LMFDB - Embedded newform 3024.2.ca.e.2033.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3024,2,Mod(2033,3024)]

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([0, 0, 1, 1]))

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

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

chi := DirichletCharacter("3024.2033");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3024 = 2^{4} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3024.ca (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:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			2033.3
Character	$\chi$	$=$	3024.2033
Dual form			3024.2.ca.e.2609.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.76701 + 3.06054i) q^{5} +(-1.34480 + 2.27849i) q^{7} +O(q^{10})$	$q+(-1.76701 + 3.06054i) q^{5} +(-1.34480 + 2.27849i) q^{7} +(-1.57467 + 0.909136i) q^{11} +(-2.78280 + 1.60665i) q^{13} +(-2.93434 + 5.08242i) q^{17} +(2.09143 - 1.20749i) q^{19} +(-3.33308 - 1.92436i) q^{23} +(-3.74462 - 6.48586i) q^{25} +(-5.79110 - 3.34349i) q^{29} +4.87236i q^{31} +(-4.59714 - 8.14192i) q^{35} +(-0.905385 - 1.56817i) q^{37} +(5.03152 + 8.71485i) q^{41} +(2.36232 - 4.09166i) q^{43} +7.92151 q^{47} +(-3.38302 - 6.12823i) q^{49} +(2.26517 + 1.30780i) q^{53} -6.42580i q^{55} +8.81208 q^{59} +10.3744i q^{61} -11.3558i q^{65} +7.84769 q^{67} +7.62952i q^{71} +(-11.7672 - 6.79382i) q^{73} +(0.0461599 - 4.81048i) q^{77} +1.84254 q^{79} +(5.61748 - 9.72975i) q^{83} +(-10.3700 - 17.9613i) q^{85} +(-6.89792 - 11.9475i) q^{89} +(0.0815748 - 8.50119i) q^{91} +8.53455i q^{95} +(13.7982 + 7.96638i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q - 12 q^{23} - 24 q^{25} - 18 q^{29} - 6 q^{41} + 6 q^{43} + 36 q^{47} + 6 q^{49} - 12 q^{53} + 36 q^{77} + 12 q^{79} - 18 q^{89} - 6 q^{91}+O(q^{100}) $ 48 * q - 12 * q^23 - 24 * q^25 - 18 * q^29 - 6 * q^41 + 6 * q^43 + 36 * q^47 + 6 * q^49 - 12 * q^53 + 36 * q^77 + 12 * q^79 - 18 * q^89 - 6 * q^91

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	−1.76701	+	3.06054i	−0.790229	+	1.36872i	0.135596	+	0.990764i	$0.456705\pi$
$5$	−1.76701	+	3.06054i	−0.790229	+	1.36872i	−0.925825	+	0.377952i	$0.876628\pi$
$6$		0			0
$7$	−1.34480	+	2.27849i	−0.508287	+	0.861188i
$7$	−1.34480	+	2.27849i	−0.508287	+	0.861188i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.57467	+	0.909136i	−0.474781	+	0.274115i	−0.718239	−	0.695796i	$-0.755052\pi$
$11$	−1.57467	+	0.909136i	−0.474781	+	0.274115i	0.243458	+	0.969911i	$0.421718\pi$
$12$		0			0
$13$	−2.78280	+	1.60665i	−0.771809	+	0.445604i	−0.833519	−	0.552490i	$-0.813678\pi$
$13$	−2.78280	+	1.60665i	−0.771809	+	0.445604i	0.0617107	+	0.998094i	$0.480344\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.93434	+	5.08242i	−0.711682	+	1.23267i	0.252544	+	0.967585i	$0.418733\pi$
$17$	−2.93434	+	5.08242i	−0.711682	+	1.23267i	−0.964225	+	0.265083i	$0.914600\pi$
$18$		0			0
$19$	2.09143	−	1.20749i	0.479807	−	0.277017i	−0.240529	−	0.970642i	$-0.577321\pi$
$19$	2.09143	−	1.20749i	0.479807	−	0.277017i	0.720336	+	0.693625i	$0.243988\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.33308	−	1.92436i	−0.694996	−	0.401256i	0.110485	−	0.993878i	$-0.464760\pi$
$23$	−3.33308	−	1.92436i	−0.694996	−	0.401256i	−0.805481	+	0.592622i	$0.798093\pi$
$24$		0			0
$25$	−3.74462	−	6.48586i	−0.748923	−	1.29717i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−5.79110	−	3.34349i	−1.07538	−	0.620871i	−0.145734	−	0.989324i	$-0.546554\pi$
$29$	−5.79110	−	3.34349i	−1.07538	−	0.620871i	−0.929647	+	0.368452i	$0.879888\pi$
$30$		0			0
$31$			4.87236i			0.875102i	0.899193	+	0.437551i	$0.144154\pi$
$31$			4.87236i			0.875102i	−0.899193	+	0.437551i	$0.855846\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−4.59714	−	8.14192i	−0.777059	−	1.37624i
$36$		0			0
$37$	−0.905385	−	1.56817i	−0.148844	−	0.257806i	0.781956	−	0.623333i	$-0.214222\pi$
$37$	−0.905385	−	1.56817i	−0.148844	−	0.257806i	−0.930801	+	0.365527i	$0.880889\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	5.03152	+	8.71485i	0.785792	+	1.36103i	0.928525	+	0.371270i	$0.121078\pi$
$41$	5.03152	+	8.71485i	0.785792	+	1.36103i	−0.142733	+	0.989761i	$0.545589\pi$
$42$		0			0
$43$	2.36232	−	4.09166i	0.360251	−	0.623973i	−0.627751	−	0.778414i	$-0.716024\pi$
$43$	2.36232	−	4.09166i	0.360251	−	0.623973i	0.988002	+	0.154441i	$0.0493577\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	7.92151			1.15547			0.577736	−	0.816224i	$-0.303936\pi$
$47$	7.92151			1.15547			0.577736	+	0.816224i	$0.303936\pi$
$48$		0			0
$49$	−3.38302	−	6.12823i	−0.483289	−	0.875461i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	2.26517	+	1.30780i	0.311146	+	0.179640i	0.647439	−	0.762117i	$-0.275840\pi$
$53$	2.26517	+	1.30780i	0.311146	+	0.179640i	−0.336293	+	0.941757i	$0.609173\pi$
$54$		0			0
$55$		−	6.42580i		−	0.866454i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	8.81208			1.14724			0.573618	−	0.819123i	$-0.305540\pi$
$59$	8.81208			1.14724			0.573618	+	0.819123i	$0.305540\pi$
$60$		0			0
$61$			10.3744i			1.32830i	0.747599	+	0.664151i	$0.231207\pi$
$61$			10.3744i			1.32830i	−0.747599	+	0.664151i	$0.768793\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$		−	11.3558i		−	1.40852i
$66$		0			0
$67$	7.84769			0.958748			0.479374	−	0.877611i	$-0.340864\pi$
$67$	7.84769			0.958748			0.479374	+	0.877611i	$0.340864\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			7.62952i			0.905458i	0.891648	+	0.452729i	$0.149549\pi$
$71$			7.62952i			0.905458i	−0.891648	+	0.452729i	$0.850451\pi$
$72$		0			0
$73$	−11.7672	−	6.79382i	−1.37725	−	0.795156i	−0.385423	−	0.922740i	$-0.625945\pi$
$73$	−11.7672	−	6.79382i	−1.37725	−	0.795156i	−0.991828	+	0.127584i	$0.959278\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.0461599	−	4.81048i	0.00526041	−	0.548205i
$78$		0			0
$79$	1.84254			0.207301			0.103651	−	0.994614i	$-0.466948\pi$
$79$	1.84254			0.207301			0.103651	+	0.994614i	$0.466948\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	5.61748	−	9.72975i	0.616598	−	1.06798i	−0.373504	−	0.927629i	$-0.621844\pi$
$83$	5.61748	−	9.72975i	0.616598	−	1.06798i	0.990102	−	0.140351i	$-0.0448230\pi$
$84$		0			0
$85$	−10.3700	−	17.9613i	−1.12478	−	1.94818i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−6.89792	−	11.9475i	−0.731178	−	1.26644i	−0.956380	−	0.292125i	$-0.905638\pi$
$89$	−6.89792	−	11.9475i	−0.731178	−	1.26644i	0.225202	−	0.974312i	$-0.427696\pi$
$90$		0			0
$91$	0.0815748	−	8.50119i	0.00855137	−	0.891167i
$92$		0			0
$93$		0			0
$94$		0			0
$95$			8.53455i			0.875627i
$96$		0			0
$97$	13.7982	+	7.96638i	1.40099	+	0.808863i	0.994494	−	0.104789i	$-0.0334168\pi$
$97$	13.7982	+	7.96638i	1.40099	+	0.808863i	0.406497	+	0.913652i	$0.366750\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−5.56250	−	9.63453i	−0.553489	−	0.958671i	−0.998019	−	0.0629076i	$-0.979963\pi$
$101$	−5.56250	−	9.63453i	−0.553489	−	0.958671i	0.444530	−	0.895764i	$-0.353371\pi$
$102$		0			0
$103$	−0.522237	−	0.301514i	−0.0514576	−	0.0297091i	0.474050	−	0.880498i	$-0.342791\pi$
$103$	−0.522237	−	0.301514i	−0.0514576	−	0.0297091i	−0.525508	+	0.850789i	$0.676125\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	11.3342	−	6.54381i	1.09572	−	0.632614i	0.160627	−	0.987015i	$-0.448649\pi$
$107$	11.3342	−	6.54381i	1.09572	−	0.632614i	0.935094	+	0.354401i	$0.115315\pi$
$108$		0			0
$109$	−1.37061	+	2.37396i	−0.131280	+	0.227384i	−0.924170	−	0.381981i	$-0.875242\pi$
$109$	−1.37061	+	2.37396i	−0.131280	+	0.227384i	0.792890	+	0.609365i	$0.208575\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−6.65125	+	3.84010i	−0.625697	+	0.361246i	−0.779084	−	0.626920i	$-0.784315\pi$
$113$	−6.65125	+	3.84010i	−0.625697	+	0.361246i	0.153387	+	0.988166i	$0.450982\pi$
$114$		0			0
$115$	11.7792	−	6.80070i	1.09841	−	0.634168i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−7.63415	−	13.5207i	−0.699821	−	1.23944i
$120$		0			0
$121$	−3.84694	+	6.66310i	−0.349722	+	0.605736i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	8.79697			0.786825
$126$		0			0
$127$	−17.9246			−1.59055			−0.795277	−	0.606246i	$-0.792675\pi$
$127$	−17.9246			−1.59055			−0.795277	+	0.606246i	$0.792675\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	8.48534	−	14.6970i	0.741367	−	1.28409i	−0.210506	−	0.977593i	$-0.567511\pi$
$131$	8.48534	−	14.6970i	0.741367	−	1.28409i	0.951873	−	0.306493i	$-0.0991556\pi$
$132$		0			0
$133$	−0.0613082	+	6.38913i	−0.00531609	+	0.554008i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−4.81631	+	2.78070i	−0.411485	+	0.237571i	−0.691428	−	0.722446i	$-0.743018\pi$
$137$	−4.81631	+	2.78070i	−0.411485	+	0.237571i	0.279943	+	0.960017i	$0.409685\pi$
$138$		0			0
$139$	−12.4503	+	7.18817i	−1.05602	+	0.609693i	−0.924328	−	0.381598i	$-0.875374\pi$
$139$	−12.4503	+	7.18817i	−1.05602	+	0.609693i	−0.131690	+	0.991291i	$0.542040\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	2.92132	−	5.05988i	0.244293	−	0.423129i
$144$		0			0
$145$	20.4658	−	11.8159i	1.69959	−	0.981261i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	5.56086	+	3.21056i	0.455563	+	0.263019i	0.710177	−	0.704023i	$-0.248615\pi$
$149$	5.56086	+	3.21056i	0.455563	+	0.263019i	−0.254614	+	0.967043i	$0.581948\pi$
$150$		0			0
$151$	7.99627	+	13.8499i	0.650727	+	1.12709i	0.982947	+	0.183890i	$0.0588690\pi$
$151$	7.99627	+	13.8499i	0.650727	+	1.12709i	−0.332220	+	0.943202i	$0.607798\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−14.9121	−	8.60949i	−1.19777	−	0.691531i
$156$		0			0
$157$		−	13.9271i		−	1.11151i	−0.831348	−	0.555753i	$-0.812430\pi$
$157$		−	13.9271i		−	1.11151i	0.831348	−	0.555753i	$-0.187570\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	8.86696	−	5.00652i	0.698814	−	0.394569i
$162$		0			0
$163$	−7.79498	−	13.5013i	−0.610550	−	1.05750i	−0.991148	−	0.132762i	$-0.957615\pi$
$163$	−7.79498	−	13.5013i	−0.610550	−	1.05750i	0.380598	−	0.924740i	$-0.375718\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	6.58728	+	11.4095i	0.509739	+	0.882893i	0.999936	+	0.0112821i	$0.00359127\pi$
$167$	6.58728	+	11.4095i	0.509739	+	0.882893i	−0.490198	+	0.871611i	$0.663075\pi$
$168$		0			0
$169$	−1.33736	+	2.31638i	−0.102874	+	0.178183i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	11.2080			0.852132			0.426066	−	0.904692i	$-0.359899\pi$
$173$	11.2080			0.852132			0.426066	+	0.904692i	$0.359899\pi$
$174$		0			0
$175$	19.8137	+	0.190127i	1.49778	+	0.0143722i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−9.22783	−	5.32769i	−0.689721	−	0.398210i	0.113787	−	0.993505i	$-0.463702\pi$
$179$	−9.22783	−	5.32769i	−0.689721	−	0.398210i	−0.803507	+	0.595295i	$0.797035\pi$
$180$		0			0
$181$			11.8897i			0.883754i	0.897076	+	0.441877i	$0.145687\pi$
$181$			11.8897i			0.883754i	−0.897076	+	0.441877i	$0.854313\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	6.39928			0.470484
$186$		0			0
$187$		−	10.6709i		−	0.780330i
$188$		0			0
$189$		0			0
$190$		0			0
$191$			0.223967i			0.0162057i	0.999967	+	0.00810283i	$0.00257924\pi$
$191$			0.223967i			0.0162057i	−0.999967	+	0.00810283i	$0.997421\pi$
$192$		0			0
$193$	26.0745			1.87688			0.938442	−	0.345437i	$-0.112269\pi$
$193$	26.0745			1.87688			0.938442	+	0.345437i	$0.112269\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			1.56289i			0.111352i	0.998449	+	0.0556758i	$0.0177313\pi$
$197$			1.56289i			0.111352i	−0.998449	+	0.0556758i	$0.982269\pi$
$198$		0			0
$199$	−13.4725	−	7.77832i	−0.955037	−	0.551391i	−0.0603949	−	0.998175i	$-0.519236\pi$
$199$	−13.4725	−	7.77832i	−0.955037	−	0.551391i	−0.894642	+	0.446784i	$0.852569\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	15.4060	−	8.69863i	1.08129	−	0.610524i
$204$		0			0
$205$	−35.5629			−2.48382
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−2.19554	+	3.80279i	−0.151869	+	0.263045i
$210$		0			0
$211$	−6.98216	−	12.0935i	−0.480672	−	0.832548i	0.519082	−	0.854724i	$-0.326274\pi$
$211$	−6.98216	−	12.0935i	−0.480672	−	0.832548i	−0.999754	+	0.0221763i	$0.992941\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	8.34848	+	14.4600i	0.569361	+	0.986163i
$216$		0			0
$217$	−11.1016	−	6.55236i	−0.753628	−	0.444803i
$218$		0			0
$219$		0			0
$220$		0			0
$221$		−	18.8578i		−	1.26851i
$222$		0			0
$223$	−21.4242	−	12.3693i	−1.43467	−	0.828307i	−0.437198	−	0.899366i	$-0.644029\pi$
$223$	−21.4242	−	12.3693i	−1.43467	−	0.828307i	−0.997472	+	0.0710586i	$0.977362\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−3.12076	−	5.40532i	−0.207132	−	0.358764i	0.743678	−	0.668538i	$-0.233080\pi$
$227$	−3.12076	−	5.40532i	−0.207132	−	0.358764i	−0.950810	+	0.309775i	$0.899746\pi$
$228$		0			0
$229$	−13.7329	−	7.92870i	−0.907496	−	0.523943i	−0.0278714	−	0.999612i	$-0.508873\pi$
$229$	−13.7329	−	7.92870i	−0.907496	−	0.523943i	−0.879625	+	0.475668i	$0.842206\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	2.94574	−	1.70072i	0.192982	−	0.111418i	−0.400396	−	0.916342i	$-0.631127\pi$
$233$	2.94574	−	1.70072i	0.192982	−	0.111418i	0.593378	+	0.804924i	$0.297794\pi$
$234$		0			0
$235$	−13.9974	+	24.2441i	−0.913087	+	1.58151i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−16.3482	+	9.43864i	−1.05748	+	0.610535i	−0.924733	−	0.380615i	$-0.875712\pi$
$239$	−16.3482	+	9.43864i	−1.05748	+	0.610535i	−0.132744	+	0.991150i	$0.542379\pi$
$240$		0			0
$241$	−9.68610	+	5.59227i	−0.623937	+	0.360230i	−0.778400	−	0.627768i	$-0.783968\pi$
$241$	−9.68610	+	5.59227i	−0.623937	+	0.360230i	0.154463	+	0.987999i	$0.450635\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	24.7335	+	0.474714i	1.58017	+	0.0303284i
$246$		0			0
$247$	−3.88002	+	6.72039i	−0.246880	+	0.427608i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−15.4537			−0.975431			−0.487716	−	0.873003i	$-0.662170\pi$
$251$	−15.4537			−0.975431			−0.487716	+	0.873003i	$0.662170\pi$
$252$		0			0
$253$	6.99801			0.439961
$254$		0			0
$255$		0			0
$256$		0			0
$257$	5.32238	−	9.21864i	0.332001	−	0.575043i	−0.650903	−	0.759161i	$-0.725610\pi$
$257$	5.32238	−	9.21864i	0.332001	−	0.575043i	0.982904	+	0.184118i	$0.0589429\pi$
$258$		0			0
$259$	4.79063	+	0.0459694i	0.297675	+	0.00285640i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	9.60206	−	5.54375i	0.592088	−	0.341842i	−0.173835	−	0.984775i	$-0.555616\pi$
$263$	9.60206	−	5.54375i	0.592088	−	0.341842i	0.765923	+	0.642933i	$0.222282\pi$
$264$		0			0
$265$	−8.00515	+	4.62178i	−0.491753	+	0.283913i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−3.14147	+	5.44119i	−0.191539	+	0.331755i	−0.945760	−	0.324865i	$-0.894681\pi$
$269$	−3.14147	+	5.44119i	−0.191539	+	0.331755i	0.754221	+	0.656620i	$0.228014\pi$
$270$		0			0
$271$	−0.954533	+	0.551100i	−0.0579838	+	0.0334769i	−0.528712	−	0.848802i	$-0.677325\pi$
$271$	−0.954533	+	0.551100i	−0.0579838	+	0.0334769i	0.470728	+	0.882278i	$0.343991\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	11.7931	+	6.80873i	0.711149	+	0.410582i
$276$		0			0
$277$	7.68081	+	13.3036i	0.461495	+	0.799333i	0.999036	−	0.0439049i	$-0.0139798\pi$
$277$	7.68081	+	13.3036i	0.461495	+	0.799333i	−0.537541	+	0.843238i	$0.680647\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−18.9133	−	10.9196i	−1.12827	−	0.651407i	−0.184771	−	0.982782i	$-0.559154\pi$
$281$	−18.9133	−	10.9196i	−1.12827	−	0.651407i	−0.943499	+	0.331374i	$0.892488\pi$
$282$		0			0
$283$			11.0785i			0.658548i	0.944234	+	0.329274i	$0.106804\pi$
$283$			11.0785i			0.658548i	−0.944234	+	0.329274i	$0.893196\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−26.6231	−	0.255467i	−1.57151	−	0.0150797i
$288$		0			0
$289$	−8.72069	−	15.1047i	−0.512982	−	0.888511i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	12.6330	+	21.8810i	0.738027	+	1.27830i	0.953382	+	0.301765i	$0.0975757\pi$
$293$	12.6330	+	21.8810i	0.738027	+	1.27830i	−0.215355	+	0.976536i	$0.569091\pi$
$294$		0			0
$295$	−15.5710	+	26.9698i	−0.906578	+	1.57024i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	12.3671			0.715206
$300$		0			0
$301$	6.14596	+	10.8850i	0.354247	+	0.627401i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−31.7512	−	18.3316i	−1.81807	−	1.04966i
$306$		0			0
$307$			12.2163i			0.697219i	0.937268	+	0.348610i	$0.113346\pi$
$307$			12.2163i			0.697219i	−0.937268	+	0.348610i	$0.886654\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−9.48967			−0.538110			−0.269055	−	0.963125i	$-0.586711\pi$
$311$	−9.48967			−0.538110			−0.269055	+	0.963125i	$0.586711\pi$
$312$		0			0
$313$		−	13.5513i		−	0.765964i	−0.923756	−	0.382982i	$-0.874897\pi$
$313$		−	13.5513i		−	0.765964i	0.923756	−	0.382982i	$-0.125103\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		−	15.8839i		−	0.892131i	−0.895000	−	0.446065i	$-0.852825\pi$
$317$		−	15.8839i		−	0.892131i	0.895000	−	0.446065i	$-0.147175\pi$
$318$		0			0
$319$	12.1588			0.680761
$320$		0			0
$321$		0			0
$322$		0			0
$323$			14.1727i			0.788591i
$324$		0			0
$325$	20.8410	+	12.0326i	1.15605	+	0.667446i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−10.6529	+	18.0491i	−0.587311	+	0.995078i
$330$		0			0
$331$	−10.9739			−0.603183			−0.301591	−	0.953437i	$-0.597518\pi$
$331$	−10.9739			−0.603183			−0.301591	+	0.953437i	$0.597518\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−13.8669	+	24.0182i	−0.757630	+	1.31225i
$336$		0			0
$337$	2.80751	+	4.86275i	0.152935	+	0.264891i	0.932305	−	0.361673i	$-0.117794\pi$
$337$	2.80751	+	4.86275i	0.152935	+	0.264891i	−0.779370	+	0.626564i	$0.784461\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−4.42964	−	7.67237i	−0.239879	−	0.415482i
$342$		0			0
$343$	18.5126	+	0.533054i	0.999586	+	0.0287822i
$344$		0			0
$345$		0			0
$346$		0			0
$347$			4.82668i			0.259110i	0.991572	+	0.129555i	$0.0413549\pi$
$347$			4.82668i			0.259110i	−0.991572	+	0.129555i	$0.958645\pi$
$348$		0			0
$349$	−22.7167	−	13.1155i	−1.21600	−	0.702056i	−0.251937	−	0.967744i	$-0.581068\pi$
$349$	−22.7167	−	13.1155i	−1.21600	−	0.702056i	−0.964059	+	0.265688i	$0.914401\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	17.4957	+	30.3034i	0.931201	+	1.61289i	0.781271	+	0.624192i	$0.214572\pi$
$353$	17.4957	+	30.3034i	0.931201	+	1.61289i	0.149930	+	0.988697i	$0.452095\pi$
$354$		0			0
$355$	−23.3505	−	13.4814i	−1.23931	−	0.715519i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	21.6396	−	12.4936i	1.14209	−	0.659388i	0.195146	−	0.980774i	$-0.437482\pi$
$359$	21.6396	−	12.4936i	1.14209	−	0.659388i	0.946948	+	0.321386i	$0.104149\pi$
$360$		0			0
$361$	−6.58394	+	11.4037i	−0.346523	+	0.600196i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	41.5855	−	24.0094i	2.17669	−	1.25671i
$366$		0			0
$367$	21.3100	−	12.3034i	1.11237	−	0.642230i	0.172931	−	0.984934i	$-0.444676\pi$
$367$	21.3100	−	12.3034i	1.11237	−	0.642230i	0.939443	+	0.342704i	$0.111343\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−6.02601	+	3.40245i	−0.312855	+	0.176646i
$372$		0			0
$373$	5.21870	−	9.03905i	0.270214	−	0.468024i	−0.698703	−	0.715412i	$-0.746239\pi$
$373$	5.21870	−	9.03905i	0.270214	−	0.468024i	0.968916	+	0.247388i	$0.0795723\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	21.4873			1.10665
$378$		0			0
$379$	−31.8728			−1.63719			−0.818597	−	0.574368i	$-0.805248\pi$
$379$	−31.8728			−1.63719			−0.818597	+	0.574368i	$0.805248\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−12.3860	+	21.4531i	−0.632893	+	1.09620i	0.354065	+	0.935221i	$0.384799\pi$
$383$	−12.3860	+	21.4531i	−0.632893	+	1.09620i	−0.986957	+	0.160982i	$0.948534\pi$
$384$		0			0
$385$	14.6411	+	8.64141i	0.746180	+	0.440407i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−19.9382	+	11.5113i	−1.01091	+	0.583647i	−0.911457	−	0.411395i	$-0.865042\pi$
$389$	−19.9382	+	11.5113i	−1.01091	+	0.583647i	−0.0994499	+	0.995043i	$0.531708\pi$
$390$		0			0
$391$	19.5608	−	11.2934i	0.989232	−	0.571133i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−3.25577	+	5.63916i	−0.163816	+	0.283737i
$396$		0			0
$397$	23.9247	−	13.8129i	1.20075	−	0.693251i	0.240025	−	0.970767i	$-0.422844\pi$
$397$	23.9247	−	13.8129i	1.20075	−	0.693251i	0.960721	+	0.277515i	$0.0895109\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−4.61058	−	2.66192i	−0.230241	−	0.132930i	0.380442	−	0.924805i	$-0.375772\pi$
$401$	−4.61058	−	2.66192i	−0.230241	−	0.132930i	−0.610683	+	0.791875i	$0.709105\pi$
$402$		0			0
$403$	−7.82817	−	13.5588i	−0.389949	−	0.675412i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	2.85137	+	1.64624i	0.141337	+	0.0816009i
$408$		0			0
$409$			7.06575i			0.349379i	0.984624	+	0.174690i	$0.0558922\pi$
$409$			7.06575i			0.349379i	−0.984624	+	0.174690i	$0.944108\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−11.8505	+	20.0782i	−0.583124	+	0.987985i
$414$		0			0
$415$	19.8522	+	34.3851i	0.974507	+	1.68790i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	1.94504	+	3.36891i	0.0950215	+	0.164582i	0.909618	−	0.415447i	$-0.136375\pi$
$419$	1.94504	+	3.36891i	0.0950215	+	0.164582i	−0.814596	+	0.580029i	$0.803041\pi$
$420$		0			0
$421$	−2.18533	+	3.78510i	−0.106506	+	0.184475i	−0.914353	−	0.404919i	$-0.867300\pi$
$421$	−2.18533	+	3.78510i	−0.106506	+	0.184475i	0.807846	+	0.589393i	$0.200633\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	43.9519			2.13198
$426$		0			0
$427$	−23.6379	−	13.9515i	−1.14392	−	0.675158i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−10.7505	−	6.20681i	−0.517834	−	0.298971i	0.218214	−	0.975901i	$-0.429977\pi$
$431$	−10.7505	−	6.20681i	−0.517834	−	0.298971i	−0.736048	+	0.676929i	$0.763310\pi$
$432$		0			0
$433$			25.2979i			1.21574i	0.794036	+	0.607870i	$0.207976\pi$
$433$			25.2979i			1.21574i	−0.794036	+	0.607870i	$0.792024\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−9.29455			−0.444619
$438$		0			0
$439$		−	26.8362i		−	1.28082i	−0.768033	−	0.640410i	$-0.778764\pi$
$439$		−	26.8362i		−	1.28082i	0.768033	−	0.640410i	$-0.221236\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$		−	13.0540i		−	0.620213i	−0.950702	−	0.310107i	$-0.899635\pi$
$443$		−	13.0540i		−	0.620213i	0.950702	−	0.310107i	$-0.100365\pi$
$444$		0			0
$445$	48.7546			2.31119
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	0.468645i		−	0.0221167i	−0.999939	−	0.0110584i	$-0.996480\pi$
$449$		−	0.468645i		−	0.0221167i	0.999939	−	0.0110584i	$-0.00352006\pi$
$450$		0			0
$451$	−15.8460	−	9.14868i	−0.746158	−	0.430795i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	25.8741	+	15.2713i	1.21300	+	0.715930i
$456$		0			0
$457$	−4.12972			−0.193180			−0.0965901	−	0.995324i	$-0.530794\pi$
$457$	−4.12972			−0.193180			−0.0965901	+	0.995324i	$0.530794\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	12.9115	−	22.3633i	0.601347	−	1.04156i	−0.391271	−	0.920276i	$-0.627964\pi$
$461$	12.9115	−	22.3633i	0.601347	−	1.04156i	0.992617	−	0.121288i	$-0.0387023\pi$
$462$		0			0
$463$	2.56402	+	4.44101i	0.119160	+	0.206391i	0.919435	−	0.393242i	$-0.128647\pi$
$463$	2.56402	+	4.44101i	0.119160	+	0.206391i	−0.800275	+	0.599633i	$0.795313\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	1.26091	+	2.18396i	0.0583480	+	0.101062i	0.893724	−	0.448617i	$-0.148083\pi$
$467$	1.26091	+	2.18396i	0.0583480	+	0.101062i	−0.835376	+	0.549679i	$0.814750\pi$
$468$		0			0
$469$	−10.5536	+	17.8809i	−0.487319	+	0.825662i
$470$		0			0
$471$		0			0
$472$		0			0
$473$			8.59070i			0.395001i
$474$		0			0
$475$	−15.6632	−	9.04316i	−0.718677	−	0.414929i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−5.74622	−	9.95275i	−0.262552	−	0.454753i	0.704368	−	0.709835i	$-0.251231\pi$
$479$	−5.74622	−	9.95275i	−0.262552	−	0.454753i	−0.966919	+	0.255083i	$0.917897\pi$
$480$		0			0
$481$	5.03900	+	2.90927i	0.229759	+	0.132651i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−48.7629	+	28.1533i	−2.21421	+	1.27837i
$486$		0			0
$487$	10.8463	−	18.7864i	0.491493	−	0.851292i	−0.508459	−	0.861086i	$-0.669785\pi$
$487$	10.8463	−	18.7864i	0.491493	−	0.851292i	0.999952	+	0.00979483i	$0.00311784\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−19.3592	+	11.1771i	−0.873669	+	0.504413i	−0.868566	−	0.495574i	$-0.834958\pi$
$491$	−19.3592	+	11.1771i	−0.873669	+	0.504413i	−0.00510349	+	0.999987i	$0.501624\pi$
$492$		0			0
$493$	33.9861	−	19.6219i	1.53066	−	0.883726i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−17.3838	−	10.2602i	−0.779769	−	0.460232i
$498$		0			0
$499$	8.76231	−	15.1768i	0.392255	−	0.679405i	−0.600492	−	0.799631i	$-0.705028\pi$
$499$	8.76231	−	15.1768i	0.392255	−	0.679405i	0.992747	+	0.120226i	$0.0383618\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	7.60926			0.339280			0.169640	−	0.985506i	$-0.445739\pi$
$503$	7.60926			0.339280			0.169640	+	0.985506i	$0.445739\pi$
$504$		0			0
$505$	39.3159			1.74953
$506$		0			0
$507$		0			0
$508$		0			0
$509$	3.39373	−	5.87811i	0.150424	−	0.260543i	−0.780959	−	0.624582i	$-0.785269\pi$
$509$	3.39373	−	5.87811i	0.150424	−	0.260543i	0.931384	+	0.364039i	$0.118603\pi$
$510$		0			0
$511$	31.3042	−	17.6752i	1.38482	−	0.781905i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	1.84559	−	1.06555i	0.0813265	−	0.0469539i
$516$		0			0
$517$	−12.4738	+	7.20174i	−0.548596	+	0.316732i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−13.8435	+	23.9777i	−0.606497	+	1.05048i	0.385316	+	0.922785i	$0.374092\pi$
$521$	−13.8435	+	23.9777i	−0.606497	+	1.05048i	−0.991813	+	0.127698i	$0.959241\pi$
$522$		0			0
$523$	0.834923	−	0.482043i	0.0365086	−	0.0210783i	−0.481635	−	0.876372i	$-0.659957\pi$
$523$	0.834923	−	0.482043i	0.0365086	−	0.0210783i	0.518143	+	0.855294i	$0.326623\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−24.7634	−	14.2972i	−1.07871	−	0.622794i
$528$		0			0
$529$	−4.09370	−	7.09049i	−0.177987	−	0.308282i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−28.0034	−	16.1678i	−1.21296	−	0.700304i
$534$		0			0
$535$			46.2518i			1.99964i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	10.8985	+	6.57430i	0.469433	+	0.283175i
$540$		0			0
$541$	2.36867	+	4.10266i	0.101837	+	0.176387i	0.912442	−	0.409207i	$-0.134195\pi$
$541$	2.36867	+	4.10266i	0.101837	+	0.176387i	−0.810604	+	0.585594i	$0.800861\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−4.84374	−	8.38960i	−0.207483	−	0.359371i
$546$		0			0
$547$	0.840875	−	1.45644i	0.0359532	−	0.0622728i	−0.847489	−	0.530813i	$-0.821887\pi$
$547$	0.840875	−	1.45644i	0.0359532	−	0.0622728i	0.883442	+	0.468540i	$0.155220\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−16.1489			−0.687967
$552$		0			0
$553$	−2.47784	+	4.19820i	−0.105369	+	0.178525i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	8.14983	+	4.70530i	0.345319	+	0.199370i	0.662622	−	0.748954i	$-0.269444\pi$
$557$	8.14983	+	4.70530i	0.345319	+	0.199370i	−0.317303	+	0.948324i	$0.602777\pi$
$558$		0			0
$559$			15.1817i			0.642117i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−31.0638			−1.30918			−0.654591	−	0.755983i	$-0.727159\pi$
$563$	−31.0638			−1.30918			−0.654591	+	0.755983i	$0.727159\pi$
$564$		0			0
$565$		−	27.1419i		−	1.14187i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		−	20.1032i		−	0.842769i	−0.906882	−	0.421384i	$-0.861544\pi$
$569$		−	20.1032i		−	0.842769i	0.906882	−	0.421384i	$-0.138456\pi$
$570$		0			0
$571$	7.87413			0.329522			0.164761	−	0.986333i	$-0.447315\pi$
$571$	7.87413			0.329522			0.164761	+	0.986333i	$0.447315\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			28.8239i			1.20204i
$576$		0			0
$577$	−2.77842	−	1.60412i	−0.115667	−	0.0667805i	0.441050	−	0.897482i	$-0.354606\pi$
$577$	−2.77842	−	1.60412i	−0.115667	−	0.0667805i	−0.556717	+	0.830702i	$0.687939\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	14.6148	+	25.8839i	0.606322	+	1.07385i
$582$		0			0
$583$	−4.75587			−0.196968
$584$		0			0
$585$		0			0
$586$		0			0
$587$	2.37708	−	4.11722i	0.0981125	−	0.169936i	−0.812791	−	0.582556i	$-0.802053\pi$
$587$	2.37708	−	4.11722i	0.0981125	−	0.169936i	0.910903	+	0.412620i	$0.135386\pi$
$588$		0			0
$589$	5.88332	+	10.1902i	0.242418	+	0.419880i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	13.0354	+	22.5780i	0.535300	+	0.927166i	0.999149	+	0.0412519i	$0.0131346\pi$
$593$	13.0354	+	22.5780i	0.535300	+	0.927166i	−0.463849	+	0.885914i	$0.653532\pi$
$594$		0			0
$595$	54.8703	+	0.526519i	2.24946	+	0.0215852i
$596$		0			0
$597$		0			0
$598$		0			0
$599$			27.5024i			1.12372i	0.827233	+	0.561859i	$0.189914\pi$
$599$			27.5024i			1.12372i	−0.827233	+	0.561859i	$0.810086\pi$
$600$		0			0
$601$	26.8647	+	15.5104i	1.09584	+	0.632681i	0.935124	−	0.354320i	$-0.115288\pi$
$601$	26.8647	+	15.5104i	1.09584	+	0.632681i	0.160712	+	0.987001i	$0.448621\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−13.5951	−	23.5475i	−0.552721	−	0.957340i
$606$		0			0
$607$	33.9745	+	19.6152i	1.37898	+	0.796156i	0.992037	−	0.125947i	$-0.0401969\pi$
$607$	33.9745	+	19.6152i	1.37898	+	0.796156i	0.386945	+	0.922103i	$0.373530\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−22.0440	+	12.7271i	−0.891803	+	0.514883i
$612$		0			0
$613$	−11.5364	+	19.9817i	−0.465951	+	0.807051i	−0.999244	−	0.0388795i	$-0.987621\pi$
$613$	−11.5364	+	19.9817i	−0.465951	+	0.807051i	0.533293	+	0.845931i	$0.320954\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−5.15715	+	2.97748i	−0.207619	+	0.119869i	−0.600204	−	0.799847i	$-0.704914\pi$
$617$	−5.15715	+	2.97748i	−0.207619	+	0.119869i	0.392585	+	0.919716i	$0.371581\pi$
$618$		0			0
$619$	28.0289	−	16.1825i	1.12658	−	0.650429i	0.183504	−	0.983019i	$-0.441256\pi$
$619$	28.0289	−	16.1825i	1.12658	−	0.650429i	0.943072	+	0.332590i	$0.107922\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	36.4987	+	0.350230i	1.46229	+	0.0140317i
$624$		0			0
$625$	3.17879	−	5.50582i	0.127152	−	0.220233i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	10.6268			0.423719
$630$		0			0
$631$	35.6689			1.41996			0.709978	−	0.704224i	$-0.248705\pi$
$631$	35.6689			1.41996			0.709978	+	0.704224i	$0.248705\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	31.6729	−	54.8591i	1.25690	−	2.17702i
$636$		0			0
$637$	19.2602	+	11.6183i	0.763116	+	0.460333i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−21.5239	+	12.4268i	−0.850141	+	0.490829i	−0.860699	−	0.509115i	$-0.829973\pi$
$641$	−21.5239	+	12.4268i	−0.850141	+	0.490829i	0.0105572	+	0.999944i	$0.496639\pi$
$642$		0			0
$643$	14.8270	−	8.56038i	0.584720	−	0.337588i	−0.178287	−	0.983979i	$-0.557056\pi$
$643$	14.8270	−	8.56038i	0.584720	−	0.337588i	0.763007	+	0.646390i	$0.223722\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−16.7208	+	28.9613i	−0.657363	+	1.13859i	0.323933	+	0.946080i	$0.394995\pi$
$647$	−16.7208	+	28.9613i	−0.657363	+	1.13859i	−0.981296	+	0.192506i	$0.938339\pi$
$648$		0			0
$649$	−13.8761	+	8.01138i	−0.544686	+	0.314474i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−22.8837	−	13.2119i	−0.895508	−	0.517022i	−0.0197678	−	0.999805i	$-0.506293\pi$
$653$	−22.8837	−	13.2119i	−0.895508	−	0.517022i	−0.875740	+	0.482783i	$0.839626\pi$
$654$		0			0
$655$	29.9873	+	51.9395i	1.17170	+	2.02944i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	25.8862	+	14.9454i	1.00838	+	0.582191i	0.910718	−	0.413029i	$-0.135529\pi$
$659$	25.8862	+	14.9454i	1.00838	+	0.582191i	0.0976658	+	0.995219i	$0.468862\pi$
$660$		0			0
$661$		−	4.53368i		−	0.176340i	−0.996105	−	0.0881699i	$-0.971898\pi$
$661$		−	4.53368i		−	0.176340i	0.996105	−	0.0881699i	$-0.0281018\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−19.4459	−	11.4773i	−0.754079	−	0.445069i
$666$		0			0
$667$	12.8682	+	22.2883i	0.498257	+	0.863006i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−9.43172	−	16.3362i	−0.364107	−	0.630652i
$672$		0			0
$673$	4.12239	−	7.14019i	0.158907	−	0.275234i	−0.775568	−	0.631264i	$-0.782536\pi$
$673$	4.12239	−	7.14019i	0.158907	−	0.275234i	0.934475	+	0.356030i	$0.115870\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−5.51263			−0.211867			−0.105934	−	0.994373i	$-0.533783\pi$
$677$	−5.51263			−0.211867			−0.105934	+	0.994373i	$0.533783\pi$
$678$		0			0
$679$	−36.7071	+	20.7258i	−1.40869	+	0.795383i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−24.0097	−	13.8620i	−0.918706	−	0.530415i	−0.0354840	−	0.999370i	$-0.511297\pi$
$683$	−24.0097	−	13.8620i	−0.918706	−	0.530415i	−0.883222	+	0.468955i	$0.844631\pi$
$684$		0			0
$685$		−	19.6540i		−	0.750942i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−8.40469			−0.320193
$690$		0			0
$691$			42.1826i			1.60470i	0.596853	+	0.802351i	$0.296418\pi$
$691$			42.1826i			1.60470i	−0.596853	+	0.802351i	$0.703582\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		−	50.8061i		−	1.92719i
$696$		0			0
$697$	−59.0568			−2.23693
$698$		0			0
$699$		0			0
$700$		0			0
$701$			1.07738i			0.0406922i	0.999793	+	0.0203461i	$0.00647681\pi$
$701$			1.07738i			0.0406922i	−0.999793	+	0.0203461i	$0.993523\pi$
$702$		0			0
$703$	−3.78710	−	2.18648i	−0.142833	−	0.0824648i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	29.4326	+	0.282426i	1.10693	+	0.0106217i
$708$		0			0
$709$	−21.9612			−0.824769			−0.412385	−	0.911010i	$-0.635304\pi$
$709$	−21.9612			−0.824769			−0.412385	+	0.911010i	$0.635304\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	9.37617	−	16.2400i	0.351140	−	0.608193i
$714$		0			0
$715$	10.3240	+	17.8817i	0.386095	+	0.668737i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	5.89267	+	10.2064i	0.219760	+	0.380635i	0.954734	−	0.297460i	$-0.0961394\pi$
$719$	5.89267	+	10.2064i	0.219760	+	0.380635i	−0.734975	+	0.678094i	$0.762806\pi$
$720$		0			0
$721$	1.38930	−	0.784436i	0.0517403	−	0.0292139i
$722$		0			0
$723$		0			0
$724$		0			0
$725$			50.0804i			1.85994i
$726$		0			0
$727$	−10.1963	−	5.88682i	−0.378159	−	0.218330i	0.298858	−	0.954298i	$-0.403394\pi$
$727$	−10.1963	−	5.88682i	−0.378159	−	0.218330i	−0.677017	+	0.735967i	$0.736728\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	13.8637	+	24.0127i	0.512768	+	0.888140i
$732$		0			0
$733$	−37.9020	−	21.8828i	−1.39994	−	0.808258i	−0.405558	−	0.914069i	$-0.632923\pi$
$733$	−37.9020	−	21.8828i	−1.39994	−	0.808258i	−0.994386	+	0.105812i	$0.966256\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−12.3575	+	7.13462i	−0.455195	+	0.262807i
$738$		0			0
$739$	−13.9728	+	24.2016i	−0.513998	+	0.890270i	0.485870	+	0.874031i	$0.338503\pi$
$739$	−13.9728	+	24.2016i	−0.513998	+	0.890270i	−0.999868	+	0.0162393i	$0.994831\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	31.0951	−	17.9528i	1.14077	−	0.658623i	0.194147	−	0.980972i	$-0.437806\pi$
$743$	31.0951	−	17.9528i	1.14077	−	0.658623i	0.946621	+	0.322350i	$0.104473\pi$
$744$		0			0
$745$	−19.6521	+	11.3462i	−0.719998	+	0.415691i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−0.332251	+	34.6250i	−0.0121402	+	1.26517i
$750$		0			0
$751$	−1.17516	+	2.03543i	−0.0428821	+	0.0742740i	−0.886670	−	0.462403i	$-0.846987\pi$
$751$	−1.17516	+	2.03543i	−0.0428821	+	0.0742740i	0.843788	+	0.536677i	$0.180321\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−56.5178			−2.05689
$756$		0			0
$757$	8.88061			0.322771			0.161386	−	0.986891i	$-0.448404\pi$
$757$	8.88061			0.322771			0.161386	+	0.986891i	$0.448404\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−13.4883	+	23.3624i	−0.488951	+	0.846888i	−0.999919	−	0.0127118i	$-0.995954\pi$
$761$	−13.4883	+	23.3624i	−0.488951	+	0.846888i	0.510968	+	0.859600i	$0.329287\pi$
$762$		0			0
$763$	−3.56585	−	6.31541i	−0.129092	−	0.228633i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−24.5222	+	14.1579i	−0.885446	+	0.511213i
$768$		0			0
$769$	−7.88232	+	4.55086i	−0.284244	+	0.164108i	−0.635343	−	0.772230i	$-0.719141\pi$
$769$	−7.88232	+	4.55086i	−0.284244	+	0.164108i	0.351099	+	0.936338i	$0.385808\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−6.46864	+	11.2040i	−0.232661	+	0.402980i	−0.958590	−	0.284789i	$-0.908077\pi$
$773$	−6.46864	+	11.2040i	−0.232661	+	0.402980i	0.725929	+	0.687769i	$0.241410\pi$
$774$		0			0
$775$	31.6015	−	18.2451i	1.13516	−	0.655384i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	21.0462	+	12.1510i	0.754057	+	0.435355i
$780$		0			0
$781$	−6.93628	−	12.0140i	−0.248199	−	0.429894i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	42.6245	+	24.6093i	1.52134	+	0.878343i
$786$		0			0
$787$		−	24.8566i		−	0.886043i	−0.896511	−	0.443022i	$-0.853906\pi$
$787$		−	24.8566i		−	0.886043i	0.896511	−	0.443022i	$-0.146094\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	0.194975	−	20.3190i	0.00693250	−	0.722460i
$792$		0			0
$793$	−16.6680	−	28.8697i	−0.591896	−	1.02519i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	6.71671	+	11.6337i	0.237918	+	0.412086i	0.960117	−	0.279600i	$-0.0902017\pi$
$797$	6.71671	+	11.6337i	0.237918	+	0.412086i	−0.722199	+	0.691686i	$0.756868\pi$
$798$		0			0
$799$	−23.2444	+	40.2605i	−0.822328	+	1.42431i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	24.7060			0.871857
$804$		0			0
$805$	−0.345294	+	35.9843i	−0.0121700	+	1.26828i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−9.38524	−	5.41857i	−0.329967	−	0.190507i	0.325859	−	0.945418i	$-0.394346\pi$
$809$	−9.38524	−	5.41857i	−0.329967	−	0.190507i	−0.655827	+	0.754912i	$0.727680\pi$
$810$		0			0
$811$		−	35.3334i		−	1.24072i	−0.784316	−	0.620361i	$-0.786986\pi$
$811$		−	35.3334i		−	1.24072i	0.784316	−	0.620361i	$-0.213014\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	55.0951			1.92990
$816$		0			0
$817$		−	11.4099i		−	0.399182i
$818$		0			0
$819$		0			0
$820$		0			0
$821$			19.2156i			0.670631i	0.942106	+	0.335315i	$0.108843\pi$
$821$			19.2156i			0.670631i	−0.942106	+	0.335315i	$0.891157\pi$
$822$		0			0
$823$	−29.8148			−1.03928			−0.519639	−	0.854386i	$-0.673934\pi$
$823$	−29.8148			−1.03928			−0.519639	+	0.854386i	$0.673934\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			0.356137i			0.0123841i	0.999981	+	0.00619205i	$0.00197100\pi$
$827$			0.356137i			0.0123841i	−0.999981	+	0.00619205i	$0.998029\pi$
$828$		0			0
$829$	−17.5571	−	10.1366i	−0.609783	−	0.352058i	0.163098	−	0.986610i	$-0.447851\pi$
$829$	−17.5571	−	10.1366i	−0.609783	−	0.352058i	−0.772880	+	0.634552i	$0.781185\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	41.0732	+	0.788324i	1.42310	+	0.0273138i
$834$		0			0
$835$	−46.5590			−1.61124
$836$		0			0
$837$		0			0
$838$		0			0
$839$	0.662663	−	1.14777i	0.0228777	−	0.0396253i	−0.854360	−	0.519682i	$-0.826051\pi$
$839$	0.662663	−	1.14777i	0.0228777	−	0.0396253i	0.877238	+	0.480056i	$0.159384\pi$
$840$		0			0
$841$	7.85791	+	13.6103i	0.270962	+	0.469321i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−4.72626	−	8.18612i	−0.162588	−	0.281611i
$846$		0			0
$847$	−10.0084	−	17.7258i	−0.343894	−	0.609064i
$848$		0			0
$849$		0			0
$850$		0			0
$851$			6.96914i			0.238899i
$852$		0			0
$853$	41.7558	+	24.1077i	1.42969	+	0.825432i	0.997096	−	0.0761571i	$-0.0242650\pi$
$853$	41.7558	+	24.1077i	1.42969	+	0.825432i	0.432594	+	0.901589i	$0.357598\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	10.4387	+	18.0803i	0.356578	+	0.617611i	0.987387	−	0.158328i	$-0.0506102\pi$
$857$	10.4387	+	18.0803i	0.356578	+	0.617611i	−0.630809	+	0.775938i	$0.717277\pi$
$858$		0			0
$859$	−11.8727	−	6.85469i	−0.405090	−	0.233879i	0.283588	−	0.958946i	$-0.408475\pi$
$859$	−11.8727	−	6.85469i	−0.405090	−	0.233879i	−0.688678	+	0.725067i	$0.741809\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−28.1125	+	16.2307i	−0.956959	+	0.552501i	−0.895236	−	0.445593i	$-0.852993\pi$
$863$	−28.1125	+	16.2307i	−0.956959	+	0.552501i	−0.0617233	+	0.998093i	$0.519660\pi$
$864$		0			0
$865$	−19.8047	+	34.3027i	−0.673379	+	1.16633i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−2.90139	+	1.67512i	−0.0984228	+	0.0568244i
$870$		0			0
$871$	−21.8385	+	12.6085i	−0.739970	+	0.427222i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−11.8302	+	20.0438i	−0.399933	+	0.677604i
$876$		0			0
$877$	−10.9669	+	18.9953i	−0.370326	+	0.641424i	−0.989616	−	0.143739i	$-0.954087\pi$
$877$	−10.9669	+	18.9953i	−0.370326	+	0.641424i	0.619289	+	0.785163i	$0.287421\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	21.8019			0.734526			0.367263	−	0.930117i	$-0.380295\pi$
$881$	21.8019			0.734526			0.367263	+	0.930117i	$0.380295\pi$
$882$		0			0
$883$	24.4085			0.821411			0.410705	−	0.911768i	$-0.365283\pi$
$883$	24.4085			0.821411			0.410705	+	0.911768i	$0.365283\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−16.8722	+	29.2235i	−0.566513	+	0.981230i	0.430394	+	0.902641i	$0.358375\pi$
$887$	−16.8722	+	29.2235i	−0.566513	+	0.981230i	−0.996907	+	0.0785887i	$0.974959\pi$
$888$		0			0
$889$	24.1051	−	40.8411i	0.808458	−	1.36977i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	16.5673	−	9.56513i	0.554403	−	0.320085i
$894$		0			0
$895$	32.6113	−	18.8281i	1.09007	−	0.629355i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	16.2907	−	28.2164i	0.543326	−	0.941068i
$900$		0			0
$901$	−13.2936	+	7.67505i	−0.442873	+	0.255693i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−36.3889	−	21.0092i	−1.20961	−	0.698368i
$906$		0			0
$907$	7.52832	+	13.0394i	0.249974	+	0.432967i	0.963518	−	0.267643i	$-0.0862447\pi$
$907$	7.52832	+	13.0394i	0.249974	+	0.432967i	−0.713544	+	0.700610i	$0.752911\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−21.5047	−	12.4157i	−0.712481	−	0.411351i	0.0994977	−	0.995038i	$-0.468276\pi$
$911$	−21.5047	−	12.4157i	−0.712481	−	0.411351i	−0.811979	+	0.583686i	$0.801610\pi$
$912$		0			0
$913$			20.4282i			0.676075i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	22.0759	+	39.0983i	0.729012	+	1.29114i
$918$		0			0
$919$	12.0689	+	20.9039i	0.398115	+	0.689555i	0.993493	−	0.113890i	$-0.0363312\pi$
$919$	12.0689	+	20.9039i	0.398115	+	0.689555i	−0.595378	+	0.803445i	$0.702998\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−12.2580	−	21.2314i	−0.403476	−	0.698840i
$924$		0			0
$925$	−6.78064	+	11.7444i	−0.222946	+	0.386154i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	26.6620			0.874752			0.437376	−	0.899279i	$-0.355908\pi$
$929$	26.6620			0.874752			0.437376	+	0.899279i	$0.355908\pi$
$930$		0			0
$931$	−14.4751	−	8.73180i	−0.474403	−	0.286173i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	32.6586	+	18.8555i	1.06805	+	0.616640i
$936$		0			0
$937$			8.17165i			0.266956i	0.991052	+	0.133478i	$0.0426146\pi$
$937$			8.17165i			0.266956i	−0.991052	+	0.133478i	$0.957385\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−32.0272			−1.04406			−0.522028	−	0.852928i	$-0.674824\pi$
$941$	−32.0272			−1.04406			−0.522028	+	0.852928i	$0.674824\pi$
$942$		0			0
$943$		−	38.7298i		−	1.26122i
$944$		0			0
$945$		0			0
$946$		0			0
$947$		−	17.9002i		−	0.581678i	−0.956772	−	0.290839i	$-0.906066\pi$
$947$		−	17.9002i		−	0.581678i	0.956772	−	0.290839i	$-0.0939344\pi$
$948$		0			0
$949$	43.6611			1.41730
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	11.2737i		−	0.365191i	−0.983188	−	0.182596i	$-0.941550\pi$
$953$		−	11.2737i		−	0.365191i	0.983188	−	0.182596i	$-0.0584499\pi$
$954$		0			0
$955$	−0.685459	−	0.395750i	−0.0221809	−	0.0128062i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	0.141185	−	14.7134i	0.00455911	−	0.475120i
$960$		0			0
$961$	7.26007			0.234196
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−46.0738	+	79.8022i	−1.48317	+	2.56892i
$966$		0			0
$967$	−15.3313	−	26.5546i	−0.493022	−	0.853939i	0.506946	−	0.861978i	$-0.330774\pi$
$967$	−15.3313	−	26.5546i	−0.493022	−	0.853939i	−0.999968	+	0.00803913i	$0.997441\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−19.0807	−	33.0488i	−0.612330	−	1.06059i	−0.990847	−	0.134992i	$-0.956899\pi$
$971$	−19.0807	−	33.0488i	−0.612330	−	1.06059i	0.378517	−	0.925595i	$-0.376434\pi$
$972$		0			0
$973$	0.364967	−	38.0345i	0.0117003	−	1.21933i
$974$		0			0
$975$		0			0
$976$		0			0
$977$			30.6991i			0.982151i	0.871117	+	0.491076i	$0.163396\pi$
$977$			30.6991i			0.982151i	−0.871117	+	0.491076i	$0.836604\pi$
$978$		0			0
$979$	21.7239	+	12.5423i	0.694299	+	0.400854i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	12.9028	+	22.3484i	0.411536	+	0.712802i	0.995058	−	0.0992957i	$-0.0316590\pi$
$983$	12.9028	+	22.3484i	0.411536	+	0.712802i	−0.583522	+	0.812098i	$0.698326\pi$
$984$		0			0
$985$	−4.78330	−	2.76164i	−0.152409	−	0.0879932i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−15.7476	+	9.09191i	−0.500746	+	0.289106i
$990$		0			0
$991$	11.4388	−	19.8126i	0.363366	−	0.629369i	−0.625146	−	0.780508i	$-0.714961\pi$
$991$	11.4388	−	19.8126i	0.363366	−	0.629369i	0.988513	+	0.151139i	$0.0482940\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	47.6118	−	27.4887i	1.50940	−	0.871450i
$996$		0			0
$997$	−35.9753	+	20.7704i	−1.13935	+	0.657804i	−0.946269	−	0.323379i	$-0.895181\pi$
$997$	−35.9753	+	20.7704i	−1.13935	+	0.657804i	−0.193080	+	0.981183i	$0.561848\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.ca.e.2033.3		48
3.2	odd	2		1008.2.ca.e.353.24		48
4.3	odd	2		1512.2.bs.a.521.3		48
7.5	odd	6		3024.2.df.e.1601.3		48
9.4	even	3		1008.2.df.e.689.18		48
9.5	odd	6		3024.2.df.e.17.3		48
12.11	even	2		504.2.bs.a.353.1	yes	48
21.5	even	6		1008.2.df.e.929.18		48
28.19	even	6		1512.2.cx.a.89.3		48
36.23	even	6		1512.2.cx.a.17.3		48
36.31	odd	6		504.2.cx.a.185.7	yes	48
63.5	even	6	inner	3024.2.ca.e.2609.3		48
63.40	odd	6		1008.2.ca.e.257.24		48
84.47	odd	6		504.2.cx.a.425.7	yes	48
252.103	even	6		504.2.bs.a.257.1	✓	48
252.131	odd	6		1512.2.bs.a.1097.3		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bs.a.257.1	✓	48	252.103	even	6
504.2.bs.a.353.1	yes	48	12.11	even	2
504.2.cx.a.185.7	yes	48	36.31	odd	6
504.2.cx.a.425.7	yes	48	84.47	odd	6
1008.2.ca.e.257.24		48	63.40	odd	6
1008.2.ca.e.353.24		48	3.2	odd	2
1008.2.df.e.689.18		48	9.4	even	3
1008.2.df.e.929.18		48	21.5	even	6
1512.2.bs.a.521.3		48	4.3	odd	2
1512.2.bs.a.1097.3		48	252.131	odd	6
1512.2.cx.a.17.3		48	36.23	even	6
1512.2.cx.a.89.3		48	28.19	even	6
3024.2.ca.e.2033.3		48	1.1	even	1	trivial
3024.2.ca.e.2609.3		48	63.5	even	6	inner
3024.2.df.e.17.3		48	9.5	odd	6
3024.2.df.e.1601.3		48	7.5	odd	6

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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.ca (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.76701 + 3.06054i) q^{5} +(-1.34480 + 2.27849i) q^{7} +O(q^{10})\)	\(q+(-1.76701 + 3.06054i) q^{5} +(-1.34480 + 2.27849i) q^{7} +(-1.57467 + 0.909136i) q^{11} +(-2.78280 + 1.60665i) q^{13} +(-2.93434 + 5.08242i) q^{17} +(2.09143 - 1.20749i) q^{19} +(-3.33308 - 1.92436i) q^{23} +(-3.74462 - 6.48586i) q^{25} +(-5.79110 - 3.34349i) q^{29} +4.87236i q^{31} +(-4.59714 - 8.14192i) q^{35} +(-0.905385 - 1.56817i) q^{37} +(5.03152 + 8.71485i) q^{41} +(2.36232 - 4.09166i) q^{43} +7.92151 q^{47} +(-3.38302 - 6.12823i) q^{49} +(2.26517 + 1.30780i) q^{53} -6.42580i q^{55} +8.81208 q^{59} +10.3744i q^{61} -11.3558i q^{65} +7.84769 q^{67} +7.62952i q^{71} +(-11.7672 - 6.79382i) q^{73} +(0.0461599 - 4.81048i) q^{77} +1.84254 q^{79} +(5.61748 - 9.72975i) q^{83} +(-10.3700 - 17.9613i) q^{85} +(-6.89792 - 11.9475i) q^{89} +(0.0815748 - 8.50119i) q^{91} +8.53455i q^{95} +(13.7982 + 7.96638i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q - 12 q^{23} - 24 q^{25} - 18 q^{29} - 6 q^{41} + 6 q^{43} + 36 q^{47} + 6 q^{49} - 12 q^{53} + 36 q^{77} + 12 q^{79} - 18 q^{89} - 6 q^{91}+O(q^{100}) \) 48 * q - 12 * q^23 - 24 * q^25 - 18 * q^29 - 6 * q^41 + 6 * q^43 + 36 * q^47 + 6 * q^49 - 12 * q^53 + 36 * q^77 + 12 * q^79 - 18 * q^89 - 6 * q^91

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