LMFDB - Embedded newform 2166.2.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2166,2,Mod(1,2166)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2166, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2166.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2166 = 2 \cdot 3 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2166.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:	$17.2955970778$
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	$\chi$	$=$	2166.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.00000 q^{5} -1.00000 q^{6} +4.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$

\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.00000 q^{5} -1.00000 q^{6} +4.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -2.00000 q^{10} -2.00000 q^{11} +1.00000 q^{12} -4.00000 q^{13} -4.00000 q^{14} +2.00000 q^{15} +1.00000 q^{16} +6.00000 q^{17} -1.00000 q^{18} +2.00000 q^{20} +4.00000 q^{21} +2.00000 q^{22} -2.00000 q^{23} -1.00000 q^{24} -1.00000 q^{25} +4.00000 q^{26} +1.00000 q^{27} +4.00000 q^{28} +10.0000 q^{29} -2.00000 q^{30} -8.00000 q^{31} -1.00000 q^{32} -2.00000 q^{33} -6.00000 q^{34} +8.00000 q^{35} +1.00000 q^{36} +8.00000 q^{37} -4.00000 q^{39} -2.00000 q^{40} +2.00000 q^{41} -4.00000 q^{42} +4.00000 q^{43} -2.00000 q^{44} +2.00000 q^{45} +2.00000 q^{46} +6.00000 q^{47} +1.00000 q^{48} +9.00000 q^{49} +1.00000 q^{50} +6.00000 q^{51} -4.00000 q^{52} +10.0000 q^{53} -1.00000 q^{54} -4.00000 q^{55} -4.00000 q^{56} -10.0000 q^{58} +4.00000 q^{59} +2.00000 q^{60} -14.0000 q^{61} +8.00000 q^{62} +4.00000 q^{63} +1.00000 q^{64} -8.00000 q^{65} +2.00000 q^{66} -8.00000 q^{67} +6.00000 q^{68} -2.00000 q^{69} -8.00000 q^{70} -1.00000 q^{72} +10.0000 q^{73} -8.00000 q^{74} -1.00000 q^{75} -8.00000 q^{77} +4.00000 q^{78} +12.0000 q^{79} +2.00000 q^{80} +1.00000 q^{81} -2.00000 q^{82} +2.00000 q^{83} +4.00000 q^{84} +12.0000 q^{85} -4.00000 q^{86} +10.0000 q^{87} +2.00000 q^{88} -6.00000 q^{89} -2.00000 q^{90} -16.0000 q^{91} -2.00000 q^{92} -8.00000 q^{93} -6.00000 q^{94} -1.00000 q^{96} -12.0000 q^{97} -9.00000 q^{98} -2.00000 q^{99} +O(q^{100})\)

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
$5$	2.00000	0.894427	0.447214	−	0.894427i	$-0.352416\pi$
$5$	2.00000	0.894427	0.447214	+	0.894427i	$0.352416\pi$
$6$	−1.00000	−0.408248
$7$	4.00000	1.51186	0.755929	−	0.654654i	$-0.227186\pi$
$7$	4.00000	1.51186	0.755929	+	0.654654i	$0.227186\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−2.00000	−0.632456
$11$	−2.00000	−0.603023	−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000	−0.603023	−0.301511	+	0.953463i	$0.597491\pi$
$12$	1.00000	0.288675
$13$	−4.00000	−1.10940	−0.554700	−	0.832050i	$-0.687167\pi$
$13$	−4.00000	−1.10940	−0.554700	+	0.832050i	$0.687167\pi$
$14$	−4.00000	−1.06904
$15$	2.00000	0.516398
$16$	1.00000	0.250000
$17$	6.00000	1.45521	0.727607	−	0.685994i	$-0.240633\pi$
$17$	6.00000	1.45521	0.727607	+	0.685994i	$0.240633\pi$
$18$	−1.00000	−0.235702
$19$	0	0
$19$	0	0
$20$	2.00000	0.447214
$21$	4.00000	0.872872
$22$	2.00000	0.426401
$23$	−2.00000	−0.417029	−0.208514	−	0.978019i	$-0.566863\pi$
$23$	−2.00000	−0.417029	−0.208514	+	0.978019i	$0.566863\pi$
$24$	−1.00000	−0.204124
$25$	−1.00000	−0.200000
$26$	4.00000	0.784465
$27$	1.00000	0.192450
$28$	4.00000	0.755929
$29$	10.0000	1.85695	0.928477	−	0.371391i	$-0.121119\pi$
$29$	10.0000	1.85695	0.928477	+	0.371391i	$0.121119\pi$
$30$	−2.00000	−0.365148
$31$	−8.00000	−1.43684	−0.718421	−	0.695608i	$-0.755135\pi$
$31$	−8.00000	−1.43684	−0.718421	+	0.695608i	$0.755135\pi$
$32$	−1.00000	−0.176777
$33$	−2.00000	−0.348155
$34$	−6.00000	−1.02899
$35$	8.00000	1.35225
$36$	1.00000	0.166667
$37$	8.00000	1.31519	0.657596	−	0.753371i	$-0.271573\pi$
$37$	8.00000	1.31519	0.657596	+	0.753371i	$0.271573\pi$
$38$	0	0
$39$	−4.00000	−0.640513
$40$	−2.00000	−0.316228
$41$	2.00000	0.312348	0.156174	−	0.987730i	$-0.450084\pi$
$41$	2.00000	0.312348	0.156174	+	0.987730i	$0.450084\pi$
$42$	−4.00000	−0.617213
$43$	4.00000	0.609994	0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000	0.609994	0.304997	+	0.952353i	$0.401344\pi$
$44$	−2.00000	−0.301511
$45$	2.00000	0.298142
$46$	2.00000	0.294884
$47$	6.00000	0.875190	0.437595	−	0.899172i	$-0.355830\pi$
$47$	6.00000	0.875190	0.437595	+	0.899172i	$0.355830\pi$
$48$	1.00000	0.144338
$49$	9.00000	1.28571
$50$	1.00000	0.141421
$51$	6.00000	0.840168
$52$	−4.00000	−0.554700
$53$	10.0000	1.37361	0.686803	−	0.726844i	$-0.259014\pi$
$53$	10.0000	1.37361	0.686803	+	0.726844i	$0.259014\pi$
$54$	−1.00000	−0.136083
$55$	−4.00000	−0.539360
$56$	−4.00000	−0.534522
$57$	0	0
$58$	−10.0000	−1.31306
$59$	4.00000	0.520756	0.260378	−	0.965507i	$-0.416153\pi$
$59$	4.00000	0.520756	0.260378	+	0.965507i	$0.416153\pi$
$60$	2.00000	0.258199
$61$	−14.0000	−1.79252	−0.896258	−	0.443533i	$-0.853725\pi$
$61$	−14.0000	−1.79252	−0.896258	+	0.443533i	$0.853725\pi$
$62$	8.00000	1.01600
$63$	4.00000	0.503953
$64$	1.00000	0.125000
$65$	−8.00000	−0.992278
$66$	2.00000	0.246183
$67$	−8.00000	−0.977356	−0.488678	−	0.872464i	$-0.662521\pi$
$67$	−8.00000	−0.977356	−0.488678	+	0.872464i	$0.662521\pi$
$68$	6.00000	0.727607
$69$	−2.00000	−0.240772
$70$	−8.00000	−0.956183
$71$	0	0		−	1.00000i	$-0.5\pi$
$71$	0	0			1.00000i	$0.5\pi$
$72$	−1.00000	−0.117851
$73$	10.0000	1.17041	0.585206	−	0.810885i	$-0.301014\pi$
$73$	10.0000	1.17041	0.585206	+	0.810885i	$0.301014\pi$
$74$	−8.00000	−0.929981
$75$	−1.00000	−0.115470
$76$	0	0
$77$	−8.00000	−0.911685
$78$	4.00000	0.452911
$79$	12.0000	1.35011	0.675053	−	0.737769i	$-0.264121\pi$
$79$	12.0000	1.35011	0.675053	+	0.737769i	$0.264121\pi$
$80$	2.00000	0.223607
$81$	1.00000	0.111111
$82$	−2.00000	−0.220863
$83$	2.00000	0.219529	0.109764	−	0.993958i	$-0.464990\pi$
$83$	2.00000	0.219529	0.109764	+	0.993958i	$0.464990\pi$
$84$	4.00000	0.436436
$85$	12.0000	1.30158
$86$	−4.00000	−0.431331
$87$	10.0000	1.07211
$88$	2.00000	0.213201
$89$	−6.00000	−0.635999	−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000	−0.635999	−0.317999	+	0.948091i	$0.603011\pi$
$90$	−2.00000	−0.210819
$91$	−16.0000	−1.67726
$92$	−2.00000	−0.208514
$93$	−8.00000	−0.829561
$94$	−6.00000	−0.618853
$95$	0	0
$96$	−1.00000	−0.102062
$97$	−12.0000	−1.21842	−0.609208	−	0.793011i	$-0.708512\pi$
$97$	−12.0000	−1.21842	−0.609208	+	0.793011i	$0.708512\pi$
$98$	−9.00000	−0.909137
$99$	−2.00000	−0.201008
$100$	−1.00000	−0.100000
$101$	−18.0000	−1.79107	−0.895533	−	0.444994i	$-0.853206\pi$
$101$	−18.0000	−1.79107	−0.895533	+	0.444994i	$0.853206\pi$
$102$	−6.00000	−0.594089
$103$	−20.0000	−1.97066	−0.985329	−	0.170664i	$-0.945409\pi$
$103$	−20.0000	−1.97066	−0.985329	+	0.170664i	$0.945409\pi$
$104$	4.00000	0.392232
$105$	8.00000	0.780720
$106$	−10.0000	−0.971286
$107$	−4.00000	−0.386695	−0.193347	−	0.981130i	$-0.561934\pi$
$107$	−4.00000	−0.386695	−0.193347	+	0.981130i	$0.561934\pi$
$108$	1.00000	0.0962250
$109$	4.00000	0.383131	0.191565	−	0.981480i	$-0.438644\pi$
$109$	4.00000	0.383131	0.191565	+	0.981480i	$0.438644\pi$
$110$	4.00000	0.381385
$111$	8.00000	0.759326
$112$	4.00000	0.377964
$113$	2.00000	0.188144	0.0940721	−	0.995565i	$-0.470012\pi$
$113$	2.00000	0.188144	0.0940721	+	0.995565i	$0.470012\pi$
$114$	0	0
$115$	−4.00000	−0.373002
$116$	10.0000	0.928477
$117$	−4.00000	−0.369800
$118$	−4.00000	−0.368230
$119$	24.0000	2.20008
$120$	−2.00000	−0.182574
$121$	−7.00000	−0.636364
$122$	14.0000	1.26750
$123$	2.00000	0.180334
$124$	−8.00000	−0.718421
$125$	−12.0000	−1.07331
$126$	−4.00000	−0.356348
$127$	16.0000	1.41977	0.709885	−	0.704317i	$-0.248747\pi$
$127$	16.0000	1.41977	0.709885	+	0.704317i	$0.248747\pi$
$128$	−1.00000	−0.0883883
$129$	4.00000	0.352180
$130$	8.00000	0.701646
$131$	14.0000	1.22319	0.611593	−	0.791173i	$-0.290529\pi$
$131$	14.0000	1.22319	0.611593	+	0.791173i	$0.290529\pi$
$132$	−2.00000	−0.174078
$133$	0	0
$134$	8.00000	0.691095
$135$	2.00000	0.172133
$136$	−6.00000	−0.514496
$137$	−2.00000	−0.170872	−0.0854358	−	0.996344i	$-0.527228\pi$
$137$	−2.00000	−0.170872	−0.0854358	+	0.996344i	$0.527228\pi$
$138$	2.00000	0.170251
$139$	−8.00000	−0.678551	−0.339276	−	0.940687i	$-0.610182\pi$
$139$	−8.00000	−0.678551	−0.339276	+	0.940687i	$0.610182\pi$
$140$	8.00000	0.676123
$141$	6.00000	0.505291
$142$	0	0
$143$	8.00000	0.668994
$144$	1.00000	0.0833333
$145$	20.0000	1.66091
$146$	−10.0000	−0.827606
$147$	9.00000	0.742307
$148$	8.00000	0.657596
$149$	6.00000	0.491539	0.245770	−	0.969328i	$-0.420959\pi$
$149$	6.00000	0.491539	0.245770	+	0.969328i	$0.420959\pi$
$150$	1.00000	0.0816497
$151$	4.00000	0.325515	0.162758	−	0.986666i	$-0.447961\pi$
$151$	4.00000	0.325515	0.162758	+	0.986666i	$0.447961\pi$
$152$	0	0
$153$	6.00000	0.485071
$154$	8.00000	0.644658
$155$	−16.0000	−1.28515
$156$	−4.00000	−0.320256
$157$	14.0000	1.11732	0.558661	−	0.829396i	$-0.311315\pi$
$157$	14.0000	1.11732	0.558661	+	0.829396i	$0.311315\pi$
$158$	−12.0000	−0.954669
$159$	10.0000	0.793052
$160$	−2.00000	−0.158114
$161$	−8.00000	−0.630488
$162$	−1.00000	−0.0785674
$163$	8.00000	0.626608	0.313304	−	0.949653i	$-0.398564\pi$
$163$	8.00000	0.626608	0.313304	+	0.949653i	$0.398564\pi$
$164$	2.00000	0.156174
$165$	−4.00000	−0.311400
$166$	−2.00000	−0.155230
$167$	−16.0000	−1.23812	−0.619059	−	0.785345i	$-0.712486\pi$
$167$	−16.0000	−1.23812	−0.619059	+	0.785345i	$0.712486\pi$
$168$	−4.00000	−0.308607
$169$	3.00000	0.230769
$170$	−12.0000	−0.920358
$171$	0	0
$172$	4.00000	0.304997
$173$	−10.0000	−0.760286	−0.380143	−	0.924928i	$-0.624125\pi$
$173$	−10.0000	−0.760286	−0.380143	+	0.924928i	$0.624125\pi$
$174$	−10.0000	−0.758098
$175$	−4.00000	−0.302372
$176$	−2.00000	−0.150756
$177$	4.00000	0.300658
$178$	6.00000	0.449719
$179$	12.0000	0.896922	0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000	0.896922	0.448461	+	0.893802i	$0.351972\pi$
$180$	2.00000	0.149071
$181$	−4.00000	−0.297318	−0.148659	−	0.988889i	$-0.547496\pi$
$181$	−4.00000	−0.297318	−0.148659	+	0.988889i	$0.547496\pi$
$182$	16.0000	1.18600
$183$	−14.0000	−1.03491
$184$	2.00000	0.147442
$185$	16.0000	1.17634
$186$	8.00000	0.586588
$187$	−12.0000	−0.877527
$188$	6.00000	0.437595
$189$	4.00000	0.290957
$190$	0	0
$191$	10.0000	0.723575	0.361787	−	0.932261i	$-0.382167\pi$
$191$	10.0000	0.723575	0.361787	+	0.932261i	$0.382167\pi$
$192$	1.00000	0.0721688
$193$	8.00000	0.575853	0.287926	−	0.957653i	$-0.407034\pi$
$193$	8.00000	0.575853	0.287926	+	0.957653i	$0.407034\pi$
$194$	12.0000	0.861550
$195$	−8.00000	−0.572892
$196$	9.00000	0.642857
$197$	18.0000	1.28245	0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000	1.28245	0.641223	+	0.767354i	$0.278427\pi$
$198$	2.00000	0.142134
$199$	0	0		−	1.00000i	$-0.5\pi$
$199$	0	0			1.00000i	$0.5\pi$
$200$	1.00000	0.0707107
$201$	−8.00000	−0.564276
$202$	18.0000	1.26648
$203$	40.0000	2.80745
$204$	6.00000	0.420084
$205$	4.00000	0.279372
$206$	20.0000	1.39347
$207$	−2.00000	−0.139010
$208$	−4.00000	−0.277350
$209$	0	0
$210$	−8.00000	−0.552052
$211$	−24.0000	−1.65223	−0.826114	−	0.563503i	$-0.809453\pi$
$211$	−24.0000	−1.65223	−0.826114	+	0.563503i	$0.809453\pi$
$212$	10.0000	0.686803
$213$	0	0
$214$	4.00000	0.273434
$215$	8.00000	0.545595
$216$	−1.00000	−0.0680414
$217$	−32.0000	−2.17230
$218$	−4.00000	−0.270914
$219$	10.0000	0.675737
$220$	−4.00000	−0.269680
$221$	−24.0000	−1.61441
$222$	−8.00000	−0.536925
$223$	−4.00000	−0.267860	−0.133930	−	0.990991i	$-0.542760\pi$
$223$	−4.00000	−0.267860	−0.133930	+	0.990991i	$0.542760\pi$
$224$	−4.00000	−0.267261
$225$	−1.00000	−0.0666667
$226$	−2.00000	−0.133038
$227$	4.00000	0.265489	0.132745	−	0.991150i	$-0.457621\pi$
$227$	4.00000	0.265489	0.132745	+	0.991150i	$0.457621\pi$
$228$	0	0
$229$	2.00000	0.132164	0.0660819	−	0.997814i	$-0.478950\pi$
$229$	2.00000	0.132164	0.0660819	+	0.997814i	$0.478950\pi$
$230$	4.00000	0.263752
$231$	−8.00000	−0.526361
$232$	−10.0000	−0.656532
$233$	−14.0000	−0.917170	−0.458585	−	0.888650i	$-0.651644\pi$
$233$	−14.0000	−0.917170	−0.458585	+	0.888650i	$0.651644\pi$
$234$	4.00000	0.261488
$235$	12.0000	0.782794
$236$	4.00000	0.260378
$237$	12.0000	0.779484
$238$	−24.0000	−1.55569
$239$	−6.00000	−0.388108	−0.194054	−	0.980991i	$-0.562164\pi$
$239$	−6.00000	−0.388108	−0.194054	+	0.980991i	$0.562164\pi$
$240$	2.00000	0.129099
$241$	4.00000	0.257663	0.128831	−	0.991667i	$-0.458877\pi$
$241$	4.00000	0.257663	0.128831	+	0.991667i	$0.458877\pi$
$242$	7.00000	0.449977
$243$	1.00000	0.0641500
$244$	−14.0000	−0.896258
$245$	18.0000	1.14998
$246$	−2.00000	−0.127515
$247$	0	0
$248$	8.00000	0.508001
$249$	2.00000	0.126745
$250$	12.0000	0.758947
$251$	−6.00000	−0.378717	−0.189358	−	0.981908i	$-0.560641\pi$
$251$	−6.00000	−0.378717	−0.189358	+	0.981908i	$0.560641\pi$
$252$	4.00000	0.251976
$253$	4.00000	0.251478
$254$	−16.0000	−1.00393
$255$	12.0000	0.751469
$256$	1.00000	0.0625000
$257$	−10.0000	−0.623783	−0.311891	−	0.950118i	$-0.600963\pi$
$257$	−10.0000	−0.623783	−0.311891	+	0.950118i	$0.600963\pi$
$258$	−4.00000	−0.249029
$259$	32.0000	1.98838
$260$	−8.00000	−0.496139
$261$	10.0000	0.618984
$262$	−14.0000	−0.864923
$263$	−22.0000	−1.35658	−0.678289	−	0.734795i	$-0.737278\pi$
$263$	−22.0000	−1.35658	−0.678289	+	0.734795i	$0.737278\pi$
$264$	2.00000	0.123091
$265$	20.0000	1.22859
$266$	0	0
$267$	−6.00000	−0.367194
$268$	−8.00000	−0.488678
$269$	6.00000	0.365826	0.182913	−	0.983129i	$-0.441447\pi$
$269$	6.00000	0.365826	0.182913	+	0.983129i	$0.441447\pi$
$270$	−2.00000	−0.121716
$271$	−32.0000	−1.94386	−0.971931	−	0.235267i	$-0.924404\pi$
$271$	−32.0000	−1.94386	−0.971931	+	0.235267i	$0.924404\pi$
$272$	6.00000	0.363803
$273$	−16.0000	−0.968364
$274$	2.00000	0.120824
$275$	2.00000	0.120605
$276$	−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
$279$	−8.00000	−0.478947
$280$	−8.00000	−0.478091
$281$	30.0000	1.78965	0.894825	−	0.446417i	$-0.147300\pi$
$281$	30.0000	1.78965	0.894825	+	0.446417i	$0.147300\pi$
$282$	−6.00000	−0.357295
$283$	−28.0000	−1.66443	−0.832214	−	0.554455i	$-0.812927\pi$
$283$	−28.0000	−1.66443	−0.832214	+	0.554455i	$0.812927\pi$
$284$	0	0
$285$	0	0
$286$	−8.00000	−0.473050
$287$	8.00000	0.472225
$288$	−1.00000	−0.0589256
$289$	19.0000	1.11765
$290$	−20.0000	−1.17444
$291$	−12.0000	−0.703452
$292$	10.0000	0.585206
$293$	30.0000	1.75262	0.876309	−	0.481749i	$-0.159998\pi$
$293$	30.0000	1.75262	0.876309	+	0.481749i	$0.159998\pi$
$294$	−9.00000	−0.524891
$295$	8.00000	0.465778
$296$	−8.00000	−0.464991
$297$	−2.00000	−0.116052
$298$	−6.00000	−0.347571
$299$	8.00000	0.462652
$300$	−1.00000	−0.0577350
$301$	16.0000	0.922225
$302$	−4.00000	−0.230174
$303$	−18.0000	−1.03407
$304$	0	0
$305$	−28.0000	−1.60328
$306$	−6.00000	−0.342997
$307$	−12.0000	−0.684876	−0.342438	−	0.939540i	$-0.611253\pi$
$307$	−12.0000	−0.684876	−0.342438	+	0.939540i	$0.611253\pi$
$308$	−8.00000	−0.455842
$309$	−20.0000	−1.13776
$310$	16.0000	0.908739
$311$	−18.0000	−1.02069	−0.510343	−	0.859971i	$-0.670482\pi$
$311$	−18.0000	−1.02069	−0.510343	+	0.859971i	$0.670482\pi$
$312$	4.00000	0.226455
$313$	14.0000	0.791327	0.395663	−	0.918396i	$-0.370515\pi$
$313$	14.0000	0.791327	0.395663	+	0.918396i	$0.370515\pi$
$314$	−14.0000	−0.790066
$315$	8.00000	0.450749
$316$	12.0000	0.675053
$317$	−2.00000	−0.112331	−0.0561656	−	0.998421i	$-0.517887\pi$
$317$	−2.00000	−0.112331	−0.0561656	+	0.998421i	$0.517887\pi$
$318$	−10.0000	−0.560772
$319$	−20.0000	−1.11979
$320$	2.00000	0.111803
$321$	−4.00000	−0.223258
$322$	8.00000	0.445823
$323$	0	0
$324$	1.00000	0.0555556
$325$	4.00000	0.221880
$326$	−8.00000	−0.443079
$327$	4.00000	0.221201
$328$	−2.00000	−0.110432
$329$	24.0000	1.32316
$330$	4.00000	0.220193
$331$	12.0000	0.659580	0.329790	−	0.944054i	$-0.393022\pi$
$331$	12.0000	0.659580	0.329790	+	0.944054i	$0.393022\pi$
$332$	2.00000	0.109764
$333$	8.00000	0.438397
$334$	16.0000	0.875481
$335$	−16.0000	−0.874173
$336$	4.00000	0.218218
$337$	−4.00000	−0.217894	−0.108947	−	0.994048i	$-0.534748\pi$
$337$	−4.00000	−0.217894	−0.108947	+	0.994048i	$0.534748\pi$
$338$	−3.00000	−0.163178
$339$	2.00000	0.108625
$340$	12.0000	0.650791
$341$	16.0000	0.866449
$342$	0	0
$343$	8.00000	0.431959
$344$	−4.00000	−0.215666
$345$	−4.00000	−0.215353
$346$	10.0000	0.537603
$347$	30.0000	1.61048	0.805242	−	0.592946i	$-0.202035\pi$
$347$	30.0000	1.61048	0.805242	+	0.592946i	$0.202035\pi$
$348$	10.0000	0.536056
$349$	−14.0000	−0.749403	−0.374701	−	0.927146i	$-0.622255\pi$
$349$	−14.0000	−0.749403	−0.374701	+	0.927146i	$0.622255\pi$
$350$	4.00000	0.213809
$351$	−4.00000	−0.213504
$352$	2.00000	0.106600
$353$	−10.0000	−0.532246	−0.266123	−	0.963939i	$-0.585743\pi$
$353$	−10.0000	−0.532246	−0.266123	+	0.963939i	$0.585743\pi$
$354$	−4.00000	−0.212598
$355$	0	0
$356$	−6.00000	−0.317999
$357$	24.0000	1.27021
$358$	−12.0000	−0.634220
$359$	−30.0000	−1.58334	−0.791670	−	0.610949i	$-0.790788\pi$
$359$	−30.0000	−1.58334	−0.791670	+	0.610949i	$0.790788\pi$
$360$	−2.00000	−0.105409
$361$	0	0
$362$	4.00000	0.210235
$363$	−7.00000	−0.367405
$364$	−16.0000	−0.838628
$365$	20.0000	1.04685
$366$	14.0000	0.731792
$367$	8.00000	0.417597	0.208798	−	0.977959i	$-0.433045\pi$
$367$	8.00000	0.417597	0.208798	+	0.977959i	$0.433045\pi$
$368$	−2.00000	−0.104257
$369$	2.00000	0.104116
$370$	−16.0000	−0.831800
$371$	40.0000	2.07670
$372$	−8.00000	−0.414781
$373$	0	0		−	1.00000i	$-0.5\pi$
$373$	0	0			1.00000i	$0.5\pi$
$374$	12.0000	0.620505
$375$	−12.0000	−0.619677
$376$	−6.00000	−0.309426
$377$	−40.0000	−2.06010
$378$	−4.00000	−0.205738
$379$	4.00000	0.205466	0.102733	−	0.994709i	$-0.467241\pi$
$379$	4.00000	0.205466	0.102733	+	0.994709i	$0.467241\pi$
$380$	0	0
$381$	16.0000	0.819705
$382$	−10.0000	−0.511645
$383$	24.0000	1.22634	0.613171	−	0.789950i	$-0.289894\pi$
$383$	24.0000	1.22634	0.613171	+	0.789950i	$0.289894\pi$
$384$	−1.00000	−0.0510310
$385$	−16.0000	−0.815436
$386$	−8.00000	−0.407189
$387$	4.00000	0.203331
$388$	−12.0000	−0.609208
$389$	−30.0000	−1.52106	−0.760530	−	0.649303i	$-0.775061\pi$
$389$	−30.0000	−1.52106	−0.760530	+	0.649303i	$0.775061\pi$
$390$	8.00000	0.405096
$391$	−12.0000	−0.606866
$392$	−9.00000	−0.454569
$393$	14.0000	0.706207
$394$	−18.0000	−0.906827
$395$	24.0000	1.20757
$396$	−2.00000	−0.100504
$397$	2.00000	0.100377	0.0501886	−	0.998740i	$-0.484018\pi$
$397$	2.00000	0.100377	0.0501886	+	0.998740i	$0.484018\pi$
$398$	0	0
$399$	0	0
$400$	−1.00000	−0.0500000
$401$	34.0000	1.69788	0.848939	−	0.528490i	$-0.177242\pi$
$401$	34.0000	1.69788	0.848939	+	0.528490i	$0.177242\pi$
$402$	8.00000	0.399004
$403$	32.0000	1.59403
$404$	−18.0000	−0.895533
$405$	2.00000	0.0993808
$406$	−40.0000	−1.98517
$407$	−16.0000	−0.793091
$408$	−6.00000	−0.297044
$409$	−20.0000	−0.988936	−0.494468	−	0.869196i	$-0.664637\pi$
$409$	−20.0000	−0.988936	−0.494468	+	0.869196i	$0.664637\pi$
$410$	−4.00000	−0.197546
$411$	−2.00000	−0.0986527
$412$	−20.0000	−0.985329
$413$	16.0000	0.787309
$414$	2.00000	0.0982946
$415$	4.00000	0.196352
$416$	4.00000	0.196116
$417$	−8.00000	−0.391762
$418$	0	0
$419$	14.0000	0.683945	0.341972	−	0.939710i	$-0.388905\pi$
$419$	14.0000	0.683945	0.341972	+	0.939710i	$0.388905\pi$
$420$	8.00000	0.390360
$421$	20.0000	0.974740	0.487370	−	0.873195i	$-0.337956\pi$
$421$	20.0000	0.974740	0.487370	+	0.873195i	$0.337956\pi$
$422$	24.0000	1.16830
$423$	6.00000	0.291730
$424$	−10.0000	−0.485643
$425$	−6.00000	−0.291043
$426$	0	0
$427$	−56.0000	−2.71003
$428$	−4.00000	−0.193347
$429$	8.00000	0.386244
$430$	−8.00000	−0.385794
$431$	−24.0000	−1.15604	−0.578020	−	0.816023i	$-0.696174\pi$
$431$	−24.0000	−1.15604	−0.578020	+	0.816023i	$0.696174\pi$
$432$	1.00000	0.0481125
$433$	−16.0000	−0.768911	−0.384455	−	0.923144i	$-0.625611\pi$
$433$	−16.0000	−0.768911	−0.384455	+	0.923144i	$0.625611\pi$
$434$	32.0000	1.53605
$435$	20.0000	0.958927
$436$	4.00000	0.191565
$437$	0	0
$438$	−10.0000	−0.477818
$439$	−28.0000	−1.33637	−0.668184	−	0.743996i	$-0.732928\pi$
$439$	−28.0000	−1.33637	−0.668184	+	0.743996i	$0.732928\pi$
$440$	4.00000	0.190693
$441$	9.00000	0.428571
$442$	24.0000	1.14156
$443$	6.00000	0.285069	0.142534	−	0.989790i	$-0.454475\pi$
$443$	6.00000	0.285069	0.142534	+	0.989790i	$0.454475\pi$
$444$	8.00000	0.379663
$445$	−12.0000	−0.568855
$446$	4.00000	0.189405
$447$	6.00000	0.283790
$448$	4.00000	0.188982
$449$	22.0000	1.03824	0.519122	−	0.854700i	$-0.326259\pi$
$449$	22.0000	1.03824	0.519122	+	0.854700i	$0.326259\pi$
$450$	1.00000	0.0471405
$451$	−4.00000	−0.188353
$452$	2.00000	0.0940721
$453$	4.00000	0.187936
$454$	−4.00000	−0.187729
$455$	−32.0000	−1.50018
$456$	0	0
$457$	22.0000	1.02912	0.514558	−	0.857455i	$-0.327956\pi$
$457$	22.0000	1.02912	0.514558	+	0.857455i	$0.327956\pi$
$458$	−2.00000	−0.0934539
$459$	6.00000	0.280056
$460$	−4.00000	−0.186501
$461$	−10.0000	−0.465746	−0.232873	−	0.972507i	$-0.574813\pi$
$461$	−10.0000	−0.465746	−0.232873	+	0.972507i	$0.574813\pi$
$462$	8.00000	0.372194
$463$	−24.0000	−1.11537	−0.557687	−	0.830051i	$-0.688311\pi$
$463$	−24.0000	−1.11537	−0.557687	+	0.830051i	$0.688311\pi$
$464$	10.0000	0.464238
$465$	−16.0000	−0.741982
$466$	14.0000	0.648537
$467$	−6.00000	−0.277647	−0.138823	−	0.990317i	$-0.544332\pi$
$467$	−6.00000	−0.277647	−0.138823	+	0.990317i	$0.544332\pi$
$468$	−4.00000	−0.184900
$469$	−32.0000	−1.47762
$470$	−12.0000	−0.553519
$471$	14.0000	0.645086
$472$	−4.00000	−0.184115
$473$	−8.00000	−0.367840
$474$	−12.0000	−0.551178
$475$	0	0
$476$	24.0000	1.10004
$477$	10.0000	0.457869
$478$	6.00000	0.274434
$479$	2.00000	0.0913823	0.0456912	−	0.998956i	$-0.485451\pi$
$479$	2.00000	0.0913823	0.0456912	+	0.998956i	$0.485451\pi$
$480$	−2.00000	−0.0912871
$481$	−32.0000	−1.45907
$482$	−4.00000	−0.182195
$483$	−8.00000	−0.364013
$484$	−7.00000	−0.318182
$485$	−24.0000	−1.08978
$486$	−1.00000	−0.0453609
$487$	−24.0000	−1.08754	−0.543772	−	0.839233i	$-0.683004\pi$
$487$	−24.0000	−1.08754	−0.543772	+	0.839233i	$0.683004\pi$
$488$	14.0000	0.633750
$489$	8.00000	0.361773
$490$	−18.0000	−0.813157
$491$	−34.0000	−1.53440	−0.767199	−	0.641409i	$-0.778350\pi$
$491$	−34.0000	−1.53440	−0.767199	+	0.641409i	$0.778350\pi$
$492$	2.00000	0.0901670
$493$	60.0000	2.70226
$494$	0	0
$495$	−4.00000	−0.179787
$496$	−8.00000	−0.359211
$497$	0	0
$498$	−2.00000	−0.0896221
$499$	−24.0000	−1.07439	−0.537194	−	0.843459i	$-0.680516\pi$
$499$	−24.0000	−1.07439	−0.537194	+	0.843459i	$0.680516\pi$
$500$	−12.0000	−0.536656
$501$	−16.0000	−0.714827
$502$	6.00000	0.267793
$503$	−6.00000	−0.267527	−0.133763	−	0.991013i	$-0.542706\pi$
$503$	−6.00000	−0.267527	−0.133763	+	0.991013i	$0.542706\pi$
$504$	−4.00000	−0.178174
$505$	−36.0000	−1.60198
$506$	−4.00000	−0.177822
$507$	3.00000	0.133235
$508$	16.0000	0.709885
$509$	−18.0000	−0.797836	−0.398918	−	0.916987i	$-0.630614\pi$
$509$	−18.0000	−0.797836	−0.398918	+	0.916987i	$0.630614\pi$
$510$	−12.0000	−0.531369
$511$	40.0000	1.76950
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	10.0000	0.441081
$515$	−40.0000	−1.76261
$516$	4.00000	0.176090
$517$	−12.0000	−0.527759
$518$	−32.0000	−1.40600
$519$	−10.0000	−0.438951
$520$	8.00000	0.350823
$521$	−30.0000	−1.31432	−0.657162	−	0.753749i	$-0.728243\pi$
$521$	−30.0000	−1.31432	−0.657162	+	0.753749i	$0.728243\pi$
$522$	−10.0000	−0.437688
$523$	−16.0000	−0.699631	−0.349816	−	0.936819i	$-0.613756\pi$
$523$	−16.0000	−0.699631	−0.349816	+	0.936819i	$0.613756\pi$
$524$	14.0000	0.611593
$525$	−4.00000	−0.174574
$526$	22.0000	0.959246
$527$	−48.0000	−2.09091
$528$	−2.00000	−0.0870388
$529$	−19.0000	−0.826087
$530$	−20.0000	−0.868744
$531$	4.00000	0.173585
$532$	0	0
$533$	−8.00000	−0.346518
$534$	6.00000	0.259645
$535$	−8.00000	−0.345870
$536$	8.00000	0.345547
$537$	12.0000	0.517838
$538$	−6.00000	−0.258678
$539$	−18.0000	−0.775315
$540$	2.00000	0.0860663
$541$	2.00000	0.0859867	0.0429934	−	0.999075i	$-0.486311\pi$
$541$	2.00000	0.0859867	0.0429934	+	0.999075i	$0.486311\pi$
$542$	32.0000	1.37452
$543$	−4.00000	−0.171656
$544$	−6.00000	−0.257248
$545$	8.00000	0.342682
$546$	16.0000	0.684737
$547$	−20.0000	−0.855138	−0.427569	−	0.903983i	$-0.640630\pi$
$547$	−20.0000	−0.855138	−0.427569	+	0.903983i	$0.640630\pi$
$548$	−2.00000	−0.0854358
$549$	−14.0000	−0.597505
$550$	−2.00000	−0.0852803
$551$	0	0
$552$	2.00000	0.0851257
$553$	48.0000	2.04117
$554$	−2.00000	−0.0849719
$555$	16.0000	0.679162
$556$	−8.00000	−0.339276
$557$	22.0000	0.932170	0.466085	−	0.884740i	$-0.345664\pi$
$557$	22.0000	0.932170	0.466085	+	0.884740i	$0.345664\pi$
$558$	8.00000	0.338667
$559$	−16.0000	−0.676728
$560$	8.00000	0.338062
$561$	−12.0000	−0.506640
$562$	−30.0000	−1.26547
$563$	−4.00000	−0.168580	−0.0842900	−	0.996441i	$-0.526862\pi$
$563$	−4.00000	−0.168580	−0.0842900	+	0.996441i	$0.526862\pi$
$564$	6.00000	0.252646
$565$	4.00000	0.168281
$566$	28.0000	1.17693
$567$	4.00000	0.167984
$568$	0	0
$569$	−18.0000	−0.754599	−0.377300	−	0.926091i	$-0.623147\pi$
$569$	−18.0000	−0.754599	−0.377300	+	0.926091i	$0.623147\pi$
$570$	0	0
$571$	−4.00000	−0.167395	−0.0836974	−	0.996491i	$-0.526673\pi$
$571$	−4.00000	−0.167395	−0.0836974	+	0.996491i	$0.526673\pi$
$572$	8.00000	0.334497
$573$	10.0000	0.417756
$574$	−8.00000	−0.333914
$575$	2.00000	0.0834058
$576$	1.00000	0.0416667
$577$	22.0000	0.915872	0.457936	−	0.888985i	$-0.348589\pi$
$577$	22.0000	0.915872	0.457936	+	0.888985i	$0.348589\pi$
$578$	−19.0000	−0.790296
$579$	8.00000	0.332469
$580$	20.0000	0.830455
$581$	8.00000	0.331896
$582$	12.0000	0.497416
$583$	−20.0000	−0.828315
$584$	−10.0000	−0.413803
$585$	−8.00000	−0.330759
$586$	−30.0000	−1.23929
$587$	−14.0000	−0.577842	−0.288921	−	0.957353i	$-0.593296\pi$
$587$	−14.0000	−0.577842	−0.288921	+	0.957353i	$0.593296\pi$
$588$	9.00000	0.371154
$589$	0	0
$590$	−8.00000	−0.329355
$591$	18.0000	0.740421
$592$	8.00000	0.328798
$593$	−30.0000	−1.23195	−0.615976	−	0.787765i	$-0.711238\pi$
$593$	−30.0000	−1.23195	−0.615976	+	0.787765i	$0.711238\pi$
$594$	2.00000	0.0820610
$595$	48.0000	1.96781
$596$	6.00000	0.245770
$597$	0	0
$598$	−8.00000	−0.327144
$599$	8.00000	0.326871	0.163436	−	0.986554i	$-0.447742\pi$
$599$	8.00000	0.326871	0.163436	+	0.986554i	$0.447742\pi$
$600$	1.00000	0.0408248
$601$	−8.00000	−0.326327	−0.163163	−	0.986599i	$-0.552170\pi$
$601$	−8.00000	−0.326327	−0.163163	+	0.986599i	$0.552170\pi$
$602$	−16.0000	−0.652111
$603$	−8.00000	−0.325785
$604$	4.00000	0.162758
$605$	−14.0000	−0.569181
$606$	18.0000	0.731200
$607$	−16.0000	−0.649420	−0.324710	−	0.945814i	$-0.605267\pi$
$607$	−16.0000	−0.649420	−0.324710	+	0.945814i	$0.605267\pi$
$608$	0	0
$609$	40.0000	1.62088
$610$	28.0000	1.13369
$611$	−24.0000	−0.970936
$612$	6.00000	0.242536
$613$	−10.0000	−0.403896	−0.201948	−	0.979396i	$-0.564727\pi$
$613$	−10.0000	−0.403896	−0.201948	+	0.979396i	$0.564727\pi$
$614$	12.0000	0.484281
$615$	4.00000	0.161296
$616$	8.00000	0.322329
$617$	−18.0000	−0.724653	−0.362326	−	0.932051i	$-0.618017\pi$
$617$	−18.0000	−0.724653	−0.362326	+	0.932051i	$0.618017\pi$
$618$	20.0000	0.804518
$619$	32.0000	1.28619	0.643094	−	0.765787i	$-0.277650\pi$
$619$	32.0000	1.28619	0.643094	+	0.765787i	$0.277650\pi$
$620$	−16.0000	−0.642575
$621$	−2.00000	−0.0802572
$622$	18.0000	0.721734
$623$	−24.0000	−0.961540
$624$	−4.00000	−0.160128
$625$	−19.0000	−0.760000
$626$	−14.0000	−0.559553
$627$	0	0
$628$	14.0000	0.558661
$629$	48.0000	1.91389
$630$	−8.00000	−0.318728
$631$	28.0000	1.11466	0.557331	−	0.830290i	$-0.311825\pi$
$631$	28.0000	1.11466	0.557331	+	0.830290i	$0.311825\pi$
$632$	−12.0000	−0.477334
$633$	−24.0000	−0.953914
$634$	2.00000	0.0794301
$635$	32.0000	1.26988
$636$	10.0000	0.396526
$637$	−36.0000	−1.42637
$638$	20.0000	0.791808
$639$	0	0
$640$	−2.00000	−0.0790569
$641$	10.0000	0.394976	0.197488	−	0.980305i	$-0.436722\pi$
$641$	10.0000	0.394976	0.197488	+	0.980305i	$0.436722\pi$
$642$	4.00000	0.157867
$643$	4.00000	0.157745	0.0788723	−	0.996885i	$-0.474868\pi$
$643$	4.00000	0.157745	0.0788723	+	0.996885i	$0.474868\pi$
$644$	−8.00000	−0.315244
$645$	8.00000	0.315000
$646$	0	0
$647$	−2.00000	−0.0786281	−0.0393141	−	0.999227i	$-0.512517\pi$
$647$	−2.00000	−0.0786281	−0.0393141	+	0.999227i	$0.512517\pi$
$648$	−1.00000	−0.0392837
$649$	−8.00000	−0.314027
$650$	−4.00000	−0.156893
$651$	−32.0000	−1.25418
$652$	8.00000	0.313304
$653$	−10.0000	−0.391330	−0.195665	−	0.980671i	$-0.562687\pi$
$653$	−10.0000	−0.391330	−0.195665	+	0.980671i	$0.562687\pi$
$654$	−4.00000	−0.156412
$655$	28.0000	1.09405
$656$	2.00000	0.0780869
$657$	10.0000	0.390137
$658$	−24.0000	−0.935617
$659$	−20.0000	−0.779089	−0.389545	−	0.921008i	$-0.627368\pi$
$659$	−20.0000	−0.779089	−0.389545	+	0.921008i	$0.627368\pi$
$660$	−4.00000	−0.155700
$661$	−8.00000	−0.311164	−0.155582	−	0.987823i	$-0.549725\pi$
$661$	−8.00000	−0.311164	−0.155582	+	0.987823i	$0.549725\pi$
$662$	−12.0000	−0.466393
$663$	−24.0000	−0.932083
$664$	−2.00000	−0.0776151
$665$	0	0
$666$	−8.00000	−0.309994
$667$	−20.0000	−0.774403
$668$	−16.0000	−0.619059
$669$	−4.00000	−0.154649
$670$	16.0000	0.618134
$671$	28.0000	1.08093
$672$	−4.00000	−0.154303
$673$	−8.00000	−0.308377	−0.154189	−	0.988041i	$-0.549276\pi$
$673$	−8.00000	−0.308377	−0.154189	+	0.988041i	$0.549276\pi$
$674$	4.00000	0.154074
$675$	−1.00000	−0.0384900
$676$	3.00000	0.115385
$677$	18.0000	0.691796	0.345898	−	0.938272i	$-0.387574\pi$
$677$	18.0000	0.691796	0.345898	+	0.938272i	$0.387574\pi$
$678$	−2.00000	−0.0768095
$679$	−48.0000	−1.84207
$680$	−12.0000	−0.460179
$681$	4.00000	0.153280
$682$	−16.0000	−0.612672
$683$	−20.0000	−0.765279	−0.382639	−	0.923898i	$-0.624985\pi$
$683$	−20.0000	−0.765279	−0.382639	+	0.923898i	$0.624985\pi$
$684$	0	0
$685$	−4.00000	−0.152832
$686$	−8.00000	−0.305441
$687$	2.00000	0.0763048
$688$	4.00000	0.152499
$689$	−40.0000	−1.52388
$690$	4.00000	0.152277
$691$	20.0000	0.760836	0.380418	−	0.924815i	$-0.375780\pi$
$691$	20.0000	0.760836	0.380418	+	0.924815i	$0.375780\pi$
$692$	−10.0000	−0.380143
$693$	−8.00000	−0.303895
$694$	−30.0000	−1.13878
$695$	−16.0000	−0.606915
$696$	−10.0000	−0.379049
$697$	12.0000	0.454532
$698$	14.0000	0.529908
$699$	−14.0000	−0.529529
$700$	−4.00000	−0.151186
$701$	30.0000	1.13308	0.566542	−	0.824033i	$-0.308281\pi$
$701$	30.0000	1.13308	0.566542	+	0.824033i	$0.308281\pi$
$702$	4.00000	0.150970
$703$	0	0
$704$	−2.00000	−0.0753778
$705$	12.0000	0.451946
$706$	10.0000	0.376355
$707$	−72.0000	−2.70784
$708$	4.00000	0.150329
$709$	6.00000	0.225335	0.112667	−	0.993633i	$-0.464061\pi$
$709$	6.00000	0.225335	0.112667	+	0.993633i	$0.464061\pi$
$710$	0	0
$711$	12.0000	0.450035
$712$	6.00000	0.224860
$713$	16.0000	0.599205
$714$	−24.0000	−0.898177
$715$	16.0000	0.598366
$716$	12.0000	0.448461
$717$	−6.00000	−0.224074
$718$	30.0000	1.11959
$719$	6.00000	0.223762	0.111881	−	0.993722i	$-0.464312\pi$
$719$	6.00000	0.223762	0.111881	+	0.993722i	$0.464312\pi$
$720$	2.00000	0.0745356
$721$	−80.0000	−2.97936
$722$	0	0
$723$	4.00000	0.148762
$724$	−4.00000	−0.148659
$725$	−10.0000	−0.371391
$726$	7.00000	0.259794
$727$	0	0		−	1.00000i	$-0.5\pi$
$727$	0	0			1.00000i	$0.5\pi$
$728$	16.0000	0.592999
$729$	1.00000	0.0370370
$730$	−20.0000	−0.740233
$731$	24.0000	0.887672
$732$	−14.0000	−0.517455
$733$	34.0000	1.25582	0.627909	−	0.778287i	$-0.283911\pi$
$733$	34.0000	1.25582	0.627909	+	0.778287i	$0.283911\pi$
$734$	−8.00000	−0.295285
$735$	18.0000	0.663940
$736$	2.00000	0.0737210
$737$	16.0000	0.589368
$738$	−2.00000	−0.0736210
$739$	16.0000	0.588570	0.294285	−	0.955718i	$-0.404919\pi$
$739$	16.0000	0.588570	0.294285	+	0.955718i	$0.404919\pi$
$740$	16.0000	0.588172
$741$	0	0
$742$	−40.0000	−1.46845
$743$	−48.0000	−1.76095	−0.880475	−	0.474093i	$-0.842776\pi$
$743$	−48.0000	−1.76095	−0.880475	+	0.474093i	$0.842776\pi$
$744$	8.00000	0.293294
$745$	12.0000	0.439646
$746$	0	0
$747$	2.00000	0.0731762
$748$	−12.0000	−0.438763
$749$	−16.0000	−0.584627
$750$	12.0000	0.438178
$751$	44.0000	1.60558	0.802791	−	0.596260i	$-0.203347\pi$
$751$	44.0000	1.60558	0.802791	+	0.596260i	$0.203347\pi$
$752$	6.00000	0.218797
$753$	−6.00000	−0.218652
$754$	40.0000	1.45671
$755$	8.00000	0.291150
$756$	4.00000	0.145479
$757$	−2.00000	−0.0726912	−0.0363456	−	0.999339i	$-0.511572\pi$
$757$	−2.00000	−0.0726912	−0.0363456	+	0.999339i	$0.511572\pi$
$758$	−4.00000	−0.145287
$759$	4.00000	0.145191
$760$	0	0
$761$	−34.0000	−1.23250	−0.616250	−	0.787551i	$-0.711349\pi$
$761$	−34.0000	−1.23250	−0.616250	+	0.787551i	$0.711349\pi$
$762$	−16.0000	−0.579619
$763$	16.0000	0.579239
$764$	10.0000	0.361787
$765$	12.0000	0.433861
$766$	−24.0000	−0.867155
$767$	−16.0000	−0.577727
$768$	1.00000	0.0360844
$769$	6.00000	0.216366	0.108183	−	0.994131i	$-0.465497\pi$
$769$	6.00000	0.216366	0.108183	+	0.994131i	$0.465497\pi$
$770$	16.0000	0.576600
$771$	−10.0000	−0.360141
$772$	8.00000	0.287926
$773$	−50.0000	−1.79838	−0.899188	−	0.437564i	$-0.855842\pi$
$773$	−50.0000	−1.79838	−0.899188	+	0.437564i	$0.855842\pi$
$774$	−4.00000	−0.143777
$775$	8.00000	0.287368
$776$	12.0000	0.430775
$777$	32.0000	1.14799
$778$	30.0000	1.07555
$779$	0	0
$780$	−8.00000	−0.286446
$781$	0	0
$782$	12.0000	0.429119
$783$	10.0000	0.357371
$784$	9.00000	0.321429
$785$	28.0000	0.999363
$786$	−14.0000	−0.499363
$787$	16.0000	0.570338	0.285169	−	0.958477i	$-0.407950\pi$
$787$	16.0000	0.570338	0.285169	+	0.958477i	$0.407950\pi$
$788$	18.0000	0.641223
$789$	−22.0000	−0.783221
$790$	−24.0000	−0.853882
$791$	8.00000	0.284447
$792$	2.00000	0.0710669
$793$	56.0000	1.98862
$794$	−2.00000	−0.0709773
$795$	20.0000	0.709327
$796$	0	0
$797$	30.0000	1.06265	0.531327	−	0.847167i	$-0.321693\pi$
$797$	30.0000	1.06265	0.531327	+	0.847167i	$0.321693\pi$
$798$	0	0
$799$	36.0000	1.27359
$800$	1.00000	0.0353553
$801$	−6.00000	−0.212000
$802$	−34.0000	−1.20058
$803$	−20.0000	−0.705785
$804$	−8.00000	−0.282138
$805$	−16.0000	−0.563926
$806$	−32.0000	−1.12715
$807$	6.00000	0.211210
$808$	18.0000	0.633238
$809$	10.0000	0.351581	0.175791	−	0.984428i	$-0.443752\pi$
$809$	10.0000	0.351581	0.175791	+	0.984428i	$0.443752\pi$
$810$	−2.00000	−0.0702728
$811$	44.0000	1.54505	0.772524	−	0.634985i	$-0.218994\pi$
$811$	44.0000	1.54505	0.772524	+	0.634985i	$0.218994\pi$
$812$	40.0000	1.40372
$813$	−32.0000	−1.12229
$814$	16.0000	0.560800
$815$	16.0000	0.560456
$816$	6.00000	0.210042
$817$	0	0
$818$	20.0000	0.699284
$819$	−16.0000	−0.559085
$820$	4.00000	0.139686
$821$	30.0000	1.04701	0.523504	−	0.852023i	$-0.324625\pi$
$821$	30.0000	1.04701	0.523504	+	0.852023i	$0.324625\pi$
$822$	2.00000	0.0697580
$823$	−4.00000	−0.139431	−0.0697156	−	0.997567i	$-0.522209\pi$
$823$	−4.00000	−0.139431	−0.0697156	+	0.997567i	$0.522209\pi$
$824$	20.0000	0.696733
$825$	2.00000	0.0696311
$826$	−16.0000	−0.556711
$827$	−36.0000	−1.25184	−0.625921	−	0.779886i	$-0.715277\pi$
$827$	−36.0000	−1.25184	−0.625921	+	0.779886i	$0.715277\pi$
$828$	−2.00000	−0.0695048
$829$	12.0000	0.416777	0.208389	−	0.978046i	$-0.433178\pi$
$829$	12.0000	0.416777	0.208389	+	0.978046i	$0.433178\pi$
$830$	−4.00000	−0.138842
$831$	2.00000	0.0693792
$832$	−4.00000	−0.138675
$833$	54.0000	1.87099
$834$	8.00000	0.277017
$835$	−32.0000	−1.10741
$836$	0	0
$837$	−8.00000	−0.276520
$838$	−14.0000	−0.483622
$839$	−24.0000	−0.828572	−0.414286	−	0.910147i	$-0.635969\pi$
$839$	−24.0000	−0.828572	−0.414286	+	0.910147i	$0.635969\pi$
$840$	−8.00000	−0.276026
$841$	71.0000	2.44828
$842$	−20.0000	−0.689246
$843$	30.0000	1.03325
$844$	−24.0000	−0.826114
$845$	6.00000	0.206406
$846$	−6.00000	−0.206284
$847$	−28.0000	−0.962091
$848$	10.0000	0.343401
$849$	−28.0000	−0.960958
$850$	6.00000	0.205798
$851$	−16.0000	−0.548473
$852$	0	0
$853$	−10.0000	−0.342393	−0.171197	−	0.985237i	$-0.554763\pi$
$853$	−10.0000	−0.342393	−0.171197	+	0.985237i	$0.554763\pi$
$854$	56.0000	1.91628
$855$	0	0
$856$	4.00000	0.136717
$857$	18.0000	0.614868	0.307434	−	0.951569i	$-0.400530\pi$
$857$	18.0000	0.614868	0.307434	+	0.951569i	$0.400530\pi$
$858$	−8.00000	−0.273115
$859$	40.0000	1.36478	0.682391	−	0.730987i	$-0.260940\pi$
$859$	40.0000	1.36478	0.682391	+	0.730987i	$0.260940\pi$
$860$	8.00000	0.272798
$861$	8.00000	0.272639
$862$	24.0000	0.817443
$863$	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
$865$	−20.0000	−0.680020
$866$	16.0000	0.543702
$867$	19.0000	0.645274
$868$	−32.0000	−1.08615
$869$	−24.0000	−0.814144
$870$	−20.0000	−0.678064
$871$	32.0000	1.08428
$872$	−4.00000	−0.135457
$873$	−12.0000	−0.406138
$874$	0	0
$875$	−48.0000	−1.62270
$876$	10.0000	0.337869
$877$	8.00000	0.270141	0.135070	−	0.990836i	$-0.456874\pi$
$877$	8.00000	0.270141	0.135070	+	0.990836i	$0.456874\pi$
$878$	28.0000	0.944954
$879$	30.0000	1.01187
$880$	−4.00000	−0.134840
$881$	6.00000	0.202145	0.101073	−	0.994879i	$-0.467773\pi$
$881$	6.00000	0.202145	0.101073	+	0.994879i	$0.467773\pi$
$882$	−9.00000	−0.303046
$883$	−24.0000	−0.807664	−0.403832	−	0.914833i	$-0.632322\pi$
$883$	−24.0000	−0.807664	−0.403832	+	0.914833i	$0.632322\pi$
$884$	−24.0000	−0.807207
$885$	8.00000	0.268917
$886$	−6.00000	−0.201574
$887$	24.0000	0.805841	0.402921	−	0.915235i	$-0.367995\pi$
$887$	24.0000	0.805841	0.402921	+	0.915235i	$0.367995\pi$
$888$	−8.00000	−0.268462
$889$	64.0000	2.14649
$890$	12.0000	0.402241
$891$	−2.00000	−0.0670025
$892$	−4.00000	−0.133930
$893$	0	0
$894$	−6.00000	−0.200670
$895$	24.0000	0.802232
$896$	−4.00000	−0.133631
$897$	8.00000	0.267112
$898$	−22.0000	−0.734150
$899$	−80.0000	−2.66815
$900$	−1.00000	−0.0333333
$901$	60.0000	1.99889
$902$	4.00000	0.133185
$903$	16.0000	0.532447
$904$	−2.00000	−0.0665190
$905$	−8.00000	−0.265929
$906$	−4.00000	−0.132891
$907$	−48.0000	−1.59381	−0.796907	−	0.604102i	$-0.793532\pi$
$907$	−48.0000	−1.59381	−0.796907	+	0.604102i	$0.793532\pi$
$908$	4.00000	0.132745
$909$	−18.0000	−0.597022
$910$	32.0000	1.06079
$911$	16.0000	0.530104	0.265052	−	0.964234i	$-0.414611\pi$
$911$	16.0000	0.530104	0.265052	+	0.964234i	$0.414611\pi$
$912$	0	0
$913$	−4.00000	−0.132381
$914$	−22.0000	−0.727695
$915$	−28.0000	−0.925651
$916$	2.00000	0.0660819
$917$	56.0000	1.84928
$918$	−6.00000	−0.198030
$919$	36.0000	1.18753	0.593765	−	0.804638i	$-0.297641\pi$
$919$	36.0000	1.18753	0.593765	+	0.804638i	$0.297641\pi$
$920$	4.00000	0.131876
$921$	−12.0000	−0.395413
$922$	10.0000	0.329332
$923$	0	0
$924$	−8.00000	−0.263181
$925$	−8.00000	−0.263038
$926$	24.0000	0.788689
$927$	−20.0000	−0.656886
$928$	−10.0000	−0.328266
$929$	−22.0000	−0.721797	−0.360898	−	0.932605i	$-0.617530\pi$
$929$	−22.0000	−0.721797	−0.360898	+	0.932605i	$0.617530\pi$
$930$	16.0000	0.524661
$931$	0	0
$932$	−14.0000	−0.458585
$933$	−18.0000	−0.589294
$934$	6.00000	0.196326
$935$	−24.0000	−0.784884
$936$	4.00000	0.130744
$937$	−26.0000	−0.849383	−0.424691	−	0.905338i	$-0.639617\pi$
$937$	−26.0000	−0.849383	−0.424691	+	0.905338i	$0.639617\pi$
$938$	32.0000	1.04484
$939$	14.0000	0.456873
$940$	12.0000	0.391397
$941$	6.00000	0.195594	0.0977972	−	0.995206i	$-0.468820\pi$
$941$	6.00000	0.195594	0.0977972	+	0.995206i	$0.468820\pi$
$942$	−14.0000	−0.456145
$943$	−4.00000	−0.130258
$944$	4.00000	0.130189
$945$	8.00000	0.260240
$946$	8.00000	0.260102
$947$	−18.0000	−0.584921	−0.292461	−	0.956278i	$-0.594474\pi$
$947$	−18.0000	−0.584921	−0.292461	+	0.956278i	$0.594474\pi$
$948$	12.0000	0.389742
$949$	−40.0000	−1.29845
$950$	0	0
$951$	−2.00000	−0.0648544
$952$	−24.0000	−0.777844
$953$	−26.0000	−0.842223	−0.421111	−	0.907009i	$-0.638360\pi$
$953$	−26.0000	−0.842223	−0.421111	+	0.907009i	$0.638360\pi$
$954$	−10.0000	−0.323762
$955$	20.0000	0.647185
$956$	−6.00000	−0.194054
$957$	−20.0000	−0.646508
$958$	−2.00000	−0.0646171
$959$	−8.00000	−0.258333
$960$	2.00000	0.0645497
$961$	33.0000	1.06452
$962$	32.0000	1.03172
$963$	−4.00000	−0.128898
$964$	4.00000	0.128831
$965$	16.0000	0.515058
$966$	8.00000	0.257396
$967$	4.00000	0.128631	0.0643157	−	0.997930i	$-0.479514\pi$
$967$	4.00000	0.128631	0.0643157	+	0.997930i	$0.479514\pi$
$968$	7.00000	0.224989
$969$	0	0
$970$	24.0000	0.770594
$971$	20.0000	0.641831	0.320915	−	0.947108i	$-0.396010\pi$
$971$	20.0000	0.641831	0.320915	+	0.947108i	$0.396010\pi$
$972$	1.00000	0.0320750
$973$	−32.0000	−1.02587
$974$	24.0000	0.769010
$975$	4.00000	0.128103
$976$	−14.0000	−0.448129
$977$	2.00000	0.0639857	0.0319928	−	0.999488i	$-0.489815\pi$
$977$	2.00000	0.0639857	0.0319928	+	0.999488i	$0.489815\pi$
$978$	−8.00000	−0.255812
$979$	12.0000	0.383522
$980$	18.0000	0.574989
$981$	4.00000	0.127710
$982$	34.0000	1.08498
$983$	−32.0000	−1.02064	−0.510321	−	0.859984i	$-0.670473\pi$
$983$	−32.0000	−1.02064	−0.510321	+	0.859984i	$0.670473\pi$
$984$	−2.00000	−0.0637577
$985$	36.0000	1.14706
$986$	−60.0000	−1.91079
$987$	24.0000	0.763928
$988$	0	0
$989$	−8.00000	−0.254385
$990$	4.00000	0.127128
$991$	8.00000	0.254128	0.127064	−	0.991894i	$-0.459445\pi$
$991$	8.00000	0.254128	0.127064	+	0.991894i	$0.459445\pi$
$992$	8.00000	0.254000
$993$	12.0000	0.380808
$994$	0	0
$995$	0	0
$996$	2.00000	0.0633724
$997$	6.00000	0.190022	0.0950110	−	0.995476i	$-0.469711\pi$
$997$	6.00000	0.190022	0.0950110	+	0.995476i	$0.469711\pi$
$998$	24.0000	0.759707
$999$	8.00000	0.253109

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2166.2.a.e.1.1	✓	1
3.2	odd	2		6498.2.a.r.1.1		1
19.18	odd	2		2166.2.a.g.1.1	yes	1
57.56	even	2		6498.2.a.d.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2166.2.a.e.1.1	✓	1	1.1	even	1	trivial
2166.2.a.g.1.1	yes	1	19.18	odd	2
6498.2.a.d.1.1		1	57.56	even	2
6498.2.a.r.1.1		1	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2166 = 2 \cdot 3 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2166.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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