LMFDB - Embedded newform 2340.2.dj.d.361.1

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			361.1
Root			$-1.27597 + 0.609843i$ of defining polynomial
Character	$\chi$	$=$	2340.361
Dual form			2340.2.dj.d.901.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{5} +(0.346241 + 0.199902i) q^{7} +O(q^{10})$	$q-1.00000i q^{5} +(0.346241 + 0.199902i) q^{7} +(-1.50000 + 0.866025i) q^{11} +(-0.619491 + 3.55193i) q^{13} +(-0.346241 + 0.599706i) q^{17} +(-4.65213 - 2.68591i) q^{19} +(0.0535636 + 0.0927749i) q^{23} -1.00000 q^{25} +(-2.45174 - 4.24653i) q^{29} -7.86488i q^{31} +(0.199902 - 0.346241i) q^{35} +(1.96128 - 1.13234i) q^{37} +(-6.69615 + 3.86603i) q^{41} +(3.00530 - 5.20533i) q^{43} -3.46410i q^{47} +(-3.42008 - 5.92375i) q^{49} -11.7189 q^{53} +(0.866025 + 1.50000i) q^{55} +(6.30059 + 3.63765i) q^{59} +(-4.34461 + 7.52509i) q^{61} +(3.55193 + 0.619491i) q^{65} +(-1.15009 + 0.664004i) q^{67} +(3.35847 + 1.93902i) q^{71} -10.2251i q^{73} -0.692481 q^{77} -13.1533 q^{79} +14.0791i q^{83} +(0.599706 + 0.346241i) q^{85} +(-0.300587 + 0.173544i) q^{89} +(-0.924532 + 1.10599i) q^{91} +(-2.68591 + 4.65213i) q^{95} +(-7.66436 - 4.42502i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	0.346241	+	0.199902i	0.130867	+	0.0755559i	0.564004	−	0.825772i	$-0.309260\pi$
$7$	0.346241	+	0.199902i	0.130867	+	0.0755559i	−0.433137	+	0.901328i	$0.642594\pi$
$8$		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
$13$	−0.619491	+	3.55193i	−0.171816	+	0.985129i
$13$	−0.619491	+	3.55193i	−0.171816	+	0.985129i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.346241	+	0.599706i	−0.0839757	+	0.145450i	−0.904954	−	0.425509i	$-0.860095\pi$
$17$	−0.346241	+	0.599706i	−0.0839757	+	0.145450i	0.820979	+	0.570959i	$0.193428\pi$
$18$		0			0
$19$	−4.65213	−	2.68591i	−1.06727	−	0.616190i	−0.139837	−	0.990175i	$-0.544658\pi$
$19$	−4.65213	−	2.68591i	−1.06727	−	0.616190i	−0.927435	+	0.373985i	$0.877991\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.0535636	+	0.0927749i	0.0111688	+	0.0193449i	0.871556	−	0.490296i	$-0.163111\pi$
$23$	0.0535636	+	0.0927749i	0.0111688	+	0.0193449i	−0.860387	+	0.509641i	$0.829778\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−2.45174	−	4.24653i	−0.455276	−	0.788562i	0.543428	−	0.839456i	$-0.317126\pi$
$29$	−2.45174	−	4.24653i	−0.455276	−	0.788562i	−0.998704	+	0.0508943i	$0.983793\pi$
$30$		0			0
$31$		−	7.86488i		−	1.41257i	−0.707925	−	0.706287i	$-0.750369\pi$
$31$		−	7.86488i		−	1.41257i	0.707925	−	0.706287i	$-0.249631\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	0.199902	−	0.346241i	0.0337896	−	0.0585254i
$36$		0			0
$37$	1.96128	−	1.13234i	0.322432	−	0.186156i	−0.330044	−	0.943966i	$-0.607064\pi$
$37$	1.96128	−	1.13234i	0.322432	−	0.186156i	0.652476	+	0.757809i	$0.273730\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−6.69615	+	3.86603i	−1.04576	+	0.603772i	−0.921460	−	0.388473i	$-0.873003\pi$
$41$	−6.69615	+	3.86603i	−1.04576	+	0.603772i	−0.124303	+	0.992244i	$0.539669\pi$
$42$		0			0
$43$	3.00530	−	5.20533i	0.458304	−	0.793806i	−0.540567	−	0.841301i	$-0.681790\pi$
$43$	3.00530	−	5.20533i	0.458304	−	0.793806i	0.998871	+	0.0474947i	$0.0151237\pi$
$44$		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
$49$	−3.42008	−	5.92375i	−0.488583	−	0.846250i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−11.7189			−1.60972			−0.804858	−	0.593468i	$-0.797758\pi$
$53$	−11.7189			−1.60972			−0.804858	+	0.593468i	$0.797758\pi$
$54$		0			0
$55$	0.866025	+	1.50000i	0.116775	+	0.202260i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	6.30059	+	3.63765i	0.820267	+	0.473581i	0.850508	−	0.525961i	$-0.176294\pi$
$59$	6.30059	+	3.63765i	0.820267	+	0.473581i	−0.0302418	+	0.999543i	$0.509628\pi$
$60$		0			0
$61$	−4.34461	+	7.52509i	−0.556270	+	0.963489i	0.441533	+	0.897245i	$0.354435\pi$
$61$	−4.34461	+	7.52509i	−0.556270	+	0.963489i	−0.997803	+	0.0662436i	$0.978899\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	3.55193	+	0.619491i	0.440563	+	0.0768384i
$66$		0			0
$67$	−1.15009	+	0.664004i	−0.140506	+	0.0811210i	−0.568605	−	0.822611i	$-0.692517\pi$
$67$	−1.15009	+	0.664004i	−0.140506	+	0.0811210i	0.428099	+	0.903732i	$0.359183\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	3.35847	+	1.93902i	0.398577	+	0.230119i	0.685870	−	0.727724i	$-0.259422\pi$
$71$	3.35847	+	1.93902i	0.398577	+	0.230119i	−0.287293	+	0.957843i	$0.592755\pi$
$72$		0			0
$73$		−	10.2251i		−	1.19676i	−0.801213	−	0.598380i	$-0.795811\pi$
$73$		−	10.2251i		−	1.19676i	0.801213	−	0.598380i	$-0.204189\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.692481			−0.0789156
$78$		0			0
$79$	−13.1533			−1.47986			−0.739932	−	0.672681i	$-0.765142\pi$
$79$	−13.1533			−1.47986			−0.739932	+	0.672681i	$0.765142\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$			14.0791i			1.54539i	0.634780	+	0.772693i	$0.281091\pi$
$83$			14.0791i			1.54539i	−0.634780	+	0.772693i	$0.718909\pi$
$84$		0			0
$85$	0.599706	+	0.346241i	0.0650473	+	0.0375551i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−0.300587	+	0.173544i	−0.0318622	+	0.0183956i	−0.515846	−	0.856681i	$-0.672523\pi$
$89$	−0.300587	+	0.173544i	−0.0318622	+	0.0183956i	0.483984	+	0.875077i	$0.339189\pi$
$90$		0			0
$91$	−0.924532	+	1.10599i	−0.0969173	+	0.115939i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−2.68591	+	4.65213i	−0.275568	+	0.477298i
$96$		0			0
$97$	−7.66436	−	4.42502i	−0.778198	−	0.449293i	0.0575932	−	0.998340i	$-0.481657\pi$
$97$	−7.66436	−	4.42502i	−0.778198	−	0.449293i	−0.835791	+	0.549047i	$0.814991\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−2.05193	−	3.55405i	−0.204175	−	0.353641i	0.745695	−	0.666288i	$-0.232118\pi$
$101$	−2.05193	−	3.55405i	−0.204175	−	0.353641i	−0.949870	+	0.312646i	$0.898784\pi$
$102$		0			0
$103$	−11.2325			−1.10677			−0.553384	−	0.832926i	$-0.686664\pi$
$103$	−11.2325			−1.10677			−0.553384	+	0.832926i	$0.686664\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−8.80165	−	15.2449i	−0.850888	−	1.47378i	−0.880408	−	0.474216i	$-0.842731\pi$
$107$	−8.80165	−	15.2449i	−0.850888	−	1.47378i	0.0295208	−	0.999564i	$-0.490602\pi$
$108$		0			0
$109$			15.1830i			1.45427i	0.686495	+	0.727134i	$0.259148\pi$
$109$			15.1830i			1.45427i	−0.686495	+	0.727134i	$0.740852\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	4.45011	−	7.70781i	0.418631	−	0.725090i	−0.577171	−	0.816623i	$-0.695843\pi$
$113$	4.45011	−	7.70781i	0.418631	−	0.725090i	0.995802	+	0.0915332i	$0.0291768\pi$
$114$		0			0
$115$	0.0927749	−	0.0535636i	0.00865131	−	0.00499483i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−0.239765	+	0.138429i	−0.0219792	+	0.0126897i
$120$		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
$127$	6.07829	+	10.5279i	0.539361	+	0.934201i	0.998939	+	0.0460632i	$0.0146676\pi$
$127$	6.07829	+	10.5279i	0.539361	+	0.934201i	−0.459577	+	0.888138i	$0.651999\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	2.11773			0.185027			0.0925135	−	0.995711i	$-0.470510\pi$
$131$	2.11773			0.185027			0.0925135	+	0.995711i	$0.470510\pi$
$132$		0			0
$133$	−1.07384	−	1.85994i	−0.0931135	−	0.161277i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−15.6171	−	9.01652i	−1.33426	−	0.770334i	−0.348308	−	0.937380i	$-0.613244\pi$
$137$	−15.6171	−	9.01652i	−1.33426	−	0.770334i	−0.985949	+	0.167046i	$0.946577\pi$
$138$		0			0
$139$	4.92008	−	8.52183i	0.417316	−	0.722812i	−0.578353	−	0.815787i	$-0.696304\pi$
$139$	4.92008	−	8.52183i	0.417316	−	0.722812i	0.995668	+	0.0929749i	$0.0296376\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−2.14683	−	5.86440i	−0.179527	−	0.490405i
$144$		0			0
$145$	−4.24653	+	2.45174i	−0.352655	+	0.203606i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	7.69289	+	4.44149i	0.630226	+	0.363861i	0.780840	−	0.624731i	$-0.214792\pi$
$149$	7.69289	+	4.44149i	0.630226	+	0.363861i	−0.150613	+	0.988593i	$0.548125\pi$
$150$		0			0
$151$		−	4.43937i		−	0.361271i	−0.983550	−	0.180636i	$-0.942185\pi$
$151$		−	4.43937i		−	0.361271i	0.983550	−	0.180636i	$-0.0578155\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−7.86488			−0.631723
$156$		0			0
$157$	−4.16719			−0.332578			−0.166289	−	0.986077i	$-0.553178\pi$
$157$	−4.16719			−0.332578			−0.166289	+	0.986077i	$0.553178\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$			0.0428299i			0.00337547i
$162$		0			0
$163$	3.20145	+	1.84836i	0.250757	+	0.144775i	0.620111	−	0.784514i	$-0.287088\pi$
$163$	3.20145	+	1.84836i	0.250757	+	0.144775i	−0.369354	+	0.929289i	$0.620421\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	18.6171	−	10.7486i	1.44063	−	0.831750i	0.442741	−	0.896650i	$-0.354006\pi$
$167$	18.6171	−	10.7486i	1.44063	−	0.831750i	0.997892	+	0.0648999i	$0.0206728\pi$
$168$		0			0
$169$	−12.2325	−	4.40078i	−0.940959	−	0.338522i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	5.80589	−	10.0561i	0.441414	−	0.764551i	−0.556381	−	0.830927i	$-0.687811\pi$
$173$	5.80589	−	10.0561i	0.441414	−	0.764551i	0.997795	+	0.0663766i	$0.0211439\pi$
$174$		0			0
$175$	−0.346241	−	0.199902i	−0.0261733	−	0.0151112i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	2.48516	+	4.30442i	0.185749	+	0.321728i	0.943829	−	0.330435i	$-0.107195\pi$
$179$	2.48516	+	4.30442i	0.185749	+	0.321728i	−0.758079	+	0.652162i	$0.773862\pi$
$180$		0			0
$181$	−17.3695			−1.29107			−0.645534	−	0.763732i	$-0.723365\pi$
$181$	−17.3695			−1.29107			−0.645534	+	0.763732i	$0.723365\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−1.13234	−	1.96128i	−0.0832516	−	0.144196i
$186$		0			0
$187$		−	1.19941i		−	0.0877098i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−10.2523	+	17.7575i	−0.741832	+	1.28489i	0.209828	+	0.977738i	$0.432710\pi$
$191$	−10.2523	+	17.7575i	−0.741832	+	1.28489i	−0.951660	+	0.307153i	$0.900624\pi$
$192$		0			0
$193$	−23.0428	+	13.3038i	−1.65866	+	0.957626i	−0.685322	+	0.728240i	$0.740338\pi$
$193$	−23.0428	+	13.3038i	−1.65866	+	0.957626i	−0.973336	+	0.229386i	$0.926328\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−0.353583	+	0.204141i	−0.0251917	+	0.0145445i	−0.512543	−	0.858662i	$-0.671296\pi$
$197$	−0.353583	+	0.204141i	−0.0251917	+	0.0145445i	0.487351	+	0.873206i	$0.337963\pi$
$198$		0			0
$199$	12.1998	−	21.1307i	0.864823	−	1.49792i	−0.00240070	−	0.999997i	$-0.500764\pi$
$199$	12.1998	−	21.1307i	0.864823	−	1.49792i	0.867223	−	0.497919i	$-0.165902\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		−	1.96043i		−	0.137595i
$204$		0			0
$205$	3.86603	+	6.69615i	0.270015	+	0.467680i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	9.30426			0.643589
$210$		0			0
$211$	−0.880509	−	1.52509i	−0.0606167	−	0.104991i	0.834125	−	0.551576i	$-0.185973\pi$
$211$	−0.880509	−	1.52509i	−0.0606167	−	0.104991i	−0.894741	+	0.446585i	$0.852640\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−5.20533	−	3.00530i	−0.355001	−	0.204960i
$216$		0			0
$217$	1.57221	−	2.72314i	0.106728	−	0.184859i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−1.91562	−	1.60134i	−0.128859	−	0.107718i
$222$		0			0
$223$	9.80263	−	5.65955i	0.656433	−	0.378991i	−0.134484	−	0.990916i	$-0.542938\pi$
$223$	9.80263	−	5.65955i	0.656433	−	0.378991i	0.790916	+	0.611924i	$0.209604\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	6.98084	+	4.03039i	0.463334	+	0.267506i	0.713445	−	0.700711i	$-0.247134\pi$
$227$	6.98084	+	4.03039i	0.463334	+	0.267506i	−0.250111	+	0.968217i	$0.580467\pi$
$228$		0			0
$229$		−	11.5715i		−	0.764666i	−0.924025	−	0.382333i	$-0.875121\pi$
$229$		−	11.5715i		−	0.764666i	0.924025	−	0.382333i	$-0.124879\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	24.0900			1.57819			0.789094	−	0.614272i	$-0.210550\pi$
$233$	24.0900			1.57819			0.789094	+	0.614272i	$0.210550\pi$
$234$		0			0
$235$	−3.46410			−0.225973
$236$		0			0
$237$		0			0
$238$		0			0
$239$		−	30.7089i		−	1.98639i	−0.116459	−	0.993196i	$-0.537154\pi$
$239$		−	30.7089i		−	1.98639i	0.116459	−	0.993196i	$-0.462846\pi$
$240$		0			0
$241$	6.86541	+	3.96374i	0.442240	+	0.255327i	0.704547	−	0.709657i	$-0.251150\pi$
$241$	6.86541	+	3.96374i	0.442240	+	0.255327i	−0.262308	+	0.964984i	$0.584483\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−5.92375	+	3.42008i	−0.378454	+	0.218501i
$246$		0			0
$247$	12.4221	−	14.8602i	0.790401	−	0.945529i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−11.3112	+	19.5916i	−0.713956	+	1.23661i	0.249405	+	0.968399i	$0.419765\pi$
$251$	−11.3112	+	19.5916i	−0.713956	+	1.23661i	−0.963361	+	0.268209i	$0.913568\pi$
$252$		0			0
$253$	−0.160691	−	0.0927749i	−0.0101025	−	0.00583271i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−12.8982	−	22.3403i	−0.804566	−	1.39355i	−0.916584	−	0.399843i	$-0.869065\pi$
$257$	−12.8982	−	22.3403i	−0.804566	−	1.39355i	0.112018	−	0.993706i	$-0.464269\pi$
$258$		0			0
$259$	0.905432			0.0562608
$260$		0			0
$261$		0			0
$262$		0			0
$263$	0.795286	+	1.37748i	0.0490394	+	0.0849388i	0.889503	−	0.456929i	$-0.151051\pi$
$263$	0.795286	+	1.37748i	0.0490394	+	0.0849388i	−0.840464	+	0.541868i	$0.817717\pi$
$264$		0			0
$265$			11.7189i			0.719887i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−13.9114	+	24.0952i	−0.848192	+	1.46911i	0.0346278	+	0.999400i	$0.488975\pi$
$269$	−13.9114	+	24.0952i	−0.848192	+	1.46911i	−0.882820	+	0.469712i	$0.844358\pi$
$270$		0			0
$271$	−20.3520	+	11.7502i	−1.23629	+	0.713774i	−0.968335	−	0.249656i	$-0.919682\pi$
$271$	−20.3520	+	11.7502i	−1.23629	+	0.713774i	−0.267959	+	0.963430i	$0.586349\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	1.50000	−	0.866025i	0.0904534	−	0.0522233i
$276$		0			0
$277$	−1.49837	+	2.59525i	−0.0900283	+	0.155934i	−0.907523	−	0.420003i	$-0.862029\pi$
$277$	−1.49837	+	2.59525i	−0.0900283	+	0.155934i	0.817494	+	0.575936i	$0.195362\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$			24.6085i			1.46802i	0.679138	+	0.734011i	$0.262354\pi$
$281$			24.6085i			1.46802i	−0.679138	+	0.734011i	$0.737646\pi$
$282$		0			0
$283$	4.08444	+	7.07446i	0.242795	+	0.420533i	0.961509	−	0.274772i	$-0.0886025\pi$
$283$	4.08444	+	7.07446i	0.242795	+	0.420533i	−0.718715	+	0.695305i	$0.755269\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−3.09131			−0.182474
$288$		0			0
$289$	8.26023	+	14.3071i	0.485896	+	0.841597i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	6.49837	+	3.75184i	0.379639	+	0.219185i	0.677661	−	0.735374i	$-0.262994\pi$
$293$	6.49837	+	3.75184i	0.379639	+	0.219185i	−0.298022	+	0.954559i	$0.596327\pi$
$294$		0			0
$295$	3.63765	−	6.30059i	0.211792	−	0.366834i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−0.362712	+	0.132781i	−0.0209762	+	0.00767893i
$300$		0			0
$301$	2.08112	−	1.20153i	0.119953	−	0.0692552i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	7.52509	+	4.34461i	0.430885	+	0.248772i
$306$		0			0
$307$		−	5.95293i		−	0.339752i	−0.985465	−	0.169876i	$-0.945663\pi$
$307$		−	5.95293i		−	0.339752i	0.985465	−	0.169876i	$-0.0543367\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	17.9247			1.01642			0.508208	−	0.861235i	$-0.330308\pi$
$311$	17.9247			1.01642			0.508208	+	0.861235i	$0.330308\pi$
$312$		0			0
$313$	−17.0073			−0.961312			−0.480656	−	0.876909i	$-0.659601\pi$
$313$	−17.0073			−0.961312			−0.480656	+	0.876909i	$0.659601\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$			3.09300i			0.173720i	0.996221	+	0.0868601i	$0.0276833\pi$
$317$			3.09300i			0.173720i	−0.996221	+	0.0868601i	$0.972317\pi$
$318$		0			0
$319$	7.35521	+	4.24653i	0.411813	+	0.237760i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	3.22151	−	1.85994i	0.179250	−	0.103490i
$324$		0			0
$325$	0.619491	−	3.55193i	0.0343632	−	0.197026i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	0.692481	−	1.19941i	0.0381777	−	0.0661258i
$330$		0			0
$331$	19.5481	+	11.2861i	1.07446	+	0.620340i	0.929397	−	0.369082i	$-0.120328\pi$
$331$	19.5481	+	11.2861i	1.07446	+	0.620340i	0.145064	+	0.989422i	$0.453661\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	0.664004	+	1.15009i	0.0362784	+	0.0628360i
$336$		0			0
$337$	18.0603			0.983808			0.491904	−	0.870649i	$-0.336301\pi$
$337$	18.0603			0.983808			0.491904	+	0.870649i	$0.336301\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	6.81119	+	11.7973i	0.368847	+	0.638861i
$342$		0			0
$343$		−	5.53335i		−	0.298773i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	13.2359	−	22.9252i	0.710538	−	1.23069i	−0.254118	−	0.967173i	$-0.581785\pi$
$347$	13.2359	−	22.9252i	0.710538	−	1.23069i	0.964655	−	0.263514i	$-0.0848816\pi$
$348$		0			0
$349$	10.7190	−	6.18860i	0.573773	−	0.331268i	−0.184882	−	0.982761i	$-0.559190\pi$
$349$	10.7190	−	6.18860i	0.573773	−	0.331268i	0.758655	+	0.651493i	$0.225857\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−16.6978	+	9.64047i	−0.888733	+	0.513110i	−0.873528	−	0.486774i	$-0.838174\pi$
$353$	−16.6978	+	9.64047i	−0.888733	+	0.513110i	−0.0152053	+	0.999884i	$0.504840\pi$
$354$		0			0
$355$	1.93902	−	3.35847i	0.102912	−	0.178249i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	26.5506i		−	1.40129i	−0.713512	−	0.700643i	$-0.752897\pi$
$359$		−	26.5506i		−	1.40129i	0.713512	−	0.700643i	$-0.247103\pi$
$360$		0			0
$361$	4.92820	+	8.53590i	0.259379	+	0.449258i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−10.2251			−0.535207
$366$		0			0
$367$	−3.68718	−	6.38638i	−0.192469	−	0.333366i	0.753599	−	0.657335i	$-0.228316\pi$
$367$	−3.68718	−	6.38638i	−0.192469	−	0.333366i	−0.946068	+	0.323968i	$0.894983\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−4.05756	−	2.34263i	−0.210658	−	0.121624i
$372$		0			0
$373$	14.1574	−	24.5214i	0.733044	−	1.26967i	−0.222532	−	0.974925i	$-0.571432\pi$
$373$	14.1574	−	24.5214i	0.733044	−	1.26967i	0.955576	−	0.294744i	$-0.0952344\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	16.6022	−	6.07772i	0.855059	−	0.313018i
$378$		0			0
$379$	9.02975	−	5.21333i	0.463827	−	0.267791i	−0.249825	−	0.968291i	$-0.580373\pi$
$379$	9.02975	−	5.21333i	0.463827	−	0.267791i	0.713652	+	0.700500i	$0.247040\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	9.39811	+	5.42600i	0.480221	+	0.277256i	0.720509	−	0.693446i	$-0.243908\pi$
$383$	9.39811	+	5.42600i	0.480221	+	0.277256i	−0.240288	+	0.970702i	$0.577242\pi$
$384$		0			0
$385$			0.692481i			0.0352921i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−20.2893			−1.02871			−0.514353	−	0.857578i	$-0.671968\pi$
$389$	−20.2893			−1.02871			−0.514353	+	0.857578i	$0.671968\pi$
$390$		0			0
$391$	−0.0741836			−0.00375163
$392$		0			0
$393$		0			0
$394$		0			0
$395$			13.1533i			0.661815i
$396$		0			0
$397$	21.8695	+	12.6263i	1.09760	+	0.633698i	0.935589	−	0.353091i	$-0.114870\pi$
$397$	21.8695	+	12.6263i	1.09760	+	0.633698i	0.162008	+	0.986789i	$0.448203\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−10.8377	+	6.25714i	−0.541208	+	0.312467i	−0.745568	−	0.666429i	$-0.767822\pi$
$401$	−10.8377	+	6.25714i	−0.541208	+	0.312467i	0.204360	+	0.978896i	$0.434489\pi$
$402$		0			0
$403$	27.9355	+	4.87223i	1.39157	+	0.242703i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−1.96128	+	3.39703i	−0.0972169	+	0.168385i
$408$		0			0
$409$	5.19248	+	2.99788i	0.256752	+	0.148236i	0.622852	−	0.782340i	$-0.285974\pi$
$409$	5.19248	+	2.99788i	0.256752	+	0.148236i	−0.366100	+	0.930575i	$0.619307\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	1.45435	+	2.51900i	0.0715637	+	0.123952i
$414$		0			0
$415$	14.0791			0.691118
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−5.48516	−	9.50057i	−0.267968	−	0.464133i	0.700369	−	0.713781i	$-0.253019\pi$
$419$	−5.48516	−	9.50057i	−0.267968	−	0.464133i	−0.968337	+	0.249647i	$0.919685\pi$
$420$		0			0
$421$			36.6085i			1.78419i	0.451848	+	0.892095i	$0.350765\pi$
$421$			36.6085i			1.78419i	−0.451848	+	0.892095i	$0.649235\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	0.346241	−	0.599706i	0.0167951	−	0.0290900i
$426$		0			0
$427$	−3.00856	+	1.73699i	−0.145595	+	0.0840590i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	10.4873	−	6.05484i	0.505155	−	0.291651i	−0.225685	−	0.974200i	$-0.572462\pi$
$431$	10.4873	−	6.05484i	0.505155	−	0.291651i	0.730840	+	0.682549i	$0.239129\pi$
$432$		0			0
$433$	−4.50897	+	7.80977i	−0.216687	+	0.375314i	−0.953793	−	0.300464i	$-0.902859\pi$
$433$	−4.50897	+	7.80977i	−0.216687	+	0.375314i	0.737106	+	0.675777i	$0.236192\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		−	0.575468i		−	0.0275284i
$438$		0			0
$439$	−6.07547	−	10.5230i	−0.289966	−	0.502236i	0.683835	−	0.729637i	$-0.260311\pi$
$439$	−6.07547	−	10.5230i	−0.289966	−	0.502236i	−0.973801	+	0.227400i	$0.926977\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−15.3116			−0.727476			−0.363738	−	0.931501i	$-0.618500\pi$
$443$	−15.3116			−0.727476			−0.363738	+	0.931501i	$0.618500\pi$
$444$		0			0
$445$	0.173544	+	0.300587i	0.00822678	+	0.0142492i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	19.6929	+	11.3697i	0.929365	+	0.536569i	0.886611	−	0.462516i	$-0.153053\pi$
$449$	19.6929	+	11.3697i	0.929365	+	0.536569i	0.0427543	+	0.999086i	$0.486387\pi$
$450$		0			0
$451$	6.69615	−	11.5981i	0.315310	−	0.546132i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	1.10599	+	0.924532i	0.0518494	+	0.0433427i
$456$		0			0
$457$	−9.30548	+	5.37252i	−0.435292	+	0.251316i	−0.701599	−	0.712572i	$-0.747530\pi$
$457$	−9.30548	+	5.37252i	−0.435292	+	0.251316i	0.266307	+	0.963888i	$0.414197\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−10.2973	−	5.94516i	−0.479594	−	0.276894i	0.240653	−	0.970611i	$-0.422638\pi$
$461$	−10.2973	−	5.94516i	−0.479594	−	0.276894i	−0.720247	+	0.693717i	$0.755972\pi$
$462$		0			0
$463$		−	3.39726i		−	0.157884i	−0.996879	−	0.0789420i	$-0.974846\pi$
$463$		−	3.39726i		−	0.157884i	0.996879	−	0.0789420i	$-0.0251542\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	6.39426			0.295891			0.147946	−	0.988996i	$-0.452734\pi$
$467$	6.39426			0.295891			0.147946	+	0.988996i	$0.452734\pi$
$468$		0			0
$469$	−0.530943			−0.0245167
$470$		0			0
$471$		0			0
$472$		0			0
$473$			10.4107i			0.478683i
$474$		0			0
$475$	4.65213	+	2.68591i	0.213454	+	0.123238i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−14.1330	+	8.15968i	−0.645752	+	0.372825i	−0.786827	−	0.617174i	$-0.788278\pi$
$479$	−14.1330	+	8.15968i	−0.645752	+	0.372825i	0.141075	+	0.989999i	$0.454944\pi$
$480$		0			0
$481$	2.80702	+	7.66781i	0.127989	+	0.349622i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−4.42502	+	7.66436i	−0.200930	+	0.348021i
$486$		0			0
$487$	−10.3356	−	5.96728i	−0.468352	−	0.270403i	0.247197	−	0.968965i	$-0.420490\pi$
$487$	−10.3356	−	5.96728i	−0.468352	−	0.270403i	−0.715550	+	0.698562i	$0.753824\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	17.0259	+	29.4896i	0.768366	+	1.33085i	0.938448	+	0.345419i	$0.112263\pi$
$491$	17.0259	+	29.4896i	0.768366	+	1.33085i	−0.170082	+	0.985430i	$0.554403\pi$
$492$		0			0
$493$	3.39557			0.152929
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.775227	+	1.34273i	0.0347737	+	0.0602298i
$498$		0			0
$499$			12.5854i			0.563398i	0.959503	+	0.281699i	$0.0908979\pi$
$499$			12.5854i			0.563398i	−0.959503	+	0.281699i	$0.909102\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−9.09433	+	15.7518i	−0.405496	+	0.702340i	−0.994379	−	0.105879i	$-0.966235\pi$
$503$	−9.09433	+	15.7518i	−0.405496	+	0.702340i	0.588883	+	0.808218i	$0.299568\pi$
$504$		0			0
$505$	−3.55405	+	2.05193i	−0.158153	+	0.0913098i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	25.1265	−	14.5068i	1.11371	−	0.643001i	0.173923	−	0.984759i	$-0.444356\pi$
$509$	25.1265	−	14.5068i	1.11371	−	0.643001i	0.939788	+	0.341758i	$0.111022\pi$
$510$		0			0
$511$	2.04402	−	3.54035i	0.0904223	−	0.156616i
$512$		0			0
$513$		0			0
$514$		0			0
$515$			11.2325i			0.494961i
$516$		0			0
$517$	3.00000	+	5.19615i	0.131940	+	0.228527i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−35.0240			−1.53443			−0.767214	−	0.641391i	$-0.778358\pi$
$521$	−35.0240			−1.53443			−0.767214	+	0.641391i	$0.778358\pi$
$522$		0			0
$523$	4.63870	+	8.03447i	0.202836	+	0.351323i	0.949441	−	0.313945i	$-0.101651\pi$
$523$	4.63870	+	8.03447i	0.202836	+	0.351323i	−0.746605	+	0.665268i	$0.768317\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	4.71662	+	2.72314i	0.205459	+	0.118622i
$528$		0			0
$529$	11.4943	−	19.9086i	0.499751	−	0.865593i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−9.58366	−	26.1793i	−0.415114	−	1.13395i
$534$		0			0
$535$	−15.2449	+	8.80165i	−0.659095	+	0.380528i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	10.2602	+	5.92375i	0.441940	+	0.255154i
$540$		0			0
$541$		−	24.3814i		−	1.04824i	−0.851644	−	0.524120i	$-0.824394\pi$
$541$		−	24.3814i		−	1.04824i	0.851644	−	0.524120i	$-0.175606\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	15.1830			0.650369
$546$		0			0
$547$	26.5270			1.13421			0.567106	−	0.823645i	$-0.308063\pi$
$547$	26.5270			1.13421			0.567106	+	0.823645i	$0.308063\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$			26.3406i			1.12215i
$552$		0			0
$553$	−4.55422	−	2.62938i	−0.193665	−	0.111813i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	2.78142	−	1.60586i	0.117853	−	0.0680423i	−0.439915	−	0.898039i	$-0.644991\pi$
$557$	2.78142	−	1.60586i	0.117853	−	0.0680423i	0.557768	+	0.829997i	$0.311658\pi$
$558$		0			0
$559$	16.6272	+	13.8993i	0.703257	+	0.587877i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	17.1426	−	29.6918i	0.722474	−	1.25136i	−0.237531	−	0.971380i	$-0.576338\pi$
$563$	17.1426	−	29.6918i	0.722474	−	1.25136i	0.960005	−	0.279982i	$-0.0903284\pi$
$564$		0			0
$565$	−7.70781	−	4.45011i	−0.324270	−	0.187217i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	17.8228	+	30.8701i	0.747172	+	1.29414i	0.949173	+	0.314755i	$0.101922\pi$
$569$	17.8228	+	30.8701i	0.747172	+	1.29414i	−0.202001	+	0.979385i	$0.564744\pi$
$570$		0			0
$571$	−4.53590			−0.189821			−0.0949107	−	0.995486i	$-0.530257\pi$
$571$	−4.53590			−0.189821			−0.0949107	+	0.995486i	$0.530257\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−0.0535636	−	0.0927749i	−0.00223376	−	0.00386898i
$576$		0			0
$577$		−	18.4475i		−	0.767981i	−0.923337	−	0.383991i	$-0.874550\pi$
$577$		−	18.4475i		−	0.767981i	0.923337	−	0.383991i	$-0.125450\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−2.81445	+	4.87477i	−0.116763	+	0.202240i
$582$		0			0
$583$	17.5784	−	10.1489i	0.728021	−	0.420323i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	37.2316	−	21.4957i	1.53671	−	0.887222i	0.537685	−	0.843146i	$-0.319299\pi$
$587$	37.2316	−	21.4957i	1.53671	−	0.887222i	0.999028	−	0.0440760i	$-0.0140344\pi$
$588$		0			0
$589$	−21.1244	+	36.5885i	−0.870414	+	1.50760i
$590$		0			0
$591$		0			0
$592$		0			0
$593$		−	12.8614i		−	0.528153i	−0.964502	−	0.264076i	$-0.914933\pi$
$593$		−	12.8614i		−	0.528153i	0.964502	−	0.264076i	$-0.0850671\pi$
$594$		0			0
$595$	0.138429	+	0.239765i	0.00567502	+	0.00982942i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−28.3170			−1.15700			−0.578500	−	0.815682i	$-0.696362\pi$
$599$	−28.3170			−1.15700			−0.578500	+	0.815682i	$0.696362\pi$
$600$		0			0
$601$	3.56734	+	6.17882i	0.145515	+	0.252039i	0.929565	−	0.368658i	$-0.120183\pi$
$601$	3.56734	+	6.17882i	0.145515	+	0.252039i	−0.784050	+	0.620698i	$0.786849\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	6.92820	+	4.00000i	0.281672	+	0.162623i
$606$		0			0
$607$	11.0901	−	19.2086i	0.450133	−	0.779653i	−0.548261	−	0.836307i	$-0.684710\pi$
$607$	11.0901	−	19.2086i	0.450133	−	0.779653i	0.998394	+	0.0566544i	$0.0180433\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	12.3043	+	2.14598i	0.497777	+	0.0868171i
$612$		0			0
$613$	−0.279399	+	0.161311i	−0.0112848	+	0.00651530i	−0.505632	−	0.862749i	$-0.668741\pi$
$613$	−0.279399	+	0.161311i	−0.0112848	+	0.00651530i	0.494347	+	0.869265i	$0.335407\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	32.2150	+	18.5993i	1.29693	+	0.748781i	0.979872	−	0.199626i	$-0.0639728\pi$
$617$	32.2150	+	18.5993i	1.29693	+	0.748781i	0.317055	+	0.948407i	$0.397306\pi$
$618$		0			0
$619$			3.94911i			0.158728i	0.996846	+	0.0793641i	$0.0252890\pi$
$619$			3.94911i			0.158728i	−0.996846	+	0.0793641i	$0.974711\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−0.138767			−0.00555959
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$		0			0
$628$		0			0
$629$			1.56825i			0.0625304i
$630$		0			0
$631$	29.0824	+	16.7908i	1.15775	+	0.668429i	0.950765	−	0.309914i	$-0.100300\pi$
$631$	29.0824	+	16.7908i	1.15775	+	0.668429i	0.206989	+	0.978343i	$0.433634\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	10.5279	−	6.07829i	0.417787	−	0.241210i
$636$		0			0
$637$	23.1595	−	8.47818i	0.917612	−	0.335918i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−16.5900	+	28.7347i	−0.655266	+	1.13495i	0.326561	+	0.945176i	$0.394110\pi$
$641$	−16.5900	+	28.7347i	−0.655266	+	1.13495i	−0.981827	+	0.189778i	$0.939223\pi$
$642$		0			0
$643$	27.1643	+	15.6833i	1.07125	+	0.618489i	0.928524	−	0.371273i	$-0.121078\pi$
$643$	27.1643	+	15.6833i	1.07125	+	0.618489i	0.142730	+	0.989762i	$0.454412\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−9.79529	−	16.9659i	−0.385092	−	0.667000i	0.606690	−	0.794939i	$-0.292497\pi$
$647$	−9.79529	−	16.9659i	−0.385092	−	0.667000i	−0.991782	+	0.127939i	$0.959164\pi$
$648$		0			0
$649$	−12.6012			−0.494639
$650$		0			0
$651$		0			0
$652$		0			0
$653$	3.55626	+	6.15962i	0.139167	+	0.241044i	0.927182	−	0.374612i	$-0.122224\pi$
$653$	3.55626	+	6.15962i	0.139167	+	0.241044i	−0.788015	+	0.615657i	$0.788891\pi$
$654$		0			0
$655$		−	2.11773i		−	0.0827466i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	9.29211	−	16.0944i	0.361969	−	0.626949i	−0.626316	−	0.779570i	$-0.715438\pi$
$659$	9.29211	−	16.0944i	0.361969	−	0.626949i	0.988285	+	0.152621i	$0.0487712\pi$
$660$		0			0
$661$	14.5413	−	8.39540i	0.565590	−	0.326543i	−0.189796	−	0.981823i	$-0.560783\pi$
$661$	14.5413	−	8.39540i	0.565590	−	0.326543i	0.755386	+	0.655280i	$0.227449\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−1.85994	+	1.07384i	−0.0721254	+	0.0416416i
$666$		0			0
$667$	0.262648	−	0.454919i	0.0101698	−	0.0176146i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		−	15.0502i		−	0.581005i
$672$		0			0
$673$	11.2957	+	19.5647i	0.435417	+	0.754165i	0.997330	−	0.0730322i	$-0.0232676\pi$
$673$	11.2957	+	19.5647i	0.435417	+	0.754165i	−0.561912	+	0.827197i	$0.689934\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−5.31616			−0.204317			−0.102158	−	0.994768i	$-0.532575\pi$
$677$	−5.31616			−0.204317			−0.102158	+	0.994768i	$0.532575\pi$
$678$		0			0
$679$	−1.76914	−	3.06424i	−0.0678935	−	0.117595i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−3.42419	−	1.97695i	−0.131023	−	0.0756461i	0.433056	−	0.901367i	$-0.357435\pi$
$683$	−3.42419	−	1.97695i	−0.131023	−	0.0756461i	−0.564079	+	0.825721i	$0.690769\pi$
$684$		0			0
$685$	−9.01652	+	15.6171i	−0.344504	+	0.596698i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	7.25976	−	41.6248i	0.276575	−	1.58578i
$690$		0			0
$691$	−11.1493	+	6.43704i	−0.424139	+	0.244877i	−0.696846	−	0.717220i	$-0.745414\pi$
$691$	−11.1493	+	6.43704i	−0.424139	+	0.244877i	0.272708	+	0.962097i	$0.412081\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−8.52183	−	4.92008i	−0.323251	−	0.186629i
$696$		0			0
$697$		−	5.35430i		−	0.202809i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−34.9777			−1.32109			−0.660544	−	0.750787i	$-0.729674\pi$
$701$	−34.9777			−1.32109			−0.660544	+	0.750787i	$0.729674\pi$
$702$		0			0
$703$	−12.1655			−0.458830
$704$		0			0
$705$		0			0
$706$		0			0
$707$		−	1.64074i		−	0.0617065i
$708$		0			0
$709$	−17.1183	−	9.88325i	−0.642891	−	0.371173i	0.142836	−	0.989746i	$-0.454378\pi$
$709$	−17.1183	−	9.88325i	−0.642891	−	0.371173i	−0.785727	+	0.618573i	$0.787711\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	0.729664	−	0.421272i	0.0273261	−	0.0157767i
$714$		0			0
$715$	−5.86440	+	2.14683i	−0.219316	+	0.0802868i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	22.1234	−	38.3188i	0.825062	−	1.42905i	−0.0768099	−	0.997046i	$-0.524473\pi$
$719$	22.1234	−	38.3188i	0.825062	−	1.42905i	0.901872	−	0.432004i	$-0.142193\pi$
$720$		0			0
$721$	−3.88914	−	2.24539i	−0.144839	−	0.0836228i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	2.45174	+	4.24653i	0.0910553	+	0.157712i
$726$		0			0
$727$	−31.4877			−1.16781			−0.583907	−	0.811821i	$-0.698477\pi$
$727$	−31.4877			−1.16781			−0.583907	+	0.811821i	$0.698477\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	2.08112	+	3.60460i	0.0769728	+	0.133321i
$732$		0			0
$733$			42.4714i			1.56872i	0.620307	+	0.784359i	$0.287008\pi$
$733$			42.4714i			1.56872i	−0.620307	+	0.784359i	$0.712992\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	1.15009	−	1.99201i	0.0423640	−	0.0733767i
$738$		0			0
$739$	−11.9368	+	6.89173i	−0.439103	+	0.253516i	−0.703217	−	0.710975i	$-0.748254\pi$
$739$	−11.9368	+	6.89173i	−0.439103	+	0.253516i	0.264114	+	0.964492i	$0.414921\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	13.8038	−	7.96961i	0.506411	−	0.292377i	−0.224946	−	0.974371i	$-0.572221\pi$
$743$	13.8038	−	7.96961i	0.506411	−	0.292377i	0.731357	+	0.681995i	$0.238887\pi$
$744$		0			0
$745$	4.44149	−	7.69289i	0.162724	−	0.281846i
$746$		0			0
$747$		0			0
$748$		0			0
$749$		−	7.03787i		−	0.257158i
$750$		0			0
$751$	−0.758540	−	1.31383i	−0.0276795	−	0.0479423i	0.851854	−	0.523780i	$-0.175478\pi$
$751$	−0.758540	−	1.31383i	−0.0276795	−	0.0479423i	−0.879533	+	0.475837i	$0.842145\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−4.43937			−0.161565
$756$		0			0
$757$	−23.7414	−	41.1214i	−0.862897	−	1.49458i	−0.869120	−	0.494601i	$-0.835314\pi$
$757$	−23.7414	−	41.1214i	−0.862897	−	1.49458i	0.00622310	−	0.999981i	$-0.498019\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	33.3805	+	19.2722i	1.21004	+	0.698618i	0.962768	−	0.270327i	$-0.0871320\pi$
$761$	33.3805	+	19.2722i	1.21004	+	0.698618i	0.247274	+	0.968946i	$0.420465\pi$
$762$		0			0
$763$	−3.03512	+	5.25697i	−0.109879	+	0.190315i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−16.8238	+	20.1258i	−0.607473	+	0.726700i
$768$		0			0
$769$	34.5236	−	19.9322i	1.24495	−	0.718775i	0.274856	−	0.961486i	$-0.411370\pi$
$769$	34.5236	−	19.9322i	1.24495	−	0.718775i	0.970099	+	0.242711i	$0.0780366\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−28.5396	−	16.4774i	−1.02650	−	0.592650i	−0.110519	−	0.993874i	$-0.535251\pi$
$773$	−28.5396	−	16.4774i	−1.02650	−	0.592650i	−0.915980	+	0.401224i	$0.868585\pi$
$774$		0			0
$775$			7.86488i			0.282515i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	41.5352			1.48815
$780$		0			0
$781$	−6.71695			−0.240351
$782$		0			0
$783$		0			0
$784$		0			0
$785$			4.16719i			0.148733i
$786$		0			0
$787$	−0.934698	−	0.539648i	−0.0333184	−	0.0192364i	0.483248	−	0.875483i	$-0.339457\pi$
$787$	−0.934698	−	0.539648i	−0.0333184	−	0.0192364i	−0.516567	+	0.856247i	$0.672790\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	3.08162	−	1.77917i	0.109570	−	0.0632601i
$792$		0			0
$793$	−24.0372	−	20.0935i	−0.853584	−	0.713541i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	9.55071	−	16.5423i	0.338304	−	0.585959i	−0.645810	−	0.763498i	$-0.723480\pi$
$797$	9.55071	−	16.5423i	0.338304	−	0.585959i	0.984114	+	0.177539i	$0.0568136\pi$
$798$		0			0
$799$	2.07744	+	1.19941i	0.0734947	+	0.0424322i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	8.85521	+	15.3377i	0.312494	+	0.541255i
$804$		0			0
$805$	0.0428299			0.00150956
$806$		0			0
$807$		0			0
$808$		0			0
$809$	0.881702	+	1.52715i	0.0309990	+	0.0536918i	0.881109	−	0.472914i	$-0.156798\pi$
$809$	0.881702	+	1.52715i	0.0309990	+	0.0536918i	−0.850110	+	0.526606i	$0.823464\pi$
$810$		0			0
$811$			52.3298i			1.83755i	0.394784	+	0.918774i	$0.370819\pi$
$811$			52.3298i			1.83755i	−0.394784	+	0.918774i	$0.629181\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	1.84836	−	3.20145i	0.0647452	−	0.112142i
$816$		0			0
$817$	−27.9621	+	16.1439i	−0.978270	+	0.564804i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	12.3585	−	7.13517i	0.431314	−	0.249019i	−0.268592	−	0.963254i	$-0.586558\pi$
$821$	12.3585	−	7.13517i	0.431314	−	0.249019i	0.699906	+	0.714235i	$0.253225\pi$
$822$		0			0
$823$	21.8573	−	37.8579i	0.761896	−	1.31964i	−0.179976	−	0.983671i	$-0.557602\pi$
$823$	21.8573	−	37.8579i	0.761896	−	1.31964i	0.941872	−	0.335972i	$-0.109065\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	22.5962i		−	0.785748i	−0.919592	−	0.392874i	$-0.871481\pi$
$827$		−	22.5962i		−	0.785748i	0.919592	−	0.392874i	$-0.128519\pi$
$828$		0			0
$829$	27.0473	+	46.8473i	0.939392	+	1.62708i	0.766608	+	0.642116i	$0.221943\pi$
$829$	27.0473	+	46.8473i	0.939392	+	1.62708i	0.172784	+	0.984960i	$0.444724\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	4.73668			0.164116
$834$		0			0
$835$	−10.7486	−	18.6171i	−0.371970	−	0.644271i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−19.2550	−	11.1169i	−0.664755	−	0.383796i	0.129332	−	0.991601i	$-0.458717\pi$
$839$	−19.2550	−	11.1169i	−0.664755	−	0.383796i	−0.794086	+	0.607805i	$0.792050\pi$
$840$		0			0
$841$	2.47796	−	4.29196i	0.0854471	−	0.147999i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−4.40078	+	12.2325i	−0.151392	+	0.420809i
$846$		0			0
$847$	−2.76993	+	1.59922i	−0.0951758	+	0.0549498i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	0.210106	+	0.121305i	0.00720235	+	0.00415828i
$852$		0			0
$853$			16.5312i			0.566019i	0.959117	+	0.283009i	$0.0913328\pi$
$853$			16.5312i			0.566019i	−0.959117	+	0.283009i	$0.908667\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−27.5842			−0.942259			−0.471129	−	0.882064i	$-0.656154\pi$
$857$	−27.5842			−0.942259			−0.471129	+	0.882064i	$0.656154\pi$
$858$		0			0
$859$	−32.5016			−1.10894			−0.554469	−	0.832204i	$-0.687079\pi$
$859$	−32.5016			−1.10894			−0.554469	+	0.832204i	$0.687079\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	29.7986i		−	1.01436i	−0.861842	−	0.507178i	$-0.830689\pi$
$863$		−	29.7986i		−	1.01436i	0.861842	−	0.507178i	$-0.169311\pi$
$864$		0			0
$865$	−10.0561	−	5.80589i	−0.341917	−	0.197406i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	19.7300	−	11.3911i	0.669294	−	0.386417i
$870$		0			0
$871$	−1.64603	−	4.49638i	−0.0557735	−	0.152354i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−0.199902	+	0.346241i	−0.00675793	+	0.0117051i
$876$		0			0
$877$	−12.4739	−	7.20181i	−0.421214	−	0.243188i	0.274383	−	0.961621i	$-0.411526\pi$
$877$	−12.4739	−	7.20181i	−0.421214	−	0.243188i	−0.695597	+	0.718433i	$0.744860\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	3.68457	+	6.38186i	0.124136	+	0.215010i	0.921395	−	0.388627i	$-0.127051\pi$
$881$	3.68457	+	6.38186i	0.124136	+	0.215010i	−0.797259	+	0.603638i	$0.793717\pi$
$882$		0			0
$883$	24.3646			0.819933			0.409967	−	0.912101i	$-0.365540\pi$
$883$	24.3646			0.819933			0.409967	+	0.912101i	$0.365540\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−12.0322	−	20.8404i	−0.404002	−	0.699752i	0.590203	−	0.807255i	$-0.299048\pi$
$887$	−12.0322	−	20.8404i	−0.404002	−	0.699752i	−0.994205	+	0.107503i	$0.965714\pi$
$888$		0			0
$889$			4.86025i			0.163008i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−9.30426	+	16.1154i	−0.311355	+	0.539283i
$894$		0			0
$895$	4.30442	−	2.48516i	0.143881	−	0.0830697i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−33.3985	+	19.2826i	−1.11390	+	0.643112i
$900$		0			0
$901$	4.05756	−	7.02790i	0.135177	−	0.234133i
$902$		0			0
$903$		0			0
$904$		0			0
$905$			17.3695i			0.577383i
$906$		0			0
$907$	18.7536	+	32.4823i	0.622705	+	1.07856i	0.988980	+	0.148050i	$0.0472995\pi$
$907$	18.7536	+	32.4823i	0.622705	+	1.07856i	−0.366275	+	0.930507i	$0.619367\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−12.6000			−0.417458			−0.208729	−	0.977974i	$-0.566933\pi$
$911$	−12.6000			−0.417458			−0.208729	+	0.977974i	$0.566933\pi$
$912$		0			0
$913$	−12.1929	−	21.1187i	−0.403526	−	0.698927i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	0.733244	+	0.423339i	0.0242139	+	0.0139799i
$918$		0			0
$919$	15.8332	−	27.4239i	0.522288	−	0.904630i	−0.477375	−	0.878699i	$-0.658412\pi$
$919$	15.8332	−	27.4239i	0.522288	−	0.904630i	0.999664	−	0.0259305i	$-0.00825486\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−8.96780	+	10.7279i	−0.295179	+	0.353112i
$924$		0			0
$925$	−1.96128	+	1.13234i	−0.0644864	+	0.0372313i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−25.7537	−	14.8689i	−0.844952	−	0.487833i	0.0139925	−	0.999902i	$-0.495546\pi$
$929$	−25.7537	−	14.8689i	−0.844952	−	0.487833i	−0.858944	+	0.512069i	$0.828879\pi$
$930$		0			0
$931$			36.7441i			1.20424i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−1.19941			−0.0392250
$936$		0			0
$937$	−52.3124			−1.70897			−0.854486	−	0.519474i	$-0.826128\pi$
$937$	−52.3124			−1.70897			−0.854486	+	0.519474i	$0.826128\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		−	29.5767i		−	0.964174i	−0.876123	−	0.482087i	$-0.839879\pi$
$941$		−	29.5767i		−	0.964174i	0.876123	−	0.482087i	$-0.160121\pi$
$942$		0			0
$943$	−0.717340	−	0.414157i	−0.0233598	−	0.0134868i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−41.5978	+	24.0165i	−1.35175	+	0.780432i	−0.988494	−	0.151258i	$-0.951668\pi$
$947$	−41.5978	+	24.0165i	−1.35175	+	0.780432i	−0.363254	+	0.931690i	$0.618334\pi$
$948$		0			0
$949$	36.3189	+	6.33437i	1.17896	+	0.205622i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−14.8912	+	25.7923i	−0.482373	+	0.835494i	−0.999795	−	0.0202363i	$-0.993558\pi$
$953$	−14.8912	+	25.7923i	−0.482373	+	0.835494i	0.517423	+	0.855730i	$0.326891\pi$
$954$		0			0
$955$	17.7575	+	10.2523i	0.574621	+	0.331757i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−3.60485	−	6.24378i	−0.116407	−	0.201622i
$960$		0			0
$961$	−30.8564			−0.995368
$962$		0			0
$963$		0			0
$964$		0			0
$965$	13.3038	+	23.0428i	0.428263	+	0.741774i
$966$		0			0
$967$			20.6730i			0.664798i	0.943139	+	0.332399i	$0.107858\pi$
$967$			20.6730i			0.664798i	−0.943139	+	0.332399i	$0.892142\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−9.99307	+	17.3085i	−0.320693	+	0.555456i	−0.980631	−	0.195863i	$-0.937249\pi$
$971$	−9.99307	+	17.3085i	−0.320693	+	0.555456i	0.659938	+	0.751320i	$0.270582\pi$
$972$		0			0
$973$	3.40706	−	1.96707i	0.109225	−	0.0630613i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	39.5147	−	22.8138i	1.26419	−	0.729878i	0.290305	−	0.956934i	$-0.406243\pi$
$977$	39.5147	−	22.8138i	1.26419	−	0.729878i	0.973882	+	0.227056i	$0.0729101\pi$
$978$		0			0
$979$	0.300587	−	0.520632i	0.00960680	−	0.0166395i
$980$		0			0
$981$		0			0
$982$		0			0
$983$			54.1966i			1.72860i	0.502975	+	0.864301i	$0.332239\pi$
$983$			54.1966i			1.72860i	−0.502975	+	0.864301i	$0.667761\pi$
$984$		0			0
$985$	0.204141	+	0.353583i	0.00650448	+	0.0112661i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	0.643899			0.0204748
$990$		0			0
$991$	−23.2639	−	40.2943i	−0.739002	−	1.27999i	−0.952945	−	0.303143i	$-0.901964\pi$
$991$	−23.2639	−	40.2943i	−0.739002	−	1.27999i	0.213943	−	0.976846i	$-0.431369\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−21.1307	−	12.1998i	−0.669889	−	0.386760i
$996$		0			0
$997$	19.5514	−	33.8641i	0.619200	−	1.07249i	−0.370432	−	0.928860i	$-0.620790\pi$
$997$	19.5514	−	33.8641i	0.619200	−	1.07249i	0.989632	−	0.143626i	$-0.0458763\pi$
$998$		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.361.1		8
3.2	odd	2		260.2.x.a.101.4	✓	8
12.11	even	2		1040.2.da.c.881.1		8
13.4	even	6	inner	2340.2.dj.d.901.3		8
15.2	even	4		1300.2.ba.c.49.3		8
15.8	even	4		1300.2.ba.b.49.2		8
15.14	odd	2		1300.2.y.b.101.1		8
39.2	even	12		3380.2.a.q.1.1		4
39.11	even	12		3380.2.a.p.1.1		4
39.17	odd	6		260.2.x.a.121.4	yes	8
39.23	odd	6		3380.2.f.i.3041.1		8
39.29	odd	6		3380.2.f.i.3041.2		8
156.95	even	6		1040.2.da.c.641.1		8
195.17	even	12		1300.2.ba.b.849.2		8
195.134	odd	6		1300.2.y.b.901.1		8
195.173	even	12		1300.2.ba.c.849.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.x.a.101.4	✓	8	3.2	odd	2
260.2.x.a.121.4	yes	8	39.17	odd	6
1040.2.da.c.641.1		8	156.95	even	6
1040.2.da.c.881.1		8	12.11	even	2
1300.2.y.b.101.1		8	15.14	odd	2
1300.2.y.b.901.1		8	195.134	odd	6
1300.2.ba.b.49.2		8	15.8	even	4
1300.2.ba.b.849.2		8	195.17	even	12
1300.2.ba.c.49.3		8	15.2	even	4
1300.2.ba.c.849.3		8	195.173	even	12
2340.2.dj.d.361.1		8	1.1	even	1	trivial
2340.2.dj.d.901.3		8	13.4	even	6	inner
3380.2.a.p.1.1		4	39.11	even	12
3380.2.a.q.1.1		4	39.2	even	12
3380.2.f.i.3041.1		8	39.23	odd	6
3380.2.f.i.3041.2		8	39.29	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)

\(f(q)\)	\(=\)	\(q-1.00000i q^{5} +(0.346241 + 0.199902i) q^{7} +O(q^{10})\)	\(q-1.00000i q^{5} +(0.346241 + 0.199902i) q^{7} +(-1.50000 + 0.866025i) q^{11} +(-0.619491 + 3.55193i) q^{13} +(-0.346241 + 0.599706i) q^{17} +(-4.65213 - 2.68591i) q^{19} +(0.0535636 + 0.0927749i) q^{23} -1.00000 q^{25} +(-2.45174 - 4.24653i) q^{29} -7.86488i q^{31} +(0.199902 - 0.346241i) q^{35} +(1.96128 - 1.13234i) q^{37} +(-6.69615 + 3.86603i) q^{41} +(3.00530 - 5.20533i) q^{43} -3.46410i q^{47} +(-3.42008 - 5.92375i) q^{49} -11.7189 q^{53} +(0.866025 + 1.50000i) q^{55} +(6.30059 + 3.63765i) q^{59} +(-4.34461 + 7.52509i) q^{61} +(3.55193 + 0.619491i) q^{65} +(-1.15009 + 0.664004i) q^{67} +(3.35847 + 1.93902i) q^{71} -10.2251i q^{73} -0.692481 q^{77} -13.1533 q^{79} +14.0791i q^{83} +(0.599706 + 0.346241i) q^{85} +(-0.300587 + 0.173544i) q^{89} +(-0.924532 + 1.10599i) q^{91} +(-2.68591 + 4.65213i) q^{95} +(-7.66436 - 4.42502i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{7}+O(q^{10}) \) 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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