LMFDB - Embedded newform 4641.2.a.t.1.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [4641,2,Mod(1,4641)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("4641.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(4641, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 4641 = 3 \cdot 7 \cdot 13 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4641.a (trivial)

Newform invariants

comment:select newform

sage:traces = [12,1,-12,15,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	yes
Analytic conductor:	$37.0585715781$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} - 19 x^{10} + 16 x^{9} + 136 x^{8} - 91 x^{7} - 456 x^{6} + 220 x^{5} + 722 x^{4} + \cdots + 85 $ x^12 - x^11 - 19x^10 + 16x^9 + 136x^8 - 91x^7 - 456x^6 + 220x^5 + 722x^4 - 204x^3 - 465x^2 + 36x + 85
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$2.54577$ of defining polynomial
Character	$\chi$	$=$	4641.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.54577 q^{2} -1.00000 q^{3} +4.48097 q^{4} -3.15427 q^{5} -2.54577 q^{6} -1.00000 q^{7} +6.31598 q^{8} +1.00000 q^{9} -8.03006 q^{10} +4.13299 q^{11} -4.48097 q^{12} -1.00000 q^{13} -2.54577 q^{14} +3.15427 q^{15} +7.11712 q^{16} +1.00000 q^{17} +2.54577 q^{18} -6.50785 q^{19} -14.1342 q^{20} +1.00000 q^{21} +10.5217 q^{22} +5.73526 q^{23} -6.31598 q^{24} +4.94943 q^{25} -2.54577 q^{26} -1.00000 q^{27} -4.48097 q^{28} +6.53293 q^{29} +8.03006 q^{30} +7.10660 q^{31} +5.48663 q^{32} -4.13299 q^{33} +2.54577 q^{34} +3.15427 q^{35} +4.48097 q^{36} -1.02262 q^{37} -16.5675 q^{38} +1.00000 q^{39} -19.9223 q^{40} -0.0855998 q^{41} +2.54577 q^{42} -4.66443 q^{43} +18.5198 q^{44} -3.15427 q^{45} +14.6007 q^{46} +5.66410 q^{47} -7.11712 q^{48} +1.00000 q^{49} +12.6001 q^{50} -1.00000 q^{51} -4.48097 q^{52} -6.08088 q^{53} -2.54577 q^{54} -13.0366 q^{55} -6.31598 q^{56} +6.50785 q^{57} +16.6314 q^{58} +6.40060 q^{59} +14.1342 q^{60} +14.2478 q^{61} +18.0918 q^{62} -1.00000 q^{63} -0.266532 q^{64} +3.15427 q^{65} -10.5217 q^{66} +9.50679 q^{67} +4.48097 q^{68} -5.73526 q^{69} +8.03006 q^{70} -8.12213 q^{71} +6.31598 q^{72} +7.24232 q^{73} -2.60336 q^{74} -4.94943 q^{75} -29.1615 q^{76} -4.13299 q^{77} +2.54577 q^{78} +10.5200 q^{79} -22.4493 q^{80} +1.00000 q^{81} -0.217918 q^{82} +5.99614 q^{83} +4.48097 q^{84} -3.15427 q^{85} -11.8746 q^{86} -6.53293 q^{87} +26.1039 q^{88} +6.22645 q^{89} -8.03006 q^{90} +1.00000 q^{91} +25.6995 q^{92} -7.10660 q^{93} +14.4195 q^{94} +20.5275 q^{95} -5.48663 q^{96} +16.9109 q^{97} +2.54577 q^{98} +4.13299 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + q^{2} - 12 q^{3} + 15 q^{4} - 3 q^{5} - q^{6} - 12 q^{7} + 6 q^{8} + 12 q^{9} + q^{10} + 14 q^{11} - 15 q^{12} - 12 q^{13} - q^{14} + 3 q^{15} + 5 q^{16} + 12 q^{17} + q^{18} + 6 q^{19} - q^{20}+ \cdots + 14 q^{99}+O(q^{100}) $ 12 * q + q^2 - 12 * q^3 + 15 * q^4 - 3 * q^5 - q^6 - 12 * q^7 + 6 * q^8 + 12 * q^9 + q^10 + 14 * q^11 - 15 * q^12 - 12 * q^13 - q^14 + 3 * q^15 + 5 * q^16 + 12 * q^17 + q^18 + 6 * q^19 - q^20 + 12 * q^21 + 16 * q^22 + 11 * q^23 - 6 * q^24 + 13 * q^25 - q^26 - 12 * q^27 - 15 * q^28 + 6 * q^29 - q^30 + 23 * q^31 + 8 * q^32 - 14 * q^33 + q^34 + 3 * q^35 + 15 * q^36 + 22 * q^37 - 19 * q^38 + 12 * q^39 - 20 * q^40 - 6 * q^41 + q^42 - 14 * q^43 + 12 * q^44 - 3 * q^45 + 7 * q^46 - 11 * q^47 - 5 * q^48 + 12 * q^49 + 11 * q^50 - 12 * q^51 - 15 * q^52 - 11 * q^53 - q^54 - 5 * q^55 - 6 * q^56 - 6 * q^57 + 22 * q^58 + 15 * q^59 + q^60 + 3 * q^61 + 7 * q^62 - 12 * q^63 - 2 * q^64 + 3 * q^65 - 16 * q^66 + 13 * q^67 + 15 * q^68 - 11 * q^69 - q^70 + 54 * q^71 + 6 * q^72 + 10 * q^73 + 28 * q^74 - 13 * q^75 + 43 * q^76 - 14 * q^77 + q^78 + 44 * q^79 - 43 * q^80 + 12 * q^81 + 6 * q^82 + q^83 + 15 * q^84 - 3 * q^85 + 9 * q^86 - 6 * q^87 + 87 * q^88 - 15 * q^89 + q^90 + 12 * q^91 + 44 * q^92 - 23 * q^93 + 33 * q^94 + 60 * q^95 - 8 * q^96 - q^97 + q^98 + 14 * q^99

Coefficient data

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

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

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

$2$	2.54577	1.80013	0.900067	−	0.435751i	$-0.143517\pi$
$2$	2.54577	1.80013	0.900067	+	0.435751i	$0.143517\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.48097	2.24048
$5$	−3.15427	−1.41063	−0.705317	−	0.708892i	$-0.749195\pi$
$5$	−3.15427	−1.41063	−0.705317	+	0.708892i	$0.749195\pi$
$6$	−2.54577	−1.03931
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	6.31598	2.23304
$9$	1.00000	0.333333
$10$	−8.03006	−2.53933
$11$	4.13299	1.24614	0.623072	−	0.782165i	$-0.285884\pi$
$11$	4.13299	1.24614	0.623072	+	0.782165i	$0.285884\pi$
$12$	−4.48097	−1.29354
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−2.54577	−0.680387
$15$	3.15427	0.814430
$16$	7.11712	1.77928
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	2.54577	0.600045
$19$	−6.50785	−1.49300	−0.746502	−	0.665383i	$-0.768268\pi$
$19$	−6.50785	−1.49300	−0.746502	+	0.665383i	$0.768268\pi$
$20$	−14.1342	−3.16050
$21$	1.00000	0.218218
$22$	10.5217	2.24323
$23$	5.73526	1.19588	0.597942	−	0.801539i	$-0.295985\pi$
$23$	5.73526	1.19588	0.597942	+	0.801539i	$0.295985\pi$
$24$	−6.31598	−1.28924
$25$	4.94943	0.989886
$26$	−2.54577	−0.499267
$27$	−1.00000	−0.192450
$28$	−4.48097	−0.846823
$29$	6.53293	1.21314	0.606568	−	0.795032i	$-0.292546\pi$
$29$	6.53293	1.21314	0.606568	+	0.795032i	$0.292546\pi$
$30$	8.03006	1.46608
$31$	7.10660	1.27638	0.638192	−	0.769878i	$-0.279683\pi$
$31$	7.10660	1.27638	0.638192	+	0.769878i	$0.279683\pi$
$32$	5.48663	0.969908
$33$	−4.13299	−0.719461
$34$	2.54577	0.436597
$35$	3.15427	0.533169
$36$	4.48097	0.746828
$37$	−1.02262	−0.168118	−0.0840590	−	0.996461i	$-0.526788\pi$
$37$	−1.02262	−0.168118	−0.0840590	+	0.996461i	$0.526788\pi$
$38$	−16.5675	−2.68761
$39$	1.00000	0.160128
$40$	−19.9223	−3.14999
$41$	−0.0855998	−0.0133684	−0.00668422	−	0.999978i	$-0.502128\pi$
$41$	−0.0855998	−0.0133684	−0.00668422	+	0.999978i	$0.502128\pi$
$42$	2.54577	0.392821
$43$	−4.66443	−0.711320	−0.355660	−	0.934615i	$-0.615744\pi$
$43$	−4.66443	−0.711320	−0.355660	+	0.934615i	$0.615744\pi$
$44$	18.5198	2.79196
$45$	−3.15427	−0.470211
$46$	14.6007	2.15275
$47$	5.66410	0.826194	0.413097	−	0.910687i	$-0.364447\pi$
$47$	5.66410	0.826194	0.413097	+	0.910687i	$0.364447\pi$
$48$	−7.11712	−1.02727
$49$	1.00000	0.142857
$50$	12.6001	1.78193
$51$	−1.00000	−0.140028
$52$	−4.48097	−0.621398
$53$	−6.08088	−0.835273	−0.417636	−	0.908614i	$-0.637141\pi$
$53$	−6.08088	−0.835273	−0.417636	+	0.908614i	$0.637141\pi$
$54$	−2.54577	−0.346436
$55$	−13.0366	−1.75785
$56$	−6.31598	−0.844008
$57$	6.50785	0.861986
$58$	16.6314	2.18381
$59$	6.40060	0.833288	0.416644	−	0.909070i	$-0.363206\pi$
$59$	6.40060	0.833288	0.416644	+	0.909070i	$0.363206\pi$
$60$	14.1342	1.82472
$61$	14.2478	1.82424	0.912122	−	0.409919i	$-0.134443\pi$
$61$	14.2478	1.82424	0.912122	+	0.409919i	$0.134443\pi$
$62$	18.0918	2.29766
$63$	−1.00000	−0.125988
$64$	−0.266532	−0.0333165
$65$	3.15427	0.391239
$66$	−10.5217	−1.29513
$67$	9.50679	1.16144	0.580720	−	0.814104i	$-0.302771\pi$
$67$	9.50679	1.16144	0.580720	+	0.814104i	$0.302771\pi$
$68$	4.48097	0.543397
$69$	−5.73526	−0.690444
$70$	8.03006	0.959776
$71$	−8.12213	−0.963919	−0.481960	−	0.876193i	$-0.660075\pi$
$71$	−8.12213	−0.963919	−0.481960	+	0.876193i	$0.660075\pi$
$72$	6.31598	0.744345
$73$	7.24232	0.847650	0.423825	−	0.905744i	$-0.360687\pi$
$73$	7.24232	0.847650	0.423825	+	0.905744i	$0.360687\pi$
$74$	−2.60336	−0.302635
$75$	−4.94943	−0.571511
$76$	−29.1615	−3.34505
$77$	−4.13299	−0.470998
$78$	2.54577	0.288252
$79$	10.5200	1.18360	0.591798	−	0.806086i	$-0.298418\pi$
$79$	10.5200	1.18360	0.591798	+	0.806086i	$0.298418\pi$
$80$	−22.4493	−2.50991
$81$	1.00000	0.111111
$82$	−0.217918	−0.0240650
$83$	5.99614	0.658162	0.329081	−	0.944302i	$-0.393261\pi$
$83$	5.99614	0.658162	0.329081	+	0.944302i	$0.393261\pi$
$84$	4.48097	0.488913
$85$	−3.15427	−0.342129
$86$	−11.8746	−1.28047
$87$	−6.53293	−0.700404
$88$	26.1039	2.78268
$89$	6.22645	0.660003	0.330001	−	0.943980i	$-0.392951\pi$
$89$	6.22645	0.660003	0.330001	+	0.943980i	$0.392951\pi$
$90$	−8.03006	−0.846443
$91$	1.00000	0.104828
$92$	25.6995	2.67936
$93$	−7.10660	−0.736920
$94$	14.4195	1.48726
$95$	20.5275	2.10608
$96$	−5.48663	−0.559976
$97$	16.9109	1.71705	0.858523	−	0.512775i	$-0.171383\pi$
$97$	16.9109	1.71705	0.858523	+	0.512775i	$0.171383\pi$
$98$	2.54577	0.257162
$99$	4.13299	0.415381
$100$	22.1782	2.21782
$101$	0.965937	0.0961144	0.0480572	−	0.998845i	$-0.484697\pi$
$101$	0.965937	0.0961144	0.0480572	+	0.998845i	$0.484697\pi$
$102$	−2.54577	−0.252069
$103$	−7.19639	−0.709081	−0.354541	−	0.935041i	$-0.615363\pi$
$103$	−7.19639	−0.709081	−0.354541	+	0.935041i	$0.615363\pi$
$104$	−6.31598	−0.619333
$105$	−3.15427	−0.307825
$106$	−15.4805	−1.50360
$107$	11.0427	1.06753	0.533767	−	0.845631i	$-0.320776\pi$
$107$	11.0427	1.06753	0.533767	+	0.845631i	$0.320776\pi$
$108$	−4.48097	−0.431181
$109$	−9.79322	−0.938020	−0.469010	−	0.883193i	$-0.655389\pi$
$109$	−9.79322	−0.938020	−0.469010	+	0.883193i	$0.655389\pi$
$110$	−33.1882	−3.16437
$111$	1.02262	0.0970630
$112$	−7.11712	−0.672505
$113$	1.18694	0.111658	0.0558288	−	0.998440i	$-0.482220\pi$
$113$	1.18694	0.111658	0.0558288	+	0.998440i	$0.482220\pi$
$114$	16.5675	1.55169
$115$	−18.0906	−1.68695
$116$	29.2739	2.71801
$117$	−1.00000	−0.0924500
$118$	16.2945	1.50003
$119$	−1.00000	−0.0916698
$120$	19.9223	1.81865
$121$	6.08161	0.552873
$122$	36.2717	3.28388
$123$	0.0855998	0.00771827
$124$	31.8444	2.85971
$125$	0.159508	0.0142668
$126$	−2.54577	−0.226796
$127$	−4.92916	−0.437392	−0.218696	−	0.975793i	$-0.570180\pi$
$127$	−4.92916	−0.437392	−0.218696	+	0.975793i	$0.570180\pi$
$128$	−11.6518	−1.02988
$129$	4.66443	0.410681
$130$	8.03006	0.704283
$131$	12.7160	1.11100	0.555500	−	0.831516i	$-0.312527\pi$
$131$	12.7160	1.11100	0.555500	+	0.831516i	$0.312527\pi$
$132$	−18.5198	−1.61194
$133$	6.50785	0.564302
$134$	24.2021	2.09075
$135$	3.15427	0.271477
$136$	6.31598	0.541591
$137$	12.6797	1.08330	0.541650	−	0.840604i	$-0.317800\pi$
$137$	12.6797	1.08330	0.541650	+	0.840604i	$0.317800\pi$
$138$	−14.6007	−1.24289
$139$	−10.8498	−0.920268	−0.460134	−	0.887849i	$-0.652199\pi$
$139$	−10.8498	−0.920268	−0.460134	+	0.887849i	$0.652199\pi$
$140$	14.1342	1.19456
$141$	−5.66410	−0.477003
$142$	−20.6771	−1.73518
$143$	−4.13299	−0.345618
$144$	7.11712	0.593093
$145$	−20.6067	−1.71129
$146$	18.4373	1.52588
$147$	−1.00000	−0.0824786
$148$	−4.58233	−0.376666
$149$	−1.21810	−0.0997906	−0.0498953	−	0.998754i	$-0.515889\pi$
$149$	−1.21810	−0.0997906	−0.0498953	+	0.998754i	$0.515889\pi$
$150$	−12.6001	−1.02880
$151$	−14.2229	−1.15744	−0.578721	−	0.815525i	$-0.696448\pi$
$151$	−14.2229	−1.15744	−0.578721	+	0.815525i	$0.696448\pi$
$152$	−41.1034	−3.33393
$153$	1.00000	0.0808452
$154$	−10.5217	−0.847859
$155$	−22.4162	−1.80051
$156$	4.48097	0.358764
$157$	7.00956	0.559424	0.279712	−	0.960084i	$-0.409761\pi$
$157$	7.00956	0.559424	0.279712	+	0.960084i	$0.409761\pi$
$158$	26.7816	2.13063
$159$	6.08088	0.482245
$160$	−17.3063	−1.36818
$161$	−5.73526	−0.452002
$162$	2.54577	0.200015
$163$	12.2210	0.957225	0.478613	−	0.878026i	$-0.341140\pi$
$163$	12.2210	0.957225	0.478613	+	0.878026i	$0.341140\pi$
$164$	−0.383570	−0.0299518
$165$	13.0366	1.01490
$166$	15.2648	1.18478
$167$	−15.6958	−1.21458	−0.607289	−	0.794481i	$-0.707743\pi$
$167$	−15.6958	−1.21458	−0.607289	+	0.794481i	$0.707743\pi$
$168$	6.31598	0.487288
$169$	1.00000	0.0769231
$170$	−8.03006	−0.615878
$171$	−6.50785	−0.497668
$172$	−20.9012	−1.59370
$173$	1.32542	0.100769	0.0503847	−	0.998730i	$-0.483955\pi$
$173$	1.32542	0.100769	0.0503847	+	0.998730i	$0.483955\pi$
$174$	−16.6314	−1.26082
$175$	−4.94943	−0.374142
$176$	29.4150	2.21724
$177$	−6.40060	−0.481099
$178$	15.8511	1.18809
$179$	−18.7262	−1.39966	−0.699832	−	0.714308i	$-0.746742\pi$
$179$	−18.7262	−1.39966	−0.699832	+	0.714308i	$0.746742\pi$
$180$	−14.1342	−1.05350
$181$	−18.0445	−1.34124	−0.670618	−	0.741803i	$-0.733971\pi$
$181$	−18.0445	−1.34124	−0.670618	+	0.741803i	$0.733971\pi$
$182$	2.54577	0.188705
$183$	−14.2478	−1.05323
$184$	36.2238	2.67045
$185$	3.22563	0.237153
$186$	−18.0918	−1.32656
$187$	4.13299	0.302234
$188$	25.3806	1.85107
$189$	1.00000	0.0727393
$190$	52.2585	3.79123
$191$	12.6411	0.914681	0.457340	−	0.889292i	$-0.348802\pi$
$191$	12.6411	0.914681	0.457340	+	0.889292i	$0.348802\pi$
$192$	0.266532	0.0192353
$193$	−22.3038	−1.60546	−0.802732	−	0.596340i	$-0.796621\pi$
$193$	−22.3038	−1.60546	−0.802732	+	0.596340i	$0.796621\pi$
$194$	43.0514	3.09091
$195$	−3.15427	−0.225882
$196$	4.48097	0.320069
$197$	6.25251	0.445473	0.222736	−	0.974879i	$-0.428501\pi$
$197$	6.25251	0.445473	0.222736	+	0.974879i	$0.428501\pi$
$198$	10.5217	0.747742
$199$	4.00708	0.284054	0.142027	−	0.989863i	$-0.454638\pi$
$199$	4.00708	0.284054	0.142027	+	0.989863i	$0.454638\pi$
$200$	31.2605	2.21045
$201$	−9.50679	−0.670557
$202$	2.45906	0.173019
$203$	−6.53293	−0.458522
$204$	−4.48097	−0.313730
$205$	0.270005	0.0188580
$206$	−18.3204	−1.27644
$207$	5.73526	0.398628
$208$	−7.11712	−0.493484
$209$	−26.8969	−1.86050
$210$	−8.03006	−0.554127
$211$	−19.2145	−1.32278	−0.661390	−	0.750042i	$-0.730033\pi$
$211$	−19.2145	−1.32278	−0.661390	+	0.750042i	$0.730033\pi$
$212$	−27.2482	−1.87141
$213$	8.12213	0.556519
$214$	28.1121	1.92171
$215$	14.7129	1.00341
$216$	−6.31598	−0.429748
$217$	−7.10660	−0.482427
$218$	−24.9313	−1.68856
$219$	−7.24232	−0.489391
$220$	−58.4164	−3.93844
$221$	−1.00000	−0.0672673
$222$	2.60336	0.174726
$223$	28.4425	1.90465	0.952327	−	0.305080i	$-0.0986832\pi$
$223$	28.4425	1.90465	0.952327	+	0.305080i	$0.0986832\pi$
$224$	−5.48663	−0.366591
$225$	4.94943	0.329962
$226$	3.02167	0.200999
$227$	−8.61175	−0.571582	−0.285791	−	0.958292i	$-0.592256\pi$
$227$	−8.61175	−0.571582	−0.285791	+	0.958292i	$0.592256\pi$
$228$	29.1615	1.93126
$229$	11.2774	0.745230	0.372615	−	0.927986i	$-0.378461\pi$
$229$	11.2774	0.745230	0.372615	+	0.927986i	$0.378461\pi$
$230$	−46.0545	−3.03674
$231$	4.13299	0.271931
$232$	41.2619	2.70897
$233$	−28.3564	−1.85769	−0.928845	−	0.370469i	$-0.879197\pi$
$233$	−28.3564	−1.85769	−0.928845	+	0.370469i	$0.879197\pi$
$234$	−2.54577	−0.166422
$235$	−17.8661	−1.16546
$236$	28.6809	1.86697
$237$	−10.5200	−0.683349
$238$	−2.54577	−0.165018
$239$	23.4574	1.51733	0.758667	−	0.651479i	$-0.225851\pi$
$239$	23.4574	1.51733	0.758667	+	0.651479i	$0.225851\pi$
$240$	22.4493	1.44910
$241$	22.9025	1.47528	0.737639	−	0.675196i	$-0.235941\pi$
$241$	22.9025	1.47528	0.737639	+	0.675196i	$0.235941\pi$
$242$	15.4824	0.995246
$243$	−1.00000	−0.0641500
$244$	63.8439	4.08719
$245$	−3.15427	−0.201519
$246$	0.217918	0.0138939
$247$	6.50785	0.414085
$248$	44.8851	2.85021
$249$	−5.99614	−0.379990
$250$	0.406070	0.0256821
$251$	−15.6624	−0.988603	−0.494301	−	0.869291i	$-0.664576\pi$
$251$	−15.6624	−0.988603	−0.494301	+	0.869291i	$0.664576\pi$
$252$	−4.48097	−0.282274
$253$	23.7038	1.49024
$254$	−12.5485	−0.787364
$255$	3.15427	0.197528
$256$	−29.1297	−1.82061
$257$	2.02593	0.126374	0.0631870	−	0.998002i	$-0.479874\pi$
$257$	2.02593	0.126374	0.0631870	+	0.998002i	$0.479874\pi$
$258$	11.8746	0.739280
$259$	1.02262	0.0635426
$260$	14.1342	0.876565
$261$	6.53293	0.404379
$262$	32.3720	1.99995
$263$	−12.8555	−0.792702	−0.396351	−	0.918099i	$-0.629724\pi$
$263$	−12.8555	−0.792702	−0.396351	+	0.918099i	$0.629724\pi$
$264$	−26.1039	−1.60658
$265$	19.1807	1.17826
$266$	16.5675	1.01582
$267$	−6.22645	−0.381053
$268$	42.5996	2.60219
$269$	0.171368	0.0104485	0.00522426	−	0.999986i	$-0.498337\pi$
$269$	0.171368	0.0104485	0.00522426	+	0.999986i	$0.498337\pi$
$270$	8.03006	0.488694
$271$	−11.8633	−0.720643	−0.360322	−	0.932828i	$-0.617333\pi$
$271$	−11.8633	−0.720643	−0.360322	+	0.932828i	$0.617333\pi$
$272$	7.11712	0.431539
$273$	−1.00000	−0.0605228
$274$	32.2797	1.95009
$275$	20.4560	1.23354
$276$	−25.6995	−1.54693
$277$	5.30509	0.318752	0.159376	−	0.987218i	$-0.449052\pi$
$277$	5.30509	0.318752	0.159376	+	0.987218i	$0.449052\pi$
$278$	−27.6211	−1.65661
$279$	7.10660	0.425461
$280$	19.9223	1.19059
$281$	−9.15077	−0.545889	−0.272945	−	0.962030i	$-0.587998\pi$
$281$	−9.15077	−0.545889	−0.272945	+	0.962030i	$0.587998\pi$
$282$	−14.4195	−0.858670
$283$	−15.5926	−0.926883	−0.463441	−	0.886128i	$-0.653385\pi$
$283$	−15.5926	−0.926883	−0.463441	+	0.886128i	$0.653385\pi$
$284$	−36.3950	−2.15964
$285$	−20.5275	−1.21595
$286$	−10.5217	−0.622159
$287$	0.0855998	0.00505280
$288$	5.48663	0.323303
$289$	1.00000	0.0588235
$290$	−52.4599	−3.08055
$291$	−16.9109	−0.991337
$292$	32.4526	1.89914
$293$	−24.2607	−1.41733	−0.708664	−	0.705546i	$-0.750702\pi$
$293$	−24.2607	−1.41733	−0.708664	+	0.705546i	$0.750702\pi$
$294$	−2.54577	−0.148473
$295$	−20.1892	−1.17546
$296$	−6.45886	−0.375413
$297$	−4.13299	−0.239820
$298$	−3.10100	−0.179636
$299$	−5.73526	−0.331678
$300$	−22.1782	−1.28046
$301$	4.66443	0.268854
$302$	−36.2083	−2.08355
$303$	−0.965937	−0.0554917
$304$	−46.3172	−2.65647
$305$	−44.9414	−2.57334
$306$	2.54577	0.145532
$307$	−29.9263	−1.70799	−0.853993	−	0.520284i	$-0.825826\pi$
$307$	−29.9263	−1.70799	−0.853993	+	0.520284i	$0.825826\pi$
$308$	−18.5198	−1.05526
$309$	7.19639	0.409388
$310$	−57.0665	−3.24116
$311$	32.1375	1.82235	0.911175	−	0.412020i	$-0.135177\pi$
$311$	32.1375	1.82235	0.911175	+	0.412020i	$0.135177\pi$
$312$	6.31598	0.357572
$313$	2.56467	0.144964	0.0724818	−	0.997370i	$-0.476908\pi$
$313$	2.56467	0.144964	0.0724818	+	0.997370i	$0.476908\pi$
$314$	17.8448	1.00704
$315$	3.15427	0.177723
$316$	47.1399	2.65183
$317$	−22.1859	−1.24609	−0.623043	−	0.782187i	$-0.714104\pi$
$317$	−22.1859	−1.24609	−0.623043	+	0.782187i	$0.714104\pi$
$318$	15.4805	0.868106
$319$	27.0006	1.51174
$320$	0.840714	0.0469974
$321$	−11.0427	−0.616342
$322$	−14.6007	−0.813663
$323$	−6.50785	−0.362107
$324$	4.48097	0.248943
$325$	−4.94943	−0.274545
$326$	31.1120	1.72313
$327$	9.79322	0.541566
$328$	−0.540646	−0.0298522
$329$	−5.66410	−0.312272
$330$	33.1882	1.82695
$331$	19.6461	1.07984	0.539922	−	0.841715i	$-0.318454\pi$
$331$	19.6461	1.07984	0.539922	+	0.841715i	$0.318454\pi$
$332$	26.8685	1.47460
$333$	−1.02262	−0.0560393
$334$	−39.9580	−2.18640
$335$	−29.9870	−1.63837
$336$	7.11712	0.388271
$337$	−9.76246	−0.531795	−0.265898	−	0.964001i	$-0.585668\pi$
$337$	−9.76246	−0.531795	−0.265898	+	0.964001i	$0.585668\pi$
$338$	2.54577	0.138472
$339$	−1.18694	−0.0644655
$340$	−14.1342	−0.766534
$341$	29.3715	1.59056
$342$	−16.5675	−0.895869
$343$	−1.00000	−0.0539949
$344$	−29.4605	−1.58840
$345$	18.0906	0.973963
$346$	3.37421	0.181399
$347$	−15.6076	−0.837861	−0.418931	−	0.908018i	$-0.637595\pi$
$347$	−15.6076	−0.837861	−0.418931	+	0.908018i	$0.637595\pi$
$348$	−29.2739	−1.56924
$349$	20.0358	1.07249	0.536245	−	0.844063i	$-0.319842\pi$
$349$	20.0358	1.07249	0.536245	+	0.844063i	$0.319842\pi$
$350$	−12.6001	−0.673505
$351$	1.00000	0.0533761
$352$	22.6762	1.20864
$353$	8.74194	0.465286	0.232643	−	0.972562i	$-0.425263\pi$
$353$	8.74194	0.465286	0.232643	+	0.972562i	$0.425263\pi$
$354$	−16.2945	−0.866043
$355$	25.6194	1.35974
$356$	27.9005	1.47872
$357$	1.00000	0.0529256
$358$	−47.6727	−2.51958
$359$	−12.5703	−0.663435	−0.331717	−	0.943379i	$-0.607628\pi$
$359$	−12.5703	−0.663435	−0.331717	+	0.943379i	$0.607628\pi$
$360$	−19.9223	−1.05000
$361$	23.3521	1.22906
$362$	−45.9372	−2.41440
$363$	−6.08161	−0.319202
$364$	4.48097	0.234866
$365$	−22.8442	−1.19572
$366$	−36.2717	−1.89595
$367$	−3.62825	−0.189393	−0.0946966	−	0.995506i	$-0.530188\pi$
$367$	−3.62825	−0.189393	−0.0946966	+	0.995506i	$0.530188\pi$
$368$	40.8185	2.12781
$369$	−0.0855998	−0.00445615
$370$	8.21172	0.426907
$371$	6.08088	0.315703
$372$	−31.8444	−1.65106
$373$	25.9286	1.34253	0.671265	−	0.741217i	$-0.265751\pi$
$373$	25.9286	1.34253	0.671265	+	0.741217i	$0.265751\pi$
$374$	10.5217	0.544062
$375$	−0.159508	−0.00823694
$376$	35.7743	1.84492
$377$	−6.53293	−0.336463
$378$	2.54577	0.130940
$379$	14.9731	0.769117	0.384559	−	0.923101i	$-0.374354\pi$
$379$	14.9731	0.769117	0.384559	+	0.923101i	$0.374354\pi$
$380$	91.9832	4.71864
$381$	4.92916	0.252528
$382$	32.1815	1.64655
$383$	13.1427	0.671558	0.335779	−	0.941941i	$-0.391000\pi$
$383$	13.1427	0.671558	0.335779	+	0.941941i	$0.391000\pi$
$384$	11.6518	0.594602
$385$	13.0366	0.664405
$386$	−56.7805	−2.89005
$387$	−4.66443	−0.237107
$388$	75.7773	3.84701
$389$	−19.6275	−0.995152	−0.497576	−	0.867420i	$-0.665777\pi$
$389$	−19.6275	−0.995152	−0.497576	+	0.867420i	$0.665777\pi$
$390$	−8.03006	−0.406618
$391$	5.73526	0.290044
$392$	6.31598	0.319005
$393$	−12.7160	−0.641436
$394$	15.9175	0.801911
$395$	−33.1830	−1.66962
$396$	18.5198	0.930654
$397$	−35.2252	−1.76790	−0.883950	−	0.467581i	$-0.845126\pi$
$397$	−35.2252	−1.76790	−0.883950	+	0.467581i	$0.845126\pi$
$398$	10.2011	0.511336
$399$	−6.50785	−0.325800
$400$	35.2257	1.76128
$401$	29.9875	1.49750	0.748752	−	0.662851i	$-0.230654\pi$
$401$	29.9875	1.49750	0.748752	+	0.662851i	$0.230654\pi$
$402$	−24.2021	−1.20709
$403$	−7.10660	−0.354005
$404$	4.32833	0.215343
$405$	−3.15427	−0.156737
$406$	−16.6314	−0.825401
$407$	−4.22649	−0.209499
$408$	−6.31598	−0.312687
$409$	24.5822	1.21551	0.607755	−	0.794125i	$-0.292070\pi$
$409$	24.5822	1.21551	0.607755	+	0.794125i	$0.292070\pi$
$410$	0.687372	0.0339469
$411$	−12.6797	−0.625444
$412$	−32.2468	−1.58868
$413$	−6.40060	−0.314953
$414$	14.6007	0.717584
$415$	−18.9134	−0.928425
$416$	−5.48663	−0.269004
$417$	10.8498	0.531317
$418$	−68.4734	−3.34914
$419$	13.0003	0.635106	0.317553	−	0.948241i	$-0.397139\pi$
$419$	13.0003	0.635106	0.317553	+	0.948241i	$0.397139\pi$
$420$	−14.1342	−0.689678
$421$	31.6749	1.54374	0.771870	−	0.635781i	$-0.219322\pi$
$421$	31.6749	1.54374	0.771870	+	0.635781i	$0.219322\pi$
$422$	−48.9157	−2.38118
$423$	5.66410	0.275398
$424$	−38.4067	−1.86519
$425$	4.94943	0.240083
$426$	20.6771	1.00181
$427$	−14.2478	−0.689499
$428$	49.4818	2.39179
$429$	4.13299	0.199543
$430$	37.4557	1.80627
$431$	4.15999	0.200380	0.100190	−	0.994968i	$-0.468055\pi$
$431$	4.15999	0.200380	0.100190	+	0.994968i	$0.468055\pi$
$432$	−7.11712	−0.342423
$433$	−19.4173	−0.933136	−0.466568	−	0.884485i	$-0.654510\pi$
$433$	−19.4173	−0.933136	−0.466568	+	0.884485i	$0.654510\pi$
$434$	−18.0918	−0.868434
$435$	20.6067	0.988013
$436$	−43.8831	−2.10162
$437$	−37.3242	−1.78546
$438$	−18.4373	−0.880969
$439$	−11.9638	−0.571002	−0.285501	−	0.958378i	$-0.592160\pi$
$439$	−11.9638	−0.571002	−0.285501	+	0.958378i	$0.592160\pi$
$440$	−82.3387	−3.92534
$441$	1.00000	0.0476190
$442$	−2.54577	−0.121090
$443$	−28.4275	−1.35063	−0.675316	−	0.737529i	$-0.735993\pi$
$443$	−28.4275	−1.35063	−0.675316	+	0.737529i	$0.735993\pi$
$444$	4.58233	0.217468
$445$	−19.6399	−0.931022
$446$	72.4083	3.42863
$447$	1.21810	0.0576141
$448$	0.266532	0.0125925
$449$	−9.61885	−0.453942	−0.226971	−	0.973902i	$-0.572882\pi$
$449$	−9.61885	−0.453942	−0.226971	+	0.973902i	$0.572882\pi$
$450$	12.6001	0.593976
$451$	−0.353783	−0.0166590
$452$	5.31862	0.250167
$453$	14.2229	0.668250
$454$	−21.9236	−1.02892
$455$	−3.15427	−0.147875
$456$	41.1034	1.92485
$457$	3.89971	0.182421	0.0912104	−	0.995832i	$-0.470926\pi$
$457$	3.89971	0.182421	0.0912104	+	0.995832i	$0.470926\pi$
$458$	28.7096	1.34151
$459$	−1.00000	−0.0466760
$460$	−81.0632	−3.77959
$461$	−23.9682	−1.11631	−0.558156	−	0.829736i	$-0.688491\pi$
$461$	−23.9682	−1.11631	−0.558156	+	0.829736i	$0.688491\pi$
$462$	10.5217	0.489512
$463$	29.2461	1.35918	0.679590	−	0.733592i	$-0.262158\pi$
$463$	29.2461	1.35918	0.679590	+	0.733592i	$0.262158\pi$
$464$	46.4957	2.15851
$465$	22.4162	1.03952
$466$	−72.1890	−3.34409
$467$	−19.0239	−0.880323	−0.440161	−	0.897919i	$-0.645079\pi$
$467$	−19.0239	−0.880323	−0.440161	+	0.897919i	$0.645079\pi$
$468$	−4.48097	−0.207133
$469$	−9.50679	−0.438983
$470$	−45.4831	−2.09798
$471$	−7.00956	−0.322983
$472$	40.4261	1.86076
$473$	−19.2781	−0.886406
$474$	−26.7816	−1.23012
$475$	−32.2102	−1.47790
$476$	−4.48097	−0.205385
$477$	−6.08088	−0.278424
$478$	59.7173	2.73140
$479$	−36.7134	−1.67748	−0.838740	−	0.544532i	$-0.816707\pi$
$479$	−36.7134	−1.67748	−0.838740	+	0.544532i	$0.816707\pi$
$480$	17.3063	0.789921
$481$	1.02262	0.0466275
$482$	58.3045	2.65570
$483$	5.73526	0.260963
$484$	27.2515	1.23870
$485$	−53.3417	−2.42212
$486$	−2.54577	−0.115479
$487$	6.41120	0.290519	0.145260	−	0.989394i	$-0.453598\pi$
$487$	6.41120	0.290519	0.145260	+	0.989394i	$0.453598\pi$
$488$	89.9888	4.07360
$489$	−12.2210	−0.552654
$490$	−8.03006	−0.362761
$491$	−0.156927	−0.00708201	−0.00354100	−	0.999994i	$-0.501127\pi$
$491$	−0.156927	−0.00708201	−0.00354100	+	0.999994i	$0.501127\pi$
$492$	0.383570	0.0172927
$493$	6.53293	0.294229
$494$	16.5675	0.745408
$495$	−13.0366	−0.585950
$496$	50.5785	2.27104
$497$	8.12213	0.364327
$498$	−15.2648	−0.684033
$499$	27.5514	1.23337	0.616686	−	0.787209i	$-0.288475\pi$
$499$	27.5514	1.23337	0.616686	+	0.787209i	$0.288475\pi$
$500$	0.714748	0.0319645
$501$	15.6958	0.701237
$502$	−39.8730	−1.77962
$503$	−13.9464	−0.621840	−0.310920	−	0.950436i	$-0.600637\pi$
$503$	−13.9464	−0.621840	−0.310920	+	0.950436i	$0.600637\pi$
$504$	−6.31598	−0.281336
$505$	−3.04683	−0.135582
$506$	60.3444	2.68264
$507$	−1.00000	−0.0444116
$508$	−22.0874	−0.979969
$509$	−20.7317	−0.918916	−0.459458	−	0.888199i	$-0.651956\pi$
$509$	−20.7317	−0.918916	−0.459458	+	0.888199i	$0.651956\pi$
$510$	8.03006	0.355577
$511$	−7.24232	−0.320381
$512$	−50.8542	−2.24746
$513$	6.50785	0.287329
$514$	5.15756	0.227490
$515$	22.6994	1.00025
$516$	20.9012	0.920123
$517$	23.4097	1.02956
$518$	2.60336	0.114385
$519$	−1.32542	−0.0581793
$520$	19.9223	0.873651
$521$	−22.0325	−0.965263	−0.482631	−	0.875824i	$-0.660319\pi$
$521$	−22.0325	−0.965263	−0.482631	+	0.875824i	$0.660319\pi$
$522$	16.6314	0.727936
$523$	2.69828	0.117988	0.0589938	−	0.998258i	$-0.481211\pi$
$523$	2.69828	0.117988	0.0589938	+	0.998258i	$0.481211\pi$
$524$	56.9799	2.48918
$525$	4.94943	0.216011
$526$	−32.7271	−1.42697
$527$	7.10660	0.309568
$528$	−29.4150	−1.28012
$529$	9.89317	0.430138
$530$	48.8298	2.12103
$531$	6.40060	0.277763
$532$	29.1615	1.26431
$533$	0.0855998	0.00370774
$534$	−15.8511	−0.685946
$535$	−34.8316	−1.50590
$536$	60.0447	2.59354
$537$	18.7262	0.808096
$538$	0.436265	0.0188087
$539$	4.13299	0.178020
$540$	14.1342	0.608238
$541$	−12.3023	−0.528916	−0.264458	−	0.964397i	$-0.585193\pi$
$541$	−12.3023	−0.528916	−0.264458	+	0.964397i	$0.585193\pi$
$542$	−30.2012	−1.29725
$543$	18.0445	0.774363
$544$	5.48663	0.235237
$545$	30.8905	1.32320
$546$	−2.54577	−0.108949
$547$	35.9351	1.53647	0.768236	−	0.640167i	$-0.221135\pi$
$547$	35.9351	1.53647	0.768236	+	0.640167i	$0.221135\pi$
$548$	56.8173	2.42712
$549$	14.2478	0.608081
$550$	52.0762	2.22054
$551$	−42.5154	−1.81122
$552$	−36.2238	−1.54179
$553$	−10.5200	−0.447357
$554$	13.5056	0.573796
$555$	−3.22563	−0.136920
$556$	−48.6176	−2.06185
$557$	14.5081	0.614726	0.307363	−	0.951592i	$-0.400553\pi$
$557$	14.5081	0.614726	0.307363	+	0.951592i	$0.400553\pi$
$558$	18.0918	0.765887
$559$	4.66443	0.197285
$560$	22.4493	0.948657
$561$	−4.13299	−0.174495
$562$	−23.2958	−0.982674
$563$	−17.7216	−0.746877	−0.373439	−	0.927655i	$-0.621821\pi$
$563$	−17.7216	−0.746877	−0.373439	+	0.927655i	$0.621821\pi$
$564$	−25.3806	−1.06872
$565$	−3.74392	−0.157508
$566$	−39.6952	−1.66851
$567$	−1.00000	−0.0419961
$568$	−51.2992	−2.15247
$569$	−15.7632	−0.660827	−0.330414	−	0.943836i	$-0.607188\pi$
$569$	−15.7632	−0.660827	−0.330414	+	0.943836i	$0.607188\pi$
$570$	−52.2585	−2.18887
$571$	−23.6618	−0.990216	−0.495108	−	0.868831i	$-0.664871\pi$
$571$	−23.6618	−0.990216	−0.495108	+	0.868831i	$0.664871\pi$
$572$	−18.5198	−0.774351
$573$	−12.6411	−0.528091
$574$	0.217918	0.00909571
$575$	28.3863	1.18379
$576$	−0.266532	−0.0111055
$577$	21.3107	0.887175	0.443587	−	0.896231i	$-0.353706\pi$
$577$	21.3107	0.887175	0.443587	+	0.896231i	$0.353706\pi$
$578$	2.54577	0.105890
$579$	22.3038	0.926915
$580$	−92.3377	−3.83411
$581$	−5.99614	−0.248762
$582$	−43.0514	−1.78454
$583$	−25.1322	−1.04087
$584$	45.7423	1.89283
$585$	3.15427	0.130413
$586$	−61.7624	−2.55138
$587$	−17.1640	−0.708435	−0.354218	−	0.935163i	$-0.615253\pi$
$587$	−17.1640	−0.708435	−0.354218	+	0.935163i	$0.615253\pi$
$588$	−4.48097	−0.184792
$589$	−46.2487	−1.90564
$590$	−51.3973	−2.11599
$591$	−6.25251	−0.257194
$592$	−7.27812	−0.299129
$593$	−28.9180	−1.18752	−0.593760	−	0.804642i	$-0.702357\pi$
$593$	−28.9180	−1.18752	−0.593760	+	0.804642i	$0.702357\pi$
$594$	−10.5217	−0.431709
$595$	3.15427	0.129313
$596$	−5.45826	−0.223579
$597$	−4.00708	−0.163999
$598$	−14.6007	−0.597066
$599$	−42.4291	−1.73361	−0.866803	−	0.498651i	$-0.833829\pi$
$599$	−42.4291	−1.73361	−0.866803	+	0.498651i	$0.833829\pi$
$600$	−31.2605	−1.27620
$601$	2.25928	0.0921578	0.0460789	−	0.998938i	$-0.485327\pi$
$601$	2.25928	0.0921578	0.0460789	+	0.998938i	$0.485327\pi$
$602$	11.8746	0.483972
$603$	9.50679	0.387147
$604$	−63.7323	−2.59323
$605$	−19.1830	−0.779902
$606$	−2.45906	−0.0998924
$607$	−7.84333	−0.318351	−0.159176	−	0.987250i	$-0.550884\pi$
$607$	−7.84333	−0.318351	−0.159176	+	0.987250i	$0.550884\pi$
$608$	−35.7061	−1.44808
$609$	6.53293	0.264728
$610$	−114.411	−4.63235
$611$	−5.66410	−0.229145
$612$	4.48097	0.181132
$613$	1.31345	0.0530498	0.0265249	−	0.999648i	$-0.491556\pi$
$613$	1.31345	0.0530498	0.0265249	+	0.999648i	$0.491556\pi$
$614$	−76.1857	−3.07461
$615$	−0.270005	−0.0108877
$616$	−26.1039	−1.05176
$617$	21.7400	0.875220	0.437610	−	0.899165i	$-0.355825\pi$
$617$	21.7400	0.875220	0.437610	+	0.899165i	$0.355825\pi$
$618$	18.3204	0.736954
$619$	−1.17955	−0.0474102	−0.0237051	−	0.999719i	$-0.507546\pi$
$619$	−1.17955	−0.0474102	−0.0237051	+	0.999719i	$0.507546\pi$
$620$	−100.446	−4.03401
$621$	−5.73526	−0.230148
$622$	81.8148	3.28047
$623$	−6.22645	−0.249458
$624$	7.11712	0.284913
$625$	−25.2503	−1.01001
$626$	6.52907	0.260954
$627$	26.8969	1.07416
$628$	31.4096	1.25338
$629$	−1.02262	−0.0407746
$630$	8.03006	0.319925
$631$	40.5780	1.61539	0.807693	−	0.589603i	$-0.200716\pi$
$631$	40.5780	1.61539	0.807693	+	0.589603i	$0.200716\pi$
$632$	66.4443	2.64301
$633$	19.2145	0.763707
$634$	−56.4804	−2.24312
$635$	15.5479	0.617000
$636$	27.2482	1.08046
$637$	−1.00000	−0.0396214
$638$	68.7373	2.72134
$639$	−8.12213	−0.321306
$640$	36.7529	1.45279
$641$	44.6505	1.76359	0.881794	−	0.471635i	$-0.156336\pi$
$641$	44.6505	1.76359	0.881794	+	0.471635i	$0.156336\pi$
$642$	−28.1121	−1.10950
$643$	−3.61769	−0.142668	−0.0713339	−	0.997452i	$-0.522726\pi$
$643$	−3.61769	−0.142668	−0.0713339	+	0.997452i	$0.522726\pi$
$644$	−25.6995	−1.01270
$645$	−14.7129	−0.579320
$646$	−16.5675	−0.651840
$647$	6.50439	0.255714	0.127857	−	0.991793i	$-0.459190\pi$
$647$	6.50439	0.255714	0.127857	+	0.991793i	$0.459190\pi$
$648$	6.31598	0.248115
$649$	26.4536	1.03840
$650$	−12.6001	−0.494218
$651$	7.10660	0.278530
$652$	54.7620	2.14465
$653$	−24.8163	−0.971137	−0.485568	−	0.874199i	$-0.661387\pi$
$653$	−24.8163	−0.971137	−0.485568	+	0.874199i	$0.661387\pi$
$654$	24.9313	0.974892
$655$	−40.1097	−1.56721
$656$	−0.609224	−0.0237862
$657$	7.24232	0.282550
$658$	−14.4195	−0.562131
$659$	21.1253	0.822925	0.411463	−	0.911427i	$-0.365018\pi$
$659$	21.1253	0.822925	0.411463	+	0.911427i	$0.365018\pi$
$660$	58.4164	2.27386
$661$	−47.4167	−1.84430	−0.922148	−	0.386836i	$-0.873568\pi$
$661$	−47.4167	−1.84430	−0.922148	+	0.386836i	$0.873568\pi$
$662$	50.0144	1.94387
$663$	1.00000	0.0388368
$664$	37.8715	1.46970
$665$	−20.5275	−0.796024
$666$	−2.60336	−0.100878
$667$	37.4681	1.45077
$668$	−70.3324	−2.72124
$669$	−28.4425	−1.09965
$670$	−76.3401	−2.94928
$671$	58.8860	2.27327
$672$	5.48663	0.211651
$673$	0.432183	0.0166594	0.00832972	−	0.999965i	$-0.497349\pi$
$673$	0.432183	0.0166594	0.00832972	+	0.999965i	$0.497349\pi$
$674$	−24.8530	−0.957303
$675$	−4.94943	−0.190504
$676$	4.48097	0.172345
$677$	17.2110	0.661472	0.330736	−	0.943723i	$-0.392703\pi$
$677$	17.2110	0.661472	0.330736	+	0.943723i	$0.392703\pi$
$678$	−3.02167	−0.116047
$679$	−16.9109	−0.648982
$680$	−19.9223	−0.763986
$681$	8.61175	0.330003
$682$	74.7732	2.86322
$683$	−33.5602	−1.28415	−0.642073	−	0.766644i	$-0.721925\pi$
$683$	−33.5602	−1.28415	−0.642073	+	0.766644i	$0.721925\pi$
$684$	−29.1615	−1.11502
$685$	−39.9952	−1.52814
$686$	−2.54577	−0.0971981
$687$	−11.2774	−0.430259
$688$	−33.1973	−1.26564
$689$	6.08088	0.231663
$690$	46.0545	1.75326
$691$	−2.77976	−0.105747	−0.0528735	−	0.998601i	$-0.516838\pi$
$691$	−2.77976	−0.105747	−0.0528735	+	0.998601i	$0.516838\pi$
$692$	5.93914	0.225772
$693$	−4.13299	−0.156999
$694$	−39.7335	−1.50826
$695$	34.2232	1.29816
$696$	−41.2619	−1.56403
$697$	−0.0855998	−0.00324232
$698$	51.0065	1.93062
$699$	28.3564	1.07254
$700$	−22.1782	−0.838258
$701$	24.9009	0.940496	0.470248	−	0.882534i	$-0.344165\pi$
$701$	24.9009	0.940496	0.470248	+	0.882534i	$0.344165\pi$
$702$	2.54577	0.0960840
$703$	6.65507	0.251001
$704$	−1.10157	−0.0415171
$705$	17.8661	0.672877
$706$	22.2550	0.837578
$707$	−0.965937	−0.0363278
$708$	−28.6809	−1.07789
$709$	13.6773	0.513661	0.256831	−	0.966456i	$-0.417322\pi$
$709$	13.6773	0.513661	0.256831	+	0.966456i	$0.417322\pi$
$710$	65.2212	2.44771
$711$	10.5200	0.394532
$712$	39.3261	1.47381
$713$	40.7582	1.52641
$714$	2.54577	0.0952732
$715$	13.0366	0.487540
$716$	−83.9116	−3.13592
$717$	−23.4574	−0.876033
$718$	−32.0011	−1.19427
$719$	35.8378	1.33653	0.668263	−	0.743925i	$-0.267038\pi$
$719$	35.8378	1.33653	0.668263	+	0.743925i	$0.267038\pi$
$720$	−22.4493	−0.836637
$721$	7.19639	0.268008
$722$	59.4492	2.21247
$723$	−22.9025	−0.851752
$724$	−80.8567	−3.00502
$725$	32.3343	1.20087
$726$	−15.4824	−0.574606
$727$	−23.7865	−0.882193	−0.441096	−	0.897460i	$-0.645410\pi$
$727$	−23.7865	−0.882193	−0.441096	+	0.897460i	$0.645410\pi$
$728$	6.31598	0.234086
$729$	1.00000	0.0370370
$730$	−58.1563	−2.15246
$731$	−4.66443	−0.172520
$732$	−63.8439	−2.35974
$733$	50.4632	1.86390	0.931950	−	0.362587i	$-0.118106\pi$
$733$	50.4632	1.86390	0.931950	+	0.362587i	$0.118106\pi$
$734$	−9.23671	−0.340933
$735$	3.15427	0.116347
$736$	31.4672	1.15990
$737$	39.2915	1.44732
$738$	−0.217918	−0.00802166
$739$	−7.13749	−0.262557	−0.131278	−	0.991346i	$-0.541908\pi$
$739$	−7.13749	−0.262557	−0.131278	+	0.991346i	$0.541908\pi$
$740$	14.4539	0.531337
$741$	−6.50785	−0.239072
$742$	15.4805	0.568309
$743$	16.8059	0.616548	0.308274	−	0.951298i	$-0.400249\pi$
$743$	16.8059	0.616548	0.308274	+	0.951298i	$0.400249\pi$
$744$	−44.8851	−1.64557
$745$	3.84222	0.140768
$746$	66.0083	2.41673
$747$	5.99614	0.219387
$748$	18.5198	0.677150
$749$	−11.0427	−0.403490
$750$	−0.406070	−0.0148276
$751$	35.7909	1.30603	0.653014	−	0.757345i	$-0.273504\pi$
$751$	35.7909	1.30603	0.653014	+	0.757345i	$0.273504\pi$
$752$	40.3121	1.47003
$753$	15.6624	0.570770
$754$	−16.6314	−0.605679
$755$	44.8629	1.63273
$756$	4.48097	0.162971
$757$	10.2051	0.370912	0.185456	−	0.982653i	$-0.440624\pi$
$757$	10.2051	0.370912	0.185456	+	0.982653i	$0.440624\pi$
$758$	38.1182	1.38451
$759$	−23.7038	−0.860392
$760$	129.651	4.70295
$761$	−43.0722	−1.56137	−0.780683	−	0.624927i	$-0.785129\pi$
$761$	−43.0722	−1.56137	−0.780683	+	0.624927i	$0.785129\pi$
$762$	12.5485	0.454585
$763$	9.79322	0.354538
$764$	56.6445	2.04933
$765$	−3.15427	−0.114043
$766$	33.4582	1.20889
$767$	−6.40060	−0.231112
$768$	29.1297	1.05113
$769$	−24.7662	−0.893093	−0.446546	−	0.894761i	$-0.647346\pi$
$769$	−24.7662	−0.893093	−0.446546	+	0.894761i	$0.647346\pi$
$770$	33.1882	1.19602
$771$	−2.02593	−0.0729620
$772$	−99.9426	−3.59701
$773$	−9.91199	−0.356510	−0.178255	−	0.983984i	$-0.557045\pi$
$773$	−9.91199	−0.356510	−0.178255	+	0.983984i	$0.557045\pi$
$774$	−11.8746	−0.426824
$775$	35.1736	1.26347
$776$	106.809	3.83422
$777$	−1.02262	−0.0366864
$778$	−49.9671	−1.79141
$779$	0.557071	0.0199591
$780$	−14.1342	−0.506085
$781$	−33.5687	−1.20118
$782$	14.6007	0.522119
$783$	−6.53293	−0.233468
$784$	7.11712	0.254183
$785$	−22.1101	−0.789142
$786$	−32.3720	−1.15467
$787$	25.5234	0.909812	0.454906	−	0.890540i	$-0.349673\pi$
$787$	25.5234	0.909812	0.454906	+	0.890540i	$0.349673\pi$
$788$	28.0173	0.998074
$789$	12.8555	0.457667
$790$	−84.4765	−3.00554
$791$	−1.18694	−0.0422026
$792$	26.1039	0.927561
$793$	−14.2478	−0.505954
$794$	−89.6753	−3.18246
$795$	−19.1807	−0.680271
$796$	17.9556	0.636419
$797$	42.9948	1.52295	0.761477	−	0.648192i	$-0.224474\pi$
$797$	42.9948	1.52295	0.761477	+	0.648192i	$0.224474\pi$
$798$	−16.5675	−0.586484
$799$	5.66410	0.200381
$800$	27.1557	0.960098
$801$	6.22645	0.220001
$802$	76.3413	2.69571
$803$	29.9324	1.05629
$804$	−42.5996	−1.50237
$805$	18.0906	0.637608
$806$	−18.0918	−0.637256
$807$	−0.171368	−0.00603245
$808$	6.10084	0.214627
$809$	42.8395	1.50616	0.753078	−	0.657931i	$-0.228568\pi$
$809$	42.8395	1.50616	0.753078	+	0.657931i	$0.228568\pi$
$810$	−8.03006	−0.282148
$811$	36.3519	1.27649	0.638244	−	0.769834i	$-0.279661\pi$
$811$	36.3519	1.27649	0.638244	+	0.769834i	$0.279661\pi$
$812$	−29.2739	−1.02731
$813$	11.8633	0.416064
$814$	−10.7597	−0.377127
$815$	−38.5485	−1.35029
$816$	−7.11712	−0.249149
$817$	30.3554	1.06200
$818$	62.5806	2.18808
$819$	1.00000	0.0349428
$820$	1.20988	0.0422509
$821$	35.0137	1.22199	0.610993	−	0.791636i	$-0.290770\pi$
$821$	35.0137	1.22199	0.610993	+	0.791636i	$0.290770\pi$
$822$	−32.2797	−1.12588
$823$	−15.5256	−0.541187	−0.270594	−	0.962694i	$-0.587220\pi$
$823$	−15.5256	−0.541187	−0.270594	+	0.962694i	$0.587220\pi$
$824$	−45.4522	−1.58340
$825$	−20.4560	−0.712185
$826$	−16.2945	−0.566958
$827$	25.2378	0.877603	0.438801	−	0.898584i	$-0.355403\pi$
$827$	25.2378	0.877603	0.438801	+	0.898584i	$0.355403\pi$
$828$	25.6995	0.893119
$829$	4.84894	0.168411	0.0842053	−	0.996448i	$-0.473165\pi$
$829$	4.84894	0.168411	0.0842053	+	0.996448i	$0.473165\pi$
$830$	−48.1494	−1.67129
$831$	−5.30509	−0.184031
$832$	0.266532	0.00924033
$833$	1.00000	0.0346479
$834$	27.6211	0.956442
$835$	49.5089	1.71332
$836$	−120.524	−4.16841
$837$	−7.10660	−0.245640
$838$	33.0958	1.14328
$839$	36.3460	1.25480	0.627402	−	0.778696i	$-0.284118\pi$
$839$	36.3460	1.25480	0.627402	+	0.778696i	$0.284118\pi$
$840$	−19.9223	−0.687385
$841$	13.6792	0.471698
$842$	80.6371	2.77894
$843$	9.15077	0.315169
$844$	−86.0994	−2.96366
$845$	−3.15427	−0.108510
$846$	14.4195	0.495753
$847$	−6.08161	−0.208967
$848$	−43.2783	−1.48618
$849$	15.5926	0.535136
$850$	12.6001	0.432181
$851$	−5.86500	−0.201050
$852$	36.3950	1.24687
$853$	−16.7917	−0.574938	−0.287469	−	0.957790i	$-0.592814\pi$
$853$	−16.7917	−0.574938	−0.287469	+	0.957790i	$0.592814\pi$
$854$	−36.2717	−1.24119
$855$	20.5275	0.702027
$856$	69.7452	2.38384
$857$	−56.7908	−1.93994	−0.969968	−	0.243232i	$-0.921792\pi$
$857$	−56.7908	−1.93994	−0.969968	+	0.243232i	$0.921792\pi$
$858$	10.5217	0.359204
$859$	−10.2346	−0.349199	−0.174600	−	0.984640i	$-0.555863\pi$
$859$	−10.2346	−0.349199	−0.174600	+	0.984640i	$0.555863\pi$
$860$	65.9280	2.24813
$861$	−0.0855998	−0.00291723
$862$	10.5904	0.360710
$863$	4.84076	0.164781	0.0823907	−	0.996600i	$-0.473744\pi$
$863$	4.84076	0.164781	0.0823907	+	0.996600i	$0.473744\pi$
$864$	−5.48663	−0.186659
$865$	−4.18072	−0.142149
$866$	−49.4320	−1.67977
$867$	−1.00000	−0.0339618
$868$	−31.8444	−1.08087
$869$	43.4792	1.47493
$870$	52.4599	1.77856
$871$	−9.50679	−0.322125
$872$	−61.8538	−2.09463
$873$	16.9109	0.572349
$874$	−95.0190	−3.21406
$875$	−0.159508	−0.00539234
$876$	−32.4526	−1.09647
$877$	10.8794	0.367371	0.183685	−	0.982985i	$-0.441197\pi$
$877$	10.8794	0.367371	0.183685	+	0.982985i	$0.441197\pi$
$878$	−30.4572	−1.02788
$879$	24.2607	0.818295
$880$	−92.7829	−3.12771
$881$	15.7543	0.530777	0.265389	−	0.964142i	$-0.414500\pi$
$881$	15.7543	0.530777	0.265389	+	0.964142i	$0.414500\pi$
$882$	2.54577	0.0857207
$883$	−42.8373	−1.44159	−0.720795	−	0.693149i	$-0.756223\pi$
$883$	−42.8373	−1.44159	−0.720795	+	0.693149i	$0.756223\pi$
$884$	−4.48097	−0.150711
$885$	20.1892	0.678654
$886$	−72.3700	−2.43132
$887$	46.3244	1.55542	0.777711	−	0.628622i	$-0.216381\pi$
$887$	46.3244	1.55542	0.777711	+	0.628622i	$0.216381\pi$
$888$	6.45886	0.216745
$889$	4.92916	0.165319
$890$	−49.9988	−1.67596
$891$	4.13299	0.138460
$892$	127.450	4.26734
$893$	−36.8611	−1.23351
$894$	3.10100	0.103713
$895$	59.0676	1.97441
$896$	11.6518	0.389259
$897$	5.73526	0.191495
$898$	−24.4874	−0.817156
$899$	46.4270	1.54843
$900$	22.1782	0.739274
$901$	−6.08088	−0.202583
$902$	−0.900652	−0.0299884
$903$	−4.66443	−0.155223
$904$	7.49666	0.249335
$905$	56.9172	1.89199
$906$	36.2083	1.20294
$907$	−6.49832	−0.215773	−0.107887	−	0.994163i	$-0.534408\pi$
$907$	−6.49832	−0.215773	−0.107887	+	0.994163i	$0.534408\pi$
$908$	−38.5889	−1.28062
$909$	0.965937	0.0320381
$910$	−8.03006	−0.266194
$911$	−16.0457	−0.531617	−0.265808	−	0.964026i	$-0.585639\pi$
$911$	−16.0457	−0.531617	−0.265808	+	0.964026i	$0.585639\pi$
$912$	46.3172	1.53371
$913$	24.7820	0.820164
$914$	9.92778	0.328382
$915$	44.9414	1.48572
$916$	50.5335	1.66967
$917$	−12.7160	−0.419919
$918$	−2.54577	−0.0840231
$919$	35.5943	1.17415	0.587074	−	0.809533i	$-0.300280\pi$
$919$	35.5943	1.17415	0.587074	+	0.809533i	$0.300280\pi$
$920$	−114.260	−3.76703
$921$	29.9263	0.986107
$922$	−61.0177	−2.00951
$923$	8.12213	0.267343
$924$	18.5198	0.609256
$925$	−5.06140	−0.166418
$926$	74.4538	2.44671
$927$	−7.19639	−0.236360
$928$	35.8438	1.17663
$929$	−27.9906	−0.918341	−0.459170	−	0.888348i	$-0.651853\pi$
$929$	−27.9906	−0.918341	−0.459170	+	0.888348i	$0.651853\pi$
$930$	57.0665	1.87128
$931$	−6.50785	−0.213286
$932$	−127.064	−4.16212
$933$	−32.1375	−1.05213
$934$	−48.4307	−1.58470
$935$	−13.0366	−0.426342
$936$	−6.31598	−0.206444
$937$	−5.88871	−0.192376	−0.0961879	−	0.995363i	$-0.530665\pi$
$937$	−5.88871	−0.192376	−0.0961879	+	0.995363i	$0.530665\pi$
$938$	−24.2021	−0.790228
$939$	−2.56467	−0.0836948
$940$	−80.0574	−2.61119
$941$	29.3389	0.956422	0.478211	−	0.878245i	$-0.341285\pi$
$941$	29.3389	0.956422	0.478211	+	0.878245i	$0.341285\pi$
$942$	−17.8448	−0.581413
$943$	−0.490937	−0.0159871
$944$	45.5539	1.48265
$945$	−3.15427	−0.102608
$946$	−49.0776	−1.59565
$947$	7.35287	0.238936	0.119468	−	0.992838i	$-0.461881\pi$
$947$	7.35287	0.238936	0.119468	+	0.992838i	$0.461881\pi$
$948$	−47.1399	−1.53103
$949$	−7.24232	−0.235096
$950$	−81.9998	−2.66042
$951$	22.1859	0.719429
$952$	−6.31598	−0.204702
$953$	50.2970	1.62928	0.814639	−	0.579968i	$-0.196935\pi$
$953$	50.2970	1.62928	0.814639	+	0.579968i	$0.196935\pi$
$954$	−15.4805	−0.501201
$955$	−39.8736	−1.29028
$956$	105.112	3.39956
$957$	−27.0006	−0.872804
$958$	−93.4641	−3.01969
$959$	−12.6797	−0.409449
$960$	−0.840714	−0.0271339
$961$	19.5038	0.629154
$962$	2.60336	0.0839358
$963$	11.0427	0.355845
$964$	102.625	3.30533
$965$	70.3523	2.26472
$966$	14.6007	0.469769
$967$	−51.6293	−1.66029	−0.830143	−	0.557551i	$-0.811741\pi$
$967$	−51.6293	−1.66029	−0.830143	+	0.557551i	$0.811741\pi$
$968$	38.4113	1.23459
$969$	6.50785	0.209062
$970$	−135.796	−4.36014
$971$	−31.7100	−1.01762	−0.508811	−	0.860878i	$-0.669915\pi$
$971$	−31.7100	−1.01762	−0.508811	+	0.860878i	$0.669915\pi$
$972$	−4.48097	−0.143727
$973$	10.8498	0.347829
$974$	16.3215	0.522974
$975$	4.94943	0.158509
$976$	101.403	3.24584
$977$	−32.1955	−1.03003	−0.515013	−	0.857182i	$-0.672213\pi$
$977$	−32.1955	−1.03003	−0.515013	+	0.857182i	$0.672213\pi$
$978$	−31.1120	−0.994852
$979$	25.7339	0.822458
$980$	−14.1342	−0.451500
$981$	−9.79322	−0.312673
$982$	−0.399500	−0.0127486
$983$	−10.6940	−0.341086	−0.170543	−	0.985350i	$-0.554552\pi$
$983$	−10.6940	−0.341086	−0.170543	+	0.985350i	$0.554552\pi$
$984$	0.540646	0.0172352
$985$	−19.7221	−0.628399
$986$	16.6314	0.529651
$987$	5.66410	0.180290
$988$	29.1615	0.927750
$989$	−26.7517	−0.850656
$990$	−33.1882	−1.05479
$991$	52.7633	1.67608	0.838041	−	0.545607i	$-0.183701\pi$
$991$	52.7633	1.67608	0.838041	+	0.545607i	$0.183701\pi$
$992$	38.9913	1.23797
$993$	−19.6461	−0.623449
$994$	20.6771	0.655838
$995$	−12.6394	−0.400697
$996$	−26.8685	−0.851361
$997$	−9.99229	−0.316459	−0.158229	−	0.987402i	$-0.550579\pi$
$997$	−9.99229	−0.316459	−0.158229	+	0.987402i	$0.550579\pi$
$998$	70.1397	2.22023
$999$	1.02262	0.0323543

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4641.2.a.t.1.11	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4641.2.a.t.1.11	✓	12	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 4641 = 3 \cdot 7 \cdot 13 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4641.a (trivial)

\(f(q)\)	\(=\)	\(q+2.54577 q^{2} -1.00000 q^{3} +4.48097 q^{4} -3.15427 q^{5} -2.54577 q^{6} -1.00000 q^{7} +6.31598 q^{8} +1.00000 q^{9} -8.03006 q^{10} +4.13299 q^{11} -4.48097 q^{12} -1.00000 q^{13} -2.54577 q^{14} +3.15427 q^{15} +7.11712 q^{16} +1.00000 q^{17} +2.54577 q^{18} -6.50785 q^{19} -14.1342 q^{20} +1.00000 q^{21} +10.5217 q^{22} +5.73526 q^{23} -6.31598 q^{24} +4.94943 q^{25} -2.54577 q^{26} -1.00000 q^{27} -4.48097 q^{28} +6.53293 q^{29} +8.03006 q^{30} +7.10660 q^{31} +5.48663 q^{32} -4.13299 q^{33} +2.54577 q^{34} +3.15427 q^{35} +4.48097 q^{36} -1.02262 q^{37} -16.5675 q^{38} +1.00000 q^{39} -19.9223 q^{40} -0.0855998 q^{41} +2.54577 q^{42} -4.66443 q^{43} +18.5198 q^{44} -3.15427 q^{45} +14.6007 q^{46} +5.66410 q^{47} -7.11712 q^{48} +1.00000 q^{49} +12.6001 q^{50} -1.00000 q^{51} -4.48097 q^{52} -6.08088 q^{53} -2.54577 q^{54} -13.0366 q^{55} -6.31598 q^{56} +6.50785 q^{57} +16.6314 q^{58} +6.40060 q^{59} +14.1342 q^{60} +14.2478 q^{61} +18.0918 q^{62} -1.00000 q^{63} -0.266532 q^{64} +3.15427 q^{65} -10.5217 q^{66} +9.50679 q^{67} +4.48097 q^{68} -5.73526 q^{69} +8.03006 q^{70} -8.12213 q^{71} +6.31598 q^{72} +7.24232 q^{73} -2.60336 q^{74} -4.94943 q^{75} -29.1615 q^{76} -4.13299 q^{77} +2.54577 q^{78} +10.5200 q^{79} -22.4493 q^{80} +1.00000 q^{81} -0.217918 q^{82} +5.99614 q^{83} +4.48097 q^{84} -3.15427 q^{85} -11.8746 q^{86} -6.53293 q^{87} +26.1039 q^{88} +6.22645 q^{89} -8.03006 q^{90} +1.00000 q^{91} +25.6995 q^{92} -7.10660 q^{93} +14.4195 q^{94} +20.5275 q^{95} -5.48663 q^{96} +16.9109 q^{97} +2.54577 q^{98} +4.13299 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + q^{2} - 12 q^{3} + 15 q^{4} - 3 q^{5} - q^{6} - 12 q^{7} + 6 q^{8} + 12 q^{9} + q^{10} + 14 q^{11} - 15 q^{12} - 12 q^{13} - q^{14} + 3 q^{15} + 5 q^{16} + 12 q^{17} + q^{18} + 6 q^{19} - q^{20}+ \cdots + 14 q^{99}+O(q^{100}) \) 12 * q + q^2 - 12 * q^3 + 15 * q^4 - 3 * q^5 - q^6 - 12 * q^7 + 6 * q^8 + 12 * q^9 + q^10 + 14 * q^11 - 15 * q^12 - 12 * q^13 - q^14 + 3 * q^15 + 5 * q^16 + 12 * q^17 + q^18 + 6 * q^19 - q^20 + 12 * q^21 + 16 * q^22 + 11 * q^23 - 6 * q^24 + 13 * q^25 - q^26 - 12 * q^27 - 15 * q^28 + 6 * q^29 - q^30 + 23 * q^31 + 8 * q^32 - 14 * q^33 + q^34 + 3 * q^35 + 15 * q^36 + 22 * q^37 - 19 * q^38 + 12 * q^39 - 20 * q^40 - 6 * q^41 + q^42 - 14 * q^43 + 12 * q^44 - 3 * q^45 + 7 * q^46 - 11 * q^47 - 5 * q^48 + 12 * q^49 + 11 * q^50 - 12 * q^51 - 15 * q^52 - 11 * q^53 - q^54 - 5 * q^55 - 6 * q^56 - 6 * q^57 + 22 * q^58 + 15 * q^59 + q^60 + 3 * q^61 + 7 * q^62 - 12 * q^63 - 2 * q^64 + 3 * q^65 - 16 * q^66 + 13 * q^67 + 15 * q^68 - 11 * q^69 - q^70 + 54 * q^71 + 6 * q^72 + 10 * q^73 + 28 * q^74 - 13 * q^75 + 43 * q^76 - 14 * q^77 + q^78 + 44 * q^79 - 43 * q^80 + 12 * q^81 + 6 * q^82 + q^83 + 15 * q^84 - 3 * q^85 + 9 * q^86 - 6 * q^87 + 87 * q^88 - 15 * q^89 + q^90 + 12 * q^91 + 44 * q^92 - 23 * q^93 + 33 * q^94 + 60 * q^95 - 8 * q^96 - q^97 + q^98 + 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more