LMFDB - Embedded newform 2008.1.bd.a.339.1

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			339.1
Root			$0.984564 - 0.175023i$ of defining polynomial
Character	$\chi$	$=$	2008.339
Dual form			2008.1.bd.a.1931.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.992115 - 0.125333i) q^{2} +(0.216489 - 0.527330i) q^{3} +(0.968583 + 0.248690i) q^{4} +(-0.280874 + 0.496038i) q^{6} +(-0.929776 - 0.368125i) q^{8} +(0.480326 + 0.474328i) q^{9} +O(q^{10})$	\(q+(-0.992115 - 0.125333i) q^{2} +(0.216489 - 0.527330i) q^{3} +(0.968583 + 0.248690i) q^{4} +(-0.280874 + 0.496038i) q^{6} +(-0.929776 - 0.368125i) q^{8} +(0.480326 + 0.474328i) q^{9} +(0.891606 + 0.302139i) q^{11} +(0.340829 - 0.456924i) q^{12} +(0.876307 + 0.481754i) q^{16} +(-0.562476 - 0.256098i) q^{17} +(-0.417090 - 0.530789i) q^{18} +(0.635213 + 0.567148i) q^{19} +(-0.846707 - 0.411504i) q^{22} +(-0.395409 + 0.410604i) q^{24} +(-0.425779 + 0.904827i) q^{25} +(0.878680 - 0.373702i) q^{27} +(-0.809017 - 0.587785i) q^{32} +(0.352349 - 0.404761i) q^{33} +(0.525944 + 0.324576i) q^{34} +(0.347276 + 0.578879i) q^{36} +(-0.559121 - 0.642289i) q^{38} +(-0.618115 + 1.15860i) q^{41} +(1.35024 + 0.0339424i) q^{43} +(0.788455 + 0.514380i) q^{44} +(0.443754 - 0.357808i) q^{48} +(-0.470704 - 0.882291i) q^{49} +(0.535827 - 0.844328i) q^{50} +(-0.256818 + 0.241168i) q^{51} +(-0.918589 + 0.260627i) q^{54} +(0.436590 - 0.212185i) q^{57} +(-0.0228729 + 0.0104141i) q^{59} +(0.728969 + 0.684547i) q^{64} +(-0.400301 + 0.357408i) q^{66} +(1.70118 + 0.302413i) q^{67} +(-0.481116 - 0.387935i) q^{68} +(-0.271984 - 0.617839i) q^{72} +(0.0886310 - 0.364131i) q^{73} +(0.384966 + 0.420411i) q^{75} +(0.474212 + 0.707301i) q^{76} +(0.00164310 + 0.130746i) q^{81} +(0.758452 - 1.07199i) q^{82} +(-0.520201 - 1.92528i) q^{83} +(-1.33534 - 0.202905i) q^{86} +(-0.717769 - 0.609144i) q^{88} +(-0.00850716 + 0.0748988i) q^{89} +(-0.485100 + 0.299370i) q^{96} +(-1.54144 + 1.00562i) q^{97} +(0.356412 + 0.934329i) q^{98} +(0.284949 + 0.568039i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2008\mathbb{Z}\right)^\times$.

$n$	$257$	$503$	$1005$
$\chi(n)$	$e\left(\frac{83}{125}\right)$	$-1$	$-1$

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 $

$2$	−0.992115	−	0.125333i	−0.992115	−	0.125333i
$2$	−0.992115	−	0.125333i	−0.992115	−	0.125333i
$3$	0.216489	−	0.527330i	0.216489	−	0.527330i	−0.778462	−	0.627691i	$-0.784000\pi$
$3$	0.216489	−	0.527330i	0.216489	−	0.527330i	0.994951	+	0.100362i	$0.0320000\pi$
$4$	0.968583	+	0.248690i	0.968583	+	0.248690i
$5$		0			0		−0.535827	−	0.844328i	$-0.680000\pi$
$5$		0			0		0.535827	+	0.844328i	$0.320000\pi$
$6$	−0.280874	+	0.496038i	−0.280874	+	0.496038i
$7$		0			0		0.514440	−	0.857527i	$-0.328000\pi$
$7$		0			0		−0.514440	+	0.857527i	$0.672000\pi$
$8$	−0.929776	−	0.368125i	−0.929776	−	0.368125i
$9$	0.480326	+	0.474328i	0.480326	+	0.474328i
$10$		0			0
$11$	0.891606	+	0.302139i	0.891606	+	0.302139i	0.728969	−	0.684547i	$-0.240000\pi$
$11$	0.891606	+	0.302139i	0.891606	+	0.302139i	0.162637	+	0.986686i	$0.448000\pi$
$12$	0.340829	−	0.456924i	0.340829	−	0.456924i
$13$		0			0		0.888136	−	0.459580i	$-0.152000\pi$
$13$		0			0		−0.888136	+	0.459580i	$0.848000\pi$
$14$		0			0
$15$		0			0
$16$	0.876307	+	0.481754i	0.876307	+	0.481754i
$17$	−0.562476	−	0.256098i	−0.562476	−	0.256098i	0.112856	−	0.993611i	$-0.464000\pi$
$17$	−0.562476	−	0.256098i	−0.562476	−	0.256098i	−0.675333	+	0.737513i	$0.736000\pi$
$18$	−0.417090	−	0.530789i	−0.417090	−	0.530789i
$19$	0.635213	+	0.567148i	0.635213	+	0.567148i	0.920232	−	0.391374i	$-0.128000\pi$
$19$	0.635213	+	0.567148i	0.635213	+	0.567148i	−0.285019	+	0.958522i	$0.592000\pi$
$20$		0			0
$21$		0			0
$22$	−0.846707	−	0.411504i	−0.846707	−	0.411504i
$23$		0			0		0.979855	−	0.199710i	$-0.0640000\pi$
$23$		0			0		−0.979855	+	0.199710i	$0.936000\pi$
$24$	−0.395409	+	0.410604i	−0.395409	+	0.410604i
$25$	−0.425779	+	0.904827i	−0.425779	+	0.904827i
$26$		0			0
$27$	0.878680	−	0.373702i	0.878680	−	0.373702i
$28$		0			0
$29$		0			0		−0.938734	−	0.344643i	$-0.888000\pi$
$29$		0			0		0.938734	+	0.344643i	$0.112000\pi$
$30$		0			0
$31$		0			0		0.0125660	−	0.999921i	$-0.496000\pi$
$31$		0			0		−0.0125660	+	0.999921i	$0.504000\pi$
$32$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$33$	0.352349	−	0.404761i	0.352349	−	0.404761i
$34$	0.525944	+	0.324576i	0.525944	+	0.324576i
$35$		0			0
$36$	0.347276	+	0.578879i	0.347276	+	0.578879i
$37$		0			0		−0.162637	−	0.986686i	$-0.552000\pi$
$37$		0			0		0.162637	+	0.986686i	$0.448000\pi$
$38$	−0.559121	−	0.642289i	−0.559121	−	0.642289i
$39$		0			0
$40$		0			0
$41$	−0.618115	+	1.15860i	−0.618115	+	1.15860i	0.356412	+	0.934329i	$0.384000\pi$
$41$	−0.618115	+	1.15860i	−0.618115	+	1.15860i	−0.974527	+	0.224271i	$0.928000\pi$
$42$		0			0
$43$	1.35024	+	0.0339424i	1.35024	+	0.0339424i	0.693653	−	0.720309i	$-0.256000\pi$
$43$	1.35024	+	0.0339424i	1.35024	+	0.0339424i	0.656586	+	0.754251i	$0.272000\pi$
$44$	0.788455	+	0.514380i	0.788455	+	0.514380i
$45$		0			0
$46$		0			0
$47$		0			0		0.876307	−	0.481754i	$-0.160000\pi$
$47$		0			0		−0.876307	+	0.481754i	$0.840000\pi$
$48$	0.443754	−	0.357808i	0.443754	−	0.357808i
$49$	−0.470704	−	0.882291i	−0.470704	−	0.882291i
$50$	0.535827	−	0.844328i	0.535827	−	0.844328i
$51$	−0.256818	+	0.241168i	−0.256818	+	0.241168i
$52$		0			0
$53$		0			0		−0.332820	−	0.942991i	$-0.608000\pi$
$53$		0			0		0.332820	+	0.942991i	$0.392000\pi$
$54$	−0.918589	+	0.260627i	−0.918589	+	0.260627i
$55$		0			0
$56$		0			0
$57$	0.436590	−	0.212185i	0.436590	−	0.212185i
$58$		0			0
$59$	−0.0228729	+	0.0104141i	−0.0228729	+	0.0104141i	−0.425779	−	0.904827i	$-0.640000\pi$
$59$	−0.0228729	+	0.0104141i	−0.0228729	+	0.0104141i	0.402906	+	0.915241i	$0.368000\pi$
$60$		0			0
$61$		0			0		0.285019	−	0.958522i	$-0.408000\pi$
$61$		0			0		−0.285019	+	0.958522i	$0.592000\pi$
$62$		0			0
$63$		0			0
$64$	0.728969	+	0.684547i	0.728969	+	0.684547i
$65$		0			0
$66$	−0.400301	+	0.357408i	−0.400301	+	0.357408i
$67$	1.70118	+	0.302413i	1.70118	+	0.302413i	0.938734	−	0.344643i	$-0.112000\pi$
$67$	1.70118	+	0.302413i	1.70118	+	0.302413i	0.762443	+	0.647056i	$0.224000\pi$
$68$	−0.481116	−	0.387935i	−0.481116	−	0.387935i
$69$		0			0
$70$		0			0
$71$		0			0		0.448383	−	0.893841i	$-0.352000\pi$
$71$		0			0		−0.448383	+	0.893841i	$0.648000\pi$
$72$	−0.271984	−	0.617839i	−0.271984	−	0.617839i
$73$	0.0886310	−	0.364131i	0.0886310	−	0.364131i	−0.910106	−	0.414376i	$-0.864000\pi$
$73$	0.0886310	−	0.364131i	0.0886310	−	0.364131i	0.998737	+	0.0502443i	$0.0160000\pi$
$74$		0			0
$75$	0.384966	+	0.420411i	0.384966	+	0.420411i
$76$	0.474212	+	0.707301i	0.474212	+	0.707301i
$77$		0			0
$78$		0			0
$79$		0			0		−0.962028	−	0.272952i	$-0.912000\pi$
$79$		0			0		0.962028	+	0.272952i	$0.0880000\pi$
$80$		0			0
$81$	0.00164310	+	0.130746i	0.00164310	+	0.130746i
$82$	0.758452	−	1.07199i	0.758452	−	1.07199i
$83$	−0.520201	−	1.92528i	−0.520201	−	1.92528i	−0.332820	−	0.942991i	$-0.608000\pi$
$83$	−0.520201	−	1.92528i	−0.520201	−	1.92528i	−0.187381	−	0.982287i	$-0.560000\pi$
$84$		0			0
$85$		0			0
$86$	−1.33534	−	0.202905i	−1.33534	−	0.202905i
$87$		0			0
$88$	−0.717769	−	0.609144i	−0.717769	−	0.609144i
$89$	−0.00850716	+	0.0748988i	−0.00850716	+	0.0748988i	−0.997159	−	0.0753268i	$-0.976000\pi$
$89$	−0.00850716	+	0.0748988i	−0.00850716	+	0.0748988i	0.988652	+	0.150226i	$0.0480000\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	−0.485100	+	0.299370i	−0.485100	+	0.299370i
$97$	−1.54144	+	1.00562i	−1.54144	+	1.00562i	−0.556876	+	0.830596i	$0.688000\pi$
$97$	−1.54144	+	1.00562i	−1.54144	+	1.00562i	−0.984564	+	0.175023i	$0.944000\pi$
$98$	0.356412	+	0.934329i	0.356412	+	0.934329i
$99$	0.284949	+	0.568039i	0.284949	+	0.568039i
$100$	−0.637424	+	0.770513i	−0.637424	+	0.770513i
$101$		0			0		−0.577573	−	0.816339i	$-0.696000\pi$
$101$		0			0		0.577573	+	0.816339i	$0.304000\pi$
$102$	0.285019	−	0.207079i	0.285019	−	0.207079i
$103$		0			0		0.0878512	−	0.996134i	$-0.472000\pi$
$103$		0			0		−0.0878512	+	0.996134i	$0.528000\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.452605	−	1.52211i	−0.452605	−	1.52211i	−0.809017	−	0.587785i	$-0.800000\pi$
$107$	−0.452605	−	1.52211i	−0.452605	−	1.52211i	0.356412	−	0.934329i	$-0.384000\pi$
$108$	0.944011	−	0.143442i	0.944011	−	0.143442i
$109$		0			0		0.556876	−	0.830596i	$-0.312000\pi$
$109$		0			0		−0.556876	+	0.830596i	$0.688000\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.304522	−	0.937223i	0.304522	−	0.937223i	−0.675333	−	0.737513i	$-0.736000\pi$
$113$	0.304522	−	0.937223i	0.304522	−	0.937223i	0.979855	−	0.199710i	$-0.0640000\pi$
$114$	−0.459742	+	0.155793i	−0.459742	+	0.155793i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	0.0239977	−	0.00746527i	0.0239977	−	0.00746527i
$119$		0			0
$120$		0			0
$121$	−0.0903174	−	0.0691528i	−0.0903174	−	0.0691528i
$122$		0			0
$123$	0.477149	+	0.576774i	0.477149	+	0.576774i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		0.260842	−	0.965382i	$-0.416000\pi$
$127$		0			0		−0.260842	+	0.965382i	$0.584000\pi$
$128$	−0.637424	−	0.770513i	−0.637424	−	0.770513i
$129$	0.310210	−	0.704673i	0.310210	−	0.704673i
$130$		0			0
$131$	0.123051	+	0.0250798i	0.123051	+	0.0250798i	0.260842	−	0.965382i	$-0.416000\pi$
$131$	0.123051	+	0.0250798i	0.123051	+	0.0250798i	−0.137790	+	0.990461i	$0.544000\pi$
$132$	0.441940	−	0.304418i	0.441940	−	0.304418i
$133$		0			0
$134$	−1.64986	−	0.513242i	−1.64986	−	0.513242i
$135$		0			0
$136$	0.428701	+	0.445175i	0.428701	+	0.445175i
$137$	0.630426	−	0.213633i	0.630426	−	0.213633i	0.0125660	−	0.999921i	$-0.496000\pi$
$137$	0.630426	−	0.213633i	0.630426	−	0.213633i	0.617860	+	0.786288i	$0.288000\pi$
$138$		0			0
$139$	0.656200	−	0.382531i	0.656200	−	0.382531i	−0.137790	−	0.990461i	$-0.544000\pi$
$139$	0.656200	−	0.382531i	0.656200	−	0.382531i	0.793990	+	0.607930i	$0.208000\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	0.192404	+	0.647056i	0.192404	+	0.647056i
$145$		0			0
$146$	−0.133570	+	0.350152i	−0.133570	+	0.350152i
$147$	−0.567160	+	0.0572100i	−0.567160	+	0.0572100i
$148$		0			0
$149$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$149$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$150$	−0.329239	−	0.465345i	−0.329239	−	0.465345i
$151$		0			0		0.637424	−	0.770513i	$-0.280000\pi$
$151$		0			0		−0.637424	+	0.770513i	$0.720000\pi$
$152$	−0.381825	−	0.761158i	−0.381825	−	0.761158i
$153$	−0.148698	−	0.389809i	−0.148698	−	0.389809i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.929776	−	0.368125i	$-0.120000\pi$
$157$		0			0		−0.929776	+	0.368125i	$0.880000\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	0.0147567	−	0.129921i	0.0147567	−	0.129921i
$163$	1.43146	+	1.21483i	1.43146	+	1.21483i	0.938734	+	0.344643i	$0.112000\pi$
$163$	1.43146	+	1.21483i	1.43146	+	1.21483i	0.492727	+	0.870184i	$0.336000\pi$
$164$	−0.886828	+	0.968481i	−0.886828	+	0.968481i
$165$		0			0
$166$	0.274798	+	1.97529i	0.274798	+	1.97529i
$167$		0			0		−0.379779	−	0.925077i	$-0.624000\pi$
$167$		0			0		0.379779	+	0.925077i	$0.376000\pi$
$168$		0			0
$169$	0.577573	−	0.816339i	0.577573	−	0.816339i
$170$		0			0
$171$	0.0360951	+	0.573715i	0.0360951	+	0.573715i
$172$	1.29938	+	0.368667i	1.29938	+	0.368667i
$173$		0			0		0.0376902	−	0.999289i	$-0.488000\pi$
$173$		0			0		−0.0376902	+	0.999289i	$0.512000\pi$
$174$		0			0
$175$		0			0
$176$	0.635764	+	0.694301i	0.635764	+	0.694301i
$177$	0.000539959		0.0143161i	0.000539959		0.0143161i
$178$	0.0178274	−	0.0732420i	0.0178274	−	0.0732420i
$179$	0.131055	+	0.297704i	0.131055	+	0.297704i	0.968583	−	0.248690i	$-0.0800000\pi$
$179$	0.131055	+	0.297704i	0.131055	+	0.297704i	−0.837528	+	0.546394i	$0.816000\pi$
$180$		0			0
$181$		0			0		−0.994951	−	0.100362i	$-0.968000\pi$
$181$		0			0		0.994951	+	0.100362i	$0.0320000\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−0.424130	−	0.398285i	−0.424130	−	0.398285i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		−0.997159	−	0.0753268i	$-0.976000\pi$
$191$		0			0		0.997159	+	0.0753268i	$0.0240000\pi$
$192$	0.518795	−	0.236210i	0.518795	−	0.236210i
$193$	−1.02593	−	0.530882i	−1.02593	−	0.530882i	−0.137790	−	0.990461i	$-0.544000\pi$
$193$	−1.02593	−	0.530882i	−1.02593	−	0.530882i	−0.888136	+	0.459580i	$0.848000\pi$
$194$	1.65532	−	0.804496i	1.65532	−	0.804496i
$195$		0			0
$196$	−0.236499	−	0.971632i	−0.236499	−	0.971632i
$197$		0			0		0.962028	−	0.272952i	$-0.0880000\pi$
$197$		0			0		−0.962028	+	0.272952i	$0.912000\pi$
$198$	−0.211508	−	0.599273i	−0.211508	−	0.599273i
$199$		0			0		0.974527	−	0.224271i	$-0.0720000\pi$
$199$		0			0		−0.974527	+	0.224271i	$0.928000\pi$
$200$	0.728969	−	0.684547i	0.728969	−	0.684547i
$201$	0.527757	−	0.831612i	0.527757	−	0.831612i
$202$		0			0
$203$		0			0
$204$	−0.308726	+	0.169723i	−0.308726	+	0.169723i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	0.395002	+	0.697595i	0.395002	+	0.697595i
$210$		0			0
$211$	−0.231551	−	1.21383i	−0.231551	−	1.21383i	−0.888136	−	0.459580i	$-0.848000\pi$
$211$	−0.231551	−	1.21383i	−0.231551	−	1.21383i	0.656586	−	0.754251i	$-0.272000\pi$
$212$		0			0
$213$		0			0
$214$	0.258265	+	1.56684i	0.258265	+	1.56684i
$215$		0			0
$216$	−0.954545	+	0.0239954i	−0.954545	+	0.0239954i
$217$		0			0
$218$		0			0
$219$	−0.172830	−	0.125568i	−0.172830	−	0.125568i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.711536	−	0.702650i	$-0.248000\pi$
$223$		0			0		−0.711536	+	0.702650i	$0.752000\pi$
$224$		0			0
$225$	−0.633698	+	0.232653i	−0.633698	+	0.232653i
$226$	−0.419586	+	0.891666i	−0.419586	+	0.891666i
$227$	−1.28989	+	1.33945i	−1.28989	+	1.33945i	−0.379779	+	0.925077i	$0.624000\pi$
$227$	−1.28989	+	1.33945i	−1.28989	+	1.33945i	−0.910106	+	0.414376i	$0.864000\pi$
$228$	0.475642	−	0.0969435i	0.475642	−	0.0969435i
$229$		0			0		−0.899405	−	0.437116i	$-0.856000\pi$
$229$		0			0		0.899405	+	0.437116i	$0.144000\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	0.139459	+	0.177475i	0.139459	+	0.177475i	0.850994	−	0.525175i	$-0.176000\pi$
$233$	0.139459	+	0.177475i	0.139459	+	0.177475i	−0.711536	+	0.702650i	$0.752000\pi$
$234$		0			0
$235$		0			0
$236$	−0.0247441	+	0.00439869i	−0.0247441	+	0.00439869i
$237$		0			0
$238$		0			0
$239$		0			0		0.597905	−	0.801567i	$-0.296000\pi$
$239$		0			0		−0.597905	+	0.801567i	$0.704000\pi$
$240$		0			0
$241$	−0.381825	−	0.811419i	−0.381825	−	0.811419i	−0.999684	−	0.0251301i	$-0.992000\pi$
$241$	−0.381825	−	0.811419i	−0.381825	−	0.811419i	0.617860	−	0.786288i	$-0.288000\pi$
$242$	0.0809381	+	0.0799273i	0.0809381	+	0.0799273i
$243$	0.957096	+	0.378941i	0.957096	+	0.378941i
$244$		0			0
$245$		0			0
$246$	−0.401098	−	0.632029i	−0.401098	−	0.632029i
$247$		0			0
$248$		0			0
$249$	−1.12787	−	0.142484i	−1.12787	−	0.142484i
$250$		0			0
$251$	−0.514440	−	0.857527i	−0.514440	−	0.857527i
$251$	−0.514440	−	0.857527i	−0.514440	−	0.857527i
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.535827	+	0.844328i	0.535827	+	0.844328i
$257$	−0.933322	+	1.64830i	−0.933322	+	1.64830i	−0.187381	+	0.982287i	$0.560000\pi$
$257$	−0.933322	+	1.64830i	−0.933322	+	1.64830i	−0.745941	+	0.666012i	$0.768000\pi$
$258$	−0.396083	+	0.660237i	−0.396083	+	0.660237i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−0.118938	−	0.0403044i	−0.118938	−	0.0403044i
$263$		0			0		0.597905	−	0.801567i	$-0.296000\pi$
$263$		0			0		−0.597905	+	0.801567i	$0.704000\pi$
$264$	−0.476608	+	0.246628i	−0.476608	+	0.246628i
$265$		0			0
$266$		0			0
$267$	0.0376546	+	0.0207008i	0.0376546	+	0.0207008i
$268$	1.57252	+	0.715978i	1.57252	+	0.715978i
$269$		0			0		−0.617860	−	0.786288i	$-0.712000\pi$
$269$		0			0		0.617860	+	0.786288i	$0.288000\pi$
$270$		0			0
$271$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$271$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$272$	−0.369526	−	0.495396i	−0.369526	−	0.495396i
$273$		0			0
$274$	−0.652230	+	0.132935i	−0.652230	+	0.132935i
$275$	−0.653011	+	0.678105i	−0.653011	+	0.678105i
$276$		0			0
$277$		0			0		0.938734	−	0.344643i	$-0.112000\pi$
$277$		0			0		−0.938734	+	0.344643i	$0.888000\pi$
$278$	−0.698970	+	0.297271i	−0.698970	+	0.297271i
$279$		0			0
$280$		0			0
$281$	−1.94659	+	0.0979289i	−1.94659	+	0.0979289i	−0.984564	−	0.175023i	$-0.944000\pi$
$281$	−1.94659	+	0.0979289i	−1.94659	+	0.0979289i	−0.962028	+	0.272952i	$0.912000\pi$
$282$		0			0
$283$	−0.725499	−	0.527106i	−0.725499	−	0.527106i	0.162637	−	0.986686i	$-0.448000\pi$
$283$	−0.725499	−	0.527106i	−0.725499	−	0.527106i	−0.888136	+	0.459580i	$0.848000\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.109789	−	0.666068i	−0.109789	−	0.666068i
$289$	−0.405792	−	0.466153i	−0.405792	−	0.466153i
$290$		0			0
$291$	0.196588	+	1.03055i	0.196588	+	1.03055i
$292$	0.176402	−	0.330650i	0.176402	−	0.330650i
$293$		0			0		−0.492727	−	0.870184i	$-0.664000\pi$
$293$		0			0		0.492727	+	0.870184i	$0.336000\pi$
$294$	0.569859	+	0.0143251i	0.569859	+	0.0143251i
$295$		0			0
$296$		0			0
$297$	0.896346	−	0.0677113i	0.896346	−	0.0677113i
$298$		0			0
$299$		0			0
$300$	0.268319	+	0.502940i	0.268319	+	0.502940i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	0.283415	+	0.803012i	0.283415	+	0.803012i
$305$		0			0
$306$	0.0986692	+	0.405372i	0.0986692	+	0.405372i
$307$	−1.41034	+	1.07985i	−1.41034	+	1.07985i	−0.425779	+	0.904827i	$0.640000\pi$
$307$	−1.41034	+	1.07985i	−1.41034	+	1.07985i	−0.984564	+	0.175023i	$0.944000\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.997159	−	0.0753268i	$-0.976000\pi$
$311$		0			0		0.997159	+	0.0753268i	$0.0240000\pi$
$312$		0			0
$313$	−0.170270	+	1.22393i	−0.170270	+	1.22393i	0.693653	+	0.720309i	$0.256000\pi$
$313$	−0.170270	+	1.22393i	−0.170270	+	1.22393i	−0.863923	+	0.503623i	$0.832000\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		0.745941	−	0.666012i	$-0.232000\pi$
$317$		0			0		−0.745941	+	0.666012i	$0.768000\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−0.900640	−	0.0908485i	−0.900640	−	0.0908485i
$322$		0			0
$323$	−0.212046	−	0.481684i	−0.212046	−	0.481684i
$324$	−0.0309239	+	0.127047i	−0.0309239	+	0.127047i
$325$		0			0
$326$	−1.26792	−	1.38466i	−1.26792	−	1.38466i
$327$		0			0
$328$	1.00122	−	0.849695i	1.00122	−	0.849695i
$329$		0			0
$330$		0			0
$331$	0.0725322	+	1.15287i	0.0725322	+	1.15287i	0.850994	+	0.525175i	$0.176000\pi$
$331$	0.0725322	+	1.15287i	0.0725322	+	1.15287i	−0.778462	+	0.627691i	$0.784000\pi$
$332$	−0.0250607	−	1.99416i	−0.0250607	−	1.99416i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−1.94678	−	0.295814i	−1.94678	−	0.295814i	−0.947098	−	0.320944i	$-0.896000\pi$
$337$	−1.94678	−	0.295814i	−1.94678	−	0.295814i	−0.999684	+	0.0251301i	$0.992000\pi$
$338$	−0.675333	+	0.737513i	−0.675333	+	0.737513i
$339$	−0.428300	−	0.363482i	−0.428300	−	0.363482i
$340$		0			0
$341$		0			0
$342$	0.0360951	−	0.573715i	0.0360951	−	0.573715i
$343$		0			0
$344$	−1.24293	−	0.528615i	−1.24293	−	0.528615i
$345$		0			0
$346$		0			0
$347$	−1.01763	+	0.628009i	−1.01763	+	0.628009i	−0.929776	−	0.368125i	$-0.880000\pi$
$347$	−1.01763	+	0.628009i	−1.01763	+	0.628009i	−0.0878512	+	0.996134i	$0.528000\pi$
$348$		0			0
$349$		0			0		−0.356412	−	0.934329i	$-0.616000\pi$
$349$		0			0		0.356412	+	0.934329i	$0.384000\pi$
$350$		0			0
$351$		0			0
$352$	−0.543731	−	0.768508i	−0.543731	−	0.768508i
$353$	−1.56720	+	1.13864i	−1.56720	+	1.13864i	−0.637424	+	0.770513i	$0.720000\pi$
$353$	−1.56720	+	1.13864i	−1.56720	+	1.13864i	−0.929776	+	0.368125i	$0.880000\pi$
$354$	0.00125858	−	0.0142709i	0.00125858	−	0.0142709i
$355$		0			0
$356$	−0.0268665	+	0.0704301i	−0.0268665	+	0.0704301i
$357$		0			0
$358$	−0.0927094	−	0.311783i	−0.0927094	−	0.311783i
$359$		0			0		0.988652	−	0.150226i	$-0.0480000\pi$
$359$		0			0		−0.988652	+	0.150226i	$0.952000\pi$
$360$		0			0
$361$	−0.0310183	−	0.273092i	−0.0310183	−	0.273092i
$362$		0			0
$363$	−0.0560190	+	0.0326562i	−0.0560190	+	0.0326562i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.823533	−	0.567269i	$-0.808000\pi$
$367$		0			0		0.823533	+	0.567269i	$0.192000\pi$
$368$		0			0
$369$	−0.846453	+	0.263317i	−0.846453	+	0.263317i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.402906	−	0.915241i	$-0.368000\pi$
$373$		0			0		−0.402906	+	0.915241i	$0.632000\pi$
$374$	0.370867	+	0.448302i	0.370867	+	0.448302i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−1.26841	−	1.53325i	−1.26841	−	1.53325i	−0.711536	−	0.702650i	$-0.752000\pi$
$379$	−1.26841	−	1.53325i	−1.26841	−	1.53325i	−0.556876	−	0.830596i	$-0.688000\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.823533	−	0.567269i	$-0.192000\pi$
$383$		0			0		−0.823533	+	0.567269i	$0.808000\pi$
$384$	−0.544310	+	0.169325i	−0.544310	+	0.169325i
$385$		0			0
$386$	0.951300	+	0.655278i	0.951300	+	0.655278i
$387$	0.632456	+	0.656760i	0.632456	+	0.656760i
$388$	−1.74310	+	0.590685i	−1.74310	+	0.590685i
$389$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$389$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$390$		0			0
$391$		0			0
$392$	0.112856	+	0.993611i	0.112856	+	0.993611i
$393$	0.0398645	−	0.0594591i	0.0398645	−	0.0594591i
$394$		0			0
$395$		0			0
$396$	0.134731	+	0.621057i	0.134731	+	0.621057i
$397$		0			0		0.356412	−	0.934329i	$-0.384000\pi$
$397$		0			0		−0.356412	+	0.934329i	$0.616000\pi$
$398$		0			0
$399$		0			0
$400$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$401$	1.15369	+	1.63062i	1.15369	+	1.63062i	0.617860	+	0.786288i	$0.288000\pi$
$401$	1.15369	+	1.63062i	1.15369	+	1.63062i	0.535827	+	0.844328i	$0.320000\pi$
$402$	−0.627824	+	0.758909i	−0.627824	+	0.758909i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	0.327563	−	0.129691i	0.327563	−	0.129691i
$409$	−0.435268	−	0.185119i	−0.435268	−	0.185119i	0.162637	−	0.986686i	$-0.448000\pi$
$409$	−0.435268	−	0.185119i	−0.435268	−	0.185119i	−0.597905	+	0.801567i	$0.704000\pi$
$410$		0			0
$411$	0.0238252	−	0.378691i	0.0238252	−	0.378691i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−0.0596601	−	0.428847i	−0.0596601	−	0.428847i
$418$	−0.304455	−	0.741601i	−0.304455	−	0.741601i
$419$	−0.123378	−	0.456624i	−0.123378	−	0.456624i	0.876307	−	0.481754i	$-0.160000\pi$
$419$	−0.123378	−	0.456624i	−0.123378	−	0.456624i	−0.999684	+	0.0251301i	$0.992000\pi$
$420$		0			0
$421$		0			0		−0.0125660	−	0.999921i	$-0.504000\pi$
$421$		0			0		0.0125660	+	0.999921i	$0.496000\pi$
$422$	0.0775915	+	1.23328i	0.0775915	+	1.23328i
$423$		0			0
$424$		0			0
$425$	0.471215	−	0.399903i	0.471215	−	0.399903i
$426$		0			0
$427$		0			0
$428$	−0.0598513	−	1.58685i	−0.0598513	−	1.58685i
$429$		0			0
$430$		0			0
$431$		0			0		0.448383	−	0.893841i	$-0.352000\pi$
$431$		0			0		−0.448383	+	0.893841i	$0.648000\pi$
$432$	0.950025	+	0.0958300i	0.950025	+	0.0958300i
$433$	0.238883	−	1.25227i	0.238883	−	1.25227i	−0.637424	−	0.770513i	$-0.720000\pi$
$433$	0.238883	−	1.25227i	0.238883	−	1.25227i	0.876307	−	0.481754i	$-0.160000\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	0.155729	+	0.146239i	0.155729	+	0.146239i
$439$		0			0		0.968583	−	0.248690i	$-0.0800000\pi$
$439$		0			0		−0.968583	+	0.248690i	$0.920000\pi$
$440$		0			0
$441$	0.192404	−	0.647056i	0.192404	−	0.647056i
$442$		0			0
$443$	1.47258	−	0.670474i	1.47258	−	0.670474i	0.492727	−	0.870184i	$-0.336000\pi$
$443$	1.47258	−	0.670474i	1.47258	−	0.670474i	0.979855	+	0.199710i	$0.0640000\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−0.566455	−	1.60496i	−0.566455	−	1.60496i	−0.778462	−	0.627691i	$-0.784000\pi$
$449$	−0.566455	−	1.60496i	−0.566455	−	1.60496i	0.212007	−	0.977268i	$-0.432000\pi$
$450$	0.657860	−	0.151395i	0.657860	−	0.151395i
$451$	−0.901173	+	0.846258i	−0.901173	+	0.846258i
$452$	0.528033	−	0.832047i	0.528033	−	0.832047i
$453$		0			0
$454$	1.44759	−	1.16723i	1.44759	−	1.16723i
$455$		0			0
$456$	−0.484042	+	0.0365652i	−0.484042	+	0.0365652i
$457$	−0.420671	+	1.93912i	−0.420671	+	1.93912i	−0.0878512	+	0.996134i	$0.528000\pi$
$457$	−0.420671	+	1.93912i	−0.420671	+	1.93912i	−0.332820	+	0.942991i	$0.608000\pi$
$458$		0			0
$459$	−0.589941	−	0.0148300i	−0.589941	−	0.0148300i
$460$		0			0
$461$		0			0		0.470704	−	0.882291i	$-0.344000\pi$
$461$		0			0		−0.470704	+	0.882291i	$0.656000\pi$
$462$		0			0
$463$		0			0		−0.0878512	−	0.996134i	$-0.528000\pi$
$463$		0			0		0.0878512	+	0.996134i	$0.472000\pi$
$464$		0			0
$465$		0			0
$466$	−0.116116	−	0.193555i	−0.116116	−	0.193555i
$467$	−0.521518	+	0.0131099i	−0.521518	+	0.0131099i	−0.285019	−	0.958522i	$-0.592000\pi$
$467$	−0.521518	+	0.0131099i	−0.521518	+	0.0131099i	−0.236499	+	0.971632i	$0.576000\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	0.0251003	−	0.00126274i	0.0251003	−	0.00126274i
$473$	1.19363	+	0.438223i	1.19363	+	0.438223i
$474$		0			0
$475$	−0.783631	+	0.333278i	−0.783631	+	0.333278i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.979855	−	0.199710i	$-0.0640000\pi$
$479$		0			0		−0.979855	+	0.199710i	$0.936000\pi$
$480$		0			0
$481$		0			0
$482$	0.277116	+	0.852876i	0.277116	+	0.852876i
$483$		0			0
$484$	−0.0702823	−	0.0894413i	−0.0702823	−	0.0894413i
$485$		0			0
$486$	−0.902055	−	0.495909i	−0.902055	−	0.495909i
$487$		0			0		0.984564	−	0.175023i	$-0.0560000\pi$
$487$		0			0		−0.984564	+	0.175023i	$0.944000\pi$
$488$		0			0
$489$	0.950509	−	0.491856i	0.950509	−	0.491856i
$490$		0			0
$491$	0.974450	+	0.330212i	0.974450	+	0.330212i	0.762443	−	0.647056i	$-0.224000\pi$
$491$	0.974450	+	0.330212i	0.974450	+	0.330212i	0.212007	+	0.977268i	$0.432000\pi$
$492$	0.318721	+	0.677316i	0.318721	+	0.677316i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	1.10112	+	0.282720i	1.10112	+	0.282720i
$499$	−0.161032	+	0.392246i	−0.161032	+	0.392246i	−0.984564	−	0.175023i	$-0.944000\pi$
$499$	−0.161032	+	0.392246i	−0.161032	+	0.392246i	0.823533	+	0.567269i	$0.192000\pi$
$500$		0			0
$501$		0			0
$502$	0.402906	+	0.915241i	0.402906	+	0.915241i
$503$		0			0		1.00000			$0$
$503$		0			0		−1.00000			$\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.305442	−	0.481299i	−0.305442	−	0.481299i
$508$		0			0
$509$		0			0		0.514440	−	0.857527i	$-0.328000\pi$
$509$		0			0		−0.514440	+	0.857527i	$0.672000\pi$
$510$		0			0
$511$		0			0
$512$	−0.425779	−	0.904827i	−0.425779	−	0.904827i
$513$	0.770093	+	0.260962i	0.770093	+	0.260962i
$514$	1.13255	−	1.51833i	1.13255	−	1.51833i
$515$		0			0
$516$	0.475710	−	0.605388i	0.475710	−	0.605388i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−0.242636	−	0.216637i	−0.242636	−	0.216637i	0.535827	−	0.844328i	$-0.320000\pi$
$521$	−0.242636	−	0.216637i	−0.242636	−	0.216637i	−0.778462	+	0.627691i	$0.784000\pi$
$522$		0			0
$523$	−0.426201	−	0.571376i	−0.426201	−	0.571376i	0.535827	−	0.844328i	$-0.320000\pi$
$523$	−0.426201	−	0.571376i	−0.426201	−	0.571376i	−0.962028	+	0.272952i	$0.912000\pi$
$524$	0.112948	+	0.0548935i	0.112948	+	0.0548935i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	0.503761	−	0.184949i	0.503761	−	0.184949i
$529$	0.920232	−	0.391374i	0.920232	−	0.391374i
$530$		0			0
$531$	−0.0159261	−	0.00584706i	−0.0159261	−	0.00584706i
$532$		0			0
$533$		0			0
$534$	−0.0347632	−	0.0252570i	−0.0347632	−	0.0252570i
$535$		0			0
$536$	−1.47039	−	0.907421i	−1.47039	−	0.907421i
$537$	0.185360	−	0.00465959i	0.185360	−	0.00465959i
$538$		0			0
$539$	−0.153108	−	0.928874i	−0.153108	−	0.928874i
$540$		0			0
$541$		0			0		−0.0878512	−	0.996134i	$-0.528000\pi$
$541$		0			0		0.0878512	+	0.996134i	$0.472000\pi$
$542$		0			0
$543$		0			0
$544$	0.304522	+	0.537803i	0.304522	+	0.537803i
$545$		0			0
$546$		0			0
$547$	0.0898940	−	0.414376i	0.0898940	−	0.414376i	−0.910106	−	0.414376i	$-0.864000\pi$
$547$	0.0898940	−	0.414376i	0.0898940	−	0.414376i	1.00000			$0$
$548$	0.663748	−	0.0501405i	0.663748	−	0.0501405i
$549$		0			0
$550$	0.732851	−	0.590914i	0.732851	−	0.590914i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	0.730716	−	0.207323i	0.730716	−	0.207323i
$557$		0			0		−0.236499	−	0.971632i	$-0.576000\pi$
$557$		0			0		0.236499	+	0.971632i	$0.424000\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−0.301847	+	0.137432i	−0.301847	+	0.137432i
$562$	1.94352	+	0.146816i	1.94352	+	0.146816i
$563$	0.530008	−	1.78242i	0.530008	−	1.78242i	−0.0878512	−	0.996134i	$-0.528000\pi$
$563$	0.530008	−	1.78242i	0.530008	−	1.78242i	0.617860	−	0.786288i	$-0.288000\pi$
$564$		0			0
$565$		0			0
$566$	0.653715	+	0.613879i	0.653715	+	0.613879i
$567$		0			0
$568$		0			0
$569$	1.86496	+	0.331528i	1.86496	+	0.331528i	0.988652	−	0.150226i	$-0.0480000\pi$
$569$	1.86496	+	0.331528i	1.86496	+	0.331528i	0.876307	+	0.481754i	$0.160000\pi$
$570$		0			0
$571$	−0.337063	+	1.76695i	−0.337063	+	1.76695i	0.260842	+	0.965382i	$0.416000\pi$
$571$	−0.337063	+	1.76695i	−0.337063	+	1.76695i	−0.597905	+	0.801567i	$0.704000\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.0254430	+	0.674576i	0.0254430	+	0.674576i
$577$	−1.34385	−	1.46758i	−1.34385	−	1.46758i	−0.745941	−	0.666012i	$-0.768000\pi$
$577$	−1.34385	−	1.46758i	−1.34385	−	1.46758i	−0.597905	−	0.801567i	$-0.704000\pi$
$578$	0.344168	+	0.513336i	0.344168	+	0.513336i
$579$	−0.502051	+	0.426072i	−0.502051	+	0.426072i
$580$		0			0
$581$		0			0
$582$	−0.0658757	−	1.04706i	−0.0658757	−	1.04706i
$583$		0			0
$584$	−0.216453	+	0.305933i	−0.216453	+	0.305933i
$585$		0			0
$586$		0			0
$587$	0.265116	+	1.90570i	0.265116	+	1.90570i	0.402906	+	0.915241i	$0.368000\pi$
$587$	0.265116	+	1.90570i	0.265116	+	1.90570i	−0.137790	+	0.990461i	$0.544000\pi$
$588$	−0.563570	−	0.0856344i	−0.563570	−	0.0856344i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	0.0997101	−	1.58485i	0.0997101	−	1.58485i	−0.556876	−	0.830596i	$-0.688000\pi$
$593$	0.0997101	−	1.58485i	0.0997101	−	1.58485i	0.656586	−	0.754251i	$-0.272000\pi$
$594$	−0.897765	−	0.0451646i	−0.897765	−	0.0451646i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		0.837528	−	0.546394i	$-0.184000\pi$
$599$		0			0		−0.837528	+	0.546394i	$0.816000\pi$
$600$	−0.203169	−	0.532603i	−0.203169	−	0.532603i
$601$	0.653715	+	1.30316i	0.653715	+	1.30316i	0.938734	+	0.344643i	$0.112000\pi$
$601$	0.653715	+	1.30316i	0.653715	+	1.30316i	−0.285019	+	0.958522i	$0.592000\pi$
$602$		0			0
$603$	0.673677	+	0.952173i	0.673677	+	0.952173i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		0.356412	−	0.934329i	$-0.384000\pi$
$607$		0			0		−0.356412	+	0.934329i	$0.616000\pi$
$608$	−0.180536	−	0.832201i	−0.180536	−	0.832201i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−0.0470845	−	0.414542i	−0.0470845	−	0.414542i
$613$		0			0		−0.974527	−	0.224271i	$-0.928000\pi$
$613$		0			0		0.974527	+	0.224271i	$0.0720000\pi$
$614$	1.53456	−	0.894572i	1.53456	−	0.894572i
$615$		0			0
$616$		0			0
$617$	1.32469	+	1.37560i	1.32469	+	1.37560i	0.876307	+	0.481754i	$0.160000\pi$
$617$	1.32469	+	1.37560i	1.32469	+	1.37560i	0.448383	+	0.893841i	$0.352000\pi$
$618$		0			0
$619$	0.215525	+	0.0670461i	0.215525	+	0.0670461i	0.402906	−	0.915241i	$-0.368000\pi$
$619$	0.215525	+	0.0670461i	0.215525	+	0.0670461i	−0.187381	+	0.982287i	$0.560000\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.637424	−	0.770513i	−0.637424	−	0.770513i
$626$	0.322327	−	1.19294i	0.322327	−	1.19294i
$627$	0.453376	−	0.0572747i	0.453376	−	0.0572747i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		0.402906	−	0.915241i	$-0.368000\pi$
$631$		0			0		−0.402906	+	0.915241i	$0.632000\pi$
$632$		0			0
$633$	−0.690217	−	0.140677i	−0.690217	−	0.140677i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−0.925827	+	0.539710i	−0.925827	+	0.539710i	−0.888136	−	0.459580i	$-0.848000\pi$
$641$	−0.925827	+	0.539710i	−0.925827	+	0.539710i	−0.0376902	+	0.999289i	$0.512000\pi$
$642$	0.882152	+	0.203012i	0.882152	+	0.203012i
$643$	−0.175709	−	1.54698i	−0.175709	−	1.54698i	−0.711536	−	0.702650i	$-0.752000\pi$
$643$	−0.175709	−	1.54698i	−0.175709	−	1.54698i	0.535827	−	0.844328i	$-0.320000\pi$
$644$		0			0
$645$		0			0
$646$	0.150003	+	0.504462i	0.150003	+	0.504462i
$647$		0			0		−0.212007	−	0.977268i	$-0.568000\pi$
$647$		0			0		0.212007	+	0.977268i	$0.432000\pi$
$648$	0.0466033	−	0.122170i	0.0466033	−	0.122170i
$649$	−0.0235401	+	0.00237451i	−0.0235401	+	0.00237451i
$650$		0			0
$651$		0			0
$652$	1.08437	+	1.53265i	1.08437	+	1.53265i
$653$		0			0		0.637424	−	0.770513i	$-0.280000\pi$
$653$		0			0		−0.637424	+	0.770513i	$0.720000\pi$
$654$		0			0
$655$		0			0
$656$	−1.09982	+	0.717509i	−1.09982	+	0.717509i
$657$	0.215290	−	0.132862i	0.215290	−	0.132862i
$658$		0			0
$659$	−0.116762	+	0.0462295i	−0.116762	+	0.0462295i	−0.425779	−	0.904827i	$-0.640000\pi$
$659$	−0.116762	+	0.0462295i	−0.116762	+	0.0462295i	0.309017	+	0.951057i	$0.400000\pi$
$660$		0			0
$661$		0			0		−0.998737	−	0.0502443i	$-0.984000\pi$
$661$		0			0		0.998737	+	0.0502443i	$0.0160000\pi$
$662$	0.0725322	−	1.15287i	0.0725322	−	1.15287i
$663$		0			0
$664$	−0.225071	+	1.98158i	−0.225071	+	1.98158i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.0699330	−	1.11155i	−0.0699330	−	1.11155i	−0.863923	−	0.503623i	$-0.832000\pi$
$673$	−0.0699330	−	1.11155i	−0.0699330	−	1.11155i	0.793990	−	0.607930i	$-0.208000\pi$
$674$	1.89436	+	0.537477i	1.89436	+	0.537477i
$675$	−0.0359883	+	0.954168i	−0.0359883	+	0.954168i
$676$	0.762443	−	0.647056i	0.762443	−	0.647056i
$677$		0			0		−0.556876	−	0.830596i	$-0.688000\pi$
$677$		0			0		0.556876	+	0.830596i	$0.312000\pi$
$678$	0.379366	+	0.414296i	0.379366	+	0.414296i
$679$		0			0
$680$		0			0
$681$	0.427088	+	0.970171i	0.427088	+	0.970171i
$682$		0			0
$683$	−0.274189	−	0.0276577i	−0.274189	−	0.0276577i	−0.0376902	−	0.999289i	$-0.512000\pi$
$683$	−0.274189	−	0.0276577i	−0.274189	−	0.0276577i	−0.236499	+	0.971632i	$0.576000\pi$
$684$	−0.107716	+	0.564668i	−0.107716	+	0.564668i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	1.16687	+	0.680227i	1.16687	+	0.680227i
$689$		0			0
$690$		0			0
$691$	0.0242101	−	0.174026i	0.0242101	−	0.174026i	−0.974527	−	0.224271i	$-0.928000\pi$
$691$	0.0242101	−	0.174026i	0.0242101	−	0.174026i	0.998737	+	0.0502443i	$0.0160000\pi$
$692$		0			0
$693$		0			0
$694$	1.08831	−	0.495514i	1.08831	−	0.495514i
$695$		0			0
$696$		0			0
$697$	0.644390	−	0.493387i	0.644390	−	0.493387i
$698$		0			0
$699$	0.123779	−	0.0351194i	0.123779	−	0.0351194i
$700$		0			0
$701$		0			0		0.974527	−	0.224271i	$-0.0720000\pi$
$701$		0			0		−0.974527	+	0.224271i	$0.928000\pi$
$702$		0			0
$703$		0			0
$704$	0.443124	+	0.830596i	0.443124	+	0.830596i
$705$		0			0
$706$	1.69755	−	0.933237i	1.69755	−	0.933237i
$707$		0			0
$708$	−0.00303727	+	0.0140006i	−0.00303727	+	0.0140006i
$709$		0			0		−0.837528	−	0.546394i	$-0.816000\pi$
$709$		0			0		0.837528	+	0.546394i	$0.184000\pi$
$710$		0			0
$711$		0			0
$712$	0.0354818	−	0.0665074i	0.0354818	−	0.0665074i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	0.0529017	+	0.320944i	0.0529017	+	0.320944i
$717$		0			0
$718$		0			0
$719$		0			0		−0.850994	−	0.525175i	$-0.824000\pi$
$719$		0			0		0.850994	+	0.525175i	$0.176000\pi$
$720$		0			0
$721$		0			0
$722$	−0.00345375	+	0.274826i	−0.00345375	+	0.274826i
$723$	−0.510546	+	0.0256845i	−0.510546	+	0.0256845i
$724$		0			0
$725$		0			0
$726$	0.0596702	−	0.0253777i	0.0596702	−	0.0253777i
$727$		0			0		0.938734	−	0.344643i	$-0.112000\pi$
$727$		0			0		−0.938734	+	0.344643i	$0.888000\pi$
$728$		0			0
$729$	0.316327	−	0.328483i	0.316327	−	0.328483i
$730$		0			0
$731$	−0.750785	−	0.364886i	−0.750785	−	0.364886i
$732$		0			0
$733$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$733$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	1.42541	+	0.783625i	1.42541	+	0.783625i
$738$	0.872781	−	0.155152i	0.872781	−	0.155152i
$739$	−0.170270	+	0.216686i	−0.170270	+	0.216686i	−0.863923	−	0.503623i	$-0.832000\pi$
$739$	−0.170270	+	0.216686i	−0.170270	+	0.216686i	0.693653	+	0.720309i	$0.256000\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		−0.425779	−	0.904827i	$-0.640000\pi$
$743$		0			0		0.425779	+	0.904827i	$0.360000\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	0.663347	−	1.17151i	0.663347	−	1.17151i
$748$	−0.311756	−	0.491249i	−0.311756	−	0.491249i
$749$		0			0
$750$		0			0
$751$		0			0		−0.992115	−	0.125333i	$-0.960000\pi$
$751$		0			0		0.992115	+	0.125333i	$0.0400000\pi$
$752$		0			0
$753$	−0.563570	+	0.0856344i	−0.563570	+	0.0856344i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		−0.968583	−	0.248690i	$-0.920000\pi$
$757$		0			0		0.968583	+	0.248690i	$0.0800000\pi$
$758$	1.06624	+	1.68013i	1.06624	+	1.68013i
$759$		0			0
$760$		0			0
$761$	1.85427	+	0.734157i	1.85427	+	0.734157i	0.954865	+	0.297042i	$0.0960000\pi$
$761$	1.85427	+	0.734157i	1.85427	+	0.734157i	0.899405	+	0.437116i	$0.144000\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	0.561240	−	0.0997699i	0.561240	−	0.0997699i
$769$	1.21571	+	0.668340i	1.21571	+	0.668340i	0.954865	−	0.297042i	$-0.0960000\pi$
$769$	1.21571	+	0.668340i	1.21571	+	0.668340i	0.260842	+	0.965382i	$0.416000\pi$
$770$		0			0
$771$	0.667143	+	0.849007i	0.667143	+	0.849007i
$772$	−0.861670	−	0.769341i	−0.861670	−	0.769341i
$773$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$773$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$774$	−0.545155	−	0.730849i	−0.545155	−	0.730849i
$775$		0			0
$776$	1.80339	−	0.367559i	1.80339	−	0.367559i
$777$		0			0
$778$		0			0
$779$	−1.04973	+	0.385394i	−1.04973	+	0.385394i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.0125660	−	0.999921i	0.0125660	−	0.999921i
$785$		0			0
$786$	−0.0470024	+	0.0539939i	−0.0470024	+	0.0539939i
$787$	−1.54899	−	0.955929i	−1.54899	−	0.955929i	−0.992115	−	0.125333i	$-0.960000\pi$
$787$	−1.54899	−	0.955929i	−1.54899	−	0.955929i	−0.556876	−	0.830596i	$-0.688000\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−0.0558297	−	0.633046i	−0.0558297	−	0.633046i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.837528	−	0.546394i	$-0.816000\pi$
$797$		0			0		0.837528	+	0.546394i	$0.184000\pi$
$798$		0			0
$799$		0			0
$800$	0.876307	−	0.481754i	0.876307	−	0.481754i
$801$	−0.0396128	+	0.0319407i	−0.0396128	+	0.0319407i
$802$	−0.940219	−	1.76235i	−0.940219	−	1.76235i
$803$	0.189042	−	0.297883i	0.189042	−	0.297883i
$804$	0.717990	−	0.674237i	0.717990	−	0.674237i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	1.10151	−	0.843386i	1.10151	−	0.843386i	0.112856	−	0.993611i	$-0.464000\pi$
$809$	1.10151	−	0.843386i	1.10151	−	0.843386i	0.988652	+	0.150226i	$0.0480000\pi$
$810$		0			0
$811$	−1.66745	−	0.862846i	−1.66745	−	0.862846i	−0.992115	−	0.125333i	$-0.960000\pi$
$811$	−1.66745	−	0.862846i	−1.66745	−	0.862846i	−0.675333	−	0.737513i	$-0.736000\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	−0.341235	+	0.0876142i	−0.341235	+	0.0876142i
$817$	0.838439	+	0.787346i	0.838439	+	0.787346i
$818$	0.408634	+	0.238213i	0.408634	+	0.238213i
$819$		0			0
$820$		0			0
$821$		0			0		−0.778462	−	0.627691i	$-0.784000\pi$
$821$		0			0		0.778462	+	0.627691i	$0.216000\pi$
$822$	−0.0711000	+	0.372719i	−0.0711000	+	0.372719i
$823$		0			0		−0.994951	−	0.100362i	$-0.968000\pi$
$823$		0			0		0.994951	+	0.100362i	$0.0320000\pi$
$824$		0			0
$825$	0.216215	+	0.491154i	0.216215	+	0.491154i
$826$		0			0
$827$	−0.0196623	−	0.521312i	−0.0196623	−	0.521312i	−0.974527	−	0.224271i	$-0.928000\pi$
$827$	−0.0196623	−	0.521312i	−0.0196623	−	0.521312i	0.954865	−	0.297042i	$-0.0960000\pi$
$828$		0			0
$829$		0			0		−0.556876	−	0.830596i	$-0.688000\pi$
$829$		0			0		0.556876	+	0.830596i	$0.312000\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	0.0388067	+	0.616814i	0.0388067	+	0.616814i
$834$	0.00544081	+	0.432943i	0.00544081	+	0.432943i
$835$		0			0
$836$	0.209107	+	0.773912i	0.209107	+	0.773912i
$837$		0			0
$838$	0.0651745	+	0.468486i	0.0651745	+	0.468486i
$839$		0			0		−0.988652	−	0.150226i	$-0.952000\pi$
$839$		0			0		0.988652	+	0.150226i	$0.0480000\pi$
$840$		0			0
$841$	0.762443	+	0.647056i	0.762443	+	0.647056i
$842$		0			0
$843$	−0.369774	+	1.04770i	−0.369774	+	1.04770i
$844$	0.0775915	−	1.23328i	0.0775915	−	1.23328i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−0.435021	+	0.268465i	−0.435021	+	0.268465i
$850$	−0.517621	+	0.337690i	−0.517621	+	0.337690i
$851$		0			0
$852$		0			0
$853$		0			0		0.637424	−	0.770513i	$-0.280000\pi$
$853$		0			0		−0.637424	+	0.770513i	$0.720000\pi$
$854$		0			0
$855$		0			0
$856$	−0.139506	+	1.58184i	−0.139506	+	1.58184i
$857$	1.86799	−	0.188426i	1.86799	−	0.188426i	0.899405	−	0.437116i	$-0.144000\pi$
$857$	1.86799	−	0.188426i	1.86799	−	0.188426i	0.968583	+	0.248690i	$0.0800000\pi$
$858$		0			0
$859$	−0.407913	−	1.88032i	−0.407913	−	1.88032i	−0.470704	−	0.882291i	$-0.656000\pi$
$859$	−0.407913	−	1.88032i	−0.407913	−	1.88032i	0.0627905	−	0.998027i	$-0.480000\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.112856	−	0.993611i	$-0.536000\pi$
$863$		0			0		0.112856	+	0.993611i	$0.464000\pi$
$864$	−0.930524	−	0.214144i	−0.930524	−	0.214144i
$865$		0			0
$866$	−0.393950	+	1.21245i	−0.393950	+	1.21245i
$867$	−0.333666	+	0.113069i	−0.333666	+	0.113069i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−1.21739	−	0.248123i	−1.21739	−	0.248123i
$874$		0			0
$875$		0			0
$876$	−0.136172	−	0.164604i	−0.136172	−	0.164604i
$877$		0			0		0.260842	−	0.965382i	$-0.416000\pi$
$877$		0			0		−0.260842	+	0.965382i	$0.584000\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	0.175662	+	0.212338i	0.175662	+	0.212338i	0.850994	−	0.525175i	$-0.176000\pi$
$881$	0.175662	+	0.212338i	0.175662	+	0.212338i	−0.675333	+	0.737513i	$0.736000\pi$
$882$	−0.271984	+	0.617839i	−0.271984	+	0.617839i
$883$	−0.297558	−	0.227830i	−0.297558	−	0.227830i	0.448383	−	0.893841i	$-0.352000\pi$
$883$	−0.297558	−	0.227830i	−0.297558	−	0.227830i	−0.745941	+	0.666012i	$0.768000\pi$
$884$		0			0
$885$		0			0
$886$	−1.54500	+	0.480623i	−1.54500	+	0.480623i
$887$		0			0		−0.954865	−	0.297042i	$-0.904000\pi$
$887$		0			0		0.954865	+	0.297042i	$0.0960000\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−0.0380386	+	0.117071i	−0.0380386	+	0.117071i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	0.360834	+	1.66330i	0.360834	+	1.66330i
$899$		0			0
$900$	−0.671648	+	0.0677498i	−0.671648	+	0.0677498i
$901$		0			0
$902$	1.00013	−	0.726638i	1.00013	−	0.726638i
$903$		0			0
$904$	−0.628152	+	0.759306i	−0.628152	+	0.759306i
$905$		0			0
$906$		0			0
$907$	1.30397	−	0.850695i	1.30397	−	0.850695i	0.309017	−	0.951057i	$-0.400000\pi$
$907$	1.30397	−	0.850695i	1.30397	−	0.850695i	0.994951	+	0.100362i	$0.0320000\pi$
$908$	−1.58247	+	0.976590i	−1.58247	+	0.976590i
$909$		0			0
$910$		0			0
$911$		0			0		−0.920232	−	0.391374i	$-0.872000\pi$
$911$		0			0		0.920232	+	0.391374i	$0.128000\pi$
$912$	0.484808	+	0.0243897i	0.484808	+	0.0243897i
$913$	0.117887	−	1.87376i	0.117887	−	1.87376i
$914$	0.660390	−	1.87111i	0.660390	−	1.87111i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	0.583431	+	0.0886523i	0.583431	+	0.0886523i
$919$		0			0		−0.137790	−	0.990461i	$-0.544000\pi$
$919$		0			0		0.137790	+	0.990461i	$0.456000\pi$
$920$		0			0
$921$	0.264113	+	0.977491i	0.264113	+	0.977491i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	1.19958	+	1.31002i	1.19958	+	1.31002i	0.938734	+	0.344643i	$0.112000\pi$
$929$	1.19958	+	1.31002i	1.19958	+	1.31002i	0.260842	+	0.965382i	$0.416000\pi$
$930$		0			0
$931$	0.201393	−	0.827401i	0.201393	−	0.827401i
$932$	0.0909411	+	0.206582i	0.0909411	+	0.206582i
$933$		0			0
$934$	0.519049	+	0.0523570i	0.519049	+	0.0523570i
$935$		0			0
$936$		0			0
$937$	0.271327	+	0.0482330i	0.271327	+	0.0482330i	0.309017	−	0.951057i	$-0.400000\pi$
$937$	0.271327	+	0.0482330i	0.271327	+	0.0482330i	−0.0376902	+	0.999289i	$0.512000\pi$
$938$		0			0
$939$	0.608554	+	0.354756i	0.608554	+	0.354756i
$940$		0			0
$941$		0			0		0.968583	−	0.248690i	$-0.0800000\pi$
$941$		0			0		−0.968583	+	0.248690i	$0.920000\pi$
$942$		0			0
$943$		0			0
$944$	−0.0250607	−	0.00189312i	−0.0250607	−	0.00189312i
$945$		0			0
$946$	−1.12929	−	0.584368i	−1.12929	−	0.584368i
$947$	1.57631	−	0.766095i	1.57631	−	0.766095i	0.577573	−	0.816339i	$-0.304000\pi$
$947$	1.57631	−	0.766095i	1.57631	−	0.766095i	0.998737	+	0.0502443i	$0.0160000\pi$
$948$		0			0
$949$		0			0
$950$	0.819223	−	0.232435i	0.819223	−	0.232435i
$951$		0			0
$952$		0			0
$953$	0.164538	−	0.154511i	0.164538	−	0.154511i	−0.597905	−	0.801567i	$-0.704000\pi$
$953$	0.164538	−	0.154511i	0.164538	−	0.154511i	0.762443	+	0.647056i	$0.224000\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.999684	−	0.0251301i	−0.999684	−	0.0251301i
$962$		0			0
$963$	0.504583	−	0.945795i	0.504583	−	0.945795i
$964$	−0.168037	−	0.880882i	−0.168037	−	0.880882i
$965$		0			0
$966$		0			0
$967$		0			0		−0.162637	−	0.986686i	$-0.552000\pi$
$967$		0			0		0.162637	+	0.986686i	$0.448000\pi$
$968$	0.0585181	+	0.0975447i	0.0585181	+	0.0975447i
$969$	−0.299912	+	0.00753920i	−0.299912	+	0.00753920i
$970$		0			0
$971$	0.957261	−	1.09965i	0.957261	−	1.09965i	−0.0376902	−	0.999289i	$-0.512000\pi$
$971$	0.957261	−	1.09965i	0.957261	−	1.09965i	0.994951	−	0.100362i	$-0.0320000\pi$
$972$	0.832788	+	0.605056i	0.832788	+	0.605056i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−0.698970	+	0.297271i	−0.698970	+	0.297271i	−0.711536	−	0.702650i	$-0.752000\pi$
$977$	−0.698970	+	0.297271i	−0.698970	+	0.297271i	0.0125660	+	0.999921i	$0.496000\pi$
$978$	−1.00466	+	0.368847i	−1.00466	+	0.368847i
$979$	−0.0302149	+	0.0642098i	−0.0302149	+	0.0642098i
$980$		0			0
$981$		0			0
$982$	−0.925379	−	0.449739i	−0.925379	−	0.449739i
$983$		0			0		−0.597905	−	0.801567i	$-0.704000\pi$
$983$		0			0		0.597905	+	0.801567i	$0.296000\pi$
$984$	−0.231317	−	0.711921i	−0.231317	−	0.711921i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.888136	−	0.459580i	$-0.152000\pi$
$991$		0			0		−0.888136	+	0.459580i	$0.848000\pi$
$992$		0			0
$993$	0.623643	+	0.211334i	0.623643	+	0.211334i
$994$		0			0
$995$		0			0
$996$	−1.05701	−	0.418498i	−1.05701	−	0.418498i
$997$		0			0		0.514440	−	0.857527i	$-0.328000\pi$
$997$		0			0		−0.514440	+	0.857527i	$0.672000\pi$
$998$	0.208923	−	0.368970i	0.208923	−	0.368970i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2008.1.bd.a.339.1	✓	100
8.3	odd	2	CM	2008.1.bd.a.339.1	✓	100
251.174	even	125	inner	2008.1.bd.a.1931.1	yes	100
2008.1931	odd	250	inner	2008.1.bd.a.1931.1	yes	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2008.1.bd.a.339.1	✓	100	1.1	even	1	trivial
2008.1.bd.a.339.1	✓	100	8.3	odd	2	CM
2008.1.bd.a.1931.1	yes	100	251.174	even	125	inner
2008.1.bd.a.1931.1	yes	100	2008.1931	odd	250	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.992115 - 0.125333i) q^{2} +(0.216489 - 0.527330i) q^{3} +(0.968583 + 0.248690i) q^{4} +(-0.280874 + 0.496038i) q^{6} +(-0.929776 - 0.368125i) q^{8} +(0.480326 + 0.474328i) q^{9} +O(q^{10})\)	\(q+(-0.992115 - 0.125333i) q^{2} +(0.216489 - 0.527330i) q^{3} +(0.968583 + 0.248690i) q^{4} +(-0.280874 + 0.496038i) q^{6} +(-0.929776 - 0.368125i) q^{8} +(0.480326 + 0.474328i) q^{9} +(0.891606 + 0.302139i) q^{11} +(0.340829 - 0.456924i) q^{12} +(0.876307 + 0.481754i) q^{16} +(-0.562476 - 0.256098i) q^{17} +(-0.417090 - 0.530789i) q^{18} +(0.635213 + 0.567148i) q^{19} +(-0.846707 - 0.411504i) q^{22} +(-0.395409 + 0.410604i) q^{24} +(-0.425779 + 0.904827i) q^{25} +(0.878680 - 0.373702i) q^{27} +(-0.809017 - 0.587785i) q^{32} +(0.352349 - 0.404761i) q^{33} +(0.525944 + 0.324576i) q^{34} +(0.347276 + 0.578879i) q^{36} +(-0.559121 - 0.642289i) q^{38} +(-0.618115 + 1.15860i) q^{41} +(1.35024 + 0.0339424i) q^{43} +(0.788455 + 0.514380i) q^{44} +(0.443754 - 0.357808i) q^{48} +(-0.470704 - 0.882291i) q^{49} +(0.535827 - 0.844328i) q^{50} +(-0.256818 + 0.241168i) q^{51} +(-0.918589 + 0.260627i) q^{54} +(0.436590 - 0.212185i) q^{57} +(-0.0228729 + 0.0104141i) q^{59} +(0.728969 + 0.684547i) q^{64} +(-0.400301 + 0.357408i) q^{66} +(1.70118 + 0.302413i) q^{67} +(-0.481116 - 0.387935i) q^{68} +(-0.271984 - 0.617839i) q^{72} +(0.0886310 - 0.364131i) q^{73} +(0.384966 + 0.420411i) q^{75} +(0.474212 + 0.707301i) q^{76} +(0.00164310 + 0.130746i) q^{81} +(0.758452 - 1.07199i) q^{82} +(-0.520201 - 1.92528i) q^{83} +(-1.33534 - 0.202905i) q^{86} +(-0.717769 - 0.609144i) q^{88} +(-0.00850716 + 0.0748988i) q^{89} +(-0.485100 + 0.299370i) q^{96} +(-1.54144 + 1.00562i) q^{97} +(0.356412 + 0.934329i) q^{98} +(0.284949 + 0.568039i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q+O(q^{10}) \) 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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Database

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