LMFDB - Embedded newform 832.2.i.n.321.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [832,2,Mod(321,832)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(832, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("832.321");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 832 = 2^{6} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	832.i (of order $3$, 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:	$6.64355344817$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{11})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 11x^{2} + 121 $ x^4 + 11*x^2 + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 416)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			321.2
Root			$1.65831 - 2.87228i$ of defining polynomial
Character	$\chi$	$=$	832.321
Dual form			832.2.i.n.705.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.65831 - 2.87228i) q^{3} +(-1.65831 - 2.87228i) q^{7} +(-4.00000 - 6.92820i) q^{9} +(1.65831 - 2.87228i) q^{11} +(1.00000 + 3.46410i) q^{13} +(1.50000 + 2.59808i) q^{17} +(1.65831 + 2.87228i) q^{19} -11.0000 q^{21} +(1.65831 - 2.87228i) q^{23} -5.00000 q^{25} -16.5831 q^{27} +(-2.50000 + 4.33013i) q^{29} +(-5.50000 - 9.52628i) q^{33} +(4.50000 - 7.79423i) q^{37} +(11.6082 + 2.87228i) q^{39} +(1.50000 - 2.59808i) q^{41} +(4.97494 + 8.61684i) q^{43} -6.63325 q^{47} +(-2.00000 + 3.46410i) q^{49} +9.94987 q^{51} +8.00000 q^{53} +11.0000 q^{57} +(1.65831 + 2.87228i) q^{59} +(-4.50000 - 7.79423i) q^{61} +(-13.2665 + 22.9783i) q^{63} +(4.97494 - 8.61684i) q^{67} +(-5.50000 - 9.52628i) q^{69} +(-4.97494 - 8.61684i) q^{71} -4.00000 q^{73} +(-8.29156 + 14.3614i) q^{75} -11.0000 q^{77} +6.63325 q^{79} +(-15.5000 + 26.8468i) q^{81} +13.2665 q^{83} +(8.29156 + 14.3614i) q^{87} +(0.500000 - 0.866025i) q^{89} +(8.29156 - 8.61684i) q^{91} +(-3.50000 - 6.06218i) q^{97} -26.5330 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 16 q^{9} + 4 q^{13} + 6 q^{17} - 44 q^{21} - 20 q^{25} - 10 q^{29} - 22 q^{33} + 18 q^{37} + 6 q^{41} - 8 q^{49} + 32 q^{53} + 44 q^{57} - 18 q^{61} - 22 q^{69} - 16 q^{73} - 44 q^{77} - 62 q^{81}+ \cdots - 14 q^{97}+O(q^{100}) $ 4 * q - 16 * q^9 + 4 * q^13 + 6 * q^17 - 44 * q^21 - 20 * q^25 - 10 * q^29 - 22 * q^33 + 18 * q^37 + 6 * q^41 - 8 * q^49 + 32 * q^53 + 44 * q^57 - 18 * q^61 - 22 * q^69 - 16 * q^73 - 44 * q^77 - 62 * q^81 + 2 * q^89 - 14 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/832\mathbb{Z}\right)^\times$.

$n$	$261$	$703$	$769$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.65831	−	2.87228i	0.957427	−	1.65831i	0.228714	−	0.973494i	$-0.426548\pi$
$3$	1.65831	−	2.87228i	0.957427	−	1.65831i	0.728714	−	0.684819i	$-0.240119\pi$
$4$		0			0
$5$		0			0			−	1.00000i	$-0.5\pi$
$5$		0			0				1.00000i	$0.5\pi$
$6$		0			0
$7$	−1.65831	−	2.87228i	−0.626783	−	1.08562i	−0.988193	−	0.153213i	$-0.951038\pi$
$7$	−1.65831	−	2.87228i	−0.626783	−	1.08562i	0.361410	−	0.932407i	$-0.382295\pi$
$8$		0			0
$9$	−4.00000	−	6.92820i	−1.33333	−	2.30940i
$10$		0			0
$11$	1.65831	−	2.87228i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$11$	1.65831	−	2.87228i	0.500000	−	0.866025i	1.00000			$0$
$12$		0			0
$13$	1.00000	+	3.46410i	0.277350	+	0.960769i
$13$	1.00000	+	3.46410i	0.277350	+	0.960769i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	0.988583	−	0.150675i	$-0.0481447\pi$
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	−0.624780	+	0.780801i	$0.714811\pi$
$18$		0			0
$19$	1.65831	+	2.87228i	0.380443	+	0.658947i	0.991126	−	0.132929i	$-0.0424382\pi$
$19$	1.65831	+	2.87228i	0.380443	+	0.658947i	−0.610683	+	0.791875i	$0.709105\pi$
$20$		0			0
$21$	−11.0000			−2.40040
$22$		0			0
$23$	1.65831	−	2.87228i	0.345782	−	0.598912i	−0.639713	−	0.768613i	$-0.720947\pi$
$23$	1.65831	−	2.87228i	0.345782	−	0.598912i	0.985496	+	0.169701i	$0.0542803\pi$
$24$		0			0
$25$	−5.00000			−1.00000
$26$		0			0
$27$	−16.5831			−3.19142
$28$		0			0
$29$	−2.50000	+	4.33013i	−0.464238	+	0.804084i	−0.999167	−	0.0408130i	$-0.987005\pi$
$29$	−2.50000	+	4.33013i	−0.464238	+	0.804084i	0.534928	+	0.844897i	$0.320339\pi$
$30$		0			0
$31$		0			0			−	1.00000i	$-0.5\pi$
$31$		0			0				1.00000i	$0.5\pi$
$32$		0			0
$33$	−5.50000	−	9.52628i	−0.957427	−	1.65831i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	4.50000	−	7.79423i	0.739795	−	1.28136i	−0.212792	−	0.977098i	$-0.568256\pi$
$37$	4.50000	−	7.79423i	0.739795	−	1.28136i	0.952587	−	0.304266i	$-0.0984111\pi$
$38$		0			0
$39$	11.6082	+	2.87228i	1.85880	+	0.459933i
$40$		0			0
$41$	1.50000	−	2.59808i	0.234261	−	0.405751i	−0.724797	−	0.688963i	$-0.758066\pi$
$41$	1.50000	−	2.59808i	0.234261	−	0.405751i	0.959058	+	0.283211i	$0.0913998\pi$
$42$		0			0
$43$	4.97494	+	8.61684i	0.758671	+	1.31406i	0.943529	+	0.331291i	$0.107484\pi$
$43$	4.97494	+	8.61684i	0.758671	+	1.31406i	−0.184858	+	0.982765i	$0.559182\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−6.63325			−0.967559			−0.483779	−	0.875190i	$-0.660736\pi$
$47$	−6.63325			−0.967559			−0.483779	+	0.875190i	$0.660736\pi$
$48$		0			0
$49$	−2.00000	+	3.46410i	−0.285714	+	0.494872i
$50$		0			0
$51$	9.94987			1.39326
$52$		0			0
$53$	8.00000			1.09888			0.549442	−	0.835532i	$-0.314840\pi$
$53$	8.00000			1.09888			0.549442	+	0.835532i	$0.314840\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	11.0000			1.45699
$58$		0			0
$59$	1.65831	+	2.87228i	0.215894	+	0.373939i	0.953549	−	0.301239i	$-0.0974001\pi$
$59$	1.65831	+	2.87228i	0.215894	+	0.373939i	−0.737655	+	0.675178i	$0.764067\pi$
$60$		0			0
$61$	−4.50000	−	7.79423i	−0.576166	−	0.997949i	−0.995914	−	0.0903080i	$-0.971215\pi$
$61$	−4.50000	−	7.79423i	−0.576166	−	0.997949i	0.419748	−	0.907641i	$-0.362118\pi$
$62$		0			0
$63$	−13.2665	+	22.9783i	−1.67142	+	2.89499i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	4.97494	−	8.61684i	0.607785	−	1.05272i	−0.383819	−	0.923408i	$-0.625391\pi$
$67$	4.97494	−	8.61684i	0.607785	−	1.05272i	0.991605	−	0.129307i	$-0.0412752\pi$
$68$		0			0
$69$	−5.50000	−	9.52628i	−0.662122	−	1.14683i
$70$		0			0
$71$	−4.97494	−	8.61684i	−0.590416	−	1.02263i	−0.994176	−	0.107766i	$-0.965630\pi$
$71$	−4.97494	−	8.61684i	−0.590416	−	1.02263i	0.403760	−	0.914865i	$-0.367703\pi$
$72$		0			0
$73$	−4.00000			−0.468165			−0.234082	−	0.972217i	$-0.575209\pi$
$73$	−4.00000			−0.468165			−0.234082	+	0.972217i	$0.575209\pi$
$74$		0			0
$75$	−8.29156	+	14.3614i	−0.957427	+	1.65831i
$76$		0			0
$77$	−11.0000			−1.25357
$78$		0			0
$79$	6.63325			0.746299			0.373149	−	0.927771i	$-0.378278\pi$
$79$	6.63325			0.746299			0.373149	+	0.927771i	$0.378278\pi$
$80$		0			0
$81$	−15.5000	+	26.8468i	−1.72222	+	2.98298i
$82$		0			0
$83$	13.2665			1.45619			0.728094	−	0.685478i	$-0.240407\pi$
$83$	13.2665			1.45619			0.728094	+	0.685478i	$0.240407\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	8.29156	+	14.3614i	0.888949	+	1.53970i
$88$		0			0
$89$	0.500000	−	0.866025i	0.0529999	−	0.0917985i	−0.838308	−	0.545197i	$-0.816455\pi$
$89$	0.500000	−	0.866025i	0.0529999	−	0.0917985i	0.891308	+	0.453398i	$0.149788\pi$
$90$		0			0
$91$	8.29156	−	8.61684i	0.869192	−	0.903291i
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−3.50000	−	6.06218i	−0.355371	−	0.615521i	0.631810	−	0.775123i	$-0.282312\pi$
$97$	−3.50000	−	6.06218i	−0.355371	−	0.615521i	−0.987181	+	0.159602i	$0.948979\pi$
$98$		0			0
$99$	−26.5330			−2.66667
$100$		0			0
$101$	−7.50000	+	12.9904i	−0.746278	+	1.29259i	0.203317	+	0.979113i	$0.434828\pi$
$101$	−7.50000	+	12.9904i	−0.746278	+	1.29259i	−0.949595	+	0.313478i	$0.898506\pi$
$102$		0			0
$103$		0			0			−	1.00000i	$-0.5\pi$
$103$		0			0				1.00000i	$0.5\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.65831	−	2.87228i	0.160315	−	0.277674i	−0.774667	−	0.632370i	$-0.782082\pi$
$107$	1.65831	−	2.87228i	0.160315	−	0.277674i	0.934982	+	0.354696i	$0.115416\pi$
$108$		0			0
$109$	16.0000			1.53252			0.766261	−	0.642529i	$-0.222115\pi$
$109$	16.0000			1.53252			0.766261	+	0.642529i	$0.222115\pi$
$110$		0			0
$111$	−14.9248	−	25.8505i	−1.41660	−	2.45362i
$112$		0			0
$113$	5.50000	+	9.52628i	0.517396	+	0.896157i	0.999796	+	0.0202056i	$0.00643208\pi$
$113$	5.50000	+	9.52628i	0.517396	+	0.896157i	−0.482399	+	0.875951i	$0.660235\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	20.0000	−	20.7846i	1.84900	−	1.92154i
$118$		0			0
$119$	4.97494	−	8.61684i	0.456052	−	0.789905i
$120$		0			0
$121$		0			0
$122$		0			0
$123$	−4.97494	−	8.61684i	−0.448575	−	0.776955i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	4.97494	−	8.61684i	0.441454	−	0.764621i	−0.556343	−	0.830952i	$-0.687796\pi$
$127$	4.97494	−	8.61684i	0.441454	−	0.764621i	0.997798	+	0.0663312i	$0.0211294\pi$
$128$		0			0
$129$	33.0000			2.90549
$130$		0			0
$131$	−13.2665			−1.15910			−0.579550	−	0.814937i	$-0.696772\pi$
$131$	−13.2665			−1.15910			−0.579550	+	0.814937i	$0.696772\pi$
$132$		0			0
$133$	5.50000	−	9.52628i	0.476910	−	0.826033i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	4.50000	+	7.79423i	0.384461	+	0.665906i	0.991694	−	0.128618i	$-0.0410540\pi$
$137$	4.50000	+	7.79423i	0.384461	+	0.665906i	−0.607233	+	0.794524i	$0.707721\pi$
$138$		0			0
$139$	1.65831	+	2.87228i	0.140656	+	0.243624i	0.927744	−	0.373217i	$-0.121745\pi$
$139$	1.65831	+	2.87228i	0.140656	+	0.243624i	−0.787088	+	0.616841i	$0.788412\pi$
$140$		0			0
$141$	−11.0000	+	19.0526i	−0.926367	+	1.60451i
$142$		0			0
$143$	11.6082	+	2.87228i	0.970725	+	0.240192i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	6.63325	+	11.4891i	0.547101	+	0.947607i
$148$		0			0
$149$	−0.500000	−	0.866025i	−0.0409616	−	0.0709476i	0.844818	−	0.535054i	$-0.179709\pi$
$149$	−0.500000	−	0.866025i	−0.0409616	−	0.0709476i	−0.885779	+	0.464107i	$0.846375\pi$
$150$		0			0
$151$		0			0			−	1.00000i	$-0.5\pi$
$151$		0			0				1.00000i	$0.5\pi$
$152$		0			0
$153$	12.0000	−	20.7846i	0.970143	−	1.68034i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	8.00000			0.638470			0.319235	−	0.947676i	$-0.396574\pi$
$157$	8.00000			0.638470			0.319235	+	0.947676i	$0.396574\pi$
$158$		0			0
$159$	13.2665	−	22.9783i	1.05210	−	1.82229i
$160$		0			0
$161$	−11.0000			−0.866921
$162$		0			0
$163$	−8.29156	−	14.3614i	−0.649445	−	1.12487i	−0.983256	−	0.182232i	$-0.941668\pi$
$163$	−8.29156	−	14.3614i	−0.649445	−	1.12487i	0.333810	−	0.942640i	$-0.391665\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	1.65831	−	2.87228i	0.128324	−	0.222264i	−0.794703	−	0.606998i	$-0.792374\pi$
$167$	1.65831	−	2.87228i	0.128324	−	0.222264i	0.923027	+	0.384734i	$0.125707\pi$
$168$		0			0
$169$	−11.0000	+	6.92820i	−0.846154	+	0.532939i
$170$		0			0
$171$	13.2665	−	22.9783i	1.01451	−	1.75719i
$172$		0			0
$173$	3.50000	+	6.06218i	0.266100	+	0.460899i	0.967851	−	0.251523i	$-0.0809315\pi$
$173$	3.50000	+	6.06218i	0.266100	+	0.460899i	−0.701751	+	0.712422i	$0.747598\pi$
$174$		0			0
$175$	8.29156	+	14.3614i	0.626783	+	1.08562i
$176$		0			0
$177$	11.0000			0.826811
$178$		0			0
$179$	1.65831	−	2.87228i	0.123948	−	0.214684i	−0.797373	−	0.603487i	$-0.793778\pi$
$179$	1.65831	−	2.87228i	0.123948	−	0.214684i	0.921321	+	0.388802i	$0.127111\pi$
$180$		0			0
$181$	8.00000			0.594635			0.297318	−	0.954779i	$-0.403908\pi$
$181$	8.00000			0.594635			0.297318	+	0.954779i	$0.403908\pi$
$182$		0			0
$183$	−29.8496			−2.20655
$184$		0			0
$185$		0			0
$186$		0			0
$187$	9.94987			0.727607
$188$		0			0
$189$	27.5000	+	47.6314i	2.00033	+	3.46467i
$190$		0			0
$191$	11.6082	+	20.1060i	0.839939	+	1.45482i	0.889945	+	0.456068i	$0.150743\pi$
$191$	11.6082	+	20.1060i	0.839939	+	1.45482i	−0.0500060	+	0.998749i	$0.515924\pi$
$192$		0			0
$193$	−6.50000	+	11.2583i	−0.467880	+	0.810392i	−0.999326	−	0.0366998i	$-0.988315\pi$
$193$	−6.50000	+	11.2583i	−0.467880	+	0.810392i	0.531446	+	0.847092i	$0.321649\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−6.50000	+	11.2583i	−0.463106	+	0.802123i	−0.999114	−	0.0420901i	$-0.986598\pi$
$197$	−6.50000	+	11.2583i	−0.463106	+	0.802123i	0.536008	+	0.844213i	$0.319932\pi$
$198$		0			0
$199$	−4.97494	−	8.61684i	−0.352664	−	0.610832i	0.634051	−	0.773291i	$-0.281391\pi$
$199$	−4.97494	−	8.61684i	−0.352664	−	0.610832i	−0.986715	+	0.162459i	$0.948057\pi$
$200$		0			0
$201$	−16.5000	−	28.5788i	−1.16382	−	2.01580i
$202$		0			0
$203$	16.5831			1.16391
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−26.5330			−1.84417
$208$		0			0
$209$	11.0000			0.760886
$210$		0			0
$211$	1.65831	−	2.87228i	0.114163	−	0.197736i	−0.803282	−	0.595599i	$-0.796915\pi$
$211$	1.65831	−	2.87228i	0.114163	−	0.197736i	0.917445	+	0.397863i	$0.130248\pi$
$212$		0			0
$213$	−33.0000			−2.26112
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−6.63325	+	11.4891i	−0.448233	+	0.776363i
$220$		0			0
$221$	−7.50000	+	7.79423i	−0.504505	+	0.524297i
$222$		0			0
$223$	1.65831	−	2.87228i	0.111049	−	0.192342i	−0.805145	−	0.593079i	$-0.797912\pi$
$223$	1.65831	−	2.87228i	0.111049	−	0.192342i	0.916193	+	0.400736i	$0.131246\pi$
$224$		0			0
$225$	20.0000	+	34.6410i	1.33333	+	2.30940i
$226$		0			0
$227$	1.65831	+	2.87228i	0.110066	+	0.190640i	0.915797	−	0.401642i	$-0.131560\pi$
$227$	1.65831	+	2.87228i	0.110066	+	0.190640i	−0.805731	+	0.592282i	$0.798227\pi$
$228$		0			0
$229$	−8.00000			−0.528655			−0.264327	−	0.964433i	$-0.585150\pi$
$229$	−8.00000			−0.528655			−0.264327	+	0.964433i	$0.585150\pi$
$230$		0			0
$231$	−18.2414	+	31.5951i	−1.20020	+	2.07880i
$232$		0			0
$233$	4.00000			0.262049			0.131024	−	0.991379i	$-0.458173\pi$
$233$	4.00000			0.262049			0.131024	+	0.991379i	$0.458173\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	11.0000	−	19.0526i	0.714527	−	1.23760i
$238$		0			0
$239$	26.5330			1.71628			0.858138	−	0.513418i	$-0.171621\pi$
$239$	26.5330			1.71628			0.858138	+	0.513418i	$0.171621\pi$
$240$		0			0
$241$	−6.50000	−	11.2583i	−0.418702	−	0.725213i	0.577107	−	0.816668i	$-0.304181\pi$
$241$	−6.50000	−	11.2583i	−0.418702	−	0.725213i	−0.995809	+	0.0914555i	$0.970848\pi$
$242$		0			0
$243$	26.5330	+	45.9565i	1.70209	+	2.94811i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−8.29156	+	8.61684i	−0.527579	+	0.548277i
$248$		0			0
$249$	22.0000	−	38.1051i	1.39419	−	2.41481i
$250$		0			0
$251$	−8.29156	−	14.3614i	−0.523359	−	0.906484i	−0.999630	−	0.0271858i	$-0.991345\pi$
$251$	−8.29156	−	14.3614i	−0.523359	−	0.906484i	0.476272	−	0.879298i	$-0.341988\pi$
$252$		0			0
$253$	−5.50000	−	9.52628i	−0.345782	−	0.598912i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−6.50000	+	11.2583i	−0.405459	+	0.702275i	−0.994375	−	0.105919i	$-0.966222\pi$
$257$	−6.50000	+	11.2583i	−0.405459	+	0.702275i	0.588916	+	0.808194i	$0.299555\pi$
$258$		0			0
$259$	−29.8496			−1.85477
$260$		0			0
$261$	40.0000			2.47594
$262$		0			0
$263$	−11.6082	+	20.1060i	−0.715791	+	1.23979i	0.246862	+	0.969051i	$0.420601\pi$
$263$	−11.6082	+	20.1060i	−0.715791	+	1.23979i	−0.962653	+	0.270737i	$0.912733\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−1.65831	−	2.87228i	−0.101487	−	0.175781i
$268$		0			0
$269$	14.5000	+	25.1147i	0.884081	+	1.53127i	0.846764	+	0.531969i	$0.178548\pi$
$269$	14.5000	+	25.1147i	0.884081	+	1.53127i	0.0373168	+	0.999303i	$0.488119\pi$
$270$		0			0
$271$	14.9248	−	25.8505i	0.906618	−	1.57031i	0.0878869	−	0.996130i	$-0.471989\pi$
$271$	14.9248	−	25.8505i	0.906618	−	1.57031i	0.818731	−	0.574178i	$-0.194678\pi$
$272$		0			0
$273$	−11.0000	−	38.1051i	−0.665750	−	2.30623i
$274$		0			0
$275$	−8.29156	+	14.3614i	−0.500000	+	0.866025i
$276$		0			0
$277$	2.50000	+	4.33013i	0.150210	+	0.260172i	0.931305	−	0.364241i	$-0.118672\pi$
$277$	2.50000	+	4.33013i	0.150210	+	0.260172i	−0.781094	+	0.624413i	$0.785338\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	20.0000			1.19310			0.596550	−	0.802576i	$-0.296538\pi$
$281$	20.0000			1.19310			0.596550	+	0.802576i	$0.296538\pi$
$282$		0			0
$283$	−11.6082	+	20.1060i	−0.690035	+	1.19518i	0.281791	+	0.959476i	$0.409072\pi$
$283$	−11.6082	+	20.1060i	−0.690035	+	1.19518i	−0.971826	+	0.235700i	$0.924262\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−9.94987			−0.587323
$288$		0			0
$289$	4.00000	−	6.92820i	0.235294	−	0.407541i
$290$		0			0
$291$	−23.2164			−1.36097
$292$		0			0
$293$	3.50000	+	6.06218i	0.204472	+	0.354156i	0.949964	−	0.312358i	$-0.101119\pi$
$293$	3.50000	+	6.06218i	0.204472	+	0.354156i	−0.745492	+	0.666514i	$0.767786\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−27.5000	+	47.6314i	−1.59571	+	2.76385i
$298$		0			0
$299$	11.6082	+	2.87228i	0.671319	+	0.166108i
$300$		0			0
$301$	16.5000	−	28.5788i	0.951044	−	1.64726i
$302$		0			0
$303$	24.8747	+	43.0842i	1.42901	+	2.47512i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−13.2665			−0.757159			−0.378580	−	0.925569i	$-0.623587\pi$
$307$	−13.2665			−0.757159			−0.378580	+	0.925569i	$0.623587\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	26.5330			1.50455			0.752274	−	0.658850i	$-0.228957\pi$
$311$	26.5330			1.50455			0.752274	+	0.658850i	$0.228957\pi$
$312$		0			0
$313$	4.00000			0.226093			0.113047	−	0.993590i	$-0.463939\pi$
$313$	4.00000			0.226093			0.113047	+	0.993590i	$0.463939\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−18.0000			−1.01098			−0.505490	−	0.862832i	$-0.668688\pi$
$317$	−18.0000			−1.01098			−0.505490	+	0.862832i	$0.668688\pi$
$318$		0			0
$319$	8.29156	+	14.3614i	0.464238	+	0.804084i
$320$		0			0
$321$	−5.50000	−	9.52628i	−0.306980	−	0.531705i
$322$		0			0
$323$	−4.97494	+	8.61684i	−0.276813	+	0.479454i
$324$		0			0
$325$	−5.00000	−	17.3205i	−0.277350	−	0.960769i
$326$		0			0
$327$	26.5330	−	45.9565i	1.46728	−	2.54140i
$328$		0			0
$329$	11.0000	+	19.0526i	0.606450	+	1.05040i
$330$		0			0
$331$	4.97494	+	8.61684i	0.273447	+	0.473625i	0.969742	−	0.244131i	$-0.0785028\pi$
$331$	4.97494	+	8.61684i	0.273447	+	0.473625i	−0.696295	+	0.717756i	$0.745169\pi$
$332$		0			0
$333$	−72.0000			−3.94558
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−12.0000			−0.653682			−0.326841	−	0.945079i	$-0.605984\pi$
$337$	−12.0000			−0.653682			−0.326841	+	0.945079i	$0.605984\pi$
$338$		0			0
$339$	36.4829			1.98148
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−9.94987			−0.537243
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−8.29156	−	14.3614i	−0.445114	−	0.770961i	0.552946	−	0.833217i	$-0.313504\pi$
$347$	−8.29156	−	14.3614i	−0.445114	−	0.770961i	−0.998060	+	0.0622565i	$0.980170\pi$
$348$		0			0
$349$	0.500000	−	0.866025i	0.0267644	−	0.0463573i	−0.852333	−	0.523000i	$-0.824813\pi$
$349$	0.500000	−	0.866025i	0.0267644	−	0.0463573i	0.879097	+	0.476642i	$0.158146\pi$
$350$		0			0
$351$	−16.5831	−	57.4456i	−0.885142	−	3.06622i
$352$		0			0
$353$	−15.5000	+	26.8468i	−0.824982	+	1.42891i	0.0769515	+	0.997035i	$0.475481\pi$
$353$	−15.5000	+	26.8468i	−0.824982	+	1.42891i	−0.901933	+	0.431875i	$0.857852\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−16.5000	−	28.5788i	−0.873273	−	1.51255i
$358$		0			0
$359$	−26.5330			−1.40036			−0.700179	−	0.713967i	$-0.746897\pi$
$359$	−26.5330			−1.40036			−0.700179	+	0.713967i	$0.746897\pi$
$360$		0			0
$361$	4.00000	−	6.92820i	0.210526	−	0.364642i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−11.6082	+	20.1060i	−0.605942	+	1.04952i	0.385959	+	0.922516i	$0.373870\pi$
$367$	−11.6082	+	20.1060i	−0.605942	+	1.04952i	−0.991902	+	0.127007i	$0.959463\pi$
$368$		0			0
$369$	−24.0000			−1.24939
$370$		0			0
$371$	−13.2665	−	22.9783i	−0.688762	−	1.19297i
$372$		0			0
$373$	6.50000	+	11.2583i	0.336557	+	0.582934i	0.983783	−	0.179364i	$-0.0574041\pi$
$373$	6.50000	+	11.2583i	0.336557	+	0.582934i	−0.647225	+	0.762299i	$0.724071\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−17.5000	−	4.33013i	−0.901296	−	0.223013i
$378$		0			0
$379$	14.9248	−	25.8505i	0.766636	−	1.32785i	−0.172741	−	0.984967i	$-0.555262\pi$
$379$	14.9248	−	25.8505i	0.766636	−	1.32785i	0.939377	−	0.342885i	$-0.111404\pi$
$380$		0			0
$381$	−16.5000	−	28.5788i	−0.845321	−	1.46414i
$382$		0			0
$383$	−1.65831	−	2.87228i	−0.0847358	−	0.146767i	0.820543	−	0.571585i	$-0.193671\pi$
$383$	−1.65831	−	2.87228i	−0.0847358	−	0.146767i	−0.905279	+	0.424818i	$0.860338\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	39.7995	−	68.9348i	2.02312	−	3.50415i
$388$		0			0
$389$	10.0000			0.507020			0.253510	−	0.967333i	$-0.418415\pi$
$389$	10.0000			0.507020			0.253510	+	0.967333i	$0.418415\pi$
$390$		0			0
$391$	9.94987			0.503187
$392$		0			0
$393$	−22.0000	+	38.1051i	−1.10975	+	1.92215i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	2.50000	+	4.33013i	0.125471	+	0.217323i	0.921917	−	0.387387i	$-0.126622\pi$
$397$	2.50000	+	4.33013i	0.125471	+	0.217323i	−0.796446	+	0.604710i	$0.793289\pi$
$398$		0			0
$399$	−18.2414	−	31.5951i	−0.913214	−	1.58173i
$400$		0			0
$401$	5.50000	−	9.52628i	0.274657	−	0.475720i	−0.695392	−	0.718631i	$-0.744769\pi$
$401$	5.50000	−	9.52628i	0.274657	−	0.475720i	0.970049	+	0.242911i	$0.0781024\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−14.9248	−	25.8505i	−0.739795	−	1.28136i
$408$		0			0
$409$	−6.50000	−	11.2583i	−0.321404	−	0.556689i	0.659374	−	0.751815i	$-0.270822\pi$
$409$	−6.50000	−	11.2583i	−0.321404	−	0.556689i	−0.980778	+	0.195127i	$0.937488\pi$
$410$		0			0
$411$	29.8496			1.47237
$412$		0			0
$413$	5.50000	−	9.52628i	0.270637	−	0.468758i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	11.0000			0.538672
$418$		0			0
$419$	−8.29156	+	14.3614i	−0.405069	+	0.701601i	−0.994330	−	0.106343i	$-0.966086\pi$
$419$	−8.29156	+	14.3614i	−0.405069	+	0.701601i	0.589260	+	0.807943i	$0.299419\pi$
$420$		0			0
$421$		0			0			−	1.00000i	$-0.5\pi$
$421$		0			0				1.00000i	$0.5\pi$
$422$		0			0
$423$	26.5330	+	45.9565i	1.29008	+	2.23448i
$424$		0			0
$425$	−7.50000	−	12.9904i	−0.363803	−	0.630126i
$426$		0			0
$427$	−14.9248	+	25.8505i	−0.722262	+	1.25099i
$428$		0			0
$429$	27.5000	−	28.5788i	1.32771	−	1.37980i
$430$		0			0
$431$	−8.29156	+	14.3614i	−0.399390	+	0.691765i	−0.993651	−	0.112508i	$-0.964112\pi$
$431$	−8.29156	+	14.3614i	−0.399390	+	0.691765i	0.594260	+	0.804273i	$0.297445\pi$
$432$		0			0
$433$	−10.5000	−	18.1865i	−0.504598	−	0.873989i	−0.999986	−	0.00531724i	$-0.998307\pi$
$433$	−10.5000	−	18.1865i	−0.504598	−	0.873989i	0.495388	−	0.868672i	$-0.335026\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	11.0000			0.526201
$438$		0			0
$439$	−8.29156	+	14.3614i	−0.395735	+	0.685433i	−0.993195	−	0.116466i	$-0.962843\pi$
$439$	−8.29156	+	14.3614i	−0.395735	+	0.685433i	0.597460	+	0.801899i	$0.296177\pi$
$440$		0			0
$441$	32.0000			1.52381
$442$		0			0
$443$	13.2665			0.630310			0.315155	−	0.949040i	$-0.397943\pi$
$443$	13.2665			0.630310			0.315155	+	0.949040i	$0.397943\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−3.31662			−0.156871
$448$		0			0
$449$	1.50000	+	2.59808i	0.0707894	+	0.122611i	0.899247	−	0.437440i	$-0.144115\pi$
$449$	1.50000	+	2.59808i	0.0707894	+	0.122611i	−0.828458	+	0.560051i	$0.810782\pi$
$450$		0			0
$451$	−4.97494	−	8.61684i	−0.234261	−	0.405751i
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	0.500000	−	0.866025i	0.0233890	−	0.0405110i	−0.854094	−	0.520119i	$-0.825888\pi$
$457$	0.500000	−	0.866025i	0.0233890	−	0.0405110i	0.877483	+	0.479608i	$0.159221\pi$
$458$		0			0
$459$	−24.8747	−	43.0842i	−1.16105	−	2.01100i
$460$		0			0
$461$	−1.50000	−	2.59808i	−0.0698620	−	0.121004i	0.828978	−	0.559281i	$-0.188923\pi$
$461$	−1.50000	−	2.59808i	−0.0698620	−	0.121004i	−0.898840	+	0.438276i	$0.855589\pi$
$462$		0			0
$463$	−26.5330			−1.23309			−0.616547	−	0.787318i	$-0.711469\pi$
$463$	−26.5330			−1.23309			−0.616547	+	0.787318i	$0.711469\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−19.8997			−0.920851			−0.460425	−	0.887698i	$-0.652303\pi$
$467$	−19.8997			−0.920851			−0.460425	+	0.887698i	$0.652303\pi$
$468$		0			0
$469$	−33.0000			−1.52380
$470$		0			0
$471$	13.2665	−	22.9783i	0.611288	−	1.05878i
$472$		0			0
$473$	33.0000			1.51734
$474$		0			0
$475$	−8.29156	−	14.3614i	−0.380443	−	0.658947i
$476$		0			0
$477$	−32.0000	−	55.4256i	−1.46518	−	2.53777i
$478$		0			0
$479$	4.97494	−	8.61684i	0.227311	−	0.393714i	−0.729700	−	0.683768i	$-0.760340\pi$
$479$	4.97494	−	8.61684i	0.227311	−	0.393714i	0.957010	+	0.290054i	$0.0936734\pi$
$480$		0			0
$481$	31.5000	+	7.79423i	1.43628	+	0.355386i
$482$		0			0
$483$	−18.2414	+	31.5951i	−0.830014	+	1.43763i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−4.97494	−	8.61684i	−0.225436	−	0.390466i	0.731014	−	0.682362i	$-0.239047\pi$
$487$	−4.97494	−	8.61684i	−0.225436	−	0.390466i	−0.956450	+	0.291896i	$0.905714\pi$
$488$		0			0
$489$	−55.0000			−2.48719
$490$		0			0
$491$	−8.29156	+	14.3614i	−0.374193	+	0.648121i	−0.990206	−	0.139615i	$-0.955414\pi$
$491$	−8.29156	+	14.3614i	−0.374193	+	0.648121i	0.616013	+	0.787736i	$0.288747\pi$
$492$		0			0
$493$	−15.0000			−0.675566
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−16.5000	+	28.5788i	−0.740126	+	1.28194i
$498$		0			0
$499$	13.2665			0.593890			0.296945	−	0.954895i	$-0.404032\pi$
$499$	13.2665			0.593890			0.296945	+	0.954895i	$0.404032\pi$
$500$		0			0
$501$	−5.50000	−	9.52628i	−0.245722	−	0.425603i
$502$		0			0
$503$	−1.65831	−	2.87228i	−0.0739405	−	0.128069i	0.826685	−	0.562666i	$-0.190224\pi$
$503$	−1.65831	−	2.87228i	−0.0739405	−	0.128069i	−0.900625	+	0.434597i	$0.856891\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	1.65831	+	43.0842i	0.0736482	+	1.91344i
$508$		0			0
$509$	−19.5000	+	33.7750i	−0.864322	+	1.49705i	0.00339621	+	0.999994i	$0.498919\pi$
$509$	−19.5000	+	33.7750i	−0.864322	+	1.49705i	−0.867719	+	0.497056i	$0.834414\pi$
$510$		0			0
$511$	6.63325	+	11.4891i	0.293438	+	0.508249i
$512$		0			0
$513$	−27.5000	−	47.6314i	−1.21415	−	2.10298i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−11.0000	+	19.0526i	−0.483779	+	0.837931i
$518$		0			0
$519$	23.2164			1.01909
$520$		0			0
$521$	−12.0000			−0.525730			−0.262865	−	0.964833i	$-0.584667\pi$
$521$	−12.0000			−0.525730			−0.262865	+	0.964833i	$0.584667\pi$
$522$		0			0
$523$	−8.29156	+	14.3614i	−0.362565	+	0.627980i	−0.988382	−	0.151989i	$-0.951432\pi$
$523$	−8.29156	+	14.3614i	−0.362565	+	0.627980i	0.625817	+	0.779970i	$0.284765\pi$
$524$		0			0
$525$	55.0000			2.40040
$526$		0			0
$527$		0			0
$528$		0			0
$529$	6.00000	+	10.3923i	0.260870	+	0.451839i
$530$		0			0
$531$	13.2665	−	22.9783i	0.575717	−	0.997171i
$532$		0			0
$533$	10.5000	+	2.59808i	0.454805	+	0.112535i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−5.50000	−	9.52628i	−0.237343	−	0.411089i
$538$		0			0
$539$	6.63325	+	11.4891i	0.285714	+	0.494872i
$540$		0			0
$541$	18.0000			0.773880			0.386940	−	0.922105i	$-0.373532\pi$
$541$	18.0000			0.773880			0.386940	+	0.922105i	$0.373532\pi$
$542$		0			0
$543$	13.2665	−	22.9783i	0.569320	−	0.986091i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	13.2665			0.567235			0.283617	−	0.958938i	$-0.408465\pi$
$547$	13.2665			0.567235			0.283617	+	0.958938i	$0.408465\pi$
$548$		0			0
$549$	−36.0000	+	62.3538i	−1.53644	+	2.66120i
$550$		0			0
$551$	−16.5831			−0.706465
$552$		0			0
$553$	−11.0000	−	19.0526i	−0.467768	−	0.810197i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−18.5000	+	32.0429i	−0.783870	+	1.35770i	0.145802	+	0.989314i	$0.453424\pi$
$557$	−18.5000	+	32.0429i	−0.783870	+	1.35770i	−0.929672	+	0.368389i	$0.879909\pi$
$558$		0			0
$559$	−24.8747	+	25.8505i	−1.05209	+	1.09336i
$560$		0			0
$561$	16.5000	−	28.5788i	0.696631	−	1.20660i
$562$		0			0
$563$	1.65831	+	2.87228i	0.0698895	+	0.121052i	0.898853	−	0.438251i	$-0.144402\pi$
$563$	1.65831	+	2.87228i	0.0698895	+	0.121052i	−0.828963	+	0.559303i	$0.811069\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	102.815			4.31784
$568$		0			0
$569$	−7.50000	+	12.9904i	−0.314416	+	0.544585i	−0.979313	−	0.202350i	$-0.935142\pi$
$569$	−7.50000	+	12.9904i	−0.314416	+	0.544585i	0.664897	+	0.746935i	$0.268475\pi$
$570$		0			0
$571$	−13.2665			−0.555186			−0.277593	−	0.960699i	$-0.589537\pi$
$571$	−13.2665			−0.555186			−0.277593	+	0.960699i	$0.589537\pi$
$572$		0			0
$573$	77.0000			3.21672
$574$		0			0
$575$	−8.29156	+	14.3614i	−0.345782	+	0.598912i
$576$		0			0
$577$	20.0000			0.832611			0.416305	−	0.909225i	$-0.363325\pi$
$577$	20.0000			0.832611			0.416305	+	0.909225i	$0.363325\pi$
$578$		0			0
$579$	21.5581	+	37.3397i	0.895922	+	1.55178i
$580$		0			0
$581$	−22.0000	−	38.1051i	−0.912714	−	1.58087i
$582$		0			0
$583$	13.2665	−	22.9783i	0.549442	−	0.951662i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−21.5581	+	37.3397i	−0.889796	+	1.54117i	−0.0496808	+	0.998765i	$0.515820\pi$
$587$	−21.5581	+	37.3397i	−0.889796	+	1.54117i	−0.840116	+	0.542407i	$0.817513\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$	21.5581	+	37.3397i	0.886780	+	1.53595i
$592$		0			0
$593$	−36.0000			−1.47834			−0.739171	−	0.673517i	$-0.764783\pi$
$593$	−36.0000			−1.47834			−0.739171	+	0.673517i	$0.764783\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−33.0000			−1.35060
$598$		0			0
$599$	−33.1662			−1.35514			−0.677568	−	0.735460i	$-0.736966\pi$
$599$	−33.1662			−1.35514			−0.677568	+	0.735460i	$0.736966\pi$
$600$		0			0
$601$	−14.5000	+	25.1147i	−0.591467	+	1.02445i	0.402568	+	0.915390i	$0.368118\pi$
$601$	−14.5000	+	25.1147i	−0.591467	+	1.02445i	−0.994035	+	0.109061i	$0.965216\pi$
$602$		0			0
$603$	−79.5990			−3.24152
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−4.97494	−	8.61684i	−0.201926	−	0.349747i	0.747223	−	0.664574i	$-0.231387\pi$
$607$	−4.97494	−	8.61684i	−0.201926	−	0.349747i	−0.949149	+	0.314827i	$0.898054\pi$
$608$		0			0
$609$	27.5000	−	47.6314i	1.11436	−	1.93012i
$610$		0			0
$611$	−6.63325	−	22.9783i	−0.268353	−	0.929601i
$612$		0			0
$613$	−3.50000	+	6.06218i	−0.141364	+	0.244849i	−0.928010	−	0.372554i	$-0.878482\pi$
$613$	−3.50000	+	6.06218i	−0.141364	+	0.244849i	0.786647	+	0.617403i	$0.211815\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	8.50000	+	14.7224i	0.342197	+	0.592703i	0.984840	−	0.173463i	$-0.0554956\pi$
$617$	8.50000	+	14.7224i	0.342197	+	0.592703i	−0.642643	+	0.766165i	$0.722162\pi$
$618$		0			0
$619$	39.7995			1.59968			0.799838	−	0.600215i	$-0.204918\pi$
$619$	39.7995			1.59968			0.799838	+	0.600215i	$0.204918\pi$
$620$		0			0
$621$	−27.5000	+	47.6314i	−1.10354	+	1.91138i
$622$		0			0
$623$	−3.31662			−0.132878
$624$		0			0
$625$	25.0000			1.00000
$626$		0			0
$627$	18.2414	−	31.5951i	0.728493	−	1.26179i
$628$		0			0
$629$	27.0000			1.07656
$630$		0			0
$631$	−4.97494	−	8.61684i	−0.198049	−	0.343031i	0.749847	−	0.661612i	$-0.230127\pi$
$631$	−4.97494	−	8.61684i	−0.198049	−	0.343031i	−0.947896	+	0.318580i	$0.896794\pi$
$632$		0			0
$633$	−5.50000	−	9.52628i	−0.218605	−	0.378636i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−14.0000	−	3.46410i	−0.554700	−	0.137253i
$638$		0			0
$639$	−39.7995	+	68.9348i	−1.57444	+	2.72702i
$640$		0			0
$641$	−10.5000	−	18.1865i	−0.414725	−	0.718325i	0.580674	−	0.814136i	$-0.302789\pi$
$641$	−10.5000	−	18.1865i	−0.414725	−	0.718325i	−0.995400	+	0.0958109i	$0.969456\pi$
$642$		0			0
$643$	18.2414	+	31.5951i	0.719372	+	1.24599i	0.961249	+	0.275682i	$0.0889037\pi$
$643$	18.2414	+	31.5951i	0.719372	+	1.24599i	−0.241877	+	0.970307i	$0.577763\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	4.97494	−	8.61684i	0.195585	−	0.338763i	−0.751507	−	0.659725i	$-0.770673\pi$
$647$	4.97494	−	8.61684i	0.195585	−	0.338763i	0.947092	+	0.320962i	$0.104006\pi$
$648$		0			0
$649$	11.0000			0.431788
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−7.50000	+	12.9904i	−0.293498	+	0.508353i	−0.974634	−	0.223803i	$-0.928153\pi$
$653$	−7.50000	+	12.9904i	−0.293498	+	0.508353i	0.681137	+	0.732156i	$0.261486\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	16.0000	+	27.7128i	0.624219	+	1.08118i
$658$		0			0
$659$	−21.5581	−	37.3397i	−0.839783	−	1.45455i	−0.890076	−	0.455812i	$-0.849349\pi$
$659$	−21.5581	−	37.3397i	−0.839783	−	1.45455i	0.0502932	−	0.998734i	$-0.483984\pi$
$660$		0			0
$661$	8.50000	−	14.7224i	0.330612	−	0.572636i	−0.652020	−	0.758202i	$-0.726078\pi$
$661$	8.50000	−	14.7224i	0.330612	−	0.572636i	0.982632	+	0.185565i	$0.0594116\pi$
$662$		0			0
$663$	9.94987	+	34.4674i	0.386421	+	1.33860i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	8.29156	+	14.3614i	0.321051	+	0.556076i
$668$		0			0
$669$	−5.50000	−	9.52628i	−0.212642	−	0.368307i
$670$		0			0
$671$	−29.8496			−1.15233
$672$		0			0
$673$	24.5000	−	42.4352i	0.944406	−	1.63576i	0.187469	−	0.982271i	$-0.439972\pi$
$673$	24.5000	−	42.4352i	0.944406	−	1.63576i	0.756937	−	0.653488i	$-0.226695\pi$
$674$		0			0
$675$	82.9156			3.19142
$676$		0			0
$677$	24.0000			0.922395			0.461197	−	0.887298i	$-0.347420\pi$
$677$	24.0000			0.922395			0.461197	+	0.887298i	$0.347420\pi$
$678$		0			0
$679$	−11.6082	+	20.1060i	−0.445481	+	0.771596i
$680$		0			0
$681$	11.0000			0.421521
$682$		0			0
$683$	14.9248	+	25.8505i	0.571082	+	0.989143i	0.996455	+	0.0841251i	$0.0268095\pi$
$683$	14.9248	+	25.8505i	0.571082	+	0.989143i	−0.425373	+	0.905018i	$0.639857\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−13.2665	+	22.9783i	−0.506149	+	0.876675i
$688$		0			0
$689$	8.00000	+	27.7128i	0.304776	+	1.05577i
$690$		0			0
$691$	−11.6082	+	20.1060i	−0.441596	+	0.764867i	−0.997808	−	0.0661734i	$-0.978921\pi$
$691$	−11.6082	+	20.1060i	−0.441596	+	0.764867i	0.556212	+	0.831041i	$0.312254\pi$
$692$		0			0
$693$	44.0000	+	76.2102i	1.67142	+	2.89499i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	9.00000			0.340899
$698$		0			0
$699$	6.63325	−	11.4891i	0.250893	−	0.434559i
$700$		0			0
$701$	32.0000			1.20862			0.604312	−	0.796748i	$-0.293448\pi$
$701$	32.0000			1.20862			0.604312	+	0.796748i	$0.293448\pi$
$702$		0			0
$703$	29.8496			1.12580
$704$		0			0
$705$		0			0
$706$		0			0
$707$	49.7494			1.87102
$708$		0			0
$709$	14.5000	+	25.1147i	0.544559	+	0.943204i	0.998635	+	0.0522406i	$0.0166363\pi$
$709$	14.5000	+	25.1147i	0.544559	+	0.943204i	−0.454076	+	0.890963i	$0.650030\pi$
$710$		0			0
$711$	−26.5330	−	45.9565i	−0.995065	−	1.72350i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$	44.0000	−	76.2102i	1.64321	−	2.84612i
$718$		0			0
$719$	−14.9248	−	25.8505i	−0.556602	−	0.964062i	−0.997777	−	0.0666413i	$-0.978772\pi$
$719$	−14.9248	−	25.8505i	−0.556602	−	0.964062i	0.441175	−	0.897421i	$-0.354562\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−43.1161			−1.60351
$724$		0			0
$725$	12.5000	−	21.6506i	0.464238	−	0.804084i
$726$		0			0
$727$	−26.5330			−0.984054			−0.492027	−	0.870580i	$-0.663744\pi$
$727$	−26.5330			−0.984054			−0.492027	+	0.870580i	$0.663744\pi$
$728$		0			0
$729$	83.0000			3.07407
$730$		0			0
$731$	−14.9248	+	25.8505i	−0.552014	+	0.956116i
$732$		0			0
$733$	−18.0000			−0.664845			−0.332423	−	0.943131i	$-0.607866\pi$
$733$	−18.0000			−0.664845			−0.332423	+	0.943131i	$0.607866\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−16.5000	−	28.5788i	−0.607785	−	1.05272i
$738$		0			0
$739$	4.97494	−	8.61684i	0.183006	−	0.316976i	−0.759897	−	0.650044i	$-0.774751\pi$
$739$	4.97494	−	8.61684i	0.183006	−	0.316976i	0.942903	+	0.333068i	$0.108084\pi$
$740$		0			0
$741$	11.0000	+	38.1051i	0.404095	+	1.39983i
$742$		0			0
$743$	−21.5581	+	37.3397i	−0.790889	+	1.36986i	0.134529	+	0.990910i	$0.457048\pi$
$743$	−21.5581	+	37.3397i	−0.790889	+	1.36986i	−0.925417	+	0.378949i	$0.876285\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−53.0660	−	91.9130i	−1.94158	−	3.36292i
$748$		0			0
$749$	−11.0000			−0.401931
$750$		0			0
$751$	14.9248	−	25.8505i	0.544614	−	0.943299i	−0.454017	−	0.890993i	$-0.650009\pi$
$751$	14.9248	−	25.8505i	0.544614	−	0.943299i	0.998631	−	0.0523063i	$-0.0166572\pi$
$752$		0			0
$753$	−55.0000			−2.00431
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−3.50000	+	6.06218i	−0.127210	+	0.220334i	−0.922595	−	0.385771i	$-0.873935\pi$
$757$	−3.50000	+	6.06218i	−0.127210	+	0.220334i	0.795385	+	0.606105i	$0.207269\pi$
$758$		0			0
$759$	−36.4829			−1.32424
$760$		0			0
$761$	13.5000	+	23.3827i	0.489375	+	0.847622i	0.999925	−	0.0122260i	$-0.00389175\pi$
$761$	13.5000	+	23.3827i	0.489375	+	0.847622i	−0.510551	+	0.859848i	$0.670558\pi$
$762$		0			0
$763$	−26.5330	−	45.9565i	−0.960559	−	1.66374i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−8.29156	+	8.61684i	−0.299391	+	0.311136i
$768$		0			0
$769$	13.5000	−	23.3827i	0.486822	−	0.843201i	−0.513063	−	0.858351i	$-0.671489\pi$
$769$	13.5000	−	23.3827i	0.486822	−	0.843201i	0.999885	+	0.0151499i	$0.00482254\pi$
$770$		0			0
$771$	21.5581	+	37.3397i	0.776395	+	1.34475i
$772$		0			0
$773$	10.5000	+	18.1865i	0.377659	+	0.654124i	0.990721	−	0.135910i	$-0.0433959\pi$
$773$	10.5000	+	18.1865i	0.377659	+	0.654124i	−0.613062	+	0.790034i	$0.710063\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−49.5000	+	85.7365i	−1.77580	+	3.07578i
$778$		0			0
$779$	9.94987			0.356491
$780$		0			0
$781$	−33.0000			−1.18083
$782$		0			0
$783$	41.4578	−	71.8070i	1.48158	−	2.56617i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	4.97494	+	8.61684i	0.177337	+	0.307157i	0.940968	−	0.338496i	$-0.109918\pi$
$787$	4.97494	+	8.61684i	0.177337	+	0.307157i	−0.763630	+	0.645654i	$0.776585\pi$
$788$		0			0
$789$	38.5000	+	66.6840i	1.37064	+	2.37401i
$790$		0			0
$791$	18.2414	−	31.5951i	0.648591	−	1.12339i
$792$		0			0
$793$	22.5000	−	23.3827i	0.798998	−	0.830344i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−16.5000	−	28.5788i	−0.584460	−	1.01231i	−0.994943	−	0.100446i	$-0.967973\pi$
$797$	−16.5000	−	28.5788i	−0.584460	−	1.01231i	0.410483	−	0.911868i	$-0.365360\pi$
$798$		0			0
$799$	−9.94987	−	17.2337i	−0.352001	−	0.609684i
$800$		0			0
$801$	−8.00000			−0.282666
$802$		0			0
$803$	−6.63325	+	11.4891i	−0.234082	+	0.405442i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	96.1821			3.38577
$808$		0			0
$809$	9.50000	−	16.4545i	0.334002	−	0.578509i	−0.649290	−	0.760541i	$-0.724934\pi$
$809$	9.50000	−	16.4545i	0.334002	−	0.578509i	0.983293	+	0.182032i	$0.0582674\pi$
$810$		0			0
$811$	6.63325			0.232925			0.116462	−	0.993195i	$-0.462845\pi$
$811$	6.63325			0.232925			0.116462	+	0.993195i	$0.462845\pi$
$812$		0			0
$813$	−49.5000	−	85.7365i	−1.73604	−	3.00691i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−16.5000	+	28.5788i	−0.577262	+	0.999847i
$818$		0			0
$819$	−92.8655	−	22.9783i	−3.24498	−	0.802925i
$820$		0			0
$821$	13.5000	−	23.3827i	0.471153	−	0.816061i	−0.528302	−	0.849056i	$-0.677171\pi$
$821$	13.5000	−	23.3827i	0.471153	−	0.816061i	0.999456	+	0.0329950i	$0.0105045\pi$
$822$		0			0
$823$	−18.2414	−	31.5951i	−0.635856	−	1.10134i	−0.986333	−	0.164764i	$-0.947314\pi$
$823$	−18.2414	−	31.5951i	−0.635856	−	1.10134i	0.350476	−	0.936572i	$-0.386020\pi$
$824$		0			0
$825$	27.5000	+	47.6314i	0.957427	+	1.65831i
$826$		0			0
$827$	13.2665			0.461321			0.230661	−	0.973034i	$-0.425911\pi$
$827$	13.2665			0.461321			0.230661	+	0.973034i	$0.425911\pi$
$828$		0			0
$829$	5.50000	−	9.52628i	0.191023	−	0.330861i	−0.754567	−	0.656223i	$-0.772153\pi$
$829$	5.50000	−	9.52628i	0.191023	−	0.330861i	0.945589	+	0.325362i	$0.105486\pi$
$830$		0			0
$831$	16.5831			0.575262
$832$		0			0
$833$	−12.0000			−0.415775
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−4.97494	−	8.61684i	−0.171754	−	0.297486i	0.767279	−	0.641313i	$-0.221610\pi$
$839$	−4.97494	−	8.61684i	−0.171754	−	0.297486i	−0.939033	+	0.343827i	$0.888277\pi$
$840$		0			0
$841$	2.00000	+	3.46410i	0.0689655	+	0.119452i
$842$		0			0
$843$	33.1662	−	57.4456i	1.14231	−	1.97853i
$844$		0			0
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	38.5000	+	66.6840i	1.32132	+	2.28859i
$850$		0			0
$851$	−14.9248	−	25.8505i	−0.511616	−	0.886145i
$852$		0			0
$853$	−56.0000			−1.91740			−0.958702	−	0.284413i	$-0.908201\pi$
$853$	−56.0000			−1.91740			−0.958702	+	0.284413i	$0.908201\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	28.0000			0.956462			0.478231	−	0.878234i	$-0.341278\pi$
$857$	28.0000			0.956462			0.478231	+	0.878234i	$0.341278\pi$
$858$		0			0
$859$	13.2665			0.452647			0.226324	−	0.974052i	$-0.427329\pi$
$859$	13.2665			0.452647			0.226324	+	0.974052i	$0.427329\pi$
$860$		0			0
$861$	−16.5000	+	28.5788i	−0.562318	+	0.973964i
$862$		0			0
$863$	53.0660			1.80639			0.903194	−	0.429233i	$-0.141216\pi$
$863$	53.0660			1.80639			0.903194	+	0.429233i	$0.141216\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−13.2665	−	22.9783i	−0.450554	−	0.780382i
$868$		0			0
$869$	11.0000	−	19.0526i	0.373149	−	0.646314i
$870$		0			0
$871$	34.8246	+	8.61684i	1.17999	+	0.291971i
$872$		0			0
$873$	−28.0000	+	48.4974i	−0.947656	+	1.64139i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	7.50000	+	12.9904i	0.253257	+	0.438654i	0.964421	−	0.264373i	$-0.0851648\pi$
$877$	7.50000	+	12.9904i	0.253257	+	0.438654i	−0.711164	+	0.703027i	$0.751832\pi$
$878$		0			0
$879$	23.2164			0.783069
$880$		0			0
$881$	−2.50000	+	4.33013i	−0.0842271	+	0.145886i	−0.905062	−	0.425280i	$-0.860175\pi$
$881$	−2.50000	+	4.33013i	−0.0842271	+	0.145886i	0.820834	+	0.571166i	$0.193509\pi$
$882$		0			0
$883$	−13.2665			−0.446453			−0.223227	−	0.974767i	$-0.571659\pi$
$883$	−13.2665			−0.446453			−0.223227	+	0.974767i	$0.571659\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−21.5581	+	37.3397i	−0.723849	+	1.25374i	0.235597	+	0.971851i	$0.424295\pi$
$887$	−21.5581	+	37.3397i	−0.723849	+	1.25374i	−0.959446	+	0.281892i	$0.909038\pi$
$888$		0			0
$889$	−33.0000			−1.10678
$890$		0			0
$891$	51.4077	+	89.0407i	1.72222	+	2.98298i
$892$		0			0
$893$	−11.0000	−	19.0526i	−0.368101	−	0.637570i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	27.5000	−	28.5788i	0.918198	−	0.954220i
$898$		0			0
$899$		0			0
$900$		0			0
$901$	12.0000	+	20.7846i	0.399778	+	0.692436i
$902$		0			0
$903$	−54.7243	−	94.7853i	−1.82111	−	3.15426i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−24.8747	+	43.0842i	−0.825950	+	1.43059i	0.0752404	+	0.997165i	$0.476028\pi$
$907$	−24.8747	+	43.0842i	−0.825950	+	1.43059i	−0.901191	+	0.433423i	$0.857306\pi$
$908$		0			0
$909$	120.000			3.98015
$910$		0			0
$911$	26.5330			0.879077			0.439539	−	0.898224i	$-0.355142\pi$
$911$	26.5330			0.879077			0.439539	+	0.898224i	$0.355142\pi$
$912$		0			0
$913$	22.0000	−	38.1051i	0.728094	−	1.26110i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	22.0000	+	38.1051i	0.726504	+	1.25834i
$918$		0			0
$919$	−1.65831	−	2.87228i	−0.0547027	−	0.0947478i	0.837377	−	0.546625i	$-0.184088\pi$
$919$	−1.65831	−	2.87228i	−0.0547027	−	0.0947478i	−0.892080	+	0.451877i	$0.850754\pi$
$920$		0			0
$921$	−22.0000	+	38.1051i	−0.724925	+	1.25561i
$922$		0			0
$923$	24.8747	−	25.8505i	0.818760	−	0.850881i
$924$		0			0
$925$	−22.5000	+	38.9711i	−0.739795	+	1.28136i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−6.50000	−	11.2583i	−0.213258	−	0.369374i	0.739474	−	0.673185i	$-0.235074\pi$
$929$	−6.50000	−	11.2583i	−0.213258	−	0.369374i	−0.952732	+	0.303811i	$0.901741\pi$
$930$		0			0
$931$	−13.2665			−0.434792
$932$		0			0
$933$	44.0000	−	76.2102i	1.44050	−	2.49501i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	20.0000			0.653372			0.326686	−	0.945133i	$-0.394068\pi$
$937$	20.0000			0.653372			0.326686	+	0.945133i	$0.394068\pi$
$938$		0			0
$939$	6.63325	−	11.4891i	0.216468	−	0.374933i
$940$		0			0
$941$	−30.0000			−0.977972			−0.488986	−	0.872292i	$-0.662633\pi$
$941$	−30.0000			−0.977972			−0.488986	+	0.872292i	$0.662633\pi$
$942$		0			0
$943$	−4.97494	−	8.61684i	−0.162006	−	0.280603i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	1.65831	−	2.87228i	0.0538879	−	0.0933366i	−0.837823	−	0.545942i	$-0.816172\pi$
$947$	1.65831	−	2.87228i	0.0538879	−	0.0933366i	0.891711	+	0.452605i	$0.149505\pi$
$948$		0			0
$949$	−4.00000	−	13.8564i	−0.129845	−	0.449798i
$950$		0			0
$951$	−29.8496	+	51.7011i	−0.967940	+	1.67652i
$952$		0			0
$953$	−7.50000	−	12.9904i	−0.242949	−	0.420800i	0.718604	−	0.695419i	$-0.244781\pi$
$953$	−7.50000	−	12.9904i	−0.242949	−	0.420800i	−0.961553	+	0.274620i	$0.911448\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	55.0000			1.77790
$958$		0			0
$959$	14.9248	−	25.8505i	0.481947	−	0.834757i
$960$		0			0
$961$	−31.0000			−1.00000
$962$		0			0
$963$	−26.5330			−0.855014
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−26.5330			−0.853244			−0.426622	−	0.904430i	$-0.640296\pi$
$967$	−26.5330			−0.853244			−0.426622	+	0.904430i	$0.640296\pi$
$968$		0			0
$969$	16.5000	+	28.5788i	0.530056	+	0.918085i
$970$		0			0
$971$	−8.29156	−	14.3614i	−0.266089	−	0.460879i	0.701759	−	0.712414i	$-0.252398\pi$
$971$	−8.29156	−	14.3614i	−0.266089	−	0.460879i	−0.967848	+	0.251535i	$0.919065\pi$
$972$		0			0
$973$	5.50000	−	9.52628i	0.176322	−	0.305398i
$974$		0			0
$975$	−58.0409	−	14.3614i	−1.85880	−	0.459933i
$976$		0			0
$977$	−3.50000	+	6.06218i	−0.111975	+	0.193946i	−0.916566	−	0.399882i	$-0.869051\pi$
$977$	−3.50000	+	6.06218i	−0.111975	+	0.193946i	0.804592	+	0.593829i	$0.202384\pi$
$978$		0			0
$979$	−1.65831	−	2.87228i	−0.0529999	−	0.0917985i
$980$		0			0
$981$	−64.0000	−	110.851i	−2.04336	−	3.53921i
$982$		0			0
$983$	53.0660			1.69254			0.846271	−	0.532752i	$-0.178842\pi$
$983$	53.0660			1.69254			0.846271	+	0.532752i	$0.178842\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	72.9657			2.32253
$988$		0			0
$989$	33.0000			1.04934
$990$		0			0
$991$	−21.5581	+	37.3397i	−0.684814	+	1.18613i	0.288681	+	0.957425i	$0.406783\pi$
$991$	−21.5581	+	37.3397i	−0.684814	+	1.18613i	−0.973495	+	0.228708i	$0.926550\pi$
$992$		0			0
$993$	33.0000			1.04722
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−8.50000	−	14.7224i	−0.269198	−	0.466264i	0.699457	−	0.714675i	$-0.253425\pi$
$997$	−8.50000	−	14.7224i	−0.269198	−	0.466264i	−0.968655	+	0.248410i	$0.920092\pi$
$998$		0			0
$999$	−74.6241	+	129.253i	−2.36100	+	4.08937i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	832.2.i.n.321.2		4
4.3	odd	2	inner	832.2.i.n.321.1		4
8.3	odd	2		416.2.i.d.321.2	yes	4
8.5	even	2		416.2.i.d.321.1	yes	4
13.3	even	3	inner	832.2.i.n.705.2		4
52.3	odd	6	inner	832.2.i.n.705.1		4
104.3	odd	6		416.2.i.d.289.2	yes	4
104.29	even	6		416.2.i.d.289.1	✓	4
104.35	odd	6		5408.2.a.x.1.1		2
104.43	odd	6		5408.2.a.w.1.1		2
104.61	even	6		5408.2.a.x.1.2		2
104.69	even	6		5408.2.a.w.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
416.2.i.d.289.1	✓	4	104.29	even	6
416.2.i.d.289.2	yes	4	104.3	odd	6
416.2.i.d.321.1	yes	4	8.5	even	2
416.2.i.d.321.2	yes	4	8.3	odd	2
832.2.i.n.321.1		4	4.3	odd	2	inner
832.2.i.n.321.2		4	1.1	even	1	trivial
832.2.i.n.705.1		4	52.3	odd	6	inner
832.2.i.n.705.2		4	13.3	even	3	inner
5408.2.a.w.1.1		2	104.43	odd	6
5408.2.a.w.1.2		2	104.69	even	6
5408.2.a.x.1.1		2	104.35	odd	6
5408.2.a.x.1.2		2	104.61	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 832 = 2^{6} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	832.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.65831 - 2.87228i) q^{3} +(-1.65831 - 2.87228i) q^{7} +(-4.00000 - 6.92820i) q^{9} +(1.65831 - 2.87228i) q^{11} +(1.00000 + 3.46410i) q^{13} +(1.50000 + 2.59808i) q^{17} +(1.65831 + 2.87228i) q^{19} -11.0000 q^{21} +(1.65831 - 2.87228i) q^{23} -5.00000 q^{25} -16.5831 q^{27} +(-2.50000 + 4.33013i) q^{29} +(-5.50000 - 9.52628i) q^{33} +(4.50000 - 7.79423i) q^{37} +(11.6082 + 2.87228i) q^{39} +(1.50000 - 2.59808i) q^{41} +(4.97494 + 8.61684i) q^{43} -6.63325 q^{47} +(-2.00000 + 3.46410i) q^{49} +9.94987 q^{51} +8.00000 q^{53} +11.0000 q^{57} +(1.65831 + 2.87228i) q^{59} +(-4.50000 - 7.79423i) q^{61} +(-13.2665 + 22.9783i) q^{63} +(4.97494 - 8.61684i) q^{67} +(-5.50000 - 9.52628i) q^{69} +(-4.97494 - 8.61684i) q^{71} -4.00000 q^{73} +(-8.29156 + 14.3614i) q^{75} -11.0000 q^{77} +6.63325 q^{79} +(-15.5000 + 26.8468i) q^{81} +13.2665 q^{83} +(8.29156 + 14.3614i) q^{87} +(0.500000 - 0.866025i) q^{89} +(8.29156 - 8.61684i) q^{91} +(-3.50000 - 6.06218i) q^{97} -26.5330 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 16 q^{9} + 4 q^{13} + 6 q^{17} - 44 q^{21} - 20 q^{25} - 10 q^{29} - 22 q^{33} + 18 q^{37} + 6 q^{41} - 8 q^{49} + 32 q^{53} + 44 q^{57} - 18 q^{61} - 22 q^{69} - 16 q^{73} - 44 q^{77} - 62 q^{81}+ \cdots - 14 q^{97}+O(q^{100}) \) 4 * q - 16 * q^9 + 4 * q^13 + 6 * q^17 - 44 * q^21 - 20 * q^25 - 10 * q^29 - 22 * q^33 + 18 * q^37 + 6 * q^41 - 8 * q^49 + 32 * q^53 + 44 * q^57 - 18 * q^61 - 22 * q^69 - 16 * q^73 - 44 * q^77 - 62 * q^81 + 2 * q^89 - 14 * q^97

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