LMFDB - Embedded newform 5586.2.a.s.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:	$0$
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)

$f(q)$

$=$

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

\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -1.00000 q^{11} +1.00000 q^{12} +4.00000 q^{13} +1.00000 q^{15} +1.00000 q^{16} -2.00000 q^{17} -1.00000 q^{18} -1.00000 q^{19} +1.00000 q^{20} +1.00000 q^{22} +2.00000 q^{23} -1.00000 q^{24} -4.00000 q^{25} -4.00000 q^{26} +1.00000 q^{27} +5.00000 q^{29} -1.00000 q^{30} -5.00000 q^{31} -1.00000 q^{32} -1.00000 q^{33} +2.00000 q^{34} +1.00000 q^{36} -6.00000 q^{37} +1.00000 q^{38} +4.00000 q^{39} -1.00000 q^{40} +2.00000 q^{41} +8.00000 q^{43} -1.00000 q^{44} +1.00000 q^{45} -2.00000 q^{46} +10.0000 q^{47} +1.00000 q^{48} +4.00000 q^{50} -2.00000 q^{51} +4.00000 q^{52} +13.0000 q^{53} -1.00000 q^{54} -1.00000 q^{55} -1.00000 q^{57} -5.00000 q^{58} -3.00000 q^{59} +1.00000 q^{60} +10.0000 q^{61} +5.00000 q^{62} +1.00000 q^{64} +4.00000 q^{65} +1.00000 q^{66} +10.0000 q^{67} -2.00000 q^{68} +2.00000 q^{69} -4.00000 q^{71} -1.00000 q^{72} -14.0000 q^{73} +6.00000 q^{74} -4.00000 q^{75} -1.00000 q^{76} -4.00000 q^{78} -5.00000 q^{79} +1.00000 q^{80} +1.00000 q^{81} -2.00000 q^{82} +3.00000 q^{83} -2.00000 q^{85} -8.00000 q^{86} +5.00000 q^{87} +1.00000 q^{88} -4.00000 q^{89} -1.00000 q^{90} +2.00000 q^{92} -5.00000 q^{93} -10.0000 q^{94} -1.00000 q^{95} -1.00000 q^{96} +13.0000 q^{97} -1.00000 q^{99} +O(q^{100})\)

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
$5$	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
$11$	−1.00000	−0.301511	−0.150756	−	0.988571i	$-0.548171\pi$
$11$	−1.00000	−0.301511	−0.150756	+	0.988571i	$0.548171\pi$
$12$	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
$17$	−2.00000	−0.485071	−0.242536	−	0.970143i	$-0.577979\pi$
$17$	−2.00000	−0.485071	−0.242536	+	0.970143i	$0.577979\pi$
$18$	−1.00000	−0.235702
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	1.00000	0.223607
$21$	0	0
$22$	1.00000	0.213201
$23$	2.00000	0.417029	0.208514	−	0.978019i	$-0.433137\pi$
$23$	2.00000	0.417029	0.208514	+	0.978019i	$0.433137\pi$
$24$	−1.00000	−0.204124
$25$	−4.00000	−0.800000
$26$	−4.00000	−0.784465
$27$	1.00000	0.192450
$28$	0	0
$29$	5.00000	0.928477	0.464238	−	0.885710i	$-0.346328\pi$
$29$	5.00000	0.928477	0.464238	+	0.885710i	$0.346328\pi$
$30$	−1.00000	−0.182574
$31$	−5.00000	−0.898027	−0.449013	−	0.893525i	$-0.648224\pi$
$31$	−5.00000	−0.898027	−0.449013	+	0.893525i	$0.648224\pi$
$32$	−1.00000	−0.176777
$33$	−1.00000	−0.174078
$34$	2.00000	0.342997
$35$	0	0
$36$	1.00000	0.166667
$37$	−6.00000	−0.986394	−0.493197	−	0.869918i	$-0.664172\pi$
$37$	−6.00000	−0.986394	−0.493197	+	0.869918i	$0.664172\pi$
$38$	1.00000	0.162221
$39$	4.00000	0.640513
$40$	−1.00000	−0.158114
$41$	2.00000	0.312348	0.156174	−	0.987730i	$-0.450084\pi$
$41$	2.00000	0.312348	0.156174	+	0.987730i	$0.450084\pi$
$42$	0	0
$43$	8.00000	1.21999	0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000	1.21999	0.609994	+	0.792406i	$0.291172\pi$
$44$	−1.00000	−0.150756
$45$	1.00000	0.149071
$46$	−2.00000	−0.294884
$47$	10.0000	1.45865	0.729325	−	0.684167i	$-0.239834\pi$
$47$	10.0000	1.45865	0.729325	+	0.684167i	$0.239834\pi$
$48$	1.00000	0.144338
$49$	0	0
$50$	4.00000	0.565685
$51$	−2.00000	−0.280056
$52$	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
$55$	−1.00000	−0.134840
$56$	0	0
$57$	−1.00000	−0.132453
$58$	−5.00000	−0.656532
$59$	−3.00000	−0.390567	−0.195283	−	0.980747i	$-0.562563\pi$
$59$	−3.00000	−0.390567	−0.195283	+	0.980747i	$0.562563\pi$
$60$	1.00000	0.129099
$61$	10.0000	1.28037	0.640184	−	0.768221i	$-0.278858\pi$
$61$	10.0000	1.28037	0.640184	+	0.768221i	$0.278858\pi$
$62$	5.00000	0.635001
$63$	0	0
$64$	1.00000	0.125000
$65$	4.00000	0.496139
$66$	1.00000	0.123091
$67$	10.0000	1.22169	0.610847	−	0.791748i	$-0.290829\pi$
$67$	10.0000	1.22169	0.610847	+	0.791748i	$0.290829\pi$
$68$	−2.00000	−0.242536
$69$	2.00000	0.240772
$70$	0	0
$71$	−4.00000	−0.474713	−0.237356	−	0.971423i	$-0.576281\pi$
$71$	−4.00000	−0.474713	−0.237356	+	0.971423i	$0.576281\pi$
$72$	−1.00000	−0.117851
$73$	−14.0000	−1.63858	−0.819288	−	0.573382i	$-0.805631\pi$
$73$	−14.0000	−1.63858	−0.819288	+	0.573382i	$0.805631\pi$
$74$	6.00000	0.697486
$75$	−4.00000	−0.461880
$76$	−1.00000	−0.114708
$77$	0	0
$78$	−4.00000	−0.452911
$79$	−5.00000	−0.562544	−0.281272	−	0.959628i	$-0.590756\pi$
$79$	−5.00000	−0.562544	−0.281272	+	0.959628i	$0.590756\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	−2.00000	−0.220863
$83$	3.00000	0.329293	0.164646	−	0.986353i	$-0.447352\pi$
$83$	3.00000	0.329293	0.164646	+	0.986353i	$0.447352\pi$
$84$	0	0
$85$	−2.00000	−0.216930
$86$	−8.00000	−0.862662
$87$	5.00000	0.536056
$88$	1.00000	0.106600
$89$	−4.00000	−0.423999	−0.212000	−	0.977270i	$-0.567998\pi$
$89$	−4.00000	−0.423999	−0.212000	+	0.977270i	$0.567998\pi$
$90$	−1.00000	−0.105409
$91$	0	0
$92$	2.00000	0.208514
$93$	−5.00000	−0.518476
$94$	−10.0000	−1.03142
$95$	−1.00000	−0.102598
$96$	−1.00000	−0.102062
$97$	13.0000	1.31995	0.659975	−	0.751288i	$-0.270567\pi$
$97$	13.0000	1.31995	0.659975	+	0.751288i	$0.270567\pi$
$98$	0	0
$99$	−1.00000	−0.100504
$100$	−4.00000	−0.400000
$101$	6.00000	0.597022	0.298511	−	0.954406i	$-0.403510\pi$
$101$	6.00000	0.597022	0.298511	+	0.954406i	$0.403510\pi$
$102$	2.00000	0.198030
$103$	8.00000	0.788263	0.394132	−	0.919054i	$-0.371045\pi$
$103$	8.00000	0.788263	0.394132	+	0.919054i	$0.371045\pi$
$104$	−4.00000	−0.392232
$105$	0	0
$106$	−13.0000	−1.26267
$107$	15.0000	1.45010	0.725052	−	0.688694i	$-0.241816\pi$
$107$	15.0000	1.45010	0.725052	+	0.688694i	$0.241816\pi$
$108$	1.00000	0.0962250
$109$	−16.0000	−1.53252	−0.766261	−	0.642529i	$-0.777885\pi$
$109$	−16.0000	−1.53252	−0.766261	+	0.642529i	$0.777885\pi$
$110$	1.00000	0.0953463
$111$	−6.00000	−0.569495
$112$	0	0
$113$	2.00000	0.188144	0.0940721	−	0.995565i	$-0.470012\pi$
$113$	2.00000	0.188144	0.0940721	+	0.995565i	$0.470012\pi$
$114$	1.00000	0.0936586
$115$	2.00000	0.186501
$116$	5.00000	0.464238
$117$	4.00000	0.369800
$118$	3.00000	0.276172
$119$	0	0
$120$	−1.00000	−0.0912871
$121$	−10.0000	−0.909091
$122$	−10.0000	−0.905357
$123$	2.00000	0.180334
$124$	−5.00000	−0.449013
$125$	−9.00000	−0.804984
$126$	0	0
$127$	−3.00000	−0.266207	−0.133103	−	0.991102i	$-0.542494\pi$
$127$	−3.00000	−0.266207	−0.133103	+	0.991102i	$0.542494\pi$
$128$	−1.00000	−0.0883883
$129$	8.00000	0.704361
$130$	−4.00000	−0.350823
$131$	15.0000	1.31056	0.655278	−	0.755388i	$-0.272551\pi$
$131$	15.0000	1.31056	0.655278	+	0.755388i	$0.272551\pi$
$132$	−1.00000	−0.0870388
$133$	0	0
$134$	−10.0000	−0.863868
$135$	1.00000	0.0860663
$136$	2.00000	0.171499
$137$	22.0000	1.87959	0.939793	−	0.341743i	$-0.111017\pi$
$137$	22.0000	1.87959	0.939793	+	0.341743i	$0.111017\pi$
$138$	−2.00000	−0.170251
$139$	8.00000	0.678551	0.339276	−	0.940687i	$-0.389818\pi$
$139$	8.00000	0.678551	0.339276	+	0.940687i	$0.389818\pi$
$140$	0	0
$141$	10.0000	0.842152
$142$	4.00000	0.335673
$143$	−4.00000	−0.334497
$144$	1.00000	0.0833333
$145$	5.00000	0.415227
$146$	14.0000	1.15865
$147$	0	0
$148$	−6.00000	−0.493197
$149$	6.00000	0.491539	0.245770	−	0.969328i	$-0.420959\pi$
$149$	6.00000	0.491539	0.245770	+	0.969328i	$0.420959\pi$
$150$	4.00000	0.326599
$151$	−5.00000	−0.406894	−0.203447	−	0.979086i	$-0.565214\pi$
$151$	−5.00000	−0.406894	−0.203447	+	0.979086i	$0.565214\pi$
$152$	1.00000	0.0811107
$153$	−2.00000	−0.161690
$154$	0	0
$155$	−5.00000	−0.401610
$156$	4.00000	0.320256
$157$	−4.00000	−0.319235	−0.159617	−	0.987179i	$-0.551026\pi$
$157$	−4.00000	−0.319235	−0.159617	+	0.987179i	$0.551026\pi$
$158$	5.00000	0.397779
$159$	13.0000	1.03097
$160$	−1.00000	−0.0790569
$161$	0	0
$162$	−1.00000	−0.0785674
$163$	4.00000	0.313304	0.156652	−	0.987654i	$-0.449930\pi$
$163$	4.00000	0.313304	0.156652	+	0.987654i	$0.449930\pi$
$164$	2.00000	0.156174
$165$	−1.00000	−0.0778499
$166$	−3.00000	−0.232845
$167$	−12.0000	−0.928588	−0.464294	−	0.885681i	$-0.653692\pi$
$167$	−12.0000	−0.928588	−0.464294	+	0.885681i	$0.653692\pi$
$168$	0	0
$169$	3.00000	0.230769
$170$	2.00000	0.153393
$171$	−1.00000	−0.0764719
$172$	8.00000	0.609994
$173$	−6.00000	−0.456172	−0.228086	−	0.973641i	$-0.573247\pi$
$173$	−6.00000	−0.456172	−0.228086	+	0.973641i	$0.573247\pi$
$174$	−5.00000	−0.379049
$175$	0	0
$176$	−1.00000	−0.0753778
$177$	−3.00000	−0.225494
$178$	4.00000	0.299813
$179$	24.0000	1.79384	0.896922	−	0.442189i	$-0.145798\pi$
$179$	24.0000	1.79384	0.896922	+	0.442189i	$0.145798\pi$
$180$	1.00000	0.0745356
$181$	16.0000	1.18927	0.594635	−	0.803996i	$-0.297296\pi$
$181$	16.0000	1.18927	0.594635	+	0.803996i	$0.297296\pi$
$182$	0	0
$183$	10.0000	0.739221
$184$	−2.00000	−0.147442
$185$	−6.00000	−0.441129
$186$	5.00000	0.366618
$187$	2.00000	0.146254
$188$	10.0000	0.729325
$189$	0	0
$190$	1.00000	0.0725476
$191$	−12.0000	−0.868290	−0.434145	−	0.900843i	$-0.642949\pi$
$191$	−12.0000	−0.868290	−0.434145	+	0.900843i	$0.642949\pi$
$192$	1.00000	0.0721688
$193$	−1.00000	−0.0719816	−0.0359908	−	0.999352i	$-0.511459\pi$
$193$	−1.00000	−0.0719816	−0.0359908	+	0.999352i	$0.511459\pi$
$194$	−13.0000	−0.933346
$195$	4.00000	0.286446
$196$	0	0
$197$	−6.00000	−0.427482	−0.213741	−	0.976890i	$-0.568565\pi$
$197$	−6.00000	−0.427482	−0.213741	+	0.976890i	$0.568565\pi$
$198$	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
$201$	10.0000	0.705346
$202$	−6.00000	−0.422159
$203$	0	0
$204$	−2.00000	−0.140028
$205$	2.00000	0.139686
$206$	−8.00000	−0.557386
$207$	2.00000	0.139010
$208$	4.00000	0.277350
$209$	1.00000	0.0691714
$210$	0	0
$211$	4.00000	0.275371	0.137686	−	0.990476i	$-0.456034\pi$
$211$	4.00000	0.275371	0.137686	+	0.990476i	$0.456034\pi$
$212$	13.0000	0.892844
$213$	−4.00000	−0.274075
$214$	−15.0000	−1.02538
$215$	8.00000	0.545595
$216$	−1.00000	−0.0680414
$217$	0	0
$218$	16.0000	1.08366
$219$	−14.0000	−0.946032
$220$	−1.00000	−0.0674200
$221$	−8.00000	−0.538138
$222$	6.00000	0.402694
$223$	−15.0000	−1.00447	−0.502237	−	0.864730i	$-0.667490\pi$
$223$	−15.0000	−1.00447	−0.502237	+	0.864730i	$0.667490\pi$
$224$	0	0
$225$	−4.00000	−0.266667
$226$	−2.00000	−0.133038
$227$	15.0000	0.995585	0.497792	−	0.867296i	$-0.334144\pi$
$227$	15.0000	0.995585	0.497792	+	0.867296i	$0.334144\pi$
$228$	−1.00000	−0.0662266
$229$	−12.0000	−0.792982	−0.396491	−	0.918039i	$-0.629772\pi$
$229$	−12.0000	−0.792982	−0.396491	+	0.918039i	$0.629772\pi$
$230$	−2.00000	−0.131876
$231$	0	0
$232$	−5.00000	−0.328266
$233$	−16.0000	−1.04819	−0.524097	−	0.851658i	$-0.675597\pi$
$233$	−16.0000	−1.04819	−0.524097	+	0.851658i	$0.675597\pi$
$234$	−4.00000	−0.261488
$235$	10.0000	0.652328
$236$	−3.00000	−0.195283
$237$	−5.00000	−0.324785
$238$	0	0
$239$	−16.0000	−1.03495	−0.517477	−	0.855697i	$-0.673129\pi$
$239$	−16.0000	−1.03495	−0.517477	+	0.855697i	$0.673129\pi$
$240$	1.00000	0.0645497
$241$	17.0000	1.09507	0.547533	−	0.836784i	$-0.315567\pi$
$241$	17.0000	1.09507	0.547533	+	0.836784i	$0.315567\pi$
$242$	10.0000	0.642824
$243$	1.00000	0.0641500
$244$	10.0000	0.640184
$245$	0	0
$246$	−2.00000	−0.127515
$247$	−4.00000	−0.254514
$248$	5.00000	0.317500
$249$	3.00000	0.190117
$250$	9.00000	0.569210
$251$	7.00000	0.441836	0.220918	−	0.975292i	$-0.429095\pi$
$251$	7.00000	0.441836	0.220918	+	0.975292i	$0.429095\pi$
$252$	0	0
$253$	−2.00000	−0.125739
$254$	3.00000	0.188237
$255$	−2.00000	−0.125245
$256$	1.00000	0.0625000
$257$	−18.0000	−1.12281	−0.561405	−	0.827541i	$-0.689739\pi$
$257$	−18.0000	−1.12281	−0.561405	+	0.827541i	$0.689739\pi$
$258$	−8.00000	−0.498058
$259$	0	0
$260$	4.00000	0.248069
$261$	5.00000	0.309492
$262$	−15.0000	−0.926703
$263$	−12.0000	−0.739952	−0.369976	−	0.929041i	$-0.620634\pi$
$263$	−12.0000	−0.739952	−0.369976	+	0.929041i	$0.620634\pi$
$264$	1.00000	0.0615457
$265$	13.0000	0.798584
$266$	0	0
$267$	−4.00000	−0.244796
$268$	10.0000	0.610847
$269$	−3.00000	−0.182913	−0.0914566	−	0.995809i	$-0.529152\pi$
$269$	−3.00000	−0.182913	−0.0914566	+	0.995809i	$0.529152\pi$
$270$	−1.00000	−0.0608581
$271$	17.0000	1.03268	0.516338	−	0.856385i	$-0.327295\pi$
$271$	17.0000	1.03268	0.516338	+	0.856385i	$0.327295\pi$
$272$	−2.00000	−0.121268
$273$	0	0
$274$	−22.0000	−1.32907
$275$	4.00000	0.241209
$276$	2.00000	0.120386
$277$	2.00000	0.120168	0.0600842	−	0.998193i	$-0.480863\pi$
$277$	2.00000	0.120168	0.0600842	+	0.998193i	$0.480863\pi$
$278$	−8.00000	−0.479808
$279$	−5.00000	−0.299342
$280$	0	0
$281$	30.0000	1.78965	0.894825	−	0.446417i	$-0.147300\pi$
$281$	30.0000	1.78965	0.894825	+	0.446417i	$0.147300\pi$
$282$	−10.0000	−0.595491
$283$	16.0000	0.951101	0.475551	−	0.879688i	$-0.342249\pi$
$283$	16.0000	0.951101	0.475551	+	0.879688i	$0.342249\pi$
$284$	−4.00000	−0.237356
$285$	−1.00000	−0.0592349
$286$	4.00000	0.236525
$287$	0	0
$288$	−1.00000	−0.0589256
$289$	−13.0000	−0.764706
$290$	−5.00000	−0.293610
$291$	13.0000	0.762073
$292$	−14.0000	−0.819288
$293$	9.00000	0.525786	0.262893	−	0.964825i	$-0.415323\pi$
$293$	9.00000	0.525786	0.262893	+	0.964825i	$0.415323\pi$
$294$	0	0
$295$	−3.00000	−0.174667
$296$	6.00000	0.348743
$297$	−1.00000	−0.0580259
$298$	−6.00000	−0.347571
$299$	8.00000	0.462652
$300$	−4.00000	−0.230940
$301$	0	0
$302$	5.00000	0.287718
$303$	6.00000	0.344691
$304$	−1.00000	−0.0573539
$305$	10.0000	0.572598
$306$	2.00000	0.114332
$307$	2.00000	0.114146	0.0570730	−	0.998370i	$-0.481823\pi$
$307$	2.00000	0.114146	0.0570730	+	0.998370i	$0.481823\pi$
$308$	0	0
$309$	8.00000	0.455104
$310$	5.00000	0.283981
$311$	18.0000	1.02069	0.510343	−	0.859971i	$-0.329518\pi$
$311$	18.0000	1.02069	0.510343	+	0.859971i	$0.329518\pi$
$312$	−4.00000	−0.226455
$313$	1.00000	0.0565233	0.0282617	−	0.999601i	$-0.491003\pi$
$313$	1.00000	0.0565233	0.0282617	+	0.999601i	$0.491003\pi$
$314$	4.00000	0.225733
$315$	0	0
$316$	−5.00000	−0.281272
$317$	−15.0000	−0.842484	−0.421242	−	0.906948i	$-0.638406\pi$
$317$	−15.0000	−0.842484	−0.421242	+	0.906948i	$0.638406\pi$
$318$	−13.0000	−0.729004
$319$	−5.00000	−0.279946
$320$	1.00000	0.0559017
$321$	15.0000	0.837218
$322$	0	0
$323$	2.00000	0.111283
$324$	1.00000	0.0555556
$325$	−16.0000	−0.887520
$326$	−4.00000	−0.221540
$327$	−16.0000	−0.884802
$328$	−2.00000	−0.110432
$329$	0	0
$330$	1.00000	0.0550482
$331$	−22.0000	−1.20923	−0.604615	−	0.796518i	$-0.706673\pi$
$331$	−22.0000	−1.20923	−0.604615	+	0.796518i	$0.706673\pi$
$332$	3.00000	0.164646
$333$	−6.00000	−0.328798
$334$	12.0000	0.656611
$335$	10.0000	0.546358
$336$	0	0
$337$	−33.0000	−1.79762	−0.898812	−	0.438334i	$-0.855569\pi$
$337$	−33.0000	−1.79762	−0.898812	+	0.438334i	$0.855569\pi$
$338$	−3.00000	−0.163178
$339$	2.00000	0.108625
$340$	−2.00000	−0.108465
$341$	5.00000	0.270765
$342$	1.00000	0.0540738
$343$	0	0
$344$	−8.00000	−0.431331
$345$	2.00000	0.107676
$346$	6.00000	0.322562
$347$	24.0000	1.28839	0.644194	−	0.764862i	$-0.277193\pi$
$347$	24.0000	1.28839	0.644194	+	0.764862i	$0.277193\pi$
$348$	5.00000	0.268028
$349$	8.00000	0.428230	0.214115	−	0.976808i	$-0.431313\pi$
$349$	8.00000	0.428230	0.214115	+	0.976808i	$0.431313\pi$
$350$	0	0
$351$	4.00000	0.213504
$352$	1.00000	0.0533002
$353$	−26.0000	−1.38384	−0.691920	−	0.721974i	$-0.743235\pi$
$353$	−26.0000	−1.38384	−0.691920	+	0.721974i	$0.743235\pi$
$354$	3.00000	0.159448
$355$	−4.00000	−0.212298
$356$	−4.00000	−0.212000
$357$	0	0
$358$	−24.0000	−1.26844
$359$	−10.0000	−0.527780	−0.263890	−	0.964553i	$-0.585006\pi$
$359$	−10.0000	−0.527780	−0.263890	+	0.964553i	$0.585006\pi$
$360$	−1.00000	−0.0527046
$361$	1.00000	0.0526316
$362$	−16.0000	−0.840941
$363$	−10.0000	−0.524864
$364$	0	0
$365$	−14.0000	−0.732793
$366$	−10.0000	−0.522708
$367$	35.0000	1.82699	0.913493	−	0.406855i	$-0.133375\pi$
$367$	35.0000	1.82699	0.913493	+	0.406855i	$0.133375\pi$
$368$	2.00000	0.104257
$369$	2.00000	0.104116
$370$	6.00000	0.311925
$371$	0	0
$372$	−5.00000	−0.259238
$373$	12.0000	0.621336	0.310668	−	0.950518i	$-0.399447\pi$
$373$	12.0000	0.621336	0.310668	+	0.950518i	$0.399447\pi$
$374$	−2.00000	−0.103418
$375$	−9.00000	−0.464758
$376$	−10.0000	−0.515711
$377$	20.0000	1.03005
$378$	0	0
$379$	−8.00000	−0.410932	−0.205466	−	0.978664i	$-0.565871\pi$
$379$	−8.00000	−0.410932	−0.205466	+	0.978664i	$0.565871\pi$
$380$	−1.00000	−0.0512989
$381$	−3.00000	−0.153695
$382$	12.0000	0.613973
$383$	22.0000	1.12415	0.562074	−	0.827087i	$-0.310004\pi$
$383$	22.0000	1.12415	0.562074	+	0.827087i	$0.310004\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	1.00000	0.0508987
$387$	8.00000	0.406663
$388$	13.0000	0.659975
$389$	−18.0000	−0.912636	−0.456318	−	0.889817i	$-0.650832\pi$
$389$	−18.0000	−0.912636	−0.456318	+	0.889817i	$0.650832\pi$
$390$	−4.00000	−0.202548
$391$	−4.00000	−0.202289
$392$	0	0
$393$	15.0000	0.756650
$394$	6.00000	0.302276
$395$	−5.00000	−0.251577
$396$	−1.00000	−0.0502519
$397$	−20.0000	−1.00377	−0.501886	−	0.864934i	$-0.667360\pi$
$397$	−20.0000	−1.00377	−0.501886	+	0.864934i	$0.667360\pi$
$398$	−8.00000	−0.401004
$399$	0	0
$400$	−4.00000	−0.200000
$401$	8.00000	0.399501	0.199750	−	0.979847i	$-0.435987\pi$
$401$	8.00000	0.399501	0.199750	+	0.979847i	$0.435987\pi$
$402$	−10.0000	−0.498755
$403$	−20.0000	−0.996271
$404$	6.00000	0.298511
$405$	1.00000	0.0496904
$406$	0	0
$407$	6.00000	0.297409
$408$	2.00000	0.0990148
$409$	17.0000	0.840596	0.420298	−	0.907386i	$-0.361926\pi$
$409$	17.0000	0.840596	0.420298	+	0.907386i	$0.361926\pi$
$410$	−2.00000	−0.0987730
$411$	22.0000	1.08518
$412$	8.00000	0.394132
$413$	0	0
$414$	−2.00000	−0.0982946
$415$	3.00000	0.147264
$416$	−4.00000	−0.196116
$417$	8.00000	0.391762
$418$	−1.00000	−0.0489116
$419$	36.0000	1.75872	0.879358	−	0.476162i	$-0.157972\pi$
$419$	36.0000	1.75872	0.879358	+	0.476162i	$0.157972\pi$
$420$	0	0
$421$	38.0000	1.85201	0.926003	−	0.377515i	$-0.123221\pi$
$421$	38.0000	1.85201	0.926003	+	0.377515i	$0.123221\pi$
$422$	−4.00000	−0.194717
$423$	10.0000	0.486217
$424$	−13.0000	−0.631336
$425$	8.00000	0.388057
$426$	4.00000	0.193801
$427$	0	0
$428$	15.0000	0.725052
$429$	−4.00000	−0.193122
$430$	−8.00000	−0.385794
$431$	−2.00000	−0.0963366	−0.0481683	−	0.998839i	$-0.515338\pi$
$431$	−2.00000	−0.0963366	−0.0481683	+	0.998839i	$0.515338\pi$
$432$	1.00000	0.0481125
$433$	−14.0000	−0.672797	−0.336399	−	0.941720i	$-0.609209\pi$
$433$	−14.0000	−0.672797	−0.336399	+	0.941720i	$0.609209\pi$
$434$	0	0
$435$	5.00000	0.239732
$436$	−16.0000	−0.766261
$437$	−2.00000	−0.0956730
$438$	14.0000	0.668946
$439$	−25.0000	−1.19318	−0.596592	−	0.802544i	$-0.703479\pi$
$439$	−25.0000	−1.19318	−0.596592	+	0.802544i	$0.703479\pi$
$440$	1.00000	0.0476731
$441$	0	0
$442$	8.00000	0.380521
$443$	−21.0000	−0.997740	−0.498870	−	0.866677i	$-0.666252\pi$
$443$	−21.0000	−0.997740	−0.498870	+	0.866677i	$0.666252\pi$
$444$	−6.00000	−0.284747
$445$	−4.00000	−0.189618
$446$	15.0000	0.710271
$447$	6.00000	0.283790
$448$	0	0
$449$	−34.0000	−1.60456	−0.802280	−	0.596948i	$-0.796380\pi$
$449$	−34.0000	−1.60456	−0.802280	+	0.596948i	$0.796380\pi$
$450$	4.00000	0.188562
$451$	−2.00000	−0.0941763
$452$	2.00000	0.0940721
$453$	−5.00000	−0.234920
$454$	−15.0000	−0.703985
$455$	0	0
$456$	1.00000	0.0468293
$457$	−33.0000	−1.54367	−0.771837	−	0.635820i	$-0.780662\pi$
$457$	−33.0000	−1.54367	−0.771837	+	0.635820i	$0.780662\pi$
$458$	12.0000	0.560723
$459$	−2.00000	−0.0933520
$460$	2.00000	0.0932505
$461$	6.00000	0.279448	0.139724	−	0.990190i	$-0.455378\pi$
$461$	6.00000	0.279448	0.139724	+	0.990190i	$0.455378\pi$
$462$	0	0
$463$	−16.0000	−0.743583	−0.371792	−	0.928316i	$-0.621256\pi$
$463$	−16.0000	−0.743583	−0.371792	+	0.928316i	$0.621256\pi$
$464$	5.00000	0.232119
$465$	−5.00000	−0.231869
$466$	16.0000	0.741186
$467$	36.0000	1.66588	0.832941	−	0.553362i	$-0.186655\pi$
$467$	36.0000	1.66588	0.832941	+	0.553362i	$0.186655\pi$
$468$	4.00000	0.184900
$469$	0	0
$470$	−10.0000	−0.461266
$471$	−4.00000	−0.184310
$472$	3.00000	0.138086
$473$	−8.00000	−0.367840
$474$	5.00000	0.229658
$475$	4.00000	0.183533
$476$	0	0
$477$	13.0000	0.595229
$478$	16.0000	0.731823
$479$	−14.0000	−0.639676	−0.319838	−	0.947472i	$-0.603629\pi$
$479$	−14.0000	−0.639676	−0.319838	+	0.947472i	$0.603629\pi$
$480$	−1.00000	−0.0456435
$481$	−24.0000	−1.09431
$482$	−17.0000	−0.774329
$483$	0	0
$484$	−10.0000	−0.454545
$485$	13.0000	0.590300
$486$	−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	$0.550698\pi$
$488$	−10.0000	−0.452679
$489$	4.00000	0.180886
$490$	0	0
$491$	19.0000	0.857458	0.428729	−	0.903433i	$-0.358962\pi$
$491$	19.0000	0.857458	0.428729	+	0.903433i	$0.358962\pi$
$492$	2.00000	0.0901670
$493$	−10.0000	−0.450377
$494$	4.00000	0.179969
$495$	−1.00000	−0.0449467
$496$	−5.00000	−0.224507
$497$	0	0
$498$	−3.00000	−0.134433
$499$	−38.0000	−1.70111	−0.850557	−	0.525883i	$-0.823735\pi$
$499$	−38.0000	−1.70111	−0.850557	+	0.525883i	$0.823735\pi$
$500$	−9.00000	−0.402492
$501$	−12.0000	−0.536120
$502$	−7.00000	−0.312425
$503$	22.0000	0.980932	0.490466	−	0.871460i	$-0.336827\pi$
$503$	22.0000	0.980932	0.490466	+	0.871460i	$0.336827\pi$
$504$	0	0
$505$	6.00000	0.266996
$506$	2.00000	0.0889108
$507$	3.00000	0.133235
$508$	−3.00000	−0.133103
$509$	13.0000	0.576215	0.288107	−	0.957598i	$-0.406974\pi$
$509$	13.0000	0.576215	0.288107	+	0.957598i	$0.406974\pi$
$510$	2.00000	0.0885615
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	−1.00000	−0.0441511
$514$	18.0000	0.793946
$515$	8.00000	0.352522
$516$	8.00000	0.352180
$517$	−10.0000	−0.439799
$518$	0	0
$519$	−6.00000	−0.263371
$520$	−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	$0.429703\pi$
$522$	−5.00000	−0.218844
$523$	10.0000	0.437269	0.218635	−	0.975807i	$-0.429840\pi$
$523$	10.0000	0.437269	0.218635	+	0.975807i	$0.429840\pi$
$524$	15.0000	0.655278
$525$	0	0
$526$	12.0000	0.523225
$527$	10.0000	0.435607
$528$	−1.00000	−0.0435194
$529$	−19.0000	−0.826087
$530$	−13.0000	−0.564684
$531$	−3.00000	−0.130189
$532$	0	0
$533$	8.00000	0.346518
$534$	4.00000	0.173097
$535$	15.0000	0.648507
$536$	−10.0000	−0.431934
$537$	24.0000	1.03568
$538$	3.00000	0.129339
$539$	0	0
$540$	1.00000	0.0430331
$541$	20.0000	0.859867	0.429934	−	0.902861i	$-0.358537\pi$
$541$	20.0000	0.859867	0.429934	+	0.902861i	$0.358537\pi$
$542$	−17.0000	−0.730213
$543$	16.0000	0.686626
$544$	2.00000	0.0857493
$545$	−16.0000	−0.685365
$546$	0	0
$547$	−2.00000	−0.0855138	−0.0427569	−	0.999086i	$-0.513614\pi$
$547$	−2.00000	−0.0855138	−0.0427569	+	0.999086i	$0.513614\pi$
$548$	22.0000	0.939793
$549$	10.0000	0.426790
$550$	−4.00000	−0.170561
$551$	−5.00000	−0.213007
$552$	−2.00000	−0.0851257
$553$	0	0
$554$	−2.00000	−0.0849719
$555$	−6.00000	−0.254686
$556$	8.00000	0.339276
$557$	17.0000	0.720313	0.360157	−	0.932892i	$-0.382723\pi$
$557$	17.0000	0.720313	0.360157	+	0.932892i	$0.382723\pi$
$558$	5.00000	0.211667
$559$	32.0000	1.35346
$560$	0	0
$561$	2.00000	0.0844401
$562$	−30.0000	−1.26547
$563$	−15.0000	−0.632175	−0.316087	−	0.948730i	$-0.602369\pi$
$563$	−15.0000	−0.632175	−0.316087	+	0.948730i	$0.602369\pi$
$564$	10.0000	0.421076
$565$	2.00000	0.0841406
$566$	−16.0000	−0.672530
$567$	0	0
$568$	4.00000	0.167836
$569$	0	0		−	1.00000i	$-0.5\pi$
$569$	0	0			1.00000i	$0.5\pi$
$570$	1.00000	0.0418854
$571$	−20.0000	−0.836974	−0.418487	−	0.908223i	$-0.637439\pi$
$571$	−20.0000	−0.836974	−0.418487	+	0.908223i	$0.637439\pi$
$572$	−4.00000	−0.167248
$573$	−12.0000	−0.501307
$574$	0	0
$575$	−8.00000	−0.333623
$576$	1.00000	0.0416667
$577$	43.0000	1.79011	0.895057	−	0.445952i	$-0.147135\pi$
$577$	43.0000	1.79011	0.895057	+	0.445952i	$0.147135\pi$
$578$	13.0000	0.540729
$579$	−1.00000	−0.0415586
$580$	5.00000	0.207614
$581$	0	0
$582$	−13.0000	−0.538867
$583$	−13.0000	−0.538405
$584$	14.0000	0.579324
$585$	4.00000	0.165380
$586$	−9.00000	−0.371787
$587$	17.0000	0.701665	0.350833	−	0.936438i	$-0.385899\pi$
$587$	17.0000	0.701665	0.350833	+	0.936438i	$0.385899\pi$
$588$	0	0
$589$	5.00000	0.206021
$590$	3.00000	0.123508
$591$	−6.00000	−0.246807
$592$	−6.00000	−0.246598
$593$	36.0000	1.47834	0.739171	−	0.673517i	$-0.235217\pi$
$593$	36.0000	1.47834	0.739171	+	0.673517i	$0.235217\pi$
$594$	1.00000	0.0410305
$595$	0	0
$596$	6.00000	0.245770
$597$	8.00000	0.327418
$598$	−8.00000	−0.327144
$599$	12.0000	0.490307	0.245153	−	0.969484i	$-0.421162\pi$
$599$	12.0000	0.490307	0.245153	+	0.969484i	$0.421162\pi$
$600$	4.00000	0.163299
$601$	25.0000	1.01977	0.509886	−	0.860242i	$-0.329688\pi$
$601$	25.0000	1.01977	0.509886	+	0.860242i	$0.329688\pi$
$602$	0	0
$603$	10.0000	0.407231
$604$	−5.00000	−0.203447
$605$	−10.0000	−0.406558
$606$	−6.00000	−0.243733
$607$	13.0000	0.527654	0.263827	−	0.964570i	$-0.415015\pi$
$607$	13.0000	0.527654	0.263827	+	0.964570i	$0.415015\pi$
$608$	1.00000	0.0405554
$609$	0	0
$610$	−10.0000	−0.404888
$611$	40.0000	1.61823
$612$	−2.00000	−0.0808452
$613$	−10.0000	−0.403896	−0.201948	−	0.979396i	$-0.564727\pi$
$613$	−10.0000	−0.403896	−0.201948	+	0.979396i	$0.564727\pi$
$614$	−2.00000	−0.0807134
$615$	2.00000	0.0806478
$616$	0	0
$617$	12.0000	0.483102	0.241551	−	0.970388i	$-0.422344\pi$
$617$	12.0000	0.483102	0.241551	+	0.970388i	$0.422344\pi$
$618$	−8.00000	−0.321807
$619$	10.0000	0.401934	0.200967	−	0.979598i	$-0.435592\pi$
$619$	10.0000	0.401934	0.200967	+	0.979598i	$0.435592\pi$
$620$	−5.00000	−0.200805
$621$	2.00000	0.0802572
$622$	−18.0000	−0.721734
$623$	0	0
$624$	4.00000	0.160128
$625$	11.0000	0.440000
$626$	−1.00000	−0.0399680
$627$	1.00000	0.0399362
$628$	−4.00000	−0.159617
$629$	12.0000	0.478471
$630$	0	0
$631$	−5.00000	−0.199047	−0.0995234	−	0.995035i	$-0.531732\pi$
$631$	−5.00000	−0.199047	−0.0995234	+	0.995035i	$0.531732\pi$
$632$	5.00000	0.198889
$633$	4.00000	0.158986
$634$	15.0000	0.595726
$635$	−3.00000	−0.119051
$636$	13.0000	0.515484
$637$	0	0
$638$	5.00000	0.197952
$639$	−4.00000	−0.158238
$640$	−1.00000	−0.0395285
$641$	0	0		−	1.00000i	$-0.5\pi$
$641$	0	0			1.00000i	$0.5\pi$
$642$	−15.0000	−0.592003
$643$	−44.0000	−1.73519	−0.867595	−	0.497271i	$-0.834335\pi$
$643$	−44.0000	−1.73519	−0.867595	+	0.497271i	$0.834335\pi$
$644$	0	0
$645$	8.00000	0.315000
$646$	−2.00000	−0.0786889
$647$	−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
$649$	3.00000	0.117760
$650$	16.0000	0.627572
$651$	0	0
$652$	4.00000	0.156652
$653$	9.00000	0.352197	0.176099	−	0.984373i	$-0.443652\pi$
$653$	9.00000	0.352197	0.176099	+	0.984373i	$0.443652\pi$
$654$	16.0000	0.625650
$655$	15.0000	0.586098
$656$	2.00000	0.0780869
$657$	−14.0000	−0.546192
$658$	0	0
$659$	0	0		−	1.00000i	$-0.5\pi$
$659$	0	0			1.00000i	$0.5\pi$
$660$	−1.00000	−0.0389249
$661$	−20.0000	−0.777910	−0.388955	−	0.921257i	$-0.627164\pi$
$661$	−20.0000	−0.777910	−0.388955	+	0.921257i	$0.627164\pi$
$662$	22.0000	0.855054
$663$	−8.00000	−0.310694
$664$	−3.00000	−0.116423
$665$	0	0
$666$	6.00000	0.232495
$667$	10.0000	0.387202
$668$	−12.0000	−0.464294
$669$	−15.0000	−0.579934
$670$	−10.0000	−0.386334
$671$	−10.0000	−0.386046
$672$	0	0
$673$	−29.0000	−1.11787	−0.558934	−	0.829212i	$-0.688789\pi$
$673$	−29.0000	−1.11787	−0.558934	+	0.829212i	$0.688789\pi$
$674$	33.0000	1.27111
$675$	−4.00000	−0.153960
$676$	3.00000	0.115385
$677$	35.0000	1.34516	0.672580	−	0.740025i	$-0.265186\pi$
$677$	35.0000	1.34516	0.672580	+	0.740025i	$0.265186\pi$
$678$	−2.00000	−0.0768095
$679$	0	0
$680$	2.00000	0.0766965
$681$	15.0000	0.574801
$682$	−5.00000	−0.191460
$683$	−1.00000	−0.0382639	−0.0191320	−	0.999817i	$-0.506090\pi$
$683$	−1.00000	−0.0382639	−0.0191320	+	0.999817i	$0.506090\pi$
$684$	−1.00000	−0.0382360
$685$	22.0000	0.840577
$686$	0	0
$687$	−12.0000	−0.457829
$688$	8.00000	0.304997
$689$	52.0000	1.98104
$690$	−2.00000	−0.0761387
$691$	−14.0000	−0.532585	−0.266293	−	0.963892i	$-0.585799\pi$
$691$	−14.0000	−0.532585	−0.266293	+	0.963892i	$0.585799\pi$
$692$	−6.00000	−0.228086
$693$	0	0
$694$	−24.0000	−0.911028
$695$	8.00000	0.303457
$696$	−5.00000	−0.189525
$697$	−4.00000	−0.151511
$698$	−8.00000	−0.302804
$699$	−16.0000	−0.605176
$700$	0	0
$701$	39.0000	1.47301	0.736505	−	0.676432i	$-0.236475\pi$
$701$	39.0000	1.47301	0.736505	+	0.676432i	$0.236475\pi$
$702$	−4.00000	−0.150970
$703$	6.00000	0.226294
$704$	−1.00000	−0.0376889
$705$	10.0000	0.376622
$706$	26.0000	0.978523
$707$	0	0
$708$	−3.00000	−0.112747
$709$	16.0000	0.600893	0.300446	−	0.953799i	$-0.402864\pi$
$709$	16.0000	0.600893	0.300446	+	0.953799i	$0.402864\pi$
$710$	4.00000	0.150117
$711$	−5.00000	−0.187515
$712$	4.00000	0.149906
$713$	−10.0000	−0.374503
$714$	0	0
$715$	−4.00000	−0.149592
$716$	24.0000	0.896922
$717$	−16.0000	−0.597531
$718$	10.0000	0.373197
$719$	26.0000	0.969636	0.484818	−	0.874615i	$-0.338886\pi$
$719$	26.0000	0.969636	0.484818	+	0.874615i	$0.338886\pi$
$720$	1.00000	0.0372678
$721$	0	0
$722$	−1.00000	−0.0372161
$723$	17.0000	0.632237
$724$	16.0000	0.594635
$725$	−20.0000	−0.742781
$726$	10.0000	0.371135
$727$	−3.00000	−0.111264	−0.0556319	−	0.998451i	$-0.517717\pi$
$727$	−3.00000	−0.111264	−0.0556319	+	0.998451i	$0.517717\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	14.0000	0.518163
$731$	−16.0000	−0.591781
$732$	10.0000	0.369611
$733$	0	0		−	1.00000i	$-0.5\pi$
$733$	0	0			1.00000i	$0.5\pi$
$734$	−35.0000	−1.29187
$735$	0	0
$736$	−2.00000	−0.0737210
$737$	−10.0000	−0.368355
$738$	−2.00000	−0.0736210
$739$	−4.00000	−0.147142	−0.0735712	−	0.997290i	$-0.523440\pi$
$739$	−4.00000	−0.147142	−0.0735712	+	0.997290i	$0.523440\pi$
$740$	−6.00000	−0.220564
$741$	−4.00000	−0.146944
$742$	0	0
$743$	6.00000	0.220119	0.110059	−	0.993925i	$-0.464896\pi$
$743$	6.00000	0.220119	0.110059	+	0.993925i	$0.464896\pi$
$744$	5.00000	0.183309
$745$	6.00000	0.219823
$746$	−12.0000	−0.439351
$747$	3.00000	0.109764
$748$	2.00000	0.0731272
$749$	0	0
$750$	9.00000	0.328634
$751$	−19.0000	−0.693320	−0.346660	−	0.937991i	$-0.612684\pi$
$751$	−19.0000	−0.693320	−0.346660	+	0.937991i	$0.612684\pi$
$752$	10.0000	0.364662
$753$	7.00000	0.255094
$754$	−20.0000	−0.728357
$755$	−5.00000	−0.181969
$756$	0	0
$757$	−8.00000	−0.290765	−0.145382	−	0.989376i	$-0.546441\pi$
$757$	−8.00000	−0.290765	−0.145382	+	0.989376i	$0.546441\pi$
$758$	8.00000	0.290573
$759$	−2.00000	−0.0725954
$760$	1.00000	0.0362738
$761$	−36.0000	−1.30500	−0.652499	−	0.757789i	$-0.726280\pi$
$761$	−36.0000	−1.30500	−0.652499	+	0.757789i	$0.726280\pi$
$762$	3.00000	0.108679
$763$	0	0
$764$	−12.0000	−0.434145
$765$	−2.00000	−0.0723102
$766$	−22.0000	−0.794892
$767$	−12.0000	−0.433295
$768$	1.00000	0.0360844
$769$	−47.0000	−1.69486	−0.847432	−	0.530904i	$-0.821852\pi$
$769$	−47.0000	−1.69486	−0.847432	+	0.530904i	$0.821852\pi$
$770$	0	0
$771$	−18.0000	−0.648254
$772$	−1.00000	−0.0359908
$773$	42.0000	1.51064	0.755318	−	0.655359i	$-0.227483\pi$
$773$	42.0000	1.51064	0.755318	+	0.655359i	$0.227483\pi$
$774$	−8.00000	−0.287554
$775$	20.0000	0.718421
$776$	−13.0000	−0.466673
$777$	0	0
$778$	18.0000	0.645331
$779$	−2.00000	−0.0716574
$780$	4.00000	0.143223
$781$	4.00000	0.143131
$782$	4.00000	0.143040
$783$	5.00000	0.178685
$784$	0	0
$785$	−4.00000	−0.142766
$786$	−15.0000	−0.535032
$787$	−14.0000	−0.499046	−0.249523	−	0.968369i	$-0.580274\pi$
$787$	−14.0000	−0.499046	−0.249523	+	0.968369i	$0.580274\pi$
$788$	−6.00000	−0.213741
$789$	−12.0000	−0.427211
$790$	5.00000	0.177892
$791$	0	0
$792$	1.00000	0.0355335
$793$	40.0000	1.42044
$794$	20.0000	0.709773
$795$	13.0000	0.461062
$796$	8.00000	0.283552
$797$	−41.0000	−1.45229	−0.726147	−	0.687539i	$-0.758691\pi$
$797$	−41.0000	−1.45229	−0.726147	+	0.687539i	$0.758691\pi$
$798$	0	0
$799$	−20.0000	−0.707549
$800$	4.00000	0.141421
$801$	−4.00000	−0.141333
$802$	−8.00000	−0.282490
$803$	14.0000	0.494049
$804$	10.0000	0.352673
$805$	0	0
$806$	20.0000	0.704470
$807$	−3.00000	−0.105605
$808$	−6.00000	−0.211079
$809$	−22.0000	−0.773479	−0.386739	−	0.922189i	$-0.626399\pi$
$809$	−22.0000	−0.773479	−0.386739	+	0.922189i	$0.626399\pi$
$810$	−1.00000	−0.0351364
$811$	−8.00000	−0.280918	−0.140459	−	0.990086i	$-0.544858\pi$
$811$	−8.00000	−0.280918	−0.140459	+	0.990086i	$0.544858\pi$
$812$	0	0
$813$	17.0000	0.596216
$814$	−6.00000	−0.210300
$815$	4.00000	0.140114
$816$	−2.00000	−0.0700140
$817$	−8.00000	−0.279885
$818$	−17.0000	−0.594391
$819$	0	0
$820$	2.00000	0.0698430
$821$	−25.0000	−0.872506	−0.436253	−	0.899824i	$-0.643695\pi$
$821$	−25.0000	−0.872506	−0.436253	+	0.899824i	$0.643695\pi$
$822$	−22.0000	−0.767338
$823$	16.0000	0.557725	0.278862	−	0.960331i	$-0.410043\pi$
$823$	16.0000	0.557725	0.278862	+	0.960331i	$0.410043\pi$
$824$	−8.00000	−0.278693
$825$	4.00000	0.139262
$826$	0	0
$827$	9.00000	0.312961	0.156480	−	0.987681i	$-0.449985\pi$
$827$	9.00000	0.312961	0.156480	+	0.987681i	$0.449985\pi$
$828$	2.00000	0.0695048
$829$	28.0000	0.972480	0.486240	−	0.873825i	$-0.338368\pi$
$829$	28.0000	0.972480	0.486240	+	0.873825i	$0.338368\pi$
$830$	−3.00000	−0.104132
$831$	2.00000	0.0693792
$832$	4.00000	0.138675
$833$	0	0
$834$	−8.00000	−0.277017
$835$	−12.0000	−0.415277
$836$	1.00000	0.0345857
$837$	−5.00000	−0.172825
$838$	−36.0000	−1.24360
$839$	54.0000	1.86429	0.932144	−	0.362089i	$-0.117936\pi$
$839$	54.0000	1.86429	0.932144	+	0.362089i	$0.117936\pi$
$840$	0	0
$841$	−4.00000	−0.137931
$842$	−38.0000	−1.30957
$843$	30.0000	1.03325
$844$	4.00000	0.137686
$845$	3.00000	0.103203
$846$	−10.0000	−0.343807
$847$	0	0
$848$	13.0000	0.446422
$849$	16.0000	0.549119
$850$	−8.00000	−0.274398
$851$	−12.0000	−0.411355
$852$	−4.00000	−0.137038
$853$	−32.0000	−1.09566	−0.547830	−	0.836590i	$-0.684546\pi$
$853$	−32.0000	−1.09566	−0.547830	+	0.836590i	$0.684546\pi$
$854$	0	0
$855$	−1.00000	−0.0341993
$856$	−15.0000	−0.512689
$857$	10.0000	0.341593	0.170797	−	0.985306i	$-0.445366\pi$
$857$	10.0000	0.341593	0.170797	+	0.985306i	$0.445366\pi$
$858$	4.00000	0.136558
$859$	2.00000	0.0682391	0.0341196	−	0.999418i	$-0.489137\pi$
$859$	2.00000	0.0682391	0.0341196	+	0.999418i	$0.489137\pi$
$860$	8.00000	0.272798
$861$	0	0
$862$	2.00000	0.0681203
$863$	8.00000	0.272323	0.136162	−	0.990687i	$-0.456523\pi$
$863$	8.00000	0.272323	0.136162	+	0.990687i	$0.456523\pi$
$864$	−1.00000	−0.0340207
$865$	−6.00000	−0.204006
$866$	14.0000	0.475739
$867$	−13.0000	−0.441503
$868$	0	0
$869$	5.00000	0.169613
$870$	−5.00000	−0.169516
$871$	40.0000	1.35535
$872$	16.0000	0.541828
$873$	13.0000	0.439983
$874$	2.00000	0.0676510
$875$	0	0
$876$	−14.0000	−0.473016
$877$	38.0000	1.28317	0.641584	−	0.767052i	$-0.278277\pi$
$877$	38.0000	1.28317	0.641584	+	0.767052i	$0.278277\pi$
$878$	25.0000	0.843709
$879$	9.00000	0.303562
$880$	−1.00000	−0.0337100
$881$	−10.0000	−0.336909	−0.168454	−	0.985709i	$-0.553878\pi$
$881$	−10.0000	−0.336909	−0.168454	+	0.985709i	$0.553878\pi$
$882$	0	0
$883$	−38.0000	−1.27880	−0.639401	−	0.768874i	$-0.720818\pi$
$883$	−38.0000	−1.27880	−0.639401	+	0.768874i	$0.720818\pi$
$884$	−8.00000	−0.269069
$885$	−3.00000	−0.100844
$886$	21.0000	0.705509
$887$	14.0000	0.470074	0.235037	−	0.971986i	$-0.424479\pi$
$887$	14.0000	0.470074	0.235037	+	0.971986i	$0.424479\pi$
$888$	6.00000	0.201347
$889$	0	0
$890$	4.00000	0.134080
$891$	−1.00000	−0.0335013
$892$	−15.0000	−0.502237
$893$	−10.0000	−0.334637
$894$	−6.00000	−0.200670
$895$	24.0000	0.802232
$896$	0	0
$897$	8.00000	0.267112
$898$	34.0000	1.13459
$899$	−25.0000	−0.833797
$900$	−4.00000	−0.133333
$901$	−26.0000	−0.866186
$902$	2.00000	0.0665927
$903$	0	0
$904$	−2.00000	−0.0665190
$905$	16.0000	0.531858
$906$	5.00000	0.166114
$907$	−10.0000	−0.332045	−0.166022	−	0.986122i	$-0.553092\pi$
$907$	−10.0000	−0.332045	−0.166022	+	0.986122i	$0.553092\pi$
$908$	15.0000	0.497792
$909$	6.00000	0.199007
$910$	0	0
$911$	−22.0000	−0.728893	−0.364446	−	0.931224i	$-0.618742\pi$
$911$	−22.0000	−0.728893	−0.364446	+	0.931224i	$0.618742\pi$
$912$	−1.00000	−0.0331133
$913$	−3.00000	−0.0992855
$914$	33.0000	1.09154
$915$	10.0000	0.330590
$916$	−12.0000	−0.396491
$917$	0	0
$918$	2.00000	0.0660098
$919$	8.00000	0.263896	0.131948	−	0.991257i	$-0.457877\pi$
$919$	8.00000	0.263896	0.131948	+	0.991257i	$0.457877\pi$
$920$	−2.00000	−0.0659380
$921$	2.00000	0.0659022
$922$	−6.00000	−0.197599
$923$	−16.0000	−0.526646
$924$	0	0
$925$	24.0000	0.789115
$926$	16.0000	0.525793
$927$	8.00000	0.262754
$928$	−5.00000	−0.164133
$929$	−40.0000	−1.31236	−0.656179	−	0.754606i	$-0.727828\pi$
$929$	−40.0000	−1.31236	−0.656179	+	0.754606i	$0.727828\pi$
$930$	5.00000	0.163956
$931$	0	0
$932$	−16.0000	−0.524097
$933$	18.0000	0.589294
$934$	−36.0000	−1.17796
$935$	2.00000	0.0654070
$936$	−4.00000	−0.130744
$937$	−33.0000	−1.07806	−0.539032	−	0.842286i	$-0.681210\pi$
$937$	−33.0000	−1.07806	−0.539032	+	0.842286i	$0.681210\pi$
$938$	0	0
$939$	1.00000	0.0326338
$940$	10.0000	0.326164
$941$	−45.0000	−1.46696	−0.733479	−	0.679712i	$-0.762105\pi$
$941$	−45.0000	−1.46696	−0.733479	+	0.679712i	$0.762105\pi$
$942$	4.00000	0.130327
$943$	4.00000	0.130258
$944$	−3.00000	−0.0976417
$945$	0	0
$946$	8.00000	0.260102
$947$	12.0000	0.389948	0.194974	−	0.980808i	$-0.437538\pi$
$947$	12.0000	0.389948	0.194974	+	0.980808i	$0.437538\pi$
$948$	−5.00000	−0.162392
$949$	−56.0000	−1.81784
$950$	−4.00000	−0.129777
$951$	−15.0000	−0.486408
$952$	0	0
$953$	−54.0000	−1.74923	−0.874616	−	0.484817i	$-0.838886\pi$
$953$	−54.0000	−1.74923	−0.874616	+	0.484817i	$0.838886\pi$
$954$	−13.0000	−0.420891
$955$	−12.0000	−0.388311
$956$	−16.0000	−0.517477
$957$	−5.00000	−0.161627
$958$	14.0000	0.452319
$959$	0	0
$960$	1.00000	0.0322749
$961$	−6.00000	−0.193548
$962$	24.0000	0.773791
$963$	15.0000	0.483368
$964$	17.0000	0.547533
$965$	−1.00000	−0.0321911
$966$	0	0
$967$	−7.00000	−0.225105	−0.112552	−	0.993646i	$-0.535903\pi$
$967$	−7.00000	−0.225105	−0.112552	+	0.993646i	$0.535903\pi$
$968$	10.0000	0.321412
$969$	2.00000	0.0642493
$970$	−13.0000	−0.417405
$971$	3.00000	0.0962746	0.0481373	−	0.998841i	$-0.484672\pi$
$971$	3.00000	0.0962746	0.0481373	+	0.998841i	$0.484672\pi$
$972$	1.00000	0.0320750
$973$	0	0
$974$	7.00000	0.224294
$975$	−16.0000	−0.512410
$976$	10.0000	0.320092
$977$	18.0000	0.575871	0.287936	−	0.957650i	$-0.407031\pi$
$977$	18.0000	0.575871	0.287936	+	0.957650i	$0.407031\pi$
$978$	−4.00000	−0.127906
$979$	4.00000	0.127841
$980$	0	0
$981$	−16.0000	−0.510841
$982$	−19.0000	−0.606314
$983$	−36.0000	−1.14822	−0.574111	−	0.818778i	$-0.694652\pi$
$983$	−36.0000	−1.14822	−0.574111	+	0.818778i	$0.694652\pi$
$984$	−2.00000	−0.0637577
$985$	−6.00000	−0.191176
$986$	10.0000	0.318465
$987$	0	0
$988$	−4.00000	−0.127257
$989$	16.0000	0.508770
$990$	1.00000	0.0317821
$991$	−41.0000	−1.30241	−0.651204	−	0.758903i	$-0.725736\pi$
$991$	−41.0000	−1.30241	−0.651204	+	0.758903i	$0.725736\pi$
$992$	5.00000	0.158750
$993$	−22.0000	−0.698149
$994$	0	0
$995$	8.00000	0.253617
$996$	3.00000	0.0950586
$997$	30.0000	0.950110	0.475055	−	0.879956i	$-0.342428\pi$
$997$	30.0000	0.950110	0.475055	+	0.879956i	$0.342428\pi$
$998$	38.0000	1.20287
$999$	−6.00000	−0.189832

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5586.2.a.s.1.1		1
7.2	even	3		798.2.j.c.571.1	yes	2
7.4	even	3		798.2.j.c.457.1	✓	2
7.6	odd	2		5586.2.a.e.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.j.c.457.1	✓	2	7.4	even	3
798.2.j.c.571.1	yes	2	7.2	even	3
5586.2.a.e.1.1		1	7.6	odd	2
5586.2.a.s.1.1		1	1.1	even	1	trivial

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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