LMFDB - Embedded newform 124.4.d.c.123.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [124,4,Mod(123,124)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(124, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("124.123");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 124 = 2^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	124.d (of order $2$, degree $1$, 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:	$7.31623684071$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			123.13
Character	$\chi$	$=$	124.123
Dual form			124.4.d.c.123.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.63773 - 2.30605i) q^{2} -0.254294 q^{3} +(-2.63571 + 7.55335i) q^{4} +3.31209 q^{5} +(0.416464 + 0.586414i) q^{6} -7.54711i q^{7} +(21.7349 - 6.29225i) q^{8} -26.9353 q^{9} +O(q^{10})$	\(q+(-1.63773 - 2.30605i) q^{2} -0.254294 q^{3} +(-2.63571 + 7.55335i) q^{4} +3.31209 q^{5} +(0.416464 + 0.586414i) q^{6} -7.54711i q^{7} +(21.7349 - 6.29225i) q^{8} -26.9353 q^{9} +(-5.42430 - 7.63784i) q^{10} -43.9165 q^{11} +(0.670244 - 1.92077i) q^{12} +69.9680i q^{13} +(-17.4040 + 12.3601i) q^{14} -0.842245 q^{15} +(-50.1061 - 39.8168i) q^{16} +85.3861i q^{17} +(44.1127 + 62.1141i) q^{18} -8.51264i q^{19} +(-8.72970 + 25.0174i) q^{20} +1.91918i q^{21} +(71.9232 + 101.274i) q^{22} +129.606 q^{23} +(-5.52706 + 1.60008i) q^{24} -114.030 q^{25} +(161.350 - 114.588i) q^{26} +13.7154 q^{27} +(57.0059 + 19.8920i) q^{28} +100.032i q^{29} +(1.37937 + 1.94226i) q^{30} +(-160.311 + 63.9632i) q^{31} +(-9.75932 + 180.756i) q^{32} +11.1677 q^{33} +(196.904 - 139.839i) q^{34} -24.9967i q^{35} +(70.9936 - 203.452i) q^{36} +297.853i q^{37} +(-19.6305 + 13.9414i) q^{38} -17.7924i q^{39} +(71.9881 - 20.8405i) q^{40} -134.617 q^{41} +(4.42573 - 3.14310i) q^{42} -495.642 q^{43} +(115.751 - 331.717i) q^{44} -89.2123 q^{45} +(-212.259 - 298.877i) q^{46} -440.259i q^{47} +(12.7417 + 10.1252i) q^{48} +286.041 q^{49} +(186.750 + 262.959i) q^{50} -21.7132i q^{51} +(-528.493 - 184.415i) q^{52} -174.570i q^{53} +(-22.4621 - 31.6284i) q^{54} -145.455 q^{55} +(-47.4883 - 164.036i) q^{56} +2.16471i q^{57} +(230.678 - 163.824i) q^{58} +365.006i q^{59} +(2.21991 - 6.36177i) q^{60} -608.459i q^{61} +(410.048 + 264.931i) q^{62} +203.284i q^{63} +(432.815 - 273.524i) q^{64} +231.740i q^{65} +(-18.2896 - 25.7532i) q^{66} -790.555i q^{67} +(-644.951 - 225.053i) q^{68} -32.9580 q^{69} +(-57.6436 + 40.9378i) q^{70} +586.695i q^{71} +(-585.438 + 169.484i) q^{72} -771.852i q^{73} +(686.863 - 487.801i) q^{74} +28.9971 q^{75} +(64.2989 + 22.4368i) q^{76} +331.443i q^{77} +(-41.0302 + 29.1391i) q^{78} -307.149 q^{79} +(-165.956 - 131.877i) q^{80} +723.766 q^{81} +(220.466 + 310.433i) q^{82} +862.812 q^{83} +(-14.4963 - 5.05840i) q^{84} +282.807i q^{85} +(811.726 + 1142.97i) q^{86} -25.4374i q^{87} +(-954.523 + 276.334i) q^{88} +413.044i q^{89} +(146.105 + 205.728i) q^{90} +528.056 q^{91} +(-341.603 + 978.957i) q^{92} +(40.7662 - 16.2655i) q^{93} +(-1015.26 + 721.023i) q^{94} -28.1946i q^{95} +(2.48173 - 45.9652i) q^{96} -1383.16 q^{97} +(-468.457 - 659.624i) q^{98} +1182.91 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 2 q^{2} + 10 q^{4} - 4 q^{5} + 94 q^{8} + 536 q^{9}+O(q^{10}) $ 40 * q - 2 * q^2 + 10 * q^4 - 4 * q^5 + 94 * q^8 + 536 * q^9	$ 40 q - 2 q^{2} + 10 q^{4} - 4 q^{5} + 94 q^{8} + 536 q^{9} + 228 q^{10} - 104 q^{14} - 78 q^{16} + 114 q^{18} - 44 q^{20} + 28 q^{25} + 48 q^{28} - 602 q^{32} - 136 q^{33} - 482 q^{36} + 420 q^{38} - 516 q^{40} - 4 q^{41} - 1596 q^{45} + 1876 q^{49} - 662 q^{50} + 1576 q^{56} - 838 q^{62} - 302 q^{64} - 3900 q^{66} - 872 q^{69} - 912 q^{70} - 2166 q^{72} + 3220 q^{76} - 476 q^{78} + 572 q^{80} - 2056 q^{81} + 3096 q^{82} - 6220 q^{90} - 2904 q^{93} + 6408 q^{94} - 1836 q^{97} - 1358 q^{98}+O(q^{100}) $ 40 * q - 2 * q^2 + 10 * q^4 - 4 * q^5 + 94 * q^8 + 536 * q^9 + 228 * q^10 - 104 * q^14 - 78 * q^16 + 114 * q^18 - 44 * q^20 + 28 * q^25 + 48 * q^28 - 602 * q^32 - 136 * q^33 - 482 * q^36 + 420 * q^38 - 516 * q^40 - 4 * q^41 - 1596 * q^45 + 1876 * q^49 - 662 * q^50 + 1576 * q^56 - 838 * q^62 - 302 * q^64 - 3900 * q^66 - 872 * q^69 - 912 * q^70 - 2166 * q^72 + 3220 * q^76 - 476 * q^78 + 572 * q^80 - 2056 * q^81 + 3096 * q^82 - 6220 * q^90 - 2904 * q^93 + 6408 * q^94 - 1836 * q^97 - 1358 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/124\mathbb{Z}\right)^\times$.

$n$	$63$	$65$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.63773	−	2.30605i	−0.579024	−	0.815311i
$2$	−1.63773	−	2.30605i	−0.579024	−	0.815311i
$3$	−0.254294			−0.0489389			−0.0244694	−	0.999701i	$-0.507790\pi$
$3$	−0.254294			−0.0489389			−0.0244694	+	0.999701i	$0.507790\pi$
$4$	−2.63571	+	7.55335i	−0.329463	+	0.944168i
$5$	3.31209			0.296242			0.148121	−	0.988969i	$-0.452677\pi$
$5$	3.31209			0.296242			0.148121	+	0.988969i	$0.452677\pi$
$6$	0.416464	+	0.586414i	0.0283368	+	0.0399004i
$7$		−	7.54711i		−	0.407506i	−0.979022	−	0.203753i	$-0.934686\pi$
$7$		−	7.54711i		−	0.407506i	0.979022	−	0.203753i	$-0.0653139\pi$
$8$	21.7349	−	6.29225i	0.960558	−	0.278081i
$9$	−26.9353			−0.997605
$10$	−5.42430	−	7.63784i	−0.171531	−	0.241530i
$11$	−43.9165			−1.20376			−0.601878	−	0.798588i	$-0.705581\pi$
$11$	−43.9165			−1.20376			−0.601878	+	0.798588i	$0.705581\pi$
$12$	0.670244	−	1.92077i	0.0161236	−	0.0462065i
$13$			69.9680i			1.49274i	0.665531	+	0.746371i	$0.268205\pi$
$13$			69.9680i			1.49274i	−0.665531	+	0.746371i	$0.731795\pi$
$14$	−17.4040	+	12.3601i	−0.332244	+	0.235955i
$15$	−0.842245			−0.0144978
$16$	−50.1061	−	39.8168i	−0.782908	−	0.622137i
$17$			85.3861i			1.21819i	0.793099	+	0.609093i	$0.208467\pi$
$17$			85.3861i			1.21819i	−0.793099	+	0.609093i	$0.791533\pi$
$18$	44.1127	+	62.1141i	0.577637	+	0.813358i
$19$		−	8.51264i		−	0.102786i	−0.998679	−	0.0513930i	$-0.983634\pi$
$19$		−	8.51264i		−	0.102786i	0.998679	−	0.0513930i	$-0.0163661\pi$
$20$	−8.72970	+	25.0174i	−0.0976010	+	0.279703i
$21$			1.91918i			0.0199429i
$22$	71.9232	+	101.274i	0.697004	+	0.981436i
$23$	129.606			1.17499			0.587493	−	0.809229i	$-0.300115\pi$
$23$	129.606			1.17499			0.587493	+	0.809229i	$0.300115\pi$
$24$	−5.52706	+	1.60008i	−0.0470086	+	0.0136090i
$25$	−114.030			−0.912240
$26$	161.350	−	114.588i	1.21705	−	0.864332i
$27$	13.7154			0.0977606
$28$	57.0059	+	19.8920i	0.384754	+	0.134258i
$29$			100.032i			0.640531i	0.947328	+	0.320265i	$0.103772\pi$
$29$			100.032i			0.640531i	−0.947328	+	0.320265i	$0.896228\pi$
$30$	1.37937	+	1.94226i	0.00839455	+	0.0118202i
$31$	−160.311	+	63.9632i	−0.928799	+	0.370585i
$31$	−160.311	+	63.9632i	−0.928799	+	0.370585i
$32$	−9.75932	+	180.756i	−0.0539131	+	0.998546i
$33$	11.1677			0.0589105
$34$	196.904	−	139.839i	0.993201	−	0.705359i
$35$		−	24.9967i		−	0.120720i
$36$	70.9936	−	203.452i	0.328674	−	0.941907i
$37$			297.853i			1.32342i	0.749758	+	0.661712i	$0.230170\pi$
$37$			297.853i			1.32342i	−0.749758	+	0.661712i	$0.769830\pi$
$38$	−19.6305	+	13.9414i	−0.0838025	+	0.0595155i
$39$		−	17.7924i		−	0.0730531i
$40$	71.9881	−	20.8405i	0.284558	−	0.0823794i
$41$	−134.617			−0.512772			−0.256386	−	0.966575i	$-0.582532\pi$
$41$	−134.617			−0.512772			−0.256386	+	0.966575i	$0.582532\pi$
$42$	4.42573	−	3.14310i	0.0162596	−	0.0115474i
$43$	−495.642			−1.75778			−0.878892	−	0.477020i	$-0.841717\pi$
$43$	−495.642			−1.75778			−0.878892	+	0.477020i	$0.841717\pi$
$44$	115.751	−	331.717i	0.396594	−	1.13655i
$45$	−89.2123			−0.295533
$46$	−212.259	−	298.877i	−0.680344	−	0.957978i
$47$		−	440.259i		−	1.36635i	−0.730256	−	0.683174i	$-0.760599\pi$
$47$		−	440.259i		−	1.36635i	0.730256	−	0.683174i	$-0.239401\pi$
$48$	12.7417	+	10.1252i	0.0383146	+	0.0304467i
$49$	286.041			0.833939
$50$	186.750	+	262.959i	0.528209	+	0.743759i
$51$		−	21.7132i		−	0.0596167i
$52$	−528.493	−	184.415i	−1.40940	−	0.491803i
$53$		−	174.570i		−	0.452435i	−0.974077	−	0.226218i	$-0.927364\pi$
$53$		−	174.570i		−	0.452435i	0.974077	−	0.226218i	$-0.0726360\pi$
$54$	−22.4621	−	31.6284i	−0.0566057	−	0.0797052i
$55$	−145.455			−0.356604
$56$	−47.4883	−	164.036i	−0.113320	−	0.391433i
$57$			2.16471i			0.00503023i
$58$	230.678	−	163.824i	0.522232	−	0.370883i
$59$			365.006i			0.805419i	0.915328	+	0.402709i	$0.131931\pi$
$59$			365.006i			0.805419i	−0.915328	+	0.402709i	$0.868069\pi$
$60$	2.21991	−	6.36177i	0.00477648	−	0.0136883i
$61$		−	608.459i		−	1.27714i	−0.769566	−	0.638568i	$-0.779527\pi$
$61$		−	608.459i		−	1.27714i	0.769566	−	0.638568i	$-0.220473\pi$
$62$	410.048	+	264.931i	0.839938	+	0.542682i
$63$			203.284i			0.406530i
$64$	432.815	−	273.524i	0.845342	−	0.534226i
$65$			231.740i			0.442213i
$66$	−18.2896	−	25.7532i	−0.0341106	−	0.0480304i
$67$		−	790.555i		−	1.44152i	−0.693186	−	0.720759i	$-0.743794\pi$
$67$		−	790.555i		−	1.44152i	0.693186	−	0.720759i	$-0.256206\pi$
$68$	−644.951	−	225.053i	−1.15017	−	0.401348i
$69$	−32.9580			−0.0575025
$70$	−57.6436	+	40.9378i	−0.0984247	+	0.0699000i
$71$			586.695i			0.980675i	0.871533	+	0.490337i	$0.163126\pi$
$71$			586.695i			0.980675i	−0.871533	+	0.490337i	$0.836874\pi$
$72$	−585.438	+	169.484i	−0.958257	+	0.277415i
$73$		−	771.852i		−	1.23751i	−0.785583	−	0.618756i	$-0.787637\pi$
$73$		−	771.852i		−	1.23751i	0.785583	−	0.618756i	$-0.212363\pi$
$74$	686.863	−	487.801i	1.07900	−	0.766294i
$75$	28.9971			0.0446440
$76$	64.2989	+	22.4368i	0.0970473	+	0.0338642i
$77$			331.443i			0.490538i
$78$	−41.0302	+	29.1391i	−0.0595610	+	0.0422995i
$79$	−307.149			−0.437430			−0.218715	−	0.975789i	$-0.570186\pi$
$79$	−307.149			−0.437430			−0.218715	+	0.975789i	$0.570186\pi$
$80$	−165.956	−	131.877i	−0.231931	−	0.184304i
$81$	723.766			0.992821
$82$	220.466	+	310.433i	0.296907	+	0.418068i
$83$	862.812			1.14103			0.570517	−	0.821286i	$-0.306743\pi$
$83$	862.812			1.14103			0.570517	+	0.821286i	$0.306743\pi$
$84$	−14.4963	−	5.05840i	−0.0188294	−	0.00657044i
$85$			282.807i			0.360879i
$86$	811.726	+	1142.97i	1.01780	+	1.43314i
$87$		−	25.4374i		−	0.0313469i
$88$	−954.523	+	276.334i	−1.15628	+	0.334742i
$89$			413.044i			0.491939i	0.969278	+	0.245970i	$0.0791063\pi$
$89$			413.044i			0.491939i	−0.969278	+	0.245970i	$0.920894\pi$
$90$	146.105	+	205.728i	0.171121	+	0.240951i
$91$	528.056			0.608300
$92$	−341.603	+	978.957i	−0.387114	+	1.10938i
$93$	40.7662	−	16.2655i	0.0454544	−	0.0181360i
$94$	−1015.26	+	721.023i	−1.11400	+	0.791147i
$95$		−	28.1946i		−	0.0304496i
$96$	2.48173	−	45.9652i	0.00263845	−	0.0488677i
$97$	−1383.16			−1.44782			−0.723912	−	0.689892i	$-0.757658\pi$
$97$	−1383.16			−1.44782			−0.723912	+	0.689892i	$0.757658\pi$
$98$	−468.457	−	659.624i	−0.482871	−	0.679920i
$99$	1182.91			1.20087
$100$	300.550	−	861.309i	0.300550	−	0.861309i
$101$	−639.767			−0.630289			−0.315144	−	0.949044i	$-0.602053\pi$
$101$	−639.767			−0.630289			−0.315144	+	0.949044i	$0.602053\pi$
$102$	−50.0716	+	35.5602i	−0.0486061	+	0.0345195i
$103$		−	101.841i		−	0.0974246i	−0.998813	−	0.0487123i	$-0.984488\pi$
$103$		−	101.841i		−	0.0974246i	0.998813	−	0.0487123i	$-0.0155118\pi$
$104$	440.256	+	1520.75i	0.415103	+	1.43386i
$105$			6.35651i			0.00590792i
$106$	−402.567	+	285.898i	−0.368875	+	0.261971i
$107$			1555.62i			1.40549i	0.711440	+	0.702747i	$0.248044\pi$
$107$			1555.62i			1.40549i	−0.711440	+	0.702747i	$0.751956\pi$
$108$	−36.1498	+	103.597i	−0.0322085	+	0.0923024i
$109$	1293.84			1.13694			0.568472	−	0.822703i	$-0.307535\pi$
$109$	1293.84			1.13694			0.568472	+	0.822703i	$0.307535\pi$
$110$	238.216	+	335.427i	0.206482	+	0.290743i
$111$		−	75.7422i		−	0.0647669i
$112$	−300.502	+	378.156i	−0.253525	+	0.319039i
$113$	817.838			0.680847			0.340424	−	0.940272i	$-0.389430\pi$
$113$	817.838			0.680847			0.340424	+	0.940272i	$0.389430\pi$
$114$	4.99193	−	3.54521i	0.00410120	−	0.00291262i
$115$	429.266			0.348081
$116$	−755.573	−	263.654i	−0.604769	−	0.211031i
$117$		−	1884.61i		−	1.48917i
$118$	841.720	−	597.779i	0.656666	−	0.466356i
$119$	644.418			0.496418
$120$	−18.3061	+	5.29962i	−0.0139259	+	0.00403156i
$121$	597.660			0.449031
$122$	−1403.14	+	996.490i	−1.04126	+	0.739492i
$123$	34.2323			0.0250945
$124$	−60.6032	−	1379.47i	−0.0438897	−	0.999036i
$125$	−791.689			−0.566487
$126$	468.782	−	332.923i	0.331448	−	0.235390i
$127$	−1639.55			−1.14557			−0.572783	−	0.819707i	$-0.694136\pi$
$127$	−1639.55			−1.14557			−0.572783	+	0.819707i	$0.694136\pi$
$128$	−1339.59	−	550.135i	−0.925033	−	0.379887i
$129$	126.039			0.0860240
$130$	534.404	−	379.527i	0.360541	−	0.256052i
$131$			318.639i			0.212516i	0.994339	+	0.106258i	$0.0338869\pi$
$131$			318.639i			0.212516i	−0.994339	+	0.106258i	$0.966113\pi$
$132$	−29.4348	+	84.3535i	−0.0194088	+	0.0556214i
$133$	−64.2458			−0.0418859
$134$	−1823.06	+	1294.71i	−1.17528	+	0.834673i
$135$	45.4267			0.0289608
$136$	537.271	+	1855.86i	0.338755	+	1.17014i
$137$			591.386i			0.368800i	0.982851	+	0.184400i	$0.0590341\pi$
$137$			591.386i			0.368800i	−0.982851	+	0.184400i	$0.940966\pi$
$138$	53.9761	+	76.0026i	0.0332953	+	0.0468824i
$139$	1096.04			0.668812			0.334406	−	0.942429i	$-0.391464\pi$
$139$	1096.04			0.668812			0.334406	+	0.942429i	$0.391464\pi$
$140$	188.809	+	65.8840i	0.113980	+	0.0397729i
$141$			111.955i			0.0668675i
$142$	1352.95	−	960.846i	0.799555	−	0.567834i
$143$		−	3072.75i		−	1.79690i
$144$	1349.62	+	1072.48i	0.781033	+	0.620647i
$145$			331.314i			0.189752i
$146$	−1779.93	+	1264.08i	−1.00896	+	0.716549i
$147$	−72.7385			−0.0408121
$148$	−2249.79	−	785.052i	−1.24954	−	0.436020i
$149$	−1250.78			−0.687703			−0.343852	−	0.939024i	$-0.611732\pi$
$149$	−1250.78			−0.687703			−0.343852	+	0.939024i	$0.611732\pi$
$150$	−47.4894	−	66.8688i	−0.0258499	−	0.0363988i
$151$	−1548.18			−0.834363			−0.417182	−	0.908823i	$-0.636982\pi$
$151$	−1548.18			−0.834363			−0.417182	+	0.908823i	$0.636982\pi$
$152$	−53.5637	−	185.022i	−0.0285828	−	0.0987318i
$153$		−	2299.90i		−	1.21527i
$154$	764.322	−	542.812i	0.399941	−	0.284033i
$155$	−530.966	+	211.852i	−0.275150	+	0.109783i
$156$	134.392	+	46.8956i	0.0689744	+	0.0240683i
$157$	2588.68			1.31592			0.657960	−	0.753053i	$-0.271419\pi$
$157$	2588.68			1.31592			0.657960	+	0.753053i	$0.271419\pi$
$158$	503.026	+	708.300i	0.253282	+	0.356641i
$159$			44.3921i			0.0221417i
$160$	−32.3237	+	598.681i	−0.0159714	+	0.295812i
$161$		−	978.149i		−	0.478813i
$162$	−1185.33	−	1669.04i	−0.574867	−	0.809457i
$163$			3228.28i			1.55128i	0.631178	+	0.775638i	$0.282572\pi$
$163$			3228.28i			1.55128i	−0.631178	+	0.775638i	$0.717428\pi$
$164$	354.811	−	1016.81i	0.168939	−	0.484143i
$165$	36.9884			0.0174518
$166$	−1413.05	−	1989.68i	−0.660686	−	0.930298i
$167$	1146.90			0.531437			0.265718	−	0.964051i	$-0.414391\pi$
$167$	1146.90			0.531437			0.265718	+	0.964051i	$0.414391\pi$
$168$	12.0760	+	41.7133i	0.00554573	+	0.0191563i
$169$	−2698.52			−1.22828
$170$	652.165	−	463.160i	0.294228	−	0.208957i
$171$			229.291i			0.102540i
$172$	1306.37	−	3743.76i	0.579125	−	1.65964i
$173$	2816.55			1.23779			0.618897	−	0.785472i	$-0.287580\pi$
$173$	2816.55			1.23779			0.618897	+	0.785472i	$0.287580\pi$
$174$	−58.6599	+	41.6595i	−0.0255574	+	0.0181506i
$175$			860.597i			0.371743i
$176$	2200.49	+	1748.61i	0.942431	+	0.748902i
$177$		−	92.8187i		−	0.0394163i
$178$	952.499	−	676.453i	0.401083	−	0.284844i
$179$	773.303			0.322902			0.161451	−	0.986881i	$-0.448383\pi$
$179$	773.303			0.322902			0.161451	+	0.986881i	$0.448383\pi$
$180$	235.137	−	673.851i	0.0973672	−	0.279033i
$181$			371.050i			0.152375i	0.997093	+	0.0761877i	$0.0242748\pi$
$181$			371.050i			0.152375i	−0.997093	+	0.0761877i	$0.975725\pi$
$182$	−864.811	−	1217.72i	−0.352220	−	0.495954i
$183$			154.728i			0.0625016i
$184$	2816.97	−	815.512i	1.12864	−	0.326741i
$185$			986.516i			0.392054i
$186$	−104.273	−	67.3704i	−0.0411056	−	0.0265582i
$187$		−	3749.86i		−	1.46640i
$188$	3325.43	+	1160.39i	1.29006	+	0.450161i
$189$		−	103.512i		−	0.0398380i
$190$	−65.0182	+	46.1751i	−0.0248259	+	0.0176310i
$191$		−	569.138i		−	0.215609i	−0.994172	−	0.107805i	$-0.965618\pi$
$191$		−	569.138i		−	0.215609i	0.994172	−	0.107805i	$-0.0343821\pi$
$192$	−110.062	+	69.5554i	−0.0413701	+	0.0261444i
$193$	−1769.86			−0.660090			−0.330045	−	0.943965i	$-0.607064\pi$
$193$	−1769.86			−0.660090			−0.330045	+	0.943965i	$0.607064\pi$
$194$	2265.24	+	3189.64i	0.838325	+	1.18043i
$195$		−	58.9302i		−	0.0216414i
$196$	−753.920	+	2160.57i	−0.274752	+	0.787379i
$197$			2328.97i			0.842297i	0.906992	+	0.421149i	$0.138373\pi$
$197$			2328.97i			0.842297i	−0.906992	+	0.421149i	$0.861627\pi$
$198$	−1937.28	−	2727.84i	−0.695334	−	0.979085i
$199$	−618.363			−0.220274			−0.110137	−	0.993916i	$-0.535129\pi$
$199$	−618.363			−0.220274			−0.110137	+	0.993916i	$0.535129\pi$
$200$	−2478.44	+	717.506i	−0.876259	+	0.253677i
$201$			201.033i			0.0705463i
$202$	1047.76	+	1475.33i	0.364952	+	0.513881i
$203$	754.949			0.261020
$204$	164.007	+	57.2295i	0.0562882	+	0.0196415i
$205$	−445.864			−0.151905
$206$	−234.851	+	166.788i	−0.0794314	+	0.0564112i
$207$	−3490.97			−1.17217
$208$	2785.90	−	3505.82i	0.928690	−	1.16868i
$209$			373.845i			0.123729i
$210$	14.6584	−	10.4102i	0.00481679	−	0.00342083i
$211$		−	2118.53i		−	0.691210i	−0.938380	−	0.345605i	$-0.887674\pi$
$211$		−	2118.53i		−	0.691210i	0.938380	−	0.345605i	$-0.112326\pi$
$212$	1318.59	+	460.116i	0.427175	+	0.149061i
$213$		−	149.193i		−	0.0479931i
$214$	3587.34	−	2547.69i	1.14591	−	0.813815i
$215$	−1641.61			−0.520730
$216$	298.104	−	86.3009i	0.0939046	−	0.0271853i
$217$	482.737	+	1209.89i	0.151015	+	0.378491i
$218$	−2118.95	−	2983.64i	−0.658318	−	0.926963i
$219$			196.277i			0.0605625i
$220$	383.378	−	1098.68i	0.117488	−	0.336694i
$221$	−5974.30			−1.81844
$222$	−174.665	+	124.045i	−0.0528052	+	0.0375016i
$223$	−5812.07			−1.74531			−0.872657	−	0.488333i	$-0.837605\pi$
$223$	−5812.07			−1.74531			−0.872657	+	0.488333i	$0.837605\pi$
$224$	1364.19	+	73.6546i	0.406913	+	0.0219699i
$225$	3071.44			0.910056
$226$	−1339.40	−	1885.97i	−0.394227	−	0.555102i
$227$			2947.54i			0.861828i	0.902393	+	0.430914i	$0.141809\pi$
$227$			2947.54i			0.861828i	−0.902393	+	0.430914i	$0.858191\pi$
$228$	−16.3508	−	5.70554i	−0.00474938	−	0.00165728i
$229$			2779.57i			0.802092i	0.916058	+	0.401046i	$0.131353\pi$
$229$			2779.57i			0.802092i	−0.916058	+	0.401046i	$0.868647\pi$
$230$	−703.020	−	989.908i	−0.201547	−	0.283794i
$231$		−	84.2838i		−	0.0240064i
$232$	629.424	+	2174.18i	0.178119	+	0.615267i
$233$	2701.56			0.759592			0.379796	−	0.925070i	$-0.375994\pi$
$233$	2701.56			0.759592			0.379796	+	0.925070i	$0.375994\pi$
$234$	−4346.00	+	3086.48i	−1.21413	+	0.862262i
$235$		−	1458.18i		−	0.404770i
$236$	−2757.02	−	962.048i	−0.760451	−	0.265356i
$237$	78.1061			0.0214073
$238$	−1055.38	−	1486.06i	−0.287438	−	0.404735i
$239$	−572.010			−0.154813			−0.0774064	−	0.997000i	$-0.524664\pi$
$239$	−572.010			−0.154813			−0.0774064	+	0.997000i	$0.524664\pi$
$240$	42.2016	+	33.5355i	0.0113504	+	0.00901961i
$241$			6274.76i			1.67715i	0.544788	+	0.838574i	$0.316610\pi$
$241$			6274.76i			1.67715i	−0.544788	+	0.838574i	$0.683390\pi$
$242$	−978.803	−	1378.23i	−0.259999	−	0.366099i
$243$	−554.366			−0.146348
$244$	4595.91	+	1603.72i	1.20583	+	0.420769i
$245$	947.394			0.247048
$246$	−56.0631	−	78.9412i	−0.0145303	−	0.0204598i
$247$	595.612			0.153433
$248$	−3081.88	+	2398.96i	−0.789112	+	0.614249i
$249$	−219.408			−0.0558410
$250$	1296.57	+	1825.67i	0.328009	+	0.461863i
$251$	5552.68			1.39634			0.698171	−	0.715931i	$-0.253998\pi$
$251$	5552.68			1.39634			0.698171	+	0.715931i	$0.253998\pi$
$252$	−1535.47	−	535.797i	−0.383832	−	0.133937i
$253$	−5691.83			−1.41440
$254$	2685.14	+	3780.89i	0.663310	+	0.933992i
$255$		−	71.9160i		−	0.0176610i
$256$	925.245	+	3990.13i	0.225890	+	0.974153i
$257$	−2975.80			−0.722277			−0.361139	−	0.932512i	$-0.617612\pi$
$257$	−2975.80			−0.722277			−0.361139	+	0.932512i	$0.617612\pi$
$258$	−206.417	−	290.651i	−0.0498099	−	0.0701363i
$259$	2247.93			0.539303
$260$	−1750.42	−	610.800i	−0.417524	−	0.145693i
$261$		−	2694.38i		−	0.638997i
$262$	734.795	−	521.843i	0.173266	−	0.123052i
$263$	−6729.44			−1.57778			−0.788888	−	0.614538i	$-0.789343\pi$
$263$	−6729.44			−1.57778			−0.788888	+	0.614538i	$0.789343\pi$
$264$	242.729	−	70.2700i	0.0565869	−	0.0163819i
$265$		−	578.192i		−	0.134030i
$266$	105.217	+	148.154i	0.0242529	+	0.0341500i
$267$		−	105.035i		−	0.0240750i
$268$	5971.34	+	2083.67i	1.36104	+	0.474927i
$269$		−	1562.25i		−	0.354097i	−0.984202	−	0.177049i	$-0.943345\pi$
$269$		−	1562.25i		−	0.354097i	0.984202	−	0.177049i	$-0.0566550\pi$
$270$	−74.3966	−	104.756i	−0.0167690	−	0.0236121i
$271$	−764.866			−0.171448			−0.0857238	−	0.996319i	$-0.527320\pi$
$271$	−764.866			−0.171448			−0.0857238	+	0.996319i	$0.527320\pi$
$272$	3399.80	−	4278.37i	0.757880	−	0.953728i
$273$	−134.281			−0.0297695
$274$	1363.76	−	968.529i	0.300686	−	0.213544i
$275$	5007.80			1.09812
$276$	86.8675	−	248.943i	0.0189450	−	0.0542920i
$277$			7760.51i			1.68333i	0.539996	+	0.841667i	$0.318426\pi$
$277$			7760.51i			1.68333i	−0.539996	+	0.841667i	$0.681574\pi$
$278$	−1795.01	−	2527.52i	−0.387258	−	0.545290i
$279$	4318.04	−	1722.87i	0.926574	−	0.369697i
$280$	−157.286	−	543.302i	−0.0335701	−	0.115959i
$281$	5414.44			1.14946			0.574730	−	0.818343i	$-0.305107\pi$
$281$	5414.44			1.14946			0.574730	+	0.818343i	$0.305107\pi$
$282$	258.174	−	183.352i	0.0545178	−	0.0387179i
$283$		−	4629.55i		−	0.972431i	−0.873839	−	0.486216i	$-0.838377\pi$
$283$		−	4629.55i		−	0.972431i	0.873839	−	0.486216i	$-0.161623\pi$
$284$	−4431.51	−	1546.36i	−0.925922	−	0.323096i
$285$			7.16972i			0.00149017i
$286$	−7085.91	+	5032.32i	−1.46503	+	1.04045i
$287$			1015.97i			0.208957i
$288$	262.870	−	4868.73i	0.0537840	−	0.996154i
$289$	−2377.79			−0.483979
$290$	764.025	−	542.601i	0.154707	−	0.109871i
$291$	351.730			0.0708549
$292$	5830.07	+	2034.37i	1.16842	+	0.407715i
$293$	3032.55			0.604654			0.302327	−	0.953204i	$-0.402236\pi$
$293$	3032.55			0.604654			0.302327	+	0.953204i	$0.402236\pi$
$294$	119.126	+	167.738i	0.0236311	+	0.0332745i
$295$			1208.93i			0.238599i
$296$	1874.17	+	6473.81i	0.368019	+	1.27123i
$297$	−602.334			−0.117680
$298$	2048.43	+	2884.35i	0.398197	+	0.560692i
$299$			9068.26i			1.75395i
$300$	−76.4279	+	219.026i	−0.0147086	+	0.0421515i
$301$			3740.67i			0.716307i
$302$	2535.49	+	3570.17i	0.483116	+	0.680265i
$303$	162.689			0.0308456
$304$	−338.946	+	426.535i	−0.0639470	+	0.0804719i
$305$		−	2015.27i		−	0.378342i
$306$	−5303.69	+	3766.61i	−0.990822	+	0.703670i
$307$			9450.07i			1.75682i	0.477908	+	0.878410i	$0.341395\pi$
$307$			9450.07i			1.75682i	−0.477908	+	0.878410i	$0.658605\pi$
$308$	−2503.50	−	873.585i	−0.463150	−	0.161614i
$309$			25.8977i			0.00476785i
$310$	1358.12	+	877.476i	0.248825	+	0.160765i
$311$		−	5098.01i		−	0.929523i	−0.885436	−	0.464761i	$-0.846140\pi$
$311$		−	5098.01i		−	0.929523i	0.885436	−	0.464761i	$-0.153860\pi$
$312$	−111.955	−	386.718i	−0.0203147	−	0.0701717i
$313$		−	1091.40i		−	0.197091i	−0.995133	−	0.0985454i	$-0.968581\pi$
$313$		−	1091.40i		−	0.197091i	0.995133	−	0.0985454i	$-0.0314190\pi$
$314$	−4239.56	−	5969.63i	−0.761949	−	1.07288i
$315$			673.295i			0.120431i
$316$	809.554	−	2320.00i	0.144117	−	0.413007i
$317$	−1596.31			−0.282831			−0.141416	−	0.989950i	$-0.545165\pi$
$317$	−1596.31			−0.282831			−0.141416	+	0.989950i	$0.545165\pi$
$318$	102.370	−	72.7022i	0.0180523	−	0.0128205i
$319$		−	4393.04i		−	0.771044i
$320$	1433.52	−	905.935i	0.250426	−	0.158260i
$321$		−	395.586i		−	0.0687833i
$322$	−2255.66	+	1601.94i	−0.390382	+	0.277244i
$323$	726.861			0.125212
$324$	−1907.63	+	5466.86i	−0.327098	+	0.937390i
$325$		−	7978.46i		−	1.36174i
$326$	7444.56	−	5287.03i	1.26477	−	0.898226i
$327$	−329.014			−0.0556408
$328$	−2925.89	+	847.044i	−0.492547	+	0.142592i
$329$	−3322.68			−0.556794
$330$	−60.5769	−	85.2971i	−0.0101050	−	0.0142286i
$331$	2811.47			0.466865			0.233433	−	0.972373i	$-0.425004\pi$
$331$	2811.47			0.466865			0.233433	+	0.972373i	$0.425004\pi$
$332$	−2274.12	+	6517.12i	−0.375929	+	1.07733i
$333$		−	8022.77i		−	1.32025i
$334$	−1878.31	−	2644.81i	−0.307714	−	0.433286i
$335$		−	2618.39i		−	0.427039i
$336$	76.4158	−	96.1628i	0.0124072	−	0.0156134i
$337$		−	5091.39i		−	0.822985i	−0.911413	−	0.411492i	$-0.865008\pi$
$337$		−	5091.39i		−	0.822985i	0.911413	−	0.411492i	$-0.134992\pi$
$338$	4419.44	+	6222.92i	0.711201	+	1.00143i
$339$	−207.971			−0.0333199
$340$	−2136.14	−	745.395i	−0.340730	−	0.118896i
$341$	7040.31	−	2809.04i	1.11805	−	0.446094i
$342$	528.755	−	375.516i	0.0836018	−	0.0593730i
$343$		−	4747.44i		−	0.747340i
$344$	−10772.8	+	3118.71i	−1.68845	+	0.488806i
$345$	−109.160			−0.0170347
$346$	−4612.74	−	6495.09i	−0.716712	−	1.00919i
$347$	7491.16			1.15892			0.579462	−	0.814999i	$-0.303263\pi$
$347$	7491.16			1.15892			0.579462	+	0.814999i	$0.303263\pi$
$348$	192.138	+	67.0455i	0.0295967	+	0.0103276i
$349$	7605.90			1.16657			0.583287	−	0.812266i	$-0.301766\pi$
$349$	7605.90			1.16657			0.583287	+	0.812266i	$0.301766\pi$
$350$	1984.58	−	1409.42i	0.303086	−	0.215248i
$351$			959.641i			0.145931i
$352$	428.595	−	7938.18i	0.0648983	−	1.20201i
$353$		−	9966.45i		−	1.50272i	−0.659891	−	0.751361i	$-0.729398\pi$
$353$		−	9966.45i		−	1.50272i	0.659891	−	0.751361i	$-0.270602\pi$
$354$	−214.044	+	152.012i	−0.0321365	+	0.0228230i
$355$			1943.19i			0.290518i
$356$	−3119.87	−	1088.66i	−0.464473	−	0.162076i
$357$	−163.872			−0.0242941
$358$	−1266.46	−	1783.27i	−0.186968	−	0.263265i
$359$		−	672.502i		−	0.0988672i	−0.998777	−	0.0494336i	$-0.984258\pi$
$359$		−	672.502i		−	0.0988672i	0.998777	−	0.0494336i	$-0.0157416\pi$
$360$	−1939.02	+	561.346i	−0.283876	+	0.0821821i
$361$	6786.53			0.989435
$362$	855.659	−	607.679i	0.124233	−	0.0882290i
$363$	−151.981			−0.0219751
$364$	−1391.80	+	3988.59i	−0.200413	+	0.574338i
$365$		−	2556.44i		−	0.366604i
$366$	356.809	−	253.401i	0.0509582	−	0.0361899i
$367$	−7222.78			−1.02732			−0.513659	−	0.857994i	$-0.671710\pi$
$367$	−7222.78			−1.02732			−0.513659	+	0.857994i	$0.671710\pi$
$368$	−6494.04	−	5160.49i	−0.919906	−	0.731003i
$369$	3625.95			0.511544
$370$	2274.95	−	1615.64i	0.319646	−	0.227009i
$371$	−1317.50			−0.184370
$372$	15.4110	+	350.792i	0.00214791	+	0.0488917i
$373$	−196.403			−0.0272637			−0.0136319	−	0.999907i	$-0.504339\pi$
$373$	−196.403			−0.0272637			−0.0136319	+	0.999907i	$0.504339\pi$
$374$	−8647.35	+	6141.24i	−1.19557	+	0.849081i
$375$	201.322			0.0277232
$376$	−2770.22	−	9568.99i	−0.379955	−	1.31246i
$377$	−6999.01			−0.956147
$378$	−238.703	+	169.524i	−0.0324803	+	0.0230671i
$379$			5719.37i			0.775157i	0.921837	+	0.387578i	$0.126688\pi$
$379$			5719.37i			0.775157i	−0.921837	+	0.387578i	$0.873312\pi$
$380$	212.964	+	74.3128i	0.0287495	+	0.0100320i
$381$	416.928			0.0560627
$382$	−1312.46	+	932.092i	−0.175789	+	0.124843i
$383$	−7947.30			−1.06028			−0.530141	−	0.847910i	$-0.677861\pi$
$383$	−7947.30			−1.06028			−0.530141	+	0.847910i	$0.677861\pi$
$384$	340.650	+	139.896i	0.0452701	+	0.0185912i
$385$			1097.77i			0.145318i
$386$	2898.55	+	4081.38i	0.382208	+	0.538179i
$387$	13350.3			1.75357
$388$	3645.61	−	10447.5i	0.477005	−	1.36699i
$389$		−	3400.99i		−	0.443283i	−0.975128	−	0.221642i	$-0.928858\pi$
$389$		−	3400.99i		−	0.443283i	0.975128	−	0.221642i	$-0.0711415\pi$
$390$	−135.896	+	96.5115i	−0.0176445	+	0.0125309i
$391$			11066.5i			1.43135i
$392$	6217.09	−	1799.84i	0.801047	−	0.231903i
$393$		−	81.0278i		−	0.0104003i
$394$	5370.72	−	3814.22i	0.686734	−	0.487710i
$395$	−1017.30			−0.129585
$396$	−3117.79	+	8934.90i	−0.395644	+	1.13383i
$397$	−3050.88			−0.385691			−0.192845	−	0.981229i	$-0.561772\pi$
$397$	−3050.88			−0.385691			−0.192845	+	0.981229i	$0.561772\pi$
$398$	1012.71	+	1425.97i	0.127544	+	0.179592i
$399$	16.3373			0.00204985
$400$	5713.60	+	4540.31i	0.714200	+	0.567539i
$401$		−	6544.36i		−	0.814987i	−0.913208	−	0.407494i	$-0.866403\pi$
$401$		−	6544.36i		−	0.814987i	0.913208	−	0.407494i	$-0.133597\pi$
$402$	463.592	−	329.238i	0.0575171	−	0.0408480i
$403$	−4475.38	−	11216.7i	−0.553187	−	1.38646i
$404$	1686.24	−	4832.38i	0.207657	−	0.595099i
$405$	2397.18			0.294116
$406$	−1236.40	−	1740.95i	−0.151137	−	0.212812i
$407$		−	13080.7i		−	1.59308i
$408$	−136.625	−	471.934i	−0.0165783	−	0.0572653i
$409$			4665.46i			0.564040i	0.959409	+	0.282020i	$0.0910045\pi$
$409$			4665.46i			0.564040i	−0.959409	+	0.282020i	$0.908996\pi$
$410$	730.203	+	1028.18i	0.0879564	+	0.123850i
$411$		−	150.386i		−	0.0180486i
$412$	769.244	+	268.424i	0.0919853	+	0.0320978i
$413$	2754.74			0.328213
$414$	5717.26	+	8050.35i	0.678715	+	0.955684i
$415$	2857.71			0.338023
$416$	−12647.1	−	682.840i	−1.49057	−	0.0804783i
$417$	−278.716			−0.0327309
$418$	862.105	−	612.256i	0.100878	−	0.0716422i
$419$		−	675.794i		−	0.0787940i	−0.999224	−	0.0393970i	$-0.987456\pi$
$419$		−	675.794i		−	0.0787940i	0.999224	−	0.0393970i	$-0.0125437\pi$
$420$	−48.0129	−	16.7539i	−0.00557808	−	0.00194644i
$421$	−3357.85			−0.388721			−0.194360	−	0.980930i	$-0.562263\pi$
$421$	−3357.85			−0.388721			−0.194360	+	0.980930i	$0.562263\pi$
$422$	−4885.42	+	3469.56i	−0.563551	+	0.400227i
$423$			11858.5i			1.36307i
$424$	−1098.44	−	3794.27i	−0.125814	−	0.434590i
$425$		−	9736.58i		−	1.11128i
$426$	−344.046	+	244.337i	−0.0391293	+	0.0277892i
$427$	−4592.11			−0.520440
$428$	−11750.2	−	4100.17i	−1.32702	−	0.463059i
$429$			781.382i			0.0879381i
$430$	2688.51	+	3785.64i	0.301515	+	0.424557i
$431$			14771.0i			1.65080i	0.564550	+	0.825399i	$0.309050\pi$
$431$			14771.0i			1.65080i	−0.564550	+	0.825399i	$0.690950\pi$
$432$	−687.227	−	546.104i	−0.0765375	−	0.0608205i
$433$			7371.91i			0.818179i	0.912494	+	0.409089i	$0.134154\pi$
$433$			7371.91i			0.818179i	−0.912494	+	0.409089i	$0.865846\pi$
$434$	1999.46	−	3094.68i	0.221146	−	0.342280i
$435$		−	84.2511i		−	0.00928627i
$436$	−3410.17	+	9772.79i	−0.374581	+	1.07347i
$437$		−	1103.29i		−	0.120772i
$438$	452.624	−	321.448i	0.0493772	−	0.0350671i
$439$		−	11074.2i		−	1.20397i	−0.798509	−	0.601983i	$-0.794377\pi$
$439$		−	11074.2i		−	1.20397i	0.798509	−	0.601983i	$-0.205623\pi$
$440$	−3161.47	+	915.243i	−0.342539	+	0.0991648i
$441$	−7704.61			−0.831942
$442$	9784.26	+	13777.0i	1.05292	+	1.48259i
$443$		−	5129.44i		−	0.550128i	−0.961426	−	0.275064i	$-0.911301\pi$
$443$		−	5129.44i		−	0.550128i	0.961426	−	0.275064i	$-0.0886991\pi$
$444$	572.107	+	199.634i	0.0611509	+	0.0213383i
$445$			1368.04i			0.145733i
$446$	9518.58	+	13402.9i	1.01058	+	1.42297i
$447$	318.065			0.0336554
$448$	−2064.31	−	3266.50i	−0.217700	−	0.344482i
$449$			14692.4i			1.54427i	0.635458	+	0.772136i	$0.280811\pi$
$449$			14692.4i			1.54427i	−0.635458	+	0.772136i	$0.719189\pi$
$450$	−5030.17	−	7082.88i	−0.526944	−	0.741978i
$451$	5911.91			0.617252
$452$	−2155.58	+	6177.42i	−0.224314	+	0.642835i
$453$	393.692			0.0408328
$454$	6797.16	−	4827.26i	0.702657	−	0.499019i
$455$	1748.97			0.180204
$456$	13.6209	+	47.0499i	0.00139881	+	0.00483183i
$457$			16297.2i			1.66816i	0.551640	+	0.834082i	$0.314002\pi$
$457$			16297.2i			1.66816i	−0.551640	+	0.834082i	$0.685998\pi$
$458$	6409.82	−	4552.17i	0.653954	−	0.464430i
$459$			1171.11i			0.119091i
$460$	−1131.42	+	3242.40i	−0.114680	+	0.328647i
$461$			11529.5i			1.16482i	0.812894	+	0.582412i	$0.197891\pi$
$461$			11529.5i			1.16482i	−0.812894	+	0.582412i	$0.802109\pi$
$462$	−194.363	+	138.034i	−0.0195726	+	0.0139003i
$463$	8266.23			0.829728			0.414864	−	0.909883i	$-0.363829\pi$
$463$	8266.23			0.829728			0.414864	+	0.909883i	$0.363829\pi$
$464$	3982.94	−	5012.19i	0.398498	−	0.501477i
$465$	135.021	−	53.8727i	0.0134655	−	0.00537266i
$466$	−4424.41	−	6229.92i	−0.439822	−	0.619304i
$467$		−	4155.28i		−	0.411742i	−0.978579	−	0.205871i	$-0.933997\pi$
$467$		−	4155.28i		−	0.411742i	0.978579	−	0.205871i	$-0.0660027\pi$
$468$	14235.1	+	4967.28i	1.40602	+	0.490625i
$469$	−5966.41			−0.587426
$470$	−3362.62	+	2388.09i	−0.330013	+	0.234371i
$471$	−658.287			−0.0643997
$472$	2296.71	+	7933.38i	0.223972	+	0.773651i
$473$	21766.9			2.11595
$474$	−127.916	−	180.116i	−0.0123953	−	0.0174536i
$475$			970.697i			0.0937655i
$476$	−1698.50	+	4867.52i	−0.163551	+	0.468702i
$477$			4702.11i			0.451351i
$478$	936.796	+	1319.08i	0.0896403	+	0.126221i
$479$			8267.70i			0.788645i	0.918972	+	0.394323i	$0.129021\pi$
$479$			8267.70i			0.788645i	−0.918972	+	0.394323i	$0.870979\pi$
$480$	8.21973	−	152.241i	0.000781620	−	0.0144767i
$481$	−20840.2			−1.97553
$482$	14469.9	−	10276.3i	1.36740	−	0.971109i
$483$			248.737i			0.0234326i
$484$	−1575.25	+	4514.33i	−0.147939	+	0.423960i
$485$	−4581.16			−0.428907
$486$	907.899	+	1278.39i	0.0847390	+	0.119319i
$487$	−11387.9			−1.05962			−0.529808	−	0.848118i	$-0.677736\pi$
$487$	−11387.9			−1.05962			−0.529808	+	0.848118i	$0.677736\pi$
$488$	−3828.58	−	13224.8i	−0.355147	−	1.22676i
$489$		−	820.931i		−	0.0759177i
$490$	−1551.57	−	2184.74i	−0.143047	−	0.201421i
$491$	15627.6			1.43638			0.718189	−	0.695848i	$-0.244971\pi$
$491$	15627.6			1.43638			0.718189	+	0.695848i	$0.244971\pi$
$492$	−90.2262	+	258.568i	−0.00826770	+	0.0236934i
$493$	−8541.31			−0.780286
$494$	−975.450	−	1373.51i	−0.0888412	−	0.125095i
$495$	3917.89			0.355750
$496$	10579.4	+	3178.13i	0.957719	+	0.287706i
$497$	4427.85			0.399631
$498$	359.330	+	505.965i	0.0323332	+	0.0455277i
$499$	−10452.1			−0.937675			−0.468838	−	0.883284i	$-0.655327\pi$
$499$	−10452.1			−0.937675			−0.468838	+	0.883284i	$0.655327\pi$
$500$	2086.66	−	5979.90i	0.186637	−	0.534859i
$501$	−291.650			−0.0260079
$502$	−9093.76	−	12804.7i	−0.808515	−	1.13845i
$503$			2735.35i			0.242471i	0.992624	+	0.121236i	$0.0386857\pi$
$503$			2735.35i			0.242471i	−0.992624	+	0.121236i	$0.961314\pi$
$504$	1279.11	+	4418.36i	0.113048	+	0.390495i
$505$	−2118.97			−0.186718
$506$	9321.66	+	13125.6i	0.818969	+	1.15317i
$507$	686.218			0.0601104
$508$	4321.38	−	12384.1i	0.377422	−	1.08161i
$509$			4536.68i			0.395059i	0.980297	+	0.197529i	$0.0632918\pi$
$509$			4536.68i			0.395059i	−0.980297	+	0.197529i	$0.936708\pi$
$510$	−165.842	+	117.779i	−0.0143992	+	0.0102261i
$511$	−5825.25			−0.504293
$512$	7686.13	−	8668.40i	0.663442	−	0.748228i
$513$		−	116.754i		−	0.0100484i
$514$	4873.54	+	6862.33i	0.418216	+	0.588880i
$515$		−	337.308i		−	0.0288613i
$516$	−332.201	+	952.015i	−0.0283417	+	0.0812212i
$517$			19334.6i			1.64475i
$518$	−3681.49	−	5183.83i	−0.312269	−	0.439699i
$519$	−716.231			−0.0605762
$520$	1458.17	+	5036.86i	0.122971	+	0.424771i
$521$	−9023.61			−0.758794			−0.379397	−	0.925234i	$-0.623869\pi$
$521$	−9023.61			−0.758794			−0.379397	+	0.925234i	$0.623869\pi$
$522$	−6213.38	+	4412.66i	−0.520981	+	0.369994i
$523$	−14888.0			−1.24475			−0.622376	−	0.782718i	$-0.713833\pi$
$523$	−14888.0			−1.24475			−0.622376	+	0.782718i	$0.713833\pi$
$524$	−2406.79	−	839.837i	−0.200651	−	0.0700162i
$525$		−	218.845i		−	0.0181927i
$526$	11021.0	+	15518.4i	0.913569	+	1.28638i
$527$	−5461.57	−	13688.4i	−0.451442	−	1.13145i
$528$	−559.570	−	444.662i	−0.0461215	−	0.0366504i
$529$	4630.65			0.380591
$530$	−1333.34	+	946.921i	−0.109276	+	0.0776068i
$531$		−	9831.55i		−	0.803490i
$532$	169.333	−	485.271i	0.0137998	−	0.0395473i
$533$		−	9418.88i		−	0.765435i
$534$	−242.215	+	172.018i	−0.0196286	+	0.0139400i
$535$			5152.37i			0.416367i
$536$	−4974.37	−	17182.7i	−0.400859	−	1.38466i
$537$	−196.646			−0.0158024
$538$	−3602.62	+	2558.54i	−0.288699	+	0.205031i
$539$	−12561.9			−1.00386
$540$	−119.732	+	343.124i	−0.00954153	+	0.0273439i
$541$	2012.71			0.159950			0.0799752	−	0.996797i	$-0.474516\pi$
$541$	2012.71			0.159950			0.0799752	+	0.996797i	$0.474516\pi$
$542$	1252.64	+	1763.82i	0.0992722	+	0.139783i
$543$		−	94.3558i		−	0.00745708i
$544$	−15434.1	−	833.310i	−1.21641	−	0.0656762i
$545$	4285.30			0.336811
$546$	219.916	+	309.659i	0.0172373	+	0.0242714i
$547$			12730.7i			0.995110i	0.867432	+	0.497555i	$0.165769\pi$
$547$			12730.7i			0.995110i	−0.867432	+	0.497555i	$0.834231\pi$
$548$	−4466.95	−	1558.72i	−0.348209	−	0.121506i
$549$			16389.1i			1.27408i
$550$	−8201.41	−	11548.2i	−0.635835	−	0.895305i
$551$	851.533			0.0658376
$552$	−716.339	+	207.380i	−0.0552344	+	0.0159903i
$553$			2318.09i			0.178255i
$554$	17896.1	−	12709.6i	1.37244	−	0.974691i
$555$		−	250.865i		−	0.0191867i
$556$	−2888.84	+	8278.77i	−0.220349	+	0.631471i
$557$		−	18857.2i		−	1.43448i	−0.696826	−	0.717240i	$-0.745405\pi$
$557$		−	18857.2i		−	1.43448i	0.696826	−	0.717240i	$-0.254595\pi$
$558$	−11044.8	−	7136.01i	−0.837927	−	0.541382i
$559$		−	34679.1i		−	2.62392i
$560$	−995.289	+	1252.49i	−0.0751047	+	0.0945130i
$561$			953.566i			0.0717640i
$562$	−8867.37	−	12486.0i	−0.665565	−	0.937167i
$563$			4877.93i			0.365151i	0.983192	+	0.182576i	$0.0584434\pi$
$563$			4877.93i			0.365151i	−0.983192	+	0.182576i	$0.941557\pi$
$564$	−845.636	−	295.081i	−0.0631342	−	0.0220304i
$565$	2708.75			0.201696
$566$	−10676.0	+	7581.93i	−0.792834	+	0.563061i
$567$		−	5462.34i		−	0.404580i
$568$	3691.64	+	12751.8i	0.272707	+	0.941995i
$569$		−	4867.18i		−	0.358599i	−0.983795	−	0.179299i	$-0.942617\pi$
$569$		−	4867.18i		−	0.358599i	0.983795	−	0.179299i	$-0.0573831\pi$
$570$	16.5337	−	11.7420i	0.00121495	−	0.000862842i
$571$	36.0698			0.00264356			0.00132178	−	0.999999i	$-0.499579\pi$
$571$	36.0698			0.00264356			0.00132178	+	0.999999i	$0.499579\pi$
$572$	23209.6	+	8098.87i	1.69657	+	0.592012i
$573$			144.728i			0.0105517i
$574$	2342.87	−	1663.88i	0.170365	−	0.120991i
$575$	−14779.0			−1.07187
$576$	−11658.0	+	7367.45i	−0.843317	+	0.532946i
$577$	2400.44			0.173192			0.0865960	−	0.996244i	$-0.472401\pi$
$577$	2400.44			0.173192			0.0865960	+	0.996244i	$0.472401\pi$
$578$	3894.16	+	5483.29i	0.280235	+	0.394593i
$579$	450.065			0.0323041
$580$	−2502.53	−	873.245i	−0.179158	−	0.0625165i
$581$		−	6511.73i		−	0.464978i
$582$	−576.038	−	811.106i	−0.0410267	−	0.0577688i
$583$			7666.51i			0.544622i
$584$	−4856.69	−	16776.2i	−0.344129	−	1.18870i
$585$		−	6242.01i		−	0.441154i
$586$	−4966.49	−	6993.21i	−0.350109	−	0.492981i
$587$	−14386.5			−1.01157			−0.505786	−	0.862659i	$-0.668798\pi$
$587$	−14386.5			−1.01157			−0.505786	+	0.862659i	$0.668798\pi$
$588$	191.717	−	549.419i	0.0134461	−	0.0385334i
$589$	544.496	+	1364.67i	0.0380909	+	0.0954674i
$590$	2787.85	−	1979.90i	0.194532	−	0.138155i
$591$		−	592.244i		−	0.0412211i
$592$	11859.5	−	14924.2i	0.823352	−	1.03612i
$593$	8232.72			0.570113			0.285057	−	0.958511i	$-0.407988\pi$
$593$	8232.72			0.570113			0.285057	+	0.958511i	$0.407988\pi$
$594$	986.458	+	1389.01i	0.0681395	+	0.0959457i
$595$	2134.37			0.147060
$596$	3296.68	−	9447.57i	0.226573	−	0.649308i
$597$	157.246			0.0107800
$598$	20911.8	−	14851.3i	1.43001	−	1.01558i
$599$			23212.3i			1.58335i	0.610939	+	0.791677i	$0.290792\pi$
$599$			23212.3i			1.58335i	−0.610939	+	0.791677i	$0.709208\pi$
$600$	630.251	−	182.457i	0.0428832	−	0.0124147i
$601$			15750.6i			1.06902i	0.845162	+	0.534511i	$0.179504\pi$
$601$			15750.6i			1.06902i	−0.845162	+	0.534511i	$0.820496\pi$
$602$	8626.15	−	6126.19i	0.584013	−	0.414759i
$603$			21293.9i			1.43807i
$604$	4080.54	−	11693.9i	0.274892	−	0.787779i
$605$	1979.50			0.133022
$606$	−266.440	−	375.168i	−0.0178604	−	0.0251488i
$607$		−	19200.9i		−	1.28392i	−0.766737	−	0.641962i	$-0.778121\pi$
$607$		−	19200.9i		−	1.28392i	0.766737	−	0.641962i	$-0.221879\pi$
$608$	1538.71	+	83.0775i	0.102636	+	0.00554151i
$609$	−191.979			−0.0127740
$610$	−4647.31	+	3300.47i	−0.308466	+	0.219069i
$611$	30804.0			2.03960
$612$	17372.0	+	6061.87i	1.14742	+	0.400386i
$613$		−	24894.6i		−	1.64027i	−0.572173	−	0.820133i	$-0.693899\pi$
$613$		−	24894.6i		−	1.64027i	0.572173	−	0.820133i	$-0.306101\pi$
$614$	21792.3	−	15476.6i	1.43235	−	1.01724i
$615$	113.380			0.00743405
$616$	2085.52	+	7203.89i	0.136409	+	0.471190i
$617$	−11643.7			−0.759739			−0.379870	−	0.925040i	$-0.624031\pi$
$617$	−11643.7			−0.759739			−0.379870	+	0.925040i	$0.624031\pi$
$618$	59.7212	−	42.4133i	0.00388728	−	0.00276070i
$619$	−21215.8			−1.37760			−0.688800	−	0.724951i	$-0.741862\pi$
$619$	−21215.8			−1.37760			−0.688800	+	0.724951i	$0.741862\pi$
$620$	−200.723	−	4568.95i	−0.0130020	−	0.295957i
$621$	1777.60			0.114867
$622$	−11756.2	+	8349.14i	−0.757850	+	0.538216i
$623$	3117.29			0.200468
$624$	−708.438	+	891.510i	−0.0454491	+	0.0571938i
$625$	11631.6			0.744423
$626$	−2516.81	+	1787.41i	−0.160690	+	0.114120i
$627$		−	95.0666i		−	0.00605517i
$628$	−6823.01	+	19553.2i	−0.433547	+	1.24245i
$629$	−25432.5			−1.61218
$630$	1552.65	−	1102.67i	0.0981890	−	0.0697326i
$631$	15927.2			1.00484			0.502419	−	0.864624i	$-0.332443\pi$
$631$	15927.2			1.00484			0.502419	+	0.864624i	$0.332443\pi$
$632$	−6675.86	+	1932.66i	−0.420176	+	0.121641i
$633$			538.728i			0.0338270i
$634$	2614.32	+	3681.16i	0.163766	+	0.230596i
$635$	−5430.35			−0.339365
$636$	−335.309	−	117.005i	−0.0209055	−	0.00729486i
$637$			20013.7i			1.24486i
$638$	−10130.6	+	7194.59i	−0.628640	+	0.446452i
$639$		−	15802.8i		−	0.978326i
$640$	−4436.85	−	1822.10i	−0.274034	−	0.112539i
$641$		−	31973.0i		−	1.97014i	−0.172161	−	0.985069i	$-0.555075\pi$
$641$		−	31973.0i		−	1.97014i	0.172161	−	0.985069i	$-0.444925\pi$
$642$	−912.240	+	647.861i	−0.0560798	+	0.0398272i
$643$	25813.1			1.58315			0.791577	−	0.611070i	$-0.209260\pi$
$643$	25813.1			1.58315			0.791577	+	0.611070i	$0.209260\pi$
$644$	7388.30	+	2578.11i	0.452080	+	0.157751i
$645$	417.452			0.0254840
$646$	−1190.40	−	1676.18i	−0.0725010	−	0.102087i
$647$	11157.2			0.677953			0.338977	−	0.940795i	$-0.389919\pi$
$647$	11157.2			0.677953			0.338977	+	0.940795i	$0.389919\pi$
$648$	15731.0	−	4554.12i	0.953661	−	0.276085i
$649$		−	16029.8i		−	0.969528i
$650$	−18398.7	+	13066.5i	−1.11024	+	0.788479i
$651$	−122.757	−	307.667i	−0.00739053	−	0.0185229i
$652$	−24384.3	−	8508.78i	−1.46467	−	0.511089i
$653$	830.406			0.0497646			0.0248823	−	0.999690i	$-0.492079\pi$
$653$	830.406			0.0497646			0.0248823	+	0.999690i	$0.492079\pi$
$654$	538.835	+	758.723i	0.0322173	+	0.0453645i
$655$			1055.36i			0.0629562i
$656$	6745.13	+	5360.02i	0.401453	+	0.319014i
$657$			20790.1i			1.23455i
$658$	5441.64	+	7662.26i	0.322397	+	0.453960i
$659$		−	3359.50i		−	0.198585i	−0.995058	−	0.0992925i	$-0.968342\pi$
$659$		−	3359.50i		−	0.198585i	0.995058	−	0.0992925i	$-0.0316580\pi$
$660$	−97.4906	+	279.387i	−0.00574972	+	0.0164774i
$661$	26429.0			1.55517			0.777586	−	0.628777i	$-0.216444\pi$
$661$	26429.0			1.55517			0.777586	+	0.628777i	$0.216444\pi$
$662$	−4604.42	−	6483.38i	−0.270326	−	0.380640i
$663$	1519.23			0.0889923
$664$	18753.2	−	5429.03i	1.09603	−	0.317300i
$665$	−212.788			−0.0124084
$666$	−18500.9	+	13139.1i	−1.07642	+	0.764459i
$667$			12964.7i			0.752615i
$668$	−3022.90	+	8662.95i	−0.175089	+	0.501766i
$669$	1477.97			0.0854138
$670$	−6038.13	+	4288.21i	−0.348169	+	0.247266i
$671$			26721.4i			1.53736i
$672$	−346.904	−	18.7299i	−0.0199139	−	0.00107518i
$673$		−	26238.9i		−	1.50287i	−0.659805	−	0.751437i	$-0.729361\pi$
$673$		−	26238.9i		−	1.50287i	0.659805	−	0.751437i	$-0.270639\pi$
$674$	−11741.0	+	8338.31i	−0.670988	+	0.476528i
$675$	−1563.97			−0.0891811
$676$	7112.51	−	20382.9i	0.404672	−	1.15970i
$677$			5965.38i			0.338653i	0.985560	+	0.169327i	$0.0541593\pi$
$677$			5965.38i			0.338653i	−0.985560	+	0.169327i	$0.945841\pi$
$678$	340.600	+	479.592i	0.0192930	+	0.0271661i
$679$			10438.9i			0.589997i
$680$	1779.49	+	6146.78i	0.100353	+	0.346645i
$681$		−	749.540i		−	0.0421769i
$682$	−18007.9	−	11634.8i	−1.01108	−	0.653257i
$683$		−	35146.5i		−	1.96902i	−0.175317	−	0.984512i	$-0.556095\pi$
$683$		−	35146.5i		−	1.96902i	0.175317	−	0.984512i	$-0.443905\pi$
$684$	−1731.91	−	604.343i	−0.0968148	−	0.0337831i
$685$			1958.73i			0.109254i
$686$	−10947.8	+	7775.01i	−0.609315	+	0.432728i
$687$		−	706.828i		−	0.0392535i
$688$	24834.7	+	19734.9i	1.37618	+	1.09358i
$689$	12214.3			0.675368
$690$	178.774	+	251.727i	0.00986348	+	0.0138886i
$691$			11059.7i			0.608872i	0.952533	+	0.304436i	$0.0984680\pi$
$691$			11059.7i			0.608872i	−0.952533	+	0.304436i	$0.901532\pi$
$692$	−7423.59	+	21274.4i	−0.407807	+	1.16869i
$693$		−	8927.52i		−	0.489363i
$694$	−12268.5	−	17275.0i	−0.671045	−	0.944884i
$695$	3630.18			0.198130
$696$	−160.059	−	552.881i	−0.00871697	−	0.0301105i
$697$		−	11494.4i		−	0.624652i
$698$	−12456.4	−	17539.6i	−0.675474	−	0.951121i
$699$	−686.990			−0.0371736
$700$	−6500.39	−	2268.28i	−0.350988	−	0.122476i
$701$	29547.7			1.59201			0.796007	−	0.605287i	$-0.206942\pi$
$701$	29547.7			1.59201			0.796007	+	0.605287i	$0.206942\pi$
$702$	2212.98	−	1571.63i	0.118979	−	0.0844976i
$703$	2535.51			0.136029
$704$	−19007.7	+	12012.2i	−1.01759	+	0.643078i
$705$			370.805i			0.0198090i
$706$	−22983.1	+	16322.3i	−1.22519	+	0.870112i
$707$			4828.39i			0.256846i
$708$	701.092	+	244.643i	0.0372156	+	0.0129862i
$709$		−	8386.02i		−	0.444208i	−0.975023	−	0.222104i	$-0.928708\pi$
$709$		−	8386.02i		−	0.444208i	0.975023	−	0.222104i	$-0.0712925\pi$
$710$	4481.08	−	3182.41i	0.236862	−	0.168217i
$711$	8273.16			0.436382
$712$	2598.98	+	8977.49i	0.136799	+	0.472536i
$713$	−20777.3	+	8290.00i	−1.09132	+	0.435432i
$714$	268.377	+	377.896i	0.0140669	+	0.0198073i
$715$		−	10177.2i		−	0.532317i
$716$	−2038.20	+	5841.03i	−0.106384	+	0.304874i
$717$	145.459			0.00757637
$718$	−1550.82	+	1101.37i	−0.0806075	+	0.0572464i
$719$	−10001.6			−0.518773			−0.259386	−	0.965774i	$-0.583520\pi$
$719$	−10001.6			−0.518773			−0.259386	+	0.965774i	$0.583520\pi$
$720$	4470.08	+	3552.15i	0.231375	+	0.183862i
$721$	−768.609			−0.0397011
$722$	−11114.5	−	15650.1i	−0.572906	−	0.806697i
$723$		−	1595.63i		−	0.0820778i
$724$	−2802.67	−	977.979i	−0.143868	−	0.0502021i
$725$		−	11406.6i		−	0.584318i
$726$	248.904	+	350.476i	0.0127241	+	0.0179165i
$727$			33431.0i			1.70548i	0.522333	+	0.852741i	$0.325062\pi$
$727$			33431.0i			1.70548i	−0.522333	+	0.852741i	$0.674938\pi$
$728$	11477.3	−	3322.66i	0.584308	−	0.169157i
$729$	−19400.7			−0.985659
$730$	−5895.28	+	4186.76i	−0.298896	+	0.212272i
$731$		−	42321.0i		−	2.14131i
$732$	−1168.71	−	407.816i	−0.0590120	−	0.0205920i
$733$	−17296.9			−0.871589			−0.435794	−	0.900046i	$-0.643532\pi$
$733$	−17296.9			−0.871589			−0.435794	+	0.900046i	$0.643532\pi$
$734$	11828.9	+	16656.1i	0.594842	+	0.837584i
$735$	−240.917			−0.0120903
$736$	−1264.86	+	23427.0i	−0.0633471	+	1.17328i
$737$			34718.4i			1.73524i
$738$	−5938.32	−	8361.62i	−0.296196	−	0.417067i
$739$	−492.420			−0.0245114			−0.0122557	−	0.999925i	$-0.503901\pi$
$739$	−492.420			−0.0245114			−0.0122557	+	0.999925i	$0.503901\pi$
$740$	−7451.50	−	2600.17i	−0.370165	−	0.129168i
$741$	−151.461			−0.00750883
$742$	2157.70	+	3038.22i	0.106754	+	0.150319i
$743$	38658.8			1.90882			0.954409	−	0.298501i	$-0.0964867\pi$
$743$	38658.8			1.90882			0.954409	+	0.298501i	$0.0964867\pi$
$744$	783.704	−	610.040i	0.0386183	−	0.0300607i
$745$	−4142.69			−0.203727
$746$	321.654	+	452.915i	0.0157863	+	0.0222284i
$747$	−23240.1			−1.13830
$748$	28324.0	+	9883.53i	1.38453	+	0.483125i
$749$	11740.5			0.572747
$750$	−329.710	−	464.257i	−0.0160524	−	0.0226030i
$751$			34183.5i			1.66095i	0.557056	+	0.830475i	$0.311931\pi$
$751$			34183.5i			1.66095i	−0.557056	+	0.830475i	$0.688069\pi$
$752$	−17529.7	+	22059.6i	−0.850056	+	1.06972i
$753$	−1412.01			−0.0683354
$754$	11462.5	+	16140.0i	0.553632	+	0.779557i
$755$	−5127.70			−0.247174
$756$	781.861	+	272.827i	0.0376138	+	0.0131251i
$757$			6543.95i			0.314193i	0.987583	+	0.157096i	$0.0502133\pi$
$757$			6543.95i			0.314193i	−0.987583	+	0.157096i	$0.949787\pi$
$758$	13189.1	−	9366.76i	0.631994	−	0.448834i
$759$	1447.40			0.0692190
$760$	−177.408	−	612.809i	−0.00846744	−	0.0292486i
$761$		−	16185.9i		−	0.771010i	−0.922706	−	0.385505i	$-0.874027\pi$
$761$		−	16185.9i		−	0.771010i	0.922706	−	0.385505i	$-0.125973\pi$
$762$	−682.815	−	961.457i	−0.0324616	−	0.0457085i
$763$		−	9764.71i		−	0.463311i
$764$	4298.90	+	1500.08i	0.203572	+	0.0710354i
$765$		−	7617.49i		−	0.360014i
$766$	13015.5	+	18326.8i	0.613928	+	0.864459i
$767$	−25538.7			−1.20228
$768$	−235.284	−	1014.67i	−0.0110548	−	0.0476740i
$769$	−17988.3			−0.843531			−0.421766	−	0.906705i	$-0.638589\pi$
$769$	−17988.3			−0.843531			−0.421766	+	0.906705i	$0.638589\pi$
$770$	2531.51	−	1797.84i	0.118479	−	0.0841426i
$771$	756.727			0.0353474
$772$	4664.83	−	13368.4i	0.217475	−	0.623237i
$773$			25688.1i			1.19526i	0.801771	+	0.597631i	$0.203891\pi$
$773$			25688.1i			1.19526i	−0.801771	+	0.597631i	$0.796109\pi$
$774$	−21864.1	−	30786.4i	−1.01536	−	1.42971i
$775$	18280.3	−	7293.73i	0.847288	−	0.338063i
$776$	−30063.0	+	8703.22i	−1.39072	+	0.402613i
$777$	−571.634			−0.0263929
$778$	−7842.85	+	5569.90i	−0.361414	+	0.256672i
$779$			1145.95i			0.0527057i
$780$	445.120	+	155.323i	0.0204331	+	0.00713005i
$781$		−	25765.6i		−	1.18049i
$782$	25519.9	−	18123.9i	1.16700	−	0.828786i
$783$			1371.98i			0.0626187i
$784$	−14332.4	−	11389.2i	−0.652898	−	0.518825i
$785$	8573.96			0.389832
$786$	−186.854	+	132.701i	−0.00847947	+	0.00602201i
$787$	5508.29			0.249491			0.124745	−	0.992189i	$-0.460189\pi$
$787$	5508.29			0.249491			0.124745	+	0.992189i	$0.460189\pi$
$788$	−17591.6	−	6138.49i	−0.795271	−	0.277506i
$789$	1711.25			0.0772146
$790$	1666.07	+	2345.95i	0.0750329	+	0.105652i
$791$		−	6172.31i		−	0.277449i
$792$	25710.4	−	7443.14i	1.15351	−	0.333940i
$793$	42572.7			1.90643
$794$	4996.51	+	7035.47i	0.223324	+	0.314458i
$795$			147.031i			0.00655930i
$796$	1629.82	−	4670.71i	0.0725722	−	0.207976i
$797$			20862.7i			0.927219i	0.886040	+	0.463609i	$0.153446\pi$
$797$			20862.7i			0.927219i	−0.886040	+	0.463609i	$0.846554\pi$
$798$	−26.7561	−	37.6746i	−0.00118691	−	0.00167126i
$799$	37592.0			1.66447
$800$	1112.86	−	20611.6i	0.0491817	−	0.910914i
$801$		−	11125.5i		−	0.490761i
$802$	−15091.6	+	10717.9i	−0.664468	+	0.471897i
$803$			33897.0i			1.48966i
$804$	−1518.47	−	529.865i	−0.0666076	−	0.0232424i
$805$		−	3239.72i		−	0.141845i
$806$	−18536.7	+	28690.3i	−0.810084	+	1.25381i
$807$			397.271i			0.0173291i
$808$	−13905.3	+	4025.58i	−0.605429	+	0.175271i
$809$			5034.12i			0.218776i	0.993999	+	0.109388i	$0.0348892\pi$
$809$			5034.12i			0.218776i	−0.993999	+	0.109388i	$0.965111\pi$
$810$	−3925.92	−	5528.01i	−0.170300	−	0.239796i
$811$		−	28241.3i		−	1.22279i	−0.791324	−	0.611397i	$-0.790608\pi$
$811$		−	28241.3i		−	1.22279i	0.791324	−	0.611397i	$-0.209392\pi$
$812$	−1989.82	+	5702.39i	−0.0859965	+	0.246447i
$813$	194.501			0.00839045
$814$	−30164.6	+	21422.5i	−1.29886	+	0.922432i
$815$			10692.3i			0.459554i
$816$	−864.549	+	1087.96i	−0.0370898	+	0.0466744i
$817$			4219.22i			0.180676i
$818$	10758.8	−	7640.75i	0.459868	−	0.326593i
$819$	−14223.4			−0.606843
$820$	1175.17	−	3367.76i	0.0500470	−	0.143424i
$821$		−	2171.40i		−	0.0923049i	−0.998934	−	0.0461525i	$-0.985304\pi$
$821$		−	2171.40i		−	0.0923049i	0.998934	−	0.0461525i	$-0.0146960\pi$
$822$	−346.797	+	246.291i	−0.0147152	+	0.0104506i
$823$	33084.5			1.40128			0.700640	−	0.713515i	$-0.252898\pi$
$823$	33084.5			1.40128			0.700640	+	0.713515i	$0.252898\pi$
$824$	−640.812	−	2213.52i	−0.0270919	−	0.0935820i
$825$	−1273.45			−0.0537406
$826$	−4511.51	−	6352.56i	−0.190043	−	0.267595i
$827$	−20883.5			−0.878102			−0.439051	−	0.898462i	$-0.644685\pi$
$827$	−20883.5			−0.878102			−0.439051	+	0.898462i	$0.644685\pi$
$828$	9201.18	−	26368.5i	0.386187	−	1.10673i
$829$		−	15700.8i		−	0.657793i	−0.944366	−	0.328896i	$-0.893323\pi$
$829$		−	15700.8i		−	0.657793i	0.944366	−	0.328896i	$-0.106677\pi$
$830$	−4680.15	−	6590.02i	−0.195723	−	0.275594i
$831$		−	1973.45i		−	0.0823805i
$832$	19137.9	+	30283.2i	0.797460	+	1.26188i
$833$			24423.9i			1.01589i
$834$	456.461	+	642.733i	0.0189520	+	0.0266859i
$835$	3798.64			0.157434
$836$	−2823.78	−	985.346i	−0.116821	−	0.0407643i
$837$	−2198.74	+	877.283i	−0.0907999	+	0.0362286i
$838$	−1558.41	+	1106.77i	−0.0642416	+	0.0456236i
$839$		−	30848.0i		−	1.26936i	−0.772777	−	0.634678i	$-0.781133\pi$
$839$		−	30848.0i		−	1.26936i	0.772777	−	0.634678i	$-0.218867\pi$
$840$	39.9968	+	138.158i	0.00164288	+	0.00567490i
$841$	14382.7			0.589720
$842$	5499.23	+	7743.35i	0.225078	+	0.316928i
$843$	−1376.86			−0.0562533
$844$	16002.0	+	5583.81i	0.652619	+	0.227728i
$845$	−8937.75			−0.363867
$846$	27346.3	−	19421.0i	1.11133	−	0.789253i
$847$		−	4510.60i		−	0.182982i
$848$	−6950.83	+	8747.03i	−0.281477	+	0.354215i
$849$			1177.27i			0.0475897i
$850$	−22453.0	+	15945.9i	−0.906038	+	0.643457i
$851$			38603.4i			1.55500i
$852$	1126.91	+	393.229i	0.0453136	+	0.0158120i
$853$	−44381.2			−1.78146			−0.890729	−	0.454536i	$-0.849805\pi$
$853$	−44381.2			−1.78146			−0.890729	+	0.454536i	$0.849805\pi$
$854$	7520.62	+	10589.6i	0.301347	+	0.424320i
$855$			759.432i			0.0303766i
$856$	9788.39	+	33811.4i	0.390841	+	1.35006i
$857$	−34614.5			−1.37971			−0.689853	−	0.723949i	$-0.742325\pi$
$857$	−34614.5			−1.37971			−0.689853	+	0.723949i	$0.742325\pi$
$858$	1801.90	−	1279.69i	0.0716969	−	0.0509183i
$859$	−45906.5			−1.82341			−0.911705	−	0.410846i	$-0.865234\pi$
$859$	−45906.5			−1.82341			−0.911705	+	0.410846i	$0.865234\pi$
$860$	4326.81	−	12399.7i	0.171562	−	0.491657i
$861$		−	258.355i		−	0.0102261i
$862$	34062.6	−	24190.8i	1.34591	−	0.955851i
$863$	−32299.9			−1.27405			−0.637023	−	0.770845i	$-0.719834\pi$
$863$	−32299.9			−1.27405			−0.637023	+	0.770845i	$0.719834\pi$
$864$	−133.853	+	2479.15i	−0.00527058	+	0.0976184i
$865$	9328.67			0.366687
$866$	17000.0	−	12073.2i	0.667070	−	0.473745i
$867$	604.657			0.0236854
$868$	−10411.0	+	457.379i	−0.407113	+	0.0178853i
$869$	13488.9			0.526559
$870$	−194.287	+	137.980i	−0.00757120	+	0.00537697i
$871$	55313.6			2.15181
$872$	28121.4	−	8141.14i	1.09210	−	0.316163i
$873$	37256.0			1.44436
$874$	−2544.23	+	1806.88i	−0.0984667	+	0.0699299i
$875$			5974.97i			0.230847i
$876$	−1482.55	−	517.329i	−0.0571812	−	0.0199531i
$877$	−30009.7			−1.15548			−0.577740	−	0.816221i	$-0.696065\pi$
$877$	−30009.7			−1.15548			−0.577740	+	0.816221i	$0.696065\pi$
$878$	−25537.6	+	18136.5i	−0.981607	+	0.697125i
$879$	−771.160			−0.0295911
$880$	7288.21	+	5791.57i	0.279188	+	0.221857i
$881$		−	20757.3i		−	0.793794i	−0.917863	−	0.396897i	$-0.870087\pi$
$881$		−	20757.3i		−	0.793794i	0.917863	−	0.396897i	$-0.129913\pi$
$882$	12618.0	+	17767.2i	0.481714	+	0.678291i
$883$	−1445.20			−0.0550792			−0.0275396	−	0.999621i	$-0.508767\pi$
$883$	−1445.20			−0.0550792			−0.0275396	+	0.999621i	$0.508767\pi$
$884$	15746.5	−	45125.9i	0.599108	−	1.71691i
$885$		−	307.424i		−	0.0116768i
$886$	−11828.7	+	8400.61i	−0.448526	+	0.318537i
$887$		−	18388.7i		−	0.696091i	−0.937478	−	0.348045i	$-0.886846\pi$
$887$		−	18388.7i		−	0.696091i	0.937478	−	0.348045i	$-0.113154\pi$
$888$	−476.589	−	1646.25i	−0.0180104	−	0.0622124i
$889$			12373.9i			0.466824i
$890$	3154.76	−	2240.47i	0.118818	−	0.0843830i
$891$	−31785.3			−1.19511
$892$	15318.9	−	43900.6i	0.575017	−	1.64787i
$893$	−3747.76			−0.140441
$894$	−520.904	−	733.474i	−0.0194873	−	0.0274396i
$895$	2561.25			0.0956572
$896$	−4151.93	+	10110.0i	−0.154806	+	0.376956i
$897$		−	2306.00i		−	0.0858363i
$898$	33881.4	−	24062.1i	1.25906	−	0.894170i
$899$	−6398.34	−	16036.2i	−0.237371	−	0.594924i
$900$	−8095.41	+	23199.6i	−0.299830	+	0.859246i
$901$	14905.9			0.551150
$902$	−9682.08	−	13633.1i	−0.357404	−	0.503252i
$903$		−	951.229i		−	0.0350553i
$904$	17775.7	−	5146.05i	0.653993	−	0.189331i
$905$			1228.95i			0.0451401i
$906$	−644.759	−	907.872i	−0.0236432	−	0.0332914i
$907$		−	16982.4i		−	0.621711i	−0.950457	−	0.310856i	$-0.899384\pi$
$907$		−	16982.4i		−	0.621711i	0.950457	−	0.310856i	$-0.100616\pi$
$908$	−22263.8	−	7768.84i	−0.813710	−	0.283940i
$909$	17232.3			0.628779
$910$	−2864.33	−	4033.21i	−0.104343	−	0.146923i
$911$	24069.3			0.875360			0.437680	−	0.899131i	$-0.355800\pi$
$911$	24069.3			0.875360			0.437680	+	0.899131i	$0.355800\pi$
$912$	86.1919	−	108.465i	0.00312949	−	0.00393821i
$913$	−37891.7			−1.37353
$914$	37582.1	−	26690.4i	1.36007	−	0.965907i
$915$			512.472i			0.0185156i
$916$	−20995.1	−	7326.13i	−0.757310	−	0.264260i
$917$	2404.80			0.0866014
$918$	2700.63	−	1917.95i	0.0970958	−	0.0689563i
$919$			37725.7i			1.35414i	0.735918	+	0.677070i	$0.236751\pi$
$919$			37725.7i			1.35414i	−0.735918	+	0.677070i	$0.763249\pi$
$920$	9330.07	−	2701.05i	0.334351	−	0.0967946i
$921$		−	2403.09i		−	0.0859768i
$922$	26587.6	−	18882.2i	0.949694	−	0.674461i
$923$	−41049.9			−1.46389
$924$	636.625	+	222.147i	0.0226661	+	0.00790921i
$925$		−	33964.2i		−	1.20728i
$926$	−13537.8	−	19062.3i	−0.480432	−	0.676486i
$927$			2743.13i			0.0971913i
$928$	−18081.3	−	976.240i	−0.639599	−	0.0345330i
$929$			35621.0i			1.25801i	0.777403	+	0.629003i	$0.216537\pi$
$929$			35621.0i			1.25801i	−0.777403	+	0.629003i	$0.783463\pi$
$930$	−345.361	−	223.137i	−0.0121772	−	0.00786768i
$931$		−	2434.96i		−	0.0857172i
$932$	−7120.51	+	20405.8i	−0.250258	+	0.717183i
$933$			1296.39i			0.0454898i
$934$	−9582.27	+	6805.21i	−0.335697	+	0.238408i
$935$		−	12419.9i		−	0.434410i
$936$	−11858.5	−	40961.9i	−0.414109	−	1.43043i
$937$	33636.8			1.17275			0.586375	−	0.810040i	$-0.300554\pi$
$937$	33636.8			1.17275			0.586375	+	0.810040i	$0.300554\pi$
$938$	9771.34	+	13758.8i	0.340134	+	0.478935i
$939$			277.536i			0.00964540i
$940$	11014.1	+	3843.32i	0.382171	+	0.133357i
$941$			29827.9i			1.03333i	0.856189	+	0.516663i	$0.172826\pi$
$941$			29827.9i			1.03333i	−0.856189	+	0.516663i	$0.827174\pi$
$942$	1078.09	+	1518.04i	0.0372889	+	0.0525058i
$943$	−17447.1			−0.602499
$944$	14533.4	−	18289.0i	0.501081	−	0.630569i
$945$		−	342.841i		−	0.0118017i
$946$	−35648.2	−	50195.4i	−1.22518	−	1.72515i
$947$	−23876.5			−0.819304			−0.409652	−	0.912242i	$-0.634350\pi$
$947$	−23876.5			−0.819304			−0.409652	+	0.912242i	$0.634350\pi$
$948$	−205.865	+	589.962i	−0.00705292	+	0.0202121i
$949$	54004.9			1.84729
$950$	2238.47	−	1589.74i	0.0764480	−	0.0542924i
$951$	405.931			0.0138415
$952$	14006.4	−	4054.84i	0.476838	−	0.138044i
$953$			11318.3i			0.384716i	0.981325	+	0.192358i	$0.0616135\pi$
$953$			11318.3i			0.384716i	−0.981325	+	0.192358i	$0.938387\pi$
$954$	10843.3	−	7700.76i	0.367992	−	0.261343i
$955$		−	1885.04i		−	0.0638726i
$956$	1507.65	−	4320.59i	0.0510051	−	0.146169i
$957$			1117.12i			0.0377340i
$958$	19065.7	−	13540.2i	0.642991	−	0.456644i
$959$	4463.26			0.150288
$960$	−364.536	+	230.374i	−0.0122556	+	0.00774508i
$961$	21608.4	−	20508.1i	0.725333	−	0.688398i
$962$	34130.5	+	48058.4i	1.14388	+	1.61067i
$963$		−	41901.3i		−	1.40213i
$964$	−47395.4	−	16538.4i	−1.58351	−	0.552559i
$965$	−5861.94			−0.195547
$966$	573.600	−	407.364i	0.0191048	−	0.0135680i
$967$	−4187.89			−0.139269			−0.0696347	−	0.997573i	$-0.522183\pi$
$967$	−4187.89			−0.139269			−0.0696347	+	0.997573i	$0.522183\pi$
$968$	12990.1	−	3760.63i	0.431320	−	0.124867i
$969$	−184.836			−0.00612776
$970$	7502.69	+	10564.4i	0.248347	+	0.349693i
$971$			9016.68i			0.298001i	0.988837	+	0.149001i	$0.0476056\pi$
$971$			9016.68i			0.298001i	−0.988837	+	0.149001i	$0.952394\pi$
$972$	1461.15	−	4187.32i	0.0482163	−	0.138177i
$973$		−	8271.93i		−	0.272545i
$974$	18650.2	+	26260.9i	0.613543	+	0.863916i
$975$			2028.87i			0.0666420i
$976$	−24226.9	+	30487.5i	−0.794554	+	0.999879i
$977$	−31564.4			−1.03361			−0.516805	−	0.856103i	$-0.672879\pi$
$977$	−31564.4			−1.03361			−0.516805	+	0.856103i	$0.672879\pi$
$978$	−1893.11	+	1344.46i	−0.0618965	+	0.0439582i
$979$		−	18139.5i		−	0.592175i
$980$	−2497.05	+	7156.00i	−0.0813933	+	0.233255i
$981$	−34849.9			−1.13422
$982$	−25593.7	−	36037.9i	−0.831697	−	1.17109i
$983$	9130.14			0.296242			0.148121	−	0.988969i	$-0.452677\pi$
$983$	9130.14			0.296242			0.148121	+	0.988969i	$0.452677\pi$
$984$	744.036	−	215.398i	0.0241047	−	0.00697829i
$985$			7713.78i			0.249524i
$986$	13988.3	+	19696.7i	0.451804	+	0.636176i
$987$	844.937			0.0272489
$988$	−1569.86	+	4498.87i	−0.0505505	+	0.144866i
$989$	−64238.1			−2.06537
$990$	−6416.43	−	9034.84i	−0.205988	−	0.290047i
$991$	−29567.1			−0.947759			−0.473879	−	0.880590i	$-0.657147\pi$
$991$	−29567.1			−0.947759			−0.473879	+	0.880590i	$0.657147\pi$
$992$	−9997.21	−	29601.5i	−0.319972	−	0.947427i
$993$	−714.940			−0.0228479
$994$	−7251.61	−	10210.8i	−0.231396	−	0.325823i
$995$	−2048.07			−0.0652546
$996$	578.294	−	1657.26i	0.0183975	−	0.0527233i
$997$	−1381.81			−0.0438940			−0.0219470	−	0.999759i	$-0.506987\pi$
$997$	−1381.81			−0.0438940			−0.0219470	+	0.999759i	$0.506987\pi$
$998$	17117.7	+	24103.0i	0.542936	+	0.764497i
$999$			4085.18i			0.129379i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	124.4.d.c.123.13	✓	40
4.3	odd	2	inner	124.4.d.c.123.16	yes	40
31.30	odd	2	inner	124.4.d.c.123.14	yes	40
124.123	even	2	inner	124.4.d.c.123.15	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
124.4.d.c.123.13	✓	40	1.1	even	1	trivial
124.4.d.c.123.14	yes	40	31.30	odd	2	inner
124.4.d.c.123.15	yes	40	124.123	even	2	inner
124.4.d.c.123.16	yes	40	4.3	odd	2	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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	124.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.63773 - 2.30605i) q^{2} -0.254294 q^{3} +(-2.63571 + 7.55335i) q^{4} +3.31209 q^{5} +(0.416464 + 0.586414i) q^{6} -7.54711i q^{7} +(21.7349 - 6.29225i) q^{8} -26.9353 q^{9} +O(q^{10})\)	\(q+(-1.63773 - 2.30605i) q^{2} -0.254294 q^{3} +(-2.63571 + 7.55335i) q^{4} +3.31209 q^{5} +(0.416464 + 0.586414i) q^{6} -7.54711i q^{7} +(21.7349 - 6.29225i) q^{8} -26.9353 q^{9} +(-5.42430 - 7.63784i) q^{10} -43.9165 q^{11} +(0.670244 - 1.92077i) q^{12} +69.9680i q^{13} +(-17.4040 + 12.3601i) q^{14} -0.842245 q^{15} +(-50.1061 - 39.8168i) q^{16} +85.3861i q^{17} +(44.1127 + 62.1141i) q^{18} -8.51264i q^{19} +(-8.72970 + 25.0174i) q^{20} +1.91918i q^{21} +(71.9232 + 101.274i) q^{22} +129.606 q^{23} +(-5.52706 + 1.60008i) q^{24} -114.030 q^{25} +(161.350 - 114.588i) q^{26} +13.7154 q^{27} +(57.0059 + 19.8920i) q^{28} +100.032i q^{29} +(1.37937 + 1.94226i) q^{30} +(-160.311 + 63.9632i) q^{31} +(-9.75932 + 180.756i) q^{32} +11.1677 q^{33} +(196.904 - 139.839i) q^{34} -24.9967i q^{35} +(70.9936 - 203.452i) q^{36} +297.853i q^{37} +(-19.6305 + 13.9414i) q^{38} -17.7924i q^{39} +(71.9881 - 20.8405i) q^{40} -134.617 q^{41} +(4.42573 - 3.14310i) q^{42} -495.642 q^{43} +(115.751 - 331.717i) q^{44} -89.2123 q^{45} +(-212.259 - 298.877i) q^{46} -440.259i q^{47} +(12.7417 + 10.1252i) q^{48} +286.041 q^{49} +(186.750 + 262.959i) q^{50} -21.7132i q^{51} +(-528.493 - 184.415i) q^{52} -174.570i q^{53} +(-22.4621 - 31.6284i) q^{54} -145.455 q^{55} +(-47.4883 - 164.036i) q^{56} +2.16471i q^{57} +(230.678 - 163.824i) q^{58} +365.006i q^{59} +(2.21991 - 6.36177i) q^{60} -608.459i q^{61} +(410.048 + 264.931i) q^{62} +203.284i q^{63} +(432.815 - 273.524i) q^{64} +231.740i q^{65} +(-18.2896 - 25.7532i) q^{66} -790.555i q^{67} +(-644.951 - 225.053i) q^{68} -32.9580 q^{69} +(-57.6436 + 40.9378i) q^{70} +586.695i q^{71} +(-585.438 + 169.484i) q^{72} -771.852i q^{73} +(686.863 - 487.801i) q^{74} +28.9971 q^{75} +(64.2989 + 22.4368i) q^{76} +331.443i q^{77} +(-41.0302 + 29.1391i) q^{78} -307.149 q^{79} +(-165.956 - 131.877i) q^{80} +723.766 q^{81} +(220.466 + 310.433i) q^{82} +862.812 q^{83} +(-14.4963 - 5.05840i) q^{84} +282.807i q^{85} +(811.726 + 1142.97i) q^{86} -25.4374i q^{87} +(-954.523 + 276.334i) q^{88} +413.044i q^{89} +(146.105 + 205.728i) q^{90} +528.056 q^{91} +(-341.603 + 978.957i) q^{92} +(40.7662 - 16.2655i) q^{93} +(-1015.26 + 721.023i) q^{94} -28.1946i q^{95} +(2.48173 - 45.9652i) q^{96} -1383.16 q^{97} +(-468.457 - 659.624i) q^{98} +1182.91 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 2 q^{2} + 10 q^{4} - 4 q^{5} + 94 q^{8} + 536 q^{9}+O(q^{10}) \) 40 * q - 2 * q^2 + 10 * q^4 - 4 * q^5 + 94 * q^8 + 536 * q^9	\( 40 q - 2 q^{2} + 10 q^{4} - 4 q^{5} + 94 q^{8} + 536 q^{9} + 228 q^{10} - 104 q^{14} - 78 q^{16} + 114 q^{18} - 44 q^{20} + 28 q^{25} + 48 q^{28} - 602 q^{32} - 136 q^{33} - 482 q^{36} + 420 q^{38} - 516 q^{40} - 4 q^{41} - 1596 q^{45} + 1876 q^{49} - 662 q^{50} + 1576 q^{56} - 838 q^{62} - 302 q^{64} - 3900 q^{66} - 872 q^{69} - 912 q^{70} - 2166 q^{72} + 3220 q^{76} - 476 q^{78} + 572 q^{80} - 2056 q^{81} + 3096 q^{82} - 6220 q^{90} - 2904 q^{93} + 6408 q^{94} - 1836 q^{97} - 1358 q^{98}+O(q^{100}) \) 40 * q - 2 * q^2 + 10 * q^4 - 4 * q^5 + 94 * q^8 + 536 * q^9 + 228 * q^10 - 104 * q^14 - 78 * q^16 + 114 * q^18 - 44 * q^20 + 28 * q^25 + 48 * q^28 - 602 * q^32 - 136 * q^33 - 482 * q^36 + 420 * q^38 - 516 * q^40 - 4 * q^41 - 1596 * q^45 + 1876 * q^49 - 662 * q^50 + 1576 * q^56 - 838 * q^62 - 302 * q^64 - 3900 * q^66 - 872 * q^69 - 912 * q^70 - 2166 * q^72 + 3220 * q^76 - 476 * q^78 + 572 * q^80 - 2056 * q^81 + 3096 * q^82 - 6220 * q^90 - 2904 * q^93 + 6408 * q^94 - 1836 * q^97 - 1358 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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