LMFDB - Embedded newform 124.5.b.a.63.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [124,5,Mod(63,124)]

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, 0]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("124.63");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 124 = 2^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	124.b (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:	$12.8178754224$
Analytic rank:	$0$
Dimension:	$60$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			63.4
Character	$\chi$	$=$	124.63
Dual form			124.5.b.a.63.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.93534 + 0.716318i) q^{2} +7.84728i q^{3} +(14.9738 - 5.63791i) q^{4} +18.4905 q^{5} +(-5.62115 - 30.8817i) q^{6} +83.1629i q^{7} +(-54.8883 + 32.9131i) q^{8} +19.4202 q^{9} +O(q^{10})$	\(q+(-3.93534 + 0.716318i) q^{2} +7.84728i q^{3} +(14.9738 - 5.63791i) q^{4} +18.4905 q^{5} +(-5.62115 - 30.8817i) q^{6} +83.1629i q^{7} +(-54.8883 + 32.9131i) q^{8} +19.4202 q^{9} +(-72.7665 + 13.2451i) q^{10} -117.150i q^{11} +(44.2423 + 117.503i) q^{12} +273.773 q^{13} +(-59.5711 - 327.274i) q^{14} +145.101i q^{15} +(192.428 - 168.842i) q^{16} +200.666 q^{17} +(-76.4249 + 13.9110i) q^{18} +137.612i q^{19} +(276.873 - 104.248i) q^{20} -652.603 q^{21} +(83.9167 + 461.025i) q^{22} +274.117i q^{23} +(-258.278 - 430.724i) q^{24} -283.100 q^{25} +(-1077.39 + 196.108i) q^{26} +788.025i q^{27} +(468.865 + 1245.26i) q^{28} -1168.51 q^{29} +(-103.938 - 571.020i) q^{30} -172.601i q^{31} +(-636.325 + 802.288i) q^{32} +919.310 q^{33} +(-789.689 + 143.741i) q^{34} +1537.73i q^{35} +(290.793 - 109.489i) q^{36} -829.122 q^{37} +(-98.5738 - 541.549i) q^{38} +2148.37i q^{39} +(-1014.92 + 608.581i) q^{40} +3247.43 q^{41} +(2568.21 - 467.471i) q^{42} +3049.24i q^{43} +(-660.482 - 1754.18i) q^{44} +359.089 q^{45} +(-196.355 - 1078.74i) q^{46} -1579.93i q^{47} +(1324.95 + 1510.04i) q^{48} -4515.06 q^{49} +(1114.09 - 202.790i) q^{50} +1574.68i q^{51} +(4099.41 - 1543.51i) q^{52} -2084.55 q^{53} +(-564.477 - 3101.15i) q^{54} -2166.17i q^{55} +(-2737.15 - 4564.67i) q^{56} -1079.88 q^{57} +(4598.50 - 837.028i) q^{58} -439.358i q^{59} +(818.064 + 2172.70i) q^{60} -4482.10 q^{61} +(123.637 + 679.242i) q^{62} +1615.04i q^{63} +(1929.46 - 3613.09i) q^{64} +5062.21 q^{65} +(-3617.80 + 658.518i) q^{66} -2037.44i q^{67} +(3004.73 - 1131.34i) q^{68} -2151.07 q^{69} +(-1101.50 - 6051.47i) q^{70} +3863.86i q^{71} +(-1065.94 + 639.177i) q^{72} +4998.86 q^{73} +(3262.87 - 593.915i) q^{74} -2221.56i q^{75} +(775.843 + 2060.57i) q^{76} +9742.54 q^{77} +(-1538.92 - 8454.57i) q^{78} +880.062i q^{79} +(3558.10 - 3121.97i) q^{80} -4610.83 q^{81} +(-12779.7 + 2326.20i) q^{82} -11266.2i q^{83} +(-9771.92 + 3679.31i) q^{84} +3710.43 q^{85} +(-2184.22 - 11999.8i) q^{86} -9169.66i q^{87} +(3855.77 + 6430.17i) q^{88} +1682.25 q^{89} +(-1413.14 + 257.222i) q^{90} +22767.7i q^{91} +(1545.45 + 4104.57i) q^{92} +1354.45 q^{93} +(1131.73 + 6217.57i) q^{94} +2544.52i q^{95} +(-6295.78 - 4993.42i) q^{96} -2834.27 q^{97} +(17768.3 - 3234.22i) q^{98} -2275.07i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 6 q^{2} - 6 q^{4} + 24 q^{5} + 45 q^{8} - 1732 q^{9}+O(q^{10}) $ 60 * q + 6 * q^2 - 6 * q^4 + 24 * q^5 + 45 * q^8 - 1732 * q^9	$ 60 q + 6 q^{2} - 6 q^{4} + 24 q^{5} + 45 q^{8} - 1732 q^{9} + 53 q^{10} + 130 q^{12} + 120 q^{13} - 231 q^{14} - 590 q^{16} - 648 q^{17} + 230 q^{18} + 1113 q^{20} + 608 q^{21} + 1080 q^{22} - 1028 q^{24} + 8340 q^{25} - 1554 q^{26} - 165 q^{28} - 168 q^{29} - 2238 q^{30} - 1674 q^{32} - 1120 q^{33} + 1844 q^{34} + 1966 q^{36} - 2248 q^{37} - 5055 q^{38} - 1716 q^{40} + 6072 q^{41} + 5794 q^{42} - 120 q^{44} - 4040 q^{45} + 8850 q^{46} + 2276 q^{48} - 17604 q^{49} - 4539 q^{50} + 5896 q^{52} + 3480 q^{53} + 5148 q^{54} - 396 q^{56} - 10912 q^{57} - 7484 q^{58} + 22812 q^{60} + 2200 q^{61} - 19299 q^{64} - 9168 q^{65} - 468 q^{66} - 21930 q^{68} + 6496 q^{69} - 9615 q^{70} - 10079 q^{72} + 13752 q^{73} - 2106 q^{74} + 20099 q^{76} + 16608 q^{77} + 39460 q^{78} - 5787 q^{80} + 20732 q^{81} - 30525 q^{82} - 21760 q^{84} - 21200 q^{85} - 13398 q^{86} + 34690 q^{88} + 22296 q^{89} - 25419 q^{90} - 18852 q^{92} + 3196 q^{94} + 20790 q^{96} + 12120 q^{97} + 21921 q^{98}+O(q^{100}) $ 60 * q + 6 * q^2 - 6 * q^4 + 24 * q^5 + 45 * q^8 - 1732 * q^9 + 53 * q^10 + 130 * q^12 + 120 * q^13 - 231 * q^14 - 590 * q^16 - 648 * q^17 + 230 * q^18 + 1113 * q^20 + 608 * q^21 + 1080 * q^22 - 1028 * q^24 + 8340 * q^25 - 1554 * q^26 - 165 * q^28 - 168 * q^29 - 2238 * q^30 - 1674 * q^32 - 1120 * q^33 + 1844 * q^34 + 1966 * q^36 - 2248 * q^37 - 5055 * q^38 - 1716 * q^40 + 6072 * q^41 + 5794 * q^42 - 120 * q^44 - 4040 * q^45 + 8850 * q^46 + 2276 * q^48 - 17604 * q^49 - 4539 * q^50 + 5896 * q^52 + 3480 * q^53 + 5148 * q^54 - 396 * q^56 - 10912 * q^57 - 7484 * q^58 + 22812 * q^60 + 2200 * q^61 - 19299 * q^64 - 9168 * q^65 - 468 * q^66 - 21930 * q^68 + 6496 * q^69 - 9615 * q^70 - 10079 * q^72 + 13752 * q^73 - 2106 * q^74 + 20099 * q^76 + 16608 * q^77 + 39460 * q^78 - 5787 * q^80 + 20732 * q^81 - 30525 * q^82 - 21760 * q^84 - 21200 * q^85 - 13398 * q^86 + 34690 * q^88 + 22296 * q^89 - 25419 * q^90 - 18852 * q^92 + 3196 * q^94 + 20790 * q^96 + 12120 * q^97 + 21921 * 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 $

$2$	−3.93534	+	0.716318i	−0.983835	+	0.179080i
$2$	−3.93534	+	0.716318i	−0.983835	+	0.179080i
$3$			7.84728i			0.871920i	0.899966	+	0.435960i	$0.143591\pi$
$3$			7.84728i			0.871920i	−0.899966	+	0.435960i	$0.856409\pi$
$4$	14.9738	−	5.63791i	0.935861	−	0.352369i
$5$	18.4905			0.739622			0.369811	−	0.929107i	$-0.379422\pi$
$5$	18.4905			0.739622			0.369811	+	0.929107i	$0.379422\pi$
$6$	−5.62115	−	30.8817i	−0.156143	−	0.857825i
$7$			83.1629i			1.69720i	0.529034	+	0.848601i	$0.322554\pi$
$7$			83.1629i			1.69720i	−0.529034	+	0.848601i	$0.677446\pi$
$8$	−54.8883	+	32.9131i	−0.857630	+	0.514267i
$9$	19.4202			0.239755
$10$	−72.7665	+	13.2451i	−0.727665	+	0.132451i
$11$		−	117.150i		−	0.968183i	−0.875017	−	0.484091i	$-0.839150\pi$
$11$		−	117.150i		−	0.968183i	0.875017	−	0.484091i	$-0.160850\pi$
$12$	44.2423	+	117.503i	0.307238	+	0.815996i
$13$	273.773			1.61996			0.809978	−	0.586460i	$-0.199479\pi$
$13$	273.773			1.61996			0.809978	+	0.586460i	$0.199479\pi$
$14$	−59.5711	−	327.274i	−0.303934	−	1.66977i
$15$			145.101i			0.644891i
$16$	192.428	−	168.842i	0.751672	−	0.659537i
$17$	200.666			0.694347			0.347173	−	0.937801i	$-0.387142\pi$
$17$	200.666			0.694347			0.347173	+	0.937801i	$0.387142\pi$
$18$	−76.4249	+	13.9110i	−0.235879	+	0.0429352i
$19$			137.612i			0.381196i	0.981668	+	0.190598i	$0.0610427\pi$
$19$			137.612i			0.381196i	−0.981668	+	0.190598i	$0.938957\pi$
$20$	276.873	−	104.248i	0.692183	−	0.260620i
$21$	−652.603			−1.47982
$22$	83.9167	+	461.025i	0.173382	+	0.952532i
$23$			274.117i			0.518180i	0.965853	+	0.259090i	$0.0834226\pi$
$23$			274.117i			0.518180i	−0.965853	+	0.259090i	$0.916577\pi$
$24$	−258.278	−	430.724i	−0.448400	−	0.747785i
$25$	−283.100			−0.452960
$26$	−1077.39	+	196.108i	−1.59377	+	0.290101i
$27$			788.025i			1.08097i
$28$	468.865	+	1245.26i	0.598042	+	1.58834i
$29$	−1168.51			−1.38943			−0.694717	−	0.719283i	$-0.744471\pi$
$29$	−1168.51			−1.38943			−0.694717	+	0.719283i	$0.744471\pi$
$30$	−103.938	−	571.020i	−0.115487	−	0.634466i
$31$		−	172.601i		−	0.179605i
$31$		−	172.601i		−	0.179605i
$32$	−636.325	+	802.288i	−0.621411	+	0.783485i
$33$	919.310			0.844178
$34$	−789.689	+	143.741i	−0.683122	+	0.124343i
$35$			1537.73i			1.25529i
$36$	290.793	−	109.489i	0.224377	−	0.0844823i
$37$	−829.122			−0.605640			−0.302820	−	0.953048i	$-0.597928\pi$
$37$	−829.122			−0.605640			−0.302820	+	0.953048i	$0.597928\pi$
$38$	−98.5738	−	541.549i	−0.0682644	−	0.375034i
$39$			2148.37i			1.41247i
$40$	−1014.92	+	608.581i	−0.634322	+	0.380363i
$41$	3247.43			1.93185			0.965923	−	0.258830i	$-0.0833368\pi$
$41$	3247.43			1.93185			0.965923	+	0.258830i	$0.0833368\pi$
$42$	2568.21	−	467.471i	1.45590	−	0.265006i
$43$			3049.24i			1.64913i	0.565769	+	0.824564i	$0.308579\pi$
$43$			3049.24i			1.64913i	−0.565769	+	0.824564i	$0.691421\pi$
$44$	−660.482	−	1754.18i	−0.341158	−	0.906084i
$45$	359.089			0.177328
$46$	−196.355	−	1078.74i	−0.0927954	−	0.509803i
$47$		−	1579.93i		−	0.715225i	−0.933870	−	0.357613i	$-0.883591\pi$
$47$		−	1579.93i		−	0.715225i	0.933870	−	0.357613i	$-0.116409\pi$
$48$	1324.95	+	1510.04i	0.575064	+	0.655398i
$49$	−4515.06			−1.88049
$50$	1114.09	−	202.790i	0.445637	−	0.0811158i
$51$			1574.68i			0.605415i
$52$	4099.41	−	1543.51i	1.51605	−	0.570823i
$53$	−2084.55			−0.742097			−0.371048	−	0.928614i	$-0.621002\pi$
$53$	−2084.55			−0.742097			−0.371048	+	0.928614i	$0.621002\pi$
$54$	−564.477	−	3101.15i	−0.193579	−	1.06349i
$55$		−	2166.17i		−	0.716089i
$56$	−2737.15	−	4564.67i	−0.872814	−	1.45557i
$57$	−1079.88			−0.332373
$58$	4598.50	−	837.028i	1.36697	−	0.248819i
$59$		−	439.358i		−	0.126216i	−0.998007	−	0.0631080i	$-0.979899\pi$
$59$		−	439.358i		−	0.126216i	0.998007	−	0.0631080i	$-0.0201013\pi$
$60$	818.064	+	2172.70i	0.227240	+	0.603529i
$61$	−4482.10			−1.20454			−0.602271	−	0.798292i	$-0.705737\pi$
$61$	−4482.10			−1.20454			−0.602271	+	0.798292i	$0.705737\pi$
$62$	123.637	+	679.242i	0.0321636	+	0.176702i
$63$			1615.04i			0.406912i
$64$	1929.46	−	3613.09i	0.471060	−	0.882101i
$65$	5062.21			1.19816
$66$	−3617.80	+	658.518i	−0.830532	+	0.151175i
$67$		−	2037.44i		−	0.453875i	−0.973909	−	0.226937i	$-0.927129\pi$
$67$		−	2037.44i		−	0.453875i	0.973909	−	0.226937i	$-0.0728713\pi$
$68$	3004.73	−	1131.34i	0.649812	−	0.244666i
$69$	−2151.07			−0.451811
$70$	−1101.50	−	6051.47i	−0.224796	−	1.23499i
$71$			3863.86i			0.766487i	0.923647	+	0.383243i	$0.125193\pi$
$71$			3863.86i			0.766487i	−0.923647	+	0.383243i	$0.874807\pi$
$72$	−1065.94	+	639.177i	−0.205621	+	0.123298i
$73$	4998.86			0.938048			0.469024	−	0.883185i	$-0.344606\pi$
$73$	4998.86			0.938048			0.469024	+	0.883185i	$0.344606\pi$
$74$	3262.87	−	593.915i	0.595850	−	0.108458i
$75$		−	2221.56i		−	0.394945i
$76$	775.843	+	2060.57i	0.134322	+	0.356746i
$77$	9742.54			1.64320
$78$	−1538.92	−	8454.57i	−0.252945	−	1.38964i
$79$			880.062i			0.141013i	0.997511	+	0.0705065i	$0.0224615\pi$
$79$			880.062i			0.141013i	−0.997511	+	0.0705065i	$0.977538\pi$
$80$	3558.10	−	3121.97i	0.555953	−	0.487808i
$81$	−4610.83			−0.702763
$82$	−12779.7	+	2326.20i	−1.90062	+	0.345954i
$83$		−	11266.2i		−	1.63538i	−0.575656	−	0.817692i	$-0.695253\pi$
$83$		−	11266.2i		−	1.63538i	0.575656	−	0.817692i	$-0.304747\pi$
$84$	−9771.92	+	3679.31i	−1.38491	+	0.521445i
$85$	3710.43			0.513554
$86$	−2184.22	−	11999.8i	−0.295325	−	1.62247i
$87$		−	9169.66i		−	1.21148i
$88$	3855.77	+	6430.17i	0.497904	+	0.830343i
$89$	1682.25			0.212378			0.106189	−	0.994346i	$-0.466135\pi$
$89$	1682.25			0.212378			0.106189	+	0.994346i	$0.466135\pi$
$90$	−1413.14	+	257.222i	−0.174461	+	0.0317558i
$91$			22767.7i			2.74939i
$92$	1545.45	+	4104.57i	0.182591	+	0.484944i
$93$	1354.45			0.156602
$94$	1131.73	+	6217.57i	0.128082	+	0.703664i
$95$			2544.52i			0.281941i
$96$	−6295.78	−	4993.42i	−0.683136	−	0.541821i
$97$	−2834.27			−0.301230			−0.150615	−	0.988593i	$-0.548125\pi$
$97$	−2834.27			−0.301230			−0.150615	+	0.988593i	$0.548125\pi$
$98$	17768.3	−	3234.22i	1.85009	−	0.336758i
$99$		−	2275.07i		−	0.232127i
$100$	−4239.07	+	1596.09i	−0.423907	+	0.159609i
$101$	13913.4			1.36393			0.681963	−	0.731386i	$-0.261126\pi$
$101$	13913.4			1.36393			0.681963	+	0.731386i	$0.261126\pi$
$102$	−1127.97	−	6196.92i	−0.108417	−	0.595628i
$103$			2833.55i			0.267089i	0.991043	+	0.133545i	$0.0426359\pi$
$103$			2833.55i			0.267089i	−0.991043	+	0.133545i	$0.957364\pi$
$104$	−15026.9	+	9010.70i	−1.38932	+	0.833090i
$105$	−12067.0			−1.09451
$106$	8203.41	−	1493.20i	0.730100	−	0.132894i
$107$		−	18634.2i		−	1.62758i	−0.581159	−	0.813790i	$-0.697401\pi$
$107$		−	18634.2i		−	1.62758i	0.581159	−	0.813790i	$-0.302599\pi$
$108$	4442.82	+	11799.7i	0.380900	+	1.01164i
$109$	−5066.07			−0.426401			−0.213201	−	0.977008i	$-0.568389\pi$
$109$	−5066.07			−0.426401			−0.213201	+	0.977008i	$0.568389\pi$
$110$	1551.67	+	8524.61i	0.128237	+	0.704513i
$111$		−	6506.35i		−	0.528070i
$112$	14041.3	+	16002.9i	1.11937	+	1.27574i
$113$	5807.88			0.454842			0.227421	−	0.973796i	$-0.426971\pi$
$113$	5807.88			0.454842			0.227421	+	0.973796i	$0.426971\pi$
$114$	4249.69	−	773.537i	0.327000	−	0.0595211i
$115$			5068.57i			0.383257i
$116$	−17497.1	+	6587.98i	−1.30032	+	0.489594i
$117$	5316.71			0.388393
$118$	314.720	+	1729.02i	0.0226027	+	0.124176i
$119$			16688.0i			1.17845i
$120$	−4775.70	−	7964.33i	−0.331646	−	0.553078i
$121$	916.854			0.0626224
$122$	17638.6	−	3210.61i	1.18507	−	0.215709i
$123$			25483.5i			1.68442i
$124$	−973.107	−	2584.48i	−0.0632874	−	0.168086i
$125$	−16791.3			−1.07464
$126$	−1156.88	−	6355.71i	−0.0728697	−	0.400335i
$127$			11477.2i			0.711585i	0.934565	+	0.355792i	$0.115789\pi$
$127$			11477.2i			0.711585i	−0.934565	+	0.355792i	$0.884211\pi$
$128$	−5004.96	+	15600.8i	−0.305478	+	0.952199i
$129$	−23928.2			−1.43791
$130$	−19921.5	+	3626.15i	−1.17879	+	0.214565i
$131$		−	27622.5i		−	1.60961i	−0.593539	−	0.804805i	$-0.702270\pi$
$131$		−	27622.5i		−	1.60961i	0.593539	−	0.804805i	$-0.297730\pi$
$132$	13765.5	−	5182.99i	0.790033	−	0.297462i
$133$	−11444.2			−0.646966
$134$	1459.46	+	8018.03i	0.0812797	+	0.446538i
$135$			14571.0i			0.799507i
$136$	−11014.2	+	6604.54i	−0.595493	+	0.357079i
$137$	−10875.2			−0.579424			−0.289712	−	0.957114i	$-0.593560\pi$
$137$	−10875.2			−0.579424			−0.289712	+	0.957114i	$0.593560\pi$
$138$	8465.20	−	1540.85i	0.444508	−	0.0809102i
$139$		−	8322.55i		−	0.430751i	−0.976531	−	0.215376i	$-0.930902\pi$
$139$		−	8322.55i		−	0.430751i	0.976531	−	0.215376i	$-0.0690976\pi$
$140$	8669.56	+	23025.6i	0.442325	+	1.17477i
$141$	12398.2			0.623620
$142$	−2767.75	−	15205.6i	−0.137262	−	0.754096i
$143$		−	32072.5i		−	1.56841i
$144$	3736.98	−	3278.93i	0.180217	−	0.158127i
$145$	−21606.5			−1.02766
$146$	−19672.2	+	3580.77i	−0.922884	+	0.167985i
$147$		−	35431.0i		−	1.63964i
$148$	−12415.1	+	4674.51i	−0.566795	+	0.213409i
$149$	23802.5			1.07214			0.536069	−	0.844174i	$-0.319909\pi$
$149$	23802.5			1.07214			0.536069	+	0.844174i	$0.319909\pi$
$150$	1591.35	+	8742.61i	0.0707265	+	0.388560i
$151$		−	32418.8i		−	1.42181i	−0.703287	−	0.710906i	$-0.748285\pi$
$151$		−	32418.8i		−	1.42181i	0.703287	−	0.710906i	$-0.251715\pi$
$152$	−4529.23	−	7553.28i	−0.196036	−	0.326925i
$153$	3896.97			0.166473
$154$	−38340.2	+	6978.76i	−1.61664	+	0.294264i
$155$		−	3191.48i		−	0.132840i
$156$	12112.3	+	32169.2i	0.497712	+	1.32188i
$157$	37949.4			1.53959			0.769797	−	0.638289i	$-0.220357\pi$
$157$	37949.4			1.53959			0.769797	+	0.638289i	$0.220357\pi$
$158$	−630.404	−	3463.34i	−0.0252525	−	0.138733i
$159$		−	16358.0i		−	0.647049i
$160$	−11766.0	+	14834.7i	−0.459609	+	0.579482i
$161$	−22796.4			−0.879455
$162$	18145.2	−	3302.82i	0.691402	−	0.125850i
$163$			43554.8i			1.63931i	0.572860	+	0.819654i	$0.305834\pi$
$163$			43554.8i			1.63931i	−0.572860	+	0.819654i	$0.694166\pi$
$164$	48626.3	−	18308.7i	1.80794	−	0.680723i
$165$	16998.5			0.624372
$166$	8070.16	+	44336.2i	0.292864	+	1.60895i
$167$			3825.32i			0.137162i	0.997646	+	0.0685811i	$0.0218472\pi$
$167$			3825.32i			0.137162i	−0.997646	+	0.0685811i	$0.978153\pi$
$168$	35820.3	−	21479.2i	1.26914	−	0.761024i
$169$	46390.5			1.62426
$170$	−14601.8	+	2657.85i	−0.505252	+	0.0919670i
$171$			2672.44i			0.0913936i
$172$	17191.3	+	45658.6i	0.581102	+	1.54335i
$173$	9428.07			0.315015			0.157507	−	0.987518i	$-0.449654\pi$
$173$	9428.07			0.315015			0.157507	+	0.987518i	$0.449654\pi$
$174$	6568.40	+	36085.7i	0.216951	+	1.19189i
$175$		−	23543.4i		−	0.768764i
$176$	−19779.8	−	22543.0i	−0.638553	−	0.727756i
$177$	3447.77			0.110050
$178$	−6620.20	+	1205.02i	−0.208945	+	0.0380325i
$179$			14352.2i			0.447932i	0.974597	+	0.223966i	$0.0719005\pi$
$179$			14352.2i			0.447932i	−0.974597	+	0.223966i	$0.928100\pi$
$180$	5376.92	−	2024.51i	0.165954	−	0.0624849i
$181$	38854.9			1.18601			0.593006	−	0.805198i	$-0.297941\pi$
$181$	38854.9			1.18601			0.593006	+	0.805198i	$0.297941\pi$
$182$	−16308.9	−	89598.7i	−0.492360	−	2.70495i
$183$		−	35172.3i		−	1.05026i
$184$	−9022.03	−	15045.8i	−0.266483	−	0.444407i
$185$	−15330.9			−0.447945
$186$	−5330.21	+	970.215i	−0.154070	+	0.0280441i
$187$		−	23508.1i		−	0.672254i
$188$	−8907.52	−	23657.6i	−0.252023	−	0.669352i
$189$	−65534.4			−1.83462
$190$	−1822.68	−	10013.5i	−0.0504898	−	0.277383i
$191$			23860.5i			0.654054i	0.945015	+	0.327027i	$0.106047\pi$
$191$			23860.5i			0.654054i	−0.945015	+	0.327027i	$0.893953\pi$
$192$	28352.9	+	15141.0i	0.769122	+	0.410726i
$193$	−72244.7			−1.93951			−0.969754	−	0.244086i	$-0.921512\pi$
$193$	−72244.7			−1.93951			−0.969754	+	0.244086i	$0.921512\pi$
$194$	11153.8	−	2030.24i	0.296360	−	0.0539441i
$195$			39724.6i			1.04470i
$196$	−67607.5	+	25455.5i	−1.75988	+	0.662628i
$197$	−14777.8			−0.380784			−0.190392	−	0.981708i	$-0.560976\pi$
$197$	−14777.8			−0.380784			−0.190392	+	0.981708i	$0.560976\pi$
$198$	1629.68	+	8953.18i	0.0415691	+	0.228374i
$199$			49204.1i			1.24250i	0.783614	+	0.621248i	$0.213374\pi$
$199$			49204.1i			1.24250i	−0.783614	+	0.621248i	$0.786626\pi$
$200$	15538.9	−	9317.68i	0.388472	−	0.232942i
$201$	15988.4			0.395743
$202$	−54754.0	+	9966.43i	−1.34188	+	0.244251i
$203$		−	97177.0i		−	2.35815i
$204$	8877.93	+	23579.0i	0.213330	+	0.566584i
$205$	60046.8			1.42884
$206$	−2029.72	−	11151.0i	−0.0478302	−	0.262772i
$207$			5323.39i			0.124236i
$208$	52681.5	−	46224.2i	1.21768	−	1.06842i
$209$	16121.2			0.369067
$210$	47487.6	−	8643.79i	1.07682	−	0.196004i
$211$		−	86799.9i		−	1.94964i	−0.222993	−	0.974820i	$-0.571583\pi$
$211$		−	86799.9i		−	1.94964i	0.222993	−	0.974820i	$-0.428417\pi$
$212$	−31213.6	+	11752.5i	−0.694499	+	0.261492i
$213$	−30320.8			−0.668315
$214$	13348.0	+	73331.7i	0.291466	+	1.60127i
$215$			56382.0i			1.21973i
$216$	−25936.3	−	43253.4i	−0.555906	−	0.927071i
$217$	14354.0			0.304826
$218$	19936.7	−	3628.92i	0.419508	−	0.0763598i
$219$			39227.4i			0.817903i
$220$	−12212.7	−	32435.7i	−0.252328	−	0.670160i
$221$	54936.9			1.12481
$222$	4660.62	+	25604.7i	0.0945666	+	0.519534i
$223$			4816.74i			0.0968598i	0.998827	+	0.0484299i	$0.0154217\pi$
$223$			4816.74i			0.0968598i	−0.998827	+	0.0484299i	$0.984578\pi$
$224$	−66720.6	−	52918.6i	−1.32973	−	1.05466i
$225$	−5497.84			−0.108599
$226$	−22856.0	+	4160.29i	−0.447490	+	0.0814530i
$227$			34124.9i			0.662246i	0.943588	+	0.331123i	$0.107428\pi$
$227$			34124.9i			0.662246i	−0.943588	+	0.331123i	$0.892572\pi$
$228$	−16169.9	+	6088.26i	−0.311054	+	0.117118i
$229$	−13652.9			−0.260348			−0.130174	−	0.991491i	$-0.541554\pi$
$229$	−13652.9			−0.260348			−0.130174	+	0.991491i	$0.541554\pi$
$230$	−3630.71	−	19946.5i	−0.0686335	−	0.377061i
$231$			76452.5i			1.43274i
$232$	64137.8	−	38459.4i	1.19162	−	0.714540i
$233$	8425.43			0.155196			0.0775979	−	0.996985i	$-0.475275\pi$
$233$	8425.43			0.155196			0.0775979	+	0.996985i	$0.475275\pi$
$234$	−20923.0	+	3808.45i	−0.382114	+	0.0695532i
$235$		−	29213.8i		−	0.528996i
$236$	−2477.06	−	6578.85i	−0.0444746	−	0.118121i
$237$	−6906.09			−0.122952
$238$	−11953.9	−	65672.8i	−0.211036	−	1.15940i
$239$			42088.1i			0.736824i	0.929663	+	0.368412i	$0.120098\pi$
$239$			42088.1i			0.736824i	−0.929663	+	0.368412i	$0.879902\pi$
$240$	24499.0	+	27921.4i	0.425330	+	0.484747i
$241$	16685.4			0.287278			0.143639	−	0.989630i	$-0.454120\pi$
$241$	16685.4			0.287278			0.143639	+	0.989630i	$0.454120\pi$
$242$	−3608.13	+	656.760i	−0.0616101	+	0.0112144i
$243$			27647.6i			0.468215i
$244$	−67113.9	+	25269.7i	−1.12728	+	0.424443i
$245$	−83486.0			−1.39085
$246$	−18254.3	−	100286.i	−0.301644	−	1.65719i
$247$			37674.3i			0.617521i
$248$	5680.82	+	9473.77i	0.0923650	+	0.154035i
$249$	88408.8			1.42592
$250$	66079.3	−	12027.9i	1.05727	−	0.192446i
$251$		−	95746.1i		−	1.51976i	−0.650066	−	0.759878i	$-0.725259\pi$
$251$		−	95746.1i		−	1.51976i	0.650066	−	0.759878i	$-0.274741\pi$
$252$	9105.42	+	24183.2i	0.143383	+	0.380814i
$253$	32112.8			0.501692
$254$	−8221.29	−	45166.5i	−0.127430	−	0.700082i
$255$			29116.8i			0.447778i
$256$	8521.04	−	64979.7i	0.130021	−	0.991511i
$257$	20979.5			0.317635			0.158818	−	0.987308i	$-0.449232\pi$
$257$	20979.5			0.317635			0.158818	+	0.987308i	$0.449232\pi$
$258$	94165.6	−	17140.2i	1.41466	−	0.257500i
$259$		−	68952.1i		−	1.02789i
$260$	75800.3	−	28540.3i	1.12131	−	0.422193i
$261$	−22692.7			−0.333124
$262$	19786.5	+	108704.i	0.288248	+	1.58359i
$263$		−	73583.5i		−	1.06382i	−0.846800	−	0.531911i	$-0.821474\pi$
$263$		−	73583.5i		−	1.06382i	0.846800	−	0.531911i	$-0.178526\pi$
$264$	−50459.4	+	30257.3i	−0.723993	+	0.434133i
$265$	−38544.5			−0.548871
$266$	45036.8	−	8197.68i	0.636508	−	0.115858i
$267$			13201.1i			0.185177i
$268$	−11486.9	−	30508.2i	−0.159932	−	0.424764i
$269$	52381.7			0.723894			0.361947	−	0.932199i	$-0.382112\pi$
$269$	52381.7			0.723894			0.361947	+	0.932199i	$0.382112\pi$
$270$	−10437.5	−	57341.9i	−0.143175	−	0.786583i
$271$			64082.1i			0.872566i	0.899809	+	0.436283i	$0.143705\pi$
$271$			64082.1i			0.872566i	−0.899809	+	0.436283i	$0.856295\pi$
$272$	38613.8	−	33880.8i	0.521921	−	0.457948i
$273$	−178665.			−2.39725
$274$	42797.6	−	7790.11i	0.570058	−	0.103763i
$275$			33165.2i			0.438548i
$276$	−32209.7	+	12127.6i	−0.422833	+	0.159204i
$277$	18084.9			0.235698			0.117849	−	0.993032i	$-0.462400\pi$
$277$	18084.9			0.235698			0.117849	+	0.993032i	$0.462400\pi$
$278$	5961.59	+	32752.0i	0.0771388	+	0.423788i
$279$		−	3351.93i		−	0.0430613i
$280$	−50611.3	−	84403.3i	−0.645552	−	1.07657i
$281$	−6219.16			−0.0787625			−0.0393812	−	0.999224i	$-0.512539\pi$
$281$	−6219.16			−0.0787625			−0.0393812	+	0.999224i	$0.512539\pi$
$282$	−48791.0	+	8881.04i	−0.613539	+	0.111678i
$283$		−	128863.i		−	1.60900i	−0.593954	−	0.804499i	$-0.702434\pi$
$283$		−	128863.i		−	1.60900i	0.593954	−	0.804499i	$-0.297566\pi$
$284$	21784.1	+	57856.6i	0.270086	+	0.717325i
$285$	−19967.5			−0.245830
$286$	22974.1	+	126216.i	0.280871	+	1.54306i
$287$			270066.i			3.27873i
$288$	−12357.5	+	15580.6i	−0.148986	+	0.187844i
$289$	−43254.1			−0.517883
$290$	85028.8	−	15477.1i	1.01104	−	0.184032i
$291$		−	22241.3i		−	0.262648i
$292$	74851.8	−	28183.1i	0.877883	−	0.330539i
$293$	−4923.94			−0.0573558			−0.0286779	−	0.999589i	$-0.509130\pi$
$293$	−4923.94			−0.0573558			−0.0286779	+	0.999589i	$0.509130\pi$
$294$	25379.8	+	139433.i	0.293626	+	1.61313i
$295$		−	8123.97i		−	0.0933521i
$296$	45509.1	−	27288.9i	0.519416	−	0.311461i
$297$	92317.2			1.04657
$298$	−93671.0	+	17050.2i	−1.05481	+	0.191998i
$299$			75045.7i			0.839428i
$300$	−12525.0	−	33265.2i	−0.139166	−	0.369613i
$301$	−253583.			−2.79890
$302$	23222.1	+	127579.i	0.254618	+	1.39883i
$303$			109182.i			1.18924i
$304$	23234.6	+	26480.3i	0.251413	+	0.286534i
$305$	−82876.4			−0.890905
$306$	−15335.9	+	2791.47i	−0.163782	+	0.0298119i
$307$			88194.5i			0.935761i	0.883792	+	0.467880i	$0.154982\pi$
$307$			88194.5i			0.935761i	−0.883792	+	0.467880i	$0.845018\pi$
$308$	145883.	−	54927.5i	1.53781	−	0.579014i
$309$	−22235.7			−0.232880
$310$	2286.12	+	12559.6i	0.0237889	+	0.130693i
$311$		−	22159.1i		−	0.229103i	−0.993417	−	0.114551i	$-0.963457\pi$
$311$		−	22159.1i		−	0.229103i	0.993417	−	0.114551i	$-0.0365431\pi$
$312$	−70709.5	−	117921.i	−0.726388	−	1.21138i
$313$	116064.			1.18471			0.592353	−	0.805679i	$-0.298199\pi$
$313$	116064.			1.18471			0.592353	+	0.805679i	$0.298199\pi$
$314$	−149344.	+	27183.9i	−1.51471	+	0.275710i
$315$			29862.9i			0.300961i
$316$	4961.71	+	13177.9i	0.0496886	+	0.131969i
$317$	56962.1			0.566849			0.283424	−	0.958995i	$-0.408530\pi$
$317$	56962.1			0.566849			0.283424	+	0.958995i	$0.408530\pi$
$318$	11717.6	+	64374.5i	0.115873	+	0.636589i
$319$			136892.i			1.34523i
$320$	35676.8	−	66808.0i	0.348406	−	0.652421i
$321$	146228.			1.41912
$322$	89711.4	−	16329.4i	0.865238	−	0.157492i
$323$			27614.0i			0.264682i
$324$	−69041.5	+	25995.4i	−0.657688	+	0.247632i
$325$	−77505.0			−0.733775
$326$	−31199.1	−	171403.i	−0.293566	−	1.61281i
$327$		−	39754.9i		−	0.371788i
$328$	−178246.	+	106883.i	−1.65681	+	0.993484i
$329$	131392.			1.21388
$330$	−66895.0	+	12176.4i	−0.614279	+	0.111812i
$331$			80951.1i			0.738868i	0.929257	+	0.369434i	$0.120448\pi$
$331$			80951.1i			0.738868i	−0.929257	+	0.369434i	$0.879552\pi$
$332$	−63517.6	−	168697.i	−0.576259	−	1.53049i
$333$	−16101.7			−0.145205
$334$	−2740.14	−	15053.9i	−0.0245629	−	0.134945i
$335$		−	37673.4i		−	0.335696i
$336$	−125579.	+	110186.i	−1.11234	+	0.976000i
$337$	−132058.			−1.16280			−0.581400	−	0.813618i	$-0.697495\pi$
$337$	−132058.			−1.16280			−0.581400	+	0.813618i	$0.697495\pi$
$338$	−182562.	+	33230.3i	−1.59800	+	0.290872i
$339$			45576.1i			0.396586i
$340$	55559.1	−	20919.0i	0.480615	−	0.180961i
$341$	−20220.2			−0.173891
$342$	−1914.32	−	10517.0i	−0.0163667	−	0.0899162i
$343$		−	175811.i		−	1.49437i
$344$	−100360.	−	167368.i	−0.848091	−	1.41434i
$345$	−39774.5			−0.334169
$346$	−37102.7	+	6753.50i	−0.309922	+	0.0564127i
$347$		−	146727.i		−	1.21857i	−0.792950	−	0.609286i	$-0.791456\pi$
$347$		−	146727.i		−	1.21857i	0.792950	−	0.609286i	$-0.208544\pi$
$348$	−51697.7	−	137305.i	−0.426887	−	1.13377i
$349$	46409.5			0.381028			0.190514	−	0.981685i	$-0.438985\pi$
$349$	46409.5			0.381028			0.190514	+	0.981685i	$0.438985\pi$
$350$	16864.6	+	92651.2i	0.137670	+	0.756336i
$351$			215740.i			1.75112i
$352$	93988.2	+	74545.5i	0.758556	+	0.601639i
$353$	240926.			1.93345			0.966726	−	0.255814i	$-0.0823435\pi$
$353$	240926.			1.93345			0.966726	+	0.255814i	$0.0823435\pi$
$354$	−13568.1	+	2469.70i	−0.108271	+	0.0197078i
$355$			71444.9i			0.566910i
$356$	25189.6	−	9484.34i	0.198756	−	0.0748354i
$357$	−130955.			−1.02751
$358$	−10280.7	−	56480.7i	−0.0802155	−	0.440691i
$359$			26487.3i			0.205518i	0.994706	+	0.102759i	$0.0327670\pi$
$359$			26487.3i			0.205518i	−0.994706	+	0.102759i	$0.967233\pi$
$360$	−19709.8	+	11818.7i	−0.152082	+	0.0911939i
$361$	111384.			0.854690
$362$	−152907.	+	27832.5i	−1.16684	+	0.212391i
$363$			7194.82i			0.0546017i
$364$	128362.	+	340919.i	0.968802	+	2.57305i
$365$	92431.6			0.693801
$366$	25194.6	+	138415.i	0.188081	+	1.03329i
$367$		−	223792.i		−	1.66155i	−0.556611	−	0.830773i	$-0.687899\pi$
$367$		−	223792.i		−	1.66155i	0.556611	−	0.830773i	$-0.312101\pi$
$368$	46282.3	+	52747.8i	0.341759	+	0.389501i
$369$	63065.6			0.463170
$370$	60332.3	−	10981.8i	0.440704	−	0.0802178i
$371$		−	173357.i		−	1.25949i
$372$	20281.2	−	7636.25i	0.146557	−	0.0551816i
$373$	158318.			1.13792			0.568960	−	0.822365i	$-0.307346\pi$
$373$	158318.			1.13792			0.568960	+	0.822365i	$0.307346\pi$
$374$	16839.3	+	92512.2i	0.120387	+	0.661387i
$375$		−	131766.i		−	0.937001i
$376$	52000.4	+	86719.9i	0.367817	+	0.613399i
$377$	−319907.			−2.25082
$378$	257900.	−	46943.5i	1.80496	−	0.328543i
$379$		−	144528.i		−	1.00617i	−0.864236	−	0.503087i	$-0.832197\pi$
$379$		−	144528.i		−	1.00617i	0.864236	−	0.503087i	$-0.167803\pi$
$380$	14345.8	+	38101.0i	0.0993473	+	0.263857i
$381$	−90064.5			−0.620445
$382$	−17091.7	−	93899.3i	−0.117128	−	0.643481i
$383$		−	164229.i		−	1.11957i	−0.828638	−	0.559785i	$-0.810884\pi$
$383$		−	164229.i		−	1.11957i	0.828638	−	0.559785i	$-0.189116\pi$
$384$	−122424.	−	39275.3i	−0.830242	−	0.266353i
$385$	180145.			1.21535
$386$	284307.	−	51750.2i	1.90815	−	0.347326i
$387$			59216.6i			0.395387i
$388$	−42439.8	+	15979.4i	−0.281909	+	0.106144i
$389$	−126118.			−0.833445			−0.416722	−	0.909034i	$-0.636821\pi$
$389$	−126118.			−0.833445			−0.416722	+	0.909034i	$0.636821\pi$
$390$	−28455.4	−	156330.i	−0.187084	−	1.02781i
$391$			55006.0i			0.359796i
$392$	247824.	−	148605.i	1.61277	−	0.967075i
$393$	216762.			1.40345
$394$	58155.8	−	10585.6i	0.374628	−	0.0681906i
$395$			16272.8i			0.104296i
$396$	−12826.7	−	34066.4i	−0.0817943	−	0.217238i
$397$	8723.57			0.0553494			0.0276747	−	0.999617i	$-0.491190\pi$
$397$	8723.57			0.0553494			0.0276747	+	0.999617i	$0.491190\pi$
$398$	−35245.8	−	193635.i	−0.222506	−	1.22241i
$399$		−	89805.8i		−	0.564103i
$400$	−54476.3	+	47799.0i	−0.340477	+	0.298744i
$401$	−42838.9			−0.266410			−0.133205	−	0.991089i	$-0.542527\pi$
$401$	−42838.9			−0.266410			−0.133205	+	0.991089i	$0.542527\pi$
$402$	−62919.8	+	11452.8i	−0.389345	+	0.0708694i
$403$		−	47253.4i		−	0.290953i
$404$	208336.	−	78442.6i	1.27645	−	0.480606i
$405$	−85256.7			−0.519778
$406$	69609.7	+	382424.i	0.422297	+	2.32003i
$407$			97131.7i			0.586370i
$408$	−51827.7	−	86431.8i	−0.311345	−	0.519222i
$409$	20454.8			0.122278			0.0611392	−	0.998129i	$-0.480527\pi$
$409$	20454.8			0.122278			0.0611392	+	0.998129i	$0.480527\pi$
$410$	−236304.	+	43012.6i	−1.40574	+	0.255875i
$411$		−	85340.9i		−	0.505212i
$412$	15975.3	+	42428.9i	0.0941140	+	0.249958i
$413$	36538.3			0.214214
$414$	−3813.24	−	20949.4i	−0.0222482	−	0.122228i
$415$		−	208317.i		−	1.20957i
$416$	−174208.	+	219645.i	−1.00666	+	1.26921i
$417$	65309.4			0.375581
$418$	−63442.5	+	11547.9i	−0.363101	+	0.0660924i
$419$			45936.3i			0.261655i	0.991405	+	0.130827i	$0.0417633\pi$
$419$			45936.3i			0.261655i	−0.991405	+	0.130827i	$0.958237\pi$
$420$	−180688.	+	68032.5i	−1.02431	+	0.385672i
$421$	−92790.5			−0.523527			−0.261764	−	0.965132i	$-0.584304\pi$
$421$	−92790.5			−0.523527			−0.261764	+	0.965132i	$0.584304\pi$
$422$	62176.4	+	341587.i	0.349141	+	1.91812i
$423$		−	30682.5i		−	0.171479i
$424$	114417.	−	68608.9i	0.636445	−	0.381636i
$425$	−56808.5			−0.314511
$426$	119323.	−	21719.3i	0.657512	−	0.119682i
$427$		−	372744.i		−	2.04435i
$428$	−105058.	−	279024.i	−0.573509	−	1.52319i
$429$	251682.			1.36753
$430$	−40387.5	−	221882.i	−0.218429	−	1.20001i
$431$		−	61892.0i		−	0.333181i	−0.986026	−	0.166590i	$-0.946724\pi$
$431$		−	61892.0i		−	0.333181i	0.986026	−	0.166590i	$-0.0532757\pi$
$432$	133051.	+	151638.i	0.712939	+	0.812533i
$433$	−152291.			−0.812268			−0.406134	−	0.913814i	$-0.633123\pi$
$433$	−152291.			−0.812268			−0.406134	+	0.913814i	$0.633123\pi$
$434$	−56487.7	+	10282.0i	−0.299899	+	0.0545882i
$435$		−	169552.i		−	0.896034i
$436$	−75858.3	+	28562.1i	−0.399052	+	0.150251i
$437$	−37721.7			−0.197528
$438$	−28099.3	−	154373.i	−0.146470	−	0.804681i
$439$		−	210910.i		−	1.09438i	−0.837008	−	0.547191i	$-0.815697\pi$
$439$		−	210910.i		−	1.09438i	0.837008	−	0.547191i	$-0.184303\pi$
$440$	71295.3	+	118897.i	0.368261	+	0.614140i
$441$	−87683.2			−0.450857
$442$	−216195.	+	39352.3i	−1.10663	+	0.201431i
$443$		−	257731.i		−	1.31329i	−0.754202	−	0.656643i	$-0.771976\pi$
$443$		−	257731.i		−	1.31329i	0.754202	−	0.656643i	$-0.228024\pi$
$444$	−36682.2	−	97424.7i	−0.186076	−	0.494200i
$445$	31105.6			0.157079
$446$	−3450.32	−	18955.5i	−0.0173456	−	0.0952940i
$447$			186785.i			0.934819i
$448$	300475.	+	160459.i	1.49710	+	0.799483i
$449$	−181124.			−0.898427			−0.449213	−	0.893424i	$-0.648296\pi$
$449$	−181124.			−0.898427			−0.449213	+	0.893424i	$0.648296\pi$
$450$	21635.9	−	3938.20i	0.106844	−	0.0194479i
$451$		−	380437.i		−	1.87038i
$452$	86965.9	−	32744.3i	0.425669	−	0.160273i
$453$	254399.			1.23971
$454$	−24444.3	−	134293.i	−0.118595	−	0.651540i
$455$			420988.i			2.03351i
$456$	59272.7	−	35542.1i	0.285053	−	0.170928i
$457$	125730.			0.602015			0.301008	−	0.953622i	$-0.402677\pi$
$457$	125730.			0.602015			0.301008	+	0.953622i	$0.402677\pi$
$458$	53728.8	−	9779.83i	0.256139	−	0.0466230i
$459$			158130.i			0.750566i
$460$	28576.2	+	75895.7i	0.135048	+	0.358675i
$461$	−84294.7			−0.396642			−0.198321	−	0.980137i	$-0.563549\pi$
$461$	−84294.7			−0.396642			−0.198321	+	0.980137i	$0.563549\pi$
$462$	−54764.3	−	300866.i	−0.256574	−	1.40958i
$463$		−	8839.34i		−	0.0412342i	−0.999787	−	0.0206171i	$-0.993437\pi$
$463$		−	8839.34i		−	0.0412342i	0.999787	−	0.0206171i	$-0.00656310\pi$
$464$	−224855.	+	197294.i	−1.04440	+	0.916384i
$465$	25044.5			0.115826
$466$	−33156.9	+	6035.29i	−0.152687	+	0.0277924i
$467$		−	10197.9i		−	0.0467604i	−0.999727	−	0.0233802i	$-0.992557\pi$
$467$		−	10197.9i		−	0.0467604i	0.999727	−	0.0233802i	$-0.00744282\pi$
$468$	79611.2	−	29975.1i	0.363482	−	0.136858i
$469$	169440.			0.770317
$470$	20926.4	+	114966.i	0.0947324	+	0.520445i
$471$			297800.i			1.34240i
$472$	14460.6	+	24115.6i	0.0649087	+	0.108247i
$473$	357218.			1.59666
$474$	27177.8	−	4946.96i	0.120965	−	0.0220182i
$475$		−	38957.9i		−	0.172666i
$476$	94085.3	+	249882.i	0.415248	+	1.10286i
$477$	−40482.3			−0.177921
$478$	−30148.5	−	165631.i	−0.131950	−	0.724913i
$479$			186885.i			0.814525i	0.913311	+	0.407262i	$0.133517\pi$
$479$			186885.i			0.814525i	−0.913311	+	0.407262i	$0.866483\pi$
$480$	−116412.	−	92331.1i	−0.505262	−	0.400742i
$481$	−226991.			−0.981111
$482$	−65662.6	+	11952.0i	−0.282634	+	0.0514456i
$483$		−	178889.i		−	0.766815i
$484$	13728.8	−	5169.14i	0.0586059	−	0.0220662i
$485$	−52407.2			−0.222796
$486$	−19804.5	−	108803.i	−0.0838477	−	0.460646i
$487$		−	45288.8i		−	0.190956i	−0.995432	−	0.0954779i	$-0.969562\pi$
$487$		−	45288.8i		−	0.190956i	0.995432	−	0.0954779i	$-0.0304379\pi$
$488$	246015.	−	147520.i	1.03305	−	0.619456i
$489$	−341786.			−1.42935
$490$	328546.	−	59802.5i	1.36837	−	0.249073i
$491$			258607.i			1.07270i	0.843997	+	0.536348i	$0.180197\pi$
$491$			258607.i			1.07270i	−0.843997	+	0.536348i	$0.819803\pi$
$492$	143674.	+	381585.i	0.593536	+	1.57638i
$493$	−234481.			−0.964749
$494$	−26986.8	−	148261.i	−0.110585	−	0.607539i
$495$		−	42067.3i		−	0.171686i
$496$	−29142.2	−	33213.2i	−0.118456	−	0.135004i
$497$	−321330.			−1.30088
$498$	−347918.	+	63328.8i	−1.40287	+	0.255354i
$499$		−	35213.1i		−	0.141418i	−0.997497	−	0.0707088i	$-0.977474\pi$
$499$		−	35213.1i		−	0.141418i	0.997497	−	0.0707088i	$-0.0225261\pi$
$500$	−251429.	+	94667.6i	−1.00571	+	0.378670i
$501$	−30018.3			−0.119594
$502$	68584.7	+	376793.i	0.272157	+	1.49519i
$503$			75552.7i			0.298617i	0.988791	+	0.149308i	$0.0477047\pi$
$503$			75552.7i			0.298617i	−0.988791	+	0.149308i	$0.952295\pi$
$504$	−53155.8	−	88646.6i	−0.209262	−	0.348980i
$505$	257267.			1.00879
$506$	−126375.	+	23003.0i	−0.493582	+	0.0898429i
$507$			364039.i			1.41622i
$508$	64707.1	+	171856.i	0.250741	+	0.665945i
$509$	−454349.			−1.75369			−0.876847	−	0.480769i	$-0.840358\pi$
$509$	−454349.			−1.75369			−0.876847	+	0.480769i	$0.840358\pi$
$510$	−20856.9	−	114584.i	−0.0801879	−	0.440540i
$511$			415719.i			1.59206i
$512$	13012.9	+	261821.i	0.0496405	+	0.998767i
$513$	−108442.			−0.412060
$514$	−82561.3	+	15028.0i	−0.312500	+	0.0568819i
$515$			52393.9i			0.197545i
$516$	−358296.	+	134905.i	−1.34568	+	0.506675i
$517$	−185089.			−0.692469
$518$	49391.7	+	271350.i	0.184075	+	1.01128i
$519$			73984.8i			0.274668i
$520$	−277856.	+	166613.i	−1.02757	+	0.616171i
$521$	−8465.06			−0.0311856			−0.0155928	−	0.999878i	$-0.504964\pi$
$521$	−8465.06			−0.0311856			−0.0155928	+	0.999878i	$0.504964\pi$
$522$	89303.6	−	16255.2i	0.327739	−	0.0596557i
$523$		−	242093.i		−	0.885074i	−0.896750	−	0.442537i	$-0.854079\pi$
$523$		−	242093.i		−	0.885074i	0.896750	−	0.442537i	$-0.145921\pi$
$524$	−155733.	−	413614.i	−0.567177	−	1.50637i
$525$	184752.			0.670301
$526$	52709.2	+	289576.i	0.190509	+	1.04662i
$527$		−	34635.1i		−	0.124708i
$528$	176901.	−	155218.i	0.634545	−	0.556767i
$529$	204701.			0.731490
$530$	151685.	−	27610.1i	0.539998	−	0.0982915i
$531$		−	8532.40i		−	0.0302609i
$532$	−171363.	+	64521.3i	−0.605471	+	0.227971i
$533$	889058.			3.12951
$534$	−9456.15	−	51950.6i	−0.0331613	−	0.182183i
$535$		−	344556.i		−	1.20379i
$536$	67058.5	+	111832.i	0.233413	+	0.389257i
$537$	−112626.			−0.390561
$538$	−206140.	+	37522.0i	−0.712192	+	0.129635i
$539$			528940.i			1.82066i
$540$	82150.1	+	218183.i	0.281722	+	0.748228i
$541$	111044.			0.379404			0.189702	−	0.981842i	$-0.439248\pi$
$541$	111044.			0.379404			0.189702	+	0.981842i	$0.439248\pi$
$542$	−45903.2	−	252185.i	−0.156259	−	0.858461i
$543$			304906.i			1.03411i
$544$	−127689.	+	160992.i	−0.431475	+	0.544010i
$545$	−93674.5			−0.315376
$546$	703106.	−	127981.i	2.35850	−	0.429299i
$547$			460550.i			1.53922i	0.638511	+	0.769612i	$0.279551\pi$
$547$			460550.i			1.53922i	−0.638511	+	0.769612i	$0.720449\pi$
$548$	−162843.	+	61313.5i	−0.542261	+	0.204171i
$549$	−87043.0			−0.288795
$550$	−23756.8	−	130516.i	−0.0785349	−	0.431458i
$551$		−	160801.i		−	0.529647i
$552$	118069.	−	70798.4i	0.387487	−	0.232352i
$553$	−73188.5			−0.239327
$554$	−71170.1	+	12954.5i	−0.231888	+	0.0422087i
$555$		−	120306.i		−	0.390572i
$556$	−46921.8	−	124620.i	−0.151784	−	0.403123i
$557$	−247301.			−0.797106			−0.398553	−	0.917145i	$-0.630487\pi$
$557$	−247301.			−0.797106			−0.398553	+	0.917145i	$0.630487\pi$
$558$	2401.05	+	13191.0i	0.00771139	+	0.0423652i
$559$			834798.i			2.67151i
$560$	259632.	+	295902.i	0.827909	+	0.943564i
$561$	184474.			0.586152
$562$	24474.5	−	4454.90i	0.0774892	−	0.0141047i
$563$		−	332750.i		−	1.04979i	−0.851168	−	0.524893i	$-0.824105\pi$
$563$		−	332750.i		−	1.04979i	0.851168	−	0.524893i	$-0.175895\pi$
$564$	185648.	−	69899.8i	0.583621	−	0.219744i
$565$	107391.			0.336411
$566$	92306.9	+	507119.i	0.288139	+	1.58299i
$567$		−	383449.i		−	1.19273i
$568$	−127171.	−	212081.i	−0.394179	−	0.657362i
$569$	−284446.			−0.878569			−0.439284	−	0.898348i	$-0.644768\pi$
$569$	−284446.			−0.878569			−0.439284	+	0.898348i	$0.644768\pi$
$570$	78579.0	−	14303.1i	0.241856	−	0.0440231i
$571$		−	605350.i		−	1.85667i	−0.371746	−	0.928334i	$-0.621241\pi$
$571$		−	605350.i		−	1.85667i	0.371746	−	0.928334i	$-0.378759\pi$
$572$	−180822.	−	480246.i	−0.552661	−	1.46782i
$573$	−187240.			−0.570283
$574$	−193453.	−	1.06280e6i	−0.587154	−	3.22573i
$575$		−	77602.5i		−	0.234714i
$576$	37470.4	−	70166.7i	0.112939	−	0.211488i
$577$	321282.			0.965017			0.482509	−	0.875891i	$-0.339726\pi$
$577$	321282.			0.965017			0.482509	+	0.875891i	$0.339726\pi$
$578$	170219.	−	30983.7i	0.509511	−	0.0927422i
$579$		−	566925.i		−	1.69110i
$580$	−323530.	+	121815.i	−0.961743	+	0.362114i
$581$	936926.			2.77558
$582$	15931.9	+	87527.2i	0.0470350	+	0.258403i
$583$			244205.i			0.718485i
$584$	−274379.	+	164528.i	−0.804498	+	0.482407i
$585$	98308.8			0.287264
$586$	19377.4	−	3527.11i	0.0564286	−	0.0102712i
$587$			523810.i			1.52019i	0.649813	+	0.760094i	$0.274847\pi$
$587$			523810.i			1.52019i	−0.649813	+	0.760094i	$0.725153\pi$
$588$	−199757.	−	530535.i	−0.577759	−	1.53447i
$589$	23751.9			0.0684648
$590$	5819.34	+	31970.6i	0.0167174	+	0.0918430i
$591$		−	115966.i		−	0.332013i
$592$	−159546.	+	139990.i	−0.455243	+	0.399442i
$593$	−92379.2			−0.262703			−0.131351	−	0.991336i	$-0.541932\pi$
$593$	−92379.2			−0.262703			−0.131351	+	0.991336i	$0.541932\pi$
$594$	−363300.	+	66128.5i	−1.02966	+	0.187420i
$595$			308570.i			0.871604i
$596$	356414.	−	134197.i	1.00337	−	0.377789i
$597$	−386118.			−1.08336
$598$	−53756.6	−	295330.i	−0.150324	−	0.825859i
$599$			230188.i			0.641549i	0.947156	+	0.320774i	$0.103943\pi$
$599$			230188.i			0.641549i	−0.947156	+	0.320774i	$0.896057\pi$
$600$	73118.5	+	121938.i	0.203107	+	0.338717i
$601$	−227415.			−0.629607			−0.314803	−	0.949157i	$-0.601939\pi$
$601$	−227415.			−0.629607			−0.314803	+	0.949157i	$0.601939\pi$
$602$	997936.	−	181646.i	2.75366	−	0.501226i
$603$		−	39567.5i		−	0.108819i
$604$	−182774.	−	485431.i	−0.501003	−	1.33062i
$605$	16953.1			0.0463169
$606$	−78209.4	−	429670.i	−0.212968	−	1.17001i
$607$			410195.i			1.11330i	0.830746	+	0.556651i	$0.187914\pi$
$607$			410195.i			1.11330i	−0.830746	+	0.556651i	$0.812086\pi$
$608$	−110404.	−	87565.8i	−0.298661	−	0.236879i
$609$	762576.			2.05612
$610$	326147.	−	59365.9i	0.876503	−	0.159543i
$611$		−	432542.i		−	1.15863i
$612$	58352.3	−	21970.8i	0.155796	−	0.0586600i
$613$	283510.			0.754481			0.377240	−	0.926115i	$-0.376873\pi$
$613$	283510.			0.754481			0.377240	+	0.926115i	$0.376873\pi$
$614$	−63175.3	−	347075.i	−0.167576	−	0.920634i
$615$			471204.i			1.24583i
$616$	−534752.	+	320657.i	−1.40926	+	0.845043i
$617$	−721640.			−1.89562			−0.947808	−	0.318841i	$-0.896707\pi$
$617$	−721640.			−1.89562			−0.947808	+	0.318841i	$0.896707\pi$
$618$	87504.8	−	15927.8i	0.229116	−	0.0417041i
$619$		−	177679.i		−	0.463720i	−0.972749	−	0.231860i	$-0.925519\pi$
$619$		−	177679.i		−	0.463720i	0.972749	−	0.231860i	$-0.0744811\pi$
$620$	−17993.3	−	47788.5i	−0.0468087	−	0.124320i
$621$	−216011.			−0.560135
$622$	15872.9	+	87203.4i	0.0410276	+	0.225399i
$623$			139900.i			0.360448i
$624$	362734.	+	413407.i	0.931579	+	1.06172i
$625$	−133542.			−0.341868
$626$	−456753.	+	83139.0i	−1.16555	+	0.212156i
$627$			126508.i			0.321797i
$628$	568247.	−	213956.i	1.44085	−	0.542506i
$629$	−166377.			−0.420524
$630$	−21391.3	−	117521.i	−0.0538960	−	0.296096i
$631$			83678.9i			0.210163i	0.994464	+	0.105082i	$0.0335104\pi$
$631$			83678.9i			0.210163i	−0.994464	+	0.105082i	$0.966490\pi$
$632$	−28965.5	−	48305.1i	−0.0725183	−	0.120937i
$633$	681144.			1.69993
$634$	−224165.	+	40803.0i	−0.557685	+	0.101511i
$635$			212219.i			0.526304i
$636$	−92225.2	−	244942.i	−0.228000	−	0.605548i
$637$	−1.23610e6			−3.04632
$638$	−98057.9	−	538715.i	−0.240903	−	1.32348i
$639$			75036.7i			0.183769i
$640$	−92544.4	+	288468.i	−0.225938	+	0.704267i
$641$	−286666.			−0.697686			−0.348843	−	0.937181i	$-0.613425\pi$
$641$	−286666.			−0.697686			−0.348843	+	0.937181i	$0.613425\pi$
$642$	−575455.	+	104745.i	−1.39618	+	0.254135i
$643$			16118.0i			0.0389843i	0.999810	+	0.0194922i	$0.00620494\pi$
$643$			16118.0i			0.0389843i	−0.999810	+	0.0194922i	$0.993795\pi$
$644$	−341348.	+	128524.i	−0.823048	+	0.309893i
$645$	−442446.			−1.06351
$646$	−19780.4	−	108671.i	−0.0473992	−	0.260403i
$647$		−	323853.i		−	0.773640i	−0.922155	−	0.386820i	$-0.873573\pi$
$647$		−	323853.i		−	0.773640i	0.922155	−	0.386820i	$-0.126427\pi$
$648$	253081.	−	151756.i	0.602710	−	0.361407i
$649$	−51470.8			−0.122200
$650$	305008.	−	55518.2i	0.721913	−	0.131404i
$651$			112640.i			0.265784i
$652$	245558.	+	652179.i	0.577642	+	1.53416i
$653$	67486.8			0.158268			0.0791339	−	0.996864i	$-0.474785\pi$
$653$	67486.8			0.158268			0.0791339	+	0.996864i	$0.474785\pi$
$654$	28477.2	+	156449.i	0.0665796	+	0.365778i
$655$		−	510756.i		−	1.19050i
$656$	624897.	−	548302.i	1.45211	−	1.27412i
$657$	97078.6			0.224902
$658$	−517071.	+	94118.3i	−1.19426	+	0.217381i
$659$		−	237756.i		−	0.547470i	−0.961805	−	0.273735i	$-0.911741\pi$
$659$		−	237756.i		−	0.547470i	0.961805	−	0.273735i	$-0.0882591\pi$
$660$	254532.	−	95836.2i	0.584326	−	0.220010i
$661$	835981.			1.91335			0.956673	−	0.291164i	$-0.0940426\pi$
$661$	835981.			1.91335			0.956673	+	0.291164i	$0.0940426\pi$
$662$	−57986.7	−	318570.i	−0.132316	−	0.726924i
$663$			431106.i			0.980746i
$664$	370804.	+	618381.i	0.841024	+	1.40256i
$665$	−211609.			−0.478510
$666$	63365.5	−	11533.9i	0.142858	−	0.0260033i
$667$		−	320310.i		−	0.719977i
$668$	21566.8	+	57279.4i	0.0483317	+	0.128365i
$669$	−37798.3			−0.0844540
$670$	26986.2	+	148258.i	0.0601162	+	0.330269i
$671$			525078.i			1.16622i
$672$	415267.	−	523575.i	0.919579	−	1.15942i
$673$	−265644.			−0.586502			−0.293251	−	0.956035i	$-0.594737\pi$
$673$	−265644.			−0.586502			−0.293251	+	0.956035i	$0.594737\pi$
$674$	519693.	−	94595.5i	1.14400	−	0.208234i
$675$		−	223090.i		−	0.489635i
$676$	694641.	−	261545.i	1.52008	−	0.572339i
$677$	72700.4			0.158621			0.0793103	−	0.996850i	$-0.474728\pi$
$677$	72700.4			0.158621			0.0793103	+	0.996850i	$0.474728\pi$
$678$	−32647.0	−	179357.i	−0.0710205	−	0.390175i
$679$		−	235706.i		−	0.511248i
$680$	−203659.	+	122122.i	−0.440439	+	0.264104i
$681$	−267788.			−0.577426
$682$	79573.3	−	14484.1i	0.171080	−	0.0311403i
$683$			505608.i			1.08386i	0.840424	+	0.541929i	$0.182306\pi$
$683$			505608.i			1.08386i	−0.840424	+	0.541929i	$0.817694\pi$
$684$	15067.0	+	40016.5i	0.0322043	+	0.0855317i
$685$	−201089.			−0.428555
$686$	125937.	+	691878.i	0.267612	+	1.47022i
$687$		−	107138.i		−	0.227003i
$688$	514838.	+	586758.i	1.08766	+	1.23960i
$689$	−570693.			−1.20216
$690$	156526.	−	28491.2i	0.328767	−	0.0598429i
$691$		−	361431.i		−	0.756954i	−0.925611	−	0.378477i	$-0.876448\pi$
$691$		−	361431.i		−	0.756954i	0.925611	−	0.378477i	$-0.123552\pi$
$692$	141174.	−	53154.6i	0.294810	−	0.111002i
$693$	189202.			0.393966
$694$	105103.	+	577421.i	0.218221	+	1.19887i
$695$		−	153888.i		−	0.318593i
$696$	301802.	+	503308.i	0.623022	+	1.03900i
$697$	651650.			1.34137
$698$	−182637.	+	33244.0i	−0.374868	+	0.0682343i
$699$			66116.7i			0.135318i
$700$	−132735.	−	352533.i	−0.270889	−	0.719456i
$701$	−250708.			−0.510191			−0.255096	−	0.966916i	$-0.582107\pi$
$701$	−250708.			−0.510191			−0.255096	+	0.966916i	$0.582107\pi$
$702$	−154538.	−	849009.i	−0.313590	−	1.72281i
$703$		−	114097.i		−	0.230868i
$704$	−423274.	−	226036.i	−0.854035	−	0.456072i
$705$	229249.			0.461243
$706$	−948123.	+	172579.i	−1.90220	+	0.346242i
$707$			1.15708e6i			2.31486i
$708$	51626.1	−	19438.2i	0.102992	−	0.0387783i
$709$	819779.			1.63081			0.815407	−	0.578888i	$-0.196513\pi$
$709$	819779.			1.63081			0.815407	+	0.578888i	$0.196513\pi$
$710$	−51177.2	−	281160.i	−0.101522	−	0.557746i
$711$			17090.9i			0.0338086i
$712$	−92335.6	+	55367.8i	−0.182142	+	0.109219i
$713$	47312.8			0.0930678
$714$	515353.	−	93805.6i	1.01090	−	0.184006i
$715$		−	593038.i		−	1.16003i
$716$	80916.4	+	214907.i	0.157838	+	0.419202i
$717$	−330278.			−0.642452
$718$	−18973.4	−	104237.i	−0.0368040	−	0.202195i
$719$		−	690272.i		−	1.33525i	−0.744498	−	0.667625i	$-0.767311\pi$
$719$		−	690272.i		−	1.33525i	0.744498	−	0.667625i	$-0.232689\pi$
$720$	69098.8	−	60629.2i	0.133292	−	0.116954i
$721$	−235646.			−0.453304
$722$	−438334.	+	79786.4i	−0.840873	+	0.153057i
$723$			130935.i			0.250483i
$724$	581805.	−	219061.i	1.10994	−	0.417914i
$725$	330806.			0.629358
$726$	−5153.78	−	28314.0i	−0.00977805	−	0.0537191i
$727$		−	412926.i		−	0.781274i	−0.920545	−	0.390637i	$-0.872255\pi$
$727$		−	412926.i		−	0.781274i	0.920545	−	0.390637i	$-0.127745\pi$
$728$	−749356.	−	1.24968e6i	−1.41392	−	2.35796i
$729$	−590435.			−1.11101
$730$	−363750.	+	66210.4i	−0.682585	+	0.124246i
$731$			611879.i			1.14507i
$732$	−198298.	−	526662.i	−0.370081	−	0.982901i
$733$	−81228.4			−0.151182			−0.0755909	−	0.997139i	$-0.524084\pi$
$733$	−81228.4			−0.151182			−0.0755909	+	0.997139i	$0.524084\pi$
$734$	160306.	+	880697.i	0.297549	+	1.63469i
$735$		−	655138.i		−	1.21271i
$736$	−219921.	−	174427.i	−0.405986	−	0.322002i
$737$	−238687.			−0.439434
$738$	−248185.	+	45175.1i	−0.455682	+	0.0829442i
$739$		−	653298.i		−	1.19625i	−0.801402	−	0.598126i	$-0.795912\pi$
$739$		−	653298.i		−	1.19625i	0.801402	−	0.598126i	$-0.204088\pi$
$740$	−229562.	+	86434.3i	−0.419214	+	0.157842i
$741$	−295641.			−0.538429
$742$	124179.	+	682219.i	0.225548	+	1.23913i
$743$		−	119172.i		−	0.215872i	−0.994158	−	0.107936i	$-0.965576\pi$
$743$		−	119172.i		−	0.215872i	0.994158	−	0.107936i	$-0.0344242\pi$
$744$	−74343.3	+	44579.0i	−0.134306	+	0.0805349i
$745$	440122.			0.792977
$746$	−623034.	+	113406.i	−1.11953	+	0.203778i
$747$		−	218791.i		−	0.392092i
$748$	−132536.	−	352004.i	−0.236882	−	0.629137i
$749$	1.54967e6			2.76233
$750$	94386.2	+	518543.i	0.167798	+	0.921854i
$751$			877095.i			1.55513i	0.628803	+	0.777565i	$0.283545\pi$
$751$			877095.i			1.55513i	−0.628803	+	0.777565i	$0.716455\pi$
$752$	−266758.	−	304023.i	−0.471718	−	0.537615i
$753$	751347.			1.32511
$754$	1.25894e6	−	229155.i	2.21444	−	0.403077i
$755$		−	599440.i		−	1.05160i
$756$	−981298.	+	369477.i	−1.71695	+	0.646464i
$757$	−395564.			−0.690279			−0.345139	−	0.938551i	$-0.612168\pi$
$757$	−395564.			−0.690279			−0.345139	+	0.938551i	$0.612168\pi$
$758$	103528.	+	568766.i	0.180185	+	0.989910i
$759$			251998.i			0.437436i
$760$	−83747.8	−	139664.i	−0.144993	−	0.241801i
$761$	399402.			0.689669			0.344835	−	0.938663i	$-0.387935\pi$
$761$	399402.			0.689669			0.344835	+	0.938663i	$0.387935\pi$
$762$	354434.	−	64514.8i	0.610416	−	0.111109i
$763$		−	421309.i		−	0.723689i
$764$	134524.	+	357283.i	0.230469	+	0.612104i
$765$	72057.1			0.123127
$766$	117640.	+	646296.i	0.200492	+	1.10147i
$767$		−	120284.i		−	0.204464i
$768$	509914.	+	66867.0i	0.864519	+	0.113368i
$769$	245944.			0.415894			0.207947	−	0.978140i	$-0.433322\pi$
$769$	245944.			0.415894			0.207947	+	0.978140i	$0.433322\pi$
$770$	−708931.	+	129041.i	−1.19570	+	0.217644i
$771$			164632.i			0.276952i
$772$	−1.08178e6	+	407309.i	−1.81511	+	0.683423i
$773$	−717936.			−1.20151			−0.600754	−	0.799434i	$-0.705133\pi$
$773$	−717936.			−1.20151			−0.600754	+	0.799434i	$0.705133\pi$
$774$	−42418.0	−	233038.i	−0.0708056	−	0.388995i
$775$			48863.2i			0.0813540i
$776$	155568.	−	93284.6i	0.258344	−	0.154913i
$777$	541087.			0.896241
$778$	496316.	−	90340.4i	0.819972	−	0.149253i
$779$			446885.i			0.736412i
$780$	223963.	+	594827.i	0.368119	+	0.977690i
$781$	452651.			0.742099
$782$	−39401.8	−	216467.i	−0.0644322	−	0.353980i
$783$		−	920819.i		−	1.50193i
$784$	−868824.	+	762330.i	−1.41351	+	1.24026i
$785$	701706.			1.13872
$786$	−853031.	+	155270.i	−1.38076	+	0.251330i
$787$		−	452983.i		−	0.731362i	−0.930740	−	0.365681i	$-0.880836\pi$
$787$		−	452983.i		−	0.731362i	0.930740	−	0.365681i	$-0.119164\pi$
$788$	−221280.	+	83316.1i	−0.356361	+	0.134177i
$789$	577430.			0.927567
$790$	−11656.5	−	64039.1i	−0.0186773	−	0.102610i
$791$			483000.i			0.771959i
$792$	74879.6	+	124875.i	0.119375	+	0.199079i
$793$	−1.22708e6			−1.95131
$794$	−34330.2	+	6248.85i	−0.0544547	+	0.00991195i
$795$		−	302469.i		−	0.478572i
$796$	277408.	+	736771.i	0.437817	+	1.16280i
$797$	179265.			0.282214			0.141107	−	0.989994i	$-0.454934\pi$
$797$	179265.			0.282214			0.141107	+	0.989994i	$0.454934\pi$
$798$	64329.5	+	353416.i	0.101019	+	0.554984i
$799$		−	317039.i		−	0.496614i
$800$	180143.	−	227128.i	0.281474	−	0.354887i
$801$	32669.5			0.0509187
$802$	168586.	−	30686.3i	0.262103	−	0.0477085i
$803$		−	585617.i		−	0.908202i
$804$	239407.	−	90141.1i	0.370360	−	0.139448i
$805$	−421517.			−0.650464
$806$	33848.4	+	185958.i	0.0521037	+	0.286249i
$807$			411054.i			0.631178i
$808$	−763684.	+	457933.i	−1.16974	+	0.701422i
$809$	−634047.			−0.968778			−0.484389	−	0.874853i	$-0.660958\pi$
$809$	−634047.			−0.968778			−0.484389	+	0.874853i	$0.660958\pi$
$810$	335514.	−	61070.9i	0.511376	−	0.0930817i
$811$		−	396405.i		−	0.602695i	−0.953514	−	0.301348i	$-0.902564\pi$
$811$		−	396405.i		−	0.602695i	0.953514	−	0.301348i	$-0.0974365\pi$
$812$	−547875.	−	1.45511e6i	−0.830940	−	2.20690i
$813$	−502871.			−0.760808
$814$	−69577.2	−	382246.i	−0.105007	−	0.576892i
$815$			805351.i			1.21247i
$816$	265872.	+	303013.i	0.399294	+	0.455073i
$817$	−419611.			−0.628641
$818$	−80496.7	+	14652.2i	−0.120302	+	0.0218975i
$819$			442153.i			0.659181i
$820$	899127.	−	338538.i	1.33719	−	0.503478i
$821$	−745575.			−1.10613			−0.553063	−	0.833139i	$-0.686541\pi$
$821$	−745575.			−1.10613			−0.553063	+	0.833139i	$0.686541\pi$
$822$	61131.2	+	335845.i	0.0904731	+	0.497045i
$823$		−	213584.i		−	0.315333i	−0.987492	−	0.157666i	$-0.949603\pi$
$823$		−	213584.i		−	0.315333i	0.987492	−	0.157666i	$-0.0503970\pi$
$824$	−93260.8	−	155529.i	−0.137355	−	0.229064i
$825$	−260256.			−0.382379
$826$	−143790.	+	26173.0i	−0.210751	+	0.0383613i
$827$			720755.i			1.05385i	0.849913	+	0.526923i	$0.176654\pi$
$827$			720755.i			1.05385i	−0.849913	+	0.526923i	$0.823346\pi$
$828$	30012.8	+	79711.3i	0.0437770	+	0.116268i
$829$	−771321.			−1.12234			−0.561172	−	0.827699i	$-0.689649\pi$
$829$	−771321.			−1.12234			−0.561172	+	0.827699i	$0.689649\pi$
$830$	149222.	+	819800.i	0.216609	+	1.19001i
$831$			141917.i			0.205510i
$832$	528233.	−	989165.i	0.763096	−	1.42897i
$833$	−906020.			−1.30571
$834$	−257014.	+	46782.3i	−0.369509	+	0.0672588i
$835$			70732.2i			0.101448i
$836$	241396.	−	90890.0i	0.345396	−	0.130048i
$837$	136014.			0.194148
$838$	−32905.0	−	180775.i	−0.0468570	−	0.257425i
$839$			392382.i			0.557423i	0.960375	+	0.278711i	$0.0899073\pi$
$839$			392382.i			0.557423i	−0.960375	+	0.278711i	$0.910093\pi$
$840$	662336.	−	397161.i	0.938685	−	0.562870i
$841$	658145.			0.930529
$842$	365162.	−	66467.5i	0.515064	−	0.0937530i
$843$		−	48803.5i		−	0.0686746i
$844$	−489370.	−	1.29972e6i	−0.686993	−	1.82459i
$845$	857785.			1.20134
$846$	21978.5	+	120746.i	0.0307084	+	0.168707i
$847$			76248.2i			0.106283i
$848$	−401126.	+	351959.i	−0.557813	+	0.489440i
$849$	1.01122e6			1.40292
$850$	223561.	−	40693.0i	0.309427	−	0.0563225i
$851$		−	227276.i		−	0.313830i
$852$	−454017.	+	170946.i	−0.625450	+	0.235494i
$853$	270209.			0.371365			0.185683	−	0.982610i	$-0.440550\pi$
$853$	270209.			0.371365			0.185683	+	0.982610i	$0.440550\pi$
$854$	267003.	+	1.46687e6i	0.366101	+	2.01130i
$855$			49414.9i			0.0675967i
$856$	613307.	+	1.02280e6i	0.837010	+	1.39586i
$857$	1.25609e6			1.71025			0.855125	−	0.518421i	$-0.173480\pi$
$857$	1.25609e6			1.71025			0.855125	+	0.518421i	$0.173480\pi$
$858$	−990454.	+	180284.i	−1.34543	+	0.244897i
$859$			471190.i			0.638572i	0.947658	+	0.319286i	$0.103443\pi$
$859$			471190.i			0.638572i	−0.947658	+	0.319286i	$0.896557\pi$
$860$	317877.	+	844252.i	0.429796	+	1.14150i
$861$	−2.11928e6			−2.85879
$862$	44334.3	+	243566.i	0.0596658	+	0.327795i
$863$		−	428036.i		−	0.574723i	−0.957822	−	0.287361i	$-0.907222\pi$
$863$		−	428036.i		−	0.574723i	0.957822	−	0.287361i	$-0.0927781\pi$
$864$	−632224.	−	501440.i	−0.846922	−	0.671725i
$865$	174330.			0.232992
$866$	599318.	−	109089.i	0.799137	−	0.145461i
$867$		−	339427.i		−	0.451552i
$868$	214933.	−	80926.4i	0.285275	−	0.107411i
$869$	103099.			0.136526
$870$	121453.	+	667245.i	0.160461	+	0.881549i
$871$		−	557796.i		−	0.735257i
$872$	278068.	−	166740.i	0.365695	−	0.219284i
$873$	−55042.0			−0.0722214
$874$	148448.	−	27020.8i	0.194335	−	0.0353732i
$875$		−	1.39641e6i		−	1.82388i
$876$	221161.	+	587383.i	0.288204	+	0.765444i
$877$	812405.			1.05627			0.528133	−	0.849162i	$-0.322892\pi$
$877$	812405.			1.05627			0.528133	+	0.849162i	$0.322892\pi$
$878$	151079.	+	830004.i	0.195981	+	1.07669i
$879$		−	38639.5i		−	0.0500097i
$880$	−365739.	−	416831.i	−0.472287	−	0.538264i
$881$	903568.			1.16415			0.582075	−	0.813135i	$-0.302241\pi$
$881$	903568.			1.16415			0.582075	+	0.813135i	$0.302241\pi$
$882$	345063.	−	62809.1i	0.443569	−	0.0807393i
$883$			86204.8i			0.110563i	0.998471	+	0.0552815i	$0.0176056\pi$
$883$			86204.8i			0.110563i	−0.998471	+	0.0552815i	$0.982394\pi$
$884$	822613.	−	309729.i	1.05267	−	0.396349i
$885$	63751.1			0.0813956
$886$	184617.	+	1.01426e6i	0.235183	+	1.29206i
$887$			911055.i			1.15797i	0.815338	+	0.578985i	$0.196551\pi$
$887$			911055.i			1.15797i	−0.815338	+	0.578985i	$0.803449\pi$
$888$	214144.	+	357123.i	0.271569	+	0.452889i
$889$	−954473.			−1.20770
$890$	−122411.	+	22281.5i	−0.154540	+	0.0281297i
$891$			540159.i			0.680403i
$892$	27156.3	+	72124.8i	0.0341304	+	0.0906473i
$893$	217417.			0.272641
$894$	−133798.	−	735063.i	−0.167407	−	0.919707i
$895$			265380.i			0.331300i
$896$	−1.29741e6	−	416227.i	−1.61607	−	0.518458i
$897$	−588905.			−0.731915
$898$	712783.	−	129742.i	0.883903	−	0.160890i
$899$			201686.i			0.249550i
$900$	−82323.4	+	30996.3i	−0.101634	+	0.0382671i
$901$	−418299.			−0.515272
$902$	272514.	+	1.49715e6i	0.334947	+	1.84014i
$903$		−	1.98994e6i		−	2.44042i
$904$	−318785.	+	191155.i	−0.390087	+	0.233910i
$905$	718449.			0.877200
$906$	−1.00115e6	+	182231.i	−1.21967	+	0.222006i
$907$			1.05793e6i			1.28600i	0.765865	+	0.643001i	$0.222311\pi$
$907$			1.05793e6i			1.28600i	−0.765865	+	0.643001i	$0.777689\pi$
$908$	192393.	+	510978.i	0.233355	+	0.619770i
$909$	270201.			0.327008
$910$	−301561.	−	1.65673e6i	−0.364160	−	2.00064i
$911$		−	656550.i		−	0.791100i	−0.918444	−	0.395550i	$-0.870554\pi$
$911$		−	656550.i		−	0.791100i	0.918444	−	0.395550i	$-0.129446\pi$
$912$	−207799.	+	182328.i	−0.249835	+	0.219212i
$913$	−1.31983e6			−1.58335
$914$	−494791.	+	90062.9i	−0.592283	+	0.107809i
$915$		−	650355.i		−	0.776798i
$916$	−204436.	+	76973.9i	−0.243650	+	0.0917386i
$917$	2.29717e6			2.73183
$918$	−113271.	−	622295.i	−0.134411	−	0.738433i
$919$		−	664925.i		−	0.787302i	−0.919260	−	0.393651i	$-0.871212\pi$
$919$		−	664925.i		−	0.787302i	0.919260	−	0.393651i	$-0.128788\pi$
$920$	−166822.	−	278206.i	−0.197096	−	0.328693i
$921$	−692087.			−0.815909
$922$	331728.	−	60381.8i	0.390230	−	0.0710304i
$923$			1.05782e6i			1.24168i
$924$	431032.	+	1.14478e6i	0.504854	+	1.34085i
$925$	234724.			0.274331
$926$	6331.78	+	34785.8i	0.00738421	+	0.0405677i
$927$			55028.0i			0.0640360i
$928$	743555.	−	937486.i	0.863410	−	1.08860i
$929$	−1.62881e6			−1.88729			−0.943644	−	0.330961i	$-0.892627\pi$
$929$	−1.62881e6			−1.88729			−0.943644	+	0.330961i	$0.892627\pi$
$930$	−98558.4	+	17939.8i	−0.113954	+	0.0207420i
$931$		−	621326.i		−	0.716836i
$932$	126160.	−	47501.8i	0.145242	−	0.0546862i
$933$	173888.			0.199759
$934$	7304.96	+	40132.3i	0.00837383	+	0.0460045i
$935$		−	434677.i		−	0.497214i
$936$	−291825.	+	174989.i	−0.333097	+	0.199737i
$937$	1.50110e6			1.70974			0.854868	−	0.518846i	$-0.173638\pi$
$937$	1.50110e6			1.70974			0.854868	+	0.518846i	$0.173638\pi$
$938$	−666802.	+	121373.i	−0.757864	+	0.137948i
$939$			910790.i			1.03297i
$940$	−164705.	−	437441.i	−0.186402	−	0.495067i
$941$	835896.			0.944003			0.472001	−	0.881598i	$-0.343532\pi$
$941$	835896.			0.944003			0.472001	+	0.881598i	$0.343532\pi$
$942$	−213320.	−	1.17194e6i	−0.240397	−	1.32070i
$943$			890177.i			1.00104i
$944$	−74181.9	−	84544.7i	−0.0832442	−	0.0948730i
$945$	−1.21177e6			−1.35692
$946$	−1.40578e6	+	255882.i	−1.57085	+	0.285929i
$947$			57249.6i			0.0638370i	0.999490	+	0.0319185i	$0.0101617\pi$
$947$			57249.6i			0.0638370i	−0.999490	+	0.0319185i	$0.989838\pi$
$948$	−103410.	+	38935.9i	−0.115066	+	0.0433245i
$949$	1.36855e6			1.51960
$950$	27906.2	+	153312.i	0.0309210	+	0.169875i
$951$			446997.i			0.494247i
$952$	−549252.	−	915975.i	−0.606036	−	1.01067i
$953$	−1.73599e6			−1.91144			−0.955722	−	0.294272i	$-0.904923\pi$
$953$	−1.73599e6			−1.91144			−0.955722	+	0.294272i	$0.904923\pi$
$954$	159311.	−	28998.2i	0.175045	−	0.0318621i
$955$			441195.i			0.483753i
$956$	237289.	+	630218.i	0.259634	+	0.689565i
$957$	−1.07423e6			−1.17293
$958$	−133869.	−	735457.i	−0.145865	−	0.801357i
$959$		−	904414.i		−	0.983400i
$960$	524261.	+	279966.i	0.568859	+	0.303782i
$961$	−29791.0			−0.0322581
$962$	893286.	−	162598.i	0.965251	−	0.175697i
$963$		−	361878.i		−	0.390220i
$964$	249843.	−	94070.6i	0.268852	−	0.101228i
$965$	−1.33584e6			−1.43450
$966$	128142.	+	703991.i	0.137321	+	0.754419i
$967$			1.86290e6i			1.99222i	0.0881381	+	0.996108i	$0.471908\pi$
$967$			1.86290e6i			1.99222i	−0.0881381	+	0.996108i	$0.528092\pi$
$968$	−50324.6	+	30176.5i	−0.0537069	+	0.0322046i
$969$	−216695.			−0.230782
$970$	206240.	−	37540.3i	0.219195	−	0.0398982i
$971$			819448.i			0.869126i	0.900641	+	0.434563i	$0.143097\pi$
$971$			819448.i			0.869126i	−0.900641	+	0.434563i	$0.856903\pi$
$972$	155875.	+	413989.i	0.164984	+	0.438184i
$973$	692127.			0.731072
$974$	32441.2	+	178227.i	0.0341963	+	0.187869i
$975$		−	608204.i		−	0.639793i
$976$	−862481.	+	756765.i	−0.905420	+	0.794440i
$977$	−1.80534e6			−1.89134			−0.945671	−	0.325126i	$-0.894593\pi$
$977$	−1.80534e6			−1.89134			−0.945671	+	0.325126i	$0.894593\pi$
$978$	1.34505e6	−	244828.i	1.40624	−	0.255966i
$979$		−	197075.i		−	0.205621i
$980$	−1.25010e6	+	470686.i	−1.30165	+	0.490094i
$981$	−98383.9			−0.102232
$982$	−185245.	−	1.01770e6i	−0.192098	−	1.05536i
$983$		−	1.34591e6i		−	1.39286i	−0.717622	−	0.696432i	$-0.754770\pi$
$983$		−	1.34591e6i		−	1.39286i	0.717622	−	0.696432i	$-0.245230\pi$
$984$	−838741.	−	1.39875e6i	−0.866239	−	1.44461i
$985$	−273250.			−0.281636
$986$	922763.	−	167963.i	0.949154	−	0.172767i
$987$			1.03107e6i			1.05841i
$988$	212404.	+	564127.i	0.217595	+	0.577914i
$989$	−835848.			−0.854544
$990$	30133.6	+	165549.i	0.0307454	+	0.168911i
$991$		−	1.67786e6i		−	1.70848i	−0.519882	−	0.854238i	$-0.674024\pi$
$991$		−	1.67786e6i		−	1.70848i	0.519882	−	0.854238i	$-0.325976\pi$
$992$	138476.	+	109830.i	0.140718	+	0.111609i
$993$	−635246.			−0.644234
$994$	1.26454e6	−	230174.i	1.27985	−	0.232961i
$995$			909810.i			0.918977i
$996$	1.32381e6	−	498441.i	1.33447	−	0.502452i
$997$	1.84660e6			1.85773			0.928865	−	0.370417i	$-0.120785\pi$
$997$	1.84660e6			1.85773			0.928865	+	0.370417i	$0.120785\pi$
$998$	25223.8	+	138576.i	0.0253250	+	0.139132i
$999$		−	653369.i		−	0.654678i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	124.5.b.a.63.4	yes	60
4.3	odd	2	inner	124.5.b.a.63.3	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
124.5.b.a.63.3	✓	60	4.3	odd	2	inner
124.5.b.a.63.4	yes	60	1.1	even	1	trivial

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:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	124.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.93534 + 0.716318i) q^{2} +7.84728i q^{3} +(14.9738 - 5.63791i) q^{4} +18.4905 q^{5} +(-5.62115 - 30.8817i) q^{6} +83.1629i q^{7} +(-54.8883 + 32.9131i) q^{8} +19.4202 q^{9} +O(q^{10})\)	\(q+(-3.93534 + 0.716318i) q^{2} +7.84728i q^{3} +(14.9738 - 5.63791i) q^{4} +18.4905 q^{5} +(-5.62115 - 30.8817i) q^{6} +83.1629i q^{7} +(-54.8883 + 32.9131i) q^{8} +19.4202 q^{9} +(-72.7665 + 13.2451i) q^{10} -117.150i q^{11} +(44.2423 + 117.503i) q^{12} +273.773 q^{13} +(-59.5711 - 327.274i) q^{14} +145.101i q^{15} +(192.428 - 168.842i) q^{16} +200.666 q^{17} +(-76.4249 + 13.9110i) q^{18} +137.612i q^{19} +(276.873 - 104.248i) q^{20} -652.603 q^{21} +(83.9167 + 461.025i) q^{22} +274.117i q^{23} +(-258.278 - 430.724i) q^{24} -283.100 q^{25} +(-1077.39 + 196.108i) q^{26} +788.025i q^{27} +(468.865 + 1245.26i) q^{28} -1168.51 q^{29} +(-103.938 - 571.020i) q^{30} -172.601i q^{31} +(-636.325 + 802.288i) q^{32} +919.310 q^{33} +(-789.689 + 143.741i) q^{34} +1537.73i q^{35} +(290.793 - 109.489i) q^{36} -829.122 q^{37} +(-98.5738 - 541.549i) q^{38} +2148.37i q^{39} +(-1014.92 + 608.581i) q^{40} +3247.43 q^{41} +(2568.21 - 467.471i) q^{42} +3049.24i q^{43} +(-660.482 - 1754.18i) q^{44} +359.089 q^{45} +(-196.355 - 1078.74i) q^{46} -1579.93i q^{47} +(1324.95 + 1510.04i) q^{48} -4515.06 q^{49} +(1114.09 - 202.790i) q^{50} +1574.68i q^{51} +(4099.41 - 1543.51i) q^{52} -2084.55 q^{53} +(-564.477 - 3101.15i) q^{54} -2166.17i q^{55} +(-2737.15 - 4564.67i) q^{56} -1079.88 q^{57} +(4598.50 - 837.028i) q^{58} -439.358i q^{59} +(818.064 + 2172.70i) q^{60} -4482.10 q^{61} +(123.637 + 679.242i) q^{62} +1615.04i q^{63} +(1929.46 - 3613.09i) q^{64} +5062.21 q^{65} +(-3617.80 + 658.518i) q^{66} -2037.44i q^{67} +(3004.73 - 1131.34i) q^{68} -2151.07 q^{69} +(-1101.50 - 6051.47i) q^{70} +3863.86i q^{71} +(-1065.94 + 639.177i) q^{72} +4998.86 q^{73} +(3262.87 - 593.915i) q^{74} -2221.56i q^{75} +(775.843 + 2060.57i) q^{76} +9742.54 q^{77} +(-1538.92 - 8454.57i) q^{78} +880.062i q^{79} +(3558.10 - 3121.97i) q^{80} -4610.83 q^{81} +(-12779.7 + 2326.20i) q^{82} -11266.2i q^{83} +(-9771.92 + 3679.31i) q^{84} +3710.43 q^{85} +(-2184.22 - 11999.8i) q^{86} -9169.66i q^{87} +(3855.77 + 6430.17i) q^{88} +1682.25 q^{89} +(-1413.14 + 257.222i) q^{90} +22767.7i q^{91} +(1545.45 + 4104.57i) q^{92} +1354.45 q^{93} +(1131.73 + 6217.57i) q^{94} +2544.52i q^{95} +(-6295.78 - 4993.42i) q^{96} -2834.27 q^{97} +(17768.3 - 3234.22i) q^{98} -2275.07i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 6 q^{2} - 6 q^{4} + 24 q^{5} + 45 q^{8} - 1732 q^{9}+O(q^{10}) \) 60 * q + 6 * q^2 - 6 * q^4 + 24 * q^5 + 45 * q^8 - 1732 * q^9	\( 60 q + 6 q^{2} - 6 q^{4} + 24 q^{5} + 45 q^{8} - 1732 q^{9} + 53 q^{10} + 130 q^{12} + 120 q^{13} - 231 q^{14} - 590 q^{16} - 648 q^{17} + 230 q^{18} + 1113 q^{20} + 608 q^{21} + 1080 q^{22} - 1028 q^{24} + 8340 q^{25} - 1554 q^{26} - 165 q^{28} - 168 q^{29} - 2238 q^{30} - 1674 q^{32} - 1120 q^{33} + 1844 q^{34} + 1966 q^{36} - 2248 q^{37} - 5055 q^{38} - 1716 q^{40} + 6072 q^{41} + 5794 q^{42} - 120 q^{44} - 4040 q^{45} + 8850 q^{46} + 2276 q^{48} - 17604 q^{49} - 4539 q^{50} + 5896 q^{52} + 3480 q^{53} + 5148 q^{54} - 396 q^{56} - 10912 q^{57} - 7484 q^{58} + 22812 q^{60} + 2200 q^{61} - 19299 q^{64} - 9168 q^{65} - 468 q^{66} - 21930 q^{68} + 6496 q^{69} - 9615 q^{70} - 10079 q^{72} + 13752 q^{73} - 2106 q^{74} + 20099 q^{76} + 16608 q^{77} + 39460 q^{78} - 5787 q^{80} + 20732 q^{81} - 30525 q^{82} - 21760 q^{84} - 21200 q^{85} - 13398 q^{86} + 34690 q^{88} + 22296 q^{89} - 25419 q^{90} - 18852 q^{92} + 3196 q^{94} + 20790 q^{96} + 12120 q^{97} + 21921 q^{98}+O(q^{100}) \) 60 * q + 6 * q^2 - 6 * q^4 + 24 * q^5 + 45 * q^8 - 1732 * q^9 + 53 * q^10 + 130 * q^12 + 120 * q^13 - 231 * q^14 - 590 * q^16 - 648 * q^17 + 230 * q^18 + 1113 * q^20 + 608 * q^21 + 1080 * q^22 - 1028 * q^24 + 8340 * q^25 - 1554 * q^26 - 165 * q^28 - 168 * q^29 - 2238 * q^30 - 1674 * q^32 - 1120 * q^33 + 1844 * q^34 + 1966 * q^36 - 2248 * q^37 - 5055 * q^38 - 1716 * q^40 + 6072 * q^41 + 5794 * q^42 - 120 * q^44 - 4040 * q^45 + 8850 * q^46 + 2276 * q^48 - 17604 * q^49 - 4539 * q^50 + 5896 * q^52 + 3480 * q^53 + 5148 * q^54 - 396 * q^56 - 10912 * q^57 - 7484 * q^58 + 22812 * q^60 + 2200 * q^61 - 19299 * q^64 - 9168 * q^65 - 468 * q^66 - 21930 * q^68 + 6496 * q^69 - 9615 * q^70 - 10079 * q^72 + 13752 * q^73 - 2106 * q^74 + 20099 * q^76 + 16608 * q^77 + 39460 * q^78 - 5787 * q^80 + 20732 * q^81 - 30525 * q^82 - 21760 * q^84 - 21200 * q^85 - 13398 * q^86 + 34690 * q^88 + 22296 * q^89 - 25419 * q^90 - 18852 * q^92 + 3196 * q^94 + 20790 * q^96 + 12120 * q^97 + 21921 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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