LMFDB - Embedded newform 8019.2.a.c.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8019,2,Mod(1,8019)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8019, 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("8019.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8019 = 3^{6} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8019.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:	$64.0320373809$
Analytic rank:	$1$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	8019.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.07274 q^{2} +2.29625 q^{4} -0.494134 q^{5} -1.40906 q^{7} +0.614038 q^{8} +O(q^{10})$	\(q+2.07274 q^{2} +2.29625 q^{4} -0.494134 q^{5} -1.40906 q^{7} +0.614038 q^{8} -1.02421 q^{10} +1.00000 q^{11} +4.49939 q^{13} -2.92060 q^{14} -3.31975 q^{16} +1.23869 q^{17} -1.48283 q^{19} -1.13465 q^{20} +2.07274 q^{22} -7.50682 q^{23} -4.75583 q^{25} +9.32607 q^{26} -3.23554 q^{28} -7.93322 q^{29} +3.09387 q^{31} -8.10905 q^{32} +2.56748 q^{34} +0.696261 q^{35} +4.63822 q^{37} -3.07353 q^{38} -0.303417 q^{40} +0.135826 q^{41} +0.264216 q^{43} +2.29625 q^{44} -15.5597 q^{46} +6.36115 q^{47} -5.01456 q^{49} -9.85760 q^{50} +10.3317 q^{52} -7.37462 q^{53} -0.494134 q^{55} -0.865214 q^{56} -16.4435 q^{58} +10.1217 q^{59} +3.37520 q^{61} +6.41279 q^{62} -10.1684 q^{64} -2.22330 q^{65} +3.97468 q^{67} +2.84433 q^{68} +1.44317 q^{70} -13.1390 q^{71} -11.7636 q^{73} +9.61381 q^{74} -3.40495 q^{76} -1.40906 q^{77} -6.19262 q^{79} +1.64040 q^{80} +0.281531 q^{82} -16.4083 q^{83} -0.612077 q^{85} +0.547652 q^{86} +0.614038 q^{88} +0.0825875 q^{89} -6.33989 q^{91} -17.2375 q^{92} +13.1850 q^{94} +0.732718 q^{95} +13.0622 q^{97} -10.3939 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q - 6 q^{2} + 18 q^{4} - 12 q^{5} - 18 q^{8}+O(q^{10}) $ 21 * q - 6 * q^2 + 18 * q^4 - 12 * q^5 - 18 * q^8	$ 21 q - 6 q^{2} + 18 q^{4} - 12 q^{5} - 18 q^{8} + 15 q^{10} + 21 q^{11} + 3 q^{13} - 24 q^{14} + 12 q^{16} - 12 q^{17} - 12 q^{19} - 15 q^{20} - 6 q^{22} + 15 q^{25} - 15 q^{26} + 42 q^{28} - 27 q^{29} + 6 q^{31} - 42 q^{32} - 6 q^{34} - 42 q^{35} + 3 q^{37} - 27 q^{38} + 30 q^{40} - 24 q^{41} + 6 q^{43} + 18 q^{44} - 51 q^{46} - 24 q^{47} - 9 q^{49} + 3 q^{50} + 9 q^{52} - 12 q^{53} - 12 q^{55} - 45 q^{56} + 12 q^{58} - 12 q^{59} - 30 q^{61} - 9 q^{62} + 42 q^{64} + 18 q^{67} - 30 q^{68} + 21 q^{70} - 36 q^{71} - 39 q^{73} - 27 q^{76} + 27 q^{79} - 78 q^{80} + 63 q^{82} - 42 q^{83} + 36 q^{85} - 42 q^{86} - 18 q^{88} - 36 q^{89} - 21 q^{91} - 6 q^{92} + 42 q^{94} - 24 q^{95} + 24 q^{97} - 69 q^{98}+O(q^{100}) $ 21 * q - 6 * q^2 + 18 * q^4 - 12 * q^5 - 18 * q^8 + 15 * q^10 + 21 * q^11 + 3 * q^13 - 24 * q^14 + 12 * q^16 - 12 * q^17 - 12 * q^19 - 15 * q^20 - 6 * q^22 + 15 * q^25 - 15 * q^26 + 42 * q^28 - 27 * q^29 + 6 * q^31 - 42 * q^32 - 6 * q^34 - 42 * q^35 + 3 * q^37 - 27 * q^38 + 30 * q^40 - 24 * q^41 + 6 * q^43 + 18 * q^44 - 51 * q^46 - 24 * q^47 - 9 * q^49 + 3 * q^50 + 9 * q^52 - 12 * q^53 - 12 * q^55 - 45 * q^56 + 12 * q^58 - 12 * q^59 - 30 * q^61 - 9 * q^62 + 42 * q^64 + 18 * q^67 - 30 * q^68 + 21 * q^70 - 36 * q^71 - 39 * q^73 - 27 * q^76 + 27 * q^79 - 78 * q^80 + 63 * q^82 - 42 * q^83 + 36 * q^85 - 42 * q^86 - 18 * q^88 - 36 * q^89 - 21 * q^91 - 6 * q^92 + 42 * q^94 - 24 * q^95 + 24 * q^97 - 69 * q^98

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 $

$2$	2.07274	1.46565	0.732824	−	0.680419i	$-0.238202\pi$
$2$	2.07274	1.46565	0.732824	+	0.680419i	$0.238202\pi$
$3$	0	0
$3$	0	0
$4$	2.29625	1.14812
$5$	−0.494134	−0.220983	−0.110492	−	0.993877i	$-0.535243\pi$
$5$	−0.494134	−0.220983	−0.110492	+	0.993877i	$0.535243\pi$
$6$	0	0
$7$	−1.40906	−0.532573	−0.266286	−	0.963894i	$-0.585797\pi$
$7$	−1.40906	−0.532573	−0.266286	+	0.963894i	$0.585797\pi$
$8$	0.614038	0.217095
$9$	0	0
$10$	−1.02421	−0.323884
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0	0
$13$	4.49939	1.24791	0.623954	−	0.781461i	$-0.285525\pi$
$13$	4.49939	1.24791	0.623954	+	0.781461i	$0.285525\pi$
$14$	−2.92060	−0.780564
$15$	0	0
$16$	−3.31975	−0.829937
$17$	1.23869	0.300426	0.150213	−	0.988654i	$-0.452004\pi$
$17$	1.23869	0.300426	0.150213	+	0.988654i	$0.452004\pi$
$18$	0	0
$19$	−1.48283	−0.340186	−0.170093	−	0.985428i	$-0.554407\pi$
$19$	−1.48283	−0.340186	−0.170093	+	0.985428i	$0.554407\pi$
$20$	−1.13465	−0.253716
$21$	0	0
$22$	2.07274	0.441909
$23$	−7.50682	−1.56528	−0.782640	−	0.622475i	$-0.786127\pi$
$23$	−7.50682	−1.56528	−0.782640	+	0.622475i	$0.786127\pi$
$24$	0	0
$25$	−4.75583	−0.951166
$26$	9.32607	1.82899
$27$	0	0
$28$	−3.23554	−0.611459
$29$	−7.93322	−1.47316	−0.736581	−	0.676349i	$-0.763561\pi$
$29$	−7.93322	−1.47316	−0.736581	+	0.676349i	$0.763561\pi$
$30$	0	0
$31$	3.09387	0.555676	0.277838	−	0.960628i	$-0.410382\pi$
$31$	3.09387	0.555676	0.277838	+	0.960628i	$0.410382\pi$
$32$	−8.10905	−1.43349
$33$	0	0
$34$	2.56748	0.440318
$35$	0.696261	0.117690
$36$	0	0
$37$	4.63822	0.762518	0.381259	−	0.924468i	$-0.375491\pi$
$37$	4.63822	0.762518	0.381259	+	0.924468i	$0.375491\pi$
$38$	−3.07353	−0.498592
$39$	0	0
$40$	−0.303417	−0.0479744
$41$	0.135826	0.0212124	0.0106062	−	0.999944i	$-0.496624\pi$
$41$	0.135826	0.0212124	0.0106062	+	0.999944i	$0.496624\pi$
$42$	0	0
$43$	0.264216	0.0402926	0.0201463	−	0.999797i	$-0.493587\pi$
$43$	0.264216	0.0402926	0.0201463	+	0.999797i	$0.493587\pi$
$44$	2.29625	0.346172
$45$	0	0
$46$	−15.5597	−2.29415
$47$	6.36115	0.927869	0.463934	−	0.885870i	$-0.346437\pi$
$47$	6.36115	0.927869	0.463934	+	0.885870i	$0.346437\pi$
$48$	0	0
$49$	−5.01456	−0.716366
$50$	−9.85760	−1.39407
$51$	0	0
$52$	10.3317	1.43275
$53$	−7.37462	−1.01298	−0.506491	−	0.862245i	$-0.669058\pi$
$53$	−7.37462	−1.01298	−0.506491	+	0.862245i	$0.669058\pi$
$54$	0	0
$55$	−0.494134	−0.0666290
$56$	−0.865214	−0.115619
$57$	0	0
$58$	−16.4435	−2.15914
$59$	10.1217	1.31774	0.658869	−	0.752258i	$-0.271035\pi$
$59$	10.1217	1.31774	0.658869	+	0.752258i	$0.271035\pi$
$60$	0	0
$61$	3.37520	0.432150	0.216075	−	0.976377i	$-0.430674\pi$
$61$	3.37520	0.432150	0.216075	+	0.976377i	$0.430674\pi$
$62$	6.41279	0.814426
$63$	0	0
$64$	−10.1684	−1.27105
$65$	−2.22330	−0.275767
$66$	0	0
$67$	3.97468	0.485585	0.242792	−	0.970078i	$-0.421937\pi$
$67$	3.97468	0.485585	0.242792	+	0.970078i	$0.421937\pi$
$68$	2.84433	0.344926
$69$	0	0
$70$	1.44317	0.172492
$71$	−13.1390	−1.55931	−0.779654	−	0.626211i	$-0.784605\pi$
$71$	−13.1390	−1.55931	−0.779654	+	0.626211i	$0.784605\pi$
$72$	0	0
$73$	−11.7636	−1.37682	−0.688410	−	0.725321i	$-0.741691\pi$
$73$	−11.7636	−1.37682	−0.688410	+	0.725321i	$0.741691\pi$
$74$	9.61381	1.11758
$75$	0	0
$76$	−3.40495	−0.390575
$77$	−1.40906	−0.160577
$78$	0	0
$79$	−6.19262	−0.696724	−0.348362	−	0.937360i	$-0.613262\pi$
$79$	−6.19262	−0.696724	−0.348362	+	0.937360i	$0.613262\pi$
$80$	1.64040	0.183402
$81$	0	0
$82$	0.281531	0.0310899
$83$	−16.4083	−1.80104	−0.900522	−	0.434810i	$-0.856816\pi$
$83$	−16.4083	−1.80104	−0.900522	+	0.434810i	$0.856816\pi$
$84$	0	0
$85$	−0.612077	−0.0663891
$86$	0.547652	0.0590548
$87$	0	0
$88$	0.614038	0.0654567
$89$	0.0825875	0.00875426	0.00437713	−	0.999990i	$-0.498607\pi$
$89$	0.0825875	0.00875426	0.00437713	+	0.999990i	$0.498607\pi$
$90$	0	0
$91$	−6.33989	−0.664602
$92$	−17.2375	−1.79713
$93$	0	0
$94$	13.1850	1.35993
$95$	0.732718	0.0751753
$96$	0	0
$97$	13.0622	1.32627	0.663133	−	0.748502i	$-0.269226\pi$
$97$	13.0622	1.32627	0.663133	+	0.748502i	$0.269226\pi$
$98$	−10.3939	−1.04994
$99$	0	0
$100$	−10.9206	−1.09206
$101$	3.94070	0.392115	0.196057	−	0.980592i	$-0.437186\pi$
$101$	3.94070	0.392115	0.196057	+	0.980592i	$0.437186\pi$
$102$	0	0
$103$	−11.3401	−1.11737	−0.558685	−	0.829380i	$-0.688694\pi$
$103$	−11.3401	−1.11737	−0.558685	+	0.829380i	$0.688694\pi$
$104$	2.76280	0.270915
$105$	0	0
$106$	−15.2857	−1.48467
$107$	10.5007	1.01514	0.507571	−	0.861610i	$-0.330544\pi$
$107$	10.5007	1.01514	0.507571	+	0.861610i	$0.330544\pi$
$108$	0	0
$109$	−15.3670	−1.47189	−0.735944	−	0.677042i	$-0.763261\pi$
$109$	−15.3670	−1.47189	−0.735944	+	0.677042i	$0.763261\pi$
$110$	−1.02421	−0.0976546
$111$	0	0
$112$	4.67771	0.442002
$113$	−18.2353	−1.71543	−0.857716	−	0.514124i	$-0.828117\pi$
$113$	−18.2353	−1.71543	−0.857716	+	0.514124i	$0.828117\pi$
$114$	0	0
$115$	3.70937	0.345901
$116$	−18.2166	−1.69137
$117$	0	0
$118$	20.9797	1.93134
$119$	−1.74538	−0.159999
$120$	0	0
$121$	1.00000	0.0909091
$122$	6.99591	0.633380
$123$	0	0
$124$	7.10429	0.637985
$125$	4.82068	0.431175
$126$	0	0
$127$	−0.0998170	−0.00885733	−0.00442866	−	0.999990i	$-0.501410\pi$
$127$	−0.0998170	−0.00885733	−0.00442866	+	0.999990i	$0.501410\pi$
$128$	−4.85842	−0.429428
$129$	0	0
$130$	−4.60832	−0.404177
$131$	−9.15859	−0.800189	−0.400095	−	0.916474i	$-0.631023\pi$
$131$	−9.15859	−0.800189	−0.400095	+	0.916474i	$0.631023\pi$
$132$	0	0
$133$	2.08940	0.181174
$134$	8.23848	0.711696
$135$	0	0
$136$	0.760602	0.0652211
$137$	−1.36036	−0.116223	−0.0581117	−	0.998310i	$-0.518508\pi$
$137$	−1.36036	−0.116223	−0.0581117	+	0.998310i	$0.518508\pi$
$138$	0	0
$139$	14.4699	1.22732	0.613662	−	0.789569i	$-0.289696\pi$
$139$	14.4699	1.22732	0.613662	+	0.789569i	$0.289696\pi$
$140$	1.59879	0.135122
$141$	0	0
$142$	−27.2336	−2.28540
$143$	4.49939	0.376258
$144$	0	0
$145$	3.92007	0.325544
$146$	−24.3828	−2.01793
$147$	0	0
$148$	10.6505	0.875464
$149$	4.17267	0.341838	0.170919	−	0.985285i	$-0.445326\pi$
$149$	4.17267	0.341838	0.170919	+	0.985285i	$0.445326\pi$
$150$	0	0
$151$	−5.84606	−0.475746	−0.237873	−	0.971296i	$-0.576450\pi$
$151$	−5.84606	−0.475746	−0.237873	+	0.971296i	$0.576450\pi$
$152$	−0.910518	−0.0738527
$153$	0	0
$154$	−2.92060	−0.235349
$155$	−1.52879	−0.122795
$156$	0	0
$157$	5.73997	0.458099	0.229050	−	0.973415i	$-0.426438\pi$
$157$	5.73997	0.458099	0.229050	+	0.973415i	$0.426438\pi$
$158$	−12.8357	−1.02115
$159$	0	0
$160$	4.00695	0.316777
$161$	10.5775	0.833625
$162$	0	0
$163$	−16.6998	−1.30803	−0.654014	−	0.756482i	$-0.726916\pi$
$163$	−16.6998	−1.30803	−0.654014	+	0.756482i	$0.726916\pi$
$164$	0.311889	0.0243544
$165$	0	0
$166$	−34.0101	−2.63970
$167$	−3.32915	−0.257617	−0.128809	−	0.991669i	$-0.541115\pi$
$167$	−3.32915	−0.257617	−0.128809	+	0.991669i	$0.541115\pi$
$168$	0	0
$169$	7.24455	0.557273
$170$	−1.26868	−0.0973030
$171$	0	0
$172$	0.606706	0.0462609
$173$	0.808797	0.0614917	0.0307459	−	0.999527i	$-0.490212\pi$
$173$	0.808797	0.0614917	0.0307459	+	0.999527i	$0.490212\pi$
$174$	0	0
$175$	6.70123	0.506565
$176$	−3.31975	−0.250235
$177$	0	0
$178$	0.171182	0.0128307
$179$	−6.60212	−0.493466	−0.246733	−	0.969084i	$-0.579357\pi$
$179$	−6.60212	−0.493466	−0.246733	+	0.969084i	$0.579357\pi$
$180$	0	0
$181$	−7.62062	−0.566436	−0.283218	−	0.959056i	$-0.591402\pi$
$181$	−7.62062	−0.566436	−0.283218	+	0.959056i	$0.591402\pi$
$182$	−13.1409	−0.974072
$183$	0	0
$184$	−4.60947	−0.339815
$185$	−2.29190	−0.168504
$186$	0	0
$187$	1.23869	0.0905818
$188$	14.6068	1.06531
$189$	0	0
$190$	1.51873	0.110181
$191$	−0.454915	−0.0329165	−0.0164582	−	0.999865i	$-0.505239\pi$
$191$	−0.454915	−0.0329165	−0.0164582	+	0.999865i	$0.505239\pi$
$192$	0	0
$193$	15.3130	1.10225	0.551125	−	0.834423i	$-0.314199\pi$
$193$	15.3130	1.10225	0.551125	+	0.834423i	$0.314199\pi$
$194$	27.0745	1.94384
$195$	0	0
$196$	−11.5147	−0.822476
$197$	1.11931	0.0797474	0.0398737	−	0.999205i	$-0.487304\pi$
$197$	1.11931	0.0797474	0.0398737	+	0.999205i	$0.487304\pi$
$198$	0	0
$199$	−8.39801	−0.595319	−0.297660	−	0.954672i	$-0.596206\pi$
$199$	−8.39801	−0.595319	−0.297660	+	0.954672i	$0.596206\pi$
$200$	−2.92026	−0.206494
$201$	0	0
$202$	8.16805	0.574702
$203$	11.1784	0.784566
$204$	0	0
$205$	−0.0671160	−0.00468759
$206$	−23.5050	−1.63767
$207$	0	0
$208$	−14.9369	−1.03568
$209$	−1.48283	−0.102570
$210$	0	0
$211$	−4.94839	−0.340661	−0.170331	−	0.985387i	$-0.554484\pi$
$211$	−4.94839	−0.340661	−0.170331	+	0.985387i	$0.554484\pi$
$212$	−16.9339	−1.16303
$213$	0	0
$214$	21.7652	1.48784
$215$	−0.130558	−0.00890400
$216$	0	0
$217$	−4.35944	−0.295938
$218$	−31.8517	−2.15727
$219$	0	0
$220$	−1.13465	−0.0764982
$221$	5.57334	0.374904
$222$	0	0
$223$	−15.5470	−1.04110	−0.520550	−	0.853831i	$-0.674273\pi$
$223$	−15.5470	−1.04110	−0.520550	+	0.853831i	$0.674273\pi$
$224$	11.4261	0.763438
$225$	0	0
$226$	−37.7970	−2.51422
$227$	3.73228	0.247720	0.123860	−	0.992300i	$-0.460473\pi$
$227$	3.73228	0.247720	0.123860	+	0.992300i	$0.460473\pi$
$228$	0	0
$229$	−2.72690	−0.180199	−0.0900993	−	0.995933i	$-0.528718\pi$
$229$	−2.72690	−0.180199	−0.0900993	+	0.995933i	$0.528718\pi$
$230$	7.68856	0.506968
$231$	0	0
$232$	−4.87130	−0.319817
$233$	−21.7820	−1.42699	−0.713494	−	0.700662i	$-0.752888\pi$
$233$	−21.7820	−1.42699	−0.713494	+	0.700662i	$0.752888\pi$
$234$	0	0
$235$	−3.14326	−0.205043
$236$	23.2420	1.51292
$237$	0	0
$238$	−3.61772	−0.234502
$239$	0.261108	0.0168897	0.00844485	−	0.999964i	$-0.497312\pi$
$239$	0.261108	0.0168897	0.00844485	+	0.999964i	$0.497312\pi$
$240$	0	0
$241$	19.5554	1.25967	0.629836	−	0.776728i	$-0.283122\pi$
$241$	19.5554	1.25967	0.629836	+	0.776728i	$0.283122\pi$
$242$	2.07274	0.133241
$243$	0	0
$244$	7.75029	0.496161
$245$	2.47786	0.158305
$246$	0	0
$247$	−6.67186	−0.424520
$248$	1.89976	0.120635
$249$	0	0
$250$	9.99202	0.631951
$251$	4.40913	0.278302	0.139151	−	0.990271i	$-0.455563\pi$
$251$	4.40913	0.278302	0.139151	+	0.990271i	$0.455563\pi$
$252$	0	0
$253$	−7.50682	−0.471950
$254$	−0.206895	−0.0129817
$255$	0	0
$256$	10.2666	0.641665
$257$	18.3338	1.14363	0.571815	−	0.820382i	$-0.306239\pi$
$257$	18.3338	1.14363	0.571815	+	0.820382i	$0.306239\pi$
$258$	0	0
$259$	−6.53550	−0.406096
$260$	−5.10525	−0.316614
$261$	0	0
$262$	−18.9834	−1.17280
$263$	−11.1217	−0.685795	−0.342897	−	0.939373i	$-0.611408\pi$
$263$	−11.1217	−0.685795	−0.342897	+	0.939373i	$0.611408\pi$
$264$	0	0
$265$	3.64405	0.223852
$266$	4.33077	0.265537
$267$	0	0
$268$	9.12685	0.557511
$269$	−16.6006	−1.01215	−0.506077	−	0.862488i	$-0.668905\pi$
$269$	−16.6006	−1.01215	−0.506077	+	0.862488i	$0.668905\pi$
$270$	0	0
$271$	31.1326	1.89117	0.945585	−	0.325375i	$-0.105490\pi$
$271$	31.1326	1.89117	0.945585	+	0.325375i	$0.105490\pi$
$272$	−4.11213	−0.249335
$273$	0	0
$274$	−2.81967	−0.170342
$275$	−4.75583	−0.286787
$276$	0	0
$277$	−12.8630	−0.772860	−0.386430	−	0.922319i	$-0.626292\pi$
$277$	−12.8630	−0.772860	−0.386430	+	0.922319i	$0.626292\pi$
$278$	29.9924	1.79882
$279$	0	0
$280$	0.427531	0.0255499
$281$	−18.3256	−1.09321	−0.546606	−	0.837390i	$-0.684080\pi$
$281$	−18.3256	−1.09321	−0.546606	+	0.837390i	$0.684080\pi$
$282$	0	0
$283$	22.9201	1.36246	0.681231	−	0.732069i	$-0.261445\pi$
$283$	22.9201	1.36246	0.681231	+	0.732069i	$0.261445\pi$
$284$	−30.1703	−1.79028
$285$	0	0
$286$	9.32607	0.551462
$287$	−0.191386	−0.0112972
$288$	0	0
$289$	−15.4657	−0.909744
$290$	8.12529	0.477133
$291$	0	0
$292$	−27.0120	−1.58076
$293$	−25.7384	−1.50365	−0.751826	−	0.659362i	$-0.770826\pi$
$293$	−25.7384	−1.50365	−0.751826	+	0.659362i	$0.770826\pi$
$294$	0	0
$295$	−5.00149	−0.291198
$296$	2.84804	0.165539
$297$	0	0
$298$	8.64885	0.501014
$299$	−33.7761	−1.95332
$300$	0	0
$301$	−0.372296	−0.0214588
$302$	−12.1174	−0.697276
$303$	0	0
$304$	4.92264	0.282333
$305$	−1.66780	−0.0954980
$306$	0	0
$307$	−9.16669	−0.523171	−0.261585	−	0.965180i	$-0.584245\pi$
$307$	−9.16669	−0.523171	−0.261585	+	0.965180i	$0.584245\pi$
$308$	−3.23554	−0.184362
$309$	0	0
$310$	−3.16878	−0.179974
$311$	20.5873	1.16740	0.583699	−	0.811970i	$-0.301605\pi$
$311$	20.5873	1.16740	0.583699	+	0.811970i	$0.301605\pi$
$312$	0	0
$313$	−0.182882	−0.0103371	−0.00516855	−	0.999987i	$-0.501645\pi$
$313$	−0.182882	−0.0103371	−0.00516855	+	0.999987i	$0.501645\pi$
$314$	11.8974	0.671412
$315$	0	0
$316$	−14.2198	−0.799925
$317$	−9.90192	−0.556147	−0.278074	−	0.960560i	$-0.589696\pi$
$317$	−9.90192	−0.556147	−0.278074	+	0.960560i	$0.589696\pi$
$318$	0	0
$319$	−7.93322	−0.444175
$320$	5.02457	0.280882
$321$	0	0
$322$	21.9244	1.22180
$323$	−1.83677	−0.102201
$324$	0	0
$325$	−21.3984	−1.18697
$326$	−34.6143	−1.91711
$327$	0	0
$328$	0.0834022	0.00460512
$329$	−8.96321	−0.494158
$330$	0	0
$331$	−9.02470	−0.496043	−0.248021	−	0.968755i	$-0.579780\pi$
$331$	−9.02470	−0.496043	−0.248021	+	0.968755i	$0.579780\pi$
$332$	−37.6775	−2.06782
$333$	0	0
$334$	−6.90045	−0.377576
$335$	−1.96402	−0.107306
$336$	0	0
$337$	−11.0064	−0.599556	−0.299778	−	0.954009i	$-0.596913\pi$
$337$	−11.0064	−0.599556	−0.299778	+	0.954009i	$0.596913\pi$
$338$	15.0161	0.816766
$339$	0	0
$340$	−1.40548	−0.0762228
$341$	3.09387	0.167543
$342$	0	0
$343$	16.9292	0.914090
$344$	0.162239	0.00874734
$345$	0	0
$346$	1.67643	0.0901252
$347$	25.0788	1.34630	0.673151	−	0.739505i	$-0.264941\pi$
$347$	25.0788	1.34630	0.673151	+	0.739505i	$0.264941\pi$
$348$	0	0
$349$	31.6587	1.69465	0.847325	−	0.531075i	$-0.178212\pi$
$349$	31.6587	1.69465	0.847325	+	0.531075i	$0.178212\pi$
$350$	13.8899	0.742446
$351$	0	0
$352$	−8.10905	−0.432214
$353$	11.1228	0.592009	0.296004	−	0.955187i	$-0.404346\pi$
$353$	11.1228	0.592009	0.296004	+	0.955187i	$0.404346\pi$
$354$	0	0
$355$	6.49240	0.344581
$356$	0.189641	0.0100510
$357$	0	0
$358$	−13.6845	−0.723247
$359$	−24.5289	−1.29458	−0.647292	−	0.762242i	$-0.724098\pi$
$359$	−24.5289	−1.29458	−0.647292	+	0.762242i	$0.724098\pi$
$360$	0	0
$361$	−16.8012	−0.884274
$362$	−15.7955	−0.830195
$363$	0	0
$364$	−14.5580	−0.763044
$365$	5.81277	0.304254
$366$	0	0
$367$	−28.4709	−1.48617	−0.743085	−	0.669198i	$-0.766638\pi$
$367$	−28.4709	−1.48617	−0.743085	+	0.669198i	$0.766638\pi$
$368$	24.9207	1.29908
$369$	0	0
$370$	−4.75051	−0.246967
$371$	10.3912	0.539487
$372$	0	0
$373$	32.1017	1.66216	0.831081	−	0.556152i	$-0.187723\pi$
$373$	32.1017	1.66216	0.831081	+	0.556152i	$0.187723\pi$
$374$	2.56748	0.132761
$375$	0	0
$376$	3.90599	0.201436
$377$	−35.6947	−1.83837
$378$	0	0
$379$	11.6805	0.599985	0.299993	−	0.953942i	$-0.403016\pi$
$379$	11.6805	0.599985	0.299993	+	0.953942i	$0.403016\pi$
$380$	1.68250	0.0863105
$381$	0	0
$382$	−0.942919	−0.0482439
$383$	18.1639	0.928134	0.464067	−	0.885800i	$-0.346390\pi$
$383$	18.1639	0.928134	0.464067	+	0.885800i	$0.346390\pi$
$384$	0	0
$385$	0.696261	0.0354848
$386$	31.7397	1.61551
$387$	0	0
$388$	29.9940	1.52272
$389$	11.6613	0.591254	0.295627	−	0.955304i	$-0.404472\pi$
$389$	11.6613	0.591254	0.295627	+	0.955304i	$0.404472\pi$
$390$	0	0
$391$	−9.29860	−0.470251
$392$	−3.07913	−0.155520
$393$	0	0
$394$	2.32003	0.116882
$395$	3.05998	0.153964
$396$	0	0
$397$	−11.7890	−0.591671	−0.295835	−	0.955239i	$-0.595598\pi$
$397$	−11.7890	−0.591671	−0.295835	+	0.955239i	$0.595598\pi$
$398$	−17.4069	−0.872528
$399$	0	0
$400$	15.7882	0.789408
$401$	−32.3241	−1.61419	−0.807094	−	0.590422i	$-0.798961\pi$
$401$	−32.3241	−1.61419	−0.807094	+	0.590422i	$0.798961\pi$
$402$	0	0
$403$	13.9206	0.693433
$404$	9.04882	0.450196
$405$	0	0
$406$	23.1698	1.14990
$407$	4.63822	0.229908
$408$	0	0
$409$	−25.7135	−1.27145	−0.635726	−	0.771915i	$-0.719299\pi$
$409$	−25.7135	−1.27145	−0.635726	+	0.771915i	$0.719299\pi$
$410$	−0.139114	−0.00687035
$411$	0	0
$412$	−26.0396	−1.28288
$413$	−14.2621	−0.701791
$414$	0	0
$415$	8.10789	0.398001
$416$	−36.4858	−1.78886
$417$	0	0
$418$	−3.07353	−0.150331
$419$	19.7962	0.967109	0.483555	−	0.875314i	$-0.339345\pi$
$419$	19.7962	0.967109	0.483555	+	0.875314i	$0.339345\pi$
$420$	0	0
$421$	−26.4754	−1.29033	−0.645167	−	0.764042i	$-0.723212\pi$
$421$	−26.4754	−1.29033	−0.645167	+	0.764042i	$0.723212\pi$
$422$	−10.2567	−0.499289
$423$	0	0
$424$	−4.52830	−0.219914
$425$	−5.89099	−0.285755
$426$	0	0
$427$	−4.75585	−0.230152
$428$	24.1122	1.16551
$429$	0	0
$430$	−0.270613	−0.0130501
$431$	4.31748	0.207966	0.103983	−	0.994579i	$-0.466841\pi$
$431$	4.31748	0.207966	0.103983	+	0.994579i	$0.466841\pi$
$432$	0	0
$433$	27.6139	1.32704	0.663519	−	0.748160i	$-0.269062\pi$
$433$	27.6139	1.32704	0.663519	+	0.748160i	$0.269062\pi$
$434$	−9.03598	−0.433741
$435$	0	0
$436$	−35.2863	−1.68991
$437$	11.1314	0.532486
$438$	0	0
$439$	15.9409	0.760818	0.380409	−	0.924818i	$-0.375783\pi$
$439$	15.9409	0.760818	0.380409	+	0.924818i	$0.375783\pi$
$440$	−0.303417	−0.0144648
$441$	0	0
$442$	11.5521	0.549477
$443$	28.3437	1.34665	0.673325	−	0.739347i	$-0.264866\pi$
$443$	28.3437	1.34665	0.673325	+	0.739347i	$0.264866\pi$
$444$	0	0
$445$	−0.0408093	−0.00193454
$446$	−32.2248	−1.52589
$447$	0	0
$448$	14.3279	0.676929
$449$	−7.53281	−0.355495	−0.177748	−	0.984076i	$-0.556881\pi$
$449$	−7.53281	−0.355495	−0.177748	+	0.984076i	$0.556881\pi$
$450$	0	0
$451$	0.135826	0.00639578
$452$	−41.8727	−1.96953
$453$	0	0
$454$	7.73604	0.363070
$455$	3.13275	0.146866
$456$	0	0
$457$	−8.82815	−0.412964	−0.206482	−	0.978450i	$-0.566201\pi$
$457$	−8.82815	−0.412964	−0.206482	+	0.978450i	$0.566201\pi$
$458$	−5.65215	−0.264107
$459$	0	0
$460$	8.51762	0.397136
$461$	27.3872	1.27555	0.637774	−	0.770223i	$-0.279855\pi$
$461$	27.3872	1.27555	0.637774	+	0.770223i	$0.279855\pi$
$462$	0	0
$463$	22.6957	1.05476	0.527378	−	0.849630i	$-0.323175\pi$
$463$	22.6957	1.05476	0.527378	+	0.849630i	$0.323175\pi$
$464$	26.3363	1.22263
$465$	0	0
$466$	−45.1484	−2.09146
$467$	8.17591	0.378336	0.189168	−	0.981945i	$-0.439421\pi$
$467$	8.17591	0.378336	0.189168	+	0.981945i	$0.439421\pi$
$468$	0	0
$469$	−5.60055	−0.258609
$470$	−6.51515	−0.300521
$471$	0	0
$472$	6.21514	0.286075
$473$	0.264216	0.0121487
$474$	0	0
$475$	7.05211	0.323573
$476$	−4.00782	−0.183698
$477$	0	0
$478$	0.541210	0.0247543
$479$	−18.6780	−0.853419	−0.426709	−	0.904389i	$-0.640327\pi$
$479$	−18.6780	−0.853419	−0.426709	+	0.904389i	$0.640327\pi$
$480$	0	0
$481$	20.8692	0.951552
$482$	40.5331	1.84623
$483$	0	0
$484$	2.29625	0.104375
$485$	−6.45447	−0.293082
$486$	0	0
$487$	−31.0887	−1.40876	−0.704381	−	0.709822i	$-0.748775\pi$
$487$	−31.0887	−1.40876	−0.704381	+	0.709822i	$0.748775\pi$
$488$	2.07250	0.0938178
$489$	0	0
$490$	5.13596	0.232019
$491$	14.1767	0.639785	0.319892	−	0.947454i	$-0.396353\pi$
$491$	14.1767	0.639785	0.319892	+	0.947454i	$0.396353\pi$
$492$	0	0
$493$	−9.82679	−0.442576
$494$	−13.8290	−0.622197
$495$	0	0
$496$	−10.2709	−0.461176
$497$	18.5135	0.830445
$498$	0	0
$499$	43.3174	1.93915	0.969576	−	0.244790i	$-0.0787191\pi$
$499$	43.3174	1.93915	0.969576	+	0.244790i	$0.0787191\pi$
$500$	11.0695	0.495042
$501$	0	0
$502$	9.13897	0.407892
$503$	8.23187	0.367041	0.183520	−	0.983016i	$-0.441251\pi$
$503$	8.23187	0.367041	0.183520	+	0.983016i	$0.441251\pi$
$504$	0	0
$505$	−1.94723	−0.0866508
$506$	−15.5597	−0.691712
$507$	0	0
$508$	−0.229204	−0.0101693
$509$	30.5586	1.35449	0.677244	−	0.735759i	$-0.263174\pi$
$509$	30.5586	1.35449	0.677244	+	0.735759i	$0.263174\pi$
$510$	0	0
$511$	16.5755	0.733257
$512$	30.9969	1.36988
$513$	0	0
$514$	38.0012	1.67616
$515$	5.60350	0.246920
$516$	0	0
$517$	6.36115	0.279763
$518$	−13.5464	−0.595194
$519$	0	0
$520$	−1.36519	−0.0598677
$521$	5.02853	0.220304	0.110152	−	0.993915i	$-0.464866\pi$
$521$	5.02853	0.220304	0.110152	+	0.993915i	$0.464866\pi$
$522$	0	0
$523$	−12.5758	−0.549903	−0.274952	−	0.961458i	$-0.588662\pi$
$523$	−12.5758	−0.549903	−0.274952	+	0.961458i	$0.588662\pi$
$524$	−21.0304	−0.918715
$525$	0	0
$526$	−23.0524	−1.00513
$527$	3.83234	0.166940
$528$	0	0
$529$	33.3523	1.45010
$530$	7.55316	0.328088
$531$	0	0
$532$	4.79777	0.208010
$533$	0.611133	0.0264711
$534$	0	0
$535$	−5.18875	−0.224329
$536$	2.44061	0.105418
$537$	0	0
$538$	−34.4086	−1.48346
$539$	−5.01456	−0.215993
$540$	0	0
$541$	0.930168	0.0399910	0.0199955	−	0.999800i	$-0.493635\pi$
$541$	0.930168	0.0399910	0.0199955	+	0.999800i	$0.493635\pi$
$542$	64.5297	2.77179
$543$	0	0
$544$	−10.0446	−0.430658
$545$	7.59333	0.325263
$546$	0	0
$547$	−19.9490	−0.852956	−0.426478	−	0.904498i	$-0.640246\pi$
$547$	−19.9490	−0.852956	−0.426478	+	0.904498i	$0.640246\pi$
$548$	−3.12372	−0.133439
$549$	0	0
$550$	−9.85760	−0.420329
$551$	11.7637	0.501149
$552$	0	0
$553$	8.72574	0.371056
$554$	−26.6615	−1.13274
$555$	0	0
$556$	33.2265	1.40912
$557$	8.13590	0.344729	0.172365	−	0.985033i	$-0.444859\pi$
$557$	8.13590	0.344729	0.172365	+	0.985033i	$0.444859\pi$
$558$	0	0
$559$	1.18881	0.0502815
$560$	−2.31141	−0.0976750
$561$	0	0
$562$	−37.9841	−1.60226
$563$	−29.6591	−1.24998	−0.624990	−	0.780633i	$-0.714897\pi$
$563$	−29.6591	−1.24998	−0.624990	+	0.780633i	$0.714897\pi$
$564$	0	0
$565$	9.01067	0.379082
$566$	47.5075	1.99689
$567$	0	0
$568$	−8.06783	−0.338519
$569$	−42.3253	−1.77437	−0.887184	−	0.461417i	$-0.847341\pi$
$569$	−42.3253	−1.77437	−0.887184	+	0.461417i	$0.847341\pi$
$570$	0	0
$571$	13.8865	0.581133	0.290566	−	0.956855i	$-0.406156\pi$
$571$	13.8865	0.581133	0.290566	+	0.956855i	$0.406156\pi$
$572$	10.3317	0.431991
$573$	0	0
$574$	−0.396693	−0.0165576
$575$	35.7012	1.48884
$576$	0	0
$577$	45.2284	1.88288	0.941442	−	0.337175i	$-0.109472\pi$
$577$	45.2284	1.88288	0.941442	+	0.337175i	$0.109472\pi$
$578$	−32.0563	−1.33336
$579$	0	0
$580$	9.00145	0.373765
$581$	23.1202	0.959188
$582$	0	0
$583$	−7.37462	−0.305426
$584$	−7.22328	−0.298901
$585$	0	0
$586$	−53.3489	−2.20382
$587$	27.6000	1.13918	0.569588	−	0.821931i	$-0.307103\pi$
$587$	27.6000	1.13918	0.569588	+	0.821931i	$0.307103\pi$
$588$	0	0
$589$	−4.58771	−0.189033
$590$	−10.3668	−0.426794
$591$	0	0
$592$	−15.3977	−0.632842
$593$	−43.2245	−1.77502	−0.887508	−	0.460793i	$-0.847565\pi$
$593$	−43.2245	−1.77502	−0.887508	+	0.460793i	$0.847565\pi$
$594$	0	0
$595$	0.862451	0.0353570
$596$	9.58147	0.392472
$597$	0	0
$598$	−70.0091	−2.86288
$599$	−3.01155	−0.123049	−0.0615244	−	0.998106i	$-0.519596\pi$
$599$	−3.01155	−0.123049	−0.0615244	+	0.998106i	$0.519596\pi$
$600$	0	0
$601$	−28.8625	−1.17732	−0.588662	−	0.808379i	$-0.700345\pi$
$601$	−28.8625	−1.17732	−0.588662	+	0.808379i	$0.700345\pi$
$602$	−0.771671	−0.0314510
$603$	0	0
$604$	−13.4240	−0.546215
$605$	−0.494134	−0.0200894
$606$	0	0
$607$	−0.313316	−0.0127171	−0.00635854	−	0.999980i	$-0.502024\pi$
$607$	−0.313316	−0.0127171	−0.00635854	+	0.999980i	$0.502024\pi$
$608$	12.0244	0.487653
$609$	0	0
$610$	−3.45691	−0.139966
$611$	28.6213	1.15789
$612$	0	0
$613$	29.4370	1.18895	0.594474	−	0.804115i	$-0.297360\pi$
$613$	29.4370	1.18895	0.594474	+	0.804115i	$0.297360\pi$
$614$	−19.0002	−0.766784
$615$	0	0
$616$	−0.865214	−0.0348605
$617$	4.27242	0.172001	0.0860005	−	0.996295i	$-0.472591\pi$
$617$	4.27242	0.172001	0.0860005	+	0.996295i	$0.472591\pi$
$618$	0	0
$619$	38.9449	1.56533	0.782664	−	0.622444i	$-0.213860\pi$
$619$	38.9449	1.56533	0.782664	+	0.622444i	$0.213860\pi$
$620$	−3.51047	−0.140984
$621$	0	0
$622$	42.6720	1.71099
$623$	−0.116370	−0.00466228
$624$	0	0
$625$	21.3971	0.855884
$626$	−0.379067	−0.0151506
$627$	0	0
$628$	13.1804	0.525954
$629$	5.74530	0.229080
$630$	0	0
$631$	45.5446	1.81310	0.906550	−	0.422098i	$-0.138706\pi$
$631$	45.5446	1.81310	0.906550	+	0.422098i	$0.138706\pi$
$632$	−3.80251	−0.151256
$633$	0	0
$634$	−20.5241	−0.815116
$635$	0.0493229	0.00195732
$636$	0	0
$637$	−22.5625	−0.893959
$638$	−16.4435	−0.651004
$639$	0	0
$640$	2.40071	0.0948963
$641$	6.50230	0.256825	0.128413	−	0.991721i	$-0.459012\pi$
$641$	6.50230	0.256825	0.128413	+	0.991721i	$0.459012\pi$
$642$	0	0
$643$	47.2951	1.86514	0.932569	−	0.360992i	$-0.117562\pi$
$643$	47.2951	1.86514	0.932569	+	0.360992i	$0.117562\pi$
$644$	24.2886	0.957104
$645$	0	0
$646$	−3.80714	−0.149790
$647$	−24.3774	−0.958374	−0.479187	−	0.877713i	$-0.659068\pi$
$647$	−24.3774	−0.958374	−0.479187	+	0.877713i	$0.659068\pi$
$648$	0	0
$649$	10.1217	0.397313
$650$	−44.3532	−1.73968
$651$	0	0
$652$	−38.3468	−1.50178
$653$	28.9412	1.13256	0.566279	−	0.824214i	$-0.308382\pi$
$653$	28.9412	1.13256	0.566279	+	0.824214i	$0.308382\pi$
$654$	0	0
$655$	4.52556	0.176828
$656$	−0.450907	−0.0176050
$657$	0	0
$658$	−18.5784	−0.724261
$659$	−25.7465	−1.00294	−0.501471	−	0.865175i	$-0.667207\pi$
$659$	−25.7465	−1.00294	−0.501471	+	0.865175i	$0.667207\pi$
$660$	0	0
$661$	13.7071	0.533146	0.266573	−	0.963815i	$-0.414109\pi$
$661$	13.7071	0.533146	0.266573	+	0.963815i	$0.414109\pi$
$662$	−18.7059	−0.727024
$663$	0	0
$664$	−10.0753	−0.390999
$665$	−1.03244	−0.0400363
$666$	0	0
$667$	59.5533	2.30591
$668$	−7.64454	−0.295776
$669$	0	0
$670$	−4.07091	−0.157273
$671$	3.37520	0.130298
$672$	0	0
$673$	10.5765	0.407692	0.203846	−	0.979003i	$-0.434656\pi$
$673$	10.5765	0.407692	0.203846	+	0.979003i	$0.434656\pi$
$674$	−22.8133	−0.878737
$675$	0	0
$676$	16.6353	0.639818
$677$	−47.9236	−1.84185	−0.920926	−	0.389737i	$-0.872566\pi$
$677$	−47.9236	−1.84185	−0.920926	+	0.389737i	$0.872566\pi$
$678$	0	0
$679$	−18.4054	−0.706333
$680$	−0.375839	−0.0144128
$681$	0	0
$682$	6.41279	0.245559
$683$	−28.8592	−1.10427	−0.552133	−	0.833756i	$-0.686186\pi$
$683$	−28.8592	−1.10427	−0.552133	+	0.833756i	$0.686186\pi$
$684$	0	0
$685$	0.672199	0.0256834
$686$	35.0898	1.33973
$687$	0	0
$688$	−0.877132	−0.0334403
$689$	−33.1813	−1.26411
$690$	0	0
$691$	41.6347	1.58386	0.791929	−	0.610614i	$-0.209077\pi$
$691$	41.6347	1.58386	0.791929	+	0.610614i	$0.209077\pi$
$692$	1.85720	0.0706000
$693$	0	0
$694$	51.9818	1.97320
$695$	−7.15008	−0.271218
$696$	0	0
$697$	0.168246	0.00637276
$698$	65.6202	2.48376
$699$	0	0
$700$	15.3877	0.581599
$701$	−6.23977	−0.235673	−0.117836	−	0.993033i	$-0.537596\pi$
$701$	−6.23977	−0.235673	−0.117836	+	0.993033i	$0.537596\pi$
$702$	0	0
$703$	−6.87771	−0.259398
$704$	−10.1684	−0.383237
$705$	0	0
$706$	23.0547	0.867676
$707$	−5.55267	−0.208830
$708$	0	0
$709$	−2.35124	−0.0883027	−0.0441513	−	0.999025i	$-0.514058\pi$
$709$	−2.35124	−0.0883027	−0.0441513	+	0.999025i	$0.514058\pi$
$710$	13.4571	0.505034
$711$	0	0
$712$	0.0507119	0.00190051
$713$	−23.2252	−0.869789
$714$	0	0
$715$	−2.22330	−0.0831468
$716$	−15.1601	−0.566559
$717$	0	0
$718$	−50.8419	−1.89740
$719$	−2.87468	−0.107207	−0.0536037	−	0.998562i	$-0.517071\pi$
$719$	−2.87468	−0.107207	−0.0536037	+	0.998562i	$0.517071\pi$
$720$	0	0
$721$	15.9788	0.595080
$722$	−34.8245	−1.29603
$723$	0	0
$724$	−17.4988	−0.650338
$725$	37.7291	1.40122
$726$	0	0
$727$	11.7667	0.436404	0.218202	−	0.975904i	$-0.429981\pi$
$727$	11.7667	0.436404	0.218202	+	0.975904i	$0.429981\pi$
$728$	−3.89294	−0.144282
$729$	0	0
$730$	12.0484	0.445930
$731$	0.327282	0.0121049
$732$	0	0
$733$	11.1070	0.410245	0.205123	−	0.978736i	$-0.434241\pi$
$733$	11.1070	0.410245	0.205123	+	0.978736i	$0.434241\pi$
$734$	−59.0127	−2.17820
$735$	0	0
$736$	60.8731	2.24381
$737$	3.97468	0.146409
$738$	0	0
$739$	0.846094	0.0311241	0.0155620	−	0.999879i	$-0.495046\pi$
$739$	0.846094	0.0311241	0.0155620	+	0.999879i	$0.495046\pi$
$740$	−5.26276	−0.193463
$741$	0	0
$742$	21.5383	0.790697
$743$	15.6750	0.575059	0.287529	−	0.957772i	$-0.407166\pi$
$743$	15.6750	0.575059	0.287529	+	0.957772i	$0.407166\pi$
$744$	0	0
$745$	−2.06185	−0.0755405
$746$	66.5384	2.43614
$747$	0	0
$748$	2.84433	0.103999
$749$	−14.7961	−0.540637
$750$	0	0
$751$	−27.2227	−0.993370	−0.496685	−	0.867931i	$-0.665450\pi$
$751$	−27.2227	−0.993370	−0.496685	+	0.867931i	$0.665450\pi$
$752$	−21.1174	−0.770073
$753$	0	0
$754$	−73.9858	−2.69440
$755$	2.88874	0.105132
$756$	0	0
$757$	−1.03820	−0.0377339	−0.0188670	−	0.999822i	$-0.506006\pi$
$757$	−1.03820	−0.0377339	−0.0188670	+	0.999822i	$0.506006\pi$
$758$	24.2106	0.879367
$759$	0	0
$760$	0.449917	0.0163202
$761$	−32.5316	−1.17927	−0.589635	−	0.807670i	$-0.700728\pi$
$761$	−32.5316	−1.17927	−0.589635	+	0.807670i	$0.700728\pi$
$762$	0	0
$763$	21.6529	0.783888
$764$	−1.04460	−0.0377921
$765$	0	0
$766$	37.6491	1.36032
$767$	45.5417	1.64441
$768$	0	0
$769$	47.9405	1.72878	0.864390	−	0.502823i	$-0.167705\pi$
$769$	47.9405	1.72878	0.864390	+	0.502823i	$0.167705\pi$
$770$	1.44317	0.0520082
$771$	0	0
$772$	35.1623	1.26552
$773$	22.3501	0.803877	0.401938	−	0.915667i	$-0.368337\pi$
$773$	22.3501	0.803877	0.401938	+	0.915667i	$0.368337\pi$
$774$	0	0
$775$	−14.7139	−0.528541
$776$	8.02069	0.287926
$777$	0	0
$778$	24.1709	0.866569
$779$	−0.201407	−0.00721616
$780$	0	0
$781$	−13.1390	−0.470149
$782$	−19.2736	−0.689222
$783$	0	0
$784$	16.6471	0.594539
$785$	−2.83631	−0.101232
$786$	0	0
$787$	43.2534	1.54182	0.770909	−	0.636945i	$-0.219802\pi$
$787$	43.2534	1.54182	0.770909	+	0.636945i	$0.219802\pi$
$788$	2.57021	0.0915598
$789$	0	0
$790$	6.34254	0.225657
$791$	25.6945	0.913592
$792$	0	0
$793$	15.1864	0.539284
$794$	−24.4354	−0.867181
$795$	0	0
$796$	−19.2839	−0.683500
$797$	−40.4863	−1.43410	−0.717050	−	0.697022i	$-0.754508\pi$
$797$	−40.4863	−1.43410	−0.717050	+	0.697022i	$0.754508\pi$
$798$	0	0
$799$	7.87947	0.278756
$800$	38.5653	1.36349
$801$	0	0
$802$	−66.9994	−2.36583
$803$	−11.7636	−0.415127
$804$	0	0
$805$	−5.22671	−0.184217
$806$	28.8537	1.01633
$807$	0	0
$808$	2.41974	0.0851263
$809$	−33.9667	−1.19421	−0.597103	−	0.802165i	$-0.703682\pi$
$809$	−33.9667	−1.19421	−0.597103	+	0.802165i	$0.703682\pi$
$810$	0	0
$811$	9.58136	0.336447	0.168224	−	0.985749i	$-0.446197\pi$
$811$	9.58136	0.336447	0.168224	+	0.985749i	$0.446197\pi$
$812$	25.6682	0.900778
$813$	0	0
$814$	9.61381	0.336964
$815$	8.25193	0.289052
$816$	0	0
$817$	−0.391789	−0.0137070
$818$	−53.2974	−1.86350
$819$	0	0
$820$	−0.154115	−0.00538192
$821$	51.5450	1.79893	0.899467	−	0.436990i	$-0.143955\pi$
$821$	51.5450	1.79893	0.899467	+	0.436990i	$0.143955\pi$
$822$	0	0
$823$	45.7030	1.59311	0.796553	−	0.604568i	$-0.206654\pi$
$823$	45.7030	1.59311	0.796553	+	0.604568i	$0.206654\pi$
$824$	−6.96323	−0.242576
$825$	0	0
$826$	−29.5616	−1.02858
$827$	42.1517	1.46576	0.732879	−	0.680359i	$-0.238176\pi$
$827$	42.1517	1.46576	0.732879	+	0.680359i	$0.238176\pi$
$828$	0	0
$829$	50.0343	1.73776	0.868881	−	0.495020i	$-0.164839\pi$
$829$	50.0343	1.73776	0.868881	+	0.495020i	$0.164839\pi$
$830$	16.8055	0.583329
$831$	0	0
$832$	−45.7518	−1.58616
$833$	−6.21148	−0.215215
$834$	0	0
$835$	1.64504	0.0569291
$836$	−3.40495	−0.117763
$837$	0	0
$838$	41.0324	1.41744
$839$	52.1590	1.80073	0.900364	−	0.435137i	$-0.143300\pi$
$839$	52.1590	1.80073	0.900364	+	0.435137i	$0.143300\pi$
$840$	0	0
$841$	33.9360	1.17021
$842$	−54.8766	−1.89117
$843$	0	0
$844$	−11.3627	−0.391121
$845$	−3.57977	−0.123148
$846$	0	0
$847$	−1.40906	−0.0484157
$848$	24.4819	0.840712
$849$	0	0
$850$	−12.2105	−0.418816
$851$	−34.8182	−1.19355
$852$	0	0
$853$	10.8624	0.371921	0.185960	−	0.982557i	$-0.440460\pi$
$853$	10.8624	0.371921	0.185960	+	0.982557i	$0.440460\pi$
$854$	−9.85762	−0.337321
$855$	0	0
$856$	6.44784	0.220383
$857$	−24.7152	−0.844254	−0.422127	−	0.906537i	$-0.638716\pi$
$857$	−24.7152	−0.844254	−0.422127	+	0.906537i	$0.638716\pi$
$858$	0	0
$859$	−31.3629	−1.07009	−0.535044	−	0.844824i	$-0.679705\pi$
$859$	−31.3629	−1.07009	−0.535044	+	0.844824i	$0.679705\pi$
$860$	−0.299794	−0.0102229
$861$	0	0
$862$	8.94901	0.304804
$863$	−1.80603	−0.0614778	−0.0307389	−	0.999527i	$-0.509786\pi$
$863$	−1.80603	−0.0614778	−0.0307389	+	0.999527i	$0.509786\pi$
$864$	0	0
$865$	−0.399654	−0.0135886
$866$	57.2363	1.94497
$867$	0	0
$868$	−10.0103	−0.339773
$869$	−6.19262	−0.210070
$870$	0	0
$871$	17.8837	0.605965
$872$	−9.43591	−0.319540
$873$	0	0
$874$	23.0724	0.780436
$875$	−6.79261	−0.229632
$876$	0	0
$877$	−26.7190	−0.902236	−0.451118	−	0.892464i	$-0.648975\pi$
$877$	−26.7190	−0.902236	−0.451118	+	0.892464i	$0.648975\pi$
$878$	33.0414	1.11509
$879$	0	0
$880$	1.64040	0.0552979
$881$	−41.4286	−1.39577	−0.697883	−	0.716212i	$-0.745874\pi$
$881$	−41.4286	−1.39577	−0.697883	+	0.716212i	$0.745874\pi$
$882$	0	0
$883$	−50.9268	−1.71382	−0.856911	−	0.515464i	$-0.827620\pi$
$883$	−50.9268	−1.71382	−0.856911	+	0.515464i	$0.827620\pi$
$884$	12.7978	0.430435
$885$	0	0
$886$	58.7491	1.97371
$887$	−35.4431	−1.19006	−0.595032	−	0.803702i	$-0.702860\pi$
$887$	−35.4431	−1.19006	−0.595032	+	0.803702i	$0.702860\pi$
$888$	0	0
$889$	0.140648	0.00471717
$890$	−0.0845869	−0.00283536
$891$	0	0
$892$	−35.6996	−1.19531
$893$	−9.43253	−0.315648
$894$	0	0
$895$	3.26233	0.109048
$896$	6.84578	0.228701
$897$	0	0
$898$	−15.6135	−0.521031
$899$	−24.5444	−0.818602
$900$	0	0
$901$	−9.13485	−0.304326
$902$	0.281531	0.00937396
$903$	0	0
$904$	−11.1972	−0.372412
$905$	3.76560	0.125173
$906$	0	0
$907$	−45.5762	−1.51333	−0.756666	−	0.653802i	$-0.773173\pi$
$907$	−45.5762	−1.51333	−0.756666	+	0.653802i	$0.773173\pi$
$908$	8.57022	0.284413
$909$	0	0
$910$	6.49338	0.215254
$911$	−59.1334	−1.95918	−0.979588	−	0.201017i	$-0.935575\pi$
$911$	−59.1334	−1.95918	−0.979588	+	0.201017i	$0.935575\pi$
$912$	0	0
$913$	−16.4083	−0.543035
$914$	−18.2985	−0.605259
$915$	0	0
$916$	−6.26163	−0.206890
$917$	12.9050	0.426159
$918$	0	0
$919$	33.5000	1.10506	0.552531	−	0.833492i	$-0.313662\pi$
$919$	33.5000	1.10506	0.552531	+	0.833492i	$0.313662\pi$
$920$	2.27770	0.0750934
$921$	0	0
$922$	56.7665	1.86951
$923$	−59.1174	−1.94587
$924$	0	0
$925$	−22.0586	−0.725282
$926$	47.0422	1.54590
$927$	0	0
$928$	64.3309	2.11177
$929$	19.0137	0.623820	0.311910	−	0.950112i	$-0.399031\pi$
$929$	19.0137	0.623820	0.311910	+	0.950112i	$0.399031\pi$
$930$	0	0
$931$	7.43577	0.243697
$932$	−50.0168	−1.63836
$933$	0	0
$934$	16.9465	0.554507
$935$	−0.612077	−0.0200171
$936$	0	0
$937$	50.7291	1.65725	0.828623	−	0.559807i	$-0.189125\pi$
$937$	50.7291	1.65725	0.828623	+	0.559807i	$0.189125\pi$
$938$	−11.6085	−0.379030
$939$	0	0
$940$	−7.21769	−0.235415
$941$	−29.7492	−0.969798	−0.484899	−	0.874570i	$-0.661144\pi$
$941$	−29.7492	−0.969798	−0.484899	+	0.874570i	$0.661144\pi$
$942$	0	0
$943$	−1.01962	−0.0332033
$944$	−33.6016	−1.09364
$945$	0	0
$946$	0.547652	0.0178057
$947$	31.6292	1.02781	0.513905	−	0.857847i	$-0.328198\pi$
$947$	31.6292	1.02781	0.513905	+	0.857847i	$0.328198\pi$
$948$	0	0
$949$	−52.9289	−1.71814
$950$	14.6172	0.474244
$951$	0	0
$952$	−1.07173	−0.0347350
$953$	−4.93499	−0.159860	−0.0799299	−	0.996800i	$-0.525470\pi$
$953$	−4.93499	−0.159860	−0.0799299	+	0.996800i	$0.525470\pi$
$954$	0	0
$955$	0.224789	0.00727399
$956$	0.599569	0.0193914
$957$	0	0
$958$	−38.7146	−1.25081
$959$	1.91682	0.0618974
$960$	0	0
$961$	−21.4279	−0.691224
$962$	43.2563	1.39464
$963$	0	0
$964$	44.9039	1.44626
$965$	−7.56664	−0.243579
$966$	0	0
$967$	−16.7250	−0.537839	−0.268920	−	0.963163i	$-0.586667\pi$
$967$	−16.7250	−0.537839	−0.268920	+	0.963163i	$0.586667\pi$
$968$	0.614038	0.0197359
$969$	0	0
$970$	−13.3784	−0.429556
$971$	−26.9057	−0.863444	−0.431722	−	0.902007i	$-0.642094\pi$
$971$	−26.9057	−0.863444	−0.431722	+	0.902007i	$0.642094\pi$
$972$	0	0
$973$	−20.3889	−0.653639
$974$	−64.4387	−2.06475
$975$	0	0
$976$	−11.2048	−0.358658
$977$	−40.7012	−1.30215	−0.651073	−	0.759015i	$-0.725681\pi$
$977$	−40.7012	−1.30215	−0.651073	+	0.759015i	$0.725681\pi$
$978$	0	0
$979$	0.0825875	0.00263951
$980$	5.68978	0.181753
$981$	0	0
$982$	29.3845	0.937699
$983$	34.0406	1.08573	0.542864	−	0.839821i	$-0.317340\pi$
$983$	34.0406	1.08573	0.542864	+	0.839821i	$0.317340\pi$
$984$	0	0
$985$	−0.553088	−0.0176228
$986$	−20.3684	−0.648661
$987$	0	0
$988$	−15.3202	−0.487401
$989$	−1.98342	−0.0630692
$990$	0	0
$991$	−22.9593	−0.729326	−0.364663	−	0.931140i	$-0.618816\pi$
$991$	−22.9593	−0.729326	−0.364663	+	0.931140i	$0.618816\pi$
$992$	−25.0884	−0.796557
$993$	0	0
$994$	38.3737	1.21714
$995$	4.14974	0.131556
$996$	0	0
$997$	−23.1209	−0.732248	−0.366124	−	0.930566i	$-0.619315\pi$
$997$	−23.1209	−0.732248	−0.366124	+	0.930566i	$0.619315\pi$
$998$	89.7856	2.84211
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8019.2.a.c.1.19	✓	21
3.2	odd	2		8019.2.a.f.1.3	yes	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8019.2.a.c.1.19	✓	21	1.1	even	1	trivial
8019.2.a.f.1.3	yes	21	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 8019 = 3^{6} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8019.a (trivial)

\(f(q)\)	\(=\)	\(q+2.07274 q^{2} +2.29625 q^{4} -0.494134 q^{5} -1.40906 q^{7} +0.614038 q^{8} +O(q^{10})\)	\(q+2.07274 q^{2} +2.29625 q^{4} -0.494134 q^{5} -1.40906 q^{7} +0.614038 q^{8} -1.02421 q^{10} +1.00000 q^{11} +4.49939 q^{13} -2.92060 q^{14} -3.31975 q^{16} +1.23869 q^{17} -1.48283 q^{19} -1.13465 q^{20} +2.07274 q^{22} -7.50682 q^{23} -4.75583 q^{25} +9.32607 q^{26} -3.23554 q^{28} -7.93322 q^{29} +3.09387 q^{31} -8.10905 q^{32} +2.56748 q^{34} +0.696261 q^{35} +4.63822 q^{37} -3.07353 q^{38} -0.303417 q^{40} +0.135826 q^{41} +0.264216 q^{43} +2.29625 q^{44} -15.5597 q^{46} +6.36115 q^{47} -5.01456 q^{49} -9.85760 q^{50} +10.3317 q^{52} -7.37462 q^{53} -0.494134 q^{55} -0.865214 q^{56} -16.4435 q^{58} +10.1217 q^{59} +3.37520 q^{61} +6.41279 q^{62} -10.1684 q^{64} -2.22330 q^{65} +3.97468 q^{67} +2.84433 q^{68} +1.44317 q^{70} -13.1390 q^{71} -11.7636 q^{73} +9.61381 q^{74} -3.40495 q^{76} -1.40906 q^{77} -6.19262 q^{79} +1.64040 q^{80} +0.281531 q^{82} -16.4083 q^{83} -0.612077 q^{85} +0.547652 q^{86} +0.614038 q^{88} +0.0825875 q^{89} -6.33989 q^{91} -17.2375 q^{92} +13.1850 q^{94} +0.732718 q^{95} +13.0622 q^{97} -10.3939 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q - 6 q^{2} + 18 q^{4} - 12 q^{5} - 18 q^{8}+O(q^{10}) \) 21 * q - 6 * q^2 + 18 * q^4 - 12 * q^5 - 18 * q^8	\( 21 q - 6 q^{2} + 18 q^{4} - 12 q^{5} - 18 q^{8} + 15 q^{10} + 21 q^{11} + 3 q^{13} - 24 q^{14} + 12 q^{16} - 12 q^{17} - 12 q^{19} - 15 q^{20} - 6 q^{22} + 15 q^{25} - 15 q^{26} + 42 q^{28} - 27 q^{29} + 6 q^{31} - 42 q^{32} - 6 q^{34} - 42 q^{35} + 3 q^{37} - 27 q^{38} + 30 q^{40} - 24 q^{41} + 6 q^{43} + 18 q^{44} - 51 q^{46} - 24 q^{47} - 9 q^{49} + 3 q^{50} + 9 q^{52} - 12 q^{53} - 12 q^{55} - 45 q^{56} + 12 q^{58} - 12 q^{59} - 30 q^{61} - 9 q^{62} + 42 q^{64} + 18 q^{67} - 30 q^{68} + 21 q^{70} - 36 q^{71} - 39 q^{73} - 27 q^{76} + 27 q^{79} - 78 q^{80} + 63 q^{82} - 42 q^{83} + 36 q^{85} - 42 q^{86} - 18 q^{88} - 36 q^{89} - 21 q^{91} - 6 q^{92} + 42 q^{94} - 24 q^{95} + 24 q^{97} - 69 q^{98}+O(q^{100}) \) 21 * q - 6 * q^2 + 18 * q^4 - 12 * q^5 - 18 * q^8 + 15 * q^10 + 21 * q^11 + 3 * q^13 - 24 * q^14 + 12 * q^16 - 12 * q^17 - 12 * q^19 - 15 * q^20 - 6 * q^22 + 15 * q^25 - 15 * q^26 + 42 * q^28 - 27 * q^29 + 6 * q^31 - 42 * q^32 - 6 * q^34 - 42 * q^35 + 3 * q^37 - 27 * q^38 + 30 * q^40 - 24 * q^41 + 6 * q^43 + 18 * q^44 - 51 * q^46 - 24 * q^47 - 9 * q^49 + 3 * q^50 + 9 * q^52 - 12 * q^53 - 12 * q^55 - 45 * q^56 + 12 * q^58 - 12 * q^59 - 30 * q^61 - 9 * q^62 + 42 * q^64 + 18 * q^67 - 30 * q^68 + 21 * q^70 - 36 * q^71 - 39 * q^73 - 27 * q^76 + 27 * q^79 - 78 * q^80 + 63 * q^82 - 42 * q^83 + 36 * q^85 - 42 * q^86 - 18 * q^88 - 36 * q^89 - 21 * q^91 - 6 * q^92 + 42 * q^94 - 24 * q^95 + 24 * q^97 - 69 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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