LMFDB - Embedded newform 2601.2.a.x.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("2601.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$20.7690895657$
Analytic rank:	$0$
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			1.3
Root			$1.87939$ 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)

$f(q)$	$=$	$q+1.87939 q^{2} +1.53209 q^{4} +0.120615 q^{5} +1.53209 q^{7} -0.879385 q^{8} +O(q^{10})$	$q+1.87939 q^{2} +1.53209 q^{4} +0.120615 q^{5} +1.53209 q^{7} -0.879385 q^{8} +0.226682 q^{10} +2.69459 q^{11} +4.57398 q^{13} +2.87939 q^{14} -4.71688 q^{16} -1.87939 q^{19} +0.184793 q^{20} +5.06418 q^{22} +7.41147 q^{23} -4.98545 q^{25} +8.59627 q^{26} +2.34730 q^{28} +3.41147 q^{29} -3.83750 q^{31} -7.10607 q^{32} +0.184793 q^{35} +5.24897 q^{37} -3.53209 q^{38} -0.106067 q^{40} +6.24897 q^{41} +5.49020 q^{43} +4.12836 q^{44} +13.9290 q^{46} +7.34730 q^{47} -4.65270 q^{49} -9.36959 q^{50} +7.00774 q^{52} -0.822948 q^{53} +0.325008 q^{55} -1.34730 q^{56} +6.41147 q^{58} +3.14290 q^{59} -1.22668 q^{61} -7.21213 q^{62} -3.92127 q^{64} +0.551689 q^{65} -14.6236 q^{67} +0.347296 q^{70} -0.170245 q^{71} +11.8007 q^{73} +9.86484 q^{74} -2.87939 q^{76} +4.12836 q^{77} +4.14796 q^{79} -0.568926 q^{80} +11.7442 q^{82} +2.43376 q^{83} +10.3182 q^{86} -2.36959 q^{88} +15.0915 q^{89} +7.00774 q^{91} +11.3550 q^{92} +13.8084 q^{94} -0.226682 q^{95} -11.1925 q^{97} -8.74422 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.87939	1.32893	0.664463	−	0.747321i	$-0.268660\pi$
$2$	1.87939	1.32893	0.664463	+	0.747321i	$0.268660\pi$
$3$	0	0
$3$	0	0
$4$	1.53209	0.766044
$5$	0.120615	0.0539406	0.0269703	−	0.999636i	$-0.491414\pi$
$5$	0.120615	0.0539406	0.0269703	+	0.999636i	$0.491414\pi$
$6$	0	0
$7$	1.53209	0.579075	0.289538	−	0.957167i	$-0.406498\pi$
$7$	1.53209	0.579075	0.289538	+	0.957167i	$0.406498\pi$
$8$	−0.879385	−0.310910
$9$	0	0
$10$	0.226682	0.0716830
$11$	2.69459	0.812450	0.406225	−	0.913773i	$-0.366845\pi$
$11$	2.69459	0.812450	0.406225	+	0.913773i	$0.366845\pi$
$12$	0	0
$13$	4.57398	1.26859	0.634297	−	0.773090i	$-0.281290\pi$
$13$	4.57398	1.26859	0.634297	+	0.773090i	$0.281290\pi$
$14$	2.87939	0.769548
$15$	0	0
$16$	−4.71688	−1.17922
$17$	0	0
$17$	0	0
$18$	0	0
$19$	−1.87939	−0.431161	−0.215580	−	0.976486i	$-0.569164\pi$
$19$	−1.87939	−0.431161	−0.215580	+	0.976486i	$0.569164\pi$
$20$	0.184793	0.0413209
$21$	0	0
$22$	5.06418	1.07969
$23$	7.41147	1.54540	0.772700	−	0.634772i	$-0.218906\pi$
$23$	7.41147	1.54540	0.772700	+	0.634772i	$0.218906\pi$
$24$	0	0
$25$	−4.98545	−0.997090
$26$	8.59627	1.68587
$27$	0	0
$28$	2.34730	0.443597
$29$	3.41147	0.633495	0.316747	−	0.948510i	$-0.397409\pi$
$29$	3.41147	0.633495	0.316747	+	0.948510i	$0.397409\pi$
$30$	0	0
$31$	−3.83750	−0.689235	−0.344617	−	0.938743i	$-0.611991\pi$
$31$	−3.83750	−0.689235	−0.344617	+	0.938743i	$0.611991\pi$
$32$	−7.10607	−1.25619
$33$	0	0
$34$	0	0
$35$	0.184793	0.0312356
$36$	0	0
$37$	5.24897	0.862925	0.431463	−	0.902131i	$-0.357998\pi$
$37$	5.24897	0.862925	0.431463	+	0.902131i	$0.357998\pi$
$38$	−3.53209	−0.572980
$39$	0	0
$40$	−0.106067	−0.0167706
$41$	6.24897	0.975925	0.487963	−	0.872865i	$-0.337740\pi$
$41$	6.24897	0.975925	0.487963	+	0.872865i	$0.337740\pi$
$42$	0	0
$43$	5.49020	0.837248	0.418624	−	0.908160i	$-0.362513\pi$
$43$	5.49020	0.837248	0.418624	+	0.908160i	$0.362513\pi$
$44$	4.12836	0.622373
$45$	0	0
$46$	13.9290	2.05372
$47$	7.34730	1.07171	0.535857	−	0.844309i	$-0.319989\pi$
$47$	7.34730	1.07171	0.535857	+	0.844309i	$0.319989\pi$
$48$	0	0
$49$	−4.65270	−0.664672
$50$	−9.36959	−1.32506
$51$	0	0
$52$	7.00774	0.971799
$53$	−0.822948	−0.113041	−0.0565203	−	0.998401i	$-0.518001\pi$
$53$	−0.822948	−0.113041	−0.0565203	+	0.998401i	$0.518001\pi$
$54$	0	0
$55$	0.325008	0.0438240
$56$	−1.34730	−0.180040
$57$	0	0
$58$	6.41147	0.841868
$59$	3.14290	0.409171	0.204586	−	0.978849i	$-0.434415\pi$
$59$	3.14290	0.409171	0.204586	+	0.978849i	$0.434415\pi$
$60$	0	0
$61$	−1.22668	−0.157060	−0.0785302	−	0.996912i	$-0.525023\pi$
$61$	−1.22668	−0.157060	−0.0785302	+	0.996912i	$0.525023\pi$
$62$	−7.21213	−0.915942
$63$	0	0
$64$	−3.92127	−0.490159
$65$	0.551689	0.0684286
$66$	0	0
$67$	−14.6236	−1.78656	−0.893279	−	0.449503i	$-0.851601\pi$
$67$	−14.6236	−1.78656	−0.893279	+	0.449503i	$0.851601\pi$
$68$	0	0
$69$	0	0
$70$	0.347296	0.0415099
$71$	−0.170245	−0.0202043	−0.0101022	−	0.999949i	$-0.503216\pi$
$71$	−0.170245	−0.0202043	−0.0101022	+	0.999949i	$0.503216\pi$
$72$	0	0
$73$	11.8007	1.38116	0.690581	−	0.723255i	$-0.257355\pi$
$73$	11.8007	1.38116	0.690581	+	0.723255i	$0.257355\pi$
$74$	9.86484	1.14676
$75$	0	0
$76$	−2.87939	−0.330288
$77$	4.12836	0.470470
$78$	0	0
$79$	4.14796	0.466682	0.233341	−	0.972395i	$-0.425034\pi$
$79$	4.14796	0.466682	0.233341	+	0.972395i	$0.425034\pi$
$80$	−0.568926	−0.0636078
$81$	0	0
$82$	11.7442	1.29693
$83$	2.43376	0.267140	0.133570	−	0.991039i	$-0.457356\pi$
$83$	2.43376	0.267140	0.133570	+	0.991039i	$0.457356\pi$
$84$	0	0
$85$	0	0
$86$	10.3182	1.11264
$87$	0	0
$88$	−2.36959	−0.252599
$89$	15.0915	1.59970	0.799849	−	0.600201i	$-0.204913\pi$
$89$	15.0915	1.59970	0.799849	+	0.600201i	$0.204913\pi$
$90$	0	0
$91$	7.00774	0.734611
$92$	11.3550	1.18384
$93$	0	0
$94$	13.8084	1.42423
$95$	−0.226682	−0.0232570
$96$	0	0
$97$	−11.1925	−1.13643	−0.568215	−	0.822880i	$-0.692366\pi$
$97$	−11.1925	−1.13643	−0.568215	+	0.822880i	$0.692366\pi$
$98$	−8.74422	−0.883300
$99$	0	0
$100$	−7.63816	−0.763816
$101$	−7.78106	−0.774244	−0.387122	−	0.922028i	$-0.626531\pi$
$101$	−7.78106	−0.774244	−0.387122	+	0.922028i	$0.626531\pi$
$102$	0	0
$103$	−10.8598	−1.07005	−0.535023	−	0.844837i	$-0.679697\pi$
$103$	−10.8598	−1.07005	−0.535023	+	0.844837i	$0.679697\pi$
$104$	−4.02229	−0.394418
$105$	0	0
$106$	−1.54664	−0.150223
$107$	12.0419	1.16413	0.582067	−	0.813141i	$-0.302244\pi$
$107$	12.0419	1.16413	0.582067	+	0.813141i	$0.302244\pi$
$108$	0	0
$109$	6.61081	0.633201	0.316601	−	0.948559i	$-0.397459\pi$
$109$	6.61081	0.633201	0.316601	+	0.948559i	$0.397459\pi$
$110$	0.610815	0.0582389
$111$	0	0
$112$	−7.22668	−0.682857
$113$	−5.08647	−0.478495	−0.239247	−	0.970959i	$-0.576901\pi$
$113$	−5.08647	−0.478495	−0.239247	+	0.970959i	$0.576901\pi$
$114$	0	0
$115$	0.893933	0.0833597
$116$	5.22668	0.485285
$117$	0	0
$118$	5.90673	0.543758
$119$	0	0
$120$	0	0
$121$	−3.73917	−0.339925
$122$	−2.30541	−0.208722
$123$	0	0
$124$	−5.87939	−0.527984
$125$	−1.20439	−0.107724
$126$	0	0
$127$	−2.20439	−0.195608	−0.0978041	−	0.995206i	$-0.531182\pi$
$127$	−2.20439	−0.195608	−0.0978041	+	0.995206i	$0.531182\pi$
$128$	6.84255	0.604802
$129$	0	0
$130$	1.03684	0.0909366
$131$	−1.99319	−0.174146	−0.0870730	−	0.996202i	$-0.527751\pi$
$131$	−1.99319	−0.174146	−0.0870730	+	0.996202i	$0.527751\pi$
$132$	0	0
$133$	−2.87939	−0.249674
$134$	−27.4834	−2.37420
$135$	0	0
$136$	0	0
$137$	12.6236	1.07851	0.539254	−	0.842143i	$-0.318706\pi$
$137$	12.6236	1.07851	0.539254	+	0.842143i	$0.318706\pi$
$138$	0	0
$139$	−5.23442	−0.443978	−0.221989	−	0.975049i	$-0.571255\pi$
$139$	−5.23442	−0.443978	−0.221989	+	0.975049i	$0.571255\pi$
$140$	0.283119	0.0239279
$141$	0	0
$142$	−0.319955	−0.0268500
$143$	12.3250	1.03067
$144$	0	0
$145$	0.411474	0.0341711
$146$	22.1780	1.83546
$147$	0	0
$148$	8.04189	0.661039
$149$	−9.65270	−0.790780	−0.395390	−	0.918513i	$-0.629391\pi$
$149$	−9.65270	−0.790780	−0.395390	+	0.918513i	$0.629391\pi$
$150$	0	0
$151$	1.20708	0.0982309	0.0491154	−	0.998793i	$-0.484360\pi$
$151$	1.20708	0.0982309	0.0491154	+	0.998793i	$0.484360\pi$
$152$	1.65270	0.134052
$153$	0	0
$154$	7.75877	0.625220
$155$	−0.462859	−0.0371777
$156$	0	0
$157$	15.0942	1.20465	0.602324	−	0.798251i	$-0.294241\pi$
$157$	15.0942	1.20465	0.602324	+	0.798251i	$0.294241\pi$
$158$	7.79561	0.620185
$159$	0	0
$160$	−0.857097	−0.0677594
$161$	11.3550	0.894902
$162$	0	0
$163$	6.55438	0.513378	0.256689	−	0.966494i	$-0.417368\pi$
$163$	6.55438	0.513378	0.256689	+	0.966494i	$0.417368\pi$
$164$	9.57398	0.747602
$165$	0	0
$166$	4.57398	0.355010
$167$	−3.94356	−0.305162	−0.152581	−	0.988291i	$-0.548759\pi$
$167$	−3.94356	−0.305162	−0.152581	+	0.988291i	$0.548759\pi$
$168$	0	0
$169$	7.92127	0.609329
$170$	0	0
$171$	0	0
$172$	8.41147	0.641369
$173$	−18.9341	−1.43953	−0.719765	−	0.694218i	$-0.755751\pi$
$173$	−18.9341	−1.43953	−0.719765	+	0.694218i	$0.755751\pi$
$174$	0	0
$175$	−7.63816	−0.577390
$176$	−12.7101	−0.958058
$177$	0	0
$178$	28.3628	2.12588
$179$	−7.25402	−0.542191	−0.271096	−	0.962552i	$-0.587386\pi$
$179$	−7.25402	−0.542191	−0.271096	+	0.962552i	$0.587386\pi$
$180$	0	0
$181$	−25.0993	−1.86561	−0.932807	−	0.360377i	$-0.882648\pi$
$181$	−25.0993	−1.86561	−0.932807	+	0.360377i	$0.882648\pi$
$182$	13.1702	0.976243
$183$	0	0
$184$	−6.51754	−0.480479
$185$	0.633103	0.0465467
$186$	0	0
$187$	0	0
$188$	11.2567	0.820980
$189$	0	0
$190$	−0.426022	−0.0309069
$191$	−14.1557	−1.02427	−0.512135	−	0.858905i	$-0.671145\pi$
$191$	−14.1557	−1.02427	−0.512135	+	0.858905i	$0.671145\pi$
$192$	0	0
$193$	16.4311	1.18273	0.591367	−	0.806402i	$-0.298588\pi$
$193$	16.4311	1.18273	0.591367	+	0.806402i	$0.298588\pi$
$194$	−21.0351	−1.51023
$195$	0	0
$196$	−7.12836	−0.509168
$197$	−20.2395	−1.44200	−0.721001	−	0.692934i	$-0.756318\pi$
$197$	−20.2395	−1.44200	−0.721001	+	0.692934i	$0.756318\pi$
$198$	0	0
$199$	−22.1753	−1.57197	−0.785983	−	0.618249i	$-0.787842\pi$
$199$	−22.1753	−1.57197	−0.785983	+	0.618249i	$0.787842\pi$
$200$	4.38413	0.310005
$201$	0	0
$202$	−14.6236	−1.02891
$203$	5.22668	0.366841
$204$	0	0
$205$	0.753718	0.0526420
$206$	−20.4097	−1.42201
$207$	0	0
$208$	−21.5749	−1.49595
$209$	−5.06418	−0.350297
$210$	0	0
$211$	−7.18748	−0.494807	−0.247403	−	0.968913i	$-0.579577\pi$
$211$	−7.18748	−0.494807	−0.247403	+	0.968913i	$0.579577\pi$
$212$	−1.26083	−0.0865942
$213$	0	0
$214$	22.6313	1.54705
$215$	0.662199	0.0451616
$216$	0	0
$217$	−5.87939	−0.399119
$218$	12.4243	0.841478
$219$	0	0
$220$	0.497941	0.0335711
$221$	0	0
$222$	0	0
$223$	−6.01960	−0.403102	−0.201551	−	0.979478i	$-0.564598\pi$
$223$	−6.01960	−0.403102	−0.201551	+	0.979478i	$0.564598\pi$
$224$	−10.8871	−0.727427
$225$	0	0
$226$	−9.55943	−0.635884
$227$	22.0351	1.46252	0.731260	−	0.682099i	$-0.238933\pi$
$227$	22.0351	1.46252	0.731260	+	0.682099i	$0.238933\pi$
$228$	0	0
$229$	3.69965	0.244479	0.122240	−	0.992501i	$-0.460992\pi$
$229$	3.69965	0.244479	0.122240	+	0.992501i	$0.460992\pi$
$230$	1.68004	0.110779
$231$	0	0
$232$	−3.00000	−0.196960
$233$	−29.1506	−1.90972	−0.954861	−	0.297053i	$-0.903996\pi$
$233$	−29.1506	−1.90972	−0.954861	+	0.297053i	$0.903996\pi$
$234$	0	0
$235$	0.886192	0.0578088
$236$	4.81521	0.313443
$237$	0	0
$238$	0	0
$239$	−12.4834	−0.807484	−0.403742	−	0.914873i	$-0.632291\pi$
$239$	−12.4834	−0.807484	−0.403742	+	0.914873i	$0.632291\pi$
$240$	0	0
$241$	−16.2172	−1.04464	−0.522320	−	0.852749i	$-0.674933\pi$
$241$	−16.2172	−1.04464	−0.522320	+	0.852749i	$0.674933\pi$
$242$	−7.02734	−0.451735
$243$	0	0
$244$	−1.87939	−0.120315
$245$	−0.561185	−0.0358528
$246$	0	0
$247$	−8.59627	−0.546967
$248$	3.37464	0.214290
$249$	0	0
$250$	−2.26352	−0.143157
$251$	−15.9959	−1.00965	−0.504826	−	0.863221i	$-0.668443\pi$
$251$	−15.9959	−1.00965	−0.504826	+	0.863221i	$0.668443\pi$
$252$	0	0
$253$	19.9709	1.25556
$254$	−4.14290	−0.259949
$255$	0	0
$256$	20.7023	1.29390
$257$	9.66044	0.602602	0.301301	−	0.953529i	$-0.402579\pi$
$257$	9.66044	0.602602	0.301301	+	0.953529i	$0.402579\pi$
$258$	0	0
$259$	8.04189	0.499699
$260$	0.845237	0.0524194
$261$	0	0
$262$	−3.74598	−0.231427
$263$	−27.9813	−1.72540	−0.862701	−	0.505714i	$-0.831229\pi$
$263$	−27.9813	−1.72540	−0.862701	+	0.505714i	$0.831229\pi$
$264$	0	0
$265$	−0.0992597	−0.00609748
$266$	−5.41147	−0.331799
$267$	0	0
$268$	−22.4047	−1.36858
$269$	−6.64590	−0.405207	−0.202604	−	0.979261i	$-0.564940\pi$
$269$	−6.64590	−0.405207	−0.202604	+	0.979261i	$0.564940\pi$
$270$	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
$274$	23.7246	1.43326
$275$	−13.4338	−0.810086
$276$	0	0
$277$	−20.1489	−1.21063	−0.605315	−	0.795986i	$-0.706953\pi$
$277$	−20.1489	−1.21063	−0.605315	+	0.795986i	$0.706953\pi$
$278$	−9.83750	−0.590014
$279$	0	0
$280$	−0.162504	−0.00971146
$281$	−16.4730	−0.982695	−0.491347	−	0.870964i	$-0.663495\pi$
$281$	−16.4730	−0.982695	−0.491347	+	0.870964i	$0.663495\pi$
$282$	0	0
$283$	18.4456	1.09648	0.548239	−	0.836322i	$-0.315298\pi$
$283$	18.4456	1.09648	0.548239	+	0.836322i	$0.315298\pi$
$284$	−0.260830	−0.0154774
$285$	0	0
$286$	23.1634	1.36968
$287$	9.57398	0.565134
$288$	0	0
$289$	0	0
$290$	0.773318	0.0454108
$291$	0	0
$292$	18.0797	1.05803
$293$	10.9513	0.639782	0.319891	−	0.947454i	$-0.396354\pi$
$293$	10.9513	0.639782	0.319891	+	0.947454i	$0.396354\pi$
$294$	0	0
$295$	0.379081	0.0220709
$296$	−4.61587	−0.268292
$297$	0	0
$298$	−18.1411	−1.05089
$299$	33.8999	1.96048
$300$	0	0
$301$	8.41147	0.484829
$302$	2.26857	0.130542
$303$	0	0
$304$	8.86484	0.508433
$305$	−0.147956	−0.00847193
$306$	0	0
$307$	−5.78106	−0.329942	−0.164971	−	0.986298i	$-0.552753\pi$
$307$	−5.78106	−0.329942	−0.164971	+	0.986298i	$0.552753\pi$
$308$	6.32501	0.360401
$309$	0	0
$310$	−0.869890	−0.0494064
$311$	0.120615	0.00683944	0.00341972	−	0.999994i	$-0.498911\pi$
$311$	0.120615	0.00683944	0.00341972	+	0.999994i	$0.498911\pi$
$312$	0	0
$313$	−10.3892	−0.587231	−0.293616	−	0.955924i	$-0.594859\pi$
$313$	−10.3892	−0.587231	−0.293616	+	0.955924i	$0.594859\pi$
$314$	28.3678	1.60089
$315$	0	0
$316$	6.35504	0.357499
$317$	27.8016	1.56149	0.780747	−	0.624848i	$-0.214839\pi$
$317$	27.8016	1.56149	0.780747	+	0.624848i	$0.214839\pi$
$318$	0	0
$319$	9.19253	0.514683
$320$	−0.472964	−0.0264395
$321$	0	0
$322$	21.3405	1.18926
$323$	0	0
$324$	0	0
$325$	−22.8033	−1.26490
$326$	12.3182	0.682242
$327$	0	0
$328$	−5.49525	−0.303425
$329$	11.2567	0.620603
$330$	0	0
$331$	8.77837	0.482503	0.241251	−	0.970463i	$-0.422442\pi$
$331$	8.77837	0.482503	0.241251	+	0.970463i	$0.422442\pi$
$332$	3.72874	0.204641
$333$	0	0
$334$	−7.41147	−0.405538
$335$	−1.76382	−0.0963679
$336$	0	0
$337$	−1.46110	−0.0795914	−0.0397957	−	0.999208i	$-0.512671\pi$
$337$	−1.46110	−0.0795914	−0.0397957	+	0.999208i	$0.512671\pi$
$338$	14.8871	0.809753
$339$	0	0
$340$	0	0
$341$	−10.3405	−0.559969
$342$	0	0
$343$	−17.8530	−0.963970
$344$	−4.82800	−0.260308
$345$	0	0
$346$	−35.5844	−1.91303
$347$	31.3560	1.68328	0.841638	−	0.540042i	$-0.181591\pi$
$347$	31.3560	1.68328	0.841638	+	0.540042i	$0.181591\pi$
$348$	0	0
$349$	−29.7743	−1.59378	−0.796890	−	0.604125i	$-0.793523\pi$
$349$	−29.7743	−1.59378	−0.796890	+	0.604125i	$0.793523\pi$
$350$	−14.3550	−0.767309
$351$	0	0
$352$	−19.1480	−1.02059
$353$	28.3141	1.50701	0.753503	−	0.657444i	$-0.228362\pi$
$353$	28.3141	1.50701	0.753503	+	0.657444i	$0.228362\pi$
$354$	0	0
$355$	−0.0205340	−0.00108983
$356$	23.1215	1.22544
$357$	0	0
$358$	−13.6331	−0.720532
$359$	2.81790	0.148723	0.0743614	−	0.997231i	$-0.476308\pi$
$359$	2.81790	0.148723	0.0743614	+	0.997231i	$0.476308\pi$
$360$	0	0
$361$	−15.4679	−0.814101
$362$	−47.1712	−2.47926
$363$	0	0
$364$	10.7365	0.562745
$365$	1.42333	0.0745007
$366$	0	0
$367$	8.31820	0.434207	0.217103	−	0.976149i	$-0.430339\pi$
$367$	8.31820	0.434207	0.217103	+	0.976149i	$0.430339\pi$
$368$	−34.9590	−1.82237
$369$	0	0
$370$	1.18984	0.0618571
$371$	−1.26083	−0.0654590
$372$	0	0
$373$	−9.21894	−0.477339	−0.238669	−	0.971101i	$-0.576711\pi$
$373$	−9.21894	−0.477339	−0.238669	+	0.971101i	$0.576711\pi$
$374$	0	0
$375$	0	0
$376$	−6.46110	−0.333206
$377$	15.6040	0.803647
$378$	0	0
$379$	10.3628	0.532300	0.266150	−	0.963932i	$-0.414248\pi$
$379$	10.3628	0.532300	0.266150	+	0.963932i	$0.414248\pi$
$380$	−0.347296	−0.0178159
$381$	0	0
$382$	−26.6040	−1.36118
$383$	−13.2713	−0.678130	−0.339065	−	0.940763i	$-0.610111\pi$
$383$	−13.2713	−0.678130	−0.339065	+	0.940763i	$0.610111\pi$
$384$	0	0
$385$	0.497941	0.0253774
$386$	30.8803	1.57177
$387$	0	0
$388$	−17.1480	−0.870556
$389$	26.2763	1.33226	0.666131	−	0.745835i	$-0.267949\pi$
$389$	26.2763	1.33226	0.666131	+	0.745835i	$0.267949\pi$
$390$	0	0
$391$	0	0
$392$	4.09152	0.206653
$393$	0	0
$394$	−38.0378	−1.91632
$395$	0.500305	0.0251731
$396$	0	0
$397$	25.4766	1.27863	0.639317	−	0.768944i	$-0.279217\pi$
$397$	25.4766	1.27863	0.639317	+	0.768944i	$0.279217\pi$
$398$	−41.6759	−2.08903
$399$	0	0
$400$	23.5158	1.17579
$401$	0.900740	0.0449808	0.0224904	−	0.999747i	$-0.492840\pi$
$401$	0.900740	0.0449808	0.0224904	+	0.999747i	$0.492840\pi$
$402$	0	0
$403$	−17.5526	−0.874358
$404$	−11.9213	−0.593106
$405$	0	0
$406$	9.82295	0.487505
$407$	14.1438	0.701084
$408$	0	0
$409$	−15.3259	−0.757819	−0.378910	−	0.925434i	$-0.623701\pi$
$409$	−15.3259	−0.757819	−0.378910	+	0.925434i	$0.623701\pi$
$410$	1.41653	0.0699573
$411$	0	0
$412$	−16.6382	−0.819703
$413$	4.81521	0.236941
$414$	0	0
$415$	0.293548	0.0144097
$416$	−32.5030	−1.59359
$417$	0	0
$418$	−9.51754	−0.465518
$419$	−2.38413	−0.116473	−0.0582363	−	0.998303i	$-0.518548\pi$
$419$	−2.38413	−0.116473	−0.0582363	+	0.998303i	$0.518548\pi$
$420$	0	0
$421$	−8.28581	−0.403826	−0.201913	−	0.979404i	$-0.564716\pi$
$421$	−8.28581	−0.403826	−0.201913	+	0.979404i	$0.564716\pi$
$422$	−13.5080	−0.657561
$423$	0	0
$424$	0.723689	0.0351454
$425$	0	0
$426$	0	0
$427$	−1.87939	−0.0909498
$428$	18.4492	0.891778
$429$	0	0
$430$	1.24453	0.0600164
$431$	−32.3191	−1.55676	−0.778379	−	0.627795i	$-0.783958\pi$
$431$	−32.3191	−1.55676	−0.778379	+	0.627795i	$0.783958\pi$
$432$	0	0
$433$	−15.0642	−0.723938	−0.361969	−	0.932190i	$-0.617895\pi$
$433$	−15.0642	−0.723938	−0.361969	+	0.932190i	$0.617895\pi$
$434$	−11.0496	−0.530399
$435$	0	0
$436$	10.1284	0.485060
$437$	−13.9290	−0.666315
$438$	0	0
$439$	−2.57304	−0.122805	−0.0614024	−	0.998113i	$-0.519557\pi$
$439$	−2.57304	−0.122805	−0.0614024	+	0.998113i	$0.519557\pi$
$440$	−0.285807	−0.0136253
$441$	0	0
$442$	0	0
$443$	−23.4662	−1.11491	−0.557455	−	0.830207i	$-0.688222\pi$
$443$	−23.4662	−1.11491	−0.557455	+	0.830207i	$0.688222\pi$
$444$	0	0
$445$	1.82026	0.0862886
$446$	−11.3131	−0.535693
$447$	0	0
$448$	−6.00774	−0.283839
$449$	−18.8580	−0.889965	−0.444983	−	0.895539i	$-0.646790\pi$
$449$	−18.8580	−0.889965	−0.444983	+	0.895539i	$0.646790\pi$
$450$	0	0
$451$	16.8384	0.792891
$452$	−7.79292	−0.366548
$453$	0	0
$454$	41.4124	1.94358
$455$	0.845237	0.0396253
$456$	0	0
$457$	−2.10782	−0.0985997	−0.0492999	−	0.998784i	$-0.515699\pi$
$457$	−2.10782	−0.0985997	−0.0492999	+	0.998784i	$0.515699\pi$
$458$	6.95306	0.324895
$459$	0	0
$460$	1.36959	0.0638572
$461$	21.9077	1.02034	0.510171	−	0.860073i	$-0.329582\pi$
$461$	21.9077	1.02034	0.510171	+	0.860073i	$0.329582\pi$
$462$	0	0
$463$	14.1557	0.657871	0.328936	−	0.944352i	$-0.393310\pi$
$463$	14.1557	0.657871	0.328936	+	0.944352i	$0.393310\pi$
$464$	−16.0915	−0.747030
$465$	0	0
$466$	−54.7853	−2.53788
$467$	29.6878	1.37379	0.686893	−	0.726758i	$-0.258974\pi$
$467$	29.6878	1.37379	0.686893	+	0.726758i	$0.258974\pi$
$468$	0	0
$469$	−22.4047	−1.03455
$470$	1.66550	0.0768236
$471$	0	0
$472$	−2.76382	−0.127215
$473$	14.7939	0.680222
$474$	0	0
$475$	9.36959	0.429906
$476$	0	0
$477$	0	0
$478$	−23.4611	−1.07309
$479$	38.2959	1.74978	0.874892	−	0.484317i	$-0.160932\pi$
$479$	38.2959	1.74978	0.874892	+	0.484317i	$0.160932\pi$
$480$	0	0
$481$	24.0087	1.09470
$482$	−30.4783	−1.38825
$483$	0	0
$484$	−5.72874	−0.260397
$485$	−1.34998	−0.0612996
$486$	0	0
$487$	23.3509	1.05813	0.529066	−	0.848581i	$-0.322543\pi$
$487$	23.3509	1.05813	0.529066	+	0.848581i	$0.322543\pi$
$488$	1.07873	0.0488316
$489$	0	0
$490$	−1.05468	−0.0476457
$491$	−31.3928	−1.41674	−0.708369	−	0.705843i	$-0.750569\pi$
$491$	−31.3928	−1.41674	−0.708369	+	0.705843i	$0.750569\pi$
$492$	0	0
$493$	0	0
$494$	−16.1557	−0.726879
$495$	0	0
$496$	18.1010	0.812760
$497$	−0.260830	−0.0116998
$498$	0	0
$499$	−16.1310	−0.722125	−0.361062	−	0.932542i	$-0.617586\pi$
$499$	−16.1310	−0.722125	−0.361062	+	0.932542i	$0.617586\pi$
$500$	−1.84524	−0.0825215
$501$	0	0
$502$	−30.0624	−1.34175
$503$	−34.3637	−1.53220	−0.766101	−	0.642720i	$-0.777806\pi$
$503$	−34.3637	−1.53220	−0.766101	+	0.642720i	$0.777806\pi$
$504$	0	0
$505$	−0.938511	−0.0417632
$506$	37.5330	1.66855
$507$	0	0
$508$	−3.37733	−0.149845
$509$	−20.0283	−0.887738	−0.443869	−	0.896092i	$-0.646394\pi$
$509$	−20.0283	−0.887738	−0.443869	+	0.896092i	$0.646394\pi$
$510$	0	0
$511$	18.0797	0.799797
$512$	25.2226	1.11469
$513$	0	0
$514$	18.1557	0.800813
$515$	−1.30985	−0.0577189
$516$	0	0
$517$	19.7980	0.870714
$518$	15.1138	0.664063
$519$	0	0
$520$	−0.485147	−0.0212751
$521$	−5.58584	−0.244720	−0.122360	−	0.992486i	$-0.539046\pi$
$521$	−5.58584	−0.244720	−0.122360	+	0.992486i	$0.539046\pi$
$522$	0	0
$523$	5.51249	0.241044	0.120522	−	0.992711i	$-0.461543\pi$
$523$	5.51249	0.241044	0.120522	+	0.992711i	$0.461543\pi$
$524$	−3.05375	−0.133404
$525$	0	0
$526$	−52.5877	−2.29293
$527$	0	0
$528$	0	0
$529$	31.9299	1.38826
$530$	−0.186547	−0.00810309
$531$	0	0
$532$	−4.41147	−0.191262
$533$	28.5827	1.23805
$534$	0	0
$535$	1.45243	0.0627940
$536$	12.8598	0.555458
$537$	0	0
$538$	−12.4902	−0.538491
$539$	−12.5371	−0.540013
$540$	0	0
$541$	−13.9949	−0.601690	−0.300845	−	0.953673i	$-0.597269\pi$
$541$	−13.9949	−0.601690	−0.300845	+	0.953673i	$0.597269\pi$
$542$	31.9495	1.37235
$543$	0	0
$544$	0	0
$545$	0.797362	0.0341552
$546$	0	0
$547$	29.4175	1.25780	0.628900	−	0.777486i	$-0.283506\pi$
$547$	29.4175	1.25780	0.628900	+	0.777486i	$0.283506\pi$
$548$	19.3405	0.826185
$549$	0	0
$550$	−25.2472	−1.07654
$551$	−6.41147	−0.273138
$552$	0	0
$553$	6.35504	0.270244
$554$	−37.8675	−1.60884
$555$	0	0
$556$	−8.01960	−0.340107
$557$	−32.0574	−1.35831	−0.679157	−	0.733993i	$-0.737655\pi$
$557$	−32.0574	−1.35831	−0.679157	+	0.733993i	$0.737655\pi$
$558$	0	0
$559$	25.1121	1.06213
$560$	−0.871644	−0.0368337
$561$	0	0
$562$	−30.9590	−1.30593
$563$	−18.6483	−0.785930	−0.392965	−	0.919553i	$-0.628551\pi$
$563$	−18.6483	−0.785930	−0.392965	+	0.919553i	$0.628551\pi$
$564$	0	0
$565$	−0.613503	−0.0258103
$566$	34.6664	1.45714
$567$	0	0
$568$	0.149711	0.00628172
$569$	−27.6554	−1.15937	−0.579687	−	0.814839i	$-0.696825\pi$
$569$	−27.6554	−1.15937	−0.579687	+	0.814839i	$0.696825\pi$
$570$	0	0
$571$	−33.1762	−1.38838	−0.694191	−	0.719791i	$-0.744238\pi$
$571$	−33.1762	−1.38838	−0.694191	+	0.719791i	$0.744238\pi$
$572$	18.8830	0.789538
$573$	0	0
$574$	17.9932	0.751021
$575$	−36.9495	−1.54090
$576$	0	0
$577$	2.70233	0.112500	0.0562498	−	0.998417i	$-0.482086\pi$
$577$	2.70233	0.112500	0.0562498	+	0.998417i	$0.482086\pi$
$578$	0	0
$579$	0	0
$580$	0.630415	0.0261766
$581$	3.72874	0.154694
$582$	0	0
$583$	−2.21751	−0.0918399
$584$	−10.3773	−0.429417
$585$	0	0
$586$	20.5817	0.850223
$587$	−6.31551	−0.260669	−0.130335	−	0.991470i	$-0.541605\pi$
$587$	−6.31551	−0.260669	−0.130335	+	0.991470i	$0.541605\pi$
$588$	0	0
$589$	7.21213	0.297171
$590$	0.712438	0.0293306
$591$	0	0
$592$	−24.7588	−1.01758
$593$	10.2148	0.419472	0.209736	−	0.977758i	$-0.432739\pi$
$593$	10.2148	0.419472	0.209736	+	0.977758i	$0.432739\pi$
$594$	0	0
$595$	0	0
$596$	−14.7888	−0.605773
$597$	0	0
$598$	63.7110	2.60534
$599$	21.4347	0.875798	0.437899	−	0.899024i	$-0.355723\pi$
$599$	21.4347	0.875798	0.437899	+	0.899024i	$0.355723\pi$
$600$	0	0
$601$	−17.4557	−0.712034	−0.356017	−	0.934479i	$-0.615865\pi$
$601$	−17.4557	−0.712034	−0.356017	+	0.934479i	$0.615865\pi$
$602$	15.8084	0.644302
$603$	0	0
$604$	1.84936	0.0752492
$605$	−0.450999	−0.0183357
$606$	0	0
$607$	8.50980	0.345402	0.172701	−	0.984974i	$-0.444751\pi$
$607$	8.50980	0.345402	0.172701	+	0.984974i	$0.444751\pi$
$608$	13.3550	0.541618
$609$	0	0
$610$	−0.278066	−0.0112586
$611$	33.6064	1.35957
$612$	0	0
$613$	9.78106	0.395053	0.197527	−	0.980298i	$-0.436709\pi$
$613$	9.78106	0.395053	0.197527	+	0.980298i	$0.436709\pi$
$614$	−10.8648	−0.438469
$615$	0	0
$616$	−3.63041	−0.146274
$617$	22.8512	0.919956	0.459978	−	0.887930i	$-0.347857\pi$
$617$	22.8512	0.919956	0.459978	+	0.887930i	$0.347857\pi$
$618$	0	0
$619$	41.2627	1.65849	0.829244	−	0.558887i	$-0.188771\pi$
$619$	41.2627	1.65849	0.829244	+	0.558887i	$0.188771\pi$
$620$	−0.709141	−0.0284798
$621$	0	0
$622$	0.226682	0.00908910
$623$	23.1215	0.926345
$624$	0	0
$625$	24.7820	0.991280
$626$	−19.5253	−0.780387
$627$	0	0
$628$	23.1257	0.922815
$629$	0	0
$630$	0	0
$631$	9.54252	0.379882	0.189941	−	0.981796i	$-0.439170\pi$
$631$	9.54252	0.379882	0.189941	+	0.981796i	$0.439170\pi$
$632$	−3.64765	−0.145096
$633$	0	0
$634$	52.2499	2.07511
$635$	−0.265882	−0.0105512
$636$	0	0
$637$	−21.2814	−0.843198
$638$	17.2763	0.683976
$639$	0	0
$640$	0.825312	0.0326233
$641$	9.42871	0.372412	0.186206	−	0.982511i	$-0.440381\pi$
$641$	9.42871	0.372412	0.186206	+	0.982511i	$0.440381\pi$
$642$	0	0
$643$	−11.0060	−0.434034	−0.217017	−	0.976168i	$-0.569633\pi$
$643$	−11.0060	−0.434034	−0.217017	+	0.976168i	$0.569633\pi$
$644$	17.3969	0.685535
$645$	0	0
$646$	0	0
$647$	−28.9840	−1.13948	−0.569740	−	0.821825i	$-0.692956\pi$
$647$	−28.9840	−1.13948	−0.569740	+	0.821825i	$0.692956\pi$
$648$	0	0
$649$	8.46884	0.332431
$650$	−42.8563	−1.68096
$651$	0	0
$652$	10.0419	0.393271
$653$	−14.7178	−0.575953	−0.287976	−	0.957638i	$-0.592982\pi$
$653$	−14.7178	−0.575953	−0.287976	+	0.957638i	$0.592982\pi$
$654$	0	0
$655$	−0.240408	−0.00939354
$656$	−29.4757	−1.15083
$657$	0	0
$658$	21.1557	0.824735
$659$	−2.19759	−0.0856058	−0.0428029	−	0.999084i	$-0.513629\pi$
$659$	−2.19759	−0.0856058	−0.0428029	+	0.999084i	$0.513629\pi$
$660$	0	0
$661$	−26.6023	−1.03471	−0.517354	−	0.855772i	$-0.673083\pi$
$661$	−26.6023	−1.03471	−0.517354	+	0.855772i	$0.673083\pi$
$662$	16.4979	0.641211
$663$	0	0
$664$	−2.14022	−0.0830565
$665$	−0.347296	−0.0134676
$666$	0	0
$667$	25.2841	0.979002
$668$	−6.04189	−0.233768
$669$	0	0
$670$	−3.31490	−0.128066
$671$	−3.30541	−0.127604
$672$	0	0
$673$	−7.24392	−0.279233	−0.139616	−	0.990206i	$-0.544587\pi$
$673$	−7.24392	−0.279233	−0.139616	+	0.990206i	$0.544587\pi$
$674$	−2.74598	−0.105771
$675$	0	0
$676$	12.1361	0.466773
$677$	22.9273	0.881166	0.440583	−	0.897712i	$-0.354772\pi$
$677$	22.9273	0.881166	0.440583	+	0.897712i	$0.354772\pi$
$678$	0	0
$679$	−17.1480	−0.658078
$680$	0	0
$681$	0	0
$682$	−19.4338	−0.744157
$683$	4.29591	0.164378	0.0821892	−	0.996617i	$-0.473809\pi$
$683$	4.29591	0.164378	0.0821892	+	0.996617i	$0.473809\pi$
$684$	0	0
$685$	1.52259	0.0581753
$686$	−33.5526	−1.28105
$687$	0	0
$688$	−25.8966	−0.987299
$689$	−3.76415	−0.143403
$690$	0	0
$691$	−20.6331	−0.784920	−0.392460	−	0.919769i	$-0.628376\pi$
$691$	−20.6331	−0.784920	−0.392460	+	0.919769i	$0.628376\pi$
$692$	−29.0087	−1.10274
$693$	0	0
$694$	58.9299	2.23695
$695$	−0.631349	−0.0239484
$696$	0	0
$697$	0	0
$698$	−55.9573	−2.11801
$699$	0	0
$700$	−11.7023	−0.442307
$701$	28.2772	1.06802	0.534008	−	0.845479i	$-0.320685\pi$
$701$	28.2772	1.06802	0.534008	+	0.845479i	$0.320685\pi$
$702$	0	0
$703$	−9.86484	−0.372059
$704$	−10.5662	−0.398230
$705$	0	0
$706$	53.2131	2.00270
$707$	−11.9213	−0.448346
$708$	0	0
$709$	27.1002	1.01777	0.508885	−	0.860835i	$-0.330058\pi$
$709$	27.1002	1.01777	0.508885	+	0.860835i	$0.330058\pi$
$710$	−0.0385913	−0.00144831
$711$	0	0
$712$	−13.2713	−0.497361
$713$	−28.4415	−1.06514
$714$	0	0
$715$	1.48658	0.0555949
$716$	−11.1138	−0.415342
$717$	0	0
$718$	5.29591	0.197642
$719$	25.8402	0.963676	0.481838	−	0.876260i	$-0.339969\pi$
$719$	25.8402	0.963676	0.481838	+	0.876260i	$0.339969\pi$
$720$	0	0
$721$	−16.6382	−0.619637
$722$	−29.0702	−1.08188
$723$	0	0
$724$	−38.4543	−1.42914
$725$	−17.0077	−0.631652
$726$	0	0
$727$	−31.6290	−1.17305	−0.586527	−	0.809930i	$-0.699505\pi$
$727$	−31.6290	−1.17305	−0.586527	+	0.809930i	$0.699505\pi$
$728$	−6.16250	−0.228398
$729$	0	0
$730$	2.67499	0.0990059
$731$	0	0
$732$	0	0
$733$	25.6040	0.945706	0.472853	−	0.881141i	$-0.343224\pi$
$733$	25.6040	0.945706	0.472853	+	0.881141i	$0.343224\pi$
$734$	15.6331	0.577028
$735$	0	0
$736$	−52.6664	−1.94131
$737$	−39.4047	−1.45149
$738$	0	0
$739$	21.6382	0.795972	0.397986	−	0.917391i	$-0.369709\pi$
$739$	21.6382	0.795972	0.397986	+	0.917391i	$0.369709\pi$
$740$	0.969971	0.0356568
$741$	0	0
$742$	−2.36959	−0.0869902
$743$	26.7547	0.981533	0.490766	−	0.871291i	$-0.336717\pi$
$743$	26.7547	0.981533	0.490766	+	0.871291i	$0.336717\pi$
$744$	0	0
$745$	−1.16426	−0.0426551
$746$	−17.3259	−0.634348
$747$	0	0
$748$	0	0
$749$	18.4492	0.674121
$750$	0	0
$751$	41.9513	1.53082	0.765412	−	0.643540i	$-0.222535\pi$
$751$	41.9513	1.53082	0.765412	+	0.643540i	$0.222535\pi$
$752$	−34.6563	−1.26379
$753$	0	0
$754$	29.3259	1.06799
$755$	0.145592	0.00529863
$756$	0	0
$757$	−4.99319	−0.181481	−0.0907403	−	0.995875i	$-0.528923\pi$
$757$	−4.99319	−0.181481	−0.0907403	+	0.995875i	$0.528923\pi$
$758$	19.4757	0.707388
$759$	0	0
$760$	0.199340	0.00723084
$761$	−13.2935	−0.481891	−0.240945	−	0.970539i	$-0.577457\pi$
$761$	−13.2935	−0.481891	−0.240945	+	0.970539i	$0.577457\pi$
$762$	0	0
$763$	10.1284	0.366671
$764$	−21.6878	−0.784637
$765$	0	0
$766$	−24.9418	−0.901184
$767$	14.3756	0.519072
$768$	0	0
$769$	8.25166	0.297562	0.148781	−	0.988870i	$-0.452465\pi$
$769$	8.25166	0.297562	0.148781	+	0.988870i	$0.452465\pi$
$770$	0.935822	0.0337247
$771$	0	0
$772$	25.1739	0.906027
$773$	−26.1043	−0.938907	−0.469453	−	0.882957i	$-0.655549\pi$
$773$	−26.1043	−0.938907	−0.469453	+	0.882957i	$0.655549\pi$
$774$	0	0
$775$	19.1317	0.687229
$776$	9.84255	0.353327
$777$	0	0
$778$	49.3833	1.77048
$779$	−11.7442	−0.420780
$780$	0	0
$781$	−0.458740	−0.0164150
$782$	0	0
$783$	0	0
$784$	21.9463	0.783795
$785$	1.82058	0.0649794
$786$	0	0
$787$	26.8634	0.957577	0.478789	−	0.877930i	$-0.341076\pi$
$787$	26.8634	0.957577	0.478789	+	0.877930i	$0.341076\pi$
$788$	−31.0087	−1.10464
$789$	0	0
$790$	0.940265	0.0334531
$791$	−7.79292	−0.277084
$792$	0	0
$793$	−5.61081	−0.199246
$794$	47.8803	1.69921
$795$	0	0
$796$	−33.9745	−1.20420
$797$	18.8212	0.666681	0.333340	−	0.942807i	$-0.391824\pi$
$797$	18.8212	0.666681	0.333340	+	0.942807i	$0.391824\pi$
$798$	0	0
$799$	0	0
$800$	35.4270	1.25253
$801$	0	0
$802$	1.69284	0.0597762
$803$	31.7980	1.12213
$804$	0	0
$805$	1.36959	0.0482715
$806$	−32.9881	−1.16196
$807$	0	0
$808$	6.84255	0.240720
$809$	−25.7573	−0.905580	−0.452790	−	0.891617i	$-0.649571\pi$
$809$	−25.7573	−0.905580	−0.452790	+	0.891617i	$0.649571\pi$
$810$	0	0
$811$	26.4483	0.928726	0.464363	−	0.885645i	$-0.346283\pi$
$811$	26.4483	0.928726	0.464363	+	0.885645i	$0.346283\pi$
$812$	8.00774	0.281017
$813$	0	0
$814$	26.5817	0.931689
$815$	0.790555	0.0276919
$816$	0	0
$817$	−10.3182	−0.360988
$818$	−28.8033	−1.00709
$819$	0	0
$820$	1.15476	0.0403261
$821$	−31.5030	−1.09946	−0.549731	−	0.835342i	$-0.685270\pi$
$821$	−31.5030	−1.09946	−0.549731	+	0.835342i	$0.685270\pi$
$822$	0	0
$823$	11.6895	0.407472	0.203736	−	0.979026i	$-0.434692\pi$
$823$	11.6895	0.407472	0.203736	+	0.979026i	$0.434692\pi$
$824$	9.54993	0.332688
$825$	0	0
$826$	9.04963	0.314877
$827$	−3.32264	−0.115540	−0.0577698	−	0.998330i	$-0.518399\pi$
$827$	−3.32264	−0.115540	−0.0577698	+	0.998330i	$0.518399\pi$
$828$	0	0
$829$	6.01186	0.208801	0.104400	−	0.994535i	$-0.466708\pi$
$829$	6.01186	0.208801	0.104400	+	0.994535i	$0.466708\pi$
$830$	0.551689	0.0191494
$831$	0	0
$832$	−17.9358	−0.621813
$833$	0	0
$834$	0	0
$835$	−0.475652	−0.0164606
$836$	−7.75877	−0.268343
$837$	0	0
$838$	−4.48070	−0.154783
$839$	41.4115	1.42968	0.714841	−	0.699287i	$-0.246499\pi$
$839$	41.4115	1.42968	0.714841	+	0.699287i	$0.246499\pi$
$840$	0	0
$841$	−17.3618	−0.598684
$842$	−15.5722	−0.536654
$843$	0	0
$844$	−11.0119	−0.379044
$845$	0.955423	0.0328675
$846$	0	0
$847$	−5.72874	−0.196842
$848$	3.88175	0.133300
$849$	0	0
$850$	0	0
$851$	38.9026	1.33356
$852$	0	0
$853$	−23.9982	−0.821684	−0.410842	−	0.911706i	$-0.634765\pi$
$853$	−23.9982	−0.821684	−0.410842	+	0.911706i	$0.634765\pi$
$854$	−3.53209	−0.120866
$855$	0	0
$856$	−10.5895	−0.361940
$857$	31.8553	1.08816	0.544079	−	0.839034i	$-0.316879\pi$
$857$	31.8553	1.08816	0.544079	+	0.839034i	$0.316879\pi$
$858$	0	0
$859$	24.0806	0.821619	0.410810	−	0.911721i	$-0.365246\pi$
$859$	24.0806	0.821619	0.410810	+	0.911721i	$0.365246\pi$
$860$	1.01455	0.0345958
$861$	0	0
$862$	−60.7401	−2.06882
$863$	20.8590	0.710047	0.355024	−	0.934857i	$-0.384473\pi$
$863$	20.8590	0.710047	0.355024	+	0.934857i	$0.384473\pi$
$864$	0	0
$865$	−2.28373	−0.0776491
$866$	−28.3114	−0.962060
$867$	0	0
$868$	−9.00774	−0.305743
$869$	11.1771	0.379156
$870$	0	0
$871$	−66.8881	−2.26642
$872$	−5.81345	−0.196868
$873$	0	0
$874$	−26.1780	−0.885484
$875$	−1.84524	−0.0623804
$876$	0	0
$877$	−22.3669	−0.755276	−0.377638	−	0.925953i	$-0.623264\pi$
$877$	−22.3669	−0.755276	−0.377638	+	0.925953i	$0.623264\pi$
$878$	−4.83574	−0.163198
$879$	0	0
$880$	−1.53302	−0.0516782
$881$	56.4279	1.90110	0.950552	−	0.310566i	$-0.100518\pi$
$881$	56.4279	1.90110	0.950552	+	0.310566i	$0.100518\pi$
$882$	0	0
$883$	−45.4219	−1.52857	−0.764284	−	0.644879i	$-0.776908\pi$
$883$	−45.4219	−1.52857	−0.764284	+	0.644879i	$0.776908\pi$
$884$	0	0
$885$	0	0
$886$	−44.1019	−1.48163
$887$	17.4816	0.586976	0.293488	−	0.955963i	$-0.405184\pi$
$887$	17.4816	0.586976	0.293488	+	0.955963i	$0.405184\pi$
$888$	0	0
$889$	−3.37733	−0.113272
$890$	3.42097	0.114671
$891$	0	0
$892$	−9.22256	−0.308794
$893$	−13.8084	−0.462080
$894$	0	0
$895$	−0.874942	−0.0292461
$896$	10.4834	0.350226
$897$	0	0
$898$	−35.4415	−1.18270
$899$	−13.0915	−0.436627
$900$	0	0
$901$	0	0
$902$	31.6459	1.05369
$903$	0	0
$904$	4.47296	0.148769
$905$	−3.02734	−0.100632
$906$	0	0
$907$	10.4138	0.345786	0.172893	−	0.984941i	$-0.444689\pi$
$907$	10.4138	0.345786	0.172893	+	0.984941i	$0.444689\pi$
$908$	33.7597	1.12036
$909$	0	0
$910$	1.58853	0.0526591
$911$	44.2722	1.46680	0.733402	−	0.679796i	$-0.237932\pi$
$911$	44.2722	1.46680	0.733402	+	0.679796i	$0.237932\pi$
$912$	0	0
$913$	6.55800	0.217038
$914$	−3.96141	−0.131032
$915$	0	0
$916$	5.66819	0.187282
$917$	−3.05375	−0.100844
$918$	0	0
$919$	−31.0615	−1.02462	−0.512312	−	0.858799i	$-0.671211\pi$
$919$	−31.0615	−1.02462	−0.512312	+	0.858799i	$0.671211\pi$
$920$	−0.786112	−0.0259173
$921$	0	0
$922$	41.1729	1.35596
$923$	−0.778695	−0.0256311
$924$	0	0
$925$	−26.1685	−0.860415
$926$	26.6040	0.874262
$927$	0	0
$928$	−24.2422	−0.795788
$929$	22.3969	0.734819	0.367410	−	0.930059i	$-0.380245\pi$
$929$	22.3969	0.734819	0.367410	+	0.930059i	$0.380245\pi$
$930$	0	0
$931$	8.74422	0.286580
$932$	−44.6614	−1.46293
$933$	0	0
$934$	55.7948	1.82566
$935$	0	0
$936$	0	0
$937$	58.1661	1.90020	0.950102	−	0.311939i	$-0.100978\pi$
$937$	58.1661	1.90020	0.950102	+	0.311939i	$0.100978\pi$
$938$	−42.1070	−1.37484
$939$	0	0
$940$	1.35773	0.0442841
$941$	10.4397	0.340326	0.170163	−	0.985416i	$-0.445571\pi$
$941$	10.4397	0.340326	0.170163	+	0.985416i	$0.445571\pi$
$942$	0	0
$943$	46.3141	1.50819
$944$	−14.8247	−0.482503
$945$	0	0
$946$	27.8033	0.903965
$947$	−4.04364	−0.131401	−0.0657004	−	0.997839i	$-0.520928\pi$
$947$	−4.04364	−0.131401	−0.0657004	+	0.997839i	$0.520928\pi$
$948$	0	0
$949$	53.9760	1.75213
$950$	17.6091	0.571313
$951$	0	0
$952$	0	0
$953$	−4.37639	−0.141765	−0.0708826	−	0.997485i	$-0.522582\pi$
$953$	−4.37639	−0.141765	−0.0708826	+	0.997485i	$0.522582\pi$
$954$	0	0
$955$	−1.70739	−0.0552497
$956$	−19.1257	−0.618568
$957$	0	0
$958$	71.9728	2.32533
$959$	19.3405	0.624537
$960$	0	0
$961$	−16.2736	−0.524956
$962$	45.1215	1.45478
$963$	0	0
$964$	−24.8462	−0.800241
$965$	1.98183	0.0637974
$966$	0	0
$967$	24.4371	0.785843	0.392921	−	0.919572i	$-0.371464\pi$
$967$	24.4371	0.785843	0.392921	+	0.919572i	$0.371464\pi$
$968$	3.28817	0.105686
$969$	0	0
$970$	−2.53714	−0.0814627
$971$	−20.5253	−0.658688	−0.329344	−	0.944210i	$-0.606828\pi$
$971$	−20.5253	−0.658688	−0.329344	+	0.944210i	$0.606828\pi$
$972$	0	0
$973$	−8.01960	−0.257097
$974$	43.8854	1.40618
$975$	0	0
$976$	5.78611	0.185209
$977$	−28.3073	−0.905630	−0.452815	−	0.891605i	$-0.649580\pi$
$977$	−28.3073	−0.905630	−0.452815	+	0.891605i	$0.649580\pi$
$978$	0	0
$979$	40.6655	1.29967
$980$	−0.859785	−0.0274648
$981$	0	0
$982$	−58.9992	−1.88274
$983$	−26.6742	−0.850774	−0.425387	−	0.905012i	$-0.639862\pi$
$983$	−26.6742	−0.850774	−0.425387	+	0.905012i	$0.639862\pi$
$984$	0	0
$985$	−2.44118	−0.0777824
$986$	0	0
$987$	0	0
$988$	−13.1702	−0.419001
$989$	40.6905	1.29388
$990$	0	0
$991$	−34.8857	−1.10818	−0.554090	−	0.832457i	$-0.686934\pi$
$991$	−34.8857	−1.10818	−0.554090	+	0.832457i	$0.686934\pi$
$992$	27.2695	0.865808
$993$	0	0
$994$	−0.490200	−0.0155482
$995$	−2.67467	−0.0847927
$996$	0	0
$997$	45.3164	1.43519	0.717593	−	0.696463i	$-0.245244\pi$
$997$	45.3164	1.43519	0.717593	+	0.696463i	$0.245244\pi$
$998$	−30.3164	−0.959650
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2601.2.a.x.1.3		3
3.2	odd	2		289.2.a.d.1.1	✓	3
12.11	even	2		4624.2.a.bg.1.3		3
15.14	odd	2		7225.2.a.t.1.3		3
17.16	even	2		2601.2.a.w.1.3		3
51.2	odd	8		289.2.c.d.38.1		12
51.5	even	16		289.2.d.f.110.6		24
51.8	odd	8		289.2.c.d.251.6		12
51.11	even	16		289.2.d.f.155.2		24
51.14	even	16		289.2.d.f.179.2		24
51.20	even	16		289.2.d.f.179.1		24
51.23	even	16		289.2.d.f.155.1		24
51.26	odd	8		289.2.c.d.251.5		12
51.29	even	16		289.2.d.f.110.5		24
51.32	odd	8		289.2.c.d.38.2		12
51.38	odd	4		289.2.b.d.288.6		6
51.41	even	16		289.2.d.f.134.6		24
51.44	even	16		289.2.d.f.134.5		24
51.47	odd	4		289.2.b.d.288.5		6
51.50	odd	2		289.2.a.e.1.1	yes	3
204.203	even	2		4624.2.a.bd.1.1		3
255.254	odd	2		7225.2.a.s.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.2.a.d.1.1	✓	3	3.2	odd	2
289.2.a.e.1.1	yes	3	51.50	odd	2
289.2.b.d.288.5		6	51.47	odd	4
289.2.b.d.288.6		6	51.38	odd	4
289.2.c.d.38.1		12	51.2	odd	8
289.2.c.d.38.2		12	51.32	odd	8
289.2.c.d.251.5		12	51.26	odd	8
289.2.c.d.251.6		12	51.8	odd	8
289.2.d.f.110.5		24	51.29	even	16
289.2.d.f.110.6		24	51.5	even	16
289.2.d.f.134.5		24	51.44	even	16
289.2.d.f.134.6		24	51.41	even	16
289.2.d.f.155.1		24	51.23	even	16
289.2.d.f.155.2		24	51.11	even	16
289.2.d.f.179.1		24	51.20	even	16
289.2.d.f.179.2		24	51.14	even	16
2601.2.a.w.1.3		3	17.16	even	2
2601.2.a.x.1.3		3	1.1	even	1	trivial
4624.2.a.bd.1.1		3	204.203	even	2
4624.2.a.bg.1.3		3	12.11	even	2
7225.2.a.s.1.3		3	255.254	odd	2
7225.2.a.t.1.3		3	15.14	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)

\(f(q)\)	\(=\)	\(q+1.87939 q^{2} +1.53209 q^{4} +0.120615 q^{5} +1.53209 q^{7} -0.879385 q^{8} +O(q^{10})\)	\(q+1.87939 q^{2} +1.53209 q^{4} +0.120615 q^{5} +1.53209 q^{7} -0.879385 q^{8} +0.226682 q^{10} +2.69459 q^{11} +4.57398 q^{13} +2.87939 q^{14} -4.71688 q^{16} -1.87939 q^{19} +0.184793 q^{20} +5.06418 q^{22} +7.41147 q^{23} -4.98545 q^{25} +8.59627 q^{26} +2.34730 q^{28} +3.41147 q^{29} -3.83750 q^{31} -7.10607 q^{32} +0.184793 q^{35} +5.24897 q^{37} -3.53209 q^{38} -0.106067 q^{40} +6.24897 q^{41} +5.49020 q^{43} +4.12836 q^{44} +13.9290 q^{46} +7.34730 q^{47} -4.65270 q^{49} -9.36959 q^{50} +7.00774 q^{52} -0.822948 q^{53} +0.325008 q^{55} -1.34730 q^{56} +6.41147 q^{58} +3.14290 q^{59} -1.22668 q^{61} -7.21213 q^{62} -3.92127 q^{64} +0.551689 q^{65} -14.6236 q^{67} +0.347296 q^{70} -0.170245 q^{71} +11.8007 q^{73} +9.86484 q^{74} -2.87939 q^{76} +4.12836 q^{77} +4.14796 q^{79} -0.568926 q^{80} +11.7442 q^{82} +2.43376 q^{83} +10.3182 q^{86} -2.36959 q^{88} +15.0915 q^{89} +7.00774 q^{91} +11.3550 q^{92} +13.8084 q^{94} -0.226682 q^{95} -11.1925 q^{97} -8.74422 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 6 q^{5} + 3 q^{8}+O(q^{10}) \) 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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