LMFDB - Embedded newform 567.2.c.c.566.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(566,567)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(567, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("567.566");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.c (of order $2$, degree $1$, 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:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 7x^{10} + 37x^{8} - 78x^{6} + 123x^{4} - 36x^{2} + 9 $ x^12 - 7x^10 + 37x^8 - 78x^6 + 123x^4 - 36*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			566.10
Root			$1.82904 - 1.05600i$ of defining polynomial
Character	$\chi$	$=$	567.566
Dual form			567.2.c.c.566.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.18593i q^{2} +0.593579 q^{4} +2.83797 q^{5} +(2.46050 + 0.972582i) q^{7} +3.07579i q^{8} +O(q^{10})$	\(q+1.18593i q^{2} +0.593579 q^{4} +2.83797 q^{5} +(2.46050 + 0.972582i) q^{7} +3.07579i q^{8} +3.36562i q^{10} +0.157816i q^{11} -3.94293i q^{13} +(-1.15341 + 2.91798i) q^{14} -2.46050 q^{16} -4.14487 q^{17} -6.33597i q^{19} +1.68456 q^{20} -0.187159 q^{22} -0.546125i q^{23} +3.05408 q^{25} +4.67602 q^{26} +(1.46050 + 0.577305i) q^{28} +4.65003i q^{29} +0.129426i q^{31} +3.23361i q^{32} -4.91551i q^{34} +(6.98284 + 2.76016i) q^{35} -2.46050 q^{37} +7.51399 q^{38} +8.72902i q^{40} -3.99138 q^{41} -6.56867 q^{43} +0.0936766i q^{44} +0.647664 q^{46} -8.66741 q^{47} +(5.10817 + 4.78609i) q^{49} +3.62192i q^{50} -2.34044i q^{52} -2.60234i q^{53} +0.447879i q^{55} +(-2.99146 + 7.56800i) q^{56} -5.51459 q^{58} +3.61372 q^{59} +3.36562i q^{61} -0.153489 q^{62} -8.75583 q^{64} -11.1899i q^{65} +1.32743 q^{67} -2.46031 q^{68} +(-3.27335 + 8.28114i) q^{70} -0.409310i q^{71} +15.0124i q^{73} -2.91798i q^{74} -3.76090i q^{76} +(-0.153489 + 0.388308i) q^{77} +4.32743 q^{79} -6.98284 q^{80} -4.73348i q^{82} +6.45169 q^{83} -11.7630 q^{85} -7.78996i q^{86} -0.485411 q^{88} -5.05368 q^{89} +(3.83482 - 9.70160i) q^{91} -0.324168i q^{92} -10.2789i q^{94} -17.9813i q^{95} +2.52247i q^{97} +(-5.67594 + 6.05791i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{4} + 4 q^{7}+O(q^{10}) $ 12 * q - 4 * q^4 + 4 * q^7	$ 12 q - 4 q^{4} + 4 q^{7} - 4 q^{16} + 20 q^{22} - 8 q^{28} - 4 q^{37} + 20 q^{43} - 40 q^{46} - 12 q^{49} - 4 q^{58} + 16 q^{64} - 24 q^{67} - 36 q^{70} + 12 q^{79} + 12 q^{85} - 68 q^{88} - 24 q^{91}+O(q^{100}) $ 12 * q - 4 * q^4 + 4 * q^7 - 4 * q^16 + 20 * q^22 - 8 * q^28 - 4 * q^37 + 20 * q^43 - 40 * q^46 - 12 * q^49 - 4 * q^58 + 16 * q^64 - 24 * q^67 - 36 * q^70 + 12 * q^79 + 12 * q^85 - 68 * q^88 - 24 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$			1.18593i			0.838576i	0.907853	+	0.419288i	$0.137720\pi$
$2$			1.18593i			0.838576i	−0.907853	+	0.419288i	$0.862280\pi$
$3$		0			0
$3$		0			0
$4$	0.593579			0.296790
$5$	2.83797			1.26918			0.634590	−	0.772849i	$-0.281169\pi$
$5$	2.83797			1.26918			0.634590	+	0.772849i	$0.281169\pi$
$6$		0			0
$7$	2.46050	+	0.972582i	0.929983	+	0.367601i
$7$	2.46050	+	0.972582i	0.929983	+	0.367601i
$8$			3.07579i			1.08746i
$9$		0			0
$10$			3.36562i			1.06430i
$11$			0.157816i			0.0475835i	0.999717	+	0.0237917i	$0.00757386\pi$
$11$			0.157816i			0.0475835i	−0.999717	+	0.0237917i	$0.992426\pi$
$12$		0			0
$13$		−	3.94293i		−	1.09357i	−0.837272	−	0.546786i	$-0.815851\pi$
$13$		−	3.94293i		−	1.09357i	0.837272	−	0.546786i	$-0.184149\pi$
$14$	−1.15341	+	2.91798i	−0.308262	+	0.779862i
$15$		0			0
$16$	−2.46050			−0.615126
$17$	−4.14487			−1.00528			−0.502640	−	0.864496i	$-0.667638\pi$
$17$	−4.14487			−1.00528			−0.502640	+	0.864496i	$0.667638\pi$
$18$		0			0
$19$		−	6.33597i		−	1.45357i	−0.686864	−	0.726786i	$-0.741013\pi$
$19$		−	6.33597i		−	1.45357i	0.686864	−	0.726786i	$-0.258987\pi$
$20$	1.68456			0.376679
$21$		0			0
$22$	−0.187159			−0.0399024
$23$		−	0.546125i		−	0.113875i	−0.998378	−	0.0569374i	$-0.981866\pi$
$23$		−	0.546125i		−	0.113875i	0.998378	−	0.0569374i	$-0.0181336\pi$
$24$		0			0
$25$	3.05408			0.610817
$26$	4.67602			0.917044
$27$		0			0
$28$	1.46050	+	0.577305i	0.276009	+	0.109100i
$29$			4.65003i			0.863488i	0.901996	+	0.431744i	$0.142102\pi$
$29$			4.65003i			0.863488i	−0.901996	+	0.431744i	$0.857898\pi$
$30$		0			0
$31$			0.129426i			0.0232456i	0.999932	+	0.0116228i	$0.00369973\pi$
$31$			0.129426i			0.0232456i	−0.999932	+	0.0116228i	$0.996300\pi$
$32$			3.23361i			0.571627i
$33$		0			0
$34$		−	4.91551i		−	0.843003i
$35$	6.98284	+	2.76016i	1.18032	+	0.466552i
$36$		0			0
$37$	−2.46050			−0.404505			−0.202252	−	0.979333i	$-0.564826\pi$
$37$	−2.46050			−0.404505			−0.202252	+	0.979333i	$0.564826\pi$
$38$	7.51399			1.21893
$39$		0			0
$40$			8.72902i			1.38018i
$41$	−3.99138			−0.623349			−0.311675	−	0.950189i	$-0.600890\pi$
$41$	−3.99138			−0.623349			−0.311675	+	0.950189i	$0.600890\pi$
$42$		0			0
$43$	−6.56867			−1.00171			−0.500857	−	0.865530i	$-0.666982\pi$
$43$	−6.56867			−1.00171			−0.500857	+	0.865530i	$0.666982\pi$
$44$			0.0936766i			0.0141223i
$45$		0			0
$46$	0.647664			0.0954928
$47$	−8.66741			−1.26427			−0.632135	−	0.774858i	$-0.717821\pi$
$47$	−8.66741			−1.26427			−0.632135	+	0.774858i	$0.717821\pi$
$48$		0			0
$49$	5.10817	+	4.78609i	0.729738	+	0.683727i
$50$			3.62192i			0.512217i
$51$		0			0
$52$		−	2.34044i		−	0.324561i
$53$		−	2.60234i		−	0.357459i	−0.983898	−	0.178730i	$-0.942801\pi$
$53$		−	2.60234i		−	0.357459i	0.983898	−	0.178730i	$-0.0571988\pi$
$54$		0			0
$55$			0.447879i			0.0603920i
$56$	−2.99146	+	7.56800i	−0.399751	+	1.01132i
$57$		0			0
$58$	−5.51459			−0.724101
$59$	3.61372			0.470466			0.235233	−	0.971939i	$-0.424415\pi$
$59$	3.61372			0.470466			0.235233	+	0.971939i	$0.424415\pi$
$60$		0			0
$61$			3.36562i			0.430924i	0.976512	+	0.215462i	$0.0691258\pi$
$61$			3.36562i			0.430924i	−0.976512	+	0.215462i	$0.930874\pi$
$62$	−0.153489			−0.0194932
$63$		0			0
$64$	−8.75583			−1.09448
$65$		−	11.1899i		−	1.38794i
$66$		0			0
$67$	1.32743			0.162171			0.0810857	−	0.996707i	$-0.474161\pi$
$67$	1.32743			0.162171			0.0810857	+	0.996707i	$0.474161\pi$
$68$	−2.46031			−0.298356
$69$		0			0
$70$	−3.27335	+	8.28114i	−0.391240	+	0.989785i
$71$		−	0.409310i		−	0.0485761i	−0.999705	−	0.0242881i	$-0.992268\pi$
$71$		−	0.409310i		−	0.0485761i	0.999705	−	0.0242881i	$-0.00773189\pi$
$72$		0			0
$73$			15.0124i			1.75707i	0.477681	+	0.878533i	$0.341478\pi$
$73$			15.0124i			1.75707i	−0.477681	+	0.878533i	$0.658522\pi$
$74$		−	2.91798i		−	0.339208i
$75$		0			0
$76$		−	3.76090i		−	0.431405i
$77$	−0.153489	+	0.388308i	−0.0174917	+	0.0442518i
$78$		0			0
$79$	4.32743			0.486874			0.243437	−	0.969917i	$-0.421725\pi$
$79$	4.32743			0.486874			0.243437	+	0.969917i	$0.421725\pi$
$80$	−6.98284			−0.780706
$81$		0			0
$82$		−	4.73348i		−	0.522726i
$83$	6.45169			0.708165			0.354083	−	0.935214i	$-0.384793\pi$
$83$	6.45169			0.708165			0.354083	+	0.935214i	$0.384793\pi$
$84$		0			0
$85$	−11.7630			−1.27588
$86$		−	7.78996i		−	0.840013i
$87$		0			0
$88$	−0.485411			−0.0517450
$89$	−5.05368			−0.535689			−0.267845	−	0.963462i	$-0.586311\pi$
$89$	−5.05368			−0.535689			−0.267845	+	0.963462i	$0.586311\pi$
$90$		0			0
$91$	3.83482	−	9.70160i	0.401999	−	1.01700i
$92$		−	0.324168i		−	0.0337969i
$93$		0			0
$94$		−	10.2789i		−	1.06019i
$95$		−	17.9813i		−	1.84484i
$96$		0			0
$97$			2.52247i			0.256118i	0.991767	+	0.128059i	$0.0408747\pi$
$97$			2.52247i			0.256118i	−0.991767	+	0.128059i	$0.959125\pi$
$98$	−5.67594	+	6.05791i	−0.573357	+	0.611941i
$99$		0			0
$100$	1.81284			0.181284
$101$	2.99146			0.297662			0.148831	−	0.988863i	$-0.452449\pi$
$101$	2.99146			0.297662			0.148831	+	0.988863i	$0.452449\pi$
$102$		0			0
$103$		−	13.1966i		−	1.30030i	−0.759804	−	0.650152i	$-0.774705\pi$
$103$		−	13.1966i		−	1.30030i	0.759804	−	0.650152i	$-0.225295\pi$
$104$	12.1276			1.18921
$105$		0			0
$106$	3.08619			0.299757
$107$		−	19.5555i		−	1.89051i	−0.326339	−	0.945253i	$-0.605815\pi$
$107$		−	19.5555i		−	1.89051i	0.326339	−	0.945253i	$-0.394185\pi$
$108$		0			0
$109$	13.2484			1.26897			0.634485	−	0.772935i	$-0.281212\pi$
$109$	13.2484			1.26897			0.634485	+	0.772935i	$0.281212\pi$
$110$	−0.531151			−0.0506433
$111$		0			0
$112$	−6.05408	−	2.39304i	−0.572057	−	0.226121i
$113$			10.0767i			0.947934i	0.880543	+	0.473967i	$0.157178\pi$
$113$			10.0767i			0.947934i	−0.880543	+	0.473967i	$0.842822\pi$
$114$		0			0
$115$		−	1.54989i		−	0.144528i
$116$			2.76016i			0.256274i
$117$		0			0
$118$			4.28561i			0.394522i
$119$	−10.1985	−	4.03123i	−0.934893	−	0.369542i
$120$		0			0
$121$	10.9751			0.997736
$122$	−3.99138			−0.361363
$123$		0			0
$124$			0.0768245i			0.00689904i
$125$	−5.52245			−0.493943
$126$		0			0
$127$	−12.4897			−1.10828			−0.554140	−	0.832423i	$-0.686953\pi$
$127$	−12.4897			−1.10828			−0.554140	+	0.832423i	$0.686953\pi$
$128$		−	3.91655i		−	0.346177i
$129$		0			0
$130$	13.2704			1.16389
$131$	−10.0450			−0.877635			−0.438817	−	0.898576i	$-0.644602\pi$
$131$	−10.0450			−0.877635			−0.438817	+	0.898576i	$0.644602\pi$
$132$		0			0
$133$	6.16225	−	15.5897i	0.534335	−	1.35180i
$134$			1.57423i			0.135993i
$135$		0			0
$136$		−	12.7488i		−	1.09320i
$137$		−	8.04145i		−	0.687028i	−0.939148	−	0.343514i	$-0.888383\pi$
$137$		−	8.04145i		−	0.687028i	0.939148	−	0.343514i	$-0.111617\pi$
$138$		0			0
$139$			18.9027i			1.60331i	0.597789	+	0.801654i	$0.296046\pi$
$139$			18.9027i			1.60331i	−0.597789	+	0.801654i	$0.703954\pi$
$140$	4.14487	+	1.63837i	0.350306	+	0.138468i
$141$		0			0
$142$	0.485411			0.0407348
$143$	0.622259			0.0520359
$144$		0			0
$145$			13.1966i			1.09592i
$146$	−17.8036			−1.47343
$147$		0			0
$148$	−1.46050			−0.120053
$149$		−	19.4063i		−	1.58982i	−0.606725	−	0.794912i	$-0.707517\pi$
$149$		−	19.4063i		−	1.58982i	0.606725	−	0.794912i	$-0.292483\pi$
$150$		0			0
$151$	−1.78794			−0.145500			−0.0727501	−	0.997350i	$-0.523178\pi$
$151$	−1.78794			−0.145500			−0.0727501	+	0.997350i	$0.523178\pi$
$152$	19.4881			1.58070
$153$		0			0
$154$	−0.460505	−	0.182027i	−0.0371085	−	0.0146682i
$155$			0.367307i			0.0295028i
$156$		0			0
$157$			4.39081i			0.350425i	0.984531	+	0.175212i	$0.0560612\pi$
$157$			4.39081i			0.350425i	−0.984531	+	0.175212i	$0.943939\pi$
$158$			5.13201i			0.408281i
$159$		0			0
$160$			9.17689i			0.725497i
$161$	0.531151	−	1.34374i	0.0418606	−	0.105902i
$162$		0			0
$163$	5.43560			0.425749			0.212874	−	0.977080i	$-0.431717\pi$
$163$	5.43560			0.425749			0.212874	+	0.977080i	$0.431717\pi$
$164$	−2.36920			−0.185004
$165$		0			0
$166$			7.65123i			0.593851i
$167$	−10.5055			−0.812937			−0.406468	−	0.913665i	$-0.633240\pi$
$167$	−10.5055			−0.812937			−0.406468	+	0.913665i	$0.633240\pi$
$168$		0			0
$169$	−2.54669			−0.195899
$170$		−	13.9501i		−	1.06992i
$171$		0			0
$172$	−3.89903			−0.297298
$173$	17.5590			1.33498			0.667492	−	0.744617i	$-0.267368\pi$
$173$	17.5590			1.33498			0.667492	+	0.744617i	$0.267368\pi$
$174$		0			0
$175$	7.51459	+	2.97035i	0.568050	+	0.224537i
$176$		−	0.388308i		−	0.0292698i
$177$		0			0
$178$		−	5.99330i		−	0.449217i
$179$		−	18.2033i		−	1.36058i	−0.732945	−	0.680288i	$-0.761855\pi$
$179$		−	18.2033i		−	1.36058i	0.732945	−	0.680288i	$-0.238145\pi$
$180$		0			0
$181$		−	6.60182i		−	0.490710i	−0.969433	−	0.245355i	$-0.921096\pi$
$181$		−	6.60182i		−	0.490710i	0.969433	−	0.245355i	$-0.0789045\pi$
$182$	11.5054	+	4.54782i	0.852835	+	0.337107i
$183$		0			0
$184$	1.67977			0.123834
$185$	−6.98284			−0.513389
$186$		0			0
$187$		−	0.654129i		−	0.0478347i
$188$	−5.14479			−0.375223
$189$		0			0
$190$	21.3245			1.54704
$191$		−	14.2101i		−	1.02821i	−0.857728	−	0.514104i	$-0.828125\pi$
$191$		−	14.2101i		−	1.02821i	0.857728	−	0.514104i	$-0.171875\pi$
$192$		0			0
$193$	−10.0043			−0.720123			−0.360062	−	0.932929i	$-0.617244\pi$
$193$	−10.0043			−0.720123			−0.360062	+	0.932929i	$0.617244\pi$
$194$	−2.99146			−0.214774
$195$		0			0
$196$	3.03210	+	2.84092i	0.216579	+	0.202923i
$197$			20.1017i			1.43218i	0.698006	+	0.716092i	$0.254071\pi$
$197$			20.1017i			1.43218i	−0.698006	+	0.716092i	$0.745929\pi$
$198$		0			0
$199$		−	12.9378i		−	0.917136i	−0.888659	−	0.458568i	$-0.848363\pi$
$199$		−	12.9378i		−	0.917136i	0.888659	−	0.458568i	$-0.151637\pi$
$200$			9.39373i			0.664237i
$201$		0			0
$202$			3.54765i			0.249612i
$203$	−4.52253	+	11.4414i	−0.317420	+	0.803030i
$204$		0			0
$205$	−11.3274			−0.791142
$206$	15.6502			1.09040
$207$		0			0
$208$			9.70160i			0.672685i
$209$	0.999921			0.0691660
$210$		0			0
$211$	9.01439			0.620577			0.310288	−	0.950643i	$-0.399574\pi$
$211$	9.01439			0.620577			0.310288	+	0.950643i	$0.399574\pi$
$212$		−	1.54470i		−	0.106090i
$213$		0			0
$214$	23.1914			1.58533
$215$	−18.6417			−1.27135
$216$		0			0
$217$	−0.125877	+	0.318453i	−0.00854510	+	0.0216180i
$218$			15.7117i			1.06413i
$219$		0			0
$220$			0.265852i			0.0179237i
$221$			16.3429i			1.09934i
$222$		0			0
$223$			2.25662i			0.151114i	0.997141	+	0.0755571i	$0.0240735\pi$
$223$			2.25662i			0.151114i	−0.997141	+	0.0755571i	$0.975926\pi$
$224$	−3.14495	+	7.95631i	−0.210131	+	0.531604i
$225$		0			0
$226$	−11.9502			−0.794915
$227$	−18.6417			−1.23729			−0.618647	−	0.785669i	$-0.712319\pi$
$227$	−18.6417			−1.23729			−0.618647	+	0.785669i	$0.712319\pi$
$228$		0			0
$229$		−	14.3057i		−	0.945344i	−0.881238	−	0.472672i	$-0.843289\pi$
$229$		−	14.3057i		−	0.945344i	0.881238	−	0.472672i	$-0.156711\pi$
$230$	1.83805			0.121197
$231$		0			0
$232$	−14.3025			−0.939007
$233$			17.0679i			1.11815i	0.829116	+	0.559077i	$0.188844\pi$
$233$			17.0679i			1.11815i	−0.829116	+	0.559077i	$0.811156\pi$
$234$		0			0
$235$	−24.5979			−1.60459
$236$	2.14503			0.139630
$237$		0			0
$238$	4.78074	−	12.0946i	0.309889	−	0.783979i
$239$		−	2.23504i		−	0.144573i	−0.997384	−	0.0722863i	$-0.976970\pi$
$239$		−	2.23504i		−	0.144573i	0.997384	−	0.0722863i	$-0.0230295\pi$
$240$		0			0
$241$			4.52023i			0.291174i	0.989345	+	0.145587i	$0.0465070\pi$
$241$			4.52023i			0.291174i	−0.989345	+	0.145587i	$0.953493\pi$
$242$			13.0157i			0.836678i
$243$		0			0
$244$			1.99777i			0.127894i
$245$	14.4968	+	13.5828i	0.926169	+	0.867772i
$246$		0			0
$247$	−24.9823			−1.58959
$248$	−0.398087			−0.0252786
$249$		0			0
$250$		−	6.54922i		−	0.414209i
$251$	21.1727			1.33641			0.668205	−	0.743978i	$-0.267063\pi$
$251$	21.1727			1.33641			0.668205	+	0.743978i	$0.267063\pi$
$252$		0			0
$253$	0.0861875			0.00541856
$254$		−	14.8118i		−	0.929378i
$255$		0			0
$256$	−12.8669			−0.804183
$257$	31.3005			1.95247			0.976236	−	0.216712i	$-0.0695331\pi$
$257$	31.3005			1.95247			0.976236	+	0.216712i	$0.0695331\pi$
$258$		0			0
$259$	−6.05408	−	2.39304i	−0.376182	−	0.148696i
$260$		−	6.64211i		−	0.411926i
$261$		0			0
$262$		−	11.9126i		−	0.735964i
$263$		−	6.67671i		−	0.411704i	−0.978583	−	0.205852i	$-0.934004\pi$
$263$		−	6.67671i		−	0.411704i	0.978583	−	0.205852i	$-0.0659965\pi$
$264$		0			0
$265$		−	7.38538i		−	0.453680i
$266$	18.4882	+	7.30798i	1.13359	+	0.448081i
$267$		0			0
$268$	0.787935			0.0481308
$269$	10.6589			0.649887			0.324944	−	0.945733i	$-0.394655\pi$
$269$	10.6589			0.649887			0.324944	+	0.945733i	$0.394655\pi$
$270$		0			0
$271$			7.44498i			0.452250i	0.974098	+	0.226125i	$0.0726058\pi$
$271$			7.44498i			0.452250i	−0.974098	+	0.226125i	$0.927394\pi$
$272$	10.1985			0.618373
$273$		0			0
$274$	9.53657			0.576125
$275$			0.481985i			0.0290648i
$276$		0			0
$277$	−26.5586			−1.59575			−0.797874	−	0.602824i	$-0.794042\pi$
$277$	−26.5586			−1.59575			−0.797874	+	0.602824i	$0.794042\pi$
$278$	−22.4172			−1.34450
$279$		0			0
$280$	−8.48968	+	21.4778i	−0.507356	+	1.28354i
$281$			24.3634i			1.45340i	0.686956	+	0.726699i	$0.258946\pi$
$281$			24.3634i			1.45340i	−0.686956	+	0.726699i	$0.741054\pi$
$282$		0			0
$283$			8.65219i			0.514319i	0.966369	+	0.257160i	$0.0827866\pi$
$283$			8.65219i			0.514319i	−0.966369	+	0.257160i	$0.917213\pi$
$284$		−	0.242958i		−	0.0144169i
$285$		0			0
$286$			0.737954i			0.0436361i
$287$	−9.82082	−	3.88195i	−0.579704	−	0.229144i
$288$		0			0
$289$	0.179961			0.0105860
$290$	−15.6502			−0.919014
$291$		0			0
$292$			8.91104i			0.521479i
$293$	8.80047			0.514129			0.257064	−	0.966394i	$-0.417245\pi$
$293$	8.80047			0.514129			0.257064	+	0.966394i	$0.417245\pi$
$294$		0			0
$295$	10.2556			0.597106
$296$		−	7.56800i		−	0.439881i
$297$		0			0
$298$	23.0144			1.33319
$299$	−2.15333			−0.124530
$300$		0			0
$301$	−16.1623	−	6.38857i	−0.931577	−	0.368231i
$302$		−	2.12036i		−	0.122013i
$303$		0			0
$304$			15.5897i			0.894130i
$305$			9.55155i			0.546920i
$306$		0			0
$307$			11.1747i			0.637771i	0.947793	+	0.318886i	$0.103309\pi$
$307$			11.1747i			0.637771i	−0.947793	+	0.318886i	$0.896691\pi$
$308$	−0.0911082	+	0.230492i	−0.00519137	+	0.0131335i
$309$		0			0
$310$	−0.435599			−0.0247404
$311$	16.4056			0.930275			0.465137	−	0.885239i	$-0.346005\pi$
$311$	16.4056			0.930275			0.465137	+	0.885239i	$0.346005\pi$
$312$		0			0
$313$			8.20431i			0.463735i	0.972747	+	0.231868i	$0.0744836\pi$
$313$			8.20431i			0.463735i	−0.972747	+	0.231868i	$0.925516\pi$
$314$	−5.20717			−0.293858
$315$		0			0
$316$	2.56867			0.144499
$317$			22.9124i			1.28689i	0.765494	+	0.643443i	$0.222495\pi$
$317$			22.9124i			1.28689i	−0.765494	+	0.643443i	$0.777505\pi$
$318$		0			0
$319$	−0.733851			−0.0410878
$320$	−24.8488			−1.38909
$321$		0			0
$322$	1.59358	+	0.629906i	0.0888067	+	0.0351033i
$323$			26.2618i			1.46125i
$324$		0			0
$325$		−	12.0420i		−	0.667972i
$326$			6.44622i			0.357023i
$327$		0			0
$328$		−	12.2767i		−	0.677866i
$329$	−21.3262	−	8.42976i	−1.17575	−	0.464748i
$330$		0			0
$331$	19.2632			1.05880			0.529401	−	0.848372i	$-0.322417\pi$
$331$	19.2632			1.05880			0.529401	+	0.848372i	$0.322417\pi$
$332$	3.82959			0.210176
$333$		0			0
$334$		−	12.4587i		−	0.681709i
$335$	3.76721			0.205825
$336$		0			0
$337$	4.53657			0.247123			0.123561	−	0.992337i	$-0.460568\pi$
$337$	4.53657			0.247123			0.123561	+	0.992337i	$0.460568\pi$
$338$		−	3.02019i		−	0.164277i
$339$		0			0
$340$	−6.98229			−0.378668
$341$	−0.0204255			−0.00110610
$342$		0			0
$343$	7.91381	+	16.7443i	0.427306	+	0.904107i
$344$		−	20.2039i		−	1.08932i
$345$		0			0
$346$			20.8237i			1.11949i
$347$		−	8.73293i		−	0.468808i	−0.972139	−	0.234404i	$-0.924686\pi$
$347$		−	8.73293i		−	0.468808i	0.972139	−	0.234404i	$-0.0753139\pi$
$348$		0			0
$349$		−	9.04047i		−	0.483925i	−0.970286	−	0.241963i	$-0.922209\pi$
$349$		−	9.04047i		−	0.483925i	0.970286	−	0.241963i	$-0.0777911\pi$
$350$	−3.52261	+	8.91175i	−0.188292	+	0.476353i
$351$		0			0
$352$	−0.510317			−0.0272000
$353$	1.21579			0.0647101			0.0323550	−	0.999476i	$-0.489699\pi$
$353$	1.21579			0.0647101			0.0323550	+	0.999476i	$0.489699\pi$
$354$		0			0
$355$		−	1.16161i		−	0.0616518i
$356$	−2.99976			−0.158987
$357$		0			0
$358$	21.5877			1.14095
$359$		−	17.3069i		−	0.913424i	−0.889615	−	0.456712i	$-0.849027\pi$
$359$		−	17.3069i		−	0.913424i	0.889615	−	0.456712i	$-0.150973\pi$
$360$		0			0
$361$	−21.1445			−1.11287
$362$	7.82927			0.411498
$363$		0			0
$364$	2.27627	−	5.75867i	0.119309	−	0.301836i
$365$			42.6047i			2.23003i
$366$		0			0
$367$			28.2090i			1.47250i	0.676710	+	0.736250i	$0.263405\pi$
$367$			28.2090i			1.47250i	−0.676710	+	0.736250i	$0.736595\pi$
$368$			1.34374i			0.0700474i
$369$		0			0
$370$		−	8.28114i		−	0.430516i
$371$	2.53099	−	6.40308i	0.131403	−	0.332431i
$372$		0			0
$373$	28.2527			1.46287			0.731435	−	0.681911i	$-0.238851\pi$
$373$	28.2527			1.46287			0.731435	+	0.681911i	$0.238851\pi$
$374$	0.775749			0.0401130
$375$		0			0
$376$		−	26.6591i		−	1.37484i
$377$	18.3347			0.944287
$378$		0			0
$379$	14.6447			0.752250			0.376125	−	0.926569i	$-0.377256\pi$
$379$	14.6447			0.752250			0.376125	+	0.926569i	$0.377256\pi$
$380$		−	10.6733i		−	0.547531i
$381$		0			0
$382$	16.8521			0.862231
$383$	24.7864			1.26653			0.633264	−	0.773936i	$-0.281715\pi$
$383$	24.7864			1.26653			0.633264	+	0.773936i	$0.281715\pi$
$384$		0			0
$385$	−0.435599	+	1.10201i	−0.0222002	+	0.0561635i
$386$		−	11.8643i		−	0.603878i
$387$		0			0
$388$			1.49729i			0.0760131i
$389$			5.12348i			0.259771i	0.991529	+	0.129885i	$0.0414609\pi$
$389$			5.12348i			0.259771i	−0.991529	+	0.129885i	$0.958539\pi$
$390$		0			0
$391$			2.26362i			0.114476i
$392$	−14.7210	+	15.7117i	−0.743523	+	0.793559i
$393$		0			0
$394$	−23.8391			−1.20100
$395$	12.2811			0.617930
$396$		0			0
$397$		−	1.92094i		−	0.0964093i	−0.998837	−	0.0482046i	$-0.984650\pi$
$397$		−	1.92094i		−	0.0964093i	0.998837	−	0.0482046i	$-0.0153500\pi$
$398$	15.3433			0.769089
$399$		0			0
$400$	−7.51459			−0.375729
$401$			14.3889i			0.718549i	0.933232	+	0.359274i	$0.116976\pi$
$401$			14.3889i			0.718549i	−0.933232	+	0.359274i	$0.883024\pi$
$402$		0			0
$403$	0.510317			0.0254207
$404$	1.77567			0.0883429
$405$		0			0
$406$	−13.5687	−	5.36339i	−0.673402	−	0.266181i
$407$		−	0.388308i		−	0.0192477i
$408$		0			0
$409$			9.72582i			0.480911i	0.970660	+	0.240455i	$0.0772968\pi$
$409$			9.72582i			0.480911i	−0.970660	+	0.240455i	$0.922703\pi$
$410$		−	13.4335i		−	0.663433i
$411$		0			0
$412$		−	7.83326i		−	0.385917i
$413$	8.89158	+	3.51464i	0.437526	+	0.172944i
$414$		0			0
$415$	18.3097			0.898789
$416$	12.7499			0.625115
$417$		0			0
$418$			1.18583i			0.0580010i
$419$	−29.9025			−1.46083			−0.730416	−	0.683002i	$-0.760674\pi$
$419$	−29.9025			−1.46083			−0.730416	+	0.683002i	$0.760674\pi$
$420$		0			0
$421$	25.0905			1.22283			0.611417	−	0.791309i	$-0.290600\pi$
$421$	25.0905			1.22283			0.611417	+	0.791309i	$0.290600\pi$
$422$			10.6904i			0.520401i
$423$		0			0
$424$	8.00427			0.388722
$425$	−12.6588			−0.614041
$426$		0			0
$427$	−3.27335	+	8.28114i	−0.158408	+	0.400752i
$428$		−	11.6078i		−	0.561083i
$429$		0			0
$430$		−	22.1077i		−	1.06613i
$431$		−	6.39061i		−	0.307825i	−0.988084	−	0.153913i	$-0.950813\pi$
$431$		−	6.39061i		−	0.307825i	0.988084	−	0.153913i	$-0.0491874\pi$
$432$		0			0
$433$		−	33.1771i		−	1.59439i	−0.603721	−	0.797196i	$-0.706316\pi$
$433$		−	33.1771i		−	1.59439i	0.603721	−	0.797196i	$-0.293684\pi$
$434$	−0.377662	−	0.149281i	−0.0181283	−	0.00716572i
$435$		0			0
$436$	7.86400			0.376617
$437$	−3.46023			−0.165525
$438$		0			0
$439$		−	8.46316i		−	0.403925i	−0.979393	−	0.201962i	$-0.935268\pi$
$439$		−	8.46316i		−	0.403925i	0.979393	−	0.201962i	$-0.0647319\pi$
$440$	−1.37758			−0.0656737
$441$		0			0
$442$	−19.3815			−0.921885
$443$			18.6001i			0.883718i	0.897085	+	0.441859i	$0.145681\pi$
$443$			18.6001i			0.883718i	−0.897085	+	0.441859i	$0.854319\pi$
$444$		0			0
$445$	−14.3422			−0.679886
$446$	−2.67618			−0.126721
$447$		0			0
$448$	−21.5438	−	8.51576i	−1.01785	−	0.402332i
$449$		−	20.3100i		−	0.958489i	−0.877681	−	0.479245i	$-0.840911\pi$
$449$		−	20.3100i		−	0.958489i	0.877681	−	0.479245i	$-0.159089\pi$
$450$		0			0
$451$		−	0.629906i		−	0.0296611i
$452$			5.98130i			0.281337i
$453$		0			0
$454$		−	22.1077i		−	1.03757i
$455$	10.8831	−	27.5329i	0.510208	−	1.29076i
$456$		0			0
$457$	11.3566			0.531240			0.265620	−	0.964078i	$-0.414423\pi$
$457$	11.3566			0.531240			0.265620	+	0.964078i	$0.414423\pi$
$458$	16.9654			0.792743
$459$		0			0
$460$		−	0.919981i		−	0.0428943i
$461$	−38.9967			−1.81626			−0.908129	−	0.418691i	$-0.862489\pi$
$461$	−38.9967			−1.81626			−0.908129	+	0.418691i	$0.862489\pi$
$462$		0			0
$463$	10.0689			0.467940			0.233970	−	0.972244i	$-0.424828\pi$
$463$	10.0689			0.467940			0.233970	+	0.972244i	$0.424828\pi$
$464$		−	11.4414i		−	0.531154i
$465$		0			0
$466$	−20.2412			−0.937657
$467$	−3.59330			−0.166278			−0.0831389	−	0.996538i	$-0.526495\pi$
$467$	−3.59330			−0.166278			−0.0831389	+	0.996538i	$0.526495\pi$
$468$		0			0
$469$	3.26615	+	1.29103i	0.150817	+	0.0596145i
$470$		−	29.1712i		−	1.34557i
$471$		0			0
$472$			11.1151i			0.511612i
$473$		−	1.03664i		−	0.0476650i
$474$		0			0
$475$		−	19.3506i		−	0.887866i
$476$	−6.05361	−	2.39285i	−0.277467	−	0.109676i
$477$		0			0
$478$	2.65059			0.121235
$479$	1.62218			0.0741193			0.0370597	−	0.999313i	$-0.488201\pi$
$479$	1.62218			0.0741193			0.0370597	+	0.999313i	$0.488201\pi$
$480$		0			0
$481$			9.70160i			0.442355i
$482$	−5.36066			−0.244172
$483$		0			0
$484$	6.51459			0.296118
$485$			7.15869i			0.325060i
$486$		0			0
$487$	7.99573			0.362321			0.181161	−	0.983454i	$-0.442015\pi$
$487$	7.99573			0.362321			0.181161	+	0.983454i	$0.442015\pi$
$488$	−10.3520			−0.468612
$489$		0			0
$490$	−16.1082	+	17.1922i	−0.727693	+	0.776663i
$491$		−	10.7460i		−	0.484961i	−0.970156	−	0.242480i	$-0.922039\pi$
$491$		−	10.7460i		−	0.484961i	0.970156	−	0.242480i	$-0.0779610\pi$
$492$		0			0
$493$		−	19.2738i		−	0.868047i
$494$		−	29.6272i		−	1.33299i
$495$		0			0
$496$		−	0.318453i		−	0.0142990i
$497$	0.398087	−	1.00711i	0.0178566	−	0.0451750i
$498$		0			0
$499$	16.9210			0.757488			0.378744	−	0.925501i	$-0.376356\pi$
$499$	16.9210			0.757488			0.378744	+	0.925501i	$0.376356\pi$
$500$	−3.27801			−0.146597
$501$		0			0
$502$			25.1093i			1.12068i
$503$	−33.9226			−1.51253			−0.756267	−	0.654263i	$-0.772979\pi$
$503$	−33.9226			−1.51253			−0.756267	+	0.654263i	$0.772979\pi$
$504$		0			0
$505$	8.48968			0.377786
$506$			0.102212i			0.00454388i
$507$		0			0
$508$	−7.41362			−0.328926
$509$	−10.1361			−0.449275			−0.224637	−	0.974442i	$-0.572120\pi$
$509$	−10.1361			−0.449275			−0.224637	+	0.974442i	$0.572120\pi$
$510$		0			0
$511$	−14.6008	+	36.9380i	−0.645900	+	1.63404i
$512$		−	23.0923i		−	1.02055i
$513$		0			0
$514$			37.1201i			1.63730i
$515$		−	37.4517i		−	1.65032i
$516$		0			0
$517$		−	1.36786i		−	0.0601584i
$518$	2.83797	−	7.17970i	0.124693	−	0.315458i
$519$		0			0
$520$	34.4179			1.50932
$521$	−31.6986			−1.38874			−0.694370	−	0.719618i	$-0.744317\pi$
$521$	−31.6986			−1.38874			−0.694370	+	0.719618i	$0.744317\pi$
$522$		0			0
$523$		−	8.09911i		−	0.354149i	−0.984197	−	0.177075i	$-0.943337\pi$
$523$		−	8.09911i		−	0.354149i	0.984197	−	0.177075i	$-0.0566634\pi$
$524$	−5.96250			−0.260473
$525$		0			0
$526$	7.91808			0.345245
$527$		−	0.536454i		−	0.0233683i
$528$		0			0
$529$	22.7017			0.987033
$530$	8.75851			0.380446
$531$		0			0
$532$	3.65779	−	9.25372i	0.158585	−	0.401200i
$533$			15.7377i			0.681677i
$534$		0			0
$535$		−	55.4981i		−	2.39939i
$536$			4.08290i			0.176354i
$537$		0			0
$538$			12.6407i			0.544980i
$539$	−0.755323	+	0.806153i	−0.0325341	+	0.0347235i
$540$		0			0
$541$	1.21634			0.0522944			0.0261472	−	0.999658i	$-0.491676\pi$
$541$	1.21634			0.0522944			0.0261472	+	0.999658i	$0.491676\pi$
$542$	−8.82920			−0.379246
$543$		0			0
$544$		−	13.4029i		−	0.574645i
$545$	37.5987			1.61055
$546$		0			0
$547$	−26.2556			−1.12261			−0.561305	−	0.827609i	$-0.689701\pi$
$547$	−26.2556			−1.12261			−0.561305	+	0.827609i	$0.689701\pi$
$548$		−	4.77324i		−	0.203903i
$549$		0			0
$550$	−0.571598			−0.0243730
$551$	29.4624			1.25514
$552$		0			0
$553$	10.6477	+	4.20878i	0.452785	+	0.178976i
$554$		−	31.4965i		−	1.33816i
$555$		0			0
$556$			11.2203i			0.475845i
$557$			27.2172i			1.15323i	0.817016	+	0.576615i	$0.195627\pi$
$557$			27.2172i			1.15323i	−0.817016	+	0.576615i	$0.804373\pi$
$558$		0			0
$559$			25.8998i			1.09545i
$560$	−17.1813	−	6.79139i	−0.726043	−	0.286989i
$561$		0			0
$562$	−28.8932			−1.21879
$563$	−9.36035			−0.394492			−0.197246	−	0.980354i	$-0.563200\pi$
$563$	−9.36035			−0.394492			−0.197246	+	0.980354i	$0.563200\pi$
$564$		0			0
$565$			28.5973i			1.20310i
$566$	−10.2609			−0.431296
$567$		0			0
$568$	1.25895			0.0528244
$569$		−	34.9209i		−	1.46396i	−0.681326	−	0.731980i	$-0.738596\pi$
$569$		−	34.9209i		−	1.46396i	0.681326	−	0.731980i	$-0.261404\pi$
$570$		0			0
$571$	−1.47197			−0.0616002			−0.0308001	−	0.999526i	$-0.509806\pi$
$571$	−1.47197			−0.0616002			−0.0308001	+	0.999526i	$0.509806\pi$
$572$	0.369360			0.0154437
$573$		0			0
$574$	4.60370	−	11.6468i	0.192155	−	0.486126i
$575$		−	1.66791i		−	0.0695567i
$576$		0			0
$577$			18.6196i			0.775146i	0.921839	+	0.387573i	$0.126686\pi$
$577$			18.6196i			0.775146i	−0.921839	+	0.387573i	$0.873314\pi$
$578$			0.213421i			0.00887714i
$579$		0			0
$580$			7.83326i			0.325258i
$581$	15.8744	+	6.27480i	0.658582	+	0.260323i
$582$		0			0
$583$	0.410693			0.0170092
$584$	−46.1750			−1.91073
$585$		0			0
$586$			10.4367i			0.431136i
$587$	18.5710			0.766508			0.383254	−	0.923643i	$-0.374803\pi$
$587$	18.5710			0.766508			0.383254	+	0.923643i	$0.374803\pi$
$588$		0			0
$589$	0.820039			0.0337891
$590$			12.1624i			0.500719i
$591$		0			0
$592$	6.05408			0.248821
$593$	30.9228			1.26985			0.634924	−	0.772574i	$-0.281031\pi$
$593$	30.9228			1.26985			0.634924	+	0.772574i	$0.281031\pi$
$594$		0			0
$595$	−28.9430	−	11.4405i	−1.18655	−	0.469015i
$596$		−	11.5192i		−	0.471843i
$597$		0			0
$598$		−	2.55369i		−	0.104428i
$599$		−	13.7111i		−	0.560219i	−0.959968	−	0.280109i	$-0.909629\pi$
$599$		−	13.7111i		−	0.560219i	0.959968	−	0.280109i	$-0.0903707\pi$
$600$		0			0
$601$			19.7529i			0.805736i	0.915258	+	0.402868i	$0.131987\pi$
$601$			19.7529i			0.805736i	−0.915258	+	0.402868i	$0.868013\pi$
$602$	7.57638	−	19.1672i	0.308790	−	0.781198i
$603$		0			0
$604$	−1.06128			−0.0431829
$605$	31.1470			1.26631
$606$		0			0
$607$		−	17.9231i		−	0.727477i	−0.931501	−	0.363739i	$-0.881500\pi$
$607$		−	17.9231i		−	0.727477i	0.931501	−	0.363739i	$-0.118500\pi$
$608$	20.4881			0.830901
$609$		0			0
$610$	−11.3274			−0.458634
$611$			34.1750i			1.38257i
$612$		0			0
$613$	−41.4327			−1.67345			−0.836725	−	0.547623i	$-0.815533\pi$
$613$	−41.4327			−1.67345			−0.836725	+	0.547623i	$0.815533\pi$
$614$	−13.2523			−0.534820
$615$		0			0
$616$	−1.19436	−	0.472102i	−0.0481220	−	0.0190215i
$617$		−	23.0577i		−	0.928269i	−0.885765	−	0.464134i	$-0.846365\pi$
$617$		−	23.0577i		−	0.928269i	0.885765	−	0.464134i	$-0.153635\pi$
$618$		0			0
$619$		−	1.93816i		−	0.0779014i	−0.999241	−	0.0389507i	$-0.987598\pi$
$619$		−	1.93816i		−	0.0779014i	0.999241	−	0.0389507i	$-0.0124015\pi$
$620$			0.218026i			0.00875613i
$621$		0			0
$622$			19.4558i			0.780106i
$623$	−12.4346	−	4.91512i	−0.498182	−	0.196920i
$624$		0			0
$625$	−30.9430			−1.23772
$626$	−9.72971			−0.388877
$627$		0			0
$628$			2.60629i			0.104002i
$629$	10.1985			0.406640
$630$		0			0
$631$	23.5831			0.938827			0.469414	−	0.882978i	$-0.344465\pi$
$631$	23.5831			0.938827			0.469414	+	0.882978i	$0.344465\pi$
$632$			13.3103i			0.529455i
$633$		0			0
$634$	−27.1724			−1.07915
$635$	−35.4454			−1.40661
$636$		0			0
$637$	18.8712	−	20.1411i	0.747704	−	0.798021i
$638$		−	0.870293i		−	0.0344552i
$639$		0			0
$640$		−	11.1151i		−	0.439361i
$641$			24.8368i			0.980996i	0.871442	+	0.490498i	$0.163185\pi$
$641$			24.8368i			0.980996i	−0.871442	+	0.490498i	$0.836815\pi$
$642$		0			0
$643$			43.7917i			1.72698i	0.504369	+	0.863489i	$0.331725\pi$
$643$			43.7917i			1.72698i	−0.504369	+	0.863489i	$0.668275\pi$
$644$	0.315280	−	0.797618i	0.0124238	−	0.0314305i
$645$		0			0
$646$	−31.1445			−1.22537
$647$	−29.3713			−1.15471			−0.577353	−	0.816494i	$-0.695914\pi$
$647$	−29.3713			−1.15471			−0.577353	+	0.816494i	$0.695914\pi$
$648$		0			0
$649$			0.570305i			0.0223864i
$650$	14.2810			0.560146
$651$		0			0
$652$	3.22646			0.126358
$653$			32.4258i			1.26892i	0.772955	+	0.634461i	$0.218778\pi$
$653$			32.4258i			1.26892i	−0.772955	+	0.634461i	$0.781222\pi$
$654$		0			0
$655$	−28.5074			−1.11388
$656$	9.82082			0.383438
$657$		0			0
$658$	9.99707	−	25.2913i	0.389727	−	0.985957i
$659$		−	0.234422i		−	0.00913180i	−0.999990	−	0.00456590i	$-0.998547\pi$
$659$		−	0.234422i		−	0.00913180i	0.999990	−	0.00456590i	$-0.00145338\pi$
$660$		0			0
$661$		−	3.52343i		−	0.137045i	−0.997650	−	0.0685227i	$-0.978171\pi$
$661$		−	3.52343i		−	0.137045i	0.997650	−	0.0685227i	$-0.0218286\pi$
$662$			22.8448i			0.887887i
$663$		0			0
$664$			19.8441i			0.770099i
$665$	17.4883	−	44.2431i	0.678167	−	1.71567i
$666$		0			0
$667$	2.53950			0.0983296
$668$	−6.23582			−0.241271
$669$		0			0
$670$			4.46763i			0.172600i
$671$	−0.531151			−0.0205049
$672$		0			0
$673$	−18.3317			−0.706635			−0.353318	−	0.935503i	$-0.614946\pi$
$673$	−18.3317			−0.706635			−0.353318	+	0.935503i	$0.614946\pi$
$674$			5.38004i			0.207231i
$675$		0			0
$676$	−1.51166			−0.0581409
$677$	−33.8519			−1.30103			−0.650517	−	0.759491i	$-0.725448\pi$
$677$	−33.8519			−1.30103			−0.650517	+	0.759491i	$0.725448\pi$
$678$		0			0
$679$	−2.45331	+	6.20655i	−0.0941493	+	0.238185i
$680$		−	36.1806i		−	1.38746i
$681$		0			0
$682$		−	0.0242232i		−	0.000927553i
$683$		−	28.0284i		−	1.07248i	−0.844066	−	0.536239i	$-0.819844\pi$
$683$		−	28.0284i		−	1.07248i	0.844066	−	0.536239i	$-0.180156\pi$
$684$		0			0
$685$		−	22.8214i		−	0.871962i
$686$	−19.8575	+	9.38520i	−0.758163	+	0.358328i
$687$		0			0
$688$	16.1623			0.616180
$689$	−10.2609			−0.390908
$690$		0			0
$691$		−	49.3511i		−	1.87741i	−0.344727	−	0.938703i	$-0.612029\pi$
$691$		−	49.3511i		−	1.87741i	0.344727	−	0.938703i	$-0.387971\pi$
$692$	10.4226			0.396210
$693$		0			0
$694$	10.3566			0.393131
$695$			53.6454i			2.03488i
$696$		0			0
$697$	16.5438			0.626640
$698$	10.7213			0.405808
$699$		0			0
$700$	4.46050	+	1.76314i	0.168591	+	0.0666403i
$701$			26.3889i			0.996696i	0.866977	+	0.498348i	$0.166060\pi$
$701$			26.3889i			0.996696i	−0.866977	+	0.498348i	$0.833940\pi$
$702$		0			0
$703$			15.5897i			0.587976i
$704$		−	1.38181i		−	0.0520791i
$705$		0			0
$706$			1.44184i			0.0542643i
$707$	7.36051	+	2.90944i	0.276820	+	0.109421i
$708$		0			0
$709$	−10.7132			−0.402343			−0.201172	−	0.979556i	$-0.564475\pi$
$709$	−10.7132			−0.402343			−0.201172	+	0.979556i	$0.564475\pi$
$710$	1.37758			0.0516998
$711$		0			0
$712$		−	15.5441i		−	0.582539i
$713$	0.0706827			0.00264709
$714$		0			0
$715$	1.76595			0.0660429
$716$		−	10.8051i		−	0.403805i
$717$		0			0
$718$	20.5247			0.765975
$719$	17.5794			0.655601			0.327801	−	0.944747i	$-0.393693\pi$
$719$	17.5794			0.655601			0.327801	+	0.944747i	$0.393693\pi$
$720$		0			0
$721$	12.8348	−	32.4704i	0.477994	−	1.20926i
$722$		−	25.0759i		−	0.933227i
$723$		0			0
$724$		−	3.91871i		−	0.145638i
$725$			14.2016i			0.527433i
$726$		0			0
$727$		−	50.1943i		−	1.86160i	−0.365524	−	0.930802i	$-0.619110\pi$
$727$		−	50.1943i		−	1.86160i	0.365524	−	0.930802i	$-0.380890\pi$
$728$	29.8401	+	11.7951i	1.10595	+	0.437156i
$729$		0			0
$730$	−50.5261			−1.87005
$731$	27.2263			1.00700
$732$		0			0
$733$			39.9084i			1.47405i	0.675865	+	0.737025i	$0.263770\pi$
$733$			39.9084i			1.47405i	−0.675865	+	0.737025i	$0.736230\pi$
$734$	−33.4538			−1.23480
$735$		0			0
$736$	1.76595			0.0650939
$737$			0.209490i			0.00771668i
$738$		0			0
$739$	30.3432			1.11619			0.558096	−	0.829777i	$-0.311532\pi$
$739$	30.3432			1.11619			0.558096	+	0.829777i	$0.311532\pi$
$740$	−4.14487			−0.152369
$741$		0			0
$742$	7.59358	+	3.00157i	0.278769	+	0.110191i
$743$			45.7101i			1.67694i	0.544948	+	0.838470i	$0.316549\pi$
$743$			45.7101i			1.67694i	−0.544948	+	0.838470i	$0.683451\pi$
$744$		0			0
$745$		−	55.0744i		−	2.01777i
$746$			33.5056i			1.22673i
$747$		0			0
$748$		−	0.388278i		−	0.0141968i
$749$	19.0194	−	48.1165i	0.694953	−	1.75814i
$750$		0			0
$751$	12.1551			0.443544			0.221772	−	0.975099i	$-0.428816\pi$
$751$	12.1551			0.443544			0.221772	+	0.975099i	$0.428816\pi$
$752$	21.3262			0.777686
$753$		0			0
$754$			21.7436i			0.791857i
$755$	−5.07411			−0.184666
$756$		0			0
$757$	−9.71614			−0.353139			−0.176570	−	0.984288i	$-0.556500\pi$
$757$	−9.71614			−0.353139			−0.176570	+	0.984288i	$0.556500\pi$
$758$			17.3676i			0.630819i
$759$		0			0
$760$	55.3068			2.00619
$761$	−38.8349			−1.40776			−0.703882	−	0.710317i	$-0.748552\pi$
$761$	−38.8349			−1.40776			−0.703882	+	0.710317i	$0.748552\pi$
$762$		0			0
$763$	32.5979	+	12.8852i	1.18012	+	0.466475i
$764$		−	8.43483i		−	0.305161i
$765$		0			0
$766$			29.3949i			1.06208i
$767$		−	14.2486i		−	0.514489i
$768$		0			0
$769$		−	10.8874i		−	0.392611i	−0.980543	−	0.196305i	$-0.937106\pi$
$769$		−	10.8874i		−	0.392611i	0.980543	−	0.196305i	$-0.0628944\pi$
$770$	−1.30690	−	0.516588i	−0.0470974	−	0.0186165i
$771$		0			0
$772$	−5.93833			−0.213725
$773$	37.3337			1.34280			0.671400	−	0.741096i	$-0.265693\pi$
$773$	37.3337			1.34280			0.671400	+	0.741096i	$0.265693\pi$
$774$		0			0
$775$			0.395277i			0.0141988i
$776$	−7.75859			−0.278517
$777$		0			0
$778$	−6.07607			−0.217837
$779$			25.2893i			0.906083i
$780$		0			0
$781$	0.0645958			0.00231142
$782$	−2.68448			−0.0959969
$783$		0			0
$784$	−12.5687	−	11.7762i	−0.448881	−	0.420578i
$785$			12.4610i			0.444752i
$786$		0			0
$787$		−	17.8463i		−	0.636152i	−0.948065	−	0.318076i	$-0.896963\pi$
$787$		−	17.8463i		−	0.636152i	0.948065	−	0.318076i	$-0.103037\pi$
$788$			11.9319i			0.425058i
$789$		0			0
$790$			14.5645i			0.518182i
$791$	−9.80039	+	24.7937i	−0.348462	+	0.881562i
$792$		0			0
$793$	13.2704			0.471246
$794$	2.27809			0.0808465
$795$		0			0
$796$		−	7.67961i		−	0.272197i
$797$	11.4971			0.407247			0.203624	−	0.979049i	$-0.434728\pi$
$797$	11.4971			0.407247			0.203624	+	0.979049i	$0.434728\pi$
$798$		0			0
$799$	35.9253			1.27095
$800$			9.87572i			0.349159i
$801$		0			0
$802$	−17.0642			−0.602558
$803$	−2.36920			−0.0836073
$804$		0			0
$805$	1.50739	−	3.81350i	0.0531286	−	0.134408i
$806$			0.605198i			0.0213172i
$807$		0			0
$808$			9.20112i			0.323694i
$809$		−	13.1945i		−	0.463893i	−0.972729	−	0.231946i	$-0.925491\pi$
$809$		−	13.1945i		−	0.463893i	0.972729	−	0.231946i	$-0.0745094\pi$
$810$		0			0
$811$			46.5800i			1.63565i	0.575469	+	0.817823i	$0.304819\pi$
$811$			46.5800i			1.63565i	−0.575469	+	0.817823i	$0.695181\pi$
$812$	−2.68448	+	6.79139i	−0.0942069	+	0.238331i
$813$		0			0
$814$	0.460505			0.0161407
$815$	15.4261			0.540352
$816$		0			0
$817$			41.6189i			1.45606i
$818$	−11.5341			−0.403280
$819$		0			0
$820$	−6.72373			−0.234803
$821$			39.6782i			1.38478i	0.721524	+	0.692390i	$0.243442\pi$
$821$			39.6782i			1.38478i	−0.721524	+	0.692390i	$0.756558\pi$
$822$		0			0
$823$	−39.2311			−1.36751			−0.683755	−	0.729711i	$-0.739654\pi$
$823$	−39.2311			−1.36751			−0.683755	+	0.729711i	$0.739654\pi$
$824$	40.5902			1.41403
$825$		0			0
$826$	−4.16810	+	10.5448i	−0.145027	+	0.366899i
$827$		−	21.0827i		−	0.733118i	−0.930395	−	0.366559i	$-0.880536\pi$
$827$		−	21.0827i		−	0.733118i	0.930395	−	0.366559i	$-0.119464\pi$
$828$		0			0
$829$		−	13.3261i		−	0.462834i	−0.972855	−	0.231417i	$-0.925664\pi$
$829$		−	13.3261i		−	0.462834i	0.972855	−	0.231417i	$-0.0743361\pi$
$830$			21.7140i			0.753703i
$831$		0			0
$832$			34.5236i			1.19689i
$833$	−21.1727	−	19.8377i	−0.733591	−	0.687336i
$834$		0			0
$835$	−29.8142			−1.03176
$836$	0.593532			0.0205277
$837$		0			0
$838$		−	35.4621i		−	1.22502i
$839$	16.7954			0.579840			0.289920	−	0.957051i	$-0.406371\pi$
$839$	16.7954			0.579840			0.289920	+	0.957051i	$0.406371\pi$
$840$		0			0
$841$	7.37724			0.254388
$842$			29.7554i			1.02544i
$843$		0			0
$844$	5.35076			0.184181
$845$	−7.22744			−0.248632
$846$		0			0
$847$	27.0043	+	10.6742i	0.927878	+	0.366769i
$848$			6.40308i			0.219883i
$849$		0			0
$850$		−	15.0124i		−	0.514921i
$851$			1.34374i			0.0460629i
$852$		0			0
$853$			40.9932i			1.40358i	0.712384	+	0.701790i	$0.247615\pi$
$853$			40.9932i			1.40358i	−0.712384	+	0.701790i	$0.752385\pi$
$854$	−9.82082	−	3.88195i	−0.336061	−	0.132837i
$855$		0			0
$856$	60.1488			2.05584
$857$	41.7436			1.42593			0.712967	−	0.701198i	$-0.247351\pi$
$857$	41.7436			1.42593			0.712967	+	0.701198i	$0.247351\pi$
$858$		0			0
$859$			27.7682i			0.947437i	0.880676	+	0.473719i	$0.157089\pi$
$859$			27.7682i			0.947437i	−0.880676	+	0.473719i	$0.842911\pi$
$860$	−11.0653			−0.377325
$861$		0			0
$862$	7.57880			0.258135
$863$			45.6090i			1.55255i	0.630396	+	0.776274i	$0.282893\pi$
$863$			45.6090i			1.55255i	−0.630396	+	0.776274i	$0.717107\pi$
$864$		0			0
$865$	49.8319			1.69434
$866$	39.3456			1.33702
$867$		0			0
$868$	−0.0747181	+	0.189027i	−0.00253610	+	0.00641600i
$869$			0.682940i			0.0231671i
$870$		0			0
$871$		−	5.23396i		−	0.177346i
$872$			40.7495i			1.37995i
$873$		0			0
$874$		−	4.10358i		−	0.138806i
$875$	−13.5880	−	5.37104i	−0.459359	−	0.181574i
$876$		0			0
$877$	17.6874			0.597259			0.298630	−	0.954369i	$-0.403470\pi$
$877$	17.6874			0.597259			0.298630	+	0.954369i	$0.403470\pi$
$878$	10.0367			0.338722
$879$		0			0
$880$		−	1.10201i		−	0.0371487i
$881$	11.6169			0.391384			0.195692	−	0.980665i	$-0.437305\pi$
$881$	11.6169			0.391384			0.195692	+	0.980665i	$0.437305\pi$
$882$		0			0
$883$	−35.5480			−1.19629			−0.598143	−	0.801389i	$-0.704095\pi$
$883$	−35.5480			−1.19629			−0.598143	+	0.801389i	$0.704095\pi$
$884$			9.70083i			0.326274i
$885$		0			0
$886$	−22.0584			−0.741065
$887$	24.5501			0.824313			0.412156	−	0.911113i	$-0.364776\pi$
$887$	24.5501			0.824313			0.412156	+	0.911113i	$0.364776\pi$
$888$		0			0
$889$	−30.7309	−	12.1472i	−1.03068	−	0.407405i
$890$		−	17.0088i		−	0.570136i
$891$		0			0
$892$			1.33948i			0.0448492i
$893$			54.9164i			1.83771i
$894$		0			0
$895$		−	51.6604i		−	1.72682i
$896$	3.80917	−	9.63669i	0.127255	−	0.321939i
$897$		0			0
$898$	24.0862			0.803766
$899$	−0.601834			−0.0200723
$900$		0			0
$901$			10.7864i			0.359346i
$902$	0.747022			0.0248731
$903$		0			0
$904$	−30.9938			−1.03084
$905$		−	18.7358i		−	0.622799i
$906$		0			0
$907$	36.9004			1.22526			0.612628	−	0.790371i	$-0.290112\pi$
$907$	36.9004			1.22526			0.612628	+	0.790371i	$0.290112\pi$
$908$	−11.0653			−0.367216
$909$		0			0
$910$	32.6519	+	12.9066i	1.08240	+	0.427849i
$911$		−	39.8111i		−	1.31900i	−0.751704	−	0.659500i	$-0.770768\pi$
$911$		−	39.8111i		−	1.31900i	0.751704	−	0.659500i	$-0.229232\pi$
$912$		0			0
$913$			1.01818i			0.0336970i
$914$			13.4681i			0.445485i
$915$		0			0
$916$		−	8.49154i		−	0.280568i
$917$	−24.7157	−	9.76957i	−0.816186	−	0.322620i
$918$		0			0
$919$	−56.8725			−1.87605			−0.938026	−	0.346565i	$-0.887348\pi$
$919$	−56.8725			−1.87605			−0.938026	+	0.346565i	$0.887348\pi$
$920$	4.76713			0.157168
$921$		0			0
$922$		−	46.2472i		−	1.52307i
$923$	−1.61388			−0.0531215
$924$		0			0
$925$	−7.51459			−0.247078
$926$			11.9409i			0.392403i
$927$		0			0
$928$	−15.0364			−0.493593
$929$	−45.7769			−1.50189			−0.750946	−	0.660364i	$-0.770402\pi$
$929$	−45.7769			−1.50189			−0.750946	+	0.660364i	$0.770402\pi$
$930$		0			0
$931$	30.3245	−	32.3652i	0.993846	−	1.06073i
$932$			10.1311i			0.331857i
$933$		0			0
$934$		−	4.26138i		−	0.139437i
$935$		−	1.85640i		−	0.0607108i
$936$		0			0
$937$			24.0003i			0.784054i	0.919954	+	0.392027i	$0.128226\pi$
$937$			24.0003i			0.784054i	−0.919954	+	0.392027i	$0.871774\pi$
$938$	−1.53107	+	3.87341i	−0.0499913	+	0.126471i
$939$		0			0
$940$	−14.6008			−0.476225
$941$	3.28632			0.107131			0.0535654	−	0.998564i	$-0.482941\pi$
$941$	3.28632			0.107131			0.0535654	+	0.998564i	$0.482941\pi$
$942$		0			0
$943$			2.17979i			0.0709838i
$944$	−8.89158			−0.289396
$945$		0			0
$946$	1.22938			0.0399707
$947$		−	29.9552i		−	0.973415i	−0.873565	−	0.486707i	$-0.838198\pi$
$947$		−	29.9552i		−	0.973415i	0.873565	−	0.486707i	$-0.161802\pi$
$948$		0			0
$949$	59.1928			1.92148
$950$	22.9484			0.744544
$951$		0			0
$952$	12.3992	−	31.3684i	0.401861	−	1.01666i
$953$			16.0580i			0.520169i	0.965586	+	0.260084i	$0.0837504\pi$
$953$			16.0580i			0.520169i	−0.965586	+	0.260084i	$0.916250\pi$
$954$		0			0
$955$		−	40.3279i		−	1.30498i
$956$		−	1.32667i		−	0.0429076i
$957$		0			0
$958$			1.92379i			0.0621547i
$959$	7.82097	−	19.7860i	0.252552	−	0.638924i
$960$		0			0
$961$	30.9832			0.999460
$962$	−11.5054			−0.370948
$963$		0			0
$964$			2.68312i			0.0864174i
$965$	−28.3918			−0.913966
$966$		0			0
$967$	−50.0550			−1.60966			−0.804831	−	0.593504i	$-0.797744\pi$
$967$	−50.0550			−1.60966			−0.804831	+	0.593504i	$0.797744\pi$
$968$			33.7571i			1.08499i
$969$		0			0
$970$	−8.48968			−0.272587
$971$	1.04188			0.0334354			0.0167177	−	0.999860i	$-0.494678\pi$
$971$	1.04188			0.0334354			0.0167177	+	0.999860i	$0.494678\pi$
$972$		0			0
$973$	−18.3844	+	46.5102i	−0.589378	+	1.49105i
$974$			9.48234i			0.303834i
$975$		0			0
$976$		−	8.28114i		−	0.265073i
$977$		−	24.4525i		−	0.782304i	−0.920326	−	0.391152i	$-0.872077\pi$
$977$		−	24.4525i		−	0.782304i	0.920326	−	0.391152i	$-0.127923\pi$
$978$		0			0
$979$		−	0.797555i		−	0.0254900i
$980$	8.60502	+	8.06246i	0.274877	+	0.257546i
$981$		0			0
$982$	12.7440			0.406677
$983$	−56.1576			−1.79115			−0.895575	−	0.444911i	$-0.853235\pi$
$983$	−56.1576			−1.79115			−0.895575	+	0.444911i	$0.853235\pi$
$984$		0			0
$985$			57.0480i			1.81770i
$986$	22.8573			0.727924
$987$		0			0
$988$	−14.8290			−0.471772
$989$			3.58731i			0.114070i
$990$		0			0
$991$	18.2278			0.579025			0.289513	−	0.957174i	$-0.406507\pi$
$991$	18.2278			0.579025			0.289513	+	0.957174i	$0.406507\pi$
$992$	−0.418513			−0.0132878
$993$		0			0
$994$	1.19436	+	0.472102i	0.0378827	+	0.0149742i
$995$		−	36.7171i		−	1.16401i
$996$		0			0
$997$			34.4328i			1.09050i	0.838274	+	0.545249i	$0.183565\pi$
$997$			34.4328i			1.09050i	−0.838274	+	0.545249i	$0.816435\pi$
$998$			20.0671i			0.635212i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.c.c.566.10		12
3.2	odd	2	inner	567.2.c.c.566.3		12
7.6	odd	2	inner	567.2.c.c.566.9		12
9.2	odd	6		189.2.o.a.125.2		12
9.4	even	3		189.2.o.a.62.1		12
9.5	odd	6		63.2.o.a.20.5	✓	12
9.7	even	3		63.2.o.a.41.6	yes	12
21.20	even	2	inner	567.2.c.c.566.4		12
36.7	odd	6		1008.2.cc.a.545.3		12
36.11	even	6		3024.2.cc.a.881.6		12
36.23	even	6		1008.2.cc.a.209.4		12
36.31	odd	6		3024.2.cc.a.2897.1		12
63.2	odd	6		1323.2.s.c.962.5		12
63.4	even	3		1323.2.s.c.656.6		12
63.5	even	6		441.2.i.c.227.1		12
63.11	odd	6		1323.2.i.c.1097.2		12
63.13	odd	6		189.2.o.a.62.2		12
63.16	even	3		441.2.s.c.374.2		12
63.20	even	6		189.2.o.a.125.1		12
63.23	odd	6		441.2.i.c.227.2		12
63.25	even	3		441.2.i.c.68.5		12
63.31	odd	6		1323.2.s.c.656.5		12
63.32	odd	6		441.2.s.c.362.1		12
63.34	odd	6		63.2.o.a.41.5	yes	12
63.38	even	6		1323.2.i.c.1097.1		12
63.40	odd	6		1323.2.i.c.521.6		12
63.41	even	6		63.2.o.a.20.6	yes	12
63.47	even	6		1323.2.s.c.962.6		12
63.52	odd	6		441.2.i.c.68.6		12
63.58	even	3		1323.2.i.c.521.5		12
63.59	even	6		441.2.s.c.362.2		12
63.61	odd	6		441.2.s.c.374.1		12
252.83	odd	6		3024.2.cc.a.881.1		12
252.139	even	6		3024.2.cc.a.2897.6		12
252.167	odd	6		1008.2.cc.a.209.3		12
252.223	even	6		1008.2.cc.a.545.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.o.a.20.5	✓	12	9.5	odd	6
63.2.o.a.20.6	yes	12	63.41	even	6
63.2.o.a.41.5	yes	12	63.34	odd	6
63.2.o.a.41.6	yes	12	9.7	even	3
189.2.o.a.62.1		12	9.4	even	3
189.2.o.a.62.2		12	63.13	odd	6
189.2.o.a.125.1		12	63.20	even	6
189.2.o.a.125.2		12	9.2	odd	6
441.2.i.c.68.5		12	63.25	even	3
441.2.i.c.68.6		12	63.52	odd	6
441.2.i.c.227.1		12	63.5	even	6
441.2.i.c.227.2		12	63.23	odd	6
441.2.s.c.362.1		12	63.32	odd	6
441.2.s.c.362.2		12	63.59	even	6
441.2.s.c.374.1		12	63.61	odd	6
441.2.s.c.374.2		12	63.16	even	3
567.2.c.c.566.3		12	3.2	odd	2	inner
567.2.c.c.566.4		12	21.20	even	2	inner
567.2.c.c.566.9		12	7.6	odd	2	inner
567.2.c.c.566.10		12	1.1	even	1	trivial
1008.2.cc.a.209.3		12	252.167	odd	6
1008.2.cc.a.209.4		12	36.23	even	6
1008.2.cc.a.545.3		12	36.7	odd	6
1008.2.cc.a.545.4		12	252.223	even	6
1323.2.i.c.521.5		12	63.58	even	3
1323.2.i.c.521.6		12	63.40	odd	6
1323.2.i.c.1097.1		12	63.38	even	6
1323.2.i.c.1097.2		12	63.11	odd	6
1323.2.s.c.656.5		12	63.31	odd	6
1323.2.s.c.656.6		12	63.4	even	3
1323.2.s.c.962.5		12	63.2	odd	6
1323.2.s.c.962.6		12	63.47	even	6
3024.2.cc.a.881.1		12	252.83	odd	6
3024.2.cc.a.881.6		12	36.11	even	6
3024.2.cc.a.2897.1		12	36.31	odd	6
3024.2.cc.a.2897.6		12	252.139	even	6

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:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.18593i q^{2} +0.593579 q^{4} +2.83797 q^{5} +(2.46050 + 0.972582i) q^{7} +3.07579i q^{8} +O(q^{10})\)	\(q+1.18593i q^{2} +0.593579 q^{4} +2.83797 q^{5} +(2.46050 + 0.972582i) q^{7} +3.07579i q^{8} +3.36562i q^{10} +0.157816i q^{11} -3.94293i q^{13} +(-1.15341 + 2.91798i) q^{14} -2.46050 q^{16} -4.14487 q^{17} -6.33597i q^{19} +1.68456 q^{20} -0.187159 q^{22} -0.546125i q^{23} +3.05408 q^{25} +4.67602 q^{26} +(1.46050 + 0.577305i) q^{28} +4.65003i q^{29} +0.129426i q^{31} +3.23361i q^{32} -4.91551i q^{34} +(6.98284 + 2.76016i) q^{35} -2.46050 q^{37} +7.51399 q^{38} +8.72902i q^{40} -3.99138 q^{41} -6.56867 q^{43} +0.0936766i q^{44} +0.647664 q^{46} -8.66741 q^{47} +(5.10817 + 4.78609i) q^{49} +3.62192i q^{50} -2.34044i q^{52} -2.60234i q^{53} +0.447879i q^{55} +(-2.99146 + 7.56800i) q^{56} -5.51459 q^{58} +3.61372 q^{59} +3.36562i q^{61} -0.153489 q^{62} -8.75583 q^{64} -11.1899i q^{65} +1.32743 q^{67} -2.46031 q^{68} +(-3.27335 + 8.28114i) q^{70} -0.409310i q^{71} +15.0124i q^{73} -2.91798i q^{74} -3.76090i q^{76} +(-0.153489 + 0.388308i) q^{77} +4.32743 q^{79} -6.98284 q^{80} -4.73348i q^{82} +6.45169 q^{83} -11.7630 q^{85} -7.78996i q^{86} -0.485411 q^{88} -5.05368 q^{89} +(3.83482 - 9.70160i) q^{91} -0.324168i q^{92} -10.2789i q^{94} -17.9813i q^{95} +2.52247i q^{97} +(-5.67594 + 6.05791i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{4} + 4 q^{7}+O(q^{10}) \) 12 * q - 4 * q^4 + 4 * q^7	\( 12 q - 4 q^{4} + 4 q^{7} - 4 q^{16} + 20 q^{22} - 8 q^{28} - 4 q^{37} + 20 q^{43} - 40 q^{46} - 12 q^{49} - 4 q^{58} + 16 q^{64} - 24 q^{67} - 36 q^{70} + 12 q^{79} + 12 q^{85} - 68 q^{88} - 24 q^{91}+O(q^{100}) \) 12 * q - 4 * q^4 + 4 * q^7 - 4 * q^16 + 20 * q^22 - 8 * q^28 - 4 * q^37 + 20 * q^43 - 40 * q^46 - 12 * q^49 - 4 * q^58 + 16 * q^64 - 24 * q^67 - 36 * q^70 + 12 * q^79 + 12 * q^85 - 68 * q^88 - 24 * q^91

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