LMFDB - Embedded newform 4600.2.a.m.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4600,2,Mod(1,4600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4600, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4600.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4600 = 2^{3} \cdot 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4600.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:	$36.7311849298$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	4600.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

$q+2.00000 q^{3} -3.00000 q^{7} +1.00000 q^{9} +5.00000 q^{11} -5.00000 q^{13} -4.00000 q^{17} +1.00000 q^{19} -6.00000 q^{21} -1.00000 q^{23} -4.00000 q^{27} +9.00000 q^{29} -2.00000 q^{31} +10.0000 q^{33} -2.00000 q^{37} -10.0000 q^{39} +3.00000 q^{41} -7.00000 q^{43} -12.0000 q^{47} +2.00000 q^{49} -8.00000 q^{51} +12.0000 q^{53} +2.00000 q^{57} -6.00000 q^{59} -10.0000 q^{61} -3.00000 q^{63} -8.00000 q^{67} -2.00000 q^{69} +2.00000 q^{71} +1.00000 q^{73} -15.0000 q^{77} -11.0000 q^{79} -11.0000 q^{81} +9.00000 q^{83} +18.0000 q^{87} -14.0000 q^{89} +15.0000 q^{91} -4.00000 q^{93} -16.0000 q^{97} +5.00000 q^{99} +O(q^{100})$

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	$-0.304087\pi$
$3$	2.00000	1.15470	0.577350	+	0.816497i	$0.304087\pi$
$4$	0	0
$5$	0	0
$5$	0	0
$6$	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
$13$	−5.00000	−1.38675	−0.693375	−	0.720577i	$-0.743877\pi$
$13$	−5.00000	−1.38675	−0.693375	+	0.720577i	$0.743877\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	−4.00000	−0.970143	−0.485071	−	0.874475i	$-0.661206\pi$
$17$	−4.00000	−0.970143	−0.485071	+	0.874475i	$0.661206\pi$
$18$	0	0
$19$	1.00000	0.229416	0.114708	−	0.993399i	$-0.463407\pi$
$19$	1.00000	0.229416	0.114708	+	0.993399i	$0.463407\pi$
$20$	0	0
$21$	−6.00000	−1.30931
$22$	0	0
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	0	0
$25$	0	0
$26$	0	0
$27$	−4.00000	−0.769800
$28$	0	0
$29$	9.00000	1.67126	0.835629	−	0.549294i	$-0.185103\pi$
$29$	9.00000	1.67126	0.835629	+	0.549294i	$0.185103\pi$
$30$	0	0
$31$	−2.00000	−0.359211	−0.179605	−	0.983739i	$-0.557482\pi$
$31$	−2.00000	−0.359211	−0.179605	+	0.983739i	$0.557482\pi$
$32$	0	0
$33$	10.0000	1.74078
$34$	0	0
$35$	0	0
$36$	0	0
$37$	−2.00000	−0.328798	−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000	−0.328798	−0.164399	+	0.986394i	$0.552568\pi$
$38$	0	0
$39$	−10.0000	−1.60128
$40$	0	0
$41$	3.00000	0.468521	0.234261	−	0.972174i	$-0.424733\pi$
$41$	3.00000	0.468521	0.234261	+	0.972174i	$0.424733\pi$
$42$	0	0
$43$	−7.00000	−1.06749	−0.533745	−	0.845645i	$-0.679216\pi$
$43$	−7.00000	−1.06749	−0.533745	+	0.845645i	$0.679216\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	−12.0000	−1.75038	−0.875190	−	0.483779i	$-0.839264\pi$
$47$	−12.0000	−1.75038	−0.875190	+	0.483779i	$0.839264\pi$
$48$	0	0
$49$	2.00000	0.285714
$50$	0	0
$51$	−8.00000	−1.12022
$52$	0	0
$53$	12.0000	1.64833	0.824163	−	0.566352i	$-0.191646\pi$
$53$	12.0000	1.64833	0.824163	+	0.566352i	$0.191646\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	2.00000	0.264906
$58$	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
$61$	−10.0000	−1.28037	−0.640184	−	0.768221i	$-0.721142\pi$
$61$	−10.0000	−1.28037	−0.640184	+	0.768221i	$0.721142\pi$
$62$	0	0
$63$	−3.00000	−0.377964
$64$	0	0
$65$	0	0
$66$	0	0
$67$	−8.00000	−0.977356	−0.488678	−	0.872464i	$-0.662521\pi$
$67$	−8.00000	−0.977356	−0.488678	+	0.872464i	$0.662521\pi$
$68$	0	0
$69$	−2.00000	−0.240772
$70$	0	0
$71$	2.00000	0.237356	0.118678	−	0.992933i	$-0.462134\pi$
$71$	2.00000	0.237356	0.118678	+	0.992933i	$0.462134\pi$
$72$	0	0
$73$	1.00000	0.117041	0.0585206	−	0.998286i	$-0.481362\pi$
$73$	1.00000	0.117041	0.0585206	+	0.998286i	$0.481362\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	−15.0000	−1.70941
$78$	0	0
$79$	−11.0000	−1.23760	−0.618798	−	0.785550i	$-0.712380\pi$
$79$	−11.0000	−1.23760	−0.618798	+	0.785550i	$0.712380\pi$
$80$	0	0
$81$	−11.0000	−1.22222
$82$	0	0
$83$	9.00000	0.987878	0.493939	−	0.869496i	$-0.335557\pi$
$83$	9.00000	0.987878	0.493939	+	0.869496i	$0.335557\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	18.0000	1.92980
$88$	0	0
$89$	−14.0000	−1.48400	−0.741999	−	0.670402i	$-0.766122\pi$
$89$	−14.0000	−1.48400	−0.741999	+	0.670402i	$0.766122\pi$
$90$	0	0
$91$	15.0000	1.57243
$92$	0	0
$93$	−4.00000	−0.414781
$94$	0	0
$95$	0	0
$96$	0	0
$97$	−16.0000	−1.62455	−0.812277	−	0.583272i	$-0.801772\pi$
$97$	−16.0000	−1.62455	−0.812277	+	0.583272i	$0.801772\pi$
$98$	0	0
$99$	5.00000	0.502519
$100$	0	0
$101$	−14.0000	−1.39305	−0.696526	−	0.717532i	$-0.745272\pi$
$101$	−14.0000	−1.39305	−0.696526	+	0.717532i	$0.745272\pi$
$102$	0	0
$103$	−9.00000	−0.886796	−0.443398	−	0.896325i	$-0.646227\pi$
$103$	−9.00000	−0.886796	−0.443398	+	0.896325i	$0.646227\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	16.0000	1.54678	0.773389	−	0.633932i	$-0.218560\pi$
$107$	16.0000	1.54678	0.773389	+	0.633932i	$0.218560\pi$
$108$	0	0
$109$	−10.0000	−0.957826	−0.478913	−	0.877862i	$-0.658969\pi$
$109$	−10.0000	−0.957826	−0.478913	+	0.877862i	$0.658969\pi$
$110$	0	0
$111$	−4.00000	−0.379663
$112$	0	0
$113$	8.00000	0.752577	0.376288	−	0.926503i	$-0.377200\pi$
$113$	8.00000	0.752577	0.376288	+	0.926503i	$0.377200\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	−5.00000	−0.462250
$118$	0	0
$119$	12.0000	1.10004
$120$	0	0
$121$	14.0000	1.27273
$122$	0	0
$123$	6.00000	0.541002
$124$	0	0
$125$	0	0
$126$	0	0
$127$	−10.0000	−0.887357	−0.443678	−	0.896186i	$-0.646327\pi$
$127$	−10.0000	−0.887357	−0.443678	+	0.896186i	$0.646327\pi$
$128$	0	0
$129$	−14.0000	−1.23263
$130$	0	0
$131$	6.00000	0.524222	0.262111	−	0.965038i	$-0.415581\pi$
$131$	6.00000	0.524222	0.262111	+	0.965038i	$0.415581\pi$
$132$	0	0
$133$	−3.00000	−0.260133
$134$	0	0
$135$	0	0
$136$	0	0
$137$	6.00000	0.512615	0.256307	−	0.966595i	$-0.417494\pi$
$137$	6.00000	0.512615	0.256307	+	0.966595i	$0.417494\pi$
$138$	0	0
$139$	12.0000	1.01783	0.508913	−	0.860818i	$-0.330047\pi$
$139$	12.0000	1.01783	0.508913	+	0.860818i	$0.330047\pi$
$140$	0	0
$141$	−24.0000	−2.02116
$142$	0	0
$143$	−25.0000	−2.09061
$144$	0	0
$145$	0	0
$146$	0	0
$147$	4.00000	0.329914
$148$	0	0
$149$	14.0000	1.14692	0.573462	−	0.819232i	$-0.305600\pi$
$149$	14.0000	1.14692	0.573462	+	0.819232i	$0.305600\pi$
$150$	0	0
$151$	−18.0000	−1.46482	−0.732410	−	0.680864i	$-0.761604\pi$
$151$	−18.0000	−1.46482	−0.732410	+	0.680864i	$0.761604\pi$
$152$	0	0
$153$	−4.00000	−0.323381
$154$	0	0
$155$	0	0
$156$	0	0
$157$	8.00000	0.638470	0.319235	−	0.947676i	$-0.396574\pi$
$157$	8.00000	0.638470	0.319235	+	0.947676i	$0.396574\pi$
$158$	0	0
$159$	24.0000	1.90332
$160$	0	0
$161$	3.00000	0.236433
$162$	0	0
$163$	16.0000	1.25322	0.626608	−	0.779334i	$-0.284443\pi$
$163$	16.0000	1.25322	0.626608	+	0.779334i	$0.284443\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	−14.0000	−1.08335	−0.541676	−	0.840587i	$-0.682210\pi$
$167$	−14.0000	−1.08335	−0.541676	+	0.840587i	$0.682210\pi$
$168$	0	0
$169$	12.0000	0.923077
$170$	0	0
$171$	1.00000	0.0764719
$172$	0	0
$173$	5.00000	0.380143	0.190071	−	0.981770i	$-0.439128\pi$
$173$	5.00000	0.380143	0.190071	+	0.981770i	$0.439128\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	−12.0000	−0.901975
$178$	0	0
$179$	12.0000	0.896922	0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000	0.896922	0.448461	+	0.893802i	$0.351972\pi$
$180$	0	0
$181$	−20.0000	−1.48659	−0.743294	−	0.668965i	$-0.766738\pi$
$181$	−20.0000	−1.48659	−0.743294	+	0.668965i	$0.766738\pi$
$182$	0	0
$183$	−20.0000	−1.47844
$184$	0	0
$185$	0	0
$186$	0	0
$187$	−20.0000	−1.46254
$188$	0	0
$189$	12.0000	0.872872
$190$	0	0
$191$	−1.00000	−0.0723575	−0.0361787	−	0.999345i	$-0.511519\pi$
$191$	−1.00000	−0.0723575	−0.0361787	+	0.999345i	$0.511519\pi$
$192$	0	0
$193$	2.00000	0.143963	0.0719816	−	0.997406i	$-0.477068\pi$
$193$	2.00000	0.143963	0.0719816	+	0.997406i	$0.477068\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	−23.0000	−1.63868	−0.819341	−	0.573306i	$-0.805660\pi$
$197$	−23.0000	−1.63868	−0.819341	+	0.573306i	$0.805660\pi$
$198$	0	0
$199$	5.00000	0.354441	0.177220	−	0.984171i	$-0.443289\pi$
$199$	5.00000	0.354441	0.177220	+	0.984171i	$0.443289\pi$
$200$	0	0
$201$	−16.0000	−1.12855
$202$	0	0
$203$	−27.0000	−1.89503
$204$	0	0
$205$	0	0
$206$	0	0
$207$	−1.00000	−0.0695048
$208$	0	0
$209$	5.00000	0.345857
$210$	0	0
$211$	−2.00000	−0.137686	−0.0688428	−	0.997628i	$-0.521931\pi$
$211$	−2.00000	−0.137686	−0.0688428	+	0.997628i	$0.521931\pi$
$212$	0	0
$213$	4.00000	0.274075
$214$	0	0
$215$	0	0
$216$	0	0
$217$	6.00000	0.407307
$218$	0	0
$219$	2.00000	0.135147
$220$	0	0
$221$	20.0000	1.34535
$222$	0	0
$223$	−8.00000	−0.535720	−0.267860	−	0.963458i	$-0.586316\pi$
$223$	−8.00000	−0.535720	−0.267860	+	0.963458i	$0.586316\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	20.0000	1.32745	0.663723	−	0.747978i	$-0.268975\pi$
$227$	20.0000	1.32745	0.663723	+	0.747978i	$0.268975\pi$
$228$	0	0
$229$	−30.0000	−1.98246	−0.991228	−	0.132164i	$-0.957808\pi$
$229$	−30.0000	−1.98246	−0.991228	+	0.132164i	$0.957808\pi$
$230$	0	0
$231$	−30.0000	−1.97386
$232$	0	0
$233$	−25.0000	−1.63780	−0.818902	−	0.573933i	$-0.805417\pi$
$233$	−25.0000	−1.63780	−0.818902	+	0.573933i	$0.805417\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	−22.0000	−1.42905
$238$	0	0
$239$	12.0000	0.776215	0.388108	−	0.921614i	$-0.373129\pi$
$239$	12.0000	0.776215	0.388108	+	0.921614i	$0.373129\pi$
$240$	0	0
$241$	−4.00000	−0.257663	−0.128831	−	0.991667i	$-0.541123\pi$
$241$	−4.00000	−0.257663	−0.128831	+	0.991667i	$0.541123\pi$
$242$	0	0
$243$	−10.0000	−0.641500
$244$	0	0
$245$	0	0
$246$	0	0
$247$	−5.00000	−0.318142
$248$	0	0
$249$	18.0000	1.14070
$250$	0	0
$251$	20.0000	1.26239	0.631194	−	0.775625i	$-0.282565\pi$
$251$	20.0000	1.26239	0.631194	+	0.775625i	$0.282565\pi$
$252$	0	0
$253$	−5.00000	−0.314347
$254$	0	0
$255$	0	0
$256$	0	0
$257$	−2.00000	−0.124757	−0.0623783	−	0.998053i	$-0.519869\pi$
$257$	−2.00000	−0.124757	−0.0623783	+	0.998053i	$0.519869\pi$
$258$	0	0
$259$	6.00000	0.372822
$260$	0	0
$261$	9.00000	0.557086
$262$	0	0
$263$	−16.0000	−0.986602	−0.493301	−	0.869859i	$-0.664210\pi$
$263$	−16.0000	−0.986602	−0.493301	+	0.869859i	$0.664210\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	−28.0000	−1.71357
$268$	0	0
$269$	5.00000	0.304855	0.152428	−	0.988315i	$-0.451291\pi$
$269$	5.00000	0.304855	0.152428	+	0.988315i	$0.451291\pi$
$270$	0	0
$271$	12.0000	0.728948	0.364474	−	0.931214i	$-0.381249\pi$
$271$	12.0000	0.728948	0.364474	+	0.931214i	$0.381249\pi$
$272$	0	0
$273$	30.0000	1.81568
$274$	0	0
$275$	0	0
$276$	0	0
$277$	13.0000	0.781094	0.390547	−	0.920583i	$-0.372286\pi$
$277$	13.0000	0.781094	0.390547	+	0.920583i	$0.372286\pi$
$278$	0	0
$279$	−2.00000	−0.119737
$280$	0	0
$281$	−8.00000	−0.477240	−0.238620	−	0.971113i	$-0.576695\pi$
$281$	−8.00000	−0.477240	−0.238620	+	0.971113i	$0.576695\pi$
$282$	0	0
$283$	−4.00000	−0.237775	−0.118888	−	0.992908i	$-0.537933\pi$
$283$	−4.00000	−0.237775	−0.118888	+	0.992908i	$0.537933\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	−9.00000	−0.531253
$288$	0	0
$289$	−1.00000	−0.0588235
$290$	0	0
$291$	−32.0000	−1.87587
$292$	0	0
$293$	28.0000	1.63578	0.817889	−	0.575376i	$-0.195144\pi$
$293$	28.0000	1.63578	0.817889	+	0.575376i	$0.195144\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	−20.0000	−1.16052
$298$	0	0
$299$	5.00000	0.289157
$300$	0	0
$301$	21.0000	1.21042
$302$	0	0
$303$	−28.0000	−1.60856
$304$	0	0
$305$	0	0
$306$	0	0
$307$	16.0000	0.913168	0.456584	−	0.889680i	$-0.349073\pi$
$307$	16.0000	0.913168	0.456584	+	0.889680i	$0.349073\pi$
$308$	0	0
$309$	−18.0000	−1.02398
$310$	0	0
$311$	18.0000	1.02069	0.510343	−	0.859971i	$-0.329518\pi$
$311$	18.0000	1.02069	0.510343	+	0.859971i	$0.329518\pi$
$312$	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
$315$	0	0
$316$	0	0
$317$	17.0000	0.954815	0.477408	−	0.878682i	$-0.341577\pi$
$317$	17.0000	0.954815	0.477408	+	0.878682i	$0.341577\pi$
$318$	0	0
$319$	45.0000	2.51952
$320$	0	0
$321$	32.0000	1.78607
$322$	0	0
$323$	−4.00000	−0.222566
$324$	0	0
$325$	0	0
$326$	0	0
$327$	−20.0000	−1.10600
$328$	0	0
$329$	36.0000	1.98474
$330$	0	0
$331$	26.0000	1.42909	0.714545	−	0.699590i	$-0.246634\pi$
$331$	26.0000	1.42909	0.714545	+	0.699590i	$0.246634\pi$
$332$	0	0
$333$	−2.00000	−0.109599
$334$	0	0
$335$	0	0
$336$	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
$339$	16.0000	0.869001
$340$	0	0
$341$	−10.0000	−0.541530
$342$	0	0
$343$	15.0000	0.809924
$344$	0	0
$345$	0	0
$346$	0	0
$347$	32.0000	1.71785	0.858925	−	0.512101i	$-0.171133\pi$
$347$	32.0000	1.71785	0.858925	+	0.512101i	$0.171133\pi$
$348$	0	0
$349$	−7.00000	−0.374701	−0.187351	−	0.982293i	$-0.559990\pi$
$349$	−7.00000	−0.374701	−0.187351	+	0.982293i	$0.559990\pi$
$350$	0	0
$351$	20.0000	1.06752
$352$	0	0
$353$	21.0000	1.11772	0.558859	−	0.829263i	$-0.311239\pi$
$353$	21.0000	1.11772	0.558859	+	0.829263i	$0.311239\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	24.0000	1.27021
$358$	0	0
$359$	−3.00000	−0.158334	−0.0791670	−	0.996861i	$-0.525226\pi$
$359$	−3.00000	−0.158334	−0.0791670	+	0.996861i	$0.525226\pi$
$360$	0	0
$361$	−18.0000	−0.947368
$362$	0	0
$363$	28.0000	1.46962
$364$	0	0
$365$	0	0
$366$	0	0
$367$	−15.0000	−0.782994	−0.391497	−	0.920179i	$-0.628043\pi$
$367$	−15.0000	−0.782994	−0.391497	+	0.920179i	$0.628043\pi$
$368$	0	0
$369$	3.00000	0.156174
$370$	0	0
$371$	−36.0000	−1.86903
$372$	0	0
$373$	−4.00000	−0.207112	−0.103556	−	0.994624i	$-0.533022\pi$
$373$	−4.00000	−0.207112	−0.103556	+	0.994624i	$0.533022\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	−45.0000	−2.31762
$378$	0	0
$379$	−4.00000	−0.205466	−0.102733	−	0.994709i	$-0.532759\pi$
$379$	−4.00000	−0.205466	−0.102733	+	0.994709i	$0.532759\pi$
$380$	0	0
$381$	−20.0000	−1.02463
$382$	0	0
$383$	−23.0000	−1.17525	−0.587623	−	0.809135i	$-0.699936\pi$
$383$	−23.0000	−1.17525	−0.587623	+	0.809135i	$0.699936\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	−7.00000	−0.355830
$388$	0	0
$389$	−4.00000	−0.202808	−0.101404	−	0.994845i	$-0.532333\pi$
$389$	−4.00000	−0.202808	−0.101404	+	0.994845i	$0.532333\pi$
$390$	0	0
$391$	4.00000	0.202289
$392$	0	0
$393$	12.0000	0.605320
$394$	0	0
$395$	0	0
$396$	0	0
$397$	−6.00000	−0.301131	−0.150566	−	0.988600i	$-0.548110\pi$
$397$	−6.00000	−0.301131	−0.150566	+	0.988600i	$0.548110\pi$
$398$	0	0
$399$	−6.00000	−0.300376
$400$	0	0
$401$	6.00000	0.299626	0.149813	−	0.988714i	$-0.452133\pi$
$401$	6.00000	0.299626	0.149813	+	0.988714i	$0.452133\pi$
$402$	0	0
$403$	10.0000	0.498135
$404$	0	0
$405$	0	0
$406$	0	0
$407$	−10.0000	−0.495682
$408$	0	0
$409$	−35.0000	−1.73064	−0.865319	−	0.501221i	$-0.832884\pi$
$409$	−35.0000	−1.73064	−0.865319	+	0.501221i	$0.832884\pi$
$410$	0	0
$411$	12.0000	0.591916
$412$	0	0
$413$	18.0000	0.885722
$414$	0	0
$415$	0	0
$416$	0	0
$417$	24.0000	1.17529
$418$	0	0
$419$	3.00000	0.146560	0.0732798	−	0.997311i	$-0.476653\pi$
$419$	3.00000	0.146560	0.0732798	+	0.997311i	$0.476653\pi$
$420$	0	0
$421$	−2.00000	−0.0974740	−0.0487370	−	0.998812i	$-0.515520\pi$
$421$	−2.00000	−0.0974740	−0.0487370	+	0.998812i	$0.515520\pi$
$422$	0	0
$423$	−12.0000	−0.583460
$424$	0	0
$425$	0	0
$426$	0	0
$427$	30.0000	1.45180
$428$	0	0
$429$	−50.0000	−2.41402
$430$	0	0
$431$	16.0000	0.770693	0.385346	−	0.922772i	$-0.374082\pi$
$431$	16.0000	0.770693	0.385346	+	0.922772i	$0.374082\pi$
$432$	0	0
$433$	6.00000	0.288342	0.144171	−	0.989553i	$-0.453949\pi$
$433$	6.00000	0.288342	0.144171	+	0.989553i	$0.453949\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	−1.00000	−0.0478365
$438$	0	0
$439$	0	0		−	1.00000i	$-0.5\pi$
$439$	0	0			1.00000i	$0.5\pi$
$440$	0	0
$441$	2.00000	0.0952381
$442$	0	0
$443$	14.0000	0.665160	0.332580	−	0.943075i	$-0.392081\pi$
$443$	14.0000	0.665160	0.332580	+	0.943075i	$0.392081\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	28.0000	1.32435
$448$	0	0
$449$	6.00000	0.283158	0.141579	−	0.989927i	$-0.454782\pi$
$449$	6.00000	0.283158	0.141579	+	0.989927i	$0.454782\pi$
$450$	0	0
$451$	15.0000	0.706322
$452$	0	0
$453$	−36.0000	−1.69143
$454$	0	0
$455$	0	0
$456$	0	0
$457$	−28.0000	−1.30978	−0.654892	−	0.755722i	$-0.727286\pi$
$457$	−28.0000	−1.30978	−0.654892	+	0.755722i	$0.727286\pi$
$458$	0	0
$459$	16.0000	0.746816
$460$	0	0
$461$	41.0000	1.90956	0.954780	−	0.297313i	$-0.0960904\pi$
$461$	41.0000	1.90956	0.954780	+	0.297313i	$0.0960904\pi$
$462$	0	0
$463$	24.0000	1.11537	0.557687	−	0.830051i	$-0.311689\pi$
$463$	24.0000	1.11537	0.557687	+	0.830051i	$0.311689\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	−21.0000	−0.971764	−0.485882	−	0.874024i	$-0.661502\pi$
$467$	−21.0000	−0.971764	−0.485882	+	0.874024i	$0.661502\pi$
$468$	0	0
$469$	24.0000	1.10822
$470$	0	0
$471$	16.0000	0.737241
$472$	0	0
$473$	−35.0000	−1.60930
$474$	0	0
$475$	0	0
$476$	0	0
$477$	12.0000	0.549442
$478$	0	0
$479$	−17.0000	−0.776750	−0.388375	−	0.921501i	$-0.626963\pi$
$479$	−17.0000	−0.776750	−0.388375	+	0.921501i	$0.626963\pi$
$480$	0	0
$481$	10.0000	0.455961
$482$	0	0
$483$	6.00000	0.273009
$484$	0	0
$485$	0	0
$486$	0	0
$487$	−32.0000	−1.45006	−0.725029	−	0.688718i	$-0.758174\pi$
$487$	−32.0000	−1.45006	−0.725029	+	0.688718i	$0.758174\pi$
$488$	0	0
$489$	32.0000	1.44709
$490$	0	0
$491$	−2.00000	−0.0902587	−0.0451294	−	0.998981i	$-0.514370\pi$
$491$	−2.00000	−0.0902587	−0.0451294	+	0.998981i	$0.514370\pi$
$492$	0	0
$493$	−36.0000	−1.62136
$494$	0	0
$495$	0	0
$496$	0	0
$497$	−6.00000	−0.269137
$498$	0	0
$499$	24.0000	1.07439	0.537194	−	0.843459i	$-0.319484\pi$
$499$	24.0000	1.07439	0.537194	+	0.843459i	$0.319484\pi$
$500$	0	0
$501$	−28.0000	−1.25095
$502$	0	0
$503$	−5.00000	−0.222939	−0.111469	−	0.993768i	$-0.535556\pi$
$503$	−5.00000	−0.222939	−0.111469	+	0.993768i	$0.535556\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	24.0000	1.06588
$508$	0	0
$509$	30.0000	1.32973	0.664863	−	0.746965i	$-0.268490\pi$
$509$	30.0000	1.32973	0.664863	+	0.746965i	$0.268490\pi$
$510$	0	0
$511$	−3.00000	−0.132712
$512$	0	0
$513$	−4.00000	−0.176604
$514$	0	0
$515$	0	0
$516$	0	0
$517$	−60.0000	−2.63880
$518$	0	0
$519$	10.0000	0.438951
$520$	0	0
$521$	18.0000	0.788594	0.394297	−	0.918983i	$-0.370988\pi$
$521$	18.0000	0.788594	0.394297	+	0.918983i	$0.370988\pi$
$522$	0	0
$523$	7.00000	0.306089	0.153044	−	0.988219i	$-0.451092\pi$
$523$	7.00000	0.306089	0.153044	+	0.988219i	$0.451092\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	8.00000	0.348485
$528$	0	0
$529$	1.00000	0.0434783
$530$	0	0
$531$	−6.00000	−0.260378
$532$	0	0
$533$	−15.0000	−0.649722
$534$	0	0
$535$	0	0
$536$	0	0
$537$	24.0000	1.03568
$538$	0	0
$539$	10.0000	0.430730
$540$	0	0
$541$	−23.0000	−0.988847	−0.494424	−	0.869221i	$-0.664621\pi$
$541$	−23.0000	−0.988847	−0.494424	+	0.869221i	$0.664621\pi$
$542$	0	0
$543$	−40.0000	−1.71656
$544$	0	0
$545$	0	0
$546$	0	0
$547$	44.0000	1.88130	0.940652	−	0.339372i	$-0.110215\pi$
$547$	44.0000	1.88130	0.940652	+	0.339372i	$0.110215\pi$
$548$	0	0
$549$	−10.0000	−0.426790
$550$	0	0
$551$	9.00000	0.383413
$552$	0	0
$553$	33.0000	1.40330
$554$	0	0
$555$	0	0
$556$	0	0
$557$	42.0000	1.77960	0.889799	−	0.456354i	$-0.150845\pi$
$557$	42.0000	1.77960	0.889799	+	0.456354i	$0.150845\pi$
$558$	0	0
$559$	35.0000	1.48034
$560$	0	0
$561$	−40.0000	−1.68880
$562$	0	0
$563$	−39.0000	−1.64365	−0.821827	−	0.569737i	$-0.807045\pi$
$563$	−39.0000	−1.64365	−0.821827	+	0.569737i	$0.807045\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	33.0000	1.38587
$568$	0	0
$569$	−4.00000	−0.167689	−0.0838444	−	0.996479i	$-0.526720\pi$
$569$	−4.00000	−0.167689	−0.0838444	+	0.996479i	$0.526720\pi$
$570$	0	0
$571$	−44.0000	−1.84134	−0.920671	−	0.390339i	$-0.872358\pi$
$571$	−44.0000	−1.84134	−0.920671	+	0.390339i	$0.872358\pi$
$572$	0	0
$573$	−2.00000	−0.0835512
$574$	0	0
$575$	0	0
$576$	0	0
$577$	−23.0000	−0.957503	−0.478751	−	0.877951i	$-0.658910\pi$
$577$	−23.0000	−0.957503	−0.478751	+	0.877951i	$0.658910\pi$
$578$	0	0
$579$	4.00000	0.166234
$580$	0	0
$581$	−27.0000	−1.12015
$582$	0	0
$583$	60.0000	2.48495
$584$	0	0
$585$	0	0
$586$	0	0
$587$	30.0000	1.23823	0.619116	−	0.785299i	$-0.287491\pi$
$587$	30.0000	1.23823	0.619116	+	0.785299i	$0.287491\pi$
$588$	0	0
$589$	−2.00000	−0.0824086
$590$	0	0
$591$	−46.0000	−1.89219
$592$	0	0
$593$	−17.0000	−0.698106	−0.349053	−	0.937103i	$-0.613497\pi$
$593$	−17.0000	−0.698106	−0.349053	+	0.937103i	$0.613497\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	10.0000	0.409273
$598$	0	0
$599$	−14.0000	−0.572024	−0.286012	−	0.958226i	$-0.592330\pi$
$599$	−14.0000	−0.572024	−0.286012	+	0.958226i	$0.592330\pi$
$600$	0	0
$601$	−22.0000	−0.897399	−0.448699	−	0.893683i	$-0.648113\pi$
$601$	−22.0000	−0.897399	−0.448699	+	0.893683i	$0.648113\pi$
$602$	0	0
$603$	−8.00000	−0.325785
$604$	0	0
$605$	0	0
$606$	0	0
$607$	40.0000	1.62355	0.811775	−	0.583970i	$-0.198502\pi$
$607$	40.0000	1.62355	0.811775	+	0.583970i	$0.198502\pi$
$608$	0	0
$609$	−54.0000	−2.18819
$610$	0	0
$611$	60.0000	2.42734
$612$	0	0
$613$	18.0000	0.727013	0.363507	−	0.931592i	$-0.381579\pi$
$613$	18.0000	0.727013	0.363507	+	0.931592i	$0.381579\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	−32.0000	−1.28827	−0.644136	−	0.764911i	$-0.722783\pi$
$617$	−32.0000	−1.28827	−0.644136	+	0.764911i	$0.722783\pi$
$618$	0	0
$619$	−24.0000	−0.964641	−0.482321	−	0.875995i	$-0.660206\pi$
$619$	−24.0000	−0.964641	−0.482321	+	0.875995i	$0.660206\pi$
$620$	0	0
$621$	4.00000	0.160514
$622$	0	0
$623$	42.0000	1.68269
$624$	0	0
$625$	0	0
$626$	0	0
$627$	10.0000	0.399362
$628$	0	0
$629$	8.00000	0.318981
$630$	0	0
$631$	−25.0000	−0.995234	−0.497617	−	0.867397i	$-0.665792\pi$
$631$	−25.0000	−0.995234	−0.497617	+	0.867397i	$0.665792\pi$
$632$	0	0
$633$	−4.00000	−0.158986
$634$	0	0
$635$	0	0
$636$	0	0
$637$	−10.0000	−0.396214
$638$	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
$643$	29.0000	1.14365	0.571824	−	0.820376i	$-0.306236\pi$
$643$	29.0000	1.14365	0.571824	+	0.820376i	$0.306236\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	−32.0000	−1.25805	−0.629025	−	0.777385i	$-0.716546\pi$
$647$	−32.0000	−1.25805	−0.629025	+	0.777385i	$0.716546\pi$
$648$	0	0
$649$	−30.0000	−1.17760
$650$	0	0
$651$	12.0000	0.470317
$652$	0	0
$653$	−29.0000	−1.13486	−0.567429	−	0.823422i	$-0.692062\pi$
$653$	−29.0000	−1.13486	−0.567429	+	0.823422i	$0.692062\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	1.00000	0.0390137
$658$	0	0
$659$	−45.0000	−1.75295	−0.876476	−	0.481446i	$-0.840112\pi$
$659$	−45.0000	−1.75295	−0.876476	+	0.481446i	$0.840112\pi$
$660$	0	0
$661$	8.00000	0.311164	0.155582	−	0.987823i	$-0.450275\pi$
$661$	8.00000	0.311164	0.155582	+	0.987823i	$0.450275\pi$
$662$	0	0
$663$	40.0000	1.55347
$664$	0	0
$665$	0	0
$666$	0	0
$667$	−9.00000	−0.348481
$668$	0	0
$669$	−16.0000	−0.618596
$670$	0	0
$671$	−50.0000	−1.93023
$672$	0	0
$673$	15.0000	0.578208	0.289104	−	0.957298i	$-0.406643\pi$
$673$	15.0000	0.578208	0.289104	+	0.957298i	$0.406643\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	−18.0000	−0.691796	−0.345898	−	0.938272i	$-0.612426\pi$
$677$	−18.0000	−0.691796	−0.345898	+	0.938272i	$0.612426\pi$
$678$	0	0
$679$	48.0000	1.84207
$680$	0	0
$681$	40.0000	1.53280
$682$	0	0
$683$	−34.0000	−1.30097	−0.650487	−	0.759517i	$-0.725435\pi$
$683$	−34.0000	−1.30097	−0.650487	+	0.759517i	$0.725435\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	−60.0000	−2.28914
$688$	0	0
$689$	−60.0000	−2.28582
$690$	0	0
$691$	−16.0000	−0.608669	−0.304334	−	0.952565i	$-0.598434\pi$
$691$	−16.0000	−0.608669	−0.304334	+	0.952565i	$0.598434\pi$
$692$	0	0
$693$	−15.0000	−0.569803
$694$	0	0
$695$	0	0
$696$	0	0
$697$	−12.0000	−0.454532
$698$	0	0
$699$	−50.0000	−1.89117
$700$	0	0
$701$	8.00000	0.302156	0.151078	−	0.988522i	$-0.451726\pi$
$701$	8.00000	0.302156	0.151078	+	0.988522i	$0.451726\pi$
$702$	0	0
$703$	−2.00000	−0.0754314
$704$	0	0
$705$	0	0
$706$	0	0
$707$	42.0000	1.57957
$708$	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
$711$	−11.0000	−0.412532
$712$	0	0
$713$	2.00000	0.0749006
$714$	0	0
$715$	0	0
$716$	0	0
$717$	24.0000	0.896296
$718$	0	0
$719$	−34.0000	−1.26799	−0.633993	−	0.773339i	$-0.718585\pi$
$719$	−34.0000	−1.26799	−0.633993	+	0.773339i	$0.718585\pi$
$720$	0	0
$721$	27.0000	1.00553
$722$	0	0
$723$	−8.00000	−0.297523
$724$	0	0
$725$	0	0
$726$	0	0
$727$	16.0000	0.593407	0.296704	−	0.954970i	$-0.404113\pi$
$727$	16.0000	0.593407	0.296704	+	0.954970i	$0.404113\pi$
$728$	0	0
$729$	13.0000	0.481481
$730$	0	0
$731$	28.0000	1.03562
$732$	0	0
$733$	−26.0000	−0.960332	−0.480166	−	0.877178i	$-0.659424\pi$
$733$	−26.0000	−0.960332	−0.480166	+	0.877178i	$0.659424\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	−40.0000	−1.47342
$738$	0	0
$739$	−26.0000	−0.956425	−0.478213	−	0.878244i	$-0.658715\pi$
$739$	−26.0000	−0.956425	−0.478213	+	0.878244i	$0.658715\pi$
$740$	0	0
$741$	−10.0000	−0.367359
$742$	0	0
$743$	21.0000	0.770415	0.385208	−	0.922830i	$-0.374130\pi$
$743$	21.0000	0.770415	0.385208	+	0.922830i	$0.374130\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	9.00000	0.329293
$748$	0	0
$749$	−48.0000	−1.75388
$750$	0	0
$751$	19.0000	0.693320	0.346660	−	0.937991i	$-0.387316\pi$
$751$	19.0000	0.693320	0.346660	+	0.937991i	$0.387316\pi$
$752$	0	0
$753$	40.0000	1.45768
$754$	0	0
$755$	0	0
$756$	0	0
$757$	2.00000	0.0726912	0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000	0.0726912	0.0363456	+	0.999339i	$0.488428\pi$
$758$	0	0
$759$	−10.0000	−0.362977
$760$	0	0
$761$	1.00000	0.0362500	0.0181250	−	0.999836i	$-0.494230\pi$
$761$	1.00000	0.0362500	0.0181250	+	0.999836i	$0.494230\pi$
$762$	0	0
$763$	30.0000	1.08607
$764$	0	0
$765$	0	0
$766$	0	0
$767$	30.0000	1.08324
$768$	0	0
$769$	2.00000	0.0721218	0.0360609	−	0.999350i	$-0.488519\pi$
$769$	2.00000	0.0721218	0.0360609	+	0.999350i	$0.488519\pi$
$770$	0	0
$771$	−4.00000	−0.144056
$772$	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
$775$	0	0
$776$	0	0
$777$	12.0000	0.430498
$778$	0	0
$779$	3.00000	0.107486
$780$	0	0
$781$	10.0000	0.357828
$782$	0	0
$783$	−36.0000	−1.28654
$784$	0	0
$785$	0	0
$786$	0	0
$787$	−25.0000	−0.891154	−0.445577	−	0.895244i	$-0.647001\pi$
$787$	−25.0000	−0.891154	−0.445577	+	0.895244i	$0.647001\pi$
$788$	0	0
$789$	−32.0000	−1.13923
$790$	0	0
$791$	−24.0000	−0.853342
$792$	0	0
$793$	50.0000	1.77555
$794$	0	0
$795$	0	0
$796$	0	0
$797$	18.0000	0.637593	0.318796	−	0.947823i	$-0.396721\pi$
$797$	18.0000	0.637593	0.318796	+	0.947823i	$0.396721\pi$
$798$	0	0
$799$	48.0000	1.69812
$800$	0	0
$801$	−14.0000	−0.494666
$802$	0	0
$803$	5.00000	0.176446
$804$	0	0
$805$	0	0
$806$	0	0
$807$	10.0000	0.352017
$808$	0	0
$809$	−23.0000	−0.808637	−0.404318	−	0.914618i	$-0.632491\pi$
$809$	−23.0000	−0.808637	−0.404318	+	0.914618i	$0.632491\pi$
$810$	0	0
$811$	40.0000	1.40459	0.702295	−	0.711886i	$-0.252159\pi$
$811$	40.0000	1.40459	0.702295	+	0.711886i	$0.252159\pi$
$812$	0	0
$813$	24.0000	0.841717
$814$	0	0
$815$	0	0
$816$	0	0
$817$	−7.00000	−0.244899
$818$	0	0
$819$	15.0000	0.524142
$820$	0	0
$821$	51.0000	1.77991	0.889956	−	0.456046i	$-0.150735\pi$
$821$	51.0000	1.77991	0.889956	+	0.456046i	$0.150735\pi$
$822$	0	0
$823$	12.0000	0.418294	0.209147	−	0.977884i	$-0.432931\pi$
$823$	12.0000	0.418294	0.209147	+	0.977884i	$0.432931\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	7.00000	0.243414	0.121707	−	0.992566i	$-0.461163\pi$
$827$	7.00000	0.243414	0.121707	+	0.992566i	$0.461163\pi$
$828$	0	0
$829$	−31.0000	−1.07667	−0.538337	−	0.842729i	$-0.680947\pi$
$829$	−31.0000	−1.07667	−0.538337	+	0.842729i	$0.680947\pi$
$830$	0	0
$831$	26.0000	0.901930
$832$	0	0
$833$	−8.00000	−0.277184
$834$	0	0
$835$	0	0
$836$	0	0
$837$	8.00000	0.276520
$838$	0	0
$839$	15.0000	0.517858	0.258929	−	0.965896i	$-0.416631\pi$
$839$	15.0000	0.517858	0.258929	+	0.965896i	$0.416631\pi$
$840$	0	0
$841$	52.0000	1.79310
$842$	0	0
$843$	−16.0000	−0.551069
$844$	0	0
$845$	0	0
$846$	0	0
$847$	−42.0000	−1.44314
$848$	0	0
$849$	−8.00000	−0.274559
$850$	0	0
$851$	2.00000	0.0685591
$852$	0	0
$853$	19.0000	0.650548	0.325274	−	0.945620i	$-0.394544\pi$
$853$	19.0000	0.650548	0.325274	+	0.945620i	$0.394544\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	−38.0000	−1.29806	−0.649028	−	0.760765i	$-0.724824\pi$
$857$	−38.0000	−1.29806	−0.649028	+	0.760765i	$0.724824\pi$
$858$	0	0
$859$	−2.00000	−0.0682391	−0.0341196	−	0.999418i	$-0.510863\pi$
$859$	−2.00000	−0.0682391	−0.0341196	+	0.999418i	$0.510863\pi$
$860$	0	0
$861$	−18.0000	−0.613438
$862$	0	0
$863$	36.0000	1.22545	0.612727	−	0.790295i	$-0.290072\pi$
$863$	36.0000	1.22545	0.612727	+	0.790295i	$0.290072\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	−2.00000	−0.0679236
$868$	0	0
$869$	−55.0000	−1.86575
$870$	0	0
$871$	40.0000	1.35535
$872$	0	0
$873$	−16.0000	−0.541518
$874$	0	0
$875$	0	0
$876$	0	0
$877$	22.0000	0.742887	0.371444	−	0.928456i	$-0.378863\pi$
$877$	22.0000	0.742887	0.371444	+	0.928456i	$0.378863\pi$
$878$	0	0
$879$	56.0000	1.88883
$880$	0	0
$881$	2.00000	0.0673817	0.0336909	−	0.999432i	$-0.489274\pi$
$881$	2.00000	0.0673817	0.0336909	+	0.999432i	$0.489274\pi$
$882$	0	0
$883$	16.0000	0.538443	0.269221	−	0.963078i	$-0.413234\pi$
$883$	16.0000	0.538443	0.269221	+	0.963078i	$0.413234\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	48.0000	1.61168	0.805841	−	0.592132i	$-0.201714\pi$
$887$	48.0000	1.61168	0.805841	+	0.592132i	$0.201714\pi$
$888$	0	0
$889$	30.0000	1.00617
$890$	0	0
$891$	−55.0000	−1.84257
$892$	0	0
$893$	−12.0000	−0.401565
$894$	0	0
$895$	0	0
$896$	0	0
$897$	10.0000	0.333890
$898$	0	0
$899$	−18.0000	−0.600334
$900$	0	0
$901$	−48.0000	−1.59911
$902$	0	0
$903$	42.0000	1.39767
$904$	0	0
$905$	0	0
$906$	0	0
$907$	15.0000	0.498067	0.249033	−	0.968495i	$-0.419887\pi$
$907$	15.0000	0.498067	0.249033	+	0.968495i	$0.419887\pi$
$908$	0	0
$909$	−14.0000	−0.464351
$910$	0	0
$911$	5.00000	0.165657	0.0828287	−	0.996564i	$-0.473605\pi$
$911$	5.00000	0.165657	0.0828287	+	0.996564i	$0.473605\pi$
$912$	0	0
$913$	45.0000	1.48928
$914$	0	0
$915$	0	0
$916$	0	0
$917$	−18.0000	−0.594412
$918$	0	0
$919$	0	0		−	1.00000i	$-0.5\pi$
$919$	0	0			1.00000i	$0.5\pi$
$920$	0	0
$921$	32.0000	1.05444
$922$	0	0
$923$	−10.0000	−0.329154
$924$	0	0
$925$	0	0
$926$	0	0
$927$	−9.00000	−0.295599
$928$	0	0
$929$	−13.0000	−0.426516	−0.213258	−	0.976996i	$-0.568408\pi$
$929$	−13.0000	−0.426516	−0.213258	+	0.976996i	$0.568408\pi$
$930$	0	0
$931$	2.00000	0.0655474
$932$	0	0
$933$	36.0000	1.17859
$934$	0	0
$935$	0	0
$936$	0	0
$937$	−44.0000	−1.43742	−0.718709	−	0.695311i	$-0.755266\pi$
$937$	−44.0000	−1.43742	−0.718709	+	0.695311i	$0.755266\pi$
$938$	0	0
$939$	−20.0000	−0.652675
$940$	0	0
$941$	−24.0000	−0.782378	−0.391189	−	0.920310i	$-0.627936\pi$
$941$	−24.0000	−0.782378	−0.391189	+	0.920310i	$0.627936\pi$
$942$	0	0
$943$	−3.00000	−0.0976934
$944$	0	0
$945$	0	0
$946$	0	0
$947$	18.0000	0.584921	0.292461	−	0.956278i	$-0.405526\pi$
$947$	18.0000	0.584921	0.292461	+	0.956278i	$0.405526\pi$
$948$	0	0
$949$	−5.00000	−0.162307
$950$	0	0
$951$	34.0000	1.10253
$952$	0	0
$953$	−2.00000	−0.0647864	−0.0323932	−	0.999475i	$-0.510313\pi$
$953$	−2.00000	−0.0647864	−0.0323932	+	0.999475i	$0.510313\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	90.0000	2.90929
$958$	0	0
$959$	−18.0000	−0.581250
$960$	0	0
$961$	−27.0000	−0.870968
$962$	0	0
$963$	16.0000	0.515593
$964$	0	0
$965$	0	0
$966$	0	0
$967$	12.0000	0.385894	0.192947	−	0.981209i	$-0.438195\pi$
$967$	12.0000	0.385894	0.192947	+	0.981209i	$0.438195\pi$
$968$	0	0
$969$	−8.00000	−0.256997
$970$	0	0
$971$	−41.0000	−1.31575	−0.657876	−	0.753126i	$-0.728545\pi$
$971$	−41.0000	−1.31575	−0.657876	+	0.753126i	$0.728545\pi$
$972$	0	0
$973$	−36.0000	−1.15411
$974$	0	0
$975$	0	0
$976$	0	0
$977$	−20.0000	−0.639857	−0.319928	−	0.947442i	$-0.603659\pi$
$977$	−20.0000	−0.639857	−0.319928	+	0.947442i	$0.603659\pi$
$978$	0	0
$979$	−70.0000	−2.23721
$980$	0	0
$981$	−10.0000	−0.319275
$982$	0	0
$983$	−1.00000	−0.0318950	−0.0159475	−	0.999873i	$-0.505076\pi$
$983$	−1.00000	−0.0318950	−0.0159475	+	0.999873i	$0.505076\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	72.0000	2.29179
$988$	0	0
$989$	7.00000	0.222587
$990$	0	0
$991$	40.0000	1.27064	0.635321	−	0.772248i	$-0.280868\pi$
$991$	40.0000	1.27064	0.635321	+	0.772248i	$0.280868\pi$
$992$	0	0
$993$	52.0000	1.65017
$994$	0	0
$995$	0	0
$996$	0	0
$997$	5.00000	0.158352	0.0791758	−	0.996861i	$-0.474771\pi$
$997$	5.00000	0.158352	0.0791758	+	0.996861i	$0.474771\pi$
$998$	0	0
$999$	8.00000	0.253109

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4600.2.a.m.1.1	yes	1
4.3	odd	2		9200.2.a.j.1.1		1
5.2	odd	4		4600.2.e.d.4049.1		2
5.3	odd	4		4600.2.e.d.4049.2		2
5.4	even	2		4600.2.a.d.1.1	✓	1
20.19	odd	2		9200.2.a.bc.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4600.2.a.d.1.1	✓	1	5.4	even	2
4600.2.a.m.1.1	yes	1	1.1	even	1	trivial
4600.2.e.d.4049.1		2	5.2	odd	4
4600.2.e.d.4049.2		2	5.3	odd	4
9200.2.a.j.1.1		1	4.3	odd	2
9200.2.a.bc.1.1		1	20.19	odd	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:	\( N \)	\(=\)	\( 4600 = 2^{3} \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4600.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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