LMFDB - Embedded newform 869.1.j.a.394.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [869,1,Mod(157,869)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(869, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8, 5]))

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

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

chi := DirichletCharacter("869.157");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 869 = 11 \cdot 79 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	869.j (of order $10$, degree $4$, 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:	$0.433687495978$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{10})$
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:	$\Z[a_1, \ldots, a_{11}]$
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			394.2
Root			$0.187381 + 0.982287i$ of defining polynomial
Character	$\chi$	$=$	869.394
Dual form			869.1.j.a.236.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.263146 + 0.809880i) q^{2} +(0.222357 + 0.161552i) q^{4} +(0.331159 + 1.01920i) q^{5} +(-0.878275 + 0.638104i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.263146 + 0.809880i) q^{2} +(0.222357 + 0.161552i) q^{4} +(0.331159 + 1.01920i) q^{5} +(-0.878275 + 0.638104i) q^{8} +(0.309017 - 0.951057i) q^{9} -0.912576 q^{10} +(-0.425779 + 0.904827i) q^{11} +(-0.115808 + 0.356420i) q^{13} +(-0.200741 - 0.617816i) q^{16} +(0.688925 + 0.500534i) q^{18} +(-0.101597 + 0.0738147i) q^{19} +(-0.0910184 + 0.280126i) q^{20} +(-0.620759 - 0.582932i) q^{22} +0.125581 q^{23} +(-0.120092 + 0.0872517i) q^{25} +(-0.258183 - 0.187581i) q^{26} +(0.450527 - 1.38658i) q^{31} -0.532426 q^{32} +(0.222357 - 0.161552i) q^{36} +(-0.0330462 - 0.101706i) q^{38} +(-0.941207 - 0.683827i) q^{40} +(-0.240851 + 0.132409i) q^{44} +1.07165 q^{45} +(-0.0330462 + 0.101706i) q^{46} +(0.309017 + 0.951057i) q^{49} +(-0.0390618 - 0.120220i) q^{50} +(-0.0833310 + 0.0605435i) q^{52} +(-1.06320 - 0.134314i) q^{55} +(1.00441 + 0.729747i) q^{62} +(0.340847 - 1.04902i) q^{64} -0.401616 q^{65} -1.85955 q^{67} +(0.335471 + 1.03247i) q^{72} +(1.03137 + 0.749337i) q^{73} -0.0345157 q^{76} +(0.309017 - 0.951057i) q^{79} +(0.563203 - 0.409191i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(0.190983 + 0.587785i) q^{83} +(-0.203423 - 1.06638i) q^{88} +1.75261 q^{89} +(-0.282001 + 0.867911i) q^{90} +(0.0279238 + 0.0202878i) q^{92} +(-0.108877 - 0.0791038i) q^{95} +(0.598617 - 1.84235i) q^{97} -0.851559 q^{98} +(0.728969 + 0.684547i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 5 q^{4} - 5 q^{9}+O(q^{10}) $ 20 * q - 5 * q^4 - 5 * q^9	$ 20 q - 5 q^{4} - 5 q^{9} - 5 q^{16} + 15 q^{20} - 5 q^{22} - 5 q^{25} + 15 q^{26} - 10 q^{32} - 5 q^{36} - 10 q^{40} - 5 q^{49} - 10 q^{50} - 10 q^{62} - 5 q^{64} - 10 q^{76} - 5 q^{79} - 10 q^{80} - 5 q^{81} + 15 q^{83} - 5 q^{88} + 15 q^{92} + 15 q^{95}+O(q^{100}) $ 20 * q - 5 * q^4 - 5 * q^9 - 5 * q^16 + 15 * q^20 - 5 * q^22 - 5 * q^25 + 15 * q^26 - 10 * q^32 - 5 * q^36 - 10 * q^40 - 5 * q^49 - 10 * q^50 - 10 * q^62 - 5 * q^64 - 10 * q^76 - 5 * q^79 - 10 * q^80 - 5 * q^81 + 15 * q^83 - 5 * q^88 + 15 * q^92 + 15 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/869\mathbb{Z}\right)^\times$.

$n$	$475$	$793$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$-1$

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 $

$2$	−0.263146	+	0.809880i	−0.263146	+	0.809880i	0.728969	+	0.684547i	$0.240000\pi$
$2$	−0.263146	+	0.809880i	−0.263146	+	0.809880i	−0.992115	+	0.125333i	$0.960000\pi$
$3$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$3$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$4$	0.222357	+	0.161552i	0.222357	+	0.161552i
$5$	0.331159	+	1.01920i	0.331159	+	1.01920i	0.968583	+	0.248690i	$0.0800000\pi$
$5$	0.331159	+	1.01920i	0.331159	+	1.01920i	−0.637424	+	0.770513i	$0.720000\pi$
$6$		0			0
$7$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$7$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$8$	−0.878275	+	0.638104i	−0.878275	+	0.638104i
$9$	0.309017	−	0.951057i	0.309017	−	0.951057i
$10$	−0.912576			−0.912576
$11$	−0.425779	+	0.904827i	−0.425779	+	0.904827i
$11$	−0.425779	+	0.904827i	−0.425779	+	0.904827i
$12$		0			0
$13$	−0.115808	+	0.356420i	−0.115808	+	0.356420i	−0.992115	−	0.125333i	$-0.960000\pi$
$13$	−0.115808	+	0.356420i	−0.115808	+	0.356420i	0.876307	+	0.481754i	$0.160000\pi$
$14$		0			0
$15$		0			0
$16$	−0.200741	−	0.617816i	−0.200741	−	0.617816i
$17$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$17$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$18$	0.688925	+	0.500534i	0.688925	+	0.500534i
$19$	−0.101597	+	0.0738147i	−0.101597	+	0.0738147i	−0.637424	−	0.770513i	$-0.720000\pi$
$19$	−0.101597	+	0.0738147i	−0.101597	+	0.0738147i	0.535827	+	0.844328i	$0.320000\pi$
$20$	−0.0910184	+	0.280126i	−0.0910184	+	0.280126i
$21$		0			0
$22$	−0.620759	−	0.582932i	−0.620759	−	0.582932i
$23$	0.125581			0.125581			0.0627905	−	0.998027i	$-0.480000\pi$
$23$	0.125581			0.125581			0.0627905	+	0.998027i	$0.480000\pi$
$24$		0			0
$25$	−0.120092	+	0.0872517i	−0.120092	+	0.0872517i
$26$	−0.258183	−	0.187581i	−0.258183	−	0.187581i
$27$		0			0
$28$		0			0
$29$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$29$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$30$		0			0
$31$	0.450527	−	1.38658i	0.450527	−	1.38658i	−0.425779	−	0.904827i	$-0.640000\pi$
$31$	0.450527	−	1.38658i	0.450527	−	1.38658i	0.876307	−	0.481754i	$-0.160000\pi$
$32$	−0.532426			−0.532426
$33$		0			0
$34$		0			0
$35$		0			0
$36$	0.222357	−	0.161552i	0.222357	−	0.161552i
$37$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$37$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$38$	−0.0330462	−	0.101706i	−0.0330462	−	0.101706i
$39$		0			0
$40$	−0.941207	−	0.683827i	−0.941207	−	0.683827i
$41$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$41$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$42$		0			0
$43$		0			0		1.00000			$0$
$43$		0			0		−1.00000			$\pi$
$44$	−0.240851	+	0.132409i	−0.240851	+	0.132409i
$45$	1.07165			1.07165
$46$	−0.0330462	+	0.101706i	−0.0330462	+	0.101706i
$47$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$47$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$48$		0			0
$49$	0.309017	+	0.951057i	0.309017	+	0.951057i
$50$	−0.0390618	−	0.120220i	−0.0390618	−	0.120220i
$51$		0			0
$52$	−0.0833310	+	0.0605435i	−0.0833310	+	0.0605435i
$53$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$53$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$54$		0			0
$55$	−1.06320	−	0.134314i	−1.06320	−	0.134314i
$56$		0			0
$57$		0			0
$58$		0			0
$59$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$59$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$60$		0			0
$61$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$61$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$62$	1.00441	+	0.729747i	1.00441	+	0.729747i
$63$		0			0
$64$	0.340847	−	1.04902i	0.340847	−	1.04902i
$65$	−0.401616			−0.401616
$66$		0			0
$67$	−1.85955			−1.85955			−0.929776	−	0.368125i	$-0.880000\pi$
$67$	−1.85955			−1.85955			−0.929776	+	0.368125i	$0.880000\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$71$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$72$	0.335471	+	1.03247i	0.335471	+	1.03247i
$73$	1.03137	+	0.749337i	1.03137	+	0.749337i	0.968583	−	0.248690i	$-0.0800000\pi$
$73$	1.03137	+	0.749337i	1.03137	+	0.749337i	0.0627905	+	0.998027i	$0.480000\pi$
$74$		0			0
$75$		0			0
$76$	−0.0345157			−0.0345157
$77$		0			0
$78$		0			0
$79$	0.309017	−	0.951057i	0.309017	−	0.951057i
$79$	0.309017	−	0.951057i	0.309017	−	0.951057i
$80$	0.563203	−	0.409191i	0.563203	−	0.409191i
$81$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$82$		0			0
$83$	0.190983	+	0.587785i	0.190983	+	0.587785i	1.00000			$0$
$83$	0.190983	+	0.587785i	0.190983	+	0.587785i	−0.809017	+	0.587785i	$0.800000\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$	−0.203423	−	1.06638i	−0.203423	−	1.06638i
$89$	1.75261			1.75261			0.876307	−	0.481754i	$-0.160000\pi$
$89$	1.75261			1.75261			0.876307	+	0.481754i	$0.160000\pi$
$90$	−0.282001	+	0.867911i	−0.282001	+	0.867911i
$91$		0			0
$92$	0.0279238	+	0.0202878i	0.0279238	+	0.0202878i
$93$		0			0
$94$		0			0
$95$	−0.108877	−	0.0791038i	−0.108877	−	0.0791038i
$96$		0			0
$97$	0.598617	−	1.84235i	0.598617	−	1.84235i	0.0627905	−	0.998027i	$-0.480000\pi$
$97$	0.598617	−	1.84235i	0.598617	−	1.84235i	0.535827	−	0.844328i	$-0.320000\pi$
$98$	−0.851559			−0.851559
$99$	0.728969	+	0.684547i	0.728969	+	0.684547i
$100$	−0.0407988			−0.0407988
$101$	0.541587	−	1.66683i	0.541587	−	1.66683i	−0.187381	−	0.982287i	$-0.560000\pi$
$101$	0.541587	−	1.66683i	0.541587	−	1.66683i	0.728969	−	0.684547i	$-0.240000\pi$
$102$		0			0
$103$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$103$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$104$	−0.125722	−	0.386933i	−0.125722	−	0.386933i
$105$		0			0
$106$		0			0
$107$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$107$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$108$		0			0
$109$		0			0		1.00000			$0$
$109$		0			0		−1.00000			$\pi$
$110$	0.388556	−	0.825723i	0.388556	−	0.825723i
$111$		0			0
$112$		0			0
$113$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$113$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$114$		0			0
$115$	0.0415873	+	0.127993i	0.0415873	+	0.127993i
$116$		0			0
$117$	0.303189	+	0.220280i	0.303189	+	0.220280i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.637424	−	0.770513i	−0.637424	−	0.770513i
$122$		0			0
$123$		0			0
$124$	0.324182	−	0.235532i	0.324182	−	0.235532i
$125$	0.738289	+	0.536399i	0.738289	+	0.536399i
$126$		0			0
$127$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$127$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$128$	0.329145	+	0.239138i	0.329145	+	0.239138i
$129$		0			0
$130$	0.105684	−	0.325261i	0.105684	−	0.325261i
$131$	−1.27485			−1.27485			−0.637424	−	0.770513i	$-0.720000\pi$
$131$	−1.27485			−1.27485			−0.637424	+	0.770513i	$0.720000\pi$
$132$		0			0
$133$		0			0
$134$	0.489334	−	1.50602i	0.489334	−	1.50602i
$135$		0			0
$136$		0			0
$137$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$137$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$138$		0			0
$139$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$139$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−0.273190	−	0.256543i	−0.273190	−	0.256543i
$144$	−0.649611			−0.649611
$145$		0			0
$146$	−0.878275	+	0.638104i	−0.878275	+	0.638104i
$147$		0			0
$148$		0			0
$149$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$149$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$150$		0			0
$151$	1.50441	−	1.09302i	1.50441	−	1.09302i	0.535827	−	0.844328i	$-0.320000\pi$
$151$	1.50441	−	1.09302i	1.50441	−	1.09302i	0.968583	−	0.248690i	$-0.0800000\pi$
$152$	0.0421288	−	0.129659i	0.0421288	−	0.129659i
$153$		0			0
$154$		0			0
$155$	1.56240			1.56240
$156$		0			0
$157$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$157$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$158$	0.688925	+	0.500534i	0.688925	+	0.500534i
$159$		0			0
$160$	−0.176318	−	0.542651i	−0.176318	−	0.542651i
$161$		0			0
$162$	0.688925	−	0.500534i	0.688925	−	0.500534i
$163$	−0.613161	+	1.88711i	−0.613161	+	1.88711i	−0.187381	+	0.982287i	$0.560000\pi$
$163$	−0.613161	+	1.88711i	−0.613161	+	1.88711i	−0.425779	+	0.904827i	$0.640000\pi$
$164$		0			0
$165$		0			0
$166$	−0.526292			−0.526292
$167$	0.450527	−	1.38658i	0.450527	−	1.38658i	−0.425779	−	0.904827i	$-0.640000\pi$
$167$	0.450527	−	1.38658i	0.450527	−	1.38658i	0.876307	−	0.481754i	$-0.160000\pi$
$168$		0			0
$169$	0.695393	+	0.505233i	0.695393	+	0.505233i
$170$		0			0
$171$	0.0388067	+	0.119435i	0.0388067	+	0.119435i
$172$		0			0
$173$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$173$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$174$		0			0
$175$		0			0
$176$	0.644488	+	0.0814178i	0.644488	+	0.0814178i
$177$		0			0
$178$	−0.461193	+	1.41941i	−0.461193	+	1.41941i
$179$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	−0.809017	−	0.587785i	$-0.800000\pi$
$179$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	0.309017	+	0.951057i	$0.400000\pi$
$180$	0.238289	+	0.173127i	0.238289	+	0.173127i
$181$	−0.115808	−	0.356420i	−0.115808	−	0.356420i	0.876307	−	0.481754i	$-0.160000\pi$
$181$	−0.115808	−	0.356420i	−0.115808	−	0.356420i	−0.992115	+	0.125333i	$0.960000\pi$
$182$		0			0
$183$		0			0
$184$	−0.110295	+	0.0801338i	−0.110295	+	0.0801338i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$	0.0927151	−	0.0673615i	0.0927151	−	0.0673615i
$191$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$191$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$192$		0			0
$193$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$193$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$194$	1.33456	+	0.969617i	1.33456	+	0.969617i
$195$		0			0
$196$	−0.0849327	+	0.261396i	−0.0849327	+	0.261396i
$197$		0			0		1.00000			$0$
$197$		0			0		−1.00000			$\pi$
$198$	−0.746226	+	0.410241i	−0.746226	+	0.410241i
$199$		0			0		1.00000			$0$
$199$		0			0		−1.00000			$\pi$
$200$	0.0497978	−	0.153262i	0.0497978	−	0.153262i
$201$		0			0
$202$	1.20742	+	0.877242i	1.20742	+	0.877242i
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	0.0388067	−	0.119435i	0.0388067	−	0.119435i
$208$	0.243450			0.243450
$209$	−0.0235315	−	0.123357i	−0.0235315	−	0.123357i
$210$		0			0
$211$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$211$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$		0			0
$219$		0			0
$220$	−0.214712	−	0.201628i	−0.214712	−	0.201628i
$221$		0			0
$222$		0			0
$223$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	−0.809017	−	0.587785i	$-0.800000\pi$
$223$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	0.309017	+	0.951057i	$0.400000\pi$
$224$		0			0
$225$	0.0458709	+	0.141176i	0.0458709	+	0.141176i
$226$		0			0
$227$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$227$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$228$		0			0
$229$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$229$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$230$	−0.114602			−0.114602
$231$		0			0
$232$		0			0
$233$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$233$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$234$	−0.258183	+	0.187581i	−0.258183	+	0.187581i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−0.866986	+	0.629902i	−0.866986	+	0.629902i	−0.929776	−	0.368125i	$-0.880000\pi$
$239$	−0.866986	+	0.629902i	−0.866986	+	0.629902i	0.0627905	+	0.998027i	$0.480000\pi$
$240$		0			0
$241$	−1.98423			−1.98423			−0.992115	−	0.125333i	$-0.960000\pi$
$241$	−1.98423			−1.98423			−0.992115	+	0.125333i	$0.960000\pi$
$242$	0.791759	−	0.313480i	0.791759	−	0.313480i
$243$		0			0
$244$		0			0
$245$	−0.866986	+	0.629902i	−0.866986	+	0.629902i
$246$		0			0
$247$	−0.0145433	−	0.0447596i	−0.0145433	−	0.0447596i
$248$	0.489096	+	1.50528i	0.489096	+	1.50528i
$249$		0			0
$250$	−0.628697	+	0.456775i	−0.628697	+	0.456775i
$251$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$251$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$252$		0			0
$253$	−0.0534698	+	0.113629i	−0.0534698	+	0.113629i
$254$		0			0
$255$		0			0
$256$	0.612062	−	0.444689i	0.612062	−	0.444689i
$257$	0.303189	+	0.220280i	0.303189	+	0.220280i	0.728969	−	0.684547i	$-0.240000\pi$
$257$	0.303189	+	0.220280i	0.303189	+	0.220280i	−0.425779	+	0.904827i	$0.640000\pi$
$258$		0			0
$259$		0			0
$260$	−0.0893019	−	0.0648817i	−0.0893019	−	0.0648817i
$261$		0			0
$262$	0.335471	−	1.03247i	0.335471	−	1.03247i
$263$	−1.98423			−1.98423			−0.992115	−	0.125333i	$-0.960000\pi$
$263$	−1.98423			−1.98423			−0.992115	+	0.125333i	$0.960000\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	−0.413484	−	0.300414i	−0.413484	−	0.300414i
$269$	−0.574633	−	1.76854i	−0.574633	−	1.76854i	−0.637424	−	0.770513i	$-0.720000\pi$
$269$	−0.574633	−	1.76854i	−0.574633	−	1.76854i	0.0627905	−	0.998027i	$-0.480000\pi$
$270$		0			0
$271$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$271$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−0.0278151	−	0.145812i	−0.0278151	−	0.145812i
$276$		0			0
$277$	0.331159	−	1.01920i	0.331159	−	1.01920i	−0.637424	−	0.770513i	$-0.720000\pi$
$277$	0.331159	−	1.01920i	0.331159	−	1.01920i	0.968583	−	0.248690i	$-0.0800000\pi$
$278$		0			0
$279$	−1.17950	−	0.856954i	−1.17950	−	0.856954i
$280$		0			0
$281$	0.331159	+	1.01920i	0.331159	+	1.01920i	0.968583	+	0.248690i	$0.0800000\pi$
$281$	0.331159	+	1.01920i	0.331159	+	1.01920i	−0.637424	+	0.770513i	$0.720000\pi$
$282$		0			0
$283$	−1.17950	+	0.856954i	−1.17950	+	0.856954i	−0.992115	−	0.125333i	$-0.960000\pi$
$283$	−1.17950	+	0.856954i	−1.17950	+	0.856954i	−0.187381	+	0.982287i	$0.560000\pi$
$284$		0			0
$285$		0			0
$286$	0.279658	−	0.153743i	0.279658	−	0.153743i
$287$		0			0
$288$	−0.164529	+	0.506367i	−0.164529	+	0.506367i
$289$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$290$		0			0
$291$		0			0
$292$	0.108276	+	0.333240i	0.108276	+	0.333240i
$293$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$293$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−0.0145433	+	0.0447596i	−0.0145433	+	0.0447596i
$300$		0			0
$301$		0			0
$302$	0.489334	+	1.50602i	0.489334	+	1.50602i
$303$		0			0
$304$	0.0659986	+	0.0479508i	0.0659986	+	0.0479508i
$305$		0			0
$306$		0			0
$307$		0			0		1.00000			$0$
$307$		0			0		−1.00000			$\pi$
$308$		0			0
$309$		0			0
$310$	−0.411140	+	1.26536i	−0.411140	+	1.26536i
$311$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$311$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$312$		0			0
$313$	0.450527	+	1.38658i	0.450527	+	1.38658i	0.876307	+	0.481754i	$0.160000\pi$
$313$	0.450527	+	1.38658i	0.450527	+	1.38658i	−0.425779	+	0.904827i	$0.640000\pi$
$314$		0			0
$315$		0			0
$316$	0.222357	−	0.161552i	0.222357	−	0.161552i
$317$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	0.309017	+	0.951057i	$0.400000\pi$
$317$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	−0.809017	+	0.587785i	$0.800000\pi$
$318$		0			0
$319$		0			0
$320$	1.18204			1.18204
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−0.0849327	−	0.261396i	−0.0849327	−	0.261396i
$325$	−0.0171907	−	0.0529076i	−0.0171907	−	0.0529076i
$326$	−1.36699	−	0.993173i	−1.36699	−	0.993173i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$		0			0		1.00000			$0$
$331$		0			0		−1.00000			$\pi$
$332$	−0.0524913	+	0.161552i	−0.0524913	+	0.161552i
$333$		0			0
$334$	1.00441	+	0.729747i	1.00441	+	0.729747i
$335$	−0.615808	−	1.89526i	−0.615808	−	1.89526i
$336$		0			0
$337$	−1.56720	−	1.13864i	−1.56720	−	1.13864i	−0.929776	−	0.368125i	$-0.880000\pi$
$337$	−1.56720	−	1.13864i	−1.56720	−	1.13864i	−0.637424	−	0.770513i	$-0.720000\pi$
$338$	−0.592168	+	0.430235i	−0.592168	+	0.430235i
$339$		0			0
$340$		0			0
$341$	1.06279	+	0.998027i	1.06279	+	0.998027i
$342$	−0.106940			−0.106940
$343$		0			0
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−0.574633	−	1.76854i	−0.574633	−	1.76854i	−0.637424	−	0.770513i	$-0.720000\pi$
$347$	−0.574633	−	1.76854i	−0.574633	−	1.76854i	0.0627905	−	0.998027i	$-0.480000\pi$
$348$		0			0
$349$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$349$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$350$		0			0
$351$		0			0
$352$	0.226696	−	0.481754i	0.226696	−	0.481754i
$353$		0			0		1.00000			$0$
$353$		0			0		−1.00000			$\pi$
$354$		0			0
$355$		0			0
$356$	0.389705	+	0.283137i	0.389705	+	0.283137i
$357$		0			0
$358$	−0.162633	−	0.500534i	−0.162633	−	0.500534i
$359$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$359$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$360$	−0.941207	+	0.683827i	−0.941207	+	0.683827i
$361$	−0.304144	+	0.936058i	−0.304144	+	0.936058i
$362$	0.319132			0.319132
$363$		0			0
$364$		0			0
$365$	−0.422178	+	1.29933i	−0.422178	+	1.29933i
$366$		0			0
$367$	−1.41789	−	1.03016i	−1.41789	−	1.03016i	−0.992115	−	0.125333i	$-0.960000\pi$
$367$	−1.41789	−	1.03016i	−1.41789	−	1.03016i	−0.425779	−	0.904827i	$-0.640000\pi$
$368$	−0.0252092	−	0.0775860i	−0.0252092	−	0.0775860i
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		1.00000			$0$
$373$		0			0		−1.00000			$\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$379$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$380$	−0.0114302	−	0.0351785i	−0.0114302	−	0.0351785i
$381$		0			0
$382$		0			0
$383$	−0.263146	+	0.809880i	−0.263146	+	0.809880i	0.728969	+	0.684547i	$0.240000\pi$
$383$	−0.263146	+	0.809880i	−0.263146	+	0.809880i	−0.992115	+	0.125333i	$0.960000\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		0			0
$388$	0.430742	−	0.312952i	0.430742	−	0.312952i
$389$	−1.17950	−	0.856954i	−1.17950	−	0.856954i	−0.187381	−	0.982287i	$-0.560000\pi$
$389$	−1.17950	−	0.856954i	−1.17950	−	0.856954i	−0.992115	+	0.125333i	$0.960000\pi$
$390$		0			0
$391$		0			0
$392$	−0.878275	−	0.638104i	−0.878275	−	0.638104i
$393$		0			0
$394$		0			0
$395$	1.07165			1.07165
$396$	0.0515014	+	0.269980i	0.0515014	+	0.269980i
$397$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$397$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$398$		0			0
$399$		0			0
$400$	0.0780128	+	0.0566796i	0.0780128	+	0.0566796i
$401$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$401$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$402$		0			0
$403$	0.442031	+	0.321154i	0.442031	+	0.321154i
$404$	0.389705	−	0.283137i	0.389705	−	0.283137i
$405$	0.331159	−	1.01920i	0.331159	−	1.01920i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$409$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	0.0865160	+	0.0628575i	0.0865160	+	0.0628575i
$415$	−0.535827	+	0.389301i	−0.535827	+	0.389301i
$416$	0.0616592	−	0.189768i	0.0616592	−	0.189768i
$417$		0			0
$418$	0.106096	+	0.0134031i	0.106096	+	0.0134031i
$419$		0			0		1.00000			$0$
$419$		0			0		−1.00000			$\pi$
$420$		0			0
$421$	−1.56720	+	1.13864i	−1.56720	+	1.13864i	−0.637424	+	0.770513i	$0.720000\pi$
$421$	−1.56720	+	1.13864i	−1.56720	+	1.13864i	−0.929776	+	0.368125i	$0.880000\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		0			0
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−0.393950	+	1.21245i	−0.393950	+	1.21245i	0.535827	+	0.844328i	$0.320000\pi$
$431$	−0.393950	+	1.21245i	−0.393950	+	1.21245i	−0.929776	+	0.368125i	$0.880000\pi$
$432$		0			0
$433$	−0.101597	−	0.0738147i	−0.101597	−	0.0738147i	0.535827	−	0.844328i	$-0.320000\pi$
$433$	−0.101597	−	0.0738147i	−0.101597	−	0.0738147i	−0.637424	+	0.770513i	$0.720000\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−0.0127587	+	0.00926972i	−0.0127587	+	0.00926972i
$438$		0			0
$439$	1.93717			1.93717			0.968583	−	0.248690i	$-0.0800000\pi$
$439$	1.93717			1.93717			0.968583	+	0.248690i	$0.0800000\pi$
$440$	1.01949	−	0.560470i	1.01949	−	0.560470i
$441$	1.00000			1.00000
$442$		0			0
$443$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$443$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$444$		0			0
$445$	0.580394	+	1.78627i	0.580394	+	1.78627i
$446$	−0.162633	−	0.500534i	−0.162633	−	0.500534i
$447$		0			0
$448$		0			0
$449$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$449$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$450$	−0.126407			−0.126407
$451$		0			0
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	0.541587	+	1.66683i	0.541587	+	1.66683i	0.728969	+	0.684547i	$0.240000\pi$
$457$	0.541587	+	1.66683i	0.541587	+	1.66683i	−0.187381	+	0.982287i	$0.560000\pi$
$458$		0			0
$459$		0			0
$460$	−0.0114302	+	0.0351785i	−0.0114302	+	0.0351785i
$461$		0			0		1.00000			$0$
$461$		0			0		−1.00000			$\pi$
$462$		0			0
$463$		0			0		1.00000			$0$
$463$		0			0		−1.00000			$\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−0.263146	−	0.809880i	−0.263146	−	0.809880i	−0.992115	−	0.125333i	$-0.960000\pi$
$467$	−0.263146	−	0.809880i	−0.263146	−	0.809880i	0.728969	−	0.684547i	$-0.240000\pi$
$468$	0.0318296	+	0.0979614i	0.0318296	+	0.0979614i
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$	0.00576052	−	0.0177291i	0.00576052	−	0.0177291i
$476$		0			0
$477$		0			0
$478$	−0.282001	−	0.867911i	−0.282001	−	0.867911i
$479$	0.190983	+	0.587785i	0.190983	+	0.587785i	1.00000			$0$
$479$	0.190983	+	0.587785i	0.190983	+	0.587785i	−0.809017	+	0.587785i	$0.800000\pi$
$480$		0			0
$481$		0			0
$482$	0.522142	−	1.60699i	0.522142	−	1.60699i
$483$		0			0
$484$	−0.0172578	−	0.274306i	−0.0172578	−	0.274306i
$485$	2.07597			2.07597
$486$		0			0
$487$	0.303189	−	0.220280i	0.303189	−	0.220280i	−0.425779	−	0.904827i	$-0.640000\pi$
$487$	0.303189	−	0.220280i	0.303189	−	0.220280i	0.728969	+	0.684547i	$0.240000\pi$
$488$		0			0
$489$		0			0
$490$	−0.282001	−	0.867911i	−0.282001	−	0.867911i
$491$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$491$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$492$		0			0
$493$		0			0
$494$	0.0400770			0.0400770
$495$	−0.456288	+	0.969661i	−0.456288	+	0.969661i
$496$	−0.947092			−0.947092
$497$		0			0
$498$		0			0
$499$	0.688925	+	0.500534i	0.688925	+	0.500534i	0.876307	−	0.481754i	$-0.160000\pi$
$499$	0.688925	+	0.500534i	0.688925	+	0.500534i	−0.187381	+	0.982287i	$0.560000\pi$
$500$	0.0775075	+	0.238544i	0.0775075	+	0.238544i
$501$		0			0
$502$		0			0
$503$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$503$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$504$		0			0
$505$	1.87819			1.87819
$506$	−0.0779556	−	0.0732052i	−0.0779556	−	0.0732052i
$507$		0			0
$508$		0			0
$509$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$509$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$510$		0			0
$511$		0			0
$512$	0.324805	+	0.999648i	0.324805	+	0.999648i
$513$		0			0
$514$	−0.258183	+	0.187581i	−0.258183	+	0.187581i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	0.352729	−	0.256273i	0.352729	−	0.256273i
$521$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$521$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$522$		0			0
$523$	0.541587	+	1.66683i	0.541587	+	1.66683i	0.728969	+	0.684547i	$0.240000\pi$
$523$	0.541587	+	1.66683i	0.541587	+	1.66683i	−0.187381	+	0.982287i	$0.560000\pi$
$524$	−0.283471	−	0.205954i	−0.283471	−	0.205954i
$525$		0			0
$526$	0.522142	−	1.60699i	0.522142	−	1.60699i
$527$		0			0
$528$		0			0
$529$	−0.984229			−0.984229
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	1.63320	−	1.18659i	1.63320	−	1.18659i
$537$		0			0
$538$	1.58352			1.58352
$539$	−0.992115	−	0.125333i	−0.992115	−	0.125333i
$540$		0			0
$541$	0.190983	−	0.587785i	0.190983	−	0.587785i	−0.809017	−	0.587785i	$-0.800000\pi$
$541$	0.190983	−	0.587785i	0.190983	−	0.587785i	1.00000			$0$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	1.60528	−	1.16630i	1.60528	−	1.16630i	0.728969	−	0.684547i	$-0.240000\pi$
$547$	1.60528	−	1.16630i	1.60528	−	1.16630i	0.876307	−	0.481754i	$-0.160000\pi$
$548$		0			0
$549$		0			0
$550$	0.125410	+	0.0158429i	0.125410	+	0.0158429i
$551$		0			0
$552$		0			0
$553$		0			0
$554$	0.738289	+	0.536399i	0.738289	+	0.536399i
$555$		0			0
$556$		0			0
$557$	−0.101597	−	0.0738147i	−0.101597	−	0.0738147i	0.535827	−	0.844328i	$-0.320000\pi$
$557$	−0.101597	−	0.0738147i	−0.101597	−	0.0738147i	−0.637424	+	0.770513i	$0.720000\pi$
$558$	1.00441	−	0.729747i	1.00441	−	0.729747i
$559$		0			0
$560$		0			0
$561$		0			0
$562$	−0.912576			−0.912576
$563$	0.618034	−	1.90211i	0.618034	−	1.90211i	0.309017	−	0.951057i	$-0.400000\pi$
$563$	0.618034	−	1.90211i	0.618034	−	1.90211i	0.309017	−	0.951057i	$-0.400000\pi$
$564$		0			0
$565$		0			0
$566$	−0.383650	−	1.18075i	−0.383650	−	1.18075i
$567$		0			0
$568$		0			0
$569$	−1.56720	+	1.13864i	−1.56720	+	1.13864i	−0.637424	+	0.770513i	$0.720000\pi$
$569$	−1.56720	+	1.13864i	−1.56720	+	1.13864i	−0.929776	+	0.368125i	$0.880000\pi$
$570$		0			0
$571$	1.45794			1.45794			0.728969	−	0.684547i	$-0.240000\pi$
$571$	1.45794			1.45794			0.728969	+	0.684547i	$0.240000\pi$
$572$	−0.0193008	−	0.101178i	−0.0193008	−	0.101178i
$573$		0			0
$574$		0			0
$575$	−0.0150812	+	0.0109572i	−0.0150812	+	0.0109572i
$576$	−0.892348	−	0.648329i	−0.892348	−	0.648329i
$577$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$577$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$578$	−0.263146	−	0.809880i	−0.263146	−	0.809880i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$	−1.38398			−1.38398
$585$	−0.124106	+	0.381959i	−0.124106	+	0.381959i
$586$		0			0
$587$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$587$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$588$		0			0
$589$	0.0565777	+	0.174128i	0.0565777	+	0.174128i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	1.07165			1.07165			0.535827	−	0.844328i	$-0.320000\pi$
$593$	1.07165			1.07165			0.535827	+	0.844328i	$0.320000\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$	−0.0324229	−	0.0235567i	−0.0324229	−	0.0235567i
$599$	−0.393950	−	1.21245i	−0.393950	−	1.21245i	−0.929776	−	0.368125i	$-0.880000\pi$
$599$	−0.393950	−	1.21245i	−0.393950	−	1.21245i	0.535827	−	0.844328i	$-0.320000\pi$
$600$		0			0
$601$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$601$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$602$		0			0
$603$	−0.574633	+	1.76854i	−0.574633	+	1.76854i
$604$	0.511094			0.511094
$605$	0.574221	−	0.904827i	0.574221	−	0.904827i
$606$		0			0
$607$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$607$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$608$	0.0540930	−	0.0393009i	0.0540930	−	0.0393009i
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$613$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−0.374763			−0.374763			−0.187381	−	0.982287i	$-0.560000\pi$
$617$	−0.374763			−0.374763			−0.187381	+	0.982287i	$0.560000\pi$
$618$		0			0
$619$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$619$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$620$	0.347411	+	0.252409i	0.347411	+	0.252409i
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.348079	+	1.07128i	−0.348079	+	1.07128i
$626$	−1.24152			−1.24152
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$631$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$632$	0.335471	+	1.03247i	0.335471	+	1.03247i
$633$		0			0
$634$	−1.11470	−	0.809880i	−1.11470	−	0.809880i
$635$		0			0
$636$		0			0
$637$	−0.374763			−0.374763
$638$		0			0
$639$		0			0
$640$	−0.134731	+	0.414658i	−0.134731	+	0.414658i
$641$	−0.101597	+	0.0738147i	−0.101597	+	0.0738147i	−0.637424	−	0.770513i	$-0.720000\pi$
$641$	−0.101597	+	0.0738147i	−0.101597	+	0.0738147i	0.535827	+	0.844328i	$0.320000\pi$
$642$		0			0
$643$	−0.393950	−	1.21245i	−0.393950	−	1.21245i	−0.929776	−	0.368125i	$-0.880000\pi$
$643$	−0.393950	−	1.21245i	−0.393950	−	1.21245i	0.535827	−	0.844328i	$-0.320000\pi$
$644$		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	$0.600000\pi$
$648$	1.08561			1.08561
$649$		0			0
$650$	0.0473725			0.0473725
$651$		0			0
$652$	−0.441207	+	0.320555i	−0.441207	+	0.320555i
$653$	−1.41789	−	1.03016i	−1.41789	−	1.03016i	−0.992115	−	0.125333i	$-0.960000\pi$
$653$	−1.41789	−	1.03016i	−1.41789	−	1.03016i	−0.425779	−	0.904827i	$-0.640000\pi$
$654$		0			0
$655$	−0.422178	−	1.29933i	−0.422178	−	1.29933i
$656$		0			0
$657$	1.03137	−	0.749337i	1.03137	−	0.749337i
$658$		0			0
$659$		0			0		1.00000			$0$
$659$		0			0		−1.00000			$\pi$
$660$		0			0
$661$		0			0		1.00000			$0$
$661$		0			0		−1.00000			$\pi$
$662$		0			0
$663$		0			0
$664$	−0.542804	−	0.394370i	−0.542804	−	0.394370i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	0.324182	−	0.235532i	0.324182	−	0.235532i
$669$		0			0
$670$	1.69698			1.69698
$671$		0			0
$672$		0			0
$673$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$673$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$674$	1.33456	−	0.969617i	1.33456	−	0.969617i
$675$		0			0
$676$	0.0730042	+	0.224684i	0.0730042	+	0.224684i
$677$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	−0.809017	−	0.587785i	$-0.800000\pi$
$677$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	0.309017	−	0.951057i	$-0.400000\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$	−1.08795	+	0.598106i	−1.08795	+	0.598106i
$683$	−1.27485			−1.27485			−0.637424	−	0.770513i	$-0.720000\pi$
$683$	−1.27485			−1.27485			−0.637424	+	0.770513i	$0.720000\pi$
$684$	−0.0106659	+	0.0328264i	−0.0106659	+	0.0328264i
$685$		0			0
$686$		0			0
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$691$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$692$		0			0
$693$		0			0
$694$	1.58352			1.58352
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$		0			0
$701$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$701$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$702$		0			0
$703$		0			0
$704$	0.804054	+	0.755057i	0.804054	+	0.755057i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$709$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$710$		0			0
$711$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$712$	−1.53928	+	1.11835i	−1.53928	+	1.11835i
$713$	0.0565777	−	0.174128i	0.0565777	−	0.174128i
$714$		0			0
$715$	0.171000	−	0.363393i	0.171000	−	0.363393i
$716$	−0.169865			−0.169865
$717$		0			0
$718$		0			0
$719$	1.60528	+	1.16630i	1.60528	+	1.16630i	0.876307	+	0.481754i	$0.160000\pi$
$719$	1.60528	+	1.16630i	1.60528	+	1.16630i	0.728969	+	0.684547i	$0.240000\pi$
$720$	−0.215125	−	0.662085i	−0.215125	−	0.662085i
$721$		0			0
$722$	−0.678061	−	0.492640i	−0.678061	−	0.492640i
$723$		0			0
$724$	0.0318296	−	0.0979614i	0.0318296	−	0.0979614i
$725$		0			0
$726$		0			0
$727$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$727$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$728$		0			0
$729$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$730$	−0.941207	−	0.683827i	−0.941207	−	0.683827i
$731$		0			0
$732$		0			0
$733$	1.50441	+	1.09302i	1.50441	+	1.09302i	0.968583	+	0.248690i	$0.0800000\pi$
$733$	1.50441	+	1.09302i	1.50441	+	1.09302i	0.535827	+	0.844328i	$0.320000\pi$
$734$	1.20742	−	0.877242i	1.20742	−	0.877242i
$735$		0			0
$736$	−0.0668626			−0.0668626
$737$	0.791759	−	1.68257i	0.791759	−	1.68257i
$738$		0			0
$739$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$739$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−0.115808	−	0.356420i	−0.115808	−	0.356420i	0.876307	−	0.481754i	$-0.160000\pi$
$743$	−0.115808	−	0.356420i	−0.115808	−	0.356420i	−0.992115	+	0.125333i	$0.960000\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	0.618034			0.618034
$748$		0			0
$749$		0			0
$750$		0			0
$751$	0.688925	−	0.500534i	0.688925	−	0.500534i	−0.187381	−	0.982287i	$-0.560000\pi$
$751$	0.688925	−	0.500534i	0.688925	−	0.500534i	0.876307	+	0.481754i	$0.160000\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	1.61221	+	1.17134i	1.61221	+	1.17134i
$756$		0			0
$757$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	0.309017	+	0.951057i	$0.400000\pi$
$757$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	−0.809017	+	0.587785i	$0.800000\pi$
$758$		0			0
$759$		0			0
$760$	0.146100			0.146100
$761$	0.0388067	−	0.119435i	0.0388067	−	0.119435i	−0.929776	−	0.368125i	$-0.880000\pi$
$761$	0.0388067	−	0.119435i	0.0388067	−	0.119435i	0.968583	+	0.248690i	$0.0800000\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$	−0.586660	−	0.426234i	−0.586660	−	0.426234i
$767$		0			0
$768$		0			0
$769$		0			0		1.00000			$0$
$769$		0			0		−1.00000			$\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	1.03137	−	0.749337i	1.03137	−	0.749337i	0.0627905	−	0.998027i	$-0.480000\pi$
$773$	1.03137	−	0.749337i	1.03137	−	0.749337i	0.968583	+	0.248690i	$0.0800000\pi$
$774$		0			0
$775$	0.0668769	+	0.205826i	0.0668769	+	0.205826i
$776$	0.649864	+	2.00007i	0.649864	+	2.00007i
$777$		0			0
$778$	1.00441	−	0.729747i	1.00441	−	0.729747i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.525546	−	0.381832i	0.525546	−	0.381832i
$785$		0			0
$786$		0			0
$787$	0.598617	+	1.84235i	0.598617	+	1.84235i	0.535827	+	0.844328i	$0.320000\pi$
$787$	0.598617	+	1.84235i	0.598617	+	1.84235i	0.0627905	+	0.998027i	$0.480000\pi$
$788$		0			0
$789$		0			0
$790$	−0.282001	+	0.867911i	−0.282001	+	0.867911i
$791$		0			0
$792$	−1.07705	−	0.136063i	−1.07705	−	0.136063i
$793$		0			0
$794$	−0.162633	+	0.500534i	−0.162633	+	0.500534i
$795$		0			0
$796$		0			0
$797$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$797$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$798$		0			0
$799$		0			0
$800$	0.0639399	−	0.0464551i	0.0639399	−	0.0464551i
$801$	0.541587	−	1.66683i	0.541587	−	1.66683i
$802$		0			0
$803$	−1.11716	+	0.614163i	−1.11716	+	0.614163i
$804$		0			0
$805$		0			0
$806$	−0.376415	+	0.273482i	−0.376415	+	0.273482i
$807$		0			0
$808$	0.587951	+	1.80953i	0.587951	+	1.80953i
$809$	−0.613161	−	1.88711i	−0.613161	−	1.88711i	−0.425779	−	0.904827i	$-0.640000\pi$
$809$	−0.613161	−	1.88711i	−0.613161	−	1.88711i	−0.187381	−	0.982287i	$-0.560000\pi$
$810$	0.738289	+	0.536399i	0.738289	+	0.536399i
$811$	1.30902	−	0.951057i	1.30902	−	0.951057i	0.309017	−	0.951057i	$-0.400000\pi$
$811$	1.30902	−	0.951057i	1.30902	−	0.951057i	1.00000			$0$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−2.12641			−2.12641
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−1.17950	−	0.856954i	−1.17950	−	0.856954i	−0.187381	−	0.982287i	$-0.560000\pi$
$821$	−1.17950	−	0.856954i	−1.17950	−	0.856954i	−0.992115	+	0.125333i	$0.960000\pi$
$822$		0			0
$823$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$823$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$827$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$828$	0.0279238	−	0.0202878i	0.0279238	−	0.0202878i
$829$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$829$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$830$	−0.174286	−	0.536399i	−0.174286	−	0.536399i
$831$		0			0
$832$	0.334419	+	0.242969i	0.334419	+	0.242969i
$833$		0			0
$834$		0			0
$835$	1.56240			1.56240
$836$	0.0146961	−	0.0312307i	0.0146961	−	0.0312307i
$837$		0			0
$838$		0			0
$839$	−1.56720	+	1.13864i	−1.56720	+	1.13864i	−0.637424	+	0.770513i	$0.720000\pi$
$839$	−1.56720	+	1.13864i	−1.56720	+	1.13864i	−0.929776	+	0.368125i	$0.880000\pi$
$840$		0			0
$841$	0.309017	+	0.951057i	0.309017	+	0.951057i
$842$	−0.509758	−	1.56887i	−0.509758	−	1.56887i
$843$		0			0
$844$		0			0
$845$	−0.284649	+	0.876059i	−0.284649	+	0.876059i
$846$		0			0
$847$		0			0
$848$		0			0
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$853$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$854$		0			0
$855$	−0.108877	+	0.0791038i	−0.108877	+	0.0791038i
$856$		0			0
$857$	0.125581			0.125581			0.0627905	−	0.998027i	$-0.480000\pi$
$857$	0.125581			0.125581			0.0627905	+	0.998027i	$0.480000\pi$
$858$		0			0
$859$		0			0		1.00000			$0$
$859$		0			0		−1.00000			$\pi$
$860$		0			0
$861$		0			0
$862$	−0.878275	−	0.638104i	−0.878275	−	0.638104i
$863$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	−0.809017	−	0.587785i	$-0.800000\pi$
$863$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	0.309017	−	0.951057i	$-0.400000\pi$
$864$		0			0
$865$		0			0
$866$	0.0865160	−	0.0628575i	0.0865160	−	0.0628575i
$867$		0			0
$868$		0			0
$869$	0.728969	+	0.684547i	0.728969	+	0.684547i
$870$		0			0
$871$	0.215351	−	0.662783i	0.215351	−	0.662783i
$872$		0			0
$873$	−1.56720	−	1.13864i	−1.56720	−	1.13864i
$874$	−0.00414997	−	0.0127723i	−0.00414997	−	0.0127723i
$875$		0			0
$876$		0			0
$877$	−1.17950	+	0.856954i	−1.17950	+	0.856954i	−0.992115	−	0.125333i	$-0.960000\pi$
$877$	−1.17950	+	0.856954i	−1.17950	+	0.856954i	−0.187381	+	0.982287i	$0.560000\pi$
$878$	−0.509758	+	1.56887i	−0.509758	+	1.56887i
$879$		0			0
$880$	0.130447	+	0.683827i	0.130447	+	0.683827i
$881$		0			0		1.00000			$0$
$881$		0			0		−1.00000			$\pi$
$882$	−0.263146	+	0.809880i	−0.263146	+	0.809880i
$883$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$883$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−0.866986	−	0.629902i	−0.866986	−	0.629902i	0.0627905	−	0.998027i	$-0.480000\pi$
$887$	−0.866986	−	0.629902i	−0.866986	−	0.629902i	−0.929776	+	0.368125i	$0.880000\pi$
$888$		0			0
$889$		0			0
$890$	−1.59939			−1.59939
$891$	0.876307	−	0.481754i	0.876307	−	0.481754i
$892$	−0.169865			−0.169865
$893$		0			0
$894$		0			0
$895$	−0.535827	−	0.389301i	−0.535827	−	0.389301i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$	−0.0126075	+	0.0388020i	−0.0126075	+	0.0388020i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$	0.324914	−	0.236064i	0.324914	−	0.236064i
$906$		0			0
$907$	0.190983	+	0.587785i	0.190983	+	0.587785i	1.00000			$0$
$907$	0.190983	+	0.587785i	0.190983	+	0.587785i	−0.809017	+	0.587785i	$0.800000\pi$
$908$		0			0
$909$	−1.41789	−	1.03016i	−1.41789	−	1.03016i
$910$		0			0
$911$	−0.574633	+	1.76854i	−0.574633	+	1.76854i	0.0627905	+	0.998027i	$0.480000\pi$
$911$	−0.574633	+	1.76854i	−0.574633	+	1.76854i	−0.637424	+	0.770513i	$0.720000\pi$
$912$		0			0
$913$	−0.613161	−	0.0774602i	−0.613161	−	0.0774602i
$914$	−1.49245			−1.49245
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	0.450527	+	1.38658i	0.450527	+	1.38658i	0.876307	+	0.481754i	$0.160000\pi$
$919$	0.450527	+	1.38658i	0.450527	+	1.38658i	−0.425779	+	0.904827i	$0.640000\pi$
$920$	−0.118198	−	0.0858757i	−0.118198	−	0.0858757i
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$929$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$930$		0			0
$931$	−0.101597	−	0.0738147i	−0.101597	−	0.0738147i
$932$		0			0
$933$		0			0
$934$	0.725152			0.725152
$935$		0			0
$936$	−0.406845			−0.406845
$937$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$937$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	−0.809017	−	0.587785i	$-0.800000\pi$
$941$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	0.309017	−	0.951057i	$-0.400000\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		1.00000			$0$
$947$		0			0		−1.00000			$\pi$
$948$		0			0
$949$	−0.386520	+	0.280823i	−0.386520	+	0.280823i
$950$	0.0128426	+	0.00933066i	0.0128426	+	0.00933066i
$951$		0			0
$952$		0			0
$953$	1.60528	+	1.16630i	1.60528	+	1.16630i	0.876307	+	0.481754i	$0.160000\pi$
$953$	1.60528	+	1.16630i	1.60528	+	1.16630i	0.728969	+	0.684547i	$0.240000\pi$
$954$		0			0
$955$		0			0
$956$	−0.294542			−0.294542
$957$		0			0
$958$	−0.526292			−0.526292
$959$		0			0
$960$		0			0
$961$	−0.910614	−	0.661600i	−0.910614	−	0.661600i
$962$		0			0
$963$		0			0
$964$	−0.441207	−	0.320555i	−0.441207	−	0.320555i
$965$		0			0
$966$		0			0
$967$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$967$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$968$	1.05150	+	0.269980i	1.05150	+	0.269980i
$969$		0			0
$970$	−0.546284	+	1.68129i	−0.546284	+	1.68129i
$971$	1.60528	−	1.16630i	1.60528	−	1.16630i	0.728969	−	0.684547i	$-0.240000\pi$
$971$	1.60528	−	1.16630i	1.60528	−	1.16630i	0.876307	−	0.481754i	$-0.160000\pi$
$972$		0			0
$973$		0			0
$974$	0.0986173	+	0.303513i	0.0986173	+	0.303513i
$975$		0			0
$976$		0			0
$977$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$977$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$978$		0			0
$979$	−0.746226	+	1.58581i	−0.746226	+	1.58581i
$980$	−0.294542			−0.294542
$981$		0			0
$982$		0			0
$983$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$983$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$	0.00399719	−	0.0123021i	0.00399719	−	0.0123021i
$989$		0			0
$990$	−0.665239	−	0.624701i	−0.665239	−	0.624701i
$991$		0			0		1.00000			$0$
$991$		0			0		−1.00000			$\pi$
$992$	−0.239873	+	0.738252i	−0.239873	+	0.738252i
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	1.50441	+	1.09302i	1.50441	+	1.09302i	0.968583	+	0.248690i	$0.0800000\pi$
$997$	1.50441	+	1.09302i	1.50441	+	1.09302i	0.535827	+	0.844328i	$0.320000\pi$
$998$	−0.586660	+	0.426234i	−0.586660	+	0.426234i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	869.1.j.a.394.2	yes	20
11.5	even	5	inner	869.1.j.a.236.2	✓	20
79.78	odd	2	CM	869.1.j.a.394.2	yes	20
869.236	odd	10	inner	869.1.j.a.236.2	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
869.1.j.a.236.2	✓	20	11.5	even	5	inner
869.1.j.a.236.2	✓	20	869.236	odd	10	inner
869.1.j.a.394.2	yes	20	1.1	even	1	trivial
869.1.j.a.394.2	yes	20	79.78	odd	2	CM

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:	\( N \)	\(=\)	\( 869 = 11 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	869.j (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.263146 + 0.809880i) q^{2} +(0.222357 + 0.161552i) q^{4} +(0.331159 + 1.01920i) q^{5} +(-0.878275 + 0.638104i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.263146 + 0.809880i) q^{2} +(0.222357 + 0.161552i) q^{4} +(0.331159 + 1.01920i) q^{5} +(-0.878275 + 0.638104i) q^{8} +(0.309017 - 0.951057i) q^{9} -0.912576 q^{10} +(-0.425779 + 0.904827i) q^{11} +(-0.115808 + 0.356420i) q^{13} +(-0.200741 - 0.617816i) q^{16} +(0.688925 + 0.500534i) q^{18} +(-0.101597 + 0.0738147i) q^{19} +(-0.0910184 + 0.280126i) q^{20} +(-0.620759 - 0.582932i) q^{22} +0.125581 q^{23} +(-0.120092 + 0.0872517i) q^{25} +(-0.258183 - 0.187581i) q^{26} +(0.450527 - 1.38658i) q^{31} -0.532426 q^{32} +(0.222357 - 0.161552i) q^{36} +(-0.0330462 - 0.101706i) q^{38} +(-0.941207 - 0.683827i) q^{40} +(-0.240851 + 0.132409i) q^{44} +1.07165 q^{45} +(-0.0330462 + 0.101706i) q^{46} +(0.309017 + 0.951057i) q^{49} +(-0.0390618 - 0.120220i) q^{50} +(-0.0833310 + 0.0605435i) q^{52} +(-1.06320 - 0.134314i) q^{55} +(1.00441 + 0.729747i) q^{62} +(0.340847 - 1.04902i) q^{64} -0.401616 q^{65} -1.85955 q^{67} +(0.335471 + 1.03247i) q^{72} +(1.03137 + 0.749337i) q^{73} -0.0345157 q^{76} +(0.309017 - 0.951057i) q^{79} +(0.563203 - 0.409191i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(0.190983 + 0.587785i) q^{83} +(-0.203423 - 1.06638i) q^{88} +1.75261 q^{89} +(-0.282001 + 0.867911i) q^{90} +(0.0279238 + 0.0202878i) q^{92} +(-0.108877 - 0.0791038i) q^{95} +(0.598617 - 1.84235i) q^{97} -0.851559 q^{98} +(0.728969 + 0.684547i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 5 q^{4} - 5 q^{9}+O(q^{10}) \) 20 * q - 5 * q^4 - 5 * q^9	\( 20 q - 5 q^{4} - 5 q^{9} - 5 q^{16} + 15 q^{20} - 5 q^{22} - 5 q^{25} + 15 q^{26} - 10 q^{32} - 5 q^{36} - 10 q^{40} - 5 q^{49} - 10 q^{50} - 10 q^{62} - 5 q^{64} - 10 q^{76} - 5 q^{79} - 10 q^{80} - 5 q^{81} + 15 q^{83} - 5 q^{88} + 15 q^{92} + 15 q^{95}+O(q^{100}) \) 20 * q - 5 * q^4 - 5 * q^9 - 5 * q^16 + 15 * q^20 - 5 * q^22 - 5 * q^25 + 15 * q^26 - 10 * q^32 - 5 * q^36 - 10 * q^40 - 5 * q^49 - 10 * q^50 - 10 * q^62 - 5 * q^64 - 10 * q^76 - 5 * q^79 - 10 * q^80 - 5 * q^81 + 15 * q^83 - 5 * q^88 + 15 * q^92 + 15 * q^95

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