LMFDB - Embedded newform 5586.2.a.h.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5586,2,Mod(1,5586)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5586, 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("5586.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5586 = 2 \cdot 3 \cdot 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5586.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:	$44.6044345691$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 798)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	5586.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +3.00000 q^{11} -1.00000 q^{12} +4.00000 q^{13} -1.00000 q^{15} +1.00000 q^{16} +4.00000 q^{17} -1.00000 q^{18} +1.00000 q^{19} +1.00000 q^{20} -3.00000 q^{22} -4.00000 q^{23} +1.00000 q^{24} -4.00000 q^{25} -4.00000 q^{26} -1.00000 q^{27} -7.00000 q^{29} +1.00000 q^{30} -7.00000 q^{31} -1.00000 q^{32} -3.00000 q^{33} -4.00000 q^{34} +1.00000 q^{36} -4.00000 q^{37} -1.00000 q^{38} -4.00000 q^{39} -1.00000 q^{40} -12.0000 q^{41} -6.00000 q^{43} +3.00000 q^{44} +1.00000 q^{45} +4.00000 q^{46} -10.0000 q^{47} -1.00000 q^{48} +4.00000 q^{50} -4.00000 q^{51} +4.00000 q^{52} +13.0000 q^{53} +1.00000 q^{54} +3.00000 q^{55} -1.00000 q^{57} +7.00000 q^{58} +1.00000 q^{59} -1.00000 q^{60} -14.0000 q^{61} +7.00000 q^{62} +1.00000 q^{64} +4.00000 q^{65} +3.00000 q^{66} -2.00000 q^{67} +4.00000 q^{68} +4.00000 q^{69} +14.0000 q^{71} -1.00000 q^{72} -10.0000 q^{73} +4.00000 q^{74} +4.00000 q^{75} +1.00000 q^{76} +4.00000 q^{78} -1.00000 q^{79} +1.00000 q^{80} +1.00000 q^{81} +12.0000 q^{82} -15.0000 q^{83} +4.00000 q^{85} +6.00000 q^{86} +7.00000 q^{87} -3.00000 q^{88} +6.00000 q^{89} -1.00000 q^{90} -4.00000 q^{92} +7.00000 q^{93} +10.0000 q^{94} +1.00000 q^{95} +1.00000 q^{96} -3.00000 q^{97} +3.00000 q^{99} +O(q^{100})\)

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
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−1.00000	−0.316228
$11$	3.00000	0.904534	0.452267	−	0.891883i	$-0.350615\pi$
$11$	3.00000	0.904534	0.452267	+	0.891883i	$0.350615\pi$
$12$	−1.00000	−0.288675
$13$	4.00000	1.10940	0.554700	−	0.832050i	$-0.312833\pi$
$13$	4.00000	1.10940	0.554700	+	0.832050i	$0.312833\pi$
$14$	0	0
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	4.00000	0.970143	0.485071	−	0.874475i	$-0.338794\pi$
$17$	4.00000	0.970143	0.485071	+	0.874475i	$0.338794\pi$
$18$	−1.00000	−0.235702
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	1.00000	0.223607
$21$	0	0
$22$	−3.00000	−0.639602
$23$	−4.00000	−0.834058	−0.417029	−	0.908893i	$-0.636929\pi$
$23$	−4.00000	−0.834058	−0.417029	+	0.908893i	$0.636929\pi$
$24$	1.00000	0.204124
$25$	−4.00000	−0.800000
$26$	−4.00000	−0.784465
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−7.00000	−1.29987	−0.649934	−	0.759991i	$-0.725203\pi$
$29$	−7.00000	−1.29987	−0.649934	+	0.759991i	$0.725203\pi$
$30$	1.00000	0.182574
$31$	−7.00000	−1.25724	−0.628619	−	0.777714i	$-0.716379\pi$
$31$	−7.00000	−1.25724	−0.628619	+	0.777714i	$0.716379\pi$
$32$	−1.00000	−0.176777
$33$	−3.00000	−0.522233
$34$	−4.00000	−0.685994
$35$	0	0
$36$	1.00000	0.166667
$37$	−4.00000	−0.657596	−0.328798	−	0.944400i	$-0.606644\pi$
$37$	−4.00000	−0.657596	−0.328798	+	0.944400i	$0.606644\pi$
$38$	−1.00000	−0.162221
$39$	−4.00000	−0.640513
$40$	−1.00000	−0.158114
$41$	−12.0000	−1.87409	−0.937043	−	0.349215i	$-0.886448\pi$
$41$	−12.0000	−1.87409	−0.937043	+	0.349215i	$0.886448\pi$
$42$	0	0
$43$	−6.00000	−0.914991	−0.457496	−	0.889212i	$-0.651253\pi$
$43$	−6.00000	−0.914991	−0.457496	+	0.889212i	$0.651253\pi$
$44$	3.00000	0.452267
$45$	1.00000	0.149071
$46$	4.00000	0.589768
$47$	−10.0000	−1.45865	−0.729325	−	0.684167i	$-0.760166\pi$
$47$	−10.0000	−1.45865	−0.729325	+	0.684167i	$0.760166\pi$
$48$	−1.00000	−0.144338
$49$	0	0
$50$	4.00000	0.565685
$51$	−4.00000	−0.560112
$52$	4.00000	0.554700
$53$	13.0000	1.78569	0.892844	−	0.450367i	$-0.148707\pi$
$53$	13.0000	1.78569	0.892844	+	0.450367i	$0.148707\pi$
$54$	1.00000	0.136083
$55$	3.00000	0.404520
$56$	0	0
$57$	−1.00000	−0.132453
$58$	7.00000	0.919145
$59$	1.00000	0.130189	0.0650945	−	0.997879i	$-0.479265\pi$
$59$	1.00000	0.130189	0.0650945	+	0.997879i	$0.479265\pi$
$60$	−1.00000	−0.129099
$61$	−14.0000	−1.79252	−0.896258	−	0.443533i	$-0.853725\pi$
$61$	−14.0000	−1.79252	−0.896258	+	0.443533i	$0.853725\pi$
$62$	7.00000	0.889001
$63$	0	0
$64$	1.00000	0.125000
$65$	4.00000	0.496139
$66$	3.00000	0.369274
$67$	−2.00000	−0.244339	−0.122169	−	0.992509i	$-0.538985\pi$
$67$	−2.00000	−0.244339	−0.122169	+	0.992509i	$0.538985\pi$
$68$	4.00000	0.485071
$69$	4.00000	0.481543
$70$	0	0
$71$	14.0000	1.66149	0.830747	−	0.556650i	$-0.187914\pi$
$71$	14.0000	1.66149	0.830747	+	0.556650i	$0.187914\pi$
$72$	−1.00000	−0.117851
$73$	−10.0000	−1.17041	−0.585206	−	0.810885i	$-0.698986\pi$
$73$	−10.0000	−1.17041	−0.585206	+	0.810885i	$0.698986\pi$
$74$	4.00000	0.464991
$75$	4.00000	0.461880
$76$	1.00000	0.114708
$77$	0	0
$78$	4.00000	0.452911
$79$	−1.00000	−0.112509	−0.0562544	−	0.998416i	$-0.517916\pi$
$79$	−1.00000	−0.112509	−0.0562544	+	0.998416i	$0.517916\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	12.0000	1.32518
$83$	−15.0000	−1.64646	−0.823232	−	0.567705i	$-0.807831\pi$
$83$	−15.0000	−1.64646	−0.823232	+	0.567705i	$0.807831\pi$
$84$	0	0
$85$	4.00000	0.433861
$86$	6.00000	0.646997
$87$	7.00000	0.750479
$88$	−3.00000	−0.319801
$89$	6.00000	0.635999	0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000	0.635999	0.317999	+	0.948091i	$0.396989\pi$
$90$	−1.00000	−0.105409
$91$	0	0
$92$	−4.00000	−0.417029
$93$	7.00000	0.725866
$94$	10.0000	1.03142
$95$	1.00000	0.102598
$96$	1.00000	0.102062
$97$	−3.00000	−0.304604	−0.152302	−	0.988334i	$-0.548669\pi$
$97$	−3.00000	−0.304604	−0.152302	+	0.988334i	$0.548669\pi$
$98$	0	0
$99$	3.00000	0.301511
$100$	−4.00000	−0.400000
$101$	2.00000	0.199007	0.0995037	−	0.995037i	$-0.468274\pi$
$101$	2.00000	0.199007	0.0995037	+	0.995037i	$0.468274\pi$
$102$	4.00000	0.396059
$103$	16.0000	1.57653	0.788263	−	0.615338i	$-0.210980\pi$
$103$	16.0000	1.57653	0.788263	+	0.615338i	$0.210980\pi$
$104$	−4.00000	−0.392232
$105$	0	0
$106$	−13.0000	−1.26267
$107$	−15.0000	−1.45010	−0.725052	−	0.688694i	$-0.758184\pi$
$107$	−15.0000	−1.45010	−0.725052	+	0.688694i	$0.758184\pi$
$108$	−1.00000	−0.0962250
$109$	18.0000	1.72409	0.862044	−	0.506834i	$-0.169184\pi$
$109$	18.0000	1.72409	0.862044	+	0.506834i	$0.169184\pi$
$110$	−3.00000	−0.286039
$111$	4.00000	0.379663
$112$	0	0
$113$	12.0000	1.12887	0.564433	−	0.825479i	$-0.309095\pi$
$113$	12.0000	1.12887	0.564433	+	0.825479i	$0.309095\pi$
$114$	1.00000	0.0936586
$115$	−4.00000	−0.373002
$116$	−7.00000	−0.649934
$117$	4.00000	0.369800
$118$	−1.00000	−0.0920575
$119$	0	0
$120$	1.00000	0.0912871
$121$	−2.00000	−0.181818
$122$	14.0000	1.26750
$123$	12.0000	1.08200
$124$	−7.00000	−0.628619
$125$	−9.00000	−0.804984
$126$	0	0
$127$	−11.0000	−0.976092	−0.488046	−	0.872818i	$-0.662290\pi$
$127$	−11.0000	−0.976092	−0.488046	+	0.872818i	$0.662290\pi$
$128$	−1.00000	−0.0883883
$129$	6.00000	0.528271
$130$	−4.00000	−0.350823
$131$	−7.00000	−0.611593	−0.305796	−	0.952097i	$-0.598923\pi$
$131$	−7.00000	−0.611593	−0.305796	+	0.952097i	$0.598923\pi$
$132$	−3.00000	−0.261116
$133$	0	0
$134$	2.00000	0.172774
$135$	−1.00000	−0.0860663
$136$	−4.00000	−0.342997
$137$	−6.00000	−0.512615	−0.256307	−	0.966595i	$-0.582506\pi$
$137$	−6.00000	−0.512615	−0.256307	+	0.966595i	$0.582506\pi$
$138$	−4.00000	−0.340503
$139$	−14.0000	−1.18746	−0.593732	−	0.804663i	$-0.702346\pi$
$139$	−14.0000	−1.18746	−0.593732	+	0.804663i	$0.702346\pi$
$140$	0	0
$141$	10.0000	0.842152
$142$	−14.0000	−1.17485
$143$	12.0000	1.00349
$144$	1.00000	0.0833333
$145$	−7.00000	−0.581318
$146$	10.0000	0.827606
$147$	0	0
$148$	−4.00000	−0.328798
$149$	−6.00000	−0.491539	−0.245770	−	0.969328i	$-0.579041\pi$
$149$	−6.00000	−0.491539	−0.245770	+	0.969328i	$0.579041\pi$
$150$	−4.00000	−0.326599
$151$	7.00000	0.569652	0.284826	−	0.958579i	$-0.408064\pi$
$151$	7.00000	0.569652	0.284826	+	0.958579i	$0.408064\pi$
$152$	−1.00000	−0.0811107
$153$	4.00000	0.323381
$154$	0	0
$155$	−7.00000	−0.562254
$156$	−4.00000	−0.320256
$157$	4.00000	0.319235	0.159617	−	0.987179i	$-0.448974\pi$
$157$	4.00000	0.319235	0.159617	+	0.987179i	$0.448974\pi$
$158$	1.00000	0.0795557
$159$	−13.0000	−1.03097
$160$	−1.00000	−0.0790569
$161$	0	0
$162$	−1.00000	−0.0785674
$163$	−24.0000	−1.87983	−0.939913	−	0.341415i	$-0.889094\pi$
$163$	−24.0000	−1.87983	−0.939913	+	0.341415i	$0.889094\pi$
$164$	−12.0000	−0.937043
$165$	−3.00000	−0.233550
$166$	15.0000	1.16423
$167$	−2.00000	−0.154765	−0.0773823	−	0.997001i	$-0.524656\pi$
$167$	−2.00000	−0.154765	−0.0773823	+	0.997001i	$0.524656\pi$
$168$	0	0
$169$	3.00000	0.230769
$170$	−4.00000	−0.306786
$171$	1.00000	0.0764719
$172$	−6.00000	−0.457496
$173$	−10.0000	−0.760286	−0.380143	−	0.924928i	$-0.624125\pi$
$173$	−10.0000	−0.760286	−0.380143	+	0.924928i	$0.624125\pi$
$174$	−7.00000	−0.530669
$175$	0	0
$176$	3.00000	0.226134
$177$	−1.00000	−0.0751646
$178$	−6.00000	−0.449719
$179$	4.00000	0.298974	0.149487	−	0.988764i	$-0.452238\pi$
$179$	4.00000	0.298974	0.149487	+	0.988764i	$0.452238\pi$
$180$	1.00000	0.0745356
$181$	8.00000	0.594635	0.297318	−	0.954779i	$-0.403908\pi$
$181$	8.00000	0.594635	0.297318	+	0.954779i	$0.403908\pi$
$182$	0	0
$183$	14.0000	1.03491
$184$	4.00000	0.294884
$185$	−4.00000	−0.294086
$186$	−7.00000	−0.513265
$187$	12.0000	0.877527
$188$	−10.0000	−0.729325
$189$	0	0
$190$	−1.00000	−0.0725476
$191$	−8.00000	−0.578860	−0.289430	−	0.957199i	$-0.593466\pi$
$191$	−8.00000	−0.578860	−0.289430	+	0.957199i	$0.593466\pi$
$192$	−1.00000	−0.0721688
$193$	17.0000	1.22369	0.611843	−	0.790979i	$-0.290428\pi$
$193$	17.0000	1.22369	0.611843	+	0.790979i	$0.290428\pi$
$194$	3.00000	0.215387
$195$	−4.00000	−0.286446
$196$	0	0
$197$	22.0000	1.56744	0.783718	−	0.621117i	$-0.213321\pi$
$197$	22.0000	1.56744	0.783718	+	0.621117i	$0.213321\pi$
$198$	−3.00000	−0.213201
$199$	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
$201$	2.00000	0.141069
$202$	−2.00000	−0.140720
$203$	0	0
$204$	−4.00000	−0.280056
$205$	−12.0000	−0.838116
$206$	−16.0000	−1.11477
$207$	−4.00000	−0.278019
$208$	4.00000	0.277350
$209$	3.00000	0.207514
$210$	0	0
$211$	−14.0000	−0.963800	−0.481900	−	0.876226i	$-0.660053\pi$
$211$	−14.0000	−0.963800	−0.481900	+	0.876226i	$0.660053\pi$
$212$	13.0000	0.892844
$213$	−14.0000	−0.959264
$214$	15.0000	1.02538
$215$	−6.00000	−0.409197
$216$	1.00000	0.0680414
$217$	0	0
$218$	−18.0000	−1.21911
$219$	10.0000	0.675737
$220$	3.00000	0.202260
$221$	16.0000	1.07628
$222$	−4.00000	−0.268462
$223$	−29.0000	−1.94198	−0.970992	−	0.239113i	$-0.923143\pi$
$223$	−29.0000	−1.94198	−0.970992	+	0.239113i	$0.923143\pi$
$224$	0	0
$225$	−4.00000	−0.266667
$226$	−12.0000	−0.798228
$227$	23.0000	1.52656	0.763282	−	0.646066i	$-0.223587\pi$
$227$	23.0000	1.52656	0.763282	+	0.646066i	$0.223587\pi$
$228$	−1.00000	−0.0662266
$229$	−28.0000	−1.85029	−0.925146	−	0.379611i	$-0.876058\pi$
$229$	−28.0000	−1.85029	−0.925146	+	0.379611i	$0.876058\pi$
$230$	4.00000	0.263752
$231$	0	0
$232$	7.00000	0.459573
$233$	24.0000	1.57229	0.786146	−	0.618041i	$-0.212073\pi$
$233$	24.0000	1.57229	0.786146	+	0.618041i	$0.212073\pi$
$234$	−4.00000	−0.261488
$235$	−10.0000	−0.652328
$236$	1.00000	0.0650945
$237$	1.00000	0.0649570
$238$	0	0
$239$	8.00000	0.517477	0.258738	−	0.965947i	$-0.416693\pi$
$239$	8.00000	0.517477	0.258738	+	0.965947i	$0.416693\pi$
$240$	−1.00000	−0.0645497
$241$	5.00000	0.322078	0.161039	−	0.986948i	$-0.448515\pi$
$241$	5.00000	0.322078	0.161039	+	0.986948i	$0.448515\pi$
$242$	2.00000	0.128565
$243$	−1.00000	−0.0641500
$244$	−14.0000	−0.896258
$245$	0	0
$246$	−12.0000	−0.765092
$247$	4.00000	0.254514
$248$	7.00000	0.444500
$249$	15.0000	0.950586
$250$	9.00000	0.569210
$251$	5.00000	0.315597	0.157799	−	0.987471i	$-0.449560\pi$
$251$	5.00000	0.315597	0.157799	+	0.987471i	$0.449560\pi$
$252$	0	0
$253$	−12.0000	−0.754434
$254$	11.0000	0.690201
$255$	−4.00000	−0.250490
$256$	1.00000	0.0625000
$257$	−6.00000	−0.374270	−0.187135	−	0.982334i	$-0.559920\pi$
$257$	−6.00000	−0.374270	−0.187135	+	0.982334i	$0.559920\pi$
$258$	−6.00000	−0.373544
$259$	0	0
$260$	4.00000	0.248069
$261$	−7.00000	−0.433289
$262$	7.00000	0.432461
$263$	22.0000	1.35658	0.678289	−	0.734795i	$-0.262722\pi$
$263$	22.0000	1.35658	0.678289	+	0.734795i	$0.262722\pi$
$264$	3.00000	0.184637
$265$	13.0000	0.798584
$266$	0	0
$267$	−6.00000	−0.367194
$268$	−2.00000	−0.122169
$269$	3.00000	0.182913	0.0914566	−	0.995809i	$-0.470848\pi$
$269$	3.00000	0.182913	0.0914566	+	0.995809i	$0.470848\pi$
$270$	1.00000	0.0608581
$271$	−23.0000	−1.39715	−0.698575	−	0.715537i	$-0.746182\pi$
$271$	−23.0000	−1.39715	−0.698575	+	0.715537i	$0.746182\pi$
$272$	4.00000	0.242536
$273$	0	0
$274$	6.00000	0.362473
$275$	−12.0000	−0.723627
$276$	4.00000	0.240772
$277$	−28.0000	−1.68236	−0.841178	−	0.540758i	$-0.818138\pi$
$277$	−28.0000	−1.68236	−0.841178	+	0.540758i	$0.818138\pi$
$278$	14.0000	0.839664
$279$	−7.00000	−0.419079
$280$	0	0
$281$	22.0000	1.31241	0.656205	−	0.754583i	$-0.272161\pi$
$281$	22.0000	1.31241	0.656205	+	0.754583i	$0.272161\pi$
$282$	−10.0000	−0.595491
$283$	−2.00000	−0.118888	−0.0594438	−	0.998232i	$-0.518933\pi$
$283$	−2.00000	−0.118888	−0.0594438	+	0.998232i	$0.518933\pi$
$284$	14.0000	0.830747
$285$	−1.00000	−0.0592349
$286$	−12.0000	−0.709575
$287$	0	0
$288$	−1.00000	−0.0589256
$289$	−1.00000	−0.0588235
$290$	7.00000	0.411054
$291$	3.00000	0.175863
$292$	−10.0000	−0.585206
$293$	−9.00000	−0.525786	−0.262893	−	0.964825i	$-0.584677\pi$
$293$	−9.00000	−0.525786	−0.262893	+	0.964825i	$0.584677\pi$
$294$	0	0
$295$	1.00000	0.0582223
$296$	4.00000	0.232495
$297$	−3.00000	−0.174078
$298$	6.00000	0.347571
$299$	−16.0000	−0.925304
$300$	4.00000	0.230940
$301$	0	0
$302$	−7.00000	−0.402805
$303$	−2.00000	−0.114897
$304$	1.00000	0.0573539
$305$	−14.0000	−0.801638
$306$	−4.00000	−0.228665
$307$	−4.00000	−0.228292	−0.114146	−	0.993464i	$-0.536413\pi$
$307$	−4.00000	−0.228292	−0.114146	+	0.993464i	$0.536413\pi$
$308$	0	0
$309$	−16.0000	−0.910208
$310$	7.00000	0.397573
$311$	−20.0000	−1.13410	−0.567048	−	0.823685i	$-0.691915\pi$
$311$	−20.0000	−1.13410	−0.567048	+	0.823685i	$0.691915\pi$
$312$	4.00000	0.226455
$313$	23.0000	1.30004	0.650018	−	0.759918i	$-0.274761\pi$
$313$	23.0000	1.30004	0.650018	+	0.759918i	$0.274761\pi$
$314$	−4.00000	−0.225733
$315$	0	0
$316$	−1.00000	−0.0562544
$317$	9.00000	0.505490	0.252745	−	0.967533i	$-0.418667\pi$
$317$	9.00000	0.505490	0.252745	+	0.967533i	$0.418667\pi$
$318$	13.0000	0.729004
$319$	−21.0000	−1.17577
$320$	1.00000	0.0559017
$321$	15.0000	0.837218
$322$	0	0
$323$	4.00000	0.222566
$324$	1.00000	0.0555556
$325$	−16.0000	−0.887520
$326$	24.0000	1.32924
$327$	−18.0000	−0.995402
$328$	12.0000	0.662589
$329$	0	0
$330$	3.00000	0.165145
$331$	8.00000	0.439720	0.219860	−	0.975531i	$-0.429440\pi$
$331$	8.00000	0.439720	0.219860	+	0.975531i	$0.429440\pi$
$332$	−15.0000	−0.823232
$333$	−4.00000	−0.219199
$334$	2.00000	0.109435
$335$	−2.00000	−0.109272
$336$	0	0
$337$	−3.00000	−0.163420	−0.0817102	−	0.996656i	$-0.526038\pi$
$337$	−3.00000	−0.163420	−0.0817102	+	0.996656i	$0.526038\pi$
$338$	−3.00000	−0.163178
$339$	−12.0000	−0.651751
$340$	4.00000	0.216930
$341$	−21.0000	−1.13721
$342$	−1.00000	−0.0540738
$343$	0	0
$344$	6.00000	0.323498
$345$	4.00000	0.215353
$346$	10.0000	0.537603
$347$	12.0000	0.644194	0.322097	−	0.946707i	$-0.395612\pi$
$347$	12.0000	0.644194	0.322097	+	0.946707i	$0.395612\pi$
$348$	7.00000	0.375239
$349$	18.0000	0.963518	0.481759	−	0.876304i	$-0.339998\pi$
$349$	18.0000	0.963518	0.481759	+	0.876304i	$0.339998\pi$
$350$	0	0
$351$	−4.00000	−0.213504
$352$	−3.00000	−0.159901
$353$	−4.00000	−0.212899	−0.106449	−	0.994318i	$-0.533948\pi$
$353$	−4.00000	−0.212899	−0.106449	+	0.994318i	$0.533948\pi$
$354$	1.00000	0.0531494
$355$	14.0000	0.743043
$356$	6.00000	0.317999
$357$	0	0
$358$	−4.00000	−0.211407
$359$	14.0000	0.738892	0.369446	−	0.929252i	$-0.379548\pi$
$359$	14.0000	0.738892	0.369446	+	0.929252i	$0.379548\pi$
$360$	−1.00000	−0.0527046
$361$	1.00000	0.0526316
$362$	−8.00000	−0.420471
$363$	2.00000	0.104973
$364$	0	0
$365$	−10.0000	−0.523424
$366$	−14.0000	−0.731792
$367$	23.0000	1.20059	0.600295	−	0.799779i	$-0.295050\pi$
$367$	23.0000	1.20059	0.600295	+	0.799779i	$0.295050\pi$
$368$	−4.00000	−0.208514
$369$	−12.0000	−0.624695
$370$	4.00000	0.207950
$371$	0	0
$372$	7.00000	0.362933
$373$	−16.0000	−0.828449	−0.414224	−	0.910175i	$-0.635947\pi$
$373$	−16.0000	−0.828449	−0.414224	+	0.910175i	$0.635947\pi$
$374$	−12.0000	−0.620505
$375$	9.00000	0.464758
$376$	10.0000	0.515711
$377$	−28.0000	−1.44207
$378$	0	0
$379$	8.00000	0.410932	0.205466	−	0.978664i	$-0.434129\pi$
$379$	8.00000	0.410932	0.205466	+	0.978664i	$0.434129\pi$
$380$	1.00000	0.0512989
$381$	11.0000	0.563547
$382$	8.00000	0.409316
$383$	6.00000	0.306586	0.153293	−	0.988181i	$-0.451012\pi$
$383$	6.00000	0.306586	0.153293	+	0.988181i	$0.451012\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−17.0000	−0.865277
$387$	−6.00000	−0.304997
$388$	−3.00000	−0.152302
$389$	−14.0000	−0.709828	−0.354914	−	0.934899i	$-0.615490\pi$
$389$	−14.0000	−0.709828	−0.354914	+	0.934899i	$0.615490\pi$
$390$	4.00000	0.202548
$391$	−16.0000	−0.809155
$392$	0	0
$393$	7.00000	0.353103
$394$	−22.0000	−1.10834
$395$	−1.00000	−0.0503155
$396$	3.00000	0.150756
$397$	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
$399$	0	0
$400$	−4.00000	−0.200000
$401$	24.0000	1.19850	0.599251	−	0.800561i	$-0.295465\pi$
$401$	24.0000	1.19850	0.599251	+	0.800561i	$0.295465\pi$
$402$	−2.00000	−0.0997509
$403$	−28.0000	−1.39478
$404$	2.00000	0.0995037
$405$	1.00000	0.0496904
$406$	0	0
$407$	−12.0000	−0.594818
$408$	4.00000	0.198030
$409$	−3.00000	−0.148340	−0.0741702	−	0.997246i	$-0.523631\pi$
$409$	−3.00000	−0.148340	−0.0741702	+	0.997246i	$0.523631\pi$
$410$	12.0000	0.592638
$411$	6.00000	0.295958
$412$	16.0000	0.788263
$413$	0	0
$414$	4.00000	0.196589
$415$	−15.0000	−0.736321
$416$	−4.00000	−0.196116
$417$	14.0000	0.685583
$418$	−3.00000	−0.146735
$419$	0	0		−	1.00000i	$-0.5\pi$
$419$	0	0			1.00000i	$0.5\pi$
$420$	0	0
$421$	−14.0000	−0.682318	−0.341159	−	0.940006i	$-0.610819\pi$
$421$	−14.0000	−0.682318	−0.341159	+	0.940006i	$0.610819\pi$
$422$	14.0000	0.681509
$423$	−10.0000	−0.486217
$424$	−13.0000	−0.631336
$425$	−16.0000	−0.776114
$426$	14.0000	0.678302
$427$	0	0
$428$	−15.0000	−0.725052
$429$	−12.0000	−0.579365
$430$	6.00000	0.289346
$431$	0	0		−	1.00000i	$-0.5\pi$
$431$	0	0			1.00000i	$0.5\pi$
$432$	−1.00000	−0.0481125
$433$	18.0000	0.865025	0.432512	−	0.901628i	$-0.357627\pi$
$433$	18.0000	0.865025	0.432512	+	0.901628i	$0.357627\pi$
$434$	0	0
$435$	7.00000	0.335624
$436$	18.0000	0.862044
$437$	−4.00000	−0.191346
$438$	−10.0000	−0.477818
$439$	−35.0000	−1.67046	−0.835229	−	0.549902i	$-0.814665\pi$
$439$	−35.0000	−1.67046	−0.835229	+	0.549902i	$0.814665\pi$
$440$	−3.00000	−0.143019
$441$	0	0
$442$	−16.0000	−0.761042
$443$	15.0000	0.712672	0.356336	−	0.934358i	$-0.384026\pi$
$443$	15.0000	0.712672	0.356336	+	0.934358i	$0.384026\pi$
$444$	4.00000	0.189832
$445$	6.00000	0.284427
$446$	29.0000	1.37319
$447$	6.00000	0.283790
$448$	0	0
$449$	−24.0000	−1.13263	−0.566315	−	0.824189i	$-0.691631\pi$
$449$	−24.0000	−1.13263	−0.566315	+	0.824189i	$0.691631\pi$
$450$	4.00000	0.188562
$451$	−36.0000	−1.69517
$452$	12.0000	0.564433
$453$	−7.00000	−0.328889
$454$	−23.0000	−1.07944
$455$	0	0
$456$	1.00000	0.0468293
$457$	23.0000	1.07589	0.537947	−	0.842978i	$-0.319200\pi$
$457$	23.0000	1.07589	0.537947	+	0.842978i	$0.319200\pi$
$458$	28.0000	1.30835
$459$	−4.00000	−0.186704
$460$	−4.00000	−0.186501
$461$	18.0000	0.838344	0.419172	−	0.907907i	$-0.362320\pi$
$461$	18.0000	0.838344	0.419172	+	0.907907i	$0.362320\pi$
$462$	0	0
$463$	−24.0000	−1.11537	−0.557687	−	0.830051i	$-0.688311\pi$
$463$	−24.0000	−1.11537	−0.557687	+	0.830051i	$0.688311\pi$
$464$	−7.00000	−0.324967
$465$	7.00000	0.324617
$466$	−24.0000	−1.11178
$467$	20.0000	0.925490	0.462745	−	0.886492i	$-0.346865\pi$
$467$	20.0000	0.925490	0.462745	+	0.886492i	$0.346865\pi$
$468$	4.00000	0.184900
$469$	0	0
$470$	10.0000	0.461266
$471$	−4.00000	−0.184310
$472$	−1.00000	−0.0460287
$473$	−18.0000	−0.827641
$474$	−1.00000	−0.0459315
$475$	−4.00000	−0.183533
$476$	0	0
$477$	13.0000	0.595229
$478$	−8.00000	−0.365911
$479$	−22.0000	−1.00521	−0.502603	−	0.864517i	$-0.667624\pi$
$479$	−22.0000	−1.00521	−0.502603	+	0.864517i	$0.667624\pi$
$480$	1.00000	0.0456435
$481$	−16.0000	−0.729537
$482$	−5.00000	−0.227744
$483$	0	0
$484$	−2.00000	−0.0909091
$485$	−3.00000	−0.136223
$486$	1.00000	0.0453609
$487$	−7.00000	−0.317200	−0.158600	−	0.987343i	$-0.550698\pi$
$487$	−7.00000	−0.317200	−0.158600	+	0.987343i	$0.550698\pi$
$488$	14.0000	0.633750
$489$	24.0000	1.08532
$490$	0	0
$491$	−9.00000	−0.406164	−0.203082	−	0.979162i	$-0.565096\pi$
$491$	−9.00000	−0.406164	−0.203082	+	0.979162i	$0.565096\pi$
$492$	12.0000	0.541002
$493$	−28.0000	−1.26106
$494$	−4.00000	−0.179969
$495$	3.00000	0.134840
$496$	−7.00000	−0.314309
$497$	0	0
$498$	−15.0000	−0.672166
$499$	−30.0000	−1.34298	−0.671492	−	0.741012i	$-0.734346\pi$
$499$	−30.0000	−1.34298	−0.671492	+	0.741012i	$0.734346\pi$
$500$	−9.00000	−0.402492
$501$	2.00000	0.0893534
$502$	−5.00000	−0.223161
$503$	−16.0000	−0.713405	−0.356702	−	0.934218i	$-0.616099\pi$
$503$	−16.0000	−0.713405	−0.356702	+	0.934218i	$0.616099\pi$
$504$	0	0
$505$	2.00000	0.0889988
$506$	12.0000	0.533465
$507$	−3.00000	−0.133235
$508$	−11.0000	−0.488046
$509$	−21.0000	−0.930809	−0.465404	−	0.885098i	$-0.654091\pi$
$509$	−21.0000	−0.930809	−0.465404	+	0.885098i	$0.654091\pi$
$510$	4.00000	0.177123
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	−1.00000	−0.0441511
$514$	6.00000	0.264649
$515$	16.0000	0.705044
$516$	6.00000	0.264135
$517$	−30.0000	−1.31940
$518$	0	0
$519$	10.0000	0.438951
$520$	−4.00000	−0.175412
$521$	10.0000	0.438108	0.219054	−	0.975713i	$-0.429703\pi$
$521$	10.0000	0.438108	0.219054	+	0.975713i	$0.429703\pi$
$522$	7.00000	0.306382
$523$	−16.0000	−0.699631	−0.349816	−	0.936819i	$-0.613756\pi$
$523$	−16.0000	−0.699631	−0.349816	+	0.936819i	$0.613756\pi$
$524$	−7.00000	−0.305796
$525$	0	0
$526$	−22.0000	−0.959246
$527$	−28.0000	−1.21970
$528$	−3.00000	−0.130558
$529$	−7.00000	−0.304348
$530$	−13.0000	−0.564684
$531$	1.00000	0.0433963
$532$	0	0
$533$	−48.0000	−2.07911
$534$	6.00000	0.259645
$535$	−15.0000	−0.648507
$536$	2.00000	0.0863868
$537$	−4.00000	−0.172613
$538$	−3.00000	−0.129339
$539$	0	0
$540$	−1.00000	−0.0430331
$541$	22.0000	0.945854	0.472927	−	0.881102i	$-0.343197\pi$
$541$	22.0000	0.945854	0.472927	+	0.881102i	$0.343197\pi$
$542$	23.0000	0.987935
$543$	−8.00000	−0.343313
$544$	−4.00000	−0.171499
$545$	18.0000	0.771035
$546$	0	0
$547$	28.0000	1.19719	0.598597	−	0.801050i	$-0.295725\pi$
$547$	28.0000	1.19719	0.598597	+	0.801050i	$0.295725\pi$
$548$	−6.00000	−0.256307
$549$	−14.0000	−0.597505
$550$	12.0000	0.511682
$551$	−7.00000	−0.298210
$552$	−4.00000	−0.170251
$553$	0	0
$554$	28.0000	1.18961
$555$	4.00000	0.169791
$556$	−14.0000	−0.593732
$557$	23.0000	0.974541	0.487271	−	0.873251i	$-0.337993\pi$
$557$	23.0000	0.974541	0.487271	+	0.873251i	$0.337993\pi$
$558$	7.00000	0.296334
$559$	−24.0000	−1.01509
$560$	0	0
$561$	−12.0000	−0.506640
$562$	−22.0000	−0.928014
$563$	−35.0000	−1.47507	−0.737537	−	0.675307i	$-0.764011\pi$
$563$	−35.0000	−1.47507	−0.737537	+	0.675307i	$0.764011\pi$
$564$	10.0000	0.421076
$565$	12.0000	0.504844
$566$	2.00000	0.0840663
$567$	0	0
$568$	−14.0000	−0.587427
$569$	−28.0000	−1.17382	−0.586911	−	0.809652i	$-0.699656\pi$
$569$	−28.0000	−1.17382	−0.586911	+	0.809652i	$0.699656\pi$
$570$	1.00000	0.0418854
$571$	−22.0000	−0.920671	−0.460336	−	0.887745i	$-0.652271\pi$
$571$	−22.0000	−0.920671	−0.460336	+	0.887745i	$0.652271\pi$
$572$	12.0000	0.501745
$573$	8.00000	0.334205
$574$	0	0
$575$	16.0000	0.667246
$576$	1.00000	0.0416667
$577$	17.0000	0.707719	0.353860	−	0.935299i	$-0.384869\pi$
$577$	17.0000	0.707719	0.353860	+	0.935299i	$0.384869\pi$
$578$	1.00000	0.0415945
$579$	−17.0000	−0.706496
$580$	−7.00000	−0.290659
$581$	0	0
$582$	−3.00000	−0.124354
$583$	39.0000	1.61521
$584$	10.0000	0.413803
$585$	4.00000	0.165380
$586$	9.00000	0.371787
$587$	27.0000	1.11441	0.557205	−	0.830375i	$-0.311874\pi$
$587$	27.0000	1.11441	0.557205	+	0.830375i	$0.311874\pi$
$588$	0	0
$589$	−7.00000	−0.288430
$590$	−1.00000	−0.0411693
$591$	−22.0000	−0.904959
$592$	−4.00000	−0.164399
$593$	32.0000	1.31408	0.657041	−	0.753855i	$-0.271808\pi$
$593$	32.0000	1.31408	0.657041	+	0.753855i	$0.271808\pi$
$594$	3.00000	0.123091
$595$	0	0
$596$	−6.00000	−0.245770
$597$	−4.00000	−0.163709
$598$	16.0000	0.654289
$599$	26.0000	1.06233	0.531166	−	0.847268i	$-0.321754\pi$
$599$	26.0000	1.06233	0.531166	+	0.847268i	$0.321754\pi$
$600$	−4.00000	−0.163299
$601$	−31.0000	−1.26452	−0.632258	−	0.774758i	$-0.717872\pi$
$601$	−31.0000	−1.26452	−0.632258	+	0.774758i	$0.717872\pi$
$602$	0	0
$603$	−2.00000	−0.0814463
$604$	7.00000	0.284826
$605$	−2.00000	−0.0813116
$606$	2.00000	0.0812444
$607$	−9.00000	−0.365299	−0.182649	−	0.983178i	$-0.558467\pi$
$607$	−9.00000	−0.365299	−0.182649	+	0.983178i	$0.558467\pi$
$608$	−1.00000	−0.0405554
$609$	0	0
$610$	14.0000	0.566843
$611$	−40.0000	−1.61823
$612$	4.00000	0.161690
$613$	−28.0000	−1.13091	−0.565455	−	0.824779i	$-0.691299\pi$
$613$	−28.0000	−1.13091	−0.565455	+	0.824779i	$0.691299\pi$
$614$	4.00000	0.161427
$615$	12.0000	0.483887
$616$	0	0
$617$	−2.00000	−0.0805170	−0.0402585	−	0.999189i	$-0.512818\pi$
$617$	−2.00000	−0.0805170	−0.0402585	+	0.999189i	$0.512818\pi$
$618$	16.0000	0.643614
$619$	−6.00000	−0.241160	−0.120580	−	0.992704i	$-0.538475\pi$
$619$	−6.00000	−0.241160	−0.120580	+	0.992704i	$0.538475\pi$
$620$	−7.00000	−0.281127
$621$	4.00000	0.160514
$622$	20.0000	0.801927
$623$	0	0
$624$	−4.00000	−0.160128
$625$	11.0000	0.440000
$626$	−23.0000	−0.919265
$627$	−3.00000	−0.119808
$628$	4.00000	0.159617
$629$	−16.0000	−0.637962
$630$	0	0
$631$	−3.00000	−0.119428	−0.0597141	−	0.998216i	$-0.519019\pi$
$631$	−3.00000	−0.119428	−0.0597141	+	0.998216i	$0.519019\pi$
$632$	1.00000	0.0397779
$633$	14.0000	0.556450
$634$	−9.00000	−0.357436
$635$	−11.0000	−0.436522
$636$	−13.0000	−0.515484
$637$	0	0
$638$	21.0000	0.831398
$639$	14.0000	0.553831
$640$	−1.00000	−0.0395285
$641$	−10.0000	−0.394976	−0.197488	−	0.980305i	$-0.563278\pi$
$641$	−10.0000	−0.394976	−0.197488	+	0.980305i	$0.563278\pi$
$642$	−15.0000	−0.592003
$643$	6.00000	0.236617	0.118308	−	0.992977i	$-0.462253\pi$
$643$	6.00000	0.236617	0.118308	+	0.992977i	$0.462253\pi$
$644$	0	0
$645$	6.00000	0.236250
$646$	−4.00000	−0.157378
$647$	30.0000	1.17942	0.589711	−	0.807614i	$-0.299242\pi$
$647$	30.0000	1.17942	0.589711	+	0.807614i	$0.299242\pi$
$648$	−1.00000	−0.0392837
$649$	3.00000	0.117760
$650$	16.0000	0.627572
$651$	0	0
$652$	−24.0000	−0.939913
$653$	7.00000	0.273931	0.136966	−	0.990576i	$-0.456265\pi$
$653$	7.00000	0.273931	0.136966	+	0.990576i	$0.456265\pi$
$654$	18.0000	0.703856
$655$	−7.00000	−0.273513
$656$	−12.0000	−0.468521
$657$	−10.0000	−0.390137
$658$	0	0
$659$	0	0		−	1.00000i	$-0.5\pi$
$659$	0	0			1.00000i	$0.5\pi$
$660$	−3.00000	−0.116775
$661$	−42.0000	−1.63361	−0.816805	−	0.576913i	$-0.804257\pi$
$661$	−42.0000	−1.63361	−0.816805	+	0.576913i	$0.804257\pi$
$662$	−8.00000	−0.310929
$663$	−16.0000	−0.621389
$664$	15.0000	0.582113
$665$	0	0
$666$	4.00000	0.154997
$667$	28.0000	1.08416
$668$	−2.00000	−0.0773823
$669$	29.0000	1.12120
$670$	2.00000	0.0772667
$671$	−42.0000	−1.62139
$672$	0	0
$673$	25.0000	0.963679	0.481840	−	0.876259i	$-0.339969\pi$
$673$	25.0000	0.963679	0.481840	+	0.876259i	$0.339969\pi$
$674$	3.00000	0.115556
$675$	4.00000	0.153960
$676$	3.00000	0.115385
$677$	9.00000	0.345898	0.172949	−	0.984931i	$-0.444670\pi$
$677$	9.00000	0.345898	0.172949	+	0.984931i	$0.444670\pi$
$678$	12.0000	0.460857
$679$	0	0
$680$	−4.00000	−0.153393
$681$	−23.0000	−0.881362
$682$	21.0000	0.804132
$683$	−19.0000	−0.727015	−0.363507	−	0.931591i	$-0.618421\pi$
$683$	−19.0000	−0.727015	−0.363507	+	0.931591i	$0.618421\pi$
$684$	1.00000	0.0382360
$685$	−6.00000	−0.229248
$686$	0	0
$687$	28.0000	1.06827
$688$	−6.00000	−0.228748
$689$	52.0000	1.98104
$690$	−4.00000	−0.152277
$691$	4.00000	0.152167	0.0760836	−	0.997101i	$-0.475758\pi$
$691$	4.00000	0.152167	0.0760836	+	0.997101i	$0.475758\pi$
$692$	−10.0000	−0.380143
$693$	0	0
$694$	−12.0000	−0.455514
$695$	−14.0000	−0.531050
$696$	−7.00000	−0.265334
$697$	−48.0000	−1.81813
$698$	−18.0000	−0.681310
$699$	−24.0000	−0.907763
$700$	0	0
$701$	21.0000	0.793159	0.396580	−	0.918000i	$-0.370197\pi$
$701$	21.0000	0.793159	0.396580	+	0.918000i	$0.370197\pi$
$702$	4.00000	0.150970
$703$	−4.00000	−0.150863
$704$	3.00000	0.113067
$705$	10.0000	0.376622
$706$	4.00000	0.150542
$707$	0	0
$708$	−1.00000	−0.0375823
$709$	34.0000	1.27690	0.638448	−	0.769665i	$-0.279577\pi$
$709$	34.0000	1.27690	0.638448	+	0.769665i	$0.279577\pi$
$710$	−14.0000	−0.525411
$711$	−1.00000	−0.0375029
$712$	−6.00000	−0.224860
$713$	28.0000	1.04861
$714$	0	0
$715$	12.0000	0.448775
$716$	4.00000	0.149487
$717$	−8.00000	−0.298765
$718$	−14.0000	−0.522475
$719$	42.0000	1.56634	0.783168	−	0.621810i	$-0.213603\pi$
$719$	42.0000	1.56634	0.783168	+	0.621810i	$0.213603\pi$
$720$	1.00000	0.0372678
$721$	0	0
$722$	−1.00000	−0.0372161
$723$	−5.00000	−0.185952
$724$	8.00000	0.297318
$725$	28.0000	1.03989
$726$	−2.00000	−0.0742270
$727$	−7.00000	−0.259616	−0.129808	−	0.991539i	$-0.541436\pi$
$727$	−7.00000	−0.259616	−0.129808	+	0.991539i	$0.541436\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	10.0000	0.370117
$731$	−24.0000	−0.887672
$732$	14.0000	0.517455
$733$	30.0000	1.10808	0.554038	−	0.832492i	$-0.313086\pi$
$733$	30.0000	1.10808	0.554038	+	0.832492i	$0.313086\pi$
$734$	−23.0000	−0.848945
$735$	0	0
$736$	4.00000	0.147442
$737$	−6.00000	−0.221013
$738$	12.0000	0.441726
$739$	−26.0000	−0.956425	−0.478213	−	0.878244i	$-0.658715\pi$
$739$	−26.0000	−0.956425	−0.478213	+	0.878244i	$0.658715\pi$
$740$	−4.00000	−0.147043
$741$	−4.00000	−0.146944
$742$	0	0
$743$	34.0000	1.24734	0.623670	−	0.781688i	$-0.285641\pi$
$743$	34.0000	1.24734	0.623670	+	0.781688i	$0.285641\pi$
$744$	−7.00000	−0.256632
$745$	−6.00000	−0.219823
$746$	16.0000	0.585802
$747$	−15.0000	−0.548821
$748$	12.0000	0.438763
$749$	0	0
$750$	−9.00000	−0.328634
$751$	−23.0000	−0.839282	−0.419641	−	0.907690i	$-0.637844\pi$
$751$	−23.0000	−0.839282	−0.419641	+	0.907690i	$0.637844\pi$
$752$	−10.0000	−0.364662
$753$	−5.00000	−0.182210
$754$	28.0000	1.01970
$755$	7.00000	0.254756
$756$	0	0
$757$	34.0000	1.23575	0.617876	−	0.786276i	$-0.287994\pi$
$757$	34.0000	1.23575	0.617876	+	0.786276i	$0.287994\pi$
$758$	−8.00000	−0.290573
$759$	12.0000	0.435572
$760$	−1.00000	−0.0362738
$761$	−28.0000	−1.01500	−0.507500	−	0.861652i	$-0.669430\pi$
$761$	−28.0000	−1.01500	−0.507500	+	0.861652i	$0.669430\pi$
$762$	−11.0000	−0.398488
$763$	0	0
$764$	−8.00000	−0.289430
$765$	4.00000	0.144620
$766$	−6.00000	−0.216789
$767$	4.00000	0.144432
$768$	−1.00000	−0.0360844
$769$	−45.0000	−1.62274	−0.811371	−	0.584532i	$-0.801278\pi$
$769$	−45.0000	−1.62274	−0.811371	+	0.584532i	$0.801278\pi$
$770$	0	0
$771$	6.00000	0.216085
$772$	17.0000	0.611843
$773$	−6.00000	−0.215805	−0.107903	−	0.994161i	$-0.534413\pi$
$773$	−6.00000	−0.215805	−0.107903	+	0.994161i	$0.534413\pi$
$774$	6.00000	0.215666
$775$	28.0000	1.00579
$776$	3.00000	0.107694
$777$	0	0
$778$	14.0000	0.501924
$779$	−12.0000	−0.429945
$780$	−4.00000	−0.143223
$781$	42.0000	1.50288
$782$	16.0000	0.572159
$783$	7.00000	0.250160
$784$	0	0
$785$	4.00000	0.142766
$786$	−7.00000	−0.249682
$787$	46.0000	1.63972	0.819861	−	0.572562i	$-0.194050\pi$
$787$	46.0000	1.63972	0.819861	+	0.572562i	$0.194050\pi$
$788$	22.0000	0.783718
$789$	−22.0000	−0.783221
$790$	1.00000	0.0355784
$791$	0	0
$792$	−3.00000	−0.106600
$793$	−56.0000	−1.98862
$794$	−20.0000	−0.709773
$795$	−13.0000	−0.461062
$796$	4.00000	0.141776
$797$	−23.0000	−0.814702	−0.407351	−	0.913272i	$-0.633547\pi$
$797$	−23.0000	−0.814702	−0.407351	+	0.913272i	$0.633547\pi$
$798$	0	0
$799$	−40.0000	−1.41510
$800$	4.00000	0.141421
$801$	6.00000	0.212000
$802$	−24.0000	−0.847469
$803$	−30.0000	−1.05868
$804$	2.00000	0.0705346
$805$	0	0
$806$	28.0000	0.986258
$807$	−3.00000	−0.105605
$808$	−2.00000	−0.0703598
$809$	−44.0000	−1.54696	−0.773479	−	0.633822i	$-0.781485\pi$
$809$	−44.0000	−1.54696	−0.773479	+	0.633822i	$0.781485\pi$
$810$	−1.00000	−0.0351364
$811$	10.0000	0.351147	0.175574	−	0.984466i	$-0.443822\pi$
$811$	10.0000	0.351147	0.175574	+	0.984466i	$0.443822\pi$
$812$	0	0
$813$	23.0000	0.806645
$814$	12.0000	0.420600
$815$	−24.0000	−0.840683
$816$	−4.00000	−0.140028
$817$	−6.00000	−0.209913
$818$	3.00000	0.104893
$819$	0	0
$820$	−12.0000	−0.419058
$821$	9.00000	0.314102	0.157051	−	0.987590i	$-0.449801\pi$
$821$	9.00000	0.314102	0.157051	+	0.987590i	$0.449801\pi$
$822$	−6.00000	−0.209274
$823$	−24.0000	−0.836587	−0.418294	−	0.908312i	$-0.637372\pi$
$823$	−24.0000	−0.836587	−0.418294	+	0.908312i	$0.637372\pi$
$824$	−16.0000	−0.557386
$825$	12.0000	0.417786
$826$	0	0
$827$	11.0000	0.382507	0.191254	−	0.981541i	$-0.438745\pi$
$827$	11.0000	0.382507	0.191254	+	0.981541i	$0.438745\pi$
$828$	−4.00000	−0.139010
$829$	−28.0000	−0.972480	−0.486240	−	0.873825i	$-0.661632\pi$
$829$	−28.0000	−0.972480	−0.486240	+	0.873825i	$0.661632\pi$
$830$	15.0000	0.520658
$831$	28.0000	0.971309
$832$	4.00000	0.138675
$833$	0	0
$834$	−14.0000	−0.484780
$835$	−2.00000	−0.0692129
$836$	3.00000	0.103757
$837$	7.00000	0.241955
$838$	0	0
$839$	−36.0000	−1.24286	−0.621429	−	0.783470i	$-0.713448\pi$
$839$	−36.0000	−1.24286	−0.621429	+	0.783470i	$0.713448\pi$
$840$	0	0
$841$	20.0000	0.689655
$842$	14.0000	0.482472
$843$	−22.0000	−0.757720
$844$	−14.0000	−0.481900
$845$	3.00000	0.103203
$846$	10.0000	0.343807
$847$	0	0
$848$	13.0000	0.446422
$849$	2.00000	0.0686398
$850$	16.0000	0.548795
$851$	16.0000	0.548473
$852$	−14.0000	−0.479632
$853$	−34.0000	−1.16414	−0.582069	−	0.813139i	$-0.697757\pi$
$853$	−34.0000	−1.16414	−0.582069	+	0.813139i	$0.697757\pi$
$854$	0	0
$855$	1.00000	0.0341993
$856$	15.0000	0.512689
$857$	18.0000	0.614868	0.307434	−	0.951569i	$-0.400530\pi$
$857$	18.0000	0.614868	0.307434	+	0.951569i	$0.400530\pi$
$858$	12.0000	0.409673
$859$	14.0000	0.477674	0.238837	−	0.971060i	$-0.423234\pi$
$859$	14.0000	0.477674	0.238837	+	0.971060i	$0.423234\pi$
$860$	−6.00000	−0.204598
$861$	0	0
$862$	0	0
$863$	42.0000	1.42970	0.714848	−	0.699280i	$-0.246496\pi$
$863$	42.0000	1.42970	0.714848	+	0.699280i	$0.246496\pi$
$864$	1.00000	0.0340207
$865$	−10.0000	−0.340010
$866$	−18.0000	−0.611665
$867$	1.00000	0.0339618
$868$	0	0
$869$	−3.00000	−0.101768
$870$	−7.00000	−0.237322
$871$	−8.00000	−0.271070
$872$	−18.0000	−0.609557
$873$	−3.00000	−0.101535
$874$	4.00000	0.135302
$875$	0	0
$876$	10.0000	0.337869
$877$	12.0000	0.405211	0.202606	−	0.979260i	$-0.435059\pi$
$877$	12.0000	0.405211	0.202606	+	0.979260i	$0.435059\pi$
$878$	35.0000	1.18119
$879$	9.00000	0.303562
$880$	3.00000	0.101130
$881$	−18.0000	−0.606435	−0.303218	−	0.952921i	$-0.598061\pi$
$881$	−18.0000	−0.606435	−0.303218	+	0.952921i	$0.598061\pi$
$882$	0	0
$883$	36.0000	1.21150	0.605748	−	0.795656i	$-0.292874\pi$
$883$	36.0000	1.21150	0.605748	+	0.795656i	$0.292874\pi$
$884$	16.0000	0.538138
$885$	−1.00000	−0.0336146
$886$	−15.0000	−0.503935
$887$	−36.0000	−1.20876	−0.604381	−	0.796696i	$-0.706579\pi$
$887$	−36.0000	−1.20876	−0.604381	+	0.796696i	$0.706579\pi$
$888$	−4.00000	−0.134231
$889$	0	0
$890$	−6.00000	−0.201120
$891$	3.00000	0.100504
$892$	−29.0000	−0.970992
$893$	−10.0000	−0.334637
$894$	−6.00000	−0.200670
$895$	4.00000	0.133705
$896$	0	0
$897$	16.0000	0.534224
$898$	24.0000	0.800890
$899$	49.0000	1.63424
$900$	−4.00000	−0.133333
$901$	52.0000	1.73237
$902$	36.0000	1.19867
$903$	0	0
$904$	−12.0000	−0.399114
$905$	8.00000	0.265929
$906$	7.00000	0.232559
$907$	28.0000	0.929725	0.464862	−	0.885383i	$-0.346104\pi$
$907$	28.0000	0.929725	0.464862	+	0.885383i	$0.346104\pi$
$908$	23.0000	0.763282
$909$	2.00000	0.0663358
$910$	0	0
$911$	−50.0000	−1.65657	−0.828287	−	0.560304i	$-0.810684\pi$
$911$	−50.0000	−1.65657	−0.828287	+	0.560304i	$0.810684\pi$
$912$	−1.00000	−0.0331133
$913$	−45.0000	−1.48928
$914$	−23.0000	−0.760772
$915$	14.0000	0.462826
$916$	−28.0000	−0.925146
$917$	0	0
$918$	4.00000	0.132020
$919$	0	0		−	1.00000i	$-0.5\pi$
$919$	0	0			1.00000i	$0.5\pi$
$920$	4.00000	0.131876
$921$	4.00000	0.131804
$922$	−18.0000	−0.592798
$923$	56.0000	1.84326
$924$	0	0
$925$	16.0000	0.526077
$926$	24.0000	0.788689
$927$	16.0000	0.525509
$928$	7.00000	0.229786
$929$	10.0000	0.328089	0.164045	−	0.986453i	$-0.447546\pi$
$929$	10.0000	0.328089	0.164045	+	0.986453i	$0.447546\pi$
$930$	−7.00000	−0.229539
$931$	0	0
$932$	24.0000	0.786146
$933$	20.0000	0.654771
$934$	−20.0000	−0.654420
$935$	12.0000	0.392442
$936$	−4.00000	−0.130744
$937$	37.0000	1.20874	0.604369	−	0.796705i	$-0.293425\pi$
$937$	37.0000	1.20874	0.604369	+	0.796705i	$0.293425\pi$
$938$	0	0
$939$	−23.0000	−0.750577
$940$	−10.0000	−0.326164
$941$	1.00000	0.0325991	0.0162995	−	0.999867i	$-0.494811\pi$
$941$	1.00000	0.0325991	0.0162995	+	0.999867i	$0.494811\pi$
$942$	4.00000	0.130327
$943$	48.0000	1.56310
$944$	1.00000	0.0325472
$945$	0	0
$946$	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	$0.215272\pi$
$948$	1.00000	0.0324785
$949$	−40.0000	−1.29845
$950$	4.00000	0.129777
$951$	−9.00000	−0.291845
$952$	0	0
$953$	26.0000	0.842223	0.421111	−	0.907009i	$-0.361640\pi$
$953$	26.0000	0.842223	0.421111	+	0.907009i	$0.361640\pi$
$954$	−13.0000	−0.420891
$955$	−8.00000	−0.258874
$956$	8.00000	0.258738
$957$	21.0000	0.678834
$958$	22.0000	0.710788
$959$	0	0
$960$	−1.00000	−0.0322749
$961$	18.0000	0.580645
$962$	16.0000	0.515861
$963$	−15.0000	−0.483368
$964$	5.00000	0.161039
$965$	17.0000	0.547249
$966$	0	0
$967$	43.0000	1.38279	0.691393	−	0.722478i	$-0.256997\pi$
$967$	43.0000	1.38279	0.691393	+	0.722478i	$0.256997\pi$
$968$	2.00000	0.0642824
$969$	−4.00000	−0.128499
$970$	3.00000	0.0963242
$971$	−21.0000	−0.673922	−0.336961	−	0.941519i	$-0.609399\pi$
$971$	−21.0000	−0.673922	−0.336961	+	0.941519i	$0.609399\pi$
$972$	−1.00000	−0.0320750
$973$	0	0
$974$	7.00000	0.224294
$975$	16.0000	0.512410
$976$	−14.0000	−0.448129
$977$	−54.0000	−1.72761	−0.863807	−	0.503824i	$-0.831926\pi$
$977$	−54.0000	−1.72761	−0.863807	+	0.503824i	$0.831926\pi$
$978$	−24.0000	−0.767435
$979$	18.0000	0.575282
$980$	0	0
$981$	18.0000	0.574696
$982$	9.00000	0.287202
$983$	−4.00000	−0.127580	−0.0637901	−	0.997963i	$-0.520319\pi$
$983$	−4.00000	−0.127580	−0.0637901	+	0.997963i	$0.520319\pi$
$984$	−12.0000	−0.382546
$985$	22.0000	0.700978
$986$	28.0000	0.891702
$987$	0	0
$988$	4.00000	0.127257
$989$	24.0000	0.763156
$990$	−3.00000	−0.0953463
$991$	−21.0000	−0.667087	−0.333543	−	0.942735i	$-0.608244\pi$
$991$	−21.0000	−0.667087	−0.333543	+	0.942735i	$0.608244\pi$
$992$	7.00000	0.222250
$993$	−8.00000	−0.253872
$994$	0	0
$995$	4.00000	0.126809
$996$	15.0000	0.475293
$997$	−46.0000	−1.45683	−0.728417	−	0.685134i	$-0.759744\pi$
$997$	−46.0000	−1.45683	−0.728417	+	0.685134i	$0.759744\pi$
$998$	30.0000	0.949633
$999$	4.00000	0.126554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5586.2.a.h.1.1		1
7.3	odd	6		798.2.j.e.457.1	✓	2
7.5	odd	6		798.2.j.e.571.1	yes	2
7.6	odd	2		5586.2.a.m.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.j.e.457.1	✓	2	7.3	odd	6
798.2.j.e.571.1	yes	2	7.5	odd	6
5586.2.a.h.1.1		1	1.1	even	1	trivial
5586.2.a.m.1.1		1	7.6	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:	\( N \)	\(=\)	\( 5586 = 2 \cdot 3 \cdot 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5586.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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