LMFDB - Embedded newform 1666.2.a.o.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:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 238)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.61803$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -3.23607 q^{3} +1.00000 q^{4} +1.23607 q^{5} +3.23607 q^{6} -1.00000 q^{8} +7.47214 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.23607 q^{3} +1.00000 q^{4} +1.23607 q^{5} +3.23607 q^{6} -1.00000 q^{8} +7.47214 q^{9} -1.23607 q^{10} +5.23607 q^{11} -3.23607 q^{12} +2.47214 q^{13} -4.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} -7.47214 q^{18} +8.47214 q^{19} +1.23607 q^{20} -5.23607 q^{22} +8.00000 q^{23} +3.23607 q^{24} -3.47214 q^{25} -2.47214 q^{26} -14.4721 q^{27} -5.70820 q^{29} +4.00000 q^{30} +1.52786 q^{31} -1.00000 q^{32} -16.9443 q^{33} +1.00000 q^{34} +7.47214 q^{36} -3.23607 q^{37} -8.47214 q^{38} -8.00000 q^{39} -1.23607 q^{40} +3.52786 q^{41} +2.47214 q^{43} +5.23607 q^{44} +9.23607 q^{45} -8.00000 q^{46} +2.47214 q^{47} -3.23607 q^{48} +3.47214 q^{50} +3.23607 q^{51} +2.47214 q^{52} -4.47214 q^{53} +14.4721 q^{54} +6.47214 q^{55} -27.4164 q^{57} +5.70820 q^{58} +6.00000 q^{59} -4.00000 q^{60} -1.23607 q^{61} -1.52786 q^{62} +1.00000 q^{64} +3.05573 q^{65} +16.9443 q^{66} -1.52786 q^{67} -1.00000 q^{68} -25.8885 q^{69} -2.47214 q^{71} -7.47214 q^{72} -13.4164 q^{73} +3.23607 q^{74} +11.2361 q^{75} +8.47214 q^{76} +8.00000 q^{78} -10.4721 q^{79} +1.23607 q^{80} +24.4164 q^{81} -3.52786 q^{82} -2.00000 q^{83} -1.23607 q^{85} -2.47214 q^{86} +18.4721 q^{87} -5.23607 q^{88} -2.00000 q^{89} -9.23607 q^{90} +8.00000 q^{92} -4.94427 q^{93} -2.47214 q^{94} +10.4721 q^{95} +3.23607 q^{96} +8.47214 q^{97} +39.1246 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{8} + 6 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^8 + 6 * q^9	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{8} + 6 q^{9} + 2 q^{10} + 6 q^{11} - 2 q^{12} - 4 q^{13} - 8 q^{15} + 2 q^{16} - 2 q^{17} - 6 q^{18} + 8 q^{19} - 2 q^{20} - 6 q^{22} + 16 q^{23} + 2 q^{24} + 2 q^{25} + 4 q^{26} - 20 q^{27} + 2 q^{29} + 8 q^{30} + 12 q^{31} - 2 q^{32} - 16 q^{33} + 2 q^{34} + 6 q^{36} - 2 q^{37} - 8 q^{38} - 16 q^{39} + 2 q^{40} + 16 q^{41} - 4 q^{43} + 6 q^{44} + 14 q^{45} - 16 q^{46} - 4 q^{47} - 2 q^{48} - 2 q^{50} + 2 q^{51} - 4 q^{52} + 20 q^{54} + 4 q^{55} - 28 q^{57} - 2 q^{58} + 12 q^{59} - 8 q^{60} + 2 q^{61} - 12 q^{62} + 2 q^{64} + 24 q^{65} + 16 q^{66} - 12 q^{67} - 2 q^{68} - 16 q^{69} + 4 q^{71} - 6 q^{72} + 2 q^{74} + 18 q^{75} + 8 q^{76} + 16 q^{78} - 12 q^{79} - 2 q^{80} + 22 q^{81} - 16 q^{82} - 4 q^{83} + 2 q^{85} + 4 q^{86} + 28 q^{87} - 6 q^{88} - 4 q^{89} - 14 q^{90} + 16 q^{92} + 8 q^{93} + 4 q^{94} + 12 q^{95} + 2 q^{96} + 8 q^{97} + 38 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^8 + 6 * q^9 + 2 * q^10 + 6 * q^11 - 2 * q^12 - 4 * q^13 - 8 * q^15 + 2 * q^16 - 2 * q^17 - 6 * q^18 + 8 * q^19 - 2 * q^20 - 6 * q^22 + 16 * q^23 + 2 * q^24 + 2 * q^25 + 4 * q^26 - 20 * q^27 + 2 * q^29 + 8 * q^30 + 12 * q^31 - 2 * q^32 - 16 * q^33 + 2 * q^34 + 6 * q^36 - 2 * q^37 - 8 * q^38 - 16 * q^39 + 2 * q^40 + 16 * q^41 - 4 * q^43 + 6 * q^44 + 14 * q^45 - 16 * q^46 - 4 * q^47 - 2 * q^48 - 2 * q^50 + 2 * q^51 - 4 * q^52 + 20 * q^54 + 4 * q^55 - 28 * q^57 - 2 * q^58 + 12 * q^59 - 8 * q^60 + 2 * q^61 - 12 * q^62 + 2 * q^64 + 24 * q^65 + 16 * q^66 - 12 * q^67 - 2 * q^68 - 16 * q^69 + 4 * q^71 - 6 * q^72 + 2 * q^74 + 18 * q^75 + 8 * q^76 + 16 * q^78 - 12 * q^79 - 2 * q^80 + 22 * q^81 - 16 * q^82 - 4 * q^83 + 2 * q^85 + 4 * q^86 + 28 * q^87 - 6 * q^88 - 4 * q^89 - 14 * q^90 + 16 * q^92 + 8 * q^93 + 4 * q^94 + 12 * q^95 + 2 * q^96 + 8 * q^97 + 38 * 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
$3$	−3.23607	−1.86834	−0.934172	−	0.356822i	$-0.883860\pi$
$3$	−3.23607	−1.86834	−0.934172	+	0.356822i	$0.883860\pi$
$4$	1.00000	0.500000
$5$	1.23607	0.552786	0.276393	−	0.961045i	$-0.410861\pi$
$5$	1.23607	0.552786	0.276393	+	0.961045i	$0.410861\pi$
$6$	3.23607	1.32112
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	7.47214	2.49071
$10$	−1.23607	−0.390879
$11$	5.23607	1.57873	0.789367	−	0.613922i	$-0.210409\pi$
$11$	5.23607	1.57873	0.789367	+	0.613922i	$0.210409\pi$
$12$	−3.23607	−0.934172
$13$	2.47214	0.685647	0.342824	−	0.939400i	$-0.388617\pi$
$13$	2.47214	0.685647	0.342824	+	0.939400i	$0.388617\pi$
$14$	0	0
$15$	−4.00000	−1.03280
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−7.47214	−1.76120
$19$	8.47214	1.94364	0.971821	−	0.235722i	$-0.0757453\pi$
$19$	8.47214	1.94364	0.971821	+	0.235722i	$0.0757453\pi$
$20$	1.23607	0.276393
$21$	0	0
$22$	−5.23607	−1.11633
$23$	8.00000	1.66812	0.834058	−	0.551677i	$-0.186012\pi$
$23$	8.00000	1.66812	0.834058	+	0.551677i	$0.186012\pi$
$24$	3.23607	0.660560
$25$	−3.47214	−0.694427
$26$	−2.47214	−0.484826
$27$	−14.4721	−2.78516
$28$	0	0
$29$	−5.70820	−1.05999	−0.529993	−	0.848002i	$-0.677806\pi$
$29$	−5.70820	−1.05999	−0.529993	+	0.848002i	$0.677806\pi$
$30$	4.00000	0.730297
$31$	1.52786	0.274412	0.137206	−	0.990543i	$-0.456188\pi$
$31$	1.52786	0.274412	0.137206	+	0.990543i	$0.456188\pi$
$32$	−1.00000	−0.176777
$33$	−16.9443	−2.94962
$34$	1.00000	0.171499
$35$	0	0
$36$	7.47214	1.24536
$37$	−3.23607	−0.532006	−0.266003	−	0.963972i	$-0.585703\pi$
$37$	−3.23607	−0.532006	−0.266003	+	0.963972i	$0.585703\pi$
$38$	−8.47214	−1.37436
$39$	−8.00000	−1.28103
$40$	−1.23607	−0.195440
$41$	3.52786	0.550960	0.275480	−	0.961307i	$-0.411163\pi$
$41$	3.52786	0.550960	0.275480	+	0.961307i	$0.411163\pi$
$42$	0	0
$43$	2.47214	0.376997	0.188499	−	0.982073i	$-0.439638\pi$
$43$	2.47214	0.376997	0.188499	+	0.982073i	$0.439638\pi$
$44$	5.23607	0.789367
$45$	9.23607	1.37683
$46$	−8.00000	−1.17954
$47$	2.47214	0.360598	0.180299	−	0.983612i	$-0.442293\pi$
$47$	2.47214	0.360598	0.180299	+	0.983612i	$0.442293\pi$
$48$	−3.23607	−0.467086
$49$	0	0
$50$	3.47214	0.491034
$51$	3.23607	0.453140
$52$	2.47214	0.342824
$53$	−4.47214	−0.614295	−0.307148	−	0.951662i	$-0.599375\pi$
$53$	−4.47214	−0.614295	−0.307148	+	0.951662i	$0.599375\pi$
$54$	14.4721	1.96941
$55$	6.47214	0.872703
$56$	0	0
$57$	−27.4164	−3.63139
$58$	5.70820	0.749524
$59$	6.00000	0.781133	0.390567	−	0.920575i	$-0.372279\pi$
$59$	6.00000	0.781133	0.390567	+	0.920575i	$0.372279\pi$
$60$	−4.00000	−0.516398
$61$	−1.23607	−0.158262	−0.0791311	−	0.996864i	$-0.525215\pi$
$61$	−1.23607	−0.158262	−0.0791311	+	0.996864i	$0.525215\pi$
$62$	−1.52786	−0.194039
$63$	0	0
$64$	1.00000	0.125000
$65$	3.05573	0.379016
$66$	16.9443	2.08570
$67$	−1.52786	−0.186658	−0.0933292	−	0.995635i	$-0.529751\pi$
$67$	−1.52786	−0.186658	−0.0933292	+	0.995635i	$0.529751\pi$
$68$	−1.00000	−0.121268
$69$	−25.8885	−3.11661
$70$	0	0
$71$	−2.47214	−0.293389	−0.146694	−	0.989182i	$-0.546863\pi$
$71$	−2.47214	−0.293389	−0.146694	+	0.989182i	$0.546863\pi$
$72$	−7.47214	−0.880600
$73$	−13.4164	−1.57027	−0.785136	−	0.619324i	$-0.787407\pi$
$73$	−13.4164	−1.57027	−0.785136	+	0.619324i	$0.787407\pi$
$74$	3.23607	0.376185
$75$	11.2361	1.29743
$76$	8.47214	0.971821
$77$	0	0
$78$	8.00000	0.905822
$79$	−10.4721	−1.17821	−0.589104	−	0.808057i	$-0.700519\pi$
$79$	−10.4721	−1.17821	−0.589104	+	0.808057i	$0.700519\pi$
$80$	1.23607	0.138197
$81$	24.4164	2.71293
$82$	−3.52786	−0.389587
$83$	−2.00000	−0.219529	−0.109764	−	0.993958i	$-0.535010\pi$
$83$	−2.00000	−0.219529	−0.109764	+	0.993958i	$0.535010\pi$
$84$	0	0
$85$	−1.23607	−0.134070
$86$	−2.47214	−0.266577
$87$	18.4721	1.98042
$88$	−5.23607	−0.558167
$89$	−2.00000	−0.212000	−0.106000	−	0.994366i	$-0.533804\pi$
$89$	−2.00000	−0.212000	−0.106000	+	0.994366i	$0.533804\pi$
$90$	−9.23607	−0.973567
$91$	0	0
$92$	8.00000	0.834058
$93$	−4.94427	−0.512697
$94$	−2.47214	−0.254981
$95$	10.4721	1.07442
$96$	3.23607	0.330280
$97$	8.47214	0.860215	0.430108	−	0.902778i	$-0.358476\pi$
$97$	8.47214	0.860215	0.430108	+	0.902778i	$0.358476\pi$
$98$	0	0
$99$	39.1246	3.93217
$100$	−3.47214	−0.347214
$101$	6.47214	0.644002	0.322001	−	0.946739i	$-0.395645\pi$
$101$	6.47214	0.644002	0.322001	+	0.946739i	$0.395645\pi$
$102$	−3.23607	−0.320418
$103$	4.00000	0.394132	0.197066	−	0.980390i	$-0.436859\pi$
$103$	4.00000	0.394132	0.197066	+	0.980390i	$0.436859\pi$
$104$	−2.47214	−0.242413
$105$	0	0
$106$	4.47214	0.434372
$107$	−1.23607	−0.119495	−0.0597476	−	0.998214i	$-0.519030\pi$
$107$	−1.23607	−0.119495	−0.0597476	+	0.998214i	$0.519030\pi$
$108$	−14.4721	−1.39258
$109$	12.1803	1.16666	0.583332	−	0.812233i	$-0.301748\pi$
$109$	12.1803	1.16666	0.583332	+	0.812233i	$0.301748\pi$
$110$	−6.47214	−0.617094
$111$	10.4721	0.993971
$112$	0	0
$113$	13.4164	1.26211	0.631055	−	0.775738i	$-0.282622\pi$
$113$	13.4164	1.26211	0.631055	+	0.775738i	$0.282622\pi$
$114$	27.4164	2.56778
$115$	9.88854	0.922111
$116$	−5.70820	−0.529993
$117$	18.4721	1.70775
$118$	−6.00000	−0.552345
$119$	0	0
$120$	4.00000	0.365148
$121$	16.4164	1.49240
$122$	1.23607	0.111908
$123$	−11.4164	−1.02938
$124$	1.52786	0.137206
$125$	−10.4721	−0.936656
$126$	0	0
$127$	12.0000	1.06483	0.532414	−	0.846484i	$-0.321285\pi$
$127$	12.0000	1.06483	0.532414	+	0.846484i	$0.321285\pi$
$128$	−1.00000	−0.0883883
$129$	−8.00000	−0.704361
$130$	−3.05573	−0.268005
$131$	−1.70820	−0.149246	−0.0746232	−	0.997212i	$-0.523775\pi$
$131$	−1.70820	−0.149246	−0.0746232	+	0.997212i	$0.523775\pi$
$132$	−16.9443	−1.47481
$133$	0	0
$134$	1.52786	0.131987
$135$	−17.8885	−1.53960
$136$	1.00000	0.0857493
$137$	3.52786	0.301406	0.150703	−	0.988579i	$-0.451846\pi$
$137$	3.52786	0.301406	0.150703	+	0.988579i	$0.451846\pi$
$138$	25.8885	2.20378
$139$	12.1803	1.03312	0.516561	−	0.856250i	$-0.327212\pi$
$139$	12.1803	1.03312	0.516561	+	0.856250i	$0.327212\pi$
$140$	0	0
$141$	−8.00000	−0.673722
$142$	2.47214	0.207457
$143$	12.9443	1.08245
$144$	7.47214	0.622678
$145$	−7.05573	−0.585946
$146$	13.4164	1.11035
$147$	0	0
$148$	−3.23607	−0.266003
$149$	18.9443	1.55198	0.775988	−	0.630748i	$-0.217252\pi$
$149$	18.9443	1.55198	0.775988	+	0.630748i	$0.217252\pi$
$150$	−11.2361	−0.917421
$151$	4.00000	0.325515	0.162758	−	0.986666i	$-0.447961\pi$
$151$	4.00000	0.325515	0.162758	+	0.986666i	$0.447961\pi$
$152$	−8.47214	−0.687181
$153$	−7.47214	−0.604086
$154$	0	0
$155$	1.88854	0.151691
$156$	−8.00000	−0.640513
$157$	−20.9443	−1.67153	−0.835767	−	0.549084i	$-0.814977\pi$
$157$	−20.9443	−1.67153	−0.835767	+	0.549084i	$0.814977\pi$
$158$	10.4721	0.833118
$159$	14.4721	1.14772
$160$	−1.23607	−0.0977198
$161$	0	0
$162$	−24.4164	−1.91833
$163$	−0.291796	−0.0228552	−0.0114276	−	0.999935i	$-0.503638\pi$
$163$	−0.291796	−0.0228552	−0.0114276	+	0.999935i	$0.503638\pi$
$164$	3.52786	0.275480
$165$	−20.9443	−1.63051
$166$	2.00000	0.155230
$167$	14.4721	1.11989	0.559944	−	0.828531i	$-0.310823\pi$
$167$	14.4721	1.11989	0.559944	+	0.828531i	$0.310823\pi$
$168$	0	0
$169$	−6.88854	−0.529888
$170$	1.23607	0.0948021
$171$	63.3050	4.84105
$172$	2.47214	0.188499
$173$	−20.6525	−1.57018	−0.785089	−	0.619383i	$-0.787383\pi$
$173$	−20.6525	−1.57018	−0.785089	+	0.619383i	$0.787383\pi$
$174$	−18.4721	−1.40037
$175$	0	0
$176$	5.23607	0.394683
$177$	−19.4164	−1.45943
$178$	2.00000	0.149906
$179$	−8.94427	−0.668526	−0.334263	−	0.942480i	$-0.608487\pi$
$179$	−8.94427	−0.668526	−0.334263	+	0.942480i	$0.608487\pi$
$180$	9.23607	0.688416
$181$	2.76393	0.205441	0.102721	−	0.994710i	$-0.467245\pi$
$181$	2.76393	0.205441	0.102721	+	0.994710i	$0.467245\pi$
$182$	0	0
$183$	4.00000	0.295689
$184$	−8.00000	−0.589768
$185$	−4.00000	−0.294086
$186$	4.94427	0.362532
$187$	−5.23607	−0.382899
$188$	2.47214	0.180299
$189$	0	0
$190$	−10.4721	−0.759729
$191$	12.9443	0.936615	0.468307	−	0.883566i	$-0.344864\pi$
$191$	12.9443	0.936615	0.468307	+	0.883566i	$0.344864\pi$
$192$	−3.23607	−0.233543
$193$	−11.8885	−0.855756	−0.427878	−	0.903836i	$-0.640739\pi$
$193$	−11.8885	−0.855756	−0.427878	+	0.903836i	$0.640739\pi$
$194$	−8.47214	−0.608264
$195$	−9.88854	−0.708133
$196$	0	0
$197$	21.7082	1.54665	0.773323	−	0.634013i	$-0.218593\pi$
$197$	21.7082	1.54665	0.773323	+	0.634013i	$0.218593\pi$
$198$	−39.1246	−2.78047
$199$	−14.4721	−1.02590	−0.512951	−	0.858418i	$-0.671448\pi$
$199$	−14.4721	−1.02590	−0.512951	+	0.858418i	$0.671448\pi$
$200$	3.47214	0.245517
$201$	4.94427	0.348742
$202$	−6.47214	−0.455378
$203$	0	0
$204$	3.23607	0.226570
$205$	4.36068	0.304563
$206$	−4.00000	−0.278693
$207$	59.7771	4.15479
$208$	2.47214	0.171412
$209$	44.3607	3.06849
$210$	0	0
$211$	−27.7082	−1.90751	−0.953756	−	0.300583i	$-0.902819\pi$
$211$	−27.7082	−1.90751	−0.953756	+	0.300583i	$0.902819\pi$
$212$	−4.47214	−0.307148
$213$	8.00000	0.548151
$214$	1.23607	0.0844959
$215$	3.05573	0.208399
$216$	14.4721	0.984704
$217$	0	0
$218$	−12.1803	−0.824957
$219$	43.4164	2.93381
$220$	6.47214	0.436351
$221$	−2.47214	−0.166294
$222$	−10.4721	−0.702844
$223$	−1.52786	−0.102313	−0.0511567	−	0.998691i	$-0.516291\pi$
$223$	−1.52786	−0.102313	−0.0511567	+	0.998691i	$0.516291\pi$
$224$	0	0
$225$	−25.9443	−1.72962
$226$	−13.4164	−0.892446
$227$	−27.5967	−1.83166	−0.915830	−	0.401566i	$-0.868466\pi$
$227$	−27.5967	−1.83166	−0.915830	+	0.401566i	$0.868466\pi$
$228$	−27.4164	−1.81570
$229$	4.94427	0.326727	0.163363	−	0.986566i	$-0.447766\pi$
$229$	4.94427	0.326727	0.163363	+	0.986566i	$0.447766\pi$
$230$	−9.88854	−0.652031
$231$	0	0
$232$	5.70820	0.374762
$233$	19.8885	1.30294	0.651471	−	0.758674i	$-0.274152\pi$
$233$	19.8885	1.30294	0.651471	+	0.758674i	$0.274152\pi$
$234$	−18.4721	−1.20756
$235$	3.05573	0.199334
$236$	6.00000	0.390567
$237$	33.8885	2.20130
$238$	0	0
$239$	−4.94427	−0.319818	−0.159909	−	0.987132i	$-0.551120\pi$
$239$	−4.94427	−0.319818	−0.159909	+	0.987132i	$0.551120\pi$
$240$	−4.00000	−0.258199
$241$	−11.8885	−0.765808	−0.382904	−	0.923788i	$-0.625076\pi$
$241$	−11.8885	−0.765808	−0.382904	+	0.923788i	$0.625076\pi$
$242$	−16.4164	−1.05529
$243$	−35.5967	−2.28353
$244$	−1.23607	−0.0791311
$245$	0	0
$246$	11.4164	0.727884
$247$	20.9443	1.33265
$248$	−1.52786	−0.0970195
$249$	6.47214	0.410155
$250$	10.4721	0.662316
$251$	−14.0000	−0.883672	−0.441836	−	0.897096i	$-0.645673\pi$
$251$	−14.0000	−0.883672	−0.441836	+	0.897096i	$0.645673\pi$
$252$	0	0
$253$	41.8885	2.63351
$254$	−12.0000	−0.752947
$255$	4.00000	0.250490
$256$	1.00000	0.0625000
$257$	2.00000	0.124757	0.0623783	−	0.998053i	$-0.480131\pi$
$257$	2.00000	0.124757	0.0623783	+	0.998053i	$0.480131\pi$
$258$	8.00000	0.498058
$259$	0	0
$260$	3.05573	0.189508
$261$	−42.6525	−2.64012
$262$	1.70820	0.105533
$263$	7.05573	0.435075	0.217537	−	0.976052i	$-0.430198\pi$
$263$	7.05573	0.435075	0.217537	+	0.976052i	$0.430198\pi$
$264$	16.9443	1.04285
$265$	−5.52786	−0.339574
$266$	0	0
$267$	6.47214	0.396088
$268$	−1.52786	−0.0933292
$269$	0.291796	0.0177911	0.00889556	−	0.999960i	$-0.497168\pi$
$269$	0.291796	0.0177911	0.00889556	+	0.999960i	$0.497168\pi$
$270$	17.8885	1.08866
$271$	−19.4164	−1.17946	−0.589731	−	0.807599i	$-0.700766\pi$
$271$	−19.4164	−1.17946	−0.589731	+	0.807599i	$0.700766\pi$
$272$	−1.00000	−0.0606339
$273$	0	0
$274$	−3.52786	−0.213126
$275$	−18.1803	−1.09632
$276$	−25.8885	−1.55831
$277$	−22.6525	−1.36106	−0.680528	−	0.732722i	$-0.738249\pi$
$277$	−22.6525	−1.36106	−0.680528	+	0.732722i	$0.738249\pi$
$278$	−12.1803	−0.730528
$279$	11.4164	0.683482
$280$	0	0
$281$	3.52786	0.210455	0.105227	−	0.994448i	$-0.466443\pi$
$281$	3.52786	0.210455	0.105227	+	0.994448i	$0.466443\pi$
$282$	8.00000	0.476393
$283$	−10.2918	−0.611784	−0.305892	−	0.952066i	$-0.598955\pi$
$283$	−10.2918	−0.611784	−0.305892	+	0.952066i	$0.598955\pi$
$284$	−2.47214	−0.146694
$285$	−33.8885	−2.00738
$286$	−12.9443	−0.765411
$287$	0	0
$288$	−7.47214	−0.440300
$289$	1.00000	0.0588235
$290$	7.05573	0.414327
$291$	−27.4164	−1.60718
$292$	−13.4164	−0.785136
$293$	28.0000	1.63578	0.817889	−	0.575376i	$-0.195144\pi$
$293$	28.0000	1.63578	0.817889	+	0.575376i	$0.195144\pi$
$294$	0	0
$295$	7.41641	0.431800
$296$	3.23607	0.188093
$297$	−75.7771	−4.39703
$298$	−18.9443	−1.09741
$299$	19.7771	1.14374
$300$	11.2361	0.648715
$301$	0	0
$302$	−4.00000	−0.230174
$303$	−20.9443	−1.20322
$304$	8.47214	0.485910
$305$	−1.52786	−0.0874852
$306$	7.47214	0.427154
$307$	3.52786	0.201346	0.100673	−	0.994920i	$-0.467900\pi$
$307$	3.52786	0.201346	0.100673	+	0.994920i	$0.467900\pi$
$308$	0	0
$309$	−12.9443	−0.736374
$310$	−1.88854	−0.107262
$311$	20.9443	1.18764	0.593820	−	0.804598i	$-0.297619\pi$
$311$	20.9443	1.18764	0.593820	+	0.804598i	$0.297619\pi$
$312$	8.00000	0.452911
$313$	5.41641	0.306153	0.153077	−	0.988214i	$-0.451082\pi$
$313$	5.41641	0.306153	0.153077	+	0.988214i	$0.451082\pi$
$314$	20.9443	1.18195
$315$	0	0
$316$	−10.4721	−0.589104
$317$	−28.1803	−1.58277	−0.791383	−	0.611321i	$-0.790638\pi$
$317$	−28.1803	−1.58277	−0.791383	+	0.611321i	$0.790638\pi$
$318$	−14.4721	−0.811557
$319$	−29.8885	−1.67344
$320$	1.23607	0.0690983
$321$	4.00000	0.223258
$322$	0	0
$323$	−8.47214	−0.471402
$324$	24.4164	1.35647
$325$	−8.58359	−0.476132
$326$	0.291796	0.0161611
$327$	−39.4164	−2.17973
$328$	−3.52786	−0.194794
$329$	0	0
$330$	20.9443	1.15294
$331$	−20.3607	−1.11912	−0.559562	−	0.828788i	$-0.689031\pi$
$331$	−20.3607	−1.11912	−0.559562	+	0.828788i	$0.689031\pi$
$332$	−2.00000	−0.109764
$333$	−24.1803	−1.32507
$334$	−14.4721	−0.791880
$335$	−1.88854	−0.103182
$336$	0	0
$337$	−20.4721	−1.11519	−0.557594	−	0.830114i	$-0.688275\pi$
$337$	−20.4721	−1.11519	−0.557594	+	0.830114i	$0.688275\pi$
$338$	6.88854	0.374687
$339$	−43.4164	−2.35806
$340$	−1.23607	−0.0670352
$341$	8.00000	0.433224
$342$	−63.3050	−3.42314
$343$	0	0
$344$	−2.47214	−0.133289
$345$	−32.0000	−1.72282
$346$	20.6525	1.11028
$347$	4.65248	0.249758	0.124879	−	0.992172i	$-0.460146\pi$
$347$	4.65248	0.249758	0.124879	+	0.992172i	$0.460146\pi$
$348$	18.4721	0.990210
$349$	21.5279	1.15236	0.576180	−	0.817323i	$-0.304543\pi$
$349$	21.5279	1.15236	0.576180	+	0.817323i	$0.304543\pi$
$350$	0	0
$351$	−35.7771	−1.90964
$352$	−5.23607	−0.279083
$353$	11.8885	0.632763	0.316382	−	0.948632i	$-0.397532\pi$
$353$	11.8885	0.632763	0.316382	+	0.948632i	$0.397532\pi$
$354$	19.4164	1.03197
$355$	−3.05573	−0.162181
$356$	−2.00000	−0.106000
$357$	0	0
$358$	8.94427	0.472719
$359$	22.8328	1.20507	0.602535	−	0.798092i	$-0.294157\pi$
$359$	22.8328	1.20507	0.602535	+	0.798092i	$0.294157\pi$
$360$	−9.23607	−0.486784
$361$	52.7771	2.77774
$362$	−2.76393	−0.145269
$363$	−53.1246	−2.78832
$364$	0	0
$365$	−16.5836	−0.868025
$366$	−4.00000	−0.209083
$367$	28.9443	1.51088	0.755439	−	0.655219i	$-0.227423\pi$
$367$	28.9443	1.51088	0.755439	+	0.655219i	$0.227423\pi$
$368$	8.00000	0.417029
$369$	26.3607	1.37228
$370$	4.00000	0.207950
$371$	0	0
$372$	−4.94427	−0.256349
$373$	13.4164	0.694675	0.347338	−	0.937740i	$-0.387086\pi$
$373$	13.4164	0.694675	0.347338	+	0.937740i	$0.387086\pi$
$374$	5.23607	0.270751
$375$	33.8885	1.75000
$376$	−2.47214	−0.127491
$377$	−14.1115	−0.726777
$378$	0	0
$379$	−17.5967	−0.903884	−0.451942	−	0.892047i	$-0.649269\pi$
$379$	−17.5967	−0.903884	−0.451942	+	0.892047i	$0.649269\pi$
$380$	10.4721	0.537209
$381$	−38.8328	−1.98947
$382$	−12.9443	−0.662287
$383$	8.94427	0.457031	0.228515	−	0.973540i	$-0.426613\pi$
$383$	8.94427	0.457031	0.228515	+	0.973540i	$0.426613\pi$
$384$	3.23607	0.165140
$385$	0	0
$386$	11.8885	0.605111
$387$	18.4721	0.938991
$388$	8.47214	0.430108
$389$	26.0000	1.31825	0.659126	−	0.752032i	$-0.270926\pi$
$389$	26.0000	1.31825	0.659126	+	0.752032i	$0.270926\pi$
$390$	9.88854	0.500726
$391$	−8.00000	−0.404577
$392$	0	0
$393$	5.52786	0.278844
$394$	−21.7082	−1.09364
$395$	−12.9443	−0.651297
$396$	39.1246	1.96609
$397$	−18.1803	−0.912445	−0.456223	−	0.889866i	$-0.650798\pi$
$397$	−18.1803	−0.912445	−0.456223	+	0.889866i	$0.650798\pi$
$398$	14.4721	0.725423
$399$	0	0
$400$	−3.47214	−0.173607
$401$	2.94427	0.147030	0.0735150	−	0.997294i	$-0.476578\pi$
$401$	2.94427	0.147030	0.0735150	+	0.997294i	$0.476578\pi$
$402$	−4.94427	−0.246598
$403$	3.77709	0.188150
$404$	6.47214	0.322001
$405$	30.1803	1.49967
$406$	0	0
$407$	−16.9443	−0.839896
$408$	−3.23607	−0.160209
$409$	−14.9443	−0.738947	−0.369473	−	0.929241i	$-0.620462\pi$
$409$	−14.9443	−0.738947	−0.369473	+	0.929241i	$0.620462\pi$
$410$	−4.36068	−0.215359
$411$	−11.4164	−0.563130
$412$	4.00000	0.197066
$413$	0	0
$414$	−59.7771	−2.93788
$415$	−2.47214	−0.121352
$416$	−2.47214	−0.121206
$417$	−39.4164	−1.93023
$418$	−44.3607	−2.16975
$419$	30.0689	1.46896	0.734481	−	0.678630i	$-0.237426\pi$
$419$	30.0689	1.46896	0.734481	+	0.678630i	$0.237426\pi$
$420$	0	0
$421$	−15.5279	−0.756782	−0.378391	−	0.925646i	$-0.623522\pi$
$421$	−15.5279	−0.756782	−0.378391	+	0.925646i	$0.623522\pi$
$422$	27.7082	1.34881
$423$	18.4721	0.898146
$424$	4.47214	0.217186
$425$	3.47214	0.168423
$426$	−8.00000	−0.387601
$427$	0	0
$428$	−1.23607	−0.0597476
$429$	−41.8885	−2.02240
$430$	−3.05573	−0.147360
$431$	−12.9443	−0.623504	−0.311752	−	0.950164i	$-0.600916\pi$
$431$	−12.9443	−0.623504	−0.311752	+	0.950164i	$0.600916\pi$
$432$	−14.4721	−0.696291
$433$	−10.9443	−0.525948	−0.262974	−	0.964803i	$-0.584703\pi$
$433$	−10.9443	−0.525948	−0.262974	+	0.964803i	$0.584703\pi$
$434$	0	0
$435$	22.8328	1.09475
$436$	12.1803	0.583332
$437$	67.7771	3.24222
$438$	−43.4164	−2.07452
$439$	3.05573	0.145842	0.0729210	−	0.997338i	$-0.476768\pi$
$439$	3.05573	0.145842	0.0729210	+	0.997338i	$0.476768\pi$
$440$	−6.47214	−0.308547
$441$	0	0
$442$	2.47214	0.117588
$443$	−8.36068	−0.397228	−0.198614	−	0.980078i	$-0.563644\pi$
$443$	−8.36068	−0.397228	−0.198614	+	0.980078i	$0.563644\pi$
$444$	10.4721	0.496986
$445$	−2.47214	−0.117190
$446$	1.52786	0.0723465
$447$	−61.3050	−2.89962
$448$	0	0
$449$	9.41641	0.444388	0.222194	−	0.975003i	$-0.428678\pi$
$449$	9.41641	0.444388	0.222194	+	0.975003i	$0.428678\pi$
$450$	25.9443	1.22302
$451$	18.4721	0.869819
$452$	13.4164	0.631055
$453$	−12.9443	−0.608175
$454$	27.5967	1.29518
$455$	0	0
$456$	27.4164	1.28389
$457$	15.8885	0.743235	0.371617	−	0.928386i	$-0.378803\pi$
$457$	15.8885	0.743235	0.371617	+	0.928386i	$0.378803\pi$
$458$	−4.94427	−0.231031
$459$	14.4721	0.675501
$460$	9.88854	0.461056
$461$	5.52786	0.257458	0.128729	−	0.991680i	$-0.458910\pi$
$461$	5.52786	0.257458	0.128729	+	0.991680i	$0.458910\pi$
$462$	0	0
$463$	32.9443	1.53105	0.765525	−	0.643406i	$-0.222479\pi$
$463$	32.9443	1.53105	0.765525	+	0.643406i	$0.222479\pi$
$464$	−5.70820	−0.264997
$465$	−6.11146	−0.283412
$466$	−19.8885	−0.921319
$467$	10.3607	0.479435	0.239718	−	0.970843i	$-0.422945\pi$
$467$	10.3607	0.479435	0.239718	+	0.970843i	$0.422945\pi$
$468$	18.4721	0.853875
$469$	0	0
$470$	−3.05573	−0.140950
$471$	67.7771	3.12300
$472$	−6.00000	−0.276172
$473$	12.9443	0.595178
$474$	−33.8885	−1.55655
$475$	−29.4164	−1.34972
$476$	0	0
$477$	−33.4164	−1.53003
$478$	4.94427	0.226146
$479$	19.4164	0.887158	0.443579	−	0.896235i	$-0.353709\pi$
$479$	19.4164	0.887158	0.443579	+	0.896235i	$0.353709\pi$
$480$	4.00000	0.182574
$481$	−8.00000	−0.364769
$482$	11.8885	0.541508
$483$	0	0
$484$	16.4164	0.746200
$485$	10.4721	0.475515
$486$	35.5967	1.61470
$487$	3.05573	0.138468	0.0692341	−	0.997600i	$-0.477944\pi$
$487$	3.05573	0.138468	0.0692341	+	0.997600i	$0.477944\pi$
$488$	1.23607	0.0559542
$489$	0.944272	0.0427015
$490$	0	0
$491$	−32.9443	−1.48675	−0.743377	−	0.668873i	$-0.766777\pi$
$491$	−32.9443	−1.48675	−0.743377	+	0.668873i	$0.766777\pi$
$492$	−11.4164	−0.514691
$493$	5.70820	0.257085
$494$	−20.9443	−0.942327
$495$	48.3607	2.17365
$496$	1.52786	0.0686031
$497$	0	0
$498$	−6.47214	−0.290023
$499$	−40.6525	−1.81985	−0.909927	−	0.414768i	$-0.863863\pi$
$499$	−40.6525	−1.81985	−0.909927	+	0.414768i	$0.863863\pi$
$500$	−10.4721	−0.468328
$501$	−46.8328	−2.09234
$502$	14.0000	0.624851
$503$	−12.9443	−0.577157	−0.288578	−	0.957456i	$-0.593183\pi$
$503$	−12.9443	−0.577157	−0.288578	+	0.957456i	$0.593183\pi$
$504$	0	0
$505$	8.00000	0.355995
$506$	−41.8885	−1.86217
$507$	22.2918	0.990013
$508$	12.0000	0.532414
$509$	3.05573	0.135443	0.0677214	−	0.997704i	$-0.478427\pi$
$509$	3.05573	0.135443	0.0677214	+	0.997704i	$0.478427\pi$
$510$	−4.00000	−0.177123
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	−122.610	−5.41336
$514$	−2.00000	−0.0882162
$515$	4.94427	0.217871
$516$	−8.00000	−0.352180
$517$	12.9443	0.569288
$518$	0	0
$519$	66.8328	2.93364
$520$	−3.05573	−0.134003
$521$	1.05573	0.0462523	0.0231261	−	0.999733i	$-0.492638\pi$
$521$	1.05573	0.0462523	0.0231261	+	0.999733i	$0.492638\pi$
$522$	42.6525	1.86685
$523$	42.9443	1.87782	0.938911	−	0.344160i	$-0.111836\pi$
$523$	42.9443	1.87782	0.938911	+	0.344160i	$0.111836\pi$
$524$	−1.70820	−0.0746232
$525$	0	0
$526$	−7.05573	−0.307644
$527$	−1.52786	−0.0665548
$528$	−16.9443	−0.737405
$529$	41.0000	1.78261
$530$	5.52786	0.240115
$531$	44.8328	1.94558
$532$	0	0
$533$	8.72136	0.377764
$534$	−6.47214	−0.280077
$535$	−1.52786	−0.0660553
$536$	1.52786	0.0659937
$537$	28.9443	1.24904
$538$	−0.291796	−0.0125802
$539$	0	0
$540$	−17.8885	−0.769800
$541$	−23.2361	−0.998997	−0.499498	−	0.866315i	$-0.666482\pi$
$541$	−23.2361	−0.998997	−0.499498	+	0.866315i	$0.666482\pi$
$542$	19.4164	0.834006
$543$	−8.94427	−0.383835
$544$	1.00000	0.0428746
$545$	15.0557	0.644917
$546$	0	0
$547$	41.5967	1.77855	0.889274	−	0.457374i	$-0.151210\pi$
$547$	41.5967	1.77855	0.889274	+	0.457374i	$0.151210\pi$
$548$	3.52786	0.150703
$549$	−9.23607	−0.394186
$550$	18.1803	0.775212
$551$	−48.3607	−2.06023
$552$	25.8885	1.10189
$553$	0	0
$554$	22.6525	0.962411
$555$	12.9443	0.549454
$556$	12.1803	0.516561
$557$	34.3607	1.45591	0.727954	−	0.685626i	$-0.240471\pi$
$557$	34.3607	1.45591	0.727954	+	0.685626i	$0.240471\pi$
$558$	−11.4164	−0.483295
$559$	6.11146	0.258487
$560$	0	0
$561$	16.9443	0.715388
$562$	−3.52786	−0.148814
$563$	32.8328	1.38374	0.691869	−	0.722023i	$-0.256788\pi$
$563$	32.8328	1.38374	0.691869	+	0.722023i	$0.256788\pi$
$564$	−8.00000	−0.336861
$565$	16.5836	0.697677
$566$	10.2918	0.432596
$567$	0	0
$568$	2.47214	0.103729
$569$	15.8885	0.666082	0.333041	−	0.942912i	$-0.391925\pi$
$569$	15.8885	0.666082	0.333041	+	0.942912i	$0.391925\pi$
$570$	33.8885	1.41943
$571$	−13.2361	−0.553912	−0.276956	−	0.960883i	$-0.589326\pi$
$571$	−13.2361	−0.553912	−0.276956	+	0.960883i	$0.589326\pi$
$572$	12.9443	0.541227
$573$	−41.8885	−1.74992
$574$	0	0
$575$	−27.7771	−1.15838
$576$	7.47214	0.311339
$577$	−30.0000	−1.24892	−0.624458	−	0.781058i	$-0.714680\pi$
$577$	−30.0000	−1.24892	−0.624458	+	0.781058i	$0.714680\pi$
$578$	−1.00000	−0.0415945
$579$	38.4721	1.59885
$580$	−7.05573	−0.292973
$581$	0	0
$582$	27.4164	1.13645
$583$	−23.4164	−0.969809
$584$	13.4164	0.555175
$585$	22.8328	0.944021
$586$	−28.0000	−1.15667
$587$	−21.4164	−0.883950	−0.441975	−	0.897027i	$-0.645722\pi$
$587$	−21.4164	−0.883950	−0.441975	+	0.897027i	$0.645722\pi$
$588$	0	0
$589$	12.9443	0.533359
$590$	−7.41641	−0.305329
$591$	−70.2492	−2.88967
$592$	−3.23607	−0.133002
$593$	2.94427	0.120907	0.0604534	−	0.998171i	$-0.480745\pi$
$593$	2.94427	0.120907	0.0604534	+	0.998171i	$0.480745\pi$
$594$	75.7771	3.10917
$595$	0	0
$596$	18.9443	0.775988
$597$	46.8328	1.91674
$598$	−19.7771	−0.808745
$599$	31.7771	1.29838	0.649188	−	0.760628i	$-0.275109\pi$
$599$	31.7771	1.29838	0.649188	+	0.760628i	$0.275109\pi$
$600$	−11.2361	−0.458711
$601$	−14.0000	−0.571072	−0.285536	−	0.958368i	$-0.592172\pi$
$601$	−14.0000	−0.571072	−0.285536	+	0.958368i	$0.592172\pi$
$602$	0	0
$603$	−11.4164	−0.464912
$604$	4.00000	0.162758
$605$	20.2918	0.824979
$606$	20.9443	0.850803
$607$	8.00000	0.324710	0.162355	−	0.986732i	$-0.448091\pi$
$607$	8.00000	0.324710	0.162355	+	0.986732i	$0.448091\pi$
$608$	−8.47214	−0.343590
$609$	0	0
$610$	1.52786	0.0618614
$611$	6.11146	0.247243
$612$	−7.47214	−0.302043
$613$	−44.8328	−1.81078	−0.905390	−	0.424581i	$-0.860422\pi$
$613$	−44.8328	−1.81078	−0.905390	+	0.424581i	$0.860422\pi$
$614$	−3.52786	−0.142373
$615$	−14.1115	−0.569029
$616$	0	0
$617$	10.3607	0.417105	0.208553	−	0.978011i	$-0.433125\pi$
$617$	10.3607	0.417105	0.208553	+	0.978011i	$0.433125\pi$
$618$	12.9443	0.520695
$619$	−25.7082	−1.03330	−0.516650	−	0.856197i	$-0.672821\pi$
$619$	−25.7082	−1.03330	−0.516650	+	0.856197i	$0.672821\pi$
$620$	1.88854	0.0758457
$621$	−115.777	−4.64597
$622$	−20.9443	−0.839789
$623$	0	0
$624$	−8.00000	−0.320256
$625$	4.41641	0.176656
$626$	−5.41641	−0.216483
$627$	−143.554	−5.73300
$628$	−20.9443	−0.835767
$629$	3.23607	0.129030
$630$	0	0
$631$	3.05573	0.121647	0.0608233	−	0.998149i	$-0.480627\pi$
$631$	3.05573	0.121647	0.0608233	+	0.998149i	$0.480627\pi$
$632$	10.4721	0.416559
$633$	89.6656	3.56389
$634$	28.1803	1.11918
$635$	14.8328	0.588622
$636$	14.4721	0.573858
$637$	0	0
$638$	29.8885	1.18330
$639$	−18.4721	−0.730746
$640$	−1.23607	−0.0488599
$641$	9.05573	0.357680	0.178840	−	0.983878i	$-0.442766\pi$
$641$	9.05573	0.357680	0.178840	+	0.983878i	$0.442766\pi$
$642$	−4.00000	−0.157867
$643$	−13.1246	−0.517584	−0.258792	−	0.965933i	$-0.583324\pi$
$643$	−13.1246	−0.517584	−0.258792	+	0.965933i	$0.583324\pi$
$644$	0	0
$645$	−9.88854	−0.389361
$646$	8.47214	0.333332
$647$	−20.3607	−0.800461	−0.400230	−	0.916415i	$-0.631070\pi$
$647$	−20.3607	−0.800461	−0.400230	+	0.916415i	$0.631070\pi$
$648$	−24.4164	−0.959167
$649$	31.4164	1.23320
$650$	8.58359	0.336676
$651$	0	0
$652$	−0.291796	−0.0114276
$653$	−7.59675	−0.297284	−0.148642	−	0.988891i	$-0.547490\pi$
$653$	−7.59675	−0.297284	−0.148642	+	0.988891i	$0.547490\pi$
$654$	39.4164	1.54130
$655$	−2.11146	−0.0825014
$656$	3.52786	0.137740
$657$	−100.249	−3.91109
$658$	0	0
$659$	−20.9443	−0.815873	−0.407936	−	0.913010i	$-0.633752\pi$
$659$	−20.9443	−0.815873	−0.407936	+	0.913010i	$0.633752\pi$
$660$	−20.9443	−0.815255
$661$	3.41641	0.132883	0.0664414	−	0.997790i	$-0.478835\pi$
$661$	3.41641	0.132883	0.0664414	+	0.997790i	$0.478835\pi$
$662$	20.3607	0.791340
$663$	8.00000	0.310694
$664$	2.00000	0.0776151
$665$	0	0
$666$	24.1803	0.936969
$667$	−45.6656	−1.76818
$668$	14.4721	0.559944
$669$	4.94427	0.191157
$670$	1.88854	0.0729608
$671$	−6.47214	−0.249854
$672$	0	0
$673$	−23.3050	−0.898340	−0.449170	−	0.893446i	$-0.648280\pi$
$673$	−23.3050	−0.898340	−0.449170	+	0.893446i	$0.648280\pi$
$674$	20.4721	0.788557
$675$	50.2492	1.93409
$676$	−6.88854	−0.264944
$677$	−34.1803	−1.31366	−0.656829	−	0.754040i	$-0.728102\pi$
$677$	−34.1803	−1.31366	−0.656829	+	0.754040i	$0.728102\pi$
$678$	43.4164	1.66740
$679$	0	0
$680$	1.23607	0.0474010
$681$	89.3050	3.42217
$682$	−8.00000	−0.306336
$683$	46.1803	1.76704	0.883521	−	0.468392i	$-0.155166\pi$
$683$	46.1803	1.76704	0.883521	+	0.468392i	$0.155166\pi$
$684$	63.3050	2.42053
$685$	4.36068	0.166613
$686$	0	0
$687$	−16.0000	−0.610438
$688$	2.47214	0.0942493
$689$	−11.0557	−0.421190
$690$	32.0000	1.21822
$691$	34.6525	1.31824	0.659121	−	0.752037i	$-0.270928\pi$
$691$	34.6525	1.31824	0.659121	+	0.752037i	$0.270928\pi$
$692$	−20.6525	−0.785089
$693$	0	0
$694$	−4.65248	−0.176606
$695$	15.0557	0.571096
$696$	−18.4721	−0.700185
$697$	−3.52786	−0.133627
$698$	−21.5279	−0.814842
$699$	−64.3607	−2.43434
$700$	0	0
$701$	−36.2492	−1.36911	−0.684557	−	0.728959i	$-0.740004\pi$
$701$	−36.2492	−1.36911	−0.684557	+	0.728959i	$0.740004\pi$
$702$	35.7771	1.35032
$703$	−27.4164	−1.03403
$704$	5.23607	0.197342
$705$	−9.88854	−0.372424
$706$	−11.8885	−0.447431
$707$	0	0
$708$	−19.4164	−0.729713
$709$	−23.5967	−0.886194	−0.443097	−	0.896474i	$-0.646120\pi$
$709$	−23.5967	−0.886194	−0.443097	+	0.896474i	$0.646120\pi$
$710$	3.05573	0.114679
$711$	−78.2492	−2.93458
$712$	2.00000	0.0749532
$713$	12.2229	0.457752
$714$	0	0
$715$	16.0000	0.598366
$716$	−8.94427	−0.334263
$717$	16.0000	0.597531
$718$	−22.8328	−0.852113
$719$	27.4164	1.02246	0.511230	−	0.859444i	$-0.329190\pi$
$719$	27.4164	1.02246	0.511230	+	0.859444i	$0.329190\pi$
$720$	9.23607	0.344208
$721$	0	0
$722$	−52.7771	−1.96416
$723$	38.4721	1.43079
$724$	2.76393	0.102721
$725$	19.8197	0.736084
$726$	53.1246	1.97164
$727$	37.5279	1.39183	0.695916	−	0.718123i	$-0.254999\pi$
$727$	37.5279	1.39183	0.695916	+	0.718123i	$0.254999\pi$
$728$	0	0
$729$	41.9443	1.55349
$730$	16.5836	0.613786
$731$	−2.47214	−0.0914353
$732$	4.00000	0.147844
$733$	4.58359	0.169299	0.0846494	−	0.996411i	$-0.473023\pi$
$733$	4.58359	0.169299	0.0846494	+	0.996411i	$0.473023\pi$
$734$	−28.9443	−1.06835
$735$	0	0
$736$	−8.00000	−0.294884
$737$	−8.00000	−0.294684
$738$	−26.3607	−0.970350
$739$	46.8328	1.72277	0.861386	−	0.507950i	$-0.169597\pi$
$739$	46.8328	1.72277	0.861386	+	0.507950i	$0.169597\pi$
$740$	−4.00000	−0.147043
$741$	−67.7771	−2.48985
$742$	0	0
$743$	29.5279	1.08327	0.541636	−	0.840613i	$-0.317805\pi$
$743$	29.5279	1.08327	0.541636	+	0.840613i	$0.317805\pi$
$744$	4.94427	0.181266
$745$	23.4164	0.857911
$746$	−13.4164	−0.491210
$747$	−14.9443	−0.546782
$748$	−5.23607	−0.191450
$749$	0	0
$750$	−33.8885	−1.23743
$751$	28.9443	1.05619	0.528096	−	0.849185i	$-0.322906\pi$
$751$	28.9443	1.05619	0.528096	+	0.849185i	$0.322906\pi$
$752$	2.47214	0.0901495
$753$	45.3050	1.65100
$754$	14.1115	0.513909
$755$	4.94427	0.179940
$756$	0	0
$757$	18.0000	0.654221	0.327111	−	0.944986i	$-0.393925\pi$
$757$	18.0000	0.654221	0.327111	+	0.944986i	$0.393925\pi$
$758$	17.5967	0.639143
$759$	−135.554	−4.92030
$760$	−10.4721	−0.379864
$761$	−3.88854	−0.140960	−0.0704798	−	0.997513i	$-0.522453\pi$
$761$	−3.88854	−0.140960	−0.0704798	+	0.997513i	$0.522453\pi$
$762$	38.8328	1.40676
$763$	0	0
$764$	12.9443	0.468307
$765$	−9.23607	−0.333931
$766$	−8.94427	−0.323170
$767$	14.8328	0.535582
$768$	−3.23607	−0.116772
$769$	4.83282	0.174276	0.0871379	−	0.996196i	$-0.472228\pi$
$769$	4.83282	0.174276	0.0871379	+	0.996196i	$0.472228\pi$
$770$	0	0
$771$	−6.47214	−0.233088
$772$	−11.8885	−0.427878
$773$	−4.00000	−0.143870	−0.0719350	−	0.997409i	$-0.522917\pi$
$773$	−4.00000	−0.143870	−0.0719350	+	0.997409i	$0.522917\pi$
$774$	−18.4721	−0.663967
$775$	−5.30495	−0.190559
$776$	−8.47214	−0.304132
$777$	0	0
$778$	−26.0000	−0.932145
$779$	29.8885	1.07087
$780$	−9.88854	−0.354067
$781$	−12.9443	−0.463182
$782$	8.00000	0.286079
$783$	82.6099	2.95224
$784$	0	0
$785$	−25.8885	−0.924002
$786$	−5.52786	−0.197172
$787$	−9.70820	−0.346060	−0.173030	−	0.984917i	$-0.555356\pi$
$787$	−9.70820	−0.346060	−0.173030	+	0.984917i	$0.555356\pi$
$788$	21.7082	0.773323
$789$	−22.8328	−0.812870
$790$	12.9443	0.460537
$791$	0	0
$792$	−39.1246	−1.39023
$793$	−3.05573	−0.108512
$794$	18.1803	0.645196
$795$	17.8885	0.634441
$796$	−14.4721	−0.512951
$797$	−39.4164	−1.39620	−0.698100	−	0.716000i	$-0.745971\pi$
$797$	−39.4164	−1.39620	−0.698100	+	0.716000i	$0.745971\pi$
$798$	0	0
$799$	−2.47214	−0.0874579
$800$	3.47214	0.122759
$801$	−14.9443	−0.528030
$802$	−2.94427	−0.103966
$803$	−70.2492	−2.47904
$804$	4.94427	0.174371
$805$	0	0
$806$	−3.77709	−0.133042
$807$	−0.944272	−0.0332399
$808$	−6.47214	−0.227689
$809$	1.05573	0.0371174	0.0185587	−	0.999828i	$-0.494092\pi$
$809$	1.05573	0.0371174	0.0185587	+	0.999828i	$0.494092\pi$
$810$	−30.1803	−1.06043
$811$	19.8197	0.695962	0.347981	−	0.937502i	$-0.386867\pi$
$811$	19.8197	0.695962	0.347981	+	0.937502i	$0.386867\pi$
$812$	0	0
$813$	62.8328	2.20364
$814$	16.9443	0.593896
$815$	−0.360680	−0.0126341
$816$	3.23607	0.113285
$817$	20.9443	0.732747
$818$	14.9443	0.522514
$819$	0	0
$820$	4.36068	0.152282
$821$	−43.0132	−1.50117	−0.750585	−	0.660774i	$-0.770228\pi$
$821$	−43.0132	−1.50117	−0.750585	+	0.660774i	$0.770228\pi$
$822$	11.4164	0.398193
$823$	−2.47214	−0.0861732	−0.0430866	−	0.999071i	$-0.513719\pi$
$823$	−2.47214	−0.0861732	−0.0430866	+	0.999071i	$0.513719\pi$
$824$	−4.00000	−0.139347
$825$	58.8328	2.04830
$826$	0	0
$827$	−37.5967	−1.30737	−0.653684	−	0.756768i	$-0.726777\pi$
$827$	−37.5967	−1.30737	−0.653684	+	0.756768i	$0.726777\pi$
$828$	59.7771	2.07740
$829$	−40.9443	−1.42205	−0.711027	−	0.703165i	$-0.751769\pi$
$829$	−40.9443	−1.42205	−0.711027	+	0.703165i	$0.751769\pi$
$830$	2.47214	0.0858091
$831$	73.3050	2.54292
$832$	2.47214	0.0857059
$833$	0	0
$834$	39.4164	1.36488
$835$	17.8885	0.619059
$836$	44.3607	1.53425
$837$	−22.1115	−0.764284
$838$	−30.0689	−1.03871
$839$	−7.63932	−0.263739	−0.131869	−	0.991267i	$-0.542098\pi$
$839$	−7.63932	−0.263739	−0.131869	+	0.991267i	$0.542098\pi$
$840$	0	0
$841$	3.58359	0.123572
$842$	15.5279	0.535126
$843$	−11.4164	−0.393202
$844$	−27.7082	−0.953756
$845$	−8.51471	−0.292915
$846$	−18.4721	−0.635085
$847$	0	0
$848$	−4.47214	−0.153574
$849$	33.3050	1.14302
$850$	−3.47214	−0.119093
$851$	−25.8885	−0.887448
$852$	8.00000	0.274075
$853$	21.2361	0.727109	0.363555	−	0.931573i	$-0.381563\pi$
$853$	21.2361	0.727109	0.363555	+	0.931573i	$0.381563\pi$
$854$	0	0
$855$	78.2492	2.67607
$856$	1.23607	0.0422479
$857$	3.52786	0.120510	0.0602548	−	0.998183i	$-0.480809\pi$
$857$	3.52786	0.120510	0.0602548	+	0.998183i	$0.480809\pi$
$858$	41.8885	1.43005
$859$	35.8885	1.22450	0.612251	−	0.790664i	$-0.290264\pi$
$859$	35.8885	1.22450	0.612251	+	0.790664i	$0.290264\pi$
$860$	3.05573	0.104199
$861$	0	0
$862$	12.9443	0.440884
$863$	16.9443	0.576790	0.288395	−	0.957512i	$-0.406878\pi$
$863$	16.9443	0.576790	0.288395	+	0.957512i	$0.406878\pi$
$864$	14.4721	0.492352
$865$	−25.5279	−0.867973
$866$	10.9443	0.371901
$867$	−3.23607	−0.109903
$868$	0	0
$869$	−54.8328	−1.86008
$870$	−22.8328	−0.774105
$871$	−3.77709	−0.127982
$872$	−12.1803	−0.412478
$873$	63.3050	2.14255
$874$	−67.7771	−2.29259
$875$	0	0
$876$	43.4164	1.46690
$877$	9.12461	0.308116	0.154058	−	0.988062i	$-0.450766\pi$
$877$	9.12461	0.308116	0.154058	+	0.988062i	$0.450766\pi$
$878$	−3.05573	−0.103126
$879$	−90.6099	−3.05620
$880$	6.47214	0.218176
$881$	46.9443	1.58159	0.790796	−	0.612079i	$-0.209667\pi$
$881$	46.9443	1.58159	0.790796	+	0.612079i	$0.209667\pi$
$882$	0	0
$883$	3.41641	0.114971	0.0574856	−	0.998346i	$-0.481692\pi$
$883$	3.41641	0.114971	0.0574856	+	0.998346i	$0.481692\pi$
$884$	−2.47214	−0.0831469
$885$	−24.0000	−0.806751
$886$	8.36068	0.280883
$887$	24.3607	0.817952	0.408976	−	0.912545i	$-0.365886\pi$
$887$	24.3607	0.817952	0.408976	+	0.912545i	$0.365886\pi$
$888$	−10.4721	−0.351422
$889$	0	0
$890$	2.47214	0.0828662
$891$	127.846	4.28300
$892$	−1.52786	−0.0511567
$893$	20.9443	0.700873
$894$	61.3050	2.05034
$895$	−11.0557	−0.369552
$896$	0	0
$897$	−64.0000	−2.13690
$898$	−9.41641	−0.314230
$899$	−8.72136	−0.290874
$900$	−25.9443	−0.864809
$901$	4.47214	0.148988
$902$	−18.4721	−0.615055
$903$	0	0
$904$	−13.4164	−0.446223
$905$	3.41641	0.113565
$906$	12.9443	0.430045
$907$	−6.76393	−0.224593	−0.112296	−	0.993675i	$-0.535821\pi$
$907$	−6.76393	−0.224593	−0.112296	+	0.993675i	$0.535821\pi$
$908$	−27.5967	−0.915830
$909$	48.3607	1.60402
$910$	0	0
$911$	12.3607	0.409528	0.204764	−	0.978811i	$-0.434357\pi$
$911$	12.3607	0.409528	0.204764	+	0.978811i	$0.434357\pi$
$912$	−27.4164	−0.907848
$913$	−10.4721	−0.346577
$914$	−15.8885	−0.525546
$915$	4.94427	0.163453
$916$	4.94427	0.163363
$917$	0	0
$918$	−14.4721	−0.477652
$919$	−27.0557	−0.892486	−0.446243	−	0.894912i	$-0.647238\pi$
$919$	−27.0557	−0.892486	−0.446243	+	0.894912i	$0.647238\pi$
$920$	−9.88854	−0.326016
$921$	−11.4164	−0.376183
$922$	−5.52786	−0.182051
$923$	−6.11146	−0.201161
$924$	0	0
$925$	11.2361	0.369440
$926$	−32.9443	−1.08262
$927$	29.8885	0.981669
$928$	5.70820	0.187381
$929$	30.0000	0.984268	0.492134	−	0.870519i	$-0.336217\pi$
$929$	30.0000	0.984268	0.492134	+	0.870519i	$0.336217\pi$
$930$	6.11146	0.200403
$931$	0	0
$932$	19.8885	0.651471
$933$	−67.7771	−2.21892
$934$	−10.3607	−0.339012
$935$	−6.47214	−0.211661
$936$	−18.4721	−0.603781
$937$	−20.1115	−0.657013	−0.328506	−	0.944502i	$-0.606545\pi$
$937$	−20.1115	−0.657013	−0.328506	+	0.944502i	$0.606545\pi$
$938$	0	0
$939$	−17.5279	−0.572000
$940$	3.05573	0.0996669
$941$	−59.1246	−1.92741	−0.963704	−	0.266974i	$-0.913976\pi$
$941$	−59.1246	−1.92741	−0.963704	+	0.266974i	$0.913976\pi$
$942$	−67.7771	−2.20830
$943$	28.2229	0.919064
$944$	6.00000	0.195283
$945$	0	0
$946$	−12.9443	−0.420855
$947$	−47.1246	−1.53134	−0.765672	−	0.643231i	$-0.777593\pi$
$947$	−47.1246	−1.53134	−0.765672	+	0.643231i	$0.777593\pi$
$948$	33.8885	1.10065
$949$	−33.1672	−1.07665
$950$	29.4164	0.954394
$951$	91.1935	2.95715
$952$	0	0
$953$	5.05573	0.163771	0.0818855	−	0.996642i	$-0.473906\pi$
$953$	5.05573	0.163771	0.0818855	+	0.996642i	$0.473906\pi$
$954$	33.4164	1.08190
$955$	16.0000	0.517748
$956$	−4.94427	−0.159909
$957$	96.7214	3.12656
$958$	−19.4164	−0.627316
$959$	0	0
$960$	−4.00000	−0.129099
$961$	−28.6656	−0.924698
$962$	8.00000	0.257930
$963$	−9.23607	−0.297628
$964$	−11.8885	−0.382904
$965$	−14.6950	−0.473050
$966$	0	0
$967$	44.9443	1.44531	0.722655	−	0.691209i	$-0.242921\pi$
$967$	44.9443	1.44531	0.722655	+	0.691209i	$0.242921\pi$
$968$	−16.4164	−0.527643
$969$	27.4164	0.880742
$970$	−10.4721	−0.336240
$971$	−24.8328	−0.796923	−0.398461	−	0.917185i	$-0.630456\pi$
$971$	−24.8328	−0.796923	−0.398461	+	0.917185i	$0.630456\pi$
$972$	−35.5967	−1.14177
$973$	0	0
$974$	−3.05573	−0.0979118
$975$	27.7771	0.889579
$976$	−1.23607	−0.0395656
$977$	−58.9443	−1.88579	−0.942897	−	0.333084i	$-0.891911\pi$
$977$	−58.9443	−1.88579	−0.942897	+	0.333084i	$0.891911\pi$
$978$	−0.944272	−0.0301945
$979$	−10.4721	−0.334691
$980$	0	0
$981$	91.0132	2.90583
$982$	32.9443	1.05129
$983$	−54.4721	−1.73739	−0.868696	−	0.495346i	$-0.835041\pi$
$983$	−54.4721	−1.73739	−0.868696	+	0.495346i	$0.835041\pi$
$984$	11.4164	0.363942
$985$	26.8328	0.854965
$986$	−5.70820	−0.181786
$987$	0	0
$988$	20.9443	0.666326
$989$	19.7771	0.628875
$990$	−48.3607	−1.53700
$991$	−22.2492	−0.706770	−0.353385	−	0.935478i	$-0.614969\pi$
$991$	−22.2492	−0.706770	−0.353385	+	0.935478i	$0.614969\pi$
$992$	−1.52786	−0.0485097
$993$	65.8885	2.09091
$994$	0	0
$995$	−17.8885	−0.567105
$996$	6.47214	0.205077
$997$	47.4853	1.50387	0.751937	−	0.659235i	$-0.229120\pi$
$997$	47.4853	1.50387	0.751937	+	0.659235i	$0.229120\pi$
$998$	40.6525	1.28683
$999$	46.8328	1.48172

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1666.2.a.o.1.1		2
7.6	odd	2		238.2.a.f.1.2	✓	2
21.20	even	2		2142.2.a.x.1.2		2
28.27	even	2		1904.2.a.f.1.1		2
35.34	odd	2		5950.2.a.x.1.1		2
56.13	odd	2		7616.2.a.n.1.1		2
56.27	even	2		7616.2.a.y.1.2		2
119.118	odd	2		4046.2.a.v.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
238.2.a.f.1.2	✓	2	7.6	odd	2
1666.2.a.o.1.1		2	1.1	even	1	trivial
1904.2.a.f.1.1		2	28.27	even	2
2142.2.a.x.1.2		2	21.20	even	2
4046.2.a.v.1.1		2	119.118	odd	2
5950.2.a.x.1.1		2	35.34	odd	2
7616.2.a.n.1.1		2	56.13	odd	2
7616.2.a.y.1.2		2	56.27	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.23607 q^{3} +1.00000 q^{4} +1.23607 q^{5} +3.23607 q^{6} -1.00000 q^{8} +7.47214 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.23607 q^{3} +1.00000 q^{4} +1.23607 q^{5} +3.23607 q^{6} -1.00000 q^{8} +7.47214 q^{9} -1.23607 q^{10} +5.23607 q^{11} -3.23607 q^{12} +2.47214 q^{13} -4.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} -7.47214 q^{18} +8.47214 q^{19} +1.23607 q^{20} -5.23607 q^{22} +8.00000 q^{23} +3.23607 q^{24} -3.47214 q^{25} -2.47214 q^{26} -14.4721 q^{27} -5.70820 q^{29} +4.00000 q^{30} +1.52786 q^{31} -1.00000 q^{32} -16.9443 q^{33} +1.00000 q^{34} +7.47214 q^{36} -3.23607 q^{37} -8.47214 q^{38} -8.00000 q^{39} -1.23607 q^{40} +3.52786 q^{41} +2.47214 q^{43} +5.23607 q^{44} +9.23607 q^{45} -8.00000 q^{46} +2.47214 q^{47} -3.23607 q^{48} +3.47214 q^{50} +3.23607 q^{51} +2.47214 q^{52} -4.47214 q^{53} +14.4721 q^{54} +6.47214 q^{55} -27.4164 q^{57} +5.70820 q^{58} +6.00000 q^{59} -4.00000 q^{60} -1.23607 q^{61} -1.52786 q^{62} +1.00000 q^{64} +3.05573 q^{65} +16.9443 q^{66} -1.52786 q^{67} -1.00000 q^{68} -25.8885 q^{69} -2.47214 q^{71} -7.47214 q^{72} -13.4164 q^{73} +3.23607 q^{74} +11.2361 q^{75} +8.47214 q^{76} +8.00000 q^{78} -10.4721 q^{79} +1.23607 q^{80} +24.4164 q^{81} -3.52786 q^{82} -2.00000 q^{83} -1.23607 q^{85} -2.47214 q^{86} +18.4721 q^{87} -5.23607 q^{88} -2.00000 q^{89} -9.23607 q^{90} +8.00000 q^{92} -4.94427 q^{93} -2.47214 q^{94} +10.4721 q^{95} +3.23607 q^{96} +8.47214 q^{97} +39.1246 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{8} + 6 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^8 + 6 * q^9	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{8} + 6 q^{9} + 2 q^{10} + 6 q^{11} - 2 q^{12} - 4 q^{13} - 8 q^{15} + 2 q^{16} - 2 q^{17} - 6 q^{18} + 8 q^{19} - 2 q^{20} - 6 q^{22} + 16 q^{23} + 2 q^{24} + 2 q^{25} + 4 q^{26} - 20 q^{27} + 2 q^{29} + 8 q^{30} + 12 q^{31} - 2 q^{32} - 16 q^{33} + 2 q^{34} + 6 q^{36} - 2 q^{37} - 8 q^{38} - 16 q^{39} + 2 q^{40} + 16 q^{41} - 4 q^{43} + 6 q^{44} + 14 q^{45} - 16 q^{46} - 4 q^{47} - 2 q^{48} - 2 q^{50} + 2 q^{51} - 4 q^{52} + 20 q^{54} + 4 q^{55} - 28 q^{57} - 2 q^{58} + 12 q^{59} - 8 q^{60} + 2 q^{61} - 12 q^{62} + 2 q^{64} + 24 q^{65} + 16 q^{66} - 12 q^{67} - 2 q^{68} - 16 q^{69} + 4 q^{71} - 6 q^{72} + 2 q^{74} + 18 q^{75} + 8 q^{76} + 16 q^{78} - 12 q^{79} - 2 q^{80} + 22 q^{81} - 16 q^{82} - 4 q^{83} + 2 q^{85} + 4 q^{86} + 28 q^{87} - 6 q^{88} - 4 q^{89} - 14 q^{90} + 16 q^{92} + 8 q^{93} + 4 q^{94} + 12 q^{95} + 2 q^{96} + 8 q^{97} + 38 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^8 + 6 * q^9 + 2 * q^10 + 6 * q^11 - 2 * q^12 - 4 * q^13 - 8 * q^15 + 2 * q^16 - 2 * q^17 - 6 * q^18 + 8 * q^19 - 2 * q^20 - 6 * q^22 + 16 * q^23 + 2 * q^24 + 2 * q^25 + 4 * q^26 - 20 * q^27 + 2 * q^29 + 8 * q^30 + 12 * q^31 - 2 * q^32 - 16 * q^33 + 2 * q^34 + 6 * q^36 - 2 * q^37 - 8 * q^38 - 16 * q^39 + 2 * q^40 + 16 * q^41 - 4 * q^43 + 6 * q^44 + 14 * q^45 - 16 * q^46 - 4 * q^47 - 2 * q^48 - 2 * q^50 + 2 * q^51 - 4 * q^52 + 20 * q^54 + 4 * q^55 - 28 * q^57 - 2 * q^58 + 12 * q^59 - 8 * q^60 + 2 * q^61 - 12 * q^62 + 2 * q^64 + 24 * q^65 + 16 * q^66 - 12 * q^67 - 2 * q^68 - 16 * q^69 + 4 * q^71 - 6 * q^72 + 2 * q^74 + 18 * q^75 + 8 * q^76 + 16 * q^78 - 12 * q^79 - 2 * q^80 + 22 * q^81 - 16 * q^82 - 4 * q^83 + 2 * q^85 + 4 * q^86 + 28 * q^87 - 6 * q^88 - 4 * q^89 - 14 * q^90 + 16 * q^92 + 8 * q^93 + 4 * q^94 + 12 * q^95 + 2 * q^96 + 8 * q^97 + 38 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more