LMFDB - Embedded newform 2583.2.a.l.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2583,2,Mod(1,2583)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2583, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("2583.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2583 = 3^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2583.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:	$20.6253588421$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{14})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 2x + 1 $ x^3 - x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 287)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.80194$ of defining polynomial
Character	$\chi$	$=$	2583.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.80194 q^{2} +5.85086 q^{4} +2.49396 q^{5} -1.00000 q^{7} -10.7899 q^{8} +O(q^{10})$	\(q-2.80194 q^{2} +5.85086 q^{4} +2.49396 q^{5} -1.00000 q^{7} -10.7899 q^{8} -6.98792 q^{10} +1.10992 q^{11} +5.15883 q^{13} +2.80194 q^{14} +18.5308 q^{16} +6.45473 q^{17} -1.86294 q^{19} +14.5918 q^{20} -3.10992 q^{22} +3.08815 q^{23} +1.21983 q^{25} -14.4547 q^{26} -5.85086 q^{28} -0.219833 q^{29} -0.670251 q^{31} -30.3424 q^{32} -18.0858 q^{34} -2.49396 q^{35} +1.33513 q^{37} +5.21983 q^{38} -26.9095 q^{40} -1.00000 q^{41} +11.3448 q^{43} +6.49396 q^{44} -8.65279 q^{46} -4.44504 q^{47} +1.00000 q^{49} -3.41789 q^{50} +30.1836 q^{52} +6.89008 q^{53} +2.76809 q^{55} +10.7899 q^{56} +0.615957 q^{58} -13.3056 q^{59} +6.27413 q^{61} +1.87800 q^{62} +47.9560 q^{64} +12.8659 q^{65} -14.7138 q^{67} +37.7657 q^{68} +6.98792 q^{70} +6.98792 q^{71} +5.20775 q^{73} -3.74094 q^{74} -10.8998 q^{76} -1.10992 q^{77} +0.792249 q^{79} +46.2150 q^{80} +2.80194 q^{82} +8.76809 q^{83} +16.0978 q^{85} -31.7875 q^{86} -11.9758 q^{88} -9.70709 q^{89} -5.15883 q^{91} +18.0683 q^{92} +12.4547 q^{94} -4.64609 q^{95} +8.29590 q^{97} -2.80194 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 4 q^{2} + 4 q^{4} - 2 q^{5} - 3 q^{7} - 9 q^{8}+O(q^{10}) $ 3 * q - 4 * q^2 + 4 * q^4 - 2 * q^5 - 3 * q^7 - 9 * q^8	$ 3 q - 4 q^{2} + 4 q^{4} - 2 q^{5} - 3 q^{7} - 9 q^{8} - 2 q^{10} + 4 q^{11} + 7 q^{13} + 4 q^{14} + 18 q^{16} - 3 q^{17} - 11 q^{19} + 16 q^{20} - 10 q^{22} + 13 q^{23} + 5 q^{25} - 21 q^{26} - 4 q^{28} - 2 q^{29} - 27 q^{32} - 17 q^{34} + 2 q^{35} + 3 q^{37} + 17 q^{38} - 36 q^{40} - 3 q^{41} + 11 q^{43} + 10 q^{44} - 8 q^{46} - 13 q^{47} + 3 q^{49} - 16 q^{50} + 35 q^{52} + 20 q^{53} - 12 q^{55} + 9 q^{56} + 12 q^{58} - 4 q^{59} + 8 q^{61} - 14 q^{62} + 49 q^{64} - 36 q^{67} + 52 q^{68} + 2 q^{70} + 2 q^{71} - 2 q^{73} + 3 q^{74} - 10 q^{76} - 4 q^{77} + 20 q^{79} + 58 q^{80} + 4 q^{82} + 6 q^{83} + 30 q^{85} - 31 q^{86} + 2 q^{88} + q^{89} - 7 q^{91} + q^{92} + 15 q^{94} + 26 q^{95} + 11 q^{97} - 4 q^{98}+O(q^{100}) $ 3 * q - 4 * q^2 + 4 * q^4 - 2 * q^5 - 3 * q^7 - 9 * q^8 - 2 * q^10 + 4 * q^11 + 7 * q^13 + 4 * q^14 + 18 * q^16 - 3 * q^17 - 11 * q^19 + 16 * q^20 - 10 * q^22 + 13 * q^23 + 5 * q^25 - 21 * q^26 - 4 * q^28 - 2 * q^29 - 27 * q^32 - 17 * q^34 + 2 * q^35 + 3 * q^37 + 17 * q^38 - 36 * q^40 - 3 * q^41 + 11 * q^43 + 10 * q^44 - 8 * q^46 - 13 * q^47 + 3 * q^49 - 16 * q^50 + 35 * q^52 + 20 * q^53 - 12 * q^55 + 9 * q^56 + 12 * q^58 - 4 * q^59 + 8 * q^61 - 14 * q^62 + 49 * q^64 - 36 * q^67 + 52 * q^68 + 2 * q^70 + 2 * q^71 - 2 * q^73 + 3 * q^74 - 10 * q^76 - 4 * q^77 + 20 * q^79 + 58 * q^80 + 4 * q^82 + 6 * q^83 + 30 * q^85 - 31 * q^86 + 2 * q^88 + q^89 - 7 * q^91 + q^92 + 15 * q^94 + 26 * q^95 + 11 * q^97 - 4 * 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 $

$2$	−2.80194	−1.98127	−0.990635	−	0.136540i	$-0.956402\pi$
$2$	−2.80194	−1.98127	−0.990635	+	0.136540i	$0.956402\pi$
$3$	0	0
$3$	0	0
$4$	5.85086	2.92543
$5$	2.49396	1.11533	0.557666	−	0.830065i	$-0.311697\pi$
$5$	2.49396	1.11533	0.557666	+	0.830065i	$0.311697\pi$
$6$	0	0
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−10.7899	−3.81479
$9$	0	0
$10$	−6.98792	−2.20977
$11$	1.10992	0.334652	0.167326	−	0.985902i	$-0.446487\pi$
$11$	1.10992	0.334652	0.167326	+	0.985902i	$0.446487\pi$
$12$	0	0
$13$	5.15883	1.43080	0.715402	−	0.698714i	$-0.246244\pi$
$13$	5.15883	1.43080	0.715402	+	0.698714i	$0.246244\pi$
$14$	2.80194	0.748849
$15$	0	0
$16$	18.5308	4.63270
$17$	6.45473	1.56550	0.782751	−	0.622335i	$-0.213816\pi$
$17$	6.45473	1.56550	0.782751	+	0.622335i	$0.213816\pi$
$18$	0	0
$19$	−1.86294	−0.427387	−0.213693	−	0.976901i	$-0.568549\pi$
$19$	−1.86294	−0.427387	−0.213693	+	0.976901i	$0.568549\pi$
$20$	14.5918	3.26282
$21$	0	0
$22$	−3.10992	−0.663036
$23$	3.08815	0.643923	0.321961	−	0.946753i	$-0.395658\pi$
$23$	3.08815	0.643923	0.321961	+	0.946753i	$0.395658\pi$
$24$	0	0
$25$	1.21983	0.243967
$26$	−14.4547	−2.83481
$27$	0	0
$28$	−5.85086	−1.10571
$29$	−0.219833	−0.0408219	−0.0204109	−	0.999792i	$-0.506497\pi$
$29$	−0.219833	−0.0408219	−0.0204109	+	0.999792i	$0.506497\pi$
$30$	0	0
$31$	−0.670251	−0.120381	−0.0601903	−	0.998187i	$-0.519171\pi$
$31$	−0.670251	−0.120381	−0.0601903	+	0.998187i	$0.519171\pi$
$32$	−30.3424	−5.36383
$33$	0	0
$34$	−18.0858	−3.10168
$35$	−2.49396	−0.421556
$36$	0	0
$37$	1.33513	0.219493	0.109747	−	0.993960i	$-0.464996\pi$
$37$	1.33513	0.219493	0.109747	+	0.993960i	$0.464996\pi$
$38$	5.21983	0.846769
$39$	0	0
$40$	−26.9095	−4.25476
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	11.3448	1.73007	0.865034	−	0.501713i	$-0.167297\pi$
$43$	11.3448	1.73007	0.865034	+	0.501713i	$0.167297\pi$
$44$	6.49396	0.979001
$45$	0	0
$46$	−8.65279	−1.27578
$47$	−4.44504	−0.648376	−0.324188	−	0.945993i	$-0.605091\pi$
$47$	−4.44504	−0.648376	−0.324188	+	0.945993i	$0.605091\pi$
$48$	0	0
$49$	1.00000	0.142857
$50$	−3.41789	−0.483363
$51$	0	0
$52$	30.1836	4.18571
$53$	6.89008	0.946426	0.473213	−	0.880948i	$-0.343094\pi$
$53$	6.89008	0.946426	0.473213	+	0.880948i	$0.343094\pi$
$54$	0	0
$55$	2.76809	0.373249
$56$	10.7899	1.44186
$57$	0	0
$58$	0.615957	0.0808791
$59$	−13.3056	−1.73224	−0.866120	−	0.499836i	$-0.833393\pi$
$59$	−13.3056	−1.73224	−0.866120	+	0.499836i	$0.833393\pi$
$60$	0	0
$61$	6.27413	0.803320	0.401660	−	0.915789i	$-0.368433\pi$
$61$	6.27413	0.803320	0.401660	+	0.915789i	$0.368433\pi$
$62$	1.87800	0.238507
$63$	0	0
$64$	47.9560	5.99450
$65$	12.8659	1.59582
$66$	0	0
$67$	−14.7138	−1.79758	−0.898788	−	0.438384i	$-0.855551\pi$
$67$	−14.7138	−1.79758	−0.898788	+	0.438384i	$0.855551\pi$
$68$	37.7657	4.57976
$69$	0	0
$70$	6.98792	0.835216
$71$	6.98792	0.829313	0.414657	−	0.909978i	$-0.363902\pi$
$71$	6.98792	0.829313	0.414657	+	0.909978i	$0.363902\pi$
$72$	0	0
$73$	5.20775	0.609521	0.304761	−	0.952429i	$-0.401424\pi$
$73$	5.20775	0.609521	0.304761	+	0.952429i	$0.401424\pi$
$74$	−3.74094	−0.434875
$75$	0	0
$76$	−10.8998	−1.25029
$77$	−1.10992	−0.126487
$78$	0	0
$79$	0.792249	0.0891350	0.0445675	−	0.999006i	$-0.485809\pi$
$79$	0.792249	0.0891350	0.0445675	+	0.999006i	$0.485809\pi$
$80$	46.2150	5.16700
$81$	0	0
$82$	2.80194	0.309422
$83$	8.76809	0.962422	0.481211	−	0.876605i	$-0.340197\pi$
$83$	8.76809	0.962422	0.481211	+	0.876605i	$0.340197\pi$
$84$	0	0
$85$	16.0978	1.74606
$86$	−31.7875	−3.42773
$87$	0	0
$88$	−11.9758	−1.27663
$89$	−9.70709	−1.02895	−0.514475	−	0.857506i	$-0.672013\pi$
$89$	−9.70709	−1.02895	−0.514475	+	0.857506i	$0.672013\pi$
$90$	0	0
$91$	−5.15883	−0.540793
$92$	18.0683	1.88375
$93$	0	0
$94$	12.4547	1.28461
$95$	−4.64609	−0.476679
$96$	0	0
$97$	8.29590	0.842321	0.421160	−	0.906986i	$-0.361623\pi$
$97$	8.29590	0.842321	0.421160	+	0.906986i	$0.361623\pi$
$98$	−2.80194	−0.283038
$99$	0	0
$100$	7.13706	0.713706
$101$	7.46011	0.742308	0.371154	−	0.928571i	$-0.378962\pi$
$101$	7.46011	0.742308	0.371154	+	0.928571i	$0.378962\pi$
$102$	0	0
$103$	−4.59179	−0.452443	−0.226221	−	0.974076i	$-0.572637\pi$
$103$	−4.59179	−0.452443	−0.226221	+	0.974076i	$0.572637\pi$
$104$	−55.6631	−5.45821
$105$	0	0
$106$	−19.3056	−1.87512
$107$	−0.137063	−0.0132504	−0.00662521	−	0.999978i	$-0.502109\pi$
$107$	−0.137063	−0.0132504	−0.00662521	+	0.999978i	$0.502109\pi$
$108$	0	0
$109$	−7.48188	−0.716634	−0.358317	−	0.933600i	$-0.616649\pi$
$109$	−7.48188	−0.716634	−0.358317	+	0.933600i	$0.616649\pi$
$110$	−7.75600	−0.739506
$111$	0	0
$112$	−18.5308	−1.75100
$113$	−10.7899	−1.01502	−0.507512	−	0.861645i	$-0.669435\pi$
$113$	−10.7899	−1.01502	−0.507512	+	0.861645i	$0.669435\pi$
$114$	0	0
$115$	7.70171	0.718188
$116$	−1.28621	−0.119421
$117$	0	0
$118$	37.2814	3.43203
$119$	−6.45473	−0.591704
$120$	0	0
$121$	−9.76809	−0.888008
$122$	−17.5797	−1.59159
$123$	0	0
$124$	−3.92154	−0.352165
$125$	−9.42758	−0.843229
$126$	0	0
$127$	0.963164	0.0854670	0.0427335	−	0.999087i	$-0.486393\pi$
$127$	0.963164	0.0854670	0.0427335	+	0.999087i	$0.486393\pi$
$128$	−73.6848	−6.51288
$129$	0	0
$130$	−36.0495	−3.16175
$131$	10.5918	0.925409	0.462705	−	0.886512i	$-0.346879\pi$
$131$	10.5918	0.925409	0.462705	+	0.886512i	$0.346879\pi$
$132$	0	0
$133$	1.86294	0.161537
$134$	41.2271	3.56148
$135$	0	0
$136$	−69.6456	−5.97206
$137$	6.89008	0.588660	0.294330	−	0.955704i	$-0.404904\pi$
$137$	6.89008	0.588660	0.294330	+	0.955704i	$0.404904\pi$
$138$	0	0
$139$	−7.57971	−0.642903	−0.321451	−	0.946926i	$-0.604171\pi$
$139$	−7.57971	−0.642903	−0.321451	+	0.946926i	$0.604171\pi$
$140$	−14.5918	−1.23323
$141$	0	0
$142$	−19.5797	−1.64309
$143$	5.72587	0.478822
$144$	0	0
$145$	−0.548253	−0.0455300
$146$	−14.5918	−1.20763
$147$	0	0
$148$	7.81163	0.642112
$149$	−11.2620	−0.922623	−0.461311	−	0.887238i	$-0.652621\pi$
$149$	−11.2620	−0.922623	−0.461311	+	0.887238i	$0.652621\pi$
$150$	0	0
$151$	−4.19567	−0.341439	−0.170719	−	0.985320i	$-0.554609\pi$
$151$	−4.19567	−0.341439	−0.170719	+	0.985320i	$0.554609\pi$
$152$	20.1008	1.63039
$153$	0	0
$154$	3.10992	0.250604
$155$	−1.67158	−0.134264
$156$	0	0
$157$	11.0814	0.884395	0.442198	−	0.896918i	$-0.354199\pi$
$157$	11.0814	0.884395	0.442198	+	0.896918i	$0.354199\pi$
$158$	−2.21983	−0.176600
$159$	0	0
$160$	−75.6728	−5.98246
$161$	−3.08815	−0.243380
$162$	0	0
$163$	−7.67994	−0.601539	−0.300770	−	0.953697i	$-0.597244\pi$
$163$	−7.67994	−0.601539	−0.300770	+	0.953697i	$0.597244\pi$
$164$	−5.85086	−0.456875
$165$	0	0
$166$	−24.5676	−1.90682
$167$	21.3448	1.65171	0.825856	−	0.563882i	$-0.190693\pi$
$167$	21.3448	1.65171	0.825856	+	0.563882i	$0.190693\pi$
$168$	0	0
$169$	13.6136	1.04720
$170$	−45.1051	−3.45941
$171$	0	0
$172$	66.3769	5.06119
$173$	13.3056	1.01160	0.505802	−	0.862649i	$-0.331196\pi$
$173$	13.3056	1.01160	0.505802	+	0.862649i	$0.331196\pi$
$174$	0	0
$175$	−1.21983	−0.0922107
$176$	20.5676	1.55034
$177$	0	0
$178$	27.1987	2.03863
$179$	−6.37196	−0.476263	−0.238131	−	0.971233i	$-0.576535\pi$
$179$	−6.37196	−0.476263	−0.238131	+	0.971233i	$0.576535\pi$
$180$	0	0
$181$	6.07606	0.451630	0.225815	−	0.974170i	$-0.427495\pi$
$181$	6.07606	0.451630	0.225815	+	0.974170i	$0.427495\pi$
$182$	14.4547	1.07146
$183$	0	0
$184$	−33.3207	−2.45643
$185$	3.32975	0.244808
$186$	0	0
$187$	7.16421	0.523899
$188$	−26.0073	−1.89678
$189$	0	0
$190$	13.0180	0.944429
$191$	5.87800	0.425317	0.212659	−	0.977127i	$-0.431788\pi$
$191$	5.87800	0.425317	0.212659	+	0.977127i	$0.431788\pi$
$192$	0	0
$193$	13.2862	0.956362	0.478181	−	0.878261i	$-0.341296\pi$
$193$	13.2862	0.956362	0.478181	+	0.878261i	$0.341296\pi$
$194$	−23.2446	−1.66886
$195$	0	0
$196$	5.85086	0.417918
$197$	−4.09352	−0.291651	−0.145826	−	0.989310i	$-0.546584\pi$
$197$	−4.09352	−0.291651	−0.145826	+	0.989310i	$0.546584\pi$
$198$	0	0
$199$	−1.67696	−0.118876	−0.0594381	−	0.998232i	$-0.518931\pi$
$199$	−1.67696	−0.118876	−0.0594381	+	0.998232i	$0.518931\pi$
$200$	−13.1618	−0.930681
$201$	0	0
$202$	−20.9028	−1.47071
$203$	0.219833	0.0154292
$204$	0	0
$205$	−2.49396	−0.174186
$206$	12.8659	0.896411
$207$	0	0
$208$	95.5973	6.62848
$209$	−2.06770	−0.143026
$210$	0	0
$211$	−21.6775	−1.49234	−0.746172	−	0.665753i	$-0.768110\pi$
$211$	−21.6775	−1.49234	−0.746172	+	0.665753i	$0.768110\pi$
$212$	40.3129	2.76870
$213$	0	0
$214$	0.384043	0.0262526
$215$	28.2935	1.92960
$216$	0	0
$217$	0.670251	0.0454996
$218$	20.9638	1.41984
$219$	0	0
$220$	16.1957	1.09191
$221$	33.2989	2.23993
$222$	0	0
$223$	−12.1763	−0.815385	−0.407692	−	0.913119i	$-0.633666\pi$
$223$	−12.1763	−0.815385	−0.407692	+	0.913119i	$0.633666\pi$
$224$	30.3424	2.02734
$225$	0	0
$226$	30.2325	2.01104
$227$	3.01208	0.199919	0.0999594	−	0.994992i	$-0.468129\pi$
$227$	3.01208	0.199919	0.0999594	+	0.994992i	$0.468129\pi$
$228$	0	0
$229$	−17.0834	−1.12890	−0.564450	−	0.825467i	$-0.690912\pi$
$229$	−17.0834	−1.12890	−0.564450	+	0.825467i	$0.690912\pi$
$230$	−21.5797	−1.42292
$231$	0	0
$232$	2.37196	0.155727
$233$	−14.7681	−0.967489	−0.483745	−	0.875209i	$-0.660724\pi$
$233$	−14.7681	−0.967489	−0.483745	+	0.875209i	$0.660724\pi$
$234$	0	0
$235$	−11.0858	−0.723155
$236$	−77.8491	−5.06754
$237$	0	0
$238$	18.0858	1.17233
$239$	−11.5797	−0.749029	−0.374515	−	0.927221i	$-0.622191\pi$
$239$	−11.5797	−0.749029	−0.374515	+	0.927221i	$0.622191\pi$
$240$	0	0
$241$	30.7090	1.97814	0.989070	−	0.147443i	$-0.0471045\pi$
$241$	30.7090	1.97814	0.989070	+	0.147443i	$0.0471045\pi$
$242$	27.3696	1.75938
$243$	0	0
$244$	36.7090	2.35005
$245$	2.49396	0.159333
$246$	0	0
$247$	−9.61058	−0.611507
$248$	7.23191	0.459227
$249$	0	0
$250$	26.4155	1.67066
$251$	13.3840	0.844793	0.422397	−	0.906411i	$-0.361189\pi$
$251$	13.3840	0.844793	0.422397	+	0.906411i	$0.361189\pi$
$252$	0	0
$253$	3.42758	0.215490
$254$	−2.69873	−0.169333
$255$	0	0
$256$	110.548	6.90927
$257$	−21.9191	−1.36728	−0.683639	−	0.729820i	$-0.739604\pi$
$257$	−21.9191	−1.36728	−0.683639	+	0.729820i	$0.739604\pi$
$258$	0	0
$259$	−1.33513	−0.0829607
$260$	75.2766	4.66846
$261$	0	0
$262$	−29.6775	−1.83348
$263$	−14.3720	−0.886213	−0.443107	−	0.896469i	$-0.646124\pi$
$263$	−14.3720	−0.886213	−0.443107	+	0.896469i	$0.646124\pi$
$264$	0	0
$265$	17.1836	1.05558
$266$	−5.21983	−0.320048
$267$	0	0
$268$	−86.0883	−5.25868
$269$	21.5013	1.31095	0.655477	−	0.755215i	$-0.272467\pi$
$269$	21.5013	1.31095	0.655477	+	0.755215i	$0.272467\pi$
$270$	0	0
$271$	−26.2741	−1.59604	−0.798020	−	0.602631i	$-0.794119\pi$
$271$	−26.2741	−1.59604	−0.798020	+	0.602631i	$0.794119\pi$
$272$	119.611	7.25250
$273$	0	0
$274$	−19.3056	−1.16629
$275$	1.35391	0.0816440
$276$	0	0
$277$	−3.18598	−0.191427	−0.0957135	−	0.995409i	$-0.530513\pi$
$277$	−3.18598	−0.191427	−0.0957135	+	0.995409i	$0.530513\pi$
$278$	21.2379	1.27376
$279$	0	0
$280$	26.9095	1.60815
$281$	6.58104	0.392592	0.196296	−	0.980545i	$-0.437109\pi$
$281$	6.58104	0.392592	0.196296	+	0.980545i	$0.437109\pi$
$282$	0	0
$283$	22.4155	1.33246	0.666232	−	0.745745i	$-0.267906\pi$
$283$	22.4155	1.33246	0.666232	+	0.745745i	$0.267906\pi$
$284$	40.8853	2.42610
$285$	0	0
$286$	−16.0435	−0.948674
$287$	1.00000	0.0590281
$288$	0	0
$289$	24.6635	1.45080
$290$	1.53617	0.0902071
$291$	0	0
$292$	30.4698	1.78311
$293$	12.7681	0.745920	0.372960	−	0.927848i	$-0.378343\pi$
$293$	12.7681	0.745920	0.372960	+	0.927848i	$0.378343\pi$
$294$	0	0
$295$	−33.1836	−1.93202
$296$	−14.4058	−0.837321
$297$	0	0
$298$	31.5555	1.82796
$299$	15.9312	0.921327
$300$	0	0
$301$	−11.3448	−0.653904
$302$	11.7560	0.676482
$303$	0	0
$304$	−34.5217	−1.97996
$305$	15.6474	0.895968
$306$	0	0
$307$	−12.6703	−0.723129	−0.361565	−	0.932347i	$-0.617757\pi$
$307$	−12.6703	−0.723129	−0.361565	+	0.932347i	$0.617757\pi$
$308$	−6.49396	−0.370028
$309$	0	0
$310$	4.68366	0.266014
$311$	22.0586	1.25083	0.625414	−	0.780293i	$-0.284930\pi$
$311$	22.0586	1.25083	0.625414	+	0.780293i	$0.284930\pi$
$312$	0	0
$313$	−5.30127	−0.299646	−0.149823	−	0.988713i	$-0.547870\pi$
$313$	−5.30127	−0.299646	−0.149823	+	0.988713i	$0.547870\pi$
$314$	−31.0495	−1.75223
$315$	0	0
$316$	4.63533	0.260758
$317$	32.6896	1.83603	0.918016	−	0.396543i	$-0.129790\pi$
$317$	32.6896	1.83603	0.918016	+	0.396543i	$0.129790\pi$
$318$	0	0
$319$	−0.243996	−0.0136611
$320$	119.600	6.68586
$321$	0	0
$322$	8.65279	0.482201
$323$	−12.0248	−0.669075
$324$	0	0
$325$	6.29291	0.349068
$326$	21.5187	1.19181
$327$	0	0
$328$	10.7899	0.595770
$329$	4.44504	0.245063
$330$	0	0
$331$	−0.879330	−0.0483324	−0.0241662	−	0.999708i	$-0.507693\pi$
$331$	−0.879330	−0.0483324	−0.0241662	+	0.999708i	$0.507693\pi$
$332$	51.3008	2.81550
$333$	0	0
$334$	−59.8068	−3.27248
$335$	−36.6956	−2.00489
$336$	0	0
$337$	31.5821	1.72039	0.860193	−	0.509968i	$-0.170343\pi$
$337$	31.5821	1.72039	0.860193	+	0.509968i	$0.170343\pi$
$338$	−38.1444	−2.07478
$339$	0	0
$340$	94.1861	5.10796
$341$	−0.743923	−0.0402857
$342$	0	0
$343$	−1.00000	−0.0539949
$344$	−122.409	−6.59985
$345$	0	0
$346$	−37.2814	−2.00426
$347$	15.2862	0.820607	0.410303	−	0.911949i	$-0.365423\pi$
$347$	15.2862	0.820607	0.410303	+	0.911949i	$0.365423\pi$
$348$	0	0
$349$	−18.2634	−0.977616	−0.488808	−	0.872391i	$-0.662568\pi$
$349$	−18.2634	−0.977616	−0.488808	+	0.872391i	$0.662568\pi$
$350$	3.41789	0.182694
$351$	0	0
$352$	−33.6775	−1.79502
$353$	2.23921	0.119181	0.0595906	−	0.998223i	$-0.481020\pi$
$353$	2.23921	0.119181	0.0595906	+	0.998223i	$0.481020\pi$
$354$	0	0
$355$	17.4276	0.924960
$356$	−56.7948	−3.01012
$357$	0	0
$358$	17.8538	0.943605
$359$	5.70709	0.301209	0.150604	−	0.988594i	$-0.451878\pi$
$359$	5.70709	0.301209	0.150604	+	0.988594i	$0.451878\pi$
$360$	0	0
$361$	−15.5295	−0.817340
$362$	−17.0248	−0.894801
$363$	0	0
$364$	−30.1836	−1.58205
$365$	12.9879	0.679819
$366$	0	0
$367$	24.1715	1.26174	0.630871	−	0.775888i	$-0.282698\pi$
$367$	24.1715	1.26174	0.630871	+	0.775888i	$0.282698\pi$
$368$	57.2258	2.98310
$369$	0	0
$370$	−9.32975	−0.485031
$371$	−6.89008	−0.357715
$372$	0	0
$373$	−19.9366	−1.03228	−0.516139	−	0.856505i	$-0.672631\pi$
$373$	−19.9366	−1.03228	−0.516139	+	0.856505i	$0.672631\pi$
$374$	−20.0737	−1.03798
$375$	0	0
$376$	47.9614	2.47342
$377$	−1.13408	−0.0584081
$378$	0	0
$379$	3.76702	0.193499	0.0967494	−	0.995309i	$-0.469155\pi$
$379$	3.76702	0.193499	0.0967494	+	0.995309i	$0.469155\pi$
$380$	−27.1836	−1.39449
$381$	0	0
$382$	−16.4698	−0.842668
$383$	3.36227	0.171804	0.0859021	−	0.996304i	$-0.472623\pi$
$383$	3.36227	0.171804	0.0859021	+	0.996304i	$0.472623\pi$
$384$	0	0
$385$	−2.76809	−0.141075
$386$	−37.2271	−1.89481
$387$	0	0
$388$	48.5381	2.46415
$389$	−3.11529	−0.157952	−0.0789758	−	0.996877i	$-0.525165\pi$
$389$	−3.11529	−0.157952	−0.0789758	+	0.996877i	$0.525165\pi$
$390$	0	0
$391$	19.9332	1.00806
$392$	−10.7899	−0.544970
$393$	0	0
$394$	11.4698	0.577840
$395$	1.97584	0.0994151
$396$	0	0
$397$	30.7439	1.54299	0.771497	−	0.636233i	$-0.219508\pi$
$397$	30.7439	1.54299	0.771497	+	0.636233i	$0.219508\pi$
$398$	4.69873	0.235526
$399$	0	0
$400$	22.6045	1.13022
$401$	3.55496	0.177526	0.0887631	−	0.996053i	$-0.471709\pi$
$401$	3.55496	0.177526	0.0887631	+	0.996053i	$0.471709\pi$
$402$	0	0
$403$	−3.45771	−0.172241
$404$	43.6480	2.17157
$405$	0	0
$406$	−0.615957	−0.0305694
$407$	1.48188	0.0734539
$408$	0	0
$409$	13.4577	0.665441	0.332721	−	0.943025i	$-0.392033\pi$
$409$	13.4577	0.665441	0.332721	+	0.943025i	$0.392033\pi$
$410$	6.98792	0.345109
$411$	0	0
$412$	−26.8659	−1.32359
$413$	13.3056	0.654725
$414$	0	0
$415$	21.8672	1.07342
$416$	−156.532	−7.67459
$417$	0	0
$418$	5.79358	0.283373
$419$	−14.8116	−0.723595	−0.361798	−	0.932257i	$-0.617837\pi$
$419$	−14.8116	−0.723595	−0.361798	+	0.932257i	$0.617837\pi$
$420$	0	0
$421$	21.8866	1.06669	0.533344	−	0.845898i	$-0.320935\pi$
$421$	21.8866	1.06669	0.533344	+	0.845898i	$0.320935\pi$
$422$	60.7391	2.95673
$423$	0	0
$424$	−74.3430	−3.61042
$425$	7.87369	0.381930
$426$	0	0
$427$	−6.27413	−0.303626
$428$	−0.801938	−0.0387631
$429$	0	0
$430$	−79.2766	−3.82306
$431$	−10.0242	−0.482847	−0.241423	−	0.970420i	$-0.577614\pi$
$431$	−10.0242	−0.482847	−0.241423	+	0.970420i	$0.577614\pi$
$432$	0	0
$433$	−6.17151	−0.296584	−0.148292	−	0.988944i	$-0.547377\pi$
$433$	−6.17151	−0.296584	−0.148292	+	0.988944i	$0.547377\pi$
$434$	−1.87800	−0.0901470
$435$	0	0
$436$	−43.7754	−2.09646
$437$	−5.75302	−0.275204
$438$	0	0
$439$	−25.4252	−1.21348	−0.606739	−	0.794901i	$-0.707523\pi$
$439$	−25.4252	−1.21348	−0.606739	+	0.794901i	$0.707523\pi$
$440$	−29.8672	−1.42387
$441$	0	0
$442$	−93.3014	−4.43789
$443$	−19.1454	−0.909627	−0.454813	−	0.890587i	$-0.650294\pi$
$443$	−19.1454	−0.909627	−0.454813	+	0.890587i	$0.650294\pi$
$444$	0	0
$445$	−24.2091	−1.14762
$446$	34.1172	1.61550
$447$	0	0
$448$	−47.9560	−2.26571
$449$	−15.8649	−0.748709	−0.374354	−	0.927286i	$-0.622136\pi$
$449$	−15.8649	−0.748709	−0.374354	+	0.927286i	$0.622136\pi$
$450$	0	0
$451$	−1.10992	−0.0522639
$452$	−63.1299	−2.96938
$453$	0	0
$454$	−8.43967	−0.396093
$455$	−12.8659	−0.603164
$456$	0	0
$457$	18.7004	0.874767	0.437383	−	0.899275i	$-0.355905\pi$
$457$	18.7004	0.874767	0.437383	+	0.899275i	$0.355905\pi$
$458$	47.8665	2.23666
$459$	0	0
$460$	45.0616	2.10101
$461$	−7.86725	−0.366414	−0.183207	−	0.983074i	$-0.558648\pi$
$461$	−7.86725	−0.366414	−0.183207	+	0.983074i	$0.558648\pi$
$462$	0	0
$463$	27.7995	1.29195	0.645977	−	0.763357i	$-0.276450\pi$
$463$	27.7995	1.29195	0.645977	+	0.763357i	$0.276450\pi$
$464$	−4.07367	−0.189115
$465$	0	0
$466$	41.3793	1.91686
$467$	−16.4504	−0.761235	−0.380617	−	0.924733i	$-0.624288\pi$
$467$	−16.4504	−0.761235	−0.380617	+	0.924733i	$0.624288\pi$
$468$	0	0
$469$	14.7138	0.679420
$470$	31.0616	1.43276
$471$	0	0
$472$	143.565	6.60813
$473$	12.5918	0.578971
$474$	0	0
$475$	−2.27247	−0.104268
$476$	−37.7657	−1.73099
$477$	0	0
$478$	32.4456	1.48403
$479$	29.7778	1.36058	0.680291	−	0.732942i	$-0.261854\pi$
$479$	29.7778	1.36058	0.680291	+	0.732942i	$0.261854\pi$
$480$	0	0
$481$	6.88769	0.314052
$482$	−86.0447	−3.91923
$483$	0	0
$484$	−57.1517	−2.59780
$485$	20.6896	0.939468
$486$	0	0
$487$	9.80864	0.444472	0.222236	−	0.974993i	$-0.428664\pi$
$487$	9.80864	0.444472	0.222236	+	0.974993i	$0.428664\pi$
$488$	−67.6969	−3.06450
$489$	0	0
$490$	−6.98792	−0.315682
$491$	21.5907	0.974376	0.487188	−	0.873297i	$-0.338023\pi$
$491$	21.5907	0.974376	0.487188	+	0.873297i	$0.338023\pi$
$492$	0	0
$493$	−1.41896	−0.0639067
$494$	26.9282	1.21156
$495$	0	0
$496$	−12.4203	−0.557687
$497$	−6.98792	−0.313451
$498$	0	0
$499$	9.19700	0.411714	0.205857	−	0.978582i	$-0.434002\pi$
$499$	9.19700	0.411714	0.205857	+	0.978582i	$0.434002\pi$
$500$	−55.1594	−2.46680
$501$	0	0
$502$	−37.5013	−1.67376
$503$	4.63773	0.206786	0.103393	−	0.994641i	$-0.467030\pi$
$503$	4.63773	0.206786	0.103393	+	0.994641i	$0.467030\pi$
$504$	0	0
$505$	18.6052	0.827921
$506$	−9.60388	−0.426944
$507$	0	0
$508$	5.63533	0.250028
$509$	−31.4282	−1.39303	−0.696515	−	0.717543i	$-0.745267\pi$
$509$	−31.4282	−1.39303	−0.696515	+	0.717543i	$0.745267\pi$
$510$	0	0
$511$	−5.20775	−0.230377
$512$	−162.380	−7.17625
$513$	0	0
$514$	61.4161	2.70895
$515$	−11.4517	−0.504624
$516$	0	0
$517$	−4.93362	−0.216981
$518$	3.74094	0.164367
$519$	0	0
$520$	−138.821	−6.08772
$521$	−40.4053	−1.77019	−0.885095	−	0.465410i	$-0.845907\pi$
$521$	−40.4053	−1.77019	−0.885095	+	0.465410i	$0.845907\pi$
$522$	0	0
$523$	27.5013	1.20255	0.601273	−	0.799044i	$-0.294660\pi$
$523$	27.5013	1.20255	0.601273	+	0.799044i	$0.294660\pi$
$524$	61.9711	2.70722
$525$	0	0
$526$	40.2693	1.75583
$527$	−4.32629	−0.188456
$528$	0	0
$529$	−13.4634	−0.585363
$530$	−48.1473	−2.09139
$531$	0	0
$532$	10.8998	0.472565
$533$	−5.15883	−0.223454
$534$	0	0
$535$	−0.341830	−0.0147786
$536$	158.760	6.85737
$537$	0	0
$538$	−60.2452	−2.59735
$539$	1.10992	0.0478075
$540$	0	0
$541$	24.6504	1.05980	0.529902	−	0.848059i	$-0.322229\pi$
$541$	24.6504	1.05980	0.529902	+	0.848059i	$0.322229\pi$
$542$	73.6185	3.16218
$543$	0	0
$544$	−195.852	−8.39709
$545$	−18.6595	−0.799285
$546$	0	0
$547$	37.3056	1.59507	0.797536	−	0.603272i	$-0.206136\pi$
$547$	37.3056	1.59507	0.797536	+	0.603272i	$0.206136\pi$
$548$	40.3129	1.72208
$549$	0	0
$550$	−3.79358	−0.161759
$551$	0.409534	0.0174467
$552$	0	0
$553$	−0.792249	−0.0336899
$554$	8.92692	0.379268
$555$	0	0
$556$	−44.3478	−1.88077
$557$	−1.15346	−0.0488735	−0.0244368	−	0.999701i	$-0.507779\pi$
$557$	−1.15346	−0.0488735	−0.0244368	+	0.999701i	$0.507779\pi$
$558$	0	0
$559$	58.5260	2.47539
$560$	−46.2150	−1.95294
$561$	0	0
$562$	−18.4397	−0.777830
$563$	−4.73855	−0.199706	−0.0998529	−	0.995002i	$-0.531837\pi$
$563$	−4.73855	−0.199706	−0.0998529	+	0.995002i	$0.531837\pi$
$564$	0	0
$565$	−26.9095	−1.13209
$566$	−62.8068	−2.63997
$567$	0	0
$568$	−75.3986	−3.16366
$569$	12.6116	0.528708	0.264354	−	0.964426i	$-0.414841\pi$
$569$	12.6116	0.528708	0.264354	+	0.964426i	$0.414841\pi$
$570$	0	0
$571$	29.5013	1.23459	0.617295	−	0.786732i	$-0.288229\pi$
$571$	29.5013	1.23459	0.617295	+	0.786732i	$0.288229\pi$
$572$	33.5013	1.40076
$573$	0	0
$574$	−2.80194	−0.116951
$575$	3.76702	0.157096
$576$	0	0
$577$	9.52781	0.396648	0.198324	−	0.980137i	$-0.436450\pi$
$577$	9.52781	0.396648	0.198324	+	0.980137i	$0.436450\pi$
$578$	−69.1057	−2.87442
$579$	0	0
$580$	−3.20775	−0.133195
$581$	−8.76809	−0.363761
$582$	0	0
$583$	7.64742	0.316724
$584$	−56.1909	−2.32520
$585$	0	0
$586$	−35.7754	−1.47787
$587$	39.8474	1.64468	0.822339	−	0.568998i	$-0.192669\pi$
$587$	39.8474	1.64468	0.822339	+	0.568998i	$0.192669\pi$
$588$	0	0
$589$	1.24864	0.0514491
$590$	92.9783	3.82786
$591$	0	0
$592$	24.7409	1.01685
$593$	−22.3532	−0.917935	−0.458967	−	0.888453i	$-0.651781\pi$
$593$	−22.3532	−0.917935	−0.458967	+	0.888453i	$0.651781\pi$
$594$	0	0
$595$	−16.0978	−0.659947
$596$	−65.8926	−2.69907
$597$	0	0
$598$	−44.6383	−1.82540
$599$	−13.3545	−0.545650	−0.272825	−	0.962064i	$-0.587958\pi$
$599$	−13.3545	−0.545650	−0.272825	+	0.962064i	$0.587958\pi$
$600$	0	0
$601$	0.831478	0.0339167	0.0169583	−	0.999856i	$-0.494602\pi$
$601$	0.831478	0.0339167	0.0169583	+	0.999856i	$0.494602\pi$
$602$	31.7875	1.29556
$603$	0	0
$604$	−24.5483	−0.998854
$605$	−24.3612	−0.990424
$606$	0	0
$607$	−7.75600	−0.314807	−0.157403	−	0.987534i	$-0.550312\pi$
$607$	−7.75600	−0.314807	−0.157403	+	0.987534i	$0.550312\pi$
$608$	56.5260	2.29243
$609$	0	0
$610$	−43.8431	−1.77515
$611$	−22.9312	−0.927698
$612$	0	0
$613$	24.3744	0.984471	0.492235	−	0.870462i	$-0.336180\pi$
$613$	24.3744	0.984471	0.492235	+	0.870462i	$0.336180\pi$
$614$	35.5013	1.43271
$615$	0	0
$616$	11.9758	0.482520
$617$	14.5090	0.584111	0.292056	−	0.956401i	$-0.405661\pi$
$617$	14.5090	0.584111	0.292056	+	0.956401i	$0.405661\pi$
$618$	0	0
$619$	−19.5603	−0.786196	−0.393098	−	0.919497i	$-0.628597\pi$
$619$	−19.5603	−0.786196	−0.393098	+	0.919497i	$0.628597\pi$
$620$	−9.78017	−0.392781
$621$	0	0
$622$	−61.8068	−2.47823
$623$	9.70709	0.388906
$624$	0	0
$625$	−29.6112	−1.18445
$626$	14.8538	0.593679
$627$	0	0
$628$	64.8359	2.58723
$629$	8.61788	0.343617
$630$	0	0
$631$	−5.79417	−0.230662	−0.115331	−	0.993327i	$-0.536793\pi$
$631$	−5.79417	−0.230662	−0.115331	+	0.993327i	$0.536793\pi$
$632$	−8.54825	−0.340031
$633$	0	0
$634$	−91.5943	−3.63767
$635$	2.40209	0.0953241
$636$	0	0
$637$	5.15883	0.204400
$638$	0.683661	0.0270664
$639$	0	0
$640$	−183.767	−7.26403
$641$	31.5448	1.24594	0.622972	−	0.782244i	$-0.285925\pi$
$641$	31.5448	1.24594	0.622972	+	0.782244i	$0.285925\pi$
$642$	0	0
$643$	−7.45712	−0.294080	−0.147040	−	0.989131i	$-0.546975\pi$
$643$	−7.45712	−0.294080	−0.147040	+	0.989131i	$0.546975\pi$
$644$	−18.0683	−0.711991
$645$	0	0
$646$	33.6926	1.32562
$647$	−25.5797	−1.00564	−0.502821	−	0.864390i	$-0.667705\pi$
$647$	−25.5797	−1.00564	−0.502821	+	0.864390i	$0.667705\pi$
$648$	0	0
$649$	−14.7681	−0.579698
$650$	−17.6324	−0.691598
$651$	0	0
$652$	−44.9342	−1.75976
$653$	−38.0737	−1.48994	−0.744969	−	0.667099i	$-0.767536\pi$
$653$	−38.0737	−1.48994	−0.744969	+	0.667099i	$0.767536\pi$
$654$	0	0
$655$	26.4155	1.03214
$656$	−18.5308	−0.723506
$657$	0	0
$658$	−12.4547	−0.485536
$659$	15.3357	0.597395	0.298697	−	0.954348i	$-0.403448\pi$
$659$	15.3357	0.597395	0.298697	+	0.954348i	$0.403448\pi$
$660$	0	0
$661$	23.4819	0.913339	0.456670	−	0.889636i	$-0.349042\pi$
$661$	23.4819	0.913339	0.456670	+	0.889636i	$0.349042\pi$
$662$	2.46383	0.0957594
$663$	0	0
$664$	−94.6064	−3.67144
$665$	4.64609	0.180168
$666$	0	0
$667$	−0.678875	−0.0262861
$668$	124.885	4.83196
$669$	0	0
$670$	102.819	3.97224
$671$	6.96376	0.268833
$672$	0	0
$673$	4.42029	0.170390	0.0851948	−	0.996364i	$-0.472849\pi$
$673$	4.42029	0.170390	0.0851948	+	0.996364i	$0.472849\pi$
$674$	−88.4911	−3.40855
$675$	0	0
$676$	79.6510	3.06350
$677$	39.0965	1.50260	0.751300	−	0.659960i	$-0.229427\pi$
$677$	39.0965	1.50260	0.751300	+	0.659960i	$0.229427\pi$
$678$	0	0
$679$	−8.29590	−0.318367
$680$	−173.693	−6.66083
$681$	0	0
$682$	2.08443	0.0798168
$683$	−33.8974	−1.29705	−0.648524	−	0.761195i	$-0.724613\pi$
$683$	−33.8974	−1.29705	−0.648524	+	0.761195i	$0.724613\pi$
$684$	0	0
$685$	17.1836	0.656551
$686$	2.80194	0.106978
$687$	0	0
$688$	210.228	8.01488
$689$	35.5448	1.35415
$690$	0	0
$691$	−23.0562	−0.877100	−0.438550	−	0.898707i	$-0.644508\pi$
$691$	−23.0562	−0.877100	−0.438550	+	0.898707i	$0.644508\pi$
$692$	77.8491	2.95938
$693$	0	0
$694$	−42.8310	−1.62584
$695$	−18.9035	−0.717050
$696$	0	0
$697$	−6.45473	−0.244490
$698$	51.1728	1.93692
$699$	0	0
$700$	−7.13706	−0.269756
$701$	17.9812	0.679141	0.339571	−	0.940581i	$-0.389718\pi$
$701$	17.9812	0.679141	0.339571	+	0.940581i	$0.389718\pi$
$702$	0	0
$703$	−2.48725	−0.0938086
$704$	53.2271	2.00607
$705$	0	0
$706$	−6.27413	−0.236130
$707$	−7.46011	−0.280566
$708$	0	0
$709$	24.5676	0.922657	0.461328	−	0.887229i	$-0.347373\pi$
$709$	24.5676	0.922657	0.461328	+	0.887229i	$0.347373\pi$
$710$	−48.8310	−1.83259
$711$	0	0
$712$	104.738	3.92523
$713$	−2.06983	−0.0775159
$714$	0	0
$715$	14.2801	0.534045
$716$	−37.2814	−1.39327
$717$	0	0
$718$	−15.9909	−0.596775
$719$	−37.1353	−1.38491	−0.692456	−	0.721460i	$-0.743471\pi$
$719$	−37.1353	−1.38491	−0.692456	+	0.721460i	$0.743471\pi$
$720$	0	0
$721$	4.59179	0.171007
$722$	43.5126	1.61937
$723$	0	0
$724$	35.5502	1.32121
$725$	−0.268159	−0.00995917
$726$	0	0
$727$	−27.5948	−1.02343	−0.511717	−	0.859154i	$-0.670990\pi$
$727$	−27.5948	−1.02343	−0.511717	+	0.859154i	$0.670990\pi$
$728$	55.6631	2.06301
$729$	0	0
$730$	−36.3913	−1.34690
$731$	73.2277	2.70843
$732$	0	0
$733$	−24.2586	−0.896011	−0.448006	−	0.894031i	$-0.647866\pi$
$733$	−24.2586	−0.896011	−0.448006	+	0.894031i	$0.647866\pi$
$734$	−67.7271	−2.49985
$735$	0	0
$736$	−93.7018	−3.45390
$737$	−16.3311	−0.601563
$738$	0	0
$739$	21.0019	0.772568	0.386284	−	0.922380i	$-0.373758\pi$
$739$	21.0019	0.772568	0.386284	+	0.922380i	$0.373758\pi$
$740$	19.4819	0.716168
$741$	0	0
$742$	19.3056	0.708730
$743$	36.2059	1.32827	0.664134	−	0.747614i	$-0.268801\pi$
$743$	36.2059	1.32827	0.664134	+	0.747614i	$0.268801\pi$
$744$	0	0
$745$	−28.0871	−1.02903
$746$	55.8611	2.04522
$747$	0	0
$748$	41.9168	1.53263
$749$	0.137063	0.00500819
$750$	0	0
$751$	−2.07367	−0.0756693	−0.0378347	−	0.999284i	$-0.512046\pi$
$751$	−2.07367	−0.0756693	−0.0378347	+	0.999284i	$0.512046\pi$
$752$	−82.3702	−3.00373
$753$	0	0
$754$	3.17762	0.115722
$755$	−10.4638	−0.380818
$756$	0	0
$757$	−40.3177	−1.46537	−0.732685	−	0.680568i	$-0.761733\pi$
$757$	−40.3177	−1.46537	−0.732685	+	0.680568i	$0.761733\pi$
$758$	−10.5550	−0.383373
$759$	0	0
$760$	50.1306	1.81843
$761$	15.6823	0.568484	0.284242	−	0.958753i	$-0.408258\pi$
$761$	15.6823	0.568484	0.284242	+	0.958753i	$0.408258\pi$
$762$	0	0
$763$	7.48188	0.270862
$764$	34.3913	1.24423
$765$	0	0
$766$	−9.42088	−0.340390
$767$	−68.6413	−2.47849
$768$	0	0
$769$	−28.6655	−1.03370	−0.516852	−	0.856075i	$-0.672896\pi$
$769$	−28.6655	−1.03370	−0.516852	+	0.856075i	$0.672896\pi$
$770$	7.75600	0.279507
$771$	0	0
$772$	77.7357	2.79777
$773$	−39.8254	−1.43242	−0.716209	−	0.697885i	$-0.754124\pi$
$773$	−39.8254	−1.43242	−0.716209	+	0.697885i	$0.754124\pi$
$774$	0	0
$775$	−0.817594	−0.0293689
$776$	−89.5115	−3.21328
$777$	0	0
$778$	8.72886	0.312945
$779$	1.86294	0.0667466
$780$	0	0
$781$	7.75600	0.277532
$782$	−55.8514	−1.99724
$783$	0	0
$784$	18.5308	0.661814
$785$	27.6367	0.986395
$786$	0	0
$787$	−35.4249	−1.26276	−0.631381	−	0.775473i	$-0.717512\pi$
$787$	−35.4249	−1.26276	−0.631381	+	0.775473i	$0.717512\pi$
$788$	−23.9506	−0.853205
$789$	0	0
$790$	−5.53617	−0.196968
$791$	10.7899	0.383643
$792$	0	0
$793$	32.3672	1.14939
$794$	−86.1426	−3.05708
$795$	0	0
$796$	−9.81163	−0.347764
$797$	−22.2150	−0.786897	−0.393449	−	0.919347i	$-0.628718\pi$
$797$	−22.2150	−0.786897	−0.393449	+	0.919347i	$0.628718\pi$
$798$	0	0
$799$	−28.6915	−1.01503
$800$	−37.0127	−1.30860
$801$	0	0
$802$	−9.96077	−0.351727
$803$	5.78017	0.203978
$804$	0	0
$805$	−7.70171	−0.271450
$806$	9.68830	0.341256
$807$	0	0
$808$	−80.4935	−2.83175
$809$	−32.9288	−1.15772	−0.578858	−	0.815428i	$-0.696502\pi$
$809$	−32.9288	−1.15772	−0.578858	+	0.815428i	$0.696502\pi$
$810$	0	0
$811$	−34.6112	−1.21536	−0.607681	−	0.794181i	$-0.707900\pi$
$811$	−34.6112	−1.21536	−0.607681	+	0.794181i	$0.707900\pi$
$812$	1.28621	0.0451371
$813$	0	0
$814$	−4.15213	−0.145532
$815$	−19.1535	−0.670916
$816$	0	0
$817$	−21.1347	−0.739409
$818$	−37.7077	−1.31842
$819$	0	0
$820$	−14.5918	−0.509568
$821$	49.9211	1.74226	0.871129	−	0.491055i	$-0.163389\pi$
$821$	49.9211	1.74226	0.871129	+	0.491055i	$0.163389\pi$
$822$	0	0
$823$	37.6098	1.31100	0.655498	−	0.755197i	$-0.272459\pi$
$823$	37.6098	1.31100	0.655498	+	0.755197i	$0.272459\pi$
$824$	49.5448	1.72597
$825$	0	0
$826$	−37.2814	−1.29719
$827$	−47.1245	−1.63868	−0.819340	−	0.573308i	$-0.805660\pi$
$827$	−47.1245	−1.63868	−0.819340	+	0.573308i	$0.805660\pi$
$828$	0	0
$829$	−16.4504	−0.571347	−0.285673	−	0.958327i	$-0.592217\pi$
$829$	−16.4504	−0.571347	−0.285673	+	0.958327i	$0.592217\pi$
$830$	−61.2707	−2.12674
$831$	0	0
$832$	247.397	8.57695
$833$	6.45473	0.223643
$834$	0	0
$835$	53.2331	1.84221
$836$	−12.0978	−0.418412
$837$	0	0
$838$	41.5013	1.43364
$839$	33.4467	1.15471	0.577354	−	0.816494i	$-0.304085\pi$
$839$	33.4467	1.15471	0.577354	+	0.816494i	$0.304085\pi$
$840$	0	0
$841$	−28.9517	−0.998334
$842$	−61.3250	−2.11340
$843$	0	0
$844$	−126.832	−4.36574
$845$	33.9517	1.16797
$846$	0	0
$847$	9.76809	0.335635
$848$	127.679	4.38451
$849$	0	0
$850$	−22.0616	−0.756706
$851$	4.12306	0.141337
$852$	0	0
$853$	2.00000	0.0684787	0.0342393	−	0.999414i	$-0.489099\pi$
$853$	2.00000	0.0684787	0.0342393	+	0.999414i	$0.489099\pi$
$854$	17.5797	0.601565
$855$	0	0
$856$	1.47889	0.0505475
$857$	−26.4349	−0.902998	−0.451499	−	0.892272i	$-0.649111\pi$
$857$	−26.4349	−0.902998	−0.451499	+	0.892272i	$0.649111\pi$
$858$	0	0
$859$	44.6762	1.52433	0.762166	−	0.647381i	$-0.224136\pi$
$859$	44.6762	1.52433	0.762166	+	0.647381i	$0.224136\pi$
$860$	165.541	5.64491
$861$	0	0
$862$	28.0871	0.956650
$863$	−39.8431	−1.35627	−0.678137	−	0.734935i	$-0.737212\pi$
$863$	−39.8431	−1.35627	−0.678137	+	0.734935i	$0.737212\pi$
$864$	0	0
$865$	33.1836	1.12828
$866$	17.2922	0.587612
$867$	0	0
$868$	3.92154	0.133106
$869$	0.879330	0.0298292
$870$	0	0
$871$	−75.9060	−2.57198
$872$	80.7284	2.73381
$873$	0	0
$874$	16.1196	0.545254
$875$	9.42758	0.318710
$876$	0	0
$877$	−43.2247	−1.45960	−0.729798	−	0.683663i	$-0.760386\pi$
$877$	−43.2247	−1.45960	−0.729798	+	0.683663i	$0.760386\pi$
$878$	71.2398	2.40423
$879$	0	0
$880$	51.2948	1.72915
$881$	10.0871	0.339842	0.169921	−	0.985458i	$-0.445649\pi$
$881$	10.0871	0.339842	0.169921	+	0.985458i	$0.445649\pi$
$882$	0	0
$883$	−7.96987	−0.268207	−0.134104	−	0.990967i	$-0.542816\pi$
$883$	−7.96987	−0.268207	−0.134104	+	0.990967i	$0.542816\pi$
$884$	194.827	6.55274
$885$	0	0
$886$	53.6443	1.80222
$887$	−46.0683	−1.54682	−0.773411	−	0.633905i	$-0.781451\pi$
$887$	−46.0683	−1.54682	−0.773411	+	0.633905i	$0.781451\pi$
$888$	0	0
$889$	−0.963164	−0.0323035
$890$	67.8323	2.27374
$891$	0	0
$892$	−71.2417	−2.38535
$893$	8.28083	0.277107
$894$	0	0
$895$	−15.8914	−0.531191
$896$	73.6848	2.46164
$897$	0	0
$898$	44.4523	1.48339
$899$	0.147343	0.00491416
$900$	0	0
$901$	44.4736	1.48163
$902$	3.10992	0.103549
$903$	0	0
$904$	116.421	3.87210
$905$	15.1535	0.503718
$906$	0	0
$907$	−41.9415	−1.39265	−0.696323	−	0.717729i	$-0.745182\pi$
$907$	−41.9415	−1.39265	−0.696323	+	0.717729i	$0.745182\pi$
$908$	17.6233	0.584848
$909$	0	0
$910$	36.0495	1.19503
$911$	−26.5042	−0.878125	−0.439062	−	0.898457i	$-0.644689\pi$
$911$	−26.5042	−0.878125	−0.439062	+	0.898457i	$0.644689\pi$
$912$	0	0
$913$	9.73184	0.322077
$914$	−52.3973	−1.73315
$915$	0	0
$916$	−99.9523	−3.30252
$917$	−10.5918	−0.349772
$918$	0	0
$919$	−23.6582	−0.780411	−0.390206	−	0.920728i	$-0.627596\pi$
$919$	−23.6582	−0.780411	−0.390206	+	0.920728i	$0.627596\pi$
$920$	−83.1003	−2.73974
$921$	0	0
$922$	22.0435	0.725965
$923$	36.0495	1.18658
$924$	0	0
$925$	1.62863	0.0535490
$926$	−77.8926	−2.55971
$927$	0	0
$928$	6.67025	0.218962
$929$	−25.3709	−0.832392	−0.416196	−	0.909275i	$-0.636637\pi$
$929$	−25.3709	−0.832392	−0.416196	+	0.909275i	$0.636637\pi$
$930$	0	0
$931$	−1.86294	−0.0610553
$932$	−86.4059	−2.83032
$933$	0	0
$934$	46.0930	1.50821
$935$	17.8672	0.584322
$936$	0	0
$937$	−16.6601	−0.544261	−0.272131	−	0.962260i	$-0.587728\pi$
$937$	−16.6601	−0.544261	−0.272131	+	0.962260i	$0.587728\pi$
$938$	−41.2271	−1.34611
$939$	0	0
$940$	−64.8611	−2.11554
$941$	0.102620	0.00334533	0.00167267	−	0.999999i	$-0.499468\pi$
$941$	0.102620	0.00334533	0.00167267	+	0.999999i	$0.499468\pi$
$942$	0	0
$943$	−3.08815	−0.100564
$944$	−246.563	−8.02494
$945$	0	0
$946$	−35.2814	−1.14710
$947$	10.2911	0.334416	0.167208	−	0.985922i	$-0.446525\pi$
$947$	10.2911	0.334416	0.167208	+	0.985922i	$0.446525\pi$
$948$	0	0
$949$	26.8659	0.872105
$950$	6.36732	0.206583
$951$	0	0
$952$	69.6456	2.25723
$953$	−42.8122	−1.38682	−0.693412	−	0.720541i	$-0.743893\pi$
$953$	−42.8122	−1.38682	−0.693412	+	0.720541i	$0.743893\pi$
$954$	0	0
$955$	14.6595	0.474370
$956$	−67.7512	−2.19123
$957$	0	0
$958$	−83.4355	−2.69568
$959$	−6.89008	−0.222492
$960$	0	0
$961$	−30.5508	−0.985508
$962$	−19.2989	−0.622221
$963$	0	0
$964$	179.674	5.78691
$965$	33.1353	1.06666
$966$	0	0
$967$	−29.4249	−0.946242	−0.473121	−	0.880997i	$-0.656873\pi$
$967$	−29.4249	−0.946242	−0.473121	+	0.880997i	$0.656873\pi$
$968$	105.396	3.38756
$969$	0	0
$970$	−57.9711	−1.86134
$971$	19.5163	0.626309	0.313154	−	0.949702i	$-0.398614\pi$
$971$	19.5163	0.626309	0.313154	+	0.949702i	$0.398614\pi$
$972$	0	0
$973$	7.57971	0.242994
$974$	−27.4832	−0.880619
$975$	0	0
$976$	116.265	3.72154
$977$	−4.67025	−0.149415	−0.0747073	−	0.997206i	$-0.523802\pi$
$977$	−4.67025	−0.149415	−0.0747073	+	0.997206i	$0.523802\pi$
$978$	0	0
$979$	−10.7741	−0.344340
$980$	14.5918	0.466118
$981$	0	0
$982$	−60.4959	−1.93050
$983$	54.4892	1.73793	0.868967	−	0.494869i	$-0.164784\pi$
$983$	54.4892	1.73793	0.868967	+	0.494869i	$0.164784\pi$
$984$	0	0
$985$	−10.2091	−0.325288
$986$	3.97584	0.126616
$987$	0	0
$988$	−56.2301	−1.78892
$989$	35.0344	1.11403
$990$	0	0
$991$	−19.0073	−0.603787	−0.301893	−	0.953342i	$-0.597619\pi$
$991$	−19.0073	−0.603787	−0.301893	+	0.953342i	$0.597619\pi$
$992$	20.3370	0.645702
$993$	0	0
$994$	19.5797	0.621031
$995$	−4.18226	−0.132587
$996$	0	0
$997$	−38.4626	−1.21812	−0.609062	−	0.793123i	$-0.708454\pi$
$997$	−38.4626	−1.21812	−0.609062	+	0.793123i	$0.708454\pi$
$998$	−25.7694	−0.815717
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2583.2.a.l.1.1		3
3.2	odd	2		287.2.a.d.1.3	✓	3
12.11	even	2		4592.2.a.r.1.3		3
15.14	odd	2		7175.2.a.i.1.1		3
21.20	even	2		2009.2.a.k.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.a.d.1.3	✓	3	3.2	odd	2
2009.2.a.k.1.3		3	21.20	even	2
2583.2.a.l.1.1		3	1.1	even	1	trivial
4592.2.a.r.1.3		3	12.11	even	2
7175.2.a.i.1.1		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:	\( N \)	\(=\)	\( 2583 = 3^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2583.a (trivial)

\(f(q)\)	\(=\)	\(q-2.80194 q^{2} +5.85086 q^{4} +2.49396 q^{5} -1.00000 q^{7} -10.7899 q^{8} +O(q^{10})\)	\(q-2.80194 q^{2} +5.85086 q^{4} +2.49396 q^{5} -1.00000 q^{7} -10.7899 q^{8} -6.98792 q^{10} +1.10992 q^{11} +5.15883 q^{13} +2.80194 q^{14} +18.5308 q^{16} +6.45473 q^{17} -1.86294 q^{19} +14.5918 q^{20} -3.10992 q^{22} +3.08815 q^{23} +1.21983 q^{25} -14.4547 q^{26} -5.85086 q^{28} -0.219833 q^{29} -0.670251 q^{31} -30.3424 q^{32} -18.0858 q^{34} -2.49396 q^{35} +1.33513 q^{37} +5.21983 q^{38} -26.9095 q^{40} -1.00000 q^{41} +11.3448 q^{43} +6.49396 q^{44} -8.65279 q^{46} -4.44504 q^{47} +1.00000 q^{49} -3.41789 q^{50} +30.1836 q^{52} +6.89008 q^{53} +2.76809 q^{55} +10.7899 q^{56} +0.615957 q^{58} -13.3056 q^{59} +6.27413 q^{61} +1.87800 q^{62} +47.9560 q^{64} +12.8659 q^{65} -14.7138 q^{67} +37.7657 q^{68} +6.98792 q^{70} +6.98792 q^{71} +5.20775 q^{73} -3.74094 q^{74} -10.8998 q^{76} -1.10992 q^{77} +0.792249 q^{79} +46.2150 q^{80} +2.80194 q^{82} +8.76809 q^{83} +16.0978 q^{85} -31.7875 q^{86} -11.9758 q^{88} -9.70709 q^{89} -5.15883 q^{91} +18.0683 q^{92} +12.4547 q^{94} -4.64609 q^{95} +8.29590 q^{97} -2.80194 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 4 q^{2} + 4 q^{4} - 2 q^{5} - 3 q^{7} - 9 q^{8}+O(q^{10}) \) 3 * q - 4 * q^2 + 4 * q^4 - 2 * q^5 - 3 * q^7 - 9 * q^8	\( 3 q - 4 q^{2} + 4 q^{4} - 2 q^{5} - 3 q^{7} - 9 q^{8} - 2 q^{10} + 4 q^{11} + 7 q^{13} + 4 q^{14} + 18 q^{16} - 3 q^{17} - 11 q^{19} + 16 q^{20} - 10 q^{22} + 13 q^{23} + 5 q^{25} - 21 q^{26} - 4 q^{28} - 2 q^{29} - 27 q^{32} - 17 q^{34} + 2 q^{35} + 3 q^{37} + 17 q^{38} - 36 q^{40} - 3 q^{41} + 11 q^{43} + 10 q^{44} - 8 q^{46} - 13 q^{47} + 3 q^{49} - 16 q^{50} + 35 q^{52} + 20 q^{53} - 12 q^{55} + 9 q^{56} + 12 q^{58} - 4 q^{59} + 8 q^{61} - 14 q^{62} + 49 q^{64} - 36 q^{67} + 52 q^{68} + 2 q^{70} + 2 q^{71} - 2 q^{73} + 3 q^{74} - 10 q^{76} - 4 q^{77} + 20 q^{79} + 58 q^{80} + 4 q^{82} + 6 q^{83} + 30 q^{85} - 31 q^{86} + 2 q^{88} + q^{89} - 7 q^{91} + q^{92} + 15 q^{94} + 26 q^{95} + 11 q^{97} - 4 q^{98}+O(q^{100}) \) 3 * q - 4 * q^2 + 4 * q^4 - 2 * q^5 - 3 * q^7 - 9 * q^8 - 2 * q^10 + 4 * q^11 + 7 * q^13 + 4 * q^14 + 18 * q^16 - 3 * q^17 - 11 * q^19 + 16 * q^20 - 10 * q^22 + 13 * q^23 + 5 * q^25 - 21 * q^26 - 4 * q^28 - 2 * q^29 - 27 * q^32 - 17 * q^34 + 2 * q^35 + 3 * q^37 + 17 * q^38 - 36 * q^40 - 3 * q^41 + 11 * q^43 + 10 * q^44 - 8 * q^46 - 13 * q^47 + 3 * q^49 - 16 * q^50 + 35 * q^52 + 20 * q^53 - 12 * q^55 + 9 * q^56 + 12 * q^58 - 4 * q^59 + 8 * q^61 - 14 * q^62 + 49 * q^64 - 36 * q^67 + 52 * q^68 + 2 * q^70 + 2 * q^71 - 2 * q^73 + 3 * q^74 - 10 * q^76 - 4 * q^77 + 20 * q^79 + 58 * q^80 + 4 * q^82 + 6 * q^83 + 30 * q^85 - 31 * q^86 + 2 * q^88 + q^89 - 7 * q^91 + q^92 + 15 * q^94 + 26 * q^95 + 11 * q^97 - 4 * q^98

Introduction

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