LMFDB - Embedded newform 3584.2.a.p.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3584,2,Mod(1,3584)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3584, 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("3584.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3584 = 2^{9} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3584.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:	$28.6183840844$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 19x^{8} + 44x^{7} + 86x^{6} - 236x^{5} - 58x^{4} + 368x^{3} - 194x^{2} - 12x + 18 $ x^10 - 2x^9 - 19x^8 + 44x^7 + 86x^6 - 236x^5 - 58x^4 + 368x^3 - 194x^2 - 12*x + 18
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$0.508920$ of defining polynomial
Character	$\chi$	$=$	3584.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.17593 q^{3} -4.23755 q^{5} +1.00000 q^{7} +7.08655 q^{9} +O(q^{10})$	$q-3.17593 q^{3} -4.23755 q^{5} +1.00000 q^{7} +7.08655 q^{9} +4.99251 q^{11} -0.439239 q^{13} +13.4582 q^{15} +3.50135 q^{17} +3.45080 q^{19} -3.17593 q^{21} -4.39770 q^{23} +12.9568 q^{25} -12.9786 q^{27} +0.132582 q^{29} -5.55912 q^{31} -15.8559 q^{33} -4.23755 q^{35} +0.572613 q^{37} +1.39499 q^{39} +5.42377 q^{41} -5.69770 q^{43} -30.0296 q^{45} -9.37162 q^{47} +1.00000 q^{49} -11.1201 q^{51} +3.65602 q^{53} -21.1560 q^{55} -10.9595 q^{57} -2.20605 q^{59} +9.89440 q^{61} +7.08655 q^{63} +1.86130 q^{65} -8.51595 q^{67} +13.9668 q^{69} +3.11263 q^{71} +9.87027 q^{73} -41.1500 q^{75} +4.99251 q^{77} +7.11263 q^{79} +19.9595 q^{81} +2.48092 q^{83} -14.8371 q^{85} -0.421071 q^{87} -5.06047 q^{89} -0.439239 q^{91} +17.6554 q^{93} -14.6229 q^{95} -16.6573 q^{97} +35.3796 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 10 q^{7} + 22 q^{9}+O(q^{10}) $ 10 * q + 10 * q^7 + 22 * q^9	$ 10 q + 10 q^{7} + 22 q^{9} + 16 q^{15} + 16 q^{17} + 8 q^{23} + 30 q^{25} - 8 q^{31} + 12 q^{33} + 20 q^{41} - 24 q^{47} + 10 q^{49} - 32 q^{55} + 28 q^{57} + 22 q^{63} + 32 q^{65} + 48 q^{73} + 40 q^{79} + 62 q^{81} - 8 q^{87} + 16 q^{89} - 32 q^{95} + 32 q^{97}+O(q^{100}) $ 10 * q + 10 * q^7 + 22 * q^9 + 16 * q^15 + 16 * q^17 + 8 * q^23 + 30 * q^25 - 8 * q^31 + 12 * q^33 + 20 * q^41 - 24 * q^47 + 10 * q^49 - 32 * q^55 + 28 * q^57 + 22 * q^63 + 32 * q^65 + 48 * q^73 + 40 * q^79 + 62 * q^81 - 8 * q^87 + 16 * q^89 - 32 * q^95 + 32 * q^97

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
$3$	−3.17593	−1.83363	−0.916813	−	0.399317i	$-0.869247\pi$
$3$	−3.17593	−1.83363	−0.916813	+	0.399317i	$0.869247\pi$
$4$	0	0
$5$	−4.23755	−1.89509	−0.947545	−	0.319623i	$-0.896444\pi$
$5$	−4.23755	−1.89509	−0.947545	+	0.319623i	$0.896444\pi$
$6$	0	0
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	0	0
$9$	7.08655	2.36218
$10$	0	0
$11$	4.99251	1.50530	0.752649	−	0.658422i	$-0.228776\pi$
$11$	4.99251	1.50530	0.752649	+	0.658422i	$0.228776\pi$
$12$	0	0
$13$	−0.439239	−0.121823	−0.0609115	−	0.998143i	$-0.519401\pi$
$13$	−0.439239	−0.121823	−0.0609115	+	0.998143i	$0.519401\pi$
$14$	0	0
$15$	13.4582	3.47488
$16$	0	0
$17$	3.50135	0.849202	0.424601	−	0.905380i	$-0.360414\pi$
$17$	3.50135	0.849202	0.424601	+	0.905380i	$0.360414\pi$
$18$	0	0
$19$	3.45080	0.791669	0.395834	−	0.918322i	$-0.370455\pi$
$19$	3.45080	0.791669	0.395834	+	0.918322i	$0.370455\pi$
$20$	0	0
$21$	−3.17593	−0.693045
$22$	0	0
$23$	−4.39770	−0.916983	−0.458492	−	0.888699i	$-0.651610\pi$
$23$	−4.39770	−0.916983	−0.458492	+	0.888699i	$0.651610\pi$
$24$	0	0
$25$	12.9568	2.59136
$26$	0	0
$27$	−12.9786	−2.49773
$28$	0	0
$29$	0.132582	0.0246199	0.0123099	−	0.999924i	$-0.496082\pi$
$29$	0.132582	0.0246199	0.0123099	+	0.999924i	$0.496082\pi$
$30$	0	0
$31$	−5.55912	−0.998447	−0.499224	−	0.866473i	$-0.666381\pi$
$31$	−5.55912	−0.998447	−0.499224	+	0.866473i	$0.666381\pi$
$32$	0	0
$33$	−15.8559	−2.76015
$34$	0	0
$35$	−4.23755	−0.716276
$36$	0	0
$37$	0.572613	0.0941371	0.0470685	−	0.998892i	$-0.485012\pi$
$37$	0.572613	0.0941371	0.0470685	+	0.998892i	$0.485012\pi$
$38$	0	0
$39$	1.39499	0.223378
$40$	0	0
$41$	5.42377	0.847051	0.423526	−	0.905884i	$-0.360792\pi$
$41$	5.42377	0.847051	0.423526	+	0.905884i	$0.360792\pi$
$42$	0	0
$43$	−5.69770	−0.868891	−0.434446	−	0.900698i	$-0.643056\pi$
$43$	−5.69770	−0.868891	−0.434446	+	0.900698i	$0.643056\pi$
$44$	0	0
$45$	−30.0296	−4.47655
$46$	0	0
$47$	−9.37162	−1.36699	−0.683496	−	0.729955i	$-0.739541\pi$
$47$	−9.37162	−1.36699	−0.683496	+	0.729955i	$0.739541\pi$
$48$	0	0
$49$	1.00000	0.142857
$50$	0	0
$51$	−11.1201	−1.55712
$52$	0	0
$53$	3.65602	0.502193	0.251096	−	0.967962i	$-0.419209\pi$
$53$	3.65602	0.502193	0.251096	+	0.967962i	$0.419209\pi$
$54$	0	0
$55$	−21.1560	−2.85267
$56$	0	0
$57$	−10.9595	−1.45162
$58$	0	0
$59$	−2.20605	−0.287203	−0.143602	−	0.989636i	$-0.545868\pi$
$59$	−2.20605	−0.287203	−0.143602	+	0.989636i	$0.545868\pi$
$60$	0	0
$61$	9.89440	1.26685	0.633424	−	0.773805i	$-0.281649\pi$
$61$	9.89440	1.26685	0.633424	+	0.773805i	$0.281649\pi$
$62$	0	0
$63$	7.08655	0.892821
$64$	0	0
$65$	1.86130	0.230866
$66$	0	0
$67$	−8.51595	−1.04039	−0.520194	−	0.854048i	$-0.674140\pi$
$67$	−8.51595	−1.04039	−0.520194	+	0.854048i	$0.674140\pi$
$68$	0	0
$69$	13.9668	1.68140
$70$	0	0
$71$	3.11263	0.369401	0.184700	−	0.982795i	$-0.440869\pi$
$71$	3.11263	0.369401	0.184700	+	0.982795i	$0.440869\pi$
$72$	0	0
$73$	9.87027	1.15523	0.577614	−	0.816310i	$-0.303984\pi$
$73$	9.87027	1.15523	0.577614	+	0.816310i	$0.303984\pi$
$74$	0	0
$75$	−41.1500	−4.75159
$76$	0	0
$77$	4.99251	0.568949
$78$	0	0
$79$	7.11263	0.800233	0.400116	−	0.916464i	$-0.368970\pi$
$79$	7.11263	0.800233	0.400116	+	0.916464i	$0.368970\pi$
$80$	0	0
$81$	19.9595	2.21772
$82$	0	0
$83$	2.48092	0.272317	0.136158	−	0.990687i	$-0.456524\pi$
$83$	2.48092	0.272317	0.136158	+	0.990687i	$0.456524\pi$
$84$	0	0
$85$	−14.8371	−1.60931
$86$	0	0
$87$	−0.421071	−0.0451436
$88$	0	0
$89$	−5.06047	−0.536409	−0.268204	−	0.963362i	$-0.586430\pi$
$89$	−5.06047	−0.536409	−0.268204	+	0.963362i	$0.586430\pi$
$90$	0	0
$91$	−0.439239	−0.0460448
$92$	0	0
$93$	17.6554	1.83078
$94$	0	0
$95$	−14.6229	−1.50028
$96$	0	0
$97$	−16.6573	−1.69130	−0.845648	−	0.533740i	$-0.820786\pi$
$97$	−16.6573	−1.69130	−0.845648	+	0.533740i	$0.820786\pi$
$98$	0	0
$99$	35.3796	3.55579
$100$	0	0
$101$	−10.2408	−1.01900	−0.509498	−	0.860472i	$-0.670169\pi$
$101$	−10.2408	−1.01900	−0.509498	+	0.860472i	$0.670169\pi$
$102$	0	0
$103$	10.5420	1.03874	0.519368	−	0.854551i	$-0.326168\pi$
$103$	10.5420	1.03874	0.519368	+	0.854551i	$0.326168\pi$
$104$	0	0
$105$	13.4582	1.31338
$106$	0	0
$107$	0.214131	0.0207009	0.0103504	−	0.999946i	$-0.496705\pi$
$107$	0.214131	0.0207009	0.0103504	+	0.999946i	$0.496705\pi$
$108$	0	0
$109$	19.7277	1.88957	0.944787	−	0.327685i	$-0.106268\pi$
$109$	19.7277	1.88957	0.944787	+	0.327685i	$0.106268\pi$
$110$	0	0
$111$	−1.81858	−0.172612
$112$	0	0
$113$	−4.95411	−0.466044	−0.233022	−	0.972471i	$-0.574861\pi$
$113$	−4.95411	−0.466044	−0.233022	+	0.972471i	$0.574861\pi$
$114$	0	0
$115$	18.6355	1.73777
$116$	0	0
$117$	−3.11269	−0.287768
$118$	0	0
$119$	3.50135	0.320968
$120$	0	0
$121$	13.9251	1.26592
$122$	0	0
$123$	−17.2255	−1.55317
$124$	0	0
$125$	−33.7174	−3.01578
$126$	0	0
$127$	7.77540	0.689955	0.344978	−	0.938611i	$-0.387887\pi$
$127$	7.77540	0.689955	0.344978	+	0.938611i	$0.387887\pi$
$128$	0	0
$129$	18.0955	1.59322
$130$	0	0
$131$	8.21947	0.718139	0.359069	−	0.933311i	$-0.383094\pi$
$131$	8.21947	0.718139	0.359069	+	0.933311i	$0.383094\pi$
$132$	0	0
$133$	3.45080	0.299223
$134$	0	0
$135$	54.9975	4.73343
$136$	0	0
$137$	−12.0434	−1.02893	−0.514467	−	0.857510i	$-0.672010\pi$
$137$	−12.0434	−1.02893	−0.514467	+	0.857510i	$0.672010\pi$
$138$	0	0
$139$	−6.45251	−0.547295	−0.273648	−	0.961830i	$-0.588230\pi$
$139$	−6.45251	−0.547295	−0.273648	+	0.961830i	$0.588230\pi$
$140$	0	0
$141$	29.7636	2.50655
$142$	0	0
$143$	−2.19291	−0.183380
$144$	0	0
$145$	−0.561823	−0.0466568
$146$	0	0
$147$	−3.17593	−0.261947
$148$	0	0
$149$	−14.2645	−1.16860	−0.584298	−	0.811539i	$-0.698630\pi$
$149$	−14.2645	−1.16860	−0.584298	+	0.811539i	$0.698630\pi$
$150$	0	0
$151$	2.44985	0.199366	0.0996830	−	0.995019i	$-0.468217\pi$
$151$	2.44985	0.199366	0.0996830	+	0.995019i	$0.468217\pi$
$152$	0	0
$153$	24.8125	2.00597
$154$	0	0
$155$	23.5570	1.89215
$156$	0	0
$157$	21.2893	1.69907	0.849537	−	0.527529i	$-0.176882\pi$
$157$	21.2893	1.69907	0.849537	+	0.527529i	$0.176882\pi$
$158$	0	0
$159$	−11.6113	−0.920834
$160$	0	0
$161$	−4.39770	−0.346587
$162$	0	0
$163$	−7.11574	−0.557348	−0.278674	−	0.960386i	$-0.589895\pi$
$163$	−7.11574	−0.557348	−0.278674	+	0.960386i	$0.589895\pi$
$164$	0	0
$165$	67.1900	5.23073
$166$	0	0
$167$	−9.74662	−0.754216	−0.377108	−	0.926169i	$-0.623081\pi$
$167$	−9.74662	−0.754216	−0.377108	+	0.926169i	$0.623081\pi$
$168$	0	0
$169$	−12.8071	−0.985159
$170$	0	0
$171$	24.4543	1.87007
$172$	0	0
$173$	18.7998	1.42932	0.714662	−	0.699470i	$-0.246580\pi$
$173$	18.7998	1.42932	0.714662	+	0.699470i	$0.246580\pi$
$174$	0	0
$175$	12.9568	0.979443
$176$	0	0
$177$	7.00627	0.526623
$178$	0	0
$179$	14.1728	1.05932	0.529662	−	0.848209i	$-0.322319\pi$
$179$	14.1728	1.05932	0.529662	+	0.848209i	$0.322319\pi$
$180$	0	0
$181$	−2.56453	−0.190620	−0.0953101	−	0.995448i	$-0.530384\pi$
$181$	−2.56453	−0.190620	−0.0953101	+	0.995448i	$0.530384\pi$
$182$	0	0
$183$	−31.4240	−2.32293
$184$	0	0
$185$	−2.42648	−0.178398
$186$	0	0
$187$	17.4805	1.27830
$188$	0	0
$189$	−12.9786	−0.944054
$190$	0	0
$191$	−12.9685	−0.938367	−0.469184	−	0.883101i	$-0.655452\pi$
$191$	−12.9685	−0.938367	−0.469184	+	0.883101i	$0.655452\pi$
$192$	0	0
$193$	10.1387	0.729800	0.364900	−	0.931047i	$-0.381103\pi$
$193$	10.1387	0.729800	0.364900	+	0.931047i	$0.381103\pi$
$194$	0	0
$195$	−5.91136	−0.423321
$196$	0	0
$197$	−2.84111	−0.202421	−0.101211	−	0.994865i	$-0.532272\pi$
$197$	−2.84111	−0.202421	−0.101211	+	0.994865i	$0.532272\pi$
$198$	0	0
$199$	−11.4094	−0.808789	−0.404394	−	0.914585i	$-0.632518\pi$
$199$	−11.4094	−0.808789	−0.404394	+	0.914585i	$0.632518\pi$
$200$	0	0
$201$	27.0461	1.90768
$202$	0	0
$203$	0.132582	0.00930543
$204$	0	0
$205$	−22.9835	−1.60524
$206$	0	0
$207$	−31.1645	−2.16608
$208$	0	0
$209$	17.2282	1.19170
$210$	0	0
$211$	7.70104	0.530161	0.265081	−	0.964226i	$-0.414601\pi$
$211$	7.70104	0.530161	0.265081	+	0.964226i	$0.414601\pi$
$212$	0	0
$213$	−9.88549	−0.677342
$214$	0	0
$215$	24.1443	1.64663
$216$	0	0
$217$	−5.55912	−0.377378
$218$	0	0
$219$	−31.3473	−2.11825
$220$	0	0
$221$	−1.53793	−0.103452
$222$	0	0
$223$	−21.9334	−1.46877	−0.734386	−	0.678732i	$-0.762530\pi$
$223$	−21.9334	−1.46877	−0.734386	+	0.678732i	$0.762530\pi$
$224$	0	0
$225$	91.8191	6.12127
$226$	0	0
$227$	4.75913	0.315875	0.157937	−	0.987449i	$-0.449516\pi$
$227$	4.75913	0.315875	0.157937	+	0.987449i	$0.449516\pi$
$228$	0	0
$229$	13.1430	0.868512	0.434256	−	0.900790i	$-0.357011\pi$
$229$	13.1430	0.868512	0.434256	+	0.900790i	$0.357011\pi$
$230$	0	0
$231$	−15.8559	−1.04324
$232$	0	0
$233$	21.0461	1.37877	0.689387	−	0.724393i	$-0.257880\pi$
$233$	21.0461	1.37877	0.689387	+	0.724393i	$0.257880\pi$
$234$	0	0
$235$	39.7127	2.59057
$236$	0	0
$237$	−22.5892	−1.46733
$238$	0	0
$239$	−25.3482	−1.63964	−0.819821	−	0.572620i	$-0.805927\pi$
$239$	−25.3482	−1.63964	−0.819821	+	0.572620i	$0.805927\pi$
$240$	0	0
$241$	13.4492	0.866339	0.433169	−	0.901312i	$-0.357395\pi$
$241$	13.4492	0.866339	0.433169	+	0.901312i	$0.357395\pi$
$242$	0	0
$243$	−24.4543	−1.56874
$244$	0	0
$245$	−4.23755	−0.270727
$246$	0	0
$247$	−1.51573	−0.0964435
$248$	0	0
$249$	−7.87924	−0.499327
$250$	0	0
$251$	10.2228	0.645258	0.322629	−	0.946526i	$-0.395433\pi$
$251$	10.2228	0.645258	0.322629	+	0.946526i	$0.395433\pi$
$252$	0	0
$253$	−21.9555	−1.38033
$254$	0	0
$255$	47.1218	2.95088
$256$	0	0
$257$	3.76035	0.234564	0.117282	−	0.993099i	$-0.462582\pi$
$257$	3.76035	0.234564	0.117282	+	0.993099i	$0.462582\pi$
$258$	0	0
$259$	0.572613	0.0355805
$260$	0	0
$261$	0.939549	0.0581566
$262$	0	0
$263$	22.8532	1.40919	0.704593	−	0.709611i	$-0.251130\pi$
$263$	22.8532	1.40919	0.704593	+	0.709611i	$0.251130\pi$
$264$	0	0
$265$	−15.4926	−0.951701
$266$	0	0
$267$	16.0717	0.983573
$268$	0	0
$269$	−18.7998	−1.14625	−0.573123	−	0.819470i	$-0.694268\pi$
$269$	−18.7998	−1.14625	−0.573123	+	0.819470i	$0.694268\pi$
$270$	0	0
$271$	13.9334	0.846396	0.423198	−	0.906037i	$-0.360907\pi$
$271$	13.9334	0.846396	0.423198	+	0.906037i	$0.360907\pi$
$272$	0	0
$273$	1.39499	0.0844289
$274$	0	0
$275$	64.6870	3.90077
$276$	0	0
$277$	21.0462	1.26455	0.632273	−	0.774746i	$-0.282122\pi$
$277$	21.0462	1.26455	0.632273	+	0.774746i	$0.282122\pi$
$278$	0	0
$279$	−39.3950	−2.35852
$280$	0	0
$281$	−2.38040	−0.142003	−0.0710015	−	0.997476i	$-0.522620\pi$
$281$	−2.38040	−0.142003	−0.0710015	+	0.997476i	$0.522620\pi$
$282$	0	0
$283$	−10.4422	−0.620726	−0.310363	−	0.950618i	$-0.600451\pi$
$283$	−10.4422	−0.620726	−0.310363	+	0.950618i	$0.600451\pi$
$284$	0	0
$285$	46.4415	2.75096
$286$	0	0
$287$	5.42377	0.320155
$288$	0	0
$289$	−4.74054	−0.278855
$290$	0	0
$291$	52.9026	3.10121
$292$	0	0
$293$	−15.3657	−0.897675	−0.448838	−	0.893613i	$-0.648162\pi$
$293$	−15.3657	−0.897675	−0.448838	+	0.893613i	$0.648162\pi$
$294$	0	0
$295$	9.34825	0.544276
$296$	0	0
$297$	−64.7958	−3.75983
$298$	0	0
$299$	1.93164	0.111710
$300$	0	0
$301$	−5.69770	−0.328410
$302$	0	0
$303$	32.5240	1.86846
$304$	0	0
$305$	−41.9280	−2.40079
$306$	0	0
$307$	−25.0880	−1.43185	−0.715923	−	0.698179i	$-0.753994\pi$
$307$	−25.0880	−1.43185	−0.715923	+	0.698179i	$0.753994\pi$
$308$	0	0
$309$	−33.4807	−1.90465
$310$	0	0
$311$	20.6079	1.16857	0.584283	−	0.811550i	$-0.301376\pi$
$311$	20.6079	1.16857	0.584283	+	0.811550i	$0.301376\pi$
$312$	0	0
$313$	29.5501	1.67027	0.835136	−	0.550044i	$-0.185389\pi$
$313$	29.5501	1.67027	0.835136	+	0.550044i	$0.185389\pi$
$314$	0	0
$315$	−30.0296	−1.69198
$316$	0	0
$317$	6.41069	0.360060	0.180030	−	0.983661i	$-0.442380\pi$
$317$	6.41069	0.360060	0.180030	+	0.983661i	$0.442380\pi$
$318$	0	0
$319$	0.661916	0.0370602
$320$	0	0
$321$	−0.680067	−0.0379576
$322$	0	0
$323$	12.0825	0.672287
$324$	0	0
$325$	−5.69114	−0.315688
$326$	0	0
$327$	−62.6540	−3.46477
$328$	0	0
$329$	−9.37162	−0.516674
$330$	0	0
$331$	1.45124	0.0797673	0.0398837	−	0.999204i	$-0.487301\pi$
$331$	1.45124	0.0797673	0.0398837	+	0.999204i	$0.487301\pi$
$332$	0	0
$333$	4.05785	0.222369
$334$	0	0
$335$	36.0867	1.97163
$336$	0	0
$337$	−11.1794	−0.608979	−0.304489	−	0.952516i	$-0.598486\pi$
$337$	−11.1794	−0.608979	−0.304489	+	0.952516i	$0.598486\pi$
$338$	0	0
$339$	15.7339	0.854550
$340$	0	0
$341$	−27.7539	−1.50296
$342$	0	0
$343$	1.00000	0.0539949
$344$	0	0
$345$	−59.1850	−3.18641
$346$	0	0
$347$	−20.4430	−1.09744	−0.548718	−	0.836007i	$-0.684884\pi$
$347$	−20.4430	−1.09744	−0.548718	+	0.836007i	$0.684884\pi$
$348$	0	0
$349$	24.2915	1.30030	0.650148	−	0.759808i	$-0.274707\pi$
$349$	24.2915	1.30030	0.650148	+	0.759808i	$0.274707\pi$
$350$	0	0
$351$	5.70071	0.304281
$352$	0	0
$353$	14.7810	0.786713	0.393356	−	0.919386i	$-0.371314\pi$
$353$	14.7810	0.786713	0.393356	+	0.919386i	$0.371314\pi$
$354$	0	0
$355$	−13.1899	−0.700047
$356$	0	0
$357$	−11.1201	−0.588536
$358$	0	0
$359$	−0.340137	−0.0179518	−0.00897588	−	0.999960i	$-0.502857\pi$
$359$	−0.340137	−0.0179518	−0.00897588	+	0.999960i	$0.502857\pi$
$360$	0	0
$361$	−7.09195	−0.373261
$362$	0	0
$363$	−44.2253	−2.32122
$364$	0	0
$365$	−41.8257	−2.18926
$366$	0	0
$367$	18.9163	0.987425	0.493712	−	0.869625i	$-0.335640\pi$
$367$	18.9163	0.987425	0.493712	+	0.869625i	$0.335640\pi$
$368$	0	0
$369$	38.4358	2.00089
$370$	0	0
$371$	3.65602	0.189811
$372$	0	0
$373$	34.0151	1.76124	0.880619	−	0.473826i	$-0.157127\pi$
$373$	34.0151	1.76124	0.880619	+	0.473826i	$0.157127\pi$
$374$	0	0
$375$	107.084	5.52980
$376$	0	0
$377$	−0.0582352	−0.00299927
$378$	0	0
$379$	30.1628	1.54936	0.774680	−	0.632354i	$-0.217911\pi$
$379$	30.1628	1.54936	0.774680	+	0.632354i	$0.217911\pi$
$380$	0	0
$381$	−24.6941	−1.26512
$382$	0	0
$383$	−23.3518	−1.19322	−0.596611	−	0.802531i	$-0.703486\pi$
$383$	−23.3518	−1.19322	−0.596611	+	0.802531i	$0.703486\pi$
$384$	0	0
$385$	−21.1560	−1.07821
$386$	0	0
$387$	−40.3770	−2.05248
$388$	0	0
$389$	−7.26880	−0.368543	−0.184271	−	0.982875i	$-0.558993\pi$
$389$	−7.26880	−0.368543	−0.184271	+	0.982875i	$0.558993\pi$
$390$	0	0
$391$	−15.3979	−0.778704
$392$	0	0
$393$	−26.1045	−1.31680
$394$	0	0
$395$	−30.1401	−1.51651
$396$	0	0
$397$	−11.5674	−0.580552	−0.290276	−	0.956943i	$-0.593747\pi$
$397$	−11.5674	−0.580552	−0.290276	+	0.956943i	$0.593747\pi$
$398$	0	0
$399$	−10.9595	−0.548662
$400$	0	0
$401$	−31.0029	−1.54821	−0.774105	−	0.633057i	$-0.781800\pi$
$401$	−31.0029	−1.54821	−0.774105	+	0.633057i	$0.781800\pi$
$402$	0	0
$403$	2.44178	0.121634
$404$	0	0
$405$	−84.5794	−4.20279
$406$	0	0
$407$	2.85878	0.141704
$408$	0	0
$409$	33.5825	1.66055	0.830273	−	0.557357i	$-0.188184\pi$
$409$	33.5825	1.66055	0.830273	+	0.557357i	$0.188184\pi$
$410$	0	0
$411$	38.2489	1.88668
$412$	0	0
$413$	−2.20605	−0.108553
$414$	0	0
$415$	−10.5130	−0.516064
$416$	0	0
$417$	20.4927	1.00353
$418$	0	0
$419$	12.4659	0.609001	0.304500	−	0.952512i	$-0.401511\pi$
$419$	12.4659	0.609001	0.304500	+	0.952512i	$0.401511\pi$
$420$	0	0
$421$	21.0462	1.02573	0.512866	−	0.858469i	$-0.328584\pi$
$421$	21.0462	1.02573	0.512866	+	0.858469i	$0.328584\pi$
$422$	0	0
$423$	−66.4124	−3.22908
$424$	0	0
$425$	45.3664	2.20059
$426$	0	0
$427$	9.89440	0.478824
$428$	0	0
$429$	6.96452	0.336250
$430$	0	0
$431$	8.55285	0.411976	0.205988	−	0.978554i	$-0.433959\pi$
$431$	8.55285	0.411976	0.205988	+	0.978554i	$0.433959\pi$
$432$	0	0
$433$	9.10654	0.437633	0.218816	−	0.975766i	$-0.429780\pi$
$433$	9.10654	0.437633	0.218816	+	0.975766i	$0.429780\pi$
$434$	0	0
$435$	1.78431	0.0855511
$436$	0	0
$437$	−15.1756	−0.725947
$438$	0	0
$439$	0.0179421	0.000856331 0	0.000428166	−	1.00000i	$-0.499864\pi$
$439$	0.0179421	0.000856331 0	0.000428166		1.00000i	$0.499864\pi$
$440$	0	0
$441$	7.08655	0.337455
$442$	0	0
$443$	−8.69941	−0.413322	−0.206661	−	0.978413i	$-0.566260\pi$
$443$	−8.69941	−0.413322	−0.206661	+	0.978413i	$0.566260\pi$
$444$	0	0
$445$	21.4440	1.01654
$446$	0	0
$447$	45.3032	2.14277
$448$	0	0
$449$	−4.85503	−0.229123	−0.114562	−	0.993416i	$-0.536546\pi$
$449$	−4.85503	−0.229123	−0.114562	+	0.993416i	$0.536546\pi$
$450$	0	0
$451$	27.0782	1.27506
$452$	0	0
$453$	−7.78056	−0.365563
$454$	0	0
$455$	1.86130	0.0872590
$456$	0	0
$457$	−1.27114	−0.0594613	−0.0297306	−	0.999558i	$-0.509465\pi$
$457$	−1.27114	−0.0594613	−0.0297306	+	0.999558i	$0.509465\pi$
$458$	0	0
$459$	−45.4426	−2.12108
$460$	0	0
$461$	−8.38224	−0.390400	−0.195200	−	0.980763i	$-0.562536\pi$
$461$	−8.38224	−0.390400	−0.195200	+	0.980763i	$0.562536\pi$
$462$	0	0
$463$	39.7117	1.84556	0.922780	−	0.385326i	$-0.125911\pi$
$463$	39.7117	1.84556	0.922780	+	0.385326i	$0.125911\pi$
$464$	0	0
$465$	−74.8156	−3.46949
$466$	0	0
$467$	−43.0897	−1.99396	−0.996978	−	0.0776879i	$-0.975246\pi$
$467$	−43.0897	−1.99396	−0.996978	+	0.0776879i	$0.975246\pi$
$468$	0	0
$469$	−8.51595	−0.393230
$470$	0	0
$471$	−67.6135	−3.11546
$472$	0	0
$473$	−28.4458	−1.30794
$474$	0	0
$475$	44.7114	2.05150
$476$	0	0
$477$	25.9086	1.18627
$478$	0	0
$479$	16.9224	0.773205	0.386603	−	0.922246i	$-0.373649\pi$
$479$	16.9224	0.773205	0.386603	+	0.922246i	$0.373649\pi$
$480$	0	0
$481$	−0.251514	−0.0114681
$482$	0	0
$483$	13.9668	0.635511
$484$	0	0
$485$	70.5863	3.20516
$486$	0	0
$487$	12.7727	0.578786	0.289393	−	0.957210i	$-0.406547\pi$
$487$	12.7727	0.578786	0.289393	+	0.957210i	$0.406547\pi$
$488$	0	0
$489$	22.5991	1.02197
$490$	0	0
$491$	17.4413	0.787113	0.393556	−	0.919300i	$-0.371245\pi$
$491$	17.4413	0.787113	0.393556	+	0.919300i	$0.371245\pi$
$492$	0	0
$493$	0.464216	0.0209072
$494$	0	0
$495$	−149.923	−6.73854
$496$	0	0
$497$	3.11263	0.139620
$498$	0	0
$499$	−26.0896	−1.16793	−0.583966	−	0.811778i	$-0.698500\pi$
$499$	−26.0896	−1.16793	−0.583966	+	0.811778i	$0.698500\pi$
$500$	0	0
$501$	30.9546	1.38295
$502$	0	0
$503$	13.4299	0.598808	0.299404	−	0.954126i	$-0.403212\pi$
$503$	13.4299	0.598808	0.299404	+	0.954126i	$0.403212\pi$
$504$	0	0
$505$	43.3958	1.93109
$506$	0	0
$507$	40.6744	1.80641
$508$	0	0
$509$	−0.235880	−0.0104552	−0.00522760	−	0.999986i	$-0.501664\pi$
$509$	−0.235880	−0.0104552	−0.00522760	+	0.999986i	$0.501664\pi$
$510$	0	0
$511$	9.87027	0.436635
$512$	0	0
$513$	−44.7866	−1.97738
$514$	0	0
$515$	−44.6723	−1.96850
$516$	0	0
$517$	−46.7879	−2.05773
$518$	0	0
$519$	−59.7070	−2.62085
$520$	0	0
$521$	13.7124	0.600751	0.300376	−	0.953821i	$-0.402888\pi$
$521$	13.7124	0.600751	0.300376	+	0.953821i	$0.402888\pi$
$522$	0	0
$523$	−0.594362	−0.0259897	−0.0129948	−	0.999916i	$-0.504136\pi$
$523$	−0.594362	−0.0259897	−0.0129948	+	0.999916i	$0.504136\pi$
$524$	0	0
$525$	−41.1500	−1.79593
$526$	0	0
$527$	−19.4644	−0.847884
$528$	0	0
$529$	−3.66026	−0.159142
$530$	0	0
$531$	−15.6333	−0.678427
$532$	0	0
$533$	−2.38233	−0.103190
$534$	0	0
$535$	−0.907392	−0.0392300
$536$	0	0
$537$	−45.0119	−1.94240
$538$	0	0
$539$	4.99251	0.215042
$540$	0	0
$541$	−23.2258	−0.998555	−0.499278	−	0.866442i	$-0.666401\pi$
$541$	−23.2258	−0.998555	−0.499278	+	0.866442i	$0.666401\pi$
$542$	0	0
$543$	8.14478	0.349526
$544$	0	0
$545$	−83.5972	−3.58091
$546$	0	0
$547$	−29.6868	−1.26932	−0.634659	−	0.772793i	$-0.718859\pi$
$547$	−29.6868	−1.26932	−0.634659	+	0.772793i	$0.718859\pi$
$548$	0	0
$549$	70.1172	2.99253
$550$	0	0
$551$	0.457514	0.0194908
$552$	0	0
$553$	7.11263	0.302460
$554$	0	0
$555$	7.70633	0.327115
$556$	0	0
$557$	−18.0090	−0.763065	−0.381532	−	0.924355i	$-0.624604\pi$
$557$	−18.0090	−0.763065	−0.381532	+	0.924355i	$0.624604\pi$
$558$	0	0
$559$	2.50265	0.105851
$560$	0	0
$561$	−55.5170	−2.34393
$562$	0	0
$563$	35.6985	1.50451	0.752257	−	0.658870i	$-0.228965\pi$
$563$	35.6985	1.50451	0.752257	+	0.658870i	$0.228965\pi$
$564$	0	0
$565$	20.9933	0.883195
$566$	0	0
$567$	19.9595	0.838221
$568$	0	0
$569$	40.4761	1.69685	0.848423	−	0.529318i	$-0.177552\pi$
$569$	40.4761	1.69685	0.848423	+	0.529318i	$0.177552\pi$
$570$	0	0
$571$	6.39496	0.267621	0.133810	−	0.991007i	$-0.457279\pi$
$571$	6.39496	0.267621	0.133810	+	0.991007i	$0.457279\pi$
$572$	0	0
$573$	41.1871	1.72061
$574$	0	0
$575$	−56.9802	−2.37624
$576$	0	0
$577$	25.6686	1.06860	0.534298	−	0.845296i	$-0.320576\pi$
$577$	25.6686	1.06860	0.534298	+	0.845296i	$0.320576\pi$
$578$	0	0
$579$	−32.1998	−1.33818
$580$	0	0
$581$	2.48092	0.102926
$582$	0	0
$583$	18.2527	0.755950
$584$	0	0
$585$	13.1902	0.545347
$586$	0	0
$587$	30.4700	1.25763	0.628815	−	0.777555i	$-0.283540\pi$
$587$	30.4700	1.25763	0.628815	+	0.777555i	$0.283540\pi$
$588$	0	0
$589$	−19.1834	−0.790439
$590$	0	0
$591$	9.02319	0.371164
$592$	0	0
$593$	14.9541	0.614091	0.307045	−	0.951695i	$-0.400660\pi$
$593$	14.9541	0.614091	0.307045	+	0.951695i	$0.400660\pi$
$594$	0	0
$595$	−14.8371	−0.608264
$596$	0	0
$597$	36.2354	1.48302
$598$	0	0
$599$	27.9316	1.14125	0.570627	−	0.821210i	$-0.306700\pi$
$599$	27.9316	1.14125	0.570627	+	0.821210i	$0.306700\pi$
$600$	0	0
$601$	33.5110	1.36694	0.683471	−	0.729978i	$-0.260470\pi$
$601$	33.5110	1.36694	0.683471	+	0.729978i	$0.260470\pi$
$602$	0	0
$603$	−60.3487	−2.45759
$604$	0	0
$605$	−59.0084	−2.39903
$606$	0	0
$607$	16.0723	0.652356	0.326178	−	0.945308i	$-0.394239\pi$
$607$	16.0723	0.652356	0.326178	+	0.945308i	$0.394239\pi$
$608$	0	0
$609$	−0.421071	−0.0170627
$610$	0	0
$611$	4.11638	0.166531
$612$	0	0
$613$	−27.4341	−1.10805	−0.554026	−	0.832500i	$-0.686909\pi$
$613$	−27.4341	−1.10805	−0.554026	+	0.832500i	$0.686909\pi$
$614$	0	0
$615$	72.9941	2.94340
$616$	0	0
$617$	−16.0290	−0.645303	−0.322651	−	0.946518i	$-0.604574\pi$
$617$	−16.0290	−0.645303	−0.322651	+	0.946518i	$0.604574\pi$
$618$	0	0
$619$	−6.58966	−0.264861	−0.132430	−	0.991192i	$-0.542278\pi$
$619$	−6.58966	−0.264861	−0.132430	+	0.991192i	$0.542278\pi$
$620$	0	0
$621$	57.0760	2.29038
$622$	0	0
$623$	−5.06047	−0.202743
$624$	0	0
$625$	78.0950	3.12380
$626$	0	0
$627$	−54.7155	−2.18513
$628$	0	0
$629$	2.00492	0.0799414
$630$	0	0
$631$	15.2225	0.606000	0.303000	−	0.952991i	$-0.402012\pi$
$631$	15.2225	0.606000	0.303000	+	0.952991i	$0.402012\pi$
$632$	0	0
$633$	−24.4580	−0.972117
$634$	0	0
$635$	−32.9486	−1.30753
$636$	0	0
$637$	−0.439239	−0.0174033
$638$	0	0
$639$	22.0578	0.872592
$640$	0	0
$641$	13.0371	0.514934	0.257467	−	0.966287i	$-0.417112\pi$
$641$	13.0371	0.514934	0.257467	+	0.966287i	$0.417112\pi$
$642$	0	0
$643$	15.6242	0.616159	0.308079	−	0.951361i	$-0.400314\pi$
$643$	15.6242	0.616159	0.308079	+	0.951361i	$0.400314\pi$
$644$	0	0
$645$	−76.6806	−3.01930
$646$	0	0
$647$	−14.5276	−0.571139	−0.285570	−	0.958358i	$-0.592183\pi$
$647$	−14.5276	−0.571139	−0.285570	+	0.958358i	$0.592183\pi$
$648$	0	0
$649$	−11.0137	−0.432326
$650$	0	0
$651$	17.6554	0.691969
$652$	0	0
$653$	34.8479	1.36370	0.681851	−	0.731491i	$-0.261175\pi$
$653$	34.8479	1.36370	0.681851	+	0.731491i	$0.261175\pi$
$654$	0	0
$655$	−34.8304	−1.36094
$656$	0	0
$657$	69.9461	2.72886
$658$	0	0
$659$	−48.8820	−1.90417	−0.952087	−	0.305828i	$-0.901067\pi$
$659$	−48.8820	−1.90417	−0.952087	+	0.305828i	$0.901067\pi$
$660$	0	0
$661$	−1.21595	−0.0472948	−0.0236474	−	0.999720i	$-0.507528\pi$
$661$	−1.21595	−0.0472948	−0.0236474	+	0.999720i	$0.507528\pi$
$662$	0	0
$663$	4.88437	0.189693
$664$	0	0
$665$	−14.6229	−0.567054
$666$	0	0
$667$	−0.583055	−0.0225760
$668$	0	0
$669$	69.6591	2.69318
$670$	0	0
$671$	49.3979	1.90698
$672$	0	0
$673$	15.3381	0.591240	0.295620	−	0.955306i	$-0.404474\pi$
$673$	15.3381	0.591240	0.295620	+	0.955306i	$0.404474\pi$
$674$	0	0
$675$	−168.161	−6.47253
$676$	0	0
$677$	34.1184	1.31128	0.655639	−	0.755074i	$-0.272399\pi$
$677$	34.1184	1.31128	0.655639	+	0.755074i	$0.272399\pi$
$678$	0	0
$679$	−16.6573	−0.639250
$680$	0	0
$681$	−15.1147	−0.579196
$682$	0	0
$683$	21.4966	0.822545	0.411272	−	0.911512i	$-0.365084\pi$
$683$	21.4966	0.822545	0.411272	+	0.911512i	$0.365084\pi$
$684$	0	0
$685$	51.0343	1.94992
$686$	0	0
$687$	−41.7412	−1.59253
$688$	0	0
$689$	−1.60587	−0.0611787
$690$	0	0
$691$	47.8380	1.81984	0.909922	−	0.414778i	$-0.136141\pi$
$691$	47.8380	1.81984	0.909922	+	0.414778i	$0.136141\pi$
$692$	0	0
$693$	35.3796	1.34396
$694$	0	0
$695$	27.3428	1.03717
$696$	0	0
$697$	18.9905	0.719318
$698$	0	0
$699$	−66.8409	−2.52815
$700$	0	0
$701$	25.1274	0.949047	0.474524	−	0.880243i	$-0.342620\pi$
$701$	25.1274	0.949047	0.474524	+	0.880243i	$0.342620\pi$
$702$	0	0
$703$	1.97598	0.0745254
$704$	0	0
$705$	−126.125	−4.75014
$706$	0	0
$707$	−10.2408	−0.385144
$708$	0	0
$709$	47.8088	1.79550	0.897749	−	0.440507i	$-0.145201\pi$
$709$	47.8088	1.79550	0.897749	+	0.440507i	$0.145201\pi$
$710$	0	0
$711$	50.4040	1.89030
$712$	0	0
$713$	24.4473	0.915560
$714$	0	0
$715$	9.29254	0.347521
$716$	0	0
$717$	80.5043	3.00649
$718$	0	0
$719$	53.1845	1.98345	0.991723	−	0.128393i	$-0.0409820\pi$
$719$	53.1845	1.98345	0.991723	+	0.128393i	$0.0409820\pi$
$720$	0	0
$721$	10.5420	0.392605
$722$	0	0
$723$	−42.7137	−1.58854
$724$	0	0
$725$	1.71784	0.0637990
$726$	0	0
$727$	35.4638	1.31528	0.657639	−	0.753333i	$-0.271555\pi$
$727$	35.4638	1.31528	0.657639	+	0.753333i	$0.271555\pi$
$728$	0	0
$729$	17.7866	0.658763
$730$	0	0
$731$	−19.9497	−0.737865
$732$	0	0
$733$	13.6131	0.502810	0.251405	−	0.967882i	$-0.419107\pi$
$733$	13.6131	0.502810	0.251405	+	0.967882i	$0.419107\pi$
$734$	0	0
$735$	13.4582	0.496412
$736$	0	0
$737$	−42.5159	−1.56609
$738$	0	0
$739$	17.4117	0.640498	0.320249	−	0.947333i	$-0.396233\pi$
$739$	17.4117	0.640498	0.320249	+	0.947333i	$0.396233\pi$
$740$	0	0
$741$	4.81385	0.176841
$742$	0	0
$743$	−14.7947	−0.542767	−0.271383	−	0.962471i	$-0.587481\pi$
$743$	−14.7947	−0.542767	−0.271383	+	0.962471i	$0.587481\pi$
$744$	0	0
$745$	60.4467	2.21459
$746$	0	0
$747$	17.5812	0.643261
$748$	0	0
$749$	0.214131	0.00782419
$750$	0	0
$751$	−3.48677	−0.127234	−0.0636170	−	0.997974i	$-0.520264\pi$
$751$	−3.48677	−0.127234	−0.0636170	+	0.997974i	$0.520264\pi$
$752$	0	0
$753$	−32.4670	−1.18316
$754$	0	0
$755$	−10.3814	−0.377817
$756$	0	0
$757$	−35.4628	−1.28892	−0.644458	−	0.764640i	$-0.722917\pi$
$757$	−35.4628	−1.28892	−0.644458	+	0.764640i	$0.722917\pi$
$758$	0	0
$759$	69.7293	2.53101
$760$	0	0
$761$	−47.1553	−1.70938	−0.854689	−	0.519140i	$-0.826252\pi$
$761$	−47.1553	−1.70938	−0.854689	+	0.519140i	$0.826252\pi$
$762$	0	0
$763$	19.7277	0.714192
$764$	0	0
$765$	−105.144	−3.80149
$766$	0	0
$767$	0.968984	0.0349880
$768$	0	0
$769$	22.9478	0.827520	0.413760	−	0.910386i	$-0.364215\pi$
$769$	22.9478	0.827520	0.413760	+	0.910386i	$0.364215\pi$
$770$	0	0
$771$	−11.9426	−0.430103
$772$	0	0
$773$	−32.9936	−1.18670	−0.593348	−	0.804946i	$-0.702194\pi$
$773$	−32.9936	−1.18670	−0.593348	+	0.804946i	$0.702194\pi$
$774$	0	0
$775$	−72.0285	−2.58734
$776$	0	0
$777$	−1.81858	−0.0652413
$778$	0	0
$779$	18.7164	0.670584
$780$	0	0
$781$	15.5398	0.556058
$782$	0	0
$783$	−1.72073	−0.0614938
$784$	0	0
$785$	−90.2146	−3.21990
$786$	0	0
$787$	−11.0916	−0.395372	−0.197686	−	0.980265i	$-0.563343\pi$
$787$	−11.0916	−0.395372	−0.197686	+	0.980265i	$0.563343\pi$
$788$	0	0
$789$	−72.5801	−2.58392
$790$	0	0
$791$	−4.95411	−0.176148
$792$	0	0
$793$	−4.34601	−0.154331
$794$	0	0
$795$	49.2033	1.74506
$796$	0	0
$797$	−8.23745	−0.291785	−0.145893	−	0.989300i	$-0.546605\pi$
$797$	−8.23745	−0.291785	−0.145893	+	0.989300i	$0.546605\pi$
$798$	0	0
$799$	−32.8133	−1.16085
$800$	0	0
$801$	−35.8613	−1.26710
$802$	0	0
$803$	49.2774	1.73896
$804$	0	0
$805$	18.6355	0.656814
$806$	0	0
$807$	59.7070	2.10179
$808$	0	0
$809$	12.9074	0.453799	0.226899	−	0.973918i	$-0.427141\pi$
$809$	12.9074	0.453799	0.226899	+	0.973918i	$0.427141\pi$
$810$	0	0
$811$	19.4515	0.683034	0.341517	−	0.939876i	$-0.389059\pi$
$811$	19.4515	0.683034	0.341517	+	0.939876i	$0.389059\pi$
$812$	0	0
$813$	−44.2517	−1.55197
$814$	0	0
$815$	30.1533	1.05622
$816$	0	0
$817$	−19.6617	−0.687874
$818$	0	0
$819$	−3.11269	−0.108766
$820$	0	0
$821$	−21.7594	−0.759408	−0.379704	−	0.925108i	$-0.623974\pi$
$821$	−21.7594	−0.759408	−0.379704	+	0.925108i	$0.623974\pi$
$822$	0	0
$823$	13.8847	0.483989	0.241995	−	0.970278i	$-0.422198\pi$
$823$	13.8847	0.483989	0.241995	+	0.970278i	$0.422198\pi$
$824$	0	0
$825$	−205.442	−7.15256
$826$	0	0
$827$	−32.2565	−1.12167	−0.560833	−	0.827929i	$-0.689519\pi$
$827$	−32.2565	−1.12167	−0.560833	+	0.827929i	$0.689519\pi$
$828$	0	0
$829$	−41.1781	−1.43018	−0.715088	−	0.699035i	$-0.753613\pi$
$829$	−41.1781	−1.43018	−0.715088	+	0.699035i	$0.753613\pi$
$830$	0	0
$831$	−66.8415	−2.31870
$832$	0	0
$833$	3.50135	0.121315
$834$	0	0
$835$	41.3018	1.42931
$836$	0	0
$837$	72.1496	2.49385
$838$	0	0
$839$	−22.9026	−0.790686	−0.395343	−	0.918534i	$-0.629374\pi$
$839$	−22.9026	−0.790686	−0.395343	+	0.918534i	$0.629374\pi$
$840$	0	0
$841$	−28.9824	−0.999394
$842$	0	0
$843$	7.56000	0.260380
$844$	0	0
$845$	54.2706	1.86696
$846$	0	0
$847$	13.9251	0.478473
$848$	0	0
$849$	33.1638	1.13818
$850$	0	0
$851$	−2.51818	−0.0863221
$852$	0	0
$853$	37.8914	1.29738	0.648688	−	0.761054i	$-0.275318\pi$
$853$	37.8914	1.29738	0.648688	+	0.761054i	$0.275318\pi$
$854$	0	0
$855$	−103.626	−3.54394
$856$	0	0
$857$	−4.47323	−0.152802	−0.0764012	−	0.997077i	$-0.524343\pi$
$857$	−4.47323	−0.152802	−0.0764012	+	0.997077i	$0.524343\pi$
$858$	0	0
$859$	−40.5244	−1.38268	−0.691338	−	0.722532i	$-0.742978\pi$
$859$	−40.5244	−1.38268	−0.691338	+	0.722532i	$0.742978\pi$
$860$	0	0
$861$	−17.2255	−0.587045
$862$	0	0
$863$	−43.2050	−1.47071	−0.735357	−	0.677680i	$-0.762986\pi$
$863$	−43.2050	−1.47071	−0.735357	+	0.677680i	$0.762986\pi$
$864$	0	0
$865$	−79.6652	−2.70870
$866$	0	0
$867$	15.0556	0.511316
$868$	0	0
$869$	35.5098	1.20459
$870$	0	0
$871$	3.74054	0.126743
$872$	0	0
$873$	−118.043	−3.99515
$874$	0	0
$875$	−33.7174	−1.13986
$876$	0	0
$877$	−28.0420	−0.946910	−0.473455	−	0.880818i	$-0.656993\pi$
$877$	−28.0420	−0.946910	−0.473455	+	0.880818i	$0.656993\pi$
$878$	0	0
$879$	48.8005	1.64600
$880$	0	0
$881$	−49.2769	−1.66018	−0.830091	−	0.557628i	$-0.811712\pi$
$881$	−49.2769	−1.66018	−0.830091	+	0.557628i	$0.811712\pi$
$882$	0	0
$883$	−15.5295	−0.522610	−0.261305	−	0.965256i	$-0.584153\pi$
$883$	−15.5295	−0.522610	−0.261305	+	0.965256i	$0.584153\pi$
$884$	0	0
$885$	−29.6894	−0.997998
$886$	0	0
$887$	−31.0779	−1.04350	−0.521748	−	0.853100i	$-0.674720\pi$
$887$	−31.0779	−1.04350	−0.521748	+	0.853100i	$0.674720\pi$
$888$	0	0
$889$	7.77540	0.260779
$890$	0	0
$891$	99.6480	3.33834
$892$	0	0
$893$	−32.3396	−1.08220
$894$	0	0
$895$	−60.0579	−2.00752
$896$	0	0
$897$	−6.13476	−0.204834
$898$	0	0
$899$	−0.737039	−0.0245816
$900$	0	0
$901$	12.8010	0.426464
$902$	0	0
$903$	18.0955	0.602181
$904$	0	0
$905$	10.8673	0.361242
$906$	0	0
$907$	21.3972	0.710482	0.355241	−	0.934775i	$-0.384399\pi$
$907$	21.3972	0.710482	0.355241	+	0.934775i	$0.384399\pi$
$908$	0	0
$909$	−72.5718	−2.40706
$910$	0	0
$911$	−22.0861	−0.731745	−0.365872	−	0.930665i	$-0.619229\pi$
$911$	−22.0861	−0.731745	−0.365872	+	0.930665i	$0.619229\pi$
$912$	0	0
$913$	12.3860	0.409917
$914$	0	0
$915$	133.161	4.40215
$916$	0	0
$917$	8.21947	0.271431
$918$	0	0
$919$	−6.21964	−0.205167	−0.102583	−	0.994724i	$-0.532711\pi$
$919$	−6.21964	−0.205167	−0.102583	+	0.994724i	$0.532711\pi$
$920$	0	0
$921$	79.6777	2.62547
$922$	0	0
$923$	−1.36719	−0.0450015
$924$	0	0
$925$	7.41925	0.243943
$926$	0	0
$927$	74.7065	2.45368
$928$	0	0
$929$	11.2163	0.367993	0.183997	−	0.982927i	$-0.441096\pi$
$929$	11.2163	0.367993	0.183997	+	0.982927i	$0.441096\pi$
$930$	0	0
$931$	3.45080	0.113096
$932$	0	0
$933$	−65.4493	−2.14271
$934$	0	0
$935$	−74.0746	−2.42250
$936$	0	0
$937$	−1.58518	−0.0517854	−0.0258927	−	0.999665i	$-0.508243\pi$
$937$	−1.58518	−0.0517854	−0.0258927	+	0.999665i	$0.508243\pi$
$938$	0	0
$939$	−93.8492	−3.06265
$940$	0	0
$941$	49.6193	1.61754	0.808772	−	0.588122i	$-0.200133\pi$
$941$	49.6193	1.61754	0.808772	+	0.588122i	$0.200133\pi$
$942$	0	0
$943$	−23.8521	−0.776732
$944$	0	0
$945$	54.9975	1.78907
$946$	0	0
$947$	11.2446	0.365399	0.182699	−	0.983169i	$-0.441516\pi$
$947$	11.2446	0.365399	0.182699	+	0.983169i	$0.441516\pi$
$948$	0	0
$949$	−4.33541	−0.140733
$950$	0	0
$951$	−20.3599	−0.660216
$952$	0	0
$953$	22.3174	0.722931	0.361466	−	0.932385i	$-0.382277\pi$
$953$	22.3174	0.722931	0.361466	+	0.932385i	$0.382277\pi$
$954$	0	0
$955$	54.9546	1.77829
$956$	0	0
$957$	−2.10220	−0.0679545
$958$	0	0
$959$	−12.0434	−0.388901
$960$	0	0
$961$	−0.0961895	−0.00310289
$962$	0	0
$963$	1.51745	0.0488992
$964$	0	0
$965$	−42.9632	−1.38304
$966$	0	0
$967$	23.9831	0.771244	0.385622	−	0.922657i	$-0.373987\pi$
$967$	23.9831	0.771244	0.385622	+	0.922657i	$0.373987\pi$
$968$	0	0
$969$	−38.3731	−1.23272
$970$	0	0
$971$	4.04470	0.129801	0.0649004	−	0.997892i	$-0.479327\pi$
$971$	4.04470	0.129801	0.0649004	+	0.997892i	$0.479327\pi$
$972$	0	0
$973$	−6.45251	−0.206858
$974$	0	0
$975$	18.0747	0.578853
$976$	0	0
$977$	38.0146	1.21619	0.608097	−	0.793863i	$-0.291933\pi$
$977$	38.0146	1.21619	0.608097	+	0.793863i	$0.291933\pi$
$978$	0	0
$979$	−25.2644	−0.807455
$980$	0	0
$981$	139.802	4.46352
$982$	0	0
$983$	−21.6742	−0.691301	−0.345650	−	0.938363i	$-0.612342\pi$
$983$	−21.6742	−0.691301	−0.345650	+	0.938363i	$0.612342\pi$
$984$	0	0
$985$	12.0394	0.383606
$986$	0	0
$987$	29.7636	0.947387
$988$	0	0
$989$	25.0568	0.796759
$990$	0	0
$991$	26.3460	0.836908	0.418454	−	0.908238i	$-0.362572\pi$
$991$	26.3460	0.836908	0.418454	+	0.908238i	$0.362572\pi$
$992$	0	0
$993$	−4.60904	−0.146263
$994$	0	0
$995$	48.3478	1.53273
$996$	0	0
$997$	6.87457	0.217720	0.108860	−	0.994057i	$-0.465280\pi$
$997$	6.87457	0.217720	0.108860	+	0.994057i	$0.465280\pi$
$998$	0	0
$999$	−7.43172	−0.235129

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3584.2.a.p.1.1	yes	10
4.3	odd	2		3584.2.a.o.1.10	yes	10
8.3	odd	2		3584.2.a.o.1.1	✓	10
8.5	even	2	inner	3584.2.a.p.1.10	yes	10
16.3	odd	4		3584.2.b.h.1793.10		10
16.5	even	4		3584.2.b.g.1793.10		10
16.11	odd	4		3584.2.b.h.1793.1		10
16.13	even	4		3584.2.b.g.1793.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3584.2.a.o.1.1	✓	10	8.3	odd	2
3584.2.a.o.1.10	yes	10	4.3	odd	2
3584.2.a.p.1.1	yes	10	1.1	even	1	trivial
3584.2.a.p.1.10	yes	10	8.5	even	2	inner
3584.2.b.g.1793.1		10	16.13	even	4
3584.2.b.g.1793.10		10	16.5	even	4
3584.2.b.h.1793.1		10	16.11	odd	4
3584.2.b.h.1793.10		10	16.3	odd	4

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:	\( N \)	\(=\)	\( 3584 = 2^{9} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3584.a (trivial)

\(f(q)\)	\(=\)	\(q-3.17593 q^{3} -4.23755 q^{5} +1.00000 q^{7} +7.08655 q^{9} +O(q^{10})\)	\(q-3.17593 q^{3} -4.23755 q^{5} +1.00000 q^{7} +7.08655 q^{9} +4.99251 q^{11} -0.439239 q^{13} +13.4582 q^{15} +3.50135 q^{17} +3.45080 q^{19} -3.17593 q^{21} -4.39770 q^{23} +12.9568 q^{25} -12.9786 q^{27} +0.132582 q^{29} -5.55912 q^{31} -15.8559 q^{33} -4.23755 q^{35} +0.572613 q^{37} +1.39499 q^{39} +5.42377 q^{41} -5.69770 q^{43} -30.0296 q^{45} -9.37162 q^{47} +1.00000 q^{49} -11.1201 q^{51} +3.65602 q^{53} -21.1560 q^{55} -10.9595 q^{57} -2.20605 q^{59} +9.89440 q^{61} +7.08655 q^{63} +1.86130 q^{65} -8.51595 q^{67} +13.9668 q^{69} +3.11263 q^{71} +9.87027 q^{73} -41.1500 q^{75} +4.99251 q^{77} +7.11263 q^{79} +19.9595 q^{81} +2.48092 q^{83} -14.8371 q^{85} -0.421071 q^{87} -5.06047 q^{89} -0.439239 q^{91} +17.6554 q^{93} -14.6229 q^{95} -16.6573 q^{97} +35.3796 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{7} + 22 q^{9}+O(q^{10}) \) 10 * q + 10 * q^7 + 22 * q^9	\( 10 q + 10 q^{7} + 22 q^{9} + 16 q^{15} + 16 q^{17} + 8 q^{23} + 30 q^{25} - 8 q^{31} + 12 q^{33} + 20 q^{41} - 24 q^{47} + 10 q^{49} - 32 q^{55} + 28 q^{57} + 22 q^{63} + 32 q^{65} + 48 q^{73} + 40 q^{79} + 62 q^{81} - 8 q^{87} + 16 q^{89} - 32 q^{95} + 32 q^{97}+O(q^{100}) \) 10 * q + 10 * q^7 + 22 * q^9 + 16 * q^15 + 16 * q^17 + 8 * q^23 + 30 * q^25 - 8 * q^31 + 12 * q^33 + 20 * q^41 - 24 * q^47 + 10 * q^49 - 32 * q^55 + 28 * q^57 + 22 * q^63 + 32 * q^65 + 48 * q^73 + 40 * q^79 + 62 * q^81 - 8 * q^87 + 16 * q^89 - 32 * q^95 + 32 * q^97

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