LMFDB - Embedded newform 2520.2.bi.k.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2520,2,Mod(361,2520)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2520, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("2520.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2520 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2520.bi (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$20.1223013094$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 280)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.1
Root			$-0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	2520.361
Dual form			2520.2.bi.k.1801.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{5} +(-2.62132 - 0.358719i) q^{7} +O(q^{10})$	$q+(0.500000 + 0.866025i) q^{5} +(-2.62132 - 0.358719i) q^{7} +(-2.41421 + 4.18154i) q^{11} +2.00000 q^{13} +(1.82843 - 3.16693i) q^{17} +(-2.82843 - 4.89898i) q^{19} +(-4.20711 - 7.28692i) q^{23} +(-0.500000 + 0.866025i) q^{25} +2.17157 q^{29} +(2.41421 - 4.18154i) q^{31} +(-1.00000 - 2.44949i) q^{35} +(2.82843 + 4.89898i) q^{37} -0.171573 q^{41} +12.8995 q^{43} +(0.171573 + 0.297173i) q^{47} +(6.74264 + 1.88064i) q^{49} +(2.82843 - 4.89898i) q^{53} -4.82843 q^{55} +(-2.00000 + 3.46410i) q^{59} +(2.32843 + 4.03295i) q^{61} +(1.00000 + 1.73205i) q^{65} +(-3.44975 + 5.97514i) q^{67} +12.0000 q^{71} +(3.82843 - 6.63103i) q^{73} +(7.82843 - 10.0951i) q^{77} +(2.00000 + 3.46410i) q^{79} +13.2426 q^{83} +3.65685 q^{85} +(-8.32843 - 14.4253i) q^{89} +(-5.24264 - 0.717439i) q^{91} +(2.82843 - 4.89898i) q^{95} +6.00000 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{5} - 2 q^{7}+O(q^{10}) $ 4 * q + 2 * q^5 - 2 * q^7	$ 4 q + 2 q^{5} - 2 q^{7} - 4 q^{11} + 8 q^{13} - 4 q^{17} - 14 q^{23} - 2 q^{25} + 20 q^{29} + 4 q^{31} - 4 q^{35} - 12 q^{41} + 12 q^{43} + 12 q^{47} + 10 q^{49} - 8 q^{55} - 8 q^{59} - 2 q^{61} + 4 q^{65} + 6 q^{67} + 48 q^{71} + 4 q^{73} + 20 q^{77} + 8 q^{79} + 36 q^{83} - 8 q^{85} - 22 q^{89} - 4 q^{91} + 24 q^{97}+O(q^{100}) $ 4 * q + 2 * q^5 - 2 * q^7 - 4 * q^11 + 8 * q^13 - 4 * q^17 - 14 * q^23 - 2 * q^25 + 20 * q^29 + 4 * q^31 - 4 * q^35 - 12 * q^41 + 12 * q^43 + 12 * q^47 + 10 * q^49 - 8 * q^55 - 8 * q^59 - 2 * q^61 + 4 * q^65 + 6 * q^67 + 48 * q^71 + 4 * q^73 + 20 * q^77 + 8 * q^79 + 36 * q^83 - 8 * q^85 - 22 * q^89 - 4 * q^91 + 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2520\mathbb{Z}\right)^\times$.

$n$	$281$	$631$	$1081$	$1261$	$2017$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$	−2.62132	−	0.358719i	−0.990766	−	0.135583i
$7$	−2.62132	−	0.358719i	−0.990766	−	0.135583i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−2.41421	+	4.18154i	−0.727913	+	1.26078i	0.229851	+	0.973226i	$0.426176\pi$
$11$	−2.41421	+	4.18154i	−0.727913	+	1.26078i	−0.957764	+	0.287556i	$0.907157\pi$
$12$		0			0
$13$	2.00000			0.554700			0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000			0.554700			0.277350	+	0.960769i	$0.410544\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.82843	−	3.16693i	0.443459	−	0.768093i	−0.554485	−	0.832194i	$-0.687085\pi$
$17$	1.82843	−	3.16693i	0.443459	−	0.768093i	0.997943	+	0.0641009i	$0.0204179\pi$
$18$		0			0
$19$	−2.82843	−	4.89898i	−0.648886	−	1.12390i	−0.983389	−	0.181509i	$-0.941902\pi$
$19$	−2.82843	−	4.89898i	−0.648886	−	1.12390i	0.334504	−	0.942394i	$-0.391431\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−4.20711	−	7.28692i	−0.877242	−	1.51943i	−0.854355	−	0.519690i	$-0.826047\pi$
$23$	−4.20711	−	7.28692i	−0.877242	−	1.51943i	−0.0228877	−	0.999738i	$-0.507286\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	2.17157			0.403251			0.201625	−	0.979463i	$-0.435378\pi$
$29$	2.17157			0.403251			0.201625	+	0.979463i	$0.435378\pi$
$30$		0			0
$31$	2.41421	−	4.18154i	0.433606	−	0.751027i	−0.563575	−	0.826065i	$-0.690574\pi$
$31$	2.41421	−	4.18154i	0.433606	−	0.751027i	0.997181	+	0.0750380i	$0.0239078\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−1.00000	−	2.44949i	−0.169031	−	0.414039i
$36$		0			0
$37$	2.82843	+	4.89898i	0.464991	+	0.805387i	0.999201	−	0.0399642i	$-0.0127244\pi$
$37$	2.82843	+	4.89898i	0.464991	+	0.805387i	−0.534211	+	0.845351i	$0.679391\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−0.171573			−0.0267952			−0.0133976	−	0.999910i	$-0.504265\pi$
$41$	−0.171573			−0.0267952			−0.0133976	+	0.999910i	$0.504265\pi$
$42$		0			0
$43$	12.8995			1.96715			0.983577	−	0.180488i	$-0.0577676\pi$
$43$	12.8995			1.96715			0.983577	+	0.180488i	$0.0577676\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	0.171573	+	0.297173i	0.0250265	+	0.0433471i	0.878267	−	0.478170i	$-0.158700\pi$
$47$	0.171573	+	0.297173i	0.0250265	+	0.0433471i	−0.853241	+	0.521517i	$0.825366\pi$
$48$		0			0
$49$	6.74264	+	1.88064i	0.963234	+	0.268662i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	2.82843	−	4.89898i	0.388514	−	0.672927i	−0.603736	−	0.797185i	$-0.706322\pi$
$53$	2.82843	−	4.89898i	0.388514	−	0.672927i	0.992250	+	0.124258i	$0.0396551\pi$
$54$		0			0
$55$	−4.82843			−0.651065
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−2.00000	+	3.46410i	−0.260378	+	0.450988i	−0.966342	−	0.257260i	$-0.917180\pi$
$59$	−2.00000	+	3.46410i	−0.260378	+	0.450988i	0.705965	+	0.708247i	$0.250514\pi$
$60$		0			0
$61$	2.32843	+	4.03295i	0.298125	+	0.516367i	0.975707	−	0.219080i	$-0.0703056\pi$
$61$	2.32843	+	4.03295i	0.298125	+	0.516367i	−0.677582	+	0.735447i	$0.736972\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	1.00000	+	1.73205i	0.124035	+	0.214834i
$66$		0			0
$67$	−3.44975	+	5.97514i	−0.421454	+	0.729979i	−0.996082	−	0.0884353i	$-0.971813\pi$
$67$	−3.44975	+	5.97514i	−0.421454	+	0.729979i	0.574628	+	0.818415i	$0.305147\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	12.0000			1.42414			0.712069	−	0.702109i	$-0.247758\pi$
$71$	12.0000			1.42414			0.712069	+	0.702109i	$0.247758\pi$
$72$		0			0
$73$	3.82843	−	6.63103i	0.448084	−	0.776103i	−0.550178	−	0.835048i	$-0.685440\pi$
$73$	3.82843	−	6.63103i	0.448084	−	0.776103i	0.998261	+	0.0589442i	$0.0187734\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	7.82843	−	10.0951i	0.892132	−	1.15045i
$78$		0			0
$79$	2.00000	+	3.46410i	0.225018	+	0.389742i	0.956325	−	0.292306i	$-0.0944227\pi$
$79$	2.00000	+	3.46410i	0.225018	+	0.389742i	−0.731307	+	0.682048i	$0.761089\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	13.2426			1.45357			0.726784	−	0.686866i	$-0.241014\pi$
$83$	13.2426			1.45357			0.726784	+	0.686866i	$0.241014\pi$
$84$		0			0
$85$	3.65685			0.396642
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−8.32843	−	14.4253i	−0.882812	−	1.52907i	−0.848202	−	0.529673i	$-0.822314\pi$
$89$	−8.32843	−	14.4253i	−0.882812	−	1.52907i	−0.0346099	−	0.999401i	$-0.511019\pi$
$90$		0			0
$91$	−5.24264	−	0.717439i	−0.549578	−	0.0752080i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	2.82843	−	4.89898i	0.290191	−	0.502625i
$96$		0			0
$97$	6.00000			0.609208			0.304604	−	0.952479i	$-0.401476\pi$
$97$	6.00000			0.609208			0.304604	+	0.952479i	$0.401476\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	2.74264	−	4.75039i	0.272903	−	0.472682i	−0.696701	−	0.717362i	$-0.745350\pi$
$101$	2.74264	−	4.75039i	0.272903	−	0.472682i	0.969604	+	0.244680i	$0.0786829\pi$
$102$		0			0
$103$	−5.20711	−	9.01897i	−0.513071	−	0.888666i	−0.999885	−	0.0151600i	$-0.995174\pi$
$103$	−5.20711	−	9.01897i	−0.513071	−	0.888666i	0.486814	−	0.873506i	$-0.338159\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−4.20711	−	7.28692i	−0.406716	−	0.704453i	0.587803	−	0.809004i	$-0.299993\pi$
$107$	−4.20711	−	7.28692i	−0.406716	−	0.704453i	−0.994520	+	0.104551i	$0.966660\pi$
$108$		0			0
$109$	2.15685	−	3.73578i	0.206589	−	0.357823i	−0.744049	−	0.668125i	$-0.767097\pi$
$109$	2.15685	−	3.73578i	0.206589	−	0.357823i	0.950638	+	0.310302i	$0.100430\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	11.3137			1.06430			0.532152	−	0.846649i	$-0.321383\pi$
$113$	11.3137			1.06430			0.532152	+	0.846649i	$0.321383\pi$
$114$		0			0
$115$	4.20711	−	7.28692i	0.392315	−	0.679509i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−5.92893	+	7.64564i	−0.543504	+	0.700875i
$120$		0			0
$121$	−6.15685	−	10.6640i	−0.559714	−	0.969453i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−15.6569			−1.38932			−0.694661	−	0.719338i	$-0.744445\pi$
$127$	−15.6569			−1.38932			−0.694661	+	0.719338i	$0.744445\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	1.17157	+	2.02922i	0.102361	+	0.177294i	0.912657	−	0.408727i	$-0.134027\pi$
$131$	1.17157	+	2.02922i	0.102361	+	0.177294i	−0.810296	+	0.586021i	$0.800694\pi$
$132$		0			0
$133$	5.65685	+	13.8564i	0.490511	+	1.20150i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−2.00000	+	3.46410i	−0.170872	+	0.295958i	−0.938725	−	0.344668i	$-0.887992\pi$
$137$	−2.00000	+	3.46410i	−0.170872	+	0.295958i	0.767853	+	0.640626i	$0.221325\pi$
$138$		0			0
$139$	−14.4853			−1.22863			−0.614313	−	0.789063i	$-0.710567\pi$
$139$	−14.4853			−1.22863			−0.614313	+	0.789063i	$0.710567\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−4.82843	+	8.36308i	−0.403773	+	0.699356i
$144$		0			0
$145$	1.08579	+	1.88064i	0.0901697	+	0.156178i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−3.32843	−	5.76500i	−0.272675	−	0.472288i	0.696871	−	0.717197i	$-0.254575\pi$
$149$	−3.32843	−	5.76500i	−0.272675	−	0.472288i	−0.969546	+	0.244909i	$0.921242\pi$
$150$		0			0
$151$	8.41421	−	14.5738i	0.684739	−	1.18600i	−0.288780	−	0.957396i	$-0.593250\pi$
$151$	8.41421	−	14.5738i	0.684739	−	1.18600i	0.973519	−	0.228607i	$-0.0734171\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	4.82843			0.387829
$156$		0			0
$157$	10.6569	−	18.4582i	0.850510	−	1.47313i	−0.0302396	−	0.999543i	$-0.509627\pi$
$157$	10.6569	−	18.4582i	0.850510	−	1.47313i	0.880749	−	0.473583i	$-0.157040\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	8.41421	+	20.6105i	0.663133	+	1.62434i
$162$		0			0
$163$	2.17157	+	3.76127i	0.170091	+	0.294606i	0.938451	−	0.345411i	$-0.112261\pi$
$163$	2.17157	+	3.76127i	0.170091	+	0.294606i	−0.768361	+	0.640017i	$0.778927\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	12.0711			0.934087			0.467044	−	0.884234i	$-0.345319\pi$
$167$	12.0711			0.934087			0.467044	+	0.884234i	$0.345319\pi$
$168$		0			0
$169$	−9.00000			−0.692308
$170$		0			0
$171$		0			0
$172$		0			0
$173$	10.8284	+	18.7554i	0.823270	+	1.42595i	0.903234	+	0.429148i	$0.141186\pi$
$173$	10.8284	+	18.7554i	0.823270	+	1.42595i	−0.0799642	+	0.996798i	$0.525481\pi$
$174$		0			0
$175$	1.62132	−	2.09077i	0.122560	−	0.158047i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	5.24264	−	9.08052i	0.391853	−	0.678710i	−0.600841	−	0.799369i	$-0.705167\pi$
$179$	5.24264	−	9.08052i	0.391853	−	0.678710i	0.992694	+	0.120659i	$0.0385007\pi$
$180$		0			0
$181$	−9.82843			−0.730541			−0.365271	−	0.930901i	$-0.619024\pi$
$181$	−9.82843			−0.730541			−0.365271	+	0.930901i	$0.619024\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−2.82843	+	4.89898i	−0.207950	+	0.360180i
$186$		0			0
$187$	8.82843	+	15.2913i	0.645599	+	1.11821i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−11.2426	−	19.4728i	−0.813489	−	1.40900i	−0.910408	−	0.413712i	$-0.864232\pi$
$191$	−11.2426	−	19.4728i	−0.813489	−	1.40900i	0.0969189	−	0.995292i	$-0.469101\pi$
$192$		0			0
$193$	−8.65685	+	14.9941i	−0.623134	+	1.07930i	0.365765	+	0.930707i	$0.380808\pi$
$193$	−8.65685	+	14.9941i	−0.623134	+	1.07930i	−0.988899	+	0.148592i	$0.952526\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−11.6569			−0.830516			−0.415258	−	0.909704i	$-0.636309\pi$
$197$	−11.6569			−0.830516			−0.415258	+	0.909704i	$0.636309\pi$
$198$		0			0
$199$	0.343146	−	0.594346i	0.0243250	−	0.0421321i	−0.853607	−	0.520918i	$-0.825590\pi$
$199$	0.343146	−	0.594346i	0.0243250	−	0.0421321i	0.877932	+	0.478786i	$0.158923\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−5.69239	−	0.778985i	−0.399527	−	0.0546741i
$204$		0			0
$205$	−0.0857864	−	0.148586i	−0.00599158	−	0.0103777i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	27.3137			1.88933
$210$		0			0
$211$	−18.6274			−1.28236			−0.641182	−	0.767389i	$-0.721556\pi$
$211$	−18.6274			−1.28236			−0.641182	+	0.767389i	$0.721556\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	6.44975	+	11.1713i	0.439869	+	0.761876i
$216$		0			0
$217$	−7.82843	+	10.0951i	−0.531428	+	0.685302i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	3.65685	−	6.33386i	0.245987	−	0.426061i
$222$		0			0
$223$	18.9706			1.27036			0.635181	−	0.772363i	$-0.280925\pi$
$223$	18.9706			1.27036			0.635181	+	0.772363i	$0.280925\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	7.00000	−	12.1244i	0.464606	−	0.804722i	−0.534577	−	0.845120i	$-0.679529\pi$
$227$	7.00000	−	12.1244i	0.464606	−	0.804722i	0.999184	+	0.0403978i	$0.0128625\pi$
$228$		0			0
$229$	7.00000	+	12.1244i	0.462573	+	0.801200i	0.999088	−	0.0426906i	$-0.0135930\pi$
$229$	7.00000	+	12.1244i	0.462573	+	0.801200i	−0.536515	+	0.843891i	$0.680260\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	0.171573	+	0.297173i	0.0112401	+	0.0194684i	0.871591	−	0.490234i	$-0.163089\pi$
$233$	0.171573	+	0.297173i	0.0112401	+	0.0194684i	−0.860351	+	0.509703i	$0.829755\pi$
$234$		0			0
$235$	−0.171573	+	0.297173i	−0.0111922	+	0.0193854i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	13.5147			0.874194			0.437097	−	0.899414i	$-0.356007\pi$
$239$	13.5147			0.874194			0.437097	+	0.899414i	$0.356007\pi$
$240$		0			0
$241$	5.00000	−	8.66025i	0.322078	−	0.557856i	−0.658838	−	0.752285i	$-0.728952\pi$
$241$	5.00000	−	8.66025i	0.322078	−	0.557856i	0.980917	+	0.194429i	$0.0622852\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	1.74264	+	6.77962i	0.111333	+	0.433134i
$246$		0			0
$247$	−5.65685	−	9.79796i	−0.359937	−	0.623429i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−23.4558			−1.48052			−0.740260	−	0.672321i	$-0.765298\pi$
$251$	−23.4558			−1.48052			−0.740260	+	0.672321i	$0.765298\pi$
$252$		0			0
$253$	40.6274			2.55422
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−3.65685	−	6.33386i	−0.228108	−	0.395095i	0.729139	−	0.684365i	$-0.239921\pi$
$257$	−3.65685	−	6.33386i	−0.228108	−	0.395095i	−0.957247	+	0.289270i	$0.906587\pi$
$258$		0			0
$259$	−5.65685	−	13.8564i	−0.351500	−	0.860995i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	4.86396	−	8.42463i	0.299925	−	0.519485i	−0.676194	−	0.736724i	$-0.736372\pi$
$263$	4.86396	−	8.42463i	0.299925	−	0.519485i	0.976118	+	0.217239i	$0.0697051\pi$
$264$		0			0
$265$	5.65685			0.347498
$266$		0			0
$267$		0			0
$268$		0			0
$269$	2.32843	−	4.03295i	0.141967	−	0.245894i	−0.786270	−	0.617882i	$-0.787991\pi$
$269$	2.32843	−	4.03295i	0.141967	−	0.245894i	0.928237	+	0.371989i	$0.121324\pi$
$270$		0			0
$271$	−9.65685	−	16.7262i	−0.586612	−	1.01604i	−0.994672	−	0.103087i	$-0.967128\pi$
$271$	−9.65685	−	16.7262i	−0.586612	−	1.01604i	0.408060	−	0.912955i	$-0.366205\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−2.41421	−	4.18154i	−0.145583	−	0.252156i
$276$		0			0
$277$	8.31371	−	14.3998i	0.499522	−	0.865198i	−0.500478	−	0.865750i	$-0.666842\pi$
$277$	8.31371	−	14.3998i	0.499522	−	0.865198i	1.00000		0.000551476i	$0.000175540\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−25.3137			−1.51009			−0.755045	−	0.655673i	$-0.772385\pi$
$281$	−25.3137			−1.51009			−0.755045	+	0.655673i	$0.772385\pi$
$282$		0			0
$283$	−9.00000	+	15.5885i	−0.534994	+	0.926638i	0.464169	+	0.885747i	$0.346353\pi$
$283$	−9.00000	+	15.5885i	−0.534994	+	0.926638i	−0.999164	+	0.0408910i	$0.986980\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	0.449747	+	0.0615465i	0.0265478	+	0.00363298i
$288$		0			0
$289$	1.81371	+	3.14144i	0.106689	+	0.184790i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	16.9706			0.991431			0.495715	−	0.868485i	$-0.334906\pi$
$293$	16.9706			0.991431			0.495715	+	0.868485i	$0.334906\pi$
$294$		0			0
$295$	−4.00000			−0.232889
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−8.41421	−	14.5738i	−0.486607	−	0.842827i
$300$		0			0
$301$	−33.8137	−	4.62730i	−1.94899	−	0.266713i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−2.32843	+	4.03295i	−0.133325	+	0.230926i
$306$		0			0
$307$	13.2426			0.755797			0.377899	−	0.925847i	$-0.376647\pi$
$307$	13.2426			0.755797			0.377899	+	0.925847i	$0.376647\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	5.17157	−	8.95743i	0.293253	−	0.507929i	−0.681324	−	0.731982i	$-0.738596\pi$
$311$	5.17157	−	8.95743i	0.293253	−	0.507929i	0.974577	+	0.224053i	$0.0719288\pi$
$312$		0			0
$313$	6.48528	+	11.2328i	0.366570	+	0.634917i	0.989027	−	0.147737i	$-0.0471988\pi$
$313$	6.48528	+	11.2328i	0.366570	+	0.634917i	−0.622457	+	0.782654i	$0.713865\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−11.0000	−	19.0526i	−0.617822	−	1.07010i	−0.989882	−	0.141890i	$-0.954682\pi$
$317$	−11.0000	−	19.0526i	−0.617822	−	1.07010i	0.372061	−	0.928208i	$-0.378651\pi$
$318$		0			0
$319$	−5.24264	+	9.08052i	−0.293532	+	0.508412i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−20.6863			−1.15102
$324$		0			0
$325$	−1.00000	+	1.73205i	−0.0554700	+	0.0960769i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−0.343146	−	0.840532i	−0.0189182	−	0.0463400i
$330$		0			0
$331$	−4.75736	−	8.23999i	−0.261488	−	0.452911i	0.705149	−	0.709059i	$-0.250880\pi$
$331$	−4.75736	−	8.23999i	−0.261488	−	0.452911i	−0.966638	+	0.256148i	$0.917547\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−6.89949			−0.376960
$336$		0			0
$337$	−8.97056			−0.488658			−0.244329	−	0.969692i	$-0.578568\pi$
$337$	−8.97056			−0.488658			−0.244329	+	0.969692i	$0.578568\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	11.6569	+	20.1903i	0.631254	+	1.09336i
$342$		0			0
$343$	−17.0000	−	7.34847i	−0.917914	−	0.396780i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−12.6924	+	21.9839i	−0.681363	+	1.18016i	0.293202	+	0.956051i	$0.405279\pi$
$347$	−12.6924	+	21.9839i	−0.681363	+	1.18016i	−0.974565	+	0.224105i	$0.928054\pi$
$348$		0			0
$349$	4.17157			0.223299			0.111650	−	0.993748i	$-0.464387\pi$
$349$	4.17157			0.223299			0.111650	+	0.993748i	$0.464387\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	11.1716	−	19.3497i	0.594603	−	1.02988i	−0.399000	−	0.916951i	$-0.630643\pi$
$353$	11.1716	−	19.3497i	0.594603	−	1.02988i	0.993603	−	0.112931i	$-0.0360240\pi$
$354$		0			0
$355$	6.00000	+	10.3923i	0.318447	+	0.551566i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	5.24264	+	9.08052i	0.276696	+	0.479252i	0.970562	−	0.240853i	$-0.0774272\pi$
$359$	5.24264	+	9.08052i	0.276696	+	0.479252i	−0.693866	+	0.720105i	$0.744094\pi$
$360$		0			0
$361$	−6.50000	+	11.2583i	−0.342105	+	0.592544i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	7.65685			0.400778
$366$		0			0
$367$	−12.2071	+	21.1433i	−0.637206	+	1.10367i	0.348837	+	0.937183i	$0.386577\pi$
$367$	−12.2071	+	21.1433i	−0.637206	+	1.10367i	−0.986043	+	0.166490i	$0.946757\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−9.17157	+	11.8272i	−0.476164	+	0.614037i
$372$		0			0
$373$	−6.00000	−	10.3923i	−0.310668	−	0.538093i	0.667839	−	0.744306i	$-0.267219\pi$
$373$	−6.00000	−	10.3923i	−0.310668	−	0.538093i	−0.978507	+	0.206213i	$0.933886\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	4.34315			0.223683
$378$		0			0
$379$	27.3137			1.40301			0.701505	−	0.712664i	$-0.252512\pi$
$379$	27.3137			1.40301			0.701505	+	0.712664i	$0.252512\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	9.44975	+	16.3674i	0.482860	+	0.836337i	0.999806	−	0.0196803i	$-0.00626483\pi$
$383$	9.44975	+	16.3674i	0.482860	+	0.836337i	−0.516947	+	0.856018i	$0.672931\pi$
$384$		0			0
$385$	12.6569	+	1.73205i	0.645053	+	0.0882735i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−8.65685	+	14.9941i	−0.438920	+	0.760232i	−0.997606	−	0.0691473i	$-0.977972\pi$
$389$	−8.65685	+	14.9941i	−0.438920	+	0.760232i	0.558687	+	0.829379i	$0.311305\pi$
$390$		0			0
$391$	−30.7696			−1.55608
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−2.00000	+	3.46410i	−0.100631	+	0.174298i
$396$		0			0
$397$	−10.3137	−	17.8639i	−0.517630	−	0.896562i	−0.999790	−	0.0204787i	$-0.993481\pi$
$397$	−10.3137	−	17.8639i	−0.517630	−	0.896562i	0.482160	−	0.876083i	$-0.339852\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−4.84315	−	8.38857i	−0.241855	−	0.418905i	0.719388	−	0.694609i	$-0.244423\pi$
$401$	−4.84315	−	8.38857i	−0.241855	−	0.418905i	−0.961243	+	0.275703i	$0.911089\pi$
$402$		0			0
$403$	4.82843	−	8.36308i	0.240521	−	0.416595i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−27.3137			−1.35389
$408$		0			0
$409$	−1.57107	+	2.72117i	−0.0776843	+	0.134553i	−0.902250	−	0.431212i	$-0.858086\pi$
$409$	−1.57107	+	2.72117i	−0.0776843	+	0.134553i	0.824566	+	0.565766i	$0.191419\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	6.48528	−	8.36308i	0.319120	−	0.411520i
$414$		0			0
$415$	6.62132	+	11.4685i	0.325028	+	0.562965i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−7.31371			−0.357298			−0.178649	−	0.983913i	$-0.557173\pi$
$419$	−7.31371			−0.357298			−0.178649	+	0.983913i	$0.557173\pi$
$420$		0			0
$421$	38.6569			1.88402			0.942010	−	0.335585i	$-0.108934\pi$
$421$	38.6569			1.88402			0.942010	+	0.335585i	$0.108934\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	1.82843	+	3.16693i	0.0886917	+	0.153619i
$426$		0			0
$427$	−4.65685	−	11.4069i	−0.225361	−	0.552019i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	2.41421	−	4.18154i	0.116289	−	0.201418i	−0.802006	−	0.597317i	$-0.796234\pi$
$431$	2.41421	−	4.18154i	0.116289	−	0.201418i	0.918294	+	0.395899i	$0.129567\pi$
$432$		0			0
$433$	3.31371			0.159247			0.0796233	−	0.996825i	$-0.474628\pi$
$433$	3.31371			0.159247			0.0796233	+	0.996825i	$0.474628\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−23.7990	+	41.2211i	−1.13846	+	1.97187i
$438$		0			0
$439$	14.8284	+	25.6836i	0.707722	+	1.22581i	0.965700	+	0.259660i	$0.0836105\pi$
$439$	14.8284	+	25.6836i	0.707722	+	1.22581i	−0.257978	+	0.966151i	$0.583056\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−9.20711	−	15.9472i	−0.437443	−	0.757673i	0.560049	−	0.828460i	$-0.310782\pi$
$443$	−9.20711	−	15.9472i	−0.437443	−	0.757673i	−0.997491	+	0.0707865i	$0.977449\pi$
$444$		0			0
$445$	8.32843	−	14.4253i	0.394805	−	0.683823i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−9.48528			−0.447638			−0.223819	−	0.974631i	$-0.571852\pi$
$449$	−9.48528			−0.447638			−0.223819	+	0.974631i	$0.571852\pi$
$450$		0			0
$451$	0.414214	−	0.717439i	0.0195046	−	0.0337829i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−2.00000	−	4.89898i	−0.0937614	−	0.229668i
$456$		0			0
$457$	2.48528	+	4.30463i	0.116257	+	0.201362i	0.918281	−	0.395928i	$-0.129577\pi$
$457$	2.48528	+	4.30463i	0.116257	+	0.201362i	−0.802025	+	0.597291i	$0.796244\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	21.3137			0.992678			0.496339	−	0.868129i	$-0.334677\pi$
$461$	21.3137			0.992678			0.496339	+	0.868129i	$0.334677\pi$
$462$		0			0
$463$	−4.89949			−0.227699			−0.113849	−	0.993498i	$-0.536318\pi$
$463$	−4.89949			−0.227699			−0.113849	+	0.993498i	$0.536318\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	7.93503	+	13.7439i	0.367189	+	0.635991i	0.989125	−	0.147078i	$-0.0469868\pi$
$467$	7.93503	+	13.7439i	0.367189	+	0.635991i	−0.621936	+	0.783068i	$0.713653\pi$
$468$		0			0
$469$	11.1863	−	14.4253i	0.516535	−	0.666097i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−31.1421	+	53.9398i	−1.43192	+	2.48015i
$474$		0			0
$475$	5.65685			0.259554
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−9.24264	+	16.0087i	−0.422307	+	0.731457i	−0.996165	−	0.0874978i	$-0.972113\pi$
$479$	−9.24264	+	16.0087i	−0.422307	+	0.731457i	0.573858	+	0.818955i	$0.305446\pi$
$480$		0			0
$481$	5.65685	+	9.79796i	0.257930	+	0.446748i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	3.00000	+	5.19615i	0.136223	+	0.235945i
$486$		0			0
$487$	−9.14214	+	15.8346i	−0.414270	+	0.717536i	−0.995351	−	0.0963090i	$-0.969296\pi$
$487$	−9.14214	+	15.8346i	−0.414270	+	0.717536i	0.581082	+	0.813845i	$0.302630\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−18.4853			−0.834229			−0.417115	−	0.908854i	$-0.636959\pi$
$491$	−18.4853			−0.834229			−0.417115	+	0.908854i	$0.636959\pi$
$492$		0			0
$493$	3.97056	−	6.87722i	0.178825	−	0.309734i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−31.4558	−	4.30463i	−1.41099	−	0.193089i
$498$		0			0
$499$	−7.92893	−	13.7333i	−0.354948	−	0.614788i	0.632161	−	0.774837i	$-0.282168\pi$
$499$	−7.92893	−	13.7333i	−0.354948	−	0.614788i	−0.987109	+	0.160049i	$0.948835\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	18.0711			0.805749			0.402875	−	0.915255i	$-0.368011\pi$
$503$	18.0711			0.805749			0.402875	+	0.915255i	$0.368011\pi$
$504$		0			0
$505$	5.48528			0.244092
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−8.25736	−	14.3022i	−0.366001	−	0.633932i	0.622935	−	0.782273i	$-0.285940\pi$
$509$	−8.25736	−	14.3022i	−0.366001	−	0.633932i	−0.988936	+	0.148341i	$0.952607\pi$
$510$		0			0
$511$	−12.4142	+	16.0087i	−0.549172	+	0.708184i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	5.20711	−	9.01897i	0.229453	−	0.397423i
$516$		0			0
$517$	−1.65685			−0.0728684
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−4.31371	+	7.47156i	−0.188987	+	0.327335i	−0.944913	−	0.327322i	$-0.893854\pi$
$521$	−4.31371	+	7.47156i	−0.188987	+	0.327335i	0.755926	+	0.654657i	$0.227187\pi$
$522$		0			0
$523$	19.9706	+	34.5900i	0.873252	+	1.51252i	0.858613	+	0.512624i	$0.171326\pi$
$523$	19.9706	+	34.5900i	0.873252	+	1.51252i	0.0146382	+	0.999893i	$0.495340\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−8.82843	−	15.2913i	−0.384572	−	0.666099i
$528$		0			0
$529$	−23.8995	+	41.3951i	−1.03911	+	1.79979i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−0.343146			−0.0148633
$534$		0			0
$535$	4.20711	−	7.28692i	0.181889	−	0.315041i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−24.1421	+	23.6544i	−1.03988	+	1.01887i
$540$		0			0
$541$	3.25736	+	5.64191i	0.140045	+	0.242565i	0.927513	−	0.373790i	$-0.121942\pi$
$541$	3.25736	+	5.64191i	0.140045	+	0.242565i	−0.787468	+	0.616355i	$0.788609\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	4.31371			0.184779
$546$		0			0
$547$	−27.7279			−1.18556			−0.592780	−	0.805364i	$-0.701970\pi$
$547$	−27.7279			−1.18556			−0.592780	+	0.805364i	$0.701970\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−6.14214	−	10.6385i	−0.261664	−	0.453215i
$552$		0			0
$553$	−4.00000	−	9.79796i	−0.170097	−	0.416652i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	2.65685	−	4.60181i	0.112575	−	0.194985i	−0.804233	−	0.594314i	$-0.797424\pi$
$557$	2.65685	−	4.60181i	0.112575	−	0.194985i	0.916808	+	0.399329i	$0.130757\pi$
$558$		0			0
$559$	25.7990			1.09118
$560$		0			0
$561$		0			0
$562$		0			0
$563$	5.03553	−	8.72180i	0.212222	−	0.367580i	−0.740187	−	0.672401i	$-0.765263\pi$
$563$	5.03553	−	8.72180i	0.212222	−	0.367580i	0.952410	+	0.304821i	$0.0985965\pi$
$564$		0			0
$565$	5.65685	+	9.79796i	0.237986	+	0.412203i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	4.31371	+	7.47156i	0.180840	+	0.313224i	0.942167	−	0.335144i	$-0.108785\pi$
$569$	4.31371	+	7.47156i	0.180840	+	0.313224i	−0.761327	+	0.648368i	$0.775452\pi$
$570$		0			0
$571$	−6.48528	+	11.2328i	−0.271401	+	0.470080i	−0.969221	−	0.246193i	$-0.920820\pi$
$571$	−6.48528	+	11.2328i	−0.271401	+	0.470080i	0.697820	+	0.716273i	$0.254153\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	8.41421			0.350897
$576$		0			0
$577$	−17.1421	+	29.6910i	−0.713636	+	1.23605i	0.249847	+	0.968285i	$0.419620\pi$
$577$	−17.1421	+	29.6910i	−0.713636	+	1.23605i	−0.963483	+	0.267769i	$0.913714\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−34.7132	−	4.75039i	−1.44015	−	0.197080i
$582$		0			0
$583$	13.6569	+	23.6544i	0.565609	+	0.979664i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	45.3137			1.87030			0.935148	−	0.354256i	$-0.115266\pi$
$587$	45.3137			1.87030			0.935148	+	0.354256i	$0.115266\pi$
$588$		0			0
$589$	−27.3137			−1.12544
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−18.9706	−	32.8580i	−0.779028	−	1.34932i	−0.932503	−	0.361163i	$-0.882380\pi$
$593$	−18.9706	−	32.8580i	−0.779028	−	1.34932i	0.153475	−	0.988153i	$-0.450954\pi$
$594$		0			0
$595$	−9.58579	−	1.31178i	−0.392979	−	0.0537779i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−1.31371	+	2.27541i	−0.0536767	+	0.0929707i	−0.891615	−	0.452794i	$-0.850427\pi$
$599$	−1.31371	+	2.27541i	−0.0536767	+	0.0929707i	0.837939	+	0.545765i	$0.183761\pi$
$600$		0			0
$601$	−34.0000			−1.38689			−0.693444	−	0.720510i	$-0.743908\pi$
$601$	−34.0000			−1.38689			−0.693444	+	0.720510i	$0.743908\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	6.15685	−	10.6640i	0.250312	−	0.433553i
$606$		0			0
$607$	−9.37868	−	16.2443i	−0.380669	−	0.659338i	0.610489	−	0.792025i	$-0.290973\pi$
$607$	−9.37868	−	16.2443i	−0.380669	−	0.659338i	−0.991158	+	0.132687i	$0.957640\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	0.343146	+	0.594346i	0.0138822	+	0.0240447i
$612$		0			0
$613$	−2.51472	+	4.35562i	−0.101569	+	0.175922i	−0.912331	−	0.409453i	$-0.865719\pi$
$613$	−2.51472	+	4.35562i	−0.101569	+	0.175922i	0.810763	+	0.585375i	$0.199053\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	35.3137			1.42168			0.710838	−	0.703356i	$-0.248316\pi$
$617$	35.3137			1.42168			0.710838	+	0.703356i	$0.248316\pi$
$618$		0			0
$619$	5.72792	−	9.92105i	0.230225	−	0.398761i	−0.727649	−	0.685949i	$-0.759387\pi$
$619$	5.72792	−	9.92105i	0.230225	−	0.398761i	0.957874	+	0.287188i	$0.0927206\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	16.6569	+	40.8008i	0.667343	+	1.63465i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	20.6863			0.824816
$630$		0			0
$631$	−18.4853			−0.735887			−0.367944	−	0.929848i	$-0.619938\pi$
$631$	−18.4853			−0.735887			−0.367944	+	0.929848i	$0.619938\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−7.82843	−	13.5592i	−0.310662	−	0.538082i
$636$		0			0
$637$	13.4853	+	3.76127i	0.534306	+	0.149027i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−24.0563	+	41.6668i	−0.950169	+	1.64574i	−0.205113	+	0.978738i	$0.565756\pi$
$641$	−24.0563	+	41.6668i	−0.950169	+	1.64574i	−0.745056	+	0.667002i	$0.767577\pi$
$642$		0			0
$643$	26.0000			1.02534			0.512670	−	0.858586i	$-0.328656\pi$
$643$	26.0000			1.02534			0.512670	+	0.858586i	$0.328656\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−14.6213	+	25.3249i	−0.574823	+	0.995623i	0.421237	+	0.906950i	$0.361596\pi$
$647$	−14.6213	+	25.3249i	−0.574823	+	0.995623i	−0.996061	+	0.0886729i	$0.971737\pi$
$648$		0			0
$649$	−9.65685	−	16.7262i	−0.379065	−	0.656559i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−2.17157	−	3.76127i	−0.0849802	−	0.147190i	0.820403	−	0.571786i	$-0.193749\pi$
$653$	−2.17157	−	3.76127i	−0.0849802	−	0.147190i	−0.905383	+	0.424596i	$0.860416\pi$
$654$		0			0
$655$	−1.17157	+	2.02922i	−0.0457771	+	0.0792883i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−35.3137			−1.37563			−0.687813	−	0.725888i	$-0.741429\pi$
$659$	−35.3137			−1.37563			−0.687813	+	0.725888i	$0.741429\pi$
$660$		0			0
$661$	13.8431	−	23.9770i	0.538436	−	0.932598i	−0.460553	−	0.887632i	$-0.652349\pi$
$661$	13.8431	−	23.9770i	0.538436	−	0.932598i	0.998989	−	0.0449660i	$-0.0143180\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−9.17157	+	11.8272i	−0.355658	+	0.458638i
$666$		0			0
$667$	−9.13604	−	15.8241i	−0.353749	−	0.612711i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−22.4853			−0.868035
$672$		0			0
$673$	5.65685			0.218056			0.109028	−	0.994039i	$-0.465226\pi$
$673$	5.65685			0.218056			0.109028	+	0.994039i	$0.465226\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−5.48528	−	9.50079i	−0.210816	−	0.365145i	0.741154	−	0.671335i	$-0.234279\pi$
$677$	−5.48528	−	9.50079i	−0.210816	−	0.365145i	−0.951970	+	0.306190i	$0.900946\pi$
$678$		0			0
$679$	−15.7279	−	2.15232i	−0.603582	−	0.0825983i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−8.03553	+	13.9180i	−0.307471	+	0.532556i	−0.977808	−	0.209501i	$-0.932816\pi$
$683$	−8.03553	+	13.9180i	−0.307471	+	0.532556i	0.670337	+	0.742057i	$0.266149\pi$
$684$		0			0
$685$	−4.00000			−0.152832
$686$		0			0
$687$		0			0
$688$		0			0
$689$	5.65685	−	9.79796i	0.215509	−	0.373273i
$690$		0			0
$691$	−15.3848	−	26.6472i	−0.585264	−	1.01371i	−0.994842	−	0.101433i	$-0.967657\pi$
$691$	−15.3848	−	26.6472i	−0.585264	−	1.01371i	0.409578	−	0.912275i	$-0.365676\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−7.24264	−	12.5446i	−0.274729	−	0.475845i
$696$		0			0
$697$	−0.313708	+	0.543359i	−0.0118826	+	0.0205812i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	11.0000			0.415464			0.207732	−	0.978186i	$-0.433392\pi$
$701$	11.0000			0.415464			0.207732	+	0.978186i	$0.433392\pi$
$702$		0			0
$703$	16.0000	−	27.7128i	0.603451	−	1.04521i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−8.89340	+	11.4685i	−0.334471	+	0.431316i
$708$		0			0
$709$	−24.7132	−	42.8045i	−0.928124	−	1.60756i	−0.786459	−	0.617643i	$-0.788088\pi$
$709$	−24.7132	−	42.8045i	−0.928124	−	1.60756i	−0.141665	−	0.989915i	$-0.545246\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−40.6274			−1.52151
$714$		0			0
$715$	−9.65685			−0.361146
$716$		0			0
$717$		0			0
$718$		0			0
$719$	6.89949	+	11.9503i	0.257308	+	0.445670i	0.965520	−	0.260330i	$-0.0838313\pi$
$719$	6.89949	+	11.9503i	0.257308	+	0.445670i	−0.708212	+	0.706000i	$0.750498\pi$
$720$		0			0
$721$	10.4142	+	25.5095i	0.387846	+	0.950024i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−1.08579	+	1.88064i	−0.0403251	+	0.0698451i
$726$		0			0
$727$	23.9289			0.887475			0.443737	−	0.896157i	$-0.353652\pi$
$727$	23.9289			0.887475			0.443737	+	0.896157i	$0.353652\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	23.5858	−	40.8518i	0.872352	−	1.51096i
$732$		0			0
$733$	1.82843	+	3.16693i	0.0675345	+	0.116973i	0.897815	−	0.440372i	$-0.145153\pi$
$733$	1.82843	+	3.16693i	0.0675345	+	0.116973i	−0.830281	+	0.557345i	$0.811820\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−16.6569	−	28.8505i	−0.613563	−	1.06272i
$738$		0			0
$739$	−5.58579	+	9.67487i	−0.205476	+	0.355896i	−0.950284	−	0.311383i	$-0.899208\pi$
$739$	−5.58579	+	9.67487i	−0.205476	+	0.355896i	0.744808	+	0.667279i	$0.232541\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	19.2426			0.705944			0.352972	−	0.935634i	$-0.385171\pi$
$743$	19.2426			0.705944			0.352972	+	0.935634i	$0.385171\pi$
$744$		0			0
$745$	3.32843	−	5.76500i	0.121944	−	0.211213i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	8.41421	+	20.6105i	0.307449	+	0.753092i
$750$		0			0
$751$	6.00000	+	10.3923i	0.218943	+	0.379221i	0.954485	−	0.298259i	$-0.0964058\pi$
$751$	6.00000	+	10.3923i	0.218943	+	0.379221i	−0.735542	+	0.677479i	$0.763072\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	16.8284			0.612449
$756$		0			0
$757$	6.00000			0.218074			0.109037	−	0.994038i	$-0.465223\pi$
$757$	6.00000			0.218074			0.109037	+	0.994038i	$0.465223\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	11.9706	+	20.7336i	0.433933	+	0.751593i	0.997208	−	0.0746761i	$-0.0237923\pi$
$761$	11.9706	+	20.7336i	0.433933	+	0.751593i	−0.563275	+	0.826269i	$0.690459\pi$
$762$		0			0
$763$	−6.99390	+	9.01897i	−0.253196	+	0.326509i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−4.00000	+	6.92820i	−0.144432	+	0.250163i
$768$		0			0
$769$	−47.2548			−1.70405			−0.852026	−	0.523499i	$-0.824626\pi$
$769$	−47.2548			−1.70405			−0.852026	+	0.523499i	$0.824626\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	17.8284	−	30.8797i	0.641244	−	1.11067i	−0.343911	−	0.939002i	$-0.611752\pi$
$773$	17.8284	−	30.8797i	0.641244	−	1.11067i	0.985155	−	0.171665i	$-0.0549147\pi$
$774$		0			0
$775$	2.41421	+	4.18154i	0.0867211	+	0.150205i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	0.485281	+	0.840532i	0.0173870	+	0.0301152i
$780$		0			0
$781$	−28.9706	+	50.1785i	−1.03665	+	1.79553i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	21.3137			0.760719
$786$		0			0
$787$	2.20711	−	3.82282i	0.0786749	−	0.136269i	−0.824004	−	0.566585i	$-0.808264\pi$
$787$	2.20711	−	3.82282i	0.0786749	−	0.136269i	0.902678	+	0.430316i	$0.141598\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−29.6569	−	4.05845i	−1.05448	−	0.144302i
$792$		0			0
$793$	4.65685	+	8.06591i	0.165370	+	0.286429i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	12.6863			0.449372			0.224686	−	0.974431i	$-0.427864\pi$
$797$	12.6863			0.449372			0.224686	+	0.974431i	$0.427864\pi$
$798$		0			0
$799$	1.25483			0.0443928
$800$		0			0
$801$		0			0
$802$		0			0
$803$	18.4853	+	32.0174i	0.652331	+	1.12987i
$804$		0			0
$805$	−13.6421	+	17.5922i	−0.480822	+	0.620043i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−1.01472	+	1.75754i	−0.0356756	+	0.0617920i	−0.883312	−	0.468786i	$-0.844692\pi$
$809$	−1.01472	+	1.75754i	−0.0356756	+	0.0617920i	0.847636	+	0.530578i	$0.178025\pi$
$810$		0			0
$811$	23.8579			0.837763			0.418881	−	0.908041i	$-0.362422\pi$
$811$	23.8579			0.837763			0.418881	+	0.908041i	$0.362422\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−2.17157	+	3.76127i	−0.0760669	+	0.131752i
$816$		0			0
$817$	−36.4853	−	63.1944i	−1.27646	−	2.21089i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	6.31371	+	10.9357i	0.220350	+	0.381657i	0.954914	−	0.296882i	$-0.0959467\pi$
$821$	6.31371	+	10.9357i	0.220350	+	0.381657i	−0.734564	+	0.678539i	$0.762613\pi$
$822$		0			0
$823$	26.0061	−	45.0439i	0.906516	−	1.57013i	0.0876457	−	0.996152i	$-0.472066\pi$
$823$	26.0061	−	45.0439i	0.906516	−	1.57013i	0.818870	−	0.573979i	$-0.194601\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	51.5269			1.79177			0.895883	−	0.444290i	$-0.146544\pi$
$827$	51.5269			1.79177			0.895883	+	0.444290i	$0.146544\pi$
$828$		0			0
$829$	8.65685	−	14.9941i	0.300665	−	0.520767i	−0.675622	−	0.737248i	$-0.736125\pi$
$829$	8.65685	−	14.9941i	0.300665	−	0.520767i	0.976287	+	0.216481i	$0.0694581\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	18.2843	−	17.9149i	0.633512	−	0.620713i
$834$		0			0
$835$	6.03553	+	10.4539i	0.208868	+	0.361770i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	8.14214			0.281098			0.140549	−	0.990074i	$-0.455113\pi$
$839$	8.14214			0.281098			0.140549	+	0.990074i	$0.455113\pi$
$840$		0			0
$841$	−24.2843			−0.837389
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−4.50000	−	7.79423i	−0.154805	−	0.268130i
$846$		0			0
$847$	12.3137	+	30.1623i	0.423104	+	1.03639i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	23.7990	−	41.2211i	0.815819	−	1.41304i
$852$		0			0
$853$	35.3137			1.20912			0.604559	−	0.796560i	$-0.293349\pi$
$853$	35.3137			1.20912			0.604559	+	0.796560i	$0.293349\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	7.48528	−	12.9649i	0.255692	−	0.442872i	−0.709391	−	0.704815i	$-0.751030\pi$
$857$	7.48528	−	12.9649i	0.255692	−	0.442872i	0.965083	+	0.261943i	$0.0843633\pi$
$858$		0			0
$859$	−7.31371	−	12.6677i	−0.249541	−	0.432217i	0.713858	−	0.700291i	$-0.246946\pi$
$859$	−7.31371	−	12.6677i	−0.249541	−	0.432217i	−0.963398	+	0.268074i	$0.913613\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	13.0061	+	22.5272i	0.442733	+	0.766835i	0.997891	−	0.0649091i	$-0.0206757\pi$
$863$	13.0061	+	22.5272i	0.442733	+	0.766835i	−0.555159	+	0.831745i	$0.687342\pi$
$864$		0			0
$865$	−10.8284	+	18.7554i	−0.368178	+	0.637702i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−19.3137			−0.655173
$870$		0			0
$871$	−6.89949	+	11.9503i	−0.233780	+	0.404920i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	2.62132	+	0.358719i	0.0886168	+	0.0121269i
$876$		0			0
$877$	−14.1421	−	24.4949i	−0.477546	−	0.827134i	0.522123	−	0.852870i	$-0.325140\pi$
$877$	−14.1421	−	24.4949i	−0.477546	−	0.827134i	−0.999669	+	0.0257364i	$0.991807\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−24.4558			−0.823938			−0.411969	−	0.911198i	$-0.635159\pi$
$881$	−24.4558			−0.823938			−0.411969	+	0.911198i	$0.635159\pi$
$882$		0			0
$883$	29.3137			0.986485			0.493242	−	0.869892i	$-0.335812\pi$
$883$	29.3137			0.986485			0.493242	+	0.869892i	$0.335812\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	10.2071	+	17.6792i	0.342721	+	0.593610i	0.984937	−	0.172913i	$-0.0553181\pi$
$887$	10.2071	+	17.6792i	0.342721	+	0.593610i	−0.642216	+	0.766524i	$0.721985\pi$
$888$		0			0
$889$	41.0416	+	5.61642i	1.37649	+	0.188369i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	0.970563	−	1.68106i	0.0324786	−	0.0562547i
$894$		0			0
$895$	10.4853			0.350484
$896$		0			0
$897$		0			0
$898$		0			0
$899$	5.24264	−	9.08052i	0.174852	−	0.302852i
$900$		0			0
$901$	−10.3431	−	17.9149i	−0.344580	−	0.596830i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−4.91421	−	8.51167i	−0.163354	−	0.282937i
$906$		0			0
$907$	−1.89340	+	3.27946i	−0.0628693	+	0.108893i	−0.895747	−	0.444565i	$-0.853358\pi$
$907$	−1.89340	+	3.27946i	−0.0628693	+	0.108893i	0.832878	+	0.553457i	$0.186692\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	1.51472			0.0501849			0.0250924	−	0.999685i	$-0.492012\pi$
$911$	1.51472			0.0501849			0.0250924	+	0.999685i	$0.492012\pi$
$912$		0			0
$913$	−31.9706	+	55.3746i	−1.05807	+	1.83263i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−2.34315	−	5.73951i	−0.0773775	−	0.189535i
$918$		0			0
$919$	−28.6274	−	49.5841i	−0.944331	−	1.63563i	−0.757084	−	0.653317i	$-0.773377\pi$
$919$	−28.6274	−	49.5841i	−0.944331	−	1.63563i	−0.187247	−	0.982313i	$-0.559956\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	24.0000			0.789970
$924$		0			0
$925$	−5.65685			−0.185996
$926$		0			0
$927$		0			0
$928$		0			0
$929$	24.3995	+	42.2612i	0.800521	+	1.38654i	0.919273	+	0.393620i	$0.128777\pi$
$929$	24.3995	+	42.2612i	0.800521	+	1.38654i	−0.118752	+	0.992924i	$0.537889\pi$
$930$		0			0
$931$	−9.85786	−	38.3513i	−0.323078	−	1.25691i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−8.82843	+	15.2913i	−0.288720	+	0.500078i
$936$		0			0
$937$	−26.6274			−0.869880			−0.434940	−	0.900459i	$-0.643230\pi$
$937$	−26.6274			−0.869880			−0.434940	+	0.900459i	$0.643230\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−5.00000	+	8.66025i	−0.162995	+	0.282316i	−0.935942	−	0.352155i	$-0.885449\pi$
$941$	−5.00000	+	8.66025i	−0.162995	+	0.282316i	0.772946	+	0.634472i	$0.218782\pi$
$942$		0			0
$943$	0.721825	+	1.25024i	0.0235059	+	0.0407134i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	15.4497	+	26.7597i	0.502049	+	0.869575i	0.999997	+	0.00236799i	$0.000753754\pi$
$947$	15.4497	+	26.7597i	0.502049	+	0.869575i	−0.497948	+	0.867207i	$0.665913\pi$
$948$		0			0
$949$	7.65685	−	13.2621i	0.248552	−	0.430505i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	9.37258			0.303608			0.151804	−	0.988411i	$-0.451492\pi$
$953$	9.37258			0.303608			0.151804	+	0.988411i	$0.451492\pi$
$954$		0			0
$955$	11.2426	−	19.4728i	0.363803	−	0.630126i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	6.48528	−	8.36308i	0.209421	−	0.270058i
$960$		0			0
$961$	3.84315	+	6.65652i	0.123972	+	0.214727i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−17.3137			−0.557348
$966$		0			0
$967$	−33.2426			−1.06901			−0.534506	−	0.845165i	$-0.679502\pi$
$967$	−33.2426			−1.06901			−0.534506	+	0.845165i	$0.679502\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	4.00000	+	6.92820i	0.128366	+	0.222337i	0.923044	−	0.384695i	$-0.125693\pi$
$971$	4.00000	+	6.92820i	0.128366	+	0.222337i	−0.794678	+	0.607032i	$0.792360\pi$
$972$		0			0
$973$	37.9706	+	5.19615i	1.21728	+	0.166581i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−13.1421	+	22.7628i	−0.420454	+	0.728248i	−0.995984	−	0.0895329i	$-0.971463\pi$
$977$	−13.1421	+	22.7628i	−0.420454	+	0.728248i	0.575530	+	0.817781i	$0.304796\pi$
$978$		0			0
$979$	80.4264			2.57044
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−2.30761	+	3.99690i	−0.0736014	+	0.127481i	−0.900477	−	0.434903i	$-0.856783\pi$
$983$	−2.30761	+	3.99690i	−0.0736014	+	0.127481i	0.826876	+	0.562385i	$0.190116\pi$
$984$		0			0
$985$	−5.82843	−	10.0951i	−0.185709	−	0.321658i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−54.2696	−	93.9976i	−1.72567	−	2.98895i
$990$		0			0
$991$	0.414214	−	0.717439i	0.0131579	−	0.0227902i	−0.859371	−	0.511352i	$-0.829145\pi$
$991$	0.414214	−	0.717439i	0.0131579	−	0.0227902i	0.872529	+	0.488562i	$0.162478\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	0.686292			0.0217569
$996$		0			0
$997$	12.8284	−	22.2195i	0.406280	−	0.703698i	−0.588189	−	0.808723i	$-0.700159\pi$
$997$	12.8284	−	22.2195i	0.406280	−	0.703698i	0.994470	+	0.105025i	$0.0334923\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2520.2.bi.k.361.1		4
3.2	odd	2		280.2.q.d.81.2	✓	4
7.2	even	3	inner	2520.2.bi.k.1801.1		4
12.11	even	2		560.2.q.j.81.1		4
15.2	even	4		1400.2.bh.g.249.1		8
15.8	even	4		1400.2.bh.g.249.4		8
15.14	odd	2		1400.2.q.h.1201.1		4
21.2	odd	6		280.2.q.d.121.2	yes	4
21.5	even	6		1960.2.q.q.961.1		4
21.11	odd	6		1960.2.a.p.1.1		2
21.17	even	6		1960.2.a.t.1.2		2
21.20	even	2		1960.2.q.q.361.1		4
84.11	even	6		3920.2.a.bz.1.2		2
84.23	even	6		560.2.q.j.401.1		4
84.59	odd	6		3920.2.a.bp.1.1		2
105.2	even	12		1400.2.bh.g.849.4		8
105.23	even	12		1400.2.bh.g.849.1		8
105.44	odd	6		1400.2.q.h.401.1		4
105.59	even	6		9800.2.a.br.1.1		2
105.74	odd	6		9800.2.a.bz.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.q.d.81.2	✓	4	3.2	odd	2
280.2.q.d.121.2	yes	4	21.2	odd	6
560.2.q.j.81.1		4	12.11	even	2
560.2.q.j.401.1		4	84.23	even	6
1400.2.q.h.401.1		4	105.44	odd	6
1400.2.q.h.1201.1		4	15.14	odd	2
1400.2.bh.g.249.1		8	15.2	even	4
1400.2.bh.g.249.4		8	15.8	even	4
1400.2.bh.g.849.1		8	105.23	even	12
1400.2.bh.g.849.4		8	105.2	even	12
1960.2.a.p.1.1		2	21.11	odd	6
1960.2.a.t.1.2		2	21.17	even	6
1960.2.q.q.361.1		4	21.20	even	2
1960.2.q.q.961.1		4	21.5	even	6
2520.2.bi.k.361.1		4	1.1	even	1	trivial
2520.2.bi.k.1801.1		4	7.2	even	3	inner
3920.2.a.bp.1.1		2	84.59	odd	6
3920.2.a.bz.1.2		2	84.11	even	6
9800.2.a.br.1.1		2	105.59	even	6
9800.2.a.bz.1.2		2	105.74	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2520 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2520.bi (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{5} +(-2.62132 - 0.358719i) q^{7} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{5} +(-2.62132 - 0.358719i) q^{7} +(-2.41421 + 4.18154i) q^{11} +2.00000 q^{13} +(1.82843 - 3.16693i) q^{17} +(-2.82843 - 4.89898i) q^{19} +(-4.20711 - 7.28692i) q^{23} +(-0.500000 + 0.866025i) q^{25} +2.17157 q^{29} +(2.41421 - 4.18154i) q^{31} +(-1.00000 - 2.44949i) q^{35} +(2.82843 + 4.89898i) q^{37} -0.171573 q^{41} +12.8995 q^{43} +(0.171573 + 0.297173i) q^{47} +(6.74264 + 1.88064i) q^{49} +(2.82843 - 4.89898i) q^{53} -4.82843 q^{55} +(-2.00000 + 3.46410i) q^{59} +(2.32843 + 4.03295i) q^{61} +(1.00000 + 1.73205i) q^{65} +(-3.44975 + 5.97514i) q^{67} +12.0000 q^{71} +(3.82843 - 6.63103i) q^{73} +(7.82843 - 10.0951i) q^{77} +(2.00000 + 3.46410i) q^{79} +13.2426 q^{83} +3.65685 q^{85} +(-8.32843 - 14.4253i) q^{89} +(-5.24264 - 0.717439i) q^{91} +(2.82843 - 4.89898i) q^{95} +6.00000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{5} - 2 q^{7}+O(q^{10}) \) 4 * q + 2 * q^5 - 2 * q^7	\( 4 q + 2 q^{5} - 2 q^{7} - 4 q^{11} + 8 q^{13} - 4 q^{17} - 14 q^{23} - 2 q^{25} + 20 q^{29} + 4 q^{31} - 4 q^{35} - 12 q^{41} + 12 q^{43} + 12 q^{47} + 10 q^{49} - 8 q^{55} - 8 q^{59} - 2 q^{61} + 4 q^{65} + 6 q^{67} + 48 q^{71} + 4 q^{73} + 20 q^{77} + 8 q^{79} + 36 q^{83} - 8 q^{85} - 22 q^{89} - 4 q^{91} + 24 q^{97}+O(q^{100}) \) 4 * q + 2 * q^5 - 2 * q^7 - 4 * q^11 + 8 * q^13 - 4 * q^17 - 14 * q^23 - 2 * q^25 + 20 * q^29 + 4 * q^31 - 4 * q^35 - 12 * q^41 + 12 * q^43 + 12 * q^47 + 10 * q^49 - 8 * q^55 - 8 * q^59 - 2 * q^61 + 4 * q^65 + 6 * q^67 + 48 * q^71 + 4 * q^73 + 20 * q^77 + 8 * q^79 + 36 * q^83 - 8 * q^85 - 22 * q^89 - 4 * q^91 + 24 * q^97

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