LMFDB - Embedded newform 76.5.b.a.39.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,5,Mod(39,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, 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("76.39");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	76.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:	$7.85611719437$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			39.18
Character	$\chi$	$=$	76.39
Dual form			76.5.b.a.39.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.591318 + 3.95605i) q^{2} -4.43430i q^{3} +(-15.3007 - 4.67857i) q^{4} +13.1035 q^{5} +(17.5423 + 2.62208i) q^{6} +8.96798i q^{7} +(27.5562 - 57.7638i) q^{8} +61.3370 q^{9} +O(q^{10})$	\(q+(-0.591318 + 3.95605i) q^{2} -4.43430i q^{3} +(-15.3007 - 4.67857i) q^{4} +13.1035 q^{5} +(17.5423 + 2.62208i) q^{6} +8.96798i q^{7} +(27.5562 - 57.7638i) q^{8} +61.3370 q^{9} +(-7.74835 + 51.8382i) q^{10} +193.669i q^{11} +(-20.7462 + 67.8478i) q^{12} +173.528 q^{13} +(-35.4778 - 5.30293i) q^{14} -58.1049i q^{15} +(212.222 + 143.171i) q^{16} +83.2927 q^{17} +(-36.2697 + 242.652i) q^{18} +82.8191i q^{19} +(-200.493 - 61.3057i) q^{20} +39.7667 q^{21} +(-766.166 - 114.520i) q^{22} +684.081i q^{23} +(-256.142 - 122.193i) q^{24} -453.298 q^{25} +(-102.610 + 686.485i) q^{26} -631.165i q^{27} +(41.9573 - 137.216i) q^{28} +1433.18 q^{29} +(229.866 + 34.3585i) q^{30} -750.769i q^{31} +(-691.881 + 754.902i) q^{32} +858.787 q^{33} +(-49.2525 + 329.510i) q^{34} +117.512i q^{35} +(-938.498 - 286.969i) q^{36} +437.540 q^{37} +(-327.637 - 48.9724i) q^{38} -769.474i q^{39} +(361.084 - 756.909i) q^{40} +895.241 q^{41} +(-23.5147 + 157.319i) q^{42} -928.943i q^{43} +(906.096 - 2963.27i) q^{44} +803.731 q^{45} +(-2706.26 - 404.510i) q^{46} -2116.78i q^{47} +(634.861 - 941.055i) q^{48} +2320.58 q^{49} +(268.043 - 1793.27i) q^{50} -369.344i q^{51} +(-2655.09 - 811.862i) q^{52} -3581.37 q^{53} +(2496.92 + 373.219i) q^{54} +2537.75i q^{55} +(518.024 + 247.124i) q^{56} +367.244 q^{57} +(-847.467 + 5669.75i) q^{58} -306.954i q^{59} +(-271.848 + 889.045i) q^{60} -7090.53 q^{61} +(2970.08 + 443.943i) q^{62} +550.069i q^{63} +(-2577.31 - 3183.50i) q^{64} +2273.83 q^{65} +(-507.817 + 3397.41i) q^{66} +4562.45i q^{67} +(-1274.43 - 389.691i) q^{68} +3033.42 q^{69} +(-464.884 - 69.4870i) q^{70} -149.139i q^{71} +(1690.22 - 3543.06i) q^{72} -2829.51 q^{73} +(-258.725 + 1730.93i) q^{74} +2010.06i q^{75} +(387.475 - 1267.19i) q^{76} -1736.82 q^{77} +(3044.08 + 455.004i) q^{78} +6895.61i q^{79} +(2780.86 + 1876.04i) q^{80} +2169.53 q^{81} +(-529.372 + 3541.62i) q^{82} -7842.11i q^{83} +(-608.457 - 186.051i) q^{84} +1091.43 q^{85} +(3674.95 + 549.301i) q^{86} -6355.16i q^{87} +(11187.1 + 5336.80i) q^{88} -8713.81 q^{89} +(-475.261 + 3179.60i) q^{90} +1556.19i q^{91} +(3200.52 - 10466.9i) q^{92} -3329.13 q^{93} +(8374.09 + 1251.69i) q^{94} +1085.22i q^{95} +(3347.46 + 3068.01i) q^{96} -2174.99 q^{97} +(-1372.20 + 9180.32i) q^{98} +11879.1i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 6 q^{2} - 6 q^{4} + 24 q^{5} + 66 q^{6} + 216 q^{8} - 972 q^{9}+O(q^{10}) $ 36 * q + 6 * q^2 - 6 * q^4 + 24 * q^5 + 66 * q^6 + 216 * q^8 - 972 * q^9	$ 36 q + 6 q^{2} - 6 q^{4} + 24 q^{5} + 66 q^{6} + 216 q^{8} - 972 q^{9} + 152 q^{10} + 160 q^{12} + 120 q^{13} - 60 q^{14} - 38 q^{16} - 600 q^{17} + 286 q^{18} - 600 q^{20} + 608 q^{21} + 1080 q^{22} + 958 q^{24} + 4604 q^{25} - 2766 q^{26} - 2250 q^{28} - 168 q^{29} - 1380 q^{30} + 3576 q^{32} + 1440 q^{33} + 908 q^{34} - 5836 q^{36} - 2248 q^{37} - 1716 q^{40} + 1800 q^{41} - 5006 q^{42} - 2520 q^{44} + 88 q^{45} + 6404 q^{46} + 1064 q^{48} - 12188 q^{49} + 3354 q^{50} + 15492 q^{52} - 6600 q^{53} + 1654 q^{54} + 12924 q^{56} + 5450 q^{58} - 11188 q^{60} + 2200 q^{61} - 9972 q^{62} + 12570 q^{64} - 15792 q^{65} + 10500 q^{66} - 22614 q^{68} + 19904 q^{69} + 900 q^{70} - 11376 q^{72} + 11560 q^{73} + 17304 q^{74} + 1680 q^{77} - 24740 q^{78} + 12900 q^{80} + 13604 q^{81} - 18420 q^{82} + 5644 q^{84} - 11552 q^{85} + 24564 q^{86} - 15304 q^{88} + 13800 q^{89} - 60212 q^{90} - 2142 q^{92} + 34592 q^{93} - 23096 q^{94} - 35770 q^{96} + 8200 q^{97} + 25566 q^{98}+O(q^{100}) $ 36 * q + 6 * q^2 - 6 * q^4 + 24 * q^5 + 66 * q^6 + 216 * q^8 - 972 * q^9 + 152 * q^10 + 160 * q^12 + 120 * q^13 - 60 * q^14 - 38 * q^16 - 600 * q^17 + 286 * q^18 - 600 * q^20 + 608 * q^21 + 1080 * q^22 + 958 * q^24 + 4604 * q^25 - 2766 * q^26 - 2250 * q^28 - 168 * q^29 - 1380 * q^30 + 3576 * q^32 + 1440 * q^33 + 908 * q^34 - 5836 * q^36 - 2248 * q^37 - 1716 * q^40 + 1800 * q^41 - 5006 * q^42 - 2520 * q^44 + 88 * q^45 + 6404 * q^46 + 1064 * q^48 - 12188 * q^49 + 3354 * q^50 + 15492 * q^52 - 6600 * q^53 + 1654 * q^54 + 12924 * q^56 + 5450 * q^58 - 11188 * q^60 + 2200 * q^61 - 9972 * q^62 + 12570 * q^64 - 15792 * q^65 + 10500 * q^66 - 22614 * q^68 + 19904 * q^69 + 900 * q^70 - 11376 * q^72 + 11560 * q^73 + 17304 * q^74 + 1680 * q^77 - 24740 * q^78 + 12900 * q^80 + 13604 * q^81 - 18420 * q^82 + 5644 * q^84 - 11552 * q^85 + 24564 * q^86 - 15304 * q^88 + 13800 * q^89 - 60212 * q^90 - 2142 * q^92 + 34592 * q^93 - 23096 * q^94 - 35770 * q^96 + 8200 * q^97 + 25566 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$1$	$-1$

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 $

$2$	−0.591318	+	3.95605i	−0.147830	+	0.989013i
$2$	−0.591318	+	3.95605i	−0.147830	+	0.989013i
$3$		−	4.43430i		−	0.492700i	−0.969181	−	0.246350i	$-0.920769\pi$
$3$		−	4.43430i		−	0.492700i	0.969181	−	0.246350i	$-0.0792312\pi$
$4$	−15.3007	−	4.67857i	−0.956293	−	0.292411i
$5$	13.1035			0.524141			0.262070	−	0.965049i	$-0.415595\pi$
$5$	13.1035			0.524141			0.262070	+	0.965049i	$0.415595\pi$
$6$	17.5423	+	2.62208i	0.487286	+	0.0728356i
$7$			8.96798i			0.183020i	0.995804	+	0.0915100i	$0.0291693\pi$
$7$			8.96798i			0.183020i	−0.995804	+	0.0915100i	$0.970831\pi$
$8$	27.5562	−	57.7638i	0.430566	−	0.902559i
$9$	61.3370			0.757247
$10$	−7.74835	+	51.8382i	−0.0774835	+	0.518382i
$11$			193.669i			1.60057i	0.599618	+	0.800287i	$0.295319\pi$
$11$			193.669i			1.60057i	−0.599618	+	0.800287i	$0.704681\pi$
$12$	−20.7462	+	67.8478i	−0.144071	+	0.471165i
$13$	173.528			1.02679			0.513396	−	0.858152i	$-0.328387\pi$
$13$	173.528			1.02679			0.513396	+	0.858152i	$0.328387\pi$
$14$	−35.4778	−	5.30293i	−0.181009	−	0.0270557i
$15$		−	58.1049i		−	0.258244i
$16$	212.222	+	143.171i	0.828992	+	0.559260i
$17$	83.2927			0.288210			0.144105	−	0.989562i	$-0.453970\pi$
$17$	83.2927			0.288210			0.144105	+	0.989562i	$0.453970\pi$
$18$	−36.2697	+	242.652i	−0.111943	+	0.748927i
$19$			82.8191i			0.229416i
$19$			82.8191i			0.229416i
$20$	−200.493	−	61.3057i	−0.501232	−	0.153264i
$21$	39.7667			0.0901738
$22$	−766.166	−	114.520i	−1.58299	−	0.236612i
$23$			684.081i			1.29316i	0.762846	+	0.646580i	$0.223801\pi$
$23$			684.081i			1.29316i	−0.762846	+	0.646580i	$0.776199\pi$
$24$	−256.142	−	122.193i	−0.444691	−	0.212140i
$25$	−453.298			−0.725276
$26$	−102.610	+	686.485i	−0.151790	+	1.01551i
$27$		−	631.165i		−	0.865795i
$28$	41.9573	−	137.216i	0.0535170	−	0.175021i
$29$	1433.18			1.70414			0.852071	−	0.523426i	$-0.175346\pi$
$29$	1433.18			1.70414			0.852071	+	0.523426i	$0.175346\pi$
$30$	229.866	+	34.3585i	0.255407	+	0.0381761i
$31$		−	750.769i		−	0.781237i	−0.920553	−	0.390619i	$-0.872261\pi$
$31$		−	750.769i		−	0.781237i	0.920553	−	0.390619i	$-0.127739\pi$
$32$	−691.881	+	754.902i	−0.675665	+	0.737209i
$33$	858.787			0.788602
$34$	−49.2525	+	329.510i	−0.0426059	+	0.285043i
$35$			117.512i			0.0959282i
$36$	−938.498	−	286.969i	−0.724150	−	0.221427i
$37$	437.540			0.319606			0.159803	−	0.987149i	$-0.448914\pi$
$37$	437.540			0.319606			0.159803	+	0.987149i	$0.448914\pi$
$38$	−327.637	−	48.9724i	−0.226895	−	0.0339144i
$39$		−	769.474i		−	0.505900i
$40$	361.084	−	756.909i	0.225677	−	0.473068i
$41$	895.241			0.532565			0.266282	−	0.963895i	$-0.414205\pi$
$41$	895.241			0.532565			0.266282	+	0.963895i	$0.414205\pi$
$42$	−23.5147	+	157.319i	−0.0133304	+	0.0891831i
$43$		−	928.943i		−	0.502403i	−0.967935	−	0.251202i	$-0.919174\pi$
$43$		−	928.943i		−	0.502403i	0.967935	−	0.251202i	$-0.0808257\pi$
$44$	906.096	−	2963.27i	0.468025	−	1.53062i
$45$	803.731			0.396904
$46$	−2706.26	−	404.510i	−1.27895	−	0.191167i
$47$		−	2116.78i		−	0.958252i	−0.877746	−	0.479126i	$-0.840954\pi$
$47$		−	2116.78i		−	0.958252i	0.877746	−	0.479126i	$-0.159046\pi$
$48$	634.861	−	941.055i	0.275547	−	0.408444i
$49$	2320.58			0.966504
$50$	268.043	−	1793.27i	0.107217	−	0.717308i
$51$		−	369.344i		−	0.142001i
$52$	−2655.09	−	811.862i	−0.981914	−	0.300245i
$53$	−3581.37			−1.27496			−0.637481	−	0.770466i	$-0.720024\pi$
$53$	−3581.37			−1.27496			−0.637481	+	0.770466i	$0.720024\pi$
$54$	2496.92	+	373.219i	0.856282	+	0.127990i
$55$			2537.75i			0.838926i
$56$	518.024	+	247.124i	0.165186	+	0.0788022i
$57$	367.244			0.113033
$58$	−847.467	+	5669.75i	−0.251922	+	1.68542i
$59$		−	306.954i		−	0.0881797i	−0.999028	−	0.0440899i	$-0.985961\pi$
$59$		−	306.954i		−	0.0881797i	0.999028	−	0.0440899i	$-0.0140388\pi$
$60$	−271.848	+	889.045i	−0.0755133	+	0.246957i
$61$	−7090.53			−1.90554			−0.952772	−	0.303687i	$-0.901782\pi$
$61$	−7090.53			−1.90554			−0.952772	+	0.303687i	$0.901782\pi$
$62$	2970.08	+	443.943i	0.772654	+	0.115490i
$63$			550.069i			0.138591i
$64$	−2577.31	−	3183.50i	−0.629226	−	0.777223i
$65$	2273.83			0.538184
$66$	−507.817	+	3397.41i	−0.116579	+	0.779937i
$67$			4562.45i			1.01636i	0.861250	+	0.508181i	$0.169682\pi$
$67$			4562.45i			1.01636i	−0.861250	+	0.508181i	$0.830318\pi$
$68$	−1274.43	−	389.691i	−0.275613	−	0.0842756i
$69$	3033.42			0.637139
$70$	−464.884	−	69.4870i	−0.0948742	−	0.0141810i
$71$		−	149.139i		−	0.0295853i	−0.999891	−	0.0147926i	$-0.995291\pi$
$71$		−	149.139i		−	0.0295853i	0.999891	−	0.0147926i	$-0.00470882\pi$
$72$	1690.22	−	3543.06i	0.326045	−	0.683460i
$73$	−2829.51			−0.530964			−0.265482	−	0.964116i	$-0.585531\pi$
$73$	−2829.51			−0.530964			−0.265482	+	0.964116i	$0.585531\pi$
$74$	−258.725	+	1730.93i	−0.0472471	+	0.316094i
$75$			2010.06i			0.357343i
$76$	387.475	−	1267.19i	0.0670836	−	0.219389i
$77$	−1736.82			−0.292937
$78$	3044.08	+	455.004i	0.500342	+	0.0747870i
$79$			6895.61i			1.10489i	0.833550	+	0.552444i	$0.186305\pi$
$79$			6895.61i			1.10489i	−0.833550	+	0.552444i	$0.813695\pi$
$80$	2780.86	+	1876.04i	0.434509	+	0.293131i
$81$	2169.53			0.330670
$82$	−529.372	+	3541.62i	−0.0787288	+	0.526713i
$83$		−	7842.11i		−	1.13835i	−0.822216	−	0.569176i	$-0.807262\pi$
$83$		−	7842.11i		−	1.13835i	0.822216	−	0.569176i	$-0.192738\pi$
$84$	−608.457	−	186.051i	−0.0862326	−	0.0263678i
$85$	1091.43			0.151063
$86$	3674.95	+	549.301i	0.496883	+	0.0742700i
$87$		−	6355.16i		−	0.839630i
$88$	11187.1	+	5336.80i	1.44461	+	0.689153i
$89$	−8713.81			−1.10009			−0.550045	−	0.835135i	$-0.685389\pi$
$89$	−8713.81			−1.10009			−0.550045	+	0.835135i	$0.685389\pi$
$90$	−475.261	+	3179.60i	−0.0586742	+	0.392543i
$91$			1556.19i			0.187923i
$92$	3200.52	−	10466.9i	0.378134	−	1.23664i
$93$	−3329.13			−0.384915
$94$	8374.09	+	1251.69i	0.947724	+	0.141658i
$95$			1085.22i			0.120246i
$96$	3347.46	+	3068.01i	0.363222	+	0.332900i
$97$	−2174.99			−0.231161			−0.115580	−	0.993298i	$-0.536873\pi$
$97$	−2174.99			−0.231161			−0.115580	+	0.993298i	$0.536873\pi$
$98$	−1372.20	+	9180.32i	−0.142878	+	0.955885i
$99$			11879.1i			1.21203i
$100$	6935.77	+	2120.78i	0.693577	+	0.212078i
$101$	−4516.78			−0.442778			−0.221389	−	0.975186i	$-0.571059\pi$
$101$	−4516.78			−0.442778			−0.221389	+	0.975186i	$0.571059\pi$
$102$	1461.15	+	218.400i	0.140441	+	0.0209919i
$103$			2460.95i			0.231968i	0.993251	+	0.115984i	$0.0370021\pi$
$103$			2460.95i			0.231968i	−0.993251	+	0.115984i	$0.962998\pi$
$104$	4781.77	−	10023.6i	0.442102	−	0.926740i
$105$	521.083			0.0472638
$106$	2117.73	−	14168.1i	0.188477	−	1.26095i
$107$		−	8505.12i		−	0.742870i	−0.928459	−	0.371435i	$-0.878866\pi$
$107$		−	8505.12i		−	0.742870i	0.928459	−	0.371435i	$-0.121134\pi$
$108$	−2952.95	+	9657.25i	−0.253168	+	0.827954i
$109$	−2706.22			−0.227777			−0.113888	−	0.993494i	$-0.536331\pi$
$109$	−2706.22			−0.227777			−0.113888	+	0.993494i	$0.536331\pi$
$110$	−10039.5	−	1500.62i	−0.829709	−	0.124018i
$111$		−	1940.18i		−	0.157470i
$112$	−1283.95	+	1903.20i	−0.102356	+	0.151722i
$113$	6191.77			0.484907			0.242453	−	0.970163i	$-0.422048\pi$
$113$	6191.77			0.484907			0.242453	+	0.970163i	$0.422048\pi$
$114$	−217.158	+	1452.84i	−0.0167096	+	0.111791i
$115$			8963.88i			0.677798i
$116$	−21928.7	−	6705.25i	−1.62966	−	0.498309i
$117$	10643.7			0.777535
$118$	1214.32	+	181.507i	0.0872109	+	0.0130356i
$119$			746.967i			0.0527482i
$120$	−3356.36	−	1601.15i	−0.233081	−	0.111191i
$121$	−22866.8			−1.56184
$122$	4192.76	−	28050.5i	0.281696	−	1.88461i
$123$		−	3969.77i		−	0.262394i
$124$	−3512.53	+	11487.3i	−0.228442	+	0.747092i
$125$	−14129.5			−0.904288
$126$	−2176.10	−	325.266i	−0.137069	−	0.0204879i
$127$			2796.70i			0.173396i	0.996235	+	0.0866979i	$0.0276315\pi$
$127$			2796.70i			0.173396i	−0.996235	+	0.0866979i	$0.972369\pi$
$128$	14118.1	−	8313.50i	0.861701	−	0.507416i
$129$	−4119.21			−0.247534
$130$	−1344.55	+	8995.37i	−0.0795594	+	0.532271i
$131$		−	24318.3i		−	1.41707i	−0.705676	−	0.708535i	$-0.749356\pi$
$131$		−	24318.3i		−	1.41707i	0.705676	−	0.708535i	$-0.250644\pi$
$132$	−13140.0	−	4017.90i	−0.754134	−	0.230596i
$133$	−742.719			−0.0419876
$134$	−18049.3	−	2697.86i	−1.00520	−	0.150248i
$135$		−	8270.48i		−	0.453799i
$136$	2295.23	−	4811.30i	0.124093	−	0.260126i
$137$	24493.0			1.30497			0.652485	−	0.757801i	$-0.273726\pi$
$137$	24493.0			1.30497			0.652485	+	0.757801i	$0.273726\pi$
$138$	−1793.72	+	12000.4i	−0.0941880	+	0.630139i
$139$		−	30575.5i		−	1.58250i	−0.611493	−	0.791250i	$-0.709431\pi$
$139$		−	30575.5i		−	1.58250i	0.611493	−	0.791250i	$-0.290569\pi$
$140$	549.788	−	1798.02i	0.0280504	−	0.0917355i
$141$	−9386.43			−0.472131
$142$	590.003	+	88.1889i	0.0292602	+	0.00437358i
$143$			33607.0i			1.64346i
$144$	13017.1	+	8781.66i	0.627752	+	0.423498i
$145$	18779.8			0.893211
$146$	1673.14	−	11193.7i	0.0784922	−	0.525131i
$147$		−	10290.1i		−	0.476196i
$148$	−6694.66	−	2047.06i	−0.305637	−	0.0934561i
$149$	42569.0			1.91744			0.958718	−	0.284357i	$-0.0917802\pi$
$149$	42569.0			1.91744			0.958718	+	0.284357i	$0.0917802\pi$
$150$	−7951.89	−	1188.58i	−0.353417	−	0.0528259i
$151$			32464.1i			1.42380i	0.702280	+	0.711901i	$0.252166\pi$
$151$			32464.1i			1.42380i	−0.702280	+	0.711901i	$0.747834\pi$
$152$	4783.94	+	2282.18i	0.207061	+	0.0987786i
$153$	5108.92			0.218246
$154$	1027.01	−	6870.96i	0.0433047	−	0.289718i
$155$		−	9837.72i		−	0.409479i
$156$	−3600.04	+	11773.5i	−0.147931	+	0.483789i
$157$	195.182			0.00791845			0.00395923	−	0.999992i	$-0.498740\pi$
$157$	195.182			0.00791845			0.00395923	+	0.999992i	$0.498740\pi$
$158$	−27279.4	−	4077.50i	−1.09275	−	0.163335i
$159$			15880.8i			0.628173i
$160$	−9066.08	+	9891.87i	−0.354144	+	0.386401i
$161$	−6134.82			−0.236674
$162$	−1282.88	+	8582.76i	−0.0488828	+	0.327037i
$163$		−	21326.3i		−	0.802678i	−0.915930	−	0.401339i	$-0.868545\pi$
$163$		−	21326.3i		−	0.802678i	0.915930	−	0.401339i	$-0.131455\pi$
$164$	−13697.8	−	4188.45i	−0.509288	−	0.155728i
$165$	11253.1			0.413339
$166$	31023.8	+	4637.18i	1.12585	+	0.168282i
$167$		−	20994.1i		−	0.752774i	−0.926462	−	0.376387i	$-0.877166\pi$
$167$		−	20994.1i		−	0.752774i	0.926462	−	0.376387i	$-0.122834\pi$
$168$	1095.82	−	2297.07i	0.0388258	−	0.0813872i
$169$	1550.90			0.0543015
$170$	−645.381	+	4317.74i	−0.0223315	+	0.149403i
$171$			5079.87i			0.173724i
$172$	−4346.13	+	14213.5i	−0.146908	+	0.480445i
$173$	34458.3			1.15134			0.575668	−	0.817684i	$-0.304742\pi$
$173$	34458.3			1.15134			0.575668	+	0.817684i	$0.304742\pi$
$174$	25141.3	+	3757.92i	0.830405	+	0.124122i
$175$		−	4065.16i		−	0.132740i
$176$	−27727.8	+	41100.9i	−0.895137	+	1.32686i
$177$	−1361.12			−0.0434461
$178$	5152.63	−	34472.3i	0.162626	−	1.08800i
$179$		−	26297.9i		−	0.820756i	−0.911915	−	0.410378i	$-0.865397\pi$
$179$		−	26297.9i		−	0.820756i	0.911915	−	0.410378i	$-0.134603\pi$
$180$	−12297.6	−	3760.31i	−0.379557	−	0.116059i
$181$	−24396.4			−0.744677			−0.372339	−	0.928097i	$-0.621444\pi$
$181$	−24396.4			−0.744677			−0.372339	+	0.928097i	$0.621444\pi$
$182$	−6156.38	−	920.205i	−0.185859	−	0.0277806i
$183$			31441.5i			0.938861i
$184$	39515.1	+	18850.7i	1.16715	+	0.556791i
$185$	5733.32			0.167518
$186$	1968.58	−	13170.2i	0.0569019	−	0.380686i
$187$			16131.2i			0.461301i
$188$	−9903.50	+	32388.2i	−0.280203	+	0.916370i
$189$	5660.27			0.158458
$190$	−4293.19	−	641.711i	−0.118925	−	0.0177759i
$191$			20922.9i			0.573527i	0.958001	+	0.286764i	$0.0925795\pi$
$191$			20922.9i			0.573527i	−0.958001	+	0.286764i	$0.907421\pi$
$192$	−14116.6	+	11428.5i	−0.382937	+	0.310019i
$193$	55571.2			1.49188			0.745942	−	0.666011i	$-0.232000\pi$
$193$	55571.2			1.49188			0.745942	+	0.666011i	$0.232000\pi$
$194$	1286.11	−	8604.37i	0.0341723	−	0.228621i
$195$		−	10082.8i		−	0.265163i
$196$	−35506.4	−	10857.0i	−0.924261	−	0.282616i
$197$	−50210.5			−1.29378			−0.646892	−	0.762582i	$-0.723932\pi$
$197$	−50210.5			−1.29378			−0.646892	+	0.762582i	$0.723932\pi$
$198$	−46994.3	−	7024.33i	−1.19871	−	0.179174i
$199$			4943.87i			0.124842i	0.998050	+	0.0624211i	$0.0198822\pi$
$199$			4943.87i			0.124842i	−0.998050	+	0.0624211i	$0.980118\pi$
$200$	−12491.2	+	26184.2i	−0.312279	+	0.654605i
$201$	20231.3			0.500761
$202$	2670.86	−	17868.6i	0.0654557	−	0.437914i
$203$			12852.8i			0.311892i
$204$	−1728.00	+	5651.22i	−0.0415226	+	0.135794i
$205$	11730.8			0.279139
$206$	−9735.63	−	1455.20i	−0.229419	−	0.0342917i
$207$			41959.5i			0.979241i
$208$	36826.4	+	24844.1i	0.851202	+	0.574244i
$209$	−16039.5			−0.367197
$210$	−308.126	+	2061.43i	−0.00698699	+	0.0467445i
$211$			67805.4i			1.52300i	0.648166	+	0.761499i	$0.275536\pi$
$211$			67805.4i			1.52300i	−0.648166	+	0.761499i	$0.724464\pi$
$212$	54797.4	+	16755.7i	1.21924	+	0.372812i
$213$	−661.329			−0.0145767
$214$	33646.7	+	5029.23i	0.734708	+	0.109818i
$215$		−	12172.4i		−	0.263330i
$216$	−36458.4	−	17392.5i	−0.781431	−	0.372782i
$217$	6732.88			0.142982
$218$	1600.24	−	10705.9i	0.0336721	−	0.225274i
$219$			12546.9i			0.261606i
$220$	11873.0	−	38829.3i	0.245311	−	0.802259i
$221$	14453.6			0.295932
$222$	7675.46	+	1147.26i	0.155739	+	0.0232786i
$223$		−	35884.4i		−	0.721598i	−0.932644	−	0.360799i	$-0.882504\pi$
$223$		−	35884.4i		−	0.721598i	0.932644	−	0.360799i	$-0.117496\pi$
$224$	−6769.94	−	6204.77i	−0.134924	−	0.123660i
$225$	−27803.9			−0.549213
$226$	−3661.31	+	24495.0i	−0.0716835	+	0.479579i
$227$		−	79862.5i		−	1.54985i	−0.632050	−	0.774927i	$-0.717786\pi$
$227$		−	79862.5i		−	1.54985i	0.632050	−	0.774927i	$-0.282214\pi$
$228$	−5619.09	−	1718.18i	−0.108093	−	0.0330521i
$229$	−56160.1			−1.07092			−0.535460	−	0.844561i	$-0.679862\pi$
$229$	−56160.1			−1.07092			−0.535460	+	0.844561i	$0.679862\pi$
$230$	−35461.6	−	5300.50i	−0.670351	−	0.100199i
$231$			7701.58i			0.144330i
$232$	39493.1	−	82786.1i	0.733746	−	1.53809i
$233$	−71608.6			−1.31903			−0.659513	−	0.751694i	$-0.729237\pi$
$233$	−71608.6			−1.31903			−0.659513	+	0.751694i	$0.729237\pi$
$234$	−6293.80	+	42106.9i	−0.114943	+	0.768992i
$235$		−	27737.3i		−	0.502259i
$236$	−1436.10	+	4696.60i	−0.0257847	+	0.0843256i
$237$	30577.2			0.544378
$238$	−2955.04	−	441.695i	−0.0521686	−	0.00779773i
$239$		−	11359.8i		−	0.198873i	−0.995044	−	0.0994366i	$-0.968296\pi$
$239$		−	11359.8i		−	0.198873i	0.995044	−	0.0994366i	$-0.0317040\pi$
$240$	8318.92	−	12331.1i	0.144426	−	0.214082i
$241$	−42161.8			−0.725914			−0.362957	−	0.931806i	$-0.618233\pi$
$241$	−42161.8			−0.725914			−0.362957	+	0.931806i	$0.618233\pi$
$242$	13521.6	−	90462.3i	0.230885	−	1.54467i
$243$		−	60744.7i		−	1.02872i
$244$	108490.	+	33173.5i	1.82226	+	0.557201i
$245$	30407.7			0.506584
$246$	15704.6	+	2347.39i	0.259511	+	0.0387896i
$247$			14371.4i			0.235562i
$248$	−43367.3	−	20688.4i	−0.705113	−	0.336374i
$249$	−34774.2			−0.560866
$250$	8355.03	−	55897.0i	0.133680	−	0.894352i
$251$			7549.02i			0.119824i	0.998204	+	0.0599119i	$0.0190820\pi$
$251$			7549.02i			0.119824i	−0.998204	+	0.0599119i	$0.980918\pi$
$252$	2573.54	−	8416.43i	0.0405256	−	0.132534i
$253$	−132486.			−2.06980
$254$	−11063.9	−	1653.74i	−0.171491	−	0.0256330i
$255$		−	4839.71i		−	0.0744285i
$256$	24540.3	+	60767.9i	0.374456	+	0.927245i
$257$	−24834.0			−0.375994			−0.187997	−	0.982170i	$-0.560200\pi$
$257$	−24834.0			−0.375994			−0.187997	+	0.982170i	$0.560200\pi$
$258$	2435.76	−	16295.8i	0.0365928	−	0.244814i
$259$			3923.85i			0.0584942i
$260$	−34791.1	−	10638.3i	−0.514661	−	0.157371i
$261$	87907.2			1.29046
$262$	96204.6	+	14379.9i	1.40150	+	0.209485i
$263$			10991.3i			0.158905i	0.996839	+	0.0794527i	$0.0253173\pi$
$263$			10991.3i			0.158905i	−0.996839	+	0.0794527i	$0.974683\pi$
$264$	23664.9	−	49606.8i	0.339545	−	0.711760i
$265$	−46928.5			−0.668260
$266$	439.183	−	2938.24i	0.00620701	−	0.0415263i
$267$			38639.6i			0.542014i
$268$	21345.7	−	69808.6i	0.297195	−	0.971940i
$269$	123859.			1.71168			0.855839	−	0.517242i	$-0.173041\pi$
$269$	123859.			1.71168			0.855839	+	0.517242i	$0.173041\pi$
$270$	32718.4	+	4890.48i	0.448813	+	0.0670848i
$271$			38457.3i			0.523649i	0.965116	+	0.261824i	$0.0843241\pi$
$271$			38457.3i			0.523649i	−0.965116	+	0.261824i	$0.915676\pi$
$272$	17676.5	+	11925.1i	0.238924	+	0.161184i
$273$	6900.62			0.0925898
$274$	−14483.2	+	96895.6i	−0.192913	+	1.29063i
$275$		−	87789.9i		−	1.16086i
$276$	−46413.4	−	14192.1i	−0.609292	−	0.186306i
$277$	−63456.0			−0.827015			−0.413508	−	0.910501i	$-0.635696\pi$
$277$	−63456.0			−0.827015			−0.413508	+	0.910501i	$0.635696\pi$
$278$	120958.	+	18079.8i	1.56511	+	0.233940i
$279$		−	46049.9i		−	0.591590i
$280$	6787.94	+	3238.19i	0.0865809	+	0.0413034i
$281$	−49117.0			−0.622041			−0.311020	−	0.950403i	$-0.600671\pi$
$281$	−49117.0			−0.622041			−0.311020	+	0.950403i	$0.600671\pi$
$282$	5550.37	−	37133.2i	0.0697948	−	0.466943i
$283$		−	71155.9i		−	0.888460i	−0.895913	−	0.444230i	$-0.853477\pi$
$283$		−	71155.9i		−	0.888460i	0.895913	−	0.444230i	$-0.146523\pi$
$284$	−697.759	+	2281.94i	−0.00865105	+	0.0282922i
$285$	4812.20			0.0592453
$286$	−132951.	−	19872.4i	−1.62540	−	0.242951i
$287$			8028.50i			0.0974699i
$288$	−42437.9	+	46303.4i	−0.511645	+	0.558249i
$289$	−76583.3			−0.916935
$290$	−11104.8	+	74293.7i	−0.132043	+	0.883397i
$291$			9644.55i			0.113893i
$292$	43293.4	+	13238.1i	0.507758	+	0.155260i
$293$	2819.70			0.0328448			0.0164224	−	0.999865i	$-0.494772\pi$
$293$	2819.70			0.0328448			0.0164224	+	0.999865i	$0.494772\pi$
$294$	40708.2	+	6084.73i	0.470964	+	0.0703958i
$295$		−	4022.17i		−	0.0462186i
$296$	12057.0	−	25274.0i	0.137611	−	0.288463i
$297$	122237.			1.38577
$298$	−25171.8	+	168405.i	−0.283454	+	1.89637i
$299$			118707.i			1.32781i
$300$	9404.19	−	30755.2i	0.104491	−	0.341725i
$301$	8330.74			0.0919498
$302$	−128430.	−	19196.6i	−1.40816	−	0.210480i
$303$			20028.8i			0.218157i
$304$	−11857.3	+	17576.0i	−0.128303	+	0.190184i
$305$	−92910.9			−0.998774
$306$	−3021.00	+	20211.2i	−0.0322632	+	0.215848i
$307$		−	161051.i		−	1.70878i	−0.519631	−	0.854391i	$-0.673931\pi$
$307$		−	161051.i		−	1.70878i	0.519631	−	0.854391i	$-0.326069\pi$
$308$	26574.6	+	8125.84i	0.280133	+	0.0856578i
$309$	10912.6			0.114290
$310$	38918.5	+	5817.22i	0.404980	+	0.0605330i
$311$			138439.i			1.43133i	0.698446	+	0.715663i	$0.253875\pi$
$311$			138439.i			1.43133i	−0.698446	+	0.715663i	$0.746125\pi$
$312$	−44447.7	−	21203.8i	−0.456605	−	0.217823i
$313$	26633.8			0.271860			0.135930	−	0.990718i	$-0.456598\pi$
$313$	26633.8			0.271860			0.135930	+	0.990718i	$0.456598\pi$
$314$	−115.415	+	772.150i	−0.00117058	+	0.00783145i
$315$			7207.84i			0.0726414i
$316$	32261.6	−	105508.i	0.323081	−	1.05660i
$317$	−45290.4			−0.450700			−0.225350	−	0.974278i	$-0.572353\pi$
$317$	−45290.4			−0.450700			−0.225350	+	0.974278i	$0.572353\pi$
$318$	−62825.4	−	9390.63i	−0.621271	−	0.0928625i
$319$			277564.i			2.72760i
$320$	−33771.8	−	41715.1i	−0.329803	−	0.407374i
$321$	−37714.2			−0.366012
$322$	3627.63	−	24269.7i	0.0349874	−	0.234074i
$323$			6898.22i			0.0661199i
$324$	−33195.3	−	10150.3i	−0.316218	−	0.0966915i
$325$	−78659.8			−0.744708
$326$	84368.1	+	12610.7i	0.793859	+	0.118659i
$327$			12000.2i			0.112226i
$328$	24669.5	−	51712.5i	0.229304	−	0.480671i
$329$	18983.2			0.175379
$330$	−6654.19	+	44518.0i	−0.0611036	+	0.408797i
$331$		−	1136.55i		−	0.0103737i	−0.999987	−	0.00518685i	$-0.998349\pi$
$331$		−	1136.55i		−	0.0103737i	0.999987	−	0.00518685i	$-0.00165103\pi$
$332$	−36689.9	+	119990.i	−0.332866	+	1.08860i
$333$	26837.4			0.242020
$334$	83053.8	+	12414.2i	0.744504	+	0.111282i
$335$			59784.2i			0.532717i
$336$	8439.36	+	5693.42i	0.0747534	+	0.0504307i
$337$	126361.			1.11263			0.556317	−	0.830970i	$-0.312214\pi$
$337$	126361.			1.11263			0.556317	+	0.830970i	$0.312214\pi$
$338$	−917.078	+	6135.46i	−0.00802736	+	0.0537049i
$339$		−	27456.2i		−	0.238913i
$340$	−16699.6	−	5106.32i	−0.144460	−	0.0441723i
$341$	145401.			1.25043
$342$	−20096.2	−	3003.82i	−0.171816	−	0.0256816i
$343$			42343.0i			0.359909i
$344$	−53659.3	−	25598.2i	−0.453449	−	0.216318i
$345$	39748.5			0.333951
$346$	−20375.8	+	136319.i	−0.170201	+	1.13869i
$347$		−	164302.i		−	1.36453i	−0.731103	−	0.682267i	$-0.760994\pi$
$347$		−	164302.i		−	1.36453i	0.731103	−	0.682267i	$-0.239006\pi$
$348$	−29733.1	+	97238.3i	−0.245517	+	0.802932i
$349$	−57342.3			−0.470787			−0.235394	−	0.971900i	$-0.575638\pi$
$349$	−57342.3			−0.470787			−0.235394	+	0.971900i	$0.575638\pi$
$350$	16082.0	+	2403.80i	0.131282	+	0.0196229i
$351$		−	109525.i		−	0.888991i
$352$	−146201.	−	133996.i	−1.17996	−	1.08145i
$353$	229162.			1.83905			0.919524	−	0.393034i	$-0.128575\pi$
$353$	229162.			1.83905			0.919524	+	0.393034i	$0.128575\pi$
$354$	804.857	−	5384.67i	0.00642262	−	0.0429688i
$355$		−	1954.25i		−	0.0155069i
$356$	133327.	+	40768.2i	1.05201	+	0.321678i
$357$	3312.27			0.0259890
$358$	104036.	+	15550.4i	0.811739	+	0.121332i
$359$			140525.i			1.09035i	0.838322	+	0.545175i	$0.183537\pi$
$359$			140525.i			1.09035i	−0.838322	+	0.545175i	$0.816463\pi$
$360$	22147.8	−	46426.5i	0.170894	−	0.358229i
$361$	−6859.00			−0.0526316
$362$	14426.0	−	96513.3i	0.110085	−	0.736495i
$363$			101398.i			0.769516i
$364$	7280.76	−	23810.8i	0.0549508	−	0.179710i
$365$	−37076.5			−0.278300
$366$	−124384.	−	18591.9i	−0.928545	−	0.138791i
$367$		−	181307.i		−	1.34612i	−0.739589	−	0.673059i	$-0.764980\pi$
$367$		−	181307.i		−	1.34612i	0.739589	−	0.673059i	$-0.235020\pi$
$368$	−97940.4	+	145177.i	−0.723213	+	1.07202i
$369$	54911.4			0.403283
$370$	−3390.21	+	22681.3i	−0.0247642	+	0.165678i
$371$		−	32117.6i		−	0.233343i
$372$	50938.0	+	15575.6i	0.368092	+	0.112553i
$373$	181780.			1.30656			0.653280	−	0.757117i	$-0.273393\pi$
$373$	181780.			1.30656			0.653280	+	0.757117i	$0.273393\pi$
$374$	−63816.0	−	9538.69i	−0.456233	−	0.0681939i
$375$			62654.4i			0.445542i
$376$	−122273.	−	58330.5i	−0.864879	−	0.412591i
$377$	248697.			1.74980
$378$	−3347.02	+	22392.3i	−0.0234247	+	0.156717i
$379$		−	151291.i		−	1.05326i	−0.850095	−	0.526629i	$-0.823456\pi$
$379$		−	151291.i		−	1.05326i	0.850095	−	0.526629i	$-0.176544\pi$
$380$	5077.29	−	16604.6i	0.0351613	−	0.114991i
$381$	12401.4			0.0854320
$382$	−82771.9	−	12372.1i	−0.567226	−	0.0847843i
$383$		−	150881.i		−	1.02858i	−0.857616	−	0.514290i	$-0.828055\pi$
$383$		−	150881.i		−	1.02858i	0.857616	−	0.514290i	$-0.171945\pi$
$384$	−36864.5	−	62603.9i	−0.250004	−	0.424560i
$385$	−22758.5			−0.153540
$386$	−32860.2	+	219842.i	−0.220544	+	1.47549i
$387$		−	56978.6i		−	0.380443i
$388$	33278.8	+	10175.8i	0.221057	+	0.0675938i
$389$	−1428.09			−0.00943750			−0.00471875	−	0.999989i	$-0.501502\pi$
$389$	−1428.09			−0.00943750			−0.00471875	+	0.999989i	$0.501502\pi$
$390$	39888.2	+	5962.15i	0.262250	+	0.0391989i
$391$			56979.0i			0.372701i
$392$	63946.3	−	134045.i	0.416144	−	0.872327i
$393$	−107835.			−0.698190
$394$	29690.4	−	198635.i	0.191259	−	1.27957i
$395$			90356.8i			0.579117i
$396$	55577.2	−	181758.i	0.354410	−	1.15906i
$397$	−208771.			−1.32461			−0.662307	−	0.749233i	$-0.730423\pi$
$397$	−208771.			−1.32461			−0.662307	+	0.749233i	$0.730423\pi$
$398$	−19558.2	−	2923.40i	−0.123471	−	0.0184554i
$399$			3293.44i			0.0206873i
$400$	−96199.7	−	64898.9i	−0.601248	−	0.405618i
$401$	237252.			1.47544			0.737719	−	0.675108i	$-0.235903\pi$
$401$	237252.			1.47544			0.737719	+	0.675108i	$0.235903\pi$
$402$	−11963.1	+	80035.9i	−0.0740273	+	0.495259i
$403$		−	130279.i		−	0.802168i
$404$	69109.9	+	21132.1i	0.423426	+	0.129473i
$405$	28428.4			0.173318
$406$	−50846.2	−	7600.07i	−0.308465	−	0.0461068i
$407$			84738.1i			0.511552i
$408$	−21334.7	−	10177.7i	−0.128164	−	0.0611408i
$409$	−315975.			−1.88889			−0.944443	−	0.328676i	$-0.893397\pi$
$409$	−315975.			−1.88889			−0.944443	+	0.328676i	$0.893397\pi$
$410$	−6936.64	+	46407.7i	−0.0412650	+	0.276072i
$411$		−	108609.i		−	0.642959i
$412$	11513.7	−	37654.2i	0.0678298	−	0.221829i
$413$	2752.75			0.0161386
$414$	−165994.	−	24811.4i	−0.968482	−	0.144761i
$415$		−	102759.i		−	0.596657i
$416$	−120061.	+	130996.i	−0.693767	+	0.756960i
$417$	−135581.			−0.779697
$418$	9484.46	−	63453.2i	0.0542825	−	0.363162i
$419$			233329.i			1.32905i	0.747266	+	0.664525i	$0.231366\pi$
$419$			233329.i			1.32905i	−0.747266	+	0.664525i	$0.768634\pi$
$420$	−7972.93	−	2437.92i	−0.0451980	−	0.0138204i
$421$	−162883.			−0.918992			−0.459496	−	0.888180i	$-0.651970\pi$
$421$	−162883.			−0.918992			−0.459496	+	0.888180i	$0.651970\pi$
$422$	−268242.	−	40094.6i	−1.50626	−	0.225144i
$423$		−	129837.i		−	0.725634i
$424$	−98689.0	+	206873.i	−0.548955	+	1.15073i
$425$	−37756.4			−0.209032
$426$	391.056	−	2616.25i	0.00215486	−	0.0144165i
$427$		−	63587.7i		−	0.348752i
$428$	−39791.8	+	130134.i	−0.217223	+	0.710401i
$429$	149024.			0.809730
$430$	48154.8	+	7197.78i	0.260437	+	0.0389280i
$431$		−	353158.i		−	1.90114i	−0.310512	−	0.950570i	$-0.600500\pi$
$431$		−	353158.i		−	1.90114i	0.310512	−	0.950570i	$-0.399500\pi$
$432$	90364.2	−	133947.i	0.484205	−	0.717737i
$433$	107507.			0.573406			0.286703	−	0.958020i	$-0.407441\pi$
$433$	107507.			0.573406			0.286703	+	0.958020i	$0.407441\pi$
$434$	−3981.27	+	26635.6i	−0.0211370	+	0.141411i
$435$		−	83275.0i		−	0.440085i
$436$	41407.0	+	12661.2i	0.217821	+	0.0666044i
$437$	−56655.0			−0.296671
$438$	−49636.1	−	7419.20i	−0.258732	−	0.0386731i
$439$			365722.i			1.89767i	0.315766	+	0.948837i	$0.397739\pi$
$439$			365722.i			1.89767i	−0.315766	+	0.948837i	$0.602261\pi$
$440$	146590.	+	69930.9i	0.757180	+	0.361213i
$441$	142337.			0.731882
$442$	−8546.67	+	57179.2i	−0.0437474	+	0.292680i
$443$		−	11929.3i		−	0.0607867i	−0.999538	−	0.0303934i	$-0.990324\pi$
$443$		−	11929.3i		−	0.0607867i	0.999538	−	0.0303934i	$-0.00967600\pi$
$444$	−9077.28	+	29686.1i	−0.0460458	+	0.150587i
$445$	−114182.			−0.576602
$446$	141960.	+	21219.1i	0.713670	+	0.106674i
$447$		−	188764.i		−	0.944720i
$448$	28549.6	−	23113.2i	0.142247	−	0.115161i
$449$	−85864.7			−0.425914			−0.212957	−	0.977062i	$-0.568309\pi$
$449$	−85864.7			−0.425914			−0.212957	+	0.977062i	$0.568309\pi$
$450$	16441.0	−	109994.i	0.0811899	−	0.543179i
$451$			173381.i			0.852409i
$452$	−94738.4	−	28968.6i	−0.463713	−	0.141792i
$453$	143955.			0.701507
$454$	315940.	+	47224.1i	1.53283	+	0.229114i
$455$			20391.6i			0.0984983i
$456$	10119.9	−	21213.4i	0.0486682	−	0.102019i
$457$	−281117.			−1.34603			−0.673015	−	0.739629i	$-0.735001\pi$
$457$	−281117.			−1.34603			−0.673015	+	0.739629i	$0.735001\pi$
$458$	33208.5	−	222172.i	0.158313	−	1.05915i
$459$		−	52571.4i		−	0.249531i
$460$	41938.1	−	137153.i	0.198195	−	0.648173i
$461$	−7044.46			−0.0331471			−0.0165736	−	0.999863i	$-0.505276\pi$
$461$	−7044.46			−0.0331471			−0.0165736	+	0.999863i	$0.505276\pi$
$462$	−30467.9	−	4554.09i	−0.142744	−	0.0213362i
$463$			216166.i			1.00838i	0.863592	+	0.504192i	$0.168209\pi$
$463$			216166.i			1.00838i	−0.863592	+	0.504192i	$0.831791\pi$
$464$	304153.	+	205190.i	1.41272	+	0.953059i
$465$	−43623.4			−0.201750
$466$	42343.4	−	283287.i	0.194991	−	1.30453i
$467$			211192.i			0.968373i	0.874965	+	0.484187i	$0.160884\pi$
$467$			211192.i			0.968373i	−0.874965	+	0.484187i	$0.839116\pi$
$468$	−162856.	−	49797.2i	−0.743551	−	0.227360i
$469$	−40915.9			−0.186014
$470$	109730.	+	16401.6i	0.496741	+	0.0742488i
$471$		−	865.495i		−	0.00390142i
$472$	−17730.8	−	8458.49i	−0.0795874	−	0.0379672i
$473$	179908.			0.804133
$474$	−18080.8	+	120965.i	−0.0804752	+	0.538397i
$475$		−	37541.7i		−	0.166390i
$476$	3494.73	−	11429.1i	0.0154241	−	0.0504427i
$477$	−219670.			−0.965461
$478$	44940.1	+	6717.28i	0.196688	+	0.0293993i
$479$			318333.i			1.38743i	0.720251	+	0.693714i	$0.244027\pi$
$479$			318333.i			1.38743i	−0.720251	+	0.693714i	$0.755973\pi$
$480$	43863.5	+	40201.7i	0.190380	+	0.174487i
$481$	75925.4			0.328168
$482$	24931.1	−	166794.i	0.107312	−	0.717939i
$483$			27203.6i			0.116609i
$484$	349878.	+	106984.i	1.49357	+	0.456697i
$485$	−28500.0			−0.121161
$486$	240309.	+	35919.4i	1.01741	+	0.152075i
$487$			158377.i			0.667780i	0.942612	+	0.333890i	$0.108361\pi$
$487$			158377.i			0.667780i	−0.942612	+	0.333890i	$0.891639\pi$
$488$	−195388.	+	409576.i	−0.820463	+	1.71987i
$489$	−94567.3			−0.395479
$490$	−17980.6	+	120294.i	−0.0748881	+	0.501018i
$491$			38055.1i			0.157852i	0.996880	+	0.0789260i	$0.0251491\pi$
$491$			38055.1i			0.157852i	−0.996880	+	0.0789260i	$0.974851\pi$
$492$	−18572.8	+	60740.1i	−0.0767269	+	0.250926i
$493$	119374.			0.491151
$494$	−56854.1	−	8498.08i	−0.232974	−	0.0348230i
$495$			155658.i			0.635274i
$496$	107488.	−	159330.i	0.436915	−	0.647640i
$497$	1337.48			0.00541470
$498$	20562.6	−	137569.i	0.0829125	−	0.554704i
$499$		−	477988.i		−	1.91962i	−0.280644	−	0.959812i	$-0.590548\pi$
$499$		−	477988.i		−	1.91962i	0.280644	−	0.959812i	$-0.409452\pi$
$500$	216191.	+	66105.8i	0.864764	+	0.264423i
$501$	−93094.2			−0.370892
$502$	−29864.3	−	4463.87i	−0.118507	−	0.0177135i
$503$		−	157454.i		−	0.622327i	−0.950356	−	0.311163i	$-0.899281\pi$
$503$		−	157454.i		−	0.622327i	0.950356	−	0.311163i	$-0.100719\pi$
$504$	31774.1	+	15157.8i	0.125087	+	0.0596727i
$505$	−59185.8			−0.232078
$506$	78341.1	−	524120.i	0.305977	−	2.04706i
$507$		−	6877.17i		−	0.0267543i
$508$	13084.6	−	42791.4i	0.0507028	−	0.165817i
$509$	−85407.2			−0.329654			−0.164827	−	0.986322i	$-0.552707\pi$
$509$	−85407.2			−0.329654			−0.164827	+	0.986322i	$0.552707\pi$
$510$	19146.2	+	2861.81i	0.0736107	+	0.0110027i
$511$		−	25375.0i		−	0.0971771i
$512$	−254912.	+	61149.7i	−0.972413	+	0.233267i
$513$	52272.5			0.198627
$514$	14684.8	−	98244.7i	0.0555830	−	0.371863i
$515$			32247.1i			0.121584i
$516$	63026.8	+	19272.0i	0.236715	+	0.0723815i
$517$	409955.			1.53375
$518$	−15522.9	−	2320.24i	−0.0578515	−	0.00864717i
$519$		−	152798.i		−	0.567263i
$520$	62658.1	−	131345.i	0.231724	−	0.485743i
$521$	−181842.			−0.669915			−0.334957	−	0.942233i	$-0.608722\pi$
$521$	−181842.			−0.669915			−0.334957	+	0.942233i	$0.608722\pi$
$522$	−51981.1	+	347765.i	−0.190768	+	1.27628i
$523$			479579.i			1.75330i	0.481128	+	0.876651i	$0.340227\pi$
$523$			479579.i			1.75330i	−0.481128	+	0.876651i	$0.659773\pi$
$524$	−113775.	+	372087.i	−0.414366	+	1.35513i
$525$	−18026.1			−0.0654009
$526$	−43482.2	−	6499.37i	−0.157159	−	0.0234909i
$527$		−	62533.6i		−	0.225160i
$528$	182254.	+	122953.i	0.653745	+	0.441034i
$529$	−188126.			−0.672262
$530$	27749.7	−	185652.i	0.0987885	−	0.660917i
$531$		−	18827.6i		−	0.0667738i
$532$	11364.1	+	3474.86i	0.0401525	+	0.0122776i
$533$	155349.			0.546833
$534$	−152860.	−	22848.3i	−0.536058	−	0.0801256i
$535$		−	111447.i		−	0.389368i
$536$	263544.	+	125724.i	0.917327	+	0.437611i
$537$	−116612.			−0.404386
$538$	−73239.9	+	489992.i	−0.253037	+	1.69287i
$539$			449424.i			1.54696i
$540$	−38694.0	+	126544.i	−0.132696	+	0.433964i
$541$	−90387.3			−0.308825			−0.154413	−	0.988006i	$-0.549349\pi$
$541$	−90387.3			−0.308825			−0.154413	+	0.988006i	$0.549349\pi$
$542$	−152139.	−	22740.5i	−0.517895	−	0.0774107i
$543$			108181.i			0.366902i
$544$	−57628.6	+	62877.8i	−0.194733	+	0.212471i
$545$	−35461.0			−0.119387
$546$	−4080.46	+	27299.2i	−0.0136875	+	0.0915725i
$547$		−	106106.i		−	0.354622i	−0.984155	−	0.177311i	$-0.943260\pi$
$547$		−	106106.i		−	0.354622i	0.984155	−	0.177311i	$-0.0567398\pi$
$548$	−374760.	−	114592.i	−1.24793	−	0.381587i
$549$	−434912.			−1.44297
$550$	347301.	+	51911.7i	1.14810	+	0.171609i
$551$			118695.i			0.390957i
$552$	83589.6	−	175222.i	0.274331	−	0.575056i
$553$	−61839.7			−0.202217
$554$	37522.7	−	251035.i	0.122257	−	0.817929i
$555$		−	25423.2i		−	0.0825362i
$556$	−143049.	+	467826.i	−0.462740	+	1.51333i
$557$	−566621.			−1.82634			−0.913171	−	0.407576i	$-0.866374\pi$
$557$	−566621.			−1.82634			−0.913171	+	0.407576i	$0.866374\pi$
$558$	182176.	+	27230.2i	0.585090	+	0.0874544i
$559$		−	161198.i		−	0.515863i
$560$	−16824.3	+	24938.6i	−0.0536489	+	0.0795237i
$561$	71530.7			0.227283
$562$	29043.7	−	194309.i	0.0919560	−	0.615206i
$563$			568120.i			1.79235i	0.443698	+	0.896176i	$0.353666\pi$
$563$			568120.i			1.79235i	−0.443698	+	0.896176i	$0.646334\pi$
$564$	143619.	+	43915.1i	0.451495	+	0.138056i
$565$	81134.0			0.254159
$566$	281496.	+	42075.8i	0.878699	+	0.131341i
$567$			19456.3i			0.0605192i
$568$	−8614.86	−	4109.72i	−0.0267025	−	0.0127384i
$569$	−86245.2			−0.266386			−0.133193	−	0.991090i	$-0.542523\pi$
$569$	−86245.2			−0.266386			−0.133193	+	0.991090i	$0.542523\pi$
$570$	−2845.54	+	19037.3i	−0.00875820	+	0.0585943i
$571$			75126.1i			0.230419i	0.993341	+	0.115210i	$0.0367540\pi$
$571$			75126.1i			0.230419i	−0.993341	+	0.115210i	$0.963246\pi$
$572$	157233.	−	514211.i	0.480564	−	1.57162i
$573$	92778.2			0.282577
$574$	−31761.2	−	4747.40i	−0.0963990	−	0.0144089i
$575$		−	310092.i		−	0.937898i
$576$	−158084.	−	195267.i	−0.476479	−	0.588550i
$577$	489075.			1.46901			0.734504	−	0.678604i	$-0.237415\pi$
$577$	489075.			1.46901			0.734504	+	0.678604i	$0.237415\pi$
$578$	45285.1	−	302968.i	0.135550	−	0.906861i
$579$		−	246419.i		−	0.735050i
$580$	−287343.	−	87862.4i	−0.854171	−	0.261184i
$581$	70327.9			0.208341
$582$	−38154.3	−	5703.00i	−0.112641	−	0.0168367i
$583$		−	693601.i		−	2.04067i
$584$	−77970.6	+	163443.i	−0.228615	+	0.479227i
$585$	139470.			0.407538
$586$	−1667.34	+	11154.9i	−0.00485544	+	0.0324840i
$587$		−	562634.i		−	1.63286i	−0.577442	−	0.816432i	$-0.695949\pi$
$587$		−	562634.i		−	1.63286i	0.577442	−	0.816432i	$-0.304051\pi$
$588$	−48143.0	+	157446.i	−0.139245	+	0.455383i
$589$	62178.0			0.179228
$590$	15911.9	+	2378.38i	0.0457108	+	0.00683247i
$591$			222648.i			0.637447i
$592$	92855.6	+	62642.9i	0.264951	+	0.178743i
$593$	−354885.			−1.00920			−0.504602	−	0.863352i	$-0.668361\pi$
$593$	−354885.			−1.00920			−0.504602	+	0.863352i	$0.668361\pi$
$594$	−72281.1	+	483577.i	−0.204857	+	1.37054i
$595$			9787.89i			0.0276475i
$596$	−651335.	−	199162.i	−1.83363	−	0.560679i
$597$	21922.6			0.0615097
$598$	−469612.	−	70193.7i	−1.31322	−	0.196289i
$599$		−	214683.i		−	0.598333i	−0.954201	−	0.299167i	$-0.903291\pi$
$599$		−	214683.i		−	0.598333i	0.954201	−	0.299167i	$-0.0967087\pi$
$600$	116108.	+	55389.6i	0.322523	+	0.153860i
$601$	79153.3			0.219139			0.109570	−	0.993979i	$-0.465053\pi$
$601$	79153.3			0.219139			0.109570	+	0.993979i	$0.465053\pi$
$602$	−4926.12	+	32956.8i	−0.0135929	+	0.0909395i
$603$			279847.i			0.769637i
$604$	151886.	−	496723.i	0.416335	−	1.36157i
$605$	−299636.			−0.818622
$606$	−79234.8	−	11843.4i	−0.215760	−	0.0322500i
$607$		−	483102.i		−	1.31118i	−0.755118	−	0.655589i	$-0.772420\pi$
$607$		−	483102.i		−	1.31118i	0.755118	−	0.655589i	$-0.227580\pi$
$608$	−62520.3	−	57301.0i	−0.169127	−	0.155008i
$609$	56992.9			0.153669
$610$	54939.9	−	367560.i	0.147648	−	0.987800i
$611$		−	367320.i		−	0.983926i
$612$	−78170.0	−	23902.5i	−0.208707	−	0.0638175i
$613$	199537.			0.531010			0.265505	−	0.964109i	$-0.414461\pi$
$613$	199537.			0.531010			0.265505	+	0.964109i	$0.414461\pi$
$614$	637126.	+	95232.3i	1.69001	+	0.252608i
$615$		−	52017.9i		−	0.137532i
$616$	−47860.3	+	100325.i	−0.126129	+	0.264393i
$617$	121881.			0.320159			0.160079	−	0.987104i	$-0.448825\pi$
$617$	121881.			0.320159			0.160079	+	0.987104i	$0.448825\pi$
$618$	−6452.80	+	43170.7i	−0.0168955	+	0.113035i
$619$		−	133551.i		−	0.348550i	−0.984697	−	0.174275i	$-0.944242\pi$
$619$		−	133551.i		−	0.348550i	0.984697	−	0.174275i	$-0.0557582\pi$
$620$	−46026.5	+	150524.i	−0.119736	+	0.391581i
$621$	431768.			1.11961
$622$	−547673.	−	81861.7i	−1.41560	−	0.211592i
$623$		−	78145.2i		−	0.201338i
$624$	110166.	−	163299.i	0.282930	−	0.419387i
$625$	98164.8			0.251302
$626$	−15749.1	+	105365.i	−0.0401889	+	0.268873i
$627$			71124.0i			0.180918i
$628$	−2986.42	−	913.172i	−0.00757236	−	0.00231544i
$629$	36443.9			0.0921135
$630$	−28514.6	−	4262.13i	−0.0718432	−	0.0107385i
$631$			559153.i			1.40434i	0.712010	+	0.702169i	$0.247785\pi$
$631$			559153.i			1.40434i	−0.712010	+	0.702169i	$0.752215\pi$
$632$	398316.	+	190017.i	0.997227	+	0.475728i
$633$	300669.			0.750380
$634$	26781.0	−	179171.i	0.0666267	−	0.445748i
$635$			36646.6i			0.0908838i
$636$	74299.6	−	242988.i	0.183685	−	0.600718i
$637$	402684.			0.992398
$638$	−1.09806e6	−	164128.i	−2.69764	−	0.403220i
$639$		−	9147.77i		−	0.0224034i
$640$	184997.	−	108936.i	0.451653	−	0.265957i
$641$	523535.			1.27418			0.637089	−	0.770791i	$-0.280139\pi$
$641$	523535.			1.27418			0.637089	+	0.770791i	$0.280139\pi$
$642$	22301.1	−	149199.i	0.0541073	−	0.361990i
$643$			508744.i			1.23049i	0.788337	+	0.615244i	$0.210943\pi$
$643$			508744.i			1.23049i	−0.788337	+	0.615244i	$0.789057\pi$
$644$	93867.0	+	28702.2i	0.226330	+	0.0692060i
$645$	−53976.2			−0.129743
$646$	−27289.7	−	4079.04i	−0.0653934	−	0.00977447i
$647$			303404.i			0.724792i	0.932024	+	0.362396i	$0.118041\pi$
$647$			303404.i			0.724792i	−0.932024	+	0.362396i	$0.881959\pi$
$648$	59784.0	−	125320.i	0.142375	−	0.298449i
$649$	59447.5			0.141138
$650$	46512.9	−	311182.i	0.110090	−	0.736526i
$651$		−	29855.6i		−	0.0704472i
$652$	−99776.8	+	326308.i	−0.234711	+	0.767595i
$653$	479003.			1.12334			0.561671	−	0.827361i	$-0.310159\pi$
$653$	479003.			1.12334			0.561671	+	0.827361i	$0.310159\pi$
$654$	−47473.3	−	7095.92i	−0.110993	−	0.0165903i
$655$		−	318656.i		−	0.742745i
$656$	189990.	+	128172.i	0.441492	+	0.297842i
$657$	−173554.			−0.402071
$658$	−11225.1	+	75098.6i	−0.0259262	+	0.173452i
$659$			28254.6i			0.0650606i	0.999471	+	0.0325303i	$0.0103565\pi$
$659$			28254.6i			0.0650606i	−0.999471	+	0.0325303i	$0.989643\pi$
$660$	−172181.	−	52648.6i	−0.395273	−	0.120865i
$661$	546615.			1.25106			0.625530	−	0.780200i	$-0.284883\pi$
$661$	546615.			1.25106			0.625530	+	0.780200i	$0.284883\pi$
$662$	4496.26	+	672.065i	0.0102597	+	0.00153354i
$663$		−	64091.5i		−	0.145805i
$664$	−452990.	−	216099.i	−1.02743	−	0.490136i
$665$	−9732.24			−0.0220074
$666$	−15869.4	+	106170.i	−0.0357778	+	0.239361i
$667$			980414.i			2.20373i
$668$	−98222.5	+	321225.i	−0.220119	+	0.719873i
$669$	−159122.			−0.355531
$670$	−236509.	−	35351.5i	−0.526864	−	0.0787513i
$671$		−	1.37322e6i		−	3.04996i
$672$	−27513.8	+	30019.9i	−0.0609273	+	0.0664769i
$673$	146970.			0.324489			0.162244	−	0.986751i	$-0.448127\pi$
$673$	146970.			0.324489			0.162244	+	0.986751i	$0.448127\pi$
$674$	−74719.3	+	499889.i	−0.164480	+	1.10041i
$675$			286105.i			0.627941i
$676$	−23729.9	−	7256.02i	−0.0519281	−	0.0158783i
$677$	−636186.			−1.38806			−0.694028	−	0.719948i	$-0.744166\pi$
$677$	−636186.			−1.38806			−0.694028	+	0.719948i	$0.744166\pi$
$678$	108618.	+	16235.3i	0.236288	+	0.0353184i
$679$		−	19505.2i		−	0.0423070i
$680$	30075.6	−	63045.0i	0.0650425	−	0.136343i
$681$	−354134.			−0.763613
$682$	−85978.2	+	575214.i	−0.184850	+	1.23669i
$683$			471150.i			1.00999i	0.863122	+	0.504996i	$0.168506\pi$
$683$			471150.i			1.00999i	−0.863122	+	0.504996i	$0.831494\pi$
$684$	23766.5	−	77725.6i	0.0507989	−	0.166131i
$685$	320945.			0.683989
$686$	−167511.	−	25038.2i	−0.355955	−	0.0532052i
$687$			249030.i			0.527641i
$688$	132997.	−	197142.i	0.280974	−	0.416488i
$689$	−621467.			−1.30912
$690$	−23504.0	+	157247.i	−0.0493678	+	0.330282i
$691$		−	727652.i		−	1.52394i	−0.647613	−	0.761970i	$-0.724233\pi$
$691$		−	727652.i		−	1.52394i	0.647613	−	0.761970i	$-0.275767\pi$
$692$	−527236.	−	161216.i	−1.10101	−	0.336663i
$693$	−106531.			−0.221826
$694$	649988.	+	97154.8i	1.34954	+	0.201718i
$695$		−	400646.i		−	0.829453i
$696$	−367098.	−	175124.i	−0.757816	−	0.361516i
$697$	74567.0			0.153490
$698$	33907.6	−	226849.i	0.0695962	−	0.465614i
$699$			317534.i			0.649883i
$700$	−19019.1	+	62199.8i	−0.0388146	+	0.126938i
$701$	610269.			1.24190			0.620948	−	0.783852i	$-0.286748\pi$
$701$	610269.			1.24190			0.620948	+	0.783852i	$0.286748\pi$
$702$	433285.	+	64763.9i	0.879224	+	0.131419i
$703$			36236.7i			0.0733226i
$704$	616547.	−	499146.i	1.24400	−	1.00712i
$705$	−122995.			−0.247463
$706$	−135508.	+	906576.i	−0.271866	+	1.81884i
$707$		−	40506.4i		−	0.0810373i
$708$	20826.1	+	6368.11i	0.0415472	+	0.0127041i
$709$	31766.6			0.0631943			0.0315972	−	0.999501i	$-0.489941\pi$
$709$	31766.6			0.0631943			0.0315972	+	0.999501i	$0.489941\pi$
$710$	7731.12	+	1155.58i	0.0153365	+	0.00229237i
$711$			422956.i			0.836674i
$712$	−240120.	+	503342.i	−0.473661	+	0.992896i
$713$	513587.			1.01026
$714$	−1958.61	+	13103.5i	−0.00384194	+	0.0257035i
$715$			440370.i			0.861402i
$716$	−123036.	+	402375.i	−0.239998	+	0.784883i
$717$	−50372.9			−0.0979848
$718$	−555926.	−	83095.2i	−1.07837	−	0.161186i
$719$			63172.8i			0.122200i	0.998132	+	0.0611001i	$0.0194609\pi$
$719$			63172.8i			0.122200i	−0.998132	+	0.0611001i	$0.980539\pi$
$720$	170569.	+	115071.i	0.329030	+	0.221973i
$721$	−22069.7			−0.0424547
$722$	4055.85	−	27134.6i	0.00778050	−	0.0520533i
$723$			186958.i			0.357658i
$724$	373281.	+	114140.i	0.712130	+	0.217752i
$725$	−649659.			−1.23597
$726$	−401137.	−	59958.6i	−0.761061	−	0.113757i
$727$		−	259499.i		−	0.490984i	−0.969399	−	0.245492i	$-0.921050\pi$
$727$		−	259499.i		−	0.490984i	0.969399	−	0.245492i	$-0.0789496\pi$
$728$	89891.6	+	42882.8i	0.169612	+	0.0809134i
$729$	−93628.2			−0.176178
$730$	21924.0	−	146677.i	0.0411410	−	0.275242i
$731$		−	77374.2i		−	0.144798i
$732$	147101.	−	481077.i	0.274533	−	0.897826i
$733$	−176670.			−0.328817			−0.164409	−	0.986392i	$-0.552572\pi$
$733$	−176670.			−0.328817			−0.164409	+	0.986392i	$0.552572\pi$
$734$	717261.	+	107210.i	1.33133	+	0.198996i
$735$		−	134837.i		−	0.249594i
$736$	−516414.	−	473303.i	−0.953328	−	0.873743i
$737$	−883607.			−1.62676
$738$	−32470.1	+	217232.i	−0.0596171	+	0.398852i
$739$			309358.i			0.566465i	0.959051	+	0.283232i	$0.0914068\pi$
$739$			309358.i			0.566465i	−0.959051	+	0.283232i	$0.908593\pi$
$740$	−87723.7	−	26823.7i	−0.160197	−	0.0489841i
$741$	63727.1			0.116061
$742$	127059.	+	18991.7i	0.230780	+	0.0344950i
$743$			173374.i			0.314055i	0.987594	+	0.157028i	$0.0501911\pi$
$743$			173374.i			0.314055i	−0.987594	+	0.157028i	$0.949809\pi$
$744$	−91738.4	+	192303.i	−0.165732	+	0.347409i
$745$	557804.			1.00501
$746$	−107490.	+	719132.i	−0.193148	+	1.29220i
$747$		−	481012.i		−	0.862014i
$748$	75471.1	−	246819.i	0.134889	−	0.441139i
$749$	76273.7			0.135960
$750$	−247864.	−	37048.7i	−0.440647	−	0.0658643i
$751$			357686.i			0.634194i	0.948393	+	0.317097i	$0.102708\pi$
$751$			357686.i			0.634194i	−0.948393	+	0.317097i	$0.897292\pi$
$752$	303061.	−	449227.i	0.535913	−	0.794384i
$753$	33474.6			0.0590372
$754$	−147059.	+	983859.i	−0.258672	+	1.73057i
$755$			425394.i			0.746273i
$756$	−86606.0	−	26482.0i	−0.151532	−	0.0463347i
$757$	423414.			0.738880			0.369440	−	0.929255i	$-0.379550\pi$
$757$	423414.			0.738880			0.369440	+	0.929255i	$0.379550\pi$
$758$	598515.	+	89461.1i	1.04169	+	0.155703i
$759$			587481.i			1.01979i
$760$	62686.5	+	29904.6i	0.108529	+	0.0517739i
$761$	660959.			1.14131			0.570657	−	0.821189i	$-0.306689\pi$
$761$	660959.			1.14131			0.570657	+	0.821189i	$0.306689\pi$
$762$	−7333.17	+	49060.6i	−0.0126294	+	0.0844934i
$763$		−	24269.3i		−	0.0416877i
$764$	97889.0	−	320134.i	0.167706	−	0.548460i
$765$	66944.9			0.114392
$766$	596895.	+	89218.9i	1.01728	+	0.152055i
$767$		−	53265.0i		−	0.0905422i
$768$	269463.	−	108819.i	0.456853	−	0.184494i
$769$	−557564.			−0.942849			−0.471424	−	0.881906i	$-0.656260\pi$
$769$	−557564.			−0.942849			−0.471424	+	0.881906i	$0.656260\pi$
$770$	13457.5	−	90033.8i	0.0226978	−	0.151853i
$771$			110121.i			0.185252i
$772$	−850277.	−	259993.i	−1.42668	−	0.436242i
$773$	159973.			0.267725			0.133862	−	0.991000i	$-0.457262\pi$
$773$	159973.			0.267725			0.133862	+	0.991000i	$0.457262\pi$
$774$	225410.	+	33692.5i	0.376263	+	0.0562408i
$775$			340322.i			0.566613i
$776$	−59934.5	+	125636.i	−0.0995299	+	0.208636i
$777$	17399.5			0.0288201
$778$	844.457	−	5649.61i	0.00139514	−	0.00933381i
$779$			74143.1i			0.122179i
$780$	−47173.2	+	154274.i	−0.0775364	+	0.253573i
$781$	28883.7			0.0473534
$782$	−225412.	−	33692.7i	−0.368606	−	0.0550963i
$783$		−	904575.i		−	1.47544i
$784$	492477.	+	332238.i	0.801224	+	0.540527i
$785$	2557.57			0.00415038
$786$	63764.6	−	426600.i	0.103213	−	0.690519i
$787$		−	536068.i		−	0.865506i	−0.901512	−	0.432753i	$-0.857542\pi$
$787$		−	536068.i		−	0.865506i	0.901512	−	0.432753i	$-0.142458\pi$
$788$	768254.	+	234913.i	1.23724	+	0.378316i
$789$	48738.8			0.0782926
$790$	−357456.	−	53429.6i	−0.572755	−	0.0856106i
$791$			55527.7i			0.0887476i
$792$	686182.	+	327343.i	1.09393	+	0.521859i
$793$	−1.23040e6			−1.95660
$794$	123450.	−	825909.i	0.195817	−	1.31006i
$795$			208095.i			0.329251i
$796$	23130.3	−	75644.7i	0.0365052	−	0.119386i
$797$	169520.			0.266873			0.133437	−	0.991057i	$-0.457399\pi$
$797$	169520.			0.266873			0.133437	+	0.991057i	$0.457399\pi$
$798$	−13029.0	−	1947.47i	−0.0204600	−	0.00305819i
$799$		−	176312.i		−	0.276178i
$800$	313628.	−	342195.i	0.490044	−	0.534680i
$801$	−534479.			−0.833039
$802$	−140291.	+	938581.i	−0.218113	+	1.45923i
$803$		−	547989.i		−	0.849848i
$804$	−309552.	−	94653.3i	−0.478874	−	0.146428i
$805$	−80387.8			−0.124050
$806$	515392.	+	77036.5i	0.793355	+	0.118584i
$807$		−	549226.i		−	0.843343i
$808$	−124466.	+	260906.i	−0.190645	+	0.399634i
$809$	−951147.			−1.45328			−0.726642	−	0.687016i	$-0.758920\pi$
$809$	−951147.			−1.45328			−0.726642	+	0.687016i	$0.758920\pi$
$810$	−16810.3	+	112464.i	−0.0256215	+	0.171414i
$811$		−	418188.i		−	0.635814i	−0.948122	−	0.317907i	$-0.897020\pi$
$811$		−	418188.i		−	0.635814i	0.948122	−	0.317907i	$-0.102980\pi$
$812$	60132.5	−	196656.i	0.0912005	−	0.298260i
$813$	170531.			0.258002
$814$	−335228.	−	50107.2i	−0.505932	−	0.0756225i
$815$		−	279450.i		−	0.420716i
$816$	52879.3	−	78383.0i	0.0794155	−	0.117718i
$817$	76934.2			0.115259
$818$	186842.	−	1.25001e6i	0.279233	−	1.86813i
$819$			95452.2i			0.142304i
$820$	−179490.	−	54883.4i	−0.266939	−	0.0816232i
$821$	−754344.			−1.11914			−0.559568	−	0.828784i	$-0.689033\pi$
$821$	−754344.			−1.11914			−0.559568	+	0.828784i	$0.689033\pi$
$822$	429664.	+	64222.6i	0.635894	+	0.0950483i
$823$		−	520834.i		−	0.768953i	−0.923135	−	0.384477i	$-0.874382\pi$
$823$		−	520834.i		−	0.768953i	0.923135	−	0.384477i	$-0.125618\pi$
$824$	142154.	+	67814.4i	0.209365	+	0.0998774i
$825$	−389286.			−0.571954
$826$	−1627.75	+	10890.0i	−0.00238577	+	0.0159613i
$827$			633719.i			0.926585i	0.886205	+	0.463293i	$0.153332\pi$
$827$			633719.i			0.926585i	−0.886205	+	0.463293i	$0.846668\pi$
$828$	196310.	−	642009.i	0.286341	−	0.936441i
$829$	68381.2			0.0995011			0.0497505	−	0.998762i	$-0.484157\pi$
$829$	68381.2			0.0995011			0.0497505	+	0.998762i	$0.484157\pi$
$830$	406521.	+	60763.4i	0.590102	+	0.0882035i
$831$			281383.i			0.407470i
$832$	−447235.	−	552427.i	−0.646084	−	0.798046i
$833$	193287.			0.278556
$834$	80171.3	−	536364.i	0.115262	−	0.771130i
$835$		−	275097.i		−	0.394560i
$836$	245416.	+	75042.0i	0.351148	+	0.107372i
$837$	−473859.			−0.676391
$838$	−923062.	−	137972.i	−1.31445	−	0.196473i
$839$		−	57238.5i		−	0.0813139i	−0.999173	−	0.0406569i	$-0.987055\pi$
$839$		−	57238.5i		−	0.0813139i	0.999173	−	0.0406569i	$-0.0129451\pi$
$840$	14359.1	−	30099.7i	0.0203502	−	0.0426584i
$841$	1.34673e6			1.90410
$842$	96315.7	−	644373.i	0.135854	−	0.908895i
$843$			217799.i			0.306479i
$844$	317232.	−	1.03747e6i	0.445341	−	1.45643i
$845$	20322.3			0.0284616
$846$	513642.	+	76774.9i	0.717661	+	0.107270i
$847$		−	205069.i		−	0.285847i
$848$	−760045.	−	512747.i	−1.05693	−	0.713036i
$849$	−315526.			−0.437744
$850$	22326.0	−	149366.i	0.0309011	−	0.206735i
$851$			299313.i			0.413301i
$852$	10118.8	+	3094.07i	0.0139396	+	0.00426237i
$853$	−158388.			−0.217684			−0.108842	−	0.994059i	$-0.534714\pi$
$853$	−158388.			−0.217684			−0.108842	+	0.994059i	$0.534714\pi$
$854$	251556.	+	37600.5i	0.344921	+	0.0515559i
$855$			66564.3i			0.0910561i
$856$	−491288.	−	234369.i	−0.670484	−	0.319855i
$857$	958773.			1.30543			0.652716	−	0.757603i	$-0.273630\pi$
$857$	958773.			1.30543			0.652716	+	0.757603i	$0.273630\pi$
$858$	−88120.3	+	589545.i	−0.119702	+	0.800833i
$859$			1.28765e6i			1.74507i	0.488555	+	0.872533i	$0.337524\pi$
$859$			1.28765e6i			1.74507i	−0.488555	+	0.872533i	$0.662476\pi$
$860$	−56949.6	+	186247.i	−0.0770005	+	0.251821i
$861$	35600.8			0.0480234
$862$	1.39711e6	+	208828.i	1.88025	+	0.281044i
$863$		−	1.04487e6i		−	1.40295i	−0.712696	−	0.701473i	$-0.752526\pi$
$863$		−	1.04487e6i		−	1.40295i	0.712696	−	0.701473i	$-0.247474\pi$
$864$	476467.	+	436691.i	0.638272	+	0.584988i
$865$	451526.			0.603462
$866$	−63571.0	+	425304.i	−0.0847663	+	0.567106i
$867$			339593.i			0.451774i
$868$	−103018.	−	31500.2i	−0.136733	−	0.0418094i
$869$	−1.33547e6			−1.76846
$870$	329440.	+	49242.0i	0.435249	+	0.0650575i
$871$			791712.i			1.04359i
$872$	−74573.1	+	156321.i	−0.0980730	+	0.205582i
$873$	−133407.			−0.175046
$874$	33501.1	−	224130.i	0.0438568	−	0.293412i
$875$		−	126713.i		−	0.165503i
$876$	58701.5	−	191976.i	0.0764964	−	0.250172i
$877$	−1.30314e6			−1.69431			−0.847156	−	0.531344i	$-0.821687\pi$
$877$	−1.30314e6			−1.69431			−0.847156	+	0.531344i	$0.821687\pi$
$878$	−1.44681e6	−	216258.i	−1.87682	−	0.280532i
$879$		−	12503.4i		−	0.0161826i
$880$	−363331.	+	538567.i	−0.469178	+	0.695463i
$881$	−1.09260e6			−1.40769			−0.703846	−	0.710353i	$-0.748535\pi$
$881$	−1.09260e6			−1.40769			−0.703846	+	0.710353i	$0.748535\pi$
$882$	−84166.5	+	563093.i	−0.108194	+	0.723841i
$883$		−	941564.i		−	1.20761i	−0.797130	−	0.603807i	$-0.793650\pi$
$883$		−	941564.i		−	1.20761i	0.797130	−	0.603807i	$-0.206350\pi$
$884$	−221150.	−	67622.1i	−0.282997	−	0.0865335i
$885$	−17835.5			−0.0227719
$886$	47193.0	+	7054.03i	0.0601188	+	0.00898607i
$887$			1.09323e6i			1.38952i	0.719242	+	0.694759i	$0.244489\pi$
$887$			1.09323e6i			1.38952i	−0.719242	+	0.694759i	$0.755511\pi$
$888$	−112072.	−	53464.1i	−0.142126	−	0.0678011i
$889$	−25080.7			−0.0317349
$890$	67517.6	−	451708.i	0.0852388	−	0.570267i
$891$			420171.i			0.529262i
$892$	−167888.	+	549055.i	−0.211003	+	0.690059i
$893$	175310.			0.219838
$894$	746759.	+	111619.i	0.934341	+	0.139658i
$895$		−	344595.i		−	0.430192i
$896$	74555.3	+	126611.i	0.0928672	+	0.157709i
$897$	526383.			0.654209
$898$	50773.4	−	339685.i	0.0629627	−	0.421235i
$899$		−	1.07599e6i		−	1.33134i
$900$	425419.	+	130083.i	0.525209	+	0.160596i
$901$	−298302.			−0.367457
$902$	−685903.	−	102523.i	−0.843043	−	0.126011i
$903$		−	36941.0i		−	0.0453036i
$904$	170622.	−	357660.i	0.208784	−	0.437657i
$905$	−319678.			−0.390316
$906$	−85123.5	+	569495.i	−0.103703	+	0.693799i
$907$			543026.i			0.660095i	0.943964	+	0.330047i	$0.107065\pi$
$907$			543026.i			0.660095i	−0.943964	+	0.330047i	$0.892935\pi$
$908$	−373642.	+	1.22195e6i	−0.453194	+	1.48211i
$909$	−277046.			−0.335293
$910$	−80670.3	−	12057.9i	−0.0974161	−	0.0145610i
$911$		−	1.63167e6i		−	1.96606i	−0.183454	−	0.983028i	$-0.558728\pi$
$911$		−	1.63167e6i		−	1.96606i	0.183454	−	0.983028i	$-0.441272\pi$
$912$	77937.3	+	52578.6i	0.0937035	+	0.0632149i
$913$	1.51878e6			1.82202
$914$	166229.	−	1.11211e6i	0.198983	−	1.33124i
$915$			411995.i			0.492095i
$916$	859287.	+	262749.i	1.02411	+	0.313148i
$917$	218086.			0.259352
$918$	207975.	+	31086.4i	0.246789	+	0.0368880i
$919$			327137.i			0.387346i	0.981066	+	0.193673i	$0.0620401\pi$
$919$			327137.i			0.387346i	−0.981066	+	0.193673i	$0.937960\pi$
$920$	517787.	+	247011.i	0.611753	+	0.291837i
$921$	−714148.			−0.841916
$922$	4165.52	−	27868.3i	0.00490013	−	0.0327829i
$923$		−	25879.8i		−	0.0303779i
$924$	36032.4	−	117840.i	0.0422036	−	0.138022i
$925$	−198336.			−0.231802
$926$	−855164.	−	127823.i	−0.997304	−	0.149069i
$927$			150947.i			0.175657i
$928$	−991593.	+	1.08191e6i	−1.15143	+	1.25631i
$929$	−16017.8			−0.0185598			−0.00927988	−	0.999957i	$-0.502954\pi$
$929$	−16017.8			−0.0185598			−0.00927988	+	0.999957i	$0.502954\pi$
$930$	25795.3	−	172576.i	0.0298246	−	0.199533i
$931$			192188.i			0.221731i
$932$	1.09566e6	+	335026.i	1.26137	+	0.385697i
$933$	613881.			0.705214
$934$	−835485.	−	124881.i	−0.957733	−	0.143154i
$935$			211376.i			0.241787i
$936$	293300.	−	614819.i	0.334780	−	0.701771i
$937$	753326.			0.858032			0.429016	−	0.903297i	$-0.358860\pi$
$937$	753326.			0.858032			0.429016	+	0.903297i	$0.358860\pi$
$938$	24194.3	−	161866.i	0.0274984	−	0.183971i
$939$		−	118102.i		−	0.133945i
$940$	−129771.	+	424399.i	−0.146866	+	0.480307i
$941$	−433839.			−0.489947			−0.244974	−	0.969530i	$-0.578779\pi$
$941$	−433839.			−0.489947			−0.244974	+	0.969530i	$0.578779\pi$
$942$	3423.94	+	511.783i	0.00385855	+	0.000576745i
$943$			612418.i			0.688691i
$944$	43946.7	−	65142.3i	0.0493154	−	0.0731003i
$945$	74169.5			0.0830542
$946$	−106383.	+	711725.i	−0.118875	+	0.795298i
$947$		−	495248.i		−	0.552233i	−0.961124	−	0.276117i	$-0.910952\pi$
$947$		−	495248.i		−	0.552233i	0.961124	−	0.276117i	$-0.0890476\pi$
$948$	−467852.	−	143057.i	−0.520585	−	0.159182i
$949$	−490999.			−0.545190
$950$	148517.	+	22199.1i	0.164562	+	0.0245973i
$951$			200831.i			0.222060i
$952$	43147.6	+	20583.6i	0.0476083	+	0.0227116i
$953$	655146.			0.721360			0.360680	−	0.932690i	$-0.382545\pi$
$953$	655146.			0.721360			0.360680	+	0.932690i	$0.382545\pi$
$954$	129895.	−	869027.i	0.142724	−	0.954853i
$955$			274163.i			0.300609i
$956$	−53147.8	+	173813.i	−0.0581526	+	0.190181i
$957$	1.23080e6			1.34389
$958$	−1.25934e6	−	188236.i	−1.37218	−	0.205103i
$959$			219653.i			0.238836i
$960$	−184977.	+	149754.i	−0.200713	+	0.162494i
$961$	359867.			0.389668
$962$	−44896.0	+	300365.i	−0.0485130	+	0.324563i
$963$		−	521678.i		−	0.562536i
$964$	645105.	+	197257.i	0.694187	+	0.212265i
$965$	728178.			0.781957
$966$	−107619.	−	16086.0i	−0.115328	−	0.0172383i
$967$		−	300375.i		−	0.321226i	−0.987017	−	0.160613i	$-0.948653\pi$
$967$		−	300375.i		−	0.321226i	0.987017	−	0.160613i	$-0.0513471\pi$
$968$	−630124.	+	1.32087e6i	−0.672473	+	1.40965i
$969$	30588.8			0.0325772
$970$	16852.6	−	112748.i	0.0179111	−	0.119829i
$971$			994951.i			1.05527i	0.849471	+	0.527635i	$0.176921\pi$
$971$			994951.i			1.05527i	−0.849471	+	0.527635i	$0.823079\pi$
$972$	−284198.	+	929435.i	−0.300807	+	0.983754i
$973$	274200.			0.289629
$974$	−626547.	−	93651.1i	−0.660443	−	0.0987177i
$975$			348801.i			0.366917i
$976$	−1.50477e6	−	1.01516e6i	−1.57968	−	1.06570i
$977$	1.39627e6			1.46278			0.731391	−	0.681959i	$-0.238872\pi$
$977$	1.39627e6			1.46278			0.731391	+	0.681959i	$0.238872\pi$
$978$	55919.4	−	374113.i	0.0584635	−	0.391134i
$979$		−	1.68760e6i		−	1.76077i
$980$	−465259.	−	142265.i	−0.484443	−	0.148131i
$981$	−165991.			−0.172483
$982$	−150548.	−	22502.7i	−0.156118	−	0.0233352i
$983$			1.17073e6i			1.21157i	0.795629	+	0.605784i	$0.207141\pi$
$983$			1.17073e6i			1.21157i	−0.795629	+	0.605784i	$0.792859\pi$
$984$	−229309.	−	109392.i	−0.236826	−	0.112978i
$985$	−657934.			−0.678125
$986$	−70587.8	+	472248.i	−0.0726066	+	0.485754i
$987$		−	84177.3i		−	0.0864093i
$988$	67237.7	−	219892.i	0.0688809	−	0.225266i
$989$	635473.			0.649687
$990$	−615791.	−	92043.4i	−0.628294	−	0.0939123i
$991$		−	28788.9i		−	0.0293142i	−0.999893	−	0.0146571i	$-0.995334\pi$
$991$		−	28788.9i		−	0.0293142i	0.999893	−	0.0146571i	$-0.00466567\pi$
$992$	566757.	+	519443.i	0.575935	+	0.527855i
$993$	−5039.82			−0.00511112
$994$	−790.876	+	5291.14i	−0.000800452	+	0.00535521i
$995$			64782.2i			0.0654349i
$996$	532070.	+	162694.i	0.536352	+	0.164003i
$997$	954503.			0.960256			0.480128	−	0.877198i	$-0.340590\pi$
$997$	954503.			0.960256			0.480128	+	0.877198i	$0.340590\pi$
$998$	1.89095e6	+	282643.i	1.89853	+	0.283777i
$999$		−	276160.i		−	0.276713i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.5.b.a.39.18	yes	36
4.3	odd	2	inner	76.5.b.a.39.17	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.5.b.a.39.17	✓	36	4.3	odd	2	inner
76.5.b.a.39.18	yes	36	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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	76.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.591318 + 3.95605i) q^{2} -4.43430i q^{3} +(-15.3007 - 4.67857i) q^{4} +13.1035 q^{5} +(17.5423 + 2.62208i) q^{6} +8.96798i q^{7} +(27.5562 - 57.7638i) q^{8} +61.3370 q^{9} +O(q^{10})\)	\(q+(-0.591318 + 3.95605i) q^{2} -4.43430i q^{3} +(-15.3007 - 4.67857i) q^{4} +13.1035 q^{5} +(17.5423 + 2.62208i) q^{6} +8.96798i q^{7} +(27.5562 - 57.7638i) q^{8} +61.3370 q^{9} +(-7.74835 + 51.8382i) q^{10} +193.669i q^{11} +(-20.7462 + 67.8478i) q^{12} +173.528 q^{13} +(-35.4778 - 5.30293i) q^{14} -58.1049i q^{15} +(212.222 + 143.171i) q^{16} +83.2927 q^{17} +(-36.2697 + 242.652i) q^{18} +82.8191i q^{19} +(-200.493 - 61.3057i) q^{20} +39.7667 q^{21} +(-766.166 - 114.520i) q^{22} +684.081i q^{23} +(-256.142 - 122.193i) q^{24} -453.298 q^{25} +(-102.610 + 686.485i) q^{26} -631.165i q^{27} +(41.9573 - 137.216i) q^{28} +1433.18 q^{29} +(229.866 + 34.3585i) q^{30} -750.769i q^{31} +(-691.881 + 754.902i) q^{32} +858.787 q^{33} +(-49.2525 + 329.510i) q^{34} +117.512i q^{35} +(-938.498 - 286.969i) q^{36} +437.540 q^{37} +(-327.637 - 48.9724i) q^{38} -769.474i q^{39} +(361.084 - 756.909i) q^{40} +895.241 q^{41} +(-23.5147 + 157.319i) q^{42} -928.943i q^{43} +(906.096 - 2963.27i) q^{44} +803.731 q^{45} +(-2706.26 - 404.510i) q^{46} -2116.78i q^{47} +(634.861 - 941.055i) q^{48} +2320.58 q^{49} +(268.043 - 1793.27i) q^{50} -369.344i q^{51} +(-2655.09 - 811.862i) q^{52} -3581.37 q^{53} +(2496.92 + 373.219i) q^{54} +2537.75i q^{55} +(518.024 + 247.124i) q^{56} +367.244 q^{57} +(-847.467 + 5669.75i) q^{58} -306.954i q^{59} +(-271.848 + 889.045i) q^{60} -7090.53 q^{61} +(2970.08 + 443.943i) q^{62} +550.069i q^{63} +(-2577.31 - 3183.50i) q^{64} +2273.83 q^{65} +(-507.817 + 3397.41i) q^{66} +4562.45i q^{67} +(-1274.43 - 389.691i) q^{68} +3033.42 q^{69} +(-464.884 - 69.4870i) q^{70} -149.139i q^{71} +(1690.22 - 3543.06i) q^{72} -2829.51 q^{73} +(-258.725 + 1730.93i) q^{74} +2010.06i q^{75} +(387.475 - 1267.19i) q^{76} -1736.82 q^{77} +(3044.08 + 455.004i) q^{78} +6895.61i q^{79} +(2780.86 + 1876.04i) q^{80} +2169.53 q^{81} +(-529.372 + 3541.62i) q^{82} -7842.11i q^{83} +(-608.457 - 186.051i) q^{84} +1091.43 q^{85} +(3674.95 + 549.301i) q^{86} -6355.16i q^{87} +(11187.1 + 5336.80i) q^{88} -8713.81 q^{89} +(-475.261 + 3179.60i) q^{90} +1556.19i q^{91} +(3200.52 - 10466.9i) q^{92} -3329.13 q^{93} +(8374.09 + 1251.69i) q^{94} +1085.22i q^{95} +(3347.46 + 3068.01i) q^{96} -2174.99 q^{97} +(-1372.20 + 9180.32i) q^{98} +11879.1i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 6 q^{2} - 6 q^{4} + 24 q^{5} + 66 q^{6} + 216 q^{8} - 972 q^{9}+O(q^{10}) \) 36 * q + 6 * q^2 - 6 * q^4 + 24 * q^5 + 66 * q^6 + 216 * q^8 - 972 * q^9	\( 36 q + 6 q^{2} - 6 q^{4} + 24 q^{5} + 66 q^{6} + 216 q^{8} - 972 q^{9} + 152 q^{10} + 160 q^{12} + 120 q^{13} - 60 q^{14} - 38 q^{16} - 600 q^{17} + 286 q^{18} - 600 q^{20} + 608 q^{21} + 1080 q^{22} + 958 q^{24} + 4604 q^{25} - 2766 q^{26} - 2250 q^{28} - 168 q^{29} - 1380 q^{30} + 3576 q^{32} + 1440 q^{33} + 908 q^{34} - 5836 q^{36} - 2248 q^{37} - 1716 q^{40} + 1800 q^{41} - 5006 q^{42} - 2520 q^{44} + 88 q^{45} + 6404 q^{46} + 1064 q^{48} - 12188 q^{49} + 3354 q^{50} + 15492 q^{52} - 6600 q^{53} + 1654 q^{54} + 12924 q^{56} + 5450 q^{58} - 11188 q^{60} + 2200 q^{61} - 9972 q^{62} + 12570 q^{64} - 15792 q^{65} + 10500 q^{66} - 22614 q^{68} + 19904 q^{69} + 900 q^{70} - 11376 q^{72} + 11560 q^{73} + 17304 q^{74} + 1680 q^{77} - 24740 q^{78} + 12900 q^{80} + 13604 q^{81} - 18420 q^{82} + 5644 q^{84} - 11552 q^{85} + 24564 q^{86} - 15304 q^{88} + 13800 q^{89} - 60212 q^{90} - 2142 q^{92} + 34592 q^{93} - 23096 q^{94} - 35770 q^{96} + 8200 q^{97} + 25566 q^{98}+O(q^{100}) \) 36 * q + 6 * q^2 - 6 * q^4 + 24 * q^5 + 66 * q^6 + 216 * q^8 - 972 * q^9 + 152 * q^10 + 160 * q^12 + 120 * q^13 - 60 * q^14 - 38 * q^16 - 600 * q^17 + 286 * q^18 - 600 * q^20 + 608 * q^21 + 1080 * q^22 + 958 * q^24 + 4604 * q^25 - 2766 * q^26 - 2250 * q^28 - 168 * q^29 - 1380 * q^30 + 3576 * q^32 + 1440 * q^33 + 908 * q^34 - 5836 * q^36 - 2248 * q^37 - 1716 * q^40 + 1800 * q^41 - 5006 * q^42 - 2520 * q^44 + 88 * q^45 + 6404 * q^46 + 1064 * q^48 - 12188 * q^49 + 3354 * q^50 + 15492 * q^52 - 6600 * q^53 + 1654 * q^54 + 12924 * q^56 + 5450 * q^58 - 11188 * q^60 + 2200 * q^61 - 9972 * q^62 + 12570 * q^64 - 15792 * q^65 + 10500 * q^66 - 22614 * q^68 + 19904 * q^69 + 900 * q^70 - 11376 * q^72 + 11560 * q^73 + 17304 * q^74 + 1680 * q^77 - 24740 * q^78 + 12900 * q^80 + 13604 * q^81 - 18420 * q^82 + 5644 * q^84 - 11552 * q^85 + 24564 * q^86 - 15304 * q^88 + 13800 * q^89 - 60212 * q^90 - 2142 * q^92 + 34592 * q^93 - 23096 * q^94 - 35770 * q^96 + 8200 * q^97 + 25566 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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