LMFDB - Embedded newform 124.6.f.a.97.1

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			97.1
Character	$\chi$	$=$	124.97
Dual form			124.6.f.a.101.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-8.98126 + 27.6415i) q^{3} -66.9725 q^{5} +(161.853 - 117.593i) q^{7} +(-486.797 - 353.679i) q^{9} +O(q^{10})$	\(q+(-8.98126 + 27.6415i) q^{3} -66.9725 q^{5} +(161.853 - 117.593i) q^{7} +(-486.797 - 353.679i) q^{9} +(330.253 - 239.943i) q^{11} +(-52.8570 + 162.677i) q^{13} +(601.498 - 1851.22i) q^{15} +(-853.146 - 619.847i) q^{17} +(-165.095 - 508.110i) q^{19} +(1796.80 + 5529.97i) q^{21} +(2844.20 + 2066.43i) q^{23} +1360.32 q^{25} +(8434.54 - 6128.05i) q^{27} +(-421.602 - 1297.56i) q^{29} +(-2636.30 + 4656.08i) q^{31} +(3666.29 + 11283.7i) q^{33} +(-10839.7 + 7875.49i) q^{35} +11293.3 q^{37} +(-4021.91 - 2922.09i) q^{39} +(-6199.77 - 19080.9i) q^{41} +(3412.56 + 10502.8i) q^{43} +(32602.0 + 23686.8i) q^{45} +(7545.52 - 23222.7i) q^{47} +(7174.54 - 22081.0i) q^{49} +(24795.8 - 18015.2i) q^{51} +(7365.48 + 5351.33i) q^{53} +(-22117.9 + 16069.6i) q^{55} +15527.7 q^{57} +(12113.3 - 37280.8i) q^{59} +32765.0 q^{61} -120379. q^{63} +(3539.97 - 10894.9i) q^{65} -8859.53 q^{67} +(-82663.7 + 60058.7i) q^{69} +(-44404.4 - 32261.7i) q^{71} +(27202.2 - 19763.5i) q^{73} +(-12217.4 + 37601.3i) q^{75} +(25236.8 - 77670.8i) q^{77} +(66707.5 + 48465.9i) q^{79} +(48452.2 + 149120. i) q^{81} +(2765.73 + 8512.05i) q^{83} +(57137.4 + 41512.7i) q^{85} +39652.9 q^{87} +(-60402.9 + 43885.3i) q^{89} +(10574.6 + 32545.3i) q^{91} +(-105024. - 114689. i) q^{93} +(11056.8 + 34029.4i) q^{95} +(-39242.2 + 28511.1i) q^{97} -245629. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/124\mathbb{Z}\right)^\times$.

$n$	$63$	$65$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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
$3$	−8.98126	+	27.6415i	−0.576148	+	1.77320i	0.0560880	+	0.998426i	$0.482137\pi$
$3$	−8.98126	+	27.6415i	−0.576148	+	1.77320i	−0.632236	+	0.774776i	$0.717863\pi$
$4$		0			0
$5$	−66.9725			−1.19804			−0.599021	−	0.800734i	$-0.704443\pi$
$5$	−66.9725			−1.19804			−0.599021	+	0.800734i	$0.704443\pi$
$6$		0			0
$7$	161.853	−	117.593i	1.24846	−	0.907059i	0.250328	−	0.968161i	$-0.419462\pi$
$7$	161.853	−	117.593i	1.24846	−	0.907059i	0.998132	+	0.0611022i	$0.0194616\pi$
$8$		0			0
$9$	−486.797	−	353.679i	−2.00328	−	1.45547i
$10$		0			0
$11$	330.253	−	239.943i	0.822934	−	0.597897i	−0.0946171	−	0.995514i	$-0.530163\pi$
$11$	330.253	−	239.943i	0.822934	−	0.597897i	0.917552	+	0.397617i	$0.130163\pi$
$12$		0			0
$13$	−52.8570	+	162.677i	−0.0867449	+	0.266973i	−0.985015	−	0.172471i	$-0.944825\pi$
$13$	−52.8570	+	162.677i	−0.0867449	+	0.266973i	0.898270	+	0.439445i	$0.144825\pi$
$14$		0			0
$15$	601.498	−	1851.22i	0.690249	−	2.12437i
$16$		0			0
$17$	−853.146	−	619.847i	−0.715981	−	0.520190i	0.169117	−	0.985596i	$-0.445908\pi$
$17$	−853.146	−	619.847i	−0.715981	−	0.520190i	−0.885098	+	0.465406i	$0.845908\pi$
$18$		0			0
$19$	−165.095	−	508.110i	−0.104918	−	0.322904i	0.884793	−	0.465984i	$-0.154299\pi$
$19$	−165.095	−	508.110i	−0.104918	−	0.322904i	−0.989711	+	0.143080i	$0.954299\pi$
$20$		0			0
$21$	1796.80	+	5529.97i	0.889101	+	2.73637i
$22$		0			0
$23$	2844.20	+	2066.43i	1.12109	+	0.814519i	0.984374	−	0.176091i	$-0.0563454\pi$
$23$	2844.20	+	2066.43i	1.12109	+	0.814519i	0.136715	+	0.990610i	$0.456345\pi$
$24$		0			0
$25$	1360.32			0.435303
$26$		0			0
$27$	8434.54	−	6128.05i	2.22665	−	1.61776i
$28$		0			0
$29$	−421.602	−	1297.56i	−0.0930910	−	0.286505i	0.893660	−	0.448744i	$-0.148128\pi$
$29$	−421.602	−	1297.56i	−0.0930910	−	0.286505i	−0.986751	+	0.162239i	$0.948128\pi$
$30$		0			0
$31$	−2636.30	+	4656.08i	−0.492709	+	0.870194i
$31$	−2636.30	+	4656.08i	−0.492709	+	0.870194i
$32$		0			0
$33$	3666.29	+	11283.7i	0.586060	+	1.80371i
$34$		0			0
$35$	−10839.7	+	7875.49i	−1.49571	+	1.08669i
$36$		0			0
$37$	11293.3			1.35618			0.678089	−	0.734980i	$-0.262808\pi$
$37$	11293.3			1.35618			0.678089	+	0.734980i	$0.262808\pi$
$38$		0			0
$39$	−4021.91	−	2922.09i	−0.423420	−	0.307632i
$40$		0			0
$41$	−6199.77	−	19080.9i	−0.575991	−	1.77272i	−0.632779	−	0.774333i	$-0.718086\pi$
$41$	−6199.77	−	19080.9i	−0.575991	−	1.77272i	0.0567873	−	0.998386i	$-0.481914\pi$
$42$		0			0
$43$	3412.56	+	10502.8i	0.281455	+	0.866230i	0.987439	+	0.158002i	$0.0505051\pi$
$43$	3412.56	+	10502.8i	0.281455	+	0.866230i	−0.705984	+	0.708228i	$0.749495\pi$
$44$		0			0
$45$	32602.0	+	23686.8i	2.40001	+	1.74371i
$46$		0			0
$47$	7545.52	−	23222.7i	0.498247	−	1.53345i	−0.313588	−	0.949559i	$-0.601531\pi$
$47$	7545.52	−	23222.7i	0.498247	−	1.53345i	0.811835	−	0.583887i	$-0.198469\pi$
$48$		0			0
$49$	7174.54	−	22081.0i	0.426878	−	1.31380i
$50$		0			0
$51$	24795.8	−	18015.2i	1.33491	−	0.969871i
$52$		0			0
$53$	7365.48	+	5351.33i	0.360173	+	0.261681i	0.753124	−	0.657878i	$-0.228546\pi$
$53$	7365.48	+	5351.33i	0.360173	+	0.261681i	−0.392951	+	0.919559i	$0.628546\pi$
$54$		0			0
$55$	−22117.9	+	16069.6i	−0.985909	+	0.716305i
$56$		0			0
$57$	15527.7			0.633022
$58$		0			0
$59$	12113.3	−	37280.8i	0.453034	−	1.39430i	−0.420394	−	0.907342i	$-0.638108\pi$
$59$	12113.3	−	37280.8i	0.453034	−	1.39430i	0.873428	−	0.486954i	$-0.161892\pi$
$60$		0			0
$61$	32765.0			1.12742			0.563710	−	0.825972i	$-0.309373\pi$
$61$	32765.0			1.12742			0.563710	+	0.825972i	$0.309373\pi$
$62$		0			0
$63$	−120379.			−3.82121
$64$		0			0
$65$	3539.97	−	10894.9i	0.103924	−	0.319845i
$66$		0			0
$67$	−8859.53			−0.241115			−0.120557	−	0.992706i	$-0.538468\pi$
$67$	−8859.53			−0.241115			−0.120557	+	0.992706i	$0.538468\pi$
$68$		0			0
$69$	−82663.7	+	60058.7i	−2.09022	+	1.51863i
$70$		0			0
$71$	−44404.4	−	32261.7i	−1.04540	−	0.759524i	−0.0740638	−	0.997254i	$-0.523597\pi$
$71$	−44404.4	−	32261.7i	−1.04540	−	0.759524i	−0.971331	+	0.237729i	$0.923597\pi$
$72$		0			0
$73$	27202.2	−	19763.5i	0.597443	−	0.434067i	−0.247528	−	0.968881i	$-0.579618\pi$
$73$	27202.2	−	19763.5i	0.597443	−	0.434067i	0.844970	+	0.534813i	$0.179618\pi$
$74$		0			0
$75$	−12217.4	+	37601.3i	−0.250799	+	0.771880i
$76$		0			0
$77$	25236.8	−	77670.8i	0.485073	−	1.49290i
$78$		0			0
$79$	66707.5	+	48465.9i	1.20256	+	0.873712i	0.994534	−	0.104411i	$-0.0332958\pi$
$79$	66707.5	+	48465.9i	1.20256	+	0.873712i	0.208027	+	0.978123i	$0.433296\pi$
$80$		0			0
$81$	48452.2	+	149120.i	0.820542	+	2.52537i
$82$		0			0
$83$	2765.73	+	8512.05i	0.0440672	+	0.135625i	0.970669	−	0.240418i	$-0.0772845\pi$
$83$	2765.73	+	8512.05i	0.0440672	+	0.135625i	−0.926602	+	0.376043i	$0.877285\pi$
$84$		0			0
$85$	57137.4	+	41512.7i	0.857774	+	0.623210i
$86$		0			0
$87$	39652.9			0.561665
$88$		0			0
$89$	−60402.9	+	43885.3i	−0.808319	+	0.587278i	−0.913343	−	0.407191i	$-0.866508\pi$
$89$	−60402.9	+	43885.3i	−0.808319	+	0.587278i	0.105024	+	0.994470i	$0.466508\pi$
$90$		0			0
$91$	10574.6	+	32545.3i	0.133863	+	0.411988i
$92$		0			0
$93$	−105024.	−	114689.i	−1.25916	−	1.37503i
$94$		0			0
$95$	11056.8	+	34029.4i	0.125696	+	0.386852i
$96$		0			0
$97$	−39242.2	+	28511.1i	−0.423471	+	0.307670i	−0.779033	−	0.626983i	$-0.784290\pi$
$97$	−39242.2	+	28511.1i	−0.423471	+	0.307670i	0.355562	+	0.934653i	$0.384290\pi$
$98$		0			0
$99$	−245629.			−2.51879
$100$		0			0
$101$	−56076.8	−	40742.2i	−0.546991	−	0.397412i	0.279684	−	0.960092i	$-0.409770\pi$
$101$	−56076.8	−	40742.2i	−0.546991	−	0.397412i	−0.826675	+	0.562680i	$0.809770\pi$
$102$		0			0
$103$	−7063.15	−	21738.2i	−0.0656003	−	0.201897i	0.912884	−	0.408220i	$-0.133850\pi$
$103$	−7063.15	−	21738.2i	−0.0656003	−	0.201897i	−0.978484	+	0.206323i	$0.933850\pi$
$104$		0			0
$105$	−120336.	−	370356.i	−1.06518	−	3.27829i
$106$		0			0
$107$	113668.	+	82584.7i	0.959796	+	0.697333i	0.953103	−	0.302645i	$-0.0978695\pi$
$107$	113668.	+	82584.7i	0.959796	+	0.697333i	0.00669296	+	0.999978i	$0.497870\pi$
$108$		0			0
$109$	61019.7	−	187799.i	0.491930	−	1.51401i	−0.329757	−	0.944066i	$-0.606967\pi$
$109$	61019.7	−	187799.i	0.491930	−	1.51401i	0.821687	−	0.569939i	$-0.193033\pi$
$110$		0			0
$111$	−101428.	+	312164.i	−0.781359	+	2.40478i
$112$		0			0
$113$	−17358.4	+	12611.6i	−0.127883	+	0.0929124i	−0.649888	−	0.760030i	$-0.725184\pi$
$113$	−17358.4	+	12611.6i	−0.127883	+	0.0929124i	0.522005	+	0.852942i	$0.325184\pi$
$114$		0			0
$115$	−190483.	−	138394.i	−1.34311	−	0.975827i
$116$		0			0
$117$	83266.1	−	60496.3i	0.562346	−	0.408568i
$118$		0			0
$119$	−210973.			−1.36572
$120$		0			0
$121$	1727.02	−	5315.21i	0.0107234	−	0.0330032i
$122$		0			0
$123$	583107.			3.47524
$124$		0			0
$125$	118185.			0.676530
$126$		0			0
$127$	110246.	−	339304.i	0.606534	−	1.86672i	0.120655	−	0.992694i	$-0.461500\pi$
$127$	110246.	−	339304.i	0.606534	−	1.86672i	0.485879	−	0.874026i	$-0.338500\pi$
$128$		0			0
$129$	−320961.			−1.69816
$130$		0			0
$131$	152427.	−	110745.i	0.776038	−	0.563825i	−0.127749	−	0.991806i	$-0.540775\pi$
$131$	152427.	−	110745.i	0.776038	−	0.563825i	0.903787	+	0.427982i	$0.140775\pi$
$132$		0			0
$133$	−86471.0	−	62824.9i	−0.423879	−	0.307966i
$134$		0			0
$135$	−564882.	+	410411.i	−2.66762	+	1.93814i
$136$		0			0
$137$	3990.11	−	12280.3i	0.0181628	−	0.0558994i	−0.941564	−	0.336833i	$-0.890644\pi$
$137$	3990.11	−	12280.3i	0.0181628	−	0.0558994i	0.959727	+	0.280934i	$0.0906441\pi$
$138$		0			0
$139$	6859.57	−	21111.6i	0.0301134	−	0.0926795i	−0.934870	−	0.354990i	$-0.884484\pi$
$139$	6859.57	−	21111.6i	0.0301134	−	0.0926795i	0.964984	+	0.262310i	$0.0844844\pi$
$140$		0			0
$141$	574142.	+	417139.i	2.43205	+	1.76698i
$142$		0			0
$143$	21577.0	+	66407.3i	0.0882372	+	0.271566i
$144$		0			0
$145$	28235.8	+	86900.8i	0.111527	+	0.343244i
$146$		0			0
$147$	545914.	+	396630.i	2.08368	+	1.51388i
$148$		0			0
$149$	1437.73			0.00530531			0.00265266	−	0.999996i	$-0.499156\pi$
$149$	1437.73			0.00530531			0.00265266	+	0.999996i	$0.499156\pi$
$150$		0			0
$151$	−48978.5	+	35585.0i	−0.174809	+	0.127006i	−0.671749	−	0.740779i	$-0.734457\pi$
$151$	−48978.5	+	35585.0i	−0.174809	+	0.127006i	0.496940	+	0.867785i	$0.334457\pi$
$152$		0			0
$153$	196082.	+	603480.i	0.677189	+	2.08417i
$154$		0			0
$155$	176560.	−	311829.i	0.590286	−	1.04253i
$156$		0			0
$157$	−160238.	−	493163.i	−0.518821	−	1.59677i	−0.776221	−	0.630461i	$-0.782866\pi$
$157$	−160238.	−	493163.i	−0.518821	−	1.59677i	0.257401	−	0.966305i	$-0.417134\pi$
$158$		0			0
$159$	−214070.	+	155531.i	−0.671526	+	0.487893i
$160$		0			0
$161$	703338.			2.13845
$162$		0			0
$163$	325407.	+	236422.i	0.959307	+	0.696978i	0.952990	−	0.303002i	$-0.0979890\pi$
$163$	325407.	+	236422.i	0.959307	+	0.696978i	0.00631765	+	0.999980i	$0.497989\pi$
$164$		0			0
$165$	−245541.	−	755696.i	−0.702124	−	2.16091i
$166$		0			0
$167$	−179241.	−	551648.i	−0.497333	−	1.53063i	−0.813289	−	0.581859i	$-0.802325\pi$
$167$	−179241.	−	551648.i	−0.497333	−	1.53063i	0.315957	−	0.948774i	$-0.397675\pi$
$168$		0			0
$169$	276712.	+	201043.i	0.745267	+	0.541468i
$170$		0			0
$171$	−99339.9	+	305737.i	−0.259797	+	0.799572i
$172$		0			0
$173$	−60324.2	+	185659.i	−0.153241	+	0.471629i	−0.997978	−	0.0635529i	$-0.979757\pi$
$173$	−60324.2	+	185659.i	−0.153241	+	0.471629i	0.844737	+	0.535182i	$0.179757\pi$
$174$		0			0
$175$	220172.	−	159964.i	0.543458	−	0.394845i
$176$		0			0
$177$	921703.	+	669657.i	2.21135	+	1.60664i
$178$		0			0
$179$	−131709.	+	95692.5i	−0.307245	+	0.223226i	−0.730713	−	0.682685i	$-0.760812\pi$
$179$	−131709.	+	95692.5i	−0.307245	+	0.223226i	0.423469	+	0.905911i	$0.360812\pi$
$180$		0			0
$181$	−340400.			−0.772312			−0.386156	−	0.922433i	$-0.626197\pi$
$181$	−340400.			−0.772312			−0.386156	+	0.922433i	$0.626197\pi$
$182$		0			0
$183$	−294271.	+	905674.i	−0.649561	+	1.99914i
$184$		0			0
$185$	−756341.			−1.62476
$186$		0			0
$187$	−430482.			−0.900225
$188$		0			0
$189$	644537.	−	1.98368e6i	1.31248	−	4.03940i
$190$		0			0
$191$	−732987.			−1.45383			−0.726914	−	0.686728i	$-0.759046\pi$
$191$	−732987.			−1.45383			−0.726914	+	0.686728i	$0.759046\pi$
$192$		0			0
$193$	256659.	−	186474.i	0.495979	−	0.360350i	−0.311500	−	0.950246i	$-0.600831\pi$
$193$	256659.	−	186474.i	0.495979	−	0.360350i	0.807479	+	0.589896i	$0.200831\pi$
$194$		0			0
$195$	269358.	+	195700.i	0.507274	+	0.368556i
$196$		0			0
$197$	−87095.1	+	63278.3i	−0.159893	+	0.116169i	−0.664855	−	0.746973i	$-0.731506\pi$
$197$	−87095.1	+	63278.3i	−0.159893	+	0.116169i	0.504962	+	0.863142i	$0.331506\pi$
$198$		0			0
$199$	66823.3	−	205661.i	0.119618	−	0.368145i	−0.873265	−	0.487246i	$-0.838001\pi$
$199$	66823.3	−	205661.i	0.119618	−	0.368145i	0.992882	+	0.119101i	$0.0380014\pi$
$200$		0			0
$201$	79569.8	−	244891.i	0.138918	−	0.427545i
$202$		0			0
$203$	−220821.	−	160436.i	−0.376097	−	0.273250i
$204$		0			0
$205$	415214.	+	1.27790e6i	0.690061	+	2.12379i
$206$		0			0
$207$	−653694.	−	2.01186e6i	−1.06035	−	3.26342i
$208$		0			0
$209$	−176440.	−	128191.i	−0.279404	−	0.202999i
$210$		0			0
$211$	−218626.			−0.338062			−0.169031	−	0.985611i	$-0.554064\pi$
$211$	−218626.			−0.338062			−0.169031	+	0.985611i	$0.554064\pi$
$212$		0			0
$213$	1.29057e6	−	937653.i	1.94909	−	1.41610i
$214$		0			0
$215$	−228548.	−	703398.i	−0.337195	−	1.03778i
$216$		0			0
$217$	120829.	+	1.06361e6i	0.174190	+	1.53332i
$218$		0			0
$219$	301983.	+	929409.i	0.425474	+	1.30947i
$220$		0			0
$221$	145930.	−	106024.i	0.200985	−	0.146024i
$222$		0			0
$223$	−1.04350e6			−1.40518			−0.702588	−	0.711596i	$-0.747972\pi$
$223$	−1.04350e6			−1.40518			−0.702588	+	0.711596i	$0.747972\pi$
$224$		0			0
$225$	−662201.	−	481117.i	−0.872034	−	0.633570i
$226$		0			0
$227$	−274162.	−	843785.i	−0.353137	−	1.08684i	−0.957082	−	0.289818i	$-0.906405\pi$
$227$	−274162.	−	843785.i	−0.353137	−	1.08684i	0.603945	−	0.797026i	$-0.293595\pi$
$228$		0			0
$229$	126252.	+	388562.i	0.159092	+	0.489635i	0.998552	−	0.0537860i	$-0.0171289\pi$
$229$	126252.	+	388562.i	0.159092	+	0.489635i	−0.839461	+	0.543421i	$0.817129\pi$
$230$		0			0
$231$	1.92028e6	+	1.39516e6i	2.36774	+	1.72026i
$232$		0			0
$233$	260376.	−	801356.i	0.314204	−	0.967020i	−0.661877	−	0.749613i	$-0.730240\pi$
$233$	260376.	−	801356.i	0.314204	−	0.967020i	0.976081	−	0.217408i	$-0.0697601\pi$
$234$		0			0
$235$	−505343.	+	1.55529e6i	−0.596920	+	1.83713i
$236$		0			0
$237$	−1.93879e6	+	1.40861e6i	−2.24212	+	1.62900i
$238$		0			0
$239$	83848.7	+	60919.6i	0.0949514	+	0.0689862i	0.634248	−	0.773130i	$-0.281310\pi$
$239$	83848.7	+	60919.6i	0.0949514	+	0.0689862i	−0.539297	+	0.842116i	$0.681310\pi$
$240$		0			0
$241$	65479.3	−	47573.5i	0.0726209	−	0.0527622i	−0.550882	−	0.834583i	$-0.685709\pi$
$241$	65479.3	−	47573.5i	0.0726209	−	0.0527622i	0.623503	+	0.781821i	$0.285709\pi$
$242$		0			0
$243$	−2.02364e6			−2.19845
$244$		0			0
$245$	−480497.	+	1.47882e6i	−0.511418	+	1.57398i
$246$		0			0
$247$	91384.2			0.0953079
$248$		0			0
$249$	−260125.			−0.265879
$250$		0			0
$251$	−183740.	+	565494.i	−0.184086	+	0.566557i	−0.999931	−	0.0117124i	$-0.996272\pi$
$251$	−183740.	+	565494.i	−0.184086	+	0.566557i	0.815846	+	0.578269i	$0.196272\pi$
$252$		0			0
$253$	1.43513e6			1.40958
$254$		0			0
$255$	−1.66064e6	+	1.20653e6i	−1.59928	+	1.16195i
$256$		0			0
$257$	−550493.	−	399956.i	−0.519899	−	0.377729i	0.296667	−	0.954981i	$-0.404125\pi$
$257$	−550493.	−	399956.i	−0.519899	−	0.377729i	−0.816566	+	0.577252i	$0.804125\pi$
$258$		0			0
$259$	1.82785e6	−	1.32801e6i	1.69313	−	1.23013i
$260$		0			0
$261$	−253684.	+	780759.i	−0.230511	+	0.709440i
$262$		0			0
$263$	−120517.	+	370913.i	−0.107438	+	0.330661i	−0.990295	−	0.138982i	$-0.955617\pi$
$263$	−120517.	+	370913.i	−0.107438	+	0.330661i	0.882857	+	0.469642i	$0.155617\pi$
$264$		0			0
$265$	−493285.	−	358392.i	−0.431502	−	0.313505i
$266$		0			0
$267$	−670560.	−	2.06377e6i	−0.575651	−	1.77167i
$268$		0			0
$269$	−159068.	−	489561.i	−0.134030	−	0.412502i	0.861408	−	0.507914i	$-0.169583\pi$
$269$	−159068.	−	489561.i	−0.134030	−	0.412502i	−0.995438	+	0.0954117i	$0.969583\pi$
$270$		0			0
$271$	−1.07982e6	−	784538.i	−0.893161	−	0.648920i	0.0435390	−	0.999052i	$-0.486137\pi$
$271$	−1.07982e6	−	784538.i	−0.893161	−	0.648920i	−0.936700	+	0.350132i	$0.886137\pi$
$272$		0			0
$273$	−994573.			−0.807663
$274$		0			0
$275$	449251.	−	326400.i	0.358226	−	0.260266i
$276$		0			0
$277$	247942.	+	763087.i	0.194156	+	0.597550i	0.999985	+	0.00540282i	$0.00171978\pi$
$277$	247942.	+	763087.i	0.194156	+	0.597550i	−0.805829	+	0.592148i	$0.798280\pi$
$278$		0			0
$279$	2.93010e6	−	1.33416e6i	2.25357	−	1.02612i
$280$		0			0
$281$	807350.	+	2.48477e6i	0.609952	+	1.87724i	0.458277	+	0.888809i	$0.348467\pi$
$281$	807350.	+	2.48477e6i	0.609952	+	1.87724i	0.151675	+	0.988430i	$0.451533\pi$
$282$		0			0
$283$	1.48301e6	−	1.07747e6i	1.10073	−	0.799724i	0.119547	−	0.992829i	$-0.461856\pi$
$283$	1.48301e6	−	1.07747e6i	1.10073	−	0.799724i	0.981178	+	0.193105i	$0.0618558\pi$
$284$		0			0
$285$	−1.03993e6			−0.758387
$286$		0			0
$287$	−3.24723e6	−	2.35925e6i	−2.32706	−	1.69071i
$288$		0			0
$289$	−95111.6	−	292723.i	−0.0669867	−	0.206164i
$290$		0			0
$291$	−435645.	−	1.34078e6i	−0.301578	−	0.928163i
$292$		0			0
$293$	−508652.	−	369558.i	−0.346140	−	0.251486i	0.401108	−	0.916031i	$-0.368625\pi$
$293$	−508652.	−	369558.i	−0.346140	−	0.251486i	−0.747248	+	0.664545i	$0.768625\pi$
$294$		0			0
$295$	−811256.	+	2.49679e6i	−0.542754	+	1.67042i
$296$		0			0
$297$	1.31515e6	−	4.04762e6i	0.865135	−	2.66261i
$298$		0			0
$299$	−486497.	+	353460.i	−0.314704	+	0.228646i
$300$		0			0
$301$	1.78738e6	+	1.29861e6i	1.13711	+	0.826156i
$302$		0			0
$303$	1.62982e6	−	1.18413e6i	1.01984	−	0.740957i
$304$		0			0
$305$	−2.19436e6			−1.35070
$306$		0			0
$307$	−925795.	+	2.84931e6i	−0.560621	+	1.72541i	0.119997	+	0.992774i	$0.461711\pi$
$307$	−925795.	+	2.84931e6i	−0.560621	+	1.72541i	−0.680618	+	0.732639i	$0.738289\pi$
$308$		0			0
$309$	664311.			0.395799
$310$		0			0
$311$	1.27260e6			0.746090			0.373045	−	0.927813i	$-0.378314\pi$
$311$	1.27260e6			0.746090			0.373045	+	0.927813i	$0.378314\pi$
$312$		0			0
$313$	693270.	−	2.13367e6i	0.399983	−	1.23102i	−0.525029	−	0.851084i	$-0.675946\pi$
$313$	693270.	−	2.13367e6i	0.399983	−	1.23102i	0.925012	−	0.379937i	$-0.124054\pi$
$314$		0			0
$315$	8.06212e6			4.57797
$316$		0			0
$317$	−1.50762e6	+	1.09535e6i	−0.842644	+	0.612217i	−0.923108	−	0.384541i	$-0.874360\pi$
$317$	−1.50762e6	+	1.09535e6i	−0.842644	+	0.612217i	0.0804637	+	0.996758i	$0.474360\pi$
$318$		0			0
$319$	−450575.	−	327362.i	−0.247908	−	0.180116i
$320$		0			0
$321$	−3.30365e6	+	2.40024e6i	−1.78950	+	1.30015i
$322$		0			0
$323$	−174100.	+	535826.i	−0.0928524	+	0.285770i
$324$		0			0
$325$	−71902.5	+	221293.i	−0.0377603	+	0.116214i
$326$		0			0
$327$	4.64301e6	+	3.37335e6i	2.40121	+	1.74458i
$328$		0			0
$329$	−1.50956e6	−	4.64596e6i	−0.768885	−	2.36638i
$330$		0			0
$331$	1.11381e6	+	3.42795e6i	0.558780	+	1.71975i	0.685746	+	0.727841i	$0.259476\pi$
$331$	1.11381e6	+	3.42795e6i	0.558780	+	1.71975i	−0.126965	+	0.991907i	$0.540524\pi$
$332$		0			0
$333$	−5.49755e6	−	3.99420e6i	−2.71680	−	1.97387i
$334$		0			0
$335$	593346.			0.288866
$336$		0			0
$337$	−750822.	+	545504.i	−0.360133	+	0.261652i	−0.753107	−	0.657898i	$-0.771446\pi$
$337$	−750822.	+	545504.i	−0.360133	+	0.261652i	0.392975	+	0.919549i	$0.371446\pi$
$338$		0			0
$339$	−192703.	−	593078.i	−0.0910729	−	0.280293i
$340$		0			0
$341$	246547.	+	2.17025e6i	0.114819	+	1.01070i
$342$		0			0
$343$	−396299.	−	1.21968e6i	−0.181881	−	0.559773i
$344$		0			0
$345$	5.53620e6	−	4.02228e6i	2.50417	−	1.81939i
$346$		0			0
$347$	−971851.			−0.433287			−0.216644	−	0.976251i	$-0.569511\pi$
$347$	−971851.			−0.433287			−0.216644	+	0.976251i	$0.569511\pi$
$348$		0			0
$349$	988928.	+	718498.i	0.434611	+	0.315764i	0.783490	−	0.621404i	$-0.213438\pi$
$349$	988928.	+	718498.i	0.434611	+	0.315764i	−0.348879	+	0.937168i	$0.613438\pi$
$350$		0			0
$351$	551069.	+	1.69602e6i	0.238747	+	0.734788i
$352$		0			0
$353$	884351.	+	2.72175e6i	0.377736	+	1.16255i	0.941614	+	0.336693i	$0.109309\pi$
$353$	884351.	+	2.72175e6i	0.377736	+	1.16255i	−0.563879	+	0.825858i	$0.690691\pi$
$354$		0			0
$355$	2.97388e6	+	2.16065e6i	1.25243	+	0.909941i
$356$		0			0
$357$	1.89481e6	−	5.83162e6i	0.786855	−	2.42169i
$358$		0			0
$359$	−445753.	+	1.37189e6i	−0.182540	+	0.561800i	−0.999897	−	0.0143308i	$-0.995438\pi$
$359$	−445753.	+	1.37189e6i	−0.182540	+	0.561800i	0.817357	+	0.576131i	$0.195438\pi$
$360$		0			0
$361$	1.77229e6	−	1.28764e6i	0.715758	−	0.520028i
$362$		0			0
$363$	131409.	+	95474.5i	0.0523431	+	0.0380295i
$364$		0			0
$365$	−1.82180e6	+	1.32361e6i	−0.715761	+	0.520031i
$366$		0			0
$367$	−3.95861e6			−1.53418			−0.767092	−	0.641537i	$-0.778297\pi$
$367$	−3.95861e6			−1.53418			−0.767092	+	0.641537i	$0.778297\pi$
$368$		0			0
$369$	−3.73049e6	+	1.14813e7i	−1.42626	+	4.38959i
$370$		0			0
$371$	1.82140e6			0.687022
$372$		0			0
$373$	−2.86304e6			−1.06550			−0.532752	−	0.846272i	$-0.678842\pi$
$373$	−2.86304e6			−1.06550			−0.532752	+	0.846272i	$0.678842\pi$
$374$		0			0
$375$	−1.06145e6	+	3.26681e6i	−0.389782	+	1.19962i
$376$		0			0
$377$	233368.			0.0845643
$378$		0			0
$379$	3.21021e6	−	2.33235e6i	1.14798	−	0.834057i	0.159770	−	0.987154i	$-0.448925\pi$
$379$	3.21021e6	−	2.33235e6i	1.14798	−	0.834057i	0.988211	+	0.153097i	$0.0489246\pi$
$380$		0			0
$381$	8.38870e6	+	6.09475e6i	2.96062	+	2.15102i
$382$		0			0
$383$	1.76790e6	−	1.28445e6i	0.615830	−	0.447426i	−0.235633	−	0.971842i	$-0.575716\pi$
$383$	1.76790e6	−	1.28445e6i	0.615830	−	0.447426i	0.851462	+	0.524416i	$0.175716\pi$
$384$		0			0
$385$	−1.69017e6	+	5.20181e6i	−0.581137	+	1.78856i
$386$		0			0
$387$	2.05339e6	−	6.31967e6i	0.696936	−	2.14495i
$388$		0			0
$389$	9373.14	+	6809.99i	0.00314059	+	0.00228177i	0.589354	−	0.807875i	$-0.299382\pi$
$389$	9373.14	+	6809.99i	0.00314059	+	0.00228177i	−0.586214	+	0.810156i	$0.699382\pi$
$390$		0			0
$391$	−1.14565e6	−	3.52594e6i	−0.378973	−	1.16636i
$392$		0			0
$393$	1.69216e6	+	5.20793e6i	0.552662	+	1.70092i
$394$		0			0
$395$	−4.46757e6	−	3.24588e6i	−1.44072	−	1.04674i
$396$		0			0
$397$	3.40649e6			1.08475			0.542376	−	0.840136i	$-0.317525\pi$
$397$	3.40649e6			1.08475			0.542376	+	0.840136i	$0.317525\pi$
$398$		0			0
$399$	2.51319e6	−	1.82594e6i	0.790303	−	0.574188i
$400$		0			0
$401$	−1.31972e6	−	4.06169e6i	−0.409847	−	1.26138i	−0.916780	−	0.399393i	$-0.869221\pi$
$401$	−1.31972e6	−	4.06169e6i	−0.409847	−	1.26138i	0.506933	−	0.861986i	$-0.330779\pi$
$402$		0			0
$403$	−618090.	−	674972.i	−0.189579	−	0.207025i
$404$		0			0
$405$	−3.24497e6	−	9.98698e6i	−0.983043	−	3.02549i
$406$		0			0
$407$	3.72965e6	−	2.70975e6i	1.11605	−	0.810854i
$408$		0			0
$409$	2.72195e6			0.804584			0.402292	−	0.915511i	$-0.368214\pi$
$409$	2.72195e6			0.804584			0.402292	+	0.915511i	$0.368214\pi$
$410$		0			0
$411$	303609.	+	220585.i	0.0886564	+	0.0644126i
$412$		0			0
$413$	−2.42339e6	−	7.45842e6i	−0.699113	−	2.15165i
$414$		0			0
$415$	−185228.	−	570074.i	−0.0527943	−	0.162484i
$416$		0			0
$417$	521947.	+	379217.i	0.146990	+	0.106794i
$418$		0			0
$419$	−511454.	+	1.57409e6i	−0.142322	+	0.438021i	−0.996657	−	0.0817013i	$-0.973965\pi$
$419$	−511454.	+	1.57409e6i	−0.142322	+	0.438021i	0.854335	+	0.519722i	$0.173965\pi$
$420$		0			0
$421$	−1.28553e6	+	3.95645e6i	−0.353489	+	1.08793i	0.603391	+	0.797445i	$0.293816\pi$
$421$	−1.28553e6	+	3.95645e6i	−0.353489	+	1.08793i	−0.956880	+	0.290483i	$0.906184\pi$
$422$		0			0
$423$	−1.18865e7	+	8.63606e6i	−3.23001	+	2.34674i
$424$		0			0
$425$	−1.16055e6	−	843192.i	−0.311669	−	0.226440i
$426$		0			0
$427$	5.30311e6	−	3.85293e6i	1.40754	−	1.02264i
$428$		0			0
$429$	−2.02938e6			−0.532379
$430$		0			0
$431$	955431.	−	2.94051e6i	0.247746	−	0.762483i	−0.747427	−	0.664344i	$-0.768711\pi$
$431$	955431.	−	2.94051e6i	0.247746	−	0.762483i	0.995173	−	0.0981391i	$-0.0312890\pi$
$432$		0			0
$433$	−3.03129e6			−0.776976			−0.388488	−	0.921454i	$-0.627002\pi$
$433$	−3.03129e6			−0.776976			−0.388488	+	0.921454i	$0.627002\pi$
$434$		0			0
$435$	−2.65566e6			−0.672898
$436$		0			0
$437$	580411.	−	1.78632e6i	0.145389	−	0.447462i
$438$		0			0
$439$	−2.80508e6			−0.694679			−0.347340	−	0.937739i	$-0.612915\pi$
$439$	−2.80508e6			−0.694679			−0.347340	+	0.937739i	$0.612915\pi$
$440$		0			0
$441$	−1.13021e7	+	8.21147e6i	−2.76735	+	2.01059i
$442$		0			0
$443$	−4.55565e6	−	3.30987e6i	−1.10291	−	0.801313i	−0.121380	−	0.992606i	$-0.538732\pi$
$443$	−4.55565e6	−	3.30987e6i	−1.10291	−	0.801313i	−0.981533	+	0.191293i	$0.938732\pi$
$444$		0			0
$445$	4.04534e6	−	2.93911e6i	0.968400	−	0.703584i
$446$		0			0
$447$	−12912.6	+	39740.9i	−0.00305664	+	0.00940738i
$448$		0			0
$449$	444218.	−	1.36716e6i	0.103987	−	0.320040i	−0.885504	−	0.464631i	$-0.846187\pi$
$449$	444218.	−	1.36716e6i	0.103987	−	0.320040i	0.989491	+	0.144592i	$0.0461869\pi$
$450$		0			0
$451$	−6.62583e6	−	4.81395e6i	−1.53391	−	1.11445i
$452$		0			0
$453$	−543733.	−	1.67344e6i	−0.124492	−	0.383146i
$454$		0			0
$455$	−708208.	−	2.17964e6i	−0.160374	−	0.493579i
$456$		0			0
$457$	2.05625e6	+	1.49395e6i	0.460559	+	0.334616i	0.793751	−	0.608243i	$-0.208125\pi$
$457$	2.05625e6	+	1.49395e6i	0.460559	+	0.334616i	−0.333191	+	0.942859i	$0.608125\pi$
$458$		0			0
$459$	−1.09943e7			−2.43578
$460$		0			0
$461$	−3.35854e6	+	2.44012e6i	−0.736034	+	0.534760i	−0.891466	−	0.453087i	$-0.850323\pi$
$461$	−3.35854e6	+	2.44012e6i	−0.736034	+	0.534760i	0.155433	+	0.987846i	$0.450323\pi$
$462$		0			0
$463$	−958317.	−	2.94940e6i	−0.207758	−	0.639412i	−0.999589	−	0.0286721i	$-0.990872\pi$
$463$	−958317.	−	2.94940e6i	−0.207758	−	0.639412i	0.791831	−	0.610740i	$-0.209128\pi$
$464$		0			0
$465$	7.03370e6	+	7.68099e6i	1.50852	+	1.64735i
$466$		0			0
$467$	−509690.	−	1.56867e6i	−0.108147	−	0.332842i	0.882309	−	0.470670i	$-0.155988\pi$
$467$	−509690.	−	1.56867e6i	−0.108147	−	0.332842i	−0.990456	+	0.137828i	$0.955988\pi$
$468$		0			0
$469$	−1.43394e6	+	1.04182e6i	−0.301022	+	0.218705i
$470$		0			0
$471$	1.50709e7			3.13030
$472$		0			0
$473$	3.64708e6	+	2.64976e6i	0.749535	+	0.544569i
$474$		0			0
$475$	−224582.	−	691193.i	−0.0456711	−	0.140561i
$476$		0			0
$477$	−1.69284e6	−	5.21003e6i	−0.340659	−	1.04844i
$478$		0			0
$479$	5.16868e6	+	3.75526e6i	1.02930	+	0.747828i	0.968168	−	0.250302i	$-0.0805298\pi$
$479$	5.16868e6	+	3.75526e6i	1.02930	+	0.747828i	0.0611292	+	0.998130i	$0.480530\pi$
$480$		0			0
$481$	−596930.	+	1.83716e6i	−0.117642	+	0.362063i
$482$		0			0
$483$	−6.31686e6	+	1.94413e7i	−1.23206	+	3.79190i
$484$		0			0
$485$	2.62815e6	−	1.90946e6i	0.507336	−	0.368601i
$486$		0			0
$487$	4.90424e6	+	3.56314e6i	0.937021	+	0.680786i	0.947702	−	0.319157i	$-0.103400\pi$
$487$	4.90424e6	+	3.56314e6i	0.937021	+	0.680786i	−0.0106805	+	0.999943i	$0.503400\pi$
$488$		0			0
$489$	−9.45762e6	+	6.87136e6i	−1.78859	+	1.29948i
$490$		0			0
$491$	−238187.			−0.0445876			−0.0222938	−	0.999751i	$-0.507097\pi$
$491$	−238187.			−0.0445876			−0.0222938	+	0.999751i	$0.507097\pi$
$492$		0			0
$493$	−444599.	+	1.36834e6i	−0.0823856	+	0.253557i
$494$		0			0
$495$	1.64504e7			3.01761
$496$		0			0
$497$	−1.09807e7			−1.99407
$498$		0			0
$499$	2.85826e6	−	8.79682e6i	0.513867	−	1.58152i	−0.271468	−	0.962448i	$-0.587509\pi$
$499$	2.85826e6	−	8.79682e6i	0.513867	−	1.58152i	0.785334	−	0.619072i	$-0.212491\pi$
$500$		0			0
$501$	1.68582e7			3.00066
$502$		0			0
$503$	2.53378e6	−	1.84090e6i	0.446527	−	0.324421i	−0.341696	−	0.939811i	$-0.611001\pi$
$503$	2.53378e6	−	1.84090e6i	0.446527	−	0.324421i	0.788223	+	0.615389i	$0.211001\pi$
$504$		0			0
$505$	3.75561e6	+	2.72861e6i	0.655318	+	0.476116i
$506$		0			0
$507$	−8.04236e6	+	5.84312e6i	−1.38952	+	1.00954i
$508$		0			0
$509$	770933.	−	2.37269e6i	0.131893	−	0.405925i	−0.863201	−	0.504861i	$-0.831544\pi$
$509$	770933.	−	2.37269e6i	0.131893	−	0.405925i	0.995094	+	0.0989356i	$0.0315438\pi$
$510$		0			0
$511$	2.07869e6	−	6.39755e6i	0.352158	−	1.08383i
$512$		0			0
$513$	−4.50622e6	−	3.27396e6i	−0.755995	−	0.549263i
$514$		0			0
$515$	473037.	+	1.45586e6i	0.0785918	+	0.241881i
$516$		0			0
$517$	−3.08020e6	−	9.47987e6i	−0.506818	−	1.55983i
$518$		0			0
$519$	−4.59010e6	−	3.33490e6i	−0.748003	−	0.543456i
$520$		0			0
$521$	−25850.6			−0.00417231			−0.00208615	−	0.999998i	$-0.500664\pi$
$521$	−25850.6			−0.00417231			−0.00208615	+	0.999998i	$0.500664\pi$
$522$		0			0
$523$	−8.58592e6	+	6.23804e6i	−1.37256	+	0.997227i	−0.375033	+	0.927012i	$0.622369\pi$
$523$	−8.58592e6	+	6.23804e6i	−1.37256	+	0.997227i	−0.997532	+	0.0702150i	$0.977631\pi$
$524$		0			0
$525$	2.44422e6	+	7.52255e6i	0.387028	+	1.19115i
$526$		0			0
$527$	5.13521e6	−	2.33821e6i	0.805437	−	0.366740i
$528$		0			0
$529$	1.83038e6	+	5.63335e6i	0.284383	+	0.875240i
$530$		0			0
$531$	−1.90821e7	+	1.38640e7i	−2.93691	+	2.13379i
$532$		0			0
$533$	3.43173e6			0.523233
$534$		0			0
$535$	−7.61264e6	−	5.53091e6i	−1.14988	−	0.835434i
$536$		0			0
$537$	−1.46216e6	−	4.50008e6i	−0.218807	−	0.673418i
$538$		0			0
$539$	−2.92876e6	−	9.01379e6i	−0.434222	−	1.33640i
$540$		0			0
$541$	1.62817e6	+	1.18293e6i	0.239169	+	0.173767i	0.700913	−	0.713247i	$-0.252776\pi$
$541$	1.62817e6	+	1.18293e6i	0.239169	+	0.173767i	−0.461744	+	0.887013i	$0.652776\pi$
$542$		0			0
$543$	3.05722e6	−	9.40915e6i	0.444966	−	1.36947i
$544$		0			0
$545$	−4.08664e6	+	1.25774e7i	−0.589353	+	1.81384i
$546$		0			0
$547$	−4.22068e6	+	3.06651e6i	−0.603135	+	0.438203i	−0.846990	−	0.531609i	$-0.821588\pi$
$547$	−4.22068e6	+	3.06651e6i	−0.603135	+	0.438203i	0.243855	+	0.969812i	$0.421588\pi$
$548$		0			0
$549$	−1.59499e7	−	1.15883e7i	−2.25854	−	1.64093i
$550$		0			0
$551$	−589697.	+	428440.i	−0.0827466	+	0.0601189i
$552$		0			0
$553$	1.64960e7			2.29386
$554$		0			0
$555$	6.79290e6	−	2.09064e7i	0.936101	−	2.88102i
$556$		0			0
$557$	−3.18823e6			−0.435423			−0.217712	−	0.976013i	$-0.569859\pi$
$557$	−3.18823e6			−0.435423			−0.217712	+	0.976013i	$0.569859\pi$
$558$		0			0
$559$	−1.88894e6			−0.255675
$560$		0			0
$561$	3.86627e6	−	1.18992e7i	0.518663	−	1.59628i
$562$		0			0
$563$	1.60053e6			0.212811			0.106405	−	0.994323i	$-0.466066\pi$
$563$	1.60053e6			0.212811			0.106405	+	0.994323i	$0.466066\pi$
$564$		0			0
$565$	1.16253e6	−	844630.i	0.153209	−	0.111313i
$566$		0			0
$567$	2.53776e7	+	1.84379e7i	3.31507	+	2.40854i
$568$		0			0
$569$	3.21958e6	−	2.33916e6i	0.416887	−	0.302886i	−0.359497	−	0.933146i	$-0.617052\pi$
$569$	3.21958e6	−	2.33916e6i	0.416887	−	0.302886i	0.776384	+	0.630260i	$0.217052\pi$
$570$		0			0
$571$	−526924.	+	1.62171e6i	−0.0676329	+	0.208153i	−0.979161	−	0.203085i	$-0.934903\pi$
$571$	−526924.	+	1.62171e6i	−0.0676329	+	0.208153i	0.911528	+	0.411237i	$0.134903\pi$
$572$		0			0
$573$	6.58315e6	−	2.02609e7i	0.837620	−	2.57793i
$574$		0			0
$575$	3.86902e6	+	2.81101e6i	0.488013	+	0.354563i
$576$		0			0
$577$	2.09975e6	+	6.46237e6i	0.262560	+	0.808076i	0.992246	+	0.124293i	$0.0396663\pi$
$577$	2.09975e6	+	6.46237e6i	0.262560	+	0.808076i	−0.729686	+	0.683783i	$0.760334\pi$
$578$		0			0
$579$	2.84929e6	+	8.76920e6i	0.353216	+	1.08709i
$580$		0			0
$581$	1.44860e6	+	1.05247e6i	0.178036	+	0.129351i
$582$		0			0
$583$	3.71649e6			0.452857
$584$		0			0
$585$	−5.57654e6	+	4.05159e6i	−0.673713	+	0.489481i
$586$		0			0
$587$	−228695.	−	703851.i	−0.0273944	−	0.0843112i	0.936425	−	0.350869i	$-0.114114\pi$
$587$	−228695.	−	703851.i	−0.0273944	−	0.0843112i	−0.963819	+	0.266558i	$0.914114\pi$
$588$		0			0
$589$	2.80104e6	+	570835.i	0.332683	+	0.0677988i
$590$		0			0
$591$	−966882.	−	2.97576e6i	−0.113869	−	0.350452i
$592$		0			0
$593$	9.09938e6	−	6.61109e6i	1.06261	−	0.772033i	0.0880427	−	0.996117i	$-0.471939\pi$
$593$	9.09938e6	−	6.61109e6i	1.06261	−	0.772033i	0.974570	+	0.224083i	$0.0719388\pi$
$594$		0			0
$595$	1.41294e7			1.63618
$596$		0			0
$597$	5.08461e6	+	3.69419e6i	0.583878	+	0.424212i
$598$		0			0
$599$	−3.03332e6	−	9.33560e6i	−0.345423	−	1.06310i	−0.961357	−	0.275305i	$-0.911221\pi$
$599$	−3.03332e6	−	9.33560e6i	−0.345423	−	1.06310i	0.615934	−	0.787798i	$-0.288779\pi$
$600$		0			0
$601$	−3.45955e6	−	1.06474e7i	−0.390691	−	1.20242i	−0.932267	−	0.361771i	$-0.882172\pi$
$601$	−3.45955e6	−	1.06474e7i	−0.390691	−	1.20242i	0.541576	−	0.840652i	$-0.317828\pi$
$602$		0			0
$603$	4.31280e6	+	3.13343e6i	0.483021	+	0.350935i
$604$		0			0
$605$	−115663.	+	355973.i	−0.0128471	+	0.0395393i
$606$		0			0
$607$	−1.86553e6	+	5.74151e6i	−0.205509	+	0.632491i	0.794183	+	0.607678i	$0.207899\pi$
$607$	−1.86553e6	+	5.74151e6i	−0.205509	+	0.632491i	−0.999692	+	0.0248130i	$0.992101\pi$
$608$		0			0
$609$	6.41793e6	−	4.66290e6i	0.701216	−	0.509463i
$610$		0			0
$611$	3.37897e6	+	2.45497e6i	0.366169	+	0.266037i
$612$		0			0
$613$	−1.30330e7	+	9.46906e6i	−1.40086	+	1.01778i	−0.406286	+	0.913746i	$0.633176\pi$
$613$	−1.30330e7	+	9.46906e6i	−1.40086	+	1.01778i	−0.994573	+	0.104038i	$0.966824\pi$
$614$		0			0
$615$	−3.90522e7			−4.16349
$616$		0			0
$617$	−3.07120e6	+	9.45217e6i	−0.324784	+	0.999583i	0.646754	+	0.762699i	$0.276126\pi$
$617$	−3.07120e6	+	9.45217e6i	−0.324784	+	0.999583i	−0.971538	+	0.236884i	$0.923874\pi$
$618$		0			0
$619$	1.51106e7			1.58510			0.792548	−	0.609810i	$-0.208754\pi$
$619$	1.51106e7			1.58510			0.792548	+	0.609810i	$0.208754\pi$
$620$		0			0
$621$	3.66527e7			3.81396
$622$		0			0
$623$	−4.61577e6	+	1.42059e7i	−0.476458	+	1.46639i
$624$		0			0
$625$	−1.21662e7			−1.24581
$626$		0			0
$627$	5.12806e6	−	3.72575e6i	0.520936	−	0.378482i
$628$		0			0
$629$	−9.63484e6	−	7.00012e6i	−0.970997	−	0.705471i
$630$		0			0
$631$	2.99132e6	−	2.17332e6i	0.299081	−	0.217295i	−0.428116	−	0.903724i	$-0.640822\pi$
$631$	2.99132e6	−	2.17332e6i	0.299081	−	0.217295i	0.727197	+	0.686428i	$0.240822\pi$
$632$		0			0
$633$	1.96354e6	−	6.04316e6i	0.194774	−	0.599452i
$634$		0			0
$635$	−7.38349e6	+	2.27240e7i	−0.726653	+	2.23641i
$636$		0			0
$637$	3.21284e6	+	2.33427e6i	0.313719	+	0.227930i
$638$		0			0
$639$	1.02057e7	+	3.14098e7i	0.988756	+	3.04308i
$640$		0			0
$641$	1.69418e6	+	5.21413e6i	0.162860	+	0.501230i	0.998872	−	0.0474800i	$-0.0151191\pi$
$641$	1.69418e6	+	5.21413e6i	0.162860	+	0.501230i	−0.836013	+	0.548710i	$0.815119\pi$
$642$		0			0
$643$	−2.44218e6	−	1.77435e6i	−0.232943	−	0.169243i	0.465190	−	0.885211i	$-0.345986\pi$
$643$	−2.44218e6	−	1.77435e6i	−0.232943	−	0.169243i	−0.698134	+	0.715967i	$0.745986\pi$
$644$		0			0
$645$	2.14956e7			2.03447
$646$		0			0
$647$	3.02858e6	−	2.20039e6i	0.284432	−	0.206652i	−0.436416	−	0.899745i	$-0.643752\pi$
$647$	3.02858e6	−	2.20039e6i	0.284432	−	0.206652i	0.720848	+	0.693093i	$0.243752\pi$
$648$		0			0
$649$	−4.94482e6	−	1.52186e7i	−0.460828	−	1.41828i
$650$		0			0
$651$	−3.04849e7	−	6.21264e6i	−2.81924	−	0.574545i
$652$		0			0
$653$	−1.87834e6	−	5.78095e6i	−0.172382	−	0.530537i	0.827122	−	0.562022i	$-0.189976\pi$
$653$	−1.87834e6	−	5.78095e6i	−0.172382	−	0.530537i	−0.999504	+	0.0314847i	$0.989976\pi$
$654$		0			0
$655$	−1.02084e7	+	7.41684e6i	−0.929725	+	0.675485i
$656$		0			0
$657$	−2.02319e7			−1.82862
$658$		0			0
$659$	8.04429e6	+	5.84452e6i	0.721563	+	0.524246i	0.886883	−	0.461994i	$-0.152866\pi$
$659$	8.04429e6	+	5.84452e6i	0.721563	+	0.524246i	−0.165320	+	0.986240i	$0.552866\pi$
$660$		0			0
$661$	−573469.	−	1.76496e6i	−0.0510513	−	0.157120i	0.922281	−	0.386521i	$-0.126323\pi$
$661$	−573469.	−	1.76496e6i	−0.0510513	−	0.157120i	−0.973332	+	0.229401i	$0.926323\pi$
$662$		0			0
$663$	1.62003e6	+	4.98594e6i	0.143133	+	0.440518i
$664$		0			0
$665$	5.79119e6	+	4.20754e6i	0.507824	+	0.368956i
$666$		0			0
$667$	1.48219e6	−	4.56172e6i	0.129000	−	0.397022i
$668$		0			0
$669$	9.37196e6	−	2.88439e7i	0.809590	−	2.49166i
$670$		0			0
$671$	1.08208e7	−	7.86174e6i	0.927793	−	0.674081i
$672$		0			0
$673$	1.21424e7	+	8.82198e6i	1.03340	+	0.750807i	0.968986	−	0.247117i	$-0.0794831\pi$
$673$	1.21424e7	+	8.82198e6i	1.03340	+	0.750807i	0.0644112	+	0.997923i	$0.479483\pi$
$674$		0			0
$675$	1.14737e7	−	8.33612e6i	0.969267	−	0.704214i
$676$		0			0
$677$	1.37874e7			1.15614			0.578072	−	0.815986i	$-0.303805\pi$
$677$	1.37874e7			1.15614			0.578072	+	0.815986i	$0.303805\pi$
$678$		0			0
$679$	−2.99875e6	+	9.22919e6i	−0.249612	+	0.768226i
$680$		0			0
$681$	2.57858e7			2.13065
$682$		0			0
$683$	−1.64831e7			−1.35203			−0.676017	−	0.736886i	$-0.736295\pi$
$683$	−1.64831e7			−1.35203			−0.676017	+	0.736886i	$0.736295\pi$
$684$		0			0
$685$	−267228.	+	822442.i	−0.0217598	+	0.0669698i
$686$		0			0
$687$	−1.18743e7			−0.959881
$688$		0			0
$689$	−1.25986e6	+	915339.i	−0.101105	+	0.0734571i
$690$		0			0
$691$	6.04906e6	+	4.39490e6i	0.481940	+	0.350150i	0.802076	−	0.597222i	$-0.203729\pi$
$691$	6.04906e6	+	4.39490e6i	0.481940	+	0.350150i	−0.320136	+	0.947372i	$0.603729\pi$
$692$		0			0
$693$	−3.97557e7	+	2.88842e7i	−3.14460	+	2.28469i
$694$		0			0
$695$	−459403.	+	1.41390e6i	−0.0360771	+	0.111034i
$696$		0			0
$697$	−6.53795e6	+	2.01217e7i	−0.509753	+	1.56886i
$698$		0			0
$699$	1.98122e7	+	1.43944e7i	1.53369	+	1.11429i
$700$		0			0
$701$	−77012.0	−	237018.i	−0.00591920	−	0.0182174i	0.948053	−	0.318112i	$-0.103049\pi$
$701$	−77012.0	−	237018.i	−0.00591920	−	0.0182174i	−0.953972	+	0.299894i	$0.903049\pi$
$702$		0			0
$703$	−1.86447e6	−	5.73824e6i	−0.142287	−	0.437915i
$704$		0			0
$705$	−3.84518e7	−	2.79368e7i	−2.91369	−	2.11692i
$706$		0			0
$707$	−1.38672e7			−1.04337
$708$		0			0
$709$	−1.12597e7	+	8.18066e6i	−0.841224	+	0.611185i	−0.922712	−	0.385489i	$-0.874033\pi$
$709$	−1.12597e7	+	8.18066e6i	−0.841224	+	0.611185i	0.0814885	+	0.996674i	$0.474033\pi$
$710$		0			0
$711$	−1.53317e7	−	4.71861e7i	−1.13741	−	3.50058i
$712$		0			0
$713$	−1.71196e7	+	7.79508e6i	−1.26116	+	0.574244i
$714$		0			0
$715$	−1.44507e6	−	4.44746e6i	−0.105712	−	0.325347i
$716$		0			0
$717$	−2.43698e6	+	1.77057e6i	−0.177033	+	0.128622i
$718$		0			0
$719$	1.54293e7			1.11308			0.556538	−	0.830822i	$-0.312129\pi$
$719$	1.54293e7			1.11308			0.556538	+	0.830822i	$0.312129\pi$
$720$		0			0
$721$	−3.69944e6	−	2.68780e6i	−0.265032	−	0.192557i
$722$		0			0
$723$	726915.	+	2.23721e6i	0.0517176	+	0.159170i
$724$		0			0
$725$	−573515.	−	1.76510e6i	−0.0405228	−	0.124716i
$726$		0			0
$727$	−2.70666e6	−	1.96650e6i	−0.189932	−	0.137993i	0.488756	−	0.872421i	$-0.337451\pi$
$727$	−2.70666e6	−	1.96650e6i	−0.189932	−	0.137993i	−0.678687	+	0.734427i	$0.737451\pi$
$728$		0			0
$729$	6.40092e6	−	1.97000e7i	0.446091	−	1.37293i
$730$		0			0
$731$	3.59870e6	−	1.10757e7i	0.249088	−	0.766614i
$732$		0			0
$733$	8.47302e6	−	6.15601e6i	0.582476	−	0.423194i	−0.257140	−	0.966374i	$-0.582780\pi$
$733$	8.47302e6	−	6.15601e6i	0.582476	−	0.423194i	0.839616	+	0.543180i	$0.182780\pi$
$734$		0			0
$735$	−3.65613e7	−	2.65633e7i	−2.49634	−	1.81369i
$736$		0			0
$737$	−2.92589e6	+	2.12578e6i	−0.198422	+	0.144162i
$738$		0			0
$739$	3.20137e6			0.215638			0.107819	−	0.994171i	$-0.465613\pi$
$739$	3.20137e6			0.215638			0.107819	+	0.994171i	$0.465613\pi$
$740$		0			0
$741$	−820745.	+	2.52599e6i	−0.0549115	+	0.169000i
$742$		0			0
$743$	6.93714e6			0.461008			0.230504	−	0.973071i	$-0.425963\pi$
$743$	6.93714e6			0.461008			0.230504	+	0.973071i	$0.425963\pi$
$744$		0			0
$745$	−96288.2			−0.00635598
$746$		0			0
$747$	1.66418e6	−	5.12182e6i	0.109119	−	0.335833i
$748$		0			0
$749$	2.81088e7			1.83079
$750$		0			0
$751$	3.35724e6	−	2.43917e6i	0.217211	−	0.157813i	−0.473859	−	0.880601i	$-0.657139\pi$
$751$	3.35724e6	−	2.43917e6i	0.217211	−	0.157813i	0.691070	+	0.722788i	$0.257139\pi$
$752$		0			0
$753$	−1.39809e7	−	1.01577e7i	−0.898559	−	0.652841i
$754$		0			0
$755$	3.28022e6	−	2.38322e6i	0.209428	−	0.152159i
$756$		0			0
$757$	2.91863e6	−	8.98262e6i	0.185114	−	0.569723i	−0.814836	−	0.579691i	$-0.803173\pi$
$757$	2.91863e6	−	8.98262e6i	0.185114	−	0.569723i	0.999950	+	0.00996864i	$0.00317317\pi$
$758$		0			0
$759$	−1.28893e7	+	3.96691e7i	−0.812127	+	2.49947i
$760$		0			0
$761$	−2.65996e6	−	1.93258e6i	−0.166500	−	0.120969i	0.501415	−	0.865207i	$-0.332813\pi$
$761$	−2.65996e6	−	1.93258e6i	−0.166500	−	0.120969i	−0.667915	+	0.744238i	$0.732813\pi$
$762$		0			0
$763$	−1.22076e7	−	3.75712e7i	−0.759137	−	2.33638i
$764$		0			0
$765$	−1.31321e7	−	4.04166e7i	−0.811301	−	2.49693i
$766$		0			0
$767$	5.42446e6	+	3.94110e6i	0.332941	+	0.241896i
$768$		0			0
$769$	7.17705e6			0.437653			0.218826	−	0.975764i	$-0.429777\pi$
$769$	7.17705e6			0.437653			0.218826	+	0.975764i	$0.429777\pi$
$770$		0			0
$771$	1.59995e7	−	1.16243e7i	0.969328	−	0.704258i
$772$		0			0
$773$	7.78915e6	+	2.39725e7i	0.468858	+	1.44300i	0.854065	+	0.520166i	$0.174130\pi$
$773$	7.78915e6	+	2.39725e7i	0.468858	+	1.44300i	−0.385207	+	0.922830i	$0.625870\pi$
$774$		0			0
$775$	−3.58622e6	+	6.33377e6i	−0.214478	+	0.378798i
$776$		0			0
$777$	2.02918e7	+	6.24517e7i	1.20578	+	3.71100i
$778$		0			0
$779$	−8.67166e6	+	6.30033e6i	−0.511986	+	0.371980i
$780$		0			0
$781$	−2.24057e7			−1.31441
$782$		0			0
$783$	−1.15075e7	−	8.36070e6i	−0.670776	−	0.487347i
$784$		0			0
$785$	1.07316e7	+	3.30284e7i	0.621568	+	1.91299i
$786$		0			0
$787$	1.02777e7	+	3.16315e7i	0.591505	+	1.82047i	0.571406	+	0.820668i	$0.306398\pi$
$787$	1.02777e7	+	3.16315e7i	0.591505	+	1.82047i	0.0200995	+	0.999798i	$0.493602\pi$
$788$		0			0
$789$	−9.17018e6	−	6.66253e6i	−0.524428	−	0.381019i
$790$		0			0
$791$	−1.32646e6	+	4.08243e6i	−0.0753796	+	0.231995i
$792$		0			0
$793$	−1.73186e6	+	5.33012e6i	−0.0977980	+	0.300991i
$794$		0			0
$795$	1.43368e7	−	1.04163e7i	0.804516	−	0.584515i
$796$		0			0
$797$	5.81053e6	+	4.22160e6i	0.324019	+	0.235413i	0.737888	−	0.674923i	$-0.235823\pi$
$797$	5.81053e6	+	4.22160e6i	0.324019	+	0.235413i	−0.413870	+	0.910336i	$0.635823\pi$
$798$		0			0
$799$	−2.08320e7	+	1.51353e7i	−1.15442	+	0.838735i
$800$		0			0
$801$	4.49253e7			2.47406
$802$		0			0
$803$	4.24148e6	−	1.30539e7i	0.232128	−	0.714418i
$804$		0			0
$805$	−4.71043e7			−2.56195
$806$		0			0
$807$	1.49608e7			0.808671
$808$		0			0
$809$	−4.11061e6	+	1.26512e7i	−0.220818	+	0.679609i	0.777871	+	0.628424i	$0.216300\pi$
$809$	−4.11061e6	+	1.26512e7i	−0.220818	+	0.679609i	−0.998689	+	0.0511847i	$0.983700\pi$
$810$		0			0
$811$	−1.84738e7			−0.986286			−0.493143	−	0.869948i	$-0.664152\pi$
$811$	−1.84738e7			−0.986286			−0.493143	+	0.869948i	$0.664152\pi$
$812$		0			0
$813$	3.13840e7	−	2.28018e7i	1.66526	−	1.20988i
$814$		0			0
$815$	−2.17933e7	−	1.58338e7i	−1.14929	−	0.835008i
$816$		0			0
$817$	4.77317e6	−	3.46791e6i	0.250179	−	0.181766i
$818$		0			0
$819$	6.36289e6	−	1.95830e7i	0.331470	−	1.02016i
$820$		0			0
$821$	−1.72388e6	+	5.30555e6i	−0.0892583	+	0.274709i	−0.985715	−	0.168423i	$-0.946133\pi$
$821$	−1.72388e6	+	5.30555e6i	−0.0892583	+	0.274709i	0.896457	+	0.443132i	$0.146133\pi$
$822$		0			0
$823$	−1.33012e7	−	9.66387e6i	−0.684527	−	0.497338i	0.190329	−	0.981720i	$-0.439044\pi$
$823$	−1.33012e7	−	9.66387e6i	−0.684527	−	0.497338i	−0.874856	+	0.484382i	$0.839044\pi$
$824$		0			0
$825$	4.98733e6	+	1.53494e7i	0.255113	+	0.785159i
$826$		0			0
$827$	−448116.	−	1.37916e6i	−0.0227838	−	0.0701214i	0.939018	−	0.343868i	$-0.111737\pi$
$827$	−448116.	−	1.37916e6i	−0.0227838	−	0.0701214i	−0.961802	+	0.273746i	$0.911737\pi$
$828$		0			0
$829$	−8.11955e6	−	5.89920e6i	−0.410342	−	0.298131i	0.363398	−	0.931634i	$-0.381616\pi$
$829$	−8.11955e6	−	5.89920e6i	−0.410342	−	0.298131i	−0.773740	+	0.633503i	$0.781616\pi$
$830$		0			0
$831$	−2.33197e7			−1.17144
$832$		0			0
$833$	−1.98078e7	+	1.43912e7i	−0.989061	+	0.718595i
$834$		0			0
$835$	1.20043e7	+	3.69453e7i	0.595825	+	1.83376i
$836$		0			0
$837$	6.29671e6	+	5.54272e7i	0.310671	+	2.73470i
$838$		0			0
$839$	7.76070e6	+	2.38850e7i	0.380624	+	1.17144i	0.939605	+	0.342260i	$0.111192\pi$
$839$	7.76070e6	+	2.38850e7i	0.380624	+	1.17144i	−0.558981	+	0.829180i	$0.688808\pi$
$840$		0			0
$841$	1.50880e7	−	1.09620e7i	0.735598	−	0.534443i
$842$		0			0
$843$	−7.59336e7			−3.68015
$844$		0			0
$845$	−1.85321e7	−	1.34644e7i	−0.892861	−	0.648701i
$846$		0			0
$847$	−345508.	−	1.06336e6i	−0.0165482	−	0.0509300i
$848$		0			0
$849$	1.64636e7	+	5.06697e7i	0.783890	+	2.41257i
$850$		0			0
$851$	3.21204e7	+	2.33368e7i	1.52040	+	1.10463i
$852$		0			0
$853$	−2.75640e6	+	8.48331e6i	−0.129709	+	0.399202i	−0.994730	−	0.102534i	$-0.967305\pi$
$853$	−2.75640e6	+	8.48331e6i	−0.129709	+	0.399202i	0.865021	+	0.501736i	$0.167305\pi$
$854$		0			0
$855$	6.65305e6	−	2.04760e7i	0.311247	−	0.957920i
$856$		0			0
$857$	2.37289e7	−	1.72401e7i	1.10364	−	0.801839i	0.121987	−	0.992532i	$-0.461073\pi$
$857$	2.37289e7	−	1.72401e7i	1.10364	−	0.801839i	0.981650	+	0.190692i	$0.0610733\pi$
$858$		0			0
$859$	1.07280e7	+	7.79434e6i	0.496062	+	0.360410i	0.807511	−	0.589853i	$-0.200814\pi$
$859$	1.07280e7	+	7.79434e6i	0.496062	+	0.360410i	−0.311449	+	0.950263i	$0.600814\pi$
$860$		0			0
$861$	9.43773e7	−	6.85691e7i	4.33870	−	3.15225i
$862$		0			0
$863$	4.95040e6			0.226263			0.113131	−	0.993580i	$-0.463912\pi$
$863$	4.95040e6			0.226263			0.113131	+	0.993580i	$0.463912\pi$
$864$		0			0
$865$	4.04006e6	−	1.24340e7i	0.183590	−	0.565031i
$866$		0			0
$867$	8.94553e6			0.404165
$868$		0			0
$869$	3.36594e7			1.51202
$870$		0			0
$871$	468288.	−	1.44124e6i	0.0209155	−	0.0643712i
$872$		0			0
$873$	2.91867e7			1.29613
$874$		0			0
$875$	1.91285e7	−	1.38977e7i	0.844621	−	0.613653i
$876$		0			0
$877$	4.92819e6	+	3.58054e6i	0.216366	+	0.157199i	0.690689	−	0.723152i	$-0.257307\pi$
$877$	4.92819e6	+	3.58054e6i	0.216366	+	0.157199i	−0.474324	+	0.880351i	$0.657307\pi$
$878$		0			0
$879$	1.47835e7	−	1.07408e7i	0.645363	−	0.468883i
$880$		0			0
$881$	−2.10277e6	+	6.47168e6i	−0.0912752	+	0.280916i	−0.986265	−	0.165170i	$-0.947183\pi$
$881$	−2.10277e6	+	6.47168e6i	−0.0912752	+	0.280916i	0.894990	+	0.446087i	$0.147183\pi$
$882$		0			0
$883$	5.87697e6	−	1.80875e7i	0.253660	−	0.780685i	−0.740431	−	0.672133i	$-0.765378\pi$
$883$	5.87697e6	−	1.80875e7i	0.253660	−	0.780685i	0.994091	−	0.108552i	$-0.0346216\pi$
$884$		0			0
$885$	−6.17288e7	−	4.48486e7i	−2.64929	−	1.92482i
$886$		0			0
$887$	−573817.	−	1.76603e6i	−0.0244886	−	0.0753682i	0.938065	−	0.346458i	$-0.112616\pi$
$887$	−573817.	−	1.76603e6i	−0.0244886	−	0.0753682i	−0.962554	+	0.271090i	$0.912616\pi$
$888$		0			0
$889$	−2.20560e7	−	6.78814e7i	−0.935992	−	2.88069i
$890$		0			0
$891$	5.17819e7	+	3.76217e7i	2.18516	+	1.58761i
$892$		0			0
$893$	−1.30454e7			−0.547431
$894$		0			0
$895$	8.82091e6	−	6.40877e6i	0.368092	−	0.267434i
$896$		0			0
$897$	−5.40082e6	−	1.66220e7i	−0.224119	−	0.689767i
$898$		0			0
$899$	7.15300e6	+	1.45774e6i	0.295181	+	0.0601562i
$900$		0			0
$901$	−2.96682e6	−	9.13094e6i	−0.121753	−	0.374717i
$902$		0			0
$903$	−5.19484e7	+	3.77427e7i	−2.12008	+	1.54033i
$904$		0			0
$905$	2.27974e7			0.925262
$906$		0			0
$907$	2.00098e6	+	1.45380e6i	0.0807652	+	0.0586793i	0.627435	−	0.778669i	$-0.284105\pi$
$907$	2.00098e6	+	1.45380e6i	0.0807652	+	0.0586793i	−0.546670	+	0.837348i	$0.684105\pi$
$908$		0			0
$909$	1.28884e7	+	3.96664e7i	0.517355	+	1.59226i
$910$		0			0
$911$	1.51796e7	+	4.67181e7i	0.605990	+	1.86505i	0.489836	+	0.871815i	$0.337057\pi$
$911$	1.51796e7	+	4.67181e7i	0.605990	+	1.86505i	0.116154	+	0.993231i	$0.462943\pi$
$912$		0			0
$913$	2.95580e6	+	2.14751e6i	0.117354	+	0.0852627i
$914$		0			0
$915$	1.97081e7	−	6.06553e7i	0.778201	−	2.39506i
$916$		0			0
$917$	1.16479e7	−	3.58486e7i	0.457430	−	1.40782i
$918$		0			0
$919$	−1.62909e7	+	1.18360e7i	−0.636292	+	0.462293i	−0.858574	−	0.512689i	$-0.828649\pi$
$919$	−1.62909e7	+	1.18360e7i	−0.636292	+	0.462293i	0.222283	+	0.974982i	$0.428649\pi$
$920$		0			0
$921$	−7.04442e7	−	5.11807e7i	−2.73650	−	1.98819i
$922$		0			0
$923$	7.59533e6	−	5.51833e6i	0.293455	−	0.213208i
$924$		0			0
$925$	1.53625e7			0.590348
$926$		0			0
$927$	−4.25000e6	+	1.30802e7i	−0.162439	+	0.499935i
$928$		0			0
$929$	−3.62009e7			−1.37619			−0.688097	−	0.725619i	$-0.741554\pi$
$929$	−3.62009e7			−1.37619			−0.688097	+	0.725619i	$0.741554\pi$
$930$		0			0
$931$	−1.24040e7			−0.469017
$932$		0			0
$933$	−1.14296e7	+	3.51765e7i	−0.429858	+	1.32297i
$934$		0			0
$935$	2.88305e7			1.07851
$936$		0			0
$937$	1.31920e7	−	9.58452e6i	0.490863	−	0.356633i	−0.314653	−	0.949207i	$-0.601888\pi$
$937$	1.31920e7	−	9.58452e6i	0.490863	−	0.356633i	0.805516	+	0.592574i	$0.201888\pi$
$938$		0			0
$939$	5.27512e7	+	3.83260e7i	1.95240	+	1.41850i
$940$		0			0
$941$	−1.92041e7	+	1.39526e7i	−0.706999	+	0.513665i	−0.882204	−	0.470867i	$-0.843941\pi$
$941$	−1.92041e7	+	1.39526e7i	−0.706999	+	0.513665i	0.175205	+	0.984532i	$0.443941\pi$
$942$		0			0
$943$	2.17960e7	−	6.70813e7i	0.798176	−	2.45653i
$944$		0			0
$945$	−4.31663e7	+	1.32852e8i	−1.57241	+	4.83937i
$946$		0			0
$947$	1.35012e7	+	9.80921e6i	0.489213	+	0.355434i	0.804882	−	0.593435i	$-0.202229\pi$
$947$	1.35012e7	+	9.80921e6i	0.489213	+	0.355434i	−0.315668	+	0.948870i	$0.602229\pi$
$948$		0			0
$949$	1.77725e6	+	5.46981e6i	0.0640593	+	0.197154i
$950$		0			0
$951$	−1.67368e7	−	5.15105e7i	−0.600096	−	1.84691i
$952$		0			0
$953$	1.91432e7	+	1.39083e7i	0.682781	+	0.496070i	0.874279	−	0.485423i	$-0.161335\pi$
$953$	1.91432e7	+	1.39083e7i	0.682781	+	0.496070i	−0.191498	+	0.981493i	$0.561335\pi$
$954$		0			0
$955$	4.90900e7			1.74175
$956$		0			0
$957$	1.30955e7	−	9.51444e6i	0.462213	−	0.335818i
$958$		0			0
$959$	−798264.	−	2.45680e6i	−0.0280285	−	0.0862628i
$960$		0			0
$961$	−1.47290e7	−	2.45496e7i	−0.514475	−	0.857505i
$962$		0			0
$963$	−2.61248e7	−	8.04040e7i	−0.907795	−	2.79391i
$964$		0			0
$965$	−1.71891e7	+	1.24886e7i	−0.594203	+	0.431714i
$966$		0			0
$967$	−3.20470e6			−0.110210			−0.0551050	−	0.998481i	$-0.517549\pi$
$967$	−3.20470e6			−0.110210			−0.0551050	+	0.998481i	$0.517549\pi$
$968$		0			0
$969$	−1.32474e7	−	9.62478e6i	−0.453232	−	0.329292i
$970$		0			0
$971$	−3.00621e6	−	9.25216e6i	−0.102323	−	0.314916i	0.886770	−	0.462211i	$-0.152944\pi$
$971$	−3.00621e6	−	9.25216e6i	−0.102323	−	0.314916i	−0.989093	+	0.147294i	$0.952944\pi$
$972$		0			0
$973$	−1.37233e6	−	4.22360e6i	−0.0464704	−	0.143021i
$974$		0			0
$975$	−5.47110e6	−	3.97498e6i	−0.184316	−	0.133913i
$976$		0			0
$977$	1.43249e7	−	4.40875e7i	0.480126	−	1.47768i	−0.358792	−	0.933417i	$-0.616811\pi$
$977$	1.43249e7	−	4.40875e7i	0.480126	−	1.47768i	0.838918	−	0.544258i	$-0.183189\pi$
$978$		0			0
$979$	−9.41829e6	+	2.89865e7i	−0.314062	+	0.966583i
$980$		0			0
$981$	−9.61248e7	+	6.98387e7i	−3.18906	+	2.31699i
$982$		0			0
$983$	1.16797e7	+	8.48577e6i	0.385520	+	0.280096i	0.763617	−	0.645669i	$-0.223422\pi$
$983$	1.16797e7	+	8.48577e6i	0.385520	+	0.280096i	−0.378097	+	0.925766i	$0.623422\pi$
$984$		0			0
$985$	5.83298e6	−	4.23791e6i	0.191558	−	0.139175i
$986$		0			0
$987$	1.41979e8			4.63907
$988$		0			0
$989$	−1.19973e7	+	3.69238e7i	−0.390024	+	1.20037i
$990$		0			0
$991$	−2.14795e7			−0.694770			−0.347385	−	0.937723i	$-0.612930\pi$
$991$	−2.14795e7			−0.694770			−0.347385	+	0.937723i	$0.612930\pi$
$992$		0			0
$993$	−1.04757e8			−3.37140
$994$		0			0
$995$	−4.47532e6	+	1.37736e7i	−0.143307	+	0.441053i
$996$		0			0
$997$	2.18005e7			0.694590			0.347295	−	0.937756i	$-0.387100\pi$
$997$	2.18005e7			0.694590			0.347295	+	0.937756i	$0.387100\pi$
$998$		0			0
$999$	9.52538e7	−	6.92059e7i	3.01973	−	2.19396i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	124.6.f.a.97.1	✓	56
31.8	even	5	inner	124.6.f.a.101.1	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
124.6.f.a.97.1	✓	56	1.1	even	1	trivial
124.6.f.a.101.1	yes	56	31.8	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)

\(f(q)\)	\(=\)	\(q+(-8.98126 + 27.6415i) q^{3} -66.9725 q^{5} +(161.853 - 117.593i) q^{7} +(-486.797 - 353.679i) q^{9} +O(q^{10})\)	\(q+(-8.98126 + 27.6415i) q^{3} -66.9725 q^{5} +(161.853 - 117.593i) q^{7} +(-486.797 - 353.679i) q^{9} +(330.253 - 239.943i) q^{11} +(-52.8570 + 162.677i) q^{13} +(601.498 - 1851.22i) q^{15} +(-853.146 - 619.847i) q^{17} +(-165.095 - 508.110i) q^{19} +(1796.80 + 5529.97i) q^{21} +(2844.20 + 2066.43i) q^{23} +1360.32 q^{25} +(8434.54 - 6128.05i) q^{27} +(-421.602 - 1297.56i) q^{29} +(-2636.30 + 4656.08i) q^{31} +(3666.29 + 11283.7i) q^{33} +(-10839.7 + 7875.49i) q^{35} +11293.3 q^{37} +(-4021.91 - 2922.09i) q^{39} +(-6199.77 - 19080.9i) q^{41} +(3412.56 + 10502.8i) q^{43} +(32602.0 + 23686.8i) q^{45} +(7545.52 - 23222.7i) q^{47} +(7174.54 - 22081.0i) q^{49} +(24795.8 - 18015.2i) q^{51} +(7365.48 + 5351.33i) q^{53} +(-22117.9 + 16069.6i) q^{55} +15527.7 q^{57} +(12113.3 - 37280.8i) q^{59} +32765.0 q^{61} -120379. q^{63} +(3539.97 - 10894.9i) q^{65} -8859.53 q^{67} +(-82663.7 + 60058.7i) q^{69} +(-44404.4 - 32261.7i) q^{71} +(27202.2 - 19763.5i) q^{73} +(-12217.4 + 37601.3i) q^{75} +(25236.8 - 77670.8i) q^{77} +(66707.5 + 48465.9i) q^{79} +(48452.2 + 149120. i) q^{81} +(2765.73 + 8512.05i) q^{83} +(57137.4 + 41512.7i) q^{85} +39652.9 q^{87} +(-60402.9 + 43885.3i) q^{89} +(10574.6 + 32545.3i) q^{91} +(-105024. - 114689. i) q^{93} +(11056.8 + 34029.4i) q^{95} +(-39242.2 + 28511.1i) q^{97} -245629. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 2 q^{3} - 58 q^{5} + 104 q^{7} - 1234 q^{9}+O(q^{10}) \) 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

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Groups

Database

Properties

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