LMFDB - Embedded newform 2541.2.a.g.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2541,2,Mod(1,2541)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2541, 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("2541.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2541 = 3 \cdot 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2541.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:	$20.2899871536$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	2541.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} -1.00000 q^{3} -1.00000 q^{4} -3.00000 q^{5} -1.00000 q^{6} +1.00000 q^{7} -3.00000 q^{8} +1.00000 q^{9} +O(q^{10})$

\(q+1.00000 q^{2} -1.00000 q^{3} -1.00000 q^{4} -3.00000 q^{5} -1.00000 q^{6} +1.00000 q^{7} -3.00000 q^{8} +1.00000 q^{9} -3.00000 q^{10} +1.00000 q^{12} +7.00000 q^{13} +1.00000 q^{14} +3.00000 q^{15} -1.00000 q^{16} +3.00000 q^{17} +1.00000 q^{18} -2.00000 q^{19} +3.00000 q^{20} -1.00000 q^{21} -4.00000 q^{23} +3.00000 q^{24} +4.00000 q^{25} +7.00000 q^{26} -1.00000 q^{27} -1.00000 q^{28} +7.00000 q^{29} +3.00000 q^{30} -10.0000 q^{31} +5.00000 q^{32} +3.00000 q^{34} -3.00000 q^{35} -1.00000 q^{36} +1.00000 q^{37} -2.00000 q^{38} -7.00000 q^{39} +9.00000 q^{40} -5.00000 q^{41} -1.00000 q^{42} +6.00000 q^{43} -3.00000 q^{45} -4.00000 q^{46} -6.00000 q^{47} +1.00000 q^{48} +1.00000 q^{49} +4.00000 q^{50} -3.00000 q^{51} -7.00000 q^{52} -5.00000 q^{53} -1.00000 q^{54} -3.00000 q^{56} +2.00000 q^{57} +7.00000 q^{58} -6.00000 q^{59} -3.00000 q^{60} +10.0000 q^{61} -10.0000 q^{62} +1.00000 q^{63} +7.00000 q^{64} -21.0000 q^{65} -8.00000 q^{67} -3.00000 q^{68} +4.00000 q^{69} -3.00000 q^{70} -10.0000 q^{71} -3.00000 q^{72} +10.0000 q^{73} +1.00000 q^{74} -4.00000 q^{75} +2.00000 q^{76} -7.00000 q^{78} -2.00000 q^{79} +3.00000 q^{80} +1.00000 q^{81} -5.00000 q^{82} -16.0000 q^{83} +1.00000 q^{84} -9.00000 q^{85} +6.00000 q^{86} -7.00000 q^{87} +3.00000 q^{89} -3.00000 q^{90} +7.00000 q^{91} +4.00000 q^{92} +10.0000 q^{93} -6.00000 q^{94} +6.00000 q^{95} -5.00000 q^{96} -19.0000 q^{97} +1.00000 q^{98} +O(q^{100})\)

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 $

$2$	1.00000	0.707107	0.353553	−	0.935414i	$-0.384973\pi$
$2$	1.00000	0.707107	0.353553	+	0.935414i	$0.384973\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.00000	−0.500000
$5$	−3.00000	−1.34164	−0.670820	−	0.741620i	$-0.734058\pi$
$5$	−3.00000	−1.34164	−0.670820	+	0.741620i	$0.734058\pi$
$6$	−1.00000	−0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−3.00000	−1.06066
$9$	1.00000	0.333333
$10$	−3.00000	−0.948683
$11$	0	0
$11$	0	0
$12$	1.00000	0.288675
$13$	7.00000	1.94145	0.970725	−	0.240192i	$-0.0772105\pi$
$13$	7.00000	1.94145	0.970725	+	0.240192i	$0.0772105\pi$
$14$	1.00000	0.267261
$15$	3.00000	0.774597
$16$	−1.00000	−0.250000
$17$	3.00000	0.727607	0.363803	−	0.931476i	$-0.381478\pi$
$17$	3.00000	0.727607	0.363803	+	0.931476i	$0.381478\pi$
$18$	1.00000	0.235702
$19$	−2.00000	−0.458831	−0.229416	−	0.973329i	$-0.573682\pi$
$19$	−2.00000	−0.458831	−0.229416	+	0.973329i	$0.573682\pi$
$20$	3.00000	0.670820
$21$	−1.00000	−0.218218
$22$	0	0
$23$	−4.00000	−0.834058	−0.417029	−	0.908893i	$-0.636929\pi$
$23$	−4.00000	−0.834058	−0.417029	+	0.908893i	$0.636929\pi$
$24$	3.00000	0.612372
$25$	4.00000	0.800000
$26$	7.00000	1.37281
$27$	−1.00000	−0.192450
$28$	−1.00000	−0.188982
$29$	7.00000	1.29987	0.649934	−	0.759991i	$-0.274797\pi$
$29$	7.00000	1.29987	0.649934	+	0.759991i	$0.274797\pi$
$30$	3.00000	0.547723
$31$	−10.0000	−1.79605	−0.898027	−	0.439941i	$-0.854999\pi$
$31$	−10.0000	−1.79605	−0.898027	+	0.439941i	$0.854999\pi$
$32$	5.00000	0.883883
$33$	0	0
$34$	3.00000	0.514496
$35$	−3.00000	−0.507093
$36$	−1.00000	−0.166667
$37$	1.00000	0.164399	0.0821995	−	0.996616i	$-0.473806\pi$
$37$	1.00000	0.164399	0.0821995	+	0.996616i	$0.473806\pi$
$38$	−2.00000	−0.324443
$39$	−7.00000	−1.12090
$40$	9.00000	1.42302
$41$	−5.00000	−0.780869	−0.390434	−	0.920631i	$-0.627675\pi$
$41$	−5.00000	−0.780869	−0.390434	+	0.920631i	$0.627675\pi$
$42$	−1.00000	−0.154303
$43$	6.00000	0.914991	0.457496	−	0.889212i	$-0.348747\pi$
$43$	6.00000	0.914991	0.457496	+	0.889212i	$0.348747\pi$
$44$	0	0
$45$	−3.00000	−0.447214
$46$	−4.00000	−0.589768
$47$	−6.00000	−0.875190	−0.437595	−	0.899172i	$-0.644170\pi$
$47$	−6.00000	−0.875190	−0.437595	+	0.899172i	$0.644170\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	4.00000	0.565685
$51$	−3.00000	−0.420084
$52$	−7.00000	−0.970725
$53$	−5.00000	−0.686803	−0.343401	−	0.939189i	$-0.611579\pi$
$53$	−5.00000	−0.686803	−0.343401	+	0.939189i	$0.611579\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	−3.00000	−0.400892
$57$	2.00000	0.264906
$58$	7.00000	0.919145
$59$	−6.00000	−0.781133	−0.390567	−	0.920575i	$-0.627721\pi$
$59$	−6.00000	−0.781133	−0.390567	+	0.920575i	$0.627721\pi$
$60$	−3.00000	−0.387298
$61$	10.0000	1.28037	0.640184	−	0.768221i	$-0.278858\pi$
$61$	10.0000	1.28037	0.640184	+	0.768221i	$0.278858\pi$
$62$	−10.0000	−1.27000
$63$	1.00000	0.125988
$64$	7.00000	0.875000
$65$	−21.0000	−2.60473
$66$	0	0
$67$	−8.00000	−0.977356	−0.488678	−	0.872464i	$-0.662521\pi$
$67$	−8.00000	−0.977356	−0.488678	+	0.872464i	$0.662521\pi$
$68$	−3.00000	−0.363803
$69$	4.00000	0.481543
$70$	−3.00000	−0.358569
$71$	−10.0000	−1.18678	−0.593391	−	0.804914i	$-0.702211\pi$
$71$	−10.0000	−1.18678	−0.593391	+	0.804914i	$0.702211\pi$
$72$	−3.00000	−0.353553
$73$	10.0000	1.17041	0.585206	−	0.810885i	$-0.301014\pi$
$73$	10.0000	1.17041	0.585206	+	0.810885i	$0.301014\pi$
$74$	1.00000	0.116248
$75$	−4.00000	−0.461880
$76$	2.00000	0.229416
$77$	0	0
$78$	−7.00000	−0.792594
$79$	−2.00000	−0.225018	−0.112509	−	0.993651i	$-0.535889\pi$
$79$	−2.00000	−0.225018	−0.112509	+	0.993651i	$0.535889\pi$
$80$	3.00000	0.335410
$81$	1.00000	0.111111
$82$	−5.00000	−0.552158
$83$	−16.0000	−1.75623	−0.878114	−	0.478451i	$-0.841198\pi$
$83$	−16.0000	−1.75623	−0.878114	+	0.478451i	$0.841198\pi$
$84$	1.00000	0.109109
$85$	−9.00000	−0.976187
$86$	6.00000	0.646997
$87$	−7.00000	−0.750479
$88$	0	0
$89$	3.00000	0.317999	0.159000	−	0.987279i	$-0.449173\pi$
$89$	3.00000	0.317999	0.159000	+	0.987279i	$0.449173\pi$
$90$	−3.00000	−0.316228
$91$	7.00000	0.733799
$92$	4.00000	0.417029
$93$	10.0000	1.03695
$94$	−6.00000	−0.618853
$95$	6.00000	0.615587
$96$	−5.00000	−0.510310
$97$	−19.0000	−1.92916	−0.964579	−	0.263795i	$-0.915026\pi$
$97$	−19.0000	−1.92916	−0.964579	+	0.263795i	$0.915026\pi$
$98$	1.00000	0.101015
$99$	0	0
$100$	−4.00000	−0.400000
$101$	−2.00000	−0.199007	−0.0995037	−	0.995037i	$-0.531726\pi$
$101$	−2.00000	−0.199007	−0.0995037	+	0.995037i	$0.531726\pi$
$102$	−3.00000	−0.297044
$103$	−16.0000	−1.57653	−0.788263	−	0.615338i	$-0.789020\pi$
$103$	−16.0000	−1.57653	−0.788263	+	0.615338i	$0.789020\pi$
$104$	−21.0000	−2.05922
$105$	3.00000	0.292770
$106$	−5.00000	−0.485643
$107$	−14.0000	−1.35343	−0.676716	−	0.736245i	$-0.736597\pi$
$107$	−14.0000	−1.35343	−0.676716	+	0.736245i	$0.736597\pi$
$108$	1.00000	0.0962250
$109$	−7.00000	−0.670478	−0.335239	−	0.942133i	$-0.608817\pi$
$109$	−7.00000	−0.670478	−0.335239	+	0.942133i	$0.608817\pi$
$110$	0	0
$111$	−1.00000	−0.0949158
$112$	−1.00000	−0.0944911
$113$	9.00000	0.846649	0.423324	−	0.905978i	$-0.360863\pi$
$113$	9.00000	0.846649	0.423324	+	0.905978i	$0.360863\pi$
$114$	2.00000	0.187317
$115$	12.0000	1.11901
$116$	−7.00000	−0.649934
$117$	7.00000	0.647150
$118$	−6.00000	−0.552345
$119$	3.00000	0.275010
$120$	−9.00000	−0.821584
$121$	0	0
$122$	10.0000	0.905357
$123$	5.00000	0.450835
$124$	10.0000	0.898027
$125$	3.00000	0.268328
$126$	1.00000	0.0890871
$127$	8.00000	0.709885	0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000	0.709885	0.354943	+	0.934888i	$0.384500\pi$
$128$	−3.00000	−0.265165
$129$	−6.00000	−0.528271
$130$	−21.0000	−1.84182
$131$	−4.00000	−0.349482	−0.174741	−	0.984614i	$-0.555909\pi$
$131$	−4.00000	−0.349482	−0.174741	+	0.984614i	$0.555909\pi$
$132$	0	0
$133$	−2.00000	−0.173422
$134$	−8.00000	−0.691095
$135$	3.00000	0.258199
$136$	−9.00000	−0.771744
$137$	2.00000	0.170872	0.0854358	−	0.996344i	$-0.472772\pi$
$137$	2.00000	0.170872	0.0854358	+	0.996344i	$0.472772\pi$
$138$	4.00000	0.340503
$139$	−4.00000	−0.339276	−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000	−0.339276	−0.169638	+	0.985506i	$0.554260\pi$
$140$	3.00000	0.253546
$141$	6.00000	0.505291
$142$	−10.0000	−0.839181
$143$	0	0
$144$	−1.00000	−0.0833333
$145$	−21.0000	−1.74396
$146$	10.0000	0.827606
$147$	−1.00000	−0.0824786
$148$	−1.00000	−0.0821995
$149$	−21.0000	−1.72039	−0.860194	−	0.509968i	$-0.829657\pi$
$149$	−21.0000	−1.72039	−0.860194	+	0.509968i	$0.829657\pi$
$150$	−4.00000	−0.326599
$151$	2.00000	0.162758	0.0813788	−	0.996683i	$-0.474068\pi$
$151$	2.00000	0.162758	0.0813788	+	0.996683i	$0.474068\pi$
$152$	6.00000	0.486664
$153$	3.00000	0.242536
$154$	0	0
$155$	30.0000	2.40966
$156$	7.00000	0.560449
$157$	−14.0000	−1.11732	−0.558661	−	0.829396i	$-0.688685\pi$
$157$	−14.0000	−1.11732	−0.558661	+	0.829396i	$0.688685\pi$
$158$	−2.00000	−0.159111
$159$	5.00000	0.396526
$160$	−15.0000	−1.18585
$161$	−4.00000	−0.315244
$162$	1.00000	0.0785674
$163$	10.0000	0.783260	0.391630	−	0.920123i	$-0.371911\pi$
$163$	10.0000	0.783260	0.391630	+	0.920123i	$0.371911\pi$
$164$	5.00000	0.390434
$165$	0	0
$166$	−16.0000	−1.24184
$167$	12.0000	0.928588	0.464294	−	0.885681i	$-0.346308\pi$
$167$	12.0000	0.928588	0.464294	+	0.885681i	$0.346308\pi$
$168$	3.00000	0.231455
$169$	36.0000	2.76923
$170$	−9.00000	−0.690268
$171$	−2.00000	−0.152944
$172$	−6.00000	−0.457496
$173$	−10.0000	−0.760286	−0.380143	−	0.924928i	$-0.624125\pi$
$173$	−10.0000	−0.760286	−0.380143	+	0.924928i	$0.624125\pi$
$174$	−7.00000	−0.530669
$175$	4.00000	0.302372
$176$	0	0
$177$	6.00000	0.450988
$178$	3.00000	0.224860
$179$	−10.0000	−0.747435	−0.373718	−	0.927543i	$-0.621917\pi$
$179$	−10.0000	−0.747435	−0.373718	+	0.927543i	$0.621917\pi$
$180$	3.00000	0.223607
$181$	23.0000	1.70958	0.854788	−	0.518977i	$-0.173687\pi$
$181$	23.0000	1.70958	0.854788	+	0.518977i	$0.173687\pi$
$182$	7.00000	0.518875
$183$	−10.0000	−0.739221
$184$	12.0000	0.884652
$185$	−3.00000	−0.220564
$186$	10.0000	0.733236
$187$	0	0
$188$	6.00000	0.437595
$189$	−1.00000	−0.0727393
$190$	6.00000	0.435286
$191$	22.0000	1.59186	0.795932	−	0.605386i	$-0.206981\pi$
$191$	22.0000	1.59186	0.795932	+	0.605386i	$0.206981\pi$
$192$	−7.00000	−0.505181
$193$	11.0000	0.791797	0.395899	−	0.918294i	$-0.370433\pi$
$193$	11.0000	0.791797	0.395899	+	0.918294i	$0.370433\pi$
$194$	−19.0000	−1.36412
$195$	21.0000	1.50384
$196$	−1.00000	−0.0714286
$197$	−1.00000	−0.0712470	−0.0356235	−	0.999365i	$-0.511342\pi$
$197$	−1.00000	−0.0712470	−0.0356235	+	0.999365i	$0.511342\pi$
$198$	0	0
$199$	−2.00000	−0.141776	−0.0708881	−	0.997484i	$-0.522583\pi$
$199$	−2.00000	−0.141776	−0.0708881	+	0.997484i	$0.522583\pi$
$200$	−12.0000	−0.848528
$201$	8.00000	0.564276
$202$	−2.00000	−0.140720
$203$	7.00000	0.491304
$204$	3.00000	0.210042
$205$	15.0000	1.04765
$206$	−16.0000	−1.11477
$207$	−4.00000	−0.278019
$208$	−7.00000	−0.485363
$209$	0	0
$210$	3.00000	0.207020
$211$	8.00000	0.550743	0.275371	−	0.961338i	$-0.411199\pi$
$211$	8.00000	0.550743	0.275371	+	0.961338i	$0.411199\pi$
$212$	5.00000	0.343401
$213$	10.0000	0.685189
$214$	−14.0000	−0.957020
$215$	−18.0000	−1.22759
$216$	3.00000	0.204124
$217$	−10.0000	−0.678844
$218$	−7.00000	−0.474100
$219$	−10.0000	−0.675737
$220$	0	0
$221$	21.0000	1.41261
$222$	−1.00000	−0.0671156
$223$	−24.0000	−1.60716	−0.803579	−	0.595198i	$-0.797074\pi$
$223$	−24.0000	−1.60716	−0.803579	+	0.595198i	$0.797074\pi$
$224$	5.00000	0.334077
$225$	4.00000	0.266667
$226$	9.00000	0.598671
$227$	2.00000	0.132745	0.0663723	−	0.997795i	$-0.478857\pi$
$227$	2.00000	0.132745	0.0663723	+	0.997795i	$0.478857\pi$
$228$	−2.00000	−0.132453
$229$	−13.0000	−0.859064	−0.429532	−	0.903052i	$-0.641321\pi$
$229$	−13.0000	−0.859064	−0.429532	+	0.903052i	$0.641321\pi$
$230$	12.0000	0.791257
$231$	0	0
$232$	−21.0000	−1.37872
$233$	−23.0000	−1.50678	−0.753390	−	0.657574i	$-0.771583\pi$
$233$	−23.0000	−1.50678	−0.753390	+	0.657574i	$0.771583\pi$
$234$	7.00000	0.457604
$235$	18.0000	1.17419
$236$	6.00000	0.390567
$237$	2.00000	0.129914
$238$	3.00000	0.194461
$239$	12.0000	0.776215	0.388108	−	0.921614i	$-0.373129\pi$
$239$	12.0000	0.776215	0.388108	+	0.921614i	$0.373129\pi$
$240$	−3.00000	−0.193649
$241$	14.0000	0.901819	0.450910	−	0.892570i	$-0.351100\pi$
$241$	14.0000	0.901819	0.450910	+	0.892570i	$0.351100\pi$
$242$	0	0
$243$	−1.00000	−0.0641500
$244$	−10.0000	−0.640184
$245$	−3.00000	−0.191663
$246$	5.00000	0.318788
$247$	−14.0000	−0.890799
$248$	30.0000	1.90500
$249$	16.0000	1.01396
$250$	3.00000	0.189737
$251$	−12.0000	−0.757433	−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000	−0.757433	−0.378717	+	0.925513i	$0.623635\pi$
$252$	−1.00000	−0.0629941
$253$	0	0
$254$	8.00000	0.501965
$255$	9.00000	0.563602
$256$	−17.0000	−1.06250
$257$	−29.0000	−1.80897	−0.904485	−	0.426505i	$-0.859745\pi$
$257$	−29.0000	−1.80897	−0.904485	+	0.426505i	$0.859745\pi$
$258$	−6.00000	−0.373544
$259$	1.00000	0.0621370
$260$	21.0000	1.30236
$261$	7.00000	0.433289
$262$	−4.00000	−0.247121
$263$	24.0000	1.47990	0.739952	−	0.672660i	$-0.234848\pi$
$263$	24.0000	1.47990	0.739952	+	0.672660i	$0.234848\pi$
$264$	0	0
$265$	15.0000	0.921443
$266$	−2.00000	−0.122628
$267$	−3.00000	−0.183597
$268$	8.00000	0.488678
$269$	−23.0000	−1.40233	−0.701167	−	0.712997i	$-0.747337\pi$
$269$	−23.0000	−1.40233	−0.701167	+	0.712997i	$0.747337\pi$
$270$	3.00000	0.182574
$271$	−8.00000	−0.485965	−0.242983	−	0.970031i	$-0.578126\pi$
$271$	−8.00000	−0.485965	−0.242983	+	0.970031i	$0.578126\pi$
$272$	−3.00000	−0.181902
$273$	−7.00000	−0.423659
$274$	2.00000	0.120824
$275$	0	0
$276$	−4.00000	−0.240772
$277$	5.00000	0.300421	0.150210	−	0.988654i	$-0.452005\pi$
$277$	5.00000	0.300421	0.150210	+	0.988654i	$0.452005\pi$
$278$	−4.00000	−0.239904
$279$	−10.0000	−0.598684
$280$	9.00000	0.537853
$281$	18.0000	1.07379	0.536895	−	0.843649i	$-0.319597\pi$
$281$	18.0000	1.07379	0.536895	+	0.843649i	$0.319597\pi$
$282$	6.00000	0.357295
$283$	−22.0000	−1.30776	−0.653882	−	0.756596i	$-0.726861\pi$
$283$	−22.0000	−1.30776	−0.653882	+	0.756596i	$0.726861\pi$
$284$	10.0000	0.593391
$285$	−6.00000	−0.355409
$286$	0	0
$287$	−5.00000	−0.295141
$288$	5.00000	0.294628
$289$	−8.00000	−0.470588
$290$	−21.0000	−1.23316
$291$	19.0000	1.11380
$292$	−10.0000	−0.585206
$293$	−27.0000	−1.57736	−0.788678	−	0.614806i	$-0.789234\pi$
$293$	−27.0000	−1.57736	−0.788678	+	0.614806i	$0.789234\pi$
$294$	−1.00000	−0.0583212
$295$	18.0000	1.04800
$296$	−3.00000	−0.174371
$297$	0	0
$298$	−21.0000	−1.21650
$299$	−28.0000	−1.61928
$300$	4.00000	0.230940
$301$	6.00000	0.345834
$302$	2.00000	0.115087
$303$	2.00000	0.114897
$304$	2.00000	0.114708
$305$	−30.0000	−1.71780
$306$	3.00000	0.171499
$307$	−12.0000	−0.684876	−0.342438	−	0.939540i	$-0.611253\pi$
$307$	−12.0000	−0.684876	−0.342438	+	0.939540i	$0.611253\pi$
$308$	0	0
$309$	16.0000	0.910208
$310$	30.0000	1.70389
$311$	−10.0000	−0.567048	−0.283524	−	0.958965i	$-0.591504\pi$
$311$	−10.0000	−0.567048	−0.283524	+	0.958965i	$0.591504\pi$
$312$	21.0000	1.18889
$313$	9.00000	0.508710	0.254355	−	0.967111i	$-0.418137\pi$
$313$	9.00000	0.508710	0.254355	+	0.967111i	$0.418137\pi$
$314$	−14.0000	−0.790066
$315$	−3.00000	−0.169031
$316$	2.00000	0.112509
$317$	18.0000	1.01098	0.505490	−	0.862832i	$-0.331312\pi$
$317$	18.0000	1.01098	0.505490	+	0.862832i	$0.331312\pi$
$318$	5.00000	0.280386
$319$	0	0
$320$	−21.0000	−1.17394
$321$	14.0000	0.781404
$322$	−4.00000	−0.222911
$323$	−6.00000	−0.333849
$324$	−1.00000	−0.0555556
$325$	28.0000	1.55316
$326$	10.0000	0.553849
$327$	7.00000	0.387101
$328$	15.0000	0.828236
$329$	−6.00000	−0.330791
$330$	0	0
$331$	18.0000	0.989369	0.494685	−	0.869072i	$-0.335284\pi$
$331$	18.0000	0.989369	0.494685	+	0.869072i	$0.335284\pi$
$332$	16.0000	0.878114
$333$	1.00000	0.0547997
$334$	12.0000	0.656611
$335$	24.0000	1.31126
$336$	1.00000	0.0545545
$337$	−5.00000	−0.272367	−0.136184	−	0.990684i	$-0.543484\pi$
$337$	−5.00000	−0.272367	−0.136184	+	0.990684i	$0.543484\pi$
$338$	36.0000	1.95814
$339$	−9.00000	−0.488813
$340$	9.00000	0.488094
$341$	0	0
$342$	−2.00000	−0.108148
$343$	1.00000	0.0539949
$344$	−18.0000	−0.970495
$345$	−12.0000	−0.646058
$346$	−10.0000	−0.537603
$347$	26.0000	1.39575	0.697877	−	0.716218i	$-0.254128\pi$
$347$	26.0000	1.39575	0.697877	+	0.716218i	$0.254128\pi$
$348$	7.00000	0.375239
$349$	3.00000	0.160586	0.0802932	−	0.996771i	$-0.474414\pi$
$349$	3.00000	0.160586	0.0802932	+	0.996771i	$0.474414\pi$
$350$	4.00000	0.213809
$351$	−7.00000	−0.373632
$352$	0	0
$353$	−21.0000	−1.11772	−0.558859	−	0.829263i	$-0.688761\pi$
$353$	−21.0000	−1.11772	−0.558859	+	0.829263i	$0.688761\pi$
$354$	6.00000	0.318896
$355$	30.0000	1.59223
$356$	−3.00000	−0.159000
$357$	−3.00000	−0.158777
$358$	−10.0000	−0.528516
$359$	12.0000	0.633336	0.316668	−	0.948536i	$-0.397436\pi$
$359$	12.0000	0.633336	0.316668	+	0.948536i	$0.397436\pi$
$360$	9.00000	0.474342
$361$	−15.0000	−0.789474
$362$	23.0000	1.20885
$363$	0	0
$364$	−7.00000	−0.366900
$365$	−30.0000	−1.57027
$366$	−10.0000	−0.522708
$367$	10.0000	0.521996	0.260998	−	0.965339i	$-0.415948\pi$
$367$	10.0000	0.521996	0.260998	+	0.965339i	$0.415948\pi$
$368$	4.00000	0.208514
$369$	−5.00000	−0.260290
$370$	−3.00000	−0.155963
$371$	−5.00000	−0.259587
$372$	−10.0000	−0.518476
$373$	6.00000	0.310668	0.155334	−	0.987862i	$-0.450355\pi$
$373$	6.00000	0.310668	0.155334	+	0.987862i	$0.450355\pi$
$374$	0	0
$375$	−3.00000	−0.154919
$376$	18.0000	0.928279
$377$	49.0000	2.52363
$378$	−1.00000	−0.0514344
$379$	16.0000	0.821865	0.410932	−	0.911666i	$-0.365203\pi$
$379$	16.0000	0.821865	0.410932	+	0.911666i	$0.365203\pi$
$380$	−6.00000	−0.307794
$381$	−8.00000	−0.409852
$382$	22.0000	1.12562
$383$	16.0000	0.817562	0.408781	−	0.912633i	$-0.365954\pi$
$383$	16.0000	0.817562	0.408781	+	0.912633i	$0.365954\pi$
$384$	3.00000	0.153093
$385$	0	0
$386$	11.0000	0.559885
$387$	6.00000	0.304997
$388$	19.0000	0.964579
$389$	7.00000	0.354914	0.177457	−	0.984129i	$-0.443213\pi$
$389$	7.00000	0.354914	0.177457	+	0.984129i	$0.443213\pi$
$390$	21.0000	1.06338
$391$	−12.0000	−0.606866
$392$	−3.00000	−0.151523
$393$	4.00000	0.201773
$394$	−1.00000	−0.0503793
$395$	6.00000	0.301893
$396$	0	0
$397$	−33.0000	−1.65622	−0.828111	−	0.560564i	$-0.810584\pi$
$397$	−33.0000	−1.65622	−0.828111	+	0.560564i	$0.810584\pi$
$398$	−2.00000	−0.100251
$399$	2.00000	0.100125
$400$	−4.00000	−0.200000
$401$	−15.0000	−0.749064	−0.374532	−	0.927214i	$-0.622197\pi$
$401$	−15.0000	−0.749064	−0.374532	+	0.927214i	$0.622197\pi$
$402$	8.00000	0.399004
$403$	−70.0000	−3.48695
$404$	2.00000	0.0995037
$405$	−3.00000	−0.149071
$406$	7.00000	0.347404
$407$	0	0
$408$	9.00000	0.445566
$409$	5.00000	0.247234	0.123617	−	0.992330i	$-0.460551\pi$
$409$	5.00000	0.247234	0.123617	+	0.992330i	$0.460551\pi$
$410$	15.0000	0.740797
$411$	−2.00000	−0.0986527
$412$	16.0000	0.788263
$413$	−6.00000	−0.295241
$414$	−4.00000	−0.196589
$415$	48.0000	2.35623
$416$	35.0000	1.71602
$417$	4.00000	0.195881
$418$	0	0
$419$	16.0000	0.781651	0.390826	−	0.920465i	$-0.372190\pi$
$419$	16.0000	0.781651	0.390826	+	0.920465i	$0.372190\pi$
$420$	−3.00000	−0.146385
$421$	−15.0000	−0.731055	−0.365528	−	0.930800i	$-0.619111\pi$
$421$	−15.0000	−0.731055	−0.365528	+	0.930800i	$0.619111\pi$
$422$	8.00000	0.389434
$423$	−6.00000	−0.291730
$424$	15.0000	0.728464
$425$	12.0000	0.582086
$426$	10.0000	0.484502
$427$	10.0000	0.483934
$428$	14.0000	0.676716
$429$	0	0
$430$	−18.0000	−0.868037
$431$	−14.0000	−0.674356	−0.337178	−	0.941441i	$-0.609472\pi$
$431$	−14.0000	−0.674356	−0.337178	+	0.941441i	$0.609472\pi$
$432$	1.00000	0.0481125
$433$	1.00000	0.0480569	0.0240285	−	0.999711i	$-0.492351\pi$
$433$	1.00000	0.0480569	0.0240285	+	0.999711i	$0.492351\pi$
$434$	−10.0000	−0.480015
$435$	21.0000	1.00687
$436$	7.00000	0.335239
$437$	8.00000	0.382692
$438$	−10.0000	−0.477818
$439$	4.00000	0.190910	0.0954548	−	0.995434i	$-0.469569\pi$
$439$	4.00000	0.190910	0.0954548	+	0.995434i	$0.469569\pi$
$440$	0	0
$441$	1.00000	0.0476190
$442$	21.0000	0.998868
$443$	4.00000	0.190046	0.0950229	−	0.995475i	$-0.469708\pi$
$443$	4.00000	0.190046	0.0950229	+	0.995475i	$0.469708\pi$
$444$	1.00000	0.0474579
$445$	−9.00000	−0.426641
$446$	−24.0000	−1.13643
$447$	21.0000	0.993266
$448$	7.00000	0.330719
$449$	−27.0000	−1.27421	−0.637104	−	0.770778i	$-0.719868\pi$
$449$	−27.0000	−1.27421	−0.637104	+	0.770778i	$0.719868\pi$
$450$	4.00000	0.188562
$451$	0	0
$452$	−9.00000	−0.423324
$453$	−2.00000	−0.0939682
$454$	2.00000	0.0938647
$455$	−21.0000	−0.984495
$456$	−6.00000	−0.280976
$457$	−33.0000	−1.54367	−0.771837	−	0.635820i	$-0.780662\pi$
$457$	−33.0000	−1.54367	−0.771837	+	0.635820i	$0.780662\pi$
$458$	−13.0000	−0.607450
$459$	−3.00000	−0.140028
$460$	−12.0000	−0.559503
$461$	−15.0000	−0.698620	−0.349310	−	0.937007i	$-0.613584\pi$
$461$	−15.0000	−0.698620	−0.349310	+	0.937007i	$0.613584\pi$
$462$	0	0
$463$	22.0000	1.02243	0.511213	−	0.859454i	$-0.329196\pi$
$463$	22.0000	1.02243	0.511213	+	0.859454i	$0.329196\pi$
$464$	−7.00000	−0.324967
$465$	−30.0000	−1.39122
$466$	−23.0000	−1.06545
$467$	8.00000	0.370196	0.185098	−	0.982720i	$-0.440740\pi$
$467$	8.00000	0.370196	0.185098	+	0.982720i	$0.440740\pi$
$468$	−7.00000	−0.323575
$469$	−8.00000	−0.369406
$470$	18.0000	0.830278
$471$	14.0000	0.645086
$472$	18.0000	0.828517
$473$	0	0
$474$	2.00000	0.0918630
$475$	−8.00000	−0.367065
$476$	−3.00000	−0.137505
$477$	−5.00000	−0.228934
$478$	12.0000	0.548867
$479$	−26.0000	−1.18797	−0.593985	−	0.804476i	$-0.702446\pi$
$479$	−26.0000	−1.18797	−0.593985	+	0.804476i	$0.702446\pi$
$480$	15.0000	0.684653
$481$	7.00000	0.319173
$482$	14.0000	0.637683
$483$	4.00000	0.182006
$484$	0	0
$485$	57.0000	2.58824
$486$	−1.00000	−0.0453609
$487$	−38.0000	−1.72194	−0.860972	−	0.508652i	$-0.830144\pi$
$487$	−38.0000	−1.72194	−0.860972	+	0.508652i	$0.830144\pi$
$488$	−30.0000	−1.35804
$489$	−10.0000	−0.452216
$490$	−3.00000	−0.135526
$491$	−36.0000	−1.62466	−0.812329	−	0.583200i	$-0.801800\pi$
$491$	−36.0000	−1.62466	−0.812329	+	0.583200i	$0.801800\pi$
$492$	−5.00000	−0.225417
$493$	21.0000	0.945792
$494$	−14.0000	−0.629890
$495$	0	0
$496$	10.0000	0.449013
$497$	−10.0000	−0.448561
$498$	16.0000	0.716977
$499$	−32.0000	−1.43252	−0.716258	−	0.697835i	$-0.754147\pi$
$499$	−32.0000	−1.43252	−0.716258	+	0.697835i	$0.754147\pi$
$500$	−3.00000	−0.134164
$501$	−12.0000	−0.536120
$502$	−12.0000	−0.535586
$503$	16.0000	0.713405	0.356702	−	0.934218i	$-0.383901\pi$
$503$	16.0000	0.713405	0.356702	+	0.934218i	$0.383901\pi$
$504$	−3.00000	−0.133631
$505$	6.00000	0.266996
$506$	0	0
$507$	−36.0000	−1.59882
$508$	−8.00000	−0.354943
$509$	−42.0000	−1.86162	−0.930809	−	0.365507i	$-0.880896\pi$
$509$	−42.0000	−1.86162	−0.930809	+	0.365507i	$0.880896\pi$
$510$	9.00000	0.398527
$511$	10.0000	0.442374
$512$	−11.0000	−0.486136
$513$	2.00000	0.0883022
$514$	−29.0000	−1.27914
$515$	48.0000	2.11513
$516$	6.00000	0.264135
$517$	0	0
$518$	1.00000	0.0439375
$519$	10.0000	0.438951
$520$	63.0000	2.76273
$521$	−2.00000	−0.0876216	−0.0438108	−	0.999040i	$-0.513950\pi$
$521$	−2.00000	−0.0876216	−0.0438108	+	0.999040i	$0.513950\pi$
$522$	7.00000	0.306382
$523$	20.0000	0.874539	0.437269	−	0.899331i	$-0.355946\pi$
$523$	20.0000	0.874539	0.437269	+	0.899331i	$0.355946\pi$
$524$	4.00000	0.174741
$525$	−4.00000	−0.174574
$526$	24.0000	1.04645
$527$	−30.0000	−1.30682
$528$	0	0
$529$	−7.00000	−0.304348
$530$	15.0000	0.651558
$531$	−6.00000	−0.260378
$532$	2.00000	0.0867110
$533$	−35.0000	−1.51602
$534$	−3.00000	−0.129823
$535$	42.0000	1.81582
$536$	24.0000	1.03664
$537$	10.0000	0.431532
$538$	−23.0000	−0.991600
$539$	0	0
$540$	−3.00000	−0.129099
$541$	30.0000	1.28980	0.644900	−	0.764267i	$-0.276899\pi$
$541$	30.0000	1.28980	0.644900	+	0.764267i	$0.276899\pi$
$542$	−8.00000	−0.343629
$543$	−23.0000	−0.987024
$544$	15.0000	0.643120
$545$	21.0000	0.899541
$546$	−7.00000	−0.299572
$547$	2.00000	0.0855138	0.0427569	−	0.999086i	$-0.486386\pi$
$547$	2.00000	0.0855138	0.0427569	+	0.999086i	$0.486386\pi$
$548$	−2.00000	−0.0854358
$549$	10.0000	0.426790
$550$	0	0
$551$	−14.0000	−0.596420
$552$	−12.0000	−0.510754
$553$	−2.00000	−0.0850487
$554$	5.00000	0.212430
$555$	3.00000	0.127343
$556$	4.00000	0.169638
$557$	−6.00000	−0.254228	−0.127114	−	0.991888i	$-0.540571\pi$
$557$	−6.00000	−0.254228	−0.127114	+	0.991888i	$0.540571\pi$
$558$	−10.0000	−0.423334
$559$	42.0000	1.77641
$560$	3.00000	0.126773
$561$	0	0
$562$	18.0000	0.759284
$563$	−18.0000	−0.758610	−0.379305	−	0.925272i	$-0.623837\pi$
$563$	−18.0000	−0.758610	−0.379305	+	0.925272i	$0.623837\pi$
$564$	−6.00000	−0.252646
$565$	−27.0000	−1.13590
$566$	−22.0000	−0.924729
$567$	1.00000	0.0419961
$568$	30.0000	1.25877
$569$	10.0000	0.419222	0.209611	−	0.977785i	$-0.432780\pi$
$569$	10.0000	0.419222	0.209611	+	0.977785i	$0.432780\pi$
$570$	−6.00000	−0.251312
$571$	−16.0000	−0.669579	−0.334790	−	0.942293i	$-0.608665\pi$
$571$	−16.0000	−0.669579	−0.334790	+	0.942293i	$0.608665\pi$
$572$	0	0
$573$	−22.0000	−0.919063
$574$	−5.00000	−0.208696
$575$	−16.0000	−0.667246
$576$	7.00000	0.291667
$577$	37.0000	1.54033	0.770165	−	0.637845i	$-0.220174\pi$
$577$	37.0000	1.54033	0.770165	+	0.637845i	$0.220174\pi$
$578$	−8.00000	−0.332756
$579$	−11.0000	−0.457144
$580$	21.0000	0.871978
$581$	−16.0000	−0.663792
$582$	19.0000	0.787575
$583$	0	0
$584$	−30.0000	−1.24141
$585$	−21.0000	−0.868243
$586$	−27.0000	−1.11536
$587$	−42.0000	−1.73353	−0.866763	−	0.498721i	$-0.833803\pi$
$587$	−42.0000	−1.73353	−0.866763	+	0.498721i	$0.833803\pi$
$588$	1.00000	0.0412393
$589$	20.0000	0.824086
$590$	18.0000	0.741048
$591$	1.00000	0.0411345
$592$	−1.00000	−0.0410997
$593$	7.00000	0.287456	0.143728	−	0.989617i	$-0.454091\pi$
$593$	7.00000	0.287456	0.143728	+	0.989617i	$0.454091\pi$
$594$	0	0
$595$	−9.00000	−0.368964
$596$	21.0000	0.860194
$597$	2.00000	0.0818546
$598$	−28.0000	−1.14501
$599$	10.0000	0.408589	0.204294	−	0.978909i	$-0.434510\pi$
$599$	10.0000	0.408589	0.204294	+	0.978909i	$0.434510\pi$
$600$	12.0000	0.489898
$601$	33.0000	1.34610	0.673049	−	0.739598i	$-0.264984\pi$
$601$	33.0000	1.34610	0.673049	+	0.739598i	$0.264984\pi$
$602$	6.00000	0.244542
$603$	−8.00000	−0.325785
$604$	−2.00000	−0.0813788
$605$	0	0
$606$	2.00000	0.0812444
$607$	4.00000	0.162355	0.0811775	−	0.996700i	$-0.474132\pi$
$607$	4.00000	0.162355	0.0811775	+	0.996700i	$0.474132\pi$
$608$	−10.0000	−0.405554
$609$	−7.00000	−0.283654
$610$	−30.0000	−1.21466
$611$	−42.0000	−1.69914
$612$	−3.00000	−0.121268
$613$	−7.00000	−0.282727	−0.141364	−	0.989958i	$-0.545149\pi$
$613$	−7.00000	−0.282727	−0.141364	+	0.989958i	$0.545149\pi$
$614$	−12.0000	−0.484281
$615$	−15.0000	−0.604858
$616$	0	0
$617$	−3.00000	−0.120775	−0.0603877	−	0.998175i	$-0.519234\pi$
$617$	−3.00000	−0.120775	−0.0603877	+	0.998175i	$0.519234\pi$
$618$	16.0000	0.643614
$619$	−42.0000	−1.68812	−0.844061	−	0.536247i	$-0.819842\pi$
$619$	−42.0000	−1.68812	−0.844061	+	0.536247i	$0.819842\pi$
$620$	−30.0000	−1.20483
$621$	4.00000	0.160514
$622$	−10.0000	−0.400963
$623$	3.00000	0.120192
$624$	7.00000	0.280224
$625$	−29.0000	−1.16000
$626$	9.00000	0.359712
$627$	0	0
$628$	14.0000	0.558661
$629$	3.00000	0.119618
$630$	−3.00000	−0.119523
$631$	14.0000	0.557331	0.278666	−	0.960388i	$-0.410108\pi$
$631$	14.0000	0.557331	0.278666	+	0.960388i	$0.410108\pi$
$632$	6.00000	0.238667
$633$	−8.00000	−0.317971
$634$	18.0000	0.714871
$635$	−24.0000	−0.952411
$636$	−5.00000	−0.198263
$637$	7.00000	0.277350
$638$	0	0
$639$	−10.0000	−0.395594
$640$	9.00000	0.355756
$641$	9.00000	0.355479	0.177739	−	0.984078i	$-0.443122\pi$
$641$	9.00000	0.355479	0.177739	+	0.984078i	$0.443122\pi$
$642$	14.0000	0.552536
$643$	12.0000	0.473234	0.236617	−	0.971603i	$-0.423961\pi$
$643$	12.0000	0.473234	0.236617	+	0.971603i	$0.423961\pi$
$644$	4.00000	0.157622
$645$	18.0000	0.708749
$646$	−6.00000	−0.236067
$647$	0	0		−	1.00000i	$-0.5\pi$
$647$	0	0			1.00000i	$0.5\pi$
$648$	−3.00000	−0.117851
$649$	0	0
$650$	28.0000	1.09825
$651$	10.0000	0.391931
$652$	−10.0000	−0.391630
$653$	−18.0000	−0.704394	−0.352197	−	0.935926i	$-0.614565\pi$
$653$	−18.0000	−0.704394	−0.352197	+	0.935926i	$0.614565\pi$
$654$	7.00000	0.273722
$655$	12.0000	0.468879
$656$	5.00000	0.195217
$657$	10.0000	0.390137
$658$	−6.00000	−0.233904
$659$	6.00000	0.233727	0.116863	−	0.993148i	$-0.462716\pi$
$659$	6.00000	0.233727	0.116863	+	0.993148i	$0.462716\pi$
$660$	0	0
$661$	35.0000	1.36134	0.680671	−	0.732589i	$-0.261688\pi$
$661$	35.0000	1.36134	0.680671	+	0.732589i	$0.261688\pi$
$662$	18.0000	0.699590
$663$	−21.0000	−0.815572
$664$	48.0000	1.86276
$665$	6.00000	0.232670
$666$	1.00000	0.0387492
$667$	−28.0000	−1.08416
$668$	−12.0000	−0.464294
$669$	24.0000	0.927894
$670$	24.0000	0.927201
$671$	0	0
$672$	−5.00000	−0.192879
$673$	46.0000	1.77317	0.886585	−	0.462566i	$-0.153071\pi$
$673$	46.0000	1.77317	0.886585	+	0.462566i	$0.153071\pi$
$674$	−5.00000	−0.192593
$675$	−4.00000	−0.153960
$676$	−36.0000	−1.38462
$677$	33.0000	1.26829	0.634147	−	0.773213i	$-0.281352\pi$
$677$	33.0000	1.26829	0.634147	+	0.773213i	$0.281352\pi$
$678$	−9.00000	−0.345643
$679$	−19.0000	−0.729153
$680$	27.0000	1.03540
$681$	−2.00000	−0.0766402
$682$	0	0
$683$	−4.00000	−0.153056	−0.0765279	−	0.997067i	$-0.524383\pi$
$683$	−4.00000	−0.153056	−0.0765279	+	0.997067i	$0.524383\pi$
$684$	2.00000	0.0764719
$685$	−6.00000	−0.229248
$686$	1.00000	0.0381802
$687$	13.0000	0.495981
$688$	−6.00000	−0.228748
$689$	−35.0000	−1.33339
$690$	−12.0000	−0.456832
$691$	22.0000	0.836919	0.418460	−	0.908235i	$-0.362570\pi$
$691$	22.0000	0.836919	0.418460	+	0.908235i	$0.362570\pi$
$692$	10.0000	0.380143
$693$	0	0
$694$	26.0000	0.986947
$695$	12.0000	0.455186
$696$	21.0000	0.796003
$697$	−15.0000	−0.568166
$698$	3.00000	0.113552
$699$	23.0000	0.869940
$700$	−4.00000	−0.151186
$701$	−29.0000	−1.09531	−0.547657	−	0.836703i	$-0.684480\pi$
$701$	−29.0000	−1.09531	−0.547657	+	0.836703i	$0.684480\pi$
$702$	−7.00000	−0.264198
$703$	−2.00000	−0.0754314
$704$	0	0
$705$	−18.0000	−0.677919
$706$	−21.0000	−0.790345
$707$	−2.00000	−0.0752177
$708$	−6.00000	−0.225494
$709$	−6.00000	−0.225335	−0.112667	−	0.993633i	$-0.535939\pi$
$709$	−6.00000	−0.225335	−0.112667	+	0.993633i	$0.535939\pi$
$710$	30.0000	1.12588
$711$	−2.00000	−0.0750059
$712$	−9.00000	−0.337289
$713$	40.0000	1.49801
$714$	−3.00000	−0.112272
$715$	0	0
$716$	10.0000	0.373718
$717$	−12.0000	−0.448148
$718$	12.0000	0.447836
$719$	30.0000	1.11881	0.559406	−	0.828894i	$-0.311029\pi$
$719$	30.0000	1.11881	0.559406	+	0.828894i	$0.311029\pi$
$720$	3.00000	0.111803
$721$	−16.0000	−0.595871
$722$	−15.0000	−0.558242
$723$	−14.0000	−0.520666
$724$	−23.0000	−0.854788
$725$	28.0000	1.03989
$726$	0	0
$727$	−14.0000	−0.519231	−0.259616	−	0.965712i	$-0.583596\pi$
$727$	−14.0000	−0.519231	−0.259616	+	0.965712i	$0.583596\pi$
$728$	−21.0000	−0.778312
$729$	1.00000	0.0370370
$730$	−30.0000	−1.11035
$731$	18.0000	0.665754
$732$	10.0000	0.369611
$733$	−1.00000	−0.0369358	−0.0184679	−	0.999829i	$-0.505879\pi$
$733$	−1.00000	−0.0369358	−0.0184679	+	0.999829i	$0.505879\pi$
$734$	10.0000	0.369107
$735$	3.00000	0.110657
$736$	−20.0000	−0.737210
$737$	0	0
$738$	−5.00000	−0.184053
$739$	−30.0000	−1.10357	−0.551784	−	0.833987i	$-0.686053\pi$
$739$	−30.0000	−1.10357	−0.551784	+	0.833987i	$0.686053\pi$
$740$	3.00000	0.110282
$741$	14.0000	0.514303
$742$	−5.00000	−0.183556
$743$	−6.00000	−0.220119	−0.110059	−	0.993925i	$-0.535104\pi$
$743$	−6.00000	−0.220119	−0.110059	+	0.993925i	$0.535104\pi$
$744$	−30.0000	−1.09985
$745$	63.0000	2.30814
$746$	6.00000	0.219676
$747$	−16.0000	−0.585409
$748$	0	0
$749$	−14.0000	−0.511549
$750$	−3.00000	−0.109545
$751$	14.0000	0.510867	0.255434	−	0.966827i	$-0.417782\pi$
$751$	14.0000	0.510867	0.255434	+	0.966827i	$0.417782\pi$
$752$	6.00000	0.218797
$753$	12.0000	0.437304
$754$	49.0000	1.78447
$755$	−6.00000	−0.218362
$756$	1.00000	0.0363696
$757$	−39.0000	−1.41748	−0.708740	−	0.705470i	$-0.750736\pi$
$757$	−39.0000	−1.41748	−0.708740	+	0.705470i	$0.750736\pi$
$758$	16.0000	0.581146
$759$	0	0
$760$	−18.0000	−0.652929
$761$	15.0000	0.543750	0.271875	−	0.962333i	$-0.412356\pi$
$761$	15.0000	0.543750	0.271875	+	0.962333i	$0.412356\pi$
$762$	−8.00000	−0.289809
$763$	−7.00000	−0.253417
$764$	−22.0000	−0.795932
$765$	−9.00000	−0.325396
$766$	16.0000	0.578103
$767$	−42.0000	−1.51653
$768$	17.0000	0.613435
$769$	−15.0000	−0.540914	−0.270457	−	0.962732i	$-0.587175\pi$
$769$	−15.0000	−0.540914	−0.270457	+	0.962732i	$0.587175\pi$
$770$	0	0
$771$	29.0000	1.04441
$772$	−11.0000	−0.395899
$773$	−18.0000	−0.647415	−0.323708	−	0.946157i	$-0.604929\pi$
$773$	−18.0000	−0.647415	−0.323708	+	0.946157i	$0.604929\pi$
$774$	6.00000	0.215666
$775$	−40.0000	−1.43684
$776$	57.0000	2.04618
$777$	−1.00000	−0.0358748
$778$	7.00000	0.250962
$779$	10.0000	0.358287
$780$	−21.0000	−0.751921
$781$	0	0
$782$	−12.0000	−0.429119
$783$	−7.00000	−0.250160
$784$	−1.00000	−0.0357143
$785$	42.0000	1.49904
$786$	4.00000	0.142675
$787$	40.0000	1.42585	0.712923	−	0.701242i	$-0.247371\pi$
$787$	40.0000	1.42585	0.712923	+	0.701242i	$0.247371\pi$
$788$	1.00000	0.0356235
$789$	−24.0000	−0.854423
$790$	6.00000	0.213470
$791$	9.00000	0.320003
$792$	0	0
$793$	70.0000	2.48577
$794$	−33.0000	−1.17113
$795$	−15.0000	−0.531995
$796$	2.00000	0.0708881
$797$	2.00000	0.0708436	0.0354218	−	0.999372i	$-0.488723\pi$
$797$	2.00000	0.0708436	0.0354218	+	0.999372i	$0.488723\pi$
$798$	2.00000	0.0707992
$799$	−18.0000	−0.636794
$800$	20.0000	0.707107
$801$	3.00000	0.106000
$802$	−15.0000	−0.529668
$803$	0	0
$804$	−8.00000	−0.282138
$805$	12.0000	0.422944
$806$	−70.0000	−2.46564
$807$	23.0000	0.809638
$808$	6.00000	0.211079
$809$	18.0000	0.632846	0.316423	−	0.948618i	$-0.397518\pi$
$809$	18.0000	0.632846	0.316423	+	0.948618i	$0.397518\pi$
$810$	−3.00000	−0.105409
$811$	38.0000	1.33436	0.667180	−	0.744896i	$-0.267501\pi$
$811$	38.0000	1.33436	0.667180	+	0.744896i	$0.267501\pi$
$812$	−7.00000	−0.245652
$813$	8.00000	0.280572
$814$	0	0
$815$	−30.0000	−1.05085
$816$	3.00000	0.105021
$817$	−12.0000	−0.419827
$818$	5.00000	0.174821
$819$	7.00000	0.244600
$820$	−15.0000	−0.523823
$821$	10.0000	0.349002	0.174501	−	0.984657i	$-0.444169\pi$
$821$	10.0000	0.349002	0.174501	+	0.984657i	$0.444169\pi$
$822$	−2.00000	−0.0697580
$823$	28.0000	0.976019	0.488009	−	0.872838i	$-0.337723\pi$
$823$	28.0000	0.976019	0.488009	+	0.872838i	$0.337723\pi$
$824$	48.0000	1.67216
$825$	0	0
$826$	−6.00000	−0.208767
$827$	46.0000	1.59958	0.799788	−	0.600282i	$-0.204945\pi$
$827$	46.0000	1.59958	0.799788	+	0.600282i	$0.204945\pi$
$828$	4.00000	0.139010
$829$	−25.0000	−0.868286	−0.434143	−	0.900844i	$-0.642949\pi$
$829$	−25.0000	−0.868286	−0.434143	+	0.900844i	$0.642949\pi$
$830$	48.0000	1.66610
$831$	−5.00000	−0.173448
$832$	49.0000	1.69877
$833$	3.00000	0.103944
$834$	4.00000	0.138509
$835$	−36.0000	−1.24583
$836$	0	0
$837$	10.0000	0.345651
$838$	16.0000	0.552711
$839$	30.0000	1.03572	0.517858	−	0.855467i	$-0.326730\pi$
$839$	30.0000	1.03572	0.517858	+	0.855467i	$0.326730\pi$
$840$	−9.00000	−0.310530
$841$	20.0000	0.689655
$842$	−15.0000	−0.516934
$843$	−18.0000	−0.619953
$844$	−8.00000	−0.275371
$845$	−108.000	−3.71531
$846$	−6.00000	−0.206284
$847$	0	0
$848$	5.00000	0.171701
$849$	22.0000	0.755038
$850$	12.0000	0.411597
$851$	−4.00000	−0.137118
$852$	−10.0000	−0.342594
$853$	−37.0000	−1.26686	−0.633428	−	0.773802i	$-0.718353\pi$
$853$	−37.0000	−1.26686	−0.633428	+	0.773802i	$0.718353\pi$
$854$	10.0000	0.342193
$855$	6.00000	0.205196
$856$	42.0000	1.43553
$857$	−26.0000	−0.888143	−0.444072	−	0.895991i	$-0.646466\pi$
$857$	−26.0000	−0.888143	−0.444072	+	0.895991i	$0.646466\pi$
$858$	0	0
$859$	0	0		−	1.00000i	$-0.5\pi$
$859$	0	0			1.00000i	$0.5\pi$
$860$	18.0000	0.613795
$861$	5.00000	0.170400
$862$	−14.0000	−0.476842
$863$	−14.0000	−0.476566	−0.238283	−	0.971196i	$-0.576585\pi$
$863$	−14.0000	−0.476566	−0.238283	+	0.971196i	$0.576585\pi$
$864$	−5.00000	−0.170103
$865$	30.0000	1.02003
$866$	1.00000	0.0339814
$867$	8.00000	0.271694
$868$	10.0000	0.339422
$869$	0	0
$870$	21.0000	0.711967
$871$	−56.0000	−1.89749
$872$	21.0000	0.711150
$873$	−19.0000	−0.643053
$874$	8.00000	0.270604
$875$	3.00000	0.101419
$876$	10.0000	0.337869
$877$	45.0000	1.51954	0.759771	−	0.650191i	$-0.225311\pi$
$877$	45.0000	1.51954	0.759771	+	0.650191i	$0.225311\pi$
$878$	4.00000	0.134993
$879$	27.0000	0.910687
$880$	0	0
$881$	35.0000	1.17918	0.589590	−	0.807703i	$-0.299289\pi$
$881$	35.0000	1.17918	0.589590	+	0.807703i	$0.299289\pi$
$882$	1.00000	0.0336718
$883$	6.00000	0.201916	0.100958	−	0.994891i	$-0.467809\pi$
$883$	6.00000	0.201916	0.100958	+	0.994891i	$0.467809\pi$
$884$	−21.0000	−0.706306
$885$	−18.0000	−0.605063
$886$	4.00000	0.134383
$887$	−8.00000	−0.268614	−0.134307	−	0.990940i	$-0.542881\pi$
$887$	−8.00000	−0.268614	−0.134307	+	0.990940i	$0.542881\pi$
$888$	3.00000	0.100673
$889$	8.00000	0.268311
$890$	−9.00000	−0.301681
$891$	0	0
$892$	24.0000	0.803579
$893$	12.0000	0.401565
$894$	21.0000	0.702345
$895$	30.0000	1.00279
$896$	−3.00000	−0.100223
$897$	28.0000	0.934893
$898$	−27.0000	−0.901002
$899$	−70.0000	−2.33463
$900$	−4.00000	−0.133333
$901$	−15.0000	−0.499722
$902$	0	0
$903$	−6.00000	−0.199667
$904$	−27.0000	−0.898007
$905$	−69.0000	−2.29364
$906$	−2.00000	−0.0664455
$907$	18.0000	0.597680	0.298840	−	0.954303i	$-0.403400\pi$
$907$	18.0000	0.597680	0.298840	+	0.954303i	$0.403400\pi$
$908$	−2.00000	−0.0663723
$909$	−2.00000	−0.0663358
$910$	−21.0000	−0.696143
$911$	12.0000	0.397578	0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000	0.397578	0.198789	+	0.980042i	$0.436299\pi$
$912$	−2.00000	−0.0662266
$913$	0	0
$914$	−33.0000	−1.09154
$915$	30.0000	0.991769
$916$	13.0000	0.429532
$917$	−4.00000	−0.132092
$918$	−3.00000	−0.0990148
$919$	−46.0000	−1.51740	−0.758700	−	0.651440i	$-0.774165\pi$
$919$	−46.0000	−1.51740	−0.758700	+	0.651440i	$0.774165\pi$
$920$	−36.0000	−1.18688
$921$	12.0000	0.395413
$922$	−15.0000	−0.493999
$923$	−70.0000	−2.30408
$924$	0	0
$925$	4.00000	0.131519
$926$	22.0000	0.722965
$927$	−16.0000	−0.525509
$928$	35.0000	1.14893
$929$	−21.0000	−0.688988	−0.344494	−	0.938789i	$-0.611949\pi$
$929$	−21.0000	−0.688988	−0.344494	+	0.938789i	$0.611949\pi$
$930$	−30.0000	−0.983739
$931$	−2.00000	−0.0655474
$932$	23.0000	0.753390
$933$	10.0000	0.327385
$934$	8.00000	0.261768
$935$	0	0
$936$	−21.0000	−0.686406
$937$	25.0000	0.816714	0.408357	−	0.912822i	$-0.366102\pi$
$937$	25.0000	0.816714	0.408357	+	0.912822i	$0.366102\pi$
$938$	−8.00000	−0.261209
$939$	−9.00000	−0.293704
$940$	−18.0000	−0.587095
$941$	17.0000	0.554184	0.277092	−	0.960843i	$-0.410629\pi$
$941$	17.0000	0.554184	0.277092	+	0.960843i	$0.410629\pi$
$942$	14.0000	0.456145
$943$	20.0000	0.651290
$944$	6.00000	0.195283
$945$	3.00000	0.0975900
$946$	0	0
$947$	−54.0000	−1.75476	−0.877382	−	0.479792i	$-0.840712\pi$
$947$	−54.0000	−1.75476	−0.877382	+	0.479792i	$0.840712\pi$
$948$	−2.00000	−0.0649570
$949$	70.0000	2.27230
$950$	−8.00000	−0.259554
$951$	−18.0000	−0.583690
$952$	−9.00000	−0.291692
$953$	29.0000	0.939402	0.469701	−	0.882826i	$-0.344362\pi$
$953$	29.0000	0.939402	0.469701	+	0.882826i	$0.344362\pi$
$954$	−5.00000	−0.161881
$955$	−66.0000	−2.13571
$956$	−12.0000	−0.388108
$957$	0	0
$958$	−26.0000	−0.840022
$959$	2.00000	0.0645834
$960$	21.0000	0.677772
$961$	69.0000	2.22581
$962$	7.00000	0.225689
$963$	−14.0000	−0.451144
$964$	−14.0000	−0.450910
$965$	−33.0000	−1.06231
$966$	4.00000	0.128698
$967$	14.0000	0.450210	0.225105	−	0.974335i	$-0.427728\pi$
$967$	14.0000	0.450210	0.225105	+	0.974335i	$0.427728\pi$
$968$	0	0
$969$	6.00000	0.192748
$970$	57.0000	1.83016
$971$	4.00000	0.128366	0.0641831	−	0.997938i	$-0.479556\pi$
$971$	4.00000	0.128366	0.0641831	+	0.997938i	$0.479556\pi$
$972$	1.00000	0.0320750
$973$	−4.00000	−0.128234
$974$	−38.0000	−1.21760
$975$	−28.0000	−0.896718
$976$	−10.0000	−0.320092
$977$	−23.0000	−0.735835	−0.367918	−	0.929858i	$-0.619929\pi$
$977$	−23.0000	−0.735835	−0.367918	+	0.929858i	$0.619929\pi$
$978$	−10.0000	−0.319765
$979$	0	0
$980$	3.00000	0.0958315
$981$	−7.00000	−0.223493
$982$	−36.0000	−1.14881
$983$	58.0000	1.84991	0.924956	−	0.380073i	$-0.124101\pi$
$983$	58.0000	1.84991	0.924956	+	0.380073i	$0.124101\pi$
$984$	−15.0000	−0.478183
$985$	3.00000	0.0955879
$986$	21.0000	0.668776
$987$	6.00000	0.190982
$988$	14.0000	0.445399
$989$	−24.0000	−0.763156
$990$	0	0
$991$	2.00000	0.0635321	0.0317660	−	0.999495i	$-0.489887\pi$
$991$	2.00000	0.0635321	0.0317660	+	0.999495i	$0.489887\pi$
$992$	−50.0000	−1.58750
$993$	−18.0000	−0.571213
$994$	−10.0000	−0.317181
$995$	6.00000	0.190213
$996$	−16.0000	−0.506979
$997$	43.0000	1.36182	0.680912	−	0.732365i	$-0.261584\pi$
$997$	43.0000	1.36182	0.680912	+	0.732365i	$0.261584\pi$
$998$	−32.0000	−1.01294
$999$	−1.00000	−0.0316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2541.2.a.g.1.1	yes	1
3.2	odd	2		7623.2.a.h.1.1		1
11.10	odd	2		2541.2.a.c.1.1	✓	1
33.32	even	2		7623.2.a.o.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2541.2.a.c.1.1	✓	1	11.10	odd	2
2541.2.a.g.1.1	yes	1	1.1	even	1	trivial
7623.2.a.h.1.1		1	3.2	odd	2
7623.2.a.o.1.1		1	33.32	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2541 = 3 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2541.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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