LMFDB - Embedded newform 1320.2.ba.a.329.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1320,2,Mod(329,1320)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1320, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1320.329");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1320 = 2^{3} \cdot 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1320.ba (of order $2$, degree $1$, 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:	$10.5402530668$
Analytic rank:	$0$
Dimension:	$72$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			329.4
Character	$\chi$	$=$	1320.329
Dual form			1320.2.ba.a.329.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.72947 + 0.0944935i) q^{3} +(1.89340 - 1.18956i) q^{5} +2.85425 q^{7} +(2.98214 - 0.326848i) q^{9} +O(q^{10})$	\(q+(-1.72947 + 0.0944935i) q^{3} +(1.89340 - 1.18956i) q^{5} +2.85425 q^{7} +(2.98214 - 0.326848i) q^{9} +(-0.833543 + 3.21017i) q^{11} +3.11005 q^{13} +(-3.16217 + 2.23622i) q^{15} +1.53160i q^{17} +5.78889i q^{19} +(-4.93635 + 0.269708i) q^{21} +3.49565 q^{23} +(2.16991 - 4.50461i) q^{25} +(-5.12664 + 0.847066i) q^{27} -4.02861 q^{29} -4.83886 q^{31} +(1.13825 - 5.63067i) q^{33} +(5.40423 - 3.39529i) q^{35} -1.57664i q^{37} +(-5.37873 + 0.293879i) q^{39} +1.72289 q^{41} +9.34300 q^{43} +(5.25758 - 4.16628i) q^{45} -2.91856 q^{47} +1.14675 q^{49} +(-0.144726 - 2.64885i) q^{51} -2.08253 q^{53} +(2.24045 + 7.06968i) q^{55} +(-0.547012 - 10.0117i) q^{57} +8.46884i q^{59} +12.6324i q^{61} +(8.51178 - 0.932905i) q^{63} +(5.88855 - 3.69957i) q^{65} -4.93483i q^{67} +(-6.04563 + 0.330316i) q^{69} -9.89348i q^{71} +16.6216 q^{73} +(-3.32715 + 7.99563i) q^{75} +(-2.37914 + 9.16264i) q^{77} +12.6160i q^{79} +(8.78634 - 1.94941i) q^{81} +2.80377i q^{83} +(1.82192 + 2.89992i) q^{85} +(6.96736 - 0.380677i) q^{87} -14.9751i q^{89} +8.87685 q^{91} +(8.36867 - 0.457241i) q^{93} +(6.88621 + 10.9607i) q^{95} +3.53318i q^{97} +(-1.43651 + 9.84563i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q+O(q^{10}) $ 72 * q	$ 72 q - 6 q^{15} - 4 q^{25} + 34 q^{45} + 96 q^{49} - 28 q^{55} + 28 q^{69} + 14 q^{75} + 16 q^{81} - 48 q^{91} - 4 q^{99}+O(q^{100}) $ 72 * q - 6 * q^15 - 4 * q^25 + 34 * q^45 + 96 * q^49 - 28 * q^55 + 28 * q^69 + 14 * q^75 + 16 * q^81 - 48 * q^91 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1320\mathbb{Z}\right)^\times$.

$n$	$661$	$881$	$991$	$1057$	$1201$
$\chi(n)$	$1$	$-1$	$1$	$-1$	$-1$

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
$3$	−1.72947	+	0.0944935i	−0.998511	+	0.0545558i
$3$	−1.72947	+	0.0944935i	−0.998511	+	0.0545558i
$4$		0			0
$5$	1.89340	−	1.18956i	0.846753	−	0.531986i
$5$	1.89340	−	1.18956i	0.846753	−	0.531986i
$6$		0			0
$7$	2.85425			1.07881			0.539403	−	0.842048i	$-0.318650\pi$
$7$	2.85425			1.07881			0.539403	+	0.842048i	$0.318650\pi$
$8$		0			0
$9$	2.98214	−	0.326848i	0.994047	−	0.108949i
$10$		0			0
$11$	−0.833543	+	3.21017i	−0.251323	+	0.967903i
$11$	−0.833543	+	3.21017i	−0.251323	+	0.967903i
$12$		0			0
$13$	3.11005			0.862571			0.431286	−	0.902215i	$-0.358060\pi$
$13$	3.11005			0.862571			0.431286	+	0.902215i	$0.358060\pi$
$14$		0			0
$15$	−3.16217	+	2.23622i	−0.816469	+	0.577389i
$16$		0			0
$17$			1.53160i			0.371467i	0.982600	+	0.185733i	$0.0594660\pi$
$17$			1.53160i			0.371467i	−0.982600	+	0.185733i	$0.940534\pi$
$18$		0			0
$19$			5.78889i			1.32806i	0.747705	+	0.664031i	$0.231156\pi$
$19$			5.78889i			1.32806i	−0.747705	+	0.664031i	$0.768844\pi$
$20$		0			0
$21$	−4.93635	+	0.269708i	−1.07720	+	0.0588551i
$22$		0			0
$23$	3.49565			0.728894			0.364447	−	0.931224i	$-0.381258\pi$
$23$	3.49565			0.728894			0.364447	+	0.931224i	$0.381258\pi$
$24$		0			0
$25$	2.16991	−	4.50461i	0.433983	−	0.900921i
$26$		0			0
$27$	−5.12664	+	0.847066i	−0.986623	+	0.163018i
$28$		0			0
$29$	−4.02861			−0.748093			−0.374047	−	0.927410i	$-0.622030\pi$
$29$	−4.02861			−0.748093			−0.374047	+	0.927410i	$0.622030\pi$
$30$		0			0
$31$	−4.83886			−0.869085			−0.434543	−	0.900651i	$-0.643090\pi$
$31$	−4.83886			−0.869085			−0.434543	+	0.900651i	$0.643090\pi$
$32$		0			0
$33$	1.13825	−	5.63067i	0.198144	−	0.980173i
$34$		0			0
$35$	5.40423	−	3.39529i	0.913482	−	0.573909i
$36$		0			0
$37$		−	1.57664i		−	0.259199i	−0.991566	−	0.129599i	$-0.958631\pi$
$37$		−	1.57664i		−	0.259199i	0.991566	−	0.129599i	$-0.0413691\pi$
$38$		0			0
$39$	−5.37873	+	0.293879i	−0.861287	+	0.0470583i
$40$		0			0
$41$	1.72289			0.269069			0.134535	−	0.990909i	$-0.457046\pi$
$41$	1.72289			0.269069			0.134535	+	0.990909i	$0.457046\pi$
$42$		0			0
$43$	9.34300			1.42479			0.712397	−	0.701777i	$-0.247610\pi$
$43$	9.34300			1.42479			0.712397	+	0.701777i	$0.247610\pi$
$44$		0			0
$45$	5.25758	−	4.16628i	0.783754	−	0.621072i
$46$		0			0
$47$	−2.91856			−0.425716			−0.212858	−	0.977083i	$-0.568277\pi$
$47$	−2.91856			−0.425716			−0.212858	+	0.977083i	$0.568277\pi$
$48$		0			0
$49$	1.14675			0.163822
$50$		0			0
$51$	−0.144726	−	2.64885i	−0.0202657	−	0.370913i
$52$		0			0
$53$	−2.08253			−0.286058			−0.143029	−	0.989719i	$-0.545684\pi$
$53$	−2.08253			−0.286058			−0.143029	+	0.989719i	$0.545684\pi$
$54$		0			0
$55$	2.24045	+	7.06968i	0.302102	+	0.953276i
$56$		0			0
$57$	−0.547012	−	10.0117i	−0.0724536	−	1.32608i
$58$		0			0
$59$			8.46884i			1.10255i	0.834324	+	0.551274i	$0.185858\pi$
$59$			8.46884i			1.10255i	−0.834324	+	0.551274i	$0.814142\pi$
$60$		0			0
$61$			12.6324i			1.61742i	0.588210	+	0.808708i	$0.299833\pi$
$61$			12.6324i			1.61742i	−0.588210	+	0.808708i	$0.700167\pi$
$62$		0			0
$63$	8.51178	−	0.932905i	1.07238	−	0.117535i
$64$		0			0
$65$	5.88855	−	3.69957i	0.730385	−	0.458876i
$66$		0			0
$67$		−	4.93483i		−	0.602885i	−0.953484	−	0.301443i	$-0.902532\pi$
$67$		−	4.93483i		−	0.602885i	0.953484	−	0.301443i	$-0.0974682\pi$
$68$		0			0
$69$	−6.04563	+	0.330316i	−0.727808	+	0.0397654i
$70$		0			0
$71$		−	9.89348i		−	1.17414i	−0.809536	−	0.587070i	$-0.800281\pi$
$71$		−	9.89348i		−	1.17414i	0.809536	−	0.587070i	$-0.199719\pi$
$72$		0			0
$73$	16.6216			1.94541			0.972707	−	0.232037i	$-0.0745390\pi$
$73$	16.6216			1.94541			0.972707	+	0.232037i	$0.0745390\pi$
$74$		0			0
$75$	−3.32715	+	7.99563i	−0.384186	+	0.923256i
$76$		0			0
$77$	−2.37914	+	9.16264i	−0.271128	+	1.04418i
$78$		0			0
$79$			12.6160i			1.41941i	0.704498	+	0.709706i	$0.251172\pi$
$79$			12.6160i			1.41941i	−0.704498	+	0.709706i	$0.748828\pi$
$80$		0			0
$81$	8.78634	−	1.94941i	0.976260	−	0.216601i
$82$		0			0
$83$			2.80377i			0.307754i	0.988090	+	0.153877i	$0.0491759\pi$
$83$			2.80377i			0.307754i	−0.988090	+	0.153877i	$0.950824\pi$
$84$		0			0
$85$	1.82192	+	2.89992i	0.197615	+	0.314541i
$86$		0			0
$87$	6.96736	−	0.380677i	0.746979	−	0.0408129i
$88$		0			0
$89$		−	14.9751i		−	1.58735i	−0.608339	−	0.793677i	$-0.708164\pi$
$89$		−	14.9751i		−	1.58735i	0.608339	−	0.793677i	$-0.291836\pi$
$90$		0			0
$91$	8.87685			0.930547
$92$		0			0
$93$	8.36867	−	0.457241i	0.867791	−	0.0474137i
$94$		0			0
$95$	6.88621	+	10.9607i	0.706510	+	1.12454i
$96$		0			0
$97$			3.53318i			0.358740i	0.983782	+	0.179370i	$0.0574060\pi$
$97$			3.53318i			0.358740i	−0.983782	+	0.179370i	$0.942594\pi$
$98$		0			0
$99$	−1.43651	+	9.84563i	−0.144374	+	0.989523i
$100$		0			0
$101$	14.1409			1.40708			0.703538	−	0.710658i	$-0.251603\pi$
$101$	14.1409			1.40708			0.703538	+	0.710658i	$0.251603\pi$
$102$		0			0
$103$		−	9.04284i		−	0.891017i	−0.895278	−	0.445509i	$-0.853023\pi$
$103$		−	9.04284i		−	0.891017i	0.895278	−	0.445509i	$-0.146977\pi$
$104$		0			0
$105$	−9.02564	+	6.38272i	−0.880812	+	0.622890i
$106$		0			0
$107$			13.8773i			1.34157i	0.741652	+	0.670785i	$0.234043\pi$
$107$			13.8773i			1.34157i	−0.741652	+	0.670785i	$0.765957\pi$
$108$		0			0
$109$		−	12.1610i		−	1.16481i	−0.812899	−	0.582405i	$-0.802112\pi$
$109$		−	12.1610i		−	1.16481i	0.812899	−	0.582405i	$-0.197888\pi$
$110$		0			0
$111$	0.148982	+	2.72676i	0.0141408	+	0.258812i
$112$		0			0
$113$	4.29497			0.404037			0.202018	−	0.979382i	$-0.435250\pi$
$113$	4.29497			0.404037			0.202018	+	0.979382i	$0.435250\pi$
$114$		0			0
$115$	6.61866	−	4.15827i	0.617193	−	0.387761i
$116$		0			0
$117$	9.27460	−	1.01651i	0.857437	−	0.0939764i
$118$		0			0
$119$			4.37156i			0.400740i
$120$		0			0
$121$	−9.61041	−	5.35164i	−0.873674	−	0.486512i
$122$		0			0
$123$	−2.97968	+	0.162801i	−0.268669	+	0.0146793i
$124$		0			0
$125$	−1.24997	−	11.1102i	−0.111801	−	0.993731i
$126$		0			0
$127$	−16.7890			−1.48978			−0.744890	−	0.667187i	$-0.767498\pi$
$127$	−16.7890			−1.48978			−0.744890	+	0.667187i	$0.767498\pi$
$128$		0			0
$129$	−16.1585	+	0.882853i	−1.42267	+	0.0777308i
$130$		0			0
$131$	16.5944			1.44986			0.724932	−	0.688821i	$-0.241871\pi$
$131$	16.5944			1.44986			0.724932	+	0.688821i	$0.241871\pi$
$132$		0			0
$133$			16.5229i			1.43272i
$134$		0			0
$135$	−8.69915	+	7.70226i	−0.748703	+	0.662905i
$136$		0			0
$137$	15.8798			1.35670			0.678352	−	0.734737i	$-0.262695\pi$
$137$	15.8798			1.35670			0.678352	+	0.734737i	$0.262695\pi$
$138$		0			0
$139$		−	19.2178i		−	1.63004i	−0.579436	−	0.815018i	$-0.696727\pi$
$139$		−	19.2178i		−	1.63004i	0.579436	−	0.815018i	$-0.303273\pi$
$140$		0			0
$141$	5.04756	−	0.275785i	0.425082	−	0.0232253i
$142$		0			0
$143$	−2.59236	+	9.98378i	−0.216784	+	0.834886i
$144$		0			0
$145$	−7.62775	+	4.79225i	−0.633450	+	0.397975i
$146$		0			0
$147$	−1.98327	+	0.108361i	−0.163578	+	0.00893743i
$148$		0			0
$149$	−4.62393			−0.378807			−0.189403	−	0.981899i	$-0.560655\pi$
$149$	−4.62393			−0.378807			−0.189403	+	0.981899i	$0.560655\pi$
$150$		0			0
$151$			3.71459i			0.302289i	0.988512	+	0.151144i	$0.0482958\pi$
$151$			3.71459i			0.302289i	−0.988512	+	0.151144i	$0.951704\pi$
$152$		0			0
$153$	0.500598	+	4.56744i	0.0404710	+	0.369255i
$154$		0			0
$155$	−9.16189	+	5.75610i	−0.735901	+	0.462341i
$156$		0			0
$157$			12.1138i			0.966787i	0.875403	+	0.483394i	$0.160596\pi$
$157$			12.1138i			0.966787i	−0.875403	+	0.483394i	$0.839404\pi$
$158$		0			0
$159$	3.60168	−	0.196786i	0.285632	−	0.0156061i
$160$		0			0
$161$	9.97747			0.786335
$162$		0			0
$163$		−	14.7433i		−	1.15479i	−0.816466	−	0.577393i	$-0.804070\pi$
$163$		−	14.7433i		−	1.15479i	0.816466	−	0.577393i	$-0.195930\pi$
$164$		0			0
$165$	−4.54283	−	12.0151i	−0.353659	−	0.935374i
$166$		0			0
$167$		−	15.9065i		−	1.23089i	−0.788182	−	0.615443i	$-0.788977\pi$
$167$		−	15.9065i		−	1.23089i	0.788182	−	0.615443i	$-0.211023\pi$
$168$		0			0
$169$	−3.32762			−0.255971
$170$		0			0
$171$	1.89208	+	17.2633i	0.144691	+	1.32016i
$172$		0			0
$173$			6.73933i			0.512382i	0.966626	+	0.256191i	$0.0824675\pi$
$173$			6.73933i			0.512382i	−0.966626	+	0.256191i	$0.917532\pi$
$174$		0			0
$175$	6.19348	−	12.8573i	0.468183	−	0.971919i
$176$		0			0
$177$	−0.800250	−	14.6466i	−0.0601505	−	1.10091i
$178$		0			0
$179$			11.5261i			0.861499i	0.902472	+	0.430749i	$0.141751\pi$
$179$			11.5261i			0.861499i	−0.902472	+	0.430749i	$0.858249\pi$
$180$		0			0
$181$	−20.8383			−1.54890			−0.774448	−	0.632638i	$-0.781972\pi$
$181$	−20.8383			−1.54890			−0.774448	+	0.632638i	$0.781972\pi$
$182$		0			0
$183$	−1.19368	−	21.8474i	−0.0882395	−	1.61501i
$184$		0			0
$185$	−1.87551	−	2.98521i	−0.137890	−	0.219477i
$186$		0			0
$187$	−4.91669	−	1.27665i	−0.359544	−	0.0933580i
$188$		0			0
$189$	−14.6327	+	2.41774i	−1.06437	+	0.175865i
$190$		0			0
$191$		−	5.85510i		−	0.423660i	−0.977306	−	0.211830i	$-0.932058\pi$
$191$		−	5.85510i		−	0.423660i	0.977306	−	0.211830i	$-0.0679424\pi$
$192$		0			0
$193$	−5.63637			−0.405715			−0.202857	−	0.979208i	$-0.565023\pi$
$193$	−5.63637			−0.405715			−0.202857	+	0.979208i	$0.565023\pi$
$194$		0			0
$195$	−9.83450	+	6.95473i	−0.704263	+	0.498039i
$196$		0			0
$197$			7.09270i			0.505334i	0.967553	+	0.252667i	$0.0813077\pi$
$197$			7.09270i			0.505334i	−0.967553	+	0.252667i	$0.918692\pi$
$198$		0			0
$199$	1.55075			0.109930			0.0549650	−	0.998488i	$-0.482495\pi$
$199$	1.55075			0.109930			0.0549650	+	0.998488i	$0.482495\pi$
$200$		0			0
$201$	0.466309	+	8.53465i	0.0328909	+	0.601988i
$202$		0			0
$203$	−11.4987			−0.807047
$204$		0			0
$205$	3.26211	−	2.04947i	0.227836	−	0.143141i
$206$		0			0
$207$	10.4245	−	1.14254i	0.724555	−	0.0794124i
$208$		0			0
$209$	−18.5833	−	4.82529i	−1.28544	−	0.333772i
$210$		0			0
$211$		−	12.0173i		−	0.827307i	−0.910434	−	0.413653i	$-0.864253\pi$
$211$		−	12.0173i		−	0.827307i	0.910434	−	0.413653i	$-0.135747\pi$
$212$		0			0
$213$	0.934870	+	17.1105i	0.0640562	+	1.17239i
$214$		0			0
$215$	17.6900	−	11.1140i	1.20645	−	0.757970i
$216$		0			0
$217$	−13.8113			−0.937574
$218$		0			0
$219$	−28.7466	+	1.57064i	−1.94252	+	0.106134i
$220$		0			0
$221$			4.76333i			0.320416i
$222$		0			0
$223$		−	25.8792i		−	1.73300i	−0.499180	−	0.866498i	$-0.666365\pi$
$223$		−	25.8792i		−	1.73300i	0.499180	−	0.866498i	$-0.333635\pi$
$224$		0			0
$225$	4.99867	−	14.1426i	0.333245	−	0.942840i
$226$		0			0
$227$		−	11.3114i		−	0.750765i	−0.926870	−	0.375382i	$-0.877511\pi$
$227$		−	11.3114i		−	0.750765i	0.926870	−	0.375382i	$-0.122489\pi$
$228$		0			0
$229$	−4.41353			−0.291654			−0.145827	−	0.989310i	$-0.546584\pi$
$229$	−4.41353			−0.291654			−0.145827	+	0.989310i	$0.546584\pi$
$230$		0			0
$231$	3.24885	−	16.0713i	0.213759	−	1.05742i
$232$		0			0
$233$		−	5.66292i		−	0.370990i	−0.982645	−	0.185495i	$-0.940611\pi$
$233$		−	5.66292i		−	0.370990i	0.982645	−	0.185495i	$-0.0593888\pi$
$234$		0			0
$235$	−5.52599	+	3.47179i	−0.360476	+	0.226475i
$236$		0			0
$237$	−1.19213	−	21.8190i	−0.0774372	−	1.41730i
$238$		0			0
$239$	−22.1548			−1.43307			−0.716536	−	0.697550i	$-0.754273\pi$
$239$	−22.1548			−1.43307			−0.716536	+	0.697550i	$0.754273\pi$
$240$		0			0
$241$		−	11.1130i		−	0.715854i	−0.933749	−	0.357927i	$-0.883484\pi$
$241$		−	11.1130i		−	0.715854i	0.933749	−	0.357927i	$-0.116516\pi$
$242$		0			0
$243$	−15.0115	+	4.20170i	−0.962989	+	0.269539i
$244$		0			0
$245$	2.17126	−	1.36413i	0.138717	−	0.0871508i
$246$		0			0
$247$			18.0037i			1.14555i
$248$		0			0
$249$	−0.264938	−	4.84904i	−0.0167898	−	0.307295i
$250$		0			0
$251$			8.01227i			0.505730i	0.967502	+	0.252865i	$0.0813729\pi$
$251$			8.01227i			0.505730i	−0.967502	+	0.252865i	$0.918627\pi$
$252$		0			0
$253$	−2.91378	+	11.2216i	−0.183188	+	0.705499i
$254$		0			0
$255$	−3.42498	−	4.84317i	−0.214481	−	0.303291i
$256$		0			0
$257$	16.5090			1.02980			0.514902	−	0.857249i	$-0.327828\pi$
$257$	16.5090			1.02980			0.514902	+	0.857249i	$0.327828\pi$
$258$		0			0
$259$		−	4.50014i		−	0.279625i
$260$		0			0
$261$	−12.0139	+	1.31674i	−0.743640	+	0.0815041i
$262$		0			0
$263$			16.9046i			1.04238i	0.853440	+	0.521192i	$0.174512\pi$
$263$			16.9046i			1.04238i	−0.853440	+	0.521192i	$0.825488\pi$
$264$		0			0
$265$	−3.94306	+	2.47729i	−0.242220	+	0.152178i
$266$		0			0
$267$	1.41505	+	25.8990i	0.0865995	+	1.58499i
$268$		0			0
$269$			11.6816i			0.712237i	0.934441	+	0.356119i	$0.115900\pi$
$269$			11.6816i			0.712237i	−0.934441	+	0.356119i	$0.884100\pi$
$270$		0			0
$271$			0.450474i			0.0273644i	0.999906	+	0.0136822i	$0.00435531\pi$
$271$			0.450474i			0.0273644i	−0.999906	+	0.0136822i	$0.995645\pi$
$272$		0			0
$273$	−15.3523	+	0.838805i	−0.929161	+	0.0507668i
$274$		0			0
$275$	12.6518	+	10.7206i	0.762935	+	0.646475i
$276$		0			0
$277$	−19.2776			−1.15828			−0.579141	−	0.815228i	$-0.696612\pi$
$277$	−19.2776			−1.15828			−0.579141	+	0.815228i	$0.696612\pi$
$278$		0			0
$279$	−14.4302	+	1.58157i	−0.863912	+	0.0946861i
$280$		0			0
$281$	5.61183			0.334774			0.167387	−	0.985891i	$-0.446467\pi$
$281$	5.61183			0.334774			0.167387	+	0.985891i	$0.446467\pi$
$282$		0			0
$283$	−15.2333			−0.905524			−0.452762	−	0.891631i	$-0.649561\pi$
$283$	−15.2333			−0.905524			−0.452762	+	0.891631i	$0.649561\pi$
$284$		0			0
$285$	−12.9452	−	18.3055i	−0.766808	−	1.08432i
$286$		0			0
$287$	4.91755			0.290274
$288$		0			0
$289$	14.6542			0.862013
$290$		0			0
$291$	−0.333863	−	6.11054i	−0.0195714	−	0.358206i
$292$		0			0
$293$		−	30.2814i		−	1.76906i	−0.466485	−	0.884529i	$-0.654480\pi$
$293$		−	30.2814i		−	1.76906i	0.466485	−	0.884529i	$-0.345520\pi$
$294$		0			0
$295$	10.0742	+	16.0349i	0.586540	+	0.933587i
$296$		0			0
$297$	1.55405	−	17.1635i	0.0901752	−	0.995926i
$298$		0			0
$299$	10.8716			0.628723
$300$		0			0
$301$	26.6673			1.53708
$302$		0			0
$303$	−24.4563	+	1.33623i	−1.40498	+	0.0767642i
$304$		0			0
$305$	15.0270	+	23.9182i	0.860443	+	1.36955i
$306$		0			0
$307$	−3.95142			−0.225520			−0.112760	−	0.993622i	$-0.535969\pi$
$307$	−3.95142			−0.225520			−0.112760	+	0.993622i	$0.535969\pi$
$308$		0			0
$309$	0.854489	+	15.6393i	0.0486102	+	0.889690i
$310$		0			0
$311$		−	25.7829i		−	1.46201i	−0.682371	−	0.731006i	$-0.739051\pi$
$311$		−	25.7829i		−	1.46201i	0.682371	−	0.731006i	$-0.260949\pi$
$312$		0			0
$313$			22.3603i			1.26388i	0.775019	+	0.631939i	$0.217740\pi$
$313$			22.3603i			1.26388i	−0.775019	+	0.631939i	$0.782260\pi$
$314$		0			0
$315$	15.0065	−	11.8916i	0.845518	−	0.670016i
$316$		0			0
$317$	−15.7447			−0.884311			−0.442156	−	0.896938i	$-0.645786\pi$
$317$	−15.7447			−0.884311			−0.442156	+	0.896938i	$0.645786\pi$
$318$		0			0
$319$	3.35802	−	12.9325i	0.188013	−	0.724082i
$320$		0			0
$321$	−1.31132	−	24.0004i	−0.0731905	−	1.33957i
$322$		0			0
$323$	−8.86624			−0.493331
$324$		0			0
$325$	6.74853	−	14.0095i	0.374341	−	0.777109i
$326$		0			0
$327$	1.14913	+	21.0320i	0.0635471	+	1.16307i
$328$		0			0
$329$	−8.33030			−0.459264
$330$		0			0
$331$	−5.04784			−0.277455			−0.138727	−	0.990331i	$-0.544301\pi$
$331$	−5.04784			−0.277455			−0.138727	+	0.990331i	$0.544301\pi$
$332$		0			0
$333$	−0.515322	−	4.70177i	−0.0282395	−	0.257656i
$334$		0			0
$335$	−5.87026	−	9.34360i	−0.320726	−	0.510495i
$336$		0			0
$337$	−15.0466			−0.819639			−0.409819	−	0.912167i	$-0.634408\pi$
$337$	−15.0466			−0.819639			−0.409819	+	0.912167i	$0.634408\pi$
$338$		0			0
$339$	−7.42803	+	0.405847i	−0.403435	+	0.0220426i
$340$		0			0
$341$	4.03340	−	15.5336i	0.218421	−	0.841191i
$342$		0			0
$343$	−16.7066			−0.902074
$344$		0			0
$345$	−11.0539	+	7.81703i	−0.595119	+	0.420855i
$346$		0			0
$347$			1.80479i			0.0968863i	0.998826	+	0.0484432i	$0.0154260\pi$
$347$			1.80479i			0.0968863i	−0.998826	+	0.0484432i	$0.984574\pi$
$348$		0			0
$349$			24.5453i			1.31388i	0.753943	+	0.656940i	$0.228150\pi$
$349$			24.5453i			1.31388i	−0.753943	+	0.656940i	$0.771850\pi$
$350$		0			0
$351$	−15.9441	+	2.63441i	−0.851033	+	0.140615i
$352$		0			0
$353$	11.2136			0.596839			0.298419	−	0.954435i	$-0.403541\pi$
$353$	11.2136			0.596839			0.298419	+	0.954435i	$0.403541\pi$
$354$		0			0
$355$	−11.7688	−	18.7323i	−0.624626	−	0.994207i
$356$		0			0
$357$	−0.413084	−	7.56049i	−0.0218627	−	0.400143i
$358$		0			0
$359$	−3.81900			−0.201559			−0.100780	−	0.994909i	$-0.532134\pi$
$359$	−3.81900			−0.201559			−0.100780	+	0.994909i	$0.532134\pi$
$360$		0			0
$361$	−14.5113			−0.763750
$362$		0			0
$363$	17.1266	+	8.34738i	0.898915	+	0.438124i
$364$		0			0
$365$	31.4714	−	19.7724i	1.64729	−	1.03493i
$366$		0			0
$367$		−	24.9646i		−	1.30314i	−0.758588	−	0.651571i	$-0.774110\pi$
$367$		−	24.9646i		−	1.30314i	0.758588	−	0.651571i	$-0.225890\pi$
$368$		0			0
$369$	5.13789	−	0.563121i	0.267468	−	0.0293149i
$370$		0			0
$371$	−5.94406			−0.308600
$372$		0			0
$373$	−3.56378			−0.184525			−0.0922627	−	0.995735i	$-0.529410\pi$
$373$	−3.56378			−0.184525			−0.0922627	+	0.995735i	$0.529410\pi$
$374$		0			0
$375$	3.21164	+	19.0967i	0.165848	+	0.986151i
$376$		0			0
$377$	−12.5291			−0.645284
$378$		0			0
$379$	−1.36403			−0.0700653			−0.0350326	−	0.999386i	$-0.511154\pi$
$379$	−1.36403			−0.0700653			−0.0350326	+	0.999386i	$0.511154\pi$
$380$		0			0
$381$	29.0360	−	1.58645i	1.48756	−	0.0812762i
$382$		0			0
$383$	33.1317			1.69295			0.846476	−	0.532426i	$-0.178720\pi$
$383$	33.1317			1.69295			0.846476	+	0.532426i	$0.178720\pi$
$384$		0			0
$385$	6.39481	+	20.1786i	0.325910	+	1.02840i
$386$		0			0
$387$	27.8622	−	3.05374i	1.41631	−	0.155230i
$388$		0			0
$389$			0.703620i			0.0356749i	0.999841	+	0.0178375i	$0.00567814\pi$
$389$			0.703620i			0.0356749i	−0.999841	+	0.0178375i	$0.994322\pi$
$390$		0			0
$391$			5.35392i			0.270760i
$392$		0			0
$393$	−28.6996	+	1.56807i	−1.44770	+	0.0790985i
$394$		0			0
$395$	15.0075	+	23.8871i	0.755107	+	1.20189i
$396$		0			0
$397$		−	16.3397i		−	0.820067i	−0.912071	−	0.410033i	$-0.865517\pi$
$397$		−	16.3397i		−	0.820067i	0.912071	−	0.410033i	$-0.134483\pi$
$398$		0			0
$399$	−1.56131	−	28.5760i	−0.0781633	−	1.43059i
$400$		0			0
$401$			27.8574i			1.39113i	0.718463	+	0.695566i	$0.244846\pi$
$401$			27.8574i			1.39113i	−0.718463	+	0.695566i	$0.755154\pi$
$402$		0			0
$403$	−15.0491			−0.749648
$404$		0			0
$405$	14.3171	−	14.1429i	0.711423	−	0.702764i
$406$		0			0
$407$	5.06130	+	1.31420i	0.250879	+	0.0651425i
$408$		0			0
$409$			17.0592i			0.843525i	0.906706	+	0.421763i	$0.138588\pi$
$409$			17.0592i			0.843525i	−0.906706	+	0.421763i	$0.861412\pi$
$410$		0			0
$411$	−27.4637	+	1.50054i	−1.35468	+	0.0740161i
$412$		0			0
$413$			24.1722i			1.18944i
$414$		0			0
$415$	3.33524	+	5.30865i	0.163721	+	0.260591i
$416$		0			0
$417$	1.81596	+	33.2367i	0.0889280	+	1.62761i
$418$		0			0
$419$			23.0521i			1.12617i	0.826399	+	0.563085i	$0.190386\pi$
$419$			23.0521i			1.12617i	−0.826399	+	0.563085i	$0.809614\pi$
$420$		0			0
$421$	−6.43047			−0.313402			−0.156701	−	0.987646i	$-0.550086\pi$
$421$	−6.43047			−0.313402			−0.156701	+	0.987646i	$0.550086\pi$
$422$		0			0
$423$	−8.70356	+	0.953924i	−0.423181	+	0.0463814i
$424$		0			0
$425$	6.89924	+	3.32343i	0.334662	+	0.161210i
$426$		0			0
$427$			36.0561i			1.74488i
$428$		0			0
$429$	3.54001	−	17.5116i	0.170913	−	0.845469i
$430$		0			0
$431$	30.9821			1.49236			0.746178	−	0.665746i	$-0.231887\pi$
$431$	30.9821			1.49236			0.746178	+	0.665746i	$0.231887\pi$
$432$		0			0
$433$			19.6214i			0.942943i	0.881881	+	0.471472i	$0.156277\pi$
$433$			19.6214i			0.942943i	−0.881881	+	0.471472i	$0.843723\pi$
$434$		0			0
$435$	12.7391	−	9.00883i	0.610795	−	0.431941i
$436$		0			0
$437$			20.2359i			0.968016i
$438$		0			0
$439$		−	3.47009i		−	0.165618i	−0.996565	−	0.0828091i	$-0.973611\pi$
$439$		−	3.47009i		−	0.165618i	0.996565	−	0.0828091i	$-0.0263892\pi$
$440$		0			0
$441$	3.41978	−	0.374813i	0.162847	−	0.0178482i
$442$		0			0
$443$	1.74196			0.0827631			0.0413815	−	0.999143i	$-0.486824\pi$
$443$	1.74196			0.0827631			0.0413815	+	0.999143i	$0.486824\pi$
$444$		0			0
$445$	−17.8137	−	28.3538i	−0.844450	−	1.34410i
$446$		0			0
$447$	7.99695	−	0.436931i	0.378243	−	0.0206661i
$448$		0			0
$449$		−	29.9424i		−	1.41307i	−0.707679	−	0.706534i	$-0.750258\pi$
$449$		−	29.9424i		−	1.41307i	0.707679	−	0.706534i	$-0.249742\pi$
$450$		0			0
$451$	−1.43610	+	5.53076i	−0.0676233	+	0.260433i
$452$		0			0
$453$	−0.351004	−	6.42427i	−0.0164916	−	0.301839i
$454$		0			0
$455$	16.8074	−	10.5595i	0.787944	−	0.495038i
$456$		0			0
$457$	14.3336			0.670495			0.335248	−	0.942130i	$-0.391180\pi$
$457$	14.3336			0.670495			0.335248	+	0.942130i	$0.391180\pi$
$458$		0			0
$459$	−1.29736	−	7.85195i	−0.0605557	−	0.366497i
$460$		0			0
$461$	−16.3747			−0.762646			−0.381323	−	0.924442i	$-0.624531\pi$
$461$	−16.3747			−0.762646			−0.381323	+	0.924442i	$0.624531\pi$
$462$		0			0
$463$		−	17.6647i		−	0.820950i	−0.911872	−	0.410475i	$-0.865363\pi$
$463$		−	17.6647i		−	0.820950i	0.911872	−	0.410475i	$-0.134637\pi$
$464$		0			0
$465$	15.3013	−	10.8207i	0.709582	−	0.501800i
$466$		0			0
$467$	−35.6501			−1.64969			−0.824845	−	0.565358i	$-0.808738\pi$
$467$	−35.6501			−1.64969			−0.824845	+	0.565358i	$0.808738\pi$
$468$		0			0
$469$		−	14.0852i		−	0.650396i
$470$		0			0
$471$	−1.14468	−	20.9505i	−0.0527439	−	0.965347i
$472$		0			0
$473$	−7.78780	+	29.9926i	−0.358083	+	1.37906i
$474$		0			0
$475$	26.0767	+	12.5614i	1.19648	+	0.576356i
$476$		0			0
$477$	−6.21040	+	0.680670i	−0.284355	+	0.0311657i
$478$		0			0
$479$	−34.2573			−1.56525			−0.782627	−	0.622491i	$-0.786121\pi$
$479$	−34.2573			−1.56525			−0.782627	+	0.622491i	$0.786121\pi$
$480$		0			0
$481$		−	4.90343i		−	0.223577i
$482$		0			0
$483$	−17.2557	+	0.942806i	−0.785163	+	0.0428991i
$484$		0			0
$485$	4.20292	+	6.68972i	0.190845	+	0.303765i
$486$		0			0
$487$			2.65422i			0.120274i	0.998190	+	0.0601371i	$0.0191538\pi$
$487$			2.65422i			0.120274i	−0.998190	+	0.0601371i	$0.980846\pi$
$488$		0			0
$489$	1.39315	+	25.4982i	0.0630003	+	1.15307i
$490$		0			0
$491$	1.84041			0.0830567			0.0415283	−	0.999137i	$-0.486777\pi$
$491$	1.84041			0.0830567			0.0415283	+	0.999137i	$0.486777\pi$
$492$		0			0
$493$		−	6.17019i		−	0.277892i
$494$		0			0
$495$	8.99205	+	20.3505i	0.404162	+	0.914687i
$496$		0			0
$497$		−	28.2385i		−	1.26667i
$498$		0			0
$499$	10.8478			0.485615			0.242807	−	0.970075i	$-0.421932\pi$
$499$	10.8478			0.485615			0.242807	+	0.970075i	$0.421932\pi$
$500$		0			0
$501$	1.50306	+	27.5099i	0.0671520	+	1.22905i
$502$		0			0
$503$		−	3.36875i		−	0.150205i	−0.997176	−	0.0751025i	$-0.976072\pi$
$503$		−	3.36875i		−	0.150205i	0.997176	−	0.0751025i	$-0.0239284\pi$
$504$		0			0
$505$	26.7744	−	16.8214i	1.19145	−	0.748544i
$506$		0			0
$507$	5.75502	−	0.314438i	0.255590	−	0.0139647i
$508$		0			0
$509$			19.5352i			0.865884i	0.901422	+	0.432942i	$0.142524\pi$
$509$			19.5352i			0.865884i	−0.901422	+	0.432942i	$0.857476\pi$
$510$		0			0
$511$	47.4423			2.09872
$512$		0			0
$513$	−4.90357	−	29.6776i	−0.216498	−	1.31030i
$514$		0			0
$515$	−10.7570	−	17.1217i	−0.474008	−	0.754472i
$516$		0			0
$517$	2.43275	−	9.36908i	0.106992	−	0.412052i
$518$		0			0
$519$	−0.636823	−	11.6555i	−0.0279534	−	0.511619i
$520$		0			0
$521$			27.5830i			1.20843i	0.796820	+	0.604217i	$0.206514\pi$
$521$			27.5830i			1.20843i	−0.796820	+	0.604217i	$0.793486\pi$
$522$		0			0
$523$	22.8074			0.997298			0.498649	−	0.866804i	$-0.333830\pi$
$523$	22.8074			0.997298			0.498649	+	0.866804i	$0.333830\pi$
$524$		0			0
$525$	−9.49651	+	22.8215i	−0.414462	+	0.996014i
$526$		0			0
$527$		−	7.41118i		−	0.322836i
$528$		0			0
$529$	−10.7804			−0.468714
$530$		0			0
$531$	2.76802	+	25.2553i	0.120122	+	1.09599i
$532$		0			0
$533$	5.35825			0.232092
$534$		0			0
$535$	16.5078	+	26.2753i	0.713696	+	1.13598i
$536$		0			0
$537$	−1.08914	−	19.9340i	−0.0469998	−	0.860216i
$538$		0			0
$539$	−0.955867	+	3.68127i	−0.0411721	+	0.158564i
$540$		0			0
$541$			7.48613i			0.321854i	0.986966	+	0.160927i	$0.0514484\pi$
$541$			7.48613i			0.321854i	−0.986966	+	0.160927i	$0.948552\pi$
$542$		0			0
$543$	36.0392	−	1.96908i	1.54659	−	0.0845013i
$544$		0			0
$545$	−14.4661	−	23.0255i	−0.619662	−	0.986306i
$546$		0			0
$547$	−19.3067			−0.825495			−0.412748	−	0.910845i	$-0.635431\pi$
$547$	−19.3067			−0.825495			−0.412748	+	0.910845i	$0.635431\pi$
$548$		0			0
$549$	4.12888	+	37.6717i	0.176216	+	1.60779i
$550$		0			0
$551$		−	23.3212i		−	0.993515i
$552$		0			0
$553$			36.0093i			1.53127i
$554$		0			0
$555$	3.52572	+	4.98562i	0.149658	+	0.211628i
$556$		0			0
$557$		−	1.75354i		−	0.0742999i	−0.999310	−	0.0371499i	$-0.988172\pi$
$557$		−	1.75354i		−	0.0742999i	0.999310	−	0.0371499i	$-0.0118279\pi$
$558$		0			0
$559$	29.0572			1.22899
$560$		0			0
$561$	8.62390	+	1.74334i	0.364101	+	0.0736038i
$562$		0			0
$563$		−	42.8178i		−	1.80456i	−0.431156	−	0.902278i	$-0.641894\pi$
$563$		−	42.8178i		−	1.80456i	0.431156	−	0.902278i	$-0.358106\pi$
$564$		0			0
$565$	8.13209	−	5.10911i	0.342120	−	0.214942i
$566$		0			0
$567$	25.0784	−	5.56411i	1.05319	−	0.233671i
$568$		0			0
$569$	−35.0195			−1.46810			−0.734048	−	0.679098i	$-0.762371\pi$
$569$	−35.0195			−1.46810			−0.734048	+	0.679098i	$0.762371\pi$
$570$		0			0
$571$		−	1.23069i		−	0.0515027i	−0.999668	−	0.0257514i	$-0.991802\pi$
$571$		−	1.23069i		−	0.0515027i	0.999668	−	0.0257514i	$-0.00819782\pi$
$572$		0			0
$573$	0.553269	+	10.1262i	0.0231131	+	0.423029i
$574$		0			0
$575$	7.58526	−	15.7465i	0.316327	−	0.656676i
$576$		0			0
$577$			15.4170i			0.641816i	0.947110	+	0.320908i	$0.103988\pi$
$577$			15.4170i			0.641816i	−0.947110	+	0.320908i	$0.896012\pi$
$578$		0			0
$579$	9.74795	−	0.532601i	0.405111	−	0.0221341i
$580$		0			0
$581$			8.00266i			0.332006i
$582$		0			0
$583$	1.73588	−	6.68528i	0.0718928	−	0.276876i
$584$		0			0
$585$	16.3513	−	12.9573i	0.676043	−	0.535719i
$586$		0			0
$587$	−30.1973			−1.24638			−0.623188	−	0.782072i	$-0.714163\pi$
$587$	−30.1973			−1.24638			−0.623188	+	0.782072i	$0.714163\pi$
$588$		0			0
$589$		−	28.0116i		−	1.15420i
$590$		0			0
$591$	−0.670214	−	12.2666i	−0.0275689	−	0.504581i
$592$		0			0
$593$		−	10.2410i		−	0.420547i	−0.977643	−	0.210273i	$-0.932565\pi$
$593$		−	10.2410i		−	0.420547i	0.977643	−	0.210273i	$-0.0674354\pi$
$594$		0			0
$595$	5.20021	+	8.27710i	0.213188	+	0.339328i
$596$		0			0
$597$	−2.68198	+	0.146536i	−0.109766	+	0.00599732i
$598$		0			0
$599$		−	23.8017i		−	0.972510i	−0.873817	−	0.486255i	$-0.838363\pi$
$599$		−	23.8017i		−	0.972510i	0.873817	−	0.486255i	$-0.161637\pi$
$600$		0			0
$601$			23.9489i			0.976894i	0.872594	+	0.488447i	$0.162436\pi$
$601$			23.9489i			0.976894i	−0.872594	+	0.488447i	$0.837564\pi$
$602$		0			0
$603$	−1.61294	−	14.7164i	−0.0656839	−	0.599297i
$604$		0			0
$605$	−24.5624	+	1.29934i	−0.998604	+	0.0528258i
$606$		0			0
$607$	−16.2526			−0.659673			−0.329836	−	0.944038i	$-0.606994\pi$
$607$	−16.2526			−0.659673			−0.329836	+	0.944038i	$0.606994\pi$
$608$		0			0
$609$	19.8866	−	1.08655i	0.805845	−	0.0440291i
$610$		0			0
$611$	−9.07685			−0.367210
$612$		0			0
$613$	24.3624			0.983989			0.491995	−	0.870598i	$-0.336268\pi$
$613$	24.3624			0.983989			0.491995	+	0.870598i	$0.336268\pi$
$614$		0			0
$615$	−5.44806	+	3.85275i	−0.219687	+	0.155358i
$616$		0			0
$617$	−38.6638			−1.55655			−0.778273	−	0.627926i	$-0.783904\pi$
$617$	−38.6638			−1.55655			−0.778273	+	0.627926i	$0.783904\pi$
$618$		0			0
$619$	−44.2276			−1.77766			−0.888828	−	0.458240i	$-0.848480\pi$
$619$	−44.2276			−1.77766			−0.888828	+	0.458240i	$0.848480\pi$
$620$		0			0
$621$	−17.9210	+	2.96105i	−0.719143	+	0.118823i
$622$		0			0
$623$		−	42.7426i		−	1.71245i
$624$		0			0
$625$	−15.5830	−	19.5492i	−0.623318	−	0.781968i
$626$		0			0
$627$	32.5953	+	6.58920i	1.30173	+	0.263147i
$628$		0			0
$629$	2.41478			0.0962836
$630$		0			0
$631$	−29.4500			−1.17239			−0.586193	−	0.810171i	$-0.699374\pi$
$631$	−29.4500			−1.17239			−0.586193	+	0.810171i	$0.699374\pi$
$632$		0			0
$633$	1.13556	+	20.7836i	0.0451344	+	0.826075i
$634$		0			0
$635$	−31.7882	+	19.9714i	−1.26148	+	0.792541i
$636$		0			0
$637$	3.56645			0.141308
$638$		0			0
$639$	−3.23366	−	29.5038i	−0.127922	−	1.16715i
$640$		0			0
$641$		−	10.5555i		−	0.416917i	−0.978031	−	0.208459i	$-0.933155\pi$
$641$		−	10.5555i		−	0.416917i	0.978031	−	0.208459i	$-0.0668447\pi$
$642$		0			0
$643$		−	21.1520i		−	0.834154i	−0.908871	−	0.417077i	$-0.863054\pi$
$643$		−	21.1520i		−	0.834154i	0.908871	−	0.417077i	$-0.136946\pi$
$644$		0			0
$645$	−29.5442	+	20.8930i	−1.16330	+	0.822660i
$646$		0			0
$647$	40.9567			1.61017			0.805087	−	0.593156i	$-0.202118\pi$
$647$	40.9567			1.61017			0.805087	+	0.593156i	$0.202118\pi$
$648$		0			0
$649$	−27.1864	−	7.05914i	−1.06716	−	0.277096i
$650$		0			0
$651$	23.8863	−	1.30508i	0.936178	−	0.0511501i
$652$		0			0
$653$	−44.7908			−1.75280			−0.876400	−	0.481584i	$-0.840062\pi$
$653$	−44.7908			−1.75280			−0.876400	+	0.481584i	$0.840062\pi$
$654$		0			0
$655$	31.4199	−	19.7400i	1.22768	−	0.771307i
$656$		0			0
$657$	49.5680	−	5.43274i	1.93383	−	0.211951i
$658$		0			0
$659$	−22.1491			−0.862806			−0.431403	−	0.902159i	$-0.641981\pi$
$659$	−22.1491			−0.862806			−0.431403	+	0.902159i	$0.641981\pi$
$660$		0			0
$661$	30.6906			1.19372			0.596862	−	0.802344i	$-0.296414\pi$
$661$	30.6906			1.19372			0.596862	+	0.802344i	$0.296414\pi$
$662$		0			0
$663$	−0.450104	−	8.23805i	−0.0174806	−	0.319939i
$664$		0			0
$665$	19.6550	+	31.2845i	0.762187	+	1.21316i
$666$		0			0
$667$	−14.0826			−0.545280
$668$		0			0
$669$	2.44541	+	44.7573i	0.0945451	+	1.73042i
$670$		0			0
$671$	−40.5523	−	10.5297i	−1.56550	−	0.406494i
$672$		0			0
$673$	24.6146			0.948825			0.474412	−	0.880303i	$-0.342661\pi$
$673$	24.6146			0.948825			0.474412	+	0.880303i	$0.342661\pi$
$674$		0			0
$675$	−7.30867	+	24.9316i	−0.281311	+	0.959617i
$676$		0			0
$677$		−	9.01530i		−	0.346486i	−0.984879	−	0.173243i	$-0.944575\pi$
$677$		−	9.01530i		−	0.346486i	0.984879	−	0.173243i	$-0.0554246\pi$
$678$		0			0
$679$			10.0846i			0.387011i
$680$		0			0
$681$	1.06885	+	19.5628i	0.0409586	+	0.749647i
$682$		0			0
$683$	5.47492			0.209492			0.104746	−	0.994499i	$-0.466597\pi$
$683$	5.47492			0.209492			0.104746	+	0.994499i	$0.466597\pi$
$684$		0			0
$685$	30.0668	−	18.8899i	1.14879	−	0.721747i
$686$		0			0
$687$	7.63308	−	0.417050i	0.291220	−	0.0159114i
$688$		0			0
$689$	−6.47676			−0.246745
$690$		0			0
$691$	40.6040			1.54465			0.772325	−	0.635228i	$-0.219094\pi$
$691$	40.6040			1.54465			0.772325	+	0.635228i	$0.219094\pi$
$692$		0			0
$693$	−4.10016	+	28.1019i	−0.155752	+	1.06750i
$694$		0			0
$695$	−22.8607	−	36.3870i	−0.867156	−	1.38024i
$696$		0			0
$697$			2.63876i			0.0999503i
$698$		0			0
$699$	0.535109	+	9.79385i	0.0202397	+	0.370437i
$700$		0			0
$701$	1.21074			0.0457290			0.0228645	−	0.999739i	$-0.492721\pi$
$701$	1.21074			0.0457290			0.0228645	+	0.999739i	$0.492721\pi$
$702$		0			0
$703$	9.12701			0.344232
$704$		0			0
$705$	9.22899	−	6.52653i	0.347584	−	0.245803i
$706$		0			0
$707$	40.3618			1.51796
$708$		0			0
$709$	−31.8172			−1.19492			−0.597461	−	0.801898i	$-0.703824\pi$
$709$	−31.8172			−1.19492			−0.597461	+	0.801898i	$0.703824\pi$
$710$		0			0
$711$	4.12351	+	37.6227i	0.154644	+	1.41096i
$712$		0			0
$713$	−16.9150			−0.633471
$714$		0			0
$715$	6.96790	+	21.9870i	0.260585	+	0.822268i
$716$		0			0
$717$	38.3160	−	2.09348i	1.43094	−	0.0781824i
$718$		0			0
$719$		−	8.98425i		−	0.335056i	−0.985867	−	0.167528i	$-0.946422\pi$
$719$		−	8.98425i		−	0.335056i	0.985867	−	0.167528i	$-0.0535785\pi$
$720$		0			0
$721$		−	25.8105i		−	0.961235i
$722$		0			0
$723$	1.05011	+	19.2197i	0.0390540	+	0.714788i
$724$		0			0
$725$	−8.74172	+	18.1473i	−0.324659	+	0.673973i
$726$		0			0
$727$		−	33.4630i		−	1.24107i	−0.784177	−	0.620537i	$-0.786915\pi$
$727$		−	33.4630i		−	1.24107i	0.784177	−	0.620537i	$-0.213085\pi$
$728$		0			0
$729$	25.5650	−	8.68522i	0.946850	−	0.321675i
$730$		0			0
$731$			14.3097i			0.529263i
$732$		0			0
$733$	−13.4593			−0.497132			−0.248566	−	0.968615i	$-0.579959\pi$
$733$	−13.4593			−0.497132			−0.248566	+	0.968615i	$0.579959\pi$
$734$		0			0
$735$	−3.62623	+	2.56439i	−0.133755	+	0.0945888i
$736$		0			0
$737$	15.8417	+	4.11339i	0.583535	+	0.151519i
$738$		0			0
$739$			44.2072i			1.62619i	0.582132	+	0.813094i	$0.302219\pi$
$739$			44.2072i			1.62619i	−0.582132	+	0.813094i	$0.697781\pi$
$740$		0			0
$741$	−1.70123	−	31.1369i	−0.0624964	−	1.14384i
$742$		0			0
$743$			15.5730i			0.571319i	0.958331	+	0.285659i	$0.0922126\pi$
$743$			15.5730i			0.571319i	−0.958331	+	0.285659i	$0.907787\pi$
$744$		0			0
$745$	−8.75494	+	5.50042i	−0.320756	+	0.201520i
$746$		0			0
$747$	0.916405	+	8.36124i	0.0335295	+	0.305922i
$748$		0			0
$749$			39.6093i			1.44729i
$750$		0			0
$751$	−16.8398			−0.614493			−0.307247	−	0.951630i	$-0.599408\pi$
$751$	−16.8398			−0.614493			−0.307247	+	0.951630i	$0.599408\pi$
$752$		0			0
$753$	−0.757108	−	13.8570i	−0.0275905	−	0.504977i
$754$		0			0
$755$	4.41871	+	7.03319i	0.160813	+	0.255964i
$756$		0			0
$757$		−	28.0102i		−	1.01805i	−0.860753	−	0.509023i	$-0.830007\pi$
$757$		−	28.0102i		−	1.01805i	0.860753	−	0.509023i	$-0.169993\pi$
$758$		0			0
$759$	3.97892	−	19.6828i	0.144426	−	0.714442i
$760$		0			0
$761$	18.0535			0.654437			0.327219	−	0.944949i	$-0.393889\pi$
$761$	18.0535			0.654437			0.327219	+	0.944949i	$0.393889\pi$
$762$		0			0
$763$		−	34.7104i		−	1.25660i
$764$		0			0
$765$	6.38105	+	8.05248i	0.230707	+	0.291138i
$766$		0			0
$767$			26.3385i			0.951027i
$768$		0			0
$769$			50.2306i			1.81136i	0.423961	+	0.905680i	$0.360639\pi$
$769$			50.2306i			1.81136i	−0.423961	+	0.905680i	$0.639361\pi$
$770$		0			0
$771$	−28.5519	+	1.56000i	−1.02827	+	0.0561818i
$772$		0			0
$773$	3.37504			0.121392			0.0606959	−	0.998156i	$-0.480668\pi$
$773$	3.37504			0.121392			0.0606959	+	0.998156i	$0.480668\pi$
$774$		0			0
$775$	−10.4999	+	21.7972i	−0.377168	+	0.782977i
$776$		0			0
$777$	0.425234	+	7.78286i	0.0152552	+	0.279208i
$778$		0			0
$779$			9.97359i			0.357341i
$780$		0			0
$781$	31.7598	+	8.24665i	1.13645	+	0.295088i
$782$		0			0
$783$	20.6532	−	3.41250i	0.738086	−	0.121953i
$784$		0			0
$785$	14.4101	+	22.9363i	0.514317	+	0.818630i
$786$		0			0
$787$	33.6114			1.19812			0.599058	−	0.800706i	$-0.295542\pi$
$787$	33.6114			1.19812			0.599058	+	0.800706i	$0.295542\pi$
$788$		0			0
$789$	−1.59738	−	29.2360i	−0.0568681	−	1.04083i
$790$		0			0
$791$	12.2589			0.435877
$792$		0			0
$793$			39.2874i			1.39514i
$794$		0			0
$795$	6.58532	−	4.65699i	0.233557	−	0.165166i
$796$		0			0
$797$	14.5377			0.514952			0.257476	−	0.966285i	$-0.417109\pi$
$797$	14.5377			0.514952			0.257476	+	0.966285i	$0.417109\pi$
$798$		0			0
$799$		−	4.47005i		−	0.158139i
$800$		0			0
$801$	−4.89457	−	44.6578i	−0.172941	−	1.57791i
$802$		0			0
$803$	−13.8548	+	53.3583i	−0.488927	+	1.88297i
$804$		0			0
$805$	18.8913	−	11.8688i	0.665831	−	0.418319i
$806$		0			0
$807$	−1.10383	−	20.2029i	−0.0388567	−	0.711177i
$808$		0			0
$809$	43.5054			1.52957			0.764785	−	0.644286i	$-0.222845\pi$
$809$	43.5054			1.52957			0.764785	+	0.644286i	$0.222845\pi$
$810$		0			0
$811$			3.57717i			0.125612i	0.998026	+	0.0628058i	$0.0200049\pi$
$811$			3.57717i			0.125612i	−0.998026	+	0.0628058i	$0.979995\pi$
$812$		0			0
$813$	−0.0425669	−	0.779082i	−0.00149289	−	0.0273236i
$814$		0			0
$815$	−17.5380	−	27.9150i	−0.614330	−	0.977819i
$816$		0			0
$817$			54.0856i			1.89222i
$818$		0			0
$819$	26.4720	−	2.90138i	0.925008	−	0.101382i
$820$		0			0
$821$	−30.4349			−1.06219			−0.531093	−	0.847314i	$-0.678218\pi$
$821$	−30.4349			−1.06219			−0.531093	+	0.847314i	$0.678218\pi$
$822$		0			0
$823$			26.8246i			0.935048i	0.883980	+	0.467524i	$0.154854\pi$
$823$			26.8246i			0.935048i	−0.883980	+	0.467524i	$0.845146\pi$
$824$		0			0
$825$	−22.8940	−	17.3454i	−0.797068	−	0.603890i
$826$		0			0
$827$		−	12.9746i		−	0.451171i	−0.974223	−	0.225585i	$-0.927571\pi$
$827$		−	12.9746i		−	0.451171i	0.974223	−	0.225585i	$-0.0724294\pi$
$828$		0			0
$829$	25.4042			0.882324			0.441162	−	0.897428i	$-0.354566\pi$
$829$	25.4042			0.882324			0.441162	+	0.897428i	$0.354566\pi$
$830$		0			0
$831$	33.3401	−	1.82161i	1.15656	−	0.0631910i
$832$		0			0
$833$			1.75636i			0.0608543i
$834$		0			0
$835$	−18.9217	−	30.1174i	−0.654813	−	1.04226i
$836$		0			0
$837$	24.8071	−	4.09884i	0.857460	−	0.141677i
$838$		0			0
$839$			25.8716i			0.893185i	0.894737	+	0.446593i	$0.147363\pi$
$839$			25.8716i			0.893185i	−0.894737	+	0.446593i	$0.852637\pi$
$840$		0			0
$841$	−12.7703			−0.440357
$842$		0			0
$843$	−9.70550	+	0.530281i	−0.334275	+	0.0182639i
$844$		0			0
$845$	−6.30051	+	3.95839i	−0.216744	+	0.136173i
$846$		0			0
$847$	−27.4305	−	15.2749i	−0.942524	−	0.524852i
$848$		0			0
$849$	26.3455	−	1.43945i	0.904176	−	0.0494016i
$850$		0			0
$851$		−	5.51139i		−	0.188928i
$852$		0			0
$853$	40.5474			1.38831			0.694157	−	0.719823i	$-0.255777\pi$
$853$	40.5474			1.38831			0.694157	+	0.719823i	$0.255777\pi$
$854$		0			0
$855$	24.1181	+	30.4355i	0.824822	+	1.04087i
$856$		0			0
$857$		−	22.8235i		−	0.779635i	−0.920892	−	0.389818i	$-0.872538\pi$
$857$		−	22.8235i		−	0.779635i	0.920892	−	0.389818i	$-0.127462\pi$
$858$		0			0
$859$	13.3018			0.453851			0.226926	−	0.973912i	$-0.427133\pi$
$859$	13.3018			0.453851			0.226926	+	0.973912i	$0.427133\pi$
$860$		0			0
$861$	−8.50476	+	0.464676i	−0.289841	+	0.0158361i
$862$		0			0
$863$	17.6076			0.599370			0.299685	−	0.954038i	$-0.403118\pi$
$863$	17.6076			0.599370			0.299685	+	0.954038i	$0.403118\pi$
$864$		0			0
$865$	8.01681	+	12.7602i	0.272580	+	0.433861i
$866$		0			0
$867$	−25.3440	+	1.38473i	−0.860729	+	0.0470278i
$868$		0			0
$869$	−40.4996	−	10.5160i	−1.37385	−	0.356731i
$870$		0			0
$871$		−	15.3475i		−	0.520032i
$872$		0			0
$873$	1.15481	+	10.5364i	0.0390845	+	0.356605i
$874$		0			0
$875$	−3.56773	−	31.7114i	−0.120611	−	1.07204i
$876$		0			0
$877$	−43.2099			−1.45909			−0.729547	−	0.683930i	$-0.760269\pi$
$877$	−43.2099			−1.45909			−0.729547	+	0.683930i	$0.760269\pi$
$878$		0			0
$879$	2.86140	+	52.3708i	0.0965125	+	1.76642i
$880$		0			0
$881$		−	23.8470i		−	0.803427i	−0.915765	−	0.401714i	$-0.868415\pi$
$881$		−	23.8470i		−	0.803427i	0.915765	−	0.401714i	$-0.131585\pi$
$882$		0			0
$883$		−	48.6588i		−	1.63750i	−0.574152	−	0.818749i	$-0.694668\pi$
$883$		−	48.6588i		−	1.63750i	0.574152	−	0.818749i	$-0.305332\pi$
$884$		0			0
$885$	−18.9382	−	26.7799i	−0.636599	−	0.900197i
$886$		0			0
$887$		−	5.99894i		−	0.201425i	−0.994916	−	0.100712i	$-0.967888\pi$
$887$		−	5.99894i		−	0.201425i	0.994916	−	0.100712i	$-0.0321122\pi$
$888$		0			0
$889$	−47.9199			−1.60718
$890$		0			0
$891$	−1.06585	+	29.8306i	−0.0357073	+	0.999362i
$892$		0			0
$893$		−	16.8952i		−	0.565377i
$894$		0			0
$895$	13.7109	+	21.8234i	0.458305	+	0.729477i
$896$		0			0
$897$	−18.8022	+	1.02730i	−0.627786	+	0.0343005i
$898$		0			0
$899$	19.4939			0.650157
$900$		0			0
$901$		−	3.18959i		−	0.106261i
$902$		0			0
$903$	−46.1203	+	2.51988i	−1.53479	+	0.0838565i
$904$		0			0
$905$	−39.4551	+	24.7883i	−1.31153	+	0.823990i
$906$		0			0
$907$			43.4114i			1.44145i	0.693220	+	0.720726i	$0.256191\pi$
$907$			43.4114i			1.44145i	−0.693220	+	0.720726i	$0.743809\pi$
$908$		0			0
$909$	42.1703	−	4.62193i	1.39870	−	0.153300i
$910$		0			0
$911$			51.4001i			1.70296i	0.524385	+	0.851481i	$0.324295\pi$
$911$			51.4001i			1.70296i	−0.524385	+	0.851481i	$0.675705\pi$
$912$		0			0
$913$	−9.00058	−	2.33706i	−0.297876	−	0.0773455i
$914$		0			0
$915$	−28.2489	−	39.9459i	−0.933878	−	1.32057i
$916$		0			0
$917$	47.3647			1.56412
$918$		0			0
$919$		−	59.0084i		−	1.94651i	−0.229733	−	0.973254i	$-0.573785\pi$
$919$		−	59.0084i		−	1.94651i	0.229733	−	0.973254i	$-0.426215\pi$
$920$		0			0
$921$	6.83387	−	0.373384i	0.225184	−	0.0123034i
$922$		0			0
$923$		−	30.7692i		−	1.01278i
$924$		0			0
$925$	−7.10216	−	3.42118i	−0.233517	−	0.112488i
$926$		0			0
$927$	−2.95563	−	26.9670i	−0.0970756	−	0.885713i
$928$		0			0
$929$		−	55.7545i		−	1.82925i	−0.404306	−	0.914624i	$-0.632487\pi$
$929$		−	55.7545i		−	1.82925i	0.404306	−	0.914624i	$-0.367513\pi$
$930$		0			0
$931$			6.63842i			0.217565i
$932$		0			0
$933$	2.43631	+	44.5907i	0.0797613	+	1.45983i
$934$		0			0
$935$	−10.8279	+	3.43146i	−0.354110	+	0.112221i
$936$		0			0
$937$	0.426723			0.0139404			0.00697022	−	0.999976i	$-0.497781\pi$
$937$	0.426723			0.0139404			0.00697022	+	0.999976i	$0.497781\pi$
$938$		0			0
$939$	−2.11290	−	38.6714i	−0.0689519	−	1.26199i
$940$		0			0
$941$	−5.83536			−0.190227			−0.0951136	−	0.995466i	$-0.530321\pi$
$941$	−5.83536			−0.190227			−0.0951136	+	0.995466i	$0.530321\pi$
$942$		0			0
$943$	6.02261			0.196123
$944$		0			0
$945$	−24.8295	+	21.9842i	−0.807705	+	0.715146i
$946$		0			0
$947$	38.0982			1.23803			0.619013	−	0.785381i	$-0.287533\pi$
$947$	38.0982			1.23803			0.619013	+	0.785381i	$0.287533\pi$
$948$		0			0
$949$	51.6940			1.67806
$950$		0			0
$951$	27.2300	−	1.48777i	0.882994	−	0.0482443i
$952$		0			0
$953$		−	32.9366i		−	1.06692i	−0.845825	−	0.533461i	$-0.820891\pi$
$953$		−	32.9366i		−	1.06692i	0.845825	−	0.533461i	$-0.179109\pi$
$954$		0			0
$955$	−6.96497	−	11.0860i	−0.225381	−	0.358736i
$956$		0			0
$957$	−4.58556	+	22.6837i	−0.148230	+	0.733261i
$958$		0			0
$959$	45.3250			1.46362
$960$		0			0
$961$	−7.58541			−0.244691
$962$		0			0
$963$	4.53577	+	41.3841i	0.146163	+	1.33358i
$964$		0			0
$965$	−10.6719	+	6.70478i	−0.343541	+	0.215835i
$966$		0			0
$967$	−27.2073			−0.874928			−0.437464	−	0.899236i	$-0.644123\pi$
$967$	−27.2073			−0.874928			−0.437464	+	0.899236i	$0.644123\pi$
$968$		0			0
$969$	15.3339	−	0.837802i	0.492596	−	0.0269141i
$970$		0			0
$971$			21.2003i			0.680351i	0.940362	+	0.340176i	$0.110487\pi$
$971$			21.2003i			0.680351i	−0.940362	+	0.340176i	$0.889513\pi$
$972$		0			0
$973$		−	54.8525i		−	1.75849i
$974$		0			0
$975$	−10.3476	+	24.8668i	−0.331388	+	0.796374i
$976$		0			0
$977$	−35.4560			−1.13434			−0.567169	−	0.823601i	$-0.691961\pi$
$977$	−35.4560			−1.13434			−0.567169	+	0.823601i	$0.691961\pi$
$978$		0			0
$979$	48.0726	+	12.4824i	1.53641	+	0.398938i
$980$		0			0
$981$	−3.97478	−	36.2657i	−0.126905	−	1.15788i
$982$		0			0
$983$	24.3822			0.777670			0.388835	−	0.921307i	$-0.372878\pi$
$983$	24.3822			0.777670			0.388835	+	0.921307i	$0.372878\pi$
$984$		0			0
$985$	8.43716	+	13.4293i	0.268830	+	0.427893i
$986$		0			0
$987$	14.4070	−	0.787159i	0.458580	−	0.0250556i
$988$		0			0
$989$	32.6599			1.03852
$990$		0			0
$991$	−37.2746			−1.18407			−0.592034	−	0.805913i	$-0.701675\pi$
$991$	−37.2746			−1.18407			−0.592034	+	0.805913i	$0.701675\pi$
$992$		0			0
$993$	8.73010	−	0.476988i	0.277041	−	0.0151368i
$994$		0			0
$995$	2.93619	−	1.84471i	0.0930835	−	0.0584811i
$996$		0			0
$997$	−29.9697			−0.949151			−0.474575	−	0.880215i	$-0.657398\pi$
$997$	−29.9697			−0.949151			−0.474575	+	0.880215i	$0.657398\pi$
$998$		0			0
$999$	1.33552	+	8.08289i	0.0422540	+	0.255731i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1320.2.ba.a.329.4	yes	72
3.2	odd	2	inner	1320.2.ba.a.329.72	yes	72
5.4	even	2	inner	1320.2.ba.a.329.69	yes	72
11.10	odd	2	inner	1320.2.ba.a.329.3	yes	72
15.14	odd	2	inner	1320.2.ba.a.329.1	✓	72
33.32	even	2	inner	1320.2.ba.a.329.71	yes	72
55.54	odd	2	inner	1320.2.ba.a.329.70	yes	72
165.164	even	2	inner	1320.2.ba.a.329.2	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1320.2.ba.a.329.1	✓	72	15.14	odd	2	inner
1320.2.ba.a.329.2	yes	72	165.164	even	2	inner
1320.2.ba.a.329.3	yes	72	11.10	odd	2	inner
1320.2.ba.a.329.4	yes	72	1.1	even	1	trivial
1320.2.ba.a.329.69	yes	72	5.4	even	2	inner
1320.2.ba.a.329.70	yes	72	55.54	odd	2	inner
1320.2.ba.a.329.71	yes	72	33.32	even	2	inner
1320.2.ba.a.329.72	yes	72	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 1320 = 2^{3} \cdot 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1320.ba (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.72947 + 0.0944935i) q^{3} +(1.89340 - 1.18956i) q^{5} +2.85425 q^{7} +(2.98214 - 0.326848i) q^{9} +O(q^{10})\)	\(q+(-1.72947 + 0.0944935i) q^{3} +(1.89340 - 1.18956i) q^{5} +2.85425 q^{7} +(2.98214 - 0.326848i) q^{9} +(-0.833543 + 3.21017i) q^{11} +3.11005 q^{13} +(-3.16217 + 2.23622i) q^{15} +1.53160i q^{17} +5.78889i q^{19} +(-4.93635 + 0.269708i) q^{21} +3.49565 q^{23} +(2.16991 - 4.50461i) q^{25} +(-5.12664 + 0.847066i) q^{27} -4.02861 q^{29} -4.83886 q^{31} +(1.13825 - 5.63067i) q^{33} +(5.40423 - 3.39529i) q^{35} -1.57664i q^{37} +(-5.37873 + 0.293879i) q^{39} +1.72289 q^{41} +9.34300 q^{43} +(5.25758 - 4.16628i) q^{45} -2.91856 q^{47} +1.14675 q^{49} +(-0.144726 - 2.64885i) q^{51} -2.08253 q^{53} +(2.24045 + 7.06968i) q^{55} +(-0.547012 - 10.0117i) q^{57} +8.46884i q^{59} +12.6324i q^{61} +(8.51178 - 0.932905i) q^{63} +(5.88855 - 3.69957i) q^{65} -4.93483i q^{67} +(-6.04563 + 0.330316i) q^{69} -9.89348i q^{71} +16.6216 q^{73} +(-3.32715 + 7.99563i) q^{75} +(-2.37914 + 9.16264i) q^{77} +12.6160i q^{79} +(8.78634 - 1.94941i) q^{81} +2.80377i q^{83} +(1.82192 + 2.89992i) q^{85} +(6.96736 - 0.380677i) q^{87} -14.9751i q^{89} +8.87685 q^{91} +(8.36867 - 0.457241i) q^{93} +(6.88621 + 10.9607i) q^{95} +3.53318i q^{97} +(-1.43651 + 9.84563i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q+O(q^{10}) \) 72 * q	\( 72 q - 6 q^{15} - 4 q^{25} + 34 q^{45} + 96 q^{49} - 28 q^{55} + 28 q^{69} + 14 q^{75} + 16 q^{81} - 48 q^{91} - 4 q^{99}+O(q^{100}) \) 72 * q - 6 * q^15 - 4 * q^25 + 34 * q^45 + 96 * q^49 - 28 * q^55 + 28 * q^69 + 14 * q^75 + 16 * q^81 - 48 * q^91 - 4 * q^99

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