LMFDB - Embedded newform 124.6.f.a.97.2

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			97.2
Character	$\chi$	$=$	124.97
Dual form			124.6.f.a.101.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-8.90517 + 27.4073i) q^{3} +53.9543 q^{5} +(-68.0214 + 49.4205i) q^{7} +(-475.267 - 345.302i) q^{9} +O(q^{10})$	\(q+(-8.90517 + 27.4073i) q^{3} +53.9543 q^{5} +(-68.0214 + 49.4205i) q^{7} +(-475.267 - 345.302i) q^{9} +(-570.436 + 414.446i) q^{11} +(202.866 - 624.358i) q^{13} +(-480.472 + 1478.74i) q^{15} +(806.268 + 585.788i) q^{17} +(402.834 + 1239.80i) q^{19} +(-748.739 - 2304.38i) q^{21} +(-3265.95 - 2372.85i) q^{23} -213.934 q^{25} +(8030.80 - 5834.72i) q^{27} +(-102.805 - 316.400i) q^{29} +(-3100.80 - 4360.53i) q^{31} +(-6279.02 - 19324.8i) q^{33} +(-3670.05 + 2666.45i) q^{35} +11970.3 q^{37} +(15305.4 + 11120.0i) q^{39} +(-3537.21 - 10886.4i) q^{41} +(-260.609 - 802.072i) q^{43} +(-25642.7 - 18630.5i) q^{45} +(1714.66 - 5277.19i) q^{47} +(-3009.12 + 9261.11i) q^{49} +(-23234.8 + 16881.1i) q^{51} +(10514.0 + 7638.88i) q^{53} +(-30777.5 + 22361.2i) q^{55} -37566.7 q^{57} +(-2773.07 + 8534.64i) q^{59} +14715.9 q^{61} +49393.3 q^{63} +(10945.5 - 33686.8i) q^{65} -61044.5 q^{67} +(94117.2 - 68380.1i) q^{69} +(43492.9 + 31599.4i) q^{71} +(-42090.7 + 30580.7i) q^{73} +(1905.12 - 5863.35i) q^{75} +(18319.8 - 56382.5i) q^{77} +(-33933.8 - 24654.4i) q^{79} +(44285.0 + 136295. i) q^{81} +(-11345.9 - 34919.2i) q^{83} +(43501.6 + 31605.8i) q^{85} +9587.17 q^{87} +(-116170. + 84402.6i) q^{89} +(17056.8 + 52495.4i) q^{91} +(147123. - 46153.2i) q^{93} +(21734.6 + 66892.3i) q^{95} +(-50225.9 + 36491.3i) q^{97} +414218. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−8.90517	+	27.4073i	−0.571267	+	1.75818i	0.0772855	+	0.997009i	$0.475375\pi$
$3$	−8.90517	+	27.4073i	−0.571267	+	1.75818i	−0.648552	+	0.761170i	$0.724625\pi$
$4$		0			0
$5$	53.9543			0.965164			0.482582	−	0.875851i	$-0.339699\pi$
$5$	53.9543			0.965164			0.482582	+	0.875851i	$0.339699\pi$
$6$		0			0
$7$	−68.0214	+	49.4205i	−0.524687	+	0.381208i	−0.818367	−	0.574696i	$-0.805120\pi$
$7$	−68.0214	+	49.4205i	−0.524687	+	0.381208i	0.293679	+	0.955904i	$0.405120\pi$
$8$		0			0
$9$	−475.267	−	345.302i	−1.95583	−	1.42099i
$10$		0			0
$11$	−570.436	+	414.446i	−1.42143	+	1.03273i	−0.429897	+	0.902878i	$0.641450\pi$
$11$	−570.436	+	414.446i	−1.42143	+	1.03273i	−0.991533	+	0.129851i	$0.958550\pi$
$12$		0			0
$13$	202.866	−	624.358i	0.332929	−	1.02465i	−0.634805	−	0.772673i	$-0.718919\pi$
$13$	202.866	−	624.358i	0.332929	−	1.02465i	0.967733	−	0.251976i	$-0.0810806\pi$
$14$		0			0
$15$	−480.472	+	1478.74i	−0.551366	+	1.69693i
$16$		0			0
$17$	806.268	+	585.788i	0.676639	+	0.491607i	0.872241	−	0.489076i	$-0.162666\pi$
$17$	806.268	+	585.788i	0.676639	+	0.491607i	−0.195602	+	0.980683i	$0.562666\pi$
$18$		0			0
$19$	402.834	+	1239.80i	0.256001	+	0.787891i	0.993631	+	0.112685i	$0.0359451\pi$
$19$	402.834	+	1239.80i	0.256001	+	0.787891i	−0.737630	+	0.675206i	$0.764055\pi$
$20$		0			0
$21$	−748.739	−	2304.38i	−0.370495	−	1.14027i
$22$		0			0
$23$	−3265.95	−	2372.85i	−1.28733	−	0.935299i	−0.287581	−	0.957756i	$-0.592851\pi$
$23$	−3265.95	−	2372.85i	−1.28733	−	0.935299i	−0.999748	+	0.0224574i	$0.992851\pi$
$24$		0			0
$25$	−213.934			−0.0684589
$26$		0			0
$27$	8030.80	−	5834.72i	2.12007	−	1.54032i
$28$		0			0
$29$	−102.805	−	316.400i	−0.0226996	−	0.0698622i	0.939065	−	0.343740i	$-0.111694\pi$
$29$	−102.805	−	316.400i	−0.0226996	−	0.0698622i	−0.961765	+	0.273877i	$0.911694\pi$
$30$		0			0
$31$	−3100.80	−	4360.53i	−0.579521	−	0.814957i
$31$	−3100.80	−	4360.53i	−0.579521	−	0.814957i
$32$		0			0
$33$	−6279.02	−	19324.8i	−1.00371	−	3.08909i
$34$		0			0
$35$	−3670.05	+	2666.45i	−0.506409	+	0.367928i
$36$		0			0
$37$	11970.3			1.43748			0.718741	−	0.695278i	$-0.244719\pi$
$37$	11970.3			1.43748			0.718741	+	0.695278i	$0.244719\pi$
$38$		0			0
$39$	15305.4	+	11120.0i	1.61133	+	1.17070i
$40$		0			0
$41$	−3537.21	−	10886.4i	−0.328625	−	1.01141i	−0.969777	−	0.243991i	$-0.921543\pi$
$41$	−3537.21	−	10886.4i	−0.328625	−	1.01141i	0.641152	−	0.767414i	$-0.278457\pi$
$42$		0			0
$43$	−260.609	−	802.072i	−0.0214940	−	0.0661519i	0.939734	−	0.341906i	$-0.111072\pi$
$43$	−260.609	−	802.072i	−0.0214940	−	0.0661519i	−0.961228	+	0.275754i	$0.911072\pi$
$44$		0			0
$45$	−25642.7	−	18630.5i	−1.88770	−	1.37149i
$46$		0			0
$47$	1714.66	−	5277.19i	0.113223	−	0.348464i	−0.878349	−	0.478019i	$-0.841355\pi$
$47$	1714.66	−	5277.19i	0.113223	−	0.348464i	0.991572	+	0.129555i	$0.0413549\pi$
$48$		0			0
$49$	−3009.12	+	9261.11i	−0.179039	+	0.551027i
$50$		0			0
$51$	−23234.8	+	16881.1i	−1.25087	+	0.908814i
$52$		0			0
$53$	10514.0	+	7638.88i	0.514137	+	0.373543i	0.814391	−	0.580317i	$-0.197071\pi$
$53$	10514.0	+	7638.88i	0.514137	+	0.373543i	−0.300253	+	0.953859i	$0.597071\pi$
$54$		0			0
$55$	−30777.5	+	22361.2i	−1.37191	+	0.996753i
$56$		0			0
$57$	−37566.7			−1.53150
$58$		0			0
$59$	−2773.07	+	8534.64i	−0.103713	+	0.319194i	−0.989426	−	0.145038i	$-0.953670\pi$
$59$	−2773.07	+	8534.64i	−0.103713	+	0.319194i	0.885714	+	0.464232i	$0.153670\pi$
$60$		0			0
$61$	14715.9			0.506365			0.253182	−	0.967419i	$-0.418523\pi$
$61$	14715.9			0.506365			0.253182	+	0.967419i	$0.418523\pi$
$62$		0			0
$63$	49393.3			1.56789
$64$		0			0
$65$	10945.5	−	33686.8i	0.321331	−	0.988954i
$66$		0			0
$67$	−61044.5			−1.66134			−0.830672	−	0.556762i	$-0.812043\pi$
$67$	−61044.5			−1.66134			−0.830672	+	0.556762i	$0.812043\pi$
$68$		0			0
$69$	94117.2	−	68380.1i	2.37983	−	1.72905i
$70$		0			0
$71$	43492.9	+	31599.4i	1.02393	+	0.743932i	0.967086	−	0.254451i	$-0.0818946\pi$
$71$	43492.9	+	31599.4i	1.02393	+	0.743932i	0.0568491	+	0.998383i	$0.481895\pi$
$72$		0			0
$73$	−42090.7	+	30580.7i	−0.924441	+	0.671646i	−0.944626	−	0.328150i	$-0.893575\pi$
$73$	−42090.7	+	30580.7i	−0.924441	+	0.671646i	0.0201841	+	0.999796i	$0.493575\pi$
$74$		0			0
$75$	1905.12	−	5863.35i	0.0391083	−	0.120363i
$76$		0			0
$77$	18319.8	−	56382.5i	0.352122	−	1.08372i
$78$		0			0
$79$	−33933.8	−	24654.4i	−0.611738	−	0.444454i	0.238288	−	0.971195i	$-0.423414\pi$
$79$	−33933.8	−	24654.4i	−0.611738	−	0.444454i	−0.850026	+	0.526741i	$0.823414\pi$
$80$		0			0
$81$	44285.0	+	136295.i	0.749971	+	2.30817i
$82$		0			0
$83$	−11345.9	−	34919.2i	−0.180778	−	0.556377i	0.819072	−	0.573690i	$-0.194489\pi$
$83$	−11345.9	−	34919.2i	−0.180778	−	0.556377i	−0.999850	+	0.0173132i	$0.994489\pi$
$84$		0			0
$85$	43501.6	+	31605.8i	0.653067	+	0.474481i
$86$		0			0
$87$	9587.17			0.135798
$88$		0			0
$89$	−116170.	+	84402.6i	−1.55460	+	1.12949i	−0.614338	+	0.789043i	$0.710577\pi$
$89$	−116170.	+	84402.6i	−1.55460	+	1.12949i	−0.940265	+	0.340442i	$0.889423\pi$
$90$		0			0
$91$	17056.8	+	52495.4i	0.215921	+	0.664535i
$92$		0			0
$93$	147123.	−	46153.2i	1.76390	−	0.553343i
$94$		0			0
$95$	21734.6	+	66892.3i	0.247083	+	0.760443i
$96$		0			0
$97$	−50225.9	+	36491.3i	−0.541999	+	0.393786i	−0.824827	−	0.565385i	$-0.808728\pi$
$97$	−50225.9	+	36491.3i	−0.541999	+	0.393786i	0.282828	+	0.959171i	$0.408728\pi$
$98$		0			0
$99$	414218.			4.24758
$100$		0			0
$101$	−108431.	−	78779.7i	−1.05767	−	0.768441i	−0.0840132	−	0.996465i	$-0.526774\pi$
$101$	−108431.	−	78779.7i	−1.05767	−	0.768441i	−0.973656	+	0.228023i	$0.926774\pi$
$102$		0			0
$103$	21834.2	+	67198.7i	0.202789	+	0.624120i	0.999797	+	0.0201511i	$0.00641472\pi$
$103$	21834.2	+	67198.7i	0.202789	+	0.624120i	−0.797008	+	0.603968i	$0.793585\pi$
$104$		0			0
$105$	−40397.7	−	124331.i	−0.357588	−	1.10054i
$106$		0			0
$107$	−74260.5	−	53953.4i	−0.627045	−	0.455575i	0.228330	−	0.973584i	$-0.426673\pi$
$107$	−74260.5	−	53953.4i	−0.627045	−	0.455575i	−0.855375	+	0.518009i	$0.826673\pi$
$108$		0			0
$109$	−64436.0	+	198314.i	−0.519472	+	1.59877i	0.255522	+	0.966803i	$0.417753\pi$
$109$	−64436.0	+	198314.i	−0.519472	+	1.59877i	−0.774994	+	0.631969i	$0.782247\pi$
$110$		0			0
$111$	−106598.	+	328075.i	−0.821186	+	2.52735i
$112$		0			0
$113$	−142981.	+	103882.i	−1.05338	+	0.765323i	−0.972852	−	0.231430i	$-0.925660\pi$
$113$	−142981.	+	103882.i	−1.05338	+	0.765323i	−0.0805250	+	0.996753i	$0.525660\pi$
$114$		0			0
$115$	−176212.	−	128025.i	−1.24248	−	0.902717i
$116$		0			0
$117$	−312007.	+	226687.i	−2.10717	+	1.53095i
$118$		0			0
$119$	−83793.4			−0.542428
$120$		0			0
$121$	103864.	−	319662.i	0.644916	−	1.98485i
$122$		0			0
$123$	329867.			1.96596
$124$		0			0
$125$	−180150.			−1.03124
$126$		0			0
$127$	71553.8	−	220220.i	0.393662	−	1.21157i	−0.536337	−	0.844004i	$-0.680192\pi$
$127$	71553.8	−	220220.i	0.393662	−	1.21157i	0.929999	−	0.367563i	$-0.119808\pi$
$128$		0			0
$129$	24303.4			0.128586
$130$		0			0
$131$	−92114.4	+	66925.0i	−0.468974	+	0.340730i	−0.797041	−	0.603925i	$-0.793603\pi$
$131$	−92114.4	+	66925.0i	−0.468974	+	0.340730i	0.328067	+	0.944654i	$0.393603\pi$
$132$		0			0
$133$	−88672.6	−	64424.4i	−0.434671	−	0.315807i
$134$		0			0
$135$	433296.	−	314808.i	2.04621	−	1.48666i
$136$		0			0
$137$	−91253.4	+	280849.i	−0.415382	+	1.27841i	0.496527	+	0.868021i	$0.334608\pi$
$137$	−91253.4	+	280849.i	−0.415382	+	1.27841i	−0.911909	+	0.410393i	$0.865392\pi$
$138$		0			0
$139$	68483.8	−	210771.i	0.300643	−	0.925283i	−0.680625	−	0.732632i	$-0.738292\pi$
$139$	68483.8	−	210771.i	0.300643	−	0.925283i	0.981267	−	0.192651i	$-0.0617085\pi$
$140$		0			0
$141$	129364.	+	93988.6i	0.547982	+	0.398132i
$142$		0			0
$143$	143041.	+	440234.i	0.584950	+	1.80029i
$144$		0			0
$145$	−5546.76	−	17071.2i	−0.0219088	−	0.0674284i
$146$		0			0
$147$	−227025.	−	164943.i	−0.866524	−	0.629567i
$148$		0			0
$149$	294859.			1.08805			0.544025	−	0.839069i	$-0.316900\pi$
$149$	294859.			1.08805			0.544025	+	0.839069i	$0.316900\pi$
$150$		0			0
$151$	227053.	−	164963.i	0.810371	−	0.588769i	−0.103567	−	0.994622i	$-0.533026\pi$
$151$	227053.	−	164963.i	0.810371	−	0.588769i	0.913938	+	0.405853i	$0.133026\pi$
$152$		0			0
$153$	−180919.	−	556811.i	−0.624821	−	1.92300i
$154$		0			0
$155$	−167301.	−	235269.i	−0.559333	−	0.786567i
$156$		0			0
$157$	−501.124	−	1542.30i	−0.00162254	−	0.00499367i	0.950242	−	0.311513i	$-0.100836\pi$
$157$	−501.124	−	1542.30i	−0.00162254	−	0.00499367i	−0.951865	+	0.306519i	$0.900836\pi$
$158$		0			0
$159$	−302990.	+	220135.i	−0.950464	+	0.690553i
$160$		0			0
$161$	339422.			1.03199
$162$		0			0
$163$	240608.	+	174812.i	0.709320	+	0.515351i	0.882954	−	0.469459i	$-0.155551\pi$
$163$	240608.	+	174812.i	0.709320	+	0.515351i	−0.173635	+	0.984810i	$0.555551\pi$
$164$		0			0
$165$	−338780.	−	1.04266e6i	−0.968742	−	2.98148i
$166$		0			0
$167$	−82293.1	−	253272.i	−0.228335	−	0.702742i	−0.997936	−	0.0642173i	$-0.979545\pi$
$167$	−82293.1	−	253272.i	−0.228335	−	0.702742i	0.769601	−	0.638525i	$-0.220455\pi$
$168$		0			0
$169$	−48285.6	−	35081.6i	−0.130047	−	0.0944849i
$170$		0			0
$171$	236650.	−	728333.i	0.618893	−	1.90476i
$172$		0			0
$173$	−22381.9	+	68884.4i	−0.0568567	+	0.174987i	−0.975452	−	0.220213i	$-0.929325\pi$
$173$	−22381.9	+	68884.4i	−0.0568567	+	0.174987i	0.918595	+	0.395200i	$0.129325\pi$
$174$		0			0
$175$	14552.1	−	10572.7i	0.0359195	−	0.0260970i
$176$		0			0
$177$	−209217.	−	152005.i	−0.501953	−	0.364690i
$178$		0			0
$179$	−438676.	+	318717.i	−1.02332	+	0.743485i	−0.966961	−	0.254926i	$-0.917949\pi$
$179$	−438676.	+	318717.i	−1.02332	+	0.743485i	−0.0563586	+	0.998411i	$0.517949\pi$
$180$		0			0
$181$	−9769.79			−0.0221661			−0.0110830	−	0.999939i	$-0.503528\pi$
$181$	−9769.79			−0.0221661			−0.0110830	+	0.999939i	$0.503528\pi$
$182$		0			0
$183$	−131048.	+	403324.i	−0.289270	+	0.890280i
$184$		0			0
$185$	645851.			1.38741
$186$		0			0
$187$	−702702.			−1.46949
$188$		0			0
$189$	−257912.	+	793772.i	−0.525191	+	1.61637i
$190$		0			0
$191$	−32844.9			−0.0651455			−0.0325727	−	0.999469i	$-0.510370\pi$
$191$	−32844.9			−0.0651455			−0.0325727	+	0.999469i	$0.510370\pi$
$192$		0			0
$193$	−705496.	+	512573.i	−1.36333	+	0.990518i	−0.365105	+	0.930966i	$0.618967\pi$
$193$	−705496.	+	512573.i	−1.36333	+	0.990518i	−0.998225	+	0.0595513i	$0.981033\pi$
$194$		0			0
$195$	825792.	+	599973.i	1.55519	+	1.12991i
$196$		0			0
$197$	−511749.	+	371807.i	−0.939488	+	0.682578i	−0.948297	−	0.317383i	$-0.897196\pi$
$197$	−511749.	+	371807.i	−0.939488	+	0.682578i	0.00880928	+	0.999961i	$0.497196\pi$
$198$		0			0
$199$	22057.7	−	67886.6i	0.0394846	−	0.121521i	−0.929371	−	0.369146i	$-0.879650\pi$
$199$	22057.7	−	67886.6i	0.0394846	−	0.121521i	0.968856	+	0.247625i	$0.0796502\pi$
$200$		0			0
$201$	543612.	−	1.67306e6i	0.949071	−	2.92094i
$202$		0			0
$203$	22629.6	+	16441.3i	0.0385422	+	0.0280025i
$204$		0			0
$205$	−190848.	−	587369.i	−0.317177	−	0.976172i
$206$		0			0
$207$	732847.	+	2.25547e6i	1.18874	+	3.65857i
$208$		0			0
$209$	−743620.	−	540271.i	−1.17757	−	0.855551i
$210$		0			0
$211$	−48639.8			−0.0752117			−0.0376058	−	0.999293i	$-0.511973\pi$
$211$	−48639.8			−0.0752117			−0.0376058	+	0.999293i	$0.511973\pi$
$212$		0			0
$213$	−1.25337e6	+	910624.i	−1.89291	+	1.37528i
$214$		0			0
$215$	−14061.0	−	43275.2i	−0.0207453	−	0.0638474i
$216$		0			0
$217$	426420.	+	143366.i	0.614735	+	0.206680i
$218$		0			0
$219$	−463309.	−	1.42592e6i	−0.652771	−	2.00902i
$220$		0			0
$221$	529306.	−	384563.i	0.728997	−	0.529647i
$222$		0			0
$223$	173540.			0.233688			0.116844	−	0.993150i	$-0.462722\pi$
$223$	173540.			0.233688			0.116844	+	0.993150i	$0.462722\pi$
$224$		0			0
$225$	101676.	+	73871.7i	0.133894	+	0.0972796i
$226$		0			0
$227$	404916.	+	1.24620e6i	0.521556	+	1.60518i	0.771028	+	0.636802i	$0.219743\pi$
$227$	404916.	+	1.24620e6i	0.521556	+	1.60518i	−0.249472	+	0.968382i	$0.580257\pi$
$228$		0			0
$229$	−188917.	−	581427.i	−0.238058	−	0.732666i	−0.996701	−	0.0811602i	$-0.974137\pi$
$229$	−188917.	−	581427.i	−0.238058	−	0.732666i	0.758643	−	0.651506i	$-0.225863\pi$
$230$		0			0
$231$	1.38215e6	+	1.00419e6i	1.70422	+	1.23819i
$232$		0			0
$233$	−265291.	+	816481.i	−0.320134	+	0.985273i	0.653455	+	0.756966i	$0.273319\pi$
$233$	−265291.	+	816481.i	−0.320134	+	0.985273i	−0.973589	+	0.228307i	$0.926681\pi$
$234$		0			0
$235$	92513.5	−	284727.i	0.109279	−	0.336325i
$236$		0			0
$237$	977897.	−	710484.i	1.13089	−	0.821643i
$238$		0			0
$239$	876983.	+	637166.i	0.993108	+	0.721535i	0.960600	−	0.277936i	$-0.0896503\pi$
$239$	876983.	+	637166.i	0.993108	+	0.721535i	0.0325088	+	0.999471i	$0.489650\pi$
$240$		0			0
$241$	485664.	−	352855.i	0.538633	−	0.391340i	−0.284944	−	0.958544i	$-0.591975\pi$
$241$	485664.	−	352855.i	0.538633	−	0.391340i	0.823577	+	0.567204i	$0.191975\pi$
$242$		0			0
$243$	−1.71768e6			−1.86607
$244$		0			0
$245$	−162355.	+	499677.i	−0.172802	+	0.531831i
$246$		0			0
$247$	855797.			0.892541
$248$		0			0
$249$	1.05808e6			1.08148
$250$		0			0
$251$	179763.	−	553254.i	0.180101	−	0.554294i	−0.819729	−	0.572752i	$-0.805876\pi$
$251$	179763.	−	553254.i	0.180101	−	0.554294i	0.999830	+	0.0184582i	$0.00587575\pi$
$252$		0			0
$253$	2.84643e6			2.79576
$254$		0			0
$255$	−1.25362e6	+	910807.i	−1.20730	+	0.877154i
$256$		0			0
$257$	819807.	+	595625.i	0.774246	+	0.562523i	0.903247	−	0.429122i	$-0.141177\pi$
$257$	819807.	+	595625.i	0.774246	+	0.562523i	−0.129001	+	0.991645i	$0.541177\pi$
$258$		0			0
$259$	−814240.	+	591580.i	−0.754228	+	0.547979i
$260$		0			0
$261$	−60393.9	+	185873.i	−0.0548772	+	0.168895i
$262$		0			0
$263$	−196728.	+	605465.i	−0.175378	+	0.539759i	−0.999651	−	0.0264346i	$-0.991585\pi$
$263$	−196728.	+	605465.i	−0.175378	+	0.539759i	0.824272	+	0.566194i	$0.191585\pi$
$264$		0			0
$265$	567277.	+	412151.i	0.496227	+	0.360530i
$266$		0			0
$267$	−1.27873e6	−	3.93553e6i	−1.09774	−	3.37851i
$268$		0			0
$269$	−362199.	−	1.11473e6i	−0.305187	−	0.939269i	−0.979607	−	0.200921i	$-0.935606\pi$
$269$	−362199.	−	1.11473e6i	−0.305187	−	0.939269i	0.674420	−	0.738348i	$-0.264394\pi$
$270$		0			0
$271$	−789260.	−	573431.i	−0.652825	−	0.474305i	0.211407	−	0.977398i	$-0.432195\pi$
$271$	−789260.	−	573431.i	−0.652825	−	0.474305i	−0.864232	+	0.503093i	$0.832195\pi$
$272$		0			0
$273$	−1.59065e6			−1.29172
$274$		0			0
$275$	122036.	−	88664.1i	0.0973095	−	0.0706995i
$276$		0			0
$277$	140391.	+	432078.i	0.109936	+	0.338347i	0.990857	−	0.134915i	$-0.0430762\pi$
$277$	140391.	+	432078.i	0.109936	+	0.338347i	−0.880921	+	0.473263i	$0.843076\pi$
$278$		0			0
$279$	−31990.9	+	3.14312e6i	−0.0246046	+	2.41741i
$280$		0			0
$281$	158577.	+	488051.i	0.119805	+	0.368722i	0.992919	−	0.118794i	$-0.0379029\pi$
$281$	158577.	+	488051.i	0.119805	+	0.368722i	−0.873114	+	0.487517i	$0.837903\pi$
$282$		0			0
$283$	1.71186e6	−	1.24374e6i	1.27058	−	0.923129i	0.271352	−	0.962480i	$-0.412529\pi$
$283$	1.71186e6	−	1.24374e6i	1.27058	−	0.923129i	0.999225	+	0.0393513i	$0.0125291\pi$
$284$		0			0
$285$	−2.02689e6			−1.47815
$286$		0			0
$287$	778617.	+	565699.i	0.557981	+	0.405397i
$288$		0			0
$289$	−131840.	−	405760.i	−0.0928541	−	0.285776i
$290$		0			0
$291$	−552857.	−	1.70152e6i	−0.382719	−	1.17789i
$292$		0			0
$293$	350063.	+	254335.i	0.238219	+	0.173076i	0.700490	−	0.713663i	$-0.252965\pi$
$293$	350063.	+	254335.i	0.238219	+	0.173076i	−0.462270	+	0.886739i	$0.652965\pi$
$294$		0			0
$295$	−149619.	+	460480.i	−0.100100	+	0.308075i
$296$		0			0
$297$	−2.16288e6	+	6.65667e6i	−1.42279	+	4.37891i
$298$		0			0
$299$	−2.14406e6	+	1.55775e6i	−1.38694	+	1.00767i
$300$		0			0
$301$	57365.8	+	41678.7i	0.0364953	+	0.0265154i
$302$		0			0
$303$	3.12473e6	−	2.27025e6i	1.95527	−	1.42059i
$304$		0			0
$305$	793989.			0.488725
$306$		0			0
$307$	−311652.	+	959167.i	−0.188723	+	0.580829i	−0.999993	−	0.00384306i	$-0.998777\pi$
$307$	−311652.	+	959167.i	−0.188723	+	0.580829i	0.811270	+	0.584672i	$0.198777\pi$
$308$		0			0
$309$	−2.03617e6			−1.21316
$310$		0			0
$311$	1.22144e6			0.716094			0.358047	−	0.933704i	$-0.383443\pi$
$311$	1.22144e6			0.716094			0.358047	+	0.933704i	$0.383443\pi$
$312$		0			0
$313$	310025.	−	954159.i	0.178869	−	0.550503i	−0.820920	−	0.571044i	$-0.806539\pi$
$313$	310025.	−	954159.i	0.178869	−	0.550503i	0.999789	+	0.0205403i	$0.00653865\pi$
$314$		0			0
$315$	2.66498e6			1.51327
$316$		0			0
$317$	−1.90578e6	+	1.38463e6i	−1.06518	+	0.773901i	−0.975040	−	0.222027i	$-0.928733\pi$
$317$	−1.90578e6	+	1.38463e6i	−1.06518	+	0.773901i	−0.0901434	+	0.995929i	$0.528733\pi$
$318$		0			0
$319$	189775.	+	137879.i	0.104415	+	0.0758616i
$320$		0			0
$321$	2.14002e6	−	1.55482e6i	1.15919	−	0.842202i
$322$		0			0
$323$	−401465.	+	1.23558e6i	−0.214112	+	0.658969i
$324$		0			0
$325$	−43400.0	+	133571.i	−0.0227919	+	0.0701463i
$326$		0			0
$327$	−4.86143e6	−	3.53203e6i	−2.51417	−	1.82665i
$328$		0			0
$329$	144167.	+	443702.i	0.0734307	+	0.225996i
$330$		0			0
$331$	−219788.	−	676437.i	−0.110264	−	0.339357i	0.880666	−	0.473738i	$-0.157096\pi$
$331$	−219788.	−	676437.i	−0.110264	−	0.339357i	−0.990930	+	0.134380i	$0.957096\pi$
$332$		0			0
$333$	−5.68911e6	−	4.13338e6i	−2.81147	−	2.04265i
$334$		0			0
$335$	−3.29361e6			−1.60347
$336$		0			0
$337$	1.12711e6	−	818893.i	0.540619	−	0.392783i	−0.283696	−	0.958914i	$-0.591561\pi$
$337$	1.12711e6	−	818893.i	0.540619	−	0.392783i	0.824315	+	0.566132i	$0.191561\pi$
$338$		0			0
$339$	−1.57385e6	−	4.84382e6i	−0.743815	−	2.28923i
$340$		0			0
$341$	3.57601e6	+	1.20229e6i	1.66538	+	0.559916i
$342$		0			0
$343$	−689681.	−	2.12262e6i	−0.316529	−	0.974175i
$344$		0			0
$345$	5.07803e6	−	3.68940e6i	2.29693	−	1.66882i
$346$		0			0
$347$	2.65173e6			1.18224			0.591119	−	0.806584i	$-0.298686\pi$
$347$	2.65173e6			1.18224			0.591119	+	0.806584i	$0.298686\pi$
$348$		0			0
$349$	462270.	+	335859.i	0.203157	+	0.147602i	0.684712	−	0.728813i	$-0.259928\pi$
$349$	462270.	+	335859.i	0.203157	+	0.147602i	−0.481555	+	0.876416i	$0.659928\pi$
$350$		0			0
$351$	−2.01377e6	−	6.19776e6i	−0.872455	−	2.68514i
$352$		0			0
$353$	−38003.9	−	116964.i	−0.0162327	−	0.0499592i	0.942612	−	0.333890i	$-0.108361\pi$
$353$	−38003.9	−	116964.i	−0.0162327	−	0.0499592i	−0.958845	+	0.283931i	$0.908361\pi$
$354$		0			0
$355$	2.34663e6	+	1.70492e6i	0.988265	+	0.718016i
$356$		0			0
$357$	746194.	−	2.29655e6i	0.309871	−	0.953686i
$358$		0			0
$359$	856226.	−	2.63519e6i	0.350633	−	1.07914i	−0.607866	−	0.794040i	$-0.707974\pi$
$359$	856226.	−	2.63519e6i	0.350633	−	1.07914i	0.958499	−	0.285097i	$-0.0920258\pi$
$360$		0			0
$361$	628390.	−	456552.i	0.253782	−	0.184383i
$362$		0			0
$363$	7.83614e6	+	5.69329e6i	3.12130	+	2.26776i
$364$		0			0
$365$	−2.27098e6	+	1.64996e6i	−0.892237	+	0.648248i
$366$		0			0
$367$	−3.92298e6			−1.52038			−0.760188	−	0.649704i	$-0.774893\pi$
$367$	−3.92298e6			−1.52038			−0.760188	+	0.649704i	$0.774893\pi$
$368$		0			0
$369$	−2.07798e6	+	6.39535e6i	−0.794465	+	2.44511i
$370$		0			0
$371$	−1.09270e6			−0.412159
$372$		0			0
$373$	1.00314e6			0.373327			0.186664	−	0.982424i	$-0.440233\pi$
$373$	1.00314e6			0.373327			0.186664	+	0.982424i	$0.440233\pi$
$374$		0			0
$375$	1.60427e6	−	4.93742e6i	0.589112	−	1.81310i
$376$		0			0
$377$	−218403.			−0.0791415
$378$		0			0
$379$	−3.54942e6	+	2.57881e6i	−1.26929	+	0.922191i	−0.999174	−	0.0406372i	$-0.987061\pi$
$379$	−3.54942e6	+	2.57881e6i	−1.26929	+	0.922191i	−0.270113	+	0.962829i	$0.587061\pi$
$380$		0			0
$381$	5.39844e6	+	3.92219e6i	1.90527	+	1.38426i
$382$		0			0
$383$	−370603.	+	269259.i	−0.129096	+	0.0937937i	−0.650459	−	0.759541i	$-0.725424\pi$
$383$	−370603.	+	269259.i	−0.129096	+	0.0937937i	0.521363	+	0.853335i	$0.325424\pi$
$384$		0			0
$385$	988430.	−	3.04208e6i	0.339855	−	1.04597i
$386$		0			0
$387$	−153098.	+	471187.i	−0.0519627	+	0.159925i
$388$		0			0
$389$	2.02536e6	+	1.47151e6i	0.678623	+	0.493048i	0.872901	−	0.487898i	$-0.162236\pi$
$389$	2.02536e6	+	1.47151e6i	0.678623	+	0.493048i	−0.194278	+	0.980947i	$0.562236\pi$
$390$		0			0
$391$	−1.24324e6	−	3.82630e6i	−0.411257	−	1.26572i
$392$		0			0
$393$	−1.01394e6	−	3.12059e6i	−0.331155	−	1.01919i
$394$		0			0
$395$	−1.83088e6	−	1.33021e6i	−0.590427	−	0.428971i
$396$		0			0
$397$	−2.98442e6			−0.950350			−0.475175	−	0.879891i	$-0.657615\pi$
$397$	−2.98442e6			−0.950350			−0.475175	+	0.879891i	$0.657615\pi$
$398$		0			0
$399$	2.55534e6	−	1.85657e6i	0.803557	−	0.583819i
$400$		0			0
$401$	875623.	+	2.69489e6i	0.271929	+	0.836913i	0.990016	+	0.140958i	$0.0450184\pi$
$401$	875623.	+	2.69489e6i	0.271929	+	0.836913i	−0.718086	+	0.695954i	$0.754982\pi$
$402$		0			0
$403$	−3.35158e6	+	1.05140e6i	−1.02798	+	0.322483i
$404$		0			0
$405$	2.38937e6	+	7.35372e6i	0.723845	+	2.22776i
$406$		0			0
$407$	−6.82832e6	+	4.96106e6i	−2.04328	+	1.48453i
$408$		0			0
$409$	5.69151e6			1.68236			0.841181	−	0.540754i	$-0.181861\pi$
$409$	5.69151e6			1.68236			0.841181	+	0.540754i	$0.181861\pi$
$410$		0			0
$411$	−6.88469e6	−	5.00202e6i	−2.01039	−	1.46063i
$412$		0			0
$413$	−233157.	−	717585.i	−0.0672627	−	0.207013i
$414$		0			0
$415$	−612162.	−	1.88404e6i	−0.174480	−	0.536995i
$416$		0			0
$417$	5.16682e6	+	3.75391e6i	1.45507	+	1.05717i
$418$		0			0
$419$	−1.40547e6	+	4.32558e6i	−0.391098	+	1.20368i	0.540861	+	0.841112i	$0.318099\pi$
$419$	−1.40547e6	+	4.32558e6i	−0.391098	+	1.20368i	−0.931959	+	0.362564i	$0.881901\pi$
$420$		0			0
$421$	1.27734e6	−	3.93126e6i	0.351238	−	1.08100i	−0.606920	−	0.794763i	$-0.707595\pi$
$421$	1.27734e6	−	3.93126e6i	0.351238	−	1.08100i	0.958159	−	0.286238i	$-0.0924048\pi$
$422$		0			0
$423$	−2.63715e6	+	1.91600e6i	−0.716611	+	0.520648i
$424$		0			0
$425$	−172488.	−	125320.i	−0.0463219	−	0.0336549i
$426$		0			0
$427$	−1.00100e6	+	727269.i	−0.265683	+	0.193030i
$428$		0			0
$429$	−1.33394e7			−3.49940
$430$		0			0
$431$	−1.73237e6	+	5.33170e6i	−0.449209	+	1.38252i	0.428592	+	0.903498i	$0.359010\pi$
$431$	−1.73237e6	+	5.33170e6i	−0.449209	+	1.38252i	−0.877801	+	0.479025i	$0.840990\pi$
$432$		0			0
$433$	−280591.			−0.0719207			−0.0359604	−	0.999353i	$-0.511449\pi$
$433$	−280591.			−0.0719207			−0.0359604	+	0.999353i	$0.511449\pi$
$434$		0			0
$435$	517269.			0.131067
$436$		0			0
$437$	1.62621e6	−	5.00497e6i	0.407356	−	1.25371i
$438$		0			0
$439$	6.54210e6			1.62015			0.810077	−	0.586324i	$-0.199425\pi$
$439$	6.54210e6			1.62015			0.810077	+	0.586324i	$0.199425\pi$
$440$		0			0
$441$	4.62801e6	−	3.36244e6i	1.13318	−	0.823301i
$442$		0			0
$443$	3.65597e6	+	2.65622e6i	0.885103	+	0.643065i	0.934596	−	0.355710i	$-0.115761\pi$
$443$	3.65597e6	+	2.65622e6i	0.885103	+	0.643065i	−0.0494938	+	0.998774i	$0.515761\pi$
$444$		0			0
$445$	−6.26788e6	+	4.55388e6i	−1.50045	+	1.09014i
$446$		0			0
$447$	−2.62577e6	+	8.08130e6i	−0.621567	+	1.91299i
$448$		0			0
$449$	1.43245e6	−	4.40863e6i	0.335324	−	1.03202i	−0.631239	−	0.775589i	$-0.717453\pi$
$449$	1.43245e6	−	4.40863e6i	0.335324	−	1.03202i	0.966562	−	0.256432i	$-0.0825468\pi$
$450$		0			0
$451$	6.52959e6	+	4.74402e6i	1.51163	+	1.09826i
$452$		0			0
$453$	2.49926e6	+	7.69193e6i	0.572223	+	1.76112i
$454$		0			0
$455$	920288.	+	2.83235e6i	0.208399	+	0.641386i
$456$		0			0
$457$	−3.98364e6	−	2.89428e6i	−0.892255	−	0.648262i	0.0442097	−	0.999022i	$-0.485923\pi$
$457$	−3.98364e6	−	2.89428e6i	−0.892255	−	0.648262i	−0.936465	+	0.350761i	$0.885923\pi$
$458$		0			0
$459$	9.89288e6			2.19175
$460$		0			0
$461$	−3.14038e6	+	2.28162e6i	−0.688224	+	0.500024i	−0.876076	−	0.482173i	$-0.839848\pi$
$461$	−3.14038e6	+	2.28162e6i	−0.688224	+	0.500024i	0.187852	+	0.982197i	$0.439848\pi$
$462$		0			0
$463$	−524374.	−	1.61386e6i	−0.113681	−	0.349875i	0.877988	−	0.478682i	$-0.158885\pi$
$463$	−524374.	−	1.61386e6i	−0.113681	−	0.349875i	−0.991670	+	0.128807i	$0.958885\pi$
$464$		0			0
$465$	7.93794e6	−	2.49017e6i	1.70245	−	0.534067i
$466$		0			0
$467$	−1.04586e6	−	3.21884e6i	−0.221913	−	0.682978i	−0.998590	−	0.0530793i	$-0.983096\pi$
$467$	−1.04586e6	−	3.21884e6i	−0.221913	−	0.682978i	0.776677	−	0.629899i	$-0.216904\pi$
$468$		0			0
$469$	4.15233e6	−	3.01685e6i	0.871686	−	0.633317i
$470$		0			0
$471$	46732.9			0.00970667
$472$		0			0
$473$	481077.	+	349523.i	0.0988693	+	0.0718327i
$474$		0			0
$475$	−86179.8	−	265234.i	−0.0175255	−	0.0539381i
$476$		0			0
$477$	−2.35925e6	−	7.26101e6i	−0.474764	−	1.46117i
$478$		0			0
$479$	4.45416e6	+	3.23614e6i	0.887008	+	0.644449i	0.935096	−	0.354394i	$-0.115313\pi$
$479$	4.45416e6	+	3.23614e6i	0.887008	+	0.644449i	−0.0480883	+	0.998843i	$0.515313\pi$
$480$		0			0
$481$	2.42838e6	−	7.47378e6i	0.478579	−	1.47291i
$482$		0			0
$483$	−3.02261e6	+	9.30263e6i	−0.589541	+	1.81442i
$484$		0			0
$485$	−2.70990e6	+	1.96886e6i	−0.523118	+	0.380068i
$486$		0			0
$487$	−6.34348e6	−	4.60881e6i	−1.21201	−	0.880575i	−0.216596	−	0.976261i	$-0.569495\pi$
$487$	−6.34348e6	−	4.60881e6i	−1.21201	−	0.880575i	−0.995412	+	0.0956865i	$0.969495\pi$
$488$		0			0
$489$	−6.93379e6	+	5.03770e6i	−1.31129	+	0.952708i
$490$		0			0
$491$	−7.81989e6			−1.46385			−0.731925	−	0.681385i	$-0.761378\pi$
$491$	−7.81989e6			−1.46385			−0.731925	+	0.681385i	$0.761378\pi$
$492$		0			0
$493$	102455.	−	315325.i	0.0189853	−	0.0584307i
$494$		0			0
$495$	2.23489e7			4.09961
$496$		0			0
$497$	−4.52011e6			−0.820838
$498$		0			0
$499$	−1.60718e6	+	4.94640e6i	−0.288944	+	0.889278i	0.696245	+	0.717804i	$0.254853\pi$
$499$	−1.60718e6	+	4.94640e6i	−0.288944	+	0.889278i	−0.985189	+	0.171474i	$0.945147\pi$
$500$		0			0
$501$	7.67434e6			1.36599
$502$		0			0
$503$	−2.23990e6	+	1.62738e6i	−0.394737	+	0.286793i	−0.767394	−	0.641176i	$-0.778447\pi$
$503$	−2.23990e6	+	1.62738e6i	−0.394737	+	0.286793i	0.372657	+	0.927969i	$0.378447\pi$
$504$		0			0
$505$	−5.85031e6	−	4.25050e6i	−1.02082	−	0.741672i
$506$		0			0
$507$	1.39148e6	−	1.01097e6i	0.240413	−	0.174670i
$508$		0			0
$509$	379324.	−	1.16744e6i	0.0648957	−	0.199729i	−0.913351	−	0.407173i	$-0.866515\pi$
$509$	379324.	−	1.16744e6i	0.0648957	−	0.199729i	0.978247	+	0.207444i	$0.0665146\pi$
$510$		0			0
$511$	1.35176e6	−	4.16029e6i	0.229006	−	0.704808i
$512$		0			0
$513$	1.04689e7	+	7.60613e6i	1.75634	+	1.27606i
$514$		0			0
$515$	1.17805e6	+	3.62566e6i	0.195724	+	0.602378i
$516$		0			0
$517$	1.20901e6	+	3.72094e6i	0.198931	+	0.612247i
$518$		0			0
$519$	−1.68862e6	−	1.22685e6i	−0.275178	−	0.199929i
$520$		0			0
$521$	5.51363e6			0.889904			0.444952	−	0.895554i	$-0.353221\pi$
$521$	5.51363e6			0.889904			0.444952	+	0.895554i	$0.353221\pi$
$522$		0			0
$523$	6.28959e6	−	4.56965e6i	1.00547	−	0.730515i	0.0422137	−	0.999109i	$-0.486559\pi$
$523$	6.28959e6	−	4.56965e6i	1.00547	−	0.730515i	0.963254	+	0.268594i	$0.0865590\pi$
$524$		0			0
$525$	160181.	+	492985.i	0.0253637	+	0.0780613i
$526$		0			0
$527$	54271.1	−	5.33216e6i	0.00851220	−	0.836328i
$528$		0			0
$529$	3.04705e6	+	9.37787e6i	0.473414	+	1.45702i
$530$		0			0
$531$	4.26497e6	−	3.09868e6i	0.656417	−	0.476915i
$532$		0			0
$533$	−7.51460e6			−1.14574
$534$		0			0
$535$	−4.00668e6	−	2.91102e6i	−0.605201	−	0.439704i
$536$		0			0
$537$	−4.82868e6	−	1.48611e7i	−0.722591	−	2.22391i
$538$		0			0
$539$	−2.12172e6	−	6.52999e6i	−0.314570	−	0.968145i
$540$		0			0
$541$	−9.09907e6	−	6.61086e6i	−1.33661	−	0.971102i	−0.999561	−	0.0296131i	$-0.990572\pi$
$541$	−9.09907e6	−	6.61086e6i	−1.33661	−	0.971102i	−0.337045	−	0.941488i	$-0.609428\pi$
$542$		0			0
$543$	87001.6	−	267763.i	0.0126627	−	0.0389719i
$544$		0			0
$545$	−3.47660e6	+	1.06999e7i	−0.501376	+	1.54308i
$546$		0			0
$547$	−5.83453e6	+	4.23903e6i	−0.833753	+	0.605757i	−0.920619	−	0.390463i	$-0.872315\pi$
$547$	−5.83453e6	+	4.23903e6i	−0.833753	+	0.605757i	0.0868657	+	0.996220i	$0.472315\pi$
$548$		0			0
$549$	−6.99400e6	−	5.08144e6i	−0.990364	−	0.719541i
$550$		0			0
$551$	350858.	−	254914.i	0.0492326	−	0.0357696i
$552$		0			0
$553$	3.52666e6			0.490400
$554$		0			0
$555$	−5.75142e6	+	1.77010e7i	−0.792579	+	2.43931i
$556$		0			0
$557$	1.16795e7			1.59509			0.797544	−	0.603260i	$-0.206132\pi$
$557$	1.16795e7			1.59509			0.797544	+	0.603260i	$0.206132\pi$
$558$		0			0
$559$	−553649.			−0.0749384
$560$		0			0
$561$	6.25768e6	−	1.92592e7i	0.839472	−	2.58363i
$562$		0			0
$563$	−1.20801e7			−1.60621			−0.803103	−	0.595840i	$-0.796819\pi$
$563$	−1.20801e7			−1.60621			−0.803103	+	0.595840i	$0.796819\pi$
$564$		0			0
$565$	−7.71446e6	+	5.60489e6i	−1.01668	+	0.738662i
$566$		0			0
$567$	−9.74811e6	−	7.08241e6i	−1.27339	−	0.925175i
$568$		0			0
$569$	−233842.	+	169896.i	−0.0302790	+	0.0219990i	−0.602822	−	0.797876i	$-0.705957\pi$
$569$	−233842.	+	169896.i	−0.0302790	+	0.0219990i	0.572543	+	0.819875i	$0.305957\pi$
$570$		0			0
$571$	−934724.	+	2.87678e6i	−0.119976	+	0.369247i	−0.992952	−	0.118515i	$-0.962187\pi$
$571$	−934724.	+	2.87678e6i	−0.119976	+	0.369247i	0.872977	+	0.487762i	$0.162187\pi$
$572$		0			0
$573$	292489.	−	900189.i	0.0372155	−	0.114537i
$574$		0			0
$575$	698697.	+	507633.i	0.0881291	+	0.0640295i
$576$		0			0
$577$	4.54243e6	+	1.39801e7i	0.568000	+	1.74812i	0.658866	+	0.752261i	$0.271037\pi$
$577$	4.54243e6	+	1.39801e7i	0.568000	+	1.74812i	−0.0908657	+	0.995863i	$0.528963\pi$
$578$		0			0
$579$	−7.76567e6	−	2.39003e7i	−0.962681	−	2.96283i
$580$		0			0
$581$	2.49749e6	+	1.81453e6i	0.306947	+	0.223010i
$582$		0			0
$583$	−9.16349e6			−1.11658
$584$		0			0
$585$	−1.68341e7	+	1.22307e7i	−2.03377	+	1.47762i
$586$		0			0
$587$	−1.11278e6	−	3.42478e6i	−0.133295	−	0.410239i	0.862026	−	0.506864i	$-0.169195\pi$
$587$	−1.11278e6	−	3.42478e6i	−0.133295	−	0.410239i	−0.995321	+	0.0966248i	$0.969195\pi$
$588$		0			0
$589$	4.15705e6	−	5.60092e6i	0.493739	−	0.665229i
$590$		0			0
$591$	−5.63302e6	−	1.73367e7i	−0.663396	−	2.04172i
$592$		0			0
$593$	−7.10341e6	+	5.16093e6i	−0.829526	+	0.602686i	−0.919425	−	0.393265i	$-0.871346\pi$
$593$	−7.10341e6	+	5.16093e6i	−0.829526	+	0.602686i	0.0898991	+	0.995951i	$0.471346\pi$
$594$		0			0
$595$	−4.52101e6			−0.523532
$596$		0			0
$597$	1.66416e6	+	1.20908e6i	0.191099	+	0.138842i
$598$		0			0
$599$	3.60536e6	+	1.10962e7i	0.410565	+	1.26359i	0.916159	+	0.400816i	$0.131273\pi$
$599$	3.60536e6	+	1.10962e7i	0.410565	+	1.26359i	−0.505594	+	0.862772i	$0.668727\pi$
$600$		0			0
$601$	3.01311e6	+	9.27339e6i	0.340274	+	1.04725i	0.964066	+	0.265664i	$0.0855913\pi$
$601$	3.01311e6	+	9.27339e6i	0.340274	+	1.04725i	−0.623792	+	0.781590i	$0.714409\pi$
$602$		0			0
$603$	2.90124e7	+	2.10788e7i	3.24931	+	2.36076i
$604$		0			0
$605$	5.60393e6	−	1.72471e7i	0.622450	−	1.91570i
$606$		0			0
$607$	−1.01612e6	+	3.12730e6i	−0.111937	+	0.344507i	−0.991296	−	0.131653i	$-0.957972\pi$
$607$	−1.01612e6	+	3.12730e6i	−0.111937	+	0.344507i	0.879359	+	0.476160i	$0.157972\pi$
$608$		0			0
$609$	−652133.	+	473802.i	−0.0712513	+	0.0517671i
$610$		0			0
$611$	−2.94701e6	−	2.14113e6i	−0.319359	−	0.232028i
$612$		0			0
$613$	3.77345e6	−	2.74157e6i	0.405590	−	0.294678i	−0.366224	−	0.930527i	$-0.619350\pi$
$613$	3.77345e6	−	2.74157e6i	0.405590	−	0.294678i	0.771814	+	0.635848i	$0.219350\pi$
$614$		0			0
$615$	1.77977e7			1.89748
$616$		0			0
$617$	1.98660e6	−	6.11413e6i	0.210086	−	0.646579i	−0.789380	−	0.613905i	$-0.789598\pi$
$617$	1.98660e6	−	6.11413e6i	0.210086	−	0.646579i	0.999466	−	0.0326741i	$-0.0104023\pi$
$618$		0			0
$619$	1.17953e7			1.23732			0.618658	−	0.785660i	$-0.287677\pi$
$619$	1.17953e7			1.23732			0.618658	+	0.785660i	$0.287677\pi$
$620$		0			0
$621$	−4.00731e7			−4.16988
$622$		0			0
$623$	3.73085e6	−	1.14824e7i	0.385112	−	1.18525i
$624$		0			0
$625$	−9.05131e6			−0.926855
$626$		0			0
$627$	2.14294e7	−	1.55694e7i	2.17692	−	1.58162i
$628$		0			0
$629$	9.65130e6	+	7.01208e6i	0.972656	+	0.706676i
$630$		0			0
$631$	−107690.	+	78241.4i	−0.0107672	+	0.00782282i	−0.593156	−	0.805088i	$-0.702118\pi$
$631$	−107690.	+	78241.4i	−0.0107672	+	0.00782282i	0.582389	+	0.812910i	$0.302118\pi$
$632$		0			0
$633$	433145.	−	1.33308e6i	0.0429660	−	0.132236i
$634$		0			0
$635$	3.86064e6	−	1.18818e7i	0.379948	−	1.16936i
$636$		0			0
$637$	5.17180e6	+	3.75753e6i	0.505002	+	0.366905i
$638$		0			0
$639$	−9.75939e6	−	3.00363e7i	−0.945520	−	2.91001i
$640$		0			0
$641$	2.76689e6	+	8.51562e6i	0.265979	+	0.818599i	0.991466	+	0.130363i	$0.0416144\pi$
$641$	2.76689e6	+	8.51562e6i	0.265979	+	0.818599i	−0.725487	+	0.688235i	$0.758386\pi$
$642$		0			0
$643$	1.11989e7	+	8.13648e6i	1.06819	+	0.776085i	0.975586	−	0.219618i	$-0.0704811\pi$
$643$	1.11989e7	+	8.13648e6i	1.06819	+	0.776085i	0.0926033	+	0.995703i	$0.470481\pi$
$644$		0			0
$645$	1.31127e6			0.124106
$646$		0			0
$647$	5.70709e6	−	4.14644e6i	0.535987	−	0.389417i	−0.286606	−	0.958049i	$-0.592527\pi$
$647$	5.70709e6	−	4.14644e6i	0.535987	−	0.389417i	0.822592	+	0.568632i	$0.192527\pi$
$648$		0			0
$649$	−1.95529e6	−	6.01776e6i	−0.182221	−	0.560819i
$650$		0			0
$651$	−7.72663e6	+	1.04103e7i	−0.714558	+	0.962745i
$652$		0			0
$653$	−6.48315e6	−	1.99531e7i	−0.594981	−	1.83116i	−0.554821	−	0.831970i	$-0.687213\pi$
$653$	−6.48315e6	−	1.99531e7i	−0.594981	−	1.83116i	−0.0401604	−	0.999193i	$-0.512787\pi$
$654$		0			0
$655$	−4.96997e6	+	3.61089e6i	−0.452637	+	0.328860i
$656$		0			0
$657$	3.05639e7			2.76246
$658$		0			0
$659$	1.16781e6	+	848467.i	0.104751	+	0.0761064i	0.638928	−	0.769267i	$-0.279378\pi$
$659$	1.16781e6	+	848467.i	0.104751	+	0.0761064i	−0.534176	+	0.845373i	$0.679378\pi$
$660$		0			0
$661$	−5.73184e6	−	1.76408e7i	−0.510259	−	1.57042i	−0.791746	−	0.610850i	$-0.790828\pi$
$661$	−5.73184e6	−	1.76408e7i	−0.510259	−	1.57042i	0.281487	−	0.959565i	$-0.409172\pi$
$662$		0			0
$663$	5.82628e6	+	1.79314e7i	0.514763	+	1.58428i
$664$		0			0
$665$	−4.78427e6	−	3.47597e6i	−0.419528	−	0.304805i
$666$		0			0
$667$	−415016.	+	1.27729e6i	−0.0361202	+	0.111166i
$668$		0			0
$669$	−1.54540e6	+	4.75626e6i	−0.133498	+	0.410866i
$670$		0			0
$671$	−8.39451e6	+	6.09897e6i	−0.719762	+	0.522938i
$672$		0			0
$673$	−1.85850e6	−	1.35028e6i	−0.158171	−	0.114918i	0.505885	−	0.862601i	$-0.331166\pi$
$673$	−1.85850e6	−	1.35028e6i	−0.158171	−	0.114918i	−0.664055	+	0.747683i	$0.731166\pi$
$674$		0			0
$675$	−1.71806e6	+	1.24824e6i	−0.145137	+	0.105448i
$676$		0			0
$677$	3.18695e6			0.267242			0.133621	−	0.991033i	$-0.457340\pi$
$677$	3.18695e6			0.267242			0.133621	+	0.991033i	$0.457340\pi$
$678$		0			0
$679$	1.61302e6	−	4.96438e6i	0.134266	−	0.413229i
$680$		0			0
$681$	−3.77610e7			−3.12015
$682$		0			0
$683$	−3.83940e6			−0.314928			−0.157464	−	0.987525i	$-0.550332\pi$
$683$	−3.83940e6			−0.314928			−0.157464	+	0.987525i	$0.550332\pi$
$684$		0			0
$685$	−4.92351e6	+	1.51530e7i	−0.400912	+	1.23388i
$686$		0			0
$687$	1.76177e7			1.42415
$688$		0			0
$689$	6.90233e6	−	5.01484e6i	0.553921	−	0.402447i
$690$		0			0
$691$	1.10853e7	+	8.05391e6i	0.883183	+	0.641670i	0.934092	−	0.357033i	$-0.116212\pi$
$691$	1.10853e7	+	8.05391e6i	0.883183	+	0.641670i	−0.0509084	+	0.998703i	$0.516212\pi$
$692$		0			0
$693$	−2.81757e7	+	2.04709e7i	−2.22865	+	1.61921i
$694$		0			0
$695$	3.69499e6	−	1.13720e7i	0.290170	−	0.893050i
$696$		0			0
$697$	3.52519e6	−	1.08494e7i	0.274853	−	0.845911i
$698$		0			0
$699$	−2.00151e7	−	1.45418e7i	−1.54940	−	1.12571i
$700$		0			0
$701$	3.65855e6	+	1.12598e7i	0.281199	+	0.865441i	0.987512	+	0.157542i	$0.0503569\pi$
$701$	3.65855e6	+	1.12598e7i	0.281199	+	0.865441i	−0.706314	+	0.707899i	$0.749643\pi$
$702$		0			0
$703$	4.82206e6	+	1.48408e7i	0.367997	+	1.13258i
$704$		0			0
$705$	6.97976e6	+	5.07109e6i	0.528893	+	0.384263i
$706$		0			0
$707$	1.12690e7			0.847881
$708$		0			0
$709$	1.77050e7	−	1.28634e7i	1.32276	−	0.961039i	0.322864	−	0.946446i	$-0.395355\pi$
$709$	1.77050e7	−	1.28634e7i	1.32276	−	0.961039i	0.999894	−	0.0145937i	$-0.00464550\pi$
$710$		0			0
$711$	7.61443e6	+	2.34348e7i	0.564890	+	1.73855i
$712$		0			0
$713$	−219836.	+	2.15990e7i	−0.0161947	+	1.59114i
$714$		0			0
$715$	7.71765e6	+	2.37525e7i	0.564573	+	1.73758i
$716$		0			0
$717$	−2.52727e7	+	1.83617e7i	−1.83592	+	1.33387i
$718$		0			0
$719$	−940278.			−0.0678319			−0.0339159	−	0.999425i	$-0.510798\pi$
$719$	−940278.			−0.0678319			−0.0339159	+	0.999425i	$0.510798\pi$
$720$		0			0
$721$	−4.80618e6	−	3.49190e6i	−0.344320	−	0.250163i
$722$		0			0
$723$	5.34589e6	+	1.64530e7i	0.380342	+	1.17057i
$724$		0			0
$725$	21993.4	+	67688.8i	0.00155399	+	0.00478268i
$726$		0			0
$727$	9.18975e6	+	6.67674e6i	0.644863	+	0.468520i	0.861517	−	0.507728i	$-0.169514\pi$
$727$	9.18975e6	+	6.67674e6i	0.644863	+	0.468520i	−0.216654	+	0.976248i	$0.569514\pi$
$728$		0			0
$729$	4.53501e6	−	1.39573e7i	0.316052	−	0.972709i
$730$		0			0
$731$	259723.	−	799346.i	0.0179770	−	0.0553276i
$732$		0			0
$733$	9.90721e6	−	7.19801e6i	0.681070	−	0.494826i	−0.192643	−	0.981269i	$-0.561706\pi$
$733$	9.90721e6	−	7.19801e6i	0.681070	−	0.494826i	0.873712	+	0.486443i	$0.161706\pi$
$734$		0			0
$735$	−1.22490e7	−	8.89941e6i	−0.836338	−	0.607635i
$736$		0			0
$737$	3.48220e7	−	2.52997e7i	2.36148	−	1.71572i
$738$		0			0
$739$	−1.82301e7			−1.22794			−0.613970	−	0.789329i	$-0.710428\pi$
$739$	−1.82301e7			−1.22794			−0.613970	+	0.789329i	$0.710428\pi$
$740$		0			0
$741$	−7.62102e6	+	2.34551e7i	−0.509879	+	1.56925i
$742$		0			0
$743$	−1.99488e7			−1.32570			−0.662849	−	0.748753i	$-0.730653\pi$
$743$	−1.99488e7			−1.32570			−0.662849	+	0.748753i	$0.730653\pi$
$744$		0			0
$745$	1.59089e7			1.05015
$746$		0			0
$747$	−6.66531e6	+	2.05137e7i	−0.437038	+	1.34506i
$748$		0			0
$749$	7.71771e6			0.502671
$750$		0			0
$751$	−1.31550e6	+	955764.i	−0.0851118	+	0.0618373i	−0.629527	−	0.776978i	$-0.716751\pi$
$751$	−1.31550e6	+	955764.i	−0.0851118	+	0.0618373i	0.544416	+	0.838816i	$0.316751\pi$
$752$		0			0
$753$	1.35624e7	+	9.85364e6i	0.871662	+	0.633300i
$754$		0			0
$755$	1.22505e7	−	8.90048e6i	0.782141	−	0.568259i
$756$		0			0
$757$	−3.99567e6	+	1.22974e7i	−0.253426	+	0.779964i	0.740710	+	0.671825i	$0.234489\pi$
$757$	−3.99567e6	+	1.22974e7i	−0.253426	+	0.779964i	−0.994136	+	0.108139i	$0.965511\pi$
$758$		0			0
$759$	−2.53480e7	+	7.80130e7i	−1.59712	+	4.91544i
$760$		0			0
$761$	−1.34643e7	−	9.78241e6i	−0.842797	−	0.612328i	0.0803535	−	0.996766i	$-0.474395\pi$
$761$	−1.34643e7	−	9.78241e6i	−0.842797	−	0.612328i	−0.923151	+	0.384438i	$0.874395\pi$
$762$		0			0
$763$	−5.41772e6	−	1.66740e7i	−0.336903	−	1.03688i
$764$		0			0
$765$	−9.76135e6	−	3.00423e7i	−0.603054	−	1.85601i
$766$		0			0
$767$	4.76611e6	+	3.46278e6i	0.292533	+	0.212538i
$768$		0			0
$769$	−6.20254e6			−0.378228			−0.189114	−	0.981955i	$-0.560562\pi$
$769$	−6.20254e6			−0.378228			−0.189114	+	0.981955i	$0.560562\pi$
$770$		0			0
$771$	−2.36250e7	+	1.71646e7i	−1.43132	+	1.03991i
$772$		0			0
$773$	5.43939e6	+	1.67407e7i	0.327417	+	1.00769i	0.970338	+	0.241754i	$0.0777227\pi$
$773$	5.43939e6	+	1.67407e7i	0.327417	+	1.00769i	−0.642920	+	0.765933i	$0.722277\pi$
$774$		0			0
$775$	663366.	+	932865.i	0.0396733	+	0.0557911i
$776$		0			0
$777$	−8.96266e6	−	2.75842e7i	−0.532579	−	1.63911i
$778$		0			0
$779$	1.20720e7	−	8.77083e6i	0.712748	−	0.517842i
$780$		0			0
$781$	−3.79062e7			−2.22373
$782$		0			0
$783$	−2.67171e6	−	1.94111e6i	−0.155735	−	0.113148i
$784$		0			0
$785$	−27037.8	−	83213.8i	−0.00156602	−	0.00481971i
$786$		0			0
$787$	4.41165e6	+	1.35777e7i	0.253901	+	0.781427i	0.994044	+	0.108978i	$0.0347577\pi$
$787$	4.41165e6	+	1.35777e7i	0.253901	+	0.781427i	−0.740143	+	0.672449i	$0.765242\pi$
$788$		0			0
$789$	−1.48423e7	−	1.07835e7i	−0.848805	−	0.616693i
$790$		0			0
$791$	4.59190e6	−	1.41324e7i	0.260946	−	0.803111i
$792$		0			0
$793$	2.98537e6	−	9.18802e6i	0.168583	−	0.518846i
$794$		0			0
$795$	−1.63476e7	+	1.18772e7i	−0.917354	+	0.666497i
$796$		0			0
$797$	−228365.	−	165917.i	−0.0127346	−	0.00925221i	0.581400	−	0.813618i	$-0.302505\pi$
$797$	−228365.	−	165917.i	−0.0127346	−	0.00925221i	−0.594134	+	0.804366i	$0.702505\pi$
$798$		0			0
$799$	4.47380e6	−	3.25040e6i	0.247919	−	0.180123i
$800$		0			0
$801$	8.43561e7			4.64553
$802$		0			0
$803$	1.13360e7	−	3.48887e7i	0.620400	−	1.90940i
$804$		0			0
$805$	1.83133e7			0.996038
$806$		0			0
$807$	3.37772e7			1.82575
$808$		0			0
$809$	2.54987e6	−	7.84768e6i	0.136977	−	0.421570i	−0.858916	−	0.512117i	$-0.828861\pi$
$809$	2.54987e6	−	7.84768e6i	0.136977	−	0.421570i	0.995892	+	0.0905466i	$0.0288614\pi$
$810$		0			0
$811$	3.39057e7			1.81018			0.905088	−	0.425225i	$-0.139805\pi$
$811$	3.39057e7			1.81018			0.905088	+	0.425225i	$0.139805\pi$
$812$		0			0
$813$	2.27447e7	−	1.65250e7i	1.20685	−	0.876829i
$814$		0			0
$815$	1.29819e7	+	9.43187e6i	0.684610	+	0.497398i
$816$		0			0
$817$	889423.	−	646203.i	0.0466179	−	0.0338699i
$818$		0			0
$819$	1.00202e7	−	3.08391e7i	0.521997	−	1.60654i
$820$		0			0
$821$	−5.53971e6	+	1.70495e7i	−0.286833	+	0.882781i	0.699010	+	0.715112i	$0.253624\pi$
$821$	−5.53971e6	+	1.70495e7i	−0.286833	+	0.882781i	−0.985843	+	0.167670i	$0.946376\pi$
$822$		0			0
$823$	740122.	+	537730.i	0.0380894	+	0.0276735i	0.606667	−	0.794956i	$-0.292506\pi$
$823$	740122.	+	537730.i	0.0380894	+	0.0276735i	−0.568578	+	0.822630i	$0.692506\pi$
$824$		0			0
$825$	1.34330e6	+	4.13424e6i	0.0687126	+	0.211476i
$826$		0			0
$827$	−1.02311e7	−	3.14882e7i	−0.520187	−	1.60097i	−0.773641	−	0.633624i	$-0.781567\pi$
$827$	−1.02311e7	−	3.14882e7i	−0.520187	−	1.60097i	0.253454	−	0.967348i	$-0.418433\pi$
$828$		0			0
$829$	−2.12393e7	−	1.54312e7i	−1.07338	−	0.779856i	−0.0968626	−	0.995298i	$-0.530881\pi$
$829$	−2.12393e7	−	1.54312e7i	−1.07338	−	0.779856i	−0.976517	+	0.215442i	$0.930881\pi$
$830$		0			0
$831$	−1.30923e7			−0.657678
$832$		0			0
$833$	−7.85120e6	+	5.70423e6i	−0.392034	+	0.284829i
$834$		0			0
$835$	−4.44006e6	−	1.36651e7i	−0.220380	−	0.678261i
$836$		0			0
$837$	−5.03443e7	−	1.69263e7i	−2.48392	−	0.835117i
$838$		0			0
$839$	9.51862e6	+	2.92953e7i	0.466841	+	1.43679i	0.856652	+	0.515895i	$0.172540\pi$
$839$	9.51862e6	+	2.92953e7i	0.466841	+	1.43679i	−0.389811	+	0.920895i	$0.627460\pi$
$840$		0			0
$841$	1.65043e7	−	1.19911e7i	0.804652	−	0.584614i
$842$		0			0
$843$	−1.47883e7			−0.716721
$844$		0			0
$845$	−2.60522e6	−	1.89280e6i	−0.125517	−	0.0911934i
$846$		0			0
$847$	8.73283e6	+	2.68769e7i	0.418260	+	1.28727i
$848$		0			0
$849$	1.88431e7	+	5.79930e7i	0.897186	+	2.76126i
$850$		0			0
$851$	−3.90945e7	−	2.84038e7i	−1.85051	−	1.34448i
$852$		0			0
$853$	1.06149e7	−	3.26692e7i	0.499508	−	1.53733i	−0.310304	−	0.950637i	$-0.600431\pi$
$853$	1.06149e7	−	3.26692e7i	0.499508	−	1.53733i	0.809812	−	0.586690i	$-0.199569\pi$
$854$		0			0
$855$	1.27683e7	−	3.92967e7i	0.597333	−	1.83840i
$856$		0			0
$857$	−2.06646e7	+	1.50137e7i	−0.961114	+	0.698291i	−0.953409	−	0.301680i	$-0.902453\pi$
$857$	−2.06646e7	+	1.50137e7i	−0.961114	+	0.698291i	−0.00770518	+	0.999970i	$0.502453\pi$
$858$		0			0
$859$	−2.55473e7	−	1.85612e7i	−1.18130	−	0.858267i	−0.188985	−	0.981980i	$-0.560520\pi$
$859$	−2.55473e7	−	1.85612e7i	−1.18130	−	0.858267i	−0.992318	+	0.123713i	$0.960520\pi$
$860$		0			0
$861$	−2.24380e7	+	1.63022e7i	−1.03152	+	0.749441i
$862$		0			0
$863$	1.94115e7			0.887219			0.443610	−	0.896220i	$-0.353698\pi$
$863$	1.94115e7			0.887219			0.443610	+	0.896220i	$0.353698\pi$
$864$		0			0
$865$	−1.20760e6	+	3.71661e6i	−0.0548760	+	0.168891i
$866$		0			0
$867$	1.22948e7			0.555489
$868$		0			0
$869$	2.95750e7			1.32854
$870$		0			0
$871$	−1.23839e7	+	3.81136e7i	−0.553109	+	1.70229i
$872$		0			0
$873$	3.64712e7			1.61963
$874$		0			0
$875$	1.22540e7	−	8.90309e6i	0.541077	−	0.393116i
$876$		0			0
$877$	−2.60671e7	−	1.89389e7i	−1.14444	−	0.831487i	−0.156712	−	0.987644i	$-0.550089\pi$
$877$	−2.60671e7	−	1.89389e7i	−1.14444	−	0.831487i	−0.987732	+	0.156157i	$0.950089\pi$
$878$		0			0
$879$	−1.00880e7	+	7.32937e6i	−0.440386	+	0.319959i
$880$		0			0
$881$	4.44010e6	−	1.36652e7i	0.192732	−	0.593167i	−0.807264	−	0.590191i	$-0.799053\pi$
$881$	4.44010e6	−	1.36652e7i	0.192732	−	0.593167i	0.999996	−	0.00297633i	$-0.000947398\pi$
$882$		0			0
$883$	−9.21852e6	+	2.83717e7i	−0.397887	+	1.22457i	0.528804	+	0.848744i	$0.322641\pi$
$883$	−9.21852e6	+	2.83717e7i	−0.397887	+	1.22457i	−0.926691	+	0.375825i	$0.877359\pi$
$884$		0			0
$885$	−1.12881e7	−	8.20131e6i	−0.484467	−	0.351986i
$886$		0			0
$887$	−3.30506e6	−	1.01719e7i	−0.141049	−	0.434105i	0.855433	−	0.517914i	$-0.173291\pi$
$887$	−3.30506e6	−	1.01719e7i	−0.141049	−	0.434105i	−0.996482	+	0.0838094i	$0.973291\pi$
$888$		0			0
$889$	6.01618e6	+	1.85159e7i	0.255309	+	0.785761i
$890$		0			0
$891$	−8.17489e7	−	5.93940e7i	−3.44975	−	2.50639i
$892$		0			0
$893$	7.23337e6			0.303537
$894$		0			0
$895$	−2.36684e7	+	1.71961e7i	−0.987671	+	0.717585i
$896$		0			0
$897$	−2.36005e7	−	7.26348e7i	−0.979354	−	3.01414i
$898$		0			0
$899$	−1.06090e6	+	1.42938e6i	−0.0437798	+	0.0589858i
$900$		0			0
$901$	4.00235e6	+	1.23180e7i	0.164249	+	0.505507i
$902$		0			0
$903$	−1.65315e6	+	1.20108e6i	−0.0674673	+	0.0490178i
$904$		0			0
$905$	−527122.			−0.0213939
$906$		0			0
$907$	−6.37695e6	−	4.63313e6i	−0.257392	−	0.187006i	0.451605	−	0.892218i	$-0.350852\pi$
$907$	−6.37695e6	−	4.63313e6i	−0.257392	−	0.187006i	−0.708996	+	0.705212i	$0.750852\pi$
$908$		0			0
$909$	2.43309e7	+	7.48827e7i	0.976670	+	3.00588i
$910$		0			0
$911$	−672853.	−	2.07083e6i	−0.0268611	−	0.0826700i	0.936727	−	0.350060i	$-0.113839\pi$
$911$	−672853.	−	2.07083e6i	−0.0268611	−	0.0826700i	−0.963588	+	0.267390i	$0.913839\pi$
$912$		0			0
$913$	2.09443e7	+	1.52169e7i	0.831550	+	0.604157i
$914$		0			0
$915$	−7.07060e6	+	2.17611e7i	−0.279193	+	0.859266i
$916$		0			0
$917$	2.95829e6	−	9.10467e6i	0.116176	−	0.357553i
$918$		0			0
$919$	3.29502e7	−	2.39397e7i	1.28697	−	0.935040i	0.287233	−	0.957861i	$-0.407265\pi$
$919$	3.29502e7	−	2.39397e7i	1.28697	−	0.935040i	0.999740	+	0.0228206i	$0.00726466\pi$
$920$		0			0
$921$	−2.35128e7	−	1.70831e7i	−0.913390	−	0.663617i
$922$		0			0
$923$	2.85526e7	−	2.07447e7i	1.10317	−	0.801498i
$924$		0			0
$925$	−2.56086e6			−0.0984084
$926$		0			0
$927$	1.28268e7	−	3.94767e7i	0.490250	−	1.50883i
$928$		0			0
$929$	−1.49192e7			−0.567161			−0.283580	−	0.958948i	$-0.591522\pi$
$929$	−1.49192e7			−0.567161			−0.283580	+	0.958948i	$0.591522\pi$
$930$		0			0
$931$	−1.26940e7			−0.479983
$932$		0			0
$933$	−1.08771e7	+	3.34763e7i	−0.409081	+	1.25902i
$934$		0			0
$935$	−3.79138e7			−1.41830
$936$		0			0
$937$	2.07422e7	−	1.50701e7i	0.771804	−	0.560748i	−0.130704	−	0.991421i	$-0.541724\pi$
$937$	2.07422e7	−	1.50701e7i	0.771804	−	0.560748i	0.902508	+	0.430673i	$0.141724\pi$
$938$		0			0
$939$	2.33901e7	+	1.69939e7i	0.865701	+	0.628969i
$940$		0			0
$941$	−6.83697e6	+	4.96735e6i	−0.251704	+	0.182873i	−0.706481	−	0.707732i	$-0.749719\pi$
$941$	−6.83697e6	+	4.96735e6i	−0.251704	+	0.182873i	0.454778	+	0.890605i	$0.349719\pi$
$942$		0			0
$943$	−1.42795e7	+	4.39477e7i	−0.522917	+	1.60937i
$944$		0			0
$945$	−1.39155e7	+	4.28274e7i	−0.506895	+	1.56006i
$946$		0			0
$947$	−1.34811e7	−	9.79462e6i	−0.488485	−	0.354905i	0.316116	−	0.948720i	$-0.397621\pi$
$947$	−1.34811e7	−	9.79462e6i	−0.488485	−	0.354905i	−0.804601	+	0.593815i	$0.797621\pi$
$948$		0			0
$949$	1.05545e7	+	3.24835e7i	0.380428	+	1.17084i
$950$		0			0
$951$	−2.09777e7	−	6.45626e7i	−0.752153	−	2.31489i
$952$		0			0
$953$	1.65271e7	+	1.20077e7i	0.589475	+	0.428278i	0.842127	−	0.539279i	$-0.181303\pi$
$953$	1.65271e7	+	1.20077e7i	0.589475	+	0.428278i	−0.252653	+	0.967557i	$0.581303\pi$
$954$		0			0
$955$	−1.77212e6			−0.0628760
$956$		0			0
$957$	−5.46887e6	+	3.97337e6i	−0.193027	+	0.140242i
$958$		0			0
$959$	−7.67251e6	−	2.36135e7i	−0.269396	−	0.829115i
$960$		0			0
$961$	−9.39926e6	+	2.70422e7i	−0.328311	+	0.944570i
$962$		0			0
$963$	1.66634e7	+	5.12846e7i	0.579024	+	1.78205i
$964$		0			0
$965$	−3.80645e7	+	2.76555e7i	−1.31584	+	0.956012i
$966$		0			0
$967$	−1.03866e7			−0.357197			−0.178599	−	0.983922i	$-0.557156\pi$
$967$	−1.03866e7			−0.357197			−0.178599	+	0.983922i	$0.557156\pi$
$968$		0			0
$969$	−3.02889e7	−	2.20061e7i	−1.03627	−	0.752895i
$970$		0			0
$971$	−1.20171e7	−	3.69850e7i	−0.409028	−	1.25886i	−0.917484	−	0.397772i	$-0.869784\pi$
$971$	−1.20171e7	−	3.69850e7i	−0.409028	−	1.25886i	0.508456	−	0.861088i	$-0.330216\pi$
$972$		0			0
$973$	5.75806e6	+	1.77215e7i	0.194982	+	0.600092i
$974$		0			0
$975$	−3.27435e6	−	2.37895e6i	−0.110310	−	0.0801445i
$976$		0			0
$977$	2.44183e6	−	7.51519e6i	0.0818426	−	0.251886i	−0.901759	−	0.432238i	$-0.857724\pi$
$977$	2.44183e6	−	7.51519e6i	0.0818426	−	0.251886i	0.983602	+	0.180353i	$0.0577239\pi$
$978$		0			0
$979$	3.12874e7	−	9.62926e7i	1.04331	−	3.21097i
$980$		0			0
$981$	9.91023e7	−	7.20021e7i	3.28785	−	2.38876i
$982$		0			0
$983$	−1.60199e7	−	1.16391e7i	−0.528780	−	0.384181i	0.291121	−	0.956686i	$-0.405972\pi$
$983$	−1.60199e7	−	1.16391e7i	−0.528780	−	0.384181i	−0.819901	+	0.572505i	$0.805972\pi$
$984$		0			0
$985$	−2.76110e7	+	2.00606e7i	−0.906760	+	0.658800i
$986$		0			0
$987$	−1.34445e7			−0.439291
$988$		0			0
$989$	−1.05206e6	+	3.23791e6i	−0.0342019	+	0.105263i
$990$		0			0
$991$	2.81340e6			0.0910012			0.0455006	−	0.998964i	$-0.485512\pi$
$991$	2.81340e6			0.0910012			0.0455006	+	0.998964i	$0.485512\pi$
$992$		0			0
$993$	2.04966e7			0.659641
$994$		0			0
$995$	1.19011e6	−	3.66277e6i	0.0381091	−	0.117288i
$996$		0			0
$997$	−4.34742e7			−1.38514			−0.692570	−	0.721351i	$-0.743522\pi$
$997$	−4.34742e7			−1.38514			−0.692570	+	0.721351i	$0.743522\pi$
$998$		0			0
$999$	9.61314e7	−	6.98436e7i	3.04756	−	2.21418i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	124.6.f.a.97.2	✓	56
31.8	even	5	inner	124.6.f.a.101.2	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
124.6.f.a.97.2	✓	56	1.1	even	1	trivial
124.6.f.a.101.2	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)

\(f(q)\)	\(=\)	\(q+(-8.90517 + 27.4073i) q^{3} +53.9543 q^{5} +(-68.0214 + 49.4205i) q^{7} +(-475.267 - 345.302i) q^{9} +O(q^{10})\)	\(q+(-8.90517 + 27.4073i) q^{3} +53.9543 q^{5} +(-68.0214 + 49.4205i) q^{7} +(-475.267 - 345.302i) q^{9} +(-570.436 + 414.446i) q^{11} +(202.866 - 624.358i) q^{13} +(-480.472 + 1478.74i) q^{15} +(806.268 + 585.788i) q^{17} +(402.834 + 1239.80i) q^{19} +(-748.739 - 2304.38i) q^{21} +(-3265.95 - 2372.85i) q^{23} -213.934 q^{25} +(8030.80 - 5834.72i) q^{27} +(-102.805 - 316.400i) q^{29} +(-3100.80 - 4360.53i) q^{31} +(-6279.02 - 19324.8i) q^{33} +(-3670.05 + 2666.45i) q^{35} +11970.3 q^{37} +(15305.4 + 11120.0i) q^{39} +(-3537.21 - 10886.4i) q^{41} +(-260.609 - 802.072i) q^{43} +(-25642.7 - 18630.5i) q^{45} +(1714.66 - 5277.19i) q^{47} +(-3009.12 + 9261.11i) q^{49} +(-23234.8 + 16881.1i) q^{51} +(10514.0 + 7638.88i) q^{53} +(-30777.5 + 22361.2i) q^{55} -37566.7 q^{57} +(-2773.07 + 8534.64i) q^{59} +14715.9 q^{61} +49393.3 q^{63} +(10945.5 - 33686.8i) q^{65} -61044.5 q^{67} +(94117.2 - 68380.1i) q^{69} +(43492.9 + 31599.4i) q^{71} +(-42090.7 + 30580.7i) q^{73} +(1905.12 - 5863.35i) q^{75} +(18319.8 - 56382.5i) q^{77} +(-33933.8 - 24654.4i) q^{79} +(44285.0 + 136295. i) q^{81} +(-11345.9 - 34919.2i) q^{83} +(43501.6 + 31605.8i) q^{85} +9587.17 q^{87} +(-116170. + 84402.6i) q^{89} +(17056.8 + 52495.4i) q^{91} +(147123. - 46153.2i) q^{93} +(21734.6 + 66892.3i) q^{95} +(-50225.9 + 36491.3i) q^{97} +414218. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 2 q^{3} - 58 q^{5} + 104 q^{7} - 1234 q^{9}+O(q^{10}) \) 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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