LMFDB - Embedded newform 3024.2.t.l.1873.4

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			1873.4
Character	$\chi$	$=$	3024.1873
Dual form			3024.2.t.l.289.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.68316 q^{5} +(-0.960133 - 2.46539i) q^{7} +O(q^{10})$	$q-1.68316 q^{5} +(-0.960133 - 2.46539i) q^{7} +1.24498 q^{11} +(1.96039 - 3.39550i) q^{13} +(1.62691 - 2.81788i) q^{17} +(-2.36192 - 4.09097i) q^{19} -0.398135 q^{23} -2.16699 q^{25} +(3.19896 + 5.54076i) q^{29} +(-0.289184 - 0.500881i) q^{31} +(1.61605 + 4.14963i) q^{35} +(2.72146 + 4.71371i) q^{37} +(-4.20216 + 7.27836i) q^{41} +(-2.46299 - 4.26603i) q^{43} +(0.212595 - 0.368225i) q^{47} +(-5.15629 + 4.73420i) q^{49} +(0.466315 - 0.807681i) q^{53} -2.09550 q^{55} +(-3.02527 - 5.23992i) q^{59} +(-5.10459 + 8.84140i) q^{61} +(-3.29965 + 5.71516i) q^{65} +(-4.70976 - 8.15754i) q^{67} +8.46617 q^{71} +(6.82340 - 11.8185i) q^{73} +(-1.19535 - 3.06936i) q^{77} +(-2.76670 + 4.79207i) q^{79} +(-8.03669 - 13.9199i) q^{83} +(-2.73833 + 4.74293i) q^{85} +(6.03776 + 10.4577i) q^{89} +(-10.2535 - 1.57300i) q^{91} +(3.97549 + 6.88575i) q^{95} +(-5.86046 - 10.1506i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times$.

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

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
$5$	−1.68316			−0.752730			−0.376365	−	0.926471i	$-0.622826\pi$
$5$	−1.68316			−0.752730			−0.376365	+	0.926471i	$0.622826\pi$
$6$		0			0
$7$	−0.960133	−	2.46539i	−0.362896	−	0.931830i
$7$	−0.960133	−	2.46539i	−0.362896	−	0.931830i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.24498			0.375376			0.187688	−	0.982229i	$-0.439901\pi$
$11$	1.24498			0.375376			0.187688	+	0.982229i	$0.439901\pi$
$12$		0			0
$13$	1.96039	−	3.39550i	0.543715	−	0.941743i	−0.454971	−	0.890506i	$-0.650350\pi$
$13$	1.96039	−	3.39550i	0.543715	−	0.941743i	0.998687	−	0.0512366i	$-0.0163162\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.62691	−	2.81788i	0.394582	−	0.683437i	−0.598465	−	0.801149i	$-0.704223\pi$
$17$	1.62691	−	2.81788i	0.394582	−	0.683437i	0.993048	+	0.117712i	$0.0375559\pi$
$18$		0			0
$19$	−2.36192	−	4.09097i	−0.541863	−	0.938534i	−0.998797	−	0.0490333i	$-0.984386\pi$
$19$	−2.36192	−	4.09097i	−0.541863	−	0.938534i	0.456935	−	0.889500i	$-0.348947\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.398135			−0.0830170			−0.0415085	−	0.999138i	$-0.513216\pi$
$23$	−0.398135			−0.0830170			−0.0415085	+	0.999138i	$0.513216\pi$
$24$		0			0
$25$	−2.16699			−0.433397
$26$		0			0
$27$		0			0
$28$		0			0
$29$	3.19896	+	5.54076i	0.594032	+	1.02889i	0.993683	+	0.112226i	$0.0357979\pi$
$29$	3.19896	+	5.54076i	0.594032	+	1.02889i	−0.399651	+	0.916667i	$0.630869\pi$
$30$		0			0
$31$	−0.289184	−	0.500881i	−0.0519389	−	0.0899608i	0.838887	−	0.544306i	$-0.183207\pi$
$31$	−0.289184	−	0.500881i	−0.0519389	−	0.0899608i	−0.890826	+	0.454345i	$0.849873\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	1.61605	+	4.14963i	0.273163	+	0.701416i
$36$		0			0
$37$	2.72146	+	4.71371i	0.447405	+	0.774928i	0.998216	−	0.0597015i	$-0.0190149\pi$
$37$	2.72146	+	4.71371i	0.447405	+	0.774928i	−0.550811	+	0.834630i	$0.685682\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−4.20216	+	7.27836i	−0.656267	+	1.13669i	0.325307	+	0.945608i	$0.394532\pi$
$41$	−4.20216	+	7.27836i	−0.656267	+	1.13669i	−0.981574	+	0.191080i	$0.938801\pi$
$42$		0			0
$43$	−2.46299	−	4.26603i	−0.375603	−	0.650563i	0.614814	−	0.788672i	$-0.289231\pi$
$43$	−2.46299	−	4.26603i	−0.375603	−	0.650563i	−0.990417	+	0.138109i	$0.955898\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	0.212595	−	0.368225i	0.0310101	−	0.0537112i	−0.850104	−	0.526615i	$-0.823461\pi$
$47$	0.212595	−	0.368225i	0.0310101	−	0.0537112i	0.881114	+	0.472904i	$0.156794\pi$
$48$		0			0
$49$	−5.15629	+	4.73420i	−0.736613	+	0.676315i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	0.466315	−	0.807681i	0.0640533	−	0.110944i	−0.832220	−	0.554445i	$-0.812931\pi$
$53$	0.466315	−	0.807681i	0.0640533	−	0.110944i	0.896274	+	0.443501i	$0.146264\pi$
$54$		0			0
$55$	−2.09550			−0.282557
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−3.02527	−	5.23992i	−0.393856	−	0.682179i	0.599098	−	0.800676i	$-0.295526\pi$
$59$	−3.02527	−	5.23992i	−0.393856	−	0.682179i	−0.992954	+	0.118496i	$0.962193\pi$
$60$		0			0
$61$	−5.10459	+	8.84140i	−0.653575	+	1.13203i	0.328674	+	0.944444i	$0.393398\pi$
$61$	−5.10459	+	8.84140i	−0.653575	+	1.13203i	−0.982249	+	0.187582i	$0.939935\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−3.29965	+	5.71516i	−0.409271	+	0.708878i
$66$		0			0
$67$	−4.70976	−	8.15754i	−0.575389	−	0.996602i	−0.995999	−	0.0893612i	$-0.971517\pi$
$67$	−4.70976	−	8.15754i	−0.575389	−	0.996602i	0.420611	−	0.907241i	$-0.361816\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	8.46617			1.00475			0.502375	−	0.864650i	$-0.332460\pi$
$71$	8.46617			1.00475			0.502375	+	0.864650i	$0.332460\pi$
$72$		0			0
$73$	6.82340	−	11.8185i	0.798619	−	1.38325i	−0.121897	−	0.992543i	$-0.538898\pi$
$73$	6.82340	−	11.8185i	0.798619	−	1.38325i	0.920516	−	0.390705i	$-0.127769\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.19535	−	3.06936i	−0.136222	−	0.349786i
$78$		0			0
$79$	−2.76670	+	4.79207i	−0.311278	+	0.539149i	−0.978639	−	0.205585i	$-0.934090\pi$
$79$	−2.76670	+	4.79207i	−0.311278	+	0.539149i	0.667361	+	0.744734i	$0.267424\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−8.03669	−	13.9199i	−0.882141	−	1.52791i	−0.848956	−	0.528463i	$-0.822768\pi$
$83$	−8.03669	−	13.9199i	−0.882141	−	1.52791i	−0.0331848	−	0.999449i	$-0.510565\pi$
$84$		0			0
$85$	−2.73833	+	4.74293i	−0.297014	+	0.514444i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	6.03776	+	10.4577i	0.640001	+	1.10851i	0.985432	+	0.170070i	$0.0543993\pi$
$89$	6.03776	+	10.4577i	0.640001	+	1.10851i	−0.345431	+	0.938444i	$0.612267\pi$
$90$		0			0
$91$	−10.2535	−	1.57300i	−1.07486	−	0.164895i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	3.97549	+	6.88575i	0.407876	+	0.706463i
$96$		0			0
$97$	−5.86046	−	10.1506i	−0.595040	−	1.03064i	−0.993541	−	0.113472i	$-0.963803\pi$
$97$	−5.86046	−	10.1506i	−0.595040	−	1.03064i	0.398501	−	0.917168i	$-0.369530\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−5.40605			−0.537922			−0.268961	−	0.963151i	$-0.586680\pi$
$101$	−5.40605			−0.537922			−0.268961	+	0.963151i	$0.586680\pi$
$102$		0			0
$103$	−14.6204			−1.44059			−0.720294	−	0.693669i	$-0.755993\pi$
$103$	−14.6204			−1.44059			−0.720294	+	0.693669i	$0.755993\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−3.40209	−	5.89259i	−0.328892	−	0.569658i	0.653400	−	0.757013i	$-0.273342\pi$
$107$	−3.40209	−	5.89259i	−0.328892	−	0.569658i	−0.982292	+	0.187354i	$0.940009\pi$
$108$		0			0
$109$	8.37636	−	14.5083i	0.802310	−	1.38964i	−0.115783	−	0.993275i	$-0.536938\pi$
$109$	8.37636	−	14.5083i	0.802310	−	1.38964i	0.918092	−	0.396367i	$-0.129729\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−6.77154	+	11.7287i	−0.637013	+	1.10334i	0.349072	+	0.937096i	$0.386497\pi$
$113$	−6.77154	+	11.7287i	−0.637013	+	1.10334i	−0.986085	+	0.166243i	$0.946836\pi$
$114$		0			0
$115$	0.670124			0.0624894
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−8.50922	−	1.30541i	−0.780039	−	0.119667i
$120$		0			0
$121$	−9.45002			−0.859093
$122$		0			0
$123$		0			0
$124$		0			0
$125$	12.0632			1.07896
$126$		0			0
$127$	−10.5904			−0.939748			−0.469874	−	0.882734i	$-0.655701\pi$
$127$	−10.5904			−0.939748			−0.469874	+	0.882734i	$0.655701\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−22.3638			−1.95394			−0.976968	−	0.213387i	$-0.931551\pi$
$131$	−22.3638			−1.95394			−0.976968	+	0.213387i	$0.931551\pi$
$132$		0			0
$133$	−7.81808	+	9.75094i	−0.677914	+	0.845514i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−17.9540			−1.53391			−0.766957	−	0.641699i	$-0.778230\pi$
$137$	−17.9540			−1.53391			−0.766957	+	0.641699i	$0.778230\pi$
$138$		0			0
$139$	−0.570825	+	0.988699i	−0.0484168	+	0.0838603i	−0.889218	−	0.457483i	$-0.848751\pi$
$139$	−0.570825	+	0.988699i	−0.0484168	+	0.0838603i	0.840801	+	0.541344i	$0.182084\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	2.44065	−	4.22733i	0.204098	−	0.353507i
$144$		0			0
$145$	−5.38434	−	9.32596i	−0.447145	−	0.774479i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−17.6583			−1.44663			−0.723313	−	0.690521i	$-0.757381\pi$
$149$	−17.6583			−1.44663			−0.723313	+	0.690521i	$0.757381\pi$
$150$		0			0
$151$	15.2354			1.23984			0.619919	−	0.784666i	$-0.287166\pi$
$151$	15.2354			1.23984			0.619919	+	0.784666i	$0.287166\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	0.486741	+	0.843060i	0.0390960	+	0.0677162i
$156$		0			0
$157$	6.81439	+	11.8029i	0.543847	+	0.941971i	0.998678	+	0.0513933i	$0.0163662\pi$
$157$	6.81439	+	11.8029i	0.543847	+	0.941971i	−0.454831	+	0.890578i	$0.650300\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	0.382263	+	0.981559i	0.0301265	+	0.0773577i
$162$		0			0
$163$	4.04726	+	7.01005i	0.317006	+	0.549070i	0.979862	−	0.199677i	$-0.0639893\pi$
$163$	4.04726	+	7.01005i	0.317006	+	0.549070i	−0.662856	+	0.748747i	$0.730656\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−2.07739	+	3.59814i	−0.160753	+	0.278433i	−0.935139	−	0.354281i	$-0.884726\pi$
$167$	−2.07739	+	3.59814i	−0.160753	+	0.278433i	0.774386	+	0.632714i	$0.218059\pi$
$168$		0			0
$169$	−1.18629	−	2.05471i	−0.0912529	−	0.158055i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	6.91730	−	11.9811i	0.525913	−	0.910907i	−0.473632	−	0.880723i	$-0.657057\pi$
$173$	6.91730	−	11.9811i	0.525913	−	0.910907i	0.999544	−	0.0301845i	$-0.00960947\pi$
$174$		0			0
$175$	2.08059	+	5.34247i	0.157278	+	0.403852i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−4.71167	+	8.16084i	−0.352166	+	0.609970i	−0.986629	−	0.162984i	$-0.947888\pi$
$179$	−4.71167	+	8.16084i	−0.352166	+	0.609970i	0.634462	+	0.772954i	$0.281222\pi$
$180$		0			0
$181$	1.32133			0.0982136			0.0491068	−	0.998794i	$-0.484363\pi$
$181$	1.32133			0.0982136			0.0491068	+	0.998794i	$0.484363\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−4.58064	−	7.93390i	−0.336775	−	0.583312i
$186$		0			0
$187$	2.02546	−	3.50821i	0.148117	−	0.256546i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−8.14271	+	14.1036i	−0.589186	+	1.02050i	0.405153	+	0.914249i	$0.367218\pi$
$191$	−8.14271	+	14.1036i	−0.589186	+	1.02050i	−0.994339	+	0.106251i	$0.966115\pi$
$192$		0			0
$193$	−1.28077	−	2.21837i	−0.0921921	−	0.159681i	0.816241	−	0.577711i	$-0.196054\pi$
$193$	−1.28077	−	2.21837i	−0.0921921	−	0.159681i	−0.908433	+	0.418030i	$0.862721\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−21.6916			−1.54546			−0.772730	−	0.634735i	$-0.781109\pi$
$197$	−21.6916			−1.54546			−0.772730	+	0.634735i	$0.781109\pi$
$198$		0			0
$199$	5.59684	−	9.69402i	0.396750	−	0.687191i	−0.596573	−	0.802559i	$-0.703471\pi$
$199$	5.59684	−	9.69402i	0.396750	−	0.687191i	0.993323	+	0.115368i	$0.0368047\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	10.5887	−	13.2065i	0.743181	−	0.926917i
$204$		0			0
$205$	7.07289	−	12.2506i	0.493992	−	0.855620i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−2.94055	−	5.09318i	−0.203402	−	0.352303i
$210$		0			0
$211$	14.1807	−	24.5616i	0.976237	−	1.69089i	0.300444	−	0.953799i	$-0.402865\pi$
$211$	14.1807	−	24.5616i	0.976237	−	1.69089i	0.675793	−	0.737092i	$-0.263801\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	4.14560	+	7.18039i	0.282728	+	0.489699i
$216$		0			0
$217$	−0.957211	+	1.19386i	−0.0649797	+	0.0810446i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−6.37875	−	11.0483i	−0.429081	−	0.743190i
$222$		0			0
$223$	12.6962	+	21.9905i	0.850202	+	1.47259i	0.881026	+	0.473068i	$0.156853\pi$
$223$	12.6962	+	21.9905i	0.850202	+	1.47259i	−0.0308242	+	0.999525i	$0.509813\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	4.62860			0.307211			0.153606	−	0.988132i	$-0.450911\pi$
$227$	4.62860			0.307211			0.153606	+	0.988132i	$0.450911\pi$
$228$		0			0
$229$	2.32592			0.153701			0.0768506	−	0.997043i	$-0.475514\pi$
$229$	2.32592			0.153701			0.0768506	+	0.997043i	$0.475514\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	6.37989	+	11.0503i	0.417960	+	0.723929i	0.995734	−	0.0922683i	$-0.0294117\pi$
$233$	6.37989	+	11.0503i	0.417960	+	0.723929i	−0.577774	+	0.816197i	$0.696078\pi$
$234$		0			0
$235$	−0.357830	+	0.619780i	−0.0233423	+	0.0404300i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−11.0492	+	19.1378i	−0.714714	+	1.23792i	0.248355	+	0.968669i	$0.420110\pi$
$239$	−11.0492	+	19.1378i	−0.714714	+	1.23792i	−0.963070	+	0.269252i	$0.913223\pi$
$240$		0			0
$241$	20.0177			1.28945			0.644726	−	0.764414i	$-0.276972\pi$
$241$	20.0177			1.28945			0.644726	+	0.764414i	$0.276972\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	8.67884	−	7.96840i	0.554471	−	0.509082i
$246$		0			0
$247$	−18.5212			−1.17848
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−2.12390			−0.134059			−0.0670297	−	0.997751i	$-0.521352\pi$
$251$	−2.12390			−0.134059			−0.0670297	+	0.997751i	$0.521352\pi$
$252$		0			0
$253$	−0.495671			−0.0311625
$254$		0			0
$255$		0			0
$256$		0			0
$257$	12.7630			0.796134			0.398067	−	0.917356i	$-0.369681\pi$
$257$	12.7630			0.796134			0.398067	+	0.917356i	$0.369681\pi$
$258$		0			0
$259$	9.00816	−	11.2352i	0.559740	−	0.698124i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−11.0686			−0.682522			−0.341261	−	0.939969i	$-0.610854\pi$
$263$	−11.0686			−0.682522			−0.341261	+	0.939969i	$0.610854\pi$
$264$		0			0
$265$	−0.784881	+	1.35945i	−0.0482148	+	0.0835105i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	1.77479	−	3.07403i	0.108211	−	0.187427i	−0.806835	−	0.590777i	$-0.798821\pi$
$269$	1.77479	−	3.07403i	0.108211	−	0.187427i	0.915046	+	0.403351i	$0.132154\pi$
$270$		0			0
$271$	0.687666	+	1.19107i	0.0417727	+	0.0723525i	0.886156	−	0.463387i	$-0.153366\pi$
$271$	0.687666	+	1.19107i	0.0417727	+	0.0723525i	−0.844383	+	0.535740i	$0.820033\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−2.69786			−0.162687
$276$		0			0
$277$	−29.1617			−1.75216			−0.876079	−	0.482168i	$-0.839849\pi$
$277$	−29.1617			−1.75216			−0.876079	+	0.482168i	$0.839849\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−6.29603	−	10.9050i	−0.375590	−	0.650540i	0.614826	−	0.788663i	$-0.289226\pi$
$281$	−6.29603	−	10.9050i	−0.375590	−	0.650540i	−0.990415	+	0.138123i	$0.955893\pi$
$282$		0			0
$283$	−4.73028	−	8.19309i	−0.281186	−	0.487029i	0.690491	−	0.723341i	$-0.257394\pi$
$283$	−4.73028	−	8.19309i	−0.281186	−	0.487029i	−0.971677	+	0.236312i	$0.924061\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	21.9786	+	3.37178i	1.29736	+	0.199030i
$288$		0			0
$289$	3.20636	+	5.55358i	0.188609	+	0.326681i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	8.32726	−	14.4232i	0.486484	−	0.842614i	−0.513396	−	0.858152i	$-0.671613\pi$
$293$	8.32726	−	14.4232i	0.486484	−	0.842614i	0.999879	+	0.0155376i	$0.00494598\pi$
$294$		0			0
$295$	5.09200	+	8.81960i	0.296468	+	0.513497i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−0.780502	+	1.35187i	−0.0451376	+	0.0781806i
$300$		0			0
$301$	−8.15262	+	10.1682i	−0.469909	+	0.586085i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	8.59181	−	14.8815i	0.491966	−	0.852110i
$306$		0			0
$307$	9.55966			0.545599			0.272799	−	0.962071i	$-0.412051\pi$
$307$	9.55966			0.545599			0.272799	+	0.962071i	$0.412051\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−13.1851	−	22.8373i	−0.747658	−	1.29498i	−0.948943	−	0.315449i	$-0.897845\pi$
$311$	−13.1851	−	22.8373i	−0.747658	−	1.29498i	0.201284	−	0.979533i	$-0.435488\pi$
$312$		0			0
$313$	6.35091	−	11.0001i	0.358975	−	0.621762i	−0.628815	−	0.777555i	$-0.716460\pi$
$313$	6.35091	−	11.0001i	0.358975	−	0.621762i	0.987790	+	0.155792i	$0.0497931\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	0.0165768	−	0.0287119i	0.000931047	−	0.00161262i	−0.865560	−	0.500806i	$-0.833037\pi$
$317$	0.0165768	−	0.0287119i	0.000931047	−	0.00161262i	0.866491	+	0.499193i	$0.166370\pi$
$318$		0			0
$319$	3.98264	+	6.89813i	0.222985	+	0.386221i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−15.3705			−0.855238
$324$		0			0
$325$	−4.24815	+	7.35801i	−0.235645	+	0.408149i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−1.11194	−	0.170584i	−0.0613031	−	0.00940461i
$330$		0			0
$331$	−2.42694	+	4.20358i	−0.133397	+	0.231050i	−0.924984	−	0.380006i	$-0.875922\pi$
$331$	−2.42694	+	4.20358i	−0.133397	+	0.231050i	0.791587	+	0.611056i	$0.209255\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	7.92726	+	13.7304i	0.433112	+	0.750173i
$336$		0			0
$337$	−4.32200	+	7.48592i	−0.235434	+	0.407784i	−0.959399	−	0.282053i	$-0.908985\pi$
$337$	−4.32200	+	7.48592i	−0.235434	+	0.407784i	0.723965	+	0.689837i	$0.242318\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−0.360028	−	0.623586i	−0.0194966	−	0.0337691i
$342$		0			0
$343$	16.6224	+	8.16680i	0.897524	+	0.440966i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	11.6116	+	20.1119i	0.623344	+	1.07966i	0.988859	+	0.148858i	$0.0475596\pi$
$347$	11.6116	+	20.1119i	0.623344	+	1.07966i	−0.365515	+	0.930806i	$0.619107\pi$
$348$		0			0
$349$	−3.76025	−	6.51295i	−0.201282	−	0.348630i	0.747660	−	0.664082i	$-0.231177\pi$
$349$	−3.76025	−	6.51295i	−0.201282	−	0.348630i	−0.948942	+	0.315452i	$0.897844\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	0.919056			0.0489164			0.0244582	−	0.999701i	$-0.492214\pi$
$353$	0.919056			0.0489164			0.0244582	+	0.999701i	$0.492214\pi$
$354$		0			0
$355$	−14.2499			−0.756306
$356$		0			0
$357$		0			0
$358$		0			0
$359$	8.24300	+	14.2773i	0.435049	+	0.753527i	0.997300	−	0.0734398i	$-0.0233977\pi$
$359$	8.24300	+	14.2773i	0.435049	+	0.753527i	−0.562251	+	0.826967i	$0.690064\pi$
$360$		0			0
$361$	−1.65737	+	2.87066i	−0.0872302	+	0.151087i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−11.4848	+	19.8923i	−0.601144	+	1.04121i
$366$		0			0
$367$	12.6784			0.661808			0.330904	−	0.943664i	$-0.392646\pi$
$367$	12.6784			0.661808			0.330904	+	0.943664i	$0.392646\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−2.43897	−	0.374167i	−0.126625	−	0.0194258i
$372$		0			0
$373$	22.6821			1.17443			0.587217	−	0.809430i	$-0.300224\pi$
$373$	22.6821			1.17443			0.587217	+	0.809430i	$0.300224\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	25.0849			1.29194
$378$		0			0
$379$	−19.0925			−0.980717			−0.490358	−	0.871521i	$-0.663134\pi$
$379$	−19.0925			−0.980717			−0.490358	+	0.871521i	$0.663134\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−6.07925			−0.310635			−0.155318	−	0.987865i	$-0.549640\pi$
$383$	−6.07925			−0.310635			−0.155318	+	0.987865i	$0.549640\pi$
$384$		0			0
$385$	2.01195	+	5.16621i	0.102539	+	0.263295i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	0.631562			0.0320214			0.0160107	−	0.999872i	$-0.494903\pi$
$389$	0.631562			0.0320214			0.0160107	+	0.999872i	$0.494903\pi$
$390$		0			0
$391$	−0.647728	+	1.12190i	−0.0327570	+	0.0567368i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	4.65679	−	8.06579i	0.234308	−	0.405834i
$396$		0			0
$397$	−18.1830	−	31.4939i	−0.912578	−	1.58063i	−0.810408	−	0.585865i	$-0.800755\pi$
$397$	−18.1830	−	31.4939i	−0.912578	−	1.58063i	−0.102170	−	0.994767i	$-0.532579\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	31.6137			1.57871			0.789357	−	0.613934i	$-0.210414\pi$
$401$	31.6137			1.57871			0.789357	+	0.613934i	$0.210414\pi$
$402$		0			0
$403$	−2.26765			−0.112960
$404$		0			0
$405$		0			0
$406$		0			0
$407$	3.38816	+	5.86847i	0.167945	+	0.290889i
$408$		0			0
$409$	−10.0906	−	17.4774i	−0.498948	−	0.864203i	0.501051	−	0.865418i	$-0.332947\pi$
$409$	−10.0906	−	17.4774i	−0.498948	−	0.864203i	−0.999999	+	0.00121422i	$0.999614\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−10.0138	+	12.4895i	−0.492746	+	0.614567i
$414$		0			0
$415$	13.5270	+	23.4294i	0.664014	+	1.15011i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−12.4159	+	21.5049i	−0.606555	+	1.05058i	0.385248	+	0.922813i	$0.374116\pi$
$419$	−12.4159	+	21.5049i	−0.606555	+	1.05058i	−0.991804	+	0.127772i	$0.959217\pi$
$420$		0			0
$421$	−5.71841	−	9.90458i	−0.278698	−	0.482720i	0.692363	−	0.721549i	$-0.256570\pi$
$421$	−5.71841	−	9.90458i	−0.278698	−	0.482720i	−0.971062	+	0.238829i	$0.923236\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−3.52548	+	6.10631i	−0.171011	+	0.296200i
$426$		0			0
$427$	26.6986	+	4.09587i	1.29203	+	0.198213i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	2.80157	−	4.85246i	0.134947	−	0.233735i	−0.790630	−	0.612294i	$-0.790247\pi$
$431$	2.80157	−	4.85246i	0.134947	−	0.233735i	0.925577	+	0.378559i	$0.123580\pi$
$432$		0			0
$433$	−4.22555			−0.203067			−0.101534	−	0.994832i	$-0.532375\pi$
$433$	−4.22555			−0.203067			−0.101534	+	0.994832i	$0.532375\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	0.940366	+	1.62876i	0.0449838	+	0.0779142i
$438$		0			0
$439$	−17.7316	+	30.7120i	−0.846281	+	1.46580i	0.0382233	+	0.999269i	$0.487830\pi$
$439$	−17.7316	+	30.7120i	−0.846281	+	1.46580i	−0.884504	+	0.466532i	$0.845503\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	11.4658	−	19.8593i	0.544755	−	0.943543i	−0.453867	−	0.891069i	$-0.649956\pi$
$443$	11.4658	−	19.8593i	0.544755	−	0.943543i	0.998622	−	0.0524740i	$-0.0167107\pi$
$444$		0			0
$445$	−10.1625	−	17.6019i	−0.481748	−	0.834412i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−20.4850			−0.966747			−0.483373	−	0.875414i	$-0.660589\pi$
$449$	−20.4850			−0.966747			−0.483373	+	0.875414i	$0.660589\pi$
$450$		0			0
$451$	−5.23161	+	9.06141i	−0.246347	+	0.426685i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	17.2582	+	2.64761i	0.809076	+	0.124122i
$456$		0			0
$457$	−7.72677	+	13.3832i	−0.361443	+	0.626038i	−0.988199	−	0.153178i	$-0.951049\pi$
$457$	−7.72677	+	13.3832i	−0.361443	+	0.626038i	0.626755	+	0.779216i	$0.284383\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−14.0815	−	24.3898i	−0.655839	−	1.13595i	−0.981683	−	0.190523i	$-0.938982\pi$
$461$	−14.0815	−	24.3898i	−0.655839	−	1.13595i	0.325844	−	0.945424i	$-0.394352\pi$
$462$		0			0
$463$	15.3193	−	26.5338i	0.711948	−	1.23313i	−0.252177	−	0.967681i	$-0.581146\pi$
$463$	15.3193	−	26.5338i	0.711948	−	1.23313i	0.964125	−	0.265449i	$-0.0855202\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−6.61798	−	11.4627i	−0.306244	−	0.530429i	0.671294	−	0.741191i	$-0.265739\pi$
$467$	−6.61798	−	11.4627i	−0.306244	−	0.530429i	−0.977537	+	0.210762i	$0.932406\pi$
$468$		0			0
$469$	−15.5895	+	19.4437i	−0.719857	+	0.897827i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−3.06638	−	5.31112i	−0.140992	−	0.244206i
$474$		0			0
$475$	5.11826	+	8.86508i	0.234842	+	0.406758i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	14.0872			0.643658			0.321829	−	0.946798i	$-0.395702\pi$
$479$	14.0872			0.643658			0.321829	+	0.946798i	$0.395702\pi$
$480$		0			0
$481$	21.3405			0.973044
$482$		0			0
$483$		0			0
$484$		0			0
$485$	9.86407	+	17.0851i	0.447904	+	0.775793i
$486$		0			0
$487$	−3.45654	+	5.98690i	−0.156631	+	0.271292i	−0.933652	−	0.358183i	$-0.883397\pi$
$487$	−3.45654	+	5.98690i	−0.156631	+	0.271292i	0.777021	+	0.629475i	$0.216730\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−15.3481	+	26.5837i	−0.692651	+	1.19971i	0.278315	+	0.960490i	$0.410224\pi$
$491$	−15.3481	+	26.5837i	−0.692651	+	1.19971i	−0.970966	+	0.239217i	$0.923109\pi$
$492$		0			0
$493$	20.8176			0.937578
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−8.12865	−	20.8724i	−0.364620	−	0.936256i
$498$		0			0
$499$	22.0371			0.986518			0.493259	−	0.869882i	$-0.335805\pi$
$499$	22.0371			0.986518			0.493259	+	0.869882i	$0.335805\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	38.9653			1.73737			0.868687	−	0.495361i	$-0.164964\pi$
$503$	38.9653			1.73737			0.868687	+	0.495361i	$0.164964\pi$
$504$		0			0
$505$	9.09922			0.404910
$506$		0			0
$507$		0			0
$508$		0			0
$509$	28.2941			1.25412			0.627058	−	0.778973i	$-0.284259\pi$
$509$	28.2941			1.25412			0.627058	+	0.778973i	$0.284259\pi$
$510$		0			0
$511$	−35.6885	−	5.47503i	−1.57877	−	0.242201i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	24.6084			1.08437
$516$		0			0
$517$	0.264676	−	0.458433i	0.0116405	−	0.0201619i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	5.98150	−	10.3603i	0.262054	−	0.453892i	−0.704733	−	0.709472i	$-0.748933\pi$
$521$	5.98150	−	10.3603i	0.262054	−	0.453892i	0.966788	+	0.255581i	$0.0822667\pi$
$522$		0			0
$523$	3.15056	+	5.45693i	0.137764	+	0.238615i	0.926650	−	0.375925i	$-0.122675\pi$
$523$	3.15056	+	5.45693i	0.137764	+	0.238615i	−0.788886	+	0.614540i	$0.789342\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.88190			−0.0819767
$528$		0			0
$529$	−22.8415			−0.993108
$530$		0			0
$531$		0			0
$532$		0			0
$533$	16.4758	+	28.5369i	0.713645	+	1.23607i
$534$		0			0
$535$	5.72625	+	9.91815i	0.247567	+	0.428799i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−6.41948	+	5.89399i	−0.276507	+	0.253872i
$540$		0			0
$541$	9.88191	+	17.1160i	0.424857	+	0.735873i	0.996407	−	0.0846937i	$-0.0269912\pi$
$541$	9.88191	+	17.1160i	0.424857	+	0.735873i	−0.571550	+	0.820567i	$0.693658\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−14.0987	+	24.4197i	−0.603923	+	1.04602i
$546$		0			0
$547$	−21.6125	−	37.4340i	−0.924085	−	1.60056i	−0.793026	−	0.609188i	$-0.791496\pi$
$547$	−21.6125	−	37.4340i	−0.924085	−	1.60056i	−0.131059	−	0.991375i	$-0.541838\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	15.1114	−	26.1737i	0.643767	−	1.11504i
$552$		0			0
$553$	14.4707	+	2.21997i	0.615357	+	0.0944029i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	14.0838	−	24.3938i	0.596748	−	1.03360i	−0.396550	−	0.918013i	$-0.629793\pi$
$557$	14.0838	−	24.3938i	0.596748	−	1.03360i	0.993298	−	0.115584i	$-0.0368740\pi$
$558$		0			0
$559$	−19.3137			−0.816884
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−12.8472	−	22.2520i	−0.541445	−	0.937810i	−0.998821	−	0.0485366i	$-0.984544\pi$
$563$	−12.8472	−	22.2520i	−0.541445	−	0.937810i	0.457377	−	0.889273i	$-0.348789\pi$
$564$		0			0
$565$	11.3976	−	19.7411i	0.479499	−	0.830516i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	17.7441	−	30.7336i	0.743870	−	1.28842i	−0.206851	−	0.978373i	$-0.566321\pi$
$569$	17.7441	−	30.7336i	0.743870	−	1.28842i	0.950721	−	0.310048i	$-0.100345\pi$
$570$		0			0
$571$	10.8412	+	18.7775i	0.453689	+	0.785813i	0.998612	−	0.0526737i	$-0.0167743\pi$
$571$	10.8412	+	18.7775i	0.453689	+	0.785813i	−0.544923	+	0.838486i	$0.683441\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	0.862754			0.0359793
$576$		0			0
$577$	−7.60727	+	13.1762i	−0.316695	+	0.548531i	−0.979796	−	0.199998i	$-0.935906\pi$
$577$	−7.60727	+	13.1762i	−0.316695	+	0.548531i	0.663102	+	0.748529i	$0.269240\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−26.6018	+	33.1786i	−1.10363	+	1.37648i
$582$		0			0
$583$	0.580553	−	1.00555i	0.0240440	−	0.0416455i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−19.1924	−	33.2423i	−0.792157	−	1.37206i	−0.924629	−	0.380869i	$-0.875625\pi$
$587$	−19.1924	−	33.2423i	−0.792157	−	1.37206i	0.132472	−	0.991187i	$-0.457708\pi$
$588$		0			0
$589$	−1.36606	+	2.36608i	−0.0562875	+	0.0974928i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	9.25559	+	16.0311i	0.380081	+	0.658320i	0.991074	−	0.133316i	$-0.0425626\pi$
$593$	9.25559	+	16.0311i	0.380081	+	0.658320i	−0.610992	+	0.791637i	$0.709229\pi$
$594$		0			0
$595$	14.3223	+	2.19721i	0.587159	+	0.0900770i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	10.8413	+	18.7776i	0.442962	+	0.767233i	0.997908	−	0.0646536i	$-0.0205942\pi$
$599$	10.8413	+	18.7776i	0.442962	+	0.767233i	−0.554946	+	0.831887i	$0.687261\pi$
$600$		0			0
$601$	3.95776	+	6.85505i	0.161441	+	0.279623i	0.935386	−	0.353630i	$-0.115053\pi$
$601$	3.95776	+	6.85505i	0.161441	+	0.279623i	−0.773945	+	0.633253i	$0.781719\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	15.9059			0.646665
$606$		0			0
$607$	−35.9247			−1.45814			−0.729068	−	0.684441i	$-0.760046\pi$
$607$	−35.9247			−1.45814			−0.729068	+	0.684441i	$0.760046\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−0.833539	−	1.44373i	−0.0337214	−	0.0584072i
$612$		0			0
$613$	−1.60252	+	2.77565i	−0.0647253	+	0.112108i	−0.896572	−	0.442898i	$-0.853950\pi$
$613$	−1.60252	+	2.77565i	−0.0647253	+	0.112108i	0.831847	+	0.555005i	$0.187284\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−15.9357	+	27.6015i	−0.641549	+	1.11120i	0.343538	+	0.939139i	$0.388374\pi$
$617$	−15.9357	+	27.6015i	−0.641549	+	1.11120i	−0.985087	+	0.172056i	$0.944959\pi$
$618$		0			0
$619$	20.9726			0.842959			0.421480	−	0.906838i	$-0.361511\pi$
$619$	20.9726			0.842959			0.421480	+	0.906838i	$0.361511\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	19.9853	−	24.9262i	0.800692	−	0.998647i
$624$		0			0
$625$	−9.46924			−0.378769
$626$		0			0
$627$		0			0
$628$		0			0
$629$	17.7102			0.706153
$630$		0			0
$631$	−26.4435			−1.05270			−0.526349	−	0.850268i	$-0.676440\pi$
$631$	−26.4435			−1.05270			−0.526349	+	0.850268i	$0.676440\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	17.8253			0.707377
$636$		0			0
$637$	5.96663	+	26.7891i	0.236407	+	1.06142i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	27.9618			1.10443			0.552213	−	0.833703i	$-0.313783\pi$
$641$	27.9618			1.10443			0.552213	+	0.833703i	$0.313783\pi$
$642$		0			0
$643$	6.12936	−	10.6164i	0.241718	−	0.418669i	−0.719485	−	0.694508i	$-0.755622\pi$
$643$	6.12936	−	10.6164i	0.241718	−	0.418669i	0.961204	+	0.275839i	$0.0889556\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	4.49923	−	7.79290i	0.176883	−	0.306371i	−0.763928	−	0.645301i	$-0.776732\pi$
$647$	4.49923	−	7.79290i	0.176883	−	0.306371i	0.940811	+	0.338931i	$0.110065\pi$
$648$		0			0
$649$	−3.76640	−	6.52360i	−0.147844	−	0.256074i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	22.7901			0.891844			0.445922	−	0.895072i	$-0.352876\pi$
$653$	22.7901			0.891844			0.445922	+	0.895072i	$0.352876\pi$
$654$		0			0
$655$	37.6418			1.47079
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−19.3311	−	33.4824i	−0.753033	−	1.30429i	−0.946347	−	0.323154i	$-0.895257\pi$
$659$	−19.3311	−	33.4824i	−0.753033	−	1.30429i	0.193314	−	0.981137i	$-0.438076\pi$
$660$		0			0
$661$	5.75399	+	9.96621i	0.223804	+	0.387641i	0.955960	−	0.293497i	$-0.0948190\pi$
$661$	5.75399	+	9.96621i	0.223804	+	0.387641i	−0.732156	+	0.681137i	$0.761486\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	13.1590	−	16.4124i	0.510286	−	0.636444i
$666$		0			0
$667$	−1.27362	−	2.20597i	−0.0493147	−	0.0854156i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−6.35511	+	11.0074i	−0.245336	+	0.424935i
$672$		0			0
$673$	−10.6642	−	18.4709i	−0.411075	−	0.712002i	0.583933	−	0.811802i	$-0.301513\pi$
$673$	−10.6642	−	18.4709i	−0.411075	−	0.712002i	−0.995008	+	0.0997997i	$0.968180\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	13.8799	−	24.0407i	0.533449	−	0.923961i	−0.465788	−	0.884896i	$-0.654229\pi$
$677$	13.8799	−	24.0407i	0.533449	−	0.923961i	0.999237	−	0.0390641i	$-0.0124377\pi$
$678$		0			0
$679$	−19.3984	+	24.1943i	−0.744443	+	0.928491i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−8.66854	+	15.0143i	−0.331692	+	0.574508i	−0.982844	−	0.184440i	$-0.940953\pi$
$683$	−8.66854	+	15.0143i	−0.331692	+	0.574508i	0.651151	+	0.758948i	$0.274286\pi$
$684$		0			0
$685$	30.2194			1.15462
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−1.82832	−	3.16675i	−0.0696535	−	0.120643i
$690$		0			0
$691$	19.8023	−	34.2986i	0.753315	−	1.30478i	−0.192892	−	0.981220i	$-0.561787\pi$
$691$	19.8023	−	34.2986i	0.753315	−	1.30478i	0.946207	−	0.323560i	$-0.104880\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	0.960788	−	1.66413i	0.0364448	−	0.0631242i
$696$		0			0
$697$	13.6730	+	23.6824i	0.517903	+	0.897035i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−7.28469			−0.275139			−0.137570	−	0.990492i	$-0.543929\pi$
$701$	−7.28469			−0.275139			−0.137570	+	0.990492i	$0.543929\pi$
$702$		0			0
$703$	12.8558	−	22.2668i	0.484864	−	0.839809i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	5.19052	+	13.3280i	0.195210	+	0.501251i
$708$		0			0
$709$	−6.00541	+	10.4017i	−0.225538	+	0.390643i	−0.956481	−	0.291796i	$-0.905747\pi$
$709$	−6.00541	+	10.4017i	−0.225538	+	0.390643i	0.730943	+	0.682439i	$0.239081\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	0.115134	+	0.199418i	0.00431181	+	0.00746827i
$714$		0			0
$715$	−4.10800	+	7.11526i	−0.153630	+	0.266096i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−2.15819	−	3.73809i	−0.0804868	−	0.139407i	0.822972	−	0.568081i	$-0.192314\pi$
$719$	−2.15819	−	3.73809i	−0.0804868	−	0.139407i	−0.903459	+	0.428674i	$0.858981\pi$
$720$		0			0
$721$	14.0375	+	36.0449i	0.522783	+	1.34238i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−6.93210	−	12.0067i	−0.257452	−	0.445919i
$726$		0			0
$727$	−10.2483	−	17.7506i	−0.380090	−	0.658334i	0.610985	−	0.791642i	$-0.290774\pi$
$727$	−10.2483	−	17.7506i	−0.380090	−	0.658334i	−0.991075	+	0.133308i	$0.957440\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−16.0282			−0.592825
$732$		0			0
$733$	25.3322			0.935666			0.467833	−	0.883817i	$-0.345035\pi$
$733$	25.3322			0.935666			0.467833	+	0.883817i	$0.345035\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−5.86356	−	10.1560i	−0.215987	−	0.374100i
$738$		0			0
$739$	6.63391	−	11.4903i	0.244032	−	0.422676i	−0.717827	−	0.696222i	$-0.754863\pi$
$739$	6.63391	−	11.4903i	0.244032	−	0.422676i	0.961859	+	0.273545i	$0.0881964\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	22.6116	−	39.1644i	0.829538	−	1.43680i	−0.0688624	−	0.997626i	$-0.521937\pi$
$743$	22.6116	−	39.1644i	0.829538	−	1.43680i	0.898401	−	0.439176i	$-0.144730\pi$
$744$		0			0
$745$	29.7217			1.08892
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−11.2611	+	14.0451i	−0.411471	+	0.513199i
$750$		0			0
$751$	28.3797			1.03559			0.517795	−	0.855505i	$-0.326753\pi$
$751$	28.3797			1.03559			0.517795	+	0.855505i	$0.326753\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−25.6435			−0.933263
$756$		0			0
$757$	5.08483			0.184811			0.0924056	−	0.995721i	$-0.470544\pi$
$757$	5.08483			0.184811			0.0924056	+	0.995721i	$0.470544\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−37.7225			−1.36744			−0.683720	−	0.729745i	$-0.739639\pi$
$761$	−37.7225			−1.36744			−0.683720	+	0.729745i	$0.739639\pi$
$762$		0			0
$763$	−43.8110	−	6.72111i	−1.58606	−	0.243321i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−23.7229			−0.856583
$768$		0			0
$769$	11.8729	−	20.5644i	0.428147	−	0.741572i	−0.568562	−	0.822641i	$-0.692500\pi$
$769$	11.8729	−	20.5644i	0.428147	−	0.741572i	0.996709	+	0.0810688i	$0.0258333\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−19.5347	+	33.8351i	−0.702614	+	1.21696i	0.264932	+	0.964267i	$0.414650\pi$
$773$	−19.5347	+	33.8351i	−0.702614	+	1.21696i	−0.967546	+	0.252696i	$0.918683\pi$
$774$		0			0
$775$	0.626657	+	1.08540i	0.0225102	+	0.0389888i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	39.7008			1.42243
$780$		0			0
$781$	10.5402			0.377159
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−11.4697	−	19.8661i	−0.409370	−	0.709050i
$786$		0			0
$787$	1.90458	+	3.29882i	0.0678908	+	0.117590i	0.897973	−	0.440051i	$-0.145040\pi$
$787$	1.90458	+	3.29882i	0.0678908	+	0.117590i	−0.830082	+	0.557642i	$0.811706\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	35.4173	+	5.43342i	1.25929	+	0.193190i
$792$		0			0
$793$	20.0140	+	34.6653i	0.710718	+	1.23100i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	10.8239	−	18.7476i	0.383404	−	0.664075i	−0.608143	−	0.793828i	$-0.708085\pi$
$797$	10.8239	−	18.7476i	0.383404	−	0.664075i	0.991546	+	0.129753i	$0.0414184\pi$
$798$		0			0
$799$	−0.691743	−	1.19813i	−0.0244721	−	0.0423870i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	8.49500	−	14.7138i	0.299782	−	0.519238i
$804$		0			0
$805$	−0.643408	−	1.65212i	−0.0226771	−	0.0582294i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	18.5128	−	32.0652i	0.650877	−	1.12735i	−0.332034	−	0.943268i	$-0.607735\pi$
$809$	18.5128	−	32.0652i	0.650877	−	1.12735i	0.982910	−	0.184084i	$-0.0589319\pi$
$810$		0			0
$811$	−5.37416			−0.188712			−0.0943561	−	0.995539i	$-0.530079\pi$
$811$	−5.37416			−0.188712			−0.0943561	+	0.995539i	$0.530079\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−6.81216	−	11.7990i	−0.238620	−	0.413301i
$816$		0			0
$817$	−11.6348	+	20.1521i	−0.407050	+	0.705032i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	1.11119	−	1.92464i	0.0387809	−	0.0671706i	−0.845983	−	0.533209i	$-0.820986\pi$
$821$	1.11119	−	1.92464i	0.0387809	−	0.0671706i	0.884764	+	0.466039i	$0.154319\pi$
$822$		0			0
$823$	18.5537	+	32.1359i	0.646740	+	1.12019i	0.983897	+	0.178738i	$0.0572015\pi$
$823$	18.5537	+	32.1359i	0.646740	+	1.12019i	−0.337157	+	0.941449i	$0.609465\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	19.4790			0.677351			0.338676	−	0.940903i	$-0.390021\pi$
$827$	19.4790			0.677351			0.338676	+	0.940903i	$0.390021\pi$
$828$		0			0
$829$	0.137129	−	0.237514i	0.00476267	−	0.00824919i	−0.863634	−	0.504119i	$-0.831817\pi$
$829$	0.137129	−	0.237514i	0.00476267	−	0.00824919i	0.868397	+	0.495870i	$0.165151\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	4.95163	+	22.2319i	0.171564	+	0.770290i
$834$		0			0
$835$	3.49657	−	6.05623i	0.121004	−	0.209585i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	21.0711	+	36.4962i	0.727455	+	1.25999i	0.957956	+	0.286917i	$0.0926303\pi$
$839$	21.0711	+	36.4962i	0.727455	+	1.25999i	−0.230501	+	0.973072i	$0.574036\pi$
$840$		0			0
$841$	−5.96666	+	10.3346i	−0.205747	+	0.356364i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	1.99671	+	3.45840i	0.0686888	+	0.118973i
$846$		0			0
$847$	9.07328	+	23.2980i	0.311762	+	0.800528i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−1.08351	−	1.87669i	−0.0371422	−	0.0643322i
$852$		0			0
$853$	22.3086	+	38.6397i	0.763833	+	1.32300i	0.940862	+	0.338791i	$0.110018\pi$
$853$	22.3086	+	38.6397i	0.763833	+	1.32300i	−0.177029	+	0.984206i	$0.556649\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	7.33227			0.250466			0.125233	−	0.992127i	$-0.460032\pi$
$857$	7.33227			0.250466			0.125233	+	0.992127i	$0.460032\pi$
$858$		0			0
$859$	2.70146			0.0921725			0.0460863	−	0.998937i	$-0.485325\pi$
$859$	2.70146			0.0921725			0.0460863	+	0.998937i	$0.485325\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	7.40188	+	12.8204i	0.251963	+	0.436413i	0.964066	−	0.265662i	$-0.0855905\pi$
$863$	7.40188	+	12.8204i	0.251963	+	0.436413i	−0.712103	+	0.702075i	$0.752257\pi$
$864$		0			0
$865$	−11.6429	+	20.1661i	−0.395870	+	0.685668i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−3.44449	+	5.96603i	−0.116846	+	0.202384i
$870$		0			0
$871$	−36.9319			−1.25139
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−11.5822	−	29.7404i	−0.391551	−	1.00541i
$876$		0			0
$877$	−11.0961			−0.374690			−0.187345	−	0.982294i	$-0.559988\pi$
$877$	−11.0961			−0.374690			−0.187345	+	0.982294i	$0.559988\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−15.0536			−0.507168			−0.253584	−	0.967313i	$-0.581609\pi$
$881$	−15.0536			−0.507168			−0.253584	+	0.967313i	$0.581609\pi$
$882$		0			0
$883$	−2.39418			−0.0805704			−0.0402852	−	0.999188i	$-0.512827\pi$
$883$	−2.39418			−0.0805704			−0.0402852	+	0.999188i	$0.512827\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−4.93394			−0.165666			−0.0828328	−	0.996563i	$-0.526397\pi$
$887$	−4.93394			−0.165666			−0.0828328	+	0.996563i	$0.526397\pi$
$888$		0			0
$889$	10.1682	+	26.1095i	0.341031	+	0.875685i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−2.00853			−0.0672130
$894$		0			0
$895$	7.93047	−	13.7360i	0.265086	−	0.459143i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	1.85017	−	3.20459i	0.0617067	−	0.106879i
$900$		0			0
$901$	−1.51730	−	2.62804i	−0.0505486	−	0.0875527i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−2.22400			−0.0739284
$906$		0			0
$907$	3.39631			0.112773			0.0563863	−	0.998409i	$-0.482042\pi$
$907$	3.39631			0.112773			0.0563863	+	0.998409i	$0.482042\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	4.65142	+	8.05649i	0.154108	+	0.266924i	0.932734	−	0.360565i	$-0.117416\pi$
$911$	4.65142	+	8.05649i	0.154108	+	0.266924i	−0.778626	+	0.627489i	$0.784083\pi$
$912$		0			0
$913$	−10.0055	−	17.3301i	−0.331134	−	0.573541i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	21.4722	+	55.1355i	0.709076	+	1.82073i
$918$		0			0
$919$	−8.92656	−	15.4613i	−0.294460	−	0.510020i	0.680399	−	0.732842i	$-0.261806\pi$
$919$	−8.92656	−	15.4613i	−0.294460	−	0.510020i	−0.974859	+	0.222822i	$0.928473\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	16.5970	−	28.7469i	0.546298	−	0.946216i
$924$		0			0
$925$	−5.89737	−	10.2145i	−0.193904	−	0.335852i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−23.6430	+	40.9510i	−0.775703	+	1.34356i	0.158695	+	0.987328i	$0.449271\pi$
$929$	−23.6430	+	40.9510i	−0.775703	+	1.34356i	−0.934398	+	0.356230i	$0.884062\pi$
$930$		0			0
$931$	31.5463	+	9.91242i	1.03389	+	0.324866i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−3.40917	+	5.90486i	−0.111492	+	0.193110i
$936$		0			0
$937$	21.2493			0.694183			0.347092	−	0.937831i	$-0.387169\pi$
$937$	21.2493			0.694183			0.347092	+	0.937831i	$0.387169\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−30.0405	−	52.0316i	−0.979292	−	1.69618i	−0.664977	−	0.746864i	$-0.731559\pi$
$941$	−30.0405	−	52.0316i	−0.979292	−	1.69618i	−0.314315	−	0.949319i	$-0.601775\pi$
$942$		0			0
$943$	1.67303	−	2.89777i	0.0544813	−	0.0943644i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−1.83468	+	3.17775i	−0.0596189	+	0.103263i	−0.894294	−	0.447479i	$-0.852322\pi$
$947$	−1.83468	+	3.17775i	−0.0596189	+	0.103263i	0.834675	+	0.550742i	$0.185655\pi$
$948$		0			0
$949$	−26.7531	−	46.3377i	−0.868442	−	1.50419i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−0.837421			−0.0271267			−0.0135634	−	0.999908i	$-0.504317\pi$
$953$	−0.837421			−0.0271267			−0.0135634	+	0.999908i	$0.504317\pi$
$954$		0			0
$955$	13.7055	−	23.7385i	0.443498	−	0.768161i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	17.2382	+	44.2636i	0.556651	+	1.42935i
$960$		0			0
$961$	15.3327	−	26.5571i	0.494605	−	0.856680i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	2.15574	+	3.73386i	0.0693958	+	0.120197i
$966$		0			0
$967$	−21.8856	+	37.9070i	−0.703795	+	1.21901i	0.263330	+	0.964706i	$0.415179\pi$
$967$	−21.8856	+	37.9070i	−0.703795	+	1.21901i	−0.967125	+	0.254302i	$0.918154\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−20.3059	−	35.1709i	−0.651648	−	1.12869i	−0.982723	−	0.185083i	$-0.940745\pi$
$971$	−20.3059	−	35.1709i	−0.651648	−	1.12869i	0.331075	−	0.943605i	$-0.392589\pi$
$972$		0			0
$973$	2.98560	+	0.458025i	0.0957138	+	0.0146836i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	28.7479	+	49.7929i	0.919728	+	1.59302i	0.799827	+	0.600230i	$0.204924\pi$
$977$	28.7479	+	49.7929i	0.919728	+	1.59302i	0.119901	+	0.992786i	$0.461742\pi$
$978$		0			0
$979$	7.51689	+	13.0196i	0.240241	+	0.416109i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−13.4594			−0.429289			−0.214644	−	0.976692i	$-0.568859\pi$
$983$	−13.4594			−0.429289			−0.214644	+	0.976692i	$0.568859\pi$
$984$		0			0
$985$	36.5103			1.16331
$986$		0			0
$987$		0			0
$988$		0			0
$989$	0.980604	+	1.69846i	0.0311814	+	0.0540078i
$990$		0			0
$991$	17.7821	−	30.7995i	0.564867	−	0.978379i	−0.432195	−	0.901780i	$-0.642261\pi$
$991$	17.7821	−	30.7995i	0.564867	−	0.978379i	0.997062	−	0.0765983i	$-0.0244059\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−9.42036	+	16.3165i	−0.298645	+	0.517269i
$996$		0			0
$997$	32.7289			1.03653			0.518267	−	0.855219i	$-0.326577\pi$
$997$	32.7289			1.03653			0.518267	+	0.855219i	$0.326577\pi$
$998$		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.1873.4		22
3.2	odd	2		1008.2.t.k.193.6		22
4.3	odd	2		1512.2.t.d.361.4		22
7.2	even	3		3024.2.q.k.2305.8		22
9.2	odd	6		1008.2.q.k.529.11		22
9.7	even	3		3024.2.q.k.2881.8		22
12.11	even	2		504.2.t.d.193.6	yes	22
21.2	odd	6		1008.2.q.k.625.11		22
28.23	odd	6		1512.2.q.c.793.8		22
36.7	odd	6		1512.2.q.c.1369.8		22
36.11	even	6		504.2.q.d.25.1	✓	22
63.2	odd	6		1008.2.t.k.961.6		22
63.16	even	3	inner	3024.2.t.l.289.4		22
84.23	even	6		504.2.q.d.121.1	yes	22
252.79	odd	6		1512.2.t.d.289.4		22
252.191	even	6		504.2.t.d.457.6	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.d.25.1	✓	22	36.11	even	6
504.2.q.d.121.1	yes	22	84.23	even	6
504.2.t.d.193.6	yes	22	12.11	even	2
504.2.t.d.457.6	yes	22	252.191	even	6
1008.2.q.k.529.11		22	9.2	odd	6
1008.2.q.k.625.11		22	21.2	odd	6
1008.2.t.k.193.6		22	3.2	odd	2
1008.2.t.k.961.6		22	63.2	odd	6
1512.2.q.c.793.8		22	28.23	odd	6
1512.2.q.c.1369.8		22	36.7	odd	6
1512.2.t.d.289.4		22	252.79	odd	6
1512.2.t.d.361.4		22	4.3	odd	2
3024.2.q.k.2305.8		22	7.2	even	3
3024.2.q.k.2881.8		22	9.7	even	3
3024.2.t.l.289.4		22	63.16	even	3	inner
3024.2.t.l.1873.4		22	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:	\( N \)	\(=\)	\( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3024.t (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.68316 q^{5} +(-0.960133 - 2.46539i) q^{7} +O(q^{10})\)	\(q-1.68316 q^{5} +(-0.960133 - 2.46539i) q^{7} +1.24498 q^{11} +(1.96039 - 3.39550i) q^{13} +(1.62691 - 2.81788i) q^{17} +(-2.36192 - 4.09097i) q^{19} -0.398135 q^{23} -2.16699 q^{25} +(3.19896 + 5.54076i) q^{29} +(-0.289184 - 0.500881i) q^{31} +(1.61605 + 4.14963i) q^{35} +(2.72146 + 4.71371i) q^{37} +(-4.20216 + 7.27836i) q^{41} +(-2.46299 - 4.26603i) q^{43} +(0.212595 - 0.368225i) q^{47} +(-5.15629 + 4.73420i) q^{49} +(0.466315 - 0.807681i) q^{53} -2.09550 q^{55} +(-3.02527 - 5.23992i) q^{59} +(-5.10459 + 8.84140i) q^{61} +(-3.29965 + 5.71516i) q^{65} +(-4.70976 - 8.15754i) q^{67} +8.46617 q^{71} +(6.82340 - 11.8185i) q^{73} +(-1.19535 - 3.06936i) q^{77} +(-2.76670 + 4.79207i) q^{79} +(-8.03669 - 13.9199i) q^{83} +(-2.73833 + 4.74293i) q^{85} +(6.03776 + 10.4577i) q^{89} +(-10.2535 - 1.57300i) q^{91} +(3.97549 + 6.88575i) q^{95} +(-5.86046 - 10.1506i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 6 q^{5} - 7 q^{7}+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more