LMFDB - Embedded newform 8085.2.a.w.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8085,2,Mod(1,8085)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8085, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("8085.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8085 = 3 \cdot 5 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8085.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:	$64.5590500342$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1155)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	8085.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} +1.00000 q^{3} -1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -3.00000 q^{8} +1.00000 q^{9} +O(q^{10})$

\(q+1.00000 q^{2} +1.00000 q^{3} -1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -3.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{11} -1.00000 q^{12} +2.00000 q^{13} +1.00000 q^{15} -1.00000 q^{16} -6.00000 q^{17} +1.00000 q^{18} -4.00000 q^{19} -1.00000 q^{20} -1.00000 q^{22} -4.00000 q^{23} -3.00000 q^{24} +1.00000 q^{25} +2.00000 q^{26} +1.00000 q^{27} +10.0000 q^{29} +1.00000 q^{30} +4.00000 q^{31} +5.00000 q^{32} -1.00000 q^{33} -6.00000 q^{34} -1.00000 q^{36} -2.00000 q^{37} -4.00000 q^{38} +2.00000 q^{39} -3.00000 q^{40} -10.0000 q^{41} +12.0000 q^{43} +1.00000 q^{44} +1.00000 q^{45} -4.00000 q^{46} -1.00000 q^{48} +1.00000 q^{50} -6.00000 q^{51} -2.00000 q^{52} +10.0000 q^{53} +1.00000 q^{54} -1.00000 q^{55} -4.00000 q^{57} +10.0000 q^{58} +12.0000 q^{59} -1.00000 q^{60} +2.00000 q^{61} +4.00000 q^{62} +7.00000 q^{64} +2.00000 q^{65} -1.00000 q^{66} +4.00000 q^{67} +6.00000 q^{68} -4.00000 q^{69} +8.00000 q^{71} -3.00000 q^{72} +14.0000 q^{73} -2.00000 q^{74} +1.00000 q^{75} +4.00000 q^{76} +2.00000 q^{78} +4.00000 q^{79} -1.00000 q^{80} +1.00000 q^{81} -10.0000 q^{82} -8.00000 q^{83} -6.00000 q^{85} +12.0000 q^{86} +10.0000 q^{87} +3.00000 q^{88} -6.00000 q^{89} +1.00000 q^{90} +4.00000 q^{92} +4.00000 q^{93} -4.00000 q^{95} +5.00000 q^{96} +10.0000 q^{97} -1.00000 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107	0.353553	−	0.935414i	$-0.384973\pi$
$2$	1.00000	0.707107	0.353553	+	0.935414i	$0.384973\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.00000	−0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.00000	0.408248
$7$	0	0
$7$	0	0
$8$	−3.00000	−1.06066
$9$	1.00000	0.333333
$10$	1.00000	0.316228
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−1.00000	−0.288675
$13$	2.00000	0.554700	0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000	0.554700	0.277350	+	0.960769i	$0.410544\pi$
$14$	0	0
$15$	1.00000	0.258199
$16$	−1.00000	−0.250000
$17$	−6.00000	−1.45521	−0.727607	−	0.685994i	$-0.759367\pi$
$17$	−6.00000	−1.45521	−0.727607	+	0.685994i	$0.759367\pi$
$18$	1.00000	0.235702
$19$	−4.00000	−0.917663	−0.458831	−	0.888523i	$-0.651732\pi$
$19$	−4.00000	−0.917663	−0.458831	+	0.888523i	$0.651732\pi$
$20$	−1.00000	−0.223607
$21$	0	0
$22$	−1.00000	−0.213201
$23$	−4.00000	−0.834058	−0.417029	−	0.908893i	$-0.636929\pi$
$23$	−4.00000	−0.834058	−0.417029	+	0.908893i	$0.636929\pi$
$24$	−3.00000	−0.612372
$25$	1.00000	0.200000
$26$	2.00000	0.392232
$27$	1.00000	0.192450
$28$	0	0
$29$	10.0000	1.85695	0.928477	−	0.371391i	$-0.121119\pi$
$29$	10.0000	1.85695	0.928477	+	0.371391i	$0.121119\pi$
$30$	1.00000	0.182574
$31$	4.00000	0.718421	0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000	0.718421	0.359211	+	0.933257i	$0.383046\pi$
$32$	5.00000	0.883883
$33$	−1.00000	−0.174078
$34$	−6.00000	−1.02899
$35$	0	0
$36$	−1.00000	−0.166667
$37$	−2.00000	−0.328798	−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000	−0.328798	−0.164399	+	0.986394i	$0.552568\pi$
$38$	−4.00000	−0.648886
$39$	2.00000	0.320256
$40$	−3.00000	−0.474342
$41$	−10.0000	−1.56174	−0.780869	−	0.624695i	$-0.785223\pi$
$41$	−10.0000	−1.56174	−0.780869	+	0.624695i	$0.785223\pi$
$42$	0	0
$43$	12.0000	1.82998	0.914991	−	0.403473i	$-0.132197\pi$
$43$	12.0000	1.82998	0.914991	+	0.403473i	$0.132197\pi$
$44$	1.00000	0.150756
$45$	1.00000	0.149071
$46$	−4.00000	−0.589768
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	−1.00000	−0.144338
$49$	0	0
$50$	1.00000	0.141421
$51$	−6.00000	−0.840168
$52$	−2.00000	−0.277350
$53$	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
$55$	−1.00000	−0.134840
$56$	0	0
$57$	−4.00000	−0.529813
$58$	10.0000	1.31306
$59$	12.0000	1.56227	0.781133	−	0.624364i	$-0.214642\pi$
$59$	12.0000	1.56227	0.781133	+	0.624364i	$0.214642\pi$
$60$	−1.00000	−0.129099
$61$	2.00000	0.256074	0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000	0.256074	0.128037	+	0.991769i	$0.459132\pi$
$62$	4.00000	0.508001
$63$	0	0
$64$	7.00000	0.875000
$65$	2.00000	0.248069
$66$	−1.00000	−0.123091
$67$	4.00000	0.488678	0.244339	−	0.969690i	$-0.421429\pi$
$67$	4.00000	0.488678	0.244339	+	0.969690i	$0.421429\pi$
$68$	6.00000	0.727607
$69$	−4.00000	−0.481543
$70$	0	0
$71$	8.00000	0.949425	0.474713	−	0.880141i	$-0.342552\pi$
$71$	8.00000	0.949425	0.474713	+	0.880141i	$0.342552\pi$
$72$	−3.00000	−0.353553
$73$	14.0000	1.63858	0.819288	−	0.573382i	$-0.194369\pi$
$73$	14.0000	1.63858	0.819288	+	0.573382i	$0.194369\pi$
$74$	−2.00000	−0.232495
$75$	1.00000	0.115470
$76$	4.00000	0.458831
$77$	0	0
$78$	2.00000	0.226455
$79$	4.00000	0.450035	0.225018	−	0.974355i	$-0.427756\pi$
$79$	4.00000	0.450035	0.225018	+	0.974355i	$0.427756\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	−10.0000	−1.10432
$83$	−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
$85$	−6.00000	−0.650791
$86$	12.0000	1.29399
$87$	10.0000	1.07211
$88$	3.00000	0.319801
$89$	−6.00000	−0.635999	−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000	−0.635999	−0.317999	+	0.948091i	$0.603011\pi$
$90$	1.00000	0.105409
$91$	0	0
$92$	4.00000	0.417029
$93$	4.00000	0.414781
$94$	0	0
$95$	−4.00000	−0.410391
$96$	5.00000	0.510310
$97$	10.0000	1.01535	0.507673	−	0.861550i	$-0.330506\pi$
$97$	10.0000	1.01535	0.507673	+	0.861550i	$0.330506\pi$
$98$	0	0
$99$	−1.00000	−0.100504
$100$	−1.00000	−0.100000
$101$	2.00000	0.199007	0.0995037	−	0.995037i	$-0.468274\pi$
$101$	2.00000	0.199007	0.0995037	+	0.995037i	$0.468274\pi$
$102$	−6.00000	−0.594089
$103$	−8.00000	−0.788263	−0.394132	−	0.919054i	$-0.628955\pi$
$103$	−8.00000	−0.788263	−0.394132	+	0.919054i	$0.628955\pi$
$104$	−6.00000	−0.588348
$105$	0	0
$106$	10.0000	0.971286
$107$	4.00000	0.386695	0.193347	−	0.981130i	$-0.438066\pi$
$107$	4.00000	0.386695	0.193347	+	0.981130i	$0.438066\pi$
$108$	−1.00000	−0.0962250
$109$	14.0000	1.34096	0.670478	−	0.741929i	$-0.266089\pi$
$109$	14.0000	1.34096	0.670478	+	0.741929i	$0.266089\pi$
$110$	−1.00000	−0.0953463
$111$	−2.00000	−0.189832
$112$	0	0
$113$	−18.0000	−1.69330	−0.846649	−	0.532152i	$-0.821383\pi$
$113$	−18.0000	−1.69330	−0.846649	+	0.532152i	$0.821383\pi$
$114$	−4.00000	−0.374634
$115$	−4.00000	−0.373002
$116$	−10.0000	−0.928477
$117$	2.00000	0.184900
$118$	12.0000	1.10469
$119$	0	0
$120$	−3.00000	−0.273861
$121$	1.00000	0.0909091
$122$	2.00000	0.181071
$123$	−10.0000	−0.901670
$124$	−4.00000	−0.359211
$125$	1.00000	0.0894427
$126$	0	0
$127$	8.00000	0.709885	0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000	0.709885	0.354943	+	0.934888i	$0.384500\pi$
$128$	−3.00000	−0.265165
$129$	12.0000	1.05654
$130$	2.00000	0.175412
$131$	4.00000	0.349482	0.174741	−	0.984614i	$-0.444091\pi$
$131$	4.00000	0.349482	0.174741	+	0.984614i	$0.444091\pi$
$132$	1.00000	0.0870388
$133$	0	0
$134$	4.00000	0.345547
$135$	1.00000	0.0860663
$136$	18.0000	1.54349
$137$	−10.0000	−0.854358	−0.427179	−	0.904167i	$-0.640493\pi$
$137$	−10.0000	−0.854358	−0.427179	+	0.904167i	$0.640493\pi$
$138$	−4.00000	−0.340503
$139$	4.00000	0.339276	0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000	0.339276	0.169638	+	0.985506i	$0.445740\pi$
$140$	0	0
$141$	0	0
$142$	8.00000	0.671345
$143$	−2.00000	−0.167248
$144$	−1.00000	−0.0833333
$145$	10.0000	0.830455
$146$	14.0000	1.15865
$147$	0	0
$148$	2.00000	0.164399
$149$	18.0000	1.47462	0.737309	−	0.675556i	$-0.236096\pi$
$149$	18.0000	1.47462	0.737309	+	0.675556i	$0.236096\pi$
$150$	1.00000	0.0816497
$151$	−4.00000	−0.325515	−0.162758	−	0.986666i	$-0.552039\pi$
$151$	−4.00000	−0.325515	−0.162758	+	0.986666i	$0.552039\pi$
$152$	12.0000	0.973329
$153$	−6.00000	−0.485071
$154$	0	0
$155$	4.00000	0.321288
$156$	−2.00000	−0.160128
$157$	14.0000	1.11732	0.558661	−	0.829396i	$-0.311315\pi$
$157$	14.0000	1.11732	0.558661	+	0.829396i	$0.311315\pi$
$158$	4.00000	0.318223
$159$	10.0000	0.793052
$160$	5.00000	0.395285
$161$	0	0
$162$	1.00000	0.0785674
$163$	−20.0000	−1.56652	−0.783260	−	0.621694i	$-0.786445\pi$
$163$	−20.0000	−1.56652	−0.783260	+	0.621694i	$0.786445\pi$
$164$	10.0000	0.780869
$165$	−1.00000	−0.0778499
$166$	−8.00000	−0.620920
$167$	12.0000	0.928588	0.464294	−	0.885681i	$-0.346308\pi$
$167$	12.0000	0.928588	0.464294	+	0.885681i	$0.346308\pi$
$168$	0	0
$169$	−9.00000	−0.692308
$170$	−6.00000	−0.460179
$171$	−4.00000	−0.305888
$172$	−12.0000	−0.914991
$173$	−26.0000	−1.97674	−0.988372	−	0.152057i	$-0.951410\pi$
$173$	−26.0000	−1.97674	−0.988372	+	0.152057i	$0.951410\pi$
$174$	10.0000	0.758098
$175$	0	0
$176$	1.00000	0.0753778
$177$	12.0000	0.901975
$178$	−6.00000	−0.449719
$179$	−4.00000	−0.298974	−0.149487	−	0.988764i	$-0.547762\pi$
$179$	−4.00000	−0.298974	−0.149487	+	0.988764i	$0.547762\pi$
$180$	−1.00000	−0.0745356
$181$	10.0000	0.743294	0.371647	−	0.928374i	$-0.378793\pi$
$181$	10.0000	0.743294	0.371647	+	0.928374i	$0.378793\pi$
$182$	0	0
$183$	2.00000	0.147844
$184$	12.0000	0.884652
$185$	−2.00000	−0.147043
$186$	4.00000	0.293294
$187$	6.00000	0.438763
$188$	0	0
$189$	0	0
$190$	−4.00000	−0.290191
$191$	16.0000	1.15772	0.578860	−	0.815427i	$-0.303498\pi$
$191$	16.0000	1.15772	0.578860	+	0.815427i	$0.303498\pi$
$192$	7.00000	0.505181
$193$	14.0000	1.00774	0.503871	−	0.863779i	$-0.331909\pi$
$193$	14.0000	1.00774	0.503871	+	0.863779i	$0.331909\pi$
$194$	10.0000	0.717958
$195$	2.00000	0.143223
$196$	0	0
$197$	26.0000	1.85242	0.926212	−	0.377004i	$-0.123046\pi$
$197$	26.0000	1.85242	0.926212	+	0.377004i	$0.123046\pi$
$198$	−1.00000	−0.0710669
$199$	−4.00000	−0.283552	−0.141776	−	0.989899i	$-0.545281\pi$
$199$	−4.00000	−0.283552	−0.141776	+	0.989899i	$0.545281\pi$
$200$	−3.00000	−0.212132
$201$	4.00000	0.282138
$202$	2.00000	0.140720
$203$	0	0
$204$	6.00000	0.420084
$205$	−10.0000	−0.698430
$206$	−8.00000	−0.557386
$207$	−4.00000	−0.278019
$208$	−2.00000	−0.138675
$209$	4.00000	0.276686
$210$	0	0
$211$	−16.0000	−1.10149	−0.550743	−	0.834675i	$-0.685655\pi$
$211$	−16.0000	−1.10149	−0.550743	+	0.834675i	$0.685655\pi$
$212$	−10.0000	−0.686803
$213$	8.00000	0.548151
$214$	4.00000	0.273434
$215$	12.0000	0.818393
$216$	−3.00000	−0.204124
$217$	0	0
$218$	14.0000	0.948200
$219$	14.0000	0.946032
$220$	1.00000	0.0674200
$221$	−12.0000	−0.807207
$222$	−2.00000	−0.134231
$223$	24.0000	1.60716	0.803579	−	0.595198i	$-0.202926\pi$
$223$	24.0000	1.60716	0.803579	+	0.595198i	$0.202926\pi$
$224$	0	0
$225$	1.00000	0.0666667
$226$	−18.0000	−1.19734
$227$	−8.00000	−0.530979	−0.265489	−	0.964114i	$-0.585534\pi$
$227$	−8.00000	−0.530979	−0.265489	+	0.964114i	$0.585534\pi$
$228$	4.00000	0.264906
$229$	−14.0000	−0.925146	−0.462573	−	0.886581i	$-0.653074\pi$
$229$	−14.0000	−0.925146	−0.462573	+	0.886581i	$0.653074\pi$
$230$	−4.00000	−0.263752
$231$	0	0
$232$	−30.0000	−1.96960
$233$	−26.0000	−1.70332	−0.851658	−	0.524097i	$-0.824403\pi$
$233$	−26.0000	−1.70332	−0.851658	+	0.524097i	$0.824403\pi$
$234$	2.00000	0.130744
$235$	0	0
$236$	−12.0000	−0.781133
$237$	4.00000	0.259828
$238$	0	0
$239$	24.0000	1.55243	0.776215	−	0.630468i	$-0.217137\pi$
$239$	24.0000	1.55243	0.776215	+	0.630468i	$0.217137\pi$
$240$	−1.00000	−0.0645497
$241$	−2.00000	−0.128831	−0.0644157	−	0.997923i	$-0.520518\pi$
$241$	−2.00000	−0.128831	−0.0644157	+	0.997923i	$0.520518\pi$
$242$	1.00000	0.0642824
$243$	1.00000	0.0641500
$244$	−2.00000	−0.128037
$245$	0	0
$246$	−10.0000	−0.637577
$247$	−8.00000	−0.509028
$248$	−12.0000	−0.762001
$249$	−8.00000	−0.506979
$250$	1.00000	0.0632456
$251$	−12.0000	−0.757433	−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000	−0.757433	−0.378717	+	0.925513i	$0.623635\pi$
$252$	0	0
$253$	4.00000	0.251478
$254$	8.00000	0.501965
$255$	−6.00000	−0.375735
$256$	−17.0000	−1.06250
$257$	2.00000	0.124757	0.0623783	−	0.998053i	$-0.480131\pi$
$257$	2.00000	0.124757	0.0623783	+	0.998053i	$0.480131\pi$
$258$	12.0000	0.747087
$259$	0	0
$260$	−2.00000	−0.124035
$261$	10.0000	0.618984
$262$	4.00000	0.247121
$263$	−24.0000	−1.47990	−0.739952	−	0.672660i	$-0.765152\pi$
$263$	−24.0000	−1.47990	−0.739952	+	0.672660i	$0.765152\pi$
$264$	3.00000	0.184637
$265$	10.0000	0.614295
$266$	0	0
$267$	−6.00000	−0.367194
$268$	−4.00000	−0.244339
$269$	−10.0000	−0.609711	−0.304855	−	0.952399i	$-0.598608\pi$
$269$	−10.0000	−0.609711	−0.304855	+	0.952399i	$0.598608\pi$
$270$	1.00000	0.0608581
$271$	8.00000	0.485965	0.242983	−	0.970031i	$-0.421874\pi$
$271$	8.00000	0.485965	0.242983	+	0.970031i	$0.421874\pi$
$272$	6.00000	0.363803
$273$	0	0
$274$	−10.0000	−0.604122
$275$	−1.00000	−0.0603023
$276$	4.00000	0.240772
$277$	2.00000	0.120168	0.0600842	−	0.998193i	$-0.480863\pi$
$277$	2.00000	0.120168	0.0600842	+	0.998193i	$0.480863\pi$
$278$	4.00000	0.239904
$279$	4.00000	0.239474
$280$	0	0
$281$	30.0000	1.78965	0.894825	−	0.446417i	$-0.147300\pi$
$281$	30.0000	1.78965	0.894825	+	0.446417i	$0.147300\pi$
$282$	0	0
$283$	28.0000	1.66443	0.832214	−	0.554455i	$-0.187073\pi$
$283$	28.0000	1.66443	0.832214	+	0.554455i	$0.187073\pi$
$284$	−8.00000	−0.474713
$285$	−4.00000	−0.236940
$286$	−2.00000	−0.118262
$287$	0	0
$288$	5.00000	0.294628
$289$	19.0000	1.11765
$290$	10.0000	0.587220
$291$	10.0000	0.586210
$292$	−14.0000	−0.819288
$293$	−18.0000	−1.05157	−0.525786	−	0.850617i	$-0.676229\pi$
$293$	−18.0000	−1.05157	−0.525786	+	0.850617i	$0.676229\pi$
$294$	0	0
$295$	12.0000	0.698667
$296$	6.00000	0.348743
$297$	−1.00000	−0.0580259
$298$	18.0000	1.04271
$299$	−8.00000	−0.462652
$300$	−1.00000	−0.0577350
$301$	0	0
$302$	−4.00000	−0.230174
$303$	2.00000	0.114897
$304$	4.00000	0.229416
$305$	2.00000	0.114520
$306$	−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	$0.611253\pi$
$308$	0	0
$309$	−8.00000	−0.455104
$310$	4.00000	0.227185
$311$	−8.00000	−0.453638	−0.226819	−	0.973937i	$-0.572833\pi$
$311$	−8.00000	−0.453638	−0.226819	+	0.973937i	$0.572833\pi$
$312$	−6.00000	−0.339683
$313$	−30.0000	−1.69570	−0.847850	−	0.530236i	$-0.822103\pi$
$313$	−30.0000	−1.69570	−0.847850	+	0.530236i	$0.822103\pi$
$314$	14.0000	0.790066
$315$	0	0
$316$	−4.00000	−0.225018
$317$	18.0000	1.01098	0.505490	−	0.862832i	$-0.331312\pi$
$317$	18.0000	1.01098	0.505490	+	0.862832i	$0.331312\pi$
$318$	10.0000	0.560772
$319$	−10.0000	−0.559893
$320$	7.00000	0.391312
$321$	4.00000	0.223258
$322$	0	0
$323$	24.0000	1.33540
$324$	−1.00000	−0.0555556
$325$	2.00000	0.110940
$326$	−20.0000	−1.10770
$327$	14.0000	0.774202
$328$	30.0000	1.65647
$329$	0	0
$330$	−1.00000	−0.0550482
$331$	−12.0000	−0.659580	−0.329790	−	0.944054i	$-0.606978\pi$
$331$	−12.0000	−0.659580	−0.329790	+	0.944054i	$0.606978\pi$
$332$	8.00000	0.439057
$333$	−2.00000	−0.109599
$334$	12.0000	0.656611
$335$	4.00000	0.218543
$336$	0	0
$337$	22.0000	1.19842	0.599208	−	0.800593i	$-0.295482\pi$
$337$	22.0000	1.19842	0.599208	+	0.800593i	$0.295482\pi$
$338$	−9.00000	−0.489535
$339$	−18.0000	−0.977626
$340$	6.00000	0.325396
$341$	−4.00000	−0.216612
$342$	−4.00000	−0.216295
$343$	0	0
$344$	−36.0000	−1.94099
$345$	−4.00000	−0.215353
$346$	−26.0000	−1.39777
$347$	−28.0000	−1.50312	−0.751559	−	0.659665i	$-0.770698\pi$
$347$	−28.0000	−1.50312	−0.751559	+	0.659665i	$0.770698\pi$
$348$	−10.0000	−0.536056
$349$	−30.0000	−1.60586	−0.802932	−	0.596071i	$-0.796728\pi$
$349$	−30.0000	−1.60586	−0.802932	+	0.596071i	$0.796728\pi$
$350$	0	0
$351$	2.00000	0.106752
$352$	−5.00000	−0.266501
$353$	18.0000	0.958043	0.479022	−	0.877803i	$-0.340992\pi$
$353$	18.0000	0.958043	0.479022	+	0.877803i	$0.340992\pi$
$354$	12.0000	0.637793
$355$	8.00000	0.424596
$356$	6.00000	0.317999
$357$	0	0
$358$	−4.00000	−0.211407
$359$	24.0000	1.26667	0.633336	−	0.773877i	$-0.281685\pi$
$359$	24.0000	1.26667	0.633336	+	0.773877i	$0.281685\pi$
$360$	−3.00000	−0.158114
$361$	−3.00000	−0.157895
$362$	10.0000	0.525588
$363$	1.00000	0.0524864
$364$	0	0
$365$	14.0000	0.732793
$366$	2.00000	0.104542
$367$	8.00000	0.417597	0.208798	−	0.977959i	$-0.433045\pi$
$367$	8.00000	0.417597	0.208798	+	0.977959i	$0.433045\pi$
$368$	4.00000	0.208514
$369$	−10.0000	−0.520579
$370$	−2.00000	−0.103975
$371$	0	0
$372$	−4.00000	−0.207390
$373$	−6.00000	−0.310668	−0.155334	−	0.987862i	$-0.549645\pi$
$373$	−6.00000	−0.310668	−0.155334	+	0.987862i	$0.549645\pi$
$374$	6.00000	0.310253
$375$	1.00000	0.0516398
$376$	0	0
$377$	20.0000	1.03005
$378$	0	0
$379$	4.00000	0.205466	0.102733	−	0.994709i	$-0.467241\pi$
$379$	4.00000	0.205466	0.102733	+	0.994709i	$0.467241\pi$
$380$	4.00000	0.205196
$381$	8.00000	0.409852
$382$	16.0000	0.818631
$383$	32.0000	1.63512	0.817562	−	0.575841i	$-0.195325\pi$
$383$	32.0000	1.63512	0.817562	+	0.575841i	$0.195325\pi$
$384$	−3.00000	−0.153093
$385$	0	0
$386$	14.0000	0.712581
$387$	12.0000	0.609994
$388$	−10.0000	−0.507673
$389$	22.0000	1.11544	0.557722	−	0.830028i	$-0.311675\pi$
$389$	22.0000	1.11544	0.557722	+	0.830028i	$0.311675\pi$
$390$	2.00000	0.101274
$391$	24.0000	1.21373
$392$	0	0
$393$	4.00000	0.201773
$394$	26.0000	1.30986
$395$	4.00000	0.201262
$396$	1.00000	0.0502519
$397$	6.00000	0.301131	0.150566	−	0.988600i	$-0.451890\pi$
$397$	6.00000	0.301131	0.150566	+	0.988600i	$0.451890\pi$
$398$	−4.00000	−0.200502
$399$	0	0
$400$	−1.00000	−0.0500000
$401$	18.0000	0.898877	0.449439	−	0.893311i	$-0.351624\pi$
$401$	18.0000	0.898877	0.449439	+	0.893311i	$0.351624\pi$
$402$	4.00000	0.199502
$403$	8.00000	0.398508
$404$	−2.00000	−0.0995037
$405$	1.00000	0.0496904
$406$	0	0
$407$	2.00000	0.0991363
$408$	18.0000	0.891133
$409$	22.0000	1.08783	0.543915	−	0.839140i	$-0.316941\pi$
$409$	22.0000	1.08783	0.543915	+	0.839140i	$0.316941\pi$
$410$	−10.0000	−0.493865
$411$	−10.0000	−0.493264
$412$	8.00000	0.394132
$413$	0	0
$414$	−4.00000	−0.196589
$415$	−8.00000	−0.392705
$416$	10.0000	0.490290
$417$	4.00000	0.195881
$418$	4.00000	0.195646
$419$	−4.00000	−0.195413	−0.0977064	−	0.995215i	$-0.531151\pi$
$419$	−4.00000	−0.195413	−0.0977064	+	0.995215i	$0.531151\pi$
$420$	0	0
$421$	6.00000	0.292422	0.146211	−	0.989253i	$-0.453292\pi$
$421$	6.00000	0.292422	0.146211	+	0.989253i	$0.453292\pi$
$422$	−16.0000	−0.778868
$423$	0	0
$424$	−30.0000	−1.45693
$425$	−6.00000	−0.291043
$426$	8.00000	0.387601
$427$	0	0
$428$	−4.00000	−0.193347
$429$	−2.00000	−0.0965609
$430$	12.0000	0.578691
$431$	40.0000	1.92673	0.963366	−	0.268190i	$-0.0864254\pi$
$431$	40.0000	1.92673	0.963366	+	0.268190i	$0.0864254\pi$
$432$	−1.00000	−0.0481125
$433$	2.00000	0.0961139	0.0480569	−	0.998845i	$-0.484697\pi$
$433$	2.00000	0.0961139	0.0480569	+	0.998845i	$0.484697\pi$
$434$	0	0
$435$	10.0000	0.479463
$436$	−14.0000	−0.670478
$437$	16.0000	0.765384
$438$	14.0000	0.668946
$439$	8.00000	0.381819	0.190910	−	0.981608i	$-0.438856\pi$
$439$	8.00000	0.381819	0.190910	+	0.981608i	$0.438856\pi$
$440$	3.00000	0.143019
$441$	0	0
$442$	−12.0000	−0.570782
$443$	−8.00000	−0.380091	−0.190046	−	0.981775i	$-0.560864\pi$
$443$	−8.00000	−0.380091	−0.190046	+	0.981775i	$0.560864\pi$
$444$	2.00000	0.0949158
$445$	−6.00000	−0.284427
$446$	24.0000	1.13643
$447$	18.0000	0.851371
$448$	0	0
$449$	18.0000	0.849473	0.424736	−	0.905317i	$-0.360367\pi$
$449$	18.0000	0.849473	0.424736	+	0.905317i	$0.360367\pi$
$450$	1.00000	0.0471405
$451$	10.0000	0.470882
$452$	18.0000	0.846649
$453$	−4.00000	−0.187936
$454$	−8.00000	−0.375459
$455$	0	0
$456$	12.0000	0.561951
$457$	−18.0000	−0.842004	−0.421002	−	0.907060i	$-0.638322\pi$
$457$	−18.0000	−0.842004	−0.421002	+	0.907060i	$0.638322\pi$
$458$	−14.0000	−0.654177
$459$	−6.00000	−0.280056
$460$	4.00000	0.186501
$461$	−30.0000	−1.39724	−0.698620	−	0.715493i	$-0.746202\pi$
$461$	−30.0000	−1.39724	−0.698620	+	0.715493i	$0.746202\pi$
$462$	0	0
$463$	16.0000	0.743583	0.371792	−	0.928316i	$-0.378744\pi$
$463$	16.0000	0.743583	0.371792	+	0.928316i	$0.378744\pi$
$464$	−10.0000	−0.464238
$465$	4.00000	0.185496
$466$	−26.0000	−1.20443
$467$	4.00000	0.185098	0.0925490	−	0.995708i	$-0.470499\pi$
$467$	4.00000	0.185098	0.0925490	+	0.995708i	$0.470499\pi$
$468$	−2.00000	−0.0924500
$469$	0	0
$470$	0	0
$471$	14.0000	0.645086
$472$	−36.0000	−1.65703
$473$	−12.0000	−0.551761
$474$	4.00000	0.183726
$475$	−4.00000	−0.183533
$476$	0	0
$477$	10.0000	0.457869
$478$	24.0000	1.09773
$479$	8.00000	0.365529	0.182765	−	0.983157i	$-0.441495\pi$
$479$	8.00000	0.365529	0.182765	+	0.983157i	$0.441495\pi$
$480$	5.00000	0.228218
$481$	−4.00000	−0.182384
$482$	−2.00000	−0.0910975
$483$	0	0
$484$	−1.00000	−0.0454545
$485$	10.0000	0.454077
$486$	1.00000	0.0453609
$487$	−8.00000	−0.362515	−0.181257	−	0.983436i	$-0.558017\pi$
$487$	−8.00000	−0.362515	−0.181257	+	0.983436i	$0.558017\pi$
$488$	−6.00000	−0.271607
$489$	−20.0000	−0.904431
$490$	0	0
$491$	−12.0000	−0.541552	−0.270776	−	0.962642i	$-0.587280\pi$
$491$	−12.0000	−0.541552	−0.270776	+	0.962642i	$0.587280\pi$
$492$	10.0000	0.450835
$493$	−60.0000	−2.70226
$494$	−8.00000	−0.359937
$495$	−1.00000	−0.0449467
$496$	−4.00000	−0.179605
$497$	0	0
$498$	−8.00000	−0.358489
$499$	4.00000	0.179065	0.0895323	−	0.995984i	$-0.471463\pi$
$499$	4.00000	0.179065	0.0895323	+	0.995984i	$0.471463\pi$
$500$	−1.00000	−0.0447214
$501$	12.0000	0.536120
$502$	−12.0000	−0.535586
$503$	20.0000	0.891756	0.445878	−	0.895094i	$-0.352892\pi$
$503$	20.0000	0.891756	0.445878	+	0.895094i	$0.352892\pi$
$504$	0	0
$505$	2.00000	0.0889988
$506$	4.00000	0.177822
$507$	−9.00000	−0.399704
$508$	−8.00000	−0.354943
$509$	6.00000	0.265945	0.132973	−	0.991120i	$-0.457548\pi$
$509$	6.00000	0.265945	0.132973	+	0.991120i	$0.457548\pi$
$510$	−6.00000	−0.265684
$511$	0	0
$512$	−11.0000	−0.486136
$513$	−4.00000	−0.176604
$514$	2.00000	0.0882162
$515$	−8.00000	−0.352522
$516$	−12.0000	−0.528271
$517$	0	0
$518$	0	0
$519$	−26.0000	−1.14127
$520$	−6.00000	−0.263117
$521$	−22.0000	−0.963837	−0.481919	−	0.876216i	$-0.660060\pi$
$521$	−22.0000	−0.963837	−0.481919	+	0.876216i	$0.660060\pi$
$522$	10.0000	0.437688
$523$	4.00000	0.174908	0.0874539	−	0.996169i	$-0.472127\pi$
$523$	4.00000	0.174908	0.0874539	+	0.996169i	$0.472127\pi$
$524$	−4.00000	−0.174741
$525$	0	0
$526$	−24.0000	−1.04645
$527$	−24.0000	−1.04546
$528$	1.00000	0.0435194
$529$	−7.00000	−0.304348
$530$	10.0000	0.434372
$531$	12.0000	0.520756
$532$	0	0
$533$	−20.0000	−0.866296
$534$	−6.00000	−0.259645
$535$	4.00000	0.172935
$536$	−12.0000	−0.518321
$537$	−4.00000	−0.172613
$538$	−10.0000	−0.431131
$539$	0	0
$540$	−1.00000	−0.0430331
$541$	−18.0000	−0.773880	−0.386940	−	0.922105i	$-0.626468\pi$
$541$	−18.0000	−0.773880	−0.386940	+	0.922105i	$0.626468\pi$
$542$	8.00000	0.343629
$543$	10.0000	0.429141
$544$	−30.0000	−1.28624
$545$	14.0000	0.599694
$546$	0	0
$547$	44.0000	1.88130	0.940652	−	0.339372i	$-0.110215\pi$
$547$	44.0000	1.88130	0.940652	+	0.339372i	$0.110215\pi$
$548$	10.0000	0.427179
$549$	2.00000	0.0853579
$550$	−1.00000	−0.0426401
$551$	−40.0000	−1.70406
$552$	12.0000	0.510754
$553$	0	0
$554$	2.00000	0.0849719
$555$	−2.00000	−0.0848953
$556$	−4.00000	−0.169638
$557$	18.0000	0.762684	0.381342	−	0.924434i	$-0.375462\pi$
$557$	18.0000	0.762684	0.381342	+	0.924434i	$0.375462\pi$
$558$	4.00000	0.169334
$559$	24.0000	1.01509
$560$	0	0
$561$	6.00000	0.253320
$562$	30.0000	1.26547
$563$	24.0000	1.01148	0.505740	−	0.862686i	$-0.331220\pi$
$563$	24.0000	1.01148	0.505740	+	0.862686i	$0.331220\pi$
$564$	0	0
$565$	−18.0000	−0.757266
$566$	28.0000	1.17693
$567$	0	0
$568$	−24.0000	−1.00702
$569$	−26.0000	−1.08998	−0.544988	−	0.838444i	$-0.683466\pi$
$569$	−26.0000	−1.08998	−0.544988	+	0.838444i	$0.683466\pi$
$570$	−4.00000	−0.167542
$571$	8.00000	0.334790	0.167395	−	0.985890i	$-0.446465\pi$
$571$	8.00000	0.334790	0.167395	+	0.985890i	$0.446465\pi$
$572$	2.00000	0.0836242
$573$	16.0000	0.668410
$574$	0	0
$575$	−4.00000	−0.166812
$576$	7.00000	0.291667
$577$	2.00000	0.0832611	0.0416305	−	0.999133i	$-0.486745\pi$
$577$	2.00000	0.0832611	0.0416305	+	0.999133i	$0.486745\pi$
$578$	19.0000	0.790296
$579$	14.0000	0.581820
$580$	−10.0000	−0.415227
$581$	0	0
$582$	10.0000	0.414513
$583$	−10.0000	−0.414158
$584$	−42.0000	−1.73797
$585$	2.00000	0.0826898
$586$	−18.0000	−0.743573
$587$	−12.0000	−0.495293	−0.247647	−	0.968850i	$-0.579657\pi$
$587$	−12.0000	−0.495293	−0.247647	+	0.968850i	$0.579657\pi$
$588$	0	0
$589$	−16.0000	−0.659269
$590$	12.0000	0.494032
$591$	26.0000	1.06950
$592$	2.00000	0.0821995
$593$	2.00000	0.0821302	0.0410651	−	0.999156i	$-0.486925\pi$
$593$	2.00000	0.0821302	0.0410651	+	0.999156i	$0.486925\pi$
$594$	−1.00000	−0.0410305
$595$	0	0
$596$	−18.0000	−0.737309
$597$	−4.00000	−0.163709
$598$	−8.00000	−0.327144
$599$	−32.0000	−1.30748	−0.653742	−	0.756717i	$-0.726802\pi$
$599$	−32.0000	−1.30748	−0.653742	+	0.756717i	$0.726802\pi$
$600$	−3.00000	−0.122474
$601$	6.00000	0.244745	0.122373	−	0.992484i	$-0.460950\pi$
$601$	6.00000	0.244745	0.122373	+	0.992484i	$0.460950\pi$
$602$	0	0
$603$	4.00000	0.162893
$604$	4.00000	0.162758
$605$	1.00000	0.0406558
$606$	2.00000	0.0812444
$607$	32.0000	1.29884	0.649420	−	0.760430i	$-0.275012\pi$
$607$	32.0000	1.29884	0.649420	+	0.760430i	$0.275012\pi$
$608$	−20.0000	−0.811107
$609$	0	0
$610$	2.00000	0.0809776
$611$	0	0
$612$	6.00000	0.242536
$613$	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
$615$	−10.0000	−0.403239
$616$	0	0
$617$	−18.0000	−0.724653	−0.362326	−	0.932051i	$-0.618017\pi$
$617$	−18.0000	−0.724653	−0.362326	+	0.932051i	$0.618017\pi$
$618$	−8.00000	−0.321807
$619$	0	0		−	1.00000i	$-0.5\pi$
$619$	0	0			1.00000i	$0.5\pi$
$620$	−4.00000	−0.160644
$621$	−4.00000	−0.160514
$622$	−8.00000	−0.320771
$623$	0	0
$624$	−2.00000	−0.0800641
$625$	1.00000	0.0400000
$626$	−30.0000	−1.19904
$627$	4.00000	0.159745
$628$	−14.0000	−0.558661
$629$	12.0000	0.478471
$630$	0	0
$631$	8.00000	0.318475	0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000	0.318475	0.159237	+	0.987240i	$0.449096\pi$
$632$	−12.0000	−0.477334
$633$	−16.0000	−0.635943
$634$	18.0000	0.714871
$635$	8.00000	0.317470
$636$	−10.0000	−0.396526
$637$	0	0
$638$	−10.0000	−0.395904
$639$	8.00000	0.316475
$640$	−3.00000	−0.118585
$641$	−30.0000	−1.18493	−0.592464	−	0.805597i	$-0.701845\pi$
$641$	−30.0000	−1.18493	−0.592464	+	0.805597i	$0.701845\pi$
$642$	4.00000	0.157867
$643$	−36.0000	−1.41970	−0.709851	−	0.704352i	$-0.751238\pi$
$643$	−36.0000	−1.41970	−0.709851	+	0.704352i	$0.751238\pi$
$644$	0	0
$645$	12.0000	0.472500
$646$	24.0000	0.944267
$647$	0	0		−	1.00000i	$-0.5\pi$
$647$	0	0			1.00000i	$0.5\pi$
$648$	−3.00000	−0.117851
$649$	−12.0000	−0.471041
$650$	2.00000	0.0784465
$651$	0	0
$652$	20.0000	0.783260
$653$	−30.0000	−1.17399	−0.586995	−	0.809590i	$-0.699689\pi$
$653$	−30.0000	−1.17399	−0.586995	+	0.809590i	$0.699689\pi$
$654$	14.0000	0.547443
$655$	4.00000	0.156293
$656$	10.0000	0.390434
$657$	14.0000	0.546192
$658$	0	0
$659$	36.0000	1.40236	0.701180	−	0.712984i	$-0.252657\pi$
$659$	36.0000	1.40236	0.701180	+	0.712984i	$0.252657\pi$
$660$	1.00000	0.0389249
$661$	−38.0000	−1.47803	−0.739014	−	0.673690i	$-0.764708\pi$
$661$	−38.0000	−1.47803	−0.739014	+	0.673690i	$0.764708\pi$
$662$	−12.0000	−0.466393
$663$	−12.0000	−0.466041
$664$	24.0000	0.931381
$665$	0	0
$666$	−2.00000	−0.0774984
$667$	−40.0000	−1.54881
$668$	−12.0000	−0.464294
$669$	24.0000	0.927894
$670$	4.00000	0.154533
$671$	−2.00000	−0.0772091
$672$	0	0
$673$	−26.0000	−1.00223	−0.501113	−	0.865382i	$-0.667076\pi$
$673$	−26.0000	−1.00223	−0.501113	+	0.865382i	$0.667076\pi$
$674$	22.0000	0.847408
$675$	1.00000	0.0384900
$676$	9.00000	0.346154
$677$	6.00000	0.230599	0.115299	−	0.993331i	$-0.463217\pi$
$677$	6.00000	0.230599	0.115299	+	0.993331i	$0.463217\pi$
$678$	−18.0000	−0.691286
$679$	0	0
$680$	18.0000	0.690268
$681$	−8.00000	−0.306561
$682$	−4.00000	−0.153168
$683$	−40.0000	−1.53056	−0.765279	−	0.643699i	$-0.777399\pi$
$683$	−40.0000	−1.53056	−0.765279	+	0.643699i	$0.777399\pi$
$684$	4.00000	0.152944
$685$	−10.0000	−0.382080
$686$	0	0
$687$	−14.0000	−0.534133
$688$	−12.0000	−0.457496
$689$	20.0000	0.761939
$690$	−4.00000	−0.152277
$691$	8.00000	0.304334	0.152167	−	0.988355i	$-0.451375\pi$
$691$	8.00000	0.304334	0.152167	+	0.988355i	$0.451375\pi$
$692$	26.0000	0.988372
$693$	0	0
$694$	−28.0000	−1.06287
$695$	4.00000	0.151729
$696$	−30.0000	−1.13715
$697$	60.0000	2.27266
$698$	−30.0000	−1.13552
$699$	−26.0000	−0.983410
$700$	0	0
$701$	−14.0000	−0.528773	−0.264386	−	0.964417i	$-0.585169\pi$
$701$	−14.0000	−0.528773	−0.264386	+	0.964417i	$0.585169\pi$
$702$	2.00000	0.0754851
$703$	8.00000	0.301726
$704$	−7.00000	−0.263822
$705$	0	0
$706$	18.0000	0.677439
$707$	0	0
$708$	−12.0000	−0.450988
$709$	6.00000	0.225335	0.112667	−	0.993633i	$-0.464061\pi$
$709$	6.00000	0.225335	0.112667	+	0.993633i	$0.464061\pi$
$710$	8.00000	0.300235
$711$	4.00000	0.150012
$712$	18.0000	0.674579
$713$	−16.0000	−0.599205
$714$	0	0
$715$	−2.00000	−0.0747958
$716$	4.00000	0.149487
$717$	24.0000	0.896296
$718$	24.0000	0.895672
$719$	48.0000	1.79010	0.895049	−	0.445968i	$-0.147140\pi$
$719$	48.0000	1.79010	0.895049	+	0.445968i	$0.147140\pi$
$720$	−1.00000	−0.0372678
$721$	0	0
$722$	−3.00000	−0.111648
$723$	−2.00000	−0.0743808
$724$	−10.0000	−0.371647
$725$	10.0000	0.371391
$726$	1.00000	0.0371135
$727$	8.00000	0.296704	0.148352	−	0.988935i	$-0.452603\pi$
$727$	8.00000	0.296704	0.148352	+	0.988935i	$0.452603\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	14.0000	0.518163
$731$	−72.0000	−2.66302
$732$	−2.00000	−0.0739221
$733$	−38.0000	−1.40356	−0.701781	−	0.712393i	$-0.747612\pi$
$733$	−38.0000	−1.40356	−0.701781	+	0.712393i	$0.747612\pi$
$734$	8.00000	0.295285
$735$	0	0
$736$	−20.0000	−0.737210
$737$	−4.00000	−0.147342
$738$	−10.0000	−0.368105
$739$	0	0		−	1.00000i	$-0.5\pi$
$739$	0	0			1.00000i	$0.5\pi$
$740$	2.00000	0.0735215
$741$	−8.00000	−0.293887
$742$	0	0
$743$	24.0000	0.880475	0.440237	−	0.897881i	$-0.354894\pi$
$743$	24.0000	0.880475	0.440237	+	0.897881i	$0.354894\pi$
$744$	−12.0000	−0.439941
$745$	18.0000	0.659469
$746$	−6.00000	−0.219676
$747$	−8.00000	−0.292705
$748$	−6.00000	−0.219382
$749$	0	0
$750$	1.00000	0.0365148
$751$	8.00000	0.291924	0.145962	−	0.989290i	$-0.453372\pi$
$751$	8.00000	0.291924	0.145962	+	0.989290i	$0.453372\pi$
$752$	0	0
$753$	−12.0000	−0.437304
$754$	20.0000	0.728357
$755$	−4.00000	−0.145575
$756$	0	0
$757$	−18.0000	−0.654221	−0.327111	−	0.944986i	$-0.606075\pi$
$757$	−18.0000	−0.654221	−0.327111	+	0.944986i	$0.606075\pi$
$758$	4.00000	0.145287
$759$	4.00000	0.145191
$760$	12.0000	0.435286
$761$	6.00000	0.217500	0.108750	−	0.994069i	$-0.465315\pi$
$761$	6.00000	0.217500	0.108750	+	0.994069i	$0.465315\pi$
$762$	8.00000	0.289809
$763$	0	0
$764$	−16.0000	−0.578860
$765$	−6.00000	−0.216930
$766$	32.0000	1.15621
$767$	24.0000	0.866590
$768$	−17.0000	−0.613435
$769$	30.0000	1.08183	0.540914	−	0.841078i	$-0.318079\pi$
$769$	30.0000	1.08183	0.540914	+	0.841078i	$0.318079\pi$
$770$	0	0
$771$	2.00000	0.0720282
$772$	−14.0000	−0.503871
$773$	6.00000	0.215805	0.107903	−	0.994161i	$-0.465587\pi$
$773$	6.00000	0.215805	0.107903	+	0.994161i	$0.465587\pi$
$774$	12.0000	0.431331
$775$	4.00000	0.143684
$776$	−30.0000	−1.07694
$777$	0	0
$778$	22.0000	0.788738
$779$	40.0000	1.43315
$780$	−2.00000	−0.0716115
$781$	−8.00000	−0.286263
$782$	24.0000	0.858238
$783$	10.0000	0.357371
$784$	0	0
$785$	14.0000	0.499681
$786$	4.00000	0.142675
$787$	−28.0000	−0.998092	−0.499046	−	0.866575i	$-0.666316\pi$
$787$	−28.0000	−0.998092	−0.499046	+	0.866575i	$0.666316\pi$
$788$	−26.0000	−0.926212
$789$	−24.0000	−0.854423
$790$	4.00000	0.142314
$791$	0	0
$792$	3.00000	0.106600
$793$	4.00000	0.142044
$794$	6.00000	0.212932
$795$	10.0000	0.354663
$796$	4.00000	0.141776
$797$	46.0000	1.62940	0.814702	−	0.579880i	$-0.196901\pi$
$797$	46.0000	1.62940	0.814702	+	0.579880i	$0.196901\pi$
$798$	0	0
$799$	0	0
$800$	5.00000	0.176777
$801$	−6.00000	−0.212000
$802$	18.0000	0.635602
$803$	−14.0000	−0.494049
$804$	−4.00000	−0.141069
$805$	0	0
$806$	8.00000	0.281788
$807$	−10.0000	−0.352017
$808$	−6.00000	−0.211079
$809$	−18.0000	−0.632846	−0.316423	−	0.948618i	$-0.602482\pi$
$809$	−18.0000	−0.632846	−0.316423	+	0.948618i	$0.602482\pi$
$810$	1.00000	0.0351364
$811$	52.0000	1.82597	0.912983	−	0.407997i	$-0.133772\pi$
$811$	52.0000	1.82597	0.912983	+	0.407997i	$0.133772\pi$
$812$	0	0
$813$	8.00000	0.280572
$814$	2.00000	0.0701000
$815$	−20.0000	−0.700569
$816$	6.00000	0.210042
$817$	−48.0000	−1.67931
$818$	22.0000	0.769212
$819$	0	0
$820$	10.0000	0.349215
$821$	10.0000	0.349002	0.174501	−	0.984657i	$-0.444169\pi$
$821$	10.0000	0.349002	0.174501	+	0.984657i	$0.444169\pi$
$822$	−10.0000	−0.348790
$823$	−32.0000	−1.11545	−0.557725	−	0.830026i	$-0.688326\pi$
$823$	−32.0000	−1.11545	−0.557725	+	0.830026i	$0.688326\pi$
$824$	24.0000	0.836080
$825$	−1.00000	−0.0348155
$826$	0	0
$827$	4.00000	0.139094	0.0695468	−	0.997579i	$-0.477845\pi$
$827$	4.00000	0.139094	0.0695468	+	0.997579i	$0.477845\pi$
$828$	4.00000	0.139010
$829$	−14.0000	−0.486240	−0.243120	−	0.969996i	$-0.578171\pi$
$829$	−14.0000	−0.486240	−0.243120	+	0.969996i	$0.578171\pi$
$830$	−8.00000	−0.277684
$831$	2.00000	0.0693792
$832$	14.0000	0.485363
$833$	0	0
$834$	4.00000	0.138509
$835$	12.0000	0.415277
$836$	−4.00000	−0.138343
$837$	4.00000	0.138260
$838$	−4.00000	−0.138178
$839$	0	0		−	1.00000i	$-0.5\pi$
$839$	0	0			1.00000i	$0.5\pi$
$840$	0	0
$841$	71.0000	2.44828
$842$	6.00000	0.206774
$843$	30.0000	1.03325
$844$	16.0000	0.550743
$845$	−9.00000	−0.309609
$846$	0	0
$847$	0	0
$848$	−10.0000	−0.343401
$849$	28.0000	0.960958
$850$	−6.00000	−0.205798
$851$	8.00000	0.274236
$852$	−8.00000	−0.274075
$853$	34.0000	1.16414	0.582069	−	0.813139i	$-0.302243\pi$
$853$	34.0000	1.16414	0.582069	+	0.813139i	$0.302243\pi$
$854$	0	0
$855$	−4.00000	−0.136797
$856$	−12.0000	−0.410152
$857$	−46.0000	−1.57133	−0.785665	−	0.618652i	$-0.787679\pi$
$857$	−46.0000	−1.57133	−0.785665	+	0.618652i	$0.787679\pi$
$858$	−2.00000	−0.0682789
$859$	−48.0000	−1.63774	−0.818869	−	0.573980i	$-0.805399\pi$
$859$	−48.0000	−1.63774	−0.818869	+	0.573980i	$0.805399\pi$
$860$	−12.0000	−0.409197
$861$	0	0
$862$	40.0000	1.36241
$863$	−20.0000	−0.680808	−0.340404	−	0.940279i	$-0.610564\pi$
$863$	−20.0000	−0.680808	−0.340404	+	0.940279i	$0.610564\pi$
$864$	5.00000	0.170103
$865$	−26.0000	−0.884027
$866$	2.00000	0.0679628
$867$	19.0000	0.645274
$868$	0	0
$869$	−4.00000	−0.135691
$870$	10.0000	0.339032
$871$	8.00000	0.271070
$872$	−42.0000	−1.42230
$873$	10.0000	0.338449
$874$	16.0000	0.541208
$875$	0	0
$876$	−14.0000	−0.473016
$877$	42.0000	1.41824	0.709120	−	0.705088i	$-0.249093\pi$
$877$	42.0000	1.41824	0.709120	+	0.705088i	$0.249093\pi$
$878$	8.00000	0.269987
$879$	−18.0000	−0.607125
$880$	1.00000	0.0337100
$881$	−14.0000	−0.471672	−0.235836	−	0.971793i	$-0.575783\pi$
$881$	−14.0000	−0.471672	−0.235836	+	0.971793i	$0.575783\pi$
$882$	0	0
$883$	−12.0000	−0.403832	−0.201916	−	0.979403i	$-0.564717\pi$
$883$	−12.0000	−0.403832	−0.201916	+	0.979403i	$0.564717\pi$
$884$	12.0000	0.403604
$885$	12.0000	0.403376
$886$	−8.00000	−0.268765
$887$	−52.0000	−1.74599	−0.872995	−	0.487730i	$-0.837825\pi$
$887$	−52.0000	−1.74599	−0.872995	+	0.487730i	$0.837825\pi$
$888$	6.00000	0.201347
$889$	0	0
$890$	−6.00000	−0.201120
$891$	−1.00000	−0.0335013
$892$	−24.0000	−0.803579
$893$	0	0
$894$	18.0000	0.602010
$895$	−4.00000	−0.133705
$896$	0	0
$897$	−8.00000	−0.267112
$898$	18.0000	0.600668
$899$	40.0000	1.33407
$900$	−1.00000	−0.0333333
$901$	−60.0000	−1.99889
$902$	10.0000	0.332964
$903$	0	0
$904$	54.0000	1.79601
$905$	10.0000	0.332411
$906$	−4.00000	−0.132891
$907$	12.0000	0.398453	0.199227	−	0.979953i	$-0.436157\pi$
$907$	12.0000	0.398453	0.199227	+	0.979953i	$0.436157\pi$
$908$	8.00000	0.265489
$909$	2.00000	0.0663358
$910$	0	0
$911$	−48.0000	−1.59031	−0.795155	−	0.606406i	$-0.792611\pi$
$911$	−48.0000	−1.59031	−0.795155	+	0.606406i	$0.792611\pi$
$912$	4.00000	0.132453
$913$	8.00000	0.264761
$914$	−18.0000	−0.595387
$915$	2.00000	0.0661180
$916$	14.0000	0.462573
$917$	0	0
$918$	−6.00000	−0.198030
$919$	20.0000	0.659739	0.329870	−	0.944027i	$-0.392995\pi$
$919$	20.0000	0.659739	0.329870	+	0.944027i	$0.392995\pi$
$920$	12.0000	0.395628
$921$	−12.0000	−0.395413
$922$	−30.0000	−0.987997
$923$	16.0000	0.526646
$924$	0	0
$925$	−2.00000	−0.0657596
$926$	16.0000	0.525793
$927$	−8.00000	−0.262754
$928$	50.0000	1.64133
$929$	−6.00000	−0.196854	−0.0984268	−	0.995144i	$-0.531381\pi$
$929$	−6.00000	−0.196854	−0.0984268	+	0.995144i	$0.531381\pi$
$930$	4.00000	0.131165
$931$	0	0
$932$	26.0000	0.851658
$933$	−8.00000	−0.261908
$934$	4.00000	0.130884
$935$	6.00000	0.196221
$936$	−6.00000	−0.196116
$937$	38.0000	1.24141	0.620703	−	0.784046i	$-0.286847\pi$
$937$	38.0000	1.24141	0.620703	+	0.784046i	$0.286847\pi$
$938$	0	0
$939$	−30.0000	−0.979013
$940$	0	0
$941$	−14.0000	−0.456387	−0.228193	−	0.973616i	$-0.573282\pi$
$941$	−14.0000	−0.456387	−0.228193	+	0.973616i	$0.573282\pi$
$942$	14.0000	0.456145
$943$	40.0000	1.30258
$944$	−12.0000	−0.390567
$945$	0	0
$946$	−12.0000	−0.390154
$947$	−24.0000	−0.779895	−0.389948	−	0.920837i	$-0.627507\pi$
$947$	−24.0000	−0.779895	−0.389948	+	0.920837i	$0.627507\pi$
$948$	−4.00000	−0.129914
$949$	28.0000	0.908918
$950$	−4.00000	−0.129777
$951$	18.0000	0.583690
$952$	0	0
$953$	38.0000	1.23094	0.615470	−	0.788160i	$-0.288966\pi$
$953$	38.0000	1.23094	0.615470	+	0.788160i	$0.288966\pi$
$954$	10.0000	0.323762
$955$	16.0000	0.517748
$956$	−24.0000	−0.776215
$957$	−10.0000	−0.323254
$958$	8.00000	0.258468
$959$	0	0
$960$	7.00000	0.225924
$961$	−15.0000	−0.483871
$962$	−4.00000	−0.128965
$963$	4.00000	0.128898
$964$	2.00000	0.0644157
$965$	14.0000	0.450676
$966$	0	0
$967$	8.00000	0.257263	0.128631	−	0.991692i	$-0.458942\pi$
$967$	8.00000	0.257263	0.128631	+	0.991692i	$0.458942\pi$
$968$	−3.00000	−0.0964237
$969$	24.0000	0.770991
$970$	10.0000	0.321081
$971$	44.0000	1.41203	0.706014	−	0.708198i	$-0.250492\pi$
$971$	44.0000	1.41203	0.706014	+	0.708198i	$0.250492\pi$
$972$	−1.00000	−0.0320750
$973$	0	0
$974$	−8.00000	−0.256337
$975$	2.00000	0.0640513
$976$	−2.00000	−0.0640184
$977$	−26.0000	−0.831814	−0.415907	−	0.909407i	$-0.636536\pi$
$977$	−26.0000	−0.831814	−0.415907	+	0.909407i	$0.636536\pi$
$978$	−20.0000	−0.639529
$979$	6.00000	0.191761
$980$	0	0
$981$	14.0000	0.446986
$982$	−12.0000	−0.382935
$983$	32.0000	1.02064	0.510321	−	0.859984i	$-0.329527\pi$
$983$	32.0000	1.02064	0.510321	+	0.859984i	$0.329527\pi$
$984$	30.0000	0.956365
$985$	26.0000	0.828429
$986$	−60.0000	−1.91079
$987$	0	0
$988$	8.00000	0.254514
$989$	−48.0000	−1.52631
$990$	−1.00000	−0.0317821
$991$	−16.0000	−0.508257	−0.254128	−	0.967170i	$-0.581789\pi$
$991$	−16.0000	−0.508257	−0.254128	+	0.967170i	$0.581789\pi$
$992$	20.0000	0.635001
$993$	−12.0000	−0.380808
$994$	0	0
$995$	−4.00000	−0.126809
$996$	8.00000	0.253490
$997$	2.00000	0.0633406	0.0316703	−	0.999498i	$-0.489917\pi$
$997$	2.00000	0.0633406	0.0316703	+	0.999498i	$0.489917\pi$
$998$	4.00000	0.126618
$999$	−2.00000	−0.0632772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8085.2.a.w.1.1		1
7.6	odd	2		1155.2.a.j.1.1	✓	1
21.20	even	2		3465.2.a.g.1.1		1
35.34	odd	2		5775.2.a.f.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.a.j.1.1	✓	1	7.6	odd	2
3465.2.a.g.1.1		1	21.20	even	2
5775.2.a.f.1.1		1	35.34	odd	2
8085.2.a.w.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:	\( N \)	\(=\)	\( 8085 = 3 \cdot 5 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8085.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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