LMFDB - Embedded newform 342.2.bb.a.143.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,2,Mod(53,342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("342.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	342.bb (of order $18$, degree $6$, 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:	$2.73088374913$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			143.2
Character	$\chi$	$=$	342.143
Dual form			342.2.bb.a.287.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.173648 + 0.984808i) q^{2} +(-0.939693 + 0.342020i) q^{4} +(-0.0466858 + 0.128268i) q^{5} +(-2.51073 + 4.34872i) q^{7} +(-0.500000 - 0.866025i) q^{8} +O(q^{10})$	\(q+(0.173648 + 0.984808i) q^{2} +(-0.939693 + 0.342020i) q^{4} +(-0.0466858 + 0.128268i) q^{5} +(-2.51073 + 4.34872i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.134426 - 0.0237030i) q^{10} +(3.11116 - 1.79623i) q^{11} +(-2.32138 + 2.76651i) q^{13} +(-4.71864 - 1.71744i) q^{14} +(0.766044 - 0.642788i) q^{16} +(-5.05668 + 0.891629i) q^{17} +(-4.27353 + 0.858478i) q^{19} -0.136500i q^{20} +(2.30918 + 2.75198i) q^{22} +(2.33023 + 6.40226i) q^{23} +(3.81595 + 3.20196i) q^{25} +(-3.12759 - 1.80571i) q^{26} +(0.871969 - 4.94518i) q^{28} +(1.24964 - 7.08707i) q^{29} +(3.67105 + 2.11948i) q^{31} +(0.766044 + 0.642788i) q^{32} +(-1.75617 - 4.82502i) q^{34} +(-0.440587 - 0.525071i) q^{35} -0.852851i q^{37} +(-1.58753 - 4.05953i) q^{38} +(0.134426 - 0.0237030i) q^{40} +(-2.61979 + 2.19827i) q^{41} +(4.48830 + 1.63361i) q^{43} +(-2.30918 + 2.75198i) q^{44} +(-5.90035 + 3.40657i) q^{46} +(6.64017 + 1.17084i) q^{47} +(-9.10757 - 15.7748i) q^{49} +(-2.49068 + 4.31399i) q^{50} +(1.23518 - 3.39363i) q^{52} +(2.63008 - 0.957270i) q^{53} +(0.0851519 + 0.482920i) q^{55} +5.02147 q^{56} +7.19640 q^{58} +(-1.77228 - 10.0511i) q^{59} +(3.59208 - 1.30741i) q^{61} +(-1.44981 + 3.98332i) q^{62} +(-0.500000 + 0.866025i) q^{64} +(-0.246480 - 0.426916i) q^{65} +(6.32389 + 1.11507i) q^{67} +(4.44677 - 2.56734i) q^{68} +(0.440587 - 0.525071i) q^{70} +(14.3392 + 5.21904i) q^{71} +(3.54200 - 2.97209i) q^{73} +(0.839894 - 0.148096i) q^{74} +(3.72218 - 2.26834i) q^{76} +18.0394i q^{77} +(4.45498 + 5.30924i) q^{79} +(0.0466858 + 0.128268i) q^{80} +(-2.61979 - 2.19827i) q^{82} +(-1.38926 - 0.802089i) q^{83} +(0.121707 - 0.690237i) q^{85} +(-0.829404 + 4.70379i) q^{86} +(-3.11116 - 1.79623i) q^{88} +(4.51237 + 3.78633i) q^{89} +(-6.20242 - 17.0410i) q^{91} +(-4.37940 - 5.21917i) q^{92} +6.74261i q^{94} +(0.0893976 - 0.588236i) q^{95} +(-5.49864 + 0.969559i) q^{97} +(13.9536 - 11.7085i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{8}+O(q^{10}) $ 24 * q - 12 * q^8	$ 24 q - 12 q^{8} - 12 q^{17} + 24 q^{19} + 12 q^{22} + 36 q^{25} - 36 q^{26} + 12 q^{29} + 12 q^{34} + 48 q^{35} + 12 q^{38} + 12 q^{41} - 12 q^{44} - 36 q^{46} - 60 q^{47} - 36 q^{49} + 24 q^{50} + 48 q^{53} - 60 q^{55} - 24 q^{58} - 24 q^{59} - 60 q^{61} - 24 q^{62} - 12 q^{64} + 24 q^{65} - 48 q^{70} + 36 q^{71} + 24 q^{79} + 12 q^{82} - 72 q^{83} + 36 q^{86} + 120 q^{89} - 24 q^{91} - 12 q^{95}+O(q^{100}) $ 24 * q - 12 * q^8 - 12 * q^17 + 24 * q^19 + 12 * q^22 + 36 * q^25 - 36 * q^26 + 12 * q^29 + 12 * q^34 + 48 * q^35 + 12 * q^38 + 12 * q^41 - 12 * q^44 - 36 * q^46 - 60 * q^47 - 36 * q^49 + 24 * q^50 + 48 * q^53 - 60 * q^55 - 24 * q^58 - 24 * q^59 - 60 * q^61 - 24 * q^62 - 12 * q^64 + 24 * q^65 - 48 * q^70 + 36 * q^71 + 24 * q^79 + 12 * q^82 - 72 * q^83 + 36 * q^86 + 120 * q^89 - 24 * q^91 - 12 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/342\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$-1$	$e\left(\frac{17}{18}\right)$

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 $

$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$3$		0			0
$3$		0			0
$4$	−0.939693	+	0.342020i	−0.469846	+	0.171010i
$5$	−0.0466858	+	0.128268i	−0.0208785	+	0.0573633i	−0.949694	−	0.313179i	$-0.898606\pi$
$5$	−0.0466858	+	0.128268i	−0.0208785	+	0.0573633i	0.928816	+	0.370542i	$0.120828\pi$
$6$		0			0
$7$	−2.51073	+	4.34872i	−0.948968	+	1.64366i	−0.201365	+	0.979516i	$0.564538\pi$
$7$	−2.51073	+	4.34872i	−0.948968	+	1.64366i	−0.747604	+	0.664145i	$0.768796\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$		0			0
$10$	−0.134426	−	0.0237030i	−0.0425094	−	0.00749555i
$11$	3.11116	−	1.79623i	0.938049	−	0.541583i	0.0487005	−	0.998813i	$-0.484492\pi$
$11$	3.11116	−	1.79623i	0.938049	−	0.541583i	0.889348	+	0.457231i	$0.151159\pi$
$12$		0			0
$13$	−2.32138	+	2.76651i	−0.643835	+	0.767292i	−0.984971	−	0.172722i	$-0.944744\pi$
$13$	−2.32138	+	2.76651i	−0.643835	+	0.767292i	0.341136	+	0.940014i	$0.389188\pi$
$14$	−4.71864	−	1.71744i	−1.26111	−	0.459006i
$15$		0			0
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	−5.05668	+	0.891629i	−1.22642	+	0.216252i	−0.749089	−	0.662470i	$-0.769508\pi$
$17$	−5.05668	+	0.891629i	−1.22642	+	0.216252i	−0.477335	+	0.878721i	$0.658397\pi$
$18$		0			0
$19$	−4.27353	+	0.858478i	−0.980414	+	0.196948i
$19$	−4.27353	+	0.858478i	−0.980414	+	0.196948i
$20$		−	0.136500i		−	0.0305224i
$21$		0			0
$22$	2.30918	+	2.75198i	0.492320	+	0.586724i
$23$	2.33023	+	6.40226i	0.485887	+	1.33496i	0.904374	+	0.426740i	$0.140338\pi$
$23$	2.33023	+	6.40226i	0.485887	+	1.33496i	−0.418487	+	0.908223i	$0.637440\pi$
$24$		0			0
$25$	3.81595	+	3.20196i	0.763190	+	0.640392i
$26$	−3.12759	−	1.80571i	−0.613370	−	0.354129i
$27$		0			0
$28$	0.871969	−	4.94518i	0.164787	−	0.934551i
$29$	1.24964	−	7.08707i	0.232053	−	1.31604i	−0.616680	−	0.787214i	$-0.711523\pi$
$29$	1.24964	−	7.08707i	0.232053	−	1.31604i	0.848733	−	0.528822i	$-0.177366\pi$
$30$		0			0
$31$	3.67105	+	2.11948i	0.659340	+	0.380670i	0.792025	−	0.610488i	$-0.209027\pi$
$31$	3.67105	+	2.11948i	0.659340	+	0.380670i	−0.132685	+	0.991158i	$0.542360\pi$
$32$	0.766044	+	0.642788i	0.135419	+	0.113630i
$33$		0			0
$34$	−1.75617	−	4.82502i	−0.301180	−	0.827485i
$35$	−0.440587	−	0.525071i	−0.0744727	−	0.0887531i
$36$		0			0
$37$		−	0.852851i		−	0.140208i	−0.997540	−	0.0701039i	$-0.977667\pi$
$37$		−	0.852851i		−	0.140208i	0.997540	−	0.0701039i	$-0.0223331\pi$
$38$	−1.58753	−	4.05953i	−0.257531	−	0.658542i
$39$		0			0
$40$	0.134426	−	0.0237030i	0.0212547	−	0.00374777i
$41$	−2.61979	+	2.19827i	−0.409142	+	0.343311i	−0.824015	−	0.566568i	$-0.808271\pi$
$41$	−2.61979	+	2.19827i	−0.409142	+	0.343311i	0.414872	+	0.909880i	$0.363826\pi$
$42$		0			0
$43$	4.48830	+	1.63361i	0.684459	+	0.249123i	0.660761	−	0.750596i	$-0.270234\pi$
$43$	4.48830	+	1.63361i	0.684459	+	0.249123i	0.0236983	+	0.999719i	$0.492456\pi$
$44$	−2.30918	+	2.75198i	−0.348123	+	0.414876i
$45$		0			0
$46$	−5.90035	+	3.40657i	−0.869959	+	0.502271i
$47$	6.64017	+	1.17084i	0.968568	+	0.170785i	0.635486	−	0.772113i	$-0.280800\pi$
$47$	6.64017	+	1.17084i	0.968568	+	0.170785i	0.333083	+	0.942898i	$0.391911\pi$
$48$		0			0
$49$	−9.10757	−	15.7748i	−1.30108	−	2.25354i
$50$	−2.49068	+	4.31399i	−0.352236	+	0.610090i
$51$		0			0
$52$	1.23518	−	3.39363i	0.171289	−	0.470612i
$53$	2.63008	−	0.957270i	0.361269	−	0.131491i	−0.155007	−	0.987913i	$-0.549540\pi$
$53$	2.63008	−	0.957270i	0.361269	−	0.131491i	0.516276	+	0.856422i	$0.327318\pi$
$54$		0			0
$55$	0.0851519	+	0.482920i	0.0114819	+	0.0651170i
$56$	5.02147			0.671022
$57$		0			0
$58$	7.19640			0.944933
$59$	−1.77228	−	10.0511i	−0.230732	−	1.30855i	−0.851419	−	0.524487i	$-0.824257\pi$
$59$	−1.77228	−	10.0511i	−0.230732	−	1.30855i	0.620687	−	0.784059i	$-0.286854\pi$
$60$		0			0
$61$	3.59208	−	1.30741i	0.459919	−	0.167397i	−0.101661	−	0.994819i	$-0.532416\pi$
$61$	3.59208	−	1.30741i	0.459919	−	0.167397i	0.561580	+	0.827422i	$0.310194\pi$
$62$	−1.44981	+	3.98332i	−0.184126	+	0.505882i
$63$		0			0
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−0.246480	−	0.426916i	−0.0305721	−	0.0529524i
$66$		0			0
$67$	6.32389	+	1.11507i	0.772587	+	0.136228i	0.546025	−	0.837769i	$-0.316140\pi$
$67$	6.32389	+	1.11507i	0.772587	+	0.136228i	0.226562	+	0.973997i	$0.427252\pi$
$68$	4.44677	−	2.56734i	0.539250	−	0.311336i
$69$		0			0
$70$	0.440587	−	0.525071i	0.0526602	−	0.0627579i
$71$	14.3392	+	5.21904i	1.70175	+	0.619386i	0.996023	−	0.0890999i	$-0.0283990\pi$
$71$	14.3392	+	5.21904i	1.70175	+	0.619386i	0.705725	+	0.708486i	$0.250621\pi$
$72$		0			0
$73$	3.54200	−	2.97209i	0.414560	−	0.347857i	−0.411529	−	0.911397i	$-0.635005\pi$
$73$	3.54200	−	2.97209i	0.414560	−	0.347857i	0.826089	+	0.563540i	$0.190561\pi$
$74$	0.839894	−	0.148096i	0.0976357	−	0.0172158i
$75$		0			0
$76$	3.72218	−	2.26834i	0.426964	−	0.260196i
$77$			18.0394i			2.05578i
$78$		0			0
$79$	4.45498	+	5.30924i	0.501225	+	0.597336i	0.956035	−	0.293252i	$-0.0947375\pi$
$79$	4.45498	+	5.30924i	0.501225	+	0.597336i	−0.454811	+	0.890588i	$0.650293\pi$
$80$	0.0466858	+	0.128268i	0.00521963	+	0.0143408i
$81$		0			0
$82$	−2.61979	−	2.19827i	−0.289307	−	0.242758i
$83$	−1.38926	−	0.802089i	−0.152491	−	0.0880407i	0.421813	−	0.906683i	$-0.361394\pi$
$83$	−1.38926	−	0.802089i	−0.152491	−	0.0880407i	−0.574304	+	0.818642i	$0.694727\pi$
$84$		0			0
$85$	0.121707	−	0.690237i	0.0132010	−	0.0748667i
$86$	−0.829404	+	4.70379i	−0.0894370	+	0.507222i
$87$		0			0
$88$	−3.11116	−	1.79623i	−0.331650	−	0.191478i
$89$	4.51237	+	3.78633i	0.478311	+	0.401350i	0.849815	−	0.527081i	$-0.176713\pi$
$89$	4.51237	+	3.78633i	0.478311	+	0.401350i	−0.371504	+	0.928431i	$0.621158\pi$
$90$		0			0
$91$	−6.20242	−	17.0410i	−0.650190	−	1.78638i
$92$	−4.37940	−	5.21917i	−0.456584	−	0.544136i
$93$		0			0
$94$			6.74261i			0.695447i
$95$	0.0893976	−	0.588236i	0.00917200	−	0.0603517i
$96$		0			0
$97$	−5.49864	+	0.969559i	−0.558303	+	0.0984438i	−0.445677	−	0.895194i	$-0.647037\pi$
$97$	−5.49864	+	0.969559i	−0.558303	+	0.0984438i	−0.112625	+	0.993638i	$0.535926\pi$
$98$	13.9536	−	11.7085i	1.40953	−	1.18273i
$99$		0			0
$100$	−4.68095	−	1.70373i	−0.468095	−	0.170373i
$101$	−1.83905	+	2.19170i	−0.182993	+	0.218082i	−0.849740	−	0.527201i	$-0.823241\pi$
$101$	−1.83905	+	2.19170i	−0.182993	+	0.218082i	0.666748	+	0.745283i	$0.267686\pi$
$102$		0			0
$103$	−9.24761	+	5.33911i	−0.911194	+	0.526078i	−0.880815	−	0.473460i	$-0.843005\pi$
$103$	−9.24761	+	5.33911i	−0.911194	+	0.526078i	−0.0303790	+	0.999538i	$0.509671\pi$
$104$	3.55656	+	0.627117i	0.348749	+	0.0614939i
$105$		0			0
$106$	1.39944	+	2.42389i	0.135925	+	0.235429i
$107$	−1.13008	+	1.95735i	−0.109249	+	0.189225i	−0.915466	−	0.402395i	$-0.868178\pi$
$107$	−1.13008	+	1.95735i	−0.109249	+	0.189225i	0.806217	+	0.591620i	$0.201511\pi$
$108$		0			0
$109$	−4.25449	+	11.6891i	−0.407507	+	1.11962i	0.550990	+	0.834512i	$0.314250\pi$
$109$	−4.25449	+	11.6891i	−0.407507	+	1.11962i	−0.958497	+	0.285103i	$0.907972\pi$
$110$	−0.460797	+	0.167716i	−0.0439353	+	0.0159911i
$111$		0			0
$112$	0.871969	+	4.94518i	0.0823933	+	0.467276i
$113$	−10.8537			−1.02103			−0.510514	−	0.859869i	$-0.670545\pi$
$113$	−10.8537			−1.02103			−0.510514	+	0.859869i	$0.670545\pi$
$114$		0			0
$115$	−0.929994			−0.0867224
$116$	1.24964	+	7.08707i	0.116026	+	0.658018i
$117$		0			0
$118$	9.59067	−	3.49072i	0.882893	−	0.321347i
$119$	8.81853	−	24.2287i	0.808393	−	2.22104i
$120$		0			0
$121$	0.952858	−	1.65040i	0.0866235	−	0.150036i
$122$	1.91131	+	3.31048i	0.173042	+	0.299717i
$123$		0			0
$124$	−4.17456	−	0.736088i	−0.374887	−	0.0661027i
$125$	−1.17992	+	0.681229i	−0.105536	+	0.0609310i
$126$		0			0
$127$	10.4784	−	12.4876i	0.929805	−	1.10810i	−0.0641088	−	0.997943i	$-0.520420\pi$
$127$	10.4784	−	12.4876i	0.929805	−	1.10810i	0.993914	−	0.110156i	$-0.0351351\pi$
$128$	−0.939693	−	0.342020i	−0.0830579	−	0.0302306i
$129$		0			0
$130$	0.377629	−	0.316868i	0.0331203	−	0.0277912i
$131$	−13.3343	+	2.35120i	−1.16503	+	0.205425i	−0.722526	−	0.691344i	$-0.757019\pi$
$131$	−13.3343	+	2.35120i	−1.16503	+	0.205425i	−0.442499	+	0.896769i	$0.645908\pi$
$132$		0			0
$133$	6.99641	−	20.7398i	0.606666	−	1.79837i
$134$			6.42145i			0.554729i
$135$		0			0
$136$	3.30051	+	3.93340i	0.283017	+	0.337286i
$137$	−0.996983	−	2.73919i	−0.0851780	−	0.234025i	0.889790	−	0.456370i	$-0.150851\pi$
$137$	−0.996983	−	2.73919i	−0.0851780	−	0.234025i	−0.974968	+	0.222346i	$0.928629\pi$
$138$		0			0
$139$	14.7330	+	12.3625i	1.24964	+	1.04857i	0.996707	+	0.0810850i	$0.0258385\pi$
$139$	14.7330	+	12.3625i	1.24964	+	1.04857i	0.252930	+	0.967485i	$0.418606\pi$
$140$	0.593601	+	0.342716i	0.0501684	+	0.0289647i
$141$		0			0
$142$	−2.64977	+	15.0276i	−0.222364	+	1.26109i
$143$	−2.25289	+	12.7768i	−0.188396	+	1.06845i
$144$		0			0
$145$	0.850705	+	0.491155i	0.0706472	+	0.0407882i
$146$	3.54200	+	2.97209i	0.293138	+	0.245972i
$147$		0			0
$148$	0.291692	+	0.801417i	0.0239769	+	0.0658761i
$149$	−8.33690	−	9.93553i	−0.682985	−	0.813950i	0.307503	−	0.951547i	$-0.400507\pi$
$149$	−8.33690	−	9.93553i	−0.682985	−	0.813950i	−0.990488	+	0.137597i	$0.956062\pi$
$150$		0			0
$151$			4.19318i			0.341236i	0.985337	+	0.170618i	$0.0545764\pi$
$151$			4.19318i			0.341236i	−0.985337	+	0.170618i	$0.945424\pi$
$152$	2.88023	+	3.27174i	0.233617	+	0.265373i
$153$		0			0
$154$	−17.7653	+	3.13251i	−1.43157	+	0.252425i
$155$	−0.443248	+	0.371929i	−0.0356025	+	0.0298741i
$156$		0			0
$157$	−6.46975	−	2.35480i	−0.516342	−	0.187933i	0.0706875	−	0.997499i	$-0.477481\pi$
$157$	−6.46975	−	2.35480i	−0.516342	−	0.187933i	−0.587030	+	0.809565i	$0.699703\pi$
$158$	−4.45498	+	5.30924i	−0.354419	+	0.422380i
$159$		0			0
$160$	−0.118213	+	0.0682501i	−0.00934552	+	0.00539564i
$161$	−33.6922	−	5.94085i	−2.65532	−	0.468204i
$162$		0			0
$163$	2.75667	+	4.77469i	0.215919	+	0.373983i	0.953556	−	0.301214i	$-0.0973919\pi$
$163$	2.75667	+	4.77469i	0.215919	+	0.373983i	−0.737637	+	0.675197i	$0.764059\pi$
$164$	1.70995	−	2.96171i	0.133524	−	0.231271i
$165$		0			0
$166$	0.548661	−	1.50743i	0.0425844	−	0.117000i
$167$	−2.77319	+	1.00936i	−0.214596	+	0.0781064i	−0.447081	−	0.894493i	$-0.647536\pi$
$167$	−2.77319	+	1.00936i	−0.214596	+	0.0781064i	0.232485	+	0.972600i	$0.425314\pi$
$168$		0			0
$169$	−0.00736016	−	0.0417415i	−0.000566166	−	0.00321089i
$170$	0.700885			0.0537554
$171$		0			0
$172$	−4.77635			−0.364193
$173$	−2.31080	−	13.1052i	−0.175687	−	0.996368i	−0.937348	−	0.348393i	$-0.886727\pi$
$173$	−2.31080	−	13.1052i	−0.175687	−	0.996368i	0.761662	−	0.647975i	$-0.224384\pi$
$174$		0			0
$175$	−23.5053	+	8.55522i	−1.77683	+	0.646714i
$176$	1.22869	−	3.37580i	0.0926161	−	0.254461i
$177$		0			0
$178$	−2.94524	+	5.10131i	−0.220755	+	0.382359i
$179$	−10.3499	−	17.9266i	−0.773590	−	1.33990i	−0.935584	−	0.353105i	$-0.885126\pi$
$179$	−10.3499	−	17.9266i	−0.773590	−	1.33990i	0.161994	−	0.986792i	$-0.448207\pi$
$180$		0			0
$181$	22.3567	+	3.94209i	1.66176	+	0.293013i	0.924098	−	0.382156i	$-0.124818\pi$
$181$	22.3567	+	3.94209i	1.66176	+	0.293013i	0.737663	+	0.675169i	$0.235929\pi$
$182$	15.7051	−	9.06733i	1.16414	−	0.672115i
$183$		0			0
$184$	4.37940	−	5.21917i	0.322854	−	0.384762i
$185$	0.109394	+	0.0398160i	0.00804278	+	0.00292733i
$186$		0			0
$187$	−14.1305	+	11.8569i	−1.03333	+	0.867065i
$188$	−6.64017	+	1.17084i	−0.484284	+	0.0853924i
$189$		0			0
$190$	0.594823	−	0.0141067i	0.0431530	−	0.00102341i
$191$			2.42275i			0.175304i	0.996151	+	0.0876518i	$0.0279363\pi$
$191$			2.42275i			0.175304i	−0.996151	+	0.0876518i	$0.972064\pi$
$192$		0			0
$193$	−13.0355	−	15.5351i	−0.938313	−	1.11824i	−0.992807	−	0.119723i	$-0.961799\pi$
$193$	−13.0355	−	15.5351i	−0.938313	−	1.11824i	0.0544947	−	0.998514i	$-0.482645\pi$
$194$	−1.90966	−	5.24675i	−0.137106	−	0.376694i
$195$		0			0
$196$	13.9536	+	11.7085i	0.996687	+	0.836319i
$197$	−13.7220	−	7.92240i	−0.977652	−	0.564448i	−0.0760915	−	0.997101i	$-0.524244\pi$
$197$	−13.7220	−	7.92240i	−0.977652	−	0.564448i	−0.901560	+	0.432653i	$0.857577\pi$
$198$		0			0
$199$	−3.80369	+	21.5718i	−0.269636	+	1.52918i	0.485864	+	0.874034i	$0.338505\pi$
$199$	−3.80369	+	21.5718i	−0.269636	+	1.52918i	−0.755500	+	0.655148i	$0.772606\pi$
$200$	0.865005	−	4.90569i	0.0611651	−	0.346885i
$201$		0			0
$202$	−2.47775	−	1.43053i	−0.174334	−	0.100652i
$203$	27.6822	+	23.2281i	1.94291	+	1.63029i
$204$		0			0
$205$	−0.159660	−	0.438663i	−0.0111512	−	0.0306376i
$206$	−6.86383	−	8.17999i	−0.478226	−	0.569927i
$207$		0			0
$208$			3.61142i			0.250407i
$209$	−11.7536	+	10.3471i	−0.813012	+	0.715722i
$210$		0			0
$211$	1.74189	−	0.307143i	0.119917	−	0.0211446i	−0.113368	−	0.993553i	$-0.536164\pi$
$211$	1.74189	−	0.307143i	0.119917	−	0.0211446i	0.233284	+	0.972409i	$0.425053\pi$
$212$	−2.14406	+	1.79908i	−0.147255	+	0.123561i
$213$		0			0
$214$	−2.12385	−	0.773020i	−0.145184	−	0.0528425i
$215$	−0.419080	+	0.499440i	−0.0285810	+	0.0340615i
$216$		0			0
$217$	−18.4341	+	10.6429i	−1.25139	+	0.722488i
$218$	−12.2503	−	2.16006i	−0.829697	−	0.146298i
$219$		0			0
$220$	−0.245185	−	0.424673i	−0.0165304	−	0.0286315i
$221$	9.27176	−	16.0592i	0.623686	−	1.08026i
$222$		0			0
$223$	2.45660	−	6.74945i	0.164506	−	0.451977i	−0.829861	−	0.557971i	$-0.811580\pi$
$223$	2.45660	−	6.74945i	0.164506	−	0.451977i	0.994367	+	0.105994i	$0.0338024\pi$
$224$	−4.71864	+	1.71744i	−0.315277	+	0.114752i
$225$		0			0
$226$	−1.88472	−	10.6888i	−0.125370	−	0.711008i
$227$	23.5253			1.56143			0.780714	−	0.624889i	$-0.214856\pi$
$227$	23.5253			1.56143			0.780714	+	0.624889i	$0.214856\pi$
$228$		0			0
$229$	−0.534218			−0.0353021			−0.0176511	−	0.999844i	$-0.505619\pi$
$229$	−0.534218			−0.0353021			−0.0176511	+	0.999844i	$0.505619\pi$
$230$	−0.161492	−	0.915866i	−0.0106485	−	0.0603904i
$231$		0			0
$232$	−6.76240	+	2.46131i	−0.443974	+	0.161593i
$233$	−9.67989	+	26.5953i	−0.634151	+	1.74231i	0.0352132	+	0.999380i	$0.488789\pi$
$233$	−9.67989	+	26.5953i	−0.634151	+	1.74231i	−0.669364	+	0.742935i	$0.733433\pi$
$234$		0			0
$235$	−0.460183	+	0.797061i	−0.0300190	+	0.0519945i
$236$	5.10309	+	8.83881i	0.332183	+	0.575358i
$237$		0			0
$238$	25.3919	+	4.47728i	1.64592	+	0.290219i
$239$	−10.4910	+	6.05698i	−0.678606	+	0.391794i	−0.799330	−	0.600893i	$-0.794812\pi$
$239$	−10.4910	+	6.05698i	−0.678606	+	0.391794i	0.120723	+	0.992686i	$0.461479\pi$
$240$		0			0
$241$	12.3500	−	14.7182i	0.795536	−	0.948083i	−0.203986	−	0.978974i	$-0.565390\pi$
$241$	12.3500	−	14.7182i	0.795536	−	0.948083i	0.999523	+	0.0308903i	$0.00983426\pi$
$242$	1.79079	+	0.651793i	0.115116	+	0.0418989i
$243$		0			0
$244$	−2.92829	+	2.45713i	−0.187465	+	0.157302i
$245$	2.44860	−	0.431754i	0.156435	−	0.0275837i
$246$		0			0
$247$	7.54548	−	13.8156i	0.480108	−	0.879066i
$248$		−	4.23896i		−	0.269174i
$249$		0			0
$250$	−0.875771	−	1.04370i	−0.0553886	−	0.0660096i
$251$	9.67564	+	26.5836i	0.610721	+	1.67794i	0.728621	+	0.684917i	$0.240161\pi$
$251$	9.67564	+	26.5836i	0.610721	+	1.67794i	−0.117900	+	0.993025i	$0.537616\pi$
$252$		0			0
$253$	18.7496	+	15.7328i	1.17878	+	0.989112i
$254$	14.1175	+	8.15073i	0.885809	+	0.511422i
$255$		0			0
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	1.22863	−	6.96791i	0.0766398	−	0.434646i	−0.922210	−	0.386690i	$-0.873618\pi$
$257$	1.22863	−	6.96791i	0.0766398	−	0.434646i	0.998849	−	0.0479557i	$-0.0152706\pi$
$258$		0			0
$259$	3.70881	+	2.14128i	0.230454	+	0.133053i
$260$	0.377629	+	0.316868i	0.0234196	+	0.0196513i
$261$		0			0
$262$	−4.63096	−	12.7235i	−0.286102	−	0.786058i
$263$	−7.85486	−	9.36106i	−0.484352	−	0.577228i	0.467420	−	0.884035i	$-0.345184\pi$
$263$	−7.85486	−	9.36106i	−0.484352	−	0.577228i	−0.951772	+	0.306808i	$0.900739\pi$
$264$		0			0
$265$			0.382046i			0.0234689i
$266$	21.6396	+	3.28869i	1.32681	+	0.201643i
$267$		0			0
$268$	−6.32389	+	1.11507i	−0.386293	+	0.0681139i
$269$	19.3684	−	16.2520i	1.18091	−	0.990901i	0.180937	−	0.983495i	$-0.442087\pi$
$269$	19.3684	−	16.2520i	1.18091	−	0.990901i	0.999973	−	0.00740578i	$-0.00235735\pi$
$270$		0			0
$271$	−0.498930	−	0.181596i	−0.0303078	−	0.0110311i	0.326822	−	0.945086i	$-0.394022\pi$
$271$	−0.498930	−	0.181596i	−0.0303078	−	0.0110311i	−0.357130	+	0.934055i	$0.616245\pi$
$272$	−3.30051	+	3.93340i	−0.200123	+	0.238497i
$273$		0			0
$274$	2.52445	−	1.45749i	0.152508	−	0.0880503i
$275$	17.6235	+	3.10749i	1.06273	+	0.187389i
$276$		0			0
$277$	−5.63747	−	9.76438i	−0.338722	−	0.586685i	0.645470	−	0.763785i	$-0.276661\pi$
$277$	−5.63747	−	9.76438i	−0.338722	−	0.586685i	−0.984193	+	0.177101i	$0.943328\pi$
$278$	−9.61628	+	16.6559i	−0.576746	+	0.998954i
$279$		0			0
$280$	−0.234431	+	0.644095i	−0.0140099	+	0.0384920i
$281$	28.9491	−	10.5366i	1.72696	−	0.628562i	0.728552	−	0.684990i	$-0.240194\pi$
$281$	28.9491	−	10.5366i	1.72696	−	0.628562i	0.998407	+	0.0564289i	$0.0179714\pi$
$282$		0			0
$283$	0.170286	+	0.965738i	0.0101224	+	0.0574072i	0.989451	−	0.144871i	$-0.0462767\pi$
$283$	0.170286	+	0.965738i	0.0101224	+	0.0574072i	−0.979328	+	0.202278i	$0.935166\pi$
$284$	−15.2594			−0.905481
$285$		0			0
$286$	−12.9739			−0.767161
$287$	−2.98204	−	16.9120i	−0.176024	−	0.998283i
$288$		0			0
$289$	8.80020	−	3.20301i	0.517659	−	0.188412i
$290$	−0.335970	+	0.923069i	−0.0197288	+	0.0542045i
$291$		0			0
$292$	−2.31188	+	4.00429i	−0.135292	+	0.234333i
$293$	10.7790	+	18.6698i	0.629717	+	1.09070i	0.987608	+	0.156938i	$0.0501623\pi$
$293$	10.7790	+	18.6698i	0.629717	+	1.09070i	−0.357892	+	0.933763i	$0.616504\pi$
$294$		0			0
$295$	1.37198	+	0.241917i	0.0798798	+	0.0140850i
$296$	−0.738590	+	0.426425i	−0.0429297	+	0.0247855i
$297$		0			0
$298$	8.33690	−	9.93553i	0.482944	−	0.575550i
$299$	−23.1213	−	8.41545i	−1.33714	−	0.486678i
$300$		0			0
$301$	−18.3730	+	15.4168i	−1.05900	+	0.888610i
$302$	−4.12948	+	0.728138i	−0.237625	+	0.0418996i
$303$		0			0
$304$	−2.72189	+	3.40460i	−0.156111	+	0.195267i
$305$			0.521787i			0.0298775i
$306$		0			0
$307$	−3.67412	−	4.37864i	−0.209693	−	0.249902i	0.650939	−	0.759130i	$-0.274375\pi$
$307$	−3.67412	−	4.37864i	−0.209693	−	0.249902i	−0.860632	+	0.509228i	$0.829931\pi$
$308$	−6.16983	−	16.9515i	−0.351559	−	0.965900i
$309$		0			0
$310$	−0.443248	−	0.371929i	−0.0251748	−	0.0211242i
$311$	−14.6645	−	8.46656i	−0.831548	−	0.480094i	0.0228345	−	0.999739i	$-0.492731\pi$
$311$	−14.6645	−	8.46656i	−0.831548	−	0.480094i	−0.854382	+	0.519645i	$0.826064\pi$
$312$		0			0
$313$	1.72542	−	9.78537i	0.0975268	−	0.553102i	−0.896417	−	0.443212i	$-0.853839\pi$
$313$	1.72542	−	9.78537i	0.0975268	−	0.553102i	0.993944	−	0.109890i	$-0.0350499\pi$
$314$	1.19556	−	6.78037i	0.0674694	−	0.382638i
$315$		0			0
$316$	−6.00218	−	3.46536i	−0.337649	−	0.194942i
$317$	22.2580	+	18.6767i	1.25013	+	1.04899i	0.996662	+	0.0816425i	$0.0260166\pi$
$317$	22.2580	+	18.6767i	1.25013	+	1.04899i	0.253471	+	0.967343i	$0.418428\pi$
$318$		0			0
$319$	−8.84215	−	24.2936i	−0.495065	−	1.36018i
$320$	−0.0877406	−	0.104565i	−0.00490485	−	0.00584537i
$321$		0			0
$322$		−	34.2120i		−	1.90656i
$323$	20.8444	−	8.15144i	1.15981	−	0.453558i
$324$		0			0
$325$	−17.7165	+	3.12390i	−0.982736	+	0.173283i
$326$	−4.22346	+	3.54391i	−0.233916	+	0.196279i
$327$		0			0
$328$	3.21365	+	1.16967i	0.177444	+	0.0645844i
$329$	−21.7634	+	25.9366i	−1.19985	+	1.42993i
$330$		0			0
$331$	7.09963	−	4.09897i	0.390231	−	0.225300i	−0.292029	−	0.956409i	$-0.594330\pi$
$331$	7.09963	−	4.09897i	0.390231	−	0.225300i	0.682260	+	0.731109i	$0.260997\pi$
$332$	1.57981	+	0.278563i	0.0867031	+	0.0152881i
$333$		0			0
$334$	−1.47558	−	2.55578i	−0.0807402	−	0.139846i
$335$	−0.438264	+	0.759096i	−0.0239449	+	0.0414738i
$336$		0			0
$337$	−0.164795	+	0.452771i	−0.00897697	+	0.0246640i	−0.944100	−	0.329659i	$-0.893066\pi$
$337$	−0.164795	+	0.452771i	−0.00897697	+	0.0246640i	0.935123	+	0.354323i	$0.115289\pi$
$338$	0.0398293	−	0.0144967i	0.00216643	−	0.000788516i
$339$		0			0
$340$	0.121707	+	0.690237i	0.00660051	+	0.0374334i
$341$	15.2283			0.824657
$342$		0			0
$343$	56.3165			3.04081
$344$	−0.829404	−	4.70379i	−0.0447185	−	0.253611i
$345$		0			0
$346$	12.5048	−	4.55138i	0.672263	−	0.244684i
$347$	3.16613	−	8.69887i	0.169967	−	0.466980i	−0.825239	−	0.564784i	$-0.808960\pi$
$347$	3.16613	−	8.69887i	0.169967	−	0.466980i	0.995206	+	0.0978040i	$0.0311818\pi$
$348$		0			0
$349$	−10.1245	+	17.5361i	−0.541951	+	0.938686i	0.456841	+	0.889548i	$0.348981\pi$
$349$	−10.1245	+	17.5361i	−0.541951	+	0.938686i	−0.998792	+	0.0491379i	$0.984353\pi$
$350$	−12.5069	−	21.6626i	−0.668521	−	1.15791i
$351$		0			0
$352$	3.53788	+	0.623823i	0.188569	+	0.0332499i
$353$	8.44596	−	4.87628i	0.449533	−	0.259538i	−0.258100	−	0.966118i	$-0.583096\pi$
$353$	8.44596	−	4.87628i	0.449533	−	0.259538i	0.707633	+	0.706580i	$0.249763\pi$
$354$		0			0
$355$	−1.33887	+	1.59561i	−0.0710600	+	0.0846860i
$356$	−5.53525	−	2.01466i	−0.293367	−	0.106777i
$357$		0			0
$358$	15.8570	−	13.3056i	0.838069	−	0.703223i
$359$	1.37537	−	0.242514i	0.0725891	−	0.0127994i	−0.137236	−	0.990538i	$-0.543822\pi$
$359$	1.37537	−	0.242514i	0.0725891	−	0.0127994i	0.209825	+	0.977739i	$0.432711\pi$
$360$		0			0
$361$	17.5260	−	7.33745i	0.922423	−	0.386182i
$362$			22.7016i			1.19317i
$363$		0			0
$364$	11.6567	+	13.8920i	0.610979	+	0.728136i
$365$	0.215864	+	0.593080i	0.0112988	+	0.0310432i
$366$		0			0
$367$	−7.38029	−	6.19280i	−0.385248	−	0.323262i	0.429510	−	0.903062i	$-0.358686\pi$
$367$	−7.38029	−	6.19280i	−0.385248	−	0.323262i	−0.814759	+	0.579800i	$0.803131\pi$
$368$	5.90035	+	3.40657i	0.307577	+	0.177580i
$369$		0			0
$370$	−0.0202151	+	0.114646i	−0.00105093	+	0.00596014i
$371$	−2.44053	+	13.8409i	−0.126706	+	0.718585i
$372$		0			0
$373$	18.1885	+	10.5011i	0.941765	+	0.543728i	0.890513	−	0.454957i	$-0.150346\pi$
$373$	18.1885	+	10.5011i	0.941765	+	0.543728i	0.0512520	+	0.998686i	$0.483679\pi$
$374$	−14.1305	−	11.8569i	−0.730673	−	0.613107i
$375$		0			0
$376$	−2.30611	−	6.33598i	−0.118928	−	0.326753i
$377$	16.7056	+	19.9089i	0.860381	+	1.02536i
$378$		0			0
$379$		−	2.87543i		−	0.147701i	−0.997269	−	0.0738506i	$-0.976471\pi$
$379$		−	2.87543i		−	0.147701i	0.997269	−	0.0738506i	$-0.0235288\pi$
$380$	0.117182	+	0.583337i	0.00601132	+	0.0299245i
$381$		0			0
$382$	−2.38594	+	0.420705i	−0.122075	+	0.0215252i
$383$	−2.77066	+	2.32486i	−0.141574	+	0.118795i	−0.710824	−	0.703369i	$-0.751678\pi$
$383$	−2.77066	+	2.32486i	−0.141574	+	0.118795i	0.569250	+	0.822164i	$0.307234\pi$
$384$		0			0
$385$	−2.31388	−	0.842183i	−0.117926	−	0.0429216i
$386$	13.0355	−	15.5351i	0.663487	−	0.790713i
$387$		0			0
$388$	4.83543	−	2.79173i	0.245482	−	0.141729i
$389$	−3.28260	−	0.578811i	−0.166434	−	0.0293469i	0.0898099	−	0.995959i	$-0.471374\pi$
$389$	−3.28260	−	0.578811i	−0.166434	−	0.0293469i	−0.256244	+	0.966612i	$0.582485\pi$
$390$		0			0
$391$	−17.4917	−	30.2964i	−0.884591	−	1.53216i
$392$	−9.10757	+	15.7748i	−0.460002	+	0.796747i
$393$		0			0
$394$	5.41924	−	14.8892i	0.273017	−	0.750109i
$395$	−0.888991	+	0.323566i	−0.0447300	+	0.0162804i
$396$		0			0
$397$	−1.36071	−	7.71696i	−0.0682920	−	0.387303i	−0.999726	−	0.0233937i	$-0.992553\pi$
$397$	−1.36071	−	7.71696i	−0.0682920	−	0.387303i	0.931434	−	0.363909i	$-0.118558\pi$
$398$	−21.9046			−1.09798
$399$		0			0
$400$	4.98137			0.249068
$401$	−1.60123	−	9.08105i	−0.0799618	−	0.453486i	−0.998330	−	0.0577600i	$-0.981604\pi$
$401$	−1.60123	−	9.08105i	−0.0799618	−	0.453486i	0.918369	−	0.395726i	$-0.129507\pi$
$402$		0			0
$403$	−14.3855	+	5.23588i	−0.716591	+	0.260818i
$404$	0.978539	−	2.68851i	0.0486842	−	0.133759i
$405$		0			0
$406$	−18.0682	+	31.2951i	−0.896712	+	1.55315i
$407$	−1.53191	−	2.65335i	−0.0759341	−	0.131522i
$408$		0			0
$409$	−36.6709	−	6.46607i	−1.81326	−	0.319727i	−0.838826	−	0.544400i	$-0.816757\pi$
$409$	−36.6709	−	6.46607i	−1.81326	−	0.319727i	−0.974434	+	0.224673i	$0.927868\pi$
$410$	0.404274	−	0.233408i	0.0199657	−	0.0115272i
$411$		0			0
$412$	6.86383	−	8.17999i	0.338157	−	0.402999i
$413$	48.1593	+	17.5285i	2.36976	+	0.862523i
$414$		0			0
$415$	0.167741	−	0.140751i	0.00823409	−	0.00690922i
$416$	−3.55656	+	0.627117i	−0.174375	+	0.0307470i
$417$		0			0
$418$	−12.2309	−	9.77827i	−0.598231	−	0.478271i
$419$		−	7.44965i		−	0.363939i	−0.983304	−	0.181970i	$-0.941753\pi$
$419$		−	7.44965i		−	0.363939i	0.983304	−	0.181970i	$-0.0582472\pi$
$420$		0			0
$421$	24.4503	+	29.1388i	1.19164	+	1.42014i	0.883267	+	0.468870i	$0.155339\pi$
$421$	24.4503	+	29.1388i	1.19164	+	1.42014i	0.308370	+	0.951267i	$0.400217\pi$
$422$	0.604953	+	1.66210i	0.0294487	+	0.0809095i
$423$		0			0
$424$	−2.14406	−	1.79908i	−0.104125	−	0.0873710i
$425$	−22.1510	−	12.7889i	−1.07448	−	0.620352i
$426$		0			0
$427$	−3.33320	+	18.9035i	−0.161305	+	0.914806i
$428$	0.392472	−	2.22582i	0.0189709	−	0.107589i
$429$		0			0
$430$	−0.564625	−	0.325986i	−0.0272286	−	0.0157204i
$431$	−26.0302	−	21.8420i	−1.25383	−	1.05209i	−0.996311	−	0.0858183i	$-0.972650\pi$
$431$	−26.0302	−	21.8420i	−1.25383	−	1.05209i	−0.257522	−	0.966272i	$-0.582906\pi$
$432$		0			0
$433$	−0.158394	−	0.435184i	−0.00761193	−	0.0209136i	0.935828	−	0.352456i	$-0.114653\pi$
$433$	−0.158394	−	0.435184i	−0.00761193	−	0.0209136i	−0.943440	+	0.331542i	$0.892431\pi$
$434$	−13.6823	−	16.3059i	−0.656770	−	0.782708i
$435$		0			0
$436$		−	12.4393i		−	0.595735i
$437$	−15.4545	−	25.3598i	−0.739289	−	1.21312i
$438$		0			0
$439$	−17.4342	+	3.07412i	−0.832089	+	0.146720i	−0.573436	−	0.819250i	$-0.694390\pi$
$439$	−17.4342	+	3.07412i	−0.832089	+	0.146720i	−0.258653	+	0.965970i	$0.583279\pi$
$440$	0.375645	−	0.315204i	0.0179082	−	0.0150268i
$441$		0			0
$442$	17.4252	+	6.34226i	0.828833	+	0.301670i
$443$	−19.7271	+	23.5099i	−0.937264	+	1.11699i	0.0556857	+	0.998448i	$0.482266\pi$
$443$	−19.7271	+	23.5099i	−0.937264	+	1.11699i	−0.992949	+	0.118539i	$0.962179\pi$
$444$		0			0
$445$	−0.696330	+	0.402026i	−0.0330092	+	0.0190579i
$446$	7.07350	+	1.24725i	0.334940	+	0.0590589i
$447$		0			0
$448$	−2.51073	−	4.34872i	−0.118621	−	0.205458i
$449$	2.84947	−	4.93543i	0.134475	−	0.232917i	−0.790922	−	0.611917i	$-0.790399\pi$
$449$	2.84947	−	4.93543i	0.134475	−	0.232917i	0.925397	+	0.379000i	$0.123732\pi$
$450$		0			0
$451$	−4.20199	+	11.5449i	−0.197864	+	0.543627i
$452$	10.1991	−	3.71218i	0.479726	−	0.174606i
$453$		0			0
$454$	4.08512	+	23.1679i	0.191724	+	1.08732i
$455$	2.47538			0.116048
$456$		0			0
$457$	26.1284			1.22224			0.611118	−	0.791540i	$-0.290720\pi$
$457$	26.1284			1.22224			0.611118	+	0.791540i	$0.290720\pi$
$458$	−0.0927660	−	0.526102i	−0.00433467	−	0.0245831i
$459$		0			0
$460$	0.873909	−	0.318077i	0.0407462	−	0.0148304i
$461$	5.02602	−	13.8089i	0.234085	−	0.643143i	−0.765915	−	0.642942i	$-0.777714\pi$
$461$	5.02602	−	13.8089i	0.234085	−	0.643143i	1.00000		0.000201404i	$-6.41089e-5\pi$
$462$		0			0
$463$	6.76150	−	11.7113i	0.314233	−	0.544268i	−0.665041	−	0.746807i	$-0.731586\pi$
$463$	6.76150	−	11.7113i	0.314233	−	0.544268i	0.979274	+	0.202539i	$0.0649192\pi$
$464$	−3.59820	−	6.23226i	−0.167042	−	0.289326i
$465$		0			0
$466$	−27.8721	−	4.91461i	−1.29115	−	0.227665i
$467$	1.81507	−	1.04793i	0.0839913	−	0.0484924i	−0.457416	−	0.889253i	$-0.651225\pi$
$467$	1.81507	−	1.04793i	0.0839913	−	0.0484924i	0.541407	+	0.840760i	$0.317892\pi$
$468$		0			0
$469$	−20.7268	+	24.7012i	−0.957073	+	1.14059i
$470$	−0.864862	−	0.314784i	−0.0398931	−	0.0145199i
$471$		0			0
$472$	−7.81839	+	6.56041i	−0.359871	+	0.301967i
$473$	16.8981	−	2.97960i	0.776977	−	0.137002i
$474$		0			0
$475$	−19.0564	−	10.4078i	−0.874366	−	0.477541i
$476$			25.7837i			1.18179i
$477$		0			0
$478$	−7.78671	−	9.27984i	−0.356156	−	0.424450i
$479$	6.33708	+	17.4110i	0.289549	+	0.795528i	0.996130	+	0.0878961i	$0.0280143\pi$
$479$	6.33708	+	17.4110i	0.289549	+	0.795528i	−0.706581	+	0.707632i	$0.749763\pi$
$480$		0			0
$481$	2.35942	+	1.97979i	0.107580	+	0.0902706i
$482$	16.6392	+	9.60663i	0.757894	+	0.437570i
$483$		0			0
$484$	−0.330924	+	1.87676i	−0.0150420	+	0.0853075i
$485$	0.132345	−	0.750566i	0.00600947	−	0.0340814i
$486$		0			0
$487$	24.6299	+	14.2201i	1.11609	+	0.644374i	0.940399	−	0.340072i	$-0.110452\pi$
$487$	24.6299	+	14.2201i	1.11609	+	0.644374i	0.175688	+	0.984446i	$0.443785\pi$
$488$	−2.92829	−	2.45713i	−0.132558	−	0.111229i
$489$		0			0
$490$	0.850389	+	2.33642i	0.0384166	+	0.105549i
$491$	0.594649	+	0.708675i	0.0268361	+	0.0319821i	0.779296	−	0.626657i	$-0.215577\pi$
$491$	0.594649	+	0.708675i	0.0268361	+	0.0319821i	−0.752459	+	0.658639i	$0.771133\pi$
$492$		0			0
$493$			36.9512i			1.66420i
$494$	14.9160	+	5.03179i	0.671102	+	0.226391i
$495$		0			0
$496$	4.17456	−	0.736088i	0.187443	−	0.0330513i
$497$	−58.6980	+	49.2535i	−2.63297	+	2.20932i
$498$		0			0
$499$	25.3488	+	9.22619i	1.13477	+	0.413021i	0.840020	−	0.542555i	$-0.182543\pi$
$499$	25.3488	+	9.22619i	1.13477	+	0.413021i	0.294746	+	0.955576i	$0.404765\pi$
$500$	0.875771	−	1.04370i	0.0391657	−	0.0466758i
$501$		0			0
$502$	−24.4996	+	14.1448i	−1.09347	+	0.631315i
$503$	20.8654	+	3.67913i	0.930340	+	0.164044i	0.618226	−	0.786000i	$-0.287852\pi$
$503$	20.8654	+	3.67913i	0.930340	+	0.164044i	0.312114	+	0.950045i	$0.398963\pi$
$504$		0			0
$505$	−0.195267	−	0.338213i	−0.00868928	−	0.0150503i
$506$	−12.2379	+	21.1967i	−0.544043	+	0.942310i
$507$		0			0
$508$	−5.57543	+	15.3184i	−0.247370	+	0.679642i
$509$	34.0484	−	12.3926i	1.50917	−	0.549292i	0.550753	−	0.834669i	$-0.314341\pi$
$509$	34.0484	−	12.3926i	1.50917	−	0.549292i	0.958416	+	0.285376i	$0.0921186\pi$
$510$		0			0
$511$	4.03177	+	22.8653i	0.178355	+	1.01150i
$512$	1.00000			0.0441942
$513$		0			0
$514$	7.07540			0.312082
$515$	−0.253106	−	1.43543i	−0.0111532	−	0.0632528i
$516$		0			0
$517$	22.7617	−	8.28458i	1.00106	−	0.364355i
$518$	−1.46472	+	4.02429i	−0.0643562	+	0.176817i
$519$		0			0
$520$	−0.246480	+	0.426916i	−0.0108089	+	0.0187215i
$521$	−15.4645	−	26.7854i	−0.677514	−	1.17349i	−0.975727	−	0.218989i	$-0.929724\pi$
$521$	−15.4645	−	26.7854i	−0.677514	−	1.17349i	0.298213	−	0.954499i	$-0.403609\pi$
$522$		0			0
$523$	−37.4570	−	6.60468i	−1.63788	−	0.288803i	−0.722494	−	0.691378i	$-0.757004\pi$
$523$	−37.4570	−	6.60468i	−1.63788	−	0.288803i	−0.915387	+	0.402575i	$0.868115\pi$
$524$	11.7260	−	6.77001i	0.512253	−	0.295749i
$525$		0			0
$526$	7.85486	−	9.36106i	0.342488	−	0.408162i
$527$	−20.4531	−	7.44432i	−0.890951	−	0.324280i
$528$		0			0
$529$	−17.9399	+	15.0534i	−0.779996	+	0.654494i
$530$	−0.376242	+	0.0663416i	−0.0163429	+	0.00288170i
$531$		0			0
$532$	0.518946	+	21.8819i	0.0224992	+	0.948702i
$533$		−	12.3507i		−	0.534968i
$534$		0			0
$535$	−0.198308	−	0.236334i	−0.00857358	−	0.0102176i
$536$	−2.19627	−	6.03419i	−0.0948642	−	0.260637i
$537$		0			0
$538$	19.3684	+	16.2520i	0.835029	+	0.700672i
$539$	−56.6702	−	32.7185i	−2.44096	−	1.40929i
$540$		0			0
$541$	5.56860	−	31.5811i	0.239413	−	1.35778i	−0.593706	−	0.804682i	$-0.702336\pi$
$541$	5.56860	−	31.5811i	0.239413	−	1.35778i	0.833118	−	0.553095i	$-0.186553\pi$
$542$	0.0921985	−	0.522884i	0.00396026	−	0.0224598i
$543$		0			0
$544$	−4.44677	−	2.56734i	−0.190654	−	0.110074i
$545$	−1.30072	−	1.09143i	−0.0557166	−	0.0467518i
$546$		0			0
$547$	−0.117215	−	0.322046i	−0.00501176	−	0.0137697i	0.937162	−	0.348896i	$-0.113443\pi$
$547$	−0.117215	−	0.322046i	−0.00501176	−	0.0137697i	−0.942173	+	0.335126i	$0.891221\pi$
$548$	1.87371	+	2.23301i	0.0800411	+	0.0953893i
$549$		0			0
$550$			17.8953i			0.763059i
$551$	0.743715	+	31.3596i	0.0316833	+	1.33596i
$552$		0			0
$553$	−34.2737	+	6.04337i	−1.45746	+	0.256990i
$554$	8.63710	−	7.24739i	0.366955	−	0.307912i
$555$		0			0
$556$	−18.0727	−	6.57792i	−0.766453	−	0.278966i
$557$	10.0448	−	11.9709i	0.425611	−	0.507223i	−0.510040	−	0.860151i	$-0.670369\pi$
$557$	10.0448	−	11.9709i	0.425611	−	0.507223i	0.935651	+	0.352928i	$0.114814\pi$
$558$		0			0
$559$	−14.9384	+	8.62471i	−0.631829	+	0.364786i
$560$	−0.675018	−	0.119024i	−0.0285247	−	0.00502968i
$561$		0			0
$562$	15.4035	+	26.6796i	0.649757	+	1.12541i
$563$	3.43337	−	5.94678i	0.144699	−	0.250627i	−0.784561	−	0.620051i	$-0.787112\pi$
$563$	3.43337	−	5.94678i	0.144699	−	0.250627i	0.929261	+	0.369424i	$0.120445\pi$
$564$		0			0
$565$	0.506713	−	1.39218i	0.0213176	−	0.0585695i
$566$	−0.921496	+	0.335397i	−0.0387334	+	0.0140978i
$567$		0			0
$568$	−2.64977	−	15.0276i	−0.111182	−	0.630545i
$569$	24.4652			1.02563			0.512817	−	0.858498i	$-0.328602\pi$
$569$	24.4652			1.02563			0.512817	+	0.858498i	$0.328602\pi$
$570$		0			0
$571$	−9.07578			−0.379810			−0.189905	−	0.981803i	$-0.560818\pi$
$571$	−9.07578			−0.379810			−0.189905	+	0.981803i	$0.560818\pi$
$572$	−2.25289	−	12.7768i	−0.0941980	−	0.534224i
$573$		0			0
$574$	16.1372	−	5.87347i	0.673555	−	0.245154i
$575$	−11.6077	+	31.8920i	−0.484076	+	1.32999i
$576$		0			0
$577$	0.184936	−	0.320318i	0.00769897	−	0.0133350i	−0.862150	−	0.506653i	$-0.830883\pi$
$577$	0.184936	−	0.320318i	0.00769897	−	0.0133350i	0.869849	+	0.493318i	$0.164216\pi$
$578$	4.68249	+	8.11031i	0.194766	+	0.337344i
$579$		0			0
$580$	−0.967386	−	0.170576i	−0.0401685	−	0.00708279i
$581$	6.97612	−	4.02766i	0.289418	−	0.167096i
$582$		0			0
$583$	6.46311	−	7.70243i	0.267675	−	0.319002i
$584$	−4.34491	−	1.58142i	−0.179794	−	0.0654395i
$585$		0			0
$586$	−16.5144	+	13.8572i	−0.682204	+	0.572437i
$587$	5.26876	−	0.929025i	0.217465	−	0.0383449i	−0.0638540	−	0.997959i	$-0.520339\pi$
$587$	5.26876	−	0.929025i	0.217465	−	0.0383449i	0.281319	+	0.959614i	$0.409228\pi$
$588$		0			0
$589$	−17.5079	−	5.90614i	−0.721398	−	0.243358i
$590$			1.39315i			0.0573549i
$591$		0			0
$592$	−0.548202	−	0.653321i	−0.0225310	−	0.0268513i
$593$	−9.96880	−	27.3891i	−0.409370	−	1.12473i	−0.957523	−	0.288356i	$-0.906891\pi$
$593$	−9.96880	−	27.3891i	−0.409370	−	1.12473i	0.548154	−	0.836378i	$-0.315331\pi$
$594$		0			0
$595$	2.69607	+	2.26227i	0.110528	+	0.0927442i
$596$	11.2323	+	6.48496i	0.460092	+	0.265634i
$597$		0			0
$598$	4.27264	−	24.2313i	0.174721	−	0.990893i
$599$	−0.982727	+	5.57332i	−0.0401531	+	0.227720i	−0.998280	−	0.0586238i	$-0.981329\pi$
$599$	−0.982727	+	5.57332i	−0.0401531	+	0.227720i	0.958127	+	0.286344i	$0.0924399\pi$
$600$		0			0
$601$	9.28297	+	5.35952i	0.378660	+	0.218620i	0.677235	−	0.735767i	$-0.263178\pi$
$601$	9.28297	+	5.35952i	0.378660	+	0.218620i	−0.298575	+	0.954386i	$0.596511\pi$
$602$	−18.3730	−	15.4168i	−0.748829	−	0.628342i
$603$		0			0
$604$	−1.43415	−	3.94030i	−0.0583548	−	0.160329i
$605$	0.167209	+	0.199272i	0.00679800	+	0.00810154i
$606$		0			0
$607$		−	2.58035i		−	0.104733i	−0.998628	−	0.0523665i	$-0.983324\pi$
$607$		−	2.58035i		−	0.104733i	0.998628	−	0.0523665i	$-0.0166764\pi$
$608$	−3.82553	−	2.08934i	−0.155146	−	0.0847338i
$609$		0			0
$610$	−0.513860	+	0.0906074i	−0.0208056	+	0.00366859i
$611$	−18.6535	+	15.6521i	−0.754640	+	0.633218i
$612$		0			0
$613$	−7.40442	−	2.69499i	−0.299062	−	0.108850i	0.188131	−	0.982144i	$-0.439757\pi$
$613$	−7.40442	−	2.69499i	−0.299062	−	0.108850i	−0.487193	+	0.873294i	$0.661979\pi$
$614$	3.67412	−	4.37864i	0.148275	−	0.176708i
$615$		0			0
$616$	15.6226	−	9.01969i	0.629451	−	0.363414i
$617$	−15.0528	−	2.65421i	−0.606001	−	0.106854i	−0.137776	−	0.990463i	$-0.543995\pi$
$617$	−15.0528	−	2.65421i	−0.606001	−	0.106854i	−0.468225	+	0.883609i	$0.655106\pi$
$618$		0			0
$619$	−23.8851	−	41.3701i	−0.960021	−	1.66281i	−0.722434	−	0.691440i	$-0.756977\pi$
$619$	−23.8851	−	41.3701i	−0.960021	−	1.66281i	−0.237587	−	0.971366i	$-0.576357\pi$
$620$	0.289310	−	0.501099i	0.0116189	−	0.0201246i
$621$		0			0
$622$	5.79147	−	15.9119i	0.232217	−	0.638010i
$623$	−27.7951	+	10.1166i	−1.11359	+	0.405312i
$624$		0			0
$625$	4.29273	+	24.3453i	0.171709	+	0.973812i
$626$	9.93632			0.397135
$627$		0			0
$628$	6.88497			0.274740
$629$	0.760426	+	4.31259i	0.0303202	+	0.171954i
$630$		0			0
$631$	−7.99316	+	2.90927i	−0.318202	+	0.115816i	−0.496183	−	0.868218i	$-0.665266\pi$
$631$	−7.99316	+	2.90927i	−0.318202	+	0.115816i	0.177981	+	0.984034i	$0.443043\pi$
$632$	2.37045	−	6.51275i	0.0942913	−	0.259063i
$633$		0			0
$634$	−14.5279	+	25.1630i	−0.576975	+	0.999350i
$635$	1.11258	+	1.92704i	0.0441512	+	0.0764721i
$636$		0			0
$637$	64.7832	+	11.4230i	2.56681	+	0.452597i
$638$	22.3891	−	12.9264i	0.886394	−	0.511760i
$639$		0			0
$640$	0.0877406	−	0.104565i	0.00346825	−	0.00413330i
$641$	−0.712852	−	0.259457i	−0.0281559	−	0.0102479i	0.327904	−	0.944711i	$-0.393658\pi$
$641$	−0.712852	−	0.259457i	−0.0281559	−	0.0102479i	−0.356060	+	0.934463i	$0.615880\pi$
$642$		0			0
$643$	24.6624	−	20.6942i	0.972591	−	0.816101i	−0.0103641	−	0.999946i	$-0.503299\pi$
$643$	24.6624	−	20.6942i	0.972591	−	0.816101i	0.982955	+	0.183845i	$0.0588546\pi$
$644$	33.6922	−	5.94085i	1.32766	−	0.234102i
$645$		0			0
$646$	11.6472	+	19.1122i	0.458253	+	0.751961i
$647$		−	9.88512i		−	0.388624i	−0.980940	−	0.194312i	$-0.937753\pi$
$647$		−	9.88512i		−	0.388624i	0.980940	−	0.194312i	$-0.0622474\pi$
$648$		0			0
$649$	−23.5680	−	28.0872i	−0.925123	−	1.10252i
$650$	−6.15289	−	16.9049i	−0.241336	−	0.663065i
$651$		0			0
$652$	−4.22346	−	3.54391i	−0.165404	−	0.138790i
$653$	18.2549	+	10.5395i	0.714368	+	0.412441i	0.812676	−	0.582715i	$-0.198010\pi$
$653$	18.2549	+	10.5395i	0.714368	+	0.412441i	−0.0983080	+	0.995156i	$0.531343\pi$
$654$		0			0
$655$	0.320939	−	1.82014i	0.0125401	−	0.0711186i
$656$	−0.593858	+	3.36794i	−0.0231863	+	0.131496i
$657$		0			0
$658$	−29.3217	−	16.9289i	−1.14308	−	0.659957i
$659$	3.22064	+	2.70244i	0.125458	+	0.105272i	0.703358	−	0.710836i	$-0.251683\pi$
$659$	3.22064	+	2.70244i	0.125458	+	0.105272i	−0.577900	+	0.816108i	$0.696128\pi$
$660$		0			0
$661$	−1.34653	−	3.69957i	−0.0523741	−	0.143897i	0.910747	−	0.412964i	$-0.135507\pi$
$661$	−1.34653	−	3.69957i	−0.0523741	−	0.143897i	−0.963121	+	0.269068i	$0.913284\pi$
$662$	5.26954	+	6.27999i	0.204806	+	0.244079i
$663$		0			0
$664$			1.60418i			0.0622542i
$665$	2.33362	+	1.86567i	0.0904939	+	0.0723475i
$666$		0			0
$667$	48.2852	−	8.51398i	1.86961	−	0.329663i
$668$	2.26072	−	1.89697i	0.0874699	−	0.0733960i
$669$		0			0
$670$	−0.823668	−	0.299790i	−0.0318211	−	0.0115819i
$671$	8.82712	−	10.5198i	0.340767	−	0.406111i
$672$		0			0
$673$	30.0889	−	17.3719i	1.15984	−	0.669636i	0.208577	−	0.978006i	$-0.433117\pi$
$673$	30.0889	−	17.3719i	1.15984	−	0.669636i	0.951266	+	0.308370i	$0.0997835\pi$
$674$	−0.474509	−	0.0836688i	−0.0182774	−	0.00322280i
$675$		0			0
$676$	0.0211927	+	0.0367069i	0.000815105	+	0.00141180i
$677$	3.64635	−	6.31567i	0.140141	−	0.242731i	−0.787409	−	0.616431i	$-0.788578\pi$
$677$	3.64635	−	6.31567i	0.140141	−	0.242731i	0.927549	+	0.373700i	$0.121911\pi$
$678$		0			0
$679$	9.58929	−	26.3464i	0.368003	−	1.01108i
$680$	−0.658616	+	0.239717i	−0.0252568	+	0.00919272i
$681$		0			0
$682$	2.64436	+	14.9969i	0.101258	+	0.574262i
$683$	−23.0454			−0.881809			−0.440904	−	0.897554i	$-0.645342\pi$
$683$	−23.0454			−0.881809			−0.440904	+	0.897554i	$0.645342\pi$
$684$		0			0
$685$	0.397896			0.0152028
$686$	9.77926	+	55.4609i	0.373374	+	2.11751i
$687$		0			0
$688$	4.48830	−	1.63361i	0.171115	−	0.0622807i
$689$	−3.45711	+	9.49833i	−0.131705	+	0.361858i
$690$		0			0
$691$	13.3725	−	23.1619i	0.508714	−	0.881119i	−0.491235	−	0.871027i	$-0.663454\pi$
$691$	13.3725	−	23.1619i	0.508714	−	0.881119i	0.999949	−	0.0100920i	$-0.00321243\pi$
$692$	6.65367	+	11.5245i	0.252935	+	0.438096i
$693$		0			0
$694$	9.11650	+	1.60749i	0.346058	+	0.0610193i
$695$	−2.27353	+	1.31262i	−0.0862399	+	0.0497907i
$696$		0			0
$697$	11.2874	−	13.4518i	0.427541	−	0.509523i
$698$	−19.0278	−	6.92555i	−0.720212	−	0.262136i
$699$		0			0
$700$	19.1617	−	16.0785i	0.724243	−	0.607712i
$701$	−22.5009	+	3.96751i	−0.849846	+	0.149851i	−0.581575	−	0.813493i	$-0.697563\pi$
$701$	−22.5009	+	3.96751i	−0.849846	+	0.149851i	−0.268271	+	0.963343i	$0.586452\pi$
$702$		0			0
$703$	0.732153	+	3.64468i	0.0276137	+	0.137462i
$704$			3.59245i			0.135396i
$705$		0			0
$706$	6.26882	+	7.47089i	0.235930	+	0.281171i
$707$	−4.91370	−	13.5003i	−0.184799	−	0.507731i
$708$		0			0
$709$	−15.5025	−	13.0081i	−0.582208	−	0.488531i	0.303463	−	0.952843i	$-0.401857\pi$
$709$	−15.5025	−	13.0081i	−0.582208	−	0.488531i	−0.885672	+	0.464312i	$0.846302\pi$
$710$	−1.80386	−	1.04146i	−0.0676976	−	0.0390852i
$711$		0			0
$712$	1.02287	−	5.80100i	0.0383338	−	0.217402i
$713$	−5.01507	+	28.4419i	−0.187816	+	1.06516i
$714$		0			0
$715$	−1.53367	−	0.885467i	−0.0573562	−	0.0331146i
$716$	15.8570	+	13.3056i	0.592604	+	0.497254i
$717$		0			0
$718$	0.477660	+	1.31236i	0.0178261	+	0.0489769i
$719$	14.9828	+	17.8557i	0.558762	+	0.665907i	0.969284	−	0.245944i	$-0.0790978\pi$
$719$	14.9828	+	17.8557i	0.558762	+	0.665907i	−0.410522	+	0.911851i	$0.634653\pi$
$720$		0			0
$721$		−	53.6204i		−	1.99693i
$722$	10.2693	+	15.9856i	0.382185	+	0.594924i
$723$		0			0
$724$	−22.3567	+	3.94209i	−0.830880	+	0.146507i
$725$	27.4611	−	23.0426i	1.01988	−	0.855780i
$726$		0			0
$727$	−22.1905	−	8.07667i	−0.822999	−	0.299547i	−0.104017	−	0.994576i	$-0.533170\pi$
$727$	−22.1905	−	8.07667i	−0.822999	−	0.299547i	−0.718982	+	0.695028i	$0.755392\pi$
$728$	−11.6567	+	13.8920i	−0.432027	+	0.514870i
$729$		0			0
$730$	−0.546586	+	0.315572i	−0.0202301	+	0.0116798i
$731$	−24.1525	−	4.25873i	−0.893311	−	0.157515i
$732$		0			0
$733$	19.0248	+	32.9519i	0.702697	+	1.21711i	0.967516	+	0.252809i	$0.0813544\pi$
$733$	19.0248	+	32.9519i	0.702697	+	1.21711i	−0.264819	+	0.964298i	$0.585312\pi$
$734$	4.81714	−	8.34354i	0.177804	−	0.307966i
$735$		0			0
$736$	−2.33023	+	6.40226i	−0.0858935	+	0.235990i
$737$	21.6775	−	7.88998i	0.798502	−	0.290631i
$738$		0			0
$739$	−0.653731	−	3.70749i	−0.0240479	−	0.136382i	0.970420	−	0.241423i	$-0.0776140\pi$
$739$	−0.653731	−	3.70749i	−0.0240479	−	0.136382i	−0.994468	+	0.105040i	$0.966503\pi$
$740$	−0.116414			−0.00427947
$741$		0			0
$742$	−14.0544			−0.515955
$743$	−7.46064	−	42.3114i	−0.273704	−	1.55225i	−0.743047	−	0.669239i	$-0.766620\pi$
$743$	−7.46064	−	42.3114i	−0.273704	−	1.55225i	0.469343	−	0.883016i	$-0.344491\pi$
$744$		0			0
$745$	1.66363	−	0.605511i	0.0609506	−	0.0221842i
$746$	−7.18320	+	19.7357i	−0.262996	+	0.722575i
$747$		0			0
$748$	9.22305	−	15.9748i	0.337228	−	0.584097i
$749$	−5.67466	−	9.82879i	−0.207347	−	0.359136i
$750$		0			0
$751$	−7.98396	−	1.40779i	−0.291339	−	0.0513709i	0.0260686	−	0.999660i	$-0.491701\pi$
$751$	−7.98396	−	1.40779i	−0.291339	−	0.0513709i	−0.317407	+	0.948289i	$0.602812\pi$
$752$	5.83927	−	3.37130i	0.212936	−	0.122939i
$753$		0			0
$754$	−16.7056	+	19.9089i	−0.608381	+	0.725040i
$755$	−0.537851	−	0.195762i	−0.0195744	−	0.00712450i
$756$		0			0
$757$	−27.2362	+	22.8539i	−0.989917	+	0.830639i	−0.985556	−	0.169351i	$-0.945833\pi$
$757$	−27.2362	+	22.8539i	−0.989917	+	0.830639i	−0.00436167	+	0.999990i	$0.501388\pi$
$758$	2.83175	−	0.499314i	0.102854	−	0.0181359i
$759$		0			0
$760$	−0.554126	+	0.216697i	−0.0201003	+	0.00786044i
$761$		−	39.5085i		−	1.43218i	−0.698007	−	0.716091i	$-0.745929\pi$
$761$		−	39.5085i		−	1.43218i	0.698007	−	0.716091i	$-0.254071\pi$
$762$		0			0
$763$	−40.1508	−	47.8499i	−1.45356	−	1.73228i
$764$	−0.828628	−	2.27664i	−0.0299787	−	0.0823658i
$765$		0			0
$766$	−2.77066	−	2.32486i	−0.100108	−	0.0840006i
$767$	31.9207	+	18.4294i	1.15259	+	0.665448i
$768$		0			0
$769$	−5.64622	+	32.0213i	−0.203608	+	1.15472i	0.696007	+	0.718035i	$0.254958\pi$
$769$	−5.64622	+	32.0213i	−0.203608	+	1.15472i	−0.899615	+	0.436684i	$0.856153\pi$
$770$	0.427588	−	2.42497i	0.0154092	−	0.0873898i
$771$		0			0
$772$	17.5626	+	10.1398i	0.632093	+	0.364939i
$773$	17.3760	+	14.5802i	0.624970	+	0.524412i	0.899361	−	0.437206i	$-0.144032\pi$
$773$	17.3760	+	14.5802i	0.624970	+	0.524412i	−0.274391	+	0.961618i	$0.588476\pi$
$774$		0			0
$775$	7.22204	+	19.8424i	0.259423	+	0.712760i
$776$	3.58898	+	4.27719i	0.128837	+	0.153542i
$777$		0			0
$778$		−	3.33324i		−	0.119502i
$779$	9.30858	−	11.6434i	0.333514	−	0.417167i
$780$		0			0
$781$	53.9860	−	9.51919i	1.93177	−	0.340623i
$782$	26.7988	−	22.4868i	0.958322	−	0.804128i
$783$		0			0
$784$	−17.1166	−	6.22995i	−0.611309	−	0.222498i
$785$	0.604091	−	0.719927i	0.0215609	−	0.0256953i
$786$		0			0
$787$	12.3080	−	7.10603i	0.438733	−	0.253303i	−0.264327	−	0.964433i	$-0.585150\pi$
$787$	12.3080	−	7.10603i	0.438733	−	0.253303i	0.703060	+	0.711131i	$0.251817\pi$
$788$	15.6041	+	2.75142i	0.555872	+	0.0980153i
$789$		0			0
$790$	−0.473022	−	0.819298i	−0.0168294	−	0.0291493i
$791$	27.2507	−	47.1996i	0.968924	−	1.67823i
$792$		0			0
$793$	−4.72162	+	12.9725i	−0.167670	+	0.460668i
$794$	7.36344	−	2.68007i	0.261319	−	0.0951122i
$795$		0			0
$796$	−3.80369	−	21.5718i	−0.134818	−	0.764591i
$797$	−24.9960			−0.885405			−0.442702	−	0.896669i	$-0.645980\pi$
$797$	−24.9960			−0.885405			−0.442702	+	0.896669i	$0.645980\pi$
$798$		0			0
$799$	−34.6212			−1.22481
$800$	0.865005	+	4.90569i	0.0305826	+	0.173442i
$801$		0			0
$802$	8.66503	−	3.15381i	0.305973	−	0.111365i
$803$	5.68117	−	15.6089i	0.200484	−	0.550825i
$804$		0			0
$805$	2.33497	−	4.04428i	0.0822968	−	0.142542i
$806$	−7.65435	−	13.2577i	−0.269613	−	0.466983i
$807$		0			0
$808$	2.81759	+	0.496817i	0.0991225	+	0.0174780i
$809$	−35.0162	+	20.2166i	−1.23110	+	0.710778i	−0.967260	−	0.253787i	$-0.918324\pi$
$809$	−35.0162	+	20.2166i	−1.23110	+	0.710778i	−0.263844	+	0.964565i	$0.584990\pi$
$810$		0			0
$811$	16.6165	−	19.8028i	0.583485	−	0.695370i	−0.390855	−	0.920452i	$-0.627821\pi$
$811$	16.6165	−	19.8028i	0.583485	−	0.695370i	0.974340	+	0.225082i	$0.0722650\pi$
$812$	−33.9572	−	12.3594i	−1.19166	−	0.433730i
$813$		0			0
$814$	2.34703	−	1.96939i	0.0822632	−	0.0690271i
$815$	−0.741138	+	0.130683i	−0.0259609	+	0.00457761i
$816$		0			0
$817$	−20.5833	−	3.12816i	−0.720118	−	0.109440i
$818$		−	37.2366i		−	1.30195i
$819$		0			0
$820$	0.300063	+	0.357602i	0.0104787	+	0.0124880i
$821$	15.3364	+	42.1365i	0.535245	+	1.47057i	0.852751	+	0.522318i	$0.174932\pi$
$821$	15.3364	+	42.1365i	0.535245	+	1.47057i	−0.317506	+	0.948256i	$0.602845\pi$
$822$		0			0
$823$	23.2702	+	19.5260i	0.811148	+	0.680634i	0.950882	−	0.309555i	$-0.100180\pi$
$823$	23.2702	+	19.5260i	0.811148	+	0.680634i	−0.139733	+	0.990189i	$0.544624\pi$
$824$	9.24761	+	5.33911i	0.322156	+	0.185997i
$825$		0			0
$826$	−8.89947	+	50.4714i	−0.309652	+	1.75613i
$827$	−6.19896	+	35.1560i	−0.215559	+	1.22250i	0.664375	+	0.747399i	$0.268698\pi$
$827$	−6.19896	+	35.1560i	−0.215559	+	1.22250i	−0.879934	+	0.475096i	$0.842413\pi$
$828$		0			0
$829$	−7.76319	−	4.48208i	−0.269627	−	0.155669i	0.359091	−	0.933302i	$-0.383087\pi$
$829$	−7.76319	−	4.48208i	−0.269627	−	0.155669i	−0.628718	+	0.777633i	$0.716420\pi$
$830$	0.167741	+	0.140751i	0.00582238	+	0.00488555i
$831$		0			0
$832$	−1.23518	−	3.39363i	−0.0428222	−	0.117653i
$833$	60.1193	+	71.6474i	2.08301	+	2.48244i
$834$		0			0
$835$		−	0.402834i		−	0.0139406i
$836$	7.50584	−	13.7430i	0.259595	−	0.475313i
$837$		0			0
$838$	7.33647	−	1.29362i	0.253434	−	0.0446873i
$839$	−30.1991	+	25.3400i	−1.04259	+	0.874835i	−0.992295	−	0.123900i	$-0.960460\pi$
$839$	−30.1991	+	25.3400i	−1.04259	+	0.874835i	−0.0502927	+	0.998735i	$0.516015\pi$
$840$		0			0
$841$	−21.4139	−	7.79401i	−0.738409	−	0.268759i
$842$	−24.4503	+	29.1388i	−0.842614	+	1.00419i
$843$		0			0
$844$	−1.53180	+	0.884382i	−0.0527266	+	0.0304417i
$845$	0.00569773	+	0.00100466i	0.000196008	+	3.45614e-5i
$846$		0			0
$847$	4.78475	+	8.28743i	0.164406	+	0.284759i
$848$	1.39944	−	2.42389i	0.0480568	−	0.0832369i
$849$		0			0
$850$	8.74811	−	24.0352i	0.300058	−	0.824401i
$851$	5.46017	−	1.98734i	0.187172	−	0.0681251i
$852$		0			0
$853$	−0.570307	−	3.23437i	−0.0195270	−	0.110743i	0.973486	−	0.228745i	$-0.0734622\pi$
$853$	−0.570307	−	3.23437i	−0.0195270	−	0.110743i	−0.993013	+	0.118002i	$0.962351\pi$
$854$	−19.1951			−0.656844
$855$		0			0
$856$	2.26016			0.0772506
$857$	4.32778	+	24.5441i	0.147834	+	0.838409i	0.965048	+	0.262074i	$0.0844066\pi$
$857$	4.32778	+	24.5441i	0.147834	+	0.838409i	−0.817213	+	0.576335i	$0.804482\pi$
$858$		0			0
$859$	14.2154	−	5.17397i	0.485022	−	0.176534i	−0.0879233	−	0.996127i	$-0.528023\pi$
$859$	14.2154	−	5.17397i	0.485022	−	0.176534i	0.572945	+	0.819594i	$0.305801\pi$
$860$	0.222988	−	0.612654i	0.00760382	−	0.0208913i
$861$		0			0
$862$	16.9900	−	29.4276i	0.578683	−	1.00231i
$863$	12.2712	+	21.2544i	0.417717	+	0.723508i	0.995709	−	0.0925347i	$-0.0294969\pi$
$863$	12.2712	+	21.2544i	0.417717	+	0.723508i	−0.577992	+	0.816042i	$0.696164\pi$
$864$		0			0
$865$	1.78886	+	0.315424i	0.0608230	+	0.0107247i
$866$	0.401068	−	0.231557i	0.0136288	−	0.00786861i
$867$		0			0
$868$	13.6823	−	16.3059i	0.464406	−	0.553458i
$869$	23.3967	+	8.51572i	0.793680	+	0.288876i
$870$		0			0
$871$	−17.7650	+	14.9066i	−0.601945	+	0.505091i
$872$	12.2503	−	2.16006i	0.414848	−	0.0731490i
$873$		0			0
$874$	22.2908	−	19.6234i	0.753999	−	0.663771i
$875$		−	6.84154i		−	0.231286i
$876$		0			0
$877$	−4.39656	−	5.23962i	−0.148461	−	0.176929i	0.686689	−	0.726952i	$-0.259064\pi$
$877$	−4.39656	−	5.23962i	−0.148461	−	0.176929i	−0.835150	+	0.550022i	$0.814619\pi$
$878$	−6.05484	−	16.6355i	−0.204341	−	0.561422i
$879$		0			0
$880$	0.375645	+	0.315204i	0.0126630	+	0.0106255i
$881$	46.2511	+	26.7031i	1.55824	+	0.899649i	0.997426	+	0.0717059i	$0.0228443\pi$
$881$	46.2511	+	26.7031i	1.55824	+	0.899649i	0.560812	+	0.827943i	$0.310489\pi$
$882$		0			0
$883$	0.286000	−	1.62199i	0.00962468	−	0.0545843i	−0.979617	−	0.200874i	$-0.935622\pi$
$883$	0.286000	−	1.62199i	0.00962468	−	0.0545843i	0.989242	+	0.146289i	$0.0467331\pi$
$884$	−3.22005	+	18.2618i	−0.108302	+	0.614211i
$885$		0			0
$886$	−26.5783	−	15.3450i	−0.892915	−	0.515524i
$887$	15.2850	+	12.8257i	0.513221	+	0.430644i	0.862261	−	0.506464i	$-0.169048\pi$
$887$	15.2850	+	12.8257i	0.513221	+	0.430644i	−0.349040	+	0.937108i	$0.613492\pi$
$888$		0			0
$889$	27.9968	+	76.9207i	0.938984	+	2.57984i
$890$	−0.516835	−	0.615940i	−0.0173243	−	0.0206463i
$891$		0			0
$892$			7.18262i			0.240492i
$893$	−29.3821	+	0.696818i	−0.983234	+	0.0233181i
$894$		0			0
$895$	2.78261	−	0.490648i	0.0930122	−	0.0164006i
$896$	3.84667	−	3.22774i	0.128508	−	0.107831i
$897$		0			0
$898$	5.35526	+	1.94915i	0.178707	+	0.0650441i
$899$	19.6084	−	23.3684i	0.653977	−	0.779380i
$900$		0			0
$901$	−12.4459	+	7.18566i	−0.414634	+	0.239389i
$902$	−12.0992	−	2.13341i	−0.402858	−	0.0710347i
$903$		0			0
$904$	5.42684	+	9.39956i	0.180494	+	0.312625i
$905$	−1.54939	+	2.68361i	−0.0515033	+	0.0892063i
$906$		0			0
$907$	−11.7415	+	32.2595i	−0.389870	+	1.07116i	0.577190	+	0.816610i	$0.304149\pi$
$907$	−11.7415	+	32.2595i	−0.389870	+	1.07116i	−0.967060	+	0.254549i	$0.918073\pi$
$908$	−22.1065	+	8.04612i	−0.733631	+	0.267020i
$909$		0			0
$910$	0.429846	+	2.43778i	0.0142492	+	0.0808115i
$911$	−23.9136			−0.792294			−0.396147	−	0.918187i	$-0.629653\pi$
$911$	−23.9136			−0.792294			−0.396147	+	0.918187i	$0.629653\pi$
$912$		0			0
$913$	−5.76293			−0.190725
$914$	4.53715	+	25.7315i	0.150076	+	0.851121i
$915$		0			0
$916$	0.502001	−	0.182713i	0.0165866	−	0.00603702i
$917$	23.2542	−	63.8905i	0.767922	−	2.10985i
$918$		0			0
$919$	6.86047	−	11.8827i	0.226306	−	0.391974i	−0.730404	−	0.683015i	$-0.760668\pi$
$919$	6.86047	−	11.8827i	0.226306	−	0.391974i	0.956710	+	0.291041i	$0.0940017\pi$
$920$	0.464997	+	0.805399i	0.0153305	+	0.0265532i
$921$		0			0
$922$	14.4718	+	2.55178i	0.476605	+	0.0840383i
$923$	−47.7252	+	27.5542i	−1.57089	+	0.906956i
$924$		0			0
$925$	2.73079	−	3.25443i	0.0897880	−	0.107005i
$926$	12.7075	+	4.62514i	0.417593	+	0.151991i
$927$		0			0
$928$	5.51276	−	4.62576i	0.180965	−	0.151848i
$929$	16.3896	−	2.88993i	0.537725	−	0.0948155i	0.101811	−	0.994804i	$-0.467536\pi$
$929$	16.3896	−	2.88993i	0.537725	−	0.0948155i	0.435914	+	0.899988i	$0.356425\pi$
$930$		0			0
$931$	52.4637	+	59.5953i	1.71943	+	1.95316i
$932$		−	28.3021i		−	0.927066i
$933$		0			0
$934$	1.34719	+	1.60552i	0.0440815	+	0.0525342i
$935$	−0.861171	−	2.36605i	−0.0281633	−	0.0773781i
$936$		0			0
$937$	−33.7481	−	28.3181i	−1.10250	−	0.925110i	−0.104913	−	0.994481i	$-0.533456\pi$
$937$	−33.7481	−	28.3181i	−1.10250	−	0.925110i	−0.997591	+	0.0693710i	$0.977901\pi$
$938$	−27.9251	−	16.1226i	−0.911786	−	0.526420i
$939$		0			0
$940$	0.159820	−	0.906384i	0.00521275	−	0.0295630i
$941$	8.23823	−	46.7213i	0.268559	−	1.52307i	−0.490147	−	0.871640i	$-0.663057\pi$
$941$	8.23823	−	46.7213i	0.268559	−	1.52307i	0.758706	−	0.651433i	$-0.225832\pi$
$942$		0			0
$943$	−20.1786	−	11.6501i	−0.657105	−	0.379380i
$944$	−7.81839	−	6.56041i	−0.254467	−	0.213523i
$945$		0			0
$946$	5.86866	+	16.1240i	0.190807	+	0.524237i
$947$	−35.3270	−	42.1011i	−1.14797	−	1.36810i	−0.918804	−	0.394714i	$-0.870844\pi$
$947$	−35.3270	−	42.1011i	−1.14797	−	1.36810i	−0.229169	−	0.973387i	$-0.573601\pi$
$948$		0			0
$949$			16.6983i			0.542051i
$950$	6.94054	−	20.5741i	0.225181	−	0.667513i
$951$		0			0
$952$	−25.3919	+	4.47728i	−0.822958	+	0.145110i
$953$	13.5273	−	11.3507i	0.438191	−	0.367686i	−0.396841	−	0.917888i	$-0.629893\pi$
$953$	13.5273	−	11.3507i	0.438191	−	0.367686i	0.835032	+	0.550201i	$0.185449\pi$
$954$		0			0
$955$	−0.310761	−	0.113108i	−0.0100560	−	0.00366008i
$956$	7.78671	−	9.27984i	0.251840	−	0.300131i
$957$		0			0
$958$	−16.0461	+	9.26419i	−0.518424	+	0.299312i
$959$	14.4151	+	2.54177i	0.465488	+	0.0820782i
$960$		0			0
$961$	−6.51559	−	11.2853i	−0.210180	−	0.364043i
$962$	−1.54000	+	2.66736i	−0.0496517	+	0.0859992i
$963$		0			0
$964$	−6.57132	+	18.0546i	−0.211648	+	0.581498i
$965$	2.60122	−	0.946768i	0.0837363	−	0.0304775i
$966$		0			0
$967$	−5.05432	−	28.6645i	−0.162536	−	0.921787i	−0.951569	−	0.307436i	$-0.900529\pi$
$967$	−5.05432	−	28.6645i	−0.162536	−	0.921787i	0.789033	−	0.614351i	$-0.210582\pi$
$968$	−1.90572			−0.0612520
$969$		0			0
$970$	0.762144			0.0244710
$971$	−0.732840	−	4.15614i	−0.0235180	−	0.133377i	0.970788	−	0.239938i	$-0.0771271\pi$
$971$	−0.732840	−	4.15614i	−0.0235180	−	0.133377i	−0.994306	+	0.106561i	$0.966016\pi$
$972$		0			0
$973$	−90.7515	+	33.0308i	−2.90936	+	1.05892i
$974$	−9.72711	+	26.7250i	−0.311677	+	0.856325i
$975$		0			0
$976$	1.91131	−	3.31048i	0.0611795	−	0.105966i
$977$	−27.0378	−	46.8308i	−0.865016	−	1.49825i	−0.867032	−	0.498253i	$-0.833975\pi$
$977$	−27.0378	−	46.8308i	−0.865016	−	1.49825i	0.00201614	−	0.999998i	$-0.499358\pi$
$978$		0			0
$979$	20.8398	+	3.67462i	0.666043	+	0.117441i
$980$	−2.15326	+	1.24318i	−0.0687834	+	0.0397121i
$981$		0			0
$982$	−0.594649	+	0.708675i	−0.0189760	+	0.0226147i
$983$	9.02234	+	3.28386i	0.287768	+	0.104739i	0.481871	−	0.876242i	$-0.339957\pi$
$983$	9.02234	+	3.28386i	0.287768	+	0.104739i	−0.194103	+	0.980981i	$0.562180\pi$
$984$		0			0
$985$	1.65681	−	1.39023i	0.0527905	−	0.0442965i
$986$	−36.3899	+	6.41651i	−1.15889	+	0.204343i
$987$		0			0
$988$	−2.36522	+	15.5631i	−0.0752476	+	0.495129i
$989$			32.5419i			1.03477i
$990$		0			0
$991$	−9.68306	−	11.5398i	−0.307593	−	0.366575i	0.589998	−	0.807405i	$-0.299129\pi$
$991$	−9.68306	−	11.5398i	−0.307593	−	0.366575i	−0.897591	+	0.440830i	$0.854684\pi$
$992$	1.44981	+	3.98332i	0.0460315	+	0.126471i
$993$		0			0
$994$	−58.6980	−	49.2535i	−1.86179	−	1.56223i
$995$	−2.58939	−	1.49499i	−0.0820893	−	0.0473943i
$996$		0			0
$997$	−0.478914	+	2.71605i	−0.0151674	+	0.0860183i	−0.991452	−	0.130473i	$-0.958350\pi$
$997$	−0.478914	+	2.71605i	−0.0151674	+	0.0860183i	0.976284	+	0.216492i	$0.0694614\pi$
$998$	−4.68426	+	26.5658i	−0.148278	+	0.840924i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.2.bb.a.143.2	✓	24
3.2	odd	2		342.2.bb.b.143.3	yes	24
19.2	odd	18		342.2.bb.b.287.3	yes	24
57.2	even	18	inner	342.2.bb.a.287.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
342.2.bb.a.143.2	✓	24	1.1	even	1	trivial
342.2.bb.a.287.2	yes	24	57.2	even	18	inner
342.2.bb.b.143.3	yes	24	3.2	odd	2
342.2.bb.b.287.3	yes	24	19.2	odd	18

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:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	342.bb (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.173648 + 0.984808i) q^{2} +(-0.939693 + 0.342020i) q^{4} +(-0.0466858 + 0.128268i) q^{5} +(-2.51073 + 4.34872i) q^{7} +(-0.500000 - 0.866025i) q^{8} +O(q^{10})\)	\(q+(0.173648 + 0.984808i) q^{2} +(-0.939693 + 0.342020i) q^{4} +(-0.0466858 + 0.128268i) q^{5} +(-2.51073 + 4.34872i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.134426 - 0.0237030i) q^{10} +(3.11116 - 1.79623i) q^{11} +(-2.32138 + 2.76651i) q^{13} +(-4.71864 - 1.71744i) q^{14} +(0.766044 - 0.642788i) q^{16} +(-5.05668 + 0.891629i) q^{17} +(-4.27353 + 0.858478i) q^{19} -0.136500i q^{20} +(2.30918 + 2.75198i) q^{22} +(2.33023 + 6.40226i) q^{23} +(3.81595 + 3.20196i) q^{25} +(-3.12759 - 1.80571i) q^{26} +(0.871969 - 4.94518i) q^{28} +(1.24964 - 7.08707i) q^{29} +(3.67105 + 2.11948i) q^{31} +(0.766044 + 0.642788i) q^{32} +(-1.75617 - 4.82502i) q^{34} +(-0.440587 - 0.525071i) q^{35} -0.852851i q^{37} +(-1.58753 - 4.05953i) q^{38} +(0.134426 - 0.0237030i) q^{40} +(-2.61979 + 2.19827i) q^{41} +(4.48830 + 1.63361i) q^{43} +(-2.30918 + 2.75198i) q^{44} +(-5.90035 + 3.40657i) q^{46} +(6.64017 + 1.17084i) q^{47} +(-9.10757 - 15.7748i) q^{49} +(-2.49068 + 4.31399i) q^{50} +(1.23518 - 3.39363i) q^{52} +(2.63008 - 0.957270i) q^{53} +(0.0851519 + 0.482920i) q^{55} +5.02147 q^{56} +7.19640 q^{58} +(-1.77228 - 10.0511i) q^{59} +(3.59208 - 1.30741i) q^{61} +(-1.44981 + 3.98332i) q^{62} +(-0.500000 + 0.866025i) q^{64} +(-0.246480 - 0.426916i) q^{65} +(6.32389 + 1.11507i) q^{67} +(4.44677 - 2.56734i) q^{68} +(0.440587 - 0.525071i) q^{70} +(14.3392 + 5.21904i) q^{71} +(3.54200 - 2.97209i) q^{73} +(0.839894 - 0.148096i) q^{74} +(3.72218 - 2.26834i) q^{76} +18.0394i q^{77} +(4.45498 + 5.30924i) q^{79} +(0.0466858 + 0.128268i) q^{80} +(-2.61979 - 2.19827i) q^{82} +(-1.38926 - 0.802089i) q^{83} +(0.121707 - 0.690237i) q^{85} +(-0.829404 + 4.70379i) q^{86} +(-3.11116 - 1.79623i) q^{88} +(4.51237 + 3.78633i) q^{89} +(-6.20242 - 17.0410i) q^{91} +(-4.37940 - 5.21917i) q^{92} +6.74261i q^{94} +(0.0893976 - 0.588236i) q^{95} +(-5.49864 + 0.969559i) q^{97} +(13.9536 - 11.7085i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{8}+O(q^{10}) \) 24 * q - 12 * q^8	\( 24 q - 12 q^{8} - 12 q^{17} + 24 q^{19} + 12 q^{22} + 36 q^{25} - 36 q^{26} + 12 q^{29} + 12 q^{34} + 48 q^{35} + 12 q^{38} + 12 q^{41} - 12 q^{44} - 36 q^{46} - 60 q^{47} - 36 q^{49} + 24 q^{50} + 48 q^{53} - 60 q^{55} - 24 q^{58} - 24 q^{59} - 60 q^{61} - 24 q^{62} - 12 q^{64} + 24 q^{65} - 48 q^{70} + 36 q^{71} + 24 q^{79} + 12 q^{82} - 72 q^{83} + 36 q^{86} + 120 q^{89} - 24 q^{91} - 12 q^{95}+O(q^{100}) \) 24 * q - 12 * q^8 - 12 * q^17 + 24 * q^19 + 12 * q^22 + 36 * q^25 - 36 * q^26 + 12 * q^29 + 12 * q^34 + 48 * q^35 + 12 * q^38 + 12 * q^41 - 12 * q^44 - 36 * q^46 - 60 * q^47 - 36 * q^49 + 24 * q^50 + 48 * q^53 - 60 * q^55 - 24 * q^58 - 24 * q^59 - 60 * q^61 - 24 * q^62 - 12 * q^64 + 24 * q^65 - 48 * q^70 + 36 * q^71 + 24 * q^79 + 12 * q^82 - 72 * q^83 + 36 * q^86 + 120 * q^89 - 24 * q^91 - 12 * q^95

Introduction

L-functions

Modular forms

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Database

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