LMFDB - Embedded newform 3542.2.a.o.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3542,2,Mod(1,3542)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3542, 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("3542.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3542 = 2 \cdot 7 \cdot 11 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3542.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:	$28.2830123959$
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	$\chi$	$=$	3542.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.00000 q^{9} +1.00000 q^{10} +1.00000 q^{11} -1.00000 q^{12} -1.00000 q^{13} +1.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} -2.00000 q^{17} -2.00000 q^{18} -5.00000 q^{19} +1.00000 q^{20} -1.00000 q^{21} +1.00000 q^{22} +1.00000 q^{23} -1.00000 q^{24} -4.00000 q^{25} -1.00000 q^{26} +5.00000 q^{27} +1.00000 q^{28} -10.0000 q^{29} -1.00000 q^{30} -8.00000 q^{31} +1.00000 q^{32} -1.00000 q^{33} -2.00000 q^{34} +1.00000 q^{35} -2.00000 q^{36} -2.00000 q^{37} -5.00000 q^{38} +1.00000 q^{39} +1.00000 q^{40} +7.00000 q^{41} -1.00000 q^{42} -6.00000 q^{43} +1.00000 q^{44} -2.00000 q^{45} +1.00000 q^{46} +3.00000 q^{47} -1.00000 q^{48} +1.00000 q^{49} -4.00000 q^{50} +2.00000 q^{51} -1.00000 q^{52} -6.00000 q^{53} +5.00000 q^{54} +1.00000 q^{55} +1.00000 q^{56} +5.00000 q^{57} -10.0000 q^{58} -1.00000 q^{60} +12.0000 q^{61} -8.00000 q^{62} -2.00000 q^{63} +1.00000 q^{64} -1.00000 q^{65} -1.00000 q^{66} +13.0000 q^{67} -2.00000 q^{68} -1.00000 q^{69} +1.00000 q^{70} -8.00000 q^{71} -2.00000 q^{72} -1.00000 q^{73} -2.00000 q^{74} +4.00000 q^{75} -5.00000 q^{76} +1.00000 q^{77} +1.00000 q^{78} +1.00000 q^{80} +1.00000 q^{81} +7.00000 q^{82} -11.0000 q^{83} -1.00000 q^{84} -2.00000 q^{85} -6.00000 q^{86} +10.0000 q^{87} +1.00000 q^{88} -15.0000 q^{89} -2.00000 q^{90} -1.00000 q^{91} +1.00000 q^{92} +8.00000 q^{93} +3.00000 q^{94} -5.00000 q^{95} -1.00000 q^{96} -7.00000 q^{97} +1.00000 q^{98} -2.00000 q^{99} +O(q^{100})\)

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
$2$	1.00000	0.707107
$3$	−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
$5$	1.00000	0.447214	0.223607	−	0.974679i	$-0.428217\pi$
$5$	1.00000	0.447214	0.223607	+	0.974679i	$0.428217\pi$
$6$	−1.00000	−0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	−2.00000	−0.666667
$10$	1.00000	0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.00000	−0.288675
$13$	−1.00000	−0.277350	−0.138675	−	0.990338i	$-0.544284\pi$
$13$	−1.00000	−0.277350	−0.138675	+	0.990338i	$0.544284\pi$
$14$	1.00000	0.267261
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	−2.00000	−0.485071	−0.242536	−	0.970143i	$-0.577979\pi$
$17$	−2.00000	−0.485071	−0.242536	+	0.970143i	$0.577979\pi$
$18$	−2.00000	−0.471405
$19$	−5.00000	−1.14708	−0.573539	−	0.819178i	$-0.694430\pi$
$19$	−5.00000	−1.14708	−0.573539	+	0.819178i	$0.694430\pi$
$20$	1.00000	0.223607
$21$	−1.00000	−0.218218
$22$	1.00000	0.213201
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−1.00000	−0.204124
$25$	−4.00000	−0.800000
$26$	−1.00000	−0.196116
$27$	5.00000	0.962250
$28$	1.00000	0.188982
$29$	−10.0000	−1.85695	−0.928477	−	0.371391i	$-0.878881\pi$
$29$	−10.0000	−1.85695	−0.928477	+	0.371391i	$0.878881\pi$
$30$	−1.00000	−0.182574
$31$	−8.00000	−1.43684	−0.718421	−	0.695608i	$-0.755135\pi$
$31$	−8.00000	−1.43684	−0.718421	+	0.695608i	$0.755135\pi$
$32$	1.00000	0.176777
$33$	−1.00000	−0.174078
$34$	−2.00000	−0.342997
$35$	1.00000	0.169031
$36$	−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	$0.552568\pi$
$38$	−5.00000	−0.811107
$39$	1.00000	0.160128
$40$	1.00000	0.158114
$41$	7.00000	1.09322	0.546608	−	0.837389i	$-0.315919\pi$
$41$	7.00000	1.09322	0.546608	+	0.837389i	$0.315919\pi$
$42$	−1.00000	−0.154303
$43$	−6.00000	−0.914991	−0.457496	−	0.889212i	$-0.651253\pi$
$43$	−6.00000	−0.914991	−0.457496	+	0.889212i	$0.651253\pi$
$44$	1.00000	0.150756
$45$	−2.00000	−0.298142
$46$	1.00000	0.147442
$47$	3.00000	0.437595	0.218797	−	0.975770i	$-0.429787\pi$
$47$	3.00000	0.437595	0.218797	+	0.975770i	$0.429787\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	−4.00000	−0.565685
$51$	2.00000	0.280056
$52$	−1.00000	−0.138675
$53$	−6.00000	−0.824163	−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000	−0.824163	−0.412082	+	0.911147i	$0.635198\pi$
$54$	5.00000	0.680414
$55$	1.00000	0.134840
$56$	1.00000	0.133631
$57$	5.00000	0.662266
$58$	−10.0000	−1.31306
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	−1.00000	−0.129099
$61$	12.0000	1.53644	0.768221	−	0.640184i	$-0.221142\pi$
$61$	12.0000	1.53644	0.768221	+	0.640184i	$0.221142\pi$
$62$	−8.00000	−1.01600
$63$	−2.00000	−0.251976
$64$	1.00000	0.125000
$65$	−1.00000	−0.124035
$66$	−1.00000	−0.123091
$67$	13.0000	1.58820	0.794101	−	0.607785i	$-0.207942\pi$
$67$	13.0000	1.58820	0.794101	+	0.607785i	$0.207942\pi$
$68$	−2.00000	−0.242536
$69$	−1.00000	−0.120386
$70$	1.00000	0.119523
$71$	−8.00000	−0.949425	−0.474713	−	0.880141i	$-0.657448\pi$
$71$	−8.00000	−0.949425	−0.474713	+	0.880141i	$0.657448\pi$
$72$	−2.00000	−0.235702
$73$	−1.00000	−0.117041	−0.0585206	−	0.998286i	$-0.518638\pi$
$73$	−1.00000	−0.117041	−0.0585206	+	0.998286i	$0.518638\pi$
$74$	−2.00000	−0.232495
$75$	4.00000	0.461880
$76$	−5.00000	−0.573539
$77$	1.00000	0.113961
$78$	1.00000	0.113228
$79$	0	0		−	1.00000i	$-0.5\pi$
$79$	0	0			1.00000i	$0.5\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	7.00000	0.773021
$83$	−11.0000	−1.20741	−0.603703	−	0.797209i	$-0.706309\pi$
$83$	−11.0000	−1.20741	−0.603703	+	0.797209i	$0.706309\pi$
$84$	−1.00000	−0.109109
$85$	−2.00000	−0.216930
$86$	−6.00000	−0.646997
$87$	10.0000	1.07211
$88$	1.00000	0.106600
$89$	−15.0000	−1.59000	−0.794998	−	0.606612i	$-0.792528\pi$
$89$	−15.0000	−1.59000	−0.794998	+	0.606612i	$0.792528\pi$
$90$	−2.00000	−0.210819
$91$	−1.00000	−0.104828
$92$	1.00000	0.104257
$93$	8.00000	0.829561
$94$	3.00000	0.309426
$95$	−5.00000	−0.512989
$96$	−1.00000	−0.102062
$97$	−7.00000	−0.710742	−0.355371	−	0.934725i	$-0.615646\pi$
$97$	−7.00000	−0.710742	−0.355371	+	0.934725i	$0.615646\pi$
$98$	1.00000	0.101015
$99$	−2.00000	−0.201008
$100$	−4.00000	−0.400000
$101$	2.00000	0.199007	0.0995037	−	0.995037i	$-0.468274\pi$
$101$	2.00000	0.199007	0.0995037	+	0.995037i	$0.468274\pi$
$102$	2.00000	0.198030
$103$	4.00000	0.394132	0.197066	−	0.980390i	$-0.436859\pi$
$103$	4.00000	0.394132	0.197066	+	0.980390i	$0.436859\pi$
$104$	−1.00000	−0.0980581
$105$	−1.00000	−0.0975900
$106$	−6.00000	−0.582772
$107$	−12.0000	−1.16008	−0.580042	−	0.814587i	$-0.696964\pi$
$107$	−12.0000	−1.16008	−0.580042	+	0.814587i	$0.696964\pi$
$108$	5.00000	0.481125
$109$	−5.00000	−0.478913	−0.239457	−	0.970907i	$-0.576969\pi$
$109$	−5.00000	−0.478913	−0.239457	+	0.970907i	$0.576969\pi$
$110$	1.00000	0.0953463
$111$	2.00000	0.189832
$112$	1.00000	0.0944911
$113$	4.00000	0.376288	0.188144	−	0.982141i	$-0.439753\pi$
$113$	4.00000	0.376288	0.188144	+	0.982141i	$0.439753\pi$
$114$	5.00000	0.468293
$115$	1.00000	0.0932505
$116$	−10.0000	−0.928477
$117$	2.00000	0.184900
$118$	0	0
$119$	−2.00000	−0.183340
$120$	−1.00000	−0.0912871
$121$	1.00000	0.0909091
$122$	12.0000	1.08643
$123$	−7.00000	−0.631169
$124$	−8.00000	−0.718421
$125$	−9.00000	−0.804984
$126$	−2.00000	−0.178174
$127$	8.00000	0.709885	0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000	0.709885	0.354943	+	0.934888i	$0.384500\pi$
$128$	1.00000	0.0883883
$129$	6.00000	0.528271
$130$	−1.00000	−0.0877058
$131$	−8.00000	−0.698963	−0.349482	−	0.936943i	$-0.613642\pi$
$131$	−8.00000	−0.698963	−0.349482	+	0.936943i	$0.613642\pi$
$132$	−1.00000	−0.0870388
$133$	−5.00000	−0.433555
$134$	13.0000	1.12303
$135$	5.00000	0.430331
$136$	−2.00000	−0.171499
$137$	−12.0000	−1.02523	−0.512615	−	0.858619i	$-0.671323\pi$
$137$	−12.0000	−1.02523	−0.512615	+	0.858619i	$0.671323\pi$
$138$	−1.00000	−0.0851257
$139$	20.0000	1.69638	0.848189	−	0.529694i	$-0.177693\pi$
$139$	20.0000	1.69638	0.848189	+	0.529694i	$0.177693\pi$
$140$	1.00000	0.0845154
$141$	−3.00000	−0.252646
$142$	−8.00000	−0.671345
$143$	−1.00000	−0.0836242
$144$	−2.00000	−0.166667
$145$	−10.0000	−0.830455
$146$	−1.00000	−0.0827606
$147$	−1.00000	−0.0824786
$148$	−2.00000	−0.164399
$149$	5.00000	0.409616	0.204808	−	0.978802i	$-0.434343\pi$
$149$	5.00000	0.409616	0.204808	+	0.978802i	$0.434343\pi$
$150$	4.00000	0.326599
$151$	−23.0000	−1.87171	−0.935857	−	0.352381i	$-0.885372\pi$
$151$	−23.0000	−1.87171	−0.935857	+	0.352381i	$0.885372\pi$
$152$	−5.00000	−0.405554
$153$	4.00000	0.323381
$154$	1.00000	0.0805823
$155$	−8.00000	−0.642575
$156$	1.00000	0.0800641
$157$	18.0000	1.43656	0.718278	−	0.695756i	$-0.244931\pi$
$157$	18.0000	1.43656	0.718278	+	0.695756i	$0.244931\pi$
$158$	0	0
$159$	6.00000	0.475831
$160$	1.00000	0.0790569
$161$	1.00000	0.0788110
$162$	1.00000	0.0785674
$163$	−16.0000	−1.25322	−0.626608	−	0.779334i	$-0.715557\pi$
$163$	−16.0000	−1.25322	−0.626608	+	0.779334i	$0.715557\pi$
$164$	7.00000	0.546608
$165$	−1.00000	−0.0778499
$166$	−11.0000	−0.853766
$167$	18.0000	1.39288	0.696441	−	0.717614i	$-0.254766\pi$
$167$	18.0000	1.39288	0.696441	+	0.717614i	$0.254766\pi$
$168$	−1.00000	−0.0771517
$169$	−12.0000	−0.923077
$170$	−2.00000	−0.153393
$171$	10.0000	0.764719
$172$	−6.00000	−0.457496
$173$	9.00000	0.684257	0.342129	−	0.939653i	$-0.388852\pi$
$173$	9.00000	0.684257	0.342129	+	0.939653i	$0.388852\pi$
$174$	10.0000	0.758098
$175$	−4.00000	−0.302372
$176$	1.00000	0.0753778
$177$	0	0
$178$	−15.0000	−1.12430
$179$	0	0		−	1.00000i	$-0.5\pi$
$179$	0	0			1.00000i	$0.5\pi$
$180$	−2.00000	−0.149071
$181$	7.00000	0.520306	0.260153	−	0.965567i	$-0.416227\pi$
$181$	7.00000	0.520306	0.260153	+	0.965567i	$0.416227\pi$
$182$	−1.00000	−0.0741249
$183$	−12.0000	−0.887066
$184$	1.00000	0.0737210
$185$	−2.00000	−0.147043
$186$	8.00000	0.586588
$187$	−2.00000	−0.146254
$188$	3.00000	0.218797
$189$	5.00000	0.363696
$190$	−5.00000	−0.362738
$191$	7.00000	0.506502	0.253251	−	0.967401i	$-0.418500\pi$
$191$	7.00000	0.506502	0.253251	+	0.967401i	$0.418500\pi$
$192$	−1.00000	−0.0721688
$193$	4.00000	0.287926	0.143963	−	0.989583i	$-0.454015\pi$
$193$	4.00000	0.287926	0.143963	+	0.989583i	$0.454015\pi$
$194$	−7.00000	−0.502571
$195$	1.00000	0.0716115
$196$	1.00000	0.0714286
$197$	8.00000	0.569976	0.284988	−	0.958531i	$-0.408010\pi$
$197$	8.00000	0.569976	0.284988	+	0.958531i	$0.408010\pi$
$198$	−2.00000	−0.142134
$199$	−10.0000	−0.708881	−0.354441	−	0.935079i	$-0.615329\pi$
$199$	−10.0000	−0.708881	−0.354441	+	0.935079i	$0.615329\pi$
$200$	−4.00000	−0.282843
$201$	−13.0000	−0.916949
$202$	2.00000	0.140720
$203$	−10.0000	−0.701862
$204$	2.00000	0.140028
$205$	7.00000	0.488901
$206$	4.00000	0.278693
$207$	−2.00000	−0.139010
$208$	−1.00000	−0.0693375
$209$	−5.00000	−0.345857
$210$	−1.00000	−0.0690066
$211$	−3.00000	−0.206529	−0.103264	−	0.994654i	$-0.532929\pi$
$211$	−3.00000	−0.206529	−0.103264	+	0.994654i	$0.532929\pi$
$212$	−6.00000	−0.412082
$213$	8.00000	0.548151
$214$	−12.0000	−0.820303
$215$	−6.00000	−0.409197
$216$	5.00000	0.340207
$217$	−8.00000	−0.543075
$218$	−5.00000	−0.338643
$219$	1.00000	0.0675737
$220$	1.00000	0.0674200
$221$	2.00000	0.134535
$222$	2.00000	0.134231
$223$	−11.0000	−0.736614	−0.368307	−	0.929704i	$-0.620063\pi$
$223$	−11.0000	−0.736614	−0.368307	+	0.929704i	$0.620063\pi$
$224$	1.00000	0.0668153
$225$	8.00000	0.533333
$226$	4.00000	0.266076
$227$	3.00000	0.199117	0.0995585	−	0.995032i	$-0.468257\pi$
$227$	3.00000	0.199117	0.0995585	+	0.995032i	$0.468257\pi$
$228$	5.00000	0.331133
$229$	−5.00000	−0.330409	−0.165205	−	0.986259i	$-0.552828\pi$
$229$	−5.00000	−0.330409	−0.165205	+	0.986259i	$0.552828\pi$
$230$	1.00000	0.0659380
$231$	−1.00000	−0.0657952
$232$	−10.0000	−0.656532
$233$	24.0000	1.57229	0.786146	−	0.618041i	$-0.212073\pi$
$233$	24.0000	1.57229	0.786146	+	0.618041i	$0.212073\pi$
$234$	2.00000	0.130744
$235$	3.00000	0.195698
$236$	0	0
$237$	0	0
$238$	−2.00000	−0.129641
$239$	−15.0000	−0.970269	−0.485135	−	0.874439i	$-0.661229\pi$
$239$	−15.0000	−0.970269	−0.485135	+	0.874439i	$0.661229\pi$
$240$	−1.00000	−0.0645497
$241$	−18.0000	−1.15948	−0.579741	−	0.814801i	$-0.696846\pi$
$241$	−18.0000	−1.15948	−0.579741	+	0.814801i	$0.696846\pi$
$242$	1.00000	0.0642824
$243$	−16.0000	−1.02640
$244$	12.0000	0.768221
$245$	1.00000	0.0638877
$246$	−7.00000	−0.446304
$247$	5.00000	0.318142
$248$	−8.00000	−0.508001
$249$	11.0000	0.697097
$250$	−9.00000	−0.569210
$251$	−18.0000	−1.13615	−0.568075	−	0.822977i	$-0.692312\pi$
$251$	−18.0000	−1.13615	−0.568075	+	0.822977i	$0.692312\pi$
$252$	−2.00000	−0.125988
$253$	1.00000	0.0628695
$254$	8.00000	0.501965
$255$	2.00000	0.125245
$256$	1.00000	0.0625000
$257$	8.00000	0.499026	0.249513	−	0.968371i	$-0.419729\pi$
$257$	8.00000	0.499026	0.249513	+	0.968371i	$0.419729\pi$
$258$	6.00000	0.373544
$259$	−2.00000	−0.124274
$260$	−1.00000	−0.0620174
$261$	20.0000	1.23797
$262$	−8.00000	−0.494242
$263$	−26.0000	−1.60323	−0.801614	−	0.597841i	$-0.796025\pi$
$263$	−26.0000	−1.60323	−0.801614	+	0.597841i	$0.796025\pi$
$264$	−1.00000	−0.0615457
$265$	−6.00000	−0.368577
$266$	−5.00000	−0.306570
$267$	15.0000	0.917985
$268$	13.0000	0.794101
$269$	0	0		−	1.00000i	$-0.5\pi$
$269$	0	0			1.00000i	$0.5\pi$
$270$	5.00000	0.304290
$271$	12.0000	0.728948	0.364474	−	0.931214i	$-0.381249\pi$
$271$	12.0000	0.728948	0.364474	+	0.931214i	$0.381249\pi$
$272$	−2.00000	−0.121268
$273$	1.00000	0.0605228
$274$	−12.0000	−0.724947
$275$	−4.00000	−0.241209
$276$	−1.00000	−0.0601929
$277$	−32.0000	−1.92269	−0.961347	−	0.275340i	$-0.911209\pi$
$277$	−32.0000	−1.92269	−0.961347	+	0.275340i	$0.911209\pi$
$278$	20.0000	1.19952
$279$	16.0000	0.957895
$280$	1.00000	0.0597614
$281$	17.0000	1.01413	0.507067	−	0.861906i	$-0.330729\pi$
$281$	17.0000	1.01413	0.507067	+	0.861906i	$0.330729\pi$
$282$	−3.00000	−0.178647
$283$	9.00000	0.534994	0.267497	−	0.963559i	$-0.413803\pi$
$283$	9.00000	0.534994	0.267497	+	0.963559i	$0.413803\pi$
$284$	−8.00000	−0.474713
$285$	5.00000	0.296174
$286$	−1.00000	−0.0591312
$287$	7.00000	0.413197
$288$	−2.00000	−0.117851
$289$	−13.0000	−0.764706
$290$	−10.0000	−0.587220
$291$	7.00000	0.410347
$292$	−1.00000	−0.0585206
$293$	−26.0000	−1.51894	−0.759468	−	0.650545i	$-0.774541\pi$
$293$	−26.0000	−1.51894	−0.759468	+	0.650545i	$0.774541\pi$
$294$	−1.00000	−0.0583212
$295$	0	0
$296$	−2.00000	−0.116248
$297$	5.00000	0.290129
$298$	5.00000	0.289642
$299$	−1.00000	−0.0578315
$300$	4.00000	0.230940
$301$	−6.00000	−0.345834
$302$	−23.0000	−1.32350
$303$	−2.00000	−0.114897
$304$	−5.00000	−0.286770
$305$	12.0000	0.687118
$306$	4.00000	0.228665
$307$	−2.00000	−0.114146	−0.0570730	−	0.998370i	$-0.518177\pi$
$307$	−2.00000	−0.114146	−0.0570730	+	0.998370i	$0.518177\pi$
$308$	1.00000	0.0569803
$309$	−4.00000	−0.227552
$310$	−8.00000	−0.454369
$311$	7.00000	0.396934	0.198467	−	0.980108i	$-0.436404\pi$
$311$	7.00000	0.396934	0.198467	+	0.980108i	$0.436404\pi$
$312$	1.00000	0.0566139
$313$	29.0000	1.63918	0.819588	−	0.572953i	$-0.194202\pi$
$313$	29.0000	1.63918	0.819588	+	0.572953i	$0.194202\pi$
$314$	18.0000	1.01580
$315$	−2.00000	−0.112687
$316$	0	0
$317$	23.0000	1.29181	0.645904	−	0.763418i	$-0.276480\pi$
$317$	23.0000	1.29181	0.645904	+	0.763418i	$0.276480\pi$
$318$	6.00000	0.336463
$319$	−10.0000	−0.559893
$320$	1.00000	0.0559017
$321$	12.0000	0.669775
$322$	1.00000	0.0557278
$323$	10.0000	0.556415
$324$	1.00000	0.0555556
$325$	4.00000	0.221880
$326$	−16.0000	−0.886158
$327$	5.00000	0.276501
$328$	7.00000	0.386510
$329$	3.00000	0.165395
$330$	−1.00000	−0.0550482
$331$	−8.00000	−0.439720	−0.219860	−	0.975531i	$-0.570560\pi$
$331$	−8.00000	−0.439720	−0.219860	+	0.975531i	$0.570560\pi$
$332$	−11.0000	−0.603703
$333$	4.00000	0.219199
$334$	18.0000	0.984916
$335$	13.0000	0.710266
$336$	−1.00000	−0.0545545
$337$	3.00000	0.163420	0.0817102	−	0.996656i	$-0.473962\pi$
$337$	3.00000	0.163420	0.0817102	+	0.996656i	$0.473962\pi$
$338$	−12.0000	−0.652714
$339$	−4.00000	−0.217250
$340$	−2.00000	−0.108465
$341$	−8.00000	−0.433224
$342$	10.0000	0.540738
$343$	1.00000	0.0539949
$344$	−6.00000	−0.323498
$345$	−1.00000	−0.0538382
$346$	9.00000	0.483843
$347$	3.00000	0.161048	0.0805242	−	0.996753i	$-0.474341\pi$
$347$	3.00000	0.161048	0.0805242	+	0.996753i	$0.474341\pi$
$348$	10.0000	0.536056
$349$	10.0000	0.535288	0.267644	−	0.963518i	$-0.413755\pi$
$349$	10.0000	0.535288	0.267644	+	0.963518i	$0.413755\pi$
$350$	−4.00000	−0.213809
$351$	−5.00000	−0.266880
$352$	1.00000	0.0533002
$353$	4.00000	0.212899	0.106449	−	0.994318i	$-0.466052\pi$
$353$	4.00000	0.212899	0.106449	+	0.994318i	$0.466052\pi$
$354$	0	0
$355$	−8.00000	−0.424596
$356$	−15.0000	−0.794998
$357$	2.00000	0.105851
$358$	0	0
$359$	−30.0000	−1.58334	−0.791670	−	0.610949i	$-0.790788\pi$
$359$	−30.0000	−1.58334	−0.791670	+	0.610949i	$0.790788\pi$
$360$	−2.00000	−0.105409
$361$	6.00000	0.315789
$362$	7.00000	0.367912
$363$	−1.00000	−0.0524864
$364$	−1.00000	−0.0524142
$365$	−1.00000	−0.0523424
$366$	−12.0000	−0.627250
$367$	−2.00000	−0.104399	−0.0521996	−	0.998637i	$-0.516623\pi$
$367$	−2.00000	−0.104399	−0.0521996	+	0.998637i	$0.516623\pi$
$368$	1.00000	0.0521286
$369$	−14.0000	−0.728811
$370$	−2.00000	−0.103975
$371$	−6.00000	−0.311504
$372$	8.00000	0.414781
$373$	29.0000	1.50156	0.750782	−	0.660551i	$-0.229677\pi$
$373$	29.0000	1.50156	0.750782	+	0.660551i	$0.229677\pi$
$374$	−2.00000	−0.103418
$375$	9.00000	0.464758
$376$	3.00000	0.154713
$377$	10.0000	0.515026
$378$	5.00000	0.257172
$379$	−25.0000	−1.28416	−0.642082	−	0.766636i	$-0.721929\pi$
$379$	−25.0000	−1.28416	−0.642082	+	0.766636i	$0.721929\pi$
$380$	−5.00000	−0.256495
$381$	−8.00000	−0.409852
$382$	7.00000	0.358151
$383$	14.0000	0.715367	0.357683	−	0.933843i	$-0.383567\pi$
$383$	14.0000	0.715367	0.357683	+	0.933843i	$0.383567\pi$
$384$	−1.00000	−0.0510310
$385$	1.00000	0.0509647
$386$	4.00000	0.203595
$387$	12.0000	0.609994
$388$	−7.00000	−0.355371
$389$	20.0000	1.01404	0.507020	−	0.861934i	$-0.330747\pi$
$389$	20.0000	1.01404	0.507020	+	0.861934i	$0.330747\pi$
$390$	1.00000	0.0506370
$391$	−2.00000	−0.101144
$392$	1.00000	0.0505076
$393$	8.00000	0.403547
$394$	8.00000	0.403034
$395$	0	0
$396$	−2.00000	−0.100504
$397$	−32.0000	−1.60603	−0.803017	−	0.595956i	$-0.796773\pi$
$397$	−32.0000	−1.60603	−0.803017	+	0.595956i	$0.796773\pi$
$398$	−10.0000	−0.501255
$399$	5.00000	0.250313
$400$	−4.00000	−0.200000
$401$	22.0000	1.09863	0.549314	−	0.835616i	$-0.314889\pi$
$401$	22.0000	1.09863	0.549314	+	0.835616i	$0.314889\pi$
$402$	−13.0000	−0.648381
$403$	8.00000	0.398508
$404$	2.00000	0.0995037
$405$	1.00000	0.0496904
$406$	−10.0000	−0.496292
$407$	−2.00000	−0.0991363
$408$	2.00000	0.0990148
$409$	−5.00000	−0.247234	−0.123617	−	0.992330i	$-0.539449\pi$
$409$	−5.00000	−0.247234	−0.123617	+	0.992330i	$0.539449\pi$
$410$	7.00000	0.345705
$411$	12.0000	0.591916
$412$	4.00000	0.197066
$413$	0	0
$414$	−2.00000	−0.0982946
$415$	−11.0000	−0.539969
$416$	−1.00000	−0.0490290
$417$	−20.0000	−0.979404
$418$	−5.00000	−0.244558
$419$	−30.0000	−1.46560	−0.732798	−	0.680446i	$-0.761786\pi$
$419$	−30.0000	−1.46560	−0.732798	+	0.680446i	$0.761786\pi$
$420$	−1.00000	−0.0487950
$421$	−18.0000	−0.877266	−0.438633	−	0.898666i	$-0.644537\pi$
$421$	−18.0000	−0.877266	−0.438633	+	0.898666i	$0.644537\pi$
$422$	−3.00000	−0.146038
$423$	−6.00000	−0.291730
$424$	−6.00000	−0.291386
$425$	8.00000	0.388057
$426$	8.00000	0.387601
$427$	12.0000	0.580721
$428$	−12.0000	−0.580042
$429$	1.00000	0.0482805
$430$	−6.00000	−0.289346
$431$	−18.0000	−0.867029	−0.433515	−	0.901146i	$-0.642727\pi$
$431$	−18.0000	−0.867029	−0.433515	+	0.901146i	$0.642727\pi$
$432$	5.00000	0.240563
$433$	29.0000	1.39365	0.696826	−	0.717241i	$-0.254595\pi$
$433$	29.0000	1.39365	0.696826	+	0.717241i	$0.254595\pi$
$434$	−8.00000	−0.384012
$435$	10.0000	0.479463
$436$	−5.00000	−0.239457
$437$	−5.00000	−0.239182
$438$	1.00000	0.0477818
$439$	20.0000	0.954548	0.477274	−	0.878755i	$-0.341625\pi$
$439$	20.0000	0.954548	0.477274	+	0.878755i	$0.341625\pi$
$440$	1.00000	0.0476731
$441$	−2.00000	−0.0952381
$442$	2.00000	0.0951303
$443$	4.00000	0.190046	0.0950229	−	0.995475i	$-0.469708\pi$
$443$	4.00000	0.190046	0.0950229	+	0.995475i	$0.469708\pi$
$444$	2.00000	0.0949158
$445$	−15.0000	−0.711068
$446$	−11.0000	−0.520865
$447$	−5.00000	−0.236492
$448$	1.00000	0.0472456
$449$	15.0000	0.707894	0.353947	−	0.935266i	$-0.384839\pi$
$449$	15.0000	0.707894	0.353947	+	0.935266i	$0.384839\pi$
$450$	8.00000	0.377124
$451$	7.00000	0.329617
$452$	4.00000	0.188144
$453$	23.0000	1.08063
$454$	3.00000	0.140797
$455$	−1.00000	−0.0468807
$456$	5.00000	0.234146
$457$	−17.0000	−0.795226	−0.397613	−	0.917553i	$-0.630161\pi$
$457$	−17.0000	−0.795226	−0.397613	+	0.917553i	$0.630161\pi$
$458$	−5.00000	−0.233635
$459$	−10.0000	−0.466760
$460$	1.00000	0.0466252
$461$	2.00000	0.0931493	0.0465746	−	0.998915i	$-0.485169\pi$
$461$	2.00000	0.0931493	0.0465746	+	0.998915i	$0.485169\pi$
$462$	−1.00000	−0.0465242
$463$	−26.0000	−1.20832	−0.604161	−	0.796862i	$-0.706492\pi$
$463$	−26.0000	−1.20832	−0.604161	+	0.796862i	$0.706492\pi$
$464$	−10.0000	−0.464238
$465$	8.00000	0.370991
$466$	24.0000	1.11178
$467$	28.0000	1.29569	0.647843	−	0.761774i	$-0.275671\pi$
$467$	28.0000	1.29569	0.647843	+	0.761774i	$0.275671\pi$
$468$	2.00000	0.0924500
$469$	13.0000	0.600284
$470$	3.00000	0.138380
$471$	−18.0000	−0.829396
$472$	0	0
$473$	−6.00000	−0.275880
$474$	0	0
$475$	20.0000	0.917663
$476$	−2.00000	−0.0916698
$477$	12.0000	0.549442
$478$	−15.0000	−0.686084
$479$	−5.00000	−0.228456	−0.114228	−	0.993455i	$-0.536439\pi$
$479$	−5.00000	−0.228456	−0.114228	+	0.993455i	$0.536439\pi$
$480$	−1.00000	−0.0456435
$481$	2.00000	0.0911922
$482$	−18.0000	−0.819878
$483$	−1.00000	−0.0455016
$484$	1.00000	0.0454545
$485$	−7.00000	−0.317854
$486$	−16.0000	−0.725775
$487$	−12.0000	−0.543772	−0.271886	−	0.962329i	$-0.587647\pi$
$487$	−12.0000	−0.543772	−0.271886	+	0.962329i	$0.587647\pi$
$488$	12.0000	0.543214
$489$	16.0000	0.723545
$490$	1.00000	0.0451754
$491$	7.00000	0.315906	0.157953	−	0.987447i	$-0.449511\pi$
$491$	7.00000	0.315906	0.157953	+	0.987447i	$0.449511\pi$
$492$	−7.00000	−0.315584
$493$	20.0000	0.900755
$494$	5.00000	0.224961
$495$	−2.00000	−0.0898933
$496$	−8.00000	−0.359211
$497$	−8.00000	−0.358849
$498$	11.0000	0.492922
$499$	30.0000	1.34298	0.671492	−	0.741012i	$-0.265654\pi$
$499$	30.0000	1.34298	0.671492	+	0.741012i	$0.265654\pi$
$500$	−9.00000	−0.402492
$501$	−18.0000	−0.804181
$502$	−18.0000	−0.803379
$503$	−1.00000	−0.0445878	−0.0222939	−	0.999751i	$-0.507097\pi$
$503$	−1.00000	−0.0445878	−0.0222939	+	0.999751i	$0.507097\pi$
$504$	−2.00000	−0.0890871
$505$	2.00000	0.0889988
$506$	1.00000	0.0444554
$507$	12.0000	0.532939
$508$	8.00000	0.354943
$509$	20.0000	0.886484	0.443242	−	0.896402i	$-0.353828\pi$
$509$	20.0000	0.886484	0.443242	+	0.896402i	$0.353828\pi$
$510$	2.00000	0.0885615
$511$	−1.00000	−0.0442374
$512$	1.00000	0.0441942
$513$	−25.0000	−1.10378
$514$	8.00000	0.352865
$515$	4.00000	0.176261
$516$	6.00000	0.264135
$517$	3.00000	0.131940
$518$	−2.00000	−0.0878750
$519$	−9.00000	−0.395056
$520$	−1.00000	−0.0438529
$521$	42.0000	1.84005	0.920027	−	0.391856i	$-0.128167\pi$
$521$	42.0000	1.84005	0.920027	+	0.391856i	$0.128167\pi$
$522$	20.0000	0.875376
$523$	24.0000	1.04945	0.524723	−	0.851273i	$-0.324169\pi$
$523$	24.0000	1.04945	0.524723	+	0.851273i	$0.324169\pi$
$524$	−8.00000	−0.349482
$525$	4.00000	0.174574
$526$	−26.0000	−1.13365
$527$	16.0000	0.696971
$528$	−1.00000	−0.0435194
$529$	1.00000	0.0434783
$530$	−6.00000	−0.260623
$531$	0	0
$532$	−5.00000	−0.216777
$533$	−7.00000	−0.303204
$534$	15.0000	0.649113
$535$	−12.0000	−0.518805
$536$	13.0000	0.561514
$537$	0	0
$538$	0	0
$539$	1.00000	0.0430730
$540$	5.00000	0.215166
$541$	22.0000	0.945854	0.472927	−	0.881102i	$-0.343197\pi$
$541$	22.0000	0.945854	0.472927	+	0.881102i	$0.343197\pi$
$542$	12.0000	0.515444
$543$	−7.00000	−0.300399
$544$	−2.00000	−0.0857493
$545$	−5.00000	−0.214176
$546$	1.00000	0.0427960
$547$	28.0000	1.19719	0.598597	−	0.801050i	$-0.295725\pi$
$547$	28.0000	1.19719	0.598597	+	0.801050i	$0.295725\pi$
$548$	−12.0000	−0.512615
$549$	−24.0000	−1.02430
$550$	−4.00000	−0.170561
$551$	50.0000	2.13007
$552$	−1.00000	−0.0425628
$553$	0	0
$554$	−32.0000	−1.35955
$555$	2.00000	0.0848953
$556$	20.0000	0.848189
$557$	3.00000	0.127114	0.0635570	−	0.997978i	$-0.479756\pi$
$557$	3.00000	0.127114	0.0635570	+	0.997978i	$0.479756\pi$
$558$	16.0000	0.677334
$559$	6.00000	0.253773
$560$	1.00000	0.0422577
$561$	2.00000	0.0844401
$562$	17.0000	0.717102
$563$	24.0000	1.01148	0.505740	−	0.862686i	$-0.331220\pi$
$563$	24.0000	1.01148	0.505740	+	0.862686i	$0.331220\pi$
$564$	−3.00000	−0.126323
$565$	4.00000	0.168281
$566$	9.00000	0.378298
$567$	1.00000	0.0419961
$568$	−8.00000	−0.335673
$569$	45.0000	1.88650	0.943249	−	0.332086i	$-0.107752\pi$
$569$	45.0000	1.88650	0.943249	+	0.332086i	$0.107752\pi$
$570$	5.00000	0.209427
$571$	−28.0000	−1.17176	−0.585882	−	0.810397i	$-0.699252\pi$
$571$	−28.0000	−1.17176	−0.585882	+	0.810397i	$0.699252\pi$
$572$	−1.00000	−0.0418121
$573$	−7.00000	−0.292429
$574$	7.00000	0.292174
$575$	−4.00000	−0.166812
$576$	−2.00000	−0.0833333
$577$	18.0000	0.749350	0.374675	−	0.927156i	$-0.377754\pi$
$577$	18.0000	0.749350	0.374675	+	0.927156i	$0.377754\pi$
$578$	−13.0000	−0.540729
$579$	−4.00000	−0.166234
$580$	−10.0000	−0.415227
$581$	−11.0000	−0.456357
$582$	7.00000	0.290159
$583$	−6.00000	−0.248495
$584$	−1.00000	−0.0413803
$585$	2.00000	0.0826898
$586$	−26.0000	−1.07405
$587$	−12.0000	−0.495293	−0.247647	−	0.968850i	$-0.579657\pi$
$587$	−12.0000	−0.495293	−0.247647	+	0.968850i	$0.579657\pi$
$588$	−1.00000	−0.0412393
$589$	40.0000	1.64817
$590$	0	0
$591$	−8.00000	−0.329076
$592$	−2.00000	−0.0821995
$593$	9.00000	0.369586	0.184793	−	0.982777i	$-0.440839\pi$
$593$	9.00000	0.369586	0.184793	+	0.982777i	$0.440839\pi$
$594$	5.00000	0.205152
$595$	−2.00000	−0.0819920
$596$	5.00000	0.204808
$597$	10.0000	0.409273
$598$	−1.00000	−0.0408930
$599$	0	0		−	1.00000i	$-0.5\pi$
$599$	0	0			1.00000i	$0.5\pi$
$600$	4.00000	0.163299
$601$	2.00000	0.0815817	0.0407909	−	0.999168i	$-0.487012\pi$
$601$	2.00000	0.0815817	0.0407909	+	0.999168i	$0.487012\pi$
$602$	−6.00000	−0.244542
$603$	−26.0000	−1.05880
$604$	−23.0000	−0.935857
$605$	1.00000	0.0406558
$606$	−2.00000	−0.0812444
$607$	18.0000	0.730597	0.365299	−	0.930890i	$-0.380967\pi$
$607$	18.0000	0.730597	0.365299	+	0.930890i	$0.380967\pi$
$608$	−5.00000	−0.202777
$609$	10.0000	0.405220
$610$	12.0000	0.485866
$611$	−3.00000	−0.121367
$612$	4.00000	0.161690
$613$	−21.0000	−0.848182	−0.424091	−	0.905620i	$-0.639406\pi$
$613$	−21.0000	−0.848182	−0.424091	+	0.905620i	$0.639406\pi$
$614$	−2.00000	−0.0807134
$615$	−7.00000	−0.282267
$616$	1.00000	0.0402911
$617$	18.0000	0.724653	0.362326	−	0.932051i	$-0.381983\pi$
$617$	18.0000	0.724653	0.362326	+	0.932051i	$0.381983\pi$
$618$	−4.00000	−0.160904
$619$	20.0000	0.803868	0.401934	−	0.915669i	$-0.368338\pi$
$619$	20.0000	0.803868	0.401934	+	0.915669i	$0.368338\pi$
$620$	−8.00000	−0.321288
$621$	5.00000	0.200643
$622$	7.00000	0.280674
$623$	−15.0000	−0.600962
$624$	1.00000	0.0400320
$625$	11.0000	0.440000
$626$	29.0000	1.15907
$627$	5.00000	0.199681
$628$	18.0000	0.718278
$629$	4.00000	0.159490
$630$	−2.00000	−0.0796819
$631$	−8.00000	−0.318475	−0.159237	−	0.987240i	$-0.550904\pi$
$631$	−8.00000	−0.318475	−0.159237	+	0.987240i	$0.550904\pi$
$632$	0	0
$633$	3.00000	0.119239
$634$	23.0000	0.913447
$635$	8.00000	0.317470
$636$	6.00000	0.237915
$637$	−1.00000	−0.0396214
$638$	−10.0000	−0.395904
$639$	16.0000	0.632950
$640$	1.00000	0.0395285
$641$	−18.0000	−0.710957	−0.355479	−	0.934684i	$-0.615682\pi$
$641$	−18.0000	−0.710957	−0.355479	+	0.934684i	$0.615682\pi$
$642$	12.0000	0.473602
$643$	4.00000	0.157745	0.0788723	−	0.996885i	$-0.474868\pi$
$643$	4.00000	0.157745	0.0788723	+	0.996885i	$0.474868\pi$
$644$	1.00000	0.0394055
$645$	6.00000	0.236250
$646$	10.0000	0.393445
$647$	−37.0000	−1.45462	−0.727310	−	0.686309i	$-0.759230\pi$
$647$	−37.0000	−1.45462	−0.727310	+	0.686309i	$0.759230\pi$
$648$	1.00000	0.0392837
$649$	0	0
$650$	4.00000	0.156893
$651$	8.00000	0.313545
$652$	−16.0000	−0.626608
$653$	29.0000	1.13486	0.567429	−	0.823422i	$-0.307938\pi$
$653$	29.0000	1.13486	0.567429	+	0.823422i	$0.307938\pi$
$654$	5.00000	0.195515
$655$	−8.00000	−0.312586
$656$	7.00000	0.273304
$657$	2.00000	0.0780274
$658$	3.00000	0.116952
$659$	10.0000	0.389545	0.194772	−	0.980848i	$-0.437603\pi$
$659$	10.0000	0.389545	0.194772	+	0.980848i	$0.437603\pi$
$660$	−1.00000	−0.0389249
$661$	2.00000	0.0777910	0.0388955	−	0.999243i	$-0.487616\pi$
$661$	2.00000	0.0777910	0.0388955	+	0.999243i	$0.487616\pi$
$662$	−8.00000	−0.310929
$663$	−2.00000	−0.0776736
$664$	−11.0000	−0.426883
$665$	−5.00000	−0.193892
$666$	4.00000	0.154997
$667$	−10.0000	−0.387202
$668$	18.0000	0.696441
$669$	11.0000	0.425285
$670$	13.0000	0.502234
$671$	12.0000	0.463255
$672$	−1.00000	−0.0385758
$673$	−26.0000	−1.00223	−0.501113	−	0.865382i	$-0.667076\pi$
$673$	−26.0000	−1.00223	−0.501113	+	0.865382i	$0.667076\pi$
$674$	3.00000	0.115556
$675$	−20.0000	−0.769800
$676$	−12.0000	−0.461538
$677$	28.0000	1.07613	0.538064	−	0.842904i	$-0.319156\pi$
$677$	28.0000	1.07613	0.538064	+	0.842904i	$0.319156\pi$
$678$	−4.00000	−0.153619
$679$	−7.00000	−0.268635
$680$	−2.00000	−0.0766965
$681$	−3.00000	−0.114960
$682$	−8.00000	−0.306336
$683$	4.00000	0.153056	0.0765279	−	0.997067i	$-0.475617\pi$
$683$	4.00000	0.153056	0.0765279	+	0.997067i	$0.475617\pi$
$684$	10.0000	0.382360
$685$	−12.0000	−0.458496
$686$	1.00000	0.0381802
$687$	5.00000	0.190762
$688$	−6.00000	−0.228748
$689$	6.00000	0.228582
$690$	−1.00000	−0.0380693
$691$	−13.0000	−0.494543	−0.247272	−	0.968946i	$-0.579534\pi$
$691$	−13.0000	−0.494543	−0.247272	+	0.968946i	$0.579534\pi$
$692$	9.00000	0.342129
$693$	−2.00000	−0.0759737
$694$	3.00000	0.113878
$695$	20.0000	0.758643
$696$	10.0000	0.379049
$697$	−14.0000	−0.530288
$698$	10.0000	0.378506
$699$	−24.0000	−0.907763
$700$	−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	$0.487975\pi$
$702$	−5.00000	−0.188713
$703$	10.0000	0.377157
$704$	1.00000	0.0376889
$705$	−3.00000	−0.112987
$706$	4.00000	0.150542
$707$	2.00000	0.0752177
$708$	0	0
$709$	−40.0000	−1.50223	−0.751116	−	0.660171i	$-0.770484\pi$
$709$	−40.0000	−1.50223	−0.751116	+	0.660171i	$0.770484\pi$
$710$	−8.00000	−0.300235
$711$	0	0
$712$	−15.0000	−0.562149
$713$	−8.00000	−0.299602
$714$	2.00000	0.0748481
$715$	−1.00000	−0.0373979
$716$	0	0
$717$	15.0000	0.560185
$718$	−30.0000	−1.11959
$719$	0	0		−	1.00000i	$-0.5\pi$
$719$	0	0			1.00000i	$0.5\pi$
$720$	−2.00000	−0.0745356
$721$	4.00000	0.148968
$722$	6.00000	0.223297
$723$	18.0000	0.669427
$724$	7.00000	0.260153
$725$	40.0000	1.48556
$726$	−1.00000	−0.0371135
$727$	8.00000	0.296704	0.148352	−	0.988935i	$-0.452603\pi$
$727$	8.00000	0.296704	0.148352	+	0.988935i	$0.452603\pi$
$728$	−1.00000	−0.0370625
$729$	13.0000	0.481481
$730$	−1.00000	−0.0370117
$731$	12.0000	0.443836
$732$	−12.0000	−0.443533
$733$	−46.0000	−1.69905	−0.849524	−	0.527549i	$-0.823111\pi$
$733$	−46.0000	−1.69905	−0.849524	+	0.527549i	$0.823111\pi$
$734$	−2.00000	−0.0738213
$735$	−1.00000	−0.0368856
$736$	1.00000	0.0368605
$737$	13.0000	0.478861
$738$	−14.0000	−0.515347
$739$	−20.0000	−0.735712	−0.367856	−	0.929883i	$-0.619908\pi$
$739$	−20.0000	−0.735712	−0.367856	+	0.929883i	$0.619908\pi$
$740$	−2.00000	−0.0735215
$741$	−5.00000	−0.183680
$742$	−6.00000	−0.220267
$743$	−6.00000	−0.220119	−0.110059	−	0.993925i	$-0.535104\pi$
$743$	−6.00000	−0.220119	−0.110059	+	0.993925i	$0.535104\pi$
$744$	8.00000	0.293294
$745$	5.00000	0.183186
$746$	29.0000	1.06177
$747$	22.0000	0.804938
$748$	−2.00000	−0.0731272
$749$	−12.0000	−0.438470
$750$	9.00000	0.328634
$751$	32.0000	1.16770	0.583848	−	0.811863i	$-0.301546\pi$
$751$	32.0000	1.16770	0.583848	+	0.811863i	$0.301546\pi$
$752$	3.00000	0.109399
$753$	18.0000	0.655956
$754$	10.0000	0.364179
$755$	−23.0000	−0.837056
$756$	5.00000	0.181848
$757$	−22.0000	−0.799604	−0.399802	−	0.916602i	$-0.630921\pi$
$757$	−22.0000	−0.799604	−0.399802	+	0.916602i	$0.630921\pi$
$758$	−25.0000	−0.908041
$759$	−1.00000	−0.0362977
$760$	−5.00000	−0.181369
$761$	27.0000	0.978749	0.489375	−	0.872074i	$-0.337225\pi$
$761$	27.0000	0.978749	0.489375	+	0.872074i	$0.337225\pi$
$762$	−8.00000	−0.289809
$763$	−5.00000	−0.181012
$764$	7.00000	0.253251
$765$	4.00000	0.144620
$766$	14.0000	0.505841
$767$	0	0
$768$	−1.00000	−0.0360844
$769$	0	0		−	1.00000i	$-0.5\pi$
$769$	0	0			1.00000i	$0.5\pi$
$770$	1.00000	0.0360375
$771$	−8.00000	−0.288113
$772$	4.00000	0.143963
$773$	−26.0000	−0.935155	−0.467578	−	0.883952i	$-0.654873\pi$
$773$	−26.0000	−0.935155	−0.467578	+	0.883952i	$0.654873\pi$
$774$	12.0000	0.431331
$775$	32.0000	1.14947
$776$	−7.00000	−0.251285
$777$	2.00000	0.0717496
$778$	20.0000	0.717035
$779$	−35.0000	−1.25401
$780$	1.00000	0.0358057
$781$	−8.00000	−0.286263
$782$	−2.00000	−0.0715199
$783$	−50.0000	−1.78685
$784$	1.00000	0.0357143
$785$	18.0000	0.642448
$786$	8.00000	0.285351
$787$	13.0000	0.463400	0.231700	−	0.972787i	$-0.425571\pi$
$787$	13.0000	0.463400	0.231700	+	0.972787i	$0.425571\pi$
$788$	8.00000	0.284988
$789$	26.0000	0.925625
$790$	0	0
$791$	4.00000	0.142224
$792$	−2.00000	−0.0710669
$793$	−12.0000	−0.426132
$794$	−32.0000	−1.13564
$795$	6.00000	0.212798
$796$	−10.0000	−0.354441
$797$	33.0000	1.16892	0.584460	−	0.811423i	$-0.301306\pi$
$797$	33.0000	1.16892	0.584460	+	0.811423i	$0.301306\pi$
$798$	5.00000	0.176998
$799$	−6.00000	−0.212265
$800$	−4.00000	−0.141421
$801$	30.0000	1.06000
$802$	22.0000	0.776847
$803$	−1.00000	−0.0352892
$804$	−13.0000	−0.458475
$805$	1.00000	0.0352454
$806$	8.00000	0.281788
$807$	0	0
$808$	2.00000	0.0703598
$809$	20.0000	0.703163	0.351581	−	0.936157i	$-0.385644\pi$
$809$	20.0000	0.703163	0.351581	+	0.936157i	$0.385644\pi$
$810$	1.00000	0.0351364
$811$	−8.00000	−0.280918	−0.140459	−	0.990086i	$-0.544858\pi$
$811$	−8.00000	−0.280918	−0.140459	+	0.990086i	$0.544858\pi$
$812$	−10.0000	−0.350931
$813$	−12.0000	−0.420858
$814$	−2.00000	−0.0701000
$815$	−16.0000	−0.560456
$816$	2.00000	0.0700140
$817$	30.0000	1.04957
$818$	−5.00000	−0.174821
$819$	2.00000	0.0698857
$820$	7.00000	0.244451
$821$	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
$823$	−56.0000	−1.95204	−0.976019	−	0.217687i	$-0.930149\pi$
$823$	−56.0000	−1.95204	−0.976019	+	0.217687i	$0.930149\pi$
$824$	4.00000	0.139347
$825$	4.00000	0.139262
$826$	0	0
$827$	8.00000	0.278187	0.139094	−	0.990279i	$-0.455581\pi$
$827$	8.00000	0.278187	0.139094	+	0.990279i	$0.455581\pi$
$828$	−2.00000	−0.0695048
$829$	40.0000	1.38926	0.694629	−	0.719368i	$-0.255569\pi$
$829$	40.0000	1.38926	0.694629	+	0.719368i	$0.255569\pi$
$830$	−11.0000	−0.381816
$831$	32.0000	1.11007
$832$	−1.00000	−0.0346688
$833$	−2.00000	−0.0692959
$834$	−20.0000	−0.692543
$835$	18.0000	0.622916
$836$	−5.00000	−0.172929
$837$	−40.0000	−1.38260
$838$	−30.0000	−1.03633
$839$	−20.0000	−0.690477	−0.345238	−	0.938515i	$-0.612202\pi$
$839$	−20.0000	−0.690477	−0.345238	+	0.938515i	$0.612202\pi$
$840$	−1.00000	−0.0345033
$841$	71.0000	2.44828
$842$	−18.0000	−0.620321
$843$	−17.0000	−0.585511
$844$	−3.00000	−0.103264
$845$	−12.0000	−0.412813
$846$	−6.00000	−0.206284
$847$	1.00000	0.0343604
$848$	−6.00000	−0.206041
$849$	−9.00000	−0.308879
$850$	8.00000	0.274398
$851$	−2.00000	−0.0685591
$852$	8.00000	0.274075
$853$	39.0000	1.33533	0.667667	−	0.744460i	$-0.267293\pi$
$853$	39.0000	1.33533	0.667667	+	0.744460i	$0.267293\pi$
$854$	12.0000	0.410632
$855$	10.0000	0.341993
$856$	−12.0000	−0.410152
$857$	13.0000	0.444072	0.222036	−	0.975039i	$-0.428730\pi$
$857$	13.0000	0.444072	0.222036	+	0.975039i	$0.428730\pi$
$858$	1.00000	0.0341394
$859$	−20.0000	−0.682391	−0.341196	−	0.939992i	$-0.610832\pi$
$859$	−20.0000	−0.682391	−0.341196	+	0.939992i	$0.610832\pi$
$860$	−6.00000	−0.204598
$861$	−7.00000	−0.238559
$862$	−18.0000	−0.613082
$863$	−36.0000	−1.22545	−0.612727	−	0.790295i	$-0.709928\pi$
$863$	−36.0000	−1.22545	−0.612727	+	0.790295i	$0.709928\pi$
$864$	5.00000	0.170103
$865$	9.00000	0.306009
$866$	29.0000	0.985460
$867$	13.0000	0.441503
$868$	−8.00000	−0.271538
$869$	0	0
$870$	10.0000	0.339032
$871$	−13.0000	−0.440488
$872$	−5.00000	−0.169321
$873$	14.0000	0.473828
$874$	−5.00000	−0.169128
$875$	−9.00000	−0.304256
$876$	1.00000	0.0337869
$877$	−22.0000	−0.742887	−0.371444	−	0.928456i	$-0.621137\pi$
$877$	−22.0000	−0.742887	−0.371444	+	0.928456i	$0.621137\pi$
$878$	20.0000	0.674967
$879$	26.0000	0.876958
$880$	1.00000	0.0337100
$881$	42.0000	1.41502	0.707508	−	0.706705i	$-0.249819\pi$
$881$	42.0000	1.41502	0.707508	+	0.706705i	$0.249819\pi$
$882$	−2.00000	−0.0673435
$883$	−16.0000	−0.538443	−0.269221	−	0.963078i	$-0.586766\pi$
$883$	−16.0000	−0.538443	−0.269221	+	0.963078i	$0.586766\pi$
$884$	2.00000	0.0672673
$885$	0	0
$886$	4.00000	0.134383
$887$	−12.0000	−0.402921	−0.201460	−	0.979497i	$-0.564569\pi$
$887$	−12.0000	−0.402921	−0.201460	+	0.979497i	$0.564569\pi$
$888$	2.00000	0.0671156
$889$	8.00000	0.268311
$890$	−15.0000	−0.502801
$891$	1.00000	0.0335013
$892$	−11.0000	−0.368307
$893$	−15.0000	−0.501956
$894$	−5.00000	−0.167225
$895$	0	0
$896$	1.00000	0.0334077
$897$	1.00000	0.0333890
$898$	15.0000	0.500556
$899$	80.0000	2.66815
$900$	8.00000	0.266667
$901$	12.0000	0.399778
$902$	7.00000	0.233075
$903$	6.00000	0.199667
$904$	4.00000	0.133038
$905$	7.00000	0.232688
$906$	23.0000	0.764124
$907$	13.0000	0.431658	0.215829	−	0.976431i	$-0.430755\pi$
$907$	13.0000	0.431658	0.215829	+	0.976431i	$0.430755\pi$
$908$	3.00000	0.0995585
$909$	−4.00000	−0.132672
$910$	−1.00000	−0.0331497
$911$	−23.0000	−0.762024	−0.381012	−	0.924570i	$-0.624424\pi$
$911$	−23.0000	−0.762024	−0.381012	+	0.924570i	$0.624424\pi$
$912$	5.00000	0.165567
$913$	−11.0000	−0.364047
$914$	−17.0000	−0.562310
$915$	−12.0000	−0.396708
$916$	−5.00000	−0.165205
$917$	−8.00000	−0.264183
$918$	−10.0000	−0.330049
$919$	20.0000	0.659739	0.329870	−	0.944027i	$-0.392995\pi$
$919$	20.0000	0.659739	0.329870	+	0.944027i	$0.392995\pi$
$920$	1.00000	0.0329690
$921$	2.00000	0.0659022
$922$	2.00000	0.0658665
$923$	8.00000	0.263323
$924$	−1.00000	−0.0328976
$925$	8.00000	0.263038
$926$	−26.0000	−0.854413
$927$	−8.00000	−0.262754
$928$	−10.0000	−0.328266
$929$	50.0000	1.64045	0.820223	−	0.572043i	$-0.193849\pi$
$929$	50.0000	1.64045	0.820223	+	0.572043i	$0.193849\pi$
$930$	8.00000	0.262330
$931$	−5.00000	−0.163868
$932$	24.0000	0.786146
$933$	−7.00000	−0.229170
$934$	28.0000	0.916188
$935$	−2.00000	−0.0654070
$936$	2.00000	0.0653720
$937$	−52.0000	−1.69877	−0.849383	−	0.527777i	$-0.823026\pi$
$937$	−52.0000	−1.69877	−0.849383	+	0.527777i	$0.823026\pi$
$938$	13.0000	0.424465
$939$	−29.0000	−0.946379
$940$	3.00000	0.0978492
$941$	42.0000	1.36916	0.684580	−	0.728937i	$-0.259985\pi$
$941$	42.0000	1.36916	0.684580	+	0.728937i	$0.259985\pi$
$942$	−18.0000	−0.586472
$943$	7.00000	0.227951
$944$	0	0
$945$	5.00000	0.162650
$946$	−6.00000	−0.195077
$947$	−42.0000	−1.36482	−0.682408	−	0.730971i	$-0.739067\pi$
$947$	−42.0000	−1.36482	−0.682408	+	0.730971i	$0.739067\pi$
$948$	0	0
$949$	1.00000	0.0324614
$950$	20.0000	0.648886
$951$	−23.0000	−0.745826
$952$	−2.00000	−0.0648204
$953$	−41.0000	−1.32812	−0.664060	−	0.747679i	$-0.731168\pi$
$953$	−41.0000	−1.32812	−0.664060	+	0.747679i	$0.731168\pi$
$954$	12.0000	0.388514
$955$	7.00000	0.226515
$956$	−15.0000	−0.485135
$957$	10.0000	0.323254
$958$	−5.00000	−0.161543
$959$	−12.0000	−0.387500
$960$	−1.00000	−0.0322749
$961$	33.0000	1.06452
$962$	2.00000	0.0644826
$963$	24.0000	0.773389
$964$	−18.0000	−0.579741
$965$	4.00000	0.128765
$966$	−1.00000	−0.0321745
$967$	8.00000	0.257263	0.128631	−	0.991692i	$-0.458942\pi$
$967$	8.00000	0.257263	0.128631	+	0.991692i	$0.458942\pi$
$968$	1.00000	0.0321412
$969$	−10.0000	−0.321246
$970$	−7.00000	−0.224756
$971$	−8.00000	−0.256732	−0.128366	−	0.991727i	$-0.540973\pi$
$971$	−8.00000	−0.256732	−0.128366	+	0.991727i	$0.540973\pi$
$972$	−16.0000	−0.513200
$973$	20.0000	0.641171
$974$	−12.0000	−0.384505
$975$	−4.00000	−0.128103
$976$	12.0000	0.384111
$977$	−42.0000	−1.34370	−0.671850	−	0.740688i	$-0.734500\pi$
$977$	−42.0000	−1.34370	−0.671850	+	0.740688i	$0.734500\pi$
$978$	16.0000	0.511624
$979$	−15.0000	−0.479402
$980$	1.00000	0.0319438
$981$	10.0000	0.319275
$982$	7.00000	0.223379
$983$	−26.0000	−0.829271	−0.414636	−	0.909988i	$-0.636091\pi$
$983$	−26.0000	−0.829271	−0.414636	+	0.909988i	$0.636091\pi$
$984$	−7.00000	−0.223152
$985$	8.00000	0.254901
$986$	20.0000	0.636930
$987$	−3.00000	−0.0954911
$988$	5.00000	0.159071
$989$	−6.00000	−0.190789
$990$	−2.00000	−0.0635642
$991$	42.0000	1.33417	0.667087	−	0.744980i	$-0.267541\pi$
$991$	42.0000	1.33417	0.667087	+	0.744980i	$0.267541\pi$
$992$	−8.00000	−0.254000
$993$	8.00000	0.253872
$994$	−8.00000	−0.253745
$995$	−10.0000	−0.317021
$996$	11.0000	0.348548
$997$	−27.0000	−0.855099	−0.427549	−	0.903992i	$-0.640623\pi$
$997$	−27.0000	−0.855099	−0.427549	+	0.903992i	$0.640623\pi$
$998$	30.0000	0.949633
$999$	−10.0000	−0.316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3542.2.a.o.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3542.2.a.o.1.1	✓	1	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 3542 = 2 \cdot 7 \cdot 11 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3542.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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