LMFDB - Embedded newform 2667.2.a.h.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2667,2,Mod(1,2667)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2667, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("2667.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2667 = 3 \cdot 7 \cdot 127 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2667.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:	$21.2961022191$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{6}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 6 $ x^2 - 6
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.44949$ of defining polynomial
Character	$\chi$	$=$	2667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.44949 q^{2} +1.00000 q^{3} +4.00000 q^{4} -2.44949 q^{5} -2.44949 q^{6} +1.00000 q^{7} -4.89898 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.44949 q^{2} +1.00000 q^{3} +4.00000 q^{4} -2.44949 q^{5} -2.44949 q^{6} +1.00000 q^{7} -4.89898 q^{8} +1.00000 q^{9} +6.00000 q^{10} +4.00000 q^{12} +6.89898 q^{13} -2.44949 q^{14} -2.44949 q^{15} +4.00000 q^{16} -0.550510 q^{17} -2.44949 q^{18} -0.449490 q^{19} -9.79796 q^{20} +1.00000 q^{21} +6.00000 q^{23} -4.89898 q^{24} +1.00000 q^{25} -16.8990 q^{26} +1.00000 q^{27} +4.00000 q^{28} +1.89898 q^{29} +6.00000 q^{30} +8.00000 q^{31} +1.34847 q^{34} -2.44949 q^{35} +4.00000 q^{36} -7.00000 q^{37} +1.10102 q^{38} +6.89898 q^{39} +12.0000 q^{40} +0.550510 q^{41} -2.44949 q^{42} +2.00000 q^{43} -2.44949 q^{45} -14.6969 q^{46} -12.0000 q^{47} +4.00000 q^{48} +1.00000 q^{49} -2.44949 q^{50} -0.550510 q^{51} +27.5959 q^{52} -7.89898 q^{53} -2.44949 q^{54} -4.89898 q^{56} -0.449490 q^{57} -4.65153 q^{58} +2.44949 q^{59} -9.79796 q^{60} -0.449490 q^{61} -19.5959 q^{62} +1.00000 q^{63} -8.00000 q^{64} -16.8990 q^{65} +14.2474 q^{67} -2.20204 q^{68} +6.00000 q^{69} +6.00000 q^{70} +8.44949 q^{71} -4.89898 q^{72} -11.3485 q^{73} +17.1464 q^{74} +1.00000 q^{75} -1.79796 q^{76} -16.8990 q^{78} -5.89898 q^{79} -9.79796 q^{80} +1.00000 q^{81} -1.34847 q^{82} +6.00000 q^{83} +4.00000 q^{84} +1.34847 q^{85} -4.89898 q^{86} +1.89898 q^{87} +9.79796 q^{89} +6.00000 q^{90} +6.89898 q^{91} +24.0000 q^{92} +8.00000 q^{93} +29.3939 q^{94} +1.10102 q^{95} +12.3485 q^{97} -2.44949 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{3} + 8 q^{4} + 2 q^{7} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^3 + 8 * q^4 + 2 * q^7 + 2 * q^9	$ 2 q + 2 q^{3} + 8 q^{4} + 2 q^{7} + 2 q^{9} + 12 q^{10} + 8 q^{12} + 4 q^{13} + 8 q^{16} - 6 q^{17} + 4 q^{19} + 2 q^{21} + 12 q^{23} + 2 q^{25} - 24 q^{26} + 2 q^{27} + 8 q^{28} - 6 q^{29} + 12 q^{30} + 16 q^{31} - 12 q^{34} + 8 q^{36} - 14 q^{37} + 12 q^{38} + 4 q^{39} + 24 q^{40} + 6 q^{41} + 4 q^{43} - 24 q^{47} + 8 q^{48} + 2 q^{49} - 6 q^{51} + 16 q^{52} - 6 q^{53} + 4 q^{57} - 24 q^{58} + 4 q^{61} + 2 q^{63} - 16 q^{64} - 24 q^{65} + 4 q^{67} - 24 q^{68} + 12 q^{69} + 12 q^{70} + 12 q^{71} - 8 q^{73} + 2 q^{75} + 16 q^{76} - 24 q^{78} - 2 q^{79} + 2 q^{81} + 12 q^{82} + 12 q^{83} + 8 q^{84} - 12 q^{85} - 6 q^{87} + 12 q^{90} + 4 q^{91} + 48 q^{92} + 16 q^{93} + 12 q^{95} + 10 q^{97}+O(q^{100}) $ 2 * q + 2 * q^3 + 8 * q^4 + 2 * q^7 + 2 * q^9 + 12 * q^10 + 8 * q^12 + 4 * q^13 + 8 * q^16 - 6 * q^17 + 4 * q^19 + 2 * q^21 + 12 * q^23 + 2 * q^25 - 24 * q^26 + 2 * q^27 + 8 * q^28 - 6 * q^29 + 12 * q^30 + 16 * q^31 - 12 * q^34 + 8 * q^36 - 14 * q^37 + 12 * q^38 + 4 * q^39 + 24 * q^40 + 6 * q^41 + 4 * q^43 - 24 * q^47 + 8 * q^48 + 2 * q^49 - 6 * q^51 + 16 * q^52 - 6 * q^53 + 4 * q^57 - 24 * q^58 + 4 * q^61 + 2 * q^63 - 16 * q^64 - 24 * q^65 + 4 * q^67 - 24 * q^68 + 12 * q^69 + 12 * q^70 + 12 * q^71 - 8 * q^73 + 2 * q^75 + 16 * q^76 - 24 * q^78 - 2 * q^79 + 2 * q^81 + 12 * q^82 + 12 * q^83 + 8 * q^84 - 12 * q^85 - 6 * q^87 + 12 * q^90 + 4 * q^91 + 48 * q^92 + 16 * q^93 + 12 * q^95 + 10 * q^97

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 $

$2$	−2.44949	−1.73205	−0.866025	−	0.500000i	$-0.833333\pi$
$2$	−2.44949	−1.73205	−0.866025	+	0.500000i	$0.833333\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.00000	2.00000
$5$	−2.44949	−1.09545	−0.547723	−	0.836660i	$-0.684505\pi$
$5$	−2.44949	−1.09545	−0.547723	+	0.836660i	$0.684505\pi$
$6$	−2.44949	−1.00000
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−4.89898	−1.73205
$9$	1.00000	0.333333
$10$	6.00000	1.89737
$11$	0	0		−	1.00000i	$-0.5\pi$
$11$	0	0			1.00000i	$0.5\pi$
$12$	4.00000	1.15470
$13$	6.89898	1.91343	0.956716	−	0.291022i	$-0.0939953\pi$
$13$	6.89898	1.91343	0.956716	+	0.291022i	$0.0939953\pi$
$14$	−2.44949	−0.654654
$15$	−2.44949	−0.632456
$16$	4.00000	1.00000
$17$	−0.550510	−0.133518	−0.0667592	−	0.997769i	$-0.521266\pi$
$17$	−0.550510	−0.133518	−0.0667592	+	0.997769i	$0.521266\pi$
$18$	−2.44949	−0.577350
$19$	−0.449490	−0.103120	−0.0515600	−	0.998670i	$-0.516419\pi$
$19$	−0.449490	−0.103120	−0.0515600	+	0.998670i	$0.516419\pi$
$20$	−9.79796	−2.19089
$21$	1.00000	0.218218
$22$	0	0
$23$	6.00000	1.25109	0.625543	−	0.780189i	$-0.284877\pi$
$23$	6.00000	1.25109	0.625543	+	0.780189i	$0.284877\pi$
$24$	−4.89898	−1.00000
$25$	1.00000	0.200000
$26$	−16.8990	−3.31416
$27$	1.00000	0.192450
$28$	4.00000	0.755929
$29$	1.89898	0.352632	0.176316	−	0.984334i	$-0.443582\pi$
$29$	1.89898	0.352632	0.176316	+	0.984334i	$0.443582\pi$
$30$	6.00000	1.09545
$31$	8.00000	1.43684	0.718421	−	0.695608i	$-0.244865\pi$
$31$	8.00000	1.43684	0.718421	+	0.695608i	$0.244865\pi$
$32$	0	0
$33$	0	0
$34$	1.34847	0.231261
$35$	−2.44949	−0.414039
$36$	4.00000	0.666667
$37$	−7.00000	−1.15079	−0.575396	−	0.817875i	$-0.695152\pi$
$37$	−7.00000	−1.15079	−0.575396	+	0.817875i	$0.695152\pi$
$38$	1.10102	0.178609
$39$	6.89898	1.10472
$40$	12.0000	1.89737
$41$	0.550510	0.0859753	0.0429876	−	0.999076i	$-0.486312\pi$
$41$	0.550510	0.0859753	0.0429876	+	0.999076i	$0.486312\pi$
$42$	−2.44949	−0.377964
$43$	2.00000	0.304997	0.152499	−	0.988304i	$-0.451268\pi$
$43$	2.00000	0.304997	0.152499	+	0.988304i	$0.451268\pi$
$44$	0	0
$45$	−2.44949	−0.365148
$46$	−14.6969	−2.16695
$47$	−12.0000	−1.75038	−0.875190	−	0.483779i	$-0.839264\pi$
$47$	−12.0000	−1.75038	−0.875190	+	0.483779i	$0.839264\pi$
$48$	4.00000	0.577350
$49$	1.00000	0.142857
$50$	−2.44949	−0.346410
$51$	−0.550510	−0.0770869
$52$	27.5959	3.82687
$53$	−7.89898	−1.08501	−0.542504	−	0.840053i	$-0.682524\pi$
$53$	−7.89898	−1.08501	−0.542504	+	0.840053i	$0.682524\pi$
$54$	−2.44949	−0.333333
$55$	0	0
$56$	−4.89898	−0.654654
$57$	−0.449490	−0.0595364
$58$	−4.65153	−0.610776
$59$	2.44949	0.318896	0.159448	−	0.987206i	$-0.449029\pi$
$59$	2.44949	0.318896	0.159448	+	0.987206i	$0.449029\pi$
$60$	−9.79796	−1.26491
$61$	−0.449490	−0.0575513	−0.0287756	−	0.999586i	$-0.509161\pi$
$61$	−0.449490	−0.0575513	−0.0287756	+	0.999586i	$0.509161\pi$
$62$	−19.5959	−2.48868
$63$	1.00000	0.125988
$64$	−8.00000	−1.00000
$65$	−16.8990	−2.09606
$66$	0	0
$67$	14.2474	1.74060	0.870301	−	0.492519i	$-0.163924\pi$
$67$	14.2474	1.74060	0.870301	+	0.492519i	$0.163924\pi$
$68$	−2.20204	−0.267037
$69$	6.00000	0.722315
$70$	6.00000	0.717137
$71$	8.44949	1.00277	0.501385	−	0.865224i	$-0.332824\pi$
$71$	8.44949	1.00277	0.501385	+	0.865224i	$0.332824\pi$
$72$	−4.89898	−0.577350
$73$	−11.3485	−1.32824	−0.664119	−	0.747627i	$-0.731193\pi$
$73$	−11.3485	−1.32824	−0.664119	+	0.747627i	$0.731193\pi$
$74$	17.1464	1.99323
$75$	1.00000	0.115470
$76$	−1.79796	−0.206240
$77$	0	0
$78$	−16.8990	−1.91343
$79$	−5.89898	−0.663687	−0.331844	−	0.943334i	$-0.607671\pi$
$79$	−5.89898	−0.663687	−0.331844	+	0.943334i	$0.607671\pi$
$80$	−9.79796	−1.09545
$81$	1.00000	0.111111
$82$	−1.34847	−0.148914
$83$	6.00000	0.658586	0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000	0.658586	0.329293	+	0.944228i	$0.393190\pi$
$84$	4.00000	0.436436
$85$	1.34847	0.146262
$86$	−4.89898	−0.528271
$87$	1.89898	0.203592
$88$	0	0
$89$	9.79796	1.03858	0.519291	−	0.854598i	$-0.326196\pi$
$89$	9.79796	1.03858	0.519291	+	0.854598i	$0.326196\pi$
$90$	6.00000	0.632456
$91$	6.89898	0.723210
$92$	24.0000	2.50217
$93$	8.00000	0.829561
$94$	29.3939	3.03175
$95$	1.10102	0.112962
$96$	0	0
$97$	12.3485	1.25380	0.626899	−	0.779101i	$-0.284324\pi$
$97$	12.3485	1.25380	0.626899	+	0.779101i	$0.284324\pi$
$98$	−2.44949	−0.247436
$99$	0	0
$100$	4.00000	0.400000
$101$	0	0		−	1.00000i	$-0.5\pi$
$101$	0	0			1.00000i	$0.5\pi$
$102$	1.34847	0.133518
$103$	−4.00000	−0.394132	−0.197066	−	0.980390i	$-0.563141\pi$
$103$	−4.00000	−0.394132	−0.197066	+	0.980390i	$0.563141\pi$
$104$	−33.7980	−3.31416
$105$	−2.44949	−0.239046
$106$	19.3485	1.87929
$107$	−7.34847	−0.710403	−0.355202	−	0.934790i	$-0.615588\pi$
$107$	−7.34847	−0.710403	−0.355202	+	0.934790i	$0.615588\pi$
$108$	4.00000	0.384900
$109$	9.34847	0.895421	0.447710	−	0.894179i	$-0.352240\pi$
$109$	9.34847	0.895421	0.447710	+	0.894179i	$0.352240\pi$
$110$	0	0
$111$	−7.00000	−0.664411
$112$	4.00000	0.377964
$113$	−6.00000	−0.564433	−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000	−0.564433	−0.282216	+	0.959351i	$0.591070\pi$
$114$	1.10102	0.103120
$115$	−14.6969	−1.37050
$116$	7.59592	0.705263
$117$	6.89898	0.637811
$118$	−6.00000	−0.552345
$119$	−0.550510	−0.0504652
$120$	12.0000	1.09545
$121$	−11.0000	−1.00000
$122$	1.10102	0.0996817
$123$	0.550510	0.0496378
$124$	32.0000	2.87368
$125$	9.79796	0.876356
$126$	−2.44949	−0.218218
$127$	1.00000	0.0887357
$127$	1.00000	0.0887357
$128$	19.5959	1.73205
$129$	2.00000	0.176090
$130$	41.3939	3.63048
$131$	10.3485	0.904150	0.452075	−	0.891980i	$-0.350684\pi$
$131$	10.3485	0.904150	0.452075	+	0.891980i	$0.350684\pi$
$132$	0	0
$133$	−0.449490	−0.0389757
$134$	−34.8990	−3.01481
$135$	−2.44949	−0.210819
$136$	2.69694	0.231261
$137$	21.7980	1.86233	0.931163	−	0.364604i	$-0.118796\pi$
$137$	21.7980	1.86233	0.931163	+	0.364604i	$0.118796\pi$
$138$	−14.6969	−1.25109
$139$	−20.3485	−1.72593	−0.862967	−	0.505260i	$-0.831397\pi$
$139$	−20.3485	−1.72593	−0.862967	+	0.505260i	$0.831397\pi$
$140$	−9.79796	−0.828079
$141$	−12.0000	−1.01058
$142$	−20.6969	−1.73685
$143$	0	0
$144$	4.00000	0.333333
$145$	−4.65153	−0.386289
$146$	27.7980	2.30058
$147$	1.00000	0.0824786
$148$	−28.0000	−2.30159
$149$	8.69694	0.712481	0.356240	−	0.934394i	$-0.384058\pi$
$149$	8.69694	0.712481	0.356240	+	0.934394i	$0.384058\pi$
$150$	−2.44949	−0.200000
$151$	−5.34847	−0.435252	−0.217626	−	0.976032i	$-0.569831\pi$
$151$	−5.34847	−0.435252	−0.217626	+	0.976032i	$0.569831\pi$
$152$	2.20204	0.178609
$153$	−0.550510	−0.0445061
$154$	0	0
$155$	−19.5959	−1.57398
$156$	27.5959	2.20944
$157$	−6.44949	−0.514725	−0.257363	−	0.966315i	$-0.582853\pi$
$157$	−6.44949	−0.514725	−0.257363	+	0.966315i	$0.582853\pi$
$158$	14.4495	1.14954
$159$	−7.89898	−0.626430
$160$	0	0
$161$	6.00000	0.472866
$162$	−2.44949	−0.192450
$163$	17.0000	1.33154	0.665771	−	0.746156i	$-0.268103\pi$
$163$	17.0000	1.33154	0.665771	+	0.746156i	$0.268103\pi$
$164$	2.20204	0.171951
$165$	0	0
$166$	−14.6969	−1.14070
$167$	−11.1464	−0.862537	−0.431268	−	0.902224i	$-0.641934\pi$
$167$	−11.1464	−0.862537	−0.431268	+	0.902224i	$0.641934\pi$
$168$	−4.89898	−0.377964
$169$	34.5959	2.66122
$170$	−3.30306	−0.253333
$171$	−0.449490	−0.0343733
$172$	8.00000	0.609994
$173$	−6.24745	−0.474985	−0.237492	−	0.971389i	$-0.576325\pi$
$173$	−6.24745	−0.474985	−0.237492	+	0.971389i	$0.576325\pi$
$174$	−4.65153	−0.352632
$175$	1.00000	0.0755929
$176$	0	0
$177$	2.44949	0.184115
$178$	−24.0000	−1.79888
$179$	−3.79796	−0.283873	−0.141936	−	0.989876i	$-0.545333\pi$
$179$	−3.79796	−0.283873	−0.141936	+	0.989876i	$0.545333\pi$
$180$	−9.79796	−0.730297
$181$	−24.1464	−1.79479	−0.897395	−	0.441228i	$-0.854543\pi$
$181$	−24.1464	−1.79479	−0.897395	+	0.441228i	$0.854543\pi$
$182$	−16.8990	−1.25264
$183$	−0.449490	−0.0332272
$184$	−29.3939	−2.16695
$185$	17.1464	1.26063
$186$	−19.5959	−1.43684
$187$	0	0
$188$	−48.0000	−3.50076
$189$	1.00000	0.0727393
$190$	−2.69694	−0.195656
$191$	1.34847	0.0975718	0.0487859	−	0.998809i	$-0.484465\pi$
$191$	1.34847	0.0975718	0.0487859	+	0.998809i	$0.484465\pi$
$192$	−8.00000	−0.577350
$193$	10.4495	0.752171	0.376085	−	0.926585i	$-0.377270\pi$
$193$	10.4495	0.752171	0.376085	+	0.926585i	$0.377270\pi$
$194$	−30.2474	−2.17164
$195$	−16.8990	−1.21016
$196$	4.00000	0.285714
$197$	3.55051	0.252963	0.126482	−	0.991969i	$-0.459632\pi$
$197$	3.55051	0.252963	0.126482	+	0.991969i	$0.459632\pi$
$198$	0	0
$199$	20.0000	1.41776	0.708881	−	0.705328i	$-0.249200\pi$
$199$	20.0000	1.41776	0.708881	+	0.705328i	$0.249200\pi$
$200$	−4.89898	−0.346410
$201$	14.2474	1.00494
$202$	0	0
$203$	1.89898	0.133282
$204$	−2.20204	−0.154174
$205$	−1.34847	−0.0941812
$206$	9.79796	0.682656
$207$	6.00000	0.417029
$208$	27.5959	1.91343
$209$	0	0
$210$	6.00000	0.414039
$211$	4.69694	0.323351	0.161675	−	0.986844i	$-0.448310\pi$
$211$	4.69694	0.323351	0.161675	+	0.986844i	$0.448310\pi$
$212$	−31.5959	−2.17002
$213$	8.44949	0.578949
$214$	18.0000	1.23045
$215$	−4.89898	−0.334108
$216$	−4.89898	−0.333333
$217$	8.00000	0.543075
$218$	−22.8990	−1.55091
$219$	−11.3485	−0.766858
$220$	0	0
$221$	−3.79796	−0.255478
$222$	17.1464	1.15079
$223$	7.44949	0.498855	0.249427	−	0.968394i	$-0.419758\pi$
$223$	7.44949	0.498855	0.249427	+	0.968394i	$0.419758\pi$
$224$	0	0
$225$	1.00000	0.0666667
$226$	14.6969	0.977626
$227$	12.0000	0.796468	0.398234	−	0.917284i	$-0.369623\pi$
$227$	12.0000	0.796468	0.398234	+	0.917284i	$0.369623\pi$
$228$	−1.79796	−0.119073
$229$	2.55051	0.168542	0.0842712	−	0.996443i	$-0.473144\pi$
$229$	2.55051	0.168542	0.0842712	+	0.996443i	$0.473144\pi$
$230$	36.0000	2.37377
$231$	0	0
$232$	−9.30306	−0.610776
$233$	1.89898	0.124406	0.0622031	−	0.998064i	$-0.480187\pi$
$233$	1.89898	0.124406	0.0622031	+	0.998064i	$0.480187\pi$
$234$	−16.8990	−1.10472
$235$	29.3939	1.91745
$236$	9.79796	0.637793
$237$	−5.89898	−0.383180
$238$	1.34847	0.0874083
$239$	3.00000	0.194054	0.0970269	−	0.995282i	$-0.469067\pi$
$239$	3.00000	0.194054	0.0970269	+	0.995282i	$0.469067\pi$
$240$	−9.79796	−0.632456
$241$	−19.2474	−1.23984	−0.619919	−	0.784666i	$-0.712834\pi$
$241$	−19.2474	−1.23984	−0.619919	+	0.784666i	$0.712834\pi$
$242$	26.9444	1.73205
$243$	1.00000	0.0641500
$244$	−1.79796	−0.115103
$245$	−2.44949	−0.156492
$246$	−1.34847	−0.0859753
$247$	−3.10102	−0.197313
$248$	−39.1918	−2.48868
$249$	6.00000	0.380235
$250$	−24.0000	−1.51789
$251$	−10.3485	−0.653190	−0.326595	−	0.945164i	$-0.605901\pi$
$251$	−10.3485	−0.653190	−0.326595	+	0.945164i	$0.605901\pi$
$252$	4.00000	0.251976
$253$	0	0
$254$	−2.44949	−0.153695
$255$	1.34847	0.0844444
$256$	−32.0000	−2.00000
$257$	23.1464	1.44383	0.721917	−	0.691979i	$-0.243261\pi$
$257$	23.1464	1.44383	0.721917	+	0.691979i	$0.243261\pi$
$258$	−4.89898	−0.304997
$259$	−7.00000	−0.434959
$260$	−67.5959	−4.19212
$261$	1.89898	0.117544
$262$	−25.3485	−1.56603
$263$	11.1464	0.687318	0.343659	−	0.939094i	$-0.388334\pi$
$263$	11.1464	0.687318	0.343659	+	0.939094i	$0.388334\pi$
$264$	0	0
$265$	19.3485	1.18857
$266$	1.10102	0.0675079
$267$	9.79796	0.599625
$268$	56.9898	3.48121
$269$	2.75255	0.167826	0.0839130	−	0.996473i	$-0.473258\pi$
$269$	2.75255	0.167826	0.0839130	+	0.996473i	$0.473258\pi$
$270$	6.00000	0.365148
$271$	22.9444	1.39377	0.696886	−	0.717182i	$-0.254568\pi$
$271$	22.9444	1.39377	0.696886	+	0.717182i	$0.254568\pi$
$272$	−2.20204	−0.133518
$273$	6.89898	0.417545
$274$	−53.3939	−3.22564
$275$	0	0
$276$	24.0000	1.44463
$277$	29.7980	1.79039	0.895193	−	0.445679i	$-0.147038\pi$
$277$	29.7980	1.79039	0.895193	+	0.445679i	$0.147038\pi$
$278$	49.8434	2.98941
$279$	8.00000	0.478947
$280$	12.0000	0.717137
$281$	−24.7980	−1.47932	−0.739661	−	0.672980i	$-0.765014\pi$
$281$	−24.7980	−1.47932	−0.739661	+	0.672980i	$0.765014\pi$
$282$	29.3939	1.75038
$283$	9.65153	0.573724	0.286862	−	0.957972i	$-0.407388\pi$
$283$	9.65153	0.573724	0.286862	+	0.957972i	$0.407388\pi$
$284$	33.7980	2.00554
$285$	1.10102	0.0652188
$286$	0	0
$287$	0.550510	0.0324956
$288$	0	0
$289$	−16.6969	−0.982173
$290$	11.3939	0.669071
$291$	12.3485	0.723880
$292$	−45.3939	−2.65648
$293$	21.5505	1.25899	0.629497	−	0.777003i	$-0.283261\pi$
$293$	21.5505	1.25899	0.629497	+	0.777003i	$0.283261\pi$
$294$	−2.44949	−0.142857
$295$	−6.00000	−0.349334
$296$	34.2929	1.99323
$297$	0	0
$298$	−21.3031	−1.23405
$299$	41.3939	2.39387
$300$	4.00000	0.230940
$301$	2.00000	0.115278
$302$	13.1010	0.753879
$303$	0	0
$304$	−1.79796	−0.103120
$305$	1.10102	0.0630443
$306$	1.34847	0.0770869
$307$	25.4495	1.45248	0.726240	−	0.687442i	$-0.241266\pi$
$307$	25.4495	1.45248	0.726240	+	0.687442i	$0.241266\pi$
$308$	0	0
$309$	−4.00000	−0.227552
$310$	48.0000	2.72622
$311$	17.1464	0.972285	0.486142	−	0.873880i	$-0.338404\pi$
$311$	17.1464	0.972285	0.486142	+	0.873880i	$0.338404\pi$
$312$	−33.7980	−1.91343
$313$	20.5505	1.16158	0.580792	−	0.814052i	$-0.302743\pi$
$313$	20.5505	1.16158	0.580792	+	0.814052i	$0.302743\pi$
$314$	15.7980	0.891530
$315$	−2.44949	−0.138013
$316$	−23.5959	−1.32737
$317$	−28.8990	−1.62313	−0.811564	−	0.584263i	$-0.801384\pi$
$317$	−28.8990	−1.62313	−0.811564	+	0.584263i	$0.801384\pi$
$318$	19.3485	1.08501
$319$	0	0
$320$	19.5959	1.09545
$321$	−7.34847	−0.410152
$322$	−14.6969	−0.819028
$323$	0.247449	0.0137684
$324$	4.00000	0.222222
$325$	6.89898	0.382687
$326$	−41.6413	−2.30630
$327$	9.34847	0.516972
$328$	−2.69694	−0.148914
$329$	−12.0000	−0.661581
$330$	0	0
$331$	−13.5505	−0.744803	−0.372402	−	0.928072i	$-0.621466\pi$
$331$	−13.5505	−0.744803	−0.372402	+	0.928072i	$0.621466\pi$
$332$	24.0000	1.31717
$333$	−7.00000	−0.383598
$334$	27.3031	1.49396
$335$	−34.8990	−1.90673
$336$	4.00000	0.218218
$337$	−8.65153	−0.471279	−0.235639	−	0.971841i	$-0.575718\pi$
$337$	−8.65153	−0.471279	−0.235639	+	0.971841i	$0.575718\pi$
$338$	−84.7423	−4.60938
$339$	−6.00000	−0.325875
$340$	5.39388	0.292524
$341$	0	0
$342$	1.10102	0.0595364
$343$	1.00000	0.0539949
$344$	−9.79796	−0.528271
$345$	−14.6969	−0.791257
$346$	15.3031	0.822698
$347$	11.6969	0.627925	0.313962	−	0.949435i	$-0.398343\pi$
$347$	11.6969	0.627925	0.313962	+	0.949435i	$0.398343\pi$
$348$	7.59592	0.407184
$349$	27.0454	1.44771	0.723854	−	0.689953i	$-0.242369\pi$
$349$	27.0454	1.44771	0.723854	+	0.689953i	$0.242369\pi$
$350$	−2.44949	−0.130931
$351$	6.89898	0.368240
$352$	0	0
$353$	7.10102	0.377949	0.188975	−	0.981982i	$-0.439484\pi$
$353$	7.10102	0.377949	0.188975	+	0.981982i	$0.439484\pi$
$354$	−6.00000	−0.318896
$355$	−20.6969	−1.09848
$356$	39.1918	2.07716
$357$	−0.550510	−0.0291361
$358$	9.30306	0.491682
$359$	15.0000	0.791670	0.395835	−	0.918322i	$-0.370455\pi$
$359$	15.0000	0.791670	0.395835	+	0.918322i	$0.370455\pi$
$360$	12.0000	0.632456
$361$	−18.7980	−0.989366
$362$	59.1464	3.10867
$363$	−11.0000	−0.577350
$364$	27.5959	1.44642
$365$	27.7980	1.45501
$366$	1.10102	0.0575513
$367$	2.00000	0.104399	0.0521996	−	0.998637i	$-0.483377\pi$
$367$	2.00000	0.104399	0.0521996	+	0.998637i	$0.483377\pi$
$368$	24.0000	1.25109
$369$	0.550510	0.0286584
$370$	−42.0000	−2.18348
$371$	−7.89898	−0.410095
$372$	32.0000	1.65912
$373$	24.8990	1.28922	0.644610	−	0.764511i	$-0.277020\pi$
$373$	24.8990	1.28922	0.644610	+	0.764511i	$0.277020\pi$
$374$	0	0
$375$	9.79796	0.505964
$376$	58.7878	3.03175
$377$	13.1010	0.674737
$378$	−2.44949	−0.125988
$379$	20.0000	1.02733	0.513665	−	0.857991i	$-0.328287\pi$
$379$	20.0000	1.02733	0.513665	+	0.857991i	$0.328287\pi$
$380$	4.40408	0.225925
$381$	1.00000	0.0512316
$382$	−3.30306	−0.168999
$383$	3.24745	0.165937	0.0829684	−	0.996552i	$-0.473560\pi$
$383$	3.24745	0.165937	0.0829684	+	0.996552i	$0.473560\pi$
$384$	19.5959	1.00000
$385$	0	0
$386$	−25.5959	−1.30280
$387$	2.00000	0.101666
$388$	49.3939	2.50759
$389$	10.0454	0.509322	0.254661	−	0.967030i	$-0.418036\pi$
$389$	10.0454	0.509322	0.254661	+	0.967030i	$0.418036\pi$
$390$	41.3939	2.09606
$391$	−3.30306	−0.167043
$392$	−4.89898	−0.247436
$393$	10.3485	0.522011
$394$	−8.69694	−0.438145
$395$	14.4495	0.727033
$396$	0	0
$397$	22.6969	1.13913	0.569563	−	0.821947i	$-0.307112\pi$
$397$	22.6969	1.13913	0.569563	+	0.821947i	$0.307112\pi$
$398$	−48.9898	−2.45564
$399$	−0.449490	−0.0225026
$400$	4.00000	0.200000
$401$	−29.6969	−1.48299	−0.741497	−	0.670956i	$-0.765884\pi$
$401$	−29.6969	−1.48299	−0.741497	+	0.670956i	$0.765884\pi$
$402$	−34.8990	−1.74060
$403$	55.1918	2.74930
$404$	0	0
$405$	−2.44949	−0.121716
$406$	−4.65153	−0.230852
$407$	0	0
$408$	2.69694	0.133518
$409$	−12.6969	−0.627823	−0.313912	−	0.949452i	$-0.601640\pi$
$409$	−12.6969	−0.627823	−0.313912	+	0.949452i	$0.601640\pi$
$410$	3.30306	0.163127
$411$	21.7980	1.07521
$412$	−16.0000	−0.788263
$413$	2.44949	0.120532
$414$	−14.6969	−0.722315
$415$	−14.6969	−0.721444
$416$	0	0
$417$	−20.3485	−0.996469
$418$	0	0
$419$	7.59592	0.371085	0.185542	−	0.982636i	$-0.440596\pi$
$419$	7.59592	0.371085	0.185542	+	0.982636i	$0.440596\pi$
$420$	−9.79796	−0.478091
$421$	−38.0454	−1.85422	−0.927110	−	0.374790i	$-0.877715\pi$
$421$	−38.0454	−1.85422	−0.927110	+	0.374790i	$0.877715\pi$
$422$	−11.5051	−0.560060
$423$	−12.0000	−0.583460
$424$	38.6969	1.87929
$425$	−0.550510	−0.0267037
$426$	−20.6969	−1.00277
$427$	−0.449490	−0.0217523
$428$	−29.3939	−1.42081
$429$	0	0
$430$	12.0000	0.578691
$431$	−13.3485	−0.642973	−0.321487	−	0.946914i	$-0.604183\pi$
$431$	−13.3485	−0.642973	−0.321487	+	0.946914i	$0.604183\pi$
$432$	4.00000	0.192450
$433$	15.3485	0.737600	0.368800	−	0.929509i	$-0.379769\pi$
$433$	15.3485	0.737600	0.368800	+	0.929509i	$0.379769\pi$
$434$	−19.5959	−0.940634
$435$	−4.65153	−0.223024
$436$	37.3939	1.79084
$437$	−2.69694	−0.129012
$438$	27.7980	1.32824
$439$	0.348469	0.0166315	0.00831576	−	0.999965i	$-0.497353\pi$
$439$	0.348469	0.0166315	0.00831576	+	0.999965i	$0.497353\pi$
$440$	0	0
$441$	1.00000	0.0476190
$442$	9.30306	0.442502
$443$	26.4495	1.25665	0.628327	−	0.777950i	$-0.283740\pi$
$443$	26.4495	1.25665	0.628327	+	0.777950i	$0.283740\pi$
$444$	−28.0000	−1.32882
$445$	−24.0000	−1.13771
$446$	−18.2474	−0.864042
$447$	8.69694	0.411351
$448$	−8.00000	−0.377964
$449$	28.8990	1.36383	0.681914	−	0.731433i	$-0.261148\pi$
$449$	28.8990	1.36383	0.681914	+	0.731433i	$0.261148\pi$
$450$	−2.44949	−0.115470
$451$	0	0
$452$	−24.0000	−1.12887
$453$	−5.34847	−0.251293
$454$	−29.3939	−1.37952
$455$	−16.8990	−0.792236
$456$	2.20204	0.103120
$457$	−19.4949	−0.911933	−0.455966	−	0.889997i	$-0.650706\pi$
$457$	−19.4949	−0.911933	−0.455966	+	0.889997i	$0.650706\pi$
$458$	−6.24745	−0.291924
$459$	−0.550510	−0.0256956
$460$	−58.7878	−2.74099
$461$	29.1464	1.35748	0.678742	−	0.734377i	$-0.262525\pi$
$461$	29.1464	1.35748	0.678742	+	0.734377i	$0.262525\pi$
$462$	0	0
$463$	−19.7980	−0.920089	−0.460045	−	0.887896i	$-0.652167\pi$
$463$	−19.7980	−0.920089	−0.460045	+	0.887896i	$0.652167\pi$
$464$	7.59592	0.352632
$465$	−19.5959	−0.908739
$466$	−4.65153	−0.215478
$467$	−7.59592	−0.351497	−0.175749	−	0.984435i	$-0.556235\pi$
$467$	−7.59592	−0.351497	−0.175749	+	0.984435i	$0.556235\pi$
$468$	27.5959	1.27562
$469$	14.2474	0.657886
$470$	−72.0000	−3.32111
$471$	−6.44949	−0.297177
$472$	−12.0000	−0.552345
$473$	0	0
$474$	14.4495	0.663687
$475$	−0.449490	−0.0206240
$476$	−2.20204	−0.100930
$477$	−7.89898	−0.361669
$478$	−7.34847	−0.336111
$479$	−21.2474	−0.970821	−0.485410	−	0.874286i	$-0.661330\pi$
$479$	−21.2474	−0.970821	−0.485410	+	0.874286i	$0.661330\pi$
$480$	0	0
$481$	−48.2929	−2.20196
$482$	47.1464	2.14746
$483$	6.00000	0.273009
$484$	−44.0000	−2.00000
$485$	−30.2474	−1.37347
$486$	−2.44949	−0.111111
$487$	22.9444	1.03971	0.519855	−	0.854255i	$-0.325986\pi$
$487$	22.9444	1.03971	0.519855	+	0.854255i	$0.325986\pi$
$488$	2.20204	0.0996817
$489$	17.0000	0.768767
$490$	6.00000	0.271052
$491$	−22.8990	−1.03342	−0.516708	−	0.856162i	$-0.672843\pi$
$491$	−22.8990	−1.03342	−0.516708	+	0.856162i	$0.672843\pi$
$492$	2.20204	0.0992757
$493$	−1.04541	−0.0470828
$494$	7.59592	0.341757
$495$	0	0
$496$	32.0000	1.43684
$497$	8.44949	0.379011
$498$	−14.6969	−0.658586
$499$	−38.0454	−1.70315	−0.851573	−	0.524236i	$-0.824351\pi$
$499$	−38.0454	−1.70315	−0.851573	+	0.524236i	$0.824351\pi$
$500$	39.1918	1.75271
$501$	−11.1464	−0.497986
$502$	25.3485	1.13136
$503$	24.5505	1.09465	0.547327	−	0.836919i	$-0.315646\pi$
$503$	24.5505	1.09465	0.547327	+	0.836919i	$0.315646\pi$
$504$	−4.89898	−0.218218
$505$	0	0
$506$	0	0
$507$	34.5959	1.53646
$508$	4.00000	0.177471
$509$	37.0454	1.64201	0.821004	−	0.570922i	$-0.193414\pi$
$509$	37.0454	1.64201	0.821004	+	0.570922i	$0.193414\pi$
$510$	−3.30306	−0.146262
$511$	−11.3485	−0.502027
$512$	39.1918	1.73205
$513$	−0.449490	−0.0198455
$514$	−56.6969	−2.50079
$515$	9.79796	0.431750
$516$	8.00000	0.352180
$517$	0	0
$518$	17.1464	0.753371
$519$	−6.24745	−0.274233
$520$	82.7878	3.63048
$521$	−18.0000	−0.788594	−0.394297	−	0.918983i	$-0.629012\pi$
$521$	−18.0000	−0.788594	−0.394297	+	0.918983i	$0.629012\pi$
$522$	−4.65153	−0.203592
$523$	−3.75255	−0.164088	−0.0820438	−	0.996629i	$-0.526145\pi$
$523$	−3.75255	−0.164088	−0.0820438	+	0.996629i	$0.526145\pi$
$524$	41.3939	1.80830
$525$	1.00000	0.0436436
$526$	−27.3031	−1.19047
$527$	−4.40408	−0.191845
$528$	0	0
$529$	13.0000	0.565217
$530$	−47.3939	−2.05866
$531$	2.44949	0.106299
$532$	−1.79796	−0.0779514
$533$	3.79796	0.164508
$534$	−24.0000	−1.03858
$535$	18.0000	0.778208
$536$	−69.7980	−3.01481
$537$	−3.79796	−0.163894
$538$	−6.74235	−0.290683
$539$	0	0
$540$	−9.79796	−0.421637
$541$	0.898979	0.0386501	0.0193251	−	0.999813i	$-0.493848\pi$
$541$	0.898979	0.0386501	0.0193251	+	0.999813i	$0.493848\pi$
$542$	−56.2020	−2.41408
$543$	−24.1464	−1.03622
$544$	0	0
$545$	−22.8990	−0.980885
$546$	−16.8990	−0.723210
$547$	17.7980	0.760986	0.380493	−	0.924784i	$-0.375754\pi$
$547$	17.7980	0.760986	0.380493	+	0.924784i	$0.375754\pi$
$548$	87.1918	3.72465
$549$	−0.449490	−0.0191838
$550$	0	0
$551$	−0.853572	−0.0363634
$552$	−29.3939	−1.25109
$553$	−5.89898	−0.250850
$554$	−72.9898	−3.10104
$555$	17.1464	0.727825
$556$	−81.3939	−3.45187
$557$	2.20204	0.0933035	0.0466517	−	0.998911i	$-0.485145\pi$
$557$	2.20204	0.0933035	0.0466517	+	0.998911i	$0.485145\pi$
$558$	−19.5959	−0.829561
$559$	13.7980	0.583591
$560$	−9.79796	−0.414039
$561$	0	0
$562$	60.7423	2.56226
$563$	−34.2929	−1.44527	−0.722636	−	0.691229i	$-0.757070\pi$
$563$	−34.2929	−1.44527	−0.722636	+	0.691229i	$0.757070\pi$
$564$	−48.0000	−2.02116
$565$	14.6969	0.618305
$566$	−23.6413	−0.993719
$567$	1.00000	0.0419961
$568$	−41.3939	−1.73685
$569$	18.4949	0.775346	0.387673	−	0.921797i	$-0.373279\pi$
$569$	18.4949	0.775346	0.387673	+	0.921797i	$0.373279\pi$
$570$	−2.69694	−0.112962
$571$	−10.8536	−0.454208	−0.227104	−	0.973871i	$-0.572926\pi$
$571$	−10.8536	−0.454208	−0.227104	+	0.973871i	$0.572926\pi$
$572$	0	0
$573$	1.34847	0.0563331
$574$	−1.34847	−0.0562840
$575$	6.00000	0.250217
$576$	−8.00000	−0.333333
$577$	−35.3485	−1.47158	−0.735788	−	0.677212i	$-0.763188\pi$
$577$	−35.3485	−1.47158	−0.735788	+	0.677212i	$0.763188\pi$
$578$	40.8990	1.70117
$579$	10.4495	0.434266
$580$	−18.6061	−0.772577
$581$	6.00000	0.248922
$582$	−30.2474	−1.25380
$583$	0	0
$584$	55.5959	2.30058
$585$	−16.8990	−0.698687
$586$	−52.7878	−2.18064
$587$	−0.550510	−0.0227220	−0.0113610	−	0.999935i	$-0.503616\pi$
$587$	−0.550510	−0.0227220	−0.0113610	+	0.999935i	$0.503616\pi$
$588$	4.00000	0.164957
$589$	−3.59592	−0.148167
$590$	14.6969	0.605063
$591$	3.55051	0.146048
$592$	−28.0000	−1.15079
$593$	9.79796	0.402354	0.201177	−	0.979555i	$-0.435523\pi$
$593$	9.79796	0.402354	0.201177	+	0.979555i	$0.435523\pi$
$594$	0	0
$595$	1.34847	0.0552818
$596$	34.7878	1.42496
$597$	20.0000	0.818546
$598$	−101.394	−4.14630
$599$	−33.0000	−1.34834	−0.674172	−	0.738575i	$-0.735499\pi$
$599$	−33.0000	−1.34834	−0.674172	+	0.738575i	$0.735499\pi$
$600$	−4.89898	−0.200000
$601$	−20.3485	−0.830031	−0.415016	−	0.909814i	$-0.636224\pi$
$601$	−20.3485	−0.830031	−0.415016	+	0.909814i	$0.636224\pi$
$602$	−4.89898	−0.199667
$603$	14.2474	0.580201
$604$	−21.3939	−0.870505
$605$	26.9444	1.09545
$606$	0	0
$607$	−5.34847	−0.217088	−0.108544	−	0.994092i	$-0.534619\pi$
$607$	−5.34847	−0.217088	−0.108544	+	0.994092i	$0.534619\pi$
$608$	0	0
$609$	1.89898	0.0769505
$610$	−2.69694	−0.109196
$611$	−82.7878	−3.34923
$612$	−2.20204	−0.0890122
$613$	−10.4949	−0.423885	−0.211942	−	0.977282i	$-0.567979\pi$
$613$	−10.4949	−0.423885	−0.211942	+	0.977282i	$0.567979\pi$
$614$	−62.3383	−2.51577
$615$	−1.34847	−0.0543755
$616$	0	0
$617$	27.0000	1.08698	0.543490	−	0.839416i	$-0.317103\pi$
$617$	27.0000	1.08698	0.543490	+	0.839416i	$0.317103\pi$
$618$	9.79796	0.394132
$619$	3.65153	0.146767	0.0733837	−	0.997304i	$-0.476620\pi$
$619$	3.65153	0.146767	0.0733837	+	0.997304i	$0.476620\pi$
$620$	−78.3837	−3.14796
$621$	6.00000	0.240772
$622$	−42.0000	−1.68405
$623$	9.79796	0.392547
$624$	27.5959	1.10472
$625$	−29.0000	−1.16000
$626$	−50.3383	−2.01192
$627$	0	0
$628$	−25.7980	−1.02945
$629$	3.85357	0.153652
$630$	6.00000	0.239046
$631$	28.2020	1.12271	0.561353	−	0.827577i	$-0.310281\pi$
$631$	28.2020	1.12271	0.561353	+	0.827577i	$0.310281\pi$
$632$	28.8990	1.14954
$633$	4.69694	0.186687
$634$	70.7878	2.81134
$635$	−2.44949	−0.0972050
$636$	−31.5959	−1.25286
$637$	6.89898	0.273348
$638$	0	0
$639$	8.44949	0.334257
$640$	−48.0000	−1.89737
$641$	−7.89898	−0.311991	−0.155995	−	0.987758i	$-0.549859\pi$
$641$	−7.89898	−0.311991	−0.155995	+	0.987758i	$0.549859\pi$
$642$	18.0000	0.710403
$643$	−5.34847	−0.210923	−0.105462	−	0.994423i	$-0.533632\pi$
$643$	−5.34847	−0.210923	−0.105462	+	0.994423i	$0.533632\pi$
$644$	24.0000	0.945732
$645$	−4.89898	−0.192897
$646$	−0.606123	−0.0238476
$647$	15.3031	0.601625	0.300813	−	0.953683i	$-0.402742\pi$
$647$	15.3031	0.601625	0.300813	+	0.953683i	$0.402742\pi$
$648$	−4.89898	−0.192450
$649$	0	0
$650$	−16.8990	−0.662833
$651$	8.00000	0.313545
$652$	68.0000	2.66309
$653$	21.5505	0.843337	0.421668	−	0.906750i	$-0.361445\pi$
$653$	21.5505	0.843337	0.421668	+	0.906750i	$0.361445\pi$
$654$	−22.8990	−0.895421
$655$	−25.3485	−0.990447
$656$	2.20204	0.0859753
$657$	−11.3485	−0.442746
$658$	29.3939	1.14589
$659$	−22.8990	−0.892018	−0.446009	−	0.895029i	$-0.647155\pi$
$659$	−22.8990	−0.892018	−0.446009	+	0.895029i	$0.647155\pi$
$660$	0	0
$661$	−35.3485	−1.37490	−0.687448	−	0.726234i	$-0.741269\pi$
$661$	−35.3485	−1.37490	−0.687448	+	0.726234i	$0.741269\pi$
$662$	33.1918	1.29004
$663$	−3.79796	−0.147501
$664$	−29.3939	−1.14070
$665$	1.10102	0.0426957
$666$	17.1464	0.664411
$667$	11.3939	0.441173
$668$	−44.5857	−1.72507
$669$	7.44949	0.288014
$670$	85.4847	3.30256
$671$	0	0
$672$	0	0
$673$	14.3031	0.551343	0.275671	−	0.961252i	$-0.411100\pi$
$673$	14.3031	0.551343	0.275671	+	0.961252i	$0.411100\pi$
$674$	21.1918	0.816279
$675$	1.00000	0.0384900
$676$	138.384	5.32245
$677$	−18.5505	−0.712954	−0.356477	−	0.934304i	$-0.616022\pi$
$677$	−18.5505	−0.712954	−0.356477	+	0.934304i	$0.616022\pi$
$678$	14.6969	0.564433
$679$	12.3485	0.473891
$680$	−6.60612	−0.253333
$681$	12.0000	0.459841
$682$	0	0
$683$	13.5959	0.520233	0.260117	−	0.965577i	$-0.416239\pi$
$683$	13.5959	0.520233	0.260117	+	0.965577i	$0.416239\pi$
$684$	−1.79796	−0.0687467
$685$	−53.3939	−2.04008
$686$	−2.44949	−0.0935220
$687$	2.55051	0.0973080
$688$	8.00000	0.304997
$689$	−54.4949	−2.07609
$690$	36.0000	1.37050
$691$	37.4495	1.42465	0.712323	−	0.701852i	$-0.247643\pi$
$691$	37.4495	1.42465	0.712323	+	0.701852i	$0.247643\pi$
$692$	−24.9898	−0.949969
$693$	0	0
$694$	−28.6515	−1.08760
$695$	49.8434	1.89067
$696$	−9.30306	−0.352632
$697$	−0.303062	−0.0114793
$698$	−66.2474	−2.50750
$699$	1.89898	0.0718260
$700$	4.00000	0.151186
$701$	24.4949	0.925160	0.462580	−	0.886578i	$-0.346924\pi$
$701$	24.4949	0.925160	0.462580	+	0.886578i	$0.346924\pi$
$702$	−16.8990	−0.637811
$703$	3.14643	0.118670
$704$	0	0
$705$	29.3939	1.10704
$706$	−17.3939	−0.654627
$707$	0	0
$708$	9.79796	0.368230
$709$	−42.3939	−1.59214	−0.796068	−	0.605208i	$-0.793090\pi$
$709$	−42.3939	−1.59214	−0.796068	+	0.605208i	$0.793090\pi$
$710$	50.6969	1.90262
$711$	−5.89898	−0.221229
$712$	−48.0000	−1.79888
$713$	48.0000	1.79761
$714$	1.34847	0.0504652
$715$	0	0
$716$	−15.1918	−0.567746
$717$	3.00000	0.112037
$718$	−36.7423	−1.37121
$719$	−3.85357	−0.143714	−0.0718570	−	0.997415i	$-0.522893\pi$
$719$	−3.85357	−0.143714	−0.0718570	+	0.997415i	$0.522893\pi$
$720$	−9.79796	−0.365148
$721$	−4.00000	−0.148968
$722$	46.0454	1.71363
$723$	−19.2474	−0.715820
$724$	−96.5857	−3.58958
$725$	1.89898	0.0705263
$726$	26.9444	1.00000
$727$	−30.6413	−1.13642	−0.568212	−	0.822882i	$-0.692365\pi$
$727$	−30.6413	−1.13642	−0.568212	+	0.822882i	$0.692365\pi$
$728$	−33.7980	−1.25264
$729$	1.00000	0.0370370
$730$	−68.0908	−2.52015
$731$	−1.10102	−0.0407227
$732$	−1.79796	−0.0664545
$733$	−14.6515	−0.541167	−0.270583	−	0.962697i	$-0.587217\pi$
$733$	−14.6515	−0.541167	−0.270583	+	0.962697i	$0.587217\pi$
$734$	−4.89898	−0.180825
$735$	−2.44949	−0.0903508
$736$	0	0
$737$	0	0
$738$	−1.34847	−0.0496378
$739$	−33.6969	−1.23956	−0.619781	−	0.784775i	$-0.712779\pi$
$739$	−33.6969	−1.23956	−0.619781	+	0.784775i	$0.712779\pi$
$740$	68.5857	2.52126
$741$	−3.10102	−0.113919
$742$	19.3485	0.710305
$743$	5.69694	0.209000	0.104500	−	0.994525i	$-0.466676\pi$
$743$	5.69694	0.209000	0.104500	+	0.994525i	$0.466676\pi$
$744$	−39.1918	−1.43684
$745$	−21.3031	−0.780484
$746$	−60.9898	−2.23300
$747$	6.00000	0.219529
$748$	0	0
$749$	−7.34847	−0.268507
$750$	−24.0000	−0.876356
$751$	−39.6413	−1.44653	−0.723266	−	0.690569i	$-0.757360\pi$
$751$	−39.6413	−1.44653	−0.723266	+	0.690569i	$0.757360\pi$
$752$	−48.0000	−1.75038
$753$	−10.3485	−0.377119
$754$	−32.0908	−1.16868
$755$	13.1010	0.476795
$756$	4.00000	0.145479
$757$	−45.0908	−1.63885	−0.819427	−	0.573184i	$-0.805708\pi$
$757$	−45.0908	−1.63885	−0.819427	+	0.573184i	$0.805708\pi$
$758$	−48.9898	−1.77939
$759$	0	0
$760$	−5.39388	−0.195656
$761$	29.6413	1.07450	0.537249	−	0.843424i	$-0.319464\pi$
$761$	29.6413	1.07450	0.537249	+	0.843424i	$0.319464\pi$
$762$	−2.44949	−0.0887357
$763$	9.34847	0.338437
$764$	5.39388	0.195144
$765$	1.34847	0.0487540
$766$	−7.95459	−0.287411
$767$	16.8990	0.610187
$768$	−32.0000	−1.15470
$769$	37.4495	1.35046	0.675232	−	0.737606i	$-0.264044\pi$
$769$	37.4495	1.35046	0.675232	+	0.737606i	$0.264044\pi$
$770$	0	0
$771$	23.1464	0.833598
$772$	41.7980	1.50434
$773$	−26.7526	−0.962222	−0.481111	−	0.876660i	$-0.659767\pi$
$773$	−26.7526	−0.962222	−0.481111	+	0.876660i	$0.659767\pi$
$774$	−4.89898	−0.176090
$775$	8.00000	0.287368
$776$	−60.4949	−2.17164
$777$	−7.00000	−0.251124
$778$	−24.6061	−0.882172
$779$	−0.247449	−0.00886577
$780$	−67.5959	−2.42032
$781$	0	0
$782$	8.09082	0.289327
$783$	1.89898	0.0678640
$784$	4.00000	0.142857
$785$	15.7980	0.563853
$786$	−25.3485	−0.904150
$787$	20.8536	0.743350	0.371675	−	0.928363i	$-0.378784\pi$
$787$	20.8536	0.743350	0.371675	+	0.928363i	$0.378784\pi$
$788$	14.2020	0.505927
$789$	11.1464	0.396823
$790$	−35.3939	−1.25926
$791$	−6.00000	−0.213335
$792$	0	0
$793$	−3.10102	−0.110120
$794$	−55.5959	−1.97303
$795$	19.3485	0.686219
$796$	80.0000	2.83552
$797$	27.7980	0.984654	0.492327	−	0.870410i	$-0.336146\pi$
$797$	27.7980	0.984654	0.492327	+	0.870410i	$0.336146\pi$
$798$	1.10102	0.0389757
$799$	6.60612	0.233708
$800$	0	0
$801$	9.79796	0.346194
$802$	72.7423	2.56862
$803$	0	0
$804$	56.9898	2.00988
$805$	−14.6969	−0.517999
$806$	−135.192	−4.76193
$807$	2.75255	0.0968944
$808$	0	0
$809$	−23.1464	−0.813785	−0.406893	−	0.913476i	$-0.633388\pi$
$809$	−23.1464	−0.813785	−0.406893	+	0.913476i	$0.633388\pi$
$810$	6.00000	0.210819
$811$	−4.49490	−0.157837	−0.0789186	−	0.996881i	$-0.525147\pi$
$811$	−4.49490	−0.157837	−0.0789186	+	0.996881i	$0.525147\pi$
$812$	7.59592	0.266564
$813$	22.9444	0.804695
$814$	0	0
$815$	−41.6413	−1.45863
$816$	−2.20204	−0.0770869
$817$	−0.898979	−0.0314513
$818$	31.1010	1.08742
$819$	6.89898	0.241070
$820$	−5.39388	−0.188362
$821$	−12.7980	−0.446652	−0.223326	−	0.974744i	$-0.571691\pi$
$821$	−12.7980	−0.446652	−0.223326	+	0.974744i	$0.571691\pi$
$822$	−53.3939	−1.86233
$823$	−19.0000	−0.662298	−0.331149	−	0.943578i	$-0.607436\pi$
$823$	−19.0000	−0.662298	−0.331149	+	0.943578i	$0.607436\pi$
$824$	19.5959	0.682656
$825$	0	0
$826$	−6.00000	−0.208767
$827$	−5.20204	−0.180893	−0.0904463	−	0.995901i	$-0.528829\pi$
$827$	−5.20204	−0.180893	−0.0904463	+	0.995901i	$0.528829\pi$
$828$	24.0000	0.834058
$829$	−16.4949	−0.572891	−0.286446	−	0.958096i	$-0.592474\pi$
$829$	−16.4949	−0.572891	−0.286446	+	0.958096i	$0.592474\pi$
$830$	36.0000	1.24958
$831$	29.7980	1.03368
$832$	−55.1918	−1.91343
$833$	−0.550510	−0.0190740
$834$	49.8434	1.72593
$835$	27.3031	0.944861
$836$	0	0
$837$	8.00000	0.276520
$838$	−18.6061	−0.642738
$839$	25.8434	0.892212	0.446106	−	0.894980i	$-0.352810\pi$
$839$	25.8434	0.892212	0.446106	+	0.894980i	$0.352810\pi$
$840$	12.0000	0.414039
$841$	−25.3939	−0.875651
$842$	93.1918	3.21160
$843$	−24.7980	−0.854087
$844$	18.7878	0.646701
$845$	−84.7423	−2.91523
$846$	29.3939	1.01058
$847$	−11.0000	−0.377964
$848$	−31.5959	−1.08501
$849$	9.65153	0.331240
$850$	1.34847	0.0462521
$851$	−42.0000	−1.43974
$852$	33.7980	1.15790
$853$	−55.7423	−1.90858	−0.954291	−	0.298880i	$-0.903387\pi$
$853$	−55.7423	−1.90858	−0.954291	+	0.298880i	$0.903387\pi$
$854$	1.10102	0.0376761
$855$	1.10102	0.0376541
$856$	36.0000	1.23045
$857$	3.30306	0.112830	0.0564152	−	0.998407i	$-0.482033\pi$
$857$	3.30306	0.112830	0.0564152	+	0.998407i	$0.482033\pi$
$858$	0	0
$859$	−1.85357	−0.0632431	−0.0316215	−	0.999500i	$-0.510067\pi$
$859$	−1.85357	−0.0632431	−0.0316215	+	0.999500i	$0.510067\pi$
$860$	−19.5959	−0.668215
$861$	0.550510	0.0187613
$862$	32.6969	1.11366
$863$	−28.1010	−0.956570	−0.478285	−	0.878205i	$-0.658741\pi$
$863$	−28.1010	−0.956570	−0.478285	+	0.878205i	$0.658741\pi$
$864$	0	0
$865$	15.3031	0.520320
$866$	−37.5959	−1.27756
$867$	−16.6969	−0.567058
$868$	32.0000	1.08615
$869$	0	0
$870$	11.3939	0.386289
$871$	98.2929	3.33053
$872$	−45.7980	−1.55091
$873$	12.3485	0.417932
$874$	6.60612	0.223455
$875$	9.79796	0.331231
$876$	−45.3939	−1.53372
$877$	43.6969	1.47554	0.737770	−	0.675052i	$-0.235879\pi$
$877$	43.6969	1.47554	0.737770	+	0.675052i	$0.235879\pi$
$878$	−0.853572	−0.0288067
$879$	21.5505	0.726881
$880$	0	0
$881$	−42.2474	−1.42335	−0.711676	−	0.702507i	$-0.752064\pi$
$881$	−42.2474	−1.42335	−0.711676	+	0.702507i	$0.752064\pi$
$882$	−2.44949	−0.0824786
$883$	−19.7980	−0.666254	−0.333127	−	0.942882i	$-0.608104\pi$
$883$	−19.7980	−0.666254	−0.333127	+	0.942882i	$0.608104\pi$
$884$	−15.1918	−0.510957
$885$	−6.00000	−0.201688
$886$	−64.7878	−2.17659
$887$	−4.89898	−0.164492	−0.0822458	−	0.996612i	$-0.526209\pi$
$887$	−4.89898	−0.164492	−0.0822458	+	0.996612i	$0.526209\pi$
$888$	34.2929	1.15079
$889$	1.00000	0.0335389
$890$	58.7878	1.97057
$891$	0	0
$892$	29.7980	0.997709
$893$	5.39388	0.180499
$894$	−21.3031	−0.712481
$895$	9.30306	0.310967
$896$	19.5959	0.654654
$897$	41.3939	1.38210
$898$	−70.7878	−2.36222
$899$	15.1918	0.506676
$900$	4.00000	0.133333
$901$	4.34847	0.144869
$902$	0	0
$903$	2.00000	0.0665558
$904$	29.3939	0.977626
$905$	59.1464	1.96609
$906$	13.1010	0.435252
$907$	13.2020	0.438367	0.219183	−	0.975684i	$-0.429661\pi$
$907$	13.2020	0.438367	0.219183	+	0.975684i	$0.429661\pi$
$908$	48.0000	1.59294
$909$	0	0
$910$	41.3939	1.37219
$911$	8.69694	0.288142	0.144071	−	0.989567i	$-0.453981\pi$
$911$	8.69694	0.288142	0.144071	+	0.989567i	$0.453981\pi$
$912$	−1.79796	−0.0595364
$913$	0	0
$914$	47.7526	1.57951
$915$	1.10102	0.0363986
$916$	10.2020	0.337085
$917$	10.3485	0.341737
$918$	1.34847	0.0445061
$919$	−4.79796	−0.158270	−0.0791350	−	0.996864i	$-0.525216\pi$
$919$	−4.79796	−0.158270	−0.0791350	+	0.996864i	$0.525216\pi$
$920$	72.0000	2.37377
$921$	25.4495	0.838589
$922$	−71.3939	−2.35123
$923$	58.2929	1.91873
$924$	0	0
$925$	−7.00000	−0.230159
$926$	48.4949	1.59364
$927$	−4.00000	−0.131377
$928$	0	0
$929$	−22.2929	−0.731405	−0.365702	−	0.930732i	$-0.619171\pi$
$929$	−22.2929	−0.731405	−0.365702	+	0.930732i	$0.619171\pi$
$930$	48.0000	1.57398
$931$	−0.449490	−0.0147314
$932$	7.59592	0.248813
$933$	17.1464	0.561349
$934$	18.6061	0.608811
$935$	0	0
$936$	−33.7980	−1.10472
$937$	−42.6969	−1.39485	−0.697424	−	0.716659i	$-0.745671\pi$
$937$	−42.6969	−1.39485	−0.697424	+	0.716659i	$0.745671\pi$
$938$	−34.8990	−1.13949
$939$	20.5505	0.670641
$940$	117.576	3.83489
$941$	−28.8434	−0.940267	−0.470133	−	0.882595i	$-0.655794\pi$
$941$	−28.8434	−0.940267	−0.470133	+	0.882595i	$0.655794\pi$
$942$	15.7980	0.514725
$943$	3.30306	0.107562
$944$	9.79796	0.318896
$945$	−2.44949	−0.0796819
$946$	0	0
$947$	−51.9898	−1.68944	−0.844721	−	0.535207i	$-0.820233\pi$
$947$	−51.9898	−1.68944	−0.844721	+	0.535207i	$0.820233\pi$
$948$	−23.5959	−0.766360
$949$	−78.2929	−2.54149
$950$	1.10102	0.0357218
$951$	−28.8990	−0.937114
$952$	2.69694	0.0874083
$953$	13.3485	0.432399	0.216200	−	0.976349i	$-0.430634\pi$
$953$	13.3485	0.432399	0.216200	+	0.976349i	$0.430634\pi$
$954$	19.3485	0.626430
$955$	−3.30306	−0.106885
$956$	12.0000	0.388108
$957$	0	0
$958$	52.0454	1.68151
$959$	21.7980	0.703893
$960$	19.5959	0.632456
$961$	33.0000	1.06452
$962$	118.293	3.81391
$963$	−7.34847	−0.236801
$964$	−76.9898	−2.47967
$965$	−25.5959	−0.823962
$966$	−14.6969	−0.472866
$967$	−42.9444	−1.38100	−0.690499	−	0.723333i	$-0.742609\pi$
$967$	−42.9444	−1.38100	−0.690499	+	0.723333i	$0.742609\pi$
$968$	53.8888	1.73205
$969$	0.247449	0.00794920
$970$	74.0908	2.37891
$971$	−1.59592	−0.0512154	−0.0256077	−	0.999672i	$-0.508152\pi$
$971$	−1.59592	−0.0512154	−0.0256077	+	0.999672i	$0.508152\pi$
$972$	4.00000	0.128300
$973$	−20.3485	−0.652342
$974$	−56.2020	−1.80083
$975$	6.89898	0.220944
$976$	−1.79796	−0.0575513
$977$	−38.2020	−1.22219	−0.611096	−	0.791557i	$-0.709271\pi$
$977$	−38.2020	−1.22219	−0.611096	+	0.791557i	$0.709271\pi$
$978$	−41.6413	−1.33154
$979$	0	0
$980$	−9.79796	−0.312984
$981$	9.34847	0.298474
$982$	56.0908	1.78993
$983$	−41.9444	−1.33782	−0.668909	−	0.743344i	$-0.733238\pi$
$983$	−41.9444	−1.33782	−0.668909	+	0.743344i	$0.733238\pi$
$984$	−2.69694	−0.0859753
$985$	−8.69694	−0.277108
$986$	2.56072	0.0815498
$987$	−12.0000	−0.381964
$988$	−12.4041	−0.394626
$989$	12.0000	0.381578
$990$	0	0
$991$	5.55051	0.176318	0.0881589	−	0.996106i	$-0.471902\pi$
$991$	5.55051	0.176318	0.0881589	+	0.996106i	$0.471902\pi$
$992$	0	0
$993$	−13.5505	−0.430012
$994$	−20.6969	−0.656467
$995$	−48.9898	−1.55308
$996$	24.0000	0.760469
$997$	56.4949	1.78921	0.894606	−	0.446856i	$-0.147457\pi$
$997$	56.4949	1.78921	0.894606	+	0.446856i	$0.147457\pi$
$998$	93.1918	2.94994
$999$	−7.00000	−0.221470

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2667.2.a.h.1.1	✓	2
3.2	odd	2		8001.2.a.k.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2667.2.a.h.1.1	✓	2	1.1	even	1	trivial
8001.2.a.k.1.2		2	3.2	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:	\( N \)	\(=\)	\( 2667 = 3 \cdot 7 \cdot 127 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2667.a (trivial)

\(f(q)\)	\(=\)	\(q-2.44949 q^{2} +1.00000 q^{3} +4.00000 q^{4} -2.44949 q^{5} -2.44949 q^{6} +1.00000 q^{7} -4.89898 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.44949 q^{2} +1.00000 q^{3} +4.00000 q^{4} -2.44949 q^{5} -2.44949 q^{6} +1.00000 q^{7} -4.89898 q^{8} +1.00000 q^{9} +6.00000 q^{10} +4.00000 q^{12} +6.89898 q^{13} -2.44949 q^{14} -2.44949 q^{15} +4.00000 q^{16} -0.550510 q^{17} -2.44949 q^{18} -0.449490 q^{19} -9.79796 q^{20} +1.00000 q^{21} +6.00000 q^{23} -4.89898 q^{24} +1.00000 q^{25} -16.8990 q^{26} +1.00000 q^{27} +4.00000 q^{28} +1.89898 q^{29} +6.00000 q^{30} +8.00000 q^{31} +1.34847 q^{34} -2.44949 q^{35} +4.00000 q^{36} -7.00000 q^{37} +1.10102 q^{38} +6.89898 q^{39} +12.0000 q^{40} +0.550510 q^{41} -2.44949 q^{42} +2.00000 q^{43} -2.44949 q^{45} -14.6969 q^{46} -12.0000 q^{47} +4.00000 q^{48} +1.00000 q^{49} -2.44949 q^{50} -0.550510 q^{51} +27.5959 q^{52} -7.89898 q^{53} -2.44949 q^{54} -4.89898 q^{56} -0.449490 q^{57} -4.65153 q^{58} +2.44949 q^{59} -9.79796 q^{60} -0.449490 q^{61} -19.5959 q^{62} +1.00000 q^{63} -8.00000 q^{64} -16.8990 q^{65} +14.2474 q^{67} -2.20204 q^{68} +6.00000 q^{69} +6.00000 q^{70} +8.44949 q^{71} -4.89898 q^{72} -11.3485 q^{73} +17.1464 q^{74} +1.00000 q^{75} -1.79796 q^{76} -16.8990 q^{78} -5.89898 q^{79} -9.79796 q^{80} +1.00000 q^{81} -1.34847 q^{82} +6.00000 q^{83} +4.00000 q^{84} +1.34847 q^{85} -4.89898 q^{86} +1.89898 q^{87} +9.79796 q^{89} +6.00000 q^{90} +6.89898 q^{91} +24.0000 q^{92} +8.00000 q^{93} +29.3939 q^{94} +1.10102 q^{95} +12.3485 q^{97} -2.44949 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{3} + 8 q^{4} + 2 q^{7} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^3 + 8 * q^4 + 2 * q^7 + 2 * q^9	\( 2 q + 2 q^{3} + 8 q^{4} + 2 q^{7} + 2 q^{9} + 12 q^{10} + 8 q^{12} + 4 q^{13} + 8 q^{16} - 6 q^{17} + 4 q^{19} + 2 q^{21} + 12 q^{23} + 2 q^{25} - 24 q^{26} + 2 q^{27} + 8 q^{28} - 6 q^{29} + 12 q^{30} + 16 q^{31} - 12 q^{34} + 8 q^{36} - 14 q^{37} + 12 q^{38} + 4 q^{39} + 24 q^{40} + 6 q^{41} + 4 q^{43} - 24 q^{47} + 8 q^{48} + 2 q^{49} - 6 q^{51} + 16 q^{52} - 6 q^{53} + 4 q^{57} - 24 q^{58} + 4 q^{61} + 2 q^{63} - 16 q^{64} - 24 q^{65} + 4 q^{67} - 24 q^{68} + 12 q^{69} + 12 q^{70} + 12 q^{71} - 8 q^{73} + 2 q^{75} + 16 q^{76} - 24 q^{78} - 2 q^{79} + 2 q^{81} + 12 q^{82} + 12 q^{83} + 8 q^{84} - 12 q^{85} - 6 q^{87} + 12 q^{90} + 4 q^{91} + 48 q^{92} + 16 q^{93} + 12 q^{95} + 10 q^{97}+O(q^{100}) \) 2 * q + 2 * q^3 + 8 * q^4 + 2 * q^7 + 2 * q^9 + 12 * q^10 + 8 * q^12 + 4 * q^13 + 8 * q^16 - 6 * q^17 + 4 * q^19 + 2 * q^21 + 12 * q^23 + 2 * q^25 - 24 * q^26 + 2 * q^27 + 8 * q^28 - 6 * q^29 + 12 * q^30 + 16 * q^31 - 12 * q^34 + 8 * q^36 - 14 * q^37 + 12 * q^38 + 4 * q^39 + 24 * q^40 + 6 * q^41 + 4 * q^43 - 24 * q^47 + 8 * q^48 + 2 * q^49 - 6 * q^51 + 16 * q^52 - 6 * q^53 + 4 * q^57 - 24 * q^58 + 4 * q^61 + 2 * q^63 - 16 * q^64 - 24 * q^65 + 4 * q^67 - 24 * q^68 + 12 * q^69 + 12 * q^70 + 12 * q^71 - 8 * q^73 + 2 * q^75 + 16 * q^76 - 24 * q^78 - 2 * q^79 + 2 * q^81 + 12 * q^82 + 12 * q^83 + 8 * q^84 - 12 * q^85 - 6 * q^87 + 12 * q^90 + 4 * q^91 + 48 * q^92 + 16 * q^93 + 12 * q^95 + 10 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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