LMFDB - Embedded newform 570.2.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(1,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, 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("570.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.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:	$4.55147291521$
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	$\chi$	$=$	570.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -4.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$

\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -4.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -4.00000 q^{11} +1.00000 q^{12} -6.00000 q^{13} +4.00000 q^{14} +1.00000 q^{15} +1.00000 q^{16} -6.00000 q^{17} -1.00000 q^{18} -1.00000 q^{19} +1.00000 q^{20} -4.00000 q^{21} +4.00000 q^{22} +4.00000 q^{23} -1.00000 q^{24} +1.00000 q^{25} +6.00000 q^{26} +1.00000 q^{27} -4.00000 q^{28} +6.00000 q^{29} -1.00000 q^{30} -8.00000 q^{31} -1.00000 q^{32} -4.00000 q^{33} +6.00000 q^{34} -4.00000 q^{35} +1.00000 q^{36} +2.00000 q^{37} +1.00000 q^{38} -6.00000 q^{39} -1.00000 q^{40} +10.0000 q^{41} +4.00000 q^{42} -8.00000 q^{43} -4.00000 q^{44} +1.00000 q^{45} -4.00000 q^{46} +12.0000 q^{47} +1.00000 q^{48} +9.00000 q^{49} -1.00000 q^{50} -6.00000 q^{51} -6.00000 q^{52} +2.00000 q^{53} -1.00000 q^{54} -4.00000 q^{55} +4.00000 q^{56} -1.00000 q^{57} -6.00000 q^{58} -4.00000 q^{59} +1.00000 q^{60} -2.00000 q^{61} +8.00000 q^{62} -4.00000 q^{63} +1.00000 q^{64} -6.00000 q^{65} +4.00000 q^{66} -12.0000 q^{67} -6.00000 q^{68} +4.00000 q^{69} +4.00000 q^{70} -16.0000 q^{71} -1.00000 q^{72} -14.0000 q^{73} -2.00000 q^{74} +1.00000 q^{75} -1.00000 q^{76} +16.0000 q^{77} +6.00000 q^{78} +8.00000 q^{79} +1.00000 q^{80} +1.00000 q^{81} -10.0000 q^{82} -4.00000 q^{84} -6.00000 q^{85} +8.00000 q^{86} +6.00000 q^{87} +4.00000 q^{88} -6.00000 q^{89} -1.00000 q^{90} +24.0000 q^{91} +4.00000 q^{92} -8.00000 q^{93} -12.0000 q^{94} -1.00000 q^{95} -1.00000 q^{96} +14.0000 q^{97} -9.00000 q^{98} -4.00000 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.00000	−0.408248
$7$	−4.00000	−1.51186	−0.755929	−	0.654654i	$-0.772814\pi$
$7$	−4.00000	−1.51186	−0.755929	+	0.654654i	$0.772814\pi$
$8$	−1.00000	−0.353553
$9$	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
$13$	−6.00000	−1.66410	−0.832050	−	0.554700i	$-0.812833\pi$
$13$	−6.00000	−1.66410	−0.832050	+	0.554700i	$0.812833\pi$
$14$	4.00000	1.06904
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	−6.00000	−1.45521	−0.727607	−	0.685994i	$-0.759367\pi$
$17$	−6.00000	−1.45521	−0.727607	+	0.685994i	$0.759367\pi$
$18$	−1.00000	−0.235702
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	1.00000	0.223607
$21$	−4.00000	−0.872872
$22$	4.00000	0.852803
$23$	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
$26$	6.00000	1.17670
$27$	1.00000	0.192450
$28$	−4.00000	−0.755929
$29$	6.00000	1.11417	0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000	1.11417	0.557086	+	0.830455i	$0.311919\pi$
$30$	−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
$33$	−4.00000	−0.696311
$34$	6.00000	1.02899
$35$	−4.00000	−0.676123
$36$	1.00000	0.166667
$37$	2.00000	0.328798	0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000	0.328798	0.164399	+	0.986394i	$0.447432\pi$
$38$	1.00000	0.162221
$39$	−6.00000	−0.960769
$40$	−1.00000	−0.158114
$41$	10.0000	1.56174	0.780869	−	0.624695i	$-0.214777\pi$
$41$	10.0000	1.56174	0.780869	+	0.624695i	$0.214777\pi$
$42$	4.00000	0.617213
$43$	−8.00000	−1.21999	−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000	−1.21999	−0.609994	+	0.792406i	$0.708828\pi$
$44$	−4.00000	−0.603023
$45$	1.00000	0.149071
$46$	−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
$49$	9.00000	1.28571
$50$	−1.00000	−0.141421
$51$	−6.00000	−0.840168
$52$	−6.00000	−0.832050
$53$	2.00000	0.274721	0.137361	−	0.990521i	$-0.456138\pi$
$53$	2.00000	0.274721	0.137361	+	0.990521i	$0.456138\pi$
$54$	−1.00000	−0.136083
$55$	−4.00000	−0.539360
$56$	4.00000	0.534522
$57$	−1.00000	−0.132453
$58$	−6.00000	−0.787839
$59$	−4.00000	−0.520756	−0.260378	−	0.965507i	$-0.583847\pi$
$59$	−4.00000	−0.520756	−0.260378	+	0.965507i	$0.583847\pi$
$60$	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	$0.540868\pi$
$62$	8.00000	1.01600
$63$	−4.00000	−0.503953
$64$	1.00000	0.125000
$65$	−6.00000	−0.744208
$66$	4.00000	0.492366
$67$	−12.0000	−1.46603	−0.733017	−	0.680211i	$-0.761888\pi$
$67$	−12.0000	−1.46603	−0.733017	+	0.680211i	$0.761888\pi$
$68$	−6.00000	−0.727607
$69$	4.00000	0.481543
$70$	4.00000	0.478091
$71$	−16.0000	−1.89885	−0.949425	−	0.313993i	$-0.898333\pi$
$71$	−16.0000	−1.89885	−0.949425	+	0.313993i	$0.898333\pi$
$72$	−1.00000	−0.117851
$73$	−14.0000	−1.63858	−0.819288	−	0.573382i	$-0.805631\pi$
$73$	−14.0000	−1.63858	−0.819288	+	0.573382i	$0.805631\pi$
$74$	−2.00000	−0.232495
$75$	1.00000	0.115470
$76$	−1.00000	−0.114708
$77$	16.0000	1.82337
$78$	6.00000	0.679366
$79$	8.00000	0.900070	0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000	0.900070	0.450035	+	0.893011i	$0.351411\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	−10.0000	−1.10432
$83$	0	0		−	1.00000i	$-0.5\pi$
$83$	0	0			1.00000i	$0.5\pi$
$84$	−4.00000	−0.436436
$85$	−6.00000	−0.650791
$86$	8.00000	0.862662
$87$	6.00000	0.643268
$88$	4.00000	0.426401
$89$	−6.00000	−0.635999	−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000	−0.635999	−0.317999	+	0.948091i	$0.603011\pi$
$90$	−1.00000	−0.105409
$91$	24.0000	2.51588
$92$	4.00000	0.417029
$93$	−8.00000	−0.829561
$94$	−12.0000	−1.23771
$95$	−1.00000	−0.102598
$96$	−1.00000	−0.102062
$97$	14.0000	1.42148	0.710742	−	0.703452i	$-0.248359\pi$
$97$	14.0000	1.42148	0.710742	+	0.703452i	$0.248359\pi$
$98$	−9.00000	−0.909137
$99$	−4.00000	−0.402015
$100$	1.00000	0.100000
$101$	6.00000	0.597022	0.298511	−	0.954406i	$-0.403510\pi$
$101$	6.00000	0.597022	0.298511	+	0.954406i	$0.403510\pi$
$102$	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	$0.371045\pi$
$104$	6.00000	0.588348
$105$	−4.00000	−0.390360
$106$	−2.00000	−0.194257
$107$	−12.0000	−1.16008	−0.580042	−	0.814587i	$-0.696964\pi$
$107$	−12.0000	−1.16008	−0.580042	+	0.814587i	$0.696964\pi$
$108$	1.00000	0.0962250
$109$	6.00000	0.574696	0.287348	−	0.957826i	$-0.407226\pi$
$109$	6.00000	0.574696	0.287348	+	0.957826i	$0.407226\pi$
$110$	4.00000	0.381385
$111$	2.00000	0.189832
$112$	−4.00000	−0.377964
$113$	−10.0000	−0.940721	−0.470360	−	0.882474i	$-0.655876\pi$
$113$	−10.0000	−0.940721	−0.470360	+	0.882474i	$0.655876\pi$
$114$	1.00000	0.0936586
$115$	4.00000	0.373002
$116$	6.00000	0.557086
$117$	−6.00000	−0.554700
$118$	4.00000	0.368230
$119$	24.0000	2.20008
$120$	−1.00000	−0.0912871
$121$	5.00000	0.454545
$122$	2.00000	0.181071
$123$	10.0000	0.901670
$124$	−8.00000	−0.718421
$125$	1.00000	0.0894427
$126$	4.00000	0.356348
$127$	−16.0000	−1.41977	−0.709885	−	0.704317i	$-0.751253\pi$
$127$	−16.0000	−1.41977	−0.709885	+	0.704317i	$0.751253\pi$
$128$	−1.00000	−0.0883883
$129$	−8.00000	−0.704361
$130$	6.00000	0.526235
$131$	12.0000	1.04844	0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000	1.04844	0.524222	+	0.851581i	$0.324356\pi$
$132$	−4.00000	−0.348155
$133$	4.00000	0.346844
$134$	12.0000	1.03664
$135$	1.00000	0.0860663
$136$	6.00000	0.514496
$137$	2.00000	0.170872	0.0854358	−	0.996344i	$-0.472772\pi$
$137$	2.00000	0.170872	0.0854358	+	0.996344i	$0.472772\pi$
$138$	−4.00000	−0.340503
$139$	12.0000	1.01783	0.508913	−	0.860818i	$-0.330047\pi$
$139$	12.0000	1.01783	0.508913	+	0.860818i	$0.330047\pi$
$140$	−4.00000	−0.338062
$141$	12.0000	1.01058
$142$	16.0000	1.34269
$143$	24.0000	2.00698
$144$	1.00000	0.0833333
$145$	6.00000	0.498273
$146$	14.0000	1.15865
$147$	9.00000	0.742307
$148$	2.00000	0.164399
$149$	−10.0000	−0.819232	−0.409616	−	0.912258i	$-0.634337\pi$
$149$	−10.0000	−0.819232	−0.409616	+	0.912258i	$0.634337\pi$
$150$	−1.00000	−0.0816497
$151$	8.00000	0.651031	0.325515	−	0.945537i	$-0.394462\pi$
$151$	8.00000	0.651031	0.325515	+	0.945537i	$0.394462\pi$
$152$	1.00000	0.0811107
$153$	−6.00000	−0.485071
$154$	−16.0000	−1.28932
$155$	−8.00000	−0.642575
$156$	−6.00000	−0.480384
$157$	22.0000	1.75579	0.877896	−	0.478852i	$-0.158947\pi$
$157$	22.0000	1.75579	0.877896	+	0.478852i	$0.158947\pi$
$158$	−8.00000	−0.636446
$159$	2.00000	0.158610
$160$	−1.00000	−0.0790569
$161$	−16.0000	−1.26098
$162$	−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	$0.715557\pi$
$164$	10.0000	0.780869
$165$	−4.00000	−0.311400
$166$	0	0
$167$	0	0		−	1.00000i	$-0.5\pi$
$167$	0	0			1.00000i	$0.5\pi$
$168$	4.00000	0.308607
$169$	23.0000	1.76923
$170$	6.00000	0.460179
$171$	−1.00000	−0.0764719
$172$	−8.00000	−0.609994
$173$	−6.00000	−0.456172	−0.228086	−	0.973641i	$-0.573247\pi$
$173$	−6.00000	−0.456172	−0.228086	+	0.973641i	$0.573247\pi$
$174$	−6.00000	−0.454859
$175$	−4.00000	−0.302372
$176$	−4.00000	−0.301511
$177$	−4.00000	−0.300658
$178$	6.00000	0.449719
$179$	−12.0000	−0.896922	−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000	−0.896922	−0.448461	+	0.893802i	$0.648028\pi$
$180$	1.00000	0.0745356
$181$	−2.00000	−0.148659	−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000	−0.148659	−0.0743294	+	0.997234i	$0.523682\pi$
$182$	−24.0000	−1.77900
$183$	−2.00000	−0.147844
$184$	−4.00000	−0.294884
$185$	2.00000	0.147043
$186$	8.00000	0.586588
$187$	24.0000	1.75505
$188$	12.0000	0.875190
$189$	−4.00000	−0.290957
$190$	1.00000	0.0725476
$191$	−8.00000	−0.578860	−0.289430	−	0.957199i	$-0.593466\pi$
$191$	−8.00000	−0.578860	−0.289430	+	0.957199i	$0.593466\pi$
$192$	1.00000	0.0721688
$193$	−2.00000	−0.143963	−0.0719816	−	0.997406i	$-0.522932\pi$
$193$	−2.00000	−0.143963	−0.0719816	+	0.997406i	$0.522932\pi$
$194$	−14.0000	−1.00514
$195$	−6.00000	−0.429669
$196$	9.00000	0.642857
$197$	6.00000	0.427482	0.213741	−	0.976890i	$-0.431435\pi$
$197$	6.00000	0.427482	0.213741	+	0.976890i	$0.431435\pi$
$198$	4.00000	0.284268
$199$	−16.0000	−1.13421	−0.567105	−	0.823646i	$-0.691937\pi$
$199$	−16.0000	−1.13421	−0.567105	+	0.823646i	$0.691937\pi$
$200$	−1.00000	−0.0707107
$201$	−12.0000	−0.846415
$202$	−6.00000	−0.422159
$203$	−24.0000	−1.68447
$204$	−6.00000	−0.420084
$205$	10.0000	0.698430
$206$	−8.00000	−0.557386
$207$	4.00000	0.278019
$208$	−6.00000	−0.416025
$209$	4.00000	0.276686
$210$	4.00000	0.276026
$211$	−20.0000	−1.37686	−0.688428	−	0.725304i	$-0.741699\pi$
$211$	−20.0000	−1.37686	−0.688428	+	0.725304i	$0.741699\pi$
$212$	2.00000	0.137361
$213$	−16.0000	−1.09630
$214$	12.0000	0.820303
$215$	−8.00000	−0.545595
$216$	−1.00000	−0.0680414
$217$	32.0000	2.17230
$218$	−6.00000	−0.406371
$219$	−14.0000	−0.946032
$220$	−4.00000	−0.269680
$221$	36.0000	2.42162
$222$	−2.00000	−0.134231
$223$	−16.0000	−1.07144	−0.535720	−	0.844396i	$-0.679960\pi$
$223$	−16.0000	−1.07144	−0.535720	+	0.844396i	$0.679960\pi$
$224$	4.00000	0.267261
$225$	1.00000	0.0666667
$226$	10.0000	0.665190
$227$	−4.00000	−0.265489	−0.132745	−	0.991150i	$-0.542379\pi$
$227$	−4.00000	−0.265489	−0.132745	+	0.991150i	$0.542379\pi$
$228$	−1.00000	−0.0662266
$229$	6.00000	0.396491	0.198246	−	0.980152i	$-0.436476\pi$
$229$	6.00000	0.396491	0.198246	+	0.980152i	$0.436476\pi$
$230$	−4.00000	−0.263752
$231$	16.0000	1.05272
$232$	−6.00000	−0.393919
$233$	10.0000	0.655122	0.327561	−	0.944830i	$-0.393773\pi$
$233$	10.0000	0.655122	0.327561	+	0.944830i	$0.393773\pi$
$234$	6.00000	0.392232
$235$	12.0000	0.782794
$236$	−4.00000	−0.260378
$237$	8.00000	0.519656
$238$	−24.0000	−1.55569
$239$	16.0000	1.03495	0.517477	−	0.855697i	$-0.326871\pi$
$239$	16.0000	1.03495	0.517477	+	0.855697i	$0.326871\pi$
$240$	1.00000	0.0645497
$241$	−22.0000	−1.41714	−0.708572	−	0.705638i	$-0.750660\pi$
$241$	−22.0000	−1.41714	−0.708572	+	0.705638i	$0.750660\pi$
$242$	−5.00000	−0.321412
$243$	1.00000	0.0641500
$244$	−2.00000	−0.128037
$245$	9.00000	0.574989
$246$	−10.0000	−0.637577
$247$	6.00000	0.381771
$248$	8.00000	0.508001
$249$	0	0
$250$	−1.00000	−0.0632456
$251$	4.00000	0.252478	0.126239	−	0.992000i	$-0.459709\pi$
$251$	4.00000	0.252478	0.126239	+	0.992000i	$0.459709\pi$
$252$	−4.00000	−0.251976
$253$	−16.0000	−1.00591
$254$	16.0000	1.00393
$255$	−6.00000	−0.375735
$256$	1.00000	0.0625000
$257$	−18.0000	−1.12281	−0.561405	−	0.827541i	$-0.689739\pi$
$257$	−18.0000	−1.12281	−0.561405	+	0.827541i	$0.689739\pi$
$258$	8.00000	0.498058
$259$	−8.00000	−0.497096
$260$	−6.00000	−0.372104
$261$	6.00000	0.371391
$262$	−12.0000	−0.741362
$263$	20.0000	1.23325	0.616626	−	0.787256i	$-0.288499\pi$
$263$	20.0000	1.23325	0.616626	+	0.787256i	$0.288499\pi$
$264$	4.00000	0.246183
$265$	2.00000	0.122859
$266$	−4.00000	−0.245256
$267$	−6.00000	−0.367194
$268$	−12.0000	−0.733017
$269$	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
$271$	−8.00000	−0.485965	−0.242983	−	0.970031i	$-0.578126\pi$
$271$	−8.00000	−0.485965	−0.242983	+	0.970031i	$0.578126\pi$
$272$	−6.00000	−0.363803
$273$	24.0000	1.45255
$274$	−2.00000	−0.120824
$275$	−4.00000	−0.241209
$276$	4.00000	0.240772
$277$	−2.00000	−0.120168	−0.0600842	−	0.998193i	$-0.519137\pi$
$277$	−2.00000	−0.120168	−0.0600842	+	0.998193i	$0.519137\pi$
$278$	−12.0000	−0.719712
$279$	−8.00000	−0.478947
$280$	4.00000	0.239046
$281$	−22.0000	−1.31241	−0.656205	−	0.754583i	$-0.727839\pi$
$281$	−22.0000	−1.31241	−0.656205	+	0.754583i	$0.727839\pi$
$282$	−12.0000	−0.714590
$283$	−16.0000	−0.951101	−0.475551	−	0.879688i	$-0.657751\pi$
$283$	−16.0000	−0.951101	−0.475551	+	0.879688i	$0.657751\pi$
$284$	−16.0000	−0.949425
$285$	−1.00000	−0.0592349
$286$	−24.0000	−1.41915
$287$	−40.0000	−2.36113
$288$	−1.00000	−0.0589256
$289$	19.0000	1.11765
$290$	−6.00000	−0.352332
$291$	14.0000	0.820695
$292$	−14.0000	−0.819288
$293$	2.00000	0.116841	0.0584206	−	0.998292i	$-0.481394\pi$
$293$	2.00000	0.116841	0.0584206	+	0.998292i	$0.481394\pi$
$294$	−9.00000	−0.524891
$295$	−4.00000	−0.232889
$296$	−2.00000	−0.116248
$297$	−4.00000	−0.232104
$298$	10.0000	0.579284
$299$	−24.0000	−1.38796
$300$	1.00000	0.0577350
$301$	32.0000	1.84445
$302$	−8.00000	−0.460348
$303$	6.00000	0.344691
$304$	−1.00000	−0.0573539
$305$	−2.00000	−0.114520
$306$	6.00000	0.342997
$307$	−20.0000	−1.14146	−0.570730	−	0.821138i	$-0.693340\pi$
$307$	−20.0000	−1.14146	−0.570730	+	0.821138i	$0.693340\pi$
$308$	16.0000	0.911685
$309$	8.00000	0.455104
$310$	8.00000	0.454369
$311$	−8.00000	−0.453638	−0.226819	−	0.973937i	$-0.572833\pi$
$311$	−8.00000	−0.453638	−0.226819	+	0.973937i	$0.572833\pi$
$312$	6.00000	0.339683
$313$	−6.00000	−0.339140	−0.169570	−	0.985518i	$-0.554238\pi$
$313$	−6.00000	−0.339140	−0.169570	+	0.985518i	$0.554238\pi$
$314$	−22.0000	−1.24153
$315$	−4.00000	−0.225374
$316$	8.00000	0.450035
$317$	−14.0000	−0.786318	−0.393159	−	0.919470i	$-0.628618\pi$
$317$	−14.0000	−0.786318	−0.393159	+	0.919470i	$0.628618\pi$
$318$	−2.00000	−0.112154
$319$	−24.0000	−1.34374
$320$	1.00000	0.0559017
$321$	−12.0000	−0.669775
$322$	16.0000	0.891645
$323$	6.00000	0.333849
$324$	1.00000	0.0555556
$325$	−6.00000	−0.332820
$326$	16.0000	0.886158
$327$	6.00000	0.331801
$328$	−10.0000	−0.552158
$329$	−48.0000	−2.64633
$330$	4.00000	0.220193
$331$	4.00000	0.219860	0.109930	−	0.993939i	$-0.464937\pi$
$331$	4.00000	0.219860	0.109930	+	0.993939i	$0.464937\pi$
$332$	0	0
$333$	2.00000	0.109599
$334$	0	0
$335$	−12.0000	−0.655630
$336$	−4.00000	−0.218218
$337$	14.0000	0.762629	0.381314	−	0.924445i	$-0.375472\pi$
$337$	14.0000	0.762629	0.381314	+	0.924445i	$0.375472\pi$
$338$	−23.0000	−1.25104
$339$	−10.0000	−0.543125
$340$	−6.00000	−0.325396
$341$	32.0000	1.73290
$342$	1.00000	0.0540738
$343$	−8.00000	−0.431959
$344$	8.00000	0.431331
$345$	4.00000	0.215353
$346$	6.00000	0.322562
$347$	32.0000	1.71785	0.858925	−	0.512101i	$-0.171133\pi$
$347$	32.0000	1.71785	0.858925	+	0.512101i	$0.171133\pi$
$348$	6.00000	0.321634
$349$	−2.00000	−0.107058	−0.0535288	−	0.998566i	$-0.517047\pi$
$349$	−2.00000	−0.107058	−0.0535288	+	0.998566i	$0.517047\pi$
$350$	4.00000	0.213809
$351$	−6.00000	−0.320256
$352$	4.00000	0.213201
$353$	26.0000	1.38384	0.691920	−	0.721974i	$-0.256765\pi$
$353$	26.0000	1.38384	0.691920	+	0.721974i	$0.256765\pi$
$354$	4.00000	0.212598
$355$	−16.0000	−0.849192
$356$	−6.00000	−0.317999
$357$	24.0000	1.27021
$358$	12.0000	0.634220
$359$	−16.0000	−0.844448	−0.422224	−	0.906492i	$-0.638750\pi$
$359$	−16.0000	−0.844448	−0.422224	+	0.906492i	$0.638750\pi$
$360$	−1.00000	−0.0527046
$361$	1.00000	0.0526316
$362$	2.00000	0.105118
$363$	5.00000	0.262432
$364$	24.0000	1.25794
$365$	−14.0000	−0.732793
$366$	2.00000	0.104542
$367$	4.00000	0.208798	0.104399	−	0.994535i	$-0.466708\pi$
$367$	4.00000	0.208798	0.104399	+	0.994535i	$0.466708\pi$
$368$	4.00000	0.208514
$369$	10.0000	0.520579
$370$	−2.00000	−0.103975
$371$	−8.00000	−0.415339
$372$	−8.00000	−0.414781
$373$	10.0000	0.517780	0.258890	−	0.965907i	$-0.416643\pi$
$373$	10.0000	0.517780	0.258890	+	0.965907i	$0.416643\pi$
$374$	−24.0000	−1.24101
$375$	1.00000	0.0516398
$376$	−12.0000	−0.618853
$377$	−36.0000	−1.85409
$378$	4.00000	0.205738
$379$	4.00000	0.205466	0.102733	−	0.994709i	$-0.467241\pi$
$379$	4.00000	0.205466	0.102733	+	0.994709i	$0.467241\pi$
$380$	−1.00000	−0.0512989
$381$	−16.0000	−0.819705
$382$	8.00000	0.409316
$383$	24.0000	1.22634	0.613171	−	0.789950i	$-0.289894\pi$
$383$	24.0000	1.22634	0.613171	+	0.789950i	$0.289894\pi$
$384$	−1.00000	−0.0510310
$385$	16.0000	0.815436
$386$	2.00000	0.101797
$387$	−8.00000	−0.406663
$388$	14.0000	0.710742
$389$	−26.0000	−1.31825	−0.659126	−	0.752032i	$-0.729074\pi$
$389$	−26.0000	−1.31825	−0.659126	+	0.752032i	$0.729074\pi$
$390$	6.00000	0.303822
$391$	−24.0000	−1.21373
$392$	−9.00000	−0.454569
$393$	12.0000	0.605320
$394$	−6.00000	−0.302276
$395$	8.00000	0.402524
$396$	−4.00000	−0.201008
$397$	22.0000	1.10415	0.552074	−	0.833795i	$-0.313837\pi$
$397$	22.0000	1.10415	0.552074	+	0.833795i	$0.313837\pi$
$398$	16.0000	0.802008
$399$	4.00000	0.200250
$400$	1.00000	0.0500000
$401$	−22.0000	−1.09863	−0.549314	−	0.835616i	$-0.685111\pi$
$401$	−22.0000	−1.09863	−0.549314	+	0.835616i	$0.685111\pi$
$402$	12.0000	0.598506
$403$	48.0000	2.39105
$404$	6.00000	0.298511
$405$	1.00000	0.0496904
$406$	24.0000	1.19110
$407$	−8.00000	−0.396545
$408$	6.00000	0.297044
$409$	−6.00000	−0.296681	−0.148340	−	0.988936i	$-0.547393\pi$
$409$	−6.00000	−0.296681	−0.148340	+	0.988936i	$0.547393\pi$
$410$	−10.0000	−0.493865
$411$	2.00000	0.0986527
$412$	8.00000	0.394132
$413$	16.0000	0.787309
$414$	−4.00000	−0.196589
$415$	0	0
$416$	6.00000	0.294174
$417$	12.0000	0.587643
$418$	−4.00000	−0.195646
$419$	20.0000	0.977064	0.488532	−	0.872546i	$-0.337533\pi$
$419$	20.0000	0.977064	0.488532	+	0.872546i	$0.337533\pi$
$420$	−4.00000	−0.195180
$421$	−26.0000	−1.26716	−0.633581	−	0.773676i	$-0.718416\pi$
$421$	−26.0000	−1.26716	−0.633581	+	0.773676i	$0.718416\pi$
$422$	20.0000	0.973585
$423$	12.0000	0.583460
$424$	−2.00000	−0.0971286
$425$	−6.00000	−0.291043
$426$	16.0000	0.775203
$427$	8.00000	0.387147
$428$	−12.0000	−0.580042
$429$	24.0000	1.15873
$430$	8.00000	0.385794
$431$	−32.0000	−1.54139	−0.770693	−	0.637207i	$-0.780090\pi$
$431$	−32.0000	−1.54139	−0.770693	+	0.637207i	$0.780090\pi$
$432$	1.00000	0.0481125
$433$	14.0000	0.672797	0.336399	−	0.941720i	$-0.390791\pi$
$433$	14.0000	0.672797	0.336399	+	0.941720i	$0.390791\pi$
$434$	−32.0000	−1.53605
$435$	6.00000	0.287678
$436$	6.00000	0.287348
$437$	−4.00000	−0.191346
$438$	14.0000	0.668946
$439$	32.0000	1.52728	0.763638	−	0.645644i	$-0.223411\pi$
$439$	32.0000	1.52728	0.763638	+	0.645644i	$0.223411\pi$
$440$	4.00000	0.190693
$441$	9.00000	0.428571
$442$	−36.0000	−1.71235
$443$	8.00000	0.380091	0.190046	−	0.981775i	$-0.439136\pi$
$443$	8.00000	0.380091	0.190046	+	0.981775i	$0.439136\pi$
$444$	2.00000	0.0949158
$445$	−6.00000	−0.284427
$446$	16.0000	0.757622
$447$	−10.0000	−0.472984
$448$	−4.00000	−0.188982
$449$	10.0000	0.471929	0.235965	−	0.971762i	$-0.424175\pi$
$449$	10.0000	0.471929	0.235965	+	0.971762i	$0.424175\pi$
$450$	−1.00000	−0.0471405
$451$	−40.0000	−1.88353
$452$	−10.0000	−0.470360
$453$	8.00000	0.375873
$454$	4.00000	0.187729
$455$	24.0000	1.12514
$456$	1.00000	0.0468293
$457$	10.0000	0.467780	0.233890	−	0.972263i	$-0.424854\pi$
$457$	10.0000	0.467780	0.233890	+	0.972263i	$0.424854\pi$
$458$	−6.00000	−0.280362
$459$	−6.00000	−0.280056
$460$	4.00000	0.186501
$461$	−18.0000	−0.838344	−0.419172	−	0.907907i	$-0.637680\pi$
$461$	−18.0000	−0.838344	−0.419172	+	0.907907i	$0.637680\pi$
$462$	−16.0000	−0.744387
$463$	20.0000	0.929479	0.464739	−	0.885448i	$-0.346148\pi$
$463$	20.0000	0.929479	0.464739	+	0.885448i	$0.346148\pi$
$464$	6.00000	0.278543
$465$	−8.00000	−0.370991
$466$	−10.0000	−0.463241
$467$	−8.00000	−0.370196	−0.185098	−	0.982720i	$-0.559260\pi$
$467$	−8.00000	−0.370196	−0.185098	+	0.982720i	$0.559260\pi$
$468$	−6.00000	−0.277350
$469$	48.0000	2.21643
$470$	−12.0000	−0.553519
$471$	22.0000	1.01371
$472$	4.00000	0.184115
$473$	32.0000	1.47136
$474$	−8.00000	−0.367452
$475$	−1.00000	−0.0458831
$476$	24.0000	1.10004
$477$	2.00000	0.0915737
$478$	−16.0000	−0.731823
$479$	24.0000	1.09659	0.548294	−	0.836286i	$-0.315277\pi$
$479$	24.0000	1.09659	0.548294	+	0.836286i	$0.315277\pi$
$480$	−1.00000	−0.0456435
$481$	−12.0000	−0.547153
$482$	22.0000	1.00207
$483$	−16.0000	−0.728025
$484$	5.00000	0.227273
$485$	14.0000	0.635707
$486$	−1.00000	−0.0453609
$487$	−16.0000	−0.725029	−0.362515	−	0.931978i	$-0.618082\pi$
$487$	−16.0000	−0.725029	−0.362515	+	0.931978i	$0.618082\pi$
$488$	2.00000	0.0905357
$489$	−16.0000	−0.723545
$490$	−9.00000	−0.406579
$491$	−12.0000	−0.541552	−0.270776	−	0.962642i	$-0.587280\pi$
$491$	−12.0000	−0.541552	−0.270776	+	0.962642i	$0.587280\pi$
$492$	10.0000	0.450835
$493$	−36.0000	−1.62136
$494$	−6.00000	−0.269953
$495$	−4.00000	−0.179787
$496$	−8.00000	−0.359211
$497$	64.0000	2.87079
$498$	0	0
$499$	−28.0000	−1.25345	−0.626726	−	0.779240i	$-0.715605\pi$
$499$	−28.0000	−1.25345	−0.626726	+	0.779240i	$0.715605\pi$
$500$	1.00000	0.0447214
$501$	0	0
$502$	−4.00000	−0.178529
$503$	−12.0000	−0.535054	−0.267527	−	0.963550i	$-0.586206\pi$
$503$	−12.0000	−0.535054	−0.267527	+	0.963550i	$0.586206\pi$
$504$	4.00000	0.178174
$505$	6.00000	0.266996
$506$	16.0000	0.711287
$507$	23.0000	1.02147
$508$	−16.0000	−0.709885
$509$	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
$511$	56.0000	2.47729
$512$	−1.00000	−0.0441942
$513$	−1.00000	−0.0441511
$514$	18.0000	0.793946
$515$	8.00000	0.352522
$516$	−8.00000	−0.352180
$517$	−48.0000	−2.11104
$518$	8.00000	0.351500
$519$	−6.00000	−0.263371
$520$	6.00000	0.263117
$521$	−14.0000	−0.613351	−0.306676	−	0.951814i	$-0.599217\pi$
$521$	−14.0000	−0.613351	−0.306676	+	0.951814i	$0.599217\pi$
$522$	−6.00000	−0.262613
$523$	20.0000	0.874539	0.437269	−	0.899331i	$-0.355946\pi$
$523$	20.0000	0.874539	0.437269	+	0.899331i	$0.355946\pi$
$524$	12.0000	0.524222
$525$	−4.00000	−0.174574
$526$	−20.0000	−0.872041
$527$	48.0000	2.09091
$528$	−4.00000	−0.174078
$529$	−7.00000	−0.304348
$530$	−2.00000	−0.0868744
$531$	−4.00000	−0.173585
$532$	4.00000	0.173422
$533$	−60.0000	−2.59889
$534$	6.00000	0.259645
$535$	−12.0000	−0.518805
$536$	12.0000	0.518321
$537$	−12.0000	−0.517838
$538$	−14.0000	−0.603583
$539$	−36.0000	−1.55063
$540$	1.00000	0.0430331
$541$	−34.0000	−1.46177	−0.730887	−	0.682498i	$-0.760893\pi$
$541$	−34.0000	−1.46177	−0.730887	+	0.682498i	$0.760893\pi$
$542$	8.00000	0.343629
$543$	−2.00000	−0.0858282
$544$	6.00000	0.257248
$545$	6.00000	0.257012
$546$	−24.0000	−1.02711
$547$	−36.0000	−1.53925	−0.769624	−	0.638497i	$-0.779557\pi$
$547$	−36.0000	−1.53925	−0.769624	+	0.638497i	$0.779557\pi$
$548$	2.00000	0.0854358
$549$	−2.00000	−0.0853579
$550$	4.00000	0.170561
$551$	−6.00000	−0.255609
$552$	−4.00000	−0.170251
$553$	−32.0000	−1.36078
$554$	2.00000	0.0849719
$555$	2.00000	0.0848953
$556$	12.0000	0.508913
$557$	−26.0000	−1.10166	−0.550828	−	0.834619i	$-0.685688\pi$
$557$	−26.0000	−1.10166	−0.550828	+	0.834619i	$0.685688\pi$
$558$	8.00000	0.338667
$559$	48.0000	2.03018
$560$	−4.00000	−0.169031
$561$	24.0000	1.01328
$562$	22.0000	0.928014
$563$	−20.0000	−0.842900	−0.421450	−	0.906852i	$-0.638479\pi$
$563$	−20.0000	−0.842900	−0.421450	+	0.906852i	$0.638479\pi$
$564$	12.0000	0.505291
$565$	−10.0000	−0.420703
$566$	16.0000	0.672530
$567$	−4.00000	−0.167984
$568$	16.0000	0.671345
$569$	34.0000	1.42535	0.712677	−	0.701492i	$-0.247483\pi$
$569$	34.0000	1.42535	0.712677	+	0.701492i	$0.247483\pi$
$570$	1.00000	0.0418854
$571$	4.00000	0.167395	0.0836974	−	0.996491i	$-0.473327\pi$
$571$	4.00000	0.167395	0.0836974	+	0.996491i	$0.473327\pi$
$572$	24.0000	1.00349
$573$	−8.00000	−0.334205
$574$	40.0000	1.66957
$575$	4.00000	0.166812
$576$	1.00000	0.0416667
$577$	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
$579$	−2.00000	−0.0831172
$580$	6.00000	0.249136
$581$	0	0
$582$	−14.0000	−0.580319
$583$	−8.00000	−0.331326
$584$	14.0000	0.579324
$585$	−6.00000	−0.248069
$586$	−2.00000	−0.0826192
$587$	32.0000	1.32078	0.660391	−	0.750922i	$-0.270391\pi$
$587$	32.0000	1.32078	0.660391	+	0.750922i	$0.270391\pi$
$588$	9.00000	0.371154
$589$	8.00000	0.329634
$590$	4.00000	0.164677
$591$	6.00000	0.246807
$592$	2.00000	0.0821995
$593$	34.0000	1.39621	0.698106	−	0.715994i	$-0.254026\pi$
$593$	34.0000	1.39621	0.698106	+	0.715994i	$0.254026\pi$
$594$	4.00000	0.164122
$595$	24.0000	0.983904
$596$	−10.0000	−0.409616
$597$	−16.0000	−0.654836
$598$	24.0000	0.981433
$599$	0	0		−	1.00000i	$-0.5\pi$
$599$	0	0			1.00000i	$0.5\pi$
$600$	−1.00000	−0.0408248
$601$	2.00000	0.0815817	0.0407909	−	0.999168i	$-0.487012\pi$
$601$	2.00000	0.0815817	0.0407909	+	0.999168i	$0.487012\pi$
$602$	−32.0000	−1.30422
$603$	−12.0000	−0.488678
$604$	8.00000	0.325515
$605$	5.00000	0.203279
$606$	−6.00000	−0.243733
$607$	24.0000	0.974130	0.487065	−	0.873366i	$-0.338067\pi$
$607$	24.0000	0.974130	0.487065	+	0.873366i	$0.338067\pi$
$608$	1.00000	0.0405554
$609$	−24.0000	−0.972529
$610$	2.00000	0.0809776
$611$	−72.0000	−2.91281
$612$	−6.00000	−0.242536
$613$	46.0000	1.85792	0.928961	−	0.370177i	$-0.120703\pi$
$613$	46.0000	1.85792	0.928961	+	0.370177i	$0.120703\pi$
$614$	20.0000	0.807134
$615$	10.0000	0.403239
$616$	−16.0000	−0.644658
$617$	−14.0000	−0.563619	−0.281809	−	0.959470i	$-0.590935\pi$
$617$	−14.0000	−0.563619	−0.281809	+	0.959470i	$0.590935\pi$
$618$	−8.00000	−0.321807
$619$	−20.0000	−0.803868	−0.401934	−	0.915669i	$-0.631662\pi$
$619$	−20.0000	−0.803868	−0.401934	+	0.915669i	$0.631662\pi$
$620$	−8.00000	−0.321288
$621$	4.00000	0.160514
$622$	8.00000	0.320771
$623$	24.0000	0.961540
$624$	−6.00000	−0.240192
$625$	1.00000	0.0400000
$626$	6.00000	0.239808
$627$	4.00000	0.159745
$628$	22.0000	0.877896
$629$	−12.0000	−0.478471
$630$	4.00000	0.159364
$631$	−32.0000	−1.27390	−0.636950	−	0.770905i	$-0.719804\pi$
$631$	−32.0000	−1.27390	−0.636950	+	0.770905i	$0.719804\pi$
$632$	−8.00000	−0.318223
$633$	−20.0000	−0.794929
$634$	14.0000	0.556011
$635$	−16.0000	−0.634941
$636$	2.00000	0.0793052
$637$	−54.0000	−2.13956
$638$	24.0000	0.950169
$639$	−16.0000	−0.632950
$640$	−1.00000	−0.0395285
$641$	−14.0000	−0.552967	−0.276483	−	0.961019i	$-0.589169\pi$
$641$	−14.0000	−0.552967	−0.276483	+	0.961019i	$0.589169\pi$
$642$	12.0000	0.473602
$643$	−40.0000	−1.57745	−0.788723	−	0.614749i	$-0.789257\pi$
$643$	−40.0000	−1.57745	−0.788723	+	0.614749i	$0.789257\pi$
$644$	−16.0000	−0.630488
$645$	−8.00000	−0.315000
$646$	−6.00000	−0.236067
$647$	12.0000	0.471769	0.235884	−	0.971781i	$-0.424201\pi$
$647$	12.0000	0.471769	0.235884	+	0.971781i	$0.424201\pi$
$648$	−1.00000	−0.0392837
$649$	16.0000	0.628055
$650$	6.00000	0.235339
$651$	32.0000	1.25418
$652$	−16.0000	−0.626608
$653$	6.00000	0.234798	0.117399	−	0.993085i	$-0.462544\pi$
$653$	6.00000	0.234798	0.117399	+	0.993085i	$0.462544\pi$
$654$	−6.00000	−0.234619
$655$	12.0000	0.468879
$656$	10.0000	0.390434
$657$	−14.0000	−0.546192
$658$	48.0000	1.87123
$659$	−12.0000	−0.467454	−0.233727	−	0.972302i	$-0.575092\pi$
$659$	−12.0000	−0.467454	−0.233727	+	0.972302i	$0.575092\pi$
$660$	−4.00000	−0.155700
$661$	−10.0000	−0.388955	−0.194477	−	0.980907i	$-0.562301\pi$
$661$	−10.0000	−0.388955	−0.194477	+	0.980907i	$0.562301\pi$
$662$	−4.00000	−0.155464
$663$	36.0000	1.39812
$664$	0	0
$665$	4.00000	0.155113
$666$	−2.00000	−0.0774984
$667$	24.0000	0.929284
$668$	0	0
$669$	−16.0000	−0.618596
$670$	12.0000	0.463600
$671$	8.00000	0.308837
$672$	4.00000	0.154303
$673$	22.0000	0.848038	0.424019	−	0.905653i	$-0.360619\pi$
$673$	22.0000	0.848038	0.424019	+	0.905653i	$0.360619\pi$
$674$	−14.0000	−0.539260
$675$	1.00000	0.0384900
$676$	23.0000	0.884615
$677$	−30.0000	−1.15299	−0.576497	−	0.817099i	$-0.695581\pi$
$677$	−30.0000	−1.15299	−0.576497	+	0.817099i	$0.695581\pi$
$678$	10.0000	0.384048
$679$	−56.0000	−2.14908
$680$	6.00000	0.230089
$681$	−4.00000	−0.153280
$682$	−32.0000	−1.22534
$683$	−12.0000	−0.459167	−0.229584	−	0.973289i	$-0.573736\pi$
$683$	−12.0000	−0.459167	−0.229584	+	0.973289i	$0.573736\pi$
$684$	−1.00000	−0.0382360
$685$	2.00000	0.0764161
$686$	8.00000	0.305441
$687$	6.00000	0.228914
$688$	−8.00000	−0.304997
$689$	−12.0000	−0.457164
$690$	−4.00000	−0.152277
$691$	−20.0000	−0.760836	−0.380418	−	0.924815i	$-0.624220\pi$
$691$	−20.0000	−0.760836	−0.380418	+	0.924815i	$0.624220\pi$
$692$	−6.00000	−0.228086
$693$	16.0000	0.607790
$694$	−32.0000	−1.21470
$695$	12.0000	0.455186
$696$	−6.00000	−0.227429
$697$	−60.0000	−2.27266
$698$	2.00000	0.0757011
$699$	10.0000	0.378235
$700$	−4.00000	−0.151186
$701$	−18.0000	−0.679851	−0.339925	−	0.940452i	$-0.610402\pi$
$701$	−18.0000	−0.679851	−0.339925	+	0.940452i	$0.610402\pi$
$702$	6.00000	0.226455
$703$	−2.00000	−0.0754314
$704$	−4.00000	−0.150756
$705$	12.0000	0.451946
$706$	−26.0000	−0.978523
$707$	−24.0000	−0.902613
$708$	−4.00000	−0.150329
$709$	6.00000	0.225335	0.112667	−	0.993633i	$-0.464061\pi$
$709$	6.00000	0.225335	0.112667	+	0.993633i	$0.464061\pi$
$710$	16.0000	0.600469
$711$	8.00000	0.300023
$712$	6.00000	0.224860
$713$	−32.0000	−1.19841
$714$	−24.0000	−0.898177
$715$	24.0000	0.897549
$716$	−12.0000	−0.448461
$717$	16.0000	0.597531
$718$	16.0000	0.597115
$719$	24.0000	0.895049	0.447524	−	0.894272i	$-0.352306\pi$
$719$	24.0000	0.895049	0.447524	+	0.894272i	$0.352306\pi$
$720$	1.00000	0.0372678
$721$	−32.0000	−1.19174
$722$	−1.00000	−0.0372161
$723$	−22.0000	−0.818189
$724$	−2.00000	−0.0743294
$725$	6.00000	0.222834
$726$	−5.00000	−0.185567
$727$	28.0000	1.03846	0.519231	−	0.854634i	$-0.326218\pi$
$727$	28.0000	1.03846	0.519231	+	0.854634i	$0.326218\pi$
$728$	−24.0000	−0.889499
$729$	1.00000	0.0370370
$730$	14.0000	0.518163
$731$	48.0000	1.77534
$732$	−2.00000	−0.0739221
$733$	−50.0000	−1.84679	−0.923396	−	0.383849i	$-0.874598\pi$
$733$	−50.0000	−1.84679	−0.923396	+	0.383849i	$0.874598\pi$
$734$	−4.00000	−0.147643
$735$	9.00000	0.331970
$736$	−4.00000	−0.147442
$737$	48.0000	1.76810
$738$	−10.0000	−0.368105
$739$	44.0000	1.61857	0.809283	−	0.587419i	$-0.199856\pi$
$739$	44.0000	1.61857	0.809283	+	0.587419i	$0.199856\pi$
$740$	2.00000	0.0735215
$741$	6.00000	0.220416
$742$	8.00000	0.293689
$743$	16.0000	0.586983	0.293492	−	0.955962i	$-0.405183\pi$
$743$	16.0000	0.586983	0.293492	+	0.955962i	$0.405183\pi$
$744$	8.00000	0.293294
$745$	−10.0000	−0.366372
$746$	−10.0000	−0.366126
$747$	0	0
$748$	24.0000	0.877527
$749$	48.0000	1.75388
$750$	−1.00000	−0.0365148
$751$	−32.0000	−1.16770	−0.583848	−	0.811863i	$-0.698454\pi$
$751$	−32.0000	−1.16770	−0.583848	+	0.811863i	$0.698454\pi$
$752$	12.0000	0.437595
$753$	4.00000	0.145768
$754$	36.0000	1.31104
$755$	8.00000	0.291150
$756$	−4.00000	−0.145479
$757$	−10.0000	−0.363456	−0.181728	−	0.983349i	$-0.558169\pi$
$757$	−10.0000	−0.363456	−0.181728	+	0.983349i	$0.558169\pi$
$758$	−4.00000	−0.145287
$759$	−16.0000	−0.580763
$760$	1.00000	0.0362738
$761$	−6.00000	−0.217500	−0.108750	−	0.994069i	$-0.534685\pi$
$761$	−6.00000	−0.217500	−0.108750	+	0.994069i	$0.534685\pi$
$762$	16.0000	0.579619
$763$	−24.0000	−0.868858
$764$	−8.00000	−0.289430
$765$	−6.00000	−0.216930
$766$	−24.0000	−0.867155
$767$	24.0000	0.866590
$768$	1.00000	0.0360844
$769$	18.0000	0.649097	0.324548	−	0.945869i	$-0.394788\pi$
$769$	18.0000	0.649097	0.324548	+	0.945869i	$0.394788\pi$
$770$	−16.0000	−0.576600
$771$	−18.0000	−0.648254
$772$	−2.00000	−0.0719816
$773$	10.0000	0.359675	0.179838	−	0.983696i	$-0.442443\pi$
$773$	10.0000	0.359675	0.179838	+	0.983696i	$0.442443\pi$
$774$	8.00000	0.287554
$775$	−8.00000	−0.287368
$776$	−14.0000	−0.502571
$777$	−8.00000	−0.286998
$778$	26.0000	0.932145
$779$	−10.0000	−0.358287
$780$	−6.00000	−0.214834
$781$	64.0000	2.29010
$782$	24.0000	0.858238
$783$	6.00000	0.214423
$784$	9.00000	0.321429
$785$	22.0000	0.785214
$786$	−12.0000	−0.428026
$787$	−52.0000	−1.85360	−0.926800	−	0.375555i	$-0.877452\pi$
$787$	−52.0000	−1.85360	−0.926800	+	0.375555i	$0.877452\pi$
$788$	6.00000	0.213741
$789$	20.0000	0.712019
$790$	−8.00000	−0.284627
$791$	40.0000	1.42224
$792$	4.00000	0.142134
$793$	12.0000	0.426132
$794$	−22.0000	−0.780751
$795$	2.00000	0.0709327
$796$	−16.0000	−0.567105
$797$	−38.0000	−1.34603	−0.673015	−	0.739629i	$-0.735001\pi$
$797$	−38.0000	−1.34603	−0.673015	+	0.739629i	$0.735001\pi$
$798$	−4.00000	−0.141598
$799$	−72.0000	−2.54718
$800$	−1.00000	−0.0353553
$801$	−6.00000	−0.212000
$802$	22.0000	0.776847
$803$	56.0000	1.97620
$804$	−12.0000	−0.423207
$805$	−16.0000	−0.563926
$806$	−48.0000	−1.69073
$807$	14.0000	0.492823
$808$	−6.00000	−0.211079
$809$	42.0000	1.47664	0.738321	−	0.674450i	$-0.235619\pi$
$809$	42.0000	1.47664	0.738321	+	0.674450i	$0.235619\pi$
$810$	−1.00000	−0.0351364
$811$	28.0000	0.983213	0.491606	−	0.870817i	$-0.336410\pi$
$811$	28.0000	0.983213	0.491606	+	0.870817i	$0.336410\pi$
$812$	−24.0000	−0.842235
$813$	−8.00000	−0.280572
$814$	8.00000	0.280400
$815$	−16.0000	−0.560456
$816$	−6.00000	−0.210042
$817$	8.00000	0.279885
$818$	6.00000	0.209785
$819$	24.0000	0.838628
$820$	10.0000	0.349215
$821$	6.00000	0.209401	0.104701	−	0.994504i	$-0.466612\pi$
$821$	6.00000	0.209401	0.104701	+	0.994504i	$0.466612\pi$
$822$	−2.00000	−0.0697580
$823$	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
$825$	−4.00000	−0.139262
$826$	−16.0000	−0.556711
$827$	12.0000	0.417281	0.208640	−	0.977992i	$-0.433096\pi$
$827$	12.0000	0.417281	0.208640	+	0.977992i	$0.433096\pi$
$828$	4.00000	0.139010
$829$	−26.0000	−0.903017	−0.451509	−	0.892267i	$-0.649114\pi$
$829$	−26.0000	−0.903017	−0.451509	+	0.892267i	$0.649114\pi$
$830$	0	0
$831$	−2.00000	−0.0693792
$832$	−6.00000	−0.208013
$833$	−54.0000	−1.87099
$834$	−12.0000	−0.415526
$835$	0	0
$836$	4.00000	0.138343
$837$	−8.00000	−0.276520
$838$	−20.0000	−0.690889
$839$	0	0		−	1.00000i	$-0.5\pi$
$839$	0	0			1.00000i	$0.5\pi$
$840$	4.00000	0.138013
$841$	7.00000	0.241379
$842$	26.0000	0.896019
$843$	−22.0000	−0.757720
$844$	−20.0000	−0.688428
$845$	23.0000	0.791224
$846$	−12.0000	−0.412568
$847$	−20.0000	−0.687208
$848$	2.00000	0.0686803
$849$	−16.0000	−0.549119
$850$	6.00000	0.205798
$851$	8.00000	0.274236
$852$	−16.0000	−0.548151
$853$	−10.0000	−0.342393	−0.171197	−	0.985237i	$-0.554763\pi$
$853$	−10.0000	−0.342393	−0.171197	+	0.985237i	$0.554763\pi$
$854$	−8.00000	−0.273754
$855$	−1.00000	−0.0341993
$856$	12.0000	0.410152
$857$	6.00000	0.204956	0.102478	−	0.994735i	$-0.467323\pi$
$857$	6.00000	0.204956	0.102478	+	0.994735i	$0.467323\pi$
$858$	−24.0000	−0.819346
$859$	−44.0000	−1.50126	−0.750630	−	0.660722i	$-0.770250\pi$
$859$	−44.0000	−1.50126	−0.750630	+	0.660722i	$0.770250\pi$
$860$	−8.00000	−0.272798
$861$	−40.0000	−1.36320
$862$	32.0000	1.08992
$863$	24.0000	0.816970	0.408485	−	0.912765i	$-0.366057\pi$
$863$	24.0000	0.816970	0.408485	+	0.912765i	$0.366057\pi$
$864$	−1.00000	−0.0340207
$865$	−6.00000	−0.204006
$866$	−14.0000	−0.475739
$867$	19.0000	0.645274
$868$	32.0000	1.08615
$869$	−32.0000	−1.08553
$870$	−6.00000	−0.203419
$871$	72.0000	2.43963
$872$	−6.00000	−0.203186
$873$	14.0000	0.473828
$874$	4.00000	0.135302
$875$	−4.00000	−0.135225
$876$	−14.0000	−0.473016
$877$	18.0000	0.607817	0.303908	−	0.952701i	$-0.401708\pi$
$877$	18.0000	0.607817	0.303908	+	0.952701i	$0.401708\pi$
$878$	−32.0000	−1.07995
$879$	2.00000	0.0674583
$880$	−4.00000	−0.134840
$881$	−14.0000	−0.471672	−0.235836	−	0.971793i	$-0.575783\pi$
$881$	−14.0000	−0.471672	−0.235836	+	0.971793i	$0.575783\pi$
$882$	−9.00000	−0.303046
$883$	−16.0000	−0.538443	−0.269221	−	0.963078i	$-0.586766\pi$
$883$	−16.0000	−0.538443	−0.269221	+	0.963078i	$0.586766\pi$
$884$	36.0000	1.21081
$885$	−4.00000	−0.134459
$886$	−8.00000	−0.268765
$887$	−8.00000	−0.268614	−0.134307	−	0.990940i	$-0.542881\pi$
$887$	−8.00000	−0.268614	−0.134307	+	0.990940i	$0.542881\pi$
$888$	−2.00000	−0.0671156
$889$	64.0000	2.14649
$890$	6.00000	0.201120
$891$	−4.00000	−0.134005
$892$	−16.0000	−0.535720
$893$	−12.0000	−0.401565
$894$	10.0000	0.334450
$895$	−12.0000	−0.401116
$896$	4.00000	0.133631
$897$	−24.0000	−0.801337
$898$	−10.0000	−0.333704
$899$	−48.0000	−1.60089
$900$	1.00000	0.0333333
$901$	−12.0000	−0.399778
$902$	40.0000	1.33185
$903$	32.0000	1.06489
$904$	10.0000	0.332595
$905$	−2.00000	−0.0664822
$906$	−8.00000	−0.265782
$907$	−12.0000	−0.398453	−0.199227	−	0.979953i	$-0.563843\pi$
$907$	−12.0000	−0.398453	−0.199227	+	0.979953i	$0.563843\pi$
$908$	−4.00000	−0.132745
$909$	6.00000	0.199007
$910$	−24.0000	−0.795592
$911$	16.0000	0.530104	0.265052	−	0.964234i	$-0.414611\pi$
$911$	16.0000	0.530104	0.265052	+	0.964234i	$0.414611\pi$
$912$	−1.00000	−0.0331133
$913$	0	0
$914$	−10.0000	−0.330771
$915$	−2.00000	−0.0661180
$916$	6.00000	0.198246
$917$	−48.0000	−1.58510
$918$	6.00000	0.198030
$919$	0	0		−	1.00000i	$-0.5\pi$
$919$	0	0			1.00000i	$0.5\pi$
$920$	−4.00000	−0.131876
$921$	−20.0000	−0.659022
$922$	18.0000	0.592798
$923$	96.0000	3.15988
$924$	16.0000	0.526361
$925$	2.00000	0.0657596
$926$	−20.0000	−0.657241
$927$	8.00000	0.262754
$928$	−6.00000	−0.196960
$929$	−14.0000	−0.459325	−0.229663	−	0.973270i	$-0.573762\pi$
$929$	−14.0000	−0.459325	−0.229663	+	0.973270i	$0.573762\pi$
$930$	8.00000	0.262330
$931$	−9.00000	−0.294963
$932$	10.0000	0.327561
$933$	−8.00000	−0.261908
$934$	8.00000	0.261768
$935$	24.0000	0.784884
$936$	6.00000	0.196116
$937$	−30.0000	−0.980057	−0.490029	−	0.871706i	$-0.663014\pi$
$937$	−30.0000	−0.980057	−0.490029	+	0.871706i	$0.663014\pi$
$938$	−48.0000	−1.56726
$939$	−6.00000	−0.195803
$940$	12.0000	0.391397
$941$	46.0000	1.49956	0.749779	−	0.661689i	$-0.230160\pi$
$941$	46.0000	1.49956	0.749779	+	0.661689i	$0.230160\pi$
$942$	−22.0000	−0.716799
$943$	40.0000	1.30258
$944$	−4.00000	−0.130189
$945$	−4.00000	−0.130120
$946$	−32.0000	−1.04041
$947$	−24.0000	−0.779895	−0.389948	−	0.920837i	$-0.627507\pi$
$947$	−24.0000	−0.779895	−0.389948	+	0.920837i	$0.627507\pi$
$948$	8.00000	0.259828
$949$	84.0000	2.72676
$950$	1.00000	0.0324443
$951$	−14.0000	−0.453981
$952$	−24.0000	−0.777844
$953$	−42.0000	−1.36051	−0.680257	−	0.732974i	$-0.738132\pi$
$953$	−42.0000	−1.36051	−0.680257	+	0.732974i	$0.738132\pi$
$954$	−2.00000	−0.0647524
$955$	−8.00000	−0.258874
$956$	16.0000	0.517477
$957$	−24.0000	−0.775810
$958$	−24.0000	−0.775405
$959$	−8.00000	−0.258333
$960$	1.00000	0.0322749
$961$	33.0000	1.06452
$962$	12.0000	0.386896
$963$	−12.0000	−0.386695
$964$	−22.0000	−0.708572
$965$	−2.00000	−0.0643823
$966$	16.0000	0.514792
$967$	52.0000	1.67221	0.836104	−	0.548572i	$-0.184828\pi$
$967$	52.0000	1.67221	0.836104	+	0.548572i	$0.184828\pi$
$968$	−5.00000	−0.160706
$969$	6.00000	0.192748
$970$	−14.0000	−0.449513
$971$	28.0000	0.898563	0.449281	−	0.893390i	$-0.351680\pi$
$971$	28.0000	0.898563	0.449281	+	0.893390i	$0.351680\pi$
$972$	1.00000	0.0320750
$973$	−48.0000	−1.53881
$974$	16.0000	0.512673
$975$	−6.00000	−0.192154
$976$	−2.00000	−0.0640184
$977$	−2.00000	−0.0639857	−0.0319928	−	0.999488i	$-0.510185\pi$
$977$	−2.00000	−0.0639857	−0.0319928	+	0.999488i	$0.510185\pi$
$978$	16.0000	0.511624
$979$	24.0000	0.767043
$980$	9.00000	0.287494
$981$	6.00000	0.191565
$982$	12.0000	0.382935
$983$	0	0		−	1.00000i	$-0.5\pi$
$983$	0	0			1.00000i	$0.5\pi$
$984$	−10.0000	−0.318788
$985$	6.00000	0.191176
$986$	36.0000	1.14647
$987$	−48.0000	−1.52786
$988$	6.00000	0.190885
$989$	−32.0000	−1.01754
$990$	4.00000	0.127128
$991$	16.0000	0.508257	0.254128	−	0.967170i	$-0.418211\pi$
$991$	16.0000	0.508257	0.254128	+	0.967170i	$0.418211\pi$
$992$	8.00000	0.254000
$993$	4.00000	0.126936
$994$	−64.0000	−2.02996
$995$	−16.0000	−0.507234
$996$	0	0
$997$	46.0000	1.45683	0.728417	−	0.685134i	$-0.240256\pi$
$997$	46.0000	1.45683	0.728417	+	0.685134i	$0.240256\pi$
$998$	28.0000	0.886325
$999$	2.00000	0.0632772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.a.e.1.1	✓	1
3.2	odd	2		1710.2.a.l.1.1		1
4.3	odd	2		4560.2.a.q.1.1		1
5.2	odd	4		2850.2.d.a.799.1		2
5.3	odd	4		2850.2.d.a.799.2		2
5.4	even	2		2850.2.a.v.1.1		1
15.14	odd	2		8550.2.a.r.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.a.e.1.1	✓	1	1.1	even	1	trivial
1710.2.a.l.1.1		1	3.2	odd	2
2850.2.a.v.1.1		1	5.4	even	2
2850.2.d.a.799.1		2	5.2	odd	4
2850.2.d.a.799.2		2	5.3	odd	4
4560.2.a.q.1.1		1	4.3	odd	2
8550.2.a.r.1.1		1	15.14	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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