LMFDB - Embedded newform 2601.2.a.be.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2601,2,Mod(1,2601)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [4,2,0,6,-6,0,4,6,0,-12,-6,0,2,-4,0,6,0,0,10,-16,0,4,6,0,2,20, 0,24,-16,0,4,14,0,0,-4,0,12,12,0,-8,14,0,14,16,0,-12,-4,0,0,30,0,-8,20, 0,2,16,0,8,24,0,12,-16,0,-2,-14,0,4,0,0,-4,-4,0,20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(73)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$20.7690895657$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.7232.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 5x^{2} + 4x + 4 $ x^4 - 2x^3 - 5x^2 + 4*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
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			$3.06644$ 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)

$f(q)$	$=$	$q+1.65222 q^{2} +0.729840 q^{4} -4.06644 q^{5} -0.922382 q^{7} -2.09859 q^{8} -6.71866 q^{10} -2.27016 q^{11} +3.57461 q^{13} -1.52398 q^{14} -4.92701 q^{16} +1.72984 q^{19} -2.96785 q^{20} -3.75081 q^{22} +5.09859 q^{23} +11.5359 q^{25} +5.90604 q^{26} -0.673192 q^{28} -2.20372 q^{29} -4.13287 q^{31} -3.94335 q^{32} +3.75081 q^{35} +5.95453 q^{37} +2.85808 q^{38} +8.53377 q^{40} +5.05010 q^{41} -5.23146 q^{43} -1.65685 q^{44} +8.42400 q^{46} +6.96130 q^{47} -6.14921 q^{49} +19.0599 q^{50} +2.60889 q^{52} +2.69555 q^{53} +9.23146 q^{55} +1.93570 q^{56} -3.64104 q^{58} +7.39840 q^{59} +3.89023 q^{61} -6.82843 q^{62} +3.33873 q^{64} -14.5359 q^{65} +12.0419 q^{67} +6.19717 q^{70} -1.52398 q^{71} -1.16502 q^{73} +9.83822 q^{74} +1.26251 q^{76} +2.09396 q^{77} +11.8837 q^{79} +20.0354 q^{80} +8.34389 q^{82} +6.38508 q^{83} -8.64354 q^{86} +4.76413 q^{88} -10.3597 q^{89} -3.29715 q^{91} +3.72115 q^{92} +11.5016 q^{94} -7.03429 q^{95} +14.4695 q^{97} -10.1599 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 6 q^{4} - 6 q^{5} + 4 q^{7} + 6 q^{8} - 12 q^{10} - 6 q^{11} + 2 q^{13} - 4 q^{14} + 6 q^{16} + 10 q^{19} - 16 q^{20} + 4 q^{22} + 6 q^{23} + 2 q^{25} + 20 q^{26} + 24 q^{28} - 16 q^{29}+ \cdots - 38 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 + 6 * q^4 - 6 * q^5 + 4 * q^7 + 6 * q^8 - 12 * q^10 - 6 * q^11 + 2 * q^13 - 4 * q^14 + 6 * q^16 + 10 * q^19 - 16 * q^20 + 4 * q^22 + 6 * q^23 + 2 * q^25 + 20 * q^26 + 24 * q^28 - 16 * q^29 + 4 * q^31 + 14 * q^32 - 4 * q^35 + 12 * q^37 + 12 * q^38 - 8 * q^40 + 14 * q^41 + 14 * q^43 + 16 * q^44 - 12 * q^46 - 4 * q^47 + 30 * q^50 - 8 * q^52 + 20 * q^53 + 2 * q^55 + 16 * q^56 + 8 * q^58 + 24 * q^59 + 12 * q^61 - 16 * q^62 - 2 * q^64 - 14 * q^65 + 4 * q^67 - 4 * q^70 - 4 * q^71 + 20 * q^73 - 12 * q^74 + 40 * q^76 + 12 * q^77 + 8 * q^79 - 4 * q^82 + 4 * q^83 + 4 * q^86 + 16 * q^88 - 4 * q^89 - 28 * q^91 - 16 * q^92 + 8 * q^94 - 22 * q^95 + 24 * q^97 - 38 * q^98

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 $

$2$	1.65222	1.16830	0.584149	−	0.811646i	$-0.301428\pi$
$2$	1.65222	1.16830	0.584149	+	0.811646i	$0.301428\pi$
$3$	0	0
$3$	0	0
$4$	0.729840	0.364920
$5$	−4.06644	−1.81857	−0.909283	−	0.416179i	$-0.863369\pi$
$5$	−4.06644	−1.81857	−0.909283	+	0.416179i	$0.863369\pi$
$6$	0	0
$7$	−0.922382	−0.348628	−0.174314	−	0.984690i	$-0.555771\pi$
$7$	−0.922382	−0.348628	−0.174314	+	0.984690i	$0.555771\pi$
$8$	−2.09859	−0.741962
$9$	0	0
$10$	−6.71866	−2.12463
$11$	−2.27016	−0.684479	−0.342239	−	0.939613i	$-0.611185\pi$
$11$	−2.27016	−0.684479	−0.342239	+	0.939613i	$0.611185\pi$
$12$	0	0
$13$	3.57461	0.991417	0.495709	−	0.868489i	$-0.334908\pi$
$13$	3.57461	0.991417	0.495709	+	0.868489i	$0.334908\pi$
$14$	−1.52398	−0.407301
$15$	0	0
$16$	−4.92701	−1.23175
$17$	0	0
$17$	0	0
$18$	0	0
$19$	1.72984	0.396853	0.198426	−	0.980116i	$-0.436417\pi$
$19$	1.72984	0.396853	0.198426	+	0.980116i	$0.436417\pi$
$20$	−2.96785	−0.663631
$21$	0	0
$22$	−3.75081	−0.799675
$23$	5.09859	1.06313	0.531564	−	0.847018i	$-0.321604\pi$
$23$	5.09859	1.06313	0.531564	+	0.847018i	$0.321604\pi$
$24$	0	0
$25$	11.5359	2.30718
$26$	5.90604	1.15827
$27$	0	0
$28$	−0.673192	−0.127221
$29$	−2.20372	−0.409221	−0.204611	−	0.978843i	$-0.565593\pi$
$29$	−2.20372	−0.409221	−0.204611	+	0.978843i	$0.565593\pi$
$30$	0	0
$31$	−4.13287	−0.742286	−0.371143	−	0.928576i	$-0.621034\pi$
$31$	−4.13287	−0.742286	−0.371143	+	0.928576i	$0.621034\pi$
$32$	−3.94335	−0.697093
$33$	0	0
$34$	0	0
$35$	3.75081	0.634003
$36$	0	0
$37$	5.95453	0.978919	0.489460	−	0.872026i	$-0.337194\pi$
$37$	5.95453	0.978919	0.489460	+	0.872026i	$0.337194\pi$
$38$	2.85808	0.463642
$39$	0	0
$40$	8.53377	1.34931
$41$	5.05010	0.788693	0.394346	−	0.918962i	$-0.370971\pi$
$41$	5.05010	0.788693	0.394346	+	0.918962i	$0.370971\pi$
$42$	0	0
$43$	−5.23146	−0.797790	−0.398895	−	0.916997i	$-0.630606\pi$
$43$	−5.23146	−0.797790	−0.398895	+	0.916997i	$0.630606\pi$
$44$	−1.65685	−0.249780
$45$	0	0
$46$	8.42400	1.24205
$47$	6.96130	1.01541	0.507705	−	0.861531i	$-0.330494\pi$
$47$	6.96130	1.01541	0.507705	+	0.861531i	$0.330494\pi$
$48$	0	0
$49$	−6.14921	−0.878459
$50$	19.0599	2.69548
$51$	0	0
$52$	2.60889	0.361788
$53$	2.69555	0.370263	0.185131	−	0.982714i	$-0.440729\pi$
$53$	2.69555	0.370263	0.185131	+	0.982714i	$0.440729\pi$
$54$	0	0
$55$	9.23146	1.24477
$56$	1.93570	0.258669
$57$	0	0
$58$	−3.64104	−0.478092
$59$	7.39840	0.963190	0.481595	−	0.876394i	$-0.340058\pi$
$59$	7.39840	0.963190	0.481595	+	0.876394i	$0.340058\pi$
$60$	0	0
$61$	3.89023	0.498093	0.249047	−	0.968492i	$-0.419883\pi$
$61$	3.89023	0.498093	0.249047	+	0.968492i	$0.419883\pi$
$62$	−6.82843	−0.867211
$63$	0	0
$64$	3.33873	0.417341
$65$	−14.5359	−1.80296
$66$	0	0
$67$	12.0419	1.47116	0.735578	−	0.677440i	$-0.236910\pi$
$67$	12.0419	1.47116	0.735578	+	0.677440i	$0.236910\pi$
$68$	0	0
$69$	0	0
$70$	6.19717	0.740704
$71$	−1.52398	−0.180863	−0.0904317	−	0.995903i	$-0.528825\pi$
$71$	−1.52398	−0.180863	−0.0904317	+	0.995903i	$0.528825\pi$
$72$	0	0
$73$	−1.16502	−0.136356	−0.0681778	−	0.997673i	$-0.521719\pi$
$73$	−1.16502	−0.136356	−0.0681778	+	0.997673i	$0.521719\pi$
$74$	9.83822	1.14367
$75$	0	0
$76$	1.26251	0.144820
$77$	2.09396	0.238628
$78$	0	0
$79$	11.8837	1.33702	0.668509	−	0.743704i	$-0.266933\pi$
$79$	11.8837	1.33702	0.668509	+	0.743704i	$0.266933\pi$
$80$	20.0354	2.24002
$81$	0	0
$82$	8.34389	0.921428
$83$	6.38508	0.700854	0.350427	−	0.936590i	$-0.386036\pi$
$83$	6.38508	0.700854	0.350427	+	0.936590i	$0.386036\pi$
$84$	0	0
$85$	0	0
$86$	−8.64354	−0.932057
$87$	0	0
$88$	4.76413	0.507858
$89$	−10.3597	−1.09813	−0.549063	−	0.835781i	$-0.685015\pi$
$89$	−10.3597	−1.09813	−0.549063	+	0.835781i	$0.685015\pi$
$90$	0	0
$91$	−3.29715	−0.345636
$92$	3.72115	0.387957
$93$	0	0
$94$	11.5016	1.18630
$95$	−7.03429	−0.721703
$96$	0	0
$97$	14.4695	1.46915	0.734576	−	0.678526i	$-0.237381\pi$
$97$	14.4695	1.46915	0.734576	+	0.678526i	$0.237381\pi$
$98$	−10.1599	−1.02630
$99$	0	0
$100$	8.41937	0.841937
$101$	−0.265746	−0.0264427	−0.0132213	−	0.999913i	$-0.504209\pi$
$101$	−0.265746	−0.0264427	−0.0132213	+	0.999913i	$0.504209\pi$
$102$	0	0
$103$	−3.03429	−0.298977	−0.149489	−	0.988763i	$-0.547763\pi$
$103$	−3.03429	−0.298977	−0.149489	+	0.988763i	$0.547763\pi$
$104$	−7.50162	−0.735594
$105$	0	0
$106$	4.45366	0.432577
$107$	−19.6524	−1.89987	−0.949937	−	0.312443i	$-0.898853\pi$
$107$	−19.6524	−1.89987	−0.949937	+	0.312443i	$0.898853\pi$
$108$	0	0
$109$	0.715639	0.0685457	0.0342729	−	0.999413i	$-0.489088\pi$
$109$	0.715639	0.0685457	0.0342729	+	0.999413i	$0.489088\pi$
$110$	15.2524	1.45426
$111$	0	0
$112$	4.54459	0.429423
$113$	11.7876	1.10888	0.554442	−	0.832223i	$-0.312932\pi$
$113$	11.7876	1.10888	0.554442	+	0.832223i	$0.312932\pi$
$114$	0	0
$115$	−20.7331	−1.93337
$116$	−1.60837	−0.149333
$117$	0	0
$118$	12.2238	1.12529
$119$	0	0
$120$	0	0
$121$	−5.84638	−0.531489
$122$	6.42753	0.581921
$123$	0	0
$124$	−3.01634	−0.270875
$125$	−26.5778	−2.37719
$126$	0	0
$127$	2.81048	0.249390	0.124695	−	0.992195i	$-0.460205\pi$
$127$	2.81048	0.249390	0.124695	+	0.992195i	$0.460205\pi$
$128$	13.4030	1.18467
$129$	0	0
$130$	−24.0166	−2.10639
$131$	7.92701	0.692586	0.346293	−	0.938126i	$-0.387440\pi$
$131$	7.92701	0.692586	0.346293	+	0.938126i	$0.387440\pi$
$132$	0	0
$133$	−1.59557	−0.138354
$134$	19.8960	1.71875
$135$	0	0
$136$	0	0
$137$	0.103218	0.00881851	0.00440926	−	0.999990i	$-0.498596\pi$
$137$	0.103218	0.00881851	0.00440926	+	0.999990i	$0.498596\pi$
$138$	0	0
$139$	−14.4464	−1.22532	−0.612662	−	0.790345i	$-0.709901\pi$
$139$	−14.4464	−1.22532	−0.612662	+	0.790345i	$0.709901\pi$
$140$	2.73749	0.231360
$141$	0	0
$142$	−2.51796	−0.211302
$143$	−8.11492	−0.678604
$144$	0	0
$145$	8.96130	0.744195
$146$	−1.92488	−0.159304
$147$	0	0
$148$	4.34586	0.357227
$149$	−3.59557	−0.294561	−0.147280	−	0.989095i	$-0.547052\pi$
$149$	−3.59557	−0.294561	−0.147280	+	0.989095i	$0.547052\pi$
$150$	0	0
$151$	7.58828	0.617526	0.308763	−	0.951139i	$-0.400085\pi$
$151$	7.58828	0.617526	0.308763	+	0.951139i	$0.400085\pi$
$152$	−3.63022	−0.294450
$153$	0	0
$154$	3.45968	0.278789
$155$	16.8061	1.34990
$156$	0	0
$157$	−18.9569	−1.51292	−0.756462	−	0.654038i	$-0.773074\pi$
$157$	−18.9569	−1.51292	−0.756462	+	0.654038i	$0.773074\pi$
$158$	19.6345	1.56204
$159$	0	0
$160$	16.0354	1.26771
$161$	−4.70285	−0.370636
$162$	0	0
$163$	13.4330	1.05216	0.526079	−	0.850436i	$-0.323662\pi$
$163$	13.4330	1.05216	0.526079	+	0.850436i	$0.323662\pi$
$164$	3.68577	0.287810
$165$	0	0
$166$	10.5496	0.818806
$167$	2.13729	0.165388	0.0826941	−	0.996575i	$-0.473648\pi$
$167$	2.13729	0.165388	0.0826941	+	0.996575i	$0.473648\pi$
$168$	0	0
$169$	−0.222197	−0.0170921
$170$	0	0
$171$	0	0
$172$	−3.81813	−0.291130
$173$	5.27995	0.401427	0.200713	−	0.979650i	$-0.435674\pi$
$173$	5.27995	0.401427	0.200713	+	0.979650i	$0.435674\pi$
$174$	0	0
$175$	−10.6405	−0.804347
$176$	11.1851	0.843109
$177$	0	0
$178$	−17.1165	−1.28294
$179$	7.77619	0.581220	0.290610	−	0.956842i	$-0.406142\pi$
$179$	7.77619	0.581220	0.290610	+	0.956842i	$0.406142\pi$
$180$	0	0
$181$	0.915833	0.0680733	0.0340367	−	0.999421i	$-0.489164\pi$
$181$	0.915833	0.0680733	0.0340367	+	0.999421i	$0.489164\pi$
$182$	−5.44763	−0.403805
$183$	0	0
$184$	−10.6998	−0.788802
$185$	−24.2137	−1.78023
$186$	0	0
$187$	0	0
$188$	5.08064	0.370544
$189$	0	0
$190$	−11.6222	−0.843164
$191$	19.1658	1.38679	0.693393	−	0.720560i	$-0.256115\pi$
$191$	19.1658	1.38679	0.693393	+	0.720560i	$0.256115\pi$
$192$	0	0
$193$	4.71137	0.339132	0.169566	−	0.985519i	$-0.445763\pi$
$193$	4.71137	0.339132	0.169566	+	0.985519i	$0.445763\pi$
$194$	23.9068	1.71641
$195$	0	0
$196$	−4.48794	−0.320567
$197$	−14.8949	−1.06122	−0.530608	−	0.847618i	$-0.678036\pi$
$197$	−14.8949	−1.06122	−0.530608	+	0.847618i	$0.678036\pi$
$198$	0	0
$199$	−18.7837	−1.33154	−0.665771	−	0.746156i	$-0.731897\pi$
$199$	−18.7837	−1.33154	−0.665771	+	0.746156i	$0.731897\pi$
$200$	−24.2091	−1.71184
$201$	0	0
$202$	−0.439071	−0.0308929
$203$	2.03268	0.142666
$204$	0	0
$205$	−20.5359	−1.43429
$206$	−5.01332	−0.349294
$207$	0	0
$208$	−17.6121	−1.22118
$209$	−3.92701	−0.271637
$210$	0	0
$211$	−5.88066	−0.404841	−0.202421	−	0.979299i	$-0.564881\pi$
$211$	−5.88066	−0.404841	−0.202421	+	0.979299i	$0.564881\pi$
$212$	1.96732	0.135116
$213$	0	0
$214$	−32.4702	−2.21962
$215$	21.2734	1.45083
$216$	0	0
$217$	3.81209	0.258781
$218$	1.18239	0.0800819
$219$	0	0
$220$	6.73749	0.454242
$221$	0	0
$222$	0	0
$223$	−5.58387	−0.373923	−0.186962	−	0.982367i	$-0.559864\pi$
$223$	−5.58387	−0.373923	−0.186962	+	0.982367i	$0.559864\pi$
$224$	3.63728	0.243026
$225$	0	0
$226$	19.4757	1.29551
$227$	27.5299	1.82722	0.913611	−	0.406589i	$-0.133282\pi$
$227$	27.5299	1.82722	0.913611	+	0.406589i	$0.133282\pi$
$228$	0	0
$229$	−3.57019	−0.235925	−0.117962	−	0.993018i	$-0.537636\pi$
$229$	−3.57019	−0.235925	−0.117962	+	0.993018i	$0.537636\pi$
$230$	−34.2557	−2.25875
$231$	0	0
$232$	4.62470	0.303627
$233$	1.37088	0.0898095	0.0449047	−	0.998991i	$-0.485702\pi$
$233$	1.37088	0.0898095	0.0449047	+	0.998991i	$0.485702\pi$
$234$	0	0
$235$	−28.3077	−1.84659
$236$	5.39965	0.351487
$237$	0	0
$238$	0	0
$239$	−21.6121	−1.39797	−0.698986	−	0.715135i	$-0.746365\pi$
$239$	−21.6121	−1.39797	−0.698986	+	0.715135i	$0.746365\pi$
$240$	0	0
$241$	1.06181	0.0683969	0.0341984	−	0.999415i	$-0.489112\pi$
$241$	1.06181	0.0683969	0.0341984	+	0.999415i	$0.489112\pi$
$242$	−9.65952	−0.620937
$243$	0	0
$244$	2.83925	0.181764
$245$	25.0054	1.59753
$246$	0	0
$247$	6.18350	0.393446
$248$	8.67319	0.550748
$249$	0	0
$250$	−43.9125	−2.77727
$251$	7.29715	0.460592	0.230296	−	0.973121i	$-0.426031\pi$
$251$	7.29715	0.460592	0.230296	+	0.973121i	$0.426031\pi$
$252$	0	0
$253$	−11.5746	−0.727689
$254$	4.64354	0.291361
$255$	0	0
$256$	15.4673	0.966708
$257$	22.5569	1.40706	0.703530	−	0.710666i	$-0.251606\pi$
$257$	22.5569	1.40706	0.703530	+	0.710666i	$0.251606\pi$
$258$	0	0
$259$	−5.49236	−0.341278
$260$	−10.6089	−0.657936
$261$	0	0
$262$	13.0972	0.809147
$263$	4.24919	0.262016	0.131008	−	0.991381i	$-0.458179\pi$
$263$	4.24919	0.262016	0.131008	+	0.991381i	$0.458179\pi$
$264$	0	0
$265$	−10.9613	−0.673347
$266$	−2.63624	−0.161639
$267$	0	0
$268$	8.78869	0.536855
$269$	11.8338	0.721520	0.360760	−	0.932659i	$-0.382517\pi$
$269$	11.8338	0.721520	0.360760	+	0.932659i	$0.382517\pi$
$270$	0	0
$271$	−11.8045	−0.717070	−0.358535	−	0.933516i	$-0.616724\pi$
$271$	−11.8045	−0.717070	−0.358535	+	0.933516i	$0.616724\pi$
$272$	0	0
$273$	0	0
$274$	0.170539	0.0103027
$275$	−26.1883	−1.57922
$276$	0	0
$277$	10.4275	0.626530	0.313265	−	0.949666i	$-0.398577\pi$
$277$	10.4275	0.626530	0.313265	+	0.949666i	$0.398577\pi$
$278$	−23.8686	−1.43154
$279$	0	0
$280$	−7.87140	−0.470406
$281$	5.46697	0.326132	0.163066	−	0.986615i	$-0.447862\pi$
$281$	5.46697	0.326132	0.163066	+	0.986615i	$0.447862\pi$
$282$	0	0
$283$	17.6375	1.04844	0.524221	−	0.851582i	$-0.324357\pi$
$283$	17.6375	1.04844	0.524221	+	0.851582i	$0.324357\pi$
$284$	−1.11226	−0.0660007
$285$	0	0
$286$	−13.4077	−0.792812
$287$	−4.65812	−0.274960
$288$	0	0
$289$	0	0
$290$	14.8061	0.869442
$291$	0	0
$292$	−0.850281	−0.0497589
$293$	8.25845	0.482464	0.241232	−	0.970467i	$-0.422449\pi$
$293$	8.25845	0.482464	0.241232	+	0.970467i	$0.422449\pi$
$294$	0	0
$295$	−30.0851	−1.75162
$296$	−12.4961	−0.726321
$297$	0	0
$298$	−5.94069	−0.344135
$299$	18.2254	1.05400
$300$	0	0
$301$	4.82541	0.278132
$302$	12.5375	0.721454
$303$	0	0
$304$	−8.52295	−0.488825
$305$	−15.8194	−0.905815
$306$	0	0
$307$	−9.94601	−0.567649	−0.283824	−	0.958876i	$-0.591603\pi$
$307$	−9.94601	−0.567649	−0.283824	+	0.958876i	$0.591603\pi$
$308$	1.52825	0.0870803
$309$	0	0
$310$	27.7674	1.57708
$311$	16.5865	0.940536	0.470268	−	0.882524i	$-0.344157\pi$
$311$	16.5865	0.940536	0.470268	+	0.882524i	$0.344157\pi$
$312$	0	0
$313$	20.6116	1.16504	0.582518	−	0.812818i	$-0.302067\pi$
$313$	20.6116	1.16504	0.582518	+	0.812818i	$0.302067\pi$
$314$	−31.3210	−1.76755
$315$	0	0
$316$	8.67319	0.487905
$317$	−4.26802	−0.239716	−0.119858	−	0.992791i	$-0.538244\pi$
$317$	−4.26802	−0.239716	−0.119858	+	0.992791i	$0.538244\pi$
$318$	0	0
$319$	5.00280	0.280103
$320$	−13.5767	−0.758963
$321$	0	0
$322$	−7.77015	−0.433014
$323$	0	0
$324$	0	0
$325$	41.2363	2.28738
$326$	22.1944	1.22923
$327$	0	0
$328$	−10.5981	−0.585181
$329$	−6.42098	−0.354000
$330$	0	0
$331$	−28.6105	−1.57258	−0.786288	−	0.617860i	$-0.788000\pi$
$331$	−28.6105	−1.57258	−0.786288	+	0.617860i	$0.788000\pi$
$332$	4.66009	0.255756
$333$	0	0
$334$	3.53127	0.193223
$335$	−48.9678	−2.67540
$336$	0	0
$337$	31.3368	1.70703	0.853513	−	0.521072i	$-0.174468\pi$
$337$	31.3368	1.70703	0.853513	+	0.521072i	$0.174468\pi$
$338$	−0.367119	−0.0199686
$339$	0	0
$340$	0	0
$341$	9.38228	0.508079
$342$	0	0
$343$	12.1286	0.654883
$344$	10.9787	0.591930
$345$	0	0
$346$	8.72365	0.468986
$347$	−12.0359	−0.646121	−0.323060	−	0.946378i	$-0.604712\pi$
$347$	−12.0359	−0.646121	−0.323060	+	0.946378i	$0.604712\pi$
$348$	0	0
$349$	33.3512	1.78525	0.892625	−	0.450799i	$-0.148861\pi$
$349$	33.3512	1.78525	0.892625	+	0.450799i	$0.148861\pi$
$350$	−17.5805	−0.939718
$351$	0	0
$352$	8.95204	0.477145
$353$	6.56570	0.349457	0.174729	−	0.984617i	$-0.444095\pi$
$353$	6.56570	0.349457	0.174729	+	0.984617i	$0.444095\pi$
$354$	0	0
$355$	6.19717	0.328912
$356$	−7.56093	−0.400728
$357$	0	0
$358$	12.8480	0.679038
$359$	−21.5508	−1.13741	−0.568705	−	0.822541i	$-0.692555\pi$
$359$	−21.5508	−1.13741	−0.568705	+	0.822541i	$0.692555\pi$
$360$	0	0
$361$	−16.0077	−0.842508
$362$	1.51316	0.0795299
$363$	0	0
$364$	−2.40640	−0.126129
$365$	4.73749	0.247972
$366$	0	0
$367$	35.5644	1.85645	0.928223	−	0.372025i	$-0.121336\pi$
$367$	35.5644	1.85645	0.928223	+	0.372025i	$0.121336\pi$
$368$	−25.1208	−1.30951
$369$	0	0
$370$	−40.0065	−2.07984
$371$	−2.48633	−0.129084
$372$	0	0
$373$	−35.8452	−1.85599	−0.927997	−	0.372588i	$-0.878471\pi$
$373$	−35.8452	−1.85599	−0.927997	+	0.372588i	$0.878471\pi$
$374$	0	0
$375$	0	0
$376$	−14.6089	−0.753396
$377$	−7.87744	−0.405709
$378$	0	0
$379$	−21.9206	−1.12599	−0.562994	−	0.826461i	$-0.690350\pi$
$379$	−21.9206	−1.12599	−0.562994	+	0.826461i	$0.690350\pi$
$380$	−5.13391	−0.263364
$381$	0	0
$382$	31.6661	1.62018
$383$	34.3109	1.75321	0.876603	−	0.481215i	$-0.159804\pi$
$383$	34.3109	1.75321	0.876603	+	0.481215i	$0.159804\pi$
$384$	0	0
$385$	−8.51494	−0.433961
$386$	7.78423	0.396207
$387$	0	0
$388$	10.5604	0.536123
$389$	34.1956	1.73379	0.866894	−	0.498493i	$-0.166113\pi$
$389$	34.1956	1.73379	0.866894	+	0.498493i	$0.166113\pi$
$390$	0	0
$391$	0	0
$392$	12.9047	0.651783
$393$	0	0
$394$	−24.6096	−1.23982
$395$	−48.3242	−2.43146
$396$	0	0
$397$	0.230357	0.0115613	0.00578065	−	0.999983i	$-0.498160\pi$
$397$	0.230357	0.0115613	0.00578065	+	0.999983i	$0.498160\pi$
$398$	−31.0349	−1.55564
$399$	0	0
$400$	−56.8376	−2.84188
$401$	−0.606756	−0.0302999	−0.0151500	−	0.999885i	$-0.504823\pi$
$401$	−0.606756	−0.0302999	−0.0151500	+	0.999885i	$0.504823\pi$
$402$	0	0
$403$	−14.7734	−0.735915
$404$	−0.193952	−0.00964947
$405$	0	0
$406$	3.35843	0.166676
$407$	−13.5177	−0.670049
$408$	0	0
$409$	−1.50925	−0.0746278	−0.0373139	−	0.999304i	$-0.511880\pi$
$409$	−1.50925	−0.0746278	−0.0373139	+	0.999304i	$0.511880\pi$
$410$	−33.9299	−1.67568
$411$	0	0
$412$	−2.21454	−0.109103
$413$	−6.82416	−0.335795
$414$	0	0
$415$	−25.9645	−1.27455
$416$	−14.0959	−0.691110
$417$	0	0
$418$	−6.48830	−0.317353
$419$	12.1198	0.592090	0.296045	−	0.955174i	$-0.404332\pi$
$419$	12.1198	0.592090	0.296045	+	0.955174i	$0.404332\pi$
$420$	0	0
$421$	−17.8730	−0.871078	−0.435539	−	0.900170i	$-0.643442\pi$
$421$	−17.8730	−0.871078	−0.435539	+	0.900170i	$0.643442\pi$
$422$	−9.71616	−0.472975
$423$	0	0
$424$	−5.65685	−0.274721
$425$	0	0
$426$	0	0
$427$	−3.58828	−0.173649
$428$	−14.3431	−0.693302
$429$	0	0
$430$	35.1484	1.69501
$431$	−11.1361	−0.536408	−0.268204	−	0.963362i	$-0.586430\pi$
$431$	−11.1361	−0.536408	−0.268204	+	0.963362i	$0.586430\pi$
$432$	0	0
$433$	−29.1182	−1.39933	−0.699665	−	0.714471i	$-0.746667\pi$
$433$	−29.1182	−1.39933	−0.699665	+	0.714471i	$0.746667\pi$
$434$	6.29842	0.302334
$435$	0	0
$436$	0.522302	0.0250137
$437$	8.81974	0.421905
$438$	0	0
$439$	22.5958	1.07844	0.539219	−	0.842165i	$-0.318719\pi$
$439$	22.5958	1.07844	0.539219	+	0.842165i	$0.318719\pi$
$440$	−19.3730	−0.923572
$441$	0	0
$442$	0	0
$443$	−32.1976	−1.52975	−0.764877	−	0.644176i	$-0.777200\pi$
$443$	−32.1976	−1.52975	−0.764877	+	0.644176i	$0.777200\pi$
$444$	0	0
$445$	42.1271	1.99701
$446$	−9.22579	−0.436854
$447$	0	0
$448$	−3.07959	−0.145497
$449$	−1.12030	−0.0528702	−0.0264351	−	0.999651i	$-0.508416\pi$
$449$	−1.12030	−0.0528702	−0.0264351	+	0.999651i	$0.508416\pi$
$450$	0	0
$451$	−11.4645	−0.539844
$452$	8.60306	0.404654
$453$	0	0
$454$	45.4855	2.13474
$455$	13.4077	0.628561
$456$	0	0
$457$	40.0795	1.87484	0.937419	−	0.348203i	$-0.113208\pi$
$457$	40.0795	1.87484	0.937419	+	0.348203i	$0.113208\pi$
$458$	−5.89875	−0.275631
$459$	0	0
$460$	−15.1318	−0.705526
$461$	−4.99595	−0.232684	−0.116342	−	0.993209i	$-0.537117\pi$
$461$	−4.99595	−0.232684	−0.116342	+	0.993209i	$0.537117\pi$
$462$	0	0
$463$	39.0452	1.81458	0.907292	−	0.420502i	$-0.138146\pi$
$463$	39.0452	1.81458	0.907292	+	0.420502i	$0.138146\pi$
$464$	10.8578	0.504060
$465$	0	0
$466$	2.26500	0.104924
$467$	−10.5242	−0.487002	−0.243501	−	0.969901i	$-0.578296\pi$
$467$	−10.5242	−0.487002	−0.243501	+	0.969901i	$0.578296\pi$
$468$	0	0
$469$	−11.1073	−0.512886
$470$	−46.7706	−2.15737
$471$	0	0
$472$	−15.5262	−0.714651
$473$	11.8762	0.546070
$474$	0	0
$475$	19.9553	0.915611
$476$	0	0
$477$	0	0
$478$	−35.7081	−1.63325
$479$	25.9640	1.18632	0.593162	−	0.805083i	$-0.297879\pi$
$479$	25.9640	1.18632	0.593162	+	0.805083i	$0.297879\pi$
$480$	0	0
$481$	21.2851	0.970517
$482$	1.75434	0.0799079
$483$	0	0
$484$	−4.26692	−0.193951
$485$	−58.8392	−2.67175
$486$	0	0
$487$	25.5405	1.15735	0.578676	−	0.815557i	$-0.303570\pi$
$487$	25.5405	1.15735	0.578676	+	0.815557i	$0.303570\pi$
$488$	−8.16399	−0.369566
$489$	0	0
$490$	41.3145	1.86640
$491$	2.50764	0.113168	0.0565842	−	0.998398i	$-0.481979\pi$
$491$	2.50764	0.113168	0.0565842	+	0.998398i	$0.481979\pi$
$492$	0	0
$493$	0	0
$494$	10.2165	0.459663
$495$	0	0
$496$	20.3627	0.914313
$497$	1.40569	0.0630540
$498$	0	0
$499$	15.2270	0.681656	0.340828	−	0.940126i	$-0.389293\pi$
$499$	15.2270	0.681656	0.340828	+	0.940126i	$0.389293\pi$
$500$	−19.3976	−0.867486
$501$	0	0
$502$	12.0565	0.538109
$503$	39.0990	1.74334	0.871670	−	0.490094i	$-0.163038\pi$
$503$	39.0990	1.74334	0.871670	+	0.490094i	$0.163038\pi$
$504$	0	0
$505$	1.08064	0.0480878
$506$	−19.1238	−0.850158
$507$	0	0
$508$	2.05120	0.0910073
$509$	31.9138	1.41455	0.707277	−	0.706937i	$-0.249924\pi$
$509$	31.9138	1.41455	0.707277	+	0.706937i	$0.249924\pi$
$510$	0	0
$511$	1.07460	0.0475374
$512$	−1.25058	−0.0552685
$513$	0	0
$514$	37.2690	1.64386
$515$	12.3387	0.543709
$516$	0	0
$517$	−15.8033	−0.695027
$518$	−9.07460	−0.398715
$519$	0	0
$520$	30.5049	1.33773
$521$	4.83056	0.211631	0.105815	−	0.994386i	$-0.466255\pi$
$521$	4.83056	0.211631	0.105815	+	0.994386i	$0.466255\pi$
$522$	0	0
$523$	36.5734	1.59924	0.799622	−	0.600503i	$-0.205033\pi$
$523$	36.5734	1.59924	0.799622	+	0.600503i	$0.205033\pi$
$524$	5.78546	0.252739
$525$	0	0
$526$	7.02061	0.306113
$527$	0	0
$528$	0	0
$529$	2.99559	0.130243
$530$	−18.1105	−0.786670
$531$	0	0
$532$	−1.16451	−0.0504881
$533$	18.0521	0.781924
$534$	0	0
$535$	79.9154	3.45504
$536$	−25.2711	−1.09154
$537$	0	0
$538$	19.5521	0.842950
$539$	13.9597	0.601286
$540$	0	0
$541$	11.0291	0.474179	0.237090	−	0.971488i	$-0.423806\pi$
$541$	11.0291	0.474179	0.237090	+	0.971488i	$0.423806\pi$
$542$	−19.5036	−0.837751
$543$	0	0
$544$	0	0
$545$	−2.91010	−0.124655
$546$	0	0
$547$	−26.8766	−1.14916	−0.574580	−	0.818448i	$-0.694835\pi$
$547$	−26.8766	−1.14916	−0.574580	+	0.818448i	$0.694835\pi$
$548$	0.0753327	0.00321805
$549$	0	0
$550$	−43.2690	−1.84500
$551$	−3.81209	−0.162400
$552$	0	0
$553$	−10.9613	−0.466122
$554$	17.2286	0.731973
$555$	0	0
$556$	−10.5435	−0.447146
$557$	34.9146	1.47938	0.739690	−	0.672948i	$-0.234972\pi$
$557$	34.9146	1.47938	0.739690	+	0.672948i	$0.234972\pi$
$558$	0	0
$559$	−18.7004	−0.790943
$560$	−18.4803	−0.780935
$561$	0	0
$562$	9.03266	0.381020
$563$	7.91334	0.333507	0.166754	−	0.985999i	$-0.446672\pi$
$563$	7.91334	0.333507	0.166754	+	0.985999i	$0.446672\pi$
$564$	0	0
$565$	−47.9335	−2.01658
$566$	29.1411	1.22489
$567$	0	0
$568$	3.19821	0.134194
$569$	17.2956	0.725070	0.362535	−	0.931970i	$-0.381911\pi$
$569$	17.2956	0.725070	0.362535	+	0.931970i	$0.381911\pi$
$570$	0	0
$571$	−19.3791	−0.810988	−0.405494	−	0.914098i	$-0.632901\pi$
$571$	−19.3791	−0.810988	−0.405494	+	0.914098i	$0.632901\pi$
$572$	−5.92260	−0.247636
$573$	0	0
$574$	−7.69626	−0.321236
$575$	58.8168	2.45283
$576$	0	0
$577$	−2.89714	−0.120610	−0.0603048	−	0.998180i	$-0.519207\pi$
$577$	−2.89714	−0.120610	−0.0603048	+	0.998180i	$0.519207\pi$
$578$	0	0
$579$	0	0
$580$	6.54032	0.271572
$581$	−5.88949	−0.244337
$582$	0	0
$583$	−6.11934	−0.253437
$584$	2.44490	0.101171
$585$	0	0
$586$	13.6448	0.563662
$587$	−12.3165	−0.508357	−0.254178	−	0.967157i	$-0.581805\pi$
$587$	−12.3165	−0.508357	−0.254178	+	0.967157i	$0.581805\pi$
$588$	0	0
$589$	−7.14921	−0.294578
$590$	−49.7073	−2.04642
$591$	0	0
$592$	−29.3381	−1.20579
$593$	−43.1763	−1.77304	−0.886519	−	0.462693i	$-0.846883\pi$
$593$	−43.1763	−1.77304	−0.886519	+	0.462693i	$0.846883\pi$
$594$	0	0
$595$	0	0
$596$	−2.62420	−0.107491
$597$	0	0
$598$	30.1125	1.23139
$599$	−6.70607	−0.274003	−0.137001	−	0.990571i	$-0.543746\pi$
$599$	−6.70607	−0.274003	−0.137001	+	0.990571i	$0.543746\pi$
$600$	0	0
$601$	31.8393	1.29875	0.649375	−	0.760468i	$-0.275030\pi$
$601$	31.8393	1.29875	0.649375	+	0.760468i	$0.275030\pi$
$602$	7.97265	0.324941
$603$	0	0
$604$	5.53823	0.225348
$605$	23.7739	0.966547
$606$	0	0
$607$	27.9168	1.13311	0.566554	−	0.824025i	$-0.308276\pi$
$607$	27.9168	1.13311	0.566554	+	0.824025i	$0.308276\pi$
$608$	−6.82137	−0.276643
$609$	0	0
$610$	−26.1371	−1.05826
$611$	24.8839	1.00669
$612$	0	0
$613$	−5.84314	−0.236002	−0.118001	−	0.993013i	$-0.537649\pi$
$613$	−5.84314	−0.236002	−0.118001	+	0.993013i	$0.537649\pi$
$614$	−16.4330	−0.663183
$615$	0	0
$616$	−4.39435	−0.177053
$617$	−37.0522	−1.49166	−0.745832	−	0.666134i	$-0.767948\pi$
$617$	−37.0522	−1.49166	−0.745832	+	0.666134i	$0.767948\pi$
$618$	0	0
$619$	−16.1686	−0.649870	−0.324935	−	0.945736i	$-0.605342\pi$
$619$	−16.1686	−0.649870	−0.324935	+	0.945736i	$0.605342\pi$
$620$	12.2657	0.492604
$621$	0	0
$622$	27.4046	1.09883
$623$	9.55561	0.382837
$624$	0	0
$625$	50.3976	2.01590
$626$	34.0550	1.36111
$627$	0	0
$628$	−13.8355	−0.552097
$629$	0	0
$630$	0	0
$631$	−31.6670	−1.26064	−0.630322	−	0.776334i	$-0.717077\pi$
$631$	−31.6670	−1.26064	−0.630322	+	0.776334i	$0.717077\pi$
$632$	−24.9389	−0.992018
$633$	0	0
$634$	−7.05173	−0.280060
$635$	−11.4286	−0.453531
$636$	0	0
$637$	−21.9810	−0.870919
$638$	8.26575	0.327244
$639$	0	0
$640$	−54.5026	−2.15440
$641$	15.9293	0.629169	0.314585	−	0.949229i	$-0.398135\pi$
$641$	15.9293	0.629169	0.314585	+	0.949229i	$0.398135\pi$
$642$	0	0
$643$	−16.6863	−0.658043	−0.329022	−	0.944322i	$-0.606719\pi$
$643$	−16.6863	−0.658043	−0.329022	+	0.944322i	$0.606719\pi$
$644$	−3.43233	−0.135253
$645$	0	0
$646$	0	0
$647$	8.35044	0.328290	0.164145	−	0.986436i	$-0.447514\pi$
$647$	8.35044	0.328290	0.164145	+	0.986436i	$0.447514\pi$
$648$	0	0
$649$	−16.7956	−0.659283
$650$	68.1316	2.67234
$651$	0	0
$652$	9.80398	0.383954
$653$	−28.6977	−1.12303	−0.561514	−	0.827467i	$-0.689781\pi$
$653$	−28.6977	−1.12303	−0.561514	+	0.827467i	$0.689781\pi$
$654$	0	0
$655$	−32.2347	−1.25951
$656$	−24.8819	−0.971475
$657$	0	0
$658$	−10.6089	−0.413578
$659$	40.3690	1.57255	0.786276	−	0.617876i	$-0.212007\pi$
$659$	40.3690	1.57255	0.786276	+	0.617876i	$0.212007\pi$
$660$	0	0
$661$	−39.4706	−1.53523	−0.767614	−	0.640913i	$-0.778556\pi$
$661$	−39.4706	−1.53523	−0.767614	+	0.640913i	$0.778556\pi$
$662$	−47.2710	−1.83724
$663$	0	0
$664$	−13.3997	−0.520007
$665$	6.48830	0.251606
$666$	0	0
$667$	−11.2359	−0.435055
$668$	1.55988	0.0603535
$669$	0	0
$670$	−80.9057	−3.12566
$671$	−8.83145	−0.340934
$672$	0	0
$673$	−21.6056	−0.832834	−0.416417	−	0.909174i	$-0.636714\pi$
$673$	−21.6056	−0.832834	−0.416417	+	0.909174i	$0.636714\pi$
$674$	51.7754	1.99431
$675$	0	0
$676$	−0.162168	−0.00623724
$677$	−2.51083	−0.0964990	−0.0482495	−	0.998835i	$-0.515364\pi$
$677$	−2.51083	−0.0964990	−0.0482495	+	0.998835i	$0.515364\pi$
$678$	0	0
$679$	−13.3464	−0.512187
$680$	0	0
$681$	0	0
$682$	15.5016	0.593588
$683$	−18.7423	−0.717156	−0.358578	−	0.933500i	$-0.616738\pi$
$683$	−18.7423	−0.717156	−0.358578	+	0.933500i	$0.616738\pi$
$684$	0	0
$685$	−0.419730	−0.0160370
$686$	20.0392	0.765098
$687$	0	0
$688$	25.7755	0.982681
$689$	9.63554	0.367085
$690$	0	0
$691$	−38.5702	−1.46728	−0.733640	−	0.679538i	$-0.762180\pi$
$691$	−38.5702	−1.46728	−0.733640	+	0.679538i	$0.762180\pi$
$692$	3.85352	0.146489
$693$	0	0
$694$	−19.8860	−0.754862
$695$	58.7452	2.22833
$696$	0	0
$697$	0	0
$698$	55.1037	2.08570
$699$	0	0
$700$	−7.76588	−0.293523
$701$	28.7827	1.08711	0.543553	−	0.839375i	$-0.317079\pi$
$701$	28.7827	1.08711	0.543553	+	0.839375i	$0.317079\pi$
$702$	0	0
$703$	10.3004	0.388487
$704$	−7.57945	−0.285661
$705$	0	0
$706$	10.8480	0.408270
$707$	0.245119	0.00921866
$708$	0	0
$709$	−5.14588	−0.193258	−0.0966288	−	0.995320i	$-0.530806\pi$
$709$	−5.14588	−0.193258	−0.0966288	+	0.995320i	$0.530806\pi$
$710$	10.2391	0.384267
$711$	0	0
$712$	21.7407	0.814768
$713$	−21.0718	−0.789146
$714$	0	0
$715$	32.9988	1.23409
$716$	5.67538	0.212099
$717$	0	0
$718$	−35.6068	−1.32883
$719$	31.5022	1.17483	0.587417	−	0.809285i	$-0.300145\pi$
$719$	31.5022	1.17483	0.587417	+	0.809285i	$0.300145\pi$
$720$	0	0
$721$	2.79877	0.104232
$722$	−26.4482	−0.984300
$723$	0	0
$724$	0.668412	0.0248413
$725$	−25.4219	−0.944147
$726$	0	0
$727$	31.2775	1.16002	0.580010	−	0.814610i	$-0.303049\pi$
$727$	31.2775	1.16002	0.580010	+	0.814610i	$0.303049\pi$
$728$	6.91936	0.256449
$729$	0	0
$730$	7.82739	0.289705
$731$	0	0
$732$	0	0
$733$	18.8153	0.694960	0.347480	−	0.937687i	$-0.387037\pi$
$733$	18.8153	0.694960	0.347480	+	0.937687i	$0.387037\pi$
$734$	58.7603	2.16888
$735$	0	0
$736$	−20.1055	−0.741099
$737$	−27.3371	−1.00698
$738$	0	0
$739$	6.94762	0.255572	0.127786	−	0.991802i	$-0.459213\pi$
$739$	6.94762	0.255572	0.127786	+	0.991802i	$0.459213\pi$
$740$	−17.6722	−0.649641
$741$	0	0
$742$	−4.10797	−0.150808
$743$	33.9563	1.24574	0.622868	−	0.782327i	$-0.285967\pi$
$743$	33.9563	1.24574	0.622868	+	0.782327i	$0.285967\pi$
$744$	0	0
$745$	14.6212	0.535678
$746$	−59.2243	−2.16835
$747$	0	0
$748$	0	0
$749$	18.1271	0.662349
$750$	0	0
$751$	−6.91509	−0.252335	−0.126168	−	0.992009i	$-0.540268\pi$
$751$	−6.91509	−0.252335	−0.126168	+	0.992009i	$0.540268\pi$
$752$	−34.2984	−1.25073
$753$	0	0
$754$	−13.0153	−0.473989
$755$	−30.8573	−1.12301
$756$	0	0
$757$	1.86166	0.0676633	0.0338316	−	0.999428i	$-0.489229\pi$
$757$	1.86166	0.0676633	0.0338316	+	0.999428i	$0.489229\pi$
$758$	−36.2178	−1.31549
$759$	0	0
$760$	14.7621	0.535476
$761$	−49.2335	−1.78471	−0.892357	−	0.451330i	$-0.850950\pi$
$761$	−49.2335	−1.78471	−0.892357	+	0.451330i	$0.850950\pi$
$762$	0	0
$763$	−0.660093	−0.0238970
$764$	13.9880	0.506066
$765$	0	0
$766$	56.6893	2.04827
$767$	26.4464	0.954923
$768$	0	0
$769$	50.9303	1.83659	0.918296	−	0.395895i	$-0.129565\pi$
$769$	50.9303	1.83659	0.918296	+	0.395895i	$0.129565\pi$
$770$	−14.0686	−0.506996
$771$	0	0
$772$	3.43855	0.123756
$773$	−2.91614	−0.104886	−0.0524431	−	0.998624i	$-0.516701\pi$
$773$	−2.91614	−0.104886	−0.0524431	+	0.998624i	$0.516701\pi$
$774$	0	0
$775$	−47.6764	−1.71259
$776$	−30.3654	−1.09006
$777$	0	0
$778$	56.4988	2.02558
$779$	8.73586	0.312995
$780$	0	0
$781$	3.45968	0.123797
$782$	0	0
$783$	0	0
$784$	30.2972	1.08204
$785$	77.0870	2.75135
$786$	0	0
$787$	−50.8932	−1.81415	−0.907073	−	0.420974i	$-0.861688\pi$
$787$	−50.8932	−1.81415	−0.907073	+	0.420974i	$0.861688\pi$
$788$	−10.8709	−0.387259
$789$	0	0
$790$	−79.8424	−2.84067
$791$	−10.8727	−0.386588
$792$	0	0
$793$	13.9060	0.493818
$794$	0.380602	0.0135070
$795$	0	0
$796$	−13.7091	−0.485906
$797$	13.6061	0.481952	0.240976	−	0.970531i	$-0.422532\pi$
$797$	13.6061	0.481952	0.240976	+	0.970531i	$0.422532\pi$
$798$	0	0
$799$	0	0
$800$	−45.4901	−1.60832
$801$	0	0
$802$	−1.00250	−0.0353993
$803$	2.64479	0.0933326
$804$	0	0
$805$	19.1238	0.674026
$806$	−24.4089	−0.859768
$807$	0	0
$808$	0.557691	0.0196195
$809$	−17.3937	−0.611529	−0.305765	−	0.952107i	$-0.598912\pi$
$809$	−17.3937	−0.611529	−0.305765	+	0.952107i	$0.598912\pi$
$810$	0	0
$811$	−32.9286	−1.15628	−0.578140	−	0.815937i	$-0.696221\pi$
$811$	−32.9286	−1.15628	−0.578140	+	0.815937i	$0.696221\pi$
$812$	1.48353	0.0520617
$813$	0	0
$814$	−22.3343	−0.782817
$815$	−54.6246	−1.91342
$816$	0	0
$817$	−9.04959	−0.316605
$818$	−2.49362	−0.0871875
$819$	0	0
$820$	−14.9879	−0.523401
$821$	−43.7368	−1.52643	−0.763213	−	0.646147i	$-0.776379\pi$
$821$	−43.7368	−1.52643	−0.763213	+	0.646147i	$0.776379\pi$
$822$	0	0
$823$	1.67402	0.0583528	0.0291764	−	0.999574i	$-0.490712\pi$
$823$	1.67402	0.0583528	0.0291764	+	0.999574i	$0.490712\pi$
$824$	6.36771	0.221830
$825$	0	0
$826$	−11.2750	−0.392308
$827$	2.27016	0.0789412	0.0394706	−	0.999221i	$-0.487433\pi$
$827$	2.27016	0.0789412	0.0394706	+	0.999221i	$0.487433\pi$
$828$	0	0
$829$	19.2597	0.668918	0.334459	−	0.942410i	$-0.391446\pi$
$829$	19.2597	0.668918	0.334459	+	0.942410i	$0.391446\pi$
$830$	−42.8992	−1.48905
$831$	0	0
$832$	11.9346	0.413760
$833$	0	0
$834$	0	0
$835$	−8.69114	−0.300769
$836$	−2.86609	−0.0991259
$837$	0	0
$838$	20.0246	0.691737
$839$	−14.8059	−0.511157	−0.255579	−	0.966788i	$-0.582266\pi$
$839$	−14.8059	−0.511157	−0.255579	+	0.966788i	$0.582266\pi$
$840$	0	0
$841$	−24.1436	−0.832538
$842$	−29.5302	−1.01768
$843$	0	0
$844$	−4.29194	−0.147735
$845$	0.903549	0.0310830
$846$	0	0
$847$	5.39259	0.185292
$848$	−13.2810	−0.456073
$849$	0	0
$850$	0	0
$851$	30.3597	1.04072
$852$	0	0
$853$	6.35771	0.217684	0.108842	−	0.994059i	$-0.465286\pi$
$853$	6.35771	0.217684	0.108842	+	0.994059i	$0.465286\pi$
$854$	−5.92864	−0.202874
$855$	0	0
$856$	41.2423	1.40963
$857$	40.8311	1.39477	0.697383	−	0.716699i	$-0.254348\pi$
$857$	40.8311	1.39477	0.697383	+	0.716699i	$0.254348\pi$
$858$	0	0
$859$	22.1464	0.755626	0.377813	−	0.925882i	$-0.376676\pi$
$859$	22.1464	0.755626	0.377813	+	0.925882i	$0.376676\pi$
$860$	15.5262	0.529439
$861$	0	0
$862$	−18.3993	−0.626684
$863$	−17.3423	−0.590339	−0.295170	−	0.955445i	$-0.595376\pi$
$863$	−17.3423	−0.590339	−0.295170	+	0.955445i	$0.595376\pi$
$864$	0	0
$865$	−21.4706	−0.730021
$866$	−48.1097	−1.63483
$867$	0	0
$868$	2.78222	0.0944346
$869$	−26.9779	−0.915161
$870$	0	0
$871$	43.0452	1.45853
$872$	−1.50183	−0.0508584
$873$	0	0
$874$	14.5722	0.492911
$875$	24.5149	0.828756
$876$	0	0
$877$	30.2306	1.02081	0.510407	−	0.859933i	$-0.329495\pi$
$877$	30.2306	1.02081	0.510407	+	0.859933i	$0.329495\pi$
$878$	37.3333	1.25994
$879$	0	0
$880$	−45.4835	−1.53325
$881$	−10.5647	−0.355933	−0.177966	−	0.984037i	$-0.556952\pi$
$881$	−10.5647	−0.355933	−0.177966	+	0.984037i	$0.556952\pi$
$882$	0	0
$883$	13.9150	0.468276	0.234138	−	0.972203i	$-0.424773\pi$
$883$	13.9150	0.468276	0.234138	+	0.972203i	$0.424773\pi$
$884$	0	0
$885$	0	0
$886$	−53.1976	−1.78721
$887$	−35.9644	−1.20757	−0.603783	−	0.797149i	$-0.706341\pi$
$887$	−35.9644	−1.20757	−0.603783	+	0.797149i	$0.706341\pi$
$888$	0	0
$889$	−2.59234	−0.0869442
$890$	69.6033	2.33311
$891$	0	0
$892$	−4.07533	−0.136452
$893$	12.0419	0.402968
$894$	0	0
$895$	−31.6214	−1.05699
$896$	−12.3627	−0.413010
$897$	0	0
$898$	−1.85098	−0.0617681
$899$	9.10771	0.303759
$900$	0	0
$901$	0	0
$902$	−18.9420	−0.630698
$903$	0	0
$904$	−24.7373	−0.822750
$905$	−3.72418	−0.123796
$906$	0	0
$907$	−39.1843	−1.30109	−0.650547	−	0.759466i	$-0.725460\pi$
$907$	−39.1843	−1.30109	−0.650547	+	0.759466i	$0.725460\pi$
$908$	20.0924	0.666790
$909$	0	0
$910$	22.1524	0.734347
$911$	−9.92806	−0.328931	−0.164466	−	0.986383i	$-0.552590\pi$
$911$	−9.92806	−0.328931	−0.164466	+	0.986383i	$0.552590\pi$
$912$	0	0
$913$	−14.4952	−0.479720
$914$	66.2202	2.19037
$915$	0	0
$916$	−2.60567	−0.0860938
$917$	−7.31174	−0.241455
$918$	0	0
$919$	42.8795	1.41446	0.707232	−	0.706982i	$-0.249944\pi$
$919$	42.8795	1.41446	0.707232	+	0.706982i	$0.249944\pi$
$920$	43.5102	1.43449
$921$	0	0
$922$	−8.25442	−0.271845
$923$	−5.44763	−0.179311
$924$	0	0
$925$	68.6909	2.25854
$926$	64.5113	2.11997
$927$	0	0
$928$	8.69006	0.285265
$929$	18.1624	0.595888	0.297944	−	0.954583i	$-0.403699\pi$
$929$	18.1624	0.595888	0.297944	+	0.954583i	$0.403699\pi$
$930$	0	0
$931$	−10.6372	−0.348619
$932$	1.00053	0.0327733
$933$	0	0
$934$	−17.3883	−0.568963
$935$	0	0
$936$	0	0
$937$	1.60243	0.0523492	0.0261746	−	0.999657i	$-0.491667\pi$
$937$	1.60243	0.0523492	0.0261746	+	0.999657i	$0.491667\pi$
$938$	−18.3517	−0.599204
$939$	0	0
$940$	−20.6601	−0.673858
$941$	−32.3544	−1.05472	−0.527362	−	0.849641i	$-0.676819\pi$
$941$	−32.3544	−1.05472	−0.527362	+	0.849641i	$0.676819\pi$
$942$	0	0
$943$	25.7484	0.838482
$944$	−36.4520	−1.18641
$945$	0	0
$946$	19.6222	0.637973
$947$	−25.1819	−0.818301	−0.409151	−	0.912467i	$-0.634175\pi$
$947$	−25.1819	−0.818301	−0.409151	+	0.912467i	$0.634175\pi$
$948$	0	0
$949$	−4.16450	−0.135185
$950$	32.9706	1.06971
$951$	0	0
$952$	0	0
$953$	−54.0658	−1.75136	−0.875681	−	0.482889i	$-0.839587\pi$
$953$	−54.0658	−1.75136	−0.875681	+	0.482889i	$0.839587\pi$
$954$	0	0
$955$	−77.9364	−2.52196
$956$	−15.7734	−0.510148
$957$	0	0
$958$	42.8983	1.38598
$959$	−0.0952065	−0.00307438
$960$	0	0
$961$	−13.9194	−0.449012
$962$	35.1677	1.13385
$963$	0	0
$964$	0.774948	0.0249594
$965$	−19.1585	−0.616733
$966$	0	0
$967$	−2.17495	−0.0699418	−0.0349709	−	0.999388i	$-0.511134\pi$
$967$	−2.17495	−0.0699418	−0.0349709	+	0.999388i	$0.511134\pi$
$968$	12.2691	0.394345
$969$	0	0
$970$	−97.2154	−3.12140
$971$	−47.4481	−1.52268	−0.761340	−	0.648352i	$-0.775458\pi$
$971$	−47.4481	−1.52268	−0.761340	+	0.648352i	$0.775458\pi$
$972$	0	0
$973$	13.3251	0.427182
$974$	42.1987	1.35213
$975$	0	0
$976$	−19.1672	−0.613528
$977$	20.8226	0.666175	0.333087	−	0.942896i	$-0.391910\pi$
$977$	20.8226	0.666175	0.333087	+	0.942896i	$0.391910\pi$
$978$	0	0
$979$	23.5182	0.751644
$980$	18.2499	0.582973
$981$	0	0
$982$	4.14319	0.132214
$983$	−2.43039	−0.0775173	−0.0387586	−	0.999249i	$-0.512340\pi$
$983$	−2.43039	−0.0775173	−0.0387586	+	0.999249i	$0.512340\pi$
$984$	0	0
$985$	60.5690	1.92989
$986$	0	0
$987$	0	0
$988$	4.51297	0.143577
$989$	−26.6731	−0.848154
$990$	0	0
$991$	36.5777	1.16193	0.580964	−	0.813929i	$-0.302676\pi$
$991$	36.5777	1.16193	0.580964	+	0.813929i	$0.302676\pi$
$992$	16.2974	0.517442
$993$	0	0
$994$	2.32252	0.0736658
$995$	76.3827	2.42150
$996$	0	0
$997$	20.7109	0.655920	0.327960	−	0.944692i	$-0.393639\pi$
$997$	20.7109	0.655920	0.327960	+	0.944692i	$0.393639\pi$
$998$	25.1585	0.796378
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2601.2.a.be.1.3		4
3.2	odd	2		867.2.a.l.1.2		4
17.2	even	8		153.2.f.b.55.3		8
17.9	even	8		153.2.f.b.64.2		8
17.16	even	2		2601.2.a.bf.1.3		4
51.2	odd	8		51.2.e.a.4.2	✓	8
51.5	even	16		867.2.h.i.688.3		16
51.8	odd	8		867.2.e.g.829.3		8
51.11	even	16		867.2.h.k.733.1		16
51.14	even	16		867.2.h.k.757.1		16
51.20	even	16		867.2.h.k.757.2		16
51.23	even	16		867.2.h.k.733.2		16
51.26	odd	8		51.2.e.a.13.3	yes	8
51.29	even	16		867.2.h.i.688.4		16
51.32	odd	8		867.2.e.g.616.2		8
51.38	odd	4		867.2.d.f.577.5		8
51.41	even	16		867.2.h.i.712.3		16
51.44	even	16		867.2.h.i.712.4		16
51.47	odd	4		867.2.d.f.577.6		8
51.50	odd	2		867.2.a.k.1.2		4
68.19	odd	8		2448.2.be.x.1585.4		8
68.43	odd	8		2448.2.be.x.1441.4		8
204.155	even	8		816.2.bd.e.769.1		8
204.179	even	8		816.2.bd.e.625.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.e.a.4.2	✓	8	51.2	odd	8
51.2.e.a.13.3	yes	8	51.26	odd	8
153.2.f.b.55.3		8	17.2	even	8
153.2.f.b.64.2		8	17.9	even	8
816.2.bd.e.625.1		8	204.179	even	8
816.2.bd.e.769.1		8	204.155	even	8
867.2.a.k.1.2		4	51.50	odd	2
867.2.a.l.1.2		4	3.2	odd	2
867.2.d.f.577.5		8	51.38	odd	4
867.2.d.f.577.6		8	51.47	odd	4
867.2.e.g.616.2		8	51.32	odd	8
867.2.e.g.829.3		8	51.8	odd	8
867.2.h.i.688.3		16	51.5	even	16
867.2.h.i.688.4		16	51.29	even	16
867.2.h.i.712.3		16	51.41	even	16
867.2.h.i.712.4		16	51.44	even	16
867.2.h.k.733.1		16	51.11	even	16
867.2.h.k.733.2		16	51.23	even	16
867.2.h.k.757.1		16	51.14	even	16
867.2.h.k.757.2		16	51.20	even	16
2448.2.be.x.1441.4		8	68.43	odd	8
2448.2.be.x.1585.4		8	68.19	odd	8
2601.2.a.be.1.3		4	1.1	even	1	trivial
2601.2.a.bf.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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 2601 = 3^{2} \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2601.a (trivial)

\(f(q)\)	\(=\)	\(q+1.65222 q^{2} +0.729840 q^{4} -4.06644 q^{5} -0.922382 q^{7} -2.09859 q^{8} -6.71866 q^{10} -2.27016 q^{11} +3.57461 q^{13} -1.52398 q^{14} -4.92701 q^{16} +1.72984 q^{19} -2.96785 q^{20} -3.75081 q^{22} +5.09859 q^{23} +11.5359 q^{25} +5.90604 q^{26} -0.673192 q^{28} -2.20372 q^{29} -4.13287 q^{31} -3.94335 q^{32} +3.75081 q^{35} +5.95453 q^{37} +2.85808 q^{38} +8.53377 q^{40} +5.05010 q^{41} -5.23146 q^{43} -1.65685 q^{44} +8.42400 q^{46} +6.96130 q^{47} -6.14921 q^{49} +19.0599 q^{50} +2.60889 q^{52} +2.69555 q^{53} +9.23146 q^{55} +1.93570 q^{56} -3.64104 q^{58} +7.39840 q^{59} +3.89023 q^{61} -6.82843 q^{62} +3.33873 q^{64} -14.5359 q^{65} +12.0419 q^{67} +6.19717 q^{70} -1.52398 q^{71} -1.16502 q^{73} +9.83822 q^{74} +1.26251 q^{76} +2.09396 q^{77} +11.8837 q^{79} +20.0354 q^{80} +8.34389 q^{82} +6.38508 q^{83} -8.64354 q^{86} +4.76413 q^{88} -10.3597 q^{89} -3.29715 q^{91} +3.72115 q^{92} +11.5016 q^{94} -7.03429 q^{95} +14.4695 q^{97} -10.1599 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 6 q^{4} - 6 q^{5} + 4 q^{7} + 6 q^{8} - 12 q^{10} - 6 q^{11} + 2 q^{13} - 4 q^{14} + 6 q^{16} + 10 q^{19} - 16 q^{20} + 4 q^{22} + 6 q^{23} + 2 q^{25} + 20 q^{26} + 24 q^{28} - 16 q^{29}+ \cdots - 38 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 + 6 * q^4 - 6 * q^5 + 4 * q^7 + 6 * q^8 - 12 * q^10 - 6 * q^11 + 2 * q^13 - 4 * q^14 + 6 * q^16 + 10 * q^19 - 16 * q^20 + 4 * q^22 + 6 * q^23 + 2 * q^25 + 20 * q^26 + 24 * q^28 - 16 * q^29 + 4 * q^31 + 14 * q^32 - 4 * q^35 + 12 * q^37 + 12 * q^38 - 8 * q^40 + 14 * q^41 + 14 * q^43 + 16 * q^44 - 12 * q^46 - 4 * q^47 + 30 * q^50 - 8 * q^52 + 20 * q^53 + 2 * q^55 + 16 * q^56 + 8 * q^58 + 24 * q^59 + 12 * q^61 - 16 * q^62 - 2 * q^64 - 14 * q^65 + 4 * q^67 - 4 * q^70 - 4 * q^71 + 20 * q^73 - 12 * q^74 + 40 * q^76 + 12 * q^77 + 8 * q^79 - 4 * q^82 + 4 * q^83 + 4 * q^86 + 16 * q^88 - 4 * q^89 - 28 * q^91 - 16 * q^92 + 8 * q^94 - 22 * q^95 + 24 * q^97 - 38 * q^98

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