LMFDB - Embedded newform 3997.1.cz.a.202.1

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			202.1
Root			$-0.775409 - 0.631460i$ of defining polynomial
Character	$\chi$	$=$	3997.202
Dual form			3997.1.cz.a.930.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.315447 - 1.00854i) q^{2} +(-0.0958675 + 0.0664730i) q^{4} +(0.746821 + 0.665025i) q^{7} +(-0.736619 - 0.573334i) q^{8} +(0.618553 + 0.785743i) q^{9} +O(q^{10})$	\(q+(-0.315447 - 1.00854i) q^{2} +(-0.0958675 + 0.0664730i) q^{4} +(0.746821 + 0.665025i) q^{7} +(-0.736619 - 0.573334i) q^{8} +(0.618553 + 0.785743i) q^{9} +(-0.323988 + 1.87774i) q^{11} +(0.435121 - 0.962979i) q^{14} +(-0.386771 + 1.03302i) q^{16} +(0.597333 - 0.871695i) q^{18} +(1.99598 - 0.265574i) q^{22} +(-0.346769 - 0.958215i) q^{23} +(-0.256156 - 0.966635i) q^{25} +(-0.115802 - 0.0141107i) q^{28} +(-1.47171 + 1.28171i) q^{29} +(0.231817 + 0.0127897i) q^{32} +(-0.111530 - 0.0342101i) q^{36} +(0.264802 - 0.246477i) q^{37} +(1.11222 + 1.66207i) q^{43} +(-0.0937595 - 0.201551i) q^{44} +(-0.857010 + 0.651997i) q^{46} +(0.115485 + 0.993309i) q^{49} +(-0.894086 + 0.563266i) q^{50} +(0.632414 + 1.87576i) q^{53} +(-0.168842 - 0.918048i) q^{56} +(1.75690 + 1.07996i) q^{58} +(-0.0605901 + 0.998163i) q^{63} +(0.210555 + 0.831465i) q^{64} +(0.394576 - 0.448056i) q^{67} +(1.65521 - 0.351826i) q^{71} +(-0.00514472 - 0.933431i) q^{72} +(-0.332113 - 0.189313i) q^{74} +(-1.49071 + 1.18688i) q^{77} +(-0.0181016 - 0.142029i) q^{79} +(-0.234785 + 0.972047i) q^{81} +(1.32542 - 1.64601i) q^{86} +(1.31523 - 1.19743i) q^{88} +(0.0969394 + 0.0688108i) q^{92} +(0.965362 - 0.429807i) q^{98} +(-1.67583 + 0.906913i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/3997\mathbb{Z}\right)^\times$.

$n$	$1716$	$2285$
$\chi(n)$	$e\left(\frac{41}{285}\right)$	$-1$

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 $

$2$	−0.315447	−	1.00854i	−0.315447	−	1.00854i	−0.968033	−	0.250825i	$-0.919298\pi$
$2$	−0.315447	−	1.00854i	−0.315447	−	1.00854i	0.652586	−	0.757715i	$-0.273684\pi$
$3$		0			0		−0.899598	−	0.436719i	$-0.856140\pi$
$3$		0			0		0.899598	+	0.436719i	$0.143860\pi$
$4$	−0.0958675	+	0.0664730i	−0.0958675	+	0.0664730i
$5$		0			0		0.609854	−	0.792514i	$-0.291228\pi$
$5$		0			0		−0.609854	+	0.792514i	$0.708772\pi$
$6$		0			0
$7$	0.746821	+	0.665025i	0.746821	+	0.665025i
$7$	0.746821	+	0.665025i	0.746821	+	0.665025i
$8$	−0.736619	−	0.573334i	−0.736619	−	0.573334i
$9$	0.618553	+	0.785743i	0.618553	+	0.785743i
$10$		0			0
$11$	−0.323988	+	1.87774i	−0.323988	+	1.87774i	0.137354	+	0.990522i	$0.456140\pi$
$11$	−0.323988	+	1.87774i	−0.323988	+	1.87774i	−0.461341	+	0.887223i	$0.652632\pi$
$12$		0			0
$13$		0			0		0.421786	−	0.906696i	$-0.361404\pi$
$13$		0			0		−0.421786	+	0.906696i	$0.638596\pi$
$14$	0.435121	−	0.962979i	0.435121	−	0.962979i
$15$		0			0
$16$	−0.386771	+	1.03302i	−0.386771	+	1.03302i
$17$		0			0		−0.266796	−	0.963753i	$-0.585965\pi$
$17$		0			0		0.266796	+	0.963753i	$0.414035\pi$
$18$	0.597333	−	0.871695i	0.597333	−	0.871695i
$19$		0			0		0.693336	−	0.720615i	$-0.256140\pi$
$19$		0			0		−0.693336	+	0.720615i	$0.743860\pi$
$20$		0			0
$21$		0			0
$22$	1.99598	−	0.265574i	1.99598	−	0.265574i
$23$	−0.346769	−	0.958215i	−0.346769	−	0.958215i	−0.982493	−	0.186298i	$-0.940351\pi$
$23$	−0.346769	−	0.958215i	−0.346769	−	0.958215i	0.635724	−	0.771917i	$-0.280702\pi$
$24$		0			0
$25$	−0.256156	−	0.966635i	−0.256156	−	0.966635i
$26$		0			0
$27$		0			0
$28$	−0.115802	−	0.0141107i	−0.115802	−	0.0141107i
$29$	−1.47171	+	1.28171i	−1.47171	+	1.28171i	−0.592235	+	0.805765i	$0.701754\pi$
$29$	−1.47171	+	1.28171i	−1.47171	+	1.28171i	−0.879474	+	0.475947i	$0.842105\pi$
$30$		0			0
$31$		0			0		0.986361	−	0.164595i	$-0.0526316\pi$
$31$		0			0		−0.986361	+	0.164595i	$0.947368\pi$
$32$	0.231817	+	0.0127897i	0.231817	+	0.0127897i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	−0.111530	−	0.0342101i	−0.111530	−	0.0342101i
$37$	0.264802	−	0.246477i	0.264802	−	0.246477i	−0.537687	−	0.843145i	$-0.680702\pi$
$37$	0.264802	−	0.246477i	0.264802	−	0.246477i	0.802489	+	0.596667i	$0.203509\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		0.0275543	−	0.999620i	$-0.491228\pi$
$41$		0			0		−0.0275543	+	0.999620i	$0.508772\pi$
$42$		0			0
$43$	1.11222	+	1.66207i	1.11222	+	1.66207i	0.565270	+	0.824906i	$0.308772\pi$
$43$	1.11222	+	1.66207i	1.11222	+	1.66207i	0.546948	+	0.837166i	$0.315789\pi$
$44$	−0.0937595	−	0.201551i	−0.0937595	−	0.201551i
$45$		0			0
$46$	−0.857010	+	0.651997i	−0.857010	+	0.651997i
$47$		0			0		−0.635724	−	0.771917i	$-0.719298\pi$
$47$		0			0		0.635724	+	0.771917i	$0.280702\pi$
$48$		0			0
$49$	0.115485	+	0.993309i	0.115485	+	0.993309i
$50$	−0.894086	+	0.563266i	−0.894086	+	0.563266i
$51$		0			0
$52$		0			0
$53$	0.632414	+	1.87576i	0.632414	+	1.87576i	0.451533	+	0.892254i	$0.350877\pi$
$53$	0.632414	+	1.87576i	0.632414	+	1.87576i	0.180881	+	0.983505i	$0.442105\pi$
$54$		0			0
$55$		0			0
$56$	−0.168842	−	0.918048i	−0.168842	−	0.918048i
$57$		0			0
$58$	1.75690	+	1.07996i	1.75690	+	1.07996i
$59$		0			0		0.401695	−	0.915773i	$-0.368421\pi$
$59$		0			0		−0.401695	+	0.915773i	$0.631579\pi$
$60$		0			0
$61$		0			0		0.509516	−	0.860461i	$-0.329825\pi$
$61$		0			0		−0.509516	+	0.860461i	$0.670175\pi$
$62$		0			0
$63$	−0.0605901	+	0.998163i	−0.0605901	+	0.998163i
$64$	0.210555	+	0.831465i	0.210555	+	0.831465i
$65$		0			0
$66$		0			0
$67$	0.394576	−	0.448056i	0.394576	−	0.448056i	−0.518970	−	0.854793i	$-0.673684\pi$
$67$	0.394576	−	0.448056i	0.394576	−	0.448056i	0.913545	+	0.406737i	$0.133333\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	1.65521	−	0.351826i	1.65521	−	0.351826i	0.716783	−	0.697297i	$-0.245614\pi$
$71$	1.65521	−	0.351826i	1.65521	−	0.351826i	0.938430	+	0.345471i	$0.112281\pi$
$72$	−0.00514472	−	0.933431i	−0.00514472	−	0.933431i
$73$		0			0		−0.224056	−	0.974576i	$-0.571930\pi$
$73$		0			0		0.224056	+	0.974576i	$0.428070\pi$
$74$	−0.332113	−	0.189313i	−0.332113	−	0.189313i
$75$		0			0
$76$		0			0
$77$	−1.49071	+	1.18688i	−1.49071	+	1.18688i
$78$		0			0
$79$	−0.0181016	−	0.142029i	−0.0181016	−	0.142029i	0.980380	−	0.197117i	$-0.0631579\pi$
$79$	−0.0181016	−	0.142029i	−0.0181016	−	0.142029i	−0.998482	+	0.0550878i	$0.982456\pi$
$80$		0			0
$81$	−0.234785	+	0.972047i	−0.234785	+	0.972047i
$82$		0			0
$83$		0			0		0.930586	−	0.366074i	$-0.119298\pi$
$83$		0			0		−0.930586	+	0.366074i	$0.880702\pi$
$84$		0			0
$85$		0			0
$86$	1.32542	−	1.64601i	1.32542	−	1.64601i
$87$		0			0
$88$	1.31523	−	1.19743i	1.31523	−	1.19743i
$89$		0			0		−0.782322	−	0.622874i	$-0.785965\pi$
$89$		0			0		0.782322	+	0.622874i	$0.214035\pi$
$90$		0			0
$91$		0			0
$92$	0.0969394	+	0.0688108i	0.0969394	+	0.0688108i
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$		0			0		−0.999757	−	0.0220445i	$-0.992982\pi$
$97$		0			0		0.999757	+	0.0220445i	$0.00701754\pi$
$98$	0.965362	−	0.429807i	0.965362	−	0.429807i
$99$	−1.67583	+	0.906913i	−1.67583	+	0.906913i
$100$	0.0888122	+	0.0756414i	0.0888122	+	0.0756414i
$101$		0			0		−0.329907	−	0.944013i	$-0.607018\pi$
$101$		0			0		0.329907	+	0.944013i	$0.392982\pi$
$102$		0			0
$103$		0			0		0.669131	−	0.743145i	$-0.266667\pi$
$103$		0			0		−0.669131	+	0.743145i	$0.733333\pi$
$104$		0			0
$105$		0			0
$106$	1.69228	−	1.22952i	1.69228	−	1.22952i
$107$	−0.149582	−	0.399515i	−0.149582	−	0.399515i	0.840168	−	0.542326i	$-0.182456\pi$
$107$	−0.149582	−	0.399515i	−0.149582	−	0.399515i	−0.989750	+	0.142811i	$0.954386\pi$
$108$		0			0
$109$	−0.490424	−	0.849438i	−0.490424	−	0.849438i	0.509516	−	0.860461i	$-0.329825\pi$
$109$	−0.490424	−	0.849438i	−0.490424	−	0.849438i	−0.999939	+	0.0110229i	$0.996491\pi$
$110$		0			0
$111$		0			0
$112$	−0.975831	+	0.514268i	−0.975831	+	0.514268i
$113$	0.466452	−	0.259119i	0.466452	−	0.259119i	−0.234785	−	0.972047i	$-0.575439\pi$
$113$	0.466452	−	0.259119i	0.466452	−	0.259119i	0.701237	+	0.712928i	$0.252632\pi$
$114$		0			0
$115$		0			0
$116$	0.0558897	−	0.220703i	0.0558897	−	0.220703i
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−2.47878	−	0.881627i	−2.47878	−	0.881627i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		0			0
$126$	1.02580	−	0.253760i	1.02580	−	0.253760i
$127$	1.19407	−	1.51681i	1.19407	−	1.51681i	0.391577	−	0.920146i	$-0.371930\pi$
$127$	1.19407	−	1.51681i	1.19407	−	1.51681i	0.802489	−	0.596667i	$-0.203509\pi$
$128$	0.969936	−	0.596218i	0.969936	−	0.596218i
$129$		0			0
$130$		0			0
$131$		0			0		−0.0825793	−	0.996584i	$-0.526316\pi$
$131$		0			0		0.0825793	+	0.996584i	$0.473684\pi$
$132$		0			0
$133$		0			0
$134$	−0.576350	−	0.256608i	−0.576350	−	0.256608i
$135$		0			0
$136$		0			0
$137$	−0.210953	+	0.796054i	−0.210953	+	0.796054i	0.775409	+	0.631460i	$0.217544\pi$
$137$	−0.210953	+	0.796054i	−0.210953	+	0.796054i	−0.986361	+	0.164595i	$0.947368\pi$
$138$		0			0
$139$		0			0		−0.989750	−	0.142811i	$-0.954386\pi$
$139$		0			0		0.989750	+	0.142811i	$0.0456140\pi$
$140$		0			0
$141$		0			0
$142$	−0.876962	−	1.55836i	−0.876962	−	1.55836i
$143$		0			0
$144$	−1.05093	+	0.335074i	−1.05093	+	0.335074i
$145$		0			0
$146$		0			0
$147$		0			0
$148$	−0.00900179	+	0.0412313i	−0.00900179	+	0.0412313i
$149$	−0.432665	+	1.19557i	−0.432665	+	1.19557i	0.509516	+	0.860461i	$0.329825\pi$
$149$	−0.432665	+	1.19557i	−0.432665	+	1.19557i	−0.942181	+	0.335105i	$0.891228\pi$
$150$		0			0
$151$	−1.72145	+	0.612268i	−1.72145	+	0.612268i	−0.997024	−	0.0770854i	$-0.975439\pi$
$151$	−1.72145	+	0.612268i	−1.72145	+	0.612268i	−0.724425	+	0.689353i	$0.757895\pi$
$152$		0			0
$153$		0			0
$154$	1.66725	+	1.12904i	1.66725	+	1.12904i
$155$		0			0
$156$		0			0
$157$		0			0		−0.968033	−	0.250825i	$-0.919298\pi$
$157$		0			0		0.968033	+	0.250825i	$0.0807018\pi$
$158$	−0.137532	+	0.0630588i	−0.137532	+	0.0630588i
$159$		0			0
$160$		0			0
$161$	0.378262	−	0.946226i	0.378262	−	0.946226i
$162$	1.05441	−	0.0698393i	1.05441	−	0.0698393i
$163$	1.49038	−	1.32714i	1.49038	−	1.32714i	0.701237	−	0.712928i	$-0.252632\pi$
$163$	1.49038	−	1.32714i	1.49038	−	1.32714i	0.789141	−	0.614213i	$-0.210526\pi$
$164$		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
$169$	−0.644194	−	0.764862i	−0.644194	−	0.764862i
$170$		0			0
$171$		0			0
$172$	−0.217109	−	0.0854062i	−0.217109	−	0.0854062i
$173$		0			0		−0.583317	−	0.812244i	$-0.698246\pi$
$173$		0			0		0.583317	+	0.812244i	$0.301754\pi$
$174$		0			0
$175$	0.451533	−	0.892254i	0.451533	−	0.892254i
$176$	−1.81444	−	1.06094i	−1.81444	−	1.06094i
$177$		0			0
$178$		0			0
$179$	0.890178	−	1.46621i	0.890178	−	1.46621i	0.00551154	−	0.999985i	$-0.498246\pi$
$179$	0.890178	−	1.46621i	0.890178	−	1.46621i	0.884667	−	0.466224i	$-0.154386\pi$
$180$		0			0
$181$		0			0		0.945817	−	0.324699i	$-0.105263\pi$
$181$		0			0		−0.945817	+	0.324699i	$0.894737\pi$
$182$		0			0
$183$		0			0
$184$	−0.293940	+	0.904654i	−0.293940	+	0.904654i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−0.971899	−	1.03268i	−0.971899	−	1.03268i	−0.999453	−	0.0330634i	$-0.989474\pi$
$191$	−0.971899	−	1.03268i	−0.971899	−	1.03268i	0.0275543	−	0.999620i	$-0.491228\pi$
$192$		0			0
$193$	1.53045	+	0.325308i	1.53045	+	0.325308i	0.894729	−	0.446609i	$-0.147368\pi$
$193$	1.53045	+	0.325308i	1.53045	+	0.325308i	0.635724	+	0.771917i	$0.280702\pi$
$194$		0			0
$195$		0			0
$196$	−0.0770995	−	0.0875494i	−0.0770995	−	0.0875494i
$197$	−0.517585	−	1.21625i	−0.517585	−	1.21625i	−0.949339	−	0.314254i	$-0.898246\pi$
$197$	−0.517585	−	1.21625i	−0.517585	−	1.21625i	0.431754	−	0.901991i	$-0.357895\pi$
$198$	1.44329	+	1.40406i	1.44329	+	1.40406i
$199$		0			0		0.949339	−	0.314254i	$-0.101754\pi$
$199$		0			0		−0.949339	+	0.314254i	$0.898246\pi$
$200$	−0.365515	+	0.858905i	−0.365515	+	0.858905i
$201$		0			0
$202$		0			0
$203$	−1.95147	−	0.0215122i	−1.95147	−	0.0215122i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	0.538416	−	0.865178i	0.538416	−	0.865178i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	1.56386	+	1.18975i	1.56386	+	1.18975i	0.894729	+	0.446609i	$0.147368\pi$
$211$	1.56386	+	1.18975i	1.56386	+	1.18975i	0.669131	+	0.743145i	$0.266667\pi$
$212$	−0.185315	−	0.137786i	−0.185315	−	0.137786i
$213$		0			0
$214$	−0.355742	+	0.276885i	−0.355742	+	0.276885i
$215$		0			0
$216$		0			0
$217$		0			0
$218$	−0.701990	+	0.762564i	−0.701990	+	0.762564i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.644194	−	0.764862i	$-0.277193\pi$
$223$		0			0		−0.644194	+	0.764862i	$0.722807\pi$
$224$	0.164621	+	0.163716i	0.164621	+	0.163716i
$225$	0.601081	−	0.799188i	0.601081	−	0.799188i
$226$	−0.408472	−	0.388697i	−0.408472	−	0.388697i
$227$		0			0		0.0715891	−	0.997434i	$-0.477193\pi$
$227$		0			0		−0.0715891	+	0.997434i	$0.522807\pi$
$228$		0			0
$229$		0			0		−0.202517	−	0.979279i	$-0.564912\pi$
$229$		0			0		0.202517	+	0.979279i	$0.435088\pi$
$230$		0			0
$231$		0			0
$232$	1.81894	−	0.100354i	1.81894	−	0.100354i
$233$	−0.0533211	+	0.0836125i	−0.0533211	+	0.0836125i	−0.868768	−	0.495219i	$-0.835088\pi$
$233$	−0.0533211	+	0.0836125i	−0.0533211	+	0.0836125i	0.815447	+	0.578832i	$0.196491\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	0.213237	−	0.318656i	0.213237	−	0.318656i	−0.709053	−	0.705155i	$-0.750877\pi$
$239$	0.213237	−	0.318656i	0.213237	−	0.318656i	0.922290	+	0.386499i	$0.126316\pi$
$240$		0			0
$241$		0			0		0.828009	−	0.560715i	$-0.189474\pi$
$241$		0			0		−0.828009	+	0.560715i	$0.810526\pi$
$242$	−0.107233	+	2.77805i	−0.107233	+	2.77805i
$243$		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		−0.917973	−	0.396642i	$-0.870175\pi$
$251$		0			0		0.917973	+	0.396642i	$0.129825\pi$
$252$	−0.0605423	−	0.0997189i	−0.0605423	−	0.0997189i
$253$	1.91163	−	0.340695i	1.91163	−	0.340695i
$254$	−1.90643	−	0.725788i	−1.90643	−	0.725788i
$255$		0			0
$256$	−0.260467	−	0.226841i	−0.260467	−	0.226841i
$257$		0			0		−0.0495838	−	0.998770i	$-0.515789\pi$
$257$		0			0		0.0495838	+	0.998770i	$0.484211\pi$
$258$		0			0
$259$	0.361673	−	0.00797483i	0.361673	−	0.00797483i
$260$		0			0
$261$	−1.91743	−	0.363579i	−1.91743	−	0.363579i
$262$		0			0
$263$	−0.00952277	+	0.0316671i	−0.00952277	+	0.0316671i	−0.962268	−	0.272103i	$-0.912281\pi$
$263$	−0.00952277	+	0.0316671i	−0.00952277	+	0.0316671i	0.952745	+	0.303771i	$0.0982456\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	−0.00804335	+	0.0691827i	−0.00804335	+	0.0691827i
$269$		0			0		−0.601081	−	0.799188i	$-0.705263\pi$
$269$		0			0		0.601081	+	0.799188i	$0.294737\pi$
$270$		0			0
$271$		0			0		−0.401695	−	0.915773i	$-0.631579\pi$
$271$		0			0		0.401695	+	0.915773i	$0.368421\pi$
$272$		0			0
$273$		0			0
$274$	0.869396	−	0.0383587i	0.869396	−	0.0383587i
$275$	1.89809	−	0.167818i	1.89809	−	0.167818i
$276$		0			0
$277$	−1.65511	−	0.0547535i	−1.65511	−	0.0547535i	−0.809017	−	0.587785i	$-0.800000\pi$
$277$	−1.65511	−	0.0547535i	−1.65511	−	0.0547535i	−0.846095	+	0.533032i	$0.821053\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	1.48757	−	0.566326i	1.48757	−	0.566326i	0.528360	−	0.849020i	$-0.322807\pi$
$281$	1.48757	−	0.566326i	1.48757	−	0.566326i	0.959210	+	0.282694i	$0.0912281\pi$
$282$		0			0
$283$		0			0		−0.574329	−	0.818625i	$-0.694737\pi$
$283$		0			0		0.574329	+	0.818625i	$0.305263\pi$
$284$	−0.135294	+	0.143756i	−0.135294	+	0.143756i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.133342	+	0.190060i	0.133342	+	0.190060i
$289$	−0.857640	+	0.514250i	−0.857640	+	0.514250i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		−0.159156	−	0.987253i	$-0.550877\pi$
$293$		0			0		0.159156	+	0.987253i	$0.449123\pi$
$294$		0			0
$295$		0			0
$296$	−0.336372	+	0.0297401i	−0.336372	+	0.0297401i
$297$		0			0
$298$	1.34226	+	0.0592220i	1.34226	+	0.0592220i
$299$		0			0
$300$		0			0
$301$	−0.274690	+	1.98092i	−0.274690	+	1.98092i
$302$	1.16052	+	1.54301i	1.16052	+	1.54301i
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		0.959210	−	0.282694i	$-0.0912281\pi$
$307$		0			0		−0.959210	+	0.282694i	$0.908772\pi$
$308$	0.0640148	−	0.212875i	0.0640148	−	0.212875i
$309$		0			0
$310$		0			0
$311$		0			0		−0.884667	−	0.466224i	$-0.845614\pi$
$311$		0			0		0.884667	+	0.466224i	$0.154386\pi$
$312$		0			0
$313$		0			0		0.904357	−	0.426776i	$-0.140351\pi$
$313$		0			0		−0.904357	+	0.426776i	$0.859649\pi$
$314$		0			0
$315$		0			0
$316$	0.0111765	+	0.0124127i	0.0111765	+	0.0124127i
$317$	−0.174875	−	0.0665759i	−0.174875	−	0.0665759i	0.266796	−	0.963753i	$-0.414035\pi$
$317$	−0.174875	−	0.0665759i	−0.174875	−	0.0665759i	−0.441671	+	0.897177i	$0.645614\pi$
$318$		0			0
$319$	−1.92991	−	3.17875i	−1.92991	−	3.17875i
$320$		0			0
$321$		0			0
$322$	−1.07363	−	0.0830080i	−1.07363	−	0.0830080i
$323$		0			0
$324$	−0.0421067	−	0.108795i	−0.0421067	−	0.108795i
$325$		0			0
$326$	−1.80861	−	1.08446i	−1.80861	−	1.08446i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	0.0579930	+	0.551767i	0.0579930	+	0.551767i	0.984487	+	0.175457i	$0.0561404\pi$
$331$	0.0579930	+	0.551767i	0.0579930	+	0.551767i	−0.926494	+	0.376309i	$0.877193\pi$
$332$		0			0
$333$	0.357462	+	0.0556070i	0.357462	+	0.0556070i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−0.0617432	−	0.104271i	−0.0617432	−	0.104271i	0.828009	−	0.560715i	$-0.189474\pi$
$337$	−0.0617432	−	0.104271i	−0.0617432	−	0.104271i	−0.889752	+	0.456444i	$0.849123\pi$
$338$	−0.568185	+	0.890968i	−0.568185	+	0.890968i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−0.574329	+	0.818625i	−0.574329	+	0.818625i
$344$	0.133641	−	1.86199i	0.133641	−	1.86199i
$345$		0			0
$346$		0			0
$347$	−1.11908	−	1.11293i	−1.11908	−	1.11293i	−0.992658	−	0.120958i	$-0.961404\pi$
$347$	−1.11908	−	1.11293i	−1.11908	−	1.11293i	−0.126427	−	0.991976i	$-0.540351\pi$
$348$		0			0
$349$		0			0		−0.565270	−	0.824906i	$-0.691228\pi$
$349$		0			0		0.565270	+	0.824906i	$0.308772\pi$
$350$	−1.04231	−	0.173931i	−1.04231	−	0.173931i
$351$		0			0
$352$	−0.0991218	+	0.431150i	−0.0991218	+	0.431150i
$353$		0			0		0.677282	−	0.735724i	$-0.263158\pi$
$353$		0			0		−0.677282	+	0.735724i	$0.736842\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	−1.75953	−	0.435269i	−1.75953	−	0.435269i
$359$	−1.45894	−	1.08475i	−1.45894	−	1.08475i	−0.978148	−	0.207912i	$-0.933333\pi$
$359$	−1.45894	−	1.08475i	−1.45894	−	1.08475i	−0.480787	−	0.876837i	$-0.659649\pi$
$360$		0			0
$361$	−0.0385714	−	0.999256i	−0.0385714	−	0.999256i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.411766	−	0.911290i	$-0.635088\pi$
$367$		0			0		0.411766	+	0.911290i	$0.364912\pi$
$368$	1.12397	+	0.0123902i	1.12397	+	0.0123902i
$369$		0			0
$370$		0			0
$371$	−0.775126	+	1.82143i	−0.775126	+	1.82143i
$372$		0			0
$373$	−1.43278	−	1.39383i	−1.43278	−	1.39383i	−0.739446	−	0.673216i	$-0.764912\pi$
$373$	−1.43278	−	1.39383i	−1.43278	−	1.39383i	−0.693336	−	0.720615i	$-0.743860\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	0.236264	−	1.14246i	0.236264	−	1.14246i	−0.677282	−	0.735724i	$-0.736842\pi$
$379$	0.236264	−	1.14246i	0.236264	−	1.14246i	0.913545	−	0.406737i	$-0.133333\pi$
$380$		0			0
$381$		0			0
$382$	−0.734920	+	1.30596i	−0.734920	+	1.30596i
$383$		0			0		−0.962268	−	0.272103i	$-0.912281\pi$
$383$		0			0		0.962268	+	0.272103i	$0.0877193\pi$
$384$		0			0
$385$		0			0
$386$	−0.154691	−	1.64614i	−0.154691	−	1.64614i
$387$	−0.617996	+	1.90200i	−0.617996	+	1.90200i
$388$		0			0
$389$	0.207726	+	0.241189i	0.207726	+	0.241189i	0.851919	−	0.523673i	$-0.175439\pi$
$389$	0.207726	+	0.241189i	0.207726	+	0.241189i	−0.644194	+	0.764862i	$0.722807\pi$
$390$		0			0
$391$		0			0
$392$	0.484430	−	0.797902i	0.484430	−	0.797902i
$393$		0			0
$394$	−1.06336	+	0.905665i	−1.06336	+	0.905665i
$395$		0			0
$396$	0.100372	−	0.198341i	0.100372	−	0.198341i
$397$		0			0		−0.537687	−	0.843145i	$-0.680702\pi$
$397$		0			0		0.537687	+	0.843145i	$0.319298\pi$
$398$		0			0
$399$		0			0
$400$	1.09763	+	0.109252i	1.09763	+	0.109252i
$401$	−0.149362	+	1.80254i	−0.149362	+	1.80254i	0.350638	+	0.936511i	$0.385965\pi$
$401$	−0.149362	+	1.80254i	−0.149362	+	1.80254i	−0.500000	+	0.866025i	$0.666667\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$	0.593890	+	1.97492i	0.593890	+	1.97492i
$407$	0.377029	+	0.577086i	0.377029	+	0.577086i
$408$		0			0
$409$		0			0		0.997814	−	0.0660906i	$-0.0210526\pi$
$409$		0			0		−0.997814	+	0.0660906i	$0.978947\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	−1.04241	−	0.270096i	−1.04241	−	0.270096i
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		0.989750	−	0.142811i	$-0.0456140\pi$
$419$		0			0		−0.989750	+	0.142811i	$0.954386\pi$
$420$		0			0
$421$	0.778400	−	0.0861533i	0.778400	−	0.0861533i	0.287976	−	0.957638i	$-0.407018\pi$
$421$	0.778400	−	0.0861533i	0.778400	−	0.0861533i	0.490424	+	0.871484i	$0.336842\pi$
$422$	0.706599	−	1.95252i	0.706599	−	1.95252i
$423$		0			0
$424$	0.609588	−	1.74430i	0.609588	−	1.74430i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	0.0408970	+	0.0283573i	0.0408970	+	0.0283573i
$429$		0			0
$430$		0			0
$431$	1.38072	−	1.40374i	1.38072	−	1.40374i	0.565270	−	0.824906i	$-0.308772\pi$
$431$	1.38072	−	1.40374i	1.38072	−	1.40374i	0.815447	−	0.578832i	$-0.196491\pi$
$432$		0			0
$433$		0			0		0.980380	−	0.197117i	$-0.0631579\pi$
$433$		0			0		−0.980380	+	0.197117i	$0.936842\pi$
$434$		0			0
$435$		0			0
$436$	0.103480	+	0.0488336i	0.103480	+	0.0488336i
$437$		0			0
$438$		0			0
$439$		0			0		0.0165339	−	0.999863i	$-0.494737\pi$
$439$		0			0		−0.0165339	+	0.999863i	$0.505263\pi$
$440$		0			0
$441$	−0.709053	+	0.705155i	−0.709053	+	0.705155i
$442$		0			0
$443$	−1.00907	+	0.620275i	−1.00907	+	0.620275i	−0.926494	−	0.376309i	$-0.877193\pi$
$443$	−1.00907	+	0.620275i	−1.00907	+	0.620275i	−0.0825793	+	0.996584i	$0.526316\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	−0.395697	+	0.760980i	−0.395697	+	0.760980i
$449$	1.62378	+	0.382743i	1.62378	+	0.382743i	0.938430	−	0.345471i	$-0.112281\pi$
$449$	1.62378	+	0.382743i	1.62378	+	0.382743i	0.685350	+	0.728214i	$0.259649\pi$
$450$	−0.995622	−	0.354113i	−0.995622	−	0.354113i
$451$		0			0
$452$	−0.0274931	+	0.0558475i	−0.0274931	+	0.0558475i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	0.883587	+	1.14823i	0.883587	+	1.14823i	0.988116	+	0.153712i	$0.0491228\pi$
$457$	0.883587	+	1.14823i	0.883587	+	1.14823i	−0.104528	+	0.994522i	$0.533333\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$461$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$462$		0			0
$463$	1.24718	+	1.16087i	1.24718	+	1.16087i	0.980380	+	0.197117i	$0.0631579\pi$
$463$	1.24718	+	1.16087i	1.24718	+	1.16087i	0.266796	+	0.963753i	$0.414035\pi$
$464$	−0.754819	−	2.01603i	−0.754819	−	2.01603i
$465$		0			0
$466$	0.101147	+	0.0274011i	0.101147	+	0.0274011i
$467$		0			0		0.889752	−	0.456444i	$-0.150877\pi$
$467$		0			0		−0.889752	+	0.456444i	$0.849123\pi$
$468$		0			0
$469$	0.592646	−	0.0722152i	0.592646	−	0.0722152i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−3.48129	+	1.54997i	−3.48129	+	1.54997i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−1.08268	+	1.65717i	−1.08268	+	1.65717i
$478$	−0.388642	−	0.114539i	−0.388642	−	0.114539i
$479$		0			0		−0.815447	−	0.578832i	$-0.803509\pi$
$479$		0			0		0.815447	+	0.578832i	$0.196491\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	0.296239	−	0.0802525i	0.296239	−	0.0802525i
$485$		0			0
$486$		0			0
$487$	−0.571807	−	0.369100i	−0.571807	−	0.369100i	0.224056	−	0.974576i	$-0.428070\pi$
$487$	−0.571807	−	0.369100i	−0.571807	−	0.369100i	−0.795863	+	0.605477i	$0.792982\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	0.456244	+	0.733136i	0.456244	+	0.733136i	0.993931	−	0.110008i	$-0.0350877\pi$
$491$	0.456244	+	0.733136i	0.456244	+	0.733136i	−0.537687	+	0.843145i	$0.680702\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	1.47012	+	0.838005i	1.47012	+	0.838005i
$498$		0			0
$499$	−0.00957650	−	1.73751i	−0.00957650	−	1.73751i	−0.500000	−	0.866025i	$-0.666667\pi$
$499$	−0.00957650	−	1.73751i	−0.00957650	−	1.73751i	0.490424	−	0.871484i	$-0.336842\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		−0.768401	−	0.639969i	$-0.778947\pi$
$503$		0			0		0.768401	+	0.639969i	$0.221053\pi$
$504$	0.616912	−	0.700528i	0.616912	−	0.700528i
$505$		0			0
$506$	−0.946622	−	1.82049i	−0.946622	−	1.82049i
$507$		0			0
$508$	−0.0136449	+	0.224786i	−0.0136449	+	0.224786i
$509$		0			0		−0.451533	−	0.892254i	$-0.649123\pi$
$509$		0			0		0.451533	+	0.892254i	$0.350877\pi$
$510$		0			0
$511$		0			0
$512$	0.310728	−	0.708388i	0.310728	−	0.708388i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$	−0.122132	−	0.362246i	−0.122132	−	0.362246i
$519$		0			0
$520$		0			0
$521$		0			0		0.846095	−	0.533032i	$-0.178947\pi$
$521$		0			0		−0.846095	+	0.533032i	$0.821053\pi$
$522$	0.238163	+	2.04849i	0.238163	+	2.04849i
$523$		0			0		0.724425	−	0.689353i	$-0.242105\pi$
$523$		0			0		−0.724425	+	0.689353i	$0.757895\pi$
$524$		0			0
$525$		0			0
$526$	0.0349414		0.000385179i	0.0349414		0.000385179i
$527$		0			0
$528$		0			0
$529$	−0.0295259	+	0.0245909i	−0.0295259	+	0.0245909i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	−0.547538	+	0.103823i	−0.547538	+	0.103823i
$537$		0			0
$538$		0			0
$539$	−1.90260	−	0.104969i	−1.90260	−	0.104969i
$540$		0			0
$541$	1.38457	+	1.43904i	1.38457	+	1.43904i	0.731980	+	0.681326i	$0.238596\pi$
$541$	1.38457	+	1.43904i	1.38457	+	1.43904i	0.652586	+	0.757715i	$0.273684\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	0.714638	+	1.45166i	0.714638	+	1.45166i	0.884667	+	0.466224i	$0.154386\pi$
$547$	0.714638	+	1.45166i	0.714638	+	1.45166i	−0.170028	+	0.985439i	$0.554386\pi$
$548$	−0.0326926	−	0.0903384i	−0.0326926	−	0.0903384i
$549$		0			0
$550$	−0.767996	−	1.86136i	−0.767996	−	1.86136i
$551$		0			0
$552$		0			0
$553$	0.0809343	−	0.118108i	0.0809343	−	0.118108i
$554$	0.466879	+	1.68652i	0.466879	+	1.68652i
$555$		0			0
$556$		0			0
$557$	0.660874	−	1.46260i	0.660874	−	1.46260i	−0.213300	−	0.976987i	$-0.568421\pi$
$557$	0.660874	−	1.46260i	0.660874	−	1.46260i	0.874174	−	0.485613i	$-0.161404\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	−1.04041	−	1.32163i	−1.04041	−	1.32163i
$563$		0			0		−0.789141	−	0.614213i	$-0.789474\pi$
$563$		0			0		0.789141	+	0.614213i	$0.210526\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−0.821778	+	0.569808i	−0.821778	+	0.569808i
$568$	−1.42098	−	0.689827i	−1.42098	−	0.689827i
$569$	−0.462942	−	1.48011i	−0.462942	−	1.48011i	−0.834139	−	0.551554i	$-0.814035\pi$
$569$	−0.462942	−	1.48011i	−0.462942	−	1.48011i	0.371197	−	0.928554i	$-0.378947\pi$
$570$		0			0
$571$	0.350638	−	0.936511i	0.350638	−	0.936511i
$571$	0.350638	−	0.936511i	0.350638	−	0.936511i
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−0.837417	+	0.580652i	−0.837417	+	0.580652i
$576$	−0.523078	+	0.679747i	−0.523078	+	0.679747i
$577$		0			0		0.148264	−	0.988948i	$-0.452632\pi$
$577$		0			0		−0.148264	+	0.988948i	$0.547368\pi$
$578$	0.789182	+	0.702745i	0.789182	+	0.702745i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−3.72709	+	0.579789i	−3.72709	+	0.579789i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		0.350638	−	0.936511i	$-0.385965\pi$
$587$		0			0		−0.350638	+	0.936511i	$0.614035\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	0.152198	+	0.368875i	0.152198	+	0.368875i
$593$		0			0		0.991264	−	0.131892i	$-0.0421053\pi$
$593$		0			0		−0.991264	+	0.131892i	$0.957895\pi$
$594$		0			0
$595$		0			0
$596$	−0.0379944	−	0.143377i	−0.0379944	−	0.143377i
$597$		0			0
$598$		0			0
$599$	−1.86308	−	0.227020i	−1.86308	−	0.227020i	−0.889752	−	0.456444i	$-0.849123\pi$
$599$	−1.86308	−	0.227020i	−1.86308	−	0.227020i	−0.973327	+	0.229424i	$0.926316\pi$
$600$		0			0
$601$		0			0		−0.693336	−	0.720615i	$-0.743860\pi$
$601$		0			0		0.693336	+	0.720615i	$0.256140\pi$
$602$	2.08449	−	0.347840i	2.08449	−	0.347840i
$603$	0.596123	+	0.0328890i	0.596123	+	0.0328890i
$604$	0.124332	−	0.173127i	0.124332	−	0.173127i
$605$		0			0
$606$		0			0
$607$		0			0		−0.956036	−	0.293250i	$-0.905263\pi$
$607$		0			0		0.956036	+	0.293250i	$0.0947368\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−1.00290	+	0.835269i	−1.00290	+	0.835269i	−0.986361	−	0.164595i	$-0.947368\pi$
$613$	−1.00290	+	0.835269i	−1.00290	+	0.835269i	−0.0165339	+	0.999863i	$0.505263\pi$
$614$		0			0
$615$		0			0
$616$	1.77856	−	0.0196061i	1.77856	−	0.0196061i
$617$	0.407730	−	0.310193i	0.407730	−	0.310193i	−0.381410	−	0.924406i	$-0.624561\pi$
$617$	0.407730	−	0.310193i	0.407730	−	0.310193i	0.789141	+	0.614213i	$0.210526\pi$
$618$		0			0
$619$		0			0		0.724425	−	0.689353i	$-0.242105\pi$
$619$		0			0		−0.724425	+	0.689353i	$0.757895\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.868768	+	0.495219i	−0.868768	+	0.495219i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	−0.194736	+	0.355150i	−0.194736	+	0.355150i	−0.956036	−	0.293250i	$-0.905263\pi$
$631$	−0.194736	+	0.355150i	−0.194736	+	0.355150i	0.761300	+	0.648400i	$0.224561\pi$
$632$	−0.0680962	+	0.115000i	−0.0680962	+	0.115000i
$633$		0			0
$634$	−0.0119806	+	0.197369i	−0.0119806	+	0.197369i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	−2.59711	+	2.94912i	−2.59711	+	2.94912i
$639$	1.30028	+	1.08295i	1.30028	+	1.08295i
$640$		0			0
$641$	−0.872930	−	1.63449i	−0.872930	−	1.63449i	−0.768401	−	0.639969i	$-0.778947\pi$
$641$	−0.872930	−	1.63449i	−0.872930	−	1.63449i	−0.104528	−	0.994522i	$-0.533333\pi$
$642$		0			0
$643$		0			0		−0.00551154	−	0.999985i	$-0.501754\pi$
$643$		0			0		0.00551154	+	0.999985i	$0.498246\pi$
$644$	0.0266355	+	0.115856i	0.0266355	+	0.115856i
$645$		0			0
$646$		0			0
$647$		0			0		0.159156	−	0.987253i	$-0.449123\pi$
$647$		0			0		−0.159156	+	0.987253i	$0.550877\pi$
$648$	0.730255	−	0.581419i	0.730255	−	0.581419i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−0.0546596	+	0.226300i	−0.0546596	+	0.226300i
$653$	0.694641	−	0.196426i	0.694641	−	0.196426i	0.0935596	−	0.995614i	$-0.470175\pi$
$653$	0.694641	−	0.196426i	0.694641	−	0.196426i	0.601081	+	0.799188i	$0.294737\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$	1.28481	−	1.16974i	1.28481	−	1.16974i	0.309017	−	0.951057i	$-0.400000\pi$
$659$	1.28481	−	1.16974i	1.28481	−	1.16974i	0.975796	−	0.218681i	$-0.0701754\pi$
$660$		0			0
$661$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$661$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$662$	0.538185	−	0.232541i	0.538185	−	0.232541i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	−0.0566783	−	0.378055i	−0.0566783	−	0.378055i
$667$	1.73850	+	0.965755i	1.73850	+	0.965755i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−1.42304	+	0.173401i	−1.42304	+	0.173401i	−0.795863	−	0.605477i	$-0.792982\pi$
$673$	−1.42304	+	0.173401i	−1.42304	+	0.173401i	−0.627176	+	0.778877i	$0.715789\pi$
$674$	−0.0856846	+	0.0951624i	−0.0856846	+	0.0951624i
$675$		0			0
$676$	0.112600	+	0.0305039i	0.112600	+	0.0305039i
$677$		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
$683$	0.243024	−	0.128075i	0.243024	−	0.128075i	−0.340293	−	0.940319i	$-0.610526\pi$
$683$	0.243024	−	0.128075i	0.243024	−	0.128075i	0.583317	+	0.812244i	$0.301754\pi$
$684$		0			0
$685$		0			0
$686$	1.00679	+	0.321001i	1.00679	+	0.321001i
$687$		0			0
$688$	−2.14712	+	0.506101i	−2.14712	+	0.506101i
$689$		0			0
$690$		0			0
$691$		0			0		−0.980380	−	0.197117i	$-0.936842\pi$
$691$		0			0		0.980380	+	0.197117i	$0.0631579\pi$
$692$		0			0
$693$	−1.85466	−	0.437165i	−1.85466	−	0.437165i
$694$	−0.769426	+	1.47971i	−0.769426	+	1.47971i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	0.0160235	+	0.115553i	0.0160235	+	0.115553i
$701$	−1.09961	+	1.09357i	−1.09961	+	1.09357i	−0.104528	+	0.994522i	$0.533333\pi$
$701$	−1.09961	+	1.09357i	−1.09961	+	1.09357i	−0.995083	+	0.0990455i	$0.968421\pi$
$702$		0			0
$703$		0			0
$704$	−1.62950	+	0.125985i	−1.62950	+	0.125985i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	1.93746	−	0.389549i	1.93746	−	0.389549i	0.938430	−	0.345471i	$-0.112281\pi$
$709$	1.93746	−	0.389549i	1.93746	−	0.389549i	0.999028	−	0.0440782i	$-0.0140351\pi$
$710$		0			0
$711$	0.100402	−	0.102076i	0.100402	−	0.102076i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	0.0121242	+	0.199735i	0.0121242	+	0.199735i
$717$		0			0
$718$	−0.633796	+	1.81357i	−0.633796	+	1.81357i
$719$		0			0		0.213300	−	0.976987i	$-0.431579\pi$
$719$		0			0		−0.213300	+	0.976987i	$0.568421\pi$
$720$		0			0
$721$		0			0
$722$	−0.995622	+	0.354113i	−0.995622	+	0.354113i
$723$		0			0
$724$		0			0
$725$	1.61594	+	1.09429i	1.61594	+	1.09429i
$726$		0			0
$727$		0			0		0.277403	−	0.960754i	$-0.410526\pi$
$727$		0			0		−0.277403	+	0.960754i	$0.589474\pi$
$728$		0			0
$729$	−0.909007	+	0.416782i	−0.909007	+	0.416782i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		0.997814	−	0.0660906i	$-0.0210526\pi$
$733$		0			0		−0.997814	+	0.0660906i	$0.978947\pi$
$734$		0			0
$735$		0			0
$736$	−0.0681319	−	0.226566i	−0.0681319	−	0.226566i
$737$	0.713497	+	0.886077i	0.713497	+	0.886077i
$738$		0			0
$739$	−0.402385	+	1.45355i	−0.402385	+	1.45355i	0.431754	+	0.901991i	$0.357895\pi$
$739$	−0.402385	+	1.45355i	−0.402385	+	1.45355i	−0.834139	+	0.551554i	$0.814035\pi$
$740$		0			0
$741$		0			0
$742$	2.08149	+	0.207181i	2.08149	+	0.207181i
$743$	1.71654	+	0.675252i	1.71654	+	0.675252i	0.999757	−	0.0220445i	$-0.00701754\pi$
$743$	1.71654	+	0.675252i	1.71654	+	0.675252i	0.716783	+	0.697297i	$0.245614\pi$
$744$		0			0
$745$		0			0
$746$	−0.953768	+	1.88470i	−0.953768	+	1.88470i
$747$		0			0
$748$		0			0
$749$	0.153976	−	0.397842i	0.153976	−	0.397842i
$750$		0			0
$751$	1.54253	−	1.09494i	1.54253	−	1.09494i	0.583317	−	0.812244i	$-0.301754\pi$
$751$	1.54253	−	1.09494i	1.54253	−	1.09494i	0.959210	−	0.282694i	$-0.0912281\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	0.0189918	+	1.14850i	0.0189918	+	1.14850i	0.828009	+	0.560715i	$0.189474\pi$
$757$	0.0189918	+	1.14850i	0.0189918	+	1.14850i	−0.809017	+	0.587785i	$0.800000\pi$
$758$	−1.22675	+	0.122104i	−1.22675	+	0.122104i
$759$		0			0
$760$		0			0
$761$		0			0		0.899598	−	0.436719i	$-0.143860\pi$
$761$		0			0		−0.899598	+	0.436719i	$0.856140\pi$
$762$		0			0
$763$	0.198639	−	0.960523i	0.198639	−	0.960523i
$764$	0.161819	+	0.0343957i	0.161819	+	0.0343957i
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$		0			0		−0.716783	−	0.697297i	$-0.754386\pi$
$769$		0			0		0.716783	+	0.697297i	$0.245614\pi$
$770$		0			0
$771$		0			0
$772$	−0.168345	+	0.0705474i	−0.168345	+	0.0705474i
$773$		0			0		0.802489	−	0.596667i	$-0.203509\pi$
$773$		0			0		−0.802489	+	0.596667i	$0.796491\pi$
$774$	2.11318	+	0.0232949i	2.11318	+	0.0232949i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	0.177723	−	0.285582i	0.177723	−	0.285582i
$779$		0			0
$780$		0			0
$781$	0.124372	+	3.22205i	0.124372	+	3.22205i
$782$		0			0
$783$		0			0
$784$	−1.07077	−	0.264885i	−1.07077	−	0.264885i
$785$		0			0
$786$		0			0
$787$		0			0		0.431754	−	0.901991i	$-0.357895\pi$
$787$		0			0		−0.431754	+	0.901991i	$0.642105\pi$
$788$	0.130467	+	0.0821929i	0.130467	+	0.0821929i
$789$		0			0
$790$		0			0
$791$	0.520677	+	0.116686i	0.520677	+	0.116686i
$792$	1.75441	+	0.292760i	1.75441	+	0.292760i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.724425	−	0.689353i	$-0.757895\pi$
$797$		0			0		0.724425	+	0.689353i	$0.242105\pi$
$798$		0			0
$799$		0			0
$800$	−0.0470185	−	0.227359i	−0.0470185	−	0.227359i
$801$		0			0
$802$	1.86505	−	0.417966i	1.86505	−	0.417966i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−1.09907	−	0.170972i	−1.09907	−	0.170972i	−0.421786	−	0.906696i	$-0.638596\pi$
$809$	−1.09907	−	0.170972i	−1.09907	−	0.170972i	−0.677282	+	0.735724i	$0.736842\pi$
$810$		0			0
$811$		0			0		−0.104528	−	0.994522i	$-0.533333\pi$
$811$		0			0		0.104528	+	0.994522i	$0.466667\pi$
$812$	0.188513	−	0.127658i	0.188513	−	0.127658i
$813$		0			0
$814$	0.463081	−	0.562289i	0.463081	−	0.562289i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−0.156083	+	1.66096i	−0.156083	+	1.66096i	0.471093	+	0.882084i	$0.343860\pi$
$821$	−0.156083	+	1.66096i	−0.156083	+	1.66096i	−0.627176	+	0.778877i	$0.715789\pi$
$822$		0			0
$823$	−1.02184	−	1.68306i	−1.02184	−	1.68306i	−0.660898	−	0.750475i	$-0.729825\pi$
$823$	−1.02184	−	1.68306i	−1.02184	−	1.68306i	−0.360939	−	0.932589i	$-0.617544\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	0.481846	+	0.419640i	0.481846	+	0.419640i	0.863256	−	0.504766i	$-0.168421\pi$
$827$	0.481846	+	0.419640i	0.481846	+	0.419640i	−0.381410	+	0.924406i	$0.624561\pi$
$828$	0.00589446	+	0.118733i	0.00589446	+	0.118733i
$829$		0			0		0.904357	−	0.426776i	$-0.140351\pi$
$829$		0			0		−0.904357	+	0.426776i	$0.859649\pi$
$830$		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		0.115485	−	0.993309i	$-0.463158\pi$
$839$		0			0		−0.115485	+	0.993309i	$0.536842\pi$
$840$		0			0
$841$	0.385787	−	2.78209i	0.385787	−	2.78209i
$842$	−0.332433	−	0.757870i	−0.332433	−	0.757870i
$843$		0			0
$844$	−0.229010	−	0.0101042i	−0.229010	−	0.0101042i
$845$		0			0
$846$		0			0
$847$	−1.26490	−	2.30687i	−1.26490	−	2.30687i
$848$	−2.18229	−	0.0721934i	−2.18229	−	0.0721934i
$849$		0			0
$850$		0			0
$851$	−0.328003	−	0.168266i	−0.328003	−	0.168266i
$852$		0			0
$853$		0			0		0.857640	−	0.514250i	$-0.171930\pi$
$853$		0			0		−0.857640	+	0.514250i	$0.828070\pi$
$854$		0			0
$855$		0			0
$856$	−0.118871	+	0.380051i	−0.118871	+	0.380051i
$857$		0			0		0.298515	−	0.954405i	$-0.403509\pi$
$857$		0			0		−0.298515	+	0.954405i	$0.596491\pi$
$858$		0			0
$859$		0			0		−0.574329	−	0.818625i	$-0.694737\pi$
$859$		0			0		0.574329	+	0.818625i	$0.305263\pi$
$860$		0			0
$861$		0			0
$862$	−1.85127	−	0.949703i	−1.85127	−	0.949703i
$863$	0.186971	+	0.170225i	0.186971	+	0.170225i	0.761300	−	0.648400i	$-0.224561\pi$
$863$	0.186971	+	0.170225i	0.186971	+	0.170225i	−0.574329	+	0.818625i	$0.694737\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		0			0
$868$		0			0
$869$	0.272559	+	0.0120256i	0.272559	+	0.0120256i
$870$		0			0
$871$		0			0
$872$	−0.125756	+	0.906889i	−0.125756	+	0.906889i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−0.156210	−	0.0536269i	−0.156210	−	0.0536269i	0.245485	−	0.969400i	$-0.421053\pi$
$877$	−0.156210	−	0.0536269i	−0.156210	−	0.0536269i	−0.401695	+	0.915773i	$0.631579\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		0			0		−0.982493	−	0.186298i	$-0.940351\pi$
$881$		0			0		0.982493	+	0.186298i	$0.0596491\pi$
$882$	0.934846	+	0.492669i	0.934846	+	0.492669i
$883$	−0.209006	+	0.00460855i	−0.209006	+	0.00460855i	−0.126427	−	0.991976i	$-0.540351\pi$
$883$	−0.209006	+	0.00460855i	−0.209006	+	0.00460855i	−0.0825793	+	0.996584i	$0.526316\pi$
$884$		0			0
$885$		0			0
$886$	0.943881	+	0.822027i	0.943881	+	0.822027i
$887$		0			0		−0.669131	−	0.743145i	$-0.733333\pi$
$887$		0			0		0.669131	+	0.743145i	$0.266667\pi$
$888$		0			0
$889$	1.90047	−	0.338706i	1.90047	−	0.338706i
$890$		0			0
$891$	−1.74919	−	0.755798i	−1.74919	−	0.755798i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	1.12087	+	0.199763i	1.12087	+	0.199763i
$897$		0			0
$898$	−0.126205	−	1.75838i	−0.126205	−	1.75838i
$899$		0			0
$900$	−0.00449969	+	0.116572i	−0.00449969	+	0.116572i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	−0.492159	−	0.0765606i	−0.492159	−	0.0765606i
$905$		0			0
$906$		0			0
$907$	−0.0550786	+	0.00182208i	−0.0550786	+	0.00182208i	−0.0605901	−	0.998163i	$-0.519298\pi$
$907$	−0.0550786	+	0.00182208i	−0.0550786	+	0.00182208i	0.00551154	+	0.999985i	$0.498246\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−1.77401	+	0.397565i	−1.77401	+	0.397565i	−0.978148	−	0.207912i	$-0.933333\pi$
$911$	−1.77401	+	0.397565i	−1.77401	+	0.397565i	−0.795863	+	0.605477i	$0.792982\pi$
$912$		0			0
$913$		0			0
$914$	0.879315	−	1.25334i	0.879315	−	1.25334i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−0.774426	+	0.919489i	−0.774426	+	0.919489i	−0.998482	−	0.0550878i	$-0.982456\pi$
$919$	−0.774426	+	0.919489i	−0.774426	+	0.919489i	0.224056	+	0.974576i	$0.428070\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−0.306084	−	0.192830i	−0.306084	−	0.192830i
$926$	0.777366	−	1.62402i	0.777366	−	1.62402i
$927$		0			0
$928$	−0.357561	+	0.278301i	−0.357561	+	0.278301i
$929$		0			0		−0.970739	−	0.240139i	$-0.922807\pi$
$929$		0			0		0.970739	+	0.240139i	$0.0771930\pi$
$930$		0			0
$931$		0			0
$932$	−0.000446223	−	0.0115601i	−0.000446223	−	0.0115601i
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		−0.775409	−	0.631460i	$-0.782456\pi$
$937$		0			0		0.775409	+	0.631460i	$0.217544\pi$
$938$	−0.259780	−	0.574927i	−0.259780	−	0.574927i
$939$		0			0
$940$		0			0
$941$		0			0		0.922290	−	0.386499i	$-0.126316\pi$
$941$		0			0		−0.922290	+	0.386499i	$0.873684\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$	2.66137	+	3.02209i	2.66137	+	3.02209i
$947$	−0.0210190	−	0.762530i	−0.0210190	−	0.762530i	−0.934564	−	0.355794i	$-0.884211\pi$
$947$	−0.0210190	−	0.762530i	−0.0210190	−	0.762530i	0.913545	−	0.406737i	$-0.133333\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	0.442885	−	0.787008i	0.442885	−	0.787008i	−0.556143	−	0.831087i	$-0.687719\pi$
$953$	0.442885	−	0.787008i	0.442885	−	0.787008i	0.999028	+	0.0440782i	$0.0140351\pi$
$954$	2.01285	+	0.569180i	2.01285	+	0.569180i
$955$		0			0
$956$	0.000739553		0.0447233i	0.000739553		0.0447233i
$957$		0			0
$958$		0			0
$959$	−0.686940	+	0.454222i	−0.686940	+	0.454222i
$960$		0			0
$961$	0.945817	−	0.324699i	0.945817	−	0.324699i
$962$		0			0
$963$	0.221392	−	0.364654i	0.221392	−	0.364654i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	0.604270	−	1.19407i	0.604270	−	1.19407i	−0.360939	−	0.932589i	$-0.617544\pi$
$967$	0.604270	−	1.19407i	0.604270	−	1.19407i	0.965209	−	0.261480i	$-0.0842105\pi$
$968$	1.32045	+	2.07059i	1.32045	+	2.07059i
$969$		0			0
$970$		0			0
$971$		0			0		−0.995083	−	0.0990455i	$-0.968421\pi$
$971$		0			0		0.995083	+	0.0990455i	$0.0315789\pi$
$972$		0			0
$973$		0			0
$974$	−0.191877	+	0.693121i	−0.191877	+	0.693121i
$975$		0			0
$976$		0			0
$977$	0.0665137	+	0.221185i	0.0665137	+	0.221185i	0.984487	−	0.175457i	$-0.0561404\pi$
$977$	0.0665137	+	0.221185i	0.0665137	+	0.221185i	−0.917973	+	0.396642i	$0.870175\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	0.364088	−	0.910769i	0.364088	−	0.910769i
$982$	0.595476	−	0.691405i	0.595476	−	0.691405i
$983$		0			0		0.126427	−	0.991976i	$-0.459649\pi$
$983$		0			0		−0.126427	+	0.991976i	$0.540351\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	1.20694	−	1.64210i	1.20694	−	1.64210i
$990$		0			0
$991$	−1.87292	+	0.666143i	−1.87292	+	0.666143i	−0.899598	+	0.436719i	$0.856140\pi$
$991$	−1.87292	+	0.666143i	−1.87292	+	0.666143i	−0.973327	+	0.229424i	$0.926316\pi$
$992$		0			0
$993$		0			0
$994$	0.381417	−	1.74702i	0.381417	−	1.74702i
$995$		0			0
$996$		0			0
$997$		0			0		−0.0605901	−	0.998163i	$-0.519298\pi$
$997$		0			0		0.0605901	+	0.998163i	$0.480702\pi$
$998$	−1.74933	+	0.557750i	−1.74933	+	0.557750i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3997.1.cz.a.202.1	✓	144
7.6	odd	2	CM	3997.1.cz.a.202.1	✓	144
571.359	even	285	inner	3997.1.cz.a.930.1	yes	144
3997.930	odd	570	inner	3997.1.cz.a.930.1	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3997.1.cz.a.202.1	✓	144	1.1	even	1	trivial
3997.1.cz.a.202.1	✓	144	7.6	odd	2	CM
3997.1.cz.a.930.1	yes	144	571.359	even	285	inner
3997.1.cz.a.930.1	yes	144	3997.930	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)

\(f(q)\)	\(=\)	\(q+(-0.315447 - 1.00854i) q^{2} +(-0.0958675 + 0.0664730i) q^{4} +(0.746821 + 0.665025i) q^{7} +(-0.736619 - 0.573334i) q^{8} +(0.618553 + 0.785743i) q^{9} +O(q^{10})\)	\(q+(-0.315447 - 1.00854i) q^{2} +(-0.0958675 + 0.0664730i) q^{4} +(0.746821 + 0.665025i) q^{7} +(-0.736619 - 0.573334i) q^{8} +(0.618553 + 0.785743i) q^{9} +(-0.323988 + 1.87774i) q^{11} +(0.435121 - 0.962979i) q^{14} +(-0.386771 + 1.03302i) q^{16} +(0.597333 - 0.871695i) q^{18} +(1.99598 - 0.265574i) q^{22} +(-0.346769 - 0.958215i) q^{23} +(-0.256156 - 0.966635i) q^{25} +(-0.115802 - 0.0141107i) q^{28} +(-1.47171 + 1.28171i) q^{29} +(0.231817 + 0.0127897i) q^{32} +(-0.111530 - 0.0342101i) q^{36} +(0.264802 - 0.246477i) q^{37} +(1.11222 + 1.66207i) q^{43} +(-0.0937595 - 0.201551i) q^{44} +(-0.857010 + 0.651997i) q^{46} +(0.115485 + 0.993309i) q^{49} +(-0.894086 + 0.563266i) q^{50} +(0.632414 + 1.87576i) q^{53} +(-0.168842 - 0.918048i) q^{56} +(1.75690 + 1.07996i) q^{58} +(-0.0605901 + 0.998163i) q^{63} +(0.210555 + 0.831465i) q^{64} +(0.394576 - 0.448056i) q^{67} +(1.65521 - 0.351826i) q^{71} +(-0.00514472 - 0.933431i) q^{72} +(-0.332113 - 0.189313i) q^{74} +(-1.49071 + 1.18688i) q^{77} +(-0.0181016 - 0.142029i) q^{79} +(-0.234785 + 0.972047i) q^{81} +(1.32542 - 1.64601i) q^{86} +(1.31523 - 1.19743i) q^{88} +(0.0969394 + 0.0688108i) q^{92} +(0.965362 - 0.429807i) q^{98} +(-1.67583 + 0.906913i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + q^{2} + 5 q^{4} + 2 q^{7} + 21 q^{8} - q^{9}+O(q^{10}) \) 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

Introduction

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