LMFDB - Embedded newform 168.4.p.a.139.24

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [168,4,Mod(139,168)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("168.139"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(168, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 0, 1])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	168.p (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.91232088096$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			139.24
Character	$\chi$	$=$	168.139
Dual form			168.4.p.a.139.21

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.713005 + 2.73708i) q^{2} +3.00000i q^{3} +(-6.98325 - 3.90311i) q^{4} -14.5659 q^{5} +(-8.21125 - 2.13902i) q^{6} +(11.7275 - 14.3341i) q^{7} +(15.6622 - 16.3308i) q^{8} -9.00000 q^{9} +(10.3856 - 39.8681i) q^{10} -28.6305 q^{11} +(11.7093 - 20.9497i) q^{12} +83.2983 q^{13} +(30.8719 + 42.3194i) q^{14} -43.6977i q^{15} +(33.5315 + 54.5128i) q^{16} -27.2438i q^{17} +(6.41705 - 24.6337i) q^{18} +62.8721i q^{19} +(101.717 + 56.8524i) q^{20} +(43.0023 + 35.1824i) q^{21} +(20.4137 - 78.3642i) q^{22} -200.361i q^{23} +(48.9924 + 46.9867i) q^{24} +87.1659 q^{25} +(-59.3922 + 227.994i) q^{26} -27.0000i q^{27} +(-137.843 + 54.3249i) q^{28} +32.4096i q^{29} +(119.604 + 31.1567i) q^{30} +51.2286 q^{31} +(-173.114 + 52.9105i) q^{32} -85.8916i q^{33} +(74.5686 + 19.4250i) q^{34} +(-170.821 + 208.789i) q^{35} +(62.8492 + 35.1280i) q^{36} -353.375i q^{37} +(-172.086 - 44.8282i) q^{38} +249.895i q^{39} +(-228.135 + 237.873i) q^{40} -83.7633i q^{41} +(-126.958 + 92.6156i) q^{42} +535.865 q^{43} +(199.934 + 111.748i) q^{44} +131.093 q^{45} +(548.406 + 142.859i) q^{46} +411.590 q^{47} +(-163.538 + 100.594i) q^{48} +(-67.9328 - 336.205i) q^{49} +(-62.1497 + 238.580i) q^{50} +81.7315 q^{51} +(-581.693 - 325.123i) q^{52} -210.917i q^{53} +(73.9012 + 19.2511i) q^{54} +417.030 q^{55} +(-50.4087 - 416.023i) q^{56} -188.616 q^{57} +(-88.7077 - 23.1082i) q^{58} -103.520i q^{59} +(-170.557 + 305.152i) q^{60} -425.937 q^{61} +(-36.5263 + 140.217i) q^{62} +(-105.547 + 129.007i) q^{63} +(-21.3892 - 511.553i) q^{64} -1213.32 q^{65} +(235.092 + 61.2412i) q^{66} -796.894 q^{67} +(-106.336 + 190.250i) q^{68} +601.084 q^{69} +(-449.677 - 616.420i) q^{70} -175.826i q^{71} +(-140.960 + 146.977i) q^{72} -1030.12i q^{73} +(967.216 + 251.958i) q^{74} +261.498i q^{75} +(245.397 - 439.052i) q^{76} +(-335.764 + 410.393i) q^{77} +(-683.983 - 178.176i) q^{78} -273.289i q^{79} +(-488.416 - 794.028i) q^{80} +81.0000 q^{81} +(229.267 + 59.7237i) q^{82} +486.916i q^{83} +(-162.975 - 413.530i) q^{84} +396.831i q^{85} +(-382.075 + 1466.71i) q^{86} -97.2288 q^{87} +(-448.418 + 467.559i) q^{88} +267.978i q^{89} +(-93.4702 + 358.813i) q^{90} +(976.879 - 1194.01i) q^{91} +(-782.033 + 1399.17i) q^{92} +153.686i q^{93} +(-293.466 + 1126.56i) q^{94} -915.790i q^{95} +(-158.732 - 519.342i) q^{96} -603.135i q^{97} +(968.659 + 53.7787i) q^{98} +257.675 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 2 q^{2} + 10 q^{4} + 118 q^{8} - 432 q^{9} - 40 q^{11} + 38 q^{14} - 142 q^{16} + 18 q^{18} - 376 q^{22} + 1200 q^{25} - 274 q^{28} + 336 q^{30} + 318 q^{32} - 456 q^{35} - 90 q^{36} + 564 q^{42}+ \cdots + 360 q^{99}+O(q^{100}) $ 48 * q - 2 * q^2 + 10 * q^4 + 118 * q^8 - 432 * q^9 - 40 * q^11 + 38 * q^14 - 142 * q^16 + 18 * q^18 - 376 * q^22 + 1200 * q^25 - 274 * q^28 + 336 * q^30 + 318 * q^32 - 456 * q^35 - 90 * q^36 + 564 * q^42 - 808 * q^43 + 1584 * q^44 - 388 * q^46 + 360 * q^49 - 14 * q^50 + 226 * q^56 + 336 * q^57 - 3176 * q^58 - 192 * q^60 + 1954 * q^64 - 4104 * q^67 - 648 * q^70 - 1062 * q^72 + 2384 * q^74 - 1800 * q^78 + 3888 * q^81 + 264 * q^84 - 880 * q^86 + 4184 * q^88 + 104 * q^91 + 2044 * q^92 - 6018 * q^98 + 360 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$-1$	$-1$	$1$	$-1$

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 $

$2$	−0.713005	+	2.73708i	−0.252085	+	0.967705i
$2$	−0.713005	+	2.73708i	−0.252085	+	0.967705i
$3$			3.00000i			0.577350i
$3$			3.00000i			0.577350i
$4$	−6.98325	−	3.90311i	−0.872906	−	0.487889i
$5$	−14.5659			−1.30281			−0.651407	−	0.758728i	$-0.725821\pi$
$5$	−14.5659			−1.30281			−0.651407	+	0.758728i	$0.725821\pi$
$6$	−8.21125	−	2.13902i	−0.558705	−	0.145542i
$7$	11.7275	−	14.3341i	0.633224	−	0.773969i
$7$	11.7275	−	14.3341i	0.633224	−	0.773969i
$8$	15.6622	−	16.3308i	0.692179	−	0.721726i
$9$	−9.00000			−0.333333
$10$	10.3856	−	39.8681i	0.328421	−	1.26074i
$11$	−28.6305			−0.784767			−0.392383	−	0.919802i	$-0.628349\pi$
$11$	−28.6305			−0.784767			−0.392383	+	0.919802i	$0.628349\pi$
$12$	11.7093	−	20.9497i	0.281683	−	0.503972i
$13$	83.2983			1.77714			0.888569	−	0.458743i	$-0.151700\pi$
$13$	83.2983			1.77714			0.888569	+	0.458743i	$0.151700\pi$
$14$	30.8719	+	42.3194i	0.589347	+	0.807880i
$15$		−	43.6977i		−	0.752181i
$16$	33.5315	+	54.5128i	0.523929	+	0.851762i
$17$		−	27.2438i		−	0.388682i	−0.980934	−	0.194341i	$-0.937743\pi$
$17$		−	27.2438i		−	0.388682i	0.980934	−	0.194341i	$-0.0622569\pi$
$18$	6.41705	−	24.6337i	0.0840285	−	0.322568i
$19$			62.8721i			0.759150i	0.925161	+	0.379575i	$0.123930\pi$
$19$			62.8721i			0.759150i	−0.925161	+	0.379575i	$0.876070\pi$
$20$	101.717	+	56.8524i	1.13723	+	0.635629i
$21$	43.0023	+	35.1824i	0.446851	+	0.365592i
$22$	20.4137	−	78.3642i	0.197828	−	0.759423i
$23$		−	200.361i		−	1.81645i	−0.418487	−	0.908223i	$-0.637439\pi$
$23$		−	200.361i		−	1.81645i	0.418487	−	0.908223i	$-0.362561\pi$
$24$	48.9924	+	46.9867i	0.416688	+	0.399630i
$25$	87.1659			0.697327
$26$	−59.3922	+	227.994i	−0.447991	+	1.71975i
$27$		−	27.0000i		−	0.192450i
$28$	−137.843	+	54.3249i	−0.930355	+	0.366659i
$29$			32.4096i			0.207528i	0.994602	+	0.103764i	$0.0330887\pi$
$29$			32.4096i			0.207528i	−0.994602	+	0.103764i	$0.966911\pi$
$30$	119.604	+	31.1567i	0.727889	+	0.189614i
$31$	51.2286			0.296804			0.148402	−	0.988927i	$-0.452587\pi$
$31$	51.2286			0.296804			0.148402	+	0.988927i	$0.452587\pi$
$32$	−173.114	+	52.9105i	−0.956329	+	0.292292i
$33$		−	85.8916i		−	0.453085i
$34$	74.5686	+	19.4250i	0.376130	+	0.0979812i
$35$	−170.821	+	208.789i	−0.824974	+	1.00834i
$36$	62.8492	+	35.1280i	0.290969	+	0.162630i
$37$		−	353.375i		−	1.57012i	−0.619419	−	0.785060i	$-0.712632\pi$
$37$		−	353.375i		−	1.57012i	0.619419	−	0.785060i	$-0.287368\pi$
$38$	−172.086	−	44.8282i	−0.734633	−	0.191371i
$39$			249.895i			1.02603i
$40$	−228.135	+	237.873i	−0.901782	+	0.940275i
$41$		−	83.7633i		−	0.319064i	−0.987193	−	0.159532i	$-0.949001\pi$
$41$		−	83.7633i		−	0.319064i	0.987193	−	0.159532i	$-0.0509986\pi$
$42$	−126.958	+	92.6156i	−0.466430	+	0.340259i
$43$	535.865			1.90043			0.950217	−	0.311590i	$-0.100861\pi$
$43$	535.865			1.90043			0.950217	+	0.311590i	$0.100861\pi$
$44$	199.934	+	111.748i	0.685027	+	0.382879i
$45$	131.093			0.434272
$46$	548.406	+	142.859i	1.75778	+	0.457900i
$47$	411.590			1.27737			0.638686	−	0.769467i	$-0.279478\pi$
$47$	411.590			1.27737			0.638686	+	0.769467i	$0.279478\pi$
$48$	−163.538	+	100.594i	−0.491765	+	0.302491i
$49$	−67.9328	−	336.205i	−0.198055	−	0.980191i
$50$	−62.1497	+	238.580i	−0.175786	+	0.674807i
$51$	81.7315			0.224406
$52$	−581.693	−	325.123i	−1.55127	−	0.867046i
$53$		−	210.917i		−	0.546635i	−0.961924	−	0.273317i	$-0.911879\pi$
$53$		−	210.917i		−	0.546635i	0.961924	−	0.273317i	$-0.0881209\pi$
$54$	73.9012	+	19.2511i	0.186235	+	0.0485139i
$55$	417.030			1.02241
$56$	−50.4087	−	416.023i	−0.120288	−	0.992739i
$57$	−188.616			−0.438296
$58$	−88.7077	−	23.1082i	−0.200826	−	0.0523148i
$59$		−	103.520i		−	0.228427i	−0.993456	−	0.114213i	$-0.963565\pi$
$59$		−	103.520i		−	0.228427i	0.993456	−	0.114213i	$-0.0364348\pi$
$60$	−170.557	+	305.152i	−0.366980	+	0.656583i
$61$	−425.937			−0.894028			−0.447014	−	0.894527i	$-0.647513\pi$
$61$	−425.937			−0.894028			−0.447014	+	0.894527i	$0.647513\pi$
$62$	−36.5263	+	140.217i	−0.0748201	+	0.287219i
$63$	−105.547	+	129.007i	−0.211075	+	0.257990i
$64$	−21.3892	−	511.553i	−0.0417757	−	0.999127i
$65$	−1213.32			−2.31528
$66$	235.092	+	61.2412i	0.438453	+	0.114216i
$67$	−796.894			−1.45308			−0.726538	−	0.687126i	$-0.758872\pi$
$67$	−796.894			−1.45308			−0.726538	+	0.687126i	$0.758872\pi$
$68$	−106.336	+	190.250i	−0.189634	+	0.339283i
$69$	601.084			1.04873
$70$	−449.677	−	616.420i	−0.767810	−	1.05252i
$71$		−	175.826i		−	0.293898i	−0.989144	−	0.146949i	$-0.953055\pi$
$71$		−	175.826i		−	0.293898i	0.989144	−	0.146949i	$-0.0469453\pi$
$72$	−140.960	+	146.977i	−0.230726	+	0.240575i
$73$		−	1030.12i		−	1.65159i	−0.563971	−	0.825795i	$-0.690727\pi$
$73$		−	1030.12i		−	1.65159i	0.563971	−	0.825795i	$-0.309273\pi$
$74$	967.216	+	251.958i	1.51941	+	0.395805i
$75$			261.498i			0.402602i
$76$	245.397	−	439.052i	0.370381	−	0.662667i
$77$	−335.764	+	410.393i	−0.496933	+	0.607385i
$78$	−683.983	−	178.176i	−0.992896	−	0.258648i
$79$		−	273.289i		−	0.389208i	−0.980882	−	0.194604i	$-0.937658\pi$
$79$		−	273.289i		−	0.389208i	0.980882	−	0.194604i	$-0.0623421\pi$
$80$	−488.416	−	794.028i	−0.682583	−	1.10969i
$81$	81.0000			0.111111
$82$	229.267	+	59.7237i	0.308760	+	0.0804315i
$83$			486.916i			0.643927i	0.946752	+	0.321964i	$0.104343\pi$
$83$			486.916i			0.643927i	−0.946752	+	0.321964i	$0.895657\pi$
$84$	−162.975	−	413.530i	−0.211691	−	0.537141i
$85$			396.831i			0.506381i
$86$	−382.075	+	1466.71i	−0.479072	+	1.83906i
$87$	−97.2288			−0.119816
$88$	−448.418	+	467.559i	−0.543199	+	0.566386i
$89$			267.978i			0.319164i	0.987185	+	0.159582i	$0.0510147\pi$
$89$			267.978i			0.319164i	−0.987185	+	0.159582i	$0.948985\pi$
$90$	−93.4702	+	358.813i	−0.109474	+	0.420247i
$91$	976.879	−	1194.01i	1.12533	−	1.37545i
$92$	−782.033	+	1399.17i	−0.886224	+	1.58559i
$93$			153.686i			0.171360i
$94$	−293.466	+	1126.56i	−0.322007	+	1.23612i
$95$		−	915.790i		−	0.989032i
$96$	−158.732	−	519.342i	−0.168755	−	0.552137i
$97$		−	603.135i		−	0.631331i	−0.948871	−	0.315665i	$-0.897772\pi$
$97$		−	603.135i		−	0.631331i	0.948871	−	0.315665i	$-0.102228\pi$
$98$	968.659	+	53.7787i	0.998462	+	0.0554334i
$99$	257.675			0.261589
$100$	−608.701	−	340.218i	−0.608701	−	0.340218i
$101$	−995.901			−0.981147			−0.490574	−	0.871400i	$-0.663213\pi$
$101$	−995.901			−0.981147			−0.490574	+	0.871400i	$0.663213\pi$
$102$	−58.2750	+	223.706i	−0.0565695	+	0.217159i
$103$	−1248.41			−1.19427			−0.597135	−	0.802141i	$-0.703694\pi$
$103$	−1248.41			−1.19427			−0.597135	+	0.802141i	$0.703694\pi$
$104$	1304.64	−	1360.33i	1.23010	−	1.28261i
$105$	−626.368	−	512.464i	−0.582164	−	0.476299i
$106$	577.297	+	150.385i	0.528981	+	0.137799i
$107$	1843.63			1.66571			0.832853	−	0.553494i	$-0.186706\pi$
$107$	1843.63			1.66571			0.832853	+	0.553494i	$0.186706\pi$
$108$	−105.384	+	188.548i	−0.0938942	+	0.167991i
$109$			9.09633i			0.00799330i	0.999992	+	0.00399665i	$0.00127218\pi$
$109$			9.09633i			0.00799330i	−0.999992	+	0.00399665i	$0.998728\pi$
$110$	−297.345	+	1141.45i	−0.257734	+	0.989387i
$111$	1060.12			0.906510
$112$	1174.63	+	158.654i	0.991001	+	0.133851i
$113$	−110.854			−0.0922858			−0.0461429	−	0.998935i	$-0.514693\pi$
$113$	−110.854			−0.0922858			−0.0461429	+	0.998935i	$0.514693\pi$
$114$	134.484	−	516.259i	0.110488	−	0.424141i
$115$			2918.45i			2.36649i
$116$	126.498	−	226.324i	0.101251	−	0.181152i
$117$	−749.685			−0.592379
$118$	283.343	+	73.8105i	0.221050	+	0.0575831i
$119$	−390.516	−	319.501i	−0.300828	−	0.246123i
$120$	−713.619	−	684.404i	−0.542868	−	0.520644i
$121$	−511.292			−0.384141
$122$	303.696	−	1165.83i	0.225371	−	0.865155i
$123$	251.290			0.184212
$124$	−357.742	−	199.951i	−0.259082	−	0.144807i
$125$	551.089			0.394327
$126$	−277.847	−	380.874i	−0.196449	−	0.269293i
$127$			267.721i			0.187058i	0.995617	+	0.0935290i	$0.0298148\pi$
$127$			267.721i			0.187058i	−0.995617	+	0.0935290i	$0.970185\pi$
$128$	1415.41	+	306.196i	0.977391	+	0.211439i
$129$			1607.59i			1.09722i
$130$	865.101	−	3320.95i	0.583649	−	2.24051i
$131$			1023.29i			0.682480i	0.939976	+	0.341240i	$0.110847\pi$
$131$			1023.29i			0.682480i	−0.939976	+	0.341240i	$0.889153\pi$
$132$	−335.244	+	599.802i	−0.221055	+	0.395501i
$133$	901.215	+	737.331i	0.587558	+	0.480712i
$134$	568.190	−	2181.17i	0.366300	−	1.40615i
$135$			393.280i			0.250727i
$136$	−444.913	−	426.699i	−0.280522	−	0.269038i
$137$	545.766			0.340350			0.170175	−	0.985414i	$-0.445567\pi$
$137$	545.766			0.340350			0.170175	+	0.985414i	$0.445567\pi$
$138$	−428.576	+	1645.22i	−0.264368	+	1.01486i
$139$			1666.97i			1.01720i	0.861004	+	0.508598i	$0.169836\pi$
$139$			1666.97i			1.01720i	−0.861004	+	0.508598i	$0.830164\pi$
$140$	2007.82	−	791.292i	1.21208	−	0.477689i
$141$			1234.77i			0.737492i
$142$	481.251	+	125.365i	0.284406	+	0.0740873i
$143$	−2384.88			−1.39464
$144$	−301.783	−	490.615i	−0.174643	−	0.283921i
$145$		−	472.075i		−	0.270370i
$146$	2819.51	+	734.479i	1.59825	+	0.416342i
$147$	1008.62	−	203.798i	0.565914	−	0.114347i
$148$	−1379.26	+	2467.70i	−0.766044	+	1.37057i
$149$		−	590.888i		−	0.324882i	−0.986718	−	0.162441i	$-0.948063\pi$
$149$		−	590.888i		−	0.324882i	0.986718	−	0.162441i	$-0.0519367\pi$
$150$	−715.741	−	186.449i	−0.389600	−	0.101490i
$151$			2402.33i			1.29469i	0.762196	+	0.647346i	$0.224121\pi$
$151$			2402.33i			1.29469i	−0.762196	+	0.647346i	$0.775879\pi$
$152$	1026.75	+	984.718i	0.547898	+	0.525468i
$153$			245.194i			0.129561i
$154$	−883.878	−	1211.63i	−0.462500	−	0.633997i
$155$	−746.192			−0.386681
$156$	975.368	−	1745.08i	0.500589	−	0.895629i
$157$	1782.98			0.906352			0.453176	−	0.891421i	$-0.350291\pi$
$157$	1782.98			0.906352			0.453176	+	0.891421i	$0.350291\pi$
$158$	748.014	+	194.856i	0.376638	+	0.0981136i
$159$	632.750			0.315600
$160$	2521.56	−	770.690i	1.24592	−	0.380802i
$161$	−2872.00	−	2349.73i	−1.40587	−	1.15022i
$162$	−57.7534	+	221.704i	−0.0280095	+	0.107523i
$163$	539.014			0.259011			0.129506	−	0.991579i	$-0.458661\pi$
$163$	539.014			0.259011			0.129506	+	0.991579i	$0.458661\pi$
$164$	−326.938	+	584.940i	−0.155668	+	0.278513i
$165$			1251.09i			0.590286i
$166$	−1332.73	−	347.174i	−0.623131	−	0.162325i
$167$	1578.17			0.731272			0.365636	−	0.930758i	$-0.380852\pi$
$167$	1578.17			0.731272			0.365636	+	0.930758i	$0.380852\pi$
$168$	1248.07	−	151.226i	0.573158	−	0.0694486i
$169$	4741.61			2.15822
$170$	−1086.16	−	282.943i	−0.490028	−	0.127651i
$171$		−	565.849i		−	0.253050i
$172$	−3742.08	−	2091.54i	−1.65890	−	0.927200i
$173$	−2249.37			−0.988534			−0.494267	−	0.869310i	$-0.664563\pi$
$173$	−2249.37			−0.988534			−0.494267	+	0.869310i	$0.664563\pi$
$174$	69.3246	−	266.123i	0.0302039	−	0.115947i
$175$	1022.24	−	1249.44i	0.441564	−	0.539709i
$176$	−960.024	−	1560.73i	−0.411162	−	0.668434i
$177$	310.561			0.131882
$178$	−733.479	−	191.070i	−0.308857	−	0.0804567i
$179$	−120.656			−0.0503813			−0.0251907	−	0.999683i	$-0.508019\pi$
$179$	−120.656			−0.0503813			−0.0251907	+	0.999683i	$0.508019\pi$
$180$	−915.456	−	511.671i	−0.379078	−	0.211876i
$181$	−3481.19			−1.42958			−0.714792	−	0.699337i	$-0.753479\pi$
$181$	−3481.19			−1.42958			−0.714792	+	0.699337i	$0.753479\pi$
$182$	2571.57	+	3525.13i	1.04735	+	1.43571i
$183$		−	1277.81i		−	0.516167i
$184$	−3272.06	−	3138.11i	−1.31098	−	1.25731i
$185$			5147.23i			2.04558i
$186$	−420.651	−	109.579i	−0.165826	−	0.0431974i
$187$			780.006i			0.305025i
$188$	−2874.23	−	1606.48i	−1.11503	−	0.623216i
$189$	−387.021	−	316.642i	−0.148950	−	0.121864i
$190$	2506.59	+	652.963i	0.957091	+	0.249321i
$191$			2543.14i			0.963432i	0.876327	+	0.481716i	$0.159986\pi$
$191$			2543.14i			0.963432i	−0.876327	+	0.481716i	$0.840014\pi$
$192$	1534.66	−	64.1675i	0.576846	−	0.0241192i
$193$	651.477			0.242976			0.121488	−	0.992593i	$-0.461233\pi$
$193$	651.477			0.242976			0.121488	+	0.992593i	$0.461233\pi$
$194$	1650.83	+	430.039i	0.610942	+	0.159149i
$195$		−	3639.95i		−	1.33673i
$196$	−837.856	+	2612.95i	−0.305341	+	0.952243i
$197$		−	5020.96i		−	1.81588i	−0.419097	−	0.907941i	$-0.637653\pi$
$197$		−	5020.96i		−	1.81588i	0.419097	−	0.907941i	$-0.362347\pi$
$198$	−183.724	+	705.277i	−0.0659428	+	0.253141i
$199$	4165.94			1.48400			0.741999	−	0.670401i	$-0.233878\pi$
$199$	4165.94			1.48400			0.741999	+	0.670401i	$0.233878\pi$
$200$	1365.21	−	1423.49i	0.482675	−	0.503279i
$201$		−	2390.68i		−	0.838934i
$202$	710.083	−	2725.86i	0.247333	−	0.949461i
$203$	464.562	+	380.083i	0.160620	+	0.131412i
$204$	−570.751	−	319.007i	−0.195885	−	0.109485i
$205$			1220.09i			0.415682i
$206$	890.125	−	3417.01i	0.301058	−	1.15570i
$207$			1803.25i			0.605482i
$208$	2793.11	+	4540.82i	0.931094	+	1.51370i
$209$		−	1800.06i		−	0.595756i
$210$	1849.26	−	1349.03i	0.607672	−	0.443295i
$211$	−3009.23			−0.981819			−0.490909	−	0.871211i	$-0.663335\pi$
$211$	−3009.23			−0.981819			−0.490909	+	0.871211i	$0.663335\pi$
$212$	−823.231	+	1472.88i	−0.266697	+	0.477161i
$213$	527.479			0.169682
$214$	−1314.52	+	5046.17i	−0.419900	+	1.61191i
$215$	−7805.36			−2.47591
$216$	−440.931	−	422.880i	−0.138896	−	0.133210i
$217$	600.782	−	734.316i	0.187944	−	0.229717i
$218$	−24.8974	−	6.48573i	−0.00773516	−	0.00201500i
$219$	3090.35			0.953546
$220$	−2912.22	−	1627.71i	−0.892464	−	0.498820i
$221$		−	2269.37i		−	0.690742i
$222$	−755.875	+	2901.65i	−0.228518	+	0.877234i
$223$	1645.84			0.494231			0.247116	−	0.968986i	$-0.420517\pi$
$223$	1645.84			0.494231			0.247116	+	0.968986i	$0.420517\pi$
$224$	−1271.77	+	3101.94i	−0.379346	+	0.925255i
$225$	−784.493			−0.232442
$226$	79.0397	−	303.418i	0.0232639	−	0.0893055i
$227$			1938.99i			0.566941i	0.958981	+	0.283470i	$0.0914858\pi$
$227$			1938.99i			0.566941i	−0.958981	+	0.283470i	$0.908514\pi$
$228$	1317.15	+	736.190i	0.382591	+	0.213839i
$229$	−2397.26			−0.691770			−0.345885	−	0.938277i	$-0.612421\pi$
$229$	−2397.26			−0.691770			−0.345885	+	0.938277i	$0.612421\pi$
$230$	−7988.03	−	2080.87i	−2.29007	−	0.596559i
$231$	−1231.18	−	1007.29i	−0.350674	−	0.286904i
$232$	529.274	+	507.606i	0.149778	+	0.143647i
$233$	316.572			0.0890101			0.0445050	−	0.999009i	$-0.485829\pi$
$233$	316.572			0.0890101			0.0445050	+	0.999009i	$0.485829\pi$
$234$	534.529	−	2051.95i	0.149330	−	0.573249i
$235$	−5995.18			−1.66418
$236$	−404.051	+	722.907i	−0.111447	+	0.199395i
$237$	819.866			0.224709
$238$	1152.94	−	841.068i	0.314009	−	0.229069i
$239$		−	4069.29i		−	1.10134i	−0.834723	−	0.550670i	$-0.814372\pi$
$239$		−	4069.29i		−	1.10134i	0.834723	−	0.550670i	$-0.185628\pi$
$240$	2382.08	−	1465.25i	0.640679	−	0.394089i
$241$		−	2677.31i		−	0.715604i	−0.933797	−	0.357802i	$-0.883526\pi$
$241$		−	2677.31i		−	0.715604i	0.933797	−	0.357802i	$-0.116474\pi$
$242$	364.554	−	1399.45i	0.0968365	−	0.371736i
$243$			243.000i			0.0641500i
$244$	2974.43	+	1662.48i	0.780402	+	0.436186i
$245$	989.503	+	4897.14i	0.258029	+	1.27701i
$246$	−179.171	+	687.802i	−0.0464371	+	0.178263i
$247$			5237.14i			1.34911i
$248$	802.354	−	836.604i	0.205442	−	0.214211i
$249$	−1460.75			−0.371771
$250$	−392.929	+	1508.38i	−0.0994041	+	0.381592i
$251$		−	3625.92i		−	0.911816i	−0.890027	−	0.455908i	$-0.849315\pi$
$251$		−	3625.92i		−	0.911816i	0.890027	−	0.455908i	$-0.150685\pi$
$252$	1240.59	−	488.924i	0.310118	−	0.122220i
$253$			5736.46i			1.42549i
$254$	−732.773	−	190.886i	−0.181017	−	0.0471546i
$255$	−1190.49			−0.292359
$256$	−1847.28	+	3655.79i	−0.450997	+	0.892526i
$257$			5970.36i			1.44911i	0.689218	+	0.724554i	$0.257954\pi$
$257$			5970.36i			1.44911i	−0.689218	+	0.724554i	$0.742046\pi$
$258$	−4400.12	−	1146.22i	−1.06178	−	0.276592i
$259$	−5065.31	−	4144.19i	−1.21522	−	0.994238i
$260$	8472.89	+	4735.71i	2.02102	+	1.12960i
$261$		−	291.686i		−	0.0691760i
$262$	−2800.82	−	729.608i	−0.660439	−	0.172043i
$263$		−	3195.46i		−	0.749203i	−0.927186	−	0.374602i	$-0.877779\pi$
$263$		−	3195.46i		−	0.749203i	0.927186	−	0.374602i	$-0.122221\pi$
$264$	−1402.68	−	1345.25i	−0.327003	−	0.313616i
$265$			3072.20i			0.712164i
$266$	−2660.71	+	1940.98i	−0.613302	+	0.447403i
$267$	−803.935			−0.184270
$268$	5564.91	+	3110.37i	1.26840	+	0.708940i
$269$	7242.91			1.64167			0.820833	−	0.571169i	$-0.193510\pi$
$269$	7242.91			1.64167			0.820833	+	0.571169i	$0.193510\pi$
$270$	−1076.44	−	280.411i	−0.242630	−	0.0632046i
$271$	976.026			0.218780			0.109390	−	0.993999i	$-0.465110\pi$
$271$	976.026			0.218780			0.109390	+	0.993999i	$0.465110\pi$
$272$	1485.14	−	913.526i	0.331065	−	0.203642i
$273$	3582.02	+	2930.64i	0.794116	+	0.649708i
$274$	−389.134	+	1493.81i	−0.0857972	+	0.329358i
$275$	−2495.61			−0.547239
$276$	−4197.52	−	2346.10i	−0.915439	−	0.511661i
$277$		−	4544.70i		−	0.985793i	−0.870088	−	0.492897i	$-0.835938\pi$
$277$		−	4544.70i		−	0.985793i	0.870088	−	0.492897i	$-0.164062\pi$
$278$	−4562.63	−	1188.56i	−0.984346	−	0.256420i
$279$	−461.058			−0.0989348
$280$	734.249	+	6059.75i	0.156714	+	1.29336i
$281$	−7384.67			−1.56773			−0.783866	−	0.620930i	$-0.786755\pi$
$281$	−7384.67			−1.56773			−0.783866	+	0.620930i	$0.786755\pi$
$282$	−3379.67	−	880.397i	−0.713674	−	0.185911i
$283$			5541.22i			1.16393i	0.813215	+	0.581963i	$0.197715\pi$
$283$			5541.22i			1.16393i	−0.813215	+	0.581963i	$0.802285\pi$
$284$	−686.269	+	1227.84i	−0.143389	+	0.256545i
$285$	2747.37			0.571018
$286$	1700.43	−	6527.60i	0.351568	−	1.34960i
$287$	−1200.67	−	982.332i	−0.246946	−	0.202039i
$288$	1558.03	−	476.195i	0.318776	−	0.0974307i
$289$	4170.77			0.848926
$290$	1292.11	+	336.592i	0.261639	+	0.0681565i
$291$	1809.41			0.364499
$292$	−4020.66	+	7193.56i	−0.805792	+	1.44168i
$293$	−2110.67			−0.420842			−0.210421	−	0.977611i	$-0.567484\pi$
$293$	−2110.67			−0.420842			−0.210421	+	0.977611i	$0.567484\pi$
$294$	−161.336	+	2905.98i	−0.0320045	+	0.576463i
$295$			1507.87i			0.297598i
$296$	−5770.89	−	5534.64i	−1.13320	−	1.08681i
$297$			773.025i			0.151028i
$298$	1617.31	+	421.306i	0.314390	+	0.0818980i
$299$		−	16689.8i		−	3.22808i
$300$	1020.65	−	1826.10i	0.196425	−	0.351434i
$301$	6284.34	−	7681.14i	1.20340	−	1.47088i
$302$	−6575.37	−	1712.87i	−1.25288	−	0.326373i
$303$		−	2987.70i		−	0.566466i
$304$	−3427.33	+	2108.19i	−0.646615	+	0.397741i
$305$	6204.17			1.16475
$306$	−671.118	−	174.825i	−0.125377	−	0.0326604i
$307$		−	2979.91i		−	0.553982i	−0.960873	−	0.276991i	$-0.910663\pi$
$307$		−	2979.91i		−	0.553982i	0.960873	−	0.276991i	$-0.0893371\pi$
$308$	3946.53	−	1555.35i	0.730112	−	0.287742i
$309$		−	3745.24i		−	0.689512i
$310$	532.039	−	2042.39i	0.0974767	−	0.374193i
$311$	3460.82			0.631013			0.315507	−	0.948923i	$-0.397826\pi$
$311$	3460.82			0.631013			0.315507	+	0.948923i	$0.397826\pi$
$312$	4080.98	+	3913.91i	0.740513	+	0.710198i
$313$		−	4253.67i		−	0.768152i	−0.923301	−	0.384076i	$-0.874520\pi$
$313$		−	4253.67i		−	0.768152i	0.923301	−	0.384076i	$-0.125480\pi$
$314$	−1271.27	+	4880.16i	−0.228478	+	0.877082i
$315$	1537.39	−	1879.10i	0.274991	−	0.336113i
$316$	−1066.68	+	1908.44i	−0.189890	+	0.339742i
$317$		−	4361.84i		−	0.772824i	−0.922326	−	0.386412i	$-0.873714\pi$
$317$		−	4361.84i		−	0.772824i	0.922326	−	0.386412i	$-0.126286\pi$
$318$	−451.154	+	1731.89i	−0.0795581	+	0.305407i
$319$		−	927.904i		−	0.162861i
$320$	311.553	+	7451.24i	0.0544260	+	1.30168i
$321$			5530.89i			0.961696i
$322$	8479.17	−	6185.53i	1.46747	−	1.07052i
$323$	1712.88			0.295068
$324$	−565.643	−	316.152i	−0.0969895	−	0.0542099i
$325$	7260.77			1.23925
$326$	−384.320	+	1475.33i	−0.0652930	+	0.250646i
$327$	−27.2890			−0.00461494
$328$	−1367.92	−	1311.92i	−0.230277	−	0.220850i
$329$	4826.91	−	5899.77i	0.808863	−	0.988646i
$330$	−3424.34	−	892.034i	−0.571223	−	0.148803i
$331$	−8344.33			−1.38564			−0.692818	−	0.721112i	$-0.743631\pi$
$331$	−8344.33			−1.38564			−0.692818	+	0.721112i	$0.743631\pi$
$332$	1900.49	−	3400.25i	0.314165	−	0.562088i
$333$			3180.37i			0.523374i
$334$	−1125.24	+	4319.58i	−0.184343	+	0.707655i
$335$	11607.5			1.89309
$336$	−475.961	+	3523.89i	−0.0772791	+	0.572155i
$337$	1305.35			0.210999			0.105500	−	0.994419i	$-0.466356\pi$
$337$	1305.35			0.210999			0.105500	+	0.994419i	$0.466356\pi$
$338$	−3380.79	+	12978.2i	−0.544056	+	2.08852i
$339$		−	332.563i		−	0.0532812i
$340$	1548.88	−	2771.17i	0.247058	−	0.442023i
$341$	−1466.70			−0.232922
$342$	1548.78	+	403.453i	0.244878	+	0.0637903i
$343$	−5615.88	−	2969.09i	−0.884050	−	0.467392i
$344$	8392.84	−	8751.10i	1.31544	−	1.37159i
$345$	−8755.34			−1.36630
$346$	1603.81	−	6156.71i	0.249195	−	0.956609i
$347$	8132.24			1.25810			0.629051	−	0.777364i	$-0.283444\pi$
$347$	8132.24			1.25810			0.629051	+	0.777364i	$0.283444\pi$
$348$	678.972	+	379.495i	0.104588	+	0.0584570i
$349$	−2169.66			−0.332777			−0.166389	−	0.986060i	$-0.553211\pi$
$349$	−2169.66			−0.332777			−0.166389	+	0.986060i	$0.553211\pi$
$350$	2690.97	+	3688.80i	0.410967	+	0.563357i
$351$		−	2249.05i		−	0.342010i
$352$	4956.35	−	1514.86i	0.750495	−	0.229381i
$353$			11505.9i			1.73483i	0.497583	+	0.867416i	$0.334221\pi$
$353$			11505.9i			1.73483i	−0.497583	+	0.867416i	$0.665779\pi$
$354$	−221.431	+	850.030i	−0.0332456	+	0.127623i
$355$			2561.07i			0.382894i
$356$	1045.95	−	1871.36i	0.155717	−	0.278601i
$357$	958.504	−	1171.55i	0.142099	−	0.173683i
$358$	86.0285	−	330.246i	0.0127004	−	0.0487543i
$359$		−	200.908i		−	0.0295363i	−0.999891	−	0.0147681i	$-0.995299\pi$
$359$		−	200.908i		−	0.0295363i	0.999891	−	0.0147681i	$-0.00470101\pi$
$360$	2053.21	−	2140.86i	0.300594	−	0.313425i
$361$	2906.10			0.423691
$362$	2482.11	−	9528.30i	0.360377	−	1.38342i
$363$		−	1533.88i		−	0.221784i
$364$	−11482.1	+	4525.18i	−1.65337	+	0.651603i
$365$			15004.6i			2.15172i
$366$	3497.48	+	911.087i	0.499498	+	0.130118i
$367$	−2626.48			−0.373573			−0.186786	−	0.982401i	$-0.559807\pi$
$367$	−2626.48			−0.373573			−0.186786	+	0.982401i	$0.559807\pi$
$368$	10922.3	−	6718.41i	1.54718	−	0.951689i
$369$			753.870i			0.106355i
$370$	−14088.4	−	3670.00i	−1.97951	−	0.515660i
$371$	−3023.30	−	2473.52i	−0.423078	−	0.346142i
$372$	599.853	−	1073.23i	0.0836046	−	0.149581i
$373$		−	8413.48i		−	1.16792i	−0.811783	−	0.583959i	$-0.801503\pi$
$373$		−	8413.48i		−	1.16792i	0.811783	−	0.583959i	$-0.198497\pi$
$374$	−2134.94	−	556.148i	−0.295174	−	0.0768924i
$375$			1653.27i			0.227665i
$376$	6446.41	−	6721.58i	0.884171	−	0.921913i
$377$			2699.66i			0.368806i
$378$	1142.62	−	833.540i	0.155477	−	0.113420i
$379$	2086.39			0.282772			0.141386	−	0.989955i	$-0.454844\pi$
$379$	2086.39			0.282772			0.141386	+	0.989955i	$0.454844\pi$
$380$	−3574.43	+	6395.19i	−0.482538	+	0.863332i
$381$	−803.162			−0.107998
$382$	−6960.80	−	1813.28i	−0.932318	−	0.242867i
$383$	10741.0			1.43301			0.716503	−	0.697584i	$-0.245742\pi$
$383$	10741.0			1.43301			0.716503	+	0.697584i	$0.245742\pi$
$384$	−918.589	+	4246.24i	−0.122074	+	0.564297i
$385$	4890.71	−	5977.75i	0.647412	−	0.791310i
$386$	−464.507	+	1783.15i	−0.0612507	+	0.235129i
$387$	−4822.78			−0.633478
$388$	−2354.10	+	4211.84i	−0.308019	+	0.551092i
$389$			4661.52i			0.607580i	0.952739	+	0.303790i	$0.0982521\pi$
$389$			4661.52i			0.607580i	−0.952739	+	0.303790i	$0.901748\pi$
$390$	9962.84	+	2595.30i	1.29356	+	0.336970i
$391$	−5458.61			−0.706020
$392$	−6554.48	−	4156.33i	−0.844518	−	0.535527i
$393$	−3069.86			−0.394030
$394$	13742.8	+	3579.97i	1.75724	+	0.457758i
$395$			3980.70i			0.507065i
$396$	−1799.41	−	1005.73i	−0.228342	−	0.127626i
$397$	−10192.4			−1.28852			−0.644262	−	0.764805i	$-0.722835\pi$
$397$	−10192.4			−1.28852			−0.644262	+	0.764805i	$0.722835\pi$
$398$	−2970.34	+	11402.5i	−0.374094	+	1.43607i
$399$	−2211.99	+	2703.65i	−0.277539	+	0.339227i
$400$	2922.80	+	4751.65i	0.365350	+	0.593956i
$401$	4009.68			0.499336			0.249668	−	0.968332i	$-0.419679\pi$
$401$	4009.68			0.499336			0.249668	+	0.968332i	$0.419679\pi$
$402$	6543.50	+	1704.57i	0.811841	+	0.211483i
$403$	4267.26			0.527462
$404$	6954.62	+	3887.11i	0.856449	+	0.478691i
$405$	−1179.84			−0.144757
$406$	−1371.55	+	1000.54i	−0.167658	+	0.122306i
$407$			10117.3i			1.23218i
$408$	1280.10	−	1334.74i	0.155329	−	0.161959i
$409$			13591.3i			1.64314i	0.570106	+	0.821571i	$0.306902\pi$
$409$			13591.3i			1.64314i	−0.570106	+	0.821571i	$0.693098\pi$
$410$	−3339.49	−	869.931i	−0.402257	−	0.104787i
$411$			1637.30i			0.196501i
$412$	8717.98	+	4872.69i	1.04249	+	0.582671i
$413$	−1483.87	−	1214.03i	−0.176795	−	0.144645i
$414$	−4935.65	−	1285.73i	−0.585928	−	0.152633i
$415$		−	7092.37i		−	0.838918i
$416$	−14420.1	+	4407.36i	−1.69953	+	0.519443i
$417$	−5000.90			−0.587279
$418$	4926.92	+	1283.45i	0.576516	+	0.150181i
$419$			10132.3i			1.18137i	0.806902	+	0.590686i	$0.201143\pi$
$419$			10132.3i			1.18137i	−0.806902	+	0.590686i	$0.798857\pi$
$420$	2373.88	+	6023.45i	0.275794	+	0.699795i
$421$		−	6461.41i		−	0.748005i	−0.927428	−	0.374002i	$-0.877985\pi$
$421$		−	6461.41i		−	0.748005i	0.927428	−	0.374002i	$-0.122015\pi$
$422$	2145.60	−	8236.50i	0.247502	−	0.950111i
$423$	−3704.31			−0.425791
$424$	−3444.44	−	3303.43i	−0.394520	−	0.378369i
$425$		−	2374.73i		−	0.271039i
$426$	−376.095	+	1443.75i	−0.0427743	+	0.164202i
$427$	−4995.17	+	6105.43i	−0.566120	+	0.691949i
$428$	−12874.5	−	7195.90i	−1.45400	−	0.812679i
$429$		−	7154.63i		−	0.805195i
$430$	5565.27	−	21363.9i	0.624142	−	2.39595i
$431$		−	1736.19i		−	0.194035i	−0.995283	−	0.0970177i	$-0.969070\pi$
$431$		−	1736.19i		−	0.194035i	0.995283	−	0.0970177i	$-0.0309303\pi$
$432$	1471.84	−	905.349i	0.163922	−	0.100830i
$433$			3225.51i			0.357986i	0.983850	+	0.178993i	$0.0572839\pi$
$433$			3225.51i			0.357986i	−0.983850	+	0.178993i	$0.942716\pi$
$434$	1581.52	+	2167.96i	0.174921	+	0.239782i
$435$	1416.23			0.156098
$436$	35.5040	−	63.5219i	0.00389984	−	0.00697740i
$437$	12597.2			1.37896
$438$	−2203.44	+	8458.54i	−0.240375	+	0.922751i
$439$	4552.79			0.494972			0.247486	−	0.968891i	$-0.420396\pi$
$439$	4552.79			0.494972			0.247486	+	0.968891i	$0.420396\pi$
$440$	6531.62	−	6810.43i	0.707688	−	0.737896i
$441$	611.395	+	3025.85i	0.0660183	+	0.326730i
$442$	6211.44	+	1618.07i	0.668435	+	0.174126i
$443$	1277.86			0.137050			0.0685250	−	0.997649i	$-0.478171\pi$
$443$	1277.86			0.137050			0.0685250	+	0.997649i	$0.478171\pi$
$444$	−7403.11	−	4137.78i	−0.791298	−	0.442276i
$445$		−	3903.35i		−	0.415812i
$446$	−1173.49	+	4504.80i	−0.124589	+	0.478270i
$447$	1772.66			0.187571
$448$	−7583.49	−	5692.63i	−0.799746	−	0.600338i
$449$	2308.64			0.242653			0.121327	−	0.992613i	$-0.461285\pi$
$449$	2308.64			0.242653			0.121327	+	0.992613i	$0.461285\pi$
$450$	559.348	−	2147.22i	0.0585953	−	0.224936i
$451$			2398.19i			0.250391i
$452$	774.123	+	432.677i	0.0805568	+	0.0450252i
$453$	−7206.98			−0.747491
$454$	−5307.19	−	1382.51i	−0.548631	−	0.142918i
$455$	−14229.1	+	17391.8i	−1.46609	+	1.79196i
$456$	−2954.15	+	3080.25i	−0.303379	+	0.316329i
$457$	13074.1			1.33825			0.669126	−	0.743149i	$-0.266669\pi$
$457$	13074.1			1.33825			0.669126	+	0.743149i	$0.266669\pi$
$458$	1709.26	−	6561.50i	0.174385	−	0.669429i
$459$	−735.583			−0.0748020
$460$	11391.0	−	20380.2i	1.15459	−	2.06573i
$461$	−17759.2			−1.79421			−0.897105	−	0.441818i	$-0.854334\pi$
$461$	−17759.2			−1.79421			−0.897105	+	0.441818i	$0.854334\pi$
$462$	3634.88	−	2651.63i	0.366039	−	0.267024i
$463$			8732.94i			0.876575i	0.898835	+	0.438288i	$0.144415\pi$
$463$			8732.94i			0.876575i	−0.898835	+	0.438288i	$0.855585\pi$
$464$	−1766.74	+	1086.74i	−0.176764	+	0.108730i
$465$		−	2238.58i		−	0.223250i
$466$	−225.718	+	866.485i	−0.0224381	+	0.0861355i
$467$		−	15464.5i		−	1.53235i	−0.642629	−	0.766177i	$-0.722156\pi$
$467$		−	15464.5i		−	1.53235i	0.642629	−	0.766177i	$-0.277844\pi$
$468$	5235.23	+	2926.10i	0.517091	+	0.289015i
$469$	−9345.56	+	11422.8i	−0.920123	+	1.12464i
$470$	4274.60	−	16409.3i	0.419516	−	1.61044i
$471$			5348.94i			0.523283i
$472$	−1690.57	−	1621.36i	−0.164862	−	0.158112i
$473$	−15342.1			−1.49140
$474$	−584.569	+	2244.04i	−0.0566459	+	0.217452i
$475$			5480.30i			0.529376i
$476$	1480.02	+	3755.38i	0.142514	+	0.361613i
$477$			1898.25i			0.182212i
$478$	11138.0	+	2901.43i	1.06577	+	0.277632i
$479$	−5255.37			−0.501303			−0.250651	−	0.968077i	$-0.580645\pi$
$479$	−5255.37			−0.501303			−0.250651	+	0.968077i	$0.580645\pi$
$480$	2312.07	+	7564.69i	0.219856	+	0.719332i
$481$		−	29435.5i		−	2.79032i
$482$	7328.01	+	1908.94i	0.692494	+	0.180393i
$483$	7049.20	−	8616.00i	0.664078	−	0.811681i
$484$	3570.48	+	1995.63i	0.335319	+	0.187418i
$485$			8785.22i			0.822507i
$486$	−665.111	−	173.260i	−0.0620783	−	0.0161713i
$487$		−	1738.65i		−	0.161777i	−0.996723	−	0.0808887i	$-0.974224\pi$
$487$		−	1738.65i		−	0.161777i	0.996723	−	0.0808887i	$-0.0257758\pi$
$488$	−6671.13	+	6955.89i	−0.618828	+	0.645243i
$489$			1617.04i			0.149540i
$490$	−14109.4	−	783.336i	−1.30081	−	0.0722194i
$491$	−11634.2			−1.06934			−0.534668	−	0.845062i	$-0.679563\pi$
$491$	−11634.2			−1.06934			−0.534668	+	0.845062i	$0.679563\pi$
$492$	−1754.82	−	980.813i	−0.160800	−	0.0898749i
$493$	882.961			0.0806624
$494$	−14334.5	−	3734.11i	−1.30555	−	0.340092i
$495$	−3753.27			−0.340802
$496$	1717.77	+	2792.61i	0.155504	+	0.252807i
$497$	−2520.31	−	2062.00i	−0.227468	−	0.186103i
$498$	1041.52	−	3998.19i	0.0937182	−	0.359765i
$499$	−1402.31			−0.125804			−0.0629020	−	0.998020i	$-0.520036\pi$
$499$	−1402.31			−0.125804			−0.0629020	+	0.998020i	$0.520036\pi$
$500$	−3848.39	−	2150.96i	−0.344210	−	0.192388i
$501$			4734.51i			0.422200i
$502$	9924.44	+	2585.30i	0.882369	+	0.229856i
$503$	4445.67			0.394081			0.197040	−	0.980395i	$-0.436867\pi$
$503$	4445.67			0.394081			0.197040	+	0.980395i	$0.436867\pi$
$504$	453.679	+	3744.21i	0.0400961	+	0.330913i
$505$	14506.2			1.27825
$506$	−15701.2	−	4090.13i	−1.37945	−	0.359344i
$507$			14224.8i			1.24605i
$508$	1044.94	−	1869.56i	0.0912635	−	0.163284i
$509$	15335.2			1.33540			0.667701	−	0.744430i	$-0.267279\pi$
$509$	15335.2			1.33540			0.667701	+	0.744430i	$0.267279\pi$
$510$	848.829	−	3258.48i	0.0736995	−	0.282918i
$511$	−14765.8	−	12080.7i	−1.27828	−	1.04583i
$512$	−8689.07	−	7662.76i	−0.750012	−	0.661424i
$513$	1697.55			0.146099
$514$	−16341.4	−	4256.90i	−1.40231	−	0.365299i
$515$	18184.3			1.55591
$516$	6274.62	−	11226.2i	0.535319	−	0.957766i
$517$	−11784.0			−1.00244
$518$	14954.6	−	10909.3i	1.26847	−	0.925345i
$519$		−	6748.11i		−	0.570730i
$520$	−19003.2	+	19814.4i	−1.60259	+	1.67100i
$521$		−	21237.7i		−	1.78587i	−0.450182	−	0.892937i	$-0.648641\pi$
$521$		−	21237.7i		−	1.78587i	0.450182	−	0.892937i	$-0.351359\pi$
$522$	798.370	+	207.974i	0.0669419	+	0.0174383i
$523$			4014.77i			0.335667i	0.985815	+	0.167833i	$0.0536770\pi$
$523$			4014.77i			0.335667i	−0.985815	+	0.167833i	$0.946323\pi$
$524$	3994.00	−	7145.86i	0.332974	−	0.595741i
$525$	3748.33	+	3066.71i	0.311601	+	0.254937i
$526$	8746.24	+	2278.38i	0.725008	+	0.188863i
$527$		−	1395.66i		−	0.115363i
$528$	4682.19	−	2880.07i	0.385921	−	0.237385i
$529$	−27977.7			−2.29948
$530$	−8408.85	−	2190.49i	−0.689165	−	0.179526i
$531$			931.682i			0.0761423i
$532$	−3415.52	−	8666.51i	−0.278349	−	0.706280i
$533$		−	6977.35i		−	0.567021i
$534$	573.210	−	2200.44i	0.0464517	−	0.178319i
$535$	−26854.2			−2.17011
$536$	−12481.1	+	13013.9i	−1.00579	+	1.04872i
$537$		−	361.968i		−	0.0290877i
$538$	−5164.23	+	19824.4i	−0.413840	+	1.58865i
$539$	1944.95	+	9625.74i	0.155427	+	0.769221i
$540$	1535.01	−	2746.37i	0.122327	−	0.218861i
$541$			21640.5i			1.71978i	0.510482	+	0.859888i	$0.329467\pi$
$541$			21640.5i			1.71978i	−0.510482	+	0.859888i	$0.670533\pi$
$542$	−695.912	+	2671.46i	−0.0551512	+	0.211714i
$543$		−	10443.6i		−	0.825371i
$544$	1441.48	+	4716.29i	0.113609	+	0.371708i
$545$		−	132.496i		−	0.0104138i
$546$	−10575.4	+	7714.72i	−0.828910	+	0.604688i
$547$	12978.0			1.01444			0.507222	−	0.861816i	$-0.330672\pi$
$547$	12978.0			1.01444			0.507222	+	0.861816i	$0.330672\pi$
$548$	−3811.22	−	2130.18i	−0.297093	−	0.166053i
$549$	3833.44			0.298009
$550$	1779.38	−	6830.68i	0.137951	−	0.529566i
$551$	−2037.66			−0.157545
$552$	9414.32	−	9816.18i	0.725906	−	0.756892i
$553$	−3917.35	−	3204.99i	−0.301234	−	0.246456i
$554$	12439.2	+	3240.40i	0.953957	+	0.248504i
$555$	−15441.7			−1.18101
$556$	6506.36	−	11640.8i	0.496279	−	0.887917i
$557$			7243.32i			0.551004i	0.961301	+	0.275502i	$0.0888441\pi$
$557$			7243.32i			0.551004i	−0.961301	+	0.275502i	$0.911156\pi$
$558$	328.737	−	1261.95i	0.0249400	−	0.0957397i
$559$	44636.7			3.37733
$560$	−17109.6	−	2310.93i	−1.29109	−	0.174384i
$561$	−2340.02			−0.176106
$562$	5265.31	−	20212.5i	0.395202	−	1.51710i
$563$			6077.75i			0.454967i	0.973782	+	0.227484i	$0.0730498\pi$
$563$			6077.75i			0.454967i	−0.973782	+	0.227484i	$0.926950\pi$
$564$	4819.44	−	8622.70i	0.359814	−	0.643761i
$565$	1614.69			0.120231
$566$	−15166.8	−	3950.92i	−1.12634	−	0.293409i
$567$	949.925	−	1161.06i	0.0703582	−	0.0859965i
$568$	−2871.38	−	2753.83i	−0.212113	−	0.203430i
$569$	3114.53			0.229469			0.114734	−	0.993396i	$-0.463398\pi$
$569$	3114.53			0.229469			0.114734	+	0.993396i	$0.463398\pi$
$570$	−1958.89	+	7519.78i	−0.143945	+	0.552577i
$571$	−5473.36			−0.401143			−0.200572	−	0.979679i	$-0.564280\pi$
$571$	−5473.36			−0.401143			−0.200572	+	0.979679i	$0.564280\pi$
$572$	16654.2	+	9308.43i	1.21739	+	0.680429i
$573$	−7629.43			−0.556238
$574$	3544.81	−	2585.93i	0.257766	−	0.188039i
$575$		−	17464.7i		−	1.26666i
$576$	192.502	+	4603.98i	0.0139252	+	0.333042i
$577$		−	7756.21i		−	0.559610i	−0.960057	−	0.279805i	$-0.909730\pi$
$577$		−	7756.21i		−	0.559610i	0.960057	−	0.279805i	$-0.0902698\pi$
$578$	−2973.78	+	11415.8i	−0.214002	+	0.821510i
$579$			1954.43i			0.140282i
$580$	−1842.56	+	3296.62i	−0.131911	+	0.236008i
$581$	6979.50	+	5710.29i	0.498379	+	0.407750i
$582$	−1290.12	+	4952.49i	−0.0918849	+	0.352728i
$583$			6038.66i			0.428981i
$584$	−16822.6	−	16133.9i	−1.19199	−	1.14320i
$585$	10919.8			0.771761
$586$	1504.92	−	5777.08i	0.106088	−	0.407251i
$587$			23258.3i			1.63539i	0.575653	+	0.817694i	$0.304748\pi$
$587$			23258.3i			1.63539i	−0.575653	+	0.817694i	$0.695252\pi$
$588$	−7838.86	−	2513.57i	−0.549778	−	0.176289i
$589$			3220.85i			0.225319i
$590$	−4127.16	−	1075.12i	−0.287987	−	0.0750201i
$591$	15062.9			1.04840
$592$	19263.4	−	11849.2i	1.33737	−	0.822632i
$593$			14831.4i			1.02707i	0.858068	+	0.513536i	$0.171665\pi$
$593$			14831.4i			1.02707i	−0.858068	+	0.513536i	$0.828335\pi$
$594$	−2115.83	−	551.171i	−0.146151	−	0.0380721i
$595$	5688.22	+	4653.83i	0.391923	+	0.320653i
$596$	−2306.30	+	4126.31i	−0.158506	+	0.283591i
$597$			12497.8i			0.856786i
$598$	45681.3	+	11899.9i	3.12382	+	0.813751i
$599$			17705.2i			1.20771i	0.797095	+	0.603854i	$0.206369\pi$
$599$			17705.2i			1.20771i	−0.797095	+	0.603854i	$0.793631\pi$
$600$	4270.46	+	4095.64i	0.290568	+	0.278673i
$601$			17547.1i			1.19095i	0.803374	+	0.595475i	$0.203036\pi$
$601$			17547.1i			1.19095i	−0.803374	+	0.595475i	$0.796964\pi$
$602$	16543.2	+	22677.5i	1.12001	+	1.53532i
$603$	7172.05			0.484359
$604$	9376.54	−	16776.0i	0.631666	−	1.13014i
$605$	7447.44			0.500465
$606$	8177.59	+	2130.25i	0.548172	+	0.142798i
$607$	9956.82			0.665791			0.332895	−	0.942964i	$-0.391974\pi$
$607$	9956.82			0.665791			0.332895	+	0.942964i	$0.391974\pi$
$608$	−3326.60	−	10884.0i	−0.221894	−	0.725997i
$609$	−1140.25	+	1393.69i	−0.0758705	+	0.0927340i
$610$	−4423.61	+	16981.3i	−0.293617	+	1.12714i
$611$	34284.7			2.27007
$612$	957.021	−	1712.25i	0.0632113	−	0.113094i
$613$		−	11669.9i		−	0.768908i	−0.923144	−	0.384454i	$-0.874390\pi$
$613$		−	11669.9i		−	0.768908i	0.923144	−	0.384454i	$-0.125610\pi$
$614$	8156.26	+	2124.69i	0.536091	+	0.139651i
$615$	−3660.27			−0.239994
$616$	1443.23	+	11911.0i	0.0943983	+	0.779068i
$617$	−12179.6			−0.794703			−0.397351	−	0.917667i	$-0.630071\pi$
$617$	−12179.6			−0.794703			−0.397351	+	0.917667i	$0.630071\pi$
$618$	10251.0	+	2670.38i	0.667244	+	0.173816i
$619$		−	1022.02i		−	0.0663624i	−0.999449	−	0.0331812i	$-0.989436\pi$
$619$		−	1022.02i		−	0.0663624i	0.999449	−	0.0331812i	$-0.0105638\pi$
$620$	5210.84	+	2912.47i	0.337536	+	0.188657i
$621$	−5409.76			−0.349575
$622$	−2467.58	+	9472.56i	−0.159069	+	0.610635i
$623$	3841.23	+	3142.71i	0.247023	+	0.202103i
$624$	−13622.5	+	8379.34i	−0.873934	+	0.537568i
$625$	−18922.8			−1.21106
$626$	11642.7	+	3032.89i	0.743345	+	0.193640i
$627$	5400.19			0.343960
$628$	−12451.0	−	6959.17i	−0.791160	−	0.442199i
$629$	−9627.29			−0.610278
$630$	4047.09	+	5547.78i	0.255937	+	0.350840i
$631$			12954.3i			0.817281i	0.912696	+	0.408640i	$0.133997\pi$
$631$			12954.3i			0.817281i	−0.912696	+	0.408640i	$0.866003\pi$
$632$	−4463.02	−	4280.31i	−0.280901	−	0.269401i
$633$		−	9027.68i		−	0.566853i
$634$	11938.7	+	3110.02i	0.747866	+	0.194818i
$635$		−	3899.59i		−	0.243702i
$636$	−4418.65	−	2469.69i	−0.275489	−	0.153978i
$637$	−5658.69	−	28005.4i	−0.351971	−	1.74193i
$638$	2539.75	+	661.601i	0.157601	+	0.0410549i
$639$			1582.44i			0.0979659i
$640$	−20616.8	−	4460.03i	−1.27336	−	0.275466i
$641$	14845.7			0.914774			0.457387	−	0.889268i	$-0.348785\pi$
$641$	14845.7			0.914774			0.457387	+	0.889268i	$0.348785\pi$
$642$	−15138.5	−	3943.56i	−0.930638	−	0.242430i
$643$		−	19561.8i		−	1.19976i	−0.800092	−	0.599878i	$-0.795216\pi$
$643$		−	19561.8i		−	1.19976i	0.800092	−	0.599878i	$-0.204784\pi$
$644$	10884.6	+	27618.5i	0.666016	+	1.68994i
$645$		−	23416.1i		−	1.42947i
$646$	−1221.29	+	4688.29i	−0.0743824	+	0.285539i
$647$	−11829.2			−0.718787			−0.359394	−	0.933186i	$-0.617016\pi$
$647$	−11829.2			−0.718787			−0.359394	+	0.933186i	$0.617016\pi$
$648$	1268.64	−	1322.79i	0.0769088	−	0.0801917i
$649$			2963.84i			0.179262i
$650$	−5176.97	+	19873.3i	−0.312396	+	1.19922i
$651$	2202.95	+	1802.35i	0.132627	+	0.108509i
$652$	−3764.07	−	2103.83i	−0.226092	−	0.126369i
$653$		−	26606.4i		−	1.59447i	−0.603671	−	0.797234i	$-0.706296\pi$
$653$		−	26606.4i		−	1.59447i	0.603671	−	0.797234i	$-0.293704\pi$
$654$	19.4572	−	74.6922i	0.00116336	−	0.00446590i
$655$		−	14905.1i		−	0.889145i
$656$	4566.17	−	2808.71i	0.271767	−	0.167167i
$657$			9271.05i			0.550530i
$658$	12706.5	+	17418.2i	0.752815	+	1.03196i
$659$	−12399.6			−0.732957			−0.366479	−	0.930426i	$-0.619437\pi$
$659$	−12399.6			−0.732957			−0.366479	+	0.930426i	$0.619437\pi$
$660$	4883.14	−	8736.67i	0.287994	−	0.515264i
$661$	9888.62			0.581880			0.290940	−	0.956741i	$-0.406032\pi$
$661$	9888.62			0.581880			0.290940	+	0.956741i	$0.406032\pi$
$662$	5949.55	−	22839.1i	0.349299	−	1.34089i
$663$	6808.10			0.398800
$664$	7951.72	+	7626.19i	0.464739	+	0.445713i
$665$	−13127.0	−	10739.9i	−0.765480	−	0.626279i
$666$	−8704.95	−	2267.62i	−0.506471	−	0.131935i
$667$	6493.63			0.376963
$668$	−11020.7	−	6159.77i	−0.638331	−	0.356779i
$669$			4937.52i			0.285345i
$670$	−8276.21	+	31770.7i	−0.477221	+	1.83195i
$671$	12194.8			0.701603
$672$	−9305.82	−	3815.30i	−0.534196	−	0.219015i
$673$	−13089.8			−0.749741			−0.374870	−	0.927077i	$-0.622313\pi$
$673$	−13089.8			−0.749741			−0.374870	+	0.927077i	$0.622313\pi$
$674$	−930.720	+	3572.85i	−0.0531899	+	0.204185i
$675$		−	2353.48i		−	0.134201i
$676$	−33111.8	−	18507.0i	−1.88392	−	1.05297i
$677$	2437.50			0.138376			0.0691882	−	0.997604i	$-0.477959\pi$
$677$	2437.50			0.138376			0.0691882	+	0.997604i	$0.477959\pi$
$678$	910.253	+	237.119i	0.0515605	+	0.0134314i
$679$	−8645.40	−	7073.25i	−0.488630	−	0.399774i
$680$	6480.57	+	6215.26i	0.365468	+	0.350507i
$681$	−5816.98			−0.327323
$682$	1045.77	−	4014.49i	0.0587163	−	0.225400i
$683$	−11211.7			−0.628116			−0.314058	−	0.949404i	$-0.601689\pi$
$683$	−11211.7			−0.628116			−0.314058	+	0.949404i	$0.601689\pi$
$684$	−2208.57	+	3951.46i	−0.123460	+	0.220889i
$685$	−7949.58			−0.443413
$686$	12130.8	−	13254.2i	0.675154	−	0.737677i
$687$		−	7191.78i		−	0.399394i
$688$	17968.3	+	29211.5i	0.995692	+	1.61872i
$689$		−	17569.0i		−	0.971446i
$690$	6242.61	−	23964.1i	0.344423	−	1.32217i
$691$			7382.53i			0.406432i	0.979134	+	0.203216i	$0.0651394\pi$
$691$			7382.53i			0.406432i	−0.979134	+	0.203216i	$0.934861\pi$
$692$	15707.9	+	8779.54i	0.862897	+	0.482295i
$693$	3021.87	−	3693.54i	0.165644	−	0.202462i
$694$	−5798.33	+	22258.6i	−0.317149	+	1.21747i
$695$		−	24280.9i		−	1.32522i
$696$	−1522.82	+	1587.82i	−0.0829344	+	0.0864745i
$697$	−2282.03			−0.124015
$698$	1546.98	−	5938.54i	0.0838884	−	0.322030i
$699$			949.717i			0.0513900i
$700$	−12015.2	+	4735.28i	−0.648762	+	0.255681i
$701$		−	6460.26i		−	0.348075i	−0.984739	−	0.174038i	$-0.944319\pi$
$701$		−	6460.26i		−	0.348075i	0.984739	−	0.174038i	$-0.0556815\pi$
$702$	6155.85	+	1603.59i	0.330965	+	0.0862159i
$703$	22217.4			1.19196
$704$	612.383	+	14646.0i	0.0327842	+	0.784082i
$705$		−	17985.5i		−	0.960815i
$706$	−31492.5	−	8203.75i	−1.67881	−	0.437326i
$707$	−11679.4	+	14275.3i	−0.621286	+	0.759377i
$708$	−2168.72	−	1212.15i	−0.115121	−	0.0643439i
$709$			20534.5i			1.08772i	0.839178	+	0.543858i	$0.183037\pi$
$709$			20534.5i			1.08772i	−0.839178	+	0.543858i	$0.816963\pi$
$710$	−7009.86	−	1826.06i	−0.370529	−	0.0965221i
$711$			2459.60i			0.129736i
$712$	4376.30	+	4197.14i	0.230349	+	0.220919i
$713$		−	10264.2i		−	0.539129i
$714$	2523.20	+	3458.82i	0.132253	+	0.181293i
$715$	34737.9			1.81696
$716$	842.571	+	470.934i	0.0439782	+	0.0245805i
$717$	12207.9			0.635859
$718$	549.902	+	143.249i	0.0285824	+	0.00744567i
$719$	14397.1			0.746760			0.373380	−	0.927679i	$-0.378199\pi$
$719$	14397.1			0.746760			0.373380	+	0.927679i	$0.378199\pi$
$720$	4395.75	+	7146.25i	0.227528	+	0.369896i
$721$	−14640.7	+	17894.9i	−0.756240	+	0.924328i
$722$	−2072.06	+	7954.23i	−0.106806	+	0.410008i
$723$	8031.92			0.413154
$724$	24310.0	+	13587.5i	1.24789	+	0.697478i
$725$			2825.01i			0.144715i
$726$	4198.35	+	1093.66i	0.214622	+	0.0559086i
$727$	7782.10			0.397004			0.198502	−	0.980100i	$-0.436392\pi$
$727$	7782.10			0.397004			0.198502	+	0.980100i	$0.436392\pi$
$728$	−4198.96	−	34654.0i	−0.213769	−	1.76423i
$729$	−729.000			−0.0370370
$730$	−41068.8	−	10698.4i	−2.08223	−	0.542416i
$731$		−	14599.0i		−	0.738665i
$732$	−4987.44	+	8923.28i	−0.251832	+	0.450565i
$733$	21703.4			1.09363			0.546816	−	0.837253i	$-0.315840\pi$
$733$	21703.4			1.09363			0.546816	+	0.837253i	$0.315840\pi$
$734$	1872.69	−	7188.89i	0.0941722	−	0.361508i
$735$	−14691.4	+	2968.51i	−0.737281	+	0.148973i
$736$	10601.2	+	34685.4i	0.530933	+	1.73712i
$737$	22815.5			1.14033
$738$	−2063.40	−	537.513i	−0.102920	−	0.0268105i
$739$	−19420.2			−0.966692			−0.483346	−	0.875430i	$-0.660579\pi$
$739$	−19420.2			−0.966692			−0.483346	+	0.875430i	$0.660579\pi$
$740$	20090.2	−	35944.4i	0.998014	−	1.78560i
$741$	−15711.4			−0.778912
$742$	8925.86	−	6511.39i	0.441615	−	0.322157i
$743$			4381.43i			0.216338i	0.994133	+	0.108169i	$0.0344987\pi$
$743$			4381.43i			0.216338i	−0.994133	+	0.108169i	$0.965501\pi$
$744$	2509.81	+	2407.06i	0.123675	+	0.118612i
$745$			8606.82i			0.423261i
$746$	23028.4	+	5998.86i	1.13020	+	0.294415i
$747$		−	4382.24i		−	0.214642i
$748$	3044.45	−	5446.97i	0.148818	−	0.266258i
$749$	21621.1	−	26426.8i	1.05477	−	1.28920i
$750$	−4525.13	−	1178.79i	−0.220312	−	0.0573910i
$751$		−	8316.49i		−	0.404092i	−0.979376	−	0.202046i	$-0.935241\pi$
$751$		−	8316.49i		−	0.404092i	0.979376	−	0.202046i	$-0.0647591\pi$
$752$	13801.2	+	22436.9i	0.669253	+	1.08802i
$753$	10877.8			0.526437
$754$	−7389.20	−	1924.88i	−0.356895	−	0.0929706i
$755$		−	34992.1i		−	1.68674i
$756$	1466.77	+	3721.77i	0.0705635	+	0.179047i
$757$			5780.62i			0.277543i	0.990324	+	0.138772i	$0.0443154\pi$
$757$			5780.62i			0.277543i	−0.990324	+	0.138772i	$0.955685\pi$
$758$	−1487.61	+	5710.62i	−0.0712827	+	0.273640i
$759$	−17209.4			−0.823005
$760$	−14955.6	−	14343.3i	−0.713810	−	0.684588i
$761$		−	12785.0i		−	0.609008i	−0.952511	−	0.304504i	$-0.901509\pi$
$761$		−	12785.0i		−	0.609008i	0.952511	−	0.304504i	$-0.0984906\pi$
$762$	572.659	−	2198.32i	0.0272247	−	0.104510i
$763$	130.388	+	106.677i	0.00618657	+	0.00506155i
$764$	9926.17	−	17759.4i	0.470048	−	0.840985i
$765$		−	3571.48i		−	0.168794i
$766$	−7658.42	+	29399.1i	−0.361240	+	1.38673i
$767$		−	8623.06i		−	0.405946i
$768$	−10967.4	−	5541.85i	−0.515300	−	0.260383i
$769$		−	14960.3i		−	0.701536i	−0.936462	−	0.350768i	$-0.885921\pi$
$769$		−	14960.3i		−	0.701536i	0.936462	−	0.350768i	$-0.114079\pi$
$770$	12874.5	+	17648.4i	0.602551	+	0.825981i
$771$	−17911.1			−0.836643
$772$	−4549.43	−	2542.79i	−0.212095	−	0.118545i
$773$	3423.96			0.159316			0.0796580	−	0.996822i	$-0.474617\pi$
$773$	3423.96			0.159316			0.0796580	+	0.996822i	$0.474617\pi$
$774$	3438.67	−	13200.4i	0.159691	−	0.613020i
$775$	4465.39			0.206970
$776$	−9849.67	−	9446.44i	−0.455648	−	0.436994i
$777$	12432.6	−	15195.9i	0.574024	−	0.701610i
$778$	−12759.0	−	3323.69i	−0.587958	−	0.153162i
$779$	5266.38			0.242218
$780$	−14207.1	+	25418.7i	−0.652175	+	1.16684i
$781$			5034.00i			0.230641i
$782$	3892.02	−	14940.7i	0.177978	−	0.683219i
$783$	875.059			0.0399388
$784$	16049.6	−	14976.7i	0.731123	−	0.682246i
$785$	−25970.7			−1.18081
$786$	2188.82	−	8402.45i	0.0993292	−	0.381305i
$787$			18372.1i			0.832140i	0.909333	+	0.416070i	$0.136593\pi$
$787$			18372.1i			0.832140i	−0.909333	+	0.416070i	$0.863407\pi$
$788$	−19597.4	+	35062.6i	−0.885949	+	1.58509i
$789$	9586.38			0.432553
$790$	−10895.5	−	2838.26i	−0.490690	−	0.127824i
$791$	−1300.04	+	1589.00i	−0.0584376	+	0.0714263i
$792$	4035.76	−	4208.03i	0.181066	−	0.188795i
$793$	−35479.9			−1.58881
$794$	7267.26	−	27897.5i	0.324818	−	1.24691i
$795$	−9216.59			−0.411168
$796$	−29091.8	−	16260.1i	−1.29539	−	0.724026i
$797$	−37654.9			−1.67353			−0.836766	−	0.547561i	$-0.815556\pi$
$797$	−37654.9			−1.67353			−0.836766	+	0.547561i	$0.815556\pi$
$798$	−5822.94	−	7982.12i	−0.258308	−	0.354090i
$799$		−	11213.3i		−	0.496492i
$800$	−15089.6	+	4611.99i	−0.666874	+	0.203823i
$801$		−	2411.80i		−	0.106388i
$802$	−2858.92	+	10974.8i	−0.125875	+	0.483210i
$803$			29492.8i			1.29611i
$804$	−9331.10	+	16694.7i	−0.409307	+	0.732311i
$805$	41833.3	+	34226.0i	1.83159	+	1.49852i
$806$	−3042.58	+	11679.8i	−0.132966	+	0.510428i
$807$			21728.7i			0.947816i
$808$	−15598.0	+	16263.9i	−0.679130	+	0.708119i
$809$	33392.4			1.45119			0.725596	−	0.688121i	$-0.241564\pi$
$809$	33392.4			1.45119			0.725596	+	0.688121i	$0.241564\pi$
$810$	841.232	−	3229.32i	0.0364912	−	0.140082i
$811$		−	19389.2i		−	0.839514i	−0.907636	−	0.419757i	$-0.862115\pi$
$811$		−	19389.2i		−	0.839514i	0.907636	−	0.419757i	$-0.137885\pi$
$812$	−1760.65	−	4467.45i	−0.0760919	−	0.193075i
$813$			2928.08i			0.126313i
$814$	−27691.9	−	7213.70i	−1.19239	−	0.310614i
$815$	−7851.23			−0.337444
$816$	2740.58	+	4455.41i	0.117573	+	0.191140i
$817$			33691.0i			1.44271i
$818$	−37200.4	−	9690.65i	−1.59008	−	0.414212i
$819$	−8791.91	+	10746.1i	−0.375109	+	0.458483i
$820$	4762.14	−	8520.19i	0.202806	−	0.362851i
$821$			14520.0i			0.617238i	0.951186	+	0.308619i	$0.0998669\pi$
$821$			14520.0i			0.617238i	−0.951186	+	0.308619i	$0.900133\pi$
$822$	−4481.42	−	1167.40i	−0.190155	−	0.0495351i
$823$			36026.1i			1.52587i	0.646474	+	0.762936i	$0.276243\pi$
$823$			36026.1i			1.52587i	−0.646474	+	0.762936i	$0.723757\pi$
$824$	−19552.9	+	20387.6i	−0.826649	+	0.861935i
$825$		−	7486.82i		−	0.315949i
$826$	4380.91	−	3195.86i	0.184542	−	0.134623i
$827$	−10062.5			−0.423105			−0.211553	−	0.977367i	$-0.567852\pi$
$827$	−10062.5			−0.423105			−0.211553	+	0.977367i	$0.567852\pi$
$828$	7038.30	−	12592.6i	0.295408	−	0.528529i
$829$	28565.1			1.19675			0.598376	−	0.801216i	$-0.295813\pi$
$829$	28565.1			1.19675			0.598376	+	0.801216i	$0.295813\pi$
$830$	19412.4	+	5056.90i	0.811825	+	0.211479i
$831$	13634.1			0.569148
$832$	−1781.68	−	42611.5i	−0.0742412	−	1.77559i
$833$	−9159.53	+	1850.75i	−0.380983	+	0.0769804i
$834$	3565.67	−	13687.9i	0.148044	−	0.568312i
$835$	−22987.5			−0.952712
$836$	−7025.84	+	12570.3i	−0.290663	+	0.520039i
$837$		−	1383.17i		−	0.0571200i
$838$	−27732.9	−	7224.38i	−1.14322	−	0.297807i
$839$	4665.37			0.191974			0.0959872	−	0.995383i	$-0.469399\pi$
$839$	4665.37			0.191974			0.0959872	+	0.995383i	$0.469399\pi$
$840$	−18179.3	+	2202.75i	−0.746719	+	0.0904786i
$841$	23338.6			0.956932
$842$	17685.4	+	4607.02i	0.723848	+	0.188561i
$843$		−	22154.0i		−	0.905130i
$844$	21014.2	+	11745.3i	0.857035	+	0.479018i
$845$	−69065.9			−2.81176
$846$	2641.19	−	10139.0i	0.107336	−	0.412040i
$847$	−5996.17	+	7328.91i	−0.243248	+	0.297313i
$848$	11497.7	−	7072.35i	0.465603	−	0.286398i
$849$	−16623.6			−0.671993
$850$	6499.84	+	1693.20i	0.262285	+	0.0683249i
$851$	−70802.7			−2.85204
$852$	−3683.51	−	2058.81i	−0.148116	−	0.0827859i
$853$	−10456.2			−0.419710			−0.209855	−	0.977733i	$-0.567299\pi$
$853$	−10456.2			−0.419710			−0.209855	+	0.977733i	$0.567299\pi$
$854$	−13149.5	−	18025.4i	−0.526892	−	0.722267i
$855$			8242.11i			0.329677i
$856$	28875.4	−	30107.9i	1.15297	−	1.20218i
$857$			33383.4i			1.33064i	0.746560	+	0.665318i	$0.231704\pi$
$857$			33383.4i			1.33064i	−0.746560	+	0.665318i	$0.768296\pi$
$858$	19582.8	+	5101.29i	0.779191	+	0.202978i
$859$		−	42587.8i		−	1.69159i	−0.533508	−	0.845795i	$-0.679127\pi$
$859$		−	42587.8i		−	1.69159i	0.533508	−	0.845795i	$-0.320873\pi$
$860$	54506.8	+	30465.2i	2.16124	+	1.20797i
$861$	2947.00	−	3602.02i	0.116647	−	0.142574i
$862$	4752.09	+	1237.91i	0.187769	+	0.0489135i
$863$		−	43036.7i		−	1.69755i	−0.528754	−	0.848775i	$-0.677341\pi$
$863$		−	43036.7i		−	1.69755i	0.528754	−	0.848775i	$-0.322659\pi$
$864$	1428.58	+	4674.08i	0.0562516	+	0.184046i
$865$	32764.1			1.28788
$866$	−8828.48	−	2299.80i	−0.346425	−	0.0902431i
$867$			12512.3i			0.490128i
$868$	−7061.53	+	2782.99i	−0.276133	+	0.108826i
$869$			7824.41i			0.305437i
$870$	−1009.78	+	3876.33i	−0.0393502	+	0.151057i
$871$	−66380.0			−2.58232
$872$	148.550	+	142.469i	0.00576897	+	0.00553280i
$873$			5428.22i			0.210444i
$874$	−8981.84	+	34479.4i	−0.347615	+	1.33442i
$875$	6462.88	−	7899.36i	0.249697	−	0.305197i
$876$	−21580.7	−	12062.0i	−0.832355	−	0.465224i
$877$			33124.9i			1.27542i	0.770275	+	0.637712i	$0.220119\pi$
$877$			33124.9i			1.27542i	−0.770275	+	0.637712i	$0.779881\pi$
$878$	−3246.16	+	12461.4i	−0.124775	+	0.478987i
$879$		−	6332.02i		−	0.242973i
$880$	13983.6	+	22733.5i	0.535668	+	0.870846i
$881$			5619.22i			0.214888i	0.994211	+	0.107444i	$0.0342667\pi$
$881$			5619.22i			0.214888i	−0.994211	+	0.107444i	$0.965733\pi$
$882$	−8717.93	−	484.008i	−0.332821	−	0.0184778i
$883$	17687.6			0.674104			0.337052	−	0.941486i	$-0.390570\pi$
$883$	17687.6			0.674104			0.337052	+	0.941486i	$0.390570\pi$
$884$	−8857.58	+	15847.5i	−0.337005	+	0.602953i
$885$	−4523.60			−0.171818
$886$	−911.123	+	3497.62i	−0.0345483	+	0.132624i
$887$	−31280.9			−1.18411			−0.592057	−	0.805896i	$-0.701684\pi$
$887$	−31280.9			−1.18411			−0.592057	+	0.805896i	$0.701684\pi$
$888$	16603.9	−	17312.7i	0.627467	−	0.654251i
$889$	3837.53	+	3139.69i	0.144777	+	0.118450i
$890$	10683.8	+	2783.11i	0.402384	+	0.104820i
$891$	−2319.07			−0.0871963
$892$	−11493.3	−	6423.90i	−0.431417	−	0.241130i
$893$			25877.5i			0.969718i
$894$	−1263.92	+	4851.93i	−0.0472838	+	0.181513i
$895$	1757.47			0.0656376
$896$	20988.3	−	16697.8i	0.782555	−	0.622582i
$897$	50069.3			1.86373
$898$	−1646.07	+	6318.93i	−0.0611694	+	0.234817i
$899$			1660.30i			0.0615952i
$900$	5478.31	+	3061.96i	0.202900	+	0.113406i
$901$	−5746.18			−0.212467
$902$	−6564.04	−	1709.92i	−0.242305	−	0.0631199i
$903$	23043.4	+	18853.0i	0.849211	+	0.694783i
$904$	−1736.23	+	1810.34i	−0.0638783	+	0.0666050i
$905$	50706.7			1.86248
$906$	5138.61	−	19726.1i	0.188432	−	0.723351i
$907$	28165.6			1.03112			0.515558	−	0.856854i	$-0.327585\pi$
$907$	28165.6			1.03112			0.515558	+	0.856854i	$0.327585\pi$
$908$	7568.11	−	13540.5i	0.276604	−	0.494886i
$909$	8963.11			0.327049
$910$	−37457.3	−	51346.8i	−1.36450	−	1.87047i
$911$			18281.3i			0.664858i	0.943128	+	0.332429i	$0.107868\pi$
$911$			18281.3i			0.664858i	−0.943128	+	0.332429i	$0.892132\pi$
$912$	−6324.58	−	10282.0i	−0.229636	−	0.373323i
$913$		−	13940.7i		−	0.505332i
$914$	−9321.91	+	35784.9i	−0.337354	+	1.29503i
$915$			18612.5i			0.672470i
$916$	16740.6	+	9356.76i	0.603850	+	0.337507i
$917$	14667.9	+	12000.6i	0.528218	+	0.432163i
$918$	524.475	−	2013.35i	0.0188565	−	0.0723862i
$919$		−	13911.2i		−	0.499334i	−0.968332	−	0.249667i	$-0.919679\pi$
$919$		−	13911.2i		−	0.499334i	0.968332	−	0.249667i	$-0.0803212\pi$
$920$	47660.6	+	45709.4i	1.70796	+	1.63804i
$921$	8939.72			0.319841
$922$	12662.4	−	48608.5i	0.452294	−	1.73627i
$923$		−	14646.0i		−	0.522297i
$924$	4666.06	+	11839.6i	0.166128	+	0.421530i
$925$		−	30802.2i		−	1.09489i
$926$	−23902.8	−	6226.64i	−0.848266	−	0.220972i
$927$	11235.7			0.398090
$928$	−1714.81	−	5610.56i	−0.0606587	−	0.198465i
$929$			17100.5i			0.603928i	0.953319	+	0.301964i	$0.0976422\pi$
$929$			17100.5i			0.603928i	−0.953319	+	0.301964i	$0.902358\pi$
$930$	6127.17	+	1596.12i	0.216041	+	0.0562782i
$931$	21138.0	−	4271.08i	0.744112	−	0.150353i
$932$	−2210.70	−	1235.62i	−0.0776974	−	0.0434270i
$933$			10382.5i			0.364316i
$934$	42327.5	+	11026.2i	1.48287	+	0.386284i
$935$		−	11361.5i		−	0.397391i
$936$	−11741.7	+	12242.9i	−0.410033	+	0.427535i
$937$		−	2136.03i		−	0.0744727i	−0.999306	−	0.0372364i	$-0.988145\pi$
$937$		−	2136.03i		−	0.0744727i	0.999306	−	0.0372364i	$-0.0118554\pi$
$938$	−24601.6	−	33724.1i	−0.856366	−	1.17391i
$939$	12761.0			0.443493
$940$	41865.8	+	23399.8i	1.45267	+	0.811935i
$941$	−23551.2			−0.815883			−0.407941	−	0.913008i	$-0.633753\pi$
$941$	−23551.2			−0.815883			−0.407941	+	0.913008i	$0.633753\pi$
$942$	−14640.5	−	3813.82i	−0.506383	−	0.131912i
$943$	−16782.9			−0.579563
$944$	5643.17	−	3471.18i	0.194565	−	0.119679i
$945$	5637.31	+	4612.18i	0.194055	+	0.158766i
$946$	10939.0	−	41992.6i	0.375959	−	1.44323i
$947$	12852.6			0.441028			0.220514	−	0.975384i	$-0.429227\pi$
$947$	12852.6			0.441028			0.220514	+	0.975384i	$0.429227\pi$
$948$	−5725.33	−	3200.03i	−0.196150	−	0.109633i
$949$		−	85807.0i		−	2.93510i
$950$	−15000.0	−	3907.49i	−0.512280	−	0.133448i
$951$	13085.5			0.446190
$952$	−11334.1	+	1373.33i	−0.385860	+	0.0467540i
$953$	1149.91			0.0390862			0.0195431	−	0.999809i	$-0.493779\pi$
$953$	1149.91			0.0390862			0.0195431	+	0.999809i	$0.493779\pi$
$954$	−5195.67	−	1353.46i	−0.176327	−	0.0459329i
$955$		−	37043.2i		−	1.25517i
$956$	−15882.9	+	28416.9i	−0.537332	+	0.961367i
$957$	2783.71			0.0940278
$958$	3747.11	−	14384.4i	0.126371	−	0.485113i
$959$	6400.45	−	7823.06i	0.215518	−	0.263420i
$960$	−22353.7	+	934.658i	−0.751524	+	0.0314229i
$961$	−27166.6			−0.911907
$962$	80567.5	+	20987.7i	2.70021	+	0.703400i
$963$	−16592.7			−0.555235
$964$	−10449.8	+	18696.3i	−0.349135	+	0.624655i
$965$	−9489.36			−0.316553
$966$	18556.6	+	25437.5i	0.618063	+	0.847245i
$967$			25298.5i			0.841309i	0.907221	+	0.420654i	$0.138199\pi$
$967$			25298.5i			0.841309i	−0.907221	+	0.420654i	$0.861801\pi$
$968$	−8007.98	+	8349.80i	−0.265895	+	0.277245i
$969$			5138.63i			0.170358i
$970$	−24045.9	−	6263.91i	−0.795945	−	0.207342i
$971$			47322.4i			1.56400i	0.623275	+	0.782002i	$0.285802\pi$
$971$			47322.4i			1.56400i	−0.623275	+	0.782002i	$0.714198\pi$
$972$	948.456	−	1696.93i	0.0312981	−	0.0559969i
$973$	23894.5	+	19549.3i	0.787278	+	0.644113i
$974$	4758.82	+	1239.67i	0.156553	+	0.0407818i
$975$			21782.3i			0.715479i
$976$	−14282.3	−	23219.0i	−0.468407	−	0.761499i
$977$	−10030.5			−0.328458			−0.164229	−	0.986422i	$-0.552514\pi$
$977$	−10030.5			−0.328458			−0.164229	+	0.986422i	$0.552514\pi$
$978$	−4425.98	−	1152.96i	−0.144711	−	0.0376969i
$979$		−	7672.36i		−	0.250470i
$980$	12204.1	−	38060.1i	0.397803	−	1.24060i
$981$		−	81.8669i		−	0.00266443i
$982$	8295.24	−	31843.8i	0.269564	−	1.03480i
$983$	−20421.9			−0.662624			−0.331312	−	0.943521i	$-0.607491\pi$
$983$	−20421.9			−0.662624			−0.331312	+	0.943521i	$0.607491\pi$
$984$	3935.76	−	4103.76i	0.127508	−	0.132950i
$985$			73134.9i			2.36576i
$986$	−629.556	+	2416.74i	−0.0203338	+	0.0780574i
$987$	17699.3	+	14480.7i	0.570795	+	0.466997i
$988$	20441.1	−	36572.3i	0.658218	−	1.17765i
$989$		−	107367.i		−	3.45203i
$990$	2676.10	−	10273.0i	0.0859112	−	0.329796i
$991$			43423.7i			1.39193i	0.718077	+	0.695964i	$0.245023\pi$
$991$			43423.7i			1.39193i	−0.718077	+	0.695964i	$0.754977\pi$
$992$	−8868.40	+	2710.53i	−0.283843	+	0.0867535i
$993$		−	25033.0i		−	0.799998i
$994$	7440.85	−	5428.08i	0.237434	−	0.173208i
$995$	−60680.7			−1.93337
$996$	10200.8	+	5701.46i	0.324521	+	0.181383i
$997$	−36227.1			−1.15078			−0.575388	−	0.817881i	$-0.695149\pi$
$997$	−36227.1			−1.15078			−0.575388	+	0.817881i	$0.695149\pi$
$998$	999.857	−	3838.25i	0.0317134	−	0.121741i
$999$	−9541.12			−0.302170

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.4.p.a.139.24	yes	48
4.3	odd	2		672.4.p.a.559.43		48
7.6	odd	2	inner	168.4.p.a.139.23	yes	48
8.3	odd	2	inner	168.4.p.a.139.22	yes	48
8.5	even	2		672.4.p.a.559.11		48
28.27	even	2		672.4.p.a.559.12		48
56.13	odd	2		672.4.p.a.559.44		48
56.27	even	2	inner	168.4.p.a.139.21	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.4.p.a.139.21	✓	48	56.27	even	2	inner
168.4.p.a.139.22	yes	48	8.3	odd	2	inner
168.4.p.a.139.23	yes	48	7.6	odd	2	inner
168.4.p.a.139.24	yes	48	1.1	even	1	trivial
672.4.p.a.559.11		48	8.5	even	2
672.4.p.a.559.12		48	28.27	even	2
672.4.p.a.559.43		48	4.3	odd	2
672.4.p.a.559.44		48	56.13	odd	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	168.p (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.713005 + 2.73708i) q^{2} +3.00000i q^{3} +(-6.98325 - 3.90311i) q^{4} -14.5659 q^{5} +(-8.21125 - 2.13902i) q^{6} +(11.7275 - 14.3341i) q^{7} +(15.6622 - 16.3308i) q^{8} -9.00000 q^{9} +(10.3856 - 39.8681i) q^{10} -28.6305 q^{11} +(11.7093 - 20.9497i) q^{12} +83.2983 q^{13} +(30.8719 + 42.3194i) q^{14} -43.6977i q^{15} +(33.5315 + 54.5128i) q^{16} -27.2438i q^{17} +(6.41705 - 24.6337i) q^{18} +62.8721i q^{19} +(101.717 + 56.8524i) q^{20} +(43.0023 + 35.1824i) q^{21} +(20.4137 - 78.3642i) q^{22} -200.361i q^{23} +(48.9924 + 46.9867i) q^{24} +87.1659 q^{25} +(-59.3922 + 227.994i) q^{26} -27.0000i q^{27} +(-137.843 + 54.3249i) q^{28} +32.4096i q^{29} +(119.604 + 31.1567i) q^{30} +51.2286 q^{31} +(-173.114 + 52.9105i) q^{32} -85.8916i q^{33} +(74.5686 + 19.4250i) q^{34} +(-170.821 + 208.789i) q^{35} +(62.8492 + 35.1280i) q^{36} -353.375i q^{37} +(-172.086 - 44.8282i) q^{38} +249.895i q^{39} +(-228.135 + 237.873i) q^{40} -83.7633i q^{41} +(-126.958 + 92.6156i) q^{42} +535.865 q^{43} +(199.934 + 111.748i) q^{44} +131.093 q^{45} +(548.406 + 142.859i) q^{46} +411.590 q^{47} +(-163.538 + 100.594i) q^{48} +(-67.9328 - 336.205i) q^{49} +(-62.1497 + 238.580i) q^{50} +81.7315 q^{51} +(-581.693 - 325.123i) q^{52} -210.917i q^{53} +(73.9012 + 19.2511i) q^{54} +417.030 q^{55} +(-50.4087 - 416.023i) q^{56} -188.616 q^{57} +(-88.7077 - 23.1082i) q^{58} -103.520i q^{59} +(-170.557 + 305.152i) q^{60} -425.937 q^{61} +(-36.5263 + 140.217i) q^{62} +(-105.547 + 129.007i) q^{63} +(-21.3892 - 511.553i) q^{64} -1213.32 q^{65} +(235.092 + 61.2412i) q^{66} -796.894 q^{67} +(-106.336 + 190.250i) q^{68} +601.084 q^{69} +(-449.677 - 616.420i) q^{70} -175.826i q^{71} +(-140.960 + 146.977i) q^{72} -1030.12i q^{73} +(967.216 + 251.958i) q^{74} +261.498i q^{75} +(245.397 - 439.052i) q^{76} +(-335.764 + 410.393i) q^{77} +(-683.983 - 178.176i) q^{78} -273.289i q^{79} +(-488.416 - 794.028i) q^{80} +81.0000 q^{81} +(229.267 + 59.7237i) q^{82} +486.916i q^{83} +(-162.975 - 413.530i) q^{84} +396.831i q^{85} +(-382.075 + 1466.71i) q^{86} -97.2288 q^{87} +(-448.418 + 467.559i) q^{88} +267.978i q^{89} +(-93.4702 + 358.813i) q^{90} +(976.879 - 1194.01i) q^{91} +(-782.033 + 1399.17i) q^{92} +153.686i q^{93} +(-293.466 + 1126.56i) q^{94} -915.790i q^{95} +(-158.732 - 519.342i) q^{96} -603.135i q^{97} +(968.659 + 53.7787i) q^{98} +257.675 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 2 q^{2} + 10 q^{4} + 118 q^{8} - 432 q^{9} - 40 q^{11} + 38 q^{14} - 142 q^{16} + 18 q^{18} - 376 q^{22} + 1200 q^{25} - 274 q^{28} + 336 q^{30} + 318 q^{32} - 456 q^{35} - 90 q^{36} + 564 q^{42}+ \cdots + 360 q^{99}+O(q^{100}) \) 48 * q - 2 * q^2 + 10 * q^4 + 118 * q^8 - 432 * q^9 - 40 * q^11 + 38 * q^14 - 142 * q^16 + 18 * q^18 - 376 * q^22 + 1200 * q^25 - 274 * q^28 + 336 * q^30 + 318 * q^32 - 456 * q^35 - 90 * q^36 + 564 * q^42 - 808 * q^43 + 1584 * q^44 - 388 * q^46 + 360 * q^49 - 14 * q^50 + 226 * q^56 + 336 * q^57 - 3176 * q^58 - 192 * q^60 + 1954 * q^64 - 4104 * q^67 - 648 * q^70 - 1062 * q^72 + 2384 * q^74 - 1800 * q^78 + 3888 * q^81 + 264 * q^84 - 880 * q^86 + 4184 * q^88 + 104 * q^91 + 2044 * q^92 - 6018 * q^98 + 360 * q^99

Introduction

L-functions

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