LMFDB - Embedded newform 79.2.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [79,2,Mod(1,79)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(79, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("79.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	79.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:	$0.630818175968$
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	$\chi$	$=$	79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} -1.00000 q^{3} -1.00000 q^{4} -3.00000 q^{5} +1.00000 q^{6} -1.00000 q^{7} +3.00000 q^{8} -2.00000 q^{9} +O(q^{10})$

\(q-1.00000 q^{2} -1.00000 q^{3} -1.00000 q^{4} -3.00000 q^{5} +1.00000 q^{6} -1.00000 q^{7} +3.00000 q^{8} -2.00000 q^{9} +3.00000 q^{10} -2.00000 q^{11} +1.00000 q^{12} +3.00000 q^{13} +1.00000 q^{14} +3.00000 q^{15} -1.00000 q^{16} -6.00000 q^{17} +2.00000 q^{18} +4.00000 q^{19} +3.00000 q^{20} +1.00000 q^{21} +2.00000 q^{22} +2.00000 q^{23} -3.00000 q^{24} +4.00000 q^{25} -3.00000 q^{26} +5.00000 q^{27} +1.00000 q^{28} -6.00000 q^{29} -3.00000 q^{30} -10.0000 q^{31} -5.00000 q^{32} +2.00000 q^{33} +6.00000 q^{34} +3.00000 q^{35} +2.00000 q^{36} -2.00000 q^{37} -4.00000 q^{38} -3.00000 q^{39} -9.00000 q^{40} -10.0000 q^{41} -1.00000 q^{42} +4.00000 q^{43} +2.00000 q^{44} +6.00000 q^{45} -2.00000 q^{46} +7.00000 q^{47} +1.00000 q^{48} -6.00000 q^{49} -4.00000 q^{50} +6.00000 q^{51} -3.00000 q^{52} +8.00000 q^{53} -5.00000 q^{54} +6.00000 q^{55} -3.00000 q^{56} -4.00000 q^{57} +6.00000 q^{58} -3.00000 q^{59} -3.00000 q^{60} -4.00000 q^{61} +10.0000 q^{62} +2.00000 q^{63} +7.00000 q^{64} -9.00000 q^{65} -2.00000 q^{66} +8.00000 q^{67} +6.00000 q^{68} -2.00000 q^{69} -3.00000 q^{70} +15.0000 q^{71} -6.00000 q^{72} +2.00000 q^{73} +2.00000 q^{74} -4.00000 q^{75} -4.00000 q^{76} +2.00000 q^{77} +3.00000 q^{78} -1.00000 q^{79} +3.00000 q^{80} +1.00000 q^{81} +10.0000 q^{82} -6.00000 q^{83} -1.00000 q^{84} +18.0000 q^{85} -4.00000 q^{86} +6.00000 q^{87} -6.00000 q^{88} -7.00000 q^{89} -6.00000 q^{90} -3.00000 q^{91} -2.00000 q^{92} +10.0000 q^{93} -7.00000 q^{94} -12.0000 q^{95} +5.00000 q^{96} -19.0000 q^{97} +6.00000 q^{98} +4.00000 q^{99} +O(q^{100})\)

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	$-0.615027\pi$
$2$	−1.00000	−0.707107	−0.353553	+	0.935414i	$0.615027\pi$
$3$	−1.00000	−0.577350	−0.288675	−	0.957427i	$-0.593215\pi$
$3$	−1.00000	−0.577350	−0.288675	+	0.957427i	$0.593215\pi$
$4$	−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	−0.188982	−	0.981981i	$-0.560519\pi$
$7$	−1.00000	−0.377964	−0.188982	+	0.981981i	$0.560519\pi$
$8$	3.00000	1.06066
$9$	−2.00000	−0.666667
$10$	3.00000	0.948683
$11$	−2.00000	−0.603023	−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000	−0.603023	−0.301511	+	0.953463i	$0.597491\pi$
$12$	1.00000	0.288675
$13$	3.00000	0.832050	0.416025	−	0.909353i	$-0.363423\pi$
$13$	3.00000	0.832050	0.416025	+	0.909353i	$0.363423\pi$
$14$	1.00000	0.267261
$15$	3.00000	0.774597
$16$	−1.00000	−0.250000
$17$	−6.00000	−1.45521	−0.727607	−	0.685994i	$-0.759367\pi$
$17$	−6.00000	−1.45521	−0.727607	+	0.685994i	$0.759367\pi$
$18$	2.00000	0.471405
$19$	4.00000	0.917663	0.458831	−	0.888523i	$-0.348268\pi$
$19$	4.00000	0.917663	0.458831	+	0.888523i	$0.348268\pi$
$20$	3.00000	0.670820
$21$	1.00000	0.218218
$22$	2.00000	0.426401
$23$	2.00000	0.417029	0.208514	−	0.978019i	$-0.433137\pi$
$23$	2.00000	0.417029	0.208514	+	0.978019i	$0.433137\pi$
$24$	−3.00000	−0.612372
$25$	4.00000	0.800000
$26$	−3.00000	−0.588348
$27$	5.00000	0.962250
$28$	1.00000	0.188982
$29$	−6.00000	−1.11417	−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000	−1.11417	−0.557086	+	0.830455i	$0.688081\pi$
$30$	−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
$33$	2.00000	0.348155
$34$	6.00000	1.02899
$35$	3.00000	0.507093
$36$	2.00000	0.333333
$37$	−2.00000	−0.328798	−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000	−0.328798	−0.164399	+	0.986394i	$0.552568\pi$
$38$	−4.00000	−0.648886
$39$	−3.00000	−0.480384
$40$	−9.00000	−1.42302
$41$	−10.0000	−1.56174	−0.780869	−	0.624695i	$-0.785223\pi$
$41$	−10.0000	−1.56174	−0.780869	+	0.624695i	$0.785223\pi$
$42$	−1.00000	−0.154303
$43$	4.00000	0.609994	0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000	0.609994	0.304997	+	0.952353i	$0.401344\pi$
$44$	2.00000	0.301511
$45$	6.00000	0.894427
$46$	−2.00000	−0.294884
$47$	7.00000	1.02105	0.510527	−	0.859861i	$-0.329450\pi$
$47$	7.00000	1.02105	0.510527	+	0.859861i	$0.329450\pi$
$48$	1.00000	0.144338
$49$	−6.00000	−0.857143
$50$	−4.00000	−0.565685
$51$	6.00000	0.840168
$52$	−3.00000	−0.416025
$53$	8.00000	1.09888	0.549442	−	0.835532i	$-0.314840\pi$
$53$	8.00000	1.09888	0.549442	+	0.835532i	$0.314840\pi$
$54$	−5.00000	−0.680414
$55$	6.00000	0.809040
$56$	−3.00000	−0.400892
$57$	−4.00000	−0.529813
$58$	6.00000	0.787839
$59$	−3.00000	−0.390567	−0.195283	−	0.980747i	$-0.562563\pi$
$59$	−3.00000	−0.390567	−0.195283	+	0.980747i	$0.562563\pi$
$60$	−3.00000	−0.387298
$61$	−4.00000	−0.512148	−0.256074	−	0.966657i	$-0.582429\pi$
$61$	−4.00000	−0.512148	−0.256074	+	0.966657i	$0.582429\pi$
$62$	10.0000	1.27000
$63$	2.00000	0.251976
$64$	7.00000	0.875000
$65$	−9.00000	−1.11631
$66$	−2.00000	−0.246183
$67$	8.00000	0.977356	0.488678	−	0.872464i	$-0.337479\pi$
$67$	8.00000	0.977356	0.488678	+	0.872464i	$0.337479\pi$
$68$	6.00000	0.727607
$69$	−2.00000	−0.240772
$70$	−3.00000	−0.358569
$71$	15.0000	1.78017	0.890086	−	0.455792i	$-0.150644\pi$
$71$	15.0000	1.78017	0.890086	+	0.455792i	$0.150644\pi$
$72$	−6.00000	−0.707107
$73$	2.00000	0.234082	0.117041	−	0.993127i	$-0.462659\pi$
$73$	2.00000	0.234082	0.117041	+	0.993127i	$0.462659\pi$
$74$	2.00000	0.232495
$75$	−4.00000	−0.461880
$76$	−4.00000	−0.458831
$77$	2.00000	0.227921
$78$	3.00000	0.339683
$79$	−1.00000	−0.112509
$79$	−1.00000	−0.112509
$80$	3.00000	0.335410
$81$	1.00000	0.111111
$82$	10.0000	1.10432
$83$	−6.00000	−0.658586	−0.329293	−	0.944228i	$-0.606810\pi$
$83$	−6.00000	−0.658586	−0.329293	+	0.944228i	$0.606810\pi$
$84$	−1.00000	−0.109109
$85$	18.0000	1.95237
$86$	−4.00000	−0.431331
$87$	6.00000	0.643268
$88$	−6.00000	−0.639602
$89$	−7.00000	−0.741999	−0.370999	−	0.928633i	$-0.620985\pi$
$89$	−7.00000	−0.741999	−0.370999	+	0.928633i	$0.620985\pi$
$90$	−6.00000	−0.632456
$91$	−3.00000	−0.314485
$92$	−2.00000	−0.208514
$93$	10.0000	1.03695
$94$	−7.00000	−0.721995
$95$	−12.0000	−1.23117
$96$	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	$0.915026\pi$
$98$	6.00000	0.606092
$99$	4.00000	0.402015
$100$	−4.00000	−0.400000
$101$	11.0000	1.09454	0.547270	−	0.836956i	$-0.315667\pi$
$101$	11.0000	1.09454	0.547270	+	0.836956i	$0.315667\pi$
$102$	−6.00000	−0.594089
$103$	−9.00000	−0.886796	−0.443398	−	0.896325i	$-0.646227\pi$
$103$	−9.00000	−0.886796	−0.443398	+	0.896325i	$0.646227\pi$
$104$	9.00000	0.882523
$105$	−3.00000	−0.292770
$106$	−8.00000	−0.777029
$107$	−11.0000	−1.06341	−0.531705	−	0.846930i	$-0.678449\pi$
$107$	−11.0000	−1.06341	−0.531705	+	0.846930i	$0.678449\pi$
$108$	−5.00000	−0.481125
$109$	10.0000	0.957826	0.478913	−	0.877862i	$-0.341031\pi$
$109$	10.0000	0.957826	0.478913	+	0.877862i	$0.341031\pi$
$110$	−6.00000	−0.572078
$111$	2.00000	0.189832
$112$	1.00000	0.0944911
$113$	0	0		−	1.00000i	$-0.5\pi$
$113$	0	0			1.00000i	$0.5\pi$
$114$	4.00000	0.374634
$115$	−6.00000	−0.559503
$116$	6.00000	0.557086
$117$	−6.00000	−0.554700
$118$	3.00000	0.276172
$119$	6.00000	0.550019
$120$	9.00000	0.821584
$121$	−7.00000	−0.636364
$122$	4.00000	0.362143
$123$	10.0000	0.901670
$124$	10.0000	0.898027
$125$	3.00000	0.268328
$126$	−2.00000	−0.178174
$127$	−11.0000	−0.976092	−0.488046	−	0.872818i	$-0.662290\pi$
$127$	−11.0000	−0.976092	−0.488046	+	0.872818i	$0.662290\pi$
$128$	3.00000	0.265165
$129$	−4.00000	−0.352180
$130$	9.00000	0.789352
$131$	6.00000	0.524222	0.262111	−	0.965038i	$-0.415581\pi$
$131$	6.00000	0.524222	0.262111	+	0.965038i	$0.415581\pi$
$132$	−2.00000	−0.174078
$133$	−4.00000	−0.346844
$134$	−8.00000	−0.691095
$135$	−15.0000	−1.29099
$136$	−18.0000	−1.54349
$137$	12.0000	1.02523	0.512615	−	0.858619i	$-0.328677\pi$
$137$	12.0000	1.02523	0.512615	+	0.858619i	$0.328677\pi$
$138$	2.00000	0.170251
$139$	−21.0000	−1.78120	−0.890598	−	0.454791i	$-0.849714\pi$
$139$	−21.0000	−1.78120	−0.890598	+	0.454791i	$0.849714\pi$
$140$	−3.00000	−0.253546
$141$	−7.00000	−0.589506
$142$	−15.0000	−1.25877
$143$	−6.00000	−0.501745
$144$	2.00000	0.166667
$145$	18.0000	1.49482
$146$	−2.00000	−0.165521
$147$	6.00000	0.494872
$148$	2.00000	0.164399
$149$	−6.00000	−0.491539	−0.245770	−	0.969328i	$-0.579041\pi$
$149$	−6.00000	−0.491539	−0.245770	+	0.969328i	$0.579041\pi$
$150$	4.00000	0.326599
$151$	6.00000	0.488273	0.244137	−	0.969741i	$-0.421495\pi$
$151$	6.00000	0.488273	0.244137	+	0.969741i	$0.421495\pi$
$152$	12.0000	0.973329
$153$	12.0000	0.970143
$154$	−2.00000	−0.161165
$155$	30.0000	2.40966
$156$	3.00000	0.240192
$157$	−18.0000	−1.43656	−0.718278	−	0.695756i	$-0.755069\pi$
$157$	−18.0000	−1.43656	−0.718278	+	0.695756i	$0.755069\pi$
$158$	1.00000	0.0795557
$159$	−8.00000	−0.634441
$160$	15.0000	1.18585
$161$	−2.00000	−0.157622
$162$	−1.00000	−0.0785674
$163$	4.00000	0.313304	0.156652	−	0.987654i	$-0.449930\pi$
$163$	4.00000	0.313304	0.156652	+	0.987654i	$0.449930\pi$
$164$	10.0000	0.780869
$165$	−6.00000	−0.467099
$166$	6.00000	0.465690
$167$	18.0000	1.39288	0.696441	−	0.717614i	$-0.254766\pi$
$167$	18.0000	1.39288	0.696441	+	0.717614i	$0.254766\pi$
$168$	3.00000	0.231455
$169$	−4.00000	−0.307692
$170$	−18.0000	−1.38054
$171$	−8.00000	−0.611775
$172$	−4.00000	−0.304997
$173$	−8.00000	−0.608229	−0.304114	−	0.952636i	$-0.598361\pi$
$173$	−8.00000	−0.608229	−0.304114	+	0.952636i	$0.598361\pi$
$174$	−6.00000	−0.454859
$175$	−4.00000	−0.302372
$176$	2.00000	0.150756
$177$	3.00000	0.225494
$178$	7.00000	0.524672
$179$	−16.0000	−1.19590	−0.597948	−	0.801535i	$-0.704017\pi$
$179$	−16.0000	−1.19590	−0.597948	+	0.801535i	$0.704017\pi$
$180$	−6.00000	−0.447214
$181$	22.0000	1.63525	0.817624	−	0.575753i	$-0.195291\pi$
$181$	22.0000	1.63525	0.817624	+	0.575753i	$0.195291\pi$
$182$	3.00000	0.222375
$183$	4.00000	0.295689
$184$	6.00000	0.442326
$185$	6.00000	0.441129
$186$	−10.0000	−0.733236
$187$	12.0000	0.877527
$188$	−7.00000	−0.510527
$189$	−5.00000	−0.363696
$190$	12.0000	0.870572
$191$	−15.0000	−1.08536	−0.542681	−	0.839939i	$-0.682591\pi$
$191$	−15.0000	−1.08536	−0.542681	+	0.839939i	$0.682591\pi$
$192$	−7.00000	−0.505181
$193$	14.0000	1.00774	0.503871	−	0.863779i	$-0.331909\pi$
$193$	14.0000	1.00774	0.503871	+	0.863779i	$0.331909\pi$
$194$	19.0000	1.36412
$195$	9.00000	0.644503
$196$	6.00000	0.428571
$197$	−6.00000	−0.427482	−0.213741	−	0.976890i	$-0.568565\pi$
$197$	−6.00000	−0.427482	−0.213741	+	0.976890i	$0.568565\pi$
$198$	−4.00000	−0.284268
$199$	11.0000	0.779769	0.389885	−	0.920864i	$-0.372515\pi$
$199$	11.0000	0.779769	0.389885	+	0.920864i	$0.372515\pi$
$200$	12.0000	0.848528
$201$	−8.00000	−0.564276
$202$	−11.0000	−0.773957
$203$	6.00000	0.421117
$204$	−6.00000	−0.420084
$205$	30.0000	2.09529
$206$	9.00000	0.627060
$207$	−4.00000	−0.278019
$208$	−3.00000	−0.208013
$209$	−8.00000	−0.553372
$210$	3.00000	0.207020
$211$	−12.0000	−0.826114	−0.413057	−	0.910705i	$-0.635539\pi$
$211$	−12.0000	−0.826114	−0.413057	+	0.910705i	$0.635539\pi$
$212$	−8.00000	−0.549442
$213$	−15.0000	−1.02778
$214$	11.0000	0.751945
$215$	−12.0000	−0.818393
$216$	15.0000	1.02062
$217$	10.0000	0.678844
$218$	−10.0000	−0.677285
$219$	−2.00000	−0.135147
$220$	−6.00000	−0.404520
$221$	−18.0000	−1.21081
$222$	−2.00000	−0.134231
$223$	−26.0000	−1.74109	−0.870544	−	0.492090i	$-0.836233\pi$
$223$	−26.0000	−1.74109	−0.870544	+	0.492090i	$0.836233\pi$
$224$	5.00000	0.334077
$225$	−8.00000	−0.533333
$226$	0	0
$227$	−8.00000	−0.530979	−0.265489	−	0.964114i	$-0.585534\pi$
$227$	−8.00000	−0.530979	−0.265489	+	0.964114i	$0.585534\pi$
$228$	4.00000	0.264906
$229$	16.0000	1.05731	0.528655	−	0.848837i	$-0.322697\pi$
$229$	16.0000	1.05731	0.528655	+	0.848837i	$0.322697\pi$
$230$	6.00000	0.395628
$231$	−2.00000	−0.131590
$232$	−18.0000	−1.18176
$233$	−18.0000	−1.17922	−0.589610	−	0.807688i	$-0.700718\pi$
$233$	−18.0000	−1.17922	−0.589610	+	0.807688i	$0.700718\pi$
$234$	6.00000	0.392232
$235$	−21.0000	−1.36989
$236$	3.00000	0.195283
$237$	1.00000	0.0649570
$238$	−6.00000	−0.388922
$239$	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
$241$	−15.0000	−0.966235	−0.483117	−	0.875556i	$-0.660496\pi$
$241$	−15.0000	−0.966235	−0.483117	+	0.875556i	$0.660496\pi$
$242$	7.00000	0.449977
$243$	−16.0000	−1.02640
$244$	4.00000	0.256074
$245$	18.0000	1.14998
$246$	−10.0000	−0.637577
$247$	12.0000	0.763542
$248$	−30.0000	−1.90500
$249$	6.00000	0.380235
$250$	−3.00000	−0.189737
$251$	−5.00000	−0.315597	−0.157799	−	0.987471i	$-0.550440\pi$
$251$	−5.00000	−0.315597	−0.157799	+	0.987471i	$0.550440\pi$
$252$	−2.00000	−0.125988
$253$	−4.00000	−0.251478
$254$	11.0000	0.690201
$255$	−18.0000	−1.12720
$256$	−17.0000	−1.06250
$257$	−2.00000	−0.124757	−0.0623783	−	0.998053i	$-0.519869\pi$
$257$	−2.00000	−0.124757	−0.0623783	+	0.998053i	$0.519869\pi$
$258$	4.00000	0.249029
$259$	2.00000	0.124274
$260$	9.00000	0.558156
$261$	12.0000	0.742781
$262$	−6.00000	−0.370681
$263$	26.0000	1.60323	0.801614	−	0.597841i	$-0.203975\pi$
$263$	26.0000	1.60323	0.801614	+	0.597841i	$0.203975\pi$
$264$	6.00000	0.369274
$265$	−24.0000	−1.47431
$266$	4.00000	0.245256
$267$	7.00000	0.428393
$268$	−8.00000	−0.488678
$269$	−19.0000	−1.15845	−0.579225	−	0.815168i	$-0.696645\pi$
$269$	−19.0000	−1.15845	−0.579225	+	0.815168i	$0.696645\pi$
$270$	15.0000	0.912871
$271$	0	0		−	1.00000i	$-0.5\pi$
$271$	0	0			1.00000i	$0.5\pi$
$272$	6.00000	0.363803
$273$	3.00000	0.181568
$274$	−12.0000	−0.724947
$275$	−8.00000	−0.482418
$276$	2.00000	0.120386
$277$	11.0000	0.660926	0.330463	−	0.943819i	$-0.392795\pi$
$277$	11.0000	0.660926	0.330463	+	0.943819i	$0.392795\pi$
$278$	21.0000	1.25950
$279$	20.0000	1.19737
$280$	9.00000	0.537853
$281$	23.0000	1.37206	0.686032	−	0.727571i	$-0.259351\pi$
$281$	23.0000	1.37206	0.686032	+	0.727571i	$0.259351\pi$
$282$	7.00000	0.416844
$283$	24.0000	1.42665	0.713326	−	0.700832i	$-0.247188\pi$
$283$	24.0000	1.42665	0.713326	+	0.700832i	$0.247188\pi$
$284$	−15.0000	−0.890086
$285$	12.0000	0.710819
$286$	6.00000	0.354787
$287$	10.0000	0.590281
$288$	10.0000	0.589256
$289$	19.0000	1.11765
$290$	−18.0000	−1.05700
$291$	19.0000	1.11380
$292$	−2.00000	−0.117041
$293$	−12.0000	−0.701047	−0.350524	−	0.936554i	$-0.613996\pi$
$293$	−12.0000	−0.701047	−0.350524	+	0.936554i	$0.613996\pi$
$294$	−6.00000	−0.349927
$295$	9.00000	0.524000
$296$	−6.00000	−0.348743
$297$	−10.0000	−0.580259
$298$	6.00000	0.347571
$299$	6.00000	0.346989
$300$	4.00000	0.230940
$301$	−4.00000	−0.230556
$302$	−6.00000	−0.345261
$303$	−11.0000	−0.631933
$304$	−4.00000	−0.229416
$305$	12.0000	0.687118
$306$	−12.0000	−0.685994
$307$	12.0000	0.684876	0.342438	−	0.939540i	$-0.388747\pi$
$307$	12.0000	0.684876	0.342438	+	0.939540i	$0.388747\pi$
$308$	−2.00000	−0.113961
$309$	9.00000	0.511992
$310$	−30.0000	−1.70389
$311$	4.00000	0.226819	0.113410	−	0.993548i	$-0.463823\pi$
$311$	4.00000	0.226819	0.113410	+	0.993548i	$0.463823\pi$
$312$	−9.00000	−0.509525
$313$	−26.0000	−1.46961	−0.734803	−	0.678280i	$-0.762726\pi$
$313$	−26.0000	−1.46961	−0.734803	+	0.678280i	$0.762726\pi$
$314$	18.0000	1.01580
$315$	−6.00000	−0.338062
$316$	1.00000	0.0562544
$317$	31.0000	1.74113	0.870567	−	0.492050i	$-0.163752\pi$
$317$	31.0000	1.74113	0.870567	+	0.492050i	$0.163752\pi$
$318$	8.00000	0.448618
$319$	12.0000	0.671871
$320$	−21.0000	−1.17394
$321$	11.0000	0.613960
$322$	2.00000	0.111456
$323$	−24.0000	−1.33540
$324$	−1.00000	−0.0555556
$325$	12.0000	0.665640
$326$	−4.00000	−0.221540
$327$	−10.0000	−0.553001
$328$	−30.0000	−1.65647
$329$	−7.00000	−0.385922
$330$	6.00000	0.330289
$331$	20.0000	1.09930	0.549650	−	0.835395i	$-0.314761\pi$
$331$	20.0000	1.09930	0.549650	+	0.835395i	$0.314761\pi$
$332$	6.00000	0.329293
$333$	4.00000	0.219199
$334$	−18.0000	−0.984916
$335$	−24.0000	−1.31126
$336$	−1.00000	−0.0545545
$337$	31.0000	1.68868	0.844339	−	0.535810i	$-0.179994\pi$
$337$	31.0000	1.68868	0.844339	+	0.535810i	$0.179994\pi$
$338$	4.00000	0.217571
$339$	0	0
$340$	−18.0000	−0.976187
$341$	20.0000	1.08306
$342$	8.00000	0.432590
$343$	13.0000	0.701934
$344$	12.0000	0.646997
$345$	6.00000	0.323029
$346$	8.00000	0.430083
$347$	−14.0000	−0.751559	−0.375780	−	0.926709i	$-0.622625\pi$
$347$	−14.0000	−0.751559	−0.375780	+	0.926709i	$0.622625\pi$
$348$	−6.00000	−0.321634
$349$	12.0000	0.642345	0.321173	−	0.947021i	$-0.395923\pi$
$349$	12.0000	0.642345	0.321173	+	0.947021i	$0.395923\pi$
$350$	4.00000	0.213809
$351$	15.0000	0.800641
$352$	10.0000	0.533002
$353$	−4.00000	−0.212899	−0.106449	−	0.994318i	$-0.533948\pi$
$353$	−4.00000	−0.212899	−0.106449	+	0.994318i	$0.533948\pi$
$354$	−3.00000	−0.159448
$355$	−45.0000	−2.38835
$356$	7.00000	0.370999
$357$	−6.00000	−0.317554
$358$	16.0000	0.845626
$359$	−35.0000	−1.84723	−0.923615	−	0.383322i	$-0.874780\pi$
$359$	−35.0000	−1.84723	−0.923615	+	0.383322i	$0.874780\pi$
$360$	18.0000	0.948683
$361$	−3.00000	−0.157895
$362$	−22.0000	−1.15629
$363$	7.00000	0.367405
$364$	3.00000	0.157243
$365$	−6.00000	−0.314054
$366$	−4.00000	−0.209083
$367$	−2.00000	−0.104399	−0.0521996	−	0.998637i	$-0.516623\pi$
$367$	−2.00000	−0.104399	−0.0521996	+	0.998637i	$0.516623\pi$
$368$	−2.00000	−0.104257
$369$	20.0000	1.04116
$370$	−6.00000	−0.311925
$371$	−8.00000	−0.415339
$372$	−10.0000	−0.518476
$373$	−2.00000	−0.103556	−0.0517780	−	0.998659i	$-0.516489\pi$
$373$	−2.00000	−0.103556	−0.0517780	+	0.998659i	$0.516489\pi$
$374$	−12.0000	−0.620505
$375$	−3.00000	−0.154919
$376$	21.0000	1.08299
$377$	−18.0000	−0.927047
$378$	5.00000	0.257172
$379$	−23.0000	−1.18143	−0.590715	−	0.806880i	$-0.701154\pi$
$379$	−23.0000	−1.18143	−0.590715	+	0.806880i	$0.701154\pi$
$380$	12.0000	0.615587
$381$	11.0000	0.563547
$382$	15.0000	0.767467
$383$	2.00000	0.102195	0.0510976	−	0.998694i	$-0.483728\pi$
$383$	2.00000	0.102195	0.0510976	+	0.998694i	$0.483728\pi$
$384$	−3.00000	−0.153093
$385$	−6.00000	−0.305788
$386$	−14.0000	−0.712581
$387$	−8.00000	−0.406663
$388$	19.0000	0.964579
$389$	−9.00000	−0.456318	−0.228159	−	0.973624i	$-0.573271\pi$
$389$	−9.00000	−0.456318	−0.228159	+	0.973624i	$0.573271\pi$
$390$	−9.00000	−0.455733
$391$	−12.0000	−0.606866
$392$	−18.0000	−0.909137
$393$	−6.00000	−0.302660
$394$	6.00000	0.302276
$395$	3.00000	0.150946
$396$	−4.00000	−0.201008
$397$	−1.00000	−0.0501886	−0.0250943	−	0.999685i	$-0.507989\pi$
$397$	−1.00000	−0.0501886	−0.0250943	+	0.999685i	$0.507989\pi$
$398$	−11.0000	−0.551380
$399$	4.00000	0.200250
$400$	−4.00000	−0.200000
$401$	10.0000	0.499376	0.249688	−	0.968326i	$-0.419672\pi$
$401$	10.0000	0.499376	0.249688	+	0.968326i	$0.419672\pi$
$402$	8.00000	0.399004
$403$	−30.0000	−1.49441
$404$	−11.0000	−0.547270
$405$	−3.00000	−0.149071
$406$	−6.00000	−0.297775
$407$	4.00000	0.198273
$408$	18.0000	0.891133
$409$	0	0		−	1.00000i	$-0.5\pi$
$409$	0	0			1.00000i	$0.5\pi$
$410$	−30.0000	−1.48159
$411$	−12.0000	−0.591916
$412$	9.00000	0.443398
$413$	3.00000	0.147620
$414$	4.00000	0.196589
$415$	18.0000	0.883585
$416$	−15.0000	−0.735436
$417$	21.0000	1.02837
$418$	8.00000	0.391293
$419$	9.00000	0.439679	0.219839	−	0.975536i	$-0.429447\pi$
$419$	9.00000	0.439679	0.219839	+	0.975536i	$0.429447\pi$
$420$	3.00000	0.146385
$421$	−13.0000	−0.633581	−0.316791	−	0.948495i	$-0.602605\pi$
$421$	−13.0000	−0.633581	−0.316791	+	0.948495i	$0.602605\pi$
$422$	12.0000	0.584151
$423$	−14.0000	−0.680703
$424$	24.0000	1.16554
$425$	−24.0000	−1.16417
$426$	15.0000	0.726752
$427$	4.00000	0.193574
$428$	11.0000	0.531705
$429$	6.00000	0.289683
$430$	12.0000	0.578691
$431$	20.0000	0.963366	0.481683	−	0.876346i	$-0.340026\pi$
$431$	20.0000	0.963366	0.481683	+	0.876346i	$0.340026\pi$
$432$	−5.00000	−0.240563
$433$	−3.00000	−0.144171	−0.0720854	−	0.997398i	$-0.522965\pi$
$433$	−3.00000	−0.144171	−0.0720854	+	0.997398i	$0.522965\pi$
$434$	−10.0000	−0.480015
$435$	−18.0000	−0.863034
$436$	−10.0000	−0.478913
$437$	8.00000	0.382692
$438$	2.00000	0.0955637
$439$	−20.0000	−0.954548	−0.477274	−	0.878755i	$-0.658375\pi$
$439$	−20.0000	−0.954548	−0.477274	+	0.878755i	$0.658375\pi$
$440$	18.0000	0.858116
$441$	12.0000	0.571429
$442$	18.0000	0.856173
$443$	−4.00000	−0.190046	−0.0950229	−	0.995475i	$-0.530292\pi$
$443$	−4.00000	−0.190046	−0.0950229	+	0.995475i	$0.530292\pi$
$444$	−2.00000	−0.0949158
$445$	21.0000	0.995495
$446$	26.0000	1.23114
$447$	6.00000	0.283790
$448$	−7.00000	−0.330719
$449$	−22.0000	−1.03824	−0.519122	−	0.854700i	$-0.673741\pi$
$449$	−22.0000	−1.03824	−0.519122	+	0.854700i	$0.673741\pi$
$450$	8.00000	0.377124
$451$	20.0000	0.941763
$452$	0	0
$453$	−6.00000	−0.281905
$454$	8.00000	0.375459
$455$	9.00000	0.421927
$456$	−12.0000	−0.561951
$457$	7.00000	0.327446	0.163723	−	0.986506i	$-0.447650\pi$
$457$	7.00000	0.327446	0.163723	+	0.986506i	$0.447650\pi$
$458$	−16.0000	−0.747631
$459$	−30.0000	−1.40028
$460$	6.00000	0.279751
$461$	−10.0000	−0.465746	−0.232873	−	0.972507i	$-0.574813\pi$
$461$	−10.0000	−0.465746	−0.232873	+	0.972507i	$0.574813\pi$
$462$	2.00000	0.0930484
$463$	−19.0000	−0.883005	−0.441502	−	0.897260i	$-0.645554\pi$
$463$	−19.0000	−0.883005	−0.441502	+	0.897260i	$0.645554\pi$
$464$	6.00000	0.278543
$465$	−30.0000	−1.39122
$466$	18.0000	0.833834
$467$	6.00000	0.277647	0.138823	−	0.990317i	$-0.455668\pi$
$467$	6.00000	0.277647	0.138823	+	0.990317i	$0.455668\pi$
$468$	6.00000	0.277350
$469$	−8.00000	−0.369406
$470$	21.0000	0.968658
$471$	18.0000	0.829396
$472$	−9.00000	−0.414259
$473$	−8.00000	−0.367840
$474$	−1.00000	−0.0459315
$475$	16.0000	0.734130
$476$	−6.00000	−0.275010
$477$	−16.0000	−0.732590
$478$	−12.0000	−0.548867
$479$	0	0		−	1.00000i	$-0.5\pi$
$479$	0	0			1.00000i	$0.5\pi$
$480$	−15.0000	−0.684653
$481$	−6.00000	−0.273576
$482$	15.0000	0.683231
$483$	2.00000	0.0910032
$484$	7.00000	0.318182
$485$	57.0000	2.58824
$486$	16.0000	0.725775
$487$	18.0000	0.815658	0.407829	−	0.913058i	$-0.366286\pi$
$487$	18.0000	0.815658	0.407829	+	0.913058i	$0.366286\pi$
$488$	−12.0000	−0.543214
$489$	−4.00000	−0.180886
$490$	−18.0000	−0.813157
$491$	13.0000	0.586682	0.293341	−	0.956008i	$-0.405233\pi$
$491$	13.0000	0.586682	0.293341	+	0.956008i	$0.405233\pi$
$492$	−10.0000	−0.450835
$493$	36.0000	1.62136
$494$	−12.0000	−0.539906
$495$	−12.0000	−0.539360
$496$	10.0000	0.449013
$497$	−15.0000	−0.672842
$498$	−6.00000	−0.268866
$499$	10.0000	0.447661	0.223831	−	0.974628i	$-0.428144\pi$
$499$	10.0000	0.447661	0.223831	+	0.974628i	$0.428144\pi$
$500$	−3.00000	−0.134164
$501$	−18.0000	−0.804181
$502$	5.00000	0.223161
$503$	−13.0000	−0.579641	−0.289821	−	0.957081i	$-0.593596\pi$
$503$	−13.0000	−0.579641	−0.289821	+	0.957081i	$0.593596\pi$
$504$	6.00000	0.267261
$505$	−33.0000	−1.46848
$506$	4.00000	0.177822
$507$	4.00000	0.177646
$508$	11.0000	0.488046
$509$	−20.0000	−0.886484	−0.443242	−	0.896402i	$-0.646172\pi$
$509$	−20.0000	−0.886484	−0.443242	+	0.896402i	$0.646172\pi$
$510$	18.0000	0.797053
$511$	−2.00000	−0.0884748
$512$	11.0000	0.486136
$513$	20.0000	0.883022
$514$	2.00000	0.0882162
$515$	27.0000	1.18976
$516$	4.00000	0.176090
$517$	−14.0000	−0.615719
$518$	−2.00000	−0.0878750
$519$	8.00000	0.351161
$520$	−27.0000	−1.18403
$521$	0	0		−	1.00000i	$-0.5\pi$
$521$	0	0			1.00000i	$0.5\pi$
$522$	−12.0000	−0.525226
$523$	−6.00000	−0.262362	−0.131181	−	0.991358i	$-0.541877\pi$
$523$	−6.00000	−0.262362	−0.131181	+	0.991358i	$0.541877\pi$
$524$	−6.00000	−0.262111
$525$	4.00000	0.174574
$526$	−26.0000	−1.13365
$527$	60.0000	2.61364
$528$	−2.00000	−0.0870388
$529$	−19.0000	−0.826087
$530$	24.0000	1.04249
$531$	6.00000	0.260378
$532$	4.00000	0.173422
$533$	−30.0000	−1.29944
$534$	−7.00000	−0.302920
$535$	33.0000	1.42671
$536$	24.0000	1.03664
$537$	16.0000	0.690451
$538$	19.0000	0.819148
$539$	12.0000	0.516877
$540$	15.0000	0.645497
$541$	−29.0000	−1.24681	−0.623404	−	0.781900i	$-0.714251\pi$
$541$	−29.0000	−1.24681	−0.623404	+	0.781900i	$0.714251\pi$
$542$	0	0
$543$	−22.0000	−0.944110
$544$	30.0000	1.28624
$545$	−30.0000	−1.28506
$546$	−3.00000	−0.128388
$547$	−18.0000	−0.769624	−0.384812	−	0.922995i	$-0.625734\pi$
$547$	−18.0000	−0.769624	−0.384812	+	0.922995i	$0.625734\pi$
$548$	−12.0000	−0.512615
$549$	8.00000	0.341432
$550$	8.00000	0.341121
$551$	−24.0000	−1.02243
$552$	−6.00000	−0.255377
$553$	1.00000	0.0425243
$554$	−11.0000	−0.467345
$555$	−6.00000	−0.254686
$556$	21.0000	0.890598
$557$	−11.0000	−0.466085	−0.233042	−	0.972467i	$-0.574868\pi$
$557$	−11.0000	−0.466085	−0.233042	+	0.972467i	$0.574868\pi$
$558$	−20.0000	−0.846668
$559$	12.0000	0.507546
$560$	−3.00000	−0.126773
$561$	−12.0000	−0.506640
$562$	−23.0000	−0.970196
$563$	18.0000	0.758610	0.379305	−	0.925272i	$-0.376163\pi$
$563$	18.0000	0.758610	0.379305	+	0.925272i	$0.376163\pi$
$564$	7.00000	0.294753
$565$	0	0
$566$	−24.0000	−1.00880
$567$	−1.00000	−0.0419961
$568$	45.0000	1.88816
$569$	−30.0000	−1.25767	−0.628833	−	0.777541i	$-0.716467\pi$
$569$	−30.0000	−1.25767	−0.628833	+	0.777541i	$0.716467\pi$
$570$	−12.0000	−0.502625
$571$	26.0000	1.08807	0.544033	−	0.839064i	$-0.316897\pi$
$571$	26.0000	1.08807	0.544033	+	0.839064i	$0.316897\pi$
$572$	6.00000	0.250873
$573$	15.0000	0.626634
$574$	−10.0000	−0.417392
$575$	8.00000	0.333623
$576$	−14.0000	−0.583333
$577$	−16.0000	−0.666089	−0.333044	−	0.942911i	$-0.608076\pi$
$577$	−16.0000	−0.666089	−0.333044	+	0.942911i	$0.608076\pi$
$578$	−19.0000	−0.790296
$579$	−14.0000	−0.581820
$580$	−18.0000	−0.747409
$581$	6.00000	0.248922
$582$	−19.0000	−0.787575
$583$	−16.0000	−0.662652
$584$	6.00000	0.248282
$585$	18.0000	0.744208
$586$	12.0000	0.495715
$587$	25.0000	1.03186	0.515930	−	0.856631i	$-0.327446\pi$
$587$	25.0000	1.03186	0.515930	+	0.856631i	$0.327446\pi$
$588$	−6.00000	−0.247436
$589$	−40.0000	−1.64817
$590$	−9.00000	−0.370524
$591$	6.00000	0.246807
$592$	2.00000	0.0821995
$593$	27.0000	1.10876	0.554379	−	0.832265i	$-0.312956\pi$
$593$	27.0000	1.10876	0.554379	+	0.832265i	$0.312956\pi$
$594$	10.0000	0.410305
$595$	−18.0000	−0.737928
$596$	6.00000	0.245770
$597$	−11.0000	−0.450200
$598$	−6.00000	−0.245358
$599$	12.0000	0.490307	0.245153	−	0.969484i	$-0.421162\pi$
$599$	12.0000	0.490307	0.245153	+	0.969484i	$0.421162\pi$
$600$	−12.0000	−0.489898
$601$	−44.0000	−1.79480	−0.897399	−	0.441221i	$-0.854546\pi$
$601$	−44.0000	−1.79480	−0.897399	+	0.441221i	$0.854546\pi$
$602$	4.00000	0.163028
$603$	−16.0000	−0.651570
$604$	−6.00000	−0.244137
$605$	21.0000	0.853771
$606$	11.0000	0.446844
$607$	13.0000	0.527654	0.263827	−	0.964570i	$-0.415015\pi$
$607$	13.0000	0.527654	0.263827	+	0.964570i	$0.415015\pi$
$608$	−20.0000	−0.811107
$609$	−6.00000	−0.243132
$610$	−12.0000	−0.485866
$611$	21.0000	0.849569
$612$	−12.0000	−0.485071
$613$	6.00000	0.242338	0.121169	−	0.992632i	$-0.461336\pi$
$613$	6.00000	0.242338	0.121169	+	0.992632i	$0.461336\pi$
$614$	−12.0000	−0.484281
$615$	−30.0000	−1.20972
$616$	6.00000	0.241747
$617$	37.0000	1.48956	0.744782	−	0.667308i	$-0.232553\pi$
$617$	37.0000	1.48956	0.744782	+	0.667308i	$0.232553\pi$
$618$	−9.00000	−0.362033
$619$	37.0000	1.48716	0.743578	−	0.668649i	$-0.233127\pi$
$619$	37.0000	1.48716	0.743578	+	0.668649i	$0.233127\pi$
$620$	−30.0000	−1.20483
$621$	10.0000	0.401286
$622$	−4.00000	−0.160385
$623$	7.00000	0.280449
$624$	3.00000	0.120096
$625$	−29.0000	−1.16000
$626$	26.0000	1.03917
$627$	8.00000	0.319489
$628$	18.0000	0.718278
$629$	12.0000	0.478471
$630$	6.00000	0.239046
$631$	−7.00000	−0.278666	−0.139333	−	0.990246i	$-0.544496\pi$
$631$	−7.00000	−0.278666	−0.139333	+	0.990246i	$0.544496\pi$
$632$	−3.00000	−0.119334
$633$	12.0000	0.476957
$634$	−31.0000	−1.23117
$635$	33.0000	1.30957
$636$	8.00000	0.317221
$637$	−18.0000	−0.713186
$638$	−12.0000	−0.475085
$639$	−30.0000	−1.18678
$640$	−9.00000	−0.355756
$641$	−9.00000	−0.355479	−0.177739	−	0.984078i	$-0.556878\pi$
$641$	−9.00000	−0.355479	−0.177739	+	0.984078i	$0.556878\pi$
$642$	−11.0000	−0.434135
$643$	16.0000	0.630978	0.315489	−	0.948929i	$-0.397831\pi$
$643$	16.0000	0.630978	0.315489	+	0.948929i	$0.397831\pi$
$644$	2.00000	0.0788110
$645$	12.0000	0.472500
$646$	24.0000	0.944267
$647$	−32.0000	−1.25805	−0.629025	−	0.777385i	$-0.716546\pi$
$647$	−32.0000	−1.25805	−0.629025	+	0.777385i	$0.716546\pi$
$648$	3.00000	0.117851
$649$	6.00000	0.235521
$650$	−12.0000	−0.470679
$651$	−10.0000	−0.391931
$652$	−4.00000	−0.156652
$653$	−7.00000	−0.273931	−0.136966	−	0.990576i	$-0.543735\pi$
$653$	−7.00000	−0.273931	−0.136966	+	0.990576i	$0.543735\pi$
$654$	10.0000	0.391031
$655$	−18.0000	−0.703318
$656$	10.0000	0.390434
$657$	−4.00000	−0.156055
$658$	7.00000	0.272888
$659$	15.0000	0.584317	0.292159	−	0.956370i	$-0.405627\pi$
$659$	15.0000	0.584317	0.292159	+	0.956370i	$0.405627\pi$
$660$	6.00000	0.233550
$661$	14.0000	0.544537	0.272268	−	0.962221i	$-0.412226\pi$
$661$	14.0000	0.544537	0.272268	+	0.962221i	$0.412226\pi$
$662$	−20.0000	−0.777322
$663$	18.0000	0.699062
$664$	−18.0000	−0.698535
$665$	12.0000	0.465340
$666$	−4.00000	−0.154997
$667$	−12.0000	−0.464642
$668$	−18.0000	−0.696441
$669$	26.0000	1.00522
$670$	24.0000	0.927201
$671$	8.00000	0.308837
$672$	−5.00000	−0.192879
$673$	−30.0000	−1.15642	−0.578208	−	0.815890i	$-0.696248\pi$
$673$	−30.0000	−1.15642	−0.578208	+	0.815890i	$0.696248\pi$
$674$	−31.0000	−1.19408
$675$	20.0000	0.769800
$676$	4.00000	0.153846
$677$	−15.0000	−0.576497	−0.288248	−	0.957556i	$-0.593073\pi$
$677$	−15.0000	−0.576497	−0.288248	+	0.957556i	$0.593073\pi$
$678$	0	0
$679$	19.0000	0.729153
$680$	54.0000	2.07081
$681$	8.00000	0.306561
$682$	−20.0000	−0.765840
$683$	24.0000	0.918334	0.459167	−	0.888350i	$-0.348148\pi$
$683$	24.0000	0.918334	0.459167	+	0.888350i	$0.348148\pi$
$684$	8.00000	0.305888
$685$	−36.0000	−1.37549
$686$	−13.0000	−0.496342
$687$	−16.0000	−0.610438
$688$	−4.00000	−0.152499
$689$	24.0000	0.914327
$690$	−6.00000	−0.228416
$691$	−23.0000	−0.874961	−0.437481	−	0.899228i	$-0.644129\pi$
$691$	−23.0000	−0.874961	−0.437481	+	0.899228i	$0.644129\pi$
$692$	8.00000	0.304114
$693$	−4.00000	−0.151947
$694$	14.0000	0.531433
$695$	63.0000	2.38973
$696$	18.0000	0.682288
$697$	60.0000	2.27266
$698$	−12.0000	−0.454207
$699$	18.0000	0.680823
$700$	4.00000	0.151186
$701$	2.00000	0.0755390	0.0377695	−	0.999286i	$-0.487975\pi$
$701$	2.00000	0.0755390	0.0377695	+	0.999286i	$0.487975\pi$
$702$	−15.0000	−0.566139
$703$	−8.00000	−0.301726
$704$	−14.0000	−0.527645
$705$	21.0000	0.790906
$706$	4.00000	0.150542
$707$	−11.0000	−0.413698
$708$	−3.00000	−0.112747
$709$	38.0000	1.42712	0.713560	−	0.700594i	$-0.247082\pi$
$709$	38.0000	1.42712	0.713560	+	0.700594i	$0.247082\pi$
$710$	45.0000	1.68882
$711$	2.00000	0.0750059
$712$	−21.0000	−0.787008
$713$	−20.0000	−0.749006
$714$	6.00000	0.224544
$715$	18.0000	0.673162
$716$	16.0000	0.597948
$717$	−12.0000	−0.448148
$718$	35.0000	1.30619
$719$	6.00000	0.223762	0.111881	−	0.993722i	$-0.464312\pi$
$719$	6.00000	0.223762	0.111881	+	0.993722i	$0.464312\pi$
$720$	−6.00000	−0.223607
$721$	9.00000	0.335178
$722$	3.00000	0.111648
$723$	15.0000	0.557856
$724$	−22.0000	−0.817624
$725$	−24.0000	−0.891338
$726$	−7.00000	−0.259794
$727$	30.0000	1.11264	0.556319	−	0.830969i	$-0.312213\pi$
$727$	30.0000	1.11264	0.556319	+	0.830969i	$0.312213\pi$
$728$	−9.00000	−0.333562
$729$	13.0000	0.481481
$730$	6.00000	0.222070
$731$	−24.0000	−0.887672
$732$	−4.00000	−0.147844
$733$	34.0000	1.25582	0.627909	−	0.778287i	$-0.283911\pi$
$733$	34.0000	1.25582	0.627909	+	0.778287i	$0.283911\pi$
$734$	2.00000	0.0738213
$735$	−18.0000	−0.663940
$736$	−10.0000	−0.368605
$737$	−16.0000	−0.589368
$738$	−20.0000	−0.736210
$739$	−13.0000	−0.478213	−0.239106	−	0.970993i	$-0.576854\pi$
$739$	−13.0000	−0.478213	−0.239106	+	0.970993i	$0.576854\pi$
$740$	−6.00000	−0.220564
$741$	−12.0000	−0.440831
$742$	8.00000	0.293689
$743$	20.0000	0.733729	0.366864	−	0.930274i	$-0.380431\pi$
$743$	20.0000	0.733729	0.366864	+	0.930274i	$0.380431\pi$
$744$	30.0000	1.09985
$745$	18.0000	0.659469
$746$	2.00000	0.0732252
$747$	12.0000	0.439057
$748$	−12.0000	−0.438763
$749$	11.0000	0.401931
$750$	3.00000	0.109545
$751$	10.0000	0.364905	0.182453	−	0.983215i	$-0.441596\pi$
$751$	10.0000	0.364905	0.182453	+	0.983215i	$0.441596\pi$
$752$	−7.00000	−0.255264
$753$	5.00000	0.182210
$754$	18.0000	0.655521
$755$	−18.0000	−0.655087
$756$	5.00000	0.181848
$757$	−9.00000	−0.327111	−0.163555	−	0.986534i	$-0.552296\pi$
$757$	−9.00000	−0.327111	−0.163555	+	0.986534i	$0.552296\pi$
$758$	23.0000	0.835398
$759$	4.00000	0.145191
$760$	−36.0000	−1.30586
$761$	−10.0000	−0.362500	−0.181250	−	0.983437i	$-0.558014\pi$
$761$	−10.0000	−0.362500	−0.181250	+	0.983437i	$0.558014\pi$
$762$	−11.0000	−0.398488
$763$	−10.0000	−0.362024
$764$	15.0000	0.542681
$765$	−36.0000	−1.30158
$766$	−2.00000	−0.0722629
$767$	−9.00000	−0.324971
$768$	17.0000	0.613435
$769$	−36.0000	−1.29819	−0.649097	−	0.760706i	$-0.724853\pi$
$769$	−36.0000	−1.29819	−0.649097	+	0.760706i	$0.724853\pi$
$770$	6.00000	0.216225
$771$	2.00000	0.0720282
$772$	−14.0000	−0.503871
$773$	−6.00000	−0.215805	−0.107903	−	0.994161i	$-0.534413\pi$
$773$	−6.00000	−0.215805	−0.107903	+	0.994161i	$0.534413\pi$
$774$	8.00000	0.287554
$775$	−40.0000	−1.43684
$776$	−57.0000	−2.04618
$777$	−2.00000	−0.0717496
$778$	9.00000	0.322666
$779$	−40.0000	−1.43315
$780$	−9.00000	−0.322252
$781$	−30.0000	−1.07348
$782$	12.0000	0.429119
$783$	−30.0000	−1.07211
$784$	6.00000	0.214286
$785$	54.0000	1.92734
$786$	6.00000	0.214013
$787$	−26.0000	−0.926800	−0.463400	−	0.886149i	$-0.653371\pi$
$787$	−26.0000	−0.926800	−0.463400	+	0.886149i	$0.653371\pi$
$788$	6.00000	0.213741
$789$	−26.0000	−0.925625
$790$	−3.00000	−0.106735
$791$	0	0
$792$	12.0000	0.426401
$793$	−12.0000	−0.426132
$794$	1.00000	0.0354887
$795$	24.0000	0.851192
$796$	−11.0000	−0.389885
$797$	−10.0000	−0.354218	−0.177109	−	0.984191i	$-0.556675\pi$
$797$	−10.0000	−0.354218	−0.177109	+	0.984191i	$0.556675\pi$
$798$	−4.00000	−0.141598
$799$	−42.0000	−1.48585
$800$	−20.0000	−0.707107
$801$	14.0000	0.494666
$802$	−10.0000	−0.353112
$803$	−4.00000	−0.141157
$804$	8.00000	0.282138
$805$	6.00000	0.211472
$806$	30.0000	1.05670
$807$	19.0000	0.668832
$808$	33.0000	1.16094
$809$	−9.00000	−0.316423	−0.158212	−	0.987405i	$-0.550573\pi$
$809$	−9.00000	−0.316423	−0.158212	+	0.987405i	$0.550573\pi$
$810$	3.00000	0.105409
$811$	50.0000	1.75574	0.877869	−	0.478901i	$-0.158965\pi$
$811$	50.0000	1.75574	0.877869	+	0.478901i	$0.158965\pi$
$812$	−6.00000	−0.210559
$813$	0	0
$814$	−4.00000	−0.140200
$815$	−12.0000	−0.420342
$816$	−6.00000	−0.210042
$817$	16.0000	0.559769
$818$	0	0
$819$	6.00000	0.209657
$820$	−30.0000	−1.04765
$821$	2.00000	0.0698005	0.0349002	−	0.999391i	$-0.488889\pi$
$821$	2.00000	0.0698005	0.0349002	+	0.999391i	$0.488889\pi$
$822$	12.0000	0.418548
$823$	−48.0000	−1.67317	−0.836587	−	0.547833i	$-0.815453\pi$
$823$	−48.0000	−1.67317	−0.836587	+	0.547833i	$0.815453\pi$
$824$	−27.0000	−0.940590
$825$	8.00000	0.278524
$826$	−3.00000	−0.104383
$827$	−1.00000	−0.0347734	−0.0173867	−	0.999849i	$-0.505535\pi$
$827$	−1.00000	−0.0347734	−0.0173867	+	0.999849i	$0.505535\pi$
$828$	4.00000	0.139010
$829$	−4.00000	−0.138926	−0.0694629	−	0.997585i	$-0.522129\pi$
$829$	−4.00000	−0.138926	−0.0694629	+	0.997585i	$0.522129\pi$
$830$	−18.0000	−0.624789
$831$	−11.0000	−0.381586
$832$	21.0000	0.728044
$833$	36.0000	1.24733
$834$	−21.0000	−0.727171
$835$	−54.0000	−1.86875
$836$	8.00000	0.276686
$837$	−50.0000	−1.72825
$838$	−9.00000	−0.310900
$839$	12.0000	0.414286	0.207143	−	0.978311i	$-0.433583\pi$
$839$	12.0000	0.414286	0.207143	+	0.978311i	$0.433583\pi$
$840$	−9.00000	−0.310530
$841$	7.00000	0.241379
$842$	13.0000	0.448010
$843$	−23.0000	−0.792162
$844$	12.0000	0.413057
$845$	12.0000	0.412813
$846$	14.0000	0.481330
$847$	7.00000	0.240523
$848$	−8.00000	−0.274721
$849$	−24.0000	−0.823678
$850$	24.0000	0.823193
$851$	−4.00000	−0.137118
$852$	15.0000	0.513892
$853$	−4.00000	−0.136957	−0.0684787	−	0.997653i	$-0.521815\pi$
$853$	−4.00000	−0.136957	−0.0684787	+	0.997653i	$0.521815\pi$
$854$	−4.00000	−0.136877
$855$	24.0000	0.820783
$856$	−33.0000	−1.12792
$857$	41.0000	1.40053	0.700267	−	0.713881i	$-0.253064\pi$
$857$	41.0000	1.40053	0.700267	+	0.713881i	$0.253064\pi$
$858$	−6.00000	−0.204837
$859$	45.0000	1.53538	0.767690	−	0.640821i	$-0.221406\pi$
$859$	45.0000	1.53538	0.767690	+	0.640821i	$0.221406\pi$
$860$	12.0000	0.409197
$861$	−10.0000	−0.340799
$862$	−20.0000	−0.681203
$863$	14.0000	0.476566	0.238283	−	0.971196i	$-0.423415\pi$
$863$	14.0000	0.476566	0.238283	+	0.971196i	$0.423415\pi$
$864$	−25.0000	−0.850517
$865$	24.0000	0.816024
$866$	3.00000	0.101944
$867$	−19.0000	−0.645274
$868$	−10.0000	−0.339422
$869$	2.00000	0.0678454
$870$	18.0000	0.610257
$871$	24.0000	0.813209
$872$	30.0000	1.01593
$873$	38.0000	1.28611
$874$	−8.00000	−0.270604
$875$	−3.00000	−0.101419
$876$	2.00000	0.0675737
$877$	−30.0000	−1.01303	−0.506514	−	0.862232i	$-0.669066\pi$
$877$	−30.0000	−1.01303	−0.506514	+	0.862232i	$0.669066\pi$
$878$	20.0000	0.674967
$879$	12.0000	0.404750
$880$	−6.00000	−0.202260
$881$	−32.0000	−1.07811	−0.539054	−	0.842271i	$-0.681218\pi$
$881$	−32.0000	−1.07811	−0.539054	+	0.842271i	$0.681218\pi$
$882$	−12.0000	−0.404061
$883$	−49.0000	−1.64898	−0.824491	−	0.565876i	$-0.808538\pi$
$883$	−49.0000	−1.64898	−0.824491	+	0.565876i	$0.808538\pi$
$884$	18.0000	0.605406
$885$	−9.00000	−0.302532
$886$	4.00000	0.134383
$887$	38.0000	1.27592	0.637958	−	0.770072i	$-0.279780\pi$
$887$	38.0000	1.27592	0.637958	+	0.770072i	$0.279780\pi$
$888$	6.00000	0.201347
$889$	11.0000	0.368928
$890$	−21.0000	−0.703922
$891$	−2.00000	−0.0670025
$892$	26.0000	0.870544
$893$	28.0000	0.936984
$894$	−6.00000	−0.200670
$895$	48.0000	1.60446
$896$	−3.00000	−0.100223
$897$	−6.00000	−0.200334
$898$	22.0000	0.734150
$899$	60.0000	2.00111
$900$	8.00000	0.266667
$901$	−48.0000	−1.59911
$902$	−20.0000	−0.665927
$903$	4.00000	0.133112
$904$	0	0
$905$	−66.0000	−2.19391
$906$	6.00000	0.199337
$907$	−32.0000	−1.06254	−0.531271	−	0.847202i	$-0.678286\pi$
$907$	−32.0000	−1.06254	−0.531271	+	0.847202i	$0.678286\pi$
$908$	8.00000	0.265489
$909$	−22.0000	−0.729694
$910$	−9.00000	−0.298347
$911$	−48.0000	−1.59031	−0.795155	−	0.606406i	$-0.792611\pi$
$911$	−48.0000	−1.59031	−0.795155	+	0.606406i	$0.792611\pi$
$912$	4.00000	0.132453
$913$	12.0000	0.397142
$914$	−7.00000	−0.231539
$915$	−12.0000	−0.396708
$916$	−16.0000	−0.528655
$917$	−6.00000	−0.198137
$918$	30.0000	0.990148
$919$	56.0000	1.84727	0.923635	−	0.383274i	$-0.125203\pi$
$919$	56.0000	1.84727	0.923635	+	0.383274i	$0.125203\pi$
$920$	−18.0000	−0.593442
$921$	−12.0000	−0.395413
$922$	10.0000	0.329332
$923$	45.0000	1.48119
$924$	2.00000	0.0657952
$925$	−8.00000	−0.263038
$926$	19.0000	0.624379
$927$	18.0000	0.591198
$928$	30.0000	0.984798
$929$	12.0000	0.393707	0.196854	−	0.980433i	$-0.436928\pi$
$929$	12.0000	0.393707	0.196854	+	0.980433i	$0.436928\pi$
$930$	30.0000	0.983739
$931$	−24.0000	−0.786568
$932$	18.0000	0.589610
$933$	−4.00000	−0.130954
$934$	−6.00000	−0.196326
$935$	−36.0000	−1.17733
$936$	−18.0000	−0.588348
$937$	28.0000	0.914720	0.457360	−	0.889282i	$-0.348795\pi$
$937$	28.0000	0.914720	0.457360	+	0.889282i	$0.348795\pi$
$938$	8.00000	0.261209
$939$	26.0000	0.848478
$940$	21.0000	0.684944
$941$	−6.00000	−0.195594	−0.0977972	−	0.995206i	$-0.531180\pi$
$941$	−6.00000	−0.195594	−0.0977972	+	0.995206i	$0.531180\pi$
$942$	−18.0000	−0.586472
$943$	−20.0000	−0.651290
$944$	3.00000	0.0976417
$945$	15.0000	0.487950
$946$	8.00000	0.260102
$947$	0	0		−	1.00000i	$-0.5\pi$
$947$	0	0			1.00000i	$0.5\pi$
$948$	−1.00000	−0.0324785
$949$	6.00000	0.194768
$950$	−16.0000	−0.519109
$951$	−31.0000	−1.00524
$952$	18.0000	0.583383
$953$	9.00000	0.291539	0.145769	−	0.989319i	$-0.453434\pi$
$953$	9.00000	0.291539	0.145769	+	0.989319i	$0.453434\pi$
$954$	16.0000	0.518019
$955$	45.0000	1.45617
$956$	−12.0000	−0.388108
$957$	−12.0000	−0.387905
$958$	0	0
$959$	−12.0000	−0.387500
$960$	21.0000	0.677772
$961$	69.0000	2.22581
$962$	6.00000	0.193448
$963$	22.0000	0.708940
$964$	15.0000	0.483117
$965$	−42.0000	−1.35203
$966$	−2.00000	−0.0643489
$967$	−32.0000	−1.02905	−0.514525	−	0.857475i	$-0.672032\pi$
$967$	−32.0000	−1.02905	−0.514525	+	0.857475i	$0.672032\pi$
$968$	−21.0000	−0.674966
$969$	24.0000	0.770991
$970$	−57.0000	−1.83016
$971$	−18.0000	−0.577647	−0.288824	−	0.957382i	$-0.593264\pi$
$971$	−18.0000	−0.577647	−0.288824	+	0.957382i	$0.593264\pi$
$972$	16.0000	0.513200
$973$	21.0000	0.673229
$974$	−18.0000	−0.576757
$975$	−12.0000	−0.384308
$976$	4.00000	0.128037
$977$	−6.00000	−0.191957	−0.0959785	−	0.995383i	$-0.530598\pi$
$977$	−6.00000	−0.191957	−0.0959785	+	0.995383i	$0.530598\pi$
$978$	4.00000	0.127906
$979$	14.0000	0.447442
$980$	−18.0000	−0.574989
$981$	−20.0000	−0.638551
$982$	−13.0000	−0.414847
$983$	−40.0000	−1.27580	−0.637901	−	0.770118i	$-0.720197\pi$
$983$	−40.0000	−1.27580	−0.637901	+	0.770118i	$0.720197\pi$
$984$	30.0000	0.956365
$985$	18.0000	0.573528
$986$	−36.0000	−1.14647
$987$	7.00000	0.222812
$988$	−12.0000	−0.381771
$989$	8.00000	0.254385
$990$	12.0000	0.381385
$991$	−57.0000	−1.81066	−0.905332	−	0.424704i	$-0.860378\pi$
$991$	−57.0000	−1.81066	−0.905332	+	0.424704i	$0.860378\pi$
$992$	50.0000	1.58750
$993$	−20.0000	−0.634681
$994$	15.0000	0.475771
$995$	−33.0000	−1.04617
$996$	−6.00000	−0.190117
$997$	2.00000	0.0633406	0.0316703	−	0.999498i	$-0.489917\pi$
$997$	2.00000	0.0633406	0.0316703	+	0.999498i	$0.489917\pi$
$998$	−10.0000	−0.316544
$999$	−10.0000	−0.316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	79.2.a.a.1.1	✓	1
3.2	odd	2		711.2.a.c.1.1		1
4.3	odd	2		1264.2.a.d.1.1		1
5.4	even	2		1975.2.a.e.1.1		1
7.6	odd	2		3871.2.a.a.1.1		1
8.3	odd	2		5056.2.a.j.1.1		1
8.5	even	2		5056.2.a.r.1.1		1
11.10	odd	2		9559.2.a.d.1.1		1
79.78	odd	2		6241.2.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
79.2.a.a.1.1	✓	1	1.1	even	1	trivial
711.2.a.c.1.1		1	3.2	odd	2
1264.2.a.d.1.1		1	4.3	odd	2
1975.2.a.e.1.1		1	5.4	even	2
3871.2.a.a.1.1		1	7.6	odd	2
5056.2.a.j.1.1		1	8.3	odd	2
5056.2.a.r.1.1		1	8.5	even	2
6241.2.a.a.1.1		1	79.78	odd	2
9559.2.a.d.1.1		1	11.10	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:	\( N \)	\(=\)	\( 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	79.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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