LMFDB - Embedded newform 432.3.q.b.305.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,3,Mod(17,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("432.17");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	432.q (of order $6$, degree $2$, 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:	$11.7711474204$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-11})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x^{2} - 3x + 9 $ x^4 - x^3 - 2x^2 - 3x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			305.1
Root			$1.68614 + 0.396143i$ of defining polynomial
Character	$\chi$	$=$	432.305
Dual form			432.3.q.b.17.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-6.55842 + 3.78651i) q^{5} +(4.55842 - 7.89542i) q^{7} +O(q^{10})$	$q+(-6.55842 + 3.78651i) q^{5} +(4.55842 - 7.89542i) q^{7} +(-0.383156 - 0.221215i) q^{11} +(5.55842 + 9.62747i) q^{13} -8.01544i q^{17} +8.11684 q^{19} +(20.4416 - 11.8020i) q^{23} +(16.1753 - 28.0164i) q^{25} +(45.9090 + 26.5055i) q^{29} +(14.6753 + 25.4183i) q^{31} +69.0420i q^{35} +18.4674 q^{37} +(38.9674 - 22.4978i) q^{41} +(11.5000 - 19.9186i) q^{43} +(-7.32473 - 4.22894i) q^{47} +(-17.0584 - 29.5461i) q^{49} +60.5841i q^{53} +3.35053 q^{55} +(65.9674 - 38.0863i) q^{59} +(-2.67527 + 4.63370i) q^{61} +(-72.9090 - 42.0940i) q^{65} +(-54.8505 - 95.0039i) q^{67} -16.0309i q^{71} -4.35053 q^{73} +(-3.49317 + 2.01678i) q^{77} +(0.792110 - 1.37197i) q^{79} +(-7.32473 - 4.22894i) q^{83} +(30.3505 + 52.5687i) q^{85} +64.1236i q^{89} +101.351 q^{91} +(-53.2337 + 30.7345i) q^{95} +(-57.6168 + 99.7953i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 9 q^{5} + q^{7}+O(q^{10}) $ 4 * q - 9 * q^5 + q^7	$ 4 q - 9 q^{5} + q^{7} - 36 q^{11} + 5 q^{13} - 2 q^{19} + 99 q^{23} + 13 q^{25} + 63 q^{29} + 7 q^{31} - 64 q^{37} + 18 q^{41} + 46 q^{43} - 81 q^{47} - 51 q^{49} - 90 q^{55} + 126 q^{59} + 41 q^{61} - 171 q^{65} - 116 q^{67} + 86 q^{73} + 279 q^{77} - 83 q^{79} - 81 q^{83} + 18 q^{85} + 302 q^{91} - 144 q^{95} - 196 q^{97}+O(q^{100}) $ 4 * q - 9 * q^5 + q^7 - 36 * q^11 + 5 * q^13 - 2 * q^19 + 99 * q^23 + 13 * q^25 + 63 * q^29 + 7 * q^31 - 64 * q^37 + 18 * q^41 + 46 * q^43 - 81 * q^47 - 51 * q^49 - 90 * q^55 + 126 * q^59 + 41 * q^61 - 171 * q^65 - 116 * q^67 + 86 * q^73 + 279 * q^77 - 83 * q^79 - 81 * q^83 + 18 * q^85 + 302 * q^91 - 144 * q^95 - 196 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−6.55842	+	3.78651i	−1.31168	+	0.757301i	−0.982375	−	0.186921i	$-0.940149\pi$
$5$	−6.55842	+	3.78651i	−1.31168	+	0.757301i	−0.329309	+	0.944222i	$0.606816\pi$
$6$		0			0
$7$	4.55842	−	7.89542i	0.651203	−	1.12792i	−0.331628	−	0.943410i	$-0.607598\pi$
$7$	4.55842	−	7.89542i	0.651203	−	1.12792i	0.982831	−	0.184507i	$-0.0590688\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.383156	−	0.221215i	−0.0348324	−	0.0201105i	0.482483	−	0.875906i	$-0.339735\pi$
$11$	−0.383156	−	0.221215i	−0.0348324	−	0.0201105i	−0.517315	+	0.855795i	$0.673068\pi$
$12$		0			0
$13$	5.55842	+	9.62747i	0.427571	+	0.740575i	0.996657	−	0.0817036i	$-0.0260361\pi$
$13$	5.55842	+	9.62747i	0.427571	+	0.740575i	−0.569086	+	0.822278i	$0.692703\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	8.01544i		−	0.471497i	−0.971814	−	0.235748i	$-0.924246\pi$
$17$		−	8.01544i		−	0.471497i	0.971814	−	0.235748i	$-0.0757541\pi$
$18$		0			0
$19$	8.11684			0.427202			0.213601	−	0.976921i	$-0.431481\pi$
$19$	8.11684			0.427202			0.213601	+	0.976921i	$0.431481\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	20.4416	−	11.8020i	0.888764	−	0.513128i	0.0152262	−	0.999884i	$-0.495153\pi$
$23$	20.4416	−	11.8020i	0.888764	−	0.513128i	0.873538	+	0.486756i	$0.161820\pi$
$24$		0			0
$25$	16.1753	−	28.0164i	0.647011	−	1.12066i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	45.9090	+	26.5055i	1.58307	+	0.913984i	0.994408	+	0.105603i	$0.0336772\pi$
$29$	45.9090	+	26.5055i	1.58307	+	0.913984i	0.588659	+	0.808381i	$0.299656\pi$
$30$		0			0
$31$	14.6753	+	25.4183i	0.473396	+	0.819945i	0.999536	−	0.0304523i	$-0.00969476\pi$
$31$	14.6753	+	25.4183i	0.473396	+	0.819945i	−0.526141	+	0.850398i	$0.676361\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$			69.0420i			1.97263i
$36$		0			0
$37$	18.4674			0.499118			0.249559	−	0.968360i	$-0.419714\pi$
$37$	18.4674			0.499118			0.249559	+	0.968360i	$0.419714\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	38.9674	−	22.4978i	0.950424	−	0.548727i	0.0572112	−	0.998362i	$-0.481779\pi$
$41$	38.9674	−	22.4978i	0.950424	−	0.548727i	0.893213	+	0.449635i	$0.148446\pi$
$42$		0			0
$43$	11.5000	−	19.9186i	0.267442	−	0.463223i	−0.700759	−	0.713398i	$-0.747155\pi$
$43$	11.5000	−	19.9186i	0.267442	−	0.463223i	0.968200	+	0.250176i	$0.0804883\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−7.32473	−	4.22894i	−0.155845	−	0.0899774i	0.420049	−	0.907501i	$-0.362013\pi$
$47$	−7.32473	−	4.22894i	−0.155845	−	0.0899774i	−0.575895	+	0.817524i	$0.695346\pi$
$48$		0			0
$49$	−17.0584	−	29.5461i	−0.348131	−	0.602981i
$50$		0			0
$51$		0			0
$52$		0			0
$53$			60.5841i			1.14310i	0.820569	+	0.571548i	$0.193657\pi$
$53$			60.5841i			1.14310i	−0.820569	+	0.571548i	$0.806343\pi$
$54$		0			0
$55$	3.35053			0.0609188
$56$		0			0
$57$		0			0
$58$		0			0
$59$	65.9674	−	38.0863i	1.11809	−	0.645530i	0.177178	−	0.984179i	$-0.443303\pi$
$59$	65.9674	−	38.0863i	1.11809	−	0.645530i	0.940913	+	0.338649i	$0.109970\pi$
$60$		0			0
$61$	−2.67527	+	4.63370i	−0.0438568	+	0.0759622i	−0.887121	−	0.461538i	$-0.847298\pi$
$61$	−2.67527	+	4.63370i	−0.0438568	+	0.0759622i	0.843264	+	0.537500i	$0.180631\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−72.9090	−	42.0940i	−1.12168	−	0.647600i
$66$		0			0
$67$	−54.8505	−	95.0039i	−0.818665	−	1.41797i	−0.906666	−	0.421848i	$-0.861381\pi$
$67$	−54.8505	−	95.0039i	−0.818665	−	1.41797i	0.0880017	−	0.996120i	$-0.471952\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	16.0309i		−	0.225787i	−0.993607	−	0.112894i	$-0.963988\pi$
$71$		−	16.0309i		−	0.225787i	0.993607	−	0.112894i	$-0.0360119\pi$
$72$		0			0
$73$	−4.35053			−0.0595963			−0.0297982	−	0.999556i	$-0.509486\pi$
$73$	−4.35053			−0.0595963			−0.0297982	+	0.999556i	$0.509486\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−3.49317	+	2.01678i	−0.0453659	+	0.0261920i
$78$		0			0
$79$	0.792110	−	1.37197i	0.0100267	−	0.0173668i	−0.860969	−	0.508658i	$-0.830142\pi$
$79$	0.792110	−	1.37197i	0.0100267	−	0.0173668i	0.870995	+	0.491291i	$0.163475\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−7.32473	−	4.22894i	−0.0882498	−	0.0509511i	0.455226	−	0.890376i	$-0.349559\pi$
$83$	−7.32473	−	4.22894i	−0.0882498	−	0.0509511i	−0.543475	+	0.839425i	$0.682892\pi$
$84$		0			0
$85$	30.3505	+	52.5687i	0.357065	+	0.618455i
$86$		0			0
$87$		0			0
$88$		0			0
$89$			64.1236i			0.720489i	0.932858	+	0.360245i	$0.117307\pi$
$89$			64.1236i			0.720489i	−0.932858	+	0.360245i	$0.882693\pi$
$90$		0			0
$91$	101.351			1.11374
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−53.2337	+	30.7345i	−0.560355	+	0.323521i
$96$		0			0
$97$	−57.6168	+	99.7953i	−0.593988	+	1.02882i	0.399701	+	0.916646i	$0.369114\pi$
$97$	−57.6168	+	99.7953i	−0.593988	+	1.02882i	−0.993689	+	0.112172i	$0.964219\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−114.558	−	66.1403i	−1.13424	−	0.654855i	−0.189244	−	0.981930i	$-0.560604\pi$
$101$	−114.558	−	66.1403i	−1.13424	−	0.654855i	−0.944998	+	0.327075i	$0.893937\pi$
$102$		0			0
$103$	62.6753	+	108.557i	0.608498	+	1.05395i	0.991488	+	0.130197i	$0.0415609\pi$
$103$	62.6753	+	108.557i	0.608498	+	1.05395i	−0.382990	+	0.923752i	$0.625106\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	36.5378i		−	0.341475i	−0.985317	−	0.170737i	$-0.945385\pi$
$107$		−	36.5378i		−	0.341475i	0.985317	−	0.170737i	$-0.0546149\pi$
$108$		0			0
$109$	134.701			1.23579			0.617895	−	0.786261i	$-0.287986\pi$
$109$	134.701			1.23579			0.617895	+	0.786261i	$0.287986\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	164.727	−	95.1051i	1.45776	−	0.841638i	0.458859	−	0.888509i	$-0.348258\pi$
$113$	164.727	−	95.1051i	1.45776	−	0.841638i	0.998901	+	0.0468711i	$0.0149250\pi$
$114$		0			0
$115$	−89.3763	+	154.804i	−0.777185	+	1.34612i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−63.2853	−	36.5378i	−0.531809	−	0.307040i
$120$		0			0
$121$	−60.4021	−	104.620i	−0.499191	−	0.864624i
$122$		0			0
$123$		0			0
$124$		0			0
$125$			55.6657i			0.445325i
$126$		0			0
$127$	−184.103			−1.44963			−0.724816	−	0.688943i	$-0.758075\pi$
$127$	−184.103			−1.44963			−0.724816	+	0.688943i	$0.758075\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−109.194	+	63.0433i	−0.833544	+	0.481247i	−0.855064	−	0.518522i	$-0.826483\pi$
$131$	−109.194	+	63.0433i	−0.833544	+	0.481247i	0.0215207	+	0.999768i	$0.493149\pi$
$132$		0			0
$133$	37.0000	−	64.0859i	0.278195	−	0.481849i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−107.617	−	62.1326i	−0.785524	−	0.453523i	0.0528602	−	0.998602i	$-0.483166\pi$
$137$	−107.617	−	62.1326i	−0.785524	−	0.453523i	−0.838385	+	0.545079i	$0.816500\pi$
$138$		0			0
$139$	13.3832	+	23.1803i	0.0962817	+	0.166765i	0.910143	−	0.414295i	$-0.135972\pi$
$139$	13.3832	+	23.1803i	0.0962817	+	0.166765i	−0.813861	+	0.581059i	$0.802638\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		−	4.91843i		−	0.0343946i
$144$		0			0
$145$	−401.454			−2.76865
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−69.8437	+	40.3243i	−0.468750	+	0.270633i	−0.715716	−	0.698391i	$-0.753900\pi$
$149$	−69.8437	+	40.3243i	−0.468750	+	0.270633i	0.246966	+	0.969024i	$0.420566\pi$
$150$		0			0
$151$	49.9742	−	86.5579i	0.330955	−	0.573231i	−0.651744	−	0.758439i	$-0.725963\pi$
$151$	49.9742	−	86.5579i	0.330955	−	0.573231i	0.982699	+	0.185208i	$0.0592958\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−192.493	−	111.136i	−1.24189	−	0.717006i
$156$		0			0
$157$	34.7269	+	60.1487i	0.221190	+	0.383113i	0.955170	−	0.296059i	$-0.0956725\pi$
$157$	34.7269	+	60.1487i	0.221190	+	0.383113i	−0.733979	+	0.679172i	$0.762339\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		−	215.193i		−	1.33660i
$162$		0			0
$163$	−162.467			−0.996732			−0.498366	−	0.866967i	$-0.666066\pi$
$163$	−162.467			−0.996732			−0.498366	+	0.866967i	$0.666066\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	83.7269	−	48.3397i	0.501358	−	0.289459i	−0.227916	−	0.973681i	$-0.573191\pi$
$167$	83.7269	−	48.3397i	0.501358	−	0.289459i	0.729274	+	0.684221i	$0.239858\pi$
$168$		0			0
$169$	22.7079	−	39.3312i	0.134366	−	0.232729i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	24.2731	+	14.0141i	0.140307	+	0.0810064i	0.568510	−	0.822676i	$-0.307520\pi$
$173$	24.2731	+	14.0141i	0.140307	+	0.0810064i	−0.428203	+	0.903682i	$0.640853\pi$
$174$		0			0
$175$	−147.467	−	255.421i	−0.842671	−	1.45955i
$176$		0			0
$177$		0			0
$178$		0			0
$179$			35.6012i			0.198889i	0.995043	+	0.0994447i	$0.0317067\pi$
$179$			35.6012i			0.198889i	−0.995043	+	0.0994447i	$0.968293\pi$
$180$		0			0
$181$	−19.6358			−0.108485			−0.0542426	−	0.998528i	$-0.517274\pi$
$181$	−19.6358			−0.108485			−0.0542426	+	0.998528i	$0.517274\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−121.117	+	69.9268i	−0.654686	+	0.377983i
$186$		0			0
$187$	−1.77314	+	3.07117i	−0.00948202	+	0.0164233i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	188.662	+	108.924i	0.987757	+	0.570282i	0.904603	−	0.426255i	$-0.140167\pi$
$191$	188.662	+	108.924i	0.987757	+	0.570282i	0.0831540	+	0.996537i	$0.473501\pi$
$192$		0			0
$193$	24.5000	+	42.4352i	0.126943	+	0.219872i	0.922491	−	0.386019i	$-0.126150\pi$
$193$	24.5000	+	42.4352i	0.126943	+	0.219872i	−0.795548	+	0.605891i	$0.792817\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			359.965i			1.82723i	0.406575	+	0.913617i	$0.366723\pi$
$197$			359.965i			1.82723i	−0.406575	+	0.913617i	$0.633277\pi$
$198$		0			0
$199$	61.0652			0.306861			0.153430	−	0.988159i	$-0.450968\pi$
$199$	61.0652			0.306861			0.153430	+	0.988159i	$0.450968\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	418.545	−	241.647i	2.06180	−	1.19038i
$204$		0			0
$205$	−170.376	+	295.100i	−0.831104	+	1.43951i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−3.11002	−	1.79557i	−0.0148805	−	0.00859124i
$210$		0			0
$211$	193.493	+	335.140i	0.917029	+	1.58834i	0.803903	+	0.594761i	$0.202753\pi$
$211$	193.493	+	335.140i	0.917029	+	1.58834i	0.113126	+	0.993581i	$0.463913\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$			174.179i			0.810136i
$216$		0			0
$217$	267.584			1.23311
$218$		0			0
$219$		0			0
$220$		0			0
$221$	77.1684	−	44.5532i	0.349178	−	0.201598i
$222$		0			0
$223$	51.3763	−	88.9864i	0.230387	−	0.399042i	−0.727535	−	0.686071i	$-0.759334\pi$
$223$	51.3763	−	88.9864i	0.230387	−	0.399042i	0.957922	+	0.287028i	$0.0926674\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−293.552	−	169.482i	−1.29318	−	0.746617i	−0.313962	−	0.949435i	$-0.601657\pi$
$227$	−293.552	−	169.482i	−1.29318	−	0.746617i	−0.979216	+	0.202818i	$0.934990\pi$
$228$		0			0
$229$	148.376	+	256.995i	0.647932	+	1.12225i	0.983616	+	0.180276i	$0.0576991\pi$
$229$	148.376	+	256.995i	0.647932	+	1.12225i	−0.335685	+	0.941974i	$0.608968\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	346.537i		−	1.48728i	−0.668578	−	0.743642i	$-0.733097\pi$
$233$		−	346.537i		−	1.48728i	0.668578	−	0.743642i	$-0.266903\pi$
$234$		0			0
$235$	64.0516			0.272560
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−140.026	+	80.8439i	−0.585882	+	0.338259i	−0.763468	−	0.645846i	$-0.776505\pi$
$239$	−140.026	+	80.8439i	−0.585882	+	0.338259i	0.177586	+	0.984105i	$0.443171\pi$
$240$		0			0
$241$	162.370	−	281.232i	0.673732	−	1.16694i	−0.303105	−	0.952957i	$-0.598023\pi$
$241$	162.370	−	281.232i	0.673732	−	1.16694i	0.976838	−	0.213982i	$-0.0686433\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	223.753	+	129.184i	0.913276	+	0.527280i
$246$		0			0
$247$	45.1168	+	78.1447i	0.182659	+	0.316375i
$248$		0			0
$249$		0			0
$250$		0			0
$251$			384.012i			1.52993i	0.644074	+	0.764963i	$0.277243\pi$
$251$			384.012i			1.52993i	−0.644074	+	0.764963i	$0.722757\pi$
$252$		0			0
$253$	−10.4431			−0.0412770
$254$		0			0
$255$		0			0
$256$		0			0
$257$	11.2011	−	6.46694i	0.0435839	−	0.0251632i	−0.478050	−	0.878333i	$-0.658656\pi$
$257$	11.2011	−	6.46694i	0.0435839	−	0.0251632i	0.521634	+	0.853170i	$0.325323\pi$
$258$		0			0
$259$	84.1821	−	145.808i	0.325027	−	0.562964i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−42.8437	−	24.7358i	−0.162904	−	0.0940526i	0.416332	−	0.909213i	$-0.363316\pi$
$263$	−42.8437	−	24.7358i	−0.162904	−	0.0940526i	−0.579236	+	0.815160i	$0.696649\pi$
$264$		0			0
$265$	−229.402	−	397.336i	−0.865668	−	1.49938i
$266$		0			0
$267$		0			0
$268$		0			0
$269$			21.4434i			0.0797154i	0.999205	+	0.0398577i	$0.0126905\pi$
$269$			21.4434i			0.0797154i	−0.999205	+	0.0398577i	$0.987310\pi$
$270$		0			0
$271$	326.907			1.20630			0.603150	−	0.797628i	$-0.293912\pi$
$271$	326.907			1.20630			0.603150	+	0.797628i	$0.293912\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−12.3953	+	7.15643i	−0.0450738	+	0.0260234i
$276$		0			0
$277$	238.727	−	413.487i	0.861830	−	1.49273i	−0.00833105	−	0.999965i	$-0.502652\pi$
$277$	238.727	−	413.487i	0.861830	−	1.49273i	0.870161	−	0.492768i	$-0.164015\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	103.064	+	59.5039i	0.366775	+	0.211758i	0.672049	−	0.740507i	$-0.265415\pi$
$281$	103.064	+	59.5039i	0.366775	+	0.211758i	−0.305274	+	0.952265i	$0.598748\pi$
$282$		0			0
$283$	−195.675	−	338.920i	−0.691432	−	1.19760i	−0.971369	−	0.237577i	$-0.923647\pi$
$283$	−195.675	−	338.920i	−0.691432	−	1.19760i	0.279937	−	0.960018i	$-0.409687\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		−	410.218i		−	1.42933i
$288$		0			0
$289$	224.753			0.777691
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−62.0910	+	35.8483i	−0.211915	+	0.122349i	−0.602201	−	0.798345i	$-0.705709\pi$
$293$	−62.0910	+	35.8483i	−0.211915	+	0.122349i	0.390286	+	0.920694i	$0.372376\pi$
$294$		0			0
$295$	−288.428	+	499.572i	−0.977722	+	1.69346i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	227.246	+	131.200i	0.760020	+	0.438797i
$300$		0			0
$301$	−104.844	−	181.595i	−0.348318	−	0.603304i
$302$		0			0
$303$		0			0
$304$		0			0
$305$		−	40.5196i		−	0.132851i
$306$		0			0
$307$	172.351			0.561402			0.280701	−	0.959795i	$-0.409433\pi$
$307$	172.351			0.561402			0.280701	+	0.959795i	$0.409433\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−524.246	+	302.673i	−1.68568	+	0.973227i	−0.727915	+	0.685667i	$0.759511\pi$
$311$	−524.246	+	302.673i	−1.68568	+	0.973227i	−0.957763	+	0.287559i	$0.907156\pi$
$312$		0			0
$313$	−163.734	+	283.595i	−0.523111	+	0.906055i	0.476527	+	0.879160i	$0.341895\pi$
$313$	−163.734	+	283.595i	−0.523111	+	0.906055i	−0.999638	+	0.0268949i	$0.991438\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	59.7921	+	34.5210i	0.188619	+	0.108899i	0.591336	−	0.806425i	$-0.298601\pi$
$317$	59.7921	+	34.5210i	0.188619	+	0.108899i	−0.402717	+	0.915325i	$0.631934\pi$
$318$		0			0
$319$	−11.7269	−	20.3115i	−0.0367613	−	0.0636725i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	65.0601i		−	0.201424i
$324$		0			0
$325$	359.636			1.10657
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−66.7785	+	38.5546i	−0.202974	+	0.117187i
$330$		0			0
$331$	254.895	−	441.492i	0.770076	−	1.33381i	−0.167444	−	0.985882i	$-0.553551\pi$
$331$	254.895	−	441.492i	0.770076	−	1.33381i	0.937521	−	0.347930i	$-0.113115\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	719.466	+	415.384i	2.14766	+	1.23995i
$336$		0			0
$337$	168.720	+	292.232i	0.500653	+	0.867156i	1.00000		0.000754096i	$0.000240036\pi$
$337$	168.720	+	292.232i	0.500653	+	0.867156i	−0.499347	+	0.866402i	$0.666427\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		−	12.9856i		−	0.0380808i
$342$		0			0
$343$	135.687			0.395590
$344$		0			0
$345$		0			0
$346$		0			0
$347$	186.407	−	107.622i	0.537197	−	0.310151i	−0.206745	−	0.978395i	$-0.566287\pi$
$347$	186.407	−	107.622i	0.537197	−	0.310151i	0.743942	+	0.668244i	$0.232954\pi$
$348$		0			0
$349$	−181.012	+	313.522i	−0.518659	+	0.898345i	0.481105	+	0.876663i	$0.340235\pi$
$349$	−181.012	+	313.522i	−0.518659	+	0.898345i	−0.999765	+	0.0216818i	$0.993098\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	506.486	+	292.420i	1.43481	+	0.828385i	0.997482	−	0.0709189i	$-0.0225932\pi$
$353$	506.486	+	292.420i	1.43481	+	0.828385i	0.437323	+	0.899304i	$0.355926\pi$
$354$		0			0
$355$	60.7011	+	105.137i	0.170989	+	0.296161i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	393.693i		−	1.09664i	−0.836269	−	0.548319i	$-0.815268\pi$
$359$		−	393.693i		−	1.09664i	0.836269	−	0.548319i	$-0.184732\pi$
$360$		0			0
$361$	−295.117			−0.817498
$362$		0			0
$363$		0			0
$364$		0			0
$365$	28.5326	−	16.4733i	0.0781716	−	0.0451324i
$366$		0			0
$367$	190.428	−	329.831i	0.518877	−	0.898722i	−0.480882	−	0.876785i	$-0.659684\pi$
$367$	190.428	−	329.831i	0.518877	−	0.898722i	0.999759	−	0.0219364i	$-0.00698314\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	478.337	+	276.168i	1.28932	+	0.744388i
$372$		0			0
$373$	−66.4416	−	115.080i	−0.178128	−	0.308526i	0.763112	−	0.646267i	$-0.223671\pi$
$373$	−66.4416	−	115.080i	−0.178128	−	0.308526i	−0.941239	+	0.337741i	$0.890337\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			589.316i			1.56317i
$378$		0			0
$379$	−507.622			−1.33937			−0.669686	−	0.742644i	$-0.733571\pi$
$379$	−507.622			−1.33937			−0.669686	+	0.742644i	$0.733571\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	287.466	−	165.968i	0.750564	−	0.433338i	−0.0753339	−	0.997158i	$-0.524002\pi$
$383$	287.466	−	165.968i	0.750564	−	0.433338i	0.825898	+	0.563820i	$0.190669\pi$
$384$		0			0
$385$	15.2731	−	26.4539i	0.0396705	−	0.0687113i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−296.662	−	171.278i	−0.762626	−	0.440302i	0.0676116	−	0.997712i	$-0.478462\pi$
$389$	−296.662	−	171.278i	−0.762626	−	0.440302i	−0.830238	+	0.557409i	$0.811795\pi$
$390$		0			0
$391$	−94.5979	−	163.848i	−0.241938	−	0.419049i
$392$		0			0
$393$		0			0
$394$		0			0
$395$			11.9973i			0.0303730i
$396$		0			0
$397$	−24.8043			−0.0624792			−0.0312396	−	0.999512i	$-0.509945\pi$
$397$	−24.8043			−0.0624792			−0.0312396	+	0.999512i	$0.509945\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−52.0842	+	30.0708i	−0.129886	+	0.0749896i	−0.563535	−	0.826092i	$-0.690559\pi$
$401$	−52.0842	+	30.0708i	−0.129886	+	0.0749896i	0.433649	+	0.901082i	$0.357226\pi$
$402$		0			0
$403$	−163.143	+	282.571i	−0.404820	+	0.701170i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−7.07589	−	4.08526i	−0.0173855	−	0.0100375i
$408$		0			0
$409$	240.720	+	416.939i	0.588558	+	1.01941i	0.994422	+	0.105478i	$0.0336373\pi$
$409$	240.720	+	416.939i	0.588558	+	1.01941i	−0.405864	+	0.913933i	$0.633029\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		−	694.453i		−	1.68149i
$414$		0			0
$415$	64.0516			0.154341
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−479.531	+	276.857i	−1.14447	+	0.660758i	−0.947533	−	0.319659i	$-0.896432\pi$
$419$	−479.531	+	276.857i	−1.14447	+	0.660758i	−0.196933	+	0.980417i	$0.563098\pi$
$420$		0			0
$421$	190.947	−	330.730i	0.453556	−	0.785581i	−0.545048	−	0.838405i	$-0.683489\pi$
$421$	190.947	−	330.730i	0.453556	−	0.785581i	0.998604	+	0.0528233i	$0.0168220\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−224.564	−	129.652i	−0.528385	−	0.305063i
$426$		0			0
$427$	24.3900	+	42.2447i	0.0571194	+	0.0989337i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		−	821.321i		−	1.90562i	−0.303570	−	0.952809i	$-0.598179\pi$
$431$		−	821.321i		−	1.90562i	0.303570	−	0.952809i	$-0.401821\pi$
$432$		0			0
$433$	−199.155			−0.459942			−0.229971	−	0.973198i	$-0.573863\pi$
$433$	−199.155			−0.459942			−0.229971	+	0.973198i	$0.573863\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	165.921	−	95.7946i	0.379682	−	0.219210i
$438$		0			0
$439$	−240.830	+	417.130i	−0.548588	+	0.950182i	0.449784	+	0.893137i	$0.351501\pi$
$439$	−240.830	+	417.130i	−0.548588	+	0.950182i	−0.998372	+	0.0570445i	$0.981832\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−467.902	−	270.143i	−1.05621	−	0.609805i	−0.131830	−	0.991272i	$-0.542085\pi$
$443$	−467.902	−	270.143i	−1.05621	−	0.609805i	−0.924382	+	0.381468i	$0.875419\pi$
$444$		0			0
$445$	−242.804	−	420.549i	−0.545628	−	0.945055i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			300.318i			0.668859i	0.942421	+	0.334429i	$0.108544\pi$
$449$			300.318i			0.668859i	−0.942421	+	0.334429i	$0.891456\pi$
$450$		0			0
$451$	−19.9074			−0.0441407
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−664.700	+	383.764i	−1.46088	+	0.843438i
$456$		0			0
$457$	−77.8505	+	134.841i	−0.170351	+	0.295057i	−0.938543	−	0.345163i	$-0.887824\pi$
$457$	−77.8505	+	134.841i	−0.170351	+	0.295057i	0.768191	+	0.640220i	$0.221157\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−261.143	−	150.771i	−0.566470	−	0.327052i	0.189268	−	0.981925i	$-0.439388\pi$
$461$	−261.143	−	150.771i	−0.566470	−	0.327052i	−0.755738	+	0.654874i	$0.772722\pi$
$462$		0			0
$463$	119.390	+	206.790i	0.257862	+	0.446630i	0.965669	−	0.259776i	$-0.0836488\pi$
$463$	119.390	+	206.790i	0.257862	+	0.446630i	−0.707807	+	0.706406i	$0.750315\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			423.152i			0.906107i	0.891483	+	0.453054i	$0.149665\pi$
$467$			423.152i			0.906107i	−0.891483	+	0.453054i	$0.850335\pi$
$468$		0			0
$469$	−1000.13			−2.13247
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−8.81259	+	5.08795i	−0.0186313	+	0.0107568i
$474$		0			0
$475$	131.292	−	227.405i	0.276404	−	0.478747i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−379.284	−	218.980i	−0.791824	−	0.457160i	0.0487802	−	0.998810i	$-0.484467\pi$
$479$	−379.284	−	218.980i	−0.791824	−	0.457160i	−0.840604	+	0.541650i	$0.817800\pi$
$480$		0			0
$481$	102.649	+	177.794i	0.213408	+	0.369634i
$482$		0			0
$483$		0			0
$484$		0			0
$485$		−	872.666i		−	1.79931i
$486$		0			0
$487$	−401.945			−0.825350			−0.412675	−	0.910878i	$-0.635405\pi$
$487$	−401.945			−0.825350			−0.412675	+	0.910878i	$0.635405\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−241.084	+	139.190i	−0.491007	+	0.283483i	−0.724992	−	0.688757i	$-0.758157\pi$
$491$	−241.084	+	139.190i	−0.491007	+	0.283483i	0.233985	+	0.972240i	$0.424823\pi$
$492$		0			0
$493$	212.454	−	367.981i	0.430941	−	0.746411i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−126.571	−	73.0756i	−0.254669	−	0.147033i
$498$		0			0
$499$	272.655	+	472.252i	0.546402	+	0.946397i	0.998517	+	0.0544369i	$0.0173364\pi$
$499$	272.655	+	472.252i	0.546402	+	0.946397i	−0.452115	+	0.891960i	$0.649330\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$			306.460i			0.609264i	0.952470	+	0.304632i	$0.0985335\pi$
$503$			306.460i			0.609264i	−0.952470	+	0.304632i	$0.901466\pi$
$504$		0			0
$505$	1001.76			1.98369
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−480.208	+	277.248i	−0.943434	+	0.544692i	−0.891035	−	0.453934i	$-0.850020\pi$
$509$	−480.208	+	277.248i	−0.943434	+	0.544692i	−0.0523989	+	0.998626i	$0.516687\pi$
$510$		0			0
$511$	−19.8316	+	34.3493i	−0.0388093	+	0.0672197i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−822.102	−	474.641i	−1.59631	−	0.921632i
$516$		0			0
$517$	1.87101	+	3.24069i	0.00361898	+	0.00626825i
$518$		0			0
$519$		0			0
$520$		0			0
$521$			154.167i			0.295905i	0.988994	+	0.147953i	$0.0472683\pi$
$521$			154.167i			0.295905i	−0.988994	+	0.147953i	$0.952732\pi$
$522$		0			0
$523$	−480.598			−0.918925			−0.459463	−	0.888197i	$-0.651958\pi$
$523$	−480.598			−0.918925			−0.459463	+	0.888197i	$0.651958\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	203.739	−	117.629i	0.386602	−	0.223204i
$528$		0			0
$529$	14.0721	−	24.3735i	0.0266013	−	0.0460748i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	433.194	+	250.105i	0.812747	+	0.469240i
$534$		0			0
$535$	138.351	+	239.630i	0.258599	+	0.447907i
$536$		0			0
$537$		0			0
$538$		0			0
$539$			15.0943i			0.0280043i
$540$		0			0
$541$	−300.543			−0.555533			−0.277766	−	0.960649i	$-0.589594\pi$
$541$	−300.543			−0.555533			−0.277766	+	0.960649i	$0.589594\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−883.426	+	510.046i	−1.62097	+	0.935865i
$546$		0			0
$547$	−50.6032	+	87.6473i	−0.0925104	+	0.160233i	−0.908567	−	0.417739i	$-0.862822\pi$
$547$	−50.6032	+	87.6473i	−0.0925104	+	0.160233i	0.816056	+	0.577972i	$0.196156\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	372.636	+	215.141i	0.676290	+	0.390456i
$552$		0			0
$553$	−7.22154	−	12.5081i	−0.0130588	−	0.0226186i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	433.041i		−	0.777452i	−0.921353	−	0.388726i	$-0.872915\pi$
$557$		−	433.041i		−	0.777452i	0.921353	−	0.388726i	$-0.127085\pi$
$558$		0			0
$559$	255.687			0.457401
$560$		0			0
$561$		0			0
$562$		0			0
$563$	902.201	−	520.886i	1.60249	−	0.925197i	0.611501	−	0.791244i	$-0.290566\pi$
$563$	902.201	−	520.886i	1.60249	−	0.925197i	0.990988	−	0.133954i	$-0.0427673\pi$
$564$		0			0
$565$	−720.232	+	1247.48i	−1.27475	+	2.20793i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−257.445	−	148.636i	−0.452452	−	0.261223i	0.256413	−	0.966567i	$-0.417459\pi$
$569$	−257.445	−	148.636i	−0.452452	−	0.261223i	−0.708865	+	0.705344i	$0.750793\pi$
$570$		0			0
$571$	−339.524	−	588.073i	−0.594613	−	1.02990i	−0.993601	−	0.112945i	$-0.963972\pi$
$571$	−339.524	−	588.073i	−0.594613	−	1.02990i	0.398988	−	0.916956i	$-0.369362\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	763.599i		−	1.32800i
$576$		0			0
$577$	−148.351			−0.257107			−0.128553	−	0.991703i	$-0.541033\pi$
$577$	−148.351			−0.257107			−0.128553	+	0.991703i	$0.541033\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−66.7785	+	38.5546i	−0.114937	+	0.0663590i
$582$		0			0
$583$	13.4021	−	23.2132i	0.0229882	−	0.0398168i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	456.497	+	263.559i	0.777678	+	0.448993i	0.835607	−	0.549328i	$-0.185116\pi$
$587$	456.497	+	263.559i	0.777678	+	0.448993i	−0.0579287	+	0.998321i	$0.518450\pi$
$588$		0			0
$589$	119.117	+	206.316i	0.202236	+	0.350283i
$590$		0			0
$591$		0			0
$592$		0			0
$593$		−	473.848i		−	0.799069i	−0.916718	−	0.399534i	$-0.869172\pi$
$593$		−	473.848i		−	0.799069i	0.916718	−	0.399534i	$-0.130828\pi$
$594$		0			0
$595$	553.402			0.930088
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−601.414	+	347.227i	−1.00403	+	0.579677i	−0.909438	−	0.415839i	$-0.863488\pi$
$599$	−601.414	+	347.227i	−1.00403	+	0.579677i	−0.0945922	+	0.995516i	$0.530155\pi$
$600$		0			0
$601$	−93.3559	+	161.697i	−0.155334	+	0.269047i	−0.933181	−	0.359408i	$-0.882979\pi$
$601$	−93.3559	+	161.697i	−0.155334	+	0.269047i	0.777846	+	0.628454i	$0.216312\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	792.285	+	457.426i	1.30956	+	0.756076i
$606$		0			0
$607$	−411.194	−	712.209i	−0.677420	−	1.17333i	−0.975755	−	0.218865i	$-0.929764\pi$
$607$	−411.194	−	712.209i	−0.677420	−	1.17333i	0.298335	−	0.954461i	$-0.403569\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		−	94.0249i		−	0.153887i
$612$		0			0
$613$	−482.206			−0.786634			−0.393317	−	0.919403i	$-0.628672\pi$
$613$	−482.206			−0.786634			−0.393317	+	0.919403i	$0.628672\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	595.916	−	344.052i	0.965828	−	0.557621i	0.0678661	−	0.997694i	$-0.478381\pi$
$617$	595.916	−	344.052i	0.965828	−	0.557621i	0.897962	+	0.440073i	$0.145048\pi$
$618$		0			0
$619$	−380.253	+	658.617i	−0.614302	+	1.06400i	0.376205	+	0.926536i	$0.377229\pi$
$619$	−380.253	+	658.617i	−0.614302	+	1.06400i	−0.990507	+	0.137465i	$0.956105\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	506.282	+	292.302i	0.812652	+	0.469185i
$624$		0			0
$625$	193.603	+	335.331i	0.309765	+	0.536529i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		−	148.024i		−	0.235333i
$630$		0			0
$631$	−1008.08			−1.59758			−0.798792	−	0.601607i	$-0.794527\pi$
$631$	−1008.08			−1.59758			−0.798792	+	0.601607i	$0.794527\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	1207.43	−	697.108i	1.90146	−	1.09781i
$636$		0			0
$637$	189.636	−	328.459i	0.297701	−	0.515634i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	488.095	+	281.802i	0.761458	+	0.439628i	0.829819	−	0.558032i	$-0.188444\pi$
$641$	488.095	+	281.802i	0.761458	+	0.439628i	−0.0683607	+	0.997661i	$0.521777\pi$
$642$		0			0
$643$	−288.500	−	499.697i	−0.448678	−	0.777133i	0.549622	−	0.835413i	$-0.314772\pi$
$643$	−288.500	−	499.697i	−0.448678	−	0.777133i	−0.998300	+	0.0582801i	$0.981438\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			1024.52i			1.58349i	0.610853	+	0.791744i	$0.290827\pi$
$647$			1024.52i			1.58349i	−0.610853	+	0.791744i	$0.709173\pi$
$648$		0			0
$649$	−33.7011			−0.0519277
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−345.885	+	199.697i	−0.529686	+	0.305814i	−0.740888	−	0.671628i	$-0.765595\pi$
$653$	−345.885	+	199.697i	−0.529686	+	0.305814i	0.211203	+	0.977442i	$0.432262\pi$
$654$		0			0
$655$	477.428	−	826.929i	0.728898	−	1.26249i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−646.308	−	373.146i	−0.980741	−	0.566231i	−0.0782470	−	0.996934i	$-0.524932\pi$
$659$	−646.308	−	373.146i	−0.980741	−	0.566231i	−0.902494	+	0.430703i	$0.858266\pi$
$660$		0			0
$661$	−475.624	−	823.804i	−0.719552	−	1.24630i	−0.961178	−	0.275931i	$-0.911014\pi$
$661$	−475.624	−	823.804i	−0.719552	−	1.24630i	0.241626	−	0.970369i	$-0.422319\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$			560.403i			0.842711i
$666$		0			0
$667$	1251.27			1.87596
$668$		0			0
$669$		0			0
$670$		0			0
$671$	2.05009	−	1.18362i	0.00305527	−	0.00176396i
$672$		0			0
$673$	172.115	−	298.113i	0.255743	−	0.442961i	−0.709354	−	0.704853i	$-0.751013\pi$
$673$	172.115	−	298.113i	0.255743	−	0.442961i	0.965097	+	0.261892i	$0.0843464\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−853.610	−	492.832i	−1.26087	−	0.727965i	−0.287628	−	0.957742i	$-0.592867\pi$
$677$	−853.610	−	492.832i	−1.26087	−	0.727965i	−0.973243	+	0.229778i	$0.926200\pi$
$678$		0			0
$679$	525.284	+	909.818i	0.773614	+	1.33994i
$680$		0			0
$681$		0			0
$682$		0			0
$683$		−	166.658i		−	0.244009i	−0.992530	−	0.122004i	$-0.961068\pi$
$683$		−	166.658i		−	0.244009i	0.992530	−	0.122004i	$-0.0389322\pi$
$684$		0			0
$685$	941.062			1.37381
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−583.272	+	336.752i	−0.846548	+	0.488755i
$690$		0			0
$691$	−449.077	+	777.825i	−0.649895	+	1.12565i	0.333253	+	0.942838i	$0.391854\pi$
$691$	−449.077	+	777.825i	−0.649895	+	1.12565i	−0.983148	+	0.182813i	$0.941480\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−175.545	−	101.351i	−0.252582	−	0.145829i
$696$		0			0
$697$	−180.330	−	312.341i	−0.258723	−	0.448122i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			730.549i			1.04215i	0.853510	+	0.521076i	$0.174469\pi$
$701$			730.549i			1.04215i	−0.853510	+	0.521076i	$0.825531\pi$
$702$		0			0
$703$	149.897			0.213224
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−1044.41	+	602.991i	−1.47724	+	0.852887i
$708$		0			0
$709$	114.961	−	199.118i	0.162145	−	0.280843i	−0.773493	−	0.633805i	$-0.781492\pi$
$709$	114.961	−	199.118i	0.162145	−	0.280843i	0.935638	+	0.352962i	$0.114826\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	599.971	+	346.394i	0.841474	+	0.485825i
$714$		0			0
$715$	18.6237	+	32.2571i	0.0260471	+	0.0451149i
$716$		0			0
$717$		0			0
$718$		0			0
$719$			907.095i			1.26161i	0.775943	+	0.630803i	$0.217275\pi$
$719$			907.095i			1.26161i	−0.775943	+	0.630803i	$0.782725\pi$
$720$		0			0
$721$	1142.80			1.58502
$722$		0			0
$723$		0			0
$724$		0			0
$725$	1485.18	−	857.469i	2.04852	−	1.18272i
$726$		0			0
$727$	107.871	−	186.838i	0.148378	−	0.256999i	−0.782250	−	0.622965i	$-0.785928\pi$
$727$	107.871	−	186.838i	0.148378	−	0.256999i	0.930628	+	0.365966i	$0.119261\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−159.656	−	92.1776i	−0.218408	−	0.126098i
$732$		0			0
$733$	−314.634	−	544.963i	−0.429242	−	0.743469i	0.567564	−	0.823329i	$-0.307886\pi$
$733$	−314.634	−	544.963i	−0.429242	−	0.743469i	−0.996806	+	0.0798604i	$0.974553\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			48.5351i			0.0658549i
$738$		0			0
$739$	−547.649			−0.741068			−0.370534	−	0.928819i	$-0.620825\pi$
$739$	−547.649			−0.741068			−0.370534	+	0.928819i	$0.620825\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−462.583	+	267.072i	−0.622588	+	0.359451i	−0.777876	−	0.628418i	$-0.783703\pi$
$743$	−462.583	+	267.072i	−0.622588	+	0.359451i	0.155288	+	0.987869i	$0.450369\pi$
$744$		0			0
$745$	305.376	−	528.927i	0.409901	−	0.709970i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−288.481	−	166.555i	−0.385155	−	0.222369i
$750$		0			0
$751$	−225.545	−	390.655i	−0.300326	−	0.520180i	0.675884	−	0.737008i	$-0.263762\pi$
$751$	−225.545	−	390.655i	−0.300326	−	0.520180i	−0.976210	+	0.216828i	$0.930429\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$			756.911i			1.00253i
$756$		0			0
$757$	−352.391			−0.465511			−0.232755	−	0.972535i	$-0.574774\pi$
$757$	−352.391			−0.465511			−0.232755	+	0.972535i	$0.574774\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	929.923	−	536.891i	1.22197	−	0.705507i	0.256636	−	0.966508i	$-0.417386\pi$
$761$	929.923	−	536.891i	1.22197	−	0.705507i	0.965339	+	0.261001i	$0.0840525\pi$
$762$		0			0
$763$	614.024	−	1063.52i	0.804750	−	1.39387i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	733.349	+	423.399i	0.956126	+	0.552020i
$768$		0			0
$769$	−177.988	−	308.284i	−0.231454	−	0.400889i	0.726782	−	0.686868i	$-0.241015\pi$
$769$	−177.988	−	308.284i	−0.231454	−	0.400889i	−0.958236	+	0.285978i	$0.907681\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$			370.790i			0.479677i	0.970813	+	0.239838i	$0.0770945\pi$
$773$			370.790i			0.479677i	−0.970813	+	0.239838i	$0.922906\pi$
$774$		0			0
$775$	949.505			1.22517
$776$		0			0
$777$		0			0
$778$		0			0
$779$	316.292	−	182.611i	0.406023	−	0.234418i
$780$		0			0
$781$	−3.54628	+	6.14233i	−0.00454069	+	0.00786470i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−455.507	−	262.987i	−0.580263	−	0.335015i
$786$		0			0
$787$	576.531	+	998.581i	0.732568	+	1.26885i	0.955782	+	0.294076i	$0.0950118\pi$
$787$	576.531	+	998.581i	0.732568	+	1.26885i	−0.223214	+	0.974769i	$0.571655\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		−	1734.12i		−	2.19231i
$792$		0			0
$793$	−59.4810			−0.0750076
$794$		0			0
$795$		0			0
$796$		0			0
$797$	761.882	−	439.873i	0.955937	−	0.551910i	0.0610167	−	0.998137i	$-0.480566\pi$
$797$	761.882	−	439.873i	0.955937	−	0.551910i	0.894920	+	0.446226i	$0.147232\pi$
$798$		0			0
$799$	−33.8968	+	58.7110i	−0.0424240	+	0.0734806i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	1.66693	+	0.962404i	0.00207588	+	0.00119851i
$804$		0			0
$805$	814.830	+	1411.33i	1.01221	+	1.75320i
$806$		0			0
$807$		0			0
$808$		0			0
$809$			884.508i			1.09334i	0.837350	+	0.546668i	$0.184104\pi$
$809$			884.508i			1.09334i	−0.837350	+	0.546668i	$0.815896\pi$
$810$		0			0
$811$	961.464			1.18553			0.592765	−	0.805376i	$-0.298036\pi$
$811$	961.464			1.18553			0.592765	+	0.805376i	$0.298036\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	1065.53	−	615.184i	1.30740	−	0.754827i
$816$		0			0
$817$	93.3437	−	161.676i	0.114252	−	0.197890i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−778.064	−	449.215i	−0.947702	−	0.547156i	−0.0553360	−	0.998468i	$-0.517623\pi$
$821$	−778.064	−	449.215i	−0.947702	−	0.547156i	−0.892366	+	0.451312i	$0.850956\pi$
$822$		0			0
$823$	108.091	+	187.219i	0.131338	+	0.227484i	0.924193	−	0.381927i	$-0.124739\pi$
$823$	108.091	+	187.219i	0.131338	+	0.227484i	−0.792855	+	0.609411i	$0.791406\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	113.883i		−	0.137706i	−0.997627	−	0.0688528i	$-0.978066\pi$
$827$		−	113.883i		−	0.137706i	0.997627	−	0.0688528i	$-0.0219339\pi$
$828$		0			0
$829$	101.326			0.122227			0.0611135	−	0.998131i	$-0.480535\pi$
$829$	101.326			0.122227			0.0611135	+	0.998131i	$0.480535\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−236.825	+	136.731i	−0.284303	+	0.164143i
$834$		0			0
$835$	−366.077	+	634.065i	−0.438416	+	0.759359i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	60.4689	+	34.9117i	0.0720726	+	0.0416111i	0.535603	−	0.844470i	$-0.320084\pi$
$839$	60.4689	+	34.9117i	0.0720726	+	0.0416111i	−0.463531	+	0.886081i	$0.653418\pi$
$840$		0			0
$841$	984.588	+	1705.36i	1.17073	+	2.02777i
$842$		0			0
$843$		0			0
$844$		0			0
$845$			343.934i			0.407023i
$846$		0			0
$847$	−1101.35			−1.30030
$848$		0			0
$849$		0			0
$850$		0			0
$851$	377.502	−	217.951i	0.443598	−	0.256112i
$852$		0			0
$853$	573.325	−	993.028i	0.672127	−	1.16416i	−0.305172	−	0.952297i	$-0.598714\pi$
$853$	573.325	−	993.028i	0.672127	−	1.16416i	0.977300	−	0.211862i	$-0.0679527\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−217.871	−	125.788i	−0.254225	−	0.146777i	0.367472	−	0.930035i	$-0.380223\pi$
$857$	−217.871	−	125.788i	−0.254225	−	0.146777i	−0.621697	+	0.783258i	$0.713557\pi$
$858$		0			0
$859$	−244.266	−	423.082i	−0.284361	−	0.492528i	0.688093	−	0.725623i	$-0.258448\pi$
$859$	−244.266	−	423.082i	−0.284361	−	0.492528i	−0.972454	+	0.233095i	$0.925115\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$			596.889i			0.691644i	0.938300	+	0.345822i	$0.112400\pi$
$863$			596.889i			0.691644i	−0.938300	+	0.345822i	$0.887600\pi$
$864$		0			0
$865$	−212.258			−0.245385
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−0.607003	+	0.350454i	−0.000698508	+	0.000403284i
$870$		0			0
$871$	609.765	−	1056.14i	0.700074	−	1.21256i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	439.504	+	253.748i	0.502290	+	0.289997i
$876$		0			0
$877$	−358.208	−	620.434i	−0.408447	−	0.707451i	0.586269	−	0.810116i	$-0.300596\pi$
$877$	−358.208	−	620.434i	−0.408447	−	0.707451i	−0.994716	+	0.102666i	$0.967263\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			1200.86i			1.36306i	0.731790	+	0.681531i	$0.238685\pi$
$881$			1200.86i			1.36306i	−0.731790	+	0.681531i	$0.761315\pi$
$882$		0			0
$883$	−22.8938			−0.0259273			−0.0129636	−	0.999916i	$-0.504127\pi$
$883$	−22.8938			−0.0259273			−0.0129636	+	0.999916i	$0.504127\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	521.857	−	301.294i	0.588340	−	0.339678i	−0.176101	−	0.984372i	$-0.556349\pi$
$887$	521.857	−	301.294i	0.588340	−	0.339678i	0.764441	+	0.644694i	$0.223015\pi$
$888$		0			0
$889$	−839.220	+	1453.57i	−0.944005	+	1.63506i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−59.4537	−	34.3256i	−0.0665775	−	0.0384385i
$894$		0			0
$895$	−134.804	−	233.488i	−0.150619	−	0.260880i
$896$		0			0
$897$		0			0
$898$		0			0
$899$			1555.90i			1.73071i
$900$		0			0
$901$	485.609			0.538966
$902$		0			0
$903$		0			0
$904$		0			0
$905$	128.780	−	74.3511i	0.142298	−	0.0821560i
$906$		0			0
$907$	211.473	−	366.281i	0.233156	−	0.403838i	−0.725579	−	0.688139i	$-0.758428\pi$
$907$	211.473	−	366.281i	0.233156	−	0.403838i	0.958735	+	0.284300i	$0.0917613\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	125.376	+	72.3861i	0.137625	+	0.0794578i	0.567232	−	0.823558i	$-0.308014\pi$
$911$	125.376	+	72.3861i	0.137625	+	0.0794578i	−0.429607	+	0.903016i	$0.641348\pi$
$912$		0			0
$913$	1.87101	+	3.24069i	0.00204930	+	0.00354949i
$914$		0			0
$915$		0			0
$916$		0			0
$917$			1149.51i			1.25356i
$918$		0			0
$919$	869.093			0.945694			0.472847	−	0.881145i	$-0.343226\pi$
$919$	869.093			0.945694			0.472847	+	0.881145i	$0.343226\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	154.337	−	89.1064i	0.167212	−	0.0965400i
$924$		0			0
$925$	298.715	−	517.389i	0.322935	−	0.559340i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−82.2838	−	47.5066i	−0.0885724	−	0.0511373i	0.455060	−	0.890461i	$-0.349618\pi$
$929$	−82.2838	−	47.5066i	−0.0885724	−	0.0511373i	−0.543632	+	0.839324i	$0.682951\pi$
$930$		0			0
$931$	−138.461	−	239.821i	−0.148722	−	0.257595i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		−	26.8560i		−	0.0287230i
$936$		0			0
$937$	−1555.55			−1.66014			−0.830071	−	0.557657i	$-0.811700\pi$
$937$	−1555.55			−1.66014			−0.830071	+	0.557657i	$0.811700\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−335.246	+	193.554i	−0.356265	+	0.205690i	−0.667441	−	0.744662i	$-0.732611\pi$
$941$	−335.246	+	193.554i	−0.356265	+	0.205690i	0.311176	+	0.950352i	$0.399277\pi$
$942$		0			0
$943$	531.036	−	919.782i	0.563135	−	0.975379i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−839.861	−	484.894i	−0.886865	−	0.512032i	−0.0139492	−	0.999903i	$-0.504440\pi$
$947$	−839.861	−	484.894i	−0.886865	−	0.512032i	−0.872916	+	0.487871i	$0.837774\pi$
$948$		0			0
$949$	−24.1821	−	41.8846i	−0.0254817	−	0.0441355i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	1294.65i		−	1.35850i	−0.733909	−	0.679248i	$-0.762306\pi$
$953$		−	1294.65i		−	1.35850i	0.733909	−	0.679248i	$-0.237694\pi$
$954$		0			0
$955$	−1649.76			−1.72750
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−981.126	+	566.453i	−1.02307	+	0.590671i
$960$		0			0
$961$	49.7731	−	86.2096i	0.0517931	−	0.0897082i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−321.363	−	185.539i	−0.333018	−	0.192268i
$966$		0			0
$967$	412.036	+	713.668i	0.426098	+	0.738023i	0.996522	−	0.0833272i	$-0.0265547\pi$
$967$	412.036	+	713.668i	0.426098	+	0.738023i	−0.570425	+	0.821350i	$0.693221\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$		−	1518.35i		−	1.56370i	−0.623469	−	0.781848i	$-0.714277\pi$
$971$		−	1518.35i		−	1.56370i	0.623469	−	0.781848i	$-0.285723\pi$
$972$		0			0
$973$	244.024			0.250796
$974$		0			0
$975$		0			0
$976$		0			0
$977$	321.497	−	185.616i	0.329065	−	0.189986i	−0.326361	−	0.945245i	$-0.605822\pi$
$977$	321.497	−	185.616i	0.329065	−	0.189986i	0.655426	+	0.755259i	$0.272489\pi$
$978$		0			0
$979$	14.1851	−	24.5693i	0.0144894	−	0.0250963i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−808.039	−	466.522i	−0.822014	−	0.474590i	0.0290967	−	0.999577i	$-0.490737\pi$
$983$	−808.039	−	466.522i	−0.822014	−	0.474590i	−0.851110	+	0.524987i	$0.824070\pi$
$984$		0			0
$985$	−1363.01	−	2360.80i	−1.38377	−	2.39676i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		−	542.890i		−	0.548928i
$990$		0			0
$991$	−1615.53			−1.63020			−0.815099	−	0.579321i	$-0.803318\pi$
$991$	−1615.53			−1.63020			−0.815099	+	0.579321i	$0.803318\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−400.492	+	231.224i	−0.402504	+	0.232386i
$996$		0			0
$997$	−519.376	+	899.586i	−0.520939	+	0.902293i	0.478764	+	0.877943i	$0.341085\pi$
$997$	−519.376	+	899.586i	−0.520939	+	0.902293i	−0.999704	+	0.0243496i	$0.992249\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.3.q.b.305.1		4
3.2	odd	2		144.3.q.b.65.2		4
4.3	odd	2		108.3.g.a.89.1		4
8.3	odd	2		1728.3.q.g.1601.2		4
8.5	even	2		1728.3.q.h.1601.2		4
9.2	odd	6		1296.3.e.e.161.4		4
9.4	even	3		144.3.q.b.113.2		4
9.5	odd	6	inner	432.3.q.b.17.1		4
9.7	even	3		1296.3.e.e.161.1		4
12.11	even	2		36.3.g.a.29.1	yes	4
20.3	even	4		2700.3.u.b.2249.4		8
20.7	even	4		2700.3.u.b.2249.1		8
20.19	odd	2		2700.3.p.b.1601.2		4
24.5	odd	2		576.3.q.g.65.1		4
24.11	even	2		576.3.q.d.65.2		4
36.7	odd	6		324.3.c.b.161.1		4
36.11	even	6		324.3.c.b.161.4		4
36.23	even	6		108.3.g.a.17.1		4
36.31	odd	6		36.3.g.a.5.1	✓	4
60.23	odd	4		900.3.u.a.749.4		8
60.47	odd	4		900.3.u.a.749.1		8
60.59	even	2		900.3.p.a.101.2		4
72.5	odd	6		1728.3.q.h.449.2		4
72.13	even	6		576.3.q.g.257.1		4
72.59	even	6		1728.3.q.g.449.2		4
72.67	odd	6		576.3.q.d.257.2		4
180.23	odd	12		2700.3.u.b.449.1		8
180.59	even	6		2700.3.p.b.2501.2		4
180.67	even	12		900.3.u.a.149.4		8
180.103	even	12		900.3.u.a.149.1		8
180.139	odd	6		900.3.p.a.401.2		4
180.167	odd	12		2700.3.u.b.449.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.3.g.a.5.1	✓	4	36.31	odd	6
36.3.g.a.29.1	yes	4	12.11	even	2
108.3.g.a.17.1		4	36.23	even	6
108.3.g.a.89.1		4	4.3	odd	2
144.3.q.b.65.2		4	3.2	odd	2
144.3.q.b.113.2		4	9.4	even	3
324.3.c.b.161.1		4	36.7	odd	6
324.3.c.b.161.4		4	36.11	even	6
432.3.q.b.17.1		4	9.5	odd	6	inner
432.3.q.b.305.1		4	1.1	even	1	trivial
576.3.q.d.65.2		4	24.11	even	2
576.3.q.d.257.2		4	72.67	odd	6
576.3.q.g.65.1		4	24.5	odd	2
576.3.q.g.257.1		4	72.13	even	6
900.3.p.a.101.2		4	60.59	even	2
900.3.p.a.401.2		4	180.139	odd	6
900.3.u.a.149.1		8	180.103	even	12
900.3.u.a.149.4		8	180.67	even	12
900.3.u.a.749.1		8	60.47	odd	4
900.3.u.a.749.4		8	60.23	odd	4
1296.3.e.e.161.1		4	9.7	even	3
1296.3.e.e.161.4		4	9.2	odd	6
1728.3.q.g.449.2		4	72.59	even	6
1728.3.q.g.1601.2		4	8.3	odd	2
1728.3.q.h.449.2		4	72.5	odd	6
1728.3.q.h.1601.2		4	8.5	even	2
2700.3.p.b.1601.2		4	20.19	odd	2
2700.3.p.b.2501.2		4	180.59	even	6
2700.3.u.b.449.1		8	180.23	odd	12
2700.3.u.b.449.4		8	180.167	odd	12
2700.3.u.b.2249.1		8	20.7	even	4
2700.3.u.b.2249.4		8	20.3	even	4

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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	432.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-6.55842 + 3.78651i) q^{5} +(4.55842 - 7.89542i) q^{7} +O(q^{10})\)	\(q+(-6.55842 + 3.78651i) q^{5} +(4.55842 - 7.89542i) q^{7} +(-0.383156 - 0.221215i) q^{11} +(5.55842 + 9.62747i) q^{13} -8.01544i q^{17} +8.11684 q^{19} +(20.4416 - 11.8020i) q^{23} +(16.1753 - 28.0164i) q^{25} +(45.9090 + 26.5055i) q^{29} +(14.6753 + 25.4183i) q^{31} +69.0420i q^{35} +18.4674 q^{37} +(38.9674 - 22.4978i) q^{41} +(11.5000 - 19.9186i) q^{43} +(-7.32473 - 4.22894i) q^{47} +(-17.0584 - 29.5461i) q^{49} +60.5841i q^{53} +3.35053 q^{55} +(65.9674 - 38.0863i) q^{59} +(-2.67527 + 4.63370i) q^{61} +(-72.9090 - 42.0940i) q^{65} +(-54.8505 - 95.0039i) q^{67} -16.0309i q^{71} -4.35053 q^{73} +(-3.49317 + 2.01678i) q^{77} +(0.792110 - 1.37197i) q^{79} +(-7.32473 - 4.22894i) q^{83} +(30.3505 + 52.5687i) q^{85} +64.1236i q^{89} +101.351 q^{91} +(-53.2337 + 30.7345i) q^{95} +(-57.6168 + 99.7953i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 9 q^{5} + q^{7}+O(q^{10}) \) 4 * q - 9 * q^5 + q^7	\( 4 q - 9 q^{5} + q^{7} - 36 q^{11} + 5 q^{13} - 2 q^{19} + 99 q^{23} + 13 q^{25} + 63 q^{29} + 7 q^{31} - 64 q^{37} + 18 q^{41} + 46 q^{43} - 81 q^{47} - 51 q^{49} - 90 q^{55} + 126 q^{59} + 41 q^{61} - 171 q^{65} - 116 q^{67} + 86 q^{73} + 279 q^{77} - 83 q^{79} - 81 q^{83} + 18 q^{85} + 302 q^{91} - 144 q^{95} - 196 q^{97}+O(q^{100}) \) 4 * q - 9 * q^5 + q^7 - 36 * q^11 + 5 * q^13 - 2 * q^19 + 99 * q^23 + 13 * q^25 + 63 * q^29 + 7 * q^31 - 64 * q^37 + 18 * q^41 + 46 * q^43 - 81 * q^47 - 51 * q^49 - 90 * q^55 + 126 * q^59 + 41 * q^61 - 171 * q^65 - 116 * q^67 + 86 * q^73 + 279 * q^77 - 83 * q^79 - 81 * q^83 + 18 * q^85 + 302 * q^91 - 144 * q^95 - 196 * q^97

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