LMFDB - Embedded newform 6498.2.a.u.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6498,2,Mod(1,6498)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6498, 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("6498.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6498 = 2 \cdot 3^{2} \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6498.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:	$51.8867912334$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 114)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	6498.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{7} +1.00000 q^{8} +O(q^{10})$

$q+1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{7} +1.00000 q^{8} +2.00000 q^{11} -3.00000 q^{13} +1.00000 q^{14} +1.00000 q^{16} -4.00000 q^{17} +2.00000 q^{22} -4.00000 q^{23} -5.00000 q^{25} -3.00000 q^{26} +1.00000 q^{28} -3.00000 q^{31} +1.00000 q^{32} -4.00000 q^{34} -5.00000 q^{37} -4.00000 q^{41} -9.00000 q^{43} +2.00000 q^{44} -4.00000 q^{46} -10.0000 q^{47} -6.00000 q^{49} -5.00000 q^{50} -3.00000 q^{52} +4.00000 q^{53} +1.00000 q^{56} +14.0000 q^{59} +11.0000 q^{61} -3.00000 q^{62} +1.00000 q^{64} +3.00000 q^{67} -4.00000 q^{68} -14.0000 q^{71} -11.0000 q^{73} -5.00000 q^{74} +2.00000 q^{77} +1.00000 q^{79} -4.00000 q^{82} -8.00000 q^{83} -9.00000 q^{86} +2.00000 q^{88} +14.0000 q^{89} -3.00000 q^{91} -4.00000 q^{92} -10.0000 q^{94} +2.00000 q^{97} -6.00000 q^{98} +O(q^{100})$

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
$3$	0	0
$3$	0	0
$4$	1.00000	0.500000
$5$	0	0		−	1.00000i	$-0.5\pi$
$5$	0	0			1.00000i	$0.5\pi$
$6$	0	0
$7$	1.00000	0.377964	0.188982	−	0.981981i	$-0.439481\pi$
$7$	1.00000	0.377964	0.188982	+	0.981981i	$0.439481\pi$
$8$	1.00000	0.353553
$9$	0	0
$10$	0	0
$11$	2.00000	0.603023	0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000	0.603023	0.301511	+	0.953463i	$0.402509\pi$
$12$	0	0
$13$	−3.00000	−0.832050	−0.416025	−	0.909353i	$-0.636577\pi$
$13$	−3.00000	−0.832050	−0.416025	+	0.909353i	$0.636577\pi$
$14$	1.00000	0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	−4.00000	−0.970143	−0.485071	−	0.874475i	$-0.661206\pi$
$17$	−4.00000	−0.970143	−0.485071	+	0.874475i	$0.661206\pi$
$18$	0	0
$19$	0	0
$19$	0	0
$20$	0	0
$21$	0	0
$22$	2.00000	0.426401
$23$	−4.00000	−0.834058	−0.417029	−	0.908893i	$-0.636929\pi$
$23$	−4.00000	−0.834058	−0.417029	+	0.908893i	$0.636929\pi$
$24$	0	0
$25$	−5.00000	−1.00000
$26$	−3.00000	−0.588348
$27$	0	0
$28$	1.00000	0.188982
$29$	0	0		−	1.00000i	$-0.5\pi$
$29$	0	0			1.00000i	$0.5\pi$
$30$	0	0
$31$	−3.00000	−0.538816	−0.269408	−	0.963026i	$-0.586828\pi$
$31$	−3.00000	−0.538816	−0.269408	+	0.963026i	$0.586828\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	−4.00000	−0.685994
$35$	0	0
$36$	0	0
$37$	−5.00000	−0.821995	−0.410997	−	0.911636i	$-0.634819\pi$
$37$	−5.00000	−0.821995	−0.410997	+	0.911636i	$0.634819\pi$
$38$	0	0
$39$	0	0
$40$	0	0
$41$	−4.00000	−0.624695	−0.312348	−	0.949968i	$-0.601115\pi$
$41$	−4.00000	−0.624695	−0.312348	+	0.949968i	$0.601115\pi$
$42$	0	0
$43$	−9.00000	−1.37249	−0.686244	−	0.727372i	$-0.740742\pi$
$43$	−9.00000	−1.37249	−0.686244	+	0.727372i	$0.740742\pi$
$44$	2.00000	0.301511
$45$	0	0
$46$	−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	$0.760166\pi$
$48$	0	0
$49$	−6.00000	−0.857143
$50$	−5.00000	−0.707107
$51$	0	0
$52$	−3.00000	−0.416025
$53$	4.00000	0.549442	0.274721	−	0.961524i	$-0.411414\pi$
$53$	4.00000	0.549442	0.274721	+	0.961524i	$0.411414\pi$
$54$	0	0
$55$	0	0
$56$	1.00000	0.133631
$57$	0	0
$58$	0	0
$59$	14.0000	1.82264	0.911322	−	0.411693i	$-0.135063\pi$
$59$	14.0000	1.82264	0.911322	+	0.411693i	$0.135063\pi$
$60$	0	0
$61$	11.0000	1.40841	0.704203	−	0.709999i	$-0.251305\pi$
$61$	11.0000	1.40841	0.704203	+	0.709999i	$0.251305\pi$
$62$	−3.00000	−0.381000
$63$	0	0
$64$	1.00000	0.125000
$65$	0	0
$66$	0	0
$67$	3.00000	0.366508	0.183254	−	0.983066i	$-0.441337\pi$
$67$	3.00000	0.366508	0.183254	+	0.983066i	$0.441337\pi$
$68$	−4.00000	−0.485071
$69$	0	0
$70$	0	0
$71$	−14.0000	−1.66149	−0.830747	−	0.556650i	$-0.812086\pi$
$71$	−14.0000	−1.66149	−0.830747	+	0.556650i	$0.812086\pi$
$72$	0	0
$73$	−11.0000	−1.28745	−0.643726	−	0.765256i	$-0.722612\pi$
$73$	−11.0000	−1.28745	−0.643726	+	0.765256i	$0.722612\pi$
$74$	−5.00000	−0.581238
$75$	0	0
$76$	0	0
$77$	2.00000	0.227921
$78$	0	0
$79$	1.00000	0.112509	0.0562544	−	0.998416i	$-0.482084\pi$
$79$	1.00000	0.112509	0.0562544	+	0.998416i	$0.482084\pi$
$80$	0	0
$81$	0	0
$82$	−4.00000	−0.441726
$83$	−8.00000	−0.878114	−0.439057	−	0.898459i	$-0.644687\pi$
$83$	−8.00000	−0.878114	−0.439057	+	0.898459i	$0.644687\pi$
$84$	0	0
$85$	0	0
$86$	−9.00000	−0.970495
$87$	0	0
$88$	2.00000	0.213201
$89$	14.0000	1.48400	0.741999	−	0.670402i	$-0.233878\pi$
$89$	14.0000	1.48400	0.741999	+	0.670402i	$0.233878\pi$
$90$	0	0
$91$	−3.00000	−0.314485
$92$	−4.00000	−0.417029
$93$	0	0
$94$	−10.0000	−1.03142
$95$	0	0
$96$	0	0
$97$	2.00000	0.203069	0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000	0.203069	0.101535	+	0.994832i	$0.467625\pi$
$98$	−6.00000	−0.606092
$99$	0	0
$100$	−5.00000	−0.500000
$101$	10.0000	0.995037	0.497519	−	0.867453i	$-0.334245\pi$
$101$	10.0000	0.995037	0.497519	+	0.867453i	$0.334245\pi$
$102$	0	0
$103$	−3.00000	−0.295599	−0.147799	−	0.989017i	$-0.547219\pi$
$103$	−3.00000	−0.295599	−0.147799	+	0.989017i	$0.547219\pi$
$104$	−3.00000	−0.294174
$105$	0	0
$106$	4.00000	0.388514
$107$	10.0000	0.966736	0.483368	−	0.875417i	$-0.339413\pi$
$107$	10.0000	0.966736	0.483368	+	0.875417i	$0.339413\pi$
$108$	0	0
$109$	14.0000	1.34096	0.670478	−	0.741929i	$-0.266089\pi$
$109$	14.0000	1.34096	0.670478	+	0.741929i	$0.266089\pi$
$110$	0	0
$111$	0	0
$112$	1.00000	0.0944911
$113$	−10.0000	−0.940721	−0.470360	−	0.882474i	$-0.655876\pi$
$113$	−10.0000	−0.940721	−0.470360	+	0.882474i	$0.655876\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	0	0
$118$	14.0000	1.28880
$119$	−4.00000	−0.366679
$120$	0	0
$121$	−7.00000	−0.636364
$122$	11.0000	0.995893
$123$	0	0
$124$	−3.00000	−0.269408
$125$	0	0
$126$	0	0
$127$	−8.00000	−0.709885	−0.354943	−	0.934888i	$-0.615500\pi$
$127$	−8.00000	−0.709885	−0.354943	+	0.934888i	$0.615500\pi$
$128$	1.00000	0.0883883
$129$	0	0
$130$	0	0
$131$	6.00000	0.524222	0.262111	−	0.965038i	$-0.415581\pi$
$131$	6.00000	0.524222	0.262111	+	0.965038i	$0.415581\pi$
$132$	0	0
$133$	0	0
$134$	3.00000	0.259161
$135$	0	0
$136$	−4.00000	−0.342997
$137$	6.00000	0.512615	0.256307	−	0.966595i	$-0.417494\pi$
$137$	6.00000	0.512615	0.256307	+	0.966595i	$0.417494\pi$
$138$	0	0
$139$	−19.0000	−1.61156	−0.805779	−	0.592216i	$-0.798253\pi$
$139$	−19.0000	−1.61156	−0.805779	+	0.592216i	$0.798253\pi$
$140$	0	0
$141$	0	0
$142$	−14.0000	−1.17485
$143$	−6.00000	−0.501745
$144$	0	0
$145$	0	0
$146$	−11.0000	−0.910366
$147$	0	0
$148$	−5.00000	−0.410997
$149$	22.0000	1.80231	0.901155	−	0.433497i	$-0.142720\pi$
$149$	22.0000	1.80231	0.901155	+	0.433497i	$0.142720\pi$
$150$	0	0
$151$	−20.0000	−1.62758	−0.813788	−	0.581161i	$-0.802599\pi$
$151$	−20.0000	−1.62758	−0.813788	+	0.581161i	$0.802599\pi$
$152$	0	0
$153$	0	0
$154$	2.00000	0.161165
$155$	0	0
$156$	0	0
$157$	−21.0000	−1.67598	−0.837991	−	0.545684i	$-0.816270\pi$
$157$	−21.0000	−1.67598	−0.837991	+	0.545684i	$0.816270\pi$
$158$	1.00000	0.0795557
$159$	0	0
$160$	0	0
$161$	−4.00000	−0.315244
$162$	0	0
$163$	11.0000	0.861586	0.430793	−	0.902451i	$-0.358234\pi$
$163$	11.0000	0.861586	0.430793	+	0.902451i	$0.358234\pi$
$164$	−4.00000	−0.312348
$165$	0	0
$166$	−8.00000	−0.620920
$167$	−6.00000	−0.464294	−0.232147	−	0.972681i	$-0.574575\pi$
$167$	−6.00000	−0.464294	−0.232147	+	0.972681i	$0.574575\pi$
$168$	0	0
$169$	−4.00000	−0.307692
$170$	0	0
$171$	0	0
$172$	−9.00000	−0.686244
$173$	24.0000	1.82469	0.912343	−	0.409426i	$-0.134271\pi$
$173$	24.0000	1.82469	0.912343	+	0.409426i	$0.134271\pi$
$174$	0	0
$175$	−5.00000	−0.377964
$176$	2.00000	0.150756
$177$	0	0
$178$	14.0000	1.04934
$179$	−4.00000	−0.298974	−0.149487	−	0.988764i	$-0.547762\pi$
$179$	−4.00000	−0.298974	−0.149487	+	0.988764i	$0.547762\pi$
$180$	0	0
$181$	−18.0000	−1.33793	−0.668965	−	0.743294i	$-0.733262\pi$
$181$	−18.0000	−1.33793	−0.668965	+	0.743294i	$0.733262\pi$
$182$	−3.00000	−0.222375
$183$	0	0
$184$	−4.00000	−0.294884
$185$	0	0
$186$	0	0
$187$	−8.00000	−0.585018
$188$	−10.0000	−0.729325
$189$	0	0
$190$	0	0
$191$	8.00000	0.578860	0.289430	−	0.957199i	$-0.406534\pi$
$191$	8.00000	0.578860	0.289430	+	0.957199i	$0.406534\pi$
$192$	0	0
$193$	−13.0000	−0.935760	−0.467880	−	0.883792i	$-0.654982\pi$
$193$	−13.0000	−0.935760	−0.467880	+	0.883792i	$0.654982\pi$
$194$	2.00000	0.143592
$195$	0	0
$196$	−6.00000	−0.428571
$197$	2.00000	0.142494	0.0712470	−	0.997459i	$-0.477302\pi$
$197$	2.00000	0.142494	0.0712470	+	0.997459i	$0.477302\pi$
$198$	0	0
$199$	5.00000	0.354441	0.177220	−	0.984171i	$-0.443289\pi$
$199$	5.00000	0.354441	0.177220	+	0.984171i	$0.443289\pi$
$200$	−5.00000	−0.353553
$201$	0	0
$202$	10.0000	0.703598
$203$	0	0
$204$	0	0
$205$	0	0
$206$	−3.00000	−0.209020
$207$	0	0
$208$	−3.00000	−0.208013
$209$	0	0
$210$	0	0
$211$	25.0000	1.72107	0.860535	−	0.509390i	$-0.170129\pi$
$211$	25.0000	1.72107	0.860535	+	0.509390i	$0.170129\pi$
$212$	4.00000	0.274721
$213$	0	0
$214$	10.0000	0.683586
$215$	0	0
$216$	0	0
$217$	−3.00000	−0.203653
$218$	14.0000	0.948200
$219$	0	0
$220$	0	0
$221$	12.0000	0.807207
$222$	0	0
$223$	9.00000	0.602685	0.301342	−	0.953516i	$-0.402565\pi$
$223$	9.00000	0.602685	0.301342	+	0.953516i	$0.402565\pi$
$224$	1.00000	0.0668153
$225$	0	0
$226$	−10.0000	−0.665190
$227$	−8.00000	−0.530979	−0.265489	−	0.964114i	$-0.585534\pi$
$227$	−8.00000	−0.530979	−0.265489	+	0.964114i	$0.585534\pi$
$228$	0	0
$229$	−11.0000	−0.726900	−0.363450	−	0.931614i	$-0.618401\pi$
$229$	−11.0000	−0.726900	−0.363450	+	0.931614i	$0.618401\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	−18.0000	−1.17922	−0.589610	−	0.807688i	$-0.700718\pi$
$233$	−18.0000	−1.17922	−0.589610	+	0.807688i	$0.700718\pi$
$234$	0	0
$235$	0	0
$236$	14.0000	0.911322
$237$	0	0
$238$	−4.00000	−0.259281
$239$	12.0000	0.776215	0.388108	−	0.921614i	$-0.373129\pi$
$239$	12.0000	0.776215	0.388108	+	0.921614i	$0.373129\pi$
$240$	0	0
$241$	25.0000	1.61039	0.805196	−	0.593009i	$-0.202060\pi$
$241$	25.0000	1.61039	0.805196	+	0.593009i	$0.202060\pi$
$242$	−7.00000	−0.449977
$243$	0	0
$244$	11.0000	0.704203
$245$	0	0
$246$	0	0
$247$	0	0
$248$	−3.00000	−0.190500
$249$	0	0
$250$	0	0
$251$	18.0000	1.13615	0.568075	−	0.822977i	$-0.307688\pi$
$251$	18.0000	1.13615	0.568075	+	0.822977i	$0.307688\pi$
$252$	0	0
$253$	−8.00000	−0.502956
$254$	−8.00000	−0.501965
$255$	0	0
$256$	1.00000	0.0625000
$257$	12.0000	0.748539	0.374270	−	0.927320i	$-0.377893\pi$
$257$	12.0000	0.748539	0.374270	+	0.927320i	$0.377893\pi$
$258$	0	0
$259$	−5.00000	−0.310685
$260$	0	0
$261$	0	0
$262$	6.00000	0.370681
$263$	−18.0000	−1.10993	−0.554964	−	0.831875i	$-0.687268\pi$
$263$	−18.0000	−1.10993	−0.554964	+	0.831875i	$0.687268\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	0	0
$268$	3.00000	0.183254
$269$	−2.00000	−0.121942	−0.0609711	−	0.998140i	$-0.519420\pi$
$269$	−2.00000	−0.121942	−0.0609711	+	0.998140i	$0.519420\pi$
$270$	0	0
$271$	−16.0000	−0.971931	−0.485965	−	0.873978i	$-0.661532\pi$
$271$	−16.0000	−0.971931	−0.485965	+	0.873978i	$0.661532\pi$
$272$	−4.00000	−0.242536
$273$	0	0
$274$	6.00000	0.362473
$275$	−10.0000	−0.603023
$276$	0	0
$277$	−2.00000	−0.120168	−0.0600842	−	0.998193i	$-0.519137\pi$
$277$	−2.00000	−0.120168	−0.0600842	+	0.998193i	$0.519137\pi$
$278$	−19.0000	−1.13954
$279$	0	0
$280$	0	0
$281$	8.00000	0.477240	0.238620	−	0.971113i	$-0.423305\pi$
$281$	8.00000	0.477240	0.238620	+	0.971113i	$0.423305\pi$
$282$	0	0
$283$	−20.0000	−1.18888	−0.594438	−	0.804141i	$-0.702626\pi$
$283$	−20.0000	−1.18888	−0.594438	+	0.804141i	$0.702626\pi$
$284$	−14.0000	−0.830747
$285$	0	0
$286$	−6.00000	−0.354787
$287$	−4.00000	−0.236113
$288$	0	0
$289$	−1.00000	−0.0588235
$290$	0	0
$291$	0	0
$292$	−11.0000	−0.643726
$293$	−14.0000	−0.817889	−0.408944	−	0.912559i	$-0.634103\pi$
$293$	−14.0000	−0.817889	−0.408944	+	0.912559i	$0.634103\pi$
$294$	0	0
$295$	0	0
$296$	−5.00000	−0.290619
$297$	0	0
$298$	22.0000	1.27443
$299$	12.0000	0.693978
$300$	0	0
$301$	−9.00000	−0.518751
$302$	−20.0000	−1.15087
$303$	0	0
$304$	0	0
$305$	0	0
$306$	0	0
$307$	−12.0000	−0.684876	−0.342438	−	0.939540i	$-0.611253\pi$
$307$	−12.0000	−0.684876	−0.342438	+	0.939540i	$0.611253\pi$
$308$	2.00000	0.113961
$309$	0	0
$310$	0	0
$311$	−10.0000	−0.567048	−0.283524	−	0.958965i	$-0.591504\pi$
$311$	−10.0000	−0.567048	−0.283524	+	0.958965i	$0.591504\pi$
$312$	0	0
$313$	6.00000	0.339140	0.169570	−	0.985518i	$-0.445762\pi$
$313$	6.00000	0.339140	0.169570	+	0.985518i	$0.445762\pi$
$314$	−21.0000	−1.18510
$315$	0	0
$316$	1.00000	0.0562544
$317$	−12.0000	−0.673987	−0.336994	−	0.941507i	$-0.609410\pi$
$317$	−12.0000	−0.673987	−0.336994	+	0.941507i	$0.609410\pi$
$318$	0	0
$319$	0	0
$320$	0	0
$321$	0	0
$322$	−4.00000	−0.222911
$323$	0	0
$324$	0	0
$325$	15.0000	0.832050
$326$	11.0000	0.609234
$327$	0	0
$328$	−4.00000	−0.220863
$329$	−10.0000	−0.551318
$330$	0	0
$331$	15.0000	0.824475	0.412237	−	0.911077i	$-0.364747\pi$
$331$	15.0000	0.824475	0.412237	+	0.911077i	$0.364747\pi$
$332$	−8.00000	−0.439057
$333$	0	0
$334$	−6.00000	−0.328305
$335$	0	0
$336$	0	0
$337$	−19.0000	−1.03500	−0.517498	−	0.855684i	$-0.673136\pi$
$337$	−19.0000	−1.03500	−0.517498	+	0.855684i	$0.673136\pi$
$338$	−4.00000	−0.217571
$339$	0	0
$340$	0	0
$341$	−6.00000	−0.324918
$342$	0	0
$343$	−13.0000	−0.701934
$344$	−9.00000	−0.485247
$345$	0	0
$346$	24.0000	1.29025
$347$	−16.0000	−0.858925	−0.429463	−	0.903085i	$-0.641297\pi$
$347$	−16.0000	−0.858925	−0.429463	+	0.903085i	$0.641297\pi$
$348$	0	0
$349$	−29.0000	−1.55233	−0.776167	−	0.630527i	$-0.782839\pi$
$349$	−29.0000	−1.55233	−0.776167	+	0.630527i	$0.782839\pi$
$350$	−5.00000	−0.267261
$351$	0	0
$352$	2.00000	0.106600
$353$	12.0000	0.638696	0.319348	−	0.947638i	$-0.396536\pi$
$353$	12.0000	0.638696	0.319348	+	0.947638i	$0.396536\pi$
$354$	0	0
$355$	0	0
$356$	14.0000	0.741999
$357$	0	0
$358$	−4.00000	−0.211407
$359$	36.0000	1.90001	0.950004	−	0.312239i	$-0.101079\pi$
$359$	36.0000	1.90001	0.950004	+	0.312239i	$0.101079\pi$
$360$	0	0
$361$	0	0
$362$	−18.0000	−0.946059
$363$	0	0
$364$	−3.00000	−0.157243
$365$	0	0
$366$	0	0
$367$	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
$369$	0	0
$370$	0	0
$371$	4.00000	0.207670
$372$	0	0
$373$	26.0000	1.34623	0.673114	−	0.739538i	$-0.264956\pi$
$373$	26.0000	1.34623	0.673114	+	0.739538i	$0.264956\pi$
$374$	−8.00000	−0.413670
$375$	0	0
$376$	−10.0000	−0.515711
$377$	0	0
$378$	0	0
$379$	−13.0000	−0.667765	−0.333883	−	0.942615i	$-0.608359\pi$
$379$	−13.0000	−0.667765	−0.333883	+	0.942615i	$0.608359\pi$
$380$	0	0
$381$	0	0
$382$	8.00000	0.409316
$383$	−14.0000	−0.715367	−0.357683	−	0.933843i	$-0.616433\pi$
$383$	−14.0000	−0.715367	−0.357683	+	0.933843i	$0.616433\pi$
$384$	0	0
$385$	0	0
$386$	−13.0000	−0.661683
$387$	0	0
$388$	2.00000	0.101535
$389$	16.0000	0.811232	0.405616	−	0.914044i	$-0.367057\pi$
$389$	16.0000	0.811232	0.405616	+	0.914044i	$0.367057\pi$
$390$	0	0
$391$	16.0000	0.809155
$392$	−6.00000	−0.303046
$393$	0	0
$394$	2.00000	0.100759
$395$	0	0
$396$	0	0
$397$	15.0000	0.752828	0.376414	−	0.926451i	$-0.377157\pi$
$397$	15.0000	0.752828	0.376414	+	0.926451i	$0.377157\pi$
$398$	5.00000	0.250627
$399$	0	0
$400$	−5.00000	−0.250000
$401$	−18.0000	−0.898877	−0.449439	−	0.893311i	$-0.648376\pi$
$401$	−18.0000	−0.898877	−0.449439	+	0.893311i	$0.648376\pi$
$402$	0	0
$403$	9.00000	0.448322
$404$	10.0000	0.497519
$405$	0	0
$406$	0	0
$407$	−10.0000	−0.495682
$408$	0	0
$409$	−30.0000	−1.48340	−0.741702	−	0.670729i	$-0.765981\pi$
$409$	−30.0000	−1.48340	−0.741702	+	0.670729i	$0.765981\pi$
$410$	0	0
$411$	0	0
$412$	−3.00000	−0.147799
$413$	14.0000	0.688895
$414$	0	0
$415$	0	0
$416$	−3.00000	−0.147087
$417$	0	0
$418$	0	0
$419$	−18.0000	−0.879358	−0.439679	−	0.898155i	$-0.644908\pi$
$419$	−18.0000	−0.879358	−0.439679	+	0.898155i	$0.644908\pi$
$420$	0	0
$421$	10.0000	0.487370	0.243685	−	0.969854i	$-0.421644\pi$
$421$	10.0000	0.487370	0.243685	+	0.969854i	$0.421644\pi$
$422$	25.0000	1.21698
$423$	0	0
$424$	4.00000	0.194257
$425$	20.0000	0.970143
$426$	0	0
$427$	11.0000	0.532327
$428$	10.0000	0.483368
$429$	0	0
$430$	0	0
$431$	10.0000	0.481683	0.240842	−	0.970564i	$-0.422577\pi$
$431$	10.0000	0.481683	0.240842	+	0.970564i	$0.422577\pi$
$432$	0	0
$433$	−9.00000	−0.432512	−0.216256	−	0.976337i	$-0.569385\pi$
$433$	−9.00000	−0.432512	−0.216256	+	0.976337i	$0.569385\pi$
$434$	−3.00000	−0.144005
$435$	0	0
$436$	14.0000	0.670478
$437$	0	0
$438$	0	0
$439$	19.0000	0.906821	0.453410	−	0.891302i	$-0.350207\pi$
$439$	19.0000	0.906821	0.453410	+	0.891302i	$0.350207\pi$
$440$	0	0
$441$	0	0
$442$	12.0000	0.570782
$443$	−24.0000	−1.14027	−0.570137	−	0.821549i	$-0.693110\pi$
$443$	−24.0000	−1.14027	−0.570137	+	0.821549i	$0.693110\pi$
$444$	0	0
$445$	0	0
$446$	9.00000	0.426162
$447$	0	0
$448$	1.00000	0.0472456
$449$	36.0000	1.69895	0.849473	−	0.527633i	$-0.176920\pi$
$449$	36.0000	1.69895	0.849473	+	0.527633i	$0.176920\pi$
$450$	0	0
$451$	−8.00000	−0.376705
$452$	−10.0000	−0.470360
$453$	0	0
$454$	−8.00000	−0.375459
$455$	0	0
$456$	0	0
$457$	5.00000	0.233890	0.116945	−	0.993138i	$-0.462690\pi$
$457$	5.00000	0.233890	0.116945	+	0.993138i	$0.462690\pi$
$458$	−11.0000	−0.513996
$459$	0	0
$460$	0	0
$461$	−6.00000	−0.279448	−0.139724	−	0.990190i	$-0.544622\pi$
$461$	−6.00000	−0.279448	−0.139724	+	0.990190i	$0.544622\pi$
$462$	0	0
$463$	−9.00000	−0.418265	−0.209133	−	0.977887i	$-0.567064\pi$
$463$	−9.00000	−0.418265	−0.209133	+	0.977887i	$0.567064\pi$
$464$	0	0
$465$	0	0
$466$	−18.0000	−0.833834
$467$	−8.00000	−0.370196	−0.185098	−	0.982720i	$-0.559260\pi$
$467$	−8.00000	−0.370196	−0.185098	+	0.982720i	$0.559260\pi$
$468$	0	0
$469$	3.00000	0.138527
$470$	0	0
$471$	0	0
$472$	14.0000	0.644402
$473$	−18.0000	−0.827641
$474$	0	0
$475$	0	0
$476$	−4.00000	−0.183340
$477$	0	0
$478$	12.0000	0.548867
$479$	−6.00000	−0.274147	−0.137073	−	0.990561i	$-0.543770\pi$
$479$	−6.00000	−0.274147	−0.137073	+	0.990561i	$0.543770\pi$
$480$	0	0
$481$	15.0000	0.683941
$482$	25.0000	1.13872
$483$	0	0
$484$	−7.00000	−0.318182
$485$	0	0
$486$	0	0
$487$	32.0000	1.45006	0.725029	−	0.688718i	$-0.241826\pi$
$487$	32.0000	1.45006	0.725029	+	0.688718i	$0.241826\pi$
$488$	11.0000	0.497947
$489$	0	0
$490$	0	0
$491$	−30.0000	−1.35388	−0.676941	−	0.736038i	$-0.736695\pi$
$491$	−30.0000	−1.35388	−0.676941	+	0.736038i	$0.736695\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	0	0
$496$	−3.00000	−0.134704
$497$	−14.0000	−0.627986
$498$	0	0
$499$	5.00000	0.223831	0.111915	−	0.993718i	$-0.464301\pi$
$499$	5.00000	0.223831	0.111915	+	0.993718i	$0.464301\pi$
$500$	0	0
$501$	0	0
$502$	18.0000	0.803379
$503$	−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
$505$	0	0
$506$	−8.00000	−0.355643
$507$	0	0
$508$	−8.00000	−0.354943
$509$	−26.0000	−1.15243	−0.576215	−	0.817298i	$-0.695471\pi$
$509$	−26.0000	−1.15243	−0.576215	+	0.817298i	$0.695471\pi$
$510$	0	0
$511$	−11.0000	−0.486611
$512$	1.00000	0.0441942
$513$	0	0
$514$	12.0000	0.529297
$515$	0	0
$516$	0	0
$517$	−20.0000	−0.879599
$518$	−5.00000	−0.219687
$519$	0	0
$520$	0	0
$521$	−34.0000	−1.48957	−0.744784	−	0.667306i	$-0.767447\pi$
$521$	−34.0000	−1.48957	−0.744784	+	0.667306i	$0.767447\pi$
$522$	0	0
$523$	37.0000	1.61790	0.808949	−	0.587879i	$-0.200037\pi$
$523$	37.0000	1.61790	0.808949	+	0.587879i	$0.200037\pi$
$524$	6.00000	0.262111
$525$	0	0
$526$	−18.0000	−0.784837
$527$	12.0000	0.522728
$528$	0	0
$529$	−7.00000	−0.304348
$530$	0	0
$531$	0	0
$532$	0	0
$533$	12.0000	0.519778
$534$	0	0
$535$	0	0
$536$	3.00000	0.129580
$537$	0	0
$538$	−2.00000	−0.0862261
$539$	−12.0000	−0.516877
$540$	0	0
$541$	−31.0000	−1.33279	−0.666397	−	0.745597i	$-0.732164\pi$
$541$	−31.0000	−1.33279	−0.666397	+	0.745597i	$0.732164\pi$
$542$	−16.0000	−0.687259
$543$	0	0
$544$	−4.00000	−0.171499
$545$	0	0
$546$	0	0
$547$	11.0000	0.470326	0.235163	−	0.971956i	$-0.424438\pi$
$547$	11.0000	0.470326	0.235163	+	0.971956i	$0.424438\pi$
$548$	6.00000	0.256307
$549$	0	0
$550$	−10.0000	−0.426401
$551$	0	0
$552$	0	0
$553$	1.00000	0.0425243
$554$	−2.00000	−0.0849719
$555$	0	0
$556$	−19.0000	−0.805779
$557$	−34.0000	−1.44063	−0.720313	−	0.693649i	$-0.756002\pi$
$557$	−34.0000	−1.44063	−0.720313	+	0.693649i	$0.756002\pi$
$558$	0	0
$559$	27.0000	1.14198
$560$	0	0
$561$	0	0
$562$	8.00000	0.337460
$563$	6.00000	0.252870	0.126435	−	0.991975i	$-0.459647\pi$
$563$	6.00000	0.252870	0.126435	+	0.991975i	$0.459647\pi$
$564$	0	0
$565$	0	0
$566$	−20.0000	−0.840663
$567$	0	0
$568$	−14.0000	−0.587427
$569$	−24.0000	−1.00613	−0.503066	−	0.864248i	$-0.667795\pi$
$569$	−24.0000	−1.00613	−0.503066	+	0.864248i	$0.667795\pi$
$570$	0	0
$571$	−7.00000	−0.292941	−0.146470	−	0.989215i	$-0.546791\pi$
$571$	−7.00000	−0.292941	−0.146470	+	0.989215i	$0.546791\pi$
$572$	−6.00000	−0.250873
$573$	0	0
$574$	−4.00000	−0.166957
$575$	20.0000	0.834058
$576$	0	0
$577$	−14.0000	−0.582828	−0.291414	−	0.956597i	$-0.594126\pi$
$577$	−14.0000	−0.582828	−0.291414	+	0.956597i	$0.594126\pi$
$578$	−1.00000	−0.0415945
$579$	0	0
$580$	0	0
$581$	−8.00000	−0.331896
$582$	0	0
$583$	8.00000	0.331326
$584$	−11.0000	−0.455183
$585$	0	0
$586$	−14.0000	−0.578335
$587$	2.00000	0.0825488	0.0412744	−	0.999148i	$-0.486858\pi$
$587$	2.00000	0.0825488	0.0412744	+	0.999148i	$0.486858\pi$
$588$	0	0
$589$	0	0
$590$	0	0
$591$	0	0
$592$	−5.00000	−0.205499
$593$	−34.0000	−1.39621	−0.698106	−	0.715994i	$-0.745974\pi$
$593$	−34.0000	−1.39621	−0.698106	+	0.715994i	$0.745974\pi$
$594$	0	0
$595$	0	0
$596$	22.0000	0.901155
$597$	0	0
$598$	12.0000	0.490716
$599$	46.0000	1.87951	0.939755	−	0.341850i	$-0.111053\pi$
$599$	46.0000	1.87951	0.939755	+	0.341850i	$0.111053\pi$
$600$	0	0
$601$	27.0000	1.10135	0.550676	−	0.834719i	$-0.314370\pi$
$601$	27.0000	1.10135	0.550676	+	0.834719i	$0.314370\pi$
$602$	−9.00000	−0.366813
$603$	0	0
$604$	−20.0000	−0.813788
$605$	0	0
$606$	0	0
$607$	5.00000	0.202944	0.101472	−	0.994838i	$-0.467645\pi$
$607$	5.00000	0.202944	0.101472	+	0.994838i	$0.467645\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	30.0000	1.21367
$612$	0	0
$613$	2.00000	0.0807792	0.0403896	−	0.999184i	$-0.487140\pi$
$613$	2.00000	0.0807792	0.0403896	+	0.999184i	$0.487140\pi$
$614$	−12.0000	−0.484281
$615$	0	0
$616$	2.00000	0.0805823
$617$	42.0000	1.69086	0.845428	−	0.534089i	$-0.179345\pi$
$617$	42.0000	1.69086	0.845428	+	0.534089i	$0.179345\pi$
$618$	0	0
$619$	1.00000	0.0401934	0.0200967	−	0.999798i	$-0.493603\pi$
$619$	1.00000	0.0401934	0.0200967	+	0.999798i	$0.493603\pi$
$620$	0	0
$621$	0	0
$622$	−10.0000	−0.400963
$623$	14.0000	0.560898
$624$	0	0
$625$	25.0000	1.00000
$626$	6.00000	0.239808
$627$	0	0
$628$	−21.0000	−0.837991
$629$	20.0000	0.797452
$630$	0	0
$631$	17.0000	0.676759	0.338380	−	0.941010i	$-0.390121\pi$
$631$	17.0000	0.676759	0.338380	+	0.941010i	$0.390121\pi$
$632$	1.00000	0.0397779
$633$	0	0
$634$	−12.0000	−0.476581
$635$	0	0
$636$	0	0
$637$	18.0000	0.713186
$638$	0	0
$639$	0	0
$640$	0	0
$641$	14.0000	0.552967	0.276483	−	0.961019i	$-0.410831\pi$
$641$	14.0000	0.552967	0.276483	+	0.961019i	$0.410831\pi$
$642$	0	0
$643$	37.0000	1.45914	0.729569	−	0.683907i	$-0.239721\pi$
$643$	37.0000	1.45914	0.729569	+	0.683907i	$0.239721\pi$
$644$	−4.00000	−0.157622
$645$	0	0
$646$	0	0
$647$	−48.0000	−1.88707	−0.943537	−	0.331266i	$-0.892524\pi$
$647$	−48.0000	−1.88707	−0.943537	+	0.331266i	$0.892524\pi$
$648$	0	0
$649$	28.0000	1.09910
$650$	15.0000	0.588348
$651$	0	0
$652$	11.0000	0.430793
$653$	42.0000	1.64359	0.821794	−	0.569785i	$-0.192974\pi$
$653$	42.0000	1.64359	0.821794	+	0.569785i	$0.192974\pi$
$654$	0	0
$655$	0	0
$656$	−4.00000	−0.156174
$657$	0	0
$658$	−10.0000	−0.389841
$659$	14.0000	0.545363	0.272681	−	0.962104i	$-0.412090\pi$
$659$	14.0000	0.545363	0.272681	+	0.962104i	$0.412090\pi$
$660$	0	0
$661$	10.0000	0.388955	0.194477	−	0.980907i	$-0.437699\pi$
$661$	10.0000	0.388955	0.194477	+	0.980907i	$0.437699\pi$
$662$	15.0000	0.582992
$663$	0	0
$664$	−8.00000	−0.310460
$665$	0	0
$666$	0	0
$667$	0	0
$668$	−6.00000	−0.232147
$669$	0	0
$670$	0	0
$671$	22.0000	0.849301
$672$	0	0
$673$	−1.00000	−0.0385472	−0.0192736	−	0.999814i	$-0.506135\pi$
$673$	−1.00000	−0.0385472	−0.0192736	+	0.999814i	$0.506135\pi$
$674$	−19.0000	−0.731853
$675$	0	0
$676$	−4.00000	−0.153846
$677$	−18.0000	−0.691796	−0.345898	−	0.938272i	$-0.612426\pi$
$677$	−18.0000	−0.691796	−0.345898	+	0.938272i	$0.612426\pi$
$678$	0	0
$679$	2.00000	0.0767530
$680$	0	0
$681$	0	0
$682$	−6.00000	−0.229752
$683$	36.0000	1.37750	0.688751	−	0.724998i	$-0.258159\pi$
$683$	36.0000	1.37750	0.688751	+	0.724998i	$0.258159\pi$
$684$	0	0
$685$	0	0
$686$	−13.0000	−0.496342
$687$	0	0
$688$	−9.00000	−0.343122
$689$	−12.0000	−0.457164
$690$	0	0
$691$	4.00000	0.152167	0.0760836	−	0.997101i	$-0.475758\pi$
$691$	4.00000	0.152167	0.0760836	+	0.997101i	$0.475758\pi$
$692$	24.0000	0.912343
$693$	0	0
$694$	−16.0000	−0.607352
$695$	0	0
$696$	0	0
$697$	16.0000	0.606043
$698$	−29.0000	−1.09767
$699$	0	0
$700$	−5.00000	−0.188982
$701$	44.0000	1.66186	0.830929	−	0.556379i	$-0.187810\pi$
$701$	44.0000	1.66186	0.830929	+	0.556379i	$0.187810\pi$
$702$	0	0
$703$	0	0
$704$	2.00000	0.0753778
$705$	0	0
$706$	12.0000	0.451626
$707$	10.0000	0.376089
$708$	0	0
$709$	−31.0000	−1.16423	−0.582115	−	0.813107i	$-0.697775\pi$
$709$	−31.0000	−1.16423	−0.582115	+	0.813107i	$0.697775\pi$
$710$	0	0
$711$	0	0
$712$	14.0000	0.524672
$713$	12.0000	0.449404
$714$	0	0
$715$	0	0
$716$	−4.00000	−0.149487
$717$	0	0
$718$	36.0000	1.34351
$719$	−40.0000	−1.49175	−0.745874	−	0.666087i	$-0.767968\pi$
$719$	−40.0000	−1.49175	−0.745874	+	0.666087i	$0.767968\pi$
$720$	0	0
$721$	−3.00000	−0.111726
$722$	0	0
$723$	0	0
$724$	−18.0000	−0.668965
$725$	0	0
$726$	0	0
$727$	17.0000	0.630495	0.315248	−	0.949009i	$-0.397912\pi$
$727$	17.0000	0.630495	0.315248	+	0.949009i	$0.397912\pi$
$728$	−3.00000	−0.111187
$729$	0	0
$730$	0	0
$731$	36.0000	1.33151
$732$	0	0
$733$	−2.00000	−0.0738717	−0.0369358	−	0.999318i	$-0.511760\pi$
$733$	−2.00000	−0.0738717	−0.0369358	+	0.999318i	$0.511760\pi$
$734$	23.0000	0.848945
$735$	0	0
$736$	−4.00000	−0.147442
$737$	6.00000	0.221013
$738$	0	0
$739$	−5.00000	−0.183928	−0.0919640	−	0.995762i	$-0.529314\pi$
$739$	−5.00000	−0.183928	−0.0919640	+	0.995762i	$0.529314\pi$
$740$	0	0
$741$	0	0
$742$	4.00000	0.146845
$743$	18.0000	0.660356	0.330178	−	0.943919i	$-0.392891\pi$
$743$	18.0000	0.660356	0.330178	+	0.943919i	$0.392891\pi$
$744$	0	0
$745$	0	0
$746$	26.0000	0.951928
$747$	0	0
$748$	−8.00000	−0.292509
$749$	10.0000	0.365392
$750$	0	0
$751$	13.0000	0.474377	0.237188	−	0.971464i	$-0.423774\pi$
$751$	13.0000	0.474377	0.237188	+	0.971464i	$0.423774\pi$
$752$	−10.0000	−0.364662
$753$	0	0
$754$	0	0
$755$	0	0
$756$	0	0
$757$	5.00000	0.181728	0.0908640	−	0.995863i	$-0.471037\pi$
$757$	5.00000	0.181728	0.0908640	+	0.995863i	$0.471037\pi$
$758$	−13.0000	−0.472181
$759$	0	0
$760$	0	0
$761$	34.0000	1.23250	0.616250	−	0.787551i	$-0.288651\pi$
$761$	34.0000	1.23250	0.616250	+	0.787551i	$0.288651\pi$
$762$	0	0
$763$	14.0000	0.506834
$764$	8.00000	0.289430
$765$	0	0
$766$	−14.0000	−0.505841
$767$	−42.0000	−1.51653
$768$	0	0
$769$	27.0000	0.973645	0.486822	−	0.873501i	$-0.338156\pi$
$769$	27.0000	0.973645	0.486822	+	0.873501i	$0.338156\pi$
$770$	0	0
$771$	0	0
$772$	−13.0000	−0.467880
$773$	18.0000	0.647415	0.323708	−	0.946157i	$-0.395071\pi$
$773$	18.0000	0.647415	0.323708	+	0.946157i	$0.395071\pi$
$774$	0	0
$775$	15.0000	0.538816
$776$	2.00000	0.0717958
$777$	0	0
$778$	16.0000	0.573628
$779$	0	0
$780$	0	0
$781$	−28.0000	−1.00192
$782$	16.0000	0.572159
$783$	0	0
$784$	−6.00000	−0.214286
$785$	0	0
$786$	0	0
$787$	−47.0000	−1.67537	−0.837685	−	0.546154i	$-0.816091\pi$
$787$	−47.0000	−1.67537	−0.837685	+	0.546154i	$0.816091\pi$
$788$	2.00000	0.0712470
$789$	0	0
$790$	0	0
$791$	−10.0000	−0.355559
$792$	0	0
$793$	−33.0000	−1.17186
$794$	15.0000	0.532330
$795$	0	0
$796$	5.00000	0.177220
$797$	−26.0000	−0.920967	−0.460484	−	0.887668i	$-0.652324\pi$
$797$	−26.0000	−0.920967	−0.460484	+	0.887668i	$0.652324\pi$
$798$	0	0
$799$	40.0000	1.41510
$800$	−5.00000	−0.176777
$801$	0	0
$802$	−18.0000	−0.635602
$803$	−22.0000	−0.776363
$804$	0	0
$805$	0	0
$806$	9.00000	0.317011
$807$	0	0
$808$	10.0000	0.351799
$809$	0	0		−	1.00000i	$-0.5\pi$
$809$	0	0			1.00000i	$0.5\pi$
$810$	0	0
$811$	4.00000	0.140459	0.0702295	−	0.997531i	$-0.477627\pi$
$811$	4.00000	0.140459	0.0702295	+	0.997531i	$0.477627\pi$
$812$	0	0
$813$	0	0
$814$	−10.0000	−0.350500
$815$	0	0
$816$	0	0
$817$	0	0
$818$	−30.0000	−1.04893
$819$	0	0
$820$	0	0
$821$	−48.0000	−1.67521	−0.837606	−	0.546275i	$-0.816045\pi$
$821$	−48.0000	−1.67521	−0.837606	+	0.546275i	$0.816045\pi$
$822$	0	0
$823$	4.00000	0.139431	0.0697156	−	0.997567i	$-0.477791\pi$
$823$	4.00000	0.139431	0.0697156	+	0.997567i	$0.477791\pi$
$824$	−3.00000	−0.104510
$825$	0	0
$826$	14.0000	0.487122
$827$	−36.0000	−1.25184	−0.625921	−	0.779886i	$-0.715277\pi$
$827$	−36.0000	−1.25184	−0.625921	+	0.779886i	$0.715277\pi$
$828$	0	0
$829$	−31.0000	−1.07667	−0.538337	−	0.842729i	$-0.680947\pi$
$829$	−31.0000	−1.07667	−0.538337	+	0.842729i	$0.680947\pi$
$830$	0	0
$831$	0	0
$832$	−3.00000	−0.104006
$833$	24.0000	0.831551
$834$	0	0
$835$	0	0
$836$	0	0
$837$	0	0
$838$	−18.0000	−0.621800
$839$	12.0000	0.414286	0.207143	−	0.978311i	$-0.433583\pi$
$839$	12.0000	0.414286	0.207143	+	0.978311i	$0.433583\pi$
$840$	0	0
$841$	−29.0000	−1.00000
$842$	10.0000	0.344623
$843$	0	0
$844$	25.0000	0.860535
$845$	0	0
$846$	0	0
$847$	−7.00000	−0.240523
$848$	4.00000	0.137361
$849$	0	0
$850$	20.0000	0.685994
$851$	20.0000	0.685591
$852$	0	0
$853$	3.00000	0.102718	0.0513590	−	0.998680i	$-0.483645\pi$
$853$	3.00000	0.102718	0.0513590	+	0.998680i	$0.483645\pi$
$854$	11.0000	0.376412
$855$	0	0
$856$	10.0000	0.341793
$857$	−42.0000	−1.43469	−0.717346	−	0.696717i	$-0.754643\pi$
$857$	−42.0000	−1.43469	−0.717346	+	0.696717i	$0.754643\pi$
$858$	0	0
$859$	7.00000	0.238837	0.119418	−	0.992844i	$-0.461897\pi$
$859$	7.00000	0.238837	0.119418	+	0.992844i	$0.461897\pi$
$860$	0	0
$861$	0	0
$862$	10.0000	0.340601
$863$	22.0000	0.748889	0.374444	−	0.927249i	$-0.377833\pi$
$863$	22.0000	0.748889	0.374444	+	0.927249i	$0.377833\pi$
$864$	0	0
$865$	0	0
$866$	−9.00000	−0.305832
$867$	0	0
$868$	−3.00000	−0.101827
$869$	2.00000	0.0678454
$870$	0	0
$871$	−9.00000	−0.304953
$872$	14.0000	0.474100
$873$	0	0
$874$	0	0
$875$	0	0
$876$	0	0
$877$	−25.0000	−0.844190	−0.422095	−	0.906552i	$-0.638705\pi$
$877$	−25.0000	−0.844190	−0.422095	+	0.906552i	$0.638705\pi$
$878$	19.0000	0.641219
$879$	0	0
$880$	0	0
$881$	−36.0000	−1.21287	−0.606435	−	0.795133i	$-0.707401\pi$
$881$	−36.0000	−1.21287	−0.606435	+	0.795133i	$0.707401\pi$
$882$	0	0
$883$	−9.00000	−0.302874	−0.151437	−	0.988467i	$-0.548390\pi$
$883$	−9.00000	−0.302874	−0.151437	+	0.988467i	$0.548390\pi$
$884$	12.0000	0.403604
$885$	0	0
$886$	−24.0000	−0.806296
$887$	−18.0000	−0.604381	−0.302190	−	0.953248i	$-0.597718\pi$
$887$	−18.0000	−0.604381	−0.302190	+	0.953248i	$0.597718\pi$
$888$	0	0
$889$	−8.00000	−0.268311
$890$	0	0
$891$	0	0
$892$	9.00000	0.301342
$893$	0	0
$894$	0	0
$895$	0	0
$896$	1.00000	0.0334077
$897$	0	0
$898$	36.0000	1.20134
$899$	0	0
$900$	0	0
$901$	−16.0000	−0.533037
$902$	−8.00000	−0.266371
$903$	0	0
$904$	−10.0000	−0.332595
$905$	0	0
$906$	0	0
$907$	52.0000	1.72663	0.863316	−	0.504664i	$-0.168384\pi$
$907$	52.0000	1.72663	0.863316	+	0.504664i	$0.168384\pi$
$908$	−8.00000	−0.265489
$909$	0	0
$910$	0	0
$911$	60.0000	1.98789	0.993944	−	0.109885i	$-0.0350482\pi$
$911$	60.0000	1.98789	0.993944	+	0.109885i	$0.0350482\pi$
$912$	0	0
$913$	−16.0000	−0.529523
$914$	5.00000	0.165385
$915$	0	0
$916$	−11.0000	−0.363450
$917$	6.00000	0.198137
$918$	0	0
$919$	55.0000	1.81428	0.907141	−	0.420826i	$-0.138260\pi$
$919$	55.0000	1.81428	0.907141	+	0.420826i	$0.138260\pi$
$920$	0	0
$921$	0	0
$922$	−6.00000	−0.197599
$923$	42.0000	1.38245
$924$	0	0
$925$	25.0000	0.821995
$926$	−9.00000	−0.295758
$927$	0	0
$928$	0	0
$929$	−12.0000	−0.393707	−0.196854	−	0.980433i	$-0.563072\pi$
$929$	−12.0000	−0.393707	−0.196854	+	0.980433i	$0.563072\pi$
$930$	0	0
$931$	0	0
$932$	−18.0000	−0.589610
$933$	0	0
$934$	−8.00000	−0.261768
$935$	0	0
$936$	0	0
$937$	−25.0000	−0.816714	−0.408357	−	0.912822i	$-0.633898\pi$
$937$	−25.0000	−0.816714	−0.408357	+	0.912822i	$0.633898\pi$
$938$	3.00000	0.0979535
$939$	0	0
$940$	0	0
$941$	32.0000	1.04317	0.521585	−	0.853199i	$-0.325341\pi$
$941$	32.0000	1.04317	0.521585	+	0.853199i	$0.325341\pi$
$942$	0	0
$943$	16.0000	0.521032
$944$	14.0000	0.455661
$945$	0	0
$946$	−18.0000	−0.585230
$947$	−10.0000	−0.324956	−0.162478	−	0.986712i	$-0.551949\pi$
$947$	−10.0000	−0.324956	−0.162478	+	0.986712i	$0.551949\pi$
$948$	0	0
$949$	33.0000	1.07123
$950$	0	0
$951$	0	0
$952$	−4.00000	−0.129641
$953$	30.0000	0.971795	0.485898	−	0.874016i	$-0.338493\pi$
$953$	30.0000	0.971795	0.485898	+	0.874016i	$0.338493\pi$
$954$	0	0
$955$	0	0
$956$	12.0000	0.388108
$957$	0	0
$958$	−6.00000	−0.193851
$959$	6.00000	0.193750
$960$	0	0
$961$	−22.0000	−0.709677
$962$	15.0000	0.483619
$963$	0	0
$964$	25.0000	0.805196
$965$	0	0
$966$	0	0
$967$	51.0000	1.64005	0.820025	−	0.572328i	$-0.193960\pi$
$967$	51.0000	1.64005	0.820025	+	0.572328i	$0.193960\pi$
$968$	−7.00000	−0.224989
$969$	0	0
$970$	0	0
$971$	−6.00000	−0.192549	−0.0962746	−	0.995355i	$-0.530693\pi$
$971$	−6.00000	−0.192549	−0.0962746	+	0.995355i	$0.530693\pi$
$972$	0	0
$973$	−19.0000	−0.609112
$974$	32.0000	1.02535
$975$	0	0
$976$	11.0000	0.352101
$977$	42.0000	1.34370	0.671850	−	0.740688i	$-0.265500\pi$
$977$	42.0000	1.34370	0.671850	+	0.740688i	$0.265500\pi$
$978$	0	0
$979$	28.0000	0.894884
$980$	0	0
$981$	0	0
$982$	−30.0000	−0.957338
$983$	6.00000	0.191370	0.0956851	−	0.995412i	$-0.469496\pi$
$983$	6.00000	0.191370	0.0956851	+	0.995412i	$0.469496\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	0	0
$988$	0	0
$989$	36.0000	1.14473
$990$	0	0
$991$	−17.0000	−0.540023	−0.270011	−	0.962857i	$-0.587027\pi$
$991$	−17.0000	−0.540023	−0.270011	+	0.962857i	$0.587027\pi$
$992$	−3.00000	−0.0952501
$993$	0	0
$994$	−14.0000	−0.444053
$995$	0	0
$996$	0	0
$997$	−49.0000	−1.55185	−0.775923	−	0.630828i	$-0.782715\pi$
$997$	−49.0000	−1.55185	−0.775923	+	0.630828i	$0.782715\pi$
$998$	5.00000	0.158272
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6498.2.a.u.1.1		1
3.2	odd	2		2166.2.a.b.1.1		1
19.7	even	3		342.2.g.c.163.1		2
19.11	even	3		342.2.g.c.235.1		2
19.18	odd	2		6498.2.a.g.1.1		1
57.11	odd	6		114.2.e.b.7.1	✓	2
57.26	odd	6		114.2.e.b.49.1	yes	2
57.56	even	2		2166.2.a.h.1.1		1
76.7	odd	6		2736.2.s.k.1873.1		2
76.11	odd	6		2736.2.s.k.577.1		2
228.11	even	6		912.2.q.b.577.1		2
228.83	even	6		912.2.q.b.49.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.e.b.7.1	✓	2	57.11	odd	6
114.2.e.b.49.1	yes	2	57.26	odd	6
342.2.g.c.163.1		2	19.7	even	3
342.2.g.c.235.1		2	19.11	even	3
912.2.q.b.49.1		2	228.83	even	6
912.2.q.b.577.1		2	228.11	even	6
2166.2.a.b.1.1		1	3.2	odd	2
2166.2.a.h.1.1		1	57.56	even	2
2736.2.s.k.577.1		2	76.11	odd	6
2736.2.s.k.1873.1		2	76.7	odd	6
6498.2.a.g.1.1		1	19.18	odd	2
6498.2.a.u.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:	\( N \)	\(=\)	\( 6498 = 2 \cdot 3^{2} \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6498.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more