LMFDB - Embedded newform 1441.2.a.c.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1441,2,Mod(1,1441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1441, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1441.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1441 = 11 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1441.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:	$11.5064429313$
Analytic rank:	$1$
Dimension:	$23$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	1441.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.338964 q^{2} +0.415229 q^{3} -1.88510 q^{4} +2.48639 q^{5} +0.140748 q^{6} +1.37068 q^{7} -1.31691 q^{8} -2.82758 q^{9} +O(q^{10})$	\(q+0.338964 q^{2} +0.415229 q^{3} -1.88510 q^{4} +2.48639 q^{5} +0.140748 q^{6} +1.37068 q^{7} -1.31691 q^{8} -2.82758 q^{9} +0.842796 q^{10} +1.00000 q^{11} -0.782750 q^{12} -6.16893 q^{13} +0.464612 q^{14} +1.03242 q^{15} +3.32382 q^{16} -6.22429 q^{17} -0.958448 q^{18} -1.56753 q^{19} -4.68710 q^{20} +0.569148 q^{21} +0.338964 q^{22} -8.96877 q^{23} -0.546819 q^{24} +1.18214 q^{25} -2.09104 q^{26} -2.41978 q^{27} -2.58388 q^{28} +0.948866 q^{29} +0.349953 q^{30} +9.67708 q^{31} +3.76047 q^{32} +0.415229 q^{33} -2.10981 q^{34} +3.40806 q^{35} +5.33029 q^{36} +2.06032 q^{37} -0.531337 q^{38} -2.56152 q^{39} -3.27435 q^{40} -9.20539 q^{41} +0.192921 q^{42} +1.99435 q^{43} -1.88510 q^{44} -7.03048 q^{45} -3.04009 q^{46} +5.37046 q^{47} +1.38015 q^{48} -5.12122 q^{49} +0.400702 q^{50} -2.58451 q^{51} +11.6291 q^{52} +11.2713 q^{53} -0.820218 q^{54} +2.48639 q^{55} -1.80507 q^{56} -0.650886 q^{57} +0.321631 q^{58} -7.99539 q^{59} -1.94622 q^{60} +1.55937 q^{61} +3.28018 q^{62} -3.87573 q^{63} -5.37298 q^{64} -15.3384 q^{65} +0.140748 q^{66} -15.1043 q^{67} +11.7334 q^{68} -3.72409 q^{69} +1.15521 q^{70} -0.208535 q^{71} +3.72367 q^{72} -14.1429 q^{73} +0.698375 q^{74} +0.490859 q^{75} +2.95496 q^{76} +1.37068 q^{77} -0.868263 q^{78} +0.383560 q^{79} +8.26432 q^{80} +7.47799 q^{81} -3.12029 q^{82} +2.50056 q^{83} -1.07290 q^{84} -15.4760 q^{85} +0.676014 q^{86} +0.393997 q^{87} -1.31691 q^{88} -5.72972 q^{89} -2.38308 q^{90} -8.45567 q^{91} +16.9071 q^{92} +4.01821 q^{93} +1.82039 q^{94} -3.89750 q^{95} +1.56146 q^{96} +7.59514 q^{97} -1.73591 q^{98} -2.82758 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 23 q - 7 q^{2} - 3 q^{3} + 15 q^{4} - 9 q^{5} - 11 q^{6} - 12 q^{7} - 21 q^{8} + 12 q^{9}+O(q^{10}) $ 23 * q - 7 * q^2 - 3 * q^3 + 15 * q^4 - 9 * q^5 - 11 * q^6 - 12 * q^7 - 21 * q^8 + 12 * q^9	\( 23 q - 7 q^{2} - 3 q^{3} + 15 q^{4} - 9 q^{5} - 11 q^{6} - 12 q^{7} - 21 q^{8} + 12 q^{9} - 2 q^{10} + 23 q^{11} + 8 q^{12} - 24 q^{13} - 13 q^{14} - 27 q^{15} + 7 q^{16} - 7 q^{17} - 14 q^{18} - 18 q^{19} - 4 q^{20} - 29 q^{21} - 7 q^{22} - 26 q^{23} - 4 q^{24} + 18 q^{25} + 8 q^{26} - 3 q^{27} - 11 q^{28} - 45 q^{29} + 19 q^{30} - 23 q^{31} - 34 q^{32} - 3 q^{33} - 2 q^{34} - 18 q^{35} - 6 q^{36} - 2 q^{37} - 8 q^{38} - 40 q^{39} - 24 q^{40} - 23 q^{41} + 59 q^{42} - 14 q^{43} + 15 q^{44} - 18 q^{45} - 12 q^{46} - 55 q^{47} + 10 q^{48} + 11 q^{49} - 41 q^{50} - 21 q^{51} - 37 q^{52} - 10 q^{53} - 68 q^{54} - 9 q^{55} + 2 q^{56} - 18 q^{57} + 27 q^{58} - 75 q^{59} - 63 q^{60} - 55 q^{61} + 14 q^{62} - 16 q^{63} + 19 q^{64} - 25 q^{65} - 11 q^{66} + 17 q^{67} + 41 q^{68} - 22 q^{69} + 27 q^{70} - 105 q^{71} - 11 q^{72} - 3 q^{73} - 39 q^{74} + 25 q^{75} - 30 q^{76} - 12 q^{77} + 25 q^{78} - 48 q^{79} - 37 q^{80} + 3 q^{81} + 36 q^{82} + 4 q^{83} - 111 q^{84} - 30 q^{85} + 22 q^{86} + 5 q^{87} - 21 q^{88} - 39 q^{89} + 100 q^{90} - 22 q^{91} - 30 q^{92} - 5 q^{93} + 11 q^{94} - 88 q^{95} + 13 q^{96} + 24 q^{97} - 91 q^{98} + 12 q^{99}+O(q^{100}) \) 23 * q - 7 * q^2 - 3 * q^3 + 15 * q^4 - 9 * q^5 - 11 * q^6 - 12 * q^7 - 21 * q^8 + 12 * q^9 - 2 * q^10 + 23 * q^11 + 8 * q^12 - 24 * q^13 - 13 * q^14 - 27 * q^15 + 7 * q^16 - 7 * q^17 - 14 * q^18 - 18 * q^19 - 4 * q^20 - 29 * q^21 - 7 * q^22 - 26 * q^23 - 4 * q^24 + 18 * q^25 + 8 * q^26 - 3 * q^27 - 11 * q^28 - 45 * q^29 + 19 * q^30 - 23 * q^31 - 34 * q^32 - 3 * q^33 - 2 * q^34 - 18 * q^35 - 6 * q^36 - 2 * q^37 - 8 * q^38 - 40 * q^39 - 24 * q^40 - 23 * q^41 + 59 * q^42 - 14 * q^43 + 15 * q^44 - 18 * q^45 - 12 * q^46 - 55 * q^47 + 10 * q^48 + 11 * q^49 - 41 * q^50 - 21 * q^51 - 37 * q^52 - 10 * q^53 - 68 * q^54 - 9 * q^55 + 2 * q^56 - 18 * q^57 + 27 * q^58 - 75 * q^59 - 63 * q^60 - 55 * q^61 + 14 * q^62 - 16 * q^63 + 19 * q^64 - 25 * q^65 - 11 * q^66 + 17 * q^67 + 41 * q^68 - 22 * q^69 + 27 * q^70 - 105 * q^71 - 11 * q^72 - 3 * q^73 - 39 * q^74 + 25 * q^75 - 30 * q^76 - 12 * q^77 + 25 * q^78 - 48 * q^79 - 37 * q^80 + 3 * q^81 + 36 * q^82 + 4 * q^83 - 111 * q^84 - 30 * q^85 + 22 * q^86 + 5 * q^87 - 21 * q^88 - 39 * q^89 + 100 * q^90 - 22 * q^91 - 30 * q^92 - 5 * q^93 + 11 * q^94 - 88 * q^95 + 13 * q^96 + 24 * q^97 - 91 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	0.338964	0.239684	0.119842	−	0.992793i	$-0.461761\pi$
$2$	0.338964	0.239684	0.119842	+	0.992793i	$0.461761\pi$
$3$	0.415229	0.239733	0.119866	−	0.992790i	$-0.461753\pi$
$3$	0.415229	0.239733	0.119866	+	0.992790i	$0.461753\pi$
$4$	−1.88510	−0.942552
$5$	2.48639	1.11195	0.555974	−	0.831200i	$-0.312345\pi$
$5$	2.48639	1.11195	0.555974	+	0.831200i	$0.312345\pi$
$6$	0.140748	0.0574600
$7$	1.37068	0.518070	0.259035	−	0.965868i	$-0.416595\pi$
$7$	1.37068	0.518070	0.259035	+	0.965868i	$0.416595\pi$
$8$	−1.31691	−0.465598
$9$	−2.82758	−0.942528
$10$	0.842796	0.266516
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−0.782750	−0.225960
$13$	−6.16893	−1.71095	−0.855477	−	0.517840i	$-0.826736\pi$
$13$	−6.16893	−1.71095	−0.855477	+	0.517840i	$0.826736\pi$
$14$	0.464612	0.124173
$15$	1.03242	0.266570
$16$	3.32382	0.830956
$17$	−6.22429	−1.50961	−0.754806	−	0.655948i	$-0.772269\pi$
$17$	−6.22429	−1.50961	−0.754806	+	0.655948i	$0.772269\pi$
$18$	−0.958448	−0.225908
$19$	−1.56753	−0.359617	−0.179809	−	0.983702i	$-0.557548\pi$
$19$	−1.56753	−0.359617	−0.179809	+	0.983702i	$0.557548\pi$
$20$	−4.68710	−1.04807
$21$	0.569148	0.124198
$22$	0.338964	0.0722673
$23$	−8.96877	−1.87012	−0.935059	−	0.354492i	$-0.884654\pi$
$23$	−8.96877	−1.87012	−0.935059	+	0.354492i	$0.884654\pi$
$24$	−0.546819	−0.111619
$25$	1.18214	0.236428
$26$	−2.09104	−0.410088
$27$	−2.41978	−0.465687
$28$	−2.58388	−0.488308
$29$	0.948866	0.176200	0.0881000	−	0.996112i	$-0.471921\pi$
$29$	0.948866	0.176200	0.0881000	+	0.996112i	$0.471921\pi$
$30$	0.349953	0.0638925
$31$	9.67708	1.73806	0.869028	−	0.494764i	$-0.164745\pi$
$31$	9.67708	1.73806	0.869028	+	0.494764i	$0.164745\pi$
$32$	3.76047	0.664764
$33$	0.415229	0.0722821
$34$	−2.10981	−0.361829
$35$	3.40806	0.576067
$36$	5.33029	0.888382
$37$	2.06032	0.338715	0.169358	−	0.985555i	$-0.445831\pi$
$37$	2.06032	0.338715	0.169358	+	0.985555i	$0.445831\pi$
$38$	−0.531337	−0.0861943
$39$	−2.56152	−0.410172
$40$	−3.27435	−0.517720
$41$	−9.20539	−1.43764	−0.718820	−	0.695196i	$-0.755317\pi$
$41$	−9.20539	−1.43764	−0.718820	+	0.695196i	$0.755317\pi$
$42$	0.192921	0.0297683
$43$	1.99435	0.304136	0.152068	−	0.988370i	$-0.451407\pi$
$43$	1.99435	0.304136	0.152068	+	0.988370i	$0.451407\pi$
$44$	−1.88510	−0.284190
$45$	−7.03048	−1.04804
$46$	−3.04009	−0.448236
$47$	5.37046	0.783362	0.391681	−	0.920101i	$-0.371894\pi$
$47$	5.37046	0.783362	0.391681	+	0.920101i	$0.371894\pi$
$48$	1.38015	0.199207
$49$	−5.12122	−0.731603
$50$	0.400702	0.0566678
$51$	−2.58451	−0.361903
$52$	11.6291	1.61266
$53$	11.2713	1.54823	0.774113	−	0.633047i	$-0.218196\pi$
$53$	11.2713	1.54823	0.774113	+	0.633047i	$0.218196\pi$
$54$	−0.820218	−0.111618
$55$	2.48639	0.335265
$56$	−1.80507	−0.241212
$57$	−0.650886	−0.0862119
$58$	0.321631	0.0422322
$59$	−7.99539	−1.04091	−0.520455	−	0.853889i	$-0.674238\pi$
$59$	−7.99539	−1.04091	−0.520455	+	0.853889i	$0.674238\pi$
$60$	−1.94622	−0.251256
$61$	1.55937	0.199656	0.0998282	−	0.995005i	$-0.468171\pi$
$61$	1.55937	0.199656	0.0998282	+	0.995005i	$0.468171\pi$
$62$	3.28018	0.416583
$63$	−3.87573	−0.488296
$64$	−5.37298	−0.671623
$65$	−15.3384	−1.90249
$66$	0.140748	0.0173248
$67$	−15.1043	−1.84528	−0.922641	−	0.385659i	$-0.873974\pi$
$67$	−15.1043	−1.84528	−0.922641	+	0.385659i	$0.873974\pi$
$68$	11.7334	1.42289
$69$	−3.72409	−0.448328
$70$	1.15521	0.138074
$71$	−0.208535	−0.0247486	−0.0123743	−	0.999923i	$-0.503939\pi$
$71$	−0.208535	−0.0247486	−0.0123743	+	0.999923i	$0.503939\pi$
$72$	3.72367	0.438839
$73$	−14.1429	−1.65530	−0.827648	−	0.561248i	$-0.810322\pi$
$73$	−14.1429	−1.65530	−0.827648	+	0.561248i	$0.810322\pi$
$74$	0.698375	0.0811845
$75$	0.490859	0.0566795
$76$	2.95496	0.338958
$77$	1.37068	0.156204
$78$	−0.868263	−0.0983114
$79$	0.383560	0.0431539	0.0215770	−	0.999767i	$-0.493131\pi$
$79$	0.383560	0.0431539	0.0215770	+	0.999767i	$0.493131\pi$
$80$	8.26432	0.923979
$81$	7.47799	0.830888
$82$	−3.12029	−0.344578
$83$	2.50056	0.274472	0.137236	−	0.990538i	$-0.456178\pi$
$83$	2.50056	0.274472	0.137236	+	0.990538i	$0.456178\pi$
$84$	−1.07290	−0.117063
$85$	−15.4760	−1.67861
$86$	0.676014	0.0728964
$87$	0.393997	0.0422409
$88$	−1.31691	−0.140383
$89$	−5.72972	−0.607350	−0.303675	−	0.952776i	$-0.598214\pi$
$89$	−5.72972	−0.607350	−0.303675	+	0.952776i	$0.598214\pi$
$90$	−2.38308	−0.251198
$91$	−8.45567	−0.886395
$92$	16.9071	1.76268
$93$	4.01821	0.416669
$94$	1.82039	0.187759
$95$	−3.89750	−0.399875
$96$	1.56146	0.159366
$97$	7.59514	0.771170	0.385585	−	0.922672i	$-0.374000\pi$
$97$	7.59514	0.771170	0.385585	+	0.922672i	$0.374000\pi$
$98$	−1.73591	−0.175353
$99$	−2.82758	−0.284183
$100$	−2.22845	−0.222845
$101$	−2.66251	−0.264929	−0.132465	−	0.991188i	$-0.542289\pi$
$101$	−2.66251	−0.264929	−0.132465	+	0.991188i	$0.542289\pi$
$102$	−0.876054	−0.0867423
$103$	15.2276	1.50042	0.750210	−	0.661200i	$-0.229952\pi$
$103$	15.2276	1.50042	0.750210	+	0.661200i	$0.229952\pi$
$104$	8.12393	0.796616
$105$	1.41512	0.138102
$106$	3.82055	0.371084
$107$	5.52741	0.534355	0.267178	−	0.963647i	$-0.413909\pi$
$107$	5.52741	0.534355	0.267178	+	0.963647i	$0.413909\pi$
$108$	4.56154	0.438935
$109$	−17.4254	−1.66905	−0.834526	−	0.550969i	$-0.814258\pi$
$109$	−17.4254	−1.66905	−0.834526	+	0.550969i	$0.814258\pi$
$110$	0.842796	0.0803575
$111$	0.855507	0.0812011
$112$	4.55591	0.430493
$113$	15.5987	1.46740	0.733699	−	0.679474i	$-0.237792\pi$
$113$	15.5987	1.46740	0.733699	+	0.679474i	$0.237792\pi$
$114$	−0.220627	−0.0206636
$115$	−22.2999	−2.07947
$116$	−1.78871	−0.166078
$117$	17.4432	1.61262
$118$	−2.71015	−0.249489
$119$	−8.53154	−0.782085
$120$	−1.35961	−0.124114
$121$	1.00000	0.0909091
$122$	0.528568	0.0478543
$123$	−3.82234	−0.344649
$124$	−18.2423	−1.63821
$125$	−9.49269	−0.849052
$126$	−1.31373	−0.117036
$127$	−1.32689	−0.117743	−0.0588713	−	0.998266i	$-0.518750\pi$
$127$	−1.32689	−0.117743	−0.0588713	+	0.998266i	$0.518750\pi$
$128$	−9.34219	−0.825741
$129$	0.828114	0.0729114
$130$	−5.19915	−0.455996
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	−0.782750	−0.0681296
$133$	−2.14860	−0.186307
$134$	−5.11981	−0.442284
$135$	−6.01653	−0.517820
$136$	8.19682	0.702872
$137$	−19.1366	−1.63495	−0.817474	−	0.575966i	$-0.804626\pi$
$137$	−19.1366	−1.63495	−0.817474	+	0.575966i	$0.804626\pi$
$138$	−1.26233	−0.107457
$139$	2.95439	0.250588	0.125294	−	0.992120i	$-0.460013\pi$
$139$	2.95439	0.250588	0.125294	+	0.992120i	$0.460013\pi$
$140$	−6.42454	−0.542973
$141$	2.22997	0.187797
$142$	−0.0706859	−0.00593182
$143$	−6.16893	−0.515872
$144$	−9.39839	−0.783199
$145$	2.35925	0.195925
$146$	−4.79391	−0.396747
$147$	−2.12648	−0.175389
$148$	−3.88392	−0.319257
$149$	−16.3412	−1.33873	−0.669363	−	0.742935i	$-0.733433\pi$
$149$	−16.3412	−1.33873	−0.669363	+	0.742935i	$0.733433\pi$
$150$	0.166383	0.0135851
$151$	2.03469	0.165581	0.0827903	−	0.996567i	$-0.473617\pi$
$151$	2.03469	0.165581	0.0827903	+	0.996567i	$0.473617\pi$
$152$	2.06430	0.167437
$153$	17.5997	1.42285
$154$	0.464612	0.0374395
$155$	24.0610	1.93263
$156$	4.82873	0.386608
$157$	5.65104	0.451002	0.225501	−	0.974243i	$-0.427598\pi$
$157$	5.65104	0.451002	0.225501	+	0.974243i	$0.427598\pi$
$158$	0.130013	0.0103433
$159$	4.68015	0.371160
$160$	9.35001	0.739183
$161$	−12.2934	−0.968852
$162$	2.53477	0.199150
$163$	−11.2758	−0.883193	−0.441596	−	0.897214i	$-0.645588\pi$
$163$	−11.2758	−0.883193	−0.441596	+	0.897214i	$0.645588\pi$
$164$	17.3531	1.35505
$165$	1.03242	0.0803739
$166$	0.847598	0.0657864
$167$	23.8818	1.84803	0.924016	−	0.382355i	$-0.124887\pi$
$167$	23.8818	1.84803	0.924016	+	0.382355i	$0.124887\pi$
$168$	−0.749516	−0.0578264
$169$	25.0558	1.92737
$170$	−5.24581	−0.402335
$171$	4.43234	0.338949
$172$	−3.75957	−0.286664
$173$	13.3249	1.01307	0.506537	−	0.862218i	$-0.330925\pi$
$173$	13.3249	1.01307	0.506537	+	0.862218i	$0.330925\pi$
$174$	0.133551	0.0101244
$175$	1.62034	0.122486
$176$	3.32382	0.250543
$177$	−3.31992	−0.249540
$178$	−1.94217	−0.145572
$179$	−2.41928	−0.180825	−0.0904127	−	0.995904i	$-0.528819\pi$
$179$	−2.41928	−0.180825	−0.0904127	+	0.995904i	$0.528819\pi$
$180$	13.2532	0.987834
$181$	−2.36309	−0.175647	−0.0878237	−	0.996136i	$-0.527991\pi$
$181$	−2.36309	−0.175647	−0.0878237	+	0.996136i	$0.527991\pi$
$182$	−2.86616	−0.212454
$183$	0.647494	0.0478642
$184$	11.8111	0.870723
$185$	5.12277	0.376634
$186$	1.36203	0.0998686
$187$	−6.22429	−0.455165
$188$	−10.1239	−0.738359
$189$	−3.31676	−0.241259
$190$	−1.32111	−0.0958435
$191$	−2.29113	−0.165780	−0.0828901	−	0.996559i	$-0.526415\pi$
$191$	−2.29113	−0.165780	−0.0828901	+	0.996559i	$0.526415\pi$
$192$	−2.23102	−0.161010
$193$	−12.8841	−0.927414	−0.463707	−	0.885989i	$-0.653481\pi$
$193$	−12.8841	−0.927414	−0.463707	+	0.885989i	$0.653481\pi$
$194$	2.57448	0.184837
$195$	−6.36894	−0.456089
$196$	9.65404	0.689574
$197$	19.0039	1.35397	0.676985	−	0.735997i	$-0.263286\pi$
$197$	19.0039	1.35397	0.676985	+	0.735997i	$0.263286\pi$
$198$	−0.958448	−0.0681140
$199$	−4.25826	−0.301860	−0.150930	−	0.988544i	$-0.548227\pi$
$199$	−4.25826	−0.301860	−0.150930	+	0.988544i	$0.548227\pi$
$200$	−1.55677	−0.110080
$201$	−6.27174	−0.442375
$202$	−0.902493	−0.0634992
$203$	1.30060	0.0912839
$204$	4.87206	0.341113
$205$	−22.8882	−1.59858
$206$	5.16160	0.359626
$207$	25.3600	1.76264
$208$	−20.5044	−1.42173
$209$	−1.56753	−0.108429
$210$	0.479676	0.0331008
$211$	−4.07680	−0.280659	−0.140329	−	0.990105i	$-0.544816\pi$
$211$	−4.07680	−0.280659	−0.140329	+	0.990105i	$0.544816\pi$
$212$	−21.2475	−1.45928
$213$	−0.0865899	−0.00593304
$214$	1.87359	0.128076
$215$	4.95875	0.338184
$216$	3.18663	0.216823
$217$	13.2642	0.900435
$218$	−5.90658	−0.400044
$219$	−5.87252	−0.396828
$220$	−4.68710	−0.316005
$221$	38.3972	2.58288
$222$	0.289986	0.0194626
$223$	11.5636	0.774359	0.387179	−	0.922004i	$-0.373449\pi$
$223$	11.5636	0.774359	0.387179	+	0.922004i	$0.373449\pi$
$224$	5.15442	0.344394
$225$	−3.34260	−0.222840
$226$	5.28738	0.351711
$227$	3.23773	0.214895	0.107448	−	0.994211i	$-0.465732\pi$
$227$	3.23773	0.214895	0.107448	+	0.994211i	$0.465732\pi$
$228$	1.22699	0.0812592
$229$	8.80749	0.582015	0.291008	−	0.956721i	$-0.406009\pi$
$229$	8.80749	0.582015	0.291008	+	0.956721i	$0.406009\pi$
$230$	−7.55885	−0.498416
$231$	0.569148	0.0374472
$232$	−1.24957	−0.0820383
$233$	−0.727226	−0.0476421	−0.0238211	−	0.999716i	$-0.507583\pi$
$233$	−0.727226	−0.0476421	−0.0238211	+	0.999716i	$0.507583\pi$
$234$	5.91261	0.386519
$235$	13.3531	0.871058
$236$	15.0721	0.981112
$237$	0.159265	0.0103454
$238$	−2.89188	−0.187453
$239$	−14.7947	−0.956990	−0.478495	−	0.878090i	$-0.658817\pi$
$239$	−14.7947	−0.956990	−0.478495	+	0.878090i	$0.658817\pi$
$240$	3.43159	0.221508
$241$	27.2182	1.75328	0.876639	−	0.481150i	$-0.159781\pi$
$241$	27.2182	1.75328	0.876639	+	0.481150i	$0.159781\pi$
$242$	0.338964	0.0217894
$243$	10.3644	0.664878
$244$	−2.93957	−0.188186
$245$	−12.7334	−0.813505
$246$	−1.29564	−0.0826067
$247$	9.67002	0.615288
$248$	−12.7438	−0.809234
$249$	1.03830	0.0657999
$250$	−3.21768	−0.203504
$251$	−22.8496	−1.44226	−0.721128	−	0.692802i	$-0.756376\pi$
$251$	−22.8496	−1.44226	−0.721128	+	0.692802i	$0.756376\pi$
$252$	7.30615	0.460244
$253$	−8.96877	−0.563862
$254$	−0.449768	−0.0282209
$255$	−6.42609	−0.402418
$256$	7.57930	0.473706
$257$	−6.09784	−0.380373	−0.190186	−	0.981748i	$-0.560909\pi$
$257$	−6.09784	−0.380373	−0.190186	+	0.981748i	$0.560909\pi$
$258$	0.280701	0.0174757
$259$	2.82406	0.175478
$260$	28.9144	1.79320
$261$	−2.68300	−0.166073
$262$	0.338964	0.0209412
$263$	28.3790	1.74992	0.874962	−	0.484192i	$-0.160886\pi$
$263$	28.3790	1.74992	0.874962	+	0.484192i	$0.160886\pi$
$264$	−0.546819	−0.0336544
$265$	28.0248	1.72155
$266$	−0.728296	−0.0446547
$267$	−2.37915	−0.145602
$268$	28.4732	1.73927
$269$	−6.80621	−0.414982	−0.207491	−	0.978237i	$-0.566530\pi$
$269$	−6.80621	−0.414982	−0.207491	+	0.978237i	$0.566530\pi$
$270$	−2.03938	−0.124113
$271$	−1.44091	−0.0875290	−0.0437645	−	0.999042i	$-0.513935\pi$
$271$	−1.44091	−0.0875290	−0.0437645	+	0.999042i	$0.513935\pi$
$272$	−20.6884	−1.25442
$273$	−3.51104	−0.212498
$274$	−6.48660	−0.391870
$275$	1.18214	0.0712857
$276$	7.02030	0.422573
$277$	23.3542	1.40322	0.701609	−	0.712562i	$-0.252465\pi$
$277$	23.3542	1.40322	0.701609	+	0.712562i	$0.252465\pi$
$278$	1.00143	0.0600619
$279$	−27.3628	−1.63817
$280$	−4.48810	−0.268215
$281$	−22.0291	−1.31415	−0.657073	−	0.753827i	$-0.728206\pi$
$281$	−22.0291	−1.31415	−0.657073	+	0.753827i	$0.728206\pi$
$282$	0.755879	0.0450119
$283$	−10.9234	−0.649329	−0.324665	−	0.945829i	$-0.605251\pi$
$283$	−10.9234	−0.649329	−0.324665	+	0.945829i	$0.605251\pi$
$284$	0.393110	0.0233268
$285$	−1.61836	−0.0958632
$286$	−2.09104	−0.123646
$287$	−12.6177	−0.744798
$288$	−10.6331	−0.626559
$289$	21.7418	1.27893
$290$	0.799700	0.0469600
$291$	3.15373	0.184875
$292$	26.6607	1.56020
$293$	−7.34724	−0.429230	−0.214615	−	0.976699i	$-0.568850\pi$
$293$	−7.34724	−0.429230	−0.214615	+	0.976699i	$0.568850\pi$
$294$	−0.720800	−0.0420379
$295$	−19.8797	−1.15744
$296$	−2.71326	−0.157705
$297$	−2.41978	−0.140410
$298$	−5.53909	−0.320871
$299$	55.3278	3.19969
$300$	−0.925319	−0.0534233
$301$	2.73363	0.157564
$302$	0.689686	0.0396870
$303$	−1.10555	−0.0635122
$304$	−5.21021	−0.298826
$305$	3.87719	0.222007
$306$	5.96566	0.341034
$307$	−19.5098	−1.11348	−0.556741	−	0.830686i	$-0.687948\pi$
$307$	−19.5098	−1.11348	−0.556741	+	0.830686i	$0.687948\pi$
$308$	−2.58388	−0.147230
$309$	6.32294	0.359700
$310$	8.15581	0.463219
$311$	−9.71989	−0.551164	−0.275582	−	0.961278i	$-0.588871\pi$
$311$	−9.71989	−0.551164	−0.275582	+	0.961278i	$0.588871\pi$
$312$	3.37329	0.190975
$313$	−2.38768	−0.134960	−0.0674799	−	0.997721i	$-0.521496\pi$
$313$	−2.38768	−0.134960	−0.0674799	+	0.997721i	$0.521496\pi$
$314$	1.91550	0.108098
$315$	−9.63657	−0.542959
$316$	−0.723051	−0.0406748
$317$	16.0944	0.903953	0.451976	−	0.892030i	$-0.350719\pi$
$317$	16.0944	0.903953	0.451976	+	0.892030i	$0.350719\pi$
$318$	1.58640	0.0889610
$319$	0.948866	0.0531263
$320$	−13.3593	−0.746809
$321$	2.29514	0.128102
$322$	−4.16700	−0.232218
$323$	9.75679	0.542882
$324$	−14.0968	−0.783155
$325$	−7.29254	−0.404517
$326$	−3.82210	−0.211687
$327$	−7.23554	−0.400126
$328$	12.1227	0.669362
$329$	7.36121	0.405837
$330$	0.349953	0.0192643
$331$	1.85400	0.101905	0.0509525	−	0.998701i	$-0.483774\pi$
$331$	1.85400	0.101905	0.0509525	+	0.998701i	$0.483774\pi$
$332$	−4.71381	−0.258704
$333$	−5.82574	−0.319249
$334$	8.09507	0.442943
$335$	−37.5552	−2.05186
$336$	1.89175	0.103203
$337$	5.68194	0.309515	0.154757	−	0.987953i	$-0.450540\pi$
$337$	5.68194	0.309515	0.154757	+	0.987953i	$0.450540\pi$
$338$	8.49299	0.461958
$339$	6.47702	0.351783
$340$	29.1739	1.58218
$341$	9.67708	0.524043
$342$	1.50240	0.0812405
$343$	−16.6144	−0.897092
$344$	−2.62638	−0.141605
$345$	−9.25956	−0.498518
$346$	4.51666	0.242817
$347$	−32.0523	−1.72066	−0.860329	−	0.509739i	$-0.829742\pi$
$347$	−32.0523	−1.72066	−0.860329	+	0.509739i	$0.829742\pi$
$348$	−0.742724	−0.0398142
$349$	−2.34399	−0.125471	−0.0627355	−	0.998030i	$-0.519982\pi$
$349$	−2.34399	−0.125471	−0.0627355	+	0.998030i	$0.519982\pi$
$350$	0.549236	0.0293579
$351$	14.9275	0.796770
$352$	3.76047	0.200434
$353$	13.3577	0.710959	0.355479	−	0.934684i	$-0.384318\pi$
$353$	13.3577	0.710959	0.355479	+	0.934684i	$0.384318\pi$
$354$	−1.12533	−0.0598107
$355$	−0.518500	−0.0275191
$356$	10.8011	0.572458
$357$	−3.54254	−0.187491
$358$	−0.820048	−0.0433409
$359$	4.32430	0.228228	0.114114	−	0.993468i	$-0.463597\pi$
$359$	4.32430	0.228228	0.114114	+	0.993468i	$0.463597\pi$
$360$	9.25850	0.487966
$361$	−16.5428	−0.870676
$362$	−0.801003	−0.0420998
$363$	0.415229	0.0217939
$364$	15.9398	0.835473
$365$	−35.1647	−1.84060
$366$	0.219477	0.0114722
$367$	−1.66430	−0.0868758	−0.0434379	−	0.999056i	$-0.513831\pi$
$367$	−1.66430	−0.0868758	−0.0434379	+	0.999056i	$0.513831\pi$
$368$	−29.8106	−1.55399
$369$	26.0290	1.35502
$370$	1.73643	0.0902729
$371$	15.4493	0.802090
$372$	−7.57474	−0.392732
$373$	3.38334	0.175182	0.0875912	−	0.996157i	$-0.472083\pi$
$373$	3.38334	0.175182	0.0875912	+	0.996157i	$0.472083\pi$
$374$	−2.10981	−0.109096
$375$	−3.94164	−0.203546
$376$	−7.07241	−0.364731
$377$	−5.85349	−0.301470
$378$	−1.12426	−0.0578257
$379$	20.1808	1.03662	0.518308	−	0.855194i	$-0.326562\pi$
$379$	20.1808	1.03662	0.518308	+	0.855194i	$0.326562\pi$
$380$	7.34720	0.376903
$381$	−0.550964	−0.0282267
$382$	−0.776609	−0.0397348
$383$	−38.7297	−1.97900	−0.989499	−	0.144542i	$-0.953829\pi$
$383$	−38.7297	−1.97900	−0.989499	+	0.144542i	$0.953829\pi$
$384$	−3.87915	−0.197957
$385$	3.40806	0.173691
$386$	−4.36723	−0.222286
$387$	−5.63921	−0.286657
$388$	−14.3176	−0.726868
$389$	14.9698	0.759000	0.379500	−	0.925192i	$-0.376096\pi$
$389$	14.9698	0.759000	0.379500	+	0.925192i	$0.376096\pi$
$390$	−2.15884	−0.109317
$391$	55.8242	2.82315
$392$	6.74418	0.340633
$393$	0.415229	0.0209455
$394$	6.44162	0.324524
$395$	0.953681	0.0479849
$396$	5.33029	0.267857
$397$	8.55475	0.429351	0.214675	−	0.976685i	$-0.431131\pi$
$397$	8.55475	0.429351	0.214675	+	0.976685i	$0.431131\pi$
$398$	−1.44340	−0.0723510
$399$	−0.892159	−0.0446638
$400$	3.92922	0.196461
$401$	5.98572	0.298912	0.149456	−	0.988768i	$-0.452248\pi$
$401$	5.98572	0.298912	0.149456	+	0.988768i	$0.452248\pi$
$402$	−2.12589	−0.106030
$403$	−59.6973	−2.97373
$404$	5.01910	0.249710
$405$	18.5932	0.923904
$406$	0.440855	0.0218793
$407$	2.06032	0.102126
$408$	3.40356	0.168501
$409$	−10.8386	−0.535936	−0.267968	−	0.963428i	$-0.586352\pi$
$409$	−10.8386	−0.535936	−0.267968	+	0.963428i	$0.586352\pi$
$410$	−7.75826	−0.383153
$411$	−7.94606	−0.391950
$412$	−28.7056	−1.41422
$413$	−10.9592	−0.539265
$414$	8.59611	0.422476
$415$	6.21736	0.305198
$416$	−23.1981	−1.13738
$417$	1.22675	0.0600742
$418$	−0.531337	−0.0259886
$419$	−0.383955	−0.0187575	−0.00937873	−	0.999956i	$-0.502985\pi$
$419$	−0.383955	−0.0187575	−0.00937873	+	0.999956i	$0.502985\pi$
$420$	−2.66766	−0.130168
$421$	29.4323	1.43444	0.717221	−	0.696846i	$-0.245414\pi$
$421$	29.4323	1.43444	0.717221	+	0.696846i	$0.245414\pi$
$422$	−1.38189	−0.0672693
$423$	−15.1854	−0.738341
$424$	−14.8432	−0.720851
$425$	−7.35798	−0.356914
$426$	−0.0293508	−0.00142205
$427$	2.13740	0.103436
$428$	−10.4197	−0.503657
$429$	−2.56152	−0.123671
$430$	1.68083	0.0810570
$431$	−5.69251	−0.274199	−0.137099	−	0.990557i	$-0.543778\pi$
$431$	−5.69251	−0.274199	−0.137099	+	0.990557i	$0.543778\pi$
$432$	−8.04293	−0.386966
$433$	25.2318	1.21256	0.606281	−	0.795250i	$-0.292661\pi$
$433$	25.2318	1.21256	0.606281	+	0.795250i	$0.292661\pi$
$434$	4.49609	0.215819
$435$	0.979630	0.0469696
$436$	32.8487	1.57317
$437$	14.0589	0.672526
$438$	−1.99057	−0.0951132
$439$	−27.3494	−1.30532	−0.652658	−	0.757652i	$-0.726346\pi$
$439$	−27.3494	−1.30532	−0.652658	+	0.757652i	$0.726346\pi$
$440$	−3.27435	−0.156099
$441$	14.4807	0.689557
$442$	13.0153	0.619073
$443$	24.8918	1.18264	0.591322	−	0.806436i	$-0.298606\pi$
$443$	24.8918	1.18264	0.591322	+	0.806436i	$0.298606\pi$
$444$	−1.61272	−0.0765362
$445$	−14.2463	−0.675341
$446$	3.91966	0.185601
$447$	−6.78536	−0.320936
$448$	−7.36467	−0.347948
$449$	19.0052	0.896910	0.448455	−	0.893805i	$-0.351974\pi$
$449$	19.0052	0.896910	0.448455	+	0.893805i	$0.351974\pi$
$450$	−1.13302	−0.0534110
$451$	−9.20539	−0.433465
$452$	−29.4051	−1.38310
$453$	0.844862	0.0396951
$454$	1.09747	0.0515069
$455$	−21.0241	−0.985624
$456$	0.857157	0.0401401
$457$	4.74754	0.222081	0.111040	−	0.993816i	$-0.464582\pi$
$457$	4.74754	0.222081	0.111040	+	0.993816i	$0.464582\pi$
$458$	2.98542	0.139499
$459$	15.0614	0.703007
$460$	42.0376	1.96001
$461$	−14.2755	−0.664876	−0.332438	−	0.943125i	$-0.607871\pi$
$461$	−14.2755	−0.664876	−0.332438	+	0.943125i	$0.607871\pi$
$462$	0.192921	0.00897548
$463$	−31.7975	−1.47776	−0.738879	−	0.673839i	$-0.764644\pi$
$463$	−31.7975	−1.47776	−0.738879	+	0.673839i	$0.764644\pi$
$464$	3.15386	0.146414
$465$	9.99083	0.463314
$466$	−0.246503	−0.0114190
$467$	26.2226	1.21344	0.606718	−	0.794917i	$-0.292486\pi$
$467$	26.2226	1.21344	0.606718	+	0.794917i	$0.292486\pi$
$468$	−32.8822	−1.51998
$469$	−20.7032	−0.955986
$470$	4.52620	0.208778
$471$	2.34647	0.108120
$472$	10.5292	0.484646
$473$	1.99435	0.0917005
$474$	0.0539852	0.00247962
$475$	−1.85304	−0.0850235
$476$	16.0828	0.737156
$477$	−31.8704	−1.45925
$478$	−5.01487	−0.229375
$479$	5.02769	0.229721	0.114860	−	0.993382i	$-0.463358\pi$
$479$	5.02769	0.229721	0.114860	+	0.993382i	$0.463358\pi$
$480$	3.88239	0.177206
$481$	−12.7100	−0.579526
$482$	9.22597	0.420232
$483$	−5.10456	−0.232266
$484$	−1.88510	−0.0856865
$485$	18.8845	0.857501
$486$	3.51316	0.159360
$487$	30.8478	1.39785	0.698924	−	0.715196i	$-0.253662\pi$
$487$	30.8478	1.39785	0.698924	+	0.715196i	$0.253662\pi$
$488$	−2.05354	−0.0929595
$489$	−4.68206	−0.211730
$490$	−4.31615	−0.194984
$491$	−42.9376	−1.93774	−0.968872	−	0.247561i	$-0.920371\pi$
$491$	−42.9376	−1.93774	−0.968872	+	0.247561i	$0.920371\pi$
$492$	7.20551	0.324850
$493$	−5.90602	−0.265994
$494$	3.27778	0.147474
$495$	−7.03048	−0.315997
$496$	32.1649	1.44425
$497$	−0.285836	−0.0128215
$498$	0.351947	0.0157711
$499$	−16.6856	−0.746951	−0.373476	−	0.927640i	$-0.621834\pi$
$499$	−16.6856	−0.746951	−0.373476	+	0.927640i	$0.621834\pi$
$500$	17.8947	0.800276
$501$	9.91643	0.443033
$502$	−7.74519	−0.345685
$503$	−21.3820	−0.953375	−0.476687	−	0.879073i	$-0.658163\pi$
$503$	−21.3820	−0.953375	−0.476687	+	0.879073i	$0.658163\pi$
$504$	5.10398	0.227349
$505$	−6.62004	−0.294588
$506$	−3.04009	−0.135148
$507$	10.4039	0.462052
$508$	2.50133	0.110978
$509$	−25.5309	−1.13164	−0.565820	−	0.824529i	$-0.691440\pi$
$509$	−25.5309	−1.13164	−0.565820	+	0.824529i	$0.691440\pi$
$510$	−2.17821	−0.0964529
$511$	−19.3854	−0.857559
$512$	21.2535	0.939280
$513$	3.79309	0.167469
$514$	−2.06695	−0.0911690
$515$	37.8618	1.66839
$516$	−1.56108	−0.0687228
$517$	5.37046	0.236193
$518$	0.957252	0.0420592
$519$	5.53289	0.242867
$520$	20.1993	0.885796
$521$	18.3972	0.805994	0.402997	−	0.915201i	$-0.367968\pi$
$521$	18.3972	0.805994	0.402997	+	0.915201i	$0.367968\pi$
$522$	−0.909439	−0.0398051
$523$	−18.4488	−0.806709	−0.403354	−	0.915044i	$-0.632156\pi$
$523$	−18.4488	−0.806709	−0.403354	+	0.915044i	$0.632156\pi$
$524$	−1.88510	−0.0823511
$525$	0.672812	0.0293639
$526$	9.61945	0.419428
$527$	−60.2330	−2.62379
$528$	1.38015	0.0600632
$529$	57.4389	2.49734
$530$	9.49937	0.412626
$531$	22.6076	0.981088
$532$	4.05033	0.175604
$533$	56.7874	2.45974
$534$	−0.806445	−0.0348983
$535$	13.7433	0.594175
$536$	19.8910	0.859159
$537$	−1.00456	−0.0433498
$538$	−2.30706	−0.0994643
$539$	−5.12122	−0.220587
$540$	11.3418	0.488072
$541$	29.7609	1.27952	0.639761	−	0.768574i	$-0.279033\pi$
$541$	29.7609	1.27952	0.639761	+	0.768574i	$0.279033\pi$
$542$	−0.488416	−0.0209793
$543$	−0.981225	−0.0421084
$544$	−23.4063	−1.00354
$545$	−43.3264	−1.85590
$546$	−1.19011	−0.0509322
$547$	−30.6529	−1.31062	−0.655312	−	0.755358i	$-0.727463\pi$
$547$	−30.6529	−1.31062	−0.655312	+	0.755358i	$0.727463\pi$
$548$	36.0744	1.54102
$549$	−4.40924	−0.188182
$550$	0.400702	0.0170860
$551$	−1.48738	−0.0633645
$552$	4.90429	0.208741
$553$	0.525740	0.0223568
$554$	7.91623	0.336328
$555$	2.12712	0.0902914
$556$	−5.56933	−0.236192
$557$	22.3512	0.947050	0.473525	−	0.880780i	$-0.342981\pi$
$557$	22.3512	0.947050	0.473525	+	0.880780i	$0.342981\pi$
$558$	−9.27499	−0.392641
$559$	−12.3030	−0.520363
$560$	11.3278	0.478686
$561$	−2.58451	−0.109118
$562$	−7.46706	−0.314979
$563$	−29.1339	−1.22785	−0.613924	−	0.789365i	$-0.710410\pi$
$563$	−29.1339	−1.22785	−0.613924	+	0.789365i	$0.710410\pi$
$564$	−4.20373	−0.177009
$565$	38.7844	1.63167
$566$	−3.70264	−0.155634
$567$	10.2500	0.430458
$568$	0.274622	0.0115229
$569$	17.9251	0.751458	0.375729	−	0.926730i	$-0.377392\pi$
$569$	17.9251	0.751458	0.375729	+	0.926730i	$0.377392\pi$
$570$	−0.548564	−0.0229768
$571$	−17.8635	−0.747564	−0.373782	−	0.927517i	$-0.621939\pi$
$571$	−17.8635	−0.747564	−0.373782	+	0.927517i	$0.621939\pi$
$572$	11.6291	0.486236
$573$	−0.951342	−0.0397429
$574$	−4.27694	−0.178516
$575$	−10.6023	−0.442148
$576$	15.1926	0.633023
$577$	−24.3817	−1.01502	−0.507512	−	0.861645i	$-0.669435\pi$
$577$	−24.3817	−1.01502	−0.507512	+	0.861645i	$0.669435\pi$
$578$	7.36968	0.306538
$579$	−5.34983	−0.222331
$580$	−4.44743	−0.184670
$581$	3.42748	0.142196
$582$	1.06900	0.0443114
$583$	11.2713	0.466808
$584$	18.6249	0.770702
$585$	43.3706	1.79315
$586$	−2.49045	−0.102879
$587$	−44.4606	−1.83509	−0.917543	−	0.397636i	$-0.869831\pi$
$587$	−44.4606	−1.83509	−0.917543	+	0.397636i	$0.869831\pi$
$588$	4.00864	0.165313
$589$	−15.1692	−0.625034
$590$	−6.73848	−0.277419
$591$	7.89096	0.324591
$592$	6.84815	0.281457
$593$	−2.46507	−0.101228	−0.0506142	−	0.998718i	$-0.516118\pi$
$593$	−2.46507	−0.101228	−0.0506142	+	0.998718i	$0.516118\pi$
$594$	−0.820218	−0.0336540
$595$	−21.2127	−0.869638
$596$	30.8049	1.26182
$597$	−1.76816	−0.0723658
$598$	18.7541	0.766912
$599$	3.52304	0.143947	0.0719737	−	0.997407i	$-0.477070\pi$
$599$	3.52304	0.143947	0.0719737	+	0.997407i	$0.477070\pi$
$600$	−0.646416	−0.0263898
$601$	−22.2415	−0.907248	−0.453624	−	0.891193i	$-0.649869\pi$
$601$	−22.2415	−0.907248	−0.453624	+	0.891193i	$0.649869\pi$
$602$	0.926602	0.0377655
$603$	42.7087	1.73923
$604$	−3.83560	−0.156068
$605$	2.48639	0.101086
$606$	−0.374742	−0.0152228
$607$	10.5495	0.428193	0.214096	−	0.976813i	$-0.431319\pi$
$607$	10.5495	0.428193	0.214096	+	0.976813i	$0.431319\pi$
$608$	−5.89467	−0.239060
$609$	0.540045	0.0218837
$610$	1.31423	0.0532115
$611$	−33.1300	−1.34030
$612$	−33.1773	−1.34111
$613$	7.09999	0.286766	0.143383	−	0.989667i	$-0.454202\pi$
$613$	7.09999	0.286766	0.143383	+	0.989667i	$0.454202\pi$
$614$	−6.61311	−0.266883
$615$	−9.50384	−0.383232
$616$	−1.80507	−0.0727282
$617$	5.75473	0.231677	0.115838	−	0.993268i	$-0.463045\pi$
$617$	5.75473	0.231677	0.115838	+	0.993268i	$0.463045\pi$
$618$	2.14325	0.0862141
$619$	25.9533	1.04315	0.521575	−	0.853205i	$-0.325345\pi$
$619$	25.9533	1.04315	0.521575	+	0.853205i	$0.325345\pi$
$620$	−45.3575	−1.82160
$621$	21.7025	0.870890
$622$	−3.29469	−0.132105
$623$	−7.85365	−0.314650
$624$	−8.51404	−0.340835
$625$	−29.5132	−1.18053
$626$	−0.809337	−0.0323476
$627$	−0.650886	−0.0259939
$628$	−10.6528	−0.425093
$629$	−12.8241	−0.511329
$630$	−3.26645	−0.130138
$631$	−42.0553	−1.67419	−0.837097	−	0.547054i	$-0.815749\pi$
$631$	−42.0553	−1.67419	−0.837097	+	0.547054i	$0.815749\pi$
$632$	−0.505114	−0.0200924
$633$	−1.69281	−0.0672831
$634$	5.45542	0.216663
$635$	−3.29917	−0.130924
$636$	−8.82258	−0.349838
$637$	31.5925	1.25174
$638$	0.321631	0.0127335
$639$	0.589651	0.0233262
$640$	−23.2283	−0.918181
$641$	−28.9410	−1.14310	−0.571550	−	0.820567i	$-0.693658\pi$
$641$	−28.9410	−1.14310	−0.571550	+	0.820567i	$0.693658\pi$
$642$	0.777970	0.0307040
$643$	25.4922	1.00531	0.502657	−	0.864486i	$-0.332356\pi$
$643$	25.4922	1.00531	0.502657	+	0.864486i	$0.332356\pi$
$644$	23.1743	0.913194
$645$	2.05902	0.0810737
$646$	3.30720	0.130120
$647$	15.0479	0.591595	0.295798	−	0.955251i	$-0.404415\pi$
$647$	15.0479	0.591595	0.295798	+	0.955251i	$0.404415\pi$
$648$	−9.84783	−0.386859
$649$	−7.99539	−0.313846
$650$	−2.47191	−0.0969561
$651$	5.50769	0.215864
$652$	21.2561	0.832455
$653$	−8.00445	−0.313238	−0.156619	−	0.987659i	$-0.550060\pi$
$653$	−8.00445	−0.313238	−0.156619	+	0.987659i	$0.550060\pi$
$654$	−2.45258	−0.0959036
$655$	2.48639	0.0971513
$656$	−30.5971	−1.19461
$657$	39.9901	1.56016
$658$	2.49518	0.0972723
$659$	−32.8335	−1.27901	−0.639507	−	0.768786i	$-0.720861\pi$
$659$	−32.8335	−1.27901	−0.639507	+	0.768786i	$0.720861\pi$
$660$	−1.94622	−0.0757566
$661$	25.7576	1.00185	0.500927	−	0.865490i	$-0.332993\pi$
$661$	25.7576	1.00185	0.500927	+	0.865490i	$0.332993\pi$
$662$	0.628439	0.0244250
$663$	15.9437	0.619200
$664$	−3.29301	−0.127793
$665$	−5.34225	−0.207164
$666$	−1.97471	−0.0765186
$667$	−8.51016	−0.329515
$668$	−45.0197	−1.74187
$669$	4.80156	0.185639
$670$	−12.7298	−0.491797
$671$	1.55937	0.0601987
$672$	2.14027	0.0825626
$673$	29.1963	1.12544	0.562718	−	0.826649i	$-0.309756\pi$
$673$	29.1963	1.12544	0.562718	+	0.826649i	$0.309756\pi$
$674$	1.92597	0.0741856
$675$	−2.86052	−0.110101
$676$	−47.2327	−1.81664
$677$	−22.9748	−0.882993	−0.441497	−	0.897263i	$-0.645552\pi$
$677$	−22.9748	−0.882993	−0.441497	+	0.897263i	$0.645552\pi$
$678$	2.19547	0.0843167
$679$	10.4106	0.399520
$680$	20.3805	0.781557
$681$	1.34440	0.0515175
$682$	3.28018	0.125605
$683$	−8.03221	−0.307344	−0.153672	−	0.988122i	$-0.549110\pi$
$683$	−8.03221	−0.307344	−0.153672	+	0.988122i	$0.549110\pi$
$684$	−8.35541	−0.319477
$685$	−47.5810	−1.81798
$686$	−5.63167	−0.215018
$687$	3.65713	0.139528
$688$	6.62888	0.252724
$689$	−69.5317	−2.64895
$690$	−3.13865	−0.119486
$691$	−20.2940	−0.772021	−0.386011	−	0.922494i	$-0.626147\pi$
$691$	−20.2940	−0.772021	−0.386011	+	0.922494i	$0.626147\pi$
$692$	−25.1188	−0.954875
$693$	−3.87573	−0.147227
$694$	−10.8646	−0.412413
$695$	7.34577	0.278641
$696$	−0.518858	−0.0196672
$697$	57.2970	2.17028
$698$	−0.794528	−0.0300733
$699$	−0.301965	−0.0114214
$700$	−3.05451	−0.115450
$701$	−11.4378	−0.432001	−0.216001	−	0.976393i	$-0.569301\pi$
$701$	−11.4378	−0.432001	−0.216001	+	0.976393i	$0.569301\pi$
$702$	5.05987	0.190973
$703$	−3.22963	−0.121808
$704$	−5.37298	−0.202502
$705$	5.54458	0.208821
$706$	4.52777	0.170405
$707$	−3.64946	−0.137252
$708$	6.25839	0.235205
$709$	−28.6861	−1.07733	−0.538665	−	0.842520i	$-0.681071\pi$
$709$	−28.6861	−1.07733	−0.538665	+	0.842520i	$0.681071\pi$
$710$	−0.175753	−0.00659588
$711$	−1.08455	−0.0406738
$712$	7.54553	0.282781
$713$	−86.7915	−3.25037
$714$	−1.20079	−0.0449386
$715$	−15.3384	−0.573623
$716$	4.56059	0.170437
$717$	−6.14319	−0.229422
$718$	1.46578	0.0547025
$719$	7.54434	0.281356	0.140678	−	0.990055i	$-0.455072\pi$
$719$	7.54434	0.281356	0.140678	+	0.990055i	$0.455072\pi$
$720$	−23.3681	−0.870877
$721$	20.8722	0.777323
$722$	−5.60742	−0.208687
$723$	11.3018	0.420318
$724$	4.45468	0.165557
$725$	1.12169	0.0416586
$726$	0.140748	0.00522363
$727$	29.7992	1.10519	0.552596	−	0.833449i	$-0.313637\pi$
$727$	29.7992	1.10519	0.552596	+	0.833449i	$0.313637\pi$
$728$	11.1353	0.412703
$729$	−18.1304	−0.671495
$730$	−11.9195	−0.441162
$731$	−12.4134	−0.459128
$732$	−1.22059	−0.0451144
$733$	50.6142	1.86948	0.934740	−	0.355334i	$-0.115633\pi$
$733$	50.6142	1.86948	0.934740	+	0.355334i	$0.115633\pi$
$734$	−0.564138	−0.0208227
$735$	−5.28726	−0.195024
$736$	−33.7268	−1.24319
$737$	−15.1043	−0.556374
$738$	8.82289	0.324775
$739$	−18.9518	−0.697155	−0.348577	−	0.937280i	$-0.613335\pi$
$739$	−18.9518	−0.697155	−0.348577	+	0.937280i	$0.613335\pi$
$740$	−9.65696	−0.354997
$741$	4.01527	0.147505
$742$	5.23677	0.192248
$743$	−15.3306	−0.562426	−0.281213	−	0.959645i	$-0.590737\pi$
$743$	−15.3306	−0.562426	−0.281213	+	0.959645i	$0.590737\pi$
$744$	−5.29161	−0.194000
$745$	−40.6307	−1.48859
$746$	1.14683	0.0419883
$747$	−7.07054	−0.258697
$748$	11.7334	0.429017
$749$	7.57634	0.276833
$750$	−1.33607	−0.0487865
$751$	0.469036	0.0171154	0.00855769	−	0.999963i	$-0.497276\pi$
$751$	0.469036	0.0171154	0.00855769	+	0.999963i	$0.497276\pi$
$752$	17.8505	0.650939
$753$	−9.48783	−0.345756
$754$	−1.98412	−0.0722574
$755$	5.05903	0.184117
$756$	6.25244	0.227399
$757$	20.2911	0.737492	0.368746	−	0.929530i	$-0.379787\pi$
$757$	20.2911	0.737492	0.368746	+	0.929530i	$0.379787\pi$
$758$	6.84055	0.248460
$759$	−3.72409	−0.135176
$760$	5.13266	0.186181
$761$	−36.3870	−1.31903	−0.659515	−	0.751692i	$-0.729238\pi$
$761$	−36.3870	−1.31903	−0.659515	+	0.751692i	$0.729238\pi$
$762$	−0.186757	−0.00676548
$763$	−23.8847	−0.864686
$764$	4.31901	0.156256
$765$	43.7598	1.58214
$766$	−13.1280	−0.474333
$767$	49.3230	1.78095
$768$	3.14715	0.113563
$769$	−25.6240	−0.924024	−0.462012	−	0.886874i	$-0.652872\pi$
$769$	−25.6240	−0.924024	−0.462012	+	0.886874i	$0.652872\pi$
$770$	1.15521	0.0416308
$771$	−2.53200	−0.0911877
$772$	24.2878	0.874136
$773$	−13.2906	−0.478031	−0.239016	−	0.971016i	$-0.576825\pi$
$773$	−13.2906	−0.478031	−0.239016	+	0.971016i	$0.576825\pi$
$774$	−1.91149	−0.0687070
$775$	11.4397	0.410925
$776$	−10.0021	−0.359055
$777$	1.17263	0.0420679
$778$	5.07422	0.181920
$779$	14.4298	0.517000
$780$	12.0061	0.429888
$781$	−0.208535	−0.00746198
$782$	18.9224	0.676663
$783$	−2.29605	−0.0820541
$784$	−17.0220	−0.607930
$785$	14.0507	0.501490
$786$	0.140748	0.00502030
$787$	3.66617	0.130685	0.0653424	−	0.997863i	$-0.479186\pi$
$787$	3.66617	0.130685	0.0653424	+	0.997863i	$0.479186\pi$
$788$	−35.8243	−1.27619
$789$	11.7838	0.419514
$790$	0.323263	0.0115012
$791$	21.3808	0.760215
$792$	3.72367	0.132315
$793$	−9.61963	−0.341603
$794$	2.89975	0.102908
$795$	11.6367	0.412711
$796$	8.02727	0.284519
$797$	−10.2792	−0.364109	−0.182054	−	0.983288i	$-0.558275\pi$
$797$	−10.2792	−0.364109	−0.182054	+	0.983288i	$0.558275\pi$
$798$	−0.302410	−0.0107052
$799$	−33.4273	−1.18257
$800$	4.44540	0.157169
$801$	16.2013	0.572444
$802$	2.02894	0.0716444
$803$	−14.1429	−0.499090
$804$	11.8229	0.416961
$805$	−30.5661	−1.07731
$806$	−20.2352	−0.712755
$807$	−2.82614	−0.0994847
$808$	3.50628	0.123351
$809$	−23.8904	−0.839941	−0.419971	−	0.907538i	$-0.637960\pi$
$809$	−23.8904	−0.839941	−0.419971	+	0.907538i	$0.637960\pi$
$810$	6.30242	0.221444
$811$	1.23714	0.0434420	0.0217210	−	0.999764i	$-0.493085\pi$
$811$	1.23714	0.0434420	0.0217210	+	0.999764i	$0.493085\pi$
$812$	−2.45176	−0.0860398
$813$	−0.598307	−0.0209836
$814$	0.698375	0.0244780
$815$	−28.0362	−0.982064
$816$	−8.59044	−0.300726
$817$	−3.12622	−0.109373
$818$	−3.67390	−0.128455
$819$	23.9091	0.835452
$820$	43.1466	1.50674
$821$	−52.1824	−1.82118	−0.910590	−	0.413311i	$-0.864372\pi$
$821$	−52.1824	−1.82118	−0.910590	+	0.413311i	$0.864372\pi$
$822$	−2.69343	−0.0939440
$823$	54.2104	1.88966	0.944828	−	0.327568i	$-0.106229\pi$
$823$	54.2104	1.88966	0.944828	+	0.327568i	$0.106229\pi$
$824$	−20.0534	−0.698592
$825$	0.490859	0.0170895
$826$	−3.71476	−0.129253
$827$	−16.5724	−0.576278	−0.288139	−	0.957589i	$-0.593036\pi$
$827$	−16.5724	−0.576278	−0.288139	+	0.957589i	$0.593036\pi$
$828$	−47.8062	−1.66138
$829$	−46.8075	−1.62569	−0.812845	−	0.582479i	$-0.802083\pi$
$829$	−46.8075	−1.62569	−0.812845	+	0.582479i	$0.802083\pi$
$830$	2.10746	0.0731510
$831$	9.69735	0.336397
$832$	33.1456	1.14912
$833$	31.8760	1.10444
$834$	0.415823	0.0143988
$835$	59.3796	2.05491
$836$	2.95496	0.102200
$837$	−23.4164	−0.809391
$838$	−0.130147	−0.00449585
$839$	20.4898	0.707386	0.353693	−	0.935362i	$-0.384926\pi$
$839$	20.4898	0.707386	0.353693	+	0.935362i	$0.384926\pi$
$840$	−1.86359	−0.0643000
$841$	−28.0997	−0.968954
$842$	9.97648	0.343812
$843$	−9.14712	−0.315044
$844$	7.68520	0.264535
$845$	62.2984	2.14313
$846$	−5.14731	−0.176968
$847$	1.37068	0.0470973
$848$	37.4637	1.28651
$849$	−4.53572	−0.155665
$850$	−2.49409	−0.0855465
$851$	−18.4786	−0.633437
$852$	0.163231	0.00559220
$853$	−55.5151	−1.90080	−0.950400	−	0.311029i	$-0.899326\pi$
$853$	−55.5151	−1.90080	−0.950400	+	0.311029i	$0.899326\pi$
$854$	0.724501	0.0247919
$855$	11.0205	0.376894
$856$	−7.27910	−0.248794
$857$	11.3163	0.386556	0.193278	−	0.981144i	$-0.438088\pi$
$857$	11.3163	0.386556	0.193278	+	0.981144i	$0.438088\pi$
$858$	−0.868263	−0.0296420
$859$	29.9962	1.02346	0.511729	−	0.859147i	$-0.329005\pi$
$859$	29.9962	1.02346	0.511729	+	0.859147i	$0.329005\pi$
$860$	−9.34775	−0.318756
$861$	−5.23923	−0.178552
$862$	−1.92955	−0.0657209
$863$	25.5559	0.869932	0.434966	−	0.900447i	$-0.356760\pi$
$863$	25.5559	0.869932	0.434966	+	0.900447i	$0.356760\pi$
$864$	−9.09953	−0.309572
$865$	33.1309	1.12649
$866$	8.55266	0.290631
$867$	9.02783	0.306601
$868$	−25.0044	−0.848706
$869$	0.383560	0.0130114
$870$	0.332059	0.0112578
$871$	93.1774	3.15720
$872$	22.9477	0.777106
$873$	−21.4759	−0.726850
$874$	4.76544	0.161193
$875$	−13.0115	−0.439869
$876$	11.0703	0.374031
$877$	−20.9674	−0.708019	−0.354010	−	0.935242i	$-0.615182\pi$
$877$	−20.9674	−0.708019	−0.354010	+	0.935242i	$0.615182\pi$
$878$	−9.27046	−0.312863
$879$	−3.05079	−0.102900
$880$	8.26432	0.278590
$881$	10.3009	0.347046	0.173523	−	0.984830i	$-0.444485\pi$
$881$	10.3009	0.347046	0.173523	+	0.984830i	$0.444485\pi$
$882$	4.90843	0.165275
$883$	−44.0834	−1.48352	−0.741762	−	0.670663i	$-0.766010\pi$
$883$	−44.0834	−1.48352	−0.741762	+	0.670663i	$0.766010\pi$
$884$	−72.3828	−2.43450
$885$	−8.25461	−0.277476
$886$	8.43740	0.283460
$887$	6.80492	0.228487	0.114243	−	0.993453i	$-0.463556\pi$
$887$	6.80492	0.228487	0.114243	+	0.993453i	$0.463556\pi$
$888$	−1.12662	−0.0378070
$889$	−1.81875	−0.0609989
$890$	−4.82899	−0.161868
$891$	7.47799	0.250522
$892$	−21.7987	−0.729873
$893$	−8.41838	−0.281710
$894$	−2.29999	−0.0769232
$895$	−6.01527	−0.201068
$896$	−12.8052	−0.427792
$897$	22.9737	0.767069
$898$	6.44207	0.214975
$899$	9.18225	0.306245
$900$	6.30114	0.210038
$901$	−70.1556	−2.33722
$902$	−3.12029	−0.103894
$903$	1.13508	0.0377732
$904$	−20.5420	−0.683217
$905$	−5.87557	−0.195311
$906$	0.286378	0.00951426
$907$	30.5143	1.01321	0.506606	−	0.862178i	$-0.330900\pi$
$907$	30.5143	1.01321	0.506606	+	0.862178i	$0.330900\pi$
$908$	−6.10345	−0.202550
$909$	7.52847	0.249703
$910$	−7.12640	−0.236238
$911$	−42.6953	−1.41456	−0.707280	−	0.706934i	$-0.750078\pi$
$911$	−42.6953	−1.41456	−0.707280	+	0.706934i	$0.750078\pi$
$912$	−2.16343	−0.0716383
$913$	2.50056	0.0827564
$914$	1.60924	0.0532290
$915$	1.60992	0.0532224
$916$	−16.6030	−0.548580
$917$	1.37068	0.0452640
$918$	5.10528	0.168499
$919$	24.2852	0.801096	0.400548	−	0.916276i	$-0.368820\pi$
$919$	24.2852	0.801096	0.400548	+	0.916276i	$0.368820\pi$
$920$	29.3669	0.968198
$921$	−8.10103	−0.266938
$922$	−4.83888	−0.159360
$923$	1.28644	0.0423437
$924$	−1.07290	−0.0352959
$925$	2.43559	0.0800817
$926$	−10.7782	−0.354194
$927$	−43.0573	−1.41419
$928$	3.56818	0.117131
$929$	−20.0781	−0.658742	−0.329371	−	0.944201i	$-0.606837\pi$
$929$	−20.0781	−0.658742	−0.329371	+	0.944201i	$0.606837\pi$
$930$	3.38653	0.111049
$931$	8.02769	0.263097
$932$	1.37090	0.0449052
$933$	−4.03598	−0.132132
$934$	8.88850	0.290841
$935$	−15.4760	−0.506120
$936$	−22.9711	−0.750833
$937$	32.0430	1.04680	0.523399	−	0.852087i	$-0.324664\pi$
$937$	32.0430	1.04680	0.523399	+	0.852087i	$0.324664\pi$
$938$	−7.01764	−0.229134
$939$	−0.991435	−0.0323542
$940$	−25.1719	−0.821017
$941$	−23.9624	−0.781152	−0.390576	−	0.920571i	$-0.627724\pi$
$941$	−23.9624	−0.781152	−0.390576	+	0.920571i	$0.627724\pi$
$942$	0.795370	0.0259145
$943$	82.5610	2.68856
$944$	−26.5753	−0.864951
$945$	−8.24676	−0.268267
$946$	0.676014	0.0219791
$947$	−45.6956	−1.48491	−0.742454	−	0.669897i	$-0.766338\pi$
$947$	−45.6956	−1.48491	−0.742454	+	0.669897i	$0.766338\pi$
$948$	−0.300232	−0.00975108
$949$	87.2463	2.83214
$950$	−0.628114	−0.0203787
$951$	6.68287	0.216707
$952$	11.2353	0.364137
$953$	−30.9290	−1.00189	−0.500944	−	0.865479i	$-0.667014\pi$
$953$	−30.9290	−1.00189	−0.500944	+	0.865479i	$0.667014\pi$
$954$	−10.8029	−0.349757
$955$	−5.69664	−0.184339
$956$	27.8895	0.902012
$957$	0.393997	0.0127361
$958$	1.70420	0.0550603
$959$	−26.2302	−0.847017
$960$	−5.54718	−0.179035
$961$	62.6459	2.02084
$962$	−4.30823	−0.138903
$963$	−15.6292	−0.503645
$964$	−51.3091	−1.65255
$965$	−32.0348	−1.03124
$966$	−1.73026	−0.0556702
$967$	−34.0853	−1.09611	−0.548055	−	0.836442i	$-0.684632\pi$
$967$	−34.0853	−1.09611	−0.548055	+	0.836442i	$0.684632\pi$
$968$	−1.31691	−0.0423271
$969$	4.05130	0.130147
$970$	6.40116	0.205529
$971$	−22.3945	−0.718673	−0.359337	−	0.933208i	$-0.616997\pi$
$971$	−22.3945	−0.718673	−0.359337	+	0.933208i	$0.616997\pi$
$972$	−19.5380	−0.626682
$973$	4.04954	0.129822
$974$	10.4563	0.335041
$975$	−3.02807	−0.0969760
$976$	5.18306	0.165906
$977$	−22.7429	−0.727608	−0.363804	−	0.931475i	$-0.618522\pi$
$977$	−22.7429	−0.727608	−0.363804	+	0.931475i	$0.618522\pi$
$978$	−1.58705	−0.0507482
$979$	−5.72972	−0.183123
$980$	24.0037	0.766770
$981$	49.2718	1.57313
$982$	−14.5543	−0.464445
$983$	8.21139	0.261903	0.130951	−	0.991389i	$-0.458197\pi$
$983$	8.21139	0.261903	0.130951	+	0.991389i	$0.458197\pi$
$984$	5.03368	0.160468
$985$	47.2510	1.50554
$986$	−2.00192	−0.0637543
$987$	3.05659	0.0972923
$988$	−18.2290	−0.579941
$989$	−17.8869	−0.568771
$990$	−2.38308	−0.0757392
$991$	−14.0244	−0.445499	−0.222750	−	0.974876i	$-0.571503\pi$
$991$	−14.0244	−0.445499	−0.222750	+	0.974876i	$0.571503\pi$
$992$	36.3904	1.15540
$993$	0.769835	0.0244300
$994$	−0.0968880	−0.00307310
$995$	−10.5877	−0.335653
$996$	−1.95731	−0.0620198
$997$	−11.6199	−0.368006	−0.184003	−	0.982926i	$-0.558906\pi$
$997$	−11.6199	−0.368006	−0.184003	+	0.982926i	$0.558906\pi$
$998$	−5.65582	−0.179032
$999$	−4.98554	−0.157735

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.2.a.c.1.14	✓	23

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.2.a.c.1.14	✓	23	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:	\( N \)	\(=\)	\( 1441 = 11 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1441.a (trivial)

\(f(q)\)	\(=\)	\(q+0.338964 q^{2} +0.415229 q^{3} -1.88510 q^{4} +2.48639 q^{5} +0.140748 q^{6} +1.37068 q^{7} -1.31691 q^{8} -2.82758 q^{9} +O(q^{10})\)	\(q+0.338964 q^{2} +0.415229 q^{3} -1.88510 q^{4} +2.48639 q^{5} +0.140748 q^{6} +1.37068 q^{7} -1.31691 q^{8} -2.82758 q^{9} +0.842796 q^{10} +1.00000 q^{11} -0.782750 q^{12} -6.16893 q^{13} +0.464612 q^{14} +1.03242 q^{15} +3.32382 q^{16} -6.22429 q^{17} -0.958448 q^{18} -1.56753 q^{19} -4.68710 q^{20} +0.569148 q^{21} +0.338964 q^{22} -8.96877 q^{23} -0.546819 q^{24} +1.18214 q^{25} -2.09104 q^{26} -2.41978 q^{27} -2.58388 q^{28} +0.948866 q^{29} +0.349953 q^{30} +9.67708 q^{31} +3.76047 q^{32} +0.415229 q^{33} -2.10981 q^{34} +3.40806 q^{35} +5.33029 q^{36} +2.06032 q^{37} -0.531337 q^{38} -2.56152 q^{39} -3.27435 q^{40} -9.20539 q^{41} +0.192921 q^{42} +1.99435 q^{43} -1.88510 q^{44} -7.03048 q^{45} -3.04009 q^{46} +5.37046 q^{47} +1.38015 q^{48} -5.12122 q^{49} +0.400702 q^{50} -2.58451 q^{51} +11.6291 q^{52} +11.2713 q^{53} -0.820218 q^{54} +2.48639 q^{55} -1.80507 q^{56} -0.650886 q^{57} +0.321631 q^{58} -7.99539 q^{59} -1.94622 q^{60} +1.55937 q^{61} +3.28018 q^{62} -3.87573 q^{63} -5.37298 q^{64} -15.3384 q^{65} +0.140748 q^{66} -15.1043 q^{67} +11.7334 q^{68} -3.72409 q^{69} +1.15521 q^{70} -0.208535 q^{71} +3.72367 q^{72} -14.1429 q^{73} +0.698375 q^{74} +0.490859 q^{75} +2.95496 q^{76} +1.37068 q^{77} -0.868263 q^{78} +0.383560 q^{79} +8.26432 q^{80} +7.47799 q^{81} -3.12029 q^{82} +2.50056 q^{83} -1.07290 q^{84} -15.4760 q^{85} +0.676014 q^{86} +0.393997 q^{87} -1.31691 q^{88} -5.72972 q^{89} -2.38308 q^{90} -8.45567 q^{91} +16.9071 q^{92} +4.01821 q^{93} +1.82039 q^{94} -3.89750 q^{95} +1.56146 q^{96} +7.59514 q^{97} -1.73591 q^{98} -2.82758 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 23 q - 7 q^{2} - 3 q^{3} + 15 q^{4} - 9 q^{5} - 11 q^{6} - 12 q^{7} - 21 q^{8} + 12 q^{9}+O(q^{10}) \) 23 * q - 7 * q^2 - 3 * q^3 + 15 * q^4 - 9 * q^5 - 11 * q^6 - 12 * q^7 - 21 * q^8 + 12 * q^9	\( 23 q - 7 q^{2} - 3 q^{3} + 15 q^{4} - 9 q^{5} - 11 q^{6} - 12 q^{7} - 21 q^{8} + 12 q^{9} - 2 q^{10} + 23 q^{11} + 8 q^{12} - 24 q^{13} - 13 q^{14} - 27 q^{15} + 7 q^{16} - 7 q^{17} - 14 q^{18} - 18 q^{19} - 4 q^{20} - 29 q^{21} - 7 q^{22} - 26 q^{23} - 4 q^{24} + 18 q^{25} + 8 q^{26} - 3 q^{27} - 11 q^{28} - 45 q^{29} + 19 q^{30} - 23 q^{31} - 34 q^{32} - 3 q^{33} - 2 q^{34} - 18 q^{35} - 6 q^{36} - 2 q^{37} - 8 q^{38} - 40 q^{39} - 24 q^{40} - 23 q^{41} + 59 q^{42} - 14 q^{43} + 15 q^{44} - 18 q^{45} - 12 q^{46} - 55 q^{47} + 10 q^{48} + 11 q^{49} - 41 q^{50} - 21 q^{51} - 37 q^{52} - 10 q^{53} - 68 q^{54} - 9 q^{55} + 2 q^{56} - 18 q^{57} + 27 q^{58} - 75 q^{59} - 63 q^{60} - 55 q^{61} + 14 q^{62} - 16 q^{63} + 19 q^{64} - 25 q^{65} - 11 q^{66} + 17 q^{67} + 41 q^{68} - 22 q^{69} + 27 q^{70} - 105 q^{71} - 11 q^{72} - 3 q^{73} - 39 q^{74} + 25 q^{75} - 30 q^{76} - 12 q^{77} + 25 q^{78} - 48 q^{79} - 37 q^{80} + 3 q^{81} + 36 q^{82} + 4 q^{83} - 111 q^{84} - 30 q^{85} + 22 q^{86} + 5 q^{87} - 21 q^{88} - 39 q^{89} + 100 q^{90} - 22 q^{91} - 30 q^{92} - 5 q^{93} + 11 q^{94} - 88 q^{95} + 13 q^{96} + 24 q^{97} - 91 q^{98} + 12 q^{99}+O(q^{100}) \) 23 * q - 7 * q^2 - 3 * q^3 + 15 * q^4 - 9 * q^5 - 11 * q^6 - 12 * q^7 - 21 * q^8 + 12 * q^9 - 2 * q^10 + 23 * q^11 + 8 * q^12 - 24 * q^13 - 13 * q^14 - 27 * q^15 + 7 * q^16 - 7 * q^17 - 14 * q^18 - 18 * q^19 - 4 * q^20 - 29 * q^21 - 7 * q^22 - 26 * q^23 - 4 * q^24 + 18 * q^25 + 8 * q^26 - 3 * q^27 - 11 * q^28 - 45 * q^29 + 19 * q^30 - 23 * q^31 - 34 * q^32 - 3 * q^33 - 2 * q^34 - 18 * q^35 - 6 * q^36 - 2 * q^37 - 8 * q^38 - 40 * q^39 - 24 * q^40 - 23 * q^41 + 59 * q^42 - 14 * q^43 + 15 * q^44 - 18 * q^45 - 12 * q^46 - 55 * q^47 + 10 * q^48 + 11 * q^49 - 41 * q^50 - 21 * q^51 - 37 * q^52 - 10 * q^53 - 68 * q^54 - 9 * q^55 + 2 * q^56 - 18 * q^57 + 27 * q^58 - 75 * q^59 - 63 * q^60 - 55 * q^61 + 14 * q^62 - 16 * q^63 + 19 * q^64 - 25 * q^65 - 11 * q^66 + 17 * q^67 + 41 * q^68 - 22 * q^69 + 27 * q^70 - 105 * q^71 - 11 * q^72 - 3 * q^73 - 39 * q^74 + 25 * q^75 - 30 * q^76 - 12 * q^77 + 25 * q^78 - 48 * q^79 - 37 * q^80 + 3 * q^81 + 36 * q^82 + 4 * q^83 - 111 * q^84 - 30 * q^85 + 22 * q^86 + 5 * q^87 - 21 * q^88 - 39 * q^89 + 100 * q^90 - 22 * q^91 - 30 * q^92 - 5 * q^93 + 11 * q^94 - 88 * q^95 + 13 * q^96 + 24 * q^97 - 91 * q^98 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more