LMFDB - Embedded newform 2008.1.bd.a.195.1

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			195.1
Root			$-0.162637 + 0.986686i$ of defining polynomial
Character	$\chi$	$=$	2008.195
Dual form			2008.1.bd.a.1627.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.535827 + 0.844328i) q^{2} +(1.35024 - 0.0339424i) q^{3} +(-0.425779 + 0.904827i) q^{4} +(0.752153 + 1.12186i) q^{6} +(-0.992115 + 0.125333i) q^{8} +(0.823256 - 0.0414163i) q^{9} +O(q^{10})$	\(q+(0.535827 + 0.844328i) q^{2} +(1.35024 - 0.0339424i) q^{3} +(-0.425779 + 0.904827i) q^{4} +(0.752153 + 1.12186i) q^{6} +(-0.992115 + 0.125333i) q^{8} +(0.823256 - 0.0414163i) q^{9} +(1.22942 - 0.716692i) q^{11} +(-0.544192 + 1.23618i) q^{12} +(-0.637424 - 0.770513i) q^{16} +(1.55659 + 0.441646i) q^{17} +(0.476092 + 0.672906i) q^{18} +(-1.67249 + 0.812840i) q^{19} +(1.26388 + 0.654015i) q^{22} +(-1.33534 + 0.202905i) q^{24} +(-0.929776 - 0.368125i) q^{25} +(-0.236641 + 0.0178762i) q^{27} +(0.309017 - 0.951057i) q^{32} +(1.63569 - 1.00943i) q^{33} +(0.461171 + 1.55092i) q^{34} +(-0.313051 + 0.762539i) q^{36} +(-1.58247 - 0.976590i) q^{38} +(-1.21103 - 1.19590i) q^{41} +(1.83965 + 0.374949i) q^{43} +(0.125019 + 1.41757i) q^{44} +(-0.886828 - 1.01874i) q^{48} +(-0.711536 + 0.702650i) q^{49} +(-0.187381 - 0.982287i) q^{50} +(2.11676 + 0.543493i) q^{51} +(-0.141892 - 0.190224i) q^{54} +(-2.23067 + 1.15430i) q^{57} +(-1.91434 + 0.543148i) q^{59} +(0.968583 - 0.248690i) q^{64} +(1.72874 + 0.840177i) q^{66} +(-0.153108 - 0.928874i) q^{67} +(-1.06238 + 1.22040i) q^{68} +(-0.811574 + 0.144271i) q^{72} +(-0.0417958 + 0.118422i) q^{73} +(-1.26792 - 0.465497i) q^{75} +(-0.0233672 - 1.85941i) q^{76} +(-1.13905 + 0.114897i) q^{81} +(0.360834 - 1.66330i) q^{82} +(-0.847315 - 1.41240i) q^{83} +(0.669152 + 1.75417i) q^{86} +(-1.12990 + 0.865128i) q^{88} +(1.17994 + 1.50160i) q^{89} +(0.384966 - 1.29464i) q^{96} +(0.175203 - 1.98661i) q^{97} +(-0.974527 - 0.224271i) q^{98} +(0.982449 - 0.640939i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2008\mathbb{Z}\right)^\times$.

$n$	$257$	$503$	$1005$
$\chi(n)$	$e\left(\frac{39}{125}\right)$	$-1$	$-1$

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 $

$2$	0.535827	+	0.844328i	0.535827	+	0.844328i
$2$	0.535827	+	0.844328i	0.535827	+	0.844328i
$3$	1.35024	−	0.0339424i	1.35024	−	0.0339424i	0.656586	−	0.754251i	$-0.272000\pi$
$3$	1.35024	−	0.0339424i	1.35024	−	0.0339424i	0.693653	+	0.720309i	$0.256000\pi$
$4$	−0.425779	+	0.904827i	−0.425779	+	0.904827i
$5$		0			0		0.187381	−	0.982287i	$-0.440000\pi$
$5$		0			0		−0.187381	+	0.982287i	$0.560000\pi$
$6$	0.752153	+	1.12186i	0.752153	+	1.12186i
$7$		0			0		−0.379779	−	0.925077i	$-0.624000\pi$
$7$		0			0		0.379779	+	0.925077i	$0.376000\pi$
$8$	−0.992115	+	0.125333i	−0.992115	+	0.125333i
$9$	0.823256	−	0.0414163i	0.823256	−	0.0414163i
$10$		0			0
$11$	1.22942	−	0.716692i	1.22942	−	0.716692i	0.260842	−	0.965382i	$-0.416000\pi$
$11$	1.22942	−	0.716692i	1.22942	−	0.716692i	0.968583	+	0.248690i	$0.0800000\pi$
$12$	−0.544192	+	1.23618i	−0.544192	+	1.23618i
$13$		0			0		0.778462	−	0.627691i	$-0.216000\pi$
$13$		0			0		−0.778462	+	0.627691i	$0.784000\pi$
$14$		0			0
$15$		0			0
$16$	−0.637424	−	0.770513i	−0.637424	−	0.770513i
$17$	1.55659	+	0.441646i	1.55659	+	0.441646i	0.938734	−	0.344643i	$-0.112000\pi$
$17$	1.55659	+	0.441646i	1.55659	+	0.441646i	0.617860	+	0.786288i	$0.288000\pi$
$18$	0.476092	+	0.672906i	0.476092	+	0.672906i
$19$	−1.67249	+	0.812840i	−1.67249	+	0.812840i	−0.675333	+	0.737513i	$0.736000\pi$
$19$	−1.67249	+	0.812840i	−1.67249	+	0.812840i	−0.997159	+	0.0753268i	$0.976000\pi$
$20$		0			0
$21$		0			0
$22$	1.26388	+	0.654015i	1.26388	+	0.654015i
$23$		0			0		−0.0376902	−	0.999289i	$-0.512000\pi$
$23$		0			0		0.0376902	+	0.999289i	$0.488000\pi$
$24$	−1.33534	+	0.202905i	−1.33534	+	0.202905i
$25$	−0.929776	−	0.368125i	−0.929776	−	0.368125i
$26$		0			0
$27$	−0.236641	+	0.0178762i	−0.236641	+	0.0178762i
$28$		0			0
$29$		0			0		0.947098	−	0.320944i	$-0.104000\pi$
$29$		0			0		−0.947098	+	0.320944i	$0.896000\pi$
$30$		0			0
$31$		0			0		−0.994951	−	0.100362i	$-0.968000\pi$
$31$		0			0		0.994951	+	0.100362i	$0.0320000\pi$
$32$	0.309017	−	0.951057i	0.309017	−	0.951057i
$33$	1.63569	−	1.00943i	1.63569	−	1.00943i
$34$	0.461171	+	1.55092i	0.461171	+	1.55092i
$35$		0			0
$36$	−0.313051	+	0.762539i	−0.313051	+	0.762539i
$37$		0			0		0.260842	−	0.965382i	$-0.416000\pi$
$37$		0			0		−0.260842	+	0.965382i	$0.584000\pi$
$38$	−1.58247	−	0.976590i	−1.58247	−	0.976590i
$39$		0			0
$40$		0			0
$41$	−1.21103	−	1.19590i	−1.21103	−	1.19590i	−0.974527	−	0.224271i	$-0.928000\pi$
$41$	−1.21103	−	1.19590i	−1.21103	−	1.19590i	−0.236499	−	0.971632i	$-0.576000\pi$
$42$		0			0
$43$	1.83965	+	0.374949i	1.83965	+	0.374949i	0.988652	−	0.150226i	$-0.0480000\pi$
$43$	1.83965	+	0.374949i	1.83965	+	0.374949i	0.850994	+	0.525175i	$0.176000\pi$
$44$	0.125019	+	1.41757i	0.125019	+	1.41757i
$45$		0			0
$46$		0			0
$47$		0			0		0.637424	−	0.770513i	$-0.280000\pi$
$47$		0			0		−0.637424	+	0.770513i	$0.720000\pi$
$48$	−0.886828	−	1.01874i	−0.886828	−	1.01874i
$49$	−0.711536	+	0.702650i	−0.711536	+	0.702650i
$50$	−0.187381	−	0.982287i	−0.187381	−	0.982287i
$51$	2.11676	+	0.543493i	2.11676	+	0.543493i
$52$		0			0
$53$		0			0		−0.910106	−	0.414376i	$-0.864000\pi$
$53$		0			0		0.910106	+	0.414376i	$0.136000\pi$
$54$	−0.141892	−	0.190224i	−0.141892	−	0.190224i
$55$		0			0
$56$		0			0
$57$	−2.23067	+	1.15430i	−2.23067	+	1.15430i
$58$		0			0
$59$	−1.91434	+	0.543148i	−1.91434	+	0.543148i	−0.929776	+	0.368125i	$0.880000\pi$
$59$	−1.91434	+	0.543148i	−1.91434	+	0.543148i	−0.984564	+	0.175023i	$0.944000\pi$
$60$		0			0
$61$		0			0		0.675333	−	0.737513i	$-0.264000\pi$
$61$		0			0		−0.675333	+	0.737513i	$0.736000\pi$
$62$		0			0
$63$		0			0
$64$	0.968583	−	0.248690i	0.968583	−	0.248690i
$65$		0			0
$66$	1.72874	+	0.840177i	1.72874	+	0.840177i
$67$	−0.153108	−	0.928874i	−0.153108	−	0.928874i	−0.947098	−	0.320944i	$-0.896000\pi$
$67$	−0.153108	−	0.928874i	−0.153108	−	0.928874i	0.793990	−	0.607930i	$-0.208000\pi$
$68$	−1.06238	+	1.22040i	−1.06238	+	1.22040i
$69$		0			0
$70$		0			0
$71$		0			0		−0.837528	−	0.546394i	$-0.816000\pi$
$71$		0			0		0.837528	+	0.546394i	$0.184000\pi$
$72$	−0.811574	+	0.144271i	−0.811574	+	0.144271i
$73$	−0.0417958	+	0.118422i	−0.0417958	+	0.118422i	−0.962028	−	0.272952i	$-0.912000\pi$
$73$	−0.0417958	+	0.118422i	−0.0417958	+	0.118422i	0.920232	+	0.391374i	$0.128000\pi$
$74$		0			0
$75$	−1.26792	−	0.465497i	−1.26792	−	0.465497i
$76$	−0.0233672	−	1.85941i	−0.0233672	−	1.85941i
$77$		0			0
$78$		0			0
$79$		0			0		0.597905	−	0.801567i	$-0.296000\pi$
$79$		0			0		−0.597905	+	0.801567i	$0.704000\pi$
$80$		0			0
$81$	−1.13905	+	0.114897i	−1.13905	+	0.114897i
$82$	0.360834	−	1.66330i	0.360834	−	1.66330i
$83$	−0.847315	−	1.41240i	−0.847315	−	1.41240i	−0.910106	−	0.414376i	$-0.864000\pi$
$83$	−0.847315	−	1.41240i	−0.847315	−	1.41240i	0.0627905	−	0.998027i	$-0.480000\pi$
$84$		0			0
$85$		0			0
$86$	0.669152	+	1.75417i	0.669152	+	1.75417i
$87$		0			0
$88$	−1.12990	+	0.865128i	−1.12990	+	0.865128i
$89$	1.17994	+	1.50160i	1.17994	+	1.50160i	0.823533	+	0.567269i	$0.192000\pi$
$89$	1.17994	+	1.50160i	1.17994	+	1.50160i	0.356412	+	0.934329i	$0.384000\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	0.384966	−	1.29464i	0.384966	−	1.29464i
$97$	0.175203	−	1.98661i	0.175203	−	1.98661i	0.0125660	−	0.999921i	$-0.496000\pi$
$97$	0.175203	−	1.98661i	0.175203	−	1.98661i	0.162637	−	0.986686i	$-0.448000\pi$
$98$	−0.974527	−	0.224271i	−0.974527	−	0.224271i
$99$	0.982449	−	0.640939i	0.982449	−	0.640939i
$100$	0.728969	−	0.684547i	0.728969	−	0.684547i
$101$		0			0		−0.212007	−	0.977268i	$-0.568000\pi$
$101$		0			0		0.212007	+	0.977268i	$0.432000\pi$
$102$	0.675333	+	2.07846i	0.675333	+	2.07846i
$103$		0			0		−0.762443	−	0.647056i	$-0.776000\pi$
$103$		0			0		0.762443	+	0.647056i	$0.224000\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.665510	−	0.726786i	−0.665510	−	0.726786i	0.309017	−	0.951057i	$-0.400000\pi$
$107$	−0.665510	−	0.726786i	−0.665510	−	0.726786i	−0.974527	+	0.224271i	$0.928000\pi$
$108$	0.0845819	−	0.221730i	0.0845819	−	0.221730i
$109$		0			0		0.0125660	−	0.999921i	$-0.496000\pi$
$109$		0			0		−0.0125660	+	0.999921i	$0.504000\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.901044	−	0.654647i	0.901044	−	0.654647i	−0.0376902	−	0.999289i	$-0.512000\pi$
$113$	0.901044	−	0.654647i	0.901044	−	0.654647i	0.938734	+	0.344643i	$0.112000\pi$
$114$	−2.16986	−	1.26492i	−2.16986	−	1.26492i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	−1.48435	−	1.32530i	−1.48435	−	1.32530i
$119$		0			0
$120$		0			0
$121$	0.505111	−	0.892053i	0.505111	−	0.892053i
$122$		0			0
$123$	−1.67577	−	1.57365i	−1.67577	−	1.57365i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		0.514440	−	0.857527i	$-0.328000\pi$
$127$		0			0		−0.514440	+	0.857527i	$0.672000\pi$
$128$	0.728969	+	0.684547i	0.728969	+	0.684547i
$129$	2.49669	+	0.443829i	2.49669	+	0.443829i
$130$		0			0
$131$	−0.0660563	+	1.75137i	−0.0660563	+	1.75137i	0.448383	+	0.893841i	$0.352000\pi$
$131$	−0.0660563	+	1.75137i	−0.0660563	+	1.75137i	−0.514440	+	0.857527i	$0.672000\pi$
$132$	0.216921	+	1.90981i	0.216921	+	1.90981i
$133$		0			0
$134$	0.702235	−	0.626989i	0.702235	−	0.626989i
$135$		0			0
$136$	−1.59967	−	0.243070i	−1.59967	−	0.243070i
$137$	1.57252	+	0.916701i	1.57252	+	0.916701i	0.994951	+	0.100362i	$0.0320000\pi$
$137$	1.57252	+	0.916701i	1.57252	+	0.916701i	0.577573	+	0.816339i	$0.304000\pi$
$138$		0			0
$139$	0.941111	−	1.76403i	0.941111	−	1.76403i	0.448383	−	0.893841i	$-0.352000\pi$
$139$	0.941111	−	1.76403i	0.941111	−	1.76403i	0.492727	−	0.870184i	$-0.336000\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−0.556675	−	0.607930i	−0.556675	−	0.607930i
$145$		0			0
$146$	−0.122382	+	0.0281642i	−0.122382	+	0.0281642i
$147$	−0.936894	+	0.972897i	−0.936894	+	0.972897i
$148$		0			0
$149$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$149$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$150$	−0.286351	−	1.31996i	−0.286351	−	1.31996i
$151$		0			0		0.728969	−	0.684547i	$-0.240000\pi$
$151$		0			0		−0.728969	+	0.684547i	$0.760000\pi$
$152$	1.55743	−	1.01605i	1.55743	−	1.01605i
$153$	1.29977	+	0.299119i	1.29977	+	0.299119i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.992115	−	0.125333i	$-0.960000\pi$
$157$		0			0		0.992115	+	0.125333i	$0.0400000\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−0.707345	−	0.900167i	−0.707345	−	0.900167i
$163$	−1.50397	+	1.15154i	−1.50397	+	1.15154i	−0.556876	+	0.830596i	$0.688000\pi$
$163$	−1.50397	+	1.15154i	−1.50397	+	1.15154i	−0.947098	+	0.320944i	$0.896000\pi$
$164$	1.59771	−	0.586578i	1.59771	−	0.586578i
$165$		0			0
$166$	0.738516	−	1.47222i	0.738516	−	1.47222i
$167$		0			0		−0.999684	−	0.0251301i	$-0.992000\pi$
$167$		0			0		0.999684	+	0.0251301i	$0.00800000\pi$
$168$		0			0
$169$	0.212007	−	0.977268i	0.212007	−	0.977268i
$170$		0			0
$171$	−1.34322	+	0.738444i	−1.34322	+	0.738444i
$172$	−1.12255	+	1.50492i	−1.12255	+	1.50492i
$173$		0			0		−0.954865	−	0.297042i	$-0.904000\pi$
$173$		0			0		0.954865	+	0.297042i	$0.0960000\pi$
$174$		0			0
$175$		0			0
$176$	−1.33589	−	0.490451i	−1.33589	−	0.490451i
$177$	−2.56638	+	0.798356i	−2.56638	+	0.798356i
$178$	−0.635595	+	1.80086i	−0.635595	+	1.80086i
$179$	−0.513630	+	0.0913066i	−0.513630	+	0.0913066i	−0.425779	−	0.904827i	$-0.640000\pi$
$179$	−0.513630	+	0.0913066i	−0.513630	+	0.0913066i	−0.0878512	+	0.996134i	$0.528000\pi$
$180$		0			0
$181$		0			0		−0.693653	−	0.720309i	$-0.744000\pi$
$181$		0			0		0.693653	+	0.720309i	$0.256000\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	2.23024	−	0.572628i	2.23024	−	0.572628i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		−0.823533	−	0.567269i	$-0.808000\pi$
$191$		0			0		0.823533	+	0.567269i	$0.192000\pi$
$192$	1.29938	−	0.368667i	1.29938	−	0.368667i
$193$	−0.330079	−	0.266150i	−0.330079	−	0.266150i	0.448383	−	0.893841i	$-0.352000\pi$
$193$	−0.330079	−	0.266150i	−0.330079	−	0.266150i	−0.778462	+	0.627691i	$0.784000\pi$
$194$	1.77123	−	0.916548i	1.77123	−	0.916548i
$195$		0			0
$196$	−0.332820	−	0.942991i	−0.332820	−	0.942991i
$197$		0			0		−0.597905	−	0.801567i	$-0.704000\pi$
$197$		0			0		0.597905	+	0.801567i	$0.296000\pi$
$198$	1.06759	+	0.486077i	1.06759	+	0.486077i
$199$		0			0		−0.236499	−	0.971632i	$-0.576000\pi$
$199$		0			0		0.236499	+	0.971632i	$0.424000\pi$
$200$	0.968583	+	0.248690i	0.968583	+	0.248690i
$201$	−0.238260	−	1.24900i	−0.238260	−	1.24900i
$202$		0			0
$203$		0			0
$204$	−1.39304	+	1.68390i	−1.39304	+	1.68390i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−1.47365	+	2.19799i	−1.47365	+	2.19799i
$210$		0			0
$211$	0.0725322	−	1.15287i	0.0725322	−	1.15287i	−0.778462	−	0.627691i	$-0.784000\pi$
$211$	0.0725322	−	1.15287i	0.0725322	−	1.15287i	0.850994	−	0.525175i	$-0.176000\pi$
$212$		0			0
$213$		0			0
$214$	0.257047	−	0.951340i	0.257047	−	0.951340i
$215$		0			0
$216$	0.232534	−	0.0473942i	0.232534	−	0.0473942i
$217$		0			0
$218$		0			0
$219$	−0.0524148	+	0.161316i	−0.0524148	+	0.161316i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.998737	−	0.0502443i	$-0.984000\pi$
$223$		0			0		0.998737	+	0.0502443i	$0.0160000\pi$
$224$		0			0
$225$	−0.780691	−	0.264553i	−0.780691	−	0.264553i
$226$	1.03554	+	0.409999i	1.03554	+	0.409999i
$227$	−1.96171	+	0.298082i	−1.96171	+	0.298082i	−0.962028	+	0.272952i	$0.912000\pi$
$227$	−1.96171	+	0.298082i	−1.96171	+	0.298082i	−0.999684	+	0.0251301i	$0.992000\pi$
$228$	−0.0946640	−	2.50985i	−0.0946640	−	2.50985i
$229$		0			0		−0.888136	−	0.459580i	$-0.848000\pi$
$229$		0			0		0.888136	+	0.459580i	$0.152000\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	0.713718	+	1.00877i	0.713718	+	1.00877i	0.998737	+	0.0502443i	$0.0160000\pi$
$233$	0.713718	+	1.00877i	0.713718	+	1.00877i	−0.285019	+	0.958522i	$0.592000\pi$
$234$		0			0
$235$		0			0
$236$	0.323632	−	1.96341i	0.323632	−	1.96341i
$237$		0			0
$238$		0			0
$239$		0			0		0.402906	−	0.915241i	$-0.368000\pi$
$239$		0			0		−0.402906	+	0.915241i	$0.632000\pi$
$240$		0			0
$241$	1.55743	−	0.616629i	1.55743	−	0.616629i	0.577573	−	0.816339i	$-0.304000\pi$
$241$	1.55743	−	0.616629i	1.55743	−	0.616629i	0.979855	+	0.199710i	$0.0640000\pi$
$242$	1.02384	−	0.0515071i	1.02384	−	0.0515071i
$243$	−1.29865	+	0.164057i	−1.29865	+	0.164057i
$244$		0			0
$245$		0			0
$246$	0.430756	−	2.25810i	0.430756	−	2.25810i
$247$		0			0
$248$		0			0
$249$	−1.19202	−	1.87832i	−1.19202	−	1.87832i
$250$		0			0
$251$	−0.379779	+	0.925077i	−0.379779	+	0.925077i
$251$	−0.379779	+	0.925077i	−0.379779	+	0.925077i
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.187381	+	0.982287i	−0.187381	+	0.982287i
$257$	0.962196	+	1.43514i	0.962196	+	1.43514i	0.899405	+	0.437116i	$0.144000\pi$
$257$	0.962196	+	1.43514i	0.962196	+	1.43514i	0.0627905	+	0.998027i	$0.480000\pi$
$258$	0.963056	+	2.34584i	0.963056	+	2.34584i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−1.51412	+	0.882657i	−1.51412	+	0.882657i
$263$		0			0		0.402906	−	0.915241i	$-0.368000\pi$
$263$		0			0		−0.402906	+	0.915241i	$0.632000\pi$
$264$	−1.49628	+	1.20648i	−1.49628	+	1.20648i
$265$		0			0
$266$		0			0
$267$	1.64417	+	1.98747i	1.64417	+	1.98747i
$268$	0.905660	+	0.256959i	0.905660	+	0.256959i
$269$		0			0		−0.577573	−	0.816339i	$-0.696000\pi$
$269$		0			0		0.577573	+	0.816339i	$0.304000\pi$
$270$		0			0
$271$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$271$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$272$	−0.651916	−	1.48089i	−0.651916	−	1.48089i
$273$		0			0
$274$	0.0686041	+	1.81892i	0.0686041	+	1.81892i
$275$	−1.40692	+	0.213782i	−1.40692	+	0.213782i
$276$		0			0
$277$		0			0		−0.947098	−	0.320944i	$-0.896000\pi$
$277$		0			0		0.947098	+	0.320944i	$0.104000\pi$
$278$	1.99369	−	0.150606i	1.99369	−	0.150606i
$279$		0			0
$280$		0			0
$281$	−0.435268	+	0.185119i	−0.435268	+	0.185119i	−0.597905	−	0.801567i	$-0.704000\pi$
$281$	−0.435268	+	0.185119i	−0.435268	+	0.185119i	0.162637	+	0.986686i	$0.448000\pi$
$282$		0			0
$283$	−0.517621	+	1.59307i	−0.517621	+	1.59307i	0.260842	+	0.965382i	$0.416000\pi$
$283$	−0.517621	+	1.59307i	−0.517621	+	1.59307i	−0.778462	+	0.627691i	$0.784000\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.215011	−	0.795762i	0.215011	−	0.795762i
$289$	1.37694	+	0.849750i	1.37694	+	0.849750i
$290$		0			0
$291$	0.169136	−	2.68834i	0.169136	−	2.68834i
$292$	−0.0893554	−	0.0882395i	−0.0893554	−	0.0882395i
$293$		0			0		0.556876	−	0.830596i	$-0.312000\pi$
$293$		0			0		−0.556876	+	0.830596i	$0.688000\pi$
$294$	−1.32346	−	0.269741i	−1.32346	−	0.269741i
$295$		0			0
$296$		0			0
$297$	−0.278120	+	0.191576i	−0.278120	+	0.191576i
$298$		0			0
$299$		0			0
$300$	0.961047	−	0.949045i	0.961047	−	0.949045i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	1.69239	+	0.770553i	1.69239	+	0.770553i
$305$		0			0
$306$	0.443895	+	1.25771i	0.443895	+	1.25771i
$307$	−0.767139	−	1.35481i	−0.767139	−	1.35481i	−0.929776	−	0.368125i	$-0.880000\pi$
$307$	−0.767139	−	1.35481i	−0.767139	−	1.35481i	0.162637	−	0.986686i	$-0.448000\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.823533	−	0.567269i	$-0.808000\pi$
$311$		0			0		0.823533	+	0.567269i	$0.192000\pi$
$312$		0			0
$313$	0.517948	+	1.03252i	0.517948	+	1.03252i	0.988652	+	0.150226i	$0.0480000\pi$
$313$	0.517948	+	1.03252i	0.517948	+	1.03252i	−0.470704	+	0.882291i	$0.656000\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		−0.899405	−	0.437116i	$-0.856000\pi$
$317$		0			0		0.899405	+	0.437116i	$0.144000\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−0.923266	−	0.958746i	−0.923266	−	0.958746i
$322$		0			0
$323$	−2.96238	+	0.526613i	−2.96238	+	0.526613i
$324$	0.381022	−	1.07956i	0.381022	−	1.07956i
$325$		0			0
$326$	−1.77815	−	0.652821i	−1.77815	−	0.652821i
$327$		0			0
$328$	1.35136	+	1.03469i	1.35136	+	1.03469i
$329$		0			0
$330$		0			0
$331$	0.371566	−	0.204270i	0.371566	−	0.204270i	−0.285019	−	0.958522i	$-0.592000\pi$
$331$	0.371566	−	0.204270i	0.371566	−	0.204270i	0.656586	+	0.754251i	$0.272000\pi$
$332$	1.63875	−	0.165302i	1.63875	−	0.165302i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	0.115932	+	0.303913i	0.115932	+	0.303913i	0.979855	−	0.199710i	$-0.0640000\pi$
$337$	0.115932	+	0.303913i	0.115932	+	0.303913i	−0.863923	+	0.503623i	$0.832000\pi$
$338$	0.938734	−	0.344643i	0.938734	−	0.344643i
$339$	1.19440	−	0.914513i	1.19440	−	0.914513i
$340$		0			0
$341$		0			0
$342$	−1.34322	−	0.738444i	−1.34322	−	0.738444i
$343$		0			0
$344$	−1.87213	−	0.141424i	−1.87213	−	0.141424i
$345$		0			0
$346$		0			0
$347$	−0.229672	+	0.772389i	−0.229672	+	0.772389i	0.762443	+	0.647056i	$0.224000\pi$
$347$	−0.229672	+	0.772389i	−0.229672	+	0.772389i	−0.992115	+	0.125333i	$0.960000\pi$
$348$		0			0
$349$		0			0		−0.974527	−	0.224271i	$-0.928000\pi$
$349$		0			0		0.974527	+	0.224271i	$0.0720000\pi$
$350$		0			0
$351$		0			0
$352$	−0.301701	−	1.39072i	−0.301701	−	1.39072i
$353$	−0.263146	−	0.809880i	−0.263146	−	0.809880i	−0.992115	−	0.125333i	$-0.960000\pi$
$353$	−0.263146	−	0.809880i	−0.263146	−	0.809880i	0.728969	−	0.684547i	$-0.240000\pi$
$354$	−2.04921	−	1.73909i	−2.04921	−	1.73909i
$355$		0			0
$356$	−1.86108	+	0.428296i	−1.86108	+	0.428296i
$357$		0			0
$358$	−0.352310	−	0.384748i	−0.352310	−	0.384748i
$359$		0			0		0.356412	−	0.934329i	$-0.384000\pi$
$359$		0			0		−0.356412	+	0.934329i	$0.616000\pi$
$360$		0			0
$361$	1.51866	−	1.93265i	1.51866	−	1.93265i
$362$		0			0
$363$	0.651742	−	1.22163i	0.651742	−	1.22163i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.112856	−	0.993611i	$-0.464000\pi$
$367$		0			0		−0.112856	+	0.993611i	$0.536000\pi$
$368$		0			0
$369$	−1.04651	−	0.934378i	−1.04651	−	0.934378i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.984564	−	0.175023i	$-0.944000\pi$
$373$		0			0		0.984564	+	0.175023i	$0.0560000\pi$
$374$	1.67851	+	1.57622i	1.67851	+	1.57622i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	1.01130	+	0.949677i	1.01130	+	0.949677i	0.998737	−	0.0502443i	$-0.0160000\pi$
$379$	1.01130	+	0.949677i	1.01130	+	0.949677i	0.0125660	+	0.999921i	$0.496000\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.112856	−	0.993611i	$-0.536000\pi$
$383$		0			0		0.112856	+	0.993611i	$0.464000\pi$
$384$	1.00752	+	0.899559i	1.00752	+	0.899559i
$385$		0			0
$386$	0.0478527	−	0.421305i	0.0478527	−	0.421305i
$387$	1.53003	+	0.232488i	1.53003	+	0.232488i
$388$	1.72294	+	1.00438i	1.72294	+	1.00438i
$389$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$389$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$390$		0			0
$391$		0			0
$392$	0.617860	−	0.786288i	0.617860	−	0.786288i
$393$	−0.0297463	+	2.36701i	−0.0297463	+	2.36701i
$394$		0			0
$395$		0			0
$396$	0.161633	+	1.16185i	0.161633	+	1.16185i
$397$		0			0		0.974527	−	0.224271i	$-0.0720000\pi$
$397$		0			0		−0.974527	+	0.224271i	$0.928000\pi$
$398$		0			0
$399$		0			0
$400$	0.309017	+	0.951057i	0.309017	+	0.951057i
$401$	0.390191	+	1.79863i	0.390191	+	1.79863i	0.577573	+	0.816339i	$0.304000\pi$
$401$	0.390191	+	1.79863i	0.390191	+	1.79863i	−0.187381	+	0.982287i	$0.560000\pi$
$402$	0.926903	−	0.870420i	0.926903	−	0.870420i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−2.16819	−	0.273906i	−2.16819	−	0.273906i
$409$	0.663748	+	0.0501405i	0.663748	+	0.0501405i	0.402906	−	0.915241i	$-0.368000\pi$
$409$	0.663748	+	0.0501405i	0.663748	+	0.0501405i	0.260842	+	0.965382i	$0.416000\pi$
$410$		0			0
$411$	2.15440	+	1.18439i	2.15440	+	1.18439i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	1.21085	−	2.41380i	1.21085	−	2.41380i
$418$	−2.64544	−	0.0665012i	−2.64544	−	0.0665012i
$419$	0.342431	+	0.570803i	0.342431	+	0.570803i	0.979855	−	0.199710i	$-0.0640000\pi$
$419$	0.342431	+	0.570803i	0.342431	+	0.570803i	−0.637424	+	0.770513i	$0.720000\pi$
$420$		0			0
$421$		0			0		0.994951	−	0.100362i	$-0.0320000\pi$
$421$		0			0		−0.994951	+	0.100362i	$0.968000\pi$
$422$	1.01226	−	0.556496i	1.01226	−	0.556496i
$423$		0			0
$424$		0			0
$425$	−1.28470	−	0.983652i	−1.28470	−	0.983652i
$426$		0			0
$427$		0			0
$428$	0.940976	−	0.292721i	0.940976	−	0.292721i
$429$		0			0
$430$		0			0
$431$		0			0		−0.837528	−	0.546394i	$-0.816000\pi$
$431$		0			0		0.837528	+	0.546394i	$0.184000\pi$
$432$	0.164614	+	0.170940i	0.164614	+	0.170940i
$433$	0.0915446	+	1.45506i	0.0915446	+	1.45506i	0.728969	+	0.684547i	$0.240000\pi$
$433$	0.0915446	+	1.45506i	0.0915446	+	1.45506i	−0.637424	+	0.770513i	$0.720000\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	−0.164289	+	0.0421823i	−0.164289	+	0.0421823i
$439$		0			0		−0.425779	−	0.904827i	$-0.640000\pi$
$439$		0			0		0.425779	+	0.904827i	$0.360000\pi$
$440$		0			0
$441$	−0.556675	+	0.607930i	−0.556675	+	0.607930i
$442$		0			0
$443$	−0.594566	+	0.168694i	−0.594566	+	0.168694i	−0.556876	−	0.830596i	$-0.688000\pi$
$443$	−0.594566	+	0.168694i	−0.594566	+	0.168694i	−0.0376902	+	0.999289i	$0.512000\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	0.518795	+	0.236210i	0.518795	+	0.236210i	0.656586	−	0.754251i	$-0.272000\pi$
$449$	0.518795	+	0.236210i	0.518795	+	0.236210i	−0.137790	+	0.990461i	$0.544000\pi$
$450$	−0.194946	−	0.800914i	−0.194946	−	0.800914i
$451$	−2.34596	−	0.602340i	−2.34596	−	0.602340i
$452$	0.208696	+	1.09402i	0.208696	+	1.09402i
$453$		0			0
$454$	−1.30282	−	1.49661i	−1.30282	−	1.49661i
$455$		0			0
$456$	2.06841	−	1.42477i	2.06841	−	1.42477i
$457$	−0.147663	+	1.06143i	−0.147663	+	1.06143i	0.762443	+	0.647056i	$0.224000\pi$
$457$	−0.147663	+	1.06143i	−0.147663	+	1.06143i	−0.910106	+	0.414376i	$0.864000\pi$
$458$		0			0
$459$	−0.376249	−	0.0766854i	−0.376249	−	0.0766854i
$460$		0			0
$461$		0			0		−0.711536	−	0.702650i	$-0.752000\pi$
$461$		0			0		0.711536	+	0.702650i	$0.248000\pi$
$462$		0			0
$463$		0			0		0.762443	−	0.647056i	$-0.224000\pi$
$463$		0			0		−0.762443	+	0.647056i	$0.776000\pi$
$464$		0			0
$465$		0			0
$466$	−0.469300	+	1.14314i	−0.469300	+	1.14314i
$467$	−1.00815	+	0.205477i	−1.00815	+	0.205477i	−0.675333	−	0.737513i	$-0.736000\pi$
$467$	−1.00815	+	0.205477i	−1.00815	+	0.205477i	−0.332820	+	0.942991i	$0.608000\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	1.83117	−	0.778795i	1.83117	−	0.778795i
$473$	2.53043	−	0.857488i	2.53043	−	0.857488i
$474$		0			0
$475$	1.85427	−	0.140074i	1.85427	−	0.140074i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		−0.0376902	−	0.999289i	$-0.512000\pi$
$479$		0			0		0.0376902	+	0.999289i	$0.488000\pi$
$480$		0			0
$481$		0			0
$482$	1.35515	+	0.984573i	1.35515	+	0.984573i
$483$		0			0
$484$	0.592088	+	0.836856i	0.592088	+	0.836856i
$485$		0			0
$486$	−0.834368	−	1.00858i	−0.834368	−	1.00858i
$487$		0			0		0.162637	−	0.986686i	$-0.448000\pi$
$487$		0			0		−0.162637	+	0.986686i	$0.552000\pi$
$488$		0			0
$489$	−1.99164	+	1.60590i	−1.99164	+	1.60590i
$490$		0			0
$491$	0.656200	−	0.382531i	0.656200	−	0.382531i	−0.137790	−	0.990461i	$-0.544000\pi$
$491$	0.656200	−	0.382531i	0.656200	−	0.382531i	0.793990	+	0.607930i	$0.208000\pi$
$492$	2.13739	−	0.846251i	2.13739	−	0.846251i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	0.947203	−	2.01291i	0.947203	−	2.01291i
$499$	0.275494	−	0.00692537i	0.275494	−	0.00692537i	0.112856	−	0.993611i	$-0.464000\pi$
$499$	0.275494	−	0.00692537i	0.275494	−	0.00692537i	0.162637	+	0.986686i	$0.448000\pi$
$500$		0			0
$501$		0			0
$502$	−0.984564	+	0.175023i	−0.984564	+	0.175023i
$503$		0			0		1.00000			$0$
$503$		0			0		−1.00000			$\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.253089	−	1.32674i	0.253089	−	1.32674i
$508$		0			0
$509$		0			0		−0.379779	−	0.925077i	$-0.624000\pi$
$509$		0			0		0.379779	+	0.925077i	$0.376000\pi$
$510$		0			0
$511$		0			0
$512$	−0.929776	+	0.368125i	−0.929776	+	0.368125i
$513$	0.381250	−	0.222249i	0.381250	−	0.222249i
$514$	−0.696161	+	1.58140i	−0.696161	+	1.58140i
$515$		0			0
$516$	−1.46463	+	2.07010i	−1.46463	+	2.07010i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	0.469204	−	0.228036i	0.469204	−	0.228036i	−0.187381	−	0.982287i	$-0.560000\pi$
$521$	0.469204	−	0.228036i	0.469204	−	0.228036i	0.656586	+	0.754251i	$0.272000\pi$
$522$		0			0
$523$	−0.785286	−	1.78385i	−0.785286	−	1.78385i	−0.597905	−	0.801567i	$-0.704000\pi$
$523$	−0.785286	−	1.78385i	−0.785286	−	1.78385i	−0.187381	−	0.982287i	$-0.560000\pi$
$524$	−1.55656	−	0.805466i	−1.55656	−	0.805466i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−1.82041	−	0.616884i	−1.82041	−	0.616884i
$529$	−0.997159	+	0.0753268i	−0.997159	+	0.0753268i
$530$		0			0
$531$	−1.55350	+	0.526435i	−1.55350	+	0.526435i
$532$		0			0
$533$		0			0
$534$	−0.797080	+	2.45316i	−0.797080	+	2.45316i
$535$		0			0
$536$	0.268319	+	0.902360i	0.268319	+	0.902360i
$537$	−0.690425	+	0.140720i	−0.690425	+	0.140720i
$538$		0			0
$539$	−0.371196	+	1.37381i	−0.371196	+	1.37381i
$540$		0			0
$541$		0			0		0.762443	−	0.647056i	$-0.224000\pi$
$541$		0			0		−0.762443	+	0.647056i	$0.776000\pi$
$542$		0			0
$543$		0			0
$544$	0.901044	−	1.34393i	0.901044	−	1.34393i
$545$		0			0
$546$		0			0
$547$	0.0379723	−	0.272952i	0.0379723	−	0.272952i	−0.962028	−	0.272952i	$-0.912000\pi$
$547$	0.0379723	−	0.272952i	0.0379723	−	0.272952i	1.00000			$0$
$548$	−1.49900	+	1.03255i	−1.49900	+	1.03255i
$549$		0			0
$550$	−0.934368	−	1.07335i	−0.934368	−	1.07335i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	1.19543	+	1.60263i	1.19543	+	1.60263i
$557$		0			0		−0.332820	−	0.942991i	$-0.608000\pi$
$557$		0			0		0.332820	+	0.942991i	$0.392000\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	2.99192	−	0.848884i	2.99192	−	0.848884i
$562$	−0.389529	−	0.268317i	−0.389529	−	0.268317i
$563$	1.34002	−	1.46340i	1.34002	−	1.46340i	0.577573	−	0.816339i	$-0.304000\pi$
$563$	1.34002	−	1.46340i	1.34002	−	1.46340i	0.762443	−	0.647056i	$-0.224000\pi$
$564$		0			0
$565$		0			0
$566$	−1.62243	+	0.416570i	−1.62243	+	0.416570i
$567$		0			0
$568$		0			0
$569$	−0.281012	−	1.70484i	−0.281012	−	1.70484i	−0.637424	−	0.770513i	$-0.720000\pi$
$569$	−0.281012	−	1.70484i	−0.281012	−	1.70484i	0.356412	−	0.934329i	$-0.384000\pi$
$570$		0			0
$571$	−0.111533	−	1.77277i	−0.111533	−	1.77277i	−0.514440	−	0.857527i	$-0.672000\pi$
$571$	−0.111533	−	1.77277i	−0.111533	−	1.77277i	0.402906	−	0.915241i	$-0.368000\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.787093	−	0.244851i	0.787093	−	0.244851i
$577$	1.30231	+	0.478125i	1.30231	+	0.478125i	0.899405	−	0.437116i	$-0.144000\pi$
$577$	1.30231	+	0.478125i	1.30231	+	0.478125i	0.402906	+	0.915241i	$0.368000\pi$
$578$	0.0203323	+	1.61791i	0.0203323	+	1.61791i
$579$	−0.454719	−	0.348163i	−0.454719	−	0.348163i
$580$		0			0
$581$		0			0
$582$	2.36047	−	1.29768i	2.36047	−	1.29768i
$583$		0			0
$584$	0.0266241	−	0.122726i	0.0266241	−	0.122726i
$585$		0			0
$586$		0			0
$587$	−0.536181	+	1.06886i	−0.536181	+	1.06886i	0.448383	+	0.893841i	$0.352000\pi$
$587$	−0.536181	+	1.06886i	−0.536181	+	1.06886i	−0.984564	+	0.175023i	$0.944000\pi$
$588$	−0.481393	−	1.26197i	−0.481393	−	1.26197i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	0.863561	+	0.474746i	0.863561	+	0.474746i	0.850994	−	0.525175i	$-0.176000\pi$
$593$	0.863561	+	0.474746i	0.863561	+	0.474746i	0.0125660	+	0.999921i	$0.496000\pi$
$594$	−0.310777	−	0.132173i	−0.310777	−	0.132173i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		0.0878512	−	0.996134i	$-0.472000\pi$
$599$		0			0		−0.0878512	+	0.996134i	$0.528000\pi$
$600$	1.31626	+	0.302915i	1.31626	+	0.302915i
$601$	−1.62243	+	1.05846i	−1.62243	+	1.05846i	−0.675333	+	0.737513i	$0.736000\pi$
$601$	−1.62243	+	1.05846i	−1.62243	+	1.05846i	−0.947098	+	0.320944i	$0.896000\pi$
$602$		0			0
$603$	−0.164518	−	0.758360i	−0.164518	−	0.758360i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		0.974527	−	0.224271i	$-0.0720000\pi$
$607$		0			0		−0.974527	+	0.224271i	$0.928000\pi$
$608$	0.256228	+	1.84182i	0.256228	+	1.84182i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−0.824065	+	1.04871i	−0.824065	+	1.04871i
$613$		0			0		0.236499	−	0.971632i	$-0.424000\pi$
$613$		0			0		−0.236499	+	0.971632i	$0.576000\pi$
$614$	0.732851	−	1.37366i	0.732851	−	1.37366i
$615$		0			0
$616$		0			0
$617$	−1.47495	−	0.224119i	−1.47495	−	0.224119i	−0.637424	−	0.770513i	$-0.720000\pi$
$617$	−1.47495	−	0.224119i	−1.47495	−	0.224119i	−0.837528	+	0.546394i	$0.816000\pi$
$618$		0			0
$619$	−0.921774	+	0.823004i	−0.921774	+	0.823004i	−0.984564	−	0.175023i	$-0.944000\pi$
$619$	−0.921774	+	0.823004i	−0.921774	+	0.823004i	0.0627905	+	0.998027i	$0.480000\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.728969	+	0.684547i	0.728969	+	0.684547i
$626$	−0.594252	+	0.990568i	−0.594252	+	0.990568i
$627$	−1.91517	+	3.01783i	−1.91517	+	3.01783i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		−0.984564	−	0.175023i	$-0.944000\pi$
$631$		0			0		0.984564	+	0.175023i	$0.0560000\pi$
$632$		0			0
$633$	0.0588048	−	1.55911i	0.0588048	−	1.55911i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	0.176402	−	0.330650i	0.176402	−	0.330650i	−0.778462	−	0.627691i	$-0.784000\pi$
$641$	0.176402	−	0.330650i	0.176402	−	0.330650i	0.954865	+	0.297042i	$0.0960000\pi$
$642$	0.314785	−	1.29326i	0.314785	−	1.29326i
$643$	0.811356	−	1.03253i	0.811356	−	1.03253i	−0.187381	−	0.982287i	$-0.560000\pi$
$643$	0.811356	−	1.03253i	0.811356	−	1.03253i	0.998737	−	0.0502443i	$-0.0160000\pi$
$644$		0			0
$645$		0			0
$646$	−2.03195	−	2.21904i	−2.03195	−	2.21904i
$647$		0			0		−0.137790	−	0.990461i	$-0.544000\pi$
$647$		0			0		0.137790	+	0.990461i	$0.456000\pi$
$648$	1.11567	−	0.256752i	1.11567	−	0.256752i
$649$	−1.96427	+	2.03975i	−1.96427	+	2.03975i
$650$		0			0
$651$		0			0
$652$	−0.401583	−	1.85114i	−0.401583	−	1.85114i
$653$		0			0		0.728969	−	0.684547i	$-0.240000\pi$
$653$		0			0		−0.728969	+	0.684547i	$0.760000\pi$
$654$		0			0
$655$		0			0
$656$	−0.149522	+	1.69541i	−0.149522	+	1.69541i
$657$	−0.0295041	+	0.0992225i	−0.0295041	+	0.0992225i
$658$		0			0
$659$	−1.73879	−	0.219661i	−1.73879	−	0.219661i	−0.809017	−	0.587785i	$-0.800000\pi$
$659$	−1.73879	−	0.219661i	−1.73879	−	0.219661i	−0.929776	+	0.368125i	$0.880000\pi$
$660$		0			0
$661$		0			0		−0.920232	−	0.391374i	$-0.872000\pi$
$661$		0			0		0.920232	+	0.391374i	$0.128000\pi$
$662$	0.371566	+	0.204270i	0.371566	+	0.204270i
$663$		0			0
$664$	1.01766	+	1.29507i	1.01766	+	1.29507i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.0220234	−	0.0121075i	0.0220234	−	0.0121075i	−0.470704	−	0.882291i	$-0.656000\pi$
$673$	0.0220234	−	0.0121075i	0.0220234	−	0.0121075i	0.492727	+	0.870184i	$0.336000\pi$
$674$	−0.194483	+	0.260729i	−0.194483	+	0.260729i
$675$	0.226604	+	0.0704925i	0.226604	+	0.0704925i
$676$	0.793990	+	0.607930i	0.793990	+	0.607930i
$677$		0			0		−0.0125660	−	0.999921i	$-0.504000\pi$
$677$		0			0		0.0125660	+	0.999921i	$0.496000\pi$
$678$	1.41214	+	0.518448i	1.41214	+	0.518448i
$679$		0			0
$680$		0			0
$681$	−2.63866	+	0.469067i	−2.63866	+	0.469067i
$682$		0			0
$683$	0.622045	+	0.645949i	0.622045	+	0.645949i	0.954865	−	0.297042i	$-0.0960000\pi$
$683$	0.622045	+	0.645949i	0.622045	+	0.645949i	−0.332820	+	0.942991i	$0.608000\pi$
$684$	−0.0962469	−	1.52980i	−0.0962469	−	1.52980i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	−0.883731	−	1.65647i	−0.883731	−	1.65647i
$689$		0			0
$690$		0			0
$691$	0.683733	+	1.36301i	0.683733	+	1.36301i	0.920232	+	0.391374i	$0.128000\pi$
$691$	0.683733	+	1.36301i	0.683733	+	1.36301i	−0.236499	+	0.971632i	$0.576000\pi$
$692$		0			0
$693$		0			0
$694$	−0.775214	+	0.219948i	−0.775214	+	0.219948i
$695$		0			0
$696$		0			0
$697$	−1.35691	−	2.39638i	−1.35691	−	2.39638i
$698$		0			0
$699$	0.997929	+	1.33785i	0.997929	+	1.33785i
$700$		0			0
$701$		0			0		−0.236499	−	0.971632i	$-0.576000\pi$
$701$		0			0		0.236499	+	0.971632i	$0.424000\pi$
$702$		0			0
$703$		0			0
$704$	1.01257	−	0.999921i	1.01257	−	0.999921i
$705$		0			0
$706$	0.542804	−	0.656137i	0.542804	−	0.656137i
$707$		0			0
$708$	0.370338	−	2.66206i	0.370338	−	2.66206i
$709$		0			0		−0.0878512	−	0.996134i	$-0.528000\pi$
$709$		0			0		0.0878512	+	0.996134i	$0.472000\pi$
$710$		0			0
$711$		0			0
$712$	−1.35884	−	1.34187i	−1.35884	−	1.34187i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	0.136077	−	0.503623i	0.136077	−	0.503623i
$717$		0			0
$718$		0			0
$719$		0			0		−0.285019	−	0.958522i	$-0.592000\pi$
$719$		0			0		0.285019	+	0.958522i	$0.408000\pi$
$720$		0			0
$721$		0			0
$722$	2.44553	+	0.246683i	2.44553	+	0.246683i
$723$	2.08197	−	0.885460i	2.08197	−	0.885460i
$724$		0			0
$725$		0			0
$726$	1.38068	−	0.104298i	1.38068	−	0.104298i
$727$		0			0		−0.947098	−	0.320944i	$-0.896000\pi$
$727$		0			0		0.947098	+	0.320944i	$0.104000\pi$
$728$		0			0
$729$	−0.616076	+	0.0936128i	−0.616076	+	0.0936128i
$730$		0			0
$731$	2.69799	+	1.39611i	2.69799	+	1.39611i
$732$		0			0
$733$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$733$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−0.853951	−	1.03225i	−0.853951	−	1.03225i
$738$	0.228171	−	1.38427i	0.228171	−	1.38427i
$739$	0.517948	−	0.732066i	0.517948	−	0.732066i	−0.470704	−	0.882291i	$-0.656000\pi$
$739$	0.517948	−	0.732066i	0.517948	−	0.732066i	0.988652	+	0.150226i	$0.0480000\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		0.929776	−	0.368125i	$-0.120000\pi$
$743$		0			0		−0.929776	+	0.368125i	$0.880000\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−0.756054	−	1.12768i	−0.756054	−	1.12768i
$748$	−0.431460	+	2.26179i	−0.431460	+	2.26179i
$749$		0			0
$750$		0			0
$751$		0			0		−0.535827	−	0.844328i	$-0.680000\pi$
$751$		0			0		0.535827	+	0.844328i	$0.320000\pi$
$752$		0			0
$753$	−0.481393	+	1.26197i	−0.481393	+	1.26197i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.425779	−	0.904827i	$-0.360000\pi$
$757$		0			0		−0.425779	+	0.904827i	$0.640000\pi$
$758$	−0.259955	+	1.36273i	−0.259955	+	1.36273i
$759$		0			0
$760$		0			0
$761$	−1.63408	+	0.206432i	−1.63408	+	0.206432i	−0.888136	−	0.459580i	$-0.848000\pi$
$761$	−1.63408	+	0.206432i	−1.63408	+	0.206432i	−0.745941	+	0.666012i	$0.768000\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−0.219668	+	1.33268i	−0.219668	+	1.33268i
$769$	−1.26038	−	1.52354i	−1.26038	−	1.52354i	−0.745941	−	0.666012i	$-0.768000\pi$
$769$	−1.26038	−	1.52354i	−1.26038	−	1.52354i	−0.514440	−	0.857527i	$-0.672000\pi$
$770$		0			0
$771$	1.34791	+	1.90513i	1.34791	+	1.90513i
$772$	0.381361	−	0.185343i	0.381361	−	0.185343i
$773$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$773$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$774$	0.623535	+	1.41642i	0.623535	+	1.41642i
$775$		0			0
$776$	0.0751662	+	1.99290i	0.0751662	+	1.99290i
$777$		0			0
$778$		0			0
$779$	2.99751	+	1.01577i	2.99751	+	1.01577i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.994951	+	0.100362i	0.994951	+	0.100362i
$785$		0			0
$786$	−2.01447	+	1.24319i	−2.01447	+	1.24319i
$787$	0.548393	+	1.84425i	0.548393	+	1.84425i	0.535827	+	0.844328i	$0.320000\pi$
$787$	0.548393	+	1.84425i	0.548393	+	1.84425i	0.0125660	+	0.999921i	$0.496000\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−0.894371	+	0.759019i	−0.894371	+	0.759019i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.0878512	−	0.996134i	$-0.528000\pi$
$797$		0			0		0.0878512	+	0.996134i	$0.472000\pi$
$798$		0			0
$799$		0			0
$800$	−0.637424	+	0.770513i	−0.637424	+	0.770513i
$801$	1.03359	+	1.18733i	1.03359	+	1.18733i
$802$	−1.30956	+	1.29320i	−1.30956	+	1.29320i
$803$	0.0334871	+	0.175545i	0.0334871	+	0.175545i
$804$	1.23158	+	0.316216i	1.23158	+	0.316216i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	0.974271	+	1.72062i	0.974271	+	1.72062i	0.617860	+	0.786288i	$0.288000\pi$
$809$	0.974271	+	1.72062i	0.974271	+	1.72062i	0.356412	+	0.934329i	$0.384000\pi$
$810$		0			0
$811$	1.47456	+	1.18897i	1.47456	+	1.18897i	0.938734	+	0.344643i	$0.112000\pi$
$811$	1.47456	+	1.18897i	1.47456	+	1.18897i	0.535827	+	0.844328i	$0.320000\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	−0.930508	−	1.97743i	−0.930508	−	1.97743i
$817$	−3.38157	+	0.868239i	−3.38157	+	0.868239i
$818$	0.313319	+	0.587288i	0.313319	+	0.587288i
$819$		0			0
$820$		0			0
$821$		0			0		0.656586	−	0.754251i	$-0.272000\pi$
$821$		0			0		−0.656586	+	0.754251i	$0.728000\pi$
$822$	0.154370	+	2.45365i	0.154370	+	2.45365i
$823$		0			0		−0.693653	−	0.720309i	$-0.744000\pi$
$823$		0			0		0.693653	+	0.720309i	$0.256000\pi$
$824$		0			0
$825$	−1.89242	+	0.336411i	−1.89242	+	0.336411i
$826$		0			0
$827$	−0.982440	+	0.305620i	−0.982440	+	0.305620i	−0.745941	−	0.666012i	$-0.768000\pi$
$827$	−0.982440	+	0.305620i	−0.982440	+	0.305620i	−0.236499	+	0.971632i	$0.576000\pi$
$828$		0			0
$829$		0			0		−0.0125660	−	0.999921i	$-0.504000\pi$
$829$		0			0		0.0125660	+	0.999921i	$0.496000\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−1.41789	+	0.779494i	−1.41789	+	0.779494i
$834$	2.68684	−	0.271025i	2.68684	−	0.271025i
$835$		0			0
$836$	−1.36135	−	2.26925i	−1.36135	−	2.26925i
$837$		0			0
$838$	−0.298461	+	0.594976i	−0.298461	+	0.594976i
$839$		0			0		−0.356412	−	0.934329i	$-0.616000\pi$
$839$		0			0		0.356412	+	0.934329i	$0.384000\pi$
$840$		0			0
$841$	0.793990	−	0.607930i	0.793990	−	0.607930i
$842$		0			0
$843$	−0.581432	+	0.264729i	−0.581432	+	0.264729i
$844$	1.01226	+	0.556496i	1.01226	+	0.556496i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−0.644839	+	2.16860i	−0.644839	+	2.16860i
$850$	0.142146	−	1.61178i	0.142146	−	1.61178i
$851$		0			0
$852$		0			0
$853$		0			0		0.728969	−	0.684547i	$-0.240000\pi$
$853$		0			0		−0.728969	+	0.684547i	$0.760000\pi$
$854$		0			0
$855$		0			0
$856$	0.751353	+	0.637644i	0.751353	+	0.637644i
$857$	−1.31392	+	1.36441i	−1.31392	+	1.36441i	−0.425779	+	0.904827i	$0.640000\pi$
$857$	−1.31392	+	1.36441i	−1.31392	+	1.36441i	−0.888136	+	0.459580i	$0.848000\pi$
$858$		0			0
$859$	0.164771	+	1.18440i	0.164771	+	1.18440i	0.876307	+	0.481754i	$0.160000\pi$
$859$	0.164771	+	1.18440i	0.164771	+	1.18440i	−0.711536	+	0.702650i	$0.752000\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.617860	−	0.786288i	$-0.288000\pi$
$863$		0			0		−0.617860	+	0.786288i	$0.712000\pi$
$864$	−0.0561248	+	0.230583i	−0.0561248	+	0.230583i
$865$		0			0
$866$	−1.17950	+	0.856954i	−1.17950	+	0.856954i
$867$	1.88804	+	1.10063i	1.88804	+	1.10063i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	0.0619593	−	1.64274i	0.0619593	−	1.64274i
$874$		0			0
$875$		0			0
$876$	−0.123646	−	0.116112i	−0.123646	−	0.116112i
$877$		0			0		0.514440	−	0.857527i	$-0.328000\pi$
$877$		0			0		−0.514440	+	0.857527i	$0.672000\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	0.653715	+	0.613879i	0.653715	+	0.613879i	0.938734	−	0.344643i	$-0.112000\pi$
$881$	0.653715	+	0.613879i	0.653715	+	0.613879i	−0.285019	+	0.958522i	$0.592000\pi$
$882$	−0.811574	−	0.144271i	−0.811574	−	0.144271i
$883$	0.0618772	−	0.109279i	0.0618772	−	0.109279i	−0.837528	−	0.546394i	$-0.816000\pi$
$883$	0.0618772	−	0.109279i	0.0618772	−	0.109279i	0.899405	+	0.437116i	$0.144000\pi$
$884$		0			0
$885$		0			0
$886$	−0.461017	−	0.411618i	−0.461017	−	0.411618i
$887$		0			0		0.745941	−	0.666012i	$-0.232000\pi$
$887$		0			0		−0.745941	+	0.666012i	$0.768000\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−1.31803	+	0.957606i	−1.31803	+	0.957606i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	0.0785458	+	0.564601i	0.0785458	+	0.564601i
$899$		0			0
$900$	0.571777	−	0.593749i	0.571777	−	0.593749i
$901$		0			0
$902$	−0.748455	−	2.30351i	−0.748455	−	2.30351i
$903$		0			0
$904$	−0.811890	+	0.762415i	−0.811890	+	0.762415i
$905$		0			0
$906$		0			0
$907$	−0.115364	+	1.30809i	−0.115364	+	1.30809i	0.693653	+	0.720309i	$0.256000\pi$
$907$	−0.115364	+	1.30809i	−0.115364	+	1.30809i	−0.809017	+	0.587785i	$0.800000\pi$
$908$	0.565544	−	1.90193i	0.565544	−	1.90193i
$909$		0			0
$910$		0			0
$911$		0			0		−0.997159	−	0.0753268i	$-0.976000\pi$
$911$		0			0		0.997159	+	0.0753268i	$0.0240000\pi$
$912$	2.31129	+	0.982988i	2.31129	+	0.982988i
$913$	−2.05397	−	1.12918i	−2.05397	−	1.12918i
$914$	−0.975318	+	0.444067i	−0.975318	+	0.444067i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	−0.136856	−	0.358767i	−0.136856	−	0.358767i
$919$		0			0		0.448383	−	0.893841i	$-0.352000\pi$
$919$		0			0		−0.448383	+	0.893841i	$0.648000\pi$
$920$		0			0
$921$	−1.08181	−	1.80328i	−1.08181	−	1.80328i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−1.46154	−	0.536583i	−1.46154	−	0.536583i	−0.514440	−	0.857527i	$-0.672000\pi$
$929$	−1.46154	−	0.536583i	−1.46154	−	0.536583i	−0.947098	+	0.320944i	$0.896000\pi$
$930$		0			0
$931$	0.618896	−	1.75354i	0.618896	−	1.75354i
$932$	−1.21665	+	0.216279i	−1.21665	+	0.216279i
$933$		0			0
$934$	−0.713685	−	0.741111i	−0.713685	−	0.741111i
$935$		0			0
$936$		0			0
$937$	0.145848	+	0.884827i	0.145848	+	0.884827i	0.954865	+	0.297042i	$0.0960000\pi$
$937$	0.145848	+	0.884827i	0.145848	+	0.884827i	−0.809017	+	0.587785i	$0.800000\pi$
$938$		0			0
$939$	0.734399	+	1.37656i	0.734399	+	1.37656i
$940$		0			0
$941$		0			0		−0.425779	−	0.904827i	$-0.640000\pi$
$941$		0			0		0.425779	+	0.904827i	$0.360000\pi$
$942$		0			0
$943$		0			0
$944$	1.63875	+	1.12881i	1.63875	+	1.12881i
$945$		0			0
$946$	2.07987	+	1.67705i	2.07987	+	1.67705i
$947$	1.13224	−	0.585894i	1.13224	−	0.585894i	0.212007	−	0.977268i	$-0.432000\pi$
$947$	1.13224	−	0.585894i	1.13224	−	0.585894i	0.920232	+	0.391374i	$0.128000\pi$
$948$		0			0
$949$		0			0
$950$	1.11184	+	1.49056i	1.11184	+	1.49056i
$951$		0			0
$952$		0			0
$953$	1.19690	+	0.307311i	1.19690	+	0.307311i	0.793990	−	0.607930i	$-0.208000\pi$
$953$	1.19690	+	0.307311i	1.19690	+	0.307311i	0.402906	+	0.915241i	$0.368000\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.979855	+	0.199710i	0.979855	+	0.199710i
$962$		0			0
$963$	−0.577986	−	0.570768i	−0.577986	−	0.570768i
$964$	−0.105178	+	1.67175i	−0.105178	+	1.67175i
$965$		0			0
$966$		0			0
$967$		0			0		0.260842	−	0.965382i	$-0.416000\pi$
$967$		0			0		−0.260842	+	0.965382i	$0.584000\pi$
$968$	−0.389324	+	0.948326i	−0.389324	+	0.948326i
$969$	−3.98204	+	0.811603i	−3.98204	+	0.811603i
$970$		0			0
$971$	1.64852	−	1.01735i	1.64852	−	1.01735i	0.693653	−	0.720309i	$-0.256000\pi$
$971$	1.64852	−	1.01735i	1.64852	−	1.01735i	0.954865	−	0.297042i	$-0.0960000\pi$
$972$	0.404494	−	1.24490i	0.404494	−	1.24490i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1.99369	−	0.150606i	1.99369	−	0.150606i	0.994951	−	0.100362i	$-0.0320000\pi$
$977$	1.99369	−	0.150606i	1.99369	−	0.150606i	0.998737	−	0.0502443i	$-0.0160000\pi$
$978$	−2.42308	−	0.821111i	−2.42308	−	0.821111i
$979$	2.52684	+	1.00045i	2.52684	+	1.00045i
$980$		0			0
$981$		0			0
$982$	0.674591	+	0.349078i	0.674591	+	0.349078i
$983$		0			0		−0.402906	−	0.915241i	$-0.632000\pi$
$983$		0			0		0.402906	+	0.915241i	$0.368000\pi$
$984$	1.85978	+	1.35121i	1.85978	+	1.35121i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.778462	−	0.627691i	$-0.216000\pi$
$991$		0			0		−0.778462	+	0.627691i	$0.784000\pi$
$992$		0			0
$993$	0.494770	−	0.288426i	0.494770	−	0.288426i
$994$		0			0
$995$		0			0
$996$	2.20709	−	0.278821i	2.20709	−	0.278821i
$997$		0			0		−0.379779	−	0.925077i	$-0.624000\pi$
$997$		0			0		0.379779	+	0.925077i	$0.376000\pi$
$998$	0.153464	+	0.228896i	0.153464	+	0.228896i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2008.1.bd.a.195.1	✓	100
8.3	odd	2	CM	2008.1.bd.a.195.1	✓	100
251.121	even	125	inner	2008.1.bd.a.1627.1	yes	100
2008.1627	odd	250	inner	2008.1.bd.a.1627.1	yes	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2008.1.bd.a.195.1	✓	100	1.1	even	1	trivial
2008.1.bd.a.195.1	✓	100	8.3	odd	2	CM
2008.1.bd.a.1627.1	yes	100	251.121	even	125	inner
2008.1.bd.a.1627.1	yes	100	2008.1627	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)

\(f(q)\)	\(=\)	\(q+(0.535827 + 0.844328i) q^{2} +(1.35024 - 0.0339424i) q^{3} +(-0.425779 + 0.904827i) q^{4} +(0.752153 + 1.12186i) q^{6} +(-0.992115 + 0.125333i) q^{8} +(0.823256 - 0.0414163i) q^{9} +O(q^{10})\)	\(q+(0.535827 + 0.844328i) q^{2} +(1.35024 - 0.0339424i) q^{3} +(-0.425779 + 0.904827i) q^{4} +(0.752153 + 1.12186i) q^{6} +(-0.992115 + 0.125333i) q^{8} +(0.823256 - 0.0414163i) q^{9} +(1.22942 - 0.716692i) q^{11} +(-0.544192 + 1.23618i) q^{12} +(-0.637424 - 0.770513i) q^{16} +(1.55659 + 0.441646i) q^{17} +(0.476092 + 0.672906i) q^{18} +(-1.67249 + 0.812840i) q^{19} +(1.26388 + 0.654015i) q^{22} +(-1.33534 + 0.202905i) q^{24} +(-0.929776 - 0.368125i) q^{25} +(-0.236641 + 0.0178762i) q^{27} +(0.309017 - 0.951057i) q^{32} +(1.63569 - 1.00943i) q^{33} +(0.461171 + 1.55092i) q^{34} +(-0.313051 + 0.762539i) q^{36} +(-1.58247 - 0.976590i) q^{38} +(-1.21103 - 1.19590i) q^{41} +(1.83965 + 0.374949i) q^{43} +(0.125019 + 1.41757i) q^{44} +(-0.886828 - 1.01874i) q^{48} +(-0.711536 + 0.702650i) q^{49} +(-0.187381 - 0.982287i) q^{50} +(2.11676 + 0.543493i) q^{51} +(-0.141892 - 0.190224i) q^{54} +(-2.23067 + 1.15430i) q^{57} +(-1.91434 + 0.543148i) q^{59} +(0.968583 - 0.248690i) q^{64} +(1.72874 + 0.840177i) q^{66} +(-0.153108 - 0.928874i) q^{67} +(-1.06238 + 1.22040i) q^{68} +(-0.811574 + 0.144271i) q^{72} +(-0.0417958 + 0.118422i) q^{73} +(-1.26792 - 0.465497i) q^{75} +(-0.0233672 - 1.85941i) q^{76} +(-1.13905 + 0.114897i) q^{81} +(0.360834 - 1.66330i) q^{82} +(-0.847315 - 1.41240i) q^{83} +(0.669152 + 1.75417i) q^{86} +(-1.12990 + 0.865128i) q^{88} +(1.17994 + 1.50160i) q^{89} +(0.384966 - 1.29464i) q^{96} +(0.175203 - 1.98661i) q^{97} +(-0.974527 - 0.224271i) q^{98} +(0.982449 - 0.640939i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q+O(q^{10}) \) 100 * q	\( 100 q - 25 q^{22} - 25 q^{32}+O(q^{100}) \) 100 * q - 25 * q^22 - 25 * q^32

Introduction

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Database

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