LMFDB - Embedded newform 3716.1.t.a.319.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3716,1,Mod(95,3716)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3716, base_ring=CyclotomicField(232))

chi = DirichletCharacter(H, H._module([116, 169]))

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

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

chi := DirichletCharacter("3716.95");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 3716 = 2^{2} \cdot 929 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	3716.t (of order $232$, degree $112$, 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:	$1.85452558694$
Analytic rank:	$0$
Dimension:	$112$
Coefficient field:	$\Q(\zeta_{232})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{112} - x^{108} + x^{104} - x^{100} + x^{96} - x^{92} + x^{88} - x^{84} + x^{80} - x^{76} + x^{72} + \cdots + 1 $ x^112 - x^108 + x^104 - x^100 + x^96 - x^92 + x^88 - x^84 + x^80 - x^76 + x^72 - x^68 + x^64 - x^60 + x^56 - x^52 + x^48 - x^44 + x^40 - x^36 + x^32 - x^28 + x^24 - x^20 + x^16 - x^12 + x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{232}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{232} - \cdots)$

Embedding invariants

Embedding label			319.1
Root			$0.779413 - 0.626510i$ of defining polynomial
Character	$\chi$	$=$	3716.319
Dual form			3716.1.t.a.1095.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.970441 + 0.241338i) q^{2} +(0.883512 - 0.468408i) q^{4} +(-1.62200 + 0.0879420i) q^{5} +(-0.744352 + 0.667788i) q^{8} +(-0.241338 + 0.970441i) q^{9} +O(q^{10})$	\(q+(-0.970441 + 0.241338i) q^{2} +(0.883512 - 0.468408i) q^{4} +(-1.62200 + 0.0879420i) q^{5} +(-0.744352 + 0.667788i) q^{8} +(-0.241338 + 0.970441i) q^{9} +(1.55283 - 0.476792i) q^{10} +(-0.0103638 - 0.765297i) q^{13} +(0.561187 - 0.827689i) q^{16} +(-1.28766 - 1.06407i) q^{17} -1.00000i q^{18} +(-1.39186 + 0.837454i) q^{20} +(1.62900 - 0.177164i) q^{25} +(0.194753 + 0.740174i) q^{26} +(0.0745689 + 0.202974i) q^{29} +(-0.344846 + 0.938659i) q^{32} +(1.50640 + 0.721857i) q^{34} +(0.241338 + 0.970441i) q^{36} +(-0.150789 + 0.0600799i) q^{37} +(1.14861 - 1.14861i) q^{40} +(1.92861 - 0.397218i) q^{41} +(0.306106 - 1.59527i) q^{45} +(0.538568 - 0.842582i) q^{49} +(-1.53809 + 0.565066i) q^{50} +(-0.367628 - 0.671294i) q^{52} +(0.208356 + 1.91580i) q^{53} +(-0.121350 - 0.178978i) q^{58} +(0.0456332 + 1.68455i) q^{61} +(0.108119 - 0.994138i) q^{64} +(0.0841118 + 1.24040i) q^{65} +(-1.63608 - 0.336969i) q^{68} +(-0.468408 - 0.883512i) q^{72} +(-0.554222 - 0.950011i) q^{73} +(0.131832 - 0.0946951i) q^{74} +(-0.837454 + 1.39186i) q^{80} +(-0.883512 - 0.468408i) q^{81} +(-1.77574 + 0.850923i) q^{82} +(2.18216 + 1.61268i) q^{85} +(0.497055 - 0.198045i) q^{89} +(0.0879420 + 1.62200i) q^{90} +(1.81816 + 0.172860i) q^{97} +(-0.319302 + 0.947653i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q+O(q^{10}) $ 112 * q	$ 112 q + 4 q^{10} + 4 q^{16} - 4 q^{17} + 4 q^{25} + 4 q^{26} + 4 q^{40} + 4 q^{45} - 4 q^{52} + 4 q^{61} + 4 q^{65} + 4 q^{72} - 4 q^{74} + 4 q^{85} + 4 q^{97}+O(q^{100}) $ 112 * q + 4 * q^10 + 4 * q^16 - 4 * q^17 + 4 * q^25 + 4 * q^26 + 4 * q^40 + 4 * q^45 - 4 * q^52 + 4 * q^61 + 4 * q^65 + 4 * q^72 - 4 * q^74 + 4 * q^85 + 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3716\mathbb{Z}\right)^\times$.

$n$	$1859$	$1861$
$\chi(n)$	$-1$	$e\left(\frac{67}{232}\right)$

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 $

$2$	−0.970441	+	0.241338i	−0.970441	+	0.241338i
$2$	−0.970441	+	0.241338i	−0.970441	+	0.241338i
$3$		0			0		−0.615899	−	0.787825i	$-0.711207\pi$
$3$		0			0		0.615899	+	0.787825i	$0.288793\pi$
$4$	0.883512	−	0.468408i	0.883512	−	0.468408i
$5$	−1.62200	+	0.0879420i	−1.62200	+	0.0879420i	−0.842582	−	0.538568i	$-0.818966\pi$
$5$	−1.62200	+	0.0879420i	−1.62200	+	0.0879420i	−0.779413	+	0.626510i	$0.784483\pi$
$6$		0			0
$7$		0			0		0.877088	−	0.480329i	$-0.159483\pi$
$7$		0			0		−0.877088	+	0.480329i	$0.840517\pi$
$8$	−0.744352	+	0.667788i	−0.744352	+	0.667788i
$9$	−0.241338	+	0.970441i	−0.241338	+	0.970441i
$10$	1.55283	−	0.476792i	1.55283	−	0.476792i
$11$		0			0		−0.999633	−	0.0270794i	$-0.991379\pi$
$11$		0			0		0.999633	+	0.0270794i	$0.00862069\pi$
$12$		0			0
$13$	−0.0103638	−	0.765297i	−0.0103638	−	0.765297i	−0.928977	−	0.370138i	$-0.879310\pi$
$13$	−0.0103638	−	0.765297i	−0.0103638	−	0.765297i	0.918613	−	0.395159i	$-0.129310\pi$
$14$		0			0
$15$		0			0
$16$	0.561187	−	0.827689i	0.561187	−	0.827689i
$17$	−1.28766	−	1.06407i	−1.28766	−	1.06407i	−0.994138	−	0.108119i	$-0.965517\pi$
$17$	−1.28766	−	1.06407i	−1.28766	−	1.06407i	−0.293523	−	0.955952i	$-0.594828\pi$
$18$		−	1.00000i		−	1.00000i
$19$		0			0		−0.725995	−	0.687699i	$-0.758621\pi$
$19$		0			0		0.725995	+	0.687699i	$0.241379\pi$
$20$	−1.39186	+	0.837454i	−1.39186	+	0.837454i
$21$		0			0
$22$		0			0
$23$		0			0		0.856857	−	0.515554i	$-0.172414\pi$
$23$		0			0		−0.856857	+	0.515554i	$0.827586\pi$
$24$		0			0
$25$	1.62900	−	0.177164i	1.62900	−	0.177164i
$26$	0.194753	+	0.740174i	0.194753	+	0.740174i
$27$		0			0
$28$		0			0
$29$	0.0745689	+	0.202974i	0.0745689	+	0.202974i	0.970441	−	0.241338i	$-0.0775862\pi$
$29$	0.0745689	+	0.202974i	0.0745689	+	0.202974i	−0.895872	+	0.444312i	$0.853448\pi$
$30$		0			0
$31$		0			0		0.820014	−	0.572343i	$-0.193966\pi$
$31$		0			0		−0.820014	+	0.572343i	$0.806034\pi$
$32$	−0.344846	+	0.938659i	−0.344846	+	0.938659i
$33$		0			0
$34$	1.50640	+	0.721857i	1.50640	+	0.721857i
$35$		0			0
$36$	0.241338	+	0.970441i	0.241338	+	0.970441i
$37$	−0.150789	+	0.0600799i	−0.150789	+	0.0600799i	−0.444312	−	0.895872i	$-0.646552\pi$
$37$	−0.150789	+	0.0600799i	−0.150789	+	0.0600799i	0.293523	+	0.955952i	$0.405172\pi$
$38$		0			0
$39$		0			0
$40$	1.14861	−	1.14861i	1.14861	−	1.14861i
$41$	1.92861	−	0.397218i	1.92861	−	0.397218i	0.928977	−	0.370138i	$-0.120690\pi$
$41$	1.92861	−	0.397218i	1.92861	−	0.397218i	0.999633	−	0.0270794i	$-0.00862069\pi$
$42$		0			0
$43$		0			0		−0.615899	−	0.787825i	$-0.711207\pi$
$43$		0			0		0.615899	+	0.787825i	$0.288793\pi$
$44$		0			0
$45$	0.306106	−	1.59527i	0.306106	−	1.59527i
$46$		0			0
$47$		0			0		−0.842582	−	0.538568i	$-0.818966\pi$
$47$		0			0		0.842582	+	0.538568i	$0.181034\pi$
$48$		0			0
$49$	0.538568	−	0.842582i	0.538568	−	0.842582i
$50$	−1.53809	+	0.565066i	−1.53809	+	0.565066i
$51$		0			0
$52$	−0.367628	−	0.671294i	−0.367628	−	0.671294i
$53$	0.208356	+	1.91580i	0.208356	+	1.91580i	0.370138	+	0.928977i	$0.379310\pi$
$53$	0.208356	+	1.91580i	0.208356	+	1.91580i	−0.161782	+	0.986827i	$0.551724\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		0			0
$58$	−0.121350	−	0.178978i	−0.121350	−	0.178978i
$59$		0			0		0.254456	−	0.967084i	$-0.418103\pi$
$59$		0			0		−0.254456	+	0.967084i	$0.581897\pi$
$60$		0			0
$61$	0.0456332	+	1.68455i	0.0456332	+	1.68455i	0.561187	+	0.827689i	$0.310345\pi$
$61$	0.0456332	+	1.68455i	0.0456332	+	1.68455i	−0.515554	+	0.856857i	$0.672414\pi$
$62$		0			0
$63$		0			0
$64$	0.108119	−	0.994138i	0.108119	−	0.994138i
$65$	0.0841118	+	1.24040i	0.0841118	+	1.24040i
$66$		0			0
$67$		0			0		0.835212	−	0.549928i	$-0.185345\pi$
$67$		0			0		−0.835212	+	0.549928i	$0.814655\pi$
$68$	−1.63608	−	0.336969i	−1.63608	−	0.336969i
$69$		0			0
$70$		0			0
$71$		0			0		0.626510	−	0.779413i	$-0.284483\pi$
$71$		0			0		−0.626510	+	0.779413i	$0.715517\pi$
$72$	−0.468408	−	0.883512i	−0.468408	−	0.883512i
$73$	−0.554222	−	0.950011i	−0.554222	−	0.950011i	−0.998533	−	0.0541389i	$-0.982759\pi$
$73$	−0.554222	−	0.950011i	−0.554222	−	0.950011i	0.444312	−	0.895872i	$-0.353448\pi$
$74$	0.131832	−	0.0946951i	0.131832	−	0.0946951i
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		−0.943243	−	0.332104i	$-0.892241\pi$
$79$		0			0		0.943243	+	0.332104i	$0.107759\pi$
$80$	−0.837454	+	1.39186i	−0.837454	+	1.39186i
$81$	−0.883512	−	0.468408i	−0.883512	−	0.468408i
$82$	−1.77574	+	0.850923i	−1.77574	+	0.850923i
$83$		0			0		0.538568	−	0.842582i	$-0.318966\pi$
$83$		0			0		−0.538568	+	0.842582i	$0.681034\pi$
$84$		0			0
$85$	2.18216	+	1.61268i	2.18216	+	1.61268i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	0.497055	−	0.198045i	0.497055	−	0.198045i	−0.108119	−	0.994138i	$-0.534483\pi$
$89$	0.497055	−	0.198045i	0.497055	−	0.198045i	0.605174	+	0.796093i	$0.293103\pi$
$90$	0.0879420	+	1.62200i	0.0879420	+	1.62200i
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$	1.81816	+	0.172860i	1.81816	+	0.172860i	0.947653	−	0.319302i	$-0.103448\pi$
$97$	1.81816	+	0.172860i	1.81816	+	0.172860i	0.870504	+	0.492162i	$0.163793\pi$
$98$	−0.319302	+	0.947653i	−0.319302	+	0.947653i
$99$		0			0
$100$	1.35625	−	0.919563i	1.35625	−	0.919563i
$101$	1.23108	+	1.23108i	1.23108	+	1.23108i	0.963550	+	0.267528i	$0.0862069\pi$
$101$	1.23108	+	1.23108i	1.23108	+	1.23108i	0.267528	+	0.963550i	$0.413793\pi$
$102$		0			0
$103$		0			0		−0.468408	−	0.883512i	$-0.655172\pi$
$103$		0			0		0.468408	+	0.883512i	$0.344828\pi$
$104$	0.518770	+	0.562729i	0.518770	+	0.562729i
$105$		0			0
$106$	−0.664553	−	1.80889i	−0.664553	−	1.80889i
$107$		0			0		0.201726	−	0.979442i	$-0.435345\pi$
$107$		0			0		−0.201726	+	0.979442i	$0.564655\pi$
$108$		0			0
$109$	−1.27014	+	1.17092i	−1.27014	+	1.17092i	−0.293523	+	0.955952i	$0.594828\pi$
$109$	−1.27014	+	1.17092i	−1.27014	+	1.17092i	−0.976621	+	0.214970i	$0.931034\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	1.45523	+	1.04529i	1.45523	+	1.04529i	0.986827	+	0.161782i	$0.0517241\pi$
$113$	1.45523	+	1.04529i	1.45523	+	1.04529i	0.468408	+	0.883512i	$0.344828\pi$
$114$		0			0
$115$		0			0
$116$	0.160957	+	0.144401i	0.160957	+	0.144401i
$117$	0.745177	+	0.174638i	0.745177	+	0.174638i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	0.998533	+	0.0541389i	0.998533	+	0.0541389i
$122$	−0.450829	−	1.62374i	−0.450829	−	1.62374i
$123$		0			0
$124$		0			0
$125$	−1.02367	+	0.167822i	−1.02367	+	0.167822i
$126$		0			0
$127$		0			0		0.959839	−	0.280551i	$-0.0905172\pi$
$127$		0			0		−0.959839	+	0.280551i	$0.909483\pi$
$128$	0.135000	+	0.990846i	0.135000	+	0.990846i
$129$		0			0
$130$	−0.380980	−	1.18343i	−0.380980	−	1.18343i
$131$		0			0		−0.605174	−	0.796093i	$-0.706897\pi$
$131$		0			0		0.605174	+	0.796093i	$0.293103\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	1.66905	−	0.0678407i	1.66905	−	0.0678407i
$137$	−0.849481	−	1.71282i	−0.849481	−	1.71282i	−0.687699	−	0.725995i	$-0.741379\pi$
$137$	−0.849481	−	1.71282i	−0.849481	−	1.71282i	−0.161782	−	0.986827i	$-0.551724\pi$
$138$		0			0
$139$		0			0		−0.999175	−	0.0406129i	$-0.987069\pi$
$139$		0			0		0.999175	+	0.0406129i	$0.0129310\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	0.667788	+	0.744352i	0.667788	+	0.744352i
$145$	−0.138800	−	0.322665i	−0.138800	−	0.322665i
$146$	0.767113	+	0.788175i	0.767113	+	0.788175i
$147$		0			0
$148$	−0.105082	+	0.123712i	−0.105082	+	0.123712i
$149$	0.402363	−	1.09522i	0.402363	−	1.09522i	−0.561187	−	0.827689i	$-0.689655\pi$
$149$	0.402363	−	1.09522i	0.402363	−	1.09522i	0.963550	−	0.267528i	$-0.0862069\pi$
$150$		0			0
$151$		0			0		0.357525	−	0.933904i	$-0.383621\pi$
$151$		0			0		−0.357525	+	0.933904i	$0.616379\pi$
$152$		0			0
$153$	1.34338	−	0.992798i	1.34338	−	0.992798i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	0.955004	+	1.18808i	0.955004	+	1.18808i	0.982084	+	0.188445i	$0.0603448\pi$
$157$	0.955004	+	1.18808i	0.955004	+	1.18808i	−0.0270794	+	0.999633i	$0.508621\pi$
$158$		0			0
$159$		0			0
$160$	0.476792	−	1.55283i	0.476792	−	1.55283i
$161$		0			0
$162$	0.970441	+	0.241338i	0.970441	+	0.241338i
$163$		0			0		−0.0946475	−	0.995511i	$-0.530172\pi$
$163$		0			0		0.0946475	+	0.995511i	$0.469828\pi$
$164$	1.51789	−	1.25432i	1.51789	−	1.25432i
$165$		0			0
$166$		0			0
$167$		0			0		−0.928977	−	0.370138i	$-0.879310\pi$
$167$		0			0		0.928977	+	0.370138i	$0.120690\pi$
$168$		0			0
$169$	0.414062	−	0.0112166i	0.414062	−	0.0112166i
$170$	−2.50685	−	1.03837i	−2.50685	−	1.03837i
$171$		0			0
$172$		0			0
$173$	0.240845	−	1.46909i	0.240845	−	1.46909i	−0.538568	−	0.842582i	$-0.681034\pi$
$173$	0.240845	−	1.46909i	0.240845	−	1.46909i	0.779413	−	0.626510i	$-0.215517\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$	−0.434567	+	0.312149i	−0.434567	+	0.312149i
$179$		0			0		−0.877088	−	0.480329i	$-0.840517\pi$
$179$		0			0		0.877088	+	0.480329i	$0.159483\pi$
$180$	−0.476792	−	1.55283i	−0.476792	−	1.55283i
$181$	1.92568	+	0.451297i	1.92568	+	0.451297i	0.996701	+	0.0811587i	$0.0258621\pi$
$181$	1.92568	+	0.451297i	1.92568	+	0.451297i	0.928977	+	0.370138i	$0.120690\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	0.239296	−	0.110710i	0.239296	−	0.110710i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		−0.201726	−	0.979442i	$-0.564655\pi$
$191$		0			0		0.201726	+	0.979442i	$0.435345\pi$
$192$		0			0
$193$	0.350123	+	1.82467i	0.350123	+	1.82467i	0.538568	+	0.842582i	$0.318966\pi$
$193$	0.350123	+	1.82467i	0.350123	+	1.82467i	−0.188445	+	0.982084i	$0.560345\pi$
$194$	−1.80613	+	0.271040i	−1.80613	+	0.271040i
$195$		0			0
$196$	0.0811587	−	0.996701i	0.0811587	−	0.996701i
$197$	0.615519	−	1.48600i	0.615519	−	1.48600i	−0.241338	−	0.970441i	$-0.577586\pi$
$197$	0.615519	−	1.48600i	0.615519	−	1.48600i	0.856857	−	0.515554i	$-0.172414\pi$
$198$		0			0
$199$		0			0		−0.735241	−	0.677806i	$-0.762931\pi$
$199$		0			0		0.735241	+	0.677806i	$0.237069\pi$
$200$	−1.09424	+	1.21970i	−1.09424	+	1.21970i
$201$		0			0
$202$	−1.49179	−	0.897583i	−1.49179	−	0.897583i
$203$		0			0
$204$		0			0
$205$	−3.09326	+	0.813891i	−3.09326	+	0.813891i
$206$		0			0
$207$		0			0
$208$	−0.639244	−	0.420897i	−0.639244	−	0.420897i
$209$		0			0
$210$		0			0
$211$		0			0		−0.432140	−	0.901807i	$-0.642241\pi$
$211$		0			0		0.432140	+	0.901807i	$0.357759\pi$
$212$	1.08146	+	1.59504i	1.08146	+	1.59504i
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$	0.950011	−	1.44285i	0.950011	−	1.44285i
$219$		0			0
$220$		0			0
$221$	−0.800985	+	0.996470i	−0.800985	+	0.996470i
$222$		0			0
$223$		0			0		−0.994138	−	0.108119i	$-0.965517\pi$
$223$		0			0		0.994138	+	0.108119i	$0.0344828\pi$
$224$		0			0
$225$	−0.221211	+	1.62360i	−0.221211	+	1.62360i
$226$	−1.66449	−	0.663193i	−1.66449	−	0.663193i
$227$		0			0		−0.626510	−	0.779413i	$-0.715517\pi$
$227$		0			0		0.626510	+	0.779413i	$0.284483\pi$
$228$		0			0
$229$	0.394459	−	0.769014i	0.394459	−	0.769014i	−0.605174	−	0.796093i	$-0.706897\pi$
$229$	0.394459	−	0.769014i	0.394459	−	0.769014i	0.999633	+	0.0270794i	$0.00862069\pi$
$230$		0			0
$231$		0			0
$232$	−0.191049	−	0.101288i	−0.191049	−	0.101288i
$233$	0.341020	+	1.91715i	0.341020	+	1.91715i	0.395159	+	0.918613i	$0.370690\pi$
$233$	0.341020	+	1.91715i	0.341020	+	1.91715i	−0.0541389	+	0.998533i	$0.517241\pi$
$234$	−0.765297	+	0.0103638i	−0.765297	+	0.0103638i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		−0.997709	−	0.0676550i	$-0.978448\pi$
$239$		0			0		0.997709	+	0.0676550i	$0.0215517\pi$
$240$		0			0
$241$	−1.35251	+	0.0917139i	−1.35251	+	0.0917139i	−0.725995	−	0.687699i	$-0.758621\pi$
$241$	−1.35251	+	0.0917139i	−1.35251	+	0.0917139i	−0.626510	+	0.779413i	$0.715517\pi$
$242$	−0.982084	+	0.188445i	−0.982084	+	0.188445i
$243$		0			0
$244$	0.829373	+	1.46694i	0.829373	+	1.46694i
$245$	−0.799456	+	1.41403i	−0.799456	+	1.41403i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$	0.952907	−	0.409911i	0.952907	−	0.409911i
$251$		0			0		−0.280551	−	0.959839i	$-0.590517\pi$
$251$		0			0		0.280551	+	0.959839i	$0.409483\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.370138	−	0.928977i	−0.370138	−	0.928977i
$257$	0.611106	−	0.645137i	0.611106	−	0.645137i	−0.344846	−	0.938659i	$-0.612069\pi$
$257$	0.611106	−	0.645137i	0.611106	−	0.645137i	0.955952	+	0.293523i	$0.0948276\pi$
$258$		0			0
$259$		0			0
$260$	0.655326	+	1.05651i	0.655326	+	1.05651i
$261$	−0.214970	+	0.0233794i	−0.214970	+	0.0233794i
$262$		0			0
$263$		0			0		−0.370138	−	0.928977i	$-0.620690\pi$
$263$		0			0		0.370138	+	0.928977i	$0.379310\pi$
$264$		0			0
$265$	−0.506432	−	3.08910i	−0.506432	−	3.08910i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−0.613649	−	0.254182i	−0.613649	−	0.254182i	0.0541389	−	0.998533i	$-0.482759\pi$
$269$	−0.613649	−	0.254182i	−0.613649	−	0.254182i	−0.667788	+	0.744352i	$0.732759\pi$
$270$		0			0
$271$		0			0		0.984545	−	0.175130i	$-0.0560345\pi$
$271$		0			0		−0.984545	+	0.175130i	$0.943966\pi$
$272$	−1.60334	+	0.468639i	−1.60334	+	0.468639i
$273$		0			0
$274$	1.23774	+	1.45718i	1.23774	+	1.45718i
$275$		0			0
$276$		0			0
$277$	−0.629495	−	0.956056i	−0.629495	−	0.956056i	−0.999633	−	0.0270794i	$-0.991379\pi$
$277$	−0.629495	−	0.956056i	−0.629495	−	0.956056i	0.370138	−	0.928977i	$-0.379310\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	1.33474	−	0.331936i	1.33474	−	0.331936i	0.492162	−	0.870504i	$-0.336207\pi$
$281$	1.33474	−	0.331936i	1.33474	−	0.331936i	0.842582	+	0.538568i	$0.181034\pi$
$282$		0			0
$283$		0			0		−0.357525	−	0.933904i	$-0.616379\pi$
$283$		0			0		0.357525	+	0.933904i	$0.383621\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.827689	−	0.561187i	−0.827689	−	0.561187i
$289$	0.337377	+	1.75824i	0.337377	+	1.75824i
$290$	0.212569	+	0.279629i	0.212569	+	0.279629i
$291$		0			0
$292$	−0.934655	−	0.579744i	−0.934655	−	0.579744i
$293$	−0.0580076	+	0.180188i	−0.0580076	+	0.180188i	−0.976621	−	0.214970i	$-0.931034\pi$
$293$	−0.0580076	+	0.180188i	−0.0580076	+	0.180188i	0.918613	+	0.395159i	$0.129310\pi$
$294$		0			0
$295$		0			0
$296$	0.0721195	−	0.145416i	0.0721195	−	0.145416i
$297$		0			0
$298$	−0.126152	+	1.15995i	−0.126152	+	1.15995i
$299$		0			0
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−0.222159	−	2.72831i	−0.222159	−	2.72831i
$306$	−1.06407	+	1.28766i	−1.06407	+	1.28766i
$307$		0			0		−0.0676550	−	0.997709i	$-0.521552\pi$
$307$		0			0		0.0676550	+	0.997709i	$0.478448\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.175130	−	0.984545i	$-0.443966\pi$
$311$		0			0		−0.175130	+	0.984545i	$0.556034\pi$
$312$		0			0
$313$	0.674466	−	1.76180i	0.674466	−	1.76180i	0.0270794	−	0.999633i	$-0.491379\pi$
$313$	0.674466	−	1.76180i	0.674466	−	1.76180i	0.647386	−	0.762162i	$-0.275862\pi$
$314$	−1.21350	−	0.922482i	−1.21350	−	0.922482i
$315$		0			0
$316$		0			0
$317$	0.174348	−	0.363836i	0.174348	−	0.363836i	−0.796093	−	0.605174i	$-0.793103\pi$
$317$	0.174348	−	0.363836i	0.174348	−	0.363836i	0.970441	+	0.241338i	$0.0775862\pi$
$318$		0			0
$319$		0			0
$320$	−0.0879420	+	1.62200i	−0.0879420	+	1.62200i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−1.00000			−1.00000
$325$	−0.152466	−	1.24483i	−0.152466	−	1.24483i
$326$		0			0
$327$		0			0
$328$	−1.17031	+	1.58357i	−1.17031	+	1.58357i
$329$		0			0
$330$		0			0
$331$		0			0		−0.716617	−	0.697467i	$-0.754310\pi$
$331$		0			0		0.716617	+	0.697467i	$0.245690\pi$
$332$		0			0
$333$	−0.0219129	−	0.160832i	−0.0219129	−	0.160832i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−0.368398	+	1.67365i	−0.368398	+	1.67365i	0.319302	+	0.947653i	$0.396552\pi$
$337$	−0.368398	+	1.67365i	−0.368398	+	1.67365i	−0.687699	+	0.725995i	$0.741379\pi$
$338$	−0.399115	+	0.110814i	−0.399115	+	0.110814i
$339$		0			0
$340$	2.68335	+	0.402681i	2.68335	+	0.402681i
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$	0.120821	+	1.48379i	0.120821	+	1.48379i
$347$		0			0		−0.725995	−	0.687699i	$-0.758621\pi$
$347$		0			0		0.725995	+	0.687699i	$0.241379\pi$
$348$		0			0
$349$	−0.210442	−	0.169158i	−0.210442	−	0.169158i	0.515554	−	0.856857i	$-0.327586\pi$
$349$	−0.210442	−	0.169158i	−0.210442	−	0.169158i	−0.725995	+	0.687699i	$0.758621\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−0.0508366	−	0.0186765i	−0.0508366	−	0.0186765i	0.319302	−	0.947653i	$-0.396552\pi$
$353$	−0.0508366	−	0.0186765i	−0.0508366	−	0.0186765i	−0.370138	+	0.928977i	$0.620690\pi$
$354$		0			0
$355$		0			0
$356$	0.346388	−	0.407800i	0.346388	−	0.407800i
$357$		0			0
$358$		0			0
$359$		0			0		−0.201726	−	0.979442i	$-0.564655\pi$
$359$		0			0		0.201726	+	0.979442i	$0.435345\pi$
$360$	0.837454	+	1.39186i	0.837454	+	1.39186i
$361$	0.0541389	+	0.998533i	0.0541389	+	0.998533i
$362$	−1.97767	+	0.0267820i	−1.97767	+	0.0267820i
$363$		0			0
$364$		0			0
$365$	0.982491	+	1.49217i	0.982491	+	1.49217i
$366$		0			0
$367$		0			0		0.883512	−	0.468408i	$-0.155172\pi$
$367$		0			0		−0.883512	+	0.468408i	$0.844828\pi$
$368$		0			0
$369$	−0.0799704	+	1.96747i	−0.0799704	+	1.96747i
$370$	−0.205504	+	0.165189i	−0.205504	+	0.165189i
$371$		0			0
$372$		0			0
$373$	−1.79024	+	0.857869i	−1.79024	+	0.857869i	−0.842582	+	0.538568i	$0.818966\pi$
$373$	−1.79024	+	0.857869i	−1.79024	+	0.857869i	−0.947653	+	0.319302i	$0.896552\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	0.154562	−	0.0591709i	0.154562	−	0.0591709i
$378$		0			0
$379$		0			0		0.947653	−	0.319302i	$-0.103448\pi$
$379$		0			0		−0.947653	+	0.319302i	$0.896552\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.148405	−	0.988927i	$-0.452586\pi$
$383$		0			0		−0.148405	+	0.988927i	$0.547414\pi$
$384$		0			0
$385$		0			0
$386$	−0.780134	−	1.68623i	−0.780134	−	1.68623i
$387$		0			0
$388$	1.68733	−	0.698916i	1.68733	−	0.698916i
$389$	0.0774438	−	0.110956i	0.0774438	−	0.110956i	−0.779413	−	0.626510i	$-0.784483\pi$
$389$	0.0774438	−	0.110956i	0.0774438	−	0.110956i	0.856857	+	0.515554i	$0.172414\pi$
$390$		0			0
$391$		0			0
$392$	0.161782	+	0.986827i	0.161782	+	0.986827i
$393$		0			0
$394$	−0.238698	+	1.59062i	−0.238698	+	1.59062i
$395$		0			0
$396$		0			0
$397$	1.15732	−	0.271227i	1.15732	−	0.271227i	0.395159	−	0.918613i	$-0.370690\pi$
$397$	1.15732	−	0.271227i	1.15732	−	0.271227i	0.762162	+	0.647386i	$0.224138\pi$
$398$		0			0
$399$		0			0
$400$	0.767536	−	1.44773i	0.767536	−	1.44773i
$401$	1.84623	−	0.0750428i	1.84623	−	0.0750428i	0.907575	−	0.419889i	$-0.137931\pi$
$401$	1.84623	−	0.0750428i	1.84623	−	0.0750428i	0.938659	+	0.344846i	$0.112069\pi$
$402$		0			0
$403$		0			0
$404$	1.66432	+	0.511025i	1.66432	+	0.511025i
$405$	1.47425	+	0.682059i	1.47425	+	0.682059i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−0.402095	−	0.391350i	−0.402095	−	0.391350i	0.468408	−	0.883512i	$-0.344828\pi$
$409$	−0.402095	−	0.391350i	−0.402095	−	0.391350i	−0.870504	+	0.492162i	$0.836207\pi$
$410$	2.80541	−	1.53636i	2.80541	−	1.53636i
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$	0.721927	+	0.254182i	0.721927	+	0.254182i
$417$		0			0
$418$		0			0
$419$		0			0		−0.267528	−	0.963550i	$-0.586207\pi$
$419$		0			0		0.267528	+	0.963550i	$0.413793\pi$
$420$		0			0
$421$	0.212698	−	0.207015i	0.212698	−	0.207015i	−0.583395	−	0.812189i	$-0.698276\pi$
$421$	0.212698	−	0.207015i	0.212698	−	0.207015i	0.796093	+	0.605174i	$0.206897\pi$
$422$		0			0
$423$		0			0
$424$	−1.43444	−	1.28689i	−1.43444	−	1.28689i
$425$	−2.28611	−	1.50524i	−2.28611	−	1.50524i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		0.943243	−	0.332104i	$-0.107759\pi$
$431$		0			0		−0.943243	+	0.332104i	$0.892241\pi$
$432$		0			0
$433$	−0.0261904	−	1.93399i	−0.0261904	−	1.93399i	−0.267528	−	0.963550i	$-0.586207\pi$
$433$	−0.0261904	−	1.93399i	−0.0261904	−	1.93399i	0.241338	−	0.970441i	$-0.422414\pi$
$434$		0			0
$435$		0			0
$436$	−0.573717	+	1.62947i	−0.573717	+	1.62947i
$437$		0			0
$438$		0			0
$439$		0			0		0.267528	−	0.963550i	$-0.413793\pi$
$439$		0			0		−0.267528	+	0.963550i	$0.586207\pi$
$440$		0			0
$441$	0.687699	+	0.725995i	0.687699	+	0.725995i
$442$	0.536823	−	1.16032i	0.536823	−	1.16032i
$443$		0			0		−0.407561	−	0.913178i	$-0.633621\pi$
$443$		0			0		0.407561	+	0.913178i	$0.366379\pi$
$444$		0			0
$445$	−0.788805	+	0.364940i	−0.788805	+	0.364940i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−0.0252919	+	0.00968244i	−0.0252919	+	0.00968244i	−0.370138	−	0.928977i	$-0.620690\pi$
$449$	−0.0252919	+	0.00968244i	−0.0252919	+	0.00968244i	0.344846	+	0.938659i	$0.387931\pi$
$450$	−0.177164	−	1.62900i	−0.177164	−	1.62900i
$451$		0			0
$452$	1.77534	+	0.241886i	1.77534	+	0.241886i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−0.279720	−	0.545325i	−0.279720	−	0.545325i	0.707107	−	0.707107i	$-0.250000\pi$
$457$	−0.279720	−	0.545325i	−0.279720	−	0.545325i	−0.986827	+	0.161782i	$0.948276\pi$
$458$	−0.197207	+	0.841480i	−0.197207	+	0.841480i
$459$		0			0
$460$		0			0
$461$	−1.49097	+	0.392300i	−1.49097	+	0.392300i	−0.907575	−	0.419889i	$-0.862069\pi$
$461$	−1.49097	+	0.392300i	−1.49097	+	0.392300i	−0.583395	+	0.812189i	$0.698276\pi$
$462$		0			0
$463$		0			0		−0.407561	−	0.913178i	$-0.633621\pi$
$463$		0			0		0.407561	+	0.913178i	$0.366379\pi$
$464$	0.209846	+	0.0521864i	0.209846	+	0.0521864i
$465$		0			0
$466$	−0.793620	−	1.77818i	−0.793620	−	1.77818i
$467$		0			0		−0.982084	−	0.188445i	$-0.939655\pi$
$467$		0			0		0.982084	+	0.188445i	$0.0603448\pi$
$468$	0.740174	−	0.194753i	0.740174	−	0.194753i
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−1.90946	−	0.260159i	−1.90946	−	0.260159i
$478$		0			0
$479$		0			0		−0.108119	−	0.994138i	$-0.534483\pi$
$479$		0			0		0.108119	+	0.994138i	$0.465517\pi$
$480$		0			0
$481$	0.0475417	+	0.114776i	0.0475417	+	0.114776i
$482$	1.29039	−	0.415414i	1.29039	−	0.415414i
$483$		0			0
$484$	0.907575	−	0.419889i	0.907575	−	0.419889i
$485$	−2.96424	−	0.120486i	−2.96424	−	0.120486i
$486$		0			0
$487$		0			0		0.419889	−	0.907575i	$-0.362069\pi$
$487$		0			0		−0.419889	+	0.907575i	$0.637931\pi$
$488$	−1.15889	−	1.22342i	−1.15889	−	1.22342i
$489$		0			0
$490$	0.434567	−	1.56517i	0.434567	−	1.56517i
$491$		0			0		0.135000	−	0.990846i	$-0.456897\pi$
$491$		0			0		−0.135000	+	0.990846i	$0.543103\pi$
$492$		0			0
$493$	0.119959	−	0.340708i	0.119959	−	0.340708i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$		0			0		−0.820014	−	0.572343i	$-0.806034\pi$
$499$		0			0		0.820014	+	0.572343i	$0.193966\pi$
$500$	−0.825813	+	0.627767i	−0.825813	+	0.627767i
$501$		0			0
$502$		0			0
$503$		0			0		0.973620	−	0.228175i	$-0.0732759\pi$
$503$		0			0		−0.973620	+	0.228175i	$0.926724\pi$
$504$		0			0
$505$	−2.10507	−	1.88854i	−2.10507	−	1.88854i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−1.11210	+	0.151521i	−1.11210	+	0.151521i	−0.667788	−	0.744352i	$-0.732759\pi$
$509$	−1.11210	+	0.151521i	−1.11210	+	0.151521i	−0.444312	+	0.895872i	$0.646552\pi$
$510$		0			0
$511$		0			0
$512$	0.583395	+	0.812189i	0.583395	+	0.812189i
$513$		0			0
$514$	−0.437346	+	0.773550i	−0.437346	+	0.773550i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	−0.890930	−	0.867122i	−0.890930	−	0.867122i
$521$	1.29430	+	1.52377i	1.29430	+	1.52377i	0.667788	+	0.744352i	$0.267241\pi$
$521$	1.29430	+	1.52377i	1.29430	+	1.52377i	0.626510	+	0.779413i	$0.284483\pi$
$522$	0.202974	−	0.0745689i	0.202974	−	0.0745689i
$523$		0			0		−0.889774	−	0.456402i	$-0.849138\pi$
$523$		0			0		0.889774	+	0.456402i	$0.150862\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	0.468408	−	0.883512i	0.468408	−	0.883512i
$530$	1.23698	+	2.87557i	1.23698	+	2.87557i
$531$		0			0
$532$		0			0
$533$	−0.323977	−	1.47184i	−0.323977	−	1.47184i
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$	0.656854	+	0.0985716i	0.656854	+	0.0985716i
$539$		0			0
$540$		0			0
$541$	−1.35855	+	0.562729i	−1.35855	+	0.562729i	−0.938659	−	0.344846i	$-0.887931\pi$
$541$	−1.35855	+	0.562729i	−1.35855	+	0.562729i	−0.419889	+	0.907575i	$0.637931\pi$
$542$		0			0
$543$		0			0
$544$	1.44285	−	0.841733i	1.44285	−	0.841733i
$545$	1.95719	−	2.01093i	1.95719	−	2.01093i
$546$		0			0
$547$		0			0		−0.432140	−	0.901807i	$-0.642241\pi$
$547$		0			0		0.432140	+	0.901807i	$0.357759\pi$
$548$	−1.55283	−	1.11539i	−1.55283	−	1.11539i
$549$	−1.64577	−	0.362260i	−1.64577	−	0.362260i
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$	0.841621	+	0.775875i	0.841621	+	0.775875i
$555$		0			0
$556$		0			0
$557$	−1.95769	+	0.375647i	−1.95769	+	0.375647i	−0.963550	+	0.267528i	$0.913793\pi$
$557$	−1.95769	+	0.375647i	−1.95769	+	0.375647i	−0.994138	+	0.108119i	$0.965517\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	−1.21518	+	0.644248i	−1.21518	+	0.644248i
$563$		0			0		0.594339	−	0.804215i	$-0.297414\pi$
$563$		0			0		−0.594339	+	0.804215i	$0.702586\pi$
$564$		0			0
$565$	−2.45231	−	1.56749i	−2.45231	−	1.56749i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−0.0558230	−	0.0927786i	−0.0558230	−	0.0927786i	0.827689	−	0.561187i	$-0.189655\pi$
$569$	−0.0558230	−	0.0927786i	−0.0558230	−	0.0927786i	−0.883512	+	0.468408i	$0.844828\pi$
$570$		0			0
$571$		0			0		−0.967084	−	0.254456i	$-0.918103\pi$
$571$		0			0		0.967084	+	0.254456i	$0.0818966\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.938659	+	0.344846i	0.938659	+	0.344846i
$577$	−0.178657	+	0.448395i	−0.178657	+	0.448395i	−0.990846	−	0.135000i	$-0.956897\pi$
$577$	−0.178657	+	0.448395i	−0.178657	+	0.448395i	0.812189	+	0.583395i	$0.198276\pi$
$578$	−0.751735	−	1.62485i	−0.751735	−	1.62485i
$579$		0			0
$580$	−0.273771	−	0.220063i	−0.273771	−	0.220063i
$581$		0			0
$582$		0			0
$583$		0			0
$584$	1.04694	+	0.337040i	1.04694	+	0.337040i
$585$	−1.22403	−	0.217729i	−1.22403	−	0.217729i
$586$	0.0128068	−	0.188861i	0.0128068	−	0.188861i
$587$		0			0		0.687699	−	0.725995i	$-0.258621\pi$
$587$		0			0		−0.687699	+	0.725995i	$0.741379\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−0.0348935	+	0.158523i	−0.0348935	+	0.158523i
$593$	0.272629	−	0.174261i	0.272629	−	0.174261i	−0.395159	−	0.918613i	$-0.629310\pi$
$593$	0.272629	−	0.174261i	0.272629	−	0.174261i	0.667788	+	0.744352i	$0.267241\pi$
$594$		0			0
$595$		0			0
$596$	−0.157517	−	1.15611i	−0.157517	−	1.15611i
$597$		0			0
$598$		0			0
$599$		0			0		−0.804215	−	0.594339i	$-0.797414\pi$
$599$		0			0		0.804215	+	0.594339i	$0.202586\pi$
$600$		0			0
$601$	−0.781731	+	1.05778i	−0.781731	+	1.05778i	0.214970	+	0.976621i	$0.431034\pi$
$601$	−0.781731	+	1.05778i	−0.781731	+	1.05778i	−0.996701	+	0.0811587i	$0.974138\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−1.62438			−1.62438
$606$		0			0
$607$		0			0		0.280551	−	0.959839i	$-0.409483\pi$
$607$		0			0		−0.280551	+	0.959839i	$0.590517\pi$
$608$		0			0
$609$		0			0
$610$	0.874038	+	2.59405i	0.874038	+	2.59405i
$611$		0			0
$612$	0.721857	−	1.50640i	0.721857	−	1.50640i
$613$	1.97767	−	0.296782i	1.97767	−	0.296782i	0.986827	−	0.161782i	$-0.0517241\pi$
$613$	1.97767	−	0.296782i	1.97767	−	0.296782i	0.990846	−	0.135000i	$-0.0431034\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−0.317767	+	1.93829i	−0.317767	+	1.93829i	0.0270794	+	0.999633i	$0.491379\pi$
$617$	−0.317767	+	1.93829i	−0.317767	+	1.93829i	−0.344846	+	0.938659i	$0.612069\pi$
$618$		0			0
$619$		0			0		0.615899	−	0.787825i	$-0.288793\pi$
$619$		0			0		−0.615899	+	0.787825i	$0.711207\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.0453317	−	0.00997827i	0.0453317	−	0.00997827i
$626$	−0.229341	+	1.87249i	−0.229341	+	1.87249i
$627$		0			0
$628$	1.40026	+	0.602350i	1.40026	+	0.602350i
$629$	0.258094	+	0.0830879i	0.258094	+	0.0830879i
$630$		0			0
$631$		0			0		0.108119	−	0.994138i	$-0.465517\pi$
$631$		0			0		−0.108119	+	0.994138i	$0.534483\pi$
$632$		0			0
$633$		0			0
$634$	−0.0813871	+	0.395159i	−0.0813871	+	0.395159i
$635$		0			0
$636$		0			0
$637$	−0.650407	−	0.403432i	−0.650407	−	0.403432i
$638$		0			0
$639$		0			0
$640$	−0.306106	−	1.59527i	−0.306106	−	1.59527i
$641$	−1.00179	−	0.679232i	−1.00179	−	0.679232i	−0.0541389	−	0.998533i	$-0.517241\pi$
$641$	−1.00179	−	0.679232i	−1.00179	−	0.679232i	−0.947653	+	0.319302i	$0.896552\pi$
$642$		0			0
$643$		0			0		−0.228175	−	0.973620i	$-0.573276\pi$
$643$		0			0		0.228175	+	0.973620i	$0.426724\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		−0.332104	−	0.943243i	$-0.607759\pi$
$647$		0			0		0.332104	+	0.943243i	$0.392241\pi$
$648$	0.970441	−	0.241338i	0.970441	−	0.241338i
$649$		0			0
$650$	0.448384	+	1.17124i	0.448384	+	1.17124i
$651$		0			0
$652$		0			0
$653$	−1.04640	+	0.128162i	−1.04640	+	0.128162i	−0.626510	−	0.779413i	$-0.715517\pi$
$653$	−1.04640	+	0.128162i	−1.04640	+	0.128162i	−0.419889	+	0.907575i	$0.637931\pi$
$654$		0			0
$655$		0			0
$656$	0.753538	−	1.81920i	0.753538	−	1.81920i
$657$	1.05568	−	0.308566i	1.05568	−	0.308566i
$658$		0			0
$659$		0			0		0.753326	−	0.657647i	$-0.228448\pi$
$659$		0			0		−0.753326	+	0.657647i	$0.771552\pi$
$660$		0			0
$661$	−0.506372	+	0.924643i	−0.506372	+	0.924643i	0.492162	+	0.870504i	$0.336207\pi$
$661$	−0.506372	+	0.924643i	−0.506372	+	0.924643i	−0.998533	+	0.0541389i	$0.982759\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$	0.0600799	+	0.150789i	0.0600799	+	0.150789i
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.654043	−	1.64152i	−0.654043	−	1.64152i	−0.762162	−	0.647386i	$-0.775862\pi$
$673$	−0.654043	−	1.64152i	−0.654043	−	1.64152i	0.108119	−	0.994138i	$-0.465517\pi$
$674$	−0.0464063	−	1.71309i	−0.0464063	−	1.71309i
$675$		0			0
$676$	0.360574	−	0.203860i	0.360574	−	0.203860i
$677$	−1.11162	−	1.20582i	−1.11162	−	1.20582i	−0.976621	−	0.214970i	$-0.931034\pi$
$677$	−1.11162	−	1.20582i	−1.11162	−	1.20582i	−0.135000	−	0.990846i	$-0.543103\pi$
$678$		0			0
$679$		0			0
$680$	−2.70122	+	0.256817i	−2.70122	+	0.256817i
$681$		0			0
$682$		0			0
$683$		0			0		−0.895872	−	0.444312i	$-0.853448\pi$
$683$		0			0		0.895872	+	0.444312i	$0.146552\pi$
$684$		0			0
$685$	1.52848	+	2.70348i	1.52848	+	2.70348i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	1.46400	−	0.179309i	1.46400	−	0.179309i
$690$		0			0
$691$		0			0		0.998533	−	0.0541389i	$-0.0172414\pi$
$691$		0			0		−0.998533	+	0.0541389i	$0.982759\pi$
$692$	−0.475345	−	1.41077i	−0.475345	−	1.41077i
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−2.90606	−	1.54070i	−2.90606	−	1.54070i
$698$	0.245045	+	0.113370i	0.245045	+	0.113370i
$699$		0			0
$700$		0			0
$701$	0.548475	+	1.32414i	0.548475	+	1.32414i	0.918613	+	0.395159i	$0.129310\pi$
$701$	0.548475	+	1.32414i	0.548475	+	1.32414i	−0.370138	+	0.928977i	$0.620690\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	0.0538413	+	0.00585559i	0.0538413	+	0.00585559i
$707$		0			0
$708$		0			0
$709$	−1.72507	+	0.975312i	−1.72507	+	0.975312i	−0.796093	+	0.605174i	$0.793103\pi$
$709$	−1.72507	+	0.975312i	−1.72507	+	0.975312i	−0.928977	+	0.370138i	$0.879310\pi$
$710$		0			0
$711$		0			0
$712$	−0.237732	+	0.479342i	−0.237732	+	0.479342i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		−0.994138	−	0.108119i	$-0.965517\pi$
$719$		0			0		0.994138	+	0.108119i	$0.0344828\pi$
$720$	−1.14861	−	1.14861i	−1.14861	−	1.14861i
$721$		0			0
$722$	−0.293523	−	0.955952i	−0.293523	−	0.955952i
$723$		0			0
$724$	1.91275	−	0.503278i	1.91275	−	0.503278i
$725$	0.157432	+	0.317433i	0.157432	+	0.317433i
$726$		0			0
$727$		0			0		−0.856857	−	0.515554i	$-0.827586\pi$
$727$		0			0		0.856857	+	0.515554i	$0.172414\pi$
$728$		0			0
$729$	0.667788	−	0.744352i	0.667788	−	0.744352i
$730$	−1.31357	−	1.21096i	−1.31357	−	1.21096i
$731$		0			0
$732$		0			0
$733$	0.147315	−	1.80916i	0.147315	−	1.80916i	−0.344846	−	0.938659i	$-0.612069\pi$
$733$	0.147315	−	1.80916i	0.147315	−	1.80916i	0.492162	−	0.870504i	$-0.336207\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$	−0.397218	−	1.92861i	−0.397218	−	1.92861i
$739$		0			0		−0.895872	−	0.444312i	$-0.853448\pi$
$739$		0			0		0.895872	+	0.444312i	$0.146552\pi$
$740$	0.159563	−	0.209902i	0.159563	−	0.209902i
$741$		0			0
$742$		0			0
$743$		0			0		−0.998533	−	0.0541389i	$-0.982759\pi$
$743$		0			0		0.998533	+	0.0541389i	$0.0172414\pi$
$744$		0			0
$745$	−0.556315	+	1.81182i	−0.556315	+	1.81182i
$746$	1.53028	−	1.26456i	1.53028	−	1.26456i
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		0.812189	−	0.583395i	$-0.198276\pi$
$751$		0			0		−0.812189	+	0.583395i	$0.801724\pi$
$752$		0			0
$753$		0			0
$754$	−0.135714	+	0.0947236i	−0.135714	+	0.0947236i
$755$		0			0
$756$		0			0
$757$	−0.319849	−	0.142752i	−0.319849	−	0.142752i	0.241338	−	0.970441i	$-0.422414\pi$
$757$	−0.319849	−	0.142752i	−0.319849	−	0.142752i	−0.561187	+	0.827689i	$0.689655\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	1.50884	−	0.508387i	1.50884	−	0.508387i	0.561187	−	0.827689i	$-0.310345\pi$
$761$	1.50884	−	0.508387i	1.50884	−	0.508387i	0.947653	+	0.319302i	$0.103448\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−2.09165	+	1.72845i	−2.09165	+	1.72845i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	0.274977	−	0.895552i	0.274977	−	0.895552i	−0.707107	−	0.707107i	$-0.750000\pi$
$769$	0.274977	−	0.895552i	0.274977	−	0.895552i	0.982084	−	0.188445i	$-0.0603448\pi$
$770$		0			0
$771$		0			0
$772$	1.16403	+	1.44811i	1.16403	+	1.44811i
$773$	0.766956	−	1.78292i	0.766956	−	1.78292i	0.161782	−	0.986827i	$-0.448276\pi$
$773$	0.766956	−	1.78292i	0.766956	−	1.78292i	0.605174	−	0.796093i	$-0.293103\pi$
$774$		0			0
$775$		0			0
$776$	−1.46878	+	1.08547i	−1.46878	+	1.08547i
$777$		0			0
$778$	−0.0483767	+	0.126367i	−0.0483767	+	0.126367i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.395159	−	0.918613i	−0.395159	−	0.918613i
$785$	−1.65349	−	1.84307i	−1.65349	−	1.84307i
$786$		0			0
$787$		0			0		0.419889	−	0.907575i	$-0.362069\pi$
$787$		0			0		−0.419889	+	0.907575i	$0.637931\pi$
$788$	−0.152234	−	1.60121i	−0.152234	−	1.60121i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	1.28870	−	0.0523812i	1.28870	−	0.0523812i
$794$	−1.05765	+	0.542515i	−1.05765	+	0.542515i
$795$		0			0
$796$		0			0
$797$	−0.219266	−	0.105071i	−0.219266	−	0.105071i	0.319302	−	0.947653i	$-0.396552\pi$
$797$	−0.219266	−	0.105071i	−0.219266	−	0.105071i	−0.538568	+	0.842582i	$0.681034\pi$
$798$		0			0
$799$		0			0
$800$	−0.395457	+	1.59017i	−0.395457	+	1.59017i
$801$	0.0722327	+	0.530159i	0.0722327	+	0.530159i
$802$	−1.77355	+	0.518391i	−1.77355	+	0.518391i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	−1.73845	−	0.0942563i	−1.73845	−	0.0942563i
$809$	1.97625	+	0.242050i	1.97625	+	0.242050i	0.999633	+	0.0270794i	$0.00862069\pi$
$809$	1.97625	+	0.242050i	1.97625	+	0.242050i	0.976621	+	0.214970i	$0.0689655\pi$
$810$	−1.59527	−	0.306106i	−1.59527	−	0.306106i
$811$		0			0		0.0135409	−	0.999908i	$-0.495690\pi$
$811$		0			0		−0.0135409	+	0.999908i	$0.504310\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	0.484658	+	0.282742i	0.484658	+	0.282742i
$819$		0			0
$820$	−2.35170	+	2.16799i	−2.35170	+	2.16799i
$821$	0.905668	−	1.15848i	0.905668	−	1.15848i	−0.0811587	−	0.996701i	$-0.525862\pi$
$821$	0.905668	−	1.15848i	0.905668	−	1.15848i	0.986827	−	0.161782i	$-0.0517241\pi$
$822$		0			0
$823$		0			0		−0.344846	−	0.938659i	$-0.612069\pi$
$823$		0			0		0.344846	+	0.938659i	$0.387931\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		−0.214970	−	0.976621i	$-0.568966\pi$
$827$		0			0		0.214970	+	0.976621i	$0.431034\pi$
$828$		0			0
$829$	1.64022	−	1.11210i	1.64022	−	1.11210i	0.744352	−	0.667788i	$-0.232759\pi$
$829$	1.64022	−	1.11210i	1.64022	−	1.11210i	0.895872	−	0.444312i	$-0.146552\pi$
$830$		0			0
$831$		0			0
$832$	−0.761931	−	0.0724401i	−0.761931	−	0.0724401i
$833$	−1.59006	+	0.511885i	−1.59006	+	0.511885i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		−0.0541389	−	0.998533i	$-0.517241\pi$
$839$		0			0		0.0541389	+	0.998533i	$0.482759\pi$
$840$		0			0
$841$	0.726524	−	0.617115i	0.726524	−	0.617115i
$842$	−0.156451	+	0.252228i	−0.156451	+	0.252228i
$843$		0			0
$844$		0			0
$845$	−0.670620	+	0.0546068i	−0.670620	+	0.0546068i
$846$		0			0
$847$		0			0
$848$	1.70262	+	0.902670i	1.70262	+	0.902670i
$849$		0			0
$850$	2.58181	+	0.909024i	2.58181	+	0.909024i
$851$		0			0
$852$		0			0
$853$	1.39907	+	0.388449i	1.39907	+	0.388449i	0.883512	−	0.468408i	$-0.155172\pi$
$853$	1.39907	+	0.388449i	1.39907	+	0.388449i	0.515554	+	0.856857i	$0.327586\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−0.0507182	−	0.0956648i	−0.0507182	−	0.0956648i	0.856857	−	0.515554i	$-0.172414\pi$
$857$	−0.0507182	−	0.0956648i	−0.0507182	−	0.0956648i	−0.907575	+	0.419889i	$0.862069\pi$
$858$		0			0
$859$		0			0		0.697467	−	0.716617i	$-0.254310\pi$
$859$		0			0		−0.697467	+	0.716617i	$0.745690\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.770858	−	0.637007i	$-0.780172\pi$
$863$		0			0		0.770858	+	0.637007i	$0.219828\pi$
$864$		0			0
$865$	−0.261455	+	2.40404i	−0.261455	+	2.40404i
$866$	0.492162	+	1.87050i	0.492162	+	1.87050i
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	0.163505	−	1.71976i	0.163505	−	1.71976i
$873$	−0.606541	+	1.72270i	−0.606541	+	1.72270i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−0.611946	−	1.11742i	−0.611946	−	1.11742i	−0.982084	−	0.188445i	$-0.939655\pi$
$877$	−0.611946	−	1.11742i	−0.611946	−	1.11742i	0.370138	−	0.928977i	$-0.379310\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−0.910712	+	0.0617558i	−0.910712	+	0.0617558i	−0.515554	−	0.856857i	$-0.672414\pi$
$881$	−0.910712	+	0.0617558i	−0.910712	+	0.0617558i	−0.395159	+	0.918613i	$0.629310\pi$
$882$	−0.842582	−	0.538568i	−0.842582	−	0.538568i
$883$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$883$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$884$	−0.240925	+	1.25558i	−0.240925	+	1.25558i
$885$		0			0
$886$		0			0
$887$		0			0		−0.986827	−	0.161782i	$-0.948276\pi$
$887$		0			0		0.986827	+	0.161782i	$0.0517241\pi$
$888$		0			0
$889$		0			0
$890$	0.677415	−	0.544521i	0.677415	−	0.544521i
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	0.0222075	−	0.0155001i	0.0222075	−	0.0155001i
$899$		0			0
$900$	0.565066	+	1.53809i	0.565066	+	1.53809i
$901$	1.77026	−	2.68861i	1.77026	−	2.68861i
$902$		0			0
$903$		0			0
$904$	−1.78124	+	0.193722i	−1.78124	+	0.193722i
$905$	−3.16313	−	0.562653i	−3.16313	−	0.562653i
$906$		0			0
$907$		0			0		0.976621	−	0.214970i	$-0.0689655\pi$
$907$		0			0		−0.976621	+	0.214970i	$0.931034\pi$
$908$		0			0
$909$	−1.49179	+	0.897583i	−1.49179	+	0.897583i
$910$		0			0
$911$		0			0			−	1.00000i	$-0.5\pi$
$911$		0			0				1.00000i	$0.5\pi$
$912$		0			0
$913$		0			0
$914$	0.403059	+	0.461699i	0.403059	+	0.461699i
$915$		0			0
$916$	−0.0117032	−	0.864201i	−0.0117032	−	0.864201i
$917$		0			0
$918$		0			0
$919$		0			0		0.955952	−	0.293523i	$-0.0948276\pi$
$919$		0			0		−0.955952	+	0.293523i	$0.905172\pi$
$920$		0			0
$921$		0			0
$922$	1.35222	−	0.740531i	1.35222	−	0.740531i
$923$		0			0
$924$		0			0
$925$	−0.234991	+	0.124584i	−0.234991	+	0.124584i
$926$		0			0
$927$		0			0
$928$	−0.216238			−0.216238
$929$		−	1.00000i		−	1.00000i
$929$		−	1.00000i		−	1.00000i
$930$		0			0
$931$		0			0
$932$	1.19930	+	1.53409i	1.19930	+	1.53409i
$933$		0			0
$934$		0			0
$935$		0			0
$936$	−0.671294	+	0.367628i	−0.671294	+	0.367628i
$937$	−1.31529	+	1.18000i	−1.31529	+	1.18000i	−0.344846	+	0.938659i	$0.612069\pi$
$937$	−1.31529	+	1.18000i	−1.31529	+	1.18000i	−0.970441	+	0.241338i	$0.922414\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	0.920308	+	0.410743i	0.920308	+	0.410743i	0.812189	−	0.583395i	$-0.198276\pi$
$941$	0.920308	+	0.410743i	0.920308	+	0.410743i	0.108119	+	0.994138i	$0.465517\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0			−	1.00000i	$-0.5\pi$
$947$		0			0				1.00000i	$0.5\pi$
$948$		0			0
$949$	−0.721297	+	0.433990i	−0.721297	+	0.433990i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	1.51789	+	0.270000i	1.51789	+	0.270000i	0.870504	−	0.492162i	$-0.163793\pi$
$953$	1.51789	+	0.270000i	1.51789	+	0.270000i	0.647386	+	0.762162i	$0.275862\pi$
$954$	1.91580	−	0.208356i	1.91580	−	0.208356i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.344846	−	0.938659i	0.344846	−	0.938659i
$962$	−0.0738361	−	0.0999095i	−0.0738361	−	0.0999095i
$963$		0			0
$964$	−1.15200	+	0.714555i	−1.15200	+	0.714555i
$965$	−0.728362	−	2.92881i	−0.728362	−	2.92881i
$966$		0			0
$967$		0			0		−0.870504	−	0.492162i	$-0.836207\pi$
$967$		0			0		0.870504	+	0.492162i	$0.163793\pi$
$968$	−0.779413	+	0.626510i	−0.779413	+	0.626510i
$969$		0			0
$970$	2.90570	−	0.598460i	2.90570	−	0.598460i
$971$		0			0		−0.986827	−	0.161782i	$-0.948276\pi$
$971$		0			0		0.986827	+	0.161782i	$0.0517241\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$	1.41989	+	0.907575i	1.41989	+	0.907575i
$977$	0.958457	−	0.0649933i	0.958457	−	0.0649933i	0.419889	−	0.907575i	$-0.362069\pi$
$977$	0.958457	−	0.0649933i	0.958457	−	0.0649933i	0.538568	+	0.842582i	$0.318966\pi$
$978$		0			0
$979$		0			0
$980$	−0.0439871	+	1.62378i	−0.0439871	+	1.62378i
$981$	−0.829778	−	1.51519i	−0.829778	−	1.51519i
$982$		0			0
$983$		0			0		0.787825	−	0.615899i	$-0.211207\pi$
$983$		0			0		−0.787825	+	0.615899i	$0.788793\pi$
$984$		0			0
$985$	−0.867688	+	2.46441i	−0.867688	+	2.46441i
$986$	−0.0341876	+	0.359588i	−0.0341876	+	0.359588i
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.657647	−	0.753326i	$-0.271552\pi$
$991$		0			0		−0.657647	+	0.753326i	$0.728448\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	1.89441	+	0.390173i	1.89441	+	0.390173i	0.998533	−	0.0541389i	$-0.0172414\pi$
$997$	1.89441	+	0.390173i	1.89441	+	0.390173i	0.895872	+	0.444312i	$0.146552\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3716.1.t.a.319.1	✓	112
4.3	odd	2	CM	3716.1.t.a.319.1	✓	112
929.166	even	232	inner	3716.1.t.a.1095.1	yes	112
3716.1095	odd	232	inner	3716.1.t.a.1095.1	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3716.1.t.a.319.1	✓	112	1.1	even	1	trivial
3716.1.t.a.319.1	✓	112	4.3	odd	2	CM
3716.1.t.a.1095.1	yes	112	929.166	even	232	inner
3716.1.t.a.1095.1	yes	112	3716.1095	odd	232	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:	\( N \)	\(=\)	\( 3716 = 2^{2} \cdot 929 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3716.t (of order \(232\), degree \(112\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.970441 + 0.241338i) q^{2} +(0.883512 - 0.468408i) q^{4} +(-1.62200 + 0.0879420i) q^{5} +(-0.744352 + 0.667788i) q^{8} +(-0.241338 + 0.970441i) q^{9} +O(q^{10})\)	\(q+(-0.970441 + 0.241338i) q^{2} +(0.883512 - 0.468408i) q^{4} +(-1.62200 + 0.0879420i) q^{5} +(-0.744352 + 0.667788i) q^{8} +(-0.241338 + 0.970441i) q^{9} +(1.55283 - 0.476792i) q^{10} +(-0.0103638 - 0.765297i) q^{13} +(0.561187 - 0.827689i) q^{16} +(-1.28766 - 1.06407i) q^{17} -1.00000i q^{18} +(-1.39186 + 0.837454i) q^{20} +(1.62900 - 0.177164i) q^{25} +(0.194753 + 0.740174i) q^{26} +(0.0745689 + 0.202974i) q^{29} +(-0.344846 + 0.938659i) q^{32} +(1.50640 + 0.721857i) q^{34} +(0.241338 + 0.970441i) q^{36} +(-0.150789 + 0.0600799i) q^{37} +(1.14861 - 1.14861i) q^{40} +(1.92861 - 0.397218i) q^{41} +(0.306106 - 1.59527i) q^{45} +(0.538568 - 0.842582i) q^{49} +(-1.53809 + 0.565066i) q^{50} +(-0.367628 - 0.671294i) q^{52} +(0.208356 + 1.91580i) q^{53} +(-0.121350 - 0.178978i) q^{58} +(0.0456332 + 1.68455i) q^{61} +(0.108119 - 0.994138i) q^{64} +(0.0841118 + 1.24040i) q^{65} +(-1.63608 - 0.336969i) q^{68} +(-0.468408 - 0.883512i) q^{72} +(-0.554222 - 0.950011i) q^{73} +(0.131832 - 0.0946951i) q^{74} +(-0.837454 + 1.39186i) q^{80} +(-0.883512 - 0.468408i) q^{81} +(-1.77574 + 0.850923i) q^{82} +(2.18216 + 1.61268i) q^{85} +(0.497055 - 0.198045i) q^{89} +(0.0879420 + 1.62200i) q^{90} +(1.81816 + 0.172860i) q^{97} +(-0.319302 + 0.947653i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q+O(q^{10}) \) 112 * q	\( 112 q + 4 q^{10} + 4 q^{16} - 4 q^{17} + 4 q^{25} + 4 q^{26} + 4 q^{40} + 4 q^{45} - 4 q^{52} + 4 q^{61} + 4 q^{65} + 4 q^{72} - 4 q^{74} + 4 q^{85} + 4 q^{97}+O(q^{100}) \) 112 * q + 4 * q^10 + 4 * q^16 - 4 * q^17 + 4 * q^25 + 4 * q^26 + 4 * q^40 + 4 * q^45 - 4 * q^52 + 4 * q^61 + 4 * q^65 + 4 * q^72 - 4 * q^74 + 4 * q^85 + 4 * q^97

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