LMFDB - Embedded newform 1400.2.x.b.993.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1400,2,Mod(657,1400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1400, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 1, 2]))

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

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

chi := DirichletCharacter("1400.657");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1400 = 2^{3} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1400.x (of order $4$, degree $2$, 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:	$11.1790562830$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 280)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			993.7
Character	$\chi$	$=$	1400.993
Dual form			1400.2.x.b.657.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0703127 - 0.0703127i) q^{3} +(2.58523 - 0.562657i) q^{7} +2.99011i q^{9} +O(q^{10})$	$q+(0.0703127 - 0.0703127i) q^{3} +(2.58523 - 0.562657i) q^{7} +2.99011i q^{9} +0.777018 q^{11} +(3.93876 - 3.93876i) q^{13} +(-0.982018 - 0.982018i) q^{17} -1.14872 q^{19} +(0.142213 - 0.221337i) q^{21} +(1.46167 + 1.46167i) q^{23} +(0.421181 + 0.421181i) q^{27} +4.69033i q^{29} -6.45186i q^{31} +(0.0546342 - 0.0546342i) q^{33} +(1.30390 - 1.30390i) q^{37} -0.553890i q^{39} +9.81800i q^{41} +(7.13800 + 7.13800i) q^{43} +(-7.34914 - 7.34914i) q^{47} +(6.36683 - 2.90920i) q^{49} -0.138097 q^{51} +(2.08092 + 2.08092i) q^{53} +(-0.0807696 + 0.0807696i) q^{57} +8.29508 q^{59} -5.88837i q^{61} +(1.68241 + 7.73013i) q^{63} +(6.30957 - 6.30957i) q^{67} +0.205548 q^{69} +12.3373 q^{71} +(-7.23861 + 7.23861i) q^{73} +(2.00877 - 0.437195i) q^{77} +2.83831i q^{79} -8.91111 q^{81} +(10.4188 - 10.4188i) q^{83} +(0.329790 + 0.329790i) q^{87} +3.41911 q^{89} +(7.96643 - 12.3988i) q^{91} +(-0.453647 - 0.453647i) q^{93} +(-8.50258 - 8.50258i) q^{97} +2.32337i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{7}+O(q^{10}) $ 24 * q - 4 * q^7	$ 24 q - 4 q^{7} + 8 q^{11} + 16 q^{21} + 32 q^{23} + 8 q^{37} - 16 q^{43} - 24 q^{51} + 16 q^{53} - 20 q^{63} + 32 q^{67} - 32 q^{71} + 40 q^{77} - 72 q^{81} - 64 q^{91} - 72 q^{93}+O(q^{100}) $ 24 * q - 4 * q^7 + 8 * q^11 + 16 * q^21 + 32 * q^23 + 8 * q^37 - 16 * q^43 - 24 * q^51 + 16 * q^53 - 20 * q^63 + 32 * q^67 - 32 * q^71 + 40 * q^77 - 72 * q^81 - 64 * q^91 - 72 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1400\mathbb{Z}\right)^\times$.

$n$	$351$	$701$	$801$	$1177$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

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
$3$	0.0703127	−	0.0703127i	0.0405951	−	0.0405951i	−0.686518	−	0.727113i	$-0.740862\pi$
$3$	0.0703127	−	0.0703127i	0.0405951	−	0.0405951i	0.727113	+	0.686518i	$0.240862\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	2.58523	−	0.562657i	0.977125	−	0.212664i
$7$	2.58523	−	0.562657i	0.977125	−	0.212664i
$8$		0			0
$9$			2.99011i			0.996704i
$10$		0			0
$11$	0.777018			0.234280			0.117140	−	0.993115i	$-0.462627\pi$
$11$	0.777018			0.234280			0.117140	+	0.993115i	$0.462627\pi$
$12$		0			0
$13$	3.93876	−	3.93876i	1.09241	−	1.09241i	0.0971446	−	0.995270i	$-0.469029\pi$
$13$	3.93876	−	3.93876i	1.09241	−	1.09241i	0.995270	−	0.0971446i	$-0.0309709\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.982018	−	0.982018i	−0.238174	−	0.238174i	0.577920	−	0.816094i	$-0.303865\pi$
$17$	−0.982018	−	0.982018i	−0.238174	−	0.238174i	−0.816094	+	0.577920i	$0.803865\pi$
$18$		0			0
$19$	−1.14872			−0.263534			−0.131767	−	0.991281i	$-0.542065\pi$
$19$	−1.14872			−0.263534			−0.131767	+	0.991281i	$0.542065\pi$
$20$		0			0
$21$	0.142213	−	0.221337i	0.0310333	−	0.0482996i
$22$		0			0
$23$	1.46167	+	1.46167i	0.304780	+	0.304780i	0.842881	−	0.538101i	$-0.180858\pi$
$23$	1.46167	+	1.46167i	0.304780	+	0.304780i	−0.538101	+	0.842881i	$0.680858\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	0.421181	+	0.421181i	0.0810563	+	0.0810563i
$28$		0			0
$29$			4.69033i			0.870973i	0.900195	+	0.435486i	$0.143424\pi$
$29$			4.69033i			0.870973i	−0.900195	+	0.435486i	$0.856576\pi$
$30$		0			0
$31$		−	6.45186i		−	1.15879i	−0.815048	−	0.579394i	$-0.803289\pi$
$31$		−	6.45186i		−	1.15879i	0.815048	−	0.579394i	$-0.196711\pi$
$32$		0			0
$33$	0.0546342	−	0.0546342i	0.00951060	−	0.00951060i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	1.30390	−	1.30390i	0.214359	−	0.214359i	−0.591757	−	0.806116i	$-0.701565\pi$
$37$	1.30390	−	1.30390i	0.214359	−	0.214359i	0.806116	+	0.591757i	$0.201565\pi$
$38$		0			0
$39$		−	0.553890i		−	0.0886933i
$40$		0			0
$41$			9.81800i			1.53331i	0.642057	+	0.766657i	$0.278081\pi$
$41$			9.81800i			1.53331i	−0.642057	+	0.766657i	$0.721919\pi$
$42$		0			0
$43$	7.13800	+	7.13800i	1.08853	+	1.08853i	0.995680	+	0.0928552i	$0.0295994\pi$
$43$	7.13800	+	7.13800i	1.08853	+	1.08853i	0.0928552	+	0.995680i	$0.470401\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−7.34914	−	7.34914i	−1.07198	−	1.07198i	−0.997200	−	0.0747825i	$-0.976174\pi$
$47$	−7.34914	−	7.34914i	−1.07198	−	1.07198i	−0.0747825	−	0.997200i	$-0.523826\pi$
$48$		0			0
$49$	6.36683	−	2.90920i	0.909548	−	0.415600i
$50$		0			0
$51$	−0.138097			−0.0193374
$52$		0			0
$53$	2.08092	+	2.08092i	0.285836	+	0.285836i	0.835431	−	0.549595i	$-0.185218\pi$
$53$	2.08092	+	2.08092i	0.285836	+	0.285836i	−0.549595	+	0.835431i	$0.685218\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−0.0807696	+	0.0807696i	−0.0106982	+	0.0106982i
$58$		0			0
$59$	8.29508			1.07993			0.539964	−	0.841688i	$-0.318438\pi$
$59$	8.29508			1.07993			0.539964	+	0.841688i	$0.318438\pi$
$60$		0			0
$61$		−	5.88837i		−	0.753929i	−0.926228	−	0.376965i	$-0.876968\pi$
$61$		−	5.88837i		−	0.753929i	0.926228	−	0.376965i	$-0.123032\pi$
$62$		0			0
$63$	1.68241	+	7.73013i	0.211963	+	0.973905i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	6.30957	−	6.30957i	0.770837	−	0.770837i	−0.207416	−	0.978253i	$-0.566505\pi$
$67$	6.30957	−	6.30957i	0.770837	−	0.770837i	0.978253	+	0.207416i	$0.0665053\pi$
$68$		0			0
$69$	0.205548			0.0247451
$70$		0			0
$71$	12.3373			1.46417			0.732084	−	0.681214i	$-0.238548\pi$
$71$	12.3373			1.46417			0.732084	+	0.681214i	$0.238548\pi$
$72$		0			0
$73$	−7.23861	+	7.23861i	−0.847216	+	0.847216i	−0.989785	−	0.142569i	$-0.954464\pi$
$73$	−7.23861	+	7.23861i	−0.847216	+	0.847216i	0.142569	+	0.989785i	$0.454464\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	2.00877	−	0.437195i	0.228921	−	0.0498229i
$78$		0			0
$79$			2.83831i			0.319335i	0.987171	+	0.159668i	$0.0510423\pi$
$79$			2.83831i			0.319335i	−0.987171	+	0.159668i	$0.948958\pi$
$80$		0			0
$81$	−8.91111			−0.990123
$82$		0			0
$83$	10.4188	−	10.4188i	1.14361	−	1.14361i	0.155823	−	0.987785i	$-0.450197\pi$
$83$	10.4188	−	10.4188i	1.14361	−	1.14361i	0.987785	−	0.155823i	$-0.0498029\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	0.329790	+	0.329790i	0.0353572	+	0.0353572i
$88$		0			0
$89$	3.41911			0.362425			0.181213	−	0.983444i	$-0.441998\pi$
$89$	3.41911			0.362425			0.181213	+	0.983444i	$0.441998\pi$
$90$		0			0
$91$	7.96643	−	12.3988i	0.835108	−	1.29974i
$92$		0			0
$93$	−0.453647	−	0.453647i	−0.0470411	−	0.0470411i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−8.50258	−	8.50258i	−0.863306	−	0.863306i	0.128414	−	0.991721i	$-0.459011\pi$
$97$	−8.50258	−	8.50258i	−0.863306	−	0.863306i	−0.991721	+	0.128414i	$0.959011\pi$
$98$		0			0
$99$			2.32337i			0.233507i
$100$		0			0
$101$		−	4.88126i		−	0.485703i	−0.970063	−	0.242852i	$-0.921917\pi$
$101$		−	4.88126i		−	0.485703i	0.970063	−	0.242852i	$-0.0780828\pi$
$102$		0			0
$103$	10.0443	−	10.0443i	0.989697	−	0.989697i	−0.0102503	−	0.999947i	$-0.503263\pi$
$103$	10.0443	−	10.0443i	0.989697	−	0.989697i	0.999947	+	0.0102503i	$0.00326282\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−5.67065	+	5.67065i	−0.548203	+	0.548203i	−0.925921	−	0.377718i	$-0.876709\pi$
$107$	−5.67065	+	5.67065i	−0.548203	+	0.548203i	0.377718	+	0.925921i	$0.376709\pi$
$108$		0			0
$109$			11.9012i			1.13993i	0.821669	+	0.569965i	$0.193043\pi$
$109$			11.9012i			1.13993i	−0.821669	+	0.569965i	$0.806957\pi$
$110$		0			0
$111$		−	0.183361i		−	0.0174039i
$112$		0			0
$113$	1.36519	+	1.36519i	0.128427	+	0.128427i	0.768398	−	0.639972i	$-0.221054\pi$
$113$	1.36519	+	1.36519i	0.128427	+	0.128427i	−0.639972	+	0.768398i	$0.721054\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	11.7773	+	11.7773i	1.08881	+	1.08881i
$118$		0			0
$119$	−3.09128	−	1.98620i	−0.283377	−	0.182075i
$120$		0			0
$121$	−10.3962			−0.945113
$122$		0			0
$123$	0.690330	+	0.690330i	0.0622450	+	0.0622450i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	9.49331	−	9.49331i	0.842395	−	0.842395i	−0.146775	−	0.989170i	$-0.546889\pi$
$127$	9.49331	−	9.49331i	0.842395	−	0.842395i	0.989170	+	0.146775i	$0.0468894\pi$
$128$		0			0
$129$	1.00378			0.0883783
$130$		0			0
$131$			19.4938i			1.70318i	0.524206	+	0.851592i	$0.324362\pi$
$131$			19.4938i			1.70318i	−0.524206	+	0.851592i	$0.675638\pi$
$132$		0			0
$133$	−2.96971	+	0.646335i	−0.257506	+	0.0560444i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−5.77702	+	5.77702i	−0.493564	+	0.493564i	−0.909427	−	0.415863i	$-0.863479\pi$
$137$	−5.77702	+	5.77702i	−0.493564	+	0.493564i	0.415863	+	0.909427i	$0.363479\pi$
$138$		0			0
$139$	−15.2115			−1.29023			−0.645113	−	0.764087i	$-0.723190\pi$
$139$	−15.2115			−1.29023			−0.645113	+	0.764087i	$0.723190\pi$
$140$		0			0
$141$	−1.03348			−0.0870344
$142$		0			0
$143$	3.06048	−	3.06048i	0.255931	−	0.255931i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	0.243116	−	0.652223i	0.0200519	−	0.0537944i
$148$		0			0
$149$			16.5328i			1.35442i	0.735789	+	0.677211i	$0.236812\pi$
$149$			16.5328i			1.35442i	−0.735789	+	0.677211i	$0.763188\pi$
$150$		0			0
$151$	12.4421			1.01252			0.506262	−	0.862380i	$-0.331027\pi$
$151$	12.4421			1.01252			0.506262	+	0.862380i	$0.331027\pi$
$152$		0			0
$153$	2.93634	−	2.93634i	0.237389	−	0.237389i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	6.24218	+	6.24218i	0.498180	+	0.498180i	0.910871	−	0.412691i	$-0.135411\pi$
$157$	6.24218	+	6.24218i	0.498180	+	0.498180i	−0.412691	+	0.910871i	$0.635411\pi$
$158$		0			0
$159$	0.292630			0.0232070
$160$		0			0
$161$	4.60118	+	2.95634i	0.362624	+	0.232992i
$162$		0			0
$163$	−9.47383	−	9.47383i	−0.742048	−	0.742048i	0.230924	−	0.972972i	$-0.425825\pi$
$163$	−9.47383	−	9.47383i	−0.742048	−	0.742048i	−0.972972	+	0.230924i	$0.925825\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	0.725303	+	0.725303i	0.0561257	+	0.0561257i	0.734613	−	0.678487i	$-0.237364\pi$
$167$	0.725303	+	0.725303i	0.0561257	+	0.0561257i	−0.678487	+	0.734613i	$0.737364\pi$
$168$		0			0
$169$		−	18.0276i		−	1.38674i
$170$		0			0
$171$		−	3.43480i		−	0.262666i
$172$		0			0
$173$	−3.12344	+	3.12344i	−0.237471	+	0.237471i	−0.815802	−	0.578331i	$-0.803704\pi$
$173$	−3.12344	+	3.12344i	−0.237471	+	0.237471i	0.578331	+	0.815802i	$0.303704\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	0.583250	−	0.583250i	0.0438397	−	0.0438397i
$178$		0			0
$179$		−	9.18800i		−	0.686743i	−0.939200	−	0.343372i	$-0.888431\pi$
$179$		−	9.18800i		−	0.686743i	0.939200	−	0.343372i	$-0.111569\pi$
$180$		0			0
$181$			9.51164i			0.706995i	0.935435	+	0.353497i	$0.115008\pi$
$181$			9.51164i			0.706995i	−0.935435	+	0.353497i	$0.884992\pi$
$182$		0			0
$183$	−0.414028	−	0.414028i	−0.0306058	−	0.0306058i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−0.763045	−	0.763045i	−0.0557994	−	0.0557994i
$188$		0			0
$189$	1.32583	+	0.851870i	0.0964400	+	0.0619644i
$190$		0			0
$191$	−21.2171			−1.53522			−0.767609	−	0.640918i	$-0.778554\pi$
$191$	−21.2171			−1.53522			−0.767609	+	0.640918i	$0.778554\pi$
$192$		0			0
$193$	−5.15371	−	5.15371i	−0.370972	−	0.370972i	0.496859	−	0.867831i	$-0.334487\pi$
$193$	−5.15371	−	5.15371i	−0.370972	−	0.370972i	−0.867831	+	0.496859i	$0.834487\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−3.83269	+	3.83269i	−0.273068	+	0.273068i	−0.830334	−	0.557266i	$-0.811850\pi$
$197$	−3.83269	+	3.83269i	−0.273068	+	0.273068i	0.557266	+	0.830334i	$0.311850\pi$
$198$		0			0
$199$	−13.4648			−0.954496			−0.477248	−	0.878769i	$-0.658366\pi$
$199$	−13.4648			−0.954496			−0.477248	+	0.878769i	$0.658366\pi$
$200$		0			0
$201$		−	0.887286i		−	0.0625844i
$202$		0			0
$203$	2.63905	+	12.1256i	0.185225	+	0.851049i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−4.37057	+	4.37057i	−0.303775	+	0.303775i
$208$		0			0
$209$	−0.892576			−0.0617408
$210$		0			0
$211$	8.11050			0.558350			0.279175	−	0.960240i	$-0.409939\pi$
$211$	8.11050			0.558350			0.279175	+	0.960240i	$0.409939\pi$
$212$		0			0
$213$	0.867469	−	0.867469i	0.0594380	−	0.0594380i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−3.63018	−	16.6795i	−0.246433	−	1.13228i
$218$		0			0
$219$			1.01793i			0.0687855i
$220$		0			0
$221$	−7.73586			−0.520370
$222$		0			0
$223$	−18.5407	+	18.5407i	−1.24157	+	1.24157i	−0.282226	+	0.959348i	$0.591073\pi$
$223$	−18.5407	+	18.5407i	−1.24157	+	1.24157i	−0.959348	+	0.282226i	$0.908927\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−4.84230	−	4.84230i	−0.321395	−	0.321395i	0.527907	−	0.849302i	$-0.322977\pi$
$227$	−4.84230	−	4.84230i	−0.321395	−	0.321395i	−0.849302	+	0.527907i	$0.822977\pi$
$228$		0			0
$229$	−4.14288			−0.273769			−0.136884	−	0.990587i	$-0.543709\pi$
$229$	−4.14288			−0.273769			−0.136884	+	0.990587i	$0.543709\pi$
$230$		0			0
$231$	0.110502	−	0.171982i	0.00727048	−	0.0113156i
$232$		0			0
$233$	−17.7734	−	17.7734i	−1.16437	−	1.16437i	−0.983508	−	0.180864i	$-0.942110\pi$
$233$	−17.7734	−	17.7734i	−1.16437	−	1.16437i	−0.180864	−	0.983508i	$-0.557890\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	0.199570	+	0.199570i	0.0129634	+	0.0129634i
$238$		0			0
$239$		−	24.8714i		−	1.60880i	−0.594090	−	0.804399i	$-0.702488\pi$
$239$		−	24.8714i		−	1.60880i	0.594090	−	0.804399i	$-0.297512\pi$
$240$		0			0
$241$			5.11385i			0.329412i	0.986343	+	0.164706i	$0.0526676\pi$
$241$			5.11385i			0.329412i	−0.986343	+	0.164706i	$0.947332\pi$
$242$		0			0
$243$	−1.89011	+	1.89011i	−0.121250	+	0.121250i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−4.52453	+	4.52453i	−0.287889	+	0.287889i
$248$		0			0
$249$		−	1.46514i		−	0.0928497i
$250$		0			0
$251$		−	21.4745i		−	1.35546i	−0.735311	−	0.677729i	$-0.762964\pi$
$251$		−	21.4745i		−	1.35546i	0.735311	−	0.677729i	$-0.237036\pi$
$252$		0			0
$253$	1.13575	+	1.13575i	0.0714037	+	0.0714037i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	2.08456	+	2.08456i	0.130031	+	0.130031i	0.769127	−	0.639096i	$-0.220691\pi$
$257$	2.08456	+	2.08456i	0.130031	+	0.130031i	−0.639096	+	0.769127i	$0.720691\pi$
$258$		0			0
$259$	2.63723	−	4.10452i	0.163869	−	0.255043i
$260$		0			0
$261$	−14.0246			−0.868102
$262$		0			0
$263$	−6.37087	−	6.37087i	−0.392845	−	0.392845i	0.482855	−	0.875700i	$-0.339600\pi$
$263$	−6.37087	−	6.37087i	−0.392845	−	0.392845i	−0.875700	+	0.482855i	$0.839600\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	0.240407	−	0.240407i	0.0147127	−	0.0147127i
$268$		0			0
$269$	9.57242			0.583641			0.291820	−	0.956473i	$-0.405739\pi$
$269$	9.57242			0.583641			0.291820	+	0.956473i	$0.405739\pi$
$270$		0			0
$271$		−	12.1076i		−	0.735486i	−0.929927	−	0.367743i	$-0.880131\pi$
$271$		−	12.1076i		−	0.735486i	0.929927	−	0.367743i	$-0.119869\pi$
$272$		0			0
$273$	−0.311650	−	1.43193i	−0.0188619	−	0.0866645i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−16.2663	+	16.2663i	−0.977345	+	0.977345i	−0.999749	−	0.0224036i	$-0.992868\pi$
$277$	−16.2663	+	16.2663i	−0.977345	+	0.977345i	0.0224036	+	0.999749i	$0.492868\pi$
$278$		0			0
$279$	19.2918			1.15497
$280$		0			0
$281$	−0.910882			−0.0543387			−0.0271693	−	0.999631i	$-0.508649\pi$
$281$	−0.910882			−0.0543387			−0.0271693	+	0.999631i	$0.508649\pi$
$282$		0			0
$283$	−12.5625	+	12.5625i	−0.746766	+	0.746766i	−0.973870	−	0.227105i	$-0.927074\pi$
$283$	−12.5625	+	12.5625i	−0.746766	+	0.746766i	0.227105	+	0.973870i	$0.427074\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	5.52417	+	25.3818i	0.326081	+	1.49824i
$288$		0			0
$289$		−	15.0713i		−	0.886546i
$290$		0			0
$291$	−1.19568			−0.0700920
$292$		0			0
$293$	−6.48178	+	6.48178i	−0.378670	+	0.378670i	−0.870622	−	0.491952i	$-0.836283\pi$
$293$	−6.48178	+	6.48178i	−0.378670	+	0.378670i	0.491952	+	0.870622i	$0.336283\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	0.327265	+	0.327265i	0.0189899	+	0.0189899i
$298$		0			0
$299$	11.5144			0.665892
$300$		0			0
$301$	22.4696	+	14.4371i	1.29513	+	0.832142i
$302$		0			0
$303$	−0.343215	−	0.343215i	−0.0197172	−	0.0197172i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	8.48970	+	8.48970i	0.484533	+	0.484533i	0.906576	−	0.422043i	$-0.138687\pi$
$307$	8.48970	+	8.48970i	0.484533	+	0.484533i	−0.422043	+	0.906576i	$0.638687\pi$
$308$		0			0
$309$		−	1.41249i		−	0.0803537i
$310$		0			0
$311$			25.9749i			1.47290i	0.676490	+	0.736452i	$0.263500\pi$
$311$			25.9749i			1.47290i	−0.676490	+	0.736452i	$0.736500\pi$
$312$		0			0
$313$	−12.3142	+	12.3142i	−0.696037	+	0.696037i	−0.963553	−	0.267516i	$-0.913797\pi$
$313$	−12.3142	+	12.3142i	−0.696037	+	0.696037i	0.267516	+	0.963553i	$0.413797\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−14.4909	+	14.4909i	−0.813888	+	0.813888i	−0.985214	−	0.171327i	$-0.945195\pi$
$317$	−14.4909	+	14.4909i	−0.813888	+	0.813888i	0.171327	+	0.985214i	$0.445195\pi$
$318$		0			0
$319$			3.64447i			0.204051i
$320$		0			0
$321$			0.797438i			0.0445086i
$322$		0			0
$323$	1.12806	+	1.12806i	0.0627671	+	0.0627671i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	0.836807	+	0.836807i	0.0462755	+	0.0462755i
$328$		0			0
$329$	−23.1343	−	14.8642i	−1.27543	−	0.819489i
$330$		0			0
$331$	−27.4165			−1.50695			−0.753474	−	0.657477i	$-0.771624\pi$
$331$	−27.4165			−1.50695			−0.753474	+	0.657477i	$0.771624\pi$
$332$		0			0
$333$	3.89880	+	3.89880i	0.213653	+	0.213653i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	11.1698	−	11.1698i	0.608460	−	0.608460i	−0.334084	−	0.942543i	$-0.608427\pi$
$337$	11.1698	−	11.1698i	0.608460	−	0.608460i	0.942543	+	0.334084i	$0.108427\pi$
$338$		0			0
$339$	0.191981			0.0104270
$340$		0			0
$341$		−	5.01321i		−	0.271480i
$342$		0			0
$343$	14.8229	−	11.1033i	0.800359	−	0.599521i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	11.4376	−	11.4376i	0.614004	−	0.614004i	−0.329983	−	0.943987i	$-0.607043\pi$
$347$	11.4376	−	11.4376i	0.614004	−	0.614004i	0.943987	+	0.329983i	$0.107043\pi$
$348$		0			0
$349$	17.1401			0.917487			0.458744	−	0.888569i	$-0.348300\pi$
$349$	17.1401			0.917487			0.458744	+	0.888569i	$0.348300\pi$
$350$		0			0
$351$	3.31786			0.177094
$352$		0			0
$353$	11.1570	−	11.1570i	0.593826	−	0.593826i	−0.344837	−	0.938663i	$-0.612066\pi$
$353$	11.1570	−	11.1570i	0.593826	−	0.593826i	0.938663	+	0.344837i	$0.112066\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−0.357012	+	0.0777011i	−0.0188951	+	0.00411238i
$358$		0			0
$359$			20.9982i			1.10824i	0.832437	+	0.554120i	$0.186945\pi$
$359$			20.9982i			1.10824i	−0.832437	+	0.554120i	$0.813055\pi$
$360$		0			0
$361$	−17.6804			−0.930550
$362$		0			0
$363$	−0.730988	+	0.730988i	−0.0383669	+	0.0383669i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−2.32101	−	2.32101i	−0.121156	−	0.121156i	0.643929	−	0.765085i	$-0.277303\pi$
$367$	−2.32101	−	2.32101i	−0.121156	−	0.121156i	−0.765085	+	0.643929i	$0.777303\pi$
$368$		0			0
$369$	−29.3569			−1.52826
$370$		0			0
$371$	6.55049	+	4.20880i	0.340084	+	0.218510i
$372$		0			0
$373$	−25.8674	−	25.8674i	−1.33937	−	1.33937i	−0.896674	−	0.442691i	$-0.854024\pi$
$373$	−25.8674	−	25.8674i	−1.33937	−	1.33937i	−0.442691	−	0.896674i	$-0.645976\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	18.4741	+	18.4741i	0.951463	+	0.951463i
$378$		0			0
$379$		−	13.1682i		−	0.676406i	−0.941073	−	0.338203i	$-0.890181\pi$
$379$		−	13.1682i		−	0.676406i	0.941073	−	0.338203i	$-0.109819\pi$
$380$		0			0
$381$		−	1.33500i		−	0.0683942i
$382$		0			0
$383$	−13.7289	+	13.7289i	−0.701514	+	0.701514i	−0.964736	−	0.263221i	$-0.915215\pi$
$383$	−13.7289	+	13.7289i	−0.701514	+	0.701514i	0.263221	+	0.964736i	$0.415215\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−21.3434	+	21.3434i	−1.08495	+	1.08495i
$388$		0			0
$389$			13.4553i			0.682209i	0.940025	+	0.341104i	$0.110801\pi$
$389$			13.4553i			0.682209i	−0.940025	+	0.341104i	$0.889199\pi$
$390$		0			0
$391$		−	2.87078i		−	0.145181i
$392$		0			0
$393$	1.37066	+	1.37066i	0.0691408	+	0.0691408i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−9.78221	−	9.78221i	−0.490955	−	0.490955i	0.417652	−	0.908607i	$-0.362853\pi$
$397$	−9.78221	−	9.78221i	−0.490955	−	0.490955i	−0.908607	+	0.417652i	$0.862853\pi$
$398$		0			0
$399$	−0.163362	+	0.254254i	−0.00817835	+	0.0127286i
$400$		0			0
$401$	−10.6960			−0.534134			−0.267067	−	0.963678i	$-0.586055\pi$
$401$	−10.6960			−0.534134			−0.267067	+	0.963678i	$0.586055\pi$
$402$		0			0
$403$	−25.4123	−	25.4123i	−1.26588	−	1.26588i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	1.01315	−	1.01315i	0.0502201	−	0.0502201i
$408$		0			0
$409$	−30.2026			−1.49342			−0.746712	−	0.665148i	$-0.768369\pi$
$409$	−30.2026			−1.49342			−0.746712	+	0.665148i	$0.768369\pi$
$410$		0			0
$411$			0.812396i			0.0400725i
$412$		0			0
$413$	21.4447	−	4.66729i	1.05522	−	0.229662i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−1.06957	+	1.06957i	−0.0523768	+	0.0523768i
$418$		0			0
$419$	−29.8749			−1.45948			−0.729742	−	0.683722i	$-0.760360\pi$
$419$	−29.8749			−1.45948			−0.729742	+	0.683722i	$0.760360\pi$
$420$		0			0
$421$	35.1836			1.71474			0.857372	−	0.514697i	$-0.172096\pi$
$421$	35.1836			1.71474			0.857372	+	0.514697i	$0.172096\pi$
$422$		0			0
$423$	21.9748	−	21.9748i	1.06845	−	1.06845i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−3.31314	−	15.2228i	−0.160334	−	0.736683i
$428$		0			0
$429$		−	0.430382i		−	0.0207790i
$430$		0			0
$431$	−20.9552			−1.00937			−0.504687	−	0.863302i	$-0.668392\pi$
$431$	−20.9552			−1.00937			−0.504687	+	0.863302i	$0.668392\pi$
$432$		0			0
$433$	−12.5824	+	12.5824i	−0.604670	+	0.604670i	−0.941548	−	0.336878i	$-0.890629\pi$
$433$	−12.5824	+	12.5824i	−0.604670	+	0.604670i	0.336878	+	0.941548i	$0.390629\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−1.67905	−	1.67905i	−0.0803200	−	0.0803200i
$438$		0			0
$439$	−7.23208			−0.345168			−0.172584	−	0.984995i	$-0.555212\pi$
$439$	−7.23208			−0.345168			−0.172584	+	0.984995i	$0.555212\pi$
$440$		0			0
$441$	8.69882	+	19.0375i	0.414230	+	0.906550i
$442$		0			0
$443$	−3.46509	−	3.46509i	−0.164632	−	0.164632i	0.619983	−	0.784615i	$-0.287139\pi$
$443$	−3.46509	−	3.46509i	−0.164632	−	0.164632i	−0.784615	+	0.619983i	$0.787139\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	1.16247	+	1.16247i	0.0549829	+	0.0549829i
$448$		0			0
$449$			6.08724i			0.287274i	0.989630	+	0.143637i	$0.0458798\pi$
$449$			6.08724i			0.287274i	−0.989630	+	0.143637i	$0.954120\pi$
$450$		0			0
$451$			7.62876i			0.359224i
$452$		0			0
$453$	0.874838	−	0.874838i	0.0411035	−	0.0411035i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	19.2746	−	19.2746i	0.901630	−	0.901630i	−0.0939472	−	0.995577i	$-0.529948\pi$
$457$	19.2746	−	19.2746i	0.901630	−	0.901630i	0.995577	+	0.0939472i	$0.0299485\pi$
$458$		0			0
$459$		−	0.827214i		−	0.0386111i
$460$		0			0
$461$		−	30.3964i		−	1.41570i	−0.706363	−	0.707850i	$-0.749665\pi$
$461$		−	30.3964i		−	1.41570i	0.706363	−	0.707850i	$-0.250335\pi$
$462$		0			0
$463$	−12.0768	−	12.0768i	−0.561259	−	0.561259i	0.368406	−	0.929665i	$-0.379904\pi$
$463$	−12.0768	−	12.0768i	−0.561259	−	0.561259i	−0.929665	+	0.368406i	$0.879904\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−4.89096	−	4.89096i	−0.226327	−	0.226327i	0.584830	−	0.811156i	$-0.301161\pi$
$467$	−4.89096	−	4.89096i	−0.226327	−	0.226327i	−0.811156	+	0.584830i	$0.801161\pi$
$468$		0			0
$469$	12.7616	−	19.8618i	0.589275	−	0.917134i
$470$		0			0
$471$	0.877809			0.0404473
$472$		0			0
$473$	5.54635	+	5.54635i	0.255022	+	0.255022i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−6.22217	+	6.22217i	−0.284894	+	0.284894i
$478$		0			0
$479$	−22.8349			−1.04335			−0.521676	−	0.853144i	$-0.674693\pi$
$479$	−22.8349			−1.04335			−0.521676	+	0.853144i	$0.674693\pi$
$480$		0			0
$481$		−	10.2715i		−	0.468339i
$482$		0			0
$483$	0.531390	−	0.115653i	0.0241791	−	0.00526241i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	11.1182	−	11.1182i	0.503812	−	0.503812i	−0.408808	−	0.912620i	$-0.634056\pi$
$487$	11.1182	−	11.1182i	0.503812	−	0.503812i	0.912620	+	0.408808i	$0.134056\pi$
$488$		0			0
$489$	−1.33226			−0.0602470
$490$		0			0
$491$	4.45336			0.200977			0.100489	−	0.994938i	$-0.467959\pi$
$491$	4.45336			0.200977			0.100489	+	0.994938i	$0.467959\pi$
$492$		0			0
$493$	4.60599	−	4.60599i	0.207443	−	0.207443i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	31.8948	−	6.94167i	1.43068	−	0.311376i
$498$		0			0
$499$			27.6446i			1.23754i	0.785572	+	0.618770i	$0.212369\pi$
$499$			27.6446i			1.23754i	−0.785572	+	0.618770i	$0.787631\pi$
$500$		0			0
$501$	0.101996			0.00455685
$502$		0			0
$503$	−16.9763	+	16.9763i	−0.756936	+	0.756936i	−0.975764	−	0.218828i	$-0.929777\pi$
$503$	−16.9763	+	16.9763i	−0.756936	+	0.756936i	0.218828	+	0.975764i	$0.429777\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−1.26757	−	1.26757i	−0.0562948	−	0.0562948i
$508$		0			0
$509$	32.3762			1.43505			0.717525	−	0.696533i	$-0.245275\pi$
$509$	32.3762			1.43505			0.717525	+	0.696533i	$0.245275\pi$
$510$		0			0
$511$	−14.6406	+	22.7863i	−0.647663	+	1.00801i
$512$		0			0
$513$	−0.483819	−	0.483819i	−0.0213611	−	0.0213611i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−5.71041	−	5.71041i	−0.251144	−	0.251144i
$518$		0			0
$519$			0.439236i			0.0192803i
$520$		0			0
$521$		−	4.38603i		−	0.192156i	−0.995374	−	0.0960778i	$-0.969370\pi$
$521$		−	4.38603i		−	0.192156i	0.995374	−	0.0960778i	$-0.0306297\pi$
$522$		0			0
$523$	4.73788	−	4.73788i	0.207173	−	0.207173i	−0.595892	−	0.803065i	$-0.703201\pi$
$523$	4.73788	−	4.73788i	0.207173	−	0.207173i	0.803065	+	0.595892i	$0.203201\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−6.33583	+	6.33583i	−0.275993	+	0.275993i
$528$		0			0
$529$		−	18.7270i		−	0.814218i
$530$		0			0
$531$			24.8032i			1.07637i
$532$		0			0
$533$	38.6707	+	38.6707i	1.67502	+	1.67502i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−0.646033	−	0.646033i	−0.0278784	−	0.0278784i
$538$		0			0
$539$	4.94714	−	2.26050i	0.213089	−	0.0973665i
$540$		0			0
$541$	7.48796			0.321933			0.160966	−	0.986960i	$-0.448539\pi$
$541$	7.48796			0.321933			0.160966	+	0.986960i	$0.448539\pi$
$542$		0			0
$543$	0.668790	+	0.668790i	0.0287005	+	0.0287005i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−1.12562	+	1.12562i	−0.0481278	+	0.0481278i	−0.730761	−	0.682633i	$-0.760835\pi$
$547$	−1.12562	+	1.12562i	−0.0481278	+	0.0481278i	0.682633	+	0.730761i	$0.260835\pi$
$548$		0			0
$549$	17.6069			0.751444
$550$		0			0
$551$		−	5.38788i		−	0.229531i
$552$		0			0
$553$	1.59700	+	7.33770i	0.0679113	+	0.312031i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−20.9130	+	20.9130i	−0.886113	+	0.886113i	−0.994147	−	0.108034i	$-0.965544\pi$
$557$	−20.9130	+	20.9130i	−0.886113	+	0.886113i	0.108034	+	0.994147i	$0.465544\pi$
$558$		0			0
$559$	56.2297			2.37826
$560$		0			0
$561$	−0.107304			−0.00453036
$562$		0			0
$563$	−5.94306	+	5.94306i	−0.250470	+	0.250470i	−0.821163	−	0.570693i	$-0.806675\pi$
$563$	−5.94306	+	5.94306i	−0.250470	+	0.250470i	0.570693	+	0.821163i	$0.306675\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−23.0373	+	5.01390i	−0.967474	+	0.210564i
$568$		0			0
$569$			6.64150i			0.278426i	0.990262	+	0.139213i	$0.0444573\pi$
$569$			6.64150i			0.278426i	−0.990262	+	0.139213i	$0.955543\pi$
$570$		0			0
$571$	33.4643			1.40044			0.700218	−	0.713929i	$-0.253086\pi$
$571$	33.4643			1.40044			0.700218	+	0.713929i	$0.253086\pi$
$572$		0			0
$573$	−1.49183	+	1.49183i	−0.0623223	+	0.0623223i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−7.86048	−	7.86048i	−0.327236	−	0.327236i	0.524299	−	0.851535i	$-0.324328\pi$
$577$	−7.86048	−	7.86048i	−0.327236	−	0.327236i	−0.851535	+	0.524299i	$0.824328\pi$
$578$		0			0
$579$	−0.724743			−0.0301193
$580$		0			0
$581$	21.0727	−	32.7971i	0.874244	−	1.36065i
$582$		0			0
$583$	1.61691	+	1.61691i	0.0669655	+	0.0669655i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	7.65881	+	7.65881i	0.316113	+	0.316113i	0.847272	−	0.531159i	$-0.178243\pi$
$587$	7.65881	+	7.65881i	0.316113	+	0.316113i	−0.531159	+	0.847272i	$0.678243\pi$
$588$		0			0
$589$			7.41137i			0.305380i
$590$		0			0
$591$			0.538974i			0.0221704i
$592$		0			0
$593$	8.24682	−	8.24682i	0.338656	−	0.338656i	−0.517205	−	0.855861i	$-0.673028\pi$
$593$	8.24682	−	8.24682i	0.338656	−	0.338656i	0.855861	+	0.517205i	$0.173028\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−0.946748	+	0.946748i	−0.0387478	+	0.0387478i
$598$		0			0
$599$		−	1.72554i		−	0.0705038i	−0.999378	−	0.0352519i	$-0.988777\pi$
$599$		−	1.72554i		−	0.0705038i	0.999378	−	0.0352519i	$-0.0112233\pi$
$600$		0			0
$601$		−	39.3868i		−	1.60662i	−0.595561	−	0.803310i	$-0.703070\pi$
$601$		−	39.3868i		−	1.60662i	0.595561	−	0.803310i	$-0.296930\pi$
$602$		0			0
$603$	18.8663	+	18.8663i	0.768296	+	0.768296i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	13.0555	+	13.0555i	0.529905	+	0.529905i	0.920544	−	0.390639i	$-0.127746\pi$
$607$	13.0555	+	13.0555i	0.529905	+	0.529905i	−0.390639	+	0.920544i	$0.627746\pi$
$608$		0			0
$609$	1.03814	+	0.667024i	0.0420676	+	0.0270292i
$610$		0			0
$611$	−57.8930			−2.34210
$612$		0			0
$613$	19.5565	+	19.5565i	0.789878	+	0.789878i	0.981474	−	0.191596i	$-0.0613664\pi$
$613$	19.5565	+	19.5565i	0.789878	+	0.789878i	−0.191596	+	0.981474i	$0.561366\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	4.82431	−	4.82431i	0.194219	−	0.194219i	−0.603297	−	0.797517i	$-0.706147\pi$
$617$	4.82431	−	4.82431i	0.194219	−	0.194219i	0.797517	+	0.603297i	$0.206147\pi$
$618$		0			0
$619$	35.5806			1.43011			0.715053	−	0.699070i	$-0.246402\pi$
$619$	35.5806			1.43011			0.715053	+	0.699070i	$0.246402\pi$
$620$		0			0
$621$			1.23126i			0.0494087i
$622$		0			0
$623$	8.83919	−	1.92379i	0.354135	−	0.0770749i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−0.0627594	+	0.0627594i	−0.00250637	+	0.00250637i
$628$		0			0
$629$	−2.56090			−0.102110
$630$		0			0
$631$	28.6285			1.13968			0.569841	−	0.821755i	$-0.307005\pi$
$631$	28.6285			1.13968			0.569841	+	0.821755i	$0.307005\pi$
$632$		0			0
$633$	0.570271	−	0.570271i	0.0226663	−	0.0226663i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	13.6188	−	36.5360i	0.539596	−	1.44761i
$638$		0			0
$639$			36.8899i			1.45934i
$640$		0			0
$641$	−20.9369			−0.826956			−0.413478	−	0.910514i	$-0.635686\pi$
$641$	−20.9369			−0.826956			−0.413478	+	0.910514i	$0.635686\pi$
$642$		0			0
$643$	13.5706	−	13.5706i	0.535174	−	0.535174i	−0.386934	−	0.922108i	$-0.626466\pi$
$643$	13.5706	−	13.5706i	0.535174	−	0.535174i	0.922108	+	0.386934i	$0.126466\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	12.1526	+	12.1526i	0.477768	+	0.477768i	0.904417	−	0.426649i	$-0.140306\pi$
$647$	12.1526	+	12.1526i	0.477768	+	0.477768i	−0.426649	+	0.904417i	$0.640306\pi$
$648$		0			0
$649$	6.44543			0.253005
$650$		0			0
$651$	−1.42803	−	0.917535i	−0.0559690	−	0.0359610i
$652$		0			0
$653$	16.3014	+	16.3014i	0.637921	+	0.637921i	0.950042	−	0.312121i	$-0.101039\pi$
$653$	16.3014	+	16.3014i	0.637921	+	0.637921i	−0.312121	+	0.950042i	$0.601039\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−21.6443	−	21.6443i	−0.844423	−	0.844423i
$658$		0			0
$659$			24.5415i			0.956001i	0.878360	+	0.478000i	$0.158638\pi$
$659$			24.5415i			0.956001i	−0.878360	+	0.478000i	$0.841362\pi$
$660$		0			0
$661$			22.1516i			0.861596i	0.902448	+	0.430798i	$0.141768\pi$
$661$			22.1516i			0.861596i	−0.902448	+	0.430798i	$0.858232\pi$
$662$		0			0
$663$	−0.543929	+	0.543929i	−0.0211245	+	0.0211245i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−6.85573	+	6.85573i	−0.265455	+	0.265455i
$668$		0			0
$669$			2.60729i			0.100804i
$670$		0			0
$671$		−	4.57537i		−	0.176630i
$672$		0			0
$673$	9.43387	+	9.43387i	0.363649	+	0.363649i	0.865154	−	0.501505i	$-0.167220\pi$
$673$	9.43387	+	9.43387i	0.363649	+	0.363649i	−0.501505	+	0.865154i	$0.667220\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−10.4956	−	10.4956i	−0.403378	−	0.403378i	0.476044	−	0.879422i	$-0.342070\pi$
$677$	−10.4956	−	10.4956i	−0.403378	−	0.403378i	−0.879422	+	0.476044i	$0.842070\pi$
$678$		0			0
$679$	−26.7652	−	17.1971i	−1.02715	−	0.659964i
$680$		0			0
$681$	−0.680951			−0.0260941
$682$		0			0
$683$	−7.11456	−	7.11456i	−0.272231	−	0.272231i	0.557767	−	0.829998i	$-0.311658\pi$
$683$	−7.11456	−	7.11456i	−0.272231	−	0.272231i	−0.829998	+	0.557767i	$0.811658\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−0.291297	+	0.291297i	−0.0111137	+	0.0111137i
$688$		0			0
$689$	16.3924			0.624502
$690$		0			0
$691$		−	6.29829i		−	0.239598i	−0.992798	−	0.119799i	$-0.961775\pi$
$691$		−	6.29829i		−	0.239598i	0.992798	−	0.119799i	$-0.0382251\pi$
$692$		0			0
$693$	1.30726	+	6.00645i	0.0496587	+	0.228166i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	9.64145	−	9.64145i	0.365196	−	0.365196i
$698$		0			0
$699$	−2.49939			−0.0945356
$700$		0			0
$701$	30.1579			1.13905			0.569523	−	0.821975i	$-0.307128\pi$
$701$	30.1579			1.13905			0.569523	+	0.821975i	$0.307128\pi$
$702$		0			0
$703$	−1.49781	+	1.49781i	−0.0564911	+	0.0564911i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−2.74648	−	12.6192i	−0.103292	−	0.474593i
$708$		0			0
$709$			1.75232i			0.0658099i	0.999458	+	0.0329049i	$0.0104759\pi$
$709$			1.75232i			0.0658099i	−0.999458	+	0.0329049i	$0.989524\pi$
$710$		0			0
$711$	−8.48688			−0.318283
$712$		0			0
$713$	9.43050	−	9.43050i	0.353175	−	0.353175i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−1.74878	−	1.74878i	−0.0653093	−	0.0653093i
$718$		0			0
$719$	22.1398			0.825675			0.412837	−	0.910805i	$-0.364538\pi$
$719$	22.1398			0.825675			0.412837	+	0.910805i	$0.364538\pi$
$720$		0			0
$721$	20.3154	−	31.6184i	0.756585	−	1.17753i
$722$		0			0
$723$	0.359569	+	0.359569i	0.0133725	+	0.0133725i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−36.3804	−	36.3804i	−1.34927	−	1.34927i	−0.886450	−	0.462825i	$-0.846836\pi$
$727$	−36.3804	−	36.3804i	−1.34927	−	1.34927i	−0.462825	−	0.886450i	$-0.653164\pi$
$728$		0			0
$729$		−	26.4675i		−	0.980279i
$730$		0			0
$731$		−	14.0193i		−	0.518522i
$732$		0			0
$733$	26.3741	−	26.3741i	0.974149	−	0.974149i	−0.0255249	−	0.999674i	$-0.508126\pi$
$733$	26.3741	−	26.3741i	0.974149	−	0.974149i	0.999674	+	0.0255249i	$0.00812572\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	4.90265	−	4.90265i	0.180591	−	0.180591i
$738$		0			0
$739$			6.48932i			0.238714i	0.992851	+	0.119357i	$0.0380832\pi$
$739$			6.48932i			0.238714i	−0.992851	+	0.119357i	$0.961917\pi$
$740$		0			0
$741$			0.636264i			0.0233737i
$742$		0			0
$743$	−7.68617	−	7.68617i	−0.281978	−	0.281978i	0.551919	−	0.833897i	$-0.313896\pi$
$743$	−7.68617	−	7.68617i	−0.281978	−	0.281978i	−0.833897	+	0.551919i	$0.813896\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	31.1533	+	31.1533i	1.13984	+	1.13984i
$748$		0			0
$749$	−11.4693	+	17.8506i	−0.419079	+	0.652246i
$750$		0			0
$751$	−2.05149			−0.0748599			−0.0374300	−	0.999299i	$-0.511917\pi$
$751$	−2.05149			−0.0748599			−0.0374300	+	0.999299i	$0.511917\pi$
$752$		0			0
$753$	−1.50993	−	1.50993i	−0.0550249	−	0.0550249i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	4.22246	−	4.22246i	0.153468	−	0.153468i	−0.626197	−	0.779665i	$-0.715389\pi$
$757$	4.22246	−	4.22246i	0.153468	−	0.153468i	0.779665	+	0.626197i	$0.215389\pi$
$758$		0			0
$759$	0.159715			0.00579728
$760$		0			0
$761$			46.0616i			1.66973i	0.550453	+	0.834866i	$0.314455\pi$
$761$			46.0616i			1.66973i	−0.550453	+	0.834866i	$0.685545\pi$
$762$		0			0
$763$	6.69631	+	30.7674i	0.242423	+	1.11385i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	32.6723	−	32.6723i	1.17973	−	1.17973i
$768$		0			0
$769$	−44.8809			−1.61845			−0.809223	−	0.587501i	$-0.800112\pi$
$769$	−44.8809			−1.61845			−0.809223	+	0.587501i	$0.800112\pi$
$770$		0			0
$771$	0.293143			0.0105573
$772$		0			0
$773$	4.22724	−	4.22724i	0.152043	−	0.152043i	−0.626987	−	0.779030i	$-0.715712\pi$
$773$	4.22724	−	4.22724i	0.152043	−	0.152043i	0.779030	+	0.626987i	$0.215712\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−0.103169	−	0.474031i	−0.00370118	−	0.0170058i
$778$		0			0
$779$		−	11.2781i		−	0.404081i
$780$		0			0
$781$	9.58630			0.343025
$782$		0			0
$783$	−1.97548	+	1.97548i	−0.0705978	+	0.0705978i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−2.71942	−	2.71942i	−0.0969367	−	0.0969367i	0.656975	−	0.753912i	$-0.271836\pi$
$787$	−2.71942	−	2.71942i	−0.0969367	−	0.0969367i	−0.753912	+	0.656975i	$0.771836\pi$
$788$		0			0
$789$	−0.895906			−0.0318951
$790$		0			0
$791$	4.29748	+	2.76121i	0.152801	+	0.0981772i
$792$		0			0
$793$	−23.1929	−	23.1929i	−0.823603	−	0.823603i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	28.8991	+	28.8991i	1.02366	+	1.02366i	0.999713	+	0.0239445i	$0.00762250\pi$
$797$	28.8991	+	28.8991i	1.02366	+	1.02366i	0.0239445	+	0.999713i	$0.492377\pi$
$798$		0			0
$799$			14.4340i			0.510637i
$800$		0			0
$801$			10.2235i			0.361231i
$802$		0			0
$803$	−5.62453	+	5.62453i	−0.198485	+	0.198485i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	0.673063	−	0.673063i	0.0236929	−	0.0236929i
$808$		0			0
$809$			32.7627i			1.15187i	0.817494	+	0.575937i	$0.195363\pi$
$809$			32.7627i			1.15187i	−0.817494	+	0.575937i	$0.804637\pi$
$810$		0			0
$811$			24.6348i			0.865045i	0.901623	+	0.432523i	$0.142376\pi$
$811$			24.6348i			0.865045i	−0.901623	+	0.432523i	$0.857624\pi$
$812$		0			0
$813$	−0.851321	−	0.851321i	−0.0298571	−	0.0298571i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−8.19956	−	8.19956i	−0.286866	−	0.286866i
$818$		0			0
$819$	37.0737	+	23.8205i	1.29546	+	0.832356i
$820$		0			0
$821$	36.5320			1.27498			0.637488	−	0.770460i	$-0.279974\pi$
$821$	36.5320			1.27498			0.637488	+	0.770460i	$0.279974\pi$
$822$		0			0
$823$	14.6526	+	14.6526i	0.510758	+	0.510758i	0.914759	−	0.404001i	$-0.132381\pi$
$823$	14.6526	+	14.6526i	0.510758	+	0.510758i	−0.404001	+	0.914759i	$0.632381\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	22.1880	−	22.1880i	0.771552	−	0.771552i	−0.206826	−	0.978378i	$-0.566313\pi$
$827$	22.1880	−	22.1880i	0.771552	−	0.771552i	0.978378	+	0.206826i	$0.0663134\pi$
$828$		0			0
$829$	−46.4490			−1.61324			−0.806620	−	0.591070i	$-0.798706\pi$
$829$	−46.4490			−1.61324			−0.806620	+	0.591070i	$0.798706\pi$
$830$		0			0
$831$			2.28745i			0.0793508i
$832$		0			0
$833$	−9.10922	−	3.39546i	−0.315616	−	0.117646i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	2.71740	−	2.71740i	0.0939271	−	0.0939271i
$838$		0			0
$839$	−20.5166			−0.708312			−0.354156	−	0.935186i	$-0.615232\pi$
$839$	−20.5166			−0.708312			−0.354156	+	0.935186i	$0.615232\pi$
$840$		0			0
$841$	7.00080			0.241407
$842$		0			0
$843$	−0.0640466	+	0.0640466i	−0.00220588	+	0.00220588i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−26.8767	+	5.84952i	−0.923494	+	0.200992i
$848$		0			0
$849$			1.76661i			0.0606300i
$850$		0			0
$851$	3.81174			0.130665
$852$		0			0
$853$	17.5496	−	17.5496i	0.600887	−	0.600887i	−0.339661	−	0.940548i	$-0.610312\pi$
$853$	17.5496	−	17.5496i	0.600887	−	0.600887i	0.940548	+	0.339661i	$0.110312\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−11.1708	−	11.1708i	−0.381588	−	0.381588i	0.490086	−	0.871674i	$-0.336965\pi$
$857$	−11.1708	−	11.1708i	−0.381588	−	0.381588i	−0.871674	+	0.490086i	$0.836965\pi$
$858$		0			0
$859$	−42.5442			−1.45159			−0.725795	−	0.687911i	$-0.758528\pi$
$859$	−42.5442			−1.45159			−0.725795	+	0.687911i	$0.758528\pi$
$860$		0			0
$861$	2.17308	+	1.39624i	0.0740585	+	0.0475839i
$862$		0			0
$863$	6.66647	+	6.66647i	0.226929	+	0.226929i	0.811409	−	0.584479i	$-0.198701\pi$
$863$	6.66647	+	6.66647i	0.226929	+	0.226929i	−0.584479	+	0.811409i	$0.698701\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−1.05970	−	1.05970i	−0.0359894	−	0.0359894i
$868$		0			0
$869$			2.20542i			0.0748138i
$870$		0			0
$871$		−	49.7038i		−	1.68415i
$872$		0			0
$873$	25.4237	−	25.4237i	0.860461	−	0.860461i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	24.1080	−	24.1080i	0.814069	−	0.814069i	−0.171172	−	0.985241i	$-0.554755\pi$
$877$	24.1080	−	24.1080i	0.814069	−	0.814069i	0.985241	+	0.171172i	$0.0547555\pi$
$878$		0			0
$879$			0.911503i			0.0307442i
$880$		0			0
$881$			41.2812i			1.39080i	0.718623	+	0.695399i	$0.244773\pi$
$881$			41.2812i			1.39080i	−0.718623	+	0.695399i	$0.755227\pi$
$882$		0			0
$883$	7.58783	+	7.58783i	0.255351	+	0.255351i	0.823160	−	0.567809i	$-0.192209\pi$
$883$	7.58783	+	7.58783i	0.255351	+	0.255351i	−0.567809	+	0.823160i	$0.692209\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−21.2247	−	21.2247i	−0.712657	−	0.712657i	0.254433	−	0.967090i	$-0.418111\pi$
$887$	−21.2247	−	21.2247i	−0.712657	−	0.712657i	−0.967090	+	0.254433i	$0.918111\pi$
$888$		0			0
$889$	19.2009	−	29.8839i	0.643978	−	1.00227i
$890$		0			0
$891$	−6.92409			−0.231966
$892$		0			0
$893$	8.44210	+	8.44210i	0.282504	+	0.282504i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	0.809606	−	0.809606i	0.0270319	−	0.0270319i
$898$		0			0
$899$	30.2613			1.00927
$900$		0			0
$901$		−	4.08699i		−	0.136157i
$902$		0			0
$903$	2.59501	−	0.564786i	0.0863567	−	0.0187949i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	2.69307	−	2.69307i	0.0894219	−	0.0894219i	−0.660981	−	0.750403i	$-0.729860\pi$
$907$	2.69307	−	2.69307i	0.0894219	−	0.0894219i	0.750403	+	0.660981i	$0.229860\pi$
$908$		0			0
$909$	14.5955			0.484103
$910$		0			0
$911$	−41.2220			−1.36575			−0.682874	−	0.730536i	$-0.739270\pi$
$911$	−41.2220			−1.36575			−0.682874	+	0.730536i	$0.739270\pi$
$912$		0			0
$913$	8.09556	−	8.09556i	0.267924	−	0.267924i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	10.9683	+	50.3960i	0.362206	+	1.66422i
$918$		0			0
$919$		−	4.87087i		−	0.160675i	−0.996768	−	0.0803376i	$-0.974400\pi$
$919$		−	4.87087i		−	0.160675i	0.996768	−	0.0803376i	$-0.0255998\pi$
$920$		0			0
$921$	1.19387			0.0393393
$922$		0			0
$923$	48.5936	−	48.5936i	1.59948	−	1.59948i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	30.0337	+	30.0337i	0.986435	+	0.986435i
$928$		0			0
$929$	21.6087			0.708957			0.354479	−	0.935064i	$-0.384658\pi$
$929$	21.6087			0.708957			0.354479	+	0.935064i	$0.384658\pi$
$930$		0			0
$931$	−7.31371	+	3.34185i	−0.239697	+	0.109525i
$932$		0			0
$933$	1.82637	+	1.82637i	0.0597926	+	0.0597926i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−5.78051	−	5.78051i	−0.188841	−	0.188841i	0.606354	−	0.795195i	$-0.292631\pi$
$937$	−5.78051	−	5.78051i	−0.188841	−	0.188841i	−0.795195	+	0.606354i	$0.792631\pi$
$938$		0			0
$939$			1.73168i			0.0565113i
$940$		0			0
$941$		−	35.5016i		−	1.15732i	−0.815569	−	0.578660i	$-0.803576\pi$
$941$		−	35.5016i		−	1.15732i	0.815569	−	0.578660i	$-0.196424\pi$
$942$		0			0
$943$	−14.3507	+	14.3507i	−0.467323	+	0.467323i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−29.6185	+	29.6185i	−0.962472	+	0.962472i	−0.999321	−	0.0368489i	$-0.988268\pi$
$947$	−29.6185	+	29.6185i	−0.962472	+	0.962472i	0.0368489	+	0.999321i	$0.488268\pi$
$948$		0			0
$949$			57.0223i			1.85102i
$950$		0			0
$951$			2.03778i			0.0660797i
$952$		0			0
$953$	2.58171	+	2.58171i	0.0836298	+	0.0836298i	0.747684	−	0.664054i	$-0.231166\pi$
$953$	2.58171	+	2.58171i	0.0836298	+	0.0836298i	−0.664054	+	0.747684i	$0.731166\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	0.256253	+	0.256253i	0.00828347	+	0.00828347i
$958$		0			0
$959$	−11.6844	+	18.1854i	−0.377310	+	0.587237i
$960$		0			0
$961$	−10.6264			−0.342788
$962$		0			0
$963$	−16.9559	−	16.9559i	−0.546396	−	0.546396i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	15.8202	−	15.8202i	0.508744	−	0.508744i	−0.405397	−	0.914141i	$-0.632867\pi$
$967$	15.8202	−	15.8202i	0.508744	−	0.508744i	0.914141	+	0.405397i	$0.132867\pi$
$968$		0			0
$969$	0.158634			0.00509607
$970$		0			0
$971$		−	26.5709i		−	0.852701i	−0.904558	−	0.426351i	$-0.859799\pi$
$971$		−	26.5709i		−	0.852701i	0.904558	−	0.426351i	$-0.140201\pi$
$972$		0			0
$973$	−39.3254	+	8.55889i	−1.26071	+	0.274385i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−40.8575	+	40.8575i	−1.30715	+	1.30715i	−0.383683	+	0.923465i	$0.625344\pi$
$977$	−40.8575	+	40.8575i	−1.30715	+	1.30715i	−0.923465	+	0.383683i	$0.874656\pi$
$978$		0			0
$979$	2.65671			0.0849089
$980$		0			0
$981$	−35.5860			−1.13617
$982$		0			0
$983$	−4.75434	+	4.75434i	−0.151640	+	0.151640i	−0.778850	−	0.627210i	$-0.784197\pi$
$983$	−4.75434	+	4.75434i	−0.151640	+	0.151640i	0.627210	+	0.778850i	$0.284197\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−2.67177	+	0.581493i	−0.0850435	+	0.0185091i
$988$		0			0
$989$			20.8668i			0.663527i
$990$		0			0
$991$	27.2402			0.865312			0.432656	−	0.901559i	$-0.357576\pi$
$991$	27.2402			0.865312			0.432656	+	0.901559i	$0.357576\pi$
$992$		0			0
$993$	−1.92773	+	1.92773i	−0.0611747	+	0.0611747i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−6.58513	−	6.58513i	−0.208553	−	0.208553i	0.595099	−	0.803652i	$-0.297113\pi$
$997$	−6.58513	−	6.58513i	−0.208553	−	0.208553i	−0.803652	+	0.595099i	$0.797113\pi$
$998$		0			0
$999$	1.09835			0.0347504

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1400.2.x.b.993.7		24
5.2	odd	4	inner	1400.2.x.b.657.6		24
5.3	odd	4		280.2.x.a.97.7	yes	24
5.4	even	2		280.2.x.a.153.6	yes	24
7.6	odd	2	inner	1400.2.x.b.993.6		24
20.3	even	4		560.2.bj.d.97.6		24
20.19	odd	2		560.2.bj.d.433.7		24
35.13	even	4		280.2.x.a.97.6	✓	24
35.27	even	4	inner	1400.2.x.b.657.7		24
35.34	odd	2		280.2.x.a.153.7	yes	24
140.83	odd	4		560.2.bj.d.97.7		24
140.139	even	2		560.2.bj.d.433.6		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.x.a.97.6	✓	24	35.13	even	4
280.2.x.a.97.7	yes	24	5.3	odd	4
280.2.x.a.153.6	yes	24	5.4	even	2
280.2.x.a.153.7	yes	24	35.34	odd	2
560.2.bj.d.97.6		24	20.3	even	4
560.2.bj.d.97.7		24	140.83	odd	4
560.2.bj.d.433.6		24	140.139	even	2
560.2.bj.d.433.7		24	20.19	odd	2
1400.2.x.b.657.6		24	5.2	odd	4	inner
1400.2.x.b.657.7		24	35.27	even	4	inner
1400.2.x.b.993.6		24	7.6	odd	2	inner
1400.2.x.b.993.7		24	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1400.x (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0703127 - 0.0703127i) q^{3} +(2.58523 - 0.562657i) q^{7} +2.99011i q^{9} +O(q^{10})\)	\(q+(0.0703127 - 0.0703127i) q^{3} +(2.58523 - 0.562657i) q^{7} +2.99011i q^{9} +0.777018 q^{11} +(3.93876 - 3.93876i) q^{13} +(-0.982018 - 0.982018i) q^{17} -1.14872 q^{19} +(0.142213 - 0.221337i) q^{21} +(1.46167 + 1.46167i) q^{23} +(0.421181 + 0.421181i) q^{27} +4.69033i q^{29} -6.45186i q^{31} +(0.0546342 - 0.0546342i) q^{33} +(1.30390 - 1.30390i) q^{37} -0.553890i q^{39} +9.81800i q^{41} +(7.13800 + 7.13800i) q^{43} +(-7.34914 - 7.34914i) q^{47} +(6.36683 - 2.90920i) q^{49} -0.138097 q^{51} +(2.08092 + 2.08092i) q^{53} +(-0.0807696 + 0.0807696i) q^{57} +8.29508 q^{59} -5.88837i q^{61} +(1.68241 + 7.73013i) q^{63} +(6.30957 - 6.30957i) q^{67} +0.205548 q^{69} +12.3373 q^{71} +(-7.23861 + 7.23861i) q^{73} +(2.00877 - 0.437195i) q^{77} +2.83831i q^{79} -8.91111 q^{81} +(10.4188 - 10.4188i) q^{83} +(0.329790 + 0.329790i) q^{87} +3.41911 q^{89} +(7.96643 - 12.3988i) q^{91} +(-0.453647 - 0.453647i) q^{93} +(-8.50258 - 8.50258i) q^{97} +2.32337i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{7}+O(q^{10}) \) 24 * q - 4 * q^7	\( 24 q - 4 q^{7} + 8 q^{11} + 16 q^{21} + 32 q^{23} + 8 q^{37} - 16 q^{43} - 24 q^{51} + 16 q^{53} - 20 q^{63} + 32 q^{67} - 32 q^{71} + 40 q^{77} - 72 q^{81} - 64 q^{91} - 72 q^{93}+O(q^{100}) \) 24 * q - 4 * q^7 + 8 * q^11 + 16 * q^21 + 32 * q^23 + 8 * q^37 - 16 * q^43 - 24 * q^51 + 16 * q^53 - 20 * q^63 + 32 * q^67 - 32 * q^71 + 40 * q^77 - 72 * q^81 - 64 * q^91 - 72 * q^93

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