LMFDB - Embedded newform 1666.2.a.x.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1666, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1666.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$13.3030769767$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.4352.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 6x^{2} - 4x + 2 $ x^4 - 6x^2 - 4x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-1.74912$ of defining polynomial
Character	$\chi$	$=$	1666.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +2.22274 q^{3} +1.00000 q^{4} -3.74912 q^{5} +2.22274 q^{6} +1.00000 q^{8} +1.94059 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.22274 q^{3} +1.00000 q^{4} -3.74912 q^{5} +2.22274 q^{6} +1.00000 q^{8} +1.94059 q^{9} -3.74912 q^{10} -5.63696 q^{11} +2.22274 q^{12} -6.36147 q^{13} -8.33333 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.94059 q^{18} -4.20285 q^{19} -3.74912 q^{20} -5.63696 q^{22} +5.30205 q^{23} +2.22274 q^{24} +9.05588 q^{25} -6.36147 q^{26} -2.35480 q^{27} -3.35951 q^{29} -8.33333 q^{30} +5.31148 q^{31} +1.00000 q^{32} -12.5295 q^{33} +1.00000 q^{34} +1.94059 q^{36} -2.83667 q^{37} -4.20285 q^{38} -14.1399 q^{39} -3.74912 q^{40} -9.97186 q^{41} -2.15862 q^{43} -5.63696 q^{44} -7.27549 q^{45} +5.30205 q^{46} +0.625581 q^{47} +2.22274 q^{48} +9.05588 q^{50} +2.22274 q^{51} -6.36147 q^{52} +6.56431 q^{53} -2.35480 q^{54} +21.1336 q^{55} -9.34185 q^{57} -3.35951 q^{58} -3.13677 q^{59} -8.33333 q^{60} +13.8117 q^{61} +5.31148 q^{62} +1.00000 q^{64} +23.8499 q^{65} -12.5295 q^{66} +12.1023 q^{67} +1.00000 q^{68} +11.7851 q^{69} +3.73588 q^{71} +1.94059 q^{72} -9.49824 q^{73} -2.83667 q^{74} +20.1289 q^{75} -4.20285 q^{76} -14.1399 q^{78} -8.40569 q^{79} -3.74912 q^{80} -11.0559 q^{81} -9.97186 q^{82} -10.5295 q^{83} -3.74912 q^{85} -2.15862 q^{86} -7.46734 q^{87} -5.63696 q^{88} +5.04070 q^{89} -7.27549 q^{90} +5.30205 q^{92} +11.8060 q^{93} +0.625581 q^{94} +15.7570 q^{95} +2.22274 q^{96} -5.15286 q^{97} -10.9390 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 8 q^{5} - 4 q^{6} + 4 q^{8} + 8 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 8 * q^5 - 4 * q^6 + 4 * q^8 + 8 * q^9	$ 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 8 q^{5} - 4 q^{6} + 4 q^{8} + 8 q^{9} - 8 q^{10} - 4 q^{11} - 4 q^{12} - 8 q^{13} + 4 q^{15} + 4 q^{16} + 4 q^{17} + 8 q^{18} - 8 q^{19} - 8 q^{20} - 4 q^{22} + 4 q^{23} - 4 q^{24} + 8 q^{25} - 8 q^{26} - 4 q^{27} - 4 q^{29} + 4 q^{30} - 4 q^{31} + 4 q^{32} - 16 q^{33} + 4 q^{34} + 8 q^{36} - 24 q^{37} - 8 q^{38} - 20 q^{39} - 8 q^{40} - 20 q^{41} - 4 q^{44} - 28 q^{45} + 4 q^{46} - 4 q^{48} + 8 q^{50} - 4 q^{51} - 8 q^{52} - 4 q^{54} + 16 q^{55} - 12 q^{57} - 4 q^{58} - 16 q^{59} + 4 q^{60} + 8 q^{61} - 4 q^{62} + 4 q^{64} + 4 q^{65} - 16 q^{66} + 4 q^{68} + 16 q^{69} + 8 q^{72} - 24 q^{73} - 24 q^{74} + 16 q^{75} - 8 q^{76} - 20 q^{78} - 16 q^{79} - 8 q^{80} - 16 q^{81} - 20 q^{82} - 8 q^{83} - 8 q^{85} + 8 q^{87} - 4 q^{88} - 8 q^{89} - 28 q^{90} + 4 q^{92} + 24 q^{93} + 12 q^{95} - 4 q^{96} - 4 q^{97} - 8 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 8 * q^5 - 4 * q^6 + 4 * q^8 + 8 * q^9 - 8 * q^10 - 4 * q^11 - 4 * q^12 - 8 * q^13 + 4 * q^15 + 4 * q^16 + 4 * q^17 + 8 * q^18 - 8 * q^19 - 8 * q^20 - 4 * q^22 + 4 * q^23 - 4 * q^24 + 8 * q^25 - 8 * q^26 - 4 * q^27 - 4 * q^29 + 4 * q^30 - 4 * q^31 + 4 * q^32 - 16 * q^33 + 4 * q^34 + 8 * q^36 - 24 * q^37 - 8 * q^38 - 20 * q^39 - 8 * q^40 - 20 * q^41 - 4 * q^44 - 28 * q^45 + 4 * q^46 - 4 * q^48 + 8 * q^50 - 4 * q^51 - 8 * q^52 - 4 * q^54 + 16 * q^55 - 12 * q^57 - 4 * q^58 - 16 * q^59 + 4 * q^60 + 8 * q^61 - 4 * q^62 + 4 * q^64 + 4 * q^65 - 16 * q^66 + 4 * q^68 + 16 * q^69 + 8 * q^72 - 24 * q^73 - 24 * q^74 + 16 * q^75 - 8 * q^76 - 20 * q^78 - 16 * q^79 - 8 * q^80 - 16 * q^81 - 20 * q^82 - 8 * q^83 - 8 * q^85 + 8 * q^87 - 4 * q^88 - 8 * q^89 - 28 * q^90 + 4 * q^92 + 24 * q^93 + 12 * q^95 - 4 * q^96 - 4 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	2.22274	1.28330	0.641651	−	0.766997i	$-0.278250\pi$
$3$	2.22274	1.28330	0.641651	+	0.766997i	$0.278250\pi$
$4$	1.00000	0.500000
$5$	−3.74912	−1.67666	−0.838328	−	0.545166i	$-0.816467\pi$
$5$	−3.74912	−1.67666	−0.838328	+	0.545166i	$0.816467\pi$
$6$	2.22274	0.907431
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	1.94059	0.646863
$10$	−3.74912	−1.18558
$11$	−5.63696	−1.69961	−0.849803	−	0.527100i	$-0.823279\pi$
$11$	−5.63696	−1.69961	−0.849803	+	0.527100i	$0.823279\pi$
$12$	2.22274	0.641651
$13$	−6.36147	−1.76435	−0.882176	−	0.470919i	$-0.843922\pi$
$13$	−6.36147	−1.76435	−0.882176	+	0.470919i	$0.843922\pi$
$14$	0	0
$15$	−8.33333	−2.15166
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.94059	0.457401
$19$	−4.20285	−0.964199	−0.482099	−	0.876116i	$-0.660126\pi$
$19$	−4.20285	−0.964199	−0.482099	+	0.876116i	$0.660126\pi$
$20$	−3.74912	−0.838328
$21$	0	0
$22$	−5.63696	−1.20180
$23$	5.30205	1.10555	0.552777	−	0.833329i	$-0.313568\pi$
$23$	5.30205	1.10555	0.552777	+	0.833329i	$0.313568\pi$
$24$	2.22274	0.453716
$25$	9.05588	1.81118
$26$	−6.36147	−1.24759
$27$	−2.35480	−0.453182
$28$	0	0
$29$	−3.35951	−0.623846	−0.311923	−	0.950107i	$-0.600973\pi$
$29$	−3.35951	−0.623846	−0.311923	+	0.950107i	$0.600973\pi$
$30$	−8.33333	−1.52145
$31$	5.31148	0.953969	0.476985	−	0.878912i	$-0.341730\pi$
$31$	5.31148	0.953969	0.476985	+	0.878912i	$0.341730\pi$
$32$	1.00000	0.176777
$33$	−12.5295	−2.18111
$34$	1.00000	0.171499
$35$	0	0
$36$	1.94059	0.323431
$37$	−2.83667	−0.466345	−0.233173	−	0.972435i	$-0.574911\pi$
$37$	−2.83667	−0.466345	−0.233173	+	0.972435i	$0.574911\pi$
$38$	−4.20285	−0.681792
$39$	−14.1399	−2.26420
$40$	−3.74912	−0.592788
$41$	−9.97186	−1.55734	−0.778672	−	0.627432i	$-0.784106\pi$
$41$	−9.97186	−1.55734	−0.778672	+	0.627432i	$0.784106\pi$
$42$	0	0
$43$	−2.15862	−0.329186	−0.164593	−	0.986362i	$-0.552631\pi$
$43$	−2.15862	−0.329186	−0.164593	+	0.986362i	$0.552631\pi$
$44$	−5.63696	−0.849803
$45$	−7.27549	−1.08457
$46$	5.30205	0.781745
$47$	0.625581	0.0912504	0.0456252	−	0.998959i	$-0.485472\pi$
$47$	0.625581	0.0912504	0.0456252	+	0.998959i	$0.485472\pi$
$48$	2.22274	0.320825
$49$	0	0
$50$	9.05588	1.28070
$51$	2.22274	0.311246
$52$	−6.36147	−0.882176
$53$	6.56431	0.901677	0.450839	−	0.892605i	$-0.351125\pi$
$53$	6.56431	0.901677	0.450839	+	0.892605i	$0.351125\pi$
$54$	−2.35480	−0.320448
$55$	21.1336	2.84966
$56$	0	0
$57$	−9.34185	−1.23736
$58$	−3.35951	−0.441126
$59$	−3.13677	−0.408373	−0.204186	−	0.978932i	$-0.565455\pi$
$59$	−3.13677	−0.408373	−0.204186	+	0.978932i	$0.565455\pi$
$60$	−8.33333	−1.07583
$61$	13.8117	1.76840	0.884201	−	0.467106i	$-0.154703\pi$
$61$	13.8117	1.76840	0.884201	+	0.467106i	$0.154703\pi$
$62$	5.31148	0.674558
$63$	0	0
$64$	1.00000	0.125000
$65$	23.8499	2.95821
$66$	−12.5295	−1.54228
$67$	12.1023	1.47854	0.739268	−	0.673411i	$-0.235172\pi$
$67$	12.1023	1.47854	0.739268	+	0.673411i	$0.235172\pi$
$68$	1.00000	0.121268
$69$	11.7851	1.41876
$70$	0	0
$71$	3.73588	0.443368	0.221684	−	0.975119i	$-0.428845\pi$
$71$	3.73588	0.443368	0.221684	+	0.975119i	$0.428845\pi$
$72$	1.94059	0.228700
$73$	−9.49824	−1.11168	−0.555842	−	0.831288i	$-0.687604\pi$
$73$	−9.49824	−1.11168	−0.555842	+	0.831288i	$0.687604\pi$
$74$	−2.83667	−0.329756
$75$	20.1289	2.32429
$76$	−4.20285	−0.482099
$77$	0	0
$78$	−14.1399	−1.60103
$79$	−8.40569	−0.945714	−0.472857	−	0.881139i	$-0.656777\pi$
$79$	−8.40569	−0.945714	−0.472857	+	0.881139i	$0.656777\pi$
$80$	−3.74912	−0.419164
$81$	−11.0559	−1.22843
$82$	−9.97186	−1.10121
$83$	−10.5295	−1.15576	−0.577882	−	0.816120i	$-0.696121\pi$
$83$	−10.5295	−1.15576	−0.577882	+	0.816120i	$0.696121\pi$
$84$	0	0
$85$	−3.74912	−0.406649
$86$	−2.15862	−0.232770
$87$	−7.46734	−0.800582
$88$	−5.63696	−0.600902
$89$	5.04070	0.534313	0.267156	−	0.963653i	$-0.413916\pi$
$89$	5.04070	0.534313	0.267156	+	0.963653i	$0.413916\pi$
$90$	−7.27549	−0.766904
$91$	0	0
$92$	5.30205	0.552777
$93$	11.8060	1.22423
$94$	0.625581	0.0645238
$95$	15.7570	1.61663
$96$	2.22274	0.226858
$97$	−5.15286	−0.523193	−0.261597	−	0.965177i	$-0.584249\pi$
$97$	−5.15286	−0.523193	−0.261597	+	0.965177i	$0.584249\pi$
$98$	0	0
$99$	−10.9390	−1.09941
$100$	9.05588	0.905588
$101$	−7.91598	−0.787669	−0.393835	−	0.919181i	$-0.628852\pi$
$101$	−7.91598	−0.787669	−0.393835	+	0.919181i	$0.628852\pi$
$102$	2.22274	0.220084
$103$	1.00353	0.0988807	0.0494404	−	0.998777i	$-0.484256\pi$
$103$	1.00353	0.0988807	0.0494404	+	0.998777i	$0.484256\pi$
$104$	−6.36147	−0.623793
$105$	0	0
$106$	6.56431	0.637582
$107$	−4.52166	−0.437126	−0.218563	−	0.975823i	$-0.570137\pi$
$107$	−4.52166	−0.437126	−0.218563	+	0.975823i	$0.570137\pi$
$108$	−2.35480	−0.226591
$109$	7.21255	0.690837	0.345418	−	0.938449i	$-0.387737\pi$
$109$	7.21255	0.690837	0.345418	+	0.938449i	$0.387737\pi$
$110$	21.1336	2.01501
$111$	−6.30519	−0.598462
$112$	0	0
$113$	9.31148	0.875950	0.437975	−	0.898987i	$-0.355696\pi$
$113$	9.31148	0.875950	0.437975	+	0.898987i	$0.355696\pi$
$114$	−9.34185	−0.874944
$115$	−19.8780	−1.85363
$116$	−3.35951	−0.311923
$117$	−12.3450	−1.14129
$118$	−3.13677	−0.288763
$119$	0	0
$120$	−8.33333	−0.760725
$121$	20.7753	1.88866
$122$	13.8117	1.25045
$123$	−22.1649	−1.99854
$124$	5.31148	0.476985
$125$	−15.2060	−1.36006
$126$	0	0
$127$	−9.70331	−0.861030	−0.430515	−	0.902583i	$-0.641668\pi$
$127$	−9.70331	−0.861030	−0.430515	+	0.902583i	$0.641668\pi$
$128$	1.00000	0.0883883
$129$	−4.79806	−0.422445
$130$	23.8499	2.09177
$131$	−20.3930	−1.78175	−0.890873	−	0.454252i	$-0.849906\pi$
$131$	−20.3930	−1.78175	−0.890873	+	0.454252i	$0.849906\pi$
$132$	−12.5295	−1.09055
$133$	0	0
$134$	12.1023	1.04548
$135$	8.82843	0.759830
$136$	1.00000	0.0857493
$137$	−2.51785	−0.215115	−0.107557	−	0.994199i	$-0.534303\pi$
$137$	−2.51785	−0.215115	−0.107557	+	0.994199i	$0.534303\pi$
$138$	11.7851	1.00321
$139$	12.7987	1.08557	0.542786	−	0.839871i	$-0.317369\pi$
$139$	12.7987	1.08557	0.542786	+	0.839871i	$0.317369\pi$
$140$	0	0
$141$	1.39051	0.117102
$142$	3.73588	0.313508
$143$	35.8593	2.99871
$144$	1.94059	0.161716
$145$	12.5952	1.04598
$146$	−9.49824	−0.786080
$147$	0	0
$148$	−2.83667	−0.233173
$149$	−5.48881	−0.449661	−0.224830	−	0.974398i	$-0.572183\pi$
$149$	−5.48881	−0.449661	−0.224830	+	0.974398i	$0.572183\pi$
$150$	20.1289	1.64352
$151$	5.44235	0.442892	0.221446	−	0.975173i	$-0.428922\pi$
$151$	5.44235	0.442892	0.221446	+	0.975173i	$0.428922\pi$
$152$	−4.20285	−0.340896
$153$	1.94059	0.156887
$154$	0	0
$155$	−19.9134	−1.59948
$156$	−14.1399	−1.13210
$157$	21.0281	1.67823	0.839113	−	0.543957i	$-0.183074\pi$
$157$	21.0281	1.67823	0.839113	+	0.543957i	$0.183074\pi$
$158$	−8.40569	−0.668721
$159$	14.5908	1.15712
$160$	−3.74912	−0.296394
$161$	0	0
$162$	−11.0559	−0.868632
$163$	−15.2540	−1.19479	−0.597393	−	0.801948i	$-0.703797\pi$
$163$	−15.2540	−1.19479	−0.597393	+	0.801948i	$0.703797\pi$
$164$	−9.97186	−0.778672
$165$	46.9746	3.65697
$166$	−10.5295	−0.817248
$167$	−8.91911	−0.690182	−0.345091	−	0.938569i	$-0.612152\pi$
$167$	−8.91911	−0.690182	−0.345091	+	0.938569i	$0.612152\pi$
$168$	0	0
$169$	27.4682	2.11294
$170$	−3.74912	−0.287544
$171$	−8.15599	−0.623704
$172$	−2.15862	−0.164593
$173$	−8.26254	−0.628189	−0.314095	−	0.949392i	$-0.601701\pi$
$173$	−8.26254	−0.628189	−0.314095	+	0.949392i	$0.601701\pi$
$174$	−7.46734	−0.566097
$175$	0	0
$176$	−5.63696	−0.424902
$177$	−6.97223	−0.524065
$178$	5.04070	0.377816
$179$	−10.0492	−0.751114	−0.375557	−	0.926799i	$-0.622549\pi$
$179$	−10.0492	−0.751114	−0.375557	+	0.926799i	$0.622549\pi$
$180$	−7.27549	−0.542283
$181$	−4.14148	−0.307834	−0.153917	−	0.988084i	$-0.549189\pi$
$181$	−4.14148	−0.307834	−0.153917	+	0.988084i	$0.549189\pi$
$182$	0	0
$183$	30.6998	2.26939
$184$	5.30205	0.390873
$185$	10.6350	0.781901
$186$	11.8060	0.865662
$187$	−5.63696	−0.412215
$188$	0.625581	0.0456252
$189$	0	0
$190$	15.7570	1.14313
$191$	−5.82490	−0.421475	−0.210737	−	0.977543i	$-0.567586\pi$
$191$	−5.82490	−0.421475	−0.210737	+	0.977543i	$0.567586\pi$
$192$	2.22274	0.160413
$193$	−16.0438	−1.15486	−0.577430	−	0.816440i	$-0.695944\pi$
$193$	−16.0438	−1.15486	−0.577430	+	0.816440i	$0.695944\pi$
$194$	−5.15286	−0.369954
$195$	53.0122	3.79628
$196$	0	0
$197$	−22.5163	−1.60422	−0.802109	−	0.597178i	$-0.796289\pi$
$197$	−22.5163	−1.60422	−0.802109	+	0.597178i	$0.796289\pi$
$198$	−10.9390	−0.777402
$199$	−18.1743	−1.28834	−0.644171	−	0.764881i	$-0.722798\pi$
$199$	−18.1743	−1.28834	−0.644171	+	0.764881i	$0.722798\pi$
$200$	9.05588	0.640348
$201$	26.9004	1.89741
$202$	−7.91598	−0.556966
$203$	0	0
$204$	2.22274	0.155623
$205$	37.3857	2.61113
$206$	1.00353	0.0699192
$207$	10.2891	0.715142
$208$	−6.36147	−0.441088
$209$	23.6913	1.63876
$210$	0	0
$211$	−14.6960	−1.01171	−0.505856	−	0.862618i	$-0.668823\pi$
$211$	−14.6960	−1.01171	−0.505856	+	0.862618i	$0.668823\pi$
$212$	6.56431	0.450839
$213$	8.30391	0.568975
$214$	−4.52166	−0.309094
$215$	8.09292	0.551932
$216$	−2.35480	−0.160224
$217$	0	0
$218$	7.21255	0.488496
$219$	−21.1121	−1.42663
$220$	21.1336	1.42483
$221$	−6.36147	−0.427918
$222$	−6.30519	−0.423176
$223$	19.8464	1.32901	0.664506	−	0.747283i	$-0.268642\pi$
$223$	19.8464	1.32901	0.664506	+	0.747283i	$0.268642\pi$
$224$	0	0
$225$	17.5737	1.17158
$226$	9.31148	0.619390
$227$	−16.5329	−1.09733	−0.548664	−	0.836043i	$-0.684863\pi$
$227$	−16.5329	−1.09733	−0.548664	+	0.836043i	$0.684863\pi$
$228$	−9.34185	−0.618679
$229$	16.8467	1.11326	0.556632	−	0.830759i	$-0.312093\pi$
$229$	16.8467	1.11326	0.556632	+	0.830759i	$0.312093\pi$
$230$	−19.8780	−1.31072
$231$	0	0
$232$	−3.35951	−0.220563
$233$	−4.64390	−0.304232	−0.152116	−	0.988363i	$-0.548609\pi$
$233$	−4.64390	−0.304232	−0.152116	+	0.988363i	$0.548609\pi$
$234$	−12.3450	−0.807017
$235$	−2.34538	−0.152996
$236$	−3.13677	−0.204186
$237$	−18.6837	−1.21364
$238$	0	0
$239$	0.908017	0.0587347	0.0293674	−	0.999569i	$-0.490651\pi$
$239$	0.908017	0.0587347	0.0293674	+	0.999569i	$0.490651\pi$
$240$	−8.33333	−0.537914
$241$	18.8347	1.21325	0.606625	−	0.794988i	$-0.292523\pi$
$241$	18.8347	1.21325	0.606625	+	0.794988i	$0.292523\pi$
$242$	20.7753	1.33549
$243$	−17.5100	−1.12327
$244$	13.8117	0.884201
$245$	0	0
$246$	−22.1649	−1.41318
$247$	26.7363	1.70119
$248$	5.31148	0.337279
$249$	−23.4044	−1.48319
$250$	−15.2060	−0.961711
$251$	4.87656	0.307806	0.153903	−	0.988086i	$-0.450816\pi$
$251$	4.87656	0.307806	0.153903	+	0.988086i	$0.450816\pi$
$252$	0	0
$253$	−29.8874	−1.87901
$254$	−9.70331	−0.608840
$255$	−8.33333	−0.521853
$256$	1.00000	0.0625000
$257$	5.93430	0.370171	0.185086	−	0.982722i	$-0.440744\pi$
$257$	5.93430	0.370171	0.185086	+	0.982722i	$0.440744\pi$
$258$	−4.79806	−0.298714
$259$	0	0
$260$	23.8499	1.47911
$261$	−6.51943	−0.403543
$262$	−20.3930	−1.25988
$263$	−6.53174	−0.402764	−0.201382	−	0.979513i	$-0.564543\pi$
$263$	−6.53174	−0.402764	−0.201382	+	0.979513i	$0.564543\pi$
$264$	−12.5295	−0.771138
$265$	−24.6104	−1.51180
$266$	0	0
$267$	11.2042	0.685684
$268$	12.1023	0.739268
$269$	−10.0243	−0.611194	−0.305597	−	0.952161i	$-0.598856\pi$
$269$	−10.0243	−0.611194	−0.305597	+	0.952161i	$0.598856\pi$
$270$	8.82843	0.537281
$271$	−3.30481	−0.200753	−0.100377	−	0.994950i	$-0.532005\pi$
$271$	−3.30481	−0.200753	−0.100377	+	0.994950i	$0.532005\pi$
$272$	1.00000	0.0606339
$273$	0	0
$274$	−2.51785	−0.152109
$275$	−51.0476	−3.07829
$276$	11.7851	0.709380
$277$	16.9225	1.01678	0.508388	−	0.861128i	$-0.330242\pi$
$277$	16.9225	1.01678	0.508388	+	0.861128i	$0.330242\pi$
$278$	12.7987	0.767616
$279$	10.3074	0.617087
$280$	0	0
$281$	−4.39903	−0.262424	−0.131212	−	0.991354i	$-0.541887\pi$
$281$	−4.39903	−0.262424	−0.131212	+	0.991354i	$0.541887\pi$
$282$	1.39051	0.0828035
$283$	16.6097	0.987345	0.493673	−	0.869648i	$-0.335654\pi$
$283$	16.6097	0.987345	0.493673	+	0.869648i	$0.335654\pi$
$284$	3.73588	0.221684
$285$	35.0237	2.07462
$286$	35.8593	2.12041
$287$	0	0
$288$	1.94059	0.114350
$289$	1.00000	0.0588235
$290$	12.5952	0.739616
$291$	−11.4535	−0.671415
$292$	−9.49824	−0.555842
$293$	24.4075	1.42590	0.712951	−	0.701213i	$-0.247358\pi$
$293$	24.4075	1.42590	0.712951	+	0.701213i	$0.247358\pi$
$294$	0	0
$295$	11.7601	0.684701
$296$	−2.83667	−0.164878
$297$	13.2739	0.770231
$298$	−5.48881	−0.317958
$299$	−33.7288	−1.95059
$300$	20.1289	1.16214
$301$	0	0
$302$	5.44235	0.313172
$303$	−17.5952	−1.01082
$304$	−4.20285	−0.241050
$305$	−51.7816	−2.96500
$306$	1.94059	0.110936
$307$	−17.4205	−0.994239	−0.497120	−	0.867682i	$-0.665609\pi$
$307$	−17.4205	−0.994239	−0.497120	+	0.867682i	$0.665609\pi$
$308$	0	0
$309$	2.23059	0.126894
$310$	−19.9134	−1.13100
$311$	19.4022	1.10020	0.550098	−	0.835100i	$-0.314590\pi$
$311$	19.4022	1.10020	0.550098	+	0.835100i	$0.314590\pi$
$312$	−14.1399	−0.800514
$313$	−0.965967	−0.0545997	−0.0272998	−	0.999627i	$-0.508691\pi$
$313$	−0.965967	−0.0545997	−0.0272998	+	0.999627i	$0.508691\pi$
$314$	21.0281	1.18669
$315$	0	0
$316$	−8.40569	−0.472857
$317$	−22.8577	−1.28382	−0.641910	−	0.766780i	$-0.721858\pi$
$317$	−22.8577	−1.28382	−0.641910	+	0.766780i	$0.721858\pi$
$318$	14.5908	0.818210
$319$	18.9374	1.06029
$320$	−3.74912	−0.209582
$321$	−10.0505	−0.560964
$322$	0	0
$323$	−4.20285	−0.233853
$324$	−11.0559	−0.614216
$325$	−57.6087	−3.19555
$326$	−15.2540	−0.844842
$327$	16.0316	0.886552
$328$	−9.97186	−0.550604
$329$	0	0
$330$	46.9746	2.58587
$331$	14.6931	0.807607	0.403803	−	0.914846i	$-0.367688\pi$
$331$	14.6931	0.807607	0.403803	+	0.914846i	$0.367688\pi$
$332$	−10.5295	−0.577882
$333$	−5.50481	−0.301661
$334$	−8.91911	−0.488032
$335$	−45.3731	−2.47900
$336$	0	0
$337$	−26.3383	−1.43474	−0.717370	−	0.696693i	$-0.754654\pi$
$337$	−26.3383	−1.43474	−0.717370	+	0.696693i	$0.754654\pi$
$338$	27.4682	1.49408
$339$	20.6970	1.12411
$340$	−3.74912	−0.203324
$341$	−29.9406	−1.62137
$342$	−8.15599	−0.441026
$343$	0	0
$344$	−2.15862	−0.116385
$345$	−44.1837	−2.37877
$346$	−8.26254	−0.444197
$347$	−18.6241	−0.999796	−0.499898	−	0.866084i	$-0.666629\pi$
$347$	−18.6241	−0.999796	−0.499898	+	0.866084i	$0.666629\pi$
$348$	−7.46734	−0.400291
$349$	16.8954	0.904390	0.452195	−	0.891919i	$-0.350641\pi$
$349$	16.8954	0.904390	0.452195	+	0.891919i	$0.350641\pi$
$350$	0	0
$351$	14.9800	0.799573
$352$	−5.63696	−0.300451
$353$	12.3659	0.658170	0.329085	−	0.944300i	$-0.393260\pi$
$353$	12.3659	0.658170	0.329085	+	0.944300i	$0.393260\pi$
$354$	−6.97223	−0.370570
$355$	−14.0063	−0.743376
$356$	5.04070	0.267156
$357$	0	0
$358$	−10.0492	−0.531118
$359$	−15.0761	−0.795684	−0.397842	−	0.917454i	$-0.630241\pi$
$359$	−15.0761	−0.795684	−0.397842	+	0.917454i	$0.630241\pi$
$360$	−7.27549	−0.383452
$361$	−1.33609	−0.0703203
$362$	−4.14148	−0.217671
$363$	46.1781	2.42372
$364$	0	0
$365$	35.6100	1.86391
$366$	30.6998	1.60470
$367$	33.7172	1.76002	0.880011	−	0.474953i	$-0.157535\pi$
$367$	33.7172	1.76002	0.880011	+	0.474953i	$0.157535\pi$
$368$	5.30205	0.276389
$369$	−19.3513	−1.00739
$370$	10.6350	0.552888
$371$	0	0
$372$	11.8060	0.612115
$373$	−14.4025	−0.745735	−0.372868	−	0.927885i	$-0.621625\pi$
$373$	−14.4025	−0.745735	−0.372868	+	0.927885i	$0.621625\pi$
$374$	−5.63696	−0.291480
$375$	−33.7990	−1.74537
$376$	0.625581	0.0322619
$377$	21.3714	1.10068
$378$	0	0
$379$	18.2318	0.936503	0.468252	−	0.883595i	$-0.344884\pi$
$379$	18.2318	0.936503	0.468252	+	0.883595i	$0.344884\pi$
$380$	15.7570	0.808315
$381$	−21.5680	−1.10496
$382$	−5.82490	−0.298028
$383$	1.87175	0.0956420	0.0478210	−	0.998856i	$-0.484772\pi$
$383$	1.87175	0.0956420	0.0478210	+	0.998856i	$0.484772\pi$
$384$	2.22274	0.113429
$385$	0	0
$386$	−16.0438	−0.816609
$387$	−4.18899	−0.212938
$388$	−5.15286	−0.261597
$389$	23.5835	1.19573	0.597866	−	0.801596i	$-0.296015\pi$
$389$	23.5835	1.19573	0.597866	+	0.801596i	$0.296015\pi$
$390$	53.0122	2.68438
$391$	5.30205	0.268136
$392$	0	0
$393$	−45.3284	−2.28652
$394$	−22.5163	−1.13435
$395$	31.5139	1.58564
$396$	−10.9390	−0.549706
$397$	17.0589	0.856163	0.428081	−	0.903740i	$-0.359190\pi$
$397$	17.0589	0.856163	0.428081	+	0.903740i	$0.359190\pi$
$398$	−18.1743	−0.910996
$399$	0	0
$400$	9.05588	0.452794
$401$	−27.6515	−1.38085	−0.690424	−	0.723405i	$-0.742576\pi$
$401$	−27.6515	−1.38085	−0.690424	+	0.723405i	$0.742576\pi$
$402$	26.9004	1.34167
$403$	−33.7888	−1.68314
$404$	−7.91598	−0.393835
$405$	41.4498	2.05966
$406$	0	0
$407$	15.9902	0.792604
$408$	2.22274	0.110042
$409$	−6.63392	−0.328026	−0.164013	−	0.986458i	$-0.552444\pi$
$409$	−6.63392	−0.328026	−0.164013	+	0.986458i	$0.552444\pi$
$410$	37.3857	1.84635
$411$	−5.59654	−0.276057
$412$	1.00353	0.0494404
$413$	0	0
$414$	10.2891	0.505682
$415$	39.4764	1.93782
$416$	−6.36147	−0.311896
$417$	28.4482	1.39312
$418$	23.6913	1.15878
$419$	1.44353	0.0705213	0.0352606	−	0.999378i	$-0.488774\pi$
$419$	1.44353	0.0705213	0.0352606	+	0.999378i	$0.488774\pi$
$420$	0	0
$421$	−25.7780	−1.25634	−0.628172	−	0.778074i	$-0.716197\pi$
$421$	−25.7780	−1.25634	−0.628172	+	0.778074i	$0.716197\pi$
$422$	−14.6960	−0.715389
$423$	1.21400	0.0590265
$424$	6.56431	0.318791
$425$	9.05588	0.439275
$426$	8.30391	0.402326
$427$	0	0
$428$	−4.52166	−0.218563
$429$	79.7060	3.84824
$430$	8.09292	0.390275
$431$	−3.36223	−0.161953	−0.0809766	−	0.996716i	$-0.525804\pi$
$431$	−3.36223	−0.161953	−0.0809766	+	0.996716i	$0.525804\pi$
$432$	−2.35480	−0.113295
$433$	−38.6546	−1.85762	−0.928811	−	0.370554i	$-0.879168\pi$
$433$	−38.6546	−1.85762	−0.928811	+	0.370554i	$0.879168\pi$
$434$	0	0
$435$	27.9959	1.34230
$436$	7.21255	0.345418
$437$	−22.2837	−1.06597
$438$	−21.1121	−1.00878
$439$	−3.50989	−0.167518	−0.0837590	−	0.996486i	$-0.526693\pi$
$439$	−3.50989	−0.167518	−0.0837590	+	0.996486i	$0.526693\pi$
$440$	21.1336	1.00751
$441$	0	0
$442$	−6.36147	−0.302584
$443$	3.08883	0.146755	0.0733773	−	0.997304i	$-0.476622\pi$
$443$	3.08883	0.146755	0.0733773	+	0.997304i	$0.476622\pi$
$444$	−6.30519	−0.299231
$445$	−18.8982	−0.895859
$446$	19.8464	0.939753
$447$	−12.2002	−0.577051
$448$	0	0
$449$	−1.12235	−0.0529672	−0.0264836	−	0.999649i	$-0.508431\pi$
$449$	−1.12235	−0.0529672	−0.0264836	+	0.999649i	$0.508431\pi$
$450$	17.5737	0.828434
$451$	56.2109	2.64687
$452$	9.31148	0.437975
$453$	12.0970	0.568364
$454$	−16.5329	−0.775928
$455$	0	0
$456$	−9.34185	−0.437472
$457$	24.0196	1.12359	0.561795	−	0.827277i	$-0.310111\pi$
$457$	24.0196	1.12359	0.561795	+	0.827277i	$0.310111\pi$
$458$	16.8467	0.787197
$459$	−2.35480	−0.109913
$460$	−19.8780	−0.926817
$461$	−13.3579	−0.622141	−0.311071	−	0.950387i	$-0.600688\pi$
$461$	−13.3579	−0.622141	−0.311071	+	0.950387i	$0.600688\pi$
$462$	0	0
$463$	13.4916	0.627006	0.313503	−	0.949587i	$-0.398497\pi$
$463$	13.4916	0.627006	0.313503	+	0.949587i	$0.398497\pi$
$464$	−3.35951	−0.155961
$465$	−44.2623	−2.05261
$466$	−4.64390	−0.215125
$467$	−13.9995	−0.647818	−0.323909	−	0.946088i	$-0.604997\pi$
$467$	−13.9995	−0.647818	−0.323909	+	0.946088i	$0.604997\pi$
$468$	−12.3450	−0.570647
$469$	0	0
$470$	−2.34538	−0.108184
$471$	46.7401	2.15367
$472$	−3.13677	−0.144382
$473$	12.1680	0.559487
$474$	−18.6837	−0.858171
$475$	−38.0605	−1.74633
$476$	0	0
$477$	12.7386	0.583261
$478$	0.908017	0.0415317
$479$	−6.99963	−0.319821	−0.159911	−	0.987132i	$-0.551121\pi$
$479$	−6.99963	−0.319821	−0.159911	+	0.987132i	$0.551121\pi$
$480$	−8.33333	−0.380363
$481$	18.0454	0.822798
$482$	18.8347	0.857897
$483$	0	0
$484$	20.7753	0.944331
$485$	19.3187	0.877216
$486$	−17.5100	−0.794269
$487$	−22.9754	−1.04111	−0.520557	−	0.853827i	$-0.674276\pi$
$487$	−22.9754	−1.04111	−0.520557	+	0.853827i	$0.674276\pi$
$488$	13.8117	0.625225
$489$	−33.9058	−1.53327
$490$	0	0
$491$	31.6239	1.42717	0.713583	−	0.700571i	$-0.247071\pi$
$491$	31.6239	1.42717	0.713583	+	0.700571i	$0.247071\pi$
$492$	−22.1649	−0.999270
$493$	−3.35951	−0.151305
$494$	26.7363	1.20292
$495$	41.0116	1.84334
$496$	5.31148	0.238492
$497$	0	0
$498$	−23.4044	−1.04878
$499$	−22.6351	−1.01329	−0.506643	−	0.862156i	$-0.669114\pi$
$499$	−22.6351	−1.01329	−0.506643	+	0.862156i	$0.669114\pi$
$500$	−15.2060	−0.680032
$501$	−19.8249	−0.885711
$502$	4.87656	0.217651
$503$	−21.3834	−0.953441	−0.476720	−	0.879055i	$-0.658175\pi$
$503$	−21.3834	−0.953441	−0.476720	+	0.879055i	$0.658175\pi$
$504$	0	0
$505$	29.6779	1.32065
$506$	−29.8874	−1.32866
$507$	61.0548	2.71154
$508$	−9.70331	−0.430515
$509$	−25.5330	−1.13173	−0.565866	−	0.824497i	$-0.691458\pi$
$509$	−25.5330	−1.13173	−0.565866	+	0.824497i	$0.691458\pi$
$510$	−8.33333	−0.369006
$511$	0	0
$512$	1.00000	0.0441942
$513$	9.89687	0.436957
$514$	5.93430	0.261751
$515$	−3.76235	−0.165789
$516$	−4.79806	−0.211223
$517$	−3.52637	−0.155090
$518$	0	0
$519$	−18.3655	−0.806156
$520$	23.8499	1.04589
$521$	34.9011	1.52905	0.764523	−	0.644596i	$-0.222974\pi$
$521$	34.9011	1.52905	0.764523	+	0.644596i	$0.222974\pi$
$522$	−6.51943	−0.285348
$523$	4.51302	0.197341	0.0986704	−	0.995120i	$-0.468541\pi$
$523$	4.51302	0.197341	0.0986704	+	0.995120i	$0.468541\pi$
$524$	−20.3930	−0.890873
$525$	0	0
$526$	−6.53174	−0.284797
$527$	5.31148	0.231372
$528$	−12.5295	−0.545277
$529$	5.11176	0.222251
$530$	−24.6104	−1.06901
$531$	−6.08718	−0.264161
$532$	0	0
$533$	63.4356	2.74770
$534$	11.2042	0.484852
$535$	16.9522	0.732909
$536$	12.1023	0.522742
$537$	−22.3368	−0.963906
$538$	−10.0243	−0.432180
$539$	0	0
$540$	8.82843	0.379915
$541$	−21.8144	−0.937875	−0.468938	−	0.883231i	$-0.655363\pi$
$541$	−21.8144	−0.937875	−0.468938	+	0.883231i	$0.655363\pi$
$542$	−3.30481	−0.141954
$543$	−9.20545	−0.395044
$544$	1.00000	0.0428746
$545$	−27.0407	−1.15830
$546$	0	0
$547$	43.0665	1.84139	0.920695	−	0.390284i	$-0.127623\pi$
$547$	43.0665	1.84139	0.920695	+	0.390284i	$0.127623\pi$
$548$	−2.51785	−0.107557
$549$	26.8027	1.14391
$550$	−51.0476	−2.17668
$551$	14.1195	0.601512
$552$	11.7851	0.501607
$553$	0	0
$554$	16.9225	0.718969
$555$	23.6389	1.00341
$556$	12.7987	0.542786
$557$	26.9237	1.14079	0.570397	−	0.821369i	$-0.306789\pi$
$557$	26.9237	1.14079	0.570397	+	0.821369i	$0.306789\pi$
$558$	10.3074	0.436346
$559$	13.7320	0.580801
$560$	0	0
$561$	−12.5295	−0.528996
$562$	−4.39903	−0.185562
$563$	−29.8987	−1.26008	−0.630040	−	0.776563i	$-0.716962\pi$
$563$	−29.8987	−1.26008	−0.630040	+	0.776563i	$0.716962\pi$
$564$	1.39051	0.0585509
$565$	−34.9098	−1.46867
$566$	16.6097	0.698159
$567$	0	0
$568$	3.73588	0.156754
$569$	27.9249	1.17067	0.585336	−	0.810791i	$-0.300963\pi$
$569$	27.9249	1.17067	0.585336	+	0.810791i	$0.300963\pi$
$570$	35.0237	1.46698
$571$	16.1263	0.674864	0.337432	−	0.941350i	$-0.390442\pi$
$571$	16.1263	0.674864	0.337432	+	0.941350i	$0.390442\pi$
$572$	35.8593	1.49935
$573$	−12.9473	−0.540879
$574$	0	0
$575$	48.0148	2.00235
$576$	1.94059	0.0808578
$577$	−11.7788	−0.490359	−0.245180	−	0.969478i	$-0.578847\pi$
$577$	−11.7788	−0.490359	−0.245180	+	0.969478i	$0.578847\pi$
$578$	1.00000	0.0415945
$579$	−35.6613	−1.48203
$580$	12.5952	0.522988
$581$	0	0
$582$	−11.4535	−0.474762
$583$	−37.0027	−1.53250
$584$	−9.49824	−0.393040
$585$	46.2828	1.91356
$586$	24.4075	1.00827
$587$	30.2981	1.25054	0.625269	−	0.780409i	$-0.284989\pi$
$587$	30.2981	1.25054	0.625269	+	0.780409i	$0.284989\pi$
$588$	0	0
$589$	−22.3233	−0.919816
$590$	11.7601	0.484156
$591$	−50.0479	−2.05870
$592$	−2.83667	−0.116586
$593$	−41.6985	−1.71235	−0.856176	−	0.516685i	$-0.827166\pi$
$593$	−41.6985	−1.71235	−0.856176	+	0.516685i	$0.827166\pi$
$594$	13.2739	0.544635
$595$	0	0
$596$	−5.48881	−0.224830
$597$	−40.3968	−1.65333
$598$	−33.7288	−1.37927
$599$	37.3039	1.52420	0.762098	−	0.647462i	$-0.224170\pi$
$599$	37.3039	1.52420	0.762098	+	0.647462i	$0.224170\pi$
$600$	20.1289	0.821759
$601$	9.77401	0.398690	0.199345	−	0.979929i	$-0.436119\pi$
$601$	9.77401	0.398690	0.199345	+	0.979929i	$0.436119\pi$
$602$	0	0
$603$	23.4857	0.956410
$604$	5.44235	0.221446
$605$	−77.8890	−3.16664
$606$	−17.5952	−0.714756
$607$	37.8812	1.53755	0.768775	−	0.639520i	$-0.220867\pi$
$607$	37.8812	1.53755	0.768775	+	0.639520i	$0.220867\pi$
$608$	−4.20285	−0.170448
$609$	0	0
$610$	−51.7816	−2.09657
$611$	−3.97961	−0.160998
$612$	1.94059	0.0784436
$613$	−0.779208	−0.0314719	−0.0157360	−	0.999876i	$-0.505009\pi$
$613$	−0.779208	−0.0314719	−0.0157360	+	0.999876i	$0.505009\pi$
$614$	−17.4205	−0.703033
$615$	83.0988	3.35087
$616$	0	0
$617$	−2.09305	−0.0842630	−0.0421315	−	0.999112i	$-0.513415\pi$
$617$	−2.09305	−0.0842630	−0.0421315	+	0.999112i	$0.513415\pi$
$618$	2.23059	0.0897275
$619$	11.2684	0.452917	0.226458	−	0.974021i	$-0.427285\pi$
$619$	11.2684	0.452917	0.226458	+	0.974021i	$0.427285\pi$
$620$	−19.9134	−0.799739
$621$	−12.4853	−0.501017
$622$	19.4022	0.777956
$623$	0	0
$624$	−14.1399	−0.566049
$625$	11.7296	0.469184
$626$	−0.965967	−0.0386078
$627$	52.6596	2.10302
$628$	21.0281	0.839113
$629$	−2.83667	−0.113105
$630$	0	0
$631$	−36.7721	−1.46388	−0.731938	−	0.681371i	$-0.761384\pi$
$631$	−36.7721	−1.46388	−0.731938	+	0.681371i	$0.761384\pi$
$632$	−8.40569	−0.334360
$633$	−32.6654	−1.29833
$634$	−22.8577	−0.907797
$635$	36.3789	1.44365
$636$	14.5908	0.578562
$637$	0	0
$638$	18.9374	0.749740
$639$	7.24981	0.286798
$640$	−3.74912	−0.148197
$641$	29.8530	1.17912	0.589562	−	0.807723i	$-0.299300\pi$
$641$	29.8530	1.17912	0.589562	+	0.807723i	$0.299300\pi$
$642$	−10.0505	−0.396661
$643$	−42.1750	−1.66322	−0.831609	−	0.555361i	$-0.812580\pi$
$643$	−42.1750	−1.66322	−0.831609	+	0.555361i	$0.812580\pi$
$644$	0	0
$645$	17.9885	0.708296
$646$	−4.20285	−0.165359
$647$	41.0546	1.61402	0.807011	−	0.590536i	$-0.201084\pi$
$647$	41.0546	1.61402	0.807011	+	0.590536i	$0.201084\pi$
$648$	−11.0559	−0.434316
$649$	17.6818	0.694073
$650$	−57.6087	−2.25960
$651$	0	0
$652$	−15.2540	−0.597393
$653$	−32.7215	−1.28049	−0.640246	−	0.768170i	$-0.721168\pi$
$653$	−32.7215	−1.28049	−0.640246	+	0.768170i	$0.721168\pi$
$654$	16.0316	0.626887
$655$	76.4558	2.98738
$656$	−9.97186	−0.389336
$657$	−18.4322	−0.719107
$658$	0	0
$659$	−10.1188	−0.394173	−0.197087	−	0.980386i	$-0.563148\pi$
$659$	−10.1188	−0.394173	−0.197087	+	0.980386i	$0.563148\pi$
$660$	46.9746	1.82848
$661$	17.4336	0.678089	0.339045	−	0.940770i	$-0.389896\pi$
$661$	17.4336	0.678089	0.339045	+	0.940770i	$0.389896\pi$
$662$	14.6931	0.571064
$663$	−14.1399	−0.549148
$664$	−10.5295	−0.408624
$665$	0	0
$666$	−5.50481	−0.213307
$667$	−17.8123	−0.689696
$668$	−8.91911	−0.345091
$669$	44.1134	1.70552
$670$	−45.3731	−1.75292
$671$	−77.8558	−3.00559
$672$	0	0
$673$	−33.4919	−1.29102	−0.645509	−	0.763752i	$-0.723355\pi$
$673$	−33.4919	−1.29102	−0.645509	+	0.763752i	$0.723355\pi$
$674$	−26.3383	−1.01451
$675$	−21.3248	−0.820792
$676$	27.4682	1.05647
$677$	−27.9538	−1.07435	−0.537176	−	0.843470i	$-0.680509\pi$
$677$	−27.9538	−1.07435	−0.537176	+	0.843470i	$0.680509\pi$
$678$	20.6970	0.794864
$679$	0	0
$680$	−3.74912	−0.143772
$681$	−36.7484	−1.40820
$682$	−29.9406	−1.14648
$683$	8.95605	0.342694	0.171347	−	0.985211i	$-0.445188\pi$
$683$	8.95605	0.342694	0.171347	+	0.985211i	$0.445188\pi$
$684$	−8.15599	−0.311852
$685$	9.43973	0.360673
$686$	0	0
$687$	37.4460	1.42865
$688$	−2.15862	−0.0822966
$689$	−41.7586	−1.59088
$690$	−44.1837	−1.68205
$691$	−37.8711	−1.44068	−0.720341	−	0.693620i	$-0.756015\pi$
$691$	−37.8711	−1.44068	−0.720341	+	0.693620i	$0.756015\pi$
$692$	−8.26254	−0.314095
$693$	0	0
$694$	−18.6241	−0.706963
$695$	−47.9839	−1.82013
$696$	−7.46734	−0.283049
$697$	−9.97186	−0.377711
$698$	16.8954	0.639501
$699$	−10.3222	−0.390421
$700$	0	0
$701$	−8.93077	−0.337310	−0.168655	−	0.985675i	$-0.553942\pi$
$701$	−8.93077	−0.337310	−0.168655	+	0.985675i	$0.553942\pi$
$702$	14.9800	0.565383
$703$	11.9221	0.449650
$704$	−5.63696	−0.212451
$705$	−5.21317	−0.196339
$706$	12.3659	0.465397
$707$	0	0
$708$	−6.97223	−0.262033
$709$	5.68381	0.213460	0.106730	−	0.994288i	$-0.465962\pi$
$709$	5.68381	0.213460	0.106730	+	0.994288i	$0.465962\pi$
$710$	−14.0063	−0.525646
$711$	−16.3120	−0.611747
$712$	5.04070	0.188908
$713$	28.1617	1.05467
$714$	0	0
$715$	−134.441	−5.02780
$716$	−10.0492	−0.375557
$717$	2.01829	0.0753743
$718$	−15.0761	−0.562634
$719$	−21.2247	−0.791548	−0.395774	−	0.918348i	$-0.629524\pi$
$719$	−21.2247	−0.791548	−0.395774	+	0.918348i	$0.629524\pi$
$720$	−7.27549	−0.271142
$721$	0	0
$722$	−1.33609	−0.0497240
$723$	41.8647	1.55696
$724$	−4.14148	−0.153917
$725$	−30.4234	−1.12990
$726$	46.1781	1.71383
$727$	10.3942	0.385500	0.192750	−	0.981248i	$-0.438259\pi$
$727$	10.3942	0.385500	0.192750	+	0.981248i	$0.438259\pi$
$728$	0	0
$729$	−5.75255	−0.213058
$730$	35.6100	1.31799
$731$	−2.15862	−0.0798394
$732$	30.6998	1.13470
$733$	21.6618	0.800099	0.400049	−	0.916494i	$-0.368993\pi$
$733$	21.6618	0.800099	0.400049	+	0.916494i	$0.368993\pi$
$734$	33.7172	1.24452
$735$	0	0
$736$	5.30205	0.195436
$737$	−68.2204	−2.51293
$738$	−19.3513	−0.712330
$739$	−43.9563	−1.61696	−0.808479	−	0.588526i	$-0.799709\pi$
$739$	−43.9563	−1.61696	−0.808479	+	0.588526i	$0.799709\pi$
$740$	10.6350	0.390951
$741$	59.4278	2.18314
$742$	0	0
$743$	−22.1103	−0.811148	−0.405574	−	0.914062i	$-0.632928\pi$
$743$	−22.1103	−0.811148	−0.405574	+	0.914062i	$0.632928\pi$
$744$	11.8060	0.432831
$745$	20.5782	0.753927
$746$	−14.4025	−0.527314
$747$	−20.4334	−0.747620
$748$	−5.63696	−0.206108
$749$	0	0
$750$	−33.7990	−1.23416
$751$	9.91243	0.361710	0.180855	−	0.983510i	$-0.442114\pi$
$751$	9.91243	0.361710	0.180855	+	0.983510i	$0.442114\pi$
$752$	0.625581	0.0228126
$753$	10.8393	0.395007
$754$	21.3714	0.778301
$755$	−20.4040	−0.742578
$756$	0	0
$757$	−15.3333	−0.557298	−0.278649	−	0.960393i	$-0.589887\pi$
$757$	−15.3333	−0.557298	−0.278649	+	0.960393i	$0.589887\pi$
$758$	18.2318	0.662208
$759$	−66.4321	−2.41133
$760$	15.7570	0.571565
$761$	53.4058	1.93596	0.967980	−	0.251027i	$-0.0807684\pi$
$761$	53.4058	1.93596	0.967980	+	0.251027i	$0.0807684\pi$
$762$	−21.5680	−0.781325
$763$	0	0
$764$	−5.82490	−0.210737
$765$	−7.27549	−0.263046
$766$	1.87175	0.0676291
$767$	19.9545	0.720514
$768$	2.22274	0.0802063
$769$	21.0653	0.759634	0.379817	−	0.925062i	$-0.375987\pi$
$769$	21.0653	0.759634	0.379817	+	0.925062i	$0.375987\pi$
$770$	0	0
$771$	13.1904	0.475041
$772$	−16.0438	−0.577430
$773$	20.9907	0.754983	0.377491	−	0.926013i	$-0.376787\pi$
$773$	20.9907	0.754983	0.377491	+	0.926013i	$0.376787\pi$
$774$	−4.18899	−0.150570
$775$	48.1001	1.72781
$776$	−5.15286	−0.184977
$777$	0	0
$778$	23.5835	0.845511
$779$	41.9102	1.50159
$780$	53.0122	1.89814
$781$	−21.0590	−0.753551
$782$	5.30205	0.189601
$783$	7.91099	0.282716
$784$	0	0
$785$	−78.8369	−2.81381
$786$	−45.3284	−1.61681
$787$	15.3778	0.548161	0.274080	−	0.961707i	$-0.411627\pi$
$787$	15.3778	0.548161	0.274080	+	0.961707i	$0.411627\pi$
$788$	−22.5163	−0.802109
$789$	−14.5184	−0.516868
$790$	31.5139	1.12122
$791$	0	0
$792$	−10.9390	−0.388701
$793$	−87.8624	−3.12009
$794$	17.0589	0.605399
$795$	−54.7025	−1.94010
$796$	−18.1743	−0.644171
$797$	−7.93929	−0.281224	−0.140612	−	0.990065i	$-0.544907\pi$
$797$	−7.93929	−0.281224	−0.140612	+	0.990065i	$0.544907\pi$
$798$	0	0
$799$	0.625581	0.0221315
$800$	9.05588	0.320174
$801$	9.78192	0.345627
$802$	−27.6515	−0.976407
$803$	53.5411	1.88943
$804$	26.9004	0.948704
$805$	0	0
$806$	−33.7888	−1.19016
$807$	−22.2815	−0.784346
$808$	−7.91598	−0.278483
$809$	−38.0446	−1.33758	−0.668788	−	0.743453i	$-0.733187\pi$
$809$	−38.0446	−1.33758	−0.668788	+	0.743453i	$0.733187\pi$
$810$	41.4498	1.45640
$811$	54.2179	1.90385	0.951924	−	0.306333i	$-0.0991023\pi$
$811$	54.2179	1.90385	0.951924	+	0.306333i	$0.0991023\pi$
$812$	0	0
$813$	−7.34575	−0.257627
$814$	15.9902	0.560456
$815$	57.1891	2.00325
$816$	2.22274	0.0778116
$817$	9.07234	0.317401
$818$	−6.63392	−0.231949
$819$	0	0
$820$	37.3857	1.30556
$821$	37.7470	1.31738	0.658691	−	0.752414i	$-0.271111\pi$
$821$	37.7470	1.31738	0.658691	+	0.752414i	$0.271111\pi$
$822$	−5.59654	−0.195202
$823$	−5.81491	−0.202695	−0.101348	−	0.994851i	$-0.532315\pi$
$823$	−5.81491	−0.202695	−0.101348	+	0.994851i	$0.532315\pi$
$824$	1.00353	0.0349596
$825$	−113.466	−3.95037
$826$	0	0
$827$	13.3564	0.464446	0.232223	−	0.972663i	$-0.425400\pi$
$827$	13.3564	0.464446	0.232223	+	0.972663i	$0.425400\pi$
$828$	10.2891	0.357571
$829$	−22.0277	−0.765055	−0.382528	−	0.923944i	$-0.624946\pi$
$829$	−22.0277	−0.765055	−0.382528	+	0.923944i	$0.624946\pi$
$830$	39.4764	1.37024
$831$	37.6144	1.30483
$832$	−6.36147	−0.220544
$833$	0	0
$834$	28.4482	0.985082
$835$	33.4388	1.15720
$836$	23.6913	0.819379
$837$	−12.5075	−0.432322
$838$	1.44353	0.0498661
$839$	−16.1773	−0.558504	−0.279252	−	0.960218i	$-0.590086\pi$
$839$	−16.1773	−0.558504	−0.279252	+	0.960218i	$0.590086\pi$
$840$	0	0
$841$	−17.7137	−0.610816
$842$	−25.7780	−0.888370
$843$	−9.77791	−0.336769
$844$	−14.6960	−0.505856
$845$	−102.982	−3.54268
$846$	1.21400	0.0417380
$847$	0	0
$848$	6.56431	0.225419
$849$	36.9191	1.26706
$850$	9.05588	0.310614
$851$	−15.0402	−0.515570
$852$	8.30391	0.284487
$853$	−52.0687	−1.78280	−0.891400	−	0.453218i	$-0.850276\pi$
$853$	−52.0687	−1.78280	−0.891400	+	0.453218i	$0.850276\pi$
$854$	0	0
$855$	30.5778	1.04574
$856$	−4.52166	−0.154547
$857$	2.43383	0.0831381	0.0415690	−	0.999136i	$-0.486764\pi$
$857$	2.43383	0.0831381	0.0415690	+	0.999136i	$0.486764\pi$
$858$	79.7060	2.72112
$859$	−24.3317	−0.830185	−0.415093	−	0.909779i	$-0.636251\pi$
$859$	−24.3317	−0.830185	−0.415093	+	0.909779i	$0.636251\pi$
$860$	8.09292	0.275966
$861$	0	0
$862$	−3.36223	−0.114518
$863$	−38.9045	−1.32432	−0.662162	−	0.749361i	$-0.730361\pi$
$863$	−38.9045	−1.32432	−0.662162	+	0.749361i	$0.730361\pi$
$864$	−2.35480	−0.0801120
$865$	30.9772	1.05326
$866$	−38.6546	−1.31354
$867$	2.22274	0.0754883
$868$	0	0
$869$	47.3825	1.60734
$870$	27.9959	0.949151
$871$	−76.9886	−2.60866
$872$	7.21255	0.244248
$873$	−9.99957	−0.338434
$874$	−22.2837	−0.753758
$875$	0	0
$876$	−21.1121	−0.713313
$877$	−15.6660	−0.529002	−0.264501	−	0.964385i	$-0.585207\pi$
$877$	−15.6660	−0.529002	−0.264501	+	0.964385i	$0.585207\pi$
$878$	−3.50989	−0.118453
$879$	54.2517	1.82986
$880$	21.1336	0.712414
$881$	3.63968	0.122624	0.0613119	−	0.998119i	$-0.480472\pi$
$881$	3.63968	0.122624	0.0613119	+	0.998119i	$0.480472\pi$
$882$	0	0
$883$	13.5231	0.455088	0.227544	−	0.973768i	$-0.426930\pi$
$883$	13.5231	0.455088	0.227544	+	0.973768i	$0.426930\pi$
$884$	−6.36147	−0.213959
$885$	26.1397	0.878677
$886$	3.08883	0.103771
$887$	27.0983	0.909870	0.454935	−	0.890525i	$-0.349662\pi$
$887$	27.0983	0.909870	0.454935	+	0.890525i	$0.349662\pi$
$888$	−6.30519	−0.211588
$889$	0	0
$890$	−18.8982	−0.633468
$891$	62.3215	2.08785
$892$	19.8464	0.664506
$893$	−2.62922	−0.0879835
$894$	−12.2002	−0.408036
$895$	37.6757	1.25936
$896$	0	0
$897$	−74.9705	−2.50319
$898$	−1.12235	−0.0374534
$899$	−17.8440	−0.595130
$900$	17.5737	0.585791
$901$	6.56431	0.218689
$902$	56.2109	1.87162
$903$	0	0
$904$	9.31148	0.309695
$905$	15.5269	0.516132
$906$	12.0970	0.401894
$907$	50.4685	1.67578	0.837889	−	0.545840i	$-0.183789\pi$
$907$	50.4685	1.67578	0.837889	+	0.545840i	$0.183789\pi$
$908$	−16.5329	−0.548664
$909$	−15.3617	−0.509514
$910$	0	0
$911$	−42.4375	−1.40602	−0.703009	−	0.711181i	$-0.748160\pi$
$911$	−42.4375	−1.40602	−0.703009	+	0.711181i	$0.748160\pi$
$912$	−9.34185	−0.309339
$913$	59.3544	1.96434
$914$	24.0196	0.794498
$915$	−115.097	−3.80499
$916$	16.8467	0.556632
$917$	0	0
$918$	−2.35480	−0.0777200
$919$	11.3022	0.372825	0.186412	−	0.982472i	$-0.440314\pi$
$919$	11.3022	0.372825	0.186412	+	0.982472i	$0.440314\pi$
$920$	−19.8780	−0.655359
$921$	−38.7213	−1.27591
$922$	−13.3579	−0.439920
$923$	−23.7657	−0.782257
$924$	0	0
$925$	−25.6885	−0.844634
$926$	13.4916	0.443361
$927$	1.94744	0.0639622
$928$	−3.35951	−0.110281
$929$	−51.0425	−1.67465	−0.837326	−	0.546705i	$-0.815882\pi$
$929$	−51.0425	−1.67465	−0.837326	+	0.546705i	$0.815882\pi$
$930$	−44.2623	−1.45142
$931$	0	0
$932$	−4.64390	−0.152116
$933$	43.1260	1.41188
$934$	−13.9995	−0.458077
$935$	21.1336	0.691143
$936$	−12.3450	−0.403508
$937$	−28.2212	−0.921945	−0.460973	−	0.887414i	$-0.652499\pi$
$937$	−28.2212	−0.921945	−0.460973	+	0.887414i	$0.652499\pi$
$938$	0	0
$939$	−2.14710	−0.0700678
$940$	−2.34538	−0.0764978
$941$	−45.5410	−1.48460	−0.742298	−	0.670070i	$-0.766264\pi$
$941$	−45.5410	−1.48460	−0.742298	+	0.670070i	$0.766264\pi$
$942$	46.7401	1.52287
$943$	−52.8713	−1.72173
$944$	−3.13677	−0.102093
$945$	0	0
$946$	12.1680	0.395617
$947$	31.5104	1.02395	0.511975	−	0.859000i	$-0.328914\pi$
$947$	31.5104	1.02395	0.511975	+	0.859000i	$0.328914\pi$
$948$	−18.6837	−0.606818
$949$	60.4227	1.96140
$950$	−38.0605	−1.23484
$951$	−50.8069	−1.64753
$952$	0	0
$953$	−33.2592	−1.07737	−0.538686	−	0.842507i	$-0.681079\pi$
$953$	−33.2592	−1.07737	−0.538686	+	0.842507i	$0.681079\pi$
$954$	12.7386	0.412428
$955$	21.8382	0.706668
$956$	0.908017	0.0293674
$957$	42.0930	1.36068
$958$	−6.99963	−0.226148
$959$	0	0
$960$	−8.33333	−0.268957
$961$	−2.78821	−0.0899424
$962$	18.0454	0.581806
$963$	−8.77468	−0.282760
$964$	18.8347	0.606625
$965$	60.1502	1.93630
$966$	0	0
$967$	0.537844	0.0172959	0.00864794	−	0.999963i	$-0.497247\pi$
$967$	0.537844	0.0172959	0.00864794	+	0.999963i	$0.497247\pi$
$968$	20.7753	0.667743
$969$	−9.34185	−0.300103
$970$	19.3187	0.620285
$971$	−1.09145	−0.0350265	−0.0175132	−	0.999847i	$-0.505575\pi$
$971$	−1.09145	−0.0350265	−0.0175132	+	0.999847i	$0.505575\pi$
$972$	−17.5100	−0.561633
$973$	0	0
$974$	−22.9754	−0.736179
$975$	−128.049	−4.10086
$976$	13.8117	0.442101
$977$	36.7384	1.17537	0.587683	−	0.809091i	$-0.300040\pi$
$977$	36.7384	1.17537	0.587683	+	0.809091i	$0.300040\pi$
$978$	−33.9058	−1.08419
$979$	−28.4142	−0.908121
$980$	0	0
$981$	13.9966	0.446877
$982$	31.6239	1.00916
$983$	24.7860	0.790552	0.395276	−	0.918562i	$-0.370649\pi$
$983$	24.7860	0.790552	0.395276	+	0.918562i	$0.370649\pi$
$984$	−22.1649	−0.706591
$985$	84.4162	2.68972
$986$	−3.35951	−0.106989
$987$	0	0
$988$	26.7363	0.850594
$989$	−11.4451	−0.363933
$990$	41.0116	1.30344
$991$	−32.8049	−1.04208	−0.521041	−	0.853532i	$-0.674456\pi$
$991$	−32.8049	−1.04208	−0.521041	+	0.853532i	$0.674456\pi$
$992$	5.31148	0.168640
$993$	32.6590	1.03640
$994$	0	0
$995$	68.1376	2.16011
$996$	−23.4044	−0.741597
$997$	−45.0100	−1.42548	−0.712741	−	0.701427i	$-0.752546\pi$
$997$	−45.0100	−1.42548	−0.712741	+	0.701427i	$0.752546\pi$
$998$	−22.6351	−0.716502
$999$	6.67979	0.211339

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.22274 q^{3} +1.00000 q^{4} -3.74912 q^{5} +2.22274 q^{6} +1.00000 q^{8} +1.94059 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.22274 q^{3} +1.00000 q^{4} -3.74912 q^{5} +2.22274 q^{6} +1.00000 q^{8} +1.94059 q^{9} -3.74912 q^{10} -5.63696 q^{11} +2.22274 q^{12} -6.36147 q^{13} -8.33333 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.94059 q^{18} -4.20285 q^{19} -3.74912 q^{20} -5.63696 q^{22} +5.30205 q^{23} +2.22274 q^{24} +9.05588 q^{25} -6.36147 q^{26} -2.35480 q^{27} -3.35951 q^{29} -8.33333 q^{30} +5.31148 q^{31} +1.00000 q^{32} -12.5295 q^{33} +1.00000 q^{34} +1.94059 q^{36} -2.83667 q^{37} -4.20285 q^{38} -14.1399 q^{39} -3.74912 q^{40} -9.97186 q^{41} -2.15862 q^{43} -5.63696 q^{44} -7.27549 q^{45} +5.30205 q^{46} +0.625581 q^{47} +2.22274 q^{48} +9.05588 q^{50} +2.22274 q^{51} -6.36147 q^{52} +6.56431 q^{53} -2.35480 q^{54} +21.1336 q^{55} -9.34185 q^{57} -3.35951 q^{58} -3.13677 q^{59} -8.33333 q^{60} +13.8117 q^{61} +5.31148 q^{62} +1.00000 q^{64} +23.8499 q^{65} -12.5295 q^{66} +12.1023 q^{67} +1.00000 q^{68} +11.7851 q^{69} +3.73588 q^{71} +1.94059 q^{72} -9.49824 q^{73} -2.83667 q^{74} +20.1289 q^{75} -4.20285 q^{76} -14.1399 q^{78} -8.40569 q^{79} -3.74912 q^{80} -11.0559 q^{81} -9.97186 q^{82} -10.5295 q^{83} -3.74912 q^{85} -2.15862 q^{86} -7.46734 q^{87} -5.63696 q^{88} +5.04070 q^{89} -7.27549 q^{90} +5.30205 q^{92} +11.8060 q^{93} +0.625581 q^{94} +15.7570 q^{95} +2.22274 q^{96} -5.15286 q^{97} -10.9390 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 8 q^{5} - 4 q^{6} + 4 q^{8} + 8 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 8 * q^5 - 4 * q^6 + 4 * q^8 + 8 * q^9	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 8 q^{5} - 4 q^{6} + 4 q^{8} + 8 q^{9} - 8 q^{10} - 4 q^{11} - 4 q^{12} - 8 q^{13} + 4 q^{15} + 4 q^{16} + 4 q^{17} + 8 q^{18} - 8 q^{19} - 8 q^{20} - 4 q^{22} + 4 q^{23} - 4 q^{24} + 8 q^{25} - 8 q^{26} - 4 q^{27} - 4 q^{29} + 4 q^{30} - 4 q^{31} + 4 q^{32} - 16 q^{33} + 4 q^{34} + 8 q^{36} - 24 q^{37} - 8 q^{38} - 20 q^{39} - 8 q^{40} - 20 q^{41} - 4 q^{44} - 28 q^{45} + 4 q^{46} - 4 q^{48} + 8 q^{50} - 4 q^{51} - 8 q^{52} - 4 q^{54} + 16 q^{55} - 12 q^{57} - 4 q^{58} - 16 q^{59} + 4 q^{60} + 8 q^{61} - 4 q^{62} + 4 q^{64} + 4 q^{65} - 16 q^{66} + 4 q^{68} + 16 q^{69} + 8 q^{72} - 24 q^{73} - 24 q^{74} + 16 q^{75} - 8 q^{76} - 20 q^{78} - 16 q^{79} - 8 q^{80} - 16 q^{81} - 20 q^{82} - 8 q^{83} - 8 q^{85} + 8 q^{87} - 4 q^{88} - 8 q^{89} - 28 q^{90} + 4 q^{92} + 24 q^{93} + 12 q^{95} - 4 q^{96} - 4 q^{97} - 8 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 8 * q^5 - 4 * q^6 + 4 * q^8 + 8 * q^9 - 8 * q^10 - 4 * q^11 - 4 * q^12 - 8 * q^13 + 4 * q^15 + 4 * q^16 + 4 * q^17 + 8 * q^18 - 8 * q^19 - 8 * q^20 - 4 * q^22 + 4 * q^23 - 4 * q^24 + 8 * q^25 - 8 * q^26 - 4 * q^27 - 4 * q^29 + 4 * q^30 - 4 * q^31 + 4 * q^32 - 16 * q^33 + 4 * q^34 + 8 * q^36 - 24 * q^37 - 8 * q^38 - 20 * q^39 - 8 * q^40 - 20 * q^41 - 4 * q^44 - 28 * q^45 + 4 * q^46 - 4 * q^48 + 8 * q^50 - 4 * q^51 - 8 * q^52 - 4 * q^54 + 16 * q^55 - 12 * q^57 - 4 * q^58 - 16 * q^59 + 4 * q^60 + 8 * q^61 - 4 * q^62 + 4 * q^64 + 4 * q^65 - 16 * q^66 + 4 * q^68 + 16 * q^69 + 8 * q^72 - 24 * q^73 - 24 * q^74 + 16 * q^75 - 8 * q^76 - 20 * q^78 - 16 * q^79 - 8 * q^80 - 16 * q^81 - 20 * q^82 - 8 * q^83 - 8 * q^85 + 8 * q^87 - 4 * q^88 - 8 * q^89 - 28 * q^90 + 4 * q^92 + 24 * q^93 + 12 * q^95 - 4 * q^96 - 4 * q^97 - 8 * q^99

Introduction

L-functions

Modular forms

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Database

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