LMFDB - Embedded newform 1449.2.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1449,2,Mod(1,1449)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1449, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("1449.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1449 = 3^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1449.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:	$11.5703232529$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 483)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1449.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-2.00000 q^{2} +2.00000 q^{4} -4.00000 q^{5} -1.00000 q^{7} +O(q^{10})$

$q-2.00000 q^{2} +2.00000 q^{4} -4.00000 q^{5} -1.00000 q^{7} +8.00000 q^{10} +5.00000 q^{11} -2.00000 q^{13} +2.00000 q^{14} -4.00000 q^{16} -5.00000 q^{19} -8.00000 q^{20} -10.0000 q^{22} +1.00000 q^{23} +11.0000 q^{25} +4.00000 q^{26} -2.00000 q^{28} +2.00000 q^{29} +6.00000 q^{31} +8.00000 q^{32} +4.00000 q^{35} +6.00000 q^{37} +10.0000 q^{38} -5.00000 q^{41} +8.00000 q^{43} +10.0000 q^{44} -2.00000 q^{46} +9.00000 q^{47} +1.00000 q^{49} -22.0000 q^{50} -4.00000 q^{52} -9.00000 q^{53} -20.0000 q^{55} -4.00000 q^{58} -9.00000 q^{59} -5.00000 q^{61} -12.0000 q^{62} -8.00000 q^{64} +8.00000 q^{65} +4.00000 q^{67} -8.00000 q^{70} -12.0000 q^{71} -12.0000 q^{74} -10.0000 q^{76} -5.00000 q^{77} -10.0000 q^{79} +16.0000 q^{80} +10.0000 q^{82} +18.0000 q^{83} -16.0000 q^{86} -10.0000 q^{89} +2.00000 q^{91} +2.00000 q^{92} -18.0000 q^{94} +20.0000 q^{95} -18.0000 q^{97} -2.00000 q^{98} +O(q^{100})$

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 $

$2$	−2.00000	−1.41421	−0.707107	−	0.707107i	$-0.750000\pi$
$2$	−2.00000	−1.41421	−0.707107	+	0.707107i	$0.750000\pi$
$3$	0	0
$3$	0	0
$4$	2.00000	1.00000
$5$	−4.00000	−1.78885	−0.894427	−	0.447214i	$-0.852416\pi$
$5$	−4.00000	−1.78885	−0.894427	+	0.447214i	$0.852416\pi$
$6$	0	0
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	0	0
$9$	0	0
$10$	8.00000	2.52982
$11$	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
$13$	−2.00000	−0.554700	−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000	−0.554700	−0.277350	+	0.960769i	$0.589456\pi$
$14$	2.00000	0.534522
$15$	0	0
$16$	−4.00000	−1.00000
$17$	0	0		−	1.00000i	$-0.5\pi$
$17$	0	0			1.00000i	$0.5\pi$
$18$	0	0
$19$	−5.00000	−1.14708	−0.573539	−	0.819178i	$-0.694430\pi$
$19$	−5.00000	−1.14708	−0.573539	+	0.819178i	$0.694430\pi$
$20$	−8.00000	−1.78885
$21$	0	0
$22$	−10.0000	−2.13201
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	0	0
$25$	11.0000	2.20000
$26$	4.00000	0.784465
$27$	0	0
$28$	−2.00000	−0.377964
$29$	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
$31$	6.00000	1.07763	0.538816	−	0.842424i	$-0.318872\pi$
$31$	6.00000	1.07763	0.538816	+	0.842424i	$0.318872\pi$
$32$	8.00000	1.41421
$33$	0	0
$34$	0	0
$35$	4.00000	0.676123
$36$	0	0
$37$	6.00000	0.986394	0.493197	−	0.869918i	$-0.335828\pi$
$37$	6.00000	0.986394	0.493197	+	0.869918i	$0.335828\pi$
$38$	10.0000	1.62221
$39$	0	0
$40$	0	0
$41$	−5.00000	−0.780869	−0.390434	−	0.920631i	$-0.627675\pi$
$41$	−5.00000	−0.780869	−0.390434	+	0.920631i	$0.627675\pi$
$42$	0	0
$43$	8.00000	1.21999	0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000	1.21999	0.609994	+	0.792406i	$0.291172\pi$
$44$	10.0000	1.50756
$45$	0	0
$46$	−2.00000	−0.294884
$47$	9.00000	1.31278	0.656392	−	0.754420i	$-0.272082\pi$
$47$	9.00000	1.31278	0.656392	+	0.754420i	$0.272082\pi$
$48$	0	0
$49$	1.00000	0.142857
$50$	−22.0000	−3.11127
$51$	0	0
$52$	−4.00000	−0.554700
$53$	−9.00000	−1.23625	−0.618123	−	0.786082i	$-0.712106\pi$
$53$	−9.00000	−1.23625	−0.618123	+	0.786082i	$0.712106\pi$
$54$	0	0
$55$	−20.0000	−2.69680
$56$	0	0
$57$	0	0
$58$	−4.00000	−0.525226
$59$	−9.00000	−1.17170	−0.585850	−	0.810419i	$-0.699239\pi$
$59$	−9.00000	−1.17170	−0.585850	+	0.810419i	$0.699239\pi$
$60$	0	0
$61$	−5.00000	−0.640184	−0.320092	−	0.947386i	$-0.603714\pi$
$61$	−5.00000	−0.640184	−0.320092	+	0.947386i	$0.603714\pi$
$62$	−12.0000	−1.52400
$63$	0	0
$64$	−8.00000	−1.00000
$65$	8.00000	0.992278
$66$	0	0
$67$	4.00000	0.488678	0.244339	−	0.969690i	$-0.421429\pi$
$67$	4.00000	0.488678	0.244339	+	0.969690i	$0.421429\pi$
$68$	0	0
$69$	0	0
$70$	−8.00000	−0.956183
$71$	−12.0000	−1.42414	−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000	−1.42414	−0.712069	+	0.702109i	$0.752242\pi$
$72$	0	0
$73$	0	0		−	1.00000i	$-0.5\pi$
$73$	0	0			1.00000i	$0.5\pi$
$74$	−12.0000	−1.39497
$75$	0	0
$76$	−10.0000	−1.14708
$77$	−5.00000	−0.569803
$78$	0	0
$79$	−10.0000	−1.12509	−0.562544	−	0.826767i	$-0.690177\pi$
$79$	−10.0000	−1.12509	−0.562544	+	0.826767i	$0.690177\pi$
$80$	16.0000	1.78885
$81$	0	0
$82$	10.0000	1.10432
$83$	18.0000	1.97576	0.987878	−	0.155230i	$-0.0496119\pi$
$83$	18.0000	1.97576	0.987878	+	0.155230i	$0.0496119\pi$
$84$	0	0
$85$	0	0
$86$	−16.0000	−1.72532
$87$	0	0
$88$	0	0
$89$	−10.0000	−1.06000	−0.529999	−	0.847998i	$-0.677808\pi$
$89$	−10.0000	−1.06000	−0.529999	+	0.847998i	$0.677808\pi$
$90$	0	0
$91$	2.00000	0.209657
$92$	2.00000	0.208514
$93$	0	0
$94$	−18.0000	−1.85656
$95$	20.0000	2.05196
$96$	0	0
$97$	−18.0000	−1.82762	−0.913812	−	0.406138i	$-0.866875\pi$
$97$	−18.0000	−1.82762	−0.913812	+	0.406138i	$0.866875\pi$
$98$	−2.00000	−0.202031
$99$	0	0
$100$	22.0000	2.20000
$101$	−5.00000	−0.497519	−0.248759	−	0.968565i	$-0.580023\pi$
$101$	−5.00000	−0.497519	−0.248759	+	0.968565i	$0.580023\pi$
$102$	0	0
$103$	−19.0000	−1.87213	−0.936063	−	0.351833i	$-0.885559\pi$
$103$	−19.0000	−1.87213	−0.936063	+	0.351833i	$0.885559\pi$
$104$	0	0
$105$	0	0
$106$	18.0000	1.74831
$107$	−4.00000	−0.386695	−0.193347	−	0.981130i	$-0.561934\pi$
$107$	−4.00000	−0.386695	−0.193347	+	0.981130i	$0.561934\pi$
$108$	0	0
$109$	−12.0000	−1.14939	−0.574696	−	0.818367i	$-0.694880\pi$
$109$	−12.0000	−1.14939	−0.574696	+	0.818367i	$0.694880\pi$
$110$	40.0000	3.81385
$111$	0	0
$112$	4.00000	0.377964
$113$	2.00000	0.188144	0.0940721	−	0.995565i	$-0.470012\pi$
$113$	2.00000	0.188144	0.0940721	+	0.995565i	$0.470012\pi$
$114$	0	0
$115$	−4.00000	−0.373002
$116$	4.00000	0.371391
$117$	0	0
$118$	18.0000	1.65703
$119$	0	0
$120$	0	0
$121$	14.0000	1.27273
$122$	10.0000	0.905357
$123$	0	0
$124$	12.0000	1.07763
$125$	−24.0000	−2.14663
$126$	0	0
$127$	9.00000	0.798621	0.399310	−	0.916816i	$-0.369250\pi$
$127$	9.00000	0.798621	0.399310	+	0.916816i	$0.369250\pi$
$128$	0	0
$129$	0	0
$130$	−16.0000	−1.40329
$131$	5.00000	0.436852	0.218426	−	0.975854i	$-0.429908\pi$
$131$	5.00000	0.436852	0.218426	+	0.975854i	$0.429908\pi$
$132$	0	0
$133$	5.00000	0.433555
$134$	−8.00000	−0.691095
$135$	0	0
$136$	0	0
$137$	−9.00000	−0.768922	−0.384461	−	0.923141i	$-0.625613\pi$
$137$	−9.00000	−0.768922	−0.384461	+	0.923141i	$0.625613\pi$
$138$	0	0
$139$	12.0000	1.01783	0.508913	−	0.860818i	$-0.330047\pi$
$139$	12.0000	1.01783	0.508913	+	0.860818i	$0.330047\pi$
$140$	8.00000	0.676123
$141$	0	0
$142$	24.0000	2.01404
$143$	−10.0000	−0.836242
$144$	0	0
$145$	−8.00000	−0.664364
$146$	0	0
$147$	0	0
$148$	12.0000	0.986394
$149$	−3.00000	−0.245770	−0.122885	−	0.992421i	$-0.539215\pi$
$149$	−3.00000	−0.245770	−0.122885	+	0.992421i	$0.539215\pi$
$150$	0	0
$151$	−19.0000	−1.54620	−0.773099	−	0.634285i	$-0.781294\pi$
$151$	−19.0000	−1.54620	−0.773099	+	0.634285i	$0.781294\pi$
$152$	0	0
$153$	0	0
$154$	10.0000	0.805823
$155$	−24.0000	−1.92773
$156$	0	0
$157$	7.00000	0.558661	0.279330	−	0.960195i	$-0.409888\pi$
$157$	7.00000	0.558661	0.279330	+	0.960195i	$0.409888\pi$
$158$	20.0000	1.59111
$159$	0	0
$160$	−32.0000	−2.52982
$161$	−1.00000	−0.0788110
$162$	0	0
$163$	13.0000	1.01824	0.509119	−	0.860696i	$-0.329971\pi$
$163$	13.0000	1.01824	0.509119	+	0.860696i	$0.329971\pi$
$164$	−10.0000	−0.780869
$165$	0	0
$166$	−36.0000	−2.79414
$167$	−19.0000	−1.47026	−0.735132	−	0.677924i	$-0.762880\pi$
$167$	−19.0000	−1.47026	−0.735132	+	0.677924i	$0.762880\pi$
$168$	0	0
$169$	−9.00000	−0.692308
$170$	0	0
$171$	0	0
$172$	16.0000	1.21999
$173$	−2.00000	−0.152057	−0.0760286	−	0.997106i	$-0.524224\pi$
$173$	−2.00000	−0.152057	−0.0760286	+	0.997106i	$0.524224\pi$
$174$	0	0
$175$	−11.0000	−0.831522
$176$	−20.0000	−1.50756
$177$	0	0
$178$	20.0000	1.49906
$179$	−8.00000	−0.597948	−0.298974	−	0.954261i	$-0.596644\pi$
$179$	−8.00000	−0.597948	−0.298974	+	0.954261i	$0.596644\pi$
$180$	0	0
$181$	−14.0000	−1.04061	−0.520306	−	0.853980i	$-0.674182\pi$
$181$	−14.0000	−1.04061	−0.520306	+	0.853980i	$0.674182\pi$
$182$	−4.00000	−0.296500
$183$	0	0
$184$	0	0
$185$	−24.0000	−1.76452
$186$	0	0
$187$	0	0
$188$	18.0000	1.31278
$189$	0	0
$190$	−40.0000	−2.90191
$191$	23.0000	1.66422	0.832111	−	0.554609i	$-0.187132\pi$
$191$	23.0000	1.66422	0.832111	+	0.554609i	$0.187132\pi$
$192$	0	0
$193$	−19.0000	−1.36765	−0.683825	−	0.729646i	$-0.739685\pi$
$193$	−19.0000	−1.36765	−0.683825	+	0.729646i	$0.739685\pi$
$194$	36.0000	2.58465
$195$	0	0
$196$	2.00000	0.142857
$197$	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
$199$	3.00000	0.212664	0.106332	−	0.994331i	$-0.466089\pi$
$199$	3.00000	0.212664	0.106332	+	0.994331i	$0.466089\pi$
$200$	0	0
$201$	0	0
$202$	10.0000	0.703598
$203$	−2.00000	−0.140372
$204$	0	0
$205$	20.0000	1.39686
$206$	38.0000	2.64759
$207$	0	0
$208$	8.00000	0.554700
$209$	−25.0000	−1.72929
$210$	0	0
$211$	13.0000	0.894957	0.447478	−	0.894295i	$-0.352322\pi$
$211$	13.0000	0.894957	0.447478	+	0.894295i	$0.352322\pi$
$212$	−18.0000	−1.23625
$213$	0	0
$214$	8.00000	0.546869
$215$	−32.0000	−2.18238
$216$	0	0
$217$	−6.00000	−0.407307
$218$	24.0000	1.62549
$219$	0	0
$220$	−40.0000	−2.69680
$221$	0	0
$222$	0	0
$223$	10.0000	0.669650	0.334825	−	0.942280i	$-0.391323\pi$
$223$	10.0000	0.669650	0.334825	+	0.942280i	$0.391323\pi$
$224$	−8.00000	−0.534522
$225$	0	0
$226$	−4.00000	−0.266076
$227$	18.0000	1.19470	0.597351	−	0.801980i	$-0.296220\pi$
$227$	18.0000	1.19470	0.597351	+	0.801980i	$0.296220\pi$
$228$	0	0
$229$	−13.0000	−0.859064	−0.429532	−	0.903052i	$-0.641321\pi$
$229$	−13.0000	−0.859064	−0.429532	+	0.903052i	$0.641321\pi$
$230$	8.00000	0.527504
$231$	0	0
$232$	0	0
$233$	12.0000	0.786146	0.393073	−	0.919507i	$-0.371412\pi$
$233$	12.0000	0.786146	0.393073	+	0.919507i	$0.371412\pi$
$234$	0	0
$235$	−36.0000	−2.34838
$236$	−18.0000	−1.17170
$237$	0	0
$238$	0	0
$239$	−12.0000	−0.776215	−0.388108	−	0.921614i	$-0.626871\pi$
$239$	−12.0000	−0.776215	−0.388108	+	0.921614i	$0.626871\pi$
$240$	0	0
$241$	17.0000	1.09507	0.547533	−	0.836784i	$-0.315567\pi$
$241$	17.0000	1.09507	0.547533	+	0.836784i	$0.315567\pi$
$242$	−28.0000	−1.79991
$243$	0	0
$244$	−10.0000	−0.640184
$245$	−4.00000	−0.255551
$246$	0	0
$247$	10.0000	0.636285
$248$	0	0
$249$	0	0
$250$	48.0000	3.03579
$251$	−10.0000	−0.631194	−0.315597	−	0.948893i	$-0.602205\pi$
$251$	−10.0000	−0.631194	−0.315597	+	0.948893i	$0.602205\pi$
$252$	0	0
$253$	5.00000	0.314347
$254$	−18.0000	−1.12942
$255$	0	0
$256$	16.0000	1.00000
$257$	−17.0000	−1.06043	−0.530215	−	0.847863i	$-0.677889\pi$
$257$	−17.0000	−1.06043	−0.530215	+	0.847863i	$0.677889\pi$
$258$	0	0
$259$	−6.00000	−0.372822
$260$	16.0000	0.992278
$261$	0	0
$262$	−10.0000	−0.617802
$263$	−7.00000	−0.431638	−0.215819	−	0.976433i	$-0.569242\pi$
$263$	−7.00000	−0.431638	−0.215819	+	0.976433i	$0.569242\pi$
$264$	0	0
$265$	36.0000	2.21146
$266$	−10.0000	−0.613139
$267$	0	0
$268$	8.00000	0.488678
$269$	18.0000	1.09748	0.548740	−	0.835993i	$-0.315108\pi$
$269$	18.0000	1.09748	0.548740	+	0.835993i	$0.315108\pi$
$270$	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
$273$	0	0
$274$	18.0000	1.08742
$275$	55.0000	3.31662
$276$	0	0
$277$	7.00000	0.420589	0.210295	−	0.977638i	$-0.432558\pi$
$277$	7.00000	0.420589	0.210295	+	0.977638i	$0.432558\pi$
$278$	−24.0000	−1.43942
$279$	0	0
$280$	0	0
$281$	−2.00000	−0.119310	−0.0596550	−	0.998219i	$-0.519000\pi$
$281$	−2.00000	−0.119310	−0.0596550	+	0.998219i	$0.519000\pi$
$282$	0	0
$283$	−20.0000	−1.18888	−0.594438	−	0.804141i	$-0.702626\pi$
$283$	−20.0000	−1.18888	−0.594438	+	0.804141i	$0.702626\pi$
$284$	−24.0000	−1.42414
$285$	0	0
$286$	20.0000	1.18262
$287$	5.00000	0.295141
$288$	0	0
$289$	−17.0000	−1.00000
$290$	16.0000	0.939552
$291$	0	0
$292$	0	0
$293$	4.00000	0.233682	0.116841	−	0.993151i	$-0.462723\pi$
$293$	4.00000	0.233682	0.116841	+	0.993151i	$0.462723\pi$
$294$	0	0
$295$	36.0000	2.09600
$296$	0	0
$297$	0	0
$298$	6.00000	0.347571
$299$	−2.00000	−0.115663
$300$	0	0
$301$	−8.00000	−0.461112
$302$	38.0000	2.18665
$303$	0	0
$304$	20.0000	1.14708
$305$	20.0000	1.14520
$306$	0	0
$307$	−8.00000	−0.456584	−0.228292	−	0.973593i	$-0.573314\pi$
$307$	−8.00000	−0.456584	−0.228292	+	0.973593i	$0.573314\pi$
$308$	−10.0000	−0.569803
$309$	0	0
$310$	48.0000	2.72622
$311$	15.0000	0.850572	0.425286	−	0.905059i	$-0.360174\pi$
$311$	15.0000	0.850572	0.425286	+	0.905059i	$0.360174\pi$
$312$	0	0
$313$	−25.0000	−1.41308	−0.706542	−	0.707671i	$-0.749746\pi$
$313$	−25.0000	−1.41308	−0.706542	+	0.707671i	$0.749746\pi$
$314$	−14.0000	−0.790066
$315$	0	0
$316$	−20.0000	−1.12509
$317$	−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
$320$	32.0000	1.78885
$321$	0	0
$322$	2.00000	0.111456
$323$	0	0
$324$	0	0
$325$	−22.0000	−1.22034
$326$	−26.0000	−1.44001
$327$	0	0
$328$	0	0
$329$	−9.00000	−0.496186
$330$	0	0
$331$	29.0000	1.59398	0.796992	−	0.603990i	$-0.206423\pi$
$331$	29.0000	1.59398	0.796992	+	0.603990i	$0.206423\pi$
$332$	36.0000	1.97576
$333$	0	0
$334$	38.0000	2.07927
$335$	−16.0000	−0.874173
$336$	0	0
$337$	22.0000	1.19842	0.599208	−	0.800593i	$-0.295482\pi$
$337$	22.0000	1.19842	0.599208	+	0.800593i	$0.295482\pi$
$338$	18.0000	0.979071
$339$	0	0
$340$	0	0
$341$	30.0000	1.62459
$342$	0	0
$343$	−1.00000	−0.0539949
$344$	0	0
$345$	0	0
$346$	4.00000	0.215041
$347$	−2.00000	−0.107366	−0.0536828	−	0.998558i	$-0.517096\pi$
$347$	−2.00000	−0.107366	−0.0536828	+	0.998558i	$0.517096\pi$
$348$	0	0
$349$	−2.00000	−0.107058	−0.0535288	−	0.998566i	$-0.517047\pi$
$349$	−2.00000	−0.107058	−0.0535288	+	0.998566i	$0.517047\pi$
$350$	22.0000	1.17595
$351$	0	0
$352$	40.0000	2.13201
$353$	14.0000	0.745145	0.372572	−	0.928003i	$-0.378476\pi$
$353$	14.0000	0.745145	0.372572	+	0.928003i	$0.378476\pi$
$354$	0	0
$355$	48.0000	2.54758
$356$	−20.0000	−1.06000
$357$	0	0
$358$	16.0000	0.845626
$359$	−32.0000	−1.68890	−0.844448	−	0.535638i	$-0.820071\pi$
$359$	−32.0000	−1.68890	−0.844448	+	0.535638i	$0.820071\pi$
$360$	0	0
$361$	6.00000	0.315789
$362$	28.0000	1.47165
$363$	0	0
$364$	4.00000	0.209657
$365$	0	0
$366$	0	0
$367$	27.0000	1.40939	0.704694	−	0.709511i	$-0.251084\pi$
$367$	27.0000	1.40939	0.704694	+	0.709511i	$0.251084\pi$
$368$	−4.00000	−0.208514
$369$	0	0
$370$	48.0000	2.49540
$371$	9.00000	0.467257
$372$	0	0
$373$	−34.0000	−1.76045	−0.880227	−	0.474554i	$-0.842610\pi$
$373$	−34.0000	−1.76045	−0.880227	+	0.474554i	$0.842610\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	−4.00000	−0.206010
$378$	0	0
$379$	−30.0000	−1.54100	−0.770498	−	0.637442i	$-0.779993\pi$
$379$	−30.0000	−1.54100	−0.770498	+	0.637442i	$0.779993\pi$
$380$	40.0000	2.05196
$381$	0	0
$382$	−46.0000	−2.35356
$383$	−6.00000	−0.306586	−0.153293	−	0.988181i	$-0.548988\pi$
$383$	−6.00000	−0.306586	−0.153293	+	0.988181i	$0.548988\pi$
$384$	0	0
$385$	20.0000	1.01929
$386$	38.0000	1.93415
$387$	0	0
$388$	−36.0000	−1.82762
$389$	−6.00000	−0.304212	−0.152106	−	0.988364i	$-0.548606\pi$
$389$	−6.00000	−0.304212	−0.152106	+	0.988364i	$0.548606\pi$
$390$	0	0
$391$	0	0
$392$	0	0
$393$	0	0
$394$	−4.00000	−0.201517
$395$	40.0000	2.01262
$396$	0	0
$397$	30.0000	1.50566	0.752828	−	0.658217i	$-0.228689\pi$
$397$	30.0000	1.50566	0.752828	+	0.658217i	$0.228689\pi$
$398$	−6.00000	−0.300753
$399$	0	0
$400$	−44.0000	−2.20000
$401$	−3.00000	−0.149813	−0.0749064	−	0.997191i	$-0.523866\pi$
$401$	−3.00000	−0.149813	−0.0749064	+	0.997191i	$0.523866\pi$
$402$	0	0
$403$	−12.0000	−0.597763
$404$	−10.0000	−0.497519
$405$	0	0
$406$	4.00000	0.198517
$407$	30.0000	1.48704
$408$	0	0
$409$	14.0000	0.692255	0.346128	−	0.938187i	$-0.387496\pi$
$409$	14.0000	0.692255	0.346128	+	0.938187i	$0.387496\pi$
$410$	−40.0000	−1.97546
$411$	0	0
$412$	−38.0000	−1.87213
$413$	9.00000	0.442861
$414$	0	0
$415$	−72.0000	−3.53434
$416$	−16.0000	−0.784465
$417$	0	0
$418$	50.0000	2.44558
$419$	18.0000	0.879358	0.439679	−	0.898155i	$-0.355092\pi$
$419$	18.0000	0.879358	0.439679	+	0.898155i	$0.355092\pi$
$420$	0	0
$421$	8.00000	0.389896	0.194948	−	0.980814i	$-0.437546\pi$
$421$	8.00000	0.389896	0.194948	+	0.980814i	$0.437546\pi$
$422$	−26.0000	−1.26566
$423$	0	0
$424$	0	0
$425$	0	0
$426$	0	0
$427$	5.00000	0.241967
$428$	−8.00000	−0.386695
$429$	0	0
$430$	64.0000	3.08635
$431$	−27.0000	−1.30054	−0.650272	−	0.759701i	$-0.725345\pi$
$431$	−27.0000	−1.30054	−0.650272	+	0.759701i	$0.725345\pi$
$432$	0	0
$433$	−11.0000	−0.528626	−0.264313	−	0.964437i	$-0.585145\pi$
$433$	−11.0000	−0.528626	−0.264313	+	0.964437i	$0.585145\pi$
$434$	12.0000	0.576018
$435$	0	0
$436$	−24.0000	−1.14939
$437$	−5.00000	−0.239182
$438$	0	0
$439$	−36.0000	−1.71819	−0.859093	−	0.511819i	$-0.828972\pi$
$439$	−36.0000	−1.71819	−0.859093	+	0.511819i	$0.828972\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	36.0000	1.71041	0.855206	−	0.518289i	$-0.173431\pi$
$443$	36.0000	1.71041	0.855206	+	0.518289i	$0.173431\pi$
$444$	0	0
$445$	40.0000	1.89618
$446$	−20.0000	−0.947027
$447$	0	0
$448$	8.00000	0.377964
$449$	−6.00000	−0.283158	−0.141579	−	0.989927i	$-0.545218\pi$
$449$	−6.00000	−0.283158	−0.141579	+	0.989927i	$0.545218\pi$
$450$	0	0
$451$	−25.0000	−1.17720
$452$	4.00000	0.188144
$453$	0	0
$454$	−36.0000	−1.68956
$455$	−8.00000	−0.375046
$456$	0	0
$457$	10.0000	0.467780	0.233890	−	0.972263i	$-0.424854\pi$
$457$	10.0000	0.467780	0.233890	+	0.972263i	$0.424854\pi$
$458$	26.0000	1.21490
$459$	0	0
$460$	−8.00000	−0.373002
$461$	−2.00000	−0.0931493	−0.0465746	−	0.998915i	$-0.514831\pi$
$461$	−2.00000	−0.0931493	−0.0465746	+	0.998915i	$0.514831\pi$
$462$	0	0
$463$	−35.0000	−1.62659	−0.813294	−	0.581853i	$-0.802328\pi$
$463$	−35.0000	−1.62659	−0.813294	+	0.581853i	$0.802328\pi$
$464$	−8.00000	−0.371391
$465$	0	0
$466$	−24.0000	−1.11178
$467$	6.00000	0.277647	0.138823	−	0.990317i	$-0.455668\pi$
$467$	6.00000	0.277647	0.138823	+	0.990317i	$0.455668\pi$
$468$	0	0
$469$	−4.00000	−0.184703
$470$	72.0000	3.32111
$471$	0	0
$472$	0	0
$473$	40.0000	1.83920
$474$	0	0
$475$	−55.0000	−2.52357
$476$	0	0
$477$	0	0
$478$	24.0000	1.09773
$479$	−32.0000	−1.46212	−0.731059	−	0.682315i	$-0.760973\pi$
$479$	−32.0000	−1.46212	−0.731059	+	0.682315i	$0.760973\pi$
$480$	0	0
$481$	−12.0000	−0.547153
$482$	−34.0000	−1.54866
$483$	0	0
$484$	28.0000	1.27273
$485$	72.0000	3.26935
$486$	0	0
$487$	−20.0000	−0.906287	−0.453143	−	0.891438i	$-0.649697\pi$
$487$	−20.0000	−0.906287	−0.453143	+	0.891438i	$0.649697\pi$
$488$	0	0
$489$	0	0
$490$	8.00000	0.361403
$491$	−14.0000	−0.631811	−0.315906	−	0.948791i	$-0.602308\pi$
$491$	−14.0000	−0.631811	−0.315906	+	0.948791i	$0.602308\pi$
$492$	0	0
$493$	0	0
$494$	−20.0000	−0.899843
$495$	0	0
$496$	−24.0000	−1.07763
$497$	12.0000	0.538274
$498$	0	0
$499$	−20.0000	−0.895323	−0.447661	−	0.894203i	$-0.647743\pi$
$499$	−20.0000	−0.895323	−0.447661	+	0.894203i	$0.647743\pi$
$500$	−48.0000	−2.14663
$501$	0	0
$502$	20.0000	0.892644
$503$	36.0000	1.60516	0.802580	−	0.596544i	$-0.203460\pi$
$503$	36.0000	1.60516	0.802580	+	0.596544i	$0.203460\pi$
$504$	0	0
$505$	20.0000	0.889988
$506$	−10.0000	−0.444554
$507$	0	0
$508$	18.0000	0.798621
$509$	19.0000	0.842160	0.421080	−	0.907023i	$-0.361651\pi$
$509$	19.0000	0.842160	0.421080	+	0.907023i	$0.361651\pi$
$510$	0	0
$511$	0	0
$512$	−32.0000	−1.41421
$513$	0	0
$514$	34.0000	1.49968
$515$	76.0000	3.34896
$516$	0	0
$517$	45.0000	1.97910
$518$	12.0000	0.527250
$519$	0	0
$520$	0	0
$521$	30.0000	1.31432	0.657162	−	0.753749i	$-0.271757\pi$
$521$	30.0000	1.31432	0.657162	+	0.753749i	$0.271757\pi$
$522$	0	0
$523$	19.0000	0.830812	0.415406	−	0.909636i	$-0.363640\pi$
$523$	19.0000	0.830812	0.415406	+	0.909636i	$0.363640\pi$
$524$	10.0000	0.436852
$525$	0	0
$526$	14.0000	0.610429
$527$	0	0
$528$	0	0
$529$	1.00000	0.0434783
$530$	−72.0000	−3.12748
$531$	0	0
$532$	10.0000	0.433555
$533$	10.0000	0.433148
$534$	0	0
$535$	16.0000	0.691740
$536$	0	0
$537$	0	0
$538$	−36.0000	−1.55207
$539$	5.00000	0.215365
$540$	0	0
$541$	11.0000	0.472927	0.236463	−	0.971640i	$-0.424012\pi$
$541$	11.0000	0.472927	0.236463	+	0.971640i	$0.424012\pi$
$542$	16.0000	0.687259
$543$	0	0
$544$	0	0
$545$	48.0000	2.05609
$546$	0	0
$547$	−8.00000	−0.342055	−0.171028	−	0.985266i	$-0.554709\pi$
$547$	−8.00000	−0.342055	−0.171028	+	0.985266i	$0.554709\pi$
$548$	−18.0000	−0.768922
$549$	0	0
$550$	−110.000	−4.69042
$551$	−10.0000	−0.426014
$552$	0	0
$553$	10.0000	0.425243
$554$	−14.0000	−0.594803
$555$	0	0
$556$	24.0000	1.01783
$557$	−46.0000	−1.94908	−0.974541	−	0.224208i	$-0.928020\pi$
$557$	−46.0000	−1.94908	−0.974541	+	0.224208i	$0.928020\pi$
$558$	0	0
$559$	−16.0000	−0.676728
$560$	−16.0000	−0.676123
$561$	0	0
$562$	4.00000	0.168730
$563$	−40.0000	−1.68580	−0.842900	−	0.538071i	$-0.819153\pi$
$563$	−40.0000	−1.68580	−0.842900	+	0.538071i	$0.819153\pi$
$564$	0	0
$565$	−8.00000	−0.336563
$566$	40.0000	1.68133
$567$	0	0
$568$	0	0
$569$	17.0000	0.712677	0.356339	−	0.934357i	$-0.384025\pi$
$569$	17.0000	0.712677	0.356339	+	0.934357i	$0.384025\pi$
$570$	0	0
$571$	8.00000	0.334790	0.167395	−	0.985890i	$-0.446465\pi$
$571$	8.00000	0.334790	0.167395	+	0.985890i	$0.446465\pi$
$572$	−20.0000	−0.836242
$573$	0	0
$574$	−10.0000	−0.417392
$575$	11.0000	0.458732
$576$	0	0
$577$	−2.00000	−0.0832611	−0.0416305	−	0.999133i	$-0.513255\pi$
$577$	−2.00000	−0.0832611	−0.0416305	+	0.999133i	$0.513255\pi$
$578$	34.0000	1.41421
$579$	0	0
$580$	−16.0000	−0.664364
$581$	−18.0000	−0.746766
$582$	0	0
$583$	−45.0000	−1.86371
$584$	0	0
$585$	0	0
$586$	−8.00000	−0.330477
$587$	17.0000	0.701665	0.350833	−	0.936438i	$-0.385899\pi$
$587$	17.0000	0.701665	0.350833	+	0.936438i	$0.385899\pi$
$588$	0	0
$589$	−30.0000	−1.23613
$590$	−72.0000	−2.96419
$591$	0	0
$592$	−24.0000	−0.986394
$593$	18.0000	0.739171	0.369586	−	0.929197i	$-0.379500\pi$
$593$	18.0000	0.739171	0.369586	+	0.929197i	$0.379500\pi$
$594$	0	0
$595$	0	0
$596$	−6.00000	−0.245770
$597$	0	0
$598$	4.00000	0.163572
$599$	−42.0000	−1.71607	−0.858037	−	0.513588i	$-0.828316\pi$
$599$	−42.0000	−1.71607	−0.858037	+	0.513588i	$0.828316\pi$
$600$	0	0
$601$	0	0		−	1.00000i	$-0.5\pi$
$601$	0	0			1.00000i	$0.5\pi$
$602$	16.0000	0.652111
$603$	0	0
$604$	−38.0000	−1.54620
$605$	−56.0000	−2.27672
$606$	0	0
$607$	8.00000	0.324710	0.162355	−	0.986732i	$-0.448091\pi$
$607$	8.00000	0.324710	0.162355	+	0.986732i	$0.448091\pi$
$608$	−40.0000	−1.62221
$609$	0	0
$610$	−40.0000	−1.61955
$611$	−18.0000	−0.728202
$612$	0	0
$613$	34.0000	1.37325	0.686624	−	0.727013i	$-0.259092\pi$
$613$	34.0000	1.37325	0.686624	+	0.727013i	$0.259092\pi$
$614$	16.0000	0.645707
$615$	0	0
$616$	0	0
$617$	−18.0000	−0.724653	−0.362326	−	0.932051i	$-0.618017\pi$
$617$	−18.0000	−0.724653	−0.362326	+	0.932051i	$0.618017\pi$
$618$	0	0
$619$	−20.0000	−0.803868	−0.401934	−	0.915669i	$-0.631662\pi$
$619$	−20.0000	−0.803868	−0.401934	+	0.915669i	$0.631662\pi$
$620$	−48.0000	−1.92773
$621$	0	0
$622$	−30.0000	−1.20289
$623$	10.0000	0.400642
$624$	0	0
$625$	41.0000	1.64000
$626$	50.0000	1.99840
$627$	0	0
$628$	14.0000	0.558661
$629$	0	0
$630$	0	0
$631$	−10.0000	−0.398094	−0.199047	−	0.979990i	$-0.563785\pi$
$631$	−10.0000	−0.398094	−0.199047	+	0.979990i	$0.563785\pi$
$632$	0	0
$633$	0	0
$634$	60.0000	2.38290
$635$	−36.0000	−1.42862
$636$	0	0
$637$	−2.00000	−0.0792429
$638$	−20.0000	−0.791808
$639$	0	0
$640$	0	0
$641$	9.00000	0.355479	0.177739	−	0.984078i	$-0.443122\pi$
$641$	9.00000	0.355479	0.177739	+	0.984078i	$0.443122\pi$
$642$	0	0
$643$	−31.0000	−1.22252	−0.611260	−	0.791430i	$-0.709337\pi$
$643$	−31.0000	−1.22252	−0.611260	+	0.791430i	$0.709337\pi$
$644$	−2.00000	−0.0788110
$645$	0	0
$646$	0	0
$647$	28.0000	1.10079	0.550397	−	0.834903i	$-0.314476\pi$
$647$	28.0000	1.10079	0.550397	+	0.834903i	$0.314476\pi$
$648$	0	0
$649$	−45.0000	−1.76640
$650$	44.0000	1.72582
$651$	0	0
$652$	26.0000	1.01824
$653$	−24.0000	−0.939193	−0.469596	−	0.882881i	$-0.655601\pi$
$653$	−24.0000	−0.939193	−0.469596	+	0.882881i	$0.655601\pi$
$654$	0	0
$655$	−20.0000	−0.781465
$656$	20.0000	0.780869
$657$	0	0
$658$	18.0000	0.701713
$659$	−24.0000	−0.934907	−0.467454	−	0.884018i	$-0.654829\pi$
$659$	−24.0000	−0.934907	−0.467454	+	0.884018i	$0.654829\pi$
$660$	0	0
$661$	−5.00000	−0.194477	−0.0972387	−	0.995261i	$-0.531001\pi$
$661$	−5.00000	−0.194477	−0.0972387	+	0.995261i	$0.531001\pi$
$662$	−58.0000	−2.25423
$663$	0	0
$664$	0	0
$665$	−20.0000	−0.775567
$666$	0	0
$667$	2.00000	0.0774403
$668$	−38.0000	−1.47026
$669$	0	0
$670$	32.0000	1.23627
$671$	−25.0000	−0.965114
$672$	0	0
$673$	49.0000	1.88881	0.944406	−	0.328783i	$-0.106638\pi$
$673$	49.0000	1.88881	0.944406	+	0.328783i	$0.106638\pi$
$674$	−44.0000	−1.69482
$675$	0	0
$676$	−18.0000	−0.692308
$677$	−36.0000	−1.38359	−0.691796	−	0.722093i	$-0.743180\pi$
$677$	−36.0000	−1.38359	−0.691796	+	0.722093i	$0.743180\pi$
$678$	0	0
$679$	18.0000	0.690777
$680$	0	0
$681$	0	0
$682$	−60.0000	−2.29752
$683$	−36.0000	−1.37750	−0.688751	−	0.724998i	$-0.741841\pi$
$683$	−36.0000	−1.37750	−0.688751	+	0.724998i	$0.741841\pi$
$684$	0	0
$685$	36.0000	1.37549
$686$	2.00000	0.0763604
$687$	0	0
$688$	−32.0000	−1.21999
$689$	18.0000	0.685745
$690$	0	0
$691$	−4.00000	−0.152167	−0.0760836	−	0.997101i	$-0.524242\pi$
$691$	−4.00000	−0.152167	−0.0760836	+	0.997101i	$0.524242\pi$
$692$	−4.00000	−0.152057
$693$	0	0
$694$	4.00000	0.151838
$695$	−48.0000	−1.82074
$696$	0	0
$697$	0	0
$698$	4.00000	0.151402
$699$	0	0
$700$	−22.0000	−0.831522
$701$	15.0000	0.566542	0.283271	−	0.959040i	$-0.408580\pi$
$701$	15.0000	0.566542	0.283271	+	0.959040i	$0.408580\pi$
$702$	0	0
$703$	−30.0000	−1.13147
$704$	−40.0000	−1.50756
$705$	0	0
$706$	−28.0000	−1.05379
$707$	5.00000	0.188044
$708$	0	0
$709$	−6.00000	−0.225335	−0.112667	−	0.993633i	$-0.535939\pi$
$709$	−6.00000	−0.225335	−0.112667	+	0.993633i	$0.535939\pi$
$710$	−96.0000	−3.60282
$711$	0	0
$712$	0	0
$713$	6.00000	0.224702
$714$	0	0
$715$	40.0000	1.49592
$716$	−16.0000	−0.597948
$717$	0	0
$718$	64.0000	2.38846
$719$	24.0000	0.895049	0.447524	−	0.894272i	$-0.352306\pi$
$719$	24.0000	0.895049	0.447524	+	0.894272i	$0.352306\pi$
$720$	0	0
$721$	19.0000	0.707597
$722$	−12.0000	−0.446594
$723$	0	0
$724$	−28.0000	−1.04061
$725$	22.0000	0.817059
$726$	0	0
$727$	41.0000	1.52061	0.760303	−	0.649569i	$-0.225051\pi$
$727$	41.0000	1.52061	0.760303	+	0.649569i	$0.225051\pi$
$728$	0	0
$729$	0	0
$730$	0	0
$731$	0	0
$732$	0	0
$733$	−6.00000	−0.221615	−0.110808	−	0.993842i	$-0.535344\pi$
$733$	−6.00000	−0.221615	−0.110808	+	0.993842i	$0.535344\pi$
$734$	−54.0000	−1.99318
$735$	0	0
$736$	8.00000	0.294884
$737$	20.0000	0.736709
$738$	0	0
$739$	12.0000	0.441427	0.220714	−	0.975339i	$-0.429161\pi$
$739$	12.0000	0.441427	0.220714	+	0.975339i	$0.429161\pi$
$740$	−48.0000	−1.76452
$741$	0	0
$742$	−18.0000	−0.660801
$743$	−15.0000	−0.550297	−0.275148	−	0.961402i	$-0.588727\pi$
$743$	−15.0000	−0.550297	−0.275148	+	0.961402i	$0.588727\pi$
$744$	0	0
$745$	12.0000	0.439646
$746$	68.0000	2.48966
$747$	0	0
$748$	0	0
$749$	4.00000	0.146157
$750$	0	0
$751$	−32.0000	−1.16770	−0.583848	−	0.811863i	$-0.698454\pi$
$751$	−32.0000	−1.16770	−0.583848	+	0.811863i	$0.698454\pi$
$752$	−36.0000	−1.31278
$753$	0	0
$754$	8.00000	0.291343
$755$	76.0000	2.76592
$756$	0	0
$757$	8.00000	0.290765	0.145382	−	0.989376i	$-0.453559\pi$
$757$	8.00000	0.290765	0.145382	+	0.989376i	$0.453559\pi$
$758$	60.0000	2.17930
$759$	0	0
$760$	0	0
$761$	21.0000	0.761249	0.380625	−	0.924730i	$-0.375709\pi$
$761$	21.0000	0.761249	0.380625	+	0.924730i	$0.375709\pi$
$762$	0	0
$763$	12.0000	0.434429
$764$	46.0000	1.66422
$765$	0	0
$766$	12.0000	0.433578
$767$	18.0000	0.649942
$768$	0	0
$769$	14.0000	0.504853	0.252426	−	0.967616i	$-0.418771\pi$
$769$	14.0000	0.504853	0.252426	+	0.967616i	$0.418771\pi$
$770$	−40.0000	−1.44150
$771$	0	0
$772$	−38.0000	−1.36765
$773$	−20.0000	−0.719350	−0.359675	−	0.933078i	$-0.617112\pi$
$773$	−20.0000	−0.719350	−0.359675	+	0.933078i	$0.617112\pi$
$774$	0	0
$775$	66.0000	2.37079
$776$	0	0
$777$	0	0
$778$	12.0000	0.430221
$779$	25.0000	0.895718
$780$	0	0
$781$	−60.0000	−2.14697
$782$	0	0
$783$	0	0
$784$	−4.00000	−0.142857
$785$	−28.0000	−0.999363
$786$	0	0
$787$	−23.0000	−0.819861	−0.409931	−	0.912117i	$-0.634447\pi$
$787$	−23.0000	−0.819861	−0.409931	+	0.912117i	$0.634447\pi$
$788$	4.00000	0.142494
$789$	0	0
$790$	−80.0000	−2.84627
$791$	−2.00000	−0.0711118
$792$	0	0
$793$	10.0000	0.355110
$794$	−60.0000	−2.12932
$795$	0	0
$796$	6.00000	0.212664
$797$	−46.0000	−1.62940	−0.814702	−	0.579880i	$-0.803099\pi$
$797$	−46.0000	−1.62940	−0.814702	+	0.579880i	$0.803099\pi$
$798$	0	0
$799$	0	0
$800$	88.0000	3.11127
$801$	0	0
$802$	6.00000	0.211867
$803$	0	0
$804$	0	0
$805$	4.00000	0.140981
$806$	24.0000	0.845364
$807$	0	0
$808$	0	0
$809$	6.00000	0.210949	0.105474	−	0.994422i	$-0.466364\pi$
$809$	6.00000	0.210949	0.105474	+	0.994422i	$0.466364\pi$
$810$	0	0
$811$	2.00000	0.0702295	0.0351147	−	0.999383i	$-0.488820\pi$
$811$	2.00000	0.0702295	0.0351147	+	0.999383i	$0.488820\pi$
$812$	−4.00000	−0.140372
$813$	0	0
$814$	−60.0000	−2.10300
$815$	−52.0000	−1.82148
$816$	0	0
$817$	−40.0000	−1.39942
$818$	−28.0000	−0.978997
$819$	0	0
$820$	40.0000	1.39686
$821$	4.00000	0.139601	0.0698005	−	0.997561i	$-0.477764\pi$
$821$	4.00000	0.139601	0.0698005	+	0.997561i	$0.477764\pi$
$822$	0	0
$823$	27.0000	0.941161	0.470580	−	0.882357i	$-0.344045\pi$
$823$	27.0000	0.941161	0.470580	+	0.882357i	$0.344045\pi$
$824$	0	0
$825$	0	0
$826$	−18.0000	−0.626300
$827$	21.0000	0.730242	0.365121	−	0.930960i	$-0.381028\pi$
$827$	21.0000	0.730242	0.365121	+	0.930960i	$0.381028\pi$
$828$	0	0
$829$	26.0000	0.903017	0.451509	−	0.892267i	$-0.350886\pi$
$829$	26.0000	0.903017	0.451509	+	0.892267i	$0.350886\pi$
$830$	144.000	4.99831
$831$	0	0
$832$	16.0000	0.554700
$833$	0	0
$834$	0	0
$835$	76.0000	2.63009
$836$	−50.0000	−1.72929
$837$	0	0
$838$	−36.0000	−1.24360
$839$	−46.0000	−1.58810	−0.794048	−	0.607855i	$-0.792030\pi$
$839$	−46.0000	−1.58810	−0.794048	+	0.607855i	$0.792030\pi$
$840$	0	0
$841$	−25.0000	−0.862069
$842$	−16.0000	−0.551396
$843$	0	0
$844$	26.0000	0.894957
$845$	36.0000	1.23844
$846$	0	0
$847$	−14.0000	−0.481046
$848$	36.0000	1.23625
$849$	0	0
$850$	0	0
$851$	6.00000	0.205677
$852$	0	0
$853$	8.00000	0.273915	0.136957	−	0.990577i	$-0.456268\pi$
$853$	8.00000	0.273915	0.136957	+	0.990577i	$0.456268\pi$
$854$	−10.0000	−0.342193
$855$	0	0
$856$	0	0
$857$	−1.00000	−0.0341593	−0.0170797	−	0.999854i	$-0.505437\pi$
$857$	−1.00000	−0.0341593	−0.0170797	+	0.999854i	$0.505437\pi$
$858$	0	0
$859$	−40.0000	−1.36478	−0.682391	−	0.730987i	$-0.739060\pi$
$859$	−40.0000	−1.36478	−0.682391	+	0.730987i	$0.739060\pi$
$860$	−64.0000	−2.18238
$861$	0	0
$862$	54.0000	1.83925
$863$	30.0000	1.02121	0.510606	−	0.859815i	$-0.329421\pi$
$863$	30.0000	1.02121	0.510606	+	0.859815i	$0.329421\pi$
$864$	0	0
$865$	8.00000	0.272008
$866$	22.0000	0.747590
$867$	0	0
$868$	−12.0000	−0.407307
$869$	−50.0000	−1.69613
$870$	0	0
$871$	−8.00000	−0.271070
$872$	0	0
$873$	0	0
$874$	10.0000	0.338255
$875$	24.0000	0.811348
$876$	0	0
$877$	−17.0000	−0.574049	−0.287025	−	0.957923i	$-0.592666\pi$
$877$	−17.0000	−0.574049	−0.287025	+	0.957923i	$0.592666\pi$
$878$	72.0000	2.42988
$879$	0	0
$880$	80.0000	2.69680
$881$	−6.00000	−0.202145	−0.101073	−	0.994879i	$-0.532227\pi$
$881$	−6.00000	−0.202145	−0.101073	+	0.994879i	$0.532227\pi$
$882$	0	0
$883$	32.0000	1.07689	0.538443	−	0.842662i	$-0.319013\pi$
$883$	32.0000	1.07689	0.538443	+	0.842662i	$0.319013\pi$
$884$	0	0
$885$	0	0
$886$	−72.0000	−2.41889
$887$	16.0000	0.537227	0.268614	−	0.963248i	$-0.413434\pi$
$887$	16.0000	0.537227	0.268614	+	0.963248i	$0.413434\pi$
$888$	0	0
$889$	−9.00000	−0.301850
$890$	−80.0000	−2.68161
$891$	0	0
$892$	20.0000	0.669650
$893$	−45.0000	−1.50587
$894$	0	0
$895$	32.0000	1.06964
$896$	0	0
$897$	0	0
$898$	12.0000	0.400445
$899$	12.0000	0.400222
$900$	0	0
$901$	0	0
$902$	50.0000	1.66482
$903$	0	0
$904$	0	0
$905$	56.0000	1.86150
$906$	0	0
$907$	44.0000	1.46100	0.730498	−	0.682915i	$-0.239288\pi$
$907$	44.0000	1.46100	0.730498	+	0.682915i	$0.239288\pi$
$908$	36.0000	1.19470
$909$	0	0
$910$	16.0000	0.530395
$911$	−24.0000	−0.795155	−0.397578	−	0.917568i	$-0.630149\pi$
$911$	−24.0000	−0.795155	−0.397578	+	0.917568i	$0.630149\pi$
$912$	0	0
$913$	90.0000	2.97857
$914$	−20.0000	−0.661541
$915$	0	0
$916$	−26.0000	−0.859064
$917$	−5.00000	−0.165115
$918$	0	0
$919$	2.00000	0.0659739	0.0329870	−	0.999456i	$-0.489498\pi$
$919$	2.00000	0.0659739	0.0329870	+	0.999456i	$0.489498\pi$
$920$	0	0
$921$	0	0
$922$	4.00000	0.131733
$923$	24.0000	0.789970
$924$	0	0
$925$	66.0000	2.17007
$926$	70.0000	2.30034
$927$	0	0
$928$	16.0000	0.525226
$929$	−26.0000	−0.853032	−0.426516	−	0.904480i	$-0.640259\pi$
$929$	−26.0000	−0.853032	−0.426516	+	0.904480i	$0.640259\pi$
$930$	0	0
$931$	−5.00000	−0.163868
$932$	24.0000	0.786146
$933$	0	0
$934$	−12.0000	−0.392652
$935$	0	0
$936$	0	0
$937$	−27.0000	−0.882052	−0.441026	−	0.897494i	$-0.645385\pi$
$937$	−27.0000	−0.882052	−0.441026	+	0.897494i	$0.645385\pi$
$938$	8.00000	0.261209
$939$	0	0
$940$	−72.0000	−2.34838
$941$	−20.0000	−0.651981	−0.325991	−	0.945373i	$-0.605698\pi$
$941$	−20.0000	−0.651981	−0.325991	+	0.945373i	$0.605698\pi$
$942$	0	0
$943$	−5.00000	−0.162822
$944$	36.0000	1.17170
$945$	0	0
$946$	−80.0000	−2.60102
$947$	−32.0000	−1.03986	−0.519930	−	0.854209i	$-0.674042\pi$
$947$	−32.0000	−1.03986	−0.519930	+	0.854209i	$0.674042\pi$
$948$	0	0
$949$	0	0
$950$	110.000	3.56887
$951$	0	0
$952$	0	0
$953$	55.0000	1.78162	0.890812	−	0.454371i	$-0.150136\pi$
$953$	55.0000	1.78162	0.890812	+	0.454371i	$0.150136\pi$
$954$	0	0
$955$	−92.0000	−2.97705
$956$	−24.0000	−0.776215
$957$	0	0
$958$	64.0000	2.06775
$959$	9.00000	0.290625
$960$	0	0
$961$	5.00000	0.161290
$962$	24.0000	0.773791
$963$	0	0
$964$	34.0000	1.09507
$965$	76.0000	2.44653
$966$	0	0
$967$	28.0000	0.900419	0.450210	−	0.892923i	$-0.351349\pi$
$967$	28.0000	0.900419	0.450210	+	0.892923i	$0.351349\pi$
$968$	0	0
$969$	0	0
$970$	−144.000	−4.62356
$971$	18.0000	0.577647	0.288824	−	0.957382i	$-0.406736\pi$
$971$	18.0000	0.577647	0.288824	+	0.957382i	$0.406736\pi$
$972$	0	0
$973$	−12.0000	−0.384702
$974$	40.0000	1.28168
$975$	0	0
$976$	20.0000	0.640184
$977$	3.00000	0.0959785	0.0479893	−	0.998848i	$-0.484719\pi$
$977$	3.00000	0.0959785	0.0479893	+	0.998848i	$0.484719\pi$
$978$	0	0
$979$	−50.0000	−1.59801
$980$	−8.00000	−0.255551
$981$	0	0
$982$	28.0000	0.893516
$983$	−42.0000	−1.33959	−0.669796	−	0.742545i	$-0.733618\pi$
$983$	−42.0000	−1.33959	−0.669796	+	0.742545i	$0.733618\pi$
$984$	0	0
$985$	−8.00000	−0.254901
$986$	0	0
$987$	0	0
$988$	20.0000	0.636285
$989$	8.00000	0.254385
$990$	0	0
$991$	5.00000	0.158830	0.0794151	−	0.996842i	$-0.474695\pi$
$991$	5.00000	0.158830	0.0794151	+	0.996842i	$0.474695\pi$
$992$	48.0000	1.52400
$993$	0	0
$994$	−24.0000	−0.761234
$995$	−12.0000	−0.380426
$996$	0	0
$997$	−56.0000	−1.77354	−0.886769	−	0.462213i	$-0.847056\pi$
$997$	−56.0000	−1.77354	−0.886769	+	0.462213i	$0.847056\pi$
$998$	40.0000	1.26618
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1449.2.a.a.1.1		1
3.2	odd	2		483.2.a.b.1.1	✓	1
12.11	even	2		7728.2.a.l.1.1		1
21.20	even	2		3381.2.a.l.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.a.b.1.1	✓	1	3.2	odd	2
1449.2.a.a.1.1		1	1.1	even	1	trivial
3381.2.a.l.1.1		1	21.20	even	2
7728.2.a.l.1.1		1	12.11	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:	\( N \)	\(=\)	\( 1449 = 3^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1449.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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