LMFDB - Embedded newform 2601.2.a.w.1.2

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:	$3$
Coefficient field:	$\Q(\zeta_{18})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 3x - 1 $ x^3 - 3*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 289)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.347296$ 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)

$f(q)$	$=$	$q-0.347296 q^{2} -1.87939 q^{4} -2.34730 q^{5} +1.87939 q^{7} +1.34730 q^{8} +O(q^{10})$	$q-0.347296 q^{2} -1.87939 q^{4} -2.34730 q^{5} +1.87939 q^{7} +1.34730 q^{8} +0.815207 q^{10} -5.06418 q^{11} +4.71688 q^{13} -0.652704 q^{14} +3.29086 q^{16} +0.347296 q^{19} +4.41147 q^{20} +1.75877 q^{22} -1.77332 q^{23} +0.509800 q^{25} -1.63816 q^{26} -3.53209 q^{28} +2.22668 q^{29} -1.94356 q^{31} -3.83750 q^{32} -4.41147 q^{35} +6.17024 q^{37} -0.120615 q^{38} -3.16250 q^{40} +5.17024 q^{41} -1.47565 q^{43} +9.51754 q^{44} +0.615867 q^{46} +8.53209 q^{47} -3.46791 q^{49} -0.177052 q^{50} -8.86484 q^{52} +10.4534 q^{53} +11.8871 q^{55} +2.53209 q^{56} -0.773318 q^{58} -5.00774 q^{59} +0.184793 q^{61} +0.674992 q^{62} -5.24897 q^{64} -11.0719 q^{65} -2.44831 q^{67} +1.53209 q^{70} -9.92127 q^{71} -10.9017 q^{73} -2.14290 q^{74} -0.652704 q^{76} -9.51754 q^{77} -4.43376 q^{79} -7.72462 q^{80} -1.79561 q^{82} -13.5817 q^{83} +0.512489 q^{86} -6.82295 q^{88} +6.32770 q^{89} +8.86484 q^{91} +3.33275 q^{92} -2.96316 q^{94} -0.815207 q^{95} -9.27631 q^{97} +1.20439 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 6 q^{5} + 3 q^{8}+O(q^{10}) $ 3 * q - 6 * q^5 + 3 * q^8	$ 3 q - 6 q^{5} + 3 q^{8} + 6 q^{10} - 6 q^{11} + 6 q^{13} - 3 q^{14} - 6 q^{16} + 3 q^{20} - 6 q^{22} - 12 q^{23} + 3 q^{25} + 12 q^{26} - 6 q^{28} + 9 q^{31} - 9 q^{32} - 3 q^{35} - 3 q^{37} - 6 q^{38} - 12 q^{40} - 6 q^{41} + 15 q^{43} + 6 q^{44} - 9 q^{46} + 21 q^{47} - 15 q^{49} - 21 q^{50} - 3 q^{52} + 18 q^{53} + 6 q^{55} + 3 q^{56} - 9 q^{58} + 9 q^{59} - 3 q^{61} - 3 q^{62} - 3 q^{64} - 9 q^{67} - 21 q^{71} - 21 q^{73} - 6 q^{74} - 3 q^{76} - 6 q^{77} + 3 q^{79} + 9 q^{80} - 6 q^{82} - 9 q^{83} - 6 q^{86} + 15 q^{89} + 3 q^{91} - 9 q^{92} + 3 q^{94} - 6 q^{95} + 6 q^{97} + 3 q^{98}+O(q^{100}) $ 3 * q - 6 * q^5 + 3 * q^8 + 6 * q^10 - 6 * q^11 + 6 * q^13 - 3 * q^14 - 6 * q^16 + 3 * q^20 - 6 * q^22 - 12 * q^23 + 3 * q^25 + 12 * q^26 - 6 * q^28 + 9 * q^31 - 9 * q^32 - 3 * q^35 - 3 * q^37 - 6 * q^38 - 12 * q^40 - 6 * q^41 + 15 * q^43 + 6 * q^44 - 9 * q^46 + 21 * q^47 - 15 * q^49 - 21 * q^50 - 3 * q^52 + 18 * q^53 + 6 * q^55 + 3 * q^56 - 9 * q^58 + 9 * q^59 - 3 * q^61 - 3 * q^62 - 3 * q^64 - 9 * q^67 - 21 * q^71 - 21 * q^73 - 6 * q^74 - 3 * q^76 - 6 * q^77 + 3 * q^79 + 9 * q^80 - 6 * q^82 - 9 * q^83 - 6 * q^86 + 15 * q^89 + 3 * q^91 - 9 * q^92 + 3 * q^94 - 6 * q^95 + 6 * q^97 + 3 * 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 $

$2$	−0.347296	−0.245576	−0.122788	−	0.992433i	$-0.539183\pi$
$2$	−0.347296	−0.245576	−0.122788	+	0.992433i	$0.539183\pi$
$3$	0	0
$3$	0	0
$4$	−1.87939	−0.939693
$5$	−2.34730	−1.04974	−0.524871	−	0.851182i	$-0.675887\pi$
$5$	−2.34730	−1.04974	−0.524871	+	0.851182i	$0.675887\pi$
$6$	0	0
$7$	1.87939	0.710341	0.355170	−	0.934802i	$-0.384423\pi$
$7$	1.87939	0.710341	0.355170	+	0.934802i	$0.384423\pi$
$8$	1.34730	0.476341
$9$	0	0
$10$	0.815207	0.257791
$11$	−5.06418	−1.52691	−0.763454	−	0.645863i	$-0.776498\pi$
$11$	−5.06418	−1.52691	−0.763454	+	0.645863i	$0.776498\pi$
$12$	0	0
$13$	4.71688	1.30823	0.654114	−	0.756396i	$-0.273042\pi$
$13$	4.71688	1.30823	0.654114	+	0.756396i	$0.273042\pi$
$14$	−0.652704	−0.174442
$15$	0	0
$16$	3.29086	0.822715
$17$	0	0
$17$	0	0
$18$	0	0
$19$	0.347296	0.0796752	0.0398376	−	0.999206i	$-0.487316\pi$
$19$	0.347296	0.0796752	0.0398376	+	0.999206i	$0.487316\pi$
$20$	4.41147	0.986436
$21$	0	0
$22$	1.75877	0.374971
$23$	−1.77332	−0.369762	−0.184881	−	0.982761i	$-0.559190\pi$
$23$	−1.77332	−0.369762	−0.184881	+	0.982761i	$0.559190\pi$
$24$	0	0
$25$	0.509800	0.101960
$26$	−1.63816	−0.321269
$27$	0	0
$28$	−3.53209	−0.667502
$29$	2.22668	0.413484	0.206742	−	0.978395i	$-0.433714\pi$
$29$	2.22668	0.413484	0.206742	+	0.978395i	$0.433714\pi$
$30$	0	0
$31$	−1.94356	−0.349074	−0.174537	−	0.984651i	$-0.555843\pi$
$31$	−1.94356	−0.349074	−0.174537	+	0.984651i	$0.555843\pi$
$32$	−3.83750	−0.678380
$33$	0	0
$34$	0	0
$35$	−4.41147	−0.745675
$36$	0	0
$37$	6.17024	1.01438	0.507191	−	0.861834i	$-0.330684\pi$
$37$	6.17024	1.01438	0.507191	+	0.861834i	$0.330684\pi$
$38$	−0.120615	−0.0195663
$39$	0	0
$40$	−3.16250	−0.500036
$41$	5.17024	0.807457	0.403728	−	0.914879i	$-0.367714\pi$
$41$	5.17024	0.807457	0.403728	+	0.914879i	$0.367714\pi$
$42$	0	0
$43$	−1.47565	−0.225035	−0.112517	−	0.993650i	$-0.535891\pi$
$43$	−1.47565	−0.225035	−0.112517	+	0.993650i	$0.535891\pi$
$44$	9.51754	1.43482
$45$	0	0
$46$	0.615867	0.0908046
$47$	8.53209	1.24453	0.622267	−	0.782805i	$-0.286212\pi$
$47$	8.53209	1.24453	0.622267	+	0.782805i	$0.286212\pi$
$48$	0	0
$49$	−3.46791	−0.495416
$50$	−0.177052	−0.0250389
$51$	0	0
$52$	−8.86484	−1.22933
$53$	10.4534	1.43588	0.717940	−	0.696105i	$-0.245085\pi$
$53$	10.4534	1.43588	0.717940	+	0.696105i	$0.245085\pi$
$54$	0	0
$55$	11.8871	1.60286
$56$	2.53209	0.338365
$57$	0	0
$58$	−0.773318	−0.101542
$59$	−5.00774	−0.651952	−0.325976	−	0.945378i	$-0.605693\pi$
$59$	−5.00774	−0.651952	−0.325976	+	0.945378i	$0.605693\pi$
$60$	0	0
$61$	0.184793	0.0236603	0.0118301	−	0.999930i	$-0.496234\pi$
$61$	0.184793	0.0236603	0.0118301	+	0.999930i	$0.496234\pi$
$62$	0.674992	0.0857241
$63$	0	0
$64$	−5.24897	−0.656121
$65$	−11.0719	−1.37330
$66$	0	0
$67$	−2.44831	−0.299109	−0.149554	−	0.988754i	$-0.547784\pi$
$67$	−2.44831	−0.299109	−0.149554	+	0.988754i	$0.547784\pi$
$68$	0	0
$69$	0	0
$70$	1.53209	0.183120
$71$	−9.92127	−1.17744	−0.588719	−	0.808338i	$-0.700368\pi$
$71$	−9.92127	−1.17744	−0.588719	+	0.808338i	$0.700368\pi$
$72$	0	0
$73$	−10.9017	−1.27594	−0.637972	−	0.770059i	$-0.720227\pi$
$73$	−10.9017	−1.27594	−0.637972	+	0.770059i	$0.720227\pi$
$74$	−2.14290	−0.249107
$75$	0	0
$76$	−0.652704	−0.0748702
$77$	−9.51754	−1.08462
$78$	0	0
$79$	−4.43376	−0.498837	−0.249419	−	0.968396i	$-0.580240\pi$
$79$	−4.43376	−0.498837	−0.249419	+	0.968396i	$0.580240\pi$
$80$	−7.72462	−0.863639
$81$	0	0
$82$	−1.79561	−0.198292
$83$	−13.5817	−1.49079	−0.745394	−	0.666625i	$-0.767738\pi$
$83$	−13.5817	−1.49079	−0.745394	+	0.666625i	$0.767738\pi$
$84$	0	0
$85$	0	0
$86$	0.512489	0.0552631
$87$	0	0
$88$	−6.82295	−0.727329
$89$	6.32770	0.670734	0.335367	−	0.942087i	$-0.391140\pi$
$89$	6.32770	0.670734	0.335367	+	0.942087i	$0.391140\pi$
$90$	0	0
$91$	8.86484	0.929287
$92$	3.33275	0.347463
$93$	0	0
$94$	−2.96316	−0.305627
$95$	−0.815207	−0.0836385
$96$	0	0
$97$	−9.27631	−0.941867	−0.470933	−	0.882169i	$-0.656083\pi$
$97$	−9.27631	−0.941867	−0.470933	+	0.882169i	$0.656083\pi$
$98$	1.20439	0.121662
$99$	0	0
$100$	−0.958111	−0.0958111
$101$	7.04963	0.701464	0.350732	−	0.936476i	$-0.385933\pi$
$101$	7.04963	0.701464	0.350732	+	0.936476i	$0.385933\pi$
$102$	0	0
$103$	5.29860	0.522087	0.261043	−	0.965327i	$-0.415933\pi$
$103$	5.29860	0.522087	0.261043	+	0.965327i	$0.415933\pi$
$104$	6.35504	0.623163
$105$	0	0
$106$	−3.63041	−0.352617
$107$	−15.5963	−1.50775	−0.753874	−	0.657019i	$-0.771817\pi$
$107$	−15.5963	−1.50775	−0.753874	+	0.657019i	$0.771817\pi$
$108$	0	0
$109$	−1.87164	−0.179271	−0.0896355	−	0.995975i	$-0.528570\pi$
$109$	−1.87164	−0.179271	−0.0896355	+	0.995975i	$0.528570\pi$
$110$	−4.12836	−0.393623
$111$	0	0
$112$	6.18479	0.584408
$113$	−12.1138	−1.13957	−0.569786	−	0.821793i	$-0.692974\pi$
$113$	−12.1138	−1.13957	−0.569786	+	0.821793i	$0.692974\pi$
$114$	0	0
$115$	4.16250	0.388155
$116$	−4.18479	−0.388548
$117$	0	0
$118$	1.73917	0.160104
$119$	0	0
$120$	0	0
$121$	14.6459	1.33145
$122$	−0.0641778	−0.00581038
$123$	0	0
$124$	3.65270	0.328022
$125$	10.5398	0.942711
$126$	0	0
$127$	−11.5398	−1.02399	−0.511997	−	0.858987i	$-0.671094\pi$
$127$	−11.5398	−1.02399	−0.511997	+	0.858987i	$0.671094\pi$
$128$	9.49794	0.839507
$129$	0	0
$130$	3.84524	0.337250
$131$	−19.3746	−1.69277	−0.846385	−	0.532572i	$-0.821226\pi$
$131$	−19.3746	−1.69277	−0.846385	+	0.532572i	$0.821226\pi$
$132$	0	0
$133$	0.652704	0.0565966
$134$	0.850289	0.0734538
$135$	0	0
$136$	0	0
$137$	0.448311	0.0383018	0.0191509	−	0.999817i	$-0.493904\pi$
$137$	0.448311	0.0383018	0.0191509	+	0.999817i	$0.493904\pi$
$138$	0	0
$139$	−11.6800	−0.990688	−0.495344	−	0.868697i	$-0.664958\pi$
$139$	−11.6800	−0.990688	−0.495344	+	0.868697i	$0.664958\pi$
$140$	8.29086	0.700706
$141$	0	0
$142$	3.44562	0.289150
$143$	−23.8871	−1.99754
$144$	0	0
$145$	−5.22668	−0.434052
$146$	3.78611	0.313341
$147$	0	0
$148$	−11.5963	−0.953207
$149$	−8.46791	−0.693718	−0.346859	−	0.937917i	$-0.612752\pi$
$149$	−8.46791	−0.693718	−0.346859	+	0.937917i	$0.612752\pi$
$150$	0	0
$151$	−13.7665	−1.12030	−0.560151	−	0.828390i	$-0.689257\pi$
$151$	−13.7665	−1.12030	−0.560151	+	0.828390i	$0.689257\pi$
$152$	0.467911	0.0379526
$153$	0	0
$154$	3.30541	0.266357
$155$	4.56212	0.366438
$156$	0	0
$157$	−17.9786	−1.43485	−0.717426	−	0.696635i	$-0.754680\pi$
$157$	−17.9786	−1.43485	−0.717426	+	0.696635i	$0.754680\pi$
$158$	1.53983	0.122502
$159$	0	0
$160$	9.00774	0.712124
$161$	−3.33275	−0.262657
$162$	0	0
$163$	7.23442	0.566644	0.283322	−	0.959025i	$-0.408564\pi$
$163$	7.23442	0.566644	0.283322	+	0.959025i	$0.408564\pi$
$164$	−9.71688	−0.758761
$165$	0	0
$166$	4.71688	0.366101
$167$	−5.10607	−0.395119	−0.197560	−	0.980291i	$-0.563302\pi$
$167$	−5.10607	−0.395119	−0.197560	+	0.980291i	$0.563302\pi$
$168$	0	0
$169$	9.24897	0.711459
$170$	0	0
$171$	0	0
$172$	2.77332	0.211464
$173$	12.8256	0.975115	0.487558	−	0.873091i	$-0.337888\pi$
$173$	12.8256	0.975115	0.487558	+	0.873091i	$0.337888\pi$
$174$	0	0
$175$	0.958111	0.0724264
$176$	−16.6655	−1.25621
$177$	0	0
$178$	−2.19759	−0.164716
$179$	−4.27126	−0.319249	−0.159624	−	0.987178i	$-0.551028\pi$
$179$	−4.27126	−0.319249	−0.159624	+	0.987178i	$0.551028\pi$
$180$	0	0
$181$	0.462859	0.0344040	0.0172020	−	0.999852i	$-0.494524\pi$
$181$	0.462859	0.0344040	0.0172020	+	0.999852i	$0.494524\pi$
$182$	−3.07873	−0.228210
$183$	0	0
$184$	−2.38919	−0.176133
$185$	−14.4834	−1.06484
$186$	0	0
$187$	0	0
$188$	−16.0351	−1.16948
$189$	0	0
$190$	0.283119	0.0205396
$191$	1.43107	0.103549	0.0517745	−	0.998659i	$-0.483512\pi$
$191$	1.43107	0.103549	0.0517745	+	0.998659i	$0.483512\pi$
$192$	0	0
$193$	−24.7246	−1.77972	−0.889859	−	0.456236i	$-0.849197\pi$
$193$	−24.7246	−1.77972	−0.889859	+	0.456236i	$0.849197\pi$
$194$	3.22163	0.231299
$195$	0	0
$196$	6.51754	0.465539
$197$	11.7615	0.837969	0.418985	−	0.907993i	$-0.362386\pi$
$197$	11.7615	0.837969	0.418985	+	0.907993i	$0.362386\pi$
$198$	0	0
$199$	20.5202	1.45464	0.727320	−	0.686298i	$-0.240766\pi$
$199$	20.5202	1.45464	0.727320	+	0.686298i	$0.240766\pi$
$200$	0.686852	0.0485678
$201$	0	0
$202$	−2.44831	−0.172263
$203$	4.18479	0.293715
$204$	0	0
$205$	−12.1361	−0.847622
$206$	−1.84018	−0.128212
$207$	0	0
$208$	15.5226	1.07630
$209$	−1.75877	−0.121657
$210$	0	0
$211$	−21.7178	−1.49512	−0.747558	−	0.664197i	$-0.768774\pi$
$211$	−21.7178	−1.49512	−0.747558	+	0.664197i	$0.768774\pi$
$212$	−19.6459	−1.34929
$213$	0	0
$214$	5.41653	0.370266
$215$	3.46379	0.236229
$216$	0	0
$217$	−3.65270	−0.247962
$218$	0.650015	0.0440246
$219$	0	0
$220$	−22.3405	−1.50620
$221$	0	0
$222$	0	0
$223$	−19.9513	−1.33604	−0.668019	−	0.744144i	$-0.732858\pi$
$223$	−19.9513	−1.33604	−0.668019	+	0.744144i	$0.732858\pi$
$224$	−7.21213	−0.481881
$225$	0	0
$226$	4.20708	0.279851
$227$	−4.22163	−0.280199	−0.140100	−	0.990137i	$-0.544742\pi$
$227$	−4.22163	−0.280199	−0.140100	+	0.990137i	$0.544742\pi$
$228$	0	0
$229$	14.5057	0.958562	0.479281	−	0.877661i	$-0.340897\pi$
$229$	14.5057	0.958562	0.479281	+	0.877661i	$0.340897\pi$
$230$	−1.44562	−0.0953215
$231$	0	0
$232$	3.00000	0.196960
$233$	5.12742	0.335909	0.167954	−	0.985795i	$-0.446284\pi$
$233$	5.12742	0.335909	0.167954	+	0.985795i	$0.446284\pi$
$234$	0	0
$235$	−20.0273	−1.30644
$236$	9.41147	0.612635
$237$	0	0
$238$	0	0
$239$	15.8503	1.02527	0.512635	−	0.858607i	$-0.328669\pi$
$239$	15.8503	1.02527	0.512635	+	0.858607i	$0.328669\pi$
$240$	0	0
$241$	18.1165	1.16699	0.583493	−	0.812118i	$-0.301686\pi$
$241$	18.1165	1.16699	0.583493	+	0.812118i	$0.301686\pi$
$242$	−5.08647	−0.326970
$243$	0	0
$244$	−0.347296	−0.0222334
$245$	8.14022	0.520059
$246$	0	0
$247$	1.63816	0.104233
$248$	−2.61856	−0.166278
$249$	0	0
$250$	−3.66044	−0.231507
$251$	29.6810	1.87345	0.936723	−	0.350070i	$-0.113842\pi$
$251$	29.6810	1.87345	0.936723	+	0.350070i	$0.113842\pi$
$252$	0	0
$253$	8.98040	0.564593
$254$	4.00774	0.251468
$255$	0	0
$256$	7.19934	0.449959
$257$	−7.39693	−0.461408	−0.230704	−	0.973024i	$-0.574103\pi$
$257$	−7.39693	−0.461408	−0.230704	+	0.973024i	$0.574103\pi$
$258$	0	0
$259$	11.5963	0.720557
$260$	20.8084	1.29048
$261$	0	0
$262$	6.72874	0.415703
$263$	23.1908	1.43000	0.715002	−	0.699122i	$-0.246426\pi$
$263$	23.1908	1.43000	0.715002	+	0.699122i	$0.246426\pi$
$264$	0	0
$265$	−24.5371	−1.50730
$266$	−0.226682	−0.0138987
$267$	0	0
$268$	4.60132	0.281070
$269$	−15.9067	−0.969850	−0.484925	−	0.874556i	$-0.661153\pi$
$269$	−15.9067	−0.969850	−0.484925	+	0.874556i	$0.661153\pi$
$270$	0	0
$271$	17.0000	1.03268	0.516338	−	0.856385i	$-0.327295\pi$
$271$	17.0000	1.03268	0.516338	+	0.856385i	$0.327295\pi$
$272$	0	0
$273$	0	0
$274$	−0.155697	−0.00940598
$275$	−2.58172	−0.155683
$276$	0	0
$277$	−16.8057	−1.00976	−0.504879	−	0.863190i	$-0.668463\pi$
$277$	−16.8057	−1.00976	−0.504879	+	0.863190i	$0.668463\pi$
$278$	4.05644	0.243289
$279$	0	0
$280$	−5.94356	−0.355196
$281$	−28.3209	−1.68948	−0.844741	−	0.535175i	$-0.820246\pi$
$281$	−28.3209	−1.68948	−0.844741	+	0.535175i	$0.820246\pi$
$282$	0	0
$283$	−32.2344	−1.91614	−0.958069	−	0.286538i	$-0.907495\pi$
$283$	−32.2344	−1.91614	−0.958069	+	0.286538i	$0.907495\pi$
$284$	18.6459	1.10643
$285$	0	0
$286$	8.29591	0.490548
$287$	9.71688	0.573569
$288$	0	0
$289$	0	0
$290$	1.81521	0.106593
$291$	0	0
$292$	20.4884	1.19900
$293$	−13.9709	−0.816189	−0.408094	−	0.912940i	$-0.633807\pi$
$293$	−13.9709	−0.816189	−0.408094	+	0.912940i	$0.633807\pi$
$294$	0	0
$295$	11.7547	0.684382
$296$	8.31315	0.483192
$297$	0	0
$298$	2.94087	0.170360
$299$	−8.36453	−0.483733
$300$	0	0
$301$	−2.77332	−0.159851
$302$	4.78106	0.275119
$303$	0	0
$304$	1.14290	0.0655500
$305$	−0.433763	−0.0248372
$306$	0	0
$307$	9.04963	0.516490	0.258245	−	0.966080i	$-0.416856\pi$
$307$	9.04963	0.516490	0.258245	+	0.966080i	$0.416856\pi$
$308$	17.8871	1.01921
$309$	0	0
$310$	−1.58441	−0.0899883
$311$	−2.34730	−0.133103	−0.0665515	−	0.997783i	$-0.521200\pi$
$311$	−2.34730	−0.133103	−0.0665515	+	0.997783i	$0.521200\pi$
$312$	0	0
$313$	15.1284	0.855105	0.427553	−	0.903990i	$-0.359376\pi$
$313$	15.1284	0.855105	0.427553	+	0.903990i	$0.359376\pi$
$314$	6.24392	0.352365
$315$	0	0
$316$	8.33275	0.468754
$317$	10.3378	0.580629	0.290314	−	0.956931i	$-0.406240\pi$
$317$	10.3378	0.580629	0.290314	+	0.956931i	$0.406240\pi$
$318$	0	0
$319$	−11.2763	−0.631352
$320$	12.3209	0.688759
$321$	0	0
$322$	1.15745	0.0645022
$323$	0	0
$324$	0	0
$325$	2.40467	0.133387
$326$	−2.51249	−0.139154
$327$	0	0
$328$	6.96585	0.384625
$329$	16.0351	0.884043
$330$	0	0
$331$	18.2567	1.00348	0.501740	−	0.865019i	$-0.332693\pi$
$331$	18.2567	1.00348	0.501740	+	0.865019i	$0.332693\pi$
$332$	25.5253	1.40088
$333$	0	0
$334$	1.77332	0.0970317
$335$	5.74691	0.313987
$336$	0	0
$337$	−16.4953	−0.898554	−0.449277	−	0.893393i	$-0.648318\pi$
$337$	−16.4953	−0.898554	−0.449277	+	0.893393i	$0.648318\pi$
$338$	−3.21213	−0.174717
$339$	0	0
$340$	0	0
$341$	9.84255	0.533004
$342$	0	0
$343$	−19.6732	−1.06225
$344$	−1.98814	−0.107193
$345$	0	0
$346$	−4.45430	−0.239464
$347$	20.5722	1.10437	0.552187	−	0.833720i	$-0.313793\pi$
$347$	20.5722	1.10437	0.552187	+	0.833720i	$0.313793\pi$
$348$	0	0
$349$	6.42427	0.343883	0.171942	−	0.985107i	$-0.444996\pi$
$349$	6.42427	0.343883	0.171942	+	0.985107i	$0.444996\pi$
$350$	−0.332748	−0.0177862
$351$	0	0
$352$	19.4338	1.03582
$353$	−27.1685	−1.44603	−0.723016	−	0.690831i	$-0.757245\pi$
$353$	−27.1685	−1.44603	−0.723016	+	0.690831i	$0.757245\pi$
$354$	0	0
$355$	23.2882	1.23601
$356$	−11.8922	−0.630284
$357$	0	0
$358$	1.48339	0.0783997
$359$	−16.8949	−0.891677	−0.445838	−	0.895113i	$-0.647094\pi$
$359$	−16.8949	−0.891677	−0.445838	+	0.895113i	$0.647094\pi$
$360$	0	0
$361$	−18.8794	−0.993652
$362$	−0.160749	−0.00844879
$363$	0	0
$364$	−16.6604	−0.873245
$365$	25.5895	1.33941
$366$	0	0
$367$	1.48751	0.0776475	0.0388237	−	0.999246i	$-0.487639\pi$
$367$	1.48751	0.0776475	0.0388237	+	0.999246i	$0.487639\pi$
$368$	−5.83574	−0.304209
$369$	0	0
$370$	5.03003	0.261499
$371$	19.6459	1.01996
$372$	0	0
$373$	−24.0496	−1.24524	−0.622621	−	0.782523i	$-0.713932\pi$
$373$	−24.0496	−1.24524	−0.622621	+	0.782523i	$0.713932\pi$
$374$	0	0
$375$	0	0
$376$	11.4953	0.592822
$377$	10.5030	0.540932
$378$	0	0
$379$	20.1976	1.03748	0.518740	−	0.854932i	$-0.326401\pi$
$379$	20.1976	1.03748	0.518740	+	0.854932i	$0.326401\pi$
$380$	1.53209	0.0785945
$381$	0	0
$382$	−0.497007	−0.0254291
$383$	8.52528	0.435622	0.217811	−	0.975991i	$-0.430108\pi$
$383$	8.52528	0.435622	0.217811	+	0.975991i	$0.430108\pi$
$384$	0	0
$385$	22.3405	1.13858
$386$	8.58677	0.437055
$387$	0	0
$388$	17.4338	0.885065
$389$	12.9162	0.654878	0.327439	−	0.944872i	$-0.393814\pi$
$389$	12.9162	0.654878	0.327439	+	0.944872i	$0.393814\pi$
$390$	0	0
$391$	0	0
$392$	−4.67230	−0.235987
$393$	0	0
$394$	−4.08471	−0.205785
$395$	10.4074	0.523651
$396$	0	0
$397$	24.2249	1.21581	0.607907	−	0.794008i	$-0.292009\pi$
$397$	24.2249	1.21581	0.607907	+	0.794008i	$0.292009\pi$
$398$	−7.12660	−0.357224
$399$	0	0
$400$	1.67768	0.0838840
$401$	−25.5371	−1.27526	−0.637632	−	0.770341i	$-0.720086\pi$
$401$	−25.5371	−1.27526	−0.637632	+	0.770341i	$0.720086\pi$
$402$	0	0
$403$	−9.16756	−0.456669
$404$	−13.2490	−0.659161
$405$	0	0
$406$	−1.45336	−0.0721292
$407$	−31.2472	−1.54887
$408$	0	0
$409$	10.3523	0.511891	0.255945	−	0.966691i	$-0.417613\pi$
$409$	10.3523	0.511891	0.255945	+	0.966691i	$0.417613\pi$
$410$	4.21482	0.208155
$411$	0	0
$412$	−9.95811	−0.490601
$413$	−9.41147	−0.463108
$414$	0	0
$415$	31.8803	1.56494
$416$	−18.1010	−0.887475
$417$	0	0
$418$	0.610815	0.0298759
$419$	−1.31315	−0.0641515	−0.0320757	−	0.999485i	$-0.510212\pi$
$419$	−1.31315	−0.0641515	−0.0320757	+	0.999485i	$0.510212\pi$
$420$	0	0
$421$	8.01548	0.390651	0.195325	−	0.980739i	$-0.437424\pi$
$421$	8.01548	0.390651	0.195325	+	0.980739i	$0.437424\pi$
$422$	7.54252	0.367164
$423$	0	0
$424$	14.0838	0.683969
$425$	0	0
$426$	0	0
$427$	0.347296	0.0168068
$428$	29.3114	1.41682
$429$	0	0
$430$	−1.20296	−0.0580120
$431$	−14.7270	−0.709374	−0.354687	−	0.934985i	$-0.615413\pi$
$431$	−14.7270	−0.709374	−0.354687	+	0.934985i	$0.615413\pi$
$432$	0	0
$433$	−8.24123	−0.396048	−0.198024	−	0.980197i	$-0.563452\pi$
$433$	−8.24123	−0.396048	−0.198024	+	0.980197i	$0.563452\pi$
$434$	1.26857	0.0608933
$435$	0	0
$436$	3.51754	0.168460
$437$	−0.615867	−0.0294609
$438$	0	0
$439$	39.9564	1.90701	0.953506	−	0.301373i	$-0.0974448\pi$
$439$	39.9564	1.90701	0.953506	+	0.301373i	$0.0974448\pi$
$440$	16.0155	0.763508
$441$	0	0
$442$	0	0
$443$	−13.9463	−0.662606	−0.331303	−	0.943524i	$-0.607488\pi$
$443$	−13.9463	−0.662606	−0.331303	+	0.943524i	$0.607488\pi$
$444$	0	0
$445$	−14.8530	−0.704099
$446$	6.92902	0.328098
$447$	0	0
$448$	−9.86484	−0.466070
$449$	−10.2317	−0.482865	−0.241433	−	0.970418i	$-0.577617\pi$
$449$	−10.2317	−0.482865	−0.241433	+	0.970418i	$0.577617\pi$
$450$	0	0
$451$	−26.1830	−1.23291
$452$	22.7665	1.07085
$453$	0	0
$454$	1.46616	0.0688101
$455$	−20.8084	−0.975513
$456$	0	0
$457$	−11.7706	−0.550607	−0.275303	−	0.961357i	$-0.588778\pi$
$457$	−11.7706	−0.550607	−0.275303	+	0.961357i	$0.588778\pi$
$458$	−5.03777	−0.235400
$459$	0	0
$460$	−7.82295	−0.364747
$461$	−19.5003	−0.908220	−0.454110	−	0.890946i	$-0.650043\pi$
$461$	−19.5003	−0.908220	−0.454110	+	0.890946i	$0.650043\pi$
$462$	0	0
$463$	−1.43107	−0.0665077	−0.0332538	−	0.999447i	$-0.510587\pi$
$463$	−1.43107	−0.0665077	−0.0332538	+	0.999447i	$0.510587\pi$
$464$	7.32770	0.340180
$465$	0	0
$466$	−1.78073	−0.0824910
$467$	10.6895	0.494653	0.247326	−	0.968932i	$-0.420448\pi$
$467$	10.6895	0.494653	0.247326	+	0.968932i	$0.420448\pi$
$468$	0	0
$469$	−4.60132	−0.212469
$470$	6.95542	0.320830
$471$	0	0
$472$	−6.74691	−0.310552
$473$	7.47296	0.343607
$474$	0	0
$475$	0.177052	0.00812369
$476$	0	0
$477$	0	0
$478$	−5.50475	−0.251781
$479$	−38.8675	−1.77590	−0.887951	−	0.459938i	$-0.847872\pi$
$479$	−38.8675	−1.77590	−0.887951	+	0.459938i	$0.847872\pi$
$480$	0	0
$481$	29.1043	1.32704
$482$	−6.29179	−0.286583
$483$	0	0
$484$	−27.5253	−1.25115
$485$	21.7743	0.988718
$486$	0	0
$487$	37.0137	1.67725	0.838626	−	0.544708i	$-0.183359\pi$
$487$	37.0137	1.67725	0.838626	+	0.544708i	$0.183359\pi$
$488$	0.248970	0.0112704
$489$	0	0
$490$	−2.82707	−0.127714
$491$	25.4175	1.14707	0.573537	−	0.819180i	$-0.305571\pi$
$491$	25.4175	1.14707	0.573537	+	0.819180i	$0.305571\pi$
$492$	0	0
$493$	0	0
$494$	−0.568926	−0.0255972
$495$	0	0
$496$	−6.39599	−0.287189
$497$	−18.6459	−0.836383
$498$	0	0
$499$	−21.8239	−0.976971	−0.488486	−	0.872572i	$-0.662451\pi$
$499$	−21.8239	−0.976971	−0.488486	+	0.872572i	$0.662451\pi$
$500$	−19.8084	−0.885859
$501$	0	0
$502$	−10.3081	−0.460073
$503$	−33.4371	−1.49088	−0.745442	−	0.666570i	$-0.767762\pi$
$503$	−33.4371	−1.49088	−0.745442	+	0.666570i	$0.767762\pi$
$504$	0	0
$505$	−16.5476	−0.736357
$506$	−3.11886	−0.138650
$507$	0	0
$508$	21.6878	0.962240
$509$	19.1530	0.848942	0.424471	−	0.905441i	$-0.360460\pi$
$509$	19.1530	0.848942	0.424471	+	0.905441i	$0.360460\pi$
$510$	0	0
$511$	−20.4884	−0.906355
$512$	−21.4962	−0.950006
$513$	0	0
$514$	2.56893	0.113310
$515$	−12.4374	−0.548057
$516$	0	0
$517$	−43.2080	−1.90029
$518$	−4.02734	−0.176951
$519$	0	0
$520$	−14.9172	−0.654161
$521$	35.5330	1.55673	0.778365	−	0.627812i	$-0.216049\pi$
$521$	35.5330	1.55673	0.778365	+	0.627812i	$0.216049\pi$
$522$	0	0
$523$	−11.8307	−0.517320	−0.258660	−	0.965968i	$-0.583281\pi$
$523$	−11.8307	−0.517320	−0.258660	+	0.965968i	$0.583281\pi$
$524$	36.4124	1.59068
$525$	0	0
$526$	−8.05407	−0.351174
$527$	0	0
$528$	0	0
$529$	−19.8553	−0.863276
$530$	8.52166	0.370157
$531$	0	0
$532$	−1.22668	−0.0531834
$533$	24.3874	1.05634
$534$	0	0
$535$	36.6091	1.58275
$536$	−3.29860	−0.142478
$537$	0	0
$538$	5.52435	0.238172
$539$	17.5621	0.756454
$540$	0	0
$541$	5.55850	0.238978	0.119489	−	0.992835i	$-0.461874\pi$
$541$	5.55850	0.238978	0.119489	+	0.992835i	$0.461874\pi$
$542$	−5.90404	−0.253600
$543$	0	0
$544$	0	0
$545$	4.39330	0.188188
$546$	0	0
$547$	5.02465	0.214839	0.107419	−	0.994214i	$-0.465741\pi$
$547$	5.02465	0.214839	0.107419	+	0.994214i	$0.465741\pi$
$548$	−0.842549	−0.0359919
$549$	0	0
$550$	0.896622	0.0382321
$551$	0.773318	0.0329445
$552$	0	0
$553$	−8.33275	−0.354345
$554$	5.83656	0.247972
$555$	0	0
$556$	21.9513	0.930943
$557$	−3.86659	−0.163833	−0.0819164	−	0.996639i	$-0.526104\pi$
$557$	−3.86659	−0.163833	−0.0819164	+	0.996639i	$0.526104\pi$
$558$	0	0
$559$	−6.96048	−0.294397
$560$	−14.5175	−0.613478
$561$	0	0
$562$	9.83574	0.414896
$563$	−28.8411	−1.21551	−0.607754	−	0.794125i	$-0.707929\pi$
$563$	−28.8411	−1.21551	−0.607754	+	0.794125i	$0.707929\pi$
$564$	0	0
$565$	28.4347	1.19626
$566$	11.1949	0.470557
$567$	0	0
$568$	−13.3669	−0.560863
$569$	−2.16157	−0.0906177	−0.0453089	−	0.998973i	$-0.514427\pi$
$569$	−2.16157	−0.0906177	−0.0453089	+	0.998973i	$0.514427\pi$
$570$	0	0
$571$	−5.71925	−0.239343	−0.119671	−	0.992814i	$-0.538184\pi$
$571$	−5.71925	−0.239343	−0.119671	+	0.992814i	$0.538184\pi$
$572$	44.8931	1.87708
$573$	0	0
$574$	−3.37464	−0.140855
$575$	−0.904038	−0.0377010
$576$	0	0
$577$	−10.8007	−0.449637	−0.224819	−	0.974401i	$-0.572179\pi$
$577$	−10.8007	−0.449637	−0.224819	+	0.974401i	$0.572179\pi$
$578$	0	0
$579$	0	0
$580$	9.82295	0.407876
$581$	−25.5253	−1.05897
$582$	0	0
$583$	−52.9377	−2.19246
$584$	−14.6878	−0.607785
$585$	0	0
$586$	4.85204	0.200436
$587$	−20.8188	−0.859285	−0.429643	−	0.902999i	$-0.641360\pi$
$587$	−20.8188	−0.859285	−0.429643	+	0.902999i	$0.641360\pi$
$588$	0	0
$589$	−0.674992	−0.0278126
$590$	−4.08235	−0.168068
$591$	0	0
$592$	20.3054	0.834547
$593$	−20.6313	−0.847228	−0.423614	−	0.905843i	$-0.639239\pi$
$593$	−20.6313	−0.847228	−0.423614	+	0.905843i	$0.639239\pi$
$594$	0	0
$595$	0	0
$596$	15.9145	0.651882
$597$	0	0
$598$	2.90497	0.118793
$599$	−31.8212	−1.30018	−0.650089	−	0.759858i	$-0.725269\pi$
$599$	−31.8212	−1.30018	−0.650089	+	0.759858i	$0.725269\pi$
$600$	0	0
$601$	48.1174	1.96275	0.981375	−	0.192100i	$-0.0615296\pi$
$601$	48.1174	1.96275	0.981375	+	0.192100i	$0.0615296\pi$
$602$	0.963163	0.0392556
$603$	0	0
$604$	25.8726	1.05274
$605$	−34.3783	−1.39768
$606$	0	0
$607$	−15.4757	−0.628137	−0.314069	−	0.949400i	$-0.601692\pi$
$607$	−15.4757	−0.628137	−0.314069	+	0.949400i	$0.601692\pi$
$608$	−1.33275	−0.0540501
$609$	0	0
$610$	0.150644	0.00609941
$611$	40.2449	1.62813
$612$	0	0
$613$	−5.04963	−0.203953	−0.101976	−	0.994787i	$-0.532517\pi$
$613$	−5.04963	−0.203953	−0.101976	+	0.994787i	$0.532517\pi$
$614$	−3.14290	−0.126837
$615$	0	0
$616$	−12.8229	−0.516651
$617$	27.6064	1.11139	0.555695	−	0.831386i	$-0.312452\pi$
$617$	27.6064	1.11139	0.555695	+	0.831386i	$0.312452\pi$
$618$	0	0
$619$	14.8331	0.596191	0.298095	−	0.954536i	$-0.403649\pi$
$619$	14.8331	0.596191	0.298095	+	0.954536i	$0.403649\pi$
$620$	−8.57398	−0.344339
$621$	0	0
$622$	0.815207	0.0326868
$623$	11.8922	0.476450
$624$	0	0
$625$	−27.2891	−1.09156
$626$	−5.25402	−0.209993
$627$	0	0
$628$	33.7888	1.34832
$629$	0	0
$630$	0	0
$631$	−34.0506	−1.35553	−0.677766	−	0.735278i	$-0.737052\pi$
$631$	−34.0506	−1.35553	−0.677766	+	0.735278i	$0.737052\pi$
$632$	−5.97359	−0.237617
$633$	0	0
$634$	−3.59028	−0.142588
$635$	27.0874	1.07493
$636$	0	0
$637$	−16.3577	−0.648117
$638$	3.91622	0.155045
$639$	0	0
$640$	−22.2945	−0.881267
$641$	15.0232	0.593382	0.296691	−	0.954974i	$-0.404117\pi$
$641$	15.0232	0.593382	0.296691	+	0.954974i	$0.404117\pi$
$642$	0	0
$643$	−17.7980	−0.701883	−0.350942	−	0.936397i	$-0.614138\pi$
$643$	−17.7980	−0.701883	−0.350942	+	0.936397i	$0.614138\pi$
$644$	6.26352	0.246817
$645$	0	0
$646$	0	0
$647$	46.4971	1.82799	0.913995	−	0.405725i	$-0.132981\pi$
$647$	46.4971	1.82799	0.913995	+	0.405725i	$0.132981\pi$
$648$	0	0
$649$	25.3601	0.995471
$650$	−0.835132	−0.0327566
$651$	0	0
$652$	−13.5963	−0.532471
$653$	−30.5303	−1.19474	−0.597372	−	0.801964i	$-0.703788\pi$
$653$	−30.5303	−1.19474	−0.597372	+	0.801964i	$0.703788\pi$
$654$	0	0
$655$	45.4780	1.77697
$656$	17.0145	0.664306
$657$	0	0
$658$	−5.56893	−0.217099
$659$	9.83481	0.383110	0.191555	−	0.981482i	$-0.438647\pi$
$659$	9.83481	0.383110	0.191555	+	0.981482i	$0.438647\pi$
$660$	0	0
$661$	12.4361	0.483709	0.241855	−	0.970312i	$-0.422244\pi$
$661$	12.4361	0.483709	0.241855	+	0.970312i	$0.422244\pi$
$662$	−6.34049	−0.246430
$663$	0	0
$664$	−18.2986	−0.710123
$665$	−1.53209	−0.0594119
$666$	0	0
$667$	−3.94862	−0.152891
$668$	9.59627	0.371291
$669$	0	0
$670$	−1.99588	−0.0771076
$671$	−0.935822	−0.0361270
$672$	0	0
$673$	−12.6117	−0.486147	−0.243074	−	0.970008i	$-0.578156\pi$
$673$	−12.6117	−0.486147	−0.243074	+	0.970008i	$0.578156\pi$
$674$	5.72874	0.220663
$675$	0	0
$676$	−17.3824	−0.668553
$677$	4.54900	0.174832	0.0874162	−	0.996172i	$-0.472139\pi$
$677$	4.54900	0.174832	0.0874162	+	0.996172i	$0.472139\pi$
$678$	0	0
$679$	−17.4338	−0.669046
$680$	0	0
$681$	0	0
$682$	−3.41828	−0.130893
$683$	−4.86753	−0.186251	−0.0931253	−	0.995654i	$-0.529686\pi$
$683$	−4.86753	−0.186251	−0.0931253	+	0.995654i	$0.529686\pi$
$684$	0	0
$685$	−1.05232	−0.0402070
$686$	6.83244	0.260864
$687$	0	0
$688$	−4.85616	−0.185139
$689$	49.3073	1.87846
$690$	0	0
$691$	5.51661	0.209862	0.104931	−	0.994480i	$-0.466538\pi$
$691$	5.51661	0.209862	0.104931	+	0.994480i	$0.466538\pi$
$692$	−24.1043	−0.916308
$693$	0	0
$694$	−7.14466	−0.271208
$695$	27.4165	1.03997
$696$	0	0
$697$	0	0
$698$	−2.23112	−0.0844493
$699$	0	0
$700$	−1.80066	−0.0680585
$701$	−22.3233	−0.843138	−0.421569	−	0.906796i	$-0.638520\pi$
$701$	−22.3233	−0.843138	−0.421569	+	0.906796i	$0.638520\pi$
$702$	0	0
$703$	2.14290	0.0808211
$704$	26.5817	1.00184
$705$	0	0
$706$	9.43552	0.355110
$707$	13.2490	0.498279
$708$	0	0
$709$	34.7766	1.30606	0.653032	−	0.757331i	$-0.273497\pi$
$709$	34.7766	1.30606	0.653032	+	0.757331i	$0.273497\pi$
$710$	−8.08790	−0.303533
$711$	0	0
$712$	8.52528	0.319498
$713$	3.44656	0.129075
$714$	0	0
$715$	56.0702	2.09691
$716$	8.02734	0.299996
$717$	0	0
$718$	5.86753	0.218974
$719$	4.24990	0.158495	0.0792473	−	0.996855i	$-0.474748\pi$
$719$	4.24990	0.158495	0.0792473	+	0.996855i	$0.474748\pi$
$720$	0	0
$721$	9.95811	0.370859
$722$	6.55674	0.244017
$723$	0	0
$724$	−0.869890	−0.0323292
$725$	1.13516	0.0421589
$726$	0	0
$727$	29.1644	1.08165	0.540823	−	0.841136i	$-0.318113\pi$
$727$	29.1644	1.08165	0.540823	+	0.841136i	$0.318113\pi$
$728$	11.9436	0.442658
$729$	0	0
$730$	−8.88713	−0.328927
$731$	0	0
$732$	0	0
$733$	−0.502993	−0.0185785	−0.00928924	−	0.999957i	$-0.502957\pi$
$733$	−0.502993	−0.0185785	−0.00928924	+	0.999957i	$0.502957\pi$
$734$	−0.516607	−0.0190683
$735$	0	0
$736$	6.80510	0.250839
$737$	12.3987	0.456711
$738$	0	0
$739$	14.9581	0.550243	0.275122	−	0.961409i	$-0.411282\pi$
$739$	14.9581	0.550243	0.275122	+	0.961409i	$0.411282\pi$
$740$	27.2199	1.00062
$741$	0	0
$742$	−6.82295	−0.250478
$743$	23.3756	0.857567	0.428783	−	0.903407i	$-0.358942\pi$
$743$	23.3756	0.857567	0.428783	+	0.903407i	$0.358942\pi$
$744$	0	0
$745$	19.8767	0.728226
$746$	8.35235	0.305801
$747$	0	0
$748$	0	0
$749$	−29.3114	−1.07102
$750$	0	0
$751$	−17.0291	−0.621401	−0.310700	−	0.950508i	$-0.600564\pi$
$751$	−17.0291	−0.621401	−0.310700	+	0.950508i	$0.600564\pi$
$752$	28.0779	1.02390
$753$	0	0
$754$	−3.64765	−0.132840
$755$	32.3141	1.17603
$756$	0	0
$757$	16.3746	0.595146	0.297573	−	0.954699i	$-0.403823\pi$
$757$	16.3746	0.595146	0.297573	+	0.954699i	$0.403823\pi$
$758$	−7.01455	−0.254780
$759$	0	0
$760$	−1.09833	−0.0398405
$761$	18.8803	0.684411	0.342206	−	0.939625i	$-0.388826\pi$
$761$	18.8803	0.684411	0.342206	+	0.939625i	$0.388826\pi$
$762$	0	0
$763$	−3.51754	−0.127344
$764$	−2.68954	−0.0973042
$765$	0	0
$766$	−2.96080	−0.106978
$767$	−23.6209	−0.852902
$768$	0	0
$769$	−27.4766	−0.990831	−0.495416	−	0.868656i	$-0.664984\pi$
$769$	−27.4766	−0.990831	−0.495416	+	0.868656i	$0.664984\pi$
$770$	−7.75877	−0.279607
$771$	0	0
$772$	46.4671	1.67239
$773$	−9.90436	−0.356235	−0.178118	−	0.984009i	$-0.557001\pi$
$773$	−9.90436	−0.356235	−0.178118	+	0.984009i	$0.557001\pi$
$774$	0	0
$775$	−0.990829	−0.0355916
$776$	−12.4979	−0.448650
$777$	0	0
$778$	−4.48576	−0.160822
$779$	1.79561	0.0643343
$780$	0	0
$781$	50.2431	1.79784
$782$	0	0
$783$	0	0
$784$	−11.4124	−0.407586
$785$	42.2012	1.50623
$786$	0	0
$787$	50.8444	1.81241	0.906204	−	0.422841i	$-0.138967\pi$
$787$	50.8444	1.81241	0.906204	+	0.422841i	$0.138967\pi$
$788$	−22.1043	−0.787434
$789$	0	0
$790$	−3.61444	−0.128596
$791$	−22.7665	−0.809484
$792$	0	0
$793$	0.871644	0.0309530
$794$	−8.41323	−0.298574
$795$	0	0
$796$	−38.5654	−1.36691
$797$	−5.38650	−0.190800	−0.0953998	−	0.995439i	$-0.530413\pi$
$797$	−5.38650	−0.190800	−0.0953998	+	0.995439i	$0.530413\pi$
$798$	0	0
$799$	0	0
$800$	−1.95636	−0.0691676
$801$	0	0
$802$	8.86896	0.313174
$803$	55.2080	1.94825
$804$	0	0
$805$	7.82295	0.275723
$806$	3.18386	0.112147
$807$	0	0
$808$	9.49794	0.334136
$809$	−48.6819	−1.71156	−0.855782	−	0.517336i	$-0.826924\pi$
$809$	−48.6819	−1.71156	−0.855782	+	0.517336i	$0.826924\pi$
$810$	0	0
$811$	−15.9281	−0.559311	−0.279655	−	0.960100i	$-0.590220\pi$
$811$	−15.9281	−0.559311	−0.279655	+	0.960100i	$0.590220\pi$
$812$	−7.86484	−0.276002
$813$	0	0
$814$	10.8520	0.380364
$815$	−16.9813	−0.594830
$816$	0	0
$817$	−0.512489	−0.0179297
$818$	−3.59533	−0.125708
$819$	0	0
$820$	22.8084	0.796504
$821$	17.1010	0.596830	0.298415	−	0.954436i	$-0.403542\pi$
$821$	17.1010	0.596830	0.298415	+	0.954436i	$0.403542\pi$
$822$	0	0
$823$	−5.62267	−0.195994	−0.0979971	−	0.995187i	$-0.531244\pi$
$823$	−5.62267	−0.195994	−0.0979971	+	0.995187i	$0.531244\pi$
$824$	7.13878	0.248691
$825$	0	0
$826$	3.26857	0.113728
$827$	−17.8607	−0.621078	−0.310539	−	0.950561i	$-0.600510\pi$
$827$	−17.8607	−0.621078	−0.310539	+	0.950561i	$0.600510\pi$
$828$	0	0
$829$	35.8161	1.24395	0.621973	−	0.783039i	$-0.286331\pi$
$829$	35.8161	1.24395	0.621973	+	0.783039i	$0.286331\pi$
$830$	−11.0719	−0.384312
$831$	0	0
$832$	−24.7588	−0.858356
$833$	0	0
$834$	0	0
$835$	11.9855	0.414774
$836$	3.30541	0.114320
$837$	0	0
$838$	0.456052	0.0157540
$839$	−35.7733	−1.23503	−0.617516	−	0.786558i	$-0.711861\pi$
$839$	−35.7733	−1.23503	−0.617516	+	0.786558i	$0.711861\pi$
$840$	0	0
$841$	−24.0419	−0.829031
$842$	−2.78375	−0.0959343
$843$	0	0
$844$	40.8161	1.40495
$845$	−21.7101	−0.746849
$846$	0	0
$847$	27.5253	0.945780
$848$	34.4005	1.18132
$849$	0	0
$850$	0	0
$851$	−10.9418	−0.375080
$852$	0	0
$853$	11.0669	0.378922	0.189461	−	0.981888i	$-0.439326\pi$
$853$	11.0669	0.378922	0.189461	+	0.981888i	$0.439326\pi$
$854$	−0.120615	−0.00412735
$855$	0	0
$856$	−21.0128	−0.718202
$857$	−27.0746	−0.924851	−0.462425	−	0.886658i	$-0.653021\pi$
$857$	−27.0746	−0.924851	−0.462425	+	0.886658i	$0.653021\pi$
$858$	0	0
$859$	−51.7279	−1.76493	−0.882467	−	0.470374i	$-0.844119\pi$
$859$	−51.7279	−1.76493	−0.882467	+	0.470374i	$0.844119\pi$
$860$	−6.50980	−0.221982
$861$	0	0
$862$	5.11463	0.174205
$863$	−45.4712	−1.54786	−0.773929	−	0.633272i	$-0.781711\pi$
$863$	−45.4712	−1.54786	−0.773929	+	0.633272i	$0.781711\pi$
$864$	0	0
$865$	−30.1056	−1.02362
$866$	2.86215	0.0972598
$867$	0	0
$868$	6.86484	0.233008
$869$	22.4534	0.761678
$870$	0	0
$871$	−11.5484	−0.391302
$872$	−2.52166	−0.0853942
$873$	0	0
$874$	0.213888	0.00723488
$875$	19.8084	0.669646
$876$	0	0
$877$	37.4834	1.26572	0.632862	−	0.774265i	$-0.281880\pi$
$877$	37.4834	1.26572	0.632862	+	0.774265i	$0.281880\pi$
$878$	−13.8767	−0.468316
$879$	0	0
$880$	39.1189	1.31870
$881$	18.1958	0.613033	0.306517	−	0.951865i	$-0.400837\pi$
$881$	18.1958	0.613033	0.306517	+	0.951865i	$0.400837\pi$
$882$	0	0
$883$	0.397860	0.0133891	0.00669453	−	0.999978i	$-0.497869\pi$
$883$	0.397860	0.0133891	0.00669453	+	0.999978i	$0.497869\pi$
$884$	0	0
$885$	0	0
$886$	4.84348	0.162720
$887$	23.7834	0.798569	0.399285	−	0.916827i	$-0.369259\pi$
$887$	23.7834	0.798569	0.399285	+	0.916827i	$0.369259\pi$
$888$	0	0
$889$	−21.6878	−0.727385
$890$	5.15839	0.172909
$891$	0	0
$892$	37.4962	1.25547
$893$	2.96316	0.0991585
$894$	0	0
$895$	10.0259	0.335129
$896$	17.8503	0.596336
$897$	0	0
$898$	3.55344	0.118580
$899$	−4.32770	−0.144337
$900$	0	0
$901$	0	0
$902$	9.09327	0.302773
$903$	0	0
$904$	−16.3209	−0.542825
$905$	−1.08647	−0.0361154
$906$	0	0
$907$	−37.5212	−1.24587	−0.622935	−	0.782274i	$-0.714060\pi$
$907$	−37.5212	−1.24587	−0.622935	+	0.782274i	$0.714060\pi$
$908$	7.93407	0.263301
$909$	0	0
$910$	7.22668	0.239562
$911$	14.7648	0.489178	0.244589	−	0.969627i	$-0.421347\pi$
$911$	14.7648	0.489178	0.244589	+	0.969627i	$0.421347\pi$
$912$	0	0
$913$	68.7802	2.27629
$914$	4.08790	0.135216
$915$	0	0
$916$	−27.2618	−0.900754
$917$	−36.4124	−1.20244
$918$	0	0
$919$	−48.5476	−1.60144	−0.800718	−	0.599041i	$-0.795549\pi$
$919$	−48.5476	−1.60144	−0.800718	+	0.599041i	$0.795549\pi$
$920$	5.60813	0.184894
$921$	0	0
$922$	6.77238	0.223037
$923$	−46.7975	−1.54036
$924$	0	0
$925$	3.14559	0.103426
$926$	0.497007	0.0163327
$927$	0	0
$928$	−8.54488	−0.280499
$929$	−11.2635	−0.369544	−0.184772	−	0.982781i	$-0.559155\pi$
$929$	−11.2635	−0.369544	−0.184772	+	0.982781i	$0.559155\pi$
$930$	0	0
$931$	−1.20439	−0.0394724
$932$	−9.63640	−0.315651
$933$	0	0
$934$	−3.71244	−0.121475
$935$	0	0
$936$	0	0
$937$	2.39775	0.0783310	0.0391655	−	0.999233i	$-0.487530\pi$
$937$	2.39775	0.0783310	0.0391655	+	0.999233i	$0.487530\pi$
$938$	1.59802	0.0521772
$939$	0	0
$940$	37.6391	1.22765
$941$	34.3797	1.12075	0.560373	−	0.828240i	$-0.310658\pi$
$941$	34.3797	1.12075	0.560373	+	0.828240i	$0.310658\pi$
$942$	0	0
$943$	−9.16849	−0.298567
$944$	−16.4798	−0.536371
$945$	0	0
$946$	−2.59533	−0.0843816
$947$	20.5294	0.667116	0.333558	−	0.942730i	$-0.391751\pi$
$947$	20.5294	0.667116	0.333558	+	0.942730i	$0.391751\pi$
$948$	0	0
$949$	−51.4219	−1.66923
$950$	−0.0614894	−0.00199498
$951$	0	0
$952$	0	0
$953$	−16.5517	−0.536162	−0.268081	−	0.963396i	$-0.586389\pi$
$953$	−16.5517	−0.536162	−0.268081	+	0.963396i	$0.586389\pi$
$954$	0	0
$955$	−3.35916	−0.108700
$956$	−29.7888	−0.963439
$957$	0	0
$958$	13.4986	0.436118
$959$	0.842549	0.0272073
$960$	0	0
$961$	−27.2226	−0.878147
$962$	−10.1078	−0.325889
$963$	0	0
$964$	−34.0479	−1.09661
$965$	58.0360	1.86825
$966$	0	0
$967$	3.92665	0.126273	0.0631363	−	0.998005i	$-0.479890\pi$
$967$	3.92665	0.126273	0.0631363	+	0.998005i	$0.479890\pi$
$968$	19.7324	0.634222
$969$	0	0
$970$	−7.56212	−0.242805
$971$	4.25402	0.136518	0.0682590	−	0.997668i	$-0.478256\pi$
$971$	4.25402	0.136518	0.0682590	+	0.997668i	$0.478256\pi$
$972$	0	0
$973$	−21.9513	−0.703726
$974$	−12.8547	−0.411892
$975$	0	0
$976$	0.608126	0.0194656
$977$	48.5431	1.55303	0.776516	−	0.630097i	$-0.216985\pi$
$977$	48.5431	1.55303	0.776516	+	0.630097i	$0.216985\pi$
$978$	0	0
$979$	−32.0446	−1.02415
$980$	−15.2986	−0.488696
$981$	0	0
$982$	−8.82739	−0.281693
$983$	−35.0597	−1.11823	−0.559116	−	0.829089i	$-0.688859\pi$
$983$	−35.0597	−1.11823	−0.559116	+	0.829089i	$0.688859\pi$
$984$	0	0
$985$	−27.6076	−0.879652
$986$	0	0
$987$	0	0
$988$	−3.07873	−0.0979473
$989$	2.61680	0.0832094
$990$	0	0
$991$	−53.1995	−1.68994	−0.844968	−	0.534817i	$-0.820381\pi$
$991$	−53.1995	−1.68994	−0.844968	+	0.534817i	$0.820381\pi$
$992$	7.45842	0.236805
$993$	0	0
$994$	6.47565	0.205395
$995$	−48.1671	−1.52700
$996$	0	0
$997$	−22.5794	−0.715095	−0.357548	−	0.933895i	$-0.616387\pi$
$997$	−22.5794	−0.715095	−0.357548	+	0.933895i	$0.616387\pi$
$998$	7.57935	0.239920
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2601.2.a.w.1.2		3
3.2	odd	2		289.2.a.e.1.2	yes	3
12.11	even	2		4624.2.a.bd.1.3		3
15.14	odd	2		7225.2.a.s.1.2		3
17.16	even	2		2601.2.a.x.1.2		3
51.2	odd	8		289.2.c.d.38.3		12
51.5	even	16		289.2.d.f.110.4		24
51.8	odd	8		289.2.c.d.251.4		12
51.11	even	16		289.2.d.f.155.4		24
51.14	even	16		289.2.d.f.179.4		24
51.20	even	16		289.2.d.f.179.3		24
51.23	even	16		289.2.d.f.155.3		24
51.26	odd	8		289.2.c.d.251.3		12
51.29	even	16		289.2.d.f.110.3		24
51.32	odd	8		289.2.c.d.38.4		12
51.38	odd	4		289.2.b.d.288.4		6
51.41	even	16		289.2.d.f.134.4		24
51.44	even	16		289.2.d.f.134.3		24
51.47	odd	4		289.2.b.d.288.3		6
51.50	odd	2		289.2.a.d.1.2	✓	3
204.203	even	2		4624.2.a.bg.1.1		3
255.254	odd	2		7225.2.a.t.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.2.a.d.1.2	✓	3	51.50	odd	2
289.2.a.e.1.2	yes	3	3.2	odd	2
289.2.b.d.288.3		6	51.47	odd	4
289.2.b.d.288.4		6	51.38	odd	4
289.2.c.d.38.3		12	51.2	odd	8
289.2.c.d.38.4		12	51.32	odd	8
289.2.c.d.251.3		12	51.26	odd	8
289.2.c.d.251.4		12	51.8	odd	8
289.2.d.f.110.3		24	51.29	even	16
289.2.d.f.110.4		24	51.5	even	16
289.2.d.f.134.3		24	51.44	even	16
289.2.d.f.134.4		24	51.41	even	16
289.2.d.f.155.3		24	51.23	even	16
289.2.d.f.155.4		24	51.11	even	16
289.2.d.f.179.3		24	51.20	even	16
289.2.d.f.179.4		24	51.14	even	16
2601.2.a.w.1.2		3	1.1	even	1	trivial
2601.2.a.x.1.2		3	17.16	even	2
4624.2.a.bd.1.3		3	12.11	even	2
4624.2.a.bg.1.1		3	204.203	even	2
7225.2.a.s.1.2		3	15.14	odd	2
7225.2.a.t.1.2		3	255.254	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-0.347296 q^{2} -1.87939 q^{4} -2.34730 q^{5} +1.87939 q^{7} +1.34730 q^{8} +O(q^{10})\)	\(q-0.347296 q^{2} -1.87939 q^{4} -2.34730 q^{5} +1.87939 q^{7} +1.34730 q^{8} +0.815207 q^{10} -5.06418 q^{11} +4.71688 q^{13} -0.652704 q^{14} +3.29086 q^{16} +0.347296 q^{19} +4.41147 q^{20} +1.75877 q^{22} -1.77332 q^{23} +0.509800 q^{25} -1.63816 q^{26} -3.53209 q^{28} +2.22668 q^{29} -1.94356 q^{31} -3.83750 q^{32} -4.41147 q^{35} +6.17024 q^{37} -0.120615 q^{38} -3.16250 q^{40} +5.17024 q^{41} -1.47565 q^{43} +9.51754 q^{44} +0.615867 q^{46} +8.53209 q^{47} -3.46791 q^{49} -0.177052 q^{50} -8.86484 q^{52} +10.4534 q^{53} +11.8871 q^{55} +2.53209 q^{56} -0.773318 q^{58} -5.00774 q^{59} +0.184793 q^{61} +0.674992 q^{62} -5.24897 q^{64} -11.0719 q^{65} -2.44831 q^{67} +1.53209 q^{70} -9.92127 q^{71} -10.9017 q^{73} -2.14290 q^{74} -0.652704 q^{76} -9.51754 q^{77} -4.43376 q^{79} -7.72462 q^{80} -1.79561 q^{82} -13.5817 q^{83} +0.512489 q^{86} -6.82295 q^{88} +6.32770 q^{89} +8.86484 q^{91} +3.33275 q^{92} -2.96316 q^{94} -0.815207 q^{95} -9.27631 q^{97} +1.20439 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 6 q^{5} + 3 q^{8}+O(q^{10}) \) 3 * q - 6 * q^5 + 3 * q^8	\( 3 q - 6 q^{5} + 3 q^{8} + 6 q^{10} - 6 q^{11} + 6 q^{13} - 3 q^{14} - 6 q^{16} + 3 q^{20} - 6 q^{22} - 12 q^{23} + 3 q^{25} + 12 q^{26} - 6 q^{28} + 9 q^{31} - 9 q^{32} - 3 q^{35} - 3 q^{37} - 6 q^{38} - 12 q^{40} - 6 q^{41} + 15 q^{43} + 6 q^{44} - 9 q^{46} + 21 q^{47} - 15 q^{49} - 21 q^{50} - 3 q^{52} + 18 q^{53} + 6 q^{55} + 3 q^{56} - 9 q^{58} + 9 q^{59} - 3 q^{61} - 3 q^{62} - 3 q^{64} - 9 q^{67} - 21 q^{71} - 21 q^{73} - 6 q^{74} - 3 q^{76} - 6 q^{77} + 3 q^{79} + 9 q^{80} - 6 q^{82} - 9 q^{83} - 6 q^{86} + 15 q^{89} + 3 q^{91} - 9 q^{92} + 3 q^{94} - 6 q^{95} + 6 q^{97} + 3 q^{98}+O(q^{100}) \) 3 * q - 6 * q^5 + 3 * q^8 + 6 * q^10 - 6 * q^11 + 6 * q^13 - 3 * q^14 - 6 * q^16 + 3 * q^20 - 6 * q^22 - 12 * q^23 + 3 * q^25 + 12 * q^26 - 6 * q^28 + 9 * q^31 - 9 * q^32 - 3 * q^35 - 3 * q^37 - 6 * q^38 - 12 * q^40 - 6 * q^41 + 15 * q^43 + 6 * q^44 - 9 * q^46 + 21 * q^47 - 15 * q^49 - 21 * q^50 - 3 * q^52 + 18 * q^53 + 6 * q^55 + 3 * q^56 - 9 * q^58 + 9 * q^59 - 3 * q^61 - 3 * q^62 - 3 * q^64 - 9 * q^67 - 21 * q^71 - 21 * q^73 - 6 * q^74 - 3 * q^76 - 6 * q^77 + 3 * q^79 + 9 * q^80 - 6 * q^82 - 9 * q^83 - 6 * q^86 + 15 * q^89 + 3 * q^91 - 9 * q^92 + 3 * q^94 - 6 * q^95 + 6 * q^97 + 3 * q^98

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