LMFDB - Embedded newform 483.2.bf.a.145.28

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(10,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 11, 9]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("483.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.bf (of order $66$, degree $20$, 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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$640$
Relative dimension:	$32$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			145.28
Character	$\chi$	$=$	483.145
Dual form			483.2.bf.a.10.28

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.679230 + 1.96250i) q^{2} +(0.458227 - 0.888835i) q^{3} +(-1.81797 + 1.42966i) q^{4} +(-3.97123 - 0.379207i) q^{5} +(2.05558 + 0.295548i) q^{6} +(0.921223 + 2.48019i) q^{7} +(-0.546439 - 0.351175i) q^{8} +(-0.580057 - 0.814576i) q^{9} +O(q^{10})$	\(q+(0.679230 + 1.96250i) q^{2} +(0.458227 - 0.888835i) q^{3} +(-1.81797 + 1.42966i) q^{4} +(-3.97123 - 0.379207i) q^{5} +(2.05558 + 0.295548i) q^{6} +(0.921223 + 2.48019i) q^{7} +(-0.546439 - 0.351175i) q^{8} +(-0.580057 - 0.814576i) q^{9} +(-1.95318 - 8.05113i) q^{10} +(-3.49404 - 1.20930i) q^{11} +(0.437696 + 2.27098i) q^{12} +(-1.42333 + 4.84742i) q^{13} +(-4.24166 + 3.49252i) q^{14} +(-2.15678 + 3.35601i) q^{15} +(-0.772491 + 3.18425i) q^{16} +(-3.63594 + 1.45561i) q^{17} +(1.20462 - 1.69165i) q^{18} +(-6.01028 - 2.40615i) q^{19} +(7.76170 - 4.98814i) q^{20} +(2.62661 + 0.317673i) q^{21} -7.67846i q^{22} +(4.30517 + 2.11318i) q^{23} +(-0.562529 + 0.324777i) q^{24} +(10.7172 + 2.06558i) q^{25} +(-10.4798 + 0.499217i) q^{26} +(-0.989821 + 0.142315i) q^{27} +(-5.22059 - 3.19186i) q^{28} +(0.765412 - 5.32356i) q^{29} +(-8.05113 - 1.95318i) q^{30} +(2.45132 + 0.116771i) q^{31} +(-8.06703 + 0.770308i) q^{32} +(-2.67593 + 2.55149i) q^{33} +(-5.32628 - 6.14686i) q^{34} +(-2.71789 - 10.1987i) q^{35} +(2.21909 + 0.651585i) q^{36} +(0.999459 - 0.711711i) q^{37} +(0.639728 - 13.4295i) q^{38} +(3.65635 + 3.48632i) q^{39} +(2.03687 + 1.60181i) q^{40} +(1.81963 - 0.830995i) q^{41} +(1.16064 + 5.37051i) q^{42} +(5.70399 + 8.87559i) q^{43} +(8.08094 - 2.79684i) q^{44} +(1.99465 + 3.45483i) q^{45} +(-1.22292 + 9.88425i) q^{46} +(3.43100 + 1.98089i) q^{47} +(2.47630 + 2.14573i) q^{48} +(-5.30269 + 4.56962i) q^{49} +(3.22576 + 22.4356i) q^{50} +(-0.372286 + 3.89875i) q^{51} +(-4.34261 - 10.8473i) q^{52} +(1.54930 - 1.62486i) q^{53} +(-0.951610 - 1.84586i) q^{54} +(13.4171 + 6.12737i) q^{55} +(0.367589 - 1.67878i) q^{56} +(-4.89275 + 4.23959i) q^{57} +(10.9674 - 2.11379i) q^{58} +(-6.82986 + 1.65691i) q^{59} +(-0.877021 - 9.18458i) q^{60} +(3.80929 - 1.96382i) q^{61} +(1.43585 + 4.89004i) q^{62} +(1.48594 - 2.18906i) q^{63} +(-4.26879 - 9.34735i) q^{64} +(7.49055 - 18.7105i) q^{65} +(-6.82489 - 3.51848i) q^{66} +(0.334907 - 1.73766i) q^{67} +(4.52898 - 7.84442i) q^{68} +(3.85101 - 2.85827i) q^{69} +(18.1690 - 12.2612i) q^{70} +(-8.56281 + 9.88201i) q^{71} +(0.0309070 + 0.648817i) q^{72} +(7.91014 + 10.0586i) q^{73} +(2.07560 + 1.47803i) q^{74} +(6.74688 - 8.57936i) q^{75} +(14.3665 - 4.21838i) q^{76} +(-0.219499 - 9.77992i) q^{77} +(-4.35842 + 9.54361i) q^{78} +(-2.88983 - 3.03076i) q^{79} +(4.27523 - 12.3525i) q^{80} +(-0.327068 + 0.945001i) q^{81} +(2.86678 + 3.00659i) q^{82} +(-1.63370 + 3.57731i) q^{83} +(-5.22926 + 3.17765i) q^{84} +(14.9911 - 4.40180i) q^{85} +(-13.5441 + 17.2227i) q^{86} +(-4.38103 - 3.11972i) q^{87} +(1.48460 + 1.88783i) q^{88} +(-0.403794 - 8.47668i) q^{89} +(-5.42530 + 6.26113i) q^{90} +(-13.3337 + 0.935424i) q^{91} +(-10.8478 + 2.31326i) q^{92} +(1.22705 - 2.12531i) q^{93} +(-1.55707 + 8.07883i) q^{94} +(22.9558 + 11.8345i) q^{95} +(-3.01185 + 7.52324i) q^{96} +(1.21531 + 2.66116i) q^{97} +(-12.5696 - 7.30274i) q^{98} +(1.04168 + 3.54762i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 640 q - 4 q^{2} + 36 q^{4} + 24 q^{8} - 32 q^{9}+O(q^{10}) $ 640 * q - 4 * q^2 + 36 * q^4 + 24 * q^8 - 32 * q^9	$ 640 q - 4 q^{2} + 36 q^{4} + 24 q^{8} - 32 q^{9} + 4 q^{18} - 28 q^{23} + 56 q^{25} - 84 q^{26} - 176 q^{28} - 24 q^{29} + 12 q^{31} + 36 q^{32} - 76 q^{35} + 28 q^{36} + 44 q^{37} - 110 q^{42} - 88 q^{43} + 154 q^{44} + 8 q^{46} + 12 q^{47} - 8 q^{49} - 212 q^{50} + 44 q^{51} + 108 q^{52} - 110 q^{56} - 88 q^{57} + 2 q^{58} - 36 q^{59} - 168 q^{64} - 48 q^{70} + 16 q^{71} + 12 q^{72} - 48 q^{73} - 22 q^{74} + 48 q^{75} + 32 q^{78} - 44 q^{79} - 594 q^{80} + 32 q^{81} + 24 q^{82} + 352 q^{85} - 36 q^{87} - 330 q^{88} + 244 q^{92} - 24 q^{93} - 486 q^{94} - 154 q^{95} - 60 q^{96} - 24 q^{98} - 44 q^{99}+O(q^{100}) $ 640 * q - 4 * q^2 + 36 * q^4 + 24 * q^8 - 32 * q^9 + 4 * q^18 - 28 * q^23 + 56 * q^25 - 84 * q^26 - 176 * q^28 - 24 * q^29 + 12 * q^31 + 36 * q^32 - 76 * q^35 + 28 * q^36 + 44 * q^37 - 110 * q^42 - 88 * q^43 + 154 * q^44 + 8 * q^46 + 12 * q^47 - 8 * q^49 - 212 * q^50 + 44 * q^51 + 108 * q^52 - 110 * q^56 - 88 * q^57 + 2 * q^58 - 36 * q^59 - 168 * q^64 - 48 * q^70 + 16 * q^71 + 12 * q^72 - 48 * q^73 - 22 * q^74 + 48 * q^75 + 32 * q^78 - 44 * q^79 - 594 * q^80 + 32 * q^81 + 24 * q^82 + 352 * q^85 - 36 * q^87 - 330 * q^88 + 244 * q^92 - 24 * q^93 - 486 * q^94 - 154 * q^95 - 60 * q^96 - 24 * q^98 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{19}{22}\right)$

Coefficient data

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

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

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

$2$	0.679230	+	1.96250i	0.480288	+	1.38770i	0.881703	+	0.471804i	$0.156397\pi$
$2$	0.679230	+	1.96250i	0.480288	+	1.38770i	−0.401415	+	0.915896i	$0.631482\pi$
$3$	0.458227	−	0.888835i	0.264557	−	0.513169i
$3$	0.458227	−	0.888835i	0.264557	−	0.513169i
$4$	−1.81797	+	1.42966i	−0.908983	+	0.714832i
$5$	−3.97123	−	0.379207i	−1.77599	−	0.169586i	−0.845032	−	0.534716i	$-0.820419\pi$
$5$	−3.97123	−	0.379207i	−1.77599	−	0.169586i	−0.930957	+	0.365129i	$0.881025\pi$
$6$	2.05558	+	0.295548i	0.839189	+	0.120657i
$7$	0.921223	+	2.48019i	0.348190	+	0.937424i
$7$	0.921223	+	2.48019i	0.348190	+	0.937424i
$8$	−0.546439	−	0.351175i	−0.193195	−	0.124159i
$9$	−0.580057	−	0.814576i	−0.193352	−	0.271525i
$10$	−1.95318	−	8.05113i	−0.617651	−	2.54599i
$11$	−3.49404	−	1.20930i	−1.05349	−	0.364617i	−0.255201	−	0.966888i	$-0.582142\pi$
$11$	−3.49404	−	1.20930i	−1.05349	−	0.364617i	−0.798292	+	0.602271i	$0.794263\pi$
$12$	0.437696	+	2.27098i	0.126352	+	0.655576i
$13$	−1.42333	+	4.84742i	−0.394761	+	1.34443i	0.487275	+	0.873249i	$0.337991\pi$
$13$	−1.42333	+	4.84742i	−0.394761	+	1.34443i	−0.882036	+	0.471183i	$0.843827\pi$
$14$	−4.24166	+	3.49252i	−1.13363	+	0.933416i
$15$	−2.15678	+	3.35601i	−0.556877	+	0.866518i
$16$	−0.772491	+	3.18425i	−0.193123	+	0.796063i
$17$	−3.63594	+	1.45561i	−0.881845	+	0.353037i	−0.767991	−	0.640460i	$-0.778744\pi$
$17$	−3.63594	+	1.45561i	−0.881845	+	0.353037i	−0.113853	+	0.993498i	$0.536319\pi$
$18$	1.20462	−	1.69165i	0.283931	−	0.398725i
$19$	−6.01028	−	2.40615i	−1.37885	−	0.552010i	−0.440521	−	0.897743i	$-0.645206\pi$
$19$	−6.01028	−	2.40615i	−1.37885	−	0.552010i	−0.938333	+	0.345733i	$0.887630\pi$
$20$	7.76170	−	4.98814i	1.73557	−	1.11538i
$21$	2.62661	+	0.317673i	0.573173	+	0.0693220i
$22$		−	7.67846i		−	1.63705i
$23$	4.30517	+	2.11318i	0.897690	+	0.440628i
$23$	4.30517	+	2.11318i	0.897690	+	0.440628i
$24$	−0.562529	+	0.324777i	−0.114826	+	0.0662947i
$25$	10.7172	+	2.06558i	2.14345	+	0.413116i
$26$	−10.4798	+	0.499217i	−2.05527	+	0.0979044i
$27$	−0.989821	+	0.142315i	−0.190491	+	0.0273885i
$28$	−5.22059	−	3.19186i	−0.986600	−	0.603205i
$29$	0.765412	−	5.32356i	0.142133	−	0.988560i	−0.786508	−	0.617580i	$-0.788113\pi$
$29$	0.765412	−	5.32356i	0.142133	−	0.988560i	0.928641	−	0.370979i	$-0.120978\pi$
$30$	−8.05113	−	1.95318i	−1.46993	−	0.356601i
$31$	2.45132	+	0.116771i	0.440270	+	0.0209726i	0.266547	−	0.963822i	$-0.414117\pi$
$31$	2.45132	+	0.116771i	0.440270	+	0.0209726i	0.173723	+	0.984795i	$0.444420\pi$
$32$	−8.06703	+	0.770308i	−1.42606	+	0.136173i
$33$	−2.67593	+	2.55149i	−0.465820	+	0.444158i
$34$	−5.32628	−	6.14686i	−0.913450	−	1.05418i
$35$	−2.71789	−	10.1987i	−0.459407	−	1.72390i
$36$	2.21909	+	0.651585i	0.369849	+	0.108597i
$37$	0.999459	−	0.711711i	0.164310	−	0.117005i	−0.494944	−	0.868925i	$-0.664812\pi$
$37$	0.999459	−	0.711711i	0.164310	−	0.117005i	0.659254	+	0.751920i	$0.270872\pi$
$38$	0.639728	−	13.4295i	0.103778	−	2.17856i
$39$	3.65635	+	3.48632i	0.585484	+	0.558258i
$40$	2.03687	+	1.60181i	0.322057	+	0.253268i
$41$	1.81963	−	0.830995i	0.284178	−	0.129780i	−0.268227	−	0.963356i	$-0.586438\pi$
$41$	1.81963	−	0.830995i	0.284178	−	0.129780i	0.552405	+	0.833576i	$0.313710\pi$
$42$	1.16064	+	5.37051i	0.179090	+	0.828688i
$43$	5.70399	+	8.87559i	0.869851	+	1.35351i	0.934633	+	0.355615i	$0.115729\pi$
$43$	5.70399	+	8.87559i	0.869851	+	1.35351i	−0.0647818	+	0.997899i	$0.520635\pi$
$44$	8.08094	−	2.79684i	1.21825	−	0.421640i
$45$	1.99465	+	3.45483i	0.297345	+	0.515016i
$46$	−1.22292	+	9.88425i	−0.180310	+	1.45735i
$47$	3.43100	+	1.98089i	0.500463	+	0.288942i	0.728905	−	0.684615i	$-0.240030\pi$
$47$	3.43100	+	1.98089i	0.500463	+	0.288942i	−0.228442	+	0.973558i	$0.573363\pi$
$48$	2.47630	+	2.14573i	0.357423	+	0.309709i
$49$	−5.30269	+	4.56962i	−0.757528	+	0.652803i
$50$	3.22576	+	22.4356i	0.456191	+	3.17288i
$51$	−0.372286	+	3.89875i	−0.0521304	+	0.545934i
$52$	−4.34261	−	10.8473i	−0.602212	−	1.50425i
$53$	1.54930	−	1.62486i	0.212813	−	0.223192i	−0.608672	−	0.793422i	$-0.708297\pi$
$53$	1.54930	−	1.62486i	0.212813	−	0.223192i	0.821485	+	0.570230i	$0.193146\pi$
$54$	−0.951610	−	1.84586i	−0.129498	−	0.251190i
$55$	13.4171	+	6.12737i	1.80916	+	0.826215i
$56$	0.367589	−	1.67878i	0.0491211	−	0.224337i
$57$	−4.89275	+	4.23959i	−0.648060	+	0.561547i
$58$	10.9674	−	2.11379i	1.44009	−	0.277555i
$59$	−6.82986	+	1.65691i	−0.889172	+	0.215711i	−0.654228	−	0.756298i	$-0.727006\pi$
$59$	−6.82986	+	1.65691i	−0.889172	+	0.215711i	−0.234945	+	0.972009i	$0.575491\pi$
$60$	−0.877021	−	9.18458i	−0.113223	−	1.18572i
$61$	3.80929	−	1.96382i	0.487729	−	0.251442i	−0.196778	−	0.980448i	$-0.563048\pi$
$61$	3.80929	−	1.96382i	0.487729	−	0.251442i	0.684507	+	0.729006i	$0.260017\pi$
$62$	1.43585	+	4.89004i	0.182353	+	0.621036i
$63$	1.48594	−	2.18906i	0.187211	−	0.275795i
$64$	−4.26879	−	9.34735i	−0.533599	−	1.16842i
$65$	7.49055	−	18.7105i	0.929088	−	2.32075i
$66$	−6.82489	−	3.51848i	−0.840086	−	0.433094i
$67$	0.334907	−	1.73766i	0.0409154	−	0.212289i	−0.955717	−	0.294287i	$-0.904918\pi$
$67$	0.334907	−	1.73766i	0.0409154	−	0.212289i	0.996633	+	0.0819975i	$0.0261300\pi$
$68$	4.52898	−	7.84442i	0.549220	−	0.951276i
$69$	3.85101	−	2.85827i	0.463607	−	0.344096i
$70$	18.1690	−	12.2612i	2.17161	−	1.46549i
$71$	−8.56281	+	9.88201i	−1.01622	+	1.17278i	−0.0313444	+	0.999509i	$0.509979\pi$
$71$	−8.56281	+	9.88201i	−1.01622	+	1.17278i	−0.984874	+	0.173270i	$0.944567\pi$
$72$	0.0309070	+	0.648817i	0.00364242	+	0.0764639i
$73$	7.91014	+	10.0586i	0.925812	+	1.17727i	0.983858	+	0.178952i	$0.0572706\pi$
$73$	7.91014	+	10.0586i	0.925812	+	1.17727i	−0.0580458	+	0.998314i	$0.518487\pi$
$74$	2.07560	+	1.47803i	0.241283	+	0.171817i
$75$	6.74688	−	8.57936i	0.779063	−	0.990659i
$76$	14.3665	−	4.21838i	1.64795	−	0.483881i
$77$	−0.219499	−	9.77992i	−0.0250142	−	1.11453i
$78$	−4.35842	+	9.54361i	−0.493494	+	1.08060i
$79$	−2.88983	−	3.03076i	−0.325131	−	0.340987i	0.540800	−	0.841151i	$-0.318122\pi$
$79$	−2.88983	−	3.03076i	−0.325131	−	0.340987i	−0.865931	+	0.500164i	$0.833273\pi$
$80$	4.27523	−	12.3525i	0.477985	−	1.38105i
$81$	−0.327068	+	0.945001i	−0.0363409	+	0.105000i
$82$	2.86678	+	3.00659i	0.316582	+	0.332022i
$83$	−1.63370	+	3.57731i	−0.179322	+	0.392661i	−0.977853	−	0.209293i	$-0.932884\pi$
$83$	−1.63370	+	3.57731i	−0.179322	+	0.392661i	0.798531	+	0.601954i	$0.205611\pi$
$84$	−5.22926	+	3.17765i	−0.570559	+	0.346710i
$85$	14.9911	−	4.40180i	1.62602	−	0.477442i
$86$	−13.5441	+	17.2227i	−1.46049	+	1.85717i
$87$	−4.38103	−	3.11972i	−0.469696	−	0.334469i
$88$	1.48460	+	1.88783i	0.158259	+	0.201243i
$89$	−0.403794	−	8.47668i	−0.0428021	−	0.898527i	−0.913532	−	0.406766i	$-0.866656\pi$
$89$	−0.403794	−	8.47668i	−0.0428021	−	0.898527i	0.870730	−	0.491761i	$-0.163647\pi$
$90$	−5.42530	+	6.26113i	−0.571877	+	0.659981i
$91$	−13.3337	+	0.935424i	−1.39775	+	0.0980590i
$92$	−10.8478	+	2.31326i	−1.13096	+	0.241174i
$93$	1.22705	−	2.12531i	0.127239	−	0.220385i
$94$	−1.55707	+	8.07883i	−0.160599	+	0.833268i
$95$	22.9558	+	11.8345i	2.35522	+	1.21420i
$96$	−3.01185	+	7.52324i	−0.307396	+	0.767837i
$97$	1.21531	+	2.66116i	0.123396	+	0.270200i	0.961242	−	0.275708i	$-0.0889121\pi$
$97$	1.21531	+	2.66116i	0.123396	+	0.270200i	−0.837845	+	0.545908i	$0.816185\pi$
$98$	−12.5696	−	7.30274i	−1.26973	−	0.737688i
$99$	1.04168	+	3.54762i	0.104692	+	0.356550i
$100$	−22.4367	+	11.5669i	−2.24367	+	1.15669i
$101$	−0.521656	−	5.46303i	−0.0519067	−	0.543592i	−0.983602	−	0.180352i	$-0.942276\pi$
$101$	−0.521656	−	5.46303i	−0.0519067	−	0.543592i	0.931695	−	0.363240i	$-0.118330\pi$
$102$	−7.90419	+	1.91753i	−0.782631	+	0.189864i
$103$	1.66947	−	0.321764i	0.164498	−	0.0317044i	−0.106337	−	0.994330i	$-0.533912\pi$
$103$	1.66947	−	0.321764i	0.164498	−	0.0317044i	0.270835	+	0.962626i	$0.412700\pi$
$104$	2.48005	−	2.14898i	0.243189	−	0.210725i
$105$	−10.3104	−	2.25758i	−1.00619	−	0.220317i
$106$	4.24113	+	1.93686i	0.411935	+	0.188124i
$107$	4.56368	+	8.85230i	0.441188	+	0.855785i	0.999655	+	0.0262582i	$0.00835921\pi$
$107$	4.56368	+	8.85230i	0.441188	+	0.855785i	−0.558468	+	0.829526i	$0.688610\pi$
$108$	1.59600	−	1.67384i	0.153575	−	0.161065i
$109$	−1.71580	−	4.28587i	−0.164344	−	0.410512i	0.823221	−	0.567721i	$-0.192175\pi$
$109$	−1.71580	−	4.28587i	−0.164344	−	0.410512i	−0.987565	+	0.157209i	$0.949750\pi$
$110$	−2.91172	+	30.4930i	−0.277622	+	2.90739i
$111$	−0.174616	−	1.21448i	−0.0165738	−	0.115273i
$112$	−8.60919	+	1.01748i	−0.813492	+	0.0961430i
$113$	10.7295	+	9.29716i	1.00935	+	0.874603i	0.992125	−	0.125248i	$-0.0399728\pi$
$113$	10.7295	+	9.29716i	1.00935	+	0.874603i	0.0172206	+	0.999852i	$0.494518\pi$
$114$	−11.6435	−	6.72238i	−1.09051	−	0.629609i
$115$	−16.2955	−	10.0245i	−1.51956	−	0.934786i
$116$	6.21941	+	10.7723i	0.577457	+	1.00019i
$117$	4.77420	−	1.65237i	0.441375	−	0.152761i
$118$	−7.89073	−	12.2782i	−0.726401	−	1.13030i
$119$	−6.95971	−	7.67688i	−0.637995	−	0.703739i
$120$	2.35709	−	1.07645i	0.215172	−	0.0982658i
$121$	2.09933	+	1.65093i	0.190848	+	0.150085i
$122$	6.44139	+	6.14186i	0.583176	+	0.556058i
$123$	0.0951828	−	1.99813i	0.00858234	−	0.180165i
$124$	−4.62336	+	3.29228i	−0.415190	+	0.295655i
$125$	−22.6389	−	6.64737i	−2.02488	−	0.594559i
$126$	5.30533	+	1.42930i	0.472637	+	0.127332i
$127$	3.81487	+	4.40259i	0.338515	+	0.390667i	0.899327	−	0.437276i	$-0.144057\pi$
$127$	3.81487	+	4.40259i	0.338515	+	0.390667i	−0.560813	+	0.827943i	$0.689511\pi$
$128$	3.71484	−	3.54209i	0.328349	−	0.313080i
$129$	10.5027	−	1.00288i	0.924707	−	0.0882989i
$130$	41.8072	+	1.99152i	3.66673	+	0.174668i
$131$	9.23952	+	2.24148i	0.807260	+	0.195839i	0.618092	−	0.786105i	$-0.287906\pi$
$131$	9.23952	+	2.24148i	0.807260	+	0.195839i	0.189168	+	0.981945i	$0.439421\pi$
$132$	1.21697	−	8.46421i	0.105924	−	0.736715i
$133$	0.430909	−	17.1233i	0.0373645	−	1.48477i
$134$	3.63765	−	0.523016i	0.314245	−	0.0451817i
$135$	3.98478	−	0.189818i	0.342955	−	0.0163370i
$136$	2.49799	+	0.481449i	0.214201	+	0.0412839i
$137$	−13.6557	+	7.88413i	−1.16669	+	0.673587i	−0.952897	−	0.303293i	$-0.901914\pi$
$137$	−13.6557	+	7.88413i	−1.16669	+	0.673587i	−0.213789	+	0.976880i	$0.568580\pi$
$138$	8.22510	+	5.61620i	0.700167	+	0.478083i
$139$		−	16.7480i		−	1.42055i	−0.703927	−	0.710273i	$-0.748572\pi$
$139$		−	16.7480i		−	1.42055i	0.703927	−	0.710273i	$-0.251428\pi$
$140$	19.5218	+	14.6553i	1.64989	+	1.23860i
$141$	3.33286	−	2.14190i	0.280677	−	0.180380i
$142$	−25.2096	−	10.0924i	−2.11554	−	0.846936i
$143$	10.8351	−	15.2158i	0.906081	−	1.27241i
$144$	3.04190	−	1.21779i	0.253492	−	0.101483i
$145$	−5.05836	+	20.8508i	−0.420074	+	1.73157i
$146$	−14.3672	+	22.3558i	−1.18904	+	1.85018i
$147$	1.63180	+	6.80714i	0.134589	+	0.561444i
$148$	−0.799474	+	2.72276i	−0.0657163	+	0.223809i
$149$	2.27921	+	11.8257i	0.186720	+	0.968798i	0.947492	+	0.319778i	$0.103608\pi$
$149$	2.27921	+	11.8257i	0.186720	+	0.968798i	−0.760772	+	0.649019i	$0.775179\pi$
$150$	21.4197	+	7.41344i	1.74891	+	0.605305i
$151$	−3.36382	−	13.8659i	−0.273744	−	1.12839i	−0.928138	−	0.372235i	$-0.878592\pi$
$151$	−3.36382	−	13.8659i	−0.273744	−	1.12839i	0.654394	−	0.756153i	$-0.272924\pi$
$152$	2.43927	+	3.42548i	0.197851	+	0.277843i
$153$	3.29476	+	2.11741i	0.266365	+	0.171183i
$154$	19.0441	−	7.07358i	1.53461	−	0.570005i
$155$	−9.69048	−	1.39328i	−0.778358	−	0.111911i
$156$	−11.6314	−	1.11066i	−0.931256	−	0.0889242i
$157$	−13.9597	+	10.9780i	−1.11411	+	0.876143i	−0.993188	−	0.116519i	$-0.962826\pi$
$157$	−13.9597	+	10.9780i	−1.11411	+	0.876143i	−0.120919	+	0.992662i	$0.538584\pi$
$158$	3.98503	−	7.72988i	0.317032	−	0.614956i
$159$	−0.734303	−	2.12163i	−0.0582340	−	0.168256i
$160$	32.3282			2.55577
$161$	−1.27506	+	12.6244i	−0.100489	+	0.994938i
$162$	−2.07672			−0.163163
$163$	−7.10197	−	20.5198i	−0.556269	−	1.60723i	−0.775352	−	0.631529i	$-0.782428\pi$
$163$	−7.10197	−	20.5198i	−0.556269	−	1.60723i	0.219083	−	0.975706i	$-0.429693\pi$
$164$	−2.11997	+	4.11218i	−0.165542	+	0.321107i
$165$	11.5943	−	9.11785i	0.902614	−	0.709823i
$166$	−8.13015	−	0.776335i	−0.631022	−	0.0602553i
$167$	−4.79888	−	0.689974i	−0.371348	−	0.0533918i	−0.0458855	−	0.998947i	$-0.514611\pi$
$167$	−4.79888	−	0.689974i	−0.371348	−	0.0533918i	−0.325463	+	0.945555i	$0.605520\pi$
$168$	−1.32372	−	1.09599i	−0.102127	−	0.0845574i
$169$	−10.5353	−	6.77061i	−0.810406	−	0.520816i
$170$	18.8210	+	26.4303i	1.44350	+	2.02712i
$171$	1.52631	+	6.29154i	0.116720	+	0.481126i
$172$	−23.0588	−	7.98072i	−1.75822	−	0.608524i
$173$	3.88073	+	20.1351i	0.295046	+	1.53085i	0.762594	+	0.646878i	$0.223926\pi$
$173$	3.88073	+	20.1351i	0.295046	+	1.53085i	−0.467547	+	0.883968i	$0.654862\pi$
$174$	3.14674	−	10.7168i	0.238554	−	0.812439i
$175$	4.74994	+	28.4837i	0.359062	+	2.15316i
$176$	6.54983	−	10.1917i	0.493712	−	0.768231i
$177$	−1.65691	+	6.82986i	−0.124541	+	0.513364i
$178$	16.3613	−	6.55006i	1.22633	−	0.490948i
$179$	−4.59856	+	6.45777i	−0.343712	+	0.482677i	−0.949860	−	0.312676i	$-0.898775\pi$
$179$	−4.59856	+	6.45777i	−0.343712	+	0.482677i	0.606147	+	0.795352i	$0.292714\pi$
$180$	−8.56545	−	3.42909i	−0.638431	−	0.255589i
$181$	7.29913	−	4.69087i	0.542540	−	0.348669i	−0.240491	−	0.970651i	$-0.577309\pi$
$181$	7.29913	−	4.69087i	0.542540	−	0.348669i	0.783032	+	0.621982i	$0.213672\pi$
$182$	−10.8924	−	25.5321i	−0.807401	−	1.89257i
$183$		−	4.28571i		−	0.316809i
$184$	−1.61042	−	2.66659i	−0.118722	−	0.196584i
$185$	−4.23897	+	2.44737i	−0.311655	+	0.179934i
$186$	5.00438	+	0.964516i	0.366939	+	0.0707218i
$187$	14.4644	−	0.689024i	1.05774	−	0.0503864i
$188$	−9.06945	+	1.30399i	−0.661457	+	0.0951032i
$189$	−1.26481	−	2.32384i	−0.0920017	−	0.169035i
$190$	−7.63308	+	53.0892i	−0.553762	+	3.85150i
$191$	9.65294	+	2.34178i	0.698462	+	0.169445i	0.569241	−	0.822171i	$-0.307237\pi$
$191$	9.65294	+	2.34178i	0.698462	+	0.169445i	0.129221	+	0.991616i	$0.458752\pi$
$192$	−10.2643	−	0.488950i	−0.740764	−	0.0352869i
$193$	−22.7361	+	2.17104i	−1.63658	+	0.156275i	−0.872423	−	0.488752i	$-0.837452\pi$
$193$	−22.7361	+	2.17104i	−1.63658	+	0.156275i	−0.764160	+	0.645027i	$0.776846\pi$
$194$	−4.39707	+	4.19260i	−0.315691	+	0.301011i
$195$	−13.1982	−	15.2315i	−0.945141	−	1.09075i
$196$	3.10710	−	15.8885i	0.221935	−	1.13489i
$197$	−4.52655	−	1.32912i	−0.322504	−	0.0946956i	0.116474	−	0.993194i	$-0.462841\pi$
$197$	−4.52655	−	1.32912i	−0.322504	−	0.0946956i	−0.438977	+	0.898498i	$0.644659\pi$
$198$	−6.25469	+	4.45395i	−0.444502	+	0.316528i
$199$	0.0838509	−	1.76025i	0.00594403	−	0.124781i	−0.993945	−	0.109879i	$-0.964954\pi$
$199$	0.0838509	−	1.76025i	0.00594403	−	0.124781i	0.999889	−	0.0149013i	$-0.00474339\pi$
$200$	−5.13094	−	4.89234i	−0.362812	−	0.345941i
$201$	−1.39103	−	1.09392i	−0.0981160	−	0.0771593i
$202$	10.3669	−	4.73441i	0.729413	−	0.333112i
$203$	13.9086	−	3.00582i	0.976189	−	0.210967i
$204$	−4.89710	−	7.62004i	−0.342866	−	0.533510i
$205$	−7.54127	+	2.61006i	−0.526705	+	0.182295i
$206$	1.76542	+	3.05780i	0.123003	+	0.213047i
$207$	−0.775900	−	4.73265i	−0.0539288	−	0.328942i
$208$	−14.3359	−	8.27683i	−0.994015	−	0.573895i
$209$	18.0904	+	15.6754i	1.25134	+	1.08429i
$210$	−2.57262	−	21.7677i	−0.177528	−	1.50211i
$211$	2.33865	+	16.2657i	0.161000	+	1.11978i	0.896754	+	0.442529i	$0.145918\pi$
$211$	2.33865	+	16.2657i	0.161000	+	1.11978i	−0.735755	+	0.677248i	$0.763172\pi$
$212$	−0.493572	+	5.16892i	−0.0338987	+	0.355003i
$213$	4.85977	+	12.1391i	0.332986	+	0.831759i
$214$	−14.2729	+	14.9690i	−0.975676	+	1.02326i
$215$	−19.2862	−	37.4100i	−1.31531	−	2.55134i
$216$	0.590854	+	0.269834i	0.0402025	+	0.0183599i
$217$	1.96860	+	6.18731i	0.133637	+	0.420022i
$218$	7.24562	−	6.27836i	0.490735	−	0.425224i
$219$	12.5650	−	2.42171i	0.849067	−	0.163644i
$220$	−33.1519	+	8.04256i	−2.23510	+	0.542229i
$221$	−1.88081	−	19.6967i	−0.126517	−	1.32495i
$222$	2.26482	−	1.16759i	0.152005	−	0.0783638i
$223$	4.38539	+	14.9353i	0.293668	+	1.00014i	0.965709	+	0.259626i	$0.0835994\pi$
$223$	4.38539	+	14.9353i	0.293668	+	1.00014i	−0.672042	+	0.740513i	$0.734582\pi$
$224$	−9.34205	−	19.2982i	−0.624192	−	1.28941i
$225$	−4.53404	−	9.92816i	−0.302269	−	0.661877i
$226$	−10.9579	+	27.3716i	−0.728911	+	1.82073i
$227$	0.876476	+	0.451855i	0.0581737	+	0.0299906i	0.487068	−	0.873364i	$-0.338066\pi$
$227$	0.876476	+	0.451855i	0.0581737	+	0.0299906i	−0.428894	+	0.903355i	$0.641097\pi$
$228$	2.83366	−	14.7024i	0.187664	−	0.973691i
$229$	3.11161	−	5.38946i	0.205621	−	0.356146i	−0.744710	−	0.667389i	$-0.767412\pi$
$229$	3.11161	−	5.38946i	0.205621	−	0.356146i	0.950330	+	0.311243i	$0.100745\pi$
$230$	8.60468	−	38.7889i	0.567376	−	2.55766i
$231$	−8.79332	−	4.28632i	−0.578558	−	0.282019i
$232$	−2.28775	+	2.64020i	−0.150198	+	0.173338i
$233$	−1.20401	−	25.2753i	−0.0788772	−	1.65584i	−0.598265	−	0.801298i	$-0.704143\pi$
$233$	−1.20401	−	25.2753i	−0.0788772	−	1.65584i	0.519388	−	0.854539i	$-0.326160\pi$
$234$	6.48556	+	8.24706i	0.423974	+	0.539127i
$235$	−12.8741	−	9.16763i	−0.839816	−	0.598030i
$236$	10.0476	−	12.7766i	0.654046	−	0.831687i
$237$	−4.01804	+	1.17980i	−0.261000	+	0.0766365i
$238$	10.3387	−	18.8728i	0.670157	−	1.22334i
$239$	9.70873	−	21.2592i	0.628006	−	1.37514i	−0.281545	−	0.959548i	$-0.590847\pi$
$239$	9.70873	−	21.2592i	0.628006	−	1.37514i	0.909551	−	0.415593i	$-0.136426\pi$
$240$	−9.02029	−	9.46020i	−0.582257	−	0.610654i
$241$	2.06909	−	5.97825i	0.133282	−	0.385093i	−0.858536	−	0.512753i	$-0.828626\pi$
$241$	2.06909	−	5.97825i	0.133282	−	0.385093i	0.991818	+	0.127660i	$0.0407468\pi$
$242$	−1.81404	+	5.24131i	−0.116611	+	0.336924i
$243$	0.690079	+	0.723734i	0.0442686	+	0.0464276i
$244$	−4.11755	+	9.01617i	−0.263599	+	0.577201i
$245$	22.7911	−	16.1362i	1.45607	−	1.03090i
$246$	3.98599	−	1.17039i	0.254138	−	0.0746216i
$247$	20.2182	−	25.7096i	1.28646	−	1.63586i
$248$	−1.29849	−	0.924650i	−0.0824542	−	0.0587153i
$249$	2.43103	+	3.09131i	0.154061	+	0.195904i
$250$	−2.33149	−	48.9440i	−0.147456	−	3.09549i
$251$	−4.58825	+	5.29512i	−0.289608	+	0.334225i	−0.881846	−	0.471538i	$-0.843699\pi$
$251$	−4.58825	+	5.29512i	−0.289608	+	0.334225i	0.592238	+	0.805763i	$0.298245\pi$
$252$	0.428227	+	6.10403i	0.0269757	+	0.384518i
$253$	−12.4870	−	12.5898i	−0.785049	−	0.791512i
$254$	−6.04893	+	10.4771i	−0.379544	+	0.657389i
$255$	2.95687	−	15.3417i	0.185166	−	0.960733i
$256$	−8.79268	−	4.53294i	−0.549543	−	0.283309i
$257$	−9.10131	+	22.7340i	−0.567724	+	1.41811i	0.315397	+	0.948960i	$0.397862\pi$
$257$	−9.10131	+	22.7340i	−0.567724	+	1.41811i	−0.883121	+	0.469146i	$0.844562\pi$
$258$	9.10188	+	19.9303i	0.566658	+	1.24081i
$259$	2.68590	+	1.82320i	0.166894	+	0.113288i
$260$	13.1321	+	44.7240i	0.814421	+	2.77366i
$261$	−4.78042	+	2.46448i	−0.295901	+	0.152547i
$262$	1.87683	+	19.6551i	0.115951	+	1.21429i
$263$	−24.9953	+	6.06378i	−1.54127	+	0.373909i	−0.914269	−	0.405107i	$-0.867234\pi$
$263$	−24.9953	+	6.06378i	−1.54127	+	0.373909i	−0.627004	+	0.779016i	$0.715719\pi$
$264$	2.35825	−	0.454516i	0.145140	−	0.0279735i
$265$	−6.76879	+	5.86519i	−0.415804	+	0.360296i
$266$	33.8972	−	10.7850i	2.07837	−	0.661268i
$267$	−7.71941	−	3.52533i	−0.472420	−	0.215747i
$268$	1.87543	+	3.63782i	0.114560	+	0.222215i
$269$	−3.65099	+	3.82905i	−0.222605	+	0.233461i	−0.825561	−	0.564313i	$-0.809141\pi$
$269$	−3.65099	+	3.82905i	−0.222605	+	0.233461i	0.602956	+	0.797774i	$0.293989\pi$
$270$	3.07910	+	7.69121i	0.187388	+	0.468072i
$271$	1.05588	−	11.0576i	0.0641399	−	0.671703i	−0.905036	−	0.425334i	$-0.860156\pi$
$271$	1.05588	−	11.0576i	0.0641399	−	0.671703i	0.969176	−	0.246369i	$-0.0792374\pi$
$272$	−1.82630	−	12.7022i	−0.110736	−	0.770184i
$273$	−5.27843	+	12.2801i	−0.319465	+	0.743227i
$274$	−24.7480	−	21.4443i	−1.49508	−	1.29550i
$275$	−34.9486	−	20.1776i	−2.10748	−	1.21675i
$276$	−2.91463	+	10.7019i	−0.175440	+	0.644178i
$277$	10.9167	+	18.9083i	0.655921	+	1.13609i	0.981662	+	0.190630i	$0.0610530\pi$
$277$	10.9167	+	18.9083i	0.655921	+	1.13609i	−0.325741	+	0.945459i	$0.605614\pi$
$278$	32.8680	−	11.3757i	1.97129	−	0.682271i
$279$	−1.32679	−	2.06452i	−0.0794326	−	0.123600i
$280$	−2.09639	+	6.52745i	−0.125283	+	0.390089i
$281$	−11.2888	+	5.15544i	−0.673435	+	0.307548i	−0.722623	−	0.691242i	$-0.757064\pi$
$281$	−11.2888	+	5.15544i	−0.673435	+	0.307548i	0.0491880	+	0.998790i	$0.484337\pi$
$282$	6.46726	+	5.08591i	0.385120	+	0.302862i
$283$	2.60755	+	2.48630i	0.155003	+	0.147795i	0.763612	−	0.645675i	$-0.223424\pi$
$283$	2.60755	+	2.48630i	0.155003	+	0.147795i	−0.608609	+	0.793470i	$0.708272\pi$
$284$	1.43894	−	30.2071i	0.0853855	−	1.79246i
$285$	21.0379	−	14.9810i	1.24618	−	0.887400i
$286$	37.2207	+	10.9290i	2.20091	+	0.646245i
$287$	3.73731	+	3.74749i	0.220606	+	0.221207i
$288$	5.30681	+	6.12439i	0.312707	+	0.360883i
$289$	−1.20222	+	1.14632i	−0.0707190	+	0.0674305i
$290$	−44.3556	+	4.23545i	−2.60465	+	0.248714i
$291$	2.92223	+	0.139203i	0.171304	+	0.00816021i
$292$	−28.7607	−	6.97728i	−1.68310	−	0.408314i
$293$	0.991398	−	6.89532i	0.0579181	−	0.402829i	−0.940153	−	0.340752i	$-0.889318\pi$
$293$	0.991398	−	6.89532i	0.0579181	−	0.402829i	0.998071	−	0.0620772i	$-0.0197725\pi$
$294$	−12.2507	+	7.82604i	−0.714474	+	0.456424i
$295$	27.7513	−	3.99003i	1.61574	−	0.232309i
$296$	−0.796078	+	0.0379219i	−0.0462711	+	0.00220416i
$297$	3.63058	+	0.699737i	0.210667	+	0.0406028i
$298$	−21.6598	+	12.5053i	−1.25472	+	0.724414i
$299$	−16.3711	+	17.8612i	−0.946766	+	1.03294i
$300$			25.2428i			1.45739i
$301$	−16.7585	+	22.3234i	−0.965944	+	1.28670i
$302$	24.9270	−	16.0196i	1.43439	−	0.921826i
$303$	−5.09477	−	2.03964i	−0.292687	−	0.117174i
$304$	12.3047	−	17.2795i	0.705722	−	0.991048i
$305$	−15.8723	+	6.35429i	−0.908843	+	0.363846i
$306$	−1.91753	+	7.90419i	−0.109618	+	0.451852i
$307$	14.9711	−	23.2954i	0.854444	−	1.32954i	−0.0883249	−	0.996092i	$-0.528151\pi$
$307$	14.9711	−	23.2954i	0.854444	−	1.32954i	0.942768	−	0.333448i	$-0.108212\pi$
$308$	14.3811	+	17.4658i	0.819436	+	0.995204i
$309$	0.479001	−	1.63133i	0.0272494	−	0.0928030i
$310$	−3.84774	−	19.9640i	−0.218537	−	1.13388i
$311$	10.7203	+	3.71032i	0.607891	+	0.210393i	0.613634	−	0.789590i	$-0.289707\pi$
$311$	10.7203	+	3.71032i	0.607891	+	0.210393i	−0.00574340	+	0.999984i	$0.501828\pi$
$312$	−0.773662	−	3.18908i	−0.0438000	−	0.180546i
$313$	16.0727	+	22.5710i	0.908485	+	1.27579i	0.960824	+	0.277159i	$0.0893929\pi$
$313$	16.0727	+	22.5710i	0.908485	+	1.27579i	−0.0523392	+	0.998629i	$0.516668\pi$
$314$	−31.0263	−	19.9394i	−1.75092	−	1.12525i
$315$	−6.73113	+	8.12978i	−0.379256	+	0.458061i
$316$	9.58658	+	1.37834i	0.539287	+	0.0775378i
$317$	6.64131	+	0.634168i	0.373013	+	0.0356184i	0.279879	−	0.960035i	$-0.409706\pi$
$317$	6.64131	+	0.634168i	0.373013	+	0.0356184i	0.0931337	+	0.995654i	$0.470312\pi$
$318$	3.66495	−	2.88215i	0.205520	−	0.161623i
$319$	−9.11215	+	17.6751i	−0.510183	+	0.989616i
$320$	13.4078	+	38.7392i	0.749518	+	2.16559i
$321$	9.95944			0.555882
$322$	−25.6414	+	6.07252i	−1.42894	+	0.338408i
$323$	25.3555			1.41082
$324$	−0.756436	−	2.18558i	−0.0420242	−	0.121421i
$325$	−25.2669	+	49.0109i	−1.40155	+	2.71864i
$326$	35.4463	−	27.8753i	1.96319	−	1.54387i
$327$	−4.59566	−	0.438832i	−0.254141	−	0.0242675i
$328$	−1.28614	−	0.184919i	−0.0710151	−	0.0102104i
$329$	−1.75226	+	10.3344i	−0.0966055	+	0.569753i
$330$	25.7690	+	16.5607i	1.41854	+	0.911638i
$331$	−2.35706	−	3.31002i	−0.129556	−	0.181935i	0.744703	−	0.667396i	$-0.232591\pi$
$331$	−2.35706	−	3.31002i	−0.129556	−	0.181935i	−0.874258	+	0.485461i	$0.838652\pi$
$332$	−2.14434	−	8.83908i	−0.117686	−	0.485107i
$333$	−1.15949	−	0.401302i	−0.0635394	−	0.0219912i
$334$	−1.90546	−	9.88647i	−0.104262	−	0.540963i
$335$	−1.98893	+	6.77367i	−0.108667	+	0.370085i
$336$	−3.04058	+	8.11839i	−0.165878	+	0.442894i
$337$	1.27053	−	1.97698i	0.0692100	−	0.107693i	−0.804923	−	0.593379i	$-0.797794\pi$
$337$	1.27053	−	1.97698i	0.0692100	−	0.107693i	0.874133	+	0.485686i	$0.161430\pi$
$338$	6.13149	−	25.2743i	0.333509	−	1.37474i
$339$	13.1802	−	5.27655i	0.715849	−	0.286583i
$340$	−20.9603	+	29.4346i	−1.13673	+	1.59632i
$341$	−8.42380	−	3.37238i	−0.456174	−	0.182625i
$342$	−11.3105	+	7.26879i	−0.611600	+	0.393051i
$343$	−16.2185	−	8.94205i	−0.875717	−	0.482826i
$344$		−	6.85306i		−	0.369492i
$345$	−16.3771	+	9.89054i	−0.881715	+	0.532489i
$346$	−36.8794	+	21.2923i	−1.98265	+	1.14468i
$347$	−4.98479	−	0.960739i	−0.267597	−	0.0515752i	0.0536874	−	0.998558i	$-0.482903\pi$
$347$	−4.98479	−	0.960739i	−0.267597	−	0.0515752i	−0.321285	+	0.946983i	$0.604115\pi$
$348$	12.4247	−	0.591863i	0.666035	−	0.0317272i
$349$	10.8311	−	1.55728i	0.579777	−	0.0833594i	0.153814	−	0.988100i	$-0.450844\pi$
$349$	10.8311	−	1.55728i	0.579777	−	0.0833594i	0.425963	+	0.904740i	$0.359935\pi$
$350$	−52.6730	+	28.6687i	−2.81549	+	1.53241i
$351$	0.718983	−	5.00064i	0.0383765	−	0.266914i
$352$	29.1181	+	7.06397i	1.55200	+	0.376511i
$353$	−5.40197	−	0.257328i	−0.287518	−	0.0136962i	−0.0966724	−	0.995316i	$-0.530820\pi$
$353$	−5.40197	−	0.257328i	−0.287518	−	0.0136962i	−0.190845	+	0.981620i	$0.561123\pi$
$354$	−14.5291	+	1.38736i	−0.772211	+	0.0737372i
$355$	37.7522	−	35.9967i	2.00368	−	1.91051i
$356$	12.8529	+	14.8330i	0.681202	+	0.786149i
$357$	−10.0126	+	2.66828i	−0.529923	+	0.141220i
$358$	−15.7969	−	4.63839i	−0.834892	−	0.245146i
$359$	24.3607	−	17.3472i	1.28571	−	0.915548i	0.286611	−	0.958047i	$-0.407471\pi$
$359$	24.3607	−	17.3472i	1.28571	−	0.915548i	0.999097	+	0.0424989i	$0.0135319\pi$
$360$	0.123297	−	2.58832i	0.00649833	−	0.136417i
$361$	16.5830	+	15.8118i	0.872788	+	0.832202i
$362$	14.1636	+	11.1384i	0.744424	+	0.585422i
$363$	2.42938	−	1.10946i	0.127509	−	0.0582315i
$364$	22.9029	−	20.7633i	1.20044	−	1.08829i
$365$	−27.5987	−	42.9445i	−1.44458	−	2.24782i
$366$	8.41072	−	2.91098i	0.439635	−	0.152159i
$367$	4.19609	+	7.26784i	0.219034	+	0.379378i	0.954513	−	0.298170i	$-0.0963761\pi$
$367$	4.19609	+	7.26784i	0.219034	+	0.379378i	−0.735479	+	0.677548i	$0.763043\pi$
$368$	−10.0546	+	12.0763i	−0.524132	+	0.629522i
$369$	−1.73240	−	1.00020i	−0.0901849	−	0.0520683i
$370$	−7.68221	−	6.65667i	−0.399379	−	0.346064i
$371$	5.45722	+	2.34570i	0.283325	+	0.121783i
$372$	0.807749	+	5.61802i	0.0418798	+	0.291281i
$373$	−1.24502	+	13.0384i	−0.0644646	+	0.675104i	0.904263	+	0.426977i	$0.140421\pi$
$373$	−1.24502	+	13.0384i	−0.0644646	+	0.675104i	−0.968727	+	0.248128i	$0.920185\pi$
$374$	11.1769	+	27.9184i	0.577941	+	1.44363i
$375$	−16.2821	+	17.0762i	−0.840806	+	0.881812i
$376$	−1.17919	−	2.28732i	−0.0608122	−	0.117959i
$377$	24.7161	+	11.2874i	1.27294	+	0.581333i
$378$	3.70145	−	4.06063i	0.190382	−	0.208856i
$379$	−13.9894	+	12.1219i	−0.718587	+	0.622659i	−0.935415	−	0.353550i	$-0.884974\pi$
$379$	−13.9894	+	12.1219i	−0.718587	+	0.622659i	0.216828	+	0.976210i	$0.430429\pi$
$380$	−58.6523	+	11.3043i	−3.00880	+	0.579898i
$381$	5.66125	−	1.37340i	0.290035	−	0.0703616i
$382$	1.96081	+	20.5346i	0.100324	+	1.05064i
$383$	7.18073	−	3.70192i	0.366918	−	0.189160i	−0.264900	−	0.964276i	$-0.585339\pi$
$383$	7.18073	−	3.70192i	0.366918	−	0.189160i	0.631819	+	0.775116i	$0.282309\pi$
$384$	−1.44610	−	4.92496i	−0.0737959	−	0.251326i
$385$	−2.83693	+	38.9216i	−0.144583	+	1.98363i
$386$	−19.7037	−	43.1451i	−1.00289	−	2.19603i
$387$	3.92120	−	9.79468i	0.199326	−	0.497892i
$388$	−6.01397	−	3.10042i	−0.305313	−	0.157400i
$389$	−1.54128	+	7.99694i	−0.0781462	+	0.405461i	0.921700	+	0.387904i	$0.126801\pi$
$389$	−1.54128	+	7.99694i	−0.0781462	+	0.405461i	−0.999846	+	0.0175567i	$0.994411\pi$
$390$	20.9273	−	36.2472i	1.05970	−	1.83545i
$391$	−18.7293	−	1.41673i	−0.947181	−	0.0716472i
$392$	4.50233	−	0.634844i	0.227402	−	0.0320645i
$393$	6.22610	−	7.18530i	0.314065	−	0.362451i
$394$	−0.466172	−	9.78616i	−0.0234854	−	0.493019i
$395$	10.3269	+	13.1317i	0.519602	+	0.660728i
$396$	−6.96564	−	4.96021i	−0.350037	−	0.249260i
$397$	−0.311568	+	0.396191i	−0.0156372	+	0.0198843i	−0.793809	−	0.608167i	$-0.791905\pi$
$397$	−0.311568	+	0.396191i	−0.0156372	+	0.0198843i	0.778172	+	0.628052i	$0.216147\pi$
$398$	3.51145	−	1.03105i	0.176013	−	0.0516820i
$399$	−15.0223	−	8.22934i	−0.752056	−	0.411982i
$400$	−14.8563	+	32.5308i	−0.742815	+	1.62654i
$401$	21.2254	+	22.2605i	1.05994	+	1.11164i	0.993498	+	0.113847i	$0.0363175\pi$
$401$	21.2254	+	22.2605i	1.05994	+	1.11164i	0.0664460	+	0.997790i	$0.478834\pi$
$402$	1.20199	−	3.47293i	0.0599500	−	0.173214i
$403$	−4.05507	+	11.7164i	−0.201998	+	0.583634i
$404$	8.75866	+	9.18582i	0.435759	+	0.457011i
$405$	1.65721	−	3.62879i	0.0823476	−	0.180316i
$406$	15.3460	+	25.2540i	0.761611	+	1.25333i
$407$	−4.35282	+	1.27810i	−0.215761	+	0.0633532i
$408$	1.57258	−	1.99969i	0.0778541	−	0.0989995i
$409$	16.7756	+	11.9458i	0.829499	+	0.590683i	0.913988	−	0.405741i	$-0.132987\pi$
$409$	16.7756	+	11.9458i	0.829499	+	0.590683i	−0.0844895	+	0.996424i	$0.526926\pi$
$410$	−10.2445	−	13.0270i	−0.505940	−	0.643356i
$411$	0.750284	+	15.7504i	0.0370088	+	0.776910i
$412$	−2.57503	+	2.97174i	−0.126863	+	0.146407i
$413$	−10.4013	−	15.4130i	−0.511813	−	0.758423i
$414$	8.76083	−	4.73726i	0.430572	−	0.232824i
$415$	7.84435	−	13.5868i	0.385064	−	0.666951i
$416$	7.74804	−	40.2007i	0.379879	−	1.97100i
$417$	−14.8862	−	7.67437i	−0.728980	−	0.375816i
$418$	−18.4756	+	46.1497i	−0.903670	+	2.25726i
$419$	10.6574	+	23.3365i	0.520650	+	1.14006i	0.969193	+	0.246303i	$0.0792157\pi$
$419$	10.6574	+	23.3365i	0.520650	+	1.14006i	−0.448543	+	0.893761i	$0.648057\pi$
$420$	21.9716	−	10.6362i	1.07210	−	0.518995i
$421$	−7.86430	−	26.7833i	−0.383283	−	1.30534i	−0.894954	−	0.446159i	$-0.852792\pi$
$421$	−7.86430	−	26.7833i	−0.383283	−	1.30534i	0.511671	−	0.859181i	$-0.329027\pi$
$422$	−30.3330	+	15.6378i	−1.47659	+	0.761234i
$423$	−0.376591	−	3.94384i	−0.0183105	−	0.191756i
$424$	−1.41721	+	0.343811i	−0.0688258	+	0.0166969i
$425$	−41.9739	+	8.08981i	−2.03603	+	0.392413i
$426$	−20.5222	+	17.7826i	−0.994304	+	0.861569i
$427$	8.37986	+	7.63864i	0.405530	+	0.369660i
$428$	−20.9524	−	9.56866i	−1.01277	−	0.462519i
$429$	−8.55942	−	16.6030i	−0.413253	−	0.801599i
$430$	60.3176	−	63.2592i	2.90877	−	3.05063i
$431$	−1.54524	−	3.85981i	−0.0744314	−	0.185921i	0.886486	−	0.462755i	$-0.153139\pi$
$431$	−1.54524	−	3.85981i	−0.0744314	−	0.185921i	−0.960918	+	0.276834i	$0.910715\pi$
$432$	0.311462	−	3.26178i	0.0149852	−	0.156932i
$433$	−0.398418	−	2.77105i	−0.0191467	−	0.133168i	0.978006	−	0.208577i	$-0.0668831\pi$
$433$	−0.398418	−	2.77105i	−0.0191467	−	0.133168i	−0.997153	+	0.0754083i	$0.975974\pi$
$434$	−10.8055	+	8.06599i	−0.518681	+	0.387180i
$435$	16.2151	+	14.0504i	0.777454	+	0.673667i
$436$	9.24663	+	5.33855i	0.442833	+	0.255670i
$437$	−20.7907	−	23.0597i	−0.994552	−	1.10309i
$438$	13.2872	+	23.0141i	0.634886	+	1.09965i
$439$	−23.3028	+	8.06516i	−1.11218	+	0.384929i	−0.820534	−	0.571597i	$-0.806324\pi$
$439$	−23.3028	+	8.06516i	−1.11218	+	0.384929i	−0.291646	+	0.956526i	$0.594203\pi$
$440$	−5.17983	−	8.05997i	−0.246939	−	0.384244i
$441$	6.79817	+	1.66881i	0.323722	+	0.0794670i
$442$	37.3774	−	17.0697i	1.77786	−	0.811923i
$443$	3.97567	+	3.12650i	0.188890	+	0.148545i	0.708126	−	0.706086i	$-0.249541\pi$
$443$	3.97567	+	3.12650i	0.188890	+	0.148545i	−0.519236	+	0.854631i	$0.673783\pi$
$444$	2.05374	+	1.95824i	0.0974664	+	0.0929340i
$445$	−1.61085	+	33.8160i	−0.0763618	+	1.60303i
$446$	−26.3319	+	18.7508i	−1.24685	+	0.887878i
$447$	11.5555	+	3.39300i	0.546555	+	0.160483i
$448$	19.2507	−	19.1984i	0.909510	−	0.907040i
$449$	15.8788	+	18.3251i	0.749366	+	0.864815i	0.994507	−	0.104673i	$-0.0333795\pi$
$449$	15.8788	+	18.3251i	0.749366	+	0.864815i	−0.245140	+	0.969488i	$0.578834\pi$
$450$	16.4044	−	15.6416i	0.773311	−	0.737351i
$451$	−7.36277	+	0.703059i	−0.346699	+	0.0331058i
$452$	−32.7977	−	1.56235i	−1.54267	−	0.0734866i
$453$	−13.8659	−	3.36382i	−0.651475	−	0.158046i
$454$	−0.291439	+	2.02700i	−0.0136779	+	0.0951319i
$455$	53.3060	+	1.34145i	2.49902	+	0.0628883i
$456$	4.16242	−	0.598466i	0.194923	−	0.0280257i
$457$	−5.77976	+	0.275324i	−0.270366	+	0.0128791i	−0.182327	−	0.983238i	$-0.558363\pi$
$457$	−5.77976	+	0.275324i	−0.270366	+	0.0128791i	−0.0880388	+	0.996117i	$0.528060\pi$
$458$	12.6903	+	2.44586i	0.592981	+	0.114288i
$459$	3.39178	−	1.95824i	0.158315	−	0.0914029i
$460$	43.9563	−	5.07295i	2.04947	−	0.236528i
$461$			18.4013i			0.857036i	0.903533	+	0.428518i	$0.140964\pi$
$461$			18.4013i			0.857036i	−0.903533	+	0.428518i	$0.859036\pi$
$462$	2.43924	−	20.1683i	0.113484	−	0.938316i
$463$	31.2883	−	20.1078i	1.45409	−	0.934486i	0.455059	−	0.890461i	$-0.349618\pi$
$463$	31.2883	−	20.1078i	1.45409	−	0.934486i	0.999030	−	0.0440250i	$-0.0140181\pi$
$464$	16.3603	+	6.54966i	0.759506	+	0.304061i
$465$	−5.67883	+	7.97480i	−0.263350	+	0.369823i
$466$	48.7850	−	19.5306i	2.25992	−	0.904736i
$467$	6.64105	−	27.3748i	0.307311	−	1.26675i	−0.583400	−	0.812185i	$-0.698278\pi$
$467$	6.64105	−	27.3748i	0.307311	−	1.26675i	0.890711	−	0.454569i	$-0.150207\pi$
$468$	−6.31701	+	9.82945i	−0.292004	+	0.454367i
$469$	4.61826	−	0.770143i	0.213252	−	0.0355619i
$470$	9.24702	−	31.4925i	0.426533	−	1.45264i
$471$	3.36096	+	17.4383i	0.154865	+	0.803516i
$472$	4.31397	+	1.49308i	0.198566	+	0.0687245i
$473$	−9.19674	−	37.9095i	−0.422867	−	1.74308i
$474$	−5.04455	−	7.08407i	−0.231704	−	0.325382i
$475$	−59.4436	−	38.2021i	−2.72746	−	1.75283i
$476$	23.6279	+	4.00627i	1.08298	+	0.183627i
$477$	−2.22226	−	0.319512i	−0.101750	−	0.0146295i
$478$	48.3157	+	4.61359i	2.20991	+	0.211021i
$479$	−1.07375	+	0.844409i	−0.0490611	+	0.0385820i	−0.642388	−	0.766379i	$-0.722056\pi$
$479$	−1.07375	+	0.844409i	−0.0490611	+	0.0385820i	0.593327	+	0.804961i	$0.297814\pi$
$480$	14.8136	−	28.7344i	0.676146	−	1.31154i
$481$	2.02740	+	5.85779i	0.0924416	+	0.267092i
$482$	13.1377			0.598407
$483$	10.6367	+	6.91813i	0.483987	+	0.314786i
$484$	−6.17680			−0.280764
$485$	−3.81716	−	11.0290i	−0.173328	−	0.500799i
$486$	−0.951610	+	1.84586i	−0.0431659	+	0.0837301i
$487$	0.231200	−	0.181818i	0.0104767	−	0.00823896i	−0.612907	−	0.790155i	$-0.710000\pi$
$487$	0.231200	−	0.181818i	0.0104767	−	0.00823896i	0.623384	+	0.781916i	$0.285758\pi$
$488$	−2.77119	−	0.264616i	−0.125446	−	0.0119786i
$489$	−21.4930	−	3.09023i	−0.971949	−	0.139745i
$490$	47.1477	+	33.7674i	2.12992	+	1.52545i
$491$	19.8928	+	12.7843i	0.897748	+	0.576947i	0.906122	−	0.423017i	$-0.139029\pi$
$491$	19.8928	+	12.7843i	0.897748	+	0.576947i	−0.00837373	+	0.999965i	$0.502665\pi$
$492$	2.68362	+	3.76862i	0.120987	+	0.169902i
$493$	4.96603	+	20.4703i	0.223659	+	0.921935i
$494$	64.1880	+	22.2157i	2.88796	+	0.999531i
$495$	−2.79146	−	14.4834i	−0.125467	−	0.650983i
$496$	−2.26545	+	7.71542i	−0.101722	+	0.346432i
$497$	−32.3975	−	12.1339i	−1.45323	−	0.544278i
$498$	−4.41548	+	6.87063i	−0.197863	+	0.307880i
$499$	0.918743	−	3.78711i	0.0411286	−	0.169534i	−0.947543	−	0.319628i	$-0.896442\pi$
$499$	0.918743	−	3.78711i	0.0411286	−	0.169534i	0.988672	+	0.150093i	$0.0479574\pi$
$500$	50.6602	−	20.2813i	2.26559	−	0.907007i
$501$	−2.81225	+	3.94925i	−0.125642	+	0.176439i
$502$	−13.5082	−	5.40786i	−0.602900	−	0.241365i
$503$	28.6221	−	18.3943i	1.27619	−	0.820160i	0.285781	−	0.958295i	$-0.407747\pi$
$503$	28.6221	−	18.3943i	1.27619	−	0.820160i	0.990413	+	0.138135i	$0.0441107\pi$
$504$	−1.58072	+	0.674361i	−0.0704108	+	0.0300384i
$505$			21.8928i			0.974216i
$506$	16.2260	−	33.0571i	0.721331	−	1.46957i
$507$	−10.8455	+	6.26166i	−0.481666	+	0.278090i
$508$	−13.2295	−	2.54978i	−0.586965	−	0.113128i
$509$	−11.8111	+	0.562634i	−0.523520	+	0.0249383i	−0.307679	−	0.951490i	$-0.599552\pi$
$509$	−11.8111	+	0.562634i	−0.523520	+	0.0249383i	−0.215841	+	0.976429i	$0.569249\pi$
$510$	32.1165	−	4.61766i	1.42214	−	0.204473i
$511$	−17.6601	+	28.8848i	−0.781239	+	1.27779i
$512$	4.38464	−	30.4959i	0.193776	−	1.34774i
$513$	6.29154	+	1.52631i	0.277778	+	0.0673883i
$514$	−50.7974	−	2.41978i	−2.24058	−	0.106732i
$515$	−6.75188	+	0.644726i	−0.297523	+	0.0284100i
$516$	−17.6597	+	16.8385i	−0.777425	+	0.741273i
$517$	−9.59257	−	11.0704i	−0.421881	−	0.486876i
$518$	−1.75370	+	6.50947i	−0.0770531	+	0.286010i
$519$	19.6751	+	5.77712i	0.863640	+	0.253588i
$520$	−10.6638	+	7.59364i	−0.467637	+	0.333003i
$521$	−1.29810	+	27.2504i	−0.0568707	+	1.19386i	0.772445	+	0.635082i	$0.219034\pi$
$521$	−1.29810	+	27.2504i	−0.0568707	+	1.19386i	−0.829315	+	0.558781i	$0.811269\pi$
$522$	−8.08356	−	7.70766i	−0.353808	−	0.337355i
$523$	−28.8097	−	22.6562i	−1.25976	−	0.990686i	−0.999685	−	0.0250972i	$-0.992010\pi$
$523$	−28.8097	−	22.6562i	−1.25976	−	0.990686i	−0.260074	−	0.965589i	$-0.583747\pi$
$524$	−20.0017	+	9.13447i	−0.873778	+	0.399041i
$525$	27.4938	+	8.83005i	1.19993	+	0.385375i
$526$	−28.8777	−	44.9346i	−1.25913	−	1.95924i
$527$	−9.08282	+	3.14360i	−0.395654	+	0.136937i
$528$	−6.05747	−	10.4918i	−0.263617	−	0.456599i
$529$	14.0690	+	18.1952i	0.611694	+	0.791094i
$530$	−16.1080	−	9.29998i	−0.699688	−	0.403965i
$531$	5.31139	+	4.60234i	0.230495	+	0.199725i
$532$	23.6971	+	31.7456i	1.02740	+	1.37634i
$533$	1.43825	+	10.0033i	0.0622976	+	0.433289i
$534$	1.67524	−	17.5439i	0.0724946	−	0.759198i
$535$	−14.7666	−	36.8851i	−0.638415	−	1.59468i
$536$	−0.793230	+	0.831916i	−0.0342623	+	0.0359333i
$537$	3.63272	+	7.04649i	0.156763	+	0.304078i
$538$	−9.99438	−	4.56428i	−0.430888	−	0.196780i
$539$	24.0539	−	9.55389i	1.03607	−	0.411515i
$540$	−6.97281	+	6.04198i	−0.300062	+	0.260005i
$541$	−32.6036	+	6.28382i	−1.40174	+	0.270163i	−0.833417	−	0.552645i	$-0.813619\pi$
$541$	−32.6036	+	6.28382i	−1.40174	+	0.270163i	−0.568320	+	0.822807i	$0.692407\pi$
$542$	22.4178	−	5.43851i	0.962928	−	0.233604i
$543$	−0.824753	−	8.63721i	−0.0353935	−	0.370658i
$544$	28.2100	−	14.5433i	1.20949	−	0.623537i
$545$	5.18862	+	17.6708i	0.222256	+	0.756935i
$546$	−27.6851	−	2.01792i	−1.18481	−	0.0863590i
$547$	3.34605	+	7.32682i	0.143067	+	0.313272i	0.967578	−	0.252574i	$-0.0812770\pi$
$547$	3.34605	+	7.32682i	0.143067	+	0.313272i	−0.824511	+	0.565846i	$0.808550\pi$
$548$	13.5540	−	33.8562i	0.578997	−	1.44626i
$549$	−3.80929	−	1.96382i	−0.162576	−	0.0838140i
$550$	15.8605	−	82.2920i	0.676293	−	3.50894i
$551$	−17.4096	+	30.1544i	−0.741676	+	1.28462i
$552$	−3.10809	+	0.209494i	−0.132289	+	0.00891665i
$553$	4.85469	−	9.95933i	0.206443	−	0.423514i
$554$	−29.6927	+	34.2672i	−1.26152	+	1.45587i
$555$	0.232901	+	4.88919i	0.00988610	+	0.207535i
$556$	23.9440	+	30.4473i	1.01545	+	1.29125i
$557$	−10.2207	−	7.27815i	−0.433066	−	0.308385i	0.342654	−	0.939461i	$-0.388674\pi$
$557$	−10.2207	−	7.27815i	−0.433066	−	0.308385i	−0.775721	+	0.631077i	$0.782613\pi$
$558$	3.15044	−	4.00611i	0.133369	−	0.169592i
$559$	−51.1423	+	15.0167i	−2.16309	+	0.635141i
$560$	34.5749	−	0.775994i	1.46106	−	0.0327917i
$561$	6.01554	−	13.1722i	0.253976	−	0.556130i
$562$	−17.7853	−	18.6527i	−0.750227	−	0.786815i
$563$	−5.99076	+	17.3092i	−0.252480	+	0.729494i	0.745532	+	0.666470i	$0.232196\pi$
$563$	−5.99076	+	17.3092i	−0.252480	+	0.729494i	−0.998012	+	0.0630237i	$0.979926\pi$
$564$	−2.99683	+	8.65877i	−0.126189	+	0.364600i
$565$	−39.0838	−	40.9899i	−1.64427	−	1.72446i
$566$	−3.10824	+	6.80610i	−0.130649	+	0.286082i
$567$	−2.64509	+	0.0593659i	−0.111083	+	0.00249313i
$568$	8.14937	−	2.39287i	0.341940	−	0.100403i
$569$	13.3785	−	17.0122i	0.560858	−	0.713189i	−0.420085	−	0.907485i	$-0.638000\pi$
$569$	13.3785	−	17.0122i	0.560858	−	0.713189i	0.980943	+	0.194296i	$0.0622422\pi$
$570$	43.6899	+	31.1114i	1.82997	+	1.30312i
$571$	10.5554	+	13.4223i	0.441730	+	0.561705i	0.955032	−	0.296503i	$-0.0958204\pi$
$571$	10.5554	+	13.4223i	0.441730	+	0.561705i	−0.513302	+	0.858208i	$0.671578\pi$
$572$	2.05561	+	43.1525i	0.0859493	+	1.80430i
$573$	6.50469	−	7.50681i	0.271737	−	0.313602i
$574$	−4.81597	+	9.87989i	−0.201015	+	0.412379i
$575$	41.7746	+	31.5401i	1.74212	+	1.31531i
$576$	−5.13798	+	8.89925i	−0.214083	+	0.370802i
$577$	−2.35526	+	12.2203i	−0.0980509	+	0.508736i	0.899384	+	0.437159i	$0.144015\pi$
$577$	−2.35526	+	12.2203i	−0.0980509	+	0.508736i	−0.997435	+	0.0715773i	$0.977197\pi$
$578$	−3.06624	−	1.58076i	−0.127539	−	0.0657508i
$579$	−8.48860	+	21.2035i	−0.352774	+	0.881188i
$580$	−20.6138	−	45.1379i	−0.855940	−	1.87425i
$581$	−10.3774	−	0.756393i	−0.430528	−	0.0313805i
$582$	1.71168	+	5.82943i	0.0709512	+	0.241638i
$583$	−7.37827	+	3.80376i	−0.305577	+	0.157536i
$584$	−0.790093	−	8.27423i	−0.0326943	−	0.342390i
$585$	−19.5860	+	4.75152i	−0.809783	+	0.196451i
$586$	14.2055	−	2.73788i	0.586824	−	0.113101i
$587$	−9.92387	+	8.59908i	−0.409602	+	0.354922i	−0.835158	−	0.550010i	$-0.814624\pi$
$587$	−9.92387	+	8.59908i	−0.409602	+	0.354922i	0.425556	+	0.904932i	$0.360078\pi$
$588$	−12.6985	−	10.0422i	−0.523677	−	0.414134i
$589$	−14.4522	−	6.60008i	−0.595491	−	0.271952i
$590$	26.6799	+	51.7519i	1.09840	+	2.13059i
$591$	−3.25555	+	3.41432i	−0.133915	+	0.140447i
$592$	1.49419	+	3.73232i	0.0614110	+	0.153397i
$593$	−0.00645844	+	0.0676358i	−0.000265216	+	0.00277747i	−0.995604	−	0.0936672i	$-0.970141\pi$
$593$	−0.00645844	+	0.0676358i	−0.000265216	+	0.00277747i	0.995338	+	0.0964447i	$0.0307471\pi$
$594$	1.09276	+	7.60031i	0.0448365	+	0.311844i
$595$	24.7275	+	33.1258i	1.01373	+	1.35803i
$596$	−21.0503	−	18.2402i	−0.862253	−	0.747147i
$597$	−1.52615	−	0.881121i	−0.0624610	−	0.0360619i
$598$	−46.1724	−	19.9966i	−1.88813	−	0.817720i
$599$	12.4611	+	21.5832i	0.509146	+	0.881866i	0.999944	+	0.0105928i	$0.00337187\pi$
$599$	12.4611	+	21.5832i	0.509146	+	0.881866i	−0.490798	+	0.871273i	$0.663295\pi$
$600$	−6.69962	+	2.31876i	−0.273511	+	0.0946630i
$601$	−24.7850	−	38.5662i	−1.01100	−	1.57315i	−0.803844	−	0.594840i	$-0.797215\pi$
$601$	−24.7850	−	38.5662i	−1.01100	−	1.57315i	−0.207156	−	0.978308i	$-0.566421\pi$
$602$	−55.1926	−	17.7259i	−2.24948	−	0.722455i
$603$	−1.60972	+	0.735137i	−0.0655531	+	0.0299371i
$604$	25.9389	+	20.3985i	1.05544	+	0.830005i
$605$	−7.71089	−	7.35232i	−0.313492	−	0.298914i
$606$	0.542282	−	11.3839i	0.0220287	−	0.462439i
$607$	23.3446	−	16.6236i	0.947529	−	0.674733i	0.00190664	−	0.999998i	$-0.499393\pi$
$607$	23.3446	−	16.6236i	0.947529	−	0.674733i	0.945623	+	0.325266i	$0.105454\pi$
$608$	50.3386	+	14.7808i	2.04150	+	0.599439i
$609$	3.70159	−	13.7398i	0.149996	−	0.556763i
$610$	−23.2512	−	26.8334i	−0.941415	−	1.08645i
$611$	−14.4856	+	13.8120i	−0.586026	+	0.558775i
$612$	−9.01695	+	0.861014i	−0.364488	+	0.0348044i
$613$	−3.67932	−	0.175268i	−0.148607	−	0.00707900i	−0.0268532	−	0.999639i	$-0.508549\pi$
$613$	−3.67932	−	0.175268i	−0.148607	−	0.00707900i	−0.121753	+	0.992560i	$0.538852\pi$
$614$	55.8862	+	13.5578i	2.25538	+	0.547150i
$615$	−1.13570	+	7.89895i	−0.0457958	+	0.318516i
$616$	−3.31452	+	5.42121i	−0.133546	+	0.218427i
$617$	−4.41275	+	0.634458i	−0.177651	+	0.0255423i	−0.230566	−	0.973057i	$-0.574058\pi$
$617$	−4.41275	+	0.634458i	−0.177651	+	0.0255423i	0.0529153	+	0.998599i	$0.483149\pi$
$618$	3.52684	−	0.168004i	0.141870	−	0.00675811i
$619$	17.6734	+	3.40627i	0.710354	+	0.136909i	0.531614	−	0.846987i	$-0.321586\pi$
$619$	17.6734	+	3.40627i	0.710354	+	0.136909i	0.178740	+	0.983896i	$0.442798\pi$
$620$	19.6089	−	11.3212i	0.787512	−	0.454670i
$621$	−4.56209	−	1.47898i	−0.183070	−	0.0593493i
$622$			23.5587i			0.944620i
$623$	20.6518	−	8.81041i	0.827397	−	0.352981i
$624$	−13.9258	+	8.94958i	−0.557479	+	0.358270i
$625$	36.7202	+	14.7005i	1.46881	+	0.588022i
$626$	−33.3786	+	46.8737i	−1.33408	+	1.87345i
$627$	22.2224	−	8.89650i	0.887477	−	0.355292i
$628$	9.68338	−	39.9154i	0.386409	−	1.59280i
$629$	−2.59800	+	4.04256i	−0.103589	+	0.161188i
$630$	−20.5267	−	7.68788i	−0.817804	−	0.306292i
$631$	12.6819	−	43.1905i	0.504858	−	1.71939i	−0.173662	−	0.984805i	$-0.555560\pi$
$631$	12.6819	−	43.1905i	0.504858	−	1.71939i	0.678520	−	0.734582i	$-0.262622\pi$
$632$	0.514786	+	2.67096i	0.0204771	+	0.106245i
$633$	15.5292	+	5.37469i	0.617229	+	0.213625i
$634$	3.26641	+	13.4643i	0.129726	+	0.534737i
$635$	−13.4802	−	18.9303i	−0.534946	−	0.751227i
$636$	4.36815	+	2.80724i	0.173209	+	0.111314i
$637$	−14.6034	−	32.2084i	−0.578606	−	1.27615i
$638$	−40.8767	−	5.87719i	−1.61833	−	0.232680i
$639$	13.0166	+	1.24293i	0.514927	+	0.0491696i
$640$	−16.0957	+	12.6578i	−0.636237	+	0.500343i
$641$	7.67976	−	14.8967i	0.303332	−	0.588382i	−0.687071	−	0.726590i	$-0.741104\pi$
$641$	7.67976	−	14.8967i	0.303332	−	0.588382i	0.990403	+	0.138208i	$0.0441342\pi$
$642$	6.76475	+	19.5455i	0.266983	+	0.771397i
$643$	−30.0531			−1.18518			−0.592589	−	0.805505i	$-0.701894\pi$
$643$	−30.0531			−1.18518			−0.592589	+	0.805505i	$0.701894\pi$
$644$	−15.7306	−	24.7735i	−0.619871	−	0.976215i
$645$	−42.0888			−1.65724
$646$	17.2222	+	49.7602i	0.677597	+	1.95779i
$647$	11.7629	−	22.8169i	0.462449	−	0.897026i	−0.536151	−	0.844122i	$-0.680122\pi$
$647$	11.7629	−	22.8169i	0.462449	−	0.897026i	0.998600	−	0.0529034i	$-0.0168475\pi$
$648$	0.510583	−	0.401527i	0.0200576	−	0.0157735i
$649$	25.8675	+	2.47005i	1.01539	+	0.0969579i
$650$	−113.346	−	16.2967i	−4.44580	−	0.639210i
$651$	6.40157	+	1.08543i	0.250897	+	0.0425414i
$652$	42.2476	+	27.1509i	1.65454	+	1.06331i
$653$	1.42438	+	2.00027i	0.0557405	+	0.0782765i	0.841505	−	0.540249i	$-0.181670\pi$
$653$	1.42438	+	2.00027i	0.0557405	+	0.0782765i	−0.785765	+	0.618525i	$0.787730\pi$
$654$	−2.26030	−	9.31708i	−0.0883846	−	0.364326i
$655$	−35.8423	−	12.4051i	−1.40047	−	0.484709i
$656$	1.24045	+	6.43608i	0.0484316	+	0.251287i
$657$	3.60513	−	12.2779i	0.140650	−	0.479008i
$658$	−21.4715	+	3.58058i	−0.837044	+	0.139586i
$659$	−5.93632	+	9.23709i	−0.231246	+	0.359826i	−0.937413	−	0.348219i	$-0.886786\pi$
$659$	−5.93632	+	9.23709i	−0.231246	+	0.359826i	0.706167	+	0.708045i	$0.250423\pi$
$660$	−8.04256	+	33.1519i	−0.313056	+	1.29043i
$661$	9.10793	−	3.64627i	0.354257	−	0.141823i	−0.187706	−	0.982225i	$-0.560105\pi$
$661$	9.10793	−	3.64627i	0.354257	−	0.141823i	0.541964	+	0.840402i	$0.317681\pi$
$662$	4.89495	−	6.87400i	0.190248	−	0.267166i
$663$	−18.3690	−	7.35383i	−0.713392	−	0.285599i
$664$	2.14898	−	1.38107i	0.0833966	−	0.0535958i
$665$	−8.20449	+	67.8370i	−0.318157	+	2.63061i
$666$		−	2.54807i		−	0.0987358i
$667$	14.5448	−	21.3014i	0.563179	−	0.824792i
$668$	9.71063	−	5.60643i	0.375715	−	0.216919i
$669$	15.2845	+	2.94585i	0.590933	+	0.113893i
$670$	−14.6443	+	0.697594i	−0.565758	+	0.0269504i
$671$	−15.6847	+	2.25511i	−0.605499	+	0.0870577i
$672$	−21.4337	−	0.539381i	−0.826821	−	0.0208071i
$673$	−4.46816	+	31.0768i	−0.172235	+	1.19792i	0.701914	+	0.712262i	$0.252329\pi$
$673$	−4.46816	+	31.0768i	−0.172235	+	1.19792i	−0.874149	+	0.485659i	$0.838580\pi$
$674$	4.74281	+	1.15059i	0.182686	+	0.0443192i
$675$	−10.9021	−	0.519332i	−0.419623	−	0.0199891i
$676$	28.8325	−	2.75317i	1.10894	−	0.105891i
$677$	19.2880	−	18.3911i	0.741299	−	0.706827i	−0.222063	−	0.975032i	$-0.571279\pi$
$677$	19.2880	−	18.3911i	0.741299	−	0.706827i	0.963362	+	0.268206i	$0.0864306\pi$
$678$	19.3076	+	22.2822i	0.741505	+	0.855742i
$679$	−5.48062	+	5.46573i	−0.210327	+	0.209756i
$680$	−9.73754	−	2.85920i	−0.373418	−	0.109645i
$681$	0.803249	−	0.571991i	0.0307806	−	0.0219187i
$682$	0.896620	−	18.8224i	0.0343334	−	0.720746i
$683$	1.76121	+	1.67931i	0.0673909	+	0.0642571i	0.723026	−	0.690821i	$-0.242751\pi$
$683$	1.76121	+	1.67931i	0.0673909	+	0.0642571i	−0.655635	+	0.755078i	$0.727599\pi$
$684$	−11.7696	−	9.25569i	−0.450021	−	0.353900i
$685$	57.2197	−	26.1314i	2.18625	−	0.998428i
$686$	6.53274	−	37.9026i	0.249421	−	1.44713i
$687$	−3.36452	−	5.23530i	−0.128365	−	0.199739i
$688$	−32.6684	+	11.3066i	−1.24547	+	0.431062i
$689$	5.67121	+	9.82282i	0.216056	+	0.374220i
$690$	−30.5341	−	25.4222i	−1.16241	−	0.967808i
$691$	41.8888	+	24.1845i	1.59353	+	0.920022i	0.992696	+	0.120645i	$0.0384963\pi$
$691$	41.8888	+	24.1845i	1.59353	+	0.920022i	0.600830	+	0.799377i	$0.294837\pi$
$692$	−35.8415	−	31.0569i	−1.36249	−	1.18060i
$693$	−7.83917	+	5.85171i	−0.297785	+	0.222288i
$694$	−1.50036	−	10.4352i	−0.0569529	−	0.396116i
$695$	−6.35095	+	66.5101i	−0.240905	+	2.52287i
$696$	1.29840	+	3.24325i	0.0492157	+	0.122935i
$697$	−5.40644	+	5.67012i	−0.204784	+	0.214771i
$698$	10.4130	+	20.1984i	0.394138	+	0.764521i
$699$	−23.0173	−	10.5116i	−0.870593	−	0.397586i
$700$	−49.3573	−	44.9915i	−1.86553	−	1.70052i
$701$	29.4247	−	25.4966i	1.11136	−	0.962995i	0.111827	−	0.993728i	$-0.464330\pi$
$701$	29.4247	−	25.4966i	1.11136	−	0.962995i	0.999528	+	0.0307329i	$0.00978414\pi$
$702$	10.3021	−	1.98557i	0.388829	−	0.0749406i
$703$	−7.71952	+	1.87273i	−0.291147	+	0.0706315i
$704$	3.61159	+	37.8223i	0.136117	+	1.42548i
$705$	−14.0478	+	7.24213i	−0.529070	+	0.272754i
$706$	−3.16417	−	10.7762i	−0.119085	−	0.405567i
$707$	13.0688	−	6.32648i	0.491503	−	0.237932i
$708$	−6.75221	−	14.7853i	−0.253764	−	0.555665i
$709$	−6.88655	+	17.2018i	−0.258630	+	0.646026i	−0.999677	−	0.0254272i	$-0.991905\pi$
$709$	−6.88655	+	17.2018i	−0.258630	+	0.646026i	0.741047	+	0.671453i	$0.234330\pi$
$710$	96.2861	+	49.6389i	3.61355	+	1.86292i
$711$	−0.792523	+	4.11200i	−0.0297219	+	0.154212i
$712$	−2.75615	+	4.77379i	−0.103291	+	0.178905i
$713$	10.3066	+	5.68279i	0.385985	+	0.212822i
$714$	−12.0374	−	17.8374i	−0.450487	−	0.667548i
$715$	−48.7988	+	56.3169i	−1.82497	+	2.10613i
$716$	−0.872423	−	18.3144i	−0.0326040	−	0.684442i
$717$	−14.4471	−	18.3710i	−0.539537	−	0.686077i
$718$	50.5904	+	36.0252i	1.88802	+	1.34445i
$719$	4.97690	−	6.32864i	0.185607	−	0.236019i	−0.684341	−	0.729162i	$-0.739910\pi$
$719$	4.97690	−	6.32864i	0.185607	−	0.236019i	0.869948	+	0.493144i	$0.164152\pi$
$720$	−12.5419	+	3.68263i	−0.467409	+	0.137244i
$721$	2.33599	+	3.84419i	0.0869970	+	0.143165i
$722$	−19.7672	+	43.2840i	−0.735658	+	1.61087i
$723$	−4.36557	−	4.57848i	−0.162357	−	0.170275i
$724$	−6.56321	+	18.9631i	−0.243920	+	0.704760i
$725$	19.1993	−	55.4728i	0.713045	−	2.06021i
$726$	3.82743	+	4.01409i	0.142049	+	0.148977i
$727$	−15.1537	+	33.1819i	−0.562019	+	1.23065i	0.388920	+	0.921271i	$0.372848\pi$
$727$	−15.1537	+	33.1819i	−0.562019	+	1.23065i	−0.950939	+	0.309378i	$0.899879\pi$
$728$	7.61456	+	4.17132i	0.282214	+	0.154599i
$729$	0.959493	−	0.281733i	0.0355368	−	0.0104345i
$730$	65.5328	−	83.3318i	2.42548	−	3.08425i
$731$	−33.6588	−	23.9683i	−1.24491	−	0.886500i
$732$	6.12712	+	7.79127i	0.226465	+	0.287974i
$733$	2.04156	+	42.8576i	0.0754067	+	1.58298i	0.647030	+	0.762465i	$0.276011\pi$
$733$	2.04156	+	42.8576i	0.0754067	+	1.58298i	−0.571623	+	0.820516i	$0.693686\pi$
$734$	−11.4131	+	13.1714i	−0.421264	+	0.486164i
$735$	−3.89896	−	27.6515i	−0.143815	−	1.01994i
$736$	−36.3577	−	13.7308i	−1.34016	−	0.506122i
$737$	−3.27154	+	5.66647i	−0.120509	+	0.208727i
$738$	0.786201	−	4.07920i	0.0289405	−	0.150157i
$739$	−5.58806	−	2.88085i	−0.205560	−	0.105974i	0.352373	−	0.935860i	$-0.385375\pi$
$739$	−5.58806	−	2.88085i	−0.205560	−	0.105974i	−0.557933	+	0.829886i	$0.688405\pi$
$740$	4.20738	−	10.5095i	0.154667	−	0.386338i
$741$	−13.5871	−	29.7515i	−0.499133	−	1.09295i
$742$	−0.896752	+	12.3031i	−0.0329208	+	0.451661i
$743$	−4.75096	−	16.1803i	−0.174296	−	0.593597i	−0.999583	−	0.0288837i	$-0.990805\pi$
$743$	−4.75096	−	16.1803i	−0.174296	−	0.593597i	0.825287	−	0.564714i	$-0.191013\pi$
$744$	−1.41686	+	0.730444i	−0.0519448	+	0.0267794i
$745$	−4.56691	−	47.8268i	−0.167319	−	1.75224i
$746$	−26.4336	+	6.41273i	−0.967804	+	0.234787i
$747$	3.86163	−	0.744269i	0.141290	−	0.0272314i
$748$	−25.3107	+	21.9318i	−0.925451	+	0.801908i
$749$	−17.7512	+	19.4737i	−0.648616	+	0.711555i
$750$	−44.5715	−	20.3551i	−1.62752	−	0.743264i
$751$	−14.7403	−	28.5922i	−0.537882	−	1.04335i	−0.988584	−	0.150671i	$-0.951857\pi$
$751$	−14.7403	−	28.5922i	−0.537882	−	1.04335i	0.450702	−	0.892675i	$-0.351174\pi$
$752$	−8.95806	+	9.39495i	−0.326667	+	0.342598i
$753$	2.60404	+	6.50457i	0.0948963	+	0.237040i
$754$	−5.36379	+	56.1722i	−0.195338	+	2.04567i
$755$	8.10049	+	56.3402i	0.294807	+	2.05043i
$756$	5.62171	+	2.41641i	0.204459	+	0.0878839i
$757$	9.31597	+	8.07233i	0.338595	+	0.293394i	0.807516	−	0.589846i	$-0.200812\pi$
$757$	9.31597	+	8.07233i	0.338595	+	0.293394i	−0.468921	+	0.883240i	$0.655357\pi$
$758$	−33.2913	−	19.2207i	−1.20919	−	0.698128i
$759$	−16.9121	+	5.32990i	−0.613870	+	0.193463i
$760$	−8.38795	−	14.5284i	−0.304263	−	0.526999i
$761$	−12.1133	+	4.19244i	−0.439105	+	0.151976i	−0.537671	−	0.843155i	$-0.680696\pi$
$761$	−12.1133	+	4.19244i	−0.439105	+	0.151976i	0.0985658	+	0.995131i	$0.468575\pi$
$762$	6.54060	+	10.1774i	0.236941	+	0.368687i
$763$	9.04914	−	8.20377i	0.327601	−	0.296996i
$764$	−20.8967	+	9.54320i	−0.756015	+	0.345261i
$765$	−12.2813	−	9.65813i	−0.444032	−	0.349190i
$766$	12.1424	+	11.5778i	0.438723	+	0.418322i
$767$	1.68943	−	35.4655i	0.0610018	−	1.28059i
$768$	−8.05808	+	5.73813i	−0.290771	+	0.207057i
$769$	34.8852	+	10.2432i

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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.bf (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.679230 + 1.96250i) q^{2} +(0.458227 - 0.888835i) q^{3} +(-1.81797 + 1.42966i) q^{4} +(-3.97123 - 0.379207i) q^{5} +(2.05558 + 0.295548i) q^{6} +(0.921223 + 2.48019i) q^{7} +(-0.546439 - 0.351175i) q^{8} +(-0.580057 - 0.814576i) q^{9} +O(q^{10})\)	\(q+(0.679230 + 1.96250i) q^{2} +(0.458227 - 0.888835i) q^{3} +(-1.81797 + 1.42966i) q^{4} +(-3.97123 - 0.379207i) q^{5} +(2.05558 + 0.295548i) q^{6} +(0.921223 + 2.48019i) q^{7} +(-0.546439 - 0.351175i) q^{8} +(-0.580057 - 0.814576i) q^{9} +(-1.95318 - 8.05113i) q^{10} +(-3.49404 - 1.20930i) q^{11} +(0.437696 + 2.27098i) q^{12} +(-1.42333 + 4.84742i) q^{13} +(-4.24166 + 3.49252i) q^{14} +(-2.15678 + 3.35601i) q^{15} +(-0.772491 + 3.18425i) q^{16} +(-3.63594 + 1.45561i) q^{17} +(1.20462 - 1.69165i) q^{18} +(-6.01028 - 2.40615i) q^{19} +(7.76170 - 4.98814i) q^{20} +(2.62661 + 0.317673i) q^{21} -7.67846i q^{22} +(4.30517 + 2.11318i) q^{23} +(-0.562529 + 0.324777i) q^{24} +(10.7172 + 2.06558i) q^{25} +(-10.4798 + 0.499217i) q^{26} +(-0.989821 + 0.142315i) q^{27} +(-5.22059 - 3.19186i) q^{28} +(0.765412 - 5.32356i) q^{29} +(-8.05113 - 1.95318i) q^{30} +(2.45132 + 0.116771i) q^{31} +(-8.06703 + 0.770308i) q^{32} +(-2.67593 + 2.55149i) q^{33} +(-5.32628 - 6.14686i) q^{34} +(-2.71789 - 10.1987i) q^{35} +(2.21909 + 0.651585i) q^{36} +(0.999459 - 0.711711i) q^{37} +(0.639728 - 13.4295i) q^{38} +(3.65635 + 3.48632i) q^{39} +(2.03687 + 1.60181i) q^{40} +(1.81963 - 0.830995i) q^{41} +(1.16064 + 5.37051i) q^{42} +(5.70399 + 8.87559i) q^{43} +(8.08094 - 2.79684i) q^{44} +(1.99465 + 3.45483i) q^{45} +(-1.22292 + 9.88425i) q^{46} +(3.43100 + 1.98089i) q^{47} +(2.47630 + 2.14573i) q^{48} +(-5.30269 + 4.56962i) q^{49} +(3.22576 + 22.4356i) q^{50} +(-0.372286 + 3.89875i) q^{51} +(-4.34261 - 10.8473i) q^{52} +(1.54930 - 1.62486i) q^{53} +(-0.951610 - 1.84586i) q^{54} +(13.4171 + 6.12737i) q^{55} +(0.367589 - 1.67878i) q^{56} +(-4.89275 + 4.23959i) q^{57} +(10.9674 - 2.11379i) q^{58} +(-6.82986 + 1.65691i) q^{59} +(-0.877021 - 9.18458i) q^{60} +(3.80929 - 1.96382i) q^{61} +(1.43585 + 4.89004i) q^{62} +(1.48594 - 2.18906i) q^{63} +(-4.26879 - 9.34735i) q^{64} +(7.49055 - 18.7105i) q^{65} +(-6.82489 - 3.51848i) q^{66} +(0.334907 - 1.73766i) q^{67} +(4.52898 - 7.84442i) q^{68} +(3.85101 - 2.85827i) q^{69} +(18.1690 - 12.2612i) q^{70} +(-8.56281 + 9.88201i) q^{71} +(0.0309070 + 0.648817i) q^{72} +(7.91014 + 10.0586i) q^{73} +(2.07560 + 1.47803i) q^{74} +(6.74688 - 8.57936i) q^{75} +(14.3665 - 4.21838i) q^{76} +(-0.219499 - 9.77992i) q^{77} +(-4.35842 + 9.54361i) q^{78} +(-2.88983 - 3.03076i) q^{79} +(4.27523 - 12.3525i) q^{80} +(-0.327068 + 0.945001i) q^{81} +(2.86678 + 3.00659i) q^{82} +(-1.63370 + 3.57731i) q^{83} +(-5.22926 + 3.17765i) q^{84} +(14.9911 - 4.40180i) q^{85} +(-13.5441 + 17.2227i) q^{86} +(-4.38103 - 3.11972i) q^{87} +(1.48460 + 1.88783i) q^{88} +(-0.403794 - 8.47668i) q^{89} +(-5.42530 + 6.26113i) q^{90} +(-13.3337 + 0.935424i) q^{91} +(-10.8478 + 2.31326i) q^{92} +(1.22705 - 2.12531i) q^{93} +(-1.55707 + 8.07883i) q^{94} +(22.9558 + 11.8345i) q^{95} +(-3.01185 + 7.52324i) q^{96} +(1.21531 + 2.66116i) q^{97} +(-12.5696 - 7.30274i) q^{98} +(1.04168 + 3.54762i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 640 q - 4 q^{2} + 36 q^{4} + 24 q^{8} - 32 q^{9}+O(q^{10}) \) 640 * q - 4 * q^2 + 36 * q^4 + 24 * q^8 - 32 * q^9	\( 640 q - 4 q^{2} + 36 q^{4} + 24 q^{8} - 32 q^{9} + 4 q^{18} - 28 q^{23} + 56 q^{25} - 84 q^{26} - 176 q^{28} - 24 q^{29} + 12 q^{31} + 36 q^{32} - 76 q^{35} + 28 q^{36} + 44 q^{37} - 110 q^{42} - 88 q^{43} + 154 q^{44} + 8 q^{46} + 12 q^{47} - 8 q^{49} - 212 q^{50} + 44 q^{51} + 108 q^{52} - 110 q^{56} - 88 q^{57} + 2 q^{58} - 36 q^{59} - 168 q^{64} - 48 q^{70} + 16 q^{71} + 12 q^{72} - 48 q^{73} - 22 q^{74} + 48 q^{75} + 32 q^{78} - 44 q^{79} - 594 q^{80} + 32 q^{81} + 24 q^{82} + 352 q^{85} - 36 q^{87} - 330 q^{88} + 244 q^{92} - 24 q^{93} - 486 q^{94} - 154 q^{95} - 60 q^{96} - 24 q^{98} - 44 q^{99}+O(q^{100}) \) 640 * q - 4 * q^2 + 36 * q^4 + 24 * q^8 - 32 * q^9 + 4 * q^18 - 28 * q^23 + 56 * q^25 - 84 * q^26 - 176 * q^28 - 24 * q^29 + 12 * q^31 + 36 * q^32 - 76 * q^35 + 28 * q^36 + 44 * q^37 - 110 * q^42 - 88 * q^43 + 154 * q^44 + 8 * q^46 + 12 * q^47 - 8 * q^49 - 212 * q^50 + 44 * q^51 + 108 * q^52 - 110 * q^56 - 88 * q^57 + 2 * q^58 - 36 * q^59 - 168 * q^64 - 48 * q^70 + 16 * q^71 + 12 * q^72 - 48 * q^73 - 22 * q^74 + 48 * q^75 + 32 * q^78 - 44 * q^79 - 594 * q^80 + 32 * q^81 + 24 * q^82 + 352 * q^85 - 36 * q^87 - 330 * q^88 + 244 * q^92 - 24 * q^93 - 486 * q^94 - 154 * q^95 - 60 * q^96 - 24 * q^98 - 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more