LMFDB - Embedded newform 1331.2.a.e.1.4

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			1.4
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)

$f(q)$	$=$	$q-1.80029 q^{2} +1.01287 q^{3} +1.24105 q^{4} -2.62489 q^{5} -1.82346 q^{6} +0.974919 q^{7} +1.36633 q^{8} -1.97409 q^{9} +O(q^{10})$	\(q-1.80029 q^{2} +1.01287 q^{3} +1.24105 q^{4} -2.62489 q^{5} -1.82346 q^{6} +0.974919 q^{7} +1.36633 q^{8} -1.97409 q^{9} +4.72556 q^{10} +1.25702 q^{12} -2.09450 q^{13} -1.75514 q^{14} -2.65867 q^{15} -4.94189 q^{16} +2.98968 q^{17} +3.55394 q^{18} +2.52797 q^{19} -3.25761 q^{20} +0.987468 q^{21} -4.47928 q^{23} +1.38392 q^{24} +1.89002 q^{25} +3.77071 q^{26} -5.03811 q^{27} +1.20992 q^{28} +2.83973 q^{29} +4.78638 q^{30} +8.67577 q^{31} +6.16419 q^{32} -5.38230 q^{34} -2.55905 q^{35} -2.44995 q^{36} -3.54906 q^{37} -4.55109 q^{38} -2.12146 q^{39} -3.58646 q^{40} -10.7727 q^{41} -1.77773 q^{42} +9.83773 q^{43} +5.18177 q^{45} +8.06401 q^{46} +2.74945 q^{47} -5.00550 q^{48} -6.04953 q^{49} -3.40259 q^{50} +3.02816 q^{51} -2.59938 q^{52} +5.73496 q^{53} +9.07007 q^{54} +1.33206 q^{56} +2.56051 q^{57} -5.11234 q^{58} +4.53029 q^{59} -3.29954 q^{60} +10.2482 q^{61} -15.6189 q^{62} -1.92458 q^{63} -1.21355 q^{64} +5.49782 q^{65} +9.29468 q^{67} +3.71034 q^{68} -4.53693 q^{69} +4.60704 q^{70} -1.87271 q^{71} -2.69726 q^{72} +10.1060 q^{73} +6.38934 q^{74} +1.91435 q^{75} +3.13734 q^{76} +3.81924 q^{78} +12.6942 q^{79} +12.9719 q^{80} +0.819318 q^{81} +19.3940 q^{82} -9.93681 q^{83} +1.22550 q^{84} -7.84757 q^{85} -17.7108 q^{86} +2.87628 q^{87} -7.60087 q^{89} -9.32869 q^{90} -2.04197 q^{91} -5.55901 q^{92} +8.78743 q^{93} -4.94982 q^{94} -6.63564 q^{95} +6.24353 q^{96} +11.5219 q^{97} +10.8909 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.80029	−1.27300	−0.636499	−	0.771277i	$-0.719618\pi$
$2$	−1.80029	−1.27300	−0.636499	+	0.771277i	$0.719618\pi$
$3$	1.01287	0.584781	0.292391	−	0.956299i	$-0.405549\pi$
$3$	1.01287	0.584781	0.292391	+	0.956299i	$0.405549\pi$
$4$	1.24105	0.620525
$5$	−2.62489	−1.17388	−0.586942	−	0.809629i	$-0.699668\pi$
$5$	−2.62489	−1.17388	−0.586942	+	0.809629i	$0.699668\pi$
$6$	−1.82346	−0.744426
$7$	0.974919	0.368485	0.184242	−	0.982881i	$-0.441017\pi$
$7$	0.974919	0.368485	0.184242	+	0.982881i	$0.441017\pi$
$8$	1.36633	0.483071
$9$	−1.97409	−0.658031
$10$	4.72556	1.49435
$11$	0	0
$11$	0	0
$12$	1.25702	0.362872
$13$	−2.09450	−0.580910	−0.290455	−	0.956889i	$-0.593807\pi$
$13$	−2.09450	−0.580910	−0.290455	+	0.956889i	$0.593807\pi$
$14$	−1.75514	−0.469081
$15$	−2.65867	−0.686466
$16$	−4.94189	−1.23547
$17$	2.98968	0.725104	0.362552	−	0.931964i	$-0.381906\pi$
$17$	2.98968	0.725104	0.362552	+	0.931964i	$0.381906\pi$
$18$	3.55394	0.837672
$19$	2.52797	0.579957	0.289979	−	0.957033i	$-0.406352\pi$
$19$	2.52797	0.579957	0.289979	+	0.957033i	$0.406352\pi$
$20$	−3.25761	−0.728425
$21$	0.987468	0.215483
$22$	0	0
$23$	−4.47928	−0.933995	−0.466997	−	0.884259i	$-0.654664\pi$
$23$	−4.47928	−0.933995	−0.466997	+	0.884259i	$0.654664\pi$
$24$	1.38392	0.282491
$25$	1.89002	0.378005
$26$	3.77071	0.739497
$27$	−5.03811	−0.969585
$28$	1.20992	0.228654
$29$	2.83973	0.527325	0.263662	−	0.964615i	$-0.415070\pi$
$29$	2.83973	0.527325	0.263662	+	0.964615i	$0.415070\pi$
$30$	4.78638	0.873870
$31$	8.67577	1.55821	0.779107	−	0.626891i	$-0.215673\pi$
$31$	8.67577	1.55821	0.779107	+	0.626891i	$0.215673\pi$
$32$	6.16419	1.08969
$33$	0	0
$34$	−5.38230	−0.923056
$35$	−2.55905	−0.432559
$36$	−2.44995	−0.408325
$37$	−3.54906	−0.583462	−0.291731	−	0.956500i	$-0.594231\pi$
$37$	−3.54906	−0.583462	−0.291731	+	0.956500i	$0.594231\pi$
$38$	−4.55109	−0.738285
$39$	−2.12146	−0.339705
$40$	−3.58646	−0.567069
$41$	−10.7727	−1.68241	−0.841206	−	0.540715i	$-0.818154\pi$
$41$	−10.7727	−1.68241	−0.841206	+	0.540715i	$0.818154\pi$
$42$	−1.77773	−0.274310
$43$	9.83773	1.50024	0.750120	−	0.661302i	$-0.229996\pi$
$43$	9.83773	1.50024	0.750120	+	0.661302i	$0.229996\pi$
$44$	0	0
$45$	5.18177	0.772452
$46$	8.06401	1.18897
$47$	2.74945	0.401049	0.200524	−	0.979689i	$-0.435735\pi$
$47$	2.74945	0.401049	0.200524	+	0.979689i	$0.435735\pi$
$48$	−5.00550	−0.722482
$49$	−6.04953	−0.864219
$50$	−3.40259	−0.481199
$51$	3.02816	0.424027
$52$	−2.59938	−0.360469
$53$	5.73496	0.787758	0.393879	−	0.919162i	$-0.371133\pi$
$53$	5.73496	0.787758	0.393879	+	0.919162i	$0.371133\pi$
$54$	9.07007	1.23428
$55$	0	0
$56$	1.33206	0.178004
$57$	2.56051	0.339148
$58$	−5.11234	−0.671284
$59$	4.53029	0.589793	0.294897	−	0.955529i	$-0.404715\pi$
$59$	4.53029	0.589793	0.294897	+	0.955529i	$0.404715\pi$
$60$	−3.29954	−0.425969
$61$	10.2482	1.31215	0.656076	−	0.754695i	$-0.272215\pi$
$61$	10.2482	1.31215	0.656076	+	0.754695i	$0.272215\pi$
$62$	−15.6189	−1.98360
$63$	−1.92458	−0.242474
$64$	−1.21355	−0.151694
$65$	5.49782	0.681921
$66$	0	0
$67$	9.29468	1.13553	0.567763	−	0.823192i	$-0.307809\pi$
$67$	9.29468	1.13553	0.567763	+	0.823192i	$0.307809\pi$
$68$	3.71034	0.449945
$69$	−4.53693	−0.546183
$70$	4.60704	0.550647
$71$	−1.87271	−0.222250	−0.111125	−	0.993806i	$-0.535445\pi$
$71$	−1.87271	−0.222250	−0.111125	+	0.993806i	$0.535445\pi$
$72$	−2.69726	−0.317876
$73$	10.1060	1.18282	0.591411	−	0.806371i	$-0.298571\pi$
$73$	10.1060	1.18282	0.591411	+	0.806371i	$0.298571\pi$
$74$	6.38934	0.742746
$75$	1.91435	0.221050
$76$	3.13734	0.359878
$77$	0	0
$78$	3.81924	0.432444
$79$	12.6942	1.42821	0.714105	−	0.700039i	$-0.246834\pi$
$79$	12.6942	1.42821	0.714105	+	0.700039i	$0.246834\pi$
$80$	12.9719	1.45030
$81$	0.819318	0.0910353
$82$	19.3940	2.14171
$83$	−9.93681	−1.09071	−0.545353	−	0.838206i	$-0.683604\pi$
$83$	−9.93681	−1.09071	−0.545353	+	0.838206i	$0.683604\pi$
$84$	1.22550	0.133713
$85$	−7.84757	−0.851188
$86$	−17.7108	−1.90980
$87$	2.87628	0.308370
$88$	0	0
$89$	−7.60087	−0.805691	−0.402845	−	0.915268i	$-0.631979\pi$
$89$	−7.60087	−0.805691	−0.402845	+	0.915268i	$0.631979\pi$
$90$	−9.32869	−0.983330
$91$	−2.04197	−0.214056
$92$	−5.55901	−0.579567
$93$	8.78743	0.911214
$94$	−4.94982	−0.510535
$95$	−6.63564	−0.680803
$96$	6.24353	0.637228
$97$	11.5219	1.16988	0.584938	−	0.811078i	$-0.301119\pi$
$97$	11.5219	1.16988	0.584938	+	0.811078i	$0.301119\pi$
$98$	10.8909	1.10015
$99$	0	0
$100$	2.34561	0.234561
$101$	−2.50025	−0.248784	−0.124392	−	0.992233i	$-0.539698\pi$
$101$	−2.50025	−0.248784	−0.124392	+	0.992233i	$0.539698\pi$
$102$	−5.45157	−0.539786
$103$	6.52987	0.643407	0.321704	−	0.946840i	$-0.395745\pi$
$103$	6.52987	0.643407	0.321704	+	0.946840i	$0.395745\pi$
$104$	−2.86178	−0.280621
$105$	−2.59199	−0.252952
$106$	−10.3246	−1.00281
$107$	−5.83079	−0.563684	−0.281842	−	0.959461i	$-0.590945\pi$
$107$	−5.83079	−0.563684	−0.281842	+	0.959461i	$0.590945\pi$
$108$	−6.25255	−0.601652
$109$	−11.9792	−1.14740	−0.573699	−	0.819066i	$-0.694492\pi$
$109$	−11.9792	−1.14740	−0.573699	+	0.819066i	$0.694492\pi$
$110$	0	0
$111$	−3.59474	−0.341198
$112$	−4.81795	−0.455253
$113$	2.26114	0.212710	0.106355	−	0.994328i	$-0.466082\pi$
$113$	2.26114	0.212710	0.106355	+	0.994328i	$0.466082\pi$
$114$	−4.60967	−0.431735
$115$	11.7576	1.09640
$116$	3.52425	0.327218
$117$	4.13474	0.382256
$118$	−8.15584	−0.750806
$119$	2.91470	0.267190
$120$	−3.63262	−0.331612
$121$	0	0
$122$	−18.4498	−1.67037
$123$	−10.9113	−0.983843
$124$	10.7671	0.966911
$125$	8.16333	0.730151
$126$	3.46481	0.308670
$127$	19.6438	1.74310	0.871551	−	0.490304i	$-0.163114\pi$
$127$	19.6438	1.74310	0.871551	+	0.490304i	$0.163114\pi$
$128$	−10.1436	−0.896579
$129$	9.96435	0.877312
$130$	−9.89768	−0.868084
$131$	14.6184	1.27722	0.638609	−	0.769531i	$-0.279510\pi$
$131$	14.6184	1.27722	0.638609	+	0.769531i	$0.279510\pi$
$132$	0	0
$133$	2.46457	0.213705
$134$	−16.7331	−1.44552
$135$	13.2245	1.13818
$136$	4.08489	0.350277
$137$	22.5645	1.92782	0.963908	−	0.266235i	$-0.0857797\pi$
$137$	22.5645	1.92782	0.963908	+	0.266235i	$0.0857797\pi$
$138$	8.16780	0.695290
$139$	9.98481	0.846901	0.423450	−	0.905919i	$-0.360819\pi$
$139$	9.98481	0.846901	0.423450	+	0.905919i	$0.360819\pi$
$140$	−3.17591	−0.268414
$141$	2.78484	0.234526
$142$	3.37143	0.282924
$143$	0	0
$144$	9.75576	0.812980
$145$	−7.45397	−0.619018
$146$	−18.1938	−1.50573
$147$	−6.12740	−0.505379
$148$	−4.40456	−0.362053
$149$	−1.04382	−0.0855130	−0.0427565	−	0.999086i	$-0.513614\pi$
$149$	−1.04382	−0.0855130	−0.0427565	+	0.999086i	$0.513614\pi$
$150$	−3.44639	−0.281396
$151$	12.2956	1.00060	0.500301	−	0.865851i	$-0.333223\pi$
$151$	12.2956	1.00060	0.500301	+	0.865851i	$0.333223\pi$
$152$	3.45405	0.280160
$153$	−5.90191	−0.477141
$154$	0	0
$155$	−22.7729	−1.82916
$156$	−2.63284	−0.210796
$157$	−18.1630	−1.44956	−0.724782	−	0.688978i	$-0.758060\pi$
$157$	−18.1630	−1.44956	−0.724782	+	0.688978i	$0.758060\pi$
$158$	−22.8533	−1.81811
$159$	5.80878	0.460666
$160$	−16.1803	−1.27916
$161$	−4.36694	−0.344163
$162$	−1.47501	−0.115888
$163$	−1.15443	−0.0904218	−0.0452109	−	0.998977i	$-0.514396\pi$
$163$	−1.15443	−0.0904218	−0.0452109	+	0.998977i	$0.514396\pi$
$164$	−13.3694	−1.04398
$165$	0	0
$166$	17.8891	1.38847
$167$	10.6919	0.827366	0.413683	−	0.910421i	$-0.364242\pi$
$167$	10.6919	0.827366	0.413683	+	0.910421i	$0.364242\pi$
$168$	1.34921	0.104094
$169$	−8.61307	−0.662544
$170$	14.1279	1.08356
$171$	−4.99046	−0.381630
$172$	12.2091	0.930937
$173$	18.7684	1.42693	0.713467	−	0.700689i	$-0.247124\pi$
$173$	18.7684	1.42693	0.713467	+	0.700689i	$0.247124\pi$
$174$	−5.17815	−0.392554
$175$	1.84262	0.139289
$176$	0	0
$177$	4.58860	0.344900
$178$	13.6838	1.02564
$179$	−8.17667	−0.611153	−0.305576	−	0.952168i	$-0.598849\pi$
$179$	−8.17667	−0.611153	−0.305576	+	0.952168i	$0.598849\pi$
$180$	6.43083	0.479326
$181$	−2.45133	−0.182206	−0.0911029	−	0.995841i	$-0.529039\pi$
$181$	−2.45133	−0.182206	−0.0911029	+	0.995841i	$0.529039\pi$
$182$	3.67614	0.272493
$183$	10.3801	0.767321
$184$	−6.12018	−0.451186
$185$	9.31587	0.684917
$186$	−15.8199	−1.15997
$187$	0	0
$188$	3.41221	0.248861
$189$	−4.91175	−0.357278
$190$	11.9461	0.866661
$191$	19.5425	1.41405	0.707023	−	0.707191i	$-0.250038\pi$
$191$	19.5425	1.41405	0.707023	+	0.707191i	$0.250038\pi$
$192$	−1.22917	−0.0887078
$193$	6.53084	0.470100	0.235050	−	0.971983i	$-0.424475\pi$
$193$	6.53084	0.470100	0.235050	+	0.971983i	$0.424475\pi$
$194$	−20.7429	−1.48925
$195$	5.56858	0.398775
$196$	−7.50777	−0.536270
$197$	−27.3236	−1.94673	−0.973364	−	0.229263i	$-0.926368\pi$
$197$	−27.3236	−1.94673	−0.973364	+	0.229263i	$0.926368\pi$
$198$	0	0
$199$	19.6441	1.39253	0.696266	−	0.717784i	$-0.254843\pi$
$199$	19.6441	1.39253	0.696266	+	0.717784i	$0.254843\pi$
$200$	2.58240	0.182603
$201$	9.41431	0.664035
$202$	4.50118	0.316702
$203$	2.76851	0.194311
$204$	3.75810	0.263120
$205$	28.2771	1.97496
$206$	−11.7557	−0.819056
$207$	8.84251	0.614597
$208$	10.3508	0.717699
$209$	0	0
$210$	4.66634	0.322008
$211$	23.7702	1.63641	0.818205	−	0.574927i	$-0.194969\pi$
$211$	23.7702	1.63641	0.818205	+	0.574927i	$0.194969\pi$
$212$	7.11738	0.488824
$213$	−1.89681	−0.129968
$214$	10.4971	0.717569
$215$	−25.8229	−1.76111
$216$	−6.88373	−0.468379
$217$	8.45817	0.574178
$218$	21.5660	1.46064
$219$	10.2361	0.691692
$220$	0	0
$221$	−6.26188	−0.421220
$222$	6.47158	0.434344
$223$	−15.2035	−1.01810	−0.509052	−	0.860736i	$-0.670004\pi$
$223$	−15.2035	−1.01810	−0.509052	+	0.860736i	$0.670004\pi$
$224$	6.00959	0.401533
$225$	−3.73108	−0.248739
$226$	−4.07071	−0.270780
$227$	25.5460	1.69555	0.847774	−	0.530358i	$-0.177943\pi$
$227$	25.5460	1.69555	0.847774	+	0.530358i	$0.177943\pi$
$228$	3.17772	0.210450
$229$	−1.78897	−0.118219	−0.0591094	−	0.998252i	$-0.518826\pi$
$229$	−1.78897	−0.118219	−0.0591094	+	0.998252i	$0.518826\pi$
$230$	−21.1671	−1.39572
$231$	0	0
$232$	3.88001	0.254735
$233$	−22.6273	−1.48236	−0.741182	−	0.671304i	$-0.765734\pi$
$233$	−22.6273	−1.48236	−0.741182	+	0.671304i	$0.765734\pi$
$234$	−7.44373	−0.486612
$235$	−7.21700	−0.470785
$236$	5.62231	0.365981
$237$	12.8576	0.835190
$238$	−5.24731	−0.340132
$239$	9.10580	0.589005	0.294503	−	0.955651i	$-0.404846\pi$
$239$	9.10580	0.589005	0.294503	+	0.955651i	$0.404846\pi$
$240$	13.1389	0.848110
$241$	−16.0269	−1.03239	−0.516193	−	0.856472i	$-0.672651\pi$
$241$	−16.0269	−1.03239	−0.516193	+	0.856472i	$0.672651\pi$
$242$	0	0
$243$	15.9442	1.02282
$244$	12.7186	0.814223
$245$	15.8793	1.01449
$246$	19.6436	1.25243
$247$	−5.29484	−0.336903
$248$	11.8540	0.752728
$249$	−10.0647	−0.637825
$250$	−14.6964	−0.929481
$251$	3.76605	0.237711	0.118855	−	0.992912i	$-0.462078\pi$
$251$	3.76605	0.237711	0.118855	+	0.992912i	$0.462078\pi$
$252$	−2.38850	−0.150461
$253$	0	0
$254$	−35.3645	−2.21897
$255$	−7.94857	−0.497759
$256$	20.6886	1.29304
$257$	−28.1488	−1.75587	−0.877937	−	0.478776i	$-0.841081\pi$
$257$	−28.1488	−1.75587	−0.877937	+	0.478776i	$0.841081\pi$
$258$	−17.9387	−1.11682
$259$	−3.46005	−0.214997
$260$	6.82307	0.423149
$261$	−5.60589	−0.346996
$262$	−26.3174	−1.62590
$263$	−7.89470	−0.486808	−0.243404	−	0.969925i	$-0.578264\pi$
$263$	−7.89470	−0.486808	−0.243404	+	0.969925i	$0.578264\pi$
$264$	0	0
$265$	−15.0536	−0.924737
$266$	−4.43695	−0.272047
$267$	−7.69870	−0.471153
$268$	11.5352	0.704623
$269$	−31.4664	−1.91854	−0.959270	−	0.282491i	$-0.908839\pi$
$269$	−31.4664	−1.91854	−0.959270	+	0.282491i	$0.908839\pi$
$270$	−23.8079	−1.44890
$271$	−1.00158	−0.0608415	−0.0304207	−	0.999537i	$-0.509685\pi$
$271$	−1.00158	−0.0608415	−0.0304207	+	0.999537i	$0.509685\pi$
$272$	−14.7747	−0.895847
$273$	−2.06825	−0.125176
$274$	−40.6227	−2.45411
$275$	0	0
$276$	−5.63056	−0.338920
$277$	26.7064	1.60463	0.802315	−	0.596901i	$-0.203601\pi$
$277$	26.7064	1.60463	0.802315	+	0.596901i	$0.203601\pi$
$278$	−17.9756	−1.07810
$279$	−17.1268	−1.02535
$280$	−3.49651	−0.208956
$281$	7.79341	0.464916	0.232458	−	0.972606i	$-0.425323\pi$
$281$	7.79341	0.464916	0.232458	+	0.972606i	$0.425323\pi$
$282$	−5.01353	−0.298551
$283$	−10.1422	−0.602890	−0.301445	−	0.953483i	$-0.597469\pi$
$283$	−10.1422	−0.602890	−0.301445	+	0.953483i	$0.597469\pi$
$284$	−2.32413	−0.137912
$285$	−6.72105	−0.398121
$286$	0	0
$287$	−10.5025	−0.619943
$288$	−12.1687	−0.717046
$289$	−8.06181	−0.474224
$290$	13.4193	0.788010
$291$	11.6702	0.684122
$292$	12.5421	0.733970
$293$	13.4246	0.784271	0.392136	−	0.919907i	$-0.371736\pi$
$293$	13.4246	0.784271	0.392136	+	0.919907i	$0.371736\pi$
$294$	11.0311	0.643347
$295$	−11.8915	−0.692349
$296$	−4.84919	−0.281853
$297$	0	0
$298$	1.87918	0.108858
$299$	9.38185	0.542566
$300$	2.37580	0.137167
$301$	9.59099	0.552816
$302$	−22.1357	−1.27377
$303$	−2.53243	−0.145484
$304$	−12.4930	−0.716522
$305$	−26.9004	−1.54031
$306$	10.6252	0.607399
$307$	−2.95957	−0.168912	−0.0844558	−	0.996427i	$-0.526915\pi$
$307$	−2.95957	−0.168912	−0.0844558	+	0.996427i	$0.526915\pi$
$308$	0	0
$309$	6.61391	0.376252
$310$	40.9979	2.32852
$311$	0.272427	0.0154479	0.00772396	−	0.999970i	$-0.497541\pi$
$311$	0.272427	0.0154479	0.00772396	+	0.999970i	$0.497541\pi$
$312$	−2.89861	−0.164102
$313$	−20.9367	−1.18341	−0.591707	−	0.806153i	$-0.701546\pi$
$313$	−20.9367	−1.18341	−0.591707	+	0.806153i	$0.701546\pi$
$314$	32.6987	1.84529
$315$	5.05180	0.284637
$316$	15.7541	0.886240
$317$	−11.7946	−0.662451	−0.331226	−	0.943552i	$-0.607462\pi$
$317$	−11.7946	−0.662451	−0.331226	+	0.943552i	$0.607462\pi$
$318$	−10.4575	−0.586427
$319$	0	0
$320$	3.18543	0.178071
$321$	−5.90584	−0.329632
$322$	7.86176	0.438119
$323$	7.55784	0.420529
$324$	1.01681	0.0564897
$325$	−3.95865	−0.219587
$326$	2.07831	0.115107
$327$	−12.1334	−0.670977
$328$	−14.7191	−0.812724
$329$	2.68049	0.147780
$330$	0	0
$331$	6.96092	0.382607	0.191303	−	0.981531i	$-0.438729\pi$
$331$	6.96092	0.382607	0.191303	+	0.981531i	$0.438729\pi$
$332$	−12.3321	−0.676811
$333$	7.00617	0.383936
$334$	−19.2486	−1.05324
$335$	−24.3975	−1.33298
$336$	−4.87996	−0.266224
$337$	−34.2241	−1.86431	−0.932153	−	0.362064i	$-0.882072\pi$
$337$	−34.2241	−1.86431	−0.932153	+	0.362064i	$0.882072\pi$
$338$	15.5060	0.843418
$339$	2.29024	0.124389
$340$	−9.73923	−0.528184
$341$	0	0
$342$	8.98428	0.485814
$343$	−12.7222	−0.686936
$344$	13.4416	0.724722
$345$	11.9089	0.641155
$346$	−33.7886	−1.81648
$347$	−32.3352	−1.73585	−0.867923	−	0.496698i	$-0.834546\pi$
$347$	−32.3352	−1.73585	−0.867923	+	0.496698i	$0.834546\pi$
$348$	3.56961	0.191351
$349$	−1.55686	−0.0833369	−0.0416684	−	0.999131i	$-0.513267\pi$
$349$	−1.55686	−0.0833369	−0.0416684	+	0.999131i	$0.513267\pi$
$350$	−3.31725	−0.177315
$351$	10.5523	0.563242
$352$	0	0
$353$	−6.04993	−0.322005	−0.161003	−	0.986954i	$-0.551473\pi$
$353$	−6.04993	−0.322005	−0.161003	+	0.986954i	$0.551473\pi$
$354$	−8.26081	−0.439057
$355$	4.91565	0.260896
$356$	−9.43306	−0.499951
$357$	2.95221	0.156248
$358$	14.7204	0.777997
$359$	23.5668	1.24381	0.621904	−	0.783093i	$-0.286359\pi$
$359$	23.5668	1.24381	0.621904	+	0.783093i	$0.286359\pi$
$360$	7.08001	0.373149
$361$	−12.6093	−0.663650
$362$	4.41311	0.231948
$363$	0	0
$364$	−2.53418	−0.132827
$365$	−26.5272	−1.38850
$366$	−18.6873	−0.976799
$367$	−25.3974	−1.32573	−0.662867	−	0.748737i	$-0.730660\pi$
$367$	−25.3974	−1.32573	−0.662867	+	0.748737i	$0.730660\pi$
$368$	22.1361	1.15393
$369$	21.2663	1.10708
$370$	−16.7713	−0.871898
$371$	5.59113	0.290277
$372$	10.9056	0.565431
$373$	1.05117	0.0544275	0.0272137	−	0.999630i	$-0.491337\pi$
$373$	1.05117	0.0544275	0.0272137	+	0.999630i	$0.491337\pi$
$374$	0	0
$375$	8.26840	0.426979
$376$	3.75666	0.193735
$377$	−5.94782	−0.306328
$378$	8.84259	0.454814
$379$	−22.0826	−1.13431	−0.567154	−	0.823612i	$-0.691956\pi$
$379$	−22.0826	−1.13431	−0.567154	+	0.823612i	$0.691956\pi$
$380$	−8.23517	−0.422455
$381$	19.8966	1.01933
$382$	−35.1822	−1.80008
$383$	−12.4460	−0.635962	−0.317981	−	0.948097i	$-0.603005\pi$
$383$	−12.4460	−0.635962	−0.317981	+	0.948097i	$0.603005\pi$
$384$	−10.2742	−0.524303
$385$	0	0
$386$	−11.7574	−0.598436
$387$	−19.4206	−0.987204
$388$	14.2993	0.725938
$389$	25.2901	1.28226	0.641130	−	0.767433i	$-0.278466\pi$
$389$	25.2901	1.28226	0.641130	+	0.767433i	$0.278466\pi$
$390$	−10.0251	−0.507639
$391$	−13.3916	−0.677243
$392$	−8.26566	−0.417479
$393$	14.8066	0.746893
$394$	49.1905	2.47818
$395$	−33.3208	−1.67655
$396$	0	0
$397$	17.6107	0.883853	0.441927	−	0.897051i	$-0.354295\pi$
$397$	17.6107	0.883853	0.441927	+	0.897051i	$0.354295\pi$
$398$	−35.3651	−1.77269
$399$	2.49629	0.124971
$400$	−9.34029	−0.467015
$401$	7.27639	0.363366	0.181683	−	0.983357i	$-0.441846\pi$
$401$	7.27639	0.363366	0.181683	+	0.983357i	$0.441846\pi$
$402$	−16.9485	−0.845315
$403$	−18.1714	−0.905181
$404$	−3.10293	−0.154377
$405$	−2.15061	−0.106865
$406$	−4.98412	−0.247358
$407$	0	0
$408$	4.13747	0.204835
$409$	−14.6193	−0.722879	−0.361440	−	0.932396i	$-0.617715\pi$
$409$	−14.6193	−0.722879	−0.361440	+	0.932396i	$0.617715\pi$
$410$	−50.9070	−2.51412
$411$	22.8549	1.12735
$412$	8.10390	0.399250
$413$	4.41666	0.217330
$414$	−15.9191	−0.782381
$415$	26.0830	1.28036
$416$	−12.9109	−0.633009
$417$	10.1133	0.495252
$418$	0	0
$419$	−2.78998	−0.136300	−0.0681498	−	0.997675i	$-0.521710\pi$
$419$	−2.78998	−0.136300	−0.0681498	+	0.997675i	$0.521710\pi$
$420$	−3.21679	−0.156963
$421$	20.5083	0.999513	0.499757	−	0.866166i	$-0.333423\pi$
$421$	20.5083	0.999513	0.499757	+	0.866166i	$0.333423\pi$
$422$	−42.7933	−2.08315
$423$	−5.42767	−0.263903
$424$	7.83586	0.380543
$425$	5.65056	0.274093
$426$	3.41482	0.165449
$427$	9.99120	0.483508
$428$	−7.23631	−0.349780
$429$	0	0
$430$	46.4888	2.24189
$431$	24.8444	1.19671	0.598357	−	0.801229i	$-0.295820\pi$
$431$	24.8444	1.19671	0.598357	+	0.801229i	$0.295820\pi$
$432$	24.8978	1.19790
$433$	−8.52299	−0.409589	−0.204794	−	0.978805i	$-0.565653\pi$
$433$	−8.52299	−0.409589	−0.204794	+	0.978805i	$0.565653\pi$
$434$	−15.2272	−0.730928
$435$	−7.54991	−0.361990
$436$	−14.8668	−0.711989
$437$	−11.3235	−0.541677
$438$	−18.4280	−0.880522
$439$	−12.1355	−0.579197	−0.289599	−	0.957148i	$-0.593522\pi$
$439$	−12.1355	−0.579197	−0.289599	+	0.957148i	$0.593522\pi$
$440$	0	0
$441$	11.9423	0.568683
$442$	11.2732	0.536212
$443$	10.8822	0.517031	0.258515	−	0.966007i	$-0.416767\pi$
$443$	10.8822	0.517031	0.258515	+	0.966007i	$0.416767\pi$
$444$	−4.46125	−0.211722
$445$	19.9514	0.945788
$446$	27.3708	1.29605
$447$	−1.05725	−0.0500064
$448$	−1.18311	−0.0558969
$449$	4.18019	0.197275	0.0986377	−	0.995123i	$-0.468552\pi$
$449$	4.18019	0.197275	0.0986377	+	0.995123i	$0.468552\pi$
$450$	6.71703	0.316644
$451$	0	0
$452$	2.80619	0.131992
$453$	12.4539	0.585134
$454$	−45.9902	−2.15843
$455$	5.35993	0.251277
$456$	3.49851	0.163833
$457$	−4.19070	−0.196033	−0.0980164	−	0.995185i	$-0.531250\pi$
$457$	−4.19070	−0.196033	−0.0980164	+	0.995185i	$0.531250\pi$
$458$	3.22067	0.150492
$459$	−15.0624	−0.703050
$460$	14.5918	0.680345
$461$	25.4105	1.18348	0.591742	−	0.806128i	$-0.298441\pi$
$461$	25.4105	1.18348	0.591742	+	0.806128i	$0.298441\pi$
$462$	0	0
$463$	−13.6295	−0.633419	−0.316709	−	0.948523i	$-0.602578\pi$
$463$	−13.6295	−0.633419	−0.316709	+	0.948523i	$0.602578\pi$
$464$	−14.0337	−0.651496
$465$	−23.0660	−1.06966
$466$	40.7357	1.88705
$467$	−1.73738	−0.0803964	−0.0401982	−	0.999192i	$-0.512799\pi$
$467$	−1.73738	−0.0803964	−0.0401982	+	0.999192i	$0.512799\pi$
$468$	5.13141	0.237200
$469$	9.06157	0.418424
$470$	12.9927	0.599309
$471$	−18.3968	−0.847678
$472$	6.18987	0.284912
$473$	0	0
$474$	−23.1474	−1.06320
$475$	4.77793	0.219226
$476$	3.61729	0.165798
$477$	−11.3214	−0.518369
$478$	−16.3931	−0.749803
$479$	−18.7963	−0.858824	−0.429412	−	0.903109i	$-0.641279\pi$
$479$	−18.7963	−0.858824	−0.429412	+	0.903109i	$0.641279\pi$
$480$	−16.3885	−0.748032
$481$	7.43350	0.338939
$482$	28.8532	1.31423
$483$	−4.42314	−0.201260
$484$	0	0
$485$	−30.2438	−1.37330
$486$	−28.7042	−1.30205
$487$	6.93722	0.314355	0.157178	−	0.987570i	$-0.449760\pi$
$487$	6.93722	0.314355	0.157178	+	0.987570i	$0.449760\pi$
$488$	14.0025	0.633862
$489$	−1.16929	−0.0528770
$490$	−28.5874	−1.29145
$491$	−13.1121	−0.591741	−0.295870	−	0.955228i	$-0.595610\pi$
$491$	−13.1121	−0.591741	−0.295870	+	0.955228i	$0.595610\pi$
$492$	−13.5415	−0.610499
$493$	8.48989	0.382365
$494$	9.53226	0.428877
$495$	0	0
$496$	−42.8747	−1.92513
$497$	−1.82574	−0.0818957
$498$	18.1194	0.811950
$499$	−19.1362	−0.856654	−0.428327	−	0.903624i	$-0.640897\pi$
$499$	−19.1362	−0.856654	−0.428327	+	0.903624i	$0.640897\pi$
$500$	10.1311	0.453077
$501$	10.8295	0.483828
$502$	−6.77998	−0.302605
$503$	4.21641	0.188001	0.0940003	−	0.995572i	$-0.470035\pi$
$503$	4.21641	0.188001	0.0940003	+	0.995572i	$0.470035\pi$
$504$	−2.62961	−0.117132
$505$	6.56286	0.292044
$506$	0	0
$507$	−8.72393	−0.387443
$508$	24.3789	1.08164
$509$	26.4167	1.17090	0.585450	−	0.810708i	$-0.300918\pi$
$509$	26.4167	1.17090	0.585450	+	0.810708i	$0.300918\pi$
$510$	14.3098	0.633646
$511$	9.85256	0.435852
$512$	−16.9583	−0.749456
$513$	−12.7362	−0.562318
$514$	50.6761	2.23522
$515$	−17.1402	−0.755286
$516$	12.3663	0.544394
$517$	0	0
$518$	6.22909	0.273691
$519$	19.0100	0.834444
$520$	7.51184	0.329416
$521$	39.4482	1.72826	0.864129	−	0.503270i	$-0.167870\pi$
$521$	39.4482	1.72826	0.864129	+	0.503270i	$0.167870\pi$
$522$	10.0922	0.441725
$523$	−19.2226	−0.840547	−0.420273	−	0.907397i	$-0.638066\pi$
$523$	−19.2226	−0.840547	−0.420273	+	0.907397i	$0.638066\pi$
$524$	18.1422	0.792546
$525$	1.86634	0.0814536
$526$	14.2128	0.619706
$527$	25.9378	1.12987
$528$	0	0
$529$	−2.93605	−0.127654
$530$	27.1009	1.17719
$531$	−8.94320	−0.388102
$532$	3.05866	0.132610
$533$	22.5634	0.977329
$534$	13.8599	0.599777
$535$	15.3052	0.661700
$536$	12.6996	0.548540
$537$	−8.28191	−0.357391
$538$	56.6487	2.44230
$539$	0	0
$540$	16.4122	0.706270
$541$	39.0034	1.67689	0.838443	−	0.544989i	$-0.183466\pi$
$541$	39.0034	1.67689	0.838443	+	0.544989i	$0.183466\pi$
$542$	1.80313	0.0774511
$543$	−2.48288	−0.106551
$544$	18.4290	0.790135
$545$	31.4440	1.34691
$546$	3.72345	0.159349
$547$	−27.6581	−1.18257	−0.591287	−	0.806461i	$-0.701380\pi$
$547$	−27.6581	−1.18257	−0.591287	+	0.806461i	$0.701380\pi$
$548$	28.0037	1.19626
$549$	−20.2309	−0.863436
$550$	0	0
$551$	7.17877	0.305826
$552$	−6.19895	−0.263845
$553$	12.3758	0.526273
$554$	−48.0793	−2.04269
$555$	9.43578	0.400526
$556$	12.3917	0.525523
$557$	22.6230	0.958567	0.479283	−	0.877660i	$-0.340897\pi$
$557$	22.6230	0.958567	0.479283	+	0.877660i	$0.340897\pi$
$558$	30.8332	1.30527
$559$	−20.6051	−0.871504
$560$	12.6466	0.534415
$561$	0	0
$562$	−14.0304	−0.591837
$563$	3.83407	0.161587	0.0807933	−	0.996731i	$-0.474255\pi$
$563$	3.83407	0.161587	0.0807933	+	0.996731i	$0.474255\pi$
$564$	3.45613	0.145529
$565$	−5.93523	−0.249697
$566$	18.2589	0.767479
$567$	0.798769	0.0335451
$568$	−2.55874	−0.107362
$569$	23.9953	1.00593	0.502967	−	0.864305i	$-0.332242\pi$
$569$	23.9953	1.00593	0.502967	+	0.864305i	$0.332242\pi$
$570$	12.0999	0.506807
$571$	0.00700778	0.000293267 0	0.000146633	−	1.00000i	$-0.499953\pi$
$571$	0.00700778	0.000293267 0	0.000146633		1.00000i	$0.499953\pi$
$572$	0	0
$573$	19.7940	0.826908
$574$	18.9076	0.789187
$575$	−8.46594	−0.353054
$576$	2.39566	0.0998193
$577$	3.77605	0.157199	0.0785995	−	0.996906i	$-0.474955\pi$
$577$	3.77605	0.157199	0.0785995	+	0.996906i	$0.474955\pi$
$578$	14.5136	0.603687
$579$	6.61490	0.274906
$580$	−9.25075	−0.384116
$581$	−9.68758	−0.401909
$582$	−21.0098	−0.870886
$583$	0	0
$584$	13.8082	0.571386
$585$	−10.8532	−0.448725
$586$	−24.1681	−0.998376
$587$	6.68248	0.275816	0.137908	−	0.990445i	$-0.455962\pi$
$587$	6.68248	0.275816	0.137908	+	0.990445i	$0.455962\pi$
$588$	−7.60441	−0.313600
$589$	21.9321	0.903697
$590$	21.4081	0.881359
$591$	−27.6753	−1.13841
$592$	17.5391	0.720852
$593$	4.33276	0.177925	0.0889626	−	0.996035i	$-0.471645\pi$
$593$	4.33276	0.177925	0.0889626	+	0.996035i	$0.471645\pi$
$594$	0	0
$595$	−7.65075	−0.313650
$596$	−1.29543	−0.0530630
$597$	19.8969	0.814327
$598$	−16.8901	−0.690686
$599$	8.30327	0.339263	0.169631	−	0.985508i	$-0.445742\pi$
$599$	8.30327	0.339263	0.169631	+	0.985508i	$0.445742\pi$
$600$	2.61563	0.106783
$601$	1.79836	0.0733568	0.0366784	−	0.999327i	$-0.488322\pi$
$601$	1.79836	0.0733568	0.0366784	+	0.999327i	$0.488322\pi$
$602$	−17.2666	−0.703734
$603$	−18.3486	−0.747211
$604$	15.2595	0.620899
$605$	0	0
$606$	4.55911	0.185201
$607$	−7.52007	−0.305230	−0.152615	−	0.988286i	$-0.548770\pi$
$607$	−7.52007	−0.305230	−0.152615	+	0.988286i	$0.548770\pi$
$608$	15.5829	0.631971
$609$	2.80414	0.113630
$610$	48.4286	1.96082
$611$	−5.75873	−0.232973
$612$	−7.32456	−0.296078
$613$	12.5639	0.507450	0.253725	−	0.967276i	$-0.418344\pi$
$613$	12.5639	0.507450	0.253725	+	0.967276i	$0.418344\pi$
$614$	5.32809	0.215024
$615$	28.6410	1.15492
$616$	0	0
$617$	2.50861	0.100993	0.0504965	−	0.998724i	$-0.483920\pi$
$617$	2.50861	0.100993	0.0504965	+	0.998724i	$0.483920\pi$
$618$	−11.9070	−0.478969
$619$	6.52055	0.262083	0.131042	−	0.991377i	$-0.458168\pi$
$619$	6.52055	0.262083	0.131042	+	0.991377i	$0.458168\pi$
$620$	−28.2623	−1.13504
$621$	22.5671	0.905588
$622$	−0.490448	−0.0196652
$623$	−7.41023	−0.296885
$624$	10.4840	0.419697
$625$	−30.8779	−1.23512
$626$	37.6922	1.50648
$627$	0	0
$628$	−22.5412	−0.899491
$629$	−10.6106	−0.423070
$630$	−9.09472	−0.362342
$631$	48.6973	1.93861	0.969304	−	0.245865i	$-0.0790719\pi$
$631$	48.6973	1.93861	0.969304	+	0.245865i	$0.0790719\pi$
$632$	17.3445	0.689926
$633$	24.0762	0.956942
$634$	21.2337	0.843299
$635$	−51.5626	−2.04620
$636$	7.20899	0.285855
$637$	12.6707	0.502033
$638$	0	0
$639$	3.69690	0.146247
$640$	26.6259	1.05248
$641$	−28.1133	−1.11041	−0.555204	−	0.831714i	$-0.687360\pi$
$641$	−28.1133	−1.11041	−0.555204	+	0.831714i	$0.687360\pi$
$642$	10.6322	0.419621
$643$	31.9969	1.26183	0.630917	−	0.775850i	$-0.282679\pi$
$643$	31.9969	1.26183	0.630917	+	0.775850i	$0.282679\pi$
$644$	−5.41959	−0.213562
$645$	−26.1553	−1.02986
$646$	−13.6063	−0.535333
$647$	−18.4780	−0.726444	−0.363222	−	0.931703i	$-0.618323\pi$
$647$	−18.4780	−0.726444	−0.363222	+	0.931703i	$0.618323\pi$
$648$	1.11946	0.0439765
$649$	0	0
$650$	7.12673	0.279533
$651$	8.56704	0.335769
$652$	−1.43270	−0.0561090
$653$	−17.0764	−0.668252	−0.334126	−	0.942528i	$-0.608441\pi$
$653$	−17.0764	−0.668252	−0.334126	+	0.942528i	$0.608441\pi$
$654$	21.8436	0.854152
$655$	−38.3717	−1.49931
$656$	53.2375	2.07857
$657$	−19.9502	−0.778333
$658$	−4.82567	−0.188124
$659$	−21.0739	−0.820922	−0.410461	−	0.911878i	$-0.634632\pi$
$659$	−21.0739	−0.820922	−0.410461	+	0.911878i	$0.634632\pi$
$660$	0	0
$661$	35.5055	1.38100	0.690502	−	0.723330i	$-0.257390\pi$
$661$	35.5055	1.38100	0.690502	+	0.723330i	$0.257390\pi$
$662$	−12.5317	−0.487058
$663$	−6.34248	−0.246322
$664$	−13.5770	−0.526888
$665$	−6.46922	−0.250866
$666$	−12.6131	−0.488750
$667$	−12.7200	−0.492519
$668$	13.2692	0.513402
$669$	−15.3992	−0.595368
$670$	43.9226	1.69688
$671$	0	0
$672$	6.08694	0.234809
$673$	−8.49011	−0.327270	−0.163635	−	0.986521i	$-0.552322\pi$
$673$	−8.49011	−0.327270	−0.163635	+	0.986521i	$0.552322\pi$
$674$	61.6134	2.37326
$675$	−9.52215	−0.366508
$676$	−10.6893	−0.411125
$677$	24.0179	0.923082	0.461541	−	0.887119i	$-0.347297\pi$
$677$	24.0179	0.923082	0.461541	+	0.887119i	$0.347297\pi$
$678$	−4.12310	−0.158347
$679$	11.2330	0.431082
$680$	−10.7224	−0.411184
$681$	25.8748	0.991524
$682$	0	0
$683$	14.9898	0.573569	0.286785	−	0.957995i	$-0.407414\pi$
$683$	14.9898	0.573569	0.286785	+	0.957995i	$0.407414\pi$
$684$	−6.19341	−0.236811
$685$	−59.2293	−2.26303
$686$	22.9037	0.874469
$687$	−1.81200	−0.0691321
$688$	−48.6170	−1.85351
$689$	−12.0119	−0.457616
$690$	−21.4395	−0.816190
$691$	48.6221	1.84967	0.924835	−	0.380367i	$-0.124202\pi$
$691$	48.6221	1.84967	0.924835	+	0.380367i	$0.124202\pi$
$692$	23.2925	0.885448
$693$	0	0
$694$	58.2129	2.20973
$695$	−26.2090	−0.994164
$696$	3.92995	0.148964
$697$	−32.2069	−1.21992
$698$	2.80280	0.106088
$699$	−22.9185	−0.866859
$700$	2.28678	0.0864323
$701$	13.5539	0.511922	0.255961	−	0.966687i	$-0.417608\pi$
$701$	13.5539	0.511922	0.255961	+	0.966687i	$0.417608\pi$
$702$	−18.9973	−0.717006
$703$	−8.97193	−0.338383
$704$	0	0
$705$	−7.30989	−0.275306
$706$	10.8916	0.409912
$707$	−2.43754	−0.0916731
$708$	5.69468	0.214019
$709$	−6.41015	−0.240738	−0.120369	−	0.992729i	$-0.538408\pi$
$709$	−6.41015	−0.240738	−0.120369	+	0.992729i	$0.538408\pi$
$710$	−8.84961	−0.332120
$711$	−25.0595	−0.939806
$712$	−10.3853	−0.389206
$713$	−38.8612	−1.45536
$714$	−5.31484	−0.198903
$715$	0	0
$716$	−10.1477	−0.379236
$717$	9.22300	0.344439
$718$	−42.4271	−1.58337
$719$	−40.2958	−1.50278	−0.751390	−	0.659858i	$-0.770616\pi$
$719$	−40.2958	−1.50278	−0.751390	+	0.659858i	$0.770616\pi$
$720$	−25.6077	−0.954344
$721$	6.36610	0.237086
$722$	22.7005	0.844825
$723$	−16.2332	−0.603720
$724$	−3.04222	−0.113063
$725$	5.36716	0.199331
$726$	0	0
$727$	−20.7804	−0.770704	−0.385352	−	0.922770i	$-0.625920\pi$
$727$	−20.7804	−0.770704	−0.385352	+	0.922770i	$0.625920\pi$
$728$	−2.79000	−0.103404
$729$	13.6915	0.507091
$730$	47.7566	1.76755
$731$	29.4117	1.08783
$732$	12.8823	0.476142
$733$	36.7752	1.35832	0.679162	−	0.733988i	$-0.262343\pi$
$733$	36.7752	1.35832	0.679162	+	0.733988i	$0.262343\pi$
$734$	45.7227	1.68766
$735$	16.0837	0.593257
$736$	−27.6111	−1.01776
$737$	0	0
$738$	−38.2855	−1.40931
$739$	32.5497	1.19736	0.598680	−	0.800988i	$-0.295692\pi$
$739$	32.5497	1.19736	0.598680	+	0.800988i	$0.295692\pi$
$740$	11.5615	0.425008
$741$	−5.36299	−0.197014
$742$	−10.0657	−0.369522
$743$	−3.06275	−0.112361	−0.0561807	−	0.998421i	$-0.517892\pi$
$743$	−3.06275	−0.112361	−0.0561807	+	0.998421i	$0.517892\pi$
$744$	12.0065	0.440181
$745$	2.73991	0.100382
$746$	−1.89241	−0.0692861
$747$	19.6162	0.717718
$748$	0	0
$749$	−5.68455	−0.207709
$750$	−14.8855	−0.543543
$751$	45.1079	1.64601	0.823006	−	0.568033i	$-0.192295\pi$
$751$	45.1079	1.64601	0.823006	+	0.568033i	$0.192295\pi$
$752$	−13.5875	−0.495485
$753$	3.81452	0.139009
$754$	10.7078	0.389955
$755$	−32.2746	−1.17459
$756$	−6.09573	−0.221700
$757$	−21.0040	−0.763402	−0.381701	−	0.924286i	$-0.624662\pi$
$757$	−21.0040	−0.763402	−0.381701	+	0.924286i	$0.624662\pi$
$758$	39.7552	1.44397
$759$	0	0
$760$	−9.06649	−0.328876
$761$	−36.6522	−1.32864	−0.664320	−	0.747448i	$-0.731279\pi$
$761$	−36.6522	−1.32864	−0.664320	+	0.747448i	$0.731279\pi$
$762$	−35.8197	−1.29761
$763$	−11.6787	−0.422799
$764$	24.2532	0.877451
$765$	15.4918	0.560108
$766$	22.4065	0.809578
$767$	−9.48868	−0.342616
$768$	20.9549	0.756144
$769$	50.5190	1.82176	0.910881	−	0.412669i	$-0.135403\pi$
$769$	50.5190	1.82176	0.910881	+	0.412669i	$0.135403\pi$
$770$	0	0
$771$	−28.5111	−1.02680
$772$	8.10510	0.291709
$773$	−21.2267	−0.763471	−0.381736	−	0.924272i	$-0.624674\pi$
$773$	−21.2267	−0.763471	−0.381736	+	0.924272i	$0.624674\pi$
$774$	34.9627	1.25671
$775$	16.3974	0.589012
$776$	15.7428	0.565133
$777$	−3.50458	−0.125726
$778$	−45.5296	−1.63231
$779$	−27.2331	−0.975726
$780$	6.91089	0.247450
$781$	0	0
$782$	24.1088	0.862130
$783$	−14.3069	−0.511287
$784$	29.8962	1.06772
$785$	47.6757	1.70162
$786$	−26.6562	−0.950794
$787$	−10.6408	−0.379303	−0.189651	−	0.981851i	$-0.560736\pi$
$787$	−10.6408	−0.379303	−0.189651	+	0.981851i	$0.560736\pi$
$788$	−33.9100	−1.20799
$789$	−7.99631	−0.284676
$790$	59.9872	2.13425
$791$	2.20443	0.0783805
$792$	0	0
$793$	−21.4649	−0.762241
$794$	−31.7043	−1.12514
$795$	−15.2474	−0.540769
$796$	24.3793	0.864101
$797$	−11.4266	−0.404750	−0.202375	−	0.979308i	$-0.564866\pi$
$797$	−11.4266	−0.404750	−0.202375	+	0.979308i	$0.564866\pi$
$798$	−4.49406	−0.159088
$799$	8.21999	0.290802
$800$	11.6505	0.411906
$801$	15.0048	0.530169
$802$	−13.0996	−0.462564
$803$	0	0
$804$	11.6836	0.412050
$805$	11.4627	0.404007
$806$	32.7138	1.15229
$807$	−31.8714	−1.12193
$808$	−3.41617	−0.120180
$809$	−9.44453	−0.332052	−0.166026	−	0.986121i	$-0.553094\pi$
$809$	−9.44453	−0.332052	−0.166026	+	0.986121i	$0.553094\pi$
$810$	3.87173	0.136039
$811$	45.8965	1.61165	0.805823	−	0.592157i	$-0.201724\pi$
$811$	45.8965	1.61165	0.805823	+	0.592157i	$0.201724\pi$
$812$	3.43586	0.120575
$813$	−1.01447	−0.0355790
$814$	0	0
$815$	3.03024	0.106145
$816$	−14.9649	−0.523875
$817$	24.8695	0.870075
$818$	26.3190	0.920224
$819$	4.03103	0.140856
$820$	35.0933	1.22551
$821$	12.8585	0.448765	0.224383	−	0.974501i	$-0.427963\pi$
$821$	12.8585	0.448765	0.224383	+	0.974501i	$0.427963\pi$
$822$	−41.1456	−1.43512
$823$	31.5051	1.09820	0.549099	−	0.835757i	$-0.314971\pi$
$823$	31.5051	1.09820	0.549099	+	0.835757i	$0.314971\pi$
$824$	8.92196	0.310811
$825$	0	0
$826$	−7.95128	−0.276661
$827$	−2.57502	−0.0895422	−0.0447711	−	0.998997i	$-0.514256\pi$
$827$	−2.57502	−0.0895422	−0.0447711	+	0.998997i	$0.514256\pi$
$828$	10.9740	0.381373
$829$	−20.5722	−0.714501	−0.357251	−	0.934009i	$-0.616286\pi$
$829$	−20.5722	−0.714501	−0.357251	+	0.934009i	$0.616286\pi$
$830$	−46.9570	−1.62990
$831$	27.0501	0.938358
$832$	2.54178	0.0881205
$833$	−18.0862	−0.626649
$834$	−18.2069	−0.630455
$835$	−28.0651	−0.971232
$836$	0	0
$837$	−43.7095	−1.51082
$838$	5.02279	0.173509
$839$	−47.6533	−1.64518	−0.822588	−	0.568638i	$-0.807470\pi$
$839$	−47.6533	−1.64518	−0.822588	+	0.568638i	$0.807470\pi$
$840$	−3.54151	−0.122194
$841$	−20.9359	−0.721929
$842$	−36.9209	−1.27238
$843$	7.89372	0.271874
$844$	29.5000	1.01543
$845$	22.6083	0.777750
$846$	9.77140	0.335948
$847$	0	0
$848$	−28.3416	−0.973254
$849$	−10.2727	−0.352559
$850$	−10.1727	−0.348920
$851$	15.8972	0.544950
$852$	−2.35404	−0.0806482
$853$	7.50058	0.256815	0.128408	−	0.991721i	$-0.459013\pi$
$853$	7.50058	0.256815	0.128408	+	0.991721i	$0.459013\pi$
$854$	−17.9871	−0.615505
$855$	13.0994	0.447989
$856$	−7.96679	−0.272299
$857$	9.47247	0.323573	0.161787	−	0.986826i	$-0.448274\pi$
$857$	9.47247	0.323573	0.161787	+	0.986826i	$0.448274\pi$
$858$	0	0
$859$	−2.28687	−0.0780269	−0.0390135	−	0.999239i	$-0.512422\pi$
$859$	−2.28687	−0.0780269	−0.0390135	+	0.999239i	$0.512422\pi$
$860$	−32.0475	−1.09281
$861$	−10.6377	−0.362531
$862$	−44.7272	−1.52342
$863$	−27.3862	−0.932236	−0.466118	−	0.884723i	$-0.654348\pi$
$863$	−27.3862	−0.932236	−0.466118	+	0.884723i	$0.654348\pi$
$864$	−31.0559	−1.05654
$865$	−49.2649	−1.67506
$866$	15.3439	0.521406
$867$	−8.16557	−0.277317
$868$	10.4970	0.356292
$869$	0	0
$870$	13.5920	0.460813
$871$	−19.4677	−0.659638
$872$	−16.3675	−0.554274
$873$	−22.7454	−0.769815
$874$	20.3856	0.689554
$875$	7.95859	0.269049
$876$	12.7035	0.429212
$877$	−5.25185	−0.177343	−0.0886713	−	0.996061i	$-0.528262\pi$
$877$	−5.25185	−0.177343	−0.0886713	+	0.996061i	$0.528262\pi$
$878$	21.8475	0.737317
$879$	13.5973	0.458627
$880$	0	0
$881$	40.5420	1.36590	0.682948	−	0.730467i	$-0.260698\pi$
$881$	40.5420	1.36590	0.682948	+	0.730467i	$0.260698\pi$
$882$	−21.4997	−0.723932
$883$	36.2880	1.22119	0.610593	−	0.791944i	$-0.290931\pi$
$883$	36.2880	1.22119	0.610593	+	0.791944i	$0.290931\pi$
$884$	−7.77131	−0.261378
$885$	−12.0445	−0.404873
$886$	−19.5912	−0.658179
$887$	−5.58158	−0.187411	−0.0937056	−	0.995600i	$-0.529871\pi$
$887$	−5.58158	−0.187411	−0.0937056	+	0.995600i	$0.529871\pi$
$888$	−4.91160	−0.164823
$889$	19.1511	0.642307
$890$	−35.9184	−1.20399
$891$	0	0
$892$	−18.8684	−0.631759
$893$	6.95055	0.232591
$894$	1.90337	0.0636581
$895$	21.4628	0.717423
$896$	−9.88922	−0.330376
$897$	9.50260	0.317283
$898$	−7.52556	−0.251131
$899$	24.6368	0.821685
$900$	−4.63046	−0.154349
$901$	17.1457	0.571206
$902$	0	0
$903$	9.71444	0.323276
$904$	3.08946	0.102754
$905$	6.43446	0.213889
$906$	−22.4206	−0.744875
$907$	−40.5811	−1.34747	−0.673737	−	0.738971i	$-0.735312\pi$
$907$	−40.5811	−1.34747	−0.673737	+	0.738971i	$0.735312\pi$
$908$	31.7039	1.05213
$909$	4.93572	0.163708
$910$	−9.64944	−0.319876
$911$	22.5409	0.746815	0.373407	−	0.927667i	$-0.378189\pi$
$911$	22.5409	0.746815	0.373407	+	0.927667i	$0.378189\pi$
$912$	−12.6538	−0.419009
$913$	0	0
$914$	7.54449	0.249550
$915$	−27.2467	−0.900747
$916$	−2.22021	−0.0733577
$917$	14.2518	0.470636
$918$	27.1166	0.894982
$919$	−43.8633	−1.44692	−0.723459	−	0.690367i	$-0.757449\pi$
$919$	−43.8633	−1.44692	−0.723459	+	0.690367i	$0.757449\pi$
$920$	16.0648	0.529640
$921$	−2.99766	−0.0987763
$922$	−45.7462	−1.50657
$923$	3.92239	0.129107
$924$	0	0
$925$	−6.70780	−0.220551
$926$	24.5372	0.806341
$927$	−12.8906	−0.423382
$928$	17.5046	0.574618
$929$	−20.4639	−0.671398	−0.335699	−	0.941969i	$-0.608973\pi$
$929$	−20.4639	−0.671398	−0.335699	+	0.941969i	$0.608973\pi$
$930$	41.5255	1.36168
$931$	−15.2931	−0.501210
$932$	−28.0816	−0.919844
$933$	0.275933	0.00903365
$934$	3.12779	0.102345
$935$	0	0
$936$	5.64942	0.184657
$937$	13.7573	0.449431	0.224715	−	0.974424i	$-0.427855\pi$
$937$	13.7573	0.449431	0.224715	+	0.974424i	$0.427855\pi$
$938$	−16.3135	−0.532653
$939$	−21.2062	−0.692038
$940$	−8.95666	−0.292134
$941$	−1.03861	−0.0338576	−0.0169288	−	0.999857i	$-0.505389\pi$
$941$	−1.03861	−0.0338576	−0.0169288	+	0.999857i	$0.505389\pi$
$942$	33.1195	1.07909
$943$	48.2539	1.57136
$944$	−22.3882	−0.728674
$945$	12.8928	0.419403
$946$	0	0
$947$	39.1265	1.27144	0.635720	−	0.771920i	$-0.280703\pi$
$947$	39.1265	1.27144	0.635720	+	0.771920i	$0.280703\pi$
$948$	15.9569	0.518256
$949$	−21.1671	−0.687112
$950$	−8.60167	−0.279075
$951$	−11.9464	−0.387389
$952$	3.98244	0.129072
$953$	−46.7108	−1.51311	−0.756556	−	0.653929i	$-0.773119\pi$
$953$	−46.7108	−1.51311	−0.756556	+	0.653929i	$0.773119\pi$
$954$	20.3817	0.659883
$955$	−51.2968	−1.65993
$956$	11.3008	0.365493
$957$	0	0
$958$	33.8388	1.09328
$959$	21.9986	0.710371
$960$	3.22643	0.104133
$961$	44.2690	1.42803
$962$	−13.3825	−0.431468
$963$	11.5105	0.370921
$964$	−19.8902	−0.640621
$965$	−17.1427	−0.551843
$966$	7.96295	0.256204
$967$	−30.6093	−0.984327	−0.492164	−	0.870503i	$-0.663794\pi$
$967$	−30.6093	−0.984327	−0.492164	+	0.870503i	$0.663794\pi$
$968$	0	0
$969$	7.65511	0.245918
$970$	54.4476	1.74821
$971$	28.8244	0.925018	0.462509	−	0.886614i	$-0.346949\pi$
$971$	28.8244	0.925018	0.462509	+	0.886614i	$0.346949\pi$
$972$	19.7876	0.634686
$973$	9.73439	0.312070
$974$	−12.4890	−0.400174
$975$	−4.00960	−0.128410
$976$	−50.6457	−1.62113
$977$	51.6689	1.65303	0.826517	−	0.562912i	$-0.190319\pi$
$977$	51.6689	1.65303	0.826517	+	0.562912i	$0.190319\pi$
$978$	2.10506	0.0673123
$979$	0	0
$980$	19.7070	0.629518
$981$	23.6480	0.755023
$982$	23.6056	0.753285
$983$	7.06111	0.225214	0.112607	−	0.993640i	$-0.464080\pi$
$983$	7.06111	0.225214	0.112607	+	0.993640i	$0.464080\pi$
$984$	−14.9085	−0.475266
$985$	71.7214	2.28523
$986$	−15.2843	−0.486751
$987$	2.71500	0.0864193
$988$	−6.57117	−0.209057
$989$	−44.0660	−1.40122
$990$	0	0
$991$	−12.3494	−0.392292	−0.196146	−	0.980575i	$-0.562843\pi$
$991$	−12.3494	−0.392292	−0.196146	+	0.980575i	$0.562843\pi$
$992$	53.4791	1.69796
$993$	7.05051	0.223741
$994$	3.28687	0.104253
$995$	−51.5635	−1.63467
$996$	−12.4908	−0.395786
$997$	11.1646	0.353585	0.176793	−	0.984248i	$-0.443428\pi$
$997$	11.1646	0.353585	0.176793	+	0.984248i	$0.443428\pi$
$998$	34.4508	1.09052
$999$	17.8806	0.565716

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1331.2.a.e.1.4	yes	25
11.10	odd	2		1331.2.a.d.1.22	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1331.2.a.d.1.22	✓	25	11.10	odd	2
1331.2.a.e.1.4	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)

\(f(q)\)	\(=\)	\(q-1.80029 q^{2} +1.01287 q^{3} +1.24105 q^{4} -2.62489 q^{5} -1.82346 q^{6} +0.974919 q^{7} +1.36633 q^{8} -1.97409 q^{9} +O(q^{10})\)	\(q-1.80029 q^{2} +1.01287 q^{3} +1.24105 q^{4} -2.62489 q^{5} -1.82346 q^{6} +0.974919 q^{7} +1.36633 q^{8} -1.97409 q^{9} +4.72556 q^{10} +1.25702 q^{12} -2.09450 q^{13} -1.75514 q^{14} -2.65867 q^{15} -4.94189 q^{16} +2.98968 q^{17} +3.55394 q^{18} +2.52797 q^{19} -3.25761 q^{20} +0.987468 q^{21} -4.47928 q^{23} +1.38392 q^{24} +1.89002 q^{25} +3.77071 q^{26} -5.03811 q^{27} +1.20992 q^{28} +2.83973 q^{29} +4.78638 q^{30} +8.67577 q^{31} +6.16419 q^{32} -5.38230 q^{34} -2.55905 q^{35} -2.44995 q^{36} -3.54906 q^{37} -4.55109 q^{38} -2.12146 q^{39} -3.58646 q^{40} -10.7727 q^{41} -1.77773 q^{42} +9.83773 q^{43} +5.18177 q^{45} +8.06401 q^{46} +2.74945 q^{47} -5.00550 q^{48} -6.04953 q^{49} -3.40259 q^{50} +3.02816 q^{51} -2.59938 q^{52} +5.73496 q^{53} +9.07007 q^{54} +1.33206 q^{56} +2.56051 q^{57} -5.11234 q^{58} +4.53029 q^{59} -3.29954 q^{60} +10.2482 q^{61} -15.6189 q^{62} -1.92458 q^{63} -1.21355 q^{64} +5.49782 q^{65} +9.29468 q^{67} +3.71034 q^{68} -4.53693 q^{69} +4.60704 q^{70} -1.87271 q^{71} -2.69726 q^{72} +10.1060 q^{73} +6.38934 q^{74} +1.91435 q^{75} +3.13734 q^{76} +3.81924 q^{78} +12.6942 q^{79} +12.9719 q^{80} +0.819318 q^{81} +19.3940 q^{82} -9.93681 q^{83} +1.22550 q^{84} -7.84757 q^{85} -17.7108 q^{86} +2.87628 q^{87} -7.60087 q^{89} -9.32869 q^{90} -2.04197 q^{91} -5.55901 q^{92} +8.78743 q^{93} -4.94982 q^{94} -6.63564 q^{95} +6.24353 q^{96} +11.5219 q^{97} +10.8909 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 5 q^{2} - 3 q^{3} + 25 q^{4} - 3 q^{5} + 15 q^{6} + 19 q^{7} + 9 q^{8} + 22 q^{9}+O(q^{10}) \) 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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