LMFDB - Embedded newform 710.2.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [710,2,Mod(1,710)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(710, 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("710.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 710 = 2 \cdot 5 \cdot 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	710.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:	$5.66937854351$
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	$\chi$	$=$	710.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +3.00000 q^{7} +1.00000 q^{8} -2.00000 q^{9} +O(q^{10})$

\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +3.00000 q^{7} +1.00000 q^{8} -2.00000 q^{9} +1.00000 q^{10} +2.00000 q^{11} -1.00000 q^{12} -1.00000 q^{13} +3.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} +8.00000 q^{17} -2.00000 q^{18} -5.00000 q^{19} +1.00000 q^{20} -3.00000 q^{21} +2.00000 q^{22} -1.00000 q^{23} -1.00000 q^{24} +1.00000 q^{25} -1.00000 q^{26} +5.00000 q^{27} +3.00000 q^{28} -1.00000 q^{30} +7.00000 q^{31} +1.00000 q^{32} -2.00000 q^{33} +8.00000 q^{34} +3.00000 q^{35} -2.00000 q^{36} -12.0000 q^{37} -5.00000 q^{38} +1.00000 q^{39} +1.00000 q^{40} +12.0000 q^{41} -3.00000 q^{42} +9.00000 q^{43} +2.00000 q^{44} -2.00000 q^{45} -1.00000 q^{46} -7.00000 q^{47} -1.00000 q^{48} +2.00000 q^{49} +1.00000 q^{50} -8.00000 q^{51} -1.00000 q^{52} -6.00000 q^{53} +5.00000 q^{54} +2.00000 q^{55} +3.00000 q^{56} +5.00000 q^{57} -1.00000 q^{60} +2.00000 q^{61} +7.00000 q^{62} -6.00000 q^{63} +1.00000 q^{64} -1.00000 q^{65} -2.00000 q^{66} +8.00000 q^{67} +8.00000 q^{68} +1.00000 q^{69} +3.00000 q^{70} +1.00000 q^{71} -2.00000 q^{72} -11.0000 q^{73} -12.0000 q^{74} -1.00000 q^{75} -5.00000 q^{76} +6.00000 q^{77} +1.00000 q^{78} +10.0000 q^{79} +1.00000 q^{80} +1.00000 q^{81} +12.0000 q^{82} -16.0000 q^{83} -3.00000 q^{84} +8.00000 q^{85} +9.00000 q^{86} +2.00000 q^{88} -15.0000 q^{89} -2.00000 q^{90} -3.00000 q^{91} -1.00000 q^{92} -7.00000 q^{93} -7.00000 q^{94} -5.00000 q^{95} -1.00000 q^{96} -2.00000 q^{97} +2.00000 q^{98} -4.00000 q^{99} +O(q^{100})\)

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	−0.288675	−	0.957427i	$-0.593215\pi$
$3$	−1.00000	−0.577350	−0.288675	+	0.957427i	$0.593215\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.00000	−0.408248
$7$	3.00000	1.13389	0.566947	−	0.823754i	$-0.308125\pi$
$7$	3.00000	1.13389	0.566947	+	0.823754i	$0.308125\pi$
$8$	1.00000	0.353553
$9$	−2.00000	−0.666667
$10$	1.00000	0.316228
$11$	2.00000	0.603023	0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000	0.603023	0.301511	+	0.953463i	$0.402509\pi$
$12$	−1.00000	−0.288675
$13$	−1.00000	−0.277350	−0.138675	−	0.990338i	$-0.544284\pi$
$13$	−1.00000	−0.277350	−0.138675	+	0.990338i	$0.544284\pi$
$14$	3.00000	0.801784
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	8.00000	1.94029	0.970143	−	0.242536i	$-0.0779791\pi$
$17$	8.00000	1.94029	0.970143	+	0.242536i	$0.0779791\pi$
$18$	−2.00000	−0.471405
$19$	−5.00000	−1.14708	−0.573539	−	0.819178i	$-0.694430\pi$
$19$	−5.00000	−1.14708	−0.573539	+	0.819178i	$0.694430\pi$
$20$	1.00000	0.223607
$21$	−3.00000	−0.654654
$22$	2.00000	0.426401
$23$	−1.00000	−0.208514	−0.104257	−	0.994550i	$-0.533247\pi$
$23$	−1.00000	−0.208514	−0.104257	+	0.994550i	$0.533247\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	−1.00000	−0.196116
$27$	5.00000	0.962250
$28$	3.00000	0.566947
$29$	0	0		−	1.00000i	$-0.5\pi$
$29$	0	0			1.00000i	$0.5\pi$
$30$	−1.00000	−0.182574
$31$	7.00000	1.25724	0.628619	−	0.777714i	$-0.283621\pi$
$31$	7.00000	1.25724	0.628619	+	0.777714i	$0.283621\pi$
$32$	1.00000	0.176777
$33$	−2.00000	−0.348155
$34$	8.00000	1.37199
$35$	3.00000	0.507093
$36$	−2.00000	−0.333333
$37$	−12.0000	−1.97279	−0.986394	−	0.164399i	$-0.947432\pi$
$37$	−12.0000	−1.97279	−0.986394	+	0.164399i	$0.947432\pi$
$38$	−5.00000	−0.811107
$39$	1.00000	0.160128
$40$	1.00000	0.158114
$41$	12.0000	1.87409	0.937043	−	0.349215i	$-0.113552\pi$
$41$	12.0000	1.87409	0.937043	+	0.349215i	$0.113552\pi$
$42$	−3.00000	−0.462910
$43$	9.00000	1.37249	0.686244	−	0.727372i	$-0.259258\pi$
$43$	9.00000	1.37249	0.686244	+	0.727372i	$0.259258\pi$
$44$	2.00000	0.301511
$45$	−2.00000	−0.298142
$46$	−1.00000	−0.147442
$47$	−7.00000	−1.02105	−0.510527	−	0.859861i	$-0.670550\pi$
$47$	−7.00000	−1.02105	−0.510527	+	0.859861i	$0.670550\pi$
$48$	−1.00000	−0.144338
$49$	2.00000	0.285714
$50$	1.00000	0.141421
$51$	−8.00000	−1.12022
$52$	−1.00000	−0.138675
$53$	−6.00000	−0.824163	−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000	−0.824163	−0.412082	+	0.911147i	$0.635198\pi$
$54$	5.00000	0.680414
$55$	2.00000	0.269680
$56$	3.00000	0.400892
$57$	5.00000	0.662266
$58$	0	0
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	−1.00000	−0.129099
$61$	2.00000	0.256074	0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000	0.256074	0.128037	+	0.991769i	$0.459132\pi$
$62$	7.00000	0.889001
$63$	−6.00000	−0.755929
$64$	1.00000	0.125000
$65$	−1.00000	−0.124035
$66$	−2.00000	−0.246183
$67$	8.00000	0.977356	0.488678	−	0.872464i	$-0.337479\pi$
$67$	8.00000	0.977356	0.488678	+	0.872464i	$0.337479\pi$
$68$	8.00000	0.970143
$69$	1.00000	0.120386
$70$	3.00000	0.358569
$71$	1.00000	0.118678
$71$	1.00000	0.118678
$72$	−2.00000	−0.235702
$73$	−11.0000	−1.28745	−0.643726	−	0.765256i	$-0.722612\pi$
$73$	−11.0000	−1.28745	−0.643726	+	0.765256i	$0.722612\pi$
$74$	−12.0000	−1.39497
$75$	−1.00000	−0.115470
$76$	−5.00000	−0.573539
$77$	6.00000	0.683763
$78$	1.00000	0.113228
$79$	10.0000	1.12509	0.562544	−	0.826767i	$-0.309823\pi$
$79$	10.0000	1.12509	0.562544	+	0.826767i	$0.309823\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	12.0000	1.32518
$83$	−16.0000	−1.75623	−0.878114	−	0.478451i	$-0.841198\pi$
$83$	−16.0000	−1.75623	−0.878114	+	0.478451i	$0.841198\pi$
$84$	−3.00000	−0.327327
$85$	8.00000	0.867722
$86$	9.00000	0.970495
$87$	0	0
$88$	2.00000	0.213201
$89$	−15.0000	−1.59000	−0.794998	−	0.606612i	$-0.792528\pi$
$89$	−15.0000	−1.59000	−0.794998	+	0.606612i	$0.792528\pi$
$90$	−2.00000	−0.210819
$91$	−3.00000	−0.314485
$92$	−1.00000	−0.104257
$93$	−7.00000	−0.725866
$94$	−7.00000	−0.721995
$95$	−5.00000	−0.512989
$96$	−1.00000	−0.102062
$97$	−2.00000	−0.203069	−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000	−0.203069	−0.101535	+	0.994832i	$0.532375\pi$
$98$	2.00000	0.202031
$99$	−4.00000	−0.402015
$100$	1.00000	0.100000
$101$	−18.0000	−1.79107	−0.895533	−	0.444994i	$-0.853206\pi$
$101$	−18.0000	−1.79107	−0.895533	+	0.444994i	$0.853206\pi$
$102$	−8.00000	−0.792118
$103$	−6.00000	−0.591198	−0.295599	−	0.955312i	$-0.595519\pi$
$103$	−6.00000	−0.591198	−0.295599	+	0.955312i	$0.595519\pi$
$104$	−1.00000	−0.0980581
$105$	−3.00000	−0.292770
$106$	−6.00000	−0.582772
$107$	−17.0000	−1.64345	−0.821726	−	0.569883i	$-0.806989\pi$
$107$	−17.0000	−1.64345	−0.821726	+	0.569883i	$0.806989\pi$
$108$	5.00000	0.481125
$109$	10.0000	0.957826	0.478913	−	0.877862i	$-0.341031\pi$
$109$	10.0000	0.957826	0.478913	+	0.877862i	$0.341031\pi$
$110$	2.00000	0.190693
$111$	12.0000	1.13899
$112$	3.00000	0.283473
$113$	−6.00000	−0.564433	−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000	−0.564433	−0.282216	+	0.959351i	$0.591070\pi$
$114$	5.00000	0.468293
$115$	−1.00000	−0.0932505
$116$	0	0
$117$	2.00000	0.184900
$118$	0	0
$119$	24.0000	2.20008
$120$	−1.00000	−0.0912871
$121$	−7.00000	−0.636364
$122$	2.00000	0.181071
$123$	−12.0000	−1.08200
$124$	7.00000	0.628619
$125$	1.00000	0.0894427
$126$	−6.00000	−0.534522
$127$	8.00000	0.709885	0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000	0.709885	0.354943	+	0.934888i	$0.384500\pi$
$128$	1.00000	0.0883883
$129$	−9.00000	−0.792406
$130$	−1.00000	−0.0877058
$131$	−3.00000	−0.262111	−0.131056	−	0.991375i	$-0.541837\pi$
$131$	−3.00000	−0.262111	−0.131056	+	0.991375i	$0.541837\pi$
$132$	−2.00000	−0.174078
$133$	−15.0000	−1.30066
$134$	8.00000	0.691095
$135$	5.00000	0.430331
$136$	8.00000	0.685994
$137$	−22.0000	−1.87959	−0.939793	−	0.341743i	$-0.888983\pi$
$137$	−22.0000	−1.87959	−0.939793	+	0.341743i	$0.888983\pi$
$138$	1.00000	0.0851257
$139$	10.0000	0.848189	0.424094	−	0.905618i	$-0.360592\pi$
$139$	10.0000	0.848189	0.424094	+	0.905618i	$0.360592\pi$
$140$	3.00000	0.253546
$141$	7.00000	0.589506
$142$	1.00000	0.0839181
$143$	−2.00000	−0.167248
$144$	−2.00000	−0.166667
$145$	0	0
$146$	−11.0000	−0.910366
$147$	−2.00000	−0.164957
$148$	−12.0000	−0.986394
$149$	−5.00000	−0.409616	−0.204808	−	0.978802i	$-0.565657\pi$
$149$	−5.00000	−0.409616	−0.204808	+	0.978802i	$0.565657\pi$
$150$	−1.00000	−0.0816497
$151$	2.00000	0.162758	0.0813788	−	0.996683i	$-0.474068\pi$
$151$	2.00000	0.162758	0.0813788	+	0.996683i	$0.474068\pi$
$152$	−5.00000	−0.405554
$153$	−16.0000	−1.29352
$154$	6.00000	0.483494
$155$	7.00000	0.562254
$156$	1.00000	0.0800641
$157$	−22.0000	−1.75579	−0.877896	−	0.478852i	$-0.841053\pi$
$157$	−22.0000	−1.75579	−0.877896	+	0.478852i	$0.841053\pi$
$158$	10.0000	0.795557
$159$	6.00000	0.475831
$160$	1.00000	0.0790569
$161$	−3.00000	−0.236433
$162$	1.00000	0.0785674
$163$	14.0000	1.09656	0.548282	−	0.836293i	$-0.315282\pi$
$163$	14.0000	1.09656	0.548282	+	0.836293i	$0.315282\pi$
$164$	12.0000	0.937043
$165$	−2.00000	−0.155700
$166$	−16.0000	−1.24184
$167$	−2.00000	−0.154765	−0.0773823	−	0.997001i	$-0.524656\pi$
$167$	−2.00000	−0.154765	−0.0773823	+	0.997001i	$0.524656\pi$
$168$	−3.00000	−0.231455
$169$	−12.0000	−0.923077
$170$	8.00000	0.613572
$171$	10.0000	0.764719
$172$	9.00000	0.686244
$173$	9.00000	0.684257	0.342129	−	0.939653i	$-0.388852\pi$
$173$	9.00000	0.684257	0.342129	+	0.939653i	$0.388852\pi$
$174$	0	0
$175$	3.00000	0.226779
$176$	2.00000	0.150756
$177$	0	0
$178$	−15.0000	−1.12430
$179$	15.0000	1.12115	0.560576	−	0.828103i	$-0.310580\pi$
$179$	15.0000	1.12115	0.560576	+	0.828103i	$0.310580\pi$
$180$	−2.00000	−0.149071
$181$	−23.0000	−1.70958	−0.854788	−	0.518977i	$-0.826313\pi$
$181$	−23.0000	−1.70958	−0.854788	+	0.518977i	$0.826313\pi$
$182$	−3.00000	−0.222375
$183$	−2.00000	−0.147844
$184$	−1.00000	−0.0737210
$185$	−12.0000	−0.882258
$186$	−7.00000	−0.513265
$187$	16.0000	1.17004
$188$	−7.00000	−0.510527
$189$	15.0000	1.09109
$190$	−5.00000	−0.362738
$191$	2.00000	0.144715	0.0723575	−	0.997379i	$-0.476948\pi$
$191$	2.00000	0.144715	0.0723575	+	0.997379i	$0.476948\pi$
$192$	−1.00000	−0.0721688
$193$	14.0000	1.00774	0.503871	−	0.863779i	$-0.331909\pi$
$193$	14.0000	1.00774	0.503871	+	0.863779i	$0.331909\pi$
$194$	−2.00000	−0.143592
$195$	1.00000	0.0716115
$196$	2.00000	0.142857
$197$	13.0000	0.926212	0.463106	−	0.886303i	$-0.346735\pi$
$197$	13.0000	0.926212	0.463106	+	0.886303i	$0.346735\pi$
$198$	−4.00000	−0.284268
$199$	0	0		−	1.00000i	$-0.5\pi$
$199$	0	0			1.00000i	$0.5\pi$
$200$	1.00000	0.0707107
$201$	−8.00000	−0.564276
$202$	−18.0000	−1.26648
$203$	0	0
$204$	−8.00000	−0.560112
$205$	12.0000	0.838116
$206$	−6.00000	−0.418040
$207$	2.00000	0.139010
$208$	−1.00000	−0.0693375
$209$	−10.0000	−0.691714
$210$	−3.00000	−0.207020
$211$	2.00000	0.137686	0.0688428	−	0.997628i	$-0.478069\pi$
$211$	2.00000	0.137686	0.0688428	+	0.997628i	$0.478069\pi$
$212$	−6.00000	−0.412082
$213$	−1.00000	−0.0685189
$214$	−17.0000	−1.16210
$215$	9.00000	0.613795
$216$	5.00000	0.340207
$217$	21.0000	1.42557
$218$	10.0000	0.677285
$219$	11.0000	0.743311
$220$	2.00000	0.134840
$221$	−8.00000	−0.538138
$222$	12.0000	0.805387
$223$	−6.00000	−0.401790	−0.200895	−	0.979613i	$-0.564385\pi$
$223$	−6.00000	−0.401790	−0.200895	+	0.979613i	$0.564385\pi$
$224$	3.00000	0.200446
$225$	−2.00000	−0.133333
$226$	−6.00000	−0.399114
$227$	18.0000	1.19470	0.597351	−	0.801980i	$-0.296220\pi$
$227$	18.0000	1.19470	0.597351	+	0.801980i	$0.296220\pi$
$228$	5.00000	0.331133
$229$	10.0000	0.660819	0.330409	−	0.943838i	$-0.392813\pi$
$229$	10.0000	0.660819	0.330409	+	0.943838i	$0.392813\pi$
$230$	−1.00000	−0.0659380
$231$	−6.00000	−0.394771
$232$	0	0
$233$	29.0000	1.89985	0.949927	−	0.312473i	$-0.101157\pi$
$233$	29.0000	1.89985	0.949927	+	0.312473i	$0.101157\pi$
$234$	2.00000	0.130744
$235$	−7.00000	−0.456630
$236$	0	0
$237$	−10.0000	−0.649570
$238$	24.0000	1.55569
$239$	15.0000	0.970269	0.485135	−	0.874439i	$-0.338771\pi$
$239$	15.0000	0.970269	0.485135	+	0.874439i	$0.338771\pi$
$240$	−1.00000	−0.0645497
$241$	12.0000	0.772988	0.386494	−	0.922292i	$-0.373686\pi$
$241$	12.0000	0.772988	0.386494	+	0.922292i	$0.373686\pi$
$242$	−7.00000	−0.449977
$243$	−16.0000	−1.02640
$244$	2.00000	0.128037
$245$	2.00000	0.127775
$246$	−12.0000	−0.765092
$247$	5.00000	0.318142
$248$	7.00000	0.444500
$249$	16.0000	1.01396
$250$	1.00000	0.0632456
$251$	−23.0000	−1.45175	−0.725874	−	0.687828i	$-0.758564\pi$
$251$	−23.0000	−1.45175	−0.725874	+	0.687828i	$0.758564\pi$
$252$	−6.00000	−0.377964
$253$	−2.00000	−0.125739
$254$	8.00000	0.501965
$255$	−8.00000	−0.500979
$256$	1.00000	0.0625000
$257$	−22.0000	−1.37232	−0.686161	−	0.727450i	$-0.740706\pi$
$257$	−22.0000	−1.37232	−0.686161	+	0.727450i	$0.740706\pi$
$258$	−9.00000	−0.560316
$259$	−36.0000	−2.23693
$260$	−1.00000	−0.0620174
$261$	0	0
$262$	−3.00000	−0.185341
$263$	−6.00000	−0.369976	−0.184988	−	0.982741i	$-0.559225\pi$
$263$	−6.00000	−0.369976	−0.184988	+	0.982741i	$0.559225\pi$
$264$	−2.00000	−0.123091
$265$	−6.00000	−0.368577
$266$	−15.0000	−0.919709
$267$	15.0000	0.917985
$268$	8.00000	0.488678
$269$	15.0000	0.914566	0.457283	−	0.889321i	$-0.348823\pi$
$269$	15.0000	0.914566	0.457283	+	0.889321i	$0.348823\pi$
$270$	5.00000	0.304290
$271$	−8.00000	−0.485965	−0.242983	−	0.970031i	$-0.578126\pi$
$271$	−8.00000	−0.485965	−0.242983	+	0.970031i	$0.578126\pi$
$272$	8.00000	0.485071
$273$	3.00000	0.181568
$274$	−22.0000	−1.32907
$275$	2.00000	0.120605
$276$	1.00000	0.0601929
$277$	−2.00000	−0.120168	−0.0600842	−	0.998193i	$-0.519137\pi$
$277$	−2.00000	−0.120168	−0.0600842	+	0.998193i	$0.519137\pi$
$278$	10.0000	0.599760
$279$	−14.0000	−0.838158
$280$	3.00000	0.179284
$281$	22.0000	1.31241	0.656205	−	0.754583i	$-0.272161\pi$
$281$	22.0000	1.31241	0.656205	+	0.754583i	$0.272161\pi$
$282$	7.00000	0.416844
$283$	4.00000	0.237775	0.118888	−	0.992908i	$-0.462067\pi$
$283$	4.00000	0.237775	0.118888	+	0.992908i	$0.462067\pi$
$284$	1.00000	0.0593391
$285$	5.00000	0.296174
$286$	−2.00000	−0.118262
$287$	36.0000	2.12501
$288$	−2.00000	−0.117851
$289$	47.0000	2.76471
$290$	0	0
$291$	2.00000	0.117242
$292$	−11.0000	−0.643726
$293$	−26.0000	−1.51894	−0.759468	−	0.650545i	$-0.774541\pi$
$293$	−26.0000	−1.51894	−0.759468	+	0.650545i	$0.774541\pi$
$294$	−2.00000	−0.116642
$295$	0	0
$296$	−12.0000	−0.697486
$297$	10.0000	0.580259
$298$	−5.00000	−0.289642
$299$	1.00000	0.0578315
$300$	−1.00000	−0.0577350
$301$	27.0000	1.55625
$302$	2.00000	0.115087
$303$	18.0000	1.03407
$304$	−5.00000	−0.286770
$305$	2.00000	0.114520
$306$	−16.0000	−0.914659
$307$	18.0000	1.02731	0.513657	−	0.857996i	$-0.328290\pi$
$307$	18.0000	1.02731	0.513657	+	0.857996i	$0.328290\pi$
$308$	6.00000	0.341882
$309$	6.00000	0.341328
$310$	7.00000	0.397573
$311$	12.0000	0.680458	0.340229	−	0.940343i	$-0.389495\pi$
$311$	12.0000	0.680458	0.340229	+	0.940343i	$0.389495\pi$
$312$	1.00000	0.0566139
$313$	−11.0000	−0.621757	−0.310878	−	0.950450i	$-0.600623\pi$
$313$	−11.0000	−0.621757	−0.310878	+	0.950450i	$0.600623\pi$
$314$	−22.0000	−1.24153
$315$	−6.00000	−0.338062
$316$	10.0000	0.562544
$317$	−22.0000	−1.23564	−0.617822	−	0.786318i	$-0.711985\pi$
$317$	−22.0000	−1.23564	−0.617822	+	0.786318i	$0.711985\pi$
$318$	6.00000	0.336463
$319$	0	0
$320$	1.00000	0.0559017
$321$	17.0000	0.948847
$322$	−3.00000	−0.167183
$323$	−40.0000	−2.22566
$324$	1.00000	0.0555556
$325$	−1.00000	−0.0554700
$326$	14.0000	0.775388
$327$	−10.0000	−0.553001
$328$	12.0000	0.662589
$329$	−21.0000	−1.15777
$330$	−2.00000	−0.110096
$331$	12.0000	0.659580	0.329790	−	0.944054i	$-0.393022\pi$
$331$	12.0000	0.659580	0.329790	+	0.944054i	$0.393022\pi$
$332$	−16.0000	−0.878114
$333$	24.0000	1.31519
$334$	−2.00000	−0.109435
$335$	8.00000	0.437087
$336$	−3.00000	−0.163663
$337$	−2.00000	−0.108947	−0.0544735	−	0.998515i	$-0.517348\pi$
$337$	−2.00000	−0.108947	−0.0544735	+	0.998515i	$0.517348\pi$
$338$	−12.0000	−0.652714
$339$	6.00000	0.325875
$340$	8.00000	0.433861
$341$	14.0000	0.758143
$342$	10.0000	0.540738
$343$	−15.0000	−0.809924
$344$	9.00000	0.485247
$345$	1.00000	0.0538382
$346$	9.00000	0.483843
$347$	−12.0000	−0.644194	−0.322097	−	0.946707i	$-0.604388\pi$
$347$	−12.0000	−0.644194	−0.322097	+	0.946707i	$0.604388\pi$
$348$	0	0
$349$	5.00000	0.267644	0.133822	−	0.991005i	$-0.457275\pi$
$349$	5.00000	0.267644	0.133822	+	0.991005i	$0.457275\pi$
$350$	3.00000	0.160357
$351$	−5.00000	−0.266880
$352$	2.00000	0.106600
$353$	−6.00000	−0.319348	−0.159674	−	0.987170i	$-0.551044\pi$
$353$	−6.00000	−0.319348	−0.159674	+	0.987170i	$0.551044\pi$
$354$	0	0
$355$	1.00000	0.0530745
$356$	−15.0000	−0.794998
$357$	−24.0000	−1.27021
$358$	15.0000	0.792775
$359$	−30.0000	−1.58334	−0.791670	−	0.610949i	$-0.790788\pi$
$359$	−30.0000	−1.58334	−0.791670	+	0.610949i	$0.790788\pi$
$360$	−2.00000	−0.105409
$361$	6.00000	0.315789
$362$	−23.0000	−1.20885
$363$	7.00000	0.367405
$364$	−3.00000	−0.157243
$365$	−11.0000	−0.575766
$366$	−2.00000	−0.104542
$367$	28.0000	1.46159	0.730794	−	0.682598i	$-0.239150\pi$
$367$	28.0000	1.46159	0.730794	+	0.682598i	$0.239150\pi$
$368$	−1.00000	−0.0521286
$369$	−24.0000	−1.24939
$370$	−12.0000	−0.623850
$371$	−18.0000	−0.934513
$372$	−7.00000	−0.362933
$373$	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
$376$	−7.00000	−0.360997
$377$	0	0
$378$	15.0000	0.771517
$379$	20.0000	1.02733	0.513665	−	0.857991i	$-0.328287\pi$
$379$	20.0000	1.02733	0.513665	+	0.857991i	$0.328287\pi$
$380$	−5.00000	−0.256495
$381$	−8.00000	−0.409852
$382$	2.00000	0.102329
$383$	9.00000	0.459879	0.229939	−	0.973205i	$-0.426147\pi$
$383$	9.00000	0.459879	0.229939	+	0.973205i	$0.426147\pi$
$384$	−1.00000	−0.0510310
$385$	6.00000	0.305788
$386$	14.0000	0.712581
$387$	−18.0000	−0.914991
$388$	−2.00000	−0.101535
$389$	−5.00000	−0.253510	−0.126755	−	0.991934i	$-0.540456\pi$
$389$	−5.00000	−0.253510	−0.126755	+	0.991934i	$0.540456\pi$
$390$	1.00000	0.0506370
$391$	−8.00000	−0.404577
$392$	2.00000	0.101015
$393$	3.00000	0.151330
$394$	13.0000	0.654931
$395$	10.0000	0.503155
$396$	−4.00000	−0.201008
$397$	−22.0000	−1.10415	−0.552074	−	0.833795i	$-0.686163\pi$
$397$	−22.0000	−1.10415	−0.552074	+	0.833795i	$0.686163\pi$
$398$	0	0
$399$	15.0000	0.750939
$400$	1.00000	0.0500000
$401$	2.00000	0.0998752	0.0499376	−	0.998752i	$-0.484098\pi$
$401$	2.00000	0.0998752	0.0499376	+	0.998752i	$0.484098\pi$
$402$	−8.00000	−0.399004
$403$	−7.00000	−0.348695
$404$	−18.0000	−0.895533
$405$	1.00000	0.0496904
$406$	0	0
$407$	−24.0000	−1.18964
$408$	−8.00000	−0.396059
$409$	5.00000	0.247234	0.123617	−	0.992330i	$-0.460551\pi$
$409$	5.00000	0.247234	0.123617	+	0.992330i	$0.460551\pi$
$410$	12.0000	0.592638
$411$	22.0000	1.08518
$412$	−6.00000	−0.295599
$413$	0	0
$414$	2.00000	0.0982946
$415$	−16.0000	−0.785409
$416$	−1.00000	−0.0490290
$417$	−10.0000	−0.489702
$418$	−10.0000	−0.489116
$419$	0	0		−	1.00000i	$-0.5\pi$
$419$	0	0			1.00000i	$0.5\pi$
$420$	−3.00000	−0.146385
$421$	−3.00000	−0.146211	−0.0731055	−	0.997324i	$-0.523291\pi$
$421$	−3.00000	−0.146211	−0.0731055	+	0.997324i	$0.523291\pi$
$422$	2.00000	0.0973585
$423$	14.0000	0.680703
$424$	−6.00000	−0.291386
$425$	8.00000	0.388057
$426$	−1.00000	−0.0484502
$427$	6.00000	0.290360
$428$	−17.0000	−0.821726
$429$	2.00000	0.0965609
$430$	9.00000	0.434019
$431$	2.00000	0.0963366	0.0481683	−	0.998839i	$-0.484662\pi$
$431$	2.00000	0.0963366	0.0481683	+	0.998839i	$0.484662\pi$
$432$	5.00000	0.240563
$433$	14.0000	0.672797	0.336399	−	0.941720i	$-0.390791\pi$
$433$	14.0000	0.672797	0.336399	+	0.941720i	$0.390791\pi$
$434$	21.0000	1.00803
$435$	0	0
$436$	10.0000	0.478913
$437$	5.00000	0.239182
$438$	11.0000	0.525600
$439$	0	0		−	1.00000i	$-0.5\pi$
$439$	0	0			1.00000i	$0.5\pi$
$440$	2.00000	0.0953463
$441$	−4.00000	−0.190476
$442$	−8.00000	−0.380521
$443$	−36.0000	−1.71041	−0.855206	−	0.518289i	$-0.826569\pi$
$443$	−36.0000	−1.71041	−0.855206	+	0.518289i	$0.826569\pi$
$444$	12.0000	0.569495
$445$	−15.0000	−0.711068
$446$	−6.00000	−0.284108
$447$	5.00000	0.236492
$448$	3.00000	0.141737
$449$	10.0000	0.471929	0.235965	−	0.971762i	$-0.424175\pi$
$449$	10.0000	0.471929	0.235965	+	0.971762i	$0.424175\pi$
$450$	−2.00000	−0.0942809
$451$	24.0000	1.13012
$452$	−6.00000	−0.282216
$453$	−2.00000	−0.0939682
$454$	18.0000	0.844782
$455$	−3.00000	−0.140642
$456$	5.00000	0.234146
$457$	−2.00000	−0.0935561	−0.0467780	−	0.998905i	$-0.514895\pi$
$457$	−2.00000	−0.0935561	−0.0467780	+	0.998905i	$0.514895\pi$
$458$	10.0000	0.467269
$459$	40.0000	1.86704
$460$	−1.00000	−0.0466252
$461$	37.0000	1.72326	0.861631	−	0.507535i	$-0.169443\pi$
$461$	37.0000	1.72326	0.861631	+	0.507535i	$0.169443\pi$
$462$	−6.00000	−0.279145
$463$	34.0000	1.58011	0.790057	−	0.613033i	$-0.210051\pi$
$463$	34.0000	1.58011	0.790057	+	0.613033i	$0.210051\pi$
$464$	0	0
$465$	−7.00000	−0.324617
$466$	29.0000	1.34340
$467$	−12.0000	−0.555294	−0.277647	−	0.960683i	$-0.589555\pi$
$467$	−12.0000	−0.555294	−0.277647	+	0.960683i	$0.589555\pi$
$468$	2.00000	0.0924500
$469$	24.0000	1.10822
$470$	−7.00000	−0.322886
$471$	22.0000	1.01371
$472$	0	0
$473$	18.0000	0.827641
$474$	−10.0000	−0.459315
$475$	−5.00000	−0.229416
$476$	24.0000	1.10004
$477$	12.0000	0.549442
$478$	15.0000	0.686084
$479$	25.0000	1.14228	0.571140	−	0.820853i	$-0.306501\pi$
$479$	25.0000	1.14228	0.571140	+	0.820853i	$0.306501\pi$
$480$	−1.00000	−0.0456435
$481$	12.0000	0.547153
$482$	12.0000	0.546585
$483$	3.00000	0.136505
$484$	−7.00000	−0.318182
$485$	−2.00000	−0.0908153
$486$	−16.0000	−0.725775
$487$	−12.0000	−0.543772	−0.271886	−	0.962329i	$-0.587647\pi$
$487$	−12.0000	−0.543772	−0.271886	+	0.962329i	$0.587647\pi$
$488$	2.00000	0.0905357
$489$	−14.0000	−0.633102
$490$	2.00000	0.0903508
$491$	−8.00000	−0.361035	−0.180517	−	0.983572i	$-0.557777\pi$
$491$	−8.00000	−0.361035	−0.180517	+	0.983572i	$0.557777\pi$
$492$	−12.0000	−0.541002
$493$	0	0
$494$	5.00000	0.224961
$495$	−4.00000	−0.179787
$496$	7.00000	0.314309
$497$	3.00000	0.134568
$498$	16.0000	0.716977
$499$	5.00000	0.223831	0.111915	−	0.993718i	$-0.464301\pi$
$499$	5.00000	0.223831	0.111915	+	0.993718i	$0.464301\pi$
$500$	1.00000	0.0447214
$501$	2.00000	0.0893534
$502$	−23.0000	−1.02654
$503$	34.0000	1.51599	0.757993	−	0.652263i	$-0.226180\pi$
$503$	34.0000	1.51599	0.757993	+	0.652263i	$0.226180\pi$
$504$	−6.00000	−0.267261
$505$	−18.0000	−0.800989
$506$	−2.00000	−0.0889108
$507$	12.0000	0.532939
$508$	8.00000	0.354943
$509$	−10.0000	−0.443242	−0.221621	−	0.975133i	$-0.571135\pi$
$509$	−10.0000	−0.443242	−0.221621	+	0.975133i	$0.571135\pi$
$510$	−8.00000	−0.354246
$511$	−33.0000	−1.45983
$512$	1.00000	0.0441942
$513$	−25.0000	−1.10378
$514$	−22.0000	−0.970378
$515$	−6.00000	−0.264392
$516$	−9.00000	−0.396203
$517$	−14.0000	−0.615719
$518$	−36.0000	−1.58175
$519$	−9.00000	−0.395056
$520$	−1.00000	−0.0438529
$521$	42.0000	1.84005	0.920027	−	0.391856i	$-0.128167\pi$
$521$	42.0000	1.84005	0.920027	+	0.391856i	$0.128167\pi$
$522$	0	0
$523$	4.00000	0.174908	0.0874539	−	0.996169i	$-0.472127\pi$
$523$	4.00000	0.174908	0.0874539	+	0.996169i	$0.472127\pi$
$524$	−3.00000	−0.131056
$525$	−3.00000	−0.130931
$526$	−6.00000	−0.261612
$527$	56.0000	2.43940
$528$	−2.00000	−0.0870388
$529$	−22.0000	−0.956522
$530$	−6.00000	−0.260623
$531$	0	0
$532$	−15.0000	−0.650332
$533$	−12.0000	−0.519778
$534$	15.0000	0.649113
$535$	−17.0000	−0.734974
$536$	8.00000	0.345547
$537$	−15.0000	−0.647298
$538$	15.0000	0.646696
$539$	4.00000	0.172292
$540$	5.00000	0.215166
$541$	2.00000	0.0859867	0.0429934	−	0.999075i	$-0.486311\pi$
$541$	2.00000	0.0859867	0.0429934	+	0.999075i	$0.486311\pi$
$542$	−8.00000	−0.343629
$543$	23.0000	0.987024
$544$	8.00000	0.342997
$545$	10.0000	0.428353
$546$	3.00000	0.128388
$547$	43.0000	1.83855	0.919274	−	0.393619i	$-0.128777\pi$
$547$	43.0000	1.83855	0.919274	+	0.393619i	$0.128777\pi$
$548$	−22.0000	−0.939793
$549$	−4.00000	−0.170716
$550$	2.00000	0.0852803
$551$	0	0
$552$	1.00000	0.0425628
$553$	30.0000	1.27573
$554$	−2.00000	−0.0849719
$555$	12.0000	0.509372
$556$	10.0000	0.424094
$557$	−12.0000	−0.508456	−0.254228	−	0.967144i	$-0.581821\pi$
$557$	−12.0000	−0.508456	−0.254228	+	0.967144i	$0.581821\pi$
$558$	−14.0000	−0.592667
$559$	−9.00000	−0.380659
$560$	3.00000	0.126773
$561$	−16.0000	−0.675521
$562$	22.0000	0.928014
$563$	−36.0000	−1.51722	−0.758610	−	0.651546i	$-0.774121\pi$
$563$	−36.0000	−1.51722	−0.758610	+	0.651546i	$0.774121\pi$
$564$	7.00000	0.294753
$565$	−6.00000	−0.252422
$566$	4.00000	0.168133
$567$	3.00000	0.125988
$568$	1.00000	0.0419591
$569$	35.0000	1.46728	0.733638	−	0.679540i	$-0.237821\pi$
$569$	35.0000	1.46728	0.733638	+	0.679540i	$0.237821\pi$
$570$	5.00000	0.209427
$571$	−28.0000	−1.17176	−0.585882	−	0.810397i	$-0.699252\pi$
$571$	−28.0000	−1.17176	−0.585882	+	0.810397i	$0.699252\pi$
$572$	−2.00000	−0.0836242
$573$	−2.00000	−0.0835512
$574$	36.0000	1.50261
$575$	−1.00000	−0.0417029
$576$	−2.00000	−0.0833333
$577$	18.0000	0.749350	0.374675	−	0.927156i	$-0.377754\pi$
$577$	18.0000	0.749350	0.374675	+	0.927156i	$0.377754\pi$
$578$	47.0000	1.95494
$579$	−14.0000	−0.581820
$580$	0	0
$581$	−48.0000	−1.99138
$582$	2.00000	0.0829027
$583$	−12.0000	−0.496989
$584$	−11.0000	−0.455183
$585$	2.00000	0.0826898
$586$	−26.0000	−1.07405
$587$	−32.0000	−1.32078	−0.660391	−	0.750922i	$-0.729609\pi$
$587$	−32.0000	−1.32078	−0.660391	+	0.750922i	$0.729609\pi$
$588$	−2.00000	−0.0824786
$589$	−35.0000	−1.44215
$590$	0	0
$591$	−13.0000	−0.534749
$592$	−12.0000	−0.493197
$593$	−21.0000	−0.862367	−0.431183	−	0.902264i	$-0.641904\pi$
$593$	−21.0000	−0.862367	−0.431183	+	0.902264i	$0.641904\pi$
$594$	10.0000	0.410305
$595$	24.0000	0.983904
$596$	−5.00000	−0.204808
$597$	0	0
$598$	1.00000	0.0408930
$599$	−45.0000	−1.83865	−0.919325	−	0.393499i	$-0.871265\pi$
$599$	−45.0000	−1.83865	−0.919325	+	0.393499i	$0.871265\pi$
$600$	−1.00000	−0.0408248
$601$	−18.0000	−0.734235	−0.367118	−	0.930175i	$-0.619655\pi$
$601$	−18.0000	−0.734235	−0.367118	+	0.930175i	$0.619655\pi$
$602$	27.0000	1.10044
$603$	−16.0000	−0.651570
$604$	2.00000	0.0813788
$605$	−7.00000	−0.284590
$606$	18.0000	0.731200
$607$	28.0000	1.13648	0.568242	−	0.822861i	$-0.307624\pi$
$607$	28.0000	1.13648	0.568242	+	0.822861i	$0.307624\pi$
$608$	−5.00000	−0.202777
$609$	0	0
$610$	2.00000	0.0809776
$611$	7.00000	0.283190
$612$	−16.0000	−0.646762
$613$	34.0000	1.37325	0.686624	−	0.727013i	$-0.259092\pi$
$613$	34.0000	1.37325	0.686624	+	0.727013i	$0.259092\pi$
$614$	18.0000	0.726421
$615$	−12.0000	−0.483887
$616$	6.00000	0.241747
$617$	−7.00000	−0.281809	−0.140905	−	0.990023i	$-0.545001\pi$
$617$	−7.00000	−0.281809	−0.140905	+	0.990023i	$0.545001\pi$
$618$	6.00000	0.241355
$619$	−30.0000	−1.20580	−0.602901	−	0.797816i	$-0.705989\pi$
$619$	−30.0000	−1.20580	−0.602901	+	0.797816i	$0.705989\pi$
$620$	7.00000	0.281127
$621$	−5.00000	−0.200643
$622$	12.0000	0.481156
$623$	−45.0000	−1.80289
$624$	1.00000	0.0400320
$625$	1.00000	0.0400000
$626$	−11.0000	−0.439648
$627$	10.0000	0.399362
$628$	−22.0000	−0.877896
$629$	−96.0000	−3.82777
$630$	−6.00000	−0.239046
$631$	−8.00000	−0.318475	−0.159237	−	0.987240i	$-0.550904\pi$
$631$	−8.00000	−0.318475	−0.159237	+	0.987240i	$0.550904\pi$
$632$	10.0000	0.397779
$633$	−2.00000	−0.0794929
$634$	−22.0000	−0.873732
$635$	8.00000	0.317470
$636$	6.00000	0.237915
$637$	−2.00000	−0.0792429
$638$	0	0
$639$	−2.00000	−0.0791188
$640$	1.00000	0.0395285
$641$	17.0000	0.671460	0.335730	−	0.941958i	$-0.391017\pi$
$641$	17.0000	0.671460	0.335730	+	0.941958i	$0.391017\pi$
$642$	17.0000	0.670936
$643$	−21.0000	−0.828159	−0.414080	−	0.910241i	$-0.635896\pi$
$643$	−21.0000	−0.828159	−0.414080	+	0.910241i	$0.635896\pi$
$644$	−3.00000	−0.118217
$645$	−9.00000	−0.354375
$646$	−40.0000	−1.57378
$647$	−32.0000	−1.25805	−0.629025	−	0.777385i	$-0.716546\pi$
$647$	−32.0000	−1.25805	−0.629025	+	0.777385i	$0.716546\pi$
$648$	1.00000	0.0392837
$649$	0	0
$650$	−1.00000	−0.0392232
$651$	−21.0000	−0.823055
$652$	14.0000	0.548282
$653$	−6.00000	−0.234798	−0.117399	−	0.993085i	$-0.537456\pi$
$653$	−6.00000	−0.234798	−0.117399	+	0.993085i	$0.537456\pi$
$654$	−10.0000	−0.391031
$655$	−3.00000	−0.117220
$656$	12.0000	0.468521
$657$	22.0000	0.858302
$658$	−21.0000	−0.818665
$659$	15.0000	0.584317	0.292159	−	0.956370i	$-0.405627\pi$
$659$	15.0000	0.584317	0.292159	+	0.956370i	$0.405627\pi$
$660$	−2.00000	−0.0778499
$661$	−13.0000	−0.505641	−0.252821	−	0.967513i	$-0.581358\pi$
$661$	−13.0000	−0.505641	−0.252821	+	0.967513i	$0.581358\pi$
$662$	12.0000	0.466393
$663$	8.00000	0.310694
$664$	−16.0000	−0.620920
$665$	−15.0000	−0.581675
$666$	24.0000	0.929981
$667$	0	0
$668$	−2.00000	−0.0773823
$669$	6.00000	0.231973
$670$	8.00000	0.309067
$671$	4.00000	0.154418
$672$	−3.00000	−0.115728
$673$	4.00000	0.154189	0.0770943	−	0.997024i	$-0.475436\pi$
$673$	4.00000	0.154189	0.0770943	+	0.997024i	$0.475436\pi$
$674$	−2.00000	−0.0770371
$675$	5.00000	0.192450
$676$	−12.0000	−0.461538
$677$	−42.0000	−1.61419	−0.807096	−	0.590421i	$-0.798962\pi$
$677$	−42.0000	−1.61419	−0.807096	+	0.590421i	$0.798962\pi$
$678$	6.00000	0.230429
$679$	−6.00000	−0.230259
$680$	8.00000	0.306786
$681$	−18.0000	−0.689761
$682$	14.0000	0.536088
$683$	24.0000	0.918334	0.459167	−	0.888350i	$-0.348148\pi$
$683$	24.0000	0.918334	0.459167	+	0.888350i	$0.348148\pi$
$684$	10.0000	0.382360
$685$	−22.0000	−0.840577
$686$	−15.0000	−0.572703
$687$	−10.0000	−0.381524
$688$	9.00000	0.343122
$689$	6.00000	0.228582
$690$	1.00000	0.0380693
$691$	42.0000	1.59776	0.798878	−	0.601494i	$-0.205427\pi$
$691$	42.0000	1.59776	0.798878	+	0.601494i	$0.205427\pi$
$692$	9.00000	0.342129
$693$	−12.0000	−0.455842
$694$	−12.0000	−0.455514
$695$	10.0000	0.379322
$696$	0	0
$697$	96.0000	3.63626
$698$	5.00000	0.189253
$699$	−29.0000	−1.09688
$700$	3.00000	0.113389
$701$	27.0000	1.01978	0.509888	−	0.860241i	$-0.329687\pi$
$701$	27.0000	1.01978	0.509888	+	0.860241i	$0.329687\pi$
$702$	−5.00000	−0.188713
$703$	60.0000	2.26294
$704$	2.00000	0.0753778
$705$	7.00000	0.263635
$706$	−6.00000	−0.225813
$707$	−54.0000	−2.03088
$708$	0	0
$709$	5.00000	0.187779	0.0938895	−	0.995583i	$-0.470070\pi$
$709$	5.00000	0.187779	0.0938895	+	0.995583i	$0.470070\pi$
$710$	1.00000	0.0375293
$711$	−20.0000	−0.750059
$712$	−15.0000	−0.562149
$713$	−7.00000	−0.262152
$714$	−24.0000	−0.898177
$715$	−2.00000	−0.0747958
$716$	15.0000	0.560576
$717$	−15.0000	−0.560185
$718$	−30.0000	−1.11959
$719$	−20.0000	−0.745874	−0.372937	−	0.927857i	$-0.621649\pi$
$719$	−20.0000	−0.745874	−0.372937	+	0.927857i	$0.621649\pi$
$720$	−2.00000	−0.0745356
$721$	−18.0000	−0.670355
$722$	6.00000	0.223297
$723$	−12.0000	−0.446285
$724$	−23.0000	−0.854788
$725$	0	0
$726$	7.00000	0.259794
$727$	−37.0000	−1.37225	−0.686127	−	0.727482i	$-0.740691\pi$
$727$	−37.0000	−1.37225	−0.686127	+	0.727482i	$0.740691\pi$
$728$	−3.00000	−0.111187
$729$	13.0000	0.481481
$730$	−11.0000	−0.407128
$731$	72.0000	2.66302
$732$	−2.00000	−0.0739221
$733$	−1.00000	−0.0369358	−0.0184679	−	0.999829i	$-0.505879\pi$
$733$	−1.00000	−0.0369358	−0.0184679	+	0.999829i	$0.505879\pi$
$734$	28.0000	1.03350
$735$	−2.00000	−0.0737711
$736$	−1.00000	−0.0368605
$737$	16.0000	0.589368
$738$	−24.0000	−0.883452
$739$	−25.0000	−0.919640	−0.459820	−	0.888012i	$-0.652086\pi$
$739$	−25.0000	−0.919640	−0.459820	+	0.888012i	$0.652086\pi$
$740$	−12.0000	−0.441129
$741$	−5.00000	−0.183680
$742$	−18.0000	−0.660801
$743$	9.00000	0.330178	0.165089	−	0.986279i	$-0.447209\pi$
$743$	9.00000	0.330178	0.165089	+	0.986279i	$0.447209\pi$
$744$	−7.00000	−0.256632
$745$	−5.00000	−0.183186
$746$	14.0000	0.512576
$747$	32.0000	1.17082
$748$	16.0000	0.585018
$749$	−51.0000	−1.86350
$750$	−1.00000	−0.0365148
$751$	−8.00000	−0.291924	−0.145962	−	0.989290i	$-0.546628\pi$
$751$	−8.00000	−0.291924	−0.145962	+	0.989290i	$0.546628\pi$
$752$	−7.00000	−0.255264
$753$	23.0000	0.838167
$754$	0	0
$755$	2.00000	0.0727875
$756$	15.0000	0.545545
$757$	−7.00000	−0.254419	−0.127210	−	0.991876i	$-0.540602\pi$
$757$	−7.00000	−0.254419	−0.127210	+	0.991876i	$0.540602\pi$
$758$	20.0000	0.726433
$759$	2.00000	0.0725954
$760$	−5.00000	−0.181369
$761$	32.0000	1.16000	0.580000	−	0.814617i	$-0.303053\pi$
$761$	32.0000	1.16000	0.580000	+	0.814617i	$0.303053\pi$
$762$	−8.00000	−0.289809
$763$	30.0000	1.08607
$764$	2.00000	0.0723575
$765$	−16.0000	−0.578481
$766$	9.00000	0.325183
$767$	0	0
$768$	−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	$0.318079\pi$
$770$	6.00000	0.216225
$771$	22.0000	0.792311
$772$	14.0000	0.503871
$773$	−21.0000	−0.755318	−0.377659	−	0.925945i	$-0.623271\pi$
$773$	−21.0000	−0.755318	−0.377659	+	0.925945i	$0.623271\pi$
$774$	−18.0000	−0.646997
$775$	7.00000	0.251447
$776$	−2.00000	−0.0717958
$777$	36.0000	1.29149
$778$	−5.00000	−0.179259
$779$	−60.0000	−2.14972
$780$	1.00000	0.0358057
$781$	2.00000	0.0715656
$782$	−8.00000	−0.286079
$783$	0	0
$784$	2.00000	0.0714286
$785$	−22.0000	−0.785214
$786$	3.00000	0.107006
$787$	3.00000	0.106938	0.0534692	−	0.998569i	$-0.482972\pi$
$787$	3.00000	0.106938	0.0534692	+	0.998569i	$0.482972\pi$
$788$	13.0000	0.463106
$789$	6.00000	0.213606
$790$	10.0000	0.355784
$791$	−18.0000	−0.640006
$792$	−4.00000	−0.142134
$793$	−2.00000	−0.0710221
$794$	−22.0000	−0.780751
$795$	6.00000	0.212798
$796$	0	0
$797$	−12.0000	−0.425062	−0.212531	−	0.977154i	$-0.568171\pi$
$797$	−12.0000	−0.425062	−0.212531	+	0.977154i	$0.568171\pi$
$798$	15.0000	0.530994
$799$	−56.0000	−1.98114
$800$	1.00000	0.0353553
$801$	30.0000	1.06000
$802$	2.00000	0.0706225
$803$	−22.0000	−0.776363
$804$	−8.00000	−0.282138
$805$	−3.00000	−0.105736
$806$	−7.00000	−0.246564
$807$	−15.0000	−0.528025
$808$	−18.0000	−0.633238
$809$	−10.0000	−0.351581	−0.175791	−	0.984428i	$-0.556248\pi$
$809$	−10.0000	−0.351581	−0.175791	+	0.984428i	$0.556248\pi$
$810$	1.00000	0.0351364
$811$	−28.0000	−0.983213	−0.491606	−	0.870817i	$-0.663590\pi$
$811$	−28.0000	−0.983213	−0.491606	+	0.870817i	$0.663590\pi$
$812$	0	0
$813$	8.00000	0.280572
$814$	−24.0000	−0.841200
$815$	14.0000	0.490399
$816$	−8.00000	−0.280056
$817$	−45.0000	−1.57435
$818$	5.00000	0.174821
$819$	6.00000	0.209657
$820$	12.0000	0.419058
$821$	−18.0000	−0.628204	−0.314102	−	0.949389i	$-0.601703\pi$
$821$	−18.0000	−0.628204	−0.314102	+	0.949389i	$0.601703\pi$
$822$	22.0000	0.767338
$823$	−11.0000	−0.383436	−0.191718	−	0.981450i	$-0.561406\pi$
$823$	−11.0000	−0.383436	−0.191718	+	0.981450i	$0.561406\pi$
$824$	−6.00000	−0.209020
$825$	−2.00000	−0.0696311
$826$	0	0
$827$	−22.0000	−0.765015	−0.382507	−	0.923952i	$-0.624939\pi$
$827$	−22.0000	−0.765015	−0.382507	+	0.923952i	$0.624939\pi$
$828$	2.00000	0.0695048
$829$	30.0000	1.04194	0.520972	−	0.853574i	$-0.325570\pi$
$829$	30.0000	1.04194	0.520972	+	0.853574i	$0.325570\pi$
$830$	−16.0000	−0.555368
$831$	2.00000	0.0693792
$832$	−1.00000	−0.0346688
$833$	16.0000	0.554367
$834$	−10.0000	−0.346272
$835$	−2.00000	−0.0692129
$836$	−10.0000	−0.345857
$837$	35.0000	1.20978
$838$	0	0
$839$	−40.0000	−1.38095	−0.690477	−	0.723355i	$-0.742599\pi$
$839$	−40.0000	−1.38095	−0.690477	+	0.723355i	$0.742599\pi$
$840$	−3.00000	−0.103510
$841$	−29.0000	−1.00000
$842$	−3.00000	−0.103387
$843$	−22.0000	−0.757720
$844$	2.00000	0.0688428
$845$	−12.0000	−0.412813
$846$	14.0000	0.481330
$847$	−21.0000	−0.721569
$848$	−6.00000	−0.206041
$849$	−4.00000	−0.137280
$850$	8.00000	0.274398
$851$	12.0000	0.411355
$852$	−1.00000	−0.0342594
$853$	−26.0000	−0.890223	−0.445112	−	0.895475i	$-0.646836\pi$
$853$	−26.0000	−0.890223	−0.445112	+	0.895475i	$0.646836\pi$
$854$	6.00000	0.205316
$855$	10.0000	0.341993
$856$	−17.0000	−0.581048
$857$	23.0000	0.785665	0.392833	−	0.919610i	$-0.371495\pi$
$857$	23.0000	0.785665	0.392833	+	0.919610i	$0.371495\pi$
$858$	2.00000	0.0682789
$859$	40.0000	1.36478	0.682391	−	0.730987i	$-0.260940\pi$
$859$	40.0000	1.36478	0.682391	+	0.730987i	$0.260940\pi$
$860$	9.00000	0.306897
$861$	−36.0000	−1.22688
$862$	2.00000	0.0681203
$863$	−11.0000	−0.374444	−0.187222	−	0.982318i	$-0.559948\pi$
$863$	−11.0000	−0.374444	−0.187222	+	0.982318i	$0.559948\pi$
$864$	5.00000	0.170103
$865$	9.00000	0.306009
$866$	14.0000	0.475739
$867$	−47.0000	−1.59620
$868$	21.0000	0.712786
$869$	20.0000	0.678454
$870$	0	0
$871$	−8.00000	−0.271070
$872$	10.0000	0.338643
$873$	4.00000	0.135379
$874$	5.00000	0.169128
$875$	3.00000	0.101419
$876$	11.0000	0.371656
$877$	28.0000	0.945493	0.472746	−	0.881199i	$-0.343263\pi$
$877$	28.0000	0.945493	0.472746	+	0.881199i	$0.343263\pi$
$878$	0	0
$879$	26.0000	0.876958
$880$	2.00000	0.0674200
$881$	−3.00000	−0.101073	−0.0505363	−	0.998722i	$-0.516093\pi$
$881$	−3.00000	−0.101073	−0.0505363	+	0.998722i	$0.516093\pi$
$882$	−4.00000	−0.134687
$883$	24.0000	0.807664	0.403832	−	0.914833i	$-0.367678\pi$
$883$	24.0000	0.807664	0.403832	+	0.914833i	$0.367678\pi$
$884$	−8.00000	−0.269069
$885$	0	0
$886$	−36.0000	−1.20944
$887$	48.0000	1.61168	0.805841	−	0.592132i	$-0.201714\pi$
$887$	48.0000	1.61168	0.805841	+	0.592132i	$0.201714\pi$
$888$	12.0000	0.402694
$889$	24.0000	0.804934
$890$	−15.0000	−0.502801
$891$	2.00000	0.0670025
$892$	−6.00000	−0.200895
$893$	35.0000	1.17123
$894$	5.00000	0.167225
$895$	15.0000	0.501395
$896$	3.00000	0.100223
$897$	−1.00000	−0.0333890
$898$	10.0000	0.333704
$899$	0	0
$900$	−2.00000	−0.0666667
$901$	−48.0000	−1.59911
$902$	24.0000	0.799113
$903$	−27.0000	−0.898504
$904$	−6.00000	−0.199557
$905$	−23.0000	−0.764546
$906$	−2.00000	−0.0664455
$907$	8.00000	0.265636	0.132818	−	0.991140i	$-0.457597\pi$
$907$	8.00000	0.265636	0.132818	+	0.991140i	$0.457597\pi$
$908$	18.0000	0.597351
$909$	36.0000	1.19404
$910$	−3.00000	−0.0994490
$911$	27.0000	0.894550	0.447275	−	0.894397i	$-0.352395\pi$
$911$	27.0000	0.894550	0.447275	+	0.894397i	$0.352395\pi$
$912$	5.00000	0.165567
$913$	−32.0000	−1.05905
$914$	−2.00000	−0.0661541
$915$	−2.00000	−0.0661180
$916$	10.0000	0.330409
$917$	−9.00000	−0.297206
$918$	40.0000	1.32020
$919$	5.00000	0.164935	0.0824674	−	0.996594i	$-0.473720\pi$
$919$	5.00000	0.164935	0.0824674	+	0.996594i	$0.473720\pi$
$920$	−1.00000	−0.0329690
$921$	−18.0000	−0.593120
$922$	37.0000	1.21853
$923$	−1.00000	−0.0329154
$924$	−6.00000	−0.197386
$925$	−12.0000	−0.394558
$926$	34.0000	1.11731
$927$	12.0000	0.394132
$928$	0	0
$929$	−10.0000	−0.328089	−0.164045	−	0.986453i	$-0.552454\pi$
$929$	−10.0000	−0.328089	−0.164045	+	0.986453i	$0.552454\pi$
$930$	−7.00000	−0.229539
$931$	−10.0000	−0.327737
$932$	29.0000	0.949927
$933$	−12.0000	−0.392862
$934$	−12.0000	−0.392652
$935$	16.0000	0.523256
$936$	2.00000	0.0653720
$937$	−22.0000	−0.718709	−0.359354	−	0.933201i	$-0.617003\pi$
$937$	−22.0000	−0.718709	−0.359354	+	0.933201i	$0.617003\pi$
$938$	24.0000	0.783628
$939$	11.0000	0.358971
$940$	−7.00000	−0.228315
$941$	12.0000	0.391189	0.195594	−	0.980685i	$-0.437336\pi$
$941$	12.0000	0.391189	0.195594	+	0.980685i	$0.437336\pi$
$942$	22.0000	0.716799
$943$	−12.0000	−0.390774
$944$	0	0
$945$	15.0000	0.487950
$946$	18.0000	0.585230
$947$	48.0000	1.55979	0.779895	−	0.625910i	$-0.215272\pi$
$947$	48.0000	1.55979	0.779895	+	0.625910i	$0.215272\pi$
$948$	−10.0000	−0.324785
$949$	11.0000	0.357075
$950$	−5.00000	−0.162221
$951$	22.0000	0.713399
$952$	24.0000	0.777844
$953$	14.0000	0.453504	0.226752	−	0.973952i	$-0.427189\pi$
$953$	14.0000	0.453504	0.226752	+	0.973952i	$0.427189\pi$
$954$	12.0000	0.388514
$955$	2.00000	0.0647185
$956$	15.0000	0.485135
$957$	0	0
$958$	25.0000	0.807713
$959$	−66.0000	−2.13125
$960$	−1.00000	−0.0322749
$961$	18.0000	0.580645
$962$	12.0000	0.386896
$963$	34.0000	1.09563
$964$	12.0000	0.386494
$965$	14.0000	0.450676
$966$	3.00000	0.0965234
$967$	43.0000	1.38279	0.691393	−	0.722478i	$-0.256997\pi$
$967$	43.0000	1.38279	0.691393	+	0.722478i	$0.256997\pi$
$968$	−7.00000	−0.224989
$969$	40.0000	1.28499
$970$	−2.00000	−0.0642161
$971$	7.00000	0.224641	0.112320	−	0.993672i	$-0.464172\pi$
$971$	7.00000	0.224641	0.112320	+	0.993672i	$0.464172\pi$
$972$	−16.0000	−0.513200
$973$	30.0000	0.961756
$974$	−12.0000	−0.384505
$975$	1.00000	0.0320256
$976$	2.00000	0.0640184
$977$	−22.0000	−0.703842	−0.351921	−	0.936030i	$-0.614471\pi$
$977$	−22.0000	−0.703842	−0.351921	+	0.936030i	$0.614471\pi$
$978$	−14.0000	−0.447671
$979$	−30.0000	−0.958804
$980$	2.00000	0.0638877
$981$	−20.0000	−0.638551
$982$	−8.00000	−0.255290
$983$	24.0000	0.765481	0.382741	−	0.923856i	$-0.374980\pi$
$983$	24.0000	0.765481	0.382741	+	0.923856i	$0.374980\pi$
$984$	−12.0000	−0.382546
$985$	13.0000	0.414214
$986$	0	0
$987$	21.0000	0.668437
$988$	5.00000	0.159071
$989$	−9.00000	−0.286183
$990$	−4.00000	−0.127128
$991$	7.00000	0.222362	0.111181	−	0.993800i	$-0.464537\pi$
$991$	7.00000	0.222362	0.111181	+	0.993800i	$0.464537\pi$
$992$	7.00000	0.222250
$993$	−12.0000	−0.380808
$994$	3.00000	0.0951542
$995$	0	0
$996$	16.0000	0.506979
$997$	−62.0000	−1.96356	−0.981780	−	0.190022i	$-0.939144\pi$
$997$	−62.0000	−1.96356	−0.981780	+	0.190022i	$0.939144\pi$
$998$	5.00000	0.158272
$999$	−60.0000	−1.89832

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	710.2.a.d.1.1	✓	1
3.2	odd	2		6390.2.a.i.1.1		1
4.3	odd	2		5680.2.a.i.1.1		1
5.4	even	2		3550.2.a.f.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
710.2.a.d.1.1	✓	1	1.1	even	1	trivial
3550.2.a.f.1.1		1	5.4	even	2
5680.2.a.i.1.1		1	4.3	odd	2
6390.2.a.i.1.1		1	3.2	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:	\( N \)	\(=\)	\( 710 = 2 \cdot 5 \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	710.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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