LMFDB - Embedded newform 2601.2.a.bc.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2601,2,Mod(1,2601)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2601, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2601.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2601 = 3^{2} \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2601.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:	$20.7690895657$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{16})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 4x^{2} + 2 $ x^4 - 4*x^2 + 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 51)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.765367$ of defining polynomial
Character	$\chi$	$=$	2601.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.765367 q^{2} -1.41421 q^{4} -2.08239 q^{5} +1.23463 q^{7} -2.61313 q^{8} +O(q^{10})$	$q+0.765367 q^{2} -1.41421 q^{4} -2.08239 q^{5} +1.23463 q^{7} -2.61313 q^{8} -1.59379 q^{10} +1.49661 q^{11} +4.10973 q^{13} +0.944947 q^{14} +0.828427 q^{16} -6.81204 q^{19} +2.94495 q^{20} +1.14545 q^{22} +3.30864 q^{23} -0.663643 q^{25} +3.14545 q^{26} -1.74603 q^{28} -6.24264 q^{29} +10.2700 q^{31} +5.86030 q^{32} -2.57099 q^{35} +3.93694 q^{37} -5.21371 q^{38} +5.44155 q^{40} -12.1371 q^{41} -3.44609 q^{43} -2.11652 q^{44} +2.53233 q^{46} -1.56940 q^{47} -5.47568 q^{49} -0.507930 q^{50} -5.81204 q^{52} -3.96134 q^{53} -3.11652 q^{55} -3.22625 q^{56} -4.77791 q^{58} -8.06306 q^{59} +3.27330 q^{61} +7.86030 q^{62} +2.82843 q^{64} -8.55807 q^{65} +2.11652 q^{67} -1.96775 q^{70} +0.226626 q^{71} -0.368233 q^{73} +3.01320 q^{74} +9.63368 q^{76} +1.84776 q^{77} +2.71485 q^{79} -1.72511 q^{80} -9.28931 q^{82} -14.4138 q^{83} -2.63752 q^{86} -3.91082 q^{88} -13.6694 q^{89} +5.07401 q^{91} -4.67913 q^{92} -1.20116 q^{94} +14.1853 q^{95} -2.68457 q^{97} -4.19090 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{5} + 8 q^{7}+O(q^{10}) $ 4 * q - 4 * q^5 + 8 * q^7	$ 4 q - 4 q^{5} + 8 q^{7} + 8 q^{10} - 4 q^{11} - 4 q^{13} - 8 q^{14} - 8 q^{16} - 12 q^{19} - 8 q^{22} - 12 q^{23} - 8 q^{29} + 8 q^{31} - 16 q^{35} + 24 q^{37} - 16 q^{38} - 12 q^{41} + 4 q^{43} - 8 q^{44} + 8 q^{46} - 8 q^{47} - 4 q^{49} - 16 q^{50} - 8 q^{52} - 8 q^{53} - 12 q^{55} + 8 q^{56} - 24 q^{59} + 24 q^{61} + 8 q^{62} - 12 q^{65} + 8 q^{67} + 24 q^{70} + 24 q^{71} + 8 q^{73} + 8 q^{74} - 8 q^{76} + 8 q^{80} - 8 q^{82} - 8 q^{83} + 16 q^{86} - 16 q^{89} - 8 q^{91} - 16 q^{94} + 12 q^{95} - 16 q^{97} - 32 q^{98}+O(q^{100}) $ 4 * q - 4 * q^5 + 8 * q^7 + 8 * q^10 - 4 * q^11 - 4 * q^13 - 8 * q^14 - 8 * q^16 - 12 * q^19 - 8 * q^22 - 12 * q^23 - 8 * q^29 + 8 * q^31 - 16 * q^35 + 24 * q^37 - 16 * q^38 - 12 * q^41 + 4 * q^43 - 8 * q^44 + 8 * q^46 - 8 * q^47 - 4 * q^49 - 16 * q^50 - 8 * q^52 - 8 * q^53 - 12 * q^55 + 8 * q^56 - 24 * q^59 + 24 * q^61 + 8 * q^62 - 12 * q^65 + 8 * q^67 + 24 * q^70 + 24 * q^71 + 8 * q^73 + 8 * q^74 - 8 * q^76 + 8 * q^80 - 8 * q^82 - 8 * q^83 + 16 * q^86 - 16 * q^89 - 8 * q^91 - 16 * q^94 + 12 * q^95 - 16 * q^97 - 32 * q^98

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 $

$2$	0.765367	0.541196	0.270598	−	0.962692i	$-0.412779\pi$
$2$	0.765367	0.541196	0.270598	+	0.962692i	$0.412779\pi$
$3$	0	0
$3$	0	0
$4$	−1.41421	−0.707107
$5$	−2.08239	−0.931274	−0.465637	−	0.884976i	$-0.654175\pi$
$5$	−2.08239	−0.931274	−0.465637	+	0.884976i	$0.654175\pi$
$6$	0	0
$7$	1.23463	0.466647	0.233324	−	0.972399i	$-0.425040\pi$
$7$	1.23463	0.466647	0.233324	+	0.972399i	$0.425040\pi$
$8$	−2.61313	−0.923880
$9$	0	0
$10$	−1.59379	−0.504002
$11$	1.49661	0.451244	0.225622	−	0.974215i	$-0.427559\pi$
$11$	1.49661	0.451244	0.225622	+	0.974215i	$0.427559\pi$
$12$	0	0
$13$	4.10973	1.13983	0.569917	−	0.821702i	$-0.306975\pi$
$13$	4.10973	1.13983	0.569917	+	0.821702i	$0.306975\pi$
$14$	0.944947	0.252548
$15$	0	0
$16$	0.828427	0.207107
$17$	0	0
$17$	0	0
$18$	0	0
$19$	−6.81204	−1.56279	−0.781394	−	0.624038i	$-0.785491\pi$
$19$	−6.81204	−1.56279	−0.781394	+	0.624038i	$0.785491\pi$
$20$	2.94495	0.658510
$21$	0	0
$22$	1.14545	0.244211
$23$	3.30864	0.689900	0.344950	−	0.938621i	$-0.387896\pi$
$23$	3.30864	0.689900	0.344950	+	0.938621i	$0.387896\pi$
$24$	0	0
$25$	−0.663643	−0.132729
$26$	3.14545	0.616874
$27$	0	0
$28$	−1.74603	−0.329970
$29$	−6.24264	−1.15923	−0.579615	−	0.814891i	$-0.696797\pi$
$29$	−6.24264	−1.15923	−0.579615	+	0.814891i	$0.696797\pi$
$30$	0	0
$31$	10.2700	1.84454	0.922271	−	0.386543i	$-0.126331\pi$
$31$	10.2700	1.84454	0.922271	+	0.386543i	$0.126331\pi$
$32$	5.86030	1.03596
$33$	0	0
$34$	0	0
$35$	−2.57099	−0.434577
$36$	0	0
$37$	3.93694	0.647229	0.323614	−	0.946189i	$-0.395102\pi$
$37$	3.93694	0.647229	0.323614	+	0.946189i	$0.395102\pi$
$38$	−5.21371	−0.845775
$39$	0	0
$40$	5.44155	0.860385
$41$	−12.1371	−1.89549	−0.947746	−	0.319026i	$-0.896644\pi$
$41$	−12.1371	−1.89549	−0.947746	+	0.319026i	$0.896644\pi$
$42$	0	0
$43$	−3.44609	−0.525524	−0.262762	−	0.964861i	$-0.584633\pi$
$43$	−3.44609	−0.525524	−0.262762	+	0.964861i	$0.584633\pi$
$44$	−2.11652	−0.319077
$45$	0	0
$46$	2.53233	0.373371
$47$	−1.56940	−0.228920	−0.114460	−	0.993428i	$-0.536514\pi$
$47$	−1.56940	−0.228920	−0.114460	+	0.993428i	$0.536514\pi$
$48$	0	0
$49$	−5.47568	−0.782240
$50$	−0.507930	−0.0718322
$51$	0	0
$52$	−5.81204	−0.805985
$53$	−3.96134	−0.544131	−0.272066	−	0.962279i	$-0.587707\pi$
$53$	−3.96134	−0.544131	−0.272066	+	0.962279i	$0.587707\pi$
$54$	0	0
$55$	−3.11652	−0.420231
$56$	−3.22625	−0.431126
$57$	0	0
$58$	−4.77791	−0.627370
$59$	−8.06306	−1.04972	−0.524861	−	0.851188i	$-0.675883\pi$
$59$	−8.06306	−1.04972	−0.524861	+	0.851188i	$0.675883\pi$
$60$	0	0
$61$	3.27330	0.419103	0.209551	−	0.977798i	$-0.432800\pi$
$61$	3.27330	0.419103	0.209551	+	0.977798i	$0.432800\pi$
$62$	7.86030	0.998259
$63$	0	0
$64$	2.82843	0.353553
$65$	−8.55807	−1.06150
$66$	0	0
$67$	2.11652	0.258574	0.129287	−	0.991607i	$-0.458731\pi$
$67$	2.11652	0.258574	0.129287	+	0.991607i	$0.458731\pi$
$68$	0	0
$69$	0	0
$70$	−1.96775	−0.235191
$71$	0.226626	0.0268955	0.0134478	−	0.999910i	$-0.495719\pi$
$71$	0.226626	0.0268955	0.0134478	+	0.999910i	$0.495719\pi$
$72$	0	0
$73$	−0.368233	−0.0430984	−0.0215492	−	0.999768i	$-0.506860\pi$
$73$	−0.368233	−0.0430984	−0.0215492	+	0.999768i	$0.506860\pi$
$74$	3.01320	0.350278
$75$	0	0
$76$	9.63368	1.10506
$77$	1.84776	0.210572
$78$	0	0
$79$	2.71485	0.305444	0.152722	−	0.988269i	$-0.451196\pi$
$79$	2.71485	0.305444	0.152722	+	0.988269i	$0.451196\pi$
$80$	−1.72511	−0.192873
$81$	0	0
$82$	−9.28931	−1.02583
$83$	−14.4138	−1.58212	−0.791062	−	0.611736i	$-0.790472\pi$
$83$	−14.4138	−1.58212	−0.791062	+	0.611736i	$0.790472\pi$
$84$	0	0
$85$	0	0
$86$	−2.63752	−0.284411
$87$	0	0
$88$	−3.91082	−0.416895
$89$	−13.6694	−1.44895	−0.724477	−	0.689299i	$-0.757918\pi$
$89$	−13.6694	−1.44895	−0.724477	+	0.689299i	$0.757918\pi$
$90$	0	0
$91$	5.07401	0.531901
$92$	−4.67913	−0.487833
$93$	0	0
$94$	−1.20116	−0.123891
$95$	14.1853	1.45538
$96$	0	0
$97$	−2.68457	−0.272577	−0.136288	−	0.990669i	$-0.543517\pi$
$97$	−2.68457	−0.272577	−0.136288	+	0.990669i	$0.543517\pi$
$98$	−4.19090	−0.423345
$99$	0	0
$100$	0.938533	0.0938533
$101$	2.38009	0.236827	0.118414	−	0.992964i	$-0.462219\pi$
$101$	2.38009	0.236827	0.118414	+	0.992964i	$0.462219\pi$
$102$	0	0
$103$	−13.2909	−1.30959	−0.654796	−	0.755806i	$-0.727245\pi$
$103$	−13.2909	−1.30959	−0.654796	+	0.755806i	$0.727245\pi$
$104$	−10.7392	−1.05307
$105$	0	0
$106$	−3.03188	−0.294482
$107$	−13.0724	−1.26376	−0.631879	−	0.775067i	$-0.717716\pi$
$107$	−13.0724	−1.26376	−0.631879	+	0.775067i	$0.717716\pi$
$108$	0	0
$109$	0.956272	0.0915942	0.0457971	−	0.998951i	$-0.485417\pi$
$109$	0.956272	0.0915942	0.0457971	+	0.998951i	$0.485417\pi$
$110$	−2.38528	−0.227428
$111$	0	0
$112$	1.02280	0.0966459
$113$	−8.62951	−0.811796	−0.405898	−	0.913918i	$-0.633041\pi$
$113$	−8.62951	−0.811796	−0.405898	+	0.913918i	$0.633041\pi$
$114$	0	0
$115$	−6.88989	−0.642486
$116$	8.82843	0.819699
$117$	0	0
$118$	−6.17120	−0.568105
$119$	0	0
$120$	0	0
$121$	−8.76017	−0.796379
$122$	2.50527	0.226817
$123$	0	0
$124$	−14.5239	−1.30429
$125$	11.7939	1.05488
$126$	0	0
$127$	−14.1484	−1.25547	−0.627734	−	0.778428i	$-0.716017\pi$
$127$	−14.1484	−1.25547	−0.627734	+	0.778428i	$0.716017\pi$
$128$	−9.55582	−0.844623
$129$	0	0
$130$	−6.55007	−0.574479
$131$	2.59085	0.226364	0.113182	−	0.993574i	$-0.463896\pi$
$131$	2.59085	0.226364	0.113182	+	0.993574i	$0.463896\pi$
$132$	0	0
$133$	−8.41037	−0.729271
$134$	1.61991	0.139939
$135$	0	0
$136$	0	0
$137$	−15.2684	−1.30447	−0.652233	−	0.758018i	$-0.726168\pi$
$137$	−15.2684	−1.30447	−0.652233	+	0.758018i	$0.726168\pi$
$138$	0	0
$139$	4.04214	0.342849	0.171425	−	0.985197i	$-0.445163\pi$
$139$	4.04214	0.342849	0.171425	+	0.985197i	$0.445163\pi$
$140$	3.63593	0.307292
$141$	0	0
$142$	0.173452	0.0145557
$143$	6.15065	0.514343
$144$	0	0
$145$	12.9996	1.07956
$146$	−0.281833	−0.0233247
$147$	0	0
$148$	−5.56767	−0.457660
$149$	18.1219	1.48460	0.742302	−	0.670065i	$-0.233734\pi$
$149$	18.1219	1.48460	0.742302	+	0.670065i	$0.233734\pi$
$150$	0	0
$151$	5.27133	0.428975	0.214487	−	0.976727i	$-0.431192\pi$
$151$	5.27133	0.428975	0.214487	+	0.976727i	$0.431192\pi$
$152$	17.8007	1.44383
$153$	0	0
$154$	1.41421	0.113961
$155$	−21.3861	−1.71778
$156$	0	0
$157$	−3.80334	−0.303540	−0.151770	−	0.988416i	$-0.548497\pi$
$157$	−3.80334	−0.303540	−0.151770	+	0.988416i	$0.548497\pi$
$158$	2.07786	0.165305
$159$	0	0
$160$	−12.2034	−0.964767
$161$	4.08496	0.321940
$162$	0	0
$163$	9.06882	0.710324	0.355162	−	0.934805i	$-0.384426\pi$
$163$	9.06882	0.710324	0.355162	+	0.934805i	$0.384426\pi$
$164$	17.1644	1.34032
$165$	0	0
$166$	−11.0319	−0.856240
$167$	−8.88764	−0.687746	−0.343873	−	0.939016i	$-0.611739\pi$
$167$	−8.88764	−0.687746	−0.343873	+	0.939016i	$0.611739\pi$
$168$	0	0
$169$	3.88989	0.299223
$170$	0	0
$171$	0	0
$172$	4.87351	0.371601
$173$	−12.2472	−0.931136	−0.465568	−	0.885012i	$-0.654150\pi$
$173$	−12.2472	−0.931136	−0.465568	+	0.885012i	$0.654150\pi$
$174$	0	0
$175$	−0.819355	−0.0619374
$176$	1.23983	0.0934556
$177$	0	0
$178$	−10.4621	−0.784168
$179$	10.6173	0.793573	0.396787	−	0.917911i	$-0.370125\pi$
$179$	10.6173	0.793573	0.396787	+	0.917911i	$0.370125\pi$
$180$	0	0
$181$	16.5274	1.22847	0.614237	−	0.789122i	$-0.289464\pi$
$181$	16.5274	1.22847	0.614237	+	0.789122i	$0.289464\pi$
$182$	3.88348	0.287863
$183$	0	0
$184$	−8.64590	−0.637384
$185$	−8.19825	−0.602748
$186$	0	0
$187$	0	0
$188$	2.21946	0.161871
$189$	0	0
$190$	10.8570	0.787649
$191$	12.0167	0.869498	0.434749	−	0.900552i	$-0.356837\pi$
$191$	12.0167	0.869498	0.434749	+	0.900552i	$0.356837\pi$
$192$	0	0
$193$	−10.7183	−0.771522	−0.385761	−	0.922599i	$-0.626061\pi$
$193$	−10.7183	−0.771522	−0.385761	+	0.922599i	$0.626061\pi$
$194$	−2.05468	−0.147517
$195$	0	0
$196$	7.74378	0.553127
$197$	3.16895	0.225778	0.112889	−	0.993608i	$-0.463990\pi$
$197$	3.16895	0.225778	0.112889	+	0.993608i	$0.463990\pi$
$198$	0	0
$199$	−13.6746	−0.969366	−0.484683	−	0.874690i	$-0.661065\pi$
$199$	−13.6746	−0.969366	−0.484683	+	0.874690i	$0.661065\pi$
$200$	1.73418	0.122625
$201$	0	0
$202$	1.82164	0.128170
$203$	−7.70737	−0.540951
$204$	0	0
$205$	25.2741	1.76522
$206$	−10.1724	−0.708746
$207$	0	0
$208$	3.40461	0.236067
$209$	−10.1949	−0.705198
$210$	0	0
$211$	−5.92856	−0.408139	−0.204069	−	0.978956i	$-0.565417\pi$
$211$	−5.92856	−0.408139	−0.204069	+	0.978956i	$0.565417\pi$
$212$	5.60218	0.384759
$213$	0	0
$214$	−10.0052	−0.683941
$215$	7.17611	0.489407
$216$	0	0
$217$	12.6797	0.860751
$218$	0.731899	0.0495704
$219$	0	0
$220$	4.40743	0.297149
$221$	0	0
$222$	0	0
$223$	26.1476	1.75098	0.875488	−	0.483240i	$-0.160540\pi$
$223$	26.1476	1.75098	0.875488	+	0.483240i	$0.160540\pi$
$224$	7.23532	0.483430
$225$	0	0
$226$	−6.60474	−0.439341
$227$	10.9746	0.728408	0.364204	−	0.931319i	$-0.381341\pi$
$227$	10.9746	0.728408	0.364204	+	0.931319i	$0.381341\pi$
$228$	0	0
$229$	−14.4872	−0.957341	−0.478670	−	0.877995i	$-0.658881\pi$
$229$	−14.4872	−0.957341	−0.478670	+	0.877995i	$0.658881\pi$
$230$	−5.27330	−0.347711
$231$	0	0
$232$	16.3128	1.07099
$233$	19.0980	1.25115	0.625577	−	0.780163i	$-0.284864\pi$
$233$	19.0980	1.25115	0.625577	+	0.780163i	$0.284864\pi$
$234$	0	0
$235$	3.26810	0.213187
$236$	11.4029	0.742265
$237$	0	0
$238$	0	0
$239$	−0.740970	−0.0479294	−0.0239647	−	0.999713i	$-0.507629\pi$
$239$	−0.740970	−0.0479294	−0.0239647	+	0.999713i	$0.507629\pi$
$240$	0	0
$241$	−21.3617	−1.37603	−0.688015	−	0.725696i	$-0.741518\pi$
$241$	−21.3617	−1.37603	−0.688015	+	0.725696i	$0.741518\pi$
$242$	−6.70474	−0.430997
$243$	0	0
$244$	−4.62914	−0.296350
$245$	11.4025	0.728480
$246$	0	0
$247$	−27.9956	−1.78132
$248$	−26.8368	−1.70414
$249$	0	0
$250$	9.02668	0.570897
$251$	0.938819	0.0592577	0.0296289	−	0.999561i	$-0.490567\pi$
$251$	0.938819	0.0592577	0.0296289	+	0.999561i	$0.490567\pi$
$252$	0	0
$253$	4.95174	0.311313
$254$	−10.8287	−0.679454
$255$	0	0
$256$	−12.9706	−0.810660
$257$	15.8293	0.987403	0.493701	−	0.869631i	$-0.335644\pi$
$257$	15.8293	0.987403	0.493701	+	0.869631i	$0.335644\pi$
$258$	0	0
$259$	4.86068	0.302028
$260$	12.1029	0.750593
$261$	0	0
$262$	1.98295	0.122507
$263$	−11.4573	−0.706486	−0.353243	−	0.935532i	$-0.614921\pi$
$263$	−11.4573	−0.706486	−0.353243	+	0.935532i	$0.614921\pi$
$264$	0	0
$265$	8.24906	0.506735
$266$	−6.43702	−0.394679
$267$	0	0
$268$	−2.99321	−0.182839
$269$	19.1689	1.16875	0.584376	−	0.811483i	$-0.301339\pi$
$269$	19.1689	1.16875	0.584376	+	0.811483i	$0.301339\pi$
$270$	0	0
$271$	6.82805	0.414775	0.207387	−	0.978259i	$-0.433504\pi$
$271$	6.82805	0.414775	0.207387	+	0.978259i	$0.433504\pi$
$272$	0	0
$273$	0	0
$274$	−11.6859	−0.705972
$275$	−0.993212	−0.0598929
$276$	0	0
$277$	8.12784	0.488355	0.244177	−	0.969731i	$-0.421482\pi$
$277$	8.12784	0.488355	0.244177	+	0.969731i	$0.421482\pi$
$278$	3.09372	0.185549
$279$	0	0
$280$	6.71832	0.401497
$281$	−11.6070	−0.692417	−0.346209	−	0.938158i	$-0.612531\pi$
$281$	−11.6070	−0.692417	−0.346209	+	0.938158i	$0.612531\pi$
$282$	0	0
$283$	−6.06404	−0.360470	−0.180235	−	0.983624i	$-0.557686\pi$
$283$	−6.06404	−0.360470	−0.180235	+	0.983624i	$0.557686\pi$
$284$	−0.320497	−0.0190180
$285$	0	0
$286$	4.70750	0.278360
$287$	−14.9848	−0.884527
$288$	0	0
$289$	0	0
$290$	9.94948	0.584254
$291$	0	0
$292$	0.520760	0.0304752
$293$	−6.87547	−0.401669	−0.200835	−	0.979625i	$-0.564365\pi$
$293$	−6.87547	−0.401669	−0.200835	+	0.979625i	$0.564365\pi$
$294$	0	0
$295$	16.7905	0.977578
$296$	−10.2877	−0.597962
$297$	0	0
$298$	13.8699	0.803462
$299$	13.5976	0.786372
$300$	0	0
$301$	−4.25466	−0.245234
$302$	4.03450	0.232159
$303$	0	0
$304$	−5.64328	−0.323664
$305$	−6.81629	−0.390300
$306$	0	0
$307$	22.2451	1.26959	0.634797	−	0.772679i	$-0.281084\pi$
$307$	22.2451	1.26959	0.634797	+	0.772679i	$0.281084\pi$
$308$	−2.61313	−0.148897
$309$	0	0
$310$	−16.3682	−0.929653
$311$	5.41421	0.307012	0.153506	−	0.988148i	$-0.450944\pi$
$311$	5.41421	0.307012	0.153506	+	0.988148i	$0.450944\pi$
$312$	0	0
$313$	11.2945	0.638403	0.319202	−	0.947687i	$-0.396585\pi$
$313$	11.2945	0.638403	0.319202	+	0.947687i	$0.396585\pi$
$314$	−2.91095	−0.164274
$315$	0	0
$316$	−3.83938	−0.215982
$317$	−18.4520	−1.03637	−0.518183	−	0.855270i	$-0.673391\pi$
$317$	−18.4520	−1.03637	−0.518183	+	0.855270i	$0.673391\pi$
$318$	0	0
$319$	−9.34277	−0.523095
$320$	−5.88989	−0.329255
$321$	0	0
$322$	3.12649	0.174233
$323$	0	0
$324$	0	0
$325$	−2.72739	−0.151289
$326$	6.94097	0.384425
$327$	0	0
$328$	31.7157	1.75121
$329$	−1.93763	−0.106825
$330$	0	0
$331$	5.76606	0.316931	0.158466	−	0.987365i	$-0.449345\pi$
$331$	5.76606	0.316931	0.158466	+	0.987365i	$0.449345\pi$
$332$	20.3842	1.11873
$333$	0	0
$334$	−6.80231	−0.372206
$335$	−4.40743	−0.240803
$336$	0	0
$337$	16.2707	0.886320	0.443160	−	0.896443i	$-0.353857\pi$
$337$	16.2707	0.886320	0.443160	+	0.896443i	$0.353857\pi$
$338$	2.97720	0.161938
$339$	0	0
$340$	0	0
$341$	15.3701	0.832338
$342$	0	0
$343$	−15.4029	−0.831678
$344$	9.00506	0.485521
$345$	0	0
$346$	−9.37358	−0.503927
$347$	4.29038	0.230319	0.115160	−	0.993347i	$-0.463262\pi$
$347$	4.29038	0.230319	0.115160	+	0.993347i	$0.463262\pi$
$348$	0	0
$349$	14.1553	0.757718	0.378859	−	0.925454i	$-0.376317\pi$
$349$	14.1553	0.757718	0.378859	+	0.925454i	$0.376317\pi$
$350$	−0.627107	−0.0335203
$351$	0	0
$352$	8.77056	0.467473
$353$	−23.8142	−1.26750	−0.633752	−	0.773536i	$-0.718486\pi$
$353$	−23.8142	−1.26750	−0.633752	+	0.773536i	$0.718486\pi$
$354$	0	0
$355$	−0.471923	−0.0250471
$356$	19.3314	1.02456
$357$	0	0
$358$	8.12612	0.429479
$359$	35.2676	1.86135	0.930677	−	0.365841i	$-0.119219\pi$
$359$	35.2676	1.86135	0.930677	+	0.365841i	$0.119219\pi$
$360$	0	0
$361$	27.4039	1.44231
$362$	12.6495	0.664845
$363$	0	0
$364$	−7.17574	−0.376111
$365$	0.766805	0.0401364
$366$	0	0
$367$	−16.3212	−0.851959	−0.425980	−	0.904733i	$-0.640070\pi$
$367$	−16.3212	−0.851959	−0.425980	+	0.904733i	$0.640070\pi$
$368$	2.74097	0.142883
$369$	0	0
$370$	−6.27467	−0.326205
$371$	−4.89080	−0.253918
$372$	0	0
$373$	−25.0156	−1.29526	−0.647630	−	0.761955i	$-0.724240\pi$
$373$	−25.0156	−1.29526	−0.647630	+	0.761955i	$0.724240\pi$
$374$	0	0
$375$	0	0
$376$	4.10103	0.211495
$377$	−25.6556	−1.32133
$378$	0	0
$379$	−32.6281	−1.67599	−0.837997	−	0.545675i	$-0.816273\pi$
$379$	−32.6281	−1.67599	−0.837997	+	0.545675i	$0.816273\pi$
$380$	−20.0611	−1.02911
$381$	0	0
$382$	9.19719	0.470569
$383$	0.585258	0.0299053	0.0149526	−	0.999888i	$-0.495240\pi$
$383$	0.585258	0.0299053	0.0149526	+	0.999888i	$0.495240\pi$
$384$	0	0
$385$	−3.84776	−0.196100
$386$	−8.20345	−0.417545
$387$	0	0
$388$	3.79655	0.192741
$389$	22.1261	1.12184	0.560918	−	0.827871i	$-0.310448\pi$
$389$	22.1261	1.12184	0.560918	+	0.827871i	$0.310448\pi$
$390$	0	0
$391$	0	0
$392$	14.3086	0.722696
$393$	0	0
$394$	2.42541	0.122190
$395$	−5.65338	−0.284453
$396$	0	0
$397$	5.83031	0.292615	0.146307	−	0.989239i	$-0.453261\pi$
$397$	5.83031	0.292615	0.146307	+	0.989239i	$0.453261\pi$
$398$	−10.4661	−0.524617
$399$	0	0
$400$	−0.549780	−0.0274890
$401$	−5.19021	−0.259187	−0.129593	−	0.991567i	$-0.541367\pi$
$401$	−5.19021	−0.259187	−0.129593	+	0.991567i	$0.541367\pi$
$402$	0	0
$403$	42.2069	2.10247
$404$	−3.36595	−0.167462
$405$	0	0
$406$	−5.89897	−0.292761
$407$	5.89205	0.292058
$408$	0	0
$409$	−27.2400	−1.34693	−0.673465	−	0.739219i	$-0.735195\pi$
$409$	−27.2400	−1.34693	−0.673465	+	0.739219i	$0.735195\pi$
$410$	19.3440	0.955332
$411$	0	0
$412$	18.7962	0.926021
$413$	−9.95492	−0.489850
$414$	0	0
$415$	30.0153	1.47339
$416$	24.0843	1.18083
$417$	0	0
$418$	−7.80287	−0.381651
$419$	14.0301	0.685416	0.342708	−	0.939442i	$-0.388656\pi$
$419$	14.0301	0.685416	0.342708	+	0.939442i	$0.388656\pi$
$420$	0	0
$421$	15.3811	0.749627	0.374814	−	0.927100i	$-0.377707\pi$
$421$	15.3811	0.749627	0.374814	+	0.927100i	$0.377707\pi$
$422$	−4.53752	−0.220883
$423$	0	0
$424$	10.3515	0.502712
$425$	0	0
$426$	0	0
$427$	4.04132	0.195573
$428$	18.4872	0.893612
$429$	0	0
$430$	5.49236	0.264865
$431$	−16.3907	−0.789510	−0.394755	−	0.918786i	$-0.629171\pi$
$431$	−16.3907	−0.789510	−0.394755	+	0.918786i	$0.629171\pi$
$432$	0	0
$433$	21.7106	1.04335	0.521673	−	0.853145i	$-0.325308\pi$
$433$	21.7106	1.04335	0.521673	+	0.853145i	$0.325308\pi$
$434$	9.70459	0.465835
$435$	0	0
$436$	−1.35237	−0.0647669
$437$	−22.5386	−1.07817
$438$	0	0
$439$	−23.5304	−1.12304	−0.561522	−	0.827462i	$-0.689784\pi$
$439$	−23.5304	−1.12304	−0.561522	+	0.827462i	$0.689784\pi$
$440$	8.14386	0.388243
$441$	0	0
$442$	0	0
$443$	15.4238	0.732808	0.366404	−	0.930456i	$-0.380589\pi$
$443$	15.4238	0.732808	0.366404	+	0.930456i	$0.380589\pi$
$444$	0	0
$445$	28.4650	1.34937
$446$	20.0125	0.947621
$447$	0	0
$448$	3.49207	0.164985
$449$	13.5494	0.639438	0.319719	−	0.947512i	$-0.396411\pi$
$449$	13.5494	0.639438	0.319719	+	0.947512i	$0.396411\pi$
$450$	0	0
$451$	−18.1644	−0.855329
$452$	12.2040	0.574027
$453$	0	0
$454$	8.39957	0.394211
$455$	−10.5661	−0.495346
$456$	0	0
$457$	−15.3875	−0.719796	−0.359898	−	0.932992i	$-0.617188\pi$
$457$	−15.3875	−0.719796	−0.359898	+	0.932992i	$0.617188\pi$
$458$	−11.0880	−0.518109
$459$	0	0
$460$	9.74378	0.454306
$461$	20.8006	0.968780	0.484390	−	0.874852i	$-0.339042\pi$
$461$	20.8006	0.968780	0.484390	+	0.874852i	$0.339042\pi$
$462$	0	0
$463$	−26.4325	−1.22842	−0.614212	−	0.789141i	$-0.710526\pi$
$463$	−26.4325	−1.22842	−0.614212	+	0.789141i	$0.710526\pi$
$464$	−5.17157	−0.240084
$465$	0	0
$466$	14.6170	0.677120
$467$	7.17088	0.331829	0.165914	−	0.986140i	$-0.446942\pi$
$467$	7.17088	0.331829	0.165914	+	0.986140i	$0.446942\pi$
$468$	0	0
$469$	2.61313	0.120663
$470$	2.50130	0.115376
$471$	0	0
$472$	21.0698	0.969816
$473$	−5.15744	−0.237139
$474$	0	0
$475$	4.52076	0.207427
$476$	0	0
$477$	0	0
$478$	−0.567114	−0.0259392
$479$	2.93400	0.134058	0.0670289	−	0.997751i	$-0.478648\pi$
$479$	2.93400	0.134058	0.0670289	+	0.997751i	$0.478648\pi$
$480$	0	0
$481$	16.1798	0.737734
$482$	−16.3496	−0.744702
$483$	0	0
$484$	12.3888	0.563125
$485$	5.59032	0.253843
$486$	0	0
$487$	−23.2420	−1.05319	−0.526597	−	0.850115i	$-0.676532\pi$
$487$	−23.2420	−1.05319	−0.526597	+	0.850115i	$0.676532\pi$
$488$	−8.55354	−0.387200
$489$	0	0
$490$	8.72711	0.394251
$491$	−13.6586	−0.616403	−0.308202	−	0.951321i	$-0.599727\pi$
$491$	−13.6586	−0.616403	−0.308202	+	0.951321i	$0.599727\pi$
$492$	0	0
$493$	0	0
$494$	−21.4269	−0.964044
$495$	0	0
$496$	8.50793	0.382017
$497$	0.279799	0.0125507
$498$	0	0
$499$	7.53220	0.337187	0.168594	−	0.985686i	$-0.446077\pi$
$499$	7.53220	0.337187	0.168594	+	0.985686i	$0.446077\pi$
$500$	−16.6791	−0.745913
$501$	0	0
$502$	0.718541	0.0320700
$503$	−25.7161	−1.14662	−0.573311	−	0.819338i	$-0.694341\pi$
$503$	−25.7161	−1.14662	−0.573311	+	0.819338i	$0.694341\pi$
$504$	0	0
$505$	−4.95627	−0.220551
$506$	3.78989	0.168481
$507$	0	0
$508$	20.0089	0.887749
$509$	−34.7796	−1.54158	−0.770789	−	0.637090i	$-0.780138\pi$
$509$	−34.7796	−1.54158	−0.770789	+	0.637090i	$0.780138\pi$
$510$	0	0
$511$	−0.454632	−0.0201117
$512$	9.18440	0.405897
$513$	0	0
$514$	12.1152	0.534379
$515$	27.6769	1.21959
$516$	0	0
$517$	−2.34877	−0.103299
$518$	3.72020	0.163456
$519$	0	0
$520$	22.3633	0.980697
$521$	−44.5784	−1.95302	−0.976508	−	0.215479i	$-0.930869\pi$
$521$	−44.5784	−1.95302	−0.976508	+	0.215479i	$0.930869\pi$
$522$	0	0
$523$	19.8918	0.869808	0.434904	−	0.900477i	$-0.356782\pi$
$523$	19.8918	0.869808	0.434904	+	0.900477i	$0.356782\pi$
$524$	−3.66402	−0.160063
$525$	0	0
$526$	−8.76902	−0.382348
$527$	0	0
$528$	0	0
$529$	−12.0529	−0.524038
$530$	6.31355	0.274243
$531$	0	0
$532$	11.8941	0.515673
$533$	−49.8801	−2.16055
$534$	0	0
$535$	27.2219	1.17691
$536$	−5.53073	−0.238891
$537$	0	0
$538$	14.6713	0.632524
$539$	−8.19494	−0.352981
$540$	0	0
$541$	−0.781382	−0.0335942	−0.0167971	−	0.999859i	$-0.505347\pi$
$541$	−0.781382	−0.0335942	−0.0167971	+	0.999859i	$0.505347\pi$
$542$	5.22597	0.224474
$543$	0	0
$544$	0	0
$545$	−1.99133	−0.0852993
$546$	0	0
$547$	−39.0565	−1.66994	−0.834968	−	0.550299i	$-0.814514\pi$
$547$	−39.0565	−1.66994	−0.834968	+	0.550299i	$0.814514\pi$
$548$	21.5928	0.922397
$549$	0	0
$550$	−0.760171	−0.0324138
$551$	42.5251	1.81163
$552$	0	0
$553$	3.35184	0.142535
$554$	6.22078	0.264296
$555$	0	0
$556$	−5.71644	−0.242431
$557$	13.0371	0.552398	0.276199	−	0.961100i	$-0.410925\pi$
$557$	13.0371	0.552398	0.276199	+	0.961100i	$0.410925\pi$
$558$	0	0
$559$	−14.1625	−0.599010
$560$	−2.12988	−0.0900038
$561$	0	0
$562$	−8.88363	−0.374734
$563$	−11.2168	−0.472733	−0.236367	−	0.971664i	$-0.575957\pi$
$563$	−11.2168	−0.472733	−0.236367	+	0.971664i	$0.575957\pi$
$564$	0	0
$565$	17.9700	0.756005
$566$	−4.64121	−0.195085
$567$	0	0
$568$	−0.592201	−0.0248482
$569$	−36.4695	−1.52888	−0.764440	−	0.644694i	$-0.776985\pi$
$569$	−36.4695	−1.52888	−0.764440	+	0.644694i	$0.776985\pi$
$570$	0	0
$571$	−13.5450	−0.566842	−0.283421	−	0.958996i	$-0.591469\pi$
$571$	−13.5450	−0.566842	−0.283421	+	0.958996i	$0.591469\pi$
$572$	−8.69833	−0.363695
$573$	0	0
$574$	−11.4689	−0.478702
$575$	−2.19576	−0.0915694
$576$	0	0
$577$	−7.10617	−0.295834	−0.147917	−	0.989000i	$-0.547257\pi$
$577$	−7.10617	−0.295834	−0.147917	+	0.989000i	$0.547257\pi$
$578$	0	0
$579$	0	0
$580$	−18.3842	−0.763364
$581$	−17.7958	−0.738294
$582$	0	0
$583$	−5.92856	−0.245536
$584$	0.962238	0.0398177
$585$	0	0
$586$	−5.26226	−0.217382
$587$	−40.2951	−1.66316	−0.831578	−	0.555408i	$-0.812562\pi$
$587$	−40.2951	−1.66316	−0.831578	+	0.555408i	$0.812562\pi$
$588$	0	0
$589$	−69.9595	−2.88263
$590$	12.8509	0.529061
$591$	0	0
$592$	3.26147	0.134045
$593$	37.8418	1.55398	0.776989	−	0.629515i	$-0.216746\pi$
$593$	37.8418	1.55398	0.776989	+	0.629515i	$0.216746\pi$
$594$	0	0
$595$	0	0
$596$	−25.6282	−1.04977
$597$	0	0
$598$	10.4072	0.425581
$599$	10.1505	0.414739	0.207369	−	0.978263i	$-0.433510\pi$
$599$	10.1505	0.414739	0.207369	+	0.978263i	$0.433510\pi$
$600$	0	0
$601$	−35.2538	−1.43803	−0.719016	−	0.694994i	$-0.755407\pi$
$601$	−35.2538	−1.43803	−0.719016	+	0.694994i	$0.755407\pi$
$602$	−3.25637	−0.132720
$603$	0	0
$604$	−7.45479	−0.303331
$605$	18.2421	0.741647
$606$	0	0
$607$	−47.5878	−1.93153	−0.965764	−	0.259420i	$-0.916468\pi$
$607$	−47.5878	−1.93153	−0.965764	+	0.259420i	$0.916468\pi$
$608$	−39.9206	−1.61899
$609$	0	0
$610$	−5.21696	−0.211229
$611$	−6.44980	−0.260931
$612$	0	0
$613$	−26.9812	−1.08976	−0.544880	−	0.838514i	$-0.683425\pi$
$613$	−26.9812	−1.08976	−0.544880	+	0.838514i	$0.683425\pi$
$614$	17.0256	0.687099
$615$	0	0
$616$	−4.82843	−0.194543
$617$	14.9919	0.603553	0.301776	−	0.953379i	$-0.402420\pi$
$617$	14.9919	0.603553	0.301776	+	0.953379i	$0.402420\pi$
$618$	0	0
$619$	2.20241	0.0885225	0.0442613	−	0.999020i	$-0.485907\pi$
$619$	2.20241	0.0885225	0.0442613	+	0.999020i	$0.485907\pi$
$620$	30.2446	1.21465
$621$	0	0
$622$	4.14386	0.166154
$623$	−16.8767	−0.676150
$624$	0	0
$625$	−21.2414	−0.849655
$626$	8.64444	0.345501
$627$	0	0
$628$	5.37874	0.214635
$629$	0	0
$630$	0	0
$631$	34.7230	1.38230	0.691151	−	0.722710i	$-0.257104\pi$
$631$	34.7230	1.38230	0.691151	+	0.722710i	$0.257104\pi$
$632$	−7.09425	−0.282194
$633$	0	0
$634$	−14.1225	−0.560877
$635$	29.4625	1.16918
$636$	0	0
$637$	−22.5036	−0.891624
$638$	−7.15065	−0.283097
$639$	0	0
$640$	19.8990	0.786576
$641$	24.9301	0.984678	0.492339	−	0.870403i	$-0.336142\pi$
$641$	24.9301	0.984678	0.492339	+	0.870403i	$0.336142\pi$
$642$	0	0
$643$	35.1614	1.38663	0.693315	−	0.720634i	$-0.256149\pi$
$643$	35.1614	1.38663	0.693315	+	0.720634i	$0.256149\pi$
$644$	−5.77701	−0.227646
$645$	0	0
$646$	0	0
$647$	28.0142	1.10135	0.550677	−	0.834719i	$-0.314370\pi$
$647$	28.0142	1.10135	0.550677	+	0.834719i	$0.314370\pi$
$648$	0	0
$649$	−12.0672	−0.473680
$650$	−2.08746	−0.0818768
$651$	0	0
$652$	−12.8252	−0.502275
$653$	37.6735	1.47428	0.737138	−	0.675742i	$-0.236177\pi$
$653$	37.6735	1.47428	0.737138	+	0.675742i	$0.236177\pi$
$654$	0	0
$655$	−5.39517	−0.210807
$656$	−10.0547	−0.392569
$657$	0	0
$658$	−1.48300	−0.0578133
$659$	13.5356	0.527272	0.263636	−	0.964622i	$-0.415078\pi$
$659$	13.5356	0.527272	0.263636	+	0.964622i	$0.415078\pi$
$660$	0	0
$661$	−2.00626	−0.0780345	−0.0390172	−	0.999239i	$-0.512423\pi$
$661$	−2.00626	−0.0780345	−0.0390172	+	0.999239i	$0.512423\pi$
$662$	4.41315	0.171522
$663$	0	0
$664$	37.6652	1.46169
$665$	17.5137	0.679152
$666$	0	0
$667$	−20.6547	−0.799752
$668$	12.5690	0.486310
$669$	0	0
$670$	−3.37330	−0.130322
$671$	4.89884	0.189117
$672$	0	0
$673$	16.7634	0.646180	0.323090	−	0.946368i	$-0.395278\pi$
$673$	16.7634	0.646180	0.323090	+	0.946368i	$0.395278\pi$
$674$	12.4530	0.479673
$675$	0	0
$676$	−5.50114	−0.211582
$677$	−23.0647	−0.886449	−0.443225	−	0.896411i	$-0.646166\pi$
$677$	−23.0647	−0.886449	−0.443225	+	0.896411i	$0.646166\pi$
$678$	0	0
$679$	−3.31446	−0.127197
$680$	0	0
$681$	0	0
$682$	11.7638	0.450458
$683$	28.0179	1.07207	0.536037	−	0.844194i	$-0.319921\pi$
$683$	28.0179	1.07207	0.536037	+	0.844194i	$0.319921\pi$
$684$	0	0
$685$	31.7948	1.21482
$686$	−11.7889	−0.450101
$687$	0	0
$688$	−2.85483	−0.108840
$689$	−16.2800	−0.620220
$690$	0	0
$691$	26.6761	1.01481	0.507404	−	0.861708i	$-0.330605\pi$
$691$	26.6761	1.01481	0.507404	+	0.861708i	$0.330605\pi$
$692$	17.3201	0.658412
$693$	0	0
$694$	3.28371	0.124648
$695$	−8.41731	−0.319287
$696$	0	0
$697$	0	0
$698$	10.8340	0.410074
$699$	0	0
$700$	1.15874	0.0437964
$701$	9.75054	0.368273	0.184136	−	0.982901i	$-0.441051\pi$
$701$	9.75054	0.368273	0.184136	+	0.982901i	$0.441051\pi$
$702$	0	0
$703$	−26.8186	−1.01148
$704$	4.23304	0.159539
$705$	0	0
$706$	−18.2266	−0.685968
$707$	2.93853	0.110515
$708$	0	0
$709$	28.7535	1.07986	0.539929	−	0.841710i	$-0.318451\pi$
$709$	28.7535	1.07986	0.539929	+	0.841710i	$0.318451\pi$
$710$	−0.361194	−0.0135554
$711$	0	0
$712$	35.7199	1.33866
$713$	33.9797	1.27255
$714$	0	0
$715$	−12.8081	−0.478994
$716$	−15.0151	−0.561141
$717$	0	0
$718$	26.9927	1.00736
$719$	47.2247	1.76118	0.880592	−	0.473876i	$-0.157145\pi$
$719$	47.2247	1.76118	0.880592	+	0.473876i	$0.157145\pi$
$720$	0	0
$721$	−16.4094	−0.611118
$722$	20.9740	0.780572
$723$	0	0
$724$	−23.3733	−0.868662
$725$	4.14288	0.153863
$726$	0	0
$727$	−27.7790	−1.03027	−0.515134	−	0.857110i	$-0.672258\pi$
$727$	−27.7790	−1.03027	−0.515134	+	0.857110i	$0.672258\pi$
$728$	−13.2590	−0.491412
$729$	0	0
$730$	0.586887	0.0217217
$731$	0	0
$732$	0	0
$733$	−5.38987	−0.199080	−0.0995398	−	0.995034i	$-0.531737\pi$
$733$	−5.38987	−0.199080	−0.0995398	+	0.995034i	$0.531737\pi$
$734$	−12.4917	−0.461077
$735$	0	0
$736$	19.3897	0.714712
$737$	3.16760	0.116680
$738$	0	0
$739$	−3.61782	−0.133084	−0.0665418	−	0.997784i	$-0.521197\pi$
$739$	−3.61782	−0.133084	−0.0665418	+	0.997784i	$0.521197\pi$
$740$	11.5941	0.426207
$741$	0	0
$742$	−3.74325	−0.137419
$743$	6.18399	0.226868	0.113434	−	0.993546i	$-0.463815\pi$
$743$	6.18399	0.226868	0.113434	+	0.993546i	$0.463815\pi$
$744$	0	0
$745$	−37.7369	−1.38257
$746$	−19.1461	−0.700990
$747$	0	0
$748$	0	0
$749$	−16.1396	−0.589730
$750$	0	0
$751$	51.3317	1.87312	0.936560	−	0.350508i	$-0.113991\pi$
$751$	51.3317	1.87312	0.936560	+	0.350508i	$0.113991\pi$
$752$	−1.30013	−0.0474109
$753$	0	0
$754$	−19.6359	−0.715098
$755$	−10.9770	−0.399493
$756$	0	0
$757$	3.83750	0.139476	0.0697381	−	0.997565i	$-0.477784\pi$
$757$	3.83750	0.139476	0.0697381	+	0.997565i	$0.477784\pi$
$758$	−24.9725	−0.907041
$759$	0	0
$760$	−37.0681	−1.34460
$761$	16.5850	0.601206	0.300603	−	0.953749i	$-0.402812\pi$
$761$	16.5850	0.601206	0.300603	+	0.953749i	$0.402812\pi$
$762$	0	0
$763$	1.18064	0.0427422
$764$	−16.9942	−0.614828
$765$	0	0
$766$	0.447937	0.0161846
$767$	−33.1370	−1.19651
$768$	0	0
$769$	−27.7826	−1.00187	−0.500933	−	0.865486i	$-0.667010\pi$
$769$	−27.7826	−1.00187	−0.500933	+	0.865486i	$0.667010\pi$
$770$	−2.94495	−0.106129
$771$	0	0
$772$	15.1580	0.545548
$773$	13.9509	0.501778	0.250889	−	0.968016i	$-0.419277\pi$
$773$	13.9509	0.501778	0.250889	+	0.968016i	$0.419277\pi$
$774$	0	0
$775$	−6.81560	−0.244823
$776$	7.01511	0.251828
$777$	0	0
$778$	16.9346	0.607133
$779$	82.6782	2.96225
$780$	0	0
$781$	0.339169	0.0121364
$782$	0	0
$783$	0	0
$784$	−4.53620	−0.162007
$785$	7.92005	0.282679
$786$	0	0
$787$	−4.23206	−0.150857	−0.0754284	−	0.997151i	$-0.524032\pi$
$787$	−4.23206	−0.150857	−0.0754284	+	0.997151i	$0.524032\pi$
$788$	−4.48157	−0.159649
$789$	0	0
$790$	−4.32691	−0.153945
$791$	−10.6543	−0.378823
$792$	0	0
$793$	13.4524	0.477708
$794$	4.46232	0.158362
$795$	0	0
$796$	19.3388	0.685445
$797$	27.7502	0.982962	0.491481	−	0.870888i	$-0.336456\pi$
$797$	27.7502	0.982962	0.491481	+	0.870888i	$0.336456\pi$
$798$	0	0
$799$	0	0
$800$	−3.88915	−0.137502
$801$	0	0
$802$	−3.97242	−0.140271
$803$	−0.551099	−0.0194479
$804$	0	0
$805$	−8.50649	−0.299814
$806$	32.3037	1.13785
$807$	0	0
$808$	−6.21946	−0.218800
$809$	4.07279	0.143192	0.0715959	−	0.997434i	$-0.477191\pi$
$809$	4.07279	0.143192	0.0715959	+	0.997434i	$0.477191\pi$
$810$	0	0
$811$	−6.28674	−0.220757	−0.110379	−	0.993890i	$-0.535206\pi$
$811$	−6.28674	−0.220757	−0.110379	+	0.993890i	$0.535206\pi$
$812$	10.8999	0.382510
$813$	0	0
$814$	4.50958	0.158061
$815$	−18.8848	−0.661507
$816$	0	0
$817$	23.4749	0.821282
$818$	−20.8486	−0.728954
$819$	0	0
$820$	−35.7430	−1.24820
$821$	−19.7998	−0.691018	−0.345509	−	0.938415i	$-0.612294\pi$
$821$	−19.7998	−0.691018	−0.345509	+	0.938415i	$0.612294\pi$
$822$	0	0
$823$	−11.6739	−0.406927	−0.203463	−	0.979083i	$-0.565220\pi$
$823$	−11.6739	−0.406927	−0.203463	+	0.979083i	$0.565220\pi$
$824$	34.7308	1.20991
$825$	0	0
$826$	−7.61917	−0.265105
$827$	−13.8910	−0.483037	−0.241518	−	0.970396i	$-0.577645\pi$
$827$	−13.8910	−0.483037	−0.241518	+	0.970396i	$0.577645\pi$
$828$	0	0
$829$	−34.2670	−1.19014	−0.595071	−	0.803673i	$-0.702876\pi$
$829$	−34.2670	−1.19014	−0.595071	+	0.803673i	$0.702876\pi$
$830$	22.9727	0.797394
$831$	0	0
$832$	11.6241	0.402992
$833$	0	0
$834$	0	0
$835$	18.5076	0.640480
$836$	14.4178	0.498651
$837$	0	0
$838$	10.7382	0.370945
$839$	−24.2470	−0.837098	−0.418549	−	0.908194i	$-0.637461\pi$
$839$	−24.2470	−0.837098	−0.418549	+	0.908194i	$0.637461\pi$
$840$	0	0
$841$	9.97056	0.343813
$842$	11.7722	0.405695
$843$	0	0
$844$	8.38425	0.288598
$845$	−8.10029	−0.278658
$846$	0	0
$847$	−10.8156	−0.371628
$848$	−3.28168	−0.112693
$849$	0	0
$850$	0	0
$851$	13.0259	0.446523
$852$	0	0
$853$	7.38937	0.253007	0.126504	−	0.991966i	$-0.459624\pi$
$853$	7.38937	0.253007	0.126504	+	0.991966i	$0.459624\pi$
$854$	3.09309	0.105843
$855$	0	0
$856$	34.1599	1.16756
$857$	8.03331	0.274413	0.137206	−	0.990542i	$-0.456188\pi$
$857$	8.03331	0.274413	0.137206	+	0.990542i	$0.456188\pi$
$858$	0	0
$859$	−7.66672	−0.261585	−0.130793	−	0.991410i	$-0.541752\pi$
$859$	−7.66672	−0.261585	−0.130793	+	0.991410i	$0.541752\pi$
$860$	−10.1486	−0.346063
$861$	0	0
$862$	−12.5449	−0.427280
$863$	14.4183	0.490804	0.245402	−	0.969421i	$-0.421080\pi$
$863$	14.4183	0.490804	0.245402	+	0.969421i	$0.421080\pi$
$864$	0	0
$865$	25.5034	0.867142
$866$	16.6166	0.564655
$867$	0	0
$868$	−17.9317	−0.608643
$869$	4.06306	0.137830
$870$	0	0
$871$	8.69833	0.294732
$872$	−2.49886	−0.0846220
$873$	0	0
$874$	−17.2503	−0.583500
$875$	14.5612	0.492257
$876$	0	0
$877$	53.8226	1.81746	0.908731	−	0.417383i	$-0.137053\pi$
$877$	53.8226	1.81746	0.908731	+	0.417383i	$0.137053\pi$
$878$	−18.0094	−0.607787
$879$	0	0
$880$	−2.58181	−0.0870328
$881$	29.7945	1.00380	0.501901	−	0.864925i	$-0.332634\pi$
$881$	29.7945	1.00380	0.501901	+	0.864925i	$0.332634\pi$
$882$	0	0
$883$	−28.2666	−0.951247	−0.475624	−	0.879649i	$-0.657778\pi$
$883$	−28.2666	−0.951247	−0.475624	+	0.879649i	$0.657778\pi$
$884$	0	0
$885$	0	0
$886$	11.8049	0.396593
$887$	−25.1167	−0.843338	−0.421669	−	0.906750i	$-0.638556\pi$
$887$	−25.1167	−0.843338	−0.421669	+	0.906750i	$0.638556\pi$
$888$	0	0
$889$	−17.4681	−0.585861
$890$	21.7862	0.730275
$891$	0	0
$892$	−36.9784	−1.23813
$893$	10.6908	0.357754
$894$	0	0
$895$	−22.1094	−0.739034
$896$	−11.7979	−0.394141
$897$	0	0
$898$	10.3703	0.346061
$899$	−64.1118	−2.13825
$900$	0	0
$901$	0	0
$902$	−13.9024	−0.462901
$903$	0	0
$904$	22.5500	0.750002
$905$	−34.4166	−1.14405
$906$	0	0
$907$	49.0993	1.63032	0.815158	−	0.579238i	$-0.196650\pi$
$907$	49.0993	1.63032	0.815158	+	0.579238i	$0.196650\pi$
$908$	−15.5204	−0.515062
$909$	0	0
$910$	−8.08693	−0.268079
$911$	7.97626	0.264265	0.132133	−	0.991232i	$-0.457817\pi$
$911$	7.97626	0.264265	0.132133	+	0.991232i	$0.457817\pi$
$912$	0	0
$913$	−21.5718	−0.713924
$914$	−11.7771	−0.389551
$915$	0	0
$916$	20.4880	0.676942
$917$	3.19875	0.105632
$918$	0	0
$919$	19.8027	0.653229	0.326615	−	0.945158i	$-0.394092\pi$
$919$	19.8027	0.653229	0.326615	+	0.945158i	$0.394092\pi$
$920$	18.0042	0.593580
$921$	0	0
$922$	15.9201	0.524300
$923$	0.931370	0.0306564
$924$	0	0
$925$	−2.61272	−0.0859058
$926$	−20.2306	−0.664818
$927$	0	0
$928$	−36.5838	−1.20092
$929$	−5.57451	−0.182894	−0.0914468	−	0.995810i	$-0.529149\pi$
$929$	−5.57451	−0.182894	−0.0914468	+	0.995810i	$0.529149\pi$
$930$	0	0
$931$	37.3005	1.22248
$932$	−27.0087	−0.884699
$933$	0	0
$934$	5.48836	0.179584
$935$	0	0
$936$	0	0
$937$	0.398572	0.0130208	0.00651039	−	0.999979i	$-0.497928\pi$
$937$	0.398572	0.0130208	0.00651039	+	0.999979i	$0.497928\pi$
$938$	2.00000	0.0653023
$939$	0	0
$940$	−4.62179	−0.150746
$941$	4.30846	0.140452	0.0702259	−	0.997531i	$-0.477628\pi$
$941$	4.30846	0.140452	0.0702259	+	0.997531i	$0.477628\pi$
$942$	0	0
$943$	−40.1572	−1.30770
$944$	−6.67966	−0.217404
$945$	0	0
$946$	−3.94733	−0.128339
$947$	−11.4156	−0.370957	−0.185478	−	0.982648i	$-0.559384\pi$
$947$	−11.4156	−0.370957	−0.185478	+	0.982648i	$0.559384\pi$
$948$	0	0
$949$	−1.51334	−0.0491250
$950$	3.46004	0.112259
$951$	0	0
$952$	0	0
$953$	40.8932	1.32466	0.662330	−	0.749213i	$-0.269568\pi$
$953$	40.8932	1.32466	0.662330	+	0.749213i	$0.269568\pi$
$954$	0	0
$955$	−25.0235	−0.809741
$956$	1.04789	0.0338912
$957$	0	0
$958$	2.24558	0.0725515
$959$	−18.8509	−0.608726
$960$	0	0
$961$	74.4725	2.40234
$962$	12.3835	0.399259
$963$	0	0
$964$	30.2100	0.973000
$965$	22.3197	0.718498
$966$	0	0
$967$	23.5335	0.756788	0.378394	−	0.925645i	$-0.376476\pi$
$967$	23.5335	0.756788	0.378394	+	0.925645i	$0.376476\pi$
$968$	22.8914	0.735758
$969$	0	0
$970$	4.27865	0.137379
$971$	−6.44140	−0.206714	−0.103357	−	0.994644i	$-0.532958\pi$
$971$	−6.44140	−0.206714	−0.103357	+	0.994644i	$0.532958\pi$
$972$	0	0
$973$	4.99055	0.159990
$974$	−17.7886	−0.569985
$975$	0	0
$976$	2.71169	0.0867990
$977$	−17.8474	−0.570989	−0.285495	−	0.958380i	$-0.592158\pi$
$977$	−17.8474	−0.570989	−0.285495	+	0.958380i	$0.592158\pi$
$978$	0	0
$979$	−20.4577	−0.653831
$980$	−16.1256	−0.515113
$981$	0	0
$982$	−10.4538	−0.333595
$983$	−24.1176	−0.769232	−0.384616	−	0.923077i	$-0.625666\pi$
$983$	−24.1176	−0.769232	−0.384616	+	0.923077i	$0.625666\pi$
$984$	0	0
$985$	−6.59899	−0.210261
$986$	0	0
$987$	0	0
$988$	39.5918	1.25958
$989$	−11.4019	−0.362559
$990$	0	0
$991$	−24.2059	−0.768925	−0.384463	−	0.923141i	$-0.625613\pi$
$991$	−24.2059	−0.768925	−0.384463	+	0.923141i	$0.625613\pi$
$992$	60.1852	1.91088
$993$	0	0
$994$	0.214149	0.00679240
$995$	28.4759	0.902746
$996$	0	0
$997$	36.9151	1.16911	0.584557	−	0.811353i	$-0.301268\pi$
$997$	36.9151	1.16911	0.584557	+	0.811353i	$0.301268\pi$
$998$	5.76489	0.182484
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2601.2.a.bc.1.3		4
3.2	odd	2		867.2.a.m.1.2		4
17.5	odd	16		153.2.l.e.127.1		8
17.7	odd	16		153.2.l.e.100.1		8
17.16	even	2		2601.2.a.bd.1.3		4
51.2	odd	8		867.2.e.i.616.2		8
51.5	even	16		51.2.h.a.25.2	✓	8
51.8	odd	8		867.2.e.h.829.3		8
51.11	even	16		867.2.h.b.733.1		8
51.14	even	16		867.2.h.b.757.1		8
51.20	even	16		867.2.h.f.757.1		8
51.23	even	16		867.2.h.f.733.1		8
51.26	odd	8		867.2.e.i.829.3		8
51.29	even	16		867.2.h.g.688.2		8
51.32	odd	8		867.2.e.h.616.2		8
51.38	odd	4		867.2.d.e.577.6		8
51.41	even	16		51.2.h.a.49.2	yes	8
51.44	even	16		867.2.h.g.712.2		8
51.47	odd	4		867.2.d.e.577.5		8
51.50	odd	2		867.2.a.n.1.2		4
204.107	odd	16		816.2.bq.a.433.1		8
204.143	odd	16		816.2.bq.a.49.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.h.a.25.2	✓	8	51.5	even	16
51.2.h.a.49.2	yes	8	51.41	even	16
153.2.l.e.100.1		8	17.7	odd	16
153.2.l.e.127.1		8	17.5	odd	16
816.2.bq.a.49.1		8	204.143	odd	16
816.2.bq.a.433.1		8	204.107	odd	16
867.2.a.m.1.2		4	3.2	odd	2
867.2.a.n.1.2		4	51.50	odd	2
867.2.d.e.577.5		8	51.47	odd	4
867.2.d.e.577.6		8	51.38	odd	4
867.2.e.h.616.2		8	51.32	odd	8
867.2.e.h.829.3		8	51.8	odd	8
867.2.e.i.616.2		8	51.2	odd	8
867.2.e.i.829.3		8	51.26	odd	8
867.2.h.b.733.1		8	51.11	even	16
867.2.h.b.757.1		8	51.14	even	16
867.2.h.f.733.1		8	51.23	even	16
867.2.h.f.757.1		8	51.20	even	16
867.2.h.g.688.2		8	51.29	even	16
867.2.h.g.712.2		8	51.44	even	16
2601.2.a.bc.1.3		4	1.1	even	1	trivial
2601.2.a.bd.1.3		4	17.16	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:	\( N \)	\(=\)	\( 2601 = 3^{2} \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2601.a (trivial)

\(f(q)\)	\(=\)	\(q+0.765367 q^{2} -1.41421 q^{4} -2.08239 q^{5} +1.23463 q^{7} -2.61313 q^{8} +O(q^{10})\)	\(q+0.765367 q^{2} -1.41421 q^{4} -2.08239 q^{5} +1.23463 q^{7} -2.61313 q^{8} -1.59379 q^{10} +1.49661 q^{11} +4.10973 q^{13} +0.944947 q^{14} +0.828427 q^{16} -6.81204 q^{19} +2.94495 q^{20} +1.14545 q^{22} +3.30864 q^{23} -0.663643 q^{25} +3.14545 q^{26} -1.74603 q^{28} -6.24264 q^{29} +10.2700 q^{31} +5.86030 q^{32} -2.57099 q^{35} +3.93694 q^{37} -5.21371 q^{38} +5.44155 q^{40} -12.1371 q^{41} -3.44609 q^{43} -2.11652 q^{44} +2.53233 q^{46} -1.56940 q^{47} -5.47568 q^{49} -0.507930 q^{50} -5.81204 q^{52} -3.96134 q^{53} -3.11652 q^{55} -3.22625 q^{56} -4.77791 q^{58} -8.06306 q^{59} +3.27330 q^{61} +7.86030 q^{62} +2.82843 q^{64} -8.55807 q^{65} +2.11652 q^{67} -1.96775 q^{70} +0.226626 q^{71} -0.368233 q^{73} +3.01320 q^{74} +9.63368 q^{76} +1.84776 q^{77} +2.71485 q^{79} -1.72511 q^{80} -9.28931 q^{82} -14.4138 q^{83} -2.63752 q^{86} -3.91082 q^{88} -13.6694 q^{89} +5.07401 q^{91} -4.67913 q^{92} -1.20116 q^{94} +14.1853 q^{95} -2.68457 q^{97} -4.19090 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{5} + 8 q^{7}+O(q^{10}) \) 4 * q - 4 * q^5 + 8 * q^7	\( 4 q - 4 q^{5} + 8 q^{7} + 8 q^{10} - 4 q^{11} - 4 q^{13} - 8 q^{14} - 8 q^{16} - 12 q^{19} - 8 q^{22} - 12 q^{23} - 8 q^{29} + 8 q^{31} - 16 q^{35} + 24 q^{37} - 16 q^{38} - 12 q^{41} + 4 q^{43} - 8 q^{44} + 8 q^{46} - 8 q^{47} - 4 q^{49} - 16 q^{50} - 8 q^{52} - 8 q^{53} - 12 q^{55} + 8 q^{56} - 24 q^{59} + 24 q^{61} + 8 q^{62} - 12 q^{65} + 8 q^{67} + 24 q^{70} + 24 q^{71} + 8 q^{73} + 8 q^{74} - 8 q^{76} + 8 q^{80} - 8 q^{82} - 8 q^{83} + 16 q^{86} - 16 q^{89} - 8 q^{91} - 16 q^{94} + 12 q^{95} - 16 q^{97} - 32 q^{98}+O(q^{100}) \) 4 * q - 4 * q^5 + 8 * q^7 + 8 * q^10 - 4 * q^11 - 4 * q^13 - 8 * q^14 - 8 * q^16 - 12 * q^19 - 8 * q^22 - 12 * q^23 - 8 * q^29 + 8 * q^31 - 16 * q^35 + 24 * q^37 - 16 * q^38 - 12 * q^41 + 4 * q^43 - 8 * q^44 + 8 * q^46 - 8 * q^47 - 4 * q^49 - 16 * q^50 - 8 * q^52 - 8 * q^53 - 12 * q^55 + 8 * q^56 - 24 * q^59 + 24 * q^61 + 8 * q^62 - 12 * q^65 + 8 * q^67 + 24 * q^70 + 24 * q^71 + 8 * q^73 + 8 * q^74 - 8 * q^76 + 8 * q^80 - 8 * q^82 - 8 * q^83 + 16 * q^86 - 16 * q^89 - 8 * q^91 - 16 * q^94 + 12 * q^95 - 16 * q^97 - 32 * q^98

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