LMFDB - Embedded newform 162.4.e.b.73.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,4,Mod(19,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("162.19");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	162.e (of order $9$, degree $6$, not 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:	$9.55830942093$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			73.1
Character	$\chi$	$=$	162.73
Dual form			162.4.e.b.91.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.347296 - 1.96962i) q^{2} +(-3.75877 - 1.36808i) q^{4} +(-7.73816 + 6.49309i) q^{5} +(7.54967 - 2.74785i) q^{7} +(-4.00000 + 6.92820i) q^{8} +O(q^{10})$	\(q+(0.347296 - 1.96962i) q^{2} +(-3.75877 - 1.36808i) q^{4} +(-7.73816 + 6.49309i) q^{5} +(7.54967 - 2.74785i) q^{7} +(-4.00000 + 6.92820i) q^{8} +(10.1015 + 17.4962i) q^{10} +(-12.9632 - 10.8775i) q^{11} +(14.9620 + 84.8538i) q^{13} +(-2.79024 - 15.8243i) q^{14} +(12.2567 + 10.2846i) q^{16} +(53.3650 + 92.4308i) q^{17} +(-17.8925 + 30.9907i) q^{19} +(37.9690 - 13.8196i) q^{20} +(-25.9265 + 21.7549i) q^{22} +(85.4423 + 31.0985i) q^{23} +(-3.98707 + 22.6118i) q^{25} +172.326 q^{26} -32.1368 q^{28} +(16.6639 - 94.5057i) q^{29} +(-191.030 - 69.5291i) q^{31} +(24.5134 - 20.5692i) q^{32} +(200.587 - 73.0076i) q^{34} +(-40.5785 + 70.2840i) q^{35} +(79.7878 + 138.197i) q^{37} +(54.8257 + 46.0043i) q^{38} +(-14.0328 - 79.5839i) q^{40} +(-43.2835 - 245.473i) q^{41} +(229.519 + 192.589i) q^{43} +(33.8446 + 58.6206i) q^{44} +(90.9258 - 157.488i) q^{46} +(-462.735 + 168.422i) q^{47} +(-213.306 + 178.985i) q^{49} +(43.1519 + 15.7060i) q^{50} +(59.8481 - 339.415i) q^{52} +317.176 q^{53} +170.940 q^{55} +(-11.1610 + 63.2970i) q^{56} +(-180.353 - 65.6430i) q^{58} +(-127.954 + 107.366i) q^{59} +(-107.083 + 38.9752i) q^{61} +(-203.289 + 352.108i) q^{62} +(-32.0000 - 55.4256i) q^{64} +(-666.742 - 559.463i) q^{65} +(-97.7000 - 554.084i) q^{67} +(-74.1338 - 420.434i) q^{68} +(124.340 + 104.333i) q^{70} +(-124.798 - 216.156i) q^{71} +(-479.693 + 830.853i) q^{73} +(299.904 - 109.156i) q^{74} +(109.651 - 92.0085i) q^{76} +(-127.758 - 46.5001i) q^{77} +(222.634 - 1262.62i) q^{79} -161.623 q^{80} -498.520 q^{82} +(-109.634 + 621.765i) q^{83} +(-1013.11 - 368.741i) q^{85} +(459.038 - 385.178i) q^{86} +(127.214 - 46.3022i) q^{88} +(-427.862 + 741.078i) q^{89} +(346.124 + 599.505i) q^{91} +(-278.613 - 233.784i) q^{92} +(171.020 + 969.903i) q^{94} +(-62.7704 - 355.988i) q^{95} +(-241.282 - 202.460i) q^{97} +(278.452 + 482.293i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 12 q^{5} + 33 q^{7} - 120 q^{8}+O(q^{10}) $ 30 * q + 12 * q^5 + 33 * q^7 - 120 * q^8	$ 30 q + 12 q^{5} + 33 q^{7} - 120 q^{8} - 30 q^{10} + 39 q^{11} - 60 q^{13} + 66 q^{14} - 102 q^{17} - 171 q^{19} - 96 q^{20} + 78 q^{22} - 48 q^{23} - 432 q^{25} + 468 q^{26} + 336 q^{28} + 381 q^{29} - 801 q^{31} - 222 q^{34} - 624 q^{35} - 555 q^{37} - 606 q^{38} + 96 q^{40} - 1401 q^{41} + 648 q^{43} - 132 q^{44} - 348 q^{46} - 540 q^{47} + 15 q^{49} + 828 q^{50} - 240 q^{52} + 1794 q^{53} + 3906 q^{55} + 264 q^{56} - 444 q^{58} + 1500 q^{59} - 378 q^{61} - 744 q^{62} - 960 q^{64} - 3666 q^{65} + 3087 q^{67} + 24 q^{68} + 2118 q^{70} - 120 q^{71} - 2604 q^{73} + 1974 q^{74} - 1212 q^{76} + 6504 q^{77} - 2625 q^{79} + 480 q^{80} + 3408 q^{82} + 5211 q^{83} - 1395 q^{85} + 1296 q^{86} - 912 q^{88} - 2604 q^{89} - 3399 q^{91} - 372 q^{92} + 4500 q^{94} - 7545 q^{95} + 8940 q^{97} - 4002 q^{98}+O(q^{100}) $ 30 * q + 12 * q^5 + 33 * q^7 - 120 * q^8 - 30 * q^10 + 39 * q^11 - 60 * q^13 + 66 * q^14 - 102 * q^17 - 171 * q^19 - 96 * q^20 + 78 * q^22 - 48 * q^23 - 432 * q^25 + 468 * q^26 + 336 * q^28 + 381 * q^29 - 801 * q^31 - 222 * q^34 - 624 * q^35 - 555 * q^37 - 606 * q^38 + 96 * q^40 - 1401 * q^41 + 648 * q^43 - 132 * q^44 - 348 * q^46 - 540 * q^47 + 15 * q^49 + 828 * q^50 - 240 * q^52 + 1794 * q^53 + 3906 * q^55 + 264 * q^56 - 444 * q^58 + 1500 * q^59 - 378 * q^61 - 744 * q^62 - 960 * q^64 - 3666 * q^65 + 3087 * q^67 + 24 * q^68 + 2118 * q^70 - 120 * q^71 - 2604 * q^73 + 1974 * q^74 - 1212 * q^76 + 6504 * q^77 - 2625 * q^79 + 480 * q^80 + 3408 * q^82 + 5211 * q^83 - 1395 * q^85 + 1296 * q^86 - 912 * q^88 - 2604 * q^89 - 3399 * q^91 - 372 * q^92 + 4500 * q^94 - 7545 * q^95 + 8940 * q^97 - 4002 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{5}{9}\right)$

Coefficient data

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

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

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

$2$	0.347296	−	1.96962i	0.122788	−	0.696364i
$2$	0.347296	−	1.96962i	0.122788	−	0.696364i
$3$		0			0
$3$		0			0
$4$	−3.75877	−	1.36808i	−0.469846	−	0.171010i
$5$	−7.73816	+	6.49309i	−0.692122	+	0.580760i	−0.919520	−	0.393042i	$-0.871423\pi$
$5$	−7.73816	+	6.49309i	−0.692122	+	0.580760i	0.227398	+	0.973802i	$0.426978\pi$
$6$		0			0
$7$	7.54967	−	2.74785i	0.407644	−	0.148370i	−0.130056	−	0.991507i	$-0.541516\pi$
$7$	7.54967	−	2.74785i	0.407644	−	0.148370i	0.537700	+	0.843136i	$0.319293\pi$
$8$	−4.00000	+	6.92820i	−0.176777	+	0.306186i
$9$		0			0
$10$	10.1015	+	17.4962i	0.319436	+	0.553279i
$11$	−12.9632	−	10.8775i	−0.355324	−	0.298152i	0.447600	−	0.894234i	$-0.352279\pi$
$11$	−12.9632	−	10.8775i	−0.355324	−	0.298152i	−0.802924	+	0.596082i	$0.796723\pi$
$12$		0			0
$13$	14.9620	+	84.8538i	0.319209	+	1.81032i	0.547584	+	0.836751i	$0.315548\pi$
$13$	14.9620	+	84.8538i	0.319209	+	1.81032i	−0.228375	+	0.973573i	$0.573341\pi$
$14$	−2.79024	−	15.8243i	−0.0532660	−	0.302087i
$15$		0			0
$16$	12.2567	+	10.2846i	0.191511	+	0.160697i
$17$	53.3650	+	92.4308i	0.761347	+	1.31869i	0.942156	+	0.335174i	$0.108795\pi$
$17$	53.3650	+	92.4308i	0.761347	+	1.31869i	−0.180809	+	0.983518i	$0.557871\pi$
$18$		0			0
$19$	−17.8925	+	30.9907i	−0.216043	+	0.374197i	−0.953595	−	0.301093i	$-0.902648\pi$
$19$	−17.8925	+	30.9907i	−0.216043	+	0.374197i	0.737552	+	0.675291i	$0.235982\pi$
$20$	37.9690	−	13.8196i	0.424507	−	0.154508i
$21$		0			0
$22$	−25.9265	+	21.7549i	−0.251252	+	0.210826i
$23$	85.4423	+	31.0985i	0.774607	+	0.281934i	0.698922	−	0.715198i	$-0.253663\pi$
$23$	85.4423	+	31.0985i	0.774607	+	0.281934i	0.0756848	+	0.997132i	$0.475886\pi$
$24$		0			0
$25$	−3.98707	+	22.6118i	−0.0318966	+	0.180895i
$26$	172.326			1.29984
$27$		0			0
$28$	−32.1368			−0.216903
$29$	16.6639	−	94.5057i	0.106704	−	0.605147i	−0.883822	−	0.467823i	$-0.845039\pi$
$29$	16.6639	−	94.5057i	0.106704	−	0.605147i	0.990526	−	0.137325i	$-0.0438503\pi$
$30$		0			0
$31$	−191.030	−	69.5291i	−1.10677	−	0.402832i	−0.276963	−	0.960881i	$-0.589328\pi$
$31$	−191.030	−	69.5291i	−1.10677	−	0.402832i	−0.829808	+	0.558049i	$0.811550\pi$
$32$	24.5134	−	20.5692i	0.135419	−	0.113630i
$33$		0			0
$34$	200.587	−	73.0076i	1.01177	−	0.368256i
$35$	−40.5785	+	70.2840i	−0.195972	+	0.339433i
$36$		0			0
$37$	79.7878	+	138.197i	0.354515	+	0.614037i	0.987035	−	0.160507i	$-0.0513128\pi$
$37$	79.7878	+	138.197i	0.354515	+	0.614037i	−0.632520	+	0.774544i	$0.717979\pi$
$38$	54.8257	+	46.0043i	0.234050	+	0.196391i
$39$		0			0
$40$	−14.0328	−	79.5839i	−0.0554695	−	0.314583i
$41$	−43.2835	−	245.473i	−0.164872	−	0.935036i	−0.949196	−	0.314685i	$-0.898101\pi$
$41$	−43.2835	−	245.473i	−0.164872	−	0.935036i	0.784324	−	0.620351i	$-0.213010\pi$
$42$		0			0
$43$	229.519	+	192.589i	0.813984	+	0.683014i	0.951555	−	0.307478i	$-0.0994851\pi$
$43$	229.519	+	192.589i	0.813984	+	0.683014i	−0.137571	+	0.990492i	$0.543930\pi$
$44$	33.8446	+	58.6206i	0.115961	+	0.200850i
$45$		0			0
$46$	90.9258	−	157.488i	0.291441	−	0.504790i
$47$	−462.735	+	168.422i	−1.43610	+	0.522699i	−0.938674	−	0.344806i	$-0.887945\pi$
$47$	−462.735	+	168.422i	−1.43610	+	0.522699i	−0.497429	+	0.867504i	$0.665723\pi$
$48$		0			0
$49$	−213.306	+	178.985i	−0.621885	+	0.521823i
$50$	43.1519	+	15.7060i	0.122052	+	0.0444233i
$51$		0			0
$52$	59.8481	−	339.415i	0.159605	−	0.905162i
$53$	317.176			0.822029			0.411014	−	0.911629i	$-0.365175\pi$
$53$	317.176			0.822029			0.411014	+	0.911629i	$0.365175\pi$
$54$		0			0
$55$	170.940			0.419083
$56$	−11.1610	+	63.2970i	−0.0266330	+	0.151043i
$57$		0			0
$58$	−180.353	−	65.6430i	−0.408301	−	0.148609i
$59$	−127.954	+	107.366i	−0.282343	+	0.236914i	−0.772950	−	0.634467i	$-0.781219\pi$
$59$	−127.954	+	107.366i	−0.282343	+	0.236914i	0.490607	+	0.871381i	$0.336775\pi$
$60$		0			0
$61$	−107.083	+	38.9752i	−0.224764	+	0.0818076i	−0.451948	−	0.892044i	$-0.649271\pi$
$61$	−107.083	+	38.9752i	−0.224764	+	0.0818076i	0.227183	+	0.973852i	$0.427048\pi$
$62$	−203.289	+	352.108i	−0.416416	+	0.721253i
$63$		0			0
$64$	−32.0000	−	55.4256i	−0.0625000	−	0.108253i
$65$	−666.742	−	559.463i	−1.27229	−	1.06758i
$66$		0			0
$67$	−97.7000	−	554.084i	−0.178149	−	1.01033i	−0.934447	−	0.356103i	$-0.884105\pi$
$67$	−97.7000	−	554.084i	−0.178149	−	1.01033i	0.756298	−	0.654227i	$-0.227006\pi$
$68$	−74.1338	−	420.434i	−0.132207	−	0.749781i
$69$		0			0
$70$	124.340	+	104.333i	0.212306	+	0.178146i
$71$	−124.798	−	216.156i	−0.208602	−	0.361310i	0.742672	−	0.669655i	$-0.233558\pi$
$71$	−124.798	−	216.156i	−0.208602	−	0.361310i	−0.951274	+	0.308346i	$0.900225\pi$
$72$		0			0
$73$	−479.693	+	830.853i	−0.769094	+	1.33211i	0.168961	+	0.985623i	$0.445959\pi$
$73$	−479.693	+	830.853i	−0.769094	+	1.33211i	−0.938055	+	0.346487i	$0.887374\pi$
$74$	299.904	−	109.156i	0.471124	−	0.171475i
$75$		0			0
$76$	109.651	−	92.0085i	0.165498	−	0.138870i
$77$	−127.758	−	46.5001i	−0.189083	−	0.0688204i
$78$		0			0
$79$	222.634	−	1262.62i	0.317067	−	1.79818i	−0.243318	−	0.969947i	$-0.578236\pi$
$79$	222.634	−	1262.62i	0.317067	−	1.79818i	0.560386	−	0.828232i	$-0.310653\pi$
$80$	−161.623			−0.225875
$81$		0			0
$82$	−498.520			−0.671370
$83$	−109.634	+	621.765i	−0.144987	+	0.822259i	0.822391	+	0.568922i	$0.192639\pi$
$83$	−109.634	+	621.765i	−0.144987	+	0.822259i	−0.967378	+	0.253337i	$0.918472\pi$
$84$		0			0
$85$	−1013.11	−	368.741i	−1.29279	−	0.470537i
$86$	459.038	−	385.178i	0.575574	−	0.482964i
$87$		0			0
$88$	127.214	−	46.3022i	0.154103	−	0.0560890i
$89$	−427.862	+	741.078i	−0.509587	+	0.882631i	0.490351	+	0.871525i	$0.336869\pi$
$89$	−427.862	+	741.078i	−0.509587	+	0.882631i	−0.999938	+	0.0111059i	$0.996465\pi$
$90$		0			0
$91$	346.124	+	599.505i	0.398722	+	0.690606i
$92$	−278.613	−	233.784i	−0.315733	−	0.264931i
$93$		0			0
$94$	171.020	+	969.903i	0.187653	+	1.06423i
$95$	−62.7704	−	355.988i	−0.0677905	−	0.384459i
$96$		0			0
$97$	−241.282	−	202.460i	−0.252562	−	0.211925i	0.507713	−	0.861526i	$-0.330491\pi$
$97$	−241.282	−	202.460i	−0.252562	−	0.211925i	−0.760275	+	0.649602i	$0.774936\pi$
$98$	278.452	+	482.293i	0.287019	+	0.497132i
$99$		0			0
$100$	45.9213	−	79.5380i	0.0459213	−	0.0795380i
$101$	−1335.60	+	486.119i	−1.31581	+	0.478917i	−0.902115	−	0.431497i	$-0.857986\pi$
$101$	−1335.60	+	486.119i	−1.31581	+	0.478917i	−0.413699	+	0.910414i	$0.635763\pi$
$102$		0			0
$103$	941.870	−	790.323i	0.901022	−	0.756047i	−0.0693682	−	0.997591i	$-0.522098\pi$
$103$	941.870	−	790.323i	0.901022	−	0.756047i	0.970390	+	0.241544i	$0.0776539\pi$
$104$	−647.733	−	235.755i	−0.610725	−	0.222286i
$105$		0			0
$106$	110.154	−	624.715i	0.100935	−	0.572431i
$107$	1616.60			1.46059			0.730293	−	0.683134i	$-0.239383\pi$
$107$	1616.60			1.46059			0.730293	+	0.683134i	$0.239383\pi$
$108$		0			0
$109$	1710.94			1.50348			0.751738	−	0.659462i	$-0.229216\pi$
$109$	1710.94			1.50348			0.751738	+	0.659462i	$0.229216\pi$
$110$	59.3668	−	336.686i	0.0514582	−	0.291834i
$111$		0			0
$112$	120.795	+	43.9657i	0.101911	+	0.0370925i
$113$	1403.54	−	1177.71i	1.16844	−	0.980437i	0.168454	−	0.985710i	$-0.446123\pi$
$113$	1403.54	−	1177.71i	1.16844	−	0.980437i	0.999986	+	0.00527224i	$0.00167821\pi$
$114$		0			0
$115$	−863.092	+	314.140i	−0.699858	+	0.254728i
$116$	−191.927	+	332.428i	−0.153621	+	0.266079i
$117$		0			0
$118$	167.032	+	289.308i	0.130310	+	0.225703i
$119$	656.874	+	551.183i	0.506013	+	0.424595i
$120$		0			0
$121$	−181.399	−	1028.76i	−0.136288	−	0.772926i
$122$	39.5764	+	224.449i	0.0293695	+	0.166563i
$123$		0			0
$124$	622.915	+	522.688i	0.451124	+	0.378538i
$125$	−747.309	−	1294.38i	−0.534731	−	0.926181i
$126$		0			0
$127$	−219.777	+	380.666i	−0.153560	+	0.265973i	−0.932534	−	0.361083i	$-0.882407\pi$
$127$	−219.777	+	380.666i	−0.153560	+	0.265973i	0.778974	+	0.627056i	$0.215740\pi$
$128$	−120.281	+	43.7786i	−0.0830579	+	0.0302306i
$129$		0			0
$130$	−1333.48	+	1118.93i	−0.899648	+	0.754894i
$131$	2675.91	+	973.950i	1.78469	+	0.649576i	0.999542	+	0.0302734i	$0.00963779\pi$
$131$	2675.91	+	973.950i	1.78469	+	0.649576i	0.785153	+	0.619302i	$0.212584\pi$
$132$		0			0
$133$	−49.9244	+	283.135i	−0.0325488	+	0.184594i
$134$	−1125.26			−0.725433
$135$		0			0
$136$	−853.840			−0.538354
$137$	5.41827	−	30.7285i	0.00337893	−	0.0191629i	−0.983072	−	0.183221i	$-0.941347\pi$
$137$	5.41827	−	30.7285i	0.00337893	−	0.0191629i	0.986451	+	0.164059i	$0.0524586\pi$
$138$		0			0
$139$	1437.22	+	523.107i	0.877006	+	0.319204i	0.741001	−	0.671504i	$-0.234352\pi$
$139$	1437.22	+	523.107i	0.877006	+	0.319204i	0.136005	+	0.990708i	$0.456574\pi$
$140$	248.679	−	208.667i	0.150123	−	0.125968i
$141$		0			0
$142$	−469.086	+	170.733i	−0.277217	+	0.100899i
$143$	729.037	−	1262.73i	0.426330	−	0.738425i
$144$		0			0
$145$	484.686	+	839.501i	0.277593	+	0.480805i
$146$	1469.87	+	1233.36i	0.833198	+	0.699136i
$147$		0			0
$148$	−110.840	−	628.605i	−0.0615608	−	0.349129i
$149$	481.343	+	2729.83i	0.264652	+	1.50091i	0.770025	+	0.638014i	$0.220244\pi$
$149$	481.343	+	2729.83i	0.264652	+	1.50091i	−0.505373	+	0.862901i	$0.668645\pi$
$150$		0			0
$151$	1726.82	+	1448.97i	0.930640	+	0.780899i	0.975932	−	0.218074i	$-0.0699776\pi$
$151$	1726.82	+	1448.97i	0.930640	+	0.780899i	−0.0452925	+	0.998974i	$0.514422\pi$
$152$	−143.140	−	247.925i	−0.0763827	−	0.132299i
$153$		0			0
$154$	−135.957	+	235.485i	−0.0711411	+	0.123220i
$155$	1929.68	−	702.345i	0.999970	−	0.363959i
$156$		0			0
$157$	−681.727	+	572.037i	−0.346546	+	0.290787i	−0.799401	−	0.600797i	$-0.794850\pi$
$157$	−681.727	+	572.037i	−0.346546	+	0.290787i	0.452855	+	0.891584i	$0.350405\pi$
$158$	−2409.56	−	877.008i	−1.21326	−	0.441589i
$159$		0			0
$160$	−56.1312	+	318.336i	−0.0277347	+	0.157292i
$161$	730.515			0.357594
$162$		0			0
$163$	−645.194			−0.310034			−0.155017	−	0.987912i	$-0.549543\pi$
$163$	−645.194			−0.310034			−0.155017	+	0.987912i	$0.549543\pi$
$164$	−173.134	+	981.892i	−0.0824360	+	0.467518i
$165$		0			0
$166$	1186.56	+	431.873i	0.554789	+	0.201927i
$167$	−1207.04	+	1012.82i	−0.559301	+	0.469310i	−0.878076	−	0.478521i	$-0.841173\pi$
$167$	−1207.04	+	1012.82i	−0.559301	+	0.469310i	0.318775	+	0.947831i	$0.396729\pi$
$168$		0			0
$169$	−4911.80	+	1787.75i	−2.23569	+	0.813723i
$170$	−1078.13	+	1867.37i	−0.486404	+	0.842476i
$171$		0			0
$172$	−599.231	−	1037.90i	−0.265645	−	0.460111i
$173$	−819.070	−	687.281i	−0.359958	−	0.302041i	0.444816	−	0.895622i	$-0.353269\pi$
$173$	−819.070	−	687.281i	−0.359958	−	0.302041i	−0.804774	+	0.593581i	$0.797714\pi$
$174$		0			0
$175$	32.0329	+	181.668i	0.0138369	+	0.0784730i
$176$	−47.0165	−	266.644i	−0.0201364	−	0.114199i
$177$		0			0
$178$	1311.04	+	1100.10i	0.552062	+	0.463235i
$179$	−88.8281	−	153.855i	−0.0370912	−	0.0642438i	0.846884	−	0.531778i	$-0.178476\pi$
$179$	−88.8281	−	153.855i	−0.0370912	−	0.0642438i	−0.883975	+	0.467534i	$0.845143\pi$
$180$		0			0
$181$	1474.99	−	2554.76i	0.605718	−	1.04914i	−0.386219	−	0.922407i	$-0.626219\pi$
$181$	1474.99	−	2554.76i	0.605718	−	1.04914i	0.991938	−	0.126728i	$-0.0404475\pi$
$182$	1301.00	−	473.526i	0.529872	−	0.192857i
$183$		0			0
$184$	−557.226	+	467.568i	−0.223257	+	0.187335i
$185$	−1514.73	−	551.318i	−0.601975	−	0.219101i
$186$		0			0
$187$	313.629	−	1778.68i	0.122646	−	0.695561i
$188$	1969.73			0.764135
$189$		0			0
$190$	−722.960			−0.276048
$191$	121.192	−	687.315i	0.0459118	−	0.260379i	−0.953209	−	0.302314i	$-0.902241\pi$
$191$	121.192	−	687.315i	0.0459118	−	0.260379i	0.999120	+	0.0419347i	$0.0133522\pi$
$192$		0			0
$193$	2438.45	+	887.523i	0.909448	+	0.331012i	0.754032	−	0.656837i	$-0.228106\pi$
$193$	2438.45	+	887.523i	0.909448	+	0.331012i	0.155415	+	0.987849i	$0.450328\pi$
$194$	−482.565	+	404.920i	−0.178588	+	0.149853i
$195$		0			0
$196$	1046.64	−	380.945i	0.381427	−	0.138828i
$197$	707.674	−	1225.73i	0.255938	−	0.443297i	−0.709212	−	0.704995i	$-0.750949\pi$
$197$	707.674	−	1225.73i	0.255938	−	0.443297i	0.965150	+	0.261698i	$0.0842825\pi$
$198$		0			0
$199$	−1440.95	−	2495.80i	−0.513299	−	0.889060i	−0.999881	−	0.0154250i	$-0.995090\pi$
$199$	−1440.95	−	2495.80i	−0.513299	−	0.889060i	0.486582	−	0.873635i	$-0.338243\pi$
$200$	−140.711	−	118.071i	−0.0497489	−	0.0417442i
$201$		0			0
$202$	493.618	+	2799.45i	0.171935	+	0.975091i
$203$	−133.881	−	759.277i	−0.0462887	−	0.262516i
$204$		0			0
$205$	1928.81	+	1618.47i	0.657142	+	0.551408i
$206$	−1229.52	−	2129.60i	−0.415850	−	0.720273i
$207$		0			0
$208$	−689.303	+	1193.91i	−0.229781	+	0.397993i
$209$	569.044	−	207.115i	0.188333	−	0.0685476i
$210$		0			0
$211$	2849.13	−	2390.70i	0.929583	−	0.780013i	−0.0461594	−	0.998934i	$-0.514698\pi$
$211$	2849.13	−	2390.70i	0.929583	−	0.780013i	0.975743	+	0.218921i	$0.0702538\pi$
$212$	−1192.19	−	433.923i	−0.386227	−	0.140575i
$213$		0			0
$214$	561.440	−	3184.08i	0.179342	−	1.01710i
$215$	−3026.55			−0.960043
$216$		0			0
$217$	−1633.27			−0.510937
$218$	594.205	−	3369.90i	0.184608	−	1.04697i
$219$		0			0
$220$	−642.524	−	233.860i	−0.196904	−	0.0716673i
$221$	−7044.66	+	5911.17i	−2.14423	+	1.79922i
$222$		0			0
$223$	−2812.80	+	1023.78i	−0.844661	+	0.307431i	−0.727861	−	0.685724i	$-0.759486\pi$
$223$	−2812.80	+	1023.78i	−0.844661	+	0.307431i	−0.116799	+	0.993156i	$0.537263\pi$
$224$	128.547	−	222.650i	0.0383433	−	0.0664126i
$225$		0			0
$226$	−1832.19	−	3173.44i	−0.539271	−	0.934045i
$227$	539.330	+	452.552i	0.157694	+	0.132321i	0.718221	−	0.695815i	$-0.244957\pi$
$227$	539.330	+	452.552i	0.157694	+	0.132321i	−0.560526	+	0.828137i	$0.689401\pi$
$228$		0			0
$229$	−290.146	−	1645.50i	−0.0837267	−	0.474838i	−0.997624	−	0.0688924i	$-0.978053\pi$
$229$	−290.146	−	1645.50i	−0.0837267	−	0.474838i	0.913897	−	0.405945i	$-0.133058\pi$
$230$	318.986	+	1809.06i	0.0914491	+	0.518634i
$231$		0			0
$232$	588.099	+	493.474i	0.166425	+	0.139647i
$233$	−341.714	−	591.865i	−0.0960790	−	0.166414i	0.813979	−	0.580894i	$-0.197297\pi$
$233$	−341.714	−	591.865i	−0.0960790	−	0.166414i	−0.910058	+	0.414480i	$0.863963\pi$
$234$		0			0
$235$	2487.14	−	4307.86i	0.690397	−	1.19580i
$236$	627.836	−	228.514i	0.173172	−	0.0630295i
$237$		0			0
$238$	1313.75	−	1102.37i	0.357805	−	0.300234i
$239$	3057.22	+	1112.74i	0.827428	+	0.301159i	0.720803	−	0.693140i	$-0.243773\pi$
$239$	3057.22	+	1112.74i	0.827428	+	0.301159i	0.106625	+	0.994299i	$0.465995\pi$
$240$		0			0
$241$	417.257	−	2366.38i	0.111526	−	0.632498i	−0.876885	−	0.480700i	$-0.840383\pi$
$241$	417.257	−	2366.38i	0.111526	−	0.632498i	0.988412	−	0.151798i	$-0.0485063\pi$
$242$	−2089.27			−0.554973
$243$		0			0
$244$	455.823			0.119595
$245$	488.432	−	2770.04i	0.127366	−	0.722331i
$246$		0			0
$247$	−2897.39	−	1054.56i	−0.746381	−	0.271661i
$248$	1245.83	−	1045.38i	0.318993	−	0.267667i
$249$		0			0
$250$	−2808.96	+	1022.38i	−0.710617	+	0.258644i
$251$	962.291	−	1666.74i	0.241989	−	0.419138i	−0.719292	−	0.694708i	$-0.755533\pi$
$251$	962.291	−	1666.74i	0.241989	−	0.419138i	0.961281	+	0.275571i	$0.0888668\pi$
$252$		0			0
$253$	−769.338	−	1332.53i	−0.191177	−	0.331129i
$254$	673.437	+	565.081i	0.166359	+	0.139592i
$255$		0			0
$256$	44.4539	+	252.111i	0.0108530	+	0.0615505i
$257$	−462.872	−	2625.08i	−0.112347	−	0.637152i	−0.988030	−	0.154264i	$-0.950699\pi$
$257$	−462.872	−	2625.08i	−0.112347	−	0.637152i	0.875683	−	0.482887i	$-0.160412\pi$
$258$		0			0
$259$	982.115	+	824.093i	0.235620	+	0.197709i
$260$	1740.74	+	3015.05i	0.415216	+	0.719175i
$261$		0			0
$262$	2847.64	−	4932.26i	0.671480	−	1.16304i
$263$	121.276	−	44.1408i	0.0284342	−	0.0103492i	−0.327764	−	0.944760i	$-0.606295\pi$
$263$	121.276	−	44.1408i	0.0284342	−	0.0103492i	0.356198	+	0.934410i	$0.384073\pi$
$264$		0			0
$265$	−2454.36	+	2059.45i	−0.568944	+	0.477401i
$266$	540.329	+	196.664i	0.124548	+	0.0453317i
$267$		0			0
$268$	−390.800	+	2216.34i	−0.0890743	+	0.505165i
$269$	−2634.62			−0.597157			−0.298579	−	0.954385i	$-0.596513\pi$
$269$	−2634.62			−0.597157			−0.298579	+	0.954385i	$0.596513\pi$
$270$		0			0
$271$	353.331			0.0792006			0.0396003	−	0.999216i	$-0.487392\pi$
$271$	353.331			0.0792006			0.0396003	+	0.999216i	$0.487392\pi$
$272$	−296.535	+	1681.74i	−0.0661033	+	0.374890i
$273$		0			0
$274$	−58.6417	−	21.3438i	−0.0129295	−	0.00470594i
$275$	297.645	−	249.753i	0.0652678	−	0.0547662i
$276$		0			0
$277$	−5858.92	+	2132.47i	−1.27086	+	0.462555i	−0.887399	−	0.461002i	$-0.847490\pi$
$277$	−5858.92	+	2132.47i	−1.27086	+	0.462555i	−0.383461	+	0.923557i	$0.625268\pi$
$278$	1529.46	−	2649.11i	0.329968	−	0.571521i
$279$		0			0
$280$	−324.628	−	562.272i	−0.0692865	−	0.120008i
$281$	−1279.24	−	1073.41i	−0.271578	−	0.227881i	0.496820	−	0.867854i	$-0.334501\pi$
$281$	−1279.24	−	1073.41i	−0.271578	−	0.227881i	−0.768397	+	0.639973i	$0.778945\pi$
$282$		0			0
$283$	1174.22	+	6659.35i	0.246644	+	1.39879i	0.816643	+	0.577144i	$0.195833\pi$
$283$	1174.22	+	6659.35i	0.246644	+	1.39879i	−0.569998	+	0.821646i	$0.693056\pi$
$284$	173.367	+	983.213i	0.0362234	+	0.205433i
$285$		0			0
$286$	−2233.90	−	1874.46i	−0.461865	−	0.387550i
$287$	−1001.30	−	1734.30i	−0.205940	−	0.356699i
$288$		0			0
$289$	−3239.14	+	5610.36i	−0.659300	+	1.14194i
$290$	1821.82	−	663.090i	0.368901	−	0.134269i
$291$		0			0
$292$	2939.73	−	2466.73i	0.589160	−	0.494364i
$293$	1465.10	+	533.252i	0.292122	+	0.106324i	0.483925	−	0.875110i	$-0.339211\pi$
$293$	1465.10	+	533.252i	0.292122	+	0.106324i	−0.191802	+	0.981434i	$0.561433\pi$
$294$		0			0
$295$	292.991	−	1661.64i	0.0578258	−	0.327946i
$296$	−1276.61			−0.250680
$297$		0			0
$298$	5543.88			1.07768
$299$	−1360.43	+	7715.40i	−0.263130	+	1.49229i
$300$		0			0
$301$	2262.00	+	823.300i	0.433154	+	0.157655i
$302$	3453.64	−	2897.95i	0.658062	−	0.552179i
$303$		0			0
$304$	−538.030	+	195.827i	−0.101507	+	0.0369455i
$305$	575.560	−	996.899i	0.108054	−	0.187155i
$306$		0			0
$307$	2381.92	+	4125.61i	0.442813	+	0.766975i	0.997897	−	0.0648196i	$-0.0206472\pi$
$307$	2381.92	+	4125.61i	0.442813	+	0.766975i	−0.555084	+	0.831794i	$0.687314\pi$
$308$	416.597	+	349.566i	0.0770708	+	0.0646701i
$309$		0			0
$310$	−713.179	−	4044.64i	−0.130664	−	0.741033i
$311$	−573.411	−	3251.98i	−0.104550	−	0.592935i	−0.991399	−	0.130875i	$-0.958221\pi$
$311$	−573.411	−	3251.98i	−0.104550	−	0.592935i	0.886849	−	0.462060i	$-0.152890\pi$
$312$		0			0
$313$	5369.70	+	4505.71i	0.969691	+	0.813667i	0.982502	−	0.186251i	$-0.0596337\pi$
$313$	5369.70	+	4505.71i	0.969691	+	0.813667i	−0.0128115	+	0.999918i	$0.504078\pi$
$314$	889.932	+	1541.41i	0.159942	+	0.277028i
$315$		0			0
$316$	−2564.20	+	4441.33i	−0.456480	+	0.790646i
$317$	−1621.57	+	590.205i	−0.287308	+	0.104572i	−0.481654	−	0.876361i	$-0.659964\pi$
$317$	−1621.57	+	590.205i	−0.287308	+	0.104572i	0.194346	+	0.980933i	$0.437742\pi$
$318$		0			0
$319$	−1244.00	+	1043.84i	−0.218341	+	0.183209i
$320$	607.505	+	221.114i	0.106127	+	0.0386270i
$321$		0			0
$322$	253.705	−	1438.83i	0.0439082	−	0.249016i
$323$	−3819.33			−0.657935
$324$		0			0
$325$	−1978.35			−0.337660
$326$	−224.073	+	1270.78i	−0.0380683	+	0.215896i
$327$		0			0
$328$	1873.82	+	682.015i	0.315441	+	0.114811i
$329$	−3030.70	+	2543.06i	−0.507866	+	0.426150i
$330$		0			0
$331$	4203.34	−	1529.89i	0.697995	−	0.254050i	0.0314406	−	0.999506i	$-0.489990\pi$
$331$	4203.34	−	1529.89i	0.697995	−	0.254050i	0.666555	+	0.745456i	$0.267768\pi$
$332$	1262.71	−	2187.08i	0.208736	−	0.361541i
$333$		0			0
$334$	1575.68	+	2729.15i	0.258135	+	0.447103i
$335$	4353.74	+	3653.22i	0.710060	+	0.595811i
$336$		0			0
$337$	−698.754	−	3962.83i	−0.112948	−	0.640561i	−0.987746	−	0.156072i	$-0.950117\pi$
$337$	−698.754	−	3962.83i	−0.112948	−	0.640561i	0.874797	−	0.484489i	$-0.160994\pi$
$338$	1815.33	+	10295.2i	0.292133	+	1.65677i
$339$		0			0
$340$	3303.57	+	2772.03i	0.526946	+	0.442160i
$341$	1720.06	+	2979.24i	0.273157	+	0.473122i
$342$		0			0
$343$	−2496.43	+	4323.94i	−0.392987	+	0.680674i
$344$	−2252.37	+	819.797i	−0.353023	+	0.128490i
$345$		0			0
$346$	−1638.14	+	1374.56i	−0.254529	+	0.213575i
$347$	822.792	+	299.472i	0.127291	+	0.0463300i	0.404880	−	0.914370i	$-0.367313\pi$
$347$	822.792	+	299.472i	0.127291	+	0.0463300i	−0.277589	+	0.960700i	$0.589536\pi$
$348$		0			0
$349$	−1013.18	+	5746.05i	−0.155400	+	0.881315i	0.803020	+	0.595952i	$0.203225\pi$
$349$	−1013.18	+	5746.05i	−0.155400	+	0.881315i	−0.958420	+	0.285363i	$0.907886\pi$
$350$	368.940			0.0563448
$351$		0			0
$352$	−541.514			−0.0819966
$353$	684.653	−	3882.86i	0.103231	−	0.585450i	−0.888682	−	0.458525i	$-0.848378\pi$
$353$	684.653	−	3882.86i	0.103231	−	0.585450i	0.991912	−	0.126925i	$-0.0405108\pi$
$354$		0			0
$355$	2369.22	+	862.327i	0.354212	+	0.128923i
$356$	2622.09	−	2200.19i	0.390366	−	0.327556i
$357$		0			0
$358$	−333.884	+	121.524i	−0.0492915	+	0.0179406i
$359$	−2192.89	+	3798.20i	−0.322385	+	0.558388i	−0.980980	−	0.194110i	$-0.937818\pi$
$359$	−2192.89	+	3798.20i	−0.322385	+	0.558388i	0.658594	+	0.752498i	$0.271151\pi$
$360$		0			0
$361$	2789.22	+	4831.07i	0.406651	+	0.704340i
$362$	−4519.63	−	3792.42i	−0.656205	−	0.550622i
$363$		0			0
$364$	−480.831	−	2726.93i	−0.0692373	−	0.392664i
$365$	−1682.86	−	9543.97i	−0.241328	−	1.36864i
$366$		0			0
$367$	−4373.71	−	3669.98i	−0.622086	−	0.521992i	0.276372	−	0.961051i	$-0.410868\pi$
$367$	−4373.71	−	3669.98i	−0.622086	−	0.521992i	−0.898459	+	0.439058i	$0.855312\pi$
$368$	727.406	+	1259.90i	0.103040	+	0.178470i
$369$		0			0
$370$	−1611.95	+	2791.97i	−0.226489	+	0.392291i
$371$	2394.58	−	871.554i	0.335095	−	0.121965i
$372$		0			0
$373$	3439.72	−	2886.27i	0.477485	−	0.400657i	−0.372031	−	0.928220i	$-0.621339\pi$
$373$	3439.72	−	2886.27i	0.477485	−	0.400657i	0.849516	+	0.527563i	$0.176894\pi$
$374$	−3394.39	−	1235.46i	−0.469304	−	0.170813i
$375$		0			0
$376$	684.080	−	3879.61i	0.0938264	−	0.532116i
$377$	8268.50			1.12957
$378$		0			0
$379$	−4441.73			−0.601996			−0.300998	−	0.953625i	$-0.597320\pi$
$379$	−4441.73			−0.601996			−0.300998	+	0.953625i	$0.597320\pi$
$380$	−251.081	+	1423.95i	−0.0338953	+	0.192230i
$381$		0			0
$382$	−1311.66	−	477.404i	−0.175681	−	0.0639427i
$383$	9552.53	−	8015.52i	1.27444	−	1.06938i	0.280458	−	0.959866i	$-0.409514\pi$
$383$	9552.53	−	8015.52i	1.27444	−	1.06938i	0.993985	−	0.109518i	$-0.0349307\pi$
$384$		0			0
$385$	1290.54	−	469.718i	0.170836	−	0.0621794i
$386$	2594.94	−	4494.57i	0.342174	−	0.592663i
$387$		0			0
$388$	629.943	+	1091.09i	0.0824240	+	0.142763i
$389$	3004.66	+	2521.21i	0.391625	+	0.328612i	0.817246	−	0.576289i	$-0.195500\pi$
$389$	3004.66	+	2521.21i	0.391625	+	0.328612i	−0.425621	+	0.904902i	$0.639944\pi$
$390$		0			0
$391$	1685.17	+	9557.07i	0.217961	+	1.23612i
$392$	−386.821	−	2193.77i	−0.0498404	−	0.282659i
$393$		0			0
$394$	−2168.44	−	1819.54i	−0.277270	−	0.232657i
$395$	6475.54	+	11216.0i	0.824860	+	1.42870i
$396$		0			0
$397$	2731.23	−	4730.62i	0.345280	−	0.598043i	−0.640124	−	0.768271i	$-0.721117\pi$
$397$	2731.23	−	4730.62i	0.345280	−	0.598043i	0.985405	+	0.170228i	$0.0544505\pi$
$398$	−5416.21	+	1971.34i	−0.682136	+	0.248277i
$399$		0			0
$400$	−281.422	+	236.141i	−0.0351778	+	0.0295176i
$401$	7386.85	+	2688.59i	0.919905	+	0.334818i	0.758201	−	0.652021i	$-0.226079\pi$
$401$	7386.85	+	2688.59i	0.919905	+	0.334818i	0.161704	+	0.986839i	$0.448301\pi$
$402$		0			0
$403$	3041.62	−	17249.9i	0.375965	−	2.13220i
$404$	5685.26			0.700130
$405$		0			0
$406$	−1541.98			−0.188491
$407$	468.918	−	2659.36i	0.0571091	−	0.323882i
$408$		0			0
$409$	−15319.3	−	5575.78i	−1.85206	−	0.674094i	−0.984141	−	0.177387i	$-0.943236\pi$
$409$	−15319.3	−	5575.78i	−1.85206	−	0.674094i	−0.867918	−	0.496708i	$-0.834542\pi$
$410$	3857.63	−	3236.93i	0.464670	−	0.389904i
$411$		0			0
$412$	−4621.50	+	1682.09i	−0.552633	+	0.201142i
$413$	−670.984	+	1162.18i	−0.0799443	+	0.138468i
$414$		0			0
$415$	−3188.81	−	5523.18i	−0.377187	−	0.653306i
$416$	2112.15	+	1772.30i	0.248934	+	0.208880i
$417$		0			0
$418$	−210.310	−	1192.73i	−0.0246091	−	0.139565i
$419$	−266.207	−	1509.74i	−0.0310383	−	0.176027i	0.965348	−	0.260967i	$-0.0840413\pi$
$419$	−266.207	−	1509.74i	−0.0310383	−	0.176027i	−0.996386	+	0.0849397i	$0.972930\pi$
$420$		0			0
$421$	1201.89	+	1008.50i	0.139136	+	0.116749i	0.709700	−	0.704504i	$-0.248831\pi$
$421$	1201.89	+	1008.50i	0.139136	+	0.116749i	−0.570563	+	0.821254i	$0.693275\pi$
$422$	−3719.27	−	6441.97i	−0.429032	−	0.743105i
$423$		0			0
$424$	−1268.71	+	2197.46i	−0.145316	+	0.251694i
$425$	−2302.80	+	838.151i	−0.262829	+	0.0956618i
$426$		0			0
$427$	−701.346	+	588.499i	−0.0794860	+	0.0666967i
$428$	−6076.44	−	2211.64i	−0.686251	−	0.249775i
$429$		0			0
$430$	−1051.11	+	5961.15i	−0.117882	+	0.668540i
$431$	−11135.0			−1.24444			−0.622218	−	0.782844i	$-0.713768\pi$
$431$	−11135.0			−1.24444			−0.622218	+	0.782844i	$0.713768\pi$
$432$		0			0
$433$	9953.45			1.10469			0.552347	−	0.833615i	$-0.313732\pi$
$433$	9953.45			1.10469			0.552347	+	0.833615i	$0.313732\pi$
$434$	−567.227	+	3216.90i	−0.0627368	+	0.355798i
$435$		0			0
$436$	−6431.05	−	2340.71i	−0.706402	−	0.257109i
$437$	−2492.54	+	2091.49i	−0.272847	+	0.228946i
$438$		0			0
$439$	16220.6	−	5903.80i	1.76347	−	0.641852i	0.763482	−	0.645829i	$-0.223488\pi$
$439$	16220.6	−	5903.80i	1.76347	−	0.641852i	0.999992	+	0.00397686i	$0.00126588\pi$
$440$	−683.760	+	1184.31i	−0.0740840	+	0.128317i
$441$		0			0
$442$	9196.15	+	15928.2i	0.989630	+	1.71409i
$443$	−8781.69	−	7368.72i	−0.941830	−	0.790290i	0.0360725	−	0.999349i	$-0.488515\pi$
$443$	−8781.69	−	7368.72i	−0.941830	−	0.790290i	−0.977903	+	0.209060i	$0.932960\pi$
$444$		0			0
$445$	−1501.02	−	8512.73i	−0.159900	−	0.906836i
$446$	1039.57	+	5895.70i	0.110370	+	0.625940i
$447$		0			0
$448$	−393.891	−	330.514i	−0.0415393	−	0.0348556i
$449$	4666.36	+	8082.38i	0.490466	+	0.849512i	0.999940	−	0.0109742i	$-0.00349326\pi$
$449$	4666.36	+	8082.38i	0.490466	+	0.849512i	−0.509474	+	0.860486i	$0.670160\pi$
$450$		0			0
$451$	−2109.03	+	3652.94i	−0.220200	+	0.381398i
$452$	−6886.77	+	2506.58i	−0.716652	+	0.260840i
$453$		0			0
$454$	1078.66	−	905.104i	0.111507	−	0.0935653i
$455$	−6571.00	−	2391.65i	−0.677040	−	0.246422i
$456$		0			0
$457$	874.462	−	4959.32i	0.0895090	−	0.507631i	−0.906783	−	0.421597i	$-0.861470\pi$
$457$	874.462	−	4959.32i	0.0895090	−	0.507631i	0.996292	−	0.0860336i	$-0.0274192\pi$
$458$	−3341.77			−0.340941
$459$		0			0
$460$	3673.93			0.372387
$461$	1063.44	−	6031.05i	0.107439	−	0.609314i	−0.882780	−	0.469787i	$-0.844331\pi$
$461$	1063.44	−	6031.05i	0.107439	−	0.609314i	0.990218	−	0.139527i	$-0.0445582\pi$
$462$		0			0
$463$	1945.91	+	708.252i	0.195322	+	0.0710913i	0.437829	−	0.899058i	$-0.355748\pi$
$463$	1945.91	+	708.252i	0.195322	+	0.0710913i	−0.242507	+	0.970150i	$0.577970\pi$
$464$	1176.20	−	986.948i	0.117680	−	0.0987455i
$465$		0			0
$466$	−1284.42	+	467.492i	−0.127682	+	0.0464724i
$467$	−4163.31	+	7211.07i	−0.412538	+	0.714536i	−0.995167	−	0.0982020i	$-0.968691\pi$
$467$	−4163.31	+	7211.07i	−0.412538	+	0.714536i	0.582629	+	0.812738i	$0.302024\pi$
$468$		0			0
$469$	−2260.15	−	3914.69i	−0.222524	−	0.385423i
$470$	−7621.04	−	6394.82i	−0.747942	−	0.627598i
$471$		0			0
$472$	−232.039	−	1315.96i	−0.0226281	−	0.128330i
$473$	−880.429	−	4993.16i	−0.0855860	−	0.485382i
$474$		0			0
$475$	−629.417	−	528.144i	−0.0607992	−	0.0510166i
$476$	−1714.98	−	2970.43i	−0.165138	−	0.286028i
$477$		0			0
$478$	3253.43	−	5635.10i	0.311315	−	0.539213i
$479$	−12650.7	+	4604.47i	−1.20673	+	0.439214i	−0.865569	−	0.500790i	$-0.833043\pi$
$479$	−12650.7	+	4604.47i	−1.20673	+	0.439214i	−0.341163	+	0.940004i	$0.610821\pi$
$480$		0			0
$481$	−10532.7	+	8838.00i	−0.998442	+	0.837792i
$482$	−4515.95	−	1643.67i	−0.426755	−	0.155326i
$483$		0			0
$484$	−725.596	+	4115.06i	−0.0681439	+	0.386463i
$485$	3181.67			0.297881
$486$		0			0
$487$	−9779.35			−0.909948			−0.454974	−	0.890505i	$-0.650351\pi$
$487$	−9779.35			−0.909948			−0.454974	+	0.890505i	$0.650351\pi$
$488$	158.306	−	897.797i	0.0146848	−	0.0832815i
$489$		0			0
$490$	−5286.27	−	1924.05i	−0.487366	−	0.177387i
$491$	3955.35	−	3318.93i	0.363549	−	0.305054i	−0.442655	−	0.896692i	$-0.645963\pi$
$491$	3955.35	−	3318.93i	0.363549	−	0.305054i	0.806203	+	0.591639i	$0.201519\pi$
$492$		0			0
$493$	9624.51	−	3503.04i	0.879242	−	0.320018i
$494$	−3083.33	+	5340.49i	−0.280821	+	0.486397i
$495$		0			0
$496$	−1626.32	−	2816.86i	−0.147225	−	0.255002i
$497$	−1536.15	−	1288.98i	−0.138643	−	0.116335i
$498$		0			0
$499$	−606.796	−	3441.31i	−0.0544367	−	0.308726i	0.945416	−	0.325865i	$-0.105655\pi$
$499$	−606.796	−	3441.31i	−0.0544367	−	0.308726i	−0.999853	+	0.0171388i	$0.994544\pi$
$500$	1038.15	+	5887.64i	0.0928550	+	0.526607i
$501$		0			0
$502$	−2948.63	−	2474.20i	−0.262159	−	0.219978i
$503$	−2986.37	−	5172.54i	−0.264723	−	0.458513i	0.702768	−	0.711419i	$-0.251947\pi$
$503$	−2986.37	−	5172.54i	−0.264723	−	0.458513i	−0.967491	+	0.252906i	$0.918614\pi$
$504$		0			0
$505$	7178.68	−	12433.8i	0.632568	−	1.09564i
$506$	−2891.76	+	1052.52i	−0.254060	+	0.0924704i
$507$		0			0
$508$	1346.87	−	1130.16i	0.117634	−	0.0987063i
$509$	−5356.69	−	1949.67i	−0.466465	−	0.169780i	0.0980851	−	0.995178i	$-0.468728\pi$
$509$	−5356.69	−	1949.67i	−0.466465	−	0.169780i	−0.564551	+	0.825398i	$0.690950\pi$
$510$		0			0
$511$	−1338.46	+	7590.79i	−0.115871	+	0.657137i
$512$	512.000			0.0441942
$513$		0			0
$514$	−5331.15			−0.457484
$515$	−2156.71	+	12231.3i	−0.184536	+	1.04655i
$516$		0			0
$517$	7830.55	+	2850.09i	0.666126	+	0.242450i
$518$	1964.23	−	1648.19i	0.166609	−	0.139801i
$519$		0			0
$520$	6543.04	−	2381.47i	0.551791	−	0.200835i
$521$	3093.89	−	5358.77i	0.260165	−	0.450618i	−0.706121	−	0.708091i	$-0.749557\pi$
$521$	3093.89	−	5358.77i	0.260165	−	0.450618i	0.966285	+	0.257473i	$0.0828898\pi$
$522$		0			0
$523$	−5817.56	−	10076.3i	−0.486394	−	0.842459i	0.513484	−	0.858099i	$-0.328355\pi$
$523$	−5817.56	−	10076.3i	−0.486394	−	0.842459i	−0.999878	+	0.0156401i	$0.995021\pi$
$524$	−8725.67	−	7321.71i	−0.727448	−	0.610401i
$525$		0			0
$526$	−44.8218	−	254.197i	−0.00371544	−	0.0210713i
$527$	−3767.66	−	21367.4i	−0.311426	−	1.76619i
$528$		0			0
$529$	−2987.19	−	2506.55i	−0.245516	−	0.206012i
$530$	3203.94	+	5549.39i	0.262586	+	0.454812i
$531$		0			0
$532$	575.006	−	995.940i	0.0468603	−	0.0811644i
$533$	20181.7	−	7345.55i	1.64009	−	0.596944i
$534$		0			0
$535$	−12509.5	+	10496.7i	−1.01090	+	0.848250i
$536$	4229.61	+	1539.45i	0.340842	+	0.124056i
$537$		0			0
$538$	−914.992	+	5189.18i	−0.0733236	+	0.415839i
$539$	4712.05			0.376554
$540$		0			0
$541$	10416.3			0.827783			0.413892	−	0.910326i	$-0.364169\pi$
$541$	10416.3			0.827783			0.413892	+	0.910326i	$0.364169\pi$
$542$	122.711	−	695.927i	0.00972487	−	0.0551525i
$543$		0			0
$544$	3209.39	+	1168.12i	0.252944	+	0.0920639i
$545$	−13239.6	+	11109.3i	−1.04059	+	0.873157i
$546$		0			0
$547$	5116.89	−	1862.40i	0.399968	−	0.145576i	−0.134201	−	0.990954i	$-0.542847\pi$
$547$	5116.89	−	1862.40i	0.399968	−	0.145576i	0.534169	+	0.845378i	$0.320625\pi$
$548$	−62.4052	+	108.089i	−0.00486463	+	0.00842578i
$549$		0			0
$550$	−388.547	−	672.984i	−0.0301231	−	0.0521748i
$551$	2630.64	+	2207.37i	0.203392	+	0.170666i
$552$		0			0
$553$	−1788.69	−	10144.1i	−0.137546	−	0.780059i
$554$	2165.37	+	12280.4i	0.166061	+	0.941778i
$555$		0			0
$556$	−4686.54	−	3932.48i	−0.357471	−	0.299954i
$557$	7802.70	+	13514.7i	0.593557	+	1.02807i	0.993749	+	0.111639i	$0.0356101\pi$
$557$	7802.70	+	13514.7i	0.593557	+	1.02807i	−0.400192	+	0.916431i	$0.631057\pi$
$558$		0			0
$559$	−12907.9	+	22357.1i	−0.976645	+	1.69160i
$560$	−1220.20	+	444.117i	−0.0920767	+	0.0335132i
$561$		0			0
$562$	−2558.49	+	2146.83i	−0.192034	+	0.161136i
$563$	13679.6	+	4978.95i	1.02402	+	0.372714i	0.798802	−	0.601594i	$-0.205468\pi$
$563$	13679.6	+	4978.95i	1.02402	+	0.372714i	0.225220	+	0.974308i	$0.427690\pi$
$564$		0			0
$565$	−3213.84	+	18226.6i	−0.239305	+	1.35716i
$566$	13524.2			1.00435
$567$		0			0
$568$	1996.76			0.147504
$569$	1397.27	−	7924.31i	0.102947	−	0.583839i	−0.889074	−	0.457763i	$-0.848651\pi$
$569$	1397.27	−	7924.31i	0.102947	−	0.583839i	0.992021	−	0.126076i	$-0.0402382\pi$
$570$		0			0
$571$	2460.00	+	895.366i	0.180294	+	0.0656216i	0.430590	−	0.902548i	$-0.358306\pi$
$571$	2460.00	+	895.366i	0.180294	+	0.0656216i	−0.250296	+	0.968169i	$0.580528\pi$
$572$	−4467.80	+	3748.93i	−0.326588	+	0.274040i
$573$		0			0
$574$	−3763.66	+	1369.86i	−0.273680	+	0.0996112i
$575$	−1043.86	+	1808.01i	−0.0757076	+	0.131129i
$576$		0			0
$577$	3387.32	+	5867.01i	0.244395	+	0.423305i	0.961961	−	0.273186i	$-0.0880773\pi$
$577$	3387.32	+	5867.01i	0.244395	+	0.423305i	−0.717566	+	0.696490i	$0.754744\pi$
$578$	9925.30	+	8328.32i	0.714253	+	0.599329i
$579$		0			0
$580$	−673.319	−	3818.58i	−0.0482035	−	0.273376i
$581$	880.819	+	4995.37i	0.0628959	+	0.356701i
$582$		0			0
$583$	−4111.64	−	3450.07i	−0.292087	−	0.245090i
$584$	−3837.55	−	6646.83i	−0.271916	−	0.470972i
$585$		0			0
$586$	1559.12	−	2700.48i	0.109909	−	0.190368i
$587$	25130.2	−	9146.65i	1.76701	−	0.643139i	0.767011	−	0.641633i	$-0.221743\pi$
$587$	25130.2	−	9146.65i	1.76701	−	0.643139i	0.999999	−	0.00150576i	$-0.000479297\pi$
$588$		0			0
$589$	5572.74	−	4676.09i	0.389849	−	0.327122i
$590$	−3171.03	−	1154.16i	−0.221270	−	0.0805356i
$591$		0			0
$592$	−443.360	+	2514.42i	−0.0307804	+	0.174564i
$593$	19887.9			1.37723			0.688616	−	0.725126i	$-0.258218\pi$
$593$	19887.9			1.37723			0.688616	+	0.725126i	$0.258218\pi$
$594$		0			0
$595$	−8661.88			−0.596811
$596$	1925.37	−	10919.3i	0.132326	−	0.750457i
$597$		0			0
$598$	14723.9	+	5359.06i	1.00686	+	0.366469i
$599$	−14310.1	+	12007.6i	−0.976120	+	0.819062i	−0.983499	−	0.180911i	$-0.942095\pi$
$599$	−14310.1	+	12007.6i	−0.976120	+	0.819062i	0.00737955	+	0.999973i	$0.497651\pi$
$600$		0			0
$601$	24532.0	−	8928.91i	1.66503	−	0.606020i	0.673885	−	0.738837i	$-0.264625\pi$
$601$	24532.0	−	8928.91i	1.66503	−	0.606020i	0.991141	+	0.132817i	$0.0424023\pi$
$602$	2407.17	−	4169.34i	0.162972	−	0.282275i
$603$		0			0
$604$	−4508.41	−	7808.79i	−0.303716	−	0.526051i
$605$	8083.56	+	6782.91i	0.543212	+	0.455809i
$606$		0			0
$607$	4001.71	+	22694.8i	0.267585	+	1.51755i	0.761571	+	0.648081i	$0.224428\pi$
$607$	4001.71	+	22694.8i	0.267585	+	1.51755i	−0.493986	+	0.869470i	$0.664461\pi$
$608$	198.848	+	1127.72i	0.0132637	+	0.0752223i
$609$		0			0
$610$	−1763.62	−	1479.85i	−0.117060	−	0.0982253i
$611$	−21214.7	−	36744.9i	−1.40467	−	2.43296i
$612$		0			0
$613$	1126.75	−	1951.59i	0.0742397	−	0.128587i	−0.826516	−	0.562914i	$-0.809680\pi$
$613$	1126.75	−	1951.59i	0.0742397	−	0.128587i	0.900755	+	0.434327i	$0.143014\pi$
$614$	8953.11	−	3258.66i	0.588466	−	0.214184i
$615$		0			0
$616$	833.193	−	699.132i	0.0544973	−	0.0457286i
$617$	10993.0	+	4001.11i	0.717278	+	0.261068i	0.674770	−	0.738028i	$-0.264243\pi$
$617$	10993.0	+	4001.11i	0.717278	+	0.261068i	0.0425080	+	0.999096i	$0.486465\pi$
$618$		0			0
$619$	−1633.45	+	9263.77i	−0.106065	+	0.601523i	0.884725	+	0.466113i	$0.154346\pi$
$619$	−1633.45	+	9263.77i	−0.106065	+	0.601523i	−0.990790	+	0.135409i	$0.956765\pi$
$620$	−8214.07			−0.532073
$621$		0			0
$622$	−6604.29			−0.425736
$623$	−1193.84	+	6770.60i	−0.0767739	+	0.435406i
$624$		0			0
$625$	11490.3	+	4182.13i	0.735380	+	0.267656i
$626$	10739.4	−	9011.42i	0.685675	−	0.575350i
$627$		0			0
$628$	3345.05	−	1217.50i	0.212551	−	0.0773622i
$629$	−8515.75	+	14749.7i	−0.539817	+	0.934991i
$630$		0			0
$631$	−4148.51	−	7185.43i	−0.261727	−	0.453324i	0.704974	−	0.709233i	$-0.250959\pi$
$631$	−4148.51	−	7185.43i	−0.261727	−	0.453324i	−0.966701	+	0.255909i	$0.917625\pi$
$632$	7857.17	+	6592.94i	0.494527	+	0.414958i
$633$		0			0
$634$	599.310	+	3398.85i	0.0375420	+	0.212911i
$635$	−771.022	−	4372.69i	−0.0481844	−	0.273267i
$636$		0			0
$637$	−18379.1	−	15421.9i	−1.14318	−	0.959242i
$638$	1623.93	+	2812.72i	0.100771	+	0.174540i
$639$		0			0
$640$	646.493	−	1119.76i	0.0399295	−	0.0691599i
$641$	−23542.5	+	8568.76i	−1.45066	+	0.527997i	−0.942775	−	0.333429i	$-0.891794\pi$
$641$	−23542.5	+	8568.76i	−1.45066	+	0.527997i	−0.507883	+	0.861426i	$0.669572\pi$
$642$		0			0
$643$	12987.1	−	10897.5i	0.796517	−	0.668357i	−0.150832	−	0.988559i	$-0.548195\pi$
$643$	12987.1	−	10897.5i	0.796517	−	0.668357i	0.947349	+	0.320202i	$0.103751\pi$
$644$	−2745.84	−	999.403i	−0.168014	−	0.0611522i
$645$		0			0
$646$	−1326.44	+	7522.60i	−0.0807864	+	0.458162i
$647$	−8739.34			−0.531034			−0.265517	−	0.964106i	$-0.585543\pi$
$647$	−8739.34			−0.531034			−0.265517	+	0.964106i	$0.585543\pi$
$648$		0			0
$649$	2826.57			0.170959
$650$	−687.075	+	3896.60i	−0.0414605	+	0.235134i
$651$		0			0
$652$	2425.14	+	882.677i	0.145668	+	0.0530189i
$653$	−7274.42	+	6103.96i	−0.435942	+	0.365799i	−0.834188	−	0.551480i	$-0.814063\pi$
$653$	−7274.42	+	6103.96i	−0.435942	+	0.365799i	0.398246	+	0.917279i	$0.369619\pi$
$654$		0			0
$655$	−27030.5	+	9838.31i	−1.61247	+	0.586892i
$656$	1994.08	−	3453.85i	0.118682	−	0.205564i
$657$		0			0
$658$	3956.30	+	6852.50i	0.234396	+	0.405985i
$659$	13979.9	+	11730.5i	0.826371	+	0.693408i	0.954455	−	0.298355i	$-0.0964381\pi$
$659$	13979.9	+	11730.5i	0.826371	+	0.693408i	−0.128083	+	0.991763i	$0.540883\pi$
$660$		0			0
$661$	1260.02	+	7145.94i	0.0741440	+	0.420491i	0.999175	+	0.0406009i	$0.0129272\pi$
$661$	1260.02	+	7145.94i	0.0741440	+	0.420491i	−0.925031	+	0.379891i	$0.875962\pi$
$662$	−1553.49	−	8810.29i	−0.0912057	−	0.517253i
$663$		0			0
$664$	−3869.18	−	3246.62i	−0.226134	−	0.189749i
$665$	−1452.10	−	2515.11i	−0.0846767	−	0.146664i
$666$		0			0
$667$	4362.79	−	7556.57i	0.253265	−	0.438668i
$668$	5922.60	−	2155.65i	0.343042	−	0.124857i
$669$		0			0
$670$	8707.47	−	7306.44i	0.502088	−	0.421302i
$671$	1812.10	+	659.551i	0.104255	+	0.0379459i
$672$		0			0
$673$	−4519.12	+	25629.2i	−0.258840	+	1.46795i	0.527180	+	0.849753i	$0.323249\pi$
$673$	−4519.12	+	25629.2i	−0.258840	+	1.46795i	−0.786020	+	0.618201i	$0.787862\pi$
$674$	−8047.93			−0.459933
$675$		0			0
$676$	20908.1			1.18958
$677$	2785.45	−	15797.1i	0.158129	−	0.896795i	−0.797740	−	0.603002i	$-0.793971\pi$
$677$	2785.45	−	15797.1i	0.158129	−	0.896795i	0.955869	−	0.293793i	$-0.0949178\pi$
$678$		0			0
$679$	−2377.93	−	865.496i	−0.134399	−	0.0489171i
$680$	6607.15	−	5544.06i	0.372607	−	0.312654i
$681$		0			0
$682$	6465.32	−	2353.19i	0.363006	−	0.132123i
$683$	1821.76	−	3155.39i	0.102061	−	0.176775i	−0.810472	−	0.585777i	$-0.800790\pi$
$683$	1821.76	−	3155.39i	0.102061	−	0.176775i	0.912534	+	0.409001i	$0.134123\pi$
$684$		0			0
$685$	157.596	+	272.964i	0.00879040	+	0.0152254i
$686$	7649.51	+	6418.70i	0.425743	+	0.357241i
$687$		0			0
$688$	832.443	+	4721.02i	0.0461288	+	0.261609i
$689$	4745.60	+	26913.6i	0.262399	+	1.48814i
$690$		0			0
$691$	8506.89	+	7138.12i	0.468332	+	0.392977i	0.846186	−	0.532888i	$-0.178893\pi$
$691$	8506.89	+	7138.12i	0.468332	+	0.392977i	−0.377854	+	0.925865i	$0.623338\pi$
$692$	2138.44	+	3703.89i	0.117473	+	0.203469i
$693$		0			0
$694$	875.597	−	1516.58i	0.0478923	−	0.0829518i
$695$	−14518.1	+	5284.14i	−0.792376	+	0.288401i
$696$		0			0
$697$	20379.5	−	17100.4i	1.10750	−	0.929302i
$698$	10965.6	+	3991.16i	0.594635	+	0.216429i
$699$		0			0
$700$	128.132	−	726.671i	0.00691846	−	0.0392365i
$701$	6154.26			0.331588			0.165794	−	0.986160i	$-0.446981\pi$
$701$	6154.26			0.331588			0.165794	+	0.986160i	$0.446981\pi$
$702$		0			0
$703$	−5710.41			−0.306361
$704$	−188.066	+	1066.57i	−0.0100682	+	0.0570995i
$705$		0			0
$706$	−7409.96	−	2697.01i	−0.395011	−	0.143772i
$707$	−8747.55	+	7340.07i	−0.465326	+	0.390455i
$708$		0			0
$709$	−25252.5	+	9191.14i	−1.33762	+	0.486856i	−0.909064	−	0.416657i	$-0.863202\pi$
$709$	−25252.5	+	9191.14i	−1.33762	+	0.486856i	−0.428561	+	0.903513i	$0.640979\pi$
$710$	2521.27	−	4366.98i	0.133270	−	0.230831i
$711$		0			0
$712$	−3422.89	−	5928.63i	−0.180166	−	0.312057i
$713$	−14159.8	−	11881.4i	−0.743741	−	0.624073i
$714$		0			0
$715$	2557.61	+	14504.9i	0.133775	+	0.758675i
$716$	123.399	+	699.829i	0.00644082	+	0.0365277i
$717$		0			0
$718$	6719.40	+	5638.25i	0.349256	+	0.293061i
$719$	−18727.9	−	32437.6i	−0.971393	−	1.68250i	−0.691358	−	0.722512i	$-0.742987\pi$
$719$	−18727.9	−	32437.6i	−0.971393	−	1.68250i	−0.280035	−	0.959990i	$-0.590346\pi$
$720$		0			0
$721$	4939.11	−	8554.80i	0.255121	−	0.441882i
$722$	10484.0	−	3815.88i	0.540409	−	0.196693i
$723$		0			0
$724$	−9039.25	+	7584.84i	−0.464007	+	0.389348i
$725$	2070.51	+	753.603i	0.106064	+	0.0386043i
$726$		0			0
$727$	−5286.00	+	29978.4i	−0.269666	+	1.52935i	0.485747	+	0.874100i	$0.338548\pi$
$727$	−5286.00	+	29978.4i	−0.269666	+	1.52935i	−0.755412	+	0.655250i	$0.772563\pi$
$728$	−5537.99			−0.281939
$729$		0			0
$730$	−19382.4			−0.982705
$731$	−5552.92	+	31492.1i	−0.280960	+	1.59341i
$732$		0			0
$733$	−19933.9	−	7255.33i	−1.00447	−	0.365596i	−0.213161	−	0.977017i	$-0.568376\pi$
$733$	−19933.9	−	7255.33i	−1.00447	−	0.365596i	−0.791305	+	0.611421i	$0.790598\pi$
$734$	−8747.42	+	7339.95i	−0.439881	+	0.369104i
$735$		0			0
$736$	2734.15	−	995.151i	0.136932	−	0.0498393i
$737$	−4760.52	+	8245.46i	−0.237932	+	0.412110i
$738$		0			0
$739$	10727.4	+	18580.3i	0.533982	+	0.924884i	0.999212	+	0.0396939i	$0.0126383\pi$
$739$	10727.4	+	18580.3i	0.533982	+	0.924884i	−0.465230	+	0.885190i	$0.654028\pi$
$740$	4939.29	+	4144.56i	0.245367	+	0.205888i
$741$		0			0
$742$	−884.999	−	5019.08i	−0.0437862	−	0.248324i
$743$	−408.601	−	2317.29i	−0.0201751	−	0.114419i	0.973057	−	0.230564i	$-0.0740572\pi$
$743$	−408.601	−	2317.29i	−0.0201751	−	0.114419i	−0.993232	+	0.116146i	$0.962946\pi$
$744$		0			0
$745$	−21449.7	−	17998.5i	−1.05484	−	0.885118i
$746$	−4490.23	−	7777.31i	−0.220374	−	0.381699i
$747$		0			0
$748$	−3612.24	+	6256.58i	−0.176573	+	0.305833i
$749$	12204.8	−	4442.19i	0.595399	−	0.216708i
$750$		0			0
$751$	−654.886	+	549.515i	−0.0318204	+	0.0267005i	−0.658559	−	0.752529i	$-0.728834\pi$
$751$	−654.886	+	549.515i	−0.0318204	+	0.0267005i	0.626739	+	0.779229i	$0.284389\pi$
$752$	−7403.76	−	2694.75i	−0.359026	−	0.130675i
$753$		0			0
$754$	2871.62	−	16285.8i	0.138698	−	0.786595i
$755$	−22770.7			−1.09763
$756$		0			0
$757$	17045.5			0.818403			0.409201	−	0.912444i	$-0.365807\pi$
$757$	17045.5			0.818403			0.409201	+	0.912444i	$0.365807\pi$
$758$	−1542.60	+	8748.51i	−0.0739178	+	0.419209i
$759$		0			0
$760$	2717.44	+	989.068i	0.129700	+	0.0472069i
$761$	18552.8	−	15567.6i	0.883754	−	0.741558i	−0.0831935	−	0.996533i	$-0.526512\pi$
$761$	18552.8	−	15567.6i	0.883754	−	0.741558i	0.966947	+	0.254976i	$0.0820675\pi$
$762$		0			0
$763$	12917.1	−	4701.43i	0.612882	−	0.223071i
$764$	−1395.84	+	2417.66i	−0.0660989	+	0.114487i
$765$		0			0
$766$	−12469.9	−	21598.6i	−0.588195	−	1.01878i
$767$	−11024.9	−	9250.98i	−0.519017	−	0.435507i
$768$		0			0
$769$	−3001.66	−	17023.3i	−0.140758	−	0.798277i	−0.970676	−	0.240392i	$-0.922724\pi$
$769$	−3001.66	−	17023.3i	−0.140758	−	0.798277i	0.829918	−	0.557885i	$-0.188387\pi$
$770$	−476.964	−	2705.00i	−0.0223229	−	0.126599i
$771$		0			0
$772$	−7951.37	−	6671.99i	−0.370694	−	0.311049i
$773$	−11043.4	−	19127.7i	−0.513845	−	0.890006i	−0.999871	−	0.0160614i	$-0.994887\pi$
$773$	−11043.4	−	19127.7i	−0.513845	−	0.890006i	0.486026	−	0.873944i	$-0.338446\pi$
$774$		0			0
$775$	2333.83	−	4042.31i	0.108172	−	0.187360i
$776$	2367.81	−	861.813i	0.109535	−	0.0398676i
$777$		0			0
$778$	6009.31	−	5042.41i	0.276921	−	0.232364i
$779$	8381.83	+	3050.74i	0.385507	+	0.140313i
$780$		0			0
$781$	−733.443	+	4159.56i	−0.0336039	+	0.190577i
$782$	19409.0			0.887551
$783$		0			0
$784$	−4455.23			−0.202953
$785$	1561.03	−	8853.03i	0.0709752	−	0.402520i
$786$		0			0
$787$	27339.3	+	9950.70i	1.23830	+	0.450704i	0.876432	−	0.481525i	$-0.159917\pi$
$787$	27339.3	+	9950.70i	1.23830	+	0.450704i	0.361867	+	0.932230i	$0.382139\pi$
$788$	−4336.88	+	3639.07i	−0.196060	+	0.164514i
$789$		0			0
$790$	24340.1	−	8859.06i	1.09618	−	0.398976i
$791$	7360.07	−	12748.0i	0.330839	−	0.573031i
$792$		0			0
$793$	−4909.38	−	8503.29i	−0.219845	−	0.380783i
$794$	−8368.96	−	7022.40i	−0.374060	−	0.313873i
$795$		0			0
$796$	2001.75	+	11352.5i	0.0891334	+	0.505501i
$797$	872.127	+	4946.08i	0.0387608	+	0.219823i	0.998035	−	0.0626517i	$-0.0199557\pi$
$797$	872.127	+	4946.08i	0.0387608	+	0.219823i	−0.959275	+	0.282475i	$0.908845\pi$
$798$		0			0
$799$	−40261.2	−	33783.2i	−1.78265	−	1.49582i
$800$	367.370	+	636.304i	0.0162356	+	0.0281209i
$801$		0			0
$802$	7860.92	−	13615.5i	0.346108	−	0.599477i
$803$	15256.0	−	5552.71i	0.670449	−	0.244024i
$804$		0			0
$805$	−5652.84	+	4743.30i	−0.247499	+	0.207676i
$806$	−32919.3	−	11981.6i	−1.43863	−	0.523617i
$807$		0			0
$808$	1974.47	−	11197.8i	0.0859674	−	0.487545i
$809$	−19520.7			−0.848345			−0.424173	−	0.905581i	$-0.639435\pi$
$809$	−19520.7			−0.848345			−0.424173	+	0.905581i	$0.639435\pi$
$810$		0			0
$811$	−15288.0			−0.661941			−0.330971	−	0.943641i	$-0.607376\pi$
$811$	−15288.0			−0.661941			−0.330971	+	0.943641i	$0.607376\pi$
$812$	−535.524	+	3037.11i	−0.0231443	+	0.131258i
$813$		0			0
$814$	−5075.07	−	1847.18i	−0.218527	−	0.0795374i
$815$	4992.61	−	4189.30i	0.214581	−	0.180055i
$816$		0			0
$817$	−10075.1	+	3667.05i	−0.431437	+	0.157030i
$818$	−16302.5	+	28236.7i	−0.696826	+	1.20694i
$819$		0			0
$820$	−5035.77	−	8722.22i	−0.214460	−	0.371455i
$821$	3537.48	+	2968.30i	0.150376	+	0.126181i	0.714872	−	0.699255i	$-0.246485\pi$
$821$	3537.48	+	2968.30i	0.150376	+	0.126181i	−0.564496	+	0.825436i	$0.690929\pi$
$822$		0			0
$823$	−6219.14	−	35270.5i	−0.263409	−	1.49387i	−0.773527	−	0.633763i	$-0.781509\pi$
$823$	−6219.14	−	35270.5i	−0.263409	−	1.49387i	0.510118	−	0.860104i	$-0.329602\pi$
$824$	1708.04	+	9686.76i	0.0722115	+	0.409532i
$825$		0			0
$826$	2056.02	+	1725.20i	0.0866077	+	0.0726725i
$827$	21674.5	+	37541.3i	0.911361	+	1.57852i	0.812144	+	0.583457i	$0.198300\pi$
$827$	21674.5	+	37541.3i	0.911361	+	1.57852i	0.0992164	+	0.995066i	$0.468366\pi$
$828$		0			0
$829$	7913.41	−	13706.4i	0.331537	−	0.574239i	−0.651276	−	0.758841i	$-0.725766\pi$
$829$	7913.41	−	13706.4i	0.331537	−	0.574239i	0.982813	+	0.184602i	$0.0590995\pi$
$830$	−11986.0	+	4362.55i	−0.501253	+	0.182441i
$831$		0			0
$832$	4224.29	−	3544.60i	0.176023	−	0.147701i
$833$	−27926.9	−	10164.5i	−1.16159	−	0.422786i
$834$		0			0
$835$	2763.89	−	15674.8i	0.114549	−	0.649639i
$836$	−2422.26			−0.100210
$837$		0			0
$838$	−3066.05			−0.126390
$839$	4140.82	−	23483.8i	0.170390	−	0.966329i	−0.772942	−	0.634477i	$-0.781215\pi$
$839$	4140.82	−	23483.8i	0.170390	−	0.966329i	0.943332	−	0.331852i	$-0.107673\pi$
$840$		0			0
$841$	14264.5	+	5191.86i	0.584875	+	0.212877i
$842$	2403.77	−	2017.01i	0.0983842	−	0.0825541i
$843$		0			0
$844$	−13979.9	+	5088.26i	−0.570151	+	0.207518i
$845$	26400.3	−	45726.7i	1.07479	−	1.86159i
$846$		0			0
$847$	−4196.40	−	7268.37i	−0.170236	−	0.294857i
$848$	3887.54	+	3262.03i	0.157428	+	0.132097i
$849$		0			0
$850$	851.081	+	4826.72i	0.0343433	+	0.194771i
$851$	2519.56	+	14289.1i	0.101491	+	0.575587i
$852$		0			0
$853$	20432.3	+	17144.8i	0.820152	+	0.688189i	0.953008	−	0.302946i	$-0.0979703\pi$
$853$	20432.3	+	17144.8i	0.820152	+	0.688189i	−0.132856	+	0.991135i	$0.542415\pi$
$854$	915.543	+	1585.77i	0.0366853	+	0.0635408i
$855$		0			0
$856$	−6466.41	+	11200.1i	−0.258198	+	0.447212i
$857$	−43887.5	+	15973.7i	−1.74932	+	0.636700i	−0.999684	−	0.0251502i	$-0.991994\pi$
$857$	−43887.5	+	15973.7i	−1.74932	+	0.636700i	−0.749636	+	0.661850i	$0.769771\pi$
$858$		0			0
$859$	−409.687	+	343.768i	−0.0162728	+	0.0136545i	−0.650888	−	0.759174i	$-0.725603\pi$
$859$	−409.687	+	343.768i	−0.0162728	+	0.0136545i	0.634615	+	0.772828i	$0.281159\pi$
$860$	11376.1	+	4140.57i	0.451073	+	0.164177i
$861$		0			0
$862$	−3867.13	+	21931.6i	−0.152802	+	0.866581i
$863$	11669.8			0.460307			0.230153	−	0.973154i	$-0.426077\pi$
$863$	11669.8			0.460307			0.230153	+	0.973154i	$0.426077\pi$
$864$		0			0
$865$	10800.7			0.424548
$866$	3456.80	−	19604.5i	0.135643	−	0.769269i
$867$		0			0
$868$	6139.07	+	2234.44i	0.240062	+	0.0873753i
$869$	−16620.2	+	13946.0i	−0.648793	+	0.544402i
$870$		0			0
$871$	45554.4	−	16580.4i	1.77216	−	0.645013i
$872$	−6843.78	+	11853.8i	−0.265779	+	0.460343i
$873$		0			0
$874$	3253.78	+	5635.71i	0.125927	+	0.218113i
$875$	−9198.69	−	7718.62i	−0.355397	−	0.298214i
$876$		0			0
$877$	568.281	+	3222.88i	0.0218808	+	0.124092i	0.993792	−	0.111257i	$-0.0354877\pi$
$877$	568.281	+	3222.88i	0.0218808	+	0.124092i	−0.971911	+	0.235349i	$0.924377\pi$
$878$	−5994.88	−	33998.6i	−0.230430	−	1.30683i
$879$		0			0
$880$	2095.16	+	1758.05i	0.0802590	+	0.0673453i
$881$	10618.6	+	18392.0i	0.406074	+	0.703340i	0.994446	−	0.105250i	$-0.0335643\pi$
$881$	10618.6	+	18392.0i	0.406074	+	0.703340i	−0.588372	+	0.808590i	$0.700231\pi$
$882$		0			0
$883$	4744.05	−	8216.94i	0.180804	−	0.313162i	−0.761350	−	0.648341i	$-0.775463\pi$
$883$	4744.05	−	8216.94i	0.180804	−	0.313162i	0.942155	+	0.335179i	$0.108797\pi$
$884$	34566.2	−	12581.1i	1.31514	−	0.478674i
$885$		0			0
$886$	−17563.4	+	14737.4i	−0.665975	+	0.558819i
$887$	−11879.5	−	4323.77i	−0.449688	−	0.163673i	0.107241	−	0.994233i	$-0.465798\pi$
$887$	−11879.5	−	4323.77i	−0.449688	−	0.163673i	−0.556929	+	0.830560i	$0.688020\pi$
$888$		0			0
$889$	−613.232	+	3477.81i	−0.0231352	+	0.131206i
$890$	−17288.1			−0.651122
$891$		0			0
$892$	11973.3			0.449435
$893$	3059.97	−	17354.0i	0.114667	−	0.650312i
$894$		0			0
$895$	1686.36	+	613.785i	0.0629819	+	0.0229235i
$896$	−787.782	+	661.027i	−0.0293727	+	0.0246466i
$897$		0			0
$898$	17539.8	−	6383.96i	0.651793	−	0.237233i
$899$	−9754.19	+	16894.8i	−0.361869	+	0.626776i
$900$		0			0
$901$	16926.1	+	29316.9i	0.625850	+	1.08400i
$902$	6462.44	+	5422.63i	0.238554	+	0.200170i
$903$		0			0
$904$	2545.25	+	14434.8i	0.0936435	+	0.531079i
$905$	5174.55	+	29346.3i	0.190064	+	1.07791i
$906$		0			0
$907$	16824.4	+	14117.4i	0.615927	+	0.516824i	0.896520	−	0.443003i	$-0.146087\pi$
$907$	16824.4	+	14117.4i	0.615927	+	0.516824i	−0.280593	+	0.959827i	$0.590531\pi$
$908$	−1408.09	−	2438.89i	−0.0514638	−	0.0891380i
$909$		0			0
$910$	−6992.71	+	12111.7i	−0.254732	+	0.441209i
$911$	18773.3	−	6832.93i	0.682753	−	0.248502i	0.0227240	−	0.999742i	$-0.492766\pi$
$911$	18773.3	−	6832.93i	0.682753	−	0.248502i	0.660029	+	0.751240i	$0.270544\pi$
$912$		0			0
$913$	8184.43	−	6867.55i	0.296676	−	0.248941i
$914$	−9464.26	−	3444.71i	−0.342505	−	0.124662i
$915$		0			0
$916$	−1160.59	+	6582.01i	−0.0418633	+	0.237419i
$917$	22878.5			0.823897
$918$		0			0
$919$	−37818.2			−1.35746			−0.678731	−	0.734387i	$-0.737470\pi$
$919$	−37818.2			−1.35746			−0.678731	+	0.734387i	$0.737470\pi$
$920$	1275.94	−	7236.23i	0.0457246	−	0.259317i
$921$		0			0
$922$	−11509.5	−	4189.12i	−0.411112	−	0.149633i
$923$	16474.4	−	13823.7i	0.587500	−	0.492971i
$924$		0			0
$925$	−3443.00	+	1253.15i	−0.122384	+	0.0445441i
$926$	2070.79	−	3586.72i	0.0734886	−	0.127286i
$927$		0			0
$928$	−1535.42	−	2659.42i	−0.0543131	−	0.0940731i
$929$	21840.6	+	18326.4i	0.771330	+	0.647223i	0.941049	−	0.338270i	$-0.109842\pi$
$929$	21840.6	+	18326.4i	0.771330	+	0.647223i	−0.169719	+	0.985492i	$0.554286\pi$
$930$		0			0
$931$	−1730.30	−	9813.00i	−0.0609111	−	0.345444i
$932$	474.704	+	2692.18i	0.0166839	+	0.0946193i
$933$		0			0
$934$	12757.1	+	10704.5i	0.446923	+	0.375013i
$935$	9122.21	+	15800.1i	0.319067	+	0.552641i
$936$		0			0
$937$	−16858.7	+	29200.1i	−0.587779	+	1.01806i	0.406744	+	0.913542i	$0.366664\pi$
$937$	−16858.7	+	29200.1i	−0.587779	+	1.01806i	−0.994523	+	0.104521i	$0.966669\pi$
$938$	−8495.37	+	3092.06i	−0.295718	+	0.107633i
$939$		0			0
$940$	−15242.1	+	12789.6i	−0.528875	+	0.443779i
$941$	16979.3	+	6179.95i	0.588213	+	0.214092i	0.618943	−	0.785436i	$-0.287561\pi$
$941$	16979.3	+	6179.95i	0.588213	+	0.214092i	−0.0307305	+	0.999528i	$0.509783\pi$
$942$		0			0
$943$	3935.59	−	22319.8i	0.135907	−	0.770768i
$944$	−2672.52			−0.0921430
$945$		0			0
$946$	−10140.4			−0.348512
$947$	−8021.69	+	45493.2i	−0.275258	+	1.56107i	0.462881	+	0.886420i	$0.346816\pi$
$947$	−8021.69	+	45493.2i	−0.275258	+	1.56107i	−0.738140	+	0.674648i	$0.764295\pi$
$948$		0			0
$949$	−77678.3	−	28272.6i	−2.65705	−	0.967088i
$950$	−1258.83	+	1056.29i	−0.0429916	+	0.0360742i
$951$		0			0
$952$	−6446.20	+	2346.23i	−0.219457	+	0.0798757i
$953$	16890.0	−	29254.3i	0.574102	−	0.994374i	−0.422037	−	0.906579i	$-0.638685\pi$
$953$	16890.0	−	29254.3i	0.574102	−	0.994374i	0.996139	−	0.0877951i	$-0.0279821\pi$
$954$		0			0
$955$	3524.99	+	6105.46i	0.119441	+	0.206878i
$956$	−9969.09	−	8365.06i	−0.337263	−	0.282997i
$957$		0			0
$958$	4675.50	+	26516.1i	0.157681	+	0.894255i
$959$	−43.5314	−	246.879i	−0.00146580	−	0.00831297i
$960$		0			0
$961$	8836.76	+	7414.93i	0.296625	+	0.248898i
$962$	13749.5	+	23814.8i	0.460812	+	0.798150i
$963$		0			0
$964$	−4805.77	+	8323.84i	−0.160564	+	0.278105i
$965$	−24631.9	+	8965.27i	−0.821687	+	0.299070i
$966$		0			0
$967$	−3224.62	+	2705.78i	−0.107236	+	0.0899813i	−0.694829	−	0.719175i	$-0.744520\pi$
$967$	−3224.62	+	2705.78i	−0.107236	+	0.0899813i	0.587593	+	0.809156i	$0.300075\pi$
$968$	7853.09	+	2858.29i	0.260752	+	0.0949059i
$969$		0			0
$970$	1104.98	−	6266.67i	0.0365761	−	0.207434i
$971$	50574.5			1.67149			0.835743	−	0.549120i	$-0.185037\pi$
$971$	50574.5			1.67149			0.835743	+	0.549120i	$0.185037\pi$
$972$		0			0
$973$	12288.0			0.404866
$974$	−3396.33	+	19261.6i	−0.111731	+	0.633655i
$975$		0			0
$976$	−1713.34	−	623.603i	−0.0561911	−	0.0204519i
$977$	30451.9	−	25552.2i	0.997179	−	0.836733i	0.0105880	−	0.999944i	$-0.496630\pi$
$977$	30451.9	−	25552.2i	0.997179	−	0.836733i	0.986591	+	0.163211i	$0.0521852\pi$
$978$		0			0
$979$	13607.5	−	4952.73i	0.444227	−	0.161685i
$980$	−5625.54	+	9743.71i	−0.183369	+	0.317604i
$981$		0			0
$982$	−5163.34	−	8943.17i	−0.167789	−	0.290619i
$983$	−24940.9	−	20927.9i	−0.809247	−	0.679039i	0.141181	−	0.989984i	$-0.454910\pi$
$983$	−24940.9	−	20927.9i	−0.809247	−	0.679039i	−0.950428	+	0.310945i	$0.899355\pi$
$984$		0			0
$985$	2482.66	+	14079.9i	0.0803088	+	0.455454i
$986$	−3557.08	−	20173.2i	−0.114889	−	0.651567i
$987$		0			0
$988$	9447.88	+	7927.71i	0.304228	+	0.255277i
$989$	13621.4	+	23593.0i	0.437953	+	0.758556i
$990$		0			0
$991$	835.941	−	1447.89i	0.0267957	−	0.0464115i	−0.852317	−	0.523026i	$-0.824803\pi$
$991$	835.941	−	1447.89i	0.0267957	−	0.0464115i	0.879112	+	0.476615i	$0.158136\pi$
$992$	−6112.95	+	2224.93i	−0.195651	+	0.0712113i
$993$		0			0
$994$	−3072.29	+	2577.96i	−0.0980354	+	0.0822614i
$995$	27355.8	+	9956.70i	0.871596	+	0.317235i
$996$		0			0
$997$	−3137.83	+	17795.5i	−0.0996750	+	0.565285i	0.893539	+	0.448985i	$0.148214\pi$
$997$	−3137.83	+	17795.5i	−0.0996750	+	0.565285i	−0.993214	+	0.116300i	$0.962897\pi$
$998$	−6988.80			−0.221670
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.4.e.b.73.1		30
3.2	odd	2		54.4.e.b.25.4	yes	30
27.11	odd	18		1458.4.a.i.1.12		15
27.13	even	9	inner	162.4.e.b.91.1		30
27.14	odd	18		54.4.e.b.13.4	✓	30
27.16	even	9		1458.4.a.j.1.4		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.4.e.b.13.4	✓	30	27.14	odd	18
54.4.e.b.25.4	yes	30	3.2	odd	2
162.4.e.b.73.1		30	1.1	even	1	trivial
162.4.e.b.91.1		30	27.13	even	9	inner
1458.4.a.i.1.12		15	27.11	odd	18
1458.4.a.j.1.4		15	27.16	even	9

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	162.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.347296 - 1.96962i) q^{2} +(-3.75877 - 1.36808i) q^{4} +(-7.73816 + 6.49309i) q^{5} +(7.54967 - 2.74785i) q^{7} +(-4.00000 + 6.92820i) q^{8} +O(q^{10})\)	\(q+(0.347296 - 1.96962i) q^{2} +(-3.75877 - 1.36808i) q^{4} +(-7.73816 + 6.49309i) q^{5} +(7.54967 - 2.74785i) q^{7} +(-4.00000 + 6.92820i) q^{8} +(10.1015 + 17.4962i) q^{10} +(-12.9632 - 10.8775i) q^{11} +(14.9620 + 84.8538i) q^{13} +(-2.79024 - 15.8243i) q^{14} +(12.2567 + 10.2846i) q^{16} +(53.3650 + 92.4308i) q^{17} +(-17.8925 + 30.9907i) q^{19} +(37.9690 - 13.8196i) q^{20} +(-25.9265 + 21.7549i) q^{22} +(85.4423 + 31.0985i) q^{23} +(-3.98707 + 22.6118i) q^{25} +172.326 q^{26} -32.1368 q^{28} +(16.6639 - 94.5057i) q^{29} +(-191.030 - 69.5291i) q^{31} +(24.5134 - 20.5692i) q^{32} +(200.587 - 73.0076i) q^{34} +(-40.5785 + 70.2840i) q^{35} +(79.7878 + 138.197i) q^{37} +(54.8257 + 46.0043i) q^{38} +(-14.0328 - 79.5839i) q^{40} +(-43.2835 - 245.473i) q^{41} +(229.519 + 192.589i) q^{43} +(33.8446 + 58.6206i) q^{44} +(90.9258 - 157.488i) q^{46} +(-462.735 + 168.422i) q^{47} +(-213.306 + 178.985i) q^{49} +(43.1519 + 15.7060i) q^{50} +(59.8481 - 339.415i) q^{52} +317.176 q^{53} +170.940 q^{55} +(-11.1610 + 63.2970i) q^{56} +(-180.353 - 65.6430i) q^{58} +(-127.954 + 107.366i) q^{59} +(-107.083 + 38.9752i) q^{61} +(-203.289 + 352.108i) q^{62} +(-32.0000 - 55.4256i) q^{64} +(-666.742 - 559.463i) q^{65} +(-97.7000 - 554.084i) q^{67} +(-74.1338 - 420.434i) q^{68} +(124.340 + 104.333i) q^{70} +(-124.798 - 216.156i) q^{71} +(-479.693 + 830.853i) q^{73} +(299.904 - 109.156i) q^{74} +(109.651 - 92.0085i) q^{76} +(-127.758 - 46.5001i) q^{77} +(222.634 - 1262.62i) q^{79} -161.623 q^{80} -498.520 q^{82} +(-109.634 + 621.765i) q^{83} +(-1013.11 - 368.741i) q^{85} +(459.038 - 385.178i) q^{86} +(127.214 - 46.3022i) q^{88} +(-427.862 + 741.078i) q^{89} +(346.124 + 599.505i) q^{91} +(-278.613 - 233.784i) q^{92} +(171.020 + 969.903i) q^{94} +(-62.7704 - 355.988i) q^{95} +(-241.282 - 202.460i) q^{97} +(278.452 + 482.293i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 12 q^{5} + 33 q^{7} - 120 q^{8}+O(q^{10}) \) 30 * q + 12 * q^5 + 33 * q^7 - 120 * q^8	\( 30 q + 12 q^{5} + 33 q^{7} - 120 q^{8} - 30 q^{10} + 39 q^{11} - 60 q^{13} + 66 q^{14} - 102 q^{17} - 171 q^{19} - 96 q^{20} + 78 q^{22} - 48 q^{23} - 432 q^{25} + 468 q^{26} + 336 q^{28} + 381 q^{29} - 801 q^{31} - 222 q^{34} - 624 q^{35} - 555 q^{37} - 606 q^{38} + 96 q^{40} - 1401 q^{41} + 648 q^{43} - 132 q^{44} - 348 q^{46} - 540 q^{47} + 15 q^{49} + 828 q^{50} - 240 q^{52} + 1794 q^{53} + 3906 q^{55} + 264 q^{56} - 444 q^{58} + 1500 q^{59} - 378 q^{61} - 744 q^{62} - 960 q^{64} - 3666 q^{65} + 3087 q^{67} + 24 q^{68} + 2118 q^{70} - 120 q^{71} - 2604 q^{73} + 1974 q^{74} - 1212 q^{76} + 6504 q^{77} - 2625 q^{79} + 480 q^{80} + 3408 q^{82} + 5211 q^{83} - 1395 q^{85} + 1296 q^{86} - 912 q^{88} - 2604 q^{89} - 3399 q^{91} - 372 q^{92} + 4500 q^{94} - 7545 q^{95} + 8940 q^{97} - 4002 q^{98}+O(q^{100}) \) 30 * q + 12 * q^5 + 33 * q^7 - 120 * q^8 - 30 * q^10 + 39 * q^11 - 60 * q^13 + 66 * q^14 - 102 * q^17 - 171 * q^19 - 96 * q^20 + 78 * q^22 - 48 * q^23 - 432 * q^25 + 468 * q^26 + 336 * q^28 + 381 * q^29 - 801 * q^31 - 222 * q^34 - 624 * q^35 - 555 * q^37 - 606 * q^38 + 96 * q^40 - 1401 * q^41 + 648 * q^43 - 132 * q^44 - 348 * q^46 - 540 * q^47 + 15 * q^49 + 828 * q^50 - 240 * q^52 + 1794 * q^53 + 3906 * q^55 + 264 * q^56 - 444 * q^58 + 1500 * q^59 - 378 * q^61 - 744 * q^62 - 960 * q^64 - 3666 * q^65 + 3087 * q^67 + 24 * q^68 + 2118 * q^70 - 120 * q^71 - 2604 * q^73 + 1974 * q^74 - 1212 * q^76 + 6504 * q^77 - 2625 * q^79 + 480 * q^80 + 3408 * q^82 + 5211 * q^83 - 1395 * q^85 + 1296 * q^86 - 912 * q^88 - 2604 * q^89 - 3399 * q^91 - 372 * q^92 + 4500 * q^94 - 7545 * q^95 + 8940 * q^97 - 4002 * q^98

Introduction

L-functions

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