LMFDB - Embedded newform 380.3.h.a.39.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,3,Mod(39,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("380.39");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	380.h (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:	$10.3542500457$
Analytic rank:	$0$
Dimension:	$108$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			39.8
Character	$\chi$	$=$	380.39
Dual form			380.3.h.a.39.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.94008 + 0.485899i) q^{2} +4.64902 q^{3} +(3.52780 - 1.88537i) q^{4} +(2.66799 - 4.22869i) q^{5} +(-9.01947 + 2.25896i) q^{6} +9.90681 q^{7} +(-5.92811 + 5.37191i) q^{8} +12.6134 q^{9} +O(q^{10})$	\(q+(-1.94008 + 0.485899i) q^{2} +4.64902 q^{3} +(3.52780 - 1.88537i) q^{4} +(2.66799 - 4.22869i) q^{5} +(-9.01947 + 2.25896i) q^{6} +9.90681 q^{7} +(-5.92811 + 5.37191i) q^{8} +12.6134 q^{9} +(-3.12138 + 9.50037i) q^{10} -2.36298i q^{11} +(16.4008 - 8.76511i) q^{12} +16.5387i q^{13} +(-19.2200 + 4.81372i) q^{14} +(12.4035 - 19.6593i) q^{15} +(8.89079 - 13.3024i) q^{16} +21.4996i q^{17} +(-24.4710 + 6.12886i) q^{18} -4.35890i q^{19} +(1.43949 - 19.9481i) q^{20} +46.0570 q^{21} +(1.14817 + 4.58437i) q^{22} +6.86595 q^{23} +(-27.5600 + 24.9742i) q^{24} +(-10.7637 - 22.5642i) q^{25} +(-8.03617 - 32.0865i) q^{26} +16.7989 q^{27} +(34.9493 - 18.6780i) q^{28} -36.1705 q^{29} +(-14.5114 + 44.1674i) q^{30} -46.4134i q^{31} +(-10.7852 + 30.1277i) q^{32} -10.9856i q^{33} +(-10.4467 - 41.7109i) q^{34} +(26.4312 - 41.8929i) q^{35} +(44.4977 - 23.7809i) q^{36} +17.7479i q^{37} +(2.11799 + 8.45660i) q^{38} +76.8890i q^{39} +(6.90005 + 39.4004i) q^{40} -54.6944 q^{41} +(-89.3542 + 22.3791i) q^{42} +4.27621 q^{43} +(-4.45508 - 8.33613i) q^{44} +(33.6524 - 53.3383i) q^{45} +(-13.3205 + 3.33616i) q^{46} -40.9908 q^{47} +(41.3335 - 61.8432i) q^{48} +49.1449 q^{49} +(31.8464 + 38.5462i) q^{50} +99.9523i q^{51} +(31.1816 + 58.3455i) q^{52} -10.7606i q^{53} +(-32.5912 + 8.16258i) q^{54} +(-9.99232 - 6.30440i) q^{55} +(-58.7287 + 53.2185i) q^{56} -20.2646i q^{57} +(70.1736 - 17.5752i) q^{58} -70.4443i q^{59} +(6.69224 - 92.7393i) q^{60} +101.474 q^{61} +(22.5522 + 90.0456i) q^{62} +124.959 q^{63} +(6.28509 - 63.6906i) q^{64} +(69.9373 + 44.1251i) q^{65} +(5.33787 + 21.3128i) q^{66} +7.29760 q^{67} +(40.5346 + 75.8464i) q^{68} +31.9200 q^{69} +(-30.9229 + 94.1184i) q^{70} +31.8531i q^{71} +(-74.7738 + 67.7582i) q^{72} -83.7571i q^{73} +(-8.62369 - 34.4323i) q^{74} +(-50.0407 - 104.901i) q^{75} +(-8.21812 - 15.3773i) q^{76} -23.4096i q^{77} +(-37.3603 - 149.171i) q^{78} +137.909i q^{79} +(-32.5313 - 73.0871i) q^{80} -35.4223 q^{81} +(106.111 - 26.5760i) q^{82} +99.8691 q^{83} +(162.480 - 86.8343i) q^{84} +(90.9153 + 57.3607i) q^{85} +(-8.29618 + 2.07781i) q^{86} -168.158 q^{87} +(12.6937 + 14.0080i) q^{88} +76.9267 q^{89} +(-39.3713 + 119.832i) q^{90} +163.846i q^{91} +(24.2217 - 12.9448i) q^{92} -215.777i q^{93} +(79.5254 - 19.9174i) q^{94} +(-18.4325 - 11.6295i) q^{95} +(-50.1407 + 140.064i) q^{96} +155.574i q^{97} +(-95.3450 + 23.8795i) q^{98} -29.8053i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q + 4 q^{5} + 324 q^{9}+O(q^{10}) $ 108 * q + 4 * q^5 + 324 * q^9	$ 108 q + 4 q^{5} + 324 q^{9} - 8 q^{10} + 8 q^{14} - 104 q^{16} - 16 q^{21} - 8 q^{24} - 76 q^{25} + 80 q^{26} - 88 q^{29} - 140 q^{30} - 88 q^{34} - 256 q^{36} + 44 q^{40} - 200 q^{41} - 8 q^{44} + 108 q^{45} + 272 q^{46} + 916 q^{49} - 276 q^{50} - 320 q^{54} - 328 q^{56} + 172 q^{60} + 200 q^{61} - 216 q^{64} - 192 q^{65} + 152 q^{66} - 592 q^{69} + 200 q^{70} - 232 q^{74} + 340 q^{80} + 1052 q^{81} + 208 q^{84} + 248 q^{85} - 1048 q^{86} + 760 q^{89} + 268 q^{90} - 320 q^{94} + 720 q^{96}+O(q^{100}) $ 108 * q + 4 * q^5 + 324 * q^9 - 8 * q^10 + 8 * q^14 - 104 * q^16 - 16 * q^21 - 8 * q^24 - 76 * q^25 + 80 * q^26 - 88 * q^29 - 140 * q^30 - 88 * q^34 - 256 * q^36 + 44 * q^40 - 200 * q^41 - 8 * q^44 + 108 * q^45 + 272 * q^46 + 916 * q^49 - 276 * q^50 - 320 * q^54 - 328 * q^56 + 172 * q^60 + 200 * q^61 - 216 * q^64 - 192 * q^65 + 152 * q^66 - 592 * q^69 + 200 * q^70 - 232 * q^74 + 340 * q^80 + 1052 * q^81 + 208 * q^84 + 248 * q^85 - 1048 * q^86 + 760 * q^89 + 268 * q^90 - 320 * q^94 + 720 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.94008	+	0.485899i	−0.970039	+	0.242950i
$2$	−1.94008	+	0.485899i	−0.970039	+	0.242950i
$3$	4.64902			1.54967			0.774837	−	0.632161i	$-0.217832\pi$
$3$	4.64902			1.54967			0.774837	+	0.632161i	$0.217832\pi$
$4$	3.52780	−	1.88537i	0.881951	−	0.471341i
$5$	2.66799	−	4.22869i	0.533597	−	0.845739i
$5$	2.66799	−	4.22869i	0.533597	−	0.845739i
$6$	−9.01947	+	2.25896i	−1.50324	+	0.376493i
$7$	9.90681			1.41526			0.707630	−	0.706584i	$-0.249765\pi$
$7$	9.90681			1.41526			0.707630	+	0.706584i	$0.249765\pi$
$8$	−5.92811	+	5.37191i	−0.741014	+	0.671489i
$9$	12.6134			1.40149
$10$	−3.12138	+	9.50037i	−0.312138	+	0.950037i
$11$		−	2.36298i		−	0.214816i	−0.994215	−	0.107408i	$-0.965745\pi$
$11$		−	2.36298i		−	0.214816i	0.994215	−	0.107408i	$-0.0342552\pi$
$12$	16.4008	−	8.76511i	1.36674	−	0.730426i
$13$			16.5387i			1.27221i	0.771602	+	0.636106i	$0.219456\pi$
$13$			16.5387i			1.27221i	−0.771602	+	0.636106i	$0.780544\pi$
$14$	−19.2200	+	4.81372i	−1.37286	+	0.343837i
$15$	12.4035	−	19.6593i	0.826902	−	1.31062i
$16$	8.89079	−	13.3024i	0.555675	−	0.831400i
$17$			21.4996i			1.26468i	0.774689	+	0.632342i	$0.217906\pi$
$17$			21.4996i			1.26468i	−0.774689	+	0.632342i	$0.782094\pi$
$18$	−24.4710	+	6.12886i	−1.35950	+	0.340492i
$19$		−	4.35890i		−	0.229416i
$19$		−	4.35890i		−	0.229416i
$20$	1.43949	−	19.9481i	0.0719747	−	0.997406i
$21$	46.0570			2.19319
$22$	1.14817	+	4.58437i	0.0521896	+	0.208380i
$23$	6.86595			0.298520			0.149260	−	0.988798i	$-0.452311\pi$
$23$	6.86595			0.298520			0.149260	+	0.988798i	$0.452311\pi$
$24$	−27.5600	+	24.9742i	−1.14833	+	1.04059i
$25$	−10.7637	−	22.5642i	−0.430548	−	0.902568i
$26$	−8.03617	−	32.0865i	−0.309083	−	1.23409i
$27$	16.7989			0.622182
$28$	34.9493	−	18.6780i	1.24819	−	0.667070i
$29$	−36.1705			−1.24726			−0.623629	−	0.781720i	$-0.714342\pi$
$29$	−36.1705			−1.24726			−0.623629	+	0.781720i	$0.714342\pi$
$30$	−14.5114	+	44.1674i	−0.483712	+	1.47225i
$31$		−	46.4134i		−	1.49721i	−0.663018	−	0.748603i	$-0.730725\pi$
$31$		−	46.4134i		−	1.49721i	0.663018	−	0.748603i	$-0.269275\pi$
$32$	−10.7852	+	30.1277i	−0.337038	+	0.941491i
$33$		−	10.9856i		−	0.332896i
$34$	−10.4467	−	41.7109i	−0.307255	−	1.22679i
$35$	26.4312	−	41.8929i	0.755178	−	1.19694i
$36$	44.4977	−	23.7809i	1.23605	−	0.660581i
$37$			17.7479i			0.479673i	0.970813	+	0.239836i	$0.0770938\pi$
$37$			17.7479i			0.479673i	−0.970813	+	0.239836i	$0.922906\pi$
$38$	2.11799	+	8.45660i	0.0557365	+	0.222542i
$39$			76.8890i			1.97151i
$40$	6.90005	+	39.4004i	0.172501	+	0.985009i
$41$	−54.6944			−1.33401			−0.667005	−	0.745053i	$-0.732424\pi$
$41$	−54.6944			−1.33401			−0.667005	+	0.745053i	$0.732424\pi$
$42$	−89.3542	+	22.3791i	−2.12748	+	0.532835i
$43$	4.27621			0.0994467			0.0497234	−	0.998763i	$-0.484166\pi$
$43$	4.27621			0.0994467			0.0497234	+	0.998763i	$0.484166\pi$
$44$	−4.45508	−	8.33613i	−0.101252	−	0.189457i
$45$	33.6524	−	53.3383i	0.747832	−	1.18530i
$46$	−13.3205	+	3.33616i	−0.289576	+	0.0725252i
$47$	−40.9908			−0.872145			−0.436073	−	0.899911i	$-0.643631\pi$
$47$	−40.9908			−0.872145			−0.436073	+	0.899911i	$0.643631\pi$
$48$	41.3335	−	61.8432i	0.861115	−	1.28840i
$49$	49.1449			1.00296
$50$	31.8464	+	38.5462i	0.636927	+	0.770924i
$51$			99.9523i			1.95985i
$52$	31.1816	+	58.3455i	0.599646	+	1.12203i
$53$		−	10.7606i		−	0.203031i	−0.994834	−	0.101515i	$-0.967631\pi$
$53$		−	10.7606i		−	0.203031i	0.994834	−	0.101515i	$-0.0323691\pi$
$54$	−32.5912	+	8.16258i	−0.603541	+	0.151159i
$55$	−9.99232	−	6.30440i	−0.181679	−	0.114625i
$56$	−58.7287	+	53.2185i	−1.04873	+	0.950331i
$57$		−	20.2646i		−	0.355520i
$58$	70.1736	−	17.5752i	1.20989	−	0.303021i
$59$		−	70.4443i		−	1.19397i	−0.802252	−	0.596985i	$-0.796365\pi$
$59$		−	70.4443i		−	1.19397i	0.802252	−	0.596985i	$-0.203635\pi$
$60$	6.69224	−	92.7393i	0.111537	−	1.54566i
$61$	101.474			1.66351			0.831755	−	0.555142i	$-0.187336\pi$
$61$	101.474			1.66351			0.831755	+	0.555142i	$0.187336\pi$
$62$	22.5522	+	90.0456i	0.363746	+	1.45235i
$63$	124.959			1.98347
$64$	6.28509	−	63.6906i	0.0982045	−	0.995166i
$65$	69.9373	+	44.1251i	1.07596	+	0.678848i
$66$	5.33787	+	21.3128i	0.0808769	+	0.322922i
$67$	7.29760			0.108919			0.0544597	−	0.998516i	$-0.482656\pi$
$67$	7.29760			0.108919			0.0544597	+	0.998516i	$0.482656\pi$
$68$	40.5346	+	75.8464i	0.596098	+	1.11539i
$69$	31.9200			0.462608
$70$	−30.9229	+	94.1184i	−0.441756	+	1.34455i
$71$			31.8531i			0.448636i	0.974516	+	0.224318i	$0.0720154\pi$
$71$			31.8531i			0.448636i	−0.974516	+	0.224318i	$0.927985\pi$
$72$	−74.7738	+	67.7582i	−1.03853	+	0.941087i
$73$		−	83.7571i		−	1.14736i	−0.819080	−	0.573679i	$-0.805516\pi$
$73$		−	83.7571i		−	1.14736i	0.819080	−	0.573679i	$-0.194484\pi$
$74$	−8.62369	−	34.4323i	−0.116536	−	0.465301i
$75$	−50.0407	−	104.901i	−0.667210	−	1.39869i
$76$	−8.21812	−	15.3773i	−0.108133	−	0.202333i
$77$		−	23.4096i		−	0.304021i
$78$	−37.3603	−	149.171i	−0.478979	−	1.91245i
$79$			137.909i			1.74568i	0.488002	+	0.872842i	$0.337726\pi$
$79$			137.909i			1.74568i	−0.488002	+	0.872842i	$0.662274\pi$
$80$	−32.5313	−	73.0871i	−0.406641	−	0.913588i
$81$	−35.4223			−0.437312
$82$	106.111	−	26.5760i	1.29404	−	0.324097i
$83$	99.8691			1.20324			0.601621	−	0.798782i	$-0.294522\pi$
$83$	99.8691			1.20324			0.601621	+	0.798782i	$0.294522\pi$
$84$	162.480	−	86.8343i	1.93429	−	1.03374i
$85$	90.9153	+	57.3607i	1.06959	+	0.674832i
$86$	−8.29618	+	2.07781i	−0.0964672	+	0.0241606i
$87$	−168.158			−1.93285
$88$	12.6937	+	14.0080i	0.144247	+	0.159182i
$89$	76.9267			0.864345			0.432173	−	0.901791i	$-0.357747\pi$
$89$	76.9267			0.864345			0.432173	+	0.901791i	$0.357747\pi$
$90$	−39.3713	+	119.832i	−0.437459	+	1.33147i
$91$			163.846i			1.80051i
$92$	24.2217	−	12.9448i	0.263280	−	0.140705i
$93$		−	215.777i		−	2.32018i
$94$	79.5254	−	19.9174i	0.846015	−	0.211887i
$95$	−18.4325	−	11.6295i	−0.194026	−	0.122416i
$96$	−50.1407	+	140.064i	−0.522299	+	1.45901i
$97$			155.574i			1.60386i	0.597421	+	0.801928i	$0.296192\pi$
$97$			155.574i			1.60386i	−0.597421	+	0.801928i	$0.703808\pi$
$98$	−95.3450	+	23.8795i	−0.972908	+	0.243668i
$99$		−	29.8053i		−	0.301063i
$100$	−80.5140	−	59.3085i	−0.805140	−	0.593085i
$101$	−140.019			−1.38633			−0.693165	−	0.720779i	$-0.743784\pi$
$101$	−140.019			−1.38633			−0.693165	+	0.720779i	$0.743784\pi$
$102$	−48.5668	−	193.915i	−0.476145	−	1.90113i
$103$	−159.914			−1.55256			−0.776281	−	0.630387i	$-0.782896\pi$
$103$	−159.914			−1.55256			−0.776281	+	0.630387i	$0.782896\pi$
$104$	−88.8447	−	98.0436i	−0.854276	−	0.942727i
$105$	122.879	−	194.761i	1.17028	−	1.85487i
$106$	5.22858	+	20.8765i	0.0493263	+	0.196948i
$107$	−90.9983			−0.850451			−0.425226	−	0.905087i	$-0.639805\pi$
$107$	−90.9983			−0.850451			−0.425226	+	0.905087i	$0.639805\pi$
$108$	59.2633	−	31.6721i	0.548734	−	0.293260i
$109$	−113.080			−1.03743			−0.518714	−	0.854948i	$-0.673589\pi$
$109$	−113.080			−1.03743			−0.518714	+	0.854948i	$0.673589\pi$
$110$	22.4492	+	7.37576i	0.204083	+	0.0670523i
$111$			82.5103i			0.743336i
$112$	88.0794	−	131.784i	0.786423	−	1.17665i
$113$		−	198.266i		−	1.75457i	−0.479973	−	0.877283i	$-0.659353\pi$
$113$		−	198.266i		−	1.75457i	0.479973	−	0.877283i	$-0.340647\pi$
$114$	9.84657	+	39.3150i	0.0863734	+	0.344868i
$115$	18.3183	−	29.0340i	0.159289	−	0.252470i
$116$	−127.602	+	68.1946i	−1.10002	+	0.587885i
$117$			208.610i			1.78299i
$118$	34.2288	+	136.667i	0.290075	+	1.15820i
$119$			212.993i			1.78985i
$120$	32.0785	+	183.173i	0.267321	+	1.52644i
$121$	115.416			0.953854
$122$	−196.868	+	49.3062i	−1.61367	+	0.404149i
$123$	−254.276			−2.06728
$124$	−87.5062	−	163.737i	−0.705695	−	1.32046i
$125$	−124.134	−	14.6845i	−0.993076	−	0.117476i
$126$	−242.430	+	60.7175i	−1.92405	+	0.481885i
$127$	−27.2569			−0.214621			−0.107311	−	0.994226i	$-0.534224\pi$
$127$	−27.2569			−0.214621			−0.107311	+	0.994226i	$0.534224\pi$
$128$	18.7537	+	126.619i	0.146513	+	0.989209i
$129$	19.8802			0.154110
$130$	−157.124	−	51.6237i	−1.20865	−	0.397105i
$131$		−	80.3096i		−	0.613050i	−0.951863	−	0.306525i	$-0.900834\pi$
$131$		−	80.3096i		−	0.613050i	0.951863	−	0.306525i	$-0.0991663\pi$
$132$	−20.7118	−	38.7549i	−0.156907	−	0.293597i
$133$		−	43.1828i		−	0.324683i
$134$	−14.1579	+	3.54590i	−0.105656	+	0.0264619i
$135$	44.8193	−	71.0375i	0.331995	−	0.526204i
$136$	−115.494	−	127.452i	−0.849221	−	0.937149i
$137$			19.5334i			0.142580i	0.997456	+	0.0712899i	$0.0227116\pi$
$137$			19.5334i			0.142580i	−0.997456	+	0.0712899i	$0.977288\pi$
$138$	−61.9272	+	15.5099i	−0.448748	+	0.112391i
$139$			33.6542i			0.242116i	0.992645	+	0.121058i	$0.0386288\pi$
$139$			33.6542i			0.242116i	−0.992645	+	0.121058i	$0.961371\pi$
$140$	14.2608	−	197.622i	0.101863	−	1.41159i
$141$	−190.567			−1.35154
$142$	−15.4774	−	61.7976i	−0.108996	−	0.435194i
$143$	39.0807			0.273292
$144$	112.143	−	167.789i	0.778774	−	1.16520i
$145$	−96.5024	+	152.954i	−0.665533	+	1.05485i
$146$	40.6975	+	162.495i	0.278750	+	1.11298i
$147$	228.476			1.55426
$148$	33.4612	+	62.6110i	0.226090	+	0.423048i
$149$	−77.4715			−0.519943			−0.259971	−	0.965616i	$-0.583713\pi$
$149$	−77.4715			−0.519943			−0.259971	+	0.965616i	$0.583713\pi$
$150$	148.054	+	179.202i	0.987030	+	1.19468i
$151$		−	251.440i		−	1.66517i	−0.553899	−	0.832584i	$-0.686860\pi$
$151$		−	251.440i		−	1.66517i	0.553899	−	0.832584i	$-0.313140\pi$
$152$	23.4156	+	25.8401i	0.154050	+	0.170000i
$153$			271.184i			1.77244i
$154$	11.3747	+	45.4164i	0.0738618	+	0.294912i
$155$	−196.268	−	123.830i	−1.26625	−	0.798905i
$156$	144.964	+	271.249i	0.929256	+	1.73878i
$157$			116.908i			0.744634i	0.928106	+	0.372317i	$0.121437\pi$
$157$			116.908i			0.744634i	−0.928106	+	0.372317i	$0.878563\pi$
$158$	−67.0100	−	267.554i	−0.424114	−	1.69338i
$159$		−	50.0264i		−	0.314632i
$160$	98.6261	+	125.988i	0.616413	+	0.787423i
$161$	68.0197			0.422482
$162$	68.7220	−	17.2117i	0.424210	−	0.106245i
$163$	228.509			1.40189			0.700947	−	0.713213i	$-0.252761\pi$
$163$	228.509			1.40189			0.700947	+	0.713213i	$0.252761\pi$
$164$	−192.951	+	103.119i	−1.17653	+	0.628774i
$165$	−46.4545	−	29.3093i	−0.281543	−	0.177632i
$166$	−193.754	+	48.5263i	−1.16719	+	0.292327i
$167$	56.5778			0.338789			0.169395	−	0.985548i	$-0.445819\pi$
$167$	56.5778			0.338789			0.169395	+	0.985548i	$0.445819\pi$
$168$	−273.031	+	247.414i	−1.62519	+	1.47270i
$169$	−104.530			−0.618522
$170$	−204.254	−	67.1085i	−1.20150	−	0.394756i
$171$		−	54.9807i		−	0.321524i
$172$	15.0856	−	8.06222i	0.0877071	−	0.0468733i
$173$			51.8491i			0.299705i	0.988708	+	0.149853i	$0.0478800\pi$
$173$			51.8491i			0.299705i	−0.988708	+	0.149853i	$0.952120\pi$
$174$	326.239	−	81.7076i	1.87493	−	0.469584i
$175$	−106.634	−	223.539i	−0.609337	−	1.27737i
$176$	−31.4333	−	21.0088i	−0.178598	−	0.119368i
$177$		−	327.497i		−	1.85027i
$178$	−149.244	+	37.3787i	−0.838449	+	0.209993i
$179$		−	16.8082i		−	0.0939006i	−0.998897	−	0.0469503i	$-0.985050\pi$
$179$		−	16.8082i		−	0.0939006i	0.998897	−	0.0469503i	$-0.0149502\pi$
$180$	18.1570	−	251.614i	0.100872	−	1.39786i
$181$	54.5705			0.301494			0.150747	−	0.988572i	$-0.451832\pi$
$181$	54.5705			0.301494			0.150747	+	0.988572i	$0.451832\pi$
$182$	−79.6128	−	317.875i	−0.437433	−	1.74656i
$183$	471.756			2.57790
$184$	−40.7021	+	36.8833i	−0.221207	+	0.200453i
$185$	75.0504	+	47.3511i	0.405678	+	0.255952i
$186$	104.846	+	418.624i	0.563688	+	2.25067i
$187$	50.8032			0.271675
$188$	−144.608	+	77.2827i	−0.769189	+	0.411078i
$189$	166.424			0.880549
$190$	41.4111	+	13.6058i	0.217953	+	0.0716093i
$191$			175.909i			0.920989i	0.887663	+	0.460494i	$0.152328\pi$
$191$			175.909i			0.920989i	−0.887663	+	0.460494i	$0.847672\pi$
$192$	29.2195	−	296.099i	0.152185	−	1.54218i
$193$			27.3432i			0.141674i	0.997488	+	0.0708372i	$0.0225671\pi$
$193$			27.3432i			0.141674i	−0.997488	+	0.0708372i	$0.977433\pi$
$194$	−75.5933	−	301.826i	−0.389656	−	1.55580i
$195$	325.140	+	205.139i	1.66739	+	1.05199i
$196$	173.374	−	92.6562i	0.884560	−	0.472736i
$197$			43.0994i			0.218779i	0.993999	+	0.109389i	$0.0348895\pi$
$197$			43.0994i			0.218779i	−0.993999	+	0.109389i	$0.965110\pi$
$198$	14.4824	+	57.8246i	0.0731433	+	0.292043i
$199$			118.139i			0.593662i	0.954930	+	0.296831i	$0.0959297\pi$
$199$			118.139i			0.593662i	−0.954930	+	0.296831i	$0.904070\pi$
$200$	185.021	+	75.9414i	0.925107	+	0.379707i
$201$	33.9267			0.168790
$202$	271.648	−	68.0353i	1.34479	−	0.336808i
$203$	−358.334			−1.76519
$204$	188.447	+	352.612i	0.923758	+	1.72849i
$205$	−145.924	+	231.286i	−0.711824	+	1.12822i
$206$	310.245	−	77.7021i	1.50605	−	0.377194i
$207$	86.6031			0.418373
$208$	220.005	+	147.043i	1.05772	+	0.706936i
$209$	−10.3000			−0.0492823
$210$	−143.761	+	437.559i	−0.684578	+	2.08361i
$211$		−	237.768i		−	1.12686i	−0.826163	−	0.563432i	$-0.809481\pi$
$211$		−	237.768i		−	1.12686i	0.826163	−	0.563432i	$-0.190519\pi$
$212$	−20.2877	−	37.9614i	−0.0956968	−	0.179063i
$213$			148.086i			0.695239i
$214$	176.544	−	44.2160i	0.824971	−	0.206617i
$215$	11.4089	−	18.0828i	0.0530645	−	0.0841059i
$216$	−99.5859	+	90.2423i	−0.461046	+	0.417789i
$217$		−	459.809i		−	2.11893i
$218$	219.383	−	54.9454i	1.00635	−	0.252043i
$219$		−	389.389i		−	1.77803i
$220$	−47.1370	−	3.40150i	−0.214259	−	0.0154613i
$221$	−355.577			−1.60895
$222$	−40.0917	−	160.076i	−0.180593	−	0.721065i
$223$	126.701			0.568164			0.284082	−	0.958800i	$-0.408311\pi$
$223$	126.701			0.568164			0.284082	+	0.958800i	$0.408311\pi$
$224$	−106.847	+	298.470i	−0.476995	+	1.33245i
$225$	−135.767	−	284.612i	−0.603410	−	1.26494i
$226$	96.3374	+	384.652i	0.426272	+	1.70200i
$227$	−131.334			−0.578562			−0.289281	−	0.957244i	$-0.593416\pi$
$227$	−131.334			−0.578562			−0.289281	+	0.957244i	$0.593416\pi$
$228$	−38.2062	−	71.4896i	−0.167571	−	0.313551i
$229$	−250.971			−1.09594			−0.547972	−	0.836497i	$-0.684600\pi$
$229$	−250.971			−1.09594			−0.547972	+	0.836497i	$0.684600\pi$
$230$	−21.4312	+	65.2290i	−0.0931793	+	0.283605i
$231$		−	108.832i		−	0.471133i
$232$	214.423	−	194.305i	0.924236	−	0.837521i
$233$		−	70.9424i		−	0.304474i	−0.988344	−	0.152237i	$-0.951352\pi$
$233$		−	70.9424i		−	0.304474i	0.988344	−	0.152237i	$-0.0486477\pi$
$234$	−101.364	−	404.720i	−0.433178	−	1.72957i
$235$	−109.363	+	173.338i	−0.465374	+	0.737607i
$236$	−132.813	−	248.514i	−0.562768	−	1.05302i
$237$			641.143i			2.70524i
$238$	−103.493	−	413.222i	−0.434845	−	1.73623i
$239$			181.370i			0.758869i	0.925219	+	0.379434i	$0.123881\pi$
$239$			181.370i			0.758869i	−0.925219	+	0.379434i	$0.876119\pi$
$240$	−151.239	−	339.783i	−0.630161	−	1.41576i
$241$	138.911			0.576396			0.288198	−	0.957571i	$-0.406944\pi$
$241$	138.911			0.576396			0.288198	+	0.957571i	$0.406944\pi$
$242$	−223.917	+	56.0807i	−0.925275	+	0.231739i
$243$	−315.869			−1.29987
$244$	357.981	−	191.316i	1.46713	−	0.784081i
$245$	131.118	−	207.819i	0.535175	−	0.848241i
$246$	493.315	−	123.552i	2.00534	−	0.502246i
$247$	72.0907			0.291865
$248$	249.329	+	275.144i	1.00536	+	1.10945i
$249$	464.294			1.86463
$250$	247.966	−	31.8278i	0.991863	−	0.127311i
$251$		−	26.2115i		−	0.104428i	−0.998636	−	0.0522141i	$-0.983372\pi$
$251$		−	26.2115i		−	0.104428i	0.998636	−	0.0522141i	$-0.0166278\pi$
$252$	440.830	−	235.593i	1.74933	−	0.934893i
$253$		−	16.2241i		−	0.0641269i
$254$	52.8805	−	13.2441i	0.208191	−	0.0521422i
$255$	422.668	+	266.671i	1.65752	+	1.04577i
$256$	−97.9076	−	236.538i	−0.382451	−	0.923976i
$257$			461.193i			1.79453i	0.441497	+	0.897263i	$0.354448\pi$
$257$			461.193i			1.79453i	−0.441497	+	0.897263i	$0.645552\pi$
$258$	−38.5691	+	9.65978i	−0.149493	+	0.0374410i
$259$			175.825i			0.678861i
$260$	329.917	+	23.8074i	1.26891	+	0.0915670i
$261$	−456.234			−1.74802
$262$	39.0224	+	155.807i	0.148940	+	0.594682i
$263$	−201.128			−0.764746			−0.382373	−	0.924008i	$-0.624893\pi$
$263$	−201.128			−0.764746			−0.382373	+	0.924008i	$0.624893\pi$
$264$	59.0134	+	65.1236i	0.223536	+	0.246680i
$265$	−45.5034	−	28.7092i	−0.171711	−	0.108337i
$266$	20.9825	+	83.7780i	0.0788816	+	0.314955i
$267$	357.634			1.33945
$268$	25.7445	−	13.7586i	0.0960615	−	0.0513382i
$269$	423.980			1.57614			0.788068	−	0.615589i	$-0.211082\pi$
$269$	423.980			1.57614			0.788068	+	0.615589i	$0.211082\pi$
$270$	−52.4358	+	159.596i	−0.194207	+	0.591096i
$271$			269.541i			0.994615i	0.867574	+	0.497308i	$0.165678\pi$
$271$			269.541i			0.994615i	−0.867574	+	0.497308i	$0.834322\pi$
$272$	285.997	+	191.149i	1.05146	+	0.702753i
$273$			761.725i			2.79020i
$274$	−9.49129	−	37.8964i	−0.0346397	−	0.138308i
$275$	−53.3187	+	25.4344i	−0.193886	+	0.0924888i
$276$	112.607	−	60.1808i	0.407998	−	0.218046i
$277$		−	131.733i		−	0.475569i	−0.971318	−	0.237785i	$-0.923579\pi$
$277$		−	131.733i		−	0.475569i	0.971318	−	0.237785i	$-0.0764213\pi$
$278$	−16.3526	−	65.2917i	−0.0588221	−	0.234862i
$279$		−	585.432i		−	2.09832i
$280$	68.3576	+	390.332i	0.244134	+	1.39404i
$281$	326.949			1.16352			0.581760	−	0.813361i	$-0.302364\pi$
$281$	326.949			1.16352			0.581760	+	0.813361i	$0.302364\pi$
$282$	369.716	−	92.5966i	1.31105	−	0.328357i
$283$	172.977			0.611227			0.305613	−	0.952156i	$-0.401139\pi$
$283$	172.977			0.611227			0.305613	+	0.952156i	$0.401139\pi$
$284$	60.0548	+	112.372i	0.211461	+	0.395675i
$285$	−85.6929	−	54.0657i	−0.300677	−	0.189704i
$286$	−75.8197	+	18.9893i	−0.265104	+	0.0663962i
$287$	−541.847			−1.88797
$288$	−136.038	+	380.014i	−0.472355	+	1.31949i
$289$	−173.234			−0.599425
$290$	112.902	−	343.633i	0.389317	−	1.18494i
$291$			723.267i			2.48545i
$292$	−157.913	−	295.479i	−0.540797	−	1.01191i
$293$		−	266.991i		−	0.911232i	−0.890177	−	0.455616i	$-0.849419\pi$
$293$		−	266.991i		−	0.911232i	0.890177	−	0.455616i	$-0.150581\pi$
$294$	−443.261	+	111.016i	−1.50769	+	0.377607i
$295$	−297.887	−	187.944i	−1.00979	−	0.637099i
$296$	−95.3401	−	105.211i	−0.322095	−	0.355444i
$297$		−	39.6955i		−	0.133655i
$298$	150.301	−	37.6433i	0.504365	−	0.126320i
$299$			113.554i			0.379780i
$300$	−374.311	−	275.727i	−1.24770	−	0.919089i
$301$	42.3636			0.140743
$302$	122.175	+	487.814i	0.404552	+	1.61528i
$303$	−650.953			−2.14836
$304$	−57.9838	−	38.7541i	−0.190736	−	0.127480i
$305$	270.732	−	429.103i	0.887644	−	1.40690i
$306$	−131.768	−	526.118i	−0.430615	−	1.71934i
$307$	195.091			0.635475			0.317737	−	0.948179i	$-0.397077\pi$
$307$	195.091			0.635475			0.317737	+	0.948179i	$0.397077\pi$
$308$	−44.1357	−	82.5845i	−0.143298	−	0.268131i
$309$	−743.443			−2.40597
$310$	440.944	+	144.874i	1.42240	+	0.467335i
$311$			16.5081i			0.0530809i	0.999648	+	0.0265404i	$0.00844907\pi$
$311$			16.5081i			0.0530809i	−0.999648	+	0.0265404i	$0.991551\pi$
$312$	−413.041	−	455.807i	−1.32385	−	1.46092i
$313$			15.1760i			0.0484857i	0.999706	+	0.0242428i	$0.00771749\pi$
$313$			15.1760i			0.0484857i	−0.999706	+	0.0242428i	$0.992283\pi$
$314$	−56.8053	−	226.810i	−0.180909	−	0.722324i
$315$	333.388	−	528.413i	1.05838	−	1.67750i
$316$	260.009	+	486.516i	0.822814	+	1.53961i
$317$			377.327i			1.19030i	0.803613	+	0.595152i	$0.202908\pi$
$317$			377.327i			1.19030i	−0.803613	+	0.595152i	$0.797092\pi$
$318$	24.3078	+	97.0552i	0.0764397	+	0.305205i
$319$			85.4702i			0.267932i
$320$	−252.560	−	196.503i	−0.789249	−	0.614073i
$321$	−423.053			−1.31792
$322$	−131.963	+	33.0507i	−0.409824	+	0.102642i
$323$	93.7147			0.290138
$324$	−124.963	+	66.7840i	−0.385688	+	0.206123i
$325$	373.183	−	178.018i	1.14826	−	0.547748i
$326$	−443.325	+	111.032i	−1.35989	+	0.340590i
$327$	−525.710			−1.60768
$328$	324.235	−	293.814i	0.988521	−	0.895773i
$329$	−406.088			−1.23431
$330$	104.367	+	34.2901i	0.316263	+	0.103909i
$331$		−	353.561i		−	1.06816i	−0.845433	−	0.534081i	$-0.820658\pi$
$331$		−	353.561i		−	1.06816i	0.845433	−	0.534081i	$-0.179342\pi$
$332$	352.318	−	188.290i	1.06120	−	0.567138i
$333$			223.862i			0.672257i
$334$	−109.765	+	27.4911i	−0.328639	+	0.0823087i
$335$	19.4699	−	30.8593i	0.0581190	−	0.0921173i
$336$	409.483	−	612.669i	1.21870	−	1.82342i
$337$			404.133i			1.19921i	0.800297	+	0.599604i	$0.204675\pi$
$337$			404.133i			1.19921i	−0.800297	+	0.599604i	$0.795325\pi$
$338$	202.797	−	50.7912i	0.599990	−	0.150270i
$339$		−	921.744i		−	2.71901i
$340$	428.877	+	30.9486i	1.26140	+	0.0910252i
$341$	−109.674			−0.321624
$342$	26.7151	+	106.667i	0.0781142	+	0.311891i
$343$	1.43594			0.00418640
$344$	−25.3499	+	22.9714i	−0.0736914	+	0.0667774i
$345$	85.1620	−	134.980i	0.246846	−	0.391246i
$346$	−25.1934	−	100.591i	−0.0728134	−	0.290726i
$347$	−111.941			−0.322597			−0.161299	−	0.986906i	$-0.551568\pi$
$347$	−111.941			−0.322597			−0.161299	+	0.986906i	$0.551568\pi$
$348$	−593.227	+	317.038i	−1.70467	+	0.911030i
$349$	−280.992			−0.805136			−0.402568	−	0.915390i	$-0.631882\pi$
$349$	−280.992			−0.805136			−0.402568	+	0.915390i	$0.631882\pi$
$350$	315.496	+	381.870i	0.901417	+	1.09106i
$351$			277.833i			0.791547i
$352$	71.1912	+	25.4852i	0.202248	+	0.0724012i
$353$		−	315.995i		−	0.895170i	−0.894241	−	0.447585i	$-0.852284\pi$
$353$		−	315.995i		−	0.895170i	0.894241	−	0.447585i	$-0.147716\pi$
$354$	159.131	+	635.370i	0.449522	+	1.79483i
$355$	134.697	+	84.9837i	0.379429	+	0.239391i
$356$	271.382	−	145.035i	0.762310	−	0.407402i
$357$			990.208i			2.77369i
$358$	8.16710	+	32.6092i	0.0228131	+	0.0910873i
$359$			113.342i			0.315716i	0.987462	+	0.157858i	$0.0504588\pi$
$359$			113.342i			0.315716i	−0.987462	+	0.157858i	$0.949541\pi$
$360$	87.0333	+	496.974i	0.241759	+	1.38048i
$361$	−19.0000			−0.0526316
$362$	−105.871	+	26.5158i	−0.292461	+	0.0732480i
$363$	536.573			1.47816
$364$	308.910	+	578.018i	0.848654	+	1.58796i
$365$	−354.183	−	223.463i	−0.970365	−	0.612226i
$366$	−915.243	+	229.226i	−2.50066	+	0.626300i
$367$	−368.053			−1.00287			−0.501434	−	0.865196i	$-0.667194\pi$
$367$	−368.053			−1.00287			−0.501434	+	0.865196i	$0.667194\pi$
$368$	61.0437	−	91.3336i	0.165880	−	0.248189i
$369$	−689.884			−1.86960
$370$	−168.611	−	55.3979i	−0.455707	−	0.149724i
$371$		−	106.604i		−	0.287341i
$372$	−406.818	−	761.219i	−1.09360	−	2.04629i
$373$			151.233i			0.405450i	0.979236	+	0.202725i	$0.0649798\pi$
$373$			151.233i			0.405450i	−0.979236	+	0.202725i	$0.935020\pi$
$374$	−98.5621	+	24.6852i	−0.263535	+	0.0660033i
$375$	−577.104	−	68.2686i	−1.53894	−	0.182050i
$376$	242.998	−	220.199i	0.646272	−	0.585636i
$377$		−	598.215i		−	1.58678i
$378$	−322.875	+	80.8652i	−0.854167	+	0.213929i
$379$			382.034i			1.00801i	0.863702	+	0.504003i	$0.168140\pi$
$379$			382.034i			1.00801i	−0.863702	+	0.504003i	$0.831860\pi$
$380$	−86.9519	−	6.27461i	−0.228821	−	0.0165121i
$381$	−126.718			−0.332593
$382$	−85.4740	−	341.277i	−0.223754	−	0.893395i
$383$	−389.134			−1.01602			−0.508008	−	0.861352i	$-0.669618\pi$
$383$	−389.134			−1.01602			−0.508008	+	0.861352i	$0.669618\pi$
$384$	87.1863	+	588.654i	0.227048	+	1.53295i
$385$	−98.9920	−	62.4565i	−0.257122	−	0.162225i
$386$	−13.2860	−	53.0478i	−0.0344197	−	0.137430i
$387$	53.9376			0.139374
$388$	293.314	+	548.834i	0.755963	+	1.41452i
$389$	556.795			1.43135			0.715675	−	0.698434i	$-0.246119\pi$
$389$	556.795			1.43135			0.715675	+	0.698434i	$0.246119\pi$
$390$	−730.474	−	240.000i	−1.87301	−	0.615384i
$391$			147.615i			0.377533i
$392$	−291.337	+	264.002i	−0.743206	+	0.673475i
$393$		−	373.361i		−	0.950028i
$394$	−20.9420	−	83.6162i	−0.0531522	−	0.212224i
$395$	583.175	+	367.939i	1.47639	+	0.931492i
$396$	−56.1938	−	105.147i	−0.141904	−	0.265523i
$397$			68.1823i			0.171744i	0.996306	+	0.0858720i	$0.0273676\pi$
$397$			68.1823i			0.171744i	−0.996306	+	0.0858720i	$0.972632\pi$
$398$	−57.4035	−	229.198i	−0.144230	−	0.575875i
$399$		−	200.758i		−	0.503153i
$400$	−395.856	−	57.4304i	−0.989639	−	0.143576i
$401$	−25.4658			−0.0635058			−0.0317529	−	0.999496i	$-0.510109\pi$
$401$	−25.4658			−0.0635058			−0.0317529	+	0.999496i	$0.510109\pi$
$402$	−65.8204	+	16.4850i	−0.163732	+	0.0410074i
$403$	767.619			1.90476
$404$	−493.961	+	263.988i	−1.22267	+	0.653435i
$405$	−94.5061	+	149.790i	−0.233348	+	0.369852i
$406$	695.196	−	174.114i	1.71231	−	0.428853i
$407$	41.9379			0.103042
$408$	−536.935	−	592.529i	−1.31602	−	1.45228i
$409$	491.713			1.20223			0.601116	−	0.799162i	$-0.294723\pi$
$409$	491.713			1.20223			0.601116	+	0.799162i	$0.294723\pi$
$410$	170.722	−	519.617i	0.416395	−	1.26736i
$411$			90.8114i			0.220952i
$412$	−564.145	+	301.496i	−1.36928	+	0.731787i
$413$		−	697.878i		−	1.68978i
$414$	−168.017	+	42.0804i	−0.405838	+	0.101644i
$415$	266.449	−	422.316i	0.642046	−	1.01763i
$416$	−498.275	−	178.374i	−1.19778	−	0.428783i
$417$			156.459i			0.375202i
$418$	19.9828	−	5.00476i	0.0478057	−	0.0119731i
$419$		−	582.437i		−	1.39006i	−0.718979	−	0.695032i	$-0.755390\pi$
$419$		−	582.437i		−	1.39006i	0.718979	−	0.695032i	$-0.244610\pi$
$420$	66.2988	−	918.751i	0.157854	−	2.18750i
$421$	191.276			0.454337			0.227168	−	0.973855i	$-0.427053\pi$
$421$	191.276			0.454337			0.227168	+	0.973855i	$0.427053\pi$
$422$	115.531	+	461.289i	0.273771	+	1.09310i
$423$	−517.035			−1.22230
$424$	57.8052	+	63.7902i	0.136333	+	0.150449i
$425$	485.122	−	231.416i	1.14146	−	0.544507i
$426$	−71.9549	−	287.298i	−0.168908	−	0.674409i
$427$	1005.29			2.35430
$428$	−321.024	+	171.565i	−0.750056	+	0.400853i
$429$	181.687			0.423513
$430$	−13.3477	+	40.6256i	−0.0310411	+	0.0944780i
$431$			825.937i			1.91633i	0.286222	+	0.958163i	$0.407601\pi$
$431$			825.937i			1.91633i	−0.286222	+	0.958163i	$0.592399\pi$
$432$	149.356	−	223.466i	0.345731	−	0.517282i
$433$			654.768i			1.51217i	0.654476	+	0.756083i	$0.272889\pi$
$433$			654.768i			1.51217i	−0.654476	+	0.756083i	$0.727111\pi$
$434$	223.421	+	892.065i	0.514795	+	2.05545i
$435$	−448.642	+	711.087i	−1.03136	+	1.63468i
$436$	−398.923	+	213.197i	−0.914961	+	0.488983i
$437$		−	29.9280i		−	0.0684851i
$438$	189.204	+	755.444i	0.431972	+	1.72476i
$439$		−	650.149i		−	1.48098i	−0.672068	−	0.740489i	$-0.734594\pi$
$439$		−	650.149i		−	1.48098i	0.672068	−	0.740489i	$-0.265406\pi$
$440$	93.1023	−	16.3047i	0.211596	−	0.0370561i
$441$	619.886			1.40564
$442$	689.847	−	172.775i	1.56074	−	0.390893i
$443$	379.721			0.857157			0.428578	−	0.903505i	$-0.359015\pi$
$443$	379.721			0.857157			0.428578	+	0.903505i	$0.359015\pi$
$444$	155.562	+	291.080i	0.350365	+	0.655586i
$445$	205.239	−	325.300i	0.461212	−	0.731011i
$446$	−245.809	+	61.5637i	−0.551141	+	0.138035i
$447$	−360.167			−0.805742
$448$	62.2652	−	630.971i	0.138985	−	1.40842i
$449$	754.927			1.68135			0.840676	−	0.541538i	$-0.182158\pi$
$449$	754.927			1.68135			0.840676	+	0.541538i	$0.182158\pi$
$450$	401.692	+	486.200i	0.892648	+	1.08044i
$451$			129.242i			0.286567i
$452$	−373.804	−	699.444i	−0.827000	−	1.54744i
$453$		−	1168.95i		−	2.58047i
$454$	254.798	−	63.8150i	0.561228	−	0.140562i
$455$	692.856	+	437.140i	1.52276	+	0.960746i
$456$	108.860	+	120.131i	0.238728	+	0.263445i
$457$			33.6817i			0.0737017i	0.999321	+	0.0368508i	$0.0117326\pi$
$457$			33.6817i			0.0737017i	−0.999321	+	0.0368508i	$0.988267\pi$
$458$	486.903	−	121.947i	1.06311	−	0.266259i
$459$			361.170i			0.786863i
$460$	9.88349	−	136.963i	0.0214859	−	0.297745i
$461$	689.678			1.49605			0.748024	−	0.663672i	$-0.231003\pi$
$461$	689.678			1.49605			0.748024	+	0.663672i	$0.231003\pi$
$462$	52.8813	+	211.142i	0.114462	+	0.457018i
$463$	−214.911			−0.464171			−0.232085	−	0.972695i	$-0.574555\pi$
$463$	−214.911			−0.464171			−0.232085	+	0.972695i	$0.574555\pi$
$464$	−321.584	+	481.154i	−0.693070	+	1.03697i
$465$	−912.455	−	575.690i	−1.96227	−	1.23804i
$466$	34.4709	+	137.634i	0.0739718	+	0.295351i
$467$	−18.1000			−0.0387580			−0.0193790	−	0.999812i	$-0.506169\pi$
$467$	−18.1000			−0.0387580			−0.0193790	+	0.999812i	$0.506169\pi$
$468$	393.307	+	735.936i	0.840399	+	1.57251i
$469$	72.2959			0.154149
$470$	127.948	−	389.428i	0.272230	−	0.828570i
$471$			543.506i			1.15394i
$472$	378.421	+	417.602i	0.801739	+	0.884750i
$473$		−	10.1046i		−	0.0213628i
$474$	−311.531	−	1243.87i	−0.657238	−	2.62419i
$475$	−98.3550	+	46.9179i	−0.207063	+	0.0987746i
$476$	401.569	+	751.397i	0.843633	+	1.57856i
$477$		−	135.728i		−	0.284546i
$478$	−88.1274	−	351.871i	−0.184367	−	0.736132i
$479$			716.323i			1.49546i	0.664005	+	0.747728i	$0.268855\pi$
$479$			716.323i			1.49546i	−0.664005	+	0.747728i	$0.731145\pi$
$480$	458.515	+	585.720i	0.955240	+	1.22025i
$481$	−293.528			−0.610245
$482$	−269.499	+	67.4969i	−0.559126	+	0.140035i
$483$	316.225			0.654710
$484$	407.166	−	217.602i	0.841252	−	0.449591i
$485$	657.875	+	415.069i	1.35644	+	0.855813i
$486$	612.811	−	153.481i	1.26093	−	0.315804i
$487$	−403.442			−0.828423			−0.414212	−	0.910181i	$-0.635943\pi$
$487$	−403.442			−0.828423			−0.414212	+	0.910181i	$0.635943\pi$
$488$	−601.550	+	545.110i	−1.23269	+	1.11703i
$489$	1062.34			2.17248
$490$	−153.400	+	466.895i	−0.313061	+	0.952847i
$491$		−	238.093i		−	0.484914i	−0.970162	−	0.242457i	$-0.922047\pi$
$491$		−	238.093i		−	0.484914i	0.970162	−	0.242457i	$-0.0779534\pi$
$492$	−897.035	+	479.403i	−1.82324	+	0.974395i
$493$		−	777.652i		−	1.57739i
$494$	−139.862	+	35.0289i	−0.283121	+	0.0709086i
$495$	−126.037	−	79.5201i	−0.254621	−	0.160647i
$496$	−617.409	−	412.652i	−1.24478	−	0.831959i
$497$			315.563i			0.634936i
$498$	−900.766	+	225.600i	−1.80877	+	0.453012i
$499$		−	903.104i		−	1.80983i	−0.425595	−	0.904914i	$-0.639935\pi$
$499$		−	903.104i		−	1.80983i	0.425595	−	0.904914i	$-0.360065\pi$
$500$	−465.608	+	182.235i	−0.931215	+	0.364470i
$501$	263.031			0.525013
$502$	12.7361	+	50.8523i	0.0253708	+	0.101299i
$503$	−176.766			−0.351424			−0.175712	−	0.984442i	$-0.556223\pi$
$503$	−176.766			−0.351424			−0.175712	+	0.984442i	$0.556223\pi$
$504$	−740.771	+	671.268i	−1.46978	+	1.33188i
$505$	−373.569	+	592.099i	−0.739742	+	1.17247i
$506$	7.88328	+	31.4760i	0.0155796	+	0.0622056i
$507$	−485.964			−0.958508
$508$	−96.1570	+	51.3892i	−0.189285	+	0.101160i
$509$	62.8367			0.123451			0.0617256	−	0.998093i	$-0.480340\pi$
$509$	62.8367			0.123451			0.0617256	+	0.998093i	$0.480340\pi$
$510$	−949.583	−	311.989i	−1.86193	−	0.611743i
$511$		−	829.766i		−	1.62381i
$512$	304.882	+	411.328i	0.595472	+	0.803376i
$513$		−	73.2248i		−	0.142738i
$514$	−224.093	−	894.750i	−0.435980	−	1.74076i
$515$	−426.648	+	676.227i	−0.828442	+	1.31306i
$516$	70.1334	−	37.4814i	0.135917	−	0.0726384i
$517$			96.8605i			0.187351i
$518$	−85.4333	−	341.114i	−0.164929	−	0.658521i
$519$			241.048i			0.464446i
$520$	−651.633	+	114.118i	−1.25314	+	0.219458i
$521$	−247.559			−0.475162			−0.237581	−	0.971368i	$-0.576355\pi$
$521$	−247.559			−0.475162			−0.237581	+	0.971368i	$0.576355\pi$
$522$	885.129	−	221.684i	1.69565	−	0.424682i
$523$	−841.377			−1.60875			−0.804376	−	0.594120i	$-0.797500\pi$
$523$	−841.377			−1.60875			−0.804376	+	0.594120i	$0.797500\pi$
$524$	−151.413	−	283.316i	−0.288956	−	0.540680i
$525$	−495.744	−	1039.24i	−0.944275	−	1.97950i
$526$	390.204	−	97.7281i	0.741833	−	0.185795i
$527$	997.870			1.89349
$528$	−146.134	−	97.6703i	−0.276769	−	0.184982i
$529$	−481.859			−0.910886
$530$	102.230	+	33.5880i	0.192887	+	0.0633736i
$531$		−	888.544i		−	1.67334i
$532$	−81.4154	−	152.340i	−0.153036	−	0.286354i
$533$		−	904.577i		−	1.69714i
$534$	−693.838	+	173.774i	−1.29932	+	0.325420i
$535$	−242.782	+	384.804i	−0.453798	+	0.719260i
$536$	−43.2610	+	39.2021i	−0.0807108	+	0.0731382i
$537$		−	78.1418i		−	0.145515i
$538$	−822.555	+	206.012i	−1.52891	+	0.382922i
$539$		−	116.129i		−	0.215452i
$540$	24.1819	−	335.107i	0.0447814	−	0.620568i
$541$	73.4089			0.135691			0.0678456	−	0.997696i	$-0.478387\pi$
$541$	73.4089			0.135691			0.0678456	+	0.997696i	$0.478387\pi$
$542$	−130.970	−	522.930i	−0.241642	−	0.964816i
$543$	253.699			0.467218
$544$	−647.735	−	231.878i	−1.19069	−	0.426246i
$545$	−301.695	+	478.180i	−0.553569	+	0.877394i
$546$	−370.122	−	1477.81i	−0.677879	−	2.70661i
$547$	−740.954			−1.35458			−0.677289	−	0.735717i	$-0.736845\pi$
$547$	−740.954			−1.35458			−0.677289	+	0.735717i	$0.736845\pi$
$548$	36.8277	+	68.9101i	0.0672038	+	0.125748i
$549$	1279.94			2.33140
$550$	91.0839	−	75.2523i	0.165607	−	0.136822i
$551$			157.664i			0.286141i
$552$	−189.225	+	171.471i	−0.342799	+	0.310636i
$553$			1366.24i			2.47060i
$554$	64.0089	+	255.572i	0.115539	+	0.461321i
$555$	348.911	+	220.136i	0.628668	+	0.396642i
$556$	63.4504	+	118.725i	0.114119	+	0.213535i
$557$			887.121i			1.59268i	0.604852	+	0.796338i	$0.293232\pi$
$557$			887.121i			1.59268i	−0.604852	+	0.796338i	$0.706768\pi$
$558$	284.461	+	1135.78i	0.509787	+	2.03545i
$559$			70.7231i			0.126517i
$560$	−322.281	−	724.060i	−0.575502	−	1.29296i
$561$	236.185			0.421008
$562$	−634.306	+	158.864i	−1.12866	+	0.282677i
$563$	834.704			1.48260			0.741300	−	0.671173i	$-0.234209\pi$
$563$	834.704			1.48260			0.741300	+	0.671173i	$0.234209\pi$
$564$	−672.284	+	359.289i	−1.19199	+	0.637037i
$565$	−838.407	−	528.971i	−1.48391	−	0.936232i
$566$	−335.589	+	84.0495i	−0.592914	+	0.148497i
$567$	−350.922			−0.618910
$568$	−171.112	−	188.829i	−0.301254	−	0.332445i
$569$	322.167			0.566198			0.283099	−	0.959091i	$-0.408638\pi$
$569$	322.167			0.566198			0.283099	+	0.959091i	$0.408638\pi$
$570$	192.521	+	63.2536i	0.337757	+	0.110971i
$571$		−	545.115i		−	0.954667i	−0.878722	−	0.477333i	$-0.841603\pi$
$571$		−	545.115i		−	0.954667i	0.878722	−	0.477333i	$-0.158397\pi$
$572$	137.869	−	73.6815i	0.241030	−	0.128814i
$573$			817.805i			1.42723i
$574$	1051.23	−	263.283i	1.83140	−	0.458682i
$575$	−73.9031	−	154.925i	−0.128527	−	0.269434i
$576$	79.2765	−	803.357i	0.137633	−	1.39472i
$577$			62.1123i			0.107647i	0.998550	+	0.0538235i	$0.0171408\pi$
$577$			62.1123i			0.107647i	−0.998550	+	0.0538235i	$0.982859\pi$
$578$	336.087	−	84.1742i	0.581465	−	0.145630i
$579$			127.119i			0.219549i
$580$	−52.0672	+	721.534i	−0.0897711	+	1.24402i
$581$	989.384			1.70290
$582$	−351.435	−	1403.19i	−0.603840	−	2.41099i
$583$	−25.4271			−0.0436143
$584$	449.936	+	496.522i	0.770438	+	0.850208i
$585$	882.149	+	556.569i	1.50795	+	0.951401i
$586$	129.731	+	517.983i	0.221383	+	0.883930i
$587$	33.4054			0.0569087			0.0284544	−	0.999595i	$-0.490941\pi$
$587$	33.4054			0.0569087			0.0284544	+	0.999595i	$0.490941\pi$
$588$	806.019	−	430.761i	1.37078	−	0.732586i
$589$	−202.311			−0.343483
$590$	669.247	+	219.883i	1.13432	+	0.372684i
$591$			200.370i			0.339036i
$592$	236.089	+	157.793i	0.398800	+	0.266542i
$593$			366.613i			0.618234i	0.951024	+	0.309117i	$0.100033\pi$
$593$			366.613i			0.618234i	−0.951024	+	0.309117i	$0.899967\pi$
$594$	19.2880	+	77.0124i	0.0324714	+	0.129650i
$595$	900.681	+	568.262i	1.51375	+	0.955061i
$596$	−273.304	+	146.062i	−0.458564	+	0.245071i
$597$			549.230i			0.919983i
$598$	−55.1759	−	220.304i	−0.0922674	−	0.368401i
$599$		−	272.444i		−	0.454831i	−0.973798	−	0.227415i	$-0.926973\pi$
$599$		−	272.444i		−	0.454831i	0.973798	−	0.227415i	$-0.0730275\pi$
$600$	860.169	+	353.053i	1.43361	+	0.588422i
$601$	−984.057			−1.63737			−0.818683	−	0.574245i	$-0.805296\pi$
$601$	−984.057			−1.63737			−0.818683	+	0.574245i	$0.805296\pi$
$602$	−82.1887	+	20.5844i	−0.136526	+	0.0341934i
$603$	92.0477			0.152650
$604$	−474.057	−	887.032i	−0.784863	−	1.46860i
$605$	307.929	−	488.060i	0.508974	−	0.806711i
$606$	1262.90	−	316.298i	2.08399	−	0.521944i
$607$	866.172			1.42697			0.713486	−	0.700669i	$-0.247115\pi$
$607$	866.172			1.42697			0.713486	+	0.700669i	$0.247115\pi$
$608$	131.324	+	47.0116i	0.215993	+	0.0773217i
$609$	−1665.91			−2.73548
$610$	−316.739	+	964.042i	−0.519245	+	1.58040i
$611$		−	677.937i		−	1.10955i
$612$	511.281	+	956.684i	0.835426	+	1.56321i
$613$		−	796.409i		−	1.29920i	−0.760277	−	0.649599i	$-0.774937\pi$
$613$		−	796.409i		−	1.29920i	0.760277	−	0.649599i	$-0.225063\pi$
$614$	−378.491	+	94.7945i	−0.616435	+	0.154388i
$615$	−678.404	+	1075.25i	−1.10310	+	1.74838i
$616$	125.754	+	138.775i	0.204147	+	0.225284i
$617$		−	399.907i		−	0.648148i	−0.946032	−	0.324074i	$-0.894947\pi$
$617$		−	399.907i		−	0.648148i	0.946032	−	0.324074i	$-0.105053\pi$
$618$	1442.34	−	361.239i	2.33388	−	0.584529i
$619$			750.355i			1.21221i	0.795386	+	0.606103i	$0.207268\pi$
$619$			750.355i			1.21221i	−0.795386	+	0.606103i	$0.792732\pi$
$620$	−925.860	−	66.8118i	−1.49332	−	0.107761i
$621$	115.340			0.185733
$622$	−8.02130	−	32.0271i	−0.0128960	−	0.0514905i
$623$	762.099			1.22327
$624$	1022.81	+	683.605i	1.63912	+	1.09552i
$625$	−393.285	+	485.749i	−0.629256	+	0.777198i
$626$	−7.37402	−	29.4427i	−0.0117796	−	0.0470330i
$627$	−47.8849			−0.0763715
$628$	220.413	+	412.427i	0.350977	+	0.656730i
$629$	−381.573			−0.606634
$630$	−390.044	+	1187.16i	−0.619117	+	1.88437i
$631$		−	841.338i		−	1.33334i	−0.745353	−	0.666670i	$-0.767719\pi$
$631$		−	841.338i		−	1.33334i	0.745353	−	0.666670i	$-0.232281\pi$
$632$	−740.836	−	817.541i	−1.17221	−	1.29358i
$633$		−	1105.39i		−	1.74627i
$634$	−183.343	−	732.043i	−0.289184	−	1.15464i
$635$	−72.7210	+	115.261i	−0.114521	+	0.181514i
$636$	−94.3181	−	176.483i	−0.148299	−	0.277490i
$637$			812.796i			1.27597i
$638$	−41.5299	−	165.819i	−0.0650939	−	0.259904i
$639$			401.777i			0.628759i
$640$	585.466	+	258.513i	0.914791	+	0.403927i
$641$	378.816			0.590977			0.295488	−	0.955346i	$-0.404518\pi$
$641$	378.816			0.590977			0.295488	+	0.955346i	$0.404518\pi$
$642$	820.756	−	205.561i	1.27844	−	0.320189i
$643$	942.850			1.46633			0.733165	−	0.680051i	$-0.238042\pi$
$643$	942.850			1.46633			0.733165	+	0.680051i	$0.238042\pi$
$644$	239.960	−	128.242i	0.372609	−	0.199133i
$645$	53.0401	−	84.0673i	0.0822327	−	0.130337i
$646$	−181.814	+	45.5359i	−0.281445	+	0.0704890i
$647$	−605.603			−0.936017			−0.468009	−	0.883724i	$-0.655028\pi$
$647$	−605.603			−0.936017			−0.468009	+	0.883724i	$0.655028\pi$
$648$	209.987	−	190.285i	0.324055	−	0.293650i
$649$	−166.458			−0.256484
$650$	−637.506	+	526.699i	−0.980778	+	0.810306i
$651$		−	2137.66i		−	3.28366i
$652$	806.134	−	430.822i	1.23640	−	0.660771i
$653$		−	805.482i		−	1.23351i	−0.787155	−	0.616755i	$-0.788447\pi$
$653$		−	805.482i		−	1.23351i	0.787155	−	0.616755i	$-0.211553\pi$
$654$	1019.92	−	255.442i	1.55951	−	0.390585i
$655$	−339.605	−	214.265i	−0.518480	−	0.327122i
$656$	−486.277	+	727.567i	−0.741276	+	1.10910i
$657$		−	1056.46i		−	1.60801i
$658$	787.843	−	197.318i	1.19733	−	0.299876i
$659$			190.125i			0.288505i	0.989541	+	0.144253i	$0.0460778\pi$
$659$			190.125i			0.288505i	−0.989541	+	0.144253i	$0.953922\pi$
$660$	−219.141	−	15.8136i	−0.332032	−	0.0239601i
$661$	909.534			1.37600			0.687999	−	0.725712i	$-0.258490\pi$
$661$	909.534			1.37600			0.687999	+	0.725712i	$0.258490\pi$
$662$	171.795	+	685.937i	0.259510	+	1.03616i
$663$	−1653.09			−2.49334
$664$	−592.035	+	536.488i	−0.891619	+	0.807964i
$665$	−182.607	−	115.211i	−0.274597	−	0.173250i
$666$	−108.774	−	434.309i	−0.163325	−	0.652116i
$667$	−248.345			−0.372331
$668$	199.595	−	106.670i	0.298795	−	0.159685i
$669$	589.034			0.880470
$670$	−22.7786	+	69.3299i	−0.0339979	+	0.103477i
$671$		−	239.781i		−	0.357349i
$672$	−496.734	+	1387.59i	−0.739188	+	2.06487i
$673$		−	206.903i		−	0.307433i	−0.988115	−	0.153717i	$-0.950876\pi$
$673$		−	206.903i		−	0.307433i	0.988115	−	0.153717i	$-0.0491243\pi$
$674$	−196.368	−	784.050i	−0.291347	−	1.16328i
$675$	−180.819	−	379.054i	−0.267879	−	0.561561i
$676$	−368.762	+	197.078i	−0.545506	+	0.291535i
$677$		−	624.692i		−	0.922736i	−0.887209	−	0.461368i	$-0.847359\pi$
$677$		−	624.692i		−	0.922736i	0.887209	−	0.461368i	$-0.152641\pi$
$678$	447.875	+	1788.25i	0.660582	+	2.63754i
$679$			1541.24i			2.26987i
$680$	−847.093	+	148.349i	−1.24573	+	0.218160i
$681$	−610.573			−0.896584
$682$	212.776	−	53.2905i	0.311988	−	0.0781386i
$683$	229.301			0.335726			0.167863	−	0.985810i	$-0.446313\pi$
$683$	229.301			0.335726			0.167863	+	0.985810i	$0.446313\pi$
$684$	−103.659	−	193.961i	−0.151548	−	0.283569i
$685$	82.6009	+	52.1149i	0.120585	+	0.0760802i
$686$	−2.78583	+	0.697721i	−0.00406097	+	0.00101709i
$687$	−1166.77			−1.69836
$688$	38.0189	−	56.8838i	0.0552600	−	0.0826800i
$689$	177.967			0.258298
$690$	−99.6343	+	303.251i	−0.144398	+	0.439495i
$691$		−	536.309i		−	0.776134i	−0.921631	−	0.388067i	$-0.873143\pi$
$691$		−	536.309i		−	0.776134i	0.921631	−	0.388067i	$-0.126857\pi$
$692$	97.7544	+	182.913i	0.141264	+	0.264326i
$693$		−	295.275i		−	0.426083i
$694$	217.175	−	54.3922i	0.312932	−	0.0783750i
$695$	142.313	+	89.7889i	0.204767	+	0.129193i
$696$	996.857	−	903.328i	1.43227	−	1.29788i
$697$		−	1175.91i		−	1.68710i
$698$	545.147	−	136.534i	0.781013	−	0.195608i
$699$		−	329.813i		−	0.471835i
$700$	−797.637	−	587.558i	−1.13948	−	0.839369i
$701$	889.251			1.26855			0.634274	−	0.773109i	$-0.281299\pi$
$701$	889.251			1.26855			0.634274	+	0.773109i	$0.281299\pi$
$702$	−134.999	−	539.018i	−0.192306	−	0.767831i
$703$	77.3612			0.110044
$704$	−150.500	−	14.8515i	−0.213778	−	0.0210959i
$705$	−508.431	+	805.851i	−0.721179	+	1.14305i
$706$	153.542	+	613.055i	0.217481	+	0.868350i
$707$	−1387.15			−1.96202
$708$	−617.452	−	1155.35i	−0.872107	−	1.63184i
$709$	779.061			1.09882			0.549408	−	0.835554i	$-0.314853\pi$
$709$	779.061			1.09882			0.549408	+	0.835554i	$0.314853\pi$
$710$	−302.616	−	99.4257i	−0.426220	−	0.140036i
$711$			1739.51i			2.44656i
$712$	−456.031	+	413.244i	−0.640492	+	0.580399i
$713$		−	318.672i		−	0.446945i
$714$	−481.142	−	1921.08i	−0.673868	−	2.69059i
$715$	104.267	−	165.260i	0.145828	−	0.231134i
$716$	−31.6896	−	59.2961i	−0.0442593	−	0.0828157i
$717$			843.192i			1.17600i
$718$	−55.0729	−	219.892i	−0.0767032	−	0.306257i
$719$			622.746i			0.866128i	0.901363	+	0.433064i	$0.142568\pi$
$719$			622.746i			0.866128i	−0.901363	+	0.433064i	$0.857432\pi$
$720$	−410.331	−	921.878i	−0.569904	−	1.28039i
$721$	−1584.24			−2.19728
$722$	36.8615	−	9.23209i	0.0510547	−	0.0127868i
$723$	645.802			0.893226
$724$	192.514	−	102.885i	0.265903	−	0.142107i
$725$	389.329	+	816.158i	0.537005	+	1.12574i
$726$	−1040.99	+	260.721i	−1.43388	+	0.359119i
$727$	49.0371			0.0674513			0.0337256	−	0.999431i	$-0.489263\pi$
$727$	49.0371			0.0674513			0.0337256	+	0.999431i	$0.489263\pi$
$728$	−880.168	−	971.300i	−1.20902	−	1.33420i
$729$	−1149.68			−1.57707
$730$	795.723	+	261.438i	1.09003	+	0.358134i
$731$			91.9369i			0.125769i
$732$	1664.26	−	889.432i	2.27358	−	1.21507i
$733$			773.926i			1.05583i	0.849296	+	0.527917i	$0.177027\pi$
$733$			773.926i			1.05583i	−0.849296	+	0.527917i	$0.822973\pi$
$734$	714.051	−	178.837i	0.972821	−	0.243647i
$735$	609.571	−	966.155i	0.829348	−	1.31450i
$736$	−74.0506	+	206.855i	−0.100612	+	0.281053i
$737$		−	17.2441i		−	0.0233977i
$738$	1338.43	−	335.214i	1.81359	−	0.454220i
$739$		−	605.475i		−	0.819316i	−0.912239	−	0.409658i	$-0.865648\pi$
$739$		−	605.475i		−	0.819316i	0.912239	−	0.409658i	$-0.134352\pi$
$740$	354.037	+	25.5480i	0.478428	+	0.0345243i
$741$	335.152			0.452296
$742$	51.7986	+	206.819i	0.0698094	+	0.278732i
$743$	1323.25			1.78095			0.890477	−	0.455028i	$-0.150371\pi$
$743$	1323.25			1.78095			0.890477	+	0.455028i	$0.150371\pi$
$744$	1159.14	+	1279.15i	1.55798	+	1.71929i
$745$	−206.693	+	327.603i	−0.277440	+	0.439736i
$746$	−73.4840	−	293.404i	−0.0985040	−	0.393303i
$747$	1259.69			1.68633
$748$	179.224	−	95.7826i	0.239604	−	0.128052i
$749$	−901.503			−1.20361
$750$	1152.80	−	147.968i	1.53706	−	0.197291i
$751$			672.833i			0.895916i	0.894055	+	0.447958i	$0.147849\pi$
$751$			672.833i			0.895916i	−0.894055	+	0.447958i	$0.852151\pi$
$752$	−364.441	+	545.276i	−0.484629	+	0.725101i
$753$		−	121.858i		−	0.161830i
$754$	290.672	+	1160.58i	0.385507	+	1.53923i
$755$	−1063.26	−	670.839i	−1.40830	−	0.888529i
$756$	587.110	−	313.770i	0.776601	−	0.415039i
$757$		−	626.803i		−	0.828010i	−0.910275	−	0.414005i	$-0.864130\pi$
$757$		−	626.803i		−	0.828010i	0.910275	−	0.414005i	$-0.135870\pi$
$758$	−185.630	−	741.176i	−0.244895	−	0.977805i
$759$		−	75.4262i		−	0.0993758i
$760$	171.742	−	30.0766i	0.225977	−	0.0395745i
$761$	1142.83			1.50174			0.750871	−	0.660449i	$-0.229634\pi$
$761$	1142.83			1.50174			0.750871	+	0.660449i	$0.229634\pi$
$762$	245.843	−	61.5722i	0.322628	−	0.0808034i
$763$	−1120.26			−1.46823
$764$	331.653	+	620.572i	0.434100	+	0.812267i
$765$	1146.75	+	723.515i	1.49902	+	0.945771i
$766$	754.951	−	189.080i	0.985576	−	0.246841i
$767$	1165.06			1.51898
$768$	−455.175	−	1099.67i	−0.592675	−	1.43186i
$769$	−267.225			−0.347497			−0.173748	−	0.984790i	$-0.555588\pi$
$769$	−267.225			−0.347497			−0.173748	+	0.984790i	$0.555588\pi$
$770$	222.400	+	73.0702i	0.288831	+	0.0948964i
$771$			2144.10i			2.78093i
$772$	51.5518	+	96.4613i	0.0667770	+	0.124950i
$773$			928.535i			1.20121i	0.799546	+	0.600605i	$0.205073\pi$
$773$			928.535i			1.20121i	−0.799546	+	0.600605i	$0.794927\pi$
$774$	−104.643	+	26.2083i	−0.135198	+	0.0338608i
$775$	−1047.28	+	499.580i	−1.35133	+	0.644620i
$776$	−835.730	−	922.260i	−1.07697	−	1.18848i
$777$			817.415i			1.05201i
$778$	−1080.23	+	270.546i	−1.38846	+	0.347746i
$779$			238.407i			0.306043i
$780$	1533.79	+	110.681i	1.96640	+	0.141899i
$781$	75.2683			0.0963743
$782$	−71.7262	−	286.385i	−0.0917215	−	0.366221i
$783$	−607.625			−0.776022
$784$	436.938	−	653.746i	0.557318	−	0.833859i
$785$	494.366	+	311.908i	0.629766	+	0.397334i
$786$	181.416	+	724.350i	0.230809	+	0.921564i
$787$	1265.70			1.60826			0.804130	−	0.594454i	$-0.202632\pi$
$787$	1265.70			1.60826			0.804130	+	0.594454i	$0.202632\pi$
$788$	81.2582	+	152.046i	0.103119	+	0.192952i
$789$	−935.050			−1.18511
$790$	−1310.19	−	430.467i	−1.65846	−	0.544894i
$791$		−	1964.18i		−	2.48317i
$792$	160.111	+	176.689i	0.202161	+	0.223092i
$793$			1678.26i			2.11634i
$794$	−33.1298	−	132.279i	−0.0417251	−	0.166598i
$795$	−211.546	−	133.470i	−0.266096	−	0.167887i
$796$	222.735	+	416.770i	0.279817	+	0.523580i
$797$		−	1496.94i		−	1.87822i	−0.343612	−	0.939112i	$-0.611650\pi$
$797$		−	1496.94i		−	1.87822i	0.343612	−	0.939112i	$-0.388350\pi$
$798$	97.5481	+	389.486i	0.122241	+	0.488078i
$799$		−	881.287i		−	1.10299i
$800$	795.896	−	80.9266i	0.994870	−	0.101158i
$801$	970.310			1.21137
$802$	49.4057	−	12.3738i	0.0616031	−	0.0154287i
$803$	−197.916			−0.246471
$804$	119.687	−	63.9642i	0.148864	−	0.0795575i
$805$	181.475	−	287.634i	0.225435	−	0.357310i
$806$	−1489.24	+	372.986i	−1.84769	+	0.462762i
$807$	1971.09			2.44250
$808$	830.051	−	752.172i	1.02729	−	0.930905i
$809$	−1194.65			−1.47670			−0.738350	−	0.674418i	$-0.764395\pi$
$809$	−1194.65			−1.47670			−0.738350	+	0.674418i	$0.764395\pi$
$810$	110.566	−	336.525i	0.136502	−	0.415463i
$811$		−	1336.15i		−	1.64753i	−0.566928	−	0.823767i	$-0.691868\pi$
$811$		−	1336.15i		−	1.64753i	0.566928	−	0.823767i	$-0.308132\pi$
$812$	−1264.13	+	675.591i	−1.55681	+	0.832009i
$813$			1253.10i			1.54133i
$814$	−81.3628	+	20.3776i	−0.0999543	+	0.0250339i
$815$	609.658	−	966.294i	0.748047	−	1.18564i
$816$	1329.60	+	888.655i	1.62942	+	1.08904i
$817$		−	18.6396i		−	0.0228146i
$818$	−953.961	+	238.923i	−1.16621	+	0.292082i
$819$			2066.66i			2.52340i
$820$	−78.7323	+	1091.05i	−0.0960150	+	1.33055i
$821$	149.964			0.182661			0.0913304	−	0.995821i	$-0.470888\pi$
$821$	149.964			0.182661			0.0913304	+	0.995821i	$0.470888\pi$
$822$	−44.1252	−	176.181i	−0.0536803	−	0.214332i
$823$	−1382.88			−1.68029			−0.840147	−	0.542359i	$-0.817531\pi$
$823$	−1382.88			−1.68029			−0.840147	+	0.542359i	$0.817531\pi$
$824$	947.988	−	859.043i	1.15047	−	1.04253i
$825$	−247.880	+	118.245i	−0.300461	+	0.143328i
$826$	339.099	+	1353.94i	0.410531	+	1.63915i
$827$	1410.48			1.70554			0.852769	−	0.522288i	$-0.174922\pi$
$827$	1410.48			1.70554			0.852769	+	0.522288i	$0.174922\pi$
$828$	305.519	−	163.279i	0.368984	−	0.197196i
$829$	324.790			0.391785			0.195892	−	0.980625i	$-0.437240\pi$
$829$	324.790			0.391785			0.195892	+	0.980625i	$0.437240\pi$
$830$	−311.729	+	948.793i	−0.375577	+	1.14312i
$831$		−	612.429i		−	0.736978i
$832$	1053.36	+	103.948i	1.26606	+	0.124937i
$833$			1056.60i			1.26842i
$834$	−76.0234	−	303.543i	−0.0911552	−	0.363960i
$835$	150.949	−	239.250i	0.180777	−	0.286527i
$836$	−36.3363	+	19.4192i	−0.0434645	+	0.0232288i
$837$		−	779.695i		−	0.931535i
$838$	283.006	+	1129.97i	0.337716	+	1.34842i
$839$		−	737.034i		−	0.878468i	−0.898373	−	0.439234i	$-0.855250\pi$
$839$		−	737.034i		−	0.878468i	0.898373	−	0.439234i	$-0.144750\pi$
$840$	317.796	+	1814.66i	0.378328	+	2.16031i
$841$	467.305			0.555654
$842$	−371.090	+	92.9408i	−0.440724	+	0.110381i
$843$	1519.99			1.80308
$844$	−448.280	−	838.799i	−0.531137	−	0.993838i
$845$	−278.885	+	442.026i	−0.330042	+	0.523108i
$846$	1003.09	−	251.227i	1.18568	−	0.296959i
$847$	1143.41			1.34995
$848$	−143.142	−	95.6705i	−0.168800	−	0.112819i
$849$	804.175			0.947202
$850$	−828.729	+	684.685i	−0.974975	+	0.805511i
$851$			121.856i			0.143192i
$852$	279.196	+	522.418i	0.327695	+	0.613167i
$853$		−	815.431i		−	0.955956i	−0.878372	−	0.477978i	$-0.841370\pi$
$853$		−	815.431i		−	0.955956i	0.878372	−	0.477978i	$-0.158630\pi$
$854$	−1950.33	+	488.468i	−2.28376	+	0.571976i
$855$	−232.496	−	146.688i	−0.271926	−	0.171564i
$856$	539.448	−	488.835i	0.630197	−	0.571069i
$857$		−	1078.90i		−	1.25892i	−0.777033	−	0.629460i	$-0.783276\pi$
$857$		−	1078.90i		−	1.25892i	0.777033	−	0.629460i	$-0.216724\pi$
$858$	−352.487	+	88.2818i	−0.410825	+	0.102892i
$859$			639.829i			0.744853i	0.928062	+	0.372427i	$0.121474\pi$
$859$			639.829i			0.744853i	−0.928062	+	0.372427i	$0.878526\pi$
$860$	6.15558	−	85.3024i	0.00715765	−	0.0991888i
$861$	−2519.06			−2.92574
$862$	−401.322	−	1602.38i	−0.465571	−	1.85891i
$863$	1243.90			1.44137			0.720686	−	0.693261i	$-0.243827\pi$
$863$	1243.90			1.44137			0.720686	+	0.693261i	$0.243827\pi$
$864$	−181.180	+	506.113i	−0.209699	+	0.585779i
$865$	219.254	+	138.333i	0.253473	+	0.159922i
$866$	−318.151	−	1270.30i	−0.367380	−	1.46686i
$867$	−805.368			−0.928914
$868$	−866.908	−	1622.11i	−0.998741	−	1.86880i
$869$	325.876			0.375002
$870$	524.883	−	1597.56i	0.603314	−	1.83627i
$871$			120.693i			0.138568i
$872$	670.350	−	607.454i	0.768749	−	0.696622i
$873$			1962.32i			2.24779i
$874$	14.5420	+	58.0626i	0.0166384	+	0.0664332i
$875$	−1229.78	−	145.477i	−1.40546	−	0.166259i
$876$	−734.140	−	1373.69i	−0.838059	−	1.56814i
$877$			144.346i			0.164591i	0.996608	+	0.0822953i	$0.0262251\pi$
$877$			144.346i			0.164591i	−0.996608	+	0.0822953i	$0.973775\pi$
$878$	315.907	+	1261.34i	0.359803	+	1.43661i
$879$		−	1241.25i		−	1.41211i
$880$	−172.703	+	76.8707i	−0.196254	+	0.0873531i
$881$	−1137.49			−1.29114			−0.645568	−	0.763703i	$-0.723379\pi$
$881$	−1137.49			−1.29114			−0.645568	+	0.763703i	$0.723379\pi$
$882$	−1202.63	+	301.202i	−1.36352	+	0.341499i
$883$	−1720.92			−1.94895			−0.974474	−	0.224502i	$-0.927924\pi$
$883$	−1720.92			−1.94895			−0.974474	+	0.224502i	$0.927924\pi$
$884$	−1254.41	+	670.392i	−1.41901	+	0.758362i
$885$	−1384.89	−	873.758i	−1.56484	−	0.987297i
$886$	−736.687	+	184.506i	−0.831476	+	0.208246i
$887$	−683.386			−0.770446			−0.385223	−	0.922823i	$-0.625875\pi$
$887$	−683.386			−0.770446			−0.385223	+	0.922823i	$0.625875\pi$
$888$	−443.238	−	489.131i	−0.499142	−	0.550823i
$889$	−270.029			−0.303745
$890$	−240.118	+	730.832i	−0.269795	+	0.821160i
$891$			83.7022i			0.0939418i
$892$	446.975	−	238.877i	0.501093	−	0.267799i
$893$			178.675i			0.200084i
$894$	698.751	−	175.005i	0.781601	−	0.195755i
$895$	−71.0768	−	44.8441i	−0.0794154	−	0.0501051i
$896$	185.789	+	1254.39i	0.207354	+	1.39999i
$897$			527.916i			0.588535i
$898$	−1464.62	+	366.819i	−1.63098	+	0.408484i
$899$			1678.80i			1.86740i
$900$	−1015.56	−	748.083i	−1.12840	−	0.831204i
$901$	231.349			0.256770
$902$	−62.7985	−	250.739i	−0.0696214	−	0.277981i
$903$	196.949			0.218106
$904$	1065.07	+	1175.34i	1.17817	+	1.30016i
$905$	145.593	−	230.762i	0.160876	−	0.254985i
$906$	567.993	+	2267.86i	0.626924	+	2.50316i
$907$	−42.4586			−0.0468122			−0.0234061	−	0.999726i	$-0.507451\pi$
$907$	−42.4586			−0.0468122			−0.0234061	+	0.999726i	$0.507451\pi$
$908$	−463.319	+	247.612i	−0.510264	+	0.272700i
$909$	−1766.12			−1.94293
$910$	−1556.60	−	511.426i	−1.71055	−	0.562007i
$911$		−	1113.86i		−	1.22267i	−0.791371	−	0.611336i	$-0.790632\pi$
$911$		−	1113.86i		−	1.22267i	0.791371	−	0.611336i	$-0.209368\pi$
$912$	−269.568	−	180.169i	−0.295579	−	0.197553i
$913$		−	235.989i		−	0.258476i
$914$	−16.3659	−	65.3450i	−0.0179058	−	0.0714935i
$915$	1258.64	−	1994.91i	1.37556	−	2.18023i
$916$	−885.377	+	473.172i	−0.966569	+	0.516564i
$917$		−	795.612i		−	0.867625i
$918$	−175.492	−	700.699i	−0.191168	−	0.763288i
$919$			1160.73i			1.26303i	0.775363	+	0.631516i	$0.217567\pi$
$919$			1160.73i			1.26303i	−0.775363	+	0.631516i	$0.782433\pi$
$920$	47.3754	+	270.521i	0.0514950	+	0.294044i
$921$	906.982			0.984779
$922$	−1338.03	+	335.114i	−1.45122	+	0.363464i
$923$	−526.811			−0.570759
$924$	−205.188	−	383.937i	−0.222065	−	0.415516i
$925$	400.467	−	191.033i	0.432937	−	0.206522i
$926$	416.944	−	104.425i	0.450264	−	0.112770i
$927$	−2017.06			−2.17590
$928$	390.106	−	1089.73i	0.420373	−	1.17428i
$929$	−986.830			−1.06225			−0.531125	−	0.847293i	$-0.678231\pi$
$929$	−986.830			−1.06225			−0.531125	+	0.847293i	$0.678231\pi$
$930$	2049.96	+	673.522i	2.20426	+	0.724217i
$931$		−	214.218i		−	0.230094i
$932$	−133.752	−	250.271i	−0.143511	−	0.268531i
$933$			76.7468i			0.0822581i
$934$	35.1153	−	8.79477i	0.0375967	−	0.00941624i
$935$	135.542	−	214.831i	0.144965	−	0.229766i
$936$	−1120.64	−	1236.67i	−1.19726	−	1.32122i
$937$			51.7220i			0.0551996i	0.999619	+	0.0275998i	$0.00878640\pi$
$937$			51.7220i			0.0551996i	−0.999619	+	0.0275998i	$0.991214\pi$
$938$	−140.260	+	35.1286i	−0.149531	+	0.0374505i
$939$			70.5537i			0.0751371i
$940$	−59.0061	+	817.690i	−0.0627724	+	0.869883i
$941$	−1084.37			−1.15236			−0.576178	−	0.817324i	$-0.695456\pi$
$941$	−1084.37			−1.15236			−0.576178	+	0.817324i	$0.695456\pi$
$942$	−264.089	−	1054.44i	−0.280349	−	1.11937i
$943$	−375.529			−0.398228
$944$	−937.078	−	626.306i	−0.992667	−	0.663459i
$945$	444.016	−	703.755i	0.469858	−	0.744714i
$946$	4.90982	+	19.6037i	0.00519008	+	0.0207227i
$947$	118.622			0.125261			0.0626303	−	0.998037i	$-0.480051\pi$
$947$	118.622			0.125261			0.0626303	+	0.998037i	$0.480051\pi$
$948$	1208.79	+	2261.83i	1.27509	+	2.38589i
$949$	1385.24			1.45968
$950$	168.019	−	138.815i	0.176862	−	0.146121i
$951$			1754.20i			1.84459i
$952$	−1144.18	−	1262.65i	−1.20187	−	1.32631i
$953$		−	486.769i		−	0.510776i	−0.966839	−	0.255388i	$-0.917797\pi$
$953$		−	486.769i		−	0.510776i	0.966839	−	0.255388i	$-0.0822032\pi$
$954$	65.9504	+	263.324i	0.0691304	+	0.276021i
$955$	743.865	+	469.322i	0.778916	+	0.491437i
$956$	341.948	+	639.837i	0.357686	+	0.669285i
$957$			397.353i			0.415207i
$958$	−348.061	−	1389.72i	−0.363321	−	1.45065i
$959$			193.514i			0.201787i
$960$	−1174.16	−	913.549i	−1.22308	−	0.951614i
$961$	−1193.20			−1.24163
$962$	569.467	−	142.625i	0.591961	−	0.148259i
$963$	−1147.80			−1.19190
$964$	490.052	−	261.899i	0.508353	−	0.271679i
$965$	115.626	+	72.9511i	0.119820	+	0.0755970i
$966$	−613.501	+	153.654i	−0.635095	+	0.159062i
$967$	609.319			0.630112			0.315056	−	0.949073i	$-0.397977\pi$
$967$	609.319			0.630112			0.315056	+	0.949073i	$0.397977\pi$
$968$	−684.201	+	620.007i	−0.706819	+	0.640503i
$969$	435.682			0.449620
$970$	−1478.01	−	485.605i	−1.52372	−	0.500624i
$971$			137.028i			0.141121i	0.997508	+	0.0705604i	$0.0224787\pi$
$971$			137.028i			0.141121i	−0.997508	+	0.0705604i	$0.977521\pi$
$972$	−1114.32	+	595.529i	−1.14642	+	0.612684i
$973$			333.406i			0.342657i
$974$	782.709	−	196.032i	0.803603	−	0.201265i
$975$	1734.94	−	827.611i	1.77942	−	0.848832i
$976$	902.186	−	1349.85i	0.924371	−	1.38304i
$977$			650.081i			0.665385i	0.943035	+	0.332693i	$0.107957\pi$
$977$			650.081i			0.665385i	−0.943035	+	0.332693i	$0.892043\pi$
$978$	−2061.03	+	516.192i	−2.10739	+	0.527803i
$979$		−	181.776i		−	0.185676i
$980$	70.7439	−	980.350i	0.0721876	−	1.00036i
$981$	−1426.32			−1.45395
$982$	115.689	+	461.919i	0.117810	+	0.470386i
$983$	−810.627			−0.824646			−0.412323	−	0.911038i	$-0.635283\pi$
$983$	−810.627			−0.824646			−0.412323	+	0.911038i	$0.635283\pi$
$984$	1507.38	−	1365.95i	1.53189	−	1.38816i
$985$	182.254	+	114.989i	0.185030	+	0.116740i
$986$	377.861	+	1508.71i	0.383226	+	1.53013i
$987$	−1887.92			−1.91278
$988$	254.322	−	135.917i	0.257411	−	0.137568i
$989$	29.3602			0.0296868
$990$	283.161	+	93.0336i	0.286021	+	0.0939733i
$991$			759.263i			0.766158i	0.923716	+	0.383079i	$0.125136\pi$
$991$			759.263i			0.766158i	−0.923716	+	0.383079i	$0.874864\pi$
$992$	1398.33	+	500.578i	1.40961	+	0.504615i
$993$		−	1643.72i		−	1.65530i
$994$	−153.332	−	612.217i	−0.154257	−	0.615912i
$995$	499.572	+	315.192i	0.502083	+	0.316776i
$996$	1637.94	−	875.363i	1.64451	−	0.878879i
$997$			1757.77i			1.76306i	0.472124	+	0.881532i	$0.343487\pi$
$997$			1757.77i			1.76306i	−0.472124	+	0.881532i	$0.656513\pi$
$998$	438.818	+	1752.09i	0.439697	+	1.75560i
$999$			298.145i			0.298444i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.3.h.a.39.8	yes	108
4.3	odd	2	inner	380.3.h.a.39.102	yes	108
5.4	even	2	inner	380.3.h.a.39.101	yes	108
20.19	odd	2	inner	380.3.h.a.39.7	✓	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.3.h.a.39.7	✓	108	20.19	odd	2	inner
380.3.h.a.39.8	yes	108	1.1	even	1	trivial
380.3.h.a.39.101	yes	108	5.4	even	2	inner
380.3.h.a.39.102	yes	108	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	380.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.94008 + 0.485899i) q^{2} +4.64902 q^{3} +(3.52780 - 1.88537i) q^{4} +(2.66799 - 4.22869i) q^{5} +(-9.01947 + 2.25896i) q^{6} +9.90681 q^{7} +(-5.92811 + 5.37191i) q^{8} +12.6134 q^{9} +O(q^{10})\)	\(q+(-1.94008 + 0.485899i) q^{2} +4.64902 q^{3} +(3.52780 - 1.88537i) q^{4} +(2.66799 - 4.22869i) q^{5} +(-9.01947 + 2.25896i) q^{6} +9.90681 q^{7} +(-5.92811 + 5.37191i) q^{8} +12.6134 q^{9} +(-3.12138 + 9.50037i) q^{10} -2.36298i q^{11} +(16.4008 - 8.76511i) q^{12} +16.5387i q^{13} +(-19.2200 + 4.81372i) q^{14} +(12.4035 - 19.6593i) q^{15} +(8.89079 - 13.3024i) q^{16} +21.4996i q^{17} +(-24.4710 + 6.12886i) q^{18} -4.35890i q^{19} +(1.43949 - 19.9481i) q^{20} +46.0570 q^{21} +(1.14817 + 4.58437i) q^{22} +6.86595 q^{23} +(-27.5600 + 24.9742i) q^{24} +(-10.7637 - 22.5642i) q^{25} +(-8.03617 - 32.0865i) q^{26} +16.7989 q^{27} +(34.9493 - 18.6780i) q^{28} -36.1705 q^{29} +(-14.5114 + 44.1674i) q^{30} -46.4134i q^{31} +(-10.7852 + 30.1277i) q^{32} -10.9856i q^{33} +(-10.4467 - 41.7109i) q^{34} +(26.4312 - 41.8929i) q^{35} +(44.4977 - 23.7809i) q^{36} +17.7479i q^{37} +(2.11799 + 8.45660i) q^{38} +76.8890i q^{39} +(6.90005 + 39.4004i) q^{40} -54.6944 q^{41} +(-89.3542 + 22.3791i) q^{42} +4.27621 q^{43} +(-4.45508 - 8.33613i) q^{44} +(33.6524 - 53.3383i) q^{45} +(-13.3205 + 3.33616i) q^{46} -40.9908 q^{47} +(41.3335 - 61.8432i) q^{48} +49.1449 q^{49} +(31.8464 + 38.5462i) q^{50} +99.9523i q^{51} +(31.1816 + 58.3455i) q^{52} -10.7606i q^{53} +(-32.5912 + 8.16258i) q^{54} +(-9.99232 - 6.30440i) q^{55} +(-58.7287 + 53.2185i) q^{56} -20.2646i q^{57} +(70.1736 - 17.5752i) q^{58} -70.4443i q^{59} +(6.69224 - 92.7393i) q^{60} +101.474 q^{61} +(22.5522 + 90.0456i) q^{62} +124.959 q^{63} +(6.28509 - 63.6906i) q^{64} +(69.9373 + 44.1251i) q^{65} +(5.33787 + 21.3128i) q^{66} +7.29760 q^{67} +(40.5346 + 75.8464i) q^{68} +31.9200 q^{69} +(-30.9229 + 94.1184i) q^{70} +31.8531i q^{71} +(-74.7738 + 67.7582i) q^{72} -83.7571i q^{73} +(-8.62369 - 34.4323i) q^{74} +(-50.0407 - 104.901i) q^{75} +(-8.21812 - 15.3773i) q^{76} -23.4096i q^{77} +(-37.3603 - 149.171i) q^{78} +137.909i q^{79} +(-32.5313 - 73.0871i) q^{80} -35.4223 q^{81} +(106.111 - 26.5760i) q^{82} +99.8691 q^{83} +(162.480 - 86.8343i) q^{84} +(90.9153 + 57.3607i) q^{85} +(-8.29618 + 2.07781i) q^{86} -168.158 q^{87} +(12.6937 + 14.0080i) q^{88} +76.9267 q^{89} +(-39.3713 + 119.832i) q^{90} +163.846i q^{91} +(24.2217 - 12.9448i) q^{92} -215.777i q^{93} +(79.5254 - 19.9174i) q^{94} +(-18.4325 - 11.6295i) q^{95} +(-50.1407 + 140.064i) q^{96} +155.574i q^{97} +(-95.3450 + 23.8795i) q^{98} -29.8053i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q + 4 q^{5} + 324 q^{9}+O(q^{10}) \) 108 * q + 4 * q^5 + 324 * q^9	\( 108 q + 4 q^{5} + 324 q^{9} - 8 q^{10} + 8 q^{14} - 104 q^{16} - 16 q^{21} - 8 q^{24} - 76 q^{25} + 80 q^{26} - 88 q^{29} - 140 q^{30} - 88 q^{34} - 256 q^{36} + 44 q^{40} - 200 q^{41} - 8 q^{44} + 108 q^{45} + 272 q^{46} + 916 q^{49} - 276 q^{50} - 320 q^{54} - 328 q^{56} + 172 q^{60} + 200 q^{61} - 216 q^{64} - 192 q^{65} + 152 q^{66} - 592 q^{69} + 200 q^{70} - 232 q^{74} + 340 q^{80} + 1052 q^{81} + 208 q^{84} + 248 q^{85} - 1048 q^{86} + 760 q^{89} + 268 q^{90} - 320 q^{94} + 720 q^{96}+O(q^{100}) \) 108 * q + 4 * q^5 + 324 * q^9 - 8 * q^10 + 8 * q^14 - 104 * q^16 - 16 * q^21 - 8 * q^24 - 76 * q^25 + 80 * q^26 - 88 * q^29 - 140 * q^30 - 88 * q^34 - 256 * q^36 + 44 * q^40 - 200 * q^41 - 8 * q^44 + 108 * q^45 + 272 * q^46 + 916 * q^49 - 276 * q^50 - 320 * q^54 - 328 * q^56 + 172 * q^60 + 200 * q^61 - 216 * q^64 - 192 * q^65 + 152 * q^66 - 592 * q^69 + 200 * q^70 - 232 * q^74 + 340 * q^80 + 1052 * q^81 + 208 * q^84 + 248 * q^85 - 1048 * q^86 + 760 * q^89 + 268 * q^90 - 320 * q^94 + 720 * q^96

Introduction

L-functions

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