LMFDB - Embedded newform 2340.2.dj.d.361.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2340,2,Mod(361,2340)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2340, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))

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

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

chi := DirichletCharacter("2340.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2340 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2340.dj (of order $6$, 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:	$18.6849940730$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.22581504.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 5x^{6} + 2x^{5} - 11x^{4} + 4x^{3} + 20x^{2} - 32x + 16 $ x^8 - 4x^7 + 5x^6 + 2x^5 - 11x^4 + 4x^3 + 20x^2 - 32*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 260)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.3
Root			$0.665665 - 1.24775i$ of defining polynomial
Character	$\chi$	$=$	2340.361
Dual form			2340.2.dj.d.901.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{5} +(-1.81414 - 1.04739i) q^{7} +O(q^{10})$	$q+1.00000i q^{5} +(-1.81414 - 1.04739i) q^{7} +(-1.50000 + 0.866025i) q^{11} +(-3.59030 + 0.331331i) q^{13} +(1.81414 - 3.14218i) q^{17} +(0.926118 + 0.534695i) q^{19} +(3.90893 + 6.77046i) q^{23} -1.00000 q^{25} +(-0.263457 - 0.456321i) q^{29} -5.84325i q^{31} +(1.04739 - 1.81414i) q^{35} +(8.44242 - 4.87423i) q^{37} +(3.69615 - 2.13397i) q^{41} +(4.67238 - 8.09281i) q^{43} -3.46410i q^{47} +(-1.30593 - 2.26194i) q^{49} -12.5939 q^{53} +(-0.866025 - 1.50000i) q^{55} +(1.21564 + 0.701848i) q^{59} +(5.55440 - 9.62050i) q^{61} +(-0.331331 - 3.59030i) q^{65} +(-9.38201 + 5.41671i) q^{67} +(12.2709 + 7.08460i) q^{71} -2.64469i q^{73} +3.62828 q^{77} +13.5729 q^{79} -15.7925i q^{83} +(3.14218 + 1.81414i) q^{85} +(4.78436 - 2.76225i) q^{89} +(6.86033 + 3.15937i) q^{91} +(-0.534695 + 0.926118i) q^{95} +(-13.1589 - 7.59730i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 6 q^{7}+O(q^{10}) $ 8 * q + 6 * q^7	$ 8 q + 6 q^{7} - 12 q^{11} - 8 q^{13} - 6 q^{17} + 6 q^{23} - 8 q^{25} + 6 q^{35} + 6 q^{37} - 12 q^{41} + 10 q^{43} - 4 q^{49} - 24 q^{53} + 24 q^{59} - 4 q^{61} - 54 q^{67} + 36 q^{71} - 12 q^{77} - 16 q^{79} + 18 q^{85} + 24 q^{89} - 30 q^{97}+O(q^{100}) $ 8 * q + 6 * q^7 - 12 * q^11 - 8 * q^13 - 6 * q^17 + 6 * q^23 - 8 * q^25 + 6 * q^35 + 6 * q^37 - 12 * q^41 + 10 * q^43 - 4 * q^49 - 24 * q^53 + 24 * q^59 - 4 * q^61 - 54 * q^67 + 36 * q^71 - 12 * q^77 - 16 * q^79 + 18 * q^85 + 24 * q^89 - 30 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2340\mathbb{Z}\right)^\times$.

$n$	$937$	$1081$	$1171$	$2081$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$1$

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
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$		0			0
$7$	−1.81414	−	1.04739i	−0.685680	−	0.395878i	0.116312	−	0.993213i	$-0.462893\pi$
$7$	−1.81414	−	1.04739i	−0.685680	−	0.395878i	−0.801992	+	0.597335i	$0.796226\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.50000	+	0.866025i	−0.452267	+	0.261116i	−0.708787	−	0.705422i	$-0.750757\pi$
$11$	−1.50000	+	0.866025i	−0.452267	+	0.261116i	0.256520	+	0.966539i	$0.417424\pi$
$12$		0			0
$13$	−3.59030	+	0.331331i	−0.995769	+	0.0918946i
$13$	−3.59030	+	0.331331i	−0.995769	+	0.0918946i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.81414	−	3.14218i	0.439993	−	0.762091i	−0.557695	−	0.830046i	$-0.688314\pi$
$17$	1.81414	−	3.14218i	0.439993	−	0.762091i	0.997688	+	0.0679550i	$0.0216474\pi$
$18$		0			0
$19$	0.926118	+	0.534695i	0.212466	+	0.122667i	0.602457	−	0.798151i	$-0.294189\pi$
$19$	0.926118	+	0.534695i	0.212466	+	0.122667i	−0.389991	+	0.920819i	$0.627522\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	3.90893	+	6.77046i	0.815068	+	1.41174i	0.909279	+	0.416186i	$0.136634\pi$
$23$	3.90893	+	6.77046i	0.815068	+	1.41174i	−0.0942118	+	0.995552i	$0.530033\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−0.263457	−	0.456321i	−0.0489227	−	0.0847366i	0.840527	−	0.541770i	$-0.182245\pi$
$29$	−0.263457	−	0.456321i	−0.0489227	−	0.0847366i	−0.889450	+	0.457033i	$0.848912\pi$
$30$		0			0
$31$		−	5.84325i		−	1.04948i	−0.851263	−	0.524740i	$-0.824163\pi$
$31$		−	5.84325i		−	1.04948i	0.851263	−	0.524740i	$-0.175837\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	1.04739	−	1.81414i	0.177042	−	0.306646i
$36$		0			0
$37$	8.44242	−	4.87423i	1.38792	−	0.801319i	0.394844	−	0.918748i	$-0.370799\pi$
$37$	8.44242	−	4.87423i	1.38792	−	0.801319i	0.993081	+	0.117429i	$0.0374654\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	3.69615	−	2.13397i	0.577242	−	0.333271i	−0.182795	−	0.983151i	$-0.558514\pi$
$41$	3.69615	−	2.13397i	0.577242	−	0.333271i	0.760037	+	0.649880i	$0.225181\pi$
$42$		0			0
$43$	4.67238	−	8.09281i	0.712532	−	1.23414i	−0.251372	−	0.967891i	$-0.580882\pi$
$43$	4.67238	−	8.09281i	0.712532	−	1.23414i	0.963904	−	0.266251i	$-0.0857849\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		−	3.46410i		−	0.505291i	−0.967559	−	0.252646i	$-0.918699\pi$
$47$		−	3.46410i		−	0.505291i	0.967559	−	0.252646i	$-0.0813007\pi$
$48$		0			0
$49$	−1.30593	−	2.26194i	−0.186562	−	0.323134i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−12.5939			−1.72990			−0.864952	−	0.501854i	$-0.832651\pi$
$53$	−12.5939			−1.72990			−0.864952	+	0.501854i	$0.832651\pi$
$54$		0			0
$55$	−0.866025	−	1.50000i	−0.116775	−	0.202260i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	1.21564	+	0.701848i	0.158262	+	0.0913729i	0.577040	−	0.816716i	$-0.304208\pi$
$59$	1.21564	+	0.701848i	0.158262	+	0.0913729i	−0.418777	+	0.908089i	$0.637541\pi$
$60$		0			0
$61$	5.55440	−	9.62050i	0.711168	−	1.23178i	−0.253251	−	0.967400i	$-0.581500\pi$
$61$	5.55440	−	9.62050i	0.711168	−	1.23178i	0.964419	−	0.264378i	$-0.0851667\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−0.331331	−	3.59030i	−0.0410965	−	0.445321i
$66$		0			0
$67$	−9.38201	+	5.41671i	−1.14620	+	0.661756i	−0.947957	−	0.318398i	$-0.896855\pi$
$67$	−9.38201	+	5.41671i	−1.14620	+	0.661756i	−0.198238	+	0.980154i	$0.563522\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	12.2709	+	7.08460i	1.45629	+	0.840787i	0.998826	−	0.0484428i	$-0.0154259\pi$
$71$	12.2709	+	7.08460i	1.45629	+	0.840787i	0.457460	+	0.889230i	$0.348759\pi$
$72$		0			0
$73$		−	2.64469i		−	0.309538i	−0.987951	−	0.154769i	$-0.950537\pi$
$73$		−	2.64469i		−	0.309538i	0.987951	−	0.154769i	$-0.0494633\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	3.62828			0.413481
$78$		0			0
$79$	13.5729			1.52707			0.763535	−	0.645766i	$-0.223462\pi$
$79$	13.5729			1.52707			0.763535	+	0.645766i	$0.223462\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$		−	15.7925i		−	1.73345i	−0.498789	−	0.866724i	$-0.666222\pi$
$83$		−	15.7925i		−	1.73345i	0.498789	−	0.866724i	$-0.333778\pi$
$84$		0			0
$85$	3.14218	+	1.81414i	0.340817	+	0.196771i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	4.78436	−	2.76225i	0.507141	−	0.292798i	−0.224516	−	0.974470i	$-0.572080\pi$
$89$	4.78436	−	2.76225i	0.507141	−	0.292798i	0.731658	+	0.681672i	$0.238747\pi$
$90$		0			0
$91$	6.86033	+	3.15937i	0.719158	+	0.331192i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−0.534695	+	0.926118i	−0.0548585	+	0.0950177i
$96$		0			0
$97$	−13.1589	−	7.59730i	−1.33608	−	0.771389i	−0.349860	−	0.936802i	$-0.613771\pi$
$97$	−13.1589	−	7.59730i	−1.33608	−	0.771389i	−0.986224	+	0.165413i	$0.947104\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	1.83133	+	3.17196i	0.182224	+	0.315622i	0.942638	−	0.333818i	$-0.108337\pi$
$101$	1.83133	+	3.17196i	0.182224	+	0.315622i	−0.760413	+	0.649439i	$0.775004\pi$
$102$		0			0
$103$	13.7804			1.35783			0.678914	−	0.734218i	$-0.262451\pi$
$103$	13.7804			1.35783			0.678914	+	0.734218i	$0.262451\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.61856	+	2.80342i	0.156472	+	0.271017i	0.933594	−	0.358333i	$-0.116655\pi$
$107$	1.61856	+	2.80342i	0.156472	+	0.271017i	−0.777122	+	0.629350i	$0.783321\pi$
$108$		0			0
$109$		−	9.12979i		−	0.874476i	−0.899346	−	0.437238i	$-0.855957\pi$
$109$		−	9.12979i		−	0.874476i	0.899346	−	0.437238i	$-0.144043\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−5.47680	+	9.48610i	−0.515214	+	0.892377i	0.484630	+	0.874719i	$0.338954\pi$
$113$	−5.47680	+	9.48610i	−0.515214	+	0.892377i	−0.999844	+	0.0176577i	$0.994379\pi$
$114$		0			0
$115$	−6.77046	+	3.90893i	−0.631349	+	0.364509i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−6.58220	+	3.80024i	−0.603390	+	0.348367i
$120$		0			0
$121$	−4.00000	+	6.92820i	−0.363636	+	0.629837i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		−	1.00000i		−	0.0894427i
$126$		0			0
$127$	0.453810	+	0.786022i	0.0402691	+	0.0697482i	0.885458	−	0.464720i	$-0.153845\pi$
$127$	0.453810	+	0.786022i	0.0402691	+	0.0697482i	−0.845188	+	0.534469i	$0.820512\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	13.1626			1.15002			0.575012	−	0.818145i	$-0.304997\pi$
$131$	13.1626			1.15002			0.575012	+	0.818145i	$0.304997\pi$
$132$		0			0
$133$	−1.12007	−	1.94002i	−0.0971225	−	0.168221i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−10.4484	−	6.03240i	−0.892669	−	0.515383i	−0.0178546	−	0.999841i	$-0.505684\pi$
$137$	−10.4484	−	6.03240i	−0.892669	−	0.515383i	−0.874815	+	0.484458i	$0.839017\pi$
$138$		0			0
$139$	2.80593	−	4.86002i	0.237996	−	0.412221i	−0.722143	−	0.691744i	$-0.756843\pi$
$139$	2.80593	−	4.86002i	0.237996	−	0.412221i	0.960139	+	0.279522i	$0.0901761\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	5.09850	−	3.60628i	0.426358	−	0.301573i
$144$		0			0
$145$	0.456321	−	0.263457i	0.0378954	−	0.0218789i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−18.1767	−	10.4943i	−1.48909	−	0.859727i	−0.489168	−	0.872189i	$-0.662700\pi$
$149$	−18.1767	−	10.4943i	−1.48909	−	0.859727i	−0.999922	+	0.0124625i	$0.996033\pi$
$150$		0			0
$151$			6.99102i			0.568921i	0.958688	+	0.284460i	$0.0918144\pi$
$151$			6.99102i			0.568921i	−0.958688	+	0.284460i	$0.908186\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	5.84325			0.469341
$156$		0			0
$157$	3.74761			0.299092			0.149546	−	0.988755i	$-0.452219\pi$
$157$	3.74761			0.299092			0.149546	+	0.988755i	$0.452219\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		−	16.3767i		−	1.29067i
$162$		0			0
$163$	−5.52377	−	3.18915i	−0.432655	−	0.249793i	0.267822	−	0.963468i	$-0.413696\pi$
$163$	−5.52377	−	3.18915i	−0.432655	−	0.249793i	−0.700477	+	0.713675i	$0.747029\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	13.4484	−	7.76445i	1.04067	−	0.600831i	0.120647	−	0.992695i	$-0.461503\pi$
$167$	13.4484	−	7.76445i	1.04067	−	0.600831i	0.920023	+	0.391864i	$0.128170\pi$
$168$		0			0
$169$	12.7804	−	2.37915i	0.983111	−	0.183012i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	2.38802	−	4.13617i	0.181558	−	0.314467i	−0.760853	−	0.648924i	$-0.775219\pi$
$173$	2.38802	−	4.13617i	0.181558	−	0.314467i	0.942411	+	0.334456i	$0.108553\pi$
$174$		0			0
$175$	1.81414	+	1.04739i	0.137136	+	0.0791755i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−7.85134	−	13.5989i	−0.586837	−	1.01643i	−0.994644	−	0.103363i	$-0.967040\pi$
$179$	−7.85134	−	13.5989i	−0.586837	−	1.01643i	0.407807	−	0.913068i	$-0.366294\pi$
$180$		0			0
$181$	10.8851			0.809080			0.404540	−	0.914520i	$-0.367432\pi$
$181$	10.8851			0.809080			0.404540	+	0.914520i	$0.367432\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	4.87423	+	8.44242i	0.358361	+	0.620699i
$186$		0			0
$187$			6.28436i			0.459558i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−2.97909	+	5.15994i	−0.215560	+	0.373360i	−0.953446	−	0.301565i	$-0.902491\pi$
$191$	−2.97909	+	5.15994i	−0.215560	+	0.373360i	0.737886	+	0.674925i	$0.235824\pi$
$192$		0			0
$193$	11.0587	−	6.38473i	0.796021	−	0.459583i	−0.0460568	−	0.998939i	$-0.514666\pi$
$193$	11.0587	−	6.38473i	0.796021	−	0.459583i	0.842078	+	0.539356i	$0.181332\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	13.9499	−	8.05397i	0.993888	−	0.573822i	0.0874540	−	0.996169i	$-0.472127\pi$
$197$	13.9499	−	8.05397i	0.993888	−	0.573822i	0.906434	+	0.422347i	$0.138794\pi$
$198$		0			0
$199$	−4.26403	+	7.38551i	−0.302269	+	0.523545i	−0.976650	−	0.214839i	$-0.931077\pi$
$199$	−4.26403	+	7.38551i	−0.302269	+	0.523545i	0.674381	+	0.738384i	$0.264411\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$			1.10377i			0.0774696i
$204$		0			0
$205$	2.13397	+	3.69615i	0.149043	+	0.258150i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−1.85224			−0.128122
$210$		0			0
$211$	2.09030	+	3.62050i	0.143902	+	0.249245i	0.928963	−	0.370173i	$-0.120702\pi$
$211$	2.09030	+	3.62050i	0.143902	+	0.249245i	−0.785061	+	0.619419i	$0.787368\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	8.09281	+	4.67238i	0.551925	+	0.318654i
$216$		0			0
$217$	−6.12019	+	10.6005i	−0.415465	+	0.719607i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−5.47219	+	11.8824i	−0.368100	+	0.799299i
$222$		0			0
$223$	−9.09249	+	5.24955i	−0.608878	+	0.351536i	−0.772526	−	0.634983i	$-0.781007\pi$
$223$	−9.09249	+	5.24955i	−0.608878	+	0.351536i	0.163648	+	0.986519i	$0.447674\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−13.4977	−	7.79288i	−0.895872	−	0.517232i	−0.0200131	−	0.999800i	$-0.506371\pi$
$227$	−13.4977	−	7.79288i	−0.895872	−	0.517232i	−0.875858	+	0.482568i	$0.839704\pi$
$228$		0			0
$229$		−	19.2714i		−	1.27349i	−0.771074	−	0.636745i	$-0.780280\pi$
$229$		−	19.2714i		−	1.27349i	0.771074	−	0.636745i	$-0.219720\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−2.48794			−0.162991			−0.0814953	−	0.996674i	$-0.525970\pi$
$233$	−2.48794			−0.162991			−0.0814953	+	0.996674i	$0.525970\pi$
$234$		0			0
$235$	3.46410			0.225973
$236$		0			0
$237$		0			0
$238$		0			0
$239$			16.7775i			1.08525i	0.839976	+	0.542624i	$0.182569\pi$
$239$			16.7775i			1.08525i	−0.839976	+	0.542624i	$0.817431\pi$
$240$		0			0
$241$	25.1835	+	14.5397i	1.62221	+	0.936585i	0.986326	+	0.164803i	$0.0526990\pi$
$241$	25.1835	+	14.5397i	1.62221	+	0.936585i	0.635887	+	0.771782i	$0.280634\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	2.26194	−	1.30593i	0.144510	−	0.0834330i
$246$		0			0
$247$	−3.50220	−	1.61286i	−0.222840	−	0.102624i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−9.56040	+	16.5591i	−0.603447	+	1.04520i	0.388847	+	0.921302i	$0.372873\pi$
$251$	−9.56040	+	16.5591i	−0.603447	+	1.04520i	−0.992295	+	0.123899i	$0.960460\pi$
$252$		0			0
$253$	−11.7268	−	6.77046i	−0.737256	−	0.425655i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−6.85453	−	11.8724i	−0.427574	−	0.740580i	0.569083	−	0.822280i	$-0.307298\pi$
$257$	−6.85453	−	11.8724i	−0.427574	−	0.740580i	−0.996657	+	0.0817004i	$0.973965\pi$
$258$		0			0
$259$	−20.4210			−1.26890
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−5.95675	−	10.3174i	−0.367309	−	0.636197i	0.621835	−	0.783148i	$-0.286387\pi$
$263$	−5.95675	−	10.3174i	−0.367309	−	0.636197i	−0.989144	+	0.146951i	$0.953054\pi$
$264$		0			0
$265$		−	12.5939i		−	0.773637i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−10.4656	+	18.1270i	−0.638100	+	1.10522i	0.347749	+	0.937588i	$0.386946\pi$
$269$	−10.4656	+	18.1270i	−0.638100	+	1.10522i	−0.985849	+	0.167634i	$0.946387\pi$
$270$		0			0
$271$	1.69014	−	0.975805i	0.102669	−	0.0592760i	−0.447786	−	0.894141i	$-0.647787\pi$
$271$	1.69014	−	0.975805i	0.102669	−	0.0592760i	0.550455	+	0.834865i	$0.314454\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	1.50000	−	0.866025i	0.0904534	−	0.0522233i
$276$		0			0
$277$	6.24026	−	10.8084i	0.374941	−	0.649416i	−0.615377	−	0.788233i	$-0.710996\pi$
$277$	6.24026	−	10.8084i	0.374941	−	0.649416i	0.990318	+	0.138816i	$0.0443297\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		−	2.29553i		−	0.136940i	−0.997653	−	0.0684698i	$-0.978188\pi$
$281$		−	2.29553i		−	0.136940i	0.997653	−	0.0684698i	$-0.0218117\pi$
$282$		0			0
$283$	7.46484	+	12.9295i	0.443739	+	0.768578i	0.997963	−	0.0637892i	$-0.0203185\pi$
$283$	7.46484	+	12.9295i	0.443739	+	0.768578i	−0.554225	+	0.832367i	$0.686985\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−8.94045			−0.527738
$288$		0			0
$289$	1.91780	+	3.32172i	0.112812	+	0.195395i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−1.24026	−	0.716063i	−0.0724566	−	0.0418329i	0.463334	−	0.886184i	$-0.346653\pi$
$293$	−1.24026	−	0.716063i	−0.0724566	−	0.0418329i	−0.535791	+	0.844351i	$0.679986\pi$
$294$		0			0
$295$	−0.701848	+	1.21564i	−0.0408632	+	0.0707771i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−16.2775	−	23.0128i	−0.941350	−	1.33086i
$300$		0			0
$301$	−16.9527	+	9.78765i	−0.977138	+	0.564151i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	9.62050	+	5.55440i	0.550868	+	0.318044i
$306$		0			0
$307$		−	17.3833i		−	0.992118i	−0.868289	−	0.496059i	$-0.834780\pi$
$307$		−	17.3833i		−	0.992118i	0.868289	−	0.496059i	$-0.165220\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	20.2164			1.14637			0.573185	−	0.819426i	$-0.305708\pi$
$311$	20.2164			1.14637			0.573185	+	0.819426i	$0.305708\pi$
$312$		0			0
$313$	−4.86425			−0.274944			−0.137472	−	0.990506i	$-0.543898\pi$
$313$	−4.86425			−0.274944			−0.137472	+	0.990506i	$0.543898\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		−	23.6177i		−	1.32650i	−0.748396	−	0.663252i	$-0.769176\pi$
$317$		−	23.6177i		−	1.32650i	0.748396	−	0.663252i	$-0.230824\pi$
$318$		0			0
$319$	0.790371	+	0.456321i	0.0442523	+	0.0255491i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	3.36022	−	1.94002i	0.186967	−	0.107946i
$324$		0			0
$325$	3.59030	−	0.331331i	0.199154	−	0.0183789i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−3.62828	+	6.28436i	−0.200033	+	0.346468i
$330$		0			0
$331$	−12.8863	−	7.43991i	−0.708295	−	0.408934i	0.102134	−	0.994771i	$-0.467433\pi$
$331$	−12.8863	−	7.43991i	−0.708295	−	0.408934i	−0.810429	+	0.585836i	$0.800766\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−5.41671	−	9.38201i	−0.295946	−	0.512594i
$336$		0			0
$337$	−29.1906			−1.59012			−0.795058	−	0.606534i	$-0.792559\pi$
$337$	−29.1906			−1.59012			−0.795058	+	0.606534i	$0.792559\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	5.06040	+	8.76488i	0.274036	+	0.474645i
$342$		0			0
$343$			20.1348i			1.08718i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−12.1125	+	20.9795i	−0.650234	+	1.12624i	0.332833	+	0.942986i	$0.391996\pi$
$347$	−12.1125	+	20.9795i	−0.650234	+	1.12624i	−0.983066	+	0.183252i	$0.941338\pi$
$348$		0			0
$349$	−11.1557	+	6.44076i	−0.597152	+	0.344766i	−0.767920	−	0.640545i	$-0.778708\pi$
$349$	−11.1557	+	6.44076i	−0.597152	+	0.344766i	0.170768	+	0.985311i	$0.445375\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−14.0441	+	8.10837i	−0.747492	+	0.431565i	−0.824787	−	0.565443i	$-0.808705\pi$
$353$	−14.0441	+	8.10837i	−0.747492	+	0.431565i	0.0772948	+	0.997008i	$0.475372\pi$
$354$		0			0
$355$	−7.08460	+	12.2709i	−0.376011	+	0.651271i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			9.19261i			0.485167i	0.970131	+	0.242584i	$0.0779949\pi$
$359$			9.19261i			0.485167i	−0.970131	+	0.242584i	$0.922005\pi$
$360$		0			0
$361$	−8.92820	−	15.4641i	−0.469905	−	0.813900i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	2.64469			0.138430
$366$		0			0
$367$	2.30066	+	3.98486i	0.120094	+	0.208008i	0.919804	−	0.392377i	$-0.128347\pi$
$367$	2.30066	+	3.98486i	0.120094	+	0.208008i	−0.799711	+	0.600385i	$0.795014\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	22.8471	+	13.1908i	1.18616	+	0.684831i
$372$		0			0
$373$	10.2463	−	17.7471i	0.530532	−	0.918908i	−0.468834	−	0.883286i	$-0.655326\pi$
$373$	10.2463	−	17.7471i	0.530532	−	0.918908i	0.999365	−	0.0356212i	$-0.0113410\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	1.09708	+	1.55103i	0.0565025	+	0.0798823i
$378$		0			0
$379$	6.95307	−	4.01436i	0.357155	−	0.206204i	−0.310677	−	0.950516i	$-0.600556\pi$
$379$	6.95307	−	4.01436i	0.357155	−	0.206204i	0.667832	+	0.744312i	$0.267222\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	26.1041	+	15.0712i	1.33386	+	0.770104i	0.985889	−	0.167401i	$-0.0535375\pi$
$383$	26.1041	+	15.0712i	1.33386	+	0.770104i	0.347971	+	0.937505i	$0.386871\pi$
$384$		0			0
$385$			3.62828i			0.184914i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	35.8264			1.81647			0.908236	−	0.418459i	$-0.137430\pi$
$389$	35.8264			1.81647			0.908236	+	0.418459i	$0.137430\pi$
$390$		0			0
$391$	28.3654			1.43450
$392$		0			0
$393$		0			0
$394$		0			0
$395$			13.5729i			0.682926i
$396$		0			0
$397$	−13.3221	−	7.69152i	−0.668617	−	0.386026i	0.126935	−	0.991911i	$-0.459486\pi$
$397$	−13.3221	−	7.69152i	−0.668617	−	0.386026i	−0.795552	+	0.605885i	$0.792819\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	8.46704	−	4.88845i	0.422824	−	0.244117i	−0.273461	−	0.961883i	$-0.588168\pi$
$401$	8.46704	−	4.88845i	0.422824	−	0.244117i	0.696285	+	0.717766i	$0.254835\pi$
$402$		0			0
$403$	1.93605	+	20.9790i	0.0964415	+	1.04504i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−8.44242	+	14.6227i	−0.418475	+	0.724820i
$408$		0			0
$409$	0.871721	+	0.503289i	0.0431039	+	0.0248860i	0.521397	−	0.853314i	$-0.325411\pi$
$409$	0.871721	+	0.503289i	0.0431039	+	0.0248860i	−0.478293	+	0.878200i	$0.658744\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−1.47022	−	2.54650i	−0.0723450	−	0.125305i
$414$		0			0
$415$	15.7925			0.775221
$416$		0			0
$417$		0			0
$418$		0			0
$419$	4.85134	+	8.40278i	0.237004	+	0.410502i	0.959853	−	0.280503i	$-0.0905013\pi$
$419$	4.85134	+	8.40278i	0.237004	+	0.410502i	−0.722849	+	0.691006i	$0.757168\pi$
$420$		0			0
$421$		−	14.2955i		−	0.696721i	−0.937361	−	0.348361i	$-0.886738\pi$
$421$		−	14.2955i		−	0.696721i	0.937361	−	0.348361i	$-0.113262\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−1.81414	+	3.14218i	−0.0879987	+	0.152418i
$426$		0			0
$427$	−20.1529	+	11.6353i	−0.975267	+	0.563071i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−10.5197	+	6.07357i	−0.506718	+	0.292554i	−0.731483	−	0.681859i	$-0.761172\pi$
$431$	−10.5197	+	6.07357i	−0.506718	+	0.292554i	0.224766	+	0.974413i	$0.427838\pi$
$432$		0			0
$433$	−0.104510	+	0.181016i	−0.00502242	+	0.00869909i	−0.868526	−	0.495644i	$-0.834932\pi$
$433$	−0.104510	+	0.181016i	−0.00502242	+	0.00869909i	0.863503	+	0.504343i	$0.168265\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$			8.36033i			0.399929i
$438$		0			0
$439$	−13.8603	−	24.0068i	−0.661517	−	1.14578i	−0.980217	−	0.197926i	$-0.936579\pi$
$439$	−13.8603	−	24.0068i	−0.661517	−	1.14578i	0.318700	−	0.947856i	$-0.396754\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	7.98798			0.379521			0.189760	−	0.981830i	$-0.439229\pi$
$443$	7.98798			0.379521			0.189760	+	0.981830i	$0.439229\pi$
$444$		0			0
$445$	2.76225	+	4.78436i	0.130943	+	0.226801i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−6.17667	−	3.56610i	−0.291495	−	0.168295i	0.347121	−	0.937820i	$-0.387159\pi$
$449$	−6.17667	−	3.56610i	−0.291495	−	0.168295i	−0.638616	+	0.769526i	$0.720493\pi$
$450$		0			0
$451$	−3.69615	+	6.40192i	−0.174045	+	0.301455i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−3.15937	+	6.86033i	−0.148114	+	0.321617i
$456$		0			0
$457$	−27.4364	+	15.8404i	−1.28342	+	0.740984i	−0.977472	−	0.211064i	$-0.932307\pi$
$457$	−27.4364	+	15.8404i	−1.28342	+	0.740984i	−0.305949	+	0.952048i	$0.598974\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	10.2649	+	5.92643i	0.478083	+	0.276021i	0.719617	−	0.694371i	$-0.244317\pi$
$461$	10.2649	+	5.92643i	0.478083	+	0.276021i	−0.241534	+	0.970392i	$0.577651\pi$
$462$		0			0
$463$			12.7655i			0.593263i	0.954992	+	0.296632i	$0.0958633\pi$
$463$			12.7655i			0.593263i	−0.954992	+	0.296632i	$0.904137\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−31.3402			−1.45025			−0.725125	−	0.688617i	$-0.758218\pi$
$467$	−31.3402			−1.45025			−0.725125	+	0.688617i	$0.758218\pi$
$468$		0			0
$469$	22.6937			1.04790
$470$		0			0
$471$		0			0
$472$		0			0
$473$			16.1856i			0.744215i
$474$		0			0
$475$	−0.926118	−	0.534695i	−0.0424932	−	0.0245335i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−13.9656	+	8.06303i	−0.638103	+	0.368409i	−0.783884	−	0.620908i	$-0.786764\pi$
$479$	−13.9656	+	8.06303i	−0.638103	+	0.368409i	0.145780	+	0.989317i	$0.453431\pi$
$480$		0			0
$481$	−28.6958	+	20.2972i	−1.30842	+	0.925471i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	7.59730	−	13.1589i	0.344976	−	0.597515i
$486$		0			0
$487$	−4.84109	−	2.79501i	−0.219371	−	0.126654i	0.386288	−	0.922378i	$-0.373757\pi$
$487$	−4.84109	−	2.79501i	−0.219371	−	0.126654i	−0.605659	+	0.795724i	$0.707090\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	9.14772	+	15.8443i	0.412831	+	0.715044i	0.995198	−	0.0978817i	$-0.0312067\pi$
$491$	9.14772	+	15.8443i	0.412831	+	0.715044i	−0.582367	+	0.812926i	$0.697873\pi$
$492$		0			0
$493$	−1.91179			−0.0861027
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−14.8407	−	25.7049i	−0.665698	−	1.15302i
$498$		0			0
$499$		−	0.553868i		−	0.0247945i	−0.999923	−	0.0123973i	$-0.996054\pi$
$499$		−	0.553868i		−	0.0247945i	0.999923	−	0.0123973i	$-0.00394627\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	7.34162	−	12.7161i	0.327347	−	0.566981i	−0.654638	−	0.755943i	$-0.727179\pi$
$503$	7.34162	−	12.7161i	0.327347	−	0.566981i	0.981984	+	0.188962i	$0.0605121\pi$
$504$		0			0
$505$	−3.17196	+	1.83133i	−0.141150	+	0.0814931i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−5.99545	+	3.46148i	−0.265744	+	0.153427i	−0.626952	−	0.779058i	$-0.715698\pi$
$509$	−5.99545	+	3.46148i	−0.265744	+	0.153427i	0.361208	+	0.932485i	$0.382364\pi$
$510$		0			0
$511$	−2.77003	+	4.79784i	−0.122539	+	0.212244i
$512$		0			0
$513$		0			0
$514$		0			0
$515$			13.7804i			0.607239i
$516$		0			0
$517$	3.00000	+	5.19615i	0.131940	+	0.228527i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	18.3551			0.804152			0.402076	−	0.915606i	$-0.368289\pi$
$521$	18.3551			0.804152			0.402076	+	0.915606i	$0.368289\pi$
$522$		0			0
$523$	9.13563	+	15.8234i	0.399473	+	0.691908i	0.993661	−	0.112418i	$-0.0358597\pi$
$523$	9.13563	+	15.8234i	0.399473	+	0.691908i	−0.594188	+	0.804326i	$0.702526\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−18.3606	−	10.6005i	−0.799798	−	0.461764i
$528$		0			0
$529$	−19.0594	+	33.0119i	−0.828670	+	1.43530i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−12.5632	+	8.88625i	−0.544174	+	0.384906i
$534$		0			0
$535$	−2.80342	+	1.61856i	−0.121202	+	0.0699763i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	3.91780	+	2.26194i	0.168751	+	0.0974287i
$540$		0			0
$541$			31.8881i			1.37098i	0.728084	+	0.685488i	$0.240411\pi$
$541$			31.8881i			1.37098i	−0.728084	+	0.685488i	$0.759589\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	9.12979			0.391077
$546$		0			0
$547$	44.7966			1.91537			0.957683	−	0.287826i	$-0.0929325\pi$
$547$	44.7966			1.91537			0.957683	+	0.287826i	$0.0929325\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		−	0.563476i		−	0.0240049i
$552$		0			0
$553$	−24.6231	−	14.2162i	−1.04708	−	0.604533i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−22.7820	+	13.1532i	−0.965306	+	0.557319i	−0.897802	−	0.440400i	$-0.854837\pi$
$557$	−22.7820	+	13.1532i	−0.965306	+	0.557319i	−0.0675037	+	0.997719i	$0.521503\pi$
$558$		0			0
$559$	−14.0938	+	30.6037i	−0.596106	+	1.29440i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	2.89492	−	5.01415i	0.122006	−	0.211321i	−0.798552	−	0.601925i	$-0.794401\pi$
$563$	2.89492	−	5.01415i	0.122006	−	0.211321i	0.920559	+	0.390604i	$0.127734\pi$
$564$		0			0
$565$	−9.48610	−	5.47680i	−0.399083	−	0.230411i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−11.8184	−	20.4700i	−0.495452	−	0.858149i	0.504534	−	0.863392i	$-0.331664\pi$
$569$	−11.8184	−	20.4700i	−0.495452	−	0.858149i	−0.999986	+	0.00524320i	$0.998331\pi$
$570$		0			0
$571$	−11.4641			−0.479758			−0.239879	−	0.970803i	$-0.577108\pi$
$571$	−11.4641			−0.479758			−0.239879	+	0.970803i	$0.577108\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−3.90893	−	6.77046i	−0.163014	−	0.282348i
$576$		0			0
$577$		−	34.2415i		−	1.42549i	−0.701422	−	0.712746i	$-0.747451\pi$
$577$		−	34.2415i		−	1.42549i	0.701422	−	0.712746i	$-0.252549\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−16.5409	+	28.6497i	−0.686233	+	1.18859i
$582$		0			0
$583$	18.8908	−	10.9066i	0.782379	−	0.451707i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	4.88091	−	2.81800i	0.201457	−	0.116311i	−0.395878	−	0.918303i	$-0.629560\pi$
$587$	4.88091	−	2.81800i	0.201457	−	0.116311i	0.597335	+	0.801992i	$0.296226\pi$
$588$		0			0
$589$	3.12436	−	5.41154i	0.128737	−	0.222979i
$590$		0			0
$591$		0			0
$592$		0			0
$593$			15.3014i			0.628353i	0.949365	+	0.314177i	$0.101728\pi$
$593$			15.3014i			0.628353i	−0.949365	+	0.314177i	$0.898272\pi$
$594$		0			0
$595$	−3.80024	−	6.58220i	−0.155795	−	0.269844i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−9.82414			−0.401404			−0.200702	−	0.979652i	$-0.564322\pi$
$599$	−9.82414			−0.401404			−0.200702	+	0.979652i	$0.564322\pi$
$600$		0			0
$601$	23.0945	+	40.0008i	0.942043	+	1.63167i	0.761566	+	0.648087i	$0.224431\pi$
$601$	23.0945	+	40.0008i	0.942043	+	1.63167i	0.180476	+	0.983579i	$0.442236\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−6.92820	−	4.00000i	−0.281672	−	0.162623i
$606$		0			0
$607$	−12.3482	+	21.3877i	−0.501198	+	0.868100i	0.498801	+	0.866716i	$0.333774\pi$
$607$	−12.3482	+	21.3877i	−0.501198	+	0.868100i	−0.999999	+	0.00138384i	$0.999560\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	1.14776	+	12.4371i	0.0464335	+	0.503153i
$612$		0			0
$613$	−14.4155	+	8.32277i	−0.582235	+	0.336154i	−0.762021	−	0.647552i	$-0.775793\pi$
$613$	−14.4155	+	8.32277i	−0.582235	+	0.336154i	0.179786	+	0.983706i	$0.442459\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.39918	+	0.807820i	0.0563291	+	0.0325216i	0.527900	−	0.849307i	$-0.322980\pi$
$617$	1.39918	+	0.807820i	0.0563291	+	0.0325216i	−0.471571	+	0.881828i	$0.656313\pi$
$618$		0			0
$619$			23.3922i			0.940213i	0.882610	+	0.470106i	$0.155784\pi$
$619$			23.3922i			0.940213i	−0.882610	+	0.470106i	$0.844216\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−11.5727			−0.463649
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$		0			0
$628$		0			0
$629$		−	35.3701i		−	1.41030i
$630$		0			0
$631$	2.77458	+	1.60190i	0.110454	+	0.0637708i	0.554209	−	0.832377i	$-0.313021\pi$
$631$	2.77458	+	1.60190i	0.110454	+	0.0637708i	−0.443755	+	0.896148i	$0.646354\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−0.786022	+	0.453810i	−0.0311923	+	0.0180089i
$636$		0			0
$637$	5.43813	+	7.68834i	0.215467	+	0.304623i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	9.98794	−	17.2996i	0.394500	−	0.683294i	−0.598537	−	0.801095i	$-0.704251\pi$
$641$	9.98794	−	17.2996i	0.394500	−	0.683294i	0.993037	+	0.117801i	$0.0375845\pi$
$642$		0			0
$643$	−24.7136	−	14.2684i	−0.974607	−	0.562690i	−0.0739696	−	0.997260i	$-0.523567\pi$
$643$	−24.7136	−	14.2684i	−0.974607	−	0.562690i	−0.900638	+	0.434571i	$0.856900\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−3.04325	−	5.27107i	−0.119643	−	0.207227i	0.799983	−	0.600022i	$-0.204842\pi$
$647$	−3.04325	−	5.27107i	−0.119643	−	0.207227i	−0.919626	+	0.392795i	$0.871508\pi$
$648$		0			0
$649$	−2.43127			−0.0954359
$650$		0			0
$651$		0			0
$652$		0			0
$653$	9.81499	+	17.0001i	0.384090	+	0.665264i	0.991643	−	0.129016i	$-0.0411818\pi$
$653$	9.81499	+	17.0001i	0.384090	+	0.665264i	−0.607552	+	0.794280i	$0.707848\pi$
$654$		0			0
$655$			13.1626i			0.514306i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−9.79752	+	16.9698i	−0.381657	+	0.661049i	−0.991299	−	0.131627i	$-0.957980\pi$
$659$	−9.79752	+	16.9698i	−0.381657	+	0.661049i	0.609642	+	0.792677i	$0.291313\pi$
$660$		0			0
$661$	30.0735	−	17.3630i	1.16972	−	0.675341i	0.216109	−	0.976369i	$-0.430663\pi$
$661$	30.0735	−	17.3630i	1.16972	−	0.675341i	0.953615	+	0.301029i	$0.0973300\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	1.94002	−	1.12007i	0.0752308	−	0.0434345i
$666$		0			0
$667$	2.05967	−	3.56745i	0.0797506	−	0.138132i
$668$		0			0
$669$		0			0
$670$		0			0
$671$			19.2410i			0.742790i
$672$		0			0
$673$	−17.0051	−	29.4538i	−0.655500	−	1.13536i	−0.981768	−	0.190082i	$-0.939125\pi$
$673$	−17.0051	−	29.4538i	−0.655500	−	1.13536i	0.326268	−	0.945277i	$-0.394209\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−29.9209			−1.14995			−0.574977	−	0.818169i	$-0.694989\pi$
$677$	−29.9209			−1.14995			−0.574977	+	0.818169i	$0.694989\pi$
$678$		0			0
$679$	15.9147	+	27.5651i	0.610751	+	1.05785i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−24.1251	−	13.9286i	−0.923121	−	0.532964i	−0.0384916	−	0.999259i	$-0.512255\pi$
$683$	−24.1251	−	13.9286i	−0.923121	−	0.532964i	−0.884629	+	0.466295i	$0.845589\pi$
$684$		0			0
$685$	6.03240	−	10.4484i	0.230486	−	0.399214i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	45.2158	−	4.17274i	1.72258	−	0.158969i
$690$		0			0
$691$	31.4550	−	18.1606i	1.19661	−	0.690860i	0.236809	−	0.971556i	$-0.423899\pi$
$691$	31.4550	−	18.1606i	1.19661	−	0.690860i	0.959797	+	0.280696i	$0.0905652\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	4.86002	+	2.80593i	0.184351	+	0.106435i
$696$		0			0
$697$		−	15.4853i		−	0.586548i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−2.16156			−0.0816411			−0.0408206	−	0.999166i	$-0.512997\pi$
$701$	−2.16156			−0.0816411			−0.0408206	+	0.999166i	$0.512997\pi$
$702$		0			0
$703$	10.4249			0.393183
$704$		0			0
$705$		0			0
$706$		0			0
$707$		−	7.67250i		−	0.288554i
$708$		0			0
$709$	−41.2371	−	23.8082i	−1.54869	−	0.894137i	−0.998242	−	0.0592680i	$-0.981123\pi$
$709$	−41.2371	−	23.8082i	−1.54869	−	0.894137i	−0.550449	−	0.834869i	$-0.685543\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	39.5615	−	22.8408i	1.48159	−	0.855396i
$714$		0			0
$715$	3.60628	+	5.09850i	0.134867	+	0.190673i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	10.1469	−	17.5749i	0.378414	−	0.655433i	−0.612417	−	0.790535i	$-0.709803\pi$
$719$	10.1469	−	17.5749i	0.378414	−	0.655433i	0.990832	+	0.135102i	$0.0431361\pi$
$720$		0			0
$721$	−24.9996	−	14.4335i	−0.931035	−	0.537533i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	0.263457	+	0.456321i	0.00978454	+	0.0169473i
$726$		0			0
$727$	11.0681			0.410494			0.205247	−	0.978710i	$-0.434200\pi$
$727$	11.0681			0.410494			0.205247	+	0.978710i	$0.434200\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−16.9527	−	29.3630i	−0.627019	−	1.08603i
$732$		0			0
$733$		−	23.4002i		−	0.864304i	−0.901801	−	0.432152i	$-0.857754\pi$
$733$		−	23.4002i		−	0.864304i	0.901801	−	0.432152i	$-0.142246\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	9.38201	−	16.2501i	0.345591	−	0.598581i
$738$		0			0
$739$	−22.1617	+	12.7951i	−0.815232	+	0.470675i	−0.848770	−	0.528763i	$-0.822656\pi$
$739$	−22.1617	+	12.7951i	−0.815232	+	0.470675i	0.0335372	+	0.999437i	$0.489323\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−7.28694	+	4.20712i	−0.267332	+	0.154344i	−0.627675	−	0.778476i	$-0.715993\pi$
$743$	−7.28694	+	4.20712i	−0.267332	+	0.154344i	0.360343	+	0.932820i	$0.382660\pi$
$744$		0			0
$745$	10.4943	−	18.1767i	0.384482	−	0.665942i
$746$		0			0
$747$		0			0
$748$		0			0
$749$		−	6.78106i		−	0.247775i
$750$		0			0
$751$	20.2595	+	35.0905i	0.739279	+	1.28047i	0.952820	+	0.303535i	$0.0981671\pi$
$751$	20.2595	+	35.0905i	0.739279	+	1.28047i	−0.213541	+	0.976934i	$0.568500\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−6.99102			−0.254429
$756$		0			0
$757$	5.67593	+	9.83100i	0.206295	+	0.357314i	0.950545	−	0.310588i	$-0.100526\pi$
$757$	5.67593	+	9.83100i	0.206295	+	0.357314i	−0.744249	+	0.667902i	$0.767193\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	5.86364	+	3.38538i	0.212557	+	0.122720i	0.602499	−	0.798120i	$-0.294172\pi$
$761$	5.86364	+	3.38538i	0.212557	+	0.122720i	−0.389942	+	0.920839i	$0.627505\pi$
$762$		0			0
$763$	−9.56249	+	16.5627i	−0.346185	+	0.599611i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−4.59704	−	2.11707i	−0.165990	−	0.0764428i
$768$		0			0
$769$	−20.0563	+	11.5795i	−0.723250	+	0.417569i	−0.815948	−	0.578126i	$-0.803784\pi$
$769$	−20.0563	+	11.5795i	−0.723250	+	0.417569i	0.0926975	+	0.995694i	$0.470451\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−36.3333	−	20.9770i	−1.30682	−	0.754491i	−0.325253	−	0.945627i	$-0.605449\pi$
$773$	−36.3333	−	20.9770i	−1.30682	−	0.754491i	−0.981564	+	0.191136i	$0.938783\pi$
$774$		0			0
$775$			5.84325i			0.209896i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	4.56410			0.163526
$780$		0			0
$781$	−24.5418			−0.878174
$782$		0			0
$783$		0			0
$784$		0			0
$785$			3.74761i			0.133758i
$786$		0			0
$787$	32.4026	+	18.7076i	1.15503	+	0.666856i	0.950107	−	0.311923i	$-0.100973\pi$
$787$	32.4026	+	18.7076i	1.15503	+	0.666856i	0.204920	+	0.978779i	$0.434306\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	19.8714	−	11.4727i	0.706544	−	0.407923i
$792$		0			0
$793$	−16.7544	+	36.3808i	−0.594965	+	1.29192i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−23.6200	+	40.9110i	−0.836663	+	1.44914i	0.0560071	+	0.998430i	$0.482163\pi$
$797$	−23.6200	+	40.9110i	−0.836663	+	1.44914i	−0.892670	+	0.450712i	$0.851170\pi$
$798$		0			0
$799$	−10.8848	−	6.28436i	−0.385078	−	0.222325i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	2.29037	+	3.96704i	0.0808254	+	0.139994i
$804$		0			0
$805$	16.3767			0.577204
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−23.2371	−	40.2478i	−0.816972	−	1.41504i	−0.907903	−	0.419180i	$-0.862318\pi$
$809$	−23.2371	−	40.2478i	−0.816972	−	1.41504i	0.0909313	−	0.995857i	$-0.471016\pi$
$810$		0			0
$811$			11.4041i			0.400453i	0.979750	+	0.200227i	$0.0641678\pi$
$811$			11.4041i			0.400453i	−0.979750	+	0.200227i	$0.935832\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	3.18915	−	5.52377i	0.111711	−	0.193489i
$816$		0			0
$817$	8.65436	−	4.99660i	0.302778	−	0.174809i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	21.2709	−	12.2808i	0.742359	−	0.428601i	−0.0805674	−	0.996749i	$-0.525673\pi$
$821$	21.2709	−	12.2808i	0.742359	−	0.428601i	0.822926	+	0.568148i	$0.192340\pi$
$822$		0			0
$823$	1.48224	−	2.56731i	0.0516676	−	0.0894909i	−0.839035	−	0.544078i	$-0.816880\pi$
$823$	1.48224	−	2.56731i	0.0516676	−	0.0894909i	0.890702	+	0.454587i	$0.150213\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	17.7265i		−	0.616412i	−0.951320	−	0.308206i	$-0.900271\pi$
$827$		−	17.7265i		−	0.616412i	0.951320	−	0.308206i	$-0.0997286\pi$
$828$		0			0
$829$	−5.78791	−	10.0250i	−0.201022	−	0.348181i	0.747836	−	0.663884i	$-0.231093\pi$
$829$	−5.78791	−	10.0250i	−0.201022	−	0.348181i	−0.948858	+	0.315703i	$0.897760\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−9.47657			−0.328344
$834$		0			0
$835$	7.76445	+	13.4484i	0.268700	+	0.465402i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−37.1348	−	21.4398i	−1.28203	−	0.740183i	−0.304815	−	0.952412i	$-0.598595\pi$
$839$	−37.1348	−	21.4398i	−1.28203	−	0.740183i	−0.977220	+	0.212229i	$0.931928\pi$
$840$		0			0
$841$	14.3612	−	24.8743i	0.495213	−	0.857734i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	2.37915	+	12.7804i	0.0818453	+	0.439660i
$846$		0			0
$847$	14.5131	−	8.37915i	0.498677	−	0.287911i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	66.0016	+	38.1060i	2.26251	+	1.30626i
$852$		0			0
$853$		−	13.4599i		−	0.460857i	−0.973089	−	0.230428i	$-0.925987\pi$
$853$		−	13.4599i		−	0.460857i	0.973089	−	0.230428i	$-0.0740127\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	10.5950			0.361919			0.180960	−	0.983491i	$-0.442080\pi$
$857$	10.5950			0.361919			0.180960	+	0.983491i	$0.442080\pi$
$858$		0			0
$859$	−8.75716			−0.298791			−0.149395	−	0.988778i	$-0.547733\pi$
$859$	−8.75716			−0.298791			−0.149395	+	0.988778i	$0.547733\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	30.8640i		−	1.05062i	−0.850910	−	0.525311i	$-0.823949\pi$
$863$		−	30.8640i		−	1.05062i	0.850910	−	0.525311i	$-0.176051\pi$
$864$		0			0
$865$	4.13617	+	2.38802i	0.140634	+	0.0811951i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−20.3593	+	11.7545i	−0.690643	+	0.398743i
$870$		0			0
$871$	31.8895	−	22.5561i	1.08053	−	0.764285i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−1.04739	+	1.81414i	−0.0354084	+	0.0613291i
$876$		0			0
$877$	17.4103	+	10.0518i	0.587904	+	0.339427i	0.764268	−	0.644898i	$-0.223100\pi$
$877$	17.4103	+	10.0518i	0.587904	+	0.339427i	−0.176364	+	0.984325i	$0.556434\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−1.56698	−	2.71409i	−0.0527930	−	0.0914401i	0.838421	−	0.545023i	$-0.183479\pi$
$881$	−1.56698	−	2.71409i	−0.0527930	−	0.0914401i	−0.891214	+	0.453583i	$0.850146\pi$
$882$		0			0
$883$	−34.0429			−1.14563			−0.572817	−	0.819683i	$-0.694149\pi$
$883$	−34.0429			−1.14563			−0.572817	+	0.819683i	$0.694149\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	25.4034	+	44.0001i	0.852964	+	1.47738i	0.878521	+	0.477704i	$0.158531\pi$
$887$	25.4034	+	44.0001i	0.852964	+	1.47738i	−0.0255565	+	0.999673i	$0.508136\pi$
$888$		0			0
$889$		−	1.90127i		−	0.0637666i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	1.85224	−	3.20817i	0.0619827	−	0.107357i
$894$		0			0
$895$	13.5989	−	7.85134i	0.454562	−	0.262442i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−2.66640	+	1.53944i	−0.0889293	+	0.0513434i
$900$		0			0
$901$	−22.8471	+	39.5723i	−0.761147	+	1.31834i
$902$		0			0
$903$		0			0
$904$		0			0
$905$			10.8851i			0.361832i
$906$		0			0
$907$	−25.4803	−	44.1331i	−0.846058	−	1.46542i	−0.884699	−	0.466163i	$-0.845636\pi$
$907$	−25.4803	−	44.1331i	−0.846058	−	1.46542i	0.0386406	−	0.999253i	$-0.487697\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	23.7176			0.785800			0.392900	−	0.919581i	$-0.371472\pi$
$911$	23.7176			0.785800			0.392900	+	0.919581i	$0.371472\pi$
$912$		0			0
$913$	13.6767	+	23.6887i	0.452632	+	0.783981i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−23.8788	−	13.7864i	−0.788548	−	0.455269i
$918$		0			0
$919$	21.1516	−	36.6356i	0.697725	−	1.20850i	−0.271528	−	0.962431i	$-0.587529\pi$
$919$	21.1516	−	36.6356i	0.697725	−	1.20850i	0.969253	−	0.246065i	$-0.0791377\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−46.4034	−	21.3701i	−1.52739	−	0.703405i
$924$		0			0
$925$	−8.44242	+	4.87423i	−0.277585	+	0.160264i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	11.5432	+	6.66449i	0.378721	+	0.218655i	0.677262	−	0.735742i	$-0.263166\pi$
$929$	11.5432	+	6.66449i	0.378721	+	0.218655i	−0.298541	+	0.954397i	$0.596500\pi$
$930$		0			0
$931$		−	2.79310i		−	0.0915402i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−6.28436			−0.205521
$936$		0			0
$937$	14.0848			0.460129			0.230065	−	0.973175i	$-0.426106\pi$
$937$	14.0848			0.460129			0.230065	+	0.973175i	$0.426106\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$			49.0399i			1.59866i	0.600895	+	0.799328i	$0.294811\pi$
$941$			49.0399i			1.59866i	−0.600895	+	0.799328i	$0.705189\pi$
$942$		0			0
$943$	28.8960	+	16.6831i	0.940983	+	0.543277i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	15.5323	−	8.96760i	0.504733	−	0.291408i	−0.225933	−	0.974143i	$-0.572543\pi$
$947$	15.5323	−	8.96760i	0.504733	−	0.291408i	0.730666	+	0.682735i	$0.239210\pi$
$948$		0			0
$949$	0.876268	+	9.49523i	0.0284449	+	0.308228i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−22.1915	+	38.4368i	−0.718853	+	1.24509i	0.242601	+	0.970126i	$0.421999\pi$
$953$	−22.1915	+	38.4368i	−0.718853	+	1.24509i	−0.961454	+	0.274964i	$0.911334\pi$
$954$		0			0
$955$	−5.15994	−	2.97909i	−0.166972	−	0.0964012i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	12.6366	+	21.8872i	0.408057	+	0.706776i
$960$		0			0
$961$	−3.14359			−0.101406
$962$		0			0
$963$		0			0
$964$		0			0
$965$	6.38473	+	11.0587i	0.205532	+	0.355992i
$966$		0			0
$967$		−	24.3595i		−	0.783348i	−0.920104	−	0.391674i	$-0.871896\pi$
$967$		−	24.3595i		−	0.783348i	0.920104	−	0.391674i	$-0.128104\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−0.587359	+	1.01734i	−0.0188492	+	0.0326478i	−0.875296	−	0.483587i	$-0.839334\pi$
$971$	−0.587359	+	1.01734i	−0.0188492	+	0.0326478i	0.856447	+	0.516235i	$0.172667\pi$
$972$		0			0
$973$	−10.1807	+	5.87783i	−0.326378	+	0.188435i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−10.6609	+	6.15505i	−0.341071	+	0.196917i	−0.660746	−	0.750610i	$-0.729760\pi$
$977$	−10.6609	+	6.15505i	−0.341071	+	0.196917i	0.319675	+	0.947527i	$0.396426\pi$
$978$		0			0
$979$	−4.78436	+	8.28676i	−0.152909	+	0.264846i
$980$		0			0
$981$		0			0
$982$		0			0
$983$			2.29060i			0.0730589i	0.999333	+	0.0365295i	$0.0116303\pi$
$983$			2.29060i			0.0730589i	−0.999333	+	0.0365295i	$0.988370\pi$
$984$		0			0
$985$	8.05397	+	13.9499i	0.256621	+	0.444480i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	73.0560			2.32305
$990$		0			0
$991$	−10.8499	−	18.7926i	−0.344659	−	0.596967i	0.640633	−	0.767848i	$-0.278672\pi$
$991$	−10.8499	−	18.7926i	−0.344659	−	0.596967i	−0.985292	+	0.170880i	$0.945339\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−7.38551	−	4.26403i	−0.234136	−	0.135179i
$996$		0			0
$997$	9.53125	−	16.5086i	0.301858	−	0.522833i	−0.674699	−	0.738093i	$-0.735727\pi$
$997$	9.53125	−	16.5086i	0.301858	−	0.522833i	0.976557	+	0.215260i	$0.0690599\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2340.2.dj.d.361.3		8
3.2	odd	2		260.2.x.a.101.1	✓	8
12.11	even	2		1040.2.da.c.881.4		8
13.4	even	6	inner	2340.2.dj.d.901.1		8
15.2	even	4		1300.2.ba.b.49.1		8
15.8	even	4		1300.2.ba.c.49.4		8
15.14	odd	2		1300.2.y.b.101.4		8
39.2	even	12		3380.2.a.p.1.4		4
39.11	even	12		3380.2.a.q.1.4		4
39.17	odd	6		260.2.x.a.121.1	yes	8
39.23	odd	6		3380.2.f.i.3041.8		8
39.29	odd	6		3380.2.f.i.3041.7		8
156.95	even	6		1040.2.da.c.641.4		8
195.17	even	12		1300.2.ba.c.849.4		8
195.134	odd	6		1300.2.y.b.901.4		8
195.173	even	12		1300.2.ba.b.849.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.x.a.101.1	✓	8	3.2	odd	2
260.2.x.a.121.1	yes	8	39.17	odd	6
1040.2.da.c.641.4		8	156.95	even	6
1040.2.da.c.881.4		8	12.11	even	2
1300.2.y.b.101.4		8	15.14	odd	2
1300.2.y.b.901.4		8	195.134	odd	6
1300.2.ba.b.49.1		8	15.2	even	4
1300.2.ba.b.849.1		8	195.173	even	12
1300.2.ba.c.49.4		8	15.8	even	4
1300.2.ba.c.849.4		8	195.17	even	12
2340.2.dj.d.361.3		8	1.1	even	1	trivial
2340.2.dj.d.901.1		8	13.4	even	6	inner
3380.2.a.p.1.4		4	39.2	even	12
3380.2.a.q.1.4		4	39.11	even	12
3380.2.f.i.3041.7		8	39.29	odd	6
3380.2.f.i.3041.8		8	39.23	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:	\( N \)	\(=\)	\( 2340 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2340.dj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{5} +(-1.81414 - 1.04739i) q^{7} +O(q^{10})\)	\(q+1.00000i q^{5} +(-1.81414 - 1.04739i) q^{7} +(-1.50000 + 0.866025i) q^{11} +(-3.59030 + 0.331331i) q^{13} +(1.81414 - 3.14218i) q^{17} +(0.926118 + 0.534695i) q^{19} +(3.90893 + 6.77046i) q^{23} -1.00000 q^{25} +(-0.263457 - 0.456321i) q^{29} -5.84325i q^{31} +(1.04739 - 1.81414i) q^{35} +(8.44242 - 4.87423i) q^{37} +(3.69615 - 2.13397i) q^{41} +(4.67238 - 8.09281i) q^{43} -3.46410i q^{47} +(-1.30593 - 2.26194i) q^{49} -12.5939 q^{53} +(-0.866025 - 1.50000i) q^{55} +(1.21564 + 0.701848i) q^{59} +(5.55440 - 9.62050i) q^{61} +(-0.331331 - 3.59030i) q^{65} +(-9.38201 + 5.41671i) q^{67} +(12.2709 + 7.08460i) q^{71} -2.64469i q^{73} +3.62828 q^{77} +13.5729 q^{79} -15.7925i q^{83} +(3.14218 + 1.81414i) q^{85} +(4.78436 - 2.76225i) q^{89} +(6.86033 + 3.15937i) q^{91} +(-0.534695 + 0.926118i) q^{95} +(-13.1589 - 7.59730i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{7}+O(q^{10}) \) 8 * q + 6 * q^7	\( 8 q + 6 q^{7} - 12 q^{11} - 8 q^{13} - 6 q^{17} + 6 q^{23} - 8 q^{25} + 6 q^{35} + 6 q^{37} - 12 q^{41} + 10 q^{43} - 4 q^{49} - 24 q^{53} + 24 q^{59} - 4 q^{61} - 54 q^{67} + 36 q^{71} - 12 q^{77} - 16 q^{79} + 18 q^{85} + 24 q^{89} - 30 q^{97}+O(q^{100}) \) 8 * q + 6 * q^7 - 12 * q^11 - 8 * q^13 - 6 * q^17 + 6 * q^23 - 8 * q^25 + 6 * q^35 + 6 * q^37 - 12 * q^41 + 10 * q^43 - 4 * q^49 - 24 * q^53 + 24 * q^59 - 4 * q^61 - 54 * q^67 + 36 * q^71 - 12 * q^77 - 16 * q^79 + 18 * q^85 + 24 * q^89 - 30 * q^97

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