LMFDB - Embedded newform 1290.2.a.j.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1290,2,Mod(1,1290)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1290, 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("1290.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1290 = 2 \cdot 3 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1290.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:	$10.3007018607$
Analytic rank:	$0$
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	$\chi$	$=$	1290.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -4.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -4.00000 q^{11} -1.00000 q^{12} +4.00000 q^{13} -4.00000 q^{14} +1.00000 q^{15} +1.00000 q^{16} +4.00000 q^{17} +1.00000 q^{18} +4.00000 q^{19} -1.00000 q^{20} +4.00000 q^{21} -4.00000 q^{22} +8.00000 q^{23} -1.00000 q^{24} +1.00000 q^{25} +4.00000 q^{26} -1.00000 q^{27} -4.00000 q^{28} +6.00000 q^{29} +1.00000 q^{30} -4.00000 q^{31} +1.00000 q^{32} +4.00000 q^{33} +4.00000 q^{34} +4.00000 q^{35} +1.00000 q^{36} +2.00000 q^{37} +4.00000 q^{38} -4.00000 q^{39} -1.00000 q^{40} +10.0000 q^{41} +4.00000 q^{42} -1.00000 q^{43} -4.00000 q^{44} -1.00000 q^{45} +8.00000 q^{46} +4.00000 q^{47} -1.00000 q^{48} +9.00000 q^{49} +1.00000 q^{50} -4.00000 q^{51} +4.00000 q^{52} -2.00000 q^{53} -1.00000 q^{54} +4.00000 q^{55} -4.00000 q^{56} -4.00000 q^{57} +6.00000 q^{58} -12.0000 q^{59} +1.00000 q^{60} -4.00000 q^{62} -4.00000 q^{63} +1.00000 q^{64} -4.00000 q^{65} +4.00000 q^{66} +8.00000 q^{67} +4.00000 q^{68} -8.00000 q^{69} +4.00000 q^{70} -12.0000 q^{71} +1.00000 q^{72} -14.0000 q^{73} +2.00000 q^{74} -1.00000 q^{75} +4.00000 q^{76} +16.0000 q^{77} -4.00000 q^{78} +8.00000 q^{79} -1.00000 q^{80} +1.00000 q^{81} +10.0000 q^{82} +6.00000 q^{83} +4.00000 q^{84} -4.00000 q^{85} -1.00000 q^{86} -6.00000 q^{87} -4.00000 q^{88} -4.00000 q^{89} -1.00000 q^{90} -16.0000 q^{91} +8.00000 q^{92} +4.00000 q^{93} +4.00000 q^{94} -4.00000 q^{95} -1.00000 q^{96} +2.00000 q^{97} +9.00000 q^{98} -4.00000 q^{99} +O(q^{100})\)

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
$13$	4.00000	1.10940	0.554700	−	0.832050i	$-0.312833\pi$
$13$	4.00000	1.10940	0.554700	+	0.832050i	$0.312833\pi$
$14$	−4.00000	−1.06904
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	4.00000	0.970143	0.485071	−	0.874475i	$-0.338794\pi$
$17$	4.00000	0.970143	0.485071	+	0.874475i	$0.338794\pi$
$18$	1.00000	0.235702
$19$	4.00000	0.917663	0.458831	−	0.888523i	$-0.348268\pi$
$19$	4.00000	0.917663	0.458831	+	0.888523i	$0.348268\pi$
$20$	−1.00000	−0.223607
$21$	4.00000	0.872872
$22$	−4.00000	−0.852803
$23$	8.00000	1.66812	0.834058	−	0.551677i	$-0.186012\pi$
$23$	8.00000	1.66812	0.834058	+	0.551677i	$0.186012\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	4.00000	0.784465
$27$	−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
$31$	−4.00000	−0.718421	−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000	−0.718421	−0.359211	+	0.933257i	$0.616954\pi$
$32$	1.00000	0.176777
$33$	4.00000	0.696311
$34$	4.00000	0.685994
$35$	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	$0.447432\pi$
$38$	4.00000	0.648886
$39$	−4.00000	−0.640513
$40$	−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
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	−4.00000	−0.603023
$45$	−1.00000	−0.149071
$46$	8.00000	1.17954
$47$	4.00000	0.583460	0.291730	−	0.956501i	$-0.405769\pi$
$47$	4.00000	0.583460	0.291730	+	0.956501i	$0.405769\pi$
$48$	−1.00000	−0.144338
$49$	9.00000	1.28571
$50$	1.00000	0.141421
$51$	−4.00000	−0.560112
$52$	4.00000	0.554700
$53$	−2.00000	−0.274721	−0.137361	−	0.990521i	$-0.543862\pi$
$53$	−2.00000	−0.274721	−0.137361	+	0.990521i	$0.543862\pi$
$54$	−1.00000	−0.136083
$55$	4.00000	0.539360
$56$	−4.00000	−0.534522
$57$	−4.00000	−0.529813
$58$	6.00000	0.787839
$59$	−12.0000	−1.56227	−0.781133	−	0.624364i	$-0.785358\pi$
$59$	−12.0000	−1.56227	−0.781133	+	0.624364i	$0.785358\pi$
$60$	1.00000	0.129099
$61$	0	0		−	1.00000i	$-0.5\pi$
$61$	0	0			1.00000i	$0.5\pi$
$62$	−4.00000	−0.508001
$63$	−4.00000	−0.503953
$64$	1.00000	0.125000
$65$	−4.00000	−0.496139
$66$	4.00000	0.492366
$67$	8.00000	0.977356	0.488678	−	0.872464i	$-0.337479\pi$
$67$	8.00000	0.977356	0.488678	+	0.872464i	$0.337479\pi$
$68$	4.00000	0.485071
$69$	−8.00000	−0.963087
$70$	4.00000	0.478091
$71$	−12.0000	−1.42414	−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000	−1.42414	−0.712069	+	0.702109i	$0.752242\pi$
$72$	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
$76$	4.00000	0.458831
$77$	16.0000	1.82337
$78$	−4.00000	−0.452911
$79$	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
$83$	6.00000	0.658586	0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000	0.658586	0.329293	+	0.944228i	$0.393190\pi$
$84$	4.00000	0.436436
$85$	−4.00000	−0.433861
$86$	−1.00000	−0.107833
$87$	−6.00000	−0.643268
$88$	−4.00000	−0.426401
$89$	−4.00000	−0.423999	−0.212000	−	0.977270i	$-0.567998\pi$
$89$	−4.00000	−0.423999	−0.212000	+	0.977270i	$0.567998\pi$
$90$	−1.00000	−0.105409
$91$	−16.0000	−1.67726
$92$	8.00000	0.834058
$93$	4.00000	0.414781
$94$	4.00000	0.412568
$95$	−4.00000	−0.410391
$96$	−1.00000	−0.102062
$97$	2.00000	0.203069	0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000	0.203069	0.101535	+	0.994832i	$0.467625\pi$
$98$	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	$0.403510\pi$
$102$	−4.00000	−0.396059
$103$	6.00000	0.591198	0.295599	−	0.955312i	$-0.404481\pi$
$103$	6.00000	0.591198	0.295599	+	0.955312i	$0.404481\pi$
$104$	4.00000	0.392232
$105$	−4.00000	−0.390360
$106$	−2.00000	−0.194257
$107$	2.00000	0.193347	0.0966736	−	0.995316i	$-0.469180\pi$
$107$	2.00000	0.193347	0.0966736	+	0.995316i	$0.469180\pi$
$108$	−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
$111$	−2.00000	−0.189832
$112$	−4.00000	−0.377964
$113$	18.0000	1.69330	0.846649	−	0.532152i	$-0.178617\pi$
$113$	18.0000	1.69330	0.846649	+	0.532152i	$0.178617\pi$
$114$	−4.00000	−0.374634
$115$	−8.00000	−0.746004
$116$	6.00000	0.557086
$117$	4.00000	0.369800
$118$	−12.0000	−1.10469
$119$	−16.0000	−1.46672
$120$	1.00000	0.0912871
$121$	5.00000	0.454545
$122$	0	0
$123$	−10.0000	−0.901670
$124$	−4.00000	−0.359211
$125$	−1.00000	−0.0894427
$126$	−4.00000	−0.356348
$127$	18.0000	1.59724	0.798621	−	0.601834i	$-0.205563\pi$
$127$	18.0000	1.59724	0.798621	+	0.601834i	$0.205563\pi$
$128$	1.00000	0.0883883
$129$	1.00000	0.0880451
$130$	−4.00000	−0.350823
$131$	18.0000	1.57267	0.786334	−	0.617802i	$-0.211977\pi$
$131$	18.0000	1.57267	0.786334	+	0.617802i	$0.211977\pi$
$132$	4.00000	0.348155
$133$	−16.0000	−1.38738
$134$	8.00000	0.691095
$135$	1.00000	0.0860663
$136$	4.00000	0.342997
$137$	22.0000	1.87959	0.939793	−	0.341743i	$-0.111017\pi$
$137$	22.0000	1.87959	0.939793	+	0.341743i	$0.111017\pi$
$138$	−8.00000	−0.681005
$139$	−4.00000	−0.339276	−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000	−0.339276	−0.169638	+	0.985506i	$0.554260\pi$
$140$	4.00000	0.338062
$141$	−4.00000	−0.336861
$142$	−12.0000	−1.00702
$143$	−16.0000	−1.33799
$144$	1.00000	0.0833333
$145$	−6.00000	−0.498273
$146$	−14.0000	−1.15865
$147$	−9.00000	−0.742307
$148$	2.00000	0.164399
$149$	−14.0000	−1.14692	−0.573462	−	0.819232i	$-0.694400\pi$
$149$	−14.0000	−1.14692	−0.573462	+	0.819232i	$0.694400\pi$
$150$	−1.00000	−0.0816497
$151$	−22.0000	−1.79033	−0.895167	−	0.445730i	$-0.852944\pi$
$151$	−22.0000	−1.79033	−0.895167	+	0.445730i	$0.852944\pi$
$152$	4.00000	0.324443
$153$	4.00000	0.323381
$154$	16.0000	1.28932
$155$	4.00000	0.321288
$156$	−4.00000	−0.320256
$157$	18.0000	1.43656	0.718278	−	0.695756i	$-0.244931\pi$
$157$	18.0000	1.43656	0.718278	+	0.695756i	$0.244931\pi$
$158$	8.00000	0.636446
$159$	2.00000	0.158610
$160$	−1.00000	−0.0790569
$161$	−32.0000	−2.52195
$162$	1.00000	0.0785674
$163$	−20.0000	−1.56652	−0.783260	−	0.621694i	$-0.786445\pi$
$163$	−20.0000	−1.56652	−0.783260	+	0.621694i	$0.786445\pi$
$164$	10.0000	0.780869
$165$	−4.00000	−0.311400
$166$	6.00000	0.465690
$167$	8.00000	0.619059	0.309529	−	0.950890i	$-0.399829\pi$
$167$	8.00000	0.619059	0.309529	+	0.950890i	$0.399829\pi$
$168$	4.00000	0.308607
$169$	3.00000	0.230769
$170$	−4.00000	−0.306786
$171$	4.00000	0.305888
$172$	−1.00000	−0.0762493
$173$	18.0000	1.36851	0.684257	−	0.729241i	$-0.260127\pi$
$173$	18.0000	1.36851	0.684257	+	0.729241i	$0.260127\pi$
$174$	−6.00000	−0.454859
$175$	−4.00000	−0.302372
$176$	−4.00000	−0.301511
$177$	12.0000	0.901975
$178$	−4.00000	−0.299813
$179$	18.0000	1.34538	0.672692	−	0.739923i	$-0.265138\pi$
$179$	18.0000	1.34538	0.672692	+	0.739923i	$0.265138\pi$
$180$	−1.00000	−0.0745356
$181$	−6.00000	−0.445976	−0.222988	−	0.974821i	$-0.571581\pi$
$181$	−6.00000	−0.445976	−0.222988	+	0.974821i	$0.571581\pi$
$182$	−16.0000	−1.18600
$183$	0	0
$184$	8.00000	0.589768
$185$	−2.00000	−0.147043
$186$	4.00000	0.293294
$187$	−16.0000	−1.17004
$188$	4.00000	0.291730
$189$	4.00000	0.290957
$190$	−4.00000	−0.290191
$191$	16.0000	1.15772	0.578860	−	0.815427i	$-0.303498\pi$
$191$	16.0000	1.15772	0.578860	+	0.815427i	$0.303498\pi$
$192$	−1.00000	−0.0721688
$193$	−26.0000	−1.87152	−0.935760	−	0.352636i	$-0.885285\pi$
$193$	−26.0000	−1.87152	−0.935760	+	0.352636i	$0.885285\pi$
$194$	2.00000	0.143592
$195$	4.00000	0.286446
$196$	9.00000	0.642857
$197$	−2.00000	−0.142494	−0.0712470	−	0.997459i	$-0.522698\pi$
$197$	−2.00000	−0.142494	−0.0712470	+	0.997459i	$0.522698\pi$
$198$	−4.00000	−0.284268
$199$	10.0000	0.708881	0.354441	−	0.935079i	$-0.384671\pi$
$199$	10.0000	0.708881	0.354441	+	0.935079i	$0.384671\pi$
$200$	1.00000	0.0707107
$201$	−8.00000	−0.564276
$202$	6.00000	0.422159
$203$	−24.0000	−1.68447
$204$	−4.00000	−0.280056
$205$	−10.0000	−0.698430
$206$	6.00000	0.418040
$207$	8.00000	0.556038
$208$	4.00000	0.277350
$209$	−16.0000	−1.10674
$210$	−4.00000	−0.276026
$211$	−8.00000	−0.550743	−0.275371	−	0.961338i	$-0.588801\pi$
$211$	−8.00000	−0.550743	−0.275371	+	0.961338i	$0.588801\pi$
$212$	−2.00000	−0.137361
$213$	12.0000	0.822226
$214$	2.00000	0.136717
$215$	1.00000	0.0681994
$216$	−1.00000	−0.0680414
$217$	16.0000	1.08615
$218$	−10.0000	−0.677285
$219$	14.0000	0.946032
$220$	4.00000	0.269680
$221$	16.0000	1.07628
$222$	−2.00000	−0.134231
$223$	16.0000	1.07144	0.535720	−	0.844396i	$-0.320040\pi$
$223$	16.0000	1.07144	0.535720	+	0.844396i	$0.320040\pi$
$224$	−4.00000	−0.267261
$225$	1.00000	0.0666667
$226$	18.0000	1.19734
$227$	8.00000	0.530979	0.265489	−	0.964114i	$-0.414466\pi$
$227$	8.00000	0.530979	0.265489	+	0.964114i	$0.414466\pi$
$228$	−4.00000	−0.264906
$229$	−2.00000	−0.132164	−0.0660819	−	0.997814i	$-0.521050\pi$
$229$	−2.00000	−0.132164	−0.0660819	+	0.997814i	$0.521050\pi$
$230$	−8.00000	−0.527504
$231$	−16.0000	−1.05272
$232$	6.00000	0.393919
$233$	−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
$235$	−4.00000	−0.260931
$236$	−12.0000	−0.781133
$237$	−8.00000	−0.519656
$238$	−16.0000	−1.03713
$239$	0	0		−	1.00000i	$-0.5\pi$
$239$	0	0			1.00000i	$0.5\pi$
$240$	1.00000	0.0645497
$241$	−14.0000	−0.901819	−0.450910	−	0.892570i	$-0.648900\pi$
$241$	−14.0000	−0.901819	−0.450910	+	0.892570i	$0.648900\pi$
$242$	5.00000	0.321412
$243$	−1.00000	−0.0641500
$244$	0	0
$245$	−9.00000	−0.574989
$246$	−10.0000	−0.637577
$247$	16.0000	1.01806
$248$	−4.00000	−0.254000
$249$	−6.00000	−0.380235
$250$	−1.00000	−0.0632456
$251$	0	0		−	1.00000i	$-0.5\pi$
$251$	0	0			1.00000i	$0.5\pi$
$252$	−4.00000	−0.251976
$253$	−32.0000	−2.01182
$254$	18.0000	1.12942
$255$	4.00000	0.250490
$256$	1.00000	0.0625000
$257$	18.0000	1.12281	0.561405	−	0.827541i	$-0.310261\pi$
$257$	18.0000	1.12281	0.561405	+	0.827541i	$0.310261\pi$
$258$	1.00000	0.0622573
$259$	−8.00000	−0.497096
$260$	−4.00000	−0.248069
$261$	6.00000	0.371391
$262$	18.0000	1.11204
$263$	−32.0000	−1.97320	−0.986602	−	0.163144i	$-0.947836\pi$
$263$	−32.0000	−1.97320	−0.986602	+	0.163144i	$0.947836\pi$
$264$	4.00000	0.246183
$265$	2.00000	0.122859
$266$	−16.0000	−0.981023
$267$	4.00000	0.244796
$268$	8.00000	0.488678
$269$	−6.00000	−0.365826	−0.182913	−	0.983129i	$-0.558553\pi$
$269$	−6.00000	−0.365826	−0.182913	+	0.983129i	$0.558553\pi$
$270$	1.00000	0.0608581
$271$	16.0000	0.971931	0.485965	−	0.873978i	$-0.338468\pi$
$271$	16.0000	0.971931	0.485965	+	0.873978i	$0.338468\pi$
$272$	4.00000	0.242536
$273$	16.0000	0.968364
$274$	22.0000	1.32907
$275$	−4.00000	−0.241209
$276$	−8.00000	−0.481543
$277$	−18.0000	−1.08152	−0.540758	−	0.841178i	$-0.681862\pi$
$277$	−18.0000	−1.08152	−0.540758	+	0.841178i	$0.681862\pi$
$278$	−4.00000	−0.239904
$279$	−4.00000	−0.239474
$280$	4.00000	0.239046
$281$	22.0000	1.31241	0.656205	−	0.754583i	$-0.272161\pi$
$281$	22.0000	1.31241	0.656205	+	0.754583i	$0.272161\pi$
$282$	−4.00000	−0.238197
$283$	28.0000	1.66443	0.832214	−	0.554455i	$-0.187073\pi$
$283$	28.0000	1.66443	0.832214	+	0.554455i	$0.187073\pi$
$284$	−12.0000	−0.712069
$285$	4.00000	0.236940
$286$	−16.0000	−0.946100
$287$	−40.0000	−2.36113
$288$	1.00000	0.0589256
$289$	−1.00000	−0.0588235
$290$	−6.00000	−0.352332
$291$	−2.00000	−0.117242
$292$	−14.0000	−0.819288
$293$	−10.0000	−0.584206	−0.292103	−	0.956387i	$-0.594355\pi$
$293$	−10.0000	−0.584206	−0.292103	+	0.956387i	$0.594355\pi$
$294$	−9.00000	−0.524891
$295$	12.0000	0.698667
$296$	2.00000	0.116248
$297$	4.00000	0.232104
$298$	−14.0000	−0.810998
$299$	32.0000	1.85061
$300$	−1.00000	−0.0577350
$301$	4.00000	0.230556
$302$	−22.0000	−1.26596
$303$	−6.00000	−0.344691
$304$	4.00000	0.229416
$305$	0	0
$306$	4.00000	0.228665
$307$	−28.0000	−1.59804	−0.799022	−	0.601302i	$-0.794649\pi$
$307$	−28.0000	−1.59804	−0.799022	+	0.601302i	$0.794649\pi$
$308$	16.0000	0.911685
$309$	−6.00000	−0.341328
$310$	4.00000	0.227185
$311$	−24.0000	−1.36092	−0.680458	−	0.732787i	$-0.738219\pi$
$311$	−24.0000	−1.36092	−0.680458	+	0.732787i	$0.738219\pi$
$312$	−4.00000	−0.226455
$313$	−14.0000	−0.791327	−0.395663	−	0.918396i	$-0.629485\pi$
$313$	−14.0000	−0.791327	−0.395663	+	0.918396i	$0.629485\pi$
$314$	18.0000	1.01580
$315$	4.00000	0.225374
$316$	8.00000	0.450035
$317$	−2.00000	−0.112331	−0.0561656	−	0.998421i	$-0.517887\pi$
$317$	−2.00000	−0.112331	−0.0561656	+	0.998421i	$0.517887\pi$
$318$	2.00000	0.112154
$319$	−24.0000	−1.34374
$320$	−1.00000	−0.0559017
$321$	−2.00000	−0.111629
$322$	−32.0000	−1.78329
$323$	16.0000	0.890264
$324$	1.00000	0.0555556
$325$	4.00000	0.221880
$326$	−20.0000	−1.10770
$327$	10.0000	0.553001
$328$	10.0000	0.552158
$329$	−16.0000	−0.882109
$330$	−4.00000	−0.220193
$331$	−32.0000	−1.75888	−0.879440	−	0.476011i	$-0.842082\pi$
$331$	−32.0000	−1.75888	−0.879440	+	0.476011i	$0.842082\pi$
$332$	6.00000	0.329293
$333$	2.00000	0.109599
$334$	8.00000	0.437741
$335$	−8.00000	−0.437087
$336$	4.00000	0.218218
$337$	−2.00000	−0.108947	−0.0544735	−	0.998515i	$-0.517348\pi$
$337$	−2.00000	−0.108947	−0.0544735	+	0.998515i	$0.517348\pi$
$338$	3.00000	0.163178
$339$	−18.0000	−0.977626
$340$	−4.00000	−0.216930
$341$	16.0000	0.866449
$342$	4.00000	0.216295
$343$	−8.00000	−0.431959
$344$	−1.00000	−0.0539164
$345$	8.00000	0.430706
$346$	18.0000	0.967686
$347$	4.00000	0.214731	0.107366	−	0.994220i	$-0.465758\pi$
$347$	4.00000	0.214731	0.107366	+	0.994220i	$0.465758\pi$
$348$	−6.00000	−0.321634
$349$	−12.0000	−0.642345	−0.321173	−	0.947021i	$-0.604077\pi$
$349$	−12.0000	−0.642345	−0.321173	+	0.947021i	$0.604077\pi$
$350$	−4.00000	−0.213809
$351$	−4.00000	−0.213504
$352$	−4.00000	−0.213201
$353$	24.0000	1.27739	0.638696	−	0.769460i	$-0.279474\pi$
$353$	24.0000	1.27739	0.638696	+	0.769460i	$0.279474\pi$
$354$	12.0000	0.637793
$355$	12.0000	0.636894
$356$	−4.00000	−0.212000
$357$	16.0000	0.846810
$358$	18.0000	0.951330
$359$	8.00000	0.422224	0.211112	−	0.977462i	$-0.432292\pi$
$359$	8.00000	0.422224	0.211112	+	0.977462i	$0.432292\pi$
$360$	−1.00000	−0.0527046
$361$	−3.00000	−0.157895
$362$	−6.00000	−0.315353
$363$	−5.00000	−0.262432
$364$	−16.0000	−0.838628
$365$	14.0000	0.732793
$366$	0	0
$367$	−2.00000	−0.104399	−0.0521996	−	0.998637i	$-0.516623\pi$
$367$	−2.00000	−0.104399	−0.0521996	+	0.998637i	$0.516623\pi$
$368$	8.00000	0.417029
$369$	10.0000	0.520579
$370$	−2.00000	−0.103975
$371$	8.00000	0.415339
$372$	4.00000	0.207390
$373$	14.0000	0.724893	0.362446	−	0.932005i	$-0.381942\pi$
$373$	14.0000	0.724893	0.362446	+	0.932005i	$0.381942\pi$
$374$	−16.0000	−0.827340
$375$	1.00000	0.0516398
$376$	4.00000	0.206284
$377$	24.0000	1.23606
$378$	4.00000	0.205738
$379$	−12.0000	−0.616399	−0.308199	−	0.951322i	$-0.599726\pi$
$379$	−12.0000	−0.616399	−0.308199	+	0.951322i	$0.599726\pi$
$380$	−4.00000	−0.205196
$381$	−18.0000	−0.922168
$382$	16.0000	0.818631
$383$	32.0000	1.63512	0.817562	−	0.575841i	$-0.195325\pi$
$383$	32.0000	1.63512	0.817562	+	0.575841i	$0.195325\pi$
$384$	−1.00000	−0.0510310
$385$	−16.0000	−0.815436
$386$	−26.0000	−1.32337
$387$	−1.00000	−0.0508329
$388$	2.00000	0.101535
$389$	18.0000	0.912636	0.456318	−	0.889817i	$-0.349168\pi$
$389$	18.0000	0.912636	0.456318	+	0.889817i	$0.349168\pi$
$390$	4.00000	0.202548
$391$	32.0000	1.61831
$392$	9.00000	0.454569
$393$	−18.0000	−0.907980
$394$	−2.00000	−0.100759
$395$	−8.00000	−0.402524
$396$	−4.00000	−0.201008
$397$	−4.00000	−0.200754	−0.100377	−	0.994949i	$-0.532005\pi$
$397$	−4.00000	−0.200754	−0.100377	+	0.994949i	$0.532005\pi$
$398$	10.0000	0.501255
$399$	16.0000	0.801002
$400$	1.00000	0.0500000
$401$	−18.0000	−0.898877	−0.449439	−	0.893311i	$-0.648376\pi$
$401$	−18.0000	−0.898877	−0.449439	+	0.893311i	$0.648376\pi$
$402$	−8.00000	−0.399004
$403$	−16.0000	−0.797017
$404$	6.00000	0.298511
$405$	−1.00000	−0.0496904
$406$	−24.0000	−1.19110
$407$	−8.00000	−0.396545
$408$	−4.00000	−0.198030
$409$	10.0000	0.494468	0.247234	−	0.968956i	$-0.420478\pi$
$409$	10.0000	0.494468	0.247234	+	0.968956i	$0.420478\pi$
$410$	−10.0000	−0.493865
$411$	−22.0000	−1.08518
$412$	6.00000	0.295599
$413$	48.0000	2.36193
$414$	8.00000	0.393179
$415$	−6.00000	−0.294528
$416$	4.00000	0.196116
$417$	4.00000	0.195881
$418$	−16.0000	−0.782586
$419$	−18.0000	−0.879358	−0.439679	−	0.898155i	$-0.644908\pi$
$419$	−18.0000	−0.879358	−0.439679	+	0.898155i	$0.644908\pi$
$420$	−4.00000	−0.195180
$421$	8.00000	0.389896	0.194948	−	0.980814i	$-0.437546\pi$
$421$	8.00000	0.389896	0.194948	+	0.980814i	$0.437546\pi$
$422$	−8.00000	−0.389434
$423$	4.00000	0.194487
$424$	−2.00000	−0.0971286
$425$	4.00000	0.194029
$426$	12.0000	0.581402
$427$	0	0
$428$	2.00000	0.0966736
$429$	16.0000	0.772487
$430$	1.00000	0.0482243
$431$	24.0000	1.15604	0.578020	−	0.816023i	$-0.303826\pi$
$431$	24.0000	1.15604	0.578020	+	0.816023i	$0.303826\pi$
$432$	−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	$0.390791\pi$
$434$	16.0000	0.768025
$435$	6.00000	0.287678
$436$	−10.0000	−0.478913
$437$	32.0000	1.53077
$438$	14.0000	0.668946
$439$	28.0000	1.33637	0.668184	−	0.743996i	$-0.267072\pi$
$439$	28.0000	1.33637	0.668184	+	0.743996i	$0.267072\pi$
$440$	4.00000	0.190693
$441$	9.00000	0.428571
$442$	16.0000	0.761042
$443$	−18.0000	−0.855206	−0.427603	−	0.903967i	$-0.640642\pi$
$443$	−18.0000	−0.855206	−0.427603	+	0.903967i	$0.640642\pi$
$444$	−2.00000	−0.0949158
$445$	4.00000	0.189618
$446$	16.0000	0.757622
$447$	14.0000	0.662177
$448$	−4.00000	−0.188982
$449$	8.00000	0.377543	0.188772	−	0.982021i	$-0.439549\pi$
$449$	8.00000	0.377543	0.188772	+	0.982021i	$0.439549\pi$
$450$	1.00000	0.0471405
$451$	−40.0000	−1.88353
$452$	18.0000	0.846649
$453$	22.0000	1.03365
$454$	8.00000	0.375459
$455$	16.0000	0.750092
$456$	−4.00000	−0.187317
$457$	−10.0000	−0.467780	−0.233890	−	0.972263i	$-0.575146\pi$
$457$	−10.0000	−0.467780	−0.233890	+	0.972263i	$0.575146\pi$
$458$	−2.00000	−0.0934539
$459$	−4.00000	−0.186704
$460$	−8.00000	−0.373002
$461$	−10.0000	−0.465746	−0.232873	−	0.972507i	$-0.574813\pi$
$461$	−10.0000	−0.465746	−0.232873	+	0.972507i	$0.574813\pi$
$462$	−16.0000	−0.744387
$463$	4.00000	0.185896	0.0929479	−	0.995671i	$-0.470371\pi$
$463$	4.00000	0.185896	0.0929479	+	0.995671i	$0.470371\pi$
$464$	6.00000	0.278543
$465$	−4.00000	−0.185496
$466$	−22.0000	−1.01913
$467$	−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
$469$	−32.0000	−1.47762
$470$	−4.00000	−0.184506
$471$	−18.0000	−0.829396
$472$	−12.0000	−0.552345
$473$	4.00000	0.183920
$474$	−8.00000	−0.367452
$475$	4.00000	0.183533
$476$	−16.0000	−0.733359
$477$	−2.00000	−0.0915737
$478$	0	0
$479$	−8.00000	−0.365529	−0.182765	−	0.983157i	$-0.558505\pi$
$479$	−8.00000	−0.365529	−0.182765	+	0.983157i	$0.558505\pi$
$480$	1.00000	0.0456435
$481$	8.00000	0.364769
$482$	−14.0000	−0.637683
$483$	32.0000	1.45605
$484$	5.00000	0.227273
$485$	−2.00000	−0.0908153
$486$	−1.00000	−0.0453609
$487$	18.0000	0.815658	0.407829	−	0.913058i	$-0.366286\pi$
$487$	18.0000	0.815658	0.407829	+	0.913058i	$0.366286\pi$
$488$	0	0
$489$	20.0000	0.904431
$490$	−9.00000	−0.406579
$491$	−26.0000	−1.17336	−0.586682	−	0.809818i	$-0.699566\pi$
$491$	−26.0000	−1.17336	−0.586682	+	0.809818i	$0.699566\pi$
$492$	−10.0000	−0.450835
$493$	24.0000	1.08091
$494$	16.0000	0.719874
$495$	4.00000	0.179787
$496$	−4.00000	−0.179605
$497$	48.0000	2.15309
$498$	−6.00000	−0.268866
$499$	−4.00000	−0.179065	−0.0895323	−	0.995984i	$-0.528537\pi$
$499$	−4.00000	−0.179065	−0.0895323	+	0.995984i	$0.528537\pi$
$500$	−1.00000	−0.0447214
$501$	−8.00000	−0.357414
$502$	0	0
$503$	16.0000	0.713405	0.356702	−	0.934218i	$-0.383901\pi$
$503$	16.0000	0.713405	0.356702	+	0.934218i	$0.383901\pi$
$504$	−4.00000	−0.178174
$505$	−6.00000	−0.266996
$506$	−32.0000	−1.42257
$507$	−3.00000	−0.133235
$508$	18.0000	0.798621
$509$	42.0000	1.86162	0.930809	−	0.365507i	$-0.119104\pi$
$509$	42.0000	1.86162	0.930809	+	0.365507i	$0.119104\pi$
$510$	4.00000	0.177123
$511$	56.0000	2.47729
$512$	1.00000	0.0441942
$513$	−4.00000	−0.176604
$514$	18.0000	0.793946
$515$	−6.00000	−0.264392
$516$	1.00000	0.0440225
$517$	−16.0000	−0.703679
$518$	−8.00000	−0.351500
$519$	−18.0000	−0.790112
$520$	−4.00000	−0.175412
$521$	0	0		−	1.00000i	$-0.5\pi$
$521$	0	0			1.00000i	$0.5\pi$
$522$	6.00000	0.262613
$523$	−44.0000	−1.92399	−0.961993	−	0.273075i	$-0.911959\pi$
$523$	−44.0000	−1.92399	−0.961993	+	0.273075i	$0.911959\pi$
$524$	18.0000	0.786334
$525$	4.00000	0.174574
$526$	−32.0000	−1.39527
$527$	−16.0000	−0.696971
$528$	4.00000	0.174078
$529$	41.0000	1.78261
$530$	2.00000	0.0868744
$531$	−12.0000	−0.520756
$532$	−16.0000	−0.693688
$533$	40.0000	1.73259
$534$	4.00000	0.173097
$535$	−2.00000	−0.0864675
$536$	8.00000	0.345547
$537$	−18.0000	−0.776757
$538$	−6.00000	−0.258678
$539$	−36.0000	−1.55063
$540$	1.00000	0.0430331
$541$	10.0000	0.429934	0.214967	−	0.976621i	$-0.431036\pi$
$541$	10.0000	0.429934	0.214967	+	0.976621i	$0.431036\pi$
$542$	16.0000	0.687259
$543$	6.00000	0.257485
$544$	4.00000	0.171499
$545$	10.0000	0.428353
$546$	16.0000	0.684737
$547$	0	0		−	1.00000i	$-0.5\pi$
$547$	0	0			1.00000i	$0.5\pi$
$548$	22.0000	0.939793
$549$	0	0
$550$	−4.00000	−0.170561
$551$	24.0000	1.02243
$552$	−8.00000	−0.340503
$553$	−32.0000	−1.36078
$554$	−18.0000	−0.764747
$555$	2.00000	0.0848953
$556$	−4.00000	−0.169638
$557$	−30.0000	−1.27114	−0.635570	−	0.772043i	$-0.719235\pi$
$557$	−30.0000	−1.27114	−0.635570	+	0.772043i	$0.719235\pi$
$558$	−4.00000	−0.169334
$559$	−4.00000	−0.169182
$560$	4.00000	0.169031
$561$	16.0000	0.675521
$562$	22.0000	0.928014
$563$	−14.0000	−0.590030	−0.295015	−	0.955493i	$-0.595325\pi$
$563$	−14.0000	−0.590030	−0.295015	+	0.955493i	$0.595325\pi$
$564$	−4.00000	−0.168430
$565$	−18.0000	−0.757266
$566$	28.0000	1.17693
$567$	−4.00000	−0.167984
$568$	−12.0000	−0.503509
$569$	−6.00000	−0.251533	−0.125767	−	0.992060i	$-0.540139\pi$
$569$	−6.00000	−0.251533	−0.125767	+	0.992060i	$0.540139\pi$
$570$	4.00000	0.167542
$571$	−12.0000	−0.502184	−0.251092	−	0.967963i	$-0.580790\pi$
$571$	−12.0000	−0.502184	−0.251092	+	0.967963i	$0.580790\pi$
$572$	−16.0000	−0.668994
$573$	−16.0000	−0.668410
$574$	−40.0000	−1.66957
$575$	8.00000	0.333623
$576$	1.00000	0.0416667
$577$	22.0000	0.915872	0.457936	−	0.888985i	$-0.348589\pi$
$577$	22.0000	0.915872	0.457936	+	0.888985i	$0.348589\pi$
$578$	−1.00000	−0.0415945
$579$	26.0000	1.08052
$580$	−6.00000	−0.249136
$581$	−24.0000	−0.995688
$582$	−2.00000	−0.0829027
$583$	8.00000	0.331326
$584$	−14.0000	−0.579324
$585$	−4.00000	−0.165380
$586$	−10.0000	−0.413096
$587$	4.00000	0.165098	0.0825488	−	0.996587i	$-0.473694\pi$
$587$	4.00000	0.165098	0.0825488	+	0.996587i	$0.473694\pi$
$588$	−9.00000	−0.371154
$589$	−16.0000	−0.659269
$590$	12.0000	0.494032
$591$	2.00000	0.0822690
$592$	2.00000	0.0821995
$593$	−14.0000	−0.574911	−0.287456	−	0.957794i	$-0.592809\pi$
$593$	−14.0000	−0.574911	−0.287456	+	0.957794i	$0.592809\pi$
$594$	4.00000	0.164122
$595$	16.0000	0.655936
$596$	−14.0000	−0.573462
$597$	−10.0000	−0.409273
$598$	32.0000	1.30858
$599$	−48.0000	−1.96123	−0.980613	−	0.195952i	$-0.937220\pi$
$599$	−48.0000	−1.96123	−0.980613	+	0.195952i	$0.937220\pi$
$600$	−1.00000	−0.0408248
$601$	−6.00000	−0.244745	−0.122373	−	0.992484i	$-0.539050\pi$
$601$	−6.00000	−0.244745	−0.122373	+	0.992484i	$0.539050\pi$
$602$	4.00000	0.163028
$603$	8.00000	0.325785
$604$	−22.0000	−0.895167
$605$	−5.00000	−0.203279
$606$	−6.00000	−0.243733
$607$	−40.0000	−1.62355	−0.811775	−	0.583970i	$-0.801498\pi$
$607$	−40.0000	−1.62355	−0.811775	+	0.583970i	$0.801498\pi$
$608$	4.00000	0.162221
$609$	24.0000	0.972529
$610$	0	0
$611$	16.0000	0.647291
$612$	4.00000	0.161690
$613$	16.0000	0.646234	0.323117	−	0.946359i	$-0.395269\pi$
$613$	16.0000	0.646234	0.323117	+	0.946359i	$0.395269\pi$
$614$	−28.0000	−1.12999
$615$	10.0000	0.403239
$616$	16.0000	0.644658
$617$	−28.0000	−1.12724	−0.563619	−	0.826035i	$-0.690591\pi$
$617$	−28.0000	−1.12724	−0.563619	+	0.826035i	$0.690591\pi$
$618$	−6.00000	−0.241355
$619$	20.0000	0.803868	0.401934	−	0.915669i	$-0.368338\pi$
$619$	20.0000	0.803868	0.401934	+	0.915669i	$0.368338\pi$
$620$	4.00000	0.160644
$621$	−8.00000	−0.321029
$622$	−24.0000	−0.962312
$623$	16.0000	0.641026
$624$	−4.00000	−0.160128
$625$	1.00000	0.0400000
$626$	−14.0000	−0.559553
$627$	16.0000	0.638978
$628$	18.0000	0.718278
$629$	8.00000	0.318981
$630$	4.00000	0.159364
$631$	−2.00000	−0.0796187	−0.0398094	−	0.999207i	$-0.512675\pi$
$631$	−2.00000	−0.0796187	−0.0398094	+	0.999207i	$0.512675\pi$
$632$	8.00000	0.318223
$633$	8.00000	0.317971
$634$	−2.00000	−0.0794301
$635$	−18.0000	−0.714308
$636$	2.00000	0.0793052
$637$	36.0000	1.42637
$638$	−24.0000	−0.950169
$639$	−12.0000	−0.474713
$640$	−1.00000	−0.0395285
$641$	0	0		−	1.00000i	$-0.5\pi$
$641$	0	0			1.00000i	$0.5\pi$
$642$	−2.00000	−0.0789337
$643$	−12.0000	−0.473234	−0.236617	−	0.971603i	$-0.576039\pi$
$643$	−12.0000	−0.473234	−0.236617	+	0.971603i	$0.576039\pi$
$644$	−32.0000	−1.26098
$645$	−1.00000	−0.0393750
$646$	16.0000	0.629512
$647$	32.0000	1.25805	0.629025	−	0.777385i	$-0.283454\pi$
$647$	32.0000	1.25805	0.629025	+	0.777385i	$0.283454\pi$
$648$	1.00000	0.0392837
$649$	48.0000	1.88416
$650$	4.00000	0.156893
$651$	−16.0000	−0.627089
$652$	−20.0000	−0.783260
$653$	6.00000	0.234798	0.117399	−	0.993085i	$-0.462544\pi$
$653$	6.00000	0.234798	0.117399	+	0.993085i	$0.462544\pi$
$654$	10.0000	0.391031
$655$	−18.0000	−0.703318
$656$	10.0000	0.390434
$657$	−14.0000	−0.546192
$658$	−16.0000	−0.623745
$659$	−40.0000	−1.55818	−0.779089	−	0.626913i	$-0.784318\pi$
$659$	−40.0000	−1.55818	−0.779089	+	0.626913i	$0.784318\pi$
$660$	−4.00000	−0.155700
$661$	26.0000	1.01128	0.505641	−	0.862744i	$-0.331256\pi$
$661$	26.0000	1.01128	0.505641	+	0.862744i	$0.331256\pi$
$662$	−32.0000	−1.24372
$663$	−16.0000	−0.621389
$664$	6.00000	0.232845
$665$	16.0000	0.620453
$666$	2.00000	0.0774984
$667$	48.0000	1.85857
$668$	8.00000	0.309529
$669$	−16.0000	−0.618596
$670$	−8.00000	−0.309067
$671$	0	0
$672$	4.00000	0.154303
$673$	−34.0000	−1.31060	−0.655302	−	0.755367i	$-0.727459\pi$
$673$	−34.0000	−1.31060	−0.655302	+	0.755367i	$0.727459\pi$
$674$	−2.00000	−0.0770371
$675$	−1.00000	−0.0384900
$676$	3.00000	0.115385
$677$	6.00000	0.230599	0.115299	−	0.993331i	$-0.463217\pi$
$677$	6.00000	0.230599	0.115299	+	0.993331i	$0.463217\pi$
$678$	−18.0000	−0.691286
$679$	−8.00000	−0.307012
$680$	−4.00000	−0.153393
$681$	−8.00000	−0.306561
$682$	16.0000	0.612672
$683$	2.00000	0.0765279	0.0382639	−	0.999268i	$-0.487817\pi$
$683$	2.00000	0.0765279	0.0382639	+	0.999268i	$0.487817\pi$
$684$	4.00000	0.152944
$685$	−22.0000	−0.840577
$686$	−8.00000	−0.305441
$687$	2.00000	0.0763048
$688$	−1.00000	−0.0381246
$689$	−8.00000	−0.304776
$690$	8.00000	0.304555
$691$	8.00000	0.304334	0.152167	−	0.988355i	$-0.451375\pi$
$691$	8.00000	0.304334	0.152167	+	0.988355i	$0.451375\pi$
$692$	18.0000	0.684257
$693$	16.0000	0.607790
$694$	4.00000	0.151838
$695$	4.00000	0.151729
$696$	−6.00000	−0.227429
$697$	40.0000	1.51511
$698$	−12.0000	−0.454207
$699$	22.0000	0.832116
$700$	−4.00000	−0.151186
$701$	2.00000	0.0755390	0.0377695	−	0.999286i	$-0.487975\pi$
$701$	2.00000	0.0755390	0.0377695	+	0.999286i	$0.487975\pi$
$702$	−4.00000	−0.150970
$703$	8.00000	0.301726
$704$	−4.00000	−0.150756
$705$	4.00000	0.150649
$706$	24.0000	0.903252
$707$	−24.0000	−0.902613
$708$	12.0000	0.450988
$709$	34.0000	1.27690	0.638448	−	0.769665i	$-0.279577\pi$
$709$	34.0000	1.27690	0.638448	+	0.769665i	$0.279577\pi$
$710$	12.0000	0.450352
$711$	8.00000	0.300023
$712$	−4.00000	−0.149906
$713$	−32.0000	−1.19841
$714$	16.0000	0.598785
$715$	16.0000	0.598366
$716$	18.0000	0.672692
$717$	0	0
$718$	8.00000	0.298557
$719$	0	0		−	1.00000i	$-0.5\pi$
$719$	0	0			1.00000i	$0.5\pi$
$720$	−1.00000	−0.0372678
$721$	−24.0000	−0.893807
$722$	−3.00000	−0.111648
$723$	14.0000	0.520666
$724$	−6.00000	−0.222988
$725$	6.00000	0.222834
$726$	−5.00000	−0.185567
$727$	44.0000	1.63187	0.815935	−	0.578144i	$-0.196223\pi$
$727$	44.0000	1.63187	0.815935	+	0.578144i	$0.196223\pi$
$728$	−16.0000	−0.592999
$729$	1.00000	0.0370370
$730$	14.0000	0.518163
$731$	−4.00000	−0.147945
$732$	0	0
$733$	30.0000	1.10808	0.554038	−	0.832492i	$-0.313086\pi$
$733$	30.0000	1.10808	0.554038	+	0.832492i	$0.313086\pi$
$734$	−2.00000	−0.0738213
$735$	9.00000	0.331970
$736$	8.00000	0.294884
$737$	−32.0000	−1.17874
$738$	10.0000	0.368105
$739$	0	0		−	1.00000i	$-0.5\pi$
$739$	0	0			1.00000i	$0.5\pi$
$740$	−2.00000	−0.0735215
$741$	−16.0000	−0.587775
$742$	8.00000	0.293689
$743$	24.0000	0.880475	0.440237	−	0.897881i	$-0.354894\pi$
$743$	24.0000	0.880475	0.440237	+	0.897881i	$0.354894\pi$
$744$	4.00000	0.146647
$745$	14.0000	0.512920
$746$	14.0000	0.512576
$747$	6.00000	0.219529
$748$	−16.0000	−0.585018
$749$	−8.00000	−0.292314
$750$	1.00000	0.0365148
$751$	−2.00000	−0.0729810	−0.0364905	−	0.999334i	$-0.511618\pi$
$751$	−2.00000	−0.0729810	−0.0364905	+	0.999334i	$0.511618\pi$
$752$	4.00000	0.145865
$753$	0	0
$754$	24.0000	0.874028
$755$	22.0000	0.800662
$756$	4.00000	0.145479
$757$	2.00000	0.0726912	0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000	0.0726912	0.0363456	+	0.999339i	$0.488428\pi$
$758$	−12.0000	−0.435860
$759$	32.0000	1.16153
$760$	−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	$0.618077\pi$
$762$	−18.0000	−0.652071
$763$	40.0000	1.44810
$764$	16.0000	0.578860
$765$	−4.00000	−0.144620
$766$	32.0000	1.15621
$767$	−48.0000	−1.73318
$768$	−1.00000	−0.0360844
$769$	30.0000	1.08183	0.540914	−	0.841078i	$-0.318079\pi$
$769$	30.0000	1.08183	0.540914	+	0.841078i	$0.318079\pi$
$770$	−16.0000	−0.576600
$771$	−18.0000	−0.648254
$772$	−26.0000	−0.935760
$773$	−26.0000	−0.935155	−0.467578	−	0.883952i	$-0.654873\pi$
$773$	−26.0000	−0.935155	−0.467578	+	0.883952i	$0.654873\pi$
$774$	−1.00000	−0.0359443
$775$	−4.00000	−0.143684
$776$	2.00000	0.0717958
$777$	8.00000	0.286998
$778$	18.0000	0.645331
$779$	40.0000	1.43315
$780$	4.00000	0.143223
$781$	48.0000	1.71758
$782$	32.0000	1.14432
$783$	−6.00000	−0.214423
$784$	9.00000	0.321429
$785$	−18.0000	−0.642448
$786$	−18.0000	−0.642039
$787$	16.0000	0.570338	0.285169	−	0.958477i	$-0.407950\pi$
$787$	16.0000	0.570338	0.285169	+	0.958477i	$0.407950\pi$
$788$	−2.00000	−0.0712470
$789$	32.0000	1.13923
$790$	−8.00000	−0.284627
$791$	−72.0000	−2.56003
$792$	−4.00000	−0.142134
$793$	0	0
$794$	−4.00000	−0.141955
$795$	−2.00000	−0.0709327
$796$	10.0000	0.354441
$797$	−14.0000	−0.495905	−0.247953	−	0.968772i	$-0.579758\pi$
$797$	−14.0000	−0.495905	−0.247953	+	0.968772i	$0.579758\pi$
$798$	16.0000	0.566394
$799$	16.0000	0.566039
$800$	1.00000	0.0353553
$801$	−4.00000	−0.141333
$802$	−18.0000	−0.635602
$803$	56.0000	1.97620
$804$	−8.00000	−0.282138
$805$	32.0000	1.12785
$806$	−16.0000	−0.563576
$807$	6.00000	0.211210
$808$	6.00000	0.211079
$809$	10.0000	0.351581	0.175791	−	0.984428i	$-0.443752\pi$
$809$	10.0000	0.351581	0.175791	+	0.984428i	$0.443752\pi$
$810$	−1.00000	−0.0351364
$811$	−20.0000	−0.702295	−0.351147	−	0.936320i	$-0.614208\pi$
$811$	−20.0000	−0.702295	−0.351147	+	0.936320i	$0.614208\pi$
$812$	−24.0000	−0.842235
$813$	−16.0000	−0.561144
$814$	−8.00000	−0.280400
$815$	20.0000	0.700569
$816$	−4.00000	−0.140028
$817$	−4.00000	−0.139942
$818$	10.0000	0.349642
$819$	−16.0000	−0.559085
$820$	−10.0000	−0.349215
$821$	−42.0000	−1.46581	−0.732905	−	0.680331i	$-0.761836\pi$
$821$	−42.0000	−1.46581	−0.732905	+	0.680331i	$0.761836\pi$
$822$	−22.0000	−0.767338
$823$	−22.0000	−0.766872	−0.383436	−	0.923567i	$-0.625259\pi$
$823$	−22.0000	−0.766872	−0.383436	+	0.923567i	$0.625259\pi$
$824$	6.00000	0.209020
$825$	4.00000	0.139262
$826$	48.0000	1.67013
$827$	−34.0000	−1.18230	−0.591148	−	0.806563i	$-0.701325\pi$
$827$	−34.0000	−1.18230	−0.591148	+	0.806563i	$0.701325\pi$
$828$	8.00000	0.278019
$829$	−28.0000	−0.972480	−0.486240	−	0.873825i	$-0.661632\pi$
$829$	−28.0000	−0.972480	−0.486240	+	0.873825i	$0.661632\pi$
$830$	−6.00000	−0.208263
$831$	18.0000	0.624413
$832$	4.00000	0.138675
$833$	36.0000	1.24733
$834$	4.00000	0.138509
$835$	−8.00000	−0.276851
$836$	−16.0000	−0.553372
$837$	4.00000	0.138260
$838$	−18.0000	−0.621800
$839$	56.0000	1.93333	0.966667	−	0.256036i	$-0.0824164\pi$
$839$	56.0000	1.93333	0.966667	+	0.256036i	$0.0824164\pi$
$840$	−4.00000	−0.138013
$841$	7.00000	0.241379
$842$	8.00000	0.275698
$843$	−22.0000	−0.757720
$844$	−8.00000	−0.275371
$845$	−3.00000	−0.103203
$846$	4.00000	0.137523
$847$	−20.0000	−0.687208
$848$	−2.00000	−0.0686803
$849$	−28.0000	−0.960958
$850$	4.00000	0.137199
$851$	16.0000	0.548473
$852$	12.0000	0.411113
$853$	−44.0000	−1.50653	−0.753266	−	0.657716i	$-0.771523\pi$
$853$	−44.0000	−1.50653	−0.753266	+	0.657716i	$0.771523\pi$
$854$	0	0
$855$	−4.00000	−0.136797
$856$	2.00000	0.0683586
$857$	48.0000	1.63965	0.819824	−	0.572615i	$-0.194071\pi$
$857$	48.0000	1.63965	0.819824	+	0.572615i	$0.194071\pi$
$858$	16.0000	0.546231
$859$	−40.0000	−1.36478	−0.682391	−	0.730987i	$-0.739060\pi$
$859$	−40.0000	−1.36478	−0.682391	+	0.730987i	$0.739060\pi$
$860$	1.00000	0.0340997
$861$	40.0000	1.36320
$862$	24.0000	0.817443
$863$	−16.0000	−0.544646	−0.272323	−	0.962206i	$-0.587792\pi$
$863$	−16.0000	−0.544646	−0.272323	+	0.962206i	$0.587792\pi$
$864$	−1.00000	−0.0340207
$865$	−18.0000	−0.612018
$866$	14.0000	0.475739
$867$	1.00000	0.0339618
$868$	16.0000	0.543075
$869$	−32.0000	−1.08553
$870$	6.00000	0.203419
$871$	32.0000	1.08428
$872$	−10.0000	−0.338643
$873$	2.00000	0.0676897
$874$	32.0000	1.08242
$875$	4.00000	0.135225
$876$	14.0000	0.473016
$877$	52.0000	1.75592	0.877958	−	0.478738i	$-0.158906\pi$
$877$	52.0000	1.75592	0.877958	+	0.478738i	$0.158906\pi$
$878$	28.0000	0.944954
$879$	10.0000	0.337292
$880$	4.00000	0.134840
$881$	18.0000	0.606435	0.303218	−	0.952921i	$-0.401939\pi$
$881$	18.0000	0.606435	0.303218	+	0.952921i	$0.401939\pi$
$882$	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	$0.586766\pi$
$884$	16.0000	0.538138
$885$	−12.0000	−0.403376
$886$	−18.0000	−0.604722
$887$	−48.0000	−1.61168	−0.805841	−	0.592132i	$-0.798286\pi$
$887$	−48.0000	−1.61168	−0.805841	+	0.592132i	$0.798286\pi$
$888$	−2.00000	−0.0671156
$889$	−72.0000	−2.41480
$890$	4.00000	0.134080
$891$	−4.00000	−0.134005
$892$	16.0000	0.535720
$893$	16.0000	0.535420
$894$	14.0000	0.468230
$895$	−18.0000	−0.601674
$896$	−4.00000	−0.133631
$897$	−32.0000	−1.06845
$898$	8.00000	0.266963
$899$	−24.0000	−0.800445
$900$	1.00000	0.0333333
$901$	−8.00000	−0.266519
$902$	−40.0000	−1.33185
$903$	−4.00000	−0.133112
$904$	18.0000	0.598671
$905$	6.00000	0.199447
$906$	22.0000	0.730901
$907$	−4.00000	−0.132818	−0.0664089	−	0.997792i	$-0.521154\pi$
$907$	−4.00000	−0.132818	−0.0664089	+	0.997792i	$0.521154\pi$
$908$	8.00000	0.265489
$909$	6.00000	0.199007
$910$	16.0000	0.530395
$911$	−36.0000	−1.19273	−0.596367	−	0.802712i	$-0.703390\pi$
$911$	−36.0000	−1.19273	−0.596367	+	0.802712i	$0.703390\pi$
$912$	−4.00000	−0.132453
$913$	−24.0000	−0.794284
$914$	−10.0000	−0.330771
$915$	0	0
$916$	−2.00000	−0.0660819
$917$	−72.0000	−2.37765
$918$	−4.00000	−0.132020
$919$	−20.0000	−0.659739	−0.329870	−	0.944027i	$-0.607005\pi$
$919$	−20.0000	−0.659739	−0.329870	+	0.944027i	$0.607005\pi$
$920$	−8.00000	−0.263752
$921$	28.0000	0.922631
$922$	−10.0000	−0.329332
$923$	−48.0000	−1.57994
$924$	−16.0000	−0.526361
$925$	2.00000	0.0657596
$926$	4.00000	0.131448
$927$	6.00000	0.197066
$928$	6.00000	0.196960
$929$	−28.0000	−0.918650	−0.459325	−	0.888268i	$-0.651909\pi$
$929$	−28.0000	−0.918650	−0.459325	+	0.888268i	$0.651909\pi$
$930$	−4.00000	−0.131165
$931$	36.0000	1.17985
$932$	−22.0000	−0.720634
$933$	24.0000	0.785725
$934$	−12.0000	−0.392652
$935$	16.0000	0.523256
$936$	4.00000	0.130744
$937$	38.0000	1.24141	0.620703	−	0.784046i	$-0.286847\pi$
$937$	38.0000	1.24141	0.620703	+	0.784046i	$0.286847\pi$
$938$	−32.0000	−1.04484
$939$	14.0000	0.456873
$940$	−4.00000	−0.130466
$941$	50.0000	1.62995	0.814977	−	0.579494i	$-0.196750\pi$
$941$	50.0000	1.62995	0.814977	+	0.579494i	$0.196750\pi$
$942$	−18.0000	−0.586472
$943$	80.0000	2.60516
$944$	−12.0000	−0.390567
$945$	−4.00000	−0.130120
$946$	4.00000	0.130051
$947$	18.0000	0.584921	0.292461	−	0.956278i	$-0.405526\pi$
$947$	18.0000	0.584921	0.292461	+	0.956278i	$0.405526\pi$
$948$	−8.00000	−0.259828
$949$	−56.0000	−1.81784
$950$	4.00000	0.129777
$951$	2.00000	0.0648544
$952$	−16.0000	−0.518563
$953$	−6.00000	−0.194359	−0.0971795	−	0.995267i	$-0.530982\pi$
$953$	−6.00000	−0.194359	−0.0971795	+	0.995267i	$0.530982\pi$
$954$	−2.00000	−0.0647524
$955$	−16.0000	−0.517748
$956$	0	0
$957$	24.0000	0.775810
$958$	−8.00000	−0.258468
$959$	−88.0000	−2.84167
$960$	1.00000	0.0322749
$961$	−15.0000	−0.483871
$962$	8.00000	0.257930
$963$	2.00000	0.0644491
$964$	−14.0000	−0.450910
$965$	26.0000	0.836970
$966$	32.0000	1.02958
$967$	54.0000	1.73652	0.868261	−	0.496107i	$-0.165238\pi$
$967$	54.0000	1.73652	0.868261	+	0.496107i	$0.165238\pi$
$968$	5.00000	0.160706
$969$	−16.0000	−0.513994
$970$	−2.00000	−0.0642161
$971$	12.0000	0.385098	0.192549	−	0.981287i	$-0.438325\pi$
$971$	12.0000	0.385098	0.192549	+	0.981287i	$0.438325\pi$
$972$	−1.00000	−0.0320750
$973$	16.0000	0.512936
$974$	18.0000	0.576757
$975$	−4.00000	−0.128103
$976$	0	0
$977$	8.00000	0.255943	0.127971	−	0.991778i	$-0.459153\pi$
$977$	8.00000	0.255943	0.127971	+	0.991778i	$0.459153\pi$
$978$	20.0000	0.639529
$979$	16.0000	0.511362
$980$	−9.00000	−0.287494
$981$	−10.0000	−0.319275
$982$	−26.0000	−0.829693
$983$	−16.0000	−0.510321	−0.255160	−	0.966899i	$-0.582128\pi$
$983$	−16.0000	−0.510321	−0.255160	+	0.966899i	$0.582128\pi$
$984$	−10.0000	−0.318788
$985$	2.00000	0.0637253
$986$	24.0000	0.764316
$987$	16.0000	0.509286
$988$	16.0000	0.509028
$989$	−8.00000	−0.254385
$990$	4.00000	0.127128
$991$	2.00000	0.0635321	0.0317660	−	0.999495i	$-0.489887\pi$
$991$	2.00000	0.0635321	0.0317660	+	0.999495i	$0.489887\pi$
$992$	−4.00000	−0.127000
$993$	32.0000	1.01549
$994$	48.0000	1.52247
$995$	−10.0000	−0.317021
$996$	−6.00000	−0.190117
$997$	−38.0000	−1.20347	−0.601736	−	0.798695i	$-0.705524\pi$
$997$	−38.0000	−1.20347	−0.601736	+	0.798695i	$0.705524\pi$
$998$	−4.00000	−0.126618
$999$	−2.00000	−0.0632772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1290.2.a.j.1.1	✓	1
3.2	odd	2		3870.2.a.g.1.1		1
5.4	even	2		6450.2.a.s.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1290.2.a.j.1.1	✓	1	1.1	even	1	trivial
3870.2.a.g.1.1		1	3.2	odd	2
6450.2.a.s.1.1		1	5.4	even	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:	\( N \)	\(=\)	\( 1290 = 2 \cdot 3 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1290.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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