LMFDB - Embedded newform 166.2.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [166,2,Mod(1,166)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(166, 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("166.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 166 = 2 \cdot 83 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	166.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:	$1.32551667355$
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	$\chi$	$=$	166.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.00000 q^{5} +1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.00000 q^{9} +2.00000 q^{10} -5.00000 q^{11} -1.00000 q^{12} -2.00000 q^{13} -1.00000 q^{14} +2.00000 q^{15} +1.00000 q^{16} -3.00000 q^{17} +2.00000 q^{18} -2.00000 q^{19} -2.00000 q^{20} -1.00000 q^{21} +5.00000 q^{22} +4.00000 q^{23} +1.00000 q^{24} -1.00000 q^{25} +2.00000 q^{26} +5.00000 q^{27} +1.00000 q^{28} -3.00000 q^{29} -2.00000 q^{30} +1.00000 q^{31} -1.00000 q^{32} +5.00000 q^{33} +3.00000 q^{34} -2.00000 q^{35} -2.00000 q^{36} +1.00000 q^{37} +2.00000 q^{38} +2.00000 q^{39} +2.00000 q^{40} +6.00000 q^{41} +1.00000 q^{42} +8.00000 q^{43} -5.00000 q^{44} +4.00000 q^{45} -4.00000 q^{46} +12.0000 q^{47} -1.00000 q^{48} -6.00000 q^{49} +1.00000 q^{50} +3.00000 q^{51} -2.00000 q^{52} -14.0000 q^{53} -5.00000 q^{54} +10.0000 q^{55} -1.00000 q^{56} +2.00000 q^{57} +3.00000 q^{58} -3.00000 q^{59} +2.00000 q^{60} -7.00000 q^{61} -1.00000 q^{62} -2.00000 q^{63} +1.00000 q^{64} +4.00000 q^{65} -5.00000 q^{66} +2.00000 q^{67} -3.00000 q^{68} -4.00000 q^{69} +2.00000 q^{70} -14.0000 q^{71} +2.00000 q^{72} -4.00000 q^{73} -1.00000 q^{74} +1.00000 q^{75} -2.00000 q^{76} -5.00000 q^{77} -2.00000 q^{78} -6.00000 q^{79} -2.00000 q^{80} +1.00000 q^{81} -6.00000 q^{82} -1.00000 q^{83} -1.00000 q^{84} +6.00000 q^{85} -8.00000 q^{86} +3.00000 q^{87} +5.00000 q^{88} +4.00000 q^{89} -4.00000 q^{90} -2.00000 q^{91} +4.00000 q^{92} -1.00000 q^{93} -12.0000 q^{94} +4.00000 q^{95} +1.00000 q^{96} +12.0000 q^{97} +6.00000 q^{98} +10.0000 q^{99} +O(q^{100})\)

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
$5$	−2.00000	−0.894427	−0.447214	−	0.894427i	$-0.647584\pi$
$5$	−2.00000	−0.894427	−0.447214	+	0.894427i	$0.647584\pi$
$6$	1.00000	0.408248
$7$	1.00000	0.377964	0.188982	−	0.981981i	$-0.439481\pi$
$7$	1.00000	0.377964	0.188982	+	0.981981i	$0.439481\pi$
$8$	−1.00000	−0.353553
$9$	−2.00000	−0.666667
$10$	2.00000	0.632456
$11$	−5.00000	−1.50756	−0.753778	−	0.657129i	$-0.771771\pi$
$11$	−5.00000	−1.50756	−0.753778	+	0.657129i	$0.771771\pi$
$12$	−1.00000	−0.288675
$13$	−2.00000	−0.554700	−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000	−0.554700	−0.277350	+	0.960769i	$0.589456\pi$
$14$	−1.00000	−0.267261
$15$	2.00000	0.516398
$16$	1.00000	0.250000
$17$	−3.00000	−0.727607	−0.363803	−	0.931476i	$-0.618522\pi$
$17$	−3.00000	−0.727607	−0.363803	+	0.931476i	$0.618522\pi$
$18$	2.00000	0.471405
$19$	−2.00000	−0.458831	−0.229416	−	0.973329i	$-0.573682\pi$
$19$	−2.00000	−0.458831	−0.229416	+	0.973329i	$0.573682\pi$
$20$	−2.00000	−0.447214
$21$	−1.00000	−0.218218
$22$	5.00000	1.06600
$23$	4.00000	0.834058	0.417029	−	0.908893i	$-0.363071\pi$
$23$	4.00000	0.834058	0.417029	+	0.908893i	$0.363071\pi$
$24$	1.00000	0.204124
$25$	−1.00000	−0.200000
$26$	2.00000	0.392232
$27$	5.00000	0.962250
$28$	1.00000	0.188982
$29$	−3.00000	−0.557086	−0.278543	−	0.960424i	$-0.589851\pi$
$29$	−3.00000	−0.557086	−0.278543	+	0.960424i	$0.589851\pi$
$30$	−2.00000	−0.365148
$31$	1.00000	0.179605	0.0898027	−	0.995960i	$-0.471376\pi$
$31$	1.00000	0.179605	0.0898027	+	0.995960i	$0.471376\pi$
$32$	−1.00000	−0.176777
$33$	5.00000	0.870388
$34$	3.00000	0.514496
$35$	−2.00000	−0.338062
$36$	−2.00000	−0.333333
$37$	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
$39$	2.00000	0.320256
$40$	2.00000	0.316228
$41$	6.00000	0.937043	0.468521	−	0.883452i	$-0.344787\pi$
$41$	6.00000	0.937043	0.468521	+	0.883452i	$0.344787\pi$
$42$	1.00000	0.154303
$43$	8.00000	1.21999	0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000	1.21999	0.609994	+	0.792406i	$0.291172\pi$
$44$	−5.00000	−0.753778
$45$	4.00000	0.596285
$46$	−4.00000	−0.589768
$47$	12.0000	1.75038	0.875190	−	0.483779i	$-0.160736\pi$
$47$	12.0000	1.75038	0.875190	+	0.483779i	$0.160736\pi$
$48$	−1.00000	−0.144338
$49$	−6.00000	−0.857143
$50$	1.00000	0.141421
$51$	3.00000	0.420084
$52$	−2.00000	−0.277350
$53$	−14.0000	−1.92305	−0.961524	−	0.274721i	$-0.911414\pi$
$53$	−14.0000	−1.92305	−0.961524	+	0.274721i	$0.911414\pi$
$54$	−5.00000	−0.680414
$55$	10.0000	1.34840
$56$	−1.00000	−0.133631
$57$	2.00000	0.264906
$58$	3.00000	0.393919
$59$	−3.00000	−0.390567	−0.195283	−	0.980747i	$-0.562563\pi$
$59$	−3.00000	−0.390567	−0.195283	+	0.980747i	$0.562563\pi$
$60$	2.00000	0.258199
$61$	−7.00000	−0.896258	−0.448129	−	0.893969i	$-0.647910\pi$
$61$	−7.00000	−0.896258	−0.448129	+	0.893969i	$0.647910\pi$
$62$	−1.00000	−0.127000
$63$	−2.00000	−0.251976
$64$	1.00000	0.125000
$65$	4.00000	0.496139
$66$	−5.00000	−0.615457
$67$	2.00000	0.244339	0.122169	−	0.992509i	$-0.461015\pi$
$67$	2.00000	0.244339	0.122169	+	0.992509i	$0.461015\pi$
$68$	−3.00000	−0.363803
$69$	−4.00000	−0.481543
$70$	2.00000	0.239046
$71$	−14.0000	−1.66149	−0.830747	−	0.556650i	$-0.812086\pi$
$71$	−14.0000	−1.66149	−0.830747	+	0.556650i	$0.812086\pi$
$72$	2.00000	0.235702
$73$	−4.00000	−0.468165	−0.234082	−	0.972217i	$-0.575209\pi$
$73$	−4.00000	−0.468165	−0.234082	+	0.972217i	$0.575209\pi$
$74$	−1.00000	−0.116248
$75$	1.00000	0.115470
$76$	−2.00000	−0.229416
$77$	−5.00000	−0.569803
$78$	−2.00000	−0.226455
$79$	−6.00000	−0.675053	−0.337526	−	0.941316i	$-0.609590\pi$
$79$	−6.00000	−0.675053	−0.337526	+	0.941316i	$0.609590\pi$
$80$	−2.00000	−0.223607
$81$	1.00000	0.111111
$82$	−6.00000	−0.662589
$83$	−1.00000	−0.109764
$83$	−1.00000	−0.109764
$84$	−1.00000	−0.109109
$85$	6.00000	0.650791
$86$	−8.00000	−0.862662
$87$	3.00000	0.321634
$88$	5.00000	0.533002
$89$	4.00000	0.423999	0.212000	−	0.977270i	$-0.432002\pi$
$89$	4.00000	0.423999	0.212000	+	0.977270i	$0.432002\pi$
$90$	−4.00000	−0.421637
$91$	−2.00000	−0.209657
$92$	4.00000	0.417029
$93$	−1.00000	−0.103695
$94$	−12.0000	−1.23771
$95$	4.00000	0.410391
$96$	1.00000	0.102062
$97$	12.0000	1.21842	0.609208	−	0.793011i	$-0.291488\pi$
$97$	12.0000	1.21842	0.609208	+	0.793011i	$0.291488\pi$
$98$	6.00000	0.606092
$99$	10.0000	1.00504
$100$	−1.00000	−0.100000
$101$	−6.00000	−0.597022	−0.298511	−	0.954406i	$-0.596490\pi$
$101$	−6.00000	−0.597022	−0.298511	+	0.954406i	$0.596490\pi$
$102$	−3.00000	−0.297044
$103$	−8.00000	−0.788263	−0.394132	−	0.919054i	$-0.628955\pi$
$103$	−8.00000	−0.788263	−0.394132	+	0.919054i	$0.628955\pi$
$104$	2.00000	0.196116
$105$	2.00000	0.195180
$106$	14.0000	1.35980
$107$	10.0000	0.966736	0.483368	−	0.875417i	$-0.339413\pi$
$107$	10.0000	0.966736	0.483368	+	0.875417i	$0.339413\pi$
$108$	5.00000	0.481125
$109$	−13.0000	−1.24517	−0.622587	−	0.782551i	$-0.713918\pi$
$109$	−13.0000	−1.24517	−0.622587	+	0.782551i	$0.713918\pi$
$110$	−10.0000	−0.953463
$111$	−1.00000	−0.0949158
$112$	1.00000	0.0944911
$113$	−9.00000	−0.846649	−0.423324	−	0.905978i	$-0.639137\pi$
$113$	−9.00000	−0.846649	−0.423324	+	0.905978i	$0.639137\pi$
$114$	−2.00000	−0.187317
$115$	−8.00000	−0.746004
$116$	−3.00000	−0.278543
$117$	4.00000	0.369800
$118$	3.00000	0.276172
$119$	−3.00000	−0.275010
$120$	−2.00000	−0.182574
$121$	14.0000	1.27273
$122$	7.00000	0.633750
$123$	−6.00000	−0.541002
$124$	1.00000	0.0898027
$125$	12.0000	1.07331
$126$	2.00000	0.178174
$127$	−7.00000	−0.621150	−0.310575	−	0.950549i	$-0.600522\pi$
$127$	−7.00000	−0.621150	−0.310575	+	0.950549i	$0.600522\pi$
$128$	−1.00000	−0.0883883
$129$	−8.00000	−0.704361
$130$	−4.00000	−0.350823
$131$	−20.0000	−1.74741	−0.873704	−	0.486458i	$-0.838289\pi$
$131$	−20.0000	−1.74741	−0.873704	+	0.486458i	$0.838289\pi$
$132$	5.00000	0.435194
$133$	−2.00000	−0.173422
$134$	−2.00000	−0.172774
$135$	−10.0000	−0.860663
$136$	3.00000	0.257248
$137$	14.0000	1.19610	0.598050	−	0.801459i	$-0.295942\pi$
$137$	14.0000	1.19610	0.598050	+	0.801459i	$0.295942\pi$
$138$	4.00000	0.340503
$139$	14.0000	1.18746	0.593732	−	0.804663i	$-0.297654\pi$
$139$	14.0000	1.18746	0.593732	+	0.804663i	$0.297654\pi$
$140$	−2.00000	−0.169031
$141$	−12.0000	−1.01058
$142$	14.0000	1.17485
$143$	10.0000	0.836242
$144$	−2.00000	−0.166667
$145$	6.00000	0.498273
$146$	4.00000	0.331042
$147$	6.00000	0.494872
$148$	1.00000	0.0821995
$149$	20.0000	1.63846	0.819232	−	0.573462i	$-0.194400\pi$
$149$	20.0000	1.63846	0.819232	+	0.573462i	$0.194400\pi$
$150$	−1.00000	−0.0816497
$151$	5.00000	0.406894	0.203447	−	0.979086i	$-0.434786\pi$
$151$	5.00000	0.406894	0.203447	+	0.979086i	$0.434786\pi$
$152$	2.00000	0.162221
$153$	6.00000	0.485071
$154$	5.00000	0.402911
$155$	−2.00000	−0.160644
$156$	2.00000	0.160128
$157$	−10.0000	−0.798087	−0.399043	−	0.916932i	$-0.630658\pi$
$157$	−10.0000	−0.798087	−0.399043	+	0.916932i	$0.630658\pi$
$158$	6.00000	0.477334
$159$	14.0000	1.11027
$160$	2.00000	0.158114
$161$	4.00000	0.315244
$162$	−1.00000	−0.0785674
$163$	−14.0000	−1.09656	−0.548282	−	0.836293i	$-0.684718\pi$
$163$	−14.0000	−1.09656	−0.548282	+	0.836293i	$0.684718\pi$
$164$	6.00000	0.468521
$165$	−10.0000	−0.778499
$166$	1.00000	0.0776151
$167$	9.00000	0.696441	0.348220	−	0.937413i	$-0.386786\pi$
$167$	9.00000	0.696441	0.348220	+	0.937413i	$0.386786\pi$
$168$	1.00000	0.0771517
$169$	−9.00000	−0.692308
$170$	−6.00000	−0.460179
$171$	4.00000	0.305888
$172$	8.00000	0.609994
$173$	9.00000	0.684257	0.342129	−	0.939653i	$-0.388852\pi$
$173$	9.00000	0.684257	0.342129	+	0.939653i	$0.388852\pi$
$174$	−3.00000	−0.227429
$175$	−1.00000	−0.0755929
$176$	−5.00000	−0.376889
$177$	3.00000	0.225494
$178$	−4.00000	−0.299813
$179$	−10.0000	−0.747435	−0.373718	−	0.927543i	$-0.621917\pi$
$179$	−10.0000	−0.747435	−0.373718	+	0.927543i	$0.621917\pi$
$180$	4.00000	0.298142
$181$	−2.00000	−0.148659	−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000	−0.148659	−0.0743294	+	0.997234i	$0.523682\pi$
$182$	2.00000	0.148250
$183$	7.00000	0.517455
$184$	−4.00000	−0.294884
$185$	−2.00000	−0.147043
$186$	1.00000	0.0733236
$187$	15.0000	1.09691
$188$	12.0000	0.875190
$189$	5.00000	0.363696
$190$	−4.00000	−0.290191
$191$	−15.0000	−1.08536	−0.542681	−	0.839939i	$-0.682591\pi$
$191$	−15.0000	−1.08536	−0.542681	+	0.839939i	$0.682591\pi$
$192$	−1.00000	−0.0721688
$193$	−22.0000	−1.58359	−0.791797	−	0.610784i	$-0.790854\pi$
$193$	−22.0000	−1.58359	−0.791797	+	0.610784i	$0.790854\pi$
$194$	−12.0000	−0.861550
$195$	−4.00000	−0.286446
$196$	−6.00000	−0.428571
$197$	−17.0000	−1.21120	−0.605600	−	0.795769i	$-0.707067\pi$
$197$	−17.0000	−1.21120	−0.605600	+	0.795769i	$0.707067\pi$
$198$	−10.0000	−0.710669
$199$	8.00000	0.567105	0.283552	−	0.958957i	$-0.408487\pi$
$199$	8.00000	0.567105	0.283552	+	0.958957i	$0.408487\pi$
$200$	1.00000	0.0707107
$201$	−2.00000	−0.141069
$202$	6.00000	0.422159
$203$	−3.00000	−0.210559
$204$	3.00000	0.210042
$205$	−12.0000	−0.838116
$206$	8.00000	0.557386
$207$	−8.00000	−0.556038
$208$	−2.00000	−0.138675
$209$	10.0000	0.691714
$210$	−2.00000	−0.138013
$211$	8.00000	0.550743	0.275371	−	0.961338i	$-0.411199\pi$
$211$	8.00000	0.550743	0.275371	+	0.961338i	$0.411199\pi$
$212$	−14.0000	−0.961524
$213$	14.0000	0.959264
$214$	−10.0000	−0.683586
$215$	−16.0000	−1.09119
$216$	−5.00000	−0.340207
$217$	1.00000	0.0678844
$218$	13.0000	0.880471
$219$	4.00000	0.270295
$220$	10.0000	0.674200
$221$	6.00000	0.403604
$222$	1.00000	0.0671156
$223$	−8.00000	−0.535720	−0.267860	−	0.963458i	$-0.586316\pi$
$223$	−8.00000	−0.535720	−0.267860	+	0.963458i	$0.586316\pi$
$224$	−1.00000	−0.0668153
$225$	2.00000	0.133333
$226$	9.00000	0.598671
$227$	−4.00000	−0.265489	−0.132745	−	0.991150i	$-0.542379\pi$
$227$	−4.00000	−0.265489	−0.132745	+	0.991150i	$0.542379\pi$
$228$	2.00000	0.132453
$229$	−26.0000	−1.71813	−0.859064	−	0.511868i	$-0.828954\pi$
$229$	−26.0000	−1.71813	−0.859064	+	0.511868i	$0.828954\pi$
$230$	8.00000	0.527504
$231$	5.00000	0.328976
$232$	3.00000	0.196960
$233$	−22.0000	−1.44127	−0.720634	−	0.693316i	$-0.756149\pi$
$233$	−22.0000	−1.44127	−0.720634	+	0.693316i	$0.756149\pi$
$234$	−4.00000	−0.261488
$235$	−24.0000	−1.56559
$236$	−3.00000	−0.195283
$237$	6.00000	0.389742
$238$	3.00000	0.194461
$239$	4.00000	0.258738	0.129369	−	0.991596i	$-0.458705\pi$
$239$	4.00000	0.258738	0.129369	+	0.991596i	$0.458705\pi$
$240$	2.00000	0.129099
$241$	23.0000	1.48156	0.740780	−	0.671748i	$-0.234456\pi$
$241$	23.0000	1.48156	0.740780	+	0.671748i	$0.234456\pi$
$242$	−14.0000	−0.899954
$243$	−16.0000	−1.02640
$244$	−7.00000	−0.448129
$245$	12.0000	0.766652
$246$	6.00000	0.382546
$247$	4.00000	0.254514
$248$	−1.00000	−0.0635001
$249$	1.00000	0.0633724
$250$	−12.0000	−0.758947
$251$	16.0000	1.00991	0.504956	−	0.863145i	$-0.331509\pi$
$251$	16.0000	1.00991	0.504956	+	0.863145i	$0.331509\pi$
$252$	−2.00000	−0.125988
$253$	−20.0000	−1.25739
$254$	7.00000	0.439219
$255$	−6.00000	−0.375735
$256$	1.00000	0.0625000
$257$	26.0000	1.62184	0.810918	−	0.585160i	$-0.198968\pi$
$257$	26.0000	1.62184	0.810918	+	0.585160i	$0.198968\pi$
$258$	8.00000	0.498058
$259$	1.00000	0.0621370
$260$	4.00000	0.248069
$261$	6.00000	0.371391
$262$	20.0000	1.23560
$263$	−14.0000	−0.863277	−0.431638	−	0.902047i	$-0.642064\pi$
$263$	−14.0000	−0.863277	−0.431638	+	0.902047i	$0.642064\pi$
$264$	−5.00000	−0.307729
$265$	28.0000	1.72003
$266$	2.00000	0.122628
$267$	−4.00000	−0.244796
$268$	2.00000	0.122169
$269$	18.0000	1.09748	0.548740	−	0.835993i	$-0.315108\pi$
$269$	18.0000	1.09748	0.548740	+	0.835993i	$0.315108\pi$
$270$	10.0000	0.608581
$271$	−12.0000	−0.728948	−0.364474	−	0.931214i	$-0.618751\pi$
$271$	−12.0000	−0.728948	−0.364474	+	0.931214i	$0.618751\pi$
$272$	−3.00000	−0.181902
$273$	2.00000	0.121046
$274$	−14.0000	−0.845771
$275$	5.00000	0.301511
$276$	−4.00000	−0.240772
$277$	−22.0000	−1.32185	−0.660926	−	0.750451i	$-0.729836\pi$
$277$	−22.0000	−1.32185	−0.660926	+	0.750451i	$0.729836\pi$
$278$	−14.0000	−0.839664
$279$	−2.00000	−0.119737
$280$	2.00000	0.119523
$281$	12.0000	0.715860	0.357930	−	0.933748i	$-0.383483\pi$
$281$	12.0000	0.715860	0.357930	+	0.933748i	$0.383483\pi$
$282$	12.0000	0.714590
$283$	14.0000	0.832214	0.416107	−	0.909316i	$-0.363394\pi$
$283$	14.0000	0.832214	0.416107	+	0.909316i	$0.363394\pi$
$284$	−14.0000	−0.830747
$285$	−4.00000	−0.236940
$286$	−10.0000	−0.591312
$287$	6.00000	0.354169
$288$	2.00000	0.117851
$289$	−8.00000	−0.470588
$290$	−6.00000	−0.352332
$291$	−12.0000	−0.703452
$292$	−4.00000	−0.234082
$293$	−6.00000	−0.350524	−0.175262	−	0.984522i	$-0.556077\pi$
$293$	−6.00000	−0.350524	−0.175262	+	0.984522i	$0.556077\pi$
$294$	−6.00000	−0.349927
$295$	6.00000	0.349334
$296$	−1.00000	−0.0581238
$297$	−25.0000	−1.45065
$298$	−20.0000	−1.15857
$299$	−8.00000	−0.462652
$300$	1.00000	0.0577350
$301$	8.00000	0.461112
$302$	−5.00000	−0.287718
$303$	6.00000	0.344691
$304$	−2.00000	−0.114708
$305$	14.0000	0.801638
$306$	−6.00000	−0.342997
$307$	−32.0000	−1.82634	−0.913168	−	0.407583i	$-0.866372\pi$
$307$	−32.0000	−1.82634	−0.913168	+	0.407583i	$0.866372\pi$
$308$	−5.00000	−0.284901
$309$	8.00000	0.455104
$310$	2.00000	0.113592
$311$	8.00000	0.453638	0.226819	−	0.973937i	$-0.427167\pi$
$311$	8.00000	0.453638	0.226819	+	0.973937i	$0.427167\pi$
$312$	−2.00000	−0.113228
$313$	−13.0000	−0.734803	−0.367402	−	0.930062i	$-0.619753\pi$
$313$	−13.0000	−0.734803	−0.367402	+	0.930062i	$0.619753\pi$
$314$	10.0000	0.564333
$315$	4.00000	0.225374
$316$	−6.00000	−0.337526
$317$	31.0000	1.74113	0.870567	−	0.492050i	$-0.163752\pi$
$317$	31.0000	1.74113	0.870567	+	0.492050i	$0.163752\pi$
$318$	−14.0000	−0.785081
$319$	15.0000	0.839839
$320$	−2.00000	−0.111803
$321$	−10.0000	−0.558146
$322$	−4.00000	−0.222911
$323$	6.00000	0.333849
$324$	1.00000	0.0555556
$325$	2.00000	0.110940
$326$	14.0000	0.775388
$327$	13.0000	0.718902
$328$	−6.00000	−0.331295
$329$	12.0000	0.661581
$330$	10.0000	0.550482
$331$	10.0000	0.549650	0.274825	−	0.961494i	$-0.411380\pi$
$331$	10.0000	0.549650	0.274825	+	0.961494i	$0.411380\pi$
$332$	−1.00000	−0.0548821
$333$	−2.00000	−0.109599
$334$	−9.00000	−0.492458
$335$	−4.00000	−0.218543
$336$	−1.00000	−0.0545545
$337$	−2.00000	−0.108947	−0.0544735	−	0.998515i	$-0.517348\pi$
$337$	−2.00000	−0.108947	−0.0544735	+	0.998515i	$0.517348\pi$
$338$	9.00000	0.489535
$339$	9.00000	0.488813
$340$	6.00000	0.325396
$341$	−5.00000	−0.270765
$342$	−4.00000	−0.216295
$343$	−13.0000	−0.701934
$344$	−8.00000	−0.431331
$345$	8.00000	0.430706
$346$	−9.00000	−0.483843
$347$	26.0000	1.39575	0.697877	−	0.716218i	$-0.254128\pi$
$347$	26.0000	1.39575	0.697877	+	0.716218i	$0.254128\pi$
$348$	3.00000	0.160817
$349$	19.0000	1.01705	0.508523	−	0.861048i	$-0.330192\pi$
$349$	19.0000	1.01705	0.508523	+	0.861048i	$0.330192\pi$
$350$	1.00000	0.0534522
$351$	−10.0000	−0.533761
$352$	5.00000	0.266501
$353$	31.0000	1.64996	0.824982	−	0.565159i	$-0.191185\pi$
$353$	31.0000	1.64996	0.824982	+	0.565159i	$0.191185\pi$
$354$	−3.00000	−0.159448
$355$	28.0000	1.48609
$356$	4.00000	0.212000
$357$	3.00000	0.158777
$358$	10.0000	0.528516
$359$	−35.0000	−1.84723	−0.923615	−	0.383322i	$-0.874780\pi$
$359$	−35.0000	−1.84723	−0.923615	+	0.383322i	$0.874780\pi$
$360$	−4.00000	−0.210819
$361$	−15.0000	−0.789474
$362$	2.00000	0.105118
$363$	−14.0000	−0.734809
$364$	−2.00000	−0.104828
$365$	8.00000	0.418739
$366$	−7.00000	−0.365896
$367$	34.0000	1.77479	0.887393	−	0.461014i	$-0.152514\pi$
$367$	34.0000	1.77479	0.887393	+	0.461014i	$0.152514\pi$
$368$	4.00000	0.208514
$369$	−12.0000	−0.624695
$370$	2.00000	0.103975
$371$	−14.0000	−0.726844
$372$	−1.00000	−0.0518476
$373$	1.00000	0.0517780	0.0258890	−	0.999665i	$-0.491758\pi$
$373$	1.00000	0.0517780	0.0258890	+	0.999665i	$0.491758\pi$
$374$	−15.0000	−0.775632
$375$	−12.0000	−0.619677
$376$	−12.0000	−0.618853
$377$	6.00000	0.309016
$378$	−5.00000	−0.257172
$379$	28.0000	1.43826	0.719132	−	0.694874i	$-0.244540\pi$
$379$	28.0000	1.43826	0.719132	+	0.694874i	$0.244540\pi$
$380$	4.00000	0.205196
$381$	7.00000	0.358621
$382$	15.0000	0.767467
$383$	−9.00000	−0.459879	−0.229939	−	0.973205i	$-0.573853\pi$
$383$	−9.00000	−0.459879	−0.229939	+	0.973205i	$0.573853\pi$
$384$	1.00000	0.0510310
$385$	10.0000	0.509647
$386$	22.0000	1.11977
$387$	−16.0000	−0.813326
$388$	12.0000	0.609208
$389$	−32.0000	−1.62246	−0.811232	−	0.584724i	$-0.801203\pi$
$389$	−32.0000	−1.62246	−0.811232	+	0.584724i	$0.801203\pi$
$390$	4.00000	0.202548
$391$	−12.0000	−0.606866
$392$	6.00000	0.303046
$393$	20.0000	1.00887
$394$	17.0000	0.856448
$395$	12.0000	0.603786
$396$	10.0000	0.502519
$397$	18.0000	0.903394	0.451697	−	0.892171i	$-0.350819\pi$
$397$	18.0000	0.903394	0.451697	+	0.892171i	$0.350819\pi$
$398$	−8.00000	−0.401004
$399$	2.00000	0.100125
$400$	−1.00000	−0.0500000
$401$	30.0000	1.49813	0.749064	−	0.662497i	$-0.230503\pi$
$401$	30.0000	1.49813	0.749064	+	0.662497i	$0.230503\pi$
$402$	2.00000	0.0997509
$403$	−2.00000	−0.0996271
$404$	−6.00000	−0.298511
$405$	−2.00000	−0.0993808
$406$	3.00000	0.148888
$407$	−5.00000	−0.247841
$408$	−3.00000	−0.148522
$409$	−29.0000	−1.43396	−0.716979	−	0.697095i	$-0.754476\pi$
$409$	−29.0000	−1.43396	−0.716979	+	0.697095i	$0.754476\pi$
$410$	12.0000	0.592638
$411$	−14.0000	−0.690569
$412$	−8.00000	−0.394132
$413$	−3.00000	−0.147620
$414$	8.00000	0.393179
$415$	2.00000	0.0981761
$416$	2.00000	0.0980581
$417$	−14.0000	−0.685583
$418$	−10.0000	−0.489116
$419$	19.0000	0.928211	0.464105	−	0.885780i	$-0.346376\pi$
$419$	19.0000	0.928211	0.464105	+	0.885780i	$0.346376\pi$
$420$	2.00000	0.0975900
$421$	22.0000	1.07221	0.536107	−	0.844150i	$-0.319894\pi$
$421$	22.0000	1.07221	0.536107	+	0.844150i	$0.319894\pi$
$422$	−8.00000	−0.389434
$423$	−24.0000	−1.16692
$424$	14.0000	0.679900
$425$	3.00000	0.145521
$426$	−14.0000	−0.678302
$427$	−7.00000	−0.338754
$428$	10.0000	0.483368
$429$	−10.0000	−0.482805
$430$	16.0000	0.771589
$431$	33.0000	1.58955	0.794777	−	0.606902i	$-0.207588\pi$
$431$	33.0000	1.58955	0.794777	+	0.606902i	$0.207588\pi$
$432$	5.00000	0.240563
$433$	28.0000	1.34559	0.672797	−	0.739827i	$-0.265093\pi$
$433$	28.0000	1.34559	0.672797	+	0.739827i	$0.265093\pi$
$434$	−1.00000	−0.0480015
$435$	−6.00000	−0.287678
$436$	−13.0000	−0.622587
$437$	−8.00000	−0.382692
$438$	−4.00000	−0.191127
$439$	−20.0000	−0.954548	−0.477274	−	0.878755i	$-0.658375\pi$
$439$	−20.0000	−0.954548	−0.477274	+	0.878755i	$0.658375\pi$
$440$	−10.0000	−0.476731
$441$	12.0000	0.571429
$442$	−6.00000	−0.285391
$443$	−3.00000	−0.142534	−0.0712672	−	0.997457i	$-0.522704\pi$
$443$	−3.00000	−0.142534	−0.0712672	+	0.997457i	$0.522704\pi$
$444$	−1.00000	−0.0474579
$445$	−8.00000	−0.379236
$446$	8.00000	0.378811
$447$	−20.0000	−0.945968
$448$	1.00000	0.0472456
$449$	−2.00000	−0.0943858	−0.0471929	−	0.998886i	$-0.515028\pi$
$449$	−2.00000	−0.0943858	−0.0471929	+	0.998886i	$0.515028\pi$
$450$	−2.00000	−0.0942809
$451$	−30.0000	−1.41264
$452$	−9.00000	−0.423324
$453$	−5.00000	−0.234920
$454$	4.00000	0.187729
$455$	4.00000	0.187523
$456$	−2.00000	−0.0936586
$457$	18.0000	0.842004	0.421002	−	0.907060i	$-0.361678\pi$
$457$	18.0000	0.842004	0.421002	+	0.907060i	$0.361678\pi$
$458$	26.0000	1.21490
$459$	−15.0000	−0.700140
$460$	−8.00000	−0.373002
$461$	−36.0000	−1.67669	−0.838344	−	0.545142i	$-0.816476\pi$
$461$	−36.0000	−1.67669	−0.838344	+	0.545142i	$0.816476\pi$
$462$	−5.00000	−0.232621
$463$	7.00000	0.325318	0.162659	−	0.986682i	$-0.447993\pi$
$463$	7.00000	0.325318	0.162659	+	0.986682i	$0.447993\pi$
$464$	−3.00000	−0.139272
$465$	2.00000	0.0927478
$466$	22.0000	1.01913
$467$	−36.0000	−1.66588	−0.832941	−	0.553362i	$-0.813345\pi$
$467$	−36.0000	−1.66588	−0.832941	+	0.553362i	$0.813345\pi$
$468$	4.00000	0.184900
$469$	2.00000	0.0923514
$470$	24.0000	1.10704
$471$	10.0000	0.460776
$472$	3.00000	0.138086
$473$	−40.0000	−1.83920
$474$	−6.00000	−0.275589
$475$	2.00000	0.0917663
$476$	−3.00000	−0.137505
$477$	28.0000	1.28203
$478$	−4.00000	−0.182956
$479$	−15.0000	−0.685367	−0.342684	−	0.939451i	$-0.611336\pi$
$479$	−15.0000	−0.685367	−0.342684	+	0.939451i	$0.611336\pi$
$480$	−2.00000	−0.0912871
$481$	−2.00000	−0.0911922
$482$	−23.0000	−1.04762
$483$	−4.00000	−0.182006
$484$	14.0000	0.636364
$485$	−24.0000	−1.08978
$486$	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	$0.587647\pi$
$488$	7.00000	0.316875
$489$	14.0000	0.633102
$490$	−12.0000	−0.542105
$491$	−30.0000	−1.35388	−0.676941	−	0.736038i	$-0.736695\pi$
$491$	−30.0000	−1.35388	−0.676941	+	0.736038i	$0.736695\pi$
$492$	−6.00000	−0.270501
$493$	9.00000	0.405340
$494$	−4.00000	−0.179969
$495$	−20.0000	−0.898933
$496$	1.00000	0.0449013
$497$	−14.0000	−0.627986
$498$	−1.00000	−0.0448111
$499$	39.0000	1.74588	0.872940	−	0.487828i	$-0.162211\pi$
$499$	39.0000	1.74588	0.872940	+	0.487828i	$0.162211\pi$
$500$	12.0000	0.536656
$501$	−9.00000	−0.402090
$502$	−16.0000	−0.714115
$503$	12.0000	0.535054	0.267527	−	0.963550i	$-0.413794\pi$
$503$	12.0000	0.535054	0.267527	+	0.963550i	$0.413794\pi$
$504$	2.00000	0.0890871
$505$	12.0000	0.533993
$506$	20.0000	0.889108
$507$	9.00000	0.399704
$508$	−7.00000	−0.310575
$509$	3.00000	0.132973	0.0664863	−	0.997787i	$-0.478821\pi$
$509$	3.00000	0.132973	0.0664863	+	0.997787i	$0.478821\pi$
$510$	6.00000	0.265684
$511$	−4.00000	−0.176950
$512$	−1.00000	−0.0441942
$513$	−10.0000	−0.441511
$514$	−26.0000	−1.14681
$515$	16.0000	0.705044
$516$	−8.00000	−0.352180
$517$	−60.0000	−2.63880
$518$	−1.00000	−0.0439375
$519$	−9.00000	−0.395056
$520$	−4.00000	−0.175412
$521$	−22.0000	−0.963837	−0.481919	−	0.876216i	$-0.660060\pi$
$521$	−22.0000	−0.963837	−0.481919	+	0.876216i	$0.660060\pi$
$522$	−6.00000	−0.262613
$523$	13.0000	0.568450	0.284225	−	0.958758i	$-0.408264\pi$
$523$	13.0000	0.568450	0.284225	+	0.958758i	$0.408264\pi$
$524$	−20.0000	−0.873704
$525$	1.00000	0.0436436
$526$	14.0000	0.610429
$527$	−3.00000	−0.130682
$528$	5.00000	0.217597
$529$	−7.00000	−0.304348
$530$	−28.0000	−1.21624
$531$	6.00000	0.260378
$532$	−2.00000	−0.0867110
$533$	−12.0000	−0.519778
$534$	4.00000	0.173097
$535$	−20.0000	−0.864675
$536$	−2.00000	−0.0863868
$537$	10.0000	0.431532
$538$	−18.0000	−0.776035
$539$	30.0000	1.29219
$540$	−10.0000	−0.430331
$541$	−34.0000	−1.46177	−0.730887	−	0.682498i	$-0.760893\pi$
$541$	−34.0000	−1.46177	−0.730887	+	0.682498i	$0.760893\pi$
$542$	12.0000	0.515444
$543$	2.00000	0.0858282
$544$	3.00000	0.128624
$545$	26.0000	1.11372
$546$	−2.00000	−0.0855921
$547$	−19.0000	−0.812381	−0.406191	−	0.913788i	$-0.633143\pi$
$547$	−19.0000	−0.812381	−0.406191	+	0.913788i	$0.633143\pi$
$548$	14.0000	0.598050
$549$	14.0000	0.597505
$550$	−5.00000	−0.213201
$551$	6.00000	0.255609
$552$	4.00000	0.170251
$553$	−6.00000	−0.255146
$554$	22.0000	0.934690
$555$	2.00000	0.0848953
$556$	14.0000	0.593732
$557$	−18.0000	−0.762684	−0.381342	−	0.924434i	$-0.624538\pi$
$557$	−18.0000	−0.762684	−0.381342	+	0.924434i	$0.624538\pi$
$558$	2.00000	0.0846668
$559$	−16.0000	−0.676728
$560$	−2.00000	−0.0845154
$561$	−15.0000	−0.633300
$562$	−12.0000	−0.506189
$563$	21.0000	0.885044	0.442522	−	0.896758i	$-0.354084\pi$
$563$	21.0000	0.885044	0.442522	+	0.896758i	$0.354084\pi$
$564$	−12.0000	−0.505291
$565$	18.0000	0.757266
$566$	−14.0000	−0.588464
$567$	1.00000	0.0419961
$568$	14.0000	0.587427
$569$	−30.0000	−1.25767	−0.628833	−	0.777541i	$-0.716467\pi$
$569$	−30.0000	−1.25767	−0.628833	+	0.777541i	$0.716467\pi$
$570$	4.00000	0.167542
$571$	24.0000	1.00437	0.502184	−	0.864761i	$-0.332530\pi$
$571$	24.0000	1.00437	0.502184	+	0.864761i	$0.332530\pi$
$572$	10.0000	0.418121
$573$	15.0000	0.626634
$574$	−6.00000	−0.250435
$575$	−4.00000	−0.166812
$576$	−2.00000	−0.0833333
$577$	−2.00000	−0.0832611	−0.0416305	−	0.999133i	$-0.513255\pi$
$577$	−2.00000	−0.0832611	−0.0416305	+	0.999133i	$0.513255\pi$
$578$	8.00000	0.332756
$579$	22.0000	0.914289
$580$	6.00000	0.249136
$581$	−1.00000	−0.0414870
$582$	12.0000	0.497416
$583$	70.0000	2.89910
$584$	4.00000	0.165521
$585$	−8.00000	−0.330759
$586$	6.00000	0.247858
$587$	16.0000	0.660391	0.330195	−	0.943913i	$-0.392885\pi$
$587$	16.0000	0.660391	0.330195	+	0.943913i	$0.392885\pi$
$588$	6.00000	0.247436
$589$	−2.00000	−0.0824086
$590$	−6.00000	−0.247016
$591$	17.0000	0.699287
$592$	1.00000	0.0410997
$593$	17.0000	0.698106	0.349053	−	0.937103i	$-0.386503\pi$
$593$	17.0000	0.698106	0.349053	+	0.937103i	$0.386503\pi$
$594$	25.0000	1.02576
$595$	6.00000	0.245976
$596$	20.0000	0.819232
$597$	−8.00000	−0.327418
$598$	8.00000	0.327144
$599$	36.0000	1.47092	0.735460	−	0.677568i	$-0.236966\pi$
$599$	36.0000	1.47092	0.735460	+	0.677568i	$0.236966\pi$
$600$	−1.00000	−0.0408248
$601$	42.0000	1.71322	0.856608	−	0.515968i	$-0.172568\pi$
$601$	42.0000	1.71322	0.856608	+	0.515968i	$0.172568\pi$
$602$	−8.00000	−0.326056
$603$	−4.00000	−0.162893
$604$	5.00000	0.203447
$605$	−28.0000	−1.13836
$606$	−6.00000	−0.243733
$607$	−16.0000	−0.649420	−0.324710	−	0.945814i	$-0.605267\pi$
$607$	−16.0000	−0.649420	−0.324710	+	0.945814i	$0.605267\pi$
$608$	2.00000	0.0811107
$609$	3.00000	0.121566
$610$	−14.0000	−0.566843
$611$	−24.0000	−0.970936
$612$	6.00000	0.242536
$613$	−16.0000	−0.646234	−0.323117	−	0.946359i	$-0.604731\pi$
$613$	−16.0000	−0.646234	−0.323117	+	0.946359i	$0.604731\pi$
$614$	32.0000	1.29141
$615$	12.0000	0.483887
$616$	5.00000	0.201456
$617$	−21.0000	−0.845428	−0.422714	−	0.906263i	$-0.638923\pi$
$617$	−21.0000	−0.845428	−0.422714	+	0.906263i	$0.638923\pi$
$618$	−8.00000	−0.321807
$619$	7.00000	0.281354	0.140677	−	0.990056i	$-0.455072\pi$
$619$	7.00000	0.281354	0.140677	+	0.990056i	$0.455072\pi$
$620$	−2.00000	−0.0803219
$621$	20.0000	0.802572
$622$	−8.00000	−0.320771
$623$	4.00000	0.160257
$624$	2.00000	0.0800641
$625$	−19.0000	−0.760000
$626$	13.0000	0.519584
$627$	−10.0000	−0.399362
$628$	−10.0000	−0.399043
$629$	−3.00000	−0.119618
$630$	−4.00000	−0.159364
$631$	−8.00000	−0.318475	−0.159237	−	0.987240i	$-0.550904\pi$
$631$	−8.00000	−0.318475	−0.159237	+	0.987240i	$0.550904\pi$
$632$	6.00000	0.238667
$633$	−8.00000	−0.317971
$634$	−31.0000	−1.23117
$635$	14.0000	0.555573
$636$	14.0000	0.555136
$637$	12.0000	0.475457
$638$	−15.0000	−0.593856
$639$	28.0000	1.10766
$640$	2.00000	0.0790569
$641$	−24.0000	−0.947943	−0.473972	−	0.880540i	$-0.657180\pi$
$641$	−24.0000	−0.947943	−0.473972	+	0.880540i	$0.657180\pi$
$642$	10.0000	0.394669
$643$	32.0000	1.26196	0.630978	−	0.775800i	$-0.282654\pi$
$643$	32.0000	1.26196	0.630978	+	0.775800i	$0.282654\pi$
$644$	4.00000	0.157622
$645$	16.0000	0.629999
$646$	−6.00000	−0.236067
$647$	−46.0000	−1.80845	−0.904223	−	0.427060i	$-0.859549\pi$
$647$	−46.0000	−1.80845	−0.904223	+	0.427060i	$0.859549\pi$
$648$	−1.00000	−0.0392837
$649$	15.0000	0.588802
$650$	−2.00000	−0.0784465
$651$	−1.00000	−0.0391931
$652$	−14.0000	−0.548282
$653$	−16.0000	−0.626128	−0.313064	−	0.949732i	$-0.601356\pi$
$653$	−16.0000	−0.626128	−0.313064	+	0.949732i	$0.601356\pi$
$654$	−13.0000	−0.508340
$655$	40.0000	1.56293
$656$	6.00000	0.234261
$657$	8.00000	0.312110
$658$	−12.0000	−0.467809
$659$	−4.00000	−0.155818	−0.0779089	−	0.996960i	$-0.524824\pi$
$659$	−4.00000	−0.155818	−0.0779089	+	0.996960i	$0.524824\pi$
$660$	−10.0000	−0.389249
$661$	8.00000	0.311164	0.155582	−	0.987823i	$-0.450275\pi$
$661$	8.00000	0.311164	0.155582	+	0.987823i	$0.450275\pi$
$662$	−10.0000	−0.388661
$663$	−6.00000	−0.233021
$664$	1.00000	0.0388075
$665$	4.00000	0.155113
$666$	2.00000	0.0774984
$667$	−12.0000	−0.464642
$668$	9.00000	0.348220
$669$	8.00000	0.309298
$670$	4.00000	0.154533
$671$	35.0000	1.35116
$672$	1.00000	0.0385758
$673$	9.00000	0.346925	0.173462	−	0.984841i	$-0.444505\pi$
$673$	9.00000	0.346925	0.173462	+	0.984841i	$0.444505\pi$
$674$	2.00000	0.0770371
$675$	−5.00000	−0.192450
$676$	−9.00000	−0.346154
$677$	12.0000	0.461197	0.230599	−	0.973049i	$-0.425932\pi$
$677$	12.0000	0.461197	0.230599	+	0.973049i	$0.425932\pi$
$678$	−9.00000	−0.345643
$679$	12.0000	0.460518
$680$	−6.00000	−0.230089
$681$	4.00000	0.153280
$682$	5.00000	0.191460
$683$	4.00000	0.153056	0.0765279	−	0.997067i	$-0.475617\pi$
$683$	4.00000	0.153056	0.0765279	+	0.997067i	$0.475617\pi$
$684$	4.00000	0.152944
$685$	−28.0000	−1.06983
$686$	13.0000	0.496342
$687$	26.0000	0.991962
$688$	8.00000	0.304997
$689$	28.0000	1.06672
$690$	−8.00000	−0.304555
$691$	37.0000	1.40755	0.703773	−	0.710425i	$-0.251497\pi$
$691$	37.0000	1.40755	0.703773	+	0.710425i	$0.251497\pi$
$692$	9.00000	0.342129
$693$	10.0000	0.379869
$694$	−26.0000	−0.986947
$695$	−28.0000	−1.06210
$696$	−3.00000	−0.113715
$697$	−18.0000	−0.681799
$698$	−19.0000	−0.719161
$699$	22.0000	0.832116
$700$	−1.00000	−0.0377964
$701$	−34.0000	−1.28416	−0.642081	−	0.766637i	$-0.721929\pi$
$701$	−34.0000	−1.28416	−0.642081	+	0.766637i	$0.721929\pi$
$702$	10.0000	0.377426
$703$	−2.00000	−0.0754314
$704$	−5.00000	−0.188445
$705$	24.0000	0.903892
$706$	−31.0000	−1.16670
$707$	−6.00000	−0.225653
$708$	3.00000	0.112747
$709$	22.0000	0.826227	0.413114	−	0.910679i	$-0.364441\pi$
$709$	22.0000	0.826227	0.413114	+	0.910679i	$0.364441\pi$
$710$	−28.0000	−1.05082
$711$	12.0000	0.450035
$712$	−4.00000	−0.149906
$713$	4.00000	0.149801
$714$	−3.00000	−0.112272
$715$	−20.0000	−0.747958
$716$	−10.0000	−0.373718
$717$	−4.00000	−0.149383
$718$	35.0000	1.30619
$719$	0	0		−	1.00000i	$-0.5\pi$
$719$	0	0			1.00000i	$0.5\pi$
$720$	4.00000	0.149071
$721$	−8.00000	−0.297936
$722$	15.0000	0.558242
$723$	−23.0000	−0.855379
$724$	−2.00000	−0.0743294
$725$	3.00000	0.111417
$726$	14.0000	0.519589
$727$	35.0000	1.29808	0.649039	−	0.760755i	$-0.275171\pi$
$727$	35.0000	1.29808	0.649039	+	0.760755i	$0.275171\pi$
$728$	2.00000	0.0741249
$729$	13.0000	0.481481
$730$	−8.00000	−0.296093
$731$	−24.0000	−0.887672
$732$	7.00000	0.258727
$733$	−29.0000	−1.07114	−0.535570	−	0.844491i	$-0.679903\pi$
$733$	−29.0000	−1.07114	−0.535570	+	0.844491i	$0.679903\pi$
$734$	−34.0000	−1.25496
$735$	−12.0000	−0.442627
$736$	−4.00000	−0.147442
$737$	−10.0000	−0.368355
$738$	12.0000	0.441726
$739$	−16.0000	−0.588570	−0.294285	−	0.955718i	$-0.595081\pi$
$739$	−16.0000	−0.588570	−0.294285	+	0.955718i	$0.595081\pi$
$740$	−2.00000	−0.0735215
$741$	−4.00000	−0.146944
$742$	14.0000	0.513956
$743$	−4.00000	−0.146746	−0.0733729	−	0.997305i	$-0.523376\pi$
$743$	−4.00000	−0.146746	−0.0733729	+	0.997305i	$0.523376\pi$
$744$	1.00000	0.0366618
$745$	−40.0000	−1.46549
$746$	−1.00000	−0.0366126
$747$	2.00000	0.0731762
$748$	15.0000	0.548454
$749$	10.0000	0.365392
$750$	12.0000	0.438178
$751$	16.0000	0.583848	0.291924	−	0.956441i	$-0.405705\pi$
$751$	16.0000	0.583848	0.291924	+	0.956441i	$0.405705\pi$
$752$	12.0000	0.437595
$753$	−16.0000	−0.583072
$754$	−6.00000	−0.218507
$755$	−10.0000	−0.363937
$756$	5.00000	0.181848
$757$	3.00000	0.109037	0.0545184	−	0.998513i	$-0.482638\pi$
$757$	3.00000	0.109037	0.0545184	+	0.998513i	$0.482638\pi$
$758$	−28.0000	−1.01701
$759$	20.0000	0.725954
$760$	−4.00000	−0.145095
$761$	−20.0000	−0.724999	−0.362500	−	0.931984i	$-0.618077\pi$
$761$	−20.0000	−0.724999	−0.362500	+	0.931984i	$0.618077\pi$
$762$	−7.00000	−0.253583
$763$	−13.0000	−0.470632
$764$	−15.0000	−0.542681
$765$	−12.0000	−0.433861
$766$	9.00000	0.325183
$767$	6.00000	0.216647
$768$	−1.00000	−0.0360844
$769$	−28.0000	−1.00971	−0.504853	−	0.863205i	$-0.668453\pi$
$769$	−28.0000	−1.00971	−0.504853	+	0.863205i	$0.668453\pi$
$770$	−10.0000	−0.360375
$771$	−26.0000	−0.936367
$772$	−22.0000	−0.791797
$773$	14.0000	0.503545	0.251773	−	0.967786i	$-0.418987\pi$
$773$	14.0000	0.503545	0.251773	+	0.967786i	$0.418987\pi$
$774$	16.0000	0.575108
$775$	−1.00000	−0.0359211
$776$	−12.0000	−0.430775
$777$	−1.00000	−0.0358748
$778$	32.0000	1.14726
$779$	−12.0000	−0.429945
$780$	−4.00000	−0.143223
$781$	70.0000	2.50480
$782$	12.0000	0.429119
$783$	−15.0000	−0.536056
$784$	−6.00000	−0.214286
$785$	20.0000	0.713831
$786$	−20.0000	−0.713376
$787$	28.0000	0.998092	0.499046	−	0.866575i	$-0.333684\pi$
$787$	28.0000	0.998092	0.499046	+	0.866575i	$0.333684\pi$
$788$	−17.0000	−0.605600
$789$	14.0000	0.498413
$790$	−12.0000	−0.426941
$791$	−9.00000	−0.320003
$792$	−10.0000	−0.355335
$793$	14.0000	0.497155
$794$	−18.0000	−0.638796
$795$	−28.0000	−0.993058
$796$	8.00000	0.283552
$797$	16.0000	0.566749	0.283375	−	0.959009i	$-0.408546\pi$
$797$	16.0000	0.566749	0.283375	+	0.959009i	$0.408546\pi$
$798$	−2.00000	−0.0707992
$799$	−36.0000	−1.27359
$800$	1.00000	0.0353553
$801$	−8.00000	−0.282666
$802$	−30.0000	−1.05934
$803$	20.0000	0.705785
$804$	−2.00000	−0.0705346
$805$	−8.00000	−0.281963
$806$	2.00000	0.0704470
$807$	−18.0000	−0.633630
$808$	6.00000	0.211079
$809$	4.00000	0.140633	0.0703163	−	0.997525i	$-0.477599\pi$
$809$	4.00000	0.140633	0.0703163	+	0.997525i	$0.477599\pi$
$810$	2.00000	0.0702728
$811$	−4.00000	−0.140459	−0.0702295	−	0.997531i	$-0.522373\pi$
$811$	−4.00000	−0.140459	−0.0702295	+	0.997531i	$0.522373\pi$
$812$	−3.00000	−0.105279
$813$	12.0000	0.420858
$814$	5.00000	0.175250
$815$	28.0000	0.980797
$816$	3.00000	0.105021
$817$	−16.0000	−0.559769
$818$	29.0000	1.01396
$819$	4.00000	0.139771
$820$	−12.0000	−0.419058
$821$	24.0000	0.837606	0.418803	−	0.908077i	$-0.362450\pi$
$821$	24.0000	0.837606	0.418803	+	0.908077i	$0.362450\pi$
$822$	14.0000	0.488306
$823$	4.00000	0.139431	0.0697156	−	0.997567i	$-0.477791\pi$
$823$	4.00000	0.139431	0.0697156	+	0.997567i	$0.477791\pi$
$824$	8.00000	0.278693
$825$	−5.00000	−0.174078
$826$	3.00000	0.104383
$827$	4.00000	0.139094	0.0695468	−	0.997579i	$-0.477845\pi$
$827$	4.00000	0.139094	0.0695468	+	0.997579i	$0.477845\pi$
$828$	−8.00000	−0.278019
$829$	−34.0000	−1.18087	−0.590434	−	0.807086i	$-0.701044\pi$
$829$	−34.0000	−1.18087	−0.590434	+	0.807086i	$0.701044\pi$
$830$	−2.00000	−0.0694210
$831$	22.0000	0.763172
$832$	−2.00000	−0.0693375
$833$	18.0000	0.623663
$834$	14.0000	0.484780
$835$	−18.0000	−0.622916
$836$	10.0000	0.345857
$837$	5.00000	0.172825
$838$	−19.0000	−0.656344
$839$	−25.0000	−0.863096	−0.431548	−	0.902090i	$-0.642032\pi$
$839$	−25.0000	−0.863096	−0.431548	+	0.902090i	$0.642032\pi$
$840$	−2.00000	−0.0690066
$841$	−20.0000	−0.689655
$842$	−22.0000	−0.758170
$843$	−12.0000	−0.413302
$844$	8.00000	0.275371
$845$	18.0000	0.619219
$846$	24.0000	0.825137
$847$	14.0000	0.481046
$848$	−14.0000	−0.480762
$849$	−14.0000	−0.480479
$850$	−3.00000	−0.102899
$851$	4.00000	0.137118
$852$	14.0000	0.479632
$853$	5.00000	0.171197	0.0855984	−	0.996330i	$-0.472720\pi$
$853$	5.00000	0.171197	0.0855984	+	0.996330i	$0.472720\pi$
$854$	7.00000	0.239535
$855$	−8.00000	−0.273594
$856$	−10.0000	−0.341793
$857$	−49.0000	−1.67381	−0.836904	−	0.547350i	$-0.815637\pi$
$857$	−49.0000	−1.67381	−0.836904	+	0.547350i	$0.815637\pi$
$858$	10.0000	0.341394
$859$	−23.0000	−0.784750	−0.392375	−	0.919805i	$-0.628346\pi$
$859$	−23.0000	−0.784750	−0.392375	+	0.919805i	$0.628346\pi$
$860$	−16.0000	−0.545595
$861$	−6.00000	−0.204479
$862$	−33.0000	−1.12398
$863$	41.0000	1.39566	0.697828	−	0.716265i	$-0.254150\pi$
$863$	41.0000	1.39566	0.697828	+	0.716265i	$0.254150\pi$
$864$	−5.00000	−0.170103
$865$	−18.0000	−0.612018
$866$	−28.0000	−0.951479
$867$	8.00000	0.271694
$868$	1.00000	0.0339422
$869$	30.0000	1.01768
$870$	6.00000	0.203419
$871$	−4.00000	−0.135535
$872$	13.0000	0.440236
$873$	−24.0000	−0.812277
$874$	8.00000	0.270604
$875$	12.0000	0.405674
$876$	4.00000	0.135147
$877$	10.0000	0.337676	0.168838	−	0.985644i	$-0.445999\pi$
$877$	10.0000	0.337676	0.168838	+	0.985644i	$0.445999\pi$
$878$	20.0000	0.674967
$879$	6.00000	0.202375
$880$	10.0000	0.337100
$881$	−43.0000	−1.44871	−0.724353	−	0.689429i	$-0.757862\pi$
$881$	−43.0000	−1.44871	−0.724353	+	0.689429i	$0.757862\pi$
$882$	−12.0000	−0.404061
$883$	2.00000	0.0673054	0.0336527	−	0.999434i	$-0.489286\pi$
$883$	2.00000	0.0673054	0.0336527	+	0.999434i	$0.489286\pi$
$884$	6.00000	0.201802
$885$	−6.00000	−0.201688
$886$	3.00000	0.100787
$887$	−36.0000	−1.20876	−0.604381	−	0.796696i	$-0.706579\pi$
$887$	−36.0000	−1.20876	−0.604381	+	0.796696i	$0.706579\pi$
$888$	1.00000	0.0335578
$889$	−7.00000	−0.234772
$890$	8.00000	0.268161
$891$	−5.00000	−0.167506
$892$	−8.00000	−0.267860
$893$	−24.0000	−0.803129
$894$	20.0000	0.668900
$895$	20.0000	0.668526
$896$	−1.00000	−0.0334077
$897$	8.00000	0.267112
$898$	2.00000	0.0667409
$899$	−3.00000	−0.100056
$900$	2.00000	0.0666667
$901$	42.0000	1.39922
$902$	30.0000	0.998891
$903$	−8.00000	−0.266223
$904$	9.00000	0.299336
$905$	4.00000	0.132964
$906$	5.00000	0.166114
$907$	33.0000	1.09575	0.547874	−	0.836561i	$-0.315438\pi$
$907$	33.0000	1.09575	0.547874	+	0.836561i	$0.315438\pi$
$908$	−4.00000	−0.132745
$909$	12.0000	0.398015
$910$	−4.00000	−0.132599
$911$	−41.0000	−1.35839	−0.679195	−	0.733958i	$-0.737671\pi$
$911$	−41.0000	−1.35839	−0.679195	+	0.733958i	$0.737671\pi$
$912$	2.00000	0.0662266
$913$	5.00000	0.165476
$914$	−18.0000	−0.595387
$915$	−14.0000	−0.462826
$916$	−26.0000	−0.859064
$917$	−20.0000	−0.660458
$918$	15.0000	0.495074
$919$	20.0000	0.659739	0.329870	−	0.944027i	$-0.392995\pi$
$919$	20.0000	0.659739	0.329870	+	0.944027i	$0.392995\pi$
$920$	8.00000	0.263752
$921$	32.0000	1.05444
$922$	36.0000	1.18560
$923$	28.0000	0.921631
$924$	5.00000	0.164488
$925$	−1.00000	−0.0328798
$926$	−7.00000	−0.230034
$927$	16.0000	0.525509
$928$	3.00000	0.0984798
$929$	−27.0000	−0.885841	−0.442921	−	0.896561i	$-0.646058\pi$
$929$	−27.0000	−0.885841	−0.442921	+	0.896561i	$0.646058\pi$
$930$	−2.00000	−0.0655826
$931$	12.0000	0.393284
$932$	−22.0000	−0.720634
$933$	−8.00000	−0.261908
$934$	36.0000	1.17796
$935$	−30.0000	−0.981105
$936$	−4.00000	−0.130744
$937$	−20.0000	−0.653372	−0.326686	−	0.945133i	$-0.605932\pi$
$937$	−20.0000	−0.653372	−0.326686	+	0.945133i	$0.605932\pi$
$938$	−2.00000	−0.0653023
$939$	13.0000	0.424239
$940$	−24.0000	−0.782794
$941$	11.0000	0.358590	0.179295	−	0.983795i	$-0.442618\pi$
$941$	11.0000	0.358590	0.179295	+	0.983795i	$0.442618\pi$
$942$	−10.0000	−0.325818
$943$	24.0000	0.781548
$944$	−3.00000	−0.0976417
$945$	−10.0000	−0.325300
$946$	40.0000	1.30051
$947$	−12.0000	−0.389948	−0.194974	−	0.980808i	$-0.562462\pi$
$947$	−12.0000	−0.389948	−0.194974	+	0.980808i	$0.562462\pi$
$948$	6.00000	0.194871
$949$	8.00000	0.259691
$950$	−2.00000	−0.0648886
$951$	−31.0000	−1.00524
$952$	3.00000	0.0972306
$953$	−19.0000	−0.615470	−0.307735	−	0.951472i	$-0.599571\pi$
$953$	−19.0000	−0.615470	−0.307735	+	0.951472i	$0.599571\pi$
$954$	−28.0000	−0.906533
$955$	30.0000	0.970777
$956$	4.00000	0.129369
$957$	−15.0000	−0.484881
$958$	15.0000	0.484628
$959$	14.0000	0.452084
$960$	2.00000	0.0645497
$961$	−30.0000	−0.967742
$962$	2.00000	0.0644826
$963$	−20.0000	−0.644491
$964$	23.0000	0.740780
$965$	44.0000	1.41641
$966$	4.00000	0.128698
$967$	−50.0000	−1.60789	−0.803946	−	0.594703i	$-0.797270\pi$
$967$	−50.0000	−1.60789	−0.803946	+	0.594703i	$0.797270\pi$
$968$	−14.0000	−0.449977
$969$	−6.00000	−0.192748
$970$	24.0000	0.770594
$971$	30.0000	0.962746	0.481373	−	0.876516i	$-0.340138\pi$
$971$	30.0000	0.962746	0.481373	+	0.876516i	$0.340138\pi$
$972$	−16.0000	−0.513200
$973$	14.0000	0.448819
$974$	12.0000	0.384505
$975$	−2.00000	−0.0640513
$976$	−7.00000	−0.224065
$977$	−43.0000	−1.37569	−0.687846	−	0.725857i	$-0.741444\pi$
$977$	−43.0000	−1.37569	−0.687846	+	0.725857i	$0.741444\pi$
$978$	−14.0000	−0.447671
$979$	−20.0000	−0.639203
$980$	12.0000	0.383326
$981$	26.0000	0.830116
$982$	30.0000	0.957338
$983$	−36.0000	−1.14822	−0.574111	−	0.818778i	$-0.694652\pi$
$983$	−36.0000	−1.14822	−0.574111	+	0.818778i	$0.694652\pi$
$984$	6.00000	0.191273
$985$	34.0000	1.08333
$986$	−9.00000	−0.286618
$987$	−12.0000	−0.381964
$988$	4.00000	0.127257
$989$	32.0000	1.01754
$990$	20.0000	0.635642
$991$	45.0000	1.42947	0.714736	−	0.699394i	$-0.246547\pi$
$991$	45.0000	1.42947	0.714736	+	0.699394i	$0.246547\pi$
$992$	−1.00000	−0.0317500
$993$	−10.0000	−0.317340
$994$	14.0000	0.444053
$995$	−16.0000	−0.507234
$996$	1.00000	0.0316862
$997$	3.00000	0.0950110	0.0475055	−	0.998871i	$-0.484873\pi$
$997$	3.00000	0.0950110	0.0475055	+	0.998871i	$0.484873\pi$
$998$	−39.0000	−1.23452
$999$	5.00000	0.158193

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	166.2.a.a.1.1	✓	1
3.2	odd	2		1494.2.a.e.1.1		1
4.3	odd	2		1328.2.a.b.1.1		1
5.4	even	2		4150.2.a.n.1.1		1
7.6	odd	2		8134.2.a.b.1.1		1
8.3	odd	2		5312.2.a.f.1.1		1
8.5	even	2		5312.2.a.n.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
166.2.a.a.1.1	✓	1	1.1	even	1	trivial
1328.2.a.b.1.1		1	4.3	odd	2
1494.2.a.e.1.1		1	3.2	odd	2
4150.2.a.n.1.1		1	5.4	even	2
5312.2.a.f.1.1		1	8.3	odd	2
5312.2.a.n.1.1		1	8.5	even	2
8134.2.a.b.1.1		1	7.6	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:	\( N \)	\(=\)	\( 166 = 2 \cdot 83 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	166.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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