LMFDB - Embedded newform 2601.2.a.bc.1.4

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			1.4
Root			$1.84776$ 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)

$f(q)$	$=$	$q+1.84776 q^{2} +1.41421 q^{4} +1.61313 q^{5} +0.152241 q^{7} -1.08239 q^{8} +O(q^{10})$	$q+1.84776 q^{2} +1.41421 q^{4} +1.61313 q^{5} +0.152241 q^{7} -1.08239 q^{8} +2.98067 q^{10} -5.02734 q^{11} -3.94495 q^{13} +0.281305 q^{14} -4.82843 q^{16} -6.57900 q^{19} +2.28130 q^{20} -9.28931 q^{22} -3.44834 q^{23} -2.39782 q^{25} -7.28931 q^{26} +0.215301 q^{28} +2.24264 q^{29} -2.57446 q^{31} -6.75699 q^{32} +0.245584 q^{35} +10.6762 q^{37} -12.1564 q^{38} -1.74603 q^{40} +0.276769 q^{41} +6.34277 q^{43} -7.10973 q^{44} -6.37170 q^{46} -9.82164 q^{47} -6.97682 q^{49} -4.43060 q^{50} -5.57900 q^{52} +2.12612 q^{53} -8.10973 q^{55} -0.164784 q^{56} +4.14386 q^{58} -1.32381 q^{59} +8.27836 q^{61} -4.75699 q^{62} -2.82843 q^{64} -6.36370 q^{65} +7.10973 q^{67} +0.453780 q^{70} +6.54712 q^{71} +8.32638 q^{73} +19.7270 q^{74} -9.30411 q^{76} -0.765367 q^{77} +0.532327 q^{79} -7.78886 q^{80} +0.511402 q^{82} -2.20345 q^{83} +11.7199 q^{86} +5.44155 q^{88} +7.64847 q^{89} -0.600582 q^{91} -4.87669 q^{92} -18.1480 q^{94} -10.6128 q^{95} +3.60634 q^{97} -12.8915 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.84776	1.30656	0.653281	−	0.757115i	$-0.273392\pi$
$2$	1.84776	1.30656	0.653281	+	0.757115i	$0.273392\pi$
$3$	0	0
$3$	0	0
$4$	1.41421	0.707107
$5$	1.61313	0.721412	0.360706	−	0.932680i	$-0.382536\pi$
$5$	1.61313	0.721412	0.360706	+	0.932680i	$0.382536\pi$
$6$	0	0
$7$	0.152241	0.0575417	0.0287708	−	0.999586i	$-0.490841\pi$
$7$	0.152241	0.0575417	0.0287708	+	0.999586i	$0.490841\pi$
$8$	−1.08239	−0.382683
$9$	0	0
$10$	2.98067	0.942570
$11$	−5.02734	−1.51580	−0.757900	−	0.652371i	$-0.773774\pi$
$11$	−5.02734	−1.51580	−0.757900	+	0.652371i	$0.773774\pi$
$12$	0	0
$13$	−3.94495	−1.09413	−0.547066	−	0.837090i	$-0.684255\pi$
$13$	−3.94495	−1.09413	−0.547066	+	0.837090i	$0.684255\pi$
$14$	0.281305	0.0751818
$15$	0	0
$16$	−4.82843	−1.20711
$17$	0	0
$17$	0	0
$18$	0	0
$19$	−6.57900	−1.50933	−0.754663	−	0.656113i	$-0.772200\pi$
$19$	−6.57900	−1.50933	−0.754663	+	0.656113i	$0.772200\pi$
$20$	2.28130	0.510115
$21$	0	0
$22$	−9.28931	−1.98049
$23$	−3.44834	−0.719029	−0.359514	−	0.933140i	$-0.617058\pi$
$23$	−3.44834	−0.719029	−0.359514	+	0.933140i	$0.617058\pi$
$24$	0	0
$25$	−2.39782	−0.479565
$26$	−7.28931	−1.42955
$27$	0	0
$28$	0.215301	0.0406881
$29$	2.24264	0.416448	0.208224	−	0.978081i	$-0.433232\pi$
$29$	2.24264	0.416448	0.208224	+	0.978081i	$0.433232\pi$
$30$	0	0
$31$	−2.57446	−0.462387	−0.231194	−	0.972908i	$-0.574263\pi$
$31$	−2.57446	−0.462387	−0.231194	+	0.972908i	$0.574263\pi$
$32$	−6.75699	−1.19448
$33$	0	0
$34$	0	0
$35$	0.245584	0.0415112
$36$	0	0
$37$	10.6762	1.75515	0.877577	−	0.479436i	$-0.159159\pi$
$37$	10.6762	1.75515	0.877577	+	0.479436i	$0.159159\pi$
$38$	−12.1564	−1.97203
$39$	0	0
$40$	−1.74603	−0.276072
$41$	0.276769	0.0432240	0.0216120	−	0.999766i	$-0.493120\pi$
$41$	0.276769	0.0432240	0.0216120	+	0.999766i	$0.493120\pi$
$42$	0	0
$43$	6.34277	0.967264	0.483632	−	0.875272i	$-0.339317\pi$
$43$	6.34277	0.967264	0.483632	+	0.875272i	$0.339317\pi$
$44$	−7.10973	−1.07183
$45$	0	0
$46$	−6.37170	−0.939457
$47$	−9.82164	−1.43263	−0.716317	−	0.697775i	$-0.754173\pi$
$47$	−9.82164	−1.43263	−0.716317	+	0.697775i	$0.754173\pi$
$48$	0	0
$49$	−6.97682	−0.996689
$50$	−4.43060	−0.626582
$51$	0	0
$52$	−5.57900	−0.773668
$53$	2.12612	0.292045	0.146023	−	0.989281i	$-0.453353\pi$
$53$	2.12612	0.292045	0.146023	+	0.989281i	$0.453353\pi$
$54$	0	0
$55$	−8.10973	−1.09352
$56$	−0.164784	−0.0220202
$57$	0	0
$58$	4.14386	0.544115
$59$	−1.32381	−0.172346	−0.0861729	−	0.996280i	$-0.527464\pi$
$59$	−1.32381	−0.172346	−0.0861729	+	0.996280i	$0.527464\pi$
$60$	0	0
$61$	8.27836	1.05994	0.529968	−	0.848018i	$-0.322204\pi$
$61$	8.27836	1.05994	0.529968	+	0.848018i	$0.322204\pi$
$62$	−4.75699	−0.604138
$63$	0	0
$64$	−2.82843	−0.353553
$65$	−6.36370	−0.789319
$66$	0	0
$67$	7.10973	0.868592	0.434296	−	0.900770i	$-0.356997\pi$
$67$	7.10973	0.868592	0.434296	+	0.900770i	$0.356997\pi$
$68$	0	0
$69$	0	0
$70$	0.453780	0.0542370
$71$	6.54712	0.777000	0.388500	−	0.921449i	$-0.372993\pi$
$71$	6.54712	0.777000	0.388500	+	0.921449i	$0.372993\pi$
$72$	0	0
$73$	8.32638	0.974529	0.487265	−	0.873254i	$-0.337995\pi$
$73$	8.32638	0.974529	0.487265	+	0.873254i	$0.337995\pi$
$74$	19.7270	2.29322
$75$	0	0
$76$	−9.30411	−1.06725
$77$	−0.765367	−0.0872216
$78$	0	0
$79$	0.532327	0.0598914	0.0299457	−	0.999552i	$-0.490467\pi$
$79$	0.532327	0.0598914	0.0299457	+	0.999552i	$0.490467\pi$
$80$	−7.78886	−0.870821
$81$	0	0
$82$	0.511402	0.0564749
$83$	−2.20345	−0.241860	−0.120930	−	0.992661i	$-0.538588\pi$
$83$	−2.20345	−0.241860	−0.120930	+	0.992661i	$0.538588\pi$
$84$	0	0
$85$	0	0
$86$	11.7199	1.26379
$87$	0	0
$88$	5.44155	0.580072
$89$	7.64847	0.810737	0.405368	−	0.914153i	$-0.367143\pi$
$89$	7.64847	0.810737	0.405368	+	0.914153i	$0.367143\pi$
$90$	0	0
$91$	−0.600582	−0.0629581
$92$	−4.87669	−0.508430
$93$	0	0
$94$	−18.1480	−1.87183
$95$	−10.6128	−1.08885
$96$	0	0
$97$	3.60634	0.366168	0.183084	−	0.983097i	$-0.441392\pi$
$97$	3.60634	0.366168	0.183084	+	0.983097i	$0.441392\pi$
$98$	−12.8915	−1.30224
$99$	0	0
$100$	−3.39104	−0.339104
$101$	−9.13707	−0.909173	−0.454586	−	0.890703i	$-0.650213\pi$
$101$	−9.13707	−0.909173	−0.454586	+	0.890703i	$0.650213\pi$
$102$	0	0
$103$	7.57862	0.746744	0.373372	−	0.927682i	$-0.378202\pi$
$103$	7.57862	0.746744	0.373372	+	0.927682i	$0.378202\pi$
$104$	4.26998	0.418706
$105$	0	0
$106$	3.92856	0.381575
$107$	−18.4666	−1.78524	−0.892619	−	0.450812i	$-0.851134\pi$
$107$	−18.4666	−1.78524	−0.892619	+	0.450812i	$0.851134\pi$
$108$	0	0
$109$	10.7392	1.02863	0.514317	−	0.857600i	$-0.328046\pi$
$109$	10.7392	1.02863	0.514317	+	0.857600i	$0.328046\pi$
$110$	−14.9848	−1.42875
$111$	0	0
$112$	−0.735084	−0.0694589
$113$	−1.67497	−0.157568	−0.0787838	−	0.996892i	$-0.525104\pi$
$113$	−1.67497	−0.157568	−0.0787838	+	0.996892i	$0.525104\pi$
$114$	0	0
$115$	−5.56261	−0.518716
$116$	3.17157	0.294473
$117$	0	0
$118$	−2.44609	−0.225181
$119$	0	0
$120$	0	0
$121$	14.2741	1.29765
$122$	15.2964	1.38487
$123$	0	0
$124$	−3.64084	−0.326957
$125$	−11.9336	−1.06738
$126$	0	0
$127$	−12.1812	−1.08090	−0.540452	−	0.841375i	$-0.681747\pi$
$127$	−12.1812	−1.08090	−0.540452	+	0.841375i	$0.681747\pi$
$128$	8.28772	0.732538
$129$	0	0
$130$	−11.7586	−1.03130
$131$	−10.4512	−0.913122	−0.456561	−	0.889692i	$-0.650919\pi$
$131$	−10.4512	−0.913122	−0.456561	+	0.889692i	$0.650919\pi$
$132$	0	0
$133$	−1.00159	−0.0868491
$134$	13.1371	1.13487
$135$	0	0
$136$	0	0
$137$	−13.4928	−1.15276	−0.576382	−	0.817180i	$-0.695536\pi$
$137$	−13.4928	−1.15276	−0.576382	+	0.817180i	$0.695536\pi$
$138$	0	0
$139$	5.32798	0.451913	0.225957	−	0.974137i	$-0.427449\pi$
$139$	5.32798	0.451913	0.225957	+	0.974137i	$0.427449\pi$
$140$	0.347308	0.0293529
$141$	0	0
$142$	12.0975	1.01520
$143$	19.8326	1.65848
$144$	0	0
$145$	3.61766	0.300430
$146$	15.3852	1.27328
$147$	0	0
$148$	15.0984	1.24108
$149$	−9.31890	−0.763434	−0.381717	−	0.924279i	$-0.624667\pi$
$149$	−9.31890	−0.763434	−0.381717	+	0.924279i	$0.624667\pi$
$150$	0	0
$151$	11.9632	0.973555	0.486778	−	0.873526i	$-0.338172\pi$
$151$	11.9632	0.973555	0.486778	+	0.873526i	$0.338172\pi$
$152$	7.12106	0.577594
$153$	0	0
$154$	−1.41421	−0.113961
$155$	−4.15293	−0.333571
$156$	0	0
$157$	−18.1548	−1.44891	−0.724456	−	0.689321i	$-0.757909\pi$
$157$	−18.1548	−1.44891	−0.724456	+	0.689321i	$0.757909\pi$
$158$	0.983611	0.0782519
$159$	0	0
$160$	−10.8999	−0.861710
$161$	−0.524979	−0.0413741
$162$	0	0
$163$	−20.7225	−1.62311	−0.811555	−	0.584276i	$-0.801379\pi$
$163$	−20.7225	−1.62311	−0.811555	+	0.584276i	$0.801379\pi$
$164$	0.391410	0.0305640
$165$	0	0
$166$	−4.07144	−0.316005
$167$	8.08881	0.625931	0.312965	−	0.949765i	$-0.398678\pi$
$167$	8.08881	0.625931	0.312965	+	0.949765i	$0.398678\pi$
$168$	0	0
$169$	2.56261	0.197124
$170$	0	0
$171$	0	0
$172$	8.97003	0.683959
$173$	−1.16062	−0.0882405	−0.0441202	−	0.999026i	$-0.514048\pi$
$173$	−1.16062	−0.0882405	−0.0441202	+	0.999026i	$0.514048\pi$
$174$	0	0
$175$	−0.365047	−0.0275950
$176$	24.2741	1.82973
$177$	0	0
$178$	14.1325	1.05928
$179$	−2.89668	−0.216508	−0.108254	−	0.994123i	$-0.534526\pi$
$179$	−2.89668	−0.216508	−0.108254	+	0.994123i	$0.534526\pi$
$180$	0	0
$181$	0.842695	0.0626370	0.0313185	−	0.999509i	$-0.490029\pi$
$181$	0.842695	0.0626370	0.0313185	+	0.999509i	$0.490029\pi$
$182$	−1.10973	−0.0822588
$183$	0	0
$184$	3.73246	0.275160
$185$	17.2220	1.26619
$186$	0	0
$187$	0	0
$188$	−13.8899	−1.01302
$189$	0	0
$190$	−19.6098	−1.42265
$191$	−9.97069	−0.721454	−0.360727	−	0.932671i	$-0.617471\pi$
$191$	−9.97069	−0.721454	−0.360727	+	0.932671i	$0.617471\pi$
$192$	0	0
$193$	−3.73418	−0.268792	−0.134396	−	0.990928i	$-0.542909\pi$
$193$	−3.73418	−0.268792	−0.134396	+	0.990928i	$0.542909\pi$
$194$	6.66364	0.478422
$195$	0	0
$196$	−9.86672	−0.704766
$197$	−16.2053	−1.15458	−0.577291	−	0.816539i	$-0.695890\pi$
$197$	−16.2053	−1.15458	−0.577291	+	0.816539i	$0.695890\pi$
$198$	0	0
$199$	−16.4734	−1.16777	−0.583885	−	0.811836i	$-0.698468\pi$
$199$	−16.4734	−1.16777	−0.583885	+	0.811836i	$0.698468\pi$
$200$	2.59539	0.183522
$201$	0	0
$202$	−16.8831	−1.18789
$203$	0.341422	0.0239631
$204$	0	0
$205$	0.446463	0.0311823
$206$	14.0035	0.975668
$207$	0	0
$208$	19.0479	1.32073
$209$	33.0749	2.28784
$210$	0	0
$211$	−10.6887	−0.735842	−0.367921	−	0.929857i	$-0.619930\pi$
$211$	−10.6887	−0.735842	−0.367921	+	0.929857i	$0.619930\pi$
$212$	3.00679	0.206507
$213$	0	0
$214$	−34.1219	−2.33253
$215$	10.2317	0.697795
$216$	0	0
$217$	−0.391939	−0.0266065
$218$	19.8435	1.34397
$219$	0	0
$220$	−11.4689	−0.773233
$221$	0	0
$222$	0	0
$223$	5.41650	0.362715	0.181358	−	0.983417i	$-0.441951\pi$
$223$	5.41650	0.362715	0.181358	+	0.983417i	$0.441951\pi$
$224$	−1.02869	−0.0687322
$225$	0	0
$226$	−3.09494	−0.205872
$227$	−12.2987	−0.816291	−0.408146	−	0.912917i	$-0.633824\pi$
$227$	−12.2987	−0.816291	−0.408146	+	0.912917i	$0.633824\pi$
$228$	0	0
$229$	30.1158	1.99011	0.995053	−	0.0993441i	$-0.0316745\pi$
$229$	30.1158	1.99011	0.995053	+	0.0993441i	$0.0316745\pi$
$230$	−10.2784	−0.677735
$231$	0	0
$232$	−2.42742	−0.159368
$233$	−8.78523	−0.575539	−0.287770	−	0.957700i	$-0.592914\pi$
$233$	−8.78523	−0.575539	−0.287770	+	0.957700i	$0.592914\pi$
$234$	0	0
$235$	−15.8435	−1.03352
$236$	−1.87216	−0.121867
$237$	0	0
$238$	0	0
$239$	−14.6501	−0.947634	−0.473817	−	0.880623i	$-0.657124\pi$
$239$	−14.6501	−0.947634	−0.473817	+	0.880623i	$0.657124\pi$
$240$	0	0
$241$	−16.9552	−1.09218	−0.546091	−	0.837726i	$-0.683885\pi$
$241$	−16.9552	−1.09218	−0.546091	+	0.837726i	$0.683885\pi$
$242$	26.3752	1.69546
$243$	0	0
$244$	11.7074	0.749488
$245$	−11.2545	−0.719023
$246$	0	0
$247$	25.9538	1.65140
$248$	2.78658	0.176948
$249$	0	0
$250$	−22.0505	−1.39459
$251$	13.9453	0.880217	0.440109	−	0.897945i	$-0.354940\pi$
$251$	13.9453	0.880217	0.440109	+	0.897945i	$0.354940\pi$
$252$	0	0
$253$	17.3360	1.08990
$254$	−22.5079	−1.41227
$255$	0	0
$256$	20.9706	1.31066
$257$	−19.6603	−1.22638	−0.613189	−	0.789936i	$-0.710113\pi$
$257$	−19.6603	−1.22638	−0.613189	+	0.789936i	$0.710113\pi$
$258$	0	0
$259$	1.62535	0.100994
$260$	−8.99963	−0.558133
$261$	0	0
$262$	−19.3112	−1.19305
$263$	27.8721	1.71867	0.859334	−	0.511415i	$-0.170879\pi$
$263$	27.8721	1.71867	0.859334	+	0.511415i	$0.170879\pi$
$264$	0	0
$265$	3.42970	0.210685
$266$	−1.85070	−0.113474
$267$	0	0
$268$	10.0547	0.614187
$269$	−0.205327	−0.0125190	−0.00625951	−	0.999980i	$-0.501992\pi$
$269$	−0.205327	−0.0125190	−0.00625951	+	0.999980i	$0.501992\pi$
$270$	0	0
$271$	−8.21077	−0.498768	−0.249384	−	0.968405i	$-0.580228\pi$
$271$	−8.21077	−0.498768	−0.249384	+	0.968405i	$0.580228\pi$
$272$	0	0
$273$	0	0
$274$	−24.9314	−1.50616
$275$	12.0547	0.726924
$276$	0	0
$277$	23.5677	1.41604	0.708022	−	0.706190i	$-0.249588\pi$
$277$	23.5677	1.41604	0.708022	+	0.706190i	$0.249588\pi$
$278$	9.84482	0.590453
$279$	0	0
$280$	−0.265818	−0.0158857
$281$	10.1532	0.605690	0.302845	−	0.953040i	$-0.402064\pi$
$281$	10.1532	0.605690	0.302845	+	0.953040i	$0.402064\pi$
$282$	0	0
$283$	−9.47918	−0.563479	−0.281739	−	0.959491i	$-0.590911\pi$
$283$	−9.47918	−0.563479	−0.281739	+	0.959491i	$0.590911\pi$
$284$	9.25903	0.549422
$285$	0	0
$286$	36.6458	2.16691
$287$	0.0421355	0.00248718
$288$	0	0
$289$	0	0
$290$	6.68457	0.392531
$291$	0	0
$292$	11.7753	0.689096
$293$	−9.28515	−0.542444	−0.271222	−	0.962517i	$-0.587428\pi$
$293$	−9.28515	−0.542444	−0.271222	+	0.962517i	$0.587428\pi$
$294$	0	0
$295$	−2.13548	−0.124332
$296$	−11.5558	−0.671668
$297$	0	0
$298$	−17.2191	−0.997475
$299$	13.6035	0.786712
$300$	0	0
$301$	0.965630	0.0556580
$302$	22.1052	1.27201
$303$	0	0
$304$	31.7662	1.82192
$305$	13.3540	0.764650
$306$	0	0
$307$	−27.1418	−1.54906	−0.774531	−	0.632536i	$-0.782014\pi$
$307$	−27.1418	−1.54906	−0.774531	+	0.632536i	$0.782014\pi$
$308$	−1.08239	−0.0616750
$309$	0	0
$310$	−7.67362	−0.435832
$311$	2.58579	0.146626	0.0733132	−	0.997309i	$-0.476643\pi$
$311$	2.58579	0.146626	0.0733132	+	0.997309i	$0.476643\pi$
$312$	0	0
$313$	25.6105	1.44759	0.723796	−	0.690015i	$-0.242396\pi$
$313$	25.6105	1.44759	0.723796	+	0.690015i	$0.242396\pi$
$314$	−33.5457	−1.89309
$315$	0	0
$316$	0.752823	0.0423496
$317$	−25.5982	−1.43774	−0.718869	−	0.695146i	$-0.755340\pi$
$317$	−25.5982	−1.43774	−0.718869	+	0.695146i	$0.755340\pi$
$318$	0	0
$319$	−11.2745	−0.631252
$320$	−4.56261	−0.255058
$321$	0	0
$322$	−0.970034	−0.0540579
$323$	0	0
$324$	0	0
$325$	9.45929	0.524707
$326$	−38.2902	−2.12070
$327$	0	0
$328$	−0.299572	−0.0165411
$329$	−1.49526	−0.0824361
$330$	0	0
$331$	−0.333172	−0.0183128	−0.00915639	−	0.999958i	$-0.502915\pi$
$331$	−0.333172	−0.0183128	−0.00915639	+	0.999958i	$0.502915\pi$
$332$	−3.11615	−0.171021
$333$	0	0
$334$	14.9462	0.817818
$335$	11.4689	0.626613
$336$	0	0
$337$	−3.75539	−0.204569	−0.102285	−	0.994755i	$-0.532615\pi$
$337$	−3.75539	−0.204569	−0.102285	+	0.994755i	$0.532615\pi$
$338$	4.73508	0.257555
$339$	0	0
$340$	0	0
$341$	12.9427	0.700886
$342$	0	0
$343$	−2.12784	−0.114893
$344$	−6.86537	−0.370156
$345$	0	0
$346$	−2.14455	−0.115292
$347$	−3.30999	−0.177690	−0.0888449	−	0.996045i	$-0.528318\pi$
$347$	−3.30999	−0.177690	−0.0888449	+	0.996045i	$0.528318\pi$
$348$	0	0
$349$	2.58488	0.138366	0.0691828	−	0.997604i	$-0.477961\pi$
$349$	2.58488	0.138366	0.0691828	+	0.997604i	$0.477961\pi$
$350$	−0.674519	−0.0360546
$351$	0	0
$352$	33.9697	1.81059
$353$	−13.2848	−0.707079	−0.353539	−	0.935420i	$-0.615022\pi$
$353$	−13.2848	−0.707079	−0.353539	+	0.935420i	$0.615022\pi$
$354$	0	0
$355$	10.5613	0.560537
$356$	10.8166	0.573277
$357$	0	0
$358$	−5.35237	−0.282882
$359$	14.7281	0.777319	0.388659	−	0.921382i	$-0.372938\pi$
$359$	14.7281	0.777319	0.388659	+	0.921382i	$0.372938\pi$
$360$	0	0
$361$	24.2832	1.27806
$362$	1.55710	0.0818392
$363$	0	0
$364$	−0.849352	−0.0445181
$365$	13.4315	0.703037
$366$	0	0
$367$	0.439960	0.0229657	0.0114829	−	0.999934i	$-0.496345\pi$
$367$	0.439960	0.0229657	0.0114829	+	0.999934i	$0.496345\pi$
$368$	16.6501	0.867945
$369$	0	0
$370$	31.8222	1.65436
$371$	0.323683	0.0168048
$372$	0	0
$373$	−0.827899	−0.0428670	−0.0214335	−	0.999770i	$-0.506823\pi$
$373$	−0.827899	−0.0428670	−0.0214335	+	0.999770i	$0.506823\pi$
$374$	0	0
$375$	0	0
$376$	10.6309	0.548245
$377$	−8.84710	−0.455649
$378$	0	0
$379$	19.8083	1.01749	0.508743	−	0.860918i	$-0.330110\pi$
$379$	19.8083	1.01749	0.508743	+	0.860918i	$0.330110\pi$
$380$	−15.0087	−0.769930
$381$	0	0
$382$	−18.4234	−0.942625
$383$	16.6828	0.852453	0.426227	−	0.904616i	$-0.359843\pi$
$383$	16.6828	0.852453	0.426227	+	0.904616i	$0.359843\pi$
$384$	0	0
$385$	−1.23463	−0.0629227
$386$	−6.89987	−0.351194
$387$	0	0
$388$	5.10013	0.258920
$389$	−17.2980	−0.877042	−0.438521	−	0.898721i	$-0.644498\pi$
$389$	−17.2980	−0.877042	−0.438521	+	0.898721i	$0.644498\pi$
$390$	0	0
$391$	0	0
$392$	7.55166	0.381416
$393$	0	0
$394$	−29.9435	−1.50853
$395$	0.858710	0.0432064
$396$	0	0
$397$	6.44065	0.323247	0.161623	−	0.986852i	$-0.448327\pi$
$397$	6.44065	0.323247	0.161623	+	0.986852i	$0.448327\pi$
$398$	−30.4389	−1.52577
$399$	0	0
$400$	11.5777	0.578886
$401$	−21.0724	−1.05231	−0.526153	−	0.850390i	$-0.676366\pi$
$401$	−21.0724	−1.05231	−0.526153	+	0.850390i	$0.676366\pi$
$402$	0	0
$403$	10.1561	0.505912
$404$	−12.9218	−0.642882
$405$	0	0
$406$	0.630865	0.0313093
$407$	−53.6728	−2.66046
$408$	0	0
$409$	−27.6232	−1.36588	−0.682939	−	0.730475i	$-0.739299\pi$
$409$	−27.6232	−1.36588	−0.682939	+	0.730475i	$0.739299\pi$
$410$	0.824955	0.0407416
$411$	0	0
$412$	10.7178	0.528028
$413$	−0.201539	−0.00991707
$414$	0	0
$415$	−3.55444	−0.174481
$416$	26.6560	1.30692
$417$	0	0
$418$	61.1144	2.98920
$419$	12.0510	0.588728	0.294364	−	0.955693i	$-0.404892\pi$
$419$	12.0510	0.588728	0.294364	+	0.955693i	$0.404892\pi$
$420$	0	0
$421$	14.0183	0.683210	0.341605	−	0.939844i	$-0.389029\pi$
$421$	14.0183	0.683210	0.341605	+	0.939844i	$0.389029\pi$
$422$	−19.7502	−0.961425
$423$	0	0
$424$	−2.30130	−0.111761
$425$	0	0
$426$	0	0
$427$	1.26031	0.0609905
$428$	−26.1158	−1.26235
$429$	0	0
$430$	18.9057	0.911714
$431$	3.44381	0.165882	0.0829411	−	0.996554i	$-0.473569\pi$
$431$	3.44381	0.165882	0.0829411	+	0.996554i	$0.473569\pi$
$432$	0	0
$433$	5.56579	0.267475	0.133738	−	0.991017i	$-0.457302\pi$
$433$	5.56579	0.267475	0.133738	+	0.991017i	$0.457302\pi$
$434$	−0.724208	−0.0347631
$435$	0	0
$436$	15.1876	0.727354
$437$	22.6866	1.08525
$438$	0	0
$439$	17.5864	0.839353	0.419676	−	0.907674i	$-0.362144\pi$
$439$	17.5864	0.839353	0.419676	+	0.907674i	$0.362144\pi$
$440$	8.77791	0.418470
$441$	0	0
$442$	0	0
$443$	−5.87632	−0.279192	−0.139596	−	0.990209i	$-0.544580\pi$
$443$	−5.87632	−0.279192	−0.139596	+	0.990209i	$0.544580\pi$
$444$	0	0
$445$	12.3380	0.584875
$446$	10.0084	0.473911
$447$	0	0
$448$	−0.430602	−0.0203441
$449$	39.9812	1.88683	0.943414	−	0.331617i	$-0.107594\pi$
$449$	39.9812	1.88683	0.943414	+	0.331617i	$0.107594\pi$
$450$	0	0
$451$	−1.39141	−0.0655189
$452$	−2.36876	−0.111417
$453$	0	0
$454$	−22.7250	−1.06654
$455$	−0.968815	−0.0454188
$456$	0	0
$457$	−17.6906	−0.827533	−0.413767	−	0.910383i	$-0.635787\pi$
$457$	−17.6906	−0.827533	−0.413767	+	0.910383i	$0.635787\pi$
$458$	55.6467	2.60020
$459$	0	0
$460$	−7.86672	−0.366788
$461$	−29.8662	−1.39101	−0.695504	−	0.718522i	$-0.744819\pi$
$461$	−29.8662	−1.39101	−0.695504	+	0.718522i	$0.744819\pi$
$462$	0	0
$463$	9.45213	0.439278	0.219639	−	0.975581i	$-0.429512\pi$
$463$	9.45213	0.439278	0.219639	+	0.975581i	$0.429512\pi$
$464$	−10.8284	−0.502697
$465$	0	0
$466$	−16.2330	−0.751978
$467$	20.0094	0.925923	0.462961	−	0.886378i	$-0.346787\pi$
$467$	20.0094	0.925923	0.462961	+	0.886378i	$0.346787\pi$
$468$	0	0
$469$	1.08239	0.0499802
$470$	−29.2750	−1.35036
$471$	0	0
$472$	1.43289	0.0659539
$473$	−31.8873	−1.46618
$474$	0	0
$475$	15.7753	0.723820
$476$	0	0
$477$	0	0
$478$	−27.0698	−1.23814
$479$	1.20570	0.0550899	0.0275449	−	0.999621i	$-0.491231\pi$
$479$	1.20570	0.0550899	0.0275449	+	0.999621i	$0.491231\pi$
$480$	0	0
$481$	−42.1170	−1.92037
$482$	−31.3292	−1.42701
$483$	0	0
$484$	20.1867	0.917577
$485$	5.81748	0.264158
$486$	0	0
$487$	11.9613	0.542017	0.271009	−	0.962577i	$-0.412643\pi$
$487$	11.9613	0.542017	0.271009	+	0.962577i	$0.412643\pi$
$488$	−8.96043	−0.405620
$489$	0	0
$490$	−20.7956	−0.939449
$491$	−31.2632	−1.41089	−0.705444	−	0.708766i	$-0.749252\pi$
$491$	−31.2632	−1.41089	−0.705444	+	0.708766i	$0.749252\pi$
$492$	0	0
$493$	0	0
$494$	47.9564	2.15766
$495$	0	0
$496$	12.4306	0.558151
$497$	0.996740	0.0447099
$498$	0	0
$499$	−41.3590	−1.85148	−0.925741	−	0.378158i	$-0.876558\pi$
$499$	−41.3590	−1.85148	−0.925741	+	0.378158i	$0.876558\pi$
$500$	−16.8767	−0.754749
$501$	0	0
$502$	25.7675	1.15006
$503$	−3.08277	−0.137454	−0.0687269	−	0.997636i	$-0.521894\pi$
$503$	−3.08277	−0.137454	−0.0687269	+	0.997636i	$0.521894\pi$
$504$	0	0
$505$	−14.7392	−0.655888
$506$	32.0327	1.42403
$507$	0	0
$508$	−17.2268	−0.764315
$509$	33.8077	1.49850	0.749249	−	0.662288i	$-0.230415\pi$
$509$	33.8077	1.49850	0.749249	+	0.662288i	$0.230415\pi$
$510$	0	0
$511$	1.26762	0.0560760
$512$	22.1731	0.979922
$513$	0	0
$514$	−36.3275	−1.60234
$515$	12.2253	0.538710
$516$	0	0
$517$	49.3767	2.17159
$518$	3.00326	0.131956
$519$	0	0
$520$	6.88802	0.302059
$521$	40.9557	1.79430	0.897150	−	0.441725i	$-0.145633\pi$
$521$	40.9557	1.79430	0.897150	+	0.441725i	$0.145633\pi$
$522$	0	0
$523$	−9.06788	−0.396511	−0.198255	−	0.980150i	$-0.563528\pi$
$523$	−9.06788	−0.396511	−0.198255	+	0.980150i	$0.563528\pi$
$524$	−14.7802	−0.645674
$525$	0	0
$526$	51.5009	2.24555
$527$	0	0
$528$	0	0
$529$	−11.1089	−0.482997
$530$	6.33726	0.275273
$531$	0	0
$532$	−1.41647	−0.0614116
$533$	−1.09184	−0.0472927
$534$	0	0
$535$	−29.7890	−1.28789
$536$	−7.69552	−0.332396
$537$	0	0
$538$	−0.379395	−0.0163569
$539$	35.0749	1.51078
$540$	0	0
$541$	12.9420	0.556420	0.278210	−	0.960520i	$-0.410259\pi$
$541$	12.9420	0.556420	0.278210	+	0.960520i	$0.410259\pi$
$542$	−15.1715	−0.651672
$543$	0	0
$544$	0	0
$545$	17.3238	0.742068
$546$	0	0
$547$	−10.6598	−0.455781	−0.227891	−	0.973687i	$-0.573183\pi$
$547$	−10.6598	−0.455781	−0.227891	+	0.973687i	$0.573183\pi$
$548$	−19.0816	−0.815127
$549$	0	0
$550$	22.2741	0.949773
$551$	−14.7543	−0.628556
$552$	0	0
$553$	0.0810419	0.00344625
$554$	43.5474	1.85015
$555$	0	0
$556$	7.53490	0.319551
$557$	30.1933	1.27933	0.639667	−	0.768653i	$-0.279072\pi$
$557$	30.1933	1.27933	0.639667	+	0.768653i	$0.279072\pi$
$558$	0	0
$559$	−25.0219	−1.05831
$560$	−1.18578	−0.0501085
$561$	0	0
$562$	18.7607	0.791372
$563$	29.9236	1.26113	0.630566	−	0.776136i	$-0.282823\pi$
$563$	29.9236	1.26113	0.630566	+	0.776136i	$0.282823\pi$
$564$	0	0
$565$	−2.70193	−0.113671
$566$	−17.5152	−0.736221
$567$	0	0
$568$	−7.08655	−0.297345
$569$	−25.6952	−1.07720	−0.538599	−	0.842562i	$-0.681046\pi$
$569$	−25.6952	−1.07720	−0.538599	+	0.842562i	$0.681046\pi$
$570$	0	0
$571$	28.0143	1.17236	0.586181	−	0.810180i	$-0.300631\pi$
$571$	28.0143	1.17236	0.586181	+	0.810180i	$0.300631\pi$
$572$	28.0475	1.17273
$573$	0	0
$574$	0.0778563	0.00324966
$575$	8.26852	0.344821
$576$	0	0
$577$	−11.8072	−0.491538	−0.245769	−	0.969328i	$-0.579041\pi$
$577$	−11.8072	−0.491538	−0.245769	+	0.969328i	$0.579041\pi$
$578$	0	0
$579$	0	0
$580$	5.11615	0.212436
$581$	−0.335455	−0.0139170
$582$	0	0
$583$	−10.6887	−0.442682
$584$	−9.01241	−0.372936
$585$	0	0
$586$	−17.1567	−0.708738
$587$	−7.44230	−0.307177	−0.153588	−	0.988135i	$-0.549083\pi$
$587$	−7.44230	−0.307177	−0.153588	+	0.988135i	$0.549083\pi$
$588$	0	0
$589$	16.9374	0.697893
$590$	−3.94585	−0.162448
$591$	0	0
$592$	−51.5492	−2.11866
$593$	−7.65194	−0.314228	−0.157114	−	0.987580i	$-0.550219\pi$
$593$	−7.65194	−0.314228	−0.157114	+	0.987580i	$0.550219\pi$
$594$	0	0
$595$	0	0
$596$	−13.1789	−0.539830
$597$	0	0
$598$	25.1360	1.02789
$599$	−16.1547	−0.660062	−0.330031	−	0.943970i	$-0.607059\pi$
$599$	−16.1547	−0.660062	−0.330031	+	0.943970i	$0.607059\pi$
$600$	0	0
$601$	28.7176	1.17141	0.585707	−	0.810523i	$-0.300817\pi$
$601$	28.7176	1.17141	0.585707	+	0.810523i	$0.300817\pi$
$602$	1.78425	0.0727206
$603$	0	0
$604$	16.9186	0.688407
$605$	23.0260	0.936140
$606$	0	0
$607$	25.8129	1.04771	0.523856	−	0.851807i	$-0.324493\pi$
$607$	25.8129	1.04771	0.523856	+	0.851807i	$0.324493\pi$
$608$	44.4542	1.80286
$609$	0	0
$610$	24.6750	0.999063
$611$	38.7458	1.56749
$612$	0	0
$613$	49.1769	1.98623	0.993117	−	0.117123i	$-0.0373670\pi$
$613$	49.1769	1.98623	0.993117	+	0.117123i	$0.0373670\pi$
$614$	−50.1514	−2.02395
$615$	0	0
$616$	0.828427	0.0333783
$617$	−3.55073	−0.142947	−0.0714734	−	0.997443i	$-0.522770\pi$
$617$	−3.55073	−0.142947	−0.0714734	+	0.997443i	$0.522770\pi$
$618$	0	0
$619$	−35.2011	−1.41485	−0.707426	−	0.706787i	$-0.750144\pi$
$619$	−35.2011	−1.41485	−0.707426	+	0.706787i	$0.750144\pi$
$620$	−5.87313	−0.235871
$621$	0	0
$622$	4.77791	0.191577
$623$	1.16441	0.0466511
$624$	0	0
$625$	−7.26131	−0.290453
$626$	47.3220	1.89137
$627$	0	0
$628$	−25.6748	−1.02454
$629$	0	0
$630$	0	0
$631$	−31.4131	−1.25054	−0.625268	−	0.780410i	$-0.715010\pi$
$631$	−31.4131	−1.25054	−0.625268	+	0.780410i	$0.715010\pi$
$632$	−0.576186	−0.0229195
$633$	0	0
$634$	−47.2993	−1.87850
$635$	−19.6498	−0.779777
$636$	0	0
$637$	27.5232	1.09051
$638$	−20.8326	−0.824770
$639$	0	0
$640$	13.3691	0.528461
$641$	26.5755	1.04967	0.524834	−	0.851205i	$-0.324127\pi$
$641$	26.5755	1.04967	0.524834	+	0.851205i	$0.324127\pi$
$642$	0	0
$643$	−16.0247	−0.631952	−0.315976	−	0.948767i	$-0.602332\pi$
$643$	−16.0247	−0.631952	−0.315976	+	0.948767i	$0.602332\pi$
$644$	−0.742432	−0.0292559
$645$	0	0
$646$	0	0
$647$	−41.6554	−1.63764	−0.818822	−	0.574048i	$-0.805372\pi$
$647$	−41.6554	−1.63764	−0.818822	+	0.574048i	$0.805372\pi$
$648$	0	0
$649$	6.65526	0.261242
$650$	17.4785	0.685563
$651$	0	0
$652$	−29.3060	−1.14771
$653$	12.3264	0.482370	0.241185	−	0.970479i	$-0.422464\pi$
$653$	12.3264	0.482370	0.241185	+	0.970479i	$0.422464\pi$
$654$	0	0
$655$	−16.8590	−0.658737
$656$	−1.33636	−0.0521760
$657$	0	0
$658$	−2.76287	−0.107708
$659$	−3.46449	−0.134957	−0.0674786	−	0.997721i	$-0.521495\pi$
$659$	−3.46449	−0.134957	−0.0674786	+	0.997721i	$0.521495\pi$
$660$	0	0
$661$	−28.3233	−1.10165	−0.550825	−	0.834621i	$-0.685687\pi$
$661$	−28.3233	−1.10165	−0.550825	+	0.834621i	$0.685687\pi$
$662$	−0.615621	−0.0239268
$663$	0	0
$664$	2.38500	0.0925558
$665$	−1.61570	−0.0626540
$666$	0	0
$667$	−7.73339	−0.299438
$668$	11.4393	0.442600
$669$	0	0
$670$	21.1918	0.818709
$671$	−41.6181	−1.60665
$672$	0	0
$673$	−28.4086	−1.09507	−0.547535	−	0.836783i	$-0.684434\pi$
$673$	−28.4086	−1.09507	−0.547535	+	0.836783i	$0.684434\pi$
$674$	−6.93906	−0.267283
$675$	0	0
$676$	3.62408	0.139388
$677$	−19.2983	−0.741692	−0.370846	−	0.928694i	$-0.620932\pi$
$677$	−19.2983	−0.741692	−0.370846	+	0.928694i	$0.620932\pi$
$678$	0	0
$679$	0.549032	0.0210699
$680$	0	0
$681$	0	0
$682$	23.9150	0.915752
$683$	19.4793	0.745355	0.372678	−	0.927961i	$-0.378440\pi$
$683$	19.4793	0.745355	0.372678	+	0.927961i	$0.378440\pi$
$684$	0	0
$685$	−21.7655	−0.831618
$686$	−3.93174	−0.150115
$687$	0	0
$688$	−30.6256	−1.16759
$689$	−8.38743	−0.319536
$690$	0	0
$691$	−7.53940	−0.286812	−0.143406	−	0.989664i	$-0.545806\pi$
$691$	−7.53940	−0.286812	−0.143406	+	0.989664i	$0.545806\pi$
$692$	−1.64137	−0.0623954
$693$	0	0
$694$	−6.11607	−0.232163
$695$	8.59470	0.326015
$696$	0	0
$697$	0	0
$698$	4.77624	0.180783
$699$	0	0
$700$	−0.516255	−0.0195126
$701$	39.0875	1.47632	0.738158	−	0.674628i	$-0.235696\pi$
$701$	39.0875	1.47632	0.738158	+	0.674628i	$0.235696\pi$
$702$	0	0
$703$	−70.2386	−2.64910
$704$	14.2195	0.535916
$705$	0	0
$706$	−24.5471	−0.923843
$707$	−1.39104	−0.0523153
$708$	0	0
$709$	6.71284	0.252106	0.126053	−	0.992024i	$-0.459769\pi$
$709$	6.71284	0.252106	0.126053	+	0.992024i	$0.459769\pi$
$710$	19.5148	0.732377
$711$	0	0
$712$	−8.27865	−0.310255
$713$	8.87762	0.332470
$714$	0	0
$715$	31.9925	1.19645
$716$	−4.09653	−0.153094
$717$	0	0
$718$	27.2140	1.01562
$719$	−7.40623	−0.276206	−0.138103	−	0.990418i	$-0.544100\pi$
$719$	−7.40623	−0.276206	−0.138103	+	0.990418i	$0.544100\pi$
$720$	0	0
$721$	1.15378	0.0429689
$722$	44.8695	1.66987
$723$	0	0
$724$	1.19175	0.0442910
$725$	−5.37746	−0.199714
$726$	0	0
$727$	−6.36054	−0.235899	−0.117950	−	0.993020i	$-0.537632\pi$
$727$	−6.36054	−0.235899	−0.117950	+	0.993020i	$0.537632\pi$
$728$	0.650066	0.0240930
$729$	0	0
$730$	24.8182	0.918562
$731$	0	0
$732$	0	0
$733$	−41.3337	−1.52670	−0.763348	−	0.645988i	$-0.776446\pi$
$733$	−41.3337	−1.52670	−0.763348	+	0.645988i	$0.776446\pi$
$734$	0.812941	0.0300062
$735$	0	0
$736$	23.3004	0.858864
$737$	−35.7430	−1.31661
$738$	0	0
$739$	23.1653	0.852150	0.426075	−	0.904688i	$-0.359896\pi$
$739$	23.1653	0.852150	0.426075	+	0.904688i	$0.359896\pi$
$740$	24.3556	0.895331
$741$	0	0
$742$	0.598087	0.0219565
$743$	−38.1505	−1.39960	−0.699802	−	0.714337i	$-0.746729\pi$
$743$	−38.1505	−1.39960	−0.699802	+	0.714337i	$0.746729\pi$
$744$	0	0
$745$	−15.0326	−0.550751
$746$	−1.52976	−0.0560084
$747$	0	0
$748$	0	0
$749$	−2.81138	−0.102726
$750$	0	0
$751$	34.2073	1.24824	0.624120	−	0.781328i	$-0.285457\pi$
$751$	34.2073	1.24824	0.624120	+	0.781328i	$0.285457\pi$
$752$	47.4231	1.72934
$753$	0	0
$754$	−16.3473	−0.595334
$755$	19.2982	0.702334
$756$	0	0
$757$	−7.02190	−0.255215	−0.127608	−	0.991825i	$-0.540730\pi$
$757$	−7.02190	−0.255215	−0.127608	+	0.991825i	$0.540730\pi$
$758$	36.6011	1.32941
$759$	0	0
$760$	11.4872	0.416683
$761$	−47.2917	−1.71432	−0.857161	−	0.515048i	$-0.827774\pi$
$761$	−47.2917	−1.71432	−0.857161	+	0.515048i	$0.827774\pi$
$762$	0	0
$763$	1.63495	0.0591893
$764$	−14.1007	−0.510145
$765$	0	0
$766$	30.8259	1.11378
$767$	5.22238	0.188569
$768$	0	0
$769$	6.39156	0.230486	0.115243	−	0.993337i	$-0.463235\pi$
$769$	6.39156	0.230486	0.115243	+	0.993337i	$0.463235\pi$
$770$	−2.28130	−0.0822125
$771$	0	0
$772$	−5.28093	−0.190065
$773$	−3.67729	−0.132263	−0.0661315	−	0.997811i	$-0.521066\pi$
$773$	−3.67729	−0.132263	−0.0661315	+	0.997811i	$0.521066\pi$
$774$	0	0
$775$	6.17311	0.221745
$776$	−3.90347	−0.140126
$777$	0	0
$778$	−31.9625	−1.14591
$779$	−1.82086	−0.0652391
$780$	0	0
$781$	−32.9146	−1.17778
$782$	0	0
$783$	0	0
$784$	33.6871	1.20311
$785$	−29.2860	−1.04526
$786$	0	0
$787$	−4.06409	−0.144869	−0.0724346	−	0.997373i	$-0.523077\pi$
$787$	−4.06409	−0.144869	−0.0724346	+	0.997373i	$0.523077\pi$
$788$	−22.9178	−0.816413
$789$	0	0
$790$	1.58669	0.0564519
$791$	−0.254999	−0.00906670
$792$	0	0
$793$	−32.6577	−1.15971
$794$	11.9008	0.422343
$795$	0	0
$796$	−23.2969	−0.825738
$797$	13.8056	0.489020	0.244510	−	0.969647i	$-0.421373\pi$
$797$	13.8056	0.489020	0.244510	+	0.969647i	$0.421373\pi$
$798$	0	0
$799$	0	0
$800$	16.2021	0.572830
$801$	0	0
$802$	−38.9368	−1.37490
$803$	−41.8596	−1.47719
$804$	0	0
$805$	−0.846857	−0.0298478
$806$	18.7661	0.661006
$807$	0	0
$808$	9.88989	0.347925
$809$	18.8490	0.662695	0.331347	−	0.943509i	$-0.392497\pi$
$809$	18.8490	0.662695	0.331347	+	0.943509i	$0.392497\pi$
$810$	0	0
$811$	2.59955	0.0912825	0.0456413	−	0.998958i	$-0.485467\pi$
$811$	2.59955	0.0912825	0.0456413	+	0.998958i	$0.485467\pi$
$812$	0.482843	0.0169445
$813$	0	0
$814$	−99.1744	−3.47606
$815$	−33.4280	−1.17093
$816$	0	0
$817$	−41.7291	−1.45992
$818$	−51.0410	−1.78461
$819$	0	0
$820$	0.631394	0.0220492
$821$	−13.0073	−0.453960	−0.226980	−	0.973899i	$-0.572885\pi$
$821$	−13.0073	−0.453960	−0.226980	+	0.973899i	$0.572885\pi$
$822$	0	0
$823$	−21.6544	−0.754824	−0.377412	−	0.926046i	$-0.623186\pi$
$823$	−21.6544	−0.754824	−0.377412	+	0.926046i	$0.623186\pi$
$824$	−8.20304	−0.285767
$825$	0	0
$826$	−0.372395	−0.0129573
$827$	47.8742	1.66475	0.832375	−	0.554213i	$-0.186981\pi$
$827$	47.8742	1.66475	0.832375	+	0.554213i	$0.186981\pi$
$828$	0	0
$829$	12.9906	0.451181	0.225590	−	0.974222i	$-0.427569\pi$
$829$	12.9906	0.451181	0.225590	+	0.974222i	$0.427569\pi$
$830$	−6.56775	−0.227970
$831$	0	0
$832$	11.1580	0.386834
$833$	0	0
$834$	0	0
$835$	13.0483	0.451554
$836$	46.7749	1.61774
$837$	0	0
$838$	22.2673	0.769210
$839$	18.8727	0.651557	0.325779	−	0.945446i	$-0.394374\pi$
$839$	18.8727	0.651557	0.325779	+	0.945446i	$0.394374\pi$
$840$	0	0
$841$	−23.9706	−0.826571
$842$	25.9024	0.892657
$843$	0	0
$844$	−15.1161	−0.520319
$845$	4.13381	0.142207
$846$	0	0
$847$	2.17311	0.0746689
$848$	−10.2658	−0.352530
$849$	0	0
$850$	0	0
$851$	−36.8151	−1.26201
$852$	0	0
$853$	−6.03591	−0.206665	−0.103333	−	0.994647i	$-0.532951\pi$
$853$	−6.03591	−0.206665	−0.103333	+	0.994647i	$0.532951\pi$
$854$	2.32874	0.0796879
$855$	0	0
$856$	19.9881	0.683181
$857$	−16.0835	−0.549401	−0.274701	−	0.961530i	$-0.588579\pi$
$857$	−16.0835	−0.549401	−0.274701	+	0.961530i	$0.588579\pi$
$858$	0	0
$859$	−57.8556	−1.97401	−0.987003	−	0.160699i	$-0.948625\pi$
$859$	−57.8556	−1.97401	−0.987003	+	0.160699i	$0.948625\pi$
$860$	14.4698	0.493416
$861$	0	0
$862$	6.36332	0.216736
$863$	7.56067	0.257368	0.128684	−	0.991686i	$-0.458925\pi$
$863$	7.56067	0.257368	0.128684	+	0.991686i	$0.458925\pi$
$864$	0	0
$865$	−1.87223	−0.0636577
$866$	10.2842	0.349473
$867$	0	0
$868$	−0.554285	−0.0188137
$869$	−2.67619	−0.0907834
$870$	0	0
$871$	−28.0475	−0.950354
$872$	−11.6241	−0.393641
$873$	0	0
$874$	41.9194	1.41795
$875$	−1.81679	−0.0614186
$876$	0	0
$877$	−17.3660	−0.586407	−0.293204	−	0.956050i	$-0.594721\pi$
$877$	−17.3660	−0.586407	−0.293204	+	0.956050i	$0.594721\pi$
$878$	32.4954	1.09667
$879$	0	0
$880$	39.1572	1.31999
$881$	−41.1018	−1.38476	−0.692378	−	0.721535i	$-0.743437\pi$
$881$	−41.1018	−1.38476	−0.692378	+	0.721535i	$0.743437\pi$
$882$	0	0
$883$	28.3729	0.954824	0.477412	−	0.878680i	$-0.341575\pi$
$883$	28.3729	0.954824	0.477412	+	0.878680i	$0.341575\pi$
$884$	0	0
$885$	0	0
$886$	−10.8580	−0.364782
$887$	−21.5004	−0.721914	−0.360957	−	0.932583i	$-0.617550\pi$
$887$	−21.5004	−0.721914	−0.360957	+	0.932583i	$0.617550\pi$
$888$	0	0
$889$	−1.85447	−0.0621970
$890$	22.7976	0.764176
$891$	0	0
$892$	7.66008	0.256479
$893$	64.6165	2.16231
$894$	0	0
$895$	−4.67271	−0.156192
$896$	1.26173	0.0421514
$897$	0	0
$898$	73.8756	2.46526
$899$	−5.77359	−0.192560
$900$	0	0
$901$	0	0
$902$	−2.57099	−0.0856046
$903$	0	0
$904$	1.81297	0.0602985
$905$	1.35937	0.0451871
$906$	0	0
$907$	14.8069	0.491654	0.245827	−	0.969314i	$-0.420940\pi$
$907$	14.8069	0.491654	0.245827	+	0.969314i	$0.420940\pi$
$908$	−17.3929	−0.577205
$909$	0	0
$910$	−1.79014	−0.0593425
$911$	47.5209	1.57444	0.787220	−	0.616673i	$-0.211520\pi$
$911$	47.5209	1.57444	0.787220	+	0.616673i	$0.211520\pi$
$912$	0	0
$913$	11.0775	0.366611
$914$	−32.6880	−1.08122
$915$	0	0
$916$	42.5901	1.40722
$917$	−1.59109	−0.0525425
$918$	0	0
$919$	−52.4090	−1.72881	−0.864407	−	0.502793i	$-0.832306\pi$
$919$	−52.4090	−1.72881	−0.864407	+	0.502793i	$0.832306\pi$
$920$	6.02092	0.198504
$921$	0	0
$922$	−55.1856	−1.81744
$923$	−25.8281	−0.850141
$924$	0	0
$925$	−25.5996	−0.841710
$926$	17.4653	0.573944
$927$	0	0
$928$	−15.1535	−0.497438
$929$	−45.8975	−1.50585	−0.752924	−	0.658107i	$-0.771357\pi$
$929$	−45.8975	−1.50585	−0.752924	+	0.658107i	$0.771357\pi$
$930$	0	0
$931$	45.9005	1.50433
$932$	−12.4242	−0.406968
$933$	0	0
$934$	36.9725	1.20978
$935$	0	0
$936$	0	0
$937$	21.7579	0.710799	0.355400	−	0.934714i	$-0.384345\pi$
$937$	21.7579	0.710799	0.355400	+	0.934714i	$0.384345\pi$
$938$	2.00000	0.0653023
$939$	0	0
$940$	−22.4061	−0.730808
$941$	54.1022	1.76368	0.881841	−	0.471548i	$-0.156304\pi$
$941$	54.1022	1.76368	0.881841	+	0.471548i	$0.156304\pi$
$942$	0	0
$943$	−0.954393	−0.0310793
$944$	6.39194	0.208040
$945$	0	0
$946$	−58.9200	−1.91565
$947$	5.77608	0.187697	0.0938486	−	0.995586i	$-0.470083\pi$
$947$	5.77608	0.187697	0.0938486	+	0.995586i	$0.470083\pi$
$948$	0	0
$949$	−32.8471	−1.06626
$950$	29.1489	0.945716
$951$	0	0
$952$	0	0
$953$	31.4698	1.01941	0.509704	−	0.860350i	$-0.329755\pi$
$953$	31.4698	1.01941	0.509704	+	0.860350i	$0.329755\pi$
$954$	0	0
$955$	−16.0840	−0.520466
$956$	−20.7183	−0.670078
$957$	0	0
$958$	2.22784	0.0719784
$959$	−2.05415	−0.0663320
$960$	0	0
$961$	−24.3721	−0.786198
$962$	−77.8221	−2.50908
$963$	0	0
$964$	−23.9783	−0.772290
$965$	−6.02371	−0.193910
$966$	0	0
$967$	−5.82126	−0.187199	−0.0935996	−	0.995610i	$-0.529837\pi$
$967$	−5.82126	−0.187199	−0.0935996	+	0.995610i	$0.529837\pi$
$968$	−15.4502	−0.496589
$969$	0	0
$970$	10.7493	0.345139
$971$	−21.9049	−0.702963	−0.351481	−	0.936195i	$-0.614322\pi$
$971$	−21.9049	−0.702963	−0.351481	+	0.936195i	$0.614322\pi$
$972$	0	0
$973$	0.811136	0.0260038
$974$	22.1016	0.708180
$975$	0	0
$976$	−39.9715	−1.27946
$977$	28.0473	0.897312	0.448656	−	0.893705i	$-0.351903\pi$
$977$	28.0473	0.897312	0.448656	+	0.893705i	$0.351903\pi$
$978$	0	0
$979$	−38.4515	−1.22891
$980$	−15.9163	−0.508426
$981$	0	0
$982$	−57.7668	−1.84341
$983$	31.3271	0.999179	0.499590	−	0.866262i	$-0.333484\pi$
$983$	31.3271	0.999179	0.499590	+	0.866262i	$0.333484\pi$
$984$	0	0
$985$	−26.1412	−0.832929
$986$	0	0
$987$	0	0
$988$	36.7042	1.16772
$989$	−21.8720	−0.695491
$990$	0	0
$991$	17.9993	0.571765	0.285883	−	0.958265i	$-0.407713\pi$
$991$	17.9993	0.571765	0.285883	+	0.958265i	$0.407713\pi$
$992$	17.3956	0.552311
$993$	0	0
$994$	1.84174	0.0584163
$995$	−26.5737	−0.842443
$996$	0	0
$997$	55.5666	1.75981	0.879907	−	0.475147i	$-0.157605\pi$
$997$	55.5666	1.75981	0.879907	+	0.475147i	$0.157605\pi$
$998$	−76.4214	−2.41908
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2601.2.a.bc.1.4		4
3.2	odd	2		867.2.a.m.1.1		4
17.11	odd	16		153.2.l.e.19.2		8
17.14	odd	16		153.2.l.e.145.2		8
17.16	even	2		2601.2.a.bd.1.4		4
51.2	odd	8		867.2.e.h.616.1		8
51.5	even	16		867.2.h.f.688.2		8
51.8	odd	8		867.2.e.i.829.4		8
51.11	even	16		51.2.h.a.19.1	✓	8
51.14	even	16		51.2.h.a.43.1	yes	8
51.20	even	16		867.2.h.g.757.1		8
51.23	even	16		867.2.h.g.733.1		8
51.26	odd	8		867.2.e.h.829.4		8
51.29	even	16		867.2.h.b.688.2		8
51.32	odd	8		867.2.e.i.616.1		8
51.38	odd	4		867.2.d.e.577.8		8
51.41	even	16		867.2.h.f.712.2		8
51.44	even	16		867.2.h.b.712.2		8
51.47	odd	4		867.2.d.e.577.7		8
51.50	odd	2		867.2.a.n.1.1		4
204.11	odd	16		816.2.bq.a.529.1		8
204.167	odd	16		816.2.bq.a.145.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.h.a.19.1	✓	8	51.11	even	16
51.2.h.a.43.1	yes	8	51.14	even	16
153.2.l.e.19.2		8	17.11	odd	16
153.2.l.e.145.2		8	17.14	odd	16
816.2.bq.a.145.1		8	204.167	odd	16
816.2.bq.a.529.1		8	204.11	odd	16
867.2.a.m.1.1		4	3.2	odd	2
867.2.a.n.1.1		4	51.50	odd	2
867.2.d.e.577.7		8	51.47	odd	4
867.2.d.e.577.8		8	51.38	odd	4
867.2.e.h.616.1		8	51.2	odd	8
867.2.e.h.829.4		8	51.26	odd	8
867.2.e.i.616.1		8	51.32	odd	8
867.2.e.i.829.4		8	51.8	odd	8
867.2.h.b.688.2		8	51.29	even	16
867.2.h.b.712.2		8	51.44	even	16
867.2.h.f.688.2		8	51.5	even	16
867.2.h.f.712.2		8	51.41	even	16
867.2.h.g.733.1		8	51.23	even	16
867.2.h.g.757.1		8	51.20	even	16
2601.2.a.bc.1.4		4	1.1	even	1	trivial
2601.2.a.bd.1.4		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)

\(f(q)\)	\(=\)	\(q+1.84776 q^{2} +1.41421 q^{4} +1.61313 q^{5} +0.152241 q^{7} -1.08239 q^{8} +O(q^{10})\)	\(q+1.84776 q^{2} +1.41421 q^{4} +1.61313 q^{5} +0.152241 q^{7} -1.08239 q^{8} +2.98067 q^{10} -5.02734 q^{11} -3.94495 q^{13} +0.281305 q^{14} -4.82843 q^{16} -6.57900 q^{19} +2.28130 q^{20} -9.28931 q^{22} -3.44834 q^{23} -2.39782 q^{25} -7.28931 q^{26} +0.215301 q^{28} +2.24264 q^{29} -2.57446 q^{31} -6.75699 q^{32} +0.245584 q^{35} +10.6762 q^{37} -12.1564 q^{38} -1.74603 q^{40} +0.276769 q^{41} +6.34277 q^{43} -7.10973 q^{44} -6.37170 q^{46} -9.82164 q^{47} -6.97682 q^{49} -4.43060 q^{50} -5.57900 q^{52} +2.12612 q^{53} -8.10973 q^{55} -0.164784 q^{56} +4.14386 q^{58} -1.32381 q^{59} +8.27836 q^{61} -4.75699 q^{62} -2.82843 q^{64} -6.36370 q^{65} +7.10973 q^{67} +0.453780 q^{70} +6.54712 q^{71} +8.32638 q^{73} +19.7270 q^{74} -9.30411 q^{76} -0.765367 q^{77} +0.532327 q^{79} -7.78886 q^{80} +0.511402 q^{82} -2.20345 q^{83} +11.7199 q^{86} +5.44155 q^{88} +7.64847 q^{89} -0.600582 q^{91} -4.87669 q^{92} -18.1480 q^{94} -10.6128 q^{95} +3.60634 q^{97} -12.8915 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{5} + 8 q^{7}+O(q^{10}) \) 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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