LMFDB - Embedded newform 1331.2.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1331,2,Mod(1,1331)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1331, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1331.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1331 = 11^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1331.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:	$10.6280885090$
Analytic rank:	$0$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1331.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.67720 q^{2} -3.00139 q^{3} +5.16738 q^{4} -2.23095 q^{5} +8.03530 q^{6} +1.26098 q^{7} -8.47969 q^{8} +6.00833 q^{9} +O(q^{10})$	\(q-2.67720 q^{2} -3.00139 q^{3} +5.16738 q^{4} -2.23095 q^{5} +8.03530 q^{6} +1.26098 q^{7} -8.47969 q^{8} +6.00833 q^{9} +5.97270 q^{10} -15.5093 q^{12} +3.28144 q^{13} -3.37588 q^{14} +6.69596 q^{15} +12.3670 q^{16} +1.75744 q^{17} -16.0855 q^{18} +5.49169 q^{19} -11.5282 q^{20} -3.78468 q^{21} -0.268675 q^{23} +25.4508 q^{24} -0.0228423 q^{25} -8.78506 q^{26} -9.02918 q^{27} +6.51594 q^{28} +9.44077 q^{29} -17.9264 q^{30} -2.73526 q^{31} -16.1496 q^{32} -4.70501 q^{34} -2.81318 q^{35} +31.0473 q^{36} +1.33730 q^{37} -14.7023 q^{38} -9.84888 q^{39} +18.9178 q^{40} -2.31931 q^{41} +10.1323 q^{42} -2.97967 q^{43} -13.4043 q^{45} +0.719297 q^{46} -0.00866548 q^{47} -37.1183 q^{48} -5.40994 q^{49} +0.0611532 q^{50} -5.27476 q^{51} +16.9564 q^{52} -11.3167 q^{53} +24.1729 q^{54} -10.6927 q^{56} -16.4827 q^{57} -25.2748 q^{58} +5.67398 q^{59} +34.6006 q^{60} +5.90985 q^{61} +7.32283 q^{62} +7.57637 q^{63} +18.5015 q^{64} -7.32074 q^{65} +4.16706 q^{67} +9.08136 q^{68} +0.806399 q^{69} +7.53144 q^{70} -11.6006 q^{71} -50.9488 q^{72} -5.87068 q^{73} -3.58021 q^{74} +0.0685585 q^{75} +28.3776 q^{76} +26.3674 q^{78} +1.45115 q^{79} -27.5903 q^{80} +9.07508 q^{81} +6.20925 q^{82} -16.7451 q^{83} -19.5569 q^{84} -3.92077 q^{85} +7.97715 q^{86} -28.3354 q^{87} +15.9007 q^{89} +35.8860 q^{90} +4.13782 q^{91} -1.38835 q^{92} +8.20958 q^{93} +0.0231992 q^{94} -12.2517 q^{95} +48.4712 q^{96} +7.42771 q^{97} +14.4835 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + 5 q^{2} - 3 q^{3} + 25 q^{4} - 3 q^{5} + 15 q^{6} + 19 q^{7} + 9 q^{8} + 22 q^{9}+O(q^{10}) $ 25 * q + 5 * q^2 - 3 * q^3 + 25 * q^4 - 3 * q^5 + 15 * q^6 + 19 * q^7 + 9 * q^8 + 22 * q^9	\( 25 q + 5 q^{2} - 3 q^{3} + 25 q^{4} - 3 q^{5} + 15 q^{6} + 19 q^{7} + 9 q^{8} + 22 q^{9} + 25 q^{10} - 12 q^{12} + 46 q^{13} - 12 q^{14} - 15 q^{15} + 13 q^{16} + 14 q^{17} + 6 q^{18} + 45 q^{19} - 24 q^{20} + 49 q^{21} + 2 q^{23} + 36 q^{24} + 16 q^{25} - 7 q^{26} - 21 q^{27} + 40 q^{28} + 40 q^{29} - 15 q^{30} - 4 q^{31} + 3 q^{32} - 24 q^{34} - q^{35} + 38 q^{36} - 21 q^{37} + 30 q^{38} + 18 q^{39} + 54 q^{40} + 49 q^{41} + 13 q^{42} + 14 q^{43} - 42 q^{45} + 40 q^{46} - 2 q^{47} - 5 q^{48} + 18 q^{49} - 12 q^{50} + 7 q^{51} + 57 q^{52} - 25 q^{53} + 33 q^{54} - 11 q^{56} + 4 q^{57} + 23 q^{58} - 22 q^{59} - 12 q^{60} + 128 q^{61} - 8 q^{62} + 12 q^{63} + 31 q^{64} + 16 q^{67} - 6 q^{68} - 57 q^{69} + 38 q^{70} - 34 q^{71} - 15 q^{72} + 71 q^{73} - 21 q^{74} - 10 q^{75} + 95 q^{76} + 75 q^{78} + 53 q^{79} - 29 q^{80} + 21 q^{81} + 33 q^{82} - 6 q^{83} + 18 q^{84} + 101 q^{85} + 38 q^{86} - 16 q^{87} + 5 q^{89} - 20 q^{90} + 16 q^{91} + 53 q^{92} + 7 q^{93} + 57 q^{94} - 16 q^{95} + 32 q^{96} + 14 q^{97} - 39 q^{98}+O(q^{100}) \) 25 * q + 5 * q^2 - 3 * q^3 + 25 * q^4 - 3 * q^5 + 15 * q^6 + 19 * q^7 + 9 * q^8 + 22 * q^9 + 25 * q^10 - 12 * q^12 + 46 * q^13 - 12 * q^14 - 15 * q^15 + 13 * q^16 + 14 * q^17 + 6 * q^18 + 45 * q^19 - 24 * q^20 + 49 * q^21 + 2 * q^23 + 36 * q^24 + 16 * q^25 - 7 * q^26 - 21 * q^27 + 40 * q^28 + 40 * q^29 - 15 * q^30 - 4 * q^31 + 3 * q^32 - 24 * q^34 - q^35 + 38 * q^36 - 21 * q^37 + 30 * q^38 + 18 * q^39 + 54 * q^40 + 49 * q^41 + 13 * q^42 + 14 * q^43 - 42 * q^45 + 40 * q^46 - 2 * q^47 - 5 * q^48 + 18 * q^49 - 12 * q^50 + 7 * q^51 + 57 * q^52 - 25 * q^53 + 33 * q^54 - 11 * q^56 + 4 * q^57 + 23 * q^58 - 22 * q^59 - 12 * q^60 + 128 * q^61 - 8 * q^62 + 12 * q^63 + 31 * q^64 + 16 * q^67 - 6 * q^68 - 57 * q^69 + 38 * q^70 - 34 * q^71 - 15 * q^72 + 71 * q^73 - 21 * q^74 - 10 * q^75 + 95 * q^76 + 75 * q^78 + 53 * q^79 - 29 * q^80 + 21 * q^81 + 33 * q^82 - 6 * q^83 + 18 * q^84 + 101 * q^85 + 38 * q^86 - 16 * q^87 + 5 * q^89 - 20 * q^90 + 16 * q^91 + 53 * q^92 + 7 * q^93 + 57 * q^94 - 16 * q^95 + 32 * q^96 + 14 * q^97 - 39 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.67720	−1.89306	−0.946532	−	0.322611i	$-0.895439\pi$
$2$	−2.67720	−1.89306	−0.946532	+	0.322611i	$0.895439\pi$
$3$	−3.00139	−1.73285	−0.866426	−	0.499305i	$-0.833589\pi$
$3$	−3.00139	−1.73285	−0.866426	+	0.499305i	$0.833589\pi$
$4$	5.16738	2.58369
$5$	−2.23095	−0.997713	−0.498857	−	0.866685i	$-0.666247\pi$
$5$	−2.23095	−0.997713	−0.498857	+	0.866685i	$0.666247\pi$
$6$	8.03530	3.28040
$7$	1.26098	0.476604	0.238302	−	0.971191i	$-0.423409\pi$
$7$	1.26098	0.476604	0.238302	+	0.971191i	$0.423409\pi$
$8$	−8.47969	−2.99802
$9$	6.00833	2.00278
$10$	5.97270	1.88873
$11$	0	0
$11$	0	0
$12$	−15.5093	−4.47715
$13$	3.28144	0.910108	0.455054	−	0.890464i	$-0.349620\pi$
$13$	3.28144	0.910108	0.455054	+	0.890464i	$0.349620\pi$
$14$	−3.37588	−0.902242
$15$	6.69596	1.72889
$16$	12.3670	3.09176
$17$	1.75744	0.426242	0.213121	−	0.977026i	$-0.431637\pi$
$17$	1.75744	0.426242	0.213121	+	0.977026i	$0.431637\pi$
$18$	−16.0855	−3.79139
$19$	5.49169	1.25988	0.629940	−	0.776643i	$-0.283079\pi$
$19$	5.49169	1.25988	0.629940	+	0.776643i	$0.283079\pi$
$20$	−11.5282	−2.57778
$21$	−3.78468	−0.825885
$22$	0	0
$23$	−0.268675	−0.0560227	−0.0280113	−	0.999608i	$-0.508917\pi$
$23$	−0.268675	−0.0560227	−0.0280113	+	0.999608i	$0.508917\pi$
$24$	25.4508	5.19513
$25$	−0.0228423	−0.00456845
$26$	−8.78506	−1.72289
$27$	−9.02918	−1.73767
$28$	6.51594	1.23140
$29$	9.44077	1.75311	0.876554	−	0.481304i	$-0.159837\pi$
$29$	9.44077	1.75311	0.876554	+	0.481304i	$0.159837\pi$
$30$	−17.9264	−3.27290
$31$	−2.73526	−0.491268	−0.245634	−	0.969363i	$-0.578996\pi$
$31$	−2.73526	−0.491268	−0.245634	+	0.969363i	$0.578996\pi$
$32$	−16.1496	−2.85487
$33$	0	0
$34$	−4.70501	−0.806903
$35$	−2.81318	−0.475515
$36$	31.0473	5.17455
$37$	1.33730	0.219850	0.109925	−	0.993940i	$-0.464939\pi$
$37$	1.33730	0.219850	0.109925	+	0.993940i	$0.464939\pi$
$38$	−14.7023	−2.38503
$39$	−9.84888	−1.57708
$40$	18.9178	2.99117
$41$	−2.31931	−0.362216	−0.181108	−	0.983463i	$-0.557968\pi$
$41$	−2.31931	−0.362216	−0.181108	+	0.983463i	$0.557968\pi$
$42$	10.1323	1.56345
$43$	−2.97967	−0.454395	−0.227198	−	0.973849i	$-0.572956\pi$
$43$	−2.97967	−0.454395	−0.227198	+	0.973849i	$0.572956\pi$
$44$	0	0
$45$	−13.4043	−1.99820
$46$	0.719297	0.106054
$47$	−0.00866548	−0.00126399	−0.000631995	−	1.00000i	$-0.500201\pi$
$47$	−0.00866548	−0.00126399	−0.000631995		1.00000i	$0.500201\pi$
$48$	−37.1183	−5.35756
$49$	−5.40994	−0.772848
$50$	0.0611532	0.00864837
$51$	−5.27476	−0.738614
$52$	16.9564	2.35143
$53$	−11.3167	−1.55447	−0.777235	−	0.629210i	$-0.783379\pi$
$53$	−11.3167	−1.55447	−0.777235	+	0.629210i	$0.783379\pi$
$54$	24.1729	3.28951
$55$	0	0
$56$	−10.6927	−1.42887
$57$	−16.4827	−2.18319
$58$	−25.2748	−3.31874
$59$	5.67398	0.738689	0.369345	−	0.929292i	$-0.379582\pi$
$59$	5.67398	0.738689	0.369345	+	0.929292i	$0.379582\pi$
$60$	34.6006	4.46691
$61$	5.90985	0.756679	0.378339	−	0.925667i	$-0.376495\pi$
$61$	5.90985	0.756679	0.378339	+	0.925667i	$0.376495\pi$
$62$	7.32283	0.930000
$63$	7.57637	0.954533
$64$	18.5015	2.31269
$65$	−7.32074	−0.908026
$66$	0	0
$67$	4.16706	0.509088	0.254544	−	0.967061i	$-0.418075\pi$
$67$	4.16706	0.509088	0.254544	+	0.967061i	$0.418075\pi$
$68$	9.08136	1.10128
$69$	0.806399	0.0970791
$70$	7.53144	0.900179
$71$	−11.6006	−1.37674	−0.688372	−	0.725358i	$-0.741674\pi$
$71$	−11.6006	−1.37674	−0.688372	+	0.725358i	$0.741674\pi$
$72$	−50.9488	−6.00437
$73$	−5.87068	−0.687111	−0.343556	−	0.939132i	$-0.611631\pi$
$73$	−5.87068	−0.687111	−0.343556	+	0.939132i	$0.611631\pi$
$74$	−3.58021	−0.416190
$75$	0.0685585	0.00791646
$76$	28.3776	3.25514
$77$	0	0
$78$	26.3674	2.98552
$79$	1.45115	0.163267	0.0816337	−	0.996662i	$-0.473986\pi$
$79$	1.45115	0.163267	0.0816337	+	0.996662i	$0.473986\pi$
$80$	−27.5903	−3.08469
$81$	9.07508	1.00834
$82$	6.20925	0.685697
$83$	−16.7451	−1.83802	−0.919009	−	0.394236i	$-0.871009\pi$
$83$	−16.7451	−1.83802	−0.919009	+	0.394236i	$0.871009\pi$
$84$	−19.5569	−2.13383
$85$	−3.92077	−0.425267
$86$	7.97715	0.860199
$87$	−28.3354	−3.03788
$88$	0	0
$89$	15.9007	1.68547	0.842735	−	0.538328i	$-0.180944\pi$
$89$	15.9007	1.68547	0.842735	+	0.538328i	$0.180944\pi$
$90$	35.8860	3.78272
$91$	4.13782	0.433761
$92$	−1.38835	−0.144745
$93$	8.20958	0.851294
$94$	0.0231992	0.00239281
$95$	−12.2517	−1.25700
$96$	48.4712	4.94707
$97$	7.42771	0.754170	0.377085	−	0.926179i	$-0.376927\pi$
$97$	7.42771	0.754170	0.377085	+	0.926179i	$0.376927\pi$
$98$	14.4835	1.46305
$99$	0	0
$100$	−0.118035	−0.0118035
$101$	10.7510	1.06976	0.534882	−	0.844927i	$-0.320356\pi$
$101$	10.7510	1.06976	0.534882	+	0.844927i	$0.320356\pi$
$102$	14.1216	1.39824
$103$	8.93863	0.880750	0.440375	−	0.897814i	$-0.354846\pi$
$103$	8.93863	0.880750	0.440375	+	0.897814i	$0.354846\pi$
$104$	−27.8256	−2.72852
$105$	8.44345	0.823997
$106$	30.2971	2.94271
$107$	11.4018	1.10226	0.551128	−	0.834421i	$-0.314198\pi$
$107$	11.4018	1.10226	0.551128	+	0.834421i	$0.314198\pi$
$108$	−46.6572	−4.48959
$109$	11.6300	1.11395	0.556977	−	0.830528i	$-0.311961\pi$
$109$	11.6300	1.11395	0.556977	+	0.830528i	$0.311961\pi$
$110$	0	0
$111$	−4.01375	−0.380968
$112$	15.5945	1.47355
$113$	−2.25523	−0.212154	−0.106077	−	0.994358i	$-0.533829\pi$
$113$	−2.25523	−0.212154	−0.106077	+	0.994358i	$0.533829\pi$
$114$	44.1274	4.13291
$115$	0.599402	0.0558946
$116$	48.7840	4.52948
$117$	19.7160	1.82274
$118$	−15.1904	−1.39839
$119$	2.21609	0.203149
$120$	−56.7797	−5.18325
$121$	0	0
$122$	−15.8218	−1.43244
$123$	6.96116	0.627666
$124$	−14.1341	−1.26928
$125$	11.2057	1.00227
$126$	−20.2834	−1.80699
$127$	−14.7031	−1.30469	−0.652347	−	0.757921i	$-0.726215\pi$
$127$	−14.7031	−1.30469	−0.652347	+	0.757921i	$0.726215\pi$
$128$	−17.2331	−1.52320
$129$	8.94314	0.787400
$130$	19.5991	1.71895
$131$	−1.46120	−0.127666	−0.0638328	−	0.997961i	$-0.520332\pi$
$131$	−1.46120	−0.127666	−0.0638328	+	0.997961i	$0.520332\pi$
$132$	0	0
$133$	6.92490	0.600465
$134$	−11.1560	−0.963735
$135$	20.1437	1.73369
$136$	−14.9025	−1.27788
$137$	21.7437	1.85769	0.928843	−	0.370473i	$-0.120804\pi$
$137$	21.7437	1.85769	0.928843	+	0.370473i	$0.120804\pi$
$138$	−2.15889	−0.183777
$139$	−17.6447	−1.49660	−0.748300	−	0.663360i	$-0.769130\pi$
$139$	−17.6447	−1.49660	−0.748300	+	0.663360i	$0.769130\pi$
$140$	−14.5368	−1.22858
$141$	0.0260085	0.00219031
$142$	31.0572	2.60626
$143$	0	0
$144$	74.3052	6.19210
$145$	−21.0619	−1.74910
$146$	15.7170	1.30074
$147$	16.2373	1.33923
$148$	6.91032	0.568025
$149$	9.71319	0.795736	0.397868	−	0.917443i	$-0.369750\pi$
$149$	9.71319	0.795736	0.397868	+	0.917443i	$0.369750\pi$
$150$	−0.183545	−0.0149864
$151$	−9.22164	−0.750447	−0.375223	−	0.926934i	$-0.622434\pi$
$151$	−9.22164	−0.750447	−0.375223	+	0.926934i	$0.622434\pi$
$152$	−46.5678	−3.77715
$153$	10.5593	0.853668
$154$	0	0
$155$	6.10224	0.490144
$156$	−50.8929	−4.07469
$157$	−9.93077	−0.792561	−0.396281	−	0.918129i	$-0.629699\pi$
$157$	−9.93077	−0.792561	−0.396281	+	0.918129i	$0.629699\pi$
$158$	−3.88502	−0.309076
$159$	33.9659	2.69367
$160$	36.0290	2.84834
$161$	−0.338793	−0.0267007
$162$	−24.2958	−1.90886
$163$	10.6465	0.833899	0.416949	−	0.908930i	$-0.363099\pi$
$163$	10.6465	0.833899	0.416949	+	0.908930i	$0.363099\pi$
$164$	−11.9848	−0.935852
$165$	0	0
$166$	44.8300	3.47949
$167$	20.8110	1.61041	0.805203	−	0.593000i	$-0.202056\pi$
$167$	20.8110	1.61041	0.805203	+	0.593000i	$0.202056\pi$
$168$	32.0929	2.47602
$169$	−2.23215	−0.171704
$170$	10.4967	0.805057
$171$	32.9959	2.52326
$172$	−15.3971	−1.17402
$173$	12.4766	0.948575	0.474287	−	0.880370i	$-0.342706\pi$
$173$	12.4766	0.948575	0.474287	+	0.880370i	$0.342706\pi$
$174$	75.8595	5.75089
$175$	−0.0288036	−0.00217735
$176$	0	0
$177$	−17.0298	−1.28004
$178$	−42.5693	−3.19070
$179$	10.1784	0.760769	0.380384	−	0.924829i	$-0.375792\pi$
$179$	10.1784	0.760769	0.380384	+	0.924829i	$0.375792\pi$
$180$	−69.2652	−5.16272
$181$	−13.8874	−1.03224	−0.516121	−	0.856515i	$-0.672625\pi$
$181$	−13.8874	−1.03224	−0.516121	+	0.856515i	$0.672625\pi$
$182$	−11.0778	−0.821138
$183$	−17.7378	−1.31121
$184$	2.27828	0.167957
$185$	−2.98345	−0.219347
$186$	−21.9787	−1.61155
$187$	0	0
$188$	−0.0447778	−0.00326576
$189$	−11.3856	−0.828180
$190$	32.8002	2.37958
$191$	−11.1244	−0.804935	−0.402468	−	0.915434i	$-0.631847\pi$
$191$	−11.1244	−0.804935	−0.402468	+	0.915434i	$0.631847\pi$
$192$	−55.5303	−4.00755
$193$	13.6678	0.983832	0.491916	−	0.870643i	$-0.336297\pi$
$193$	13.6678	0.983832	0.491916	+	0.870643i	$0.336297\pi$
$194$	−19.8854	−1.42769
$195$	21.9724	1.57348
$196$	−27.9552	−1.99680
$197$	−21.9259	−1.56215	−0.781077	−	0.624435i	$-0.785329\pi$
$197$	−21.9259	−1.56215	−0.781077	+	0.624435i	$0.785329\pi$
$198$	0	0
$199$	−4.71436	−0.334192	−0.167096	−	0.985941i	$-0.553439\pi$
$199$	−4.71436	−0.334192	−0.167096	+	0.985941i	$0.553439\pi$
$200$	0.193695	0.0136963
$201$	−12.5070	−0.882174
$202$	−28.7825	−2.02513
$203$	11.9046	0.835539
$204$	−27.2567	−1.90835
$205$	5.17428	0.361387
$206$	−23.9305	−1.66731
$207$	−1.61429	−0.112201
$208$	40.5817	2.81383
$209$	0	0
$210$	−22.6048	−1.55988
$211$	16.9054	1.16382	0.581908	−	0.813255i	$-0.302307\pi$
$211$	16.9054	1.16382	0.581908	+	0.813255i	$0.302307\pi$
$212$	−58.4777	−4.01627
$213$	34.8181	2.38569
$214$	−30.5249	−2.08664
$215$	6.64750	0.453356
$216$	76.5646	5.20956
$217$	−3.44910	−0.234140
$218$	−31.1358	−2.10879
$219$	17.6202	1.19066
$220$	0	0
$221$	5.76693	0.387926
$222$	10.7456	0.721197
$223$	−0.659249	−0.0441466	−0.0220733	−	0.999756i	$-0.507027\pi$
$223$	−0.659249	−0.0441466	−0.0220733	+	0.999756i	$0.507027\pi$
$224$	−20.3642	−1.36064
$225$	−0.137244	−0.00914960
$226$	6.03769	0.401621
$227$	−0.746356	−0.0495374	−0.0247687	−	0.999693i	$-0.507885\pi$
$227$	−0.746356	−0.0495374	−0.0247687	+	0.999693i	$0.507885\pi$
$228$	−85.1723	−5.64068
$229$	−0.289348	−0.0191207	−0.00956033	−	0.999954i	$-0.503043\pi$
$229$	−0.289348	−0.0191207	−0.00956033	+	0.999954i	$0.503043\pi$
$230$	−1.60472	−0.105812
$231$	0	0
$232$	−80.0548	−5.25586
$233$	−5.68380	−0.372358	−0.186179	−	0.982516i	$-0.559610\pi$
$233$	−5.68380	−0.372358	−0.186179	+	0.982516i	$0.559610\pi$
$234$	−52.7836	−3.45057
$235$	0.0193323	0.00126110
$236$	29.3196	1.90854
$237$	−4.35547	−0.282918
$238$	−5.93291	−0.384573
$239$	−2.21840	−0.143496	−0.0717482	−	0.997423i	$-0.522858\pi$
$239$	−2.21840	−0.143496	−0.0717482	+	0.997423i	$0.522858\pi$
$240$	82.8091	5.34531
$241$	20.0521	1.29167	0.645835	−	0.763477i	$-0.276509\pi$
$241$	20.0521	1.29167	0.645835	+	0.763477i	$0.276509\pi$
$242$	0	0
$243$	−0.150297	−0.00964157
$244$	30.5384	1.95502
$245$	12.0693	0.771081
$246$	−18.6364	−1.18821
$247$	18.0207	1.14663
$248$	23.1942	1.47283
$249$	50.2587	3.18502
$250$	−29.9999	−1.89736
$251$	−16.4219	−1.03654	−0.518272	−	0.855216i	$-0.673425\pi$
$251$	−16.4219	−1.03654	−0.518272	+	0.855216i	$0.673425\pi$
$252$	39.1500	2.46622
$253$	0	0
$254$	39.3632	2.46987
$255$	11.7678	0.736925
$256$	9.13320	0.570825
$257$	−12.4260	−0.775114	−0.387557	−	0.921846i	$-0.626681\pi$
$257$	−12.4260	−0.775114	−0.387557	+	0.921846i	$0.626681\pi$
$258$	−23.9425	−1.49060
$259$	1.68630	0.104782
$260$	−37.8290	−2.34606
$261$	56.7233	3.51109
$262$	3.91192	0.241679
$263$	−12.3659	−0.762514	−0.381257	−	0.924469i	$-0.624509\pi$
$263$	−12.3659	−0.762514	−0.381257	+	0.924469i	$0.624509\pi$
$264$	0	0
$265$	25.2471	1.55092
$266$	−18.5393	−1.13672
$267$	−47.7242	−2.92067
$268$	21.5328	1.31532
$269$	24.6542	1.50320	0.751598	−	0.659622i	$-0.229283\pi$
$269$	24.6542	1.50320	0.751598	+	0.659622i	$0.229283\pi$
$270$	−53.9286	−3.28199
$271$	−7.33642	−0.445656	−0.222828	−	0.974858i	$-0.571529\pi$
$271$	−7.33642	−0.445656	−0.222828	+	0.974858i	$0.571529\pi$
$272$	21.7343	1.31784
$273$	−12.4192	−0.751645
$274$	−58.2121	−3.51672
$275$	0	0
$276$	4.16697	0.250822
$277$	21.9006	1.31588	0.657940	−	0.753071i	$-0.271428\pi$
$277$	21.9006	1.31588	0.657940	+	0.753071i	$0.271428\pi$
$278$	47.2382	2.83316
$279$	−16.4344	−0.983900
$280$	23.8549	1.42560
$281$	−19.5320	−1.16518	−0.582591	−	0.812766i	$-0.697961\pi$
$281$	−19.5320	−1.16518	−0.582591	+	0.812766i	$0.697961\pi$
$282$	−0.0696298	−0.00414639
$283$	7.25263	0.431124	0.215562	−	0.976490i	$-0.430842\pi$
$283$	7.25263	0.431124	0.215562	+	0.976490i	$0.430842\pi$
$284$	−59.9449	−3.55708
$285$	36.7722	2.17820
$286$	0	0
$287$	−2.92460	−0.172634
$288$	−97.0321	−5.71767
$289$	−13.9114	−0.818318
$290$	56.3869	3.31115
$291$	−22.2934	−1.30686
$292$	−30.3360	−1.77528
$293$	−5.09124	−0.297433	−0.148717	−	0.988880i	$-0.547514\pi$
$293$	−5.09124	−0.297433	−0.148717	+	0.988880i	$0.547514\pi$
$294$	−43.4705	−2.53525
$295$	−12.6584	−0.737000
$296$	−11.3399	−0.659116
$297$	0	0
$298$	−26.0041	−1.50638
$299$	−0.881642	−0.0509867
$300$	0.354268	0.0204537
$301$	−3.75729	−0.216567
$302$	24.6881	1.42064
$303$	−32.2679	−1.85374
$304$	67.9159	3.89525
$305$	−13.1846	−0.754949
$306$	−28.2693	−1.61605
$307$	14.6005	0.833294	0.416647	−	0.909068i	$-0.363205\pi$
$307$	14.6005	0.833294	0.416647	+	0.909068i	$0.363205\pi$
$308$	0	0
$309$	−26.8283	−1.52621
$310$	−16.3369	−0.927874
$311$	−1.55298	−0.0880615	−0.0440308	−	0.999030i	$-0.514020\pi$
$311$	−1.55298	−0.0880615	−0.0440308	+	0.999030i	$0.514020\pi$
$312$	83.5154	4.72813
$313$	−15.1019	−0.853612	−0.426806	−	0.904343i	$-0.640361\pi$
$313$	−15.1019	−0.853612	−0.426806	+	0.904343i	$0.640361\pi$
$314$	26.5866	1.50037
$315$	−16.9025	−0.952350
$316$	7.49865	0.421832
$317$	6.18045	0.347129	0.173564	−	0.984823i	$-0.444472\pi$
$317$	6.18045	0.347129	0.173564	+	0.984823i	$0.444472\pi$
$318$	−90.9333	−5.09929
$319$	0	0
$320$	−41.2761	−2.30740
$321$	−34.2213	−1.91005
$322$	0.907016	0.0505460
$323$	9.65132	0.537014
$324$	46.8944	2.60524
$325$	−0.0749555	−0.00415778
$326$	−28.5028	−1.57862
$327$	−34.9062	−1.93032
$328$	19.6670	1.08593
$329$	−0.0109270	−0.000602424 0
$330$	0	0
$331$	−13.7755	−0.757171	−0.378586	−	0.925566i	$-0.623589\pi$
$331$	−13.7755	−0.757171	−0.378586	+	0.925566i	$0.623589\pi$
$332$	−86.5285	−4.74887
$333$	8.03493	0.440311
$334$	−55.7152	−3.04860
$335$	−9.29652	−0.507923
$336$	−46.8053	−2.55344
$337$	11.6123	0.632564	0.316282	−	0.948665i	$-0.397565\pi$
$337$	11.6123	0.632564	0.316282	+	0.948665i	$0.397565\pi$
$338$	5.97590	0.325046
$339$	6.76882	0.367632
$340$	−20.2601	−1.09876
$341$	0	0
$342$	−88.3366	−4.77669
$343$	−15.6486	−0.844947
$344$	25.2667	1.36229
$345$	−1.79904	−0.0968571
$346$	−33.4022	−1.79571
$347$	13.3172	0.714903	0.357451	−	0.933932i	$-0.383646\pi$
$347$	13.3172	0.714903	0.357451	+	0.933932i	$0.383646\pi$
$348$	−146.420	−7.84893
$349$	15.9102	0.851653	0.425827	−	0.904805i	$-0.359983\pi$
$349$	15.9102	0.851653	0.425827	+	0.904805i	$0.359983\pi$
$350$	0.0771128	0.00412185
$351$	−29.6287	−1.58146
$352$	0	0
$353$	2.70847	0.144157	0.0720787	−	0.997399i	$-0.477037\pi$
$353$	2.70847	0.144157	0.0720787	+	0.997399i	$0.477037\pi$
$354$	45.5922	2.42320
$355$	25.8805	1.37360
$356$	82.1649	4.35473
$357$	−6.65135	−0.352027
$358$	−27.2495	−1.44018
$359$	3.90296	0.205990	0.102995	−	0.994682i	$-0.467157\pi$
$359$	3.90296	0.205990	0.102995	+	0.994682i	$0.467157\pi$
$360$	113.664	5.99064
$361$	11.1587	0.587300
$362$	37.1793	1.95410
$363$	0	0
$364$	21.3817	1.12070
$365$	13.0972	0.685540
$366$	47.4875	2.48221
$367$	11.3599	0.592984	0.296492	−	0.955035i	$-0.404183\pi$
$367$	11.3599	0.592984	0.296492	+	0.955035i	$0.404183\pi$
$368$	−3.32272	−0.173209
$369$	−13.9352	−0.725438
$370$	7.98728	0.415239
$371$	−14.2701	−0.740868
$372$	42.4220	2.19948
$373$	15.3465	0.794610	0.397305	−	0.917687i	$-0.369945\pi$
$373$	15.3465	0.794610	0.397305	+	0.917687i	$0.369945\pi$
$374$	0	0
$375$	−33.6328	−1.73679
$376$	0.0734806	0.00378947
$377$	30.9793	1.59552
$378$	30.4814	1.56780
$379$	−28.7987	−1.47929	−0.739644	−	0.672998i	$-0.765006\pi$
$379$	−28.7987	−1.47929	−0.739644	+	0.672998i	$0.765006\pi$
$380$	−63.3092	−3.24770
$381$	44.1299	2.26084
$382$	29.7823	1.52379
$383$	16.3952	0.837758	0.418879	−	0.908042i	$-0.362423\pi$
$383$	16.3952	0.837758	0.418879	+	0.908042i	$0.362423\pi$
$384$	51.7231	2.63948
$385$	0	0
$386$	−36.5915	−1.86246
$387$	−17.9028	−0.910053
$388$	38.3818	1.94854
$389$	−15.6471	−0.793337	−0.396669	−	0.917962i	$-0.629834\pi$
$389$	−15.6471	−0.793337	−0.396669	+	0.917962i	$0.629834\pi$
$390$	−58.8244	−2.97869
$391$	−0.472181	−0.0238792
$392$	45.8746	2.31702
$393$	4.38563	0.221226
$394$	58.6999	2.95726
$395$	−3.23746	−0.162894
$396$	0	0
$397$	27.9484	1.40269	0.701346	−	0.712821i	$-0.252583\pi$
$397$	27.9484	1.40269	0.701346	+	0.712821i	$0.252583\pi$
$398$	12.6213	0.632647
$399$	−20.7843	−1.04052
$400$	−0.282491	−0.0141245
$401$	−14.7680	−0.737481	−0.368740	−	0.929532i	$-0.620211\pi$
$401$	−14.7680	−0.737481	−0.368740	+	0.929532i	$0.620211\pi$
$402$	33.4836	1.67001
$403$	−8.97560	−0.447106
$404$	55.5544	2.76394
$405$	−20.2461	−1.00604
$406$	−31.8709	−1.58173
$407$	0	0
$408$	44.7283	2.21438
$409$	27.8962	1.37938	0.689688	−	0.724106i	$-0.257748\pi$
$409$	27.8962	1.37938	0.689688	+	0.724106i	$0.257748\pi$
$410$	−13.8526	−0.684129
$411$	−65.2612	−3.21910
$412$	46.1893	2.27558
$413$	7.15476	0.352063
$414$	4.32177	0.212404
$415$	37.3577	1.83382
$416$	−52.9939	−2.59824
$417$	52.9585	2.59339
$418$	0	0
$419$	21.5000	1.05034	0.525171	−	0.850997i	$-0.324001\pi$
$419$	21.5000	1.05034	0.525171	+	0.850997i	$0.324001\pi$
$420$	43.6305	2.12895
$421$	−5.11311	−0.249198	−0.124599	−	0.992207i	$-0.539764\pi$
$421$	−5.11311	−0.249198	−0.124599	+	0.992207i	$0.539764\pi$
$422$	−45.2590	−2.20318
$423$	−0.0520651	−0.00253149
$424$	95.9622	4.66034
$425$	−0.0401439	−0.00194727
$426$	−93.2147	−4.51627
$427$	7.45219	0.360637
$428$	58.9175	2.84788
$429$	0	0
$430$	−17.7967	−0.858231
$431$	−5.57991	−0.268775	−0.134387	−	0.990929i	$-0.542907\pi$
$431$	−5.57991	−0.268775	−0.134387	+	0.990929i	$0.542907\pi$
$432$	−111.664	−5.37244
$433$	5.82620	0.279990	0.139995	−	0.990152i	$-0.455291\pi$
$433$	5.82620	0.279990	0.139995	+	0.990152i	$0.455291\pi$
$434$	9.23392	0.443242
$435$	63.2151	3.03093
$436$	60.0967	2.87811
$437$	−1.47548	−0.0705819
$438$	−47.1727	−2.25400
$439$	−13.9593	−0.666241	−0.333121	−	0.942884i	$-0.608102\pi$
$439$	−13.9593	−0.666241	−0.333121	+	0.942884i	$0.608102\pi$
$440$	0	0
$441$	−32.5047	−1.54784
$442$	−15.4392	−0.734368
$443$	22.6223	1.07482	0.537410	−	0.843321i	$-0.319403\pi$
$443$	22.6223	1.07482	0.537410	+	0.843321i	$0.319403\pi$
$444$	−20.7405	−0.984303
$445$	−35.4737	−1.68162
$446$	1.76494	0.0835723
$447$	−29.1531	−1.37889
$448$	23.3300	1.10224
$449$	40.0403	1.88962	0.944810	−	0.327619i	$-0.106246\pi$
$449$	40.0403	1.88962	0.944810	+	0.327619i	$0.106246\pi$
$450$	0.367429	0.0173208
$451$	0	0
$452$	−11.6536	−0.548140
$453$	27.6777	1.30041
$454$	1.99814	0.0937774
$455$	−9.23129	−0.432769
$456$	139.768	6.54524
$457$	16.7777	0.784827	0.392414	−	0.919789i	$-0.371640\pi$
$457$	16.7777	0.784827	0.392414	+	0.919789i	$0.371640\pi$
$458$	0.774641	0.0361966
$459$	−15.8682	−0.740666
$460$	3.09734	0.144414
$461$	29.6735	1.38203	0.691015	−	0.722840i	$-0.257164\pi$
$461$	29.6735	1.38203	0.691015	+	0.722840i	$0.257164\pi$
$462$	0	0
$463$	39.4266	1.83231	0.916155	−	0.400824i	$-0.131276\pi$
$463$	39.4266	1.83231	0.916155	+	0.400824i	$0.131276\pi$
$464$	116.754	5.42018
$465$	−18.3152	−0.849347
$466$	15.2166	0.704897
$467$	11.9249	0.551818	0.275909	−	0.961184i	$-0.411021\pi$
$467$	11.9249	0.551818	0.275909	+	0.961184i	$0.411021\pi$
$468$	101.880	4.70940
$469$	5.25457	0.242633
$470$	−0.0517564	−0.00238734
$471$	29.8061	1.37339
$472$	−48.1136	−2.21461
$473$	0	0
$474$	11.6605	0.535582
$475$	−0.125443	−0.00575571
$476$	11.4514	0.524873
$477$	−67.9946	−3.11326
$478$	5.93909	0.271648
$479$	−23.7901	−1.08700	−0.543499	−	0.839410i	$-0.682901\pi$
$479$	−23.7901	−1.08700	−0.543499	+	0.839410i	$0.682901\pi$
$480$	−108.137	−4.93575
$481$	4.38826	0.200087
$482$	−53.6834	−2.44521
$483$	1.01685	0.0462683
$484$	0	0
$485$	−16.5709	−0.752445
$486$	0.402375	0.0182521
$487$	−37.9740	−1.72077	−0.860384	−	0.509646i	$-0.829776\pi$
$487$	−37.9740	−1.72077	−0.860384	+	0.509646i	$0.829776\pi$
$488$	−50.1137	−2.26854
$489$	−31.9543	−1.44502
$490$	−32.3119	−1.45970
$491$	1.58398	0.0714842	0.0357421	−	0.999361i	$-0.488621\pi$
$491$	1.58398	0.0714842	0.0357421	+	0.999361i	$0.488621\pi$
$492$	35.9709	1.62169
$493$	16.5916	0.747248
$494$	−48.2448	−2.17064
$495$	0	0
$496$	−33.8271	−1.51888
$497$	−14.6281	−0.656162
$498$	−134.552	−6.02944
$499$	4.42687	0.198174	0.0990869	−	0.995079i	$-0.468408\pi$
$499$	4.42687	0.198174	0.0990869	+	0.995079i	$0.468408\pi$
$500$	57.9042	2.58956
$501$	−62.4620	−2.79060
$502$	43.9648	1.96224
$503$	10.8352	0.483117	0.241559	−	0.970386i	$-0.422341\pi$
$503$	10.8352	0.483117	0.241559	+	0.970386i	$0.422341\pi$
$504$	−64.2452	−2.86171
$505$	−23.9850	−1.06732
$506$	0	0
$507$	6.69955	0.297538
$508$	−75.9767	−3.37092
$509$	30.4974	1.35177	0.675886	−	0.737006i	$-0.263761\pi$
$509$	30.4974	1.35177	0.675886	+	0.737006i	$0.263761\pi$
$510$	−31.5046	−1.39505
$511$	−7.40279	−0.327480
$512$	10.0147	0.442593
$513$	−49.5855	−2.18925
$514$	33.2669	1.46734
$515$	−19.9417	−0.878736
$516$	46.2126	2.03440
$517$	0	0
$518$	−4.51456	−0.198358
$519$	−37.4470	−1.64374
$520$	62.0776	2.72228
$521$	−14.9423	−0.654635	−0.327318	−	0.944914i	$-0.606145\pi$
$521$	−14.9423	−0.654635	−0.327318	+	0.944914i	$0.606145\pi$
$522$	−151.859	−6.64671
$523$	25.2707	1.10501	0.552504	−	0.833510i	$-0.313672\pi$
$523$	25.2707	1.10501	0.552504	+	0.833510i	$0.313672\pi$
$524$	−7.55057	−0.329848
$525$	0.0864507	0.00377302
$526$	33.1059	1.44349
$527$	−4.80706	−0.209399
$528$	0	0
$529$	−22.9278	−0.996861
$530$	−67.5914	−2.93598
$531$	34.0912	1.47943
$532$	35.7836	1.55141
$533$	−7.61068	−0.329655
$534$	127.767	5.52902
$535$	−25.4369	−1.09973
$536$	−35.3354	−1.52626
$537$	−30.5493	−1.31830
$538$	−66.0042	−2.84564
$539$	0	0
$540$	104.090	4.47932
$541$	31.6017	1.35866	0.679332	−	0.733831i	$-0.262270\pi$
$541$	31.6017	1.35866	0.679332	+	0.733831i	$0.262270\pi$
$542$	19.6410	0.843654
$543$	41.6815	1.78872
$544$	−28.3819	−1.21686
$545$	−25.9460	−1.11141
$546$	33.2486	1.42291
$547$	−36.4552	−1.55871	−0.779355	−	0.626583i	$-0.784453\pi$
$547$	−36.4552	−1.55871	−0.779355	+	0.626583i	$0.784453\pi$
$548$	112.358	4.79968
$549$	35.5084	1.51546
$550$	0	0
$551$	51.8458	2.20871
$552$	−6.83801	−0.291045
$553$	1.82987	0.0778140
$554$	−58.6322	−2.49104
$555$	8.95449	0.380097
$556$	−91.1766	−3.86675
$557$	17.7654	0.752746	0.376373	−	0.926468i	$-0.377171\pi$
$557$	17.7654	0.752746	0.376373	+	0.926468i	$0.377171\pi$
$558$	43.9980	1.86258
$559$	−9.77760	−0.413548
$560$	−34.7907	−1.47018
$561$	0	0
$562$	52.2910	2.20576
$563$	24.8667	1.04801	0.524004	−	0.851716i	$-0.324438\pi$
$563$	24.8667	1.04801	0.524004	+	0.851716i	$0.324438\pi$
$564$	0.134396	0.00565908
$565$	5.03131	0.211669
$566$	−19.4167	−0.816145
$567$	11.4435	0.480580
$568$	98.3699	4.12751
$569$	−29.6252	−1.24195	−0.620976	−	0.783830i	$-0.713263\pi$
$569$	−29.6252	−1.24195	−0.620976	+	0.783830i	$0.713263\pi$
$570$	−98.4463	−4.12346
$571$	−8.86638	−0.371047	−0.185523	−	0.982640i	$-0.559398\pi$
$571$	−8.86638	−0.371047	−0.185523	+	0.982640i	$0.559398\pi$
$572$	0	0
$573$	33.3887	1.39483
$574$	7.82972	0.326806
$575$	0.00613715	0.000255937 0
$576$	111.163	4.63181
$577$	16.2789	0.677701	0.338851	−	0.940840i	$-0.389962\pi$
$577$	16.2789	0.677701	0.338851	+	0.940840i	$0.389962\pi$
$578$	37.2436	1.54913
$579$	−41.0225	−1.70484
$580$	−108.835	−4.51913
$581$	−21.1152	−0.876008
$582$	59.6839	2.47398
$583$	0	0
$584$	49.7815	2.05997
$585$	−43.9855	−1.81858
$586$	13.6302	0.563060
$587$	−21.0784	−0.869997	−0.434998	−	0.900431i	$-0.643251\pi$
$587$	−21.0784	−0.869997	−0.434998	+	0.900431i	$0.643251\pi$
$588$	83.9044	3.46016
$589$	−15.0212	−0.618938
$590$	33.8890	1.39519
$591$	65.8081	2.70698
$592$	16.5384	0.679724
$593$	26.4627	1.08669	0.543346	−	0.839509i	$-0.317157\pi$
$593$	26.4627	1.08669	0.543346	+	0.839509i	$0.317157\pi$
$594$	0	0
$595$	−4.94400	−0.202684
$596$	50.1917	2.05593
$597$	14.1496	0.579106
$598$	2.36033	0.0965210
$599$	−35.0006	−1.43009	−0.715044	−	0.699080i	$-0.753593\pi$
$599$	−35.0006	−1.43009	−0.715044	+	0.699080i	$0.753593\pi$
$600$	−0.581355	−0.0237337
$601$	39.6972	1.61928	0.809642	−	0.586924i	$-0.199661\pi$
$601$	39.6972	1.61928	0.809642	+	0.586924i	$0.199661\pi$
$602$	10.0590	0.409974
$603$	25.0371	1.01959
$604$	−47.6517	−1.93892
$605$	0	0
$606$	86.3875	3.50925
$607$	21.8677	0.887583	0.443792	−	0.896130i	$-0.353633\pi$
$607$	21.8677	0.887583	0.443792	+	0.896130i	$0.353633\pi$
$608$	−88.6885	−3.59680
$609$	−35.7303	−1.44787
$610$	35.2978	1.42917
$611$	−0.0284353	−0.00115037
$612$	54.5638	2.20561
$613$	−22.4957	−0.908592	−0.454296	−	0.890851i	$-0.650109\pi$
$613$	−22.4957	−0.908592	−0.454296	+	0.890851i	$0.650109\pi$
$614$	−39.0884	−1.57748
$615$	−15.5300	−0.626231
$616$	0	0
$617$	−6.39149	−0.257312	−0.128656	−	0.991689i	$-0.541066\pi$
$617$	−6.39149	−0.257312	−0.128656	+	0.991689i	$0.541066\pi$
$618$	71.8246	2.88921
$619$	6.55317	0.263394	0.131697	−	0.991290i	$-0.457957\pi$
$619$	6.55317	0.263394	0.131697	+	0.991290i	$0.457957\pi$
$620$	31.5326	1.26638
$621$	2.42592	0.0973488
$622$	4.15764	0.166706
$623$	20.0504	0.803303
$624$	−121.801	−4.87596
$625$	−24.8853	−0.995411
$626$	40.4308	1.61594
$627$	0	0
$628$	−51.3160	−2.04773
$629$	2.35022	0.0937094
$630$	45.2514	1.80286
$631$	−27.7913	−1.10636	−0.553178	−	0.833063i	$-0.686585\pi$
$631$	−27.7913	−1.10636	−0.553178	+	0.833063i	$0.686585\pi$
$632$	−12.3053	−0.489479
$633$	−50.7397	−2.01672
$634$	−16.5463	−0.657136
$635$	32.8020	1.30171
$636$	175.514	6.95960
$637$	−17.7524	−0.703375
$638$	0	0
$639$	−69.7006	−2.75731
$640$	38.4462	1.51972
$641$	40.6327	1.60490	0.802448	−	0.596722i	$-0.203530\pi$
$641$	40.6327	1.60490	0.802448	+	0.596722i	$0.203530\pi$
$642$	91.6171	3.61584
$643$	35.1310	1.38543	0.692715	−	0.721211i	$-0.256414\pi$
$643$	35.1310	1.38543	0.692715	+	0.721211i	$0.256414\pi$
$644$	−1.75067	−0.0689862
$645$	−19.9517	−0.785599
$646$	−25.8385	−1.01660
$647$	−18.5830	−0.730574	−0.365287	−	0.930895i	$-0.619029\pi$
$647$	−18.5830	−0.730574	−0.365287	+	0.930895i	$0.619029\pi$
$648$	−76.9538	−3.02303
$649$	0	0
$650$	0.200671	0.00787095
$651$	10.3521	0.405731
$652$	55.0145	2.15453
$653$	25.8980	1.01347	0.506733	−	0.862103i	$-0.330853\pi$
$653$	25.8980	1.01347	0.506733	+	0.862103i	$0.330853\pi$
$654$	93.4508	3.65421
$655$	3.25987	0.127374
$656$	−28.6830	−1.11988
$657$	−35.2730	−1.37613
$658$	0.0292536	0.00114043
$659$	−0.729285	−0.0284089	−0.0142045	−	0.999899i	$-0.504522\pi$
$659$	−0.729285	−0.0284089	−0.0142045	+	0.999899i	$0.504522\pi$
$660$	0	0
$661$	6.00664	0.233631	0.116816	−	0.993154i	$-0.462731\pi$
$661$	6.00664	0.233631	0.116816	+	0.993154i	$0.462731\pi$
$662$	36.8798	1.43337
$663$	−17.3088	−0.672219
$664$	141.994	5.51042
$665$	−15.4491	−0.599092
$666$	−21.5111	−0.833537
$667$	−2.53650	−0.0982138
$668$	107.538	4.16079
$669$	1.97866	0.0764995
$670$	24.8886	0.961531
$671$	0	0
$672$	61.1210	2.35779
$673$	−21.5766	−0.831717	−0.415859	−	0.909429i	$-0.636519\pi$
$673$	−21.5766	−0.831717	−0.415859	+	0.909429i	$0.636519\pi$
$674$	−31.0885	−1.19748
$675$	0.206247	0.00793845
$676$	−11.5344	−0.443629
$677$	23.8776	0.917689	0.458845	−	0.888517i	$-0.348263\pi$
$677$	23.8776	0.917689	0.458845	+	0.888517i	$0.348263\pi$
$678$	−18.1214	−0.695950
$679$	9.36617	0.359441
$680$	33.2469	1.27496
$681$	2.24010	0.0858410
$682$	0	0
$683$	−16.5330	−0.632619	−0.316310	−	0.948656i	$-0.602444\pi$
$683$	−16.5330	−0.632619	−0.316310	+	0.948656i	$0.602444\pi$
$684$	170.502	6.51932
$685$	−48.5091	−1.85344
$686$	41.8945	1.59954
$687$	0.868446	0.0331333
$688$	−36.8496	−1.40488
$689$	−37.1351	−1.41474
$690$	4.81638	0.183357
$691$	−41.6632	−1.58494	−0.792472	−	0.609908i	$-0.791206\pi$
$691$	−41.6632	−1.58494	−0.792472	+	0.609908i	$0.791206\pi$
$692$	64.4711	2.45082
$693$	0	0
$694$	−35.6527	−1.35336
$695$	39.3644	1.49318
$696$	240.276	9.10762
$697$	−4.07605	−0.154391
$698$	−42.5947	−1.61223
$699$	17.0593	0.645242
$700$	−0.148839	−0.00562558
$701$	17.2441	0.651300	0.325650	−	0.945490i	$-0.394417\pi$
$701$	17.2441	0.651300	0.325650	+	0.945490i	$0.394417\pi$
$702$	79.3219	2.99381
$703$	7.34402	0.276985
$704$	0	0
$705$	−0.0580238	−0.00218530
$706$	−7.25111	−0.272899
$707$	13.5568	0.509854
$708$	−87.9995	−3.30722
$709$	44.0615	1.65477	0.827383	−	0.561638i	$-0.189829\pi$
$709$	44.0615	1.65477	0.827383	+	0.561638i	$0.189829\pi$
$710$	−69.2872	−2.60030
$711$	8.71901	0.326988
$712$	−134.833	−5.05308
$713$	0.734897	0.0275221
$714$	17.8070	0.666409
$715$	0	0
$716$	52.5956	1.96559
$717$	6.65828	0.248658
$718$	−10.4490	−0.389952
$719$	16.5269	0.616349	0.308174	−	0.951330i	$-0.400282\pi$
$719$	16.5269	0.616349	0.308174	+	0.951330i	$0.400282\pi$
$720$	−165.772	−6.17794
$721$	11.2714	0.419769
$722$	−29.8740	−1.11180
$723$	−60.1842	−2.23827
$724$	−71.7615	−2.66699
$725$	−0.215649	−0.00800899
$726$	0	0
$727$	−7.93153	−0.294164	−0.147082	−	0.989124i	$-0.546988\pi$
$727$	−7.93153	−0.294164	−0.147082	+	0.989124i	$0.546988\pi$
$728$	−35.0874	−1.30043
$729$	−26.7741	−0.991635
$730$	−35.0638	−1.29777
$731$	−5.23659	−0.193682
$732$	−91.6577	−3.38777
$733$	24.3955	0.901068	0.450534	−	0.892759i	$-0.351234\pi$
$733$	24.3955	0.901068	0.450534	+	0.892759i	$0.351234\pi$
$734$	−30.4128	−1.12256
$735$	−36.2247	−1.33617
$736$	4.33899	0.159937
$737$	0	0
$738$	37.3073	1.37330
$739$	−42.5226	−1.56422	−0.782110	−	0.623140i	$-0.785857\pi$
$739$	−42.5226	−1.56422	−0.782110	+	0.623140i	$0.785857\pi$
$740$	−15.4166	−0.566726
$741$	−54.0870	−1.98694
$742$	38.2039	1.40251
$743$	−30.5343	−1.12019	−0.560097	−	0.828427i	$-0.689236\pi$
$743$	−30.5343	−1.12019	−0.560097	+	0.828427i	$0.689236\pi$
$744$	−69.6147	−2.55220
$745$	−21.6697	−0.793916
$746$	−41.0855	−1.50425
$747$	−100.610	−3.68114
$748$	0	0
$749$	14.3774	0.525340
$750$	90.0415	3.28785
$751$	12.6486	0.461554	0.230777	−	0.973007i	$-0.425873\pi$
$751$	12.6486	0.461554	0.230777	+	0.973007i	$0.425873\pi$
$752$	−0.107166	−0.00390795
$753$	49.2886	1.79618
$754$	−82.9377	−3.02041
$755$	20.5731	0.748731
$756$	−58.8336	−2.13976
$757$	−12.6887	−0.461178	−0.230589	−	0.973051i	$-0.574065\pi$
$757$	−12.6887	−0.461178	−0.230589	+	0.973051i	$0.574065\pi$
$758$	77.0997	2.80039
$759$	0	0
$760$	103.891	3.76851
$761$	−5.66953	−0.205520	−0.102760	−	0.994706i	$-0.532767\pi$
$761$	−5.66953	−0.205520	−0.102760	+	0.994706i	$0.532767\pi$
$762$	−118.144	−4.27991
$763$	14.6652	0.530915
$764$	−57.4841	−2.07970
$765$	−23.5573	−0.851716
$766$	−43.8933	−1.58593
$767$	18.6188	0.672287
$768$	−27.4123	−0.989156
$769$	−13.1461	−0.474060	−0.237030	−	0.971502i	$-0.576174\pi$
$769$	−13.1461	−0.474060	−0.237030	+	0.971502i	$0.576174\pi$
$770$	0	0
$771$	37.2953	1.34316
$772$	70.6268	2.54192
$773$	−38.8636	−1.39783	−0.698913	−	0.715206i	$-0.746333\pi$
$773$	−38.8636	−1.39783	−0.698913	+	0.715206i	$0.746333\pi$
$774$	47.9294	1.72279
$775$	0.0624796	0.00224433
$776$	−62.9846	−2.26102
$777$	−5.06124	−0.181571
$778$	41.8902	1.50184
$779$	−12.7369	−0.456348
$780$	113.540	4.06537
$781$	0	0
$782$	1.26412	0.0452049
$783$	−85.2425	−3.04632
$784$	−66.9049	−2.38946
$785$	22.1551	0.790749
$786$	−11.7412	−0.418794
$787$	43.4785	1.54984	0.774920	−	0.632060i	$-0.217790\pi$
$787$	43.4785	1.54984	0.774920	+	0.632060i	$0.217790\pi$
$788$	−113.299	−4.03612
$789$	37.1149	1.32132
$790$	8.66730	0.308369
$791$	−2.84379	−0.101114
$792$	0	0
$793$	19.3928	0.688659
$794$	−74.8234	−2.65538
$795$	−75.7763	−2.68751
$796$	−24.3609	−0.863449
$797$	10.2570	0.363322	0.181661	−	0.983361i	$-0.441853\pi$
$797$	10.2570	0.363322	0.181661	+	0.983361i	$0.441853\pi$
$798$	55.6437	1.96976
$799$	−0.0152291	−0.000538766 0
$800$	0.368893	0.0130423
$801$	95.5367	3.37562
$802$	39.5369	1.39610
$803$	0	0
$804$	−64.6282	−2.27926
$805$	0.755833	0.0266396
$806$	24.0294	0.846401
$807$	−73.9970	−2.60482
$808$	−91.1650	−3.20718
$809$	25.4275	0.893983	0.446991	−	0.894538i	$-0.352495\pi$
$809$	25.4275	0.893983	0.446991	+	0.894538i	$0.352495\pi$
$810$	54.2027	1.90449
$811$	39.8342	1.39877	0.699385	−	0.714746i	$-0.253457\pi$
$811$	39.8342	1.39877	0.699385	+	0.714746i	$0.253457\pi$
$812$	61.5155	2.15877
$813$	22.0194	0.772256
$814$	0	0
$815$	−23.7519	−0.831992
$816$	−65.2331	−2.28362
$817$	−16.3634	−0.572484
$818$	−74.6835	−2.61125
$819$	24.8614	0.868728
$820$	26.7374	0.933712
$821$	25.8678	0.902793	0.451397	−	0.892323i	$-0.350926\pi$
$821$	25.8678	0.902793	0.451397	+	0.892323i	$0.350926\pi$
$822$	174.717	6.09395
$823$	18.5724	0.647393	0.323697	−	0.946161i	$-0.395074\pi$
$823$	18.5724	0.647393	0.323697	+	0.946161i	$0.395074\pi$
$824$	−75.7968	−2.64051
$825$	0	0
$826$	−19.1547	−0.666477
$827$	−43.7131	−1.52005	−0.760027	−	0.649891i	$-0.774815\pi$
$827$	−43.7131	−1.52005	−0.760027	+	0.649891i	$0.774815\pi$
$828$	−8.34165	−0.289892
$829$	−19.9227	−0.691944	−0.345972	−	0.938245i	$-0.612451\pi$
$829$	−19.9227	−0.691944	−0.345972	+	0.938245i	$0.612451\pi$
$830$	−100.014	−3.47153
$831$	−65.7322	−2.28022
$832$	60.7117	2.10480
$833$	−9.50764	−0.329420
$834$	−141.780	−4.90945
$835$	−46.4285	−1.60672
$836$	0	0
$837$	24.6972	0.853659
$838$	−57.5596	−1.98836
$839$	32.7259	1.12982	0.564912	−	0.825151i	$-0.308910\pi$
$839$	32.7259	1.12982	0.564912	+	0.825151i	$0.308910\pi$
$840$	−71.5978	−2.47036
$841$	60.1282	2.07339
$842$	13.6888	0.471747
$843$	58.6231	2.01909
$844$	87.3565	3.00694
$845$	4.97983	0.171311
$846$	0.139389	0.00479228
$847$	0	0
$848$	−139.954	−4.80605
$849$	−21.7680	−0.747074
$850$	0.107473	0.00368630
$851$	−0.359299	−0.0123166
$852$	179.918	6.16389
$853$	31.5171	1.07913	0.539563	−	0.841945i	$-0.318589\pi$
$853$	31.5171	1.07913	0.539563	+	0.841945i	$0.318589\pi$
$854$	−19.9510	−0.682708
$855$	−73.6124	−2.51749
$856$	−96.6839	−3.30459
$857$	−21.9857	−0.751019	−0.375509	−	0.926819i	$-0.622532\pi$
$857$	−21.9857	−0.751019	−0.375509	+	0.926819i	$0.622532\pi$
$858$	0	0
$859$	16.0590	0.547926	0.273963	−	0.961740i	$-0.411665\pi$
$859$	16.0590	0.547926	0.273963	+	0.961740i	$0.411665\pi$
$860$	34.3502	1.17133
$861$	8.77786	0.299149
$862$	14.9385	0.508808
$863$	−11.9927	−0.408235	−0.204117	−	0.978946i	$-0.565432\pi$
$863$	−11.9927	−0.408235	−0.204117	+	0.978946i	$0.565432\pi$
$864$	145.817	4.96081
$865$	−27.8346	−0.946406
$866$	−15.5979	−0.530038
$867$	41.7535	1.41802
$868$	−17.8228	−0.604945
$869$	0	0
$870$	−169.239	−5.73774
$871$	13.6740	0.463325
$872$	−98.6189	−3.33966
$873$	44.6282	1.51043
$874$	3.95016	0.133616
$875$	14.1302	0.477687
$876$	91.0502	3.07630
$877$	−34.8780	−1.17775	−0.588873	−	0.808226i	$-0.700428\pi$
$877$	−34.8780	−1.17775	−0.588873	+	0.808226i	$0.700428\pi$
$878$	37.3718	1.26124
$879$	15.2808	0.515408
$880$	0	0
$881$	−14.1670	−0.477299	−0.238650	−	0.971106i	$-0.576705\pi$
$881$	−14.1670	−0.477299	−0.238650	+	0.971106i	$0.576705\pi$
$882$	87.0215	2.93017
$883$	−47.3872	−1.59471	−0.797353	−	0.603513i	$-0.793767\pi$
$883$	−47.3872	−1.59471	−0.797353	+	0.603513i	$0.793767\pi$
$884$	29.7999	1.00228
$885$	37.9928	1.27711
$886$	−60.5644	−2.03470
$887$	26.7805	0.899200	0.449600	−	0.893230i	$-0.351567\pi$
$887$	26.7805	0.899200	0.449600	+	0.893230i	$0.351567\pi$
$888$	34.0353	1.14215
$889$	−18.5403	−0.621822
$890$	94.9701	3.18341
$891$	0	0
$892$	−3.40659	−0.114061
$893$	−0.0475882	−0.00159248
$894$	78.0485	2.61033
$895$	−22.7075	−0.759029
$896$	−21.7305	−0.725964
$897$	2.64615	0.0883524
$898$	−107.196	−3.57717
$899$	−25.8230	−0.861245
$900$	−0.709191	−0.0236397
$901$	−19.8885	−0.662581
$902$	0	0
$903$	11.2771	0.375278
$904$	19.1236	0.636042
$905$	30.9822	1.02988
$906$	−74.0987	−2.46177
$907$	35.7684	1.18767	0.593836	−	0.804586i	$-0.297613\pi$
$907$	35.7684	1.18767	0.593836	+	0.804586i	$0.297613\pi$
$908$	−3.85670	−0.127989
$909$	64.5956	2.14250
$910$	24.7140	0.819260
$911$	20.6503	0.684175	0.342088	−	0.939668i	$-0.388866\pi$
$911$	20.6503	0.684175	0.342088	+	0.939668i	$0.388866\pi$
$912$	−203.842	−6.74989
$913$	0	0
$914$	−44.9172	−1.48573
$915$	39.5721	1.30821
$916$	−1.49517	−0.0494018
$917$	−1.84254	−0.0608460
$918$	42.4824	1.40213
$919$	−43.1025	−1.42182	−0.710911	−	0.703282i	$-0.751717\pi$
$919$	−43.1025	−1.42182	−0.710911	+	0.703282i	$0.751717\pi$
$920$	−5.08275	−0.167573
$921$	−43.8217	−1.44398
$922$	−79.4417	−2.61627
$923$	−38.0668	−1.25298
$924$	0	0
$925$	−0.0305469	−0.00100438
$926$	−105.553	−3.46868
$927$	53.7063	1.76395
$928$	−152.465	−5.00489
$929$	8.52549	0.279712	0.139856	−	0.990172i	$-0.455336\pi$
$929$	8.52549	0.279712	0.139856	+	0.990172i	$0.455336\pi$
$930$	49.0334	1.60787
$931$	−29.7097	−0.973697
$932$	−29.3703	−0.962057
$933$	4.66110	0.152598
$934$	−31.9253	−1.04463
$935$	0	0
$936$	−167.185	−5.46463
$937$	57.0170	1.86266	0.931332	−	0.364170i	$-0.118647\pi$
$937$	57.0170	1.86266	0.931332	+	0.364170i	$0.118647\pi$
$938$	−14.0675	−0.459320
$939$	45.3268	1.47918
$940$	0.0998973	0.00325829
$941$	25.2442	0.822937	0.411468	−	0.911424i	$-0.365016\pi$
$941$	25.2442	0.822937	0.411468	+	0.911424i	$0.365016\pi$
$942$	−79.7967	−2.59992
$943$	0.623142	0.0202923
$944$	70.1703	2.28385
$945$	25.4007	0.826286
$946$	0	0
$947$	31.5430	1.02501	0.512506	−	0.858684i	$-0.328717\pi$
$947$	31.5430	1.02501	0.512506	+	0.858684i	$0.328717\pi$
$948$	−22.5064	−0.730973
$949$	−19.2643	−0.625345
$950$	0.335835	0.0108959
$951$	−18.5499	−0.601523
$952$	−18.7918	−0.609044
$953$	−37.9448	−1.22915	−0.614576	−	0.788858i	$-0.710673\pi$
$953$	−37.9448	−1.22915	−0.614576	+	0.788858i	$0.710673\pi$
$954$	182.035	5.89360
$955$	24.8181	0.803095
$956$	−11.4633	−0.370750
$957$	0	0
$958$	63.6908	2.05776
$959$	27.4183	0.885382
$960$	123.886	3.99839
$961$	−23.5183	−0.758656
$962$	−11.7482	−0.378778
$963$	68.5059	2.20757
$964$	103.617	3.33727
$965$	−30.4923	−0.981582
$966$	−2.72231	−0.0875888
$967$	−2.59815	−0.0835510	−0.0417755	−	0.999127i	$-0.513301\pi$
$967$	−2.59815	−0.0835510	−0.0417755	+	0.999127i	$0.513301\pi$
$968$	0	0
$969$	−28.9674	−0.930566
$970$	44.3635	1.42443
$971$	23.8619	0.765765	0.382882	−	0.923797i	$-0.374931\pi$
$971$	23.8619	0.765765	0.382882	+	0.923797i	$0.374931\pi$
$972$	−0.776643	−0.0249108
$973$	−22.2495	−0.713286
$974$	101.664	3.25752
$975$	0.224971	0.00720483
$976$	73.0873	2.33947
$977$	19.2117	0.614637	0.307318	−	0.951607i	$-0.400568\pi$
$977$	19.2117	0.614637	0.307318	+	0.951607i	$0.400568\pi$
$978$	85.5479	2.73552
$979$	0	0
$980$	62.3667	1.99223
$981$	69.8771	2.23100
$982$	−4.24064	−0.135324
$983$	−4.27424	−0.136327	−0.0681635	−	0.997674i	$-0.521714\pi$
$983$	−4.27424	−0.136327	−0.0681635	+	0.997674i	$0.521714\pi$
$984$	−59.0284	−1.88176
$985$	48.9156	1.55858
$986$	−44.4189	−1.41459
$987$	0.0327961	0.00104391
$988$	93.1195	2.96253
$989$	0.800563	0.0254564
$990$	0	0
$991$	−32.6540	−1.03729	−0.518645	−	0.854990i	$-0.673563\pi$
$991$	−32.6540	−1.03729	−0.518645	+	0.854990i	$0.673563\pi$
$992$	44.1733	1.40250
$993$	41.3457	1.31207
$994$	39.1624	1.24216
$995$	10.5175	0.333428
$996$	259.706	8.22909
$997$	−42.1440	−1.33471	−0.667357	−	0.744738i	$-0.732574\pi$
$997$	−42.1440	−1.33471	−0.667357	+	0.744738i	$0.732574\pi$
$998$	−11.8516	−0.375155
$999$	−12.0747	−0.382026

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1331.2.a.e.1.1	yes	25
11.10	odd	2		1331.2.a.d.1.25	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1331.2.a.d.1.25	✓	25	11.10	odd	2
1331.2.a.e.1.1	yes	25	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1331 = 11^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1331.a (trivial)

\(f(q)\)	\(=\)	\(q-2.67720 q^{2} -3.00139 q^{3} +5.16738 q^{4} -2.23095 q^{5} +8.03530 q^{6} +1.26098 q^{7} -8.47969 q^{8} +6.00833 q^{9} +O(q^{10})\)	\(q-2.67720 q^{2} -3.00139 q^{3} +5.16738 q^{4} -2.23095 q^{5} +8.03530 q^{6} +1.26098 q^{7} -8.47969 q^{8} +6.00833 q^{9} +5.97270 q^{10} -15.5093 q^{12} +3.28144 q^{13} -3.37588 q^{14} +6.69596 q^{15} +12.3670 q^{16} +1.75744 q^{17} -16.0855 q^{18} +5.49169 q^{19} -11.5282 q^{20} -3.78468 q^{21} -0.268675 q^{23} +25.4508 q^{24} -0.0228423 q^{25} -8.78506 q^{26} -9.02918 q^{27} +6.51594 q^{28} +9.44077 q^{29} -17.9264 q^{30} -2.73526 q^{31} -16.1496 q^{32} -4.70501 q^{34} -2.81318 q^{35} +31.0473 q^{36} +1.33730 q^{37} -14.7023 q^{38} -9.84888 q^{39} +18.9178 q^{40} -2.31931 q^{41} +10.1323 q^{42} -2.97967 q^{43} -13.4043 q^{45} +0.719297 q^{46} -0.00866548 q^{47} -37.1183 q^{48} -5.40994 q^{49} +0.0611532 q^{50} -5.27476 q^{51} +16.9564 q^{52} -11.3167 q^{53} +24.1729 q^{54} -10.6927 q^{56} -16.4827 q^{57} -25.2748 q^{58} +5.67398 q^{59} +34.6006 q^{60} +5.90985 q^{61} +7.32283 q^{62} +7.57637 q^{63} +18.5015 q^{64} -7.32074 q^{65} +4.16706 q^{67} +9.08136 q^{68} +0.806399 q^{69} +7.53144 q^{70} -11.6006 q^{71} -50.9488 q^{72} -5.87068 q^{73} -3.58021 q^{74} +0.0685585 q^{75} +28.3776 q^{76} +26.3674 q^{78} +1.45115 q^{79} -27.5903 q^{80} +9.07508 q^{81} +6.20925 q^{82} -16.7451 q^{83} -19.5569 q^{84} -3.92077 q^{85} +7.97715 q^{86} -28.3354 q^{87} +15.9007 q^{89} +35.8860 q^{90} +4.13782 q^{91} -1.38835 q^{92} +8.20958 q^{93} +0.0231992 q^{94} -12.2517 q^{95} +48.4712 q^{96} +7.42771 q^{97} +14.4835 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 5 q^{2} - 3 q^{3} + 25 q^{4} - 3 q^{5} + 15 q^{6} + 19 q^{7} + 9 q^{8} + 22 q^{9}+O(q^{10}) \) 25 * q + 5 * q^2 - 3 * q^3 + 25 * q^4 - 3 * q^5 + 15 * q^6 + 19 * q^7 + 9 * q^8 + 22 * q^9	\( 25 q + 5 q^{2} - 3 q^{3} + 25 q^{4} - 3 q^{5} + 15 q^{6} + 19 q^{7} + 9 q^{8} + 22 q^{9} + 25 q^{10} - 12 q^{12} + 46 q^{13} - 12 q^{14} - 15 q^{15} + 13 q^{16} + 14 q^{17} + 6 q^{18} + 45 q^{19} - 24 q^{20} + 49 q^{21} + 2 q^{23} + 36 q^{24} + 16 q^{25} - 7 q^{26} - 21 q^{27} + 40 q^{28} + 40 q^{29} - 15 q^{30} - 4 q^{31} + 3 q^{32} - 24 q^{34} - q^{35} + 38 q^{36} - 21 q^{37} + 30 q^{38} + 18 q^{39} + 54 q^{40} + 49 q^{41} + 13 q^{42} + 14 q^{43} - 42 q^{45} + 40 q^{46} - 2 q^{47} - 5 q^{48} + 18 q^{49} - 12 q^{50} + 7 q^{51} + 57 q^{52} - 25 q^{53} + 33 q^{54} - 11 q^{56} + 4 q^{57} + 23 q^{58} - 22 q^{59} - 12 q^{60} + 128 q^{61} - 8 q^{62} + 12 q^{63} + 31 q^{64} + 16 q^{67} - 6 q^{68} - 57 q^{69} + 38 q^{70} - 34 q^{71} - 15 q^{72} + 71 q^{73} - 21 q^{74} - 10 q^{75} + 95 q^{76} + 75 q^{78} + 53 q^{79} - 29 q^{80} + 21 q^{81} + 33 q^{82} - 6 q^{83} + 18 q^{84} + 101 q^{85} + 38 q^{86} - 16 q^{87} + 5 q^{89} - 20 q^{90} + 16 q^{91} + 53 q^{92} + 7 q^{93} + 57 q^{94} - 16 q^{95} + 32 q^{96} + 14 q^{97} - 39 q^{98}+O(q^{100}) \) 25 * q + 5 * q^2 - 3 * q^3 + 25 * q^4 - 3 * q^5 + 15 * q^6 + 19 * q^7 + 9 * q^8 + 22 * q^9 + 25 * q^10 - 12 * q^12 + 46 * q^13 - 12 * q^14 - 15 * q^15 + 13 * q^16 + 14 * q^17 + 6 * q^18 + 45 * q^19 - 24 * q^20 + 49 * q^21 + 2 * q^23 + 36 * q^24 + 16 * q^25 - 7 * q^26 - 21 * q^27 + 40 * q^28 + 40 * q^29 - 15 * q^30 - 4 * q^31 + 3 * q^32 - 24 * q^34 - q^35 + 38 * q^36 - 21 * q^37 + 30 * q^38 + 18 * q^39 + 54 * q^40 + 49 * q^41 + 13 * q^42 + 14 * q^43 - 42 * q^45 + 40 * q^46 - 2 * q^47 - 5 * q^48 + 18 * q^49 - 12 * q^50 + 7 * q^51 + 57 * q^52 - 25 * q^53 + 33 * q^54 - 11 * q^56 + 4 * q^57 + 23 * q^58 - 22 * q^59 - 12 * q^60 + 128 * q^61 - 8 * q^62 + 12 * q^63 + 31 * q^64 + 16 * q^67 - 6 * q^68 - 57 * q^69 + 38 * q^70 - 34 * q^71 - 15 * q^72 + 71 * q^73 - 21 * q^74 - 10 * q^75 + 95 * q^76 + 75 * q^78 + 53 * q^79 - 29 * q^80 + 21 * q^81 + 33 * q^82 - 6 * q^83 + 18 * q^84 + 101 * q^85 + 38 * q^86 - 16 * q^87 + 5 * q^89 - 20 * q^90 + 16 * q^91 + 53 * q^92 + 7 * q^93 + 57 * q^94 - 16 * q^95 + 32 * q^96 + 14 * q^97 - 39 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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