LMFDB - Embedded newform 404.1.o.a.227.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [404,1,Mod(19,404)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(404, base_ring=CyclotomicField(50))

chi = DirichletCharacter(H, H._module([25, 48]))

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

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

chi := DirichletCharacter("404.19");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 404 = 2^{2} \cdot 101 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	404.o (of order $50$, degree $20$, 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:	$0.201622265104$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\Q(\zeta_{50})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{15} + x^{10} - x^{5} + 1 $ x^20 - x^15 + x^10 - x^5 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{25}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{25} - \cdots)$

Embedding invariants

Embedding label			227.1
Root			$0.929776 + 0.368125i$ of defining polynomial
Character	$\chi$	$=$	404.227
Dual form			404.1.o.a.299.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0627905 + 0.998027i) q^{2} +(-0.992115 + 0.125333i) q^{4} +(-0.0534698 + 0.849878i) q^{5} +(-0.187381 - 0.982287i) q^{8} +(0.728969 + 0.684547i) q^{9} +O(q^{10})$	\(q+(0.0627905 + 0.998027i) q^{2} +(-0.992115 + 0.125333i) q^{4} +(-0.0534698 + 0.849878i) q^{5} +(-0.187381 - 0.982287i) q^{8} +(0.728969 + 0.684547i) q^{9} -0.851559 q^{10} +(-0.996398 + 1.57007i) q^{13} +(0.968583 - 0.248690i) q^{16} +(-0.500000 - 1.53884i) q^{17} +(-0.637424 + 0.770513i) q^{18} +(-0.0534698 - 0.849878i) q^{20} +(0.272681 + 0.0344476i) q^{25} +(-1.62954 - 0.895846i) q^{26} +(0.331159 - 0.521823i) q^{29} +(0.309017 + 0.951057i) q^{32} +(1.50441 - 0.595638i) q^{34} +(-0.809017 - 0.587785i) q^{36} +(1.84489 - 0.730444i) q^{37} +(0.844844 - 0.106729i) q^{40} +(0.598617 - 1.84235i) q^{41} +(-0.620759 + 0.582932i) q^{45} +(-0.425779 + 0.904827i) q^{49} +(-0.0172578 + 0.274306i) q^{50} +(0.791759 - 1.68257i) q^{52} +(-1.06320 - 0.134314i) q^{53} +(0.541587 + 0.297740i) q^{58} +(0.371808 - 0.0469702i) q^{61} +(-0.929776 + 0.368125i) q^{64} +(-1.28109 - 0.930769i) q^{65} +(0.688925 + 1.46404i) q^{68} +(0.535827 - 0.844328i) q^{72} +(-1.11716 - 1.35041i) q^{73} +(0.844844 + 1.79538i) q^{74} +(0.159566 + 0.836475i) q^{80} +(0.0627905 + 0.998027i) q^{81} +(1.87631 + 0.481754i) q^{82} +(1.33456 - 0.342658i) q^{85} +(1.41213 + 0.362574i) q^{89} +(-0.620759 - 0.582932i) q^{90} +(-1.06320 + 0.134314i) q^{97} +(-0.929776 - 0.368125i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q+O(q^{10}) $ 20 * q	$ 20 q - 5 q^{13} - 10 q^{17} - 5 q^{32} - 5 q^{36} - 5 q^{40} - 5 q^{45} - 5 q^{50} - 5 q^{61} - 5 q^{74} - 5 q^{80} + 20 q^{82} - 5 q^{90}+O(q^{100}) $ 20 * q - 5 * q^13 - 10 * q^17 - 5 * q^32 - 5 * q^36 - 5 * q^40 - 5 * q^45 - 5 * q^50 - 5 * q^61 - 5 * q^74 - 5 * q^80 + 20 * q^82 - 5 * q^90

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/404\mathbb{Z}\right)^\times$.

$n$	$203$	$305$
$\chi(n)$	$-1$	$e\left(\frac{12}{25}\right)$

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 $

$2$	0.0627905	+	0.998027i	0.0627905	+	0.998027i
$2$	0.0627905	+	0.998027i	0.0627905	+	0.998027i
$3$		0			0		−0.929776	−	0.368125i	$-0.880000\pi$
$3$		0			0		0.929776	+	0.368125i	$0.120000\pi$
$4$	−0.992115	+	0.125333i	−0.992115	+	0.125333i
$5$	−0.0534698	+	0.849878i	−0.0534698	+	0.849878i	0.876307	+	0.481754i	$0.160000\pi$
$5$	−0.0534698	+	0.849878i	−0.0534698	+	0.849878i	−0.929776	+	0.368125i	$0.880000\pi$
$6$		0			0
$7$		0			0		−0.535827	−	0.844328i	$-0.680000\pi$
$7$		0			0		0.535827	+	0.844328i	$0.320000\pi$
$8$	−0.187381	−	0.982287i	−0.187381	−	0.982287i
$9$	0.728969	+	0.684547i	0.728969	+	0.684547i
$10$	−0.851559			−0.851559
$11$		0			0		−0.728969	−	0.684547i	$-0.760000\pi$
$11$		0			0		0.728969	+	0.684547i	$0.240000\pi$
$12$		0			0
$13$	−0.996398	+	1.57007i	−0.996398	+	1.57007i	−0.187381	+	0.982287i	$0.560000\pi$
$13$	−0.996398	+	1.57007i	−0.996398	+	1.57007i	−0.809017	+	0.587785i	$0.800000\pi$
$14$		0			0
$15$		0			0
$16$	0.968583	−	0.248690i	0.968583	−	0.248690i
$17$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	−0.809017	−	0.587785i	$-0.800000\pi$
$17$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	0.309017	−	0.951057i	$-0.400000\pi$
$18$	−0.637424	+	0.770513i	−0.637424	+	0.770513i
$19$		0			0		−0.968583	−	0.248690i	$-0.920000\pi$
$19$		0			0		0.968583	+	0.248690i	$0.0800000\pi$
$20$	−0.0534698	−	0.849878i	−0.0534698	−	0.849878i
$21$		0			0
$22$		0			0
$23$		0			0		−0.637424	−	0.770513i	$-0.720000\pi$
$23$		0			0		0.637424	+	0.770513i	$0.280000\pi$
$24$		0			0
$25$	0.272681	+	0.0344476i	0.272681	+	0.0344476i
$26$	−1.62954	−	0.895846i	−1.62954	−	0.895846i
$27$		0			0
$28$		0			0
$29$	0.331159	−	0.521823i	0.331159	−	0.521823i	−0.637424	−	0.770513i	$-0.720000\pi$
$29$	0.331159	−	0.521823i	0.331159	−	0.521823i	0.968583	+	0.248690i	$0.0800000\pi$
$30$		0			0
$31$		0			0		−0.535827	−	0.844328i	$-0.680000\pi$
$31$		0			0		0.535827	+	0.844328i	$0.320000\pi$
$32$	0.309017	+	0.951057i	0.309017	+	0.951057i
$33$		0			0
$34$	1.50441	−	0.595638i	1.50441	−	0.595638i
$35$		0			0
$36$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$37$	1.84489	−	0.730444i	1.84489	−	0.730444i	0.876307	−	0.481754i	$-0.160000\pi$
$37$	1.84489	−	0.730444i	1.84489	−	0.730444i	0.968583	−	0.248690i	$-0.0800000\pi$
$38$		0			0
$39$		0			0
$40$	0.844844	−	0.106729i	0.844844	−	0.106729i
$41$	0.598617	−	1.84235i	0.598617	−	1.84235i	0.0627905	−	0.998027i	$-0.480000\pi$
$41$	0.598617	−	1.84235i	0.598617	−	1.84235i	0.535827	−	0.844328i	$-0.320000\pi$
$42$		0			0
$43$		0			0		−0.876307	−	0.481754i	$-0.840000\pi$
$43$		0			0		0.876307	+	0.481754i	$0.160000\pi$
$44$		0			0
$45$	−0.620759	+	0.582932i	−0.620759	+	0.582932i
$46$		0			0
$47$		0			0		0.876307	−	0.481754i	$-0.160000\pi$
$47$		0			0		−0.876307	+	0.481754i	$0.840000\pi$
$48$		0			0
$49$	−0.425779	+	0.904827i	−0.425779	+	0.904827i
$50$	−0.0172578	+	0.274306i	−0.0172578	+	0.274306i
$51$		0			0
$52$	0.791759	−	1.68257i	0.791759	−	1.68257i
$53$	−1.06320	−	0.134314i	−1.06320	−	0.134314i	−0.425779	−	0.904827i	$-0.640000\pi$
$53$	−1.06320	−	0.134314i	−1.06320	−	0.134314i	−0.637424	+	0.770513i	$0.720000\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		0			0
$58$	0.541587	+	0.297740i	0.541587	+	0.297740i
$59$		0			0		0.968583	−	0.248690i	$-0.0800000\pi$
$59$		0			0		−0.968583	+	0.248690i	$0.920000\pi$
$60$		0			0
$61$	0.371808	−	0.0469702i	0.371808	−	0.0469702i	0.0627905	−	0.998027i	$-0.480000\pi$
$61$	0.371808	−	0.0469702i	0.371808	−	0.0469702i	0.309017	+	0.951057i	$0.400000\pi$
$62$		0			0
$63$		0			0
$64$	−0.929776	+	0.368125i	−0.929776	+	0.368125i
$65$	−1.28109	−	0.930769i	−1.28109	−	0.930769i
$66$		0			0
$67$		0			0		0.929776	−	0.368125i	$-0.120000\pi$
$67$		0			0		−0.929776	+	0.368125i	$0.880000\pi$
$68$	0.688925	+	1.46404i	0.688925	+	1.46404i
$69$		0			0
$70$		0			0
$71$		0			0		−0.929776	−	0.368125i	$-0.880000\pi$
$71$		0			0		0.929776	+	0.368125i	$0.120000\pi$
$72$	0.535827	−	0.844328i	0.535827	−	0.844328i
$73$	−1.11716	−	1.35041i	−1.11716	−	1.35041i	−0.929776	−	0.368125i	$-0.880000\pi$
$73$	−1.11716	−	1.35041i	−1.11716	−	1.35041i	−0.187381	−	0.982287i	$-0.560000\pi$
$74$	0.844844	+	1.79538i	0.844844	+	1.79538i
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		0.637424	−	0.770513i	$-0.280000\pi$
$79$		0			0		−0.637424	+	0.770513i	$0.720000\pi$
$80$	0.159566	+	0.836475i	0.159566	+	0.836475i
$81$	0.0627905	+	0.998027i	0.0627905	+	0.998027i
$82$	1.87631	+	0.481754i	1.87631	+	0.481754i
$83$		0			0		0.637424	−	0.770513i	$-0.280000\pi$
$83$		0			0		−0.637424	+	0.770513i	$0.720000\pi$
$84$		0			0
$85$	1.33456	−	0.342658i	1.33456	−	0.342658i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	1.41213	+	0.362574i	1.41213	+	0.362574i	0.876307	−	0.481754i	$-0.160000\pi$
$89$	1.41213	+	0.362574i	1.41213	+	0.362574i	0.535827	+	0.844328i	$0.320000\pi$
$90$	−0.620759	−	0.582932i	−0.620759	−	0.582932i
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−1.06320	+	0.134314i	−1.06320	+	0.134314i	−0.637424	−	0.770513i	$-0.720000\pi$
$97$	−1.06320	+	0.134314i	−1.06320	+	0.134314i	−0.425779	+	0.904827i	$0.640000\pi$
$98$	−0.929776	−	0.368125i	−0.929776	−	0.368125i
$99$		0			0
$100$	−0.274848			−0.274848
$101$	−0.992115	+	0.125333i	−0.992115	+	0.125333i
$101$	−0.992115	+	0.125333i	−0.992115	+	0.125333i
$102$		0			0
$103$		0			0		−0.0627905	−	0.998027i	$-0.520000\pi$
$103$		0			0		0.0627905	+	0.998027i	$0.480000\pi$
$104$	1.72897	+	0.684547i	1.72897	+	0.684547i
$105$		0			0
$106$	0.0672897	−	1.06954i	0.0672897	−	1.06954i
$107$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$107$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$108$		0			0
$109$	−0.0235315	−	0.123357i	−0.0235315	−	0.123357i	0.968583	−	0.248690i	$-0.0800000\pi$
$109$	−0.0235315	−	0.123357i	−0.0235315	−	0.123357i	−0.992115	+	0.125333i	$0.960000\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.121636	+	0.0312307i	0.121636	+	0.0312307i	0.309017	−	0.951057i	$-0.400000\pi$
$113$	0.121636	+	0.0312307i	0.121636	+	0.0312307i	−0.187381	+	0.982287i	$0.560000\pi$
$114$		0			0
$115$		0			0
$116$	−0.263146	+	0.559214i	−0.263146	+	0.559214i
$117$	−1.80113	+	0.462452i	−1.80113	+	0.462452i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	0.0627905	+	0.998027i	0.0627905	+	0.998027i
$122$	0.0702235	+	0.368125i	0.0702235	+	0.368125i
$123$		0			0
$124$		0			0
$125$	−0.203423	+	1.06638i	−0.203423	+	1.06638i
$126$		0			0
$127$		0			0		−0.876307	−	0.481754i	$-0.840000\pi$
$127$		0			0		0.876307	+	0.481754i	$0.160000\pi$
$128$	−0.425779	−	0.904827i	−0.425779	−	0.904827i
$129$		0			0
$130$	0.848492	−	1.33701i	0.848492	−	1.33701i
$131$		0			0		−0.929776	−	0.368125i	$-0.880000\pi$
$131$		0			0		0.929776	+	0.368125i	$0.120000\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	−1.41789	+	0.779494i	−1.41789	+	0.779494i
$137$	−1.41789	−	1.03016i	−1.41789	−	1.03016i	−0.992115	−	0.125333i	$-0.960000\pi$
$137$	−1.41789	−	1.03016i	−1.41789	−	1.03016i	−0.425779	−	0.904827i	$-0.640000\pi$
$138$		0			0
$139$		0			0		0.187381	−	0.982287i	$-0.440000\pi$
$139$		0			0		−0.187381	+	0.982287i	$0.560000\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	0.876307	+	0.481754i	0.876307	+	0.481754i
$145$	0.425779	+	0.309347i	0.425779	+	0.309347i
$146$	1.27760	−	1.19975i	1.27760	−	1.19975i
$147$		0			0
$148$	−1.73879	+	0.955910i	−1.73879	+	0.955910i
$149$	−1.73879	−	0.219661i	−1.73879	−	0.219661i	−0.809017	−	0.587785i	$-0.800000\pi$
$149$	−1.73879	−	0.219661i	−1.73879	−	0.219661i	−0.929776	+	0.368125i	$0.880000\pi$
$150$		0			0
$151$		0			0		0.0627905	−	0.998027i	$-0.480000\pi$
$151$		0			0		−0.0627905	+	0.998027i	$0.520000\pi$
$152$		0			0
$153$	0.688925	−	1.46404i	0.688925	−	1.46404i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	0.0915446	−	0.0859661i	0.0915446	−	0.0859661i	−0.637424	−	0.770513i	$-0.720000\pi$
$157$	0.0915446	−	0.0859661i	0.0915446	−	0.0859661i	0.728969	+	0.684547i	$0.240000\pi$
$158$		0			0
$159$		0			0
$160$	−0.824805	+	0.211774i	−0.824805	+	0.211774i
$161$		0			0
$162$	−0.992115	+	0.125333i	−0.992115	+	0.125333i
$163$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$163$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$164$	−0.362989	+	1.90285i	−0.362989	+	1.90285i
$165$		0			0
$166$		0			0
$167$		0			0		0.876307	−	0.481754i	$-0.160000\pi$
$167$		0			0		−0.876307	+	0.481754i	$0.840000\pi$
$168$		0			0
$169$	−1.04654	−	2.22401i	−1.04654	−	2.22401i
$170$	0.425779	+	1.31041i	0.425779	+	1.31041i
$171$		0			0
$172$		0			0
$173$	−1.06320	+	1.67534i	−1.06320	+	1.67534i	−0.425779	+	0.904827i	$0.640000\pi$
$173$	−1.06320	+	1.67534i	−1.06320	+	1.67534i	−0.637424	+	0.770513i	$0.720000\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$	−0.273190	+	1.43211i	−0.273190	+	1.43211i
$179$		0			0		−0.637424	−	0.770513i	$-0.720000\pi$
$179$		0			0		0.637424	+	0.770513i	$0.280000\pi$
$180$	0.542804	−	0.656137i	0.542804	−	0.656137i
$181$	0.0702235	+	0.368125i	0.0702235	+	0.368125i	1.00000			$0$
$181$	0.0702235	+	0.368125i	0.0702235	+	0.368125i	−0.929776	+	0.368125i	$0.880000\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	0.522142	+	1.60699i	0.522142	+	1.60699i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		−0.728969	−	0.684547i	$-0.760000\pi$
$191$		0			0		0.728969	+	0.684547i	$0.240000\pi$
$192$		0			0
$193$	1.41213	+	1.32608i	1.41213	+	1.32608i	0.876307	+	0.481754i	$0.160000\pi$
$193$	1.41213	+	1.32608i	1.41213	+	1.32608i	0.535827	+	0.844328i	$0.320000\pi$
$194$	−0.200808	−	1.05267i	−0.200808	−	1.05267i
$195$		0			0
$196$	0.309017	−	0.951057i	0.309017	−	0.951057i
$197$	0.0388067	−	0.616814i	0.0388067	−	0.616814i	−0.929776	−	0.368125i	$-0.880000\pi$
$197$	0.0388067	−	0.616814i	0.0388067	−	0.616814i	0.968583	−	0.248690i	$-0.0800000\pi$
$198$		0			0
$199$		0			0		−0.929776	−	0.368125i	$-0.880000\pi$
$199$		0			0		0.929776	+	0.368125i	$0.120000\pi$
$200$	−0.0172578	−	0.274306i	−0.0172578	−	0.274306i
$201$		0			0
$202$	−0.187381	−	0.982287i	−0.187381	−	0.982287i
$203$		0			0
$204$		0			0
$205$	1.53377	+	0.607262i	1.53377	+	0.607262i
$206$		0			0
$207$		0			0
$208$	−0.574633	+	1.76854i	−0.574633	+	1.76854i
$209$		0			0
$210$		0			0
$211$		0			0		−0.728969	−	0.684547i	$-0.760000\pi$
$211$		0			0		0.728969	+	0.684547i	$0.240000\pi$
$212$	1.07165			1.07165
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$	0.121636	−	0.0312307i	0.121636	−	0.0312307i
$219$		0			0
$220$		0			0
$221$	2.91429	+	0.748263i	2.91429	+	0.748263i
$222$		0			0
$223$		0			0		−0.187381	−	0.982287i	$-0.560000\pi$
$223$		0			0		0.187381	+	0.982287i	$0.440000\pi$
$224$		0			0
$225$	0.175195	+	0.211774i	0.175195	+	0.211774i
$226$	−0.0235315	+	0.123357i	−0.0235315	+	0.123357i
$227$		0			0		−0.992115	−	0.125333i	$-0.960000\pi$
$227$		0			0		0.992115	+	0.125333i	$0.0400000\pi$
$228$		0			0
$229$	−0.456288	−	0.969661i	−0.456288	−	0.969661i	−0.992115	−	0.125333i	$-0.960000\pi$
$229$	−0.456288	−	0.969661i	−0.456288	−	0.969661i	0.535827	−	0.844328i	$-0.320000\pi$
$230$		0			0
$231$		0			0
$232$	−0.574633	−	0.227513i	−0.574633	−	0.227513i
$233$	−0.200808	−	0.316423i	−0.200808	−	0.316423i	0.728969	−	0.684547i	$-0.240000\pi$
$233$	−0.200808	−	0.316423i	−0.200808	−	0.316423i	−0.929776	+	0.368125i	$0.880000\pi$
$234$	−0.574633	−	1.76854i	−0.574633	−	1.76854i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		0.929776	−	0.368125i	$-0.120000\pi$
$239$		0			0		−0.929776	+	0.368125i	$0.880000\pi$
$240$		0			0
$241$	1.03137	−	0.749337i	1.03137	−	0.749337i	0.0627905	−	0.998027i	$-0.480000\pi$
$241$	1.03137	−	0.749337i	1.03137	−	0.749337i	0.968583	+	0.248690i	$0.0800000\pi$
$242$	−0.992115	+	0.125333i	−0.992115	+	0.125333i
$243$		0			0
$244$	−0.362989	+	0.0931997i	−0.362989	+	0.0931997i
$245$	−0.746226	−	0.410241i	−0.746226	−	0.410241i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$	−1.07705	−	0.136063i	−1.07705	−	0.136063i
$251$		0			0		0.425779	−	0.904827i	$-0.360000\pi$
$251$		0			0		−0.425779	+	0.904827i	$0.640000\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.876307	−	0.481754i	0.876307	−	0.481754i
$257$	−0.273190	+	0.256543i	−0.273190	+	0.256543i	−0.809017	−	0.587785i	$-0.800000\pi$
$257$	−0.273190	+	0.256543i	−0.273190	+	0.256543i	0.535827	+	0.844328i	$0.320000\pi$
$258$		0			0
$259$		0			0
$260$	1.38765	+	0.762866i	1.38765	+	0.762866i
$261$	0.598617	−	0.153699i	0.598617	−	0.153699i
$262$		0			0
$263$		0			0		0.992115	−	0.125333i	$-0.0400000\pi$
$263$		0			0		−0.992115	+	0.125333i	$0.960000\pi$
$264$		0			0
$265$	0.171000	−	0.896412i	0.171000	−	0.896412i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	1.18532	−	0.469303i	1.18532	−	0.469303i	0.309017	−	0.951057i	$-0.400000\pi$
$269$	1.18532	−	0.469303i	1.18532	−	0.469303i	0.876307	+	0.481754i	$0.160000\pi$
$270$		0			0
$271$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$271$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$272$	−0.866986	−	1.36615i	−0.866986	−	1.36615i
$273$		0			0
$274$	0.939097	−	1.47978i	0.939097	−	1.47978i
$275$		0			0
$276$		0			0
$277$	1.69755	+	0.933237i	1.69755	+	0.933237i	0.968583	+	0.248690i	$0.0800000\pi$
$277$	1.69755	+	0.933237i	1.69755	+	0.933237i	0.728969	+	0.684547i	$0.240000\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	1.26480	−	1.52888i	1.26480	−	1.52888i	0.535827	−	0.844328i	$-0.320000\pi$
$281$	1.26480	−	1.52888i	1.26480	−	1.52888i	0.728969	−	0.684547i	$-0.240000\pi$
$282$		0			0
$283$		0			0		−0.0627905	−	0.998027i	$-0.520000\pi$
$283$		0			0		0.0627905	+	0.998027i	$0.480000\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.425779	+	0.904827i	−0.425779	+	0.904827i
$289$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$290$	−0.282001	+	0.444363i	−0.282001	+	0.444363i
$291$		0			0
$292$	1.27760	+	1.19975i	1.27760	+	1.19975i
$293$	1.45794			1.45794			0.728969	−	0.684547i	$-0.240000\pi$
$293$	1.45794			1.45794			0.728969	+	0.684547i	$0.240000\pi$
$294$		0			0
$295$		0			0
$296$	−1.06320	−	1.67534i	−1.06320	−	1.67534i
$297$		0			0
$298$	0.110048	−	1.74915i	0.110048	−	1.74915i
$299$		0			0
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	0.0200385	+	0.318503i	0.0200385	+	0.318503i
$306$	1.50441	+	0.595638i	1.50441	+	0.595638i
$307$		0			0		0.992115	−	0.125333i	$-0.0400000\pi$
$307$		0			0		−0.992115	+	0.125333i	$0.960000\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.187381	−	0.982287i	$-0.560000\pi$
$311$		0			0		0.187381	+	0.982287i	$0.440000\pi$
$312$		0			0
$313$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$313$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$314$	0.0915446	+	0.0859661i	0.0915446	+	0.0859661i
$315$		0			0
$316$		0			0
$317$	−1.17950	+	0.856954i	−1.17950	+	0.856954i	−0.992115	−	0.125333i	$-0.960000\pi$
$317$	−1.17950	+	0.856954i	−1.17950	+	0.856954i	−0.187381	+	0.982287i	$0.560000\pi$
$318$		0			0
$319$		0			0
$320$	−0.263146	−	0.809880i	−0.263146	−	0.809880i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−0.187381	−	0.982287i	−0.187381	−	0.982287i
$325$	−0.325784	+	0.393805i	−0.325784	+	0.393805i
$326$		0			0
$327$		0			0
$328$	−1.92189	−	0.242791i	−1.92189	−	0.242791i
$329$		0			0
$330$		0			0
$331$		0			0		−0.637424	−	0.770513i	$-0.720000\pi$
$331$		0			0		0.637424	+	0.770513i	$0.280000\pi$
$332$		0			0
$333$	1.84489	+	0.730444i	1.84489	+	0.730444i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−1.62954	+	0.645180i	−1.62954	+	0.645180i	−0.992115	−	0.125333i	$-0.960000\pi$
$337$	−1.62954	+	0.645180i	−1.62954	+	0.645180i	−0.637424	+	0.770513i	$0.720000\pi$
$338$	2.15391	−	1.18412i	2.15391	−	1.18412i
$339$		0			0
$340$	−1.28109	+	0.507221i	−1.28109	+	0.507221i
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$	−1.73879	−	0.955910i	−1.73879	−	0.955910i
$347$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$347$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$348$		0			0
$349$	−1.44644	+	1.35830i	−1.44644	+	1.35830i	−0.637424	+	0.770513i	$0.720000\pi$
$349$	−1.44644	+	1.35830i	−1.44644	+	1.35830i	−0.809017	+	0.587785i	$0.800000\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	0.0388067	−	0.616814i	0.0388067	−	0.616814i	−0.929776	−	0.368125i	$-0.880000\pi$
$353$	0.0388067	−	0.616814i	0.0388067	−	0.616814i	0.968583	−	0.248690i	$-0.0800000\pi$
$354$		0			0
$355$		0			0
$356$	−1.44644	−	0.182728i	−1.44644	−	0.182728i
$357$		0			0
$358$		0			0
$359$		0			0		0.728969	−	0.684547i	$-0.240000\pi$
$359$		0			0		−0.728969	+	0.684547i	$0.760000\pi$
$360$	0.688925	+	0.500534i	0.688925	+	0.500534i
$361$	0.876307	+	0.481754i	0.876307	+	0.481754i
$362$	−0.362989	+	0.0931997i	−0.362989	+	0.0931997i
$363$		0			0
$364$		0			0
$365$	1.20742	−	0.877242i	1.20742	−	0.877242i
$366$		0			0
$367$		0			0		0.929776	−	0.368125i	$-0.120000\pi$
$367$		0			0		−0.929776	+	0.368125i	$0.880000\pi$
$368$		0			0
$369$	1.69755	−	0.933237i	1.69755	−	0.933237i
$370$	−1.57103	+	0.622015i	−1.57103	+	0.622015i
$371$		0			0
$372$		0			0
$373$	−1.06320	−	1.67534i	−1.06320	−	1.67534i	−0.637424	−	0.770513i	$-0.720000\pi$
$373$	−1.06320	−	1.67534i	−1.06320	−	1.67534i	−0.425779	−	0.904827i	$-0.640000\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	0.489334	+	1.03989i	0.489334	+	1.03989i
$378$		0			0
$379$		0			0		−0.992115	−	0.125333i	$-0.960000\pi$
$379$		0			0		0.992115	+	0.125333i	$0.0400000\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.187381	−	0.982287i	$-0.560000\pi$
$383$		0			0		0.187381	+	0.982287i	$0.440000\pi$
$384$		0			0
$385$		0			0
$386$	−1.23480	+	1.49261i	−1.23480	+	1.49261i
$387$		0			0
$388$	1.03799	−	0.266509i	1.03799	−	0.266509i
$389$	0.688925	−	1.46404i	0.688925	−	1.46404i	−0.187381	−	0.982287i	$-0.560000\pi$
$389$	0.688925	−	1.46404i	0.688925	−	1.46404i	0.876307	−	0.481754i	$-0.160000\pi$
$390$		0			0
$391$		0			0
$392$	0.968583	+	0.248690i	0.968583	+	0.248690i
$393$		0			0
$394$	0.618034			0.618034
$395$		0			0
$396$		0			0
$397$	−0.996398	−	1.57007i	−0.996398	−	1.57007i	−0.809017	−	0.587785i	$-0.800000\pi$
$397$	−0.996398	−	1.57007i	−0.996398	−	1.57007i	−0.187381	−	0.982287i	$-0.560000\pi$
$398$		0			0
$399$		0			0
$400$	0.272681	−	0.0344476i	0.272681	−	0.0344476i
$401$	1.72897	+	0.684547i	1.72897	+	0.684547i	1.00000			$0$
$401$	1.72897	+	0.684547i	1.72897	+	0.684547i	0.728969	+	0.684547i	$0.240000\pi$
$402$		0			0
$403$		0			0
$404$	0.968583	−	0.248690i	0.968583	−	0.248690i
$405$	−0.851559			−0.851559
$406$		0			0
$407$		0			0
$408$		0			0
$409$	0.00788530	−	0.125333i	0.00788530	−	0.125333i	−0.992115	−	0.125333i	$-0.960000\pi$
$409$	0.00788530	−	0.125333i	0.00788530	−	0.125333i	1.00000			$0$
$410$	−0.509758	+	1.56887i	−0.509758	+	1.56887i
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$	−1.80113	−	0.462452i	−1.80113	−	0.462452i
$417$		0			0
$418$		0			0
$419$		0			0		0.425779	−	0.904827i	$-0.360000\pi$
$419$		0			0		−0.425779	+	0.904827i	$0.640000\pi$
$420$		0			0
$421$	−0.393950	−	1.21245i	−0.393950	−	1.21245i	−0.929776	−	0.368125i	$-0.880000\pi$
$421$	−0.393950	−	1.21245i	−0.393950	−	1.21245i	0.535827	−	0.844328i	$-0.320000\pi$
$422$		0			0
$423$		0			0
$424$	0.0672897	+	1.06954i	0.0672897	+	1.06954i
$425$	−0.0833310	−	0.436836i	−0.0833310	−	0.436836i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		−0.425779	−	0.904827i	$-0.640000\pi$
$431$		0			0		0.425779	+	0.904827i	$0.360000\pi$
$432$		0			0
$433$	−0.683098	+	1.07639i	−0.683098	+	1.07639i	0.309017	+	0.951057i	$0.400000\pi$
$433$	−0.683098	+	1.07639i	−0.683098	+	1.07639i	−0.992115	+	0.125333i	$0.960000\pi$
$434$		0			0
$435$		0			0
$436$	0.0388067	+	0.119435i	0.0388067	+	0.119435i
$437$		0			0
$438$		0			0
$439$		0			0		0.876307	−	0.481754i	$-0.160000\pi$
$439$		0			0		−0.876307	+	0.481754i	$0.840000\pi$
$440$		0			0
$441$	−0.929776	+	0.368125i	−0.929776	+	0.368125i
$442$	−0.563797	+	2.95553i	−0.563797	+	2.95553i
$443$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$443$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$444$		0			0
$445$	−0.383650	+	1.18075i	−0.383650	+	1.18075i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−0.929324	+	0.872693i	−0.929324	+	0.872693i	−0.992115	−	0.125333i	$-0.960000\pi$
$449$	−0.929324	+	0.872693i	−0.929324	+	0.872693i	0.0627905	+	0.998027i	$0.480000\pi$
$450$	−0.200356	+	0.188146i	−0.200356	+	0.188146i
$451$		0			0
$452$	−0.124591	−	0.0157395i	−0.124591	−	0.0157395i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	1.84489	+	0.233064i	1.84489	+	0.233064i	0.968583	−	0.248690i	$-0.0800000\pi$
$457$	1.84489	+	0.233064i	1.84489	+	0.233064i	0.876307	+	0.481754i	$0.160000\pi$
$458$	0.939097	−	0.516273i	0.939097	−	0.516273i
$459$		0			0
$460$		0			0
$461$	−1.17950	−	0.856954i	−1.17950	−	0.856954i	−0.187381	−	0.982287i	$-0.560000\pi$
$461$	−1.17950	−	0.856954i	−1.17950	−	0.856954i	−0.992115	+	0.125333i	$0.960000\pi$
$462$		0			0
$463$		0			0		0.968583	−	0.248690i	$-0.0800000\pi$
$463$		0			0		−0.968583	+	0.248690i	$0.920000\pi$
$464$	0.190983	−	0.587785i	0.190983	−	0.587785i
$465$		0			0
$466$	0.303189	−	0.220280i	0.303189	−	0.220280i
$467$		0			0		0.187381	−	0.982287i	$-0.440000\pi$
$467$		0			0		−0.187381	+	0.982287i	$0.560000\pi$
$468$	1.72897	−	0.684547i	1.72897	−	0.684547i
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−0.683098	−	0.825723i	−0.683098	−	0.825723i
$478$		0			0
$479$		0			0		−0.876307	−	0.481754i	$-0.840000\pi$
$479$		0			0		0.876307	+	0.481754i	$0.160000\pi$
$480$		0			0
$481$	−0.691396	+	3.62442i	−0.691396	+	3.62442i
$482$	0.812619	+	0.982287i	0.812619	+	0.982287i
$483$		0			0
$484$	−0.187381	−	0.982287i	−0.187381	−	0.982287i
$485$	−0.0573011	−	0.910775i	−0.0573011	−	0.910775i
$486$		0			0
$487$		0			0		0.637424	−	0.770513i	$-0.280000\pi$
$487$		0			0		−0.637424	+	0.770513i	$0.720000\pi$
$488$	−0.115808	−	0.356420i	−0.115808	−	0.356420i
$489$		0			0
$490$	0.362576	−	0.770513i	0.362576	−	0.770513i
$491$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$491$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$492$		0			0
$493$	−0.968583	−	0.248690i	−0.968583	−	0.248690i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$499$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$500$	0.0681659	−	1.08347i	0.0681659	−	1.08347i
$501$		0			0
$502$		0			0
$503$		0			0		−0.0627905	−	0.998027i	$-0.520000\pi$
$503$		0			0		0.0627905	+	0.998027i	$0.480000\pi$
$504$		0			0
$505$	−0.0534698	−	0.849878i	−0.0534698	−	0.849878i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−0.613161	+	0.0774602i	−0.613161	+	0.0774602i	−0.425779	−	0.904827i	$-0.640000\pi$
$509$	−0.613161	+	0.0774602i	−0.613161	+	0.0774602i	−0.187381	+	0.982287i	$0.560000\pi$
$510$		0			0
$511$		0			0
$512$	0.535827	+	0.844328i	0.535827	+	0.844328i
$513$		0			0
$514$	−0.273190	−	0.256543i	−0.273190	−	0.256543i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	−0.674229	+	1.43281i	−0.674229	+	1.43281i
$521$	−0.362989	+	0.0931997i	−0.362989	+	0.0931997i	−0.425779	−	0.904827i	$-0.640000\pi$
$521$	−0.362989	+	0.0931997i	−0.362989	+	0.0931997i	0.0627905	+	0.998027i	$0.480000\pi$
$522$	0.190983	+	0.587785i	0.190983	+	0.587785i
$523$		0			0		0.637424	−	0.770513i	$-0.280000\pi$
$523$		0			0		−0.637424	+	0.770513i	$0.720000\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	−0.187381	+	0.982287i	−0.187381	+	0.982287i
$530$	0.905380	+	0.114376i	0.905380	+	0.114376i
$531$		0			0
$532$		0			0
$533$	2.29617	+	2.77559i	2.29617	+	2.77559i
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$	0.542804	+	1.15352i	0.542804	+	1.15352i
$539$		0			0
$540$		0			0
$541$	−1.17950	−	0.856954i	−1.17950	−	0.856954i	−0.187381	−	0.982287i	$-0.560000\pi$
$541$	−1.17950	−	0.856954i	−1.17950	−	0.856954i	−0.992115	+	0.125333i	$0.960000\pi$
$542$		0			0
$543$		0			0
$544$	1.30902	−	0.951057i	1.30902	−	0.951057i
$545$	0.106096	−	0.0134031i	0.106096	−	0.0134031i
$546$		0			0
$547$		0			0		0.968583	−	0.248690i	$-0.0800000\pi$
$547$		0			0		−0.968583	+	0.248690i	$0.920000\pi$
$548$	1.53583	+	0.844328i	1.53583	+	0.844328i
$549$	0.303189	+	0.220280i	0.303189	+	0.220280i
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$	−0.824805	+	1.75280i	−0.824805	+	1.75280i
$555$		0			0
$556$		0			0
$557$	−0.456288	+	0.969661i	−0.456288	+	0.969661i	0.535827	+	0.844328i	$0.320000\pi$
$557$	−0.456288	+	0.969661i	−0.456288	+	0.969661i	−0.992115	+	0.125333i	$0.960000\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	1.60528	+	1.16630i	1.60528	+	1.16630i
$563$		0			0		−0.876307	−	0.481754i	$-0.840000\pi$
$563$		0			0		0.876307	+	0.481754i	$0.160000\pi$
$564$		0			0
$565$	−0.0330462	+	0.101706i	−0.0330462	+	0.101706i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−0.574633	+	0.227513i	−0.574633	+	0.227513i	−0.637424	−	0.770513i	$-0.720000\pi$
$569$	−0.574633	+	0.227513i	−0.574633	+	0.227513i	0.0627905	+	0.998027i	$0.480000\pi$
$570$		0			0
$571$		0			0		0.876307	−	0.481754i	$-0.160000\pi$
$571$		0			0		−0.876307	+	0.481754i	$0.840000\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−0.929776	−	0.368125i	−0.929776	−	0.368125i
$577$	1.03799	−	1.63560i	1.03799	−	1.63560i	0.309017	−	0.951057i	$-0.400000\pi$
$577$	1.03799	−	1.63560i	1.03799	−	1.63560i	0.728969	−	0.684547i	$-0.240000\pi$
$578$	−1.03137	−	1.24672i	−1.03137	−	1.24672i
$579$		0			0
$580$	−0.461193	−	0.253543i	−0.461193	−	0.253543i
$581$		0			0
$582$		0			0
$583$		0			0
$584$	−1.11716	+	1.35041i	−1.11716	+	1.35041i
$585$	−0.296722	−	1.55547i	−0.296722	−	1.55547i
$586$	0.0915446	+	1.45506i	0.0915446	+	1.45506i
$587$		0			0		−0.968583	−	0.248690i	$-0.920000\pi$
$587$		0			0		0.968583	+	0.248690i	$0.0800000\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	1.60528	−	1.16630i	1.60528	−	1.16630i
$593$	−0.683098	+	1.07639i	−0.683098	+	1.07639i	0.309017	+	0.951057i	$0.400000\pi$
$593$	−0.683098	+	1.07639i	−0.683098	+	1.07639i	−0.992115	+	0.125333i	$0.960000\pi$
$594$		0			0
$595$		0			0
$596$	1.75261			1.75261
$597$		0			0
$598$		0			0
$599$		0			0		−0.535827	−	0.844328i	$-0.680000\pi$
$599$		0			0		0.535827	+	0.844328i	$0.320000\pi$
$600$		0			0
$601$	−0.101597	+	1.61484i	−0.101597	+	1.61484i	0.535827	+	0.844328i	$0.320000\pi$
$601$	−0.101597	+	1.61484i	−0.101597	+	1.61484i	−0.637424	+	0.770513i	$0.720000\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−0.851559			−0.851559
$606$		0			0
$607$		0			0		1.00000			$0$
$607$		0			0		−1.00000			$\pi$
$608$		0			0
$609$		0			0
$610$	−0.316616	+	0.0399979i	−0.316616	+	0.0399979i
$611$		0			0
$612$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$613$	−0.683098	−	1.07639i	−0.683098	−	1.07639i	−0.992115	−	0.125333i	$-0.960000\pi$
$613$	−0.683098	−	1.07639i	−0.683098	−	1.07639i	0.309017	−	0.951057i	$-0.400000\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	0.781202	+	0.733597i	0.781202	+	0.733597i	0.968583	−	0.248690i	$-0.0800000\pi$
$617$	0.781202	+	0.733597i	0.781202	+	0.733597i	−0.187381	+	0.982287i	$0.560000\pi$
$618$		0			0
$619$		0			0		0.535827	−	0.844328i	$-0.320000\pi$
$619$		0			0		−0.535827	+	0.844328i	$0.680000\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.629202	−	0.161552i	−0.629202	−	0.161552i
$626$	−0.101597	−	1.61484i	−0.101597	−	1.61484i
$627$		0			0
$628$	−0.0800484	+	0.0967619i	−0.0800484	+	0.0967619i
$629$	−2.04648	−	2.47377i	−2.04648	−	2.47377i
$630$		0			0
$631$		0			0		−0.992115	−	0.125333i	$-0.960000\pi$
$631$		0			0		0.992115	+	0.125333i	$0.0400000\pi$
$632$		0			0
$633$		0			0
$634$	−0.929324	−	1.12336i	−0.929324	−	1.12336i
$635$		0			0
$636$		0			0
$637$	−0.996398	−	1.57007i	−0.996398	−	1.57007i
$638$		0			0
$639$		0			0
$640$	0.791759	−	0.313480i	0.791759	−	0.313480i
$641$	−0.328407	+	0.180543i	−0.328407	+	0.180543i	−0.637424	−	0.770513i	$-0.720000\pi$
$641$	−0.328407	+	0.180543i	−0.328407	+	0.180543i	0.309017	+	0.951057i	$0.400000\pi$
$642$		0			0
$643$		0			0		0.929776	−	0.368125i	$-0.120000\pi$
$643$		0			0		−0.929776	+	0.368125i	$0.880000\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$647$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$648$	0.968583	−	0.248690i	0.968583	−	0.248690i
$649$		0			0
$650$	−0.413484	−	0.300414i	−0.413484	−	0.300414i
$651$		0			0
$652$		0			0
$653$	−1.41789	+	0.779494i	−1.41789	+	0.779494i	−0.992115	−	0.125333i	$-0.960000\pi$
$653$	−1.41789	+	0.779494i	−1.41789	+	0.779494i	−0.425779	+	0.904827i	$0.640000\pi$
$654$		0			0
$655$		0			0
$656$	0.121636	−	1.93334i	0.121636	−	1.93334i
$657$	0.110048	−	1.74915i	0.110048	−	1.74915i
$658$		0			0
$659$		0			0		−0.992115	−	0.125333i	$-0.960000\pi$
$659$		0			0		0.992115	+	0.125333i	$0.0400000\pi$
$660$		0			0
$661$	1.41213	−	1.32608i	1.41213	−	1.32608i	0.535827	−	0.844328i	$-0.320000\pi$
$661$	1.41213	−	1.32608i	1.41213	−	1.32608i	0.876307	−	0.481754i	$-0.160000\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$	−0.613161	+	1.88711i	−0.613161	+	1.88711i
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	1.84489	−	0.730444i	1.84489	−	0.730444i	0.876307	−	0.481754i	$-0.160000\pi$
$673$	1.84489	−	0.730444i	1.84489	−	0.730444i	0.968583	−	0.248690i	$-0.0800000\pi$
$674$	−0.746226	−	1.58581i	−0.746226	−	1.58581i
$675$		0			0
$676$	1.31703	+	2.07531i	1.31703	+	2.07531i
$677$	1.18532	+	0.469303i	1.18532	+	0.469303i	0.876307	−	0.481754i	$-0.160000\pi$
$677$	1.18532	+	0.469303i	1.18532	+	0.469303i	0.309017	+	0.951057i	$0.400000\pi$
$678$		0			0
$679$		0			0
$680$	−0.586660	−	1.24672i	−0.586660	−	1.24672i
$681$		0			0
$682$		0			0
$683$		0			0		0.187381	−	0.982287i	$-0.440000\pi$
$683$		0			0		−0.187381	+	0.982287i	$0.560000\pi$
$684$		0			0
$685$	0.951325	−	1.14995i	0.951325	−	1.14995i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	1.27026	−	1.53548i	1.27026	−	1.53548i
$690$		0			0
$691$		0			0		0.968583	−	0.248690i	$-0.0800000\pi$
$691$		0			0		−0.968583	+	0.248690i	$0.920000\pi$
$692$	0.844844	−	1.79538i	0.844844	−	1.79538i
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−3.13440			−3.13440
$698$	−1.44644	−	1.35830i	−1.44644	−	1.35830i
$699$		0			0
$700$		0			0
$701$	0.0388067	−	0.119435i	0.0388067	−	0.119435i	−0.929776	−	0.368125i	$-0.880000\pi$
$701$	0.0388067	−	0.119435i	0.0388067	−	0.119435i	0.968583	+	0.248690i	$0.0800000\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	0.618034			0.618034
$707$		0			0
$708$		0			0
$709$	0.0915446	+	1.45506i	0.0915446	+	1.45506i	0.728969	+	0.684547i	$0.240000\pi$
$709$	0.0915446	+	1.45506i	0.0915446	+	1.45506i	−0.637424	+	0.770513i	$0.720000\pi$
$710$		0			0
$711$		0			0
$712$	0.0915446	−	1.45506i	0.0915446	−	1.45506i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		−0.968583	−	0.248690i	$-0.920000\pi$
$719$		0			0		0.968583	+	0.248690i	$0.0800000\pi$
$720$	−0.456288	+	0.718995i	−0.456288	+	0.718995i
$721$		0			0
$722$	−0.425779	+	0.904827i	−0.425779	+	0.904827i
$723$		0			0
$724$	−0.115808	−	0.356420i	−0.115808	−	0.356420i
$725$	0.108276	−	0.130884i	0.108276	−	0.130884i
$726$		0			0
$727$		0			0		−0.0627905	−	0.998027i	$-0.520000\pi$
$727$		0			0		0.0627905	+	0.998027i	$0.480000\pi$
$728$		0			0
$729$	−0.637424	+	0.770513i	−0.637424	+	0.770513i
$730$	0.951325	+	1.14995i	0.951325	+	1.14995i
$731$		0			0
$732$		0			0
$733$	0.110048	+	0.0604991i	0.110048	+	0.0604991i	0.535827	−	0.844328i	$-0.320000\pi$
$733$	0.110048	+	0.0604991i	0.110048	+	0.0604991i	−0.425779	+	0.904827i	$0.640000\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$	1.03799	+	1.63560i	1.03799	+	1.63560i
$739$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$739$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$740$	−0.719434	−	1.52888i	−0.719434	−	1.52888i
$741$		0			0
$742$		0			0
$743$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$743$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$744$		0			0
$745$	0.279658	−	1.46602i	0.279658	−	1.46602i
$746$	1.60528	−	1.16630i	1.60528	−	1.16630i
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$751$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$752$		0			0
$753$		0			0
$754$	−1.00711	+	0.553664i	−1.00711	+	0.553664i
$755$		0			0
$756$		0			0
$757$	0.0915446	−	1.45506i	0.0915446	−	1.45506i	−0.637424	−	0.770513i	$-0.720000\pi$
$757$	0.0915446	−	1.45506i	0.0915446	−	1.45506i	0.728969	−	0.684547i	$-0.240000\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−1.73879	+	0.955910i	−1.73879	+	0.955910i	−0.809017	+	0.587785i	$0.800000\pi$
$761$	−1.73879	+	0.955910i	−1.73879	+	0.955910i	−0.929776	+	0.368125i	$0.880000\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	1.20742	+	0.663785i	1.20742	+	0.663785i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	−0.809017	−	0.587785i	$-0.800000\pi$
$769$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	0.309017	+	0.951057i	$0.400000\pi$
$770$		0			0
$771$		0			0
$772$	−1.56720	−	1.13864i	−1.56720	−	1.13864i
$773$	1.53583	−	0.844328i	1.53583	−	0.844328i	0.535827	−	0.844328i	$-0.320000\pi$
$773$	1.53583	−	0.844328i	1.53583	−	0.844328i	1.00000			$0$
$774$		0			0
$775$		0			0
$776$	0.331159	+	1.01920i	0.331159	+	1.01920i
$777$		0			0
$778$	1.50441	+	0.595638i	1.50441	+	0.595638i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.187381	+	0.982287i	−0.187381	+	0.982287i
$785$	0.0681659	+	0.0823984i	0.0681659	+	0.0823984i
$786$		0			0
$787$		0			0		−0.187381	−	0.982287i	$-0.560000\pi$
$787$		0			0		0.187381	+	0.982287i	$0.440000\pi$
$788$	0.0388067	+	0.616814i	0.0388067	+	0.616814i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−0.296722	+	0.630566i	−0.296722	+	0.630566i
$794$	1.50441	−	1.09302i	1.50441	−	1.09302i
$795$		0			0
$796$		0			0
$797$	−0.273190	−	0.256543i	−0.273190	−	0.256543i	0.535827	−	0.844328i	$-0.320000\pi$
$797$	−0.273190	−	0.256543i	−0.273190	−	0.256543i	−0.809017	+	0.587785i	$0.800000\pi$
$798$		0			0
$799$		0			0
$800$	0.0515014	+	0.269980i	0.0515014	+	0.269980i
$801$	0.781202	+	1.23098i	0.781202	+	1.23098i
$802$	−0.574633	+	1.76854i	−0.574633	+	1.76854i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	0.309017	+	0.951057i	0.309017	+	0.951057i
$809$	−0.374763			−0.374763			−0.187381	−	0.982287i	$-0.560000\pi$
$809$	−0.374763			−0.374763			−0.187381	+	0.982287i	$0.560000\pi$
$810$	−0.0534698	−	0.849878i	−0.0534698	−	0.849878i
$811$		0			0		−0.929776	−	0.368125i	$-0.880000\pi$
$811$		0			0		0.929776	+	0.368125i	$0.120000\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	0.125581			0.125581
$819$		0			0
$820$	−1.59779	−	0.410241i	−1.59779	−	0.410241i
$821$	1.03799	−	1.63560i	1.03799	−	1.63560i	0.309017	−	0.951057i	$-0.400000\pi$
$821$	1.03799	−	1.63560i	1.03799	−	1.63560i	0.728969	−	0.684547i	$-0.240000\pi$
$822$		0			0
$823$		0			0		0.425779	−	0.904827i	$-0.360000\pi$
$823$		0			0		−0.425779	+	0.904827i	$0.640000\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		−0.968583	−	0.248690i	$-0.920000\pi$
$827$		0			0		0.968583	+	0.248690i	$0.0800000\pi$
$828$		0			0
$829$	0.348445	+	1.82662i	0.348445	+	1.82662i	0.535827	+	0.844328i	$0.320000\pi$
$829$	0.348445	+	1.82662i	0.348445	+	1.82662i	−0.187381	+	0.982287i	$0.560000\pi$
$830$		0			0
$831$		0			0
$832$	0.348445	−	1.82662i	0.348445	−	1.82662i
$833$	1.60528	+	0.202793i	1.60528	+	0.202793i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		−0.535827	−	0.844328i	$-0.680000\pi$
$839$		0			0		0.535827	+	0.844328i	$0.320000\pi$
$840$		0			0
$841$	0.263146	+	0.559214i	0.263146	+	0.559214i
$842$	1.18532	−	0.469303i	1.18532	−	0.469303i
$843$		0			0
$844$		0			0
$845$	1.94609	−	0.770513i	1.94609	−	0.770513i
$846$		0			0
$847$		0			0
$848$	−1.06320	+	0.134314i	−1.06320	+	0.134314i
$849$		0			0
$850$	0.430742	−	0.110596i	0.430742	−	0.110596i
$851$		0			0
$852$		0			0
$853$	1.06279	−	0.998027i	1.06279	−	0.998027i	0.0627905	−	0.998027i	$-0.480000\pi$
$853$	1.06279	−	0.998027i	1.06279	−	0.998027i	1.00000			$0$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−0.746226	+	1.58581i	−0.746226	+	1.58581i	0.0627905	+	0.998027i	$0.480000\pi$
$857$	−0.746226	+	1.58581i	−0.746226	+	1.58581i	−0.809017	+	0.587785i	$0.800000\pi$
$858$		0			0
$859$		0			0		0.0627905	−	0.998027i	$-0.480000\pi$
$859$		0			0		−0.0627905	+	0.998027i	$0.520000\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.728969	−	0.684547i	$-0.240000\pi$
$863$		0			0		−0.728969	+	0.684547i	$0.760000\pi$
$864$		0			0
$865$	−1.36699	−	0.993173i	−1.36699	−	0.993173i
$866$	−1.11716	−	0.614163i	−1.11716	−	0.614163i
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	−0.116762	+	0.0462295i	−0.116762	+	0.0462295i
$873$	−0.866986	−	0.629902i	−0.866986	−	0.629902i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	0.450527	+	1.38658i	0.450527	+	1.38658i	0.876307	+	0.481754i	$0.160000\pi$
$877$	0.450527	+	1.38658i	0.450527	+	1.38658i	−0.425779	+	0.904827i	$0.640000\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−0.0800484	−	0.0967619i	−0.0800484	−	0.0967619i	0.728969	−	0.684547i	$-0.240000\pi$
$881$	−0.0800484	−	0.0967619i	−0.0800484	−	0.0967619i	−0.809017	+	0.587785i	$0.800000\pi$
$882$	−0.425779	−	0.904827i	−0.425779	−	0.904827i
$883$		0			0		−0.876307	−	0.481754i	$-0.840000\pi$
$883$		0			0		0.876307	+	0.481754i	$0.160000\pi$
$884$	−2.98509	−	0.377105i	−2.98509	−	0.377105i
$885$		0			0
$886$		0			0
$887$		0			0		0.637424	−	0.770513i	$-0.280000\pi$
$887$		0			0		−0.637424	+	0.770513i	$0.720000\pi$
$888$		0			0
$889$		0			0
$890$	−1.20251	−	0.308753i	−1.20251	−	0.308753i
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−0.929324	−	0.872693i	−0.929324	−	0.872693i
$899$		0			0
$900$	−0.200356	−	0.188146i	−0.200356	−	0.188146i
$901$	0.324914	+	1.70326i	0.324914	+	1.70326i
$902$		0			0
$903$		0			0
$904$	0.00788530	−	0.125333i	0.00788530	−	0.125333i
$905$	−0.316616	+	0.0399979i	−0.316616	+	0.0399979i
$906$		0			0
$907$		0			0		−0.0627905	−	0.998027i	$-0.520000\pi$
$907$		0			0		0.0627905	+	0.998027i	$0.480000\pi$
$908$		0			0
$909$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$910$		0			0
$911$		0			0		−0.0627905	−	0.998027i	$-0.520000\pi$
$911$		0			0		0.0627905	+	0.998027i	$0.480000\pi$
$912$		0			0
$913$		0			0
$914$	−0.116762	+	1.85588i	−0.116762	+	1.85588i
$915$		0			0
$916$	0.574221	+	0.904827i	0.574221	+	0.904827i
$917$		0			0
$918$		0			0
$919$		0			0		1.00000			$0$
$919$		0			0		−1.00000			$\pi$
$920$		0			0
$921$		0			0
$922$	0.781202	−	1.23098i	0.781202	−	1.23098i
$923$		0			0
$924$		0			0
$925$	0.528228	−	0.135626i	0.528228	−	0.135626i
$926$		0			0
$927$		0			0
$928$	0.598617	+	0.153699i	0.598617	+	0.153699i
$929$	0.0388067	+	0.616814i	0.0388067	+	0.616814i	0.968583	+	0.248690i	$0.0800000\pi$
$929$	0.0388067	+	0.616814i	0.0388067	+	0.616814i	−0.929776	+	0.368125i	$0.880000\pi$
$930$		0			0
$931$		0			0
$932$	0.238883	+	0.288760i	0.238883	+	0.288760i
$933$		0			0
$934$		0			0
$935$		0			0
$936$	0.791759	+	1.68257i	0.791759	+	1.68257i
$937$	1.18532	+	1.43281i	1.18532	+	1.43281i	0.876307	+	0.481754i	$0.160000\pi$
$937$	1.18532	+	1.43281i	1.18532	+	1.43281i	0.309017	+	0.951057i	$0.400000\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	0.541587	+	1.66683i	0.541587	+	1.66683i	0.728969	+	0.684547i	$0.240000\pi$
$941$	0.541587	+	1.66683i	0.541587	+	1.66683i	−0.187381	+	0.982287i	$0.560000\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		0.187381	−	0.982287i	$-0.440000\pi$
$947$		0			0		−0.187381	+	0.982287i	$0.560000\pi$
$948$		0			0
$949$	3.23338	−	0.408471i	3.23338	−	0.408471i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	1.30902	+	0.951057i	1.30902	+	0.951057i	1.00000			$0$
$953$	1.30902	+	0.951057i	1.30902	+	0.951057i	0.309017	+	0.951057i	$0.400000\pi$
$954$	0.781202	−	0.733597i	0.781202	−	0.733597i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.425779	+	0.904827i	−0.425779	+	0.904827i
$962$	−3.66068	−	0.462452i	−3.66068	−	0.462452i
$963$		0			0
$964$	−0.929324	+	0.872693i	−0.929324	+	0.872693i
$965$	−1.20251	+	1.12924i	−1.20251	+	1.12924i
$966$		0			0
$967$		0			0		−0.876307	−	0.481754i	$-0.840000\pi$
$967$		0			0		0.876307	+	0.481754i	$0.160000\pi$
$968$	0.968583	−	0.248690i	0.968583	−	0.248690i
$969$		0			0
$970$	0.905380	−	0.114376i	0.905380	−	0.114376i
$971$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$971$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$	0.348445	−	0.137959i	0.348445	−	0.137959i
$977$	0.791759	+	1.68257i	0.791759	+	1.68257i	0.728969	+	0.684547i	$0.240000\pi$
$977$	0.791759	+	1.68257i	0.791759	+	1.68257i	0.0627905	+	0.998027i	$0.480000\pi$
$978$		0			0
$979$		0			0
$980$	0.791759	+	0.313480i	0.791759	+	0.313480i
$981$	0.0672897	−	0.106032i	0.0672897	−	0.106032i
$982$		0			0
$983$		0			0		−0.425779	−	0.904827i	$-0.640000\pi$
$983$		0			0		0.425779	+	0.904827i	$0.360000\pi$
$984$		0			0
$985$	0.522142	+	0.0659619i	0.522142	+	0.0659619i
$986$	0.187381	−	0.982287i	0.187381	−	0.982287i
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.968583	−	0.248690i	$-0.920000\pi$
$991$		0			0		0.968583	+	0.248690i	$0.0800000\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	0.574221	−	0.904827i	0.574221	−	0.904827i	−0.425779	−	0.904827i	$-0.640000\pi$
$997$	0.574221	−	0.904827i	0.574221	−	0.904827i	1.00000			$0$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	404.1.o.a.227.1	✓	20
3.2	odd	2		3636.1.bt.a.631.1		20
4.3	odd	2	CM	404.1.o.a.227.1	✓	20
12.11	even	2		3636.1.bt.a.631.1		20
101.97	even	25	inner	404.1.o.a.299.1	yes	20
303.299	odd	50		3636.1.bt.a.703.1		20
404.299	odd	50	inner	404.1.o.a.299.1	yes	20
1212.299	even	50		3636.1.bt.a.703.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
404.1.o.a.227.1	✓	20	1.1	even	1	trivial
404.1.o.a.227.1	✓	20	4.3	odd	2	CM
404.1.o.a.299.1	yes	20	101.97	even	25	inner
404.1.o.a.299.1	yes	20	404.299	odd	50	inner
3636.1.bt.a.631.1		20	3.2	odd	2
3636.1.bt.a.631.1		20	12.11	even	2
3636.1.bt.a.703.1		20	303.299	odd	50
3636.1.bt.a.703.1		20	1212.299	even	50

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:	\( N \)	\(=\)	\( 404 = 2^{2} \cdot 101 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	404.o (of order \(50\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0627905 + 0.998027i) q^{2} +(-0.992115 + 0.125333i) q^{4} +(-0.0534698 + 0.849878i) q^{5} +(-0.187381 - 0.982287i) q^{8} +(0.728969 + 0.684547i) q^{9} +O(q^{10})\)	\(q+(0.0627905 + 0.998027i) q^{2} +(-0.992115 + 0.125333i) q^{4} +(-0.0534698 + 0.849878i) q^{5} +(-0.187381 - 0.982287i) q^{8} +(0.728969 + 0.684547i) q^{9} -0.851559 q^{10} +(-0.996398 + 1.57007i) q^{13} +(0.968583 - 0.248690i) q^{16} +(-0.500000 - 1.53884i) q^{17} +(-0.637424 + 0.770513i) q^{18} +(-0.0534698 - 0.849878i) q^{20} +(0.272681 + 0.0344476i) q^{25} +(-1.62954 - 0.895846i) q^{26} +(0.331159 - 0.521823i) q^{29} +(0.309017 + 0.951057i) q^{32} +(1.50441 - 0.595638i) q^{34} +(-0.809017 - 0.587785i) q^{36} +(1.84489 - 0.730444i) q^{37} +(0.844844 - 0.106729i) q^{40} +(0.598617 - 1.84235i) q^{41} +(-0.620759 + 0.582932i) q^{45} +(-0.425779 + 0.904827i) q^{49} +(-0.0172578 + 0.274306i) q^{50} +(0.791759 - 1.68257i) q^{52} +(-1.06320 - 0.134314i) q^{53} +(0.541587 + 0.297740i) q^{58} +(0.371808 - 0.0469702i) q^{61} +(-0.929776 + 0.368125i) q^{64} +(-1.28109 - 0.930769i) q^{65} +(0.688925 + 1.46404i) q^{68} +(0.535827 - 0.844328i) q^{72} +(-1.11716 - 1.35041i) q^{73} +(0.844844 + 1.79538i) q^{74} +(0.159566 + 0.836475i) q^{80} +(0.0627905 + 0.998027i) q^{81} +(1.87631 + 0.481754i) q^{82} +(1.33456 - 0.342658i) q^{85} +(1.41213 + 0.362574i) q^{89} +(-0.620759 - 0.582932i) q^{90} +(-1.06320 + 0.134314i) q^{97} +(-0.929776 - 0.368125i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q+O(q^{10}) \) 20 * q	\( 20 q - 5 q^{13} - 10 q^{17} - 5 q^{32} - 5 q^{36} - 5 q^{40} - 5 q^{45} - 5 q^{50} - 5 q^{61} - 5 q^{74} - 5 q^{80} + 20 q^{82} - 5 q^{90}+O(q^{100}) \) 20 * q - 5 * q^13 - 10 * q^17 - 5 * q^32 - 5 * q^36 - 5 * q^40 - 5 * q^45 - 5 * q^50 - 5 * q^61 - 5 * q^74 - 5 * q^80 + 20 * q^82 - 5 * q^90

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