LMFDB - Embedded newform 3997.1.cz.a.531.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3997,1,Mod(13,3997)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3997, base_ring=CyclotomicField(570))

chi = DirichletCharacter(H, H._module([285, 352]))

N = Newforms(chi, 1, names="a")

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

chi := DirichletCharacter("3997.13");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 3997 = 7 \cdot 571 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	3997.cz (of order $570$, degree $144$, 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:	$1.99476285549$
Analytic rank:	$0$
Dimension:	$144$
Coefficient field:	$\Q(\zeta_{570})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{144} - x^{143} + x^{142} + x^{139} - x^{138} + x^{137} - x^{129} + x^{128} - x^{127} + x^{125} + \cdots + 1 $ x^144 - x^143 + x^142 + x^139 - x^138 + x^137 - x^129 + x^128 - x^127 + x^125 - 2x^124 + 2x^123 - x^122 + x^120 - x^119 + x^118 + x^114 - x^113 + x^112 - x^110 + 2x^109 - 2x^108 + x^107 - x^105 + x^104 - x^103 - x^99 + x^98 - x^97 + x^95 - 2x^94 + 2x^93 - x^92 + x^90 - x^89 + x^88 - x^87 + x^86 - x^85 + x^84 - x^83 + x^81 - 2x^80 + 2x^79 - 2x^78 + x^77 - x^75 + x^74 - x^73 + x^72 - x^71 + x^70 - x^69 + x^67 - 2x^66 + 2x^65 - 2x^64 + x^63 - x^61 + x^60 - x^59 + x^58 - x^57 + x^56 - x^55 + x^54 - x^52 + 2x^51 - 2x^50 + x^49 - x^47 + x^46 - x^45 - x^41 + x^40 - x^39 + x^37 - 2x^36 + 2x^35 - x^34 + x^32 - x^31 + x^30 + x^26 - x^25 + x^24 - x^22 + 2x^21 - 2x^20 + x^19 - x^17 + x^16 - x^15 + x^7 - x^6 + x^5 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{285}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{285} - \cdots)$

Embedding invariants

Embedding label			531.1
Root			$0.319482 - 0.947592i$ of defining polynomial
Character	$\chi$	$=$	3997.531
Dual form			3997.1.cz.a.3583.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26766 - 1.53924i) q^{2} +(-0.570575 + 2.92103i) q^{4} +(0.922290 + 0.386499i) q^{7} +(3.46574 - 1.87557i) q^{8} +(0.775409 + 0.631460i) q^{9} +O(q^{10})$	\(q+(-1.26766 - 1.53924i) q^{2} +(-0.570575 + 2.92103i) q^{4} +(0.922290 + 0.386499i) q^{7} +(3.46574 - 1.87557i) q^{8} +(0.775409 + 0.631460i) q^{9} +(0.855563 + 0.438905i) q^{11} +(-0.574239 - 1.90958i) q^{14} +(-4.52289 - 1.83704i) q^{16} +(-0.0109903 - 1.99402i) q^{18} +(-0.408987 - 1.87330i) q^{22} +(1.13347 - 1.07859i) q^{23} +(0.815447 - 0.578832i) q^{25} +(-1.65521 + 2.47351i) q^{28} +(0.502662 - 0.488997i) q^{29} +(1.72950 + 5.52953i) q^{32} +(-2.28694 + 1.90469i) q^{36} +(-1.86763 - 0.687544i) q^{37} +(-0.671770 - 1.73571i) q^{43} +(-1.77022 + 2.24869i) q^{44} +(-3.09707 - 0.377385i) q^{46} +(0.701237 + 0.712928i) q^{49} +(-1.92467 - 0.521404i) q^{50} +(-0.0192865 + 0.317727i) q^{53} +(3.92133 - 0.390309i) q^{56} +(-1.38989 - 0.153833i) q^{58} +(0.471093 + 0.882084i) q^{63} +(3.64879 - 5.58489i) q^{64} +(-1.06056 - 0.701272i) q^{67} +(1.29170 + 1.43458i) q^{71} +(3.87171 + 0.734147i) q^{72} +(1.30923 + 3.74631i) q^{74} +(0.619441 + 0.735472i) q^{77} +(0.596215 + 1.40101i) q^{79} +(0.202517 + 0.979279i) q^{81} +(-1.82009 + 3.23431i) q^{86} +(3.78836 - 0.0835327i) q^{88} +(2.50387 + 3.92631i) q^{92} +(0.208435 - 1.98313i) q^{98} +(0.386260 + 0.880585i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + q^{2} + 5 q^{4} + 2 q^{7} + 21 q^{8} - q^{9}+O(q^{10}) $ 144 * q + q^2 + 5 * q^4 + 2 * q^7 + 21 * q^8 - q^9	$ 144 q + q^{2} + 5 q^{4} + 2 q^{7} + 21 q^{8} - q^{9} + 6 q^{11} + q^{14} + 6 q^{16} - 9 q^{18} + 21 q^{22} + 3 q^{23} - q^{25} - 10 q^{28} - 4 q^{29} - 5 q^{32} - 2 q^{37} - 9 q^{43} - 20 q^{44} - 34 q^{46} + 2 q^{49} - 2 q^{50} + 6 q^{53} - 8 q^{56} - q^{58} - q^{63} + 11 q^{64} + 20 q^{67} + 3 q^{71} + 23 q^{72} - 31 q^{74} + q^{77} + 6 q^{79} - q^{81} + 7 q^{86} - 9 q^{88} + 9 q^{92} + 6 q^{98} - 2 q^{99}+O(q^{100}) $ 144 * q + q^2 + 5 * q^4 + 2 * q^7 + 21 * q^8 - q^9 + 6 * q^11 + q^14 + 6 * q^16 - 9 * q^18 + 21 * q^22 + 3 * q^23 - q^25 - 10 * q^28 - 4 * q^29 - 5 * q^32 - 2 * q^37 - 9 * q^43 - 20 * q^44 - 34 * q^46 + 2 * q^49 - 2 * q^50 + 6 * q^53 - 8 * q^56 - q^58 - q^63 + 11 * q^64 + 20 * q^67 + 3 * q^71 + 23 * q^72 - 31 * q^74 + q^77 + 6 * q^79 - q^81 + 7 * q^86 - 9 * q^88 + 9 * q^92 + 6 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3997\mathbb{Z}\right)^\times$.

$n$	$1716$	$2285$
$\chi(n)$	$e\left(\frac{31}{285}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.26766	−	1.53924i	−1.26766	−	1.53924i	−0.693336	−	0.720615i	$-0.743860\pi$
$2$	−1.26766	−	1.53924i	−1.26766	−	1.53924i	−0.574329	−	0.818625i	$-0.694737\pi$
$3$		0			0		−0.942181	−	0.335105i	$-0.891228\pi$
$3$		0			0		0.942181	+	0.335105i	$0.108772\pi$
$4$	−0.570575	+	2.92103i	−0.570575	+	2.92103i
$5$		0			0		0.952745	−	0.303771i	$-0.0982456\pi$
$5$		0			0		−0.952745	+	0.303771i	$0.901754\pi$
$6$		0			0
$7$	0.922290	+	0.386499i	0.922290	+	0.386499i
$7$	0.922290	+	0.386499i	0.922290	+	0.386499i
$8$	3.46574	−	1.87557i	3.46574	−	1.87557i
$9$	0.775409	+	0.631460i	0.775409	+	0.631460i
$10$		0			0
$11$	0.855563	+	0.438905i	0.855563	+	0.438905i	0.828009	−	0.560715i	$-0.189474\pi$
$11$	0.855563	+	0.438905i	0.855563	+	0.438905i	0.0275543	+	0.999620i	$0.491228\pi$
$12$		0			0
$13$		0			0		−0.618553	−	0.785743i	$-0.712281\pi$
$13$		0			0		0.618553	+	0.785743i	$0.287719\pi$
$14$	−0.574239	−	1.90958i	−0.574239	−	1.90958i
$15$		0			0
$16$	−4.52289	−	1.83704i	−4.52289	−	1.83704i
$17$		0			0		0.970739	−	0.240139i	$-0.0771930\pi$
$17$		0			0		−0.970739	+	0.240139i	$0.922807\pi$
$18$	−0.0109903	−	1.99402i	−0.0109903	−	1.99402i
$19$		0			0		0.609854	−	0.792514i	$-0.291228\pi$
$19$		0			0		−0.609854	+	0.792514i	$0.708772\pi$
$20$		0			0
$21$		0			0
$22$	−0.408987	−	1.87330i	−0.408987	−	1.87330i
$23$	1.13347	−	1.07859i	1.13347	−	1.07859i	0.137354	−	0.990522i	$-0.456140\pi$
$23$	1.13347	−	1.07859i	1.13347	−	1.07859i	0.996114	−	0.0880708i	$-0.0280702\pi$
$24$		0			0
$25$	0.815447	−	0.578832i	0.815447	−	0.578832i
$26$		0			0
$27$		0			0
$28$	−1.65521	+	2.47351i	−1.65521	+	2.47351i
$29$	0.502662	−	0.488997i	0.502662	−	0.488997i	−0.401695	−	0.915773i	$-0.631579\pi$
$29$	0.502662	−	0.488997i	0.502662	−	0.488997i	0.904357	+	0.426776i	$0.140351\pi$
$30$		0			0
$31$		0			0		0.789141	−	0.614213i	$-0.210526\pi$
$31$		0			0		−0.789141	+	0.614213i	$0.789474\pi$
$32$	1.72950	+	5.52953i	1.72950	+	5.52953i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	−2.28694	+	1.90469i	−2.28694	+	1.90469i
$37$	−1.86763	−	0.687544i	−1.86763	−	0.687544i	−0.968033	−	0.250825i	$-0.919298\pi$
$37$	−1.86763	−	0.687544i	−1.86763	−	0.687544i	−0.899598	−	0.436719i	$-0.856140\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		0.592235	−	0.805765i	$-0.298246\pi$
$41$		0			0		−0.592235	+	0.805765i	$0.701754\pi$
$42$		0			0
$43$	−0.671770	−	1.73571i	−0.671770	−	1.73571i	−0.677282	−	0.735724i	$-0.736842\pi$
$43$	−0.671770	−	1.73571i	−0.671770	−	1.73571i	0.00551154	−	0.999985i	$-0.498246\pi$
$44$	−1.77022	+	2.24869i	−1.77022	+	2.24869i
$45$		0			0
$46$	−3.09707	−	0.377385i	−3.09707	−	0.377385i
$47$		0			0		−0.137354	−	0.990522i	$-0.543860\pi$
$47$		0			0		0.137354	+	0.990522i	$0.456140\pi$
$48$		0			0
$49$	0.701237	+	0.712928i	0.701237	+	0.712928i
$50$	−1.92467	−	0.521404i	−1.92467	−	0.521404i
$51$		0			0
$52$		0			0
$53$	−0.0192865	+	0.317727i	−0.0192865	+	0.317727i	0.975796	+	0.218681i	$0.0701754\pi$
$53$	−0.0192865	+	0.317727i	−0.0192865	+	0.317727i	−0.995083	+	0.0990455i	$0.968421\pi$
$54$		0			0
$55$		0			0
$56$	3.92133	−	0.390309i	3.92133	−	0.390309i
$57$		0			0
$58$	−1.38989	−	0.153833i	−1.38989	−	0.153833i
$59$		0			0		0.0825793	−	0.996584i	$-0.473684\pi$
$59$		0			0		−0.0825793	+	0.996584i	$0.526316\pi$
$60$		0			0
$61$		0			0		−0.782322	−	0.622874i	$-0.785965\pi$
$61$		0			0		0.782322	+	0.622874i	$0.214035\pi$
$62$		0			0
$63$	0.471093	+	0.882084i	0.471093	+	0.882084i
$64$	3.64879	−	5.58489i	3.64879	−	5.58489i
$65$		0			0
$66$		0			0
$67$	−1.06056	−	0.701272i	−1.06056	−	0.701272i	−0.104528	−	0.994522i	$-0.533333\pi$
$67$	−1.06056	−	0.701272i	−1.06056	−	0.701272i	−0.956036	+	0.293250i	$0.905263\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	1.29170	+	1.43458i	1.29170	+	1.43458i	0.840168	+	0.542326i	$0.182456\pi$
$71$	1.29170	+	1.43458i	1.29170	+	1.43458i	0.451533	+	0.892254i	$0.350877\pi$
$72$	3.87171	+	0.734147i	3.87171	+	0.734147i
$73$		0			0		−0.170028	−	0.985439i	$-0.554386\pi$
$73$		0			0		0.170028	+	0.985439i	$0.445614\pi$
$74$	1.30923	+	3.74631i	1.30923	+	3.74631i
$75$		0			0
$76$		0			0
$77$	0.619441	+	0.735472i	0.619441	+	0.735472i
$78$		0			0
$79$	0.596215	+	1.40101i	0.596215	+	1.40101i	0.894729	+	0.446609i	$0.147368\pi$
$79$	0.596215	+	1.40101i	0.596215	+	1.40101i	−0.298515	+	0.954405i	$0.596491\pi$
$80$		0			0
$81$	0.202517	+	0.979279i	0.202517	+	0.979279i
$82$		0			0
$83$		0			0		−0.984487	−	0.175457i	$-0.943860\pi$
$83$		0			0		0.984487	+	0.175457i	$0.0561404\pi$
$84$		0			0
$85$		0			0
$86$	−1.82009	+	3.23431i	−1.82009	+	3.23431i
$87$		0			0
$88$	3.78836	−	0.0835327i	3.78836	−	0.0835327i
$89$		0			0		0.644194	−	0.764862i	$-0.277193\pi$
$89$		0			0		−0.644194	+	0.764862i	$0.722807\pi$
$90$		0			0
$91$		0			0
$92$	2.50387	+	3.92631i	2.50387	+	3.92631i
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$		0			0		0.731980	−	0.681326i	$-0.238596\pi$
$97$		0			0		−0.731980	+	0.681326i	$0.761404\pi$
$98$	0.208435	−	1.98313i	0.208435	−	1.98313i
$99$	0.386260	+	0.880585i	0.386260	+	0.880585i
$100$	1.22551	+	2.71221i	1.22551	+	2.71221i
$101$		0			0		0.421786	−	0.906696i	$-0.361404\pi$
$101$		0			0		−0.421786	+	0.906696i	$0.638596\pi$
$102$		0			0
$103$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$103$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$104$		0			0
$105$		0			0
$106$	0.513506	−	0.373084i	0.513506	−	0.373084i
$107$	0.961644	−	0.390586i	0.961644	−	0.390586i	0.159156	−	0.987253i	$-0.449123\pi$
$107$	0.961644	−	0.390586i	0.961644	−	0.390586i	0.802489	+	0.596667i	$0.203509\pi$
$108$		0			0
$109$	0.148264	−	0.256800i	0.148264	−	0.256800i	−0.782322	−	0.622874i	$-0.785965\pi$
$109$	0.148264	−	0.256800i	0.148264	−	0.256800i	0.930586	+	0.366074i	$0.119298\pi$
$110$		0			0
$111$		0			0
$112$	−3.46140	−	3.44237i	−3.46140	−	3.44237i
$113$	−0.0748855	−	1.94003i	−0.0748855	−	1.94003i	−0.277403	−	0.960754i	$-0.589474\pi$
$113$	−0.0748855	−	1.94003i	−0.0748855	−	1.94003i	0.202517	−	0.979279i	$-0.435088\pi$
$114$		0			0
$115$		0			0
$116$	1.14157	+	1.74730i	1.14157	+	1.74730i
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.0439669	−	0.0612220i	−0.0439669	−	0.0612220i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		0			0
$126$	0.760550	−	1.84331i	0.760550	−	1.84331i
$127$	−1.40970	+	1.14800i	−1.40970	+	1.14800i	−0.441671	+	0.897177i	$0.645614\pi$
$127$	−1.40970	+	1.14800i	−1.40970	+	1.14800i	−0.968033	+	0.250825i	$0.919298\pi$
$128$	−7.46340	+	0.826048i	−7.46340	+	0.826048i
$129$		0			0
$130$		0			0
$131$		0			0		0.945817	−	0.324699i	$-0.105263\pi$
$131$		0			0		−0.945817	+	0.324699i	$0.894737\pi$
$132$		0			0
$133$		0			0
$134$	0.265014	+	2.52144i	0.265014	+	2.52144i
$135$		0			0
$136$		0			0
$137$	0.469659	+	0.333380i	0.469659	+	0.333380i	0.789141	−	0.614213i	$-0.210526\pi$
$137$	0.469659	+	0.333380i	0.469659	+	0.333380i	−0.319482	+	0.947592i	$0.603509\pi$
$138$		0			0
$139$		0			0		−0.159156	−	0.987253i	$-0.550877\pi$
$139$		0			0		0.159156	+	0.987253i	$0.449123\pi$
$140$		0			0
$141$		0			0
$142$	0.570718	−	3.80680i	0.570718	−	3.80680i
$143$		0			0
$144$	−2.34707	−	4.28048i	−2.34707	−	4.28048i
$145$		0			0
$146$		0			0
$147$		0			0
$148$	3.07396	−	5.06310i	3.07396	−	5.06310i
$149$	−0.199005	−	0.189370i	−0.199005	−	0.189370i	0.583317	−	0.812244i	$-0.301754\pi$
$149$	−0.199005	−	0.189370i	−0.199005	−	0.189370i	−0.782322	+	0.622874i	$0.785965\pi$
$150$		0			0
$151$	−0.121947	+	0.169805i	−0.121947	+	0.169805i	−0.868768	−	0.495219i	$-0.835088\pi$
$151$	−0.121947	+	0.169805i	−0.121947	+	0.169805i	0.746821	+	0.665025i	$0.231579\pi$
$152$		0			0
$153$		0			0
$154$	0.346825	−	1.88580i	0.346825	−	1.88580i
$155$		0			0
$156$		0			0
$157$		0			0		−0.693336	−	0.720615i	$-0.743860\pi$
$157$		0			0		0.693336	+	0.720615i	$0.256140\pi$
$158$	1.40070	−	2.69373i	1.40070	−	2.69373i
$159$		0			0
$160$		0			0
$161$	1.46226	−	0.556691i	1.46226	−	0.556691i
$162$	1.25062	−	1.55312i	1.25062	−	1.55312i
$163$	−1.15688	+	0.484806i	−1.15688	+	0.484806i	−0.879474	−	0.475947i	$-0.842105\pi$
$163$	−1.15688	+	0.484806i	−1.15688	+	0.484806i	−0.277403	+	0.960754i	$0.589474\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$167$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$168$		0			0
$169$	−0.234785	+	0.972047i	−0.234785	+	0.972047i
$170$		0			0
$171$		0			0
$172$	5.45335	−	0.971906i	5.45335	−	0.971906i
$173$		0			0		0.685350	−	0.728214i	$-0.259649\pi$
$173$		0			0		−0.685350	+	0.728214i	$0.740351\pi$
$174$		0			0
$175$	0.975796	−	0.218681i	0.975796	−	0.218681i
$176$	−3.06333	−	3.55682i	−3.06333	−	3.55682i
$177$		0			0
$178$		0			0
$179$	−1.69155	−	0.518857i	−1.69155	−	0.518857i	−0.709053	−	0.705155i	$-0.750877\pi$
$179$	−1.69155	−	0.518857i	−1.69155	−	0.518857i	−0.982493	+	0.186298i	$0.940351\pi$
$180$		0			0
$181$		0			0		0.245485	−	0.969400i	$-0.421053\pi$
$181$		0			0		−0.245485	+	0.969400i	$0.578947\pi$
$182$		0			0
$183$		0			0
$184$	1.90534	−	5.86402i	1.90534	−	5.86402i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−0.160481	−	0.0962261i	−0.160481	−	0.0962261i	0.431754	−	0.901991i	$-0.357895\pi$
$191$	−0.160481	−	0.0962261i	−0.160481	−	0.0962261i	−0.592235	+	0.805765i	$0.701754\pi$
$192$		0			0
$193$	−0.862100	+	0.957459i	−0.862100	+	0.957459i	−0.999453	−	0.0330634i	$-0.989474\pi$
$193$	−0.862100	+	0.957459i	−0.862100	+	0.957459i	0.137354	+	0.990522i	$0.456140\pi$
$194$		0			0
$195$		0			0
$196$	−2.48259	+	1.64155i	−2.48259	+	1.64155i
$197$	0.736830	+	1.49674i	0.736830	+	1.49674i	0.863256	+	0.504766i	$0.168421\pi$
$197$	0.736830	+	1.49674i	0.736830	+	1.49674i	−0.126427	+	0.991976i	$0.540351\pi$
$198$	0.865782	−	1.71083i	0.865782	−	1.71083i
$199$		0			0		−0.126427	−	0.991976i	$-0.540351\pi$
$199$		0			0		0.126427	+	0.991976i	$0.459649\pi$
$200$	1.74049	−	3.53551i	1.74049	−	3.53551i
$201$		0			0
$202$		0			0
$203$	0.652597	−	0.256718i	0.652597	−	0.256718i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	1.55999	−	0.120611i	1.55999	−	0.120611i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−1.97760	+	0.240975i	−1.97760	+	0.240975i	−0.978148	+	0.207912i	$0.933333\pi$
$211$	−1.97760	+	0.240975i	−1.97760	+	0.240975i	−0.999453	+	0.0330634i	$0.989474\pi$
$212$	−0.917084	−	0.237623i	−0.917084	−	0.237623i
$213$		0			0
$214$	−1.82025	−	0.985069i	−1.82025	−	0.985069i
$215$		0			0
$216$		0			0
$217$		0			0
$218$	−0.583226	+	0.0973231i	−0.583226	+	0.0973231i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.234785	−	0.972047i	$-0.575439\pi$
$223$		0			0		0.234785	+	0.972047i	$0.424561\pi$
$224$	−0.542055	+	5.76828i	−0.542055	+	5.76828i
$225$	0.997814	+	0.0660906i	0.997814	+	0.0660906i
$226$	−2.89124	+	2.57458i	−2.89124	+	2.57458i
$227$		0			0		−0.761300	−	0.648400i	$-0.775439\pi$
$227$		0			0		0.761300	+	0.648400i	$0.224561\pi$
$228$		0			0
$229$		0			0		−0.795863	−	0.605477i	$-0.792982\pi$
$229$		0			0		0.795863	+	0.605477i	$0.207018\pi$
$230$		0			0
$231$		0			0
$232$	0.824951	−	2.63751i	0.824951	−	2.63751i
$233$	−0.207779	+	0.100869i	−0.207779	+	0.100869i	−0.537687	−	0.843145i	$-0.680702\pi$
$233$	−0.207779	+	0.100869i	−0.207779	+	0.100869i	0.329907	+	0.944013i	$0.392982\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	0.694641	−	1.79480i	0.694641	−	1.79480i	0.0935596	−	0.995614i	$-0.470175\pi$
$239$	0.694641	−	1.79480i	0.694641	−	1.79480i	0.601081	−	0.799188i	$-0.294737\pi$
$240$		0			0
$241$		0			0		−0.180881	−	0.983505i	$-0.557895\pi$
$241$		0			0		0.180881	+	0.983505i	$0.442105\pi$
$242$	−0.0385001	+	0.145284i	−0.0385001	+	0.145284i
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$		0			0
$251$		0			0		0.266796	−	0.963753i	$-0.414035\pi$
$251$		0			0		−0.266796	+	0.963753i	$0.585965\pi$
$252$	−2.84538	+	0.872780i	−2.84538	+	0.872780i
$253$	1.44315	−	0.425319i	1.44315	−	0.425319i
$254$	3.55408	+	0.714590i	3.55408	+	0.714590i
$255$		0			0
$256$	5.95078	+	5.78901i	5.95078	+	5.78901i
$257$		0			0		0.115485	−	0.993309i	$-0.463158\pi$
$257$		0			0		−0.115485	+	0.993309i	$0.536842\pi$
$258$		0			0
$259$	−1.45676	−	1.35595i	−1.45676	−	1.35595i
$260$		0			0
$261$	0.698550	−	0.0617619i	0.698550	−	0.0617619i
$262$		0			0
$263$	−1.47927	+	0.821749i	−1.47927	+	0.821749i	−0.998482	−	0.0550878i	$-0.982456\pi$
$263$	−1.47927	+	0.821749i	−1.47927	+	0.821749i	−0.480787	+	0.876837i	$0.659649\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	2.65357	−	2.69781i	2.65357	−	2.69781i
$269$		0			0		0.997814	−	0.0660906i	$-0.0210526\pi$
$269$		0			0		−0.997814	+	0.0660906i	$0.978947\pi$
$270$		0			0
$271$		0			0		−0.0825793	−	0.996584i	$-0.526316\pi$
$271$		0			0		0.0825793	+	0.996584i	$0.473684\pi$
$272$		0			0
$273$		0			0
$274$	−0.0822185	−	1.14553i	−0.0822185	−	1.14553i
$275$	0.951719	−	0.137323i	0.951719	−	0.137323i
$276$		0			0
$277$	0.156192	−	0.326305i	0.156192	−	0.326305i	−0.809017	−	0.587785i	$-0.800000\pi$
$277$	0.156192	−	0.326305i	0.156192	−	0.326305i	0.965209	+	0.261480i	$0.0842105\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−1.94636	+	0.391339i	−1.94636	+	0.391339i	−0.949339	+	0.314254i	$0.898246\pi$
$281$	−1.94636	+	0.391339i	−1.94636	+	0.391339i	−0.997024	+	0.0770854i	$0.975439\pi$
$282$		0			0
$283$		0			0		0.371197	−	0.928554i	$-0.378947\pi$
$283$		0			0		−0.371197	+	0.928554i	$0.621053\pi$
$284$	−4.92746	+	2.95456i	−4.92746	+	2.95456i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−2.15060	+	5.37975i	−2.15060	+	5.37975i
$289$	0.884667	−	0.466224i	0.884667	−	0.466224i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		0.660898	−	0.750475i	$-0.270175\pi$
$293$		0			0		−0.660898	+	0.750475i	$0.729825\pi$
$294$		0			0
$295$		0			0
$296$	−7.76226	+	1.12002i	−7.76226	+	1.12002i
$297$		0			0
$298$	−0.0392150	+	0.546374i	−0.0392150	+	0.546374i
$299$		0			0
$300$		0			0
$301$	0.0512834	−	1.86046i	0.0512834	−	1.86046i
$302$	0.415958	−	0.0275512i	0.415958	−	0.0275512i
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		−0.949339	−	0.314254i	$-0.898246\pi$
$307$		0			0		0.949339	+	0.314254i	$0.101754\pi$
$308$	−2.50177	+	1.38976i	−2.50177	+	1.38976i
$309$		0			0
$310$		0			0
$311$		0			0		0.709053	−	0.705155i	$-0.249123\pi$
$311$		0			0		−0.709053	+	0.705155i	$0.750877\pi$
$312$		0			0
$313$		0			0		0.754107	−	0.656752i	$-0.228070\pi$
$313$		0			0		−0.754107	+	0.656752i	$0.771930\pi$
$314$		0			0
$315$		0			0
$316$	−4.43258	+	0.942175i	−4.43258	+	0.942175i
$317$	1.95885	+	0.393851i	1.95885	+	0.393851i	0.988116	+	0.153712i	$0.0491228\pi$
$317$	1.95885	+	0.393851i	1.95885	+	0.393851i	0.970739	+	0.240139i	$0.0771930\pi$
$318$		0			0
$319$	0.644682	−	0.197747i	0.644682	−	0.197747i
$320$		0			0
$321$		0			0
$322$	−2.71054	−	1.54507i	−2.71054	−	1.54507i
$323$		0			0
$324$	−2.97605	+	0.0328067i	−2.97605	+	0.0328067i
$325$		0			0
$326$	2.21276	+	1.16614i	2.21276	+	1.16614i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	1.81113	+	0.806367i	1.81113	+	0.806367i	0.959210	+	0.282694i	$0.0912281\pi$
$331$	1.81113	+	0.806367i	1.81113	+	0.806367i	0.851919	+	0.523673i	$0.175439\pi$
$332$		0			0
$333$	−1.01402	−	1.71246i	−1.01402	−	1.71246i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−0.737093	+	0.586863i	−0.737093	+	0.586863i	−0.917973	−	0.396642i	$-0.870175\pi$
$337$	−0.737093	+	0.586863i	−0.737093	+	0.586863i	0.180881	+	0.983505i	$0.442105\pi$
$338$	1.79384	−	0.870839i	1.79384	−	0.870839i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	0.371197	+	0.928554i	0.371197	+	0.928554i
$344$	−5.58362	−	4.75557i	−5.58362	−	4.75557i
$345$		0			0
$346$		0			0
$347$	−0.164566	+	1.75123i	−0.164566	+	1.75123i	0.391577	+	0.920146i	$0.371930\pi$
$347$	−0.164566	+	1.75123i	−0.164566	+	1.75123i	−0.556143	+	0.831087i	$0.687719\pi$
$348$		0			0
$349$		0			0		0.00551154	−	0.999985i	$-0.498246\pi$
$349$		0			0		−0.00551154	+	0.999985i	$0.501754\pi$
$350$	−1.57358	−	1.22477i	−1.57358	−	1.22477i
$351$		0			0
$352$	−0.947240	+	5.48995i	−0.947240	+	5.48995i
$353$		0			0		0.986361	−	0.164595i	$-0.0526316\pi$
$353$		0			0		−0.986361	+	0.164595i	$0.947368\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	1.34567	+	3.26143i	1.34567	+	3.26143i
$359$	0.893187	+	0.231431i	0.893187	+	0.231431i	0.669131	−	0.743145i	$-0.266667\pi$
$359$	0.893187	+	0.231431i	0.893187	+	0.231431i	0.224056	+	0.974576i	$0.428070\pi$
$360$		0			0
$361$	−0.256156	−	0.966635i	−0.256156	−	0.966635i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.287976	−	0.957638i	$-0.407018\pi$
$367$		0			0		−0.287976	+	0.957638i	$0.592982\pi$
$368$	−7.10796	+	2.79613i	−7.10796	+	2.79613i
$369$		0			0
$370$		0			0
$371$	−0.140589	+	0.285582i	−0.140589	+	0.285582i
$372$		0			0
$373$	0.389903	−	0.770469i	0.389903	−	0.770469i	−0.609854	−	0.792514i	$-0.708772\pi$
$373$	0.389903	−	0.770469i	0.389903	−	0.770469i	0.999757	+	0.0220445i	$0.00701754\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−1.09089	+	0.829927i	−1.09089	+	0.829927i	−0.986361	−	0.164595i	$-0.947368\pi$
$379$	−1.09089	+	0.829927i	−1.09089	+	0.829927i	−0.104528	+	0.994522i	$0.533333\pi$
$380$		0			0
$381$		0			0
$382$	0.0553208	+	0.369001i	0.0553208	+	0.369001i
$383$		0			0		−0.998482	−	0.0550878i	$-0.982456\pi$
$383$		0			0		0.998482	+	0.0550878i	$0.0175439\pi$
$384$		0			0
$385$		0			0
$386$	2.56661	+	0.113242i	2.56661	+	0.113242i
$387$	0.575134	−	1.77008i	0.575134	−	1.77008i
$388$		0			0
$389$	0.759146	−	1.08206i	0.759146	−	1.08206i	−0.234785	−	0.972047i	$-0.575439\pi$
$389$	0.759146	−	1.08206i	0.759146	−	1.08206i	0.993931	−	0.110008i	$-0.0350877\pi$
$390$		0			0
$391$		0			0
$392$	3.76745	+	1.15561i	3.76745	+	1.15561i
$393$		0			0
$394$	1.36979	−	3.03152i	1.36979	−	3.03152i
$395$		0			0
$396$	−2.79260	+	0.625837i	−2.79260	+	0.625837i
$397$		0			0		−0.899598	−	0.436719i	$-0.856140\pi$
$397$		0			0		0.899598	+	0.436719i	$0.143860\pi$
$398$		0			0
$399$		0			0
$400$	−4.75151	+	1.11998i	−4.75151	+	1.11998i
$401$	−1.42649	−	0.489716i	−1.42649	−	0.489716i	−0.500000	−	0.866025i	$-0.666667\pi$
$401$	−1.42649	−	0.489716i	−1.42649	−	0.489716i	−0.926494	+	0.376309i	$0.877193\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$	−1.22242	−	0.679070i	−1.22242	−	0.679070i
$407$	−1.29611	−	1.40795i	−1.29611	−	1.40795i
$408$		0			0
$409$		0			0		0.627176	−	0.778877i	$-0.284211\pi$
$409$		0			0		−0.627176	+	0.778877i	$0.715789\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	−2.16319	−	2.24830i	−2.16319	−	2.24830i
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		0.159156	−	0.987253i	$-0.449123\pi$
$419$		0			0		−0.159156	+	0.987253i	$0.550877\pi$
$420$		0			0
$421$	0.725910	+	0.503335i	0.725910	+	0.503335i	0.874174	−	0.485613i	$-0.161404\pi$
$421$	0.725910	+	0.503335i	0.725910	+	0.503335i	−0.148264	+	0.988948i	$0.547368\pi$
$422$	2.87785	+	2.73853i	2.87785	+	2.73853i
$423$		0			0
$424$	0.529075	+	1.13733i	0.529075	+	1.13733i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	0.592222	+	3.03185i	0.592222	+	3.03185i
$429$		0			0
$430$		0			0
$431$	−0.532175	+	1.84313i	−0.532175	+	1.84313i	0.00551154	+	0.999985i	$0.498246\pi$
$431$	−0.532175	+	1.84313i	−0.532175	+	1.84313i	−0.537687	+	0.843145i	$0.680702\pi$
$432$		0			0
$433$		0			0		−0.894729	−	0.446609i	$-0.852632\pi$
$433$		0			0		0.894729	+	0.446609i	$0.147368\pi$
$434$		0			0
$435$		0			0
$436$	0.665525	+	0.579606i	0.665525	+	0.579606i
$437$		0			0
$438$		0			0
$439$		0			0		0.846095	−	0.533032i	$-0.178947\pi$
$439$		0			0		−0.846095	+	0.533032i	$0.821053\pi$
$440$		0			0
$441$	0.0935596	+	0.995614i	0.0935596	+	0.995614i
$442$		0			0
$443$	1.79774	−	0.198973i	1.79774	−	0.198973i	0.851919	−	0.523673i	$-0.175439\pi$
$443$	1.79774	−	0.198973i	1.79774	−	0.198973i	0.945817	+	0.324699i	$0.105263\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	5.52380	−	3.74063i	5.52380	−	3.74063i
$449$	−0.0174718	−	1.05658i	−0.0174718	−	1.05658i	−0.857640	−	0.514250i	$-0.828070\pi$
$449$	−0.0174718	−	1.05658i	−0.0174718	−	1.05658i	0.840168	−	0.542326i	$-0.182456\pi$
$450$	−1.16316	−	1.61965i	−1.16316	−	1.61965i
$451$		0			0
$452$	5.70961	+	0.888192i	5.70961	+	0.888192i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	1.42306	+	0.453725i	1.42306	+	0.453725i	0.913545	−	0.406737i	$-0.133333\pi$
$457$	1.42306	+	0.453725i	1.42306	+	0.453725i	0.509516	+	0.860461i	$0.329825\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$461$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$462$		0			0
$463$	1.86547	−	0.686748i	1.86547	−	0.686748i	0.894729	−	0.446609i	$-0.147368\pi$
$463$	1.86547	−	0.686748i	1.86547	−	0.686748i	0.970739	−	0.240139i	$-0.0771930\pi$
$464$	−3.17179	+	1.28827i	−3.17179	+	1.28827i
$465$		0			0
$466$	0.418656	+	0.191955i	0.418656	+	0.191955i
$467$		0			0		−0.917973	−	0.396642i	$-0.870175\pi$
$467$		0			0		0.917973	+	0.396642i	$0.129825\pi$
$468$		0			0
$469$	−0.707107	−	1.05668i	−0.707107	−	1.05668i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	0.187070	−	1.77985i	0.187070	−	1.77985i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−0.215586	+	0.234189i	−0.215586	+	0.234189i
$478$	−3.64320	+	1.20599i	−3.64320	+	1.20599i
$479$		0			0		−0.537687	−	0.843145i	$-0.680702\pi$
$479$		0			0		0.537687	+	0.843145i	$0.319298\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	0.203917	−	0.0934967i	0.203917	−	0.0934967i
$485$		0			0
$486$		0			0
$487$	−1.16269	+	0.864482i	−1.16269	+	0.864482i	−0.992658	−	0.120958i	$-0.961404\pi$
$487$	−1.16269	+	0.864482i	−1.16269	+	0.864482i	−0.170028	+	0.985439i	$0.554386\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−1.72138	−	0.133089i	−1.72138	−	0.133089i	−0.821778	−	0.569808i	$-0.807018\pi$
$491$	−1.72138	−	0.133089i	−1.72138	−	0.133089i	−0.899598	+	0.436719i	$0.856140\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.636859	+	1.82234i	0.636859	+	1.82234i
$498$		0			0
$499$	−0.648264	−	0.122922i	−0.648264	−	0.122922i	−0.148264	−	0.988948i	$-0.547368\pi$
$499$	−0.648264	−	0.122922i	−0.648264	−	0.122922i	−0.500000	+	0.866025i	$0.666667\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		−0.0495838	−	0.998770i	$-0.515789\pi$
$503$		0			0		0.0495838	+	0.998770i	$0.484211\pi$
$504$	3.28709	+	2.17351i	3.28709	+	2.17351i
$505$		0			0
$506$	−2.48410	−	1.68220i	−2.48410	−	1.68220i
$507$		0			0
$508$	−2.54900	−	4.77280i	−2.54900	−	4.77280i
$509$		0			0		−0.975796	−	0.218681i	$-0.929825\pi$
$509$		0			0		0.975796	+	0.218681i	$0.0701754\pi$
$510$		0			0
$511$		0			0
$512$	0.746994	−	9.01488i	0.746994	−	9.01488i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$	−0.240451	+	3.96120i	−0.240451	+	3.96120i
$519$		0			0
$520$		0			0
$521$		0			0		−0.965209	−	0.261480i	$-0.915789\pi$
$521$		0			0		0.965209	+	0.261480i	$0.0842105\pi$
$522$	−0.980593	−	0.996943i	−0.980593	−	0.996943i
$523$		0			0		−0.746821	−	0.665025i	$-0.768421\pi$
$523$		0			0		0.746821	+	0.665025i	$0.231579\pi$
$524$		0			0
$525$		0			0
$526$	3.14009	+	1.23525i	3.14009	+	1.23525i
$527$		0			0
$528$		0			0
$529$	0.0718028	−	1.44633i	0.0718028	−	1.44633i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	−4.99093	−	0.441270i	−4.99093	−	0.441270i
$537$		0			0
$538$		0			0
$539$	0.287044	+	0.917732i	0.287044	+	0.917732i
$540$		0			0
$541$	0.364101	+	0.473154i	0.364101	+	0.473154i	0.938430	−	0.345471i	$-0.112281\pi$
$541$	0.364101	+	0.473154i	0.364101	+	0.473154i	−0.574329	+	0.818625i	$0.694737\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−1.59880	+	0.248711i	−1.59880	+	0.248711i	−0.889752	−	0.456444i	$-0.849123\pi$
$547$	−1.59880	+	0.248711i	−1.59880	+	0.248711i	−0.709053	+	0.705155i	$0.750877\pi$
$548$	−1.24179	+	1.18167i	−1.24179	+	1.18167i
$549$		0			0
$550$	−1.41783	−	1.29084i	−1.41783	−	1.29084i
$551$		0			0
$552$		0			0
$553$	0.00839187	+	1.52258i	0.00839187	+	1.52258i
$554$	−0.700261	+	0.173229i	−0.700261	+	0.173229i
$555$		0			0
$556$		0			0
$557$	−0.557541	−	1.85405i	−0.557541	−	1.85405i	−0.518970	−	0.854793i	$-0.673684\pi$
$557$	−0.557541	−	1.85405i	−0.557541	−	1.85405i	−0.0385714	−	0.999256i	$-0.512281\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	3.06970	+	2.49983i	3.06970	+	2.49983i
$563$		0			0		0.879474	−	0.475947i	$-0.157895\pi$
$563$		0			0		−0.879474	+	0.475947i	$0.842105\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−0.191711	+	0.981451i	−0.191711	+	0.981451i
$568$	7.16736	+	2.54921i	7.16736	+	2.54921i
$569$	−0.406204	−	0.493226i	−0.406204	−	0.493226i	0.528360	−	0.849020i	$-0.322807\pi$
$569$	−0.406204	−	0.493226i	−0.406204	−	0.493226i	−0.934564	+	0.355794i	$0.884211\pi$
$570$		0			0
$571$	−0.926494	−	0.376309i	−0.926494	−	0.376309i
$571$	−0.926494	−	0.376309i	−0.926494	−	0.376309i
$572$		0			0
$573$		0			0
$574$		0			0
$575$	0.299959	−	1.53562i	0.299959	−	1.53562i
$576$	6.35594	−	2.02651i	6.35594	−	2.02651i
$577$		0			0		−0.340293	−	0.940319i	$-0.610526\pi$
$577$		0			0		0.340293	+	0.940319i	$0.389474\pi$
$578$	−1.83909	−	0.770698i	−1.83909	−	0.770698i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−0.155953	+	0.263370i	−0.155953	+	0.263370i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		−0.926494	−	0.376309i	$-0.877193\pi$
$587$		0			0		0.926494	+	0.376309i	$0.122807\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	7.18404	+	6.54059i	7.18404	+	6.54059i
$593$		0			0		−0.213300	−	0.976987i	$-0.568421\pi$
$593$		0			0		0.213300	+	0.976987i	$0.431579\pi$
$594$		0			0
$595$		0			0
$596$	0.666703	−	0.473248i	0.666703	−	0.473248i
$597$		0			0
$598$		0			0
$599$	−0.934507	+	1.39651i	−0.934507	+	1.39651i	−0.0165339	+	0.999863i	$0.505263\pi$
$599$	−0.934507	+	1.39651i	−0.934507	+	1.39651i	−0.917973	+	0.396642i	$0.870175\pi$
$600$		0			0
$601$		0			0		−0.609854	−	0.792514i	$-0.708772\pi$
$601$		0			0		0.609854	+	0.792514i	$0.291228\pi$
$602$	−2.92871	+	2.27951i	−2.92871	+	2.27951i
$603$	−0.379546	−	1.21348i	−0.379546	−	1.21348i
$604$	−0.426426	−	0.453096i	−0.426426	−	0.453096i
$605$		0			0
$606$		0			0
$607$		0			0		0.768401	−	0.639969i	$-0.221053\pi$
$607$		0			0		−0.768401	+	0.639969i	$0.778947\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−0.0569547	+	1.14724i	−0.0569547	+	1.14724i	0.789141	+	0.614213i	$0.210526\pi$
$613$	−0.0569547	+	1.14724i	−0.0569547	+	1.14724i	−0.846095	+	0.533032i	$0.821053\pi$
$614$		0			0
$615$		0			0
$616$	3.52625	+	1.38716i	3.52625	+	1.38716i
$617$	−1.61892	−	0.197269i	−1.61892	−	0.197269i	−0.739446	−	0.673216i	$-0.764912\pi$
$617$	−1.61892	−	0.197269i	−1.61892	−	0.197269i	−0.879474	+	0.475947i	$0.842105\pi$
$618$		0			0
$619$		0			0		−0.746821	−	0.665025i	$-0.768421\pi$
$619$		0			0		0.746821	+	0.665025i	$0.231579\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.329907	−	0.944013i	0.329907	−	0.944013i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	−0.356636	+	1.55126i	−0.356636	+	1.55126i	0.411766	+	0.911290i	$0.364912\pi$
$631$	−0.356636	+	1.55126i	−0.356636	+	1.55126i	−0.768401	+	0.639969i	$0.778947\pi$
$632$	4.69402	+	3.73732i	4.69402	+	3.73732i
$633$		0			0
$634$	−1.87694	−	3.51442i	−1.87694	−	3.51442i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	−1.12162	−	0.741644i	−1.12162	−	0.741644i
$639$	0.0957174	+	1.92804i	0.0957174	+	1.92804i
$640$		0			0
$641$	0.963129	+	1.40551i	0.963129	+	1.40551i	0.913545	+	0.406737i	$0.133333\pi$
$641$	0.963129	+	1.40551i	0.963129	+	1.40551i	0.0495838	+	0.998770i	$0.484211\pi$
$642$		0			0
$643$		0			0		−0.982493	−	0.186298i	$-0.940351\pi$
$643$		0			0		0.982493	+	0.186298i	$0.0596491\pi$
$644$	0.791779	+	4.58894i	0.791779	+	4.58894i
$645$		0			0
$646$		0			0
$647$		0			0		−0.660898	−	0.750475i	$-0.729825\pi$
$647$		0			0		0.660898	+	0.750475i	$0.270175\pi$
$648$	2.53858	+	3.01409i	2.53858	+	3.01409i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−0.756047	−	3.65589i	−0.756047	−	3.65589i
$653$	1.99684	−	0.110169i	1.99684	−	0.110169i	0.997814	−	0.0660906i	$-0.0210526\pi$
$653$	1.99684	−	0.110169i	1.99684	−	0.110169i	0.999028	−	0.0440782i	$-0.0140351\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$	0.659655	−	0.0145453i	0.659655	−	0.0145453i	0.309017	−	0.951057i	$-0.400000\pi$
$659$	0.659655	−	0.0145453i	0.659655	−	0.0145453i	0.350638	+	0.936511i	$0.385965\pi$
$660$		0			0
$661$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$661$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$662$	−1.05471	−	3.80996i	−1.05471	−	3.80996i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	−1.35045	+	3.73165i	−1.35045	+	3.73165i
$667$	0.0423223	−	1.09643i	0.0423223	−	1.09643i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.502234	−	0.750527i	−0.502234	−	0.750527i	0.490424	−	0.871484i	$-0.336842\pi$
$673$	−0.502234	−	0.750527i	−0.502234	−	0.750527i	−0.992658	+	0.120958i	$0.961404\pi$
$674$	1.83771	+	0.390617i	1.83771	+	0.390617i
$675$		0			0
$676$	−2.70541	−	1.24044i	−2.70541	−	1.24044i
$677$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$677$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−0.0390750	−	0.0388602i	−0.0390750	−	0.0388602i	0.685350	−	0.728214i	$-0.259649\pi$
$683$	−0.0390750	−	0.0388602i	−0.0390750	−	0.0388602i	−0.724425	+	0.689353i	$0.757895\pi$
$684$		0			0
$685$		0			0
$686$	0.958714	−	1.74846i	0.958714	−	1.74846i
$687$		0			0
$688$	−0.150223	+	9.08448i	−0.150223	+	9.08448i
$689$		0			0
$690$		0			0
$691$		0			0		0.894729	−	0.446609i	$-0.147368\pi$
$691$		0			0		−0.894729	+	0.446609i	$0.852632\pi$
$692$		0			0
$693$	0.0158986	+	0.961443i	0.0158986	+	0.961443i
$694$	2.90418	−	1.96667i	2.90418	−	1.96667i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	0.0820081	+	2.97510i	0.0820081	+	2.97510i
$701$	−0.0597811	−	0.636161i	−0.0597811	−	0.636161i	−0.973327	−	0.229424i	$-0.926316\pi$
$701$	−0.0597811	−	0.636161i	−0.0597811	−	0.636161i	0.913545	−	0.406737i	$-0.133333\pi$
$702$		0			0
$703$		0			0
$704$	5.57301	−	3.17675i	5.57301	−	3.17675i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	0.911757	+	0.455108i	0.911757	+	0.455108i	0.840168	−	0.542326i	$-0.182456\pi$
$709$	0.911757	+	0.455108i	0.911757	+	0.455108i	0.0715891	+	0.997434i	$0.477193\pi$
$710$		0			0
$711$	−0.422374	+	1.46284i	−0.422374	+	1.46284i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	2.48075	−	4.64500i	2.48075	−	4.64500i
$717$		0			0
$718$	−0.776032	−	1.66821i	−0.776032	−	1.66821i
$719$		0			0		0.518970	−	0.854793i	$-0.326316\pi$
$719$		0			0		−0.518970	+	0.854793i	$0.673684\pi$
$720$		0			0
$721$		0			0
$722$	−1.16316	+	1.61965i	−1.16316	+	1.61965i
$723$		0			0
$724$		0			0
$725$	0.126847	−	0.689708i	0.126847	−	0.689708i
$726$		0			0
$727$		0			0		0.991264	−	0.131892i	$-0.0421053\pi$
$727$		0			0		−0.991264	+	0.131892i	$0.957895\pi$
$728$		0			0
$729$	−0.461341	+	0.887223i	−0.461341	+	0.887223i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		0.627176	−	0.778877i	$-0.284211\pi$
$733$		0			0		−0.627176	+	0.778877i	$0.715789\pi$
$734$		0			0
$735$		0			0
$736$	7.92444	+	4.40211i	7.92444	+	4.40211i
$737$	−0.599588	−	1.06547i	−0.599588	−	1.06547i
$738$		0			0
$739$	1.39162	+	0.344255i	1.39162	+	0.344255i	0.863256	−	0.504766i	$-0.168421\pi$
$739$	1.39162	+	0.344255i	1.39162	+	0.344255i	0.528360	+	0.849020i	$0.322807\pi$
$740$		0			0
$741$		0			0
$742$	0.617798	−	0.145622i	0.617798	−	0.145622i
$743$	1.18351	−	0.210928i	1.18351	−	0.210928i	0.451533	−	0.892254i	$-0.350877\pi$
$743$	1.18351	−	0.210928i	1.18351	−	0.210928i	0.731980	+	0.681326i	$0.238596\pi$
$744$		0			0
$745$		0			0
$746$	−1.68020	+	0.376542i	−1.68020	+	0.376542i
$747$		0			0
$748$		0			0
$749$	1.03788	+	0.0114411i	1.03788	+	0.0114411i
$750$		0			0
$751$	−0.263989	+	0.413960i	−0.263989	+	0.413960i	−0.949339	−	0.314254i	$-0.898246\pi$
$751$	−0.263989	+	0.413960i	−0.263989	+	0.413960i	0.685350	+	0.728214i	$0.259649\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−0.628136	−	0.395720i	−0.628136	−	0.395720i	0.180881	−	0.983505i	$-0.442105\pi$
$757$	−0.628136	−	0.395720i	−0.628136	−	0.395720i	−0.809017	+	0.587785i	$0.800000\pi$
$758$	2.66034	+	0.627072i	2.66034	+	0.627072i
$759$		0			0
$760$		0			0
$761$		0			0		0.942181	−	0.335105i	$-0.108772\pi$
$761$		0			0		−0.942181	+	0.335105i	$0.891228\pi$
$762$		0			0
$763$	0.235995	−	0.179540i	0.235995	−	0.179540i
$764$	0.372646	−	0.413865i	0.372646	−	0.413865i
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$		0			0		0.451533	−	0.892254i	$-0.350877\pi$
$769$		0			0		−0.451533	+	0.892254i	$0.649123\pi$
$770$		0			0
$771$		0			0
$772$	−2.30487	−	3.06452i	−2.30487	−	3.06452i
$773$		0			0		0.968033	−	0.250825i	$-0.0807018\pi$
$773$		0			0		−0.968033	+	0.250825i	$0.919298\pi$
$774$	−3.45365	+	1.35860i	−3.45365	+	1.35860i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−2.62788	+	0.203176i	−2.62788	+	0.203176i
$779$		0			0
$780$		0			0
$781$	0.475488	+	1.79431i	0.475488	+	1.79431i
$782$		0			0
$783$		0			0
$784$	−1.86194	−	4.51269i	−1.86194	−	4.51269i
$785$		0			0
$786$		0			0
$787$		0			0		−0.863256	−	0.504766i	$-0.831579\pi$
$787$		0			0		0.863256	+	0.504766i	$0.168421\pi$
$788$	−4.79244	+	1.29830i	−4.79244	+	1.29830i
$789$		0			0
$790$		0			0
$791$	0.680755	−	1.81822i	0.680755	−	1.81822i
$792$	2.99027	+	2.32742i	2.99027	+	2.32742i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.746821	−	0.665025i	$-0.231579\pi$
$797$		0			0		−0.746821	+	0.665025i	$0.768421\pi$
$798$		0			0
$799$		0			0
$800$	4.61098	+	3.50794i	4.61098	+	3.50794i
$801$		0			0
$802$	1.05453	+	2.81651i	1.05453	+	2.81651i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−0.367809	−	0.621149i	−0.367809	−	0.621149i	0.618553	−	0.785743i	$-0.287719\pi$
$809$	−0.367809	−	0.621149i	−0.367809	−	0.621149i	−0.986361	+	0.164595i	$0.947368\pi$
$810$		0			0
$811$		0			0		−0.913545	−	0.406737i	$-0.866667\pi$
$811$		0			0		0.913545	+	0.406737i	$0.133333\pi$
$812$	0.377526	+	2.05273i	0.377526	+	2.05273i
$813$		0			0
$814$	−0.524141	+	3.77983i	−0.524141	+	3.77983i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	1.05569	−	0.0465784i	1.05569	−	0.0465784i	0.490424	−	0.871484i	$-0.336842\pi$
$821$	1.05569	−	0.0465784i	1.05569	−	0.0465784i	0.565270	+	0.824906i	$0.308772\pi$
$822$		0			0
$823$	−1.83408	+	0.562577i	−1.83408	+	0.562577i	−0.834139	+	0.551554i	$0.814035\pi$
$823$	−1.83408	+	0.562577i	−1.83408	+	0.562577i	−0.999939	+	0.0110229i	$0.996491\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−0.0868598	−	0.0844986i	−0.0868598	−	0.0844986i	0.652586	−	0.757715i	$-0.273684\pi$
$827$	−0.0868598	−	0.0844986i	−0.0868598	−	0.0844986i	−0.739446	+	0.673216i	$0.764912\pi$
$828$	−0.537782	+	4.62559i	−0.537782	+	4.62559i
$829$		0			0		0.754107	−	0.656752i	$-0.228070\pi$
$829$		0			0		−0.754107	+	0.656752i	$0.771930\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		0.701237	−	0.712928i	$-0.252632\pi$
$839$		0			0		−0.701237	+	0.712928i	$0.747368\pi$
$840$		0			0
$841$	−0.0140035	+	0.508020i	−0.0140035	+	0.508020i
$842$	−0.145457	−	1.75541i	−0.145457	−	1.75541i
$843$		0			0
$844$	0.424475	−	5.91412i	0.424475	−	5.91412i
$845$		0			0
$846$		0			0
$847$	−0.0168880	−	0.0734576i	−0.0168880	−	0.0734576i
$848$	0.670907	−	1.40161i	0.670907	−	1.40161i
$849$		0			0
$850$		0			0
$851$	−2.85848	+	1.23510i	−2.85848	+	1.23510i
$852$		0			0
$853$		0			0		0.884667	−	0.466224i	$-0.154386\pi$
$853$		0			0		−0.884667	+	0.466224i	$0.845614\pi$
$854$		0			0
$855$		0			0
$856$	2.60024	−	3.15730i	2.60024	−	3.15730i
$857$		0			0		0.635724	−	0.771917i	$-0.280702\pi$
$857$		0			0		−0.635724	+	0.771917i	$0.719298\pi$
$858$		0			0
$859$		0			0		0.371197	−	0.928554i	$-0.378947\pi$
$859$		0			0		−0.371197	+	0.928554i	$0.621053\pi$
$860$		0			0
$861$		0			0
$862$	3.51164	−	1.51732i	3.51164	−	1.51732i
$863$	0.782963	+	0.0172642i	0.782963	+	0.0172642i	0.411766	−	0.911290i	$-0.364912\pi$
$863$	0.782963	+	0.0172642i	0.782963	+	0.0172642i	0.371197	+	0.928554i	$0.378947\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−0.104813	+	1.46034i	−0.104813	+	1.46034i
$870$		0			0
$871$		0			0
$872$	0.0321980	−	1.16808i	0.0321980	−	1.16808i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	0.464369	+	1.83375i	0.464369	+	1.83375i	0.546948	+	0.837166i	$0.315789\pi$
$877$	0.464369	+	1.83375i	0.464369	+	1.83375i	−0.0825793	+	0.996584i	$0.526316\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		0			0		0.996114	−	0.0880708i	$-0.0280702\pi$
$881$		0			0		−0.996114	+	0.0880708i	$0.971930\pi$
$882$	1.41389	−	1.40611i	1.41389	−	1.40611i
$883$	1.33739	+	1.24485i	1.33739	+	1.24485i	0.945817	+	0.324699i	$0.105263\pi$
$883$	1.33739	+	1.24485i	1.33739	+	1.24485i	0.391577	+	0.920146i	$0.371930\pi$
$884$		0			0
$885$		0			0
$886$	−2.58519	−	2.51492i	−2.58519	−	2.51492i
$887$		0			0		0.978148	−	0.207912i	$-0.0666667\pi$
$887$		0			0		−0.978148	+	0.207912i	$0.933333\pi$
$888$		0			0
$889$	−1.74386	+	0.513941i	−1.74386	+	0.513941i
$890$		0			0
$891$	−0.256544	+	0.926721i	−0.256544	+	0.926721i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	−7.20268	−	2.12274i	−7.20268	−	2.12274i
$897$		0			0
$898$	−1.60418	+	1.36628i	−1.60418	+	1.36628i
$899$		0			0
$900$	−0.762380	+	2.87693i	−0.762380	+	2.87693i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	−3.89819	−	6.58320i	−3.89819	−	6.58320i
$905$		0			0
$906$		0			0
$907$	−0.511400	−	1.06838i	−0.511400	−	1.06838i	−0.982493	−	0.186298i	$-0.940351\pi$
$907$	−0.511400	−	1.06838i	−0.511400	−	1.06838i	0.471093	−	0.882084i	$-0.343860\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−0.323527	−	0.864102i	−0.323527	−	0.864102i	−0.992658	−	0.120958i	$-0.961404\pi$
$911$	−0.323527	−	0.864102i	−0.323527	−	0.864102i	0.669131	−	0.743145i	$-0.266667\pi$
$912$		0			0
$913$		0			0
$914$	−1.10557	−	2.76560i	−1.10557	−	2.76560i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−0.468543	−	1.93984i	−0.468543	−	1.93984i	−0.298515	−	0.954405i	$-0.596491\pi$
$919$	−0.468543	−	1.93984i	−0.468543	−	1.93984i	−0.170028	−	0.985439i	$-0.554386\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−1.92093	+	0.520388i	−1.92093	+	0.520388i
$926$	−3.42186	−	2.00084i	−3.42186	−	2.00084i
$927$		0			0
$928$	3.57328	+	1.93376i	3.57328	+	1.93376i
$929$		0			0		−0.381410	−	0.924406i	$-0.624561\pi$
$929$		0			0		0.381410	+	0.924406i	$0.375439\pi$
$930$		0			0
$931$		0			0
$932$	−0.176086	−	0.664483i	−0.176086	−	0.664483i
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		0.319482	−	0.947592i	$-0.396491\pi$
$937$		0			0		−0.319482	+	0.947592i	$0.603509\pi$
$938$	−0.730115	+	2.42793i	−0.730115	+	2.42793i
$939$		0			0
$940$		0			0
$941$		0			0		−0.601081	−	0.799188i	$-0.705263\pi$
$941$		0			0		0.601081	+	0.799188i	$0.294737\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$	−2.97676	+	1.96831i	−2.97676	+	1.96831i
$947$	0.875852	+	1.19164i	0.875852	+	1.19164i	0.980380	+	0.197117i	$0.0631579\pi$
$947$	0.875852	+	1.19164i	0.875852	+	1.19164i	−0.104528	+	0.994522i	$0.533333\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−0.289350	−	1.93002i	−0.289350	−	1.93002i	−0.360939	−	0.932589i	$-0.617544\pi$
$953$	−0.289350	−	1.93002i	−0.289350	−	1.93002i	0.0715891	−	0.997434i	$-0.477193\pi$
$954$	0.633765	+	0.0349658i	0.633765	+	0.0349658i
$955$		0			0
$956$	4.84632	+	3.05313i	4.84632	+	3.05313i
$957$		0			0
$958$		0			0
$959$	0.304311	+	0.488996i	0.304311	+	0.488996i
$960$		0			0
$961$	0.245485	−	0.969400i	0.245485	−	0.969400i
$962$		0			0
$963$	0.992307	+	0.304376i	0.992307	+	0.304376i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−1.90895	+	0.427805i	−1.90895	+	0.427805i	−0.909007	+	0.416782i	$0.863158\pi$
$967$	−1.90895	+	0.427805i	−1.90895	+	0.427805i	−0.999939	+	0.0110229i	$0.996491\pi$
$968$	−0.267204	−	0.129717i	−0.267204	−	0.129717i
$969$		0			0
$970$		0			0
$971$		0			0		0.973327	−	0.229424i	$-0.0736842\pi$
$971$		0			0		−0.973327	+	0.229424i	$0.926316\pi$
$972$		0			0
$973$		0			0
$974$	2.80454	+	0.693780i	2.80454	+	0.693780i
$975$		0			0
$976$		0			0
$977$	1.22601	+	0.681059i	1.22601	+	0.681059i	0.959210	−	0.282694i	$-0.0912281\pi$
$977$	1.22601	+	0.681059i	1.22601	+	0.681059i	0.266796	+	0.963753i	$0.414035\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	0.277124	−	0.105503i	0.277124	−	0.105503i
$982$	1.97727	+	2.81832i	1.97727	+	2.81832i
$983$		0			0		0.391577	−	0.920146i	$-0.371930\pi$
$983$		0			0		−0.391577	+	0.920146i	$0.628070\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−2.63355	−	1.24280i	−2.63355	−	1.24280i
$990$		0			0
$991$	−0.958715	+	1.33497i	−0.958715	+	1.33497i	−0.0165339	+	0.999863i	$0.505263\pi$
$991$	−0.958715	+	1.33497i	−0.958715	+	1.33497i	−0.942181	+	0.335105i	$0.891228\pi$
$992$		0			0
$993$		0			0
$994$	1.99769	−	3.29039i	1.99769	−	3.29039i
$995$		0			0
$996$		0			0
$997$		0			0		0.471093	−	0.882084i	$-0.343860\pi$
$997$		0			0		−0.471093	+	0.882084i	$0.656140\pi$
$998$	0.632574	+	1.15366i	0.632574	+	1.15366i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3997.1.cz.a.531.1	✓	144
7.6	odd	2	CM	3997.1.cz.a.531.1	✓	144
571.157	even	285	inner	3997.1.cz.a.3583.1	yes	144
3997.3583	odd	570	inner	3997.1.cz.a.3583.1	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3997.1.cz.a.531.1	✓	144	1.1	even	1	trivial
3997.1.cz.a.531.1	✓	144	7.6	odd	2	CM
3997.1.cz.a.3583.1	yes	144	571.157	even	285	inner
3997.1.cz.a.3583.1	yes	144	3997.3583	odd	570	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3997 = 7 \cdot 571 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3997.cz (of order \(570\), degree \(144\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.26766 - 1.53924i) q^{2} +(-0.570575 + 2.92103i) q^{4} +(0.922290 + 0.386499i) q^{7} +(3.46574 - 1.87557i) q^{8} +(0.775409 + 0.631460i) q^{9} +O(q^{10})\)	\(q+(-1.26766 - 1.53924i) q^{2} +(-0.570575 + 2.92103i) q^{4} +(0.922290 + 0.386499i) q^{7} +(3.46574 - 1.87557i) q^{8} +(0.775409 + 0.631460i) q^{9} +(0.855563 + 0.438905i) q^{11} +(-0.574239 - 1.90958i) q^{14} +(-4.52289 - 1.83704i) q^{16} +(-0.0109903 - 1.99402i) q^{18} +(-0.408987 - 1.87330i) q^{22} +(1.13347 - 1.07859i) q^{23} +(0.815447 - 0.578832i) q^{25} +(-1.65521 + 2.47351i) q^{28} +(0.502662 - 0.488997i) q^{29} +(1.72950 + 5.52953i) q^{32} +(-2.28694 + 1.90469i) q^{36} +(-1.86763 - 0.687544i) q^{37} +(-0.671770 - 1.73571i) q^{43} +(-1.77022 + 2.24869i) q^{44} +(-3.09707 - 0.377385i) q^{46} +(0.701237 + 0.712928i) q^{49} +(-1.92467 - 0.521404i) q^{50} +(-0.0192865 + 0.317727i) q^{53} +(3.92133 - 0.390309i) q^{56} +(-1.38989 - 0.153833i) q^{58} +(0.471093 + 0.882084i) q^{63} +(3.64879 - 5.58489i) q^{64} +(-1.06056 - 0.701272i) q^{67} +(1.29170 + 1.43458i) q^{71} +(3.87171 + 0.734147i) q^{72} +(1.30923 + 3.74631i) q^{74} +(0.619441 + 0.735472i) q^{77} +(0.596215 + 1.40101i) q^{79} +(0.202517 + 0.979279i) q^{81} +(-1.82009 + 3.23431i) q^{86} +(3.78836 - 0.0835327i) q^{88} +(2.50387 + 3.92631i) q^{92} +(0.208435 - 1.98313i) q^{98} +(0.386260 + 0.880585i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + q^{2} + 5 q^{4} + 2 q^{7} + 21 q^{8} - q^{9}+O(q^{10}) \) 144 * q + q^2 + 5 * q^4 + 2 * q^7 + 21 * q^8 - q^9	\( 144 q + q^{2} + 5 q^{4} + 2 q^{7} + 21 q^{8} - q^{9} + 6 q^{11} + q^{14} + 6 q^{16} - 9 q^{18} + 21 q^{22} + 3 q^{23} - q^{25} - 10 q^{28} - 4 q^{29} - 5 q^{32} - 2 q^{37} - 9 q^{43} - 20 q^{44} - 34 q^{46} + 2 q^{49} - 2 q^{50} + 6 q^{53} - 8 q^{56} - q^{58} - q^{63} + 11 q^{64} + 20 q^{67} + 3 q^{71} + 23 q^{72} - 31 q^{74} + q^{77} + 6 q^{79} - q^{81} + 7 q^{86} - 9 q^{88} + 9 q^{92} + 6 q^{98} - 2 q^{99}+O(q^{100}) \) 144 * q + q^2 + 5 * q^4 + 2 * q^7 + 21 * q^8 - q^9 + 6 * q^11 + q^14 + 6 * q^16 - 9 * q^18 + 21 * q^22 + 3 * q^23 - q^25 - 10 * q^28 - 4 * q^29 - 5 * q^32 - 2 * q^37 - 9 * q^43 - 20 * q^44 - 34 * q^46 + 2 * q^49 - 2 * q^50 + 6 * q^53 - 8 * q^56 - q^58 - q^63 + 11 * q^64 + 20 * q^67 + 3 * q^71 + 23 * q^72 - 31 * q^74 + q^77 + 6 * q^79 - q^81 + 7 * q^86 - 9 * q^88 + 9 * q^92 + 6 * q^98 - 2 * q^99

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