LMFDB - Embedded newform 1444.2.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1444,2,Mod(1,1444)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1444, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1444.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1444 = 2^{2} \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1444.a (trivial)

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:	yes
Analytic conductor:	$11.5303980519$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 76)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1444.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-2.00000 q^{3} -1.00000 q^{5} -3.00000 q^{7} +1.00000 q^{9} +O(q^{10})$

$q-2.00000 q^{3} -1.00000 q^{5} -3.00000 q^{7} +1.00000 q^{9} +5.00000 q^{11} +4.00000 q^{13} +2.00000 q^{15} -3.00000 q^{17} +6.00000 q^{21} +8.00000 q^{23} -4.00000 q^{25} +4.00000 q^{27} +2.00000 q^{29} -4.00000 q^{31} -10.0000 q^{33} +3.00000 q^{35} -10.0000 q^{37} -8.00000 q^{39} -10.0000 q^{41} +1.00000 q^{43} -1.00000 q^{45} -1.00000 q^{47} +2.00000 q^{49} +6.00000 q^{51} +4.00000 q^{53} -5.00000 q^{55} -6.00000 q^{59} -13.0000 q^{61} -3.00000 q^{63} -4.00000 q^{65} +12.0000 q^{67} -16.0000 q^{69} -2.00000 q^{71} +9.00000 q^{73} +8.00000 q^{75} -15.0000 q^{77} -8.00000 q^{79} -11.0000 q^{81} -12.0000 q^{83} +3.00000 q^{85} -4.00000 q^{87} -12.0000 q^{89} -12.0000 q^{91} +8.00000 q^{93} +8.00000 q^{97} +5.00000 q^{99} +O(q^{100})$

Display 100 coefficients 10 coefficients

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	0
$2$	0	0
$3$	−2.00000	−1.15470	−0.577350	−	0.816497i	$-0.695913\pi$
$3$	−2.00000	−1.15470	−0.577350	+	0.816497i	$0.695913\pi$
$4$	0	0
$5$	−1.00000	−0.447214	−0.223607	−	0.974679i	$-0.571783\pi$
$5$	−1.00000	−0.447214	−0.223607	+	0.974679i	$0.571783\pi$
$6$	0	0
$7$	−3.00000	−1.13389	−0.566947	−	0.823754i	$-0.691875\pi$
$7$	−3.00000	−1.13389	−0.566947	+	0.823754i	$0.691875\pi$
$8$	0	0
$9$	1.00000	0.333333
$10$	0	0
$11$	5.00000	1.50756	0.753778	−	0.657129i	$-0.228229\pi$
$11$	5.00000	1.50756	0.753778	+	0.657129i	$0.228229\pi$
$12$	0	0
$13$	4.00000	1.10940	0.554700	−	0.832050i	$-0.312833\pi$
$13$	4.00000	1.10940	0.554700	+	0.832050i	$0.312833\pi$
$14$	0	0
$15$	2.00000	0.516398
$16$	0	0
$17$	−3.00000	−0.727607	−0.363803	−	0.931476i	$-0.618522\pi$
$17$	−3.00000	−0.727607	−0.363803	+	0.931476i	$0.618522\pi$
$18$	0	0
$19$	0	0
$19$	0	0
$20$	0	0
$21$	6.00000	1.30931
$22$	0	0
$23$	8.00000	1.66812	0.834058	−	0.551677i	$-0.186012\pi$
$23$	8.00000	1.66812	0.834058	+	0.551677i	$0.186012\pi$
$24$	0	0
$25$	−4.00000	−0.800000
$26$	0	0
$27$	4.00000	0.769800
$28$	0	0
$29$	2.00000	0.371391	0.185695	−	0.982607i	$-0.440546\pi$
$29$	2.00000	0.371391	0.185695	+	0.982607i	$0.440546\pi$
$30$	0	0
$31$	−4.00000	−0.718421	−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000	−0.718421	−0.359211	+	0.933257i	$0.616954\pi$
$32$	0	0
$33$	−10.0000	−1.74078
$34$	0	0
$35$	3.00000	0.507093
$36$	0	0
$37$	−10.0000	−1.64399	−0.821995	−	0.569495i	$-0.807139\pi$
$37$	−10.0000	−1.64399	−0.821995	+	0.569495i	$0.807139\pi$
$38$	0	0
$39$	−8.00000	−1.28103
$40$	0	0
$41$	−10.0000	−1.56174	−0.780869	−	0.624695i	$-0.785223\pi$
$41$	−10.0000	−1.56174	−0.780869	+	0.624695i	$0.785223\pi$
$42$	0	0
$43$	1.00000	0.152499	0.0762493	−	0.997089i	$-0.475706\pi$
$43$	1.00000	0.152499	0.0762493	+	0.997089i	$0.475706\pi$
$44$	0	0
$45$	−1.00000	−0.149071
$46$	0	0
$47$	−1.00000	−0.145865	−0.0729325	−	0.997337i	$-0.523236\pi$
$47$	−1.00000	−0.145865	−0.0729325	+	0.997337i	$0.523236\pi$
$48$	0	0
$49$	2.00000	0.285714
$50$	0	0
$51$	6.00000	0.840168
$52$	0	0
$53$	4.00000	0.549442	0.274721	−	0.961524i	$-0.411414\pi$
$53$	4.00000	0.549442	0.274721	+	0.961524i	$0.411414\pi$
$54$	0	0
$55$	−5.00000	−0.674200
$56$	0	0
$57$	0	0
$58$	0	0
$59$	−6.00000	−0.781133	−0.390567	−	0.920575i	$-0.627721\pi$
$59$	−6.00000	−0.781133	−0.390567	+	0.920575i	$0.627721\pi$
$60$	0	0
$61$	−13.0000	−1.66448	−0.832240	−	0.554416i	$-0.812942\pi$
$61$	−13.0000	−1.66448	−0.832240	+	0.554416i	$0.812942\pi$
$62$	0	0
$63$	−3.00000	−0.377964
$64$	0	0
$65$	−4.00000	−0.496139
$66$	0	0
$67$	12.0000	1.46603	0.733017	−	0.680211i	$-0.238112\pi$
$67$	12.0000	1.46603	0.733017	+	0.680211i	$0.238112\pi$
$68$	0	0
$69$	−16.0000	−1.92617
$70$	0	0
$71$	−2.00000	−0.237356	−0.118678	−	0.992933i	$-0.537866\pi$
$71$	−2.00000	−0.237356	−0.118678	+	0.992933i	$0.537866\pi$
$72$	0	0
$73$	9.00000	1.05337	0.526685	−	0.850060i	$-0.323435\pi$
$73$	9.00000	1.05337	0.526685	+	0.850060i	$0.323435\pi$
$74$	0	0
$75$	8.00000	0.923760
$76$	0	0
$77$	−15.0000	−1.70941
$78$	0	0
$79$	−8.00000	−0.900070	−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000	−0.900070	−0.450035	+	0.893011i	$0.648589\pi$
$80$	0	0
$81$	−11.0000	−1.22222
$82$	0	0
$83$	−12.0000	−1.31717	−0.658586	−	0.752506i	$-0.728845\pi$
$83$	−12.0000	−1.31717	−0.658586	+	0.752506i	$0.728845\pi$
$84$	0	0
$85$	3.00000	0.325396
$86$	0	0
$87$	−4.00000	−0.428845
$88$	0	0
$89$	−12.0000	−1.27200	−0.635999	−	0.771690i	$-0.719412\pi$
$89$	−12.0000	−1.27200	−0.635999	+	0.771690i	$0.719412\pi$
$90$	0	0
$91$	−12.0000	−1.25794
$92$	0	0
$93$	8.00000	0.829561
$94$	0	0
$95$	0	0
$96$	0	0
$97$	8.00000	0.812277	0.406138	−	0.913812i	$-0.366875\pi$
$97$	8.00000	0.812277	0.406138	+	0.913812i	$0.366875\pi$
$98$	0	0
$99$	5.00000	0.502519
$100$	0	0
$101$	−10.0000	−0.995037	−0.497519	−	0.867453i	$-0.665755\pi$
$101$	−10.0000	−0.995037	−0.497519	+	0.867453i	$0.665755\pi$
$102$	0	0
$103$	6.00000	0.591198	0.295599	−	0.955312i	$-0.404481\pi$
$103$	6.00000	0.591198	0.295599	+	0.955312i	$0.404481\pi$
$104$	0	0
$105$	−6.00000	−0.585540
$106$	0	0
$107$	−2.00000	−0.193347	−0.0966736	−	0.995316i	$-0.530820\pi$
$107$	−2.00000	−0.193347	−0.0966736	+	0.995316i	$0.530820\pi$
$108$	0	0
$109$	0	0		−	1.00000i	$-0.5\pi$
$109$	0	0			1.00000i	$0.5\pi$
$110$	0	0
$111$	20.0000	1.89832
$112$	0	0
$113$	10.0000	0.940721	0.470360	−	0.882474i	$-0.344124\pi$
$113$	10.0000	0.940721	0.470360	+	0.882474i	$0.344124\pi$
$114$	0	0
$115$	−8.00000	−0.746004
$116$	0	0
$117$	4.00000	0.369800
$118$	0	0
$119$	9.00000	0.825029
$120$	0	0
$121$	14.0000	1.27273
$122$	0	0
$123$	20.0000	1.80334
$124$	0	0
$125$	9.00000	0.804984
$126$	0	0
$127$	−6.00000	−0.532414	−0.266207	−	0.963916i	$-0.585770\pi$
$127$	−6.00000	−0.532414	−0.266207	+	0.963916i	$0.585770\pi$
$128$	0	0
$129$	−2.00000	−0.176090
$130$	0	0
$131$	−9.00000	−0.786334	−0.393167	−	0.919467i	$-0.628621\pi$
$131$	−9.00000	−0.786334	−0.393167	+	0.919467i	$0.628621\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	−4.00000	−0.344265
$136$	0	0
$137$	−11.0000	−0.939793	−0.469897	−	0.882721i	$-0.655709\pi$
$137$	−11.0000	−0.939793	−0.469897	+	0.882721i	$0.655709\pi$
$138$	0	0
$139$	−3.00000	−0.254457	−0.127228	−	0.991873i	$-0.540608\pi$
$139$	−3.00000	−0.254457	−0.127228	+	0.991873i	$0.540608\pi$
$140$	0	0
$141$	2.00000	0.168430
$142$	0	0
$143$	20.0000	1.67248
$144$	0	0
$145$	−2.00000	−0.166091
$146$	0	0
$147$	−4.00000	−0.329914
$148$	0	0
$149$	−15.0000	−1.22885	−0.614424	−	0.788976i	$-0.710612\pi$
$149$	−15.0000	−1.22885	−0.614424	+	0.788976i	$0.710612\pi$
$150$	0	0
$151$	−2.00000	−0.162758	−0.0813788	−	0.996683i	$-0.525932\pi$
$151$	−2.00000	−0.162758	−0.0813788	+	0.996683i	$0.525932\pi$
$152$	0	0
$153$	−3.00000	−0.242536
$154$	0	0
$155$	4.00000	0.321288
$156$	0	0
$157$	−2.00000	−0.159617	−0.0798087	−	0.996810i	$-0.525431\pi$
$157$	−2.00000	−0.159617	−0.0798087	+	0.996810i	$0.525431\pi$
$158$	0	0
$159$	−8.00000	−0.634441
$160$	0	0
$161$	−24.0000	−1.89146
$162$	0	0
$163$	−4.00000	−0.313304	−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000	−0.313304	−0.156652	+	0.987654i	$0.550070\pi$
$164$	0	0
$165$	10.0000	0.778499
$166$	0	0
$167$	6.00000	0.464294	0.232147	−	0.972681i	$-0.425425\pi$
$167$	6.00000	0.464294	0.232147	+	0.972681i	$0.425425\pi$
$168$	0	0
$169$	3.00000	0.230769
$170$	0	0
$171$	0	0
$172$	0	0
$173$	−6.00000	−0.456172	−0.228086	−	0.973641i	$-0.573247\pi$
$173$	−6.00000	−0.456172	−0.228086	+	0.973641i	$0.573247\pi$
$174$	0	0
$175$	12.0000	0.907115
$176$	0	0
$177$	12.0000	0.901975
$178$	0	0
$179$	−18.0000	−1.34538	−0.672692	−	0.739923i	$-0.734862\pi$
$179$	−18.0000	−1.34538	−0.672692	+	0.739923i	$0.734862\pi$
$180$	0	0
$181$	−10.0000	−0.743294	−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000	−0.743294	−0.371647	+	0.928374i	$0.621207\pi$
$182$	0	0
$183$	26.0000	1.92198
$184$	0	0
$185$	10.0000	0.735215
$186$	0	0
$187$	−15.0000	−1.09691
$188$	0	0
$189$	−12.0000	−0.872872
$190$	0	0
$191$	25.0000	1.80894	0.904468	−	0.426541i	$-0.140268\pi$
$191$	25.0000	1.80894	0.904468	+	0.426541i	$0.140268\pi$
$192$	0	0
$193$	−12.0000	−0.863779	−0.431889	−	0.901927i	$-0.642153\pi$
$193$	−12.0000	−0.863779	−0.431889	+	0.901927i	$0.642153\pi$
$194$	0	0
$195$	8.00000	0.572892
$196$	0	0
$197$	2.00000	0.142494	0.0712470	−	0.997459i	$-0.477302\pi$
$197$	2.00000	0.142494	0.0712470	+	0.997459i	$0.477302\pi$
$198$	0	0
$199$	−7.00000	−0.496217	−0.248108	−	0.968732i	$-0.579809\pi$
$199$	−7.00000	−0.496217	−0.248108	+	0.968732i	$0.579809\pi$
$200$	0	0
$201$	−24.0000	−1.69283
$202$	0	0
$203$	−6.00000	−0.421117
$204$	0	0
$205$	10.0000	0.698430
$206$	0	0
$207$	8.00000	0.556038
$208$	0	0
$209$	0	0
$210$	0	0
$211$	−18.0000	−1.23917	−0.619586	−	0.784929i	$-0.712699\pi$
$211$	−18.0000	−1.23917	−0.619586	+	0.784929i	$0.712699\pi$
$212$	0	0
$213$	4.00000	0.274075
$214$	0	0
$215$	−1.00000	−0.0681994
$216$	0	0
$217$	12.0000	0.814613
$218$	0	0
$219$	−18.0000	−1.21633
$220$	0	0
$221$	−12.0000	−0.807207
$222$	0	0
$223$	−2.00000	−0.133930	−0.0669650	−	0.997755i	$-0.521332\pi$
$223$	−2.00000	−0.133930	−0.0669650	+	0.997755i	$0.521332\pi$
$224$	0	0
$225$	−4.00000	−0.266667
$226$	0	0
$227$	−4.00000	−0.265489	−0.132745	−	0.991150i	$-0.542379\pi$
$227$	−4.00000	−0.265489	−0.132745	+	0.991150i	$0.542379\pi$
$228$	0	0
$229$	17.0000	1.12339	0.561696	−	0.827344i	$-0.310149\pi$
$229$	17.0000	1.12339	0.561696	+	0.827344i	$0.310149\pi$
$230$	0	0
$231$	30.0000	1.97386
$232$	0	0
$233$	3.00000	0.196537	0.0982683	−	0.995160i	$-0.468670\pi$
$233$	3.00000	0.196537	0.0982683	+	0.995160i	$0.468670\pi$
$234$	0	0
$235$	1.00000	0.0652328
$236$	0	0
$237$	16.0000	1.03931
$238$	0	0
$239$	21.0000	1.35838	0.679189	−	0.733964i	$-0.262332\pi$
$239$	21.0000	1.35838	0.679189	+	0.733964i	$0.262332\pi$
$240$	0	0
$241$	26.0000	1.67481	0.837404	−	0.546585i	$-0.184072\pi$
$241$	26.0000	1.67481	0.837404	+	0.546585i	$0.184072\pi$
$242$	0	0
$243$	10.0000	0.641500
$244$	0	0
$245$	−2.00000	−0.127775
$246$	0	0
$247$	0	0
$248$	0	0
$249$	24.0000	1.52094
$250$	0	0
$251$	11.0000	0.694314	0.347157	−	0.937807i	$-0.387147\pi$
$251$	11.0000	0.694314	0.347157	+	0.937807i	$0.387147\pi$
$252$	0	0
$253$	40.0000	2.51478
$254$	0	0
$255$	−6.00000	−0.375735
$256$	0	0
$257$	−32.0000	−1.99611	−0.998053	−	0.0623783i	$-0.980131\pi$
$257$	−32.0000	−1.99611	−0.998053	+	0.0623783i	$0.980131\pi$
$258$	0	0
$259$	30.0000	1.86411
$260$	0	0
$261$	2.00000	0.123797
$262$	0	0
$263$	−21.0000	−1.29492	−0.647458	−	0.762101i	$-0.724168\pi$
$263$	−21.0000	−1.29492	−0.647458	+	0.762101i	$0.724168\pi$
$264$	0	0
$265$	−4.00000	−0.245718
$266$	0	0
$267$	24.0000	1.46878
$268$	0	0
$269$	24.0000	1.46331	0.731653	−	0.681677i	$-0.238749\pi$
$269$	24.0000	1.46331	0.731653	+	0.681677i	$0.238749\pi$
$270$	0	0
$271$	−8.00000	−0.485965	−0.242983	−	0.970031i	$-0.578126\pi$
$271$	−8.00000	−0.485965	−0.242983	+	0.970031i	$0.578126\pi$
$272$	0	0
$273$	24.0000	1.45255
$274$	0	0
$275$	−20.0000	−1.20605
$276$	0	0
$277$	1.00000	0.0600842	0.0300421	−	0.999549i	$-0.490436\pi$
$277$	1.00000	0.0600842	0.0300421	+	0.999549i	$0.490436\pi$
$278$	0	0
$279$	−4.00000	−0.239474
$280$	0	0
$281$	−22.0000	−1.31241	−0.656205	−	0.754583i	$-0.727839\pi$
$281$	−22.0000	−1.31241	−0.656205	+	0.754583i	$0.727839\pi$
$282$	0	0
$283$	−3.00000	−0.178331	−0.0891657	−	0.996017i	$-0.528420\pi$
$283$	−3.00000	−0.178331	−0.0891657	+	0.996017i	$0.528420\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	30.0000	1.77084
$288$	0	0
$289$	−8.00000	−0.470588
$290$	0	0
$291$	−16.0000	−0.937937
$292$	0	0
$293$	12.0000	0.701047	0.350524	−	0.936554i	$-0.386004\pi$
$293$	12.0000	0.701047	0.350524	+	0.936554i	$0.386004\pi$
$294$	0	0
$295$	6.00000	0.349334
$296$	0	0
$297$	20.0000	1.16052
$298$	0	0
$299$	32.0000	1.85061
$300$	0	0
$301$	−3.00000	−0.172917
$302$	0	0
$303$	20.0000	1.14897
$304$	0	0
$305$	13.0000	0.744378
$306$	0	0
$307$	−12.0000	−0.684876	−0.342438	−	0.939540i	$-0.611253\pi$
$307$	−12.0000	−0.684876	−0.342438	+	0.939540i	$0.611253\pi$
$308$	0	0
$309$	−12.0000	−0.682656
$310$	0	0
$311$	7.00000	0.396934	0.198467	−	0.980108i	$-0.436404\pi$
$311$	7.00000	0.396934	0.198467	+	0.980108i	$0.436404\pi$
$312$	0	0
$313$	−10.0000	−0.565233	−0.282617	−	0.959233i	$-0.591202\pi$
$313$	−10.0000	−0.565233	−0.282617	+	0.959233i	$0.591202\pi$
$314$	0	0
$315$	3.00000	0.169031
$316$	0	0
$317$	−30.0000	−1.68497	−0.842484	−	0.538721i	$-0.818908\pi$
$317$	−30.0000	−1.68497	−0.842484	+	0.538721i	$0.818908\pi$
$318$	0	0
$319$	10.0000	0.559893
$320$	0	0
$321$	4.00000	0.223258
$322$	0	0
$323$	0	0
$324$	0	0
$325$	−16.0000	−0.887520
$326$	0	0
$327$	0	0
$328$	0	0
$329$	3.00000	0.165395
$330$	0	0
$331$	4.00000	0.219860	0.109930	−	0.993939i	$-0.464937\pi$
$331$	4.00000	0.219860	0.109930	+	0.993939i	$0.464937\pi$
$332$	0	0
$333$	−10.0000	−0.547997
$334$	0	0
$335$	−12.0000	−0.655630
$336$	0	0
$337$	32.0000	1.74315	0.871576	−	0.490261i	$-0.163099\pi$
$337$	32.0000	1.74315	0.871576	+	0.490261i	$0.163099\pi$
$338$	0	0
$339$	−20.0000	−1.08625
$340$	0	0
$341$	−20.0000	−1.08306
$342$	0	0
$343$	15.0000	0.809924
$344$	0	0
$345$	16.0000	0.861411
$346$	0	0
$347$	19.0000	1.01997	0.509987	−	0.860182i	$-0.329650\pi$
$347$	19.0000	1.01997	0.509987	+	0.860182i	$0.329650\pi$
$348$	0	0
$349$	−11.0000	−0.588817	−0.294408	−	0.955680i	$-0.595123\pi$
$349$	−11.0000	−0.588817	−0.294408	+	0.955680i	$0.595123\pi$
$350$	0	0
$351$	16.0000	0.854017
$352$	0	0
$353$	−6.00000	−0.319348	−0.159674	−	0.987170i	$-0.551044\pi$
$353$	−6.00000	−0.319348	−0.159674	+	0.987170i	$0.551044\pi$
$354$	0	0
$355$	2.00000	0.106149
$356$	0	0
$357$	−18.0000	−0.952661
$358$	0	0
$359$	21.0000	1.10834	0.554169	−	0.832404i	$-0.313036\pi$
$359$	21.0000	1.10834	0.554169	+	0.832404i	$0.313036\pi$
$360$	0	0
$361$	0	0
$362$	0	0
$363$	−28.0000	−1.46962
$364$	0	0
$365$	−9.00000	−0.471082
$366$	0	0
$367$	16.0000	0.835193	0.417597	−	0.908633i	$-0.362873\pi$
$367$	16.0000	0.835193	0.417597	+	0.908633i	$0.362873\pi$
$368$	0	0
$369$	−10.0000	−0.520579
$370$	0	0
$371$	−12.0000	−0.623009
$372$	0	0
$373$	4.00000	0.207112	0.103556	−	0.994624i	$-0.466978\pi$
$373$	4.00000	0.207112	0.103556	+	0.994624i	$0.466978\pi$
$374$	0	0
$375$	−18.0000	−0.929516
$376$	0	0
$377$	8.00000	0.412021
$378$	0	0
$379$	30.0000	1.54100	0.770498	−	0.637442i	$-0.220007\pi$
$379$	30.0000	1.54100	0.770498	+	0.637442i	$0.220007\pi$
$380$	0	0
$381$	12.0000	0.614779
$382$	0	0
$383$	−4.00000	−0.204390	−0.102195	−	0.994764i	$-0.532587\pi$
$383$	−4.00000	−0.204390	−0.102195	+	0.994764i	$0.532587\pi$
$384$	0	0
$385$	15.0000	0.764471
$386$	0	0
$387$	1.00000	0.0508329
$388$	0	0
$389$	−21.0000	−1.06474	−0.532371	−	0.846511i	$-0.678699\pi$
$389$	−21.0000	−1.06474	−0.532371	+	0.846511i	$0.678699\pi$
$390$	0	0
$391$	−24.0000	−1.21373
$392$	0	0
$393$	18.0000	0.907980
$394$	0	0
$395$	8.00000	0.402524
$396$	0	0
$397$	5.00000	0.250943	0.125471	−	0.992097i	$-0.459956\pi$
$397$	5.00000	0.250943	0.125471	+	0.992097i	$0.459956\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	−28.0000	−1.39825	−0.699127	−	0.714998i	$-0.746428\pi$
$401$	−28.0000	−1.39825	−0.699127	+	0.714998i	$0.746428\pi$
$402$	0	0
$403$	−16.0000	−0.797017
$404$	0	0
$405$	11.0000	0.546594
$406$	0	0
$407$	−50.0000	−2.47841
$408$	0	0
$409$	20.0000	0.988936	0.494468	−	0.869196i	$-0.335363\pi$
$409$	20.0000	0.988936	0.494468	+	0.869196i	$0.335363\pi$
$410$	0	0
$411$	22.0000	1.08518
$412$	0	0
$413$	18.0000	0.885722
$414$	0	0
$415$	12.0000	0.589057
$416$	0	0
$417$	6.00000	0.293821
$418$	0	0
$419$	−36.0000	−1.75872	−0.879358	−	0.476162i	$-0.842028\pi$
$419$	−36.0000	−1.75872	−0.879358	+	0.476162i	$0.842028\pi$
$420$	0	0
$421$	40.0000	1.94948	0.974740	−	0.223341i	$-0.0716964\pi$
$421$	40.0000	1.94948	0.974740	+	0.223341i	$0.0716964\pi$
$422$	0	0
$423$	−1.00000	−0.0486217
$424$	0	0
$425$	12.0000	0.582086
$426$	0	0
$427$	39.0000	1.88734
$428$	0	0
$429$	−40.0000	−1.93122
$430$	0	0
$431$	−24.0000	−1.15604	−0.578020	−	0.816023i	$-0.696174\pi$
$431$	−24.0000	−1.15604	−0.578020	+	0.816023i	$0.696174\pi$
$432$	0	0
$433$	−2.00000	−0.0961139	−0.0480569	−	0.998845i	$-0.515303\pi$
$433$	−2.00000	−0.0961139	−0.0480569	+	0.998845i	$0.515303\pi$
$434$	0	0
$435$	4.00000	0.191785
$436$	0	0
$437$	0	0
$438$	0	0
$439$	−2.00000	−0.0954548	−0.0477274	−	0.998860i	$-0.515198\pi$
$439$	−2.00000	−0.0954548	−0.0477274	+	0.998860i	$0.515198\pi$
$440$	0	0
$441$	2.00000	0.0952381
$442$	0	0
$443$	−5.00000	−0.237557	−0.118779	−	0.992921i	$-0.537898\pi$
$443$	−5.00000	−0.237557	−0.118779	+	0.992921i	$0.537898\pi$
$444$	0	0
$445$	12.0000	0.568855
$446$	0	0
$447$	30.0000	1.41895
$448$	0	0
$449$	−16.0000	−0.755087	−0.377543	−	0.925992i	$-0.623231\pi$
$449$	−16.0000	−0.755087	−0.377543	+	0.925992i	$0.623231\pi$
$450$	0	0
$451$	−50.0000	−2.35441
$452$	0	0
$453$	4.00000	0.187936
$454$	0	0
$455$	12.0000	0.562569
$456$	0	0
$457$	−13.0000	−0.608114	−0.304057	−	0.952654i	$-0.598341\pi$
$457$	−13.0000	−0.608114	−0.304057	+	0.952654i	$0.598341\pi$
$458$	0	0
$459$	−12.0000	−0.560112
$460$	0	0
$461$	−19.0000	−0.884918	−0.442459	−	0.896789i	$-0.645894\pi$
$461$	−19.0000	−0.884918	−0.442459	+	0.896789i	$0.645894\pi$
$462$	0	0
$463$	19.0000	0.883005	0.441502	−	0.897260i	$-0.354446\pi$
$463$	19.0000	0.883005	0.441502	+	0.897260i	$0.354446\pi$
$464$	0	0
$465$	−8.00000	−0.370991
$466$	0	0
$467$	−5.00000	−0.231372	−0.115686	−	0.993286i	$-0.536907\pi$
$467$	−5.00000	−0.231372	−0.115686	+	0.993286i	$0.536907\pi$
$468$	0	0
$469$	−36.0000	−1.66233
$470$	0	0
$471$	4.00000	0.184310
$472$	0	0
$473$	5.00000	0.229900
$474$	0	0
$475$	0	0
$476$	0	0
$477$	4.00000	0.183147
$478$	0	0
$479$	4.00000	0.182765	0.0913823	−	0.995816i	$-0.470871\pi$
$479$	4.00000	0.182765	0.0913823	+	0.995816i	$0.470871\pi$
$480$	0	0
$481$	−40.0000	−1.82384
$482$	0	0
$483$	48.0000	2.18408
$484$	0	0
$485$	−8.00000	−0.363261
$486$	0	0
$487$	26.0000	1.17817	0.589086	−	0.808070i	$-0.299488\pi$
$487$	26.0000	1.17817	0.589086	+	0.808070i	$0.299488\pi$
$488$	0	0
$489$	8.00000	0.361773
$490$	0	0
$491$	−28.0000	−1.26362	−0.631811	−	0.775122i	$-0.717688\pi$
$491$	−28.0000	−1.26362	−0.631811	+	0.775122i	$0.717688\pi$
$492$	0	0
$493$	−6.00000	−0.270226
$494$	0	0
$495$	−5.00000	−0.224733
$496$	0	0
$497$	6.00000	0.269137
$498$	0	0
$499$	19.0000	0.850557	0.425278	−	0.905063i	$-0.360176\pi$
$499$	19.0000	0.850557	0.425278	+	0.905063i	$0.360176\pi$
$500$	0	0
$501$	−12.0000	−0.536120
$502$	0	0
$503$	−36.0000	−1.60516	−0.802580	−	0.596544i	$-0.796540\pi$
$503$	−36.0000	−1.60516	−0.802580	+	0.596544i	$0.796540\pi$
$504$	0	0
$505$	10.0000	0.444994
$506$	0	0
$507$	−6.00000	−0.266469
$508$	0	0
$509$	0	0		−	1.00000i	$-0.5\pi$
$509$	0	0			1.00000i	$0.5\pi$
$510$	0	0
$511$	−27.0000	−1.19441
$512$	0	0
$513$	0	0
$514$	0	0
$515$	−6.00000	−0.264392
$516$	0	0
$517$	−5.00000	−0.219900
$518$	0	0
$519$	12.0000	0.526742
$520$	0	0
$521$	−32.0000	−1.40195	−0.700973	−	0.713188i	$-0.747251\pi$
$521$	−32.0000	−1.40195	−0.700973	+	0.713188i	$0.747251\pi$
$522$	0	0
$523$	−26.0000	−1.13690	−0.568450	−	0.822718i	$-0.692457\pi$
$523$	−26.0000	−1.13690	−0.568450	+	0.822718i	$0.692457\pi$
$524$	0	0
$525$	−24.0000	−1.04745
$526$	0	0
$527$	12.0000	0.522728
$528$	0	0
$529$	41.0000	1.78261
$530$	0	0
$531$	−6.00000	−0.260378
$532$	0	0
$533$	−40.0000	−1.73259
$534$	0	0
$535$	2.00000	0.0864675
$536$	0	0
$537$	36.0000	1.55351
$538$	0	0
$539$	10.0000	0.430730
$540$	0	0
$541$	11.0000	0.472927	0.236463	−	0.971640i	$-0.424012\pi$
$541$	11.0000	0.472927	0.236463	+	0.971640i	$0.424012\pi$
$542$	0	0
$543$	20.0000	0.858282
$544$	0	0
$545$	0	0
$546$	0	0
$547$	−28.0000	−1.19719	−0.598597	−	0.801050i	$-0.704275\pi$
$547$	−28.0000	−1.19719	−0.598597	+	0.801050i	$0.704275\pi$
$548$	0	0
$549$	−13.0000	−0.554826
$550$	0	0
$551$	0	0
$552$	0	0
$553$	24.0000	1.02058
$554$	0	0
$555$	−20.0000	−0.848953
$556$	0	0
$557$	1.00000	0.0423714	0.0211857	−	0.999776i	$-0.493256\pi$
$557$	1.00000	0.0423714	0.0211857	+	0.999776i	$0.493256\pi$
$558$	0	0
$559$	4.00000	0.169182
$560$	0	0
$561$	30.0000	1.26660
$562$	0	0
$563$	−42.0000	−1.77009	−0.885044	−	0.465506i	$-0.845872\pi$
$563$	−42.0000	−1.77009	−0.885044	+	0.465506i	$0.845872\pi$
$564$	0	0
$565$	−10.0000	−0.420703
$566$	0	0
$567$	33.0000	1.38587
$568$	0	0
$569$	8.00000	0.335377	0.167689	−	0.985840i	$-0.446370\pi$
$569$	8.00000	0.335377	0.167689	+	0.985840i	$0.446370\pi$
$570$	0	0
$571$	20.0000	0.836974	0.418487	−	0.908223i	$-0.362561\pi$
$571$	20.0000	0.836974	0.418487	+	0.908223i	$0.362561\pi$
$572$	0	0
$573$	−50.0000	−2.08878
$574$	0	0
$575$	−32.0000	−1.33449
$576$	0	0
$577$	−13.0000	−0.541197	−0.270599	−	0.962692i	$-0.587222\pi$
$577$	−13.0000	−0.541197	−0.270599	+	0.962692i	$0.587222\pi$
$578$	0	0
$579$	24.0000	0.997406
$580$	0	0
$581$	36.0000	1.49353
$582$	0	0
$583$	20.0000	0.828315
$584$	0	0
$585$	−4.00000	−0.165380
$586$	0	0
$587$	3.00000	0.123823	0.0619116	−	0.998082i	$-0.480280\pi$
$587$	3.00000	0.123823	0.0619116	+	0.998082i	$0.480280\pi$
$588$	0	0
$589$	0	0
$590$	0	0
$591$	−4.00000	−0.164538
$592$	0	0
$593$	22.0000	0.903432	0.451716	−	0.892162i	$-0.350812\pi$
$593$	22.0000	0.903432	0.451716	+	0.892162i	$0.350812\pi$
$594$	0	0
$595$	−9.00000	−0.368964
$596$	0	0
$597$	14.0000	0.572982
$598$	0	0
$599$	12.0000	0.490307	0.245153	−	0.969484i	$-0.421162\pi$
$599$	12.0000	0.490307	0.245153	+	0.969484i	$0.421162\pi$
$600$	0	0
$601$	−10.0000	−0.407909	−0.203954	−	0.978980i	$-0.565379\pi$
$601$	−10.0000	−0.407909	−0.203954	+	0.978980i	$0.565379\pi$
$602$	0	0
$603$	12.0000	0.488678
$604$	0	0
$605$	−14.0000	−0.569181
$606$	0	0
$607$	−32.0000	−1.29884	−0.649420	−	0.760430i	$-0.724988\pi$
$607$	−32.0000	−1.29884	−0.649420	+	0.760430i	$0.724988\pi$
$608$	0	0
$609$	12.0000	0.486265
$610$	0	0
$611$	−4.00000	−0.161823
$612$	0	0
$613$	−47.0000	−1.89831	−0.949156	−	0.314806i	$-0.898061\pi$
$613$	−47.0000	−1.89831	−0.949156	+	0.314806i	$0.898061\pi$
$614$	0	0
$615$	−20.0000	−0.806478
$616$	0	0
$617$	9.00000	0.362326	0.181163	−	0.983453i	$-0.442014\pi$
$617$	9.00000	0.362326	0.181163	+	0.983453i	$0.442014\pi$
$618$	0	0
$619$	4.00000	0.160774	0.0803868	−	0.996764i	$-0.474384\pi$
$619$	4.00000	0.160774	0.0803868	+	0.996764i	$0.474384\pi$
$620$	0	0
$621$	32.0000	1.28412
$622$	0	0
$623$	36.0000	1.44231
$624$	0	0
$625$	11.0000	0.440000
$626$	0	0
$627$	0	0
$628$	0	0
$629$	30.0000	1.19618
$630$	0	0
$631$	−7.00000	−0.278666	−0.139333	−	0.990246i	$-0.544496\pi$
$631$	−7.00000	−0.278666	−0.139333	+	0.990246i	$0.544496\pi$
$632$	0	0
$633$	36.0000	1.43087
$634$	0	0
$635$	6.00000	0.238103
$636$	0	0
$637$	8.00000	0.316972
$638$	0	0
$639$	−2.00000	−0.0791188
$640$	0	0
$641$	0	0		−	1.00000i	$-0.5\pi$
$641$	0	0			1.00000i	$0.5\pi$
$642$	0	0
$643$	−11.0000	−0.433798	−0.216899	−	0.976194i	$-0.569594\pi$
$643$	−11.0000	−0.433798	−0.216899	+	0.976194i	$0.569594\pi$
$644$	0	0
$645$	2.00000	0.0787499
$646$	0	0
$647$	−7.00000	−0.275198	−0.137599	−	0.990488i	$-0.543939\pi$
$647$	−7.00000	−0.275198	−0.137599	+	0.990488i	$0.543939\pi$
$648$	0	0
$649$	−30.0000	−1.17760
$650$	0	0
$651$	−24.0000	−0.940634
$652$	0	0
$653$	−27.0000	−1.05659	−0.528296	−	0.849060i	$-0.677169\pi$
$653$	−27.0000	−1.05659	−0.528296	+	0.849060i	$0.677169\pi$
$654$	0	0
$655$	9.00000	0.351659
$656$	0	0
$657$	9.00000	0.351123
$658$	0	0
$659$	34.0000	1.32445	0.662226	−	0.749304i	$-0.269612\pi$
$659$	34.0000	1.32445	0.662226	+	0.749304i	$0.269612\pi$
$660$	0	0
$661$	−16.0000	−0.622328	−0.311164	−	0.950356i	$-0.600719\pi$
$661$	−16.0000	−0.622328	−0.311164	+	0.950356i	$0.600719\pi$
$662$	0	0
$663$	24.0000	0.932083
$664$	0	0
$665$	0	0
$666$	0	0
$667$	16.0000	0.619522
$668$	0	0
$669$	4.00000	0.154649
$670$	0	0
$671$	−65.0000	−2.50930
$672$	0	0
$673$	10.0000	0.385472	0.192736	−	0.981251i	$-0.438264\pi$
$673$	10.0000	0.385472	0.192736	+	0.981251i	$0.438264\pi$
$674$	0	0
$675$	−16.0000	−0.615840
$676$	0	0
$677$	2.00000	0.0768662	0.0384331	−	0.999261i	$-0.487763\pi$
$677$	2.00000	0.0768662	0.0384331	+	0.999261i	$0.487763\pi$
$678$	0	0
$679$	−24.0000	−0.921035
$680$	0	0
$681$	8.00000	0.306561
$682$	0	0
$683$	20.0000	0.765279	0.382639	−	0.923898i	$-0.375015\pi$
$683$	20.0000	0.765279	0.382639	+	0.923898i	$0.375015\pi$
$684$	0	0
$685$	11.0000	0.420288
$686$	0	0
$687$	−34.0000	−1.29718
$688$	0	0
$689$	16.0000	0.609551
$690$	0	0
$691$	−33.0000	−1.25538	−0.627690	−	0.778464i	$-0.715999\pi$
$691$	−33.0000	−1.25538	−0.627690	+	0.778464i	$0.715999\pi$
$692$	0	0
$693$	−15.0000	−0.569803
$694$	0	0
$695$	3.00000	0.113796
$696$	0	0
$697$	30.0000	1.13633
$698$	0	0
$699$	−6.00000	−0.226941
$700$	0	0
$701$	−10.0000	−0.377695	−0.188847	−	0.982006i	$-0.560475\pi$
$701$	−10.0000	−0.377695	−0.188847	+	0.982006i	$0.560475\pi$
$702$	0	0
$703$	0	0
$704$	0	0
$705$	−2.00000	−0.0753244
$706$	0	0
$707$	30.0000	1.12827
$708$	0	0
$709$	−6.00000	−0.225335	−0.112667	−	0.993633i	$-0.535939\pi$
$709$	−6.00000	−0.225335	−0.112667	+	0.993633i	$0.535939\pi$
$710$	0	0
$711$	−8.00000	−0.300023
$712$	0	0
$713$	−32.0000	−1.19841
$714$	0	0
$715$	−20.0000	−0.747958
$716$	0	0
$717$	−42.0000	−1.56852
$718$	0	0
$719$	13.0000	0.484818	0.242409	−	0.970174i	$-0.422062\pi$
$719$	13.0000	0.484818	0.242409	+	0.970174i	$0.422062\pi$
$720$	0	0
$721$	−18.0000	−0.670355
$722$	0	0
$723$	−52.0000	−1.93390
$724$	0	0
$725$	−8.00000	−0.297113
$726$	0	0
$727$	7.00000	0.259616	0.129808	−	0.991539i	$-0.458564\pi$
$727$	7.00000	0.259616	0.129808	+	0.991539i	$0.458564\pi$
$728$	0	0
$729$	13.0000	0.481481
$730$	0	0
$731$	−3.00000	−0.110959
$732$	0	0
$733$	−6.00000	−0.221615	−0.110808	−	0.993842i	$-0.535344\pi$
$733$	−6.00000	−0.221615	−0.110808	+	0.993842i	$0.535344\pi$
$734$	0	0
$735$	4.00000	0.147542
$736$	0	0
$737$	60.0000	2.21013
$738$	0	0
$739$	−43.0000	−1.58178	−0.790890	−	0.611958i	$-0.790382\pi$
$739$	−43.0000	−1.58178	−0.790890	+	0.611958i	$0.790382\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	40.0000	1.46746	0.733729	−	0.679442i	$-0.237778\pi$
$743$	40.0000	1.46746	0.733729	+	0.679442i	$0.237778\pi$
$744$	0	0
$745$	15.0000	0.549557
$746$	0	0
$747$	−12.0000	−0.439057
$748$	0	0
$749$	6.00000	0.219235
$750$	0	0
$751$	16.0000	0.583848	0.291924	−	0.956441i	$-0.405705\pi$
$751$	16.0000	0.583848	0.291924	+	0.956441i	$0.405705\pi$
$752$	0	0
$753$	−22.0000	−0.801725
$754$	0	0
$755$	2.00000	0.0727875
$756$	0	0
$757$	−5.00000	−0.181728	−0.0908640	−	0.995863i	$-0.528963\pi$
$757$	−5.00000	−0.181728	−0.0908640	+	0.995863i	$0.528963\pi$
$758$	0	0
$759$	−80.0000	−2.90382
$760$	0	0
$761$	9.00000	0.326250	0.163125	−	0.986605i	$-0.447843\pi$
$761$	9.00000	0.326250	0.163125	+	0.986605i	$0.447843\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	3.00000	0.108465
$766$	0	0
$767$	−24.0000	−0.866590
$768$	0	0
$769$	31.0000	1.11789	0.558944	−	0.829205i	$-0.311207\pi$
$769$	31.0000	1.11789	0.558944	+	0.829205i	$0.311207\pi$
$770$	0	0
$771$	64.0000	2.30490
$772$	0	0
$773$	−18.0000	−0.647415	−0.323708	−	0.946157i	$-0.604929\pi$
$773$	−18.0000	−0.647415	−0.323708	+	0.946157i	$0.604929\pi$
$774$	0	0
$775$	16.0000	0.574737
$776$	0	0
$777$	−60.0000	−2.15249
$778$	0	0
$779$	0	0
$780$	0	0
$781$	−10.0000	−0.357828
$782$	0	0
$783$	8.00000	0.285897
$784$	0	0
$785$	2.00000	0.0713831
$786$	0	0
$787$	−4.00000	−0.142585	−0.0712923	−	0.997455i	$-0.522712\pi$
$787$	−4.00000	−0.142585	−0.0712923	+	0.997455i	$0.522712\pi$
$788$	0	0
$789$	42.0000	1.49524
$790$	0	0
$791$	−30.0000	−1.06668
$792$	0	0
$793$	−52.0000	−1.84657
$794$	0	0
$795$	8.00000	0.283731
$796$	0	0
$797$	12.0000	0.425062	0.212531	−	0.977154i	$-0.431829\pi$
$797$	12.0000	0.425062	0.212531	+	0.977154i	$0.431829\pi$
$798$	0	0
$799$	3.00000	0.106132
$800$	0	0
$801$	−12.0000	−0.423999
$802$	0	0
$803$	45.0000	1.58802
$804$	0	0
$805$	24.0000	0.845889
$806$	0	0
$807$	−48.0000	−1.68968
$808$	0	0
$809$	39.0000	1.37117	0.685583	−	0.727994i	$-0.259547\pi$
$809$	39.0000	1.37117	0.685583	+	0.727994i	$0.259547\pi$
$810$	0	0
$811$	0	0		−	1.00000i	$-0.5\pi$
$811$	0	0			1.00000i	$0.5\pi$
$812$	0	0
$813$	16.0000	0.561144
$814$	0	0
$815$	4.00000	0.140114
$816$	0	0
$817$	0	0
$818$	0	0
$819$	−12.0000	−0.419314
$820$	0	0
$821$	45.0000	1.57051	0.785255	−	0.619172i	$-0.212532\pi$
$821$	45.0000	1.57051	0.785255	+	0.619172i	$0.212532\pi$
$822$	0	0
$823$	53.0000	1.84746	0.923732	−	0.383040i	$-0.125123\pi$
$823$	53.0000	1.84746	0.923732	+	0.383040i	$0.125123\pi$
$824$	0	0
$825$	40.0000	1.39262
$826$	0	0
$827$	28.0000	0.973655	0.486828	−	0.873498i	$-0.338154\pi$
$827$	28.0000	0.973655	0.486828	+	0.873498i	$0.338154\pi$
$828$	0	0
$829$	48.0000	1.66711	0.833554	−	0.552437i	$-0.186302\pi$
$829$	48.0000	1.66711	0.833554	+	0.552437i	$0.186302\pi$
$830$	0	0
$831$	−2.00000	−0.0693792
$832$	0	0
$833$	−6.00000	−0.207888
$834$	0	0
$835$	−6.00000	−0.207639
$836$	0	0
$837$	−16.0000	−0.553041
$838$	0	0
$839$	10.0000	0.345238	0.172619	−	0.984989i	$-0.444777\pi$
$839$	10.0000	0.345238	0.172619	+	0.984989i	$0.444777\pi$
$840$	0	0
$841$	−25.0000	−0.862069
$842$	0	0
$843$	44.0000	1.51544
$844$	0	0
$845$	−3.00000	−0.103203
$846$	0	0
$847$	−42.0000	−1.44314
$848$	0	0
$849$	6.00000	0.205919
$850$	0	0
$851$	−80.0000	−2.74236
$852$	0	0
$853$	42.0000	1.43805	0.719026	−	0.694983i	$-0.244588\pi$
$853$	42.0000	1.43805	0.719026	+	0.694983i	$0.244588\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	−18.0000	−0.614868	−0.307434	−	0.951569i	$-0.599470\pi$
$857$	−18.0000	−0.614868	−0.307434	+	0.951569i	$0.599470\pi$
$858$	0	0
$859$	1.00000	0.0341196	0.0170598	−	0.999854i	$-0.494569\pi$
$859$	1.00000	0.0341196	0.0170598	+	0.999854i	$0.494569\pi$
$860$	0	0
$861$	−60.0000	−2.04479
$862$	0	0
$863$	−6.00000	−0.204242	−0.102121	−	0.994772i	$-0.532563\pi$
$863$	−6.00000	−0.204242	−0.102121	+	0.994772i	$0.532563\pi$
$864$	0	0
$865$	6.00000	0.204006
$866$	0	0
$867$	16.0000	0.543388
$868$	0	0
$869$	−40.0000	−1.35691
$870$	0	0
$871$	48.0000	1.62642
$872$	0	0
$873$	8.00000	0.270759
$874$	0	0
$875$	−27.0000	−0.912767
$876$	0	0
$877$	−34.0000	−1.14810	−0.574049	−	0.818821i	$-0.694628\pi$
$877$	−34.0000	−1.14810	−0.574049	+	0.818821i	$0.694628\pi$
$878$	0	0
$879$	−24.0000	−0.809500
$880$	0	0
$881$	−51.0000	−1.71823	−0.859117	−	0.511780i	$-0.828986\pi$
$881$	−51.0000	−1.71823	−0.859117	+	0.511780i	$0.828986\pi$
$882$	0	0
$883$	1.00000	0.0336527	0.0168263	−	0.999858i	$-0.494644\pi$
$883$	1.00000	0.0336527	0.0168263	+	0.999858i	$0.494644\pi$
$884$	0	0
$885$	−12.0000	−0.403376
$886$	0	0
$887$	−22.0000	−0.738688	−0.369344	−	0.929293i	$-0.620418\pi$
$887$	−22.0000	−0.738688	−0.369344	+	0.929293i	$0.620418\pi$
$888$	0	0
$889$	18.0000	0.603701
$890$	0	0
$891$	−55.0000	−1.84257
$892$	0	0
$893$	0	0
$894$	0	0
$895$	18.0000	0.601674
$896$	0	0
$897$	−64.0000	−2.13690
$898$	0	0
$899$	−8.00000	−0.266815
$900$	0	0
$901$	−12.0000	−0.399778
$902$	0	0
$903$	6.00000	0.199667
$904$	0	0
$905$	10.0000	0.332411
$906$	0	0
$907$	40.0000	1.32818	0.664089	−	0.747653i	$-0.268820\pi$
$907$	40.0000	1.32818	0.664089	+	0.747653i	$0.268820\pi$
$908$	0	0
$909$	−10.0000	−0.331679
$910$	0	0
$911$	18.0000	0.596367	0.298183	−	0.954509i	$-0.403619\pi$
$911$	18.0000	0.596367	0.298183	+	0.954509i	$0.403619\pi$
$912$	0	0
$913$	−60.0000	−1.98571
$914$	0	0
$915$	−26.0000	−0.859533
$916$	0	0
$917$	27.0000	0.891619
$918$	0	0
$919$	−28.0000	−0.923635	−0.461817	−	0.886975i	$-0.652802\pi$
$919$	−28.0000	−0.923635	−0.461817	+	0.886975i	$0.652802\pi$
$920$	0	0
$921$	24.0000	0.790827
$922$	0	0
$923$	−8.00000	−0.263323
$924$	0	0
$925$	40.0000	1.31519
$926$	0	0
$927$	6.00000	0.197066
$928$	0	0
$929$	14.0000	0.459325	0.229663	−	0.973270i	$-0.426238\pi$
$929$	14.0000	0.459325	0.229663	+	0.973270i	$0.426238\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	−14.0000	−0.458339
$934$	0	0
$935$	15.0000	0.490552
$936$	0	0
$937$	−31.0000	−1.01273	−0.506363	−	0.862320i	$-0.669010\pi$
$937$	−31.0000	−1.01273	−0.506363	+	0.862320i	$0.669010\pi$
$938$	0	0
$939$	20.0000	0.652675
$940$	0	0
$941$	26.0000	0.847576	0.423788	−	0.905761i	$-0.360700\pi$
$941$	26.0000	0.847576	0.423788	+	0.905761i	$0.360700\pi$
$942$	0	0
$943$	−80.0000	−2.60516
$944$	0	0
$945$	12.0000	0.390360
$946$	0	0
$947$	−12.0000	−0.389948	−0.194974	−	0.980808i	$-0.562462\pi$
$947$	−12.0000	−0.389948	−0.194974	+	0.980808i	$0.562462\pi$
$948$	0	0
$949$	36.0000	1.16861
$950$	0	0
$951$	60.0000	1.94563
$952$	0	0
$953$	16.0000	0.518291	0.259145	−	0.965838i	$-0.416559\pi$
$953$	16.0000	0.518291	0.259145	+	0.965838i	$0.416559\pi$
$954$	0	0
$955$	−25.0000	−0.808981
$956$	0	0
$957$	−20.0000	−0.646508
$958$	0	0
$959$	33.0000	1.06563
$960$	0	0
$961$	−15.0000	−0.483871
$962$	0	0
$963$	−2.00000	−0.0644491
$964$	0	0
$965$	12.0000	0.386294
$966$	0	0
$967$	48.0000	1.54358	0.771788	−	0.635880i	$-0.219363\pi$
$967$	48.0000	1.54358	0.771788	+	0.635880i	$0.219363\pi$
$968$	0	0
$969$	0	0
$970$	0	0
$971$	−20.0000	−0.641831	−0.320915	−	0.947108i	$-0.603990\pi$
$971$	−20.0000	−0.641831	−0.320915	+	0.947108i	$0.603990\pi$
$972$	0	0
$973$	9.00000	0.288527
$974$	0	0
$975$	32.0000	1.02482
$976$	0	0
$977$	−56.0000	−1.79160	−0.895799	−	0.444459i	$-0.853396\pi$
$977$	−56.0000	−1.79160	−0.895799	+	0.444459i	$0.853396\pi$
$978$	0	0
$979$	−60.0000	−1.91761
$980$	0	0
$981$	0	0
$982$	0	0
$983$	12.0000	0.382741	0.191370	−	0.981518i	$-0.438707\pi$
$983$	12.0000	0.382741	0.191370	+	0.981518i	$0.438707\pi$
$984$	0	0
$985$	−2.00000	−0.0637253
$986$	0	0
$987$	−6.00000	−0.190982
$988$	0	0
$989$	8.00000	0.254385
$990$	0	0
$991$	38.0000	1.20711	0.603555	−	0.797321i	$-0.293750\pi$
$991$	38.0000	1.20711	0.603555	+	0.797321i	$0.293750\pi$
$992$	0	0
$993$	−8.00000	−0.253872
$994$	0	0
$995$	7.00000	0.221915
$996$	0	0
$997$	37.0000	1.17180	0.585901	−	0.810383i	$-0.300741\pi$
$997$	37.0000	1.17180	0.585901	+	0.810383i	$0.300741\pi$
$998$	0	0
$999$	−40.0000	−1.26554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1444.2.a.a.1.1		1
4.3	odd	2		5776.2.a.p.1.1		1
19.7	even	3		1444.2.e.c.429.1		2
19.8	odd	6		1444.2.e.a.653.1		2
19.11	even	3		1444.2.e.c.653.1		2
19.12	odd	6		1444.2.e.a.429.1		2
19.18	odd	2		76.2.a.a.1.1	✓	1
57.56	even	2		684.2.a.b.1.1		1
76.75	even	2		304.2.a.a.1.1		1
95.18	even	4		1900.2.c.b.1749.2		2
95.37	even	4		1900.2.c.b.1749.1		2
95.94	odd	2		1900.2.a.b.1.1		1
133.132	even	2		3724.2.a.a.1.1		1
152.37	odd	2		1216.2.a.c.1.1		1
152.75	even	2		1216.2.a.q.1.1		1
209.208	even	2		9196.2.a.f.1.1		1
228.227	odd	2		2736.2.a.q.1.1		1
380.379	even	2		7600.2.a.p.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.2.a.a.1.1	✓	1	19.18	odd	2
304.2.a.a.1.1		1	76.75	even	2
684.2.a.b.1.1		1	57.56	even	2
1216.2.a.c.1.1		1	152.37	odd	2
1216.2.a.q.1.1		1	152.75	even	2
1444.2.a.a.1.1		1	1.1	even	1	trivial
1444.2.e.a.429.1		2	19.12	odd	6
1444.2.e.a.653.1		2	19.8	odd	6
1444.2.e.c.429.1		2	19.7	even	3
1444.2.e.c.653.1		2	19.11	even	3
1900.2.a.b.1.1		1	95.94	odd	2
1900.2.c.b.1749.1		2	95.37	even	4
1900.2.c.b.1749.2		2	95.18	even	4
2736.2.a.q.1.1		1	228.227	odd	2
3724.2.a.a.1.1		1	133.132	even	2
5776.2.a.p.1.1		1	4.3	odd	2
7600.2.a.p.1.1		1	380.379	even	2
9196.2.a.f.1.1		1	209.208	even	2

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:	\( N \)	\(=\)	\( 1444 = 2^{2} \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1444.a (trivial)

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