696722
$120$		0			0
$121$	−197955.	+	143823.i	−1.22914	+	0.893025i
$122$		0			0
$123$	220074.			1.31161
$124$		0			0
$125$	203690.			1.16599
$126$		0			0
$127$	133806.	−	97215.9i	0.736151	−	0.534845i	−0.155352	−	0.987859i	$-0.549651\pi$
$127$	133806.	−	97215.9i	0.736151	−	0.534845i	0.891503	+	0.453014i	$0.149651\pi$
$128$		0			0
$129$	−207834.			−1.09962
$130$		0			0
$131$	−928.745	−	2858.38i	−0.00472845	−	0.0145527i	0.948664	−	0.316284i	$-0.102435\pi$
$131$	−928.745	−	2858.38i	−0.00472845	−	0.0145527i	−0.953393	+	0.301732i	$0.902435\pi$
$132$		0			0
$133$	−52758.4	+	162374.i	−0.258620	+	0.795951i
$134$		0			0
$135$	155070.	+	477257.i	0.732309	+	2.25381i
$136$		0			0
$137$	247431.	−	179769.i	1.12630	−	0.818301i	0.141144	−	0.989989i	$-0.454922\pi$
$137$	247431.	−	179769.i	1.12630	−	0.818301i	0.985151	+	0.171688i	$0.0549220\pi$
$138$		0			0
$139$	−260998.	+	189626.i	−1.14578	+	0.832455i	−0.987913	−	0.155006i	$-0.950460\pi$
$139$	−260998.	+	189626.i	−1.14578	+	0.832455i	−0.157862	+	0.987461i	$0.550460\pi$
$140$		0			0
$141$	129337.	−	398057.i	0.547865	−	1.68616i
$142$		0			0
$143$	−143723.	−	104421.i	−0.587741	−	0.427019i
$144$		0			0
$145$	300091.	+	218029.i	1.18531	+	0.861179i
$146$		0			0
$147$	−75137.1	+	231248.i	−0.286788	+	0.882642i
$148$		0			0
$149$	81148.0			0.299442			0.149721	−	0.988728i	$-0.452163\pi$
$149$	81148.0			0.299442			0.149721	+	0.988728i	$0.452163\pi$
$150$		0			0
$151$	84746.8	+	260824.i	0.302469	+	0.930904i	0.980610	+	0.195972i	$0.0627861\pi$
$151$	84746.8	+	260824.i	0.302469	+	0.930904i	−0.678140	+	0.734932i	$0.737214\pi$
$152$		0			0
$153$	−450472.	−	327287.i	−1.55575	−	1.13032i
$154$		0			0
$155$	78311.8	+	485989.i	0.261817	+	1.62479i
$156$		0			0
$157$	−285793.	−	207641.i	−0.925342	−	0.672300i	0.0195060	−	0.999810i	$-0.493791\pi$
$157$	−285793.	−	207641.i	−0.925342	−	0.672300i	−0.944848	+	0.327510i	$0.893791\pi$
$158$		0			0
$159$	138661.	+	426755.i	0.434973	+	1.33871i
$160$		0			0
$161$	204580.			0.622011
$162$		0			0
$163$	−5140.88	+	15822.0i	−0.0151554	+	0.0466436i	−0.958348	−	0.285602i	$-0.907806\pi$
$163$	−5140.88	+	15822.0i	−0.0151554	+	0.0466436i	0.943193	+	0.332246i	$0.107806\pi$
$164$		0			0
$165$	1.24821e6	+	906881.i	3.56927	+	2.59323i
$166$		0			0
$167$	−335277.	−	243593.i	−0.930279	−	0.675887i	0.0157823	−	0.999875i	$-0.494976\pi$
$167$	−335277.	−	243593.i	−0.930279	−	0.675887i	−0.946061	+	0.323988i	$0.894976\pi$
$168$		0			0
$169$	−90699.1	+	279143.i	−0.244279	+	0.751814i
$170$		0			0
$171$	714580.	−	519173.i	1.86879	−	1.35776i
$172$		0			0
$173$	316373.	−	229858.i	0.803681	−	0.583908i	−0.108311	−	0.994117i	$-0.534544\pi$
$173$	316373.	−	229858.i	0.803681	−	0.583908i	0.911992	+	0.410209i	$0.134544\pi$
$174$		0			0
$175$	143562.	+	441840.i	0.354361	+	1.09061i
$176$		0			0
$177$	193226.	−	594690.i	0.463589	−	1.42678i
$178$		0			0
$179$	−211623.	−	651310.i	−0.493664	−	1.51934i	−0.819029	−	0.573752i	$-0.805487\pi$
$179$	−211623.	−	651310.i	−0.493664	−	1.51934i	0.325366	−	0.945588i	$-0.394513\pi$
$180$		0			0
$181$	160308.			0.363712			0.181856	−	0.983325i	$-0.441789\pi$
$181$	160308.			0.363712			0.181856	+	0.983325i	$0.441789\pi$
$182$		0			0
$183$	15900.5	−	11552.4i	0.0350981	−	0.0255003i
$184$		0			0
$185$	332534.			0.714343
$186$		0			0
$187$	−787865.			−1.64758
$188$		0			0
$189$	−383984.	+	278980.i	−0.781912	+	0.568093i
$190$		0			0
$191$	425784.			0.844512			0.422256	−	0.906477i	$-0.361238\pi$
$191$	425784.			0.844512			0.422256	+	0.906477i	$0.361238\pi$
$192$		0			0
$193$	−23069.6	−	71001.0i	−0.0445807	−	0.137205i	0.926289	−	0.376815i	$-0.122981\pi$
$193$	−23069.6	−	71001.0i	−0.0445807	−	0.137205i	−0.970869	+	0.239609i	$0.922981\pi$
$194$		0			0
$195$	−208756.	+	642485.i	−0.393144	+	1.20997i
$196$		0			0
$197$	−58729.3	−	180750.i	−0.107818	−	0.331828i	0.882564	−	0.470193i	$-0.155816\pi$
$197$	−58729.3	−	180750.i	−0.107818	−	0.331828i	−0.990381	+	0.138364i	$0.955816\pi$
$198$		0			0
$199$	493567.	−	358597.i	0.883513	−	0.641910i	−0.0506653	−	0.998716i	$-0.516134\pi$
$199$	493567.	−	358597.i	0.883513	−	0.641910i	0.934179	+	0.356806i	$0.116134\pi$
$200$		0			0
$201$	−1.11587e6	+	810729.i	−1.94816	+	1.41542i
$202$		0			0
$203$	−108414.	+	333664.i	−0.184649	+	0.568290i
$204$		0			0
$205$	−622146.	−	452016.i	−1.03397	−	0.751223i
$206$		0			0
$207$	−856258.	−	622108.i	−1.38892	−	1.00911i
$208$		0			0
$209$	386204.	−	1.18861e6i	0.611577	−	1.88224i
$210$		0			0
$211$	433626.			0.670515			0.335258	−	0.942126i	$-0.391177\pi$
$211$	433626.			0.670515			0.335258	+	0.942126i	$0.391177\pi$
$212$		0			0
$213$	−78811.3	−	242556.i	−0.119025	−	0.366322i
$214$		0			0
$215$	587545.	+	426877.i	0.866852	+	0.629805i
$216$		0			0
$217$	−414272.	+	212486.i	−0.597223	+	0.306324i
$218$		0			0
$219$	−1.53192e6	−	1.11300e6i	−2.15837	−	1.56815i
$220$		0			0
$221$	−106600.	−	328082.i	−0.146818	−	0.451858i
$222$		0			0
$223$	403593.			0.543478			0.271739	−	0.962371i	$-0.412401\pi$
$223$	403593.			0.543478			0.271739	+	0.962371i	$0.412401\pi$
$224$		0			0
$225$	742719.	−	2.28585e6i	0.978067	−	3.01018i
$226$		0			0
$227$	475055.	+	345147.i	0.611898	+	0.444570i	0.850082	−	0.526650i	$-0.176552\pi$
$227$	475055.	+	345147.i	0.611898	+	0.444570i	−0.238184	+	0.971220i	$0.576552\pi$
$228$		0			0
$229$	−930234.	−	675854.i	−1.17220	−	0.851657i	−0.180933	−	0.983495i	$-0.557912\pi$
$229$	−930234.	−	675854.i	−1.17220	−	0.851657i	−0.991271	+	0.131839i	$0.957912\pi$
$230$		0			0
$231$	−450944.	+	1.38786e6i	−0.556023	+	1.71126i
$232$		0			0
$233$	−703630.	+	511217.i	−0.849092	+	0.616901i	−0.924896	−	0.380221i	$-0.875848\pi$
$233$	−703630.	+	511217.i	−0.849092	+	0.616901i	0.0758036	+	0.997123i	$0.475848\pi$
$234$		0			0
$235$	−1.18321e6	+	859656.i	−1.39764	+	1.01544i
$236$		0			0
$237$	629193.	+	1.93646e6i	0.727634	+	2.23943i
$238$		0			0
$239$	235545.	−	724932.i	0.266734	−	0.820923i	−0.724555	−	0.689217i	$-0.757955\pi$
$239$	235545.	−	724932.i	0.266734	−	0.820923i	0.991289	−	0.131706i	$-0.0420454\pi$
$240$		0			0
$241$	502696.	+	1.54714e6i	0.557523	+	1.71588i	0.689185	+	0.724585i	$0.257969\pi$
$241$	502696.	+	1.54714e6i	0.557523	+	1.71588i	−0.131662	+	0.991295i	$0.542031\pi$
$242$		0			0
$243$	−424612.			−0.461293
$244$		0			0
$245$	687379.	−	499410.i	0.731613	−	0.531548i
$246$		0			0
$247$	547216.			0.570711
$248$		0			0
$249$	2.86069e6			2.92397
$250$		0			0
$251$	−1.11268e6	+	808410.i	−1.11477	+	0.809930i	−0.983409	−	0.181404i	$-0.941936\pi$
$251$	−1.11268e6	+	808410.i	−1.11477	+	0.809930i	−0.131364	+	0.991334i	$0.541936\pi$
$252$		0			0
$253$	−1.49757e6			−1.47091
$254$		0			0
$255$	925809.	+	2.84935e6i	0.891602	+	2.74407i
$256$		0			0
$257$	−172755.	+	531684.i	−0.163154	+	0.502135i	−0.998895	−	0.0469874i	$-0.985038\pi$
$257$	−172755.	+	531684.i	−0.163154	+	0.502135i	0.835742	+	0.549122i	$0.185038\pi$
$258$		0			0
$259$	97191.3	+	299124.i	0.0900280	+	0.277078i
$260$		0			0
$261$	1.46840e6	−	1.06686e6i	1.33427	−	0.969405i
$262$		0			0
$263$	−485571.	+	352788.i	−0.432876	+	0.314503i	−0.782798	−	0.622276i	$-0.786208\pi$
$263$	−485571.	+	352788.i	−0.432876	+	0.314503i	0.349922	+	0.936779i	$0.386208\pi$
$264$		0			0
$265$	484531.	−	1.49123e6i	0.423845	−	1.30446i
$266$		0			0
$267$	−2.92291e6	−	2.12362e6i	−2.50921	−	1.82305i
$268$		0			0
$269$	−1.29546e6	−	941209.i	−1.09155	−	0.793059i	−0.111892	−	0.993720i	$-0.535691\pi$
$269$	−1.29546e6	−	941209.i	−1.09155	−	0.793059i	−0.979661	+	0.200661i	$0.935691\pi$
$270$		0			0
$271$	340093.	−	1.04670e6i	0.281303	−	0.865762i	−0.706179	−	0.708033i	$-0.749583\pi$
$271$	340093.	−	1.04670e6i	0.281303	−	0.865762i	0.987482	−	0.157729i	$-0.0504172\pi$
$272$		0			0
$273$	−638947.			−0.518870
$274$		0			0
$275$	−1.05091e6	−	3.23437e6i	−0.837981	−	2.57904i
$276$		0			0
$277$	−370053.	−	268859.i	−0.289778	−	0.210536i	0.433393	−	0.901205i	$-0.357316\pi$
$277$	−370053.	−	268859.i	−0.289778	−	0.210536i	−0.723171	+	0.690669i	$0.757316\pi$
$278$		0			0
$279$	2.38006e6	+	370414.i	1.83053	+	0.284890i
$280$		0			0
$281$	1.21900e6	+	885652.i	0.920951	+	0.669110i	0.943760	−	0.330630i	$-0.107261\pi$
$281$	1.21900e6	+	885652.i	0.920951	+	0.669110i	−0.0228099	+	0.999740i	$0.507261\pi$
$282$		0			0
$283$	379910.	+	1.16924e6i	0.281977	+	0.867837i	0.987288	+	0.158939i	$0.0508073\pi$
$283$	379910.	+	1.16924e6i	0.281977	+	0.867837i	−0.705311	+	0.708898i	$0.749193\pi$
$284$		0			0
$285$	−4.75250e6			−3.46585
$286$		0			0
$287$	224764.	−	691751.i	0.161072	−	0.495730i
$288$		0			0
$289$	−89015.7	−	64673.7i	−0.0626934	−	0.0455494i
$290$		0			0
$291$	1.76027e6	+	1.27891e6i	1.21856	+	0.885333i
$292$		0			0
$293$	−256614.	+	789777.i	−0.174627	+	0.537447i	−0.999616	−	0.0277019i	$-0.991181\pi$
$293$	−256614.	+	789777.i	−0.174627	+	0.537447i	0.824989	+	0.565148i	$0.191181\pi$
$294$		0			0
$295$	−1.76770e6	+	1.28431e6i	−1.18264	+	0.859241i
$296$		0			0
$297$	2.81085e6	−	2.04220e6i	1.84904	−	1.34341i
$298$		0			0
$299$	−202626.	−	623618.i	−0.131074	−	0.403405i
$300$		0			0
$301$	−212263.	+	653279.i	−0.135039	+	0.415607i
$302$		0			0
$303$	−1.03864e6	−	3.19661e6i	−0.649918	−	2.00024i
$304$		0			0
$305$	−68678.5			−0.0422738
$306$		0			0
$307$	402908.	−	292730.i	0.243983	−	0.177264i	−0.459073	−	0.888399i	$-0.651818\pi$
$307$	402908.	−	292730.i	0.243983	−	0.177264i	0.703056	+	0.711135i	$0.251818\pi$
$308$		0			0
$309$	−4.93631e6			−2.94107
$310$		0			0
$311$	−1.84521e6			−1.08180			−0.540899	−	0.841088i	$-0.681916\pi$
$311$	−1.84521e6			−1.08180			−0.540899	+	0.841088i	$0.681916\pi$
$312$		0			0
$313$	−1.19380e6	+	867344.i	−0.688763	+	0.500415i	−0.876253	−	0.481851i	$-0.839965\pi$
$313$	−1.19380e6	+	867344.i	−0.688763	+	0.500415i	0.187491	+	0.982266i	$0.439965\pi$
$314$		0			0
$315$	3.60385e6			2.04640
$316$		0			0
$317$	749684.	+	2.30729e6i	0.419016	+	1.28960i	0.908609	+	0.417647i	$0.137145\pi$
$317$	749684.	+	2.30729e6i	0.419016	+	1.28960i	−0.489594	+	0.871951i	$0.662855\pi$
$318$		0			0
$319$	793617.	−	2.44250e6i	0.436651	−	1.34387i
$320$		0			0
$321$	1.57224e6	+	4.83887e6i	0.851642	+	2.62108i
$322$		0			0
$323$	1.96336e6	−	1.42646e6i	1.04711	−	0.760771i
$324$		0			0
$325$	1.20466e6	−	875239.i	0.632641	−	0.459641i
$326$		0			0
$327$	355786.	−	1.09500e6i	0.184001	−	0.566297i
$328$		0			0
$329$	−1.11911e6	−	813080.i	−0.570010	−	0.414137i
$330$		0			0
$331$	−298376.	−	216783.i	−0.149691	−	0.108757i	0.510419	−	0.859926i	$-0.329490\pi$
$331$	−298376.	−	216783.i	−0.149691	−	0.108757i	−0.660110	+	0.751169i	$0.729490\pi$
$332$		0			0
$333$	502818.	−	1.54752e6i	0.248485	−	0.764759i
$334$		0			0
$335$	4.81975e6			2.34645
$336$		0			0
$337$	124044.	+	381769.i	0.0594979	+	0.183116i	0.976388	−	0.216024i	$-0.0693089\pi$
$337$	124044.	+	381769.i	0.0594979	+	0.183116i	−0.916890	+	0.399140i	$0.869309\pi$
$338$		0			0
$339$	4.15664e6	+	3.01998e6i	1.96446	+	1.42726i
$340$		0			0
$341$	3.03257e6	−	1.55545e6i	1.41229	−	0.724384i
$342$		0			0
$343$	1.83330e6	+	1.33197e6i	0.841392	+	0.611307i
$344$		0			0
$345$	1.75978e6	+	5.41604e6i	0.795994	+	2.44982i
$346$		0			0
$347$	−4.31110e6			−1.92205			−0.961025	−	0.276463i	$-0.910838\pi$
$347$	−4.31110e6			−1.92205			−0.961025	+	0.276463i	$0.910838\pi$
$348$		0			0
$349$	−181554.	+	558765.i	−0.0797888	+	0.245565i	−0.982992	−	0.183649i	$-0.941209\pi$
$349$	−181554.	+	558765.i	−0.0797888	+	0.245565i	0.903203	+	0.429213i	$0.141209\pi$
$350$		0			0
$351$	1.23073e6	+	894177.i	0.533205	+	0.387396i
$352$		0			0
$353$	1.47323e6	+	1.07036e6i	0.629263	+	0.457187i	0.856145	−	0.516736i	$-0.172853\pi$
$353$	1.47323e6	+	1.07036e6i	0.629263	+	0.457187i	−0.226882	+	0.973922i	$0.572853\pi$
$354$		0			0
$355$	−275394.	+	847577.i	−0.115980	+	0.356951i
$356$		0			0
$357$	−2.29248e6	+	1.66558e6i	−0.951996	+	0.691665i
$358$		0			0
$359$	227973.	−	165632.i	0.0933570	−	0.0678278i	−0.540128	−	0.841583i	$-0.681624\pi$
$359$	227973.	−	165632.i	0.0933570	−	0.0678278i	0.633485	+	0.773755i	$0.281624\pi$
$360$		0			0
$361$	424459.	+	1.30635e6i	0.171423	+	0.527584i
$362$		0			0
$363$	1.99073e6	−	6.12683e6i	0.792949	−	2.44045i
$364$		0			0
$365$	2.04469e6	+	6.29291e6i	0.803332	+	2.47240i
$366$		0			0
$367$	−1.30343e6			−0.505152			−0.252576	−	0.967577i	$-0.581278\pi$
$367$	−1.30343e6			−0.505152			−0.252576	+	0.967577i	$0.581278\pi$
$368$		0			0
$369$	−3.04428e6	+	2.21180e6i	−1.16391	+	0.845630i
$370$		0			0
$371$	1.48302e6			0.559388
$372$		0			0
$373$	−1.89977e6			−0.707015			−0.353507	−	0.935432i	$-0.615011\pi$
$373$	−1.89977e6			−0.707015			−0.353507	+	0.935432i	$0.615011\pi$
$374$		0			0
$375$	−4.33859e6	+	3.15217e6i	−1.59320	+	1.15753i
$376$		0			0
$377$	1.12448e6			0.407474
$378$		0			0
$379$	534798.	+	1.64594e6i	0.191246	+	0.588594i	1.00000		0.000447235i	$0.000142359\pi$
$379$	534798.	+	1.64594e6i	0.191246	+	0.588594i	−0.808754	+	0.588147i	$0.799858\pi$
$380$		0			0
$381$	−1.34562e6	+	4.14139e6i	−0.474908	+	1.46162i
$382$		0			0
$383$	−1.10330e6	−	3.39562e6i	−0.384324	−	1.18283i	−0.936969	−	0.349412i	$-0.886381\pi$
$383$	−1.10330e6	−	3.39562e6i	−0.384324	−	1.18283i	0.552645	−	0.833417i	$-0.313619\pi$
$384$		0			0
$385$	4.12539e6	−	2.99727e6i	1.41845	−	1.03056i
$386$		0			0
$387$	2.87498e6	−	2.08879e6i	0.975791	−	0.708954i
$388$		0			0
$389$	190079.	−	585003.i	0.0636883	−	0.196013i	−0.914149	−	0.405378i	$-0.867140\pi$
$389$	190079.	−	585003.i	0.0636883	−	0.196013i	0.977837	+	0.209366i	$0.0671399\pi$
$390$		0			0
$391$	−2.35263e6	−	1.70928e6i	−0.778236	−	0.565421i
$392$		0			0
$393$	64016.7	+	46510.9i	0.0209080	+	0.0151905i
$394$		0			0
$395$	2.19862e6	−	6.76667e6i	0.709020	−	2.18214i
$396$		0			0
$397$	−1.74680e6			−0.556245			−0.278123	−	0.960546i	$-0.589712\pi$
$397$	−1.74680e6			−0.556245			−0.278123	+	0.960546i	$0.589712\pi$
$398$		0			0
$399$	−1.38903e6	−	4.27501e6i	−0.436798	−	1.34433i
$400$		0			0
$401$	1.90297e6	+	1.38259e6i	0.590978	+	0.429371i	0.842665	−	0.538438i	$-0.180985\pi$
$401$	1.90297e6	+	1.38259e6i	0.590978	+	0.429371i	−0.251687	+	0.967809i	$0.580985\pi$
$402$		0			0
$403$	1.05803e6	+	1.05236e6i	0.324517	+	0.322778i
$404$		0			0
$405$	−2.54667e6	−	1.85026e6i	−0.771498	−	0.560526i
$406$		0			0
$407$	−711463.	−	2.18966e6i	−0.212895	−	0.655224i
$408$		0			0
$409$	243721.			0.0720419			0.0360210	−	0.999351i	$-0.488532\pi$
$409$	243721.			0.0720419			0.0360210	+	0.999351i	$0.488532\pi$
$410$		0			0
$411$	−2.48828e6	+	7.65815e6i	−0.726600	+	2.23624i
$412$		0			0
$413$	−1.67193e6	−	1.21473e6i	−0.482328	−	0.350432i
$414$		0			0
$415$	−8.08716e6	−	5.87566e6i	−2.30502	−	1.67470i
$416$		0			0
$417$	2.62472e6	−	8.07805e6i	0.739167	−	2.27492i
$418$		0			0
$419$	1.04588e6	−	759873.i	0.291035	−	0.211449i	−0.432681	−	0.901547i	$-0.642432\pi$
$419$	1.04588e6	−	759873.i	0.291035	−	0.211449i	0.723716	+	0.690098i	$0.242432\pi$
$420$		0			0
$421$	−3.67580e6	+	2.67063e6i	−1.01076	+	0.734358i	−0.964368	−	0.264565i	$-0.914772\pi$
$421$	−3.67580e6	+	2.67063e6i	−1.01076	+	0.734358i	−0.0463897	+	0.998923i	$0.514772\pi$
$422$		0			0
$423$	2.21147e6	+	6.80620e6i	0.600939	+	1.84950i
$424$		0			0
$425$	2.04067e6	−	6.28054e6i	0.548026	−	1.68665i
$426$		0			0
$427$	−20073.0	−	61778.3i	−0.00532773	−	0.0163971i
$428$		0			0
$429$	4.67724e6			1.22701
$430$		0			0
$431$	5.08870e6	−	3.69715e6i	1.31951	−	0.958682i	0.319574	−	0.947561i	$-0.396460\pi$
$431$	5.08870e6	−	3.69715e6i	1.31951	−	0.958682i	0.999938	−	0.0111204i	$-0.00353981\pi$
$432$		0			0
$433$	−4.24187e6			−1.08727			−0.543636	−	0.839321i	$-0.682953\pi$
$433$	−4.24187e6			−1.08727			−0.543636	+	0.839321i	$0.682953\pi$
$434$		0			0
$435$	−9.76599e6			−2.47453
$436$		0			0
$437$	3.73195e6	−	2.71142e6i	0.934829	−	0.679193i
$438$		0			0
$439$	−5.51917e6			−1.36682			−0.683412	−	0.730033i	$-0.739505\pi$
$439$	−5.51917e6			−1.36682			−0.683412	+	0.730033i	$0.739505\pi$
$440$		0			0
$441$	−1.28474e6	−	3.95401e6i	−0.314570	−	0.968147i
$442$		0			0
$443$	−1.54539e6	+	4.75621e6i	−0.374134	+	1.15147i	0.569926	+	0.821696i	$0.306972\pi$
$443$	−1.54539e6	+	4.75621e6i	−0.374134	+	1.15147i	−0.944061	+	0.329772i	$0.893028\pi$
$444$		0			0
$445$	3.90128e6	+	1.20069e7i	0.933914	+	2.87429i
$446$		0			0
$447$	−1.72845e6	+	1.25579e6i	−0.409155	+	0.297269i
$448$		0			0
$449$	−1.90141e6	+	1.38146e6i	−0.445103	+	0.323387i	−0.787659	−	0.616111i	$-0.788707\pi$
$449$	−1.90141e6	+	1.38146e6i	−0.445103	+	0.323387i	0.342556	+	0.939497i	$0.388707\pi$
$450$		0			0
$451$	−1.64532e6	+	5.06378e6i	−0.380899	+	1.17229i
$452$		0			0
$453$	−5.84144e6	−	4.24406e6i	−1.33744	−	0.971707i
$454$		0			0
$455$	1.80630e6	+	1.31235e6i	0.409036	+	0.297182i
$456$		0			0
$457$	435833.	−	1.34135e6i	0.0976179	−	0.300437i	−0.890309	−	0.455356i	$-0.849512\pi$
$457$	435833.	−	1.34135e6i	0.0976179	−	0.300437i	0.987927	+	0.154920i	$0.0495118\pi$
$458$		0			0
$459$	6.74664e6			1.49471
$460$		0			0
$461$	681148.	+	2.09636e6i	0.149276	+	0.459423i	0.997536	−	0.0701562i	$-0.0223498\pi$
$461$	681148.	+	2.09636e6i	0.149276	+	0.459423i	−0.848260	+	0.529579i	$0.822350\pi$
$462$		0			0
$463$	3.30779e6	+	2.40325e6i	0.717109	+	0.521010i	0.885459	−	0.464717i	$-0.153844\pi$
$463$	3.30779e6	+	2.40325e6i	0.717109	+	0.521010i	−0.168350	+	0.985727i	$0.553844\pi$
$464$		0			0
$465$	−9.18887e6	−	9.13964e6i	−1.97074	−	1.96018i
$466$		0			0
$467$	−4.62498e6	−	3.36025e6i	−0.981336	−	0.712983i	−0.0233296	−	0.999728i	$-0.507427\pi$
$467$	−4.62498e6	−	3.36025e6i	−0.981336	−	0.712983i	−0.958007	+	0.286745i	$0.907427\pi$
$468$		0			0
$469$	1.40869e6	+	4.33550e6i	0.295722	+	0.910138i
$470$		0			0
$471$	9.30069e6			1.93180
$472$		0			0
$473$	1.55382e6	−	4.78216e6i	0.319335	−	0.982813i
$474$		0			0
$475$	8.47483e6	+	6.15733e6i	1.72344	+	1.25216i
$476$		0			0
$477$	−6.20712e6	−	4.50973e6i	−1.24909	−	0.907518i
$478$		0			0
$479$	845373.	−	2.60179e6i	0.168349	−	0.518124i	−0.830919	−	0.556394i	$-0.812185\pi$
$479$	845373.	−	2.60179e6i	0.168349	−	0.518124i	0.999267	+	0.0382699i	$0.0121847\pi$
$480$		0			0
$481$	815553.	−	592534.i	0.160727	−	0.116775i
$482$		0			0
$483$	−4.35754e6	+	3.16594e6i	−0.849912	+	0.617497i
$484$		0			0
$485$	−2.34947e6	−	7.23092e6i	−0.453540	−	1.39585i
$486$		0			0
$487$	474428.	−	1.46014e6i	0.0906458	−	0.278979i	−0.895449	−	0.445165i	$-0.853145\pi$
$487$	474428.	−	1.46014e6i	0.0906458	−	0.278979i	0.986094	+	0.166186i	$0.0531451\pi$
$488$		0			0
$489$	−135350.	−	416565.i	−0.0255968	−	0.0787790i
$490$		0			0
$491$	−2.38069e6			−0.445655			−0.222827	−	0.974858i	$-0.571529\pi$
$491$	−2.38069e6			−0.445655			−0.222827	+	0.974858i	$0.571529\pi$
$492$		0			0
$493$	4.03454e6	−	2.93126e6i	0.747612	−	0.543172i
$494$		0			0
$495$	−2.63810e7			−4.83925
$496$		0			0
$497$	−842911.			−0.153070
$498$		0			0
$499$	3.08363e6	−	2.24039e6i	0.554384	−	0.402784i	−0.275015	−	0.961440i	$-0.588683\pi$
$499$	3.08363e6	−	2.24039e6i	0.554384	−	0.402784i	0.829399	+	0.558656i	$0.188683\pi$
$500$		0			0
$501$	1.09111e7			1.94211
$502$		0			0
$503$	−216949.	−	667701.i	−0.0382329	−	0.117669i	0.930118	−	0.367260i	$-0.119704\pi$
$503$	−216949.	−	667701.i	−0.0382329	−	0.117669i	−0.968351	+	0.249591i	$0.919704\pi$
$504$		0			0
$505$	−3.62938e6	+	1.11701e7i	−0.633292	+	1.94907i
$506$		0			0
$507$	−2.38794e6	−	7.34934e6i	−0.412576	−	1.26978i
$508$		0			0
$509$	596994.	−	433742.i	0.102135	−	0.0742056i	−0.535545	−	0.844506i	$-0.679894\pi$
$509$	596994.	−	433742.i	0.102135	−	0.0742056i	0.637681	+	0.770301i	$0.279894\pi$
$510$		0			0
$511$	−5.06304e6	+	3.67851e6i	−0.857747	+	0.623190i
$512$		0			0
$513$	−3.30714e6	+	1.01783e7i	−0.554829	+	1.70759i
$514$		0			0
$515$	1.39549e7	+	1.01388e7i	2.31851	+	1.68450i
$516$		0			0
$517$	8.19214e6	+	5.95194e6i	1.34794	+	0.979337i
$518$		0			0
$519$	−3.18160e6	+	9.79195e6i	−0.518474	+	1.59570i
$520$		0			0
$521$	758303.			0.122391			0.0611954	−	0.998126i	$-0.480509\pi$
$521$	758303.			0.122391			0.0611954	+	0.998126i	$0.480509\pi$
$522$		0			0
$523$	−2.40674e6	−	7.40719e6i	−0.384747	−	1.18413i	−0.936664	−	0.350230i	$-0.886103\pi$
$523$	−2.40674e6	−	7.40719e6i	−0.384747	−	1.18413i	0.551917	−	0.833899i	$-0.313897\pi$
$524$		0			0
$525$	−9.89549e6	−	7.18949e6i	−1.56689	−	1.13841i
$526$		0			0
$527$	6.53939e6	+	1.01774e6i	1.02568	+	0.159628i
$528$		0			0
$529$	735240.	+	534183.i	0.114233	+	0.0829948i
$530$		0			0
$531$	3.30390e6	+	1.01683e7i	0.508499	+	1.56500i
$532$		0			0
$533$	−2.33127e6			−0.355447
$534$		0			0
$535$	5.49397e6	−	1.69087e7i	0.829855	−	2.55403i
$536$		0			0
$537$	1.45868e7	+	1.05979e7i	2.18285	+	1.58594i
$538$		0			0
$539$	−4.75916e6	−	3.45773e6i	−0.705599	−	0.512648i
$540$		0			0
$541$	2.41122e6	−	7.42096e6i	0.354196	−	1.09010i	−0.602279	−	0.798286i	$-0.705740\pi$
$541$	2.41122e6	−	7.42096e6i	0.354196	−	1.09010i	0.956474	−	0.291816i	$-0.0942596\pi$
$542$		0			0
$543$	−3.41455e6	+	2.48082e6i	−0.496974	+	0.361073i
$544$		0			0
$545$	−3.25485e6	+	2.36479e6i	−0.469397	+	0.341037i
$546$		0			0
$547$	−2.82431e6	−	8.69234e6i	−0.403594	−	1.24213i	−0.922064	−	0.387038i	$-0.873498\pi$
$547$	−2.82431e6	−	8.69234e6i	−0.403594	−	1.24213i	0.518470	−	0.855096i	$-0.326502\pi$
$548$		0			0
$549$	−103847.	+	319610.i	−0.0147050	+	0.0452573i
$550$		0			0
$551$	2.44456e6	+	7.52359e6i	0.343022	+	1.05571i
$552$		0			0
$553$	6.72942e6			0.935760
$554$		0			0
$555$	−7.08296e6	+	5.14607e6i	−0.976074	+	0.709159i
$556$		0			0
$557$	812063.			0.110905			0.0554526	−	0.998461i	$-0.482340\pi$
$557$	812063.			0.110905			0.0554526	+	0.998461i	$0.482340\pi$
$558$		0			0
$559$	2.20162e6			0.297998
$560$		0			0
$561$	1.67815e7	−	1.21925e7i	2.25125	−	1.63563i
$562$		0			0
$563$	3.50634e6			0.466211			0.233105	−	0.972451i	$-0.425111\pi$
$563$	3.50634e6			0.466211			0.233105	+	0.972451i	$0.425111\pi$
$564$		0			0
$565$	−5.54797e6	−	1.70749e7i	−0.731161	−	2.25028i
$566$		0			0
$567$	920038.	−	2.83159e6i	0.120184	−	0.369890i
$568$		0			0
$569$	2.32677e6	+	7.16107e6i	0.301282	+	0.927251i	0.981038	+	0.193813i	$0.0620855\pi$
$569$	2.32677e6	+	7.16107e6i	0.301282	+	0.927251i	−0.679756	+	0.733438i	$0.737914\pi$
$570$		0			0
$571$	2.60569e6	−	1.89314e6i	0.334450	−	0.242992i	−0.407866	−	0.913042i	$-0.633727\pi$
$571$	2.60569e6	−	1.89314e6i	0.334450	−	0.242992i	0.742317	+	0.670049i	$0.233727\pi$
$572$		0			0
$573$	−9.06919e6	+	6.58915e6i	−1.15394	+	0.838384i
$574$		0			0
$575$	3.87891e6	−	1.19381e7i	0.489260	−	1.50579i
$576$		0			0
$577$	2.84653e6	+	2.06813e6i	0.355940	+	0.258605i	0.751357	−	0.659896i	$-0.229400\pi$
$577$	2.84653e6	+	2.06813e6i	0.355940	+	0.258605i	−0.395417	+	0.918502i	$0.629400\pi$
$578$		0			0
$579$	1.59015e6	+	1.15531e6i	0.197125	+	0.143219i
$580$		0			0
$581$	2.92166e6	−	8.99194e6i	0.359078	−	1.10513i
$582$		0			0
$583$	−1.08561e7			−1.32282
$584$		0			0
$585$	−3.56943e6	−	1.09856e7i	−0.431230	−	1.32719i
$586$		0			0
$587$	9.66206e6	+	7.01990e6i	1.15738	+	0.840883i	0.989444	−	0.144915i	$-0.0462909\pi$
$587$	9.66206e6	+	7.01990e6i	1.15738	+	0.840883i	0.167933	+	0.985798i	$0.446291\pi$
$588$		0			0
$589$	−4.74096e6	+	9.36677e6i	−0.563090	+	1.11250i
$590$		0			0
$591$	4.04810e6	+	2.94112e6i	0.476741	+	0.346373i
$592$		0			0
$593$	1.27919e6	+	3.93693e6i	0.149382	+	0.459749i	0.997548	−	0.0699799i	$-0.0222935\pi$
$593$	1.27919e6	+	3.93693e6i	0.149382	+	0.459749i	−0.848167	+	0.529729i	$0.822294\pi$
$594$		0			0
$595$	9.90182e6			1.14663
$596$		0			0
$597$	−4.96354e6	+	1.52762e7i	−0.569975	+	1.75420i
$598$		0			0
$599$	−2.51390e6	−	1.82645e6i	−0.286273	−	0.207990i	0.435376	−	0.900249i	$-0.356616\pi$
$599$	−2.51390e6	−	1.82645e6i	−0.286273	−	0.207990i	−0.721649	+	0.692259i	$0.756616\pi$
$600$		0			0
$601$	1.92636e6	+	1.39959e6i	0.217547	+	0.158057i	0.691222	−	0.722643i	$-0.257073\pi$
$601$	1.92636e6	+	1.39959e6i	0.217547	+	0.158057i	−0.473675	+	0.880700i	$0.657073\pi$
$602$		0			0
$603$	7.28785e6	−	2.24297e7i	0.816218	−	2.51206i
$604$		0			0
$605$	−1.82118e7	+	1.32317e7i	−2.02286	+	1.46969i
$606$		0			0
$607$	−1.05726e7	+	7.68141e6i	−1.16468	+	0.846193i	−0.990363	−	0.138496i	$-0.955773\pi$
$607$	−1.05726e7	+	7.68141e6i	−1.16468	+	0.846193i	−0.174322	+	0.984689i	$0.555773\pi$
$608$		0			0
$609$	−2.85435e6	−	8.78479e6i	−0.311863	−	0.959816i
$610$		0			0
$611$	−1.37008e6	+	4.21668e6i	−0.148472	+	0.456949i
$612$		0			0
$613$	−50272.2	−	154722.i	−0.00540352	−	0.0166303i	0.948318	−	0.317320i	$-0.102783\pi$
$613$	−50272.2	−	154722.i	−0.00540352	−	0.0166303i	−0.953722	+	0.300690i	$0.902783\pi$
$614$		0			0
$615$	2.02468e7			2.15858
$616$		0			0
$617$	−4.33384e6	+	3.14872e6i	−0.458310	+	0.332982i	−0.792868	−	0.609393i	$-0.791413\pi$
$617$	−4.33384e6	+	3.14872e6i	−0.458310	+	0.332982i	0.334558	+	0.942375i	$0.391413\pi$
$618$		0			0
$619$	−1.41681e6			−0.148623			−0.0743115	−	0.997235i	$-0.523676\pi$
$619$	−1.41681e6			−0.148623			−0.0743115	+	0.997235i	$0.523676\pi$
$620$		0			0
$621$	1.28240e7			1.33443
$622$		0			0
$623$	−9.66031e6	+	7.01863e6i	−0.997174	+	0.724489i
$624$		0			0
$625$	2.05505e6			0.210437
$626$		0			0
$627$	1.01681e7	+	3.12941e7i	1.03293	+	3.17902i
$628$		0			0
$629$	1.38153e6	−	4.25191e6i	0.139230	−	0.428506i
$630$		0			0
$631$	−1.85188e6	−	5.69950e6i	−0.185157	−	0.569853i	0.814794	−	0.579750i	$-0.196850\pi$
$631$	−1.85188e6	−	5.69950e6i	−0.185157	−	0.569853i	−0.999951	+	0.00989658i	$0.996850\pi$
$632$		0			0
$633$	−9.23621e6	+	6.71050e6i	−0.916188	+	0.665650i
$634$		0			0
$635$	1.23102e7	−	8.94387e6i	1.21152	−	0.880220i
$636$		0			0
$637$	795939.	−	2.44965e6i	0.0777197	−	0.239197i
$638$		0			0
$639$	3.52796e6	+	2.56321e6i	0.341799	+	0.248332i
$640$		0			0
$641$	−2.20751e6	−	1.60385e6i	−0.212206	−	0.154176i	0.476606	−	0.879117i	$-0.341867\pi$
$641$	−2.20751e6	−	1.60385e6i	−0.212206	−	0.154176i	−0.688811	+	0.724941i	$0.741867\pi$
$642$		0			0
$643$	299728.	−	922467.i	0.0285890	−	0.0879880i	−0.935744	−	0.352680i	$-0.885270\pi$
$643$	299728.	−	922467.i	0.0285890	−	0.0879880i	0.964333	+	0.264692i	$0.0852704\pi$
$644$		0			0
$645$	−1.91208e7			−1.80970
$646$		0			0
$647$	−139635.	−	429753.i	−0.0131140	−	0.0403606i	0.944285	−	0.329128i	$-0.106755\pi$
$647$	−139635.	−	429753.i	−0.0131140	−	0.0403606i	−0.957399	+	0.288767i	$0.906755\pi$
$648$		0			0
$649$	1.22389e7	+	8.89209e6i	1.14059	+	0.828690i
$650$		0			0
$651$	5.53569e6	−	1.09369e7i	0.511941	−	1.01145i
$652$		0			0
$653$	4.77836e6	+	3.47168e6i	0.438527	+	0.318608i	0.785049	−	0.619433i	$-0.212638\pi$
$653$	4.77836e6	+	3.47168e6i	0.438527	+	0.318608i	−0.346523	+	0.938042i	$0.612638\pi$
$654$		0			0
$655$	−85444.6	−	262972.i	−0.00778183	−	0.0239500i
$656$		0			0
$657$	3.23771e7			2.92634
$658$		0			0
$659$	−5.15107e6	+	1.58534e7i	−0.462045	+	1.42203i	0.400617	+	0.916246i	$0.368796\pi$
$659$	−5.15107e6	+	1.58534e7i	−0.462045	+	1.42203i	−0.862661	+	0.505782i	$0.831204\pi$
$660$		0			0
$661$	−1.21323e7	−	8.81464e6i	−1.08004	−	0.784695i	−0.102350	−	0.994748i	$-0.532636\pi$
$661$	−1.21323e7	−	8.81464e6i	−1.08004	−	0.784695i	−0.977690	+	0.210054i	$0.932636\pi$
$662$		0			0
$663$	7.34777e6	+	5.33846e6i	0.649190	+	0.471664i
$664$		0			0
$665$	−4.85378e6	+	1.49384e7i	−0.425624	+	1.30993i
$666$		0			0
$667$	7.66885e6	−	5.57174e6i	0.667445	−	0.484927i
$668$		0			0
$669$	−8.59653e6	+	6.24574e6i	−0.742605	+	0.539534i
$670$		0			0
$671$	146939.	+	452232.i	0.0125988	+	0.0387752i
$672$		0			0
$673$	3.13440e6	−	9.64669e6i	0.266758	−	0.820995i	−0.724526	−	0.689248i	$-0.757941\pi$
$673$	3.13440e6	−	9.64669e6i	0.266758	−	0.820995i	0.991283	−	0.131748i	$-0.0420588\pi$
$674$		0			0
$675$	8.99915e6	+	2.76965e7i	0.760225	+	2.33973i
$676$		0			0
$677$	−1.00296e7			−0.841031			−0.420515	−	0.907285i	$-0.638151\pi$
$677$	−1.00296e7			−0.841031			−0.420515	+	0.907285i	$0.638151\pi$
$678$		0			0
$679$	5.81773e6	−	4.22683e6i	0.484261	−	0.351836i
$680$		0			0
$681$	−1.54599e7			−1.27744
$682$		0			0
$683$	−1.72101e7			−1.41167			−0.705833	−	0.708378i	$-0.749427\pi$
$683$	−1.72101e7			−1.41167			−0.705833	+	0.708378i	$0.749427\pi$
$684$		0			0
$685$	2.27637e7	−	1.65388e7i	1.85360	−	1.34672i
$686$		0			0
$687$	3.02730e7			2.44717
$688$		0			0
$689$	−1.46886e6	−	4.52069e6i	−0.117878	−	0.362791i
$690$		0			0
$691$	−659314.	+	2.02916e6i	−0.0525288	+	0.161667i	−0.973880	−	0.227065i	$-0.927087\pi$
$691$	−659314.	+	2.02916e6i	−0.0525288	+	0.161667i	0.921351	+	0.388732i	$0.127087\pi$
$692$		0			0
$693$	−7.71050e6	−	2.37305e7i	−0.609887	−	1.87704i
$694$		0			0
$695$	−2.40118e7	+	1.74456e7i	−1.88566	+	1.37001i
$696$		0			0
$697$	−8.36438e6	+	6.07708e6i	−0.652156	+	0.473819i
$698$		0			0
$699$	7.07604e6	−	2.17778e7i	0.547769	−	1.68586i
$700$		0			0
$701$	−1.93968e7	−	1.40926e7i	−1.49086	−	1.08317i	−0.973851	−	0.227188i	$-0.927047\pi$
$701$	−1.93968e7	−	1.40926e7i	−1.49086	−	1.08317i	−0.517005	−	0.855982i	$-0.672953\pi$
$702$		0			0
$703$	5.73743e6	+	4.16849e6i	0.437854	+	0.318120i
$704$		0			0
$705$	1.18990e7	−	3.66213e7i	0.901648	−	2.77499i
$706$		0			0
$707$	−1.11086e7			−0.835815
$708$		0			0
$709$	3.13045e6	+	9.63453e6i	0.233879	+	0.719805i	0.997268	+	0.0738663i	$0.0235338\pi$
$709$	3.13045e6	+	9.63453e6i	0.233879	+	0.719805i	−0.763389	+	0.645939i	$0.776466\pi$
$710$		0			0
$711$	−2.81656e7	−	2.04635e7i	−2.08951	−	1.51812i
$712$		0			0
$713$	1.24301e7	+	1.93451e6i	0.915692	+	0.142511i
$714$		0			0
$715$	−1.32225e7	−	9.60673e6i	−0.967274	−	0.702766i
$716$		0			0
$717$	6.20147e6	+	1.90862e7i	0.450502	+	1.38650i
$718$		0			0
$719$	−2.18439e7			−1.57583			−0.787913	−	0.615787i	$-0.788838\pi$
$719$	−2.18439e7			−1.57583			−0.787913	+	0.615787i	$0.788838\pi$
$720$		0			0
$721$	−5.04151e6	+	1.55162e7i	−0.361179	+	1.11159i
$722$		0			0
$723$	−3.46499e7	−	2.51746e7i	−2.46522	−	1.79109i
$724$		0			0
$725$	1.74151e7	+	1.26528e7i	1.23050	+	0.894008i
$726$		0			0
$727$	−5.69539e6	+	1.75286e7i	−0.399657	+	1.23002i	0.525618	+	0.850721i	$0.323834\pi$
$727$	−5.69539e6	+	1.75286e7i	−0.399657	+	1.23002i	−0.925275	+	0.379297i	$0.876166\pi$
$728$		0			0
$729$	1.57708e7	−	1.14581e7i	1.09909	−	0.798536i
$730$		0			0
$731$	7.89919e6	−	5.73910e6i	0.546751	−	0.397238i
$732$		0			0
$733$	−6.70308e6	−	2.06300e7i	−0.460802	−	1.41820i	−0.864186	−	0.503173i	$-0.832166\pi$
$733$	−6.70308e6	−	2.06300e7i	−0.460802	−	1.41820i	0.403384	−	0.915031i	$-0.367834\pi$
$734$		0			0
$735$	−6.91262e6	+	2.12748e7i	−0.471981	+	1.45261i
$736$		0			0
$737$	−1.03119e7	−	3.17369e7i	−0.699313	−	2.15226i
$738$		0			0
$739$	−2.08603e7			−1.40511			−0.702555	−	0.711630i	$-0.747957\pi$
$739$	−2.08603e7			−1.40511			−0.702555	+	0.711630i	$0.747957\pi$
$740$		0			0
$741$	−1.16557e7	+	8.46835e6i	−0.779817	+	0.566570i
$742$		0			0
$743$	−1.24362e7			−0.826447			−0.413223	−	0.910630i	$-0.635597\pi$
$743$	−1.24362e7			−0.826447			−0.413223	+	0.910630i	$0.635597\pi$
$744$		0			0
$745$	7.46562e6			0.492805
$746$		0			0
$747$	−3.95721e7	+	2.87508e7i	−2.59470	+	1.88516i
$748$		0			0
$749$	1.68156e7			1.09524
$750$		0			0
$751$	−1.98666e6	−	6.11430e6i	−0.128536	−	0.395592i	0.865993	−	0.500056i	$-0.166687\pi$
$751$	−1.98666e6	−	6.11430e6i	−0.128536	−	0.395592i	−0.994529	+	0.104464i	$0.966687\pi$
$752$		0			0
$753$	1.11897e7	−	3.44382e7i	0.719166	−	2.21337i
$754$		0			0
$755$	7.79671e6	+	2.39958e7i	0.497788	+	1.53203i
$756$		0			0
$757$	−1.18273e6	+	859304.i	−0.0750147	+	0.0545014i	−0.624661	−	0.780896i	$-0.714763\pi$
$757$	−1.18273e6	+	859304.i	−0.0750147	+	0.0545014i	0.549646	+	0.835398i	$0.314763\pi$
$758$		0			0
$759$	3.18982e7	−	2.31754e7i	2.00984	−	1.46024i
$760$		0			0
$761$	690805.	−	2.12608e6i	0.0432408	−	0.133081i	−0.927105	−	0.374800i	$-0.877711\pi$
$761$	690805.	−	2.12608e6i	0.0432408	−	0.133081i	0.970346	+	0.241719i	$0.0777112\pi$
$762$		0			0
$763$	−3.07851e6	−	2.23667e6i	−0.191438	−	0.139088i
$764$		0			0
$765$	−4.14435e7	−	3.01105e7i	−2.56037	−	1.86022i
$766$		0			0
$767$	−2.04688e6	+	6.29964e6i	−0.125633	+	0.386659i
$768$		0			0
$769$	2.30960e6			0.140838			0.0704191	−	0.997517i	$-0.477566\pi$
$769$	2.30960e6			0.140838			0.0704191	+	0.997517i	$0.477566\pi$
$770$		0			0
$771$	−4.54832e6	−	1.39983e7i	−0.275559	−	0.848084i
$772$		0			0
$773$	−5.24266e6	−	3.80901e6i	−0.315575	−	0.229279i	0.418710	−	0.908120i	$-0.362482\pi$
$773$	−5.24266e6	−	3.80901e6i	−0.315575	−	0.229279i	−0.734285	+	0.678841i	$0.762482\pi$
$774$		0			0
$775$	4.54465e6	+	2.82032e7i	0.271798	+	1.68673i
$776$		0			0
$777$	−6.69921e6	−	4.86726e6i	−0.398081	−	0.289223i
$778$		0			0
$779$	−5.06805e6	−	1.55979e7i	−0.299225	−	0.920919i
$780$		0			0
$781$	6.17031e6			0.361975
$782$		0			0
$783$	−6.79590e6	+	2.09156e7i	−0.396134	+	1.21918i
$784$		0			0
$785$	−2.62930e7	−	1.91030e7i	−1.52288	−	1.10644i
$786$		0			0
$787$	−1.31585e7	−	9.56018e6i	−0.757301	−	0.550211i	0.140781	−	0.990041i	$-0.455039\pi$
$787$	−1.31585e7	−	9.56018e6i	−0.757301	−	0.550211i	−0.898081	+	0.439830i	$0.855039\pi$
$788$		0			0
$789$	4.88314e6	−	1.50288e7i	0.279259	−	0.859470i
$790$		0			0
$791$	1.37378e7	−	9.98112e6i	0.780687	−	0.567202i
$792$		0			0
$793$	−168437.	+	122376.i	−0.00951161	+	0.00691059i
$794$		0			0
$795$	1.27568e7	+	3.92615e7i	0.715856	+	2.20318i
$796$		0			0
$797$	−8.73726e6	+	2.68905e7i	−0.487225	+	1.49952i	0.341508	+	0.939879i	$0.389062\pi$
$797$	−8.73726e6	+	2.68905e7i	−0.487225	+	1.49952i	−0.828733	+	0.559644i	$0.810938\pi$
$798$		0			0
$799$	6.07617e6	+	1.87005e7i	0.336715	+	1.03630i
$800$		0			0
$801$	6.17757e7			3.40201
$802$		0			0
$803$	3.70626e7	−	2.69276e7i	2.02837	−	1.47370i
$804$		0			0
$805$	1.88214e7			1.02367
$806$		0			0
$807$	4.21589e7			2.27879
$808$		0			0
$809$	−1.17431e7	+	8.53183e6i	−0.630826	+	0.458322i	−0.856686	−	0.515838i	$-0.827481\pi$
$809$	−1.17431e7	+	8.53183e6i	−0.630826	+	0.458322i	0.225860	+	0.974160i	$0.427481\pi$
$810$		0			0
$811$	−1.18842e7			−0.634482			−0.317241	−	0.948345i	$-0.602756\pi$
$811$	−1.18842e7			−0.634482			−0.317241	+	0.948345i	$0.602756\pi$
$812$		0			0
$813$	8.95404e6	+	2.75577e7i	0.475108	+	1.46223i
$814$		0			0
$815$	−472961.	+	1.45562e6i	−0.0249420	+	0.0767636i
$816$		0			0
$817$	4.78619e6	+	1.47304e7i	0.250862	+	0.772074i
$818$		0			0
$819$	8.83858e6	−	6.42160e6i	0.460440	−	0.334529i
$820$		0			0
$821$	−2.93998e7	+	2.13602e7i	−1.52225	+	1.10598i	−0.561891	+	0.827211i	$0.689926\pi$
$821$	−2.93998e7	+	2.13602e7i	−1.52225	+	1.10598i	−0.960359	+	0.278768i	$0.910074\pi$
$822$		0			0
$823$	−4.30367e6	+	1.32453e7i	−0.221483	+	0.681654i	0.777147	+	0.629319i	$0.216666\pi$
$823$	−4.30367e6	+	1.32453e7i	−0.221483	+	0.681654i	−0.998630	+	0.0523344i	$0.983334\pi$
$824$		0			0
$825$	7.24373e7	+	5.26288e7i	3.70533	+	2.69208i
$826$		0			0
$827$	1.51525e7	+	1.10089e7i	0.770408	+	0.559734i	0.902085	−	0.431558i	$-0.142036\pi$
$827$	1.51525e7	+	1.10089e7i	0.770408	+	0.559734i	−0.131677	+	0.991293i	$0.542036\pi$
$828$		0			0
$829$	−1.06015e7	+	3.26279e7i	−0.535771	+	1.64893i	0.206205	+	0.978509i	$0.433888\pi$
$829$	−1.06015e7	+	3.26279e7i	−0.535771	+	1.64893i	−0.741977	+	0.670426i	$0.766112\pi$
$830$		0			0
$831$	1.20428e7			0.604958
$832$		0			0
$833$	−3.52990e6	−	1.08639e7i	−0.176258	−	0.542468i
$834$		0			0
$835$	−3.08456e7	−	2.24106e7i	−1.53100	−	1.11234i
$836$		0			0
$837$	−2.59685e7	+	1.33196e7i	−1.28125	+	0.657169i
$838$		0			0
$839$	1.21668e7	+	8.83969e6i	0.596721	+	0.433543i	0.844713	−	0.535219i	$-0.179771\pi$
$839$	1.21668e7	+	8.83969e6i	0.596721	+	0.433543i	−0.247993	+	0.968762i	$0.579771\pi$
$840$		0			0
$841$	−1.31492e6	−	4.04691e6i	−0.0641076	−	0.197303i
$842$		0			0
$843$	−3.96703e7			−1.92264
$844$		0			0
$845$	−8.34432e6	+	2.56812e7i	−0.402022	+	1.23730i
$846$		0			0
$847$	−1.72251e7	−	1.25148e7i	−0.825001	−	0.599398i
$848$		0			0
$849$	−2.61865e7	−	1.90256e7i	−1.24683	−	0.905876i
$850$		0			0
$851$	2.62601e6	−	8.08202e6i	0.124300	−	0.382557i
$852$		0			0
$853$	5.58440e6	−	4.05730e6i	0.262787	−	0.190926i	−0.448588	−	0.893739i	$-0.648073\pi$
$853$	5.58440e6	−	4.05730e6i	0.262787	−	0.190926i	0.711375	+	0.702813i	$0.248073\pi$
$854$		0			0
$855$	6.57414e7	−	4.77639e7i	3.07556	−	2.23452i
$856$		0			0
$857$	2.78372e6	+	8.56742e6i	0.129472	+	0.398472i	0.994689	−	0.102924i	$-0.0328198\pi$
$857$	2.78372e6	+	8.56742e6i	0.129472	+	0.398472i	−0.865218	+	0.501396i	$0.832820\pi$
$858$		0			0
$859$	−5.04893e6	+	1.55390e7i	−0.233462	+	0.718523i	0.763859	+	0.645383i	$0.223302\pi$
$859$	−5.04893e6	+	1.55390e7i	−0.233462	+	0.718523i	−0.997322	+	0.0731403i	$0.976698\pi$
$860$		0			0
$861$	5.91762e6	+	1.82126e7i	0.272044	+	0.837266i
$862$		0			0
$863$	−2.77704e6			−0.126927			−0.0634636	−	0.997984i	$-0.520215\pi$
$863$	−2.77704e6			−0.126927			−0.0634636	+	0.997984i	$0.520215\pi$
$864$		0			0
$865$	2.91063e7	−	2.11470e7i	1.32266	−	0.960966i
$866$		0			0
$867$	2.89688e6			0.130883
$868$		0			0
$869$	−4.92609e7			−2.21285
$870$		0			0
$871$	1.18206e7	−	8.58818e6i	0.527952	−	0.383580i
$872$		0			0
$873$	−3.72032e7			−1.65213
$874$		0			0
$875$	5.47707e6	+	1.68567e7i	0.241840	+	0.744307i
$876$		0			0
$877$	1.14838e7	−	3.53436e7i	0.504182	−	1.55171i	−0.297958	−	0.954579i	$-0.596306\pi$
$877$	1.14838e7	−	3.53436e7i	0.504182	−	1.55171i	0.802141	−	0.597135i	$-0.203694\pi$
$878$		0			0
$879$	−6.75619e6	−	2.07934e7i	−0.294937	−	0.907723i
$880$		0			0
$881$	9.41929e6	−	6.84351e6i	0.408863	−	0.297057i	−0.364278	−	0.931290i	$-0.618684\pi$
$881$	9.41929e6	−	6.84351e6i	0.408863	−	0.297057i	0.773141	+	0.634234i	$0.218684\pi$
$882$		0			0
$883$	−1.35344e7	+	9.83334e6i	−0.584168	+	0.424423i	−0.840224	−	0.542239i	$-0.817577\pi$
$883$	−1.35344e7	+	9.83334e6i	−0.584168	+	0.424423i	0.256056	+	0.966662i	$0.417577\pi$
$884$		0			0
$885$	1.77769e7	−	5.47115e7i	0.762951	−	2.34812i
$886$		0			0
$887$	1.93918e7	+	1.40890e7i	0.827580	+	0.601272i	0.918874	−	0.394552i	$-0.129100\pi$
$887$	1.93918e7	+	1.40890e7i	0.827580	+	0.601272i	−0.0912935	+	0.995824i	$0.529100\pi$
$888$		0			0
$889$	1.16432e7	+	8.45930e6i	0.494105	+	0.358988i
$890$		0			0
$891$	−6.73490e6	+	2.07279e7i	−0.284208	+	0.874703i
$892$		0			0
$893$	−3.11910e7			−1.30888
$894$		0			0
$895$	−1.94694e7	−	5.99206e7i	−0.812446	−	2.50045i
$896$		0			0
$897$	1.39666e7	+	1.01473e7i	0.579576	+	0.421087i
$898$		0			0
$899$	−9.74227e6	+	1.92479e7i	−0.402032	+	0.794301i
$900$		0			0
$901$	−1.70545e7	−	1.23908e7i	−0.699885	−	0.508496i
$902$		0			0
$903$	−5.58851e6	−	1.71997e7i	−0.228075	−	0.701941i
$904$		0			0
$905$	1.47483e7			0.598579
$906$		0			0
$907$	6.64526e6	−	2.04520e7i	0.268221	−	0.825501i	−0.722712	−	0.691149i	$-0.757105\pi$
$907$	6.64526e6	−	2.04520e7i	0.268221	−	0.825501i	0.990934	−	0.134352i	$-0.0428952\pi$
$908$		0			0
$909$	4.64944e7	+	3.37801e7i	1.86634	+	1.35597i
$910$		0			0
$911$	2.94967e7	+	2.14306e7i	1.17755	+	0.855537i	0.991893	−	0.127078i	$-0.0405599\pi$
$911$	2.94967e7	+	2.14306e7i	1.17755	+	0.855537i	0.185653	+	0.982615i	$0.440560\pi$
$912$		0			0
$913$	−2.13872e7	+	6.58231e7i	−0.849136	+	2.61337i
$914$		0			0
$915$	1.46285e6	−	1.06282e6i	0.0577626	−	0.0419670i
$916$		0			0
$917$	211577.	−	153720.i	0.00830894	−	0.00603680i
$918$		0			0
$919$	1.35041e6	+	4.15613e6i	0.0527444	+	0.162330i	0.973959	−	0.226724i	$-0.0728017\pi$
$919$	1.35041e6	+	4.15613e6i	0.0527444	+	0.162330i	−0.921215	+	0.389055i	$0.872802\pi$
$920$		0			0
$921$	−4.05183e6	+	1.24703e7i	−0.157399	+	0.484425i
$922$		0			0
$923$	834860.	+	2.56944e6i	0.0322559	+	0.0992735i
$924$		0			0
$925$	1.92979e7			0.741574
$926$		0			0
$927$	6.82841e7	−	4.96113e7i	2.60988	−	1.89619i
$928$		0			0
$929$	1.31305e7			0.499163			0.249582	−	0.968354i	$-0.419707\pi$
$929$	1.31305e7			0.499163			0.249582	+	0.968354i	$0.419707\pi$
$930$		0			0
$931$	1.81202e7			0.685154
$932$		0			0
$933$	3.93030e7	−	2.85553e7i	1.47816	−	1.07395i
$934$		0			0
$935$	−7.24836e7			−2.71151
$936$		0			0
$937$	−7.70490e6	−	2.37132e7i	−0.286694	−	0.882352i	−0.985886	−	0.167419i	$-0.946457\pi$
$937$	−7.70490e6	−	2.37132e7i	−0.286694	−	0.882352i	0.699192	−	0.714934i	$-0.253543\pi$
$938$		0			0
$939$	1.20054e7	−	3.69488e7i	0.444337	−	1.36753i
$940$		0			0
$941$	3.90480e6	+	1.20177e7i	0.143756	+	0.442434i	0.996849	−	0.0793241i	$-0.0252762\pi$
$941$	3.90480e6	+	1.20177e7i	0.143756	+	0.442434i	−0.853093	+	0.521759i	$0.825276\pi$
$942$		0			0
$943$	−1.58990e7	+	1.15513e7i	−0.582225	+	0.423011i
$944$		0			0
$945$	−3.53265e7	+	2.56662e7i	−1.28683	+	0.934937i
$946$		0			0
$947$	−1.01647e7	+	3.12836e7i	−0.368314	+	1.13355i	0.579566	+	0.814926i	$0.303222\pi$
$947$	−1.01647e7	+	3.12836e7i	−0.368314	+	1.13355i	−0.947880	+	0.318628i	$0.896778\pi$
$948$		0			0
$949$	1.62279e7	+	1.17902e7i	0.584919	+	0.424968i
$950$		0			0
$951$	−5.16743e7	−	3.75436e7i	−1.85278	−	1.34612i
$952$		0			0
$953$	1.05996e6	−	3.26222e6i	0.0378057	−	0.116354i	−0.930373	−	0.366615i	$-0.880517\pi$
$953$	1.05996e6	−	3.26222e6i	0.0378057	−	0.116354i	0.968178	+	0.250261i	$0.0805165\pi$
$954$		0			0
$955$	3.91722e7			1.38985
$956$		0			0
$957$	2.08945e7	+	6.43067e7i	0.737484	+	2.26974i
$958$		0			0
$959$	2.15303e7	+	1.56427e7i	0.755969	+	0.549244i
$960$		0			0
$961$	−2.71800e7	+	8.99305e6i	−0.949383	+	0.314122i
$962$		0			0
$963$	−7.03809e7	−	5.11347e7i	−2.44562	−	1.77685i
$964$		0			0
$965$	−2.12241e6	−	6.53210e6i	−0.0733686	−	0.225805i
$966$		0			0
$967$	2.68178e6			0.0922266			0.0461133	−	0.998936i	$-0.485316\pi$
$967$	2.68178e6			0.0922266			0.0461133	+	0.998936i	$0.485316\pi$
$968$		0			0
$969$	−1.97445e7	+	6.07672e7i	−0.675517	+	2.07903i
$970$		0			0
$971$	2.76124e6	+	2.00616e6i	0.0939845	+	0.0682837i	0.633785	−	0.773509i	$-0.281500\pi$
$971$	2.76124e6	+	2.00616e6i	0.0939845	+	0.0682837i	−0.539801	+	0.841793i	$0.681500\pi$
$972$		0			0
$973$	−2.27109e7	−	1.65004e7i	−0.769045	−	0.558744i
$974$		0			0
$975$	−1.21147e7	+	3.72851e7i	−0.408132	+	1.25610i
$976$		0			0
$977$	4.00465e7	−	2.90955e7i	1.34224	−	0.975191i	0.342877	−	0.939380i	$-0.388599\pi$
$977$	4.00465e7	−	2.90955e7i	1.34224	−	0.975191i	0.999359	−	0.0358106i	$-0.0114013\pi$
$978$		0			0
$979$	7.07157e7	−	5.13780e7i	2.35808	−	1.71325i
$980$		0			0
$981$	6.08344e6	+	1.87229e7i	0.201826	+	0.621156i
$982$		0			0
$983$	−7.25715e6	+	2.23352e7i	−0.239542	+	0.737235i	0.756944	+	0.653480i	$0.226691\pi$
$983$	−7.25715e6	+	2.23352e7i	−0.239542	+	0.737235i	−0.996486	+	0.0837555i	$0.973309\pi$
$984$		0			0
$985$	−5.40310e6	−	1.66290e7i	−0.177440	−	0.546106i
$986$		0			0
$987$	3.64197e7			1.18999
$988$		0			0
$989$	1.50148e7	−	1.09089e7i	0.488122	−	0.354641i
$990$		0			0
$991$	4.34729e7			1.40616			0.703079	−	0.711111i	$-0.251808\pi$
$991$	4.34729e7			1.40616			0.703079	+	0.711111i	$0.251808\pi$
$992$		0			0
$993$	9.71020e6			0.312503
$994$		0			0
$995$	4.54082e7	−	3.29910e7i	1.45404	−	1.05642i
$996$		0			0
$997$	6.17903e7			1.96871			0.984357	−	0.176188i	$-0.0563766\pi$
$997$	6.17903e7			1.96871			0.984357	+	0.176188i	$0.0563766\pi$
$998$		0			0
$999$	6.09240e6	+	1.87505e7i	0.193141	+	0.594427i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	124.6.f.a.33.2	✓	56
31.16	even	5	inner	124.6.f.a.109.2	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
124.6.f.a.33.2	✓	56	1.1	even	1	trivial
124.6.f.a.109.2	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)

\(f(q)\)	\(=\)	\(q+(-21.3000 + 15.4753i) q^{3} +92.0001 q^{5} +(26.8893 + 82.7567i) q^{7} +(139.112 - 428.142i) q^{9} +O(q^{10})\)	\(q+(-21.3000 + 15.4753i) q^{3} +92.0001 q^{5} +(26.8893 + 82.7567i) q^{7} +(139.112 - 428.142i) q^{9} +(-196.836 - 605.799i) q^{11} +(225.634 - 163.933i) q^{13} +(-1959.60 + 1423.73i) q^{15} +(382.219 - 1176.35i) q^{17} +(1587.34 + 1153.27i) q^{19} +(-1853.43 - 1346.60i) q^{21} +(726.521 - 2236.00i) q^{23} +5339.02 q^{25} +(1685.54 + 5187.57i) q^{27} +(3261.85 + 2369.87i) q^{29} +(851.215 + 5282.48i) q^{31} +(13567.5 + 9857.39i) q^{33} +(2473.82 + 7613.63i) q^{35} +3614.50 q^{37} +(-2269.08 + 6983.52i) q^{39} +(-6762.45 - 4913.21i) q^{41} +(6386.36 + 4639.96i) q^{43} +(12798.3 - 39389.1i) q^{45} +(-12861.0 + 9344.07i) q^{47} +(7471.51 - 5428.37i) q^{49} +(10063.1 + 30971.1i) q^{51} +(5266.64 - 16209.1i) q^{53} +(-18108.9 - 55733.5i) q^{55} -51657.5 q^{57} +(-19214.1 + 13959.9i) q^{59} -746.505 q^{61} +39172.2 q^{63} +(20758.3 - 15081.8i) q^{65} +52388.5 q^{67} +(19128.0 + 58869.9i) q^{69} +(-2993.42 + 9212.79i) q^{71} +(22224.9 + 68401.1i) q^{73} +(-113721. + 82623.1i) q^{75} +(44841.1 - 32579.0i) q^{77} +(23898.1 - 73550.7i) q^{79} +(-27681.1 - 20111.5i) q^{81} +(-87903.8 - 63865.8i) q^{83} +(35164.2 - 108224. i) q^{85} -106152. q^{87} +(42405.2 + 130510. i) q^{89} +(19633.7 + 14264.7i) q^{91} +(-99879.0 - 99343.8i) q^{93} +(146035. + 106101. i) q^{95} +(-25537.7 - 78596.9i) q^{97} -286750. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 2 q^{3} - 58 q^{5} + 104 q^{7} - 1234 q^{9}+O(q^{10}) \) 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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