LMFDB - Embedded newform 714.2.a.g.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [714,2,Mod(1,714)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(714, 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("714.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 714 = 2 \cdot 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	714.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:	$5.70131870432$
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	$\chi$	$=$	714.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.00000 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.00000 q^{10} +1.00000 q^{11} -1.00000 q^{12} +1.00000 q^{13} -1.00000 q^{14} -3.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} +6.00000 q^{19} +3.00000 q^{20} +1.00000 q^{21} +1.00000 q^{22} -2.00000 q^{23} -1.00000 q^{24} +4.00000 q^{25} +1.00000 q^{26} -1.00000 q^{27} -1.00000 q^{28} -2.00000 q^{29} -3.00000 q^{30} +1.00000 q^{32} -1.00000 q^{33} -1.00000 q^{34} -3.00000 q^{35} +1.00000 q^{36} +5.00000 q^{37} +6.00000 q^{38} -1.00000 q^{39} +3.00000 q^{40} +4.00000 q^{41} +1.00000 q^{42} -9.00000 q^{43} +1.00000 q^{44} +3.00000 q^{45} -2.00000 q^{46} -1.00000 q^{48} +1.00000 q^{49} +4.00000 q^{50} +1.00000 q^{51} +1.00000 q^{52} +11.0000 q^{53} -1.00000 q^{54} +3.00000 q^{55} -1.00000 q^{56} -6.00000 q^{57} -2.00000 q^{58} +4.00000 q^{59} -3.00000 q^{60} +6.00000 q^{61} -1.00000 q^{63} +1.00000 q^{64} +3.00000 q^{65} -1.00000 q^{66} -11.0000 q^{67} -1.00000 q^{68} +2.00000 q^{69} -3.00000 q^{70} -12.0000 q^{71} +1.00000 q^{72} -5.00000 q^{73} +5.00000 q^{74} -4.00000 q^{75} +6.00000 q^{76} -1.00000 q^{77} -1.00000 q^{78} -15.0000 q^{79} +3.00000 q^{80} +1.00000 q^{81} +4.00000 q^{82} +1.00000 q^{83} +1.00000 q^{84} -3.00000 q^{85} -9.00000 q^{86} +2.00000 q^{87} +1.00000 q^{88} +9.00000 q^{89} +3.00000 q^{90} -1.00000 q^{91} -2.00000 q^{92} +18.0000 q^{95} -1.00000 q^{96} -9.00000 q^{97} +1.00000 q^{98} +1.00000 q^{99} +O(q^{100})\)

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
$5$	3.00000	1.34164	0.670820	−	0.741620i	$-0.265942\pi$
$5$	3.00000	1.34164	0.670820	+	0.741620i	$0.265942\pi$
$6$	−1.00000	−0.408248
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	3.00000	0.948683
$11$	1.00000	0.301511	0.150756	−	0.988571i	$-0.451829\pi$
$11$	1.00000	0.301511	0.150756	+	0.988571i	$0.451829\pi$
$12$	−1.00000	−0.288675
$13$	1.00000	0.277350	0.138675	−	0.990338i	$-0.455716\pi$
$13$	1.00000	0.277350	0.138675	+	0.990338i	$0.455716\pi$
$14$	−1.00000	−0.267261
$15$	−3.00000	−0.774597
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.00000	0.235702
$19$	6.00000	1.37649	0.688247	−	0.725476i	$-0.258380\pi$
$19$	6.00000	1.37649	0.688247	+	0.725476i	$0.258380\pi$
$20$	3.00000	0.670820
$21$	1.00000	0.218218
$22$	1.00000	0.213201
$23$	−2.00000	−0.417029	−0.208514	−	0.978019i	$-0.566863\pi$
$23$	−2.00000	−0.417029	−0.208514	+	0.978019i	$0.566863\pi$
$24$	−1.00000	−0.204124
$25$	4.00000	0.800000
$26$	1.00000	0.196116
$27$	−1.00000	−0.192450
$28$	−1.00000	−0.188982
$29$	−2.00000	−0.371391	−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000	−0.371391	−0.185695	+	0.982607i	$0.559454\pi$
$30$	−3.00000	−0.547723
$31$	0	0		−	1.00000i	$-0.5\pi$
$31$	0	0			1.00000i	$0.5\pi$
$32$	1.00000	0.176777
$33$	−1.00000	−0.174078
$34$	−1.00000	−0.171499
$35$	−3.00000	−0.507093
$36$	1.00000	0.166667
$37$	5.00000	0.821995	0.410997	−	0.911636i	$-0.365181\pi$
$37$	5.00000	0.821995	0.410997	+	0.911636i	$0.365181\pi$
$38$	6.00000	0.973329
$39$	−1.00000	−0.160128
$40$	3.00000	0.474342
$41$	4.00000	0.624695	0.312348	−	0.949968i	$-0.398885\pi$
$41$	4.00000	0.624695	0.312348	+	0.949968i	$0.398885\pi$
$42$	1.00000	0.154303
$43$	−9.00000	−1.37249	−0.686244	−	0.727372i	$-0.740742\pi$
$43$	−9.00000	−1.37249	−0.686244	+	0.727372i	$0.740742\pi$
$44$	1.00000	0.150756
$45$	3.00000	0.447214
$46$	−2.00000	−0.294884
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	4.00000	0.565685
$51$	1.00000	0.140028
$52$	1.00000	0.138675
$53$	11.0000	1.51097	0.755483	−	0.655168i	$-0.227402\pi$
$53$	11.0000	1.51097	0.755483	+	0.655168i	$0.227402\pi$
$54$	−1.00000	−0.136083
$55$	3.00000	0.404520
$56$	−1.00000	−0.133631
$57$	−6.00000	−0.794719
$58$	−2.00000	−0.262613
$59$	4.00000	0.520756	0.260378	−	0.965507i	$-0.416153\pi$
$59$	4.00000	0.520756	0.260378	+	0.965507i	$0.416153\pi$
$60$	−3.00000	−0.387298
$61$	6.00000	0.768221	0.384111	−	0.923287i	$-0.374508\pi$
$61$	6.00000	0.768221	0.384111	+	0.923287i	$0.374508\pi$
$62$	0	0
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	3.00000	0.372104
$66$	−1.00000	−0.123091
$67$	−11.0000	−1.34386	−0.671932	−	0.740613i	$-0.734535\pi$
$67$	−11.0000	−1.34386	−0.671932	+	0.740613i	$0.734535\pi$
$68$	−1.00000	−0.121268
$69$	2.00000	0.240772
$70$	−3.00000	−0.358569
$71$	−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
$73$	−5.00000	−0.585206	−0.292603	−	0.956234i	$-0.594521\pi$
$73$	−5.00000	−0.585206	−0.292603	+	0.956234i	$0.594521\pi$
$74$	5.00000	0.581238
$75$	−4.00000	−0.461880
$76$	6.00000	0.688247
$77$	−1.00000	−0.113961
$78$	−1.00000	−0.113228
$79$	−15.0000	−1.68763	−0.843816	−	0.536633i	$-0.819696\pi$
$79$	−15.0000	−1.68763	−0.843816	+	0.536633i	$0.819696\pi$
$80$	3.00000	0.335410
$81$	1.00000	0.111111
$82$	4.00000	0.441726
$83$	1.00000	0.109764	0.0548821	−	0.998493i	$-0.482522\pi$
$83$	1.00000	0.109764	0.0548821	+	0.998493i	$0.482522\pi$
$84$	1.00000	0.109109
$85$	−3.00000	−0.325396
$86$	−9.00000	−0.970495
$87$	2.00000	0.214423
$88$	1.00000	0.106600
$89$	9.00000	0.953998	0.476999	−	0.878904i	$-0.341725\pi$
$89$	9.00000	0.953998	0.476999	+	0.878904i	$0.341725\pi$
$90$	3.00000	0.316228
$91$	−1.00000	−0.104828
$92$	−2.00000	−0.208514
$93$	0	0
$94$	0	0
$95$	18.0000	1.84676
$96$	−1.00000	−0.102062
$97$	−9.00000	−0.913812	−0.456906	−	0.889515i	$-0.651042\pi$
$97$	−9.00000	−0.913812	−0.456906	+	0.889515i	$0.651042\pi$
$98$	1.00000	0.101015
$99$	1.00000	0.100504
$100$	4.00000	0.400000
$101$	8.00000	0.796030	0.398015	−	0.917379i	$-0.369699\pi$
$101$	8.00000	0.796030	0.398015	+	0.917379i	$0.369699\pi$
$102$	1.00000	0.0990148
$103$	−7.00000	−0.689730	−0.344865	−	0.938652i	$-0.612075\pi$
$103$	−7.00000	−0.689730	−0.344865	+	0.938652i	$0.612075\pi$
$104$	1.00000	0.0980581
$105$	3.00000	0.292770
$106$	11.0000	1.06841
$107$	−8.00000	−0.773389	−0.386695	−	0.922208i	$-0.626383\pi$
$107$	−8.00000	−0.773389	−0.386695	+	0.922208i	$0.626383\pi$
$108$	−1.00000	−0.0962250
$109$	−2.00000	−0.191565	−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000	−0.191565	−0.0957826	+	0.995402i	$0.530535\pi$
$110$	3.00000	0.286039
$111$	−5.00000	−0.474579
$112$	−1.00000	−0.0944911
$113$	−9.00000	−0.846649	−0.423324	−	0.905978i	$-0.639137\pi$
$113$	−9.00000	−0.846649	−0.423324	+	0.905978i	$0.639137\pi$
$114$	−6.00000	−0.561951
$115$	−6.00000	−0.559503
$116$	−2.00000	−0.185695
$117$	1.00000	0.0924500
$118$	4.00000	0.368230
$119$	1.00000	0.0916698
$120$	−3.00000	−0.273861
$121$	−10.0000	−0.909091
$122$	6.00000	0.543214
$123$	−4.00000	−0.360668
$124$	0	0
$125$	−3.00000	−0.268328
$126$	−1.00000	−0.0890871
$127$	−10.0000	−0.887357	−0.443678	−	0.896186i	$-0.646327\pi$
$127$	−10.0000	−0.887357	−0.443678	+	0.896186i	$0.646327\pi$
$128$	1.00000	0.0883883
$129$	9.00000	0.792406
$130$	3.00000	0.263117
$131$	−10.0000	−0.873704	−0.436852	−	0.899533i	$-0.643907\pi$
$131$	−10.0000	−0.873704	−0.436852	+	0.899533i	$0.643907\pi$
$132$	−1.00000	−0.0870388
$133$	−6.00000	−0.520266
$134$	−11.0000	−0.950255
$135$	−3.00000	−0.258199
$136$	−1.00000	−0.0857493
$137$	0	0		−	1.00000i	$-0.5\pi$
$137$	0	0			1.00000i	$0.5\pi$
$138$	2.00000	0.170251
$139$	−1.00000	−0.0848189	−0.0424094	−	0.999100i	$-0.513503\pi$
$139$	−1.00000	−0.0848189	−0.0424094	+	0.999100i	$0.513503\pi$
$140$	−3.00000	−0.253546
$141$	0	0
$142$	−12.0000	−1.00702
$143$	1.00000	0.0836242
$144$	1.00000	0.0833333
$145$	−6.00000	−0.498273
$146$	−5.00000	−0.413803
$147$	−1.00000	−0.0824786
$148$	5.00000	0.410997
$149$	−9.00000	−0.737309	−0.368654	−	0.929567i	$-0.620181\pi$
$149$	−9.00000	−0.737309	−0.368654	+	0.929567i	$0.620181\pi$
$150$	−4.00000	−0.326599
$151$	−8.00000	−0.651031	−0.325515	−	0.945537i	$-0.605538\pi$
$151$	−8.00000	−0.651031	−0.325515	+	0.945537i	$0.605538\pi$
$152$	6.00000	0.486664
$153$	−1.00000	−0.0808452
$154$	−1.00000	−0.0805823
$155$	0	0
$156$	−1.00000	−0.0800641
$157$	−10.0000	−0.798087	−0.399043	−	0.916932i	$-0.630658\pi$
$157$	−10.0000	−0.798087	−0.399043	+	0.916932i	$0.630658\pi$
$158$	−15.0000	−1.19334
$159$	−11.0000	−0.872357
$160$	3.00000	0.237171
$161$	2.00000	0.157622
$162$	1.00000	0.0785674
$163$	10.0000	0.783260	0.391630	−	0.920123i	$-0.371911\pi$
$163$	10.0000	0.783260	0.391630	+	0.920123i	$0.371911\pi$
$164$	4.00000	0.312348
$165$	−3.00000	−0.233550
$166$	1.00000	0.0776151
$167$	−3.00000	−0.232147	−0.116073	−	0.993241i	$-0.537031\pi$
$167$	−3.00000	−0.232147	−0.116073	+	0.993241i	$0.537031\pi$
$168$	1.00000	0.0771517
$169$	−12.0000	−0.923077
$170$	−3.00000	−0.230089
$171$	6.00000	0.458831
$172$	−9.00000	−0.686244
$173$	−18.0000	−1.36851	−0.684257	−	0.729241i	$-0.739873\pi$
$173$	−18.0000	−1.36851	−0.684257	+	0.729241i	$0.739873\pi$
$174$	2.00000	0.151620
$175$	−4.00000	−0.302372
$176$	1.00000	0.0753778
$177$	−4.00000	−0.300658
$178$	9.00000	0.674579
$179$	18.0000	1.34538	0.672692	−	0.739923i	$-0.265138\pi$
$179$	18.0000	1.34538	0.672692	+	0.739923i	$0.265138\pi$
$180$	3.00000	0.223607
$181$	12.0000	0.891953	0.445976	−	0.895045i	$-0.352856\pi$
$181$	12.0000	0.891953	0.445976	+	0.895045i	$0.352856\pi$
$182$	−1.00000	−0.0741249
$183$	−6.00000	−0.443533
$184$	−2.00000	−0.147442
$185$	15.0000	1.10282
$186$	0	0
$187$	−1.00000	−0.0731272
$188$	0	0
$189$	1.00000	0.0727393
$190$	18.0000	1.30586
$191$	15.0000	1.08536	0.542681	−	0.839939i	$-0.317409\pi$
$191$	15.0000	1.08536	0.542681	+	0.839939i	$0.317409\pi$
$192$	−1.00000	−0.0721688
$193$	−8.00000	−0.575853	−0.287926	−	0.957653i	$-0.592966\pi$
$193$	−8.00000	−0.575853	−0.287926	+	0.957653i	$0.592966\pi$
$194$	−9.00000	−0.646162
$195$	−3.00000	−0.214834
$196$	1.00000	0.0714286
$197$	20.0000	1.42494	0.712470	−	0.701702i	$-0.247576\pi$
$197$	20.0000	1.42494	0.712470	+	0.701702i	$0.247576\pi$
$198$	1.00000	0.0710669
$199$	8.00000	0.567105	0.283552	−	0.958957i	$-0.408487\pi$
$199$	8.00000	0.567105	0.283552	+	0.958957i	$0.408487\pi$
$200$	4.00000	0.282843
$201$	11.0000	0.775880
$202$	8.00000	0.562878
$203$	2.00000	0.140372
$204$	1.00000	0.0700140
$205$	12.0000	0.838116
$206$	−7.00000	−0.487713
$207$	−2.00000	−0.139010
$208$	1.00000	0.0693375
$209$	6.00000	0.415029
$210$	3.00000	0.207020
$211$	−10.0000	−0.688428	−0.344214	−	0.938891i	$-0.611855\pi$
$211$	−10.0000	−0.688428	−0.344214	+	0.938891i	$0.611855\pi$
$212$	11.0000	0.755483
$213$	12.0000	0.822226
$214$	−8.00000	−0.546869
$215$	−27.0000	−1.84138
$216$	−1.00000	−0.0680414
$217$	0	0
$218$	−2.00000	−0.135457
$219$	5.00000	0.337869
$220$	3.00000	0.202260
$221$	−1.00000	−0.0672673
$222$	−5.00000	−0.335578
$223$	24.0000	1.60716	0.803579	−	0.595198i	$-0.202926\pi$
$223$	24.0000	1.60716	0.803579	+	0.595198i	$0.202926\pi$
$224$	−1.00000	−0.0668153
$225$	4.00000	0.266667
$226$	−9.00000	−0.598671
$227$	12.0000	0.796468	0.398234	−	0.917284i	$-0.369623\pi$
$227$	12.0000	0.796468	0.398234	+	0.917284i	$0.369623\pi$
$228$	−6.00000	−0.397360
$229$	−17.0000	−1.12339	−0.561696	−	0.827344i	$-0.689851\pi$
$229$	−17.0000	−1.12339	−0.561696	+	0.827344i	$0.689851\pi$
$230$	−6.00000	−0.395628
$231$	1.00000	0.0657952
$232$	−2.00000	−0.131306
$233$	3.00000	0.196537	0.0982683	−	0.995160i	$-0.468670\pi$
$233$	3.00000	0.196537	0.0982683	+	0.995160i	$0.468670\pi$
$234$	1.00000	0.0653720
$235$	0	0
$236$	4.00000	0.260378
$237$	15.0000	0.974355
$238$	1.00000	0.0648204
$239$	−15.0000	−0.970269	−0.485135	−	0.874439i	$-0.661229\pi$
$239$	−15.0000	−0.970269	−0.485135	+	0.874439i	$0.661229\pi$
$240$	−3.00000	−0.193649
$241$	22.0000	1.41714	0.708572	−	0.705638i	$-0.249340\pi$
$241$	22.0000	1.41714	0.708572	+	0.705638i	$0.249340\pi$
$242$	−10.0000	−0.642824
$243$	−1.00000	−0.0641500
$244$	6.00000	0.384111
$245$	3.00000	0.191663
$246$	−4.00000	−0.255031
$247$	6.00000	0.381771
$248$	0	0
$249$	−1.00000	−0.0633724
$250$	−3.00000	−0.189737
$251$	23.0000	1.45175	0.725874	−	0.687828i	$-0.241436\pi$
$251$	23.0000	1.45175	0.725874	+	0.687828i	$0.241436\pi$
$252$	−1.00000	−0.0629941
$253$	−2.00000	−0.125739
$254$	−10.0000	−0.627456
$255$	3.00000	0.187867
$256$	1.00000	0.0625000
$257$	15.0000	0.935674	0.467837	−	0.883815i	$-0.345033\pi$
$257$	15.0000	0.935674	0.467837	+	0.883815i	$0.345033\pi$
$258$	9.00000	0.560316
$259$	−5.00000	−0.310685
$260$	3.00000	0.186052
$261$	−2.00000	−0.123797
$262$	−10.0000	−0.617802
$263$	31.0000	1.91154	0.955771	−	0.294112i	$-0.0950239\pi$
$263$	31.0000	1.91154	0.955771	+	0.294112i	$0.0950239\pi$
$264$	−1.00000	−0.0615457
$265$	33.0000	2.02717
$266$	−6.00000	−0.367884
$267$	−9.00000	−0.550791
$268$	−11.0000	−0.671932
$269$	−18.0000	−1.09748	−0.548740	−	0.835993i	$-0.684892\pi$
$269$	−18.0000	−1.09748	−0.548740	+	0.835993i	$0.684892\pi$
$270$	−3.00000	−0.182574
$271$	15.0000	0.911185	0.455593	−	0.890188i	$-0.349427\pi$
$271$	15.0000	0.911185	0.455593	+	0.890188i	$0.349427\pi$
$272$	−1.00000	−0.0606339
$273$	1.00000	0.0605228
$274$	0	0
$275$	4.00000	0.241209
$276$	2.00000	0.120386
$277$	−30.0000	−1.80253	−0.901263	−	0.433273i	$-0.857359\pi$
$277$	−30.0000	−1.80253	−0.901263	+	0.433273i	$0.857359\pi$
$278$	−1.00000	−0.0599760
$279$	0	0
$280$	−3.00000	−0.179284
$281$	26.0000	1.55103	0.775515	−	0.631329i	$-0.217490\pi$
$281$	26.0000	1.55103	0.775515	+	0.631329i	$0.217490\pi$
$282$	0	0
$283$	−21.0000	−1.24832	−0.624160	−	0.781296i	$-0.714559\pi$
$283$	−21.0000	−1.24832	−0.624160	+	0.781296i	$0.714559\pi$
$284$	−12.0000	−0.712069
$285$	−18.0000	−1.06623
$286$	1.00000	0.0591312
$287$	−4.00000	−0.236113
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	−6.00000	−0.352332
$291$	9.00000	0.527589
$292$	−5.00000	−0.292603
$293$	0	0		−	1.00000i	$-0.5\pi$
$293$	0	0			1.00000i	$0.5\pi$
$294$	−1.00000	−0.0583212
$295$	12.0000	0.698667
$296$	5.00000	0.290619
$297$	−1.00000	−0.0580259
$298$	−9.00000	−0.521356
$299$	−2.00000	−0.115663
$300$	−4.00000	−0.230940
$301$	9.00000	0.518751
$302$	−8.00000	−0.460348
$303$	−8.00000	−0.459588
$304$	6.00000	0.344124
$305$	18.0000	1.03068
$306$	−1.00000	−0.0571662
$307$	28.0000	1.59804	0.799022	−	0.601302i	$-0.205351\pi$
$307$	28.0000	1.59804	0.799022	+	0.601302i	$0.205351\pi$
$308$	−1.00000	−0.0569803
$309$	7.00000	0.398216
$310$	0	0
$311$	−3.00000	−0.170114	−0.0850572	−	0.996376i	$-0.527107\pi$
$311$	−3.00000	−0.170114	−0.0850572	+	0.996376i	$0.527107\pi$
$312$	−1.00000	−0.0566139
$313$	−30.0000	−1.69570	−0.847850	−	0.530236i	$-0.822103\pi$
$313$	−30.0000	−1.69570	−0.847850	+	0.530236i	$0.822103\pi$
$314$	−10.0000	−0.564333
$315$	−3.00000	−0.169031
$316$	−15.0000	−0.843816
$317$	−18.0000	−1.01098	−0.505490	−	0.862832i	$-0.668688\pi$
$317$	−18.0000	−1.01098	−0.505490	+	0.862832i	$0.668688\pi$
$318$	−11.0000	−0.616849
$319$	−2.00000	−0.111979
$320$	3.00000	0.167705
$321$	8.00000	0.446516
$322$	2.00000	0.111456
$323$	−6.00000	−0.333849
$324$	1.00000	0.0555556
$325$	4.00000	0.221880
$326$	10.0000	0.553849
$327$	2.00000	0.110600
$328$	4.00000	0.220863
$329$	0	0
$330$	−3.00000	−0.165145
$331$	1.00000	0.0549650	0.0274825	−	0.999622i	$-0.491251\pi$
$331$	1.00000	0.0549650	0.0274825	+	0.999622i	$0.491251\pi$
$332$	1.00000	0.0548821
$333$	5.00000	0.273998
$334$	−3.00000	−0.164153
$335$	−33.0000	−1.80298
$336$	1.00000	0.0545545
$337$	−22.0000	−1.19842	−0.599208	−	0.800593i	$-0.704518\pi$
$337$	−22.0000	−1.19842	−0.599208	+	0.800593i	$0.704518\pi$
$338$	−12.0000	−0.652714
$339$	9.00000	0.488813
$340$	−3.00000	−0.162698
$341$	0	0
$342$	6.00000	0.324443
$343$	−1.00000	−0.0539949
$344$	−9.00000	−0.485247
$345$	6.00000	0.323029
$346$	−18.0000	−0.967686
$347$	27.0000	1.44944	0.724718	−	0.689046i	$-0.241970\pi$
$347$	27.0000	1.44944	0.724718	+	0.689046i	$0.241970\pi$
$348$	2.00000	0.107211
$349$	−13.0000	−0.695874	−0.347937	−	0.937518i	$-0.613118\pi$
$349$	−13.0000	−0.695874	−0.347937	+	0.937518i	$0.613118\pi$
$350$	−4.00000	−0.213809
$351$	−1.00000	−0.0533761
$352$	1.00000	0.0533002
$353$	5.00000	0.266123	0.133062	−	0.991108i	$-0.457519\pi$
$353$	5.00000	0.266123	0.133062	+	0.991108i	$0.457519\pi$
$354$	−4.00000	−0.212598
$355$	−36.0000	−1.91068
$356$	9.00000	0.476999
$357$	−1.00000	−0.0529256
$358$	18.0000	0.951330
$359$	−8.00000	−0.422224	−0.211112	−	0.977462i	$-0.567708\pi$
$359$	−8.00000	−0.422224	−0.211112	+	0.977462i	$0.567708\pi$
$360$	3.00000	0.158114
$361$	17.0000	0.894737
$362$	12.0000	0.630706
$363$	10.0000	0.524864
$364$	−1.00000	−0.0524142
$365$	−15.0000	−0.785136
$366$	−6.00000	−0.313625
$367$	12.0000	0.626395	0.313197	−	0.949688i	$-0.398600\pi$
$367$	12.0000	0.626395	0.313197	+	0.949688i	$0.398600\pi$
$368$	−2.00000	−0.104257
$369$	4.00000	0.208232
$370$	15.0000	0.779813
$371$	−11.0000	−0.571092
$372$	0	0
$373$	32.0000	1.65690	0.828449	−	0.560065i	$-0.189224\pi$
$373$	32.0000	1.65690	0.828449	+	0.560065i	$0.189224\pi$
$374$	−1.00000	−0.0517088
$375$	3.00000	0.154919
$376$	0	0
$377$	−2.00000	−0.103005
$378$	1.00000	0.0514344
$379$	−10.0000	−0.513665	−0.256833	−	0.966456i	$-0.582679\pi$
$379$	−10.0000	−0.513665	−0.256833	+	0.966456i	$0.582679\pi$
$380$	18.0000	0.923381
$381$	10.0000	0.512316
$382$	15.0000	0.767467
$383$	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
$385$	−3.00000	−0.152894
$386$	−8.00000	−0.407189
$387$	−9.00000	−0.457496
$388$	−9.00000	−0.456906
$389$	−6.00000	−0.304212	−0.152106	−	0.988364i	$-0.548606\pi$
$389$	−6.00000	−0.304212	−0.152106	+	0.988364i	$0.548606\pi$
$390$	−3.00000	−0.151911
$391$	2.00000	0.101144
$392$	1.00000	0.0505076
$393$	10.0000	0.504433
$394$	20.0000	1.00759
$395$	−45.0000	−2.26420
$396$	1.00000	0.0502519
$397$	−4.00000	−0.200754	−0.100377	−	0.994949i	$-0.532005\pi$
$397$	−4.00000	−0.200754	−0.100377	+	0.994949i	$0.532005\pi$
$398$	8.00000	0.401004
$399$	6.00000	0.300376
$400$	4.00000	0.200000
$401$	18.0000	0.898877	0.449439	−	0.893311i	$-0.351624\pi$
$401$	18.0000	0.898877	0.449439	+	0.893311i	$0.351624\pi$
$402$	11.0000	0.548630
$403$	0	0
$404$	8.00000	0.398015
$405$	3.00000	0.149071
$406$	2.00000	0.0992583
$407$	5.00000	0.247841
$408$	1.00000	0.0495074
$409$	38.0000	1.87898	0.939490	−	0.342578i	$-0.111300\pi$
$409$	38.0000	1.87898	0.939490	+	0.342578i	$0.111300\pi$
$410$	12.0000	0.592638
$411$	0	0
$412$	−7.00000	−0.344865
$413$	−4.00000	−0.196827
$414$	−2.00000	−0.0982946
$415$	3.00000	0.147264
$416$	1.00000	0.0490290
$417$	1.00000	0.0489702
$418$	6.00000	0.293470
$419$	−26.0000	−1.27018	−0.635092	−	0.772437i	$-0.719038\pi$
$419$	−26.0000	−1.27018	−0.635092	+	0.772437i	$0.719038\pi$
$420$	3.00000	0.146385
$421$	6.00000	0.292422	0.146211	−	0.989253i	$-0.453292\pi$
$421$	6.00000	0.292422	0.146211	+	0.989253i	$0.453292\pi$
$422$	−10.0000	−0.486792
$423$	0	0
$424$	11.0000	0.534207
$425$	−4.00000	−0.194029
$426$	12.0000	0.581402
$427$	−6.00000	−0.290360
$428$	−8.00000	−0.386695
$429$	−1.00000	−0.0482805
$430$	−27.0000	−1.30206
$431$	40.0000	1.92673	0.963366	−	0.268190i	$-0.0864254\pi$
$431$	40.0000	1.92673	0.963366	+	0.268190i	$0.0864254\pi$
$432$	−1.00000	−0.0481125
$433$	−28.0000	−1.34559	−0.672797	−	0.739827i	$-0.734907\pi$
$433$	−28.0000	−1.34559	−0.672797	+	0.739827i	$0.734907\pi$
$434$	0	0
$435$	6.00000	0.287678
$436$	−2.00000	−0.0957826
$437$	−12.0000	−0.574038
$438$	5.00000	0.238909
$439$	16.0000	0.763638	0.381819	−	0.924237i	$-0.375298\pi$
$439$	16.0000	0.763638	0.381819	+	0.924237i	$0.375298\pi$
$440$	3.00000	0.143019
$441$	1.00000	0.0476190
$442$	−1.00000	−0.0475651
$443$	−4.00000	−0.190046	−0.0950229	−	0.995475i	$-0.530292\pi$
$443$	−4.00000	−0.190046	−0.0950229	+	0.995475i	$0.530292\pi$
$444$	−5.00000	−0.237289
$445$	27.0000	1.27992
$446$	24.0000	1.13643
$447$	9.00000	0.425685
$448$	−1.00000	−0.0472456
$449$	−1.00000	−0.0471929	−0.0235965	−	0.999722i	$-0.507512\pi$
$449$	−1.00000	−0.0471929	−0.0235965	+	0.999722i	$0.507512\pi$
$450$	4.00000	0.188562
$451$	4.00000	0.188353
$452$	−9.00000	−0.423324
$453$	8.00000	0.375873
$454$	12.0000	0.563188
$455$	−3.00000	−0.140642
$456$	−6.00000	−0.280976
$457$	−25.0000	−1.16945	−0.584725	−	0.811231i	$-0.698798\pi$
$457$	−25.0000	−1.16945	−0.584725	+	0.811231i	$0.698798\pi$
$458$	−17.0000	−0.794358
$459$	1.00000	0.0466760
$460$	−6.00000	−0.279751
$461$	2.00000	0.0931493	0.0465746	−	0.998915i	$-0.485169\pi$
$461$	2.00000	0.0931493	0.0465746	+	0.998915i	$0.485169\pi$
$462$	1.00000	0.0465242
$463$	8.00000	0.371792	0.185896	−	0.982569i	$-0.440481\pi$
$463$	8.00000	0.371792	0.185896	+	0.982569i	$0.440481\pi$
$464$	−2.00000	−0.0928477
$465$	0	0
$466$	3.00000	0.138972
$467$	−32.0000	−1.48078	−0.740392	−	0.672176i	$-0.765360\pi$
$467$	−32.0000	−1.48078	−0.740392	+	0.672176i	$0.765360\pi$
$468$	1.00000	0.0462250
$469$	11.0000	0.507933
$470$	0	0
$471$	10.0000	0.460776
$472$	4.00000	0.184115
$473$	−9.00000	−0.413820
$474$	15.0000	0.688973
$475$	24.0000	1.10120
$476$	1.00000	0.0458349
$477$	11.0000	0.503655
$478$	−15.0000	−0.686084
$479$	−21.0000	−0.959514	−0.479757	−	0.877401i	$-0.659275\pi$
$479$	−21.0000	−0.959514	−0.479757	+	0.877401i	$0.659275\pi$
$480$	−3.00000	−0.136931
$481$	5.00000	0.227980
$482$	22.0000	1.00207
$483$	−2.00000	−0.0910032
$484$	−10.0000	−0.454545
$485$	−27.0000	−1.22601
$486$	−1.00000	−0.0453609
$487$	23.0000	1.04223	0.521115	−	0.853487i	$-0.325516\pi$
$487$	23.0000	1.04223	0.521115	+	0.853487i	$0.325516\pi$
$488$	6.00000	0.271607
$489$	−10.0000	−0.452216
$490$	3.00000	0.135526
$491$	2.00000	0.0902587	0.0451294	−	0.998981i	$-0.485630\pi$
$491$	2.00000	0.0902587	0.0451294	+	0.998981i	$0.485630\pi$
$492$	−4.00000	−0.180334
$493$	2.00000	0.0900755
$494$	6.00000	0.269953
$495$	3.00000	0.134840
$496$	0	0
$497$	12.0000	0.538274
$498$	−1.00000	−0.0448111
$499$	36.0000	1.61158	0.805791	−	0.592200i	$-0.201741\pi$
$499$	36.0000	1.61158	0.805791	+	0.592200i	$0.201741\pi$
$500$	−3.00000	−0.134164
$501$	3.00000	0.134030
$502$	23.0000	1.02654
$503$	−16.0000	−0.713405	−0.356702	−	0.934218i	$-0.616099\pi$
$503$	−16.0000	−0.713405	−0.356702	+	0.934218i	$0.616099\pi$
$504$	−1.00000	−0.0445435
$505$	24.0000	1.06799
$506$	−2.00000	−0.0889108
$507$	12.0000	0.532939
$508$	−10.0000	−0.443678
$509$	16.0000	0.709188	0.354594	−	0.935020i	$-0.384619\pi$
$509$	16.0000	0.709188	0.354594	+	0.935020i	$0.384619\pi$
$510$	3.00000	0.132842
$511$	5.00000	0.221187
$512$	1.00000	0.0441942
$513$	−6.00000	−0.264906
$514$	15.0000	0.661622
$515$	−21.0000	−0.925371
$516$	9.00000	0.396203
$517$	0	0
$518$	−5.00000	−0.219687
$519$	18.0000	0.790112
$520$	3.00000	0.131559
$521$	−16.0000	−0.700973	−0.350486	−	0.936568i	$-0.613984\pi$
$521$	−16.0000	−0.700973	−0.350486	+	0.936568i	$0.613984\pi$
$522$	−2.00000	−0.0875376
$523$	0	0		−	1.00000i	$-0.5\pi$
$523$	0	0			1.00000i	$0.5\pi$
$524$	−10.0000	−0.436852
$525$	4.00000	0.174574
$526$	31.0000	1.35166
$527$	0	0
$528$	−1.00000	−0.0435194
$529$	−19.0000	−0.826087
$530$	33.0000	1.43343
$531$	4.00000	0.173585
$532$	−6.00000	−0.260133
$533$	4.00000	0.173259
$534$	−9.00000	−0.389468
$535$	−24.0000	−1.03761
$536$	−11.0000	−0.475128
$537$	−18.0000	−0.776757
$538$	−18.0000	−0.776035
$539$	1.00000	0.0430730
$540$	−3.00000	−0.129099
$541$	25.0000	1.07483	0.537417	−	0.843317i	$-0.319400\pi$
$541$	25.0000	1.07483	0.537417	+	0.843317i	$0.319400\pi$
$542$	15.0000	0.644305
$543$	−12.0000	−0.514969
$544$	−1.00000	−0.0428746
$545$	−6.00000	−0.257012
$546$	1.00000	0.0427960
$547$	−22.0000	−0.940652	−0.470326	−	0.882493i	$-0.655864\pi$
$547$	−22.0000	−0.940652	−0.470326	+	0.882493i	$0.655864\pi$
$548$	0	0
$549$	6.00000	0.256074
$550$	4.00000	0.170561
$551$	−12.0000	−0.511217
$552$	2.00000	0.0851257
$553$	15.0000	0.637865
$554$	−30.0000	−1.27458
$555$	−15.0000	−0.636715
$556$	−1.00000	−0.0424094
$557$	−2.00000	−0.0847427	−0.0423714	−	0.999102i	$-0.513491\pi$
$557$	−2.00000	−0.0847427	−0.0423714	+	0.999102i	$0.513491\pi$
$558$	0	0
$559$	−9.00000	−0.380659
$560$	−3.00000	−0.126773
$561$	1.00000	0.0422200
$562$	26.0000	1.09674
$563$	−11.0000	−0.463595	−0.231797	−	0.972764i	$-0.574461\pi$
$563$	−11.0000	−0.463595	−0.231797	+	0.972764i	$0.574461\pi$
$564$	0	0
$565$	−27.0000	−1.13590
$566$	−21.0000	−0.882696
$567$	−1.00000	−0.0419961
$568$	−12.0000	−0.503509
$569$	−26.0000	−1.08998	−0.544988	−	0.838444i	$-0.683466\pi$
$569$	−26.0000	−1.08998	−0.544988	+	0.838444i	$0.683466\pi$
$570$	−18.0000	−0.753937
$571$	32.0000	1.33916	0.669579	−	0.742741i	$-0.266474\pi$
$571$	32.0000	1.33916	0.669579	+	0.742741i	$0.266474\pi$
$572$	1.00000	0.0418121
$573$	−15.0000	−0.626634
$574$	−4.00000	−0.166957
$575$	−8.00000	−0.333623
$576$	1.00000	0.0416667
$577$	14.0000	0.582828	0.291414	−	0.956597i	$-0.405874\pi$
$577$	14.0000	0.582828	0.291414	+	0.956597i	$0.405874\pi$
$578$	1.00000	0.0415945
$579$	8.00000	0.332469
$580$	−6.00000	−0.249136
$581$	−1.00000	−0.0414870
$582$	9.00000	0.373062
$583$	11.0000	0.455573
$584$	−5.00000	−0.206901
$585$	3.00000	0.124035
$586$	0	0
$587$	−23.0000	−0.949312	−0.474656	−	0.880172i	$-0.657427\pi$
$587$	−23.0000	−0.949312	−0.474656	+	0.880172i	$0.657427\pi$
$588$	−1.00000	−0.0412393
$589$	0	0
$590$	12.0000	0.494032
$591$	−20.0000	−0.822690
$592$	5.00000	0.205499
$593$	18.0000	0.739171	0.369586	−	0.929197i	$-0.379500\pi$
$593$	18.0000	0.739171	0.369586	+	0.929197i	$0.379500\pi$
$594$	−1.00000	−0.0410305
$595$	3.00000	0.122988
$596$	−9.00000	−0.368654
$597$	−8.00000	−0.327418
$598$	−2.00000	−0.0817861
$599$	24.0000	0.980613	0.490307	−	0.871550i	$-0.336885\pi$
$599$	24.0000	0.980613	0.490307	+	0.871550i	$0.336885\pi$
$600$	−4.00000	−0.163299
$601$	26.0000	1.06056	0.530281	−	0.847822i	$-0.322086\pi$
$601$	26.0000	1.06056	0.530281	+	0.847822i	$0.322086\pi$
$602$	9.00000	0.366813
$603$	−11.0000	−0.447955
$604$	−8.00000	−0.325515
$605$	−30.0000	−1.21967
$606$	−8.00000	−0.324978
$607$	−32.0000	−1.29884	−0.649420	−	0.760430i	$-0.724988\pi$
$607$	−32.0000	−1.29884	−0.649420	+	0.760430i	$0.724988\pi$
$608$	6.00000	0.243332
$609$	−2.00000	−0.0810441
$610$	18.0000	0.728799
$611$	0	0
$612$	−1.00000	−0.0404226
$613$	8.00000	0.323117	0.161558	−	0.986863i	$-0.448348\pi$
$613$	8.00000	0.323117	0.161558	+	0.986863i	$0.448348\pi$
$614$	28.0000	1.12999
$615$	−12.0000	−0.483887
$616$	−1.00000	−0.0402911
$617$	43.0000	1.73111	0.865557	−	0.500810i	$-0.166964\pi$
$617$	43.0000	1.73111	0.865557	+	0.500810i	$0.166964\pi$
$618$	7.00000	0.281581
$619$	−19.0000	−0.763674	−0.381837	−	0.924230i	$-0.624709\pi$
$619$	−19.0000	−0.763674	−0.381837	+	0.924230i	$0.624709\pi$
$620$	0	0
$621$	2.00000	0.0802572
$622$	−3.00000	−0.120289
$623$	−9.00000	−0.360577
$624$	−1.00000	−0.0400320
$625$	−29.0000	−1.16000
$626$	−30.0000	−1.19904
$627$	−6.00000	−0.239617
$628$	−10.0000	−0.399043
$629$	−5.00000	−0.199363
$630$	−3.00000	−0.119523
$631$	48.0000	1.91085	0.955425	−	0.295234i	$-0.0953977\pi$
$631$	48.0000	1.91085	0.955425	+	0.295234i	$0.0953977\pi$
$632$	−15.0000	−0.596668
$633$	10.0000	0.397464
$634$	−18.0000	−0.714871
$635$	−30.0000	−1.19051
$636$	−11.0000	−0.436178
$637$	1.00000	0.0396214
$638$	−2.00000	−0.0791808
$639$	−12.0000	−0.474713
$640$	3.00000	0.118585
$641$	7.00000	0.276483	0.138242	−	0.990399i	$-0.455855\pi$
$641$	7.00000	0.276483	0.138242	+	0.990399i	$0.455855\pi$
$642$	8.00000	0.315735
$643$	11.0000	0.433798	0.216899	−	0.976194i	$-0.430406\pi$
$643$	11.0000	0.433798	0.216899	+	0.976194i	$0.430406\pi$
$644$	2.00000	0.0788110
$645$	27.0000	1.06312
$646$	−6.00000	−0.236067
$647$	4.00000	0.157256	0.0786281	−	0.996904i	$-0.474946\pi$
$647$	4.00000	0.157256	0.0786281	+	0.996904i	$0.474946\pi$
$648$	1.00000	0.0392837
$649$	4.00000	0.157014
$650$	4.00000	0.156893
$651$	0	0
$652$	10.0000	0.391630
$653$	42.0000	1.64359	0.821794	−	0.569785i	$-0.192974\pi$
$653$	42.0000	1.64359	0.821794	+	0.569785i	$0.192974\pi$
$654$	2.00000	0.0782062
$655$	−30.0000	−1.17220
$656$	4.00000	0.156174
$657$	−5.00000	−0.195069
$658$	0	0
$659$	−48.0000	−1.86981	−0.934907	−	0.354892i	$-0.884518\pi$
$659$	−48.0000	−1.86981	−0.934907	+	0.354892i	$0.884518\pi$
$660$	−3.00000	−0.116775
$661$	−22.0000	−0.855701	−0.427850	−	0.903850i	$-0.640729\pi$
$661$	−22.0000	−0.855701	−0.427850	+	0.903850i	$0.640729\pi$
$662$	1.00000	0.0388661
$663$	1.00000	0.0388368
$664$	1.00000	0.0388075
$665$	−18.0000	−0.698010
$666$	5.00000	0.193746
$667$	4.00000	0.154881
$668$	−3.00000	−0.116073
$669$	−24.0000	−0.927894
$670$	−33.0000	−1.27490
$671$	6.00000	0.231627
$672$	1.00000	0.0385758
$673$	−48.0000	−1.85026	−0.925132	−	0.379646i	$-0.876046\pi$
$673$	−48.0000	−1.85026	−0.925132	+	0.379646i	$0.876046\pi$
$674$	−22.0000	−0.847408
$675$	−4.00000	−0.153960
$676$	−12.0000	−0.461538
$677$	27.0000	1.03769	0.518847	−	0.854867i	$-0.326361\pi$
$677$	27.0000	1.03769	0.518847	+	0.854867i	$0.326361\pi$
$678$	9.00000	0.345643
$679$	9.00000	0.345388
$680$	−3.00000	−0.115045
$681$	−12.0000	−0.459841
$682$	0	0
$683$	−8.00000	−0.306111	−0.153056	−	0.988218i	$-0.548911\pi$
$683$	−8.00000	−0.306111	−0.153056	+	0.988218i	$0.548911\pi$
$684$	6.00000	0.229416
$685$	0	0
$686$	−1.00000	−0.0381802
$687$	17.0000	0.648590
$688$	−9.00000	−0.343122
$689$	11.0000	0.419067
$690$	6.00000	0.228416
$691$	21.0000	0.798878	0.399439	−	0.916760i	$-0.369205\pi$
$691$	21.0000	0.798878	0.399439	+	0.916760i	$0.369205\pi$
$692$	−18.0000	−0.684257
$693$	−1.00000	−0.0379869
$694$	27.0000	1.02491
$695$	−3.00000	−0.113796
$696$	2.00000	0.0758098
$697$	−4.00000	−0.151511
$698$	−13.0000	−0.492057
$699$	−3.00000	−0.113470
$700$	−4.00000	−0.151186
$701$	−7.00000	−0.264386	−0.132193	−	0.991224i	$-0.542202\pi$
$701$	−7.00000	−0.264386	−0.132193	+	0.991224i	$0.542202\pi$
$702$	−1.00000	−0.0377426
$703$	30.0000	1.13147
$704$	1.00000	0.0376889
$705$	0	0
$706$	5.00000	0.188177
$707$	−8.00000	−0.300871
$708$	−4.00000	−0.150329
$709$	5.00000	0.187779	0.0938895	−	0.995583i	$-0.470070\pi$
$709$	5.00000	0.187779	0.0938895	+	0.995583i	$0.470070\pi$
$710$	−36.0000	−1.35106
$711$	−15.0000	−0.562544
$712$	9.00000	0.337289
$713$	0	0
$714$	−1.00000	−0.0374241
$715$	3.00000	0.112194
$716$	18.0000	0.672692
$717$	15.0000	0.560185
$718$	−8.00000	−0.298557
$719$	−40.0000	−1.49175	−0.745874	−	0.666087i	$-0.767968\pi$
$719$	−40.0000	−1.49175	−0.745874	+	0.666087i	$0.767968\pi$
$720$	3.00000	0.111803
$721$	7.00000	0.260694
$722$	17.0000	0.632674
$723$	−22.0000	−0.818189
$724$	12.0000	0.445976
$725$	−8.00000	−0.297113
$726$	10.0000	0.371135
$727$	17.0000	0.630495	0.315248	−	0.949009i	$-0.397912\pi$
$727$	17.0000	0.630495	0.315248	+	0.949009i	$0.397912\pi$
$728$	−1.00000	−0.0370625
$729$	1.00000	0.0370370
$730$	−15.0000	−0.555175
$731$	9.00000	0.332877
$732$	−6.00000	−0.221766
$733$	−14.0000	−0.517102	−0.258551	−	0.965998i	$-0.583245\pi$
$733$	−14.0000	−0.517102	−0.258551	+	0.965998i	$0.583245\pi$
$734$	12.0000	0.442928
$735$	−3.00000	−0.110657
$736$	−2.00000	−0.0737210
$737$	−11.0000	−0.405190
$738$	4.00000	0.147242
$739$	−12.0000	−0.441427	−0.220714	−	0.975339i	$-0.570839\pi$
$739$	−12.0000	−0.441427	−0.220714	+	0.975339i	$0.570839\pi$
$740$	15.0000	0.551411
$741$	−6.00000	−0.220416
$742$	−11.0000	−0.403823
$743$	−26.0000	−0.953847	−0.476924	−	0.878945i	$-0.658248\pi$
$743$	−26.0000	−0.953847	−0.476924	+	0.878945i	$0.658248\pi$
$744$	0	0
$745$	−27.0000	−0.989203
$746$	32.0000	1.17160
$747$	1.00000	0.0365881
$748$	−1.00000	−0.0365636
$749$	8.00000	0.292314
$750$	3.00000	0.109545
$751$	−12.0000	−0.437886	−0.218943	−	0.975738i	$-0.570261\pi$
$751$	−12.0000	−0.437886	−0.218943	+	0.975738i	$0.570261\pi$
$752$	0	0
$753$	−23.0000	−0.838167
$754$	−2.00000	−0.0728357
$755$	−24.0000	−0.873449
$756$	1.00000	0.0363696
$757$	36.0000	1.30844	0.654221	−	0.756303i	$-0.272997\pi$
$757$	36.0000	1.30844	0.654221	+	0.756303i	$0.272997\pi$
$758$	−10.0000	−0.363216
$759$	2.00000	0.0725954
$760$	18.0000	0.652929
$761$	43.0000	1.55875	0.779374	−	0.626559i	$-0.215537\pi$
$761$	43.0000	1.55875	0.779374	+	0.626559i	$0.215537\pi$
$762$	10.0000	0.362262
$763$	2.00000	0.0724049
$764$	15.0000	0.542681
$765$	−3.00000	−0.108465
$766$	24.0000	0.867155
$767$	4.00000	0.144432
$768$	−1.00000	−0.0360844
$769$	−34.0000	−1.22607	−0.613036	−	0.790055i	$-0.710052\pi$
$769$	−34.0000	−1.22607	−0.613036	+	0.790055i	$0.710052\pi$
$770$	−3.00000	−0.108112
$771$	−15.0000	−0.540212
$772$	−8.00000	−0.287926
$773$	−32.0000	−1.15096	−0.575480	−	0.817816i	$-0.695185\pi$
$773$	−32.0000	−1.15096	−0.575480	+	0.817816i	$0.695185\pi$
$774$	−9.00000	−0.323498
$775$	0	0
$776$	−9.00000	−0.323081
$777$	5.00000	0.179374
$778$	−6.00000	−0.215110
$779$	24.0000	0.859889
$780$	−3.00000	−0.107417
$781$	−12.0000	−0.429394
$782$	2.00000	0.0715199
$783$	2.00000	0.0714742
$784$	1.00000	0.0357143
$785$	−30.0000	−1.07075
$786$	10.0000	0.356688
$787$	−11.0000	−0.392108	−0.196054	−	0.980593i	$-0.562813\pi$
$787$	−11.0000	−0.392108	−0.196054	+	0.980593i	$0.562813\pi$
$788$	20.0000	0.712470
$789$	−31.0000	−1.10363
$790$	−45.0000	−1.60103
$791$	9.00000	0.320003
$792$	1.00000	0.0355335
$793$	6.00000	0.213066
$794$	−4.00000	−0.141955
$795$	−33.0000	−1.17039
$796$	8.00000	0.283552
$797$	−14.0000	−0.495905	−0.247953	−	0.968772i	$-0.579758\pi$
$797$	−14.0000	−0.495905	−0.247953	+	0.968772i	$0.579758\pi$
$798$	6.00000	0.212398
$799$	0	0
$800$	4.00000	0.141421
$801$	9.00000	0.317999
$802$	18.0000	0.635602
$803$	−5.00000	−0.176446
$804$	11.0000	0.387940
$805$	6.00000	0.211472
$806$	0	0
$807$	18.0000	0.633630
$808$	8.00000	0.281439
$809$	30.0000	1.05474	0.527372	−	0.849635i	$-0.323177\pi$
$809$	30.0000	1.05474	0.527372	+	0.849635i	$0.323177\pi$
$810$	3.00000	0.105409
$811$	−29.0000	−1.01833	−0.509164	−	0.860670i	$-0.670045\pi$
$811$	−29.0000	−1.01833	−0.509164	+	0.860670i	$0.670045\pi$
$812$	2.00000	0.0701862
$813$	−15.0000	−0.526073
$814$	5.00000	0.175250
$815$	30.0000	1.05085
$816$	1.00000	0.0350070
$817$	−54.0000	−1.88922
$818$	38.0000	1.32864
$819$	−1.00000	−0.0349428
$820$	12.0000	0.419058
$821$	−2.00000	−0.0698005	−0.0349002	−	0.999391i	$-0.511111\pi$
$821$	−2.00000	−0.0698005	−0.0349002	+	0.999391i	$0.511111\pi$
$822$	0	0
$823$	9.00000	0.313720	0.156860	−	0.987621i	$-0.449863\pi$
$823$	9.00000	0.313720	0.156860	+	0.987621i	$0.449863\pi$
$824$	−7.00000	−0.243857
$825$	−4.00000	−0.139262
$826$	−4.00000	−0.139178
$827$	−11.0000	−0.382507	−0.191254	−	0.981541i	$-0.561255\pi$
$827$	−11.0000	−0.382507	−0.191254	+	0.981541i	$0.561255\pi$
$828$	−2.00000	−0.0695048
$829$	−31.0000	−1.07667	−0.538337	−	0.842729i	$-0.680947\pi$
$829$	−31.0000	−1.07667	−0.538337	+	0.842729i	$0.680947\pi$
$830$	3.00000	0.104132
$831$	30.0000	1.04069
$832$	1.00000	0.0346688
$833$	−1.00000	−0.0346479
$834$	1.00000	0.0346272
$835$	−9.00000	−0.311458
$836$	6.00000	0.207514
$837$	0	0
$838$	−26.0000	−0.898155
$839$	11.0000	0.379762	0.189881	−	0.981807i	$-0.439190\pi$
$839$	11.0000	0.379762	0.189881	+	0.981807i	$0.439190\pi$
$840$	3.00000	0.103510
$841$	−25.0000	−0.862069
$842$	6.00000	0.206774
$843$	−26.0000	−0.895488
$844$	−10.0000	−0.344214
$845$	−36.0000	−1.23844
$846$	0	0
$847$	10.0000	0.343604
$848$	11.0000	0.377742
$849$	21.0000	0.720718
$850$	−4.00000	−0.137199
$851$	−10.0000	−0.342796
$852$	12.0000	0.411113
$853$	−46.0000	−1.57501	−0.787505	−	0.616308i	$-0.788628\pi$
$853$	−46.0000	−1.57501	−0.787505	+	0.616308i	$0.788628\pi$
$854$	−6.00000	−0.205316
$855$	18.0000	0.615587
$856$	−8.00000	−0.273434
$857$	32.0000	1.09310	0.546550	−	0.837427i	$-0.315941\pi$
$857$	32.0000	1.09310	0.546550	+	0.837427i	$0.315941\pi$
$858$	−1.00000	−0.0341394
$859$	50.0000	1.70598	0.852989	−	0.521929i	$-0.174787\pi$
$859$	50.0000	1.70598	0.852989	+	0.521929i	$0.174787\pi$
$860$	−27.0000	−0.920692
$861$	4.00000	0.136320
$862$	40.0000	1.36241
$863$	−37.0000	−1.25949	−0.629747	−	0.776800i	$-0.716842\pi$
$863$	−37.0000	−1.25949	−0.629747	+	0.776800i	$0.716842\pi$
$864$	−1.00000	−0.0340207
$865$	−54.0000	−1.83606
$866$	−28.0000	−0.951479
$867$	−1.00000	−0.0339618
$868$	0	0
$869$	−15.0000	−0.508840
$870$	6.00000	0.203419
$871$	−11.0000	−0.372721
$872$	−2.00000	−0.0677285
$873$	−9.00000	−0.304604
$874$	−12.0000	−0.405906
$875$	3.00000	0.101419
$876$	5.00000	0.168934
$877$	23.0000	0.776655	0.388327	−	0.921521i	$-0.373053\pi$
$877$	23.0000	0.776655	0.388327	+	0.921521i	$0.373053\pi$
$878$	16.0000	0.539974
$879$	0	0
$880$	3.00000	0.101130
$881$	−22.0000	−0.741199	−0.370599	−	0.928793i	$-0.620848\pi$
$881$	−22.0000	−0.741199	−0.370599	+	0.928793i	$0.620848\pi$
$882$	1.00000	0.0336718
$883$	−20.0000	−0.673054	−0.336527	−	0.941674i	$-0.609252\pi$
$883$	−20.0000	−0.673054	−0.336527	+	0.941674i	$0.609252\pi$
$884$	−1.00000	−0.0336336
$885$	−12.0000	−0.403376
$886$	−4.00000	−0.134383
$887$	51.0000	1.71241	0.856206	−	0.516634i	$-0.172815\pi$
$887$	51.0000	1.71241	0.856206	+	0.516634i	$0.172815\pi$
$888$	−5.00000	−0.167789
$889$	10.0000	0.335389
$890$	27.0000	0.905042
$891$	1.00000	0.0335013
$892$	24.0000	0.803579
$893$	0	0
$894$	9.00000	0.301005
$895$	54.0000	1.80502
$896$	−1.00000	−0.0334077
$897$	2.00000	0.0667781
$898$	−1.00000	−0.0333704
$899$	0	0
$900$	4.00000	0.133333
$901$	−11.0000	−0.366463
$902$	4.00000	0.133185
$903$	−9.00000	−0.299501
$904$	−9.00000	−0.299336
$905$	36.0000	1.19668
$906$	8.00000	0.265782
$907$	−8.00000	−0.265636	−0.132818	−	0.991140i	$-0.542403\pi$
$907$	−8.00000	−0.265636	−0.132818	+	0.991140i	$0.542403\pi$
$908$	12.0000	0.398234
$909$	8.00000	0.265343
$910$	−3.00000	−0.0994490
$911$	40.0000	1.32526	0.662630	−	0.748947i	$-0.269440\pi$
$911$	40.0000	1.32526	0.662630	+	0.748947i	$0.269440\pi$
$912$	−6.00000	−0.198680
$913$	1.00000	0.0330952
$914$	−25.0000	−0.826927
$915$	−18.0000	−0.595062
$916$	−17.0000	−0.561696
$917$	10.0000	0.330229
$918$	1.00000	0.0330049
$919$	20.0000	0.659739	0.329870	−	0.944027i	$-0.392995\pi$
$919$	20.0000	0.659739	0.329870	+	0.944027i	$0.392995\pi$
$920$	−6.00000	−0.197814
$921$	−28.0000	−0.922631
$922$	2.00000	0.0658665
$923$	−12.0000	−0.394985
$924$	1.00000	0.0328976
$925$	20.0000	0.657596
$926$	8.00000	0.262896
$927$	−7.00000	−0.229910
$928$	−2.00000	−0.0656532
$929$	28.0000	0.918650	0.459325	−	0.888268i	$-0.348091\pi$
$929$	28.0000	0.918650	0.459325	+	0.888268i	$0.348091\pi$
$930$	0	0
$931$	6.00000	0.196642
$932$	3.00000	0.0982683
$933$	3.00000	0.0982156
$934$	−32.0000	−1.04707
$935$	−3.00000	−0.0981105
$936$	1.00000	0.0326860
$937$	−32.0000	−1.04539	−0.522697	−	0.852518i	$-0.675074\pi$
$937$	−32.0000	−1.04539	−0.522697	+	0.852518i	$0.675074\pi$
$938$	11.0000	0.359163
$939$	30.0000	0.979013
$940$	0	0
$941$	49.0000	1.59735	0.798677	−	0.601760i	$-0.205534\pi$
$941$	49.0000	1.59735	0.798677	+	0.601760i	$0.205534\pi$
$942$	10.0000	0.325818
$943$	−8.00000	−0.260516
$944$	4.00000	0.130189
$945$	3.00000	0.0975900
$946$	−9.00000	−0.292615
$947$	4.00000	0.129983	0.0649913	−	0.997886i	$-0.479298\pi$
$947$	4.00000	0.129983	0.0649913	+	0.997886i	$0.479298\pi$
$948$	15.0000	0.487177
$949$	−5.00000	−0.162307
$950$	24.0000	0.778663
$951$	18.0000	0.583690
$952$	1.00000	0.0324102
$953$	6.00000	0.194359	0.0971795	−	0.995267i	$-0.469018\pi$
$953$	6.00000	0.194359	0.0971795	+	0.995267i	$0.469018\pi$
$954$	11.0000	0.356138
$955$	45.0000	1.45617
$956$	−15.0000	−0.485135
$957$	2.00000	0.0646508
$958$	−21.0000	−0.678479
$959$	0	0
$960$	−3.00000	−0.0968246
$961$	−31.0000	−1.00000
$962$	5.00000	0.161206
$963$	−8.00000	−0.257796
$964$	22.0000	0.708572
$965$	−24.0000	−0.772587
$966$	−2.00000	−0.0643489
$967$	−12.0000	−0.385894	−0.192947	−	0.981209i	$-0.561805\pi$
$967$	−12.0000	−0.385894	−0.192947	+	0.981209i	$0.561805\pi$
$968$	−10.0000	−0.321412
$969$	6.00000	0.192748
$970$	−27.0000	−0.866918
$971$	53.0000	1.70085	0.850425	−	0.526096i	$-0.176345\pi$
$971$	53.0000	1.70085	0.850425	+	0.526096i	$0.176345\pi$
$972$	−1.00000	−0.0320750
$973$	1.00000	0.0320585
$974$	23.0000	0.736968
$975$	−4.00000	−0.128103
$976$	6.00000	0.192055
$977$	8.00000	0.255943	0.127971	−	0.991778i	$-0.459153\pi$
$977$	8.00000	0.255943	0.127971	+	0.991778i	$0.459153\pi$
$978$	−10.0000	−0.319765
$979$	9.00000	0.287641
$980$	3.00000	0.0958315
$981$	−2.00000	−0.0638551
$982$	2.00000	0.0638226
$983$	16.0000	0.510321	0.255160	−	0.966899i	$-0.417872\pi$
$983$	16.0000	0.510321	0.255160	+	0.966899i	$0.417872\pi$
$984$	−4.00000	−0.127515
$985$	60.0000	1.91176
$986$	2.00000	0.0636930
$987$	0	0
$988$	6.00000	0.190885
$989$	18.0000	0.572367
$990$	3.00000	0.0953463
$991$	9.00000	0.285894	0.142947	−	0.989730i	$-0.454342\pi$
$991$	9.00000	0.285894	0.142947	+	0.989730i	$0.454342\pi$
$992$	0	0
$993$	−1.00000	−0.0317340
$994$	12.0000	0.380617
$995$	24.0000	0.760851
$996$	−1.00000	−0.0316862
$997$	4.00000	0.126681	0.0633406	−	0.997992i	$-0.479825\pi$
$997$	4.00000	0.126681	0.0633406	+	0.997992i	$0.479825\pi$
$998$	36.0000	1.13956
$999$	−5.00000	−0.158193

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	714.2.a.g.1.1	✓	1
3.2	odd	2		2142.2.a.a.1.1		1
4.3	odd	2		5712.2.a.bb.1.1		1
7.6	odd	2		4998.2.a.bj.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
714.2.a.g.1.1	✓	1	1.1	even	1	trivial
2142.2.a.a.1.1		1	3.2	odd	2
4998.2.a.bj.1.1		1	7.6	odd	2
5712.2.a.bb.1.1		1	4.3	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:	\( N \)	\(=\)	\( 714 = 2 \cdot 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	714.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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