LMFDB - Embedded newform 2008.1.bd.a.595.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2008,1,Mod(3,2008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2008, base_ring=CyclotomicField(250))

chi = DirichletCharacter(H, H._module([125, 125, 16]))

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

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

chi := DirichletCharacter("2008.3");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2008 = 2^{3} \cdot 251 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2008.bd (of order $250$, degree $100$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.00212254537$
Analytic rank:	$0$
Dimension:	$100$
Coefficient field:	$\Q(\zeta_{250})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{100} - x^{75} + x^{50} - x^{25} + 1 $ x^100 - x^75 + x^50 - x^25 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{125}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{125} - \cdots)$

Embedding invariants

Embedding label			595.1
Root			$-0.994951 + 0.100362i$ of defining polynomial
Character	$\chi$	$=$	2008.595
Dual form			2008.1.bd.a.27.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.929776 + 0.368125i) q^{2} +(0.740210 - 0.170347i) q^{3} +(0.728969 - 0.684547i) q^{4} +(-0.625521 + 0.430874i) q^{6} +(-0.425779 + 0.904827i) q^{8} +(-0.380513 + 0.184931i) q^{9} +O(q^{10})$	\(q+(-0.929776 + 0.368125i) q^{2} +(0.740210 - 0.170347i) q^{3} +(0.728969 - 0.684547i) q^{4} +(-0.625521 + 0.430874i) q^{6} +(-0.425779 + 0.904827i) q^{8} +(-0.380513 + 0.184931i) q^{9} +(0.0562293 + 1.49082i) q^{11} +(0.422979 - 0.630886i) q^{12} +(0.0627905 - 0.998027i) q^{16} +(-1.28470 + 0.983652i) q^{17} +(0.285714 - 0.312021i) q^{18} +(-1.15824 + 1.55277i) q^{19} +(-0.601089 - 1.36543i) q^{22} +(-0.161032 + 0.742292i) q^{24} +(0.968583 + 0.248690i) q^{25} +(-0.841444 + 0.678475i) q^{27} +(0.309017 + 0.951057i) q^{32} +(0.295578 + 1.09394i) q^{33} +(0.832381 - 1.38751i) q^{34} +(-0.150788 + 0.395288i) q^{36} +(0.505293 - 1.87010i) q^{38} +(-0.389145 - 0.347447i) q^{41} +(0.472849 - 1.94265i) q^{43} +(1.06153 + 1.04827i) q^{44} +(-0.123532 - 0.749445i) q^{48} +(-0.745941 + 0.666012i) q^{49} +(-0.992115 + 0.125333i) q^{50} +(-0.783388 + 0.946954i) q^{51} +(0.532592 - 0.940586i) q^{54} +(-0.592833 + 1.34668i) q^{57} +(0.981149 + 0.751231i) q^{59} +(-0.637424 - 0.770513i) q^{64} +(-0.677529 - 0.908313i) q^{66} +(1.90009 + 0.191664i) q^{67} +(-0.263152 + 1.59649i) q^{68} +(-0.00531633 - 0.423038i) q^{72} +(-0.0941461 - 1.06751i) q^{73} +(0.759318 + 0.0190878i) q^{75} +(0.218622 + 1.92479i) q^{76} +(-0.245871 + 0.312895i) q^{81} +(0.489722 + 0.179794i) q^{82} +(1.29827 - 0.197272i) q^{83} +(0.275494 + 1.98030i) q^{86} +(-1.37288 - 0.583883i) q^{88} +(0.518795 - 1.74471i) q^{89} +(0.390747 + 0.651341i) q^{96} +(1.10781 - 1.09397i) q^{97} +(0.448383 - 0.893841i) q^{98} +(-0.297095 - 0.556878i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q+O(q^{10}) $ 100 * q	$ 100 q - 25 q^{22} - 25 q^{32}+O(q^{100}) $ 100 * q - 25 * q^22 - 25 * q^32

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2008\mathbb{Z}\right)^\times$.

$n$	$257$	$503$	$1005$
$\chi(n)$	$e\left(\frac{101}{125}\right)$	$-1$	$-1$

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 $

$2$	−0.929776	+	0.368125i	−0.929776	+	0.368125i
$2$	−0.929776	+	0.368125i	−0.929776	+	0.368125i
$3$	0.740210	−	0.170347i	0.740210	−	0.170347i	0.162637	−	0.986686i	$-0.448000\pi$
$3$	0.740210	−	0.170347i	0.740210	−	0.170347i	0.577573	+	0.816339i	$0.304000\pi$
$4$	0.728969	−	0.684547i	0.728969	−	0.684547i
$5$		0			0		−0.992115	−	0.125333i	$-0.960000\pi$
$5$		0			0		0.992115	+	0.125333i	$0.0400000\pi$
$6$	−0.625521	+	0.430874i	−0.625521	+	0.430874i
$7$		0			0		−0.356412	−	0.934329i	$-0.616000\pi$
$7$		0			0		0.356412	+	0.934329i	$0.384000\pi$
$8$	−0.425779	+	0.904827i	−0.425779	+	0.904827i
$9$	−0.380513	+	0.184931i	−0.380513	+	0.184931i
$10$		0			0
$11$	0.0562293	+	1.49082i	0.0562293	+	1.49082i	0.693653	+	0.720309i	$0.256000\pi$
$11$	0.0562293	+	1.49082i	0.0562293	+	1.49082i	−0.637424	+	0.770513i	$0.720000\pi$
$12$	0.422979	−	0.630886i	0.422979	−	0.630886i
$13$		0			0		−0.984564	−	0.175023i	$-0.944000\pi$
$13$		0			0		0.984564	+	0.175023i	$0.0560000\pi$
$14$		0			0
$15$		0			0
$16$	0.0627905	−	0.998027i	0.0627905	−	0.998027i
$17$	−1.28470	+	0.983652i	−1.28470	+	0.983652i	−0.285019	+	0.958522i	$0.592000\pi$
$17$	−1.28470	+	0.983652i	−1.28470	+	0.983652i	−0.999684	+	0.0251301i	$0.992000\pi$
$18$	0.285714	−	0.312021i	0.285714	−	0.312021i
$19$	−1.15824	+	1.55277i	−1.15824	+	1.55277i	−0.379779	+	0.925077i	$0.624000\pi$
$19$	−1.15824	+	1.55277i	−1.15824	+	1.55277i	−0.778462	+	0.627691i	$0.784000\pi$
$20$		0			0
$21$		0			0
$22$	−0.601089	−	1.36543i	−0.601089	−	1.36543i
$23$		0			0		−0.332820	−	0.942991i	$-0.608000\pi$
$23$		0			0		0.332820	+	0.942991i	$0.392000\pi$
$24$	−0.161032	+	0.742292i	−0.161032	+	0.742292i
$25$	0.968583	+	0.248690i	0.968583	+	0.248690i
$26$		0			0
$27$	−0.841444	+	0.678475i	−0.841444	+	0.678475i
$28$		0			0
$29$		0			0		−0.979855	−	0.199710i	$-0.936000\pi$
$29$		0			0		0.979855	+	0.199710i	$0.0640000\pi$
$30$		0			0
$31$		0			0		−0.617860	−	0.786288i	$-0.712000\pi$
$31$		0			0		0.617860	+	0.786288i	$0.288000\pi$
$32$	0.309017	+	0.951057i	0.309017	+	0.951057i
$33$	0.295578	+	1.09394i	0.295578	+	1.09394i
$34$	0.832381	−	1.38751i	0.832381	−	1.38751i
$35$		0			0
$36$	−0.150788	+	0.395288i	−0.150788	+	0.395288i
$37$		0			0		−0.693653	−	0.720309i	$-0.744000\pi$
$37$		0			0		0.693653	+	0.720309i	$0.256000\pi$
$38$	0.505293	−	1.87010i	0.505293	−	1.87010i
$39$		0			0
$40$		0			0
$41$	−0.389145	−	0.347447i	−0.389145	−	0.347447i	0.448383	−	0.893841i	$-0.352000\pi$
$41$	−0.389145	−	0.347447i	−0.389145	−	0.347447i	−0.837528	+	0.546394i	$0.816000\pi$
$42$		0			0
$43$	0.472849	−	1.94265i	0.472849	−	1.94265i	0.212007	−	0.977268i	$-0.432000\pi$
$43$	0.472849	−	1.94265i	0.472849	−	1.94265i	0.260842	−	0.965382i	$-0.416000\pi$
$44$	1.06153	+	1.04827i	1.06153	+	1.04827i
$45$		0			0
$46$		0			0
$47$		0			0		−0.0627905	−	0.998027i	$-0.520000\pi$
$47$		0			0		0.0627905	+	0.998027i	$0.480000\pi$
$48$	−0.123532	−	0.749445i	−0.123532	−	0.749445i
$49$	−0.745941	+	0.666012i	−0.745941	+	0.666012i
$50$	−0.992115	+	0.125333i	−0.992115	+	0.125333i
$51$	−0.783388	+	0.946954i	−0.783388	+	0.946954i
$52$		0			0
$53$		0			0		−0.762443	−	0.647056i	$-0.776000\pi$
$53$		0			0		0.762443	+	0.647056i	$0.224000\pi$
$54$	0.532592	−	0.940586i	0.532592	−	0.940586i
$55$		0			0
$56$		0			0
$57$	−0.592833	+	1.34668i	−0.592833	+	1.34668i
$58$		0			0
$59$	0.981149	+	0.751231i	0.981149	+	0.751231i	0.968583	−	0.248690i	$-0.0800000\pi$
$59$	0.981149	+	0.751231i	0.981149	+	0.751231i	0.0125660	+	0.999921i	$0.496000\pi$
$60$		0			0
$61$		0			0		0.379779	−	0.925077i	$-0.376000\pi$
$61$		0			0		−0.379779	+	0.925077i	$0.624000\pi$
$62$		0			0
$63$		0			0
$64$	−0.637424	−	0.770513i	−0.637424	−	0.770513i
$65$		0			0
$66$	−0.677529	−	0.908313i	−0.677529	−	0.908313i
$67$	1.90009	+	0.191664i	1.90009	+	0.191664i	0.979855	−	0.199710i	$-0.0640000\pi$
$67$	1.90009	+	0.191664i	1.90009	+	0.191664i	0.920232	+	0.391374i	$0.128000\pi$
$68$	−0.263152	+	1.59649i	−0.263152	+	1.59649i
$69$		0			0
$70$		0			0
$71$		0			0		0.470704	−	0.882291i	$-0.344000\pi$
$71$		0			0		−0.470704	+	0.882291i	$0.656000\pi$
$72$	−0.00531633	−	0.423038i	−0.00531633	−	0.423038i
$73$	−0.0941461	−	1.06751i	−0.0941461	−	1.06751i	−0.888136	−	0.459580i	$-0.848000\pi$
$73$	−0.0941461	−	1.06751i	−0.0941461	−	1.06751i	0.793990	−	0.607930i	$-0.208000\pi$
$74$		0			0
$75$	0.759318	+	0.0190878i	0.759318	+	0.0190878i
$76$	0.218622	+	1.92479i	0.218622	+	1.92479i
$77$		0			0
$78$		0			0
$79$		0			0		−0.492727	−	0.870184i	$-0.664000\pi$
$79$		0			0		0.492727	+	0.870184i	$0.336000\pi$
$80$		0			0
$81$	−0.245871	+	0.312895i	−0.245871	+	0.312895i
$82$	0.489722	+	0.179794i	0.489722	+	0.179794i
$83$	1.29827	−	0.197272i	1.29827	−	0.197272i	0.535827	−	0.844328i	$-0.320000\pi$
$83$	1.29827	−	0.197272i	1.29827	−	0.197272i	0.762443	+	0.647056i	$0.224000\pi$
$84$		0			0
$85$		0			0
$86$	0.275494	+	1.98030i	0.275494	+	1.98030i
$87$		0			0
$88$	−1.37288	−	0.583883i	−1.37288	−	0.583883i
$89$	0.518795	−	1.74471i	0.518795	−	1.74471i	−0.137790	−	0.990461i	$-0.544000\pi$
$89$	0.518795	−	1.74471i	0.518795	−	1.74471i	0.656586	−	0.754251i	$-0.272000\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	0.390747	+	0.651341i	0.390747	+	0.651341i
$97$	1.10781	−	1.09397i	1.10781	−	1.09397i	0.112856	−	0.993611i	$-0.464000\pi$
$97$	1.10781	−	1.09397i	1.10781	−	1.09397i	0.994951	−	0.100362i	$-0.0320000\pi$
$98$	0.448383	−	0.893841i	0.448383	−	0.893841i
$99$	−0.297095	−	0.556878i	−0.297095	−	0.556878i
$100$	0.876307	−	0.481754i	0.876307	−	0.481754i
$101$		0			0		0.938734	−	0.344643i	$-0.112000\pi$
$101$		0			0		−0.938734	+	0.344643i	$0.888000\pi$
$102$	0.379779	−	1.16884i	0.379779	−	1.16884i
$103$		0			0		−0.998737	−	0.0502443i	$-0.984000\pi$
$103$		0			0		0.998737	+	0.0502443i	$0.0160000\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.757400	+	1.84490i	0.757400	+	1.84490i	0.448383	+	0.893841i	$0.352000\pi$
$107$	0.757400	+	1.84490i	0.757400	+	1.84490i	0.309017	+	0.951057i	$0.400000\pi$
$108$	−0.148938	+	1.07060i	−0.148938	+	1.07060i
$109$		0			0		0.112856	−	0.993611i	$-0.464000\pi$
$109$		0			0		−0.112856	+	0.993611i	$0.536000\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−1.33250	−	0.968121i	−1.33250	−	0.968121i	−0.999684	−	0.0251301i	$-0.992000\pi$
$113$	−1.33250	−	0.968121i	−1.33250	−	0.968121i	−0.332820	−	0.942991i	$-0.608000\pi$
$114$	0.0554570	−	1.47035i	0.0554570	−	1.47035i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	−1.18880	−	0.337292i	−1.18880	−	0.337292i
$119$		0			0
$120$		0			0
$121$	−1.22223	+	0.0923290i	−1.22223	+	0.0923290i
$122$		0			0
$123$	−0.347235	−	0.190894i	−0.347235	−	0.190894i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		−0.988652	−	0.150226i	$-0.952000\pi$
$127$		0			0		0.988652	+	0.150226i	$0.0480000\pi$
$128$	0.876307	+	0.481754i	0.876307	+	0.481754i
$129$	0.0190832	−	1.51852i	0.0190832	−	1.51852i
$130$		0			0
$131$	0.124728	−	0.353398i	0.124728	−	0.353398i	−0.863923	−	0.503623i	$-0.832000\pi$
$131$	0.124728	−	0.353398i	0.124728	−	0.353398i	0.988652	+	0.150226i	$0.0480000\pi$
$132$	0.964323	+	0.595113i	0.964323	+	0.595113i
$133$		0			0
$134$	−1.83721	+	0.521264i	−1.83721	+	0.521264i
$135$		0			0
$136$	−0.343035	−	1.58125i	−0.343035	−	1.58125i
$137$	−0.0574732	+	1.52380i	−0.0574732	+	1.52380i	0.617860	+	0.786288i	$0.288000\pi$
$137$	−0.0574732	+	1.52380i	−0.0574732	+	1.52380i	−0.675333	+	0.737513i	$0.736000\pi$
$138$		0			0
$139$	−1.86108	+	0.578950i	−1.86108	+	0.578950i	−0.863923	+	0.503623i	$0.832000\pi$
$139$	−1.86108	+	0.578950i	−1.86108	+	0.578950i	−0.997159	+	0.0753268i	$0.976000\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	0.160674	+	0.391374i	0.160674	+	0.391374i
$145$		0			0
$146$	0.480511	+	0.957888i	0.480511	+	0.957888i
$147$	−0.438700	+	0.620057i	−0.438700	+	0.620057i
$148$		0			0
$149$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$149$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$150$	−0.713023	+	0.261776i	−0.713023	+	0.261776i
$151$		0			0		0.876307	−	0.481754i	$-0.160000\pi$
$151$		0			0		−0.876307	+	0.481754i	$0.840000\pi$
$152$	−0.911832	−	1.70914i	−0.911832	−	1.70914i
$153$	0.306938	−	0.611874i	0.306938	−	0.611874i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.425779	−	0.904827i	$-0.640000\pi$
$157$		0			0		0.425779	+	0.904827i	$0.360000\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	0.113420	−	0.381433i	0.113420	−	0.381433i
$163$	1.80339	+	0.766979i	1.80339	+	0.766979i	0.979855	+	0.199710i	$0.0640000\pi$
$163$	1.80339	+	0.766979i	1.80339	+	0.766979i	0.823533	+	0.567269i	$0.192000\pi$
$164$	−0.521518	+	0.0131099i	−0.521518	+	0.0131099i
$165$		0			0
$166$	−1.13448	+	0.661344i	−1.13448	+	0.661344i
$167$		0			0		−0.974527	−	0.224271i	$-0.928000\pi$
$167$		0			0		0.974527	+	0.224271i	$0.0720000\pi$
$168$		0			0
$169$	0.938734	+	0.344643i	0.938734	+	0.344643i
$170$		0			0
$171$	0.153570	−	0.805043i	0.153570	−	0.805043i
$172$	−0.985143	−	1.73982i	−0.985143	−	1.73982i
$173$		0			0		0.910106	−	0.414376i	$-0.136000\pi$
$173$		0			0		−0.910106	+	0.414376i	$0.864000\pi$
$174$		0			0
$175$		0			0
$176$	1.49141	+	0.0374911i	1.49141	+	0.0374911i
$177$	0.854226	+	0.388933i	0.854226	+	0.388933i
$178$	0.159908	+	1.81317i	0.159908	+	1.81317i
$179$	0.0174330	+	1.38720i	0.0174330	+	1.38720i	0.728969	+	0.684547i	$0.240000\pi$
$179$	0.0174330	+	1.38720i	0.0174330	+	1.38720i	−0.711536	+	0.702650i	$0.752000\pi$
$180$		0			0
$181$		0			0		−0.577573	−	0.816339i	$-0.696000\pi$
$181$		0			0		0.577573	+	0.816339i	$0.304000\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−1.53869	−	1.85995i	−1.53869	−	1.85995i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		0.656586	−	0.754251i	$-0.272000\pi$
$191$		0			0		−0.656586	+	0.754251i	$0.728000\pi$
$192$	−0.603082	−	0.461758i	−0.603082	−	0.461758i
$193$	−1.84849	+	0.328600i	−1.84849	+	0.328600i	−0.984564	−	0.175023i	$-0.944000\pi$
$193$	−1.84849	+	0.328600i	−1.84849	+	0.328600i	−0.863923	+	0.503623i	$0.832000\pi$
$194$	−0.627295	+	1.42496i	−0.627295	+	1.42496i
$195$		0			0
$196$	−0.0878512	+	0.996134i	−0.0878512	+	0.996134i
$197$		0			0		0.492727	−	0.870184i	$-0.336000\pi$
$197$		0			0		−0.492727	+	0.870184i	$0.664000\pi$
$198$	0.481233	+	0.408404i	0.481233	+	0.408404i
$199$		0			0		0.837528	−	0.546394i	$-0.184000\pi$
$199$		0			0		−0.837528	+	0.546394i	$0.816000\pi$
$200$	−0.637424	+	0.770513i	−0.637424	+	0.770513i
$201$	1.43911	−	0.181802i	1.43911	−	0.181802i
$202$		0			0
$203$		0			0
$204$	0.0771690	+	1.22657i	0.0771690	+	1.22657i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−2.38003	−	1.63942i	−2.38003	−	1.63942i
$210$		0			0
$211$	−0.723723	+	1.14040i	−0.723723	+	1.14040i	0.260842	+	0.965382i	$0.416000\pi$
$211$	−0.723723	+	1.14040i	−0.723723	+	1.14040i	−0.984564	+	0.175023i	$0.944000\pi$
$212$		0			0
$213$		0			0
$214$	−1.38337	−	1.43653i	−1.38337	−	1.43653i
$215$		0			0
$216$	−0.255633	−	1.05024i	−0.255633	−	1.05024i
$217$		0			0
$218$		0			0
$219$	−0.251535	−	0.774144i	−0.251535	−	0.774144i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.899405	−	0.437116i	$-0.856000\pi$
$223$		0			0		0.899405	+	0.437116i	$0.144000\pi$
$224$		0			0
$225$	−0.414549	+	0.0844916i	−0.414549	+	0.0844916i
$226$	1.59532	+	0.409608i	1.59532	+	0.409608i
$227$	−0.180536	+	0.832201i	−0.180536	+	0.832201i	0.793990	+	0.607930i	$0.208000\pi$
$227$	−0.180536	+	0.832201i	−0.180536	+	0.832201i	−0.974527	+	0.224271i	$0.928000\pi$
$228$	0.489708	+	1.38751i	0.489708	+	1.38751i
$229$		0			0		−0.402906	−	0.915241i	$-0.632000\pi$
$229$		0			0		0.402906	+	0.915241i	$0.368000\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	0.384966	−	0.420411i	0.384966	−	0.420411i	−0.514440	−	0.857527i	$-0.672000\pi$
$233$	0.384966	−	0.420411i	0.384966	−	0.420411i	0.899405	+	0.437116i	$0.144000\pi$
$234$		0			0
$235$		0			0
$236$	1.22948	−	0.124019i	1.22948	−	0.124019i
$237$		0			0
$238$		0			0
$239$		0			0		0.556876	−	0.830596i	$-0.312000\pi$
$239$		0			0		−0.556876	+	0.830596i	$0.688000\pi$
$240$		0			0
$241$	−0.911832	+	0.234119i	−0.911832	+	0.234119i	−0.675333	−	0.737513i	$-0.736000\pi$
$241$	−0.911832	+	0.234119i	−0.911832	+	0.234119i	−0.236499	+	0.971632i	$0.576000\pi$
$242$	1.10241	−	0.535778i	1.10241	−	0.535778i
$243$	0.331532	−	0.704541i	0.331532	−	0.704541i
$244$		0			0
$245$		0			0
$246$	0.393124	+	0.0496631i	0.393124	+	0.0496631i
$247$		0			0
$248$		0			0
$249$	0.927387	−	0.367179i	0.927387	−	0.367179i
$250$		0			0
$251$	0.356412	−	0.934329i	0.356412	−	0.934329i
$251$	0.356412	−	0.934329i	0.356412	−	0.934329i
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.992115	−	0.125333i	−0.992115	−	0.125333i
$257$	−0.0620782	+	0.0427609i	−0.0620782	+	0.0427609i	−0.597905	−	0.801567i	$-0.704000\pi$
$257$	−0.0620782	+	0.0427609i	−0.0620782	+	0.0427609i	0.535827	+	0.844328i	$0.320000\pi$
$258$	0.541260	+	1.41891i	0.541260	+	1.41891i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	0.0141249	+	0.374496i	0.0141249	+	0.374496i
$263$		0			0		0.556876	−	0.830596i	$-0.312000\pi$
$263$		0			0		−0.556876	+	0.830596i	$0.688000\pi$
$264$	−1.11568	−	0.198331i	−1.11568	−	0.198331i
$265$		0			0
$266$		0			0
$267$	0.0868115	−	1.37983i	0.0868115	−	1.37983i
$268$	1.51631	−	1.16098i	1.51631	−	1.16098i
$269$		0			0		0.675333	−	0.737513i	$-0.264000\pi$
$269$		0			0		−0.675333	+	0.737513i	$0.736000\pi$
$270$		0			0
$271$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$271$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$272$	0.901044	+	1.34393i	0.901044	+	1.34393i
$273$		0			0
$274$	−0.507512	−	1.43795i	−0.507512	−	1.43795i
$275$	−0.316290	+	1.45797i	−0.316290	+	1.45797i
$276$		0			0
$277$		0			0		0.979855	−	0.199710i	$-0.0640000\pi$
$277$		0			0		−0.979855	+	0.199710i	$0.936000\pi$
$278$	1.51726	−	1.22340i	1.51726	−	1.22340i
$279$		0			0
$280$		0			0
$281$	1.48768	−	0.769822i	1.48768	−	0.769822i	0.492727	−	0.870184i	$-0.336000\pi$
$281$	1.48768	−	0.769822i	1.48768	−	0.769822i	0.994951	+	0.100362i	$0.0320000\pi$
$282$		0			0
$283$	−0.290911	−	0.895332i	−0.290911	−	0.895332i	−0.984564	−	0.175023i	$-0.944000\pi$
$283$	−0.290911	−	0.895332i	−0.290911	−	0.895332i	0.693653	−	0.720309i	$-0.256000\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.293465	−	0.304742i	−0.293465	−	0.304742i
$289$	0.422050	−	1.56202i	0.422050	−	1.56202i
$290$		0			0
$291$	0.633655	−	0.998481i	0.633655	−	0.998481i
$292$	−0.799391	−	0.713734i	−0.799391	−	0.713734i
$293$		0			0		−0.823533	−	0.567269i	$-0.808000\pi$
$293$		0			0		0.823533	+	0.567269i	$0.192000\pi$
$294$	0.179635	−	0.738011i	0.179635	−	0.738011i
$295$		0			0
$296$		0			0
$297$	−1.05880	−	1.21629i	−1.05880	−	1.21629i
$298$		0			0
$299$		0			0
$300$	0.566586	−	0.505875i	0.566586	−	0.505875i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	1.47698	+	1.25346i	1.47698	+	1.25346i
$305$		0			0
$306$	−0.0601380	+	0.681897i	−0.0601380	+	0.681897i
$307$	1.96353	+	0.148328i	1.96353	+	0.148328i	0.994951	−	0.100362i	$-0.0320000\pi$
$307$	1.96353	+	0.148328i	1.96353	+	0.148328i	0.968583	+	0.248690i	$0.0800000\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.656586	−	0.754251i	$-0.272000\pi$
$311$		0			0		−0.656586	+	0.754251i	$0.728000\pi$
$312$		0			0
$313$	1.16687	+	0.680227i	1.16687	+	0.680227i	0.954865	−	0.297042i	$-0.0960000\pi$
$313$	1.16687	+	0.680227i	1.16687	+	0.680227i	0.212007	+	0.977268i	$0.432000\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		−0.597905	−	0.801567i	$-0.704000\pi$
$317$		0			0		0.597905	+	0.801567i	$0.296000\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	0.874907	+	1.23659i	0.874907	+	1.23659i
$322$		0			0
$323$	−0.0393870	−	3.13415i	−0.0393870	−	3.13415i
$324$	0.0349594	+	0.396401i	0.0349594	+	0.396401i
$325$		0			0
$326$	−1.95909	−	0.0492477i	−1.95909	−	0.0492477i
$327$		0			0
$328$	0.480069	−	0.204173i	0.480069	−	0.204173i
$329$		0			0
$330$		0			0
$331$	−0.351802	+	1.84421i	−0.351802	+	1.84421i	0.162637	+	0.986686i	$0.448000\pi$
$331$	−0.351802	+	1.84421i	−0.351802	+	1.84421i	−0.514440	+	0.857527i	$0.672000\pi$
$332$	0.811356	−	1.03253i	0.811356	−	1.03253i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−0.274189	−	1.97092i	−0.274189	−	1.97092i	−0.236499	−	0.971632i	$-0.576000\pi$
$337$	−0.274189	−	1.97092i	−0.274189	−	1.97092i	−0.0376902	−	0.999289i	$-0.512000\pi$
$338$	−0.999684	+	0.0251301i	−0.999684	+	0.0251301i
$339$	−1.15125	−	0.489625i	−1.15125	−	0.489625i
$340$		0			0
$341$		0			0
$342$	0.153570	+	0.805043i	0.153570	+	0.805043i
$343$		0			0
$344$	1.55643	+	1.25499i	1.55643	+	1.25499i
$345$		0			0
$346$		0			0
$347$	0.572958	+	0.955071i	0.572958	+	0.955071i	0.998737	+	0.0502443i	$0.0160000\pi$
$347$	0.572958	+	0.955071i	0.572958	+	0.955071i	−0.425779	+	0.904827i	$0.640000\pi$
$348$		0			0
$349$		0			0		0.448383	−	0.893841i	$-0.352000\pi$
$349$		0			0		−0.448383	+	0.893841i	$0.648000\pi$
$350$		0			0
$351$		0			0
$352$	−1.40048	+	0.514167i	−1.40048	+	0.514167i
$353$	0.450527	−	1.38658i	0.450527	−	1.38658i	−0.425779	−	0.904827i	$-0.640000\pi$
$353$	0.450527	−	1.38658i	0.450527	−	1.38658i	0.876307	−	0.481754i	$-0.160000\pi$
$354$	−0.937415	−	0.0471594i	−0.937415	−	0.0471594i
$355$		0			0
$356$	−0.816152	−	1.62698i	−0.816152	−	1.62698i
$357$		0			0
$358$	−0.526870	−	1.28337i	−0.526870	−	1.28337i
$359$		0			0		0.137790	−	0.990461i	$-0.456000\pi$
$359$		0			0		−0.137790	+	0.990461i	$0.544000\pi$
$360$		0			0
$361$	−0.784548	−	2.63844i	−0.784548	−	2.63844i
$362$		0			0
$363$	−0.888979	+	0.276546i	−0.888979	+	0.276546i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.850994	−	0.525175i	$-0.176000\pi$
$367$		0			0		−0.850994	+	0.525175i	$0.824000\pi$
$368$		0			0
$369$	0.212328	+	0.0602430i	0.212328	+	0.0602430i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.0125660	−	0.999921i	$-0.496000\pi$
$373$		0			0		−0.0125660	+	0.999921i	$0.504000\pi$
$374$	2.11533	+	1.16291i	2.11533	+	1.16291i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	1.01226	+	0.556496i	1.01226	+	0.556496i	0.899405	−	0.437116i	$-0.144000\pi$
$379$	1.01226	+	0.556496i	1.01226	+	0.556496i	0.112856	+	0.993611i	$0.464000\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.850994	−	0.525175i	$-0.824000\pi$
$383$		0			0		0.850994	+	0.525175i	$0.176000\pi$
$384$	0.730716	+	0.207323i	0.730716	+	0.207323i
$385$		0			0
$386$	1.59771	−	0.985998i	1.59771	−	0.985998i
$387$	0.179332	+	0.826647i	0.179332	+	0.826647i
$388$	0.0586808	−	1.55582i	0.0586808	−	1.55582i
$389$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$389$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$390$		0			0
$391$		0			0
$392$	−0.285019	−	0.958522i	−0.285019	−	0.958522i
$393$	0.0321250	−	0.282835i	0.0321250	−	0.282835i
$394$		0			0
$395$		0			0
$396$	−0.597783	−	0.202571i	−0.597783	−	0.202571i
$397$		0			0		−0.448383	−	0.893841i	$-0.648000\pi$
$397$		0			0		0.448383	+	0.893841i	$0.352000\pi$
$398$		0			0
$399$		0			0
$400$	0.309017	−	0.951057i	0.309017	−	0.951057i
$401$	−1.66745	+	0.612180i	−1.66745	+	0.612180i	−0.992115	−	0.125333i	$-0.960000\pi$
$401$	−1.66745	+	0.612180i	−1.66745	+	0.612180i	−0.675333	+	0.737513i	$0.736000\pi$
$402$	−1.27113	+	0.698808i	−1.27113	+	0.698808i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−0.523279	−	1.11202i	−0.523279	−	1.11202i
$409$	0.136778	+	0.110287i	0.136778	+	0.110287i	0.693653	−	0.720309i	$-0.256000\pi$
$409$	0.136778	+	0.110287i	0.136778	+	0.110287i	−0.556876	+	0.830596i	$0.688000\pi$
$410$		0			0
$411$	0.217032	+	1.13772i	0.217032	+	1.13772i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−1.27897	+	0.745574i	−1.27897	+	0.745574i
$418$	2.81641	+	0.648148i	2.81641	+	0.648148i
$419$	−0.173708	+	0.0263950i	−0.173708	+	0.0263950i	−0.236499	−	0.971632i	$-0.576000\pi$
$419$	−0.173708	+	0.0263950i	−0.173708	+	0.0263950i	0.0627905	+	0.998027i	$0.480000\pi$
$420$		0			0
$421$		0			0		0.617860	−	0.786288i	$-0.288000\pi$
$421$		0			0		−0.617860	+	0.786288i	$0.712000\pi$
$422$	0.253089	−	1.32674i	0.253089	−	1.32674i
$423$		0			0
$424$		0			0
$425$	−1.48897	+	0.633256i	−1.48897	+	0.633256i
$426$		0			0
$427$		0			0
$428$	1.81504	+	0.826397i	1.81504	+	0.826397i
$429$		0			0
$430$		0			0
$431$		0			0		0.470704	−	0.882291i	$-0.344000\pi$
$431$		0			0		−0.470704	+	0.882291i	$0.656000\pi$
$432$	0.624302	+	0.882386i	0.624302	+	0.882386i
$433$	0.939097	+	1.47978i	0.939097	+	1.47978i	0.876307	+	0.481754i	$0.160000\pi$
$433$	0.939097	+	1.47978i	0.939097	+	1.47978i	0.0627905	+	0.998027i	$0.480000\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	0.518852	+	0.627185i	0.518852	+	0.627185i
$439$		0			0		−0.728969	−	0.684547i	$-0.760000\pi$
$439$		0			0		0.728969	+	0.684547i	$0.240000\pi$
$440$		0			0
$441$	0.160674	−	0.391374i	0.160674	−	0.391374i
$442$		0			0
$443$	0.490713	+	0.375722i	0.490713	+	0.375722i	0.823533	−	0.567269i	$-0.192000\pi$
$443$	0.490713	+	0.375722i	0.490713	+	0.375722i	−0.332820	+	0.942991i	$0.608000\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−0.784461	−	0.665742i	−0.784461	−	0.665742i	0.162637	−	0.986686i	$-0.448000\pi$
$449$	−0.784461	−	0.665742i	−0.784461	−	0.665742i	−0.947098	+	0.320944i	$0.896000\pi$
$450$	0.354334	−	0.231164i	0.354334	−	0.231164i
$451$	0.496100	−	0.599682i	0.496100	−	0.599682i
$452$	−1.63408	+	0.206432i	−1.63408	+	0.206432i
$453$		0			0
$454$	−0.138495	−	0.840221i	−0.138495	−	0.840221i
$455$		0			0
$456$	−0.966094	−	1.10980i	−0.966094	−	1.10980i
$457$	1.76118	−	0.596812i	1.76118	−	0.596812i	0.762443	−	0.647056i	$-0.224000\pi$
$457$	1.76118	−	0.596812i	1.76118	−	0.596812i	0.998737	+	0.0502443i	$0.0160000\pi$
$458$		0			0
$459$	0.413623	−	1.69933i	0.413623	−	1.69933i
$460$		0			0
$461$		0			0		−0.745941	−	0.666012i	$-0.768000\pi$
$461$		0			0		0.745941	+	0.666012i	$0.232000\pi$
$462$		0			0
$463$		0			0		0.998737	−	0.0502443i	$-0.0160000\pi$
$463$		0			0		−0.998737	+	0.0502443i	$0.984000\pi$
$464$		0			0
$465$		0			0
$466$	−0.203169	+	0.532603i	−0.203169	+	0.532603i
$467$	−0.467630	−	1.92121i	−0.467630	−	1.92121i	−0.379779	−	0.925077i	$-0.624000\pi$
$467$	−0.467630	−	1.92121i	−0.467630	−	1.92121i	−0.0878512	−	0.996134i	$-0.528000\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−1.09749	+	0.567912i	−1.09749	+	0.567912i
$473$	2.92273	+	0.595699i	2.92273	+	0.595699i
$474$		0			0
$475$	−1.50801	+	1.21594i	−1.50801	+	1.21594i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		−0.332820	−	0.942991i	$-0.608000\pi$
$479$		0			0		0.332820	+	0.942991i	$0.392000\pi$
$480$		0			0
$481$		0			0
$482$	0.761615	−	0.553346i	0.761615	−	0.553346i
$483$		0			0
$484$	−0.827764	+	0.903979i	−0.827764	+	0.903979i
$485$		0			0
$486$	−0.0488917	+	0.777111i	−0.0488917	+	0.777111i
$487$		0			0		0.994951	−	0.100362i	$-0.0320000\pi$
$487$		0			0		−0.994951	+	0.100362i	$0.968000\pi$
$488$		0			0
$489$	1.46554	+	0.260524i	1.46554	+	0.260524i
$490$		0			0
$491$	−0.0268665	−	0.712317i	−0.0268665	−	0.712317i	−0.947098	−	0.320944i	$-0.896000\pi$
$491$	−0.0268665	−	0.712317i	−0.0268665	−	0.712317i	0.920232	−	0.391374i	$-0.128000\pi$
$492$	−0.383800	+	0.0985430i	−0.383800	+	0.0985430i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−0.727095	+	0.682788i	−0.727095	+	0.682788i
$499$	1.84595	−	0.424813i	1.84595	−	0.424813i	0.850994	−	0.525175i	$-0.176000\pi$
$499$	1.84595	−	0.424813i	1.84595	−	0.424813i	0.994951	+	0.100362i	$0.0320000\pi$
$500$		0			0
$501$		0			0
$502$	0.0125660	+	0.999921i	0.0125660	+	0.999921i
$503$		0			0		1.00000			$0$
$503$		0			0		−1.00000			$\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.753569	+	0.0951979i	0.753569	+	0.0951979i
$508$		0			0
$509$		0			0		−0.356412	−	0.934329i	$-0.616000\pi$
$509$		0			0		0.356412	+	0.934329i	$0.384000\pi$
$510$		0			0
$511$		0			0
$512$	0.968583	−	0.248690i	0.968583	−	0.248690i
$513$	−0.0789192	−	2.09241i	−0.0789192	−	2.09241i
$514$	0.0419775	−	0.0626106i	0.0419775	−	0.0626106i
$515$		0			0
$516$	−1.02559	−	1.12001i	−1.02559	−	1.12001i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−0.829478	+	1.11202i	−0.829478	+	1.11202i	0.162637	+	0.986686i	$0.448000\pi$
$521$	−0.829478	+	1.11202i	−0.829478	+	1.11202i	−0.992115	+	0.125333i	$0.960000\pi$
$522$		0			0
$523$	−0.499387	−	0.744851i	−0.499387	−	0.744851i	0.492727	−	0.870184i	$-0.336000\pi$
$523$	−0.499387	−	0.744851i	−0.499387	−	0.744851i	−0.992115	+	0.125333i	$0.960000\pi$
$524$	−0.150994	−	0.342998i	−0.150994	−	0.342998i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	1.11034	−	0.226306i	1.11034	−	0.226306i
$529$	−0.778462	+	0.627691i	−0.778462	+	0.627691i
$530$		0			0
$531$	−0.512266	−	0.104408i	−0.512266	−	0.104408i
$532$		0			0
$533$		0			0
$534$	0.427234	+	1.31489i	0.427234	+	1.31489i
$535$		0			0
$536$	−0.982440	+	1.63764i	−0.982440	+	1.63764i
$537$	0.249208	+	1.02385i	0.249208	+	1.02385i
$538$		0			0
$539$	−1.03485	−	1.07462i	−1.03485	−	1.07462i
$540$		0			0
$541$		0			0		0.998737	−	0.0502443i	$-0.0160000\pi$
$541$		0			0		−0.998737	+	0.0502443i	$0.984000\pi$
$542$		0			0
$543$		0			0
$544$	−1.33250	−	0.917860i	−1.33250	−	0.917860i
$545$		0			0
$546$		0			0
$547$	1.79399	−	0.607930i	1.79399	−	0.607930i	0.793990	−	0.607930i	$-0.208000\pi$
$547$	1.79399	−	0.607930i	1.79399	−	0.607930i	1.00000			$0$
$548$	1.00122	+	1.15015i	1.00122	+	1.15015i
$549$		0			0
$550$	−0.242636	−	1.47202i	−0.242636	−	1.47202i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	−0.960352	+	1.69603i	−0.960352	+	1.69603i
$557$		0			0		0.0878512	−	0.996134i	$-0.472000\pi$
$557$		0			0		−0.0878512	+	0.996134i	$0.528000\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−1.45579	−	1.11465i	−1.45579	−	1.11465i
$562$	−1.09982	+	1.26341i	−1.09982	+	1.26341i
$563$	0.323404	−	0.787757i	0.323404	−	0.787757i	−0.675333	−	0.737513i	$-0.736000\pi$
$563$	0.323404	−	0.787757i	0.323404	−	0.787757i	0.998737	−	0.0502443i	$-0.0160000\pi$
$564$		0			0
$565$		0			0
$566$	0.600076	+	0.725367i	0.600076	+	0.725367i
$567$		0			0
$568$		0			0
$569$	−0.0749998	−	0.00756530i	−0.0749998	−	0.00756530i	0.0627905	−	0.998027i	$-0.480000\pi$
$569$	−0.0749998	−	0.00756530i	−0.0749998	−	0.00756530i	−0.137790	+	0.990461i	$0.544000\pi$
$570$		0			0
$571$	0.431776	+	0.680370i	0.431776	+	0.680370i	0.988652	−	0.150226i	$-0.0480000\pi$
$571$	0.431776	+	0.680370i	0.431776	+	0.680370i	−0.556876	+	0.830596i	$0.688000\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.385040	+	0.175310i	0.385040	+	0.175310i
$577$	−1.15478	−	0.0290289i	−1.15478	−	0.0290289i	−0.556876	−	0.830596i	$-0.688000\pi$
$577$	−1.15478	−	0.0290289i	−1.15478	−	0.0290289i	−0.597905	+	0.801567i	$0.704000\pi$
$578$	0.182605	+	1.60770i	0.182605	+	1.60770i
$579$	−1.31229	+	0.558117i	−1.31229	+	0.558117i
$580$		0			0
$581$		0			0
$582$	−0.221592	+	1.16163i	−0.221592	+	1.16163i
$583$		0			0
$584$	1.00600	+	0.369338i	1.00600	+	0.369338i
$585$		0			0
$586$		0			0
$587$	−0.851357	+	0.496298i	−0.851357	+	0.496298i	−0.863923	−	0.503623i	$-0.832000\pi$
$587$	−0.851357	+	0.496298i	−0.851357	+	0.496298i	0.0125660	+	0.999921i	$0.496000\pi$
$588$	0.104660	+	0.752313i	0.104660	+	0.752313i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	0.373698	+	1.95899i	0.373698	+	1.95899i	0.260842	+	0.965382i	$0.416000\pi$
$593$	0.373698	+	1.95899i	0.373698	+	1.95899i	0.112856	+	0.993611i	$0.464000\pi$
$594$	1.43219	+	0.741111i	1.43219	+	0.741111i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		0.711536	−	0.702650i	$-0.248000\pi$
$599$		0			0		−0.711536	+	0.702650i	$0.752000\pi$
$600$	−0.340573	+	0.678925i	−0.340573	+	0.678925i
$601$	0.600076	+	1.12479i	0.600076	+	1.12479i	0.979855	+	0.199710i	$0.0640000\pi$
$601$	0.600076	+	1.12479i	0.600076	+	1.12479i	−0.379779	+	0.925077i	$0.624000\pi$
$602$		0			0
$603$	−0.758452	+	0.278455i	−0.758452	+	0.278455i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		−0.448383	−	0.893841i	$-0.648000\pi$
$607$		0			0		0.448383	+	0.893841i	$0.352000\pi$
$608$	−1.83469	−	0.621721i	−1.83469	−	0.621721i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−0.195108	−	0.656150i	−0.195108	−	0.656150i
$613$		0			0		−0.837528	−	0.546394i	$-0.816000\pi$
$613$		0			0		0.837528	+	0.546394i	$0.184000\pi$
$614$	−1.88025	+	0.584913i	−1.88025	+	0.584913i
$615$		0			0
$616$		0			0
$617$	−0.407913	−	1.88032i	−0.407913	−	1.88032i	−0.470704	−	0.882291i	$-0.656000\pi$
$617$	−0.407913	−	1.88032i	−0.407913	−	1.88032i	0.0627905	−	0.998027i	$-0.480000\pi$
$618$		0			0
$619$	0.548393	−	0.155593i	0.548393	−	0.155593i	0.0125660	−	0.999921i	$-0.496000\pi$
$619$	0.548393	−	0.155593i	0.548393	−	0.155593i	0.535827	+	0.844328i	$0.320000\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.876307	+	0.481754i	0.876307	+	0.481754i
$626$	−1.33534	−	0.202905i	−1.33534	−	0.202905i
$627$	−2.04099	−	0.808085i	−2.04099	−	0.808085i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		0.0125660	−	0.999921i	$-0.496000\pi$
$631$		0			0		−0.0125660	+	0.999921i	$0.504000\pi$
$632$		0			0
$633$	−0.341443	+	0.967423i	−0.341443	+	0.967423i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−1.89467	+	0.589399i	−1.89467	+	0.589399i	−0.910106	+	0.414376i	$0.864000\pi$
$641$	−1.89467	+	0.589399i	−1.89467	+	0.589399i	−0.984564	+	0.175023i	$0.944000\pi$
$642$	−1.26869	−	0.827678i	−1.26869	−	0.827678i
$643$	−0.0927094	−	0.311783i	−0.0927094	−	0.311783i	0.899405	−	0.437116i	$-0.144000\pi$
$643$	−0.0927094	−	0.311783i	−0.0927094	−	0.311783i	−0.992115	+	0.125333i	$0.960000\pi$
$644$		0			0
$645$		0			0
$646$	1.19038	+	2.89956i	1.19038	+	2.89956i
$647$		0			0		−0.947098	−	0.320944i	$-0.896000\pi$
$647$		0			0		0.947098	+	0.320944i	$0.104000\pi$
$648$	−0.178429	−	0.355695i	−0.178429	−	0.355695i
$649$	−1.06478	+	1.50496i	−1.06478	+	1.50496i
$650$		0			0
$651$		0			0
$652$	1.83965	−	0.675400i	1.83965	−	0.675400i
$653$		0			0		0.876307	−	0.481754i	$-0.160000\pi$
$653$		0			0		−0.876307	+	0.481754i	$0.840000\pi$
$654$		0			0
$655$		0			0
$656$	−0.371196	+	0.366561i	−0.371196	+	0.366561i
$657$	0.233240	+	0.388791i	0.233240	+	0.388791i
$658$		0			0
$659$	0.159566	+	0.339095i	0.159566	+	0.339095i	0.968583	−	0.248690i	$-0.0800000\pi$
$659$	0.159566	+	0.339095i	0.159566	+	0.339095i	−0.809017	+	0.587785i	$0.800000\pi$
$660$		0			0
$661$		0			0		−0.888136	−	0.459580i	$-0.848000\pi$
$661$		0			0		0.888136	+	0.459580i	$0.152000\pi$
$662$	−0.351802	−	1.84421i	−0.351802	−	1.84421i
$663$		0			0
$664$	−0.374279	+	1.25870i	−0.374279	+	1.25870i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.0422944	+	0.221715i	−0.0422944	+	0.221715i	−0.997159	−	0.0753268i	$-0.976000\pi$
$673$	−0.0422944	+	0.221715i	−0.0422944	+	0.221715i	0.954865	+	0.297042i	$0.0960000\pi$
$674$	0.980479	+	1.73158i	0.980479	+	1.73158i
$675$	−0.983739	+	0.447901i	−0.983739	+	0.447901i
$676$	0.920232	−	0.391374i	0.920232	−	0.391374i
$677$		0			0		−0.112856	−	0.993611i	$-0.536000\pi$
$677$		0			0		0.112856	+	0.993611i	$0.464000\pi$
$678$	1.25065	+	0.0314388i	1.25065	+	0.0314388i
$679$		0			0
$680$		0			0
$681$	0.00812782	+	0.646757i	0.00812782	+	0.646757i
$682$		0			0
$683$	−0.997957	−	1.41051i	−0.997957	−	1.41051i	−0.910106	−	0.414376i	$-0.864000\pi$
$683$	−0.997957	−	1.41051i	−0.997957	−	1.41051i	−0.0878512	−	0.996134i	$-0.528000\pi$
$684$	−0.439142	−	0.691977i	−0.439142	−	0.691977i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	−1.90913	−	0.593896i	−1.90913	−	0.593896i
$689$		0			0
$690$		0			0
$691$	−1.72566	−	1.00597i	−1.72566	−	1.00597i	−0.888136	−	0.459580i	$-0.848000\pi$
$691$	−1.72566	−	1.00597i	−1.72566	−	1.00597i	−0.837528	−	0.546394i	$-0.816000\pi$
$692$		0			0
$693$		0			0
$694$	−0.884308	−	0.677083i	−0.884308	−	0.677083i
$695$		0			0
$696$		0			0
$697$	0.841703	+	0.0635834i	0.841703	+	0.0635834i
$698$		0			0
$699$	0.213340	−	0.376770i	0.213340	−	0.376770i
$700$		0			0
$701$		0			0		0.837528	−	0.546394i	$-0.184000\pi$
$701$		0			0		−0.837528	+	0.546394i	$0.816000\pi$
$702$		0			0
$703$		0			0
$704$	1.11286	−	0.993611i	1.11286	−	0.993611i
$705$		0			0
$706$	0.0915446	+	1.45506i	0.0915446	+	1.45506i
$707$		0			0
$708$	0.888947	−	0.301238i	0.888947	−	0.301238i
$709$		0			0		−0.711536	−	0.702650i	$-0.752000\pi$
$709$		0			0		0.711536	+	0.702650i	$0.248000\pi$
$710$		0			0
$711$		0			0
$712$	1.35777	+	1.21228i	1.35777	+	1.21228i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	0.962310	+	0.999289i	0.962310	+	0.999289i
$717$		0			0
$718$		0			0
$719$		0			0		0.514440	−	0.857527i	$-0.328000\pi$
$719$		0			0		−0.514440	+	0.857527i	$0.672000\pi$
$720$		0			0
$721$		0			0
$722$	1.70073	+	2.16435i	1.70073	+	2.16435i
$723$	−0.635066	+	0.328624i	−0.635066	+	0.328624i
$724$		0			0
$725$		0			0
$726$	0.724749	−	0.584381i	0.724749	−	0.584381i
$727$		0			0		0.979855	−	0.199710i	$-0.0640000\pi$
$727$		0			0		−0.979855	+	0.199710i	$0.936000\pi$
$728$		0			0
$729$	0.209753	−	0.966877i	0.209753	−	0.966877i
$730$		0			0
$731$	1.30342	+	2.96085i	1.30342	+	2.96085i
$732$		0			0
$733$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$733$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−0.178896	+	2.84347i	−0.178896	+	2.84347i
$738$	−0.219595	+	0.0221507i	−0.219595	+	0.0221507i
$739$	1.16687	+	1.27431i	1.16687	+	1.27431i	0.954865	+	0.297042i	$0.0960000\pi$
$739$	1.16687	+	1.27431i	1.16687	+	1.27431i	0.212007	+	0.977268i	$0.432000\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		0.968583	−	0.248690i	$-0.0800000\pi$
$743$		0			0		−0.968583	+	0.248690i	$0.920000\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−0.457526	+	0.315155i	−0.457526	+	0.315155i
$748$	−2.39488	−	0.302544i	−2.39488	−	0.302544i
$749$		0			0
$750$		0			0
$751$		0			0		0.929776	−	0.368125i	$-0.120000\pi$
$751$		0			0		−0.929776	+	0.368125i	$0.880000\pi$
$752$		0			0
$753$	0.104660	−	0.752313i	0.104660	−	0.752313i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.728969	−	0.684547i	$-0.240000\pi$
$757$		0			0		−0.728969	+	0.684547i	$0.760000\pi$
$758$	−1.14604	−	0.144778i	−1.14604	−	0.144778i
$759$		0			0
$760$		0			0
$761$	−0.559121	+	1.18819i	−0.559121	+	1.18819i	0.402906	+	0.915241i	$0.368000\pi$
$761$	−0.559121	+	1.18819i	−0.559121	+	1.18819i	−0.962028	+	0.272952i	$0.912000\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−0.755723	+	0.0762306i	−0.755723	+	0.0762306i
$769$	0.0266241	−	0.423178i	0.0266241	−	0.423178i	−0.962028	−	0.272952i	$-0.912000\pi$
$769$	0.0266241	−	0.423178i	0.0266241	−	0.423178i	0.988652	−	0.150226i	$-0.0480000\pi$
$770$		0			0
$771$	−0.0386667	+	0.0422269i	−0.0386667	+	0.0422269i
$772$	−1.12255	+	1.50492i	−1.12255	+	1.50492i
$773$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$773$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$774$	−0.471047	−	0.702581i	−0.471047	−	0.702581i
$775$		0			0
$776$	0.518175	+	1.46817i	0.518175	+	1.46817i
$777$		0			0
$778$		0			0
$779$	0.990229	−	0.201824i	0.990229	−	0.201824i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.617860	+	0.786288i	0.617860	+	0.786288i
$785$		0			0
$786$	0.0742496	+	0.274800i	0.0742496	+	0.274800i
$787$	−0.816920	+	1.36174i	−0.816920	+	1.36174i	0.112856	+	0.993611i	$0.464000\pi$
$787$	−0.816920	+	1.36174i	−0.816920	+	1.36174i	−0.929776	+	0.368125i	$0.880000\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	0.630375	−	0.0317128i	0.630375	−	0.0317128i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.711536	−	0.702650i	$-0.752000\pi$
$797$		0			0		0.711536	+	0.702650i	$0.248000\pi$
$798$		0			0
$799$		0			0
$800$	0.0627905	+	0.998027i	0.0627905	+	0.998027i
$801$	0.125244	+	0.759827i	0.125244	+	0.759827i
$802$	1.32500	−	1.18302i	1.32500	−	1.18302i
$803$	1.58617	−	0.200380i	1.58617	−	0.200380i
$804$	0.924616	−	1.11767i	0.924616	−	1.11767i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−0.422810	−	0.0319396i	−0.422810	−	0.0319396i	−0.137790	−	0.990461i	$-0.544000\pi$
$809$	−0.422810	−	0.0319396i	−0.422810	−	0.0319396i	−0.285019	+	0.958522i	$0.592000\pi$
$810$		0			0
$811$	−1.92946	+	0.342994i	−1.92946	+	0.342994i	−0.999684	−	0.0251301i	$-0.992000\pi$
$811$	−1.92946	+	0.342994i	−1.92946	+	0.342994i	−0.929776	+	0.368125i	$0.880000\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	0.895896	+	0.841302i	0.895896	+	0.841302i
$817$	2.46881	+	2.98428i	2.46881	+	2.98428i
$818$	−0.167772	−	0.0521909i	−0.167772	−	0.0521909i
$819$		0			0
$820$		0			0
$821$		0			0		0.162637	−	0.986686i	$-0.448000\pi$
$821$		0			0		−0.162637	+	0.986686i	$0.552000\pi$
$822$	−0.620615	−	0.977933i	−0.620615	−	0.977933i
$823$		0			0		−0.577573	−	0.816339i	$-0.696000\pi$
$823$		0			0		0.577573	+	0.816339i	$0.304000\pi$
$824$		0			0
$825$	0.0142395	+	1.13308i	0.0142395	+	1.13308i
$826$		0			0
$827$	−1.79956	−	0.819346i	−1.79956	−	0.819346i	−0.962028	−	0.272952i	$-0.912000\pi$
$827$	−1.79956	−	0.819346i	−1.79956	−	0.819346i	−0.837528	−	0.546394i	$-0.816000\pi$
$828$		0			0
$829$		0			0		−0.112856	−	0.993611i	$-0.536000\pi$
$829$		0			0		0.112856	+	0.993611i	$0.464000\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	0.303189	−	1.58937i	0.303189	−	1.58937i
$834$	0.914692	−	1.16404i	0.914692	−	1.16404i
$835$		0			0
$836$	−2.85723	+	0.434156i	−2.85723	+	0.434156i
$837$		0			0
$838$	0.151793	−	0.0884878i	0.151793	−	0.0884878i
$839$		0			0		−0.137790	−	0.990461i	$-0.544000\pi$
$839$		0			0		0.137790	+	0.990461i	$0.456000\pi$
$840$		0			0
$841$	0.920232	+	0.391374i	0.920232	+	0.391374i
$842$		0			0
$843$	0.970058	−	0.823251i	0.970058	−	0.823251i
$844$	0.253089	+	1.32674i	0.253089	+	1.32674i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−0.367852	−	0.613178i	−0.367852	−	0.613178i
$850$	1.15129	−	1.13691i	1.15129	−	1.13691i
$851$		0			0
$852$		0			0
$853$		0			0		0.876307	−	0.481754i	$-0.160000\pi$
$853$		0			0		−0.876307	+	0.481754i	$0.840000\pi$
$854$		0			0
$855$		0			0
$856$	−1.99180	−	0.100203i	−1.99180	−	0.100203i
$857$	1.13188	−	1.59979i	1.13188	−	1.59979i	0.402906	−	0.915241i	$-0.368000\pi$
$857$	1.13188	−	1.59979i	1.13188	−	1.59979i	0.728969	−	0.684547i	$-0.240000\pi$
$858$		0			0
$859$	−0.933322	−	0.316275i	−0.933322	−	0.316275i	−0.187381	−	0.982287i	$-0.560000\pi$
$859$	−0.933322	−	0.316275i	−0.933322	−	0.316275i	−0.745941	+	0.666012i	$0.768000\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.285019	−	0.958522i	$-0.592000\pi$
$863$		0			0		0.285019	+	0.958522i	$0.408000\pi$
$864$	−0.905289	−	0.590601i	−0.905289	−	0.590601i
$865$		0			0
$866$	−1.41789	−	1.03016i	−1.41789	−	1.03016i
$867$	0.0463209	−	1.22812i	0.0463209	−	1.22812i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−0.219225	+	0.621139i	−0.219225	+	0.621139i
$874$		0			0
$875$		0			0
$876$	−0.713299	−	0.392139i	−0.713299	−	0.392139i
$877$		0			0		−0.988652	−	0.150226i	$-0.952000\pi$
$877$		0			0		0.988652	+	0.150226i	$0.0480000\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−1.51412	−	0.832397i	−1.51412	−	0.832397i	−0.514440	−	0.857527i	$-0.672000\pi$
$881$	−1.51412	−	0.832397i	−1.51412	−	0.832397i	−0.999684	+	0.0251301i	$0.992000\pi$
$882$	−0.00531633	+	0.423038i	−0.00531633	+	0.423038i
$883$	−1.06861	+	0.0807242i	−1.06861	+	0.0807242i	−0.597905	−	0.801567i	$-0.704000\pi$
$883$	−1.06861	+	0.0807242i	−1.06861	+	0.0807242i	−0.470704	+	0.882291i	$0.656000\pi$
$884$		0			0
$885$		0			0
$886$	−0.594566	−	0.168694i	−0.594566	−	0.168694i
$887$		0			0		0.962028	−	0.272952i	$-0.0880000\pi$
$887$		0			0		−0.962028	+	0.272952i	$0.912000\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−0.480296	−	0.348956i	−0.480296	−	0.348956i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	0.974450	+	0.330212i	0.974450	+	0.330212i
$899$		0			0
$900$	−0.244354	+	0.345370i	−0.244354	+	0.345370i
$901$		0			0
$902$	−0.240505	+	0.740197i	−0.240505	+	0.740197i
$903$		0			0
$904$	1.44333	−	0.793480i	1.44333	−	0.793480i
$905$		0			0
$906$		0			0
$907$	−0.231444	+	0.228554i	−0.231444	+	0.228554i	−0.809017	−	0.587785i	$-0.800000\pi$
$907$	−0.231444	+	0.228554i	−0.231444	+	0.228554i	0.577573	+	0.816339i	$0.304000\pi$
$908$	0.438075	+	0.730234i	0.438075	+	0.730234i
$909$		0			0
$910$		0			0
$911$		0			0		−0.778462	−	0.627691i	$-0.784000\pi$
$911$		0			0		0.778462	+	0.627691i	$0.216000\pi$
$912$	1.30680	+	0.676221i	1.30680	+	0.676221i
$913$	0.367098	+	1.92440i	0.367098	+	1.92440i
$914$	−1.41780	+	1.20323i	−1.41780	+	1.20323i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	0.240987	+	1.73226i	0.240987	+	1.73226i
$919$		0			0		0.863923	−	0.503623i	$-0.168000\pi$
$919$		0			0		−0.863923	+	0.503623i	$0.832000\pi$
$920$		0			0
$921$	1.47869	−	0.224688i	1.47869	−	0.224688i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	1.96851	+	0.0494844i	1.96851	+	0.0494844i	0.988652	−	0.150226i	$-0.0480000\pi$
$929$	1.96851	+	0.0494844i	1.96851	+	0.0494844i	0.979855	+	0.199710i	$0.0640000\pi$
$930$		0			0
$931$	−0.170182	−	1.92968i	−0.170182	−	1.92968i
$932$	−0.00716313	−	0.569994i	−0.00716313	−	0.569994i
$933$		0			0
$934$	1.14204	+	1.61415i	1.14204	+	1.61415i
$935$		0			0
$936$		0			0
$937$	−1.71912	−	0.173410i	−1.71912	−	0.173410i	−0.809017	−	0.587785i	$-0.800000\pi$
$937$	−1.71912	−	0.173410i	−1.71912	−	0.173410i	−0.910106	+	0.414376i	$0.864000\pi$
$938$		0			0
$939$	0.979604	+	0.304738i	0.979604	+	0.304738i
$940$		0			0
$941$		0			0		−0.728969	−	0.684547i	$-0.760000\pi$
$941$		0			0		0.728969	+	0.684547i	$0.240000\pi$
$942$		0			0
$943$		0			0
$944$	0.811356	−	0.932043i	0.811356	−	0.932043i
$945$		0			0
$946$	−2.93678	+	0.522063i	−2.93678	+	0.522063i
$947$	0.0505974	−	0.114937i	0.0505974	−	0.114937i	−0.888136	−	0.459580i	$-0.848000\pi$
$947$	0.0505974	−	0.114937i	0.0505974	−	0.114937i	0.938734	+	0.344643i	$0.112000\pi$
$948$		0			0
$949$		0			0
$950$	0.954495	−	1.68569i	0.954495	−	1.68569i
$951$		0			0
$952$		0			0
$953$	0.363356	−	0.439222i	0.363356	−	0.439222i	−0.556876	−	0.830596i	$-0.688000\pi$
$953$	0.363356	−	0.439222i	0.363356	−	0.439222i	0.920232	+	0.391374i	$0.128000\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.236499	+	0.971632i	−0.236499	+	0.971632i
$962$		0			0
$963$	−0.629379	−	0.561940i	−0.629379	−	0.561940i
$964$	−0.504432	+	0.794857i	−0.504432	+	0.794857i
$965$		0			0
$966$		0			0
$967$		0			0		−0.693653	−	0.720309i	$-0.744000\pi$
$967$		0			0		0.693653	+	0.720309i	$0.256000\pi$
$968$	0.436859	−	1.14522i	0.436859	−	1.14522i
$969$	−0.563047	−	2.31322i	−0.563047	−	2.31322i
$970$		0			0
$971$	−0.332533	−	1.23071i	−0.332533	−	1.23071i	−0.910106	−	0.414376i	$-0.864000\pi$
$971$	−0.332533	−	1.23071i	−0.332533	−	1.23071i	0.577573	−	0.816339i	$-0.304000\pi$
$972$	−0.240615	−	0.740538i	−0.240615	−	0.740538i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1.51726	−	1.22340i	1.51726	−	1.22340i	0.617860	−	0.786288i	$-0.288000\pi$
$977$	1.51726	−	1.22340i	1.51726	−	1.22340i	0.899405	−	0.437116i	$-0.144000\pi$
$978$	−1.45853	+	0.297271i	−1.45853	+	0.297271i
$979$	2.63023	+	0.675328i	2.63023	+	0.675328i
$980$		0			0
$981$		0			0
$982$	0.287201	+	0.652406i	0.287201	+	0.652406i
$983$		0			0		−0.556876	−	0.830596i	$-0.688000\pi$
$983$		0			0		0.556876	+	0.830596i	$0.312000\pi$
$984$	0.320572	−	0.232909i	0.320572	−	0.232909i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.984564	−	0.175023i	$-0.944000\pi$
$991$		0			0		0.984564	+	0.175023i	$0.0560000\pi$
$992$		0			0
$993$	0.0537479	+	1.42503i	0.0537479	+	1.42503i
$994$		0			0
$995$		0			0
$996$	0.424685	−	0.902502i	0.424685	−	0.902502i
$997$		0			0		−0.356412	−	0.934329i	$-0.616000\pi$
$997$		0			0		0.356412	+	0.934329i	$0.384000\pi$
$998$	−1.55993	+	1.07452i	−1.55993	+	1.07452i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2008.1.bd.a.595.1	yes	100
8.3	odd	2	CM	2008.1.bd.a.595.1	yes	100
251.27	even	125	inner	2008.1.bd.a.27.1	✓	100
2008.27	odd	250	inner	2008.1.bd.a.27.1	✓	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2008.1.bd.a.27.1	✓	100	251.27	even	125	inner
2008.1.bd.a.27.1	✓	100	2008.27	odd	250	inner
2008.1.bd.a.595.1	yes	100	1.1	even	1	trivial
2008.1.bd.a.595.1	yes	100	8.3	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:	\( N \)	\(=\)	\( 2008 = 2^{3} \cdot 251 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2008.bd (of order \(250\), degree \(100\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.929776 + 0.368125i) q^{2} +(0.740210 - 0.170347i) q^{3} +(0.728969 - 0.684547i) q^{4} +(-0.625521 + 0.430874i) q^{6} +(-0.425779 + 0.904827i) q^{8} +(-0.380513 + 0.184931i) q^{9} +O(q^{10})\)	\(q+(-0.929776 + 0.368125i) q^{2} +(0.740210 - 0.170347i) q^{3} +(0.728969 - 0.684547i) q^{4} +(-0.625521 + 0.430874i) q^{6} +(-0.425779 + 0.904827i) q^{8} +(-0.380513 + 0.184931i) q^{9} +(0.0562293 + 1.49082i) q^{11} +(0.422979 - 0.630886i) q^{12} +(0.0627905 - 0.998027i) q^{16} +(-1.28470 + 0.983652i) q^{17} +(0.285714 - 0.312021i) q^{18} +(-1.15824 + 1.55277i) q^{19} +(-0.601089 - 1.36543i) q^{22} +(-0.161032 + 0.742292i) q^{24} +(0.968583 + 0.248690i) q^{25} +(-0.841444 + 0.678475i) q^{27} +(0.309017 + 0.951057i) q^{32} +(0.295578 + 1.09394i) q^{33} +(0.832381 - 1.38751i) q^{34} +(-0.150788 + 0.395288i) q^{36} +(0.505293 - 1.87010i) q^{38} +(-0.389145 - 0.347447i) q^{41} +(0.472849 - 1.94265i) q^{43} +(1.06153 + 1.04827i) q^{44} +(-0.123532 - 0.749445i) q^{48} +(-0.745941 + 0.666012i) q^{49} +(-0.992115 + 0.125333i) q^{50} +(-0.783388 + 0.946954i) q^{51} +(0.532592 - 0.940586i) q^{54} +(-0.592833 + 1.34668i) q^{57} +(0.981149 + 0.751231i) q^{59} +(-0.637424 - 0.770513i) q^{64} +(-0.677529 - 0.908313i) q^{66} +(1.90009 + 0.191664i) q^{67} +(-0.263152 + 1.59649i) q^{68} +(-0.00531633 - 0.423038i) q^{72} +(-0.0941461 - 1.06751i) q^{73} +(0.759318 + 0.0190878i) q^{75} +(0.218622 + 1.92479i) q^{76} +(-0.245871 + 0.312895i) q^{81} +(0.489722 + 0.179794i) q^{82} +(1.29827 - 0.197272i) q^{83} +(0.275494 + 1.98030i) q^{86} +(-1.37288 - 0.583883i) q^{88} +(0.518795 - 1.74471i) q^{89} +(0.390747 + 0.651341i) q^{96} +(1.10781 - 1.09397i) q^{97} +(0.448383 - 0.893841i) q^{98} +(-0.297095 - 0.556878i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q+O(q^{10}) \) 100 * q	\( 100 q - 25 q^{22} - 25 q^{32}+O(q^{100}) \) 100 * q - 25 * q^22 - 25 * q^32

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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