LMFDB - Embedded newform 714.2.a.c.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)

$f(q)$

$=$

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

\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +5.00000 q^{11} -1.00000 q^{12} -1.00000 q^{13} -1.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} -6.00000 q^{19} +1.00000 q^{20} -1.00000 q^{21} -5.00000 q^{22} +6.00000 q^{23} +1.00000 q^{24} -4.00000 q^{25} +1.00000 q^{26} -1.00000 q^{27} +1.00000 q^{28} +6.00000 q^{29} +1.00000 q^{30} +4.00000 q^{31} -1.00000 q^{32} -5.00000 q^{33} +1.00000 q^{34} +1.00000 q^{35} +1.00000 q^{36} +11.0000 q^{37} +6.00000 q^{38} +1.00000 q^{39} -1.00000 q^{40} +1.00000 q^{42} -9.00000 q^{43} +5.00000 q^{44} +1.00000 q^{45} -6.00000 q^{46} +4.00000 q^{47} -1.00000 q^{48} +1.00000 q^{49} +4.00000 q^{50} +1.00000 q^{51} -1.00000 q^{52} -7.00000 q^{53} +1.00000 q^{54} +5.00000 q^{55} -1.00000 q^{56} +6.00000 q^{57} -6.00000 q^{58} +12.0000 q^{59} -1.00000 q^{60} +6.00000 q^{61} -4.00000 q^{62} +1.00000 q^{63} +1.00000 q^{64} -1.00000 q^{65} +5.00000 q^{66} +13.0000 q^{67} -1.00000 q^{68} -6.00000 q^{69} -1.00000 q^{70} +4.00000 q^{71} -1.00000 q^{72} -13.0000 q^{73} -11.0000 q^{74} +4.00000 q^{75} -6.00000 q^{76} +5.00000 q^{77} -1.00000 q^{78} +15.0000 q^{79} +1.00000 q^{80} +1.00000 q^{81} +13.0000 q^{83} -1.00000 q^{84} -1.00000 q^{85} +9.00000 q^{86} -6.00000 q^{87} -5.00000 q^{88} +13.0000 q^{89} -1.00000 q^{90} -1.00000 q^{91} +6.00000 q^{92} -4.00000 q^{93} -4.00000 q^{94} -6.00000 q^{95} +1.00000 q^{96} -9.00000 q^{97} -1.00000 q^{98} +5.00000 q^{99} +O(q^{100})\)

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	0.223607	−	0.974679i	$-0.428217\pi$
$5$	1.00000	0.447214	0.223607	+	0.974679i	$0.428217\pi$
$6$	1.00000	0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−1.00000	−0.316228
$11$	5.00000	1.50756	0.753778	−	0.657129i	$-0.228229\pi$
$11$	5.00000	1.50756	0.753778	+	0.657129i	$0.228229\pi$
$12$	−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	$0.544284\pi$
$14$	−1.00000	−0.267261
$15$	−1.00000	−0.258199
$16$	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	$-0.741620\pi$
$19$	−6.00000	−1.37649	−0.688247	+	0.725476i	$0.741620\pi$
$20$	1.00000	0.223607
$21$	−1.00000	−0.218218
$22$	−5.00000	−1.06600
$23$	6.00000	1.25109	0.625543	−	0.780189i	$-0.284877\pi$
$23$	6.00000	1.25109	0.625543	+	0.780189i	$0.284877\pi$
$24$	1.00000	0.204124
$25$	−4.00000	−0.800000
$26$	1.00000	0.196116
$27$	−1.00000	−0.192450
$28$	1.00000	0.188982
$29$	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	$-0.383046\pi$
$31$	4.00000	0.718421	0.359211	+	0.933257i	$0.383046\pi$
$32$	−1.00000	−0.176777
$33$	−5.00000	−0.870388
$34$	1.00000	0.171499
$35$	1.00000	0.169031
$36$	1.00000	0.166667
$37$	11.0000	1.80839	0.904194	−	0.427121i	$-0.140472\pi$
$37$	11.0000	1.80839	0.904194	+	0.427121i	$0.140472\pi$
$38$	6.00000	0.973329
$39$	1.00000	0.160128
$40$	−1.00000	−0.158114
$41$	0	0		−	1.00000i	$-0.5\pi$
$41$	0	0			1.00000i	$0.5\pi$
$42$	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	$0.740742\pi$
$44$	5.00000	0.753778
$45$	1.00000	0.149071
$46$	−6.00000	−0.884652
$47$	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
$49$	1.00000	0.142857
$50$	4.00000	0.565685
$51$	1.00000	0.140028
$52$	−1.00000	−0.138675
$53$	−7.00000	−0.961524	−0.480762	−	0.876851i	$-0.659640\pi$
$53$	−7.00000	−0.961524	−0.480762	+	0.876851i	$0.659640\pi$
$54$	1.00000	0.136083
$55$	5.00000	0.674200
$56$	−1.00000	−0.133631
$57$	6.00000	0.794719
$58$	−6.00000	−0.787839
$59$	12.0000	1.56227	0.781133	−	0.624364i	$-0.214642\pi$
$59$	12.0000	1.56227	0.781133	+	0.624364i	$0.214642\pi$
$60$	−1.00000	−0.129099
$61$	6.00000	0.768221	0.384111	−	0.923287i	$-0.374508\pi$
$61$	6.00000	0.768221	0.384111	+	0.923287i	$0.374508\pi$
$62$	−4.00000	−0.508001
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	−1.00000	−0.124035
$66$	5.00000	0.615457
$67$	13.0000	1.58820	0.794101	−	0.607785i	$-0.207942\pi$
$67$	13.0000	1.58820	0.794101	+	0.607785i	$0.207942\pi$
$68$	−1.00000	−0.121268
$69$	−6.00000	−0.722315
$70$	−1.00000	−0.119523
$71$	4.00000	0.474713	0.237356	−	0.971423i	$-0.423719\pi$
$71$	4.00000	0.474713	0.237356	+	0.971423i	$0.423719\pi$
$72$	−1.00000	−0.117851
$73$	−13.0000	−1.52153	−0.760767	−	0.649025i	$-0.775177\pi$
$73$	−13.0000	−1.52153	−0.760767	+	0.649025i	$0.775177\pi$
$74$	−11.0000	−1.27872
$75$	4.00000	0.461880
$76$	−6.00000	−0.688247
$77$	5.00000	0.569803
$78$	−1.00000	−0.113228
$79$	15.0000	1.68763	0.843816	−	0.536633i	$-0.180304\pi$
$79$	15.0000	1.68763	0.843816	+	0.536633i	$0.180304\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	0	0
$83$	13.0000	1.42694	0.713468	−	0.700688i	$-0.247124\pi$
$83$	13.0000	1.42694	0.713468	+	0.700688i	$0.247124\pi$
$84$	−1.00000	−0.109109
$85$	−1.00000	−0.108465
$86$	9.00000	0.970495
$87$	−6.00000	−0.643268
$88$	−5.00000	−0.533002
$89$	13.0000	1.37800	0.688999	−	0.724763i	$-0.258051\pi$
$89$	13.0000	1.37800	0.688999	+	0.724763i	$0.258051\pi$
$90$	−1.00000	−0.105409
$91$	−1.00000	−0.104828
$92$	6.00000	0.625543
$93$	−4.00000	−0.414781
$94$	−4.00000	−0.412568
$95$	−6.00000	−0.615587
$96$	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
$99$	5.00000	0.502519
$100$	−4.00000	−0.400000
$101$	4.00000	0.398015	0.199007	−	0.979998i	$-0.436228\pi$
$101$	4.00000	0.398015	0.199007	+	0.979998i	$0.436228\pi$
$102$	−1.00000	−0.0990148
$103$	−1.00000	−0.0985329	−0.0492665	−	0.998786i	$-0.515688\pi$
$103$	−1.00000	−0.0985329	−0.0492665	+	0.998786i	$0.515688\pi$
$104$	1.00000	0.0980581
$105$	−1.00000	−0.0975900
$106$	7.00000	0.679900
$107$	0	0		−	1.00000i	$-0.5\pi$
$107$	0	0			1.00000i	$0.5\pi$
$108$	−1.00000	−0.0962250
$109$	−14.0000	−1.34096	−0.670478	−	0.741929i	$-0.733911\pi$
$109$	−14.0000	−1.34096	−0.670478	+	0.741929i	$0.733911\pi$
$110$	−5.00000	−0.476731
$111$	−11.0000	−1.04407
$112$	1.00000	0.0944911
$113$	−13.0000	−1.22294	−0.611469	−	0.791269i	$-0.709421\pi$
$113$	−13.0000	−1.22294	−0.611469	+	0.791269i	$0.709421\pi$
$114$	−6.00000	−0.561951
$115$	6.00000	0.559503
$116$	6.00000	0.557086
$117$	−1.00000	−0.0924500
$118$	−12.0000	−1.10469
$119$	−1.00000	−0.0916698
$120$	1.00000	0.0912871
$121$	14.0000	1.27273
$122$	−6.00000	−0.543214
$123$	0	0
$124$	4.00000	0.359211
$125$	−9.00000	−0.804984
$126$	−1.00000	−0.0890871
$127$	−2.00000	−0.177471	−0.0887357	−	0.996055i	$-0.528283\pi$
$127$	−2.00000	−0.177471	−0.0887357	+	0.996055i	$0.528283\pi$
$128$	−1.00000	−0.0883883
$129$	9.00000	0.792406
$130$	1.00000	0.0877058
$131$	−6.00000	−0.524222	−0.262111	−	0.965038i	$-0.584419\pi$
$131$	−6.00000	−0.524222	−0.262111	+	0.965038i	$0.584419\pi$
$132$	−5.00000	−0.435194
$133$	−6.00000	−0.520266
$134$	−13.0000	−1.12303
$135$	−1.00000	−0.0860663
$136$	1.00000	0.0857493
$137$	−16.0000	−1.36697	−0.683486	−	0.729964i	$-0.739537\pi$
$137$	−16.0000	−1.36697	−0.683486	+	0.729964i	$0.739537\pi$
$138$	6.00000	0.510754
$139$	−17.0000	−1.44192	−0.720961	−	0.692976i	$-0.756299\pi$
$139$	−17.0000	−1.44192	−0.720961	+	0.692976i	$0.756299\pi$
$140$	1.00000	0.0845154
$141$	−4.00000	−0.336861
$142$	−4.00000	−0.335673
$143$	−5.00000	−0.418121
$144$	1.00000	0.0833333
$145$	6.00000	0.498273
$146$	13.0000	1.07589
$147$	−1.00000	−0.0824786
$148$	11.0000	0.904194
$149$	−11.0000	−0.901155	−0.450578	−	0.892737i	$-0.648782\pi$
$149$	−11.0000	−0.901155	−0.450578	+	0.892737i	$0.648782\pi$
$150$	−4.00000	−0.326599
$151$	−4.00000	−0.325515	−0.162758	−	0.986666i	$-0.552039\pi$
$151$	−4.00000	−0.325515	−0.162758	+	0.986666i	$0.552039\pi$
$152$	6.00000	0.486664
$153$	−1.00000	−0.0808452
$154$	−5.00000	−0.402911
$155$	4.00000	0.321288
$156$	1.00000	0.0800641
$157$	−14.0000	−1.11732	−0.558661	−	0.829396i	$-0.688685\pi$
$157$	−14.0000	−1.11732	−0.558661	+	0.829396i	$0.688685\pi$
$158$	−15.0000	−1.19334
$159$	7.00000	0.555136
$160$	−1.00000	−0.0790569
$161$	6.00000	0.472866
$162$	−1.00000	−0.0785674
$163$	22.0000	1.72317	0.861586	−	0.507611i	$-0.169471\pi$
$163$	22.0000	1.72317	0.861586	+	0.507611i	$0.169471\pi$
$164$	0	0
$165$	−5.00000	−0.389249
$166$	−13.0000	−1.00900
$167$	−17.0000	−1.31550	−0.657750	−	0.753237i	$-0.728492\pi$
$167$	−17.0000	−1.31550	−0.657750	+	0.753237i	$0.728492\pi$
$168$	1.00000	0.0771517
$169$	−12.0000	−0.923077
$170$	1.00000	0.0766965
$171$	−6.00000	−0.458831
$172$	−9.00000	−0.686244
$173$	−14.0000	−1.06440	−0.532200	−	0.846619i	$-0.678635\pi$
$173$	−14.0000	−1.06440	−0.532200	+	0.846619i	$0.678635\pi$
$174$	6.00000	0.454859
$175$	−4.00000	−0.302372
$176$	5.00000	0.376889
$177$	−12.0000	−0.901975
$178$	−13.0000	−0.974391
$179$	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
$181$	0	0		−	1.00000i	$-0.5\pi$
$181$	0	0			1.00000i	$0.5\pi$
$182$	1.00000	0.0741249
$183$	−6.00000	−0.443533
$184$	−6.00000	−0.442326
$185$	11.0000	0.808736
$186$	4.00000	0.293294
$187$	−5.00000	−0.365636
$188$	4.00000	0.291730
$189$	−1.00000	−0.0727393
$190$	6.00000	0.435286
$191$	21.0000	1.51951	0.759753	−	0.650211i	$-0.225320\pi$
$191$	21.0000	1.51951	0.759753	+	0.650211i	$0.225320\pi$
$192$	−1.00000	−0.0721688
$193$	16.0000	1.15171	0.575853	−	0.817554i	$-0.304670\pi$
$193$	16.0000	1.15171	0.575853	+	0.817554i	$0.304670\pi$
$194$	9.00000	0.646162
$195$	1.00000	0.0716115
$196$	1.00000	0.0714286
$197$	8.00000	0.569976	0.284988	−	0.958531i	$-0.408010\pi$
$197$	8.00000	0.569976	0.284988	+	0.958531i	$0.408010\pi$
$198$	−5.00000	−0.355335
$199$	4.00000	0.283552	0.141776	−	0.989899i	$-0.454719\pi$
$199$	4.00000	0.283552	0.141776	+	0.989899i	$0.454719\pi$
$200$	4.00000	0.282843
$201$	−13.0000	−0.916949
$202$	−4.00000	−0.281439
$203$	6.00000	0.421117
$204$	1.00000	0.0700140
$205$	0	0
$206$	1.00000	0.0696733
$207$	6.00000	0.417029
$208$	−1.00000	−0.0693375
$209$	−30.0000	−2.07514
$210$	1.00000	0.0690066
$211$	−2.00000	−0.137686	−0.0688428	−	0.997628i	$-0.521931\pi$
$211$	−2.00000	−0.137686	−0.0688428	+	0.997628i	$0.521931\pi$
$212$	−7.00000	−0.480762
$213$	−4.00000	−0.274075
$214$	0	0
$215$	−9.00000	−0.613795
$216$	1.00000	0.0680414
$217$	4.00000	0.271538
$218$	14.0000	0.948200
$219$	13.0000	0.878459
$220$	5.00000	0.337100
$221$	1.00000	0.0672673
$222$	11.0000	0.738272
$223$	−24.0000	−1.60716	−0.803579	−	0.595198i	$-0.797074\pi$
$223$	−24.0000	−1.60716	−0.803579	+	0.595198i	$0.797074\pi$
$224$	−1.00000	−0.0668153
$225$	−4.00000	−0.266667
$226$	13.0000	0.864747
$227$	4.00000	0.265489	0.132745	−	0.991150i	$-0.457621\pi$
$227$	4.00000	0.265489	0.132745	+	0.991150i	$0.457621\pi$
$228$	6.00000	0.397360
$229$	−7.00000	−0.462573	−0.231287	−	0.972886i	$-0.574293\pi$
$229$	−7.00000	−0.462573	−0.231287	+	0.972886i	$0.574293\pi$
$230$	−6.00000	−0.395628
$231$	−5.00000	−0.328976
$232$	−6.00000	−0.393919
$233$	−1.00000	−0.0655122	−0.0327561	−	0.999463i	$-0.510428\pi$
$233$	−1.00000	−0.0655122	−0.0327561	+	0.999463i	$0.510428\pi$
$234$	1.00000	0.0653720
$235$	4.00000	0.260931
$236$	12.0000	0.781133
$237$	−15.0000	−0.974355
$238$	1.00000	0.0648204
$239$	−5.00000	−0.323423	−0.161712	−	0.986838i	$-0.551701\pi$
$239$	−5.00000	−0.323423	−0.161712	+	0.986838i	$0.551701\pi$
$240$	−1.00000	−0.0645497
$241$	22.0000	1.41714	0.708572	−	0.705638i	$-0.249340\pi$
$241$	22.0000	1.41714	0.708572	+	0.705638i	$0.249340\pi$
$242$	−14.0000	−0.899954
$243$	−1.00000	−0.0641500
$244$	6.00000	0.384111
$245$	1.00000	0.0638877
$246$	0	0
$247$	6.00000	0.381771
$248$	−4.00000	−0.254000
$249$	−13.0000	−0.823842
$250$	9.00000	0.569210
$251$	−13.0000	−0.820553	−0.410276	−	0.911961i	$-0.634568\pi$
$251$	−13.0000	−0.820553	−0.410276	+	0.911961i	$0.634568\pi$
$252$	1.00000	0.0629941
$253$	30.0000	1.88608
$254$	2.00000	0.125491
$255$	1.00000	0.0626224
$256$	1.00000	0.0625000
$257$	3.00000	0.187135	0.0935674	−	0.995613i	$-0.470173\pi$
$257$	3.00000	0.187135	0.0935674	+	0.995613i	$0.470173\pi$
$258$	−9.00000	−0.560316
$259$	11.0000	0.683507
$260$	−1.00000	−0.0620174
$261$	6.00000	0.371391
$262$	6.00000	0.370681
$263$	−27.0000	−1.66489	−0.832446	−	0.554107i	$-0.813060\pi$
$263$	−27.0000	−1.66489	−0.832446	+	0.554107i	$0.813060\pi$
$264$	5.00000	0.307729
$265$	−7.00000	−0.430007
$266$	6.00000	0.367884
$267$	−13.0000	−0.795587
$268$	13.0000	0.794101
$269$	18.0000	1.09748	0.548740	−	0.835993i	$-0.315108\pi$
$269$	18.0000	1.09748	0.548740	+	0.835993i	$0.315108\pi$
$270$	1.00000	0.0608581
$271$	9.00000	0.546711	0.273356	−	0.961913i	$-0.411866\pi$
$271$	9.00000	0.546711	0.273356	+	0.961913i	$0.411866\pi$
$272$	−1.00000	−0.0606339
$273$	1.00000	0.0605228
$274$	16.0000	0.966595
$275$	−20.0000	−1.20605
$276$	−6.00000	−0.361158
$277$	−18.0000	−1.08152	−0.540758	−	0.841178i	$-0.681862\pi$
$277$	−18.0000	−1.08152	−0.540758	+	0.841178i	$0.681862\pi$
$278$	17.0000	1.01959
$279$	4.00000	0.239474
$280$	−1.00000	−0.0597614
$281$	−18.0000	−1.07379	−0.536895	−	0.843649i	$-0.680403\pi$
$281$	−18.0000	−1.07379	−0.536895	+	0.843649i	$0.680403\pi$
$282$	4.00000	0.238197
$283$	−13.0000	−0.772770	−0.386385	−	0.922338i	$-0.626276\pi$
$283$	−13.0000	−0.772770	−0.386385	+	0.922338i	$0.626276\pi$
$284$	4.00000	0.237356
$285$	6.00000	0.355409
$286$	5.00000	0.295656
$287$	0	0
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	−6.00000	−0.352332
$291$	9.00000	0.527589
$292$	−13.0000	−0.760767
$293$	12.0000	0.701047	0.350524	−	0.936554i	$-0.386004\pi$
$293$	12.0000	0.701047	0.350524	+	0.936554i	$0.386004\pi$
$294$	1.00000	0.0583212
$295$	12.0000	0.698667
$296$	−11.0000	−0.639362
$297$	−5.00000	−0.290129
$298$	11.0000	0.637213
$299$	−6.00000	−0.346989
$300$	4.00000	0.230940
$301$	−9.00000	−0.518751
$302$	4.00000	0.230174
$303$	−4.00000	−0.229794
$304$	−6.00000	−0.344124
$305$	6.00000	0.343559
$306$	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	$0.205351\pi$
$308$	5.00000	0.284901
$309$	1.00000	0.0568880
$310$	−4.00000	−0.227185
$311$	−25.0000	−1.41762	−0.708810	−	0.705399i	$-0.750768\pi$
$311$	−25.0000	−1.41762	−0.708810	+	0.705399i	$0.750768\pi$
$312$	−1.00000	−0.0566139
$313$	−6.00000	−0.339140	−0.169570	−	0.985518i	$-0.554238\pi$
$313$	−6.00000	−0.339140	−0.169570	+	0.985518i	$0.554238\pi$
$314$	14.0000	0.790066
$315$	1.00000	0.0563436
$316$	15.0000	0.843816
$317$	14.0000	0.786318	0.393159	−	0.919470i	$-0.371382\pi$
$317$	14.0000	0.786318	0.393159	+	0.919470i	$0.371382\pi$
$318$	−7.00000	−0.392541
$319$	30.0000	1.67968
$320$	1.00000	0.0559017
$321$	0	0
$322$	−6.00000	−0.334367
$323$	6.00000	0.333849
$324$	1.00000	0.0555556
$325$	4.00000	0.221880
$326$	−22.0000	−1.21847
$327$	14.0000	0.774202
$328$	0	0
$329$	4.00000	0.220527
$330$	5.00000	0.275241
$331$	−15.0000	−0.824475	−0.412237	−	0.911077i	$-0.635253\pi$
$331$	−15.0000	−0.824475	−0.412237	+	0.911077i	$0.635253\pi$
$332$	13.0000	0.713468
$333$	11.0000	0.602796
$334$	17.0000	0.930199
$335$	13.0000	0.710266
$336$	−1.00000	−0.0545545
$337$	34.0000	1.85210	0.926049	−	0.377403i	$-0.123183\pi$
$337$	34.0000	1.85210	0.926049	+	0.377403i	$0.123183\pi$
$338$	12.0000	0.652714
$339$	13.0000	0.706063
$340$	−1.00000	−0.0542326
$341$	20.0000	1.08306
$342$	6.00000	0.324443
$343$	1.00000	0.0539949
$344$	9.00000	0.485247
$345$	−6.00000	−0.323029
$346$	14.0000	0.752645
$347$	−9.00000	−0.483145	−0.241573	−	0.970383i	$-0.577663\pi$
$347$	−9.00000	−0.483145	−0.241573	+	0.970383i	$0.577663\pi$
$348$	−6.00000	−0.321634
$349$	5.00000	0.267644	0.133822	−	0.991005i	$-0.457275\pi$
$349$	5.00000	0.267644	0.133822	+	0.991005i	$0.457275\pi$
$350$	4.00000	0.213809
$351$	1.00000	0.0533761
$352$	−5.00000	−0.266501
$353$	−31.0000	−1.64996	−0.824982	−	0.565159i	$-0.808815\pi$
$353$	−31.0000	−1.64996	−0.824982	+	0.565159i	$0.808815\pi$
$354$	12.0000	0.637793
$355$	4.00000	0.212298
$356$	13.0000	0.688999
$357$	1.00000	0.0529256
$358$	−18.0000	−0.951330
$359$	0	0		−	1.00000i	$-0.5\pi$
$359$	0	0			1.00000i	$0.5\pi$
$360$	−1.00000	−0.0527046
$361$	17.0000	0.894737
$362$	0	0
$363$	−14.0000	−0.734809
$364$	−1.00000	−0.0524142
$365$	−13.0000	−0.680451
$366$	6.00000	0.313625
$367$	0	0		−	1.00000i	$-0.5\pi$
$367$	0	0			1.00000i	$0.5\pi$
$368$	6.00000	0.312772
$369$	0	0
$370$	−11.0000	−0.571863
$371$	−7.00000	−0.363422
$372$	−4.00000	−0.207390
$373$	−4.00000	−0.207112	−0.103556	−	0.994624i	$-0.533022\pi$
$373$	−4.00000	−0.207112	−0.103556	+	0.994624i	$0.533022\pi$
$374$	5.00000	0.258544
$375$	9.00000	0.464758
$376$	−4.00000	−0.206284
$377$	−6.00000	−0.309016
$378$	1.00000	0.0514344
$379$	−34.0000	−1.74646	−0.873231	−	0.487306i	$-0.837980\pi$
$379$	−34.0000	−1.74646	−0.873231	+	0.487306i	$0.837980\pi$
$380$	−6.00000	−0.307794
$381$	2.00000	0.102463
$382$	−21.0000	−1.07445
$383$	−32.0000	−1.63512	−0.817562	−	0.575841i	$-0.804675\pi$
$383$	−32.0000	−1.63512	−0.817562	+	0.575841i	$0.804675\pi$
$384$	1.00000	0.0510310
$385$	5.00000	0.254824
$386$	−16.0000	−0.814379
$387$	−9.00000	−0.457496
$388$	−9.00000	−0.456906
$389$	6.00000	0.304212	0.152106	−	0.988364i	$-0.451394\pi$
$389$	6.00000	0.304212	0.152106	+	0.988364i	$0.451394\pi$
$390$	−1.00000	−0.0506370
$391$	−6.00000	−0.303433
$392$	−1.00000	−0.0505076
$393$	6.00000	0.302660
$394$	−8.00000	−0.403034
$395$	15.0000	0.754732
$396$	5.00000	0.251259
$397$	20.0000	1.00377	0.501886	−	0.864934i	$-0.332640\pi$
$397$	20.0000	1.00377	0.501886	+	0.864934i	$0.332640\pi$
$398$	−4.00000	−0.200502
$399$	6.00000	0.300376
$400$	−4.00000	−0.200000
$401$	−30.0000	−1.49813	−0.749064	−	0.662497i	$-0.769497\pi$
$401$	−30.0000	−1.49813	−0.749064	+	0.662497i	$0.769497\pi$
$402$	13.0000	0.648381
$403$	−4.00000	−0.199254
$404$	4.00000	0.199007
$405$	1.00000	0.0496904
$406$	−6.00000	−0.297775
$407$	55.0000	2.72625
$408$	−1.00000	−0.0495074
$409$	−26.0000	−1.28562	−0.642809	−	0.766027i	$-0.722231\pi$
$409$	−26.0000	−1.28562	−0.642809	+	0.766027i	$0.722231\pi$
$410$	0	0
$411$	16.0000	0.789222
$412$	−1.00000	−0.0492665
$413$	12.0000	0.590481
$414$	−6.00000	−0.294884
$415$	13.0000	0.638145
$416$	1.00000	0.0490290
$417$	17.0000	0.832494
$418$	30.0000	1.46735
$419$	18.0000	0.879358	0.439679	−	0.898155i	$-0.355092\pi$
$419$	18.0000	0.879358	0.439679	+	0.898155i	$0.355092\pi$
$420$	−1.00000	−0.0487950
$421$	−6.00000	−0.292422	−0.146211	−	0.989253i	$-0.546708\pi$
$421$	−6.00000	−0.292422	−0.146211	+	0.989253i	$0.546708\pi$
$422$	2.00000	0.0973585
$423$	4.00000	0.194487
$424$	7.00000	0.339950
$425$	4.00000	0.194029
$426$	4.00000	0.193801
$427$	6.00000	0.290360
$428$	0	0
$429$	5.00000	0.241402
$430$	9.00000	0.434019
$431$	4.00000	0.192673	0.0963366	−	0.995349i	$-0.469287\pi$
$431$	4.00000	0.192673	0.0963366	+	0.995349i	$0.469287\pi$
$432$	−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	$0.734907\pi$
$434$	−4.00000	−0.192006
$435$	−6.00000	−0.287678
$436$	−14.0000	−0.670478
$437$	−36.0000	−1.72211
$438$	−13.0000	−0.621164
$439$	−20.0000	−0.954548	−0.477274	−	0.878755i	$-0.658375\pi$
$439$	−20.0000	−0.954548	−0.477274	+	0.878755i	$0.658375\pi$
$440$	−5.00000	−0.238366
$441$	1.00000	0.0476190
$442$	−1.00000	−0.0475651
$443$	12.0000	0.570137	0.285069	−	0.958507i	$-0.407984\pi$
$443$	12.0000	0.570137	0.285069	+	0.958507i	$0.407984\pi$
$444$	−11.0000	−0.522037
$445$	13.0000	0.616259
$446$	24.0000	1.13643
$447$	11.0000	0.520282
$448$	1.00000	0.0472456
$449$	19.0000	0.896665	0.448333	−	0.893867i	$-0.352018\pi$
$449$	19.0000	0.896665	0.448333	+	0.893867i	$0.352018\pi$
$450$	4.00000	0.188562
$451$	0	0
$452$	−13.0000	−0.611469
$453$	4.00000	0.187936
$454$	−4.00000	−0.187729
$455$	−1.00000	−0.0468807
$456$	−6.00000	−0.280976
$457$	7.00000	0.327446	0.163723	−	0.986506i	$-0.447650\pi$
$457$	7.00000	0.327446	0.163723	+	0.986506i	$0.447650\pi$
$458$	7.00000	0.327089
$459$	1.00000	0.0466760
$460$	6.00000	0.279751
$461$	10.0000	0.465746	0.232873	−	0.972507i	$-0.425187\pi$
$461$	10.0000	0.465746	0.232873	+	0.972507i	$0.425187\pi$
$462$	5.00000	0.232621
$463$	−4.00000	−0.185896	−0.0929479	−	0.995671i	$-0.529629\pi$
$463$	−4.00000	−0.185896	−0.0929479	+	0.995671i	$0.529629\pi$
$464$	6.00000	0.278543
$465$	−4.00000	−0.185496
$466$	1.00000	0.0463241
$467$	24.0000	1.11059	0.555294	−	0.831654i	$-0.312606\pi$
$467$	24.0000	1.11059	0.555294	+	0.831654i	$0.312606\pi$
$468$	−1.00000	−0.0462250
$469$	13.0000	0.600284
$470$	−4.00000	−0.184506
$471$	14.0000	0.645086
$472$	−12.0000	−0.552345
$473$	−45.0000	−2.06910
$474$	15.0000	0.688973
$475$	24.0000	1.10120
$476$	−1.00000	−0.0458349
$477$	−7.00000	−0.320508
$478$	5.00000	0.228695
$479$	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
$481$	−11.0000	−0.501557
$482$	−22.0000	−1.00207
$483$	−6.00000	−0.273009
$484$	14.0000	0.636364
$485$	−9.00000	−0.408669
$486$	1.00000	0.0453609
$487$	−23.0000	−1.04223	−0.521115	−	0.853487i	$-0.674484\pi$
$487$	−23.0000	−1.04223	−0.521115	+	0.853487i	$0.674484\pi$
$488$	−6.00000	−0.271607
$489$	−22.0000	−0.994874
$490$	−1.00000	−0.0451754
$491$	−10.0000	−0.451294	−0.225647	−	0.974209i	$-0.572450\pi$
$491$	−10.0000	−0.451294	−0.225647	+	0.974209i	$0.572450\pi$
$492$	0	0
$493$	−6.00000	−0.270226
$494$	−6.00000	−0.269953
$495$	5.00000	0.224733
$496$	4.00000	0.179605
$497$	4.00000	0.179425
$498$	13.0000	0.582544
$499$	12.0000	0.537194	0.268597	−	0.963253i	$-0.413440\pi$
$499$	12.0000	0.537194	0.268597	+	0.963253i	$0.413440\pi$
$500$	−9.00000	−0.402492
$501$	17.0000	0.759504
$502$	13.0000	0.580218
$503$	−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
$505$	4.00000	0.177998
$506$	−30.0000	−1.33366
$507$	12.0000	0.532939
$508$	−2.00000	−0.0887357
$509$	−24.0000	−1.06378	−0.531891	−	0.846813i	$-0.678518\pi$
$509$	−24.0000	−1.06378	−0.531891	+	0.846813i	$0.678518\pi$
$510$	−1.00000	−0.0442807
$511$	−13.0000	−0.575086
$512$	−1.00000	−0.0441942
$513$	6.00000	0.264906
$514$	−3.00000	−0.132324
$515$	−1.00000	−0.0440653
$516$	9.00000	0.396203
$517$	20.0000	0.879599
$518$	−11.0000	−0.483312
$519$	14.0000	0.614532
$520$	1.00000	0.0438529
$521$	20.0000	0.876216	0.438108	−	0.898922i	$-0.355649\pi$
$521$	20.0000	0.876216	0.438108	+	0.898922i	$0.355649\pi$
$522$	−6.00000	−0.262613
$523$	−20.0000	−0.874539	−0.437269	−	0.899331i	$-0.644054\pi$
$523$	−20.0000	−0.874539	−0.437269	+	0.899331i	$0.644054\pi$
$524$	−6.00000	−0.262111
$525$	4.00000	0.174574
$526$	27.0000	1.17726
$527$	−4.00000	−0.174243
$528$	−5.00000	−0.217597
$529$	13.0000	0.565217
$530$	7.00000	0.304061
$531$	12.0000	0.520756
$532$	−6.00000	−0.260133
$533$	0	0
$534$	13.0000	0.562565
$535$	0	0
$536$	−13.0000	−0.561514
$537$	−18.0000	−0.776757
$538$	−18.0000	−0.776035
$539$	5.00000	0.215365
$540$	−1.00000	−0.0430331
$541$	23.0000	0.988847	0.494424	−	0.869221i	$-0.335379\pi$
$541$	23.0000	0.988847	0.494424	+	0.869221i	$0.335379\pi$
$542$	−9.00000	−0.386583
$543$	0	0
$544$	1.00000	0.0428746
$545$	−14.0000	−0.599694
$546$	−1.00000	−0.0427960
$547$	2.00000	0.0855138	0.0427569	−	0.999086i	$-0.486386\pi$
$547$	2.00000	0.0855138	0.0427569	+	0.999086i	$0.486386\pi$
$548$	−16.0000	−0.683486
$549$	6.00000	0.256074
$550$	20.0000	0.852803
$551$	−36.0000	−1.53365
$552$	6.00000	0.255377
$553$	15.0000	0.637865
$554$	18.0000	0.764747
$555$	−11.0000	−0.466924
$556$	−17.0000	−0.720961
$557$	−6.00000	−0.254228	−0.127114	−	0.991888i	$-0.540571\pi$
$557$	−6.00000	−0.254228	−0.127114	+	0.991888i	$0.540571\pi$
$558$	−4.00000	−0.169334
$559$	9.00000	0.380659
$560$	1.00000	0.0422577
$561$	5.00000	0.211100
$562$	18.0000	0.759284
$563$	41.0000	1.72794	0.863972	−	0.503540i	$-0.167969\pi$
$563$	41.0000	1.72794	0.863972	+	0.503540i	$0.167969\pi$
$564$	−4.00000	−0.168430
$565$	−13.0000	−0.546914
$566$	13.0000	0.546431
$567$	1.00000	0.0419961
$568$	−4.00000	−0.167836
$569$	−26.0000	−1.08998	−0.544988	−	0.838444i	$-0.683466\pi$
$569$	−26.0000	−1.08998	−0.544988	+	0.838444i	$0.683466\pi$
$570$	−6.00000	−0.251312
$571$	−36.0000	−1.50655	−0.753277	−	0.657704i	$-0.771528\pi$
$571$	−36.0000	−1.50655	−0.753277	+	0.657704i	$0.771528\pi$
$572$	−5.00000	−0.209061
$573$	−21.0000	−0.877288
$574$	0	0
$575$	−24.0000	−1.00087
$576$	1.00000	0.0416667
$577$	−10.0000	−0.416305	−0.208153	−	0.978096i	$-0.566745\pi$
$577$	−10.0000	−0.416305	−0.208153	+	0.978096i	$0.566745\pi$
$578$	−1.00000	−0.0415945
$579$	−16.0000	−0.664937
$580$	6.00000	0.249136
$581$	13.0000	0.539331
$582$	−9.00000	−0.373062
$583$	−35.0000	−1.44955
$584$	13.0000	0.537944
$585$	−1.00000	−0.0413449
$586$	−12.0000	−0.495715
$587$	21.0000	0.866763	0.433381	−	0.901211i	$-0.357320\pi$
$587$	21.0000	0.866763	0.433381	+	0.901211i	$0.357320\pi$
$588$	−1.00000	−0.0412393
$589$	−24.0000	−0.988903
$590$	−12.0000	−0.494032
$591$	−8.00000	−0.329076
$592$	11.0000	0.452097
$593$	−30.0000	−1.23195	−0.615976	−	0.787765i	$-0.711238\pi$
$593$	−30.0000	−1.23195	−0.615976	+	0.787765i	$0.711238\pi$
$594$	5.00000	0.205152
$595$	−1.00000	−0.0409960
$596$	−11.0000	−0.450578
$597$	−4.00000	−0.163709
$598$	6.00000	0.245358
$599$	−16.0000	−0.653742	−0.326871	−	0.945069i	$-0.605994\pi$
$599$	−16.0000	−0.653742	−0.326871	+	0.945069i	$0.605994\pi$
$600$	−4.00000	−0.163299
$601$	2.00000	0.0815817	0.0407909	−	0.999168i	$-0.487012\pi$
$601$	2.00000	0.0815817	0.0407909	+	0.999168i	$0.487012\pi$
$602$	9.00000	0.366813
$603$	13.0000	0.529401
$604$	−4.00000	−0.162758
$605$	14.0000	0.569181
$606$	4.00000	0.162489
$607$	−8.00000	−0.324710	−0.162355	−	0.986732i	$-0.551909\pi$
$607$	−8.00000	−0.324710	−0.162355	+	0.986732i	$0.551909\pi$
$608$	6.00000	0.243332
$609$	−6.00000	−0.243132
$610$	−6.00000	−0.242933
$611$	−4.00000	−0.161823
$612$	−1.00000	−0.0404226
$613$	40.0000	1.61558	0.807792	−	0.589467i	$-0.200662\pi$
$613$	40.0000	1.61558	0.807792	+	0.589467i	$0.200662\pi$
$614$	−28.0000	−1.12999
$615$	0	0
$616$	−5.00000	−0.201456
$617$	−1.00000	−0.0402585	−0.0201292	−	0.999797i	$-0.506408\pi$
$617$	−1.00000	−0.0402585	−0.0201292	+	0.999797i	$0.506408\pi$
$618$	−1.00000	−0.0402259
$619$	−35.0000	−1.40677	−0.703384	−	0.710810i	$-0.748329\pi$
$619$	−35.0000	−1.40677	−0.703384	+	0.710810i	$0.748329\pi$
$620$	4.00000	0.160644
$621$	−6.00000	−0.240772
$622$	25.0000	1.00241
$623$	13.0000	0.520834
$624$	1.00000	0.0400320
$625$	11.0000	0.440000
$626$	6.00000	0.239808
$627$	30.0000	1.19808
$628$	−14.0000	−0.558661
$629$	−11.0000	−0.438599
$630$	−1.00000	−0.0398410
$631$	−20.0000	−0.796187	−0.398094	−	0.917345i	$-0.630328\pi$
$631$	−20.0000	−0.796187	−0.398094	+	0.917345i	$0.630328\pi$
$632$	−15.0000	−0.596668
$633$	2.00000	0.0794929
$634$	−14.0000	−0.556011
$635$	−2.00000	−0.0793676
$636$	7.00000	0.277568
$637$	−1.00000	−0.0396214
$638$	−30.0000	−1.18771
$639$	4.00000	0.158238
$640$	−1.00000	−0.0395285
$641$	3.00000	0.118493	0.0592464	−	0.998243i	$-0.481130\pi$
$641$	3.00000	0.118493	0.0592464	+	0.998243i	$0.481130\pi$
$642$	0	0
$643$	19.0000	0.749287	0.374643	−	0.927169i	$-0.377765\pi$
$643$	19.0000	0.749287	0.374643	+	0.927169i	$0.377765\pi$
$644$	6.00000	0.236433
$645$	9.00000	0.354375
$646$	−6.00000	−0.236067
$647$	−12.0000	−0.471769	−0.235884	−	0.971781i	$-0.575799\pi$
$647$	−12.0000	−0.471769	−0.235884	+	0.971781i	$0.575799\pi$
$648$	−1.00000	−0.0392837
$649$	60.0000	2.35521
$650$	−4.00000	−0.156893
$651$	−4.00000	−0.156772
$652$	22.0000	0.861586
$653$	−10.0000	−0.391330	−0.195665	−	0.980671i	$-0.562687\pi$
$653$	−10.0000	−0.391330	−0.195665	+	0.980671i	$0.562687\pi$
$654$	−14.0000	−0.547443
$655$	−6.00000	−0.234439
$656$	0	0
$657$	−13.0000	−0.507178
$658$	−4.00000	−0.155936
$659$	12.0000	0.467454	0.233727	−	0.972302i	$-0.424908\pi$
$659$	12.0000	0.467454	0.233727	+	0.972302i	$0.424908\pi$
$660$	−5.00000	−0.194625
$661$	6.00000	0.233373	0.116686	−	0.993169i	$-0.462773\pi$
$661$	6.00000	0.233373	0.116686	+	0.993169i	$0.462773\pi$
$662$	15.0000	0.582992
$663$	−1.00000	−0.0388368
$664$	−13.0000	−0.504498
$665$	−6.00000	−0.232670
$666$	−11.0000	−0.426241
$667$	36.0000	1.39393
$668$	−17.0000	−0.657750
$669$	24.0000	0.927894
$670$	−13.0000	−0.502234
$671$	30.0000	1.15814
$672$	1.00000	0.0385758
$673$	−36.0000	−1.38770	−0.693849	−	0.720121i	$-0.744086\pi$
$673$	−36.0000	−1.38770	−0.693849	+	0.720121i	$0.744086\pi$
$674$	−34.0000	−1.30963
$675$	4.00000	0.153960
$676$	−12.0000	−0.461538
$677$	−47.0000	−1.80636	−0.903178	−	0.429265i	$-0.858772\pi$
$677$	−47.0000	−1.80636	−0.903178	+	0.429265i	$0.858772\pi$
$678$	−13.0000	−0.499262
$679$	−9.00000	−0.345388
$680$	1.00000	0.0383482
$681$	−4.00000	−0.153280
$682$	−20.0000	−0.765840
$683$	32.0000	1.22445	0.612223	−	0.790685i	$-0.290275\pi$
$683$	32.0000	1.22445	0.612223	+	0.790685i	$0.290275\pi$
$684$	−6.00000	−0.229416
$685$	−16.0000	−0.611329
$686$	−1.00000	−0.0381802
$687$	7.00000	0.267067
$688$	−9.00000	−0.343122
$689$	7.00000	0.266679
$690$	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	$0.369205\pi$
$692$	−14.0000	−0.532200
$693$	5.00000	0.189934
$694$	9.00000	0.341635
$695$	−17.0000	−0.644847
$696$	6.00000	0.227429
$697$	0	0
$698$	−5.00000	−0.189253
$699$	1.00000	0.0378235
$700$	−4.00000	−0.151186
$701$	27.0000	1.01978	0.509888	−	0.860241i	$-0.329687\pi$
$701$	27.0000	1.01978	0.509888	+	0.860241i	$0.329687\pi$
$702$	−1.00000	−0.0377426
$703$	−66.0000	−2.48924
$704$	5.00000	0.188445
$705$	−4.00000	−0.150649
$706$	31.0000	1.16670
$707$	4.00000	0.150435
$708$	−12.0000	−0.450988
$709$	19.0000	0.713560	0.356780	−	0.934188i	$-0.383875\pi$
$709$	19.0000	0.713560	0.356780	+	0.934188i	$0.383875\pi$
$710$	−4.00000	−0.150117
$711$	15.0000	0.562544
$712$	−13.0000	−0.487196
$713$	24.0000	0.898807
$714$	−1.00000	−0.0374241
$715$	−5.00000	−0.186989
$716$	18.0000	0.672692
$717$	5.00000	0.186728
$718$	0	0
$719$	−48.0000	−1.79010	−0.895049	−	0.445968i	$-0.852860\pi$
$719$	−48.0000	−1.79010	−0.895049	+	0.445968i	$0.852860\pi$
$720$	1.00000	0.0372678
$721$	−1.00000	−0.0372419
$722$	−17.0000	−0.632674
$723$	−22.0000	−0.818189
$724$	0	0
$725$	−24.0000	−0.891338
$726$	14.0000	0.519589
$727$	−33.0000	−1.22390	−0.611951	−	0.790896i	$-0.709615\pi$
$727$	−33.0000	−1.22390	−0.611951	+	0.790896i	$0.709615\pi$
$728$	1.00000	0.0370625
$729$	1.00000	0.0370370
$730$	13.0000	0.481152
$731$	9.00000	0.332877
$732$	−6.00000	−0.221766
$733$	−42.0000	−1.55131	−0.775653	−	0.631160i	$-0.782579\pi$
$733$	−42.0000	−1.55131	−0.775653	+	0.631160i	$0.782579\pi$
$734$	0	0
$735$	−1.00000	−0.0368856
$736$	−6.00000	−0.221163
$737$	65.0000	2.39431
$738$	0	0
$739$	−12.0000	−0.441427	−0.220714	−	0.975339i	$-0.570839\pi$
$739$	−12.0000	−0.441427	−0.220714	+	0.975339i	$0.570839\pi$
$740$	11.0000	0.404368
$741$	−6.00000	−0.220416
$742$	7.00000	0.256978
$743$	18.0000	0.660356	0.330178	−	0.943919i	$-0.392891\pi$
$743$	18.0000	0.660356	0.330178	+	0.943919i	$0.392891\pi$
$744$	4.00000	0.146647
$745$	−11.0000	−0.403009
$746$	4.00000	0.146450
$747$	13.0000	0.475645
$748$	−5.00000	−0.182818
$749$	0	0
$750$	−9.00000	−0.328634
$751$	−4.00000	−0.145962	−0.0729810	−	0.997333i	$-0.523251\pi$
$751$	−4.00000	−0.145962	−0.0729810	+	0.997333i	$0.523251\pi$
$752$	4.00000	0.145865
$753$	13.0000	0.473746
$754$	6.00000	0.218507
$755$	−4.00000	−0.145575
$756$	−1.00000	−0.0363696
$757$	−36.0000	−1.30844	−0.654221	−	0.756303i	$-0.727003\pi$
$757$	−36.0000	−1.30844	−0.654221	+	0.756303i	$0.727003\pi$
$758$	34.0000	1.23494
$759$	−30.0000	−1.08893
$760$	6.00000	0.217643
$761$	−25.0000	−0.906249	−0.453125	−	0.891447i	$-0.649691\pi$
$761$	−25.0000	−0.906249	−0.453125	+	0.891447i	$0.649691\pi$
$762$	−2.00000	−0.0724524
$763$	−14.0000	−0.506834
$764$	21.0000	0.759753
$765$	−1.00000	−0.0361551
$766$	32.0000	1.15621
$767$	−12.0000	−0.433295
$768$	−1.00000	−0.0360844
$769$	−14.0000	−0.504853	−0.252426	−	0.967616i	$-0.581229\pi$
$769$	−14.0000	−0.504853	−0.252426	+	0.967616i	$0.581229\pi$
$770$	−5.00000	−0.180187
$771$	−3.00000	−0.108042
$772$	16.0000	0.575853
$773$	32.0000	1.15096	0.575480	−	0.817816i	$-0.304815\pi$
$773$	32.0000	1.15096	0.575480	+	0.817816i	$0.304815\pi$
$774$	9.00000	0.323498
$775$	−16.0000	−0.574737
$776$	9.00000	0.323081
$777$	−11.0000	−0.394623
$778$	−6.00000	−0.215110
$779$	0	0
$780$	1.00000	0.0358057
$781$	20.0000	0.715656
$782$	6.00000	0.214560
$783$	−6.00000	−0.214423
$784$	1.00000	0.0357143
$785$	−14.0000	−0.499681
$786$	−6.00000	−0.214013
$787$	5.00000	0.178231	0.0891154	−	0.996021i	$-0.471596\pi$
$787$	5.00000	0.178231	0.0891154	+	0.996021i	$0.471596\pi$
$788$	8.00000	0.284988
$789$	27.0000	0.961225
$790$	−15.0000	−0.533676
$791$	−13.0000	−0.462227
$792$	−5.00000	−0.177667
$793$	−6.00000	−0.213066
$794$	−20.0000	−0.709773
$795$	7.00000	0.248264
$796$	4.00000	0.141776
$797$	26.0000	0.920967	0.460484	−	0.887668i	$-0.347676\pi$
$797$	26.0000	0.920967	0.460484	+	0.887668i	$0.347676\pi$
$798$	−6.00000	−0.212398
$799$	−4.00000	−0.141510
$800$	4.00000	0.141421
$801$	13.0000	0.459332
$802$	30.0000	1.05934
$803$	−65.0000	−2.29380
$804$	−13.0000	−0.458475
$805$	6.00000	0.211472
$806$	4.00000	0.140894
$807$	−18.0000	−0.633630
$808$	−4.00000	−0.140720
$809$	−26.0000	−0.914111	−0.457056	−	0.889438i	$-0.651096\pi$
$809$	−26.0000	−0.914111	−0.457056	+	0.889438i	$0.651096\pi$
$810$	−1.00000	−0.0351364
$811$	43.0000	1.50993	0.754967	−	0.655763i	$-0.227653\pi$
$811$	43.0000	1.50993	0.754967	+	0.655763i	$0.227653\pi$
$812$	6.00000	0.210559
$813$	−9.00000	−0.315644
$814$	−55.0000	−1.92775
$815$	22.0000	0.770626
$816$	1.00000	0.0350070
$817$	54.0000	1.88922
$818$	26.0000	0.909069
$819$	−1.00000	−0.0349428
$820$	0	0
$821$	30.0000	1.04701	0.523504	−	0.852023i	$-0.324625\pi$
$821$	30.0000	1.04701	0.523504	+	0.852023i	$0.324625\pi$
$822$	−16.0000	−0.558064
$823$	23.0000	0.801730	0.400865	−	0.916137i	$-0.368710\pi$
$823$	23.0000	0.801730	0.400865	+	0.916137i	$0.368710\pi$
$824$	1.00000	0.0348367
$825$	20.0000	0.696311
$826$	−12.0000	−0.417533
$827$	1.00000	0.0347734	0.0173867	−	0.999849i	$-0.494465\pi$
$827$	1.00000	0.0347734	0.0173867	+	0.999849i	$0.494465\pi$
$828$	6.00000	0.208514
$829$	31.0000	1.07667	0.538337	−	0.842729i	$-0.319053\pi$
$829$	31.0000	1.07667	0.538337	+	0.842729i	$0.319053\pi$
$830$	−13.0000	−0.451237
$831$	18.0000	0.624413
$832$	−1.00000	−0.0346688
$833$	−1.00000	−0.0346479
$834$	−17.0000	−0.588662
$835$	−17.0000	−0.588309
$836$	−30.0000	−1.03757
$837$	−4.00000	−0.138260
$838$	−18.0000	−0.621800
$839$	25.0000	0.863096	0.431548	−	0.902090i	$-0.357968\pi$
$839$	25.0000	0.863096	0.431548	+	0.902090i	$0.357968\pi$
$840$	1.00000	0.0345033
$841$	7.00000	0.241379
$842$	6.00000	0.206774
$843$	18.0000	0.619953
$844$	−2.00000	−0.0688428
$845$	−12.0000	−0.412813
$846$	−4.00000	−0.137523
$847$	14.0000	0.481046
$848$	−7.00000	−0.240381
$849$	13.0000	0.446159
$850$	−4.00000	−0.137199
$851$	66.0000	2.26245
$852$	−4.00000	−0.137038
$853$	−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
$855$	−6.00000	−0.205196
$856$	0	0
$857$	0	0		−	1.00000i	$-0.5\pi$
$857$	0	0			1.00000i	$0.5\pi$
$858$	−5.00000	−0.170697
$859$	30.0000	1.02359	0.511793	−	0.859109i	$-0.328981\pi$
$859$	30.0000	1.02359	0.511793	+	0.859109i	$0.328981\pi$
$860$	−9.00000	−0.306897
$861$	0	0
$862$	−4.00000	−0.136241
$863$	−23.0000	−0.782929	−0.391465	−	0.920193i	$-0.628031\pi$
$863$	−23.0000	−0.782929	−0.391465	+	0.920193i	$0.628031\pi$
$864$	1.00000	0.0340207
$865$	−14.0000	−0.476014
$866$	28.0000	0.951479
$867$	−1.00000	−0.0339618
$868$	4.00000	0.135769
$869$	75.0000	2.54420
$870$	6.00000	0.203419
$871$	−13.0000	−0.440488
$872$	14.0000	0.474100
$873$	−9.00000	−0.304604
$874$	36.0000	1.21772
$875$	−9.00000	−0.304256
$876$	13.0000	0.439229
$877$	1.00000	0.0337676	0.0168838	−	0.999857i	$-0.494625\pi$
$877$	1.00000	0.0337676	0.0168838	+	0.999857i	$0.494625\pi$
$878$	20.0000	0.674967
$879$	−12.0000	−0.404750
$880$	5.00000	0.168550
$881$	−10.0000	−0.336909	−0.168454	−	0.985709i	$-0.553878\pi$
$881$	−10.0000	−0.336909	−0.168454	+	0.985709i	$0.553878\pi$
$882$	−1.00000	−0.0336718
$883$	−52.0000	−1.74994	−0.874970	−	0.484178i	$-0.839119\pi$
$883$	−52.0000	−1.74994	−0.874970	+	0.484178i	$0.839119\pi$
$884$	1.00000	0.0336336
$885$	−12.0000	−0.403376
$886$	−12.0000	−0.403148
$887$	33.0000	1.10803	0.554016	−	0.832506i	$-0.313095\pi$
$887$	33.0000	1.10803	0.554016	+	0.832506i	$0.313095\pi$
$888$	11.0000	0.369136
$889$	−2.00000	−0.0670778
$890$	−13.0000	−0.435761
$891$	5.00000	0.167506
$892$	−24.0000	−0.803579
$893$	−24.0000	−0.803129
$894$	−11.0000	−0.367895
$895$	18.0000	0.601674
$896$	−1.00000	−0.0334077
$897$	6.00000	0.200334
$898$	−19.0000	−0.634038
$899$	24.0000	0.800445
$900$	−4.00000	−0.133333
$901$	7.00000	0.233204
$902$	0	0
$903$	9.00000	0.299501
$904$	13.0000	0.432374
$905$	0	0
$906$	−4.00000	−0.132891
$907$	4.00000	0.132818	0.0664089	−	0.997792i	$-0.478846\pi$
$907$	4.00000	0.132818	0.0664089	+	0.997792i	$0.478846\pi$
$908$	4.00000	0.132745
$909$	4.00000	0.132672
$910$	1.00000	0.0331497
$911$	36.0000	1.19273	0.596367	−	0.802712i	$-0.296610\pi$
$911$	36.0000	1.19273	0.596367	+	0.802712i	$0.296610\pi$
$912$	6.00000	0.198680
$913$	65.0000	2.15119
$914$	−7.00000	−0.231539
$915$	−6.00000	−0.198354
$916$	−7.00000	−0.231287
$917$	−6.00000	−0.198137
$918$	−1.00000	−0.0330049
$919$	16.0000	0.527791	0.263896	−	0.964551i	$-0.414993\pi$
$919$	16.0000	0.527791	0.263896	+	0.964551i	$0.414993\pi$
$920$	−6.00000	−0.197814
$921$	−28.0000	−0.922631
$922$	−10.0000	−0.329332
$923$	−4.00000	−0.131662
$924$	−5.00000	−0.164488
$925$	−44.0000	−1.44671
$926$	4.00000	0.131448
$927$	−1.00000	−0.0328443
$928$	−6.00000	−0.196960
$929$	16.0000	0.524943	0.262471	−	0.964940i	$-0.415462\pi$
$929$	16.0000	0.524943	0.262471	+	0.964940i	$0.415462\pi$
$930$	4.00000	0.131165
$931$	−6.00000	−0.196642
$932$	−1.00000	−0.0327561
$933$	25.0000	0.818463
$934$	−24.0000	−0.785304
$935$	−5.00000	−0.163517
$936$	1.00000	0.0326860
$937$	52.0000	1.69877	0.849383	−	0.527777i	$-0.176974\pi$
$937$	52.0000	1.69877	0.849383	+	0.527777i	$0.176974\pi$
$938$	−13.0000	−0.424465
$939$	6.00000	0.195803
$940$	4.00000	0.130466
$941$	3.00000	0.0977972	0.0488986	−	0.998804i	$-0.484429\pi$
$941$	3.00000	0.0977972	0.0488986	+	0.998804i	$0.484429\pi$
$942$	−14.0000	−0.456145
$943$	0	0
$944$	12.0000	0.390567
$945$	−1.00000	−0.0325300
$946$	45.0000	1.46308
$947$	−4.00000	−0.129983	−0.0649913	−	0.997886i	$-0.520702\pi$
$947$	−4.00000	−0.129983	−0.0649913	+	0.997886i	$0.520702\pi$
$948$	−15.0000	−0.487177
$949$	13.0000	0.421998
$950$	−24.0000	−0.778663
$951$	−14.0000	−0.453981
$952$	1.00000	0.0324102
$953$	2.00000	0.0647864	0.0323932	−	0.999475i	$-0.489687\pi$
$953$	2.00000	0.0647864	0.0323932	+	0.999475i	$0.489687\pi$
$954$	7.00000	0.226633
$955$	21.0000	0.679544
$956$	−5.00000	−0.161712
$957$	−30.0000	−0.969762
$958$	−25.0000	−0.807713
$959$	−16.0000	−0.516667
$960$	−1.00000	−0.0322749
$961$	−15.0000	−0.483871
$962$	11.0000	0.354654
$963$	0	0
$964$	22.0000	0.708572
$965$	16.0000	0.515058
$966$	6.00000	0.193047
$967$	−4.00000	−0.128631	−0.0643157	−	0.997930i	$-0.520486\pi$
$967$	−4.00000	−0.128631	−0.0643157	+	0.997930i	$0.520486\pi$
$968$	−14.0000	−0.449977
$969$	−6.00000	−0.192748
$970$	9.00000	0.288973
$971$	25.0000	0.802288	0.401144	−	0.916015i	$-0.368613\pi$
$971$	25.0000	0.802288	0.401144	+	0.916015i	$0.368613\pi$
$972$	−1.00000	−0.0320750
$973$	−17.0000	−0.544995
$974$	23.0000	0.736968
$975$	−4.00000	−0.128103
$976$	6.00000	0.192055
$977$	12.0000	0.383914	0.191957	−	0.981403i	$-0.438517\pi$
$977$	12.0000	0.383914	0.191957	+	0.981403i	$0.438517\pi$
$978$	22.0000	0.703482
$979$	65.0000	2.07741
$980$	1.00000	0.0319438
$981$	−14.0000	−0.446986
$982$	10.0000	0.319113
$983$	32.0000	1.02064	0.510321	−	0.859984i	$-0.329527\pi$
$983$	32.0000	1.02064	0.510321	+	0.859984i	$0.329527\pi$
$984$	0	0
$985$	8.00000	0.254901
$986$	6.00000	0.191079
$987$	−4.00000	−0.127321
$988$	6.00000	0.190885
$989$	−54.0000	−1.71710
$990$	−5.00000	−0.158910
$991$	−9.00000	−0.285894	−0.142947	−	0.989730i	$-0.545658\pi$
$991$	−9.00000	−0.285894	−0.142947	+	0.989730i	$0.545658\pi$
$992$	−4.00000	−0.127000
$993$	15.0000	0.476011
$994$	−4.00000	−0.126872
$995$	4.00000	0.126809
$996$	−13.0000	−0.411921
$997$	−40.0000	−1.26681	−0.633406	−	0.773819i	$-0.718344\pi$
$997$	−40.0000	−1.26681	−0.633406	+	0.773819i	$0.718344\pi$
$998$	−12.0000	−0.379853
$999$	−11.0000	−0.348025

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
714.2.a.c.1.1	✓	1	1.1	even	1	trivial
2142.2.a.q.1.1		1	3.2	odd	2
4998.2.a.s.1.1		1	7.6	odd	2
5712.2.a.s.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

Downloads

Learn more