LMFDB - Embedded newform 3024.2.t.l.289.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3024,2,Mod(289,3024)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 0, 4, 2]))

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

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

chi := DirichletCharacter("3024.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$24.1467615712$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.5
Character	$\chi$	$=$	3024.289
Dual form			3024.2.t.l.1873.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.340200 q^{5} +(-1.09748 - 2.40739i) q^{7} +O(q^{10})$	$q-0.340200 q^{5} +(-1.09748 - 2.40739i) q^{7} -0.671588 q^{11} +(1.62370 + 2.81233i) q^{13} +(1.10014 + 1.90550i) q^{17} +(-0.242085 + 0.419303i) q^{19} +4.18990 q^{23} -4.88426 q^{25} +(-0.478868 + 0.829424i) q^{29} +(1.04132 - 1.80361i) q^{31} +(0.373363 + 0.818995i) q^{35} +(4.81613 - 8.34178i) q^{37} +(3.90207 + 6.75858i) q^{41} +(3.66119 - 6.34136i) q^{43} +(1.34951 + 2.33742i) q^{47} +(-4.59108 + 5.28413i) q^{49} +(6.12335 + 10.6059i) q^{53} +0.228474 q^{55} +(2.47148 - 4.28074i) q^{59} +(1.76059 + 3.04944i) q^{61} +(-0.552383 - 0.956755i) q^{65} +(6.16012 - 10.6696i) q^{67} -5.57304 q^{71} +(-3.71686 - 6.43779i) q^{73} +(0.737054 + 1.61677i) q^{77} +(-5.00637 - 8.67128i) q^{79} +(2.47376 - 4.28468i) q^{83} +(-0.374269 - 0.648252i) q^{85} +(8.52177 - 14.7601i) q^{89} +(4.98840 - 6.99536i) q^{91} +(0.0823572 - 0.142647i) q^{95} +(4.23657 - 7.33795i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 6 q^{5} - 7 q^{7}+O(q^{10}) $ 22 * q + 6 * q^5 - 7 * q^7	$ 22 q + 6 q^{5} - 7 q^{7} + 6 q^{11} - 3 q^{13} - 7 q^{17} + q^{19} - 4 q^{23} + 20 q^{25} - 9 q^{29} + 4 q^{31} + 14 q^{35} + 2 q^{37} - 16 q^{41} + 5 q^{47} - 15 q^{49} - 11 q^{53} - 22 q^{55} - 19 q^{59} - 13 q^{61} - 13 q^{65} - 26 q^{67} - 48 q^{71} - 35 q^{73} + 4 q^{77} - 10 q^{79} - 28 q^{83} - 20 q^{85} - 6 q^{89} + 37 q^{91} + 12 q^{95} - 29 q^{97}+O(q^{100}) $ 22 * q + 6 * q^5 - 7 * q^7 + 6 * q^11 - 3 * q^13 - 7 * q^17 + q^19 - 4 * q^23 + 20 * q^25 - 9 * q^29 + 4 * q^31 + 14 * q^35 + 2 * q^37 - 16 * q^41 + 5 * q^47 - 15 * q^49 - 11 * q^53 - 22 * q^55 - 19 * q^59 - 13 * q^61 - 13 * q^65 - 26 * q^67 - 48 * q^71 - 35 * q^73 + 4 * q^77 - 10 * q^79 - 28 * q^83 - 20 * q^85 - 6 * q^89 + 37 * q^91 + 12 * q^95 - 29 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−0.340200			−0.152142			−0.0760711	−	0.997102i	$-0.524238\pi$
$5$	−0.340200			−0.152142			−0.0760711	+	0.997102i	$0.524238\pi$
$6$		0			0
$7$	−1.09748	−	2.40739i	−0.414808	−	0.909909i
$7$	−1.09748	−	2.40739i	−0.414808	−	0.909909i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.671588			−0.202491			−0.101246	−	0.994861i	$-0.532283\pi$
$11$	−0.671588			−0.202491			−0.101246	+	0.994861i	$0.532283\pi$
$12$		0			0
$13$	1.62370	+	2.81233i	0.450333	+	0.780000i	0.998407	−	0.0564303i	$-0.0179719\pi$
$13$	1.62370	+	2.81233i	0.450333	+	0.780000i	−0.548073	+	0.836430i	$0.684639\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.10014	+	1.90550i	0.266824	+	0.462152i	0.968040	−	0.250796i	$-0.0806925\pi$
$17$	1.10014	+	1.90550i	0.266824	+	0.462152i	−0.701216	+	0.712949i	$0.747359\pi$
$18$		0			0
$19$	−0.242085	+	0.419303i	−0.0555380	+	0.0961946i	−0.892458	−	0.451131i	$-0.851021\pi$
$19$	−0.242085	+	0.419303i	−0.0555380	+	0.0961946i	0.836920	+	0.547326i	$0.184354\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	4.18990			0.873655			0.436827	−	0.899545i	$-0.356102\pi$
$23$	4.18990			0.873655			0.436827	+	0.899545i	$0.356102\pi$
$24$		0			0
$25$	−4.88426			−0.976853
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−0.478868	+	0.829424i	−0.0889235	+	0.154020i	−0.907056	−	0.421009i	$-0.861676\pi$
$29$	−0.478868	+	0.829424i	−0.0889235	+	0.154020i	0.818133	+	0.575029i	$0.195009\pi$
$30$		0			0
$31$	1.04132	−	1.80361i	0.187026	−	0.323938i	−0.757231	−	0.653147i	$-0.773449\pi$
$31$	1.04132	−	1.80361i	0.187026	−	0.323938i	0.944257	+	0.329208i	$0.106782\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	0.373363	+	0.818995i	0.0631098	+	0.138435i
$36$		0			0
$37$	4.81613	−	8.34178i	0.791767	−	1.37138i	−0.133105	−	0.991102i	$-0.542495\pi$
$37$	4.81613	−	8.34178i	0.791767	−	1.37138i	0.924872	−	0.380278i	$-0.124172\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	3.90207	+	6.75858i	0.609400	+	1.05551i	0.991339	+	0.131325i	$0.0419231\pi$
$41$	3.90207	+	6.75858i	0.609400	+	1.05551i	−0.381939	+	0.924188i	$0.624744\pi$
$42$		0			0
$43$	3.66119	−	6.34136i	0.558326	−	0.967048i	−0.439311	−	0.898335i	$-0.644777\pi$
$43$	3.66119	−	6.34136i	0.558326	−	0.967048i	0.997636	−	0.0687132i	$-0.0218893\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1.34951	+	2.33742i	0.196846	+	0.340947i	0.947504	−	0.319744i	$-0.103597\pi$
$47$	1.34951	+	2.33742i	0.196846	+	0.340947i	−0.750658	+	0.660691i	$0.770263\pi$
$48$		0			0
$49$	−4.59108	+	5.28413i	−0.655868	+	0.754876i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	6.12335	+	10.6059i	0.841107	+	1.45684i	0.888960	+	0.457985i	$0.151429\pi$
$53$	6.12335	+	10.6059i	0.841107	+	1.45684i	−0.0478535	+	0.998854i	$0.515238\pi$
$54$		0			0
$55$	0.228474			0.0308075
$56$		0			0
$57$		0			0
$58$		0			0
$59$	2.47148	−	4.28074i	0.321760	−	0.557304i	−0.659091	−	0.752063i	$-0.729059\pi$
$59$	2.47148	−	4.28074i	0.321760	−	0.557304i	0.980851	+	0.194758i	$0.0623923\pi$
$60$		0			0
$61$	1.76059	+	3.04944i	0.225421	+	0.390441i	0.956446	−	0.291910i	$-0.0942909\pi$
$61$	1.76059	+	3.04944i	0.225421	+	0.390441i	−0.731025	+	0.682351i	$0.760958\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−0.552383	−	0.956755i	−0.0685147	−	0.118671i
$66$		0			0
$67$	6.16012	−	10.6696i	0.752579	−	1.30350i	−0.193990	−	0.981003i	$-0.562143\pi$
$67$	6.16012	−	10.6696i	0.752579	−	1.30350i	0.946569	−	0.322501i	$-0.104524\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−5.57304			−0.661398			−0.330699	−	0.943736i	$-0.607285\pi$
$71$	−5.57304			−0.661398			−0.330699	+	0.943736i	$0.607285\pi$
$72$		0			0
$73$	−3.71686	−	6.43779i	−0.435026	−	0.753487i	0.562272	−	0.826952i	$-0.309927\pi$
$73$	−3.71686	−	6.43779i	−0.435026	−	0.753487i	−0.997298	+	0.0734657i	$0.976594\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.737054	+	1.61677i	0.0839951	+	0.184249i
$78$		0			0
$79$	−5.00637	−	8.67128i	−0.563260	−	0.975596i	−0.997209	−	0.0746582i	$-0.976213\pi$
$79$	−5.00637	−	8.67128i	−0.563260	−	0.975596i	0.433949	−	0.900938i	$-0.357120\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	2.47376	−	4.28468i	0.271530	−	0.470305i	−0.697723	−	0.716367i	$-0.745804\pi$
$83$	2.47376	−	4.28468i	0.271530	−	0.470305i	0.969254	+	0.246063i	$0.0791369\pi$
$84$		0			0
$85$	−0.374269	−	0.648252i	−0.0405951	−	0.0703128i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	8.52177	−	14.7601i	0.903306	−	1.56457i	0.0801310	−	0.996784i	$-0.474466\pi$
$89$	8.52177	−	14.7601i	0.903306	−	1.56457i	0.823175	−	0.567788i	$-0.192201\pi$
$90$		0			0
$91$	4.98840	−	6.99536i	0.522927	−	0.733313i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	0.0823572	−	0.142647i	0.00844967	−	0.0146353i
$96$		0			0
$97$	4.23657	−	7.33795i	0.430159	−	0.745056i	−0.566728	−	0.823905i	$-0.691791\pi$
$97$	4.23657	−	7.33795i	0.430159	−	0.745056i	0.996887	+	0.0788485i	$0.0251243\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	4.57385			0.455115			0.227558	−	0.973765i	$-0.426926\pi$
$101$	4.57385			0.455115			0.227558	+	0.973765i	$0.426926\pi$
$102$		0			0
$103$	1.80713			0.178061			0.0890307	−	0.996029i	$-0.471623\pi$
$103$	1.80713			0.178061			0.0890307	+	0.996029i	$0.471623\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	3.88188	−	6.72361i	0.375275	−	0.649996i	−0.615093	−	0.788454i	$-0.710882\pi$
$107$	3.88188	−	6.72361i	0.375275	−	0.649996i	0.990368	+	0.138459i	$0.0442149\pi$
$108$		0			0
$109$	−1.07178	−	1.85638i	−0.102658	−	0.177809i	0.810121	−	0.586263i	$-0.199401\pi$
$109$	−1.07178	−	1.85638i	−0.102658	−	0.177809i	−0.912779	+	0.408454i	$0.866068\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	7.91006	+	13.7006i	0.744116	+	1.28885i	0.950607	+	0.310398i	$0.100462\pi$
$113$	7.91006	+	13.7006i	0.744116	+	1.28885i	−0.206491	+	0.978449i	$0.566204\pi$
$114$		0			0
$115$	−1.42540			−0.132920
$116$		0			0
$117$		0			0
$118$		0			0
$119$	3.37991	−	4.73973i	0.309836	−	0.434490i
$120$		0			0
$121$	−10.5490			−0.958997
$122$		0			0
$123$		0			0
$124$		0			0
$125$	3.36263			0.300763
$126$		0			0
$127$	13.8820			1.23183			0.615915	−	0.787812i	$-0.288786\pi$
$127$	13.8820			1.23183			0.615915	+	0.787812i	$0.288786\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−4.17538			−0.364805			−0.182402	−	0.983224i	$-0.558387\pi$
$131$	−4.17538			−0.364805			−0.182402	+	0.983224i	$0.558387\pi$
$132$		0			0
$133$	1.27511	+	0.122616i	0.110566	+	0.0106322i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	12.7609			1.09023			0.545117	−	0.838360i	$-0.316485\pi$
$137$	12.7609			1.09023			0.545117	+	0.838360i	$0.316485\pi$
$138$		0			0
$139$	−5.95986	−	10.3228i	−0.505509	−	0.875567i	−0.999980	−	0.00637264i	$-0.997972\pi$
$139$	−5.95986	−	10.3228i	−0.505509	−	0.875567i	0.494471	−	0.869194i	$-0.335362\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−1.09046	−	1.88873i	−0.0911885	−	0.157943i
$144$		0			0
$145$	0.162911	−	0.282170i	0.0135290	−	0.0234329i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	10.7510			0.880753			0.440376	−	0.897813i	$-0.354845\pi$
$149$	10.7510			0.880753			0.440376	+	0.897813i	$0.354845\pi$
$150$		0			0
$151$	2.58099			0.210038			0.105019	−	0.994470i	$-0.466510\pi$
$151$	2.58099			0.210038			0.105019	+	0.994470i	$0.466510\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−0.354256	+	0.613589i	−0.0284545	+	0.0492846i
$156$		0			0
$157$	−3.99846	+	6.92554i	−0.319112	+	0.552718i	−0.980303	−	0.197499i	$-0.936718\pi$
$157$	−3.99846	+	6.92554i	−0.319112	+	0.552718i	0.661191	+	0.750218i	$0.270051\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−4.59833	−	10.0867i	−0.362399	−	0.794946i
$162$		0			0
$163$	−4.13306	+	7.15868i	−0.323727	+	0.560711i	−0.981254	−	0.192720i	$-0.938269\pi$
$163$	−4.13306	+	7.15868i	−0.323727	+	0.560711i	0.657527	+	0.753431i	$0.271602\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	8.99384	+	15.5778i	0.695964	+	1.20544i	0.969855	+	0.243684i	$0.0783560\pi$
$167$	8.99384	+	15.5778i	0.695964	+	1.20544i	−0.273891	+	0.961761i	$0.588311\pi$
$168$		0			0
$169$	1.22720	−	2.12557i	0.0944000	−	0.163506i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−8.49915	−	14.7210i	−0.646179	−	1.11921i	−0.984028	−	0.178014i	$-0.943033\pi$
$173$	−8.49915	−	14.7210i	−0.646179	−	1.11921i	0.337849	−	0.941200i	$-0.390301\pi$
$174$		0			0
$175$	5.36038	+	11.7583i	0.405207	+	0.888847i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−9.65073	−	16.7156i	−0.721329	−	1.24938i	−0.960467	−	0.278393i	$-0.910198\pi$
$179$	−9.65073	−	16.7156i	−0.721329	−	1.24938i	0.239138	−	0.970986i	$-0.423135\pi$
$180$		0			0
$181$	21.9640			1.63257			0.816287	−	0.577646i	$-0.196029\pi$
$181$	21.9640			1.63257			0.816287	+	0.577646i	$0.196029\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−1.63845	+	2.83788i	−0.120461	+	0.208645i
$186$		0			0
$187$	−0.738842	−	1.27971i	−0.0540295	−	0.0935818i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−3.32872	−	5.76552i	−0.240858	−	0.417178i	0.720101	−	0.693869i	$-0.244095\pi$
$191$	−3.32872	−	5.76552i	−0.240858	−	0.417178i	−0.960959	+	0.276691i	$0.910762\pi$
$192$		0			0
$193$	−3.17453	+	5.49845i	−0.228508	+	0.395787i	−0.957366	−	0.288878i	$-0.906718\pi$
$193$	−3.17453	+	5.49845i	−0.228508	+	0.395787i	0.728858	+	0.684665i	$0.240051\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−23.8112			−1.69648			−0.848239	−	0.529614i	$-0.822337\pi$
$197$	−23.8112			−1.69648			−0.848239	+	0.529614i	$0.822337\pi$
$198$		0			0
$199$	10.4771	+	18.1468i	0.742701	+	1.28640i	0.951261	+	0.308386i	$0.0997887\pi$
$199$	10.4771	+	18.1468i	0.742701	+	1.28640i	−0.208561	+	0.978009i	$0.566878\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	2.52230	+	0.242547i	0.177030	+	0.0170235i
$204$		0			0
$205$	−1.32748	−	2.29927i	−0.0927155	−	0.160588i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	0.162581	−	0.281599i	0.0112460	−	0.0194786i
$210$		0			0
$211$	6.32431	+	10.9540i	0.435384	+	0.754106i	0.997327	−	0.0730693i	$-0.0232794\pi$
$211$	6.32431	+	10.9540i	0.435384	+	0.754106i	−0.561943	+	0.827176i	$0.689946\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−1.24554	+	2.15733i	−0.0849448	+	0.147129i
$216$		0			0
$217$	−5.48482	−	0.527427i	−0.372334	−	0.0358041i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−3.57260	+	6.18793i	−0.240319	+	0.416245i
$222$		0			0
$223$	1.34432	−	2.32843i	0.0900225	−	0.155924i	−0.817498	−	0.575932i	$-0.804639\pi$
$223$	1.34432	−	2.32843i	0.0900225	−	0.155924i	0.907520	+	0.420008i	$0.137973\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	27.9885			1.85766			0.928829	−	0.370508i	$-0.120816\pi$
$227$	27.9885			1.85766			0.928829	+	0.370508i	$0.120816\pi$
$228$		0			0
$229$	24.5390			1.62158			0.810790	−	0.585337i	$-0.199038\pi$
$229$	24.5390			1.62158			0.810790	+	0.585337i	$0.199038\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	4.61844	−	7.99938i	0.302564	−	0.524057i	−0.674152	−	0.738593i	$-0.735491\pi$
$233$	4.61844	−	7.99938i	0.302564	−	0.524057i	0.976716	+	0.214536i	$0.0688240\pi$
$234$		0			0
$235$	−0.459103	−	0.795189i	−0.0299486	−	0.0518724i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	14.0126	+	24.2706i	0.906403	+	1.56994i	0.819023	+	0.573760i	$0.194516\pi$
$239$	14.0126	+	24.2706i	0.906403	+	1.56994i	0.0873796	+	0.996175i	$0.472151\pi$
$240$		0			0
$241$	19.8282			1.27725			0.638624	−	0.769519i	$-0.279504\pi$
$241$	19.8282			1.27725			0.638624	+	0.769519i	$0.279504\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	1.56188	−	1.79766i	0.0997851	−	0.114848i
$246$		0			0
$247$	−1.57229			−0.100042
$248$		0			0
$249$		0			0
$250$		0			0
$251$	16.5759			1.04626			0.523132	−	0.852252i	$-0.324764\pi$
$251$	16.5759			1.04626			0.523132	+	0.852252i	$0.324764\pi$
$252$		0			0
$253$	−2.81389			−0.176907
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−7.29501			−0.455050			−0.227525	−	0.973772i	$-0.573063\pi$
$257$	−7.29501			−0.455050			−0.227525	+	0.973772i	$0.573063\pi$
$258$		0			0
$259$	−25.3675	−	2.43937i	−1.57626	−	0.151575i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−26.7798			−1.65131			−0.825657	−	0.564172i	$-0.809196\pi$
$263$	−26.7798			−1.65131			−0.825657	+	0.564172i	$0.809196\pi$
$264$		0			0
$265$	−2.08316	−	3.60815i	−0.127968	−	0.221647i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−10.1791	−	17.6307i	−0.620630	−	1.07496i	−0.989369	−	0.145429i	$-0.953544\pi$
$269$	−10.1791	−	17.6307i	−0.620630	−	1.07496i	0.368739	−	0.929533i	$-0.379790\pi$
$270$		0			0
$271$	−5.45842	+	9.45427i	−0.331576	+	0.574306i	−0.982821	−	0.184561i	$-0.940914\pi$
$271$	−5.45842	+	9.45427i	−0.331576	+	0.574306i	0.651245	+	0.758867i	$0.274247\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	3.28021			0.197804
$276$		0			0
$277$	17.6738			1.06191			0.530957	−	0.847399i	$-0.321832\pi$
$277$	17.6738			1.06191			0.530957	+	0.847399i	$0.321832\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−7.17614	+	12.4294i	−0.428092	+	0.741478i	−0.996704	−	0.0811286i	$-0.974148\pi$
$281$	−7.17614	+	12.4294i	−0.428092	+	0.741478i	0.568611	+	0.822606i	$0.307481\pi$
$282$		0			0
$283$	4.86420	−	8.42505i	0.289147	−	0.500817i	−0.684459	−	0.729051i	$-0.739962\pi$
$283$	4.86420	−	8.42505i	0.289147	−	0.500817i	0.973606	+	0.228234i	$0.0732950\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	11.9881	−	16.8112i	0.707636	−	0.992334i
$288$		0			0
$289$	6.07937	−	10.5298i	0.357610	−	0.619399i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−6.26345	−	10.8486i	−0.365915	−	0.633783i	0.623008	−	0.782216i	$-0.285911\pi$
$293$	−6.26345	−	10.8486i	−0.365915	−	0.633783i	−0.988923	+	0.148433i	$0.952577\pi$
$294$		0			0
$295$	−0.840799	+	1.45631i	−0.0489532	+	0.0847895i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	6.80314	+	11.7834i	0.393436	+	0.681451i
$300$		0			0
$301$	−19.2842	−	1.85439i	−1.11152	−	0.106886i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−0.598954	−	1.03742i	−0.0342960	−	0.0594025i
$306$		0			0
$307$	−25.8747			−1.47675			−0.738375	−	0.674391i	$-0.764406\pi$
$307$	−25.8747			−1.47675			−0.738375	+	0.674391i	$0.764406\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−14.2001	+	24.5952i	−0.805211	+	1.39467i	0.110937	+	0.993827i	$0.464615\pi$
$311$	−14.2001	+	24.5952i	−0.805211	+	1.39467i	−0.916148	+	0.400840i	$0.868718\pi$
$312$		0			0
$313$	6.10074	+	10.5668i	0.344834	+	0.597270i	0.985324	−	0.170697i	$-0.0546019\pi$
$313$	6.10074	+	10.5668i	0.344834	+	0.597270i	−0.640490	+	0.767967i	$0.721269\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−1.97609	−	3.42270i	−0.110988	−	0.192238i	0.805181	−	0.593030i	$-0.202068\pi$
$317$	−1.97609	−	3.42270i	−0.110988	−	0.192238i	−0.916169	+	0.400792i	$0.868735\pi$
$318$		0			0
$319$	0.321602	−	0.557031i	0.0180062	−	0.0311877i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−1.06531			−0.0592754
$324$		0			0
$325$	−7.93058	−	13.7362i	−0.439909	−	0.761945i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	4.14602	−	5.81406i	0.228577	−	0.320540i
$330$		0			0
$331$	−4.44143	−	7.69278i	−0.244123	−	0.422834i	0.717762	−	0.696289i	$-0.245167\pi$
$331$	−4.44143	−	7.69278i	−0.244123	−	0.422834i	−0.961885	+	0.273455i	$0.911833\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−2.09567	+	3.62981i	−0.114499	+	0.198318i
$336$		0			0
$337$	−11.9741	−	20.7397i	−0.652269	−	1.12976i	−0.982571	−	0.185887i	$-0.940484\pi$
$337$	−11.9741	−	20.7397i	−0.652269	−	1.12976i	0.330302	−	0.943875i	$-0.392849\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−0.699335	+	1.21128i	−0.0378711	+	0.0655947i
$342$		0			0
$343$	17.7596	+	5.25329i	0.958928	+	0.283651i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−4.74529	+	8.21909i	−0.254741	+	0.441224i	−0.964825	−	0.262893i	$-0.915323\pi$
$347$	−4.74529	+	8.21909i	−0.254741	+	0.441224i	0.710084	+	0.704117i	$0.248657\pi$
$348$		0			0
$349$	4.26145	−	7.38104i	0.228110	−	0.395098i	−0.729138	−	0.684367i	$-0.760079\pi$
$349$	4.26145	−	7.38104i	0.228110	−	0.395098i	0.957248	+	0.289269i	$0.0934121\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	37.1744			1.97859			0.989297	−	0.145919i	$-0.0466138\pi$
$353$	37.1744			1.97859			0.989297	+	0.145919i	$0.0466138\pi$
$354$		0			0
$355$	1.89595			0.100627
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−5.30964	+	9.19657i	−0.280232	+	0.485376i	−0.971442	−	0.237278i	$-0.923745\pi$
$359$	−5.30964	+	9.19657i	−0.280232	+	0.485376i	0.691210	+	0.722654i	$0.257078\pi$
$360$		0			0
$361$	9.38279	+	16.2515i	0.493831	+	0.855340i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	1.26448	+	2.19014i	0.0661857	+	0.114637i
$366$		0			0
$367$	−22.3598			−1.16717			−0.583586	−	0.812051i	$-0.698351\pi$
$367$	−22.3598			−1.16717			−0.583586	+	0.812051i	$0.698351\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	18.8124	−	26.3811i	0.976693	−	1.36964i
$372$		0			0
$373$	−17.5853			−0.910532			−0.455266	−	0.890356i	$-0.650456\pi$
$373$	−17.5853			−0.910532			−0.455266	+	0.890356i	$0.650456\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−3.11015			−0.160181
$378$		0			0
$379$	−10.0443			−0.515939			−0.257969	−	0.966153i	$-0.583053\pi$
$379$	−10.0443			−0.515939			−0.257969	+	0.966153i	$0.583053\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−7.87238			−0.402260			−0.201130	−	0.979565i	$-0.564461\pi$
$383$	−7.87238			−0.402260			−0.201130	+	0.979565i	$0.564461\pi$
$384$		0			0
$385$	−0.250746	−	0.550027i	−0.0127792	−	0.0280320i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	3.64835			0.184979			0.0924893	−	0.995714i	$-0.470518\pi$
$389$	3.64835			0.184979			0.0924893	+	0.995714i	$0.470518\pi$
$390$		0			0
$391$	4.60949	+	7.98387i	0.233112	+	0.403762i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	1.70317	+	2.94997i	0.0856956	+	0.148429i
$396$		0			0
$397$	6.56071	−	11.3635i	0.329272	−	0.570317i	−0.653095	−	0.757276i	$-0.726530\pi$
$397$	6.56071	−	11.3635i	0.329272	−	0.570317i	0.982368	+	0.186959i	$0.0598632\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−11.4374			−0.571159			−0.285579	−	0.958355i	$-0.592186\pi$
$401$	−11.4374			−0.571159			−0.285579	+	0.958355i	$0.592186\pi$
$402$		0			0
$403$	6.76313			0.336896
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−3.23445	+	5.60224i	−0.160326	+	0.277693i
$408$		0			0
$409$	9.24106	−	16.0060i	0.456941	−	0.791445i	−0.541857	−	0.840471i	$-0.682278\pi$
$409$	9.24106	−	16.0060i	0.456941	−	0.791445i	0.998797	+	0.0490262i	$0.0156118\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−13.0178	−	1.25181i	−0.640565	−	0.0615975i
$414$		0			0
$415$	−0.841574	+	1.45765i	−0.0413112	+	0.0715531i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−10.6290	−	18.4099i	−0.519260	−	0.899385i	−0.999749	−	0.0223843i	$-0.992874\pi$
$419$	−10.6290	−	18.4099i	−0.519260	−	0.899385i	0.480489	−	0.877001i	$-0.340459\pi$
$420$		0			0
$421$	−8.60478	+	14.9039i	−0.419371	+	0.726373i	−0.995876	−	0.0907211i	$-0.971083\pi$
$421$	−8.60478	+	14.9039i	−0.419371	+	0.726373i	0.576505	+	0.817094i	$0.304416\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−5.37339	−	9.30698i	−0.260648	−	0.451455i
$426$		0			0
$427$	5.40898	−	7.58514i	0.261759	−	0.367071i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	3.02962	+	5.24745i	0.145931	+	0.252761i	0.929720	−	0.368267i	$-0.120049\pi$
$431$	3.02962	+	5.24745i	0.145931	+	0.252761i	−0.783789	+	0.621028i	$0.786715\pi$
$432$		0			0
$433$	−17.6963			−0.850432			−0.425216	−	0.905092i	$-0.639802\pi$
$433$	−17.6963			−0.850432			−0.425216	+	0.905092i	$0.639802\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−1.01431	+	1.75684i	−0.0485210	+	0.0840409i
$438$		0			0
$439$	13.6687	+	23.6748i	0.652370	+	1.12994i	0.982546	+	0.186018i	$0.0595584\pi$
$439$	13.6687	+	23.6748i	0.652370	+	1.12994i	−0.330177	+	0.943919i	$0.607108\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−0.958856	−	1.66079i	−0.0455566	−	0.0789064i	0.842348	−	0.538934i	$-0.181173\pi$
$443$	−0.958856	−	1.66079i	−0.0455566	−	0.0789064i	−0.887905	+	0.460028i	$0.847839\pi$
$444$		0			0
$445$	−2.89911	+	5.02140i	−0.137431	+	0.238037i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−28.3249			−1.33674			−0.668368	−	0.743831i	$-0.733007\pi$
$449$	−28.3249			−1.33674			−0.668368	+	0.743831i	$0.733007\pi$
$450$		0			0
$451$	−2.62058	−	4.53898i	−0.123398	−	0.213732i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−1.69706	+	2.37982i	−0.0795592	+	0.111568i
$456$		0			0
$457$	−6.50427	−	11.2657i	−0.304257	−	0.526988i	0.672839	−	0.739789i	$-0.265075\pi$
$457$	−6.50427	−	11.2657i	−0.304257	−	0.526988i	−0.977096	+	0.212801i	$0.931741\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	11.8278	−	20.4863i	0.550875	−	0.954144i	−0.447336	−	0.894366i	$-0.647627\pi$
$461$	11.8278	−	20.4863i	0.550875	−	0.954144i	0.998212	−	0.0597782i	$-0.0190393\pi$
$462$		0			0
$463$	20.2403	+	35.0572i	0.940647	+	1.62925i	0.764241	+	0.644931i	$0.223114\pi$
$463$	20.2403	+	35.0572i	0.940647	+	1.62925i	0.176406	+	0.984317i	$0.443553\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−18.6010	+	32.2179i	−0.860753	+	1.49087i	0.0104492	+	0.999945i	$0.496674\pi$
$467$	−18.6010	+	32.2179i	−0.860753	+	1.49087i	−0.871203	+	0.490923i	$0.836659\pi$
$468$		0			0
$469$	−32.4466	−	3.12011i	−1.49825	−	0.144073i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−2.45881	+	4.25878i	−0.113056	+	0.195819i
$474$		0			0
$475$	1.18240	−	2.04799i	0.0542525	−	0.0939680i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	40.5835			1.85431			0.927154	−	0.374681i	$-0.122248\pi$
$479$	40.5835			1.85431			0.927154	+	0.374681i	$0.122248\pi$
$480$		0			0
$481$	31.2798			1.42624
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−1.44128	+	2.49637i	−0.0654452	+	0.113354i
$486$		0			0
$487$	−10.5255	−	18.2307i	−0.476956	−	0.826113i	0.522695	−	0.852520i	$-0.324927\pi$
$487$	−10.5255	−	18.2307i	−0.476956	−	0.826113i	−0.999651	+	0.0264072i	$0.991593\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−4.97925	−	8.62432i	−0.224711	−	0.389210i	0.731522	−	0.681818i	$-0.238810\pi$
$491$	−4.97925	−	8.62432i	−0.224711	−	0.389210i	−0.956233	+	0.292608i	$0.905477\pi$
$492$		0			0
$493$	−2.10729			−0.0949077
$494$		0			0
$495$		0			0
$496$		0			0
$497$	6.11630	+	13.4165i	0.274354	+	0.601812i
$498$		0			0
$499$	−22.6301			−1.01306			−0.506531	−	0.862222i	$-0.669072\pi$
$499$	−22.6301			−1.01306			−0.506531	+	0.862222i	$0.669072\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−43.4520			−1.93743			−0.968714	−	0.248179i	$-0.920168\pi$
$503$	−43.4520			−1.93743			−0.968714	+	0.248179i	$0.920168\pi$
$504$		0			0
$505$	−1.55602			−0.0692422
$506$		0			0
$507$		0			0
$508$		0			0
$509$	9.55477			0.423508			0.211754	−	0.977323i	$-0.432082\pi$
$509$	9.55477			0.423508			0.211754	+	0.977323i	$0.432082\pi$
$510$		0			0
$511$	−11.4191	+	16.0133i	−0.505152	+	0.708386i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−0.614785			−0.0270906
$516$		0			0
$517$	−0.906312	−	1.56978i	−0.0398596	−	0.0690388i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−0.581462	−	1.00712i	−0.0254743	−	0.0441228i	0.853007	−	0.521899i	$-0.174776\pi$
$521$	−0.581462	−	1.00712i	−0.0254743	−	0.0441228i	−0.878482	+	0.477776i	$0.841443\pi$
$522$		0			0
$523$	3.20567	−	5.55239i	0.140174	−	0.242789i	−0.787388	−	0.616458i	$-0.788567\pi$
$523$	3.20567	−	5.55239i	0.140174	−	0.242789i	0.927562	+	0.373669i	$0.121900\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	4.58238			0.199612
$528$		0			0
$529$	−5.44474			−0.236728
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−12.6716	+	21.9478i	−0.548866	+	0.950665i
$534$		0			0
$535$	−1.32061	+	2.28737i	−0.0570952	+	0.0988917i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	3.08331	−	3.54876i	0.132808	−	0.152856i
$540$		0			0
$541$	−7.37443	+	12.7729i	−0.317052	+	0.549150i	−0.979871	−	0.199629i	$-0.936026\pi$
$541$	−7.37443	+	12.7729i	−0.317052	+	0.549150i	0.662820	+	0.748779i	$0.269360\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	0.364621	+	0.631542i	0.0156187	+	0.0270523i
$546$		0			0
$547$	−6.57905	+	11.3952i	−0.281300	+	0.487226i	−0.971705	−	0.236197i	$-0.924099\pi$
$547$	−6.57905	+	11.3952i	−0.281300	+	0.487226i	0.690405	+	0.723423i	$0.257432\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−0.231853	−	0.401581i	−0.00987727	−	0.0171079i
$552$		0			0
$553$	−15.3808	+	21.5689i	−0.654058	+	0.917201i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	12.1869	+	21.1083i	0.516374	+	0.894385i	0.999819	+	0.0190111i	$0.00605177\pi$
$557$	12.1869	+	21.1083i	0.516374	+	0.894385i	−0.483446	+	0.875374i	$0.660615\pi$
$558$		0			0
$559$	23.7787			1.00573
$560$		0			0
$561$		0			0
$562$		0			0
$563$	1.55982	−	2.70169i	0.0657388	−	0.113863i	−0.831283	−	0.555850i	$-0.812393\pi$
$563$	1.55982	−	2.70169i	0.0657388	−	0.113863i	0.897021	+	0.441987i	$0.145726\pi$
$564$		0			0
$565$	−2.69100	−	4.66096i	−0.113211	−	0.196088i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−10.7384	−	18.5995i	−0.450179	−	0.779733i	0.548218	−	0.836336i	$-0.315307\pi$
$569$	−10.7384	−	18.5995i	−0.450179	−	0.779733i	−0.998397	+	0.0566027i	$0.981973\pi$
$570$		0			0
$571$	16.5230	−	28.6187i	0.691466	−	1.19765i	−0.279891	−	0.960032i	$-0.590298\pi$
$571$	16.5230	−	28.6187i	0.691466	−	1.19765i	0.971358	−	0.237623i	$-0.0763682\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−20.4646			−0.853432
$576$		0			0
$577$	0.904826	+	1.56720i	0.0376684	+	0.0652436i	0.884245	−	0.467023i	$-0.154674\pi$
$577$	0.904826	+	1.56720i	0.0376684	+	0.0652436i	−0.846577	+	0.532267i	$0.821340\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−13.0298	−	1.25296i	−0.540567	−	0.0519816i
$582$		0			0
$583$	−4.11236	−	7.12282i	−0.170317	−	0.294997i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	1.65901	−	2.87349i	0.0684746	−	0.118601i	−0.829755	−	0.558127i	$-0.811520\pi$
$587$	1.65901	−	2.87349i	0.0684746	−	0.118601i	0.898230	+	0.439526i	$0.144853\pi$
$588$		0			0
$589$	0.504173	+	0.873253i	0.0207741	+	0.0359818i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−15.3784	+	26.6362i	−0.631516	+	1.09382i	0.355726	+	0.934590i	$0.384234\pi$
$593$	−15.3784	+	26.6362i	−0.631516	+	1.09382i	−0.987242	+	0.159228i	$0.949100\pi$
$594$		0			0
$595$	−1.14985	+	1.61246i	−0.0471391	+	0.0661042i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−6.98523	+	12.0988i	−0.285409	+	0.494342i	−0.972708	−	0.232032i	$-0.925463\pi$
$599$	−6.98523	+	12.0988i	−0.285409	+	0.494342i	0.687299	+	0.726374i	$0.258796\pi$
$600$		0			0
$601$	−7.50432	+	12.9979i	−0.306108	+	0.530194i	−0.977507	−	0.210901i	$-0.932360\pi$
$601$	−7.50432	+	12.9979i	−0.306108	+	0.530194i	0.671400	+	0.741096i	$0.265693\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	3.58876			0.145904
$606$		0			0
$607$	−23.3289			−0.946889			−0.473444	−	0.880824i	$-0.656990\pi$
$607$	−23.3289			−0.946889			−0.473444	+	0.880824i	$0.656990\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−4.38239	+	7.59052i	−0.177292	+	0.307080i
$612$		0			0
$613$	22.3374	+	38.6895i	0.902198	+	1.56265i	0.824635	+	0.565666i	$0.191381\pi$
$613$	22.3374	+	38.6895i	0.902198	+	1.56265i	0.0775635	+	0.996987i	$0.475286\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.18488	+	2.05227i	0.0477013	+	0.0826212i	0.888890	−	0.458120i	$-0.151477\pi$
$617$	1.18488	+	2.05227i	0.0477013	+	0.0826212i	−0.841189	+	0.540741i	$0.818144\pi$
$618$		0			0
$619$	22.7727			0.915311			0.457655	−	0.889130i	$-0.348689\pi$
$619$	22.7727			0.915311			0.457655	+	0.889130i	$0.348689\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−44.8859	−	4.31629i	−1.79832	−	0.172928i
$624$		0			0
$625$	23.2774			0.931094
$626$		0			0
$627$		0			0
$628$		0			0
$629$	21.1937			0.845049
$630$		0			0
$631$	−17.8652			−0.711201			−0.355600	−	0.934638i	$-0.615724\pi$
$631$	−17.8652			−0.711201			−0.355600	+	0.934638i	$0.615724\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−4.72267			−0.187413
$636$		0			0
$637$	−22.3152	−	4.33178i	−0.884162	−	0.171631i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	25.5800			1.01035			0.505175	−	0.863017i	$-0.331428\pi$
$641$	25.5800			1.01035			0.505175	+	0.863017i	$0.331428\pi$
$642$		0			0
$643$	−7.99334	−	13.8449i	−0.315227	−	0.545989i	0.664259	−	0.747503i	$-0.268747\pi$
$643$	−7.99334	−	13.8449i	−0.315227	−	0.545989i	−0.979486	+	0.201514i	$0.935414\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	7.47306	+	12.9437i	0.293796	+	0.508870i	0.974704	−	0.223499i	$-0.0717479\pi$
$647$	7.47306	+	12.9437i	0.293796	+	0.508870i	−0.680908	+	0.732369i	$0.738415\pi$
$648$		0			0
$649$	−1.65982	+	2.87489i	−0.0651536	+	0.112849i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	9.65770			0.377935			0.188967	−	0.981983i	$-0.439486\pi$
$653$	9.65770			0.377935			0.188967	+	0.981983i	$0.439486\pi$
$654$		0			0
$655$	1.42047			0.0555022
$656$		0			0
$657$		0			0
$658$		0			0
$659$	9.80353	−	16.9802i	0.381891	−	0.661455i	−0.609441	−	0.792831i	$-0.708606\pi$
$659$	9.80353	−	16.9802i	0.381891	−	0.661455i	0.991333	+	0.131376i	$0.0419396\pi$
$660$		0			0
$661$	5.13275	−	8.89018i	0.199641	−	0.345788i	−0.748771	−	0.662829i	$-0.769356\pi$
$661$	5.13275	−	8.89018i	0.199641	−	0.345788i	0.948412	+	0.317041i	$0.102689\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−0.433792	−	0.0417140i	−0.0168217	−	0.00161760i
$666$		0			0
$667$	−2.00641	+	3.47520i	−0.0776885	+	0.134560i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−1.18239	−	2.04797i	−0.0456458	−	0.0790608i
$672$		0			0
$673$	−17.1584	+	29.7191i	−0.661406	+	1.14559i	0.318840	+	0.947808i	$0.396707\pi$
$673$	−17.1584	+	29.7191i	−0.661406	+	1.14559i	−0.980246	+	0.197780i	$0.936627\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	3.73709	+	6.47283i	0.143628	+	0.248771i	0.928860	−	0.370430i	$-0.120790\pi$
$677$	3.73709	+	6.47283i	0.143628	+	0.248771i	−0.785232	+	0.619201i	$0.787456\pi$
$678$		0			0
$679$	−22.3149	−	2.14583i	−0.856367	−	0.0823493i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−18.1577	−	31.4501i	−0.694786	−	1.20340i	−0.970253	−	0.242094i	$-0.922166\pi$
$683$	−18.1577	−	31.4501i	−0.694786	−	1.20340i	0.275467	−	0.961310i	$-0.411167\pi$
$684$		0			0
$685$	−4.34125			−0.165871
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−19.8850	+	34.4417i	−0.757556	+	1.31213i
$690$		0			0
$691$	25.4812	+	44.1347i	0.969350	+	1.67896i	0.697444	+	0.716640i	$0.254321\pi$
$691$	25.4812	+	44.1347i	0.969350	+	1.67896i	0.271906	+	0.962324i	$0.412346\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	2.02755	+	3.51181i	0.0769092	+	0.133211i
$696$		0			0
$697$	−8.58566	+	14.8708i	−0.325205	+	0.563272i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−36.6075			−1.38265			−0.691324	−	0.722545i	$-0.742972\pi$
$701$	−36.6075			−1.38265			−0.691324	+	0.722545i	$0.742972\pi$
$702$		0			0
$703$	2.33182	+	4.03883i	0.0879463	+	0.152327i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−5.01971	−	11.0111i	−0.188786	−	0.414113i
$708$		0			0
$709$	2.93789	+	5.08858i	0.110335	+	0.191106i	0.915905	−	0.401394i	$-0.131474\pi$
$709$	2.93789	+	5.08858i	0.110335	+	0.191106i	−0.805570	+	0.592500i	$0.798141\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	4.36301	−	7.55695i	0.163396	−	0.283010i
$714$		0			0
$715$	0.370973	+	0.642545i	0.0138736	+	0.0240298i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−8.09642	+	14.0234i	−0.301945	+	0.522985i	−0.976577	−	0.215170i	$-0.930969\pi$
$719$	−8.09642	+	14.0234i	−0.301945	+	0.522985i	0.674631	+	0.738155i	$0.264303\pi$
$720$		0			0
$721$	−1.98328	−	4.35046i	−0.0738614	−	0.162020i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	2.33892	−	4.05112i	0.0868652	−	0.150455i
$726$		0			0
$727$	22.8771	−	39.6243i	0.848464	−	1.46958i	−0.0341138	−	0.999418i	$-0.510861\pi$
$727$	22.8771	−	39.6243i	0.848464	−	1.46958i	0.882578	−	0.470166i	$-0.155806\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	16.1113			0.595898
$732$		0			0
$733$	27.1833			1.00404			0.502019	−	0.864857i	$-0.332591\pi$
$733$	27.1833			1.00404			0.502019	+	0.864857i	$0.332591\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−4.13706	+	7.16560i	−0.152391	+	0.263948i
$738$		0			0
$739$	−12.1738	−	21.0856i	−0.447821	−	0.775648i	0.550423	−	0.834886i	$-0.314466\pi$
$739$	−12.1738	−	21.0856i	−0.447821	−	0.775648i	−0.998244	+	0.0592377i	$0.981133\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−0.0683178	−	0.118330i	−0.00250634	−	0.00434110i	0.864770	−	0.502169i	$-0.167464\pi$
$743$	−0.0683178	−	0.118330i	−0.00250634	−	0.00434110i	−0.867276	+	0.497828i	$0.834131\pi$
$744$		0			0
$745$	−3.65748			−0.134000
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−20.4466	−	1.96617i	−0.747104	−	0.0718424i
$750$		0			0
$751$	−7.42893			−0.271085			−0.135543	−	0.990772i	$-0.543278\pi$
$751$	−7.42893			−0.271085			−0.135543	+	0.990772i	$0.543278\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−0.878055			−0.0319557
$756$		0			0
$757$	−14.0794			−0.511723			−0.255861	−	0.966713i	$-0.582359\pi$
$757$	−14.0794			−0.511723			−0.255861	+	0.966713i	$0.582359\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−38.7232			−1.40372			−0.701858	−	0.712317i	$-0.747646\pi$
$761$	−38.7232			−1.40372			−0.701858	+	0.712317i	$0.747646\pi$
$762$		0			0
$763$	−3.29278	+	4.61755i	−0.119207	+	0.167167i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	16.0518			0.579597
$768$		0			0
$769$	5.14295	+	8.90786i	0.185460	+	0.321226i	0.943731	−	0.330713i	$-0.107289\pi$
$769$	5.14295	+	8.90786i	0.185460	+	0.321226i	−0.758272	+	0.651939i	$0.773956\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	22.6768	+	39.2773i	0.815627	+	1.41271i	0.908877	+	0.417064i	$0.136941\pi$
$773$	22.6768	+	39.2773i	0.815627	+	1.41271i	−0.0932501	+	0.995643i	$0.529726\pi$
$774$		0			0
$775$	−5.08606	+	8.80931i	−0.182697	+	0.316440i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−3.77852			−0.135380
$780$		0			0
$781$	3.74279			0.133927
$782$		0			0
$783$		0			0
$784$		0			0
$785$	1.36028	−	2.35607i	0.0485504	−	0.0840917i
$786$		0			0
$787$	13.0543	−	22.6108i	0.465337	−	0.805988i	−0.533879	−	0.845561i	$-0.679266\pi$
$787$	13.0543	−	22.6108i	0.465337	−	0.805988i	0.999217	+	0.0395728i	$0.0125997\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	24.3017	−	34.0788i	0.864067	−	1.21170i
$792$		0			0
$793$	−5.71735	+	9.90274i	−0.203029	+	0.351657i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	16.1618	+	27.9931i	0.572481	+	0.991567i	0.996310	+	0.0858244i	$0.0273524\pi$
$797$	16.1618	+	27.9931i	0.572481	+	0.991567i	−0.423829	+	0.905742i	$0.639314\pi$
$798$		0			0
$799$	−2.96930	+	5.14298i	−0.105046	+	0.181946i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	2.49620	+	4.32354i	0.0880889	+	0.152574i
$804$		0			0
$805$	1.56435	+	3.43151i	0.0551362	+	0.120945i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−22.4553	−	38.8938i	−0.789488	−	1.36743i	−0.926281	−	0.376833i	$-0.877013\pi$
$809$	−22.4553	−	38.8938i	−0.789488	−	1.36743i	0.136793	−	0.990600i	$-0.456320\pi$
$810$		0			0
$811$	−42.8204			−1.50363			−0.751813	−	0.659376i	$-0.770820\pi$
$811$	−42.8204			−1.50363			−0.751813	+	0.659376i	$0.770820\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	1.40607	−	2.43538i	0.0492524	−	0.0853077i
$816$		0			0
$817$	1.77263	+	3.07029i	0.0620166	+	0.107416i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−16.1100	−	27.9033i	−0.562242	−	0.973832i	−0.997300	−	0.0734300i	$-0.976605\pi$
$821$	−16.1100	−	27.9033i	−0.562242	−	0.973832i	0.435058	−	0.900402i	$-0.356728\pi$
$822$		0			0
$823$	2.19420	−	3.80047i	0.0764851	−	0.132476i	−0.825246	−	0.564773i	$-0.808964\pi$
$823$	2.19420	−	3.80047i	0.0764851	−	0.132476i	0.901731	+	0.432297i	$0.142297\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−42.0996			−1.46395			−0.731973	−	0.681333i	$-0.761400\pi$
$827$	−42.0996			−1.46395			−0.731973	+	0.681333i	$0.761400\pi$
$828$		0			0
$829$	−5.55838	−	9.62739i	−0.193050	−	0.334373i	0.753209	−	0.657781i	$-0.228505\pi$
$829$	−5.55838	−	9.62739i	−0.193050	−	0.334373i	−0.946260	+	0.323408i	$0.895171\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−15.1198	−	2.93501i	−0.523869	−	0.101692i
$834$		0			0
$835$	−3.05970	−	5.29956i	−0.105885	−	0.183399i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−27.2669	+	47.2277i	−0.941360	+	1.63048i	−0.178479	+	0.983944i	$0.557118\pi$
$839$	−27.2669	+	47.2277i	−0.941360	+	1.63048i	−0.762881	+	0.646539i	$0.776216\pi$
$840$		0			0
$841$	14.0414	+	24.3204i	0.484185	+	0.838633i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−0.417494	+	0.723120i	−0.0143622	+	0.0248761i
$846$		0			0
$847$	11.5773	+	25.3955i	0.397800	+	0.872600i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	20.1791	−	34.9512i	0.691731	−	1.19811i
$852$		0			0
$853$	−11.3669	+	19.6880i	−0.389194	+	0.674105i	−0.992341	−	0.123526i	$-0.960580\pi$
$853$	−11.3669	+	19.6880i	−0.389194	+	0.674105i	0.603147	+	0.797630i	$0.293913\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−11.2386			−0.383902			−0.191951	−	0.981405i	$-0.561481\pi$
$857$	−11.2386			−0.383902			−0.191951	+	0.981405i	$0.561481\pi$
$858$		0			0
$859$	−50.8049			−1.73344			−0.866720	−	0.498795i	$-0.833776\pi$
$859$	−50.8049			−1.73344			−0.866720	+	0.498795i	$0.833776\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−0.340985	+	0.590603i	−0.0116073	+	0.0201044i	−0.871771	−	0.489914i	$-0.837028\pi$
$863$	−0.340985	+	0.590603i	−0.0116073	+	0.0201044i	0.860163	+	0.510018i	$0.170361\pi$
$864$		0			0
$865$	2.89141	+	5.00807i	0.0983110	+	0.170280i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	3.36222	+	5.82353i	0.114055	+	0.197550i
$870$		0			0
$871$	40.0087			1.35564
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−3.69042	−	8.09516i	−0.124759	−	0.273667i
$876$		0			0
$877$	−25.3190			−0.854961			−0.427480	−	0.904025i	$-0.640599\pi$
$877$	−25.3190			−0.854961			−0.427480	+	0.904025i	$0.640599\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	30.9482			1.04267			0.521335	−	0.853352i	$-0.325434\pi$
$881$	30.9482			1.04267			0.521335	+	0.853352i	$0.325434\pi$
$882$		0			0
$883$	−9.48501			−0.319196			−0.159598	−	0.987182i	$-0.551020\pi$
$883$	−9.48501			−0.319196			−0.159598	+	0.987182i	$0.551020\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	3.94938			0.132607			0.0663036	−	0.997799i	$-0.478879\pi$
$887$	3.94938			0.132607			0.0663036	+	0.997799i	$0.478879\pi$
$888$		0			0
$889$	−15.2352	−	33.4195i	−0.510974	−	1.12085i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−1.30678			−0.0437297
$894$		0			0
$895$	3.28318	+	5.68663i	0.109745	+	0.190083i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	0.997305	+	1.72738i	0.0332620	+	0.0576115i
$900$		0			0
$901$	−13.4731	+	23.3361i	−0.448854	+	0.777439i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−7.47217			−0.248383
$906$		0			0
$907$	33.5061			1.11255			0.556276	−	0.830998i	$-0.312230\pi$
$907$	33.5061			1.11255			0.556276	+	0.830998i	$0.312230\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	5.26585	−	9.12072i	0.174465	−	0.302183i	−0.765511	−	0.643423i	$-0.777514\pi$
$911$	5.26585	−	9.12072i	0.174465	−	0.302183i	0.939976	+	0.341240i	$0.110847\pi$
$912$		0			0
$913$	−1.66135	+	2.87754i	−0.0549826	+	0.0952326i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	4.58240	+	10.0518i	0.151324	+	0.331939i
$918$		0			0
$919$	−1.81600	+	3.14540i	−0.0599042	+	0.103757i	−0.894422	−	0.447224i	$-0.852413\pi$
$919$	−1.81600	+	3.14540i	−0.0599042	+	0.103757i	0.834518	+	0.550981i	$0.185746\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−9.04894	−	15.6732i	−0.297850	−	0.515891i
$924$		0			0
$925$	−23.5232	+	40.7435i	−0.773440	+	1.33964i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	6.80291	+	11.7830i	0.223196	+	0.386587i	0.955777	−	0.294093i	$-0.0950176\pi$
$929$	6.80291	+	11.7830i	0.223196	+	0.386587i	−0.732581	+	0.680680i	$0.761684\pi$
$930$		0			0
$931$	−1.10422	−	3.20426i	−0.0361894	−	0.105015i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	0.251354	+	0.435358i	0.00822016	+	0.0142377i
$936$		0			0
$937$	9.98770			0.326284			0.163142	−	0.986603i	$-0.447837\pi$
$937$	9.98770			0.326284			0.163142	+	0.986603i	$0.447837\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	17.3105	−	29.9826i	0.564305	−	0.977405i	−0.432809	−	0.901486i	$-0.642477\pi$
$941$	17.3105	−	29.9826i	0.564305	−	0.977405i	0.997114	−	0.0759195i	$-0.0241892\pi$
$942$		0			0
$943$	16.3493	+	28.3178i	0.532405	+	0.922153i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−24.6085	−	42.6232i	−0.799670	−	1.38507i	−0.919831	−	0.392315i	$-0.871674\pi$
$947$	−24.6085	−	42.6232i	−0.799670	−	1.38507i	0.120161	−	0.992754i	$-0.461659\pi$
$948$		0			0
$949$	12.0701	−	20.9061i	0.391813	−	0.678640i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−14.2310			−0.460987			−0.230494	−	0.973074i	$-0.574034\pi$
$953$	−14.2310			−0.460987			−0.230494	+	0.973074i	$0.574034\pi$
$954$		0			0
$955$	1.13243	+	1.96143i	0.0366446	+	0.0634704i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−14.0048	−	30.7204i	−0.452238	−	0.992013i
$960$		0			0
$961$	13.3313	+	23.0905i	0.430043	+	0.744856i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	1.07998	−	1.87057i	0.0347657	−	0.0602159i
$966$		0			0
$967$	19.4246	+	33.6443i	0.624652	+	1.08193i	0.988608	+	0.150513i	$0.0480925\pi$
$967$	19.4246	+	33.6443i	0.624652	+	1.08193i	−0.363956	+	0.931416i	$0.618574\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−4.13629	+	7.16427i	−0.132740	+	0.229912i	−0.924732	−	0.380619i	$-0.875711\pi$
$971$	−4.13629	+	7.16427i	−0.132740	+	0.229912i	0.791992	+	0.610532i	$0.209044\pi$
$972$		0			0
$973$	−18.3102	+	25.6768i	−0.586997	+	0.823159i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	3.68736	−	6.38670i	0.117969	−	0.204329i	−0.800994	−	0.598673i	$-0.795695\pi$
$977$	3.68736	−	6.38670i	0.117969	−	0.204329i	0.918963	+	0.394344i	$0.129028\pi$
$978$		0			0
$979$	−5.72312	+	9.91273i	−0.182912	+	0.316812i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−4.78363			−0.152574			−0.0762870	−	0.997086i	$-0.524307\pi$
$983$	−4.78363			−0.152574			−0.0762870	+	0.997086i	$0.524307\pi$
$984$		0			0
$985$	8.10057			0.258106
$986$		0			0
$987$		0			0
$988$		0			0
$989$	15.3400	−	26.5697i	0.487784	−	0.844866i
$990$		0			0
$991$	−18.4932	−	32.0312i	−0.587456	−	1.01750i	−0.994564	−	0.104124i	$-0.966796\pi$
$991$	−18.4932	−	32.0312i	−0.587456	−	1.01750i	0.407108	−	0.913380i	$-0.366537\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−3.56430	−	6.17356i	−0.112996	−	0.195715i
$996$		0			0
$997$	48.6570			1.54098			0.770491	−	0.637451i	$-0.220011\pi$
$997$	48.6570			1.54098			0.770491	+	0.637451i	$0.220011\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.t.l.289.5		22
3.2	odd	2		1008.2.t.k.961.1		22
4.3	odd	2		1512.2.t.d.289.5		22
7.4	even	3		3024.2.q.k.2881.7		22
9.4	even	3		3024.2.q.k.2305.7		22
9.5	odd	6		1008.2.q.k.625.8		22
12.11	even	2		504.2.t.d.457.11	yes	22
21.11	odd	6		1008.2.q.k.529.8		22
28.11	odd	6		1512.2.q.c.1369.7		22
36.23	even	6		504.2.q.d.121.4	yes	22
36.31	odd	6		1512.2.q.c.793.7		22
63.4	even	3	inner	3024.2.t.l.1873.5		22
63.32	odd	6		1008.2.t.k.193.1		22
84.11	even	6		504.2.q.d.25.4	✓	22
252.67	odd	6		1512.2.t.d.361.5		22
252.95	even	6		504.2.t.d.193.11	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.d.25.4	✓	22	84.11	even	6
504.2.q.d.121.4	yes	22	36.23	even	6
504.2.t.d.193.11	yes	22	252.95	even	6
504.2.t.d.457.11	yes	22	12.11	even	2
1008.2.q.k.529.8		22	21.11	odd	6
1008.2.q.k.625.8		22	9.5	odd	6
1008.2.t.k.193.1		22	63.32	odd	6
1008.2.t.k.961.1		22	3.2	odd	2
1512.2.q.c.793.7		22	36.31	odd	6
1512.2.q.c.1369.7		22	28.11	odd	6
1512.2.t.d.289.5		22	4.3	odd	2
1512.2.t.d.361.5		22	252.67	odd	6
3024.2.q.k.2305.7		22	9.4	even	3
3024.2.q.k.2881.7		22	7.4	even	3
3024.2.t.l.289.5		22	1.1	even	1	trivial
3024.2.t.l.1873.5		22	63.4	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-0.340200 q^{5} +(-1.09748 - 2.40739i) q^{7} +O(q^{10})\)	\(q-0.340200 q^{5} +(-1.09748 - 2.40739i) q^{7} -0.671588 q^{11} +(1.62370 + 2.81233i) q^{13} +(1.10014 + 1.90550i) q^{17} +(-0.242085 + 0.419303i) q^{19} +4.18990 q^{23} -4.88426 q^{25} +(-0.478868 + 0.829424i) q^{29} +(1.04132 - 1.80361i) q^{31} +(0.373363 + 0.818995i) q^{35} +(4.81613 - 8.34178i) q^{37} +(3.90207 + 6.75858i) q^{41} +(3.66119 - 6.34136i) q^{43} +(1.34951 + 2.33742i) q^{47} +(-4.59108 + 5.28413i) q^{49} +(6.12335 + 10.6059i) q^{53} +0.228474 q^{55} +(2.47148 - 4.28074i) q^{59} +(1.76059 + 3.04944i) q^{61} +(-0.552383 - 0.956755i) q^{65} +(6.16012 - 10.6696i) q^{67} -5.57304 q^{71} +(-3.71686 - 6.43779i) q^{73} +(0.737054 + 1.61677i) q^{77} +(-5.00637 - 8.67128i) q^{79} +(2.47376 - 4.28468i) q^{83} +(-0.374269 - 0.648252i) q^{85} +(8.52177 - 14.7601i) q^{89} +(4.98840 - 6.99536i) q^{91} +(0.0823572 - 0.142647i) q^{95} +(4.23657 - 7.33795i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 6 q^{5} - 7 q^{7}+O(q^{10}) \) 22 * q + 6 * q^5 - 7 * q^7	\( 22 q + 6 q^{5} - 7 q^{7} + 6 q^{11} - 3 q^{13} - 7 q^{17} + q^{19} - 4 q^{23} + 20 q^{25} - 9 q^{29} + 4 q^{31} + 14 q^{35} + 2 q^{37} - 16 q^{41} + 5 q^{47} - 15 q^{49} - 11 q^{53} - 22 q^{55} - 19 q^{59} - 13 q^{61} - 13 q^{65} - 26 q^{67} - 48 q^{71} - 35 q^{73} + 4 q^{77} - 10 q^{79} - 28 q^{83} - 20 q^{85} - 6 q^{89} + 37 q^{91} + 12 q^{95} - 29 q^{97}+O(q^{100}) \) 22 * q + 6 * q^5 - 7 * q^7 + 6 * q^11 - 3 * q^13 - 7 * q^17 + q^19 - 4 * q^23 + 20 * q^25 - 9 * q^29 + 4 * q^31 + 14 * q^35 + 2 * q^37 - 16 * q^41 + 5 * q^47 - 15 * q^49 - 11 * q^53 - 22 * q^55 - 19 * q^59 - 13 * q^61 - 13 * q^65 - 26 * q^67 - 48 * q^71 - 35 * q^73 + 4 * q^77 - 10 * q^79 - 28 * q^83 - 20 * q^85 - 6 * q^89 + 37 * q^91 + 12 * q^95 - 29 * q^97

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