LMFDB - Embedded newform 378.3.s.d.107.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,3,Mod(53,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("378.53");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	378.s (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:	$10.2997539928$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.621801639936.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} - 34x^{6} + 116x^{5} + 413x^{4} - 1024x^{3} - 1664x^{2} + 2196x + 4467 $ x^8 - 4x^7 - 34x^6 + 116x^5 + 413x^4 - 1024x^3 - 1664x^2 + 2196*x + 4467
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			107.1
Root			$4.76613 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	378.107
Dual form			378.3.s.d.53.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22474 - 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +(-4.33729 - 2.50413i) q^{5} +(0.0413813 + 6.99988i) q^{7} -2.82843i q^{8} +O(q^{10})$	\(q+(-1.22474 - 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +(-4.33729 - 2.50413i) q^{5} +(0.0413813 + 6.99988i) q^{7} -2.82843i q^{8} +(3.54138 + 6.13385i) q^{10} +(1.32611 - 0.765629i) q^{11} +0.917237 q^{13} +(4.89898 - 8.60233i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(14.3380 - 8.27803i) q^{17} +(6.50000 - 11.2583i) q^{19} -10.0165i q^{20} -2.16553 q^{22} +(-10.3596 - 5.98115i) q^{23} +(0.0413813 + 0.0716745i) q^{25} +(-1.12338 - 0.648585i) q^{26} +(-12.0828 + 7.07155i) q^{28} -33.5266i q^{29} +(8.66553 + 15.0091i) q^{31} +(4.89898 - 2.82843i) q^{32} -23.4138 q^{34} +(17.3492 - 30.4641i) q^{35} +(27.8724 - 48.2765i) q^{37} +(-15.9217 + 9.19239i) q^{38} +(-7.08276 + 12.2677i) q^{40} -6.53953i q^{41} +32.7449 q^{43} +(2.65222 + 1.53126i) q^{44} +(8.45862 + 14.6508i) q^{46} +(-46.3841 - 26.7799i) q^{47} +(-48.9966 + 0.579328i) q^{49} -0.117044i q^{50} +(0.917237 + 1.58870i) q^{52} +(72.4078 - 41.8047i) q^{53} -7.66895 q^{55} +(19.7986 - 0.117044i) q^{56} +(-23.7069 + 41.0616i) q^{58} +(-41.4386 + 23.9246i) q^{59} +(40.2897 - 69.7838i) q^{61} -24.5098i q^{62} -8.00000 q^{64} +(-3.97832 - 2.29689i) q^{65} +(1.21033 + 2.09636i) q^{67} +(28.6759 + 16.5561i) q^{68} +(-42.7897 + 25.0431i) q^{70} -83.3216i q^{71} +(-36.0414 - 62.4255i) q^{73} +(-68.2732 + 39.4176i) q^{74} +26.0000 q^{76} +(5.41418 + 9.25091i) q^{77} +(61.1655 - 105.942i) q^{79} +(17.3492 - 10.0165i) q^{80} +(-4.62414 + 8.00925i) q^{82} +158.860i q^{83} -82.9172 q^{85} +(-40.1041 - 23.1541i) q^{86} +(-2.16553 - 3.75080i) q^{88} +(46.9922 + 27.1310i) q^{89} +(0.0379564 + 6.42055i) q^{91} -23.9246i q^{92} +(37.8724 + 65.5970i) q^{94} +(-56.3848 + 32.5538i) q^{95} +12.0828 q^{97} +(60.4180 + 33.9363i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{4} - 24 q^{7}+O(q^{10}) $ 8 * q + 8 * q^4 - 24 * q^7	$ 8 q + 8 q^{4} - 24 q^{7} + 4 q^{10} + 56 q^{13} - 16 q^{16} + 52 q^{19} + 80 q^{22} - 24 q^{25} - 48 q^{28} - 28 q^{31} + 56 q^{34} + 4 q^{37} - 8 q^{40} - 176 q^{43} + 92 q^{46} - 100 q^{49} + 56 q^{52} - 256 q^{55} - 68 q^{58} + 152 q^{61} - 64 q^{64} + 180 q^{67} - 172 q^{70} - 264 q^{73} + 208 q^{76} + 392 q^{79} + 36 q^{82} - 712 q^{85} + 80 q^{88} - 316 q^{91} + 84 q^{94} + 48 q^{97}+O(q^{100}) $ 8 * q + 8 * q^4 - 24 * q^7 + 4 * q^10 + 56 * q^13 - 16 * q^16 + 52 * q^19 + 80 * q^22 - 24 * q^25 - 48 * q^28 - 28 * q^31 + 56 * q^34 + 4 * q^37 - 8 * q^40 - 176 * q^43 + 92 * q^46 - 100 * q^49 + 56 * q^52 - 256 * q^55 - 68 * q^58 + 152 * q^61 - 64 * q^64 + 180 * q^67 - 172 * q^70 - 264 * q^73 + 208 * q^76 + 392 * q^79 + 36 * q^82 - 712 * q^85 + 80 * q^88 - 316 * q^91 + 84 * q^94 + 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−1.22474	−	0.707107i	−0.612372	−	0.353553i
$2$	−1.22474	−	0.707107i	−0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	1.00000	+	1.73205i	0.250000	+	0.433013i
$5$	−4.33729	−	2.50413i	−0.867458	−	0.500827i	−0.000955133	−	1.00000i	$-0.500304\pi$
$5$	−4.33729	−	2.50413i	−0.867458	−	0.500827i	−0.866503	+	0.499173i	$0.833637\pi$
$6$		0			0
$7$	0.0413813	+	6.99988i	0.00591161	+	0.999983i
$7$	0.0413813	+	6.99988i	0.00591161	+	0.999983i
$8$		−	2.82843i		−	0.353553i
$9$		0			0
$10$	3.54138	+	6.13385i	0.354138	+	0.613385i
$11$	1.32611	−	0.765629i	0.120555	−	0.0696026i	−0.438510	−	0.898726i	$-0.644494\pi$
$11$	1.32611	−	0.765629i	0.120555	−	0.0696026i	0.559065	+	0.829124i	$0.311160\pi$
$12$		0			0
$13$	0.917237			0.0705567			0.0352784	−	0.999378i	$-0.488768\pi$
$13$	0.917237			0.0705567			0.0352784	+	0.999378i	$0.488768\pi$
$14$	4.89898	−	8.60233i	0.349927	−	0.614452i
$15$		0			0
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$	14.3380	−	8.27803i	0.843410	−	0.486943i	−0.0150117	−	0.999887i	$-0.504779\pi$
$17$	14.3380	−	8.27803i	0.843410	−	0.486943i	0.858422	+	0.512944i	$0.171445\pi$
$18$		0			0
$19$	6.50000	−	11.2583i	0.342105	−	0.592544i	−0.642718	−	0.766103i	$-0.722193\pi$
$19$	6.50000	−	11.2583i	0.342105	−	0.592544i	0.984823	+	0.173559i	$0.0555267\pi$
$20$		−	10.0165i		−	0.500827i
$21$		0			0
$22$	−2.16553			−0.0984330
$23$	−10.3596	−	5.98115i	−0.450420	−	0.260050i	0.257588	−	0.966255i	$-0.417072\pi$
$23$	−10.3596	−	5.98115i	−0.450420	−	0.260050i	−0.708007	+	0.706205i	$0.750406\pi$
$24$		0			0
$25$	0.0413813	+	0.0716745i	0.00165525	+	0.00286698i
$26$	−1.12338	−	0.648585i	−0.0432070	−	0.0249456i
$27$		0			0
$28$	−12.0828	+	7.07155i	−0.431527	+	0.252555i
$29$		−	33.5266i		−	1.15609i	−0.816005	−	0.578045i	$-0.803816\pi$
$29$		−	33.5266i		−	1.15609i	0.816005	−	0.578045i	$-0.196184\pi$
$30$		0			0
$31$	8.66553	+	15.0091i	0.279533	+	0.484165i	0.971269	−	0.237985i	$-0.0764870\pi$
$31$	8.66553	+	15.0091i	0.279533	+	0.484165i	−0.691736	+	0.722151i	$0.743154\pi$
$32$	4.89898	−	2.82843i	0.153093	−	0.0883883i
$33$		0			0
$34$	−23.4138			−0.688642
$35$	17.3492	−	30.4641i	0.495690	−	0.870403i
$36$		0			0
$37$	27.8724	−	48.2765i	0.753309	−	1.30477i	−0.192902	−	0.981218i	$-0.561790\pi$
$37$	27.8724	−	48.2765i	0.753309	−	1.30477i	0.946211	−	0.323551i	$-0.104877\pi$
$38$	−15.9217	+	9.19239i	−0.418992	+	0.241905i
$39$		0			0
$40$	−7.08276	+	12.2677i	−0.177069	+	0.306693i
$41$		−	6.53953i		−	0.159501i	−0.996815	−	0.0797503i	$-0.974588\pi$
$41$		−	6.53953i		−	0.159501i	0.996815	−	0.0797503i	$-0.0254123\pi$
$42$		0			0
$43$	32.7449			0.761508			0.380754	−	0.924676i	$-0.375664\pi$
$43$	32.7449			0.761508			0.380754	+	0.924676i	$0.375664\pi$
$44$	2.65222	+	1.53126i	0.0602776	+	0.0348013i
$45$		0			0
$46$	8.45862	+	14.6508i	0.183883	+	0.318495i
$47$	−46.3841	−	26.7799i	−0.986895	−	0.569784i	−0.0825503	−	0.996587i	$-0.526307\pi$
$47$	−46.3841	−	26.7799i	−0.986895	−	0.569784i	−0.904345	+	0.426803i	$0.859640\pi$
$48$		0			0
$49$	−48.9966	+	0.579328i	−0.999930	+	0.0118230i
$50$		−	0.117044i		−	0.00234088i
$51$		0			0
$52$	0.917237	+	1.58870i	0.0176392	+	0.0305520i
$53$	72.4078	−	41.8047i	1.36618	−	0.788767i	0.375746	−	0.926723i	$-0.377386\pi$
$53$	72.4078	−	41.8047i	1.36618	−	0.788767i	0.990438	+	0.137955i	$0.0440530\pi$
$54$		0			0
$55$	−7.66895			−0.139435
$56$	19.7986	−	0.117044i	0.353547	−	0.00209007i
$57$		0			0
$58$	−23.7069	+	41.0616i	−0.408740	+	0.707958i
$59$	−41.4386	+	23.9246i	−0.702349	+	0.405501i	−0.808222	−	0.588878i	$-0.799570\pi$
$59$	−41.4386	+	23.9246i	−0.702349	+	0.405501i	0.105873	+	0.994380i	$0.466236\pi$
$60$		0			0
$61$	40.2897	−	69.7838i	0.660486	−	1.14400i	−0.320002	−	0.947417i	$-0.603683\pi$
$61$	40.2897	−	69.7838i	0.660486	−	1.14400i	0.980488	−	0.196579i	$-0.0629832\pi$
$62$		−	24.5098i		−	0.395319i
$63$		0			0
$64$	−8.00000			−0.125000
$65$	−3.97832	−	2.29689i	−0.0612050	−	0.0353367i
$66$		0			0
$67$	1.21033	+	2.09636i	0.0180646	+	0.0312889i	0.874916	−	0.484274i	$-0.160916\pi$
$67$	1.21033	+	2.09636i	0.0180646	+	0.0312889i	−0.856852	+	0.515563i	$0.827583\pi$
$68$	28.6759	+	16.5561i	0.421705	+	0.243472i
$69$		0			0
$70$	−42.7897	+	25.0431i	−0.611281	+	0.357758i
$71$		−	83.3216i		−	1.17354i	−0.809753	−	0.586772i	$-0.800399\pi$
$71$		−	83.3216i		−	1.17354i	0.809753	−	0.586772i	$-0.199601\pi$
$72$		0			0
$73$	−36.0414	−	62.4255i	−0.493718	−	0.855144i	0.506256	−	0.862383i	$-0.331029\pi$
$73$	−36.0414	−	62.4255i	−0.493718	−	0.855144i	−0.999974	+	0.00723922i	$0.997696\pi$
$74$	−68.2732	+	39.4176i	−0.922611	+	0.532670i
$75$		0			0
$76$	26.0000			0.342105
$77$	5.41418	+	9.25091i	0.0703141	+	0.120142i
$78$		0			0
$79$	61.1655	−	105.942i	0.774247	−	1.34104i	−0.160969	−	0.986959i	$-0.551462\pi$
$79$	61.1655	−	105.942i	0.774247	−	1.34104i	0.935217	−	0.354076i	$-0.115205\pi$
$80$	17.3492	−	10.0165i	0.216864	−	0.125207i
$81$		0			0
$82$	−4.62414	+	8.00925i	−0.0563920	+	0.0976738i
$83$			158.860i			1.91398i	0.290126	+	0.956989i	$0.406303\pi$
$83$			158.860i			1.91398i	−0.290126	+	0.956989i	$0.593697\pi$
$84$		0			0
$85$	−82.9172			−0.975497
$86$	−40.1041	−	23.1541i	−0.466327	−	0.269234i
$87$		0			0
$88$	−2.16553	−	3.75080i	−0.0246082	−	0.0426227i
$89$	46.9922	+	27.1310i	0.528003	+	0.304843i	0.740203	−	0.672384i	$-0.234729\pi$
$89$	46.9922	+	27.1310i	0.528003	+	0.304843i	−0.212200	+	0.977226i	$0.568063\pi$
$90$		0			0
$91$	0.0379564	+	6.42055i	0.000417104	+	0.0705555i
$92$		−	23.9246i		−	0.260050i
$93$		0			0
$94$	37.8724	+	65.5970i	0.402898	+	0.697840i
$95$	−56.3848	+	32.5538i	−0.593524	+	0.342671i
$96$		0			0
$97$	12.0828			0.124565			0.0622823	−	0.998059i	$-0.480162\pi$
$97$	12.0828			0.124565			0.0622823	+	0.998059i	$0.480162\pi$
$98$	60.4180	+	33.9363i	0.616510	+	0.346289i
$99$		0			0
$100$	−0.0827625	+	0.143349i	−0.000827625	+	0.00143349i
$101$	−157.468	+	90.9145i	−1.55909	+	0.900143i	−0.561750	+	0.827307i	$0.689872\pi$
$101$	−157.468	+	90.9145i	−1.55909	+	0.900143i	−0.997344	+	0.0728364i	$0.976795\pi$
$102$		0			0
$103$	57.8724	−	100.238i	0.561868	−	0.973184i	−0.435465	−	0.900206i	$-0.643416\pi$
$103$	57.8724	−	100.238i	0.561868	−	0.973184i	0.997333	−	0.0729788i	$-0.0232506\pi$
$104$		−	2.59434i		−	0.0249456i
$105$		0			0
$106$	−118.241			−1.11549
$107$	148.186	+	85.5551i	1.38491	+	0.799580i	0.992736	−	0.120310i	$-0.0383887\pi$
$107$	148.186	+	85.5551i	1.38491	+	0.799580i	0.392177	+	0.919890i	$0.371722\pi$
$108$		0			0
$109$	65.9586	+	114.244i	0.605125	+	1.04811i	0.992032	+	0.125988i	$0.0402102\pi$
$109$	65.9586	+	114.244i	0.605125	+	1.04811i	−0.386907	+	0.922119i	$0.626456\pi$
$110$	9.39251	+	5.42277i	0.0853864	+	0.0492979i
$111$		0			0
$112$	−24.3311	−	13.8564i	−0.217242	−	0.123718i
$113$			7.65629i			0.0677548i	0.999426	+	0.0338774i	$0.0107856\pi$
$113$			7.65629i			0.0677548i	−0.999426	+	0.0338774i	$0.989214\pi$
$114$		0			0
$115$	29.9552	+	51.8839i	0.260480	+	0.451165i
$116$	58.0698	−	33.5266i	0.500602	−	0.289023i
$117$		0			0
$118$	67.6689			0.573466
$119$	58.5385	+	100.022i	0.491921	+	0.840517i
$120$		0			0
$121$	−59.3276	+	102.758i	−0.490311	+	0.849243i
$122$	−98.6891	+	56.9782i	−0.808927	+	0.467034i
$123$		0			0
$124$	−17.3311	+	30.0183i	−0.139767	+	0.242083i
$125$			124.792i			0.998338i
$126$		0			0
$127$	−8.57934			−0.0675538			−0.0337769	−	0.999429i	$-0.510754\pi$
$127$	−8.57934			−0.0675538			−0.0337769	+	0.999429i	$0.510754\pi$
$128$	9.79796	+	5.65685i	0.0765466	+	0.0441942i
$129$		0			0
$130$	3.24829	+	5.62620i	0.0249868	+	0.0432785i
$131$	−60.9713	−	35.2018i	−0.465429	−	0.268716i	0.248895	−	0.968530i	$-0.419933\pi$
$131$	−60.9713	−	35.2018i	−0.465429	−	0.268716i	−0.714324	+	0.699815i	$0.753266\pi$
$132$		0			0
$133$	79.0759	+	45.0333i	0.594556	+	0.338596i
$134$		−	3.42333i		−	0.0255473i
$135$		0			0
$136$	−23.4138	−	40.5539i	−0.172160	−	0.298191i
$137$	−58.4288	+	33.7339i	−0.426488	+	0.246233i	−0.697849	−	0.716245i	$-0.745859\pi$
$137$	−58.4288	+	33.7339i	−0.426488	+	0.246233i	0.271362	+	0.962477i	$0.412526\pi$
$138$		0			0
$139$	166.572			1.19836			0.599182	−	0.800613i	$-0.295493\pi$
$139$	166.572			1.19836			0.599182	+	0.800613i	$0.295493\pi$
$140$	70.1145	−	0.414497i	0.500818	−	0.00296069i
$141$		0			0
$142$	−58.9172	+	102.048i	−0.414910	+	0.718645i
$143$	1.21636	−	0.702263i	0.00850598	−	0.00491093i
$144$		0			0
$145$	−83.9552	+	145.415i	−0.579001	+	1.00286i
$146$			101.940i			0.698222i
$147$		0			0
$148$	111.490			0.753309
$149$	196.724	+	113.578i	1.32029	+	0.762271i	0.983775	−	0.179406i	$-0.0574176\pi$
$149$	196.724	+	113.578i	1.32029	+	0.762271i	0.336517	+	0.941677i	$0.390751\pi$
$150$		0			0
$151$	137.824	+	238.719i	0.912743	+	1.58092i	0.810172	+	0.586192i	$0.199373\pi$
$151$	137.824	+	238.719i	0.912743	+	1.58092i	0.102571	+	0.994726i	$0.467293\pi$
$152$	−31.8434	−	18.3848i	−0.209496	−	0.120952i
$153$		0			0
$154$	−0.0896122	−	15.1584i	−0.000581897	−	0.0984312i
$155$		−	86.7986i		−	0.559991i
$156$		0			0
$157$	−99.6173	−	172.542i	−0.634505	−	1.09899i	−0.986620	−	0.163038i	$-0.947871\pi$
$157$	−99.6173	−	172.542i	−0.634505	−	1.09899i	0.352115	−	0.935957i	$-0.385463\pi$
$158$	−149.824	+	86.5011i	−0.948255	+	0.547475i
$159$		0			0
$160$	−28.3311			−0.177069
$161$	41.4386	−	72.7638i	0.257383	−	0.451949i
$162$		0			0
$163$	48.5000	−	84.0045i	0.297546	−	0.515365i	−0.678028	−	0.735036i	$-0.737165\pi$
$163$	48.5000	−	84.0045i	0.297546	−	0.515365i	0.975574	+	0.219671i	$0.0704985\pi$
$164$	11.3268	−	6.53953i	0.0690658	−	0.0398752i
$165$		0			0
$166$	112.331	−	194.563i	0.676693	−	1.17207i
$167$		−	21.6911i		−	0.129887i	−0.997889	−	0.0649433i	$-0.979313\pi$
$167$		−	21.6911i		−	0.129887i	0.997889	−	0.0649433i	$-0.0206867\pi$
$168$		0			0
$169$	−168.159			−0.995022
$170$	101.552	+	58.6313i	0.597367	+	0.344890i
$171$		0			0
$172$	32.7449	+	56.7158i	0.190377	+	0.329743i
$173$	−180.701	−	104.328i	−1.04451	−	0.603049i	−0.123404	−	0.992357i	$-0.539381\pi$
$173$	−180.701	−	104.328i	−1.04451	−	0.603049i	−0.921108	+	0.389307i	$0.872714\pi$
$174$		0			0
$175$	−0.500000	+	0.292630i	−0.00285714	+	0.00167217i
$176$			6.12503i			0.0348013i
$177$		0			0
$178$	−38.3690	−	66.4571i	−0.215556	−	0.373354i
$179$	−54.9489	+	31.7248i	−0.306977	+	0.177233i	−0.645573	−	0.763699i	$-0.723381\pi$
$179$	−54.9489	+	31.7248i	−0.306977	+	0.177233i	0.338596	+	0.940932i	$0.390048\pi$
$180$		0			0
$181$	−212.311			−1.17299			−0.586493	−	0.809954i	$-0.699492\pi$
$181$	−212.311			−1.17299			−0.586493	+	0.809954i	$0.699492\pi$
$182$	4.49353	−	7.89038i	0.0246897	−	0.0433537i
$183$		0			0
$184$	−16.9172	+	29.3015i	−0.0919415	+	0.159247i
$185$	−241.782	+	139.593i	−1.30693	+	0.754555i
$186$		0			0
$187$	12.6758	−	21.9551i	0.0677850	−	0.117407i
$188$		−	107.119i		−	0.569784i
$189$		0			0
$190$	92.0759			0.484610
$191$	−50.9706	−	29.4279i	−0.266862	−	0.154073i	0.360599	−	0.932721i	$-0.382572\pi$
$191$	−50.9706	−	29.4279i	−0.266862	−	0.154073i	−0.627461	+	0.778648i	$0.715906\pi$
$192$		0			0
$193$	−69.6173	−	120.581i	−0.360711	−	0.624770i	0.627367	−	0.778724i	$-0.284133\pi$
$193$	−69.6173	−	120.581i	−0.360711	−	0.624770i	−0.988078	+	0.153954i	$0.950799\pi$
$194$	−14.7983	−	8.54380i	−0.0762799	−	0.0440402i
$195$		0			0
$196$	−50.0000	−	84.2852i	−0.255102	−	0.430027i
$197$		−	317.720i		−	1.61279i	−0.591375	−	0.806396i	$-0.701415\pi$
$197$		−	317.720i		−	1.61279i	0.591375	−	0.806396i	$-0.298585\pi$
$198$		0			0
$199$	−124.869	−	216.279i	−0.627482	−	1.08683i	−0.988055	−	0.154100i	$-0.950752\pi$
$199$	−124.869	−	216.279i	−0.627482	−	1.08683i	0.360573	−	0.932731i	$-0.382581\pi$
$200$	0.202726	−	0.117044i	0.00101363	−	0.000585219i
$201$		0			0
$202$	257.145			1.27299
$203$	234.682	−	1.38737i	1.15607	−	0.00683436i
$204$		0			0
$205$	−16.3759	+	28.3638i	−0.0798822	+	0.138360i
$206$	−141.758	+	81.8440i	−0.688145	+	0.397301i
$207$		0			0
$208$	−1.83447	+	3.17740i	−0.00881959	+	0.0152760i
$209$		−	19.9063i		−	0.0952457i
$210$		0			0
$211$	−112.248			−0.531982			−0.265991	−	0.963975i	$-0.585699\pi$
$211$	−112.248			−0.531982			−0.265991	+	0.963975i	$0.585699\pi$
$212$	144.816	+	83.6093i	0.683092	+	0.394384i
$213$		0			0
$214$	−120.993	−	209.566i	−0.565389	−	0.979282i
$215$	−142.024	−	81.9975i	−0.660576	−	0.381384i
$216$		0			0
$217$	−104.703	+	61.2787i	−0.482505	+	0.282390i
$218$		−	186.559i		−	0.855776i
$219$		0			0
$220$	−7.66895	−	13.2830i	−0.0348589	−	0.0603773i
$221$	13.1513	−	7.59292i	0.0595083	−	0.0343571i
$222$		0			0
$223$	79.2346			0.355312			0.177656	−	0.984093i	$-0.443149\pi$
$223$	79.2346			0.355312			0.177656	+	0.984093i	$0.443149\pi$
$224$	20.0014	+	34.1752i	0.0892918	+	0.152568i
$225$		0			0
$226$	5.41381	−	9.37700i	0.0239549	−	0.0414911i
$227$	310.600	−	179.325i	1.36828	−	0.789977i	0.377572	−	0.925980i	$-0.376759\pi$
$227$	310.600	−	179.325i	1.36828	−	0.789977i	0.990708	+	0.136003i	$0.0434257\pi$
$228$		0			0
$229$	−61.1689	+	105.948i	−0.267113	+	0.462654i	−0.968115	−	0.250506i	$-0.919403\pi$
$229$	−61.1689	+	105.948i	−0.267113	+	0.462654i	0.701002	+	0.713159i	$0.252736\pi$
$230$		−	84.7261i		−	0.368374i
$231$		0			0
$232$	−94.8276			−0.408740
$233$	184.071	+	106.273i	0.790003	+	0.456108i	0.839964	−	0.542643i	$-0.182576\pi$
$233$	184.071	+	106.273i	0.790003	+	0.456108i	−0.0499606	+	0.998751i	$0.515910\pi$
$234$		0			0
$235$	134.121	+	232.304i	0.570726	+	0.988527i
$236$	−82.8772	−	47.8492i	−0.351175	−	0.202751i
$237$		0			0
$238$	−0.968893	−	163.894i	−0.00407098	−	0.688630i
$239$		−	342.762i		−	1.43415i	−0.696997	−	0.717074i	$-0.745481\pi$
$239$		−	342.762i		−	1.43415i	0.696997	−	0.717074i	$-0.254519\pi$
$240$		0			0
$241$	−16.3724	−	28.3579i	−0.0679354	−	0.117668i	0.830057	−	0.557679i	$-0.188308\pi$
$241$	−16.3724	−	28.3579i	−0.0679354	−	0.117668i	−0.897992	+	0.440011i	$0.854975\pi$
$242$	145.322	−	83.9019i	0.600506	−	0.346702i
$243$		0			0
$244$	161.159			0.660486
$245$	213.963	+	120.181i	0.873318	+	0.490536i
$246$		0			0
$247$	5.96204	−	10.3266i	0.0241378	−	0.0418079i
$248$	42.4522	−	24.5098i	0.171178	−	0.0988299i
$249$		0			0
$250$	88.2414	−	152.839i	0.352966	−	0.611355i
$251$			8.32425i			0.0331643i	0.999863	+	0.0165822i	$0.00527851\pi$
$251$			8.32425i			0.0331643i	−0.999863	+	0.0165822i	$0.994721\pi$
$252$		0			0
$253$	−18.3174			−0.0724006
$254$	10.5075	+	6.06651i	0.0413681	+	0.0238839i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	−13.4806	−	7.78302i	−0.0524536	−	0.0302841i	0.473544	−	0.880770i	$-0.342975\pi$
$257$	−13.4806	−	7.78302i	−0.0524536	−	0.0302841i	−0.525997	+	0.850486i	$0.676308\pi$
$258$		0			0
$259$	339.083	+	193.106i	1.30920	+	0.745583i
$260$		−	9.18754i		−	0.0353367i
$261$		0			0
$262$	49.7828	+	86.2264i	0.190011	+	0.329108i
$263$	−5.52394	+	3.18925i	−0.0210036	+	0.0121264i	−0.510465	−	0.859899i	$-0.670527\pi$
$263$	−5.52394	+	3.18925i	−0.0210036	+	0.0121264i	0.489461	+	0.872025i	$0.337193\pi$
$264$		0			0
$265$	−418.738			−1.58014
$266$	−65.0045	−	111.069i	−0.244378	−	0.417554i
$267$		0			0
$268$	−2.42066	+	4.19271i	−0.00903232	+	0.0156444i
$269$	−299.243	+	172.768i	−1.11243	+	0.642261i	−0.939457	−	0.342666i	$-0.888670\pi$
$269$	−299.243	+	172.768i	−1.11243	+	0.642261i	−0.172971	+	0.984927i	$0.555337\pi$
$270$		0			0
$271$	−109.214	+	189.164i	−0.403003	+	0.698021i	−0.994087	−	0.108589i	$-0.965367\pi$
$271$	−109.214	+	189.164i	−0.403003	+	0.698021i	0.591084	+	0.806610i	$0.298700\pi$
$272$			66.2243i			0.243472i
$273$		0			0
$274$	95.4138			0.348226
$275$	0.109752	+	0.0633654i	0.000399098	+	0.000230420i
$276$		0			0
$277$	−65.3656	−	113.217i	−0.235977	−	0.408724i	0.723579	−	0.690241i	$-0.242496\pi$
$277$	−65.3656	−	113.217i	−0.235977	−	0.408724i	−0.959556	+	0.281517i	$0.909162\pi$
$278$	−204.009	−	117.785i	−0.733845	−	0.423685i
$279$		0			0
$280$	−86.1655	−	49.0708i	−0.307734	−	0.175253i
$281$		−	430.516i		−	1.53208i	−0.642790	−	0.766042i	$-0.722223\pi$
$281$		−	430.516i		−	1.53208i	0.642790	−	0.766042i	$-0.277777\pi$
$282$		0			0
$283$	193.945	+	335.922i	0.685318	+	1.18701i	0.973337	+	0.229380i	$0.0736700\pi$
$283$	193.945	+	335.922i	0.685318	+	1.18701i	−0.288019	+	0.957625i	$0.592997\pi$
$284$	144.317	−	83.3216i	0.508159	−	0.293386i
$285$		0			0
$286$	−1.98630			−0.00694511
$287$	45.7759	−	0.270614i	0.159498	−	0.000942906i
$288$		0			0
$289$	−7.44834	+	12.9009i	−0.0257728	+	0.0446398i
$290$	205.647	−	118.731i	0.709129	−	0.409416i
$291$		0			0
$292$	72.0828	−	124.851i	0.246859	−	0.427572i
$293$		−	397.726i		−	1.35743i	−0.734404	−	0.678713i	$-0.762538\pi$
$293$		−	397.726i		−	1.35743i	0.734404	−	0.678713i	$-0.237462\pi$
$294$		0			0
$295$	239.642			0.812344
$296$	−136.546	−	78.8351i	−0.461306	−	0.266335i
$297$		0			0
$298$	−160.624	−	278.209i	−0.539007	−	0.933588i
$299$	−9.50226	−	5.48613i	−0.0317801	−	0.0183483i
$300$		0			0
$301$	1.35502	+	229.210i	0.00450174	+	0.761495i
$302$		−	389.826i		−	1.29081i
$303$		0			0
$304$	26.0000	+	45.0333i	0.0855263	+	0.148136i
$305$	−349.496	+	201.782i	−1.14589	+	0.661579i
$306$		0			0
$307$	−116.669			−0.380029			−0.190015	−	0.981781i	$-0.560854\pi$
$307$	−116.669			−0.380029			−0.190015	+	0.981781i	$0.560854\pi$
$308$	−10.6089	+	18.6286i	−0.0344444	+	0.0604823i
$309$		0			0
$310$	−61.3759	+	106.306i	−0.197987	+	0.342923i
$311$	−420.797	+	242.947i	−1.35305	+	0.781181i	−0.988675	−	0.150073i	$-0.952049\pi$
$311$	−420.797	+	242.947i	−1.35305	+	0.781181i	−0.364370	+	0.931254i	$0.618716\pi$
$312$		0			0
$313$	76.8311	−	133.075i	0.245467	−	0.425161i	−0.716796	−	0.697283i	$-0.754392\pi$
$313$	76.8311	−	133.075i	0.245467	−	0.425161i	0.962263	+	0.272122i	$0.0877255\pi$
$314$			281.760i			0.897326i
$315$		0			0
$316$	244.662			0.774247
$317$	83.8741	+	48.4247i	0.264587	+	0.152759i	0.626425	−	0.779482i	$-0.284517\pi$
$317$	83.8741	+	48.4247i	0.264587	+	0.152759i	−0.361838	+	0.932241i	$0.617851\pi$
$318$		0			0
$319$	−25.6689	−	44.4599i	−0.0804669	−	0.139373i
$320$	34.6983	+	20.0331i	0.108432	+	0.0626034i
$321$		0			0
$322$	−102.203	+	59.8156i	−0.317402	+	0.185763i
$323$		−	215.229i		−	0.666343i
$324$		0			0
$325$	0.0379564	+	0.0657425i	0.000116789	+	0.000202285i
$326$	−118.800	+	68.5894i	−0.364418	+	0.210397i
$327$		0			0
$328$	−18.4966			−0.0563920
$329$	185.536	−	325.791i	0.563940	−	0.990246i
$330$		0			0
$331$	36.6344	−	63.4527i	0.110678	−	0.191700i	−0.805366	−	0.592778i	$-0.798031\pi$
$331$	36.6344	−	63.4527i	0.110678	−	0.191700i	0.916044	+	0.401078i	$0.131364\pi$
$332$	−275.154	+	158.860i	−0.828776	+	0.478494i
$333$		0			0
$334$	−15.3379	+	26.5660i	−0.0459219	+	0.0795390i
$335$		−	12.1233i		−	0.0361890i
$336$		0			0
$337$	−165.304			−0.490515			−0.245258	−	0.969458i	$-0.578873\pi$
$337$	−165.304			−0.490515			−0.245258	+	0.969458i	$0.578873\pi$
$338$	205.951	+	118.906i	0.609324	+	0.351793i
$339$		0			0
$340$	−82.9172	−	143.617i	−0.243874	−	0.422403i
$341$	22.9828	+	13.2691i	0.0673984	+	0.0389125i
$342$		0			0
$343$	−6.08276	−	342.946i	−0.0177340	−	0.999843i
$344$		−	92.6165i		−	0.269234i
$345$		0			0
$346$	147.541	+	255.549i	0.426420	+	0.738581i
$347$	181.558	−	104.823i	0.523222	−	0.302082i	−0.215030	−	0.976607i	$-0.568985\pi$
$347$	181.558	−	104.823i	0.523222	−	0.302082i	0.738252	+	0.674525i	$0.235652\pi$
$348$		0			0
$349$	−442.655			−1.26835			−0.634177	−	0.773188i	$-0.718661\pi$
$349$	−442.655			−1.26835			−0.634177	+	0.773188i	$0.718661\pi$
$350$	0.819293	−	0.00484342i	0.00234084	−	1.38384e-5i
$351$		0			0
$352$	4.33105	−	7.50160i	0.0123041	−	0.0213114i
$353$	144.537	−	83.4483i	0.409452	−	0.236397i	−0.281102	−	0.959678i	$-0.590700\pi$
$353$	144.537	−	83.4483i	0.409452	−	0.236397i	0.690554	+	0.723280i	$0.257367\pi$
$354$		0			0
$355$	−208.648	+	361.390i	−0.587742	+	1.01800i
$356$			108.524i			0.304843i
$357$		0			0
$358$	89.7312			0.250646
$359$	16.3523	+	9.44101i	0.0455496	+	0.0262981i	0.522602	−	0.852577i	$-0.324961\pi$
$359$	16.3523	+	9.44101i	0.0455496	+	0.0262981i	−0.477052	+	0.878875i	$0.658295\pi$
$360$		0			0
$361$	96.0000	+	166.277i	0.265928	+	0.460601i
$362$	260.026	+	150.126i	0.718304	+	0.414713i
$363$		0			0
$364$	−11.0828	+	6.48629i	−0.0304471	+	0.0178195i
$365$			361.010i			0.989068i
$366$		0			0
$367$	196.110	+	339.673i	0.534361	+	0.925540i	0.999194	+	0.0401419i	$0.0127810\pi$
$367$	196.110	+	339.673i	0.534361	+	0.925540i	−0.464833	+	0.885398i	$0.653886\pi$
$368$	41.4386	−	23.9246i	0.112605	−	0.0650125i
$369$		0			0
$370$	394.828			1.06710
$371$	295.624	+	505.116i	0.796830	+	1.36150i
$372$		0			0
$373$	277.811	−	481.182i	0.744800	−	1.29003i	−0.205488	−	0.978660i	$-0.565878\pi$
$373$	277.811	−	481.182i	0.744800	−	1.29003i	0.950288	−	0.311372i	$-0.100789\pi$
$374$	−31.0492	+	17.9263i	−0.0830194	+	0.0479313i
$375$		0			0
$376$	−75.7449	+	131.194i	−0.201449	+	0.348920i
$377$		−	30.7519i		−	0.0815700i
$378$		0			0
$379$	433.552			1.14394			0.571968	−	0.820276i	$-0.306180\pi$
$379$	433.552			1.14394			0.571968	+	0.820276i	$0.306180\pi$
$380$	−112.770	−	65.1075i	−0.296762	−	0.171336i
$381$		0			0
$382$	41.6173	+	72.0833i	0.108946	+	0.188700i
$383$	118.682	+	68.5211i	0.309875	+	0.178906i	0.646871	−	0.762600i	$-0.276077\pi$
$383$	118.682	+	68.5211i	0.309875	+	0.178906i	−0.336996	+	0.941506i	$0.609411\pi$
$384$		0			0
$385$	−0.317351	−	53.6817i	−0.000824288	−	0.139433i
$386$			196.907i			0.510123i
$387$		0			0
$388$	12.0828	+	20.9280i	0.0311411	+	0.0539380i
$389$	301.317	−	173.965i	0.774594	−	0.447212i	−0.0599172	−	0.998203i	$-0.519084\pi$
$389$	301.317	−	173.965i	0.774594	−	0.447212i	0.834511	+	0.550991i	$0.185750\pi$
$390$		0			0
$391$	−198.049			−0.506518
$392$	1.63859	+	138.583i	0.00418007	+	0.353529i
$393$		0			0
$394$	−224.662	+	389.126i	−0.570208	+	0.987630i
$395$	−530.585	+	306.333i	−1.34325	+	0.775528i
$396$		0			0
$397$	−231.200	+	400.450i	−0.582368	+	1.00869i	0.412830	+	0.910808i	$0.364540\pi$
$397$	−231.200	+	400.450i	−0.582368	+	1.00869i	−0.995198	+	0.0978827i	$0.968793\pi$
$398$			353.183i			0.887394i
$399$		0			0
$400$	−0.331050			−0.000827625
$401$	383.337	+	221.320i	0.955952	+	0.551919i	0.894925	−	0.446217i	$-0.147229\pi$
$401$	383.337	+	221.320i	0.955952	+	0.551919i	0.0610272	+	0.998136i	$0.480562\pi$
$402$		0			0
$403$	7.94834	+	13.7669i	0.0197229	+	0.0341611i
$404$	−314.937	−	181.829i	−0.779547	−	0.450072i
$405$		0			0
$406$	−288.407	−	164.246i	−0.710362	−	0.404547i
$407$		−	85.3597i		−	0.209729i
$408$		0			0
$409$	−28.1139	−	48.6947i	−0.0687381	−	0.119058i	0.829608	−	0.558346i	$-0.188564\pi$
$409$	−28.1139	−	48.6947i	−0.0687381	−	0.119058i	−0.898346	+	0.439288i	$0.855231\pi$
$410$	40.1125	−	23.1590i	0.0978353	−	0.0564853i
$411$		0			0
$412$	231.490			0.561868
$413$	−169.184	−	289.075i	−0.409646	−	0.699940i
$414$		0			0
$415$	397.807	−	689.022i	0.958571	−	1.66029i
$416$	4.49353	−	2.59434i	0.0108017	−	0.00623639i
$417$		0			0
$418$	−14.0759	+	24.3802i	−0.0336744	+	0.0583258i
$419$			330.707i			0.789276i	0.918837	+	0.394638i	$0.129130\pi$
$419$			330.707i			0.789276i	−0.918837	+	0.394638i	$0.870870\pi$
$420$		0			0
$421$	−30.5930			−0.0726675			−0.0363338	−	0.999340i	$-0.511568\pi$
$421$	−30.5930			−0.0726675			−0.0363338	+	0.999340i	$0.511568\pi$
$422$	137.476	+	79.3715i	0.325771	+	0.188084i
$423$		0			0
$424$	−118.241	−	204.800i	−0.278871	−	0.483019i
$425$	1.18665	+	0.685111i	0.00279211	+	0.00161203i
$426$		0			0
$427$	490.145	+	279.135i	1.14788	+	0.653712i
$428$			342.220i			0.799580i
$429$		0			0
$430$	115.962	+	200.852i	0.269679	+	0.467098i
$431$	−580.479	+	335.140i	−1.34682	+	0.777586i	−0.987798	−	0.155744i	$-0.950223\pi$
$431$	−580.479	+	335.140i	−1.34682	+	0.777586i	−0.359021	+	0.933330i	$0.616889\pi$
$432$		0			0
$433$	−192.276			−0.444055			−0.222027	−	0.975040i	$-0.571267\pi$
$433$	−192.276			−0.444055			−0.222027	+	0.975040i	$0.571267\pi$
$434$	171.566	−	1.01425i	0.395313	−	0.00233697i
$435$		0			0
$436$	−131.917	+	228.487i	−0.302562	+	0.524054i
$437$	−134.675	+	77.7549i	−0.308182	+	0.177929i
$438$		0			0
$439$	80.5208	−	139.466i	0.183419	−	0.317691i	−0.759624	−	0.650363i	$-0.774617\pi$
$439$	80.5208	−	139.466i	0.183419	−	0.317691i	0.943043	+	0.332672i	$0.107950\pi$
$440$			21.6911i			0.0492979i
$441$		0			0
$442$	−21.4760			−0.0485883
$443$	−590.281	−	340.799i	−1.33246	−	0.769297i	−0.346785	−	0.937945i	$-0.612727\pi$
$443$	−590.281	−	340.799i	−1.33246	−	0.769297i	−0.985676	+	0.168647i	$0.946060\pi$
$444$		0			0
$445$	−135.879	−	235.350i	−0.305347	−	0.528876i
$446$	−97.0422	−	56.0273i	−0.217583	−	0.125622i
$447$		0			0
$448$	−0.331050	−	55.9990i	−0.000738951	−	0.124998i
$449$			804.351i			1.79143i	0.444630	+	0.895714i	$0.353335\pi$
$449$			804.351i			1.79143i	−0.444630	+	0.895714i	$0.646665\pi$
$450$		0			0
$451$	−5.00685	−	8.67212i	−0.0111017	−	0.0192286i
$452$	−13.2611	+	7.65629i	−0.0293387	+	0.0169387i
$453$		0			0
$454$	−507.207			−1.11720
$455$	15.9133	−	27.9428i	0.0349743	−	0.0614128i
$456$		0			0
$457$	44.4415	−	76.9749i	0.0972462	−	0.168435i	−0.813298	−	0.581848i	$-0.802330\pi$
$457$	44.4415	−	76.9749i	0.0972462	−	0.168435i	0.910544	+	0.413413i	$0.135663\pi$
$458$	149.833	−	86.5060i	0.327146	−	0.188878i
$459$		0			0
$460$	−59.9104	+	103.768i	−0.130240	+	0.225582i
$461$			862.183i			1.87024i	0.354325	+	0.935122i	$0.384711\pi$
$461$			862.183i			1.87024i	−0.354325	+	0.935122i	$0.615289\pi$
$462$		0			0
$463$	−140.938			−0.304401			−0.152201	−	0.988350i	$-0.548636\pi$
$463$	−140.938			−0.304401			−0.152201	+	0.988350i	$0.548636\pi$
$464$	116.140	+	67.0533i	0.250301	+	0.144511i
$465$		0			0
$466$	−150.293	−	260.315i	−0.322517	−	0.558616i
$467$	233.715	+	134.936i	0.500461	+	0.288941i	0.728904	−	0.684616i	$-0.240030\pi$
$467$	233.715	+	134.936i	0.500461	+	0.288941i	−0.228443	+	0.973557i	$0.573363\pi$
$468$		0			0
$469$	−14.6241	+	8.55892i	−0.0311815	+	0.0182493i
$470$		−	379.351i		−	0.807129i
$471$		0			0
$472$	67.6689	+	117.206i	0.143366	+	0.248318i
$473$	43.4232	−	25.0704i	0.0918038	−	0.0530030i
$474$		0			0
$475$	1.07591			0.00226508
$476$	−114.704	+	201.413i	−0.240974	+	0.423137i
$477$		0			0
$478$	−242.369	+	419.795i	−0.507048	+	0.878233i
$479$	652.109	−	376.495i	1.36140	−	0.786003i	0.371587	−	0.928398i	$-0.378814\pi$
$479$	652.109	−	376.495i	1.36140	−	0.786003i	0.989810	+	0.142395i	$0.0454804\pi$
$480$		0			0
$481$	25.5656	−	44.2810i	0.0531510	−	0.0920603i
$482$			46.3082i			0.0960752i
$483$		0			0
$484$	−237.311			−0.490311
$485$	−52.4064	−	30.2569i	−0.108054	−	0.0623853i
$486$		0			0
$487$	−375.969	−	651.198i	−0.772011	−	1.33716i	−0.936459	−	0.350776i	$-0.885918\pi$
$487$	−375.969	−	651.198i	−0.772011	−	1.33716i	0.164449	−	0.986386i	$-0.447415\pi$
$488$	−197.378	−	113.956i	−0.404464	−	0.233517i
$489$		0			0
$490$	−177.069	−	298.486i	−0.361365	−	0.609155i
$491$			165.492i			0.337051i	0.985697	+	0.168526i	$0.0539006\pi$
$491$			165.492i			0.337051i	−0.985697	+	0.168526i	$0.946099\pi$
$492$		0			0
$493$	−277.535	−	480.704i	−0.562950	−	0.975059i
$494$	−14.6040	+	8.43160i	−0.0295627	+	0.0170680i
$495$		0			0
$496$	−69.3242			−0.139767
$497$	583.241	−	3.44795i	1.17352	−	0.00693753i
$498$		0			0
$499$	213.341	−	369.518i	0.427538	−	0.740517i	−0.569116	−	0.822257i	$-0.692714\pi$
$499$	213.341	−	369.518i	0.427538	−	0.740517i	0.996654	+	0.0817402i	$0.0260478\pi$
$500$	−216.146	+	124.792i	−0.432293	+	0.249584i
$501$		0			0
$502$	5.88613	−	10.1951i	0.0117254	−	0.0203089i
$503$			302.442i			0.601276i	0.953738	+	0.300638i	$0.0971996\pi$
$503$			302.442i			0.601276i	−0.953738	+	0.300638i	$0.902800\pi$
$504$		0			0
$505$	910.648			1.80326
$506$	22.4341	+	12.9523i	0.0443361	+	0.0255975i
$507$		0			0
$508$	−8.57934	−	14.8598i	−0.0168885	−	0.0292517i
$509$	122.770	+	70.8814i	0.241199	+	0.139256i	0.615728	−	0.787959i	$-0.288862\pi$
$509$	122.770	+	70.8814i	0.241199	+	0.139256i	−0.374529	+	0.927215i	$0.622196\pi$
$510$		0			0
$511$	435.479	−	254.869i	0.852210	−	0.498764i
$512$			22.6274i			0.0441942i
$513$		0			0
$514$	11.0068	+	19.0644i	0.0214141	+	0.0370903i
$515$	−502.019	+	289.841i	−0.974794	+	0.562798i
$516$		0			0
$517$	−82.0137			−0.158634
$518$	−278.743	−	476.273i	−0.538115	−	0.919446i
$519$		0			0
$520$	−6.49658	+	11.2524i	−0.0124934	+	0.0216392i
$521$	−390.077	+	225.211i	−0.748708	+	0.432267i	−0.825227	−	0.564801i	$-0.808953\pi$
$521$	−390.077	+	225.211i	−0.748708	+	0.432267i	0.0765187	+	0.997068i	$0.475620\pi$
$522$		0			0
$523$	156.221	−	270.583i	0.298702	−	0.517366i	−0.677138	−	0.735856i	$-0.736780\pi$
$523$	156.221	−	270.583i	0.298702	−	0.517366i	0.975839	+	0.218490i	$0.0701132\pi$
$524$		−	140.807i		−	0.268716i
$525$		0			0
$526$	9.02055			0.0171493
$527$	248.492	+	143.467i	0.471522	+	0.272233i
$528$		0			0
$529$	−192.952	−	334.202i	−0.364748	−	0.631762i
$530$	512.847	+	296.092i	0.967636	+	0.558665i
$531$		0			0
$532$	1.07591	+	181.997i	0.00202239	+	0.342099i
$533$		−	5.99830i		−	0.0112538i
$534$		0			0
$535$	−428.483	−	742.154i	−0.800903	−	1.38720i
$536$	5.92939	−	3.42333i	0.0110623	−	0.00638682i
$537$		0			0
$538$	488.662			0.908294
$539$	−64.5312	+	38.2814i	−0.119724	+	0.0710231i
$540$		0			0
$541$	−307.173	+	532.039i	−0.567787	+	0.983436i	0.428998	+	0.903306i	$0.358867\pi$
$541$	−307.173	+	532.039i	−0.567787	+	0.983436i	−0.996784	+	0.0801300i	$0.974466\pi$
$542$	267.518	−	154.452i	0.493576	−	0.284966i
$543$		0			0
$544$	46.8276	−	81.1078i	0.0860802	−	0.149095i
$545$		−	660.677i		−	1.21225i
$546$		0			0
$547$	−675.263			−1.23448			−0.617242	−	0.786773i	$-0.711750\pi$
$547$	−675.263			−1.23448			−0.617242	+	0.786773i	$0.711750\pi$
$548$	−116.858	−	67.4678i	−0.213244	−	0.123116i
$549$		0			0
$550$	−0.0896122	−	0.155213i	−0.000162931	−	0.000282205i
$551$	−377.454	−	217.923i	−0.685034	−	0.395505i
$552$		0			0
$553$	744.111	+	423.767i	1.34559	+	0.766306i
$554$			184.882i			0.333722i
$555$		0			0
$556$	166.572	+	288.512i	0.299591	+	0.518906i
$557$	579.013	−	334.293i	1.03952	−	0.600168i	0.119823	−	0.992795i	$-0.461767\pi$
$557$	579.013	−	334.293i	1.03952	−	0.600168i	0.919698	+	0.392628i	$0.128434\pi$
$558$		0			0
$559$	30.0348			0.0537295
$560$	70.8325	+	121.027i	0.126487	+	0.216120i
$561$		0			0
$562$	−304.421	+	527.272i	−0.541674	+	0.938207i
$563$	10.9678	−	6.33228i	0.0194810	−	0.0112474i	−0.490228	−	0.871594i	$-0.663086\pi$
$563$	10.9678	−	6.33228i	0.0194810	−	0.0112474i	0.509709	+	0.860347i	$0.329753\pi$
$564$		0			0
$565$	19.1724	−	33.2075i	0.0339334	−	0.0587744i
$566$		−	548.559i		−	0.969186i
$567$		0			0
$568$	−235.669			−0.414910
$569$	−509.198	−	293.986i	−0.894900	−	0.516671i	−0.0193580	−	0.999813i	$-0.506162\pi$
$569$	−509.198	−	293.986i	−0.894900	−	0.516671i	−0.875542	+	0.483142i	$0.839496\pi$
$570$		0			0
$571$	386.759	+	669.886i	0.677336	+	1.17318i	0.975780	+	0.218753i	$0.0701990\pi$
$571$	386.759	+	669.886i	0.677336	+	1.17318i	−0.298444	+	0.954427i	$0.596468\pi$
$572$	2.43271	+	1.40453i	0.00425299	+	0.00245547i
$573$		0			0
$574$	−56.2551	−	32.0370i	−0.0980055	−	0.0558136i
$575$		−	0.990030i		−	0.00172179i
$576$		0			0
$577$	−45.7965	−	79.3219i	−0.0793700	−	0.137473i	0.823608	−	0.567159i	$-0.191958\pi$
$577$	−45.7965	−	79.3219i	−0.0793700	−	0.137473i	−0.902978	+	0.429686i	$0.858624\pi$
$578$	18.2446	−	10.5335i	0.0315651	−	0.0182241i
$579$		0			0
$580$	−335.821			−0.579001
$581$	−1112.00	+	6.57383i	−1.91394	+	0.0113147i
$582$		0			0
$583$	64.0137	−	110.875i	0.109801	−	0.190180i
$584$	−176.566	+	101.940i	−0.302339	+	0.174556i
$585$		0			0
$586$	−281.235	+	487.113i	−0.479923	+	0.831250i
$587$			237.495i			0.404592i	0.979324	+	0.202296i	$0.0648403\pi$
$587$			237.495i			0.404592i	−0.979324	+	0.202296i	$0.935160\pi$
$588$		0			0
$589$	225.304			0.382519
$590$	−293.500	−	169.452i	−0.497457	−	0.287207i
$591$		0			0
$592$	111.490	+	193.106i	0.188327	+	0.326192i
$593$	23.8699	+	13.7813i	0.0402529	+	0.0232400i	0.519991	−	0.854172i	$-0.325935\pi$
$593$	23.8699	+	13.7813i	0.0402529	+	0.0232400i	−0.479739	+	0.877412i	$0.659268\pi$
$594$		0			0
$595$	−3.43122	−	580.411i	−0.00576676	−	0.975480i
$596$			454.314i			0.762271i
$597$		0			0
$598$	7.75856	+	13.4382i	0.0129742	+	0.0224719i
$599$	815.769	−	470.985i	1.36189	−	0.786285i	0.372010	−	0.928229i	$-0.378669\pi$
$599$	815.769	−	470.985i	1.36189	−	0.786285i	0.989875	+	0.141944i	$0.0453352\pi$
$600$		0			0
$601$	−374.262			−0.622732			−0.311366	−	0.950290i	$-0.600787\pi$
$601$	−374.262			−0.622732			−0.311366	+	0.950290i	$0.600787\pi$
$602$	160.416	−	281.682i	0.266472	−	0.467910i
$603$		0			0
$604$	−275.648	+	477.437i	−0.456372	+	0.790459i
$605$	514.642	−	297.129i	0.850648	−	0.491122i
$606$		0			0
$607$	−190.328	+	329.657i	−0.313555	+	0.543092i	−0.979129	−	0.203239i	$-0.934853\pi$
$607$	−190.328	+	329.657i	−0.313555	+	0.543092i	0.665575	+	0.746331i	$0.268187\pi$
$608$		−	73.5391i		−	0.120952i
$609$		0			0
$610$	570.724			0.935614
$611$	−42.5452	−	24.5635i	−0.0696321	−	0.0402021i
$612$		0			0
$613$	455.283	+	788.573i	0.742713	+	1.28642i	0.951256	+	0.308403i	$0.0997945\pi$
$613$	455.283	+	788.573i	0.742713	+	1.28642i	−0.208543	+	0.978013i	$0.566872\pi$
$614$	142.890	+	82.4974i	0.232719	+	0.134361i
$615$		0			0
$616$	26.1655	−	15.3136i	0.0424765	−	0.0248598i
$617$		−	16.8438i		−	0.0272996i	−0.999907	−	0.0136498i	$-0.995655\pi$
$617$		−	16.8438i		−	0.0272996i	0.999907	−	0.0136498i	$-0.00434500\pi$
$618$		0			0
$619$	391.707	+	678.456i	0.632806	+	1.09605i	0.986975	+	0.160871i	$0.0514303\pi$
$619$	391.707	+	678.456i	0.632806	+	1.09605i	−0.354169	+	0.935181i	$0.615236\pi$
$620$	150.340	−	86.7986i	0.242483	−	0.139998i
$621$		0			0
$622$	687.159			1.10476
$623$	−187.969	+	330.063i	−0.301716	+	0.529796i
$624$		0			0
$625$	313.531	−	543.052i	0.501650	−	0.868883i
$626$	−188.197	+	108.656i	−0.300634	+	0.173571i
$627$		0			0
$628$	199.235	−	345.084i	0.317253	−	0.549497i
$629$		−	922.916i		−	1.46727i
$630$		0			0
$631$	−679.228			−1.07643			−0.538215	−	0.842807i	$-0.680901\pi$
$631$	−679.228			−1.07643			−0.538215	+	0.842807i	$0.680901\pi$
$632$	−299.649	−	173.002i	−0.474128	−	0.273738i
$633$		0			0
$634$	−68.4829	−	118.616i	−0.108017	−	0.187091i
$635$	37.2111	+	21.4838i	0.0586001	+	0.0338328i
$636$		0			0
$637$	−44.9415	+	0.531381i	−0.0705518	+	0.000834193i
$638$			72.6028i			0.113797i
$639$		0			0
$640$	−28.3311	−	49.0708i	−0.0442673	−	0.0766732i
$641$	−589.124	+	340.131i	−0.919070	+	0.530625i	−0.883338	−	0.468736i	$-0.844709\pi$
$641$	−589.124	+	340.131i	−0.919070	+	0.530625i	−0.0357315	+	0.999361i	$0.511376\pi$
$642$		0			0
$643$	843.966			1.31254			0.656272	−	0.754524i	$-0.272132\pi$
$643$	843.966			1.31254			0.656272	+	0.754524i	$0.272132\pi$
$644$	167.469	−	0.990030i	0.260045	−	0.00153731i
$645$		0			0
$646$	−152.190	+	263.600i	−0.235588	+	0.408050i
$647$	1111.67	−	641.824i	1.71819	−	0.992000i	0.795979	−	0.605324i	$-0.206956\pi$
$647$	1111.67	−	641.824i	1.71819	−	0.992000i	0.922216	−	0.386676i	$-0.126377\pi$
$648$		0			0
$649$	−36.6347	+	63.4532i	−0.0564479	+	0.0977707i
$650$		−	0.107357i		−	0.000165165i
$651$		0			0
$652$	194.000			0.297546
$653$	276.898	+	159.867i	0.424040	+	0.244820i	0.696804	−	0.717261i	$-0.254605\pi$
$653$	276.898	+	159.867i	0.424040	+	0.244820i	−0.272764	+	0.962081i	$0.587938\pi$
$654$		0			0
$655$	176.300	+	305.360i	0.269160	+	0.466199i
$656$	22.6536	+	13.0791i	0.0345329	+	0.0199376i
$657$		0			0
$658$	−457.604	+	267.817i	−0.695446	+	0.407017i
$659$		−	915.684i		−	1.38951i	−0.719249	−	0.694753i	$-0.755514\pi$
$659$		−	915.684i		−	1.38951i	0.719249	−	0.694753i	$-0.244486\pi$
$660$		0			0
$661$	−251.183	−	435.061i	−0.380004	−	0.658186i	0.611058	−	0.791586i	$-0.290744\pi$
$661$	−251.183	−	435.061i	−0.380004	−	0.658186i	−0.991062	+	0.133399i	$0.957411\pi$
$662$	−89.7356	+	51.8089i	−0.135552	+	0.0782612i
$663$		0			0
$664$	449.324			0.676693
$665$	−230.206	−	393.339i	−0.346174	−	0.591488i
$666$		0			0
$667$	−200.528	+	347.324i	−0.300641	+	0.520726i
$668$	37.5700	−	21.6911i	0.0562426	−	0.0324717i
$669$		0			0
$670$	−8.57249	+	14.8480i	−0.0127948	+	0.0221612i
$671$		−	123.388i		−	0.183886i
$672$		0			0
$673$	299.724			0.445356			0.222678	−	0.974892i	$-0.428520\pi$
$673$	299.724			0.445356			0.222678	+	0.974892i	$0.428520\pi$
$674$	202.455	+	116.887i	0.300378	+	0.173423i
$675$		0			0
$676$	−168.159	−	291.259i	−0.248755	−	0.430857i
$677$	286.869	+	165.624i	0.423736	+	0.244644i	0.696674	−	0.717387i	$-0.254662\pi$
$677$	286.869	+	165.624i	0.423736	+	0.244644i	−0.272939	+	0.962031i	$0.587996\pi$
$678$		0			0
$679$	0.500000	+	84.5779i	0.000736377	+	0.124562i
$680$			234.525i			0.344890i
$681$		0			0
$682$	−18.7654	−	32.5026i	−0.0275153	−	0.0476578i
$683$	858.175	−	495.468i	1.25648	−	0.725428i	0.284090	−	0.958797i	$-0.408308\pi$
$683$	858.175	−	495.468i	1.25648	−	0.725428i	0.972388	+	0.233369i	$0.0749751\pi$
$684$		0			0
$685$	337.897			0.493280
$686$	−235.050	+	424.323i	−0.342638	+	0.618546i
$687$		0			0
$688$	−65.4897	+	113.432i	−0.0951886	+	0.164871i
$689$	66.4151	−	38.3448i	0.0963935	−	0.0556528i
$690$		0			0
$691$	−326.842	+	566.106i	−0.472998	+	0.819257i	−0.999522	−	0.0309035i	$-0.990162\pi$
$691$	−326.842	+	566.106i	−0.472998	+	0.819257i	0.526524	+	0.850160i	$0.323495\pi$
$692$		−	417.310i		−	0.603049i
$693$		0			0
$694$	−296.483			−0.427209
$695$	−722.473	−	417.120i	−1.03953	−	0.600173i
$696$		0			0
$697$	−54.1344	−	93.7636i	−0.0776677	−	0.134524i
$698$	542.140	+	313.005i	0.776705	+	0.448431i
$699$		0			0
$700$	−1.00685	−	0.573396i	−0.00143836	−	0.000819137i
$701$		−	281.648i		−	0.401781i	−0.979614	−	0.200890i	$-0.935616\pi$
$701$		−	281.648i		−	0.401781i	0.979614	−	0.200890i	$-0.0643835\pi$
$702$		0			0
$703$	−362.342	−	627.594i	−0.515422	−	0.892737i
$704$	−10.6089	+	6.12503i	−0.0150694	+	0.00870033i
$705$		0			0
$706$	−236.027			−0.334316
$707$	−642.906	−	1098.50i	−0.909344	−	1.55375i
$708$		0			0
$709$	−250.372	+	433.658i	−0.353135	+	0.611647i	−0.986797	−	0.161963i	$-0.948218\pi$
$709$	−250.372	+	433.658i	−0.353135	+	0.611647i	0.633662	+	0.773610i	$0.281551\pi$
$710$	511.082	−	295.073i	0.719834	−	0.415596i
$711$		0			0
$712$	76.7380	−	132.914i	0.107778	−	0.186677i
$713$		−	207.319i		−	0.290770i
$714$		0			0
$715$	−7.03425			−0.00983811
$716$	−109.898	−	63.4495i	−0.153489	−	0.0886166i
$717$		0			0
$718$	−13.3516	−	23.1256i	−0.0185955	−	0.0322084i
$719$	371.073	+	214.239i	0.516095	+	0.297968i	0.735336	−	0.677703i	$-0.237025\pi$
$719$	371.073	+	214.239i	0.516095	+	0.297968i	−0.219240	+	0.975671i	$0.570358\pi$
$720$		0			0
$721$	704.049	+	400.952i	0.976489	+	0.556105i
$722$		−	271.529i		−	0.376079i
$723$		0			0
$724$	−212.311	−	367.733i	−0.293247	−	0.507918i
$725$	2.40300	−	1.38737i	0.00331449	−	0.00191362i
$726$		0			0
$727$	−1134.87			−1.56103			−0.780515	−	0.625137i	$-0.785043\pi$
$727$	−1134.87			−1.56103			−0.780515	+	0.625137i	$0.785043\pi$
$728$	18.1601	−	0.107357i	0.0249451	−	0.000147468i
$729$		0			0
$730$	255.273	−	442.145i	0.349688	−	0.605678i
$731$	469.495	−	271.063i	0.642264	−	0.370811i
$732$		0			0
$733$	322.786	−	559.082i	0.440363	−	0.762731i	−0.557353	−	0.830276i	$-0.688183\pi$
$733$	322.786	−	559.082i	0.440363	−	0.762731i	0.997716	+	0.0675441i	$0.0215163\pi$
$734$		−	554.684i		−	0.755700i
$735$		0			0
$736$	−67.6689			−0.0919415
$737$	3.21006	+	1.85333i	0.00435558	+	0.00251469i
$738$		0			0
$739$	396.638	+	686.997i	0.536723	+	0.929631i	0.999078	+	0.0429362i	$0.0136712\pi$
$739$	396.638	+	686.997i	0.536723	+	0.929631i	−0.462355	+	0.886695i	$0.652995\pi$
$740$	−483.563	−	279.185i	−0.653464	−	0.377277i
$741$		0			0
$742$	−4.89298	−	827.676i	−0.00659431	−	1.11547i
$743$			1254.90i			1.68896i	0.535584	+	0.844482i	$0.320092\pi$
$743$			1254.90i			1.68896i	−0.535584	+	0.844482i	$0.679908\pi$
$744$		0			0
$745$	−568.831	−	985.245i	−0.763532	−	1.32248i
$746$	−680.494	+	392.883i	−0.912190	+	0.526653i
$747$		0			0
$748$	50.7032			0.0677850
$749$	−592.743	+	1040.82i	−0.791379	+	1.38962i
$750$		0			0
$751$	427.766	−	740.912i	0.569595	−	0.986567i	−0.427011	−	0.904246i	$-0.640433\pi$
$751$	427.766	−	740.912i	0.569595	−	0.986567i	0.996606	−	0.0823207i	$-0.0262332\pi$
$752$	185.536	−	107.119i	0.246724	−	0.142446i
$753$		0			0
$754$	−21.7449	+	37.6632i	−0.0288393	+	0.0499512i
$755$		−	1380.52i		−	1.82851i
$756$		0			0
$757$	254.428			0.336100			0.168050	−	0.985778i	$-0.446253\pi$
$757$	254.428			0.336100			0.168050	+	0.985778i	$0.446253\pi$
$758$	−530.991	−	306.568i	−0.700515	−	0.404443i
$759$		0			0
$760$	92.0759	+	159.480i	0.121153	+	0.209842i
$761$	−831.324	−	479.965i	−1.09241	−	0.630703i	−0.158192	−	0.987408i	$-0.550567\pi$
$761$	−831.324	−	479.965i	−1.09241	−	0.630703i	−0.934217	+	0.356705i	$0.883900\pi$
$762$		0			0
$763$	−796.962	+	466.430i	−1.04451	+	0.611310i
$764$		−	117.711i		−	0.154073i
$765$		0			0
$766$	−96.9035	−	167.842i	−0.126506	−	0.219115i
$767$	−38.0090	+	21.9445i	−0.0495555	+	0.0286109i
$768$		0			0
$769$	563.090			0.732236			0.366118	−	0.930568i	$-0.380687\pi$
$769$	563.090			0.732236			0.366118	+	0.930568i	$0.380687\pi$
$770$	−37.5700	+	65.9708i	−0.0487922	+	0.0856764i
$771$		0			0
$772$	139.235	−	241.161i	0.180356	−	0.312385i
$773$	164.508	−	94.9789i	0.212818	−	0.122871i	−0.389802	−	0.920899i	$-0.627457\pi$
$773$	164.508	−	94.9789i	0.212818	−	0.122871i	0.602620	+	0.798028i	$0.294123\pi$
$774$		0			0
$775$	−0.717181	+	1.24219i	−0.000925395	+	0.00160283i
$776$		−	34.1752i		−	0.0440402i
$777$		0			0
$778$	−492.049			−0.632453
$779$	−73.6242	−	42.5069i	−0.0945111	−	0.0545660i
$780$		0			0
$781$	−63.7934	−	110.493i	−0.0816817	−	0.141477i

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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	378.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 - 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +(-4.33729 - 2.50413i) q^{5} +(0.0413813 + 6.99988i) q^{7} -2.82843i q^{8} +O(q^{10})\)	\(q+(-1.22474 - 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +(-4.33729 - 2.50413i) q^{5} +(0.0413813 + 6.99988i) q^{7} -2.82843i q^{8} +(3.54138 + 6.13385i) q^{10} +(1.32611 - 0.765629i) q^{11} +0.917237 q^{13} +(4.89898 - 8.60233i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(14.3380 - 8.27803i) q^{17} +(6.50000 - 11.2583i) q^{19} -10.0165i q^{20} -2.16553 q^{22} +(-10.3596 - 5.98115i) q^{23} +(0.0413813 + 0.0716745i) q^{25} +(-1.12338 - 0.648585i) q^{26} +(-12.0828 + 7.07155i) q^{28} -33.5266i q^{29} +(8.66553 + 15.0091i) q^{31} +(4.89898 - 2.82843i) q^{32} -23.4138 q^{34} +(17.3492 - 30.4641i) q^{35} +(27.8724 - 48.2765i) q^{37} +(-15.9217 + 9.19239i) q^{38} +(-7.08276 + 12.2677i) q^{40} -6.53953i q^{41} +32.7449 q^{43} +(2.65222 + 1.53126i) q^{44} +(8.45862 + 14.6508i) q^{46} +(-46.3841 - 26.7799i) q^{47} +(-48.9966 + 0.579328i) q^{49} -0.117044i q^{50} +(0.917237 + 1.58870i) q^{52} +(72.4078 - 41.8047i) q^{53} -7.66895 q^{55} +(19.7986 - 0.117044i) q^{56} +(-23.7069 + 41.0616i) q^{58} +(-41.4386 + 23.9246i) q^{59} +(40.2897 - 69.7838i) q^{61} -24.5098i q^{62} -8.00000 q^{64} +(-3.97832 - 2.29689i) q^{65} +(1.21033 + 2.09636i) q^{67} +(28.6759 + 16.5561i) q^{68} +(-42.7897 + 25.0431i) q^{70} -83.3216i q^{71} +(-36.0414 - 62.4255i) q^{73} +(-68.2732 + 39.4176i) q^{74} +26.0000 q^{76} +(5.41418 + 9.25091i) q^{77} +(61.1655 - 105.942i) q^{79} +(17.3492 - 10.0165i) q^{80} +(-4.62414 + 8.00925i) q^{82} +158.860i q^{83} -82.9172 q^{85} +(-40.1041 - 23.1541i) q^{86} +(-2.16553 - 3.75080i) q^{88} +(46.9922 + 27.1310i) q^{89} +(0.0379564 + 6.42055i) q^{91} -23.9246i q^{92} +(37.8724 + 65.5970i) q^{94} +(-56.3848 + 32.5538i) q^{95} +12.0828 q^{97} +(60.4180 + 33.9363i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{4} - 24 q^{7}+O(q^{10}) \) 8 * q + 8 * q^4 - 24 * q^7	\( 8 q + 8 q^{4} - 24 q^{7} + 4 q^{10} + 56 q^{13} - 16 q^{16} + 52 q^{19} + 80 q^{22} - 24 q^{25} - 48 q^{28} - 28 q^{31} + 56 q^{34} + 4 q^{37} - 8 q^{40} - 176 q^{43} + 92 q^{46} - 100 q^{49} + 56 q^{52} - 256 q^{55} - 68 q^{58} + 152 q^{61} - 64 q^{64} + 180 q^{67} - 172 q^{70} - 264 q^{73} + 208 q^{76} + 392 q^{79} + 36 q^{82} - 712 q^{85} + 80 q^{88} - 316 q^{91} + 84 q^{94} + 48 q^{97}+O(q^{100}) \) 8 * q + 8 * q^4 - 24 * q^7 + 4 * q^10 + 56 * q^13 - 16 * q^16 + 52 * q^19 + 80 * q^22 - 24 * q^25 - 48 * q^28 - 28 * q^31 + 56 * q^34 + 4 * q^37 - 8 * q^40 - 176 * q^43 + 92 * q^46 - 100 * q^49 + 56 * q^52 - 256 * q^55 - 68 * q^58 + 152 * q^61 - 64 * q^64 + 180 * q^67 - 172 * q^70 - 264 * q^73 + 208 * q^76 + 392 * q^79 + 36 * q^82 - 712 * q^85 + 80 * q^88 - 316 * q^91 + 84 * q^94 + 48 * q^97

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