LMFDB - Embedded newform 201.2.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,2,Mod(1,201)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(201, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("201.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	201.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:	$1.60499308063$
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	$\chi$	$=$	201.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} +1.00000 q^{3} -1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -5.00000 q^{7} +3.00000 q^{8} +1.00000 q^{9} +O(q^{10})$

\(q-1.00000 q^{2} +1.00000 q^{3} -1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -5.00000 q^{7} +3.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -4.00000 q^{11} -1.00000 q^{12} -4.00000 q^{13} +5.00000 q^{14} -1.00000 q^{15} -1.00000 q^{16} +6.00000 q^{17} -1.00000 q^{18} -2.00000 q^{19} +1.00000 q^{20} -5.00000 q^{21} +4.00000 q^{22} -3.00000 q^{23} +3.00000 q^{24} -4.00000 q^{25} +4.00000 q^{26} +1.00000 q^{27} +5.00000 q^{28} +4.00000 q^{29} +1.00000 q^{30} -7.00000 q^{31} -5.00000 q^{32} -4.00000 q^{33} -6.00000 q^{34} +5.00000 q^{35} -1.00000 q^{36} +5.00000 q^{37} +2.00000 q^{38} -4.00000 q^{39} -3.00000 q^{40} -3.00000 q^{41} +5.00000 q^{42} +7.00000 q^{43} +4.00000 q^{44} -1.00000 q^{45} +3.00000 q^{46} +8.00000 q^{47} -1.00000 q^{48} +18.0000 q^{49} +4.00000 q^{50} +6.00000 q^{51} +4.00000 q^{52} -5.00000 q^{53} -1.00000 q^{54} +4.00000 q^{55} -15.0000 q^{56} -2.00000 q^{57} -4.00000 q^{58} +3.00000 q^{59} +1.00000 q^{60} -2.00000 q^{61} +7.00000 q^{62} -5.00000 q^{63} +7.00000 q^{64} +4.00000 q^{65} +4.00000 q^{66} +1.00000 q^{67} -6.00000 q^{68} -3.00000 q^{69} -5.00000 q^{70} -12.0000 q^{71} +3.00000 q^{72} -13.0000 q^{73} -5.00000 q^{74} -4.00000 q^{75} +2.00000 q^{76} +20.0000 q^{77} +4.00000 q^{78} -8.00000 q^{79} +1.00000 q^{80} +1.00000 q^{81} +3.00000 q^{82} +1.00000 q^{83} +5.00000 q^{84} -6.00000 q^{85} -7.00000 q^{86} +4.00000 q^{87} -12.0000 q^{88} +4.00000 q^{89} +1.00000 q^{90} +20.0000 q^{91} +3.00000 q^{92} -7.00000 q^{93} -8.00000 q^{94} +2.00000 q^{95} -5.00000 q^{96} -12.0000 q^{97} -18.0000 q^{98} -4.00000 q^{99} +O(q^{100})\)

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
$3$	1.00000	0.577350
$4$	−1.00000	−0.500000
$5$	−1.00000	−0.447214	−0.223607	−	0.974679i	$-0.571783\pi$
$5$	−1.00000	−0.447214	−0.223607	+	0.974679i	$0.571783\pi$
$6$	−1.00000	−0.408248
$7$	−5.00000	−1.88982	−0.944911	−	0.327327i	$-0.893852\pi$
$7$	−5.00000	−1.88982	−0.944911	+	0.327327i	$0.893852\pi$
$8$	3.00000	1.06066
$9$	1.00000	0.333333
$10$	1.00000	0.316228
$11$	−4.00000	−1.20605	−0.603023	−	0.797724i	$-0.706037\pi$
$11$	−4.00000	−1.20605	−0.603023	+	0.797724i	$0.706037\pi$
$12$	−1.00000	−0.288675
$13$	−4.00000	−1.10940	−0.554700	−	0.832050i	$-0.687167\pi$
$13$	−4.00000	−1.10940	−0.554700	+	0.832050i	$0.687167\pi$
$14$	5.00000	1.33631
$15$	−1.00000	−0.258199
$16$	−1.00000	−0.250000
$17$	6.00000	1.45521	0.727607	−	0.685994i	$-0.240633\pi$
$17$	6.00000	1.45521	0.727607	+	0.685994i	$0.240633\pi$
$18$	−1.00000	−0.235702
$19$	−2.00000	−0.458831	−0.229416	−	0.973329i	$-0.573682\pi$
$19$	−2.00000	−0.458831	−0.229416	+	0.973329i	$0.573682\pi$
$20$	1.00000	0.223607
$21$	−5.00000	−1.09109
$22$	4.00000	0.852803
$23$	−3.00000	−0.625543	−0.312772	−	0.949828i	$-0.601257\pi$
$23$	−3.00000	−0.625543	−0.312772	+	0.949828i	$0.601257\pi$
$24$	3.00000	0.612372
$25$	−4.00000	−0.800000
$26$	4.00000	0.784465
$27$	1.00000	0.192450
$28$	5.00000	0.944911
$29$	4.00000	0.742781	0.371391	−	0.928477i	$-0.378881\pi$
$29$	4.00000	0.742781	0.371391	+	0.928477i	$0.378881\pi$
$30$	1.00000	0.182574
$31$	−7.00000	−1.25724	−0.628619	−	0.777714i	$-0.716379\pi$
$31$	−7.00000	−1.25724	−0.628619	+	0.777714i	$0.716379\pi$
$32$	−5.00000	−0.883883
$33$	−4.00000	−0.696311
$34$	−6.00000	−1.02899
$35$	5.00000	0.845154
$36$	−1.00000	−0.166667
$37$	5.00000	0.821995	0.410997	−	0.911636i	$-0.365181\pi$
$37$	5.00000	0.821995	0.410997	+	0.911636i	$0.365181\pi$
$38$	2.00000	0.324443
$39$	−4.00000	−0.640513
$40$	−3.00000	−0.474342
$41$	−3.00000	−0.468521	−0.234261	−	0.972174i	$-0.575267\pi$
$41$	−3.00000	−0.468521	−0.234261	+	0.972174i	$0.575267\pi$
$42$	5.00000	0.771517
$43$	7.00000	1.06749	0.533745	−	0.845645i	$-0.320784\pi$
$43$	7.00000	1.06749	0.533745	+	0.845645i	$0.320784\pi$
$44$	4.00000	0.603023
$45$	−1.00000	−0.149071
$46$	3.00000	0.442326
$47$	8.00000	1.16692	0.583460	−	0.812142i	$-0.301699\pi$
$47$	8.00000	1.16692	0.583460	+	0.812142i	$0.301699\pi$
$48$	−1.00000	−0.144338
$49$	18.0000	2.57143
$50$	4.00000	0.565685
$51$	6.00000	0.840168
$52$	4.00000	0.554700
$53$	−5.00000	−0.686803	−0.343401	−	0.939189i	$-0.611579\pi$
$53$	−5.00000	−0.686803	−0.343401	+	0.939189i	$0.611579\pi$
$54$	−1.00000	−0.136083
$55$	4.00000	0.539360
$56$	−15.0000	−2.00446
$57$	−2.00000	−0.264906
$58$	−4.00000	−0.525226
$59$	3.00000	0.390567	0.195283	−	0.980747i	$-0.437437\pi$
$59$	3.00000	0.390567	0.195283	+	0.980747i	$0.437437\pi$
$60$	1.00000	0.129099
$61$	−2.00000	−0.256074	−0.128037	−	0.991769i	$-0.540868\pi$
$61$	−2.00000	−0.256074	−0.128037	+	0.991769i	$0.540868\pi$
$62$	7.00000	0.889001
$63$	−5.00000	−0.629941
$64$	7.00000	0.875000
$65$	4.00000	0.496139
$66$	4.00000	0.492366
$67$	1.00000	0.122169
$67$	1.00000	0.122169
$68$	−6.00000	−0.727607
$69$	−3.00000	−0.361158
$70$	−5.00000	−0.597614
$71$	−12.0000	−1.42414	−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000	−1.42414	−0.712069	+	0.702109i	$0.752242\pi$
$72$	3.00000	0.353553
$73$	−13.0000	−1.52153	−0.760767	−	0.649025i	$-0.775177\pi$
$73$	−13.0000	−1.52153	−0.760767	+	0.649025i	$0.775177\pi$
$74$	−5.00000	−0.581238
$75$	−4.00000	−0.461880
$76$	2.00000	0.229416
$77$	20.0000	2.27921
$78$	4.00000	0.452911
$79$	−8.00000	−0.900070	−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000	−0.900070	−0.450035	+	0.893011i	$0.648589\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	3.00000	0.331295
$83$	1.00000	0.109764	0.0548821	−	0.998493i	$-0.482522\pi$
$83$	1.00000	0.109764	0.0548821	+	0.998493i	$0.482522\pi$
$84$	5.00000	0.545545
$85$	−6.00000	−0.650791
$86$	−7.00000	−0.754829
$87$	4.00000	0.428845
$88$	−12.0000	−1.27920
$89$	4.00000	0.423999	0.212000	−	0.977270i	$-0.432002\pi$
$89$	4.00000	0.423999	0.212000	+	0.977270i	$0.432002\pi$
$90$	1.00000	0.105409
$91$	20.0000	2.09657
$92$	3.00000	0.312772
$93$	−7.00000	−0.725866
$94$	−8.00000	−0.825137
$95$	2.00000	0.205196
$96$	−5.00000	−0.510310
$97$	−12.0000	−1.21842	−0.609208	−	0.793011i	$-0.708512\pi$
$97$	−12.0000	−1.21842	−0.609208	+	0.793011i	$0.708512\pi$
$98$	−18.0000	−1.81827
$99$	−4.00000	−0.402015
$100$	4.00000	0.400000
$101$	−10.0000	−0.995037	−0.497519	−	0.867453i	$-0.665755\pi$
$101$	−10.0000	−0.995037	−0.497519	+	0.867453i	$0.665755\pi$
$102$	−6.00000	−0.594089
$103$	8.00000	0.788263	0.394132	−	0.919054i	$-0.371045\pi$
$103$	8.00000	0.788263	0.394132	+	0.919054i	$0.371045\pi$
$104$	−12.0000	−1.17670
$105$	5.00000	0.487950
$106$	5.00000	0.485643
$107$	−16.0000	−1.54678	−0.773389	−	0.633932i	$-0.781440\pi$
$107$	−16.0000	−1.54678	−0.773389	+	0.633932i	$0.781440\pi$
$108$	−1.00000	−0.0962250
$109$	−10.0000	−0.957826	−0.478913	−	0.877862i	$-0.658969\pi$
$109$	−10.0000	−0.957826	−0.478913	+	0.877862i	$0.658969\pi$
$110$	−4.00000	−0.381385
$111$	5.00000	0.474579
$112$	5.00000	0.472456
$113$	6.00000	0.564433	0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000	0.564433	0.282216	+	0.959351i	$0.408930\pi$
$114$	2.00000	0.187317
$115$	3.00000	0.279751
$116$	−4.00000	−0.371391
$117$	−4.00000	−0.369800
$118$	−3.00000	−0.276172
$119$	−30.0000	−2.75010
$120$	−3.00000	−0.273861
$121$	5.00000	0.454545
$122$	2.00000	0.181071
$123$	−3.00000	−0.270501
$124$	7.00000	0.628619
$125$	9.00000	0.804984
$126$	5.00000	0.445435
$127$	−8.00000	−0.709885	−0.354943	−	0.934888i	$-0.615500\pi$
$127$	−8.00000	−0.709885	−0.354943	+	0.934888i	$0.615500\pi$
$128$	3.00000	0.265165
$129$	7.00000	0.616316
$130$	−4.00000	−0.350823
$131$	−21.0000	−1.83478	−0.917389	−	0.397991i	$-0.869707\pi$
$131$	−21.0000	−1.83478	−0.917389	+	0.397991i	$0.869707\pi$
$132$	4.00000	0.348155
$133$	10.0000	0.867110
$134$	−1.00000	−0.0863868
$135$	−1.00000	−0.0860663
$136$	18.0000	1.54349
$137$	21.0000	1.79415	0.897076	−	0.441877i	$-0.145687\pi$
$137$	21.0000	1.79415	0.897076	+	0.441877i	$0.145687\pi$
$138$	3.00000	0.255377
$139$	13.0000	1.10265	0.551323	−	0.834292i	$-0.314123\pi$
$139$	13.0000	1.10265	0.551323	+	0.834292i	$0.314123\pi$
$140$	−5.00000	−0.422577
$141$	8.00000	0.673722
$142$	12.0000	1.00702
$143$	16.0000	1.33799
$144$	−1.00000	−0.0833333
$145$	−4.00000	−0.332182
$146$	13.0000	1.07589
$147$	18.0000	1.48461
$148$	−5.00000	−0.410997
$149$	−12.0000	−0.983078	−0.491539	−	0.870855i	$-0.663566\pi$
$149$	−12.0000	−0.983078	−0.491539	+	0.870855i	$0.663566\pi$
$150$	4.00000	0.326599
$151$	−18.0000	−1.46482	−0.732410	−	0.680864i	$-0.761604\pi$
$151$	−18.0000	−1.46482	−0.732410	+	0.680864i	$0.761604\pi$
$152$	−6.00000	−0.486664
$153$	6.00000	0.485071
$154$	−20.0000	−1.61165
$155$	7.00000	0.562254
$156$	4.00000	0.320256
$157$	−9.00000	−0.718278	−0.359139	−	0.933284i	$-0.616930\pi$
$157$	−9.00000	−0.718278	−0.359139	+	0.933284i	$0.616930\pi$
$158$	8.00000	0.636446
$159$	−5.00000	−0.396526
$160$	5.00000	0.395285
$161$	15.0000	1.18217
$162$	−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	$0.449930\pi$
$164$	3.00000	0.234261
$165$	4.00000	0.311400
$166$	−1.00000	−0.0776151
$167$	3.00000	0.232147	0.116073	−	0.993241i	$-0.462969\pi$
$167$	3.00000	0.232147	0.116073	+	0.993241i	$0.462969\pi$
$168$	−15.0000	−1.15728
$169$	3.00000	0.230769
$170$	6.00000	0.460179
$171$	−2.00000	−0.152944
$172$	−7.00000	−0.533745
$173$	14.0000	1.06440	0.532200	−	0.846619i	$-0.321365\pi$
$173$	14.0000	1.06440	0.532200	+	0.846619i	$0.321365\pi$
$174$	−4.00000	−0.303239
$175$	20.0000	1.51186
$176$	4.00000	0.301511
$177$	3.00000	0.225494
$178$	−4.00000	−0.299813
$179$	−6.00000	−0.448461	−0.224231	−	0.974536i	$-0.571987\pi$
$179$	−6.00000	−0.448461	−0.224231	+	0.974536i	$0.571987\pi$
$180$	1.00000	0.0745356
$181$	7.00000	0.520306	0.260153	−	0.965567i	$-0.416227\pi$
$181$	7.00000	0.520306	0.260153	+	0.965567i	$0.416227\pi$
$182$	−20.0000	−1.48250
$183$	−2.00000	−0.147844
$184$	−9.00000	−0.663489
$185$	−5.00000	−0.367607
$186$	7.00000	0.513265
$187$	−24.0000	−1.75505
$188$	−8.00000	−0.583460
$189$	−5.00000	−0.363696
$190$	−2.00000	−0.145095
$191$	24.0000	1.73658	0.868290	−	0.496058i	$-0.165220\pi$
$191$	24.0000	1.73658	0.868290	+	0.496058i	$0.165220\pi$
$192$	7.00000	0.505181
$193$	13.0000	0.935760	0.467880	−	0.883792i	$-0.345018\pi$
$193$	13.0000	0.935760	0.467880	+	0.883792i	$0.345018\pi$
$194$	12.0000	0.861550
$195$	4.00000	0.286446
$196$	−18.0000	−1.28571
$197$	25.0000	1.78118	0.890588	−	0.454811i	$-0.150293\pi$
$197$	25.0000	1.78118	0.890588	+	0.454811i	$0.150293\pi$
$198$	4.00000	0.284268
$199$	−20.0000	−1.41776	−0.708881	−	0.705328i	$-0.750800\pi$
$199$	−20.0000	−1.41776	−0.708881	+	0.705328i	$0.750800\pi$
$200$	−12.0000	−0.848528
$201$	1.00000	0.0705346
$202$	10.0000	0.703598
$203$	−20.0000	−1.40372
$204$	−6.00000	−0.420084
$205$	3.00000	0.209529
$206$	−8.00000	−0.557386
$207$	−3.00000	−0.208514
$208$	4.00000	0.277350
$209$	8.00000	0.553372
$210$	−5.00000	−0.345033
$211$	6.00000	0.413057	0.206529	−	0.978441i	$-0.433783\pi$
$211$	6.00000	0.413057	0.206529	+	0.978441i	$0.433783\pi$
$212$	5.00000	0.343401
$213$	−12.0000	−0.822226
$214$	16.0000	1.09374
$215$	−7.00000	−0.477396
$216$	3.00000	0.204124
$217$	35.0000	2.37595
$218$	10.0000	0.677285
$219$	−13.0000	−0.878459
$220$	−4.00000	−0.269680
$221$	−24.0000	−1.61441
$222$	−5.00000	−0.335578
$223$	2.00000	0.133930	0.0669650	−	0.997755i	$-0.478668\pi$
$223$	2.00000	0.133930	0.0669650	+	0.997755i	$0.478668\pi$
$224$	25.0000	1.67038
$225$	−4.00000	−0.266667
$226$	−6.00000	−0.399114
$227$	−9.00000	−0.597351	−0.298675	−	0.954355i	$-0.596545\pi$
$227$	−9.00000	−0.597351	−0.298675	+	0.954355i	$0.596545\pi$
$228$	2.00000	0.132453
$229$	10.0000	0.660819	0.330409	−	0.943838i	$-0.392813\pi$
$229$	10.0000	0.660819	0.330409	+	0.943838i	$0.392813\pi$
$230$	−3.00000	−0.197814
$231$	20.0000	1.31590
$232$	12.0000	0.787839
$233$	1.00000	0.0655122	0.0327561	−	0.999463i	$-0.489572\pi$
$233$	1.00000	0.0655122	0.0327561	+	0.999463i	$0.489572\pi$
$234$	4.00000	0.261488
$235$	−8.00000	−0.521862
$236$	−3.00000	−0.195283
$237$	−8.00000	−0.519656
$238$	30.0000	1.94461
$239$	−14.0000	−0.905585	−0.452792	−	0.891616i	$-0.649572\pi$
$239$	−14.0000	−0.905585	−0.452792	+	0.891616i	$0.649572\pi$
$240$	1.00000	0.0645497
$241$	−25.0000	−1.61039	−0.805196	−	0.593009i	$-0.797940\pi$
$241$	−25.0000	−1.61039	−0.805196	+	0.593009i	$0.797940\pi$
$242$	−5.00000	−0.321412
$243$	1.00000	0.0641500
$244$	2.00000	0.128037
$245$	−18.0000	−1.14998
$246$	3.00000	0.191273
$247$	8.00000	0.509028
$248$	−21.0000	−1.33350
$249$	1.00000	0.0633724
$250$	−9.00000	−0.569210
$251$	−8.00000	−0.504956	−0.252478	−	0.967603i	$-0.581245\pi$
$251$	−8.00000	−0.504956	−0.252478	+	0.967603i	$0.581245\pi$
$252$	5.00000	0.314970
$253$	12.0000	0.754434
$254$	8.00000	0.501965
$255$	−6.00000	−0.375735
$256$	−17.0000	−1.06250
$257$	8.00000	0.499026	0.249513	−	0.968371i	$-0.419729\pi$
$257$	8.00000	0.499026	0.249513	+	0.968371i	$0.419729\pi$
$258$	−7.00000	−0.435801
$259$	−25.0000	−1.55342
$260$	−4.00000	−0.248069
$261$	4.00000	0.247594
$262$	21.0000	1.29738
$263$	7.00000	0.431638	0.215819	−	0.976433i	$-0.430758\pi$
$263$	7.00000	0.431638	0.215819	+	0.976433i	$0.430758\pi$
$264$	−12.0000	−0.738549
$265$	5.00000	0.307148
$266$	−10.0000	−0.613139
$267$	4.00000	0.244796
$268$	−1.00000	−0.0610847
$269$	14.0000	0.853595	0.426798	−	0.904347i	$-0.359642\pi$
$269$	14.0000	0.853595	0.426798	+	0.904347i	$0.359642\pi$
$270$	1.00000	0.0608581
$271$	−16.0000	−0.971931	−0.485965	−	0.873978i	$-0.661532\pi$
$271$	−16.0000	−0.971931	−0.485965	+	0.873978i	$0.661532\pi$
$272$	−6.00000	−0.363803
$273$	20.0000	1.21046
$274$	−21.0000	−1.26866
$275$	16.0000	0.964836
$276$	3.00000	0.180579
$277$	−23.0000	−1.38194	−0.690968	−	0.722885i	$-0.742815\pi$
$277$	−23.0000	−1.38194	−0.690968	+	0.722885i	$0.742815\pi$
$278$	−13.0000	−0.779688
$279$	−7.00000	−0.419079
$280$	15.0000	0.896421
$281$	6.00000	0.357930	0.178965	−	0.983855i	$-0.442725\pi$
$281$	6.00000	0.357930	0.178965	+	0.983855i	$0.442725\pi$
$282$	−8.00000	−0.476393
$283$	6.00000	0.356663	0.178331	−	0.983970i	$-0.442930\pi$
$283$	6.00000	0.356663	0.178331	+	0.983970i	$0.442930\pi$
$284$	12.0000	0.712069
$285$	2.00000	0.118470
$286$	−16.0000	−0.946100
$287$	15.0000	0.885422
$288$	−5.00000	−0.294628
$289$	19.0000	1.11765
$290$	4.00000	0.234888
$291$	−12.0000	−0.703452
$292$	13.0000	0.760767
$293$	30.0000	1.75262	0.876309	−	0.481749i	$-0.159998\pi$
$293$	30.0000	1.75262	0.876309	+	0.481749i	$0.159998\pi$
$294$	−18.0000	−1.04978
$295$	−3.00000	−0.174667
$296$	15.0000	0.871857
$297$	−4.00000	−0.232104
$298$	12.0000	0.695141
$299$	12.0000	0.693978
$300$	4.00000	0.230940
$301$	−35.0000	−2.01737
$302$	18.0000	1.03578
$303$	−10.0000	−0.574485
$304$	2.00000	0.114708
$305$	2.00000	0.114520
$306$	−6.00000	−0.342997
$307$	8.00000	0.456584	0.228292	−	0.973593i	$-0.426686\pi$
$307$	8.00000	0.456584	0.228292	+	0.973593i	$0.426686\pi$
$308$	−20.0000	−1.13961
$309$	8.00000	0.455104
$310$	−7.00000	−0.397573
$311$	−6.00000	−0.340229	−0.170114	−	0.985424i	$-0.554414\pi$
$311$	−6.00000	−0.340229	−0.170114	+	0.985424i	$0.554414\pi$
$312$	−12.0000	−0.679366
$313$	−10.0000	−0.565233	−0.282617	−	0.959233i	$-0.591202\pi$
$313$	−10.0000	−0.565233	−0.282617	+	0.959233i	$0.591202\pi$
$314$	9.00000	0.507899
$315$	5.00000	0.281718
$316$	8.00000	0.450035
$317$	6.00000	0.336994	0.168497	−	0.985702i	$-0.446109\pi$
$317$	6.00000	0.336994	0.168497	+	0.985702i	$0.446109\pi$
$318$	5.00000	0.280386
$319$	−16.0000	−0.895828
$320$	−7.00000	−0.391312
$321$	−16.0000	−0.893033
$322$	−15.0000	−0.835917
$323$	−12.0000	−0.667698
$324$	−1.00000	−0.0555556
$325$	16.0000	0.887520
$326$	−4.00000	−0.221540
$327$	−10.0000	−0.553001
$328$	−9.00000	−0.496942
$329$	−40.0000	−2.20527
$330$	−4.00000	−0.220193
$331$	33.0000	1.81384	0.906922	−	0.421299i	$-0.138426\pi$
$331$	33.0000	1.81384	0.906922	+	0.421299i	$0.138426\pi$
$332$	−1.00000	−0.0548821
$333$	5.00000	0.273998
$334$	−3.00000	−0.164153
$335$	−1.00000	−0.0546358
$336$	5.00000	0.272772
$337$	−14.0000	−0.762629	−0.381314	−	0.924445i	$-0.624528\pi$
$337$	−14.0000	−0.762629	−0.381314	+	0.924445i	$0.624528\pi$
$338$	−3.00000	−0.163178
$339$	6.00000	0.325875
$340$	6.00000	0.325396
$341$	28.0000	1.51629
$342$	2.00000	0.108148
$343$	−55.0000	−2.96972
$344$	21.0000	1.13224
$345$	3.00000	0.161515
$346$	−14.0000	−0.752645
$347$	24.0000	1.28839	0.644194	−	0.764862i	$-0.277193\pi$
$347$	24.0000	1.28839	0.644194	+	0.764862i	$0.277193\pi$
$348$	−4.00000	−0.214423
$349$	15.0000	0.802932	0.401466	−	0.915874i	$-0.368501\pi$
$349$	15.0000	0.802932	0.401466	+	0.915874i	$0.368501\pi$
$350$	−20.0000	−1.06904
$351$	−4.00000	−0.213504
$352$	20.0000	1.06600
$353$	−21.0000	−1.11772	−0.558859	−	0.829263i	$-0.688761\pi$
$353$	−21.0000	−1.11772	−0.558859	+	0.829263i	$0.688761\pi$
$354$	−3.00000	−0.159448
$355$	12.0000	0.636894
$356$	−4.00000	−0.212000
$357$	−30.0000	−1.58777
$358$	6.00000	0.317110
$359$	−11.0000	−0.580558	−0.290279	−	0.956942i	$-0.593748\pi$
$359$	−11.0000	−0.580558	−0.290279	+	0.956942i	$0.593748\pi$
$360$	−3.00000	−0.158114
$361$	−15.0000	−0.789474
$362$	−7.00000	−0.367912
$363$	5.00000	0.262432
$364$	−20.0000	−1.04828
$365$	13.0000	0.680451
$366$	2.00000	0.104542
$367$	16.0000	0.835193	0.417597	−	0.908633i	$-0.362873\pi$
$367$	16.0000	0.835193	0.417597	+	0.908633i	$0.362873\pi$
$368$	3.00000	0.156386
$369$	−3.00000	−0.156174
$370$	5.00000	0.259938
$371$	25.0000	1.29794
$372$	7.00000	0.362933
$373$	−18.0000	−0.932005	−0.466002	−	0.884783i	$-0.654306\pi$
$373$	−18.0000	−0.932005	−0.466002	+	0.884783i	$0.654306\pi$
$374$	24.0000	1.24101
$375$	9.00000	0.464758
$376$	24.0000	1.23771
$377$	−16.0000	−0.824042
$378$	5.00000	0.257172
$379$	9.00000	0.462299	0.231149	−	0.972918i	$-0.425751\pi$
$379$	9.00000	0.462299	0.231149	+	0.972918i	$0.425751\pi$
$380$	−2.00000	−0.102598
$381$	−8.00000	−0.409852
$382$	−24.0000	−1.22795
$383$	8.00000	0.408781	0.204390	−	0.978889i	$-0.434479\pi$
$383$	8.00000	0.408781	0.204390	+	0.978889i	$0.434479\pi$
$384$	3.00000	0.153093
$385$	−20.0000	−1.01929
$386$	−13.0000	−0.661683
$387$	7.00000	0.355830
$388$	12.0000	0.609208
$389$	−16.0000	−0.811232	−0.405616	−	0.914044i	$-0.632943\pi$
$389$	−16.0000	−0.811232	−0.405616	+	0.914044i	$0.632943\pi$
$390$	−4.00000	−0.202548
$391$	−18.0000	−0.910299
$392$	54.0000	2.72741
$393$	−21.0000	−1.05931
$394$	−25.0000	−1.25948
$395$	8.00000	0.402524
$396$	4.00000	0.201008
$397$	26.0000	1.30490	0.652451	−	0.757831i	$-0.273741\pi$
$397$	26.0000	1.30490	0.652451	+	0.757831i	$0.273741\pi$
$398$	20.0000	1.00251
$399$	10.0000	0.500626
$400$	4.00000	0.200000
$401$	−17.0000	−0.848939	−0.424470	−	0.905442i	$-0.639539\pi$
$401$	−17.0000	−0.848939	−0.424470	+	0.905442i	$0.639539\pi$
$402$	−1.00000	−0.0498755
$403$	28.0000	1.39478
$404$	10.0000	0.497519
$405$	−1.00000	−0.0496904
$406$	20.0000	0.992583
$407$	−20.0000	−0.991363
$408$	18.0000	0.891133
$409$	20.0000	0.988936	0.494468	−	0.869196i	$-0.335363\pi$
$409$	20.0000	0.988936	0.494468	+	0.869196i	$0.335363\pi$
$410$	−3.00000	−0.148159
$411$	21.0000	1.03585
$412$	−8.00000	−0.394132
$413$	−15.0000	−0.738102
$414$	3.00000	0.147442
$415$	−1.00000	−0.0490881
$416$	20.0000	0.980581
$417$	13.0000	0.636613
$418$	−8.00000	−0.391293
$419$	33.0000	1.61216	0.806078	−	0.591810i	$-0.201586\pi$
$419$	33.0000	1.61216	0.806078	+	0.591810i	$0.201586\pi$
$420$	−5.00000	−0.243975
$421$	3.00000	0.146211	0.0731055	−	0.997324i	$-0.476709\pi$
$421$	3.00000	0.146211	0.0731055	+	0.997324i	$0.476709\pi$
$422$	−6.00000	−0.292075
$423$	8.00000	0.388973
$424$	−15.0000	−0.728464
$425$	−24.0000	−1.16417
$426$	12.0000	0.581402
$427$	10.0000	0.483934
$428$	16.0000	0.773389
$429$	16.0000	0.772487
$430$	7.00000	0.337570
$431$	3.00000	0.144505	0.0722525	−	0.997386i	$-0.476981\pi$
$431$	3.00000	0.144505	0.0722525	+	0.997386i	$0.476981\pi$
$432$	−1.00000	−0.0481125
$433$	12.0000	0.576683	0.288342	−	0.957528i	$-0.406896\pi$
$433$	12.0000	0.576683	0.288342	+	0.957528i	$0.406896\pi$
$434$	−35.0000	−1.68005
$435$	−4.00000	−0.191785
$436$	10.0000	0.478913
$437$	6.00000	0.287019
$438$	13.0000	0.621164
$439$	−16.0000	−0.763638	−0.381819	−	0.924237i	$-0.624702\pi$
$439$	−16.0000	−0.763638	−0.381819	+	0.924237i	$0.624702\pi$
$440$	12.0000	0.572078
$441$	18.0000	0.857143
$442$	24.0000	1.14156
$443$	−22.0000	−1.04525	−0.522626	−	0.852562i	$-0.675047\pi$
$443$	−22.0000	−1.04525	−0.522626	+	0.852562i	$0.675047\pi$
$444$	−5.00000	−0.237289
$445$	−4.00000	−0.189618
$446$	−2.00000	−0.0947027
$447$	−12.0000	−0.567581
$448$	−35.0000	−1.65359
$449$	−12.0000	−0.566315	−0.283158	−	0.959073i	$-0.591382\pi$
$449$	−12.0000	−0.566315	−0.283158	+	0.959073i	$0.591382\pi$
$450$	4.00000	0.188562
$451$	12.0000	0.565058
$452$	−6.00000	−0.282216
$453$	−18.0000	−0.845714
$454$	9.00000	0.422391
$455$	−20.0000	−0.937614
$456$	−6.00000	−0.280976
$457$	−34.0000	−1.59045	−0.795226	−	0.606313i	$-0.792648\pi$
$457$	−34.0000	−1.59045	−0.795226	+	0.606313i	$0.792648\pi$
$458$	−10.0000	−0.467269
$459$	6.00000	0.280056
$460$	−3.00000	−0.139876
$461$	−20.0000	−0.931493	−0.465746	−	0.884918i	$-0.654214\pi$
$461$	−20.0000	−0.931493	−0.465746	+	0.884918i	$0.654214\pi$
$462$	−20.0000	−0.930484
$463$	13.0000	0.604161	0.302081	−	0.953282i	$-0.402319\pi$
$463$	13.0000	0.604161	0.302081	+	0.953282i	$0.402319\pi$
$464$	−4.00000	−0.185695
$465$	7.00000	0.324617
$466$	−1.00000	−0.0463241
$467$	−12.0000	−0.555294	−0.277647	−	0.960683i	$-0.589555\pi$
$467$	−12.0000	−0.555294	−0.277647	+	0.960683i	$0.589555\pi$
$468$	4.00000	0.184900
$469$	−5.00000	−0.230879
$470$	8.00000	0.369012
$471$	−9.00000	−0.414698
$472$	9.00000	0.414259
$473$	−28.0000	−1.28744
$474$	8.00000	0.367452
$475$	8.00000	0.367065
$476$	30.0000	1.37505
$477$	−5.00000	−0.228934
$478$	14.0000	0.640345
$479$	13.0000	0.593985	0.296993	−	0.954880i	$-0.404016\pi$
$479$	13.0000	0.593985	0.296993	+	0.954880i	$0.404016\pi$
$480$	5.00000	0.228218
$481$	−20.0000	−0.911922
$482$	25.0000	1.13872
$483$	15.0000	0.682524
$484$	−5.00000	−0.227273
$485$	12.0000	0.544892
$486$	−1.00000	−0.0453609
$487$	−7.00000	−0.317200	−0.158600	−	0.987343i	$-0.550698\pi$
$487$	−7.00000	−0.317200	−0.158600	+	0.987343i	$0.550698\pi$
$488$	−6.00000	−0.271607
$489$	4.00000	0.180886
$490$	18.0000	0.813157
$491$	−15.0000	−0.676941	−0.338470	−	0.940977i	$-0.609909\pi$
$491$	−15.0000	−0.676941	−0.338470	+	0.940977i	$0.609909\pi$
$492$	3.00000	0.135250
$493$	24.0000	1.08091
$494$	−8.00000	−0.359937
$495$	4.00000	0.179787
$496$	7.00000	0.314309
$497$	60.0000	2.69137
$498$	−1.00000	−0.0448111
$499$	0	0		−	1.00000i	$-0.5\pi$
$499$	0	0			1.00000i	$0.5\pi$
$500$	−9.00000	−0.402492
$501$	3.00000	0.134030
$502$	8.00000	0.357057
$503$	28.0000	1.24846	0.624229	−	0.781241i	$-0.285413\pi$
$503$	28.0000	1.24846	0.624229	+	0.781241i	$0.285413\pi$
$504$	−15.0000	−0.668153
$505$	10.0000	0.444994
$506$	−12.0000	−0.533465
$507$	3.00000	0.133235
$508$	8.00000	0.354943
$509$	6.00000	0.265945	0.132973	−	0.991120i	$-0.457548\pi$
$509$	6.00000	0.265945	0.132973	+	0.991120i	$0.457548\pi$
$510$	6.00000	0.265684
$511$	65.0000	2.87543
$512$	11.0000	0.486136
$513$	−2.00000	−0.0883022
$514$	−8.00000	−0.352865
$515$	−8.00000	−0.352522
$516$	−7.00000	−0.308158
$517$	−32.0000	−1.40736
$518$	25.0000	1.09844
$519$	14.0000	0.614532
$520$	12.0000	0.526235
$521$	−38.0000	−1.66481	−0.832405	−	0.554168i	$-0.813037\pi$
$521$	−38.0000	−1.66481	−0.832405	+	0.554168i	$0.813037\pi$
$522$	−4.00000	−0.175075
$523$	−4.00000	−0.174908	−0.0874539	−	0.996169i	$-0.527873\pi$
$523$	−4.00000	−0.174908	−0.0874539	+	0.996169i	$0.527873\pi$
$524$	21.0000	0.917389
$525$	20.0000	0.872872
$526$	−7.00000	−0.305215
$527$	−42.0000	−1.82955
$528$	4.00000	0.174078
$529$	−14.0000	−0.608696
$530$	−5.00000	−0.217186
$531$	3.00000	0.130189
$532$	−10.0000	−0.433555
$533$	12.0000	0.519778
$534$	−4.00000	−0.173097
$535$	16.0000	0.691740
$536$	3.00000	0.129580
$537$	−6.00000	−0.258919
$538$	−14.0000	−0.603583
$539$	−72.0000	−3.10126
$540$	1.00000	0.0430331
$541$	14.0000	0.601907	0.300954	−	0.953639i	$-0.402695\pi$
$541$	14.0000	0.601907	0.300954	+	0.953639i	$0.402695\pi$
$542$	16.0000	0.687259
$543$	7.00000	0.300399
$544$	−30.0000	−1.28624
$545$	10.0000	0.428353
$546$	−20.0000	−0.855921
$547$	−37.0000	−1.58201	−0.791003	−	0.611812i	$-0.790441\pi$
$547$	−37.0000	−1.58201	−0.791003	+	0.611812i	$0.790441\pi$
$548$	−21.0000	−0.897076
$549$	−2.00000	−0.0853579
$550$	−16.0000	−0.682242
$551$	−8.00000	−0.340811
$552$	−9.00000	−0.383065
$553$	40.0000	1.70097
$554$	23.0000	0.977176
$555$	−5.00000	−0.212238
$556$	−13.0000	−0.551323
$557$	−2.00000	−0.0847427	−0.0423714	−	0.999102i	$-0.513491\pi$
$557$	−2.00000	−0.0847427	−0.0423714	+	0.999102i	$0.513491\pi$
$558$	7.00000	0.296334
$559$	−28.0000	−1.18427
$560$	−5.00000	−0.211289
$561$	−24.0000	−1.01328
$562$	−6.00000	−0.253095
$563$	12.0000	0.505740	0.252870	−	0.967500i	$-0.418626\pi$
$563$	12.0000	0.505740	0.252870	+	0.967500i	$0.418626\pi$
$564$	−8.00000	−0.336861
$565$	−6.00000	−0.252422
$566$	−6.00000	−0.252199
$567$	−5.00000	−0.209980
$568$	−36.0000	−1.51053
$569$	12.0000	0.503066	0.251533	−	0.967849i	$-0.419065\pi$
$569$	12.0000	0.503066	0.251533	+	0.967849i	$0.419065\pi$
$570$	−2.00000	−0.0837708
$571$	22.0000	0.920671	0.460336	−	0.887745i	$-0.347729\pi$
$571$	22.0000	0.920671	0.460336	+	0.887745i	$0.347729\pi$
$572$	−16.0000	−0.668994
$573$	24.0000	1.00261
$574$	−15.0000	−0.626088
$575$	12.0000	0.500435
$576$	7.00000	0.291667
$577$	18.0000	0.749350	0.374675	−	0.927156i	$-0.377754\pi$
$577$	18.0000	0.749350	0.374675	+	0.927156i	$0.377754\pi$
$578$	−19.0000	−0.790296
$579$	13.0000	0.540262
$580$	4.00000	0.166091
$581$	−5.00000	−0.207435
$582$	12.0000	0.497416
$583$	20.0000	0.828315
$584$	−39.0000	−1.61383
$585$	4.00000	0.165380
$586$	−30.0000	−1.23929
$587$	12.0000	0.495293	0.247647	−	0.968850i	$-0.420343\pi$
$587$	12.0000	0.495293	0.247647	+	0.968850i	$0.420343\pi$
$588$	−18.0000	−0.742307
$589$	14.0000	0.576860
$590$	3.00000	0.123508
$591$	25.0000	1.02836
$592$	−5.00000	−0.205499
$593$	−45.0000	−1.84793	−0.923964	−	0.382479i	$-0.875070\pi$
$593$	−45.0000	−1.84793	−0.923964	+	0.382479i	$0.875070\pi$
$594$	4.00000	0.164122
$595$	30.0000	1.22988
$596$	12.0000	0.491539
$597$	−20.0000	−0.818546
$598$	−12.0000	−0.490716
$599$	−20.0000	−0.817178	−0.408589	−	0.912719i	$-0.633979\pi$
$599$	−20.0000	−0.817178	−0.408589	+	0.912719i	$0.633979\pi$
$600$	−12.0000	−0.489898
$601$	−2.00000	−0.0815817	−0.0407909	−	0.999168i	$-0.512988\pi$
$601$	−2.00000	−0.0815817	−0.0407909	+	0.999168i	$0.512988\pi$
$602$	35.0000	1.42649
$603$	1.00000	0.0407231
$604$	18.0000	0.732410
$605$	−5.00000	−0.203279
$606$	10.0000	0.406222
$607$	−22.0000	−0.892952	−0.446476	−	0.894795i	$-0.647321\pi$
$607$	−22.0000	−0.892952	−0.446476	+	0.894795i	$0.647321\pi$
$608$	10.0000	0.405554
$609$	−20.0000	−0.810441
$610$	−2.00000	−0.0809776
$611$	−32.0000	−1.29458
$612$	−6.00000	−0.242536
$613$	−15.0000	−0.605844	−0.302922	−	0.953015i	$-0.597962\pi$
$613$	−15.0000	−0.605844	−0.302922	+	0.953015i	$0.597962\pi$
$614$	−8.00000	−0.322854
$615$	3.00000	0.120972
$616$	60.0000	2.41747
$617$	−10.0000	−0.402585	−0.201292	−	0.979531i	$-0.564514\pi$
$617$	−10.0000	−0.402585	−0.201292	+	0.979531i	$0.564514\pi$
$618$	−8.00000	−0.321807
$619$	20.0000	0.803868	0.401934	−	0.915669i	$-0.368338\pi$
$619$	20.0000	0.803868	0.401934	+	0.915669i	$0.368338\pi$
$620$	−7.00000	−0.281127
$621$	−3.00000	−0.120386
$622$	6.00000	0.240578
$623$	−20.0000	−0.801283
$624$	4.00000	0.160128
$625$	11.0000	0.440000
$626$	10.0000	0.399680
$627$	8.00000	0.319489
$628$	9.00000	0.359139
$629$	30.0000	1.19618
$630$	−5.00000	−0.199205
$631$	−20.0000	−0.796187	−0.398094	−	0.917345i	$-0.630328\pi$
$631$	−20.0000	−0.796187	−0.398094	+	0.917345i	$0.630328\pi$
$632$	−24.0000	−0.954669
$633$	6.00000	0.238479
$634$	−6.00000	−0.238290
$635$	8.00000	0.317470
$636$	5.00000	0.198263
$637$	−72.0000	−2.85274
$638$	16.0000	0.633446
$639$	−12.0000	−0.474713
$640$	−3.00000	−0.118585
$641$	−7.00000	−0.276483	−0.138242	−	0.990399i	$-0.544145\pi$
$641$	−7.00000	−0.276483	−0.138242	+	0.990399i	$0.544145\pi$
$642$	16.0000	0.631470
$643$	12.0000	0.473234	0.236617	−	0.971603i	$-0.423961\pi$
$643$	12.0000	0.473234	0.236617	+	0.971603i	$0.423961\pi$
$644$	−15.0000	−0.591083
$645$	−7.00000	−0.275625
$646$	12.0000	0.472134
$647$	−42.0000	−1.65119	−0.825595	−	0.564263i	$-0.809160\pi$
$647$	−42.0000	−1.65119	−0.825595	+	0.564263i	$0.809160\pi$
$648$	3.00000	0.117851
$649$	−12.0000	−0.471041
$650$	−16.0000	−0.627572
$651$	35.0000	1.37176
$652$	−4.00000	−0.156652
$653$	−39.0000	−1.52619	−0.763094	−	0.646288i	$-0.776321\pi$
$653$	−39.0000	−1.52619	−0.763094	+	0.646288i	$0.776321\pi$
$654$	10.0000	0.391031
$655$	21.0000	0.820538
$656$	3.00000	0.117130
$657$	−13.0000	−0.507178
$658$	40.0000	1.55936
$659$	−21.0000	−0.818044	−0.409022	−	0.912525i	$-0.634130\pi$
$659$	−21.0000	−0.818044	−0.409022	+	0.912525i	$0.634130\pi$
$660$	−4.00000	−0.155700
$661$	42.0000	1.63361	0.816805	−	0.576913i	$-0.195743\pi$
$661$	42.0000	1.63361	0.816805	+	0.576913i	$0.195743\pi$
$662$	−33.0000	−1.28258
$663$	−24.0000	−0.932083
$664$	3.00000	0.116423
$665$	−10.0000	−0.387783
$666$	−5.00000	−0.193746
$667$	−12.0000	−0.464642
$668$	−3.00000	−0.116073
$669$	2.00000	0.0773245
$670$	1.00000	0.0386334
$671$	8.00000	0.308837
$672$	25.0000	0.964396
$673$	16.0000	0.616755	0.308377	−	0.951264i	$-0.400214\pi$
$673$	16.0000	0.616755	0.308377	+	0.951264i	$0.400214\pi$
$674$	14.0000	0.539260
$675$	−4.00000	−0.153960
$676$	−3.00000	−0.115385
$677$	9.00000	0.345898	0.172949	−	0.984931i	$-0.444670\pi$
$677$	9.00000	0.345898	0.172949	+	0.984931i	$0.444670\pi$
$678$	−6.00000	−0.230429
$679$	60.0000	2.30259
$680$	−18.0000	−0.690268
$681$	−9.00000	−0.344881
$682$	−28.0000	−1.07218
$683$	−30.0000	−1.14792	−0.573959	−	0.818884i	$-0.694593\pi$
$683$	−30.0000	−1.14792	−0.573959	+	0.818884i	$0.694593\pi$
$684$	2.00000	0.0764719
$685$	−21.0000	−0.802369
$686$	55.0000	2.09991
$687$	10.0000	0.381524
$688$	−7.00000	−0.266872
$689$	20.0000	0.761939
$690$	−3.00000	−0.114208
$691$	−6.00000	−0.228251	−0.114125	−	0.993466i	$-0.536407\pi$
$691$	−6.00000	−0.228251	−0.114125	+	0.993466i	$0.536407\pi$
$692$	−14.0000	−0.532200
$693$	20.0000	0.759737
$694$	−24.0000	−0.911028
$695$	−13.0000	−0.493118
$696$	12.0000	0.454859
$697$	−18.0000	−0.681799
$698$	−15.0000	−0.567758
$699$	1.00000	0.0378235
$700$	−20.0000	−0.755929
$701$	5.00000	0.188847	0.0944237	−	0.995532i	$-0.469899\pi$
$701$	5.00000	0.188847	0.0944237	+	0.995532i	$0.469899\pi$
$702$	4.00000	0.150970
$703$	−10.0000	−0.377157
$704$	−28.0000	−1.05529
$705$	−8.00000	−0.301297
$706$	21.0000	0.790345
$707$	50.0000	1.88044
$708$	−3.00000	−0.112747
$709$	17.0000	0.638448	0.319224	−	0.947679i	$-0.396578\pi$
$709$	17.0000	0.638448	0.319224	+	0.947679i	$0.396578\pi$
$710$	−12.0000	−0.450352
$711$	−8.00000	−0.300023
$712$	12.0000	0.449719
$713$	21.0000	0.786456
$714$	30.0000	1.12272
$715$	−16.0000	−0.598366
$716$	6.00000	0.224231
$717$	−14.0000	−0.522840
$718$	11.0000	0.410516
$719$	43.0000	1.60363	0.801815	−	0.597573i	$-0.203868\pi$
$719$	43.0000	1.60363	0.801815	+	0.597573i	$0.203868\pi$
$720$	1.00000	0.0372678
$721$	−40.0000	−1.48968
$722$	15.0000	0.558242
$723$	−25.0000	−0.929760
$724$	−7.00000	−0.260153
$725$	−16.0000	−0.594225
$726$	−5.00000	−0.185567
$727$	37.0000	1.37225	0.686127	−	0.727482i	$-0.259309\pi$
$727$	37.0000	1.37225	0.686127	+	0.727482i	$0.259309\pi$
$728$	60.0000	2.22375
$729$	1.00000	0.0370370
$730$	−13.0000	−0.481152
$731$	42.0000	1.55343
$732$	2.00000	0.0739221
$733$	−6.00000	−0.221615	−0.110808	−	0.993842i	$-0.535344\pi$
$733$	−6.00000	−0.221615	−0.110808	+	0.993842i	$0.535344\pi$
$734$	−16.0000	−0.590571
$735$	−18.0000	−0.663940
$736$	15.0000	0.552907
$737$	−4.00000	−0.147342
$738$	3.00000	0.110432
$739$	−23.0000	−0.846069	−0.423034	−	0.906114i	$-0.639035\pi$
$739$	−23.0000	−0.846069	−0.423034	+	0.906114i	$0.639035\pi$
$740$	5.00000	0.183804
$741$	8.00000	0.293887
$742$	−25.0000	−0.917779
$743$	−3.00000	−0.110059	−0.0550297	−	0.998485i	$-0.517525\pi$
$743$	−3.00000	−0.110059	−0.0550297	+	0.998485i	$0.517525\pi$
$744$	−21.0000	−0.769897
$745$	12.0000	0.439646
$746$	18.0000	0.659027
$747$	1.00000	0.0365881
$748$	24.0000	0.877527
$749$	80.0000	2.92314
$750$	−9.00000	−0.328634
$751$	26.0000	0.948753	0.474377	−	0.880322i	$-0.342673\pi$
$751$	26.0000	0.948753	0.474377	+	0.880322i	$0.342673\pi$
$752$	−8.00000	−0.291730
$753$	−8.00000	−0.291536
$754$	16.0000	0.582686
$755$	18.0000	0.655087
$756$	5.00000	0.181848
$757$	−14.0000	−0.508839	−0.254419	−	0.967094i	$-0.581884\pi$
$757$	−14.0000	−0.508839	−0.254419	+	0.967094i	$0.581884\pi$
$758$	−9.00000	−0.326895
$759$	12.0000	0.435572
$760$	6.00000	0.217643
$761$	38.0000	1.37750	0.688749	−	0.724999i	$-0.258160\pi$
$761$	38.0000	1.37750	0.688749	+	0.724999i	$0.258160\pi$
$762$	8.00000	0.289809
$763$	50.0000	1.81012
$764$	−24.0000	−0.868290
$765$	−6.00000	−0.216930
$766$	−8.00000	−0.289052
$767$	−12.0000	−0.433295
$768$	−17.0000	−0.613435
$769$	−24.0000	−0.865462	−0.432731	−	0.901523i	$-0.642450\pi$
$769$	−24.0000	−0.865462	−0.432731	+	0.901523i	$0.642450\pi$
$770$	20.0000	0.720750
$771$	8.00000	0.288113
$772$	−13.0000	−0.467880
$773$	−24.0000	−0.863220	−0.431610	−	0.902060i	$-0.642054\pi$
$773$	−24.0000	−0.863220	−0.431610	+	0.902060i	$0.642054\pi$
$774$	−7.00000	−0.251610
$775$	28.0000	1.00579
$776$	−36.0000	−1.29232
$777$	−25.0000	−0.896870
$778$	16.0000	0.573628
$779$	6.00000	0.214972
$780$	−4.00000	−0.143223
$781$	48.0000	1.71758
$782$	18.0000	0.643679
$783$	4.00000	0.142948
$784$	−18.0000	−0.642857
$785$	9.00000	0.321224
$786$	21.0000	0.749045
$787$	31.0000	1.10503	0.552515	−	0.833503i	$-0.313668\pi$
$787$	31.0000	1.10503	0.552515	+	0.833503i	$0.313668\pi$
$788$	−25.0000	−0.890588
$789$	7.00000	0.249207
$790$	−8.00000	−0.284627
$791$	−30.0000	−1.06668
$792$	−12.0000	−0.426401
$793$	8.00000	0.284088
$794$	−26.0000	−0.922705
$795$	5.00000	0.177332
$796$	20.0000	0.708881
$797$	0	0		−	1.00000i	$-0.5\pi$
$797$	0	0			1.00000i	$0.5\pi$
$798$	−10.0000	−0.353996
$799$	48.0000	1.69812
$800$	20.0000	0.707107
$801$	4.00000	0.141333
$802$	17.0000	0.600291
$803$	52.0000	1.83504
$804$	−1.00000	−0.0352673
$805$	−15.0000	−0.528681
$806$	−28.0000	−0.986258
$807$	14.0000	0.492823
$808$	−30.0000	−1.05540
$809$	39.0000	1.37117	0.685583	−	0.727994i	$-0.259547\pi$
$809$	39.0000	1.37117	0.685583	+	0.727994i	$0.259547\pi$
$810$	1.00000	0.0351364
$811$	−13.0000	−0.456492	−0.228246	−	0.973604i	$-0.573299\pi$
$811$	−13.0000	−0.456492	−0.228246	+	0.973604i	$0.573299\pi$
$812$	20.0000	0.701862
$813$	−16.0000	−0.561144
$814$	20.0000	0.701000
$815$	−4.00000	−0.140114
$816$	−6.00000	−0.210042
$817$	−14.0000	−0.489798
$818$	−20.0000	−0.699284
$819$	20.0000	0.698857
$820$	−3.00000	−0.104765
$821$	−28.0000	−0.977207	−0.488603	−	0.872506i	$-0.662493\pi$
$821$	−28.0000	−0.977207	−0.488603	+	0.872506i	$0.662493\pi$
$822$	−21.0000	−0.732459
$823$	−42.0000	−1.46403	−0.732014	−	0.681290i	$-0.761419\pi$
$823$	−42.0000	−1.46403	−0.732014	+	0.681290i	$0.761419\pi$
$824$	24.0000	0.836080
$825$	16.0000	0.557048
$826$	15.0000	0.521917
$827$	24.0000	0.834562	0.417281	−	0.908778i	$-0.362983\pi$
$827$	24.0000	0.834562	0.417281	+	0.908778i	$0.362983\pi$
$828$	3.00000	0.104257
$829$	38.0000	1.31979	0.659897	−	0.751356i	$-0.270600\pi$
$829$	38.0000	1.31979	0.659897	+	0.751356i	$0.270600\pi$
$830$	1.00000	0.0347105
$831$	−23.0000	−0.797861
$832$	−28.0000	−0.970725
$833$	108.000	3.74198
$834$	−13.0000	−0.450153
$835$	−3.00000	−0.103819
$836$	−8.00000	−0.276686
$837$	−7.00000	−0.241955
$838$	−33.0000	−1.13997
$839$	28.0000	0.966667	0.483334	−	0.875436i	$-0.339426\pi$
$839$	28.0000	0.966667	0.483334	+	0.875436i	$0.339426\pi$
$840$	15.0000	0.517549
$841$	−13.0000	−0.448276
$842$	−3.00000	−0.103387
$843$	6.00000	0.206651
$844$	−6.00000	−0.206529
$845$	−3.00000	−0.103203
$846$	−8.00000	−0.275046
$847$	−25.0000	−0.859010
$848$	5.00000	0.171701
$849$	6.00000	0.205919
$850$	24.0000	0.823193
$851$	−15.0000	−0.514193
$852$	12.0000	0.411113
$853$	−46.0000	−1.57501	−0.787505	−	0.616308i	$-0.788628\pi$
$853$	−46.0000	−1.57501	−0.787505	+	0.616308i	$0.788628\pi$
$854$	−10.0000	−0.342193
$855$	2.00000	0.0683986
$856$	−48.0000	−1.64061
$857$	−57.0000	−1.94708	−0.973541	−	0.228510i	$-0.926614\pi$
$857$	−57.0000	−1.94708	−0.973541	+	0.228510i	$0.926614\pi$
$858$	−16.0000	−0.546231
$859$	−14.0000	−0.477674	−0.238837	−	0.971060i	$-0.576766\pi$
$859$	−14.0000	−0.477674	−0.238837	+	0.971060i	$0.576766\pi$
$860$	7.00000	0.238698
$861$	15.0000	0.511199
$862$	−3.00000	−0.102180
$863$	−41.0000	−1.39566	−0.697828	−	0.716265i	$-0.745850\pi$
$863$	−41.0000	−1.39566	−0.697828	+	0.716265i	$0.745850\pi$
$864$	−5.00000	−0.170103
$865$	−14.0000	−0.476014
$866$	−12.0000	−0.407777
$867$	19.0000	0.645274
$868$	−35.0000	−1.18798
$869$	32.0000	1.08553
$870$	4.00000	0.135613
$871$	−4.00000	−0.135535
$872$	−30.0000	−1.01593
$873$	−12.0000	−0.406138
$874$	−6.00000	−0.202953
$875$	−45.0000	−1.52128
$876$	13.0000	0.439229
$877$	−46.0000	−1.55331	−0.776655	−	0.629926i	$-0.783085\pi$
$877$	−46.0000	−1.55331	−0.776655	+	0.629926i	$0.783085\pi$
$878$	16.0000	0.539974
$879$	30.0000	1.01187
$880$	−4.00000	−0.134840
$881$	36.0000	1.21287	0.606435	−	0.795133i	$-0.292599\pi$
$881$	36.0000	1.21287	0.606435	+	0.795133i	$0.292599\pi$
$882$	−18.0000	−0.606092
$883$	−35.0000	−1.17784	−0.588922	−	0.808190i	$-0.700447\pi$
$883$	−35.0000	−1.17784	−0.588922	+	0.808190i	$0.700447\pi$
$884$	24.0000	0.807207
$885$	−3.00000	−0.100844
$886$	22.0000	0.739104
$887$	17.0000	0.570804	0.285402	−	0.958408i	$-0.407873\pi$
$887$	17.0000	0.570804	0.285402	+	0.958408i	$0.407873\pi$
$888$	15.0000	0.503367
$889$	40.0000	1.34156
$890$	4.00000	0.134080
$891$	−4.00000	−0.134005
$892$	−2.00000	−0.0669650
$893$	−16.0000	−0.535420
$894$	12.0000	0.401340
$895$	6.00000	0.200558
$896$	−15.0000	−0.501115
$897$	12.0000	0.400668
$898$	12.0000	0.400445
$899$	−28.0000	−0.933852
$900$	4.00000	0.133333
$901$	−30.0000	−0.999445
$902$	−12.0000	−0.399556
$903$	−35.0000	−1.16473
$904$	18.0000	0.598671
$905$	−7.00000	−0.232688
$906$	18.0000	0.598010
$907$	20.0000	0.664089	0.332045	−	0.943264i	$-0.392262\pi$
$907$	20.0000	0.664089	0.332045	+	0.943264i	$0.392262\pi$
$908$	9.00000	0.298675
$909$	−10.0000	−0.331679
$910$	20.0000	0.662994
$911$	−36.0000	−1.19273	−0.596367	−	0.802712i	$-0.703390\pi$
$911$	−36.0000	−1.19273	−0.596367	+	0.802712i	$0.703390\pi$
$912$	2.00000	0.0662266
$913$	−4.00000	−0.132381
$914$	34.0000	1.12462
$915$	2.00000	0.0661180
$916$	−10.0000	−0.330409
$917$	105.000	3.46741
$918$	−6.00000	−0.198030
$919$	15.0000	0.494804	0.247402	−	0.968913i	$-0.420423\pi$
$919$	15.0000	0.494804	0.247402	+	0.968913i	$0.420423\pi$
$920$	9.00000	0.296721
$921$	8.00000	0.263609
$922$	20.0000	0.658665
$923$	48.0000	1.57994
$924$	−20.0000	−0.657952
$925$	−20.0000	−0.657596
$926$	−13.0000	−0.427207
$927$	8.00000	0.262754
$928$	−20.0000	−0.656532
$929$	2.00000	0.0656179	0.0328089	−	0.999462i	$-0.489555\pi$
$929$	2.00000	0.0656179	0.0328089	+	0.999462i	$0.489555\pi$
$930$	−7.00000	−0.229539
$931$	−36.0000	−1.17985
$932$	−1.00000	−0.0327561
$933$	−6.00000	−0.196431
$934$	12.0000	0.392652
$935$	24.0000	0.784884
$936$	−12.0000	−0.392232
$937$	−30.0000	−0.980057	−0.490029	−	0.871706i	$-0.663014\pi$
$937$	−30.0000	−0.980057	−0.490029	+	0.871706i	$0.663014\pi$
$938$	5.00000	0.163256
$939$	−10.0000	−0.326338
$940$	8.00000	0.260931
$941$	14.0000	0.456387	0.228193	−	0.973616i	$-0.426718\pi$
$941$	14.0000	0.456387	0.228193	+	0.973616i	$0.426718\pi$
$942$	9.00000	0.293236
$943$	9.00000	0.293080
$944$	−3.00000	−0.0976417
$945$	5.00000	0.162650
$946$	28.0000	0.910359
$947$	−3.00000	−0.0974869	−0.0487435	−	0.998811i	$-0.515522\pi$
$947$	−3.00000	−0.0974869	−0.0487435	+	0.998811i	$0.515522\pi$
$948$	8.00000	0.259828
$949$	52.0000	1.68799
$950$	−8.00000	−0.259554
$951$	6.00000	0.194563
$952$	−90.0000	−2.91692
$953$	−40.0000	−1.29573	−0.647864	−	0.761756i	$-0.724337\pi$
$953$	−40.0000	−1.29573	−0.647864	+	0.761756i	$0.724337\pi$
$954$	5.00000	0.161881
$955$	−24.0000	−0.776622
$956$	14.0000	0.452792
$957$	−16.0000	−0.517207
$958$	−13.0000	−0.420011
$959$	−105.000	−3.39063
$960$	−7.00000	−0.225924
$961$	18.0000	0.580645
$962$	20.0000	0.644826
$963$	−16.0000	−0.515593
$964$	25.0000	0.805196
$965$	−13.0000	−0.418485
$966$	−15.0000	−0.482617
$967$	6.00000	0.192947	0.0964735	−	0.995336i	$-0.469244\pi$
$967$	6.00000	0.192947	0.0964735	+	0.995336i	$0.469244\pi$
$968$	15.0000	0.482118
$969$	−12.0000	−0.385496
$970$	−12.0000	−0.385297
$971$	48.0000	1.54039	0.770197	−	0.637806i	$-0.220158\pi$
$971$	48.0000	1.54039	0.770197	+	0.637806i	$0.220158\pi$
$972$	−1.00000	−0.0320750
$973$	−65.0000	−2.08380
$974$	7.00000	0.224294
$975$	16.0000	0.512410
$976$	2.00000	0.0640184
$977$	−34.0000	−1.08776	−0.543878	−	0.839164i	$-0.683045\pi$
$977$	−34.0000	−1.08776	−0.543878	+	0.839164i	$0.683045\pi$
$978$	−4.00000	−0.127906
$979$	−16.0000	−0.511362
$980$	18.0000	0.574989
$981$	−10.0000	−0.319275
$982$	15.0000	0.478669
$983$	40.0000	1.27580	0.637901	−	0.770118i	$-0.279803\pi$
$983$	40.0000	1.27580	0.637901	+	0.770118i	$0.279803\pi$
$984$	−9.00000	−0.286910
$985$	−25.0000	−0.796566
$986$	−24.0000	−0.764316
$987$	−40.0000	−1.27321
$988$	−8.00000	−0.254514
$989$	−21.0000	−0.667761
$990$	−4.00000	−0.127128
$991$	−25.0000	−0.794151	−0.397076	−	0.917786i	$-0.629975\pi$
$991$	−25.0000	−0.794151	−0.397076	+	0.917786i	$0.629975\pi$
$992$	35.0000	1.11125
$993$	33.0000	1.04722
$994$	−60.0000	−1.90308
$995$	20.0000	0.634043
$996$	−1.00000	−0.0316862
$997$	27.0000	0.855099	0.427549	−	0.903992i	$-0.359377\pi$
$997$	27.0000	0.855099	0.427549	+	0.903992i	$0.359377\pi$
$998$	0	0
$999$	5.00000	0.158193

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.2.a.b.1.1	✓	1
3.2	odd	2		603.2.a.e.1.1		1
4.3	odd	2		3216.2.a.d.1.1		1
5.4	even	2		5025.2.a.h.1.1		1
7.6	odd	2		9849.2.a.e.1.1		1
12.11	even	2		9648.2.a.n.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.2.a.b.1.1	✓	1	1.1	even	1	trivial
603.2.a.e.1.1		1	3.2	odd	2
3216.2.a.d.1.1		1	4.3	odd	2
5025.2.a.h.1.1		1	5.4	even	2
9648.2.a.n.1.1		1	12.11	even	2
9849.2.a.e.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:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	201.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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