LMFDB - Embedded newform 1666.2.a.v.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1666,2,Mod(1,1666)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1666, 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("1666.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1666 = 2 \cdot 7^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1666.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:	$13.3030769767$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.4352.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 6x^{2} - 4x + 2 $ x^4 - 6x^2 - 4x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.27133$ of defining polynomial
Character	$\chi$	$=$	1666.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.68554 q^{3} +1.00000 q^{4} -1.11239 q^{5} +2.68554 q^{6} -1.00000 q^{8} +4.21215 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.68554 q^{3} +1.00000 q^{4} -1.11239 q^{5} +2.68554 q^{6} -1.00000 q^{8} +4.21215 q^{9} +1.11239 q^{10} -1.55710 q^{11} -2.68554 q^{12} +1.63899 q^{13} +2.98737 q^{15} +1.00000 q^{16} -1.00000 q^{17} -4.21215 q^{18} -4.18165 q^{19} -1.11239 q^{20} +1.55710 q^{22} +3.03049 q^{23} +2.68554 q^{24} -3.76259 q^{25} -1.63899 q^{26} -3.25527 q^{27} +9.69562 q^{29} -2.98737 q^{30} -0.426845 q^{31} -1.00000 q^{32} +4.18165 q^{33} +1.00000 q^{34} +4.21215 q^{36} +8.44035 q^{37} +4.18165 q^{38} -4.40158 q^{39} +1.11239 q^{40} -1.97729 q^{41} +7.88163 q^{43} -1.55710 q^{44} -4.68554 q^{45} -3.03049 q^{46} -0.871553 q^{47} -2.68554 q^{48} +3.76259 q^{50} +2.68554 q^{51} +1.63899 q^{52} -0.735321 q^{53} +3.25527 q^{54} +1.73210 q^{55} +11.2300 q^{57} -9.69562 q^{58} -6.58579 q^{59} +2.98737 q^{60} -1.14451 q^{61} +0.426845 q^{62} +1.00000 q^{64} -1.82320 q^{65} -4.18165 q^{66} +2.03212 q^{67} -1.00000 q^{68} -8.13853 q^{69} -11.3101 q^{71} -4.21215 q^{72} +10.5174 q^{73} -8.44035 q^{74} +10.1046 q^{75} -4.18165 q^{76} +4.40158 q^{78} -5.97474 q^{79} -1.11239 q^{80} -3.89426 q^{81} +1.97729 q^{82} -11.1284 q^{83} +1.11239 q^{85} -7.88163 q^{86} -26.0380 q^{87} +1.55710 q^{88} -13.0101 q^{89} +4.68554 q^{90} +3.03049 q^{92} +1.14631 q^{93} +0.871553 q^{94} +4.65162 q^{95} +2.68554 q^{96} +4.65162 q^{97} -6.55872 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 4 q^{4} - 4 q^{5} - 4 q^{8}+O(q^{10}) $ 4 * q - 4 * q^2 + 4 * q^4 - 4 * q^5 - 4 * q^8	$ 4 q - 4 q^{2} + 4 q^{4} - 4 q^{5} - 4 q^{8} + 4 q^{10} - 4 q^{15} + 4 q^{16} - 4 q^{17} - 4 q^{20} + 12 q^{23} - 12 q^{27} + 4 q^{30} - 12 q^{31} - 4 q^{32} + 4 q^{34} - 4 q^{37} + 4 q^{39} + 4 q^{40} - 20 q^{41} + 8 q^{43} - 8 q^{45} - 12 q^{46} - 8 q^{47} + 12 q^{54} - 8 q^{55} + 12 q^{57} - 32 q^{59} - 4 q^{60} + 4 q^{61} + 12 q^{62} + 4 q^{64} - 28 q^{65} - 4 q^{68} - 24 q^{71} + 4 q^{74} + 28 q^{75} - 4 q^{78} + 8 q^{79} - 4 q^{80} - 8 q^{81} + 20 q^{82} - 40 q^{83} + 4 q^{85} - 8 q^{86} - 32 q^{87} - 24 q^{89} + 8 q^{90} + 12 q^{92} - 16 q^{93} + 8 q^{94} + 28 q^{95} + 28 q^{97} - 12 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 + 4 * q^4 - 4 * q^5 - 4 * q^8 + 4 * q^10 - 4 * q^15 + 4 * q^16 - 4 * q^17 - 4 * q^20 + 12 * q^23 - 12 * q^27 + 4 * q^30 - 12 * q^31 - 4 * q^32 + 4 * q^34 - 4 * q^37 + 4 * q^39 + 4 * q^40 - 20 * q^41 + 8 * q^43 - 8 * q^45 - 12 * q^46 - 8 * q^47 + 12 * q^54 - 8 * q^55 + 12 * q^57 - 32 * q^59 - 4 * q^60 + 4 * q^61 + 12 * q^62 + 4 * q^64 - 28 * q^65 - 4 * q^68 - 24 * q^71 + 4 * q^74 + 28 * q^75 - 4 * q^78 + 8 * q^79 - 4 * q^80 - 8 * q^81 + 20 * q^82 - 40 * q^83 + 4 * q^85 - 8 * q^86 - 32 * q^87 - 24 * q^89 + 8 * q^90 + 12 * q^92 - 16 * q^93 + 8 * q^94 + 28 * q^95 + 28 * q^97 - 12 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.68554	−1.55050	−0.775250	−	0.631655i	$-0.782376\pi$
$3$	−2.68554	−1.55050	−0.775250	+	0.631655i	$0.782376\pi$
$4$	1.00000	0.500000
$5$	−1.11239	−0.497475	−0.248738	−	0.968571i	$-0.580016\pi$
$5$	−1.11239	−0.497475	−0.248738	+	0.968571i	$0.580016\pi$
$6$	2.68554	1.09637
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	4.21215	1.40405
$10$	1.11239	0.351768
$11$	−1.55710	−0.469482	−0.234741	−	0.972058i	$-0.575424\pi$
$11$	−1.55710	−0.469482	−0.234741	+	0.972058i	$0.575424\pi$
$12$	−2.68554	−0.775250
$13$	1.63899	0.454574	0.227287	−	0.973828i	$-0.427014\pi$
$13$	1.63899	0.454574	0.227287	+	0.973828i	$0.427014\pi$
$14$	0	0
$15$	2.98737	0.771335
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−4.21215	−0.992812
$19$	−4.18165	−0.959337	−0.479668	−	0.877450i	$-0.659243\pi$
$19$	−4.18165	−0.959337	−0.479668	+	0.877450i	$0.659243\pi$
$20$	−1.11239	−0.248738
$21$	0	0
$22$	1.55710	0.331974
$23$	3.03049	0.631902	0.315951	−	0.948776i	$-0.397677\pi$
$23$	3.03049	0.631902	0.315951	+	0.948776i	$0.397677\pi$
$24$	2.68554	0.548184
$25$	−3.76259	−0.752518
$26$	−1.63899	−0.321433
$27$	−3.25527	−0.626477
$28$	0	0
$29$	9.69562	1.80043	0.900216	−	0.435444i	$-0.143408\pi$
$29$	9.69562	1.80043	0.900216	+	0.435444i	$0.143408\pi$
$30$	−2.98737	−0.545416
$31$	−0.426845	−0.0766636	−0.0383318	−	0.999265i	$-0.512204\pi$
$31$	−0.426845	−0.0766636	−0.0383318	+	0.999265i	$0.512204\pi$
$32$	−1.00000	−0.176777
$33$	4.18165	0.727932
$34$	1.00000	0.171499
$35$	0	0
$36$	4.21215	0.702024
$37$	8.44035	1.38759	0.693793	−	0.720175i	$-0.255938\pi$
$37$	8.44035	1.38759	0.693793	+	0.720175i	$0.255938\pi$
$38$	4.18165	0.678353
$39$	−4.40158	−0.704817
$40$	1.11239	0.175884
$41$	−1.97729	−0.308801	−0.154400	−	0.988008i	$-0.549345\pi$
$41$	−1.97729	−0.308801	−0.154400	+	0.988008i	$0.549345\pi$
$42$	0	0
$43$	7.88163	1.20194	0.600969	−	0.799272i	$-0.294782\pi$
$43$	7.88163	1.20194	0.600969	+	0.799272i	$0.294782\pi$
$44$	−1.55710	−0.234741
$45$	−4.68554	−0.698480
$46$	−3.03049	−0.446822
$47$	−0.871553	−0.127129	−0.0635645	−	0.997978i	$-0.520247\pi$
$47$	−0.871553	−0.127129	−0.0635645	+	0.997978i	$0.520247\pi$
$48$	−2.68554	−0.387625
$49$	0	0
$50$	3.76259	0.532111
$51$	2.68554	0.376051
$52$	1.63899	0.227287
$53$	−0.735321	−0.101004	−0.0505021	−	0.998724i	$-0.516082\pi$
$53$	−0.735321	−0.101004	−0.0505021	+	0.998724i	$0.516082\pi$
$54$	3.25527	0.442986
$55$	1.73210	0.233556
$56$	0	0
$57$	11.2300	1.48745
$58$	−9.69562	−1.27310
$59$	−6.58579	−0.857396	−0.428698	−	0.903448i	$-0.641028\pi$
$59$	−6.58579	−0.857396	−0.428698	+	0.903448i	$0.641028\pi$
$60$	2.98737	0.385668
$61$	−1.14451	−0.146539	−0.0732695	−	0.997312i	$-0.523343\pi$
$61$	−1.14451	−0.146539	−0.0732695	+	0.997312i	$0.523343\pi$
$62$	0.426845	0.0542093
$63$	0	0
$64$	1.00000	0.125000
$65$	−1.82320	−0.226140
$66$	−4.18165	−0.514726
$67$	2.03212	0.248263	0.124131	−	0.992266i	$-0.460386\pi$
$67$	2.03212	0.248263	0.124131	+	0.992266i	$0.460386\pi$
$68$	−1.00000	−0.121268
$69$	−8.13853	−0.979763
$70$	0	0
$71$	−11.3101	−1.34226	−0.671131	−	0.741339i	$-0.734191\pi$
$71$	−11.3101	−1.34226	−0.671131	+	0.741339i	$0.734191\pi$
$72$	−4.21215	−0.496406
$73$	10.5174	1.23097	0.615484	−	0.788149i	$-0.288960\pi$
$73$	10.5174	1.23097	0.615484	+	0.788149i	$0.288960\pi$
$74$	−8.44035	−0.981171
$75$	10.1046	1.16678
$76$	−4.18165	−0.479668
$77$	0	0
$78$	4.40158	0.498381
$79$	−5.97474	−0.672210	−0.336105	−	0.941824i	$-0.609110\pi$
$79$	−5.97474	−0.672210	−0.336105	+	0.941824i	$0.609110\pi$
$80$	−1.11239	−0.124369
$81$	−3.89426	−0.432696
$82$	1.97729	0.218355
$83$	−11.1284	−1.22151	−0.610753	−	0.791821i	$-0.709133\pi$
$83$	−11.1284	−1.22151	−0.610753	+	0.791821i	$0.709133\pi$
$84$	0	0
$85$	1.11239	0.120655
$86$	−7.88163	−0.849898
$87$	−26.0380	−2.79157
$88$	1.55710	0.165987
$89$	−13.0101	−1.37907	−0.689533	−	0.724254i	$-0.742184\pi$
$89$	−13.0101	−1.37907	−0.689533	+	0.724254i	$0.742184\pi$
$90$	4.68554	0.493900
$91$	0	0
$92$	3.03049	0.315951
$93$	1.14631	0.118867
$94$	0.871553	0.0898938
$95$	4.65162	0.477246
$96$	2.68554	0.274092
$97$	4.65162	0.472301	0.236150	−	0.971717i	$-0.424114\pi$
$97$	4.65162	0.472301	0.236150	+	0.971717i	$0.424114\pi$
$98$	0	0
$99$	−6.55872	−0.659176
$100$	−3.76259	−0.376259
$101$	6.98482	0.695015	0.347508	−	0.937677i	$-0.387028\pi$
$101$	6.98482	0.695015	0.347508	+	0.937677i	$0.387028\pi$
$102$	−2.68554	−0.265908
$103$	17.4844	1.72278	0.861392	−	0.507940i	$-0.169593\pi$
$103$	17.4844	1.72278	0.861392	+	0.507940i	$0.169593\pi$
$104$	−1.63899	−0.160716
$105$	0	0
$106$	0.735321	0.0714207
$107$	−5.87498	−0.567956	−0.283978	−	0.958831i	$-0.591654\pi$
$107$	−5.87498	−0.567956	−0.283978	+	0.958831i	$0.591654\pi$
$108$	−3.25527	−0.313239
$109$	5.86557	0.561820	0.280910	−	0.959734i	$-0.409364\pi$
$109$	5.86557	0.561820	0.280910	+	0.959734i	$0.409364\pi$
$110$	−1.73210	−0.165149
$111$	−22.6669	−2.15145
$112$	0	0
$113$	−17.2754	−1.62514	−0.812568	−	0.582867i	$-0.801931\pi$
$113$	−17.2754	−1.62514	−0.812568	+	0.582867i	$0.801931\pi$
$114$	−11.2300	−1.05179
$115$	−3.37109	−0.314356
$116$	9.69562	0.900216
$117$	6.90367	0.638244
$118$	6.58579	0.606271
$119$	0	0
$120$	−2.98737	−0.272708
$121$	−8.57545	−0.779586
$122$	1.14451	0.103619
$123$	5.31010	0.478795
$124$	−0.426845	−0.0383318
$125$	9.74741	0.871835
$126$	0	0
$127$	−8.26535	−0.733431	−0.366716	−	0.930333i	$-0.619518\pi$
$127$	−8.26535	−0.733431	−0.366716	+	0.930333i	$0.619518\pi$
$128$	−1.00000	−0.0883883
$129$	−21.1665	−1.86360
$130$	1.82320	0.159905
$131$	−16.6376	−1.45363	−0.726816	−	0.686833i	$-0.759001\pi$
$131$	−16.6376	−1.45363	−0.726816	+	0.686833i	$0.759001\pi$
$132$	4.18165	0.363966
$133$	0	0
$134$	−2.03212	−0.175548
$135$	3.62113	0.311657
$136$	1.00000	0.0857493
$137$	−21.9543	−1.87568	−0.937842	−	0.347062i	$-0.887179\pi$
$137$	−21.9543	−1.87568	−0.937842	+	0.347062i	$0.887179\pi$
$138$	8.13853	0.692797
$139$	7.15781	0.607117	0.303559	−	0.952813i	$-0.401825\pi$
$139$	7.15781	0.607117	0.303559	+	0.952813i	$0.401825\pi$
$140$	0	0
$141$	2.34059	0.197114
$142$	11.3101	0.949122
$143$	−2.55207	−0.213415
$144$	4.21215	0.351012
$145$	−10.7853	−0.895671
$146$	−10.5174	−0.870426
$147$	0	0
$148$	8.44035	0.693793
$149$	−0.231632	−0.0189760	−0.00948801	−	0.999955i	$-0.503020\pi$
$149$	−0.231632	−0.0189760	−0.00948801	+	0.999955i	$0.503020\pi$
$150$	−10.1046	−0.825037
$151$	−18.5222	−1.50732	−0.753659	−	0.657265i	$-0.771713\pi$
$151$	−18.5222	−1.50732	−0.753659	+	0.657265i	$0.771713\pi$
$152$	4.18165	0.339177
$153$	−4.21215	−0.340532
$154$	0	0
$155$	0.474817	0.0381382
$156$	−4.40158	−0.352409
$157$	15.5527	1.24124	0.620622	−	0.784110i	$-0.286880\pi$
$157$	15.5527	1.24124	0.620622	+	0.784110i	$0.286880\pi$
$158$	5.97474	0.475325
$159$	1.97474	0.156607
$160$	1.11239	0.0879420
$161$	0	0
$162$	3.89426	0.305962
$163$	−15.9273	−1.24752	−0.623759	−	0.781616i	$-0.714396\pi$
$163$	−15.9273	−1.24752	−0.623759	+	0.781616i	$0.714396\pi$
$164$	−1.97729	−0.154400
$165$	−4.65162	−0.362128
$166$	11.1284	0.863735
$167$	−14.5333	−1.12462	−0.562308	−	0.826928i	$-0.690087\pi$
$167$	−14.5333	−1.12462	−0.562308	+	0.826928i	$0.690087\pi$
$168$	0	0
$169$	−10.3137	−0.793362
$170$	−1.11239	−0.0853163
$171$	−17.6137	−1.34696
$172$	7.88163	0.600969
$173$	−3.06081	−0.232709	−0.116354	−	0.993208i	$-0.537121\pi$
$173$	−3.06081	−0.232709	−0.116354	+	0.993208i	$0.537121\pi$
$174$	26.0380	1.97394
$175$	0	0
$176$	−1.55710	−0.117371
$177$	17.6864	1.32939
$178$	13.0101	0.975147
$179$	−19.4234	−1.45177	−0.725885	−	0.687816i	$-0.758570\pi$
$179$	−19.4234	−1.45177	−0.725885	+	0.687816i	$0.758570\pi$
$180$	−4.68554	−0.349240
$181$	−9.15781	−0.680695	−0.340347	−	0.940300i	$-0.610545\pi$
$181$	−9.15781	−0.680695	−0.340347	+	0.940300i	$0.610545\pi$
$182$	0	0
$183$	3.07362	0.227209
$184$	−3.03049	−0.223411
$185$	−9.38895	−0.690289
$186$	−1.14631	−0.0840516
$187$	1.55710	0.113866
$188$	−0.871553	−0.0635645
$189$	0	0
$190$	−4.65162	−0.337464
$191$	24.7623	1.79174	0.895870	−	0.444317i	$-0.146553\pi$
$191$	24.7623	1.79174	0.895870	+	0.444317i	$0.146553\pi$
$192$	−2.68554	−0.193812
$193$	12.3085	0.885984	0.442992	−	0.896526i	$-0.353917\pi$
$193$	12.3085	0.885984	0.442992	+	0.896526i	$0.353917\pi$
$194$	−4.65162	−0.333967
$195$	4.89627	0.350629
$196$	0	0
$197$	17.8114	1.26901	0.634506	−	0.772918i	$-0.281203\pi$
$197$	17.8114	1.26901	0.634506	+	0.772918i	$0.281203\pi$
$198$	6.55872	0.466108
$199$	−2.97891	−0.211169	−0.105585	−	0.994410i	$-0.533671\pi$
$199$	−2.97891	−0.211169	−0.105585	+	0.994410i	$0.533671\pi$
$200$	3.76259	0.266055
$201$	−5.45734	−0.384931
$202$	−6.98482	−0.491450
$203$	0	0
$204$	2.68554	0.188026
$205$	2.19951	0.153621
$206$	−17.4844	−1.21819
$207$	12.7649	0.887221
$208$	1.63899	0.113644
$209$	6.51124	0.450392
$210$	0	0
$211$	−5.92040	−0.407577	−0.203789	−	0.979015i	$-0.565326\pi$
$211$	−5.92040	−0.407577	−0.203789	+	0.979015i	$0.565326\pi$
$212$	−0.735321	−0.0505021
$213$	30.3738	2.08118
$214$	5.87498	0.401605
$215$	−8.76744	−0.597934
$216$	3.25527	0.221493
$217$	0	0
$218$	−5.86557	−0.397267
$219$	−28.2449	−1.90862
$220$	1.73210	0.116778
$221$	−1.63899	−0.110250
$222$	22.6669	1.52130
$223$	−16.4454	−1.10127	−0.550633	−	0.834748i	$-0.685614\pi$
$223$	−16.4454	−1.10127	−0.550633	+	0.834748i	$0.685614\pi$
$224$	0	0
$225$	−15.8486	−1.05657
$226$	17.2754	1.14914
$227$	−3.99240	−0.264985	−0.132492	−	0.991184i	$-0.542298\pi$
$227$	−3.99240	−0.264985	−0.132492	+	0.991184i	$0.542298\pi$
$228$	11.2300	0.743726
$229$	−29.9128	−1.97669	−0.988347	−	0.152220i	$-0.951358\pi$
$229$	−29.9128	−1.97669	−0.988347	+	0.152220i	$0.951358\pi$
$230$	3.37109	0.222283
$231$	0	0
$232$	−9.69562	−0.636549
$233$	−7.52157	−0.492755	−0.246377	−	0.969174i	$-0.579240\pi$
$233$	−7.52157	−0.492755	−0.246377	+	0.969174i	$0.579240\pi$
$234$	−6.90367	−0.451307
$235$	0.969506	0.0632436
$236$	−6.58579	−0.428698
$237$	16.0454	1.04226
$238$	0	0
$239$	−7.29355	−0.471781	−0.235890	−	0.971780i	$-0.575801\pi$
$239$	−7.29355	−0.471781	−0.235890	+	0.971780i	$0.575801\pi$
$240$	2.98737	0.192834
$241$	24.2161	1.55989	0.779947	−	0.625846i	$-0.215246\pi$
$241$	24.2161	1.55989	0.779947	+	0.625846i	$0.215246\pi$
$242$	8.57545	0.551251
$243$	20.2240	1.29737
$244$	−1.14451	−0.0732695
$245$	0	0
$246$	−5.31010	−0.338560
$247$	−6.85369	−0.436090
$248$	0.426845	0.0271047
$249$	29.8859	1.89394
$250$	−9.74741	−0.616480
$251$	−13.5239	−0.853619	−0.426809	−	0.904342i	$-0.640363\pi$
$251$	−13.5239	−0.853619	−0.426809	+	0.904342i	$0.640363\pi$
$252$	0	0
$253$	−4.71877	−0.296667
$254$	8.26535	0.518614
$255$	−2.98737	−0.187076
$256$	1.00000	0.0625000
$257$	−20.8807	−1.30250	−0.651251	−	0.758862i	$-0.725756\pi$
$257$	−20.8807	−1.30250	−0.651251	+	0.758862i	$0.725756\pi$
$258$	21.1665	1.31777
$259$	0	0
$260$	−1.82320	−0.113070
$261$	40.8394	2.52789
$262$	16.6376	1.02787
$263$	8.20436	0.505903	0.252951	−	0.967479i	$-0.418599\pi$
$263$	8.20436	0.505903	0.252951	+	0.967479i	$0.418599\pi$
$264$	−4.18165	−0.257363
$265$	0.817963	0.0502471
$266$	0	0
$267$	34.9391	2.13824
$268$	2.03212	0.124131
$269$	25.9061	1.57953	0.789763	−	0.613412i	$-0.210204\pi$
$269$	25.9061	1.57953	0.789763	+	0.613412i	$0.210204\pi$
$270$	−3.62113	−0.220375
$271$	−4.59909	−0.279375	−0.139687	−	0.990196i	$-0.544610\pi$
$271$	−4.59909	−0.279375	−0.139687	+	0.990196i	$0.544610\pi$
$272$	−1.00000	−0.0606339
$273$	0	0
$274$	21.9543	1.32631
$275$	5.85872	0.353294
$276$	−8.13853	−0.489882
$277$	27.0187	1.62340	0.811699	−	0.584076i	$-0.198543\pi$
$277$	27.0187	1.62340	0.811699	+	0.584076i	$0.198543\pi$
$278$	−7.15781	−0.429297
$279$	−1.79793	−0.107639
$280$	0	0
$281$	4.98376	0.297306	0.148653	−	0.988889i	$-0.452506\pi$
$281$	4.98376	0.297306	0.148653	+	0.988889i	$0.452506\pi$
$282$	−2.34059	−0.139380
$283$	14.6087	0.868397	0.434199	−	0.900817i	$-0.357032\pi$
$283$	14.6087	0.868397	0.434199	+	0.900817i	$0.357032\pi$
$284$	−11.3101	−0.671131
$285$	−12.4921	−0.739970
$286$	2.55207	0.150907
$287$	0	0
$288$	−4.21215	−0.248203
$289$	1.00000	0.0588235
$290$	10.7853	0.633335
$291$	−12.4921	−0.732302
$292$	10.5174	0.615484
$293$	−8.49954	−0.496548	−0.248274	−	0.968690i	$-0.579863\pi$
$293$	−8.49954	−0.496548	−0.248274	+	0.968690i	$0.579863\pi$
$294$	0	0
$295$	7.32595	0.426534
$296$	−8.44035	−0.490585
$297$	5.06877	0.294120
$298$	0.231632	0.0134181
$299$	4.96695	0.287246
$300$	10.1046	0.583390
$301$	0	0
$302$	18.5222	1.06584
$303$	−18.7580	−1.07762
$304$	−4.18165	−0.239834
$305$	1.27314	0.0728995
$306$	4.21215	0.240792
$307$	7.06746	0.403361	0.201681	−	0.979451i	$-0.435360\pi$
$307$	7.06746	0.403361	0.201681	+	0.979451i	$0.435360\pi$
$308$	0	0
$309$	−46.9550	−2.67118
$310$	−0.474817	−0.0269678
$311$	24.7623	1.40414	0.702072	−	0.712106i	$-0.252259\pi$
$311$	24.7623	1.40414	0.702072	+	0.712106i	$0.252259\pi$
$312$	4.40158	0.249191
$313$	−17.1318	−0.968347	−0.484173	−	0.874972i	$-0.660880\pi$
$313$	−17.1318	−0.968347	−0.484173	+	0.874972i	$0.660880\pi$
$314$	−15.5527	−0.877692
$315$	0	0
$316$	−5.97474	−0.336105
$317$	4.85065	0.272440	0.136220	−	0.990679i	$-0.456505\pi$
$317$	4.85065	0.272440	0.136220	+	0.990679i	$0.456505\pi$
$318$	−1.97474	−0.110738
$319$	−15.0970	−0.845271
$320$	−1.11239	−0.0621844
$321$	15.7775	0.880615
$322$	0	0
$323$	4.18165	0.232673
$324$	−3.89426	−0.216348
$325$	−6.16685	−0.342075
$326$	15.9273	0.882129
$327$	−15.7523	−0.871102
$328$	1.97729	0.109178
$329$	0	0
$330$	4.65162	0.256063
$331$	2.06784	0.113659	0.0568295	−	0.998384i	$-0.481901\pi$
$331$	2.06784	0.113659	0.0568295	+	0.998384i	$0.481901\pi$
$332$	−11.1284	−0.610753
$333$	35.5520	1.94824
$334$	14.5333	0.795224
$335$	−2.26050	−0.123505
$336$	0	0
$337$	−25.9112	−1.41147	−0.705736	−	0.708475i	$-0.749384\pi$
$337$	−25.9112	−1.41147	−0.705736	+	0.708475i	$0.749384\pi$
$338$	10.3137	0.560992
$339$	46.3939	2.51977
$340$	1.11239	0.0603277
$341$	0.664639	0.0359922
$342$	17.6137	0.952441
$343$	0	0
$344$	−7.88163	−0.424949
$345$	9.05320	0.487408
$346$	3.06081	0.164550
$347$	−8.75499	−0.469992	−0.234996	−	0.971996i	$-0.575508\pi$
$347$	−8.75499	−0.469992	−0.234996	+	0.971996i	$0.575508\pi$
$348$	−26.0380	−1.39578
$349$	7.27208	0.389265	0.194633	−	0.980876i	$-0.437649\pi$
$349$	7.27208	0.389265	0.194633	+	0.980876i	$0.437649\pi$
$350$	0	0
$351$	−5.33536	−0.284781
$352$	1.55710	0.0829935
$353$	9.65324	0.513790	0.256895	−	0.966439i	$-0.417300\pi$
$353$	9.65324	0.513790	0.256895	+	0.966439i	$0.417300\pi$
$354$	−17.6864	−0.940023
$355$	12.5812	0.667742
$356$	−13.0101	−0.689533
$357$	0	0
$358$	19.4234	1.02656
$359$	10.9789	0.579445	0.289722	−	0.957111i	$-0.406437\pi$
$359$	10.9789	0.579445	0.289722	+	0.957111i	$0.406437\pi$
$360$	4.68554	0.246950
$361$	−1.51379	−0.0796731
$362$	9.15781	0.481324
$363$	23.0297	1.20875
$364$	0	0
$365$	−11.6994	−0.612376
$366$	−3.07362	−0.160661
$367$	−17.1438	−0.894897	−0.447448	−	0.894310i	$-0.647667\pi$
$367$	−17.1438	−0.894897	−0.447448	+	0.894310i	$0.647667\pi$
$368$	3.03049	0.157975
$369$	−8.32863	−0.433571
$370$	9.38895	0.488108
$371$	0	0
$372$	1.14631	0.0594334
$373$	−9.74996	−0.504834	−0.252417	−	0.967619i	$-0.581225\pi$
$373$	−9.74996	−0.504834	−0.252417	+	0.967619i	$0.581225\pi$
$374$	−1.55710	−0.0805156
$375$	−26.1771	−1.35178
$376$	0.871553	0.0449469
$377$	15.8910	0.818430
$378$	0	0
$379$	−24.0243	−1.23404	−0.617022	−	0.786946i	$-0.711661\pi$
$379$	−24.0243	−1.23404	−0.617022	+	0.786946i	$0.711661\pi$
$380$	4.65162	0.238623
$381$	22.1970	1.13718
$382$	−24.7623	−1.26695
$383$	−1.43208	−0.0731757	−0.0365879	−	0.999330i	$-0.511649\pi$
$383$	−1.43208	−0.0731757	−0.0365879	+	0.999330i	$0.511649\pi$
$384$	2.68554	0.137046
$385$	0	0
$386$	−12.3085	−0.626485
$387$	33.1986	1.68758
$388$	4.65162	0.236150
$389$	−21.2073	−1.07525	−0.537626	−	0.843183i	$-0.680679\pi$
$389$	−21.2073	−1.07525	−0.537626	+	0.843183i	$0.680679\pi$
$390$	−4.89627	−0.247932
$391$	−3.03049	−0.153259
$392$	0	0
$393$	44.6809	2.25385
$394$	−17.8114	−0.897327
$395$	6.64623	0.334408
$396$	−6.55872	−0.329588
$397$	38.0742	1.91089	0.955446	−	0.295167i	$-0.0953754\pi$
$397$	38.0742	1.91089	0.955446	+	0.295167i	$0.0953754\pi$
$398$	2.97891	0.149319
$399$	0	0
$400$	−3.76259	−0.188130
$401$	19.4043	0.969003	0.484501	−	0.874791i	$-0.339001\pi$
$401$	19.4043	0.969003	0.484501	+	0.874791i	$0.339001\pi$
$402$	5.45734	0.272187
$403$	−0.699595	−0.0348493
$404$	6.98482	0.347508
$405$	4.33193	0.215256
$406$	0	0
$407$	−13.1424	−0.651447
$408$	−2.68554	−0.132954
$409$	−10.6692	−0.527559	−0.263780	−	0.964583i	$-0.584969\pi$
$409$	−10.6692	−0.527559	−0.263780	+	0.964583i	$0.584969\pi$
$410$	−2.19951	−0.108626
$411$	58.9593	2.90825
$412$	17.4844	0.861392
$413$	0	0
$414$	−12.7649	−0.627360
$415$	12.3792	0.607669
$416$	−1.63899	−0.0803581
$417$	−19.2226	−0.941335
$418$	−6.51124	−0.318475
$419$	31.7791	1.55251	0.776254	−	0.630420i	$-0.217117\pi$
$419$	31.7791	1.55251	0.776254	+	0.630420i	$0.217117\pi$
$420$	0	0
$421$	21.0922	1.02797	0.513985	−	0.857799i	$-0.328169\pi$
$421$	21.0922	1.02797	0.513985	+	0.857799i	$0.328169\pi$
$422$	5.92040	0.288201
$423$	−3.67111	−0.178495
$424$	0.735321	0.0357104
$425$	3.76259	0.182512
$426$	−30.3738	−1.47161
$427$	0	0
$428$	−5.87498	−0.283978
$429$	6.85369	0.330899
$430$	8.76744	0.422803
$431$	4.28471	0.206387	0.103194	−	0.994661i	$-0.467094\pi$
$431$	4.28471	0.206387	0.103194	+	0.994661i	$0.467094\pi$
$432$	−3.25527	−0.156619
$433$	34.2531	1.64610	0.823050	−	0.567970i	$-0.192271\pi$
$433$	34.2531	1.64610	0.823050	+	0.567970i	$0.192271\pi$
$434$	0	0
$435$	28.9644	1.38874
$436$	5.86557	0.280910
$437$	−12.6725	−0.606207
$438$	28.2449	1.34960
$439$	−12.1732	−0.580995	−0.290497	−	0.956876i	$-0.593821\pi$
$439$	−12.1732	−0.580995	−0.290497	+	0.956876i	$0.593821\pi$
$440$	−1.73210	−0.0825745
$441$	0	0
$442$	1.63899	0.0779589
$443$	−10.7541	−0.510944	−0.255472	−	0.966816i	$-0.582231\pi$
$443$	−10.7541	−0.510944	−0.255472	+	0.966816i	$0.582231\pi$
$444$	−22.6669	−1.07573
$445$	14.4723	0.686051
$446$	16.4454	0.778712
$447$	0.622058	0.0294223
$448$	0	0
$449$	−32.4192	−1.52996	−0.764978	−	0.644056i	$-0.777250\pi$
$449$	−32.4192	−1.52996	−0.764978	+	0.644056i	$0.777250\pi$
$450$	15.8486	0.747109
$451$	3.07883	0.144977
$452$	−17.2754	−0.812568
$453$	49.7423	2.33710
$454$	3.99240	0.187373
$455$	0	0
$456$	−11.2300	−0.525893
$457$	−37.9495	−1.77520	−0.887601	−	0.460614i	$-0.847629\pi$
$457$	−37.9495	−1.77520	−0.887601	+	0.460614i	$0.847629\pi$
$458$	29.9128	1.39773
$459$	3.25527	0.151943
$460$	−3.37109	−0.157178
$461$	−35.0876	−1.63419	−0.817097	−	0.576501i	$-0.804418\pi$
$461$	−35.0876	−1.63419	−0.817097	+	0.576501i	$0.804418\pi$
$462$	0	0
$463$	−39.3098	−1.82688	−0.913442	−	0.406970i	$-0.866585\pi$
$463$	−39.3098	−1.82688	−0.913442	+	0.406970i	$0.866585\pi$
$464$	9.69562	0.450108
$465$	−1.27514	−0.0591333
$466$	7.52157	0.348430
$467$	28.3610	1.31239	0.656195	−	0.754591i	$-0.272165\pi$
$467$	28.3610	1.31239	0.656195	+	0.754591i	$0.272165\pi$
$468$	6.90367	0.319122
$469$	0	0
$470$	−0.969506	−0.0447200
$471$	−41.7676	−1.92455
$472$	6.58579	0.303135
$473$	−12.2725	−0.564288
$474$	−16.0454	−0.736991
$475$	15.7338	0.721918
$476$	0	0
$477$	−3.09728	−0.141815
$478$	7.29355	0.333599
$479$	−35.8123	−1.63631	−0.818153	−	0.575001i	$-0.805002\pi$
$479$	−35.8123	−1.63631	−0.818153	+	0.575001i	$0.805002\pi$
$480$	−2.98737	−0.136354
$481$	13.8337	0.630761
$482$	−24.2161	−1.10301
$483$	0	0
$484$	−8.57545	−0.389793
$485$	−5.17441	−0.234958
$486$	−20.2240	−0.917381
$487$	31.0387	1.40650	0.703249	−	0.710944i	$-0.251732\pi$
$487$	31.0387	1.40650	0.703249	+	0.710944i	$0.251732\pi$
$488$	1.14451	0.0518093
$489$	42.7733	1.93428
$490$	0	0
$491$	28.4646	1.28459	0.642295	−	0.766458i	$-0.277982\pi$
$491$	28.4646	1.28459	0.642295	+	0.766458i	$0.277982\pi$
$492$	5.31010	0.239398
$493$	−9.69562	−0.436669
$494$	6.85369	0.308362
$495$	7.29585	0.327924
$496$	−0.426845	−0.0191659
$497$	0	0
$498$	−29.8859	−1.33922
$499$	−5.19583	−0.232597	−0.116299	−	0.993214i	$-0.537103\pi$
$499$	−5.19583	−0.232597	−0.116299	+	0.993214i	$0.537103\pi$
$500$	9.74741	0.435917
$501$	39.0297	1.74372
$502$	13.5239	0.603600
$503$	−27.8538	−1.24194	−0.620970	−	0.783834i	$-0.713261\pi$
$503$	−27.8538	−1.24194	−0.620970	+	0.783834i	$0.713261\pi$
$504$	0	0
$505$	−7.76983	−0.345753
$506$	4.71877	0.209775
$507$	27.6979	1.23011
$508$	−8.26535	−0.366716
$509$	−9.73571	−0.431528	−0.215764	−	0.976446i	$-0.569224\pi$
$509$	−9.73571	−0.431528	−0.215764	+	0.976446i	$0.569224\pi$
$510$	2.98737	0.132283
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	13.6124	0.601003
$514$	20.8807	0.921008
$515$	−19.4494	−0.857043
$516$	−21.1665	−0.931802
$517$	1.35709	0.0596848
$518$	0	0
$519$	8.21993	0.360815
$520$	1.82320	0.0799524
$521$	−28.8269	−1.26293	−0.631465	−	0.775404i	$-0.717546\pi$
$521$	−28.8269	−1.26293	−0.631465	+	0.775404i	$0.717546\pi$
$522$	−40.8394	−1.78749
$523$	−19.1068	−0.835482	−0.417741	−	0.908566i	$-0.637178\pi$
$523$	−19.1068	−0.835482	−0.417741	+	0.908566i	$0.637178\pi$
$524$	−16.6376	−0.726816
$525$	0	0
$526$	−8.20436	−0.357727
$527$	0.426845	0.0185937
$528$	4.18165	0.181983
$529$	−13.8161	−0.600700
$530$	−0.817963	−0.0355300
$531$	−27.7403	−1.20383
$532$	0	0
$533$	−3.24076	−0.140373
$534$	−34.9391	−1.51196
$535$	6.53526	0.282544
$536$	−2.03212	−0.0877741
$537$	52.1623	2.25097
$538$	−25.9061	−1.11689
$539$	0	0
$540$	3.62113	0.155829
$541$	−18.4498	−0.793217	−0.396609	−	0.917988i	$-0.629813\pi$
$541$	−18.4498	−0.793217	−0.396609	+	0.917988i	$0.629813\pi$
$542$	4.59909	0.197548
$543$	24.5937	1.05542
$544$	1.00000	0.0428746
$545$	−6.52480	−0.279492
$546$	0	0
$547$	−19.4578	−0.831957	−0.415978	−	0.909375i	$-0.636561\pi$
$547$	−19.4578	−0.831957	−0.415978	+	0.909375i	$0.636561\pi$
$548$	−21.9543	−0.937842
$549$	−4.82083	−0.205748
$550$	−5.85872	−0.249817
$551$	−40.5437	−1.72722
$552$	8.13853	0.346399
$553$	0	0
$554$	−27.0187	−1.14792
$555$	25.2144	1.07029
$556$	7.15781	0.303559
$557$	10.2890	0.435959	0.217980	−	0.975953i	$-0.430053\pi$
$557$	10.2890	0.435959	0.217980	+	0.975953i	$0.430053\pi$
$558$	1.79793	0.0761126
$559$	12.9179	0.546370
$560$	0	0
$561$	−4.18165	−0.176549
$562$	−4.98376	−0.210227
$563$	−37.6696	−1.58758	−0.793792	−	0.608189i	$-0.791896\pi$
$563$	−37.6696	−1.58758	−0.793792	+	0.608189i	$0.791896\pi$
$564$	2.34059	0.0985568
$565$	19.2170	0.808465
$566$	−14.6087	−0.614049
$567$	0	0
$568$	11.3101	0.474561
$569$	12.6170	0.528930	0.264465	−	0.964395i	$-0.414805\pi$
$569$	12.6170	0.528930	0.264465	+	0.964395i	$0.414805\pi$
$570$	12.4921	0.523238
$571$	−7.11144	−0.297604	−0.148802	−	0.988867i	$-0.547542\pi$
$571$	−7.11144	−0.297604	−0.148802	+	0.988867i	$0.547542\pi$
$572$	−2.55207	−0.106707
$573$	−66.5003	−2.77809
$574$	0	0
$575$	−11.4025	−0.475518
$576$	4.21215	0.175506
$577$	15.2362	0.634290	0.317145	−	0.948377i	$-0.397276\pi$
$577$	15.2362	0.634290	0.317145	+	0.948377i	$0.397276\pi$
$578$	−1.00000	−0.0415945
$579$	−33.0550	−1.37372
$580$	−10.7853	−0.447835
$581$	0	0
$582$	12.4921	0.517816
$583$	1.14497	0.0474197
$584$	−10.5174	−0.435213
$585$	−7.67956	−0.317511
$586$	8.49954	0.351113
$587$	−39.0338	−1.61110	−0.805550	−	0.592528i	$-0.798130\pi$
$587$	−39.0338	−1.61110	−0.805550	+	0.592528i	$0.798130\pi$
$588$	0	0
$589$	1.78492	0.0735462
$590$	−7.32595	−0.301605
$591$	−47.8334	−1.96760
$592$	8.44035	0.346896
$593$	4.60594	0.189143	0.0945717	−	0.995518i	$-0.469852\pi$
$593$	4.60594	0.189143	0.0945717	+	0.995518i	$0.469852\pi$
$594$	−5.06877	−0.207974
$595$	0	0
$596$	−0.231632	−0.00948801
$597$	8.00000	0.327418
$598$	−4.96695	−0.203114
$599$	7.94102	0.324461	0.162231	−	0.986753i	$-0.448131\pi$
$599$	7.94102	0.324461	0.162231	+	0.986753i	$0.448131\pi$
$600$	−10.1046	−0.412519
$601$	45.3180	1.84856	0.924280	−	0.381715i	$-0.124666\pi$
$601$	45.3180	1.84856	0.924280	+	0.381715i	$0.124666\pi$
$602$	0	0
$603$	8.55957	0.348573
$604$	−18.5222	−0.753659
$605$	9.53923	0.387825
$606$	18.7580	0.761993
$607$	17.2812	0.701423	0.350712	−	0.936483i	$-0.385940\pi$
$607$	17.2812	0.701423	0.350712	+	0.936483i	$0.385940\pi$
$608$	4.18165	0.169588
$609$	0	0
$610$	−1.27314	−0.0515477
$611$	−1.42847	−0.0577896
$612$	−4.21215	−0.170266
$613$	9.54210	0.385402	0.192701	−	0.981258i	$-0.438275\pi$
$613$	9.54210	0.385402	0.192701	+	0.981258i	$0.438275\pi$
$614$	−7.06746	−0.285219
$615$	−5.90689	−0.238189
$616$	0	0
$617$	−15.3328	−0.617276	−0.308638	−	0.951180i	$-0.599873\pi$
$617$	−15.3328	−0.617276	−0.308638	+	0.951180i	$0.599873\pi$
$618$	46.9550	1.88881
$619$	−28.3878	−1.14100	−0.570501	−	0.821297i	$-0.693251\pi$
$619$	−28.3878	−1.14100	−0.570501	+	0.821297i	$0.693251\pi$
$620$	0.474817	0.0190691
$621$	−9.86508	−0.395872
$622$	−24.7623	−0.992879
$623$	0	0
$624$	−4.40158	−0.176204
$625$	7.97005	0.318802
$626$	17.1318	0.684724
$627$	−17.4862	−0.698332
$628$	15.5527	0.620622
$629$	−8.44035	−0.336539
$630$	0	0
$631$	21.0095	0.836376	0.418188	−	0.908360i	$-0.362665\pi$
$631$	21.0095	0.836376	0.418188	+	0.908360i	$0.362665\pi$
$632$	5.97474	0.237662
$633$	15.8995	0.631948
$634$	−4.85065	−0.192644
$635$	9.19428	0.364864
$636$	1.97474	0.0783034
$637$	0	0
$638$	15.0970	0.597697
$639$	−47.6398	−1.88460
$640$	1.11239	0.0439710
$641$	−13.5479	−0.535110	−0.267555	−	0.963543i	$-0.586216\pi$
$641$	−13.5479	−0.535110	−0.267555	+	0.963543i	$0.586216\pi$
$642$	−15.7775	−0.622689
$643$	−4.09265	−0.161398	−0.0806991	−	0.996739i	$-0.525715\pi$
$643$	−4.09265	−0.161398	−0.0806991	+	0.996739i	$0.525715\pi$
$644$	0	0
$645$	23.5453	0.927097
$646$	−4.18165	−0.164525
$647$	−14.7243	−0.578872	−0.289436	−	0.957197i	$-0.593468\pi$
$647$	−14.7243	−0.578872	−0.289436	+	0.957197i	$0.593468\pi$
$648$	3.89426	0.152981
$649$	10.2547	0.402532
$650$	6.16685	0.241884
$651$	0	0
$652$	−15.9273	−0.623759
$653$	25.3344	0.991410	0.495705	−	0.868491i	$-0.334910\pi$
$653$	25.3344	0.991410	0.495705	+	0.868491i	$0.334910\pi$
$654$	15.7523	0.615962
$655$	18.5074	0.723146
$656$	−1.97729	−0.0772002
$657$	44.3008	1.72834
$658$	0	0
$659$	33.1022	1.28948	0.644740	−	0.764402i	$-0.276966\pi$
$659$	33.1022	1.28948	0.644740	+	0.764402i	$0.276966\pi$
$660$	−4.65162	−0.181064
$661$	13.1775	0.512544	0.256272	−	0.966605i	$-0.417506\pi$
$661$	13.1775	0.512544	0.256272	+	0.966605i	$0.417506\pi$
$662$	−2.06784	−0.0803690
$663$	4.40158	0.170943
$664$	11.1284	0.431868
$665$	0	0
$666$	−35.5520	−1.37761
$667$	29.3825	1.13770
$668$	−14.5333	−0.562308
$669$	44.1648	1.70751
$670$	2.26050	0.0873309
$671$	1.78211	0.0687974
$672$	0	0
$673$	−9.43208	−0.363580	−0.181790	−	0.983337i	$-0.558189\pi$
$673$	−9.43208	−0.363580	−0.181790	+	0.983337i	$0.558189\pi$
$674$	25.9112	0.998062
$675$	12.2483	0.471436
$676$	−10.3137	−0.396681
$677$	15.5739	0.598554	0.299277	−	0.954166i	$-0.403255\pi$
$677$	15.5739	0.598554	0.299277	+	0.954166i	$0.403255\pi$
$678$	−46.3939	−1.78175
$679$	0	0
$680$	−1.11239	−0.0426582
$681$	10.7218	0.410859
$682$	−0.664639	−0.0254503
$683$	−0.546760	−0.0209212	−0.0104606	−	0.999945i	$-0.503330\pi$
$683$	−0.546760	−0.0209212	−0.0104606	+	0.999945i	$0.503330\pi$
$684$	−17.6137	−0.673478
$685$	24.4217	0.933107
$686$	0	0
$687$	80.3321	3.06486
$688$	7.88163	0.300484
$689$	−1.20518	−0.0459139
$690$	−9.05320	−0.344650
$691$	−31.4537	−1.19655	−0.598277	−	0.801289i	$-0.704148\pi$
$691$	−31.4537	−1.19655	−0.598277	+	0.801289i	$0.704148\pi$
$692$	−3.06081	−0.116354
$693$	0	0
$694$	8.75499	0.332335
$695$	−7.96227	−0.302026
$696$	26.0380	0.986969
$697$	1.97729	0.0748952
$698$	−7.27208	−0.275252
$699$	20.1995	0.764016
$700$	0	0
$701$	−26.7146	−1.00900	−0.504499	−	0.863412i	$-0.668323\pi$
$701$	−26.7146	−1.00900	−0.504499	+	0.863412i	$0.668323\pi$
$702$	5.33536	0.201370
$703$	−35.2946	−1.33116
$704$	−1.55710	−0.0586853
$705$	−2.60365	−0.0980591
$706$	−9.65324	−0.363305
$707$	0	0
$708$	17.6864	0.664696
$709$	−49.3441	−1.85316	−0.926579	−	0.376101i	$-0.877265\pi$
$709$	−49.3441	−1.85316	−0.926579	+	0.376101i	$0.877265\pi$
$710$	−12.5812	−0.472165
$711$	−25.1665	−0.943816
$712$	13.0101	0.487573
$713$	−1.29355	−0.0484439
$714$	0	0
$715$	2.83889	0.106169
$716$	−19.4234	−0.725885
$717$	19.5872	0.731496
$718$	−10.9789	−0.409729
$719$	17.0935	0.637481	0.318740	−	0.947842i	$-0.396740\pi$
$719$	17.0935	0.637481	0.318740	+	0.947842i	$0.396740\pi$
$720$	−4.68554	−0.174620
$721$	0	0
$722$	1.51379	0.0563374
$723$	−65.0333	−2.41861
$724$	−9.15781	−0.340347
$725$	−36.4807	−1.35486
$726$	−23.0297	−0.854714
$727$	31.4939	1.16804	0.584021	−	0.811738i	$-0.301478\pi$
$727$	31.4939	1.16804	0.584021	+	0.811738i	$0.301478\pi$
$728$	0	0
$729$	−42.6297	−1.57888
$730$	11.6994	0.433016
$731$	−7.88163	−0.291513
$732$	3.07362	0.113604
$733$	11.7908	0.435504	0.217752	−	0.976004i	$-0.430128\pi$
$733$	11.7908	0.435504	0.217752	+	0.976004i	$0.430128\pi$
$734$	17.1438	0.632788
$735$	0	0
$736$	−3.03049	−0.111706
$737$	−3.16420	−0.116555
$738$	8.32863	0.306581
$739$	−6.62530	−0.243716	−0.121858	−	0.992548i	$-0.538885\pi$
$739$	−6.62530	−0.243716	−0.121858	+	0.992548i	$0.538885\pi$
$740$	−9.38895	−0.345145
$741$	18.4059	0.676157
$742$	0	0
$743$	7.27084	0.266741	0.133371	−	0.991066i	$-0.457420\pi$
$743$	7.27084	0.266741	0.133371	+	0.991066i	$0.457420\pi$
$744$	−1.14631	−0.0420258
$745$	0.257665	0.00944010
$746$	9.74996	0.356971
$747$	−46.8746	−1.71505
$748$	1.55710	0.0569331
$749$	0	0
$750$	26.1771	0.955852
$751$	16.7296	0.610470	0.305235	−	0.952277i	$-0.401265\pi$
$751$	16.7296	0.610470	0.305235	+	0.952277i	$0.401265\pi$
$752$	−0.871553	−0.0317823
$753$	36.3189	1.32354
$754$	−15.8910	−0.578717
$755$	20.6039	0.749854
$756$	0	0
$757$	9.31371	0.338512	0.169256	−	0.985572i	$-0.445863\pi$
$757$	9.31371	0.338512	0.169256	+	0.985572i	$0.445863\pi$
$758$	24.0243	0.872600
$759$	12.6725	0.459982
$760$	−4.65162	−0.168732
$761$	−3.25782	−0.118096	−0.0590480	−	0.998255i	$-0.518807\pi$
$761$	−3.25782	−0.118096	−0.0590480	+	0.998255i	$0.518807\pi$
$762$	−22.1970	−0.804111
$763$	0	0
$764$	24.7623	0.895870
$765$	4.68554	0.169406
$766$	1.43208	0.0517430
$767$	−10.7940	−0.389750
$768$	−2.68554	−0.0969062
$769$	−32.6462	−1.17725	−0.588627	−	0.808405i	$-0.700331\pi$
$769$	−32.6462	−1.17725	−0.588627	+	0.808405i	$0.700331\pi$
$770$	0	0
$771$	56.0760	2.01953
$772$	12.3085	0.442992
$773$	21.5826	0.776272	0.388136	−	0.921602i	$-0.373119\pi$
$773$	21.5826	0.776272	0.388136	+	0.921602i	$0.373119\pi$
$774$	−33.1986	−1.19330
$775$	1.60604	0.0576907
$776$	−4.65162	−0.166984
$777$	0	0
$778$	21.2073	0.760319
$779$	8.26834	0.296244
$780$	4.89627	0.175315
$781$	17.6109	0.630168
$782$	3.03049	0.108370
$783$	−31.5619	−1.12793
$784$	0	0
$785$	−17.3007	−0.617488
$786$	−44.6809	−1.59372
$787$	−21.8543	−0.779021	−0.389510	−	0.921022i	$-0.627356\pi$
$787$	−21.8543	−0.779021	−0.389510	+	0.921022i	$0.627356\pi$
$788$	17.8114	0.634506
$789$	−22.0332	−0.784402
$790$	−6.64623	−0.236462
$791$	0	0
$792$	6.55872	0.233054
$793$	−1.87583	−0.0666128
$794$	−38.0742	−1.35120
$795$	−2.19668	−0.0779081
$796$	−2.97891	−0.105585
$797$	−1.52387	−0.0539782	−0.0269891	−	0.999636i	$-0.508592\pi$
$797$	−1.52387	−0.0539782	−0.0269891	+	0.999636i	$0.508592\pi$
$798$	0	0
$799$	0.871553	0.0308333
$800$	3.76259	0.133028
$801$	−54.8004	−1.93628
$802$	−19.4043	−0.685188
$803$	−16.3766	−0.577918
$804$	−5.45734	−0.192466
$805$	0	0
$806$	0.699595	0.0246422
$807$	−69.5721	−2.44905
$808$	−6.98482	−0.245725
$809$	−37.9025	−1.33258	−0.666290	−	0.745693i	$-0.732119\pi$
$809$	−37.9025	−1.33258	−0.666290	+	0.745693i	$0.732119\pi$
$810$	−4.33193	−0.152209
$811$	−7.70634	−0.270606	−0.135303	−	0.990804i	$-0.543201\pi$
$811$	−7.70634	−0.270606	−0.135303	+	0.990804i	$0.543201\pi$
$812$	0	0
$813$	12.3511	0.433170
$814$	13.1424	0.460642
$815$	17.7173	0.620610
$816$	2.68554	0.0940128
$817$	−32.9582	−1.15306
$818$	10.6692	0.373041
$819$	0	0
$820$	2.19951	0.0768104
$821$	3.20454	0.111839	0.0559197	−	0.998435i	$-0.482191\pi$
$821$	3.20454	0.111839	0.0559197	+	0.998435i	$0.482191\pi$
$822$	−58.9593	−2.05644
$823$	−17.2261	−0.600465	−0.300232	−	0.953866i	$-0.597064\pi$
$823$	−17.2261	−0.600465	−0.300232	+	0.953866i	$0.597064\pi$
$824$	−17.4844	−0.609096
$825$	−15.7338	−0.547782
$826$	0	0
$827$	10.3772	0.360850	0.180425	−	0.983589i	$-0.442253\pi$
$827$	10.3772	0.360850	0.180425	+	0.983589i	$0.442253\pi$
$828$	12.7649	0.443610
$829$	−10.8499	−0.376833	−0.188416	−	0.982089i	$-0.560335\pi$
$829$	−10.8499	−0.376833	−0.188416	+	0.982089i	$0.560335\pi$
$830$	−12.3792	−0.429687
$831$	−72.5600	−2.51708
$832$	1.63899	0.0568218
$833$	0	0
$834$	19.2226	0.665625
$835$	16.1666	0.559469
$836$	6.51124	0.225196
$837$	1.38950	0.0480280
$838$	−31.7791	−1.09779
$839$	45.4474	1.56902	0.784510	−	0.620117i	$-0.212915\pi$
$839$	45.4474	1.56902	0.784510	+	0.620117i	$0.212915\pi$
$840$	0	0
$841$	65.0051	2.24156
$842$	−21.0922	−0.726884
$843$	−13.3841	−0.460973
$844$	−5.92040	−0.203789
$845$	11.4729	0.394678
$846$	3.67111	0.126215
$847$	0	0
$848$	−0.735321	−0.0252510
$849$	−39.2323	−1.34645
$850$	−3.76259	−0.129056
$851$	25.5784	0.876818
$852$	30.3738	1.04059
$853$	−36.4343	−1.24749	−0.623743	−	0.781629i	$-0.714389\pi$
$853$	−36.4343	−1.24749	−0.623743	+	0.781629i	$0.714389\pi$
$854$	0	0
$855$	19.5933	0.670077
$856$	5.87498	0.200803
$857$	35.2152	1.20293	0.601464	−	0.798900i	$-0.294584\pi$
$857$	35.2152	1.20293	0.601464	+	0.798900i	$0.294584\pi$
$858$	−6.85369	−0.233981
$859$	−23.9145	−0.815954	−0.407977	−	0.912992i	$-0.633766\pi$
$859$	−23.9145	−0.815954	−0.407977	+	0.912992i	$0.633766\pi$
$860$	−8.76744	−0.298967
$861$	0	0
$862$	−4.28471	−0.145938
$863$	35.4052	1.20521	0.602604	−	0.798041i	$-0.294130\pi$
$863$	35.4052	1.20521	0.602604	+	0.798041i	$0.294130\pi$
$864$	3.25527	0.110747
$865$	3.40481	0.115767
$866$	−34.2531	−1.16397
$867$	−2.68554	−0.0912059
$868$	0	0
$869$	9.30324	0.315591
$870$	−28.9644	−0.981985
$871$	3.33062	0.112854
$872$	−5.86557	−0.198633
$873$	19.5933	0.663133
$874$	12.6725	0.428653
$875$	0	0
$876$	−28.2449	−0.954308
$877$	6.21452	0.209849	0.104925	−	0.994480i	$-0.466540\pi$
$877$	6.21452	0.209849	0.104925	+	0.994480i	$0.466540\pi$
$878$	12.1732	0.410825
$879$	22.8259	0.769898
$880$	1.73210	0.0583890
$881$	2.86769	0.0966148	0.0483074	−	0.998833i	$-0.484617\pi$
$881$	2.86769	0.0966148	0.0483074	+	0.998833i	$0.484617\pi$
$882$	0	0
$883$	−14.7743	−0.497195	−0.248597	−	0.968607i	$-0.579970\pi$
$883$	−14.7743	−0.497195	−0.248597	+	0.968607i	$0.579970\pi$
$884$	−1.63899	−0.0551252
$885$	−19.6742	−0.661340
$886$	10.7541	0.361292
$887$	2.35036	0.0789175	0.0394588	−	0.999221i	$-0.487437\pi$
$887$	2.35036	0.0789175	0.0394588	+	0.999221i	$0.487437\pi$
$888$	22.6669	0.760652
$889$	0	0
$890$	−14.4723	−0.485111
$891$	6.06374	0.203143
$892$	−16.4454	−0.550633
$893$	3.64453	0.121960
$894$	−0.622058	−0.0208047
$895$	21.6063	0.722220
$896$	0	0
$897$	−13.3390	−0.445375
$898$	32.4192	1.08184
$899$	−4.13853	−0.138028
$900$	−15.8486	−0.528286
$901$	0.735321	0.0244971
$902$	−3.07883	−0.102514
$903$	0	0
$904$	17.2754	0.574572
$905$	10.1870	0.338629
$906$	−49.7423	−1.65258
$907$	31.2103	1.03632	0.518161	−	0.855283i	$-0.326617\pi$
$907$	31.2103	1.03632	0.518161	+	0.855283i	$0.326617\pi$
$908$	−3.99240	−0.132492
$909$	29.4211	0.975835
$910$	0	0
$911$	6.00390	0.198918	0.0994590	−	0.995042i	$-0.468289\pi$
$911$	6.00390	0.198918	0.0994590	+	0.995042i	$0.468289\pi$
$912$	11.2300	0.371863
$913$	17.3281	0.573475
$914$	37.9495	1.25526
$915$	−3.41906	−0.113031
$916$	−29.9128	−0.988347
$917$	0	0
$918$	−3.25527	−0.107440
$919$	−59.5370	−1.96394	−0.981972	−	0.189026i	$-0.939467\pi$
$919$	−59.5370	−1.96394	−0.981972	+	0.189026i	$0.939467\pi$
$920$	3.37109	0.111141
$921$	−18.9800	−0.625411
$922$	35.0876	1.15555
$923$	−18.5372	−0.610158
$924$	0	0
$925$	−31.7576	−1.04418
$926$	39.3098	1.29180
$927$	73.6466	2.41887
$928$	−9.69562	−0.318274
$929$	−7.18488	−0.235728	−0.117864	−	0.993030i	$-0.537605\pi$
$929$	−7.18488	−0.235728	−0.117864	+	0.993030i	$0.537605\pi$
$930$	1.27514	0.0418136
$931$	0	0
$932$	−7.52157	−0.246377
$933$	−66.5003	−2.17712
$934$	−28.3610	−0.928001
$935$	−1.73210	−0.0566456
$936$	−6.90367	−0.225654
$937$	45.0481	1.47166	0.735829	−	0.677168i	$-0.236793\pi$
$937$	45.0481	1.47166	0.735829	+	0.677168i	$0.236793\pi$
$938$	0	0
$939$	46.0082	1.50142
$940$	0.969506	0.0316218
$941$	−9.08388	−0.296126	−0.148063	−	0.988978i	$-0.547304\pi$
$941$	−9.08388	−0.296126	−0.148063	+	0.988978i	$0.547304\pi$
$942$	41.7676	1.36086
$943$	−5.99217	−0.195132
$944$	−6.58579	−0.214349
$945$	0	0
$946$	12.2725	0.399012
$947$	30.3613	0.986610	0.493305	−	0.869856i	$-0.335789\pi$
$947$	30.3613	0.986610	0.493305	+	0.869856i	$0.335789\pi$
$948$	16.0454	0.521131
$949$	17.2379	0.559567
$950$	−15.7338	−0.510473
$951$	−13.0266	−0.422417
$952$	0	0
$953$	3.15090	0.102068	0.0510338	−	0.998697i	$-0.483748\pi$
$953$	3.15090	0.102068	0.0510338	+	0.998697i	$0.483748\pi$
$954$	3.09728	0.100278
$955$	−27.5453	−0.891346
$956$	−7.29355	−0.235890
$957$	40.5437	1.31059
$958$	35.8123	1.15704
$959$	0	0
$960$	2.98737	0.0964169
$961$	−30.8178	−0.994123
$962$	−13.8337	−0.446015
$963$	−24.7463	−0.797438
$964$	24.2161	0.779947
$965$	−13.6918	−0.440755
$966$	0	0
$967$	60.3953	1.94218	0.971090	−	0.238712i	$-0.0767251\pi$
$967$	60.3953	1.94218	0.971090	+	0.238712i	$0.0767251\pi$
$968$	8.57545	0.275625
$969$	−11.2300	−0.360760
$970$	5.17441	0.166140
$971$	18.2651	0.586154	0.293077	−	0.956089i	$-0.405321\pi$
$971$	18.2651	0.586154	0.293077	+	0.956089i	$0.405321\pi$
$972$	20.2240	0.648686
$973$	0	0
$974$	−31.0387	−0.994544
$975$	16.5614	0.530388
$976$	−1.14451	−0.0366347
$977$	−38.2279	−1.22302	−0.611509	−	0.791237i	$-0.709437\pi$
$977$	−38.2279	−1.22302	−0.611509	+	0.791237i	$0.709437\pi$
$978$	−42.7733	−1.36774
$979$	20.2580	0.647447
$980$	0	0
$981$	24.7067	0.788823
$982$	−28.4646	−0.908342
$983$	−39.7597	−1.26814	−0.634068	−	0.773277i	$-0.718616\pi$
$983$	−39.7597	−1.26814	−0.634068	+	0.773277i	$0.718616\pi$
$984$	−5.31010	−0.169280
$985$	−19.8132	−0.631302
$986$	9.69562	0.308772
$987$	0	0
$988$	−6.85369	−0.218045
$989$	23.8852	0.759506
$990$	−7.29585	−0.231877
$991$	60.7439	1.92959	0.964797	−	0.262995i	$-0.0847103\pi$
$991$	60.7439	1.92959	0.964797	+	0.262995i	$0.0847103\pi$
$992$	0.426845	0.0135523
$993$	−5.55328	−0.176228
$994$	0	0
$995$	3.31371	0.105052
$996$	29.8859	0.946972
$997$	−49.3785	−1.56383	−0.781917	−	0.623383i	$-0.785758\pi$
$997$	−49.3785	−1.56383	−0.781917	+	0.623383i	$0.785758\pi$
$998$	5.19583	0.164471
$999$	−27.4756	−0.869291

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1666.2.a.v.1.1	✓	4
7.6	odd	2		1666.2.a.w.1.4	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1666.2.a.v.1.1	✓	4	1.1	even	1	trivial
1666.2.a.w.1.4	yes	4	7.6	odd	2

Overview	Random
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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:	\( N \)	\(=\)	\( 1666 = 2 \cdot 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1666.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.68554 q^{3} +1.00000 q^{4} -1.11239 q^{5} +2.68554 q^{6} -1.00000 q^{8} +4.21215 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.68554 q^{3} +1.00000 q^{4} -1.11239 q^{5} +2.68554 q^{6} -1.00000 q^{8} +4.21215 q^{9} +1.11239 q^{10} -1.55710 q^{11} -2.68554 q^{12} +1.63899 q^{13} +2.98737 q^{15} +1.00000 q^{16} -1.00000 q^{17} -4.21215 q^{18} -4.18165 q^{19} -1.11239 q^{20} +1.55710 q^{22} +3.03049 q^{23} +2.68554 q^{24} -3.76259 q^{25} -1.63899 q^{26} -3.25527 q^{27} +9.69562 q^{29} -2.98737 q^{30} -0.426845 q^{31} -1.00000 q^{32} +4.18165 q^{33} +1.00000 q^{34} +4.21215 q^{36} +8.44035 q^{37} +4.18165 q^{38} -4.40158 q^{39} +1.11239 q^{40} -1.97729 q^{41} +7.88163 q^{43} -1.55710 q^{44} -4.68554 q^{45} -3.03049 q^{46} -0.871553 q^{47} -2.68554 q^{48} +3.76259 q^{50} +2.68554 q^{51} +1.63899 q^{52} -0.735321 q^{53} +3.25527 q^{54} +1.73210 q^{55} +11.2300 q^{57} -9.69562 q^{58} -6.58579 q^{59} +2.98737 q^{60} -1.14451 q^{61} +0.426845 q^{62} +1.00000 q^{64} -1.82320 q^{65} -4.18165 q^{66} +2.03212 q^{67} -1.00000 q^{68} -8.13853 q^{69} -11.3101 q^{71} -4.21215 q^{72} +10.5174 q^{73} -8.44035 q^{74} +10.1046 q^{75} -4.18165 q^{76} +4.40158 q^{78} -5.97474 q^{79} -1.11239 q^{80} -3.89426 q^{81} +1.97729 q^{82} -11.1284 q^{83} +1.11239 q^{85} -7.88163 q^{86} -26.0380 q^{87} +1.55710 q^{88} -13.0101 q^{89} +4.68554 q^{90} +3.03049 q^{92} +1.14631 q^{93} +0.871553 q^{94} +4.65162 q^{95} +2.68554 q^{96} +4.65162 q^{97} -6.55872 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 4 q^{4} - 4 q^{5} - 4 q^{8}+O(q^{10}) \) 4 * q - 4 * q^2 + 4 * q^4 - 4 * q^5 - 4 * q^8	\( 4 q - 4 q^{2} + 4 q^{4} - 4 q^{5} - 4 q^{8} + 4 q^{10} - 4 q^{15} + 4 q^{16} - 4 q^{17} - 4 q^{20} + 12 q^{23} - 12 q^{27} + 4 q^{30} - 12 q^{31} - 4 q^{32} + 4 q^{34} - 4 q^{37} + 4 q^{39} + 4 q^{40} - 20 q^{41} + 8 q^{43} - 8 q^{45} - 12 q^{46} - 8 q^{47} + 12 q^{54} - 8 q^{55} + 12 q^{57} - 32 q^{59} - 4 q^{60} + 4 q^{61} + 12 q^{62} + 4 q^{64} - 28 q^{65} - 4 q^{68} - 24 q^{71} + 4 q^{74} + 28 q^{75} - 4 q^{78} + 8 q^{79} - 4 q^{80} - 8 q^{81} + 20 q^{82} - 40 q^{83} + 4 q^{85} - 8 q^{86} - 32 q^{87} - 24 q^{89} + 8 q^{90} + 12 q^{92} - 16 q^{93} + 8 q^{94} + 28 q^{95} + 28 q^{97} - 12 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 4 * q^4 - 4 * q^5 - 4 * q^8 + 4 * q^10 - 4 * q^15 + 4 * q^16 - 4 * q^17 - 4 * q^20 + 12 * q^23 - 12 * q^27 + 4 * q^30 - 12 * q^31 - 4 * q^32 + 4 * q^34 - 4 * q^37 + 4 * q^39 + 4 * q^40 - 20 * q^41 + 8 * q^43 - 8 * q^45 - 12 * q^46 - 8 * q^47 + 12 * q^54 - 8 * q^55 + 12 * q^57 - 32 * q^59 - 4 * q^60 + 4 * q^61 + 12 * q^62 + 4 * q^64 - 28 * q^65 - 4 * q^68 - 24 * q^71 + 4 * q^74 + 28 * q^75 - 4 * q^78 + 8 * q^79 - 4 * q^80 - 8 * q^81 + 20 * q^82 - 40 * q^83 + 4 * q^85 - 8 * q^86 - 32 * q^87 - 24 * q^89 + 8 * q^90 + 12 * q^92 - 16 * q^93 + 8 * q^94 + 28 * q^95 + 28 * q^97 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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