LMFDB - Embedded newform 3024.2.cz.g.2719.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3024,2,Mod(1279,3024)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3024, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 2, 5]))

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

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

chi := DirichletCharacter("3024.1279");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3024 = 2^{4} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3024.cz (of order $6$, degree $2$, 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:	$24.1467615712$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 1008)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			2719.7
Character	$\chi$	$=$	3024.2719
Dual form			3024.2.cz.g.1279.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.679706 + 0.392428i) q^{5} +(2.49091 + 0.891831i) q^{7} +O(q^{10})$	$q+(0.679706 + 0.392428i) q^{5} +(2.49091 + 0.891831i) q^{7} +(-1.22712 + 0.708477i) q^{11} +(-1.50450 + 0.868623i) q^{13} +(-5.43701 - 3.13906i) q^{17} +(-0.736632 - 1.27588i) q^{19} +(-4.85720 - 2.80431i) q^{23} +(-2.19200 - 3.79666i) q^{25} +(-3.95678 + 6.85335i) q^{29} -8.41859 q^{31} +(1.34311 + 1.58369i) q^{35} +(3.74187 + 6.48111i) q^{37} +(-7.19180 + 4.15219i) q^{41} +(-7.85087 - 4.53270i) q^{43} -0.110085 q^{47} +(5.40927 + 4.44294i) q^{49} +(4.28575 - 7.42313i) q^{53} -1.11211 q^{55} -0.0736173 q^{59} -1.23776i q^{61} -1.36349 q^{65} -11.8735i q^{67} -0.390149i q^{71} +(3.70538 + 2.13930i) q^{73} +(-3.68848 + 0.670370i) q^{77} -6.00205i q^{79} +(7.88696 - 13.6606i) q^{83} +(-2.46371 - 4.26727i) q^{85} +(-6.15579 + 3.55405i) q^{89} +(-4.52224 + 0.821903i) q^{91} -1.15630i q^{95} +(5.89647 + 3.40433i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{5} - 4 q^{7}+O(q^{10}) $ 24 * q + 3 * q^5 - 4 * q^7	$ 24 q + 3 q^{5} - 4 q^{7} - 9 q^{11} - 3 q^{13} + 3 q^{17} + 4 q^{19} - 6 q^{23} + 15 q^{25} - 18 q^{29} - 34 q^{31} - 42 q^{35} - 3 q^{37} - 36 q^{41} - 24 q^{43} - 42 q^{47} + 30 q^{49} + 12 q^{53} + 30 q^{55} - 12 q^{59} + 48 q^{73} + 48 q^{77} - 48 q^{83} - 21 q^{85} - 39 q^{89} - 9 q^{91} + 3 q^{97}+O(q^{100}) $ 24 * q + 3 * q^5 - 4 * q^7 - 9 * q^11 - 3 * q^13 + 3 * q^17 + 4 * q^19 - 6 * q^23 + 15 * q^25 - 18 * q^29 - 34 * q^31 - 42 * q^35 - 3 * q^37 - 36 * q^41 - 24 * q^43 - 42 * q^47 + 30 * q^49 + 12 * q^53 + 30 * q^55 - 12 * q^59 + 48 * q^73 + 48 * q^77 - 48 * q^83 - 21 * q^85 - 39 * q^89 - 9 * q^91 + 3 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1135$	$2593$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{6}\right)$

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			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	0.679706	+	0.392428i	0.303974	+	0.175499i	0.644227	−	0.764835i	$-0.277179\pi$
$5$	0.679706	+	0.392428i	0.303974	+	0.175499i	−0.340253	+	0.940334i	$0.610513\pi$
$6$		0			0
$7$	2.49091	+	0.891831i	0.941476	+	0.337081i
$7$	2.49091	+	0.891831i	0.941476	+	0.337081i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.22712	+	0.708477i	−0.369990	+	0.213614i	−0.673454	−	0.739229i	$-0.735190\pi$
$11$	−1.22712	+	0.708477i	−0.369990	+	0.213614i	0.303464	+	0.952843i	$0.401857\pi$
$12$		0			0
$13$	−1.50450	+	0.868623i	−0.417273	+	0.240913i	−0.693910	−	0.720062i	$-0.744113\pi$
$13$	−1.50450	+	0.868623i	−0.417273	+	0.240913i	0.276637	+	0.960975i	$0.410780\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−5.43701	−	3.13906i	−1.31867	−	0.761334i	−0.335154	−	0.942163i	$-0.608788\pi$
$17$	−5.43701	−	3.13906i	−1.31867	−	0.761334i	−0.983514	+	0.180829i	$0.942122\pi$
$18$		0			0
$19$	−0.736632	−	1.27588i	−0.168995	−	0.292708i	0.769072	−	0.639162i	$-0.220719\pi$
$19$	−0.736632	−	1.27588i	−0.168995	−	0.292708i	−0.938067	+	0.346455i	$0.887385\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−4.85720	−	2.80431i	−1.01280	−	0.584739i	−0.100787	−	0.994908i	$-0.532136\pi$
$23$	−4.85720	−	2.80431i	−1.01280	−	0.584739i	−0.912009	+	0.410169i	$0.865470\pi$
$24$		0			0
$25$	−2.19200	−	3.79666i	−0.438400	−	0.759331i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−3.95678	+	6.85335i	−0.734756	+	1.27263i	0.220075	+	0.975483i	$0.429370\pi$
$29$	−3.95678	+	6.85335i	−0.734756	+	1.27263i	−0.954830	+	0.297151i	$0.903963\pi$
$30$		0			0
$31$	−8.41859			−1.51202			−0.756011	−	0.654559i	$-0.772855\pi$
$31$	−8.41859			−1.51202			−0.756011	+	0.654559i	$0.772855\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	1.34311	+	1.58369i	0.227026	+	0.267692i
$36$		0			0
$37$	3.74187	+	6.48111i	0.615160	+	1.06549i	0.990356	+	0.138543i	$0.0442420\pi$
$37$	3.74187	+	6.48111i	0.615160	+	1.06549i	−0.375196	+	0.926945i	$0.622425\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−7.19180	+	4.15219i	−1.12317	+	0.648463i	−0.942208	−	0.335027i	$-0.891254\pi$
$41$	−7.19180	+	4.15219i	−1.12317	+	0.648463i	−0.180962	+	0.983490i	$0.557921\pi$
$42$		0			0
$43$	−7.85087	−	4.53270i	−1.19725	−	0.691230i	−0.237306	−	0.971435i	$-0.576264\pi$
$43$	−7.85087	−	4.53270i	−1.19725	−	0.691230i	−0.959940	+	0.280205i	$0.909598\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−0.110085			−0.0160576			−0.00802880	−	0.999968i	$-0.502556\pi$
$47$	−0.110085			−0.0160576			−0.00802880	+	0.999968i	$0.502556\pi$
$48$		0			0
$49$	5.40927	+	4.44294i	0.772753	+	0.634706i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	4.28575	−	7.42313i	0.588693	−	1.01965i	−0.405711	−	0.914001i	$-0.632976\pi$
$53$	4.28575	−	7.42313i	0.588693	−	1.01965i	0.994404	−	0.105644i	$-0.0336905\pi$
$54$		0			0
$55$	−1.11211			−0.149956
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−0.0736173			−0.00958415			−0.00479208	−	0.999989i	$-0.501525\pi$
$59$	−0.0736173			−0.00958415			−0.00479208	+	0.999989i	$0.501525\pi$
$60$		0			0
$61$		−	1.23776i		−	0.158479i	−0.996856	−	0.0792394i	$-0.974751\pi$
$61$		−	1.23776i		−	0.158479i	0.996856	−	0.0792394i	$-0.0252492\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.36349			−0.169120
$66$		0			0
$67$		−	11.8735i		−	1.45058i	−0.688442	−	0.725291i	$-0.741705\pi$
$67$		−	11.8735i		−	1.45058i	0.688442	−	0.725291i	$-0.258295\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	0.390149i		−	0.0463021i	−0.999732	−	0.0231511i	$-0.992630\pi$
$71$		−	0.390149i		−	0.0463021i	0.999732	−	0.0231511i	$-0.00736987\pi$
$72$		0			0
$73$	3.70538	+	2.13930i	0.433682	+	0.250386i	0.700914	−	0.713246i	$-0.252776\pi$
$73$	3.70538	+	2.13930i	0.433682	+	0.250386i	−0.267232	+	0.963632i	$0.586109\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−3.68848	+	0.670370i	−0.420342	+	0.0763958i
$78$		0			0
$79$		−	6.00205i		−	0.675283i	−0.941275	−	0.337642i	$-0.890371\pi$
$79$		−	6.00205i		−	0.675283i	0.941275	−	0.337642i	$-0.109629\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	7.88696	−	13.6606i	0.865706	−	1.49945i	−0.000637973	−	1.00000i	$-0.500203\pi$
$83$	7.88696	−	13.6606i	0.865706	−	1.49945i	0.866344	−	0.499447i	$-0.166464\pi$
$84$		0			0
$85$	−2.46371	−	4.26727i	−0.267227	−	0.462851i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−6.15579	+	3.55405i	−0.652513	+	0.376729i	−0.789418	−	0.613856i	$-0.789618\pi$
$89$	−6.15579	+	3.55405i	−0.652513	+	0.376729i	0.136905	+	0.990584i	$0.456284\pi$
$90$		0			0
$91$	−4.52224	+	0.821903i	−0.474060	+	0.0861589i
$92$		0			0
$93$		0			0
$94$		0			0
$95$		−	1.15630i		−	0.118634i
$96$		0			0
$97$	5.89647	+	3.40433i	0.598695	+	0.345657i	0.768528	−	0.639816i	$-0.220989\pi$
$97$	5.89647	+	3.40433i	0.598695	+	0.345657i	−0.169833	+	0.985473i	$0.554323\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	2.82630	−	1.63176i	0.281227	−	0.162366i	−0.352752	−	0.935717i	$-0.614754\pi$
$101$	2.82630	−	1.63176i	0.281227	−	0.162366i	0.633979	+	0.773350i	$0.281421\pi$
$102$		0			0
$103$	−8.39149	+	14.5345i	−0.826838	+	1.43212i	0.0736690	+	0.997283i	$0.476529\pi$
$103$	−8.39149	+	14.5345i	−0.826838	+	1.43212i	−0.900507	+	0.434842i	$0.856804\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	8.07017	−	4.65932i	0.780173	−	0.450433i	−0.0563185	−	0.998413i	$-0.517936\pi$
$107$	8.07017	−	4.65932i	0.780173	−	0.450433i	0.836492	+	0.547980i	$0.184603\pi$
$108$		0			0
$109$	1.10094	−	1.90688i	0.105451	−	0.182646i	−0.808471	−	0.588535i	$-0.799705\pi$
$109$	1.10094	−	1.90688i	0.105451	−	0.182646i	0.913922	+	0.405889i	$0.133038\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	3.33634	+	5.77872i	0.313857	+	0.543616i	0.979194	−	0.202927i	$-0.0650455\pi$
$113$	3.33634	+	5.77872i	0.313857	+	0.543616i	−0.665337	+	0.746543i	$0.731712\pi$
$114$		0			0
$115$	−2.20098	−	3.81221i	−0.205242	−	0.355490i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−10.7436	−	12.6680i	−0.984864	−	1.16127i
$120$		0			0
$121$	−4.49612	+	7.78751i	−0.408738	+	0.707955i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		−	7.36510i		−	0.658754i
$126$		0			0
$127$			15.5443i			1.37934i	0.724125	+	0.689669i	$0.242244\pi$
$127$			15.5443i			1.37934i	−0.724125	+	0.689669i	$0.757756\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−2.63094	+	4.55693i	−0.229867	+	0.398140i	−0.957768	−	0.287541i	$-0.907162\pi$
$131$	−2.63094	+	4.55693i	−0.229867	+	0.398140i	0.727902	+	0.685681i	$0.240496\pi$
$132$		0			0
$133$	−0.697011	−	3.83506i	−0.0604385	−	0.332542i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	6.84273	+	11.8520i	0.584614	+	1.01258i	0.994923	+	0.100635i	$0.0320875\pi$
$137$	6.84273	+	11.8520i	0.584614	+	1.01258i	−0.410309	+	0.911946i	$0.634579\pi$
$138$		0			0
$139$	−4.61572	−	7.99465i	−0.391500	−	0.678098i	0.601148	−	0.799138i	$-0.294710\pi$
$139$	−4.61572	−	7.99465i	−0.391500	−	0.678098i	−0.992648	+	0.121040i	$0.961377\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	1.23080	−	2.13181i	0.102925	−	0.178271i
$144$		0			0
$145$	−5.37889	+	3.10551i	−0.446693	+	0.257898i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−9.44849	+	16.3653i	−0.774051	+	1.34070i	0.161276	+	0.986909i	$0.448439\pi$
$149$	−9.44849	+	16.3653i	−0.774051	+	1.34070i	−0.935326	+	0.353786i	$0.884894\pi$
$150$		0			0
$151$	2.66662	−	1.53957i	0.217006	−	0.125289i	−0.387557	−	0.921846i	$-0.626681\pi$
$151$	2.66662	−	1.53957i	0.217006	−	0.125289i	0.604563	+	0.796557i	$0.293348\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−5.72216	−	3.30369i	−0.459615	−	0.265359i
$156$		0			0
$157$			15.2290i			1.21541i	0.794164	+	0.607703i	$0.207909\pi$
$157$			15.2290i			1.21541i	−0.794164	+	0.607703i	$0.792091\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−9.59789	−	11.3171i	−0.756420	−	0.891911i
$162$		0			0
$163$	−4.96129	+	2.86440i	−0.388599	+	0.224357i	−0.681553	−	0.731769i	$-0.738695\pi$
$163$	−4.96129	+	2.86440i	−0.388599	+	0.224357i	0.292954	+	0.956126i	$0.405362\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−2.28326	−	3.95472i	−0.176684	−	0.306025i	0.764059	−	0.645147i	$-0.223204\pi$
$167$	−2.28326	−	3.95472i	−0.176684	−	0.306025i	−0.940743	+	0.339121i	$0.889870\pi$
$168$		0			0
$169$	−4.99099	+	8.64464i	−0.383922	+	0.664973i
$170$		0			0
$171$		0			0
$172$		0			0
$173$		−	17.8762i		−	1.35910i	−0.733628	−	0.679551i	$-0.762174\pi$
$173$		−	17.8762i		−	1.35910i	0.733628	−	0.679551i	$-0.237826\pi$
$174$		0			0
$175$	−2.07410	−	11.4120i	−0.156787	−	0.862668i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−6.15176	−	3.55172i	−0.459804	−	0.265468i	0.252158	−	0.967686i	$-0.418860\pi$
$179$	−6.15176	−	3.55172i	−0.459804	−	0.265468i	−0.711962	+	0.702218i	$0.752193\pi$
$180$		0			0
$181$		−	6.31771i		−	0.469591i	−0.972045	−	0.234796i	$-0.924558\pi$
$181$		−	6.31771i		−	0.469591i	0.972045	−	0.234796i	$-0.0754421\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$			5.87367i			0.431841i
$186$		0			0
$187$	8.89580			0.650526
$188$		0			0
$189$		0			0
$190$		0			0
$191$		−	21.6174i		−	1.56418i	−0.623165	−	0.782090i	$-0.714153\pi$
$191$		−	21.6174i		−	1.56418i	0.623165	−	0.782090i	$-0.285847\pi$
$192$		0			0
$193$	−5.11201			−0.367970			−0.183985	−	0.982929i	$-0.558900\pi$
$193$	−5.11201			−0.367970			−0.183985	+	0.982929i	$0.558900\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	12.7051			0.905199			0.452599	−	0.891714i	$-0.350497\pi$
$197$	12.7051			0.905199			0.452599	+	0.891714i	$0.350497\pi$
$198$		0			0
$199$	−1.35332	+	2.34401i	−0.0959341	+	0.166163i	−0.909998	−	0.414612i	$-0.863917\pi$
$199$	−1.35332	+	2.34401i	−0.0959341	+	0.166163i	0.814064	+	0.580775i	$0.197250\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−15.9680	+	13.5423i	−1.12074	+	0.950483i
$204$		0			0
$205$	−6.51774			−0.455219
$206$		0			0
$207$		0			0
$208$		0			0
$209$	1.80787	+	1.04377i	0.125053	+	0.0721993i
$210$		0			0
$211$	−7.54303	+	4.35497i	−0.519284	+	0.299809i	−0.736641	−	0.676283i	$-0.763589\pi$
$211$	−7.54303	+	4.35497i	−0.519284	+	0.299809i	0.217358	+	0.976092i	$0.430256\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−3.55752	−	6.16181i	−0.242621	−	0.420232i
$216$		0			0
$217$	−20.9699	−	7.50796i	−1.42353	−	0.509673i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	10.9066			0.733660
$222$		0			0
$223$	−4.60457	+	7.97535i	−0.308345	+	0.534069i	−0.978000	−	0.208603i	$-0.933108\pi$
$223$	−4.60457	+	7.97535i	−0.308345	+	0.534069i	0.669656	+	0.742672i	$0.266442\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−4.08469	−	7.07489i	−0.271110	−	0.469577i	0.698036	−	0.716063i	$-0.254057\pi$
$227$	−4.08469	−	7.07489i	−0.271110	−	0.469577i	−0.969146	+	0.246486i	$0.920724\pi$
$228$		0			0
$229$	1.76036	+	1.01634i	0.116328	+	0.0671618i	0.557035	−	0.830489i	$-0.311939\pi$
$229$	1.76036	+	1.01634i	0.116328	+	0.0671618i	−0.440707	+	0.897651i	$0.645272\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−5.74641	−	9.95307i	−0.376460	−	0.652047i	0.614085	−	0.789240i	$-0.289525\pi$
$233$	−5.74641	−	9.95307i	−0.376460	−	0.652047i	−0.990544	+	0.137193i	$0.956192\pi$
$234$		0			0
$235$	−0.0748256	−	0.0432006i	−0.00488109	−	0.00281810i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	15.1651	−	8.75560i	0.980952	−	0.566353i	0.0783945	−	0.996922i	$-0.475021\pi$
$239$	15.1651	−	8.75560i	0.980952	−	0.566353i	0.902557	+	0.430570i	$0.141687\pi$
$240$		0			0
$241$	−17.6422	+	10.1858i	−1.13644	+	0.656122i	−0.945546	−	0.325489i	$-0.894471\pi$
$241$	−17.6422	+	10.1858i	−1.13644	+	0.656122i	−0.190891	+	0.981611i	$0.561138\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	1.93318	+	5.14265i	0.123506	+	0.328552i
$246$		0			0
$247$	2.21652	+	1.27971i	0.141034	+	0.0814260i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−7.09897			−0.448083			−0.224041	−	0.974580i	$-0.571925\pi$
$251$	−7.09897			−0.448083			−0.224041	+	0.974580i	$0.571925\pi$
$252$		0			0
$253$	7.94715			0.499633
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−22.4449	−	12.9585i	−1.40007	−	0.808332i	−0.405672	−	0.914019i	$-0.632963\pi$
$257$	−22.4449	−	12.9585i	−1.40007	−	0.808332i	−0.994399	+	0.105687i	$0.966296\pi$
$258$		0			0
$259$	3.54061	+	19.4810i	0.220003	+	1.21049i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	4.18333	−	2.41525i	0.257955	−	0.148931i	−0.365446	−	0.930832i	$-0.619084\pi$
$263$	4.18333	−	2.41525i	0.257955	−	0.148931i	0.623401	+	0.781902i	$0.285750\pi$
$264$		0			0
$265$	5.82610	−	3.36370i	0.357894	−	0.206630i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	6.63937	+	3.83324i	0.404809	+	0.233717i	0.688557	−	0.725182i	$-0.258244\pi$
$269$	6.63937	+	3.83324i	0.404809	+	0.233717i	−0.283748	+	0.958899i	$0.591578\pi$
$270$		0			0
$271$	−2.53360	−	4.38832i	−0.153905	−	0.266571i	0.778755	−	0.627328i	$-0.215852\pi$
$271$	−2.53360	−	4.38832i	−0.153905	−	0.266571i	−0.932660	+	0.360757i	$0.882518\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	5.37968	+	3.10596i	0.324407	+	0.187297i
$276$		0			0
$277$	−10.9256	−	18.9237i	−0.656455	−	1.13701i	−0.981527	−	0.191325i	$-0.938722\pi$
$277$	−10.9256	−	18.9237i	−0.656455	−	1.13701i	0.325071	−	0.945689i	$-0.394612\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−1.09695	+	1.89998i	−0.0654388	+	0.113343i	−0.896889	−	0.442257i	$-0.854178\pi$
$281$	−1.09695	+	1.89998i	−0.0654388	+	0.113343i	0.831450	+	0.555600i	$0.187511\pi$
$282$		0			0
$283$	−15.3003			−0.909509			−0.454754	−	0.890617i	$-0.650273\pi$
$283$	−15.3003			−0.909509			−0.454754	+	0.890617i	$0.650273\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−21.6172	+	3.92886i	−1.27602	+	0.231913i
$288$		0			0
$289$	11.2074	+	19.4118i	0.659258	+	1.14187i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−5.07666	+	2.93101i	−0.296581	+	0.171231i	−0.640906	−	0.767619i	$-0.721441\pi$
$293$	−5.07666	+	2.93101i	−0.296581	+	0.171231i	0.344325	+	0.938851i	$0.388108\pi$
$294$		0			0
$295$	−0.0500381	−	0.0288895i	−0.00291333	−	0.00168201i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	9.74355			0.563484
$300$		0			0
$301$	−15.5134	−	18.2922i	−0.894178	−	1.05435i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	0.485732	−	0.841312i	0.0278129	−	0.0481734i
$306$		0			0
$307$	−8.38567			−0.478596			−0.239298	−	0.970946i	$-0.576917\pi$
$307$	−8.38567			−0.478596			−0.239298	+	0.970946i	$0.576917\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	28.8576			1.63636			0.818182	−	0.574960i	$-0.194982\pi$
$311$	28.8576			1.63636			0.818182	+	0.574960i	$0.194982\pi$
$312$		0			0
$313$			28.4132i			1.60601i	0.595973	+	0.803005i	$0.296767\pi$
$313$			28.4132i			1.60601i	−0.595973	+	0.803005i	$0.703233\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	8.98308			0.504540			0.252270	−	0.967657i	$-0.418823\pi$
$317$	8.98308			0.504540			0.252270	+	0.967657i	$0.418823\pi$
$318$		0			0
$319$		−	11.2131i		−	0.627816i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			9.24932i			0.514646i
$324$		0			0
$325$	6.59573	+	3.80804i	0.365865	+	0.211232i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−0.274213	−	0.0981775i	−0.0151178	−	0.00541270i
$330$		0			0
$331$		−	6.80699i		−	0.374146i	−0.982346	−	0.187073i	$-0.940100\pi$
$331$		−	6.80699i		−	0.374146i	0.982346	−	0.187073i	$-0.0599001\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	4.65951	−	8.07051i	0.254576	−	0.440939i
$336$		0			0
$337$	8.43310	+	14.6066i	0.459380	+	0.795670i	0.998928	−	0.0462849i	$-0.0147382\pi$
$337$	8.43310	+	14.6066i	0.459380	+	0.795670i	−0.539548	+	0.841955i	$0.681405\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	10.3306	−	5.96437i	0.559433	−	0.322989i
$342$		0			0
$343$	9.51166	+	15.8911i	0.513581	+	0.858041i
$344$		0			0
$345$		0			0
$346$		0			0
$347$			33.9020i			1.81995i	0.414659	+	0.909977i	$0.363901\pi$
$347$			33.9020i			1.81995i	−0.414659	+	0.909977i	$0.636099\pi$
$348$		0			0
$349$	8.57679	+	4.95181i	0.459105	+	0.265065i	0.711668	−	0.702516i	$-0.247940\pi$
$349$	8.57679	+	4.95181i	0.459105	+	0.265065i	−0.252563	+	0.967581i	$0.581273\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	25.7683	−	14.8774i	1.37151	−	0.791842i	0.380392	−	0.924825i	$-0.375789\pi$
$353$	25.7683	−	14.8774i	1.37151	−	0.791842i	0.991118	+	0.132983i	$0.0424557\pi$
$354$		0			0
$355$	0.153105	−	0.265186i	0.00812599	−	0.0140746i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−11.8705	+	6.85344i	−0.626502	+	0.361711i	−0.779396	−	0.626532i	$-0.784474\pi$
$359$	−11.8705	+	6.85344i	−0.626502	+	0.361711i	0.152894	+	0.988243i	$0.451141\pi$
$360$		0			0
$361$	8.41475	−	14.5748i	0.442881	−	0.767093i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	1.67905	+	2.90819i	0.0878853	+	0.152222i
$366$		0			0
$367$	−16.3229	−	28.2720i	−0.852047	−	1.47579i	−0.879358	−	0.476162i	$-0.842028\pi$
$367$	−16.3229	−	28.2720i	−0.852047	−	1.47579i	0.0273109	−	0.999627i	$-0.491306\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	17.2956	−	14.6682i	0.897943	−	0.761535i
$372$		0			0
$373$	10.1393	−	17.5618i	0.524995	−	0.909317i	−0.474582	−	0.880211i	$-0.657401\pi$
$373$	10.1393	−	17.5618i	0.524995	−	0.909317i	0.999576	−	0.0291058i	$-0.00926598\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	13.7478i		−	0.708048i
$378$		0			0
$379$		−	22.3099i		−	1.14598i	−0.819561	−	0.572992i	$-0.805783\pi$
$379$		−	22.3099i		−	1.14598i	0.819561	−	0.572992i	$-0.194217\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−10.4652	+	18.1262i	−0.534746	+	0.926207i	0.464430	+	0.885610i	$0.346259\pi$
$383$	−10.4652	+	18.1262i	−0.534746	+	0.926207i	−0.999176	+	0.0405971i	$0.987074\pi$
$384$		0			0
$385$	−2.77016	−	0.991811i	−0.141180	−	0.0505474i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	6.14324	+	10.6404i	0.311475	+	0.539490i	0.978682	−	0.205382i	$-0.0658438\pi$
$389$	6.14324	+	10.6404i	0.311475	+	0.539490i	−0.667207	+	0.744872i	$0.732510\pi$
$390$		0			0
$391$	17.6058	+	30.4941i	0.890362	+	1.54215i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	2.35537	−	4.07963i	0.118512	−	0.205268i
$396$		0			0
$397$	−21.2792	+	12.2856i	−1.06797	+	0.616594i	−0.927627	−	0.373508i	$-0.878155\pi$
$397$	−21.2792	+	12.2856i	−1.06797	+	0.616594i	−0.140346	+	0.990103i	$0.544821\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−18.3595	+	31.7997i	−0.916832	+	1.58800i	−0.112634	+	0.993637i	$0.535929\pi$
$401$	−18.3595	+	31.7997i	−0.916832	+	1.58800i	−0.804197	+	0.594362i	$0.797405\pi$
$402$		0			0
$403$	12.6658	−	7.31258i	0.630926	−	0.364266i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−9.18344	−	5.30206i	−0.455206	−	0.262813i
$408$		0			0
$409$			8.40233i			0.415468i	0.978185	+	0.207734i	$0.0666089\pi$
$409$			8.40233i			0.415468i	−0.978185	+	0.207734i	$0.933391\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−0.183374	−	0.0656542i	−0.00902325	−	0.00323063i
$414$		0			0
$415$	10.7216	−	6.19013i	0.526304	−	0.303862i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−14.1563	−	24.5195i	−0.691583	−	1.19786i	−0.971319	−	0.237780i	$-0.923580\pi$
$419$	−14.1563	−	24.5195i	−0.691583	−	1.19786i	0.279736	−	0.960077i	$-0.409753\pi$
$420$		0			0
$421$	14.2835	−	24.7397i	0.696133	−	1.20574i	−0.273664	−	0.961825i	$-0.588236\pi$
$421$	14.2835	−	24.7397i	0.696133	−	1.20574i	0.969797	−	0.243912i	$-0.0784309\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$			27.5233i			1.33507i
$426$		0			0
$427$	1.10387	−	3.08315i	0.0534201	−	0.149204i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−9.31259	−	5.37663i	−0.448572	−	0.258983i	0.258655	−	0.965970i	$-0.416721\pi$
$431$	−9.31259	−	5.37663i	−0.448572	−	0.258983i	−0.707227	+	0.706987i	$0.750054\pi$
$432$		0			0
$433$		−	2.52301i		−	0.121248i	−0.998161	−	0.0606241i	$-0.980691\pi$
$433$		−	2.52301i		−	0.121248i	0.998161	−	0.0606241i	$-0.0193091\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$			8.26296i			0.395271i
$438$		0			0
$439$	2.12556			0.101447			0.0507237	−	0.998713i	$-0.483847\pi$
$439$	2.12556			0.101447			0.0507237	+	0.998713i	$0.483847\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$			34.4346i			1.63604i	0.575193	+	0.818018i	$0.304927\pi$
$443$			34.4346i			1.63604i	−0.575193	+	0.818018i	$0.695073\pi$
$444$		0			0
$445$	−5.57884			−0.264462
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−25.1970			−1.18912			−0.594560	−	0.804051i	$-0.702674\pi$
$449$	−25.1970			−1.18912			−0.594560	+	0.804051i	$0.702674\pi$
$450$		0			0
$451$	5.88346	−	10.1904i	0.277041	−	0.479849i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−3.39633	−	1.21600i	−0.159222	−	0.0570071i
$456$		0			0
$457$	38.3416			1.79354			0.896771	−	0.442494i	$-0.145906\pi$
$457$	38.3416			1.79354			0.896771	+	0.442494i	$0.145906\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	22.0353	+	12.7221i	1.02629	+	0.592527i	0.915919	−	0.401364i	$-0.131464\pi$
$461$	22.0353	+	12.7221i	1.02629	+	0.592527i	0.110368	+	0.993891i	$0.464797\pi$
$462$		0			0
$463$	19.6432	−	11.3410i	0.912897	−	0.527061i	0.0315350	−	0.999503i	$-0.489960\pi$
$463$	19.6432	−	11.3410i	0.912897	−	0.527061i	0.881362	+	0.472441i	$0.156627\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	3.19769	+	5.53857i	0.147972	+	0.256294i	0.930478	−	0.366349i	$-0.119392\pi$
$467$	3.19769	+	5.53857i	0.147972	+	0.256294i	−0.782506	+	0.622643i	$0.786059\pi$
$468$		0			0
$469$	10.5892	−	29.5759i	0.488963	−	1.36569i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	12.8453			0.590625
$474$		0			0
$475$	−3.22939	+	5.59347i	−0.148175	+	0.256646i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	16.6853	+	28.8999i	0.762373	+	1.32047i	0.941625	+	0.336665i	$0.109299\pi$
$479$	16.6853	+	28.8999i	0.762373	+	1.32047i	−0.179252	+	0.983803i	$0.557368\pi$
$480$		0			0
$481$	−11.2593	−	6.50056i	−0.513380	−	0.296400i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	2.67191	+	4.62788i	0.121325	+	0.210141i
$486$		0			0
$487$	−32.8011	−	18.9377i	−1.48636	−	0.858150i	−0.486481	−	0.873691i	$-0.661720\pi$
$487$	−32.8011	−	18.9377i	−1.48636	−	0.858150i	−0.999879	+	0.0155410i	$0.995053\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	21.1550	−	12.2138i	0.954711	−	0.551203i	0.0601697	−	0.998188i	$-0.480836\pi$
$491$	21.1550	−	12.2138i	0.954711	−	0.551203i	0.894541	+	0.446986i	$0.147502\pi$
$492$		0			0
$493$	43.0261	−	24.8411i	1.93780	−	1.11879i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.347947	−	0.971826i	0.0156075	−	0.0435923i
$498$		0			0
$499$	31.4156	+	18.1378i	1.40636	+	0.811961i	0.995035	−	0.0995293i	$-0.0317337\pi$
$499$	31.4156	+	18.1378i	1.40636	+	0.811961i	0.411322	+	0.911490i	$0.365067\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	7.84762			0.349908			0.174954	−	0.984577i	$-0.444022\pi$
$503$	7.84762			0.349908			0.174954	+	0.984577i	$0.444022\pi$
$504$		0			0
$505$	2.56140			0.113981
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−33.4820	−	19.3308i	−1.48406	−	0.856824i	−0.484228	−	0.874942i	$-0.660899\pi$
$509$	−33.4820	−	19.3308i	−1.48406	−	0.856824i	−0.999836	+	0.0181176i	$0.994233\pi$
$510$		0			0
$511$	7.32188	+	8.63339i	0.323901	+	0.381919i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−11.4075	+	6.58611i	−0.502674	+	0.290219i
$516$		0			0
$517$	0.135088	−	0.0779929i	0.00594115	−	0.00343012i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−21.3950	−	12.3524i	−0.937332	−	0.541169i	−0.0482092	−	0.998837i	$-0.515351\pi$
$521$	−21.3950	−	12.3524i	−0.937332	−	0.541169i	−0.889123	+	0.457668i	$0.848685\pi$
$522$		0			0
$523$	20.0144	+	34.6660i	0.875168	+	1.51584i	0.856583	+	0.516009i	$0.172583\pi$
$523$	20.0144	+	34.6660i	0.875168	+	1.51584i	0.0185852	+	0.999827i	$0.494084\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	45.7719	+	26.4264i	1.99386	+	1.15115i
$528$		0			0
$529$	4.22828	+	7.32359i	0.183838	+	0.318417i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	7.21337	−	12.4939i	0.312446	−	0.541172i
$534$		0			0
$535$	7.31379			0.316203
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−9.78554	−	1.61967i	−0.421493	−	0.0697642i
$540$		0			0
$541$	10.0341	+	17.3795i	0.431399	+	0.747205i	0.996994	−	0.0774780i	$-0.0246868\pi$
$541$	10.0341	+	17.3795i	0.431399	+	0.747205i	−0.565595	+	0.824683i	$0.691353\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	1.49663	−	0.864081i	0.0641086	−	0.0370131i
$546$		0			0
$547$	6.60776	+	3.81499i	0.282528	+	0.163117i	0.634567	−	0.772868i	$-0.281178\pi$
$547$	6.60776	+	3.81499i	0.282528	+	0.163117i	−0.352040	+	0.935985i	$0.614512\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	11.6588			0.496680
$552$		0			0
$553$	5.35282	−	14.9506i	0.227625	−	0.635763i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	15.0488	−	26.0653i	0.637638	−	1.10442i	−0.348312	−	0.937379i	$-0.613245\pi$
$557$	15.0488	−	26.0653i	0.637638	−	1.10442i	0.985950	−	0.167042i	$-0.0534216\pi$
$558$		0			0
$559$	15.7488			0.666105
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−1.89980			−0.0800669			−0.0400335	−	0.999198i	$-0.512746\pi$
$563$	−1.89980			−0.0800669			−0.0400335	+	0.999198i	$0.512746\pi$
$564$		0			0
$565$			5.23710i			0.220327i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−10.9733			−0.460024			−0.230012	−	0.973188i	$-0.573876\pi$
$569$	−10.9733			−0.460024			−0.230012	+	0.973188i	$0.573876\pi$
$570$		0			0
$571$			13.1336i			0.549625i	0.961498	+	0.274813i	$0.0886159\pi$
$571$			13.1336i			0.549625i	−0.961498	+	0.274813i	$0.911384\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			24.5882i			1.02540i
$576$		0			0
$577$	−24.2132	−	13.9795i	−1.00801	−	0.581973i	−0.0973997	−	0.995245i	$-0.531053\pi$
$577$	−24.2132	−	13.9795i	−1.00801	−	0.581973i	−0.910608	+	0.413272i	$0.864386\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	31.8287	−	26.9935i	1.32048	−	1.11988i
$582$		0			0
$583$			12.1454i			0.503011i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−7.27205	+	12.5956i	−0.300150	+	0.519875i	−0.976170	−	0.217009i	$-0.930370\pi$
$587$	−7.27205	+	12.5956i	−0.300150	+	0.519875i	0.676020	+	0.736883i	$0.263703\pi$
$588$		0			0
$589$	6.20140	+	10.7411i	0.255524	+	0.442581i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−37.9941	+	21.9359i	−1.56023	+	0.900800i	−0.562998	+	0.826458i	$0.690352\pi$
$593$	−37.9941	+	21.9359i	−1.56023	+	0.900800i	−0.997233	+	0.0743413i	$0.976315\pi$
$594$		0			0
$595$	−2.33120	−	12.8266i	−0.0955698	−	0.525840i
$596$		0			0
$597$		0			0
$598$		0			0
$599$		−	12.1395i		−	0.496008i	−0.968759	−	0.248004i	$-0.920225\pi$
$599$		−	12.1395i		−	0.496008i	0.968759	−	0.248004i	$-0.0797745\pi$
$600$		0			0
$601$	−34.5034	−	19.9205i	−1.40742	−	0.812576i	−0.412284	−	0.911055i	$-0.635269\pi$
$601$	−34.5034	−	19.9205i	−1.40742	−	0.812576i	−0.995139	+	0.0984793i	$0.968602\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−6.11208	+	3.52881i	−0.248491	+	0.143467i
$606$		0			0
$607$	8.03387	−	13.9151i	0.326085	−	0.564795i	−0.655647	−	0.755068i	$-0.727604\pi$
$607$	8.03387	−	13.9151i	0.326085	−	0.564795i	0.981731	+	0.190273i	$0.0609372\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	0.165623	−	0.0956227i	0.00670040	−	0.00386848i
$612$		0			0
$613$	17.8831	−	30.9744i	0.722290	−	1.25104i	−0.237789	−	0.971317i	$-0.576423\pi$
$613$	17.8831	−	30.9744i	0.722290	−	1.25104i	0.960080	−	0.279727i	$-0.0902439\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−6.64049	−	11.5017i	−0.267336	−	0.463040i	0.700837	−	0.713322i	$-0.252810\pi$
$617$	−6.64049	−	11.5017i	−0.267336	−	0.463040i	−0.968173	+	0.250282i	$0.919477\pi$
$618$		0			0
$619$	12.9291	+	22.3939i	0.519666	+	0.900088i	0.999739	+	0.0228592i	$0.00727694\pi$
$619$	12.9291	+	22.3939i	0.519666	+	0.900088i	−0.480073	+	0.877229i	$0.659390\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−18.5031	+	3.36289i	−0.741313	+	0.134731i
$624$		0			0
$625$	−8.06973	+	13.9772i	−0.322789	+	0.559087i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		−	46.9839i		−	1.87337i
$630$		0			0
$631$		−	35.8684i		−	1.42790i	−0.700198	−	0.713948i	$-0.746905\pi$
$631$		−	35.8684i		−	1.42790i	0.700198	−	0.713948i	$-0.253095\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−6.10004	+	10.5656i	−0.242073	+	0.419282i
$636$		0			0
$637$	−11.9975	−	1.98579i	−0.475358	−	0.0786798i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	12.0641	+	20.8956i	0.476502	+	0.825325i	0.999637	−	0.0269240i	$-0.00857120\pi$
$641$	12.0641	+	20.8956i	0.476502	+	0.825325i	−0.523136	+	0.852249i	$0.675238\pi$
$642$		0			0
$643$	7.71638	+	13.3652i	0.304304	+	0.527070i	0.977106	−	0.212752i	$-0.0682427\pi$
$643$	7.71638	+	13.3652i	0.304304	+	0.527070i	−0.672802	+	0.739823i	$0.734909\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−20.0842	+	34.7869i	−0.789592	+	1.36761i	0.136625	+	0.990623i	$0.456375\pi$
$647$	−20.0842	+	34.7869i	−0.789592	+	1.36761i	−0.926217	+	0.376991i	$0.876959\pi$
$648$		0			0
$649$	0.0903371	−	0.0521561i	0.00354604	−	0.00204731i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−25.2555	+	43.7438i	−0.988324	+	1.71183i	−0.362206	+	0.932098i	$0.617976\pi$
$653$	−25.2555	+	43.7438i	−0.988324	+	1.71183i	−0.626117	+	0.779729i	$0.715357\pi$
$654$		0			0
$655$	−3.57653	+	2.06491i	−0.139747	+	0.0806828i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	16.7746	+	9.68482i	0.653446	+	0.377267i	0.789775	−	0.613397i	$-0.210197\pi$
$659$	16.7746	+	9.68482i	0.653446	+	0.377267i	−0.136329	+	0.990664i	$0.543531\pi$
$660$		0			0
$661$		−	25.3992i		−	0.987915i	−0.869486	−	0.493957i	$-0.835550\pi$
$661$		−	25.3992i		−	0.987915i	0.869486	−	0.493957i	$-0.164450\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	1.03123	−	2.88024i	0.0399892	−	0.111691i
$666$		0			0
$667$	38.4378	−	22.1921i	1.48832	−	0.859280i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	0.876924	+	1.51888i	0.0338533	+	0.0586356i
$672$		0			0
$673$	−9.47290	+	16.4075i	−0.365153	+	0.632464i	−0.988801	−	0.149242i	$-0.952317\pi$
$673$	−9.47290	+	16.4075i	−0.365153	+	0.632464i	0.623647	+	0.781706i	$0.285650\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$		−	48.4853i		−	1.86344i	−0.363178	−	0.931720i	$-0.618308\pi$
$677$		−	48.4853i		−	1.86344i	0.363178	−	0.931720i	$-0.381692\pi$
$678$		0			0
$679$	11.6515	+	13.7385i	0.447143	+	0.527236i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−21.1815	−	12.2292i	−0.810489	−	0.467936i	0.0366369	−	0.999329i	$-0.488336\pi$
$683$	−21.1815	−	12.2292i	−0.810489	−	0.467936i	−0.847126	+	0.531393i	$0.821669\pi$
$684$		0			0
$685$			10.7411i			0.410398i
$686$		0			0
$687$		0			0
$688$		0			0
$689$			14.8908i			0.567294i
$690$		0			0
$691$	−38.3164			−1.45763			−0.728813	−	0.684713i	$-0.759928\pi$
$691$	−38.3164			−1.45763			−0.728813	+	0.684713i	$0.759928\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		−	7.24535i		−	0.274832i
$696$		0			0
$697$	52.1359			1.97479
$698$		0			0
$699$		0			0
$700$		0			0
$701$	33.3296			1.25884			0.629421	−	0.777064i	$-0.283292\pi$
$701$	33.3296			1.25884			0.629421	+	0.777064i	$0.283292\pi$
$702$		0			0
$703$	5.51276	−	9.54839i	0.207918	−	0.360124i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	8.49531	−	1.54400i	0.319499	−	0.0580680i
$708$		0			0
$709$	1.43783			0.0539990			0.0269995	−	0.999635i	$-0.491405\pi$
$709$	1.43783			0.0539990			0.0269995	+	0.999635i	$0.491405\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	40.8908	+	23.6083i	1.53137	+	0.884138i
$714$		0			0
$715$	1.67316	−	0.966001i	0.0625727	−	0.0361264i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	12.0257	+	20.8291i	0.448481	+	0.776793i	0.998287	−	0.0584998i	$-0.0186317\pi$
$719$	12.0257	+	20.8291i	0.448481	+	0.776793i	−0.549806	+	0.835292i	$0.685298\pi$
$720$		0			0
$721$	−33.8647	+	28.7203i	−1.26119	+	1.06960i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	34.6931			1.28847
$726$		0			0
$727$	−7.87496	+	13.6398i	−0.292066	+	0.505873i	−0.974298	−	0.225262i	$-0.927676\pi$
$727$	−7.87496	+	13.6398i	−0.292066	+	0.505873i	0.682232	+	0.731136i	$0.261009\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	28.4568	+	49.2887i	1.05251	+	1.82301i
$732$		0			0
$733$	−36.2669	−	20.9387i	−1.33955	−	0.773389i	−0.352809	−	0.935695i	$-0.614774\pi$
$733$	−36.2669	−	20.9387i	−1.33955	−	0.773389i	−0.986740	+	0.162306i	$0.948107\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	8.41212	+	14.5702i	0.309864	+	0.536701i
$738$		0			0
$739$	−1.29085	−	0.745272i	−0.0474846	−	0.0274153i	0.476070	−	0.879408i	$-0.342061\pi$
$739$	−1.29085	−	0.745272i	−0.0474846	−	0.0274153i	−0.523554	+	0.851992i	$0.675394\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	6.96436	−	4.02088i	0.255498	−	0.147512i	−0.366781	−	0.930307i	$-0.619540\pi$
$743$	6.96436	−	4.02088i	0.255498	−	0.147512i	0.622279	+	0.782796i	$0.286207\pi$
$744$		0			0
$745$	−12.8444	+	7.41571i	−0.470582	+	0.271691i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	24.2574	−	4.40871i	0.886346	−	0.161091i
$750$		0			0
$751$	−13.4437	−	7.76170i	−0.490566	−	0.283229i	0.234243	−	0.972178i	$-0.424739\pi$
$751$	−13.4437	−	7.76170i	−0.490566	−	0.283229i	−0.724809	+	0.688949i	$0.758072\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	2.41669			0.0879523
$756$		0			0
$757$	19.4868			0.708260			0.354130	−	0.935196i	$-0.384777\pi$
$757$	19.4868			0.708260			0.354130	+	0.935196i	$0.384777\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−20.0623	−	11.5830i	−0.727259	−	0.419883i	0.0901595	−	0.995927i	$-0.471262\pi$
$761$	−20.0623	−	11.5830i	−0.727259	−	0.419883i	−0.817419	+	0.576044i	$0.804596\pi$
$762$		0			0
$763$	4.44296	−	3.76803i	0.160846	−	0.136412i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	0.110757	−	0.0639457i	0.00399921	−	0.00230894i
$768$		0			0
$769$	28.2140	−	16.2894i	1.01742	−	0.587410i	0.104067	−	0.994570i	$-0.466814\pi$
$769$	28.2140	−	16.2894i	1.01742	−	0.587410i	0.913357	+	0.407160i	$0.133481\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−6.85868	−	3.95986i	−0.246690	−	0.142426i	0.371558	−	0.928410i	$-0.378824\pi$
$773$	−6.85868	−	3.95986i	−0.246690	−	0.142426i	−0.618248	+	0.785983i	$0.712157\pi$
$774$		0			0
$775$	18.4535	+	31.9625i	0.662871	+	1.14813i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	10.5954	+	6.11726i	0.379620	+	0.219174i
$780$		0			0
$781$	0.276411	+	0.478758i	0.00989077	+	0.0171313i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−5.97629	+	10.3512i	−0.213303	+	0.369452i
$786$		0			0
$787$	30.2452			1.07813			0.539063	−	0.842266i	$-0.318779\pi$
$787$	30.2452			1.07813			0.539063	+	0.842266i	$0.318779\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	3.15689	+	17.3697i	0.112246	+	0.617596i
$792$		0			0
$793$	1.07515	+	1.86221i	0.0381796	+	0.0661290i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−26.9751	+	15.5741i	−0.955507	+	0.551662i	−0.894787	−	0.446493i	$-0.852673\pi$
$797$	−26.9751	+	15.5741i	−0.955507	+	0.551662i	−0.0607197	+	0.998155i	$0.519340\pi$
$798$		0			0
$799$	0.598535	+	0.345564i	0.0211746	+	0.0122252i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−6.06259			−0.213944
$804$		0			0
$805$	−2.08260	−	11.4588i	−0.0734019	−	0.403869i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	10.0362	−	17.3832i	0.352853	−	0.611160i	−0.633895	−	0.773419i	$-0.718545\pi$
$809$	10.0362	−	17.3832i	0.352853	−	0.611160i	0.986748	+	0.162259i	$0.0518781\pi$
$810$		0			0
$811$	−20.4633			−0.718564			−0.359282	−	0.933229i	$-0.616978\pi$
$811$	−20.4633			−0.718564			−0.359282	+	0.933229i	$0.616978\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−4.49629			−0.157498
$816$		0			0
$817$			13.3557i			0.467258i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	42.5686			1.48566			0.742828	−	0.669483i	$-0.233484\pi$
$821$	42.5686			1.48566			0.742828	+	0.669483i	$0.233484\pi$
$822$		0			0
$823$		−	12.2908i		−	0.428432i	−0.976786	−	0.214216i	$-0.931280\pi$
$823$		−	12.2908i		−	0.428432i	0.976786	−	0.214216i	$-0.0687196\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	16.1935i		−	0.563104i	−0.959546	−	0.281552i	$-0.909151\pi$
$827$		−	16.1935i		−	0.563104i	0.959546	−	0.281552i	$-0.0908493\pi$
$828$		0			0
$829$	0.0315654	+	0.0182243i	0.00109631	+	0.000632956i	0.500548	−	0.865709i	$-0.333132\pi$
$829$	0.0315654	+	0.0182243i	0.00109631	+	0.000632956i	−0.499452	+	0.866342i	$0.666465\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−15.4636	−	41.1364i	−0.535782	−	1.42529i
$834$		0			0
$835$		−	3.58406i		−	0.124032i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−21.2294	+	36.7705i	−0.732921	+	1.26946i	0.222708	+	0.974885i	$0.428510\pi$
$839$	−21.2294	+	36.7705i	−0.732921	+	1.26946i	−0.955629	+	0.294572i	$0.904823\pi$
$840$		0			0
$841$	−16.8122	−	29.1196i	−0.579732	−	1.00413i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−6.78481	+	3.91721i	−0.233404	+	0.134756i
$846$		0			0
$847$	−18.1446	+	15.3882i	−0.623455	+	0.528745i
$848$		0			0
$849$		0			0
$850$		0			0
$851$		−	41.9735i		−	1.43883i
$852$		0			0
$853$	−3.60970	−	2.08406i	−0.123594	−	0.0713568i	0.436929	−	0.899496i	$-0.356066\pi$
$853$	−3.60970	−	2.08406i	−0.123594	−	0.0713568i	−0.560522	+	0.828139i	$0.689400\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	9.96984	−	5.75609i	0.340563	−	0.196624i	−0.319958	−	0.947432i	$-0.603669\pi$
$857$	9.96984	−	5.75609i	0.340563	−	0.196624i	0.660521	+	0.750808i	$0.270335\pi$
$858$		0			0
$859$	−2.10057	+	3.63829i	−0.0716704	+	0.124137i	−0.899633	−	0.436646i	$-0.856166\pi$
$859$	−2.10057	+	3.63829i	−0.0716704	+	0.124137i	0.827963	+	0.560783i	$0.189500\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	15.9911	−	9.23249i	0.544345	−	0.314278i	−0.202493	−	0.979284i	$-0.564904\pi$
$863$	15.9911	−	9.23249i	0.544345	−	0.314278i	0.746838	+	0.665006i	$0.231571\pi$
$864$		0			0
$865$	7.01513	−	12.1506i	0.238522	−	0.413132i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	4.25231	+	7.36522i	0.144250	+	0.249848i
$870$		0			0
$871$	10.3136	+	17.8637i	0.349464	+	0.605289i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	6.56842	−	18.3458i	0.222053	−	0.620201i
$876$		0			0
$877$	−2.77845	+	4.81242i	−0.0938217	+	0.162504i	−0.909116	−	0.416543i	$-0.863242\pi$
$877$	−2.77845	+	4.81242i	−0.0938217	+	0.162504i	0.815295	+	0.579046i	$0.196575\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			22.3336i			0.752438i	0.926531	+	0.376219i	$0.122776\pi$
$881$			22.3336i			0.752438i	−0.926531	+	0.376219i	$0.877224\pi$
$882$		0			0
$883$			36.9024i			1.24186i	0.783865	+	0.620932i	$0.213246\pi$
$883$			36.9024i			1.24186i	−0.783865	+	0.620932i	$0.786754\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−3.40494	+	5.89752i	−0.114327	+	0.198020i	−0.917510	−	0.397712i	$-0.869804\pi$
$887$	−3.40494	+	5.89752i	−0.114327	+	0.198020i	0.803184	+	0.595731i	$0.203138\pi$
$888$		0			0
$889$	−13.8629	+	38.7196i	−0.464948	+	1.29861i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	0.0810923	+	0.140456i	0.00271365	+	0.00470018i
$894$		0			0
$895$	−2.78759	−	4.82825i	−0.0931789	−	0.161391i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	33.3105	−	57.6955i	1.11097	−	1.92425i
$900$		0			0
$901$	−46.6033	+	26.9064i	−1.55258	+	0.896383i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	2.47925	−	4.29418i	0.0824130	−	0.142743i
$906$		0			0
$907$	3.60190	−	2.07956i	0.119599	−	0.0690506i	−0.439007	−	0.898484i	$-0.644670\pi$
$907$	3.60190	−	2.07956i	0.119599	−	0.0690506i	0.558606	+	0.829433i	$0.311336\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−4.80883	−	2.77638i	−0.159324	−	0.0919856i	0.418218	−	0.908347i	$-0.362655\pi$
$911$	−4.80883	−	2.77638i	−0.159324	−	0.0919856i	−0.577542	+	0.816361i	$0.695988\pi$
$912$		0			0
$913$			22.3509i			0.739707i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−10.6175	+	9.00454i	−0.350619	+	0.297356i
$918$		0			0
$919$	23.2582	−	13.4281i	0.767216	−	0.442952i	−0.0646648	−	0.997907i	$-0.520598\pi$
$919$	23.2582	−	13.4281i	0.767216	−	0.442952i	0.831880	+	0.554955i	$0.187264\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	0.338892	+	0.586979i	0.0111548	+	0.0193206i
$924$		0			0
$925$	16.4044	−	28.4132i	0.539372	−	0.934220i
$926$		0			0
$927$		0			0
$928$		0			0
$929$		−	28.0523i		−	0.920365i	−0.887824	−	0.460183i	$-0.847784\pi$
$929$		−	28.0523i		−	0.920365i	0.887824	−	0.460183i	$-0.152216\pi$
$930$		0			0
$931$	1.68404	−	10.1744i	0.0551921	−	0.333453i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	6.04653	+	3.49097i	0.197743	+	0.114167i
$936$		0			0
$937$		−	15.2285i		−	0.497493i	−0.968569	−	0.248746i	$-0.919981\pi$
$937$		−	15.2285i		−	0.497493i	0.968569	−	0.248746i	$-0.0800186\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$			3.21460i			0.104793i	0.998626	+	0.0523965i	$0.0166860\pi$
$941$			3.21460i			0.104793i	−0.998626	+	0.0523965i	$0.983314\pi$
$942$		0			0
$943$	46.5760			1.51672
$944$		0			0
$945$		0			0
$946$		0			0
$947$			20.4308i			0.663911i	0.943295	+	0.331956i	$0.107708\pi$
$947$			20.4308i			0.663911i	−0.943295	+	0.331956i	$0.892292\pi$
$948$		0			0
$949$	−7.43299			−0.241285
$950$		0			0
$951$		0			0
$952$		0			0
$953$	57.3984			1.85932			0.929658	−	0.368423i	$-0.120102\pi$
$953$	57.3984			1.85932			0.929658	+	0.368423i	$0.120102\pi$
$954$		0			0
$955$	8.48329	−	14.6935i	0.274513	−	0.475470i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	6.47469	+	35.6247i	0.209079	+	1.15038i
$960$		0			0
$961$	39.8726			1.28621
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−3.47466	−	2.00610i	−0.111853	−	0.0645785i
$966$		0			0
$967$	31.0281	−	17.9141i	0.997797	−	0.576078i	0.0902010	−	0.995924i	$-0.471249\pi$
$967$	31.0281	−	17.9141i	0.997797	−	0.576078i	0.907596	+	0.419845i	$0.137916\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−27.6346	−	47.8645i	−0.886836	−	1.53605i	−0.843594	−	0.536981i	$-0.819565\pi$
$971$	−27.6346	−	47.8645i	−0.886836	−	1.53605i	−0.0432421	−	0.999065i	$-0.513769\pi$
$972$		0			0
$973$	−4.36745	−	24.0304i	−0.140014	−	0.770380i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−3.30526			−0.105745			−0.0528723	−	0.998601i	$-0.516838\pi$
$977$	−3.30526			−0.105745			−0.0528723	+	0.998601i	$0.516838\pi$
$978$		0			0
$979$	5.03592	−	8.72248i	0.160949	−	0.278772i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−29.6188	−	51.3012i	−0.944692	−	1.63626i	−0.756366	−	0.654149i	$-0.773027\pi$
$983$	−29.6188	−	51.3012i	−0.944692	−	1.63626i	−0.188327	−	0.982106i	$-0.560306\pi$
$984$		0			0
$985$	8.63571	+	4.98583i	0.275157	+	0.158862i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	25.4222	+	44.0325i	0.808378	+	1.40015i
$990$		0			0
$991$	−15.3830	−	8.88141i	−0.488659	−	0.282127i	0.235359	−	0.971908i	$-0.424373\pi$
$991$	−15.3830	−	8.88141i	−0.488659	−	0.282127i	−0.724018	+	0.689781i	$0.757707\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−1.83972	+	1.06216i	−0.0583229	+	0.0336727i
$996$		0			0
$997$	−12.4110	+	7.16551i	−0.393061	+	0.226934i	−0.683486	−	0.729964i	$-0.739537\pi$
$997$	−12.4110	+	7.16551i	−0.393061	+	0.226934i	0.290424	+	0.956898i	$0.406204\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.cz.g.2719.7		24
3.2	odd	2		1008.2.cz.h.367.9	yes	24
4.3	odd	2		3024.2.cz.h.2719.7		24
7.5	odd	6		3024.2.bf.g.2287.7		24
9.4	even	3		3024.2.bf.h.1711.6		24
9.5	odd	6		1008.2.bf.g.31.7	✓	24
12.11	even	2		1008.2.cz.g.367.4	yes	24
21.5	even	6		1008.2.bf.h.943.6	yes	24
28.19	even	6		3024.2.bf.h.2287.7		24
36.23	even	6		1008.2.bf.h.31.6	yes	24
36.31	odd	6		3024.2.bf.g.1711.6		24
63.5	even	6		1008.2.cz.g.607.4	yes	24
63.40	odd	6		3024.2.cz.h.1279.7		24
84.47	odd	6		1008.2.bf.g.943.7	yes	24
252.103	even	6	inner	3024.2.cz.g.1279.7		24
252.131	odd	6		1008.2.cz.h.607.9	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.bf.g.31.7	✓	24	9.5	odd	6
1008.2.bf.g.943.7	yes	24	84.47	odd	6
1008.2.bf.h.31.6	yes	24	36.23	even	6
1008.2.bf.h.943.6	yes	24	21.5	even	6
1008.2.cz.g.367.4	yes	24	12.11	even	2
1008.2.cz.g.607.4	yes	24	63.5	even	6
1008.2.cz.h.367.9	yes	24	3.2	odd	2
1008.2.cz.h.607.9	yes	24	252.131	odd	6
3024.2.bf.g.1711.6		24	36.31	odd	6
3024.2.bf.g.2287.7		24	7.5	odd	6
3024.2.bf.h.1711.6		24	9.4	even	3
3024.2.bf.h.2287.7		24	28.19	even	6
3024.2.cz.g.1279.7		24	252.103	even	6	inner
3024.2.cz.g.2719.7		24	1.1	even	1	trivial
3024.2.cz.h.1279.7		24	63.40	odd	6
3024.2.cz.h.2719.7		24	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3024.cz (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.679706 + 0.392428i) q^{5} +(2.49091 + 0.891831i) q^{7} +O(q^{10})\)	\(q+(0.679706 + 0.392428i) q^{5} +(2.49091 + 0.891831i) q^{7} +(-1.22712 + 0.708477i) q^{11} +(-1.50450 + 0.868623i) q^{13} +(-5.43701 - 3.13906i) q^{17} +(-0.736632 - 1.27588i) q^{19} +(-4.85720 - 2.80431i) q^{23} +(-2.19200 - 3.79666i) q^{25} +(-3.95678 + 6.85335i) q^{29} -8.41859 q^{31} +(1.34311 + 1.58369i) q^{35} +(3.74187 + 6.48111i) q^{37} +(-7.19180 + 4.15219i) q^{41} +(-7.85087 - 4.53270i) q^{43} -0.110085 q^{47} +(5.40927 + 4.44294i) q^{49} +(4.28575 - 7.42313i) q^{53} -1.11211 q^{55} -0.0736173 q^{59} -1.23776i q^{61} -1.36349 q^{65} -11.8735i q^{67} -0.390149i q^{71} +(3.70538 + 2.13930i) q^{73} +(-3.68848 + 0.670370i) q^{77} -6.00205i q^{79} +(7.88696 - 13.6606i) q^{83} +(-2.46371 - 4.26727i) q^{85} +(-6.15579 + 3.55405i) q^{89} +(-4.52224 + 0.821903i) q^{91} -1.15630i q^{95} +(5.89647 + 3.40433i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{5} - 4 q^{7}+O(q^{10}) \) 24 * q + 3 * q^5 - 4 * q^7	\( 24 q + 3 q^{5} - 4 q^{7} - 9 q^{11} - 3 q^{13} + 3 q^{17} + 4 q^{19} - 6 q^{23} + 15 q^{25} - 18 q^{29} - 34 q^{31} - 42 q^{35} - 3 q^{37} - 36 q^{41} - 24 q^{43} - 42 q^{47} + 30 q^{49} + 12 q^{53} + 30 q^{55} - 12 q^{59} + 48 q^{73} + 48 q^{77} - 48 q^{83} - 21 q^{85} - 39 q^{89} - 9 q^{91} + 3 q^{97}+O(q^{100}) \) 24 * q + 3 * q^5 - 4 * q^7 - 9 * q^11 - 3 * q^13 + 3 * q^17 + 4 * q^19 - 6 * q^23 + 15 * q^25 - 18 * q^29 - 34 * q^31 - 42 * q^35 - 3 * q^37 - 36 * q^41 - 24 * q^43 - 42 * q^47 + 30 * q^49 + 12 * q^53 + 30 * q^55 - 12 * q^59 + 48 * q^73 + 48 * q^77 - 48 * q^83 - 21 * q^85 - 39 * q^89 - 9 * q^91 + 3 * q^97

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