LMFDB - Embedded newform 7280.2.a.bc.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7280,2,Mod(1,7280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7280, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 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("7280.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7280 = 2^{4} \cdot 5 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7280.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:	$58.1310926715$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{8})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 2 $ x^2 - 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 910)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.41421$ of defining polynomial
Character	$\chi$	$=$	7280.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.82843 q^{3} +1.00000 q^{5} -1.00000 q^{7} +5.00000 q^{9} +O(q^{10})$	$q+2.82843 q^{3} +1.00000 q^{5} -1.00000 q^{7} +5.00000 q^{9} -4.00000 q^{11} +1.00000 q^{13} +2.82843 q^{15} -4.82843 q^{17} +1.17157 q^{19} -2.82843 q^{21} +1.17157 q^{23} +1.00000 q^{25} +5.65685 q^{27} +6.00000 q^{29} +9.65685 q^{31} -11.3137 q^{33} -1.00000 q^{35} +7.65685 q^{37} +2.82843 q^{39} +6.48528 q^{41} +11.3137 q^{43} +5.00000 q^{45} -11.3137 q^{47} +1.00000 q^{49} -13.6569 q^{51} +3.17157 q^{53} -4.00000 q^{55} +3.31371 q^{57} -1.17157 q^{59} -0.343146 q^{61} -5.00000 q^{63} +1.00000 q^{65} -1.65685 q^{67} +3.31371 q^{69} -5.17157 q^{71} +11.6569 q^{73} +2.82843 q^{75} +4.00000 q^{77} -11.3137 q^{79} +1.00000 q^{81} +13.6569 q^{83} -4.82843 q^{85} +16.9706 q^{87} +11.1716 q^{89} -1.00000 q^{91} +27.3137 q^{93} +1.17157 q^{95} +17.3137 q^{97} -20.0000 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{5} - 2 q^{7} + 10 q^{9}+O(q^{10}) $ 2 * q + 2 * q^5 - 2 * q^7 + 10 * q^9	$ 2 q + 2 q^{5} - 2 q^{7} + 10 q^{9} - 8 q^{11} + 2 q^{13} - 4 q^{17} + 8 q^{19} + 8 q^{23} + 2 q^{25} + 12 q^{29} + 8 q^{31} - 2 q^{35} + 4 q^{37} - 4 q^{41} + 10 q^{45} + 2 q^{49} - 16 q^{51} + 12 q^{53} - 8 q^{55} - 16 q^{57} - 8 q^{59} - 12 q^{61} - 10 q^{63} + 2 q^{65} + 8 q^{67} - 16 q^{69} - 16 q^{71} + 12 q^{73} + 8 q^{77} + 2 q^{81} + 16 q^{83} - 4 q^{85} + 28 q^{89} - 2 q^{91} + 32 q^{93} + 8 q^{95} + 12 q^{97} - 40 q^{99}+O(q^{100}) $ 2 * q + 2 * q^5 - 2 * q^7 + 10 * q^9 - 8 * q^11 + 2 * q^13 - 4 * q^17 + 8 * q^19 + 8 * q^23 + 2 * q^25 + 12 * q^29 + 8 * q^31 - 2 * q^35 + 4 * q^37 - 4 * q^41 + 10 * q^45 + 2 * q^49 - 16 * q^51 + 12 * q^53 - 8 * q^55 - 16 * q^57 - 8 * q^59 - 12 * q^61 - 10 * q^63 + 2 * q^65 + 8 * q^67 - 16 * q^69 - 16 * q^71 + 12 * q^73 + 8 * q^77 + 2 * q^81 + 16 * q^83 - 4 * q^85 + 28 * q^89 - 2 * q^91 + 32 * q^93 + 8 * q^95 + 12 * q^97 - 40 * q^99

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 $

$2$	0	0
$2$	0	0
$3$	2.82843	1.63299	0.816497	−	0.577350i	$-0.195913\pi$
$3$	2.82843	1.63299	0.816497	+	0.577350i	$0.195913\pi$
$4$	0	0
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0	0
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	0	0
$9$	5.00000	1.66667
$10$	0	0
$11$	−4.00000	−1.20605	−0.603023	−	0.797724i	$-0.706037\pi$
$11$	−4.00000	−1.20605	−0.603023	+	0.797724i	$0.706037\pi$
$12$	0	0
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0	0
$15$	2.82843	0.730297
$16$	0	0
$17$	−4.82843	−1.17107	−0.585533	−	0.810649i	$-0.699115\pi$
$17$	−4.82843	−1.17107	−0.585533	+	0.810649i	$0.699115\pi$
$18$	0	0
$19$	1.17157	0.268777	0.134389	−	0.990929i	$-0.457093\pi$
$19$	1.17157	0.268777	0.134389	+	0.990929i	$0.457093\pi$
$20$	0	0
$21$	−2.82843	−0.617213
$22$	0	0
$23$	1.17157	0.244290	0.122145	−	0.992512i	$-0.461023\pi$
$23$	1.17157	0.244290	0.122145	+	0.992512i	$0.461023\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	0	0
$27$	5.65685	1.08866
$28$	0	0
$29$	6.00000	1.11417	0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000	1.11417	0.557086	+	0.830455i	$0.311919\pi$
$30$	0	0
$31$	9.65685	1.73442	0.867211	−	0.497941i	$-0.165910\pi$
$31$	9.65685	1.73442	0.867211	+	0.497941i	$0.165910\pi$
$32$	0	0
$33$	−11.3137	−1.96946
$34$	0	0
$35$	−1.00000	−0.169031
$36$	0	0
$37$	7.65685	1.25878	0.629390	−	0.777090i	$-0.283305\pi$
$37$	7.65685	1.25878	0.629390	+	0.777090i	$0.283305\pi$
$38$	0	0
$39$	2.82843	0.452911
$40$	0	0
$41$	6.48528	1.01283	0.506415	−	0.862290i	$-0.330970\pi$
$41$	6.48528	1.01283	0.506415	+	0.862290i	$0.330970\pi$
$42$	0	0
$43$	11.3137	1.72532	0.862662	−	0.505781i	$-0.168795\pi$
$43$	11.3137	1.72532	0.862662	+	0.505781i	$0.168795\pi$
$44$	0	0
$45$	5.00000	0.745356
$46$	0	0
$47$	−11.3137	−1.65027	−0.825137	−	0.564933i	$-0.808902\pi$
$47$	−11.3137	−1.65027	−0.825137	+	0.564933i	$0.808902\pi$
$48$	0	0
$49$	1.00000	0.142857
$50$	0	0
$51$	−13.6569	−1.91234
$52$	0	0
$53$	3.17157	0.435649	0.217825	−	0.975988i	$-0.430104\pi$
$53$	3.17157	0.435649	0.217825	+	0.975988i	$0.430104\pi$
$54$	0	0
$55$	−4.00000	−0.539360
$56$	0	0
$57$	3.31371	0.438911
$58$	0	0
$59$	−1.17157	−0.152526	−0.0762629	−	0.997088i	$-0.524299\pi$
$59$	−1.17157	−0.152526	−0.0762629	+	0.997088i	$0.524299\pi$
$60$	0	0
$61$	−0.343146	−0.0439353	−0.0219677	−	0.999759i	$-0.506993\pi$
$61$	−0.343146	−0.0439353	−0.0219677	+	0.999759i	$0.506993\pi$
$62$	0	0
$63$	−5.00000	−0.629941
$64$	0	0
$65$	1.00000	0.124035
$66$	0	0
$67$	−1.65685	−0.202417	−0.101208	−	0.994865i	$-0.532271\pi$
$67$	−1.65685	−0.202417	−0.101208	+	0.994865i	$0.532271\pi$
$68$	0	0
$69$	3.31371	0.398924
$70$	0	0
$71$	−5.17157	−0.613753	−0.306876	−	0.951749i	$-0.599284\pi$
$71$	−5.17157	−0.613753	−0.306876	+	0.951749i	$0.599284\pi$
$72$	0	0
$73$	11.6569	1.36433	0.682166	−	0.731198i	$-0.261038\pi$
$73$	11.6569	1.36433	0.682166	+	0.731198i	$0.261038\pi$
$74$	0	0
$75$	2.82843	0.326599
$76$	0	0
$77$	4.00000	0.455842
$78$	0	0
$79$	−11.3137	−1.27289	−0.636446	−	0.771321i	$-0.719596\pi$
$79$	−11.3137	−1.27289	−0.636446	+	0.771321i	$0.719596\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	0	0
$83$	13.6569	1.49903	0.749517	−	0.661985i	$-0.230286\pi$
$83$	13.6569	1.49903	0.749517	+	0.661985i	$0.230286\pi$
$84$	0	0
$85$	−4.82843	−0.523716
$86$	0	0
$87$	16.9706	1.81944
$88$	0	0
$89$	11.1716	1.18418	0.592092	−	0.805870i	$-0.298302\pi$
$89$	11.1716	1.18418	0.592092	+	0.805870i	$0.298302\pi$
$90$	0	0
$91$	−1.00000	−0.104828
$92$	0	0
$93$	27.3137	2.83230
$94$	0	0
$95$	1.17157	0.120201
$96$	0	0
$97$	17.3137	1.75794	0.878970	−	0.476876i	$-0.158231\pi$
$97$	17.3137	1.75794	0.878970	+	0.476876i	$0.158231\pi$
$98$	0	0
$99$	−20.0000	−2.01008
$100$	0	0
$101$	−3.65685	−0.363871	−0.181935	−	0.983311i	$-0.558236\pi$
$101$	−3.65685	−0.363871	−0.181935	+	0.983311i	$0.558236\pi$
$102$	0	0
$103$	0	0		−	1.00000i	$-0.5\pi$
$103$	0	0			1.00000i	$0.5\pi$
$104$	0	0
$105$	−2.82843	−0.276026
$106$	0	0
$107$	−8.00000	−0.773389	−0.386695	−	0.922208i	$-0.626383\pi$
$107$	−8.00000	−0.773389	−0.386695	+	0.922208i	$0.626383\pi$
$108$	0	0
$109$	6.48528	0.621177	0.310589	−	0.950544i	$-0.399474\pi$
$109$	6.48528	0.621177	0.310589	+	0.950544i	$0.399474\pi$
$110$	0	0
$111$	21.6569	2.05558
$112$	0	0
$113$	10.0000	0.940721	0.470360	−	0.882474i	$-0.344124\pi$
$113$	10.0000	0.940721	0.470360	+	0.882474i	$0.344124\pi$
$114$	0	0
$115$	1.17157	0.109250
$116$	0	0
$117$	5.00000	0.462250
$118$	0	0
$119$	4.82843	0.442621
$120$	0	0
$121$	5.00000	0.454545
$122$	0	0
$123$	18.3431	1.65395
$124$	0	0
$125$	1.00000	0.0894427
$126$	0	0
$127$	−4.48528	−0.398004	−0.199002	−	0.979999i	$-0.563770\pi$
$127$	−4.48528	−0.398004	−0.199002	+	0.979999i	$0.563770\pi$
$128$	0	0
$129$	32.0000	2.81744
$130$	0	0
$131$	−16.0000	−1.39793	−0.698963	−	0.715158i	$-0.746355\pi$
$131$	−16.0000	−1.39793	−0.698963	+	0.715158i	$0.746355\pi$
$132$	0	0
$133$	−1.17157	−0.101588
$134$	0	0
$135$	5.65685	0.486864
$136$	0	0
$137$	−10.0000	−0.854358	−0.427179	−	0.904167i	$-0.640493\pi$
$137$	−10.0000	−0.854358	−0.427179	+	0.904167i	$0.640493\pi$
$138$	0	0
$139$	19.3137	1.63817	0.819084	−	0.573674i	$-0.194482\pi$
$139$	19.3137	1.63817	0.819084	+	0.573674i	$0.194482\pi$
$140$	0	0
$141$	−32.0000	−2.69489
$142$	0	0
$143$	−4.00000	−0.334497
$144$	0	0
$145$	6.00000	0.498273
$146$	0	0
$147$	2.82843	0.233285
$148$	0	0
$149$	14.4853	1.18668	0.593340	−	0.804952i	$-0.297809\pi$
$149$	14.4853	1.18668	0.593340	+	0.804952i	$0.297809\pi$
$150$	0	0
$151$	22.1421	1.80190	0.900951	−	0.433921i	$-0.142870\pi$
$151$	22.1421	1.80190	0.900951	+	0.433921i	$0.142870\pi$
$152$	0	0
$153$	−24.1421	−1.95178
$154$	0	0
$155$	9.65685	0.775657
$156$	0	0
$157$	−2.00000	−0.159617	−0.0798087	−	0.996810i	$-0.525431\pi$
$157$	−2.00000	−0.159617	−0.0798087	+	0.996810i	$0.525431\pi$
$158$	0	0
$159$	8.97056	0.711412
$160$	0	0
$161$	−1.17157	−0.0923329
$162$	0	0
$163$	9.65685	0.756383	0.378192	−	0.925727i	$-0.376546\pi$
$163$	9.65685	0.756383	0.378192	+	0.925727i	$0.376546\pi$
$164$	0	0
$165$	−11.3137	−0.880771
$166$	0	0
$167$	−8.97056	−0.694163	−0.347081	−	0.937835i	$-0.612827\pi$
$167$	−8.97056	−0.694163	−0.347081	+	0.937835i	$0.612827\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	0	0
$171$	5.85786	0.447962
$172$	0	0
$173$	−10.0000	−0.760286	−0.380143	−	0.924928i	$-0.624125\pi$
$173$	−10.0000	−0.760286	−0.380143	+	0.924928i	$0.624125\pi$
$174$	0	0
$175$	−1.00000	−0.0755929
$176$	0	0
$177$	−3.31371	−0.249074
$178$	0	0
$179$	−12.0000	−0.896922	−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000	−0.896922	−0.448461	+	0.893802i	$0.648028\pi$
$180$	0	0
$181$	−22.9706	−1.70739	−0.853694	−	0.520775i	$-0.825643\pi$
$181$	−22.9706	−1.70739	−0.853694	+	0.520775i	$0.825643\pi$
$182$	0	0
$183$	−0.970563	−0.0717461
$184$	0	0
$185$	7.65685	0.562943
$186$	0	0
$187$	19.3137	1.41236
$188$	0	0
$189$	−5.65685	−0.411476
$190$	0	0
$191$	−21.6569	−1.56703	−0.783517	−	0.621370i	$-0.786577\pi$
$191$	−21.6569	−1.56703	−0.783517	+	0.621370i	$0.786577\pi$
$192$	0	0
$193$	6.00000	0.431889	0.215945	−	0.976406i	$-0.430717\pi$
$193$	6.00000	0.431889	0.215945	+	0.976406i	$0.430717\pi$
$194$	0	0
$195$	2.82843	0.202548
$196$	0	0
$197$	−0.343146	−0.0244481	−0.0122241	−	0.999925i	$-0.503891\pi$
$197$	−0.343146	−0.0244481	−0.0122241	+	0.999925i	$0.503891\pi$
$198$	0	0
$199$	5.65685	0.401004	0.200502	−	0.979693i	$-0.435743\pi$
$199$	5.65685	0.401004	0.200502	+	0.979693i	$0.435743\pi$
$200$	0	0
$201$	−4.68629	−0.330546
$202$	0	0
$203$	−6.00000	−0.421117
$204$	0	0
$205$	6.48528	0.452952
$206$	0	0
$207$	5.85786	0.407150
$208$	0	0
$209$	−4.68629	−0.324158
$210$	0	0
$211$	6.34315	0.436680	0.218340	−	0.975873i	$-0.429936\pi$
$211$	6.34315	0.436680	0.218340	+	0.975873i	$0.429936\pi$
$212$	0	0
$213$	−14.6274	−1.00225
$214$	0	0
$215$	11.3137	0.771589
$216$	0	0
$217$	−9.65685	−0.655550
$218$	0	0
$219$	32.9706	2.22794
$220$	0	0
$221$	−4.82843	−0.324795
$222$	0	0
$223$	−24.9706	−1.67215	−0.836076	−	0.548613i	$-0.815156\pi$
$223$	−24.9706	−1.67215	−0.836076	+	0.548613i	$0.815156\pi$
$224$	0	0
$225$	5.00000	0.333333
$226$	0	0
$227$	10.3431	0.686499	0.343249	−	0.939244i	$-0.388472\pi$
$227$	10.3431	0.686499	0.343249	+	0.939244i	$0.388472\pi$
$228$	0	0
$229$	−7.65685	−0.505979	−0.252990	−	0.967469i	$-0.581414\pi$
$229$	−7.65685	−0.505979	−0.252990	+	0.967469i	$0.581414\pi$
$230$	0	0
$231$	11.3137	0.744387
$232$	0	0
$233$	10.9706	0.718705	0.359353	−	0.933202i	$-0.382997\pi$
$233$	10.9706	0.718705	0.359353	+	0.933202i	$0.382997\pi$
$234$	0	0
$235$	−11.3137	−0.738025
$236$	0	0
$237$	−32.0000	−2.07862
$238$	0	0
$239$	−16.4853	−1.06634	−0.533172	−	0.846007i	$-0.679000\pi$
$239$	−16.4853	−1.06634	−0.533172	+	0.846007i	$0.679000\pi$
$240$	0	0
$241$	0.828427	0.0533637	0.0266818	−	0.999644i	$-0.491506\pi$
$241$	0.828427	0.0533637	0.0266818	+	0.999644i	$0.491506\pi$
$242$	0	0
$243$	−14.1421	−0.907218
$244$	0	0
$245$	1.00000	0.0638877
$246$	0	0
$247$	1.17157	0.0745454
$248$	0	0
$249$	38.6274	2.44791
$250$	0	0
$251$	8.97056	0.566217	0.283108	−	0.959088i	$-0.408634\pi$
$251$	8.97056	0.566217	0.283108	+	0.959088i	$0.408634\pi$
$252$	0	0
$253$	−4.68629	−0.294625
$254$	0	0
$255$	−13.6569	−0.855225
$256$	0	0
$257$	3.17157	0.197837	0.0989186	−	0.995096i	$-0.468462\pi$
$257$	3.17157	0.197837	0.0989186	+	0.995096i	$0.468462\pi$
$258$	0	0
$259$	−7.65685	−0.475774
$260$	0	0
$261$	30.0000	1.85695
$262$	0	0
$263$	−29.4558	−1.81633	−0.908163	−	0.418618i	$-0.862515\pi$
$263$	−29.4558	−1.81633	−0.908163	+	0.418618i	$0.862515\pi$
$264$	0	0
$265$	3.17157	0.194828
$266$	0	0
$267$	31.5980	1.93376
$268$	0	0
$269$	15.6569	0.954615	0.477308	−	0.878736i	$-0.341613\pi$
$269$	15.6569	0.954615	0.477308	+	0.878736i	$0.341613\pi$
$270$	0	0
$271$	−4.97056	−0.301940	−0.150970	−	0.988538i	$-0.548240\pi$
$271$	−4.97056	−0.301940	−0.150970	+	0.988538i	$0.548240\pi$
$272$	0	0
$273$	−2.82843	−0.171184
$274$	0	0
$275$	−4.00000	−0.241209
$276$	0	0
$277$	12.1421	0.729550	0.364775	−	0.931096i	$-0.381146\pi$
$277$	12.1421	0.729550	0.364775	+	0.931096i	$0.381146\pi$
$278$	0	0
$279$	48.2843	2.89070
$280$	0	0
$281$	−6.97056	−0.415829	−0.207914	−	0.978147i	$-0.566668\pi$
$281$	−6.97056	−0.415829	−0.207914	+	0.978147i	$0.566668\pi$
$282$	0	0
$283$	26.8284	1.59478	0.797392	−	0.603461i	$-0.206212\pi$
$283$	26.8284	1.59478	0.797392	+	0.603461i	$0.206212\pi$
$284$	0	0
$285$	3.31371	0.196287
$286$	0	0
$287$	−6.48528	−0.382814
$288$	0	0
$289$	6.31371	0.371395
$290$	0	0
$291$	48.9706	2.87071
$292$	0	0
$293$	−10.0000	−0.584206	−0.292103	−	0.956387i	$-0.594355\pi$
$293$	−10.0000	−0.584206	−0.292103	+	0.956387i	$0.594355\pi$
$294$	0	0
$295$	−1.17157	−0.0682116
$296$	0	0
$297$	−22.6274	−1.31298
$298$	0	0
$299$	1.17157	0.0677538
$300$	0	0
$301$	−11.3137	−0.652111
$302$	0	0
$303$	−10.3431	−0.594198
$304$	0	0
$305$	−0.343146	−0.0196485
$306$	0	0
$307$	−27.3137	−1.55888	−0.779438	−	0.626480i	$-0.784495\pi$
$307$	−27.3137	−1.55888	−0.779438	+	0.626480i	$0.784495\pi$
$308$	0	0
$309$	0	0
$310$	0	0
$311$	−24.9706	−1.41595	−0.707975	−	0.706237i	$-0.750391\pi$
$311$	−24.9706	−1.41595	−0.707975	+	0.706237i	$0.750391\pi$
$312$	0	0
$313$	−0.142136	−0.00803398	−0.00401699	−	0.999992i	$-0.501279\pi$
$313$	−0.142136	−0.00803398	−0.00401699	+	0.999992i	$0.501279\pi$
$314$	0	0
$315$	−5.00000	−0.281718
$316$	0	0
$317$	−1.31371	−0.0737852	−0.0368926	−	0.999319i	$-0.511746\pi$
$317$	−1.31371	−0.0737852	−0.0368926	+	0.999319i	$0.511746\pi$
$318$	0	0
$319$	−24.0000	−1.34374
$320$	0	0
$321$	−22.6274	−1.26294
$322$	0	0
$323$	−5.65685	−0.314756
$324$	0	0
$325$	1.00000	0.0554700
$326$	0	0
$327$	18.3431	1.01438
$328$	0	0
$329$	11.3137	0.623745
$330$	0	0
$331$	4.00000	0.219860	0.109930	−	0.993939i	$-0.464937\pi$
$331$	4.00000	0.219860	0.109930	+	0.993939i	$0.464937\pi$
$332$	0	0
$333$	38.2843	2.09797
$334$	0	0
$335$	−1.65685	−0.0905236
$336$	0	0
$337$	10.9706	0.597605	0.298802	−	0.954315i	$-0.403413\pi$
$337$	10.9706	0.597605	0.298802	+	0.954315i	$0.403413\pi$
$338$	0	0
$339$	28.2843	1.53619
$340$	0	0
$341$	−38.6274	−2.09179
$342$	0	0
$343$	−1.00000	−0.0539949
$344$	0	0
$345$	3.31371	0.178404
$346$	0	0
$347$	−18.3431	−0.984712	−0.492356	−	0.870394i	$-0.663864\pi$
$347$	−18.3431	−0.984712	−0.492356	+	0.870394i	$0.663864\pi$
$348$	0	0
$349$	−18.9706	−1.01547	−0.507735	−	0.861513i	$-0.669517\pi$
$349$	−18.9706	−1.01547	−0.507735	+	0.861513i	$0.669517\pi$
$350$	0	0
$351$	5.65685	0.301941
$352$	0	0
$353$	14.0000	0.745145	0.372572	−	0.928003i	$-0.378476\pi$
$353$	14.0000	0.745145	0.372572	+	0.928003i	$0.378476\pi$
$354$	0	0
$355$	−5.17157	−0.274479
$356$	0	0
$357$	13.6569	0.722797
$358$	0	0
$359$	22.1421	1.16862	0.584309	−	0.811532i	$-0.301366\pi$
$359$	22.1421	1.16862	0.584309	+	0.811532i	$0.301366\pi$
$360$	0	0
$361$	−17.6274	−0.927759
$362$	0	0
$363$	14.1421	0.742270
$364$	0	0
$365$	11.6569	0.610148
$366$	0	0
$367$	−8.97056	−0.468260	−0.234130	−	0.972205i	$-0.575224\pi$
$367$	−8.97056	−0.468260	−0.234130	+	0.972205i	$0.575224\pi$
$368$	0	0
$369$	32.4264	1.68805
$370$	0	0
$371$	−3.17157	−0.164660
$372$	0	0
$373$	−4.82843	−0.250006	−0.125003	−	0.992156i	$-0.539894\pi$
$373$	−4.82843	−0.250006	−0.125003	+	0.992156i	$0.539894\pi$
$374$	0	0
$375$	2.82843	0.146059
$376$	0	0
$377$	6.00000	0.309016
$378$	0	0
$379$	−28.9706	−1.48812	−0.744059	−	0.668114i	$-0.767102\pi$
$379$	−28.9706	−1.48812	−0.744059	+	0.668114i	$0.767102\pi$
$380$	0	0
$381$	−12.6863	−0.649938
$382$	0	0
$383$	29.6569	1.51539	0.757697	−	0.652606i	$-0.226324\pi$
$383$	29.6569	1.51539	0.757697	+	0.652606i	$0.226324\pi$
$384$	0	0
$385$	4.00000	0.203859
$386$	0	0
$387$	56.5685	2.87554
$388$	0	0
$389$	−13.3137	−0.675032	−0.337516	−	0.941320i	$-0.609587\pi$
$389$	−13.3137	−0.675032	−0.337516	+	0.941320i	$0.609587\pi$
$390$	0	0
$391$	−5.65685	−0.286079
$392$	0	0
$393$	−45.2548	−2.28280
$394$	0	0
$395$	−11.3137	−0.569254
$396$	0	0
$397$	−5.31371	−0.266687	−0.133344	−	0.991070i	$-0.542571\pi$
$397$	−5.31371	−0.266687	−0.133344	+	0.991070i	$0.542571\pi$
$398$	0	0
$399$	−3.31371	−0.165893
$400$	0	0
$401$	−6.00000	−0.299626	−0.149813	−	0.988714i	$-0.547867\pi$
$401$	−6.00000	−0.299626	−0.149813	+	0.988714i	$0.547867\pi$
$402$	0	0
$403$	9.65685	0.481042
$404$	0	0
$405$	1.00000	0.0496904
$406$	0	0
$407$	−30.6274	−1.51814
$408$	0	0
$409$	−35.4558	−1.75318	−0.876589	−	0.481239i	$-0.840187\pi$
$409$	−35.4558	−1.75318	−0.876589	+	0.481239i	$0.840187\pi$
$410$	0	0
$411$	−28.2843	−1.39516
$412$	0	0
$413$	1.17157	0.0576493
$414$	0	0
$415$	13.6569	0.670389
$416$	0	0
$417$	54.6274	2.67512
$418$	0	0
$419$	16.0000	0.781651	0.390826	−	0.920465i	$-0.372190\pi$
$419$	16.0000	0.781651	0.390826	+	0.920465i	$0.372190\pi$
$420$	0	0
$421$	−11.4558	−0.558324	−0.279162	−	0.960244i	$-0.590057\pi$
$421$	−11.4558	−0.558324	−0.279162	+	0.960244i	$0.590057\pi$
$422$	0	0
$423$	−56.5685	−2.75046
$424$	0	0
$425$	−4.82843	−0.234213
$426$	0	0
$427$	0.343146	0.0166060
$428$	0	0
$429$	−11.3137	−0.546231
$430$	0	0
$431$	35.7990	1.72438	0.862188	−	0.506588i	$-0.169093\pi$
$431$	35.7990	1.72438	0.862188	+	0.506588i	$0.169093\pi$
$432$	0	0
$433$	14.4853	0.696118	0.348059	−	0.937473i	$-0.386841\pi$
$433$	14.4853	0.696118	0.348059	+	0.937473i	$0.386841\pi$
$434$	0	0
$435$	16.9706	0.813676
$436$	0	0
$437$	1.37258	0.0656595
$438$	0	0
$439$	−28.2843	−1.34993	−0.674967	−	0.737848i	$-0.735842\pi$
$439$	−28.2843	−1.34993	−0.674967	+	0.737848i	$0.735842\pi$
$440$	0	0
$441$	5.00000	0.238095
$442$	0	0
$443$	22.6274	1.07506	0.537531	−	0.843244i	$-0.319357\pi$
$443$	22.6274	1.07506	0.537531	+	0.843244i	$0.319357\pi$
$444$	0	0
$445$	11.1716	0.529583
$446$	0	0
$447$	40.9706	1.93784
$448$	0	0
$449$	−19.6569	−0.927664	−0.463832	−	0.885923i	$-0.653526\pi$
$449$	−19.6569	−0.927664	−0.463832	+	0.885923i	$0.653526\pi$
$450$	0	0
$451$	−25.9411	−1.22152
$452$	0	0
$453$	62.6274	2.94249
$454$	0	0
$455$	−1.00000	−0.0468807
$456$	0	0
$457$	−27.9411	−1.30703	−0.653515	−	0.756913i	$-0.726707\pi$
$457$	−27.9411	−1.30703	−0.653515	+	0.756913i	$0.726707\pi$
$458$	0	0
$459$	−27.3137	−1.27489
$460$	0	0
$461$	35.6569	1.66071	0.830353	−	0.557238i	$-0.188139\pi$
$461$	35.6569	1.66071	0.830353	+	0.557238i	$0.188139\pi$
$462$	0	0
$463$	−24.0000	−1.11537	−0.557687	−	0.830051i	$-0.688311\pi$
$463$	−24.0000	−1.11537	−0.557687	+	0.830051i	$0.688311\pi$
$464$	0	0
$465$	27.3137	1.26664
$466$	0	0
$467$	−24.4853	−1.13304	−0.566522	−	0.824047i	$-0.691711\pi$
$467$	−24.4853	−1.13304	−0.566522	+	0.824047i	$0.691711\pi$
$468$	0	0
$469$	1.65685	0.0765064
$470$	0	0
$471$	−5.65685	−0.260654
$472$	0	0
$473$	−45.2548	−2.08082
$474$	0	0
$475$	1.17157	0.0537555
$476$	0	0
$477$	15.8579	0.726082
$478$	0	0
$479$	34.6274	1.58217	0.791084	−	0.611708i	$-0.209517\pi$
$479$	34.6274	1.58217	0.791084	+	0.611708i	$0.209517\pi$
$480$	0	0
$481$	7.65685	0.349123
$482$	0	0
$483$	−3.31371	−0.150779
$484$	0	0
$485$	17.3137	0.786175
$486$	0	0
$487$	16.0000	0.725029	0.362515	−	0.931978i	$-0.381918\pi$
$487$	16.0000	0.725029	0.362515	+	0.931978i	$0.381918\pi$
$488$	0	0
$489$	27.3137	1.23517
$490$	0	0
$491$	36.9706	1.66846	0.834229	−	0.551418i	$-0.185913\pi$
$491$	36.9706	1.66846	0.834229	+	0.551418i	$0.185913\pi$
$492$	0	0
$493$	−28.9706	−1.30477
$494$	0	0
$495$	−20.0000	−0.898933
$496$	0	0
$497$	5.17157	0.231977
$498$	0	0
$499$	20.0000	0.895323	0.447661	−	0.894203i	$-0.352257\pi$
$499$	20.0000	0.895323	0.447661	+	0.894203i	$0.352257\pi$
$500$	0	0
$501$	−25.3726	−1.13356
$502$	0	0
$503$	−3.31371	−0.147751	−0.0738755	−	0.997267i	$-0.523537\pi$
$503$	−3.31371	−0.147751	−0.0738755	+	0.997267i	$0.523537\pi$
$504$	0	0
$505$	−3.65685	−0.162728
$506$	0	0
$507$	2.82843	0.125615
$508$	0	0
$509$	−20.3431	−0.901694	−0.450847	−	0.892601i	$-0.648878\pi$
$509$	−20.3431	−0.901694	−0.450847	+	0.892601i	$0.648878\pi$
$510$	0	0
$511$	−11.6569	−0.515669
$512$	0	0
$513$	6.62742	0.292608
$514$	0	0
$515$	0	0
$516$	0	0
$517$	45.2548	1.99031
$518$	0	0
$519$	−28.2843	−1.24154
$520$	0	0
$521$	−16.3431	−0.716006	−0.358003	−	0.933720i	$-0.616542\pi$
$521$	−16.3431	−0.716006	−0.358003	+	0.933720i	$0.616542\pi$
$522$	0	0
$523$	−32.4853	−1.42048	−0.710241	−	0.703959i	$-0.751414\pi$
$523$	−32.4853	−1.42048	−0.710241	+	0.703959i	$0.751414\pi$
$524$	0	0
$525$	−2.82843	−0.123443
$526$	0	0
$527$	−46.6274	−2.03112
$528$	0	0
$529$	−21.6274	−0.940322
$530$	0	0
$531$	−5.85786	−0.254210
$532$	0	0
$533$	6.48528	0.280909
$534$	0	0
$535$	−8.00000	−0.345870
$536$	0	0
$537$	−33.9411	−1.46467
$538$	0	0
$539$	−4.00000	−0.172292
$540$	0	0
$541$	−11.4558	−0.492525	−0.246263	−	0.969203i	$-0.579203\pi$
$541$	−11.4558	−0.492525	−0.246263	+	0.969203i	$0.579203\pi$
$542$	0	0
$543$	−64.9706	−2.78815
$544$	0	0
$545$	6.48528	0.277799
$546$	0	0
$547$	8.97056	0.383554	0.191777	−	0.981439i	$-0.438575\pi$
$547$	8.97056	0.383554	0.191777	+	0.981439i	$0.438575\pi$
$548$	0	0
$549$	−1.71573	−0.0732255
$550$	0	0
$551$	7.02944	0.299464
$552$	0	0
$553$	11.3137	0.481108
$554$	0	0
$555$	21.6569	0.919282
$556$	0	0
$557$	12.3431	0.522996	0.261498	−	0.965204i	$-0.415784\pi$
$557$	12.3431	0.522996	0.261498	+	0.965204i	$0.415784\pi$
$558$	0	0
$559$	11.3137	0.478519
$560$	0	0
$561$	54.6274	2.30637
$562$	0	0
$563$	−1.85786	−0.0782996	−0.0391498	−	0.999233i	$-0.512465\pi$
$563$	−1.85786	−0.0782996	−0.0391498	+	0.999233i	$0.512465\pi$
$564$	0	0
$565$	10.0000	0.420703
$566$	0	0
$567$	−1.00000	−0.0419961
$568$	0	0
$569$	10.0000	0.419222	0.209611	−	0.977785i	$-0.432780\pi$
$569$	10.0000	0.419222	0.209611	+	0.977785i	$0.432780\pi$
$570$	0	0
$571$	30.3431	1.26982	0.634911	−	0.772586i	$-0.281037\pi$
$571$	30.3431	1.26982	0.634911	+	0.772586i	$0.281037\pi$
$572$	0	0
$573$	−61.2548	−2.55896
$574$	0	0
$575$	1.17157	0.0488580
$576$	0	0
$577$	−14.2843	−0.594662	−0.297331	−	0.954774i	$-0.596096\pi$
$577$	−14.2843	−0.594662	−0.297331	+	0.954774i	$0.596096\pi$
$578$	0	0
$579$	16.9706	0.705273
$580$	0	0
$581$	−13.6569	−0.566582
$582$	0	0
$583$	−12.6863	−0.525413
$584$	0	0
$585$	5.00000	0.206725
$586$	0	0
$587$	29.6569	1.22407	0.612035	−	0.790831i	$-0.290351\pi$
$587$	29.6569	1.22407	0.612035	+	0.790831i	$0.290351\pi$
$588$	0	0
$589$	11.3137	0.466173
$590$	0	0
$591$	−0.970563	−0.0399236
$592$	0	0
$593$	−35.9411	−1.47593	−0.737963	−	0.674842i	$-0.764212\pi$
$593$	−35.9411	−1.47593	−0.737963	+	0.674842i	$0.764212\pi$
$594$	0	0
$595$	4.82843	0.197946
$596$	0	0
$597$	16.0000	0.654836
$598$	0	0
$599$	−32.0000	−1.30748	−0.653742	−	0.756717i	$-0.726802\pi$
$599$	−32.0000	−1.30748	−0.653742	+	0.756717i	$0.726802\pi$
$600$	0	0
$601$	37.3137	1.52206	0.761029	−	0.648718i	$-0.224694\pi$
$601$	37.3137	1.52206	0.761029	+	0.648718i	$0.224694\pi$
$602$	0	0
$603$	−8.28427	−0.337362
$604$	0	0
$605$	5.00000	0.203279
$606$	0	0
$607$	40.0000	1.62355	0.811775	−	0.583970i	$-0.198502\pi$
$607$	40.0000	1.62355	0.811775	+	0.583970i	$0.198502\pi$
$608$	0	0
$609$	−16.9706	−0.687682
$610$	0	0
$611$	−11.3137	−0.457704
$612$	0	0
$613$	−17.3137	−0.699294	−0.349647	−	0.936881i	$-0.613698\pi$
$613$	−17.3137	−0.699294	−0.349647	+	0.936881i	$0.613698\pi$
$614$	0	0
$615$	18.3431	0.739667
$616$	0	0
$617$	−10.0000	−0.402585	−0.201292	−	0.979531i	$-0.564514\pi$
$617$	−10.0000	−0.402585	−0.201292	+	0.979531i	$0.564514\pi$
$618$	0	0
$619$	−3.51472	−0.141268	−0.0706342	−	0.997502i	$-0.522502\pi$
$619$	−3.51472	−0.141268	−0.0706342	+	0.997502i	$0.522502\pi$
$620$	0	0
$621$	6.62742	0.265949
$622$	0	0
$623$	−11.1716	−0.447580
$624$	0	0
$625$	1.00000	0.0400000
$626$	0	0
$627$	−13.2548	−0.529347
$628$	0	0
$629$	−36.9706	−1.47411
$630$	0	0
$631$	25.4558	1.01338	0.506691	−	0.862128i	$-0.330869\pi$
$631$	25.4558	1.01338	0.506691	+	0.862128i	$0.330869\pi$
$632$	0	0
$633$	17.9411	0.713096
$634$	0	0
$635$	−4.48528	−0.177993
$636$	0	0
$637$	1.00000	0.0396214
$638$	0	0
$639$	−25.8579	−1.02292
$640$	0	0
$641$	26.0000	1.02694	0.513469	−	0.858108i	$-0.328360\pi$
$641$	26.0000	1.02694	0.513469	+	0.858108i	$0.328360\pi$
$642$	0	0
$643$	−8.97056	−0.353764	−0.176882	−	0.984232i	$-0.556601\pi$
$643$	−8.97056	−0.353764	−0.176882	+	0.984232i	$0.556601\pi$
$644$	0	0
$645$	32.0000	1.26000
$646$	0	0
$647$	−8.97056	−0.352669	−0.176335	−	0.984330i	$-0.556424\pi$
$647$	−8.97056	−0.352669	−0.176335	+	0.984330i	$0.556424\pi$
$648$	0	0
$649$	4.68629	0.183953
$650$	0	0
$651$	−27.3137	−1.07051
$652$	0	0
$653$	−7.17157	−0.280645	−0.140323	−	0.990106i	$-0.544814\pi$
$653$	−7.17157	−0.280645	−0.140323	+	0.990106i	$0.544814\pi$
$654$	0	0
$655$	−16.0000	−0.625172
$656$	0	0
$657$	58.2843	2.27389
$658$	0	0
$659$	−28.0000	−1.09073	−0.545363	−	0.838200i	$-0.683608\pi$
$659$	−28.0000	−1.09073	−0.545363	+	0.838200i	$0.683608\pi$
$660$	0	0
$661$	43.2548	1.68242	0.841209	−	0.540710i	$-0.181844\pi$
$661$	43.2548	1.68242	0.841209	+	0.540710i	$0.181844\pi$
$662$	0	0
$663$	−13.6569	−0.530388
$664$	0	0
$665$	−1.17157	−0.0454316
$666$	0	0
$667$	7.02944	0.272181
$668$	0	0
$669$	−70.6274	−2.73061
$670$	0	0
$671$	1.37258	0.0529880
$672$	0	0
$673$	−33.3137	−1.28415	−0.642075	−	0.766642i	$-0.721926\pi$
$673$	−33.3137	−1.28415	−0.642075	+	0.766642i	$0.721926\pi$
$674$	0	0
$675$	5.65685	0.217732
$676$	0	0
$677$	−5.31371	−0.204222	−0.102111	−	0.994773i	$-0.532560\pi$
$677$	−5.31371	−0.204222	−0.102111	+	0.994773i	$0.532560\pi$
$678$	0	0
$679$	−17.3137	−0.664439
$680$	0	0
$681$	29.2548	1.12105
$682$	0	0
$683$	−2.62742	−0.100535	−0.0502677	−	0.998736i	$-0.516007\pi$
$683$	−2.62742	−0.100535	−0.0502677	+	0.998736i	$0.516007\pi$
$684$	0	0
$685$	−10.0000	−0.382080
$686$	0	0
$687$	−21.6569	−0.826261
$688$	0	0
$689$	3.17157	0.120827
$690$	0	0
$691$	−25.1716	−0.957572	−0.478786	−	0.877932i	$-0.658923\pi$
$691$	−25.1716	−0.957572	−0.478786	+	0.877932i	$0.658923\pi$
$692$	0	0
$693$	20.0000	0.759737
$694$	0	0
$695$	19.3137	0.732611
$696$	0	0
$697$	−31.3137	−1.18609
$698$	0	0
$699$	31.0294	1.17364
$700$	0	0
$701$	22.9706	0.867586	0.433793	−	0.901013i	$-0.357175\pi$
$701$	22.9706	0.867586	0.433793	+	0.901013i	$0.357175\pi$
$702$	0	0
$703$	8.97056	0.338331
$704$	0	0
$705$	−32.0000	−1.20519
$706$	0	0
$707$	3.65685	0.137530
$708$	0	0
$709$	6.48528	0.243560	0.121780	−	0.992557i	$-0.461140\pi$
$709$	6.48528	0.243560	0.121780	+	0.992557i	$0.461140\pi$
$710$	0	0
$711$	−56.5685	−2.12149
$712$	0	0
$713$	11.3137	0.423702
$714$	0	0
$715$	−4.00000	−0.149592
$716$	0	0
$717$	−46.6274	−1.74133
$718$	0	0
$719$	−33.9411	−1.26579	−0.632895	−	0.774237i	$-0.718134\pi$
$719$	−33.9411	−1.26579	−0.632895	+	0.774237i	$0.718134\pi$
$720$	0	0
$721$	0	0
$722$	0	0
$723$	2.34315	0.0871425
$724$	0	0
$725$	6.00000	0.222834
$726$	0	0
$727$	−32.9706	−1.22281	−0.611405	−	0.791318i	$-0.709395\pi$
$727$	−32.9706	−1.22281	−0.611405	+	0.791318i	$0.709395\pi$
$728$	0	0
$729$	−43.0000	−1.59259
$730$	0	0
$731$	−54.6274	−2.02047
$732$	0	0
$733$	−35.9411	−1.32752	−0.663758	−	0.747948i	$-0.731039\pi$
$733$	−35.9411	−1.32752	−0.663758	+	0.747948i	$0.731039\pi$
$734$	0	0
$735$	2.82843	0.104328
$736$	0	0
$737$	6.62742	0.244124
$738$	0	0
$739$	53.9411	1.98426	0.992128	−	0.125226i	$-0.0399657\pi$
$739$	53.9411	1.98426	0.992128	+	0.125226i	$0.0399657\pi$
$740$	0	0
$741$	3.31371	0.121732
$742$	0	0
$743$	40.9706	1.50306	0.751532	−	0.659697i	$-0.229315\pi$
$743$	40.9706	1.50306	0.751532	+	0.659697i	$0.229315\pi$
$744$	0	0
$745$	14.4853	0.530700
$746$	0	0
$747$	68.2843	2.49839
$748$	0	0
$749$	8.00000	0.292314
$750$	0	0
$751$	−20.6863	−0.754853	−0.377427	−	0.926039i	$-0.623191\pi$
$751$	−20.6863	−0.754853	−0.377427	+	0.926039i	$0.623191\pi$
$752$	0	0
$753$	25.3726	0.924628
$754$	0	0
$755$	22.1421	0.805835
$756$	0	0
$757$	8.82843	0.320875	0.160437	−	0.987046i	$-0.448710\pi$
$757$	8.82843	0.320875	0.160437	+	0.987046i	$0.448710\pi$
$758$	0	0
$759$	−13.2548	−0.481120
$760$	0	0
$761$	−49.1127	−1.78033	−0.890167	−	0.455634i	$-0.849412\pi$
$761$	−49.1127	−1.78033	−0.890167	+	0.455634i	$0.849412\pi$
$762$	0	0
$763$	−6.48528	−0.234783
$764$	0	0
$765$	−24.1421	−0.872861
$766$	0	0
$767$	−1.17157	−0.0423030
$768$	0	0
$769$	30.4853	1.09933	0.549664	−	0.835386i	$-0.314756\pi$
$769$	30.4853	1.09933	0.549664	+	0.835386i	$0.314756\pi$
$770$	0	0
$771$	8.97056	0.323067
$772$	0	0
$773$	−24.6274	−0.885787	−0.442893	−	0.896574i	$-0.646048\pi$
$773$	−24.6274	−0.885787	−0.442893	+	0.896574i	$0.646048\pi$
$774$	0	0
$775$	9.65685	0.346884
$776$	0	0
$777$	−21.6569	−0.776935
$778$	0	0
$779$	7.59798	0.272226
$780$	0	0
$781$	20.6863	0.740214
$782$	0	0
$783$	33.9411	1.21296
$784$	0	0
$785$	−2.00000	−0.0713831
$786$	0	0
$787$	−4.68629	−0.167048	−0.0835241	−	0.996506i	$-0.526618\pi$
$787$	−4.68629	−0.167048	−0.0835241	+	0.996506i	$0.526618\pi$
$788$	0	0
$789$	−83.3137	−2.96605
$790$	0	0
$791$	−10.0000	−0.355559
$792$	0	0
$793$	−0.343146	−0.0121855
$794$	0	0
$795$	8.97056	0.318153
$796$	0	0
$797$	38.0000	1.34603	0.673015	−	0.739629i	$-0.264999\pi$
$797$	38.0000	1.34603	0.673015	+	0.739629i	$0.264999\pi$
$798$	0	0
$799$	54.6274	1.93258
$800$	0	0
$801$	55.8579	1.97364
$802$	0	0
$803$	−46.6274	−1.64545
$804$	0	0
$805$	−1.17157	−0.0412925
$806$	0	0
$807$	44.2843	1.55888
$808$	0	0
$809$	−28.6274	−1.00649	−0.503243	−	0.864145i	$-0.667860\pi$
$809$	−28.6274	−1.00649	−0.503243	+	0.864145i	$0.667860\pi$
$810$	0	0
$811$	−22.8284	−0.801614	−0.400807	−	0.916162i	$-0.631270\pi$
$811$	−22.8284	−0.801614	−0.400807	+	0.916162i	$0.631270\pi$
$812$	0	0
$813$	−14.0589	−0.493066
$814$	0	0
$815$	9.65685	0.338265
$816$	0	0
$817$	13.2548	0.463728
$818$	0	0
$819$	−5.00000	−0.174714
$820$	0	0
$821$	33.7990	1.17959	0.589796	−	0.807552i	$-0.299208\pi$
$821$	33.7990	1.17959	0.589796	+	0.807552i	$0.299208\pi$
$822$	0	0
$823$	43.1127	1.50281	0.751407	−	0.659839i	$-0.229375\pi$
$823$	43.1127	1.50281	0.751407	+	0.659839i	$0.229375\pi$
$824$	0	0
$825$	−11.3137	−0.393893
$826$	0	0
$827$	−1.65685	−0.0576145	−0.0288072	−	0.999585i	$-0.509171\pi$
$827$	−1.65685	−0.0576145	−0.0288072	+	0.999585i	$0.509171\pi$
$828$	0	0
$829$	−14.9706	−0.519949	−0.259975	−	0.965615i	$-0.583714\pi$
$829$	−14.9706	−0.519949	−0.259975	+	0.965615i	$0.583714\pi$
$830$	0	0
$831$	34.3431	1.19135
$832$	0	0
$833$	−4.82843	−0.167295
$834$	0	0
$835$	−8.97056	−0.310439
$836$	0	0
$837$	54.6274	1.88820
$838$	0	0
$839$	32.2843	1.11458	0.557288	−	0.830319i	$-0.311842\pi$
$839$	32.2843	1.11458	0.557288	+	0.830319i	$0.311842\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	0	0
$843$	−19.7157	−0.679046
$844$	0	0
$845$	1.00000	0.0344010
$846$	0	0
$847$	−5.00000	−0.171802
$848$	0	0
$849$	75.8823	2.60427
$850$	0	0
$851$	8.97056	0.307507
$852$	0	0
$853$	17.3137	0.592810	0.296405	−	0.955062i	$-0.404212\pi$
$853$	17.3137	0.592810	0.296405	+	0.955062i	$0.404212\pi$
$854$	0	0
$855$	5.85786	0.200335
$856$	0	0
$857$	−25.5147	−0.871566	−0.435783	−	0.900052i	$-0.643529\pi$
$857$	−25.5147	−0.871566	−0.435783	+	0.900052i	$0.643529\pi$
$858$	0	0
$859$	47.5980	1.62402	0.812011	−	0.583642i	$-0.198373\pi$
$859$	47.5980	1.62402	0.812011	+	0.583642i	$0.198373\pi$
$860$	0	0
$861$	−18.3431	−0.625133
$862$	0	0
$863$	37.2548	1.26817	0.634085	−	0.773264i	$-0.281377\pi$
$863$	37.2548	1.26817	0.634085	+	0.773264i	$0.281377\pi$
$864$	0	0
$865$	−10.0000	−0.340010
$866$	0	0
$867$	17.8579	0.606485
$868$	0	0
$869$	45.2548	1.53517
$870$	0	0
$871$	−1.65685	−0.0561404
$872$	0	0
$873$	86.5685	2.92990
$874$	0	0
$875$	−1.00000	−0.0338062
$876$	0	0
$877$	−45.5980	−1.53973	−0.769867	−	0.638204i	$-0.779678\pi$
$877$	−45.5980	−1.53973	−0.769867	+	0.638204i	$0.779678\pi$
$878$	0	0
$879$	−28.2843	−0.954005
$880$	0	0
$881$	−18.6863	−0.629557	−0.314779	−	0.949165i	$-0.601930\pi$
$881$	−18.6863	−0.629557	−0.314779	+	0.949165i	$0.601930\pi$
$882$	0	0
$883$	13.6569	0.459590	0.229795	−	0.973239i	$-0.426194\pi$
$883$	13.6569	0.459590	0.229795	+	0.973239i	$0.426194\pi$
$884$	0	0
$885$	−3.31371	−0.111389
$886$	0	0
$887$	32.9706	1.10704	0.553522	−	0.832835i	$-0.313284\pi$
$887$	32.9706	1.10704	0.553522	+	0.832835i	$0.313284\pi$
$888$	0	0
$889$	4.48528	0.150432
$890$	0	0
$891$	−4.00000	−0.134005
$892$	0	0
$893$	−13.2548	−0.443556
$894$	0	0
$895$	−12.0000	−0.401116
$896$	0	0
$897$	3.31371	0.110642
$898$	0	0
$899$	57.9411	1.93244
$900$	0	0
$901$	−15.3137	−0.510174
$902$	0	0
$903$	−32.0000	−1.06489
$904$	0	0
$905$	−22.9706	−0.763567
$906$	0	0
$907$	36.2843	1.20480	0.602400	−	0.798195i	$-0.294211\pi$
$907$	36.2843	1.20480	0.602400	+	0.798195i	$0.294211\pi$
$908$	0	0
$909$	−18.2843	−0.606451
$910$	0	0
$911$	33.9411	1.12452	0.562260	−	0.826961i	$-0.309932\pi$
$911$	33.9411	1.12452	0.562260	+	0.826961i	$0.309932\pi$
$912$	0	0
$913$	−54.6274	−1.80790
$914$	0	0
$915$	−0.970563	−0.0320858
$916$	0	0
$917$	16.0000	0.528367
$918$	0	0
$919$	−13.6569	−0.450498	−0.225249	−	0.974301i	$-0.572320\pi$
$919$	−13.6569	−0.450498	−0.225249	+	0.974301i	$0.572320\pi$
$920$	0	0
$921$	−77.2548	−2.54563
$922$	0	0
$923$	−5.17157	−0.170224
$924$	0	0
$925$	7.65685	0.251756
$926$	0	0
$927$	0	0
$928$	0	0
$929$	−41.1127	−1.34886	−0.674432	−	0.738337i	$-0.735611\pi$
$929$	−41.1127	−1.34886	−0.674432	+	0.738337i	$0.735611\pi$
$930$	0	0
$931$	1.17157	0.0383968
$932$	0	0
$933$	−70.6274	−2.31224
$934$	0	0
$935$	19.3137	0.631626
$936$	0	0
$937$	16.8284	0.549761	0.274880	−	0.961478i	$-0.411362\pi$
$937$	16.8284	0.549761	0.274880	+	0.961478i	$0.411362\pi$
$938$	0	0
$939$	−0.402020	−0.0131194
$940$	0	0
$941$	−32.6274	−1.06362	−0.531812	−	0.846863i	$-0.678489\pi$
$941$	−32.6274	−1.06362	−0.531812	+	0.846863i	$0.678489\pi$
$942$	0	0
$943$	7.59798	0.247424
$944$	0	0
$945$	−5.65685	−0.184017
$946$	0	0
$947$	−22.3431	−0.726055	−0.363027	−	0.931778i	$-0.618257\pi$
$947$	−22.3431	−0.726055	−0.363027	+	0.931778i	$0.618257\pi$
$948$	0	0
$949$	11.6569	0.378398
$950$	0	0
$951$	−3.71573	−0.120491
$952$	0	0
$953$	−26.2843	−0.851431	−0.425716	−	0.904857i	$-0.639978\pi$
$953$	−26.2843	−0.851431	−0.425716	+	0.904857i	$0.639978\pi$
$954$	0	0
$955$	−21.6569	−0.700799
$956$	0	0
$957$	−67.8823	−2.19432
$958$	0	0
$959$	10.0000	0.322917
$960$	0	0
$961$	62.2548	2.00822
$962$	0	0
$963$	−40.0000	−1.28898
$964$	0	0
$965$	6.00000	0.193147
$966$	0	0
$967$	−24.0000	−0.771788	−0.385894	−	0.922543i	$-0.626107\pi$
$967$	−24.0000	−0.771788	−0.385894	+	0.922543i	$0.626107\pi$
$968$	0	0
$969$	−16.0000	−0.513994
$970$	0	0
$971$	−20.2843	−0.650953	−0.325477	−	0.945550i	$-0.605525\pi$
$971$	−20.2843	−0.650953	−0.325477	+	0.945550i	$0.605525\pi$
$972$	0	0
$973$	−19.3137	−0.619169
$974$	0	0
$975$	2.82843	0.0905822
$976$	0	0
$977$	10.6863	0.341885	0.170942	−	0.985281i	$-0.445319\pi$
$977$	10.6863	0.341885	0.170942	+	0.985281i	$0.445319\pi$
$978$	0	0
$979$	−44.6863	−1.42818
$980$	0	0
$981$	32.4264	1.03530
$982$	0	0
$983$	8.00000	0.255160	0.127580	−	0.991828i	$-0.459279\pi$
$983$	8.00000	0.255160	0.127580	+	0.991828i	$0.459279\pi$
$984$	0	0
$985$	−0.343146	−0.0109335
$986$	0	0
$987$	32.0000	1.01857
$988$	0	0
$989$	13.2548	0.421479
$990$	0	0
$991$	−20.6863	−0.657122	−0.328561	−	0.944483i	$-0.606564\pi$
$991$	−20.6863	−0.657122	−0.328561	+	0.944483i	$0.606564\pi$
$992$	0	0
$993$	11.3137	0.359030
$994$	0	0
$995$	5.65685	0.179334
$996$	0	0
$997$	38.9706	1.23421	0.617105	−	0.786881i	$-0.288305\pi$
$997$	38.9706	1.23421	0.617105	+	0.786881i	$0.288305\pi$
$998$	0	0
$999$	43.3137	1.37039

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7280.2.a.bc.1.2		2
4.3	odd	2		910.2.a.m.1.1	✓	2
12.11	even	2		8190.2.a.ck.1.2		2
20.19	odd	2		4550.2.a.bn.1.2		2
28.27	even	2		6370.2.a.bd.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
910.2.a.m.1.1	✓	2	4.3	odd	2
4550.2.a.bn.1.2		2	20.19	odd	2
6370.2.a.bd.1.2		2	28.27	even	2
7280.2.a.bc.1.2		2	1.1	even	1	trivial
8190.2.a.ck.1.2		2	12.11	even	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:	\( N \)	\(=\)	\( 7280 = 2^{4} \cdot 5 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7280.a (trivial)

\(f(q)\)	\(=\)	\(q+2.82843 q^{3} +1.00000 q^{5} -1.00000 q^{7} +5.00000 q^{9} +O(q^{10})\)	\(q+2.82843 q^{3} +1.00000 q^{5} -1.00000 q^{7} +5.00000 q^{9} -4.00000 q^{11} +1.00000 q^{13} +2.82843 q^{15} -4.82843 q^{17} +1.17157 q^{19} -2.82843 q^{21} +1.17157 q^{23} +1.00000 q^{25} +5.65685 q^{27} +6.00000 q^{29} +9.65685 q^{31} -11.3137 q^{33} -1.00000 q^{35} +7.65685 q^{37} +2.82843 q^{39} +6.48528 q^{41} +11.3137 q^{43} +5.00000 q^{45} -11.3137 q^{47} +1.00000 q^{49} -13.6569 q^{51} +3.17157 q^{53} -4.00000 q^{55} +3.31371 q^{57} -1.17157 q^{59} -0.343146 q^{61} -5.00000 q^{63} +1.00000 q^{65} -1.65685 q^{67} +3.31371 q^{69} -5.17157 q^{71} +11.6569 q^{73} +2.82843 q^{75} +4.00000 q^{77} -11.3137 q^{79} +1.00000 q^{81} +13.6569 q^{83} -4.82843 q^{85} +16.9706 q^{87} +11.1716 q^{89} -1.00000 q^{91} +27.3137 q^{93} +1.17157 q^{95} +17.3137 q^{97} -20.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{5} - 2 q^{7} + 10 q^{9}+O(q^{10}) \) 2 * q + 2 * q^5 - 2 * q^7 + 10 * q^9	\( 2 q + 2 q^{5} - 2 q^{7} + 10 q^{9} - 8 q^{11} + 2 q^{13} - 4 q^{17} + 8 q^{19} + 8 q^{23} + 2 q^{25} + 12 q^{29} + 8 q^{31} - 2 q^{35} + 4 q^{37} - 4 q^{41} + 10 q^{45} + 2 q^{49} - 16 q^{51} + 12 q^{53} - 8 q^{55} - 16 q^{57} - 8 q^{59} - 12 q^{61} - 10 q^{63} + 2 q^{65} + 8 q^{67} - 16 q^{69} - 16 q^{71} + 12 q^{73} + 8 q^{77} + 2 q^{81} + 16 q^{83} - 4 q^{85} + 28 q^{89} - 2 q^{91} + 32 q^{93} + 8 q^{95} + 12 q^{97} - 40 q^{99}+O(q^{100}) \) 2 * q + 2 * q^5 - 2 * q^7 + 10 * q^9 - 8 * q^11 + 2 * q^13 - 4 * q^17 + 8 * q^19 + 8 * q^23 + 2 * q^25 + 12 * q^29 + 8 * q^31 - 2 * q^35 + 4 * q^37 - 4 * q^41 + 10 * q^45 + 2 * q^49 - 16 * q^51 + 12 * q^53 - 8 * q^55 - 16 * q^57 - 8 * q^59 - 12 * q^61 - 10 * q^63 + 2 * q^65 + 8 * q^67 - 16 * q^69 - 16 * q^71 + 12 * q^73 + 8 * q^77 + 2 * q^81 + 16 * q^83 - 4 * q^85 + 28 * q^89 - 2 * q^91 + 32 * q^93 + 8 * q^95 + 12 * q^97 - 40 * q^99

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