LMFDB - Embedded newform 1680.2.f.l.881.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1680,2,Mod(881,1680)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1680, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 1, 0, 1]))

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

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

chi := DirichletCharacter("1680.881");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1680.f (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$13.4148675396$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + x^{14} - 4 x^{13} + 10 x^{12} - 32 x^{11} + 71 x^{10} - 70 x^{9} + 74 x^{8} + \cdots + 6561 $ x^16 - 2x^15 + x^14 - 4x^13 + 10x^12 - 32x^11 + 71x^10 - 70x^9 + 74x^8 - 210x^7 + 639x^6 - 864x^5 + 810x^4 - 972x^3 + 729x^2 - 4374x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{16} $
Twist minimal:	no (minimal twist has level 840)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			881.8
Root			$1.71703 - 0.227581i$ of defining polynomial
Character	$\chi$	$=$	1680.881
Dual form			1680.2.f.l.881.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.227581 + 1.71703i) q^{3} +1.00000 q^{5} +(1.22074 - 2.34729i) q^{7} +(-2.89641 - 0.781528i) q^{9} +O(q^{10})$	\(q+(-0.227581 + 1.71703i) q^{3} +1.00000 q^{5} +(1.22074 - 2.34729i) q^{7} +(-2.89641 - 0.781528i) q^{9} -4.73831i q^{11} +5.25541i q^{13} +(-0.227581 + 1.71703i) q^{15} -0.432719 q^{17} -6.30136i q^{19} +(3.75256 + 2.63026i) q^{21} -0.332245i q^{23} +1.00000 q^{25} +(2.00108 - 4.79538i) q^{27} -7.48606i q^{29} -0.0758169i q^{31} +(8.13584 + 1.07835i) q^{33} +(1.22074 - 2.34729i) q^{35} -2.54100 q^{37} +(-9.02372 - 1.19603i) q^{39} +4.82357 q^{41} -1.97756 q^{43} +(-2.89641 - 0.781528i) q^{45} +9.28919 q^{47} +(-4.01957 - 5.73089i) q^{49} +(0.0984785 - 0.742993i) q^{51} -13.8305i q^{53} -4.73831i q^{55} +(10.8197 + 1.43407i) q^{57} -5.65528 q^{59} +5.11428i q^{61} +(-5.37026 + 5.84469i) q^{63} +5.25541i q^{65} -6.75379 q^{67} +(0.570475 + 0.0756124i) q^{69} -9.35623i q^{71} +2.75129i q^{73} +(-0.227581 + 1.71703i) q^{75} +(-11.1222 - 5.78426i) q^{77} -0.0508016 q^{79} +(7.77843 + 4.52726i) q^{81} +4.12411 q^{83} -0.432719 q^{85} +(12.8538 + 1.70368i) q^{87} +12.4092 q^{89} +(12.3360 + 6.41551i) q^{91} +(0.130180 + 0.0172545i) q^{93} -6.30136i q^{95} +11.1116i q^{97} +(-3.70312 + 13.7241i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{5} - 2 q^{7} - 2 q^{9}+O(q^{10}) $ 16 * q + 16 * q^5 - 2 * q^7 - 2 * q^9	$ 16 q + 16 q^{5} - 2 q^{7} - 2 q^{9} + 10 q^{21} + 16 q^{25} - 6 q^{27} + 6 q^{33} - 2 q^{35} + 12 q^{37} - 6 q^{39} + 32 q^{41} - 32 q^{43} - 2 q^{45} - 4 q^{47} - 4 q^{49} - 6 q^{51} + 24 q^{59} + 24 q^{63} + 8 q^{69} - 32 q^{77} + 4 q^{79} - 6 q^{81} - 20 q^{83} - 6 q^{87} - 24 q^{89} - 20 q^{91} - 32 q^{93} + 58 q^{99}+O(q^{100}) $ 16 * q + 16 * q^5 - 2 * q^7 - 2 * q^9 + 10 * q^21 + 16 * q^25 - 6 * q^27 + 6 * q^33 - 2 * q^35 + 12 * q^37 - 6 * q^39 + 32 * q^41 - 32 * q^43 - 2 * q^45 - 4 * q^47 - 4 * q^49 - 6 * q^51 + 24 * q^59 + 24 * q^63 + 8 * q^69 - 32 * q^77 + 4 * q^79 - 6 * q^81 - 20 * q^83 - 6 * q^87 - 24 * q^89 - 20 * q^91 - 32 * q^93 + 58 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$421$	$1121$	$1471$
$\chi(n)$	$-1$	$1$	$1$	$-1$	$1$

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
$3$	−0.227581	+	1.71703i	−0.131394	+	0.991330i
$3$	−0.227581	+	1.71703i	−0.131394	+	0.991330i
$4$		0			0
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$		0			0
$7$	1.22074	−	2.34729i	0.461398	−	0.887193i
$7$	1.22074	−	2.34729i	0.461398	−	0.887193i
$8$		0			0
$9$	−2.89641	−	0.781528i	−0.965471	−	0.260509i
$10$		0			0
$11$		−	4.73831i		−	1.42865i	−0.699812	−	0.714327i	$-0.746733\pi$
$11$		−	4.73831i		−	1.42865i	0.699812	−	0.714327i	$-0.253267\pi$
$12$		0			0
$13$			5.25541i			1.45759i	0.684733	+	0.728794i	$0.259919\pi$
$13$			5.25541i			1.45759i	−0.684733	+	0.728794i	$0.740081\pi$
$14$		0			0
$15$	−0.227581	+	1.71703i	−0.0587611	+	0.443336i
$16$		0			0
$17$	−0.432719			−0.104950			−0.0524749	−	0.998622i	$-0.516711\pi$
$17$	−0.432719			−0.104950			−0.0524749	+	0.998622i	$0.516711\pi$
$18$		0			0
$19$		−	6.30136i		−	1.44563i	−0.691041	−	0.722816i	$-0.742847\pi$
$19$		−	6.30136i		−	1.44563i	0.691041	−	0.722816i	$-0.257153\pi$
$20$		0			0
$21$	3.75256	+	2.63026i	0.818877	+	0.573969i
$22$		0			0
$23$		−	0.332245i		−	0.0692778i	−0.999400	−	0.0346389i	$-0.988972\pi$
$23$		−	0.332245i		−	0.0692778i	0.999400	−	0.0346389i	$-0.0110281\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$	2.00108	−	4.79538i	0.385108	−	0.922872i
$28$		0			0
$29$		−	7.48606i		−	1.39013i	−0.718948	−	0.695064i	$-0.755376\pi$
$29$		−	7.48606i		−	1.39013i	0.718948	−	0.695064i	$-0.244624\pi$
$30$		0			0
$31$		−	0.0758169i		−	0.0136171i	−0.999977	−	0.00680856i	$-0.997833\pi$
$31$		−	0.0758169i		−	0.0136171i	0.999977	−	0.00680856i	$-0.00216725\pi$
$32$		0			0
$33$	8.13584	+	1.07835i	1.41627	+	0.187716i
$34$		0			0
$35$	1.22074	−	2.34729i	0.206343	−	0.396765i
$36$		0			0
$37$	−2.54100			−0.417738			−0.208869	−	0.977944i	$-0.566978\pi$
$37$	−2.54100			−0.417738			−0.208869	+	0.977944i	$0.566978\pi$
$38$		0			0
$39$	−9.02372	−	1.19603i	−1.44495	−	0.191518i
$40$		0			0
$41$	4.82357			0.753315			0.376658	−	0.926353i	$-0.377073\pi$
$41$	4.82357			0.753315			0.376658	+	0.926353i	$0.377073\pi$
$42$		0			0
$43$	−1.97756			−0.301575			−0.150787	−	0.988566i	$-0.548181\pi$
$43$	−1.97756			−0.301575			−0.150787	+	0.988566i	$0.548181\pi$
$44$		0			0
$45$	−2.89641	−	0.781528i	−0.431772	−	0.116503i
$46$		0			0
$47$	9.28919			1.35497			0.677484	−	0.735538i	$-0.263070\pi$
$47$	9.28919			1.35497			0.677484	+	0.735538i	$0.263070\pi$
$48$		0			0
$49$	−4.01957	−	5.73089i	−0.574224	−	0.818698i
$50$		0			0
$51$	0.0984785	−	0.742993i	0.0137897	−	0.104040i
$52$		0			0
$53$		−	13.8305i		−	1.89976i	−0.312616	−	0.949880i	$-0.601205\pi$
$53$		−	13.8305i		−	1.89976i	0.312616	−	0.949880i	$-0.398795\pi$
$54$		0			0
$55$		−	4.73831i		−	0.638913i
$56$		0			0
$57$	10.8197	+	1.43407i	1.43310	+	0.189947i
$58$		0			0
$59$	−5.65528			−0.736254			−0.368127	−	0.929775i	$-0.620001\pi$
$59$	−5.65528			−0.736254			−0.368127	+	0.929775i	$0.620001\pi$
$60$		0			0
$61$			5.11428i			0.654816i	0.944883	+	0.327408i	$0.106175\pi$
$61$			5.11428i			0.654816i	−0.944883	+	0.327408i	$0.893825\pi$
$62$		0			0
$63$	−5.37026	+	5.84469i	−0.676589	+	0.736361i
$64$		0			0
$65$			5.25541i			0.651853i
$66$		0			0
$67$	−6.75379			−0.825106			−0.412553	−	0.910934i	$-0.635363\pi$
$67$	−6.75379			−0.825106			−0.412553	+	0.910934i	$0.635363\pi$
$68$		0			0
$69$	0.570475	+	0.0756124i	0.0686772	+	0.00910267i
$70$		0			0
$71$		−	9.35623i		−	1.11038i	−0.831723	−	0.555190i	$-0.812645\pi$
$71$		−	9.35623i		−	1.11038i	0.831723	−	0.555190i	$-0.187355\pi$
$72$		0			0
$73$			2.75129i			0.322014i	0.986953	+	0.161007i	$0.0514742\pi$
$73$			2.75129i			0.322014i	−0.986953	+	0.161007i	$0.948526\pi$
$74$		0			0
$75$	−0.227581	+	1.71703i	−0.0262788	+	0.198266i
$76$		0			0
$77$	−11.1222	−	5.78426i	−1.26749	−	0.659178i
$78$		0			0
$79$	−0.0508016			−0.00571563			−0.00285781	−	0.999996i	$-0.500910\pi$
$79$	−0.0508016			−0.00571563			−0.00285781	+	0.999996i	$0.500910\pi$
$80$		0			0
$81$	7.77843	+	4.52726i	0.864270	+	0.503028i
$82$		0			0
$83$	4.12411			0.452680			0.226340	−	0.974048i	$-0.427324\pi$
$83$	4.12411			0.452680			0.226340	+	0.974048i	$0.427324\pi$
$84$		0			0
$85$	−0.432719			−0.0469349
$86$		0			0
$87$	12.8538	+	1.70368i	1.37808	+	0.182654i
$88$		0			0
$89$	12.4092			1.31538			0.657688	−	0.753291i	$-0.271535\pi$
$89$	12.4092			1.31538			0.657688	+	0.753291i	$0.271535\pi$
$90$		0			0
$91$	12.3360	+	6.41551i	1.29316	+	0.672528i
$92$		0			0
$93$	0.130180	+	0.0172545i	0.0134991	+	0.00178920i
$94$		0			0
$95$		−	6.30136i		−	0.646506i
$96$		0			0
$97$			11.1116i			1.12822i	0.825701	+	0.564108i	$0.190780\pi$
$97$			11.1116i			1.12822i	−0.825701	+	0.564108i	$0.809220\pi$
$98$		0			0
$99$	−3.70312	+	13.7241i	−0.372178	+	1.37932i
$100$		0			0
$101$	17.8460			1.77575			0.887873	−	0.460090i	$-0.152183\pi$
$101$	17.8460			1.77575			0.887873	+	0.460090i	$0.152183\pi$
$102$		0			0
$103$		−	5.87340i		−	0.578723i	−0.957220	−	0.289362i	$-0.906557\pi$
$103$		−	5.87340i		−	0.578723i	0.957220	−	0.289362i	$-0.0934430\pi$
$104$		0			0
$105$	3.75256	+	2.63026i	0.366213	+	0.256687i
$106$		0			0
$107$			9.02242i			0.872230i	0.899891	+	0.436115i	$0.143646\pi$
$107$			9.02242i			0.872230i	−0.899891	+	0.436115i	$0.856354\pi$
$108$		0			0
$109$	−2.35605			−0.225668			−0.112834	−	0.993614i	$-0.535993\pi$
$109$	−2.35605			−0.225668			−0.112834	+	0.993614i	$0.535993\pi$
$110$		0			0
$111$	0.578283	−	4.36299i	0.0548882	−	0.414116i
$112$		0			0
$113$			18.8779i			1.77589i	0.459952	+	0.887944i	$0.347867\pi$
$113$			18.8779i			1.77589i	−0.459952	+	0.887944i	$0.652133\pi$
$114$		0			0
$115$		−	0.332245i		−	0.0309820i
$116$		0			0
$117$	4.10725	−	15.2218i	0.379715	−	1.40726i
$118$		0			0
$119$	−0.528239	+	1.01572i	−0.0484236	+	0.0931107i
$120$		0			0
$121$	−11.4516			−1.04105
$122$		0			0
$123$	−1.09775	+	8.28224i	−0.0989810	+	0.746784i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	19.3495			1.71699			0.858494	−	0.512824i	$-0.171401\pi$
$127$	19.3495			1.71699			0.858494	+	0.512824i	$0.171401\pi$
$128$		0			0
$129$	0.450054	−	3.39553i	0.0396250	−	0.298960i
$130$		0			0
$131$	−3.48806			−0.304753			−0.152377	−	0.988322i	$-0.548693\pi$
$131$	−3.48806			−0.304753			−0.152377	+	0.988322i	$0.548693\pi$
$132$		0			0
$133$	−14.7911	−	7.69235i	−1.28255	−	0.667012i
$134$		0			0
$135$	2.00108	−	4.79538i	0.172225	−	0.412721i
$136$		0			0
$137$		−	15.8902i		−	1.35759i	−0.734328	−	0.678795i	$-0.762503\pi$
$137$		−	15.8902i		−	1.35759i	0.734328	−	0.678795i	$-0.237497\pi$
$138$		0			0
$139$			2.39902i			0.203483i	0.994811	+	0.101741i	$0.0324414\pi$
$139$			2.39902i			0.203483i	−0.994811	+	0.101741i	$0.967559\pi$
$140$		0			0
$141$	−2.11404	+	15.9499i	−0.178034	+	1.34322i
$142$		0			0
$143$	24.9017			2.08239
$144$		0			0
$145$		−	7.48606i		−	0.621684i
$146$		0			0
$147$	10.7549	−	5.59749i	0.887050	−	0.461674i
$148$		0			0
$149$			8.55813i			0.701109i	0.936542	+	0.350555i	$0.114007\pi$
$149$			8.55813i			0.701109i	−0.936542	+	0.350555i	$0.885993\pi$
$150$		0			0
$151$	−10.1893			−0.829192			−0.414596	−	0.910006i	$-0.636077\pi$
$151$	−10.1893			−0.829192			−0.414596	+	0.910006i	$0.636077\pi$
$152$		0			0
$153$	1.25333	+	0.338182i	0.101326	+	0.0273404i
$154$		0			0
$155$		−	0.0758169i		−	0.00608976i
$156$		0			0
$157$		−	10.2559i		−	0.818514i	−0.912419	−	0.409257i	$-0.865788\pi$
$157$		−	10.2559i		−	0.818514i	0.912419	−	0.409257i	$-0.134212\pi$
$158$		0			0
$159$	23.7474	+	3.14754i	1.88329	+	0.249617i
$160$		0			0
$161$	−0.779875	−	0.405586i	−0.0614628	−	0.0319646i
$162$		0			0
$163$	22.2713			1.74442			0.872211	−	0.489129i	$-0.162685\pi$
$163$	22.2713			1.74442			0.872211	+	0.489129i	$0.162685\pi$
$164$		0			0
$165$	8.13584	+	1.07835i	0.633374	+	0.0839492i
$166$		0			0
$167$	−15.7525			−1.21896			−0.609482	−	0.792800i	$-0.708623\pi$
$167$	−15.7525			−1.21896			−0.609482	+	0.792800i	$0.708623\pi$
$168$		0			0
$169$	−14.6193			−1.12456
$170$		0			0
$171$	−4.92469	+	18.2514i	−0.376601	+	1.39572i
$172$		0			0
$173$	−12.4793			−0.948785			−0.474393	−	0.880313i	$-0.657332\pi$
$173$	−12.4793			−0.948785			−0.474393	+	0.880313i	$0.657332\pi$
$174$		0			0
$175$	1.22074	−	2.34729i	0.0922796	−	0.177439i
$176$		0			0
$177$	1.28703	−	9.71030i	0.0967392	−	0.729871i
$178$		0			0
$179$		−	5.33402i		−	0.398683i	−0.979930	−	0.199342i	$-0.936120\pi$
$179$		−	5.33402i		−	0.398683i	0.979930	−	0.199342i	$-0.0638803\pi$
$180$		0			0
$181$		−	3.47936i		−	0.258619i	−0.991604	−	0.129310i	$-0.958724\pi$
$181$		−	3.47936i		−	0.258619i	0.991604	−	0.129310i	$-0.0412761\pi$
$182$		0			0
$183$	−8.78139	−	1.16391i	−0.649139	−	0.0860387i
$184$		0			0
$185$	−2.54100			−0.186818
$186$		0			0
$187$			2.05036i			0.149937i
$188$		0			0
$189$	−8.81336	−	10.5511i	−0.641078	−	0.767476i
$190$		0			0
$191$		−	6.87673i		−	0.497583i	−0.968557	−	0.248791i	$-0.919967\pi$
$191$		−	6.87673i		−	0.497583i	0.968557	−	0.248791i	$-0.0800333\pi$
$192$		0			0
$193$	23.3219			1.67875			0.839375	−	0.543553i	$-0.182921\pi$
$193$	23.3219			1.67875			0.839375	+	0.543553i	$0.182921\pi$
$194$		0			0
$195$	−9.02372	−	1.19603i	−0.646202	−	0.0856495i
$196$		0			0
$197$		−	12.5906i		−	0.897041i	−0.893773	−	0.448520i	$-0.851951\pi$
$197$		−	12.5906i		−	0.897041i	0.893773	−	0.448520i	$-0.148049\pi$
$198$		0			0
$199$			4.35331i			0.308598i	0.988024	+	0.154299i	$0.0493119\pi$
$199$			4.35331i			0.308598i	−0.988024	+	0.154299i	$0.950688\pi$
$200$		0			0
$201$	1.53703	−	11.5965i	0.108414	−	0.817953i
$202$		0			0
$203$	−17.5720	−	9.13857i	−1.23331	−	0.641402i
$204$		0			0
$205$	4.82357			0.336893
$206$		0			0
$207$	−0.259658	+	0.962318i	−0.0180475	+	0.0668857i
$208$		0			0
$209$	−29.8578			−2.06531
$210$		0			0
$211$	−23.3789			−1.60947			−0.804735	−	0.593635i	$-0.797692\pi$
$211$	−23.3789			−1.60947			−0.804735	+	0.593635i	$0.797692\pi$
$212$		0			0
$213$	16.0650	+	2.12930i	1.10075	+	0.145897i
$214$		0			0
$215$	−1.97756			−0.134868
$216$		0			0
$217$	−0.177964	−	0.0925530i	−0.0120810	−	0.00628291i
$218$		0			0
$219$	−4.72406	−	0.626141i	−0.319222	−	0.0423107i
$220$		0			0
$221$		−	2.27411i		−	0.152973i
$222$		0			0
$223$			24.7236i			1.65561i	0.561014	+	0.827807i	$0.310411\pi$
$223$			24.7236i			1.65561i	−0.561014	+	0.827807i	$0.689589\pi$
$224$		0			0
$225$	−2.89641	−	0.781528i	−0.193094	−	0.0521018i
$226$		0			0
$227$	−8.70057			−0.577477			−0.288739	−	0.957408i	$-0.593236\pi$
$227$	−8.70057			−0.577477			−0.288739	+	0.957408i	$0.593236\pi$
$228$		0			0
$229$			21.8801i			1.44588i	0.690911	+	0.722940i	$0.257210\pi$
$229$			21.8801i			1.44588i	−0.690911	+	0.722940i	$0.742790\pi$
$230$		0			0
$231$	12.4630	−	17.7808i	0.820004	−	1.16989i
$232$		0			0
$233$		−	14.6761i		−	0.961460i	−0.876869	−	0.480730i	$-0.840372\pi$
$233$		−	14.6761i		−	0.961460i	0.876869	−	0.480730i	$-0.159628\pi$
$234$		0			0
$235$	9.28919			0.605960
$236$		0			0
$237$	0.0115615	−	0.0872281i	0.000750998	−	0.00566607i
$238$		0			0
$239$			27.6560i			1.78892i	0.447148	+	0.894460i	$0.352440\pi$
$239$			27.6560i			1.78892i	−0.447148	+	0.894460i	$0.647560\pi$
$240$		0			0
$241$		−	6.37849i		−	0.410875i	−0.978670	−	0.205437i	$-0.934138\pi$
$241$		−	6.37849i		−	0.410875i	0.978670	−	0.205437i	$-0.0658617\pi$
$242$		0			0
$243$	−9.54367	+	12.3255i	−0.612227	+	0.790682i
$244$		0			0
$245$	−4.01957	−	5.73089i	−0.256801	−	0.366133i
$246$		0			0
$247$	33.1162			2.10714
$248$		0			0
$249$	−0.938568	+	7.08124i	−0.0594793	+	0.448755i
$250$		0			0
$251$	−22.4413			−1.41648			−0.708241	−	0.705971i	$-0.750511\pi$
$251$	−22.4413			−1.41648			−0.708241	+	0.705971i	$0.750511\pi$
$252$		0			0
$253$	−1.57428			−0.0989740
$254$		0			0
$255$	0.0984785	−	0.742993i	0.00616696	−	0.0465280i
$256$		0			0
$257$	−4.52841			−0.282474			−0.141237	−	0.989976i	$-0.545108\pi$
$257$	−4.52841			−0.282474			−0.141237	+	0.989976i	$0.545108\pi$
$258$		0			0
$259$	−3.10191	+	5.96447i	−0.192743	+	0.370614i
$260$		0			0
$261$	−5.85057	+	21.6827i	−0.362141	+	1.34213i
$262$		0			0
$263$		−	20.6412i		−	1.27279i	−0.771363	−	0.636396i	$-0.780425\pi$
$263$		−	20.6412i		−	1.27279i	0.771363	−	0.636396i	$-0.219575\pi$
$264$		0			0
$265$		−	13.8305i		−	0.849598i
$266$		0			0
$267$	−2.82410	+	21.3071i	−0.172832	+	1.30397i
$268$		0			0
$269$	−16.3501			−0.996882			−0.498441	−	0.866924i	$-0.666094\pi$
$269$	−16.3501			−0.996882			−0.498441	+	0.866924i	$0.666094\pi$
$270$		0			0
$271$		−	15.6084i		−	0.948145i	−0.880486	−	0.474073i	$-0.842783\pi$
$271$		−	15.6084i		−	0.948145i	0.880486	−	0.474073i	$-0.157217\pi$
$272$		0			0
$273$	−13.8231	+	19.7213i	−0.836611	+	1.19359i
$274$		0			0
$275$		−	4.73831i		−	0.285731i
$276$		0			0
$277$	26.3323			1.58216			0.791078	−	0.611715i	$-0.209520\pi$
$277$	26.3323			1.58216			0.791078	+	0.611715i	$0.209520\pi$
$278$		0			0
$279$	−0.0592530	+	0.219597i	−0.00354738	+	0.0131469i
$280$		0			0
$281$			23.1514i			1.38110i	0.723286	+	0.690549i	$0.242631\pi$
$281$			23.1514i			1.38110i	−0.723286	+	0.690549i	$0.757369\pi$
$282$		0			0
$283$		−	5.89091i		−	0.350178i	−0.984553	−	0.175089i	$-0.943979\pi$
$283$		−	5.89091i		−	0.350178i	0.984553	−	0.175089i	$-0.0560214\pi$
$284$		0			0
$285$	10.8197	+	1.43407i	0.640901	+	0.0849469i
$286$		0			0
$287$	5.88835	−	11.3223i	0.347578	−	0.668336i
$288$		0			0
$289$	−16.8128			−0.988986
$290$		0			0
$291$	−19.0791	−	2.52879i	−1.11843	−	0.148240i
$292$		0			0
$293$	−20.0650			−1.17221			−0.586104	−	0.810236i	$-0.699339\pi$
$293$	−20.0650			−1.17221			−0.586104	+	0.810236i	$0.699339\pi$
$294$		0			0
$295$	−5.65528			−0.329263
$296$		0			0
$297$	−22.7220	−	9.48172i	−1.31846	−	0.550185i
$298$		0			0
$299$	1.74608			0.100978
$300$		0			0
$301$	−2.41409	+	4.64191i	−0.139146	+	0.267555i
$302$		0			0
$303$	−4.06141	+	30.6422i	−0.233322	+	1.76035i
$304$		0			0
$305$			5.11428i			0.292843i
$306$		0			0
$307$			20.7614i			1.18491i	0.805602	+	0.592457i	$0.201842\pi$
$307$			20.7614i			1.18491i	−0.805602	+	0.592457i	$0.798158\pi$
$308$		0			0
$309$	10.0848	+	1.33667i	0.573706	+	0.0760407i
$310$		0			0
$311$	1.08521			0.0615368			0.0307684	−	0.999527i	$-0.490205\pi$
$311$	1.08521			0.0615368			0.0307684	+	0.999527i	$0.490205\pi$
$312$		0			0
$313$			1.20176i			0.0679273i	0.999423	+	0.0339636i	$0.0108130\pi$
$313$			1.20176i			0.0679273i	−0.999423	+	0.0339636i	$0.989187\pi$
$314$		0			0
$315$	−5.37026	+	5.84469i	−0.302580	+	0.329311i
$316$		0			0
$317$		−	0.541371i		−	0.0304064i	−0.999884	−	0.0152032i	$-0.995160\pi$
$317$		−	0.541371i		−	0.0304064i	0.999884	−	0.0152032i	$-0.00483952\pi$
$318$		0			0
$319$	−35.4713			−1.98601
$320$		0			0
$321$	−15.4918	−	2.05333i	−0.864668	−	0.114606i
$322$		0			0
$323$			2.72672i			0.151719i
$324$		0			0
$325$			5.25541i			0.291518i
$326$		0			0
$327$	0.536191	−	4.04541i	0.0296514	−	0.223712i
$328$		0			0
$329$	11.3397	−	21.8044i	0.625179	−	1.20212i
$330$		0			0
$331$	0.575398			0.0316267			0.0158134	−	0.999875i	$-0.494966\pi$
$331$	0.575398			0.0316267			0.0158134	+	0.999875i	$0.494966\pi$
$332$		0			0
$333$	7.35979	+	1.98586i	0.403314	+	0.108825i
$334$		0			0
$335$	−6.75379			−0.368999
$336$		0			0
$337$	27.7122			1.50958			0.754789	−	0.655967i	$-0.227739\pi$
$337$	27.7122			1.50958			0.754789	+	0.655967i	$0.227739\pi$
$338$		0			0
$339$	−32.4141	−	4.29626i	−1.76049	−	0.233341i
$340$		0			0
$341$	−0.359244			−0.0194541
$342$		0			0
$343$	−18.3589	+	2.43915i	−0.991289	+	0.131702i
$344$		0			0
$345$	0.570475	+	0.0756124i	0.0307134	+	0.00407084i
$346$		0			0
$347$			17.4704i			0.937862i	0.883235	+	0.468931i	$0.155361\pi$
$347$			17.4704i			0.937862i	−0.883235	+	0.468931i	$0.844639\pi$
$348$		0			0
$349$		−	13.7673i		−	0.736947i	−0.929638	−	0.368474i	$-0.879880\pi$
$349$		−	13.7673i		−	0.736947i	0.929638	−	0.368474i	$-0.120120\pi$
$350$		0			0
$351$	25.2017	+	10.5165i	1.34517	+	0.561328i
$352$		0			0
$353$	−5.26362			−0.280154			−0.140077	−	0.990141i	$-0.544735\pi$
$353$	−5.26362			−0.280154			−0.140077	+	0.990141i	$0.544735\pi$
$354$		0			0
$355$		−	9.35623i		−	0.496577i
$356$		0			0
$357$	−1.62381	−	1.13816i	−0.0859409	−	0.0602379i
$358$		0			0
$359$		−	33.9683i		−	1.79278i	−0.443270	−	0.896388i	$-0.646182\pi$
$359$		−	33.9683i		−	1.79278i	0.443270	−	0.896388i	$-0.353818\pi$
$360$		0			0
$361$	−20.7072			−1.08985
$362$		0			0
$363$	2.60616	−	19.6627i	0.136788	−	1.03203i
$364$		0			0
$365$			2.75129i			0.144009i
$366$		0			0
$367$		−	31.2891i		−	1.63328i	−0.577150	−	0.816638i	$-0.695835\pi$
$367$		−	31.2891i		−	1.63328i	0.577150	−	0.816638i	$-0.304165\pi$
$368$		0			0
$369$	−13.9711	−	3.76976i	−0.727304	−	0.196246i
$370$		0			0
$371$	−32.4641	−	16.8834i	−1.68545	−	0.876545i
$372$		0			0
$373$	−22.3471			−1.15709			−0.578544	−	0.815651i	$-0.696379\pi$
$373$	−22.3471			−1.15709			−0.578544	+	0.815651i	$0.696379\pi$
$374$		0			0
$375$	−0.227581	+	1.71703i	−0.0117522	+	0.0886673i
$376$		0			0
$377$	39.3423			2.02623
$378$		0			0
$379$	−7.52493			−0.386530			−0.193265	−	0.981147i	$-0.561908\pi$
$379$	−7.52493			−0.386530			−0.193265	+	0.981147i	$0.561908\pi$
$380$		0			0
$381$	−4.40356	+	33.2237i	−0.225601	+	1.70210i
$382$		0			0
$383$	3.56768			0.182300			0.0911499	−	0.995837i	$-0.470946\pi$
$383$	3.56768			0.182300			0.0911499	+	0.995837i	$0.470946\pi$
$384$		0			0
$385$	−11.1222	−	5.78426i	−0.566840	−	0.294793i
$386$		0			0
$387$	5.72783	+	1.54552i	0.291162	+	0.0785630i
$388$		0			0
$389$		−	28.0479i		−	1.42209i	−0.703149	−	0.711043i	$-0.748223\pi$
$389$		−	28.0479i		−	1.42209i	0.703149	−	0.711043i	$-0.251777\pi$
$390$		0			0
$391$			0.143768i			0.00727068i
$392$		0			0
$393$	0.793815	−	5.98912i	0.0400427	−	0.302111i
$394$		0			0
$395$	−0.0508016			−0.00255611
$396$		0			0
$397$			18.5765i			0.932327i	0.884699	+	0.466164i	$0.154364\pi$
$397$			18.5765i			0.932327i	−0.884699	+	0.466164i	$0.845636\pi$
$398$		0			0
$399$	16.5742	−	23.6463i	0.829749	−	1.18379i
$400$		0			0
$401$		−	15.8632i		−	0.792172i	−0.918213	−	0.396086i	$-0.870368\pi$
$401$		−	15.8632i		−	0.792172i	0.918213	−	0.396086i	$-0.129632\pi$
$402$		0			0
$403$	0.398449			0.0198481
$404$		0			0
$405$	7.77843	+	4.52726i	0.386513	+	0.224961i
$406$		0			0
$407$			12.0400i			0.596803i
$408$		0			0
$409$			32.2559i			1.59495i	0.603350	+	0.797477i	$0.293832\pi$
$409$			32.2559i			1.59495i	−0.603350	+	0.797477i	$0.706168\pi$
$410$		0			0
$411$	27.2840	+	3.61630i	1.34582	+	0.178379i
$412$		0			0
$413$	−6.90365	+	13.2746i	−0.339706	+	0.653200i
$414$		0			0
$415$	4.12411			0.202445
$416$		0			0
$417$	−4.11921	−	0.545972i	−0.201718	−	0.0267363i
$418$		0			0
$419$	32.4477			1.58517			0.792587	−	0.609758i	$-0.208733\pi$
$419$	32.4477			1.58517			0.792587	+	0.609758i	$0.208733\pi$
$420$		0			0
$421$	20.5985			1.00391			0.501955	−	0.864894i	$-0.332614\pi$
$421$	20.5985			1.00391			0.501955	+	0.864894i	$0.332614\pi$
$422$		0			0
$423$	−26.9053	−	7.25976i	−1.30818	−	0.352981i
$424$		0			0
$425$	−0.432719			−0.0209899
$426$		0			0
$427$	12.0047	+	6.24322i	0.580948	+	0.302131i
$428$		0			0
$429$	−5.66716	+	42.7572i	−0.273613	+	2.06434i
$430$		0			0
$431$		−	4.64015i		−	0.223508i	−0.993736	−	0.111754i	$-0.964353\pi$
$431$		−	4.64015i		−	0.223508i	0.993736	−	0.111754i	$-0.0356469\pi$
$432$		0			0
$433$			14.2245i			0.683585i	0.939775	+	0.341792i	$0.111034\pi$
$433$			14.2245i			0.683585i	−0.939775	+	0.341792i	$0.888966\pi$
$434$		0			0
$435$	12.8538	+	1.70368i	0.616294	+	0.0816854i
$436$		0			0
$437$	−2.09359			−0.100150
$438$		0			0
$439$			33.3643i			1.59239i	0.605038	+	0.796196i	$0.293158\pi$
$439$			33.3643i			1.59239i	−0.605038	+	0.796196i	$0.706842\pi$
$440$		0			0
$441$	7.16348	+	19.7404i	0.341118	+	0.940020i
$442$		0			0
$443$			16.7418i			0.795425i	0.917510	+	0.397712i	$0.130196\pi$
$443$			16.7418i			0.795425i	−0.917510	+	0.397712i	$0.869804\pi$
$444$		0			0
$445$	12.4092			0.588254
$446$		0			0
$447$	−14.6946	−	1.94767i	−0.695031	−	0.0921214i
$448$		0			0
$449$			26.4107i			1.24640i	0.782063	+	0.623199i	$0.214167\pi$
$449$			26.4107i			1.24640i	−0.782063	+	0.623199i	$0.785833\pi$
$450$		0			0
$451$		−	22.8556i		−	1.07623i
$452$		0			0
$453$	2.31888	−	17.4953i	0.108951	−	0.822003i
$454$		0			0
$455$	12.3360	+	6.41551i	0.578320	+	0.300764i
$456$		0			0
$457$	26.6004			1.24431			0.622157	−	0.782893i	$-0.286257\pi$
$457$	26.6004			1.24431			0.622157	+	0.782893i	$0.286257\pi$
$458$		0			0
$459$	−0.865904	+	2.07505i	−0.0404169	+	0.0968551i
$460$		0			0
$461$	−5.10914			−0.237956			−0.118978	−	0.992897i	$-0.537962\pi$
$461$	−5.10914			−0.237956			−0.118978	+	0.992897i	$0.537962\pi$
$462$		0			0
$463$	−18.9156			−0.879082			−0.439541	−	0.898222i	$-0.644859\pi$
$463$	−18.9156			−0.879082			−0.439541	+	0.898222i	$0.644859\pi$
$464$		0			0
$465$	0.130180	+	0.0172545i	0.00603696	+	0.000800156i
$466$		0			0
$467$	−33.1205			−1.53263			−0.766316	−	0.642464i	$-0.777912\pi$
$467$	−33.1205			−1.53263			−0.766316	+	0.642464i	$0.777912\pi$
$468$		0			0
$469$	−8.24465	+	15.8531i	−0.380702	+	0.732029i
$470$		0			0
$471$	17.6098	+	2.33406i	0.811417	+	0.107548i
$472$		0			0
$473$			9.37028i			0.430846i
$474$		0			0
$475$		−	6.30136i		−	0.289126i
$476$		0			0
$477$	−10.8089	+	40.0587i	−0.494905	+	1.83416i
$478$		0			0
$479$	−2.12327			−0.0970148			−0.0485074	−	0.998823i	$-0.515446\pi$
$479$	−2.12327			−0.0970148			−0.0485074	+	0.998823i	$0.515446\pi$
$480$		0			0
$481$		−	13.3540i		−	0.608890i
$482$		0			0
$483$	0.873889	−	1.24677i	0.0397633	−	0.0567300i
$484$		0			0
$485$			11.1116i			0.504553i
$486$		0			0
$487$	2.19092			0.0992800			0.0496400	−	0.998767i	$-0.484193\pi$
$487$	2.19092			0.0992800			0.0496400	+	0.998767i	$0.484193\pi$
$488$		0			0
$489$	−5.06852	+	38.2406i	−0.229206	+	1.72930i
$490$		0			0
$491$			29.2850i			1.32161i	0.750557	+	0.660806i	$0.229785\pi$
$491$			29.2850i			1.32161i	−0.750557	+	0.660806i	$0.770215\pi$
$492$		0			0
$493$			3.23936i			0.145893i
$494$		0			0
$495$	−3.70312	+	13.7241i	−0.166443	+	0.616853i
$496$		0			0
$497$	−21.9618	−	11.4216i	−0.985122	−	0.512327i
$498$		0			0
$499$	−13.4228			−0.600889			−0.300444	−	0.953799i	$-0.597135\pi$
$499$	−13.4228			−0.600889			−0.300444	+	0.953799i	$0.597135\pi$
$500$		0			0
$501$	3.58496	−	27.0476i	0.160164	−	1.20840i
$502$		0			0
$503$	26.2934			1.17236			0.586182	−	0.810180i	$-0.300631\pi$
$503$	26.2934			1.17236			0.586182	+	0.810180i	$0.300631\pi$
$504$		0			0
$505$	17.8460			0.794137
$506$		0			0
$507$	3.32708	−	25.1019i	0.147761	−	1.11481i
$508$		0			0
$509$	−1.49327			−0.0661881			−0.0330940	−	0.999452i	$-0.510536\pi$
$509$	−1.49327			−0.0661881			−0.0330940	+	0.999452i	$0.510536\pi$
$510$		0			0
$511$	6.45808	+	3.35862i	0.285689	+	0.148577i
$512$		0			0
$513$	−30.2174	−	12.6095i	−1.33413	−	0.556724i
$514$		0			0
$515$		−	5.87340i		−	0.258813i
$516$		0			0
$517$		−	44.0150i		−	1.93578i
$518$		0			0
$519$	2.84005	−	21.4274i	0.124664	−	0.940559i
$520$		0			0
$521$	11.2497			0.492858			0.246429	−	0.969161i	$-0.420743\pi$
$521$	11.2497			0.492858			0.246429	+	0.969161i	$0.420743\pi$
$522$		0			0
$523$		−	35.8696i		−	1.56847i	−0.620466	−	0.784233i	$-0.713056\pi$
$523$		−	35.8696i		−	1.56847i	0.620466	−	0.784233i	$-0.286944\pi$
$524$		0			0
$525$	3.75256	+	2.63026i	0.163775	+	0.114794i
$526$		0			0
$527$			0.0328074i			0.00142911i
$528$		0			0
$529$	22.8896			0.995201
$530$		0			0
$531$	16.3800	+	4.41976i	0.710832	+	0.191801i
$532$		0			0
$533$			25.3498i			1.09802i
$534$		0			0
$535$			9.02242i			0.390073i
$536$		0			0
$537$	9.15869	+	1.21392i	0.395227	+	0.0523845i
$538$		0			0
$539$	−27.1547	+	19.0459i	−1.16964	+	0.820367i
$540$		0			0
$541$	22.5663			0.970201			0.485100	−	0.874458i	$-0.338783\pi$
$541$	22.5663			0.970201			0.485100	+	0.874458i	$0.338783\pi$
$542$		0			0
$543$	5.97419	+	0.791836i	0.256377	+	0.0339809i
$544$		0			0
$545$	−2.35605			−0.100922
$546$		0			0
$547$	13.4861			0.576626			0.288313	−	0.957536i	$-0.406906\pi$
$547$	13.4861			0.576626			0.288313	+	0.957536i	$0.406906\pi$
$548$		0			0
$549$	3.99695	−	14.8131i	0.170586	−	0.632206i
$550$		0			0
$551$	−47.1724			−2.00961
$552$		0			0
$553$	−0.0620158	+	0.119246i	−0.00263718	+	0.00507087i
$554$		0			0
$555$	0.578283	−	4.36299i	0.0245467	−	0.185198i
$556$		0			0
$557$		−	16.8778i		−	0.715134i	−0.933888	−	0.357567i	$-0.883606\pi$
$557$		−	16.8778i		−	0.715134i	0.933888	−	0.357567i	$-0.116394\pi$
$558$		0			0
$559$		−	10.3929i		−	0.439572i
$560$		0			0
$561$	−3.52053	−	0.466621i	−0.148637	−	0.0197008i
$562$		0			0
$563$	−16.9449			−0.714143			−0.357072	−	0.934077i	$-0.616225\pi$
$563$	−16.9449			−0.714143			−0.357072	+	0.934077i	$0.616225\pi$
$564$		0			0
$565$			18.8779i			0.794201i
$566$		0			0
$567$	20.1223	−	12.7316i	0.845056	−	0.534678i
$568$		0			0
$569$			7.05526i			0.295772i	0.989004	+	0.147886i	$0.0472469\pi$
$569$			7.05526i			0.295772i	−0.989004	+	0.147886i	$0.952753\pi$
$570$		0			0
$571$	−39.5264			−1.65413			−0.827064	−	0.562108i	$-0.809991\pi$
$571$	−39.5264			−1.65413			−0.827064	+	0.562108i	$0.809991\pi$
$572$		0			0
$573$	11.8076	+	1.56501i	0.493269	+	0.0653793i
$574$		0			0
$575$		−	0.332245i		−	0.0138556i
$576$		0			0
$577$			15.0514i			0.626599i	0.949654	+	0.313299i	$0.101434\pi$
$577$			15.0514i			0.626599i	−0.949654	+	0.313299i	$0.898566\pi$
$578$		0			0
$579$	−5.30762	+	40.0446i	−0.220577	+	1.66420i
$580$		0			0
$581$	5.03448	−	9.68049i	0.208866	−	0.401615i
$582$		0			0
$583$	−65.5330			−2.71410
$584$		0			0
$585$	4.10725	−	15.2218i	0.169814	−	0.629346i
$586$		0			0
$587$	−10.9578			−0.452278			−0.226139	−	0.974095i	$-0.572610\pi$
$587$	−10.9578			−0.452278			−0.226139	+	0.974095i	$0.572610\pi$
$588$		0			0
$589$	−0.477750			−0.0196853
$590$		0			0
$591$	21.6184	+	2.86537i	0.889264	+	0.117866i
$592$		0			0
$593$	−29.9860			−1.23138			−0.615688	−	0.787990i	$-0.711122\pi$
$593$	−29.9860			−1.23138			−0.615688	+	0.787990i	$0.711122\pi$
$594$		0			0
$595$	−0.528239	+	1.01572i	−0.0216557	+	0.0416404i
$596$		0			0
$597$	−7.47478	−	0.990729i	−0.305922	−	0.0405478i
$598$		0			0
$599$			1.20400i			0.0491942i	0.999697	+	0.0245971i	$0.00783029\pi$
$599$			1.20400i			0.0491942i	−0.999697	+	0.0245971i	$0.992170\pi$
$600$		0			0
$601$		−	43.3173i		−	1.76695i	−0.468479	−	0.883475i	$-0.655198\pi$
$601$		−	43.3173i		−	1.76695i	0.468479	−	0.883475i	$-0.344802\pi$
$602$		0			0
$603$	19.5618	+	5.27827i	0.796616	+	0.214948i
$604$		0			0
$605$	−11.4516			−0.465572
$606$		0			0
$607$		−	27.3272i		−	1.10918i	−0.832125	−	0.554588i	$-0.812876\pi$
$607$		−	27.3272i		−	1.10918i	0.832125	−	0.554588i	$-0.187124\pi$
$608$		0			0
$609$	19.6903	−	28.0919i	0.797890	−	1.13834i
$610$		0			0
$611$			48.8185i			1.97498i
$612$		0			0
$613$	−0.898054			−0.0362721			−0.0181360	−	0.999836i	$-0.505773\pi$
$613$	−0.898054			−0.0362721			−0.0181360	+	0.999836i	$0.505773\pi$
$614$		0			0
$615$	−1.09775	+	8.28224i	−0.0442656	+	0.333972i
$616$		0			0
$617$			19.6207i			0.789900i	0.918703	+	0.394950i	$0.129238\pi$
$617$			19.6207i			0.789900i	−0.918703	+	0.394950i	$0.870762\pi$
$618$		0			0
$619$			39.2835i			1.57894i	0.613792	+	0.789468i	$0.289643\pi$
$619$			39.2835i			1.57894i	−0.613792	+	0.789468i	$0.710357\pi$
$620$		0			0
$621$	−1.59324	−	0.664847i	−0.0639345	−	0.0266794i
$622$		0			0
$623$	15.1485	−	29.1281i	0.606912	−	1.16699i
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	6.79506	−	51.2669i	0.271369	−	2.04740i
$628$		0			0
$629$	1.09954			0.0438415
$630$		0			0
$631$	5.66857			0.225662			0.112831	−	0.993614i	$-0.464008\pi$
$631$	5.66857			0.225662			0.112831	+	0.993614i	$0.464008\pi$
$632$		0			0
$633$	5.32058	−	40.1424i	0.211474	−	1.59552i
$634$		0			0
$635$	19.3495			0.767860
$636$		0			0
$637$	30.1182	−	21.1245i	1.19333	−	0.836982i
$638$		0			0
$639$	−7.31216	+	27.0995i	−0.289264	+	1.07204i
$640$		0			0
$641$			16.3234i			0.644737i	0.946614	+	0.322369i	$0.104479\pi$
$641$			16.3234i			0.644737i	−0.946614	+	0.322369i	$0.895521\pi$
$642$		0			0
$643$			21.2389i			0.837580i	0.908083	+	0.418790i	$0.137546\pi$
$643$			21.2389i			0.837580i	−0.908083	+	0.418790i	$0.862454\pi$
$644$		0			0
$645$	0.450054	−	3.39553i	0.0177209	−	0.133699i
$646$		0			0
$647$	47.2897			1.85915			0.929575	−	0.368634i	$-0.120174\pi$
$647$	47.2897			1.85915			0.929575	+	0.368634i	$0.120174\pi$
$648$		0			0
$649$			26.7964i			1.05185i
$650$		0			0
$651$	0.199418	−	0.284508i	0.00781581	−	0.0111507i
$652$		0			0
$653$			16.5690i			0.648396i	0.945989	+	0.324198i	$0.105094\pi$
$653$			16.5690i			0.648396i	−0.945989	+	0.324198i	$0.894906\pi$
$654$		0			0
$655$	−3.48806			−0.136290
$656$		0			0
$657$	2.15021	−	7.96888i	0.0838877	−	0.310895i
$658$		0			0
$659$			25.8101i			1.00542i	0.864456	+	0.502709i	$0.167663\pi$
$659$			25.8101i			1.00542i	−0.864456	+	0.502709i	$0.832337\pi$
$660$		0			0
$661$		−	29.6991i		−	1.15516i	−0.816333	−	0.577581i	$-0.803997\pi$
$661$		−	29.6991i		−	1.15516i	0.816333	−	0.577581i	$-0.196003\pi$
$662$		0			0
$663$	3.90473	+	0.517545i	0.151647	+	0.0200998i
$664$		0			0
$665$	−14.7911	−	7.69235i	−0.573576	−	0.298297i
$666$		0			0
$667$	−2.48720			−0.0963049
$668$		0			0
$669$	−42.4512	−	5.62661i	−1.64126	−	0.217537i
$670$		0			0
$671$	24.2330			0.935505
$672$		0			0
$673$	−3.04033			−0.117196			−0.0585980	−	0.998282i	$-0.518663\pi$
$673$	−3.04033			−0.117196			−0.0585980	+	0.998282i	$0.518663\pi$
$674$		0			0
$675$	2.00108	−	4.79538i	0.0770215	−	0.184574i
$676$		0			0
$677$	−4.42120			−0.169920			−0.0849602	−	0.996384i	$-0.527076\pi$
$677$	−4.42120			−0.169920			−0.0849602	+	0.996384i	$0.527076\pi$
$678$		0			0
$679$	26.0823	+	13.5645i	1.00095	+	0.520556i
$680$		0			0
$681$	1.98008	−	14.9392i	0.0758769	−	0.572471i
$682$		0			0
$683$		−	13.0877i		−	0.500786i	−0.968144	−	0.250393i	$-0.919440\pi$
$683$		−	13.0877i		−	0.500786i	0.968144	−	0.250393i	$-0.0805598\pi$
$684$		0			0
$685$		−	15.8902i		−	0.607133i
$686$		0			0
$687$	−37.5689	−	4.97949i	−1.43334	−	0.189980i
$688$		0			0
$689$	72.6847			2.76907
$690$		0			0
$691$		−	8.60750i		−	0.327445i	−0.986506	−	0.163722i	$-0.947650\pi$
$691$		−	8.60750i		−	0.327445i	0.986506	−	0.163722i	$-0.0523501\pi$
$692$		0			0
$693$	27.6939	+	25.4459i	1.05201	+	0.966611i
$694$		0			0
$695$			2.39902i			0.0910002i
$696$		0			0
$697$	−2.08725			−0.0790603
$698$		0			0
$699$	25.1993	+	3.33999i	0.953125	+	0.126330i
$700$		0			0
$701$		−	23.5481i		−	0.889398i	−0.895680	−	0.444699i	$-0.853311\pi$
$701$		−	23.5481i		−	0.889398i	0.895680	−	0.444699i	$-0.146689\pi$
$702$		0			0
$703$			16.0118i			0.603895i
$704$		0			0
$705$	−2.11404	+	15.9499i	−0.0796193	+	0.600706i
$706$		0			0
$707$	21.7854	−	41.8898i	0.819325	−	1.57543i
$708$		0			0
$709$	16.6983			0.627119			0.313560	−	0.949568i	$-0.398478\pi$
$709$	16.6983			0.627119			0.313560	+	0.949568i	$0.398478\pi$
$710$		0			0
$711$	0.147142	+	0.0397029i	0.00551827	+	0.00148897i
$712$		0			0
$713$	−0.0251897			−0.000943363
$714$		0			0
$715$	24.9017			0.931273
$716$		0			0
$717$	−47.4864	−	6.29398i	−1.77341	−	0.235053i
$718$		0			0
$719$	−7.24703			−0.270269			−0.135134	−	0.990827i	$-0.543147\pi$
$719$	−7.24703			−0.270269			−0.135134	+	0.990827i	$0.543147\pi$
$720$		0			0
$721$	−13.7866	−	7.16992i	−0.513440	−	0.267022i
$722$		0			0
$723$	10.9521	+	1.45162i	0.407312	+	0.0539864i
$724$		0			0
$725$		−	7.48606i		−	0.278025i
$726$		0			0
$727$			21.3688i			0.792525i	0.918137	+	0.396262i	$0.129693\pi$
$727$			21.3688i			0.792525i	−0.918137	+	0.396262i	$0.870307\pi$
$728$		0			0
$729$	−18.9914	−	19.1919i	−0.703384	−	0.710810i
$730$		0			0
$731$	0.855726			0.0316502
$732$		0			0
$733$		−	23.2849i		−	0.860047i	−0.902818	−	0.430024i	$-0.858505\pi$
$733$		−	23.2849i		−	0.860047i	0.902818	−	0.430024i	$-0.141495\pi$
$734$		0			0
$735$	10.7549	−	5.59749i	0.396701	−	0.206467i
$736$		0			0
$737$			32.0015i			1.17879i
$738$		0			0
$739$	25.3282			0.931711			0.465856	−	0.884861i	$-0.345747\pi$
$739$	25.3282			0.931711			0.465856	+	0.884861i	$0.345747\pi$
$740$		0			0
$741$	−7.53662	+	56.8617i	−0.276865	+	2.08887i
$742$		0			0
$743$			18.9806i			0.696332i	0.937433	+	0.348166i	$0.113195\pi$
$743$			18.9806i			0.696332i	−0.937433	+	0.348166i	$0.886805\pi$
$744$		0			0
$745$			8.55813i			0.313546i
$746$		0			0
$747$	−11.9451	−	3.22311i	−0.437049	−	0.117927i
$748$		0			0
$749$	21.1783	+	11.0141i	0.773837	+	0.402445i
$750$		0			0
$751$	31.5844			1.15253			0.576265	−	0.817263i	$-0.304510\pi$
$751$	31.5844			1.15253			0.576265	+	0.817263i	$0.304510\pi$
$752$		0			0
$753$	5.10721	−	38.5325i	0.186117	−	1.40420i
$754$		0			0
$755$	−10.1893			−0.370826
$756$		0			0
$757$	−36.9363			−1.34247			−0.671237	−	0.741243i	$-0.734237\pi$
$757$	−36.9363			−1.34247			−0.671237	+	0.741243i	$0.734237\pi$
$758$		0			0
$759$	0.358275	−	2.70309i	0.0130046	−	0.0981159i
$760$		0			0
$761$	−0.0965566			−0.00350017			−0.00175009	−	0.999998i	$-0.500557\pi$
$761$	−0.0965566			−0.00350017			−0.00175009	+	0.999998i	$0.500557\pi$
$762$		0			0
$763$	−2.87613	+	5.53033i	−0.104123	+	0.200211i
$764$		0			0
$765$	1.25333	+	0.338182i	0.0453143	+	0.0122270i
$766$		0			0
$767$		−	29.7208i		−	1.07316i
$768$		0			0
$769$		−	22.4069i		−	0.808015i	−0.914756	−	0.404007i	$-0.867617\pi$
$769$		−	22.4069i		−	0.808015i	0.914756	−	0.404007i	$-0.132383\pi$
$770$		0			0
$771$	1.03058	−	7.77543i	0.0371153	−	0.280025i
$772$		0			0
$773$	31.9936			1.15073			0.575365	−	0.817897i	$-0.304860\pi$
$773$	31.9936			1.15073			0.575365	+	0.817897i	$0.304860\pi$
$774$		0			0
$775$		−	0.0758169i		−	0.00272342i
$776$		0			0
$777$	−9.53527	−	6.68349i	−0.342076	−	0.239769i
$778$		0			0
$779$		−	30.3951i		−	1.08902i
$780$		0			0
$781$	−44.3327			−1.58635
$782$		0			0
$783$	−35.8985	−	14.9802i	−1.28291	−	0.535349i
$784$		0			0
$785$		−	10.2559i		−	0.366050i
$786$		0			0
$787$			36.1665i			1.28920i	0.764522	+	0.644598i	$0.222975\pi$
$787$			36.1665i			1.28920i	−0.764522	+	0.644598i	$0.777025\pi$
$788$		0			0
$789$	35.4417	+	4.69754i	1.26176	+	0.167237i
$790$		0			0
$791$	44.3121	+	23.0451i	1.57556	+	0.819391i
$792$		0			0
$793$	−26.8776			−0.954452
$794$		0			0
$795$	23.7474	+	3.14754i	0.842232	+	0.111632i
$796$		0			0
$797$	40.7592			1.44376			0.721882	−	0.692016i	$-0.243277\pi$
$797$	40.7592			1.44376			0.721882	+	0.692016i	$0.243277\pi$
$798$		0			0
$799$	−4.01961			−0.142203
$800$		0			0
$801$	−35.9423	−	9.69816i	−1.26996	−	0.342668i
$802$		0			0
$803$	13.0365			0.460047
$804$		0			0
$805$	−0.779875	−	0.405586i	−0.0274870	−	0.0142950i
$806$		0			0
$807$	3.72096	−	28.0737i	0.130984	−	0.988239i
$808$		0			0
$809$			25.3706i			0.891984i	0.895037	+	0.445992i	$0.147149\pi$
$809$			25.3706i			0.891984i	−0.895037	+	0.445992i	$0.852851\pi$
$810$		0			0
$811$		−	8.47154i		−	0.297476i	−0.988877	−	0.148738i	$-0.952479\pi$
$811$		−	8.47154i		−	0.297476i	0.988877	−	0.148738i	$-0.0475211\pi$
$812$		0			0
$813$	26.8002	+	3.55218i	0.939925	+	0.124580i
$814$		0			0
$815$	22.2713			0.780130
$816$		0			0
$817$			12.4613i			0.435966i
$818$		0			0
$819$	−30.7162	−	28.2229i	−1.07331	−	0.986188i
$820$		0			0
$821$		−	50.2670i		−	1.75433i	−0.480188	−	0.877166i	$-0.659431\pi$
$821$		−	50.2670i		−	1.75433i	0.480188	−	0.877166i	$-0.340569\pi$
$822$		0			0
$823$	29.2698			1.02028			0.510140	−	0.860091i	$-0.329593\pi$
$823$	29.2698			1.02028			0.510140	+	0.860091i	$0.329593\pi$
$824$		0			0
$825$	8.13584	+	1.07835i	0.283254	+	0.0375432i
$826$		0			0
$827$		−	19.0571i		−	0.662681i	−0.943511	−	0.331340i	$-0.892499\pi$
$827$		−	19.0571i		−	0.662681i	0.943511	−	0.331340i	$-0.107501\pi$
$828$		0			0
$829$		−	4.81787i		−	0.167331i	−0.996494	−	0.0836657i	$-0.973337\pi$
$829$		−	4.81787i		−	0.167331i	0.996494	−	0.0836657i	$-0.0266628\pi$
$830$		0			0
$831$	−5.99273	+	45.2135i	−0.207885	+	1.56844i
$832$		0			0
$833$	1.73934	+	2.47986i	0.0602646	+	0.0859222i
$834$		0			0
$835$	−15.7525			−0.545138
$836$		0			0
$837$	−0.363571	−	0.151715i	−0.0125668	−	0.00524405i
$838$		0			0
$839$	11.8273			0.408322			0.204161	−	0.978937i	$-0.434553\pi$
$839$	11.8273			0.408322			0.204161	+	0.978937i	$0.434553\pi$
$840$		0			0
$841$	−27.0412			−0.932453
$842$		0			0
$843$	−39.7518	−	5.26881i	−1.36912	−	0.181468i
$844$		0			0
$845$	−14.6193			−0.502920
$846$		0			0
$847$	−13.9794	+	26.8802i	−0.480339	+	0.923614i
$848$		0			0
$849$	10.1149	+	1.34066i	0.347143	+	0.0460113i
$850$		0			0
$851$			0.844234i			0.0289400i
$852$		0			0
$853$			9.27659i			0.317624i	0.987309	+	0.158812i	$0.0507664\pi$
$853$			9.27659i			0.317624i	−0.987309	+	0.158812i	$0.949234\pi$
$854$		0			0
$855$	−4.92469	+	18.2514i	−0.168421	+	0.624183i
$856$		0			0
$857$	5.52188			0.188624			0.0943120	−	0.995543i	$-0.469935\pi$
$857$	5.52188			0.188624			0.0943120	+	0.995543i	$0.469935\pi$
$858$		0			0
$859$			23.9698i			0.817839i	0.912570	+	0.408920i	$0.134094\pi$
$859$			23.9698i			0.817839i	−0.912570	+	0.408920i	$0.865906\pi$
$860$		0			0
$861$	18.1008	+	12.6872i	0.616872	+	0.432380i
$862$		0			0
$863$			2.74328i			0.0933823i	0.998909	+	0.0466912i	$0.0148677\pi$
$863$			2.74328i			0.0933823i	−0.998909	+	0.0466912i	$0.985132\pi$
$864$		0			0
$865$	−12.4793			−0.424310
$866$		0			0
$867$	3.82626	−	28.8681i	0.129947	−	0.980411i
$868$		0			0
$869$			0.240714i			0.00816565i
$870$		0			0
$871$		−	35.4939i		−	1.20267i
$872$		0			0
$873$	8.68405	−	32.1839i	0.293911	−	1.08926i
$874$		0			0
$875$	1.22074	−	2.34729i	0.0412687	−	0.0793530i
$876$		0			0
$877$	21.7538			0.734575			0.367287	−	0.930108i	$-0.380287\pi$
$877$	21.7538			0.734575			0.367287	+	0.930108i	$0.380287\pi$
$878$		0			0
$879$	4.56640	−	34.4523i	0.154021	−	1.16205i
$880$		0			0
$881$	13.6690			0.460520			0.230260	−	0.973129i	$-0.426042\pi$
$881$	13.6690			0.460520			0.230260	+	0.973129i	$0.426042\pi$
$882$		0			0
$883$	36.1851			1.21772			0.608862	−	0.793276i	$-0.291626\pi$
$883$	36.1851			1.21772			0.608862	+	0.793276i	$0.291626\pi$
$884$		0			0
$885$	1.28703	−	9.71030i	0.0432631	−	0.326408i
$886$		0			0
$887$	−18.1459			−0.609280			−0.304640	−	0.952468i	$-0.598536\pi$
$887$	−18.1459			−0.609280			−0.304640	+	0.952468i	$0.598536\pi$
$888$		0			0
$889$	23.6207	−	45.4189i	0.792214	−	1.52330i
$890$		0			0
$891$	21.4515	−	36.8566i	0.718653	−	1.23474i
$892$		0			0
$893$		−	58.5345i		−	1.95878i
$894$		0			0
$895$		−	5.33402i		−	0.178296i
$896$		0			0
$897$	−0.397374	+	2.99808i	−0.0132679	+	0.100103i
$898$		0			0
$899$	−0.567570			−0.0189295
$900$		0			0
$901$			5.98470i			0.199379i
$902$		0			0
$903$	−7.42091	−	5.20149i	−0.246952	−	0.173095i
$904$		0			0
$905$		−	3.47936i		−	0.115658i
$906$		0			0
$907$	−17.4826			−0.580501			−0.290251	−	0.956951i	$-0.593739\pi$
$907$	−17.4826			−0.580501			−0.290251	+	0.956951i	$0.593739\pi$
$908$		0			0
$909$	−51.6895	−	13.9472i	−1.71443	−	0.462598i
$910$		0			0
$911$			16.7926i			0.556363i	0.960528	+	0.278182i	$0.0897317\pi$
$911$			16.7926i			0.556363i	−0.960528	+	0.278182i	$0.910268\pi$
$912$		0			0
$913$		−	19.5413i		−	0.646723i
$914$		0			0
$915$	−8.78139	−	1.16391i	−0.290304	−	0.0384777i
$916$		0			0
$917$	−4.25803	+	8.18750i	−0.140613	+	0.270375i
$918$		0			0
$919$	8.76074			0.288990			0.144495	−	0.989506i	$-0.453844\pi$
$919$	8.76074			0.288990			0.144495	+	0.989506i	$0.453844\pi$
$920$		0			0
$921$	−35.6480	−	4.72489i	−1.17464	−	0.155690i
$922$		0			0
$923$	49.1708			1.61848
$924$		0			0
$925$	−2.54100			−0.0835476
$926$		0			0
$927$	−4.59023	+	17.0118i	−0.150763	+	0.558741i
$928$		0			0
$929$	−53.4297			−1.75297			−0.876486	−	0.481428i	$-0.840118\pi$
$929$	−53.4297			−1.75297			−0.876486	+	0.481428i	$0.840118\pi$
$930$		0			0
$931$	−36.1124	+	25.3288i	−1.18354	+	0.830116i
$932$		0			0
$933$	−0.246974	+	1.86335i	−0.00808556	+	0.0610033i
$934$		0			0
$935$			2.05036i			0.0670538i
$936$		0			0
$937$			35.7222i			1.16699i	0.812116	+	0.583496i	$0.198316\pi$
$937$			35.7222i			1.16699i	−0.812116	+	0.583496i	$0.801684\pi$
$938$		0			0
$939$	−2.06346	−	0.273496i	−0.0673384	−	0.00892522i
$940$		0			0
$941$	−27.1081			−0.883698			−0.441849	−	0.897089i	$-0.645677\pi$
$941$	−27.1081			−0.883698			−0.441849	+	0.897089i	$0.645677\pi$
$942$		0			0
$943$		−	1.60261i		−	0.0521880i
$944$		0			0
$945$	−8.81336	−	10.5511i	−0.286699	−	0.343226i
$946$		0			0
$947$		−	1.60157i		−	0.0520440i	−0.999661	−	0.0260220i	$-0.991716\pi$
$947$		−	1.60157i		−	0.0520440i	0.999661	−	0.0260220i	$-0.00828400\pi$
$948$		0			0
$949$	−14.4592			−0.469364
$950$		0			0
$951$	0.929553	+	0.123206i	0.0301428	+	0.00399522i
$952$		0			0
$953$			8.86213i			0.287072i	0.989645	+	0.143536i	$0.0458474\pi$
$953$			8.86213i			0.287072i	−0.989645	+	0.143536i	$0.954153\pi$
$954$		0			0
$955$		−	6.87673i		−	0.222526i
$956$		0			0
$957$	8.07258	−	60.9054i	0.260949	−	1.96879i
$958$		0			0
$959$	−37.2989	−	19.3978i	−1.20444	−	0.626389i
$960$		0			0
$961$	30.9943			0.999815
$962$		0			0
$963$	7.05127	−	26.1327i	0.227224	−	0.842113i
$964$		0			0
$965$	23.3219			0.750760
$966$		0			0
$967$	−5.63660			−0.181261			−0.0906304	−	0.995885i	$-0.528888\pi$
$967$	−5.63660			−0.181261			−0.0906304	+	0.995885i	$0.528888\pi$
$968$		0			0
$969$	−4.68187	−	0.620549i	−0.150403	−	0.0199349i
$970$		0			0
$971$	46.6619			1.49745			0.748725	−	0.662880i	$-0.230666\pi$
$971$	46.6619			1.49745			0.748725	+	0.662880i	$0.230666\pi$
$972$		0			0
$973$	5.63121	+	2.92860i	0.180528	+	0.0938865i
$974$		0			0
$975$	−9.02372	−	1.19603i	−0.288990	−	0.0383036i
$976$		0			0
$977$			57.7582i			1.84785i	0.382577	+	0.923924i	$0.375037\pi$
$977$			57.7582i			1.84785i	−0.382577	+	0.923924i	$0.624963\pi$
$978$		0			0
$979$		−	58.7988i		−	1.87922i
$980$		0			0
$981$	6.82409	+	1.84132i	0.217876	+	0.0587887i
$982$		0			0
$983$	0.633061			0.0201915			0.0100958	−	0.999949i	$-0.496786\pi$
$983$	0.633061			0.0201915			0.0100958	+	0.999949i	$0.496786\pi$
$984$		0			0
$985$		−	12.5906i		−	0.401169i
$986$		0			0
$987$	34.8583	+	24.4330i	1.10955	+	0.777710i
$988$		0			0
$989$			0.657033i			0.0208924i
$990$		0			0
$991$	33.5075			1.06440			0.532200	−	0.846619i	$-0.321365\pi$
$991$	33.5075			1.06440			0.532200	+	0.846619i	$0.321365\pi$
$992$		0			0
$993$	−0.130949	+	0.987978i	−0.00415556	+	0.0313525i
$994$		0			0
$995$			4.35331i			0.138009i
$996$		0			0
$997$			33.7645i			1.06933i	0.845063	+	0.534667i	$0.179563\pi$
$997$			33.7645i			1.06933i	−0.845063	+	0.534667i	$0.820437\pi$
$998$		0			0
$999$	−5.08474	+	12.1851i	−0.160874	+	0.385518i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1680.2.f.l.881.8		16
3.2	odd	2		1680.2.f.k.881.10		16
4.3	odd	2		840.2.f.b.41.9	yes	16
7.6	odd	2		1680.2.f.k.881.9		16
12.11	even	2		840.2.f.a.41.7	✓	16
21.20	even	2	inner	1680.2.f.l.881.7		16
28.27	even	2		840.2.f.a.41.8	yes	16
84.83	odd	2		840.2.f.b.41.10	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.f.a.41.7	✓	16	12.11	even	2
840.2.f.a.41.8	yes	16	28.27	even	2
840.2.f.b.41.9	yes	16	4.3	odd	2
840.2.f.b.41.10	yes	16	84.83	odd	2
1680.2.f.k.881.9		16	7.6	odd	2
1680.2.f.k.881.10		16	3.2	odd	2
1680.2.f.l.881.7		16	21.20	even	2	inner
1680.2.f.l.881.8		16	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1680.f (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.227581 + 1.71703i) q^{3} +1.00000 q^{5} +(1.22074 - 2.34729i) q^{7} +(-2.89641 - 0.781528i) q^{9} +O(q^{10})\)	\(q+(-0.227581 + 1.71703i) q^{3} +1.00000 q^{5} +(1.22074 - 2.34729i) q^{7} +(-2.89641 - 0.781528i) q^{9} -4.73831i q^{11} +5.25541i q^{13} +(-0.227581 + 1.71703i) q^{15} -0.432719 q^{17} -6.30136i q^{19} +(3.75256 + 2.63026i) q^{21} -0.332245i q^{23} +1.00000 q^{25} +(2.00108 - 4.79538i) q^{27} -7.48606i q^{29} -0.0758169i q^{31} +(8.13584 + 1.07835i) q^{33} +(1.22074 - 2.34729i) q^{35} -2.54100 q^{37} +(-9.02372 - 1.19603i) q^{39} +4.82357 q^{41} -1.97756 q^{43} +(-2.89641 - 0.781528i) q^{45} +9.28919 q^{47} +(-4.01957 - 5.73089i) q^{49} +(0.0984785 - 0.742993i) q^{51} -13.8305i q^{53} -4.73831i q^{55} +(10.8197 + 1.43407i) q^{57} -5.65528 q^{59} +5.11428i q^{61} +(-5.37026 + 5.84469i) q^{63} +5.25541i q^{65} -6.75379 q^{67} +(0.570475 + 0.0756124i) q^{69} -9.35623i q^{71} +2.75129i q^{73} +(-0.227581 + 1.71703i) q^{75} +(-11.1222 - 5.78426i) q^{77} -0.0508016 q^{79} +(7.77843 + 4.52726i) q^{81} +4.12411 q^{83} -0.432719 q^{85} +(12.8538 + 1.70368i) q^{87} +12.4092 q^{89} +(12.3360 + 6.41551i) q^{91} +(0.130180 + 0.0172545i) q^{93} -6.30136i q^{95} +11.1116i q^{97} +(-3.70312 + 13.7241i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{5} - 2 q^{7} - 2 q^{9}+O(q^{10}) \) 16 * q + 16 * q^5 - 2 * q^7 - 2 * q^9	\( 16 q + 16 q^{5} - 2 q^{7} - 2 q^{9} + 10 q^{21} + 16 q^{25} - 6 q^{27} + 6 q^{33} - 2 q^{35} + 12 q^{37} - 6 q^{39} + 32 q^{41} - 32 q^{43} - 2 q^{45} - 4 q^{47} - 4 q^{49} - 6 q^{51} + 24 q^{59} + 24 q^{63} + 8 q^{69} - 32 q^{77} + 4 q^{79} - 6 q^{81} - 20 q^{83} - 6 q^{87} - 24 q^{89} - 20 q^{91} - 32 q^{93} + 58 q^{99}+O(q^{100}) \) 16 * q + 16 * q^5 - 2 * q^7 - 2 * q^9 + 10 * q^21 + 16 * q^25 - 6 * q^27 + 6 * q^33 - 2 * q^35 + 12 * q^37 - 6 * q^39 + 32 * q^41 - 32 * q^43 - 2 * q^45 - 4 * q^47 - 4 * q^49 - 6 * q^51 + 24 * q^59 + 24 * q^63 + 8 * q^69 - 32 * q^77 + 4 * q^79 - 6 * q^81 - 20 * q^83 - 6 * q^87 - 24 * q^89 - 20 * q^91 - 32 * q^93 + 58 * q^99

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